LMFDB - Embedded newform 67.5.h.a.2.5

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			2.5
Character	$\chi$	$=$	67.2
Dual form			67.5.h.a.34.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.14762 - 0.245211i) q^{2} +(4.28565 - 14.5956i) q^{3} +(10.5103 + 1.00362i) q^{4} +(-36.2663 - 31.4249i) q^{5} +(-25.6399 + 74.0816i) q^{6} +(-18.7117 - 36.2956i) q^{7} +(27.7590 + 3.99113i) q^{8} +(-126.522 - 81.3110i) q^{9} +O(q^{10})$	\(q+(-5.14762 - 0.245211i) q^{2} +(4.28565 - 14.5956i) q^{3} +(10.5103 + 1.00362i) q^{4} +(-36.2663 - 31.4249i) q^{5} +(-25.6399 + 74.0816i) q^{6} +(-18.7117 - 36.2956i) q^{7} +(27.7590 + 3.99113i) q^{8} +(-126.522 - 81.3110i) q^{9} +(178.979 + 170.657i) q^{10} +(175.185 - 60.6321i) q^{11} +(59.6919 - 149.103i) q^{12} +(42.5509 + 54.1079i) q^{13} +(87.4205 + 191.424i) q^{14} +(-614.089 + 394.651i) q^{15} +(-307.791 - 59.3219i) q^{16} +(129.574 - 12.3729i) q^{17} +(631.351 + 449.583i) q^{18} +(-123.426 - 63.6305i) q^{19} +(-349.632 - 366.684i) q^{20} +(-609.946 + 117.558i) q^{21} +(-916.653 + 269.154i) q^{22} +(39.1896 + 161.542i) q^{23} +(177.218 - 388.053i) q^{24} +(238.772 + 1660.69i) q^{25} +(-205.768 - 288.961i) q^{26} +(-797.813 + 691.309i) q^{27} +(-160.239 - 400.258i) q^{28} +(813.971 - 1409.84i) q^{29} +(3257.87 - 1880.93i) q^{30} +(-309.650 + 393.752i) q^{31} +(1133.79 + 275.053i) q^{32} +(-134.179 - 2816.77i) q^{33} +(-670.034 + 31.9176i) q^{34} +(-461.983 + 1904.32i) q^{35} +(-1248.19 - 981.586i) q^{36} +(-443.122 - 767.510i) q^{37} +(619.747 + 357.811i) q^{38} +(972.094 - 389.168i) q^{39} +(-881.293 - 1017.07i) q^{40} +(1229.49 - 875.515i) q^{41} +(3168.60 - 455.576i) q^{42} +(-23.2345 - 10.6108i) q^{43} +(1902.10 - 461.445i) q^{44} +(2033.31 + 6924.81i) q^{45} +(-162.121 - 841.165i) q^{46} +(-2190.23 + 2088.38i) q^{47} +(-2184.92 + 4238.16i) q^{48} +(425.474 - 597.495i) q^{49} +(-821.885 - 8607.17i) q^{50} +(374.721 - 1944.24i) q^{51} +(392.921 + 611.397i) q^{52} +(-280.091 + 127.913i) q^{53} +(4276.35 - 3362.96i) q^{54} +(-8258.66 - 3306.27i) q^{55} +(-374.556 - 1082.21i) q^{56} +(-1457.68 + 1528.77i) q^{57} +(-4535.72 + 7057.72i) q^{58} +(279.684 - 1945.25i) q^{59} +(-6850.36 + 3531.61i) q^{60} +(2236.63 + 774.107i) q^{61} +(1690.51 - 1950.96i) q^{62} +(-583.785 + 6113.67i) q^{63} +(-956.711 - 280.916i) q^{64} +(157.172 - 3299.45i) q^{65} +14532.6i q^{66} +(1621.99 - 4185.72i) q^{67} +1374.29 q^{68} +(2525.75 + 120.316i) q^{69} +(2845.07 - 9689.43i) q^{70} +(-3150.69 - 300.855i) q^{71} +(-3187.61 - 2762.08i) q^{72} +(-2932.67 + 8473.39i) q^{73} +(2092.82 + 4059.51i) q^{74} +(25262.1 + 3632.14i) q^{75} +(-1233.39 - 792.650i) q^{76} +(-5478.68 - 5223.91i) q^{77} +(-5099.40 + 1764.92i) q^{78} +(-481.996 + 1203.97i) q^{79} +(9298.27 + 11823.7i) q^{80} +(1610.23 + 3525.92i) q^{81} +(-6543.63 + 4205.33i) q^{82} +(8187.32 + 1577.98i) q^{83} +(-6528.72 + 623.417i) q^{84} +(-5088.00 - 3623.15i) q^{85} +(117.000 + 60.3179i) q^{86} +(-17089.0 - 17922.4i) q^{87} +(5104.94 - 983.896i) q^{88} +(-2406.12 + 706.502i) q^{89} +(-8768.65 - 36144.9i) q^{90} +(1167.68 - 2556.86i) q^{91} +(249.770 + 1737.19i) q^{92} +(4419.99 + 6207.00i) q^{93} +(11786.6 - 10213.1i) q^{94} +(2476.62 + 6186.29i) q^{95} +(8873.56 - 15369.5i) q^{96} +(-6355.13 + 3669.13i) q^{97} +(-2336.69 + 2971.35i) q^{98} +(-27094.9 - 6573.14i) 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 $

$2$	−5.14762	−	0.245211i	−1.28691	−	0.0613029i	−0.607059	−	0.794657i	$-0.707651\pi$
$2$	−5.14762	−	0.245211i	−1.28691	−	0.0613029i	−0.679847	+	0.733354i	$0.737954\pi$
$3$	4.28565	−	14.5956i	0.476183	−	1.62173i	−0.274865	−	0.961483i	$-0.588633\pi$
$3$	4.28565	−	14.5956i	0.476183	−	1.62173i	0.751048	−	0.660247i	$-0.229549\pi$
$4$	10.5103	+	1.00362i	0.656896	+	0.0627259i
$5$	−36.2663	−	31.4249i	−1.45065	−	1.25700i	−0.909261	−	0.416226i	$-0.863353\pi$
$5$	−36.2663	−	31.4249i	−1.45065	−	1.25700i	−0.541391	−	0.840771i	$-0.682102\pi$
$6$	−25.6399	+	74.0816i	−0.712219	+	2.05782i
$7$	−18.7117	−	36.2956i	−0.381871	−	0.740726i	0.617062	−	0.786915i	$-0.288323\pi$
$7$	−18.7117	−	36.2956i	−0.381871	−	0.740726i	−0.998933	+	0.0461885i	$0.985293\pi$
$8$	27.7590	+	3.99113i	0.433734	+	0.0623615i
$9$	−126.522	−	81.3110i	−1.56201	−	1.00384i
$10$	178.979	+	170.657i	1.78979	+	1.70657i
$11$	175.185	−	60.6321i	1.44781	−	0.501091i	0.513666	−	0.857990i	$-0.328287\pi$
$11$	175.185	−	60.6321i	1.44781	−	0.501091i	0.934143	+	0.356899i	$0.116166\pi$
$12$	59.6919	−	149.103i	0.414527	−	1.03544i
$13$	42.5509	+	54.1079i	0.251781	+	0.320165i	0.895470	−	0.445122i	$-0.146840\pi$
$13$	42.5509	+	54.1079i	0.251781	+	0.320165i	−0.643689	+	0.765287i	$0.722597\pi$
$14$	87.4205	+	191.424i	0.446023	+	0.976654i
$15$	−614.089	+	394.651i	−2.72929	+	1.75401i
$16$	−307.791	−	59.3219i	−1.20231	−	0.231726i
$17$	129.574	−	12.3729i	0.448354	−	0.0428126i	0.131563	−	0.991308i	$-0.458001\pi$
$17$	129.574	−	12.3729i	0.448354	−	0.0428126i	0.316791	+	0.948495i	$0.397394\pi$
$18$	631.351	+	449.583i	1.94861	+	1.38760i
$19$	−123.426	−	63.6305i	−0.341900	−	0.176262i	0.278721	−	0.960372i	$-0.410089\pi$
$19$	−123.426	−	63.6305i	−0.341900	−	0.176262i	−0.620622	+	0.784110i	$0.713120\pi$
$20$	−349.632	−	366.684i	−0.874081	−	0.916710i
$21$	−609.946	+	117.558i	−1.38310	+	0.266570i
$22$	−916.653	+	269.154i	−1.89391	+	0.556102i
$23$	39.1896	+	161.542i	0.0740824	+	0.305372i	0.996783	−	0.0801450i	$-0.0255383\pi$
$23$	39.1896	+	161.542i	0.0740824	+	0.305372i	−0.922701	+	0.385517i	$0.874023\pi$
$24$	177.218	−	388.053i	0.307670	−	0.673703i
$25$	238.772	+	1660.69i	0.382035	+	2.65711i
$26$	−205.768	−	288.961i	−0.304391	−	0.427457i
$27$	−797.813	+	691.309i	−1.09439	+	0.948297i
$28$	−160.239	−	400.258i	−0.204387	−	0.510533i
$29$	813.971	−	1409.84i	0.967861	−	1.67638i	0.266136	−	0.963936i	$-0.414253\pi$
$29$	813.971	−	1409.84i	0.967861	−	1.67638i	0.701725	−	0.712448i	$-0.252414\pi$
$30$	3257.87	−	1880.93i	3.61986	−	2.08993i
$31$	−309.650	+	393.752i	−0.322217	+	0.409732i	−0.919995	−	0.391929i	$-0.871808\pi$
$31$	−309.650	+	393.752i	−0.322217	+	0.409732i	0.597779	+	0.801661i	$0.296050\pi$
$32$	1133.79	+	275.053i	1.10721	+	0.268607i
$33$	−134.179	−	2816.77i	−0.123213	−	2.58657i
$34$	−670.034	+	31.9176i	−0.579614	+	0.0276104i
$35$	−461.983	+	1904.32i	−0.377129	+	1.55455i
$36$	−1248.19	−	981.586i	−0.963108	−	0.757396i
$37$	−443.122	−	767.510i	−0.323683	−	0.560636i	0.657562	−	0.753401i	$-0.271588\pi$
$37$	−443.122	−	767.510i	−0.323683	−	0.560636i	−0.981245	+	0.192765i	$0.938254\pi$
$38$	619.747	+	357.811i	0.429188	+	0.247792i
$39$	972.094	−	389.168i	0.639115	−	0.255863i
$40$	−881.293	−	1017.07i	−0.550808	−	0.635667i
$41$	1229.49	−	875.515i	0.731403	−	0.520830i	−0.152613	−	0.988286i	$-0.548769\pi$
$41$	1229.49	−	875.515i	0.731403	−	0.520830i	0.884016	+	0.467456i	$0.154829\pi$
$42$	3168.60	−	455.576i	1.79626	−	0.258263i
$43$	−23.2345	−	10.6108i	−0.0125660	−	0.00573868i	0.409122	−	0.912480i	$-0.365835\pi$
$43$	−23.2345	−	10.6108i	−0.0125660	−	0.00573868i	−0.421688	+	0.906741i	$0.638562\pi$
$44$	1902.10	−	461.445i	0.982491	−	0.238350i
$45$	2033.31	+	6924.81i	1.00410	+	3.41966i
$46$	−162.121	−	841.165i	−0.0766169	−	0.397526i
$47$	−2190.23	+	2088.38i	−0.991504	+	0.945397i	−0.998509	−	0.0545783i	$-0.982619\pi$
$47$	−2190.23	+	2088.38i	−0.991504	+	0.945397i	0.00700551	+	0.999975i	$0.497770\pi$
$48$	−2184.92	+	4238.16i	−0.948317	+	1.83948i
$49$	425.474	−	597.495i	0.177207	−	0.248852i
$50$	−821.885	−	8607.17i	−0.328754	−	3.44287i
$51$	374.721	−	1944.24i	0.144068	−	0.747496i
$52$	392.921	+	611.397i	0.145311	+	0.226108i
$53$	−280.091	+	127.913i	−0.0997119	+	0.0455369i	−0.464647	−	0.885496i	$-0.653819\pi$
$53$	−280.091	+	127.913i	−0.0997119	+	0.0455369i	0.364935	+	0.931033i	$0.381091\pi$
$54$	4276.35	−	3362.96i	1.46651	−	1.15328i
$55$	−8258.66	−	3306.27i	−2.73014	−	1.09298i
$56$	−374.556	−	1082.21i	−0.119437	−	0.345092i
$57$	−1457.68	+	1528.77i	−0.448656	+	0.470537i
$58$	−4535.72	+	7057.72i	−1.34831	+	2.09801i
$59$	279.684	−	1945.25i	0.0803459	−	0.558818i	−0.909394	−	0.415936i	$-0.863454\pi$
$59$	279.684	−	1945.25i	0.0803459	−	0.558818i	0.989740	−	0.142882i	$-0.0456369\pi$
$60$	−6850.36	+	3531.61i	−1.90288	+	0.981002i
$61$	2236.63	+	774.107i	0.601084	+	0.208037i	0.610629	−	0.791917i	$-0.290917\pi$
$61$	2236.63	+	774.107i	0.601084	+	0.208037i	−0.00954429	+	0.999954i	$0.503038\pi$
$62$	1690.51	−	1950.96i	0.439780	−	0.507533i
$63$	−583.785	+	6113.67i	−0.147086	+	1.54036i
$64$	−956.711	−	280.916i	−0.233572	−	0.0685829i
$65$	157.172	−	3299.45i	0.0372005	−	0.780936i
$66$			14532.6i			3.33622i
$67$	1621.99	−	4185.72i	0.361325	−	0.932440i
$67$	1621.99	−	4185.72i	0.361325	−	0.932440i
$68$	1374.29			0.297207
$69$	2525.75	+	120.316i	0.530507	+	0.0252712i
$70$	2845.07	−	9689.43i	0.580627	−	1.97744i
$71$	−3150.69	−	300.855i	−0.625014	−	0.0596816i	−0.222256	−	0.974988i	$-0.571342\pi$
$71$	−3150.69	−	300.855i	−0.625014	−	0.0596816i	−0.402757	+	0.915307i	$0.631948\pi$
$72$	−3187.61	−	2762.08i	−0.614893	−	0.532808i
$73$	−2932.67	+	8473.39i	−0.550323	+	1.59005i	0.235681	+	0.971831i	$0.424268\pi$
$73$	−2932.67	+	8473.39i	−0.550323	+	1.59005i	−0.786003	+	0.618222i	$0.787853\pi$
$74$	2092.82	+	4059.51i	0.382181	+	0.741328i
$75$	25262.1	+	3632.14i	4.49103	+	0.645713i
$76$	−1233.39	−	792.650i	−0.213537	−	0.137232i
$77$	−5478.68	−	5223.91i	−0.924047	−	0.881077i
$78$	−5099.40	+	1764.92i	−0.838166	+	0.290092i
$79$	−481.996	+	1203.97i	−0.0772306	+	0.192913i	−0.961959	−	0.273195i	$-0.911920\pi$
$79$	−481.996	+	1203.97i	−0.0772306	+	0.192913i	0.884728	+	0.466107i	$0.154344\pi$
$80$	9298.27	+	11823.7i	1.45285	+	1.84745i
$81$	1610.23	+	3525.92i	0.245425	+	0.537406i
$82$	−6543.63	+	4205.33i	−0.973175	+	0.625422i
$83$	8187.32	+	1577.98i	1.18846	+	0.229057i	0.744894	−	0.667183i	$-0.232500\pi$
$83$	8187.32	+	1577.98i	1.18846	+	0.229057i	0.443569	+	0.896240i	$0.353712\pi$
$84$	−6528.72	+	623.417i	−0.925272	+	0.0883528i
$85$	−5088.00	−	3623.15i	−0.704221	−	0.501474i
$86$	117.000	+	60.3179i	0.0158194	+	0.00815547i
$87$	−17089.0	−	17922.4i	−2.25776	−	2.36787i
$88$	5104.94	−	983.896i	0.659212	−	0.127053i
$89$	−2406.12	+	706.502i	−0.303765	+	0.0891935i	−0.430063	−	0.902799i	$-0.641509\pi$
$89$	−2406.12	+	706.502i	−0.303765	+	0.0891935i	0.126298	+	0.991992i	$0.459690\pi$
$90$	−8768.65	−	36144.9i	−1.08255	−	4.46233i
$91$	1167.68	−	2556.86i	0.141007	−	0.308762i
$92$	249.770	+	1737.19i	0.0295097	+	0.205244i
$93$	4419.99	+	6207.00i	0.511040	+	0.717656i
$94$	11786.6	−	10213.1i	1.33393	−	1.15585i
$95$	2476.62	+	6186.29i	0.274418	+	0.685462i
$96$	8873.56	−	15369.5i	0.962843	−	1.66769i
$97$	−6355.13	+	3669.13i	−0.675431	+	0.389960i	−0.798131	−	0.602484i	$-0.794178\pi$
$97$	−6355.13	+	3669.13i	−0.675431	+	0.389960i	0.122701	+	0.992444i	$0.460845\pi$
$98$	−2336.69	+	2971.35i	−0.243304	+	0.309386i
$99$	−27094.9	−	6573.14i	−2.76450	−	0.670660i
$100$	842.872	+	17694.1i	0.0842872	+	1.76941i
$101$	−3293.31	+	156.880i	−0.322842	+	0.0153789i	−0.208378	−	0.978048i	$-0.566818\pi$
$101$	−3293.31	+	156.880i	−0.322842	+	0.0153789i	−0.114465	+	0.993427i	$0.536515\pi$
$102$	−2405.67	+	9916.31i	−0.231226	+	0.953125i
$103$	−1620.45	−	1274.34i	−0.152743	−	0.120118i	0.538863	−	0.842393i	$-0.318854\pi$
$103$	−1620.45	−	1274.34i	−0.152743	−	0.120118i	−0.691606	+	0.722275i	$0.743096\pi$
$104$	965.217	+	1671.80i	0.0892397	+	0.154568i
$105$	25814.7	+	14904.1i	2.34147	+	1.35185i
$106$	1473.17	−	589.767i	0.131111	−	0.0524891i
$107$	−2942.52	−	3395.85i	−0.257011	−	0.296607i	0.612550	−	0.790432i	$-0.290144\pi$
$107$	−2942.52	−	3395.85i	−0.257011	−	0.296607i	−0.869561	+	0.493825i	$0.835598\pi$
$108$	−9079.08	+	6465.19i	−0.778385	+	0.554285i
$109$	−10258.5	+	1474.95i	−0.863439	+	0.124144i	−0.559784	−	0.828638i	$-0.689116\pi$
$109$	−10258.5	+	1474.95i	−0.863439	+	0.124144i	−0.303655	+	0.952782i	$0.598207\pi$
$110$	41701.7	+	19044.5i	3.44643	+	1.57393i
$111$	−13101.3	+	3178.34i	−1.06333	+	0.257962i
$112$	3606.17	+	12281.5i	0.287481	+	0.979072i
$113$	3894.51	+	20206.6i	0.304997	+	1.58248i	0.733985	+	0.679166i	$0.237658\pi$
$113$	3894.51	+	20206.6i	0.304997	+	1.58248i	−0.428987	+	0.903310i	$0.641130\pi$
$114$	7878.48	−	7512.11i	0.606223	−	0.578033i
$115$	3655.17	−	7090.05i	0.276384	−	0.536109i
$116$	9970.04	−	14001.0i	0.740936	−	1.04050i
$117$	−984.077	−	10305.7i	−0.0718882	−	0.752847i
$118$	−1916.70	+	9944.81i	−0.137655	+	0.714220i
$119$	−2873.63	−	4471.46i	−0.202926	−	0.315759i
$120$	−18621.6	+	8504.19i	−1.29317	+	0.590569i
$121$	15504.9	−	12193.2i	1.05900	−	0.832810i
$122$	−11323.5	−	4533.26i	−0.760785	−	0.304572i
$123$	−7509.49	−	21697.2i	−0.496364	−	1.43415i
$124$	−3649.70	+	3827.70i	−0.237364	+	0.248940i
$125$	27312.9	−	42499.7i	1.74803	−	2.71998i
$126$	4504.24	−	31327.7i	0.283714	−	1.97327i
$127$	−23342.6	+	12033.9i	−1.44724	+	0.746106i	−0.989710	−	0.143086i	$-0.954297\pi$
$127$	−23342.6	+	12033.9i	−1.44724	+	0.746106i	−0.457534	+	0.889192i	$0.651267\pi$
$128$	−12784.2	−	4424.65i	−0.780285	−	0.270059i
$129$	−254.446	+	293.646i	−0.0152903	+	0.0176459i
$130$	−1618.13	+	16945.8i	−0.0957472	+	1.00271i
$131$	−3694.65	−	1084.85i	−0.215293	−	0.0632159i	0.172307	−	0.985043i	$-0.444878\pi$
$131$	−3694.65	−	1084.85i	−0.215293	−	0.0632159i	−0.387601	+	0.921827i	$0.626696\pi$
$132$	1416.68	−	29739.9i	0.0813065	−	1.70683i
$133$			5670.45i			0.320564i
$134$	−9375.77	+	21148.8i	−0.522152	+	1.17781i
$135$	50658.0			2.77959
$136$	3646.23	+	173.691i	0.197136	+	0.00939075i
$137$	9067.85	−	30882.3i	0.483129	−	1.64539i	−0.252199	−	0.967675i	$-0.581154\pi$
$137$	9067.85	−	30882.3i	0.483129	−	1.64539i	0.735328	−	0.677711i	$-0.237028\pi$
$138$	−12972.1	−	1238.68i	−0.681164	−	0.0650432i
$139$	17099.4	+	14816.7i	0.885016	+	0.766871i	0.973375	−	0.229218i	$-0.0736169\pi$
$139$	17099.4	+	14816.7i	0.885016	+	0.766871i	−0.0883592	+	0.996089i	$0.528162\pi$
$140$	−6766.80	+	19551.4i	−0.345245	+	0.997519i
$141$	21094.6	+	40917.8i	1.06104	+	2.05813i
$142$	16144.8	+	2321.27i	0.800675	+	0.115120i
$143$	10734.9	+	6898.93i	0.524962	+	0.337373i
$144$	34119.0	+	32532.4i	1.64540	+	1.56888i
$145$	−73823.8	+	25550.7i	−3.51124	+	1.21525i
$146$	17174.0	−	42898.7i	0.805688	−	2.01251i
$147$	−6897.35	−	8770.69i	−0.319189	−	0.405881i
$148$	−3887.08	−	8511.51i	−0.177460	−	0.388582i
$149$	1506.67	−	968.278i	0.0678650	−	0.0436142i	−0.506268	−	0.862376i	$-0.668975\pi$
$149$	1506.67	−	968.278i	0.0678650	−	0.0436142i	0.574133	+	0.818762i	$0.305339\pi$
$150$	−129149.	−	24891.4i	−5.73995	−	1.10628i
$151$	32232.4	−	3077.82i	1.41364	−	0.134986i	0.639884	−	0.768471i	$-0.278982\pi$
$151$	32232.4	−	3077.82i	1.41364	−	0.134986i	0.773755	+	0.633485i	$0.218376\pi$
$152$	−3172.22	−	2258.93i	−0.137302	−	0.0977720i
$153$	−17400.1	−	8970.38i	−0.743309	−	0.383202i
$154$	26921.2	+	28234.1i	1.13515	+	1.19051i
$155$	23603.5	−	4549.20i	0.982456	−	0.189353i
$156$	10607.6	−	3114.67i	0.435881	−	0.127986i
$157$	7558.66	+	31157.2i	0.306652	+	1.26404i	0.891548	+	0.452927i	$0.149620\pi$
$157$	7558.66	+	31157.2i	0.306652	+	1.26404i	−0.584896	+	0.811108i	$0.698865\pi$
$158$	2776.36	−	6079.39i	0.111215	−	0.243526i
$159$	666.596	+	4636.27i	0.0263675	+	0.183390i
$160$	−32474.7	−	45604.3i	−1.26854	−	1.78142i
$161$	5129.94	−	4445.12i	0.197907	−	0.171487i
$162$	−7424.28	−	18545.0i	−0.282894	−	0.706636i
$163$	6135.51	−	10627.0i	0.230928	−	0.399978i	−0.727154	−	0.686475i	$-0.759157\pi$
$163$	6135.51	−	10627.0i	0.230928	−	0.399978i	0.958081	+	0.286496i	$0.0924906\pi$
$164$	13801.0	−	7968.02i	0.513125	−	0.296253i
$165$	−83650.6	+	106370.i	−3.07257	+	3.90709i
$166$	−41758.3	−	10130.5i	−1.51540	−	0.367632i
$167$	−1506.23	−	31619.6i	−0.0540080	−	1.13377i	−0.849427	−	0.527706i	$-0.823052\pi$
$167$	−1506.23	−	31619.6i	−0.0540080	−	1.13377i	0.795419	−	0.606060i	$-0.207251\pi$
$168$	−17400.7	+	828.896i	−0.616520	+	0.0293685i
$169$	5616.43	−	23151.2i	0.196647	−	0.810589i
$170$	25302.7	+	19898.2i	0.875524	+	0.688520i
$171$	10442.3	+	18086.6i	0.357111	+	0.618535i
$172$	−233.553	−	134.842i	−0.00789456	−	0.00455793i
$173$	−6879.44	+	2754.11i	−0.229859	+	0.0920215i	−0.483733	−	0.875216i	$-0.660719\pi$
$173$	−6879.44	+	2754.11i	−0.229859	+	0.0920215i	0.253874	+	0.967237i	$0.418295\pi$
$174$	83573.0	+	96448.4i	2.76037	+	3.18564i
$175$	55808.0	−	39740.7i	1.82230	−	1.29766i
$176$	−57517.2	+	8269.72i	−1.85683	+	0.266972i
$177$	−27193.3	−	12418.8i	−0.867993	−	0.396399i
$178$	12559.1	−	3046.80i	0.396385	−	0.0961619i
$179$	5762.67	+	19625.9i	0.179853	+	0.612523i	0.999229	+	0.0392664i	$0.0125021\pi$
$179$	5762.67	+	19625.9i	0.179853	+	0.612523i	−0.819376	+	0.573257i	$0.805680\pi$
$180$	14420.9	+	74822.7i	0.445089	+	2.30934i
$181$	8733.86	−	8327.72i	0.266593	−	0.254196i	−0.544977	−	0.838451i	$-0.683462\pi$
$181$	8733.86	−	8327.72i	0.266593	−	0.254196i	0.811570	+	0.584255i	$0.198613\pi$
$182$	−6637.74	+	12875.4i	−0.200391	+	0.388704i
$183$	20884.0	−	29327.4i	0.623606	−	0.875733i
$184$	443.127	+	4640.64i	0.0130886	+	0.137070i
$185$	−8048.55	+	41759.8i	−0.235166	+	1.22016i
$186$	−21230.4	−	33035.1i	−0.613666	−	0.954883i
$187$	21949.3	−	10023.9i	0.627678	−	0.286651i
$188$	−25116.0	+	19751.4i	−0.710616	+	0.558834i
$189$	40019.9	+	16021.5i	1.12035	+	0.448519i
$190$	−11231.7	−	32452.0i	−0.311129	−	0.898947i
$191$	5457.60	−	5723.77i	0.149601	−	0.156897i	−0.644669	−	0.764462i	$-0.723005\pi$
$191$	5457.60	−	5723.77i	0.149601	−	0.156897i	0.794270	+	0.607564i	$0.207853\pi$
$192$	−8200.25	+	12759.8i	−0.222446	+	0.346133i
$193$	7246.17	−	50398.2i	0.194533	−	1.35301i	−0.625290	−	0.780392i	$-0.715019\pi$
$193$	7246.17	−	50398.2i	0.194533	−	1.35301i	0.819824	−	0.572616i	$-0.194071\pi$
$194$	33613.5	−	17329.0i	0.893121	−	0.460436i
$195$	−47483.8	−	16434.3i	−1.24875	−	0.432197i
$196$	5071.53	−	5852.86i	0.132016	−	0.152355i
$197$	1554.12	−	16275.5i	0.0400454	−	0.419374i	−0.953114	−	0.302610i	$-0.902142\pi$
$197$	1554.12	−	16275.5i	0.0400454	−	0.419374i	0.993160	−	0.116764i	$-0.0372520\pi$
$198$	137862.	+	40480.0i	3.51654	+	1.03255i
$199$	−725.770	+	15235.8i	−0.0183271	+	0.384733i	0.971005	+	0.239057i	$0.0768384\pi$
$199$	−725.770	+	15235.8i	−0.0183271	+	0.384733i	−0.989332	+	0.145675i	$0.953465\pi$
$200$			47052.1i			1.17630i
$201$	−54141.8	−	41612.4i	−1.34011	−	1.02998i
$202$	16991.2			0.416410
$203$	−66401.7	−	3163.10i	−1.61134	−	0.0767575i
$204$	5889.71	−	20058.5i	0.141525	−	0.481990i
$205$	−72102.0	−	6884.90i	−1.71569	−	0.163829i
$206$	8028.98	+	6957.15i	0.189202	+	0.163945i
$207$	8176.75	−	23625.2i	0.190827	−	0.551359i
$208$	−9887.02	−	19178.1i	−0.228528	−	0.443282i
$209$	−25480.4	−	3663.53i	−0.583329	−	0.0838701i
$210$	−129230.	−	83051.0i	−2.93038	−	1.88324i
$211$	16491.9	+	15725.0i	0.370430	+	0.353205i	0.852314	−	0.523031i	$-0.175199\pi$
$211$	16491.9	+	15725.0i	0.370430	+	0.353205i	−0.481884	+	0.876235i	$0.660047\pi$
$212$	−3072.22	+	1063.31i	−0.0683567	+	0.0236585i
$213$	−17893.9	+	44696.8i	−0.394408	+	0.985184i
$214$	14314.3	+	18202.1i	0.312566	+	0.397460i
$215$	509.184	+	1114.96i	0.0110153	+	0.0241202i
$216$	−24905.5	+	16005.8i	−0.533812	+	0.343060i
$217$	20085.5	+	3871.17i	0.426544	+	0.0822097i
$218$	53168.6	−	5076.99i	1.11877	−	0.106830i
$219$	111106.	+	79118.0i	2.31658	+	1.64963i
$220$	−83483.1	−	43038.5i	−1.72486	−	0.889226i
$221$	6182.98	+	6484.52i	0.126594	+	0.132768i
$222$	68220.0	−	13148.3i	1.38422	−	0.266787i
$223$	54656.0	−	16048.4i	1.09908	−	0.322718i	0.318591	−	0.947892i	$-0.396790\pi$
$223$	54656.0	−	16048.4i	1.09908	−	0.322718i	0.780485	+	0.625174i	$0.214972\pi$
$224$	−11231.8	−	46298.1i	−0.223848	−	0.922714i
$225$	104823.	−	229530.i	2.07057	−	4.53392i
$226$	−15092.6	−	104971.i	−0.295492	−	2.05519i
$227$	−31806.9	−	44666.6i	−0.617263	−	0.866824i	0.381070	−	0.924546i	$-0.375556\pi$
$227$	−31806.9	−	44666.6i	−0.617263	−	0.866824i	−0.998333	+	0.0577219i	$0.981616\pi$
$228$	−16855.0	+	14605.0i	−0.324235	+	0.280951i
$229$	−13941.0	−	34822.9i	−0.265842	−	0.664040i	0.734045	−	0.679101i	$-0.237630\pi$
$229$	−13941.0	−	34822.9i	−0.265842	−	0.664040i	−0.999887	+	0.0150605i	$0.995206\pi$
$230$	−20554.0	+	35600.6i	−0.388545	+	0.672979i
$231$	−99725.6	+	57576.6i	−1.86889	+	1.07900i
$232$	28221.8	−	35887.0i	0.524335	−	0.666747i
$233$	18833.0	+	4568.85i	0.346904	+	0.0841579i	0.405425	−	0.914128i	$-0.367123\pi$
$233$	18833.0	+	4568.85i	0.346904	+	0.0841579i	−0.0585216	+	0.998286i	$0.518639\pi$
$234$	2538.58	+	53291.3i	0.0463616	+	0.973250i
$235$	145059.	−	6910.01i	2.62669	−	0.125125i
$236$	4891.85	−	20164.5i	0.0878313	−	0.362045i
$237$	15506.9	+	12194.8i	0.276077	+	0.217109i
$238$	13695.9	+	23722.0i	0.241789	+	0.418792i
$239$	−27875.2	−	16093.7i	−0.488002	−	0.281748i	0.235743	−	0.971815i	$-0.424248\pi$
$239$	−27875.2	−	16093.7i	−0.488002	−	0.281748i	−0.723745	+	0.690067i	$0.757581\pi$
$240$	212423.	−	85041.3i	3.68790	−	1.47641i
$241$	23193.9	+	26767.1i	0.399336	+	0.460859i	0.919432	−	0.393249i	$-0.128649\pi$
$241$	23193.9	+	26767.1i	0.399336	+	0.460859i	−0.520095	+	0.854108i	$0.674104\pi$
$242$	−82803.2	+	58963.9i	−1.41389	+	1.00683i
$243$	−26274.2	+	3777.66i	−0.444956	+	0.0639749i
$244$	22730.9	+	10380.8i	0.381800	+	0.174362i
$245$	−34206.6	+	8298.43i	−0.569873	+	0.138250i
$246$	33335.6	+	113531.i	0.550856	+	1.87604i
$247$	−1808.98	−	9385.85i	−0.0296510	−	0.153844i
$248$	−10167.1	+	9694.29i	−0.165308	+	0.157621i
$249$	58119.4	−	112736.i	0.937395	−	1.81829i
$250$	−151018.	+	212075.i	−2.41629	+	3.39320i
$251$	−2998.69	−	31403.7i	−0.0475976	−	0.498464i	−0.987566	−	0.157203i	$-0.949752\pi$
$251$	−2998.69	−	31403.7i	−0.0475976	−	0.498464i	0.939969	−	0.341261i	$-0.110854\pi$
$252$	−12271.5	+	63670.8i	−0.193240	+	1.00263i
$253$	16660.0	+	25923.5i	0.260276	+	0.404998i
$254$	123110.	−	56222.3i	1.90820	−	0.871448i
$255$	−74687.3	+	58734.7i	−1.14859	+	0.903264i
$256$	79534.0	+	31840.6i	1.21359	+	0.485849i
$257$	9910.82	+	28635.4i	0.150053	+	0.433548i	0.994828	−	0.101572i	$-0.0323873\pi$
$257$	9910.82	+	28635.4i	0.150053	+	0.433548i	−0.844776	+	0.535121i	$0.820266\pi$
$258$	1381.80	−	1449.19i	0.0207589	−	0.0217713i
$259$	−19565.7	+	30444.8i	−0.291672	+	0.453851i
$260$	4963.31	−	34520.6i	0.0734218	−	0.510660i
$261$	−217621.	+	112191.i	−3.19462	+	1.64694i
$262$	18752.6	+	6490.35i	0.273187	+	0.0945509i
$263$	17541.5	−	20243.9i	0.253603	−	0.292674i	−0.614645	−	0.788804i	$-0.710701\pi$
$263$	17541.5	−	20243.9i	0.253603	−	0.292674i	0.868248	+	0.496130i	$0.165246\pi$
$264$	7517.43	−	78726.1i	0.107860	−	1.12956i
$265$	14177.5	+	4162.89i	0.201887	+	0.0592794i
$266$	1390.46	−	29189.3i	0.0196515	−	0.412535i
$267$			38146.6i			0.535098i
$268$	21248.5	−	42365.5i	0.295841	−	0.589851i
$269$	−96072.1			−1.32768			−0.663839	−	0.747876i	$-0.731074\pi$
$269$	−96072.1			−1.32768			−0.663839	+	0.747876i	$0.731074\pi$
$270$	−260768.	−	12421.9i	−3.57707	−	0.170397i
$271$	37440.6	−	127511.i	0.509806	−	1.73624i	−0.153748	−	0.988110i	$-0.549135\pi$
$271$	37440.6	−	127511.i	0.509806	−	1.73624i	0.663554	−	0.748128i	$-0.269047\pi$
$272$	−40615.9	−	3878.34i	−0.548982	−	0.0524214i
$273$	−32314.6	−	28000.7i	−0.433584	−	0.375703i
$274$	−54250.5	+	156747.i	−0.722608	+	2.08784i
$275$	142520.	+	276451.i	1.88457	+	3.65555i
$276$	26425.7	+	3799.44i	0.346903	+	0.0498771i
$277$	−39064.6	−	25105.3i	−0.509125	−	0.327195i	0.260732	−	0.965411i	$-0.416036\pi$
$277$	−39064.6	−	25105.3i	−0.509125	−	0.327195i	−0.769857	+	0.638217i	$0.779672\pi$
$278$	−84388.0	−	80463.8i	−1.09192	−	1.04114i
$279$	71194.1	−	24640.5i	0.914609	−	0.316549i
$280$	−20424.6	+	51018.1i	−0.260517	+	0.650741i
$281$	62566.1	+	79559.2i	0.792367	+	1.00758i	0.999571	+	0.0292787i	$0.00932104\pi$
$281$	62566.1	+	79559.2i	0.792367	+	1.00758i	−0.207204	+	0.978298i	$0.566437\pi$
$282$	−98553.4	−	215802.i	−1.23929	−	2.71367i
$283$	−36708.5	+	23591.1i	−0.458346	+	0.294561i	−0.749366	−	0.662156i	$-0.769642\pi$
$283$	−36708.5	+	23591.1i	−0.458346	+	0.294561i	0.291020	+	0.956717i	$0.406005\pi$
$284$	−32812.9	−	6324.17i	−0.406825	−	0.0784091i
$285$	100906.	−	9635.39i	1.24231	−	0.118626i
$286$	−53567.8	−	38145.4i	−0.654895	−	0.466348i
$287$	−54783.1	−	28242.7i	−0.665094	−	0.342880i
$288$	−121084.	−	126990.i	−1.45983	−	1.53103i
$289$	−65375.2	+	12600.0i	−0.782740	+	0.150861i
$290$	386282.	−	113423.i	4.59313	−	1.34866i
$291$	26317.3	+	108481.i	0.310781	+	1.28106i
$292$	−39327.4	+	86114.9i	−0.461242	+	1.00998i
$293$	−2463.65	−	17135.0i	−0.0286974	−	0.199595i	0.970429	−	0.241387i	$-0.0776024\pi$
$293$	−2463.65	−	17135.0i	−0.0286974	−	0.199595i	−0.999126	+	0.0417921i	$0.986693\pi$
$294$	33354.3	+	46839.5i	0.385884	+	0.541898i
$295$	−71272.3	+	61757.8i	−0.818986	+	0.709656i
$296$	−9237.37	−	23073.8i	−0.105430	−	0.263352i
$297$	−97849.2	+	169480.i	−1.10929	+	1.92134i
$298$	−7993.20	+	4614.88i	−0.0900095	+	0.0519670i
$299$	−7073.13	+	8994.21i	−0.0791168	+	0.100605i
$300$	261867.	+	63528.3i	2.90964	+	0.705870i
$301$	49.6296	+	1041.85i	0.000547783	+	0.0114994i
$302$	−166675.	+	7939.70i	−1.82750	+	0.0870543i
$303$	−11824.2	+	48740.1i	−0.128792	+	0.530886i
$304$	34214.8	+	26906.8i	0.370225	+	0.291149i
$305$	−56788.2	−	98360.1i	−0.610462	−	1.05735i
$306$	87369.6	+	50442.8i	0.933077	+	0.538712i
$307$	−63390.9	+	25377.9i	−0.672589	+	0.269264i	−0.682715	−	0.730685i	$-0.739201\pi$
$307$	−63390.9	+	25377.9i	−0.672589	+	0.269264i	0.0101260	+	0.999949i	$0.496777\pi$
$308$	−52339.9	−	60403.5i	−0.551736	−	0.636738i
$309$	−25544.3	+	18190.0i	−0.267533	+	0.190510i
$310$	−122617.	+	17629.7i	−1.27594	+	0.183452i
$311$	−29803.0	−	13610.6i	−0.308134	−	0.140720i	0.255346	−	0.966850i	$-0.417811\pi$
$311$	−29803.0	−	13610.6i	−0.308134	−	0.140720i	−0.563480	+	0.826130i	$0.690538\pi$
$312$	28537.5	−	6923.13i	0.293162	−	0.0711202i
$313$	28829.5	+	98184.3i	0.294272	+	1.00220i	0.965382	+	0.260840i	$0.0839995\pi$
$313$	28829.5	+	98184.3i	0.294272	+	1.00220i	−0.671110	+	0.741358i	$0.734182\pi$
$314$	−31269.0	−	162239.i	−0.317143	−	1.64549i
$315$	213293.	−	203375.i	2.14959	−	2.04963i
$316$	−6274.26	+	12170.4i	−0.0628331	+	0.121879i
$317$	−31646.6	+	44441.5i	−0.314926	+	0.442252i	−0.941451	−	0.337149i	$-0.890537\pi$
$317$	−31646.6	+	44441.5i	−0.314926	+	0.442252i	0.626525	+	0.779401i	$0.284477\pi$
$318$	−2294.51	−	24029.2i	−0.0226901	−	0.237622i
$319$	57113.9	−	296335.i	0.561255	−	2.91207i
$320$	25868.6	+	40252.3i	0.252623	+	0.393089i
$321$	−62174.9	+	28394.3i	−0.603400	+	0.275564i
$322$	−27497.0	+	21623.9i	−0.265200	+	0.208556i
$323$	−16780.1	−	6717.75i	−0.160839	−	0.0643901i
$324$	13385.4	+	38674.7i	0.127509	+	0.368414i
$325$	−79696.7	+	83583.4i	−0.754525	+	0.791323i
$326$	−34189.2	+	53199.4i	−0.321702	+	0.500578i
$327$	−22436.6	+	156050.i	−0.209827	+	1.45938i
$328$	37623.6	−	19396.3i	0.349714	−	0.180290i
$329$	116782.	+	40418.6i	1.07891	+	0.373413i
$330$	456685.	−	527043.i	4.19362	−	4.83969i
$331$	15649.4	−	163888.i	0.142838	−	1.49586i	−0.585516	−	0.810661i	$-0.699108\pi$
$331$	15649.4	−	163888.i	0.142838	−	1.49586i	0.728353	−	0.685202i	$-0.240286\pi$
$332$	84467.8	+	24802.0i	0.766329	+	0.225014i
$333$	−6342.14	+	133138.i	−0.0571936	+	1.20064i
$334$			163135.i			1.46236i
$335$	−190360.	+	100830.i	−1.69623	+	0.898461i
$336$	194710.			1.72468
$337$	162634.	+	7747.21i	1.43203	+	0.0682159i	0.749190	−	0.662355i	$-0.230443\pi$
$337$	162634.	+	7747.21i	1.43203	+	0.0682159i	0.682837	+	0.730571i	$0.260746\pi$
$338$	−34588.2	+	117797.i	−0.302757	+	1.03110i
$339$	311618.	+	29755.9i	2.71158	+	0.258925i
$340$	−49840.3	−	43186.9i	−0.431145	−	0.373589i
$341$	−30372.0	+	87754.2i	−0.261195	+	0.754673i
$342$	−49317.9	−	95663.4i	−0.421650	−	0.817888i
$343$	−126695.	−	18215.9i	−1.07689	−	0.154833i
$344$	−602.615	−	387.277i	−0.00509241	−	0.00327269i
$345$	−87818.5	−	83734.8i	−0.737816	−	0.703506i
$346$	36088.1	−	12490.2i	0.301448	−	0.104332i
$347$	7536.84	−	18826.1i	0.0625937	−	0.156351i	−0.893774	−	0.448518i	$-0.851952\pi$
$347$	7536.84	−	18826.1i	0.0625937	−	0.156351i	0.956367	+	0.292167i	$0.0943762\pi$
$348$	−161624.	−	205522.i	−1.33459	−	1.69707i
$349$	−18828.6	−	41228.9i	−0.154585	−	0.338494i	0.816456	−	0.577408i	$-0.195936\pi$
$349$	−18828.6	−	41228.9i	−0.154585	−	0.338494i	−0.971041	+	0.238914i	$0.923208\pi$
$350$	−297023.	+	190885.i	−2.42468	+	1.55825i
$351$	−71352.9	−	13752.1i	−0.579159	−	0.111624i
$352$	215299.	−	20558.6i	1.73763	−	0.165923i
$353$	−30725.3	−	21879.4i	−0.246574	−	0.175584i	0.450088	−	0.892984i	$-0.351393\pi$
$353$	−30725.3	−	21879.4i	−0.246574	−	0.175584i	−0.696662	+	0.717400i	$0.745332\pi$
$354$	136936.	+	70595.3i	1.09272	+	0.563338i
$355$	104810.	+	109921.i	0.831658	+	0.872217i
$356$	−25998.2	+	5010.75i	−0.205137	+	0.0395369i
$357$	−77578.9	+	22779.2i	−0.608705	+	0.178732i
$358$	−24851.6	−	102440.i	−0.193904	−	0.799285i
$359$	−30657.7	+	67130.9i	−0.237876	+	0.520875i	−0.990490	−	0.137587i	$-0.956065\pi$
$359$	−30657.7	+	67130.9i	−0.237876	+	0.520875i	0.752614	+	0.658462i	$0.228793\pi$
$360$	28804.6	+	200341.i	0.222258	+	1.54584i
$361$	−64408.5	−	90449.0i	−0.494229	−	0.694048i
$362$	−47000.7	+	40726.3i	−0.358663	+	0.310784i
$363$	−111518.	−	278558.i	−0.846313	−	2.11399i
$364$	14838.8	−	25701.5i	0.111994	−	0.193980i
$365$	372633.	−	215140.i	2.79702	−	1.61486i
$366$	−114694.	+	145845.i	−0.856207	+	1.08876i
$367$	−9194.11	−	2230.47i	−0.0682618	−	0.0165601i	0.201483	−	0.979492i	$-0.435424\pi$
$367$	−9194.11	−	2230.47i	−0.0682618	−	0.0165601i	−0.269744	+	0.962932i	$0.586939\pi$
$368$	−2479.25	−	52045.9i	−0.0183073	−	0.384318i
$369$	−226747.	+	10801.3i	−1.66528	+	0.0793273i
$370$	51670.9	−	212990.i	0.377435	−	1.55581i
$371$	9883.65	+	7772.59i	0.0718074	+	0.0564700i
$372$	40226.1	+	69673.6i	0.290685	+	0.503480i
$373$	184069.	+	106273.i	1.32301	+	0.763841i	0.984208	−	0.177015i	$-0.0566443\pi$
$373$	184069.	+	106273.i	1.32301	+	0.763841i	0.338804	+	0.940857i	$0.389978\pi$
$374$	−115445.	+	46217.0i	−0.825335	+	0.330414i
$375$	−503254.	−	580786.i	−3.57870	−	4.13003i
$376$	−69133.6	+	49229.8i	−0.489005	+	0.348219i
$377$	110919.	−	15947.7i	0.780408	−	0.112206i
$378$	−202078.	−	92286.1i	−1.41428	−	0.645881i
$379$	98799.9	−	23968.6i	0.687825	−	0.166865i	0.123410	−	0.992356i	$-0.460617\pi$
$379$	98799.9	−	23968.6i	0.687825	−	0.166865i	0.564415	+	0.825491i	$0.309102\pi$
$380$	19821.4	+	67505.6i	0.137267	+	0.467490i
$381$	75604.2	+	392272.i	0.520830	+	2.70232i
$382$	−29497.2	+	28125.5i	−0.202141	+	0.192741i
$383$	50703.8	−	98351.6i	0.345655	−	0.670477i	−0.650364	−	0.759623i	$-0.725383\pi$
$383$	50703.8	−	98351.6i	0.345655	−	0.670477i	0.996019	+	0.0891458i	$0.0284137\pi$
$384$	−119369.	+	167630.i	−0.809522	+	1.13681i
$385$	34530.4	+	361619.i	0.232959	+	2.43966i
$386$	−49658.7	+	257654.i	−0.333289	+	1.72927i
$387$	2076.90	+	3231.72i	0.0138674	+	0.0215781i
$388$	−70476.9	+	32185.7i	−0.468148	+	0.213796i
$389$	98976.9	−	77836.3i	0.654086	−	0.514379i	−0.235073	−	0.971978i	$-0.575533\pi$
$389$	98976.9	−	77836.3i	0.654086	−	0.514379i	0.889159	+	0.457599i	$0.151290\pi$
$390$	240399.	+	96241.2i	1.58053	+	0.632749i
$391$	7076.70	+	20446.8i	0.0462889	+	0.133743i
$392$	14195.4	−	14887.7i	0.0923795	−	0.0968848i
$393$	−31667.9	+	49276.3i	−0.205038	+	0.319046i
$394$	−11991.0	+	83399.0i	−0.0772434	+	0.537240i
$395$	55314.9	−	28516.8i	0.354526	−	0.182771i
$396$	−278179.	−	96278.7i	−1.77392	−	0.613960i
$397$	−127892.	+	147595.i	−0.811452	+	0.936465i	−0.998951	−	0.0457997i	$-0.985416\pi$
$397$	−127892.	+	147595.i	−0.811452	+	0.936465i	0.187499	+	0.982265i	$0.439962\pi$
$398$	7471.98	−	78250.1i	0.0471704	−	0.493991i
$399$	82763.4	+	24301.5i	0.519868	+	0.152647i
$400$	25023.7	−	525311.i	0.156398	−	3.28320i
$401$		−	10595.6i		−	0.0658925i	−0.999457	−	0.0329463i	$-0.989511\pi$
$401$		−	10595.6i		−	0.0658925i	0.999457	−	0.0329463i	$-0.0104890\pi$
$402$	268497.	+	227481.i	1.66145	+	1.40764i
$403$	−34481.0			−0.212310
$404$	−34771.3	−	1656.36i	−0.213038	−	0.0101483i
$405$	52404.6	−	178474.i	0.319491	−	1.08809i
$406$	341035.	+	32564.9i	2.06894	+	0.197559i
$407$	−124164.	−	107589.i	−0.749561	−	0.649498i
$408$	18161.6	−	52474.4i	0.109102	−	0.315230i
$409$	110845.	+	215010.i	0.662628	+	1.28532i	0.945331	+	0.326112i	$0.105739\pi$
$409$	110845.	+	215010.i	0.662628	+	1.28532i	−0.282703	+	0.959208i	$0.591231\pi$
$410$	369466.	+	53121.1i	2.19789	+	0.316009i
$411$	−411883.	−	264701.i	−2.43832	−	1.56701i
$412$	−15752.5	−	15020.0i	−0.0928017	−	0.0884862i
$413$	−75837.2	+	26247.5i	−0.444613	+	0.153882i
$414$	−47884.0	+	119608.i	−0.279376	+	0.697849i
$415$	−247336.	−	314513.i	−1.43612	−	1.82618i
$416$	33361.0	+	73050.5i	0.192776	+	0.422121i
$417$	289540.	−	186076.i	1.66509	−	1.07009i
$418$	130265.	+	25106.5i	0.745548	+	0.143693i
$419$	−57109.5	+	5453.30i	−0.325297	+	0.0310621i	−0.256427	−	0.966564i	$-0.582545\pi$
$419$	−57109.5	+	5453.30i	−0.325297	+	0.0310621i	−0.0688700	+	0.997626i	$0.521939\pi$
$420$	256363.	+	182556.i	1.45331	+	1.03490i
$421$	−147795.	−	76193.5i	−0.833863	−	0.429886i	−0.0122453	−	0.999925i	$-0.503898\pi$
$421$	−147795.	−	76193.5i	−0.833863	−	0.429886i	−0.821618	+	0.570039i	$0.806928\pi$
$422$	−81038.2	−	84990.5i	−0.455056	−	0.477249i
$423$	446922.	−	86137.1i	2.49776	−	0.481404i
$424$	−8285.54	+	2432.85i	−0.0460881	+	0.0135327i
$425$	51486.2	+	212229.i	0.285045	+	1.17497i
$426$	103071.	−	225695.i	0.567961	−	1.24366i
$427$	−13754.5	−	95664.8i	−0.0754379	−	0.524682i
$428$	−27518.7	−	38644.6i	−0.150225	−	0.210961i
$429$	146700.	−	127116.i	0.797105	−	0.690696i
$430$	−2347.68	−	5864.23i	−0.0126970	−	0.0317157i
$431$	−6826.71	+	11824.2i	−0.0367500	+	0.0636528i	−0.883815	−	0.467836i	$-0.845034\pi$
$431$	−6826.71	+	11824.2i	−0.0367500	+	0.0636528i	0.847065	+	0.531489i	$0.178367\pi$
$432$	286570.	−	165451.i	1.53555	−	0.886547i
$433$	−92440.9	+	117548.i	−0.493047	+	0.626960i	−0.967363	−	0.253395i	$-0.918453\pi$
$433$	−92440.9	+	117548.i	−0.493047	+	0.626960i	0.474316	+	0.880355i	$0.342695\pi$
$434$	−102444.	−	24852.5i	−0.543882	−	0.131944i
$435$	56543.8	+	1.18700e6i	0.298818	+	6.27296i
$436$	−109301.	+	5206.63i	−0.574976	+	0.0273895i
$437$	5441.96	−	22432.1i	0.0284966	−	0.117465i
$438$	−552529.	−	434514.i	−2.88010	−	2.26493i
$439$	43695.1	+	75682.1i	0.226727	+	0.392703i	0.956836	−	0.290628i	$-0.0938641\pi$
$439$	43695.1	+	75682.1i	0.226727	+	0.392703i	−0.730109	+	0.683331i	$0.760531\pi$
$440$	−216056.	−	124740.i	−1.11599	−	0.644318i
$441$	−102415.	+	41000.8i	−0.526606	+	0.210821i
$442$	−30237.6	−	34896.0i	−0.154775	−	0.178620i
$443$	108505.	−	77266.3i	0.552896	−	0.393716i	−0.269183	−	0.963089i	$-0.586754\pi$
$443$	108505.	−	77266.3i	0.552896	−	0.393716i	0.822079	+	0.569374i	$0.192814\pi$
$444$	−140889.	+	20256.8i	−0.714679	+	0.102755i
$445$	109463.	+	49990.1i	0.552774	+	0.252443i
$446$	−285284.	+	69209.0i	−1.43419	+	0.347931i
$447$	−7675.52	−	26140.4i	−0.0384143	−	0.130827i
$448$	7705.67	+	39980.8i	0.0383932	+	0.199203i
$449$	163218.	−	155628.i	0.809611	−	0.771963i	−0.167232	−	0.985918i	$-0.553483\pi$
$449$	163218.	−	155628.i	0.809611	−	0.771963i	0.976844	+	0.213955i	$0.0686345\pi$
$450$	−595871.	+	1.15583e6i	−2.94257	+	5.70779i
$451$	162303.	−	227923.i	0.797948	−	1.12056i
$452$	20652.9	+	216287.i	0.101089	+	1.05865i
$453$	93214.1	−	483641.i	0.454240	−	2.35682i
$454$	152777.	+	237726.i	0.741220	+	1.15336i
$455$	−122697.	+	56033.6i	−0.592665	+	0.270661i
$456$	−46565.3	+	36619.4i	−0.223941	+	0.176109i
$457$	−1765.34	−	706.737i	−0.00845272	−	0.00338396i	0.367432	−	0.930050i	$-0.380237\pi$
$457$	−1765.34	−	706.737i	−0.00845272	−	0.00338396i	−0.375885	+	0.926666i	$0.622661\pi$
$458$	63224.0	+	182674.i	0.301406	+	0.870854i
$459$	−94822.6	+	99447.1i	−0.450077	+	0.472027i
$460$	45532.8	−	70850.4i	0.215183	−	0.334832i
$461$	30545.7	−	212450.i	0.143730	−	0.999666i	−0.782484	−	0.622670i	$-0.786048\pi$
$461$	30545.7	−	212450.i	0.143730	−	0.999666i	0.926215	−	0.376996i	$-0.123043\pi$
$462$	527468.	−	271929.i	2.47122	−	1.27400i
$463$	−182884.	−	63296.7i	−0.853126	−	0.295270i	−0.134712	−	0.990885i	$-0.543011\pi$
$463$	−182884.	−	63296.7i	−0.853126	−	0.295270i	−0.718415	+	0.695615i	$0.755132\pi$
$464$	−334168.	+	385650.i	−1.55213	+	1.79125i
$465$	34758.1	−	364003.i	0.160749	−	1.68344i
$466$	−95825.1	−	28136.8i	−0.441273	−	0.129569i
$467$	−9419.60	+	197742.i	−0.0431915	+	0.906702i	0.868465	+	0.495750i	$0.165107\pi$
$467$	−9419.60	+	197742.i	−0.0431915	+	0.906702i	−0.911657	+	0.410952i	$0.865196\pi$
$468$		−	109304.i		−	0.499051i
$469$	−182273.	+	19450.9i	−0.828662	+	0.0884288i
$470$	−748403.			−3.38797
$471$	487151.	+	23205.9i	2.19595	+	0.104606i
$472$	15527.5	−	52881.7i	0.0696974	−	0.237368i
$473$	−4713.68	−	450.102i	−0.0210687	−	0.00201182i
$474$	−76833.6	−	66576.7i	−0.341975	−	0.296323i
$475$	76200.1	−	220166.i	0.337729	−	0.975804i
$476$	−25715.2	−	49880.6i	−0.113495	−	0.220149i
$477$	45838.5	+	6590.58i	0.201462	+	0.0289659i
$478$	139545.	+	89679.8i	0.610741	+	0.392499i
$479$	−118263.	−	112763.i	−0.515438	−	0.491469i	0.387125	−	0.922027i	$-0.373468\pi$
$479$	−118263.	−	112763.i	−0.515438	−	0.491469i	−0.902563	+	0.430558i	$0.858317\pi$
$480$	−804795.	+	278542.i	−3.49304	+	1.20895i
$481$	22673.1	−	56634.7i	0.0979988	−	0.244789i
$482$	−112830.	−	143475.i	−0.485656	−	0.617562i
$483$	−42894.0	−	93924.7i	−0.183866	−	0.402611i
$484$	175199.	−	112593.i	0.747894	−	0.480642i
$485$	345779.	+	66643.5i	1.46999	+	0.283318i
$486$	136176.	−	13003.2i	0.576538	−	0.0550527i
$487$	20483.9	+	14586.5i	0.0863685	+	0.0615027i	0.622425	−	0.782679i	$-0.286147\pi$
$487$	20483.9	+	14586.5i	0.0863685	+	0.0615027i	−0.536057	+	0.844182i	$0.680087\pi$
$488$	58997.1	+	30415.1i	0.247737	+	0.127717i
$489$	−128813.	−	135095.i	−0.538693	−	0.564965i
$490$	178118.	−	34329.3i	0.741847	−	0.142979i
$491$	397133.	−	116609.i	1.64730	−	0.483691i	0.679137	−	0.734011i	$-0.262354\pi$
$491$	397133.	−	116609.i	1.64730	−	0.483691i	0.968163	+	0.250320i	$0.0805359\pi$
$492$	−57151.5	−	235582.i	−0.236101	−	0.973221i
$493$	88026.0	−	192750.i	0.362174	−	0.793050i
$494$	7010.40	+	48758.4i	0.0287269	+	0.199800i
$495$	776070.	+	1.08984e6i	3.16731	+	4.44786i
$496$	118666.	−	102824.i	0.482350	−	0.417959i
$497$	48035.0	+	119986.i	0.194467	+	0.485755i
$498$	−326821.	+	566071.i	−1.31781	+	2.28251i
$499$	−26536.1	+	15320.6i	−0.106570	+	0.0615283i	−0.552338	−	0.833620i	$-0.686264\pi$
$499$	−26536.1	+	15320.6i	−0.106570	+	0.0615283i	0.445768	+	0.895149i	$0.352931\pi$
$500$	329721.	−	419274.i	1.31888	−	1.67710i
$501$	−467961.	−	113526.i	−1.86438	−	0.452294i
$502$	7735.59	+	162390.i	0.0306963	+	0.644394i
$503$	−442663.	+	21086.6i	−1.74959	+	0.0833434i	−0.897764	−	0.440476i	$-0.854810\pi$
$503$	−442663.	+	21086.6i	−1.74959	+	0.0833434i	−0.851829	+	0.523819i	$0.824507\pi$
$504$	−40605.7	+	167379.i	−0.159855	+	0.658931i
$505$	124366.	+	97802.7i	0.487663	+	0.383502i
$506$	−79402.8	−	137530.i	−0.310123	−	0.537149i
$507$	−313835.	−	181193.i	−1.22092	−	0.704897i
$508$	−257416.	+	103054.i	−0.997489	+	0.399334i
$509$	−89877.6	−	103724.i	−0.346909	−	0.400354i	0.555302	−	0.831649i	$-0.312603\pi$
$509$	−89877.6	−	103724.i	−0.346909	−	0.400354i	−0.902211	+	0.431294i	$0.858057\pi$
$510$	398864.	−	284030.i	1.53350	−	1.09200i
$511$	362422.	−	52108.4i	1.38795	−	0.199557i
$512$	−204712.	−	93488.8i	−0.780914	−	0.356632i
$513$	142459.	−	34560.2i	0.541322	−	0.131323i
$514$	−43995.4	−	149835.i	−0.166526	−	0.567135i
$515$	18721.8	+	97138.0i	0.0705884	+	0.366247i
$516$	−2969.02	+	2830.95i	−0.0111510	+	0.0106324i
$517$	−257073.	+	498651.i	−0.961778	+	1.86559i
$518$	108182.	−	151920.i	0.403177	−	0.566183i
$519$	10715.0	+	112212.i	0.0397793	+	0.416588i
$520$	17531.5	−	90962.0i	0.0648354	−	0.336398i
$521$	−194573.	−	302762.i	−0.716817	−	1.11539i	−0.988237	−	0.152928i	$-0.951130\pi$
$521$	−194573.	−	302762.i	−0.716817	−	1.11539i	0.271421	−	0.962461i	$-0.412507\pi$
$522$	1.14774e6	−	524156.i	4.21214	−	1.92362i
$523$	−391520.	+	307895.i	−1.43136	+	1.12564i	−0.460035	+	0.887901i	$0.652163\pi$
$523$	−391520.	+	307895.i	−1.43136	+	1.12564i	−0.971330	+	0.237737i	$0.923594\pi$
$524$	−37743.2	−	15110.1i	−0.137460	−	0.0550307i
$525$	−340865.	−	984864.i	−1.23670	−	3.57320i
$526$	−95261.0	+	99906.8i	−0.344305	+	0.361097i
$527$	−35250.9	+	54851.5i	−0.126925	+	0.197500i
$528$	−125797.	+	874937.i	−0.451235	+	3.13841i
$529$	224173.	−	115569.i	0.801072	−	0.412981i
$530$	−71959.7	−	24905.5i	−0.256175	−	0.0886632i
$531$	−193556.	+	223376.i	−0.686464	+	0.792222i
$532$	−5690.95	+	59598.3i	−0.0201077	+	0.210577i
$533$	99688.1	+	29271.1i	0.350905	+	0.103035i
$534$	9353.98	−	196364.i	0.0328030	−	0.688620i
$535$			215623.i			0.753335i
$536$	61730.5	−	109718.i	0.214867	−	0.381898i
$537$	311147.			1.07899
$538$	494543.	+	23558.0i	1.70860	+	0.0813904i
$539$	38309.3	−	130469.i	0.131864	−	0.449088i
$540$	532433.	+	50841.2i	1.82590	+	0.174352i
$541$	319786.	+	277096.i	1.09261	+	0.946752i	0.998807	−	0.0488382i	$-0.0155519\pi$
$541$	319786.	+	277096.i	1.09261	+	0.946752i	0.0938039	+	0.995591i	$0.470097\pi$
$542$	−223997.	+	647198.i	−0.762508	+	2.20312i
$543$	−84117.6	−	163165.i	−0.285290	−	0.553386i
$544$	150313.	+	21611.7i	0.507923	+	0.0730283i
$545$	418389.	+	268882.i	1.40860	+	0.905251i
$546$	159477.	+	152061.i	0.534950	+	0.510074i
$547$	−188035.	+	65079.4i	−0.628439	+	0.217505i	−0.622678	−	0.782479i	$-0.713955\pi$
$547$	−188035.	+	65079.4i	−0.628439	+	0.217505i	−0.00576150	+	0.999983i	$0.501834\pi$
$548$	126300.	−	315482.i	0.420574	−	1.05054i
$549$	−220041.	−	279805.i	−0.730061	−	0.928347i
$550$	−665852.	−	1.45801e6i	−2.20116	−	4.81988i
$551$	−190174.	+	122217.i	−0.626394	+	0.402559i
$552$	69631.8	+	13420.4i	0.228523	+	0.0440442i
$553$	52717.7	−	5033.93i	0.172388	−	0.0164610i
$554$	194934.	+	138812.i	0.635137	+	0.452279i
$555$	575015.	+	296441.i	1.86678	+	0.962393i
$556$	164850.	+	172890.i	0.533260	+	0.559268i
$557$	−287648.	+	55439.6i	−0.927152	+	0.178694i	−0.630408	−	0.776264i	$-0.717113\pi$
$557$	−287648.	+	55439.6i	−0.927152	+	0.178694i	−0.296743	+	0.954957i	$0.595900\pi$
$558$	−372522.	+	109382.i	−1.19642	+	0.351301i
$559$	−414.518	−	1708.67i	−0.00132654	−	0.00546807i
$560$	255162.	−	558727.i	0.813655	−	1.78166i
$561$	−52237.7	−	363321.i	−0.165981	−	1.15442i
$562$	−302558.	−	424883.i	−0.957934	−	1.34523i
$563$	330442.	−	286329.i	1.04251	−	0.903336i	0.0470809	−	0.998891i	$-0.485008\pi$
$563$	330442.	−	286329.i	1.04251	−	0.903336i	0.995424	+	0.0955553i	$0.0304627\pi$
$564$	180645.	+	451230.i	0.567895	+	1.41853i
$565$	493753.	−	855205.i	1.54672	−	2.67900i
$566$	194746.	−	112437.i	0.607906	−	0.350975i
$567$	97845.2	−	124420.i	0.304350	−	0.387012i
$568$	−86259.2	−	20926.3i	−0.267368	−	0.0648627i
$569$	12287.5	+	257947.i	0.0379524	+	0.796720i	0.934970	+	0.354726i	$0.115426\pi$
$569$	12287.5	+	257947.i	0.0379524	+	0.796720i	−0.897018	+	0.441994i	$0.854271\pi$
$570$	−521791.	+	24856.0i	−1.60600	+	0.0765034i
$571$	13191.7	−	54376.8i	0.0404602	−	0.166779i	−0.947997	−	0.318279i	$-0.896895\pi$
$571$	13191.7	−	54376.8i	0.0404602	−	0.166779i	0.988457	+	0.151500i	$0.0484103\pi$
$572$	105904.	+	83283.8i	0.323683	+	0.254547i
$573$	−60152.3	−	104187.i	−0.183207	−	0.317325i
$574$	275077.	+	158816.i	0.834893	+	0.482026i
$575$	−258914.	+	103653.i	−0.783104	+	0.313508i
$576$	98203.8	+	113333.i	0.295994	+	0.341596i
$577$	−436687.	+	310963.i	−1.31165	+	0.934023i	−0.999870	−	0.0161312i	$-0.994865\pi$
$577$	−436687.	+	310963.i	−1.31165	+	0.934023i	−0.311781	+	0.950154i	$0.600926\pi$
$578$	339617.	−	48829.5i	1.01656	−	0.146159i
$579$	−704536.	−	321751.i	−2.10158	−	0.959760i
$580$	−801556.	+	194455.i	−2.38275	+	0.578048i
$581$	−95924.9	−	326690.i	−0.284171	−	0.967796i
$582$	−108871.	−	564874.i	−0.321414	−	1.66765i
$583$	−41312.0	+	39390.9i	−0.121546	+	0.115893i
$584$	−115226.	+	223508.i	−0.337852	+	0.655340i
$585$	−288168.	+	404675.i	−0.842041	+	1.18248i
$586$	8480.21	+	88808.8i	0.0246951	+	0.258619i
$587$	−66857.2	+	346888.i	−0.194031	+	1.00673i	0.746078	+	0.665858i	$0.231934\pi$
$587$	−66857.2	+	346888.i	−0.194031	+	1.00673i	−0.940110	+	0.340872i	$0.889278\pi$
$588$	−63691.0	−	99105.1i	−0.184214	−	0.286643i
$589$	63273.5	−	28896.0i	0.182386	−	0.0832929i
$590$	382027.	−	300429.i	1.09746	−	0.863054i
$591$	−230890.	−	92434.3i	−0.661043	−	0.264642i
$592$	90859.0	+	262520.i	0.259253	+	0.749064i
$593$	270832.	−	284041.i	0.770178	−	0.807740i	−0.215477	−	0.976509i	$-0.569131\pi$
$593$	270832.	−	284041.i	0.770178	−	0.807740i	0.985656	+	0.168769i	$0.0539792\pi$
$594$	545249.	−	848424.i	1.54533	−	2.40459i
$595$	−36299.3	+	252467.i	−0.102533	+	0.713133i
$596$	16807.4	−	8664.81i	0.0473159	−	0.0243931i
$597$	219265.	+	75888.3i	0.615205	+	0.212925i
$598$	38615.3	−	44564.4i	0.107983	−	0.124619i
$599$	37129.7	−	388840.i	0.103483	−	1.08372i	−0.783335	−	0.621600i	$-0.786483\pi$
$599$	37129.7	−	388840.i	0.103483	−	1.08372i	0.886817	−	0.462120i	$-0.152911\pi$
$600$	686752.	+	201649.i	1.90764	+	0.560135i
$601$	240.165	−	5041.69i	0.000664908	−	0.0139581i	−0.998511	−	0.0545598i	$-0.982624\pi$
$601$	240.165	−	5041.69i	0.000664908	−	0.0139581i	0.999175	+	0.0406017i	$0.0129275\pi$
$602$		−	5375.24i		−	0.0148322i
$603$	−545563.	+	397702.i	−1.50041	+	1.09376i
$604$	341862.			0.937081
$605$	−945474.	−	45038.5i	−2.58309	−	0.123048i
$606$	72818.3	−	247996.i	0.198287	−	0.675305i
$607$	−406154.	−	38783.0i	−1.10233	−	0.105260i	−0.472011	−	0.881593i	$-0.656472\pi$
$607$	−406154.	−	38783.0i	−1.10233	−	0.105260i	−0.630323	+	0.776333i	$0.717078\pi$
$608$	−122437.	−	106092.i	−0.331211	−	0.286996i
$609$	−330741.	+	955614.i	−0.891772	+	2.57661i
$610$	268205.	+	520245.i	0.720788	+	1.39813i
$611$	−206194.	−	29646.3i	−0.552325	−	0.0794123i
$612$	−173878.	−	111745.i	−0.464240	−	0.298349i
$613$	259027.	+	246981.i	0.689324	+	0.657269i	0.951464	−	0.307761i	$-0.0995796\pi$
$613$	259027.	+	246981.i	0.689324	+	0.657269i	−0.262140	+	0.965030i	$0.584428\pi$
$614$	332535.	−	115092.i	0.882065	−	0.305286i
$615$	−409493.	+	1.02286e6i	−1.08267	+	2.70438i
$616$	−131233.	−	166876.i	−0.345845	−	0.439778i
$617$	156782.	+	343305.i	0.411837	+	0.901798i	0.995932	+	0.0901122i	$0.0287226\pi$
$617$	156782.	+	343305.i	0.411837	+	0.901798i	−0.584094	+	0.811686i	$0.698550\pi$
$618$	135953.	−	87371.7i	0.355969	−	0.228767i
$619$	−252469.	−	48659.5i	−0.658912	−	0.126995i	−0.151175	−	0.988507i	$-0.548306\pi$
$619$	−252469.	−	48659.5i	−0.658912	−	0.126995i	−0.507737	+	0.861512i	$0.669518\pi$
$620$	252646.	−	24124.8i	0.657248	−	0.0627596i
$621$	−142941.	−	101788.i	−0.370658	−	0.263945i
$622$	150077.	+	77370.1i	0.387912	+	0.199983i
$623$	70665.5	+	74111.8i	0.182067	+	0.190946i
$624$	−322288.	+	62116.0i	−0.827704	+	0.159527i
$625$	−1.31996e6	+	387574.i	−3.37909	+	0.992191i
$626$	−124328.	−	512485.i	−0.317262	−	1.30777i
$627$	−162671.	+	356200.i	−0.413786	+	0.906065i
$628$	48174.2	+	335059.i	0.122150	+	0.849575i
$629$	−66913.6	−	93966.9i	−0.169127	−	0.237506i
$630$	−1.14782e6	+	994594.i	−2.89197	+	2.50591i
$631$	16379.3	+	40913.5i	0.0411374	+	0.102756i	0.947514	−	0.319715i	$-0.103587\pi$
$631$	16379.3	+	40913.5i	0.0411374	+	0.102756i	−0.906376	+	0.422471i	$0.861163\pi$
$632$	−18184.9	+	31497.2i	−0.0455279	+	0.0788566i
$633$	300194.	−	173317.i	0.749195	−	0.432548i
$634$	173802.	−	221008.i	0.432392	−	0.549831i
$635$	1.22472e6	+	297113.i	3.03730	+	0.736841i
$636$	2353.11	+	49397.8i	0.00581738	+	0.122122i
$637$	50433.5	−	2402.44i	0.124291	−	0.00592072i
$638$	−366666.	+	1.51142e6i	−0.900801	+	3.71315i
$639$	374171.	+	294251.i	0.916364	+	0.720636i
$640$	324591.	+	562208.i	0.792458	+	1.37258i
$641$	595074.	+	343566.i	1.44829	+	0.836169i	0.998380	−	0.0569052i	$-0.0181233\pi$
$641$	595074.	+	343566.i	1.44829	+	0.836169i	0.449908	+	0.893075i	$0.351457\pi$
$642$	327016.	−	130917.i	0.793412	−	0.317634i
$643$	−133426.	−	153982.i	−0.322715	−	0.372433i	0.571091	−	0.820887i	$-0.306520\pi$
$643$	−133426.	−	153982.i	−0.322715	−	0.372433i	−0.893806	+	0.448454i	$0.851975\pi$
$644$	58378.6	−	41571.2i	0.140761	−	0.100235i
$645$	18455.6	−	2653.52i	0.0443618	−	0.00637826i
$646$	84730.5	+	38695.1i	0.203037	+	0.0927238i
$647$	782904.	−	189931.i	1.87025	−	0.453718i	0.870961	−	0.491353i	$-0.163497\pi$
$647$	782904.	−	189931.i	1.87025	−	0.453718i	0.999292	+	0.0376344i	$0.0119822\pi$
$648$	30626.0	+	104303.i	0.0729357	+	0.248396i
$649$	−68947.8	−	357735.i	−0.163693	−	0.849322i
$650$	430744.	−	410713.i	1.01951	−	0.972103i
$651$	142581.	−	276569.i	0.336435	−	0.652593i
$652$	75151.7	−	105536.i	0.176784	−	0.248259i
$653$	44072.8	+	461552.i	0.103358	+	1.08242i	0.887178	+	0.461427i	$0.152662\pi$
$653$	44072.8	+	461552.i	0.103358	+	1.08242i	−0.783820	+	0.620988i	$0.786731\pi$
$654$	153760.	−	797785.i	0.359492	−	1.86522i
$655$	99900.1	+	155448.i	0.232854	+	0.362327i
$656$	−430363.	+	196540.i	−1.00006	+	0.456714i
$657$	1.06003e6	−	833616.i	2.45577	−	1.93124i
$658$	−591238.	−	236696.i	−1.36556	−	0.546688i
$659$	−59567.4	−	172109.i	−0.137163	−	0.396307i	0.855411	−	0.517950i	$-0.173305\pi$
$659$	−59567.4	−	172109.i	−0.137163	−	0.396307i	−0.992574	+	0.121643i	$0.961184\pi$
$660$	−985951.	+	1.03404e6i	−2.26343	+	2.37382i
$661$	−35677.9	+	55515.8i	−0.0816575	+	0.127062i	−0.879680	−	0.475566i	$-0.842243\pi$
$661$	−35677.9	+	55515.8i	−0.0816575	+	0.127062i	0.798022	+	0.602628i	$0.205880\pi$
$662$	−120745.	+	839797.i	−0.275519	+	1.91628i
$663$	121143.	−	62453.7i	0.275596	−	0.142079i
$664$	220974.	+	76479.7i	0.501192	+	0.173464i
$665$	178193.	−	205646.i	0.402947	−	0.465026i
$666$	65293.9	−	683789.i	0.147206	−	1.54161i
$667$	259647.	+	76239.2i	0.583622	+	0.171367i
$668$	15903.0	−	333844.i	0.0356390	−	0.748154i
$669$		−	866513.i		−	1.93608i
$670$	1.00462e6	−	472355.i	2.23797	−	1.05225i
$671$	438760.			0.974501
$672$	−723883.	−	34482.8i	−1.60299	−	0.0763596i
$673$	27878.1	−	94944.0i	0.0615506	−	0.209622i	−0.922976	−	0.384858i	$-0.874251\pi$
$673$	27878.1	−	94944.0i	0.0615506	−	0.209622i	0.984527	+	0.175236i	$0.0560687\pi$
$674$	−835278.	−	79759.4i	−1.83870	−	0.175575i
$675$	−1.33855e6	−	1.15986e6i	−2.93782	−	2.54564i
$676$	82265.4	−	237690.i	0.180021	−	0.520138i
$677$	57105.0	+	110768.i	0.124594	+	0.241678i	0.942880	−	0.333133i	$-0.108106\pi$
$677$	57105.0	+	110768.i	0.124594	+	0.241678i	−0.818286	+	0.574811i	$0.805075\pi$
$678$	−1.59680e6	−	229584.i	−3.47368	−	0.499440i
$679$	252088.	+	162007.i	0.546781	+	0.351395i
$680$	−126777.	−	120882.i	−0.274172	−	0.261422i
$681$	−788248.	+	272815.i	−1.69969	+	0.588267i
$682$	177862.	−	444278.i	0.382397	−	0.955181i
$683$	415066.	+	527800.i	0.889766	+	1.13143i	0.990636	+	0.136530i	$0.0435950\pi$
$683$	415066.	+	527800.i	0.889766	+	1.13143i	−0.100870	+	0.994900i	$0.532163\pi$
$684$	91600.0	+	200576.i	0.195787	+	0.428713i
$685$	−1.29933e6	+	835029.i	−2.76910	+	1.77959i
$686$	647709.	+	124836.i	1.37636	+	0.265271i
$687$	−568007.	+	54238.1i	−1.20348	+	0.114919i
$688$	6521.91	+	4644.23i	0.0137784	+	0.00981154i
$689$	−18839.2	−	9712.30i	−0.0396848	−	0.0204590i
$690$	431524.	+	452569.i	0.906372	+	0.950576i
$691$	290712.	−	56030.2i	0.608845	−	0.117345i	0.124496	−	0.992220i	$-0.460269\pi$
$691$	290712.	−	56030.2i	0.608845	−	0.117345i	0.484349	+	0.874875i	$0.339056\pi$
$692$	−75069.3	+	22042.3i	−0.156765	+	0.0460304i
$693$	268414.	+	1.10642e6i	0.558906	+	2.30384i
$694$	−43413.2	+	95061.7i	−0.0901370	+	0.197372i
$695$	−154518.	−	1.07469e6i	−0.319896	−	2.22492i
$696$	−402842.	−	565713.i	−0.831604	−	1.16782i
$697$	148478.	−	128657.i	0.305630	−	0.264830i
$698$	86812.7	+	216848.i	0.178185	+	0.445086i
$699$	147397.	−	255299.i	0.301671	−	0.522509i
$700$	626445.	−	361678.i	1.27846	−	0.738119i
$701$	−254802.	+	324007.i	−0.518521	+	0.659353i	−0.972838	−	0.231487i	$-0.925641\pi$
$701$	−254802.	+	324007.i	−0.518521	+	0.659353i	0.454317	+	0.890840i	$0.349883\pi$
$702$	363926.	+	88287.4i	0.738479	+	0.179153i
$703$	5855.72	+	122927.i	0.0118487	+	0.248734i
$704$	−184634.	+	8795.19i	−0.372534	+	0.0177460i
$705$	520816.	−	2.14683e6i	1.04787	−	4.31936i
$706$	152797.	+	120161.i	0.306553	+	0.241076i
$707$	67317.5	+	116597.i	0.134676	+	0.233265i
$708$	−273347.	−	157817.i	−0.545316	−	0.314838i
$709$	430345.	−	172284.i	0.856099	−	0.342730i	0.0982510	−	0.995162i	$-0.468675\pi$
$709$	430345.	−	172284.i	0.856099	−	0.342730i	0.757848	+	0.652431i	$0.226251\pi$
$710$	−512567.	−	591533.i	−1.01680	−	1.17344i
$711$	158879.	−	113137.i	0.314288	−	0.223804i
$712$	−69611.2	+	10008.6i	−0.137315	+	0.0197430i
$713$	−75742.4	−	34590.4i	−0.148991	−	0.0680419i
$714$	404933.	−	98235.6i	0.794303	−	0.192696i
$715$	−172518.	−	587544.i	−0.337461	−	1.14929i
$716$	40870.8	+	212058.i	0.0797236	+	0.413645i
$717$	−354361.	+	337882.i	−0.689298	+	0.657244i
$718$	174275.	−	338047.i	0.338055	−	0.655734i
$719$	17934.4	−	25185.4i	0.0346920	−	0.0487182i	−0.796866	−	0.604157i	$-0.793510\pi$
$719$	17934.4	−	25185.4i	0.0346920	−	0.0487182i	0.831558	+	0.555438i	$0.187450\pi$
$720$	−215041.	−	2.25202e6i	−0.414818	−	4.34417i
$721$	−15931.4	+	82660.1i	−0.0306467	+	0.159010i
$722$	309371.	+	481391.i	0.593479	+	0.923472i
$723$	490082.	−	223813.i	0.937546	−	0.428163i
$724$	100154.	−	78761.7i	0.191069	−	0.150258i
$725$	2.53566e6	+	1.01513e6i	4.82409	+	1.93127i
$726$	505746.	+	1.46126e6i	0.959532	+	2.77239i
$727$	−320147.	+	335760.i	−0.605732	+	0.635273i	−0.953172	−	0.302429i	$-0.902202\pi$
$727$	−320147.	+	335760.i	−0.605732	+	0.635273i	0.347440	+	0.937702i	$0.387051\pi$
$728$	42618.3	−	66315.4i	0.0804143	−	0.125127i
$729$	−102148.	+	710453.i	−0.192209	+	1.33684i
$730$	−1.97093e6	+	1.01608e6i	−3.69849	+	1.90671i
$731$	−3141.88	−	1087.41i	−0.00587969	−	0.00203498i
$732$	248931.	−	287281.i	0.464576	−	0.536149i
$733$	−31345.0	+	328260.i	−0.0583392	+	0.610956i	0.918273	+	0.395948i	$0.129584\pi$
$733$	−31345.0	+	328260.i	−0.0583392	+	0.610956i	−0.976612	+	0.215008i	$0.931022\pi$
$734$	46780.9	+	13736.1i	0.0868312	+	0.0254960i
$735$	−25477.0	+	534829.i	−0.0471601	+	0.990012i
$736$			193933.i			0.358010i
$737$	30358.7	−	831620.i	0.0558918	−	1.53105i
$738$	1.16986e6			2.14793
$739$	121706.	+	5797.57i	0.222856	+	0.0106159i	0.158713	−	0.987325i	$-0.449266\pi$
$739$	121706.	+	5797.57i	0.222856	+	0.0106159i	0.0641428	+	0.997941i	$0.479569\pi$
$740$	−126504.	+	430832.i	−0.231015	+	0.786764i
$741$	−144745.	−	13821.4i	−0.263612	−	0.0251719i
$742$	−48971.4	−	42433.9i	−0.0889476	−	0.0770735i
$743$	109688.	−	316922.i	0.198692	−	0.574084i	−0.801006	−	0.598657i	$-0.795701\pi$
$743$	109688.	−	316922.i	0.198692	−	0.574084i	0.999698	+	0.0245729i	$0.00782260\pi$
$744$	97921.2	+	189941.i	0.176901	+	0.343141i
$745$	−85069.4	−	12231.1i	−0.153271	−	0.0220371i
$746$	−921460.	−	592187.i	−1.65577	−	1.06410i
$747$	−907573.	−	865369.i	−1.62645	−	1.55082i
$748$	240754.	−	83325.9i	0.430300	−	0.148928i
$749$	−68194.8	+	170342.i	−0.121559	+	0.303640i
$750$	2.44815e6	+	3.11307e6i	4.35226	+	5.53435i
$751$	246632.	+	540048.i	0.437289	+	0.957530i	0.992088	+	0.125545i	$0.0400681\pi$
$751$	246632.	+	540048.i	0.437289	+	0.957530i	−0.554799	+	0.831985i	$0.687205\pi$
$752$	798021.	−	512857.i	1.41117	−	0.906903i
$753$	−471207.	−	90817.7i	−0.831040	−	0.160170i
$754$	−574878.	+	54894.2i	−1.01119	+	0.0965569i
$755$	−1.26567e6	−	901279.i	−2.22038	−	1.58112i
$756$	404543.	+	208556.i	0.707816	+	0.364905i
$757$	228727.	+	239882.i	0.399140	+	0.418606i	0.892378	−	0.451288i	$-0.149035\pi$
$757$	228727.	+	239882.i	0.399140	+	0.418606i	−0.493238	+	0.869894i	$0.664187\pi$
$758$	−514462.	+	99154.4i	−0.895395	+	0.172573i
$759$	449767.	−	132064.i	0.780736	−	0.229245i
$760$	44058.0	+	181610.i	0.0762777	+	0.314421i
$761$	379089.	−	830089.i	0.654594	−	1.43336i	−0.232881	−	0.972505i	$-0.574815\pi$
$761$	379089.	−	830089.i	0.654594	−	1.43336i	0.887475	−	0.460856i	$-0.152457\pi$
$762$	−292992.	−	2.03781e6i	−0.504599	−	3.50956i
$763$	245488.	+	344740.i	0.421679	+	0.592165i
$764$	63105.7	−	54681.4i	0.108114	−	0.0936812i
$765$	349144.	+	872120.i	0.596598	+	1.49023i
$766$	−285121.	+	493844.i	−0.485928	+	0.841651i
$767$	117154.	−	67638.9i	0.199144	−	0.114976i
$768$	805587.	−	1.02439e6i	1.36581	−	1.73677i
$769$	−691939.	−	167863.i	−1.17008	−	0.283858i	−0.396788	−	0.917910i	$-0.629875\pi$
$769$	−691939.	−	167863.i	−1.17008	−	0.283858i	−0.773290	+	0.634052i	$0.781390\pi$
$770$	−89076.4	−	1.86994e6i	−0.150239	−	3.15390i
$771$	460425.	−	21932.7i	0.774551	−	0.0368964i
$772$	126740.	−	522429.i	0.212657	−	0.876583i
$773$	516749.	+	406376.i	0.864809	+	0.680093i	0.948630	−	0.316387i	$-0.102470\pi$
$773$	516749.	+	406376.i	0.864809	+	0.680093i	−0.0838209	+	0.996481i	$0.526712\pi$
$774$	−9898.66	−	17145.0i	−0.0165232	−	0.0286190i
$775$	−727837.	−	420217.i	−1.21180	−	0.699633i
$776$	−191056.	+	76487.1i	−0.317275	+	0.127018i
$777$	360507.	+	416048.i	0.597134	+	0.689130i
$778$	−528582.	+	376402.i	−0.873280	+	0.621860i
$779$	−207460.	+	29828.3i	−0.341869	+	0.0491534i
$780$	−482577.	−	220385.i	−0.793190	−	0.362238i
$781$	−570195.	+	138328.i	−0.934806	+	0.226781i
$782$	−31414.4	−	106988.i	−0.0513706	−	0.174952i
$783$	325237.	+	1.68749e6i	0.530490	+	2.75244i
$784$	−166402.	+	158664.i	−0.270723	+	0.258134i
$785$	704989.	−	1.36749e6i	1.14404	−	2.21914i
$786$	175098.	−	245890.i	0.283423	−	0.398012i
$787$	−9149.00	−	95812.7i	−0.0147715	−	0.154694i	0.985077	−	0.172116i	$-0.0550603\pi$
$787$	−9149.00	−	95812.7i	−0.0147715	−	0.154694i	−0.999848	+	0.0174216i	$0.994454\pi$
$788$	32668.6	−	169501.i	0.0526113	−	0.272973i
$789$	−220295.	−	342786.i	−0.353876	−	0.550642i
$790$	−291733.	+	133230.i	−0.467445	+	0.213475i
$791$	660539.	−	519454.i	1.05571	−	0.830221i
$792$	−725891.	−	290603.i	−1.15723	−	0.463286i
$793$	53285.6	+	153959.i	0.0847351	+	0.244826i
$794$	694532.	−	728404.i	1.10167	−	1.15540i
$795$	121520.	−	189088.i	0.192270	−	0.299178i
$796$	−22919.0	+	159405.i	−0.0361717	+	0.251580i
$797$	−673558.	+	347243.i	−1.06037	+	0.546660i	−0.897966	−	0.440064i	$-0.854956\pi$
$797$	−673558.	+	347243.i	−1.06037	+	0.546660i	−0.162406	+	0.986724i	$0.551925\pi$
$798$	−420076.	−	145390.i	−0.659663	−	0.228312i
$799$	−257959.	+	297700.i	−0.404070	+	0.466322i
$800$	−186063.	+	1.94854e6i	−0.290724	+	3.04460i
$801$	361875.	+	106256.i	0.564019	+	0.165611i
$802$	−2598.16	+	54542.1i	−0.00403940	+	0.0847975i
$803$			1.66222e6i			2.57785i
$804$	−527285.	−	491697.i	−0.815705	−	0.760651i
$805$	−325732.			−0.502653
$806$	177495.	+	8455.14i	0.273223	+	0.0130152i
$807$	−411731.	+	1.40223e6i	−0.632217	+	2.15313i
$808$	−92045.1	−	8789.24i	−0.140987	−	0.0134626i
$809$	−26512.5	−	22973.2i	−0.0405092	−	0.0351014i	0.634371	−	0.773029i	$-0.281259\pi$
$809$	−26512.5	−	22973.2i	−0.0405092	−	0.0351014i	−0.674880	+	0.737927i	$0.735805\pi$
$810$	−313523.	+	905864.i	−0.477858	+	1.38068i
$811$	−460409.	−	893069.i	−0.700006	−	1.35782i	−0.923682	−	0.383159i	$-0.874836\pi$
$811$	−460409.	−	893069.i	−0.700006	−	1.35782i	0.223676	−	0.974664i	$-0.428194\pi$
$812$	−694729.	−	99887.0i	−1.05367	−	0.151494i
$813$	−1.70064e6	−	1.09293e6i	−2.57295	−	1.65353i
$814$	612767.	+	584272.i	0.924798	+	0.881793i
$815$	−556466.	+	192595.i	−0.837767	+	0.289954i
$816$	−230672.	+	576190.i	−0.346429	+	0.865338i
$817$	2192.56	+	2788.07i	0.00328479	+	0.00417695i
$818$	−517866.	−	1.13397e6i	−0.773946	−	1.69471i
$819$	−355638.	+	228555.i	−0.530201	+	0.340740i
$820$	−750906.	−	144725.i	−1.11675	−	0.215237i
$821$	−627801.	+	59947.7i	−0.931399	+	0.0889378i	−0.549712	−	0.835354i	$-0.685263\pi$
$821$	−627801.	+	59947.7i	−0.931399	+	0.0889378i	−0.381687	+	0.924292i	$0.624657\pi$
$822$	2.05531e6	+	1.46358e6i	3.04182	+	2.16607i
$823$	981498.	+	505997.i	1.44907	+	0.747048i	0.989962	−	0.141332i	$-0.0451385\pi$
$823$	981498.	+	505997.i	1.44907	+	0.747048i	0.459109	+	0.888380i	$0.348169\pi$
$824$	−39896.0	−	41841.7i	−0.0587590	−	0.0616247i
$825$	4.64575e6	−	895396.i	6.82572	−	1.31555i
$826$	396817.	−	116516.i	0.581608	−	0.170776i
$827$	−113849.	−	469292.i	−0.166463	−	0.686171i	−0.992468	−	0.122507i	$-0.960907\pi$
$827$	−113849.	−	469292.i	−0.166463	−	0.686171i	0.826004	−	0.563664i	$-0.190609\pi$
$828$	109651.	−	240102.i	0.159938	−	0.350216i
$829$	−77296.9	−	537611.i	−0.112474	−	0.782275i	−0.965499	−	0.260405i	$-0.916144\pi$
$829$	−77296.9	−	537611.i	−0.112474	−	0.782275i	0.853025	−	0.521870i	$-0.174765\pi$
$830$	1.19607e6	+	1.67965e6i	1.73620	+	2.43816i
$831$	−533844.	+	462578.i	−0.773058	+	0.669858i
$832$	−25509.2	−	63718.8i	−0.0368510	−	0.0920495i
$833$	47737.8	−	82684.3i	0.0687975	−	0.119161i
$834$	−1.53607e6	+	886851.i	−2.20841	+	1.27503i
$835$	−939019.	+	1.19406e6i	−1.34679	+	1.71259i
$836$	−264131.	−	64077.4i	−0.377926	−	0.0916838i
$837$	−25161.5	−	528204.i	−0.0359158	−	0.753965i
$838$	295315.	−	14067.6i	0.420531	−	0.0200324i
$839$	83272.8	−	343255.i	0.118299	−	0.487633i	−0.881580	−	0.472035i	$-0.843520\pi$
$839$	83272.8	−	343255.i	0.118299	−	0.487633i	0.999878	−	0.0155983i	$-0.00496529\pi$
$840$	657105.	+	516753.i	0.931272	+	0.732360i
$841$	−971456.	−	1.68261e6i	−1.37351	−	2.37899i
$842$	742108.	+	428456.i	1.04675	+	0.604341i
$843$	1.42935e6	−	572225.i	2.01133	−	0.805214i
$844$	157554.	+	181827.i	0.221179	+	0.255254i
$845$	−931213.	+	663114.i	−1.30417	+	0.928698i
$846$	−2.32171e6	+	333811.i	−3.24389	+	0.466402i
$847$	−732680.	−	334604.i	−1.02129	−	0.466406i
$848$	93797.6	−	22755.0i	0.130437	−	0.0316436i
$849$	187006.	+	636885.i	0.259442	+	0.883579i
$850$	−212990.	−	1.10510e6i	−0.294797	−	1.52955i
$851$	106619.	−	101661.i	0.147223	−	0.140377i
$852$	−232929.	+	451820.i	−0.320882	+	0.622424i
$853$	308964.	−	433879.i	0.424629	−	0.596308i	−0.545734	−	0.837958i	$-0.683749\pi$
$853$	308964.	−	433879.i	0.424629	−	0.596308i	0.970363	+	0.241650i	$0.0776886\pi$
$854$	47345.0	+	495819.i	0.0649169	+	0.679841i
$855$	189666.	−	984081.i	0.259452	−	1.34617i
$856$	−68128.0	−	106009.i	−0.0929775	−	0.144676i
$857$	−617085.	+	281813.i	−0.840202	+	0.383707i	−0.788559	−	0.614958i	$-0.789173\pi$
$857$	−617085.	+	281813.i	−0.840202	+	0.383707i	−0.0516420	+	0.998666i	$0.516445\pi$
$858$	−786327.	+	618374.i	−1.06814	+	0.839995i
$859$	−531389.	−	212736.i	−0.720155	−	0.288307i	−0.0175094	−	0.999847i	$-0.505574\pi$
$859$	−531389.	−	212736.i	−0.720155	−	0.288307i	−0.702645	+	0.711540i	$0.747998\pi$
$860$	4232.70	+	12229.6i	0.00572296	+	0.0165354i
$861$	−646999.	+	678553.i	−0.872765	+	0.915329i
$862$	38040.7	−	59192.6i	0.0511958	−	0.0796622i
$863$	108078.	−	751700.i	0.145116	−	1.00931i	−0.778953	−	0.627082i	$-0.784249\pi$
$863$	108078.	−	751700.i	0.145116	−	1.00931i	0.924070	−	0.382224i	$-0.124842\pi$
$864$	−1.09469e6	+	564354.i	−1.46644	+	0.756005i
$865$	336040.	+	116304.i	0.449116	+	0.155440i
$866$	504675.	−	582426.i	0.672939	−	0.776613i
$867$	−96270.3	+	1.00819e6i	−0.128072	+	1.34123i
$868$	207221.	+	60845.4i	0.275038	+	0.0807586i
$869$	−11439.4	+	240142.i	−0.0151482	+	0.318000i
$870$		−	6.12410e6i		−	8.09103i
$871$	295498.	−	90344.0i	0.389509	−	0.119087i
$872$	−290652.			−0.382244
$873$	1.10241e6	+	52514.1i	1.44648	+	0.0689045i
$874$	−33513.8	+	114137.i	−0.0438733	+	0.149419i
$875$	−2.05362e6	−	196097.i	−2.68228	−	0.256127i
$876$	1.08835e6	+	943063.i	1.41828	+	1.22895i
$877$	−3178.78	+	9184.49i	−0.00413296	+	0.0119414i	−0.947048	−	0.321091i	$-0.895951\pi$
$877$	−3178.78	+	9184.49i	−0.00413296	+	0.0119414i	0.942915	+	0.333032i	$0.108072\pi$
$878$	−206368.	−	400297.i	−0.267703	−	0.519271i
$879$	−260654.	−	37476.4i	−0.337354	−	0.0485043i
$880$	2.34581e6	+	1.50756e6i	3.02920	+	1.94675i
$881$	−698654.	−	666166.i	−0.900141	−	0.858283i	0.0903429	−	0.995911i	$-0.471204\pi$
$881$	−698654.	−	666166.i	−0.900141	−	0.858283i	−0.990484	+	0.137628i	$0.956052\pi$
$882$	537247.	−	185943.i	0.690617	−	0.239025i
$883$	547451.	−	1.36747e6i	0.702140	−	1.75386i	0.0463394	−	0.998926i	$-0.485244\pi$
$883$	547451.	−	1.36747e6i	0.702140	−	1.75386i	0.655800	−	0.754934i	$-0.272331\pi$
$884$	58477.2	+	74359.8i	0.0748311	+	0.0951554i
$885$	595942.	+	1.30493e6i	0.760883	+	1.66610i
$886$	−577491.	+	371131.i	−0.735661	+	0.472781i
$887$	−371377.	−	71577.0i	−0.472028	−	0.0909759i	−0.0523107	−	0.998631i	$-0.516659\pi$
$887$	−371377.	−	71577.0i	−0.472028	−	0.0909759i	−0.419717	+	0.907655i	$0.637871\pi$
$888$	−376364.	+	35938.4i	−0.477290	+	0.0455756i
$889$	873558.	+	622058.i	1.10532	+	0.787095i
$890$	−551216.	−	284172.i	−0.695892	−	0.358757i
$891$	495872.	+	520056.i	0.624618	+	0.655081i
$892$	590559.	−	113821.i	0.742221	−	0.143051i
$893$	403216.	−	118395.i	0.505633	−	0.148467i
$894$	33100.7	+	136443.i	0.0414155	+	0.170717i
$895$	407750.	−	892849.i	0.509036	−	1.11463i
$896$	78618.3	+	546802.i	0.0979282	+	0.681105i
$897$	100963.	+	141782.i	0.125480	+	0.176213i
$898$	−878349.	+	761094.i	−1.08922	+	0.943812i
$899$	303081.	+	757060.i	0.375007	+	0.936722i
$900$	1.33208e6	−	2.30723e6i	1.64454	−	2.84843i
$901$	−34709.9	+	20039.8i	−0.0427567	+	0.0246856i
$902$	−891366.	+	1.13346e6i	−1.09558	+	1.39314i
$903$	15419.2	+	3740.65i	0.0189097	+	0.00458745i
$904$	27460.1	+	576459.i	0.0336020	+	0.705393i
$905$	−578443.	+	27554.6i	−0.706258	+	0.0336432i
$906$	−598425.	+	2.46674e6i	−0.729043	+	3.00516i
$907$	−1.11532e6	−	877097.i	−1.35577	−	1.06619i	−0.990824	−	0.135155i	$-0.956847\pi$
$907$	−1.11532e6	−	877097.i	−1.35577	−	1.06619i	−0.364941	−	0.931031i	$-0.618911\pi$
$908$	−289473.	−	501383.i	−0.351105	−	0.608132i
$909$	429434.	+	247934.i	0.519719	+	0.300060i
$910$	645335.	−	258353.i	0.779296	−	0.311983i
$911$	896196.	+	1.03426e6i	1.07986	+	1.24622i	0.967586	+	0.252543i	$0.0812670\pi$
$911$	896196.	+	1.03426e6i	1.07986	+	1.24622i	0.112271	+	0.993678i	$0.464188\pi$
$912$	539352.	−	384071.i	0.648459	−	0.461766i
$913$	1.52997e6	−	219977.i	1.83545	−	0.263897i
$914$	8914.02	+	4070.89i	0.0106704	+	0.00487301i
$915$	−1.67900e6	+	407320.i	−2.00543	+	0.486512i
$916$	−111576.	−	379992.i	−0.132978	−	0.452881i
$917$	29757.9	+	154399.i	0.0353887	+	0.183614i
$918$	512497.	−	488664.i	0.608143	−	0.579863i
$919$	488650.	−	947849.i	0.578585	−	1.12230i	−0.400012	−	0.916510i	$-0.630994\pi$
$919$	488650.	−	947849.i	0.578585	−	1.12230i	0.978597	−	0.205788i	$-0.0659758\pi$
$920$	129761.	−	182224.i	0.153309	−	0.215293i
$921$	98733.7	+	1.03399e6i	0.116398	+	1.21898i
$922$	−209333.	+	1.08612e6i	−0.246250	+	1.27767i
$923$	−117786.	−	183279.i	−0.138258	−	0.215134i
$924$	−1.10593e6	+	505063.i	−1.29534	+	0.591564i
$925$	1.16879e6	−	919150.i	1.36601	−	1.07424i
$926$	925896.	+	370673.i	1.07979	+	0.432284i
$927$	101406.	+	292993.i	0.118006	+	0.340955i
$928$	1.31065e6	−	1.37457e6i	1.52191	−	1.59614i
$929$	338716.	−	527052.i	0.392468	−	0.610691i	−0.587649	−	0.809116i	$-0.699946\pi$
$929$	338716.	−	527052.i	0.392468	−	0.610691i	0.980116	+	0.198425i	$0.0635826\pi$
$930$	−268179.	+	1.86523e6i	−0.310069	+	2.15658i
$931$	−90533.4	+	46673.2i	−0.104450	+	0.0538479i
$932$	193356.	+	66921.2i	0.222601	+	0.0770428i
$933$	−326379.	+	376662.i	−0.374938	+	0.432701i
$934$	96977.1	−	1.01559e6i	0.111167	−	1.16419i
$935$	−1.11102e6	−	326225.i	−1.27086	−	0.373159i
$936$	13814.6	−	290004.i	0.0157683	−	0.331018i
$937$			1.17169e6i			1.33454i	0.744814	+	0.667272i	$0.232538\pi$
$937$			1.17169e6i			1.33454i	−0.744814	+	0.667272i	$0.767462\pi$
$938$	943044.	−	55430.3i	1.07183	−	0.0630001i
$939$	1.55661e6			1.76542
$940$	1.53155e6	+	72956.8i	1.73331	+	0.0825677i
$941$	−133356.	+	454167.i	−0.150602	+	0.512905i	−0.999887	−	0.0150305i	$-0.995215\pi$
$941$	−133356.	+	454167.i	−0.150602	+	0.512905i	0.849285	+	0.527935i	$0.177034\pi$
$942$	−2.50198e6	−	238910.i	−2.81956	−	0.269236i
$943$	189615.	+	164303.i	0.213231	+	0.184765i
$944$	−201480.	+	582138.i	−0.226093	+	0.653254i
$945$	−947896.	−	1.83866e6i	−1.06144	−	2.05892i
$946$	24153.9	+	3472.80i	0.0269901	+	0.00388059i
$947$	189098.	+	121526.i	0.210857	+	0.135510i	0.641807	−	0.766866i	$-0.278185\pi$
$947$	189098.	+	121526.i	0.210857	+	0.135510i	−0.430950	+	0.902376i	$0.641821\pi$
$948$	150744.	+	143734.i	0.167735	+	0.159935i
$949$	−583265.	+	201870.i	−0.647640	+	0.224150i
$950$	−446237.	+	1.11465e6i	−0.494445	+	1.23506i
$951$	513022.	+	652361.i	0.567251	+	0.721318i
$952$	−61922.8	−	135592.i	−0.0683246	−	0.149610i
$953$	860258.	−	552854.i	0.947203	−	0.608730i	0.0267743	−	0.999642i	$-0.491476\pi$
$953$	860258.	−	552854.i	0.947203	−	0.608730i	0.920428	+	0.390911i	$0.127840\pi$
$954$	−234343.	−	45165.9i	−0.257487	−	0.0496266i
$955$	−377796.	+	36075.1i	−0.414239	+	0.0395550i
$956$	−276825.	−	197127.i	−0.302894	−	0.215690i
$957$	−4.08041e6	−	2.10360e6i	−4.45533	−	2.29688i
$958$	581120.	+	609461.i	0.633191	+	0.664072i
$959$	−1.29056e6	+	248736.i	−1.40327	+	0.270459i
$960$	698370.	−	205060.i	0.757780	−	0.222504i
$961$	158571.	+	653637.i	0.171702	+	0.707767i
$962$	−130600.	+	285974.i	−0.141121	+	0.309013i
$963$	96174.8	+	668910.i	0.103707	+	0.721299i
$964$	216911.	+	304609.i	0.233415	+	0.327785i
$965$	−1.84655e6	+	1.60005e6i	−1.98293	+	1.71822i
$966$	197771.	+	494007.i	0.211937	+	0.529394i
$967$	492648.	−	853291.i	0.526846	−	0.912524i	−0.472665	−	0.881242i	$-0.656708\pi$
$967$	492648.	−	853291.i	0.526846	−	0.912524i	0.999511	−	0.0312816i	$-0.00995886\pi$
$968$	479064.	−	276588.i	0.511261	−	0.295177i
$969$	−169963.	+	216126.i	−0.181012	+	0.230175i
$970$	−1.76360e6	−	427844.i	−1.87437	−	0.454718i
$971$	−17166.1	−	360360.i	−0.0182068	−	0.382207i	−0.989519	−	0.144401i	$-0.953875\pi$
$971$	−17166.1	−	360360.i	−0.0182068	−	0.382207i	0.971313	−	0.237806i	$-0.0764284\pi$
$972$	−279942.	+	13335.3i	−0.296302	+	0.0141146i
$973$	217823.	−	897878.i	0.230079	−	0.948400i
$974$	−101867.	−	80108.9i	−0.107378	−	0.0844428i
$975$	878396.	+	1.52143e6i	0.924020	+	1.60045i
$976$	−642495.	−	370945.i	−0.674482	−	0.389412i
$977$	53286.0	−	21332.5i	0.0558244	−	0.0223487i	−0.343582	−	0.939123i	$-0.611640\pi$
$977$	53286.0	−	21332.5i	0.0558244	−	0.0223487i	0.399407	+	0.916774i	$0.369216\pi$
$978$	629953.	+	727004.i	0.658613	+	0.760080i
$979$	−378680.	+	269657.i	−0.395100	+	0.281349i
$980$	−367851.	+	52889.0i	−0.383019	+	0.0550698i
$981$	1.41786e6	+	647516.i	1.47332	+	0.672841i
$982$	−2.07288e6	+	502876.i	−2.14957	+	0.521480i
$983$	−389941.	−	1.32802e6i	−0.403545	−	1.37435i	−0.871413	−	0.490550i	$-0.836796\pi$
$983$	−389941.	−	1.32802e6i	−0.403545	−	1.37435i	0.467868	−	0.883798i	$-0.345022\pi$
$984$	−121859.	−	632264.i	−0.125854	−	0.652992i
$985$	−567818.	+	541413.i	−0.585244	+	0.558029i
$986$	−500389.	+	970620.i	−0.514700	+	0.998379i
$987$	1.09042e6	−	1.53128e6i	1.11933	−	1.57188i
$988$	−9593.14	−	100464.i	−0.00982759	−	0.102919i
$989$	803.541	−	4169.17i	0.000821515	−	0.00426242i
$990$	−3.72767e6	−	5.80037e6i	−3.80336	−	5.91814i
$991$	1.50965e6	−	689433.i	1.53719	−	0.702013i	0.546416	−	0.837514i	$-0.315992\pi$
$991$	1.50965e6	−	689433.i	1.53719	−	0.702013i	0.990777	+	0.135501i	$0.0432644\pi$
$992$	−459380.	+	361260.i	−0.466819	+	0.367110i
$993$	−2.32497e6	−	930779.i	−2.35787	−	0.943948i
$994$	−217844.	−	629420.i	−0.220482	−	0.637042i
$995$	505105.	−	529739.i	0.510194	−	0.535076i
$996$	723998.	−	1.12656e6i	0.729825	−	1.13563i
$997$	44743.3	−	311196.i	0.0450129	−	0.313072i	−0.954859	−	0.297060i	$-0.903994\pi$
$997$	44743.3	−	311196.i	0.0450129	−	0.313072i	0.999872	−	0.0160120i	$-0.00509700\pi$
$998$	140355.	−	72357.8i	0.140918	−	0.0726481i
$999$	884115.	+	305995.i	0.885886	+	0.306608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.5.h.a.2.5	✓	440
67.34	odd	66	inner	67.5.h.a.34.5	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.5.h.a.2.5	✓	440	1.1	even	1	trivial
67.5.h.a.34.5	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)

\(f(q)\)	\(=\)	\(q+(-5.14762 - 0.245211i) q^{2} +(4.28565 - 14.5956i) q^{3} +(10.5103 + 1.00362i) q^{4} +(-36.2663 - 31.4249i) q^{5} +(-25.6399 + 74.0816i) q^{6} +(-18.7117 - 36.2956i) q^{7} +(27.7590 + 3.99113i) q^{8} +(-126.522 - 81.3110i) q^{9} +O(q^{10})\)	\(q+(-5.14762 - 0.245211i) q^{2} +(4.28565 - 14.5956i) q^{3} +(10.5103 + 1.00362i) q^{4} +(-36.2663 - 31.4249i) q^{5} +(-25.6399 + 74.0816i) q^{6} +(-18.7117 - 36.2956i) q^{7} +(27.7590 + 3.99113i) q^{8} +(-126.522 - 81.3110i) q^{9} +(178.979 + 170.657i) q^{10} +(175.185 - 60.6321i) q^{11} +(59.6919 - 149.103i) q^{12} +(42.5509 + 54.1079i) q^{13} +(87.4205 + 191.424i) q^{14} +(-614.089 + 394.651i) q^{15} +(-307.791 - 59.3219i) q^{16} +(129.574 - 12.3729i) q^{17} +(631.351 + 449.583i) q^{18} +(-123.426 - 63.6305i) q^{19} +(-349.632 - 366.684i) q^{20} +(-609.946 + 117.558i) q^{21} +(-916.653 + 269.154i) q^{22} +(39.1896 + 161.542i) q^{23} +(177.218 - 388.053i) q^{24} +(238.772 + 1660.69i) q^{25} +(-205.768 - 288.961i) q^{26} +(-797.813 + 691.309i) q^{27} +(-160.239 - 400.258i) q^{28} +(813.971 - 1409.84i) q^{29} +(3257.87 - 1880.93i) q^{30} +(-309.650 + 393.752i) q^{31} +(1133.79 + 275.053i) q^{32} +(-134.179 - 2816.77i) q^{33} +(-670.034 + 31.9176i) q^{34} +(-461.983 + 1904.32i) q^{35} +(-1248.19 - 981.586i) q^{36} +(-443.122 - 767.510i) q^{37} +(619.747 + 357.811i) q^{38} +(972.094 - 389.168i) q^{39} +(-881.293 - 1017.07i) q^{40} +(1229.49 - 875.515i) q^{41} +(3168.60 - 455.576i) q^{42} +(-23.2345 - 10.6108i) q^{43} +(1902.10 - 461.445i) q^{44} +(2033.31 + 6924.81i) q^{45} +(-162.121 - 841.165i) q^{46} +(-2190.23 + 2088.38i) q^{47} +(-2184.92 + 4238.16i) q^{48} +(425.474 - 597.495i) q^{49} +(-821.885 - 8607.17i) q^{50} +(374.721 - 1944.24i) q^{51} +(392.921 + 611.397i) q^{52} +(-280.091 + 127.913i) q^{53} +(4276.35 - 3362.96i) q^{54} +(-8258.66 - 3306.27i) q^{55} +(-374.556 - 1082.21i) q^{56} +(-1457.68 + 1528.77i) q^{57} +(-4535.72 + 7057.72i) q^{58} +(279.684 - 1945.25i) q^{59} +(-6850.36 + 3531.61i) q^{60} +(2236.63 + 774.107i) q^{61} +(1690.51 - 1950.96i) q^{62} +(-583.785 + 6113.67i) q^{63} +(-956.711 - 280.916i) q^{64} +(157.172 - 3299.45i) q^{65} +14532.6i q^{66} +(1621.99 - 4185.72i) q^{67} +1374.29 q^{68} +(2525.75 + 120.316i) q^{69} +(2845.07 - 9689.43i) q^{70} +(-3150.69 - 300.855i) q^{71} +(-3187.61 - 2762.08i) q^{72} +(-2932.67 + 8473.39i) q^{73} +(2092.82 + 4059.51i) q^{74} +(25262.1 + 3632.14i) q^{75} +(-1233.39 - 792.650i) q^{76} +(-5478.68 - 5223.91i) q^{77} +(-5099.40 + 1764.92i) q^{78} +(-481.996 + 1203.97i) q^{79} +(9298.27 + 11823.7i) q^{80} +(1610.23 + 3525.92i) q^{81} +(-6543.63 + 4205.33i) q^{82} +(8187.32 + 1577.98i) q^{83} +(-6528.72 + 623.417i) q^{84} +(-5088.00 - 3623.15i) q^{85} +(117.000 + 60.3179i) q^{86} +(-17089.0 - 17922.4i) q^{87} +(5104.94 - 983.896i) q^{88} +(-2406.12 + 706.502i) q^{89} +(-8768.65 - 36144.9i) q^{90} +(1167.68 - 2556.86i) q^{91} +(249.770 + 1737.19i) q^{92} +(4419.99 + 6207.00i) q^{93} +(11786.6 - 10213.1i) q^{94} +(2476.62 + 6186.29i) q^{95} +(8873.56 - 15369.5i) q^{96} +(-6355.13 + 3669.13i) q^{97} +(-2336.69 + 2971.35i) q^{98} +(-27094.9 - 6573.14i) 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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