LMFDB - Embedded newform 67.5.h.a.2.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [67,5,Mod(2,67)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(67, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 5, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("67.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 67 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	67.h (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.92578752662$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			2.15
Character	$\chi$	$=$	67.2
Dual form			67.5.h.a.34.15

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.99695 + 0.142762i) q^{2} +(-0.301492 + 1.02679i) q^{3} +(-6.96623 - 0.665194i) q^{4} +(20.3314 + 17.6172i) q^{5} +(-1.05014 + 3.03419i) q^{6} +(20.4478 + 39.6632i) q^{7} +(-68.2994 - 9.81997i) q^{8} +(67.1781 + 43.1728i) q^{9} +O(q^{10})$	\(q+(2.99695 + 0.142762i) q^{2} +(-0.301492 + 1.02679i) q^{3} +(-6.96623 - 0.665194i) q^{4} +(20.3314 + 17.6172i) q^{5} +(-1.05014 + 3.03419i) q^{6} +(20.4478 + 39.6632i) q^{7} +(-68.2994 - 9.81997i) q^{8} +(67.1781 + 43.1728i) q^{9} +(58.4170 + 55.7005i) q^{10} +(-9.39829 + 3.25278i) q^{11} +(2.78328 - 6.95229i) q^{12} +(121.695 + 154.748i) q^{13} +(55.6186 + 121.788i) q^{14} +(-24.2189 + 15.5645i) q^{15} +(-93.3446 - 17.9907i) q^{16} +(69.6223 - 6.64813i) q^{17} +(195.166 + 138.977i) q^{18} +(-205.312 - 105.846i) q^{19} +(-129.914 - 136.250i) q^{20} +(-46.8906 + 9.03741i) q^{21} +(-28.6306 + 8.40669i) q^{22} +(-117.412 - 483.979i) q^{23} +(30.6748 - 67.1684i) q^{24} +(14.0508 + 97.7255i) q^{25} +(342.621 + 481.144i) q^{26} +(-130.092 + 112.726i) q^{27} +(-116.060 - 289.905i) q^{28} +(-349.668 + 605.642i) q^{29} +(-74.8049 + 43.1886i) q^{30} +(701.196 - 891.644i) q^{31} +(795.726 + 193.041i) q^{32} +(-0.506405 - 10.6307i) q^{33} +(209.604 - 9.98465i) q^{34} +(-283.024 + 1166.64i) q^{35} +(-439.260 - 345.438i) q^{36} +(-684.199 - 1185.07i) q^{37} +(-600.199 - 346.525i) q^{38} +(-195.583 + 78.2997i) q^{39} +(-1215.62 - 1402.90i) q^{40} +(989.315 - 704.488i) q^{41} +(-141.819 + 20.3905i) q^{42} +(-722.533 - 329.970i) q^{43} +(67.6343 - 16.4079i) q^{44} +(605.238 + 2061.25i) q^{45} +(-282.784 - 1467.22i) q^{46} +(457.619 - 436.339i) q^{47} +(46.6153 - 90.4211i) q^{48} +(237.661 - 333.748i) q^{49} +(28.1580 + 294.884i) q^{50} +(-14.1644 + 73.4918i) q^{51} +(-744.818 - 1158.96i) q^{52} +(-950.518 + 434.087i) q^{53} +(-405.973 + 319.260i) q^{54} +(-248.385 - 99.4383i) q^{55} +(-1007.08 - 2909.77i) q^{56} +(170.581 - 178.900i) q^{57} +(-1134.40 + 1765.16i) q^{58} +(134.546 - 935.786i) q^{59} +(179.068 - 92.3159i) q^{60} +(2677.37 + 926.646i) q^{61} +(2228.74 - 2572.11i) q^{62} +(-338.725 + 3547.29i) q^{63} +(3816.58 + 1120.65i) q^{64} +(-252.001 + 5290.16i) q^{65} -31.9321i q^{66} +(4470.15 - 411.002i) q^{67} -489.427 q^{68} +(532.343 + 25.3586i) q^{69} +(-1014.76 + 3455.95i) q^{70} +(-2148.79 - 205.184i) q^{71} +(-4164.27 - 3608.36i) q^{72} +(-1988.46 + 5745.27i) q^{73} +(-1881.33 - 3649.26i) q^{74} +(-104.580 - 15.0363i) q^{75} +(1359.84 + 873.918i) q^{76} +(-321.190 - 306.254i) q^{77} +(-597.331 + 206.738i) q^{78} +(-2533.77 + 6329.06i) q^{79} +(-1580.88 - 2010.25i) q^{80} +(2610.48 + 5716.15i) q^{81} +(3065.50 - 1970.08i) q^{82} +(11165.3 + 2151.94i) q^{83} +(332.662 - 31.7654i) q^{84} +(1532.64 + 1091.39i) q^{85} +(-2118.29 - 1092.05i) q^{86} +(-516.444 - 541.631i) q^{87} +(673.839 - 129.872i) q^{88} +(7075.89 - 2077.67i) q^{89} +(1519.60 + 6263.87i) q^{90} +(-3649.39 + 7991.06i) q^{91} +(495.979 + 3449.61i) q^{92} +(704.124 + 988.804i) q^{93} +(1433.75 - 1242.36i) q^{94} +(-2309.56 - 5769.01i) q^{95} +(-438.118 + 758.842i) q^{96} +(11001.6 - 6351.78i) q^{97} +(759.904 - 966.296i) q^{98} +(-771.791 - 187.234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 19 q^{2} - 22 q^{3} - 191 q^{4} - 22 q^{5} - 53 q^{6} - 16 q^{7} - 517 q^{8} + 840 q^{9}+O(q^{10}) $ 440 * q - 19 * q^2 - 22 * q^3 - 191 * q^4 - 22 * q^5 - 53 * q^6 - 16 * q^7 - 517 * q^8 + 840 * q^9	\( 440 q - 19 q^{2} - 22 q^{3} - 191 q^{4} - 22 q^{5} - 53 q^{6} - 16 q^{7} - 517 q^{8} + 840 q^{9} + 854 q^{10} - 100 q^{11} - 742 q^{12} + 248 q^{13} + 308 q^{14} - 1658 q^{15} + 1585 q^{16} - 387 q^{17} + 458 q^{18} + 2011 q^{19} + 653 q^{20} - 4978 q^{21} - 5071 q^{22} + 2673 q^{23} + 7510 q^{24} + 4716 q^{25} - 307 q^{26} - 22 q^{27} + 1350 q^{28} - 412 q^{29} - 3258 q^{30} + 6228 q^{31} - 12097 q^{32} - 7165 q^{33} - 2803 q^{34} + 1835 q^{35} + 1521 q^{36} - 4085 q^{37} - 9813 q^{38} + 5901 q^{39} - 6267 q^{40} - 1009 q^{41} - 22 q^{42} + 23760 q^{43} + 3215 q^{44} - 18942 q^{45} - 15800 q^{46} + 11346 q^{47} + 38529 q^{48} - 1070 q^{49} - 22867 q^{50} - 9793 q^{51} + 7018 q^{52} + 17996 q^{53} + 91622 q^{54} + 508 q^{55} - 49204 q^{56} + 46028 q^{57} - 36454 q^{58} - 44616 q^{59} - 69860 q^{60} - 91374 q^{61} - 15694 q^{62} - 7642 q^{63} - 66563 q^{64} - 11104 q^{65} + 29958 q^{67} + 33458 q^{68} + 12995 q^{69} + 72490 q^{70} + 34293 q^{71} + 178288 q^{72} + 7050 q^{73} - 8786 q^{74} + 80014 q^{75} + 146812 q^{76} + 108149 q^{77} - 10978 q^{78} - 80964 q^{79} - 83953 q^{80} - 89880 q^{81} - 126534 q^{82} + 21228 q^{83} + 16421 q^{84} - 2014 q^{85} - 40102 q^{86} + 17510 q^{87} - 51977 q^{88} - 93609 q^{89} - 142715 q^{90} + 121690 q^{91} + 32880 q^{92} - 16047 q^{93} + 47850 q^{94} + 22766 q^{95} - 221501 q^{96} + 44892 q^{97} + 14720 q^{98} - 22428 q^{99}+O(q^{100}) \) 440 * q - 19 * q^2 - 22 * q^3 - 191 * q^4 - 22 * q^5 - 53 * q^6 - 16 * q^7 - 517 * q^8 + 840 * q^9 + 854 * q^10 - 100 * q^11 - 742 * q^12 + 248 * q^13 + 308 * q^14 - 1658 * q^15 + 1585 * q^16 - 387 * q^17 + 458 * q^18 + 2011 * q^19 + 653 * q^20 - 4978 * q^21 - 5071 * q^22 + 2673 * q^23 + 7510 * q^24 + 4716 * q^25 - 307 * q^26 - 22 * q^27 + 1350 * q^28 - 412 * q^29 - 3258 * q^30 + 6228 * q^31 - 12097 * q^32 - 7165 * q^33 - 2803 * q^34 + 1835 * q^35 + 1521 * q^36 - 4085 * q^37 - 9813 * q^38 + 5901 * q^39 - 6267 * q^40 - 1009 * q^41 - 22 * q^42 + 23760 * q^43 + 3215 * q^44 - 18942 * q^45 - 15800 * q^46 + 11346 * q^47 + 38529 * q^48 - 1070 * q^49 - 22867 * q^50 - 9793 * q^51 + 7018 * q^52 + 17996 * q^53 + 91622 * q^54 + 508 * q^55 - 49204 * q^56 + 46028 * q^57 - 36454 * q^58 - 44616 * q^59 - 69860 * q^60 - 91374 * q^61 - 15694 * q^62 - 7642 * q^63 - 66563 * q^64 - 11104 * q^65 + 29958 * q^67 + 33458 * q^68 + 12995 * q^69 + 72490 * q^70 + 34293 * q^71 + 178288 * q^72 + 7050 * q^73 - 8786 * q^74 + 80014 * q^75 + 146812 * q^76 + 108149 * q^77 - 10978 * q^78 - 80964 * q^79 - 83953 * q^80 - 89880 * q^81 - 126534 * q^82 + 21228 * q^83 + 16421 * q^84 - 2014 * q^85 - 40102 * q^86 + 17510 * q^87 - 51977 * q^88 - 93609 * q^89 - 142715 * q^90 + 121690 * q^91 + 32880 * q^92 - 16047 * q^93 + 47850 * q^94 + 22766 * q^95 - 221501 * q^96 + 44892 * q^97 + 14720 * q^98 - 22428 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{66}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.99695	+	0.142762i	0.749237	+	0.0356906i	0.418727	−	0.908112i	$-0.362476\pi$
$2$	2.99695	+	0.142762i	0.749237	+	0.0356906i	0.330510	+	0.943803i	$0.392779\pi$
$3$	−0.301492	+	1.02679i	−0.0334991	+	0.114088i	−0.974545	−	0.224190i	$-0.928026\pi$
$3$	−0.301492	+	1.02679i	−0.0334991	+	0.114088i	0.941046	+	0.338278i	$0.109844\pi$
$4$	−6.96623	−	0.665194i	−0.435389	−	0.0415746i
$5$	20.3314	+	17.6172i	0.813254	+	0.704689i	0.958620	−	0.284689i	$-0.0918904\pi$
$5$	20.3314	+	17.6172i	0.813254	+	0.704689i	−0.145366	+	0.989378i	$0.546436\pi$
$6$	−1.05014	+	3.03419i	−0.0291707	+	0.0842831i
$7$	20.4478	+	39.6632i	0.417302	+	0.809453i	0.999995	−	0.00323973i	$-0.00103124\pi$
$7$	20.4478	+	39.6632i	0.417302	+	0.809453i	−0.582693	+	0.812692i	$0.698001\pi$
$8$	−68.2994	−	9.81997i	−1.06718	−	0.153437i
$9$	67.1781	+	43.1728i	0.829360	+	0.532997i
$10$	58.4170	+	55.7005i	0.584170	+	0.557005i
$11$	−9.39829	+	3.25278i	−0.0776718	+	0.0268825i	−0.365628	−	0.930761i	$-0.619146\pi$
$11$	−9.39829	+	3.25278i	−0.0776718	+	0.0268825i	0.287956	+	0.957644i	$0.407024\pi$
$12$	2.78328	−	6.95229i	0.0193283	−	0.0482798i
$13$	121.695	+	154.748i	0.720088	+	0.915667i	0.999003	−	0.0446492i	$-0.0142170\pi$
$13$	121.695	+	154.748i	0.720088	+	0.915667i	−0.278914	+	0.960316i	$0.589975\pi$
$14$	55.6186	+	121.788i	0.283768	+	0.621366i
$15$	−24.2189	+	15.5645i	−0.107640	+	0.0691758i
$16$	−93.3446	−	17.9907i	−0.364627	−	0.0702762i
$17$	69.6223	−	6.64813i	0.240908	−	0.0230039i	0.0260963	−	0.999659i	$-0.491692\pi$
$17$	69.6223	−	6.64813i	0.240908	−	0.0230039i	0.214811	+	0.976656i	$0.431086\pi$
$18$	195.166	+	138.977i	0.602364	+	0.428942i
$19$	−205.312	−	105.846i	−0.568731	−	0.293201i	0.149777	−	0.988720i	$-0.452144\pi$
$19$	−205.312	−	105.846i	−0.568731	−	0.293201i	−0.718508	+	0.695519i	$0.755175\pi$
$20$	−129.914	−	136.250i	−0.324785	−	0.340625i
$21$	−46.8906	+	9.03741i	−0.106328	+	0.0204930i
$22$	−28.6306	+	8.40669i	−0.0591540	+	0.0173692i
$23$	−117.412	−	483.979i	−0.221951	−	0.914894i	−0.968390	−	0.249440i	$-0.919753\pi$
$23$	−117.412	−	483.979i	−0.221951	−	0.914894i	0.746439	−	0.665453i	$-0.231762\pi$
$24$	30.6748	−	67.1684i	0.0532548	−	0.116612i
$25$	14.0508	+	97.7255i	0.0224813	+	0.156361i
$26$	342.621	+	481.144i	0.506836	+	0.711752i
$27$	−130.092	+	112.726i	−0.178453	+	0.154630i
$28$	−116.060	−	289.905i	−0.148036	−	0.369776i
$29$	−349.668	+	605.642i	−0.415776	+	0.720145i	−0.995510	−	0.0946610i	$-0.969823\pi$
$29$	−349.668	+	605.642i	−0.415776	+	0.720145i	0.579734	+	0.814806i	$0.303157\pi$
$30$	−74.8049	+	43.1886i	−0.0831165	+	0.0479873i
$31$	701.196	−	891.644i	0.729653	−	0.927829i	−0.269731	−	0.962936i	$-0.586935\pi$
$31$	701.196	−	891.644i	0.729653	−	0.927829i	0.999384	+	0.0351069i	$0.0111772\pi$
$32$	795.726	+	193.041i	0.777077	+	0.188517i
$33$	−0.506405	−	10.6307i	−0.000465018	−	0.00976193i
$34$	209.604	−	9.98465i	0.181318	−	0.00863724i
$35$	−283.024	+	1166.64i	−0.231040	+	0.952359i
$36$	−439.260	−	345.438i	−0.338935	−	0.266542i
$37$	−684.199	−	1185.07i	−0.499780	−	0.865645i	0.500220	−	0.865898i	$-0.333253\pi$
$37$	−684.199	−	1185.07i	−0.499780	−	0.865645i	−1.00000		0.000253888i	$0.999919\pi$
$38$	−600.199	−	346.525i	−0.415650	−	0.239976i
$39$	−195.583	+	78.2997i	−0.128589	+	0.0514791i
$40$	−1215.62	−	1402.90i	−0.759762	−	0.876812i
$41$	989.315	−	704.488i	0.588528	−	0.419089i	−0.246622	−	0.969112i	$-0.579320\pi$
$41$	989.315	−	704.488i	0.588528	−	0.419089i	0.835149	+	0.550023i	$0.185381\pi$
$42$	−141.819	+	20.3905i	−0.0803961	+	0.0115592i
$43$	−722.533	−	329.970i	−0.390770	−	0.178459i	0.210334	−	0.977630i	$-0.432545\pi$
$43$	−722.533	−	329.970i	−0.390770	−	0.178459i	−0.601104	+	0.799171i	$0.705272\pi$
$44$	67.6343	−	16.4079i	0.0349351	−	0.00847516i
$45$	605.238	+	2061.25i	0.298883	+	1.01790i
$46$	−282.784	−	1467.22i	−0.133641	−	0.693394i
$47$	457.619	−	436.339i	0.207161	−	0.197528i	−0.579394	−	0.815047i	$-0.696711\pi$
$47$	457.619	−	436.339i	0.207161	−	0.197528i	0.786556	+	0.617519i	$0.211862\pi$
$48$	46.6153	−	90.4211i	0.0202323	−	0.0392453i
$49$	237.661	−	333.748i	0.0989841	−	0.139004i
$50$	28.1580	+	294.884i	0.0112632	+	0.117954i
$51$	−14.1644	+	73.4918i	−0.00544574	+	0.0282552i
$52$	−744.818	−	1158.96i	−0.275450	−	0.428609i
$53$	−950.518	+	434.087i	−0.338383	+	0.154534i	−0.577357	−	0.816491i	$-0.695916\pi$
$53$	−950.518	+	434.087i	−0.338383	+	0.154534i	0.238974	+	0.971026i	$0.423189\pi$
$54$	−405.973	+	319.260i	−0.139222	+	0.109486i
$55$	−248.385	−	99.4383i	−0.0821107	−	0.0328722i
$56$	−1007.08	−	2909.77i	−0.321135	−	0.927860i
$57$	170.581	−	178.900i	0.0525026	−	0.0550632i
$58$	−1134.40	+	1765.16i	−0.337217	+	0.524720i
$59$	134.546	−	935.786i	0.0386514	−	0.268827i	−0.961327	−	0.275410i	$-0.911186\pi$
$59$	134.546	−	935.786i	0.0386514	−	0.268827i	0.999978	+	0.00658323i	$0.00209552\pi$
$60$	179.068	−	92.3159i	0.0497411	−	0.0256433i
$61$	2677.37	+	926.646i	0.719529	+	0.249032i	0.662204	−	0.749324i	$-0.269621\pi$
$61$	2677.37	+	926.646i	0.719529	+	0.249032i	0.0573258	+	0.998356i	$0.481743\pi$
$62$	2228.74	−	2572.11i	0.579798	−	0.669122i
$63$	−338.725	+	3547.29i	−0.0853426	+	0.893748i
$64$	3816.58	+	1120.65i	0.931782	+	0.273596i
$65$	−252.001	+	5290.16i	−0.0596453	+	1.25211i
$66$		−	31.9321i		−	0.00733060i
$67$	4470.15	−	411.002i	0.995800	−	0.0915577i
$67$	4470.15	−	411.002i	0.995800	−	0.0915577i
$68$	−489.427			−0.105845
$69$	532.343	+	25.3586i	0.111813	+	0.00532632i
$70$	−1014.76	+	3455.95i	−0.207094	+	0.705297i
$71$	−2148.79	−	205.184i	−0.426262	−	0.0407031i	−0.120279	−	0.992740i	$-0.538379\pi$
$71$	−2148.79	−	205.184i	−0.426262	−	0.0407031i	−0.305983	+	0.952037i	$0.598985\pi$
$72$	−4164.27	−	3608.36i	−0.803293	−	0.696057i
$73$	−1988.46	+	5745.27i	−0.373139	+	1.07811i	0.589604	+	0.807693i	$0.299284\pi$
$73$	−1988.46	+	5745.27i	−0.373139	+	1.07811i	−0.962742	+	0.270421i	$0.912837\pi$
$74$	−1881.33	−	3649.26i	−0.343559	−	0.666411i
$75$	−104.580	−	15.0363i	−0.0185919	−	0.00267312i
$76$	1359.84	+	873.918i	0.235430	+	0.151302i
$77$	−321.190	−	306.254i	−0.0541727	−	0.0516535i
$78$	−597.331	+	206.738i	−0.0981807	+	0.0339807i
$79$	−2533.77	+	6329.06i	−0.405988	+	1.01411i	0.574671	+	0.818385i	$0.305130\pi$
$79$	−2533.77	+	6329.06i	−0.405988	+	1.01411i	−0.980659	+	0.195725i	$0.937294\pi$
$80$	−1580.88	−	2010.25i	−0.247012	−	0.314101i
$81$	2610.48	+	5716.15i	0.397878	+	0.871232i
$82$	3065.50	−	1970.08i	0.455904	−	0.292992i
$83$	11165.3	+	2151.94i	1.62075	+	0.312373i	0.917246	−	0.398322i	$-0.130407\pi$
$83$	11165.3	+	2151.94i	1.62075	+	0.312373i	0.703500	+	0.710695i	$0.251620\pi$
$84$	332.662	−	31.7654i	0.0471460	−	0.00450189i
$85$	1532.64	+	1091.39i	0.212130	+	0.151057i
$86$	−2118.29	−	1092.05i	−0.286410	−	0.147655i
$87$	−516.444	−	541.631i	−0.0682315	−	0.0715591i
$88$	673.839	−	129.872i	0.0870144	−	0.0167706i
$89$	7075.89	−	2077.67i	0.893308	−	0.262299i	0.197309	−	0.980341i	$-0.436780\pi$
$89$	7075.89	−	2077.67i	0.893308	−	0.262299i	0.695999	+	0.718043i	$0.254962\pi$
$90$	1519.60	+	6263.87i	0.187605	+	0.773318i
$91$	−3649.39	+	7991.06i	−0.440695	+	0.964987i
$92$	495.979	+	3449.61i	0.0585986	+	0.407562i
$93$	704.124	+	988.804i	0.0814110	+	0.114326i
$94$	1433.75	−	1242.36i	0.162263	−	0.140602i
$95$	−2309.56	−	5769.01i	−0.255907	−	0.639226i
$96$	−438.118	+	758.842i	−0.0475388	+	0.0823397i
$97$	11001.6	−	6351.78i	1.16926	−	0.675075i	0.215757	−	0.976447i	$-0.430778\pi$
$97$	11001.6	−	6351.78i	1.16926	−	0.675075i	0.953507	+	0.301372i	$0.0974447\pi$
$98$	759.904	−	966.296i	0.0791237	−	0.100614i
$99$	−771.791	−	187.234i	−0.0787461	−	0.0191036i
$100$	−32.8747	−	690.125i	−0.00328747	−	0.0690125i
$101$	−7773.06	+	370.276i	−0.761990	+	0.0362980i	−0.424980	−	0.905203i	$-0.639719\pi$
$101$	−7773.06	+	370.276i	−0.761990	+	0.0362980i	−0.337010	+	0.941501i	$0.609416\pi$
$102$	−52.9418	+	218.229i	−0.00508860	+	0.0209755i
$103$	−15301.1	−	12032.9i	−1.44228	−	1.13422i	−0.967120	−	0.254320i	$-0.918148\pi$
$103$	−15301.1	−	12032.9i	−1.44228	−	1.13422i	−0.475158	−	0.879900i	$-0.657609\pi$
$104$	−6792.07	−	11764.2i	−0.627965	−	1.08767i
$105$	−1112.56	−	642.338i	−0.100913	−	0.0582620i
$106$	−2910.63	+	1165.24i	−0.259045	+	0.103706i
$107$	−10654.5	−	12295.9i	−0.930603	−	1.07397i	−0.997094	−	0.0761859i	$-0.975726\pi$
$107$	−10654.5	−	12295.9i	−0.930603	−	1.07397i	0.0664908	−	0.997787i	$-0.478820\pi$
$108$	981.236	−	698.735i	0.0841252	−	0.0599053i
$109$	−11202.2	+	1610.64i	−0.942871	+	0.135564i	−0.596572	−	0.802560i	$-0.703471\pi$
$109$	−11202.2	+	1610.64i	−0.942871	+	0.135564i	−0.346299	+	0.938124i	$0.612562\pi$
$110$	−730.201	−	333.471i	−0.0603472	−	0.0275596i
$111$	1423.09	−	345.239i	0.115502	−	0.0280204i
$112$	−1195.12	−	4070.21i	−0.0952744	−	0.324475i
$113$	−3673.69	−	19060.9i	−0.287704	−	1.49275i	−0.781902	−	0.623401i	$-0.785750\pi$
$113$	−3673.69	−	19060.9i	−0.287704	−	1.49275i	0.494198	−	0.869349i	$-0.335462\pi$
$114$	536.763	−	511.802i	0.0413022	−	0.0393815i
$115$	6139.22	−	11908.4i	0.464213	−	0.900447i
$116$	2838.73	−	3986.44i	0.210964	−	0.296258i
$117$	1494.35	+	15649.6i	0.109164	+	1.14322i
$118$	536.821	−	2785.29i	0.0385537	−	0.200035i
$119$	1687.31	+	2625.50i	0.119152	+	0.185404i
$120$	1806.98	−	825.220i	0.125485	−	0.0573070i
$121$	−11430.9	+	8989.32i	−0.780743	+	0.613983i
$122$	7891.65	+	3159.34i	0.530210	+	0.212264i
$123$	425.089	+	1228.22i	0.0280977	+	0.0811828i
$124$	−5477.81	+	5744.96i	−0.356257	+	0.373632i
$125$	7654.30	−	11910.3i	0.489875	−	0.762261i
$126$	−1521.56	+	10582.7i	−0.0958402	+	0.666583i
$127$	22225.9	−	11458.3i	1.37801	−	0.710414i	0.399524	−	0.916723i	$-0.369175\pi$
$127$	22225.9	−	11458.3i	1.37801	−	0.710414i	0.978487	+	0.206309i	$0.0661452\pi$
$128$	−1102.27	−	381.498i	−0.0672769	−	0.0232848i
$129$	556.647	−	642.405i	0.0334504	−	0.0386038i
$130$	−1510.47	+	15818.4i	−0.0893769	+	0.935997i
$131$	−4640.68	−	1362.63i	−0.270420	−	0.0794026i	0.143711	−	0.989620i	$-0.454096\pi$
$131$	−4640.68	−	1362.63i	−0.270420	−	0.0794026i	−0.414131	+	0.910217i	$0.635915\pi$
$132$	−3.54378	+	74.3930i	−0.000203385	+	0.00426957i
$133$		−	10307.6i		−	0.582714i
$134$	13455.5	−	593.585i	0.749358	−	0.0330578i
$135$	−4630.86			−0.254094
$136$	−4820.45	−	229.626i	−0.260621	−	0.0124149i
$137$	−5809.82	+	19786.4i	−0.309543	+	1.05421i	0.646969	+	0.762516i	$0.276036\pi$
$137$	−5809.82	+	19786.4i	−0.309543	+	1.05421i	−0.956512	+	0.291692i	$0.905782\pi$
$138$	1591.78	+	151.997i	0.0835845	+	0.00798135i
$139$	7772.23	+	6734.68i	0.402269	+	0.348568i	0.832377	−	0.554209i	$-0.186979\pi$
$139$	7772.23	+	6734.68i	0.402269	+	0.348568i	−0.430109	+	0.902777i	$0.641525\pi$
$140$	2747.65	−	7938.81i	0.140186	−	0.405041i
$141$	310.059	+	601.431i	0.0155958	+	0.0302516i
$142$	−6410.51	−	921.692i	−0.317918	−	0.0457098i
$143$	−1647.08	−	1058.52i	−0.0805459	−	0.0517637i
$144$	−5494.01	−	5238.53i	−0.264950	−	0.252630i
$145$	−17778.9	+	6153.35i	−0.845610	+	0.292668i
$146$	−6779.51	+	16934.4i	−0.318048	+	0.794445i
$147$	271.036	+	344.650i	0.0125427	+	0.0159494i
$148$	3977.99	+	8710.58i	0.181610	+	0.397671i
$149$	13001.0	−	8355.22i	0.585603	−	0.376344i	−0.214035	−	0.976826i	$-0.568661\pi$
$149$	13001.0	−	8355.22i	0.585603	−	0.376344i	0.799639	+	0.600482i	$0.205024\pi$
$150$	−311.273	−	59.9930i	−0.0138344	−	0.00266636i
$151$	−14340.9	+	1369.39i	−0.628961	+	0.0600585i	−0.404669	−	0.914463i	$-0.632613\pi$
$151$	−14340.9	+	1369.39i	−0.628961	+	0.0600585i	−0.224292	+	0.974522i	$0.572007\pi$
$152$	12983.3	+	9245.35i	0.561949	+	0.400162i
$153$	4964.12	+	2559.18i	0.212060	+	0.109325i
$154$	−918.868	−	963.681i	−0.0387446	−	0.0406342i
$155$	29964.5	−	5775.19i	1.24722	−	0.240383i
$156$	1414.56	−	415.353i	0.0581263	−	0.0170674i
$157$	1235.24	+	5091.72i	0.0501131	+	0.206569i	0.991364	−	0.131139i	$-0.0418634\pi$
$157$	1235.24	+	5091.72i	0.0501131	+	0.206569i	−0.941251	+	0.337708i	$0.890348\pi$
$158$	−8497.13	+	18606.1i	−0.340376	+	0.745318i
$159$	−159.142	−	1106.85i	−0.00629491	−	0.0437821i
$160$	12777.3	+	17943.3i	0.499115	+	0.700909i
$161$	16795.3	−	14553.2i	0.647943	−	0.561446i
$162$	7007.42	+	17503.7i	0.267011	+	0.666960i
$163$	−10853.4	+	18798.7i	−0.408500	+	0.707543i	−0.994722	−	0.102608i	$-0.967281\pi$
$163$	−10853.4	+	18798.7i	−0.408500	+	0.707543i	0.586222	+	0.810151i	$0.300615\pi$
$164$	−7360.42	+	4249.54i	−0.273662	+	0.157999i
$165$	176.988	−	225.059i	0.00650094	−	0.00826662i
$166$	33154.7	+	8043.23i	1.20317	+	0.291887i
$167$	−1488.05	−	31238.0i	−0.0533562	−	1.12008i	−0.853775	−	0.520643i	$-0.825692\pi$
$167$	−1488.05	−	31238.0i	−0.0533562	−	1.12008i	0.800418	−	0.599442i	$-0.204611\pi$
$168$	3291.34	−	156.786i	0.116615	−	0.00555506i
$169$	−2403.68	+	9908.10i	−0.0841595	+	0.346910i
$170$	4437.43	+	3489.63i	0.153544	+	0.120749i
$171$	−9222.82	−	15974.4i	−0.315407	−	0.546301i
$172$	4813.84	+	2779.27i	0.162718	+	0.0939450i
$173$	−37695.6	+	15091.1i	−1.25950	+	0.504228i	−0.902829	−	0.430001i	$-0.858513\pi$
$173$	−37695.6	+	15091.1i	−1.25950	+	0.504228i	−0.356673	+	0.934229i	$0.616089\pi$
$174$	−1470.43	−	1696.97i	−0.0485676	−	0.0560500i
$175$	−3588.80	+	2555.57i	−0.117185	+	0.0834472i
$176$	935.799	−	134.548i	0.0302104	−	0.00434361i
$177$	920.289	+	420.282i	0.0293750	+	0.0134151i
$178$	21502.7	−	5216.50i	0.678661	−	0.164641i
$179$	−11954.3	−	40712.5i	−0.373093	−	1.27064i	−0.905571	−	0.424194i	$-0.860557\pi$
$179$	−11954.3	−	40712.5i	−0.373093	−	1.27064i	0.532478	−	0.846444i	$-0.321261\pi$
$180$	−2845.10	−	14761.8i	−0.0878116	−	0.455610i
$181$	−14785.4	+	14097.9i	−0.451312	+	0.430325i	−0.881334	−	0.472493i	$-0.843354\pi$
$181$	−14785.4	+	14097.9i	−0.451312	+	0.430325i	0.430022	+	0.902818i	$0.358506\pi$
$182$	−12077.9	+	23427.8i	−0.364626	+	0.707275i
$183$	−1758.68	+	2469.71i	−0.0525150	+	0.0737470i
$184$	3266.51	+	34208.4i	0.0964824	+	1.01041i
$185$	6966.90	−	36147.7i	0.203562	−	1.05618i
$186$	1969.06	+	3063.92i	0.0569158	+	0.0885627i
$187$	−632.706	+	288.947i	−0.0180933	+	0.00826295i
$188$	−3478.13	+	2735.23i	−0.0984080	+	0.0773889i
$189$	−7131.15	−	2854.88i	−0.199635	−	0.0799217i
$190$	−6098.05	−	17619.2i	−0.168921	−	0.488065i
$191$	18428.6	−	19327.4i	0.505157	−	0.529793i	−0.420935	−	0.907091i	$-0.638298\pi$
$191$	18428.6	−	19327.4i	0.505157	−	0.529793i	0.926092	+	0.377297i	$0.123147\pi$
$192$	−2301.34	+	3580.95i	−0.0624278	+	0.0971396i
$193$	−7020.87	+	48831.2i	−0.188485	+	1.31094i	0.647448	+	0.762109i	$0.275836\pi$
$193$	−7020.87	+	48831.2i	−0.188485	+	1.31094i	−0.835933	+	0.548831i	$0.815073\pi$
$194$	33878.0	−	17465.3i	0.900150	−	0.464059i
$195$	−5355.90	−	1853.69i	−0.140852	−	0.0487493i
$196$	−1877.61	+	2166.87i	−0.0488756	+	0.0564055i
$197$	1402.82	−	14691.0i	0.0361468	−	0.378546i	−0.959239	−	0.282595i	$-0.908805\pi$
$197$	1402.82	−	14691.0i	0.0361468	−	0.378546i	0.995386	−	0.0959510i	$-0.0305892\pi$
$198$	−2286.29	−	671.315i	−0.0583177	−	0.0171236i
$199$	−643.754	+	13514.1i	−0.0162560	+	0.341256i	0.976058	+	0.217510i	$0.0697936\pi$
$199$	−643.754	+	13514.1i	−0.0162560	+	0.341256i	−0.992314	+	0.123745i	$0.960509\pi$
$200$		−	6812.57i		−	0.170314i
$201$	−925.702	+	4713.81i	−0.0229128	+	0.116676i
$202$	−23348.3			−0.572207
$203$	−31171.6	−	1484.89i	−0.756428	−	0.0360331i
$204$	147.559	−	502.538i	0.00354572	−	0.0120756i
$205$	32525.2	+	3105.78i	0.773950	+	0.0739033i
$206$	−44138.9	−	38246.5i	−1.04013	−	0.901276i
$207$	13007.2	−	37581.8i	0.303559	−	0.877075i
$208$	−8575.54	−	16634.2i	−0.198214	−	0.384482i
$209$	2273.87	+	326.934i	0.0520563	+	0.00748457i
$210$	−3242.59	−	2083.89i	−0.0735281	−	0.0472537i
$211$	31535.7	+	30069.2i	0.708333	+	0.675394i	0.955972	−	0.293458i	$-0.0948061\pi$
$211$	31535.7	+	30069.2i	0.708333	+	0.675394i	−0.247639	+	0.968852i	$0.579655\pi$
$212$	6910.28	−	2391.67i	0.153753	−	0.0532145i
$213$	858.523	−	2144.49i	0.0189231	−	0.0472677i
$214$	−30175.5	−	38371.3i	−0.658912	−	0.837874i
$215$	−8876.93	−	19437.8i	−0.192037	−	0.420503i
$216$	9992.18	−	6421.58i	0.214167	−	0.137637i
$217$	49703.3	+	9579.53i	1.05552	+	0.203435i
$218$	−33802.5	+	3227.75i	−0.711272	+	0.0679183i
$219$	−5299.67	−	3773.88i	−0.110500	−	0.0786864i
$220$	1664.16	+	857.934i	0.0343835	+	0.0177259i
$221$	9501.47	+	9964.85i	0.194539	+	0.204026i
$222$	4314.23	−	831.499i	0.0875381	−	0.0168716i
$223$	−72330.8	+	21238.2i	−1.45450	+	0.427079i	−0.911026	−	0.412348i	$-0.864709\pi$
$223$	−72330.8	+	21238.2i	−1.45450	+	0.427079i	−0.543472	+	0.839427i	$0.682891\pi$
$224$	8614.22	+	35508.3i	0.171680	+	0.707675i
$225$	−3275.17	+	7171.63i	−0.0646948	+	0.141662i
$226$	−8288.69	−	57649.1i	−0.162281	−	1.12869i
$227$	−27835.7	−	39089.7i	−0.540194	−	0.758597i	0.450782	−	0.892634i	$-0.351145\pi$
$227$	−27835.7	−	39089.7i	−0.540194	−	0.758597i	−0.990976	+	0.134037i	$0.957206\pi$
$228$	−1307.31	+	1132.79i	−0.0251483	+	0.0217911i
$229$	18816.9	+	47002.3i	0.358820	+	0.896289i	0.992450	+	0.122652i	$0.0391400\pi$
$229$	18816.9	+	47002.3i	0.358820	+	0.896289i	−0.633630	+	0.773636i	$0.718436\pi$
$230$	20099.0	−	34812.5i	0.379943	−	0.658081i
$231$	411.294	−	237.461i	0.00770777	−	0.00445008i
$232$	29829.5	−	37931.3i	0.554204	−	0.704728i
$233$	53848.2	+	13063.4i	0.991880	+	0.240627i	0.698688	−	0.715426i	$-0.253767\pi$
$233$	53848.2	+	13063.4i	0.991880	+	0.240627i	0.293192	+	0.956054i	$0.405283\pi$
$234$	2244.33	+	47114.3i	0.0409878	+	0.860441i
$235$	16991.1	−	809.386i	0.307671	−	0.0146562i
$236$	−1559.76	+	6429.40i	−0.0280048	+	0.115437i
$237$	−5734.69	−	4509.81i	−0.102097	−	0.0802900i
$238$	4681.96	+	8109.38i	0.0826558	+	0.143164i
$239$	−12733.0	−	7351.38i	−0.222912	−	0.128698i	0.384386	−	0.923173i	$-0.374413\pi$
$239$	−12733.0	−	7351.38i	−0.222912	−	0.128698i	−0.607298	+	0.794474i	$0.707747\pi$
$240$	2540.72	−	1017.15i	0.0441097	−	0.0176589i
$241$	28035.9	+	32355.2i	0.482704	+	0.557070i	0.943901	−	0.330227i	$-0.107125\pi$
$241$	28035.9	+	32355.2i	0.482704	+	0.557070i	−0.461197	+	0.887298i	$0.652580\pi$
$242$	−35541.0	+	25308.7i	−0.606875	+	0.432154i
$243$	−20457.5	+	2941.34i	−0.346449	+	0.0498118i
$244$	−18034.8	−	8236.20i	−0.302922	−	0.138340i
$245$	10711.7	−	2598.62i	0.178454	−	0.0432924i
$246$	1098.63	+	3741.58i	0.0181543	+	0.0618280i
$247$	−8606.05	−	44652.4i	−0.141062	−	0.731899i
$248$	−56647.2	+	54013.0i	−0.921033	+	0.878203i
$249$	−5575.84	+	10815.6i	−0.0899315	+	0.174443i
$250$	24639.9	−	34601.9i	0.394238	−	0.553630i
$251$	−2537.74	−	26576.5i	−0.0402810	−	0.421842i	−0.993011	−	0.118023i	$-0.962344\pi$
$251$	−2537.74	−	26576.5i	−0.0402810	−	0.421842i	0.952730	−	0.303819i	$-0.0982618\pi$
$252$	4719.27	−	24485.9i	0.0743145	−	0.385580i
$253$	2677.75	+	4166.66i	0.0418339	+	0.0650948i
$254$	68245.8	−	31166.8i	1.05781	−	0.483087i
$255$	−1582.70	+	1244.65i	−0.0243399	+	0.0191411i
$256$	−62333.4	−	24954.5i	−0.951132	−	0.380776i
$257$	17921.5	+	51780.7i	0.271336	+	0.783974i	0.995536	+	0.0943841i	$0.0300882\pi$
$257$	17921.5	+	51780.7i	0.271336	+	0.783974i	−0.724200	+	0.689590i	$0.757791\pi$
$258$	1759.95	−	1845.79i	0.0264400	−	0.0277295i
$259$	33013.2	−	51369.5i	0.492139	−	0.765783i
$260$	5274.48	−	36684.8i	0.0780249	−	0.542675i
$261$	−49637.3	+	25589.8i	−0.728663	+	0.375652i
$262$	−13713.4	−	4746.24i	−0.199775	−	0.0691428i
$263$	−54242.6	+	62599.3i	−0.784204	+	0.905020i	−0.997405	−	0.0719887i	$-0.977065\pi$
$263$	−54242.6	+	62599.3i	−0.784204	+	0.905020i	0.213202	+	0.977008i	$0.431611\pi$
$264$	−69.8064	+	731.046i	−0.00100158	+	0.0104891i
$265$	−26972.7	−	7919.91i	−0.384090	−	0.112779i
$266$	1471.54	−	30891.5i	0.0207974	−	0.436591i
$267$			7891.85i			0.110702i
$268$	−31413.5	−	110.378i	−0.437367	−	0.00153678i
$269$	23246.7			0.321260			0.160630	−	0.987015i	$-0.448647\pi$
$269$	23246.7			0.321260			0.160630	+	0.987015i	$0.448647\pi$
$270$	−13878.5	−	661.112i	−0.190377	−	0.00906875i
$271$	1528.67	−	5206.18i	0.0208150	−	0.0708893i	−0.948431	−	0.316985i	$-0.897330\pi$
$271$	1528.67	−	5206.18i	0.0208150	−	0.0708893i	0.969246	+	0.246096i	$0.0791477\pi$
$272$	−6618.47	−	631.987i	−0.0894582	−	0.00854222i
$273$	−7104.86	−	6156.40i	−0.0953301	−	0.0826040i
$274$	−20236.5	+	58469.5i	−0.269547	+	0.778804i
$275$	−449.933	−	872.748i	−0.00594953	−	0.0115405i
$276$	−3691.55	−	530.765i	−0.0484608	−	0.00696762i
$277$	42398.0	+	27247.6i	0.552569	+	0.355114i	0.786937	−	0.617034i	$-0.211666\pi$
$277$	42398.0	+	27247.6i	0.552569	+	0.355114i	−0.234368	+	0.972148i	$0.575302\pi$
$278$	22331.5	+	21293.1i	0.288954	+	0.275517i
$279$	85599.8	−	29626.4i	1.09967	−	0.380601i
$280$	30786.7	−	76901.5i	0.392688	−	0.980886i
$281$	89575.4	+	113904.i	1.13443	+	1.44254i	0.879702	+	0.475525i	$0.157742\pi$
$281$	89575.4	+	113904.i	1.13443	+	1.44254i	0.254723	+	0.967014i	$0.418016\pi$
$282$	843.370	+	1846.72i	0.0106052	+	0.0232222i
$283$	−24282.2	+	15605.2i	−0.303191	+	0.194849i	−0.683386	−	0.730058i	$-0.739493\pi$
$283$	−24282.2	+	15605.2i	−0.303191	+	0.194849i	0.380195	+	0.924906i	$0.375857\pi$
$284$	14832.4	+	2858.72i	0.183898	+	0.0354434i
$285$	6619.87	−	632.121i	0.0815004	−	0.00778235i
$286$	−4785.11	−	3407.46i	−0.0585005	−	0.0416580i
$287$	48171.6	+	24834.2i	0.584826	+	0.301499i
$288$	45121.3	+	47321.9i	0.543997	+	0.570528i
$289$	−77208.6	+	14880.7i	−0.924421	+	0.178168i
$290$	−54161.1	+	15903.1i	−0.644008	+	0.189098i
$291$	3205.03	+	13211.3i	0.0378483	+	0.156013i
$292$	17673.8	−	38700.1i	0.207283	−	0.453886i
$293$	14211.3	+	98842.0i	0.165539	+	1.15135i	0.887969	+	0.459903i	$0.152116\pi$
$293$	14211.3	+	98842.0i	0.165539	+	1.15135i	−0.722430	+	0.691444i	$0.756975\pi$
$294$	763.077	+	1071.59i	0.00882823	+	0.0123975i
$295$	19221.4	−	16655.5i	0.220873	−	0.191387i
$296$	35093.0	+	87658.2i	0.400532	+	1.00048i
$297$	855.972	−	1482.59i	0.00970391	−	0.0168077i
$298$	40156.1	−	23184.1i	0.452188	−	0.261071i
$299$	60606.1	−	77067.0i	0.677914	−	0.862037i
$300$	718.524	+	174.312i	0.00798360	+	0.00193680i
$301$	−1686.55	−	35405.1i	−0.0186152	−	0.390781i
$302$	−43174.6	+	2056.66i	−0.473385	+	0.0225501i
$303$	1963.32	−	8092.92i	0.0213848	−	0.0881495i
$304$	17260.5	+	13573.8i	0.186770	+	0.146877i
$305$	38109.6	+	66007.8i	0.409671	+	0.709570i
$306$	14511.8	+	8378.42i	0.154982	+	0.0894786i
$307$	−132084.	+	52878.3i	−1.40143	+	0.561049i	−0.944518	−	0.328461i	$-0.893470\pi$
$307$	−132084.	+	52878.3i	−1.40143	+	0.561049i	−0.456915	+	0.889510i	$0.651046\pi$
$308$	2033.76	+	2347.09i	0.0214387	+	0.0247416i
$309$	16968.5	−	12083.2i	0.177716	−	0.126551i
$310$	90626.7	−	13030.2i	0.943046	−	0.135590i
$311$	−119297.	−	54481.1i	−1.23341	−	0.563281i	−0.311341	−	0.950298i	$-0.600778\pi$
$311$	−119297.	−	54481.1i	−1.23341	−	0.563281i	−0.922073	+	0.387017i	$0.873506\pi$
$312$	14127.1	−	3427.20i	0.145126	−	0.0352071i
$313$	−20858.1	−	71036.0i	−0.212905	−	0.725087i	−0.994815	−	0.101696i	$-0.967573\pi$
$313$	−20858.1	−	71036.0i	−0.212905	−	0.725087i	0.781911	−	0.623390i	$-0.214245\pi$
$314$	2975.04	+	15436.0i	0.0301741	+	0.156558i
$315$	−69380.1	+	66153.8i	−0.699220	+	0.666705i
$316$	21860.9	−	42404.2i	0.218924	−	0.424654i
$317$	−75819.2	+	106473.i	−0.754502	+	1.05955i	0.241515	+	0.970397i	$0.422356\pi$
$317$	−75819.2	+	106473.i	−0.754502	+	1.05955i	−0.996018	+	0.0891535i	$0.971584\pi$
$318$	−318.922	−	3339.91i	−0.00315378	−	0.0330278i
$319$	1316.26	−	6829.39i	0.0129348	−	0.0671120i
$320$	57853.5	+	90021.9i	0.564976	+	0.879120i
$321$	15837.5	−	7232.76i	0.153701	−	0.0701931i
$322$	52412.4	−	41217.5i	0.505501	−	0.397530i
$323$	−14998.0	−	6004.28i	−0.143756	−	0.0575514i
$324$	−14382.9	−	41556.5i	−0.137011	−	0.395867i
$325$	−13412.9	+	14067.0i	−0.126986	+	0.133179i
$326$	−35210.9	+	54789.3i	−0.331316	+	0.515538i
$327$	1723.60	−	11987.9i	0.0161191	−	0.112111i
$328$	−74487.7	+	38401.1i	−0.692368	+	0.356940i
$329$	26663.9	+	9228.47i	0.246338	+	0.0852585i
$330$	562.554	−	649.222i	0.00516579	−	0.00596164i
$331$	−9107.97	+	95383.0i	−0.0831315	+	0.870593i	0.853689	+	0.520783i	$0.174360\pi$
$331$	−9107.97	+	95383.0i	−0.0831315	+	0.870593i	−0.936821	+	0.349810i	$0.886246\pi$
$332$	−76348.7	−	22418.0i	−0.692668	−	0.203386i
$333$	5199.43	−	109149.i	0.0468886	−	0.984312i
$334$		−	93831.2i		−	0.841113i
$335$	98124.8	+	70395.3i	0.874358	+	0.627269i
$336$	4539.57			0.0402102
$337$	157258.	+	7491.11i	1.38469	+	0.0659609i	0.726642	−	0.687016i	$-0.241080\pi$
$337$	157258.	+	7491.11i	1.38469	+	0.0659609i	0.658047	+	0.752977i	$0.271383\pi$
$338$	−8618.21	+	29350.9i	−0.0754369	+	0.256914i
$339$	20679.1	+	1974.62i	0.179942	+	0.0171824i
$340$	−9950.72	−	8622.35i	−0.0860789	−	0.0745878i
$341$	−3689.72	+	10660.8i	−0.0317311	+	0.0916810i
$342$	−25359.8	−	49191.1i	−0.216817	−	0.420566i
$343$	124148.	+	17849.8i	1.05524	+	0.151721i
$344$	46108.3	+	29632.0i	0.389639	+	0.250406i
$345$	10376.5	+	9893.97i	0.0871792	+	0.0831252i
$346$	−115126.	+	39845.6i	−0.961662	+	0.332834i
$347$	64579.3	−	161311.i	0.536333	−	1.33970i	−0.374617	−	0.927180i	$-0.622226\pi$
$347$	64579.3	−	161311.i	0.536333	−	1.33970i	0.910950	−	0.412516i	$-0.135350\pi$
$348$	3237.38	+	4116.66i	0.0267322	+	0.0339928i
$349$	−43065.5	−	94300.3i	−0.353573	−	0.774216i	−0.999937	−	0.0111876i	$-0.996439\pi$
$349$	−43065.5	−	94300.3i	−0.353573	−	0.774216i	0.646365	−	0.763029i	$-0.276288\pi$
$350$	−11120.3	+	7146.57i	−0.0907778	+	0.0583394i
$351$	−33275.6	−	6413.34i	−0.270092	−	0.0520559i
$352$	−8106.38	+	774.066i	−0.0654247	+	0.00624730i
$353$	−109475.	−	77956.7i	−0.878547	−	0.625610i	0.0492132	−	0.998788i	$-0.484329\pi$
$353$	−109475.	−	77956.7i	−0.878547	−	0.625610i	−0.927760	+	0.373178i	$0.878268\pi$
$354$	2698.06	+	1390.95i	0.0215300	+	0.0110995i
$355$	−40072.9	−	42027.3i	−0.317976	−	0.333484i
$356$	−50674.3	+	9766.68i	−0.399842	+	0.0770632i
$357$	−3204.55	+	940.940i	−0.0251438	+	0.00738288i
$358$	−30014.1	−	123720.i	−0.234185	−	0.965325i
$359$	45140.5	−	98844.0i	0.350250	−	0.766940i	−0.649727	−	0.760167i	$-0.725117\pi$
$359$	45140.5	−	98844.0i	0.350250	−	0.766940i	0.999977	−	0.00677257i	$-0.00215579\pi$
$360$	−21096.0	−	146726.i	−0.162778	−	1.13214i
$361$	−44643.9	−	62693.6i	−0.342569	−	0.481071i
$362$	−46323.9	+	40139.9i	−0.353499	+	0.306308i
$363$	−5783.82	−	14447.3i	−0.0438936	−	0.109641i
$364$	30738.1	−	53240.0i	0.231993	−	0.401823i
$365$	−141644.	+	81778.0i	−1.06319	+	0.613834i
$366$	−5623.24	+	7150.54i	−0.0419783	+	0.0533797i
$367$	14417.3	+	3497.60i	0.107041	+	0.0259679i	0.288922	−	0.957353i	$-0.406703\pi$
$367$	14417.3	+	3497.60i	0.107041	+	0.0259679i	−0.181880	+	0.983321i	$0.558218\pi$
$368$	2252.66	+	47289.1i	0.0166341	+	0.349193i
$369$	96875.1	−	4614.73i	0.711474	−	0.0338917i
$370$	26040.0	−	107338.i	0.190212	−	0.784063i
$371$	−36653.3	−	28824.5i	−0.266296	−	0.209418i
$372$	−4247.34	−	7356.61i	−0.0306924	−	0.0531609i
$373$	−151181.	−	87284.6i	−1.08663	−	0.627365i	−0.153951	−	0.988078i	$-0.549200\pi$
$373$	−151181.	−	87284.6i	−1.08663	−	0.627365i	−0.932677	+	0.360714i	$0.882533\pi$
$374$	−1937.44	+	775.633i	−0.0138511	+	0.00554515i
$375$	9921.67	+	11450.2i	0.0705541	+	0.0814238i
$376$	−35540.0	+	25307.9i	−0.251386	+	0.179011i
$377$	−136274.	+	19593.3i	−0.958808	+	0.137856i
$378$	−20964.1	−	9573.99i	−0.146721	−	0.0670054i
$379$	189390.	−	45945.6i	1.31850	−	0.319864i	0.486032	−	0.873941i	$-0.338444\pi$
$379$	189390.	−	45945.6i	1.31850	−	0.319864i	0.832466	+	0.554077i	$0.186929\pi$
$380$	12251.4	+	41724.6i	0.0848438	+	0.288951i
$381$	5064.27	+	26275.9i	0.0348872	+	0.181012i
$382$	57988.9	−	55292.3i	0.397391	−	0.378912i
$383$	1895.97	−	3677.66i	0.0129251	−	0.0250711i	−0.882285	−	0.470717i	$-0.843995\pi$
$383$	1895.97	−	3677.66i	0.0129251	−	0.0250711i	0.895210	+	0.445645i	$0.147026\pi$
$384$	724.042	−	1016.77i	0.00491022	−	0.00689545i
$385$	−1134.88	−	11885.0i	−0.00765648	−	0.0801823i
$386$	−28012.4	+	145342.i	−0.188008	+	0.975478i
$387$	−34292.7	−	53360.5i	−0.228971	−	0.356285i
$388$	−80864.9	+	36929.7i	−0.537151	+	0.245309i
$389$	165994.	−	130539.i	1.09696	−	0.862663i	0.105680	−	0.994400i	$-0.466298\pi$
$389$	165994.	−	130539.i	1.09696	−	0.862663i	0.991285	+	0.131738i	$0.0420556\pi$
$390$	−15786.7	−	6320.04i	−0.103792	−	0.0415519i
$391$	−11392.0	−	32915.2i	−0.0745158	−	0.215299i
$392$	−19509.5	+	20461.0i	−0.126962	+	0.133154i
$393$	2798.26	−	4354.18i	0.0181177	−	0.0281917i
$394$	6301.50	−	43827.9i	0.0405930	−	0.282331i
$395$	−163015.	+	84040.3i	−1.04480	+	0.538633i
$396$	5251.92	+	1817.71i	0.0334910	+	0.0115913i
$397$	−115574.	+	133379.i	−0.733295	+	0.846268i	−0.992839	−	0.119464i	$-0.961883\pi$
$397$	−115574.	+	133379.i	−0.733295	+	0.846268i	0.259543	+	0.965731i	$0.416428\pi$
$398$	−3858.60	+	40409.1i	−0.0243592	+	0.255101i
$399$	10583.8	+	3107.67i	0.0664805	+	0.0195204i
$400$	446.583	−	9374.93i	0.00279114	−	0.0585933i
$401$		−	85183.4i		−	0.529744i	−0.964284	−	0.264872i	$-0.914670\pi$
$401$		−	85183.4i		−	0.529744i	0.964284	−	0.264872i	$-0.0853297\pi$
$402$	−3447.23	+	13994.9i	−0.0213314	+	0.0865999i
$403$	223312.			1.37500
$404$	54395.2	+	2591.16i	0.333271	+	0.0158757i
$405$	−47628.1	+	162207.i	−0.290371	+	0.988914i
$406$	−93207.8	−	8900.26i	−0.565458	−	0.0539947i
$407$	10285.1	+	8912.05i	0.0620895	+	0.0538008i
$408$	1689.11	−	4880.35i	0.0101470	−	0.0293177i
$409$	−105545.	−	204729.i	−0.630944	−	1.22386i	−0.960119	−	0.279592i	$-0.909801\pi$
$409$	−105545.	−	204729.i	−0.630944	−	1.22386i	0.329175	−	0.944269i	$-0.393230\pi$
$410$	97033.1	+	13951.3i	0.577234	+	0.0829938i
$411$	−18564.9	−	11930.9i	−0.109903	−	0.0706302i
$412$	98586.9	+	94002.5i	0.580798	+	0.553790i
$413$	39867.4	−	13798.2i	0.233732	−	0.0808954i
$414$	44347.1	−	110774.i	0.258741	−	0.646303i
$415$	189095.	+	240454.i	1.09795	+	1.39616i
$416$	66963.2	+	146629.i	0.386945	+	0.847292i
$417$	−9258.36	+	5949.98i	−0.0532429	+	0.0342171i
$418$	6768.01	+	1304.43i	0.0387354	+	0.00746564i
$419$	−182151.	+	17393.3i	−1.03754	+	0.0990729i	−0.599898	−	0.800077i	$-0.704792\pi$
$419$	−182151.	+	17393.3i	−1.03754	+	0.0990729i	−0.437641	+	0.899150i	$0.644186\pi$
$420$	7323.09	+	5214.75i	0.0415141	+	0.0295621i
$421$	68950.5	+	35546.5i	0.389021	+	0.200554i	0.641630	−	0.767014i	$-0.278258\pi$
$421$	68950.5	+	35546.5i	0.389021	+	0.200554i	−0.252609	+	0.967568i	$0.581289\pi$
$422$	90218.1	+	94618.0i	0.506604	+	0.531311i
$423$	49580.0	−	9555.76i	0.277093	−	0.0534053i
$424$	69182.5	−	20313.8i	0.384826	−	0.112995i
$425$	1627.94	+	6710.47i	0.00901283	+	0.0371514i
$426$	2879.10	−	6304.35i	0.0158649	−	0.0347393i
$427$	17992.5	+	125141.i	0.0986817	+	0.686346i
$428$	66042.3	+	92743.5i	0.360525	+	0.506286i
$429$	1583.46	−	1372.07i	0.00860382	−	0.00745525i
$430$	−23828.7	−	59521.3i	−0.128874	−	0.321911i
$431$	90250.3	−	156318.i	0.485841	−	0.841501i	−0.514027	−	0.857774i	$-0.671847\pi$
$431$	90250.3	−	156318.i	0.485841	−	0.841501i	0.999868	+	0.0162730i	$0.00518008\pi$
$432$	14171.4	−	8181.87i	0.0759356	−	0.0438415i
$433$	−136309.	+	173331.i	−0.727022	+	0.924484i	−0.999288	−	0.0377383i	$-0.987985\pi$
$433$	−136309.	+	173331.i	−0.727022	+	0.924484i	0.272265	+	0.962222i	$0.412227\pi$
$434$	147591.	+	35805.1i	0.783573	+	0.190093i
$435$	−957.977	−	20110.4i	−0.00506263	−	0.106278i
$436$	79108.8	−	3768.42i	0.416152	−	0.0198238i
$437$	−27121.0	+	111794.i	−0.142018	+	0.585405i
$438$	−15344.1	−	12066.7i	−0.0799820	−	0.0628986i
$439$	35186.0	+	60943.9i	0.182575	+	0.316229i	0.942757	−	0.333482i	$-0.108223\pi$
$439$	35186.0	+	60943.9i	0.182575	+	0.316229i	−0.760182	+	0.649710i	$0.774890\pi$
$440$	15988.1	+	9230.71i	0.0825829	+	0.0476793i
$441$	30374.4	−	12160.1i	0.156182	−	0.0625258i
$442$	27052.8	+	31220.6i	0.138474	+	0.159807i
$443$	−138960.	+	98952.9i	−0.708080	+	0.504221i	−0.876444	−	0.481504i	$-0.840091\pi$
$443$	−138960.	+	98952.9i	−0.708080	+	0.504221i	0.168364	+	0.985725i	$0.446151\pi$
$444$	−10143.3	+	1458.38i	−0.0514531	+	0.00739783i
$445$	180465.	+	82415.7i	0.911325	+	0.416188i
$446$	−219804.	+	53323.8i	−1.10501	+	0.268072i
$447$	4659.35	+	15868.3i	0.0233190	+	0.0794173i
$448$	33592.1	+	174293.i	0.167372	+	0.868406i
$449$	165074.	−	157398.i	0.818818	−	0.780741i	−0.159643	−	0.987175i	$-0.551034\pi$
$449$	165074.	−	157398.i	0.818818	−	0.780741i	0.978461	+	0.206434i	$0.0661858\pi$
$450$	−10839.4	+	21025.4i	−0.0535277	+	0.103829i
$451$	−7006.32	+	9839.00i	−0.0344459	+	0.0483724i
$452$	12912.6	+	135227.i	0.0632027	+	0.661889i
$453$	2917.61	−	15138.0i	0.0142177	−	0.0737686i
$454$	−77841.6	−	121124.i	−0.377659	−	0.587649i
$455$	−214977.	+	98176.8i	−1.03841	+	0.474227i
$456$	−13407.4	+	10543.7i	−0.0644784	+	0.0507064i
$457$	−349337.	−	139853.i	−1.67268	−	0.669639i	−0.675004	−	0.737814i	$-0.735858\pi$
$457$	−349337.	−	139853.i	−1.67268	−	0.669639i	−0.997673	+	0.0681751i	$0.978282\pi$
$458$	49683.1	+	143550.i	0.236852	+	0.684339i
$459$	−8307.91	+	8713.08i	−0.0394336	+	0.0413567i
$460$	−50688.6	+	78873.0i	−0.239549	+	0.372746i
$461$	32138.4	−	223527.i	0.151225	−	1.05179i	−0.762947	−	0.646461i	$-0.776248\pi$
$461$	32138.4	−	223527.i	0.151225	−	1.05179i	0.914171	−	0.405328i	$-0.132843\pi$
$462$	1266.53	−	652.940i	0.00593377	−	0.00305907i
$463$	−112406.	−	38904.1i	−0.524357	−	0.181482i	0.0520499	−	0.998644i	$-0.483425\pi$
$463$	−112406.	−	38904.1i	−0.524357	−	0.181482i	−0.576407	+	0.817163i	$0.695546\pi$
$464$	43535.5	−	50242.6i	0.202212	−	0.233365i
$465$	−3104.18	+	32508.4i	−0.0143562	+	0.150345i
$466$	159515.	+	46837.9i	0.734565	+	0.215688i
$467$	4688.87	−	98431.4i	0.0214998	−	0.451336i	−0.962292	−	0.272020i	$-0.912308\pi$
$467$	4688.87	−	98431.4i	0.0214998	−	0.451336i	0.983791	−	0.179316i	$-0.0573885\pi$
$468$		−	110013.i		−	0.502285i
$469$	107706.	+	168896.i	0.489661	+	0.767846i
$470$	51037.0			0.231041
$471$	−5600.54	−	266.786i	−0.0252457	−	0.00120260i
$472$	−18378.8	+	62592.4i	−0.0824959	+	0.280955i
$473$	7863.89	+	750.911i	0.0351492	+	0.00335634i
$474$	−16542.7	−	14334.4i	−0.0736293	−	0.0638002i
$475$	7459.02	−	21551.4i	0.0330594	−	0.0955188i
$476$	−10007.7	−	19412.2i	−0.0441693	−	0.0856765i
$477$	−82594.8	−	11875.3i	−0.363008	−	0.0521926i
$478$	−37110.5	−	23849.5i	−0.162421	−	0.104381i
$479$	63356.0	+	60409.8i	0.276132	+	0.263291i	0.815472	−	0.578797i	$-0.196478\pi$
$479$	63356.0	+	60409.8i	0.276132	+	0.263291i	−0.539340	+	0.842088i	$0.681326\pi$
$480$	−22276.2	+	7709.87i	−0.0966850	+	0.0334630i
$481$	100123.	−	250095.i	0.432756	−	1.08097i
$482$	79403.2	+	100969.i	0.341778	+	0.434606i
$483$	9879.43	+	21632.9i	0.0423485	+	0.0927302i
$484$	85609.6	−	55018.0i	0.365453	−	0.234863i
$485$	335578.	+	64677.4i	1.42663	+	0.274960i
$486$	−61729.9	+	5894.49i	−0.261350	+	0.0249559i
$487$	73753.1	+	52519.4i	0.310973	+	0.221443i	0.724878	−	0.688877i	$-0.241896\pi$
$487$	73753.1	+	52519.4i	0.310973	+	0.221443i	−0.413905	+	0.910320i	$0.635836\pi$
$488$	−173763.	−	89581.1i	−0.729655	−	0.376163i
$489$	−16030.1	−	16811.9i	−0.0670375	−	0.0703069i
$490$	32473.3	−	6258.72i	0.135249	−	0.0260671i
$491$	303872.	−	89225.0i	1.26046	−	0.370104i	0.417793	−	0.908542i	$-0.362804\pi$
$491$	303872.	−	89225.0i	1.26046	−	0.370104i	0.842665	+	0.538439i	$0.180986\pi$
$492$	−2144.27	−	8838.80i	−0.00885827	−	0.0365143i
$493$	−20318.3	+	44490.8i	−0.0835975	+	0.183053i
$494$	−19417.2	−	135050.i	−0.0795670	−	0.553401i
$495$	−12393.0	−	17403.5i	−0.0505785	−	0.0710276i
$496$	−81494.2	+	70615.1i	−0.331256	+	0.287035i
$497$	−35799.7	−	89423.2i	−0.144933	−	0.362024i
$498$	−18254.6	+	31617.9i	−0.0736060	+	0.127489i
$499$	−15748.3	+	9092.28i	−0.0632459	+	0.0365150i	−0.531289	−	0.847190i	$-0.678292\pi$
$499$	−15748.3	+	9092.28i	−0.0632459	+	0.0365150i	0.468044	+	0.883705i	$0.344959\pi$
$500$	−61244.3	+	77878.5i	−0.244977	+	0.311514i
$501$	32523.5	+	7890.11i	0.129575	+	0.0314346i
$502$	−3811.37	−	80010.6i	−0.0151243	−	0.317497i
$503$	−169850.	+	8090.94i	−0.671319	+	0.0319788i	−0.380474	−	0.924792i	$-0.624239\pi$
$503$	−169850.	+	8090.94i	−0.671319	+	0.0319788i	−0.290844	+	0.956770i	$0.593936\pi$
$504$	57969.0	−	238951.i	0.228210	−	0.940694i
$505$	−164560.	−	129411.i	−0.645270	−	0.507446i
$506$	7430.23	+	12869.5i	0.0290203	+	0.0502645i
$507$	−9448.84	−	5455.29i	−0.0367589	−	0.0212228i
$508$	−162453.	+	65036.3i	−0.629506	+	0.252016i
$509$	314535.	+	362993.i	1.21404	+	1.40108i	0.890573	+	0.454839i	$0.150303\pi$
$509$	314535.	+	362993.i	1.21404	+	1.40108i	0.323468	+	0.946239i	$0.395151\pi$
$510$	−4920.96	+	3504.20i	−0.0189195	+	0.0134725i
$511$	−268535.	+	38609.5i	−1.02839	+	0.147861i
$512$	−166271.	−	75933.5i	−0.634274	−	0.289663i
$513$	38641.0	−	9374.20i	0.146830	−	0.0356205i
$514$	46317.4	+	157743.i	0.175315	+	0.597067i
$515$	−99105.7	−	514209.i	−0.373667	−	1.93877i
$516$	−4305.06	+	4104.86i	−0.0161689	+	0.0154170i
$517$	−2881.52	+	5589.38i	−0.0107806	+	0.0209114i
$518$	106272.	−	149239.i	0.396060	−	0.556189i
$519$	−4130.38	−	43255.3i	−0.0153340	−	0.160585i
$520$	69160.7	−	358840.i	0.255772	−	1.32707i
$521$	−229558.	−	357200.i	−0.845703	−	1.31594i	−0.947049	−	0.321088i	$-0.895952\pi$
$521$	−229558.	−	357200.i	−0.845703	−	1.31594i	0.101347	−	0.994851i	$-0.467685\pi$
$522$	−152414.	+	69605.0i	−0.559349	+	0.255446i
$523$	−404923.	+	318435.i	−1.48036	+	1.16417i	−0.532104	+	0.846679i	$0.678598\pi$
$523$	−404923.	+	318435.i	−1.48036	+	1.16417i	−0.948261	+	0.317492i	$0.897159\pi$
$524$	31421.7	+	12579.3i	0.114437	+	0.0458137i
$525$	−1542.04	−	4455.42i	−0.00559469	−	0.0161648i
$526$	−171499.	+	179863.i	−0.619855	+	0.650086i
$527$	42891.2	−	66739.9i	0.154435	−	0.240306i
$528$	−143.984	+	1001.43i	−0.000516472	+	0.00359215i
$529$	28282.8	−	14580.8i	0.101067	−	0.0521038i
$530$	−79705.2	−	27586.2i	−0.283749	−	0.0982066i
$531$	49439.0	−	57055.6i	0.175340	−	0.202353i
$532$	−6856.58	+	71805.4i	−0.0242261	+	0.253708i
$533$	229413.	+	67361.6i	0.807538	+	0.237114i
$534$	−1126.66	+	23651.5i	−0.00395102	+	0.0829422i
$535$		−	437695.i		−	1.52920i
$536$	−309344.	−	15825.5i	−1.07674	−	0.0550842i
$537$	45407.3			0.157462
$538$	69669.1	+	3318.75i	0.240700	+	0.0114659i
$539$	−1148.00	+	3909.72i	−0.00395151	+	0.0134576i
$540$	32259.6	+	3080.42i	0.110630	+	0.0105639i
$541$	245840.	+	213022.i	0.839959	+	0.727828i	0.964414	−	0.264397i	$-0.0851728\pi$
$541$	245840.	+	213022.i	0.839959	+	0.727828i	−0.124455	+	0.992225i	$0.539718\pi$
$542$	5324.60	−	15384.4i	0.0181254	−	0.0523700i
$543$	−10017.9	−	19431.9i	−0.0339762	−	0.0659047i
$544$	56683.7	+	8149.88i	0.191540	+	0.0275393i
$545$	−256132.	−	164606.i	−0.862324	−	0.554182i
$546$	−20414.0	−	19464.7i	−0.0684767	−	0.0652924i
$547$	20663.9	−	7151.86i	0.0690619	−	0.0239025i	−0.292319	−	0.956321i	$-0.594427\pi$
$547$	20663.9	−	7151.86i	0.0690619	−	0.0239025i	0.361380	+	0.932418i	$0.382306\pi$
$548$	53634.4	−	133972.i	0.178600	−	0.446122i
$549$	139855.	+	177840.i	0.464016	+	0.590044i
$550$	−1223.83	−	2679.82i	−0.00404572	−	0.00885889i
$551$	135896.	−	87334.8i	0.447612	−	0.287663i
$552$	−36109.7	−	6959.57i	−0.118507	−	0.0228404i
$553$	−302841.	+	28917.8i	−0.990293	+	0.0945615i
$554$	123175.	+	87712.4i	0.401331	+	0.285786i
$555$	35015.6	+	18051.8i	0.113678	+	0.0586049i
$556$	−49663.3	−	52085.3i	−0.160652	−	0.168487i
$557$	12419.0	−	2393.57i	0.0400292	−	0.00771499i	−0.169197	−	0.985582i	$-0.554118\pi$
$557$	12419.0	−	2393.57i	0.0400292	−	0.00771499i	0.209227	+	0.977867i	$0.432905\pi$
$558$	260768.	−	76568.3i	0.837501	−	0.245912i
$559$	−36866.5	−	151966.i	−0.117980	−	0.486321i
$560$	47407.4	−	103808.i	0.151172	−	0.331019i
$561$	−105.932	−	736.770i	−0.000336589	−	0.00234103i
$562$	252192.	+	354153.i	0.798469	+	1.12129i
$563$	−357946.	+	310162.i	−1.12928	+	0.978524i	−0.999915	−	0.0130729i	$-0.995839\pi$
$563$	−357946.	+	310162.i	−1.12928	+	0.978524i	−0.129363	+	0.991597i	$0.541293\pi$
$564$	−1759.88	−	4395.96i	−0.00553253	−	0.0138196i
$565$	261109.	−	452255.i	0.817948	−	1.41673i
$566$	−75000.5	+	43301.5i	−0.234116	+	0.135167i
$567$	−173342.	+	220423.i	−0.539186	+	0.685631i
$568$	144746.	+	35115.0i	0.448652	+	0.108842i
$569$	−29901.6	−	627712.i	−0.0923570	−	1.93881i	−0.286987	−	0.957935i	$-0.592653\pi$
$569$	−29901.6	−	627712.i	−0.0923570	−	1.93881i	0.194630	−	0.980877i	$-0.437650\pi$
$570$	19929.7	−	949.367i	0.0613409	−	0.00292203i
$571$	−118496.	+	488447.i	−0.363439	+	1.49812i	0.437417	+	0.899259i	$0.355893\pi$
$571$	−118496.	+	488447.i	−0.363439	+	1.49812i	−0.800856	+	0.598857i	$0.795622\pi$
$572$	10769.8	+	8469.50i	0.0329168	+	0.0258860i
$573$	14289.1	+	24749.4i	0.0435205	+	0.0753798i
$574$	140822.	+	81303.8i	0.427413	+	0.246767i
$575$	45647.3	−	18274.4i	0.138064	−	0.0552724i
$576$	208009.	+	240055.i	0.626957	+	0.723547i
$577$	55650.7	−	39628.7i	0.167155	−	0.119031i	−0.493418	−	0.869792i	$-0.664253\pi$
$577$	55650.7	−	39628.7i	0.167155	−	0.119031i	0.660573	+	0.750762i	$0.270313\pi$
$578$	−233515.	+	33574.3i	−0.698970	+	0.100497i
$579$	−48022.6	−	21931.2i	−0.143248	−	0.0654192i
$580$	127945.	−	31039.2i	0.380337	−	0.0922688i
$581$	142953.	+	486854.i	0.423489	+	1.44227i
$582$	7719.24	+	40051.2i	0.0227892	+	0.118242i
$583$	7521.25	−	7171.50i	0.0221286	−	0.0210995i
$584$	192229.	−	372872.i	0.563628	−	1.09329i
$585$	−245320.	+	344503.i	−0.716837	+	1.00666i
$586$	28479.7	+	298253.i	0.0829356	+	0.868540i
$587$	31166.7	−	161708.i	0.0904512	−	0.469306i	−0.908253	−	0.418421i	$-0.862584\pi$
$587$	31166.7	−	161708.i	0.0904512	−	0.469306i	0.998705	−	0.0508848i	$-0.0162041\pi$
$588$	−1658.84	−	2581.20i	−0.00479788	−	0.00746564i
$589$	−238341.	+	108846.i	−0.687017	+	0.313750i
$590$	59983.4	−	47171.5i	0.172317	−	0.135511i
$591$	14661.6	+	5869.62i	0.0419765	+	0.0168049i
$592$	42546.1	+	122929.i	0.121399	+	0.350760i
$593$	341188.	−	357828.i	0.970253	−	1.01757i	−0.0295851	−	0.999562i	$-0.509419\pi$
$593$	341188.	−	357828.i	0.970253	−	1.01757i	0.999838	−	0.0180095i	$-0.00573292\pi$
$594$	2776.96	−	4321.04i	0.00787041	−	0.0122466i
$595$	−11948.8	+	83105.7i	−0.0337513	+	0.234745i
$596$	−96125.6	+	49556.2i	−0.270612	+	0.139510i
$597$	−13682.0	−	4735.39i	−0.0383885	−	0.0132864i
$598$	192636.	−	222314.i	0.538685	−	0.621675i
$599$	−32639.9	+	341821.i	−0.0909694	+	0.952674i	0.828625	+	0.559805i	$0.189124\pi$
$599$	−32639.9	+	341821.i	−0.0909694	+	0.952674i	−0.919594	+	0.392870i	$0.871482\pi$
$600$	6995.07	+	2053.94i	0.0194308	+	0.00570538i
$601$	11564.1	−	242760.i	0.0320156	−	0.672091i	−0.924635	−	0.380854i	$-0.875630\pi$
$601$	11564.1	−	242760.i	0.0320156	−	0.672091i	0.956651	−	0.291237i	$-0.0940669\pi$
$602$		−	106348.i		−	0.293452i
$603$	318040.	+	165378.i	0.874676	+	0.454824i
$604$	100813.			0.276340
$605$	−390772.	−	18614.8i	−1.06761	−	0.0508565i
$606$	7039.34	−	23973.8i	0.0191684	−	0.0652817i
$607$	−490039.	−	46793.0i	−1.33000	−	0.127000i	−0.594268	−	0.804267i	$-0.702558\pi$
$607$	−490039.	−	46793.0i	−1.33000	−	0.127000i	−0.735737	+	0.677267i	$0.763164\pi$
$608$	−142940.	−	123858.i	−0.386674	−	0.335055i
$609$	10922.7	−	31559.0i	0.0294506	−	0.0850919i
$610$	104789.	+	203263.i	0.281615	+	0.546258i
$611$	123212.	+	17715.3i	0.330044	+	0.0474532i
$612$	−32878.8	−	21129.9i	−0.0877836	−	0.0564151i
$613$	−304055.	−	289916.i	−0.809154	−	0.771527i	0.167608	−	0.985854i	$-0.446396\pi$
$613$	−304055.	−	289916.i	−0.809154	−	0.771527i	−0.976762	+	0.214327i	$0.931244\pi$
$614$	−403397.	+	139617.i	−1.07003	+	0.370341i
$615$	−12995.1	+	32460.2i	−0.0343581	+	0.0858224i
$616$	18929.7	+	24071.0i	0.0498863	+	0.0634356i
$617$	−76563.1	−	167650.i	−0.201117	−	0.440385i	0.782020	−	0.623253i	$-0.214189\pi$
$617$	−76563.1	−	167650.i	−0.201117	−	0.440385i	−0.983138	+	0.182868i	$0.941462\pi$
$618$	52578.6	−	33790.2i	0.137668	−	0.0884737i
$619$	506886.	+	97694.3i	1.32291	+	0.254969i	0.801324	−	0.598231i	$-0.204129\pi$
$619$	506886.	+	97694.3i	1.32291	+	0.254969i	0.521583	+	0.853200i	$0.325342\pi$
$620$	−212582.	+	20299.1i	−0.553022	+	0.0528072i
$621$	69831.1	+	49726.5i	0.181078	+	0.128945i
$622$	−349749.	−	180308.i	−0.904016	−	0.466053i
$623$	227093.	+	238169.i	0.585098	+	0.613633i
$624$	19665.3	−	3790.18i	0.0505047	−	0.00973397i
$625$	424656.	−	124690.i	1.08712	−	0.319207i
$626$	−52369.3	−	215869.i	−0.133637	−	0.550861i
$627$	−1021.25	+	2236.22i	−0.00259774	+	0.00568826i
$628$	−5217.97	−	36291.8i	−0.0132307	−	0.0920214i
$629$	−55514.0	−	77958.5i	−0.140314	−	0.197044i
$630$	−217373.	+	188355.i	−0.547676	+	0.474564i
$631$	287402.	+	717894.i	0.721822	+	1.80303i	0.582591	+	0.812765i	$0.302039\pi$
$631$	287402.	+	717894.i	0.721822	+	1.80303i	0.139231	+	0.990260i	$0.455537\pi$
$632$	235206.	−	407389.i	0.588863	−	1.01994i
$633$	−40382.5	+	23314.9i	−0.100783	+	0.0581869i
$634$	−242427.	+	308270.i	−0.603117	+	0.766926i
$635$	653746.	+	158597.i	1.62129	+	0.393322i
$636$	372.344	+	7816.47i	0.000920514	+	0.0193240i
$637$	80568.8	−	3837.97i	0.198558	−	0.00945850i
$638$	4919.73	−	20279.4i	0.0120865	−	0.0498212i
$639$	−135493.	−	106553.i	−0.331830	−	0.260954i
$640$	−15689.6	−	27175.2i	−0.0383047	−	0.0663458i
$641$	−478965.	−	276530.i	−1.16570	−	0.673018i	−0.213038	−	0.977044i	$-0.568336\pi$
$641$	−478965.	−	276530.i	−1.16570	−	0.673018i	−0.952664	+	0.304026i	$0.901669\pi$
$642$	48496.9	−	19415.2i	0.117664	−	0.0471056i
$643$	144910.	+	167235.i	0.350492	+	0.404489i	0.903432	−	0.428732i	$-0.141040\pi$
$643$	144910.	+	167235.i	0.350492	+	0.404489i	−0.552940	+	0.833221i	$0.686494\pi$
$644$	−126681.	+	90209.0i	−0.305449	+	0.217509i
$645$	22634.8	−	3254.39i	0.0544073	−	0.00782259i
$646$	−44091.0	−	20135.7i	−0.105654	−	0.0482504i
$647$	373220.	−	90542.2i	0.891571	−	0.216293i	0.236294	−	0.971682i	$-0.424067\pi$
$647$	373220.	−	90542.2i	0.891571	−	0.216293i	0.655277	+	0.755389i	$0.272552\pi$
$648$	−122162.	−	416045.i	−0.290928	−	0.990809i
$649$	1779.40	+	9232.43i	0.00422460	+	0.0219193i
$650$	−42206.0	+	40243.3i	−0.0998958	+	0.0952505i
$651$	−24821.3	+	48146.7i	−0.0585684	+	0.113607i
$652$	88112.3	−	123736.i	0.207272	−	0.291073i
$653$	41162.7	+	431075.i	0.0965334	+	1.01094i	0.905858	+	0.423582i	$0.139227\pi$
$653$	41162.7	+	431075.i	0.0965334	+	1.01094i	−0.809325	+	0.587362i	$0.800167\pi$
$654$	6876.98	−	35681.2i	0.0160784	−	0.0834225i
$655$	−70345.7	−	109460.i	−0.163966	−	0.255137i
$656$	−105021.	+	47961.7i	−0.244045	+	0.111452i
$657$	−381620.	+	300109.i	−0.884098	+	0.695262i
$658$	78592.9	+	31463.8i	0.181523	+	0.0726708i
$659$	116357.	+	336191.i	0.267930	+	0.774134i	0.996059	+	0.0886932i	$0.0282691\pi$
$659$	116357.	+	336191.i	0.267930	+	0.774134i	−0.728129	+	0.685440i	$0.759610\pi$
$660$	−1382.65	+	1450.08i	−0.00317412	+	0.00332892i
$661$	−255068.	+	396893.i	−0.583785	+	0.908387i	−1.00000		0.000879401i	$-0.999720\pi$
$661$	−255068.	+	396893.i	−0.583785	+	0.908387i	0.416215	+	0.909266i	$0.363356\pi$
$662$	−40913.2	+	284558.i	−0.0933572	+	0.649313i
$663$	−13096.4	+	6751.67i	−0.0297938	+	0.0153598i
$664$	−741452.	−	256619.i	−1.68169	−	0.582040i
$665$	181592.	−	209568.i	0.410632	−	0.473895i
$666$	31164.8	−	326373.i	0.0702613	−	0.735810i
$667$	334173.	+	98122.1i	0.751138	+	0.220554i
$668$	−10413.3	+	218601.i	−0.0233364	+	0.489891i
$669$		−	80671.6i		−	0.180247i
$670$	284025.	+	224980.i	0.632714	+	0.501180i
$671$	−28176.9			−0.0625817
$672$	−39056.6	−	1860.50i	−0.0864881	−	0.00411994i
$673$	16847.1	−	57375.8i	0.0371958	−	0.126677i	−0.938802	−	0.344457i	$-0.888063\pi$
$673$	16847.1	−	57375.8i	0.0371958	−	0.126677i	0.975998	+	0.217779i	$0.0698813\pi$
$674$	470224.	+	44901.0i	1.03511	+	0.0988407i
$675$	−12844.1	−	11129.4i	−0.0281900	−	0.0244268i
$676$	23335.4	−	67423.2i	0.0510648	−	0.147542i
$677$	9661.52	+	18740.7i	0.0210799	+	0.0408893i	0.899140	−	0.437661i	$-0.144193\pi$
$677$	9661.52	+	18740.7i	0.0210799	+	0.0408893i	−0.878060	+	0.478550i	$0.841163\pi$
$678$	61692.4	+	8870.03i	0.134206	+	0.0192959i
$679$	476890.	+	306479.i	1.03438	+	0.664754i
$680$	−93960.9	−	89591.5i	−0.203203	−	0.193753i
$681$	48529.1	−	16796.1i	0.104643	−	0.0362171i
$682$	−12579.9	+	31423.0i	−0.0270463	+	0.0675583i
$683$	324248.	+	412315.i	0.695083	+	0.883870i	0.997598	−	0.0692750i	$-0.0220686\pi$
$683$	324248.	+	412315.i	0.695083	+	0.883870i	−0.302515	+	0.953145i	$0.597826\pi$
$684$	53622.2	+	117416.i	0.114613	+	0.250967i
$685$	−466704.	+	299932.i	−0.994626	+	0.639208i
$686$	369518.	+	71218.7i	0.785212	+	0.151337i
$687$	−53934.5	+	5150.12i	−0.114276	+	0.0109120i
$688$	61508.2	+	43799.8i	0.129944	+	0.0925326i
$689$	−182847.	−	94264.3i	−0.385168	−	0.198568i
$690$	29685.3	+	31133.1i	0.0623511	+	0.0653919i
$691$	669663.	−	129067.i	1.40249	−	0.270308i	0.568771	−	0.822496i	$-0.307419\pi$
$691$	669663.	−	129067.i	1.40249	−	0.270308i	0.833720	+	0.552188i	$0.186207\pi$
$692$	272635.	−	80052.8i	0.569337	−	0.167172i
$693$	−8355.10	−	34440.2i	−0.0173974	−	0.0717132i
$694$	216570.	−	474223.i	0.449655	−	0.984608i
$695$	39373.7	+	273850.i	0.0815149	+	0.566948i
$696$	29954.0	+	42064.5i	0.0618353	+	0.0868356i
$697$	64194.9	−	55625.2i	0.132140	−	0.114500i
$698$	−115603.	−	288761.i	−0.237278	−	0.592691i
$699$	−29648.2	+	51352.2i	−0.0606797	+	0.105100i
$700$	26700.3	−	15415.4i	0.0544905	−	0.0314601i
$701$	371458.	−	472347.i	0.755916	−	0.961225i	−0.244048	−	0.969763i	$-0.578475\pi$
$701$	371458.	−	472347.i	0.755916	−	0.961225i	0.999964	+	0.00853789i	$0.00271773\pi$
$702$	−98809.6	−	23970.9i	−0.200505	−	0.0486419i
$703$	15040.0	+	315728.i	0.0304324	+	0.638855i
$704$	−39514.5	+	1882.31i	−0.0797281	+	0.00379792i
$705$	−4291.62	+	17690.3i	−0.00863462	+	0.0355924i
$706$	−316961.	−	249261.i	−0.635911	−	0.500086i
$707$	−173628.	−	300733.i	−0.347361	−	0.601647i
$708$	−6131.38	−	3539.95i	−0.0122318	−	0.00706205i
$709$	−438605.	+	175591.i	−0.872532	+	0.349309i	−0.764334	−	0.644821i	$-0.776932\pi$
$709$	−438605.	+	175591.i	−0.872532	+	0.349309i	−0.108197	+	0.994129i	$0.534508\pi$
$710$	−114097.	−	131675.i	−0.226337	−	0.261207i
$711$	−443457.	+	315784.i	−0.877227	+	0.624671i
$712$	−503682.	+	72418.5i	−0.993565	+	0.142853i
$713$	−513865.	−	234674.i	−1.01081	−	0.461622i
$714$	−9738.20	+	2362.46i	−0.0191021	+	0.00463413i
$715$	−14839.3	−	50538.1i	−0.0290270	−	0.0988569i
$716$	56194.5	+	291565.i	0.109614	+	0.568733i
$717$	11387.2	−	10857.7i	0.0221502	−	0.0211202i
$718$	149395.	−	289786.i	0.289793	−	0.562119i
$719$	−73800.6	+	103638.i	−0.142759	+	0.200476i	−0.879764	−	0.475410i	$-0.842300\pi$
$719$	−73800.6	+	103638.i	−0.142759	+	0.200476i	0.737006	+	0.675887i	$0.236239\pi$
$720$	−19412.4	−	203295.i	−0.0374467	−	0.392159i
$721$	164390.	−	852939.i	0.316232	−	1.64077i
$722$	−124845.	−	194263.i	−0.239496	−	0.372662i
$723$	−41674.6	+	19032.1i	−0.0797250	+	0.0364092i
$724$	112377.	−	88373.9i	0.214387	−	0.168596i
$725$	−64099.8	−	25661.7i	−0.121950	−	0.0488213i
$726$	−15271.3	−	44123.5i	−0.0289736	−	0.0837137i
$727$	−170985.	+	179324.i	−0.323512	+	0.339289i	−0.865327	−	0.501209i	$-0.832889\pi$
$727$	−170985.	+	179324.i	−0.323512	+	0.339289i	0.541815	+	0.840498i	$0.317737\pi$
$728$	327723.	−	509947.i	0.618365	−	0.962194i
$729$	−69291.5	+	481933.i	−0.130384	+	0.906842i
$730$	−436174.	+	224863.i	−0.818490	+	0.421961i
$731$	−52498.1	−	18169.8i	−0.0982447	−	0.0340028i
$732$	13894.2	−	16034.7i	0.0259305	−	0.0299254i
$733$	865.343	−	9062.28i	0.00161057	−	0.0168667i	−0.994631	−	0.103486i	$-0.967000\pi$
$733$	865.343	−	9062.28i	0.00161057	−	0.0168667i	0.996241	+	0.0866193i	$0.0276064\pi$
$734$	42708.6	+	12540.4i	0.0792725	+	0.0232765i
$735$	−561.250	+	11782.1i	−0.00103892	+	0.0218096i
$736$		−	407780.i		−	0.752784i
$737$	−40674.8	+	18403.1i	−0.0748843	+	0.0338810i
$738$	290988.			0.534273
$739$	−893455.	−	42560.5i	−1.63600	−	0.0779324i	−0.790694	−	0.612211i	$-0.790280\pi$
$739$	−893455.	−	42560.5i	−1.63600	−	0.0779324i	−0.845308	+	0.534279i	$0.820583\pi$
$740$	−72578.3	+	247179.i	−0.132539	+	0.451386i
$741$	48443.3	+	4625.77i	0.0882261	+	0.00842457i
$742$	−105733.	−	91618.1i	−0.192045	−	0.166408i
$743$	−48488.7	+	140099.i	−0.0878340	+	0.253780i	−0.980360	−	0.197216i	$-0.936810\pi$
$743$	−48488.7	+	140099.i	−0.0878340	+	0.253780i	0.892526	+	0.450996i	$0.148931\pi$
$744$	−38381.2	−	74449.2i	−0.0693383	−	0.134497i
$745$	411523.	+	59168.1i	0.741450	+	0.106604i
$746$	−440622.	−	283171.i	−0.791751	−	0.508827i
$747$	657160.	+	626601.i	1.17769	+	1.12292i
$748$	4599.78	−	1592.00i	0.00822117	−	0.00284538i
$749$	269835.	−	674015.i	0.480988	−	1.20145i
$750$	28100.1	+	35732.2i	0.0499557	+	0.0635238i
$751$	−250585.	−	548704.i	−0.444299	−	0.972878i	−0.990789	−	0.135413i	$-0.956764\pi$
$751$	−250585.	−	548704.i	−0.444299	−	0.972878i	0.546491	−	0.837465i	$-0.315963\pi$
$752$	−50566.3	+	32497.0i	−0.0894182	+	0.0574656i
$753$	28053.5	+	5406.87i	0.0494763	+	0.00953578i
$754$	−411205.	+	39265.3i	−0.723295	+	0.0690663i
$755$	−315696.	−	224806.i	−0.553828	−	0.394379i
$756$	47778.2	+	24631.4i	0.0835961	+	0.0430968i
$757$	454331.	+	476489.i	0.792832	+	0.831498i	0.988821	−	0.149108i	$-0.0476402\pi$
$757$	454331.	+	476489.i	0.792832	+	0.831498i	−0.195989	+	0.980606i	$0.562792\pi$
$758$	574153.	−	110659.i	0.999284	−	0.192596i
$759$	−5085.59	+	1493.27i	−0.00882791	+	0.00259211i
$760$	101090.	+	416700.i	0.175018	+	0.721433i
$761$	321978.	−	705033.i	0.555977	−	1.21742i	−0.397958	−	0.917404i	$-0.630281\pi$
$761$	321978.	−	705033.i	0.555977	−	1.21742i	0.953934	−	0.300015i	$-0.0969917\pi$
$762$	11426.1	+	79470.6i	0.0196784	+	0.136866i
$763$	−292944.	−	411383.i	−0.503195	−	0.706638i
$764$	−141235.	+	122380.i	−0.241966	+	0.209665i
$765$	55841.6	+	139486.i	0.0954190	+	0.238345i
$766$	6207.14	−	10751.1i	0.0105787	−	0.0183229i
$767$	161184.	−	93059.7i	0.273988	−	0.158187i
$768$	44416.0	−	56479.6i	0.0753039	−	0.0957567i
$769$	202861.	+	49213.5i	0.343041	+	0.0832208i	0.403578	−	0.914945i	$-0.367766\pi$
$769$	202861.	+	49213.5i	0.343041	+	0.0832208i	−0.0605374	+	0.998166i	$0.519281\pi$
$770$	−1704.45	−	35780.8i	−0.00287477	−	0.0603488i
$771$	−58571.0	+	2790.08i	−0.0985313	+	0.00469362i
$772$	81391.3	−	335499.i	0.136566	−	0.562933i
$773$	−604990.	−	475769.i	−1.01249	−	0.796228i	−0.0333519	−	0.999444i	$-0.510618\pi$
$773$	−604990.	−	475769.i	−1.01249	−	0.796228i	−0.979134	+	0.203216i	$0.934861\pi$
$774$	−95155.6	−	164814.i	−0.158837	−	0.275114i
$775$	96988.7	+	55996.5i	0.161480	+	0.0932303i
$776$	−813777.	+	325787.i	−1.35139	+	0.541017i
$777$	42792.4	+	49385.1i	0.0708802	+	0.0818001i
$778$	516111.	−	367521.i	0.852676	−	0.607188i
$779$	−277685.	+	39925.1i	−0.457591	+	0.0657917i
$780$	36077.3	+	16476.0i	0.0592987	+	0.0270808i
$781$	20862.3	−	5061.14i	0.0342027	−	0.00829749i
$782$	−29442.3	−	100271.i	−0.0481458	−	0.163970i
$783$	−22782.3	−	118206.i	−0.0371598	−	0.192804i
$784$	−28188.7	+	26877.9i	−0.0458609	+	0.0437283i
$785$	−64587.9	+	125283.i	−0.104812	+	0.203307i
$786$	9007.86	−	12649.8i	0.0145806	−	0.0204756i
$787$	−30750.4	−	322032.i	−0.0496479	−	0.519936i	−0.985751	−	0.168211i	$-0.946201\pi$
$787$	−30750.4	−	322032.i	−0.0496479	−	0.519936i	0.936103	−	0.351725i	$-0.114405\pi$
$788$	−19544.7	+	101408.i	−0.0314758	+	0.163312i
$789$	−47922.5	−	74568.9i	−0.0769814	−	0.119785i
$790$	−500547.	+	228592.i	−0.802029	+	0.366275i
$791$	680898.	−	535464.i	1.08825	−	0.855810i
$792$	50874.2	+	20367.0i	0.0811049	+	0.0324695i
$793$	182426.	+	527085.i	0.290095	+	0.838174i
$794$	−365411.	+	383232.i	−0.579616	+	0.607884i
$795$	16264.1	−	25307.5i	0.0257334	−	0.0400419i
$796$	13474.0	−	93713.9i	0.0212653	−	0.147903i
$797$	−845004.	+	435630.i	−1.33028	+	0.685805i	−0.969095	−	0.246690i	$-0.920657\pi$
$797$	−845004.	+	435630.i	−1.33028	+	0.685805i	−0.361182	+	0.932495i	$0.617627\pi$
$798$	31275.3	+	10824.5i	0.0491130	+	0.0169982i
$799$	28959.7	−	33421.3i	0.0453629	−	0.0523515i
$800$	−7684.45	+	80475.2i	−0.0120069	+	0.125742i
$801$	565044.	+	165912.i	0.880678	+	0.258590i
$802$	12161.0	−	255290.i	0.0189069	−	0.396904i
$803$		−	60463.7i		−	0.0937699i
$804$	9584.25	−	32221.7i	0.0148268	−	0.0498467i
$805$	597859.			0.922586
$806$	669254.	+	31880.5i	1.03020	+	0.0490744i
$807$	−7008.69	+	23869.4i	−0.0107619	+	0.0366518i
$808$	534531.	+	51041.5i	0.818748	+	0.0781810i
$809$	−638081.	−	552900.i	−0.974942	−	0.844792i	0.0129532	−	0.999916i	$-0.495877\pi$
$809$	−638081.	−	552900.i	−0.974942	−	0.844792i	−0.987895	+	0.155124i	$0.950422\pi$
$810$	−165896.	+	479325.i	−0.252852	+	0.730567i
$811$	−258054.	−	500555.i	−0.392346	−	0.761044i	0.607090	−	0.794633i	$-0.292337\pi$
$811$	−258054.	−	500555.i	−0.392346	−	0.761044i	−0.999436	+	0.0335888i	$0.989306\pi$
$812$	216161.	+	31079.3i	0.327842	+	0.0471366i
$813$	4884.76	+	3139.25i	0.00739030	+	0.00474946i
$814$	29551.5	+	28177.3i	0.0445996	+	0.0425256i
$815$	−551846.	+	190996.i	−0.830812	+	0.287547i
$816$	2644.34	−	6605.23i	0.00397133	−	0.00991991i
$817$	113419.	+	144224.i	0.169919	+	0.216069i
$818$	−287085.	−	628629.i	−0.429047	−	0.939481i
$819$	−590155.	+	379270.i	−0.879830	+	0.565432i
$820$	−224512.	−	43271.2i	−0.333897	−	0.0643534i
$821$	335700.	−	32055.5i	0.498041	−	0.0475572i	0.156987	−	0.987601i	$-0.449822\pi$
$821$	335700.	−	32055.5i	0.498041	−	0.0475572i	0.341054	+	0.940044i	$0.389216\pi$
$822$	−53934.7	−	38406.7i	−0.0798223	−	0.0568412i
$823$	−25661.6	−	13229.5i	−0.0378864	−	0.0195318i	0.439179	−	0.898399i	$-0.355269\pi$
$823$	−25661.6	−	13229.5i	−0.0378864	−	0.0195318i	−0.477066	+	0.878868i	$0.658300\pi$
$824$	926895.	+	972099.i	1.36514	+	1.43171i
$825$	1031.78	−	198.859i	0.00151593	−	0.000292171i
$826$	121450.	−	35661.1i	0.178008	−	0.0522678i
$827$	5158.00	+	21261.6i	0.00754172	+	0.0310874i	0.975458	−	0.220185i	$-0.0706661\pi$
$827$	5158.00	+	21261.6i	0.00754172	+	0.0310874i	−0.967916	+	0.251272i	$0.919151\pi$
$828$	−115610.	+	253151.i	−0.168630	+	0.369249i
$829$	−81390.8	−	566086.i	−0.118431	−	0.823708i	−0.959284	−	0.282444i	$-0.908855\pi$
$829$	−81390.8	−	566086.i	−0.118431	−	0.823708i	0.840853	−	0.541264i	$-0.182054\pi$
$830$	532380.	+	747623.i	0.772797	+	1.08524i
$831$	−40760.2	+	35318.9i	−0.0590247	+	0.0511452i
$832$	291041.	+	726984.i	0.420443	+	1.05022i
$833$	14327.7	−	24816.3i	0.0206484	−	0.0357641i
$834$	−28596.3	+	16510.1i	−0.0411128	+	0.0237365i
$835$	520073.	−	661327.i	0.745919	−	0.948513i
$836$	−15622.8	−	3790.06i	−0.0223536	−	0.00542293i
$837$	9290.83	+	195039.i	0.0132618	+	0.278400i
$838$	−548381.	+	26122.6i	−0.780898	+	0.0371988i
$839$	−34885.5	+	143800.i	−0.0495588	+	0.204284i	−0.991208	−	0.132311i	$-0.957760\pi$
$839$	−34885.5	+	143800.i	−0.0495588	+	0.204284i	0.941649	+	0.336595i	$0.109275\pi$
$840$	69679.6	+	54796.7i	0.0987523	+	0.0776597i
$841$	109106.	+	188976.i	0.154261	+	0.267187i
$842$	201567.	+	116375.i	0.284311	+	0.164147i
$843$	−143962.	+	57633.7i	−0.202578	+	0.0811001i
$844$	−199683.	−	230447.i	−0.280321	−	0.323508i
$845$	−223423.	+	159099.i	−0.312907	+	0.222820i
$846$	149953.	−	21560.0i	0.209515	−	0.0301236i
$847$	−590281.	−	269572.i	−0.822796	−	0.375758i
$848$	96535.2	−	23419.2i	0.134244	−	0.0325672i
$849$	−8702.38	−	29637.6i	−0.0120732	−	0.0411176i
$850$	3920.86	+	20343.3i	0.00542679	+	0.0281569i
$851$	−493214.	+	470279.i	−0.681046	+	0.649376i
$852$	−7407.17	+	14367.9i	−0.0102041	+	0.0197931i
$853$	34072.6	−	47848.3i	0.0468282	−	0.0657609i	−0.790498	−	0.612465i	$-0.790178\pi$
$853$	34072.6	−	47848.3i	0.0468282	−	0.0657609i	0.837326	+	0.546704i	$0.184118\pi$
$854$	36057.3	+	377609.i	0.0494399	+	0.517758i
$855$	93912.0	−	487262.i	0.128466	−	0.666546i
$856$	606948.	+	944430.i	0.828332	+	1.28891i
$857$	540463.	−	246821.i	0.735876	−	0.336063i	−0.0119766	−	0.999928i	$-0.503812\pi$
$857$	540463.	−	246821.i	0.735876	−	0.336063i	0.747852	+	0.663865i	$0.231085\pi$
$858$	4941.41	−	3885.97i	0.00671238	−	0.00527868i
$859$	−424171.	−	169812.i	−0.574850	−	0.230135i	0.0659764	−	0.997821i	$-0.478984\pi$
$859$	−424171.	−	169812.i	−0.574850	−	0.230135i	−0.640826	+	0.767686i	$0.721408\pi$
$860$	48908.8	+	141313.i	0.0661287	+	0.191066i
$861$	−40022.8	+	41974.7i	−0.0539885	+	0.0566215i
$862$	292792.	−	455593.i	0.394044	−	0.613144i
$863$	−76016.5	+	528706.i	−0.102067	+	0.709893i	0.872958	+	0.487796i	$0.162199\pi$
$863$	−76016.5	+	528706.i	−0.102067	+	0.709893i	−0.975025	+	0.222097i	$0.928710\pi$
$864$	−125278.	+	64585.5i	−0.167822	+	0.0865182i
$865$	−1.03227e6	−	357271.i	−1.37962	−	0.477491i
$866$	−433255.	+	500003.i	−0.577707	+	0.666710i
$867$	7998.43	−	83763.3i	0.0106406	−	0.111433i
$868$	−339873.	−	99795.6i	−0.451104	−	0.132456i
$869$	3226.10	−	67724.1i	0.00427206	−	0.0896816i
$870$		−	60406.6i		−	0.0798079i
$871$	607596.	+	641728.i	0.800900	+	0.845891i
$872$	780923.			1.02701
$873$	1.01329e6	+	48269.0i	1.32955	+	0.0633344i
$874$	−97240.2	+	331170.i	−0.127298	+	0.433538i
$875$	628915.	+	60054.1i	0.821440	+	0.0784380i
$876$	34408.4	+	29815.0i	0.0448390	+	0.0388532i
$877$	−263819.	+	762256.i	−0.343010	+	0.991063i	0.633153	+	0.774027i	$0.281760\pi$
$877$	−263819.	+	762256.i	−0.343010	+	0.991063i	−0.976163	+	0.217037i	$0.930361\pi$
$878$	96750.1	+	187669.i	0.125505	+	0.243447i
$879$	−105774.	−	15208.1i	−0.136900	−	0.0196832i
$880$	21396.4	+	13750.6i	0.0276297	+	0.0177565i
$881$	588693.	+	561318.i	0.758467	+	0.723197i	0.966988	−	0.254821i	$-0.0820164\pi$
$881$	588693.	+	561318.i	0.758467	+	0.723197i	−0.208521	+	0.978018i	$0.566865\pi$
$882$	92766.6	−	32106.8i	0.119249	−	0.0412725i
$883$	99915.7	−	249577.i	0.128148	−	0.320099i	−0.850394	−	0.526147i	$-0.823636\pi$
$883$	99915.7	−	249577.i	0.128148	−	0.320099i	0.978542	+	0.206048i	$0.0660604\pi$
$884$	−59560.8	−	75737.8i	−0.0762178	−	0.0969188i
$885$	11306.5	+	24757.8i	0.0144359	+	0.0316101i
$886$	−430583.	+	276719.i	−0.548516	+	0.352510i
$887$	1.00540e6	+	193776.i	1.27789	+	0.246293i	0.782649	−	0.622463i	$-0.213868\pi$
$887$	1.00540e6	+	193776.i	1.27789	+	0.246293i	0.495240	+	0.868756i	$0.335080\pi$
$888$	−100587.	+	9604.87i	−0.127560	+	0.0121805i
$889$	908943.	+	647255.i	1.15009	+	0.818977i
$890$	529079.	+	272759.i	0.667945	+	0.344350i
$891$	−43127.4	−	45230.7i	−0.0543248	−	0.0569742i
$892$	518000.	−	99836.4i	0.651029	−	0.125476i
$893$	−140139.	+	41148.6i	−0.175735	+	0.0516003i
$894$	11698.4	+	48221.6i	0.0146370	+	0.0603347i
$895$	474195.	−	1.03834e6i	0.591985	−	1.29627i
$896$	−7407.48	−	51520.1i	−0.00922687	−	0.0641743i
$897$	60859.2	+	85464.8i	0.0756382	+	0.106219i
$898$	517190.	−	448148.i	0.641354	−	0.555736i
$899$	294831.	+	736453.i	0.364799	+	0.911225i
$900$	27586.1	−	47780.6i	0.0340570	−	0.0589884i
$901$	−63291.4	+	36541.3i	−0.0779642	+	0.0450127i
$902$	−22402.2	+	28486.8i	−0.0275346	+	0.0350130i
$903$	36862.0	+	8942.64i	0.0452068	+	0.0109671i
$904$	63733.2	+	1.33793e6i	0.0779882	+	1.63717i
$905$	−548974.	+	26150.8i	−0.670277	+	0.0319292i
$906$	10905.0	−	44951.2i	0.0132853	−	0.0547627i
$907$	345043.	+	271345.i	0.419430	+	0.329843i	0.805468	−	0.592640i	$-0.201914\pi$
$907$	345043.	+	271345.i	0.419430	+	0.329843i	−0.386038	+	0.922483i	$0.626157\pi$
$908$	167907.	+	290824.i	0.203656	+	0.352743i
$909$	−538165.	−	310710.i	−0.651310	−	0.376034i
$910$	−658292.	+	263540.i	−0.794943	+	0.318247i
$911$	−379292.	−	437726.i	−0.457022	−	0.527431i	0.479735	−	0.877414i	$-0.340733\pi$
$911$	−379292.	−	437726.i	−0.457022	−	0.527431i	−0.936756	+	0.349983i	$0.886188\pi$
$912$	−19141.4	+	13630.5i	−0.0230135	+	0.0163879i
$913$	−111935.	+	16093.8i	−0.134284	+	0.0193071i
$914$	−1.02698e6	−	469006.i	−1.22933	−	0.561417i
$915$	−79265.8	+	19229.7i	−0.0946768	+	0.0229683i
$916$	−99817.0	−	339946.i	−0.118963	−	0.405152i
$917$	−40845.6	−	211927.i	−0.0485743	−	0.252027i
$918$	−26142.3	+	24926.6i	−0.0310212	+	0.0295786i
$919$	−604299.	+	1.17218e6i	−0.715518	+	1.38791i	0.197627	+	0.980277i	$0.436677\pi$
$919$	−604299.	+	1.17218e6i	−0.715518	+	1.38791i	−0.913145	+	0.407635i	$0.866354\pi$
$920$	−536245.	+	753051.i	−0.633560	+	0.889710i
$921$	−14472.6	−	151564.i	−0.0170619	−	0.178681i
$922$	128228.	−	665312.i	0.150842	−	0.782643i
$923$	−229745.	−	357489.i	−0.269676	−	0.419624i
$924$	−3023.13	+	1380.62i	−0.00354089	+	0.00161707i
$925$	106198.	−	83514.9i	0.124117	−	0.0976069i
$926$	−331321.	−	132641.i	−0.386391	−	0.154688i
$927$	−508406.	−	1.46894e6i	−0.591631	−	1.70941i
$928$	−395154.	+	414425.i	−0.458849	+	0.481227i
$929$	323996.	−	504148.i	0.375412	−	0.584153i	−0.601216	−	0.799086i	$-0.705317\pi$
$929$	323996.	−	504148.i	0.375412	−	0.584153i	0.976629	+	0.214933i	$0.0689534\pi$
$930$	−13944.0	+	96982.9i	−0.0161221	+	0.112132i
$931$	−84120.4	+	43367.1i	−0.0970514	+	0.0500335i
$932$	−366429.	−	126822.i	−0.421850	−	0.146004i
$933$	91907.7	−	106067.i	0.105582	−	0.121848i
$934$	28104.6	−	294324.i	0.0322169	−	0.337390i
$935$	−17954.2	−	5271.83i	−0.0205373	−	0.00603029i
$936$	51614.9	−	1.08353e6i	0.0589147	−	1.23677i
$937$		−	1.03462e6i		−	1.17842i	−0.807980	−	0.589210i	$-0.799439\pi$
$937$		−	1.03462e6i		−	1.17842i	0.807980	−	0.589210i	$-0.200561\pi$
$938$	298678.	+	521549.i	0.339467	+	0.592775i
$939$	79227.5			0.0898555
$940$	−118902.	−	5664.02i	−0.134566	−	0.00641016i
$941$	313333.	−	1.06711e6i	0.353856	−	1.20512i	−0.569763	−	0.821809i	$-0.692965\pi$
$941$	313333.	−	1.06711e6i	0.353856	−	1.20512i	0.923618	−	0.383313i	$-0.125217\pi$
$942$	−16746.4	−	1599.09i	−0.0188721	−	0.00180207i
$943$	−457115.	−	396092.i	−0.514046	−	0.445423i
$944$	−29394.5	+	84929.9i	−0.0329855	+	0.0953053i
$945$	−94690.9	−	183675.i	−0.106034	−	0.205677i
$946$	23460.5	+	3373.11i	0.0262153	+	0.00376919i
$947$	−732042.	−	470455.i	−0.816274	−	0.524588i	0.0646149	−	0.997910i	$-0.479418\pi$
$947$	−732042.	−	470455.i	−0.816274	−	0.524588i	−0.880889	+	0.473323i	$0.843054\pi$
$948$	36949.3	+	35231.0i	0.0411139	+	0.0392021i
$949$	−1.13105e6	+	391461.i	−1.25589	+	0.434666i
$950$	25431.0	−	63523.7i	0.0281784	−	0.0703864i
$951$	−86466.5	−	109951.i	−0.0956064	−	0.121573i
$952$	−89459.8	−	195890.i	−0.0987084	−	0.216141i
$953$	−54660.7	+	35128.3i	−0.0601851	+	0.0386786i	−0.570387	−	0.821376i	$-0.693207\pi$
$953$	−54660.7	+	35128.3i	−0.0601851	+	0.0386786i	0.510202	+	0.860054i	$0.329571\pi$
$954$	−245837.	−	47381.2i	−0.270116	−	0.0520606i
$955$	715174.	−	68290.8i	0.784160	−	0.0748782i
$956$	83810.6	+	59681.3i	0.0917029	+	0.0653014i
$957$	6615.50	+	3410.53i	0.00722335	+	0.00372389i
$958$	181250.	+	190090.i	0.197491	+	0.207123i
$959$	−903591.	+	174153.i	−0.982505	+	0.189362i
$960$	−109876.	+	32262.4i	−0.119223	+	0.0350070i
$961$	−85623.7	−	352946.i	−0.0927144	−	0.382174i
$962$	335767.	−	735228.i	0.362818	−	0.794460i
$963$	−184899.	−	1.28600e6i	−0.199380	−	1.38672i
$964$	−173782.	−	244043.i	−0.187004	−	0.262611i
$965$	−1.00301e6	+	869117.i	−1.07709	+	0.933305i
$966$	26519.8	+	66243.2i	0.0284194	+	0.0709883i
$967$	321418.	−	556711.i	0.343729	−	0.595357i	−0.641393	−	0.767213i	$-0.721643\pi$
$967$	321418.	−	556711.i	0.343729	−	0.595357i	0.985122	+	0.171856i	$0.0549764\pi$
$968$	868995.	−	501715.i	0.927399	−	0.535434i
$969$	10686.9	−	13589.5i	0.0113816	−	0.0144729i
$970$	996477.	+	241743.i	1.05907	+	0.256927i
$971$	21239.4	+	445869.i	0.0225270	+	0.472900i	0.981741	+	0.190220i	$0.0609202\pi$
$971$	21239.4	+	445869.i	0.0225270	+	0.472900i	−0.959214	+	0.282679i	$0.908777\pi$
$972$	144468.	−	6881.86i	0.152911	−	0.00728405i
$973$	−108194.	+	445981.i	−0.114282	+	0.471075i
$974$	213537.	+	167927.i	0.225089	+	0.177012i
$975$	−10400.0	−	18013.3i	−0.0109402	−	0.0189489i
$976$	−233247.	−	134665.i	−0.244859	−	0.141369i
$977$	374906.	−	150090.i	0.392765	−	0.157240i	−0.166869	−	0.985979i	$-0.553366\pi$
$977$	374906.	−	150090.i	0.392765	−	0.157240i	0.559635	+	0.828740i	$0.310942\pi$
$978$	−45641.2	−	52672.7i	−0.0477177	−	0.0550691i
$979$	−59743.1	+	42542.8i	−0.0623336	+	0.0443875i
$980$	−76348.6	+	10977.3i	−0.0794966	+	0.0114299i
$981$	−822082.	−	375432.i	−0.854234	−	0.390116i
$982$	923428.	−	224021.i	0.957591	−	0.232309i
$983$	−260974.	−	888795.i	−0.270078	−	0.919802i	−0.977130	−	0.212641i	$-0.931794\pi$
$983$	−260974.	−	888795.i	−0.270078	−	0.919802i	0.707052	−	0.707161i	$-0.250025\pi$
$984$	−16972.3	−	88060.7i	−0.0175287	−	0.0909478i
$985$	287336.	−	273974.i	0.296154	−	0.282382i
$986$	−67244.5	+	130436.i	−0.0691676	+	0.134166i
$987$	−17514.6	+	24595.9i	−0.0179791	+	0.0252481i
$988$	30249.2	+	316784.i	0.0309884	+	0.324526i
$989$	−74864.3	+	388433.i	−0.0765389	+	0.397122i
$990$	−34656.6	−	53926.8i	−0.0353603	−	0.0550217i
$991$	1.64809e6	−	752657.i	1.67816	−	0.766390i	0.678671	−	0.734443i	$-0.262556\pi$
$991$	1.64809e6	−	752657.i	1.67816	−	0.766390i	0.999490	−	0.0319475i	$-0.0101709\pi$
$992$	730084.	−	574145.i	0.741907	−	0.583442i
$993$	−95192.2	−	38109.2i	−0.0965390	−	0.0386484i
$994$	−94523.5	−	273108.i	−0.0956681	−	0.276415i
$995$	−251169.	+	263418.i	−0.253699	+	0.266072i
$996$	46037.1	−	71635.1i	0.0464076	−	0.0722116i
$997$	−268266.	+	1.86583e6i	−0.269883	+	1.87707i	0.179533	+	0.983752i	$0.442541\pi$
$997$	−268266.	+	1.86583e6i	−0.269883	+	1.87707i	−0.449415	+	0.893323i	$0.648368\pi$
$998$	−48494.8	+	25000.8i	−0.0486894	+	0.0251011i
$999$	222596.	+	77041.3i	0.223042	+	0.0771956i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.5.h.a.2.15	✓	440
67.34	odd	66	inner	67.5.h.a.34.15	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.5.h.a.2.15	✓	440	1.1	even	1	trivial
67.5.h.a.34.15	yes	440	67.34	odd	66	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	67.h (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.99695 + 0.142762i) q^{2} +(-0.301492 + 1.02679i) q^{3} +(-6.96623 - 0.665194i) q^{4} +(20.3314 + 17.6172i) q^{5} +(-1.05014 + 3.03419i) q^{6} +(20.4478 + 39.6632i) q^{7} +(-68.2994 - 9.81997i) q^{8} +(67.1781 + 43.1728i) q^{9} +O(q^{10})\)	\(q+(2.99695 + 0.142762i) q^{2} +(-0.301492 + 1.02679i) q^{3} +(-6.96623 - 0.665194i) q^{4} +(20.3314 + 17.6172i) q^{5} +(-1.05014 + 3.03419i) q^{6} +(20.4478 + 39.6632i) q^{7} +(-68.2994 - 9.81997i) q^{8} +(67.1781 + 43.1728i) q^{9} +(58.4170 + 55.7005i) q^{10} +(-9.39829 + 3.25278i) q^{11} +(2.78328 - 6.95229i) q^{12} +(121.695 + 154.748i) q^{13} +(55.6186 + 121.788i) q^{14} +(-24.2189 + 15.5645i) q^{15} +(-93.3446 - 17.9907i) q^{16} +(69.6223 - 6.64813i) q^{17} +(195.166 + 138.977i) q^{18} +(-205.312 - 105.846i) q^{19} +(-129.914 - 136.250i) q^{20} +(-46.8906 + 9.03741i) q^{21} +(-28.6306 + 8.40669i) q^{22} +(-117.412 - 483.979i) q^{23} +(30.6748 - 67.1684i) q^{24} +(14.0508 + 97.7255i) q^{25} +(342.621 + 481.144i) q^{26} +(-130.092 + 112.726i) q^{27} +(-116.060 - 289.905i) q^{28} +(-349.668 + 605.642i) q^{29} +(-74.8049 + 43.1886i) q^{30} +(701.196 - 891.644i) q^{31} +(795.726 + 193.041i) q^{32} +(-0.506405 - 10.6307i) q^{33} +(209.604 - 9.98465i) q^{34} +(-283.024 + 1166.64i) q^{35} +(-439.260 - 345.438i) q^{36} +(-684.199 - 1185.07i) q^{37} +(-600.199 - 346.525i) q^{38} +(-195.583 + 78.2997i) q^{39} +(-1215.62 - 1402.90i) q^{40} +(989.315 - 704.488i) q^{41} +(-141.819 + 20.3905i) q^{42} +(-722.533 - 329.970i) q^{43} +(67.6343 - 16.4079i) q^{44} +(605.238 + 2061.25i) q^{45} +(-282.784 - 1467.22i) q^{46} +(457.619 - 436.339i) q^{47} +(46.6153 - 90.4211i) q^{48} +(237.661 - 333.748i) q^{49} +(28.1580 + 294.884i) q^{50} +(-14.1644 + 73.4918i) q^{51} +(-744.818 - 1158.96i) q^{52} +(-950.518 + 434.087i) q^{53} +(-405.973 + 319.260i) q^{54} +(-248.385 - 99.4383i) q^{55} +(-1007.08 - 2909.77i) q^{56} +(170.581 - 178.900i) q^{57} +(-1134.40 + 1765.16i) q^{58} +(134.546 - 935.786i) q^{59} +(179.068 - 92.3159i) q^{60} +(2677.37 + 926.646i) q^{61} +(2228.74 - 2572.11i) q^{62} +(-338.725 + 3547.29i) q^{63} +(3816.58 + 1120.65i) q^{64} +(-252.001 + 5290.16i) q^{65} -31.9321i q^{66} +(4470.15 - 411.002i) q^{67} -489.427 q^{68} +(532.343 + 25.3586i) q^{69} +(-1014.76 + 3455.95i) q^{70} +(-2148.79 - 205.184i) q^{71} +(-4164.27 - 3608.36i) q^{72} +(-1988.46 + 5745.27i) q^{73} +(-1881.33 - 3649.26i) q^{74} +(-104.580 - 15.0363i) q^{75} +(1359.84 + 873.918i) q^{76} +(-321.190 - 306.254i) q^{77} +(-597.331 + 206.738i) q^{78} +(-2533.77 + 6329.06i) q^{79} +(-1580.88 - 2010.25i) q^{80} +(2610.48 + 5716.15i) q^{81} +(3065.50 - 1970.08i) q^{82} +(11165.3 + 2151.94i) q^{83} +(332.662 - 31.7654i) q^{84} +(1532.64 + 1091.39i) q^{85} +(-2118.29 - 1092.05i) q^{86} +(-516.444 - 541.631i) q^{87} +(673.839 - 129.872i) q^{88} +(7075.89 - 2077.67i) q^{89} +(1519.60 + 6263.87i) q^{90} +(-3649.39 + 7991.06i) q^{91} +(495.979 + 3449.61i) q^{92} +(704.124 + 988.804i) q^{93} +(1433.75 - 1242.36i) q^{94} +(-2309.56 - 5769.01i) q^{95} +(-438.118 + 758.842i) q^{96} +(11001.6 - 6351.78i) q^{97} +(759.904 - 966.296i) q^{98} +(-771.791 - 187.234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 19 q^{2} - 22 q^{3} - 191 q^{4} - 22 q^{5} - 53 q^{6} - 16 q^{7} - 517 q^{8} + 840 q^{9}+O(q^{10}) \) 440 * q - 19 * q^2 - 22 * q^3 - 191 * q^4 - 22 * q^5 - 53 * q^6 - 16 * q^7 - 517 * q^8 + 840 * q^9	\( 440 q - 19 q^{2} - 22 q^{3} - 191 q^{4} - 22 q^{5} - 53 q^{6} - 16 q^{7} - 517 q^{8} + 840 q^{9} + 854 q^{10} - 100 q^{11} - 742 q^{12} + 248 q^{13} + 308 q^{14} - 1658 q^{15} + 1585 q^{16} - 387 q^{17} + 458 q^{18} + 2011 q^{19} + 653 q^{20} - 4978 q^{21} - 5071 q^{22} + 2673 q^{23} + 7510 q^{24} + 4716 q^{25} - 307 q^{26} - 22 q^{27} + 1350 q^{28} - 412 q^{29} - 3258 q^{30} + 6228 q^{31} - 12097 q^{32} - 7165 q^{33} - 2803 q^{34} + 1835 q^{35} + 1521 q^{36} - 4085 q^{37} - 9813 q^{38} + 5901 q^{39} - 6267 q^{40} - 1009 q^{41} - 22 q^{42} + 23760 q^{43} + 3215 q^{44} - 18942 q^{45} - 15800 q^{46} + 11346 q^{47} + 38529 q^{48} - 1070 q^{49} - 22867 q^{50} - 9793 q^{51} + 7018 q^{52} + 17996 q^{53} + 91622 q^{54} + 508 q^{55} - 49204 q^{56} + 46028 q^{57} - 36454 q^{58} - 44616 q^{59} - 69860 q^{60} - 91374 q^{61} - 15694 q^{62} - 7642 q^{63} - 66563 q^{64} - 11104 q^{65} + 29958 q^{67} + 33458 q^{68} + 12995 q^{69} + 72490 q^{70} + 34293 q^{71} + 178288 q^{72} + 7050 q^{73} - 8786 q^{74} + 80014 q^{75} + 146812 q^{76} + 108149 q^{77} - 10978 q^{78} - 80964 q^{79} - 83953 q^{80} - 89880 q^{81} - 126534 q^{82} + 21228 q^{83} + 16421 q^{84} - 2014 q^{85} - 40102 q^{86} + 17510 q^{87} - 51977 q^{88} - 93609 q^{89} - 142715 q^{90} + 121690 q^{91} + 32880 q^{92} - 16047 q^{93} + 47850 q^{94} + 22766 q^{95} - 221501 q^{96} + 44892 q^{97} + 14720 q^{98} - 22428 q^{99}+O(q^{100}) \) 440 * q - 19 * q^2 - 22 * q^3 - 191 * q^4 - 22 * q^5 - 53 * q^6 - 16 * q^7 - 517 * q^8 + 840 * q^9 + 854 * q^10 - 100 * q^11 - 742 * q^12 + 248 * q^13 + 308 * q^14 - 1658 * q^15 + 1585 * q^16 - 387 * q^17 + 458 * q^18 + 2011 * q^19 + 653 * q^20 - 4978 * q^21 - 5071 * q^22 + 2673 * q^23 + 7510 * q^24 + 4716 * q^25 - 307 * q^26 - 22 * q^27 + 1350 * q^28 - 412 * q^29 - 3258 * q^30 + 6228 * q^31 - 12097 * q^32 - 7165 * q^33 - 2803 * q^34 + 1835 * q^35 + 1521 * q^36 - 4085 * q^37 - 9813 * q^38 + 5901 * q^39 - 6267 * q^40 - 1009 * q^41 - 22 * q^42 + 23760 * q^43 + 3215 * q^44 - 18942 * q^45 - 15800 * q^46 + 11346 * q^47 + 38529 * q^48 - 1070 * q^49 - 22867 * q^50 - 9793 * q^51 + 7018 * q^52 + 17996 * q^53 + 91622 * q^54 + 508 * q^55 - 49204 * q^56 + 46028 * q^57 - 36454 * q^58 - 44616 * q^59 - 69860 * q^60 - 91374 * q^61 - 15694 * q^62 - 7642 * q^63 - 66563 * q^64 - 11104 * q^65 + 29958 * q^67 + 33458 * q^68 + 12995 * q^69 + 72490 * q^70 + 34293 * q^71 + 178288 * q^72 + 7050 * q^73 - 8786 * q^74 + 80014 * q^75 + 146812 * q^76 + 108149 * q^77 - 10978 * q^78 - 80964 * q^79 - 83953 * q^80 - 89880 * q^81 - 126534 * q^82 + 21228 * q^83 + 16421 * q^84 - 2014 * q^85 - 40102 * q^86 + 17510 * q^87 - 51977 * q^88 - 93609 * q^89 - 142715 * q^90 + 121690 * q^91 + 32880 * q^92 - 16047 * q^93 + 47850 * q^94 + 22766 * q^95 - 221501 * q^96 + 44892 * q^97 + 14720 * q^98 - 22428 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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