LMFDB - Embedded newform 67.5.h.a.34.19

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			34.19
Character	$\chi$	$=$	67.34
Dual form			67.5.h.a.2.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.64013 - 0.268673i) q^{2} +(-4.71637 - 16.0625i) q^{3} +(15.8113 - 1.50980i) q^{4} +(10.4042 - 9.01530i) q^{5} +(-30.9165 - 89.3274i) q^{6} +(-5.20271 + 10.0919i) q^{7} +(-0.652485 + 0.0938132i) q^{8} +(-167.618 + 107.721i) q^{9} +O(q^{10})$	\(q+(5.64013 - 0.268673i) q^{2} +(-4.71637 - 16.0625i) q^{3} +(15.8113 - 1.50980i) q^{4} +(10.4042 - 9.01530i) q^{5} +(-30.9165 - 89.3274i) q^{6} +(-5.20271 + 10.0919i) q^{7} +(-0.652485 + 0.0938132i) q^{8} +(-167.618 + 107.721i) q^{9} +(56.2589 - 53.6428i) q^{10} +(61.2373 + 21.1944i) q^{11} +(-98.8233 - 246.849i) q^{12} +(172.452 - 219.291i) q^{13} +(-26.6326 + 58.3172i) q^{14} +(-193.878 - 124.598i) q^{15} +(-253.195 + 48.7992i) q^{16} +(183.683 + 17.5396i) q^{17} +(-916.445 + 652.598i) q^{18} +(374.380 - 193.007i) q^{19} +(150.893 - 158.252i) q^{20} +(186.638 + 35.9716i) q^{21} +(351.081 + 103.087i) q^{22} +(92.8144 - 382.586i) q^{23} +(4.58424 + 10.0381i) q^{24} +(-61.9748 + 431.044i) q^{25} +(913.735 - 1283.16i) q^{26} +(1496.04 + 1296.32i) q^{27} +(-67.0252 + 167.421i) q^{28} +(507.417 + 878.872i) q^{29} +(-1126.97 - 650.659i) q^{30} +(-226.585 - 288.126i) q^{31} +(-1404.69 + 340.774i) q^{32} +(51.6175 - 1083.58i) q^{33} +(1040.71 + 49.5752i) q^{34} +(36.8510 + 151.902i) q^{35} +(-2487.63 + 1956.29i) q^{36} +(-512.666 + 887.964i) q^{37} +(2059.70 - 1189.17i) q^{38} +(-4335.70 - 1735.75i) q^{39} +(-5.94284 + 6.85840i) q^{40} +(-1758.25 - 1252.05i) q^{41} +(1062.33 + 152.740i) q^{42} +(1691.13 - 772.314i) q^{43} +(1000.24 + 242.656i) q^{44} +(-772.790 + 2631.88i) q^{45} +(420.695 - 2182.77i) q^{46} +(2197.56 + 2095.37i) q^{47} +(1978.00 + 3836.78i) q^{48} +(1317.94 + 1850.79i) q^{49} +(-233.736 + 2447.80i) q^{50} +(-584.589 - 3033.14i) q^{51} +(2395.61 - 3727.65i) q^{52} +(-1397.74 - 638.324i) q^{53} +(8786.12 + 6909.48i) q^{54} +(828.199 - 331.561i) q^{55} +(2.44795 - 7.07287i) q^{56} +(-4865.88 - 5103.19i) q^{57} +(3098.03 + 4820.62i) q^{58} +(200.378 + 1393.66i) q^{59} +(-3253.59 - 1677.34i) q^{60} +(-4742.81 + 1641.50i) q^{61} +(-1355.38 - 1564.19i) q^{62} +(-215.042 - 2252.02i) q^{63} +(-3872.52 + 1137.08i) q^{64} +(-182.743 - 3836.25i) q^{65} -6125.42i q^{66} +(2355.58 + 3821.30i) q^{67} +2930.76 q^{68} +(-6583.04 + 313.589i) q^{69} +(248.656 + 846.845i) q^{70} +(1968.37 - 187.957i) q^{71} +(99.2625 - 86.0115i) q^{72} +(-2171.26 - 6273.44i) q^{73} +(-2652.93 + 5145.97i) q^{74} +(7215.94 - 1037.50i) q^{75} +(5628.05 - 3616.93i) q^{76} +(-532.491 + 507.729i) q^{77} +(-24920.3 - 8624.99i) q^{78} +(2740.84 + 6846.29i) q^{79} +(-2194.35 + 2790.34i) q^{80} +(7061.89 - 15463.4i) q^{81} +(-10253.2 - 6589.31i) q^{82} +(-9353.06 + 1802.66i) q^{83} +(3005.31 + 286.972i) q^{84} +(2069.20 - 1473.47i) q^{85} +(9330.71 - 4810.31i) q^{86} +(11723.7 - 12295.5i) q^{87} +(-41.9447 - 8.08419i) q^{88} +(-14005.3 - 4112.34i) q^{89} +(-3651.52 + 15051.8i) q^{90} +(1315.83 + 2881.27i) q^{91} +(889.892 - 6189.33i) q^{92} +(-3559.37 + 4998.43i) q^{93} +(12957.5 + 11227.7i) q^{94} +(2155.12 - 5383.23i) q^{95} +(12098.7 + 20955.6i) q^{96} +(6743.97 + 3893.63i) q^{97} +(7930.61 + 10084.6i) q^{98} +(-12547.6 + 3044.00i) 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 $\left(\mathbb{Z}/67\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{65}{66}\right)$

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 $

$2$	5.64013	−	0.268673i	1.41003	−	0.0671681i	0.671309	−	0.741177i	$-0.265732\pi$
$2$	5.64013	−	0.268673i	1.41003	−	0.0671681i	0.738723	+	0.674009i	$0.235429\pi$
$3$	−4.71637	−	16.0625i	−0.524041	−	1.78472i	−0.614610	−	0.788831i	$-0.710687\pi$
$3$	−4.71637	−	16.0625i	−0.524041	−	1.78472i	0.0905687	−	0.995890i	$-0.471132\pi$
$4$	15.8113	−	1.50980i	0.988208	−	0.0943625i
$5$	10.4042	−	9.01530i	0.416168	−	0.360612i	−0.421465	−	0.906845i	$-0.638484\pi$
$5$	10.4042	−	9.01530i	0.416168	−	0.360612i	0.837633	+	0.546233i	$0.183939\pi$
$6$	−30.9165	−	89.3274i	−0.858792	−	2.48132i
$7$	−5.20271	+	10.0919i	−0.106178	+	0.205956i	−0.935939	−	0.352163i	$-0.885446\pi$
$7$	−5.20271	+	10.0919i	−0.106178	+	0.205956i	0.829761	+	0.558119i	$0.188477\pi$
$8$	−0.652485	+	0.0938132i	−0.0101951	+	0.00146583i
$9$	−167.618	+	107.721i	−2.06936	+	1.32989i
$10$	56.2589	−	53.6428i	0.562589	−	0.536428i
$11$	61.2373	+	21.1944i	0.506093	+	0.175161i	0.568171	−	0.822911i	$-0.307651\pi$
$11$	61.2373	+	21.1944i	0.506093	+	0.175161i	−0.0620775	+	0.998071i	$0.519773\pi$
$12$	−98.8233	−	246.849i	−0.686273	−	1.71423i
$13$	172.452	−	219.291i	1.02043	−	1.29758i	0.0664200	−	0.997792i	$-0.478842\pi$
$13$	172.452	−	219.291i	1.02043	−	1.29758i	0.954006	−	0.299786i	$-0.0969153\pi$
$14$	−26.6326	+	58.3172i	−0.135881	+	0.297537i
$15$	−193.878	−	124.598i	−0.861681	−	0.553769i
$16$	−253.195	+	48.7992i	−0.989041	+	0.190622i
$17$	183.683	+	17.5396i	0.635583	+	0.0606908i	0.407873	−	0.913038i	$-0.366270\pi$
$17$	183.683	+	17.5396i	0.635583	+	0.0606908i	0.227709	+	0.973729i	$0.426876\pi$
$18$	−916.445	+	652.598i	−2.82853	+	2.01419i
$19$	374.380	−	193.007i	1.03706	−	0.534644i	0.146363	−	0.989231i	$-0.453243\pi$
$19$	374.380	−	193.007i	1.03706	−	0.534644i	0.890702	+	0.454587i	$0.150213\pi$
$20$	150.893	−	158.252i	0.377233	−	0.395630i
$21$	186.638	+	35.9716i	0.423216	+	0.0815682i
$22$	351.081	+	103.087i	0.725373	+	0.212989i
$23$	92.8144	−	382.586i	0.175453	−	0.723226i	−0.814301	−	0.580442i	$-0.802880\pi$
$23$	92.8144	−	382.586i	0.175453	−	0.723226i	0.989754	−	0.142783i	$-0.0456052\pi$
$24$	4.58424	+	10.0381i	0.00795875	+	0.0174272i
$25$	−61.9748	+	431.044i	−0.0991597	+	0.689671i
$26$	913.735	−	1283.16i	1.35168	−	1.89817i
$27$	1496.04	+	1296.32i	2.05218	+	1.77822i
$28$	−67.0252	+	167.421i	−0.0854913	+	0.213547i
$29$	507.417	+	878.872i	0.603349	+	1.04503i	0.992310	+	0.123777i	$0.0395008\pi$
$29$	507.417	+	878.872i	0.603349	+	1.04503i	−0.388961	+	0.921254i	$0.627166\pi$
$30$	−1126.97	−	650.659i	−1.25219	−	0.722955i
$31$	−226.585	−	288.126i	−0.235781	−	0.299819i	0.653736	−	0.756723i	$-0.273201\pi$
$31$	−226.585	−	288.126i	−0.235781	−	0.299819i	−0.889516	+	0.456904i	$0.848958\pi$
$32$	−1404.69	+	340.774i	−1.37177	+	0.332787i
$33$	51.6175	−	1083.58i	0.0473990	−	0.995026i
$34$	1040.71	+	49.5752i	0.900269	+	0.0428851i
$35$	36.8510	+	151.902i	0.0300824	+	0.124001i
$36$	−2487.63	+	1956.29i	−1.91946	+	1.50948i
$37$	−512.666	+	887.964i	−0.374482	+	0.648622i	−0.990249	−	0.139306i	$-0.955513\pi$
$37$	−512.666	+	887.964i	−0.374482	+	0.648622i	0.615767	+	0.787928i	$0.288846\pi$
$38$	2059.70	−	1189.17i	1.42638	−	0.823523i
$39$	−4335.70	−	1735.75i	−2.85056	−	1.14119i
$40$	−5.94284	+	6.85840i	−0.00371427	+	0.00428650i
$41$	−1758.25	−	1252.05i	−1.04596	−	0.744823i	−0.0782587	−	0.996933i	$-0.524936\pi$
$41$	−1758.25	−	1252.05i	−1.04596	−	0.744823i	−0.967698	+	0.252110i	$0.918875\pi$
$42$	1062.33	+	152.740i	0.602227	+	0.0865872i
$43$	1691.13	−	772.314i	0.914620	−	0.417693i	0.0982099	−	0.995166i	$-0.468688\pi$
$43$	1691.13	−	772.314i	0.914620	−	0.417693i	0.816410	+	0.577473i	$0.195961\pi$
$44$	1000.24	+	242.656i	0.516654	+	0.125339i
$45$	−772.790	+	2631.88i	−0.381625	+	1.29969i
$46$	420.695	−	2182.77i	0.198816	−	1.03156i
$47$	2197.56	+	2095.37i	0.994821	+	0.948559i	0.998676	−	0.0514331i	$-0.0163789\pi$
$47$	2197.56	+	2095.37i	0.994821	+	0.948559i	−0.00385589	+	0.999993i	$0.501227\pi$
$48$	1978.00	+	3836.78i	0.858506	+	1.66527i
$49$	1317.94	+	1850.79i	0.548913	+	0.770840i
$50$	−233.736	+	2447.80i	−0.0934945	+	0.979119i
$51$	−584.589	−	3033.14i	−0.224755	−	1.16614i
$52$	2395.61	−	3727.65i	0.885951	−	1.37857i
$53$	−1397.74	−	638.324i	−0.497592	−	0.227243i	0.150779	−	0.988568i	$-0.451822\pi$
$53$	−1397.74	−	638.324i	−0.497592	−	0.227243i	−0.648370	+	0.761325i	$0.724549\pi$
$54$	8786.12	+	6909.48i	3.01307	+	2.36951i
$55$	828.199	−	331.561i	0.273785	−	0.109607i
$56$	2.44795	−	7.07287i	0.000780595	−	0.00225538i
$57$	−4865.88	−	5103.19i	−1.49766	−	1.57070i
$58$	3098.03	+	4820.62i	0.920935	+	1.43300i
$59$	200.378	+	1393.66i	0.0575634	+	0.400362i	0.998150	+	0.0608069i	$0.0193674\pi$
$59$	200.378	+	1393.66i	0.0575634	+	0.400362i	−0.940586	+	0.339555i	$0.889724\pi$
$60$	−3253.59	−	1677.34i	−0.903775	−	0.465929i
$61$	−4742.81	+	1641.50i	−1.27461	+	0.441146i	−0.878801	−	0.477188i	$-0.841656\pi$
$61$	−4742.81	+	1641.50i	−1.27461	+	0.441146i	−0.395806	+	0.918334i	$0.629535\pi$
$62$	−1355.38	−	1564.19i	−0.352597	−	0.406918i
$63$	−215.042	−	2252.02i	−0.0541804	−	0.567402i
$64$	−3872.52	+	1137.08i	−0.945440	+	0.277606i
$65$	−182.743	−	3836.25i	−0.0432528	−	0.907989i
$66$		−	6125.42i		−	1.40620i
$67$	2355.58	+	3821.30i	0.524745	+	0.851259i
$67$	2355.58	+	3821.30i	0.524745	+	0.851259i
$68$	2930.76			0.633815
$69$	−6583.04	+	313.589i	−1.38270	+	0.0658661i
$70$	248.656	+	846.845i	0.0507461	+	0.172826i
$71$	1968.37	−	187.957i	0.390473	−	0.0372857i	0.102027	−	0.994782i	$-0.467467\pi$
$71$	1968.37	−	187.957i	0.390473	−	0.0372857i	0.288447	+	0.957496i	$0.406861\pi$
$72$	99.2625	−	86.0115i	0.0191479	−	0.0165917i
$73$	−2171.26	−	6273.44i	−0.407442	−	1.17723i	−0.943019	−	0.332739i	$-0.892027\pi$
$73$	−2171.26	−	6273.44i	−0.407442	−	1.17723i	0.535577	−	0.844486i	$-0.320094\pi$
$74$	−2652.93	+	5145.97i	−0.484465	+	0.939732i
$75$	7215.94	−	1037.50i	1.28283	−	0.184444i
$76$	5628.05	−	3616.93i	0.974386	−	0.626200i
$77$	−532.491	+	507.729i	−0.0898113	+	0.0856349i
$78$	−24920.3	−	8624.99i	−4.09603	−	1.41765i
$79$	2740.84	+	6846.29i	0.439167	+	1.09699i	0.968598	+	0.248633i	$0.0799814\pi$
$79$	2740.84	+	6846.29i	0.439167	+	1.09699i	−0.529431	+	0.848353i	$0.677594\pi$
$80$	−2194.35	+	2790.34i	−0.342867	+	0.435991i
$81$	7061.89	−	15463.4i	1.07634	−	2.35686i
$82$	−10253.2	−	6589.31i	−1.52486	−	0.979969i
$83$	−9353.06	+	1802.66i	−1.35768	+	0.261672i	−0.815581	−	0.578643i	$-0.803583\pi$
$83$	−9353.06	+	1802.66i	−1.35768	+	0.261672i	−0.542100	+	0.840314i	$0.682370\pi$
$84$	3005.31	+	286.972i	0.425923	+	0.0406707i
$85$	2069.20	−	1473.47i	0.286395	−	0.203941i
$86$	9330.71	−	4810.31i	1.26159	−	0.650394i
$87$	11723.7	−	12295.5i	1.54891	−	1.62445i
$88$	−41.9447	−	8.08419i	−0.00541642	−	0.00104393i
$89$	−14005.3	−	4112.34i	−1.76813	−	0.519169i	−0.774568	−	0.632490i	$-0.782033\pi$
$89$	−14005.3	−	4112.34i	−1.76813	−	0.519169i	−0.993558	+	0.113322i	$0.963851\pi$
$90$	−3651.52	+	15051.8i	−0.450805	+	1.85824i
$91$	1315.83	+	2881.27i	0.158898	+	0.347937i
$92$	889.892	−	6189.33i	0.105138	−	0.731254i
$93$	−3559.37	+	4998.43i	−0.411535	+	0.577920i
$94$	12957.5	+	11227.7i	1.46644	+	1.27068i
$95$	2155.12	−	5383.23i	0.238794	−	0.596480i
$96$	12098.7	+	20955.6i	1.31279	+	2.27383i
$97$	6743.97	+	3893.63i	0.716757	+	0.413820i	0.813558	−	0.581484i	$-0.197528\pi$
$97$	6743.97	+	3893.63i	0.716757	+	0.413820i	−0.0968007	+	0.995304i	$0.530861\pi$
$98$	7930.61	+	10084.6i	0.825761	+	1.05004i
$99$	−12547.6	+	3044.00i	−1.28023	+	0.310581i
$100$	−329.114	+	6908.96i	−0.0329114	+	0.690896i
$101$	4618.86	+	220.023i	0.452785	+	0.0215688i	0.272736	−	0.962089i	$-0.412071\pi$
$101$	4618.86	+	220.023i	0.452785	+	0.0215688i	0.180049	+	0.983658i	$0.442374\pi$
$102$	−4112.08	−	16950.2i	−0.395240	−	1.62920i
$103$	1156.04	−	909.117i	0.108967	−	0.0856930i	−0.562189	−	0.827009i	$-0.690040\pi$
$103$	1156.04	−	909.117i	0.108967	−	0.0856930i	0.671156	+	0.741316i	$0.265798\pi$
$104$	−91.9501	+	159.262i	−0.00850130	+	0.0147247i
$105$	2266.12	−	1308.34i	0.205544	−	0.118671i
$106$	−8054.91	−	3224.70i	−0.716884	−	0.286997i
$107$	11406.7	−	13164.1i	0.996309	−	1.14980i	0.00759716	−	0.999971i	$-0.497582\pi$
$107$	11406.7	−	13164.1i	0.996309	−	1.14980i	0.988712	−	0.149831i	$-0.0478728\pi$
$108$	25611.5	+	18237.9i	2.19577	+	1.56360i
$109$	−4552.06	−	654.487i	−0.383137	−	0.0550868i	−0.0519446	−	0.998650i	$-0.516542\pi$
$109$	−4552.06	−	654.487i	−0.383137	−	0.0550868i	−0.331193	+	0.943563i	$0.607451\pi$
$110$	4582.07	−	2092.56i	0.378683	−	0.172939i
$111$	16680.8	+	4046.73i	1.35385	+	0.328441i
$112$	824.824	−	2809.09i	0.0657544	−	0.223939i
$113$	−1280.22	+	6642.42i	−0.100260	+	0.520199i	0.896724	+	0.442590i	$0.145940\pi$
$113$	−1280.22	+	6642.42i	−0.100260	+	0.520199i	−0.996984	+	0.0776082i	$0.975272\pi$
$114$	−28815.3	−	27475.3i	−2.21724	−	2.11414i
$115$	−2483.47	−	4817.26i	−0.187786	−	0.364254i
$116$	9349.86	+	13130.0i	0.694847	+	0.975776i
$117$	−5283.74	+	55333.8i	−0.385984	+	4.04221i
$118$	1504.60	+	7806.59i	0.108058	+	0.560657i
$119$	−1132.66	+	1762.45i	−0.0799844	+	0.124458i
$120$	138.192	+	63.1100i	0.00959664	+	0.00438264i
$121$	−8207.80	−	6454.69i	−0.560604	−	0.440864i
$122$	−26309.1	+	10532.6i	−1.76761	+	0.707643i
$123$	−11818.4	+	34147.1i	−0.781176	+	2.25706i
$124$	−4017.63	−	4213.57i	−0.261292	−	0.274035i
$125$	7892.98	+	12281.7i	0.505151	+	0.786030i
$126$	−1817.92	−	12643.9i	−0.114507	−	0.796417i
$127$	−20683.2	−	10662.9i	−1.28236	−	0.661103i	−0.323836	−	0.946113i	$-0.604973\pi$
$127$	−20683.2	−	10662.9i	−1.28236	−	0.661103i	−0.958524	+	0.285011i	$0.908003\pi$
$128$	318.937	−	110.385i	0.0194664	−	0.00673737i
$129$	−20381.3	−	23521.3i	−1.22476	−	1.41345i
$130$	−2061.39	−	21587.9i	−0.121976	−	1.27739i
$131$	22129.4	−	6497.79i	1.28952	−	0.378637i	0.436117	−	0.899890i	$-0.356353\pi$
$131$	22129.4	−	6497.79i	1.28952	−	0.378637i	0.853402	+	0.521253i	$0.174535\pi$
$132$	−819.853	−	17210.8i	−0.0470531	−	0.987766i
$133$			4782.35i			0.270357i
$134$	14312.5	+	20919.8i	0.797085	+	1.16506i
$135$	27251.8			1.49530
$136$	−121.496	+	5.78758i	−0.00656878	+	0.000312910i
$137$	9471.60	+	32257.3i	0.504641	+	1.71865i	0.679156	+	0.733994i	$0.262346\pi$
$137$	9471.60	+	32257.3i	0.504641	+	1.71865i	−0.174516	+	0.984654i	$0.555836\pi$
$138$	−37044.9	+	3537.36i	−1.94523	+	0.185747i
$139$	−3452.67	+	2991.76i	−0.178700	+	0.154845i	−0.739618	−	0.673027i	$-0.764994\pi$
$139$	−3452.67	+	2991.76i	−0.178700	+	0.154845i	0.560918	+	0.827872i	$0.310448\pi$
$140$	812.004	+	2346.13i	0.0414288	+	0.119701i
$141$	23292.3	−	45180.8i	1.17159	−	2.27256i
$142$	11051.4	−	1588.95i	0.548075	−	0.0788013i
$143$	15208.2	−	9773.74i	0.743715	−	0.477957i
$144$	37183.2	−	35454.1i	1.79317	−	1.70979i
$145$	13202.6	+	4569.45i	0.627946	+	0.217334i
$146$	−13931.7	−	34799.6i	−0.653578	−	1.63256i
$147$	23512.4	−	29898.4i	1.08808	−	1.38361i
$148$	−6765.29	+	14813.9i	−0.308861	+	0.676311i
$149$	−1868.05	−	1200.52i	−0.0841425	−	0.0540751i	0.497893	−	0.867238i	$-0.334107\pi$
$149$	−1868.05	−	1200.52i	−0.0841425	−	0.0540751i	−0.582036	+	0.813163i	$0.697744\pi$
$150$	40420.1	−	7790.34i	1.79645	−	0.346237i
$151$	−28041.8	−	2677.67i	−1.22985	−	0.117437i	−0.540174	−	0.841554i	$-0.681641\pi$
$151$	−28041.8	−	2677.67i	−1.22985	−	0.117437i	−0.689677	+	0.724117i	$0.742248\pi$
$152$	−226.171	+	161.056i	−0.00978927	+	0.00697090i
$153$	−32678.0	+	16846.7i	−1.39596	+	0.719667i
$154$	−2866.91	+	3006.72i	−0.120885	+	0.126780i
$155$	−4954.98	−	954.995i	−0.206243	−	0.0397500i
$156$	−71173.9	−	20898.5i	−2.92463	−	0.858750i
$157$	−5113.54	+	21078.3i	−0.207454	+	0.855139i	0.768971	+	0.639284i	$0.220769\pi$
$157$	−5113.54	+	21078.3i	−0.207454	+	0.855139i	−0.976425	+	0.215855i	$0.930746\pi$
$158$	17298.1	+	37877.6i	0.692923	+	1.51729i
$159$	−3660.84	+	25461.7i	−0.144806	+	1.00715i
$160$	−11542.5	+	16209.2i	−0.450879	+	0.633171i
$161$	3378.12	+	2927.16i	0.130324	+	0.112926i
$162$	35675.4	−	89112.9i	1.35937	−	3.39555i
$163$	−1067.26	−	1848.55i	−0.0401693	−	0.0695753i	0.845242	−	0.534384i	$-0.179456\pi$
$163$	−1067.26	−	1848.55i	−0.0401693	−	0.0695753i	−0.885411	+	0.464809i	$0.846123\pi$
$164$	−29690.7	−	17141.9i	−1.10391	−	0.637341i
$165$	−9231.79	−	11739.2i	−0.339092	−	0.431191i
$166$	−52268.2	+	12680.1i	−1.89680	+	0.460158i
$167$	−721.266	+	15141.2i	−0.0258620	+	0.542911i	0.948343	+	0.317246i	$0.102758\pi$
$167$	−721.266	+	15141.2i	−0.0258620	+	0.542911i	−0.974205	+	0.225664i	$0.927545\pi$
$168$	−125.153	−	5.96179i	−0.00443429	−	0.000211231i
$169$	−11615.2	−	47878.3i	−0.406679	−	1.67635i
$170$	11274.7	−	8866.52i	0.390128	−	0.306800i
$171$	−41961.9	+	72680.2i	−1.43504	+	2.48556i
$172$	25573.0	−	14764.6i	0.864420	−	0.499073i
$173$	47965.0	+	19202.3i	1.60262	+	0.641594i	0.988988	−	0.147995i	$-0.0472818\pi$
$173$	47965.0	+	19202.3i	1.60262	+	0.641594i	0.613636	+	0.789589i	$0.289706\pi$
$174$	62819.7	−	72497.9i	2.07490	−	2.39457i
$175$	−4027.60	−	2868.04i	−0.131514	−	0.0936503i
$176$	−16539.2	−	2377.98i	−0.533936	−	0.0767685i
$177$	21440.6	−	9791.59i	0.684369	−	0.312541i
$178$	−80096.8	−	19431.3i	−2.52799	−	0.613283i
$179$	−5464.48	+	18610.3i	−0.170547	+	0.580828i	0.829214	+	0.558932i	$0.188789\pi$
$179$	−5464.48	+	18610.3i	−0.170547	+	0.580828i	−0.999760	+	0.0218966i	$0.993030\pi$
$180$	−8245.23	+	42780.3i	−0.254482	+	1.32038i
$181$	−31082.3	−	29636.9i	−0.948759	−	0.904640i	0.0467878	−	0.998905i	$-0.485102\pi$
$181$	−31082.3	−	29636.9i	−0.948759	−	0.904640i	−0.995547	+	0.0942646i	$0.969950\pi$
$182$	8195.58	+	15897.2i	0.247421	+	0.479930i
$183$	48735.5	+	68439.5i	1.45527	+	2.04364i
$184$	−24.6684	+	258.339i	−0.000728627	+	0.00763053i
$185$	2671.37	+	13860.4i	0.0780532	+	0.404979i
$186$	−18732.4	+	29148.1i	−0.541460	+	0.842529i
$187$	10876.5	+	4967.14i	0.311033	+	0.142044i
$188$	37909.9	+	29812.7i	1.07260	+	0.843501i
$189$	−20865.7	+	8353.39i	−0.584131	+	0.233851i
$190$	10708.8	−	30941.1i	0.296644	−	0.857095i
$191$	30742.9	+	32242.2i	0.842709	+	0.883808i	0.994514	−	0.104603i	$-0.0333571\pi$
$191$	30742.9	+	32242.2i	0.842709	+	0.883808i	−0.151805	+	0.988410i	$0.548509\pi$
$192$	36528.5	+	56839.5i	0.990900	+	1.54187i
$193$	−3410.52	−	23720.7i	−0.0915600	−	0.636814i	−0.982991	−	0.183656i	$-0.941207\pi$
$193$	−3410.52	−	23720.7i	−0.0915600	−	0.636814i	0.891431	−	0.453157i	$-0.149702\pi$
$194$	39083.0	+	20148.7i	1.03845	+	0.535357i
$195$	−60757.9	+	21028.5i	−1.59784	+	0.553018i
$196$	23632.7	+	27273.6i	0.615179	+	0.709954i
$197$	−4322.28	−	45265.0i	−0.111373	−	1.16635i	−0.862452	−	0.506139i	$-0.831072\pi$
$197$	−4322.28	−	45265.0i	−0.111373	−	1.16635i	0.751079	−	0.660213i	$-0.229534\pi$
$198$	−69952.0	+	20539.8i	−1.78431	+	0.523920i
$199$	−2255.68	−	47352.5i	−0.0569601	−	1.19574i	−0.828660	−	0.559753i	$-0.810896\pi$
$199$	−2255.68	−	47352.5i	−0.0569601	−	1.19574i	0.771700	−	0.635987i	$-0.219407\pi$
$200$		−	287.064i		−	0.00717661i
$201$	50269.8	−	55859.2i	1.24427	−	1.38262i
$202$	26110.1			0.639890
$203$	−11509.4	+	548.260i	−0.279293	+	0.0133044i
$204$	−13822.6	−	47075.3i	−0.332145	−	1.13118i
$205$	−29580.8	+	2824.63i	−0.703886	+	0.0672130i
$206$	6275.94	−	5438.13i	0.147892	−	0.128149i
$207$	25655.4	+	74126.4i	0.598740	+	1.72995i
$208$	−32962.7	+	63938.7i	−0.761897	+	1.47787i
$209$	27016.7	−	3884.41i	0.618500	−	0.0889269i
$210$	12429.7	−	7988.07i	0.281852	−	0.181135i
$211$	17370.6	−	16562.9i	0.390167	−	0.372024i	−0.469453	−	0.882958i	$-0.655549\pi$
$211$	17370.6	−	16562.9i	0.390167	−	0.372024i	0.859620	+	0.510934i	$0.170700\pi$
$212$	−23063.8	−	7982.46i	−0.513168	−	0.177609i
$213$	−12302.6	−	30730.5i	−0.271169	−	0.677346i
$214$	60798.7	−	77311.8i	1.32760	−	1.68818i
$215$	10632.2	−	23281.4i	0.230011	−	0.503653i
$216$	−1097.75	−	705.484i	−0.0235287	−	0.0151210i
$217$	4086.59	−	787.625i	0.0867843	−	0.0167263i
$218$	−25850.0	−	2468.38i	−0.543936	−	0.0519396i
$219$	−90526.6	+	64463.7i	−1.88750	+	1.34409i
$220$	12594.3	−	6492.84i	0.260214	−	0.134150i
$221$	35522.9	−	37255.3i	0.727316	−	0.762787i
$222$	95169.3	+	18342.4i	1.93104	+	0.372177i
$223$	12936.2	+	3798.40i	0.260133	+	0.0763820i	0.409199	−	0.912445i	$-0.365808\pi$
$223$	12936.2	+	3798.40i	0.260133	+	0.0763820i	−0.149065	+	0.988827i	$0.547626\pi$
$224$	3869.15	−	15948.9i	0.0771117	−	0.317859i
$225$	−36044.7	−	78926.8i	−0.711993	−	1.55905i
$226$	−5435.98	+	37808.1i	−0.106429	+	0.740231i
$227$	−2584.92	+	3630.01i	−0.0501644	+	0.0704460i	−0.838896	−	0.544291i	$-0.816799\pi$
$227$	−2584.92	+	3630.01i	−0.0501644	+	0.0704460i	0.788732	+	0.614737i	$0.210738\pi$
$228$	−84640.9	−	73341.8i	−1.62821	−	1.41085i
$229$	22822.2	−	57007.2i	0.435198	−	1.08707i	−0.535020	−	0.844839i	$-0.679696\pi$
$229$	22822.2	−	57007.2i	0.435198	−	1.08707i	0.970218	−	0.242233i	$-0.0778798\pi$
$230$	−15301.4	−	26502.7i	−0.289250	−	0.500997i
$231$	10666.8	+	6158.49i	0.199899	+	0.115412i
$232$	−413.532	−	525.848i	−0.00768304	−	0.00976978i
$233$	29903.5	−	7254.51i	0.550821	−	0.133628i	0.0493170	−	0.998783i	$-0.484296\pi$
$233$	29903.5	−	7254.51i	0.550821	−	0.133628i	0.501504	+	0.865156i	$0.332780\pi$
$234$	−14934.3	+	313510.i	−0.272743	+	5.72558i
$235$	41754.2	+	1989.00i	0.756075	+	0.0360163i
$236$	5272.39	+	21733.1i	0.0946637	+	0.390209i
$237$	97041.7	−	76314.4i	1.72767	−	1.35866i
$238$	−5914.82	+	10244.8i	−0.104421	+	0.180863i
$239$	69254.3	−	39984.0i	1.21241	−	0.699988i	0.249129	−	0.968470i	$-0.419856\pi$
$239$	69254.3	−	39984.0i	1.21241	−	0.699988i	0.963285	+	0.268483i	$0.0865222\pi$
$240$	55169.2	+	22086.4i	0.957798	+	0.383445i
$241$	−41458.2	+	47845.3i	−0.713800	+	0.823769i	−0.990547	−	0.137173i	$-0.956198\pi$
$241$	−41458.2	+	47845.3i	−0.713800	+	0.823769i	0.276747	+	0.960943i	$0.410744\pi$
$242$	−48027.3	−	34200.1i	−0.820082	−	0.583978i
$243$	−122976.	−	17681.3i	−2.08262	−	0.299435i
$244$	−72511.9	+	33115.1i	−1.21795	+	0.556219i
$245$	30397.5	+	7374.35i	0.506414	+	0.122855i
$246$	−57483.0	+	195769.i	−0.949881	+	3.23500i
$247$	22238.2	−	115382.i	0.364506	−	1.89124i
$248$	174.874	+	166.742i	0.00284329	+	0.00271107i
$249$	73067.7	+	141732.i	1.17849	+	2.28596i
$250$	47817.2	+	67149.9i	0.765075	+	1.07440i
$251$	1994.90	−	20891.5i	0.0316645	−	0.331606i	−0.965735	−	0.259531i	$-0.916432\pi$
$251$	1994.90	−	20891.5i	0.0316645	−	0.331606i	0.997399	−	0.0720747i	$-0.0229620\pi$
$252$	−6800.20	−	35282.8i	−0.107083	−	0.555599i
$253$	13792.4	−	21461.4i	0.215476	−	0.335287i
$254$	−119521.	−	54583.3i	−1.85257	−	0.846042i
$255$	−33426.8	−	26287.1i	−0.514061	−	0.404262i
$256$	61719.6	−	24708.8i	0.941767	−	0.377027i
$257$	−17179.2	+	49635.9i	−0.260097	+	0.751501i	0.737037	+	0.675852i	$0.236224\pi$
$257$	−17179.2	+	49635.9i	−0.260097	+	0.751501i	−0.997134	+	0.0756493i	$0.975897\pi$
$258$	−121273.	−	127187.i	−1.82190	−	1.91075i
$259$	−6293.95	−	9793.57i	−0.0938261	−	0.145996i
$260$	−8681.38	−	60380.4i	−0.128423	−	0.893201i
$261$	−179725.	−	92654.9i	−2.63833	−	1.36015i
$262$	123067.	−	42593.9i	1.79283	−	0.620505i
$263$	−59335.4	−	68476.7i	−0.857832	−	0.989991i	−1.00000		0.000148078i	$-0.999953\pi$
$263$	−59335.4	−	68476.7i	−0.857832	−	0.989991i	0.142168	−	0.989843i	$-0.454593\pi$
$264$	67.9749	+	711.865i	0.000975305	+	0.0102139i
$265$	−20297.0	+	5959.74i	−0.289028	+	0.0848663i
$266$	1284.89	+	26973.1i	0.0181594	+	0.381213i
$267$			244356.i			3.42768i
$268$	43014.3	+	56863.5i	0.598885	+	0.791705i
$269$	1408.25			0.0194614			0.00973070	−	0.999953i	$-0.496903\pi$
$269$	1408.25			0.0194614			0.00973070	+	0.999953i	$0.496903\pi$
$270$	153704.	−	7321.81i	2.10842	−	0.100436i
$271$	1866.00	+	6355.00i	0.0254081	+	0.0865321i	0.971221	−	0.238180i	$-0.0765508\pi$
$271$	1866.00	+	6355.00i	0.0254081	+	0.0865321i	−0.945813	+	0.324712i	$0.894733\pi$
$272$	−47363.5	+	4522.67i	−0.640186	+	0.0611304i
$273$	40074.4	−	34724.7i	0.537702	−	0.465921i
$274$	62087.7	+	179391.i	0.826998	+	2.38945i
$275$	−12930.9	+	25082.5i	−0.170987	+	0.331669i
$276$	−103613.	+	14897.3i	−1.36018	+	0.195565i
$277$	−74940.0	+	48161.0i	−0.976684	+	0.627677i	−0.928567	−	0.371165i	$-0.878958\pi$
$277$	−74940.0	+	48161.0i	−0.976684	+	0.627677i	−0.0481172	+	0.998842i	$0.515322\pi$
$278$	−18669.7	+	17801.5i	−0.241573	+	0.230339i
$279$	69017.1	+	23887.1i	0.886642	+	0.306870i
$280$	−38.2951	−	95.6566i	−0.000488458	−	0.00122011i
$281$	1671.64	−	2125.67i	0.0211705	−	0.0269205i	−0.775353	−	0.631529i	$-0.782428\pi$
$281$	1671.64	−	2125.67i	0.0211705	−	0.0269205i	0.796523	+	0.604608i	$0.206670\pi$
$282$	119233.	−	261084.i	1.49933	−	3.28308i
$283$	48402.4	+	31106.3i	0.604358	+	0.388397i	0.806738	−	0.590910i	$-0.201231\pi$
$283$	48402.4	+	31106.3i	0.604358	+	0.388397i	−0.202380	+	0.979307i	$0.564868\pi$
$284$	30838.9	−	5943.70i	0.382350	−	0.0736920i
$285$	−96632.4	−	9227.28i	−1.18969	−	0.113601i
$286$	83150.5	−	59211.2i	1.01656	−	0.723889i
$287$	21783.2	−	11230.0i	0.264458	−	0.136338i
$288$	198742.	−	208435.i	2.39610	−	2.51296i
$289$	−48579.7	−	9362.98i	−0.581647	−	0.112103i
$290$	75691.8	+	22225.1i	0.900022	+	0.264270i
$291$	30734.4	−	126689.i	0.362943	−	1.49607i
$292$	−43802.1	−	95913.3i	−0.513723	−	1.12490i
$293$	−4011.24	+	27898.8i	−0.0467244	+	0.324975i	0.953031	+	0.302872i	$0.0979454\pi$
$293$	−4011.24	+	27898.8i	−0.0467244	+	0.324975i	−0.999756	+	0.0221034i	$0.992964\pi$
$294$	124580.	−	174948.i	1.44130	−	2.02402i
$295$	14649.0	+	12693.5i	0.168331	+	0.145860i
$296$	251.204	−	627.478i	0.00286711	−	0.00716169i
$297$	64138.3	+	111091.i	0.727118	+	1.25941i
$298$	−10858.6	−	6269.21i	−0.122276	−	0.0705960i
$299$	−67891.6	−	86331.1i	−0.759405	−	0.965662i
$300$	112527.	−	27298.8i	1.25030	−	0.303320i
$301$	−1004.39	+	21084.8i	−0.0110859	+	0.232721i
$302$	−158879.	−	7568.34i	−1.74202	−	0.0829825i
$303$	−18250.1	−	75228.1i	−0.198784	−	0.819398i
$304$	−85372.5	+	67137.7i	−0.923785	+	0.726472i
$305$	−34546.6	+	59836.4i	−0.371369	+	0.643229i
$306$	−179782.	+	103797.i	−1.92001	+	1.10852i
$307$	−101105.	−	40476.4i	−1.07275	−	0.429462i	−0.233019	−	0.972472i	$-0.574860\pi$
$307$	−101105.	−	40476.4i	−1.07275	−	0.429462i	−0.839726	+	0.543010i	$0.817285\pi$
$308$	−7652.83	+	8831.83i	−0.0806715	+	0.0930999i
$309$	−20055.0	−	14281.1i	−0.210042	−	0.149570i
$310$	−28203.3	−	4055.03i	−0.293479	−	0.0421959i
$311$	−46695.8	+	21325.3i	−0.482789	+	0.220482i	−0.641915	−	0.766776i	$-0.721860\pi$
$311$	−46695.8	+	21325.3i	−0.482789	+	0.220482i	0.159126	+	0.987258i	$0.449132\pi$
$312$	2991.82	+	725.807i	0.0307345	+	0.00745611i
$313$	−504.027	+	1716.56i	−0.00514476	+	0.0175215i	−0.962025	−	0.272960i	$-0.911997\pi$
$313$	−504.027	+	1716.56i	−0.00514476	+	0.0175215i	0.956881	+	0.290482i	$0.0938155\pi$
$314$	−23177.9	+	120258.i	−0.235079	+	1.21971i
$315$	−22540.0	−	21491.8i	−0.227160	−	0.216597i
$316$	53672.9	+	104111.i	0.537503	+	1.04261i
$317$	−55771.8	−	78320.5i	−0.555004	−	0.779394i	0.437809	−	0.899068i	$-0.355755\pi$
$317$	−55771.8	−	78320.5i	−0.555004	−	0.779394i	−0.992813	+	0.119674i	$0.961815\pi$
$318$	−13806.7	+	144591.i	−0.136533	+	1.42984i
$319$	12445.6	+	64574.1i	0.122303	+	0.634566i
$320$	−30039.5	+	46742.3i	−0.293354	+	0.456468i
$321$	−265246.	−	121134.i	−2.57418	−	1.17559i
$322$	19839.5	+	15601.9i	0.191346	+	0.150476i
$323$	72152.7	−	28885.6i	0.691588	−	0.276870i
$324$	88311.4	−	255159.i	0.841253	−	2.43064i
$325$	83836.3	+	87925.0i	0.793717	+	0.832426i
$326$	−6516.13	−	10139.3i	−0.0613133	−	0.0954053i
$327$	10956.5	+	76204.1i	0.102465	+	0.712661i
$328$	1264.69	+	651.995i	0.0117554	+	0.00606033i
$329$	−32579.4	+	11275.8i	−0.300990	+	0.104174i
$330$	−55222.5	−	63730.2i	−0.507094	−	0.585217i
$331$	9064.92	+	94932.1i	0.0827385	+	0.866477i	0.937622	+	0.347657i	$0.113023\pi$
$331$	9064.92	+	94932.1i	0.0827385	+	0.866477i	−0.854883	+	0.518820i	$0.826371\pi$
$332$	−145163.	+	42623.6i	−1.31698	+	0.386700i
$333$	−9720.76	−	204064.i	−0.0876620	−	1.84025i
$334$			85592.3i			0.767259i
$335$	58958.1	+	18521.4i	0.525357	+	0.165038i
$336$	−49011.2			−0.434127
$337$	30924.4	−	1473.11i	0.272296	−	0.0129711i	0.0890102	−	0.996031i	$-0.471630\pi$
$337$	30924.4	−	1473.11i	0.272296	−	0.0129711i	0.183286	+	0.983060i	$0.441327\pi$
$338$	−78374.6	−	266919.i	−0.686028	−	2.33640i
$339$	112732.	−	10764.6i	0.980950	−	0.0936694i
$340$	30492.2	−	26421.7i	0.263774	−	0.228561i
$341$	−7768.78	−	22446.4i	−0.0668104	−	0.193036i
$342$	−217144.	+	421200.i	−1.85650	+	3.60110i
$343$	−52518.3	+	7550.99i	−0.446398	+	0.0641823i
$344$	−1030.99	+	662.574i	−0.00871236	+	0.00559909i
$345$	−65664.2	+	62610.7i	−0.551684	+	0.526030i
$346$	275688.	+	95416.4i	2.30285	+	0.797023i
$347$	18678.4	+	46656.5i	0.155125	+	0.387483i	0.985489	−	0.169737i	$-0.0542920\pi$
$347$	18678.4	+	46656.5i	0.155125	+	0.387483i	−0.830364	+	0.557221i	$0.811868\pi$
$348$	166804.	−	212108.i	1.37736	−	1.75145i
$349$	64356.6	−	140921.i	0.528375	−	1.15698i	−0.437795	−	0.899075i	$-0.644241\pi$
$349$	64356.6	−	140921.i	0.528375	−	1.15698i	0.966170	−	0.257905i	$-0.0830322\pi$
$350$	−23486.8	−	15094.0i	−0.191729	−	0.123217i
$351$	542266.	−	104513.i	4.40147	−	0.848314i
$352$	−93241.8	−	8903.52i	−0.752533	−	0.0718582i
$353$	−90955.0	+	64768.8i	−0.729923	+	0.519776i	−0.883541	−	0.468354i	$-0.844847\pi$
$353$	−90955.0	+	64768.8i	−0.729923	+	0.519776i	0.153617	+	0.988130i	$0.450908\pi$
$354$	118297.	−	60986.3i	0.943990	−	0.486660i
$355$	18784.9	−	19701.0i	0.149057	−	0.156326i
$356$	−227652.	−	43876.3i	−1.79627	−	0.346202i
$357$	33651.4	+	9880.95i	0.264038	+	0.0775286i
$358$	−25820.3	+	106433.i	−0.201463	+	0.830442i
$359$	66460.0	+	145527.i	0.515670	+	1.12916i	0.971053	+	0.238864i	$0.0767749\pi$
$359$	66460.0	+	145527.i	0.515670	+	1.12916i	−0.455383	+	0.890295i	$0.650498\pi$
$360$	257.329	−	1789.76i	0.00198556	−	0.0138099i
$361$	27315.6	−	38359.4i	0.209602	−	0.294345i
$362$	−183271.	−	158805.i	−1.39854	−	1.21185i
$363$	−64967.3	+	162280.i	−0.493039	+	1.23155i
$364$	25155.2	+	43570.1i	0.189856	+	0.328841i
$365$	−79147.1	−	45695.6i	−0.594086	−	0.342996i
$366$	293262.	+	372914.i	2.18924	+	2.78385i
$367$	−38198.5	+	9266.85i	−0.283605	+	0.0688018i	−0.375038	−	0.927009i	$-0.622370\pi$
$367$	−38198.5	+	9266.85i	−0.283605	+	0.0688018i	0.0914332	+	0.995811i	$0.470855\pi$
$368$	−4830.18	+	101398.i	−0.0356671	+	0.748745i
$369$	429587.	+	20463.8i	3.15499	+	0.150291i
$370$	18790.8	+	77456.7i	0.137259	+	0.565790i
$371$	13713.9	−	10784.7i	0.0996352	−	0.0783540i
$372$	−48731.7	+	84405.8i	−0.352149	+	0.609939i
$373$	−178608.	+	103119.i	−1.28376	+	0.741177i	−0.977533	−	0.210783i	$-0.932399\pi$
$373$	−178608.	+	103119.i	−1.28376	+	0.741177i	−0.306223	+	0.951960i	$0.599065\pi$
$374$	62679.5	+	25093.1i	0.448108	+	0.179395i
$375$	160049.	−	184706.i	1.13812	−	1.31347i
$376$	−1630.45	−	1161.04i	−0.0115327	−	0.00821240i
$377$	280233.	+	40291.5i	1.97168	+	0.283485i
$378$	−115441.	+	52720.2i	−0.807937	+	0.368972i
$379$	−187279.	−	45433.3i	−1.30380	−	0.316298i	−0.477052	−	0.878875i	$-0.658295\pi$
$379$	−187279.	−	45433.3i	−1.30380	−	0.316298i	−0.826745	+	0.562577i	$0.809810\pi$
$380$	25947.7	−	88369.9i	0.179693	−	0.611980i
$381$	−73723.5	+	382514.i	−0.507874	+	2.63510i
$382$	182056.	+	173590.i	1.24761	+	1.18959i
$383$	15997.3	+	31030.5i	0.109056	+	0.211539i	0.937048	−	0.349201i	$-0.113547\pi$
$383$	15997.3	+	31030.5i	0.109056	+	0.211539i	−0.827992	+	0.560740i	$0.810517\pi$
$384$	−3277.28	−	4602.30i	−0.0222255	−	0.0312114i
$385$	−962.818	+	10083.1i	−0.00649565	+	0.0680255i
$386$	−25608.9	−	132871.i	−0.171876	−	0.891778i
$387$	−200269.	+	311625.i	−1.33719	+	2.08070i
$388$	112510.	+	51381.5i	0.747355	+	0.341305i
$389$	64852.2	+	51000.3i	0.428574	+	0.337034i	0.809033	−	0.587764i	$-0.199992\pi$
$389$	64852.2	+	51000.3i	0.428574	+	0.337034i	−0.380459	+	0.924798i	$0.624234\pi$
$390$	−337033.	+	134927.i	−2.21586	+	0.887097i
$391$	23758.9	−	68646.8i	0.155408	−	0.449021i
$392$	−1033.56	−	1083.97i	−0.00672613	−	0.00705416i
$393$	−208741.	−	324808.i	−1.35152	−	2.10301i
$394$	−36539.7	−	254139.i	−0.235381	−	1.63711i
$395$	90237.6	+	46520.7i	0.578354	+	0.298162i
$396$	−193798.	+	67074.1i	−1.23583	+	0.427725i
$397$	99313.5	+	114614.i	0.630126	+	0.727204i	0.977597	−	0.210487i	$-0.0675050\pi$
$397$	99313.5	+	114614.i	0.630126	+	0.727204i	−0.347471	+	0.937691i	$0.612960\pi$
$398$	−25444.6	−	266468.i	−0.160631	−	1.68221i
$399$	76816.5	−	22555.4i	0.482513	−	0.141678i
$400$	−5342.95	−	112162.i	−0.0333935	−	0.701015i
$401$			148474.i			0.923339i	0.887052	+	0.461669i	$0.152749\pi$
$401$			148474.i			0.923339i	−0.887052	+	0.461669i	$0.847251\pi$
$402$	268521.	−	328559.i	1.66160	−	2.03311i
$403$	−102259.			−0.629636
$404$	73362.5	−	3494.69i	0.449481	−	0.0214114i
$405$	−65933.6	−	224549.i	−0.401973	−	1.36899i
$406$	−64767.2	+	6184.51i	−0.392919	+	0.0375192i
$407$	−50214.1	+	43510.8i	−0.303136	+	0.262669i
$408$	665.984	+	1924.23i	0.00400077	+	0.0115595i
$409$	56388.0	−	109377.i	0.337086	−	0.653855i	−0.657984	−	0.753032i	$-0.728591\pi$
$409$	56388.0	−	109377.i	0.337086	−	0.653855i	0.995070	+	0.0991769i	$0.0316210\pi$
$410$	−166081.	+	23878.8i	−0.987988	+	0.142051i
$411$	473461.	−	304275.i	2.80286	−	1.80129i
$412$	16905.9	−	16119.7i	0.0995964	−	0.0949650i
$413$	−15107.1	−	5228.63i	−0.0885690	−	0.0306540i
$414$	164616.	+	411190.i	0.960440	+	2.39906i
$415$	−81059.7	+	103076.i	−0.470662	+	0.598495i
$416$	−167513.	+	366802.i	−0.967970	+	2.11956i
$417$	64339.2	+	41348.3i	0.370001	+	0.237785i
$418$	151334.	−	29167.2i	0.866132	−	0.166933i
$419$	−166319.	−	15881.5i	−0.947357	−	0.0904616i	−0.390073	−	0.920784i	$-0.627550\pi$
$419$	−166319.	−	15881.5i	−0.947357	−	0.0904616i	−0.557283	+	0.830322i	$0.688156\pi$
$420$	33855.0	−	24108.0i	0.191922	−	0.136667i
$421$	−33072.9	+	17050.2i	−0.186598	+	0.0961981i	−0.548994	−	0.835826i	$-0.684989\pi$
$421$	−33072.9	+	17050.2i	−0.186598	+	0.0961981i	0.362396	+	0.932024i	$0.381959\pi$
$422$	93522.6	−	98083.7i	0.525160	−	0.550772i
$423$	−594066.	−	114497.i	−3.32012	−	0.639901i
$424$	971.885	+	285.371i	0.00540609	+	0.00158737i
$425$	−18944.1	+	78088.7i	−0.104881	+	0.432325i
$426$	−77645.0	−	170019.i	−0.427853	−	0.936867i
$427$	8109.68	−	56404.1i	0.0444783	−	0.309353i
$428$	160481.	−	225364.i	0.876063	−	1.23026i
$429$	−228718.	−	198186.i	−1.24276	−	1.07686i
$430$	53712.2	−	134167.i	0.290493	−	0.725617i
$431$	92578.4	+	160351.i	0.498374	+	0.863209i	0.999998	−	0.00187663i	$-0.000597350\pi$
$431$	92578.4	+	160351.i	0.498374	+	0.863209i	−0.501624	+	0.865086i	$0.667264\pi$
$432$	−442048.	−	255216.i	−2.36865	−	1.36754i
$433$	−70837.5	−	90077.3i	−0.377822	−	0.480440i	0.559536	−	0.828806i	$-0.310979\pi$
$433$	−70837.5	−	90077.3i	−0.377822	−	0.480440i	−0.937359	+	0.348366i	$0.886737\pi$
$434$	22837.3	−	5540.26i	0.121245	−	0.0294138i
$435$	11128.6	−	233617.i	0.0588112	−	1.23460i
$436$	−72962.2	−	3475.62i	−0.383818	−	0.0182835i
$437$	−39093.7	−	161147.i	−0.204713	−	0.843837i
$438$	−493262.	+	387906.i	−2.57116	+	2.02198i
$439$	189903.	−	328921.i	0.985377	−	1.70672i	0.345128	−	0.938556i	$-0.387835\pi$
$439$	189903.	−	328921.i	0.985377	−	1.70672i	0.640249	−	0.768167i	$-0.278831\pi$
$440$	−509.283	+	294.035i	−0.00263059	+	0.00151877i
$441$	−420280.	−	168255.i	−2.16103	−	0.865147i
$442$	190344.	−	219669.i	0.974305	−	1.12441i
$443$	224382.	+	159782.i	1.14335	+	0.814178i	0.984889	−	0.173187i	$-0.0554063\pi$
$443$	224382.	+	159782.i	1.14335	+	0.814178i	0.158464	+	0.987365i	$0.449346\pi$
$444$	269856.	+	38799.4i	1.36888	+	0.196816i
$445$	−182788.	+	83476.6i	−0.923057	+	0.421546i
$446$	73982.2	+	17947.9i	0.371927	+	0.0902285i
$447$	−10473.0	+	35667.6i	−0.0524149	+	0.178509i
$448$	8672.43	−	44996.8i	0.0432100	−	0.224195i
$449$	−43424.5	−	41405.1i	−0.215398	−	0.205382i	0.574696	−	0.818367i	$-0.305120\pi$
$449$	−43424.5	−	41405.1i	−0.215398	−	0.205382i	−0.790095	+	0.612985i	$0.789969\pi$
$450$	−224502.	−	435473.i	−1.10865	−	2.15048i
$451$	−81134.3	−	113937.i	−0.398888	−	0.560160i
$452$	−10213.3	+	106958.i	−0.0499906	+	0.523525i
$453$	89245.7	+	463051.i	0.434901	+	2.25648i
$454$	−13604.0	+	21168.2i	−0.0660017	+	0.102701i
$455$	39665.7	+	18114.7i	0.191598	+	0.0875001i
$456$	3653.66	+	2873.27i	0.0175711	+	0.0138181i
$457$	−332176.	+	132983.i	−1.59051	+	0.636743i	−0.987015	−	0.160626i	$-0.948649\pi$
$457$	−332176.	+	132983.i	−1.59051	+	0.636743i	−0.603492	+	0.797369i	$0.706225\pi$
$458$	113404.	−	327659.i	0.540627	−	1.56204i
$459$	252060.	+	264353.i	1.19641	+	1.25475i
$460$	−46540.0	−	72417.7i	−0.219943	−	0.342239i
$461$	−8883.24	−	61784.3i	−0.0417993	−	0.290721i	−0.999989	−	0.00458857i	$-0.998539\pi$
$461$	−8883.24	−	61784.3i	−0.0417993	−	0.290721i	0.958190	−	0.286132i	$-0.0923697\pi$
$462$	61816.9	+	31868.8i	0.289616	+	0.149308i
$463$	96017.9	−	33232.1i	0.447910	−	0.155023i	−0.0937958	−	0.995591i	$-0.529900\pi$
$463$	96017.9	−	33232.1i	0.447910	−	0.155023i	0.541705	+	0.840568i	$0.317779\pi$
$464$	−171363.	−	197764.i	−0.795943	−	0.918567i
$465$	8029.95	+	84093.5i	0.0371370	+	0.388917i
$466$	166711.	−	48950.6i	0.767700	−	0.225417i
$467$	−13669.4	−	286956.i	−0.0626780	−	1.31577i	−0.782952	−	0.622083i	$-0.786287\pi$
$467$	−13669.4	−	286956.i	−0.0626780	−	1.31577i	0.720274	−	0.693690i	$-0.244016\pi$
$468$			882879.i			4.03097i
$469$	−50819.5	+	3891.04i	−0.231039	+	0.0176897i
$470$	236034.			1.06851
$471$	362688.	−	17276.9i	1.63490	−	0.0778798i
$472$	−261.487	−	890.545i	−0.00117373	−	0.00399735i
$473$	119929.	−	11451.8i	0.536046	−	0.0511862i
$474$	526824.	−	456496.i	2.34482	−	2.03180i
$475$	59992.2	+	173336.i	0.265893	+	0.768249i
$476$	−15247.9	+	29576.8i	−0.0672971	+	0.130538i
$477$	303047.	−	43571.5i	1.33190	−	0.191499i
$478$	379861.	−	244122.i	1.66253	−	1.06844i
$479$	−27653.2	+	26367.3i	−0.120524	+	0.114920i	−0.747945	−	0.663761i	$-0.768959\pi$
$479$	−27653.2	+	26367.3i	−0.120524	+	0.114920i	0.627420	+	0.778681i	$0.284111\pi$
$480$	314798.	+	108953.i	1.36631	+	0.472885i
$481$	106312.	+	265554.i	0.459506	+	1.14779i
$482$	−220975.	+	280993.i	−0.951151	+	1.20949i
$483$	31085.0	−	68066.6i	0.133247	−	0.291769i
$484$	−139522.	−	89665.1i	−0.595595	−	0.382765i
$485$	105268.	−	20288.7i	0.447520	−	0.0862524i
$486$	−698354.	−	66684.7i	−2.95667	−	0.282328i
$487$	−240517.	+	171271.i	−1.01411	+	0.722148i	−0.961031	−	0.276442i	$-0.910845\pi$
$487$	−240517.	+	171271.i	−1.01411	+	0.722148i	−0.0530844	+	0.998590i	$0.516905\pi$
$488$	2940.62	−	1516.00i	0.0123481	−	0.00636588i
$489$	−24658.7	+	25861.3i	−0.103122	+	0.108151i
$490$	173427.	+	33425.3i	0.722312	+	0.139214i
$491$	−373262.	−	109600.i	−1.54828	−	0.454617i	−0.607697	−	0.794169i	$-0.707906\pi$
$491$	−373262.	−	109600.i	−1.54828	−	0.454617i	−0.940587	+	0.339552i	$0.889725\pi$
$492$	−135310.	+	557754.i	−0.558983	+	2.30416i
$493$	77788.9	+	170334.i	0.320054	+	0.700822i
$494$	94426.0	−	656747.i	0.386935	−	2.69119i
$495$	−103105.	+	144790.i	−0.420793	+	0.590921i
$496$	71430.5	+	61894.8i	0.290349	+	0.251589i
$497$	−8344.06	+	20842.4i	−0.0337804	+	0.0843793i
$498$	450191.	+	779753.i	1.81526	+	3.14411i
$499$	215819.	+	124603.i	0.866739	+	0.500412i	0.866263	−	0.499588i	$-0.166515\pi$
$499$	215819.	+	124603.i	0.866739	+	0.500412i	0.000475607		1.00000i	$0.499849\pi$
$500$	143342.	+	182274.i	0.573366	+	0.729094i
$501$	246608.	−	59826.4i	0.982497	−	0.238351i
$502$	5638.50	−	118367.i	0.0223747	−	0.469702i
$503$	70938.4	+	3379.21i	0.280379	+	0.0133561i	0.187300	−	0.982303i	$-0.440026\pi$
$503$	70938.4	+	3379.21i	0.280379	+	0.0133561i	0.0930785	+	0.995659i	$0.470329\pi$
$504$	351.581	+	1449.24i	0.00138409	+	0.00570530i
$505$	50039.2	−	39351.2i	0.196213	−	0.154303i
$506$	72024.8	−	124751.i	0.281307	−	0.487239i
$507$	−714264.	+	412380.i	−2.77871	+	1.60429i
$508$	−343128.	−	137368.i	−1.32962	−	0.532301i
$509$	−170077.	+	196280.i	−0.656465	+	0.757600i	−0.982195	−	0.187862i	$-0.939844\pi$
$509$	−170077.	+	196280.i	−0.656465	+	0.757600i	0.325731	+	0.945463i	$0.394390\pi$
$510$	−195594.	−	139282.i	−0.751996	−	0.535494i
$511$	74607.1	+	10726.9i	0.285718	+	0.0410801i
$512$	336556.	−	153700.i	1.28386	−	0.586319i
$513$	810285.	+	196573.i	3.07895	+	0.746946i
$514$	−83556.9	+	284569.i	−0.316269	+	1.07711i
$515$	3831.68	−	19880.6i	0.0144469	−	0.0749577i
$516$	−357768.	−	341131.i	−1.34370	−	1.28121i
$517$	90162.4	+	174891.i	0.337322	+	0.654313i
$518$	−38130.0	−	53546.0i	−0.142104	−	0.199557i
$519$	82215.7	−	861002.i	0.305225	−	3.19646i
$520$	479.128	+	2485.95i	0.00177192	+	0.00919362i
$521$	−100059.	+	155695.i	−0.368622	+	0.573587i	−0.975169	−	0.221461i	$-0.928918\pi$
$521$	−100059.	+	155695.i	−0.368622	+	0.573587i	0.606548	+	0.795047i	$0.292554\pi$
$522$	−1.03857e6	−	474299.i	−3.81149	−	1.74065i
$523$	−375831.	−	295557.i	−1.37401	−	1.08053i	−0.987393	−	0.158289i	$-0.949402\pi$
$523$	−375831.	−	295557.i	−1.37401	−	1.08053i	−0.386614	−	0.922242i	$-0.626355\pi$
$524$	340086.	−	136150.i	1.23858	−	0.495854i
$525$	−27072.2	+	78220.1i	−0.0982212	+	0.283792i
$526$	−353057.	−	370276.i	−1.27607	−	1.33830i
$527$	−36566.3	−	56898.2i	−0.131662	−	0.204870i
$528$	39808.8	+	276876.i	0.142794	+	0.993157i
$529$	110975.	+	57211.5i	0.396564	+	0.204443i
$530$	−112877.	+	39067.0i	−0.401839	+	0.139078i
$531$	−183714.	−	212017.i	−0.651558	−	0.751938i
$532$	7220.39	+	75615.4i	0.0255116	+	0.267169i
$533$	−577777.	+	169651.i	−2.03379	+	0.597174i
$534$	65651.7	+	1.37820e6i	0.230231	+	4.83314i
$535$		−	239797.i		−	0.837792i
$536$	−1895.47	−	2272.36i	−0.00659763	−	0.00790947i
$537$	324701.			1.12599
$538$	7942.69	−	378.357i	0.0274412	−	0.00130719i
$539$	41480.6	+	141270.i	0.142780	+	0.486265i
$540$	430887.	−	41144.8i	1.47767	−	0.141100i
$541$	−131108.	+	113605.i	−0.447954	+	0.388154i	−0.849418	−	0.527720i	$-0.823047\pi$
$541$	−131108.	+	113605.i	−0.447954	+	0.388154i	0.401464	+	0.915875i	$0.368501\pi$
$542$	12231.9	+	35341.7i	0.0416385	+	0.120306i
$543$	−329447.	+	639038.i	−1.11734	+	2.16734i
$544$	−263995.	+	37956.8i	−0.892068	+	0.128260i
$545$	−53260.9	+	34228.7i	−0.179315	+	0.115238i
$546$	216695.	−	206618.i	0.726882	−	0.693081i
$547$	−343300.	−	118817.i	−1.14736	−	0.397104i	−0.313774	−	0.949498i	$-0.601593\pi$
$547$	−343300.	−	118817.i	−1.14736	−	0.397104i	−0.833583	+	0.552394i	$0.813715\pi$
$548$	198461.	+	495731.i	0.660866	+	1.65076i
$549$	618155.	−	786048.i	2.05094	−	2.60798i
$550$	−66193.0	+	144943.i	−0.218820	+	0.479149i
$551$	359595.	+	231098.i	1.18443	+	0.761188i
$552$	4265.92	−	822.188i	0.0140002	−	0.00269832i
$553$	−83351.6	−	7959.12i	−0.272561	−	0.0260264i
$554$	−409732.	+	291769.i	−1.33500	+	0.950647i
$555$	210033.	−	108280.i	0.681871	−	0.351529i
$556$	−50074.4	+	52516.5i	−0.161982	+	0.169882i
$557$	281220.	+	54200.7i	0.906433	+	0.174701i	0.621103	−	0.783729i	$-0.286685\pi$
$557$	281220.	+	54200.7i	0.906433	+	0.174701i	0.285330	+	0.958429i	$0.407897\pi$
$558$	395683.	+	116183.i	1.27081	+	0.373142i
$559$	122278.	−	504037.i	0.391313	−	1.61302i
$560$	−16743.2	−	36662.4i	−0.0533902	−	0.116908i
$561$	28486.9	−	198131.i	0.0905149	−	0.629545i
$562$	8857.17	−	12438.2i	0.0280429	−	0.0393807i
$563$	104042.	+	90152.8i	0.328240	+	0.284421i	0.803353	−	0.595503i	$-0.203047\pi$
$563$	104042.	+	90152.8i	0.328240	+	0.284421i	−0.475113	+	0.879925i	$0.657593\pi$
$564$	300069.	−	749536.i	0.943328	−	2.35632i
$565$	46563.7	+	80650.6i	0.145865	+	0.252645i
$566$	281353.	+	162439.i	0.878252	+	0.507059i
$567$	119313.	+	151719.i	0.371127	+	0.471927i
$568$	−1266.70	+	307.299i	−0.00392625	+	0.000952498i
$569$	1447.12	−	30378.8i	0.00446972	−	0.0938311i	−0.995530	−	0.0944449i	$-0.969892\pi$
$569$	1447.12	−	30378.8i	0.00446972	−	0.0938311i	1.00000		0.000613866i	$0.000195400\pi$
$570$	−547499.	−	26080.6i	−1.68513	−	0.0802726i
$571$	109520.	+	451449.i	0.335909	+	1.38464i	0.849946	+	0.526869i	$0.176634\pi$
$571$	109520.	+	451449.i	0.335909	+	1.38464i	−0.514037	+	0.857768i	$0.671851\pi$
$572$	225706.	−	177497.i	0.689844	−	0.542500i
$573$	372895.	−	645873.i	1.13574	−	1.96715i
$574$	119843.	−	69191.2i	0.363737	−	0.210004i
$575$	159160.	+	63717.9i	0.481390	+	0.192719i
$576$	526617.	−	607748.i	1.58727	−	1.83180i
$577$	−278392.	−	198242.i	−0.836191	−	0.595449i	0.0797259	−	0.996817i	$-0.474595\pi$
$577$	−278392.	−	198242.i	−0.836191	−	0.595449i	−0.915917	+	0.401368i	$0.868535\pi$
$578$	−276512.	−	39756.4i	−0.827671	−	0.119001i
$579$	−364928.	+	166657.i	−1.08855	+	0.497126i
$580$	215649.	+	52315.9i	0.641049	+	0.155517i
$581$	30469.2	−	103768.i	0.0902627	−	0.307407i
$582$	139308.	−	722799.i	0.411273	−	2.13389i
$583$	−72064.6	−	68713.4i	−0.212024	−	0.202164i
$584$	2005.25	+	3889.63i	0.00587952	+	0.0114047i
$585$	443878.	+	623339.i	1.29703	+	1.82143i
$586$	−15128.3	+	158431.i	−0.0440549	+	0.461364i
$587$	51360.7	+	266484.i	0.149058	+	0.773385i	0.977110	+	0.212734i	$0.0682369\pi$
$587$	51360.7	+	266484.i	0.149058	+	0.773385i	−0.828052	+	0.560651i	$0.810551\pi$
$588$	326621.	−	508232.i	0.944691	−	1.46997i
$589$	−140439.	−	64136.5i	−0.404816	−	0.184873i
$590$	86032.8	+	67657.0i	0.247150	+	0.194361i
$591$	−706683.	+	282913.i	−2.02325	+	0.809987i
$592$	86472.3	−	249845.i	0.246737	−	0.712898i
$593$	310759.	+	325915.i	0.883720	+	0.926819i	0.997776	−	0.0666553i	$-0.0212328\pi$
$593$	310759.	+	325915.i	0.883720	+	0.926819i	−0.114056	+	0.993474i	$0.536384\pi$
$594$	391596.	+	609335.i	1.10985	+	1.72696i
$595$	4104.61	+	28548.2i	0.0115941	+	0.0806389i
$596$	−31348.9	−	16161.5i	−0.0882530	−	0.0454976i
$597$	−749960.	+	259564.i	−2.10421	+	0.728275i
$598$	−406112.	−	468678.i	−1.13565	−	1.31061i
$599$	−14938.1	−	156438.i	−0.0416333	−	0.436003i	−0.992125	−	0.125253i	$-0.960026\pi$
$599$	−14938.1	−	156438.i	−0.0416333	−	0.436003i	0.950492	−	0.310750i	$-0.100580\pi$
$600$	−4610.97	+	1353.90i	−0.0128082	+	0.00376084i
$601$	11004.0	+	231002.i	0.0304650	+	0.639538i	0.961533	+	0.274691i	$0.0885756\pi$
$601$	11004.0	+	231002.i	0.0304650	+	0.639538i	−0.931068	+	0.364847i	$0.881121\pi$
$602$			119191.i			0.328889i
$603$	−806474.	−	386772.i	−2.21797	−	1.06370i
$604$	−447422.			−1.22643
$605$	−143587.	+	6839.87i	−0.392286	+	0.0186869i
$606$	−123145.	−	419393.i	−0.335329	−	1.14203i
$607$	−68616.6	+	6552.09i	−0.186231	+	0.0177829i	−0.187755	−	0.982216i	$-0.560121\pi$
$607$	−68616.6	+	6552.09i	−0.186231	+	0.0177829i	0.00152378	+	0.999999i	$0.499515\pi$
$608$	−460117.	+	398693.i	−1.24469	+	1.07853i
$609$	63089.0	+	182284.i	0.170106	+	0.491488i
$610$	−178771.	+	346767.i	−0.480437	+	0.931918i
$611$	838468.	−	120554.i	2.24597	−	0.322922i
$612$	−491248.	+	315706.i	−1.31159	+	0.842907i
$613$	−3934.38	+	3751.42i	−0.0104702	+	0.00998332i	−0.695296	−	0.718723i	$-0.744727\pi$
$613$	−3934.38	+	3751.42i	−0.0104702	+	0.00998332i	0.684826	+	0.728707i	$0.259878\pi$
$614$	−581121.	−	201128.i	−1.54145	−	0.533502i
$615$	184885.	+	461820.i	0.488822	+	1.22102i
$616$	299.811	−	381.241i	0.000790107	−	0.00100470i
$617$	163372.	−	357734.i	0.429148	−	0.939703i	−0.564316	−	0.825559i	$-0.690860\pi$
$617$	163372.	−	357734.i	0.429148	−	0.939703i	0.993464	−	0.114144i	$-0.0364125\pi$
$618$	−116950.	−	75159.0i	−0.306212	−	0.196790i
$619$	397493.	−	76610.6i	1.03741	−	0.199944i	0.358012	−	0.933717i	$-0.383455\pi$
$619$	397493.	−	76610.6i	1.03741	−	0.199944i	0.679394	+	0.733774i	$0.262243\pi$
$620$	−79786.8	−	7618.71i	−0.207562	−	0.0198197i
$621$	634809.	−	452045.i	1.64611	−	1.17219i
$622$	−257641.	+	132823.i	−0.665939	+	0.343315i
$623$	114367.	−	119944.i	0.294662	−	0.309033i
$624$	1.18248e6	+	227904.i	3.03686	+	0.585306i
$625$	−68304.6	−	20056.0i	−0.174860	−	0.0513435i
$626$	−2381.59	+	9817.04i	−0.00607740	+	0.0250514i
$627$	−189814.	−	415635.i	−0.482829	−	1.05725i
$628$	−49027.9	+	340997.i	−0.124315	+	0.864631i
$629$	−109743.	+	154112.i	−0.277380	+	0.389525i
$630$	−132903.	−	115161.i	−0.334852	−	0.290151i
$631$	1623.41	−	4055.08i	0.00407727	−	0.0101845i	−0.926315	−	0.376749i	$-0.877042\pi$
$631$	1623.41	−	4055.08i	0.00407727	−	0.0101845i	0.930393	+	0.366565i	$0.119466\pi$
$632$	−2430.63	−	4209.98i	−0.00608534	−	0.0105401i
$633$	−347967.	−	200899.i	−0.868422	−	0.501384i
$634$	−335603.	−	426754.i	−0.834924	−	1.06169i
$635$	−311322.	+	75525.8i	−0.772079	+	0.187304i
$636$	−19440.7	+	408110.i	−0.0480615	+	1.00894i
$637$	633142.	+	30160.3i	1.56035	+	0.0743286i
$638$	87544.3	+	360863.i	0.215073	+	0.886544i
$639$	−309688.	+	243541.i	−0.758442	+	0.596446i
$640$	2323.13	−	4023.78i	0.00567170	−	0.00982368i
$641$	461218.	−	266284.i	1.12251	−	0.648081i	0.180469	−	0.983581i	$-0.442239\pi$
$641$	461218.	−	266284.i	1.12251	−	0.648081i	0.942040	+	0.335500i	$0.108905\pi$
$642$	−1.52857e6	−	611947.i	−3.70864	−	1.48472i
$643$	−54291.4	+	62655.7i	−0.131314	+	0.151544i	−0.817598	−	0.575789i	$-0.804695\pi$
$643$	−54291.4	+	62655.7i	−0.131314	+	0.151544i	0.686285	+	0.727333i	$0.259240\pi$
$644$	57832.0	+	41182.0i	0.139443	+	0.0992969i
$645$	−424102.	−	60976.7i	−1.01942	−	0.146570i
$646$	399190.	−	182304.i	0.956565	−	0.436849i
$647$	−132230.	−	32078.6i	−0.315879	−	0.0766315i	0.0746849	−	0.997207i	$-0.476205\pi$
$647$	−132230.	−	32078.6i	−0.315879	−	0.0766315i	−0.390564	+	0.920576i	$0.627720\pi$
$648$	−3157.11	+	10752.1i	−0.00751865	+	0.0256062i
$649$	−17267.2	+	89590.8i	−0.0409952	+	0.212703i
$650$	496471.	+	473384.i	1.17508	+	1.12044i
$651$	−31925.1	−	61926.1i	−0.0753304	−	0.146121i
$652$	−19665.7	−	27616.6i	−0.0462610	−	0.0649644i
$653$	44221.8	−	463112.i	0.103708	−	1.08607i	−0.782457	−	0.622704i	$-0.786034\pi$
$653$	44221.8	−	463112.i	0.103708	−	1.08607i	0.886165	−	0.463370i	$-0.153360\pi$
$654$	82270.1	+	426858.i	0.192347	+	0.997993i
$655$	171660.	−	267108.i	0.400116	−	0.622592i
$656$	506279.	+	231210.i	1.17647	+	0.537278i
$657$	1.03973e6	+	817649.i	2.40873	+	1.89425i
$658$	−180723.	+	72350.4i	−0.417408	+	0.167105i
$659$	108616.	−	313824.i	0.250104	−	0.722629i	−0.748148	−	0.663532i	$-0.769057\pi$
$659$	108616.	−	313824.i	0.250104	−	0.722629i	0.998252	−	0.0590969i	$-0.0188221\pi$
$660$	−163691.	−	171674.i	−0.375782	−	0.394109i
$661$	−204861.	−	318770.i	−0.468874	−	0.729582i	0.523610	−	0.851958i	$-0.324585\pi$
$661$	−204861.	−	318770.i	−0.468874	−	0.729582i	−0.992484	+	0.122376i	$0.960949\pi$
$662$	76633.0	+	532994.i	0.174864	+	1.21620i
$663$	−765952.	−	394876.i	−1.74251	−	0.898325i
$664$	5933.62	−	2053.65i	0.0134581	−	0.00465790i
$665$	43114.3	+	49756.6i	0.0974941	+	0.112514i
$666$	−109653.	−	1.14833e6i	−0.247213	−	2.58893i
$667$	383340.	−	112559.i	0.861653	−	0.253004i
$668$	11456.1	+	240492.i	0.0256733	+	0.538949i
$669$		−	225702.i		−	0.504293i
$670$	337508.	+	88622.5i	0.751855	+	0.197421i
$671$	−325228.			−0.722341
$672$	−274427.	+	13072.6i	−0.607699	+	0.0289483i
$673$	7652.47	+	26061.9i	0.0168955	+	0.0575409i	0.967509	−	0.252835i	$-0.0813631\pi$
$673$	7652.47	+	26061.9i	0.0168955	+	0.0575409i	−0.950614	+	0.310376i	$0.899545\pi$
$674$	174022.	−	16617.1i	0.383075	−	0.0365792i
$675$	−651489.	+	564519.i	−1.42988	+	1.23900i
$676$	−255938.	−	739484.i	−0.560069	−	1.61821i
$677$	88056.3	−	170805.i	0.192125	−	0.372670i	−0.773022	−	0.634379i	$-0.781256\pi$
$677$	88056.3	−	170805.i	0.192125	−	0.372670i	0.965147	+	0.261709i	$0.0842861\pi$
$678$	632930.	−	91001.5i	1.37688	−	0.197965i
$679$	−74380.9	+	47801.7i	−0.161333	+	0.103682i
$680$	−1211.89	+	1155.54i	−0.00262088	+	0.00249900i
$681$	70498.5	+	24399.8i	0.152015	+	0.0526128i
$682$	−49847.7	−	124513.i	−0.107171	−	0.267699i
$683$	334700.	−	425605.i	0.717487	−	0.912359i	−0.281397	−	0.959591i	$-0.590798\pi$
$683$	334700.	−	425605.i	0.717487	−	0.912359i	0.998884	+	0.0472324i	$0.0150401\pi$
$684$	−553741.	+	1.21252e6i	−1.18357	+	2.59166i
$685$	389354.	+	250222.i	0.829780	+	0.533267i
$686$	−294181.	+	56698.8i	−0.625125	+	0.120483i
$687$	−1.02332e6	−	97714.7i	−2.16818	−	0.207036i
$688$	−390497.	+	278072.i	−0.824975	+	0.587462i
$689$	−381021.	+	196430.i	−0.802621	+	0.413780i
$690$	−353533.	+	370774.i	−0.742560	+	0.778774i
$691$	486975.	+	93856.8i	1.01988	+	0.196566i	0.671671	−	0.740849i	$-0.265577\pi$
$691$	486975.	+	93856.8i	1.01988	+	0.196566i	0.348212	+	0.937416i	$0.386789\pi$
$692$	787382.	+	231196.i	1.64427	+	0.482801i
$693$	34561.7	−	142465.i	0.0719662	−	0.296649i
$694$	117884.	+	258130.i	0.244758	+	0.535945i
$695$	−8950.73	+	62253.7i	−0.0185306	+	0.128883i
$696$	−6496.07	+	9122.45i	−0.0134101	+	0.0188318i
$697$	−301002.	−	260819.i	−0.619588	−	0.536876i
$698$	325118.	−	812105.i	0.667314	−	1.66687i
$699$	−257562.	−	446110.i	−0.527141	−	0.913035i
$700$	−68011.9	−	39266.7i	−0.138800	−	0.0801361i
$701$	113639.	+	144504.i	0.231256	+	0.294065i	0.887807	−	0.460216i	$-0.152228\pi$
$701$	113639.	+	144504.i	0.231256	+	0.294065i	−0.656552	+	0.754281i	$0.727986\pi$
$702$	3.03037e6	−	735160.i	6.14924	−	1.49179i
$703$	−20549.4	+	431384.i	−0.0415803	+	0.872878i
$704$	−261242.	−	12444.5i	−0.527107	−	0.0251092i
$705$	−164980.	−	680058.i	−0.331935	−	1.36826i
$706$	−495597.	+	389741.i	−0.994303	+	0.781929i
$707$	−26251.1	+	45468.2i	−0.0525180	+	0.0909638i
$708$	324221.	−	187189.i	0.646807	−	0.373434i
$709$	771874.	+	309012.i	1.53551	+	0.614727i	0.976708	−	0.214571i	$-0.0688354\pi$
$709$	771874.	+	309012.i	1.53551	+	0.614727i	0.558806	+	0.829298i	$0.311260\pi$
$710$	100656.	−	116163.i	0.199675	−	0.230437i
$711$	−1.19691e6	−	852314.i	−2.36767	−	1.68601i
$712$	9524.07	+	1369.35i	0.0187872	+	0.00270119i
$713$	−131264.	+	59946.1i	−0.258205	+	0.117918i
$714$	192453.	+	46688.6i	0.377510	+	0.0915830i
$715$	70116.4	−	238795.i	0.137154	−	0.467103i
$716$	−58302.9	+	302504.i	−0.113727	+	0.590073i
$717$	−968872.	−	923817.i	−1.88464	−	1.79700i
$718$	413942.	+	802936.i	0.802955	+	1.55751i
$719$	−159485.	−	223965.i	−0.308505	−	0.433234i	0.630993	−	0.775788i	$-0.282647\pi$
$719$	−159485.	−	223965.i	−0.308505	−	0.433234i	−0.939498	+	0.342554i	$0.888708\pi$
$720$	67232.4	−	704090.i	0.129692	−	1.35820i
$721$	3160.15	+	16396.4i	0.00607907	+	0.0315412i
$722$	143757.	−	223691.i	0.275776	−	0.429115i
$723$	964048.	+	440266.i	1.84426	+	0.842245i
$724$	−536199.	−	421671.i	−1.02294	−	0.804446i
$725$	−410280.	+	164251.i	−0.780556	+	0.312487i
$726$	−322824.	+	932738.i	−0.612481	+	1.76965i
$727$	4002.35	+	4197.55i	0.00757263	+	0.00794194i	0.727509	−	0.686098i	$-0.240678\pi$
$727$	4002.35	+	4197.55i	0.00757263	+	0.00794194i	−0.719937	+	0.694040i	$0.755829\pi$
$728$	−1128.86	−	1756.54i	−0.00212999	−	0.00331433i
$729$	100033.	+	695747.i	0.188230	+	1.30917i
$730$	−458677.	−	236464.i	−0.860719	−	0.443731i
$731$	324179.	−	112199.i	0.606666	−	0.209969i
$732$	873903.	+	1.00854e6i	1.63095	+	1.88222i
$733$	−1284.10	−	13447.7i	−0.00238996	−	0.0250288i	0.994198	−	0.107563i	$-0.0343047\pi$
$733$	−1284.10	−	13447.7i	−0.00238996	−	0.0250288i	−0.996588	+	0.0825341i	$0.973699\pi$
$734$	−212955.	+	62529.1i	−0.395271	+	0.116062i
$735$	−24915.5	−	523040.i	−0.0461205	−	0.968189i
$736$			569044.i			1.05049i
$737$	63259.1	+	283931.i	0.116463	+	0.522731i
$738$	2.42843e6			4.45874
$739$	−600717.	+	28615.7i	−1.09997	+	0.0523980i	−0.589705	−	0.807619i	$-0.700756\pi$
$739$	−600717.	+	28615.7i	−1.09997	+	0.0523980i	−0.510265	+	0.860017i	$0.670453\pi$
$740$	63164.4	+	215118.i	0.115348	+	0.392838i
$741$	−1.95821e6	+	186987.i	−3.56635	+	0.340545i
$742$	74450.6	−	64511.8i	0.135226	−	0.117174i
$743$	−140418.	−	405711.i	−0.254358	−	0.734919i	−0.997811	−	0.0661307i	$-0.978935\pi$
$743$	−140418.	−	405711.i	−0.254358	−	0.734919i	0.743453	−	0.668788i	$-0.233187\pi$
$744$	1853.52	−	3595.32i	0.00334850	−	0.00649519i
$745$	−30258.6	+	4350.53i	−0.0545176	+	0.00783845i
$746$	−979665.	+	629592.i	−1.76035	+	1.13131i
$747$	1.37356e6	−	1.30968e6i	2.46153	−	2.34706i
$748$	179472.	+	62115.8i	0.320769	+	0.111019i
$749$	73504.0	+	183604.i	0.131023	+	0.327280i
$750$	853070.	−	1.08477e6i	1.51657	−	1.92848i
$751$	−58353.1	+	127775.i	−0.103463	+	0.226552i	−0.954283	−	0.298906i	$-0.903378\pi$
$751$	−58353.1	+	127775.i	−0.103463	+	0.226552i	0.850820	+	0.525457i	$0.176106\pi$
$752$	−658662.	−	423296.i	−1.16473	−	0.748530i
$753$	−344978.	+	66489.1i	−0.608418	+	0.117263i
$754$	1.59138e6	+	151958.i	2.79918	+	0.267289i
$755$	−315893.	+	224946.i	−0.554174	+	0.394625i
$756$	−317303.	+	163581.i	−0.555177	+	0.286213i
$757$	−82603.2	+	86631.7i	−0.144147	+	0.151177i	−0.791849	−	0.610717i	$-0.790881\pi$
$757$	−82603.2	+	86631.7i	−0.144147	+	0.151177i	0.647703	+	0.761893i	$0.275730\pi$
$758$	−1.06848e6	−	205933.i	−1.85964	−	0.358416i
$759$	−409774.	−	120320.i	−0.711312	−	0.208860i
$760$	−901.166	+	3714.66i	−0.00156019	+	0.00643119i
$761$	335327.	+	734263.i	0.579027	+	1.26789i	0.941850	+	0.336034i	$0.109086\pi$
$761$	335327.	+	734263.i	0.579027	+	1.26789i	−0.362823	+	0.931858i	$0.618187\pi$
$762$	−313039.	+	2.17724e6i	−0.539124	+	3.74969i
$763$	30288.0	−	42533.6i	0.0520262	−	0.0730605i
$764$	534765.	+	463376.i	0.916170	+	0.793866i
$765$	−188111.	+	469878.i	−0.321434	+	0.802902i
$766$	98564.0	+	170718.i	0.167981	+	0.290952i
$767$	340172.	+	196398.i	0.578240	+	0.333847i
$768$	−687978.	−	874835.i	−1.16641	−	1.48321i
$769$	−267990.	+	65013.7i	−0.453175	+	0.109939i	−0.455849	−	0.890057i	$-0.650664\pi$
$769$	−267990.	+	65013.7i	−0.453175	+	0.109939i	0.00267332	+	0.999996i	$0.499149\pi$
$770$	−2721.37	+	57128.6i	−0.00458993	+	0.0963545i
$771$	878300.	+	41838.6i	1.47752	+	0.0703831i
$772$	−89738.3	−	369906.i	−0.150572	−	0.620665i
$773$	365795.	−	287665.i	0.612180	−	0.481424i	−0.263277	−	0.964720i	$-0.584803\pi$
$773$	365795.	−	287665.i	0.612180	−	0.481424i	0.875457	+	0.483297i	$0.160561\pi$
$774$	−1.04582e6	+	1.81141e6i	−1.74572	+	3.02368i
$775$	138238.	−	79811.7i	0.230157	−	0.132881i
$776$	−4765.62	−	1907.86i	−0.00791399	−	0.00316828i
$777$	−127625.	+	147287.i	−0.211394	+	0.243961i
$778$	379477.	+	270224.i	0.626941	+	0.446442i
$779$	−899909.	−	129387.i	−1.48294	−	0.213215i
$780$	−928914.	+	424221.i	−1.52682	+	0.697273i
$781$	124522.	+	30208.6i	0.204147	+	0.0495255i
$782$	115560.	−	393560.i	0.188970	−	0.643573i
$783$	−380187.	+	1.97260e6i	−0.620118	+	3.21748i
$784$	−424012.	−	404295.i	−0.689836	−	0.657758i
$785$	136825.	+	265403.i	0.222037	+	0.430692i
$786$	−1.26460e6	−	1.77588e6i	−2.04695	−	2.87453i
$787$	11875.3	−	124363.i	0.0191731	−	0.200790i	−0.980810	−	0.194967i	$-0.937540\pi$
$787$	11875.3	−	124363.i	0.0191731	−	0.200790i	0.999983	−	0.00582375i	$-0.00185377\pi$
$788$	−136682.	−	709174.i	−0.220120	−	1.14209i
$789$	−820058.	+	1.27604e6i	−1.31732	+	2.04979i
$790$	521451.	+	238139.i	0.835525	+	0.381571i
$791$	−60373.7	−	47478.4i	−0.0964928	−	0.0758827i
$792$	7901.53	−	3163.30i	0.0125968	−	0.00504300i
$793$	−457942.	+	1.32314e6i	−0.728222	+	2.10406i
$794$	590934.	+	619754.i	0.937342	+	0.983056i
$795$	191456.	+	297912.i	0.302926	+	0.471361i
$796$	−107158.	−	745300.i	−0.169121	−	1.17627i
$797$	496755.	+	256095.i	0.782034	+	0.403167i	0.802521	−	0.596624i	$-0.203491\pi$
$797$	496755.	+	256095.i	0.782034	+	0.403167i	−0.0204872	+	0.999790i	$0.506522\pi$
$798$	427195.	−	147854.i	0.670842	−	0.232181i
$799$	366903.	+	423429.i	0.574722	+	0.663264i
$800$	−59833.3	−	626603.i	−0.0934896	−	0.979067i
$801$	2.79053e6	−	819374.i	4.34933	−	1.27708i
$802$	39890.8	+	837411.i	0.0620189	+	1.30194i
$803$		−	430187.i		−	0.667154i
$804$	710497.	−	959106.i	1.09913	−	1.48373i
$805$	61535.8			0.0949591
$806$	−576751.	+	27474.0i	−0.887807	+	0.0422915i
$807$	−6641.81	−	22619.9i	−0.0101986	−	0.0347332i
$808$	−3034.38	+	289.748i	−0.00464780	+	0.000443811i
$809$	−253770.	+	219893.i	−0.387742	+	0.335981i	−0.826818	−	0.562469i	$-0.809851\pi$
$809$	−253770.	+	219893.i	−0.387742	+	0.335981i	0.439076	+	0.898450i	$0.355306\pi$
$810$	−432205.	−	1.24877e6i	−0.658748	−	1.90333i
$811$	466383.	−	904657.i	0.709090	−	1.37544i	−0.208543	−	0.978013i	$-0.566872\pi$
$811$	466383.	−	904657.i	0.709090	−	1.37544i	0.917633	−	0.397429i	$-0.130098\pi$
$812$	−181151.	+	26045.6i	−0.274744	+	0.0395023i
$813$	93276.4	−	59945.1i	0.141121	−	0.0906928i
$814$	−271524.	+	258898.i	−0.409788	+	0.390733i
$815$	−27769.2	−	9611.00i	−0.0418069	−	0.0144695i
$816$	296029.	+	739446.i	0.444585	+	1.11052i
$817$	484065.	−	615539.i	0.725203	−	0.922171i
$818$	288649.	−	632053.i	0.431383	−	0.944598i
$819$	−530931.	−	341209.i	−0.791536	−	0.508689i
$820$	−463448.	+	89322.2i	−0.689244	+	0.132841i
$821$	−234872.	−	22427.6i	−0.348454	−	0.0332733i	−0.0806382	−	0.996743i	$-0.525696\pi$
$821$	−234872.	−	22427.6i	−0.348454	−	0.0332733i	−0.267816	+	0.963470i	$0.586302\pi$
$822$	2.58863e6	−	1.84336e6i	3.83113	−	2.72813i
$823$	512119.	−	264015.i	0.756085	−	0.389789i	−0.0366713	−	0.999327i	$-0.511675\pi$
$823$	512119.	−	264015.i	0.756085	−	0.389789i	0.792757	+	0.609538i	$0.208645\pi$
$824$	−669.009	+	701.637i	−0.000985321	+	0.00103338i
$825$	463874.	+	89404.3i	0.681541	+	0.131356i
$826$	−86610.9	−	25431.3i	−0.126944	−	0.0372742i
$827$	103125.	−	425085.i	0.150783	−	0.621534i	−0.845392	−	0.534147i	$-0.820633\pi$
$827$	103125.	−	425085.i	0.150783	−	0.621534i	0.996174	−	0.0873875i	$-0.0278518\pi$
$828$	517562.	+	1.13330e6i	0.754922	+	1.65305i
$829$	75726.2	−	526687.i	0.110189	−	0.766379i	−0.857546	−	0.514407i	$-0.828012\pi$
$829$	75726.2	−	526687.i	0.110189	−	0.766379i	0.967735	−	0.251972i	$-0.0810790\pi$
$830$	−429494.	+	603140.i	−0.623449	+	0.875511i
$831$	1.12703e6	+	976578.i	1.63205	+	1.41418i
$832$	−418475.	+	1.04530e6i	−0.604537	+	1.51006i
$833$	209621.	+	363075.i	0.302096	+	0.523246i
$834$	373990.	+	215923.i	0.537686	+	0.310433i
$835$	128999.	+	164035.i	0.185017	+	0.235268i
$836$	421305.	−	102208.i	0.602816	−	0.146241i
$837$	34525.3	−	724775.i	0.0492818	−	1.03455i
$838$	−942327.	−	44888.6i	−1.34188	−	0.0639216i
$839$	−194907.	−	803419.i	−0.276888	−	1.14135i	−0.925050	−	0.379846i	$-0.875977\pi$
$839$	−194907.	−	803419.i	−0.276888	−	1.14135i	0.648162	−	0.761503i	$-0.275538\pi$
$840$	−1355.87	+	1066.27i	−0.00192158	+	0.00151115i
$841$	−161303.	+	279385.i	−0.228061	+	0.395013i
$842$	−181954.	+	105051.i	−0.256648	+	0.148176i
$843$	−42027.6	−	16825.3i	−0.0591397	−	0.0236760i
$844$	249646.	−	288107.i	0.350461	−	0.404454i
$845$	−552484.	−	393422.i	−0.773760	−	0.550992i
$846$	−3.38137e6	−	486168.i	−4.72446	−	0.679275i
$847$	107843.	−	49250.1i	0.150322	−	0.0686499i
$848$	385049.	+	93411.8i	0.535456	+	0.129900i
$849$	271362.	−	924172.i	0.376472	−	1.28215i
$850$	−85866.9	+	445520.i	−0.118847	+	0.616637i
$851$	292140.	+	278555.i	0.403396	+	0.384638i
$852$	−240918.	−	467316.i	−0.331887	−	0.643771i
$853$	−675677.	−	948856.i	−0.928627	−	1.30407i	−0.952557	−	0.304360i	$-0.901557\pi$
$853$	−675677.	−	948856.i	−0.928627	−	1.30407i	0.0239305	−	0.999714i	$-0.492382\pi$
$854$	30585.4	−	320305.i	0.0419371	−	0.439186i
$855$	218653.	+	1.13448e6i	0.299104	+	1.55190i
$856$	−6207.77	+	9659.47i	−0.00847204	+	0.0131827i
$857$	992739.	+	453369.i	1.35168	+	0.617291i	0.953882	−	0.300183i	$-0.0970477\pi$
$857$	992739.	+	453369.i	1.35168	+	0.617291i	0.397797	+	0.917474i	$0.369775\pi$
$858$	−1.34325e6	−	1.05634e6i	−1.82466	−	1.43493i
$859$	−43445.9	+	17393.1i	−0.0588793	+	0.0235717i	−0.400915	−	0.916115i	$-0.631308\pi$
$859$	−43445.9	+	17393.1i	−0.0588793	+	0.0235717i	0.342036	+	0.939687i	$0.388884\pi$
$860$	132960.	−	384162.i	0.179773	−	0.519419i
$861$	−283119.	−	296927.i	−0.381912	−	0.400538i
$862$	565236.	+	879525.i	0.760704	+	1.18368i
$863$	−179195.	−	1.24633e6i	−0.240605	−	1.67344i	−0.649115	−	0.760691i	$-0.724860\pi$
$863$	−179195.	−	1.24633e6i	−0.240605	−	1.67344i	0.408510	−	0.912754i	$-0.366049\pi$
$864$	−2.54322e6	−	1.31112e6i	−3.40688	−	1.75637i
$865$	672151.	−	232634.i	0.898328	−	0.310914i
$866$	−423734.	−	489015.i	−0.565012	−	0.652059i
$867$	78727.4	+	824471.i	0.104734	+	1.09682i
$868$	63425.3	−	18623.3i	0.0841827	−	0.0247183i
$869$	22738.5	+	477339.i	0.0301107	+	0.632102i
$870$		−	1.32062e6i		−	1.74478i
$871$	1.24420e6	+	142435.i	1.64004	+	0.187750i
$872$	3031.55			0.00398687
$873$	−1.54984e6	+	73827.9i	−2.03356	+	0.0968706i
$874$	−263790.	−	898385.i	−0.345330	−	1.17609i
$875$	−165010.	+	15756.6i	−0.215524	+	0.0205800i
$876$	−1.33402e6	+	1.15593e6i	−1.73842	+	1.50635i
$877$	−118648.	−	342811.i	−0.154263	−	0.445713i	0.841216	−	0.540700i	$-0.181840\pi$
$877$	−118648.	−	342811.i	−0.154263	−	0.445713i	−0.995479	+	0.0949864i	$0.969719\pi$
$878$	982705.	−	1.90618e6i	1.27478	−	2.47272i
$879$	467043.	−	67150.6i	0.604475	−	0.0869104i
$880$	−193516.	+	124365.i	−0.249891	+	0.160595i
$881$	−460427.	+	439016.i	−0.593211	+	0.565625i	−0.926070	−	0.377351i	$-0.876835\pi$
$881$	−460427.	+	439016.i	−0.593211	+	0.565625i	0.332859	+	0.942976i	$0.391987\pi$
$882$	−2.41564e6	−	836060.i	−3.10524	−	1.07473i
$883$	−119158.	−	297643.i	−0.152828	−	0.381746i	0.832120	−	0.554595i	$-0.187127\pi$
$883$	−119158.	−	297643.i	−0.152828	−	0.381746i	−0.984948	+	0.172849i	$0.944703\pi$
$884$	505416.	−	642688.i	0.646762	−	0.822424i
$885$	134798.	−	295167.i	0.172107	−	0.376861i
$886$	1.30847e6	+	840904.i	1.66685	+	1.07122i
$887$	120056.	−	23138.9i	0.152594	−	0.0294101i	−0.112382	−	0.993665i	$-0.535848\pi$
$887$	120056.	−	23138.9i	0.152594	−	0.0294101i	0.264976	+	0.964255i	$0.414636\pi$
$888$	−11263.6	−	1075.55i	−0.0142841	−	0.00136397i
$889$	215217.	−	153256.i	0.272316	−	0.193916i
$890$	−1.00852e6	+	519929.i	−1.27323	+	0.656393i
$891$	760189.	−	797263.i	0.957560	−	1.00426i
$892$	210273.	+	40526.8i	0.264273	+	0.0509345i
$893$	1.22714e6	+	360322.i	1.53884	+	0.451843i
$894$	−49485.9	+	203984.i	−0.0619166	+	0.255224i
$895$	110924.	+	242890.i	0.138478	+	0.303224i
$896$	−545.346	+	3792.97i	−0.000679292	+	0.00472458i
$897$	−1.06649e6	+	1.49768e6i	−1.32548	+	1.86137i
$898$	−256044.	−	221863.i	−0.317513	−	0.275127i
$899$	138253.	−	345339.i	0.171063	−	0.427294i
$900$	−689078.	−	1.19352e6i	−0.850713	−	1.47348i
$901$	−245545.	−	141765.i	−0.302469	−	0.174631i
$902$	−488220.	−	620822.i	−0.600070	−	0.763051i
$903$	343411.	−	83310.7i	0.421152	−	0.102170i
$904$	212.179	−	4454.18i	0.000259636	−	0.00545043i
$905$	−590572.	−	28132.4i	−0.721068	−	0.0343487i
$906$	627766.	+	2.58769e6i	0.764789	+	3.15250i
$907$	−150712.	+	118521.i	−0.183203	+	0.144073i	−0.705549	−	0.708661i	$-0.749300\pi$
$907$	−150712.	+	118521.i	−0.183203	+	0.144073i	0.522346	+	0.852734i	$0.325057\pi$
$908$	−35390.4	+	61298.0i	−0.0429254	+	0.0743490i
$909$	−797905.	+	460671.i	−0.965658	+	0.557523i
$910$	228586.	+	91512.2i	0.276037	+	0.110509i
$911$	−417814.	+	482183.i	−0.503438	+	0.580998i	−0.949406	−	0.314050i	$-0.898314\pi$
$911$	−417814.	+	482183.i	−0.503438	+	0.580998i	0.445968	+	0.895049i	$0.352859\pi$
$912$	1.48105e6	+	1.05465e6i	1.78065	+	1.26800i
$913$	−610962.	−	87843.1i	−0.732947	−	0.105382i
$914$	−1.83779e6	+	839289.i	−2.19990	+	1.00466i
$915$	1.12406e6	+	272693.i	1.34260	+	0.325711i
$916$	274780.	−	935816.i	0.327488	−	1.11532i
$917$	−49558.4	+	257133.i	−0.0589357	+	0.305787i
$918$	1.49267e6	+	1.42326e6i	1.77125	+	1.68888i
$919$	141507.	+	274485.i	0.167551	+	0.325004i	0.957630	−	0.288001i	$-0.0929908\pi$
$919$	141507.	+	274485.i	0.167551	+	0.325004i	−0.790079	+	0.613005i	$0.789961\pi$
$920$	2072.35	+	2910.21i	0.00244843	+	0.00343834i
$921$	−173302.	+	1.81490e6i	−0.204308	+	2.13961i
$922$	−66702.4	−	346085.i	−0.0784656	−	0.407118i
$923$	298233.	−	464060.i	0.350068	−	0.544716i
$924$	177955.	+	81269.2i	0.208433	+	0.0951880i
$925$	−350979.	−	276013.i	−0.410202	−	0.322587i
$926$	532625.	−	213231.i	0.621155	−	0.248673i
$927$	−95840.9	+	276914.i	−0.111530	+	0.322245i
$928$	−1.01226e6	−	1.06163e6i	−1.17543	−	1.23275i
$929$	−135227.	−	210417.i	−0.156686	−	0.243808i	0.754031	−	0.656839i	$-0.228107\pi$
$929$	−135227.	−	210417.i	−0.156686	−	0.243808i	−0.910717	+	0.413030i	$0.864470\pi$
$930$	67883.6	+	472141.i	0.0784872	+	0.545891i
$931$	850625.	+	438527.i	0.981383	+	0.505938i
$932$	461862.	−	159852.i	0.531716	−	0.184029i
$933$	562772.	+	649474.i	0.646501	+	0.746102i
$934$	−154194.	−	1.61479e6i	−0.176756	−	1.85107i
$935$	157942.	−	46375.9i	0.180665	−	0.0530480i
$936$	−1743.48	−	36600.2i	−0.00199006	−	0.0417765i
$937$			1.38640e6i			1.57910i	0.613689	+	0.789548i	$0.289685\pi$
$937$			1.38640e6i			1.57910i	−0.613689	+	0.789548i	$0.710315\pi$
$938$	−285583.	+	35599.8i	−0.324584	+	0.0404615i
$939$	29949.4			0.0339670
$940$	663193.	−	31591.8i	0.750558	−	0.0357535i
$941$	−51392.1	−	175025.i	−0.0580386	−	0.197661i	0.925370	−	0.379065i	$-0.123754\pi$
$941$	−51392.1	−	175025.i	−0.0580386	−	0.197661i	−0.983409	+	0.181403i	$0.941936\pi$
$942$	2.04096e6	−	194888.i	2.30003	−	0.219626i
$943$	−642207.	+	556476.i	−0.722191	+	0.625782i
$944$	−118744.	−	343089.i	−0.133250	−	0.385002i
$945$	−141783.	+	275021.i	−0.158767	+	0.307966i
$946$	673339.	−	96811.5i	0.752404	−	0.108179i
$947$	393505.	−	252890.i	0.438783	−	0.281989i	−0.302541	−	0.953137i	$-0.597835\pi$
$947$	393505.	−	252890.i	0.438783	−	0.281989i	0.741324	+	0.671148i	$0.234198\pi$
$948$	1.41914e6	−	1.35315e6i	1.57910	−	1.50566i
$949$	−1.75014e6	−	605731.i	−1.94331	−	0.672585i
$950$	384935.	+	961520.i	0.426520	+	1.06540i
$951$	−994982.	+	1.26522e6i	−1.10016	+	1.39896i
$952$	573.702	−	1256.23i	0.000633013	−	0.00138611i
$953$	53374.3	+	34301.6i	0.0587687	+	0.0377683i	0.569695	−	0.821856i	$-0.307061\pi$
$953$	53374.3	+	34301.6i	0.0587687	+	0.0377683i	−0.510927	+	0.859624i	$0.670698\pi$
$954$	1.69752e6	−	327169.i	1.86516	−	0.359481i
$955$	610528.	+	58298.4i	0.669420	+	0.0639219i
$956$	1.03464e6	−	736760.i	1.13207	−	0.806140i
$957$	978523.	−	504463.i	1.06843	−	0.550815i
$958$	−148884.	+	156145.i	−0.162224	+	0.170136i
$959$	−374814.	−	72239.5i	−0.407548	−	0.0785484i
$960$	892475.	+	262054.i	0.968398	+	0.284347i
$961$	186052.	−	766918.i	0.201460	−	0.830428i
$962$	670960.	+	1.46920e6i	0.725014	+	1.58756i
$963$	−493920.	+	3.43529e6i	−0.532603	+	3.70434i
$964$	−583273.	+	819093.i	−0.627651	+	0.881412i
$965$	−249333.	−	216048.i	−0.267747	−	0.232004i
$966$	157036.	−	392256.i	0.168284	−	0.420354i
$967$	−190766.	−	330416.i	−0.204008	−	0.353352i	0.745808	−	0.666161i	$-0.232064\pi$
$967$	−190766.	−	330416.i	−0.204008	−	0.353352i	−0.949816	+	0.312809i	$0.898730\pi$
$968$	5961.01	+	3441.59i	0.00636164	+	0.00367289i
$969$	−804274.	−	1.02272e6i	−0.856557	−	1.08920i
$970$	588274.	−	142714.i	0.625224	−	0.151678i
$971$	−40634.6	+	853025.i	−0.0430980	+	0.904739i	0.869011	+	0.494792i	$0.164756\pi$
$971$	−40634.6	+	853025.i	−0.0430980	+	0.904739i	−0.912109	+	0.409947i	$0.865547\pi$
$972$	−1.97112e6	−	93895.9i	−2.08632	−	0.0993835i
$973$	−12229.1	−	50409.1i	−0.0129172	−	0.0532456i
$974$	−1.31053e6	+	1.03061e6i	−1.38143	+	1.08637i
$975$	1.01689e6	−	1.76131e6i	1.06971	−	1.85279i
$976$	1.12075e6	−	647065.i	1.17655	−	0.679280i
$977$	−236003.	−	94481.3i	−0.247245	−	0.0989821i	0.244730	−	0.969591i	$-0.421301\pi$
$977$	−236003.	−	94481.3i	−0.247245	−	0.0989821i	−0.491975	+	0.870609i	$0.663725\pi$
$978$	−132130.	+	152486.i	−0.138141	+	0.159423i
$979$	−770490.	−	548663.i	−0.803899	−	0.572454i
$980$	491759.	+	70704.3i	0.512036	+	0.0736196i
$981$	833508.	−	380650.i	0.866108	−	0.395538i
$982$	−2.13469e6	−	517871.i	−2.21367	−	0.537030i
$983$	−306341.	+	1.04330e6i	−0.317028	+	1.07970i	0.634700	+	0.772759i	$0.281124\pi$
$983$	−306341.	+	1.04330e6i	−0.317028	+	1.07970i	−0.951729	+	0.306941i	$0.900695\pi$
$984$	4507.90	−	23389.2i	0.00465569	−	0.0241560i
$985$	−453047.	−	431979.i	−0.466950	−	0.445236i
$986$	484504.	+	939806.i	0.498360	+	0.966684i
$987$	334775.	+	470126.i	0.343652	+	0.482591i
$988$	177410.	−	1.85793e6i	0.181746	−	1.90333i
$989$	−138515.	−	718686.i	−0.141614	−	0.734762i
$990$	−542623.	+	844338.i	−0.553641	+	0.861482i
$991$	57976.7	+	26477.1i	0.0590346	+	0.0269602i	0.444714	−	0.895673i	$-0.353305\pi$
$991$	57976.7	+	26477.1i	0.0590346	+	0.0269602i	−0.385679	+	0.922633i	$0.626033\pi$
$992$	416468.	+	327514.i	0.423212	+	0.332818i
$993$	1.48209e6	−	593340.i	1.50306	−	0.601735i
$994$	−41461.8	+	119796.i	−0.0419638	+	0.121247i
$995$	−450365.	−	472329.i	−0.454903	−	0.477088i
$996$	1.36928e6	+	2.13065e6i	1.38030	+	2.14779i
$997$	274849.	+	1.91162e6i	0.276505	+	1.92314i	0.373056	+	0.927809i	$0.378310\pi$
$997$	274849.	+	1.91162e6i	0.276505	+	1.92314i	−0.0965504	+	0.995328i	$0.530781\pi$
$998$	1.25072e6	+	644793.i	1.25574	+	0.647380i
$999$	−1.91805e6	+	663845.i	−1.92190	+	0.665175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	67.5.h.a.34.19	yes	440
67.2	odd	66	inner	67.5.h.a.2.19	✓	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
67.5.h.a.2.19	✓	440	67.2	odd	66	inner
67.5.h.a.34.19	yes	440	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(5.64013 - 0.268673i) q^{2} +(-4.71637 - 16.0625i) q^{3} +(15.8113 - 1.50980i) q^{4} +(10.4042 - 9.01530i) q^{5} +(-30.9165 - 89.3274i) q^{6} +(-5.20271 + 10.0919i) q^{7} +(-0.652485 + 0.0938132i) q^{8} +(-167.618 + 107.721i) q^{9} +O(q^{10})\)	\(q+(5.64013 - 0.268673i) q^{2} +(-4.71637 - 16.0625i) q^{3} +(15.8113 - 1.50980i) q^{4} +(10.4042 - 9.01530i) q^{5} +(-30.9165 - 89.3274i) q^{6} +(-5.20271 + 10.0919i) q^{7} +(-0.652485 + 0.0938132i) q^{8} +(-167.618 + 107.721i) q^{9} +(56.2589 - 53.6428i) q^{10} +(61.2373 + 21.1944i) q^{11} +(-98.8233 - 246.849i) q^{12} +(172.452 - 219.291i) q^{13} +(-26.6326 + 58.3172i) q^{14} +(-193.878 - 124.598i) q^{15} +(-253.195 + 48.7992i) q^{16} +(183.683 + 17.5396i) q^{17} +(-916.445 + 652.598i) q^{18} +(374.380 - 193.007i) q^{19} +(150.893 - 158.252i) q^{20} +(186.638 + 35.9716i) q^{21} +(351.081 + 103.087i) q^{22} +(92.8144 - 382.586i) q^{23} +(4.58424 + 10.0381i) q^{24} +(-61.9748 + 431.044i) q^{25} +(913.735 - 1283.16i) q^{26} +(1496.04 + 1296.32i) q^{27} +(-67.0252 + 167.421i) q^{28} +(507.417 + 878.872i) q^{29} +(-1126.97 - 650.659i) q^{30} +(-226.585 - 288.126i) q^{31} +(-1404.69 + 340.774i) q^{32} +(51.6175 - 1083.58i) q^{33} +(1040.71 + 49.5752i) q^{34} +(36.8510 + 151.902i) q^{35} +(-2487.63 + 1956.29i) q^{36} +(-512.666 + 887.964i) q^{37} +(2059.70 - 1189.17i) q^{38} +(-4335.70 - 1735.75i) q^{39} +(-5.94284 + 6.85840i) q^{40} +(-1758.25 - 1252.05i) q^{41} +(1062.33 + 152.740i) q^{42} +(1691.13 - 772.314i) q^{43} +(1000.24 + 242.656i) q^{44} +(-772.790 + 2631.88i) q^{45} +(420.695 - 2182.77i) q^{46} +(2197.56 + 2095.37i) q^{47} +(1978.00 + 3836.78i) q^{48} +(1317.94 + 1850.79i) q^{49} +(-233.736 + 2447.80i) q^{50} +(-584.589 - 3033.14i) q^{51} +(2395.61 - 3727.65i) q^{52} +(-1397.74 - 638.324i) q^{53} +(8786.12 + 6909.48i) q^{54} +(828.199 - 331.561i) q^{55} +(2.44795 - 7.07287i) q^{56} +(-4865.88 - 5103.19i) q^{57} +(3098.03 + 4820.62i) q^{58} +(200.378 + 1393.66i) q^{59} +(-3253.59 - 1677.34i) q^{60} +(-4742.81 + 1641.50i) q^{61} +(-1355.38 - 1564.19i) q^{62} +(-215.042 - 2252.02i) q^{63} +(-3872.52 + 1137.08i) q^{64} +(-182.743 - 3836.25i) q^{65} -6125.42i q^{66} +(2355.58 + 3821.30i) q^{67} +2930.76 q^{68} +(-6583.04 + 313.589i) q^{69} +(248.656 + 846.845i) q^{70} +(1968.37 - 187.957i) q^{71} +(99.2625 - 86.0115i) q^{72} +(-2171.26 - 6273.44i) q^{73} +(-2652.93 + 5145.97i) q^{74} +(7215.94 - 1037.50i) q^{75} +(5628.05 - 3616.93i) q^{76} +(-532.491 + 507.729i) q^{77} +(-24920.3 - 8624.99i) q^{78} +(2740.84 + 6846.29i) q^{79} +(-2194.35 + 2790.34i) q^{80} +(7061.89 - 15463.4i) q^{81} +(-10253.2 - 6589.31i) q^{82} +(-9353.06 + 1802.66i) q^{83} +(3005.31 + 286.972i) q^{84} +(2069.20 - 1473.47i) q^{85} +(9330.71 - 4810.31i) q^{86} +(11723.7 - 12295.5i) q^{87} +(-41.9447 - 8.08419i) q^{88} +(-14005.3 - 4112.34i) q^{89} +(-3651.52 + 15051.8i) q^{90} +(1315.83 + 2881.27i) q^{91} +(889.892 - 6189.33i) q^{92} +(-3559.37 + 4998.43i) q^{93} +(12957.5 + 11227.7i) q^{94} +(2155.12 - 5383.23i) q^{95} +(12098.7 + 20955.6i) q^{96} +(6743.97 + 3893.63i) q^{97} +(7930.61 + 10084.6i) q^{98} +(-12547.6 + 3044.00i) 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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