LMFDB - Embedded newform 495.2.bc.d.23.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(23,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("495.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.bc (of order $12$, degree $4$, 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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.17
Character	$\chi$	$=$	495.23
Dual form			495.2.bc.d.452.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00736284 + 0.0274785i) q^{2} +(0.724814 - 1.57310i) q^{3} +(1.73135 + 0.999595i) q^{4} +(0.674857 + 2.13180i) q^{5} +(0.0378897 + 0.0314993i) q^{6} +(3.09816 + 0.830150i) q^{7} +(-0.0804463 + 0.0804463i) q^{8} +(-1.94929 - 2.28041i) q^{9} +O(q^{10})$	\(q+(-0.00736284 + 0.0274785i) q^{2} +(0.724814 - 1.57310i) q^{3} +(1.73135 + 0.999595i) q^{4} +(0.674857 + 2.13180i) q^{5} +(0.0378897 + 0.0314993i) q^{6} +(3.09816 + 0.830150i) q^{7} +(-0.0804463 + 0.0804463i) q^{8} +(-1.94929 - 2.28041i) q^{9} +(-0.0635475 + 0.00284797i) q^{10} +(0.866025 - 0.500000i) q^{11} +(2.82737 - 1.99907i) q^{12} +(-2.89912 + 0.776816i) q^{13} +(-0.0456225 + 0.0790205i) q^{14} +(3.84268 + 0.483540i) q^{15} +(1.99757 + 3.45990i) q^{16} +(-3.59908 - 3.59908i) q^{17} +(0.0770146 - 0.0367732i) q^{18} +7.26476i q^{19} +(-0.962522 + 4.36547i) q^{20} +(3.55150 - 4.27201i) q^{21} +(0.00736284 + 0.0274785i) q^{22} +(-0.0589483 - 0.219998i) q^{23} +(0.0682415 + 0.184859i) q^{24} +(-4.08914 + 2.87732i) q^{25} -0.0853829i q^{26} +(-5.00019 + 1.41355i) q^{27} +(4.53419 + 4.53419i) q^{28} +(-2.30368 - 3.99009i) q^{29} +(-0.0415800 + 0.102031i) q^{30} +(3.22955 - 5.59375i) q^{31} +(-0.329564 + 0.0883064i) q^{32} +(-0.158842 - 1.72475i) q^{33} +(0.125397 - 0.0723979i) q^{34} +(0.321104 + 7.16489i) q^{35} +(-1.09541 - 5.89669i) q^{36} +(6.56691 - 6.56691i) q^{37} +(-0.199625 - 0.0534892i) q^{38} +(-0.879312 + 5.12365i) q^{39} +(-0.225785 - 0.117206i) q^{40} +(-1.51514 - 0.874766i) q^{41} +(0.0912393 + 0.129044i) q^{42} +(1.67608 - 6.25522i) q^{43} +1.99919 q^{44} +(3.54589 - 5.69444i) q^{45} +0.00647924 q^{46} +(3.00735 - 11.2236i) q^{47} +(6.89063 - 0.634599i) q^{48} +(2.84727 + 1.64387i) q^{49} +(-0.0489568 - 0.133549i) q^{50} +(-8.27039 + 3.05305i) q^{51} +(-5.79589 - 1.55300i) q^{52} +(-4.30627 + 4.30627i) q^{53} +(-0.00202667 - 0.147805i) q^{54} +(1.65034 + 1.50876i) q^{55} +(-0.316018 + 0.182453i) q^{56} +(11.4282 + 5.26560i) q^{57} +(0.126603 - 0.0339232i) q^{58} +(-1.55836 + 2.69917i) q^{59} +(6.16968 + 4.67830i) q^{60} +(-3.46648 - 6.00411i) q^{61} +(0.129929 + 0.129929i) q^{62} +(-4.14613 - 8.68328i) q^{63} +7.98058i q^{64} +(-3.61251 - 5.65609i) q^{65} +(0.0485631 + 0.00833432i) q^{66} +(-0.867862 - 3.23891i) q^{67} +(-2.63365 - 9.82890i) q^{68} +(-0.388806 - 0.0667262i) q^{69} +(-0.199245 - 0.0439305i) q^{70} +9.40355i q^{71} +(0.340264 + 0.0266376i) q^{72} +(1.17731 + 1.17731i) q^{73} +(0.132098 + 0.228800i) q^{74} +(1.56245 + 8.51814i) q^{75} +(-7.26182 + 12.5778i) q^{76} +(3.09816 - 0.830150i) q^{77} +(-0.134316 - 0.0618868i) q^{78} +(-6.40956 + 3.70056i) q^{79} +(-6.02773 + 6.59336i) q^{80} +(-1.40055 + 8.89036i) q^{81} +(0.0351930 - 0.0351930i) q^{82} +(-7.77308 - 2.08279i) q^{83} +(10.4192 - 3.84629i) q^{84} +(5.24365 - 10.1014i) q^{85} +(0.159543 + 0.0921124i) q^{86} +(-7.94654 + 0.731843i) q^{87} +(-0.0294454 + 0.109892i) q^{88} +7.03497 q^{89} +(0.130367 + 0.139363i) q^{90} -9.62680 q^{91} +(0.117849 - 0.439818i) q^{92} +(-6.45870 - 9.13484i) q^{93} +(0.286264 + 0.165275i) q^{94} +(-15.4870 + 4.90267i) q^{95} +(-0.0999579 + 0.582443i) q^{96} +(8.71439 + 2.33501i) q^{97} +(-0.0661352 + 0.0661352i) q^{98} +(-2.82834 - 1.00025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 2 q^{2} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 10 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) $ 116 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 10 * q^7 + 2 * q^8 + 16 * q^9	\( 116 q - 2 q^{2} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 10 q^{7} + 2 q^{8} + 16 q^{9} + 6 q^{10} - 8 q^{12} + 12 q^{13} - 10 q^{14} + 20 q^{15} + 62 q^{16} - 8 q^{17} - 54 q^{18} + 6 q^{20} - 10 q^{21} + 2 q^{22} - 14 q^{23} - 62 q^{24} - 12 q^{25} + 30 q^{27} + 18 q^{28} - 2 q^{29} - 18 q^{30} - 2 q^{31} - 48 q^{32} + 4 q^{33} - 24 q^{34} + 2 q^{35} + 24 q^{36} - 14 q^{37} - 6 q^{38} + 4 q^{39} + 98 q^{40} + 6 q^{41} - 44 q^{42} + 26 q^{43} - 120 q^{44} - 18 q^{45} - 44 q^{46} - 2 q^{47} - 20 q^{48} - 18 q^{49} - 20 q^{50} - 8 q^{51} + 102 q^{52} - 44 q^{53} + 28 q^{54} + 2 q^{55} + 42 q^{56} - 48 q^{57} - 16 q^{58} + 22 q^{59} - 8 q^{60} - 10 q^{61} - 16 q^{62} - 26 q^{63} - 108 q^{65} + 6 q^{66} - 36 q^{67} - 72 q^{68} - 76 q^{69} - 134 q^{70} + 30 q^{72} + 12 q^{73} - 8 q^{74} + 20 q^{75} - 6 q^{76} - 10 q^{77} + 210 q^{78} - 6 q^{79} + 4 q^{80} + 44 q^{81} - 50 q^{82} + 24 q^{83} + 222 q^{84} + 54 q^{85} + 90 q^{86} - 32 q^{87} - 4 q^{88} + 8 q^{89} - 74 q^{90} + 72 q^{91} + 18 q^{92} - 98 q^{93} + 42 q^{94} + 54 q^{95} + 68 q^{96} + 18 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 116 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 10 * q^7 + 2 * q^8 + 16 * q^9 + 6 * q^10 - 8 * q^12 + 12 * q^13 - 10 * q^14 + 20 * q^15 + 62 * q^16 - 8 * q^17 - 54 * q^18 + 6 * q^20 - 10 * q^21 + 2 * q^22 - 14 * q^23 - 62 * q^24 - 12 * q^25 + 30 * q^27 + 18 * q^28 - 2 * q^29 - 18 * q^30 - 2 * q^31 - 48 * q^32 + 4 * q^33 - 24 * q^34 + 2 * q^35 + 24 * q^36 - 14 * q^37 - 6 * q^38 + 4 * q^39 + 98 * q^40 + 6 * q^41 - 44 * q^42 + 26 * q^43 - 120 * q^44 - 18 * q^45 - 44 * q^46 - 2 * q^47 - 20 * q^48 - 18 * q^49 - 20 * q^50 - 8 * q^51 + 102 * q^52 - 44 * q^53 + 28 * q^54 + 2 * q^55 + 42 * q^56 - 48 * q^57 - 16 * q^58 + 22 * q^59 - 8 * q^60 - 10 * q^61 - 16 * q^62 - 26 * q^63 - 108 * q^65 + 6 * q^66 - 36 * q^67 - 72 * q^68 - 76 * q^69 - 134 * q^70 + 30 * q^72 + 12 * q^73 - 8 * q^74 + 20 * q^75 - 6 * q^76 - 10 * q^77 + 210 * q^78 - 6 * q^79 + 4 * q^80 + 44 * q^81 - 50 * q^82 + 24 * q^83 + 222 * q^84 + 54 * q^85 + 90 * q^86 - 32 * q^87 - 4 * q^88 + 8 * q^89 - 74 * q^90 + 72 * q^91 + 18 * q^92 - 98 * q^93 + 42 * q^94 + 54 * q^95 + 68 * q^96 + 18 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.00736284	+	0.0274785i	−0.00520631	+	0.0194302i	−0.968480	−	0.249091i	$-0.919868\pi$
$2$	−0.00736284	+	0.0274785i	−0.00520631	+	0.0194302i	0.963274	+	0.268521i	$0.0865349\pi$
$3$	0.724814	−	1.57310i	0.418472	−	0.908230i
$3$	0.724814	−	1.57310i	0.418472	−	0.908230i
$4$	1.73135	+	0.999595i	0.865675	+	0.499798i
$5$	0.674857	+	2.13180i	0.301805	+	0.953370i
$5$	0.674857	+	2.13180i	0.301805	+	0.953370i
$6$	0.0378897	+	0.0314993i	0.0154684	+	0.0128595i
$7$	3.09816	+	0.830150i	1.17099	+	0.313767i	0.791349	−	0.611365i	$-0.209379\pi$
$7$	3.09816	+	0.830150i	1.17099	+	0.313767i	0.379646	+	0.925132i	$0.376046\pi$
$8$	−0.0804463	+	0.0804463i	−0.0284421	+	0.0284421i
$9$	−1.94929	−	2.28041i	−0.649763	−	0.760137i
$10$	−0.0635475	+	0.00284797i	−0.0200955	+	0.000900606i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$	2.82737	−	1.99907i	0.816192	−	0.577081i
$13$	−2.89912	+	0.776816i	−0.804070	+	0.215450i	−0.637370	−	0.770558i	$-0.719978\pi$
$13$	−2.89912	+	0.776816i	−0.804070	+	0.215450i	−0.166700	+	0.986008i	$0.553311\pi$
$14$	−0.0456225	+	0.0790205i	−0.0121931	+	0.0211191i
$15$	3.84268	+	0.483540i	0.992176	+	0.124850i
$16$	1.99757	+	3.45990i	0.499393	+	0.864974i
$17$	−3.59908	−	3.59908i	−0.872906	−	0.872906i	0.119882	−	0.992788i	$-0.461748\pi$
$17$	−3.59908	−	3.59908i	−0.872906	−	0.872906i	−0.992788	+	0.119882i	$0.961748\pi$
$18$	0.0770146	−	0.0367732i	0.0181525	−	0.00866753i
$19$			7.26476i			1.66665i	0.552784	+	0.833325i	$0.313566\pi$
$19$			7.26476i			1.66665i	−0.552784	+	0.833325i	$0.686434\pi$
$20$	−0.962522	+	4.36547i	−0.215227	+	0.976150i
$21$	3.55150	−	4.27201i	0.775001	−	0.932230i
$22$	0.00736284	+	0.0274785i	0.00156976	+	0.00585843i
$23$	−0.0589483	−	0.219998i	−0.0122916	−	0.0458728i	0.959508	−	0.281682i	$-0.0908925\pi$
$23$	−0.0589483	−	0.219998i	−0.0122916	−	0.0458728i	−0.971799	+	0.235810i	$0.924226\pi$
$24$	0.0682415	+	0.184859i	0.0139297	+	0.0377341i
$25$	−4.08914	+	2.87732i	−0.817827	+	0.575464i
$26$		−	0.0853829i		−	0.0167450i
$27$	−5.00019	+	1.41355i	−0.962287	+	0.272038i
$28$	4.53419	+	4.53419i	0.856881	+	0.856881i
$29$	−2.30368	−	3.99009i	−0.427782	−	0.740940i	0.568894	−	0.822411i	$-0.307372\pi$
$29$	−2.30368	−	3.99009i	−0.427782	−	0.740940i	−0.996676	+	0.0814709i	$0.974038\pi$
$30$	−0.0415800	+	0.102031i	−0.00759143	+	0.0186282i
$31$	3.22955	−	5.59375i	0.580045	−	1.00467i	−0.415429	−	0.909626i	$-0.636368\pi$
$31$	3.22955	−	5.59375i	0.580045	−	1.00467i	0.995473	−	0.0950412i	$-0.0302983\pi$
$32$	−0.329564	+	0.0883064i	−0.0582592	+	0.0156105i
$33$	−0.158842	−	1.72475i	−0.0276509	−	0.300241i
$34$	0.125397	−	0.0723979i	0.0215054	−	0.0124161i
$35$	0.321104	+	7.16489i	0.0542765	+	1.21109i
$36$	−1.09541	−	5.89669i	−0.182569	−	0.982782i
$37$	6.56691	−	6.56691i	1.07959	−	1.07959i	0.0830473	−	0.996546i	$-0.473535\pi$
$37$	6.56691	−	6.56691i	1.07959	−	1.07959i	0.996546	−	0.0830473i	$-0.0264653\pi$
$38$	−0.199625	−	0.0534892i	−0.0323834	−	0.00867710i
$39$	−0.879312	+	5.12365i	−0.140803	+	0.820440i
$40$	−0.225785	−	0.117206i	−0.0356998	−	0.0185318i
$41$	−1.51514	−	0.874766i	−0.236625	−	0.136616i	0.377000	−	0.926213i	$-0.376956\pi$
$41$	−1.51514	−	0.874766i	−0.236625	−	0.136616i	−0.613625	+	0.789598i	$0.710289\pi$
$42$	0.0912393	+	0.129044i	0.0140785	+	0.0199119i
$43$	1.67608	−	6.25522i	0.255600	−	0.953913i	−0.712156	−	0.702022i	$-0.752281\pi$
$43$	1.67608	−	6.25522i	0.255600	−	0.953913i	0.967756	−	0.251891i	$-0.0810524\pi$
$44$	1.99919			0.301389
$45$	3.54589	−	5.69444i	0.528590	−	0.848878i
$46$	0.00647924			0.000955312
$47$	3.00735	−	11.2236i	0.438667	−	1.63713i	−0.293470	−	0.955968i	$-0.594810\pi$
$47$	3.00735	−	11.2236i	0.438667	−	1.63713i	0.732137	−	0.681158i	$-0.238523\pi$
$48$	6.89063	−	0.634599i	0.994577	−	0.0915964i
$49$	2.84727	+	1.64387i	0.406753	+	0.234839i
$50$	−0.0489568	−	0.133549i	−0.00692354	−	0.0188866i
$51$	−8.27039	+	3.05305i	−1.15809	+	0.427513i
$52$	−5.79589	−	1.55300i	−0.803745	−	0.215363i
$53$	−4.30627	+	4.30627i	−0.591512	+	0.591512i	−0.938040	−	0.346528i	$-0.887361\pi$
$53$	−4.30627	+	4.30627i	−0.591512	+	0.591512i	0.346528	+	0.938040i	$0.387361\pi$
$54$	−0.00202667	−	0.147805i	−0.000275795	−	0.0201138i
$55$	1.65034	+	1.50876i	0.222532	+	0.203442i
$56$	−0.316018	+	0.182453i	−0.0422297	+	0.0243813i
$57$	11.4282	+	5.26560i	1.51370	+	0.697446i
$58$	0.126603	−	0.0339232i	0.0166238	−	0.00445434i
$59$	−1.55836	+	2.69917i	−0.202882	+	0.351402i	−0.949456	−	0.313901i	$-0.898364\pi$
$59$	−1.55836	+	2.69917i	−0.202882	+	0.351402i	0.746574	+	0.665302i	$0.231697\pi$
$60$	6.16968	+	4.67830i	0.796502	+	0.603966i
$61$	−3.46648	−	6.00411i	−0.443837	−	0.768748i	0.554134	−	0.832428i	$-0.313050\pi$
$61$	−3.46648	−	6.00411i	−0.443837	−	0.768748i	−0.997970	+	0.0636800i	$0.979716\pi$
$62$	0.129929	+	0.129929i	0.0165010	+	0.0165010i
$63$	−4.14613	−	8.68328i	−0.522363	−	1.09399i
$64$			7.98058i			0.997573i
$65$	−3.61251	−	5.65609i	−0.448076	−	0.701552i
$66$	0.0485631	+	0.00833432i	0.00597771	+	0.00102588i
$67$	−0.867862	−	3.23891i	−0.106026	−	0.395695i	0.892433	−	0.451179i	$-0.148997\pi$
$67$	−0.867862	−	3.23891i	−0.106026	−	0.395695i	−0.998460	+	0.0554839i	$0.982330\pi$
$68$	−2.63365	−	9.82890i	−0.319376	−	1.19193i
$69$	−0.388806	−	0.0667262i	−0.0468067	−	0.00803289i
$70$	−0.199245	−	0.0439305i	−0.0238143	−	0.00525070i
$71$			9.40355i			1.11600i	0.829842	+	0.557998i	$0.188430\pi$
$71$			9.40355i			1.11600i	−0.829842	+	0.557998i	$0.811570\pi$
$72$	0.340264	+	0.0266376i	0.0401005	+	0.00313927i
$73$	1.17731	+	1.17731i	0.137794	+	0.137794i	0.772639	−	0.634845i	$-0.218936\pi$
$73$	1.17731	+	1.17731i	0.137794	+	0.137794i	−0.634845	+	0.772639i	$0.718936\pi$
$74$	0.132098	+	0.228800i	0.0153560	+	0.0265974i
$75$	1.56245	+	8.51814i	0.180416	+	0.983590i
$76$	−7.26182	+	12.5778i	−0.832987	+	1.44278i
$77$	3.09816	−	0.830150i	0.353068	−	0.0946043i
$78$	−0.134316	−	0.0618868i	−0.0152083	−	0.00700730i
$79$	−6.40956	+	3.70056i	−0.721132	+	0.416346i	−0.815169	−	0.579223i	$-0.803356\pi$
$79$	−6.40956	+	3.70056i	−0.721132	+	0.416346i	0.0940370	+	0.995569i	$0.470023\pi$
$80$	−6.02773	+	6.59336i	−0.673921	+	0.737160i
$81$	−1.40055	+	8.89036i	−0.155617	+	0.987818i
$82$	0.0351930	−	0.0351930i	0.00388642	−	0.00388642i
$83$	−7.77308	−	2.08279i	−0.853207	−	0.228616i	−0.194394	−	0.980923i	$-0.562274\pi$
$83$	−7.77308	−	2.08279i	−0.853207	−	0.228616i	−0.658812	+	0.752307i	$0.728941\pi$
$84$	10.4192	−	3.84629i	1.13683	−	0.419664i
$85$	5.24365	−	10.1014i	0.568754	−	1.09565i
$86$	0.159543	+	0.0921124i	0.0172040	+	0.00993274i
$87$	−7.94654	+	0.731843i	−0.851959	+	0.0784618i
$88$	−0.0294454	+	0.109892i	−0.00313889	+	0.0117145i
$89$	7.03497			0.745706			0.372853	−	0.927890i	$-0.378380\pi$
$89$	7.03497			0.745706			0.372853	+	0.927890i	$0.378380\pi$
$90$	0.130367	+	0.139363i	0.0137419	+	0.0146901i
$91$	−9.62680			−1.00916
$92$	0.117849	−	0.439818i	0.0122866	−	0.0458542i
$93$	−6.45870	−	9.13484i	−0.669736	−	0.947239i
$94$	0.286264	+	0.165275i	0.0295259	+	0.0170468i
$95$	−15.4870	+	4.90267i	−1.58893	+	0.503004i
$96$	−0.0999579	+	0.582443i	−0.0102019	+	0.0594453i
$97$	8.71439	+	2.33501i	0.884813	+	0.237085i	0.672482	−	0.740113i	$-0.265228\pi$
$97$	8.71439	+	2.33501i	0.884813	+	0.237085i	0.212330	+	0.977198i	$0.431895\pi$
$98$	−0.0661352	+	0.0661352i	−0.00668066	+	0.00668066i
$99$	−2.82834	−	1.00025i	−0.284259	−	0.100529i
$100$	−9.95588	+	0.894169i	−0.995588	+	0.0894169i
$101$	−5.55308	+	3.20608i	−0.552553	+	0.319016i	−0.750151	−	0.661267i	$-0.770019\pi$
$101$	−5.55308	+	3.20608i	−0.552553	+	0.319016i	0.197598	+	0.980283i	$0.436686\pi$
$102$	−0.0229997	−	0.249737i	−0.00227731	−	0.0247276i
$103$	5.12333	−	1.37279i	0.504817	−	0.135265i	0.00258222	−	0.999997i	$-0.499178\pi$
$103$	5.12333	−	1.37279i	0.504817	−	0.135265i	0.502235	+	0.864731i	$0.332511\pi$
$104$	0.170731	−	0.295715i	0.0167416	−	0.0289973i
$105$	11.5038	+	4.68809i	1.12266	+	0.457510i
$106$	−0.0866235	−	0.150036i	−0.00841361	−	0.0145728i
$107$	7.39693	+	7.39693i	0.715089	+	0.715089i	0.967595	−	0.252507i	$-0.0812549\pi$
$107$	7.39693	+	7.39693i	0.715089	+	0.715089i	−0.252507	+	0.967595i	$0.581255\pi$
$108$	−10.0701	−	2.55081i	−0.968991	−	0.245452i
$109$			16.0982i			1.54193i	0.636880	+	0.770963i	$0.280225\pi$
$109$			16.0982i			1.54193i	−0.636880	+	0.770963i	$0.719775\pi$
$110$	−0.0536098	+	0.0342402i	−0.00511149	+	0.00326467i
$111$	−5.57061	−	15.0902i	−0.528739	−	1.43230i
$112$	3.31657	+	12.3776i	0.313386	+	1.16957i
$113$	1.50258	+	5.60771i	0.141351	+	0.527529i	0.999891	+	0.0147820i	$0.00470544\pi$
$113$	1.50258	+	5.60771i	0.141351	+	0.527529i	−0.858540	+	0.512747i	$0.828628\pi$
$114$	−0.228835	+	0.275260i	−0.0214323	+	0.0257804i
$115$	0.429210	−	0.274133i	0.0400240	−	0.0255631i
$116$		−	9.21098i		−	0.855218i
$117$	7.42267	+	5.09694i	0.686226	+	0.471212i
$118$	−0.0626950	−	0.0626950i	−0.00577155	−	0.00577155i
$119$	−8.16276	−	14.1383i	−0.748279	−	1.29606i
$120$	−0.348029	+	0.270230i	−0.0317705	+	0.0246686i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	0.190507	−	0.0510462i	0.0172477	−	0.00462151i
$123$	−2.47429	+	1.74942i	−0.223099	+	0.157740i
$124$	11.1830	−	6.45649i	1.00426	−	0.579810i
$125$	−8.89345	−	6.77543i	−0.795455	−	0.606013i
$126$	0.269131	−	0.0499957i	0.0239761	−	0.00445397i
$127$	1.48023	−	1.48023i	0.131349	−	0.131349i	−0.638376	−	0.769725i	$-0.720393\pi$
$127$	1.48023	−	1.48023i	0.131349	−	0.131349i	0.769725	+	0.638376i	$0.220393\pi$
$128$	−0.878423	−	0.235373i	−0.0776423	−	0.0208042i
$129$	−8.62524	−	7.17052i	−0.759410	−	0.631329i
$130$	0.182019	−	0.0576213i	0.0159641	−	0.00505372i
$131$	−4.82135	−	2.78361i	−0.421243	−	0.243205i	0.274366	−	0.961625i	$-0.411532\pi$
$131$	−4.82135	−	2.78361i	−0.421243	−	0.243205i	−0.695609	+	0.718421i	$0.744865\pi$
$132$	1.44904	−	3.14493i	0.126123	−	0.273731i
$133$	−6.03083	+	22.5074i	−0.522940	+	1.95164i
$134$	0.0953902			0.00824046
$135$	−6.38782	−	9.70545i	−0.549776	−	0.835312i
$136$	0.579066			0.0496545
$137$	1.71383	−	6.39609i	0.146422	−	0.546455i	−0.853266	−	0.521476i	$-0.825382\pi$
$137$	1.71383	−	6.39609i	0.146422	−	0.546455i	0.999688	−	0.0249787i	$-0.00795180\pi$
$138$	0.00469625	−	0.0101925i	0.000399771	−	0.000867643i
$139$	−18.1389	−	10.4725i	−1.53852	−	0.888266i	−0.998926	−	0.0463425i	$-0.985243\pi$
$139$	−18.1389	−	10.4725i	−1.53852	−	0.888266i	−0.539597	−	0.841924i	$-0.681423\pi$
$140$	−6.60605	+	12.7259i	−0.558313	+	1.07554i
$141$	−15.4760	−	12.8659i	−1.30332	−	1.08350i
$142$	−0.258395	−	0.0692368i	−0.0216841	−	0.00581023i
$143$	−2.12230	+	2.12230i	−0.177476	+	0.177476i
$144$	3.99614	−	11.2996i	0.333012	−	0.941635i
$145$	6.95141	−	7.60371i	0.577283	−	0.631454i
$146$	−0.0410191	+	0.0236824i	−0.00339476	+	0.00195997i
$147$	4.64972	−	3.28754i	0.383503	−	0.271152i
$148$	17.9339	−	4.80536i	1.47415	−	0.394999i
$149$	−1.15178	+	1.99494i	−0.0943577	+	0.163432i	−0.909340	−	0.416053i	$-0.863413\pi$
$149$	−1.15178	+	1.99494i	−0.0943577	+	0.163432i	0.814983	+	0.579485i	$0.196746\pi$
$150$	−0.245570	−	0.0197840i	−0.0200507	−	0.00161535i
$151$	−1.39474	−	2.41577i	−0.113503	−	0.196592i	0.803678	−	0.595065i	$-0.202874\pi$
$151$	−1.39474	−	2.41577i	−0.113503	−	0.196592i	−0.917180	+	0.398473i	$0.869540\pi$
$152$	−0.584423	−	0.584423i	−0.0474030	−	0.0474030i
$153$	−1.19174	+	15.2230i	−0.0963464	+	1.23071i
$154$			0.0912450i			0.00735274i
$155$	14.1042	+	3.10977i	1.13288	+	0.249783i
$156$	−6.64397	+	7.99187i	−0.531943	+	0.639862i
$157$	0.658410	+	2.45722i	0.0525468	+	0.196107i	0.987209	−	0.159428i	$-0.0509651\pi$
$157$	0.658410	+	2.45722i	0.0525468	+	0.196107i	−0.934663	+	0.355536i	$0.884298\pi$
$158$	−0.0544933	−	0.203372i	−0.00433526	−	0.0161794i
$159$	3.65295	+	9.89544i	0.289698	+	0.784760i
$160$	−0.410660	−	0.642970i	−0.0324655	−	0.0508312i
$161$		−	0.730525i		−	0.0575735i
$162$	−0.233982	−	0.103943i	−0.0183833	−	0.00816656i
$163$	−15.3525	−	15.3525i	−1.20250	−	1.20250i	−0.973404	−	0.229097i	$-0.926423\pi$
$163$	−15.3525	−	15.3525i	−1.20250	−	1.20250i	−0.229097	−	0.973404i	$-0.573577\pi$
$164$	−1.74882	−	3.02905i	−0.136560	−	0.236529i
$165$	3.56963	−	1.50258i	0.277895	−	0.116976i
$166$	0.114464	−	0.198257i	0.00888412	−	0.0153878i
$167$	−14.1219	+	3.78396i	−1.09279	+	0.292812i	−0.759824	−	0.650128i	$-0.774715\pi$
$167$	−14.1219	+	3.78396i	−1.09279	+	0.292812i	−0.332963	+	0.942940i	$0.608048\pi$
$168$	0.0579626	+	0.629373i	0.00447191	+	0.0485572i
$169$	−3.45690	+	1.99584i	−0.265915	+	0.153526i
$170$	0.238963	+	0.218463i	0.0183276	+	0.0167553i
$171$	16.5666	−	14.1611i	1.26688	−	1.08293i
$172$	9.15458	−	9.15458i	0.698030	−	0.698030i
$173$	−15.7084	−	4.20905i	−1.19429	−	0.320008i	−0.393707	−	0.919236i	$-0.628808\pi$
$173$	−15.7084	−	4.20905i	−1.19429	−	0.320008i	−0.800578	+	0.599228i	$0.795474\pi$
$174$	0.0383992	−	0.223747i	0.00291103	−	0.0169622i
$175$	−15.0574	+	5.51981i	−1.13823	+	0.417258i
$176$	3.45990	+	1.99757i	0.260800	+	0.150573i
$177$	3.11653	+	4.40786i	0.234253	+	0.331315i
$178$	−0.0517974	+	0.193310i	−0.00388238	+	0.0144892i
$179$	23.5544			1.76054			0.880270	−	0.474473i	$-0.157361\pi$
$179$	23.5544			1.76054			0.880270	+	0.474473i	$0.157361\pi$
$180$	11.8313	−	6.31462i	0.881854	−	0.470664i
$181$	−3.83503			−0.285056			−0.142528	−	0.989791i	$-0.545523\pi$
$181$	−3.83503			−0.285056			−0.142528	+	0.989791i	$0.545523\pi$
$182$	0.0708806	−	0.264530i	0.00525402	−	0.0196083i
$183$	−11.9576	+	1.10125i	−0.883933	+	0.0814065i
$184$	0.0224402	+	0.0129559i	0.00165431	+	0.000955119i
$185$	18.4311	+	9.56760i	1.35508	+	0.703424i
$186$	0.298566	−	0.110217i	0.0218919	−	0.00808151i
$187$	−4.91644	−	1.31736i	−0.359526	−	0.0963346i
$188$	16.4258	−	16.4258i	1.19797	−	1.19797i
$189$	−16.6648	+	0.228504i	−1.21219	+	0.0166212i
$190$	−0.0206898	−	0.461657i	−0.00150100	−	0.0334921i
$191$	18.4798	−	10.6693i	1.33715	−	0.772005i	0.350767	−	0.936463i	$-0.385921\pi$
$191$	18.4798	−	10.6693i	1.33715	−	0.772005i	0.986384	+	0.164458i	$0.0525874\pi$
$192$	12.5543	+	5.78444i	0.906026	+	0.417456i
$193$	14.8767	−	3.98620i	1.07085	−	0.286933i	0.320007	−	0.947415i	$-0.396315\pi$
$193$	14.8767	−	3.98620i	1.07085	−	0.286933i	0.750842	+	0.660482i	$0.229648\pi$
$194$	−0.128325	+	0.222266i	−0.00921322	+	0.0159578i
$195$	−11.5160	+	1.58321i	−0.824678	+	0.113376i
$196$	3.28642	+	5.69224i	0.234744	+	0.406589i
$197$	12.2773	+	12.2773i	0.874724	+	0.874724i	0.992983	−	0.118259i	$-0.0377312\pi$
$197$	12.2773	+	12.2773i	0.874724	+	0.874724i	−0.118259	+	0.992983i	$0.537731\pi$
$198$	0.0483100	−	0.0703538i	0.00343324	−	0.00499983i
$199$			10.9617i			0.777056i	0.921437	+	0.388528i	$0.127016\pi$
$199$			10.9617i			0.777056i	−0.921437	+	0.388528i	$0.872984\pi$
$200$	0.0974860	−	0.560426i	0.00689330	−	0.0396281i
$201$	−5.72416	−	0.982371i	−0.403751	−	0.0692911i
$202$	−0.0472116	−	0.176196i	−0.00332180	−	0.0123971i
$203$	−3.82479	−	14.2743i	−0.268448	−	1.00186i
$204$	−17.3707	−	2.98114i	−1.21620	−	0.208721i
$205$	0.842323	−	3.82032i	0.0588304	−	0.266822i
$206$			0.150889i			0.0105129i
$207$	−0.386779	+	0.563266i	−0.0268830	+	0.0391497i
$208$	−8.47890	−	8.47890i	−0.587906	−	0.587906i
$209$	3.63238	+	6.29146i	0.251257	+	0.435190i
$210$	−0.213522	+	0.281590i	−0.0147344	+	0.0194316i
$211$	−9.95356	+	17.2401i	−0.685231	+	1.18686i	0.288133	+	0.957591i	$0.406966\pi$
$211$	−9.95356	+	17.2401i	−0.685231	+	1.18686i	−0.973364	+	0.229265i	$0.926368\pi$
$212$	−11.7602	+	3.15113i	−0.807693	+	0.216421i
$213$	14.7927	+	6.81583i	1.01358	+	0.467013i
$214$	−0.257719	+	0.148794i	−0.0176173	+	0.0101714i
$215$	14.4660	−	0.648313i	0.986573	−	0.0442146i
$216$	0.288532	−	0.515962i	0.0196321	−	0.0351067i
$217$	14.6493	−	14.6493i	0.994461	−	0.994461i
$218$	−0.442354	−	0.118528i	−0.0299600	−	0.00802775i
$219$	2.70536	−	0.998696i	0.182811	−	0.0674856i
$220$	1.34917	+	4.26187i	0.0909609	+	0.287335i
$221$	13.2300	+	7.63834i	0.889945	+	0.513810i
$222$	0.455671	−	0.0419654i	0.0305827	−	0.00281653i
$223$	−2.86914	+	10.7078i	−0.192132	+	0.717046i	0.800859	+	0.598853i	$0.204377\pi$
$223$	−2.86914	+	10.7078i	−0.192132	+	0.717046i	−0.992991	+	0.118193i	$0.962290\pi$
$224$	−1.09435			−0.0731193
$225$	14.5324	+	3.71618i	0.968825	+	0.247745i
$226$	−0.165155			−0.0109859
$227$	−6.07062	+	22.6559i	−0.402921	+	1.50372i	0.404936	+	0.914345i	$0.367294\pi$
$227$	−6.07062	+	22.6559i	−0.402921	+	1.50372i	−0.807858	+	0.589378i	$0.799373\pi$
$228$	14.5227	+	20.5402i	0.961791	+	1.36031i
$229$	11.0779	+	6.39583i	0.732048	+	0.422648i	0.819171	−	0.573549i	$-0.194434\pi$
$229$	11.0779	+	6.39583i	0.732048	+	0.422648i	−0.0871230	+	0.996198i	$0.527767\pi$
$230$	0.00437257	+	0.0138124i	0.000288318	+	0.000910766i
$231$	0.939683	−	5.47542i	0.0618266	−	0.360256i
$232$	0.506310	+	0.135665i	0.0332409	+	0.00890687i
$233$	4.58631	−	4.58631i	0.300459	−	0.300459i	−0.540734	−	0.841193i	$-0.681854\pi$
$233$	4.58631	−	4.58631i	0.300459	−	0.300459i	0.841193	+	0.540734i	$0.181854\pi$
$234$	−0.194708	+	0.166436i	−0.0127285	+	0.0108803i
$235$	25.9559	−	1.16325i	1.69318	−	0.0758821i
$236$	−5.39615	+	3.11547i	−0.351259	+	0.202800i
$237$	1.17561	+	12.7651i	0.0763643	+	0.829183i
$238$	0.448601	−	0.120202i	0.0290785	−	0.00779155i
$239$	1.43753	−	2.48987i	0.0929859	−	0.161056i	−0.815780	−	0.578362i	$-0.803692\pi$
$239$	1.43753	−	2.48987i	0.0929859	−	0.161056i	0.908766	+	0.417306i	$0.137026\pi$
$240$	6.00303	+	14.2612i	0.387494	+	0.920555i
$241$	1.09124	+	1.89009i	0.0702932	+	0.121751i	0.899030	−	0.437887i	$-0.144273\pi$
$241$	1.09124	+	1.89009i	0.0702932	+	0.121751i	−0.828737	+	0.559639i	$0.810940\pi$
$242$	0.0201157	+	0.0201157i	0.00129308	+	0.00129308i
$243$	12.9703	+	8.64706i	0.832044	+	0.554709i
$244$		−	13.8603i		−	0.887314i
$245$	−1.58291	+	7.17920i	−0.101128	+	0.458662i
$246$	−0.0298537	−	0.0808705i	−0.00190340	−	0.00515611i
$247$	−5.64338	−	21.0614i	−0.359080	−	1.34010i
$248$	0.190191	+	0.709802i	0.0120771	+	0.0450725i
$249$	−8.91048	+	10.7182i	−0.564679	+	0.679238i
$250$	0.251660	−	0.194492i	0.0159164	−	0.0123008i
$251$			20.5741i			1.29863i	0.760521	+	0.649314i	$0.224944\pi$
$251$			20.5741i			1.29863i	−0.760521	+	0.649314i	$0.775056\pi$
$252$	1.50137	−	19.1782i	0.0945776	−	1.20812i
$253$	−0.161050	−	0.161050i	−0.0101251	−	0.0101251i
$254$	0.0297757	+	0.0515730i	0.00186829	+	0.00323598i
$255$	−12.0898	−	15.5704i	−0.757094	−	0.975058i
$256$	−7.96765	+	13.8004i	−0.497978	+	0.862523i
$257$	−15.4537	+	4.14081i	−0.963976	+	0.258297i	−0.706283	−	0.707930i	$-0.749629\pi$
$257$	−15.4537	+	4.14081i	−0.963976	+	0.258297i	−0.257694	+	0.966227i	$0.582963\pi$
$258$	0.260541	−	0.184213i	0.0162206	−	0.0114686i
$259$	25.7968	−	14.8938i	1.60294	−	0.925457i
$260$	−0.600706	−	13.4037i	−0.0372542	−	0.831264i
$261$	−4.60850	+	13.0312i	−0.285259	+	0.806608i
$262$	0.111988	−	0.111988i	0.00691865	−	0.00691865i
$263$	−15.2955	−	4.09840i	−0.943158	−	0.252718i	−0.245701	−	0.969346i	$-0.579018\pi$
$263$	−15.2955	−	4.09840i	−0.943158	−	0.252718i	−0.697456	+	0.716627i	$0.745685\pi$
$264$	0.151528	+	0.125972i	0.00932592	+	0.00775302i
$265$	−12.0862	−	6.27399i	−0.742451	−	0.385408i
$266$	−0.574065	−	0.331437i	−0.0351982	−	0.0203217i
$267$	5.09905	−	11.0667i	0.312057	−	0.677272i
$268$	1.73502	−	6.47519i	0.105983	−	0.395535i
$269$	−15.4729			−0.943401			−0.471701	−	0.881759i	$-0.656360\pi$
$269$	−15.4729			−0.943401			−0.471701	+	0.881759i	$0.656360\pi$
$270$	0.313724	−	0.104068i	0.0190926	−	0.00633338i
$271$	−11.0221			−0.669544			−0.334772	−	0.942299i	$-0.608659\pi$
$271$	−11.0221			−0.669544			−0.334772	+	0.942299i	$0.608659\pi$
$272$	5.26303	−	19.6419i	0.319118	−	1.19096i
$273$	−6.97764	+	15.1439i	−0.422306	+	0.916552i
$274$	0.163136	+	0.0941868i	0.00985542	+	0.00569003i
$275$	−2.10263	+	4.53640i	−0.126794	+	0.273555i
$276$	−0.606460	−	0.504175i	−0.0365046	−	0.0303478i
$277$	−16.2374	−	4.35081i	−0.975613	−	0.261415i	−0.264417	−	0.964408i	$-0.585179\pi$
$277$	−16.2374	−	4.35081i	−0.975613	−	0.261415i	−0.711196	+	0.702994i	$0.751846\pi$
$278$	0.421323	−	0.421323i	0.0252692	−	0.0252692i
$279$	−19.0514	+	3.53912i	−1.14058	+	0.211882i
$280$	−0.602221	−	0.550557i	−0.0359896	−	0.0329021i
$281$	21.3923	−	12.3509i	1.27616	−	0.736792i	0.300020	−	0.953933i	$-0.403007\pi$
$281$	21.3923	−	12.3509i	1.27616	−	0.736792i	0.976140	+	0.217141i	$0.0696732\pi$
$282$	0.467482	−	0.330529i	0.0278382	−	0.0196827i
$283$	28.8490	−	7.73008i	1.71490	−	0.459505i	0.738281	−	0.674494i	$-0.235638\pi$
$283$	28.8490	−	7.73008i	1.71490	−	0.459505i	0.976617	+	0.214988i	$0.0689714\pi$
$284$	−9.39974	+	16.2808i	−0.557772	+	0.966090i
$285$	−3.51280	+	27.9161i	−0.208080	+	1.65361i
$286$	−0.0426915	−	0.0739438i	−0.00252440	−	0.00437239i
$287$	−3.96796	−	3.96796i	−0.234221	−	0.234221i
$288$	0.843790	+	0.579407i	0.0497208	+	0.0341419i
$289$			8.90680i			0.523929i
$290$	0.157757	+	0.246999i	0.00926378	+	0.0145043i
$291$	9.98953	−	12.0162i	0.585597	−	0.704400i
$292$	0.861502	+	3.21517i	0.0504156	+	0.188154i
$293$	5.27070	+	19.6705i	0.307917	+	1.14916i	0.930405	+	0.366534i	$0.119456\pi$
$293$	5.27070	+	19.6705i	0.307917	+	1.14916i	−0.622487	+	0.782630i	$0.713878\pi$
$294$	0.0561016	+	0.151973i	0.00327191	+	0.00886325i
$295$	−6.80575	−	1.50057i	−0.396246	−	0.0873664i
$296$			1.05657i			0.0614117i
$297$	−3.62351	+	3.72426i	−0.210258	+	0.216104i
$298$	−0.0463377	−	0.0463377i	−0.00268427	−	0.00268427i
$299$	0.341796	+	0.592008i	0.0197666	+	0.0342367i
$300$	−5.80955	+	16.3097i	−0.335414	+	0.941641i
$301$	10.3855	−	17.9883i	0.598613	−	1.03683i
$302$	0.0766510	−	0.0205386i	0.00441077	−	0.00118186i
$303$	1.01852	+	11.0594i	0.0585125	+	0.635344i
$304$	−25.1353	+	14.5119i	−1.44161	+	0.832313i
$305$	10.4602	−	11.4417i	0.598948	−	0.655153i
$306$	−0.409532	−	0.144832i	−0.0234114	−	0.00827949i
$307$	−9.57123	+	9.57123i	−0.546259	+	0.546259i	−0.925357	−	0.379098i	$-0.876234\pi$
$307$	−9.57123	+	9.57123i	−0.546259	+	0.546259i	0.379098	+	0.925357i	$0.376234\pi$
$308$	6.19381	+	1.65963i	0.352925	+	0.0945661i
$309$	1.55392	−	9.05453i	0.0883996	−	0.515094i
$310$	−0.189299	+	0.364666i	−0.0107515	+	0.0207117i
$311$	25.5791	+	14.7681i	1.45046	+	0.837421i	0.998507	−	0.0546232i	$-0.0173958\pi$
$311$	25.5791	+	14.7681i	1.45046	+	0.837421i	0.451948	+	0.892044i	$0.350729\pi$
$312$	−0.341441	−	0.482916i	−0.0193303	−	0.0273397i
$313$	5.73344	−	21.3975i	0.324073	−	1.20946i	−0.591167	−	0.806549i	$-0.701332\pi$
$313$	5.73344	−	21.3975i	0.324073	−	1.20946i	0.915240	−	0.402909i	$-0.132001\pi$
$314$	−0.0723684			−0.00408399
$315$	15.7130	−	14.6987i	0.885325	−	0.828177i
$316$	−14.7963			−0.832355
$317$	−2.28790	+	8.53857i	−0.128501	+	0.479574i	−0.999940	−	0.0109304i	$-0.996521\pi$
$317$	−2.28790	+	8.53857i	−0.128501	+	0.479574i	0.871439	+	0.490504i	$0.163187\pi$
$318$	−0.298808	+	0.0275190i	−0.0167563	+	0.00154319i
$319$	−3.99009	−	2.30368i	−0.223402	−	0.128981i
$320$	−17.0130	+	5.38576i	−0.951056	+	0.301073i
$321$	16.9975	−	6.27471i	0.948709	−	0.350220i
$322$	0.0200737	+	0.00537874i	0.00111867	+	0.000299746i
$323$	26.1465	−	26.1465i	1.45483	−	1.45483i
$324$	−11.3116	+	13.9923i	−0.628422	+	0.777352i
$325$	9.61973	−	11.5182i	0.533607	−	0.638914i
$326$	0.534902	−	0.308826i	0.0296255	−	0.0171043i
$327$	25.3240	+	11.6682i	1.40042	+	0.645252i
$328$	0.192259	−	0.0515157i	0.0106157	−	0.00284448i
$329$	18.6345	−	32.2759i	1.02735	−	1.77943i
$330$	0.0150061	+	0.109151i	0.000826057	+	0.00600858i
$331$	−0.539604	−	0.934621i	−0.0296593	−	0.0513714i	0.850815	−	0.525466i	$-0.176109\pi$
$331$	−0.539604	−	0.934621i	−0.0296593	−	0.0513714i	−0.880474	+	0.474094i	$0.842776\pi$
$332$	−11.3760	−	11.3760i	−0.624338	−	0.624338i
$333$	−27.7760	−	2.17445i	−1.52212	−	0.119159i
$334$		−	0.415910i		−	0.0227576i
$335$	6.31901	−	4.03591i	0.345245	−	0.220505i
$336$	21.8751	+	3.75417i	1.19338	+	0.204807i
$337$	0.841753	+	3.14146i	0.0458532	+	0.171126i	0.985055	−	0.172238i	$-0.0550999\pi$
$337$	0.841753	+	3.14146i	0.0458532	+	0.171126i	−0.939202	+	0.343365i	$0.888433\pi$
$338$	−0.0293901	−	0.109685i	−0.00159861	−	0.00596610i
$339$	9.91058	+	1.70084i	0.538269	+	0.0923768i
$340$	19.1759	−	12.2475i	1.03996	−	0.664214i
$341$		−	6.45911i		−	0.349780i
$342$	0.267148	+	0.559492i	0.0144457	+	0.0302539i
$343$	−8.41943	−	8.41943i	−0.454606	−	0.454606i
$344$	0.368375	+	0.638044i	0.0198615	+	0.0344010i
$345$	−0.120142	−	0.873886i	−0.00646820	−	0.0470485i
$346$	0.231316	−	0.400652i	0.0124357	−	0.0215392i
$347$	22.5501	−	6.04227i	1.21055	−	0.324366i	0.403573	−	0.914947i	$-0.367768\pi$
$347$	22.5501	−	6.04227i	1.21055	−	0.324366i	0.806978	+	0.590581i	$0.201101\pi$
$348$	−14.4898	−	6.67625i	−0.776734	−	0.357885i
$349$	23.2810	−	13.4413i	1.24620	−	0.719497i	0.275854	−	0.961199i	$-0.411039\pi$
$349$	23.2810	−	13.4413i	1.24620	−	0.719497i	0.970350	+	0.241703i	$0.0777060\pi$
$350$	−0.0408107	−	0.454396i	−0.00218143	−	0.0242885i
$351$	13.3981	−	7.98227i	0.715135	−	0.426062i
$352$	−0.241258	+	0.241258i	−0.0128591	+	0.0128591i
$353$	25.4731	+	6.82549i	1.35580	+	0.363284i	0.862271	−	0.506447i	$-0.169042\pi$
$353$	25.4731	+	6.82549i	1.35580	+	0.363284i	0.493525	+	0.869732i	$0.335708\pi$
$354$	−0.144068	+	0.0531833i	−0.00765712	+	0.00282666i
$355$	−20.0465	+	6.34605i	−1.06396	+	0.336814i
$356$	12.1800	+	7.03213i	0.645539	+	0.372702i
$357$	−28.1575	+	2.59319i	−1.49025	+	0.137246i
$358$	−0.173427	+	0.647240i	−0.00916593	+	0.0342077i
$359$	21.4338			1.13124			0.565618	−	0.824668i	$-0.308638\pi$
$359$	21.4338			1.13124			0.565618	+	0.824668i	$0.308638\pi$
$360$	0.172843	+	0.743351i	0.00910965	+	0.0391780i
$361$	−33.7767			−1.77772
$362$	0.0282367	−	0.105381i	0.00148409	−	0.00553870i
$363$	−0.999938	−	1.41426i	−0.0524831	−	0.0742293i
$364$	−16.6674	−	9.62291i	−0.873607	−	0.504377i
$365$	−1.71527	+	3.30431i	−0.0897815	+	0.172955i
$366$	0.0577814	−	0.336686i	0.00302028	−	0.0175988i
$367$	−11.9255	−	3.19542i	−0.622504	−	0.166799i	−0.0662381	−	0.997804i	$-0.521100\pi$
$367$	−11.9255	−	3.19542i	−0.622504	−	0.166799i	−0.556266	+	0.831004i	$0.687766\pi$
$368$	0.643417	−	0.643417i	0.0335404	−	0.0335404i
$369$	0.958617	+	5.16031i	0.0499036	+	0.268635i
$370$	−0.398608	+	0.436013i	−0.0207227	+	0.0226672i
$371$	−16.9164	+	9.76667i	−0.878254	+	0.507060i
$372$	−2.05113	−	22.2717i	−0.106346	−	1.15473i
$373$	14.6141	−	3.91584i	0.756691	−	0.202755i	0.140207	−	0.990122i	$-0.455223\pi$
$373$	14.6141	−	3.91584i	0.756691	−	0.202755i	0.616484	+	0.787367i	$0.288557\pi$
$374$	0.0723979	−	0.125397i	0.00374361	−	0.00648412i
$375$	−17.1045	+	9.07936i	−0.883275	+	0.468856i
$376$	0.660965	+	1.14483i	0.0340867	+	0.0590399i
$377$	9.77819	+	9.77819i	0.503602	+	0.503602i
$378$	0.116422	−	0.459607i	0.00598808	−	0.0236396i
$379$		−	4.29816i		−	0.220782i	−0.993888	−	0.110391i	$-0.964790\pi$
$379$		−	4.29816i		−	0.220782i	0.993888	−	0.110391i	$-0.0352103\pi$
$380$	−31.7141	−	6.99249i	−1.62690	−	0.358707i
$381$	−1.25565	−	3.40143i	−0.0643291	−	0.174261i
$382$	0.157113	+	0.586354i	0.00803860	+	0.0300005i
$383$	−9.69896	−	36.1970i	−0.495594	−	1.84958i	−0.526679	−	0.850064i	$-0.676563\pi$
$383$	−9.69896	−	36.1970i	−0.495594	−	1.84958i	0.0310854	−	0.999517i	$-0.490104\pi$
$384$	−1.00696	+	1.21125i	−0.0513861	+	0.0618111i
$385$	3.86053	+	6.04442i	0.196751	+	0.308052i
$386$			0.438139i			0.0223007i
$387$	−17.5316	+	8.37108i	−0.891184	+	0.425526i
$388$	12.7536	+	12.7536i	0.647466	+	0.647466i
$389$	12.9332	+	22.4010i	0.655740	+	1.13578i	0.981708	+	0.190395i	$0.0609768\pi$
$389$	12.9332	+	22.4010i	0.655740	+	1.13578i	−0.325967	+	0.945381i	$0.605690\pi$
$390$	0.0412861	−	0.328099i	0.00209060	−	0.0166140i
$391$	−0.579632	+	1.00395i	−0.0293132	+	0.0507720i
$392$	−0.361296	+	0.0968091i	−0.0182482	+	0.00488960i
$393$	−7.87347	+	5.56686i	−0.397164	+	0.280811i
$394$	−0.427759	+	0.246967i	−0.0215502	+	0.0124420i
$395$	−12.2144	−	11.1665i	−0.614573	−	0.561850i
$396$	−3.89700	−	4.55898i	−0.195832	−	0.229097i
$397$	−6.36702	+	6.36702i	−0.319552	+	0.319552i	−0.848595	−	0.529043i	$-0.822551\pi$
$397$	−6.36702	+	6.36702i	−0.319552	+	0.319552i	0.529043	+	0.848595i	$0.322551\pi$
$398$	−0.301212	−	0.0807094i	−0.0150984	−	0.00404560i
$399$	31.0351	+	25.8008i	1.55370	+	1.29165i
$400$	−18.1236	−	8.40033i	−0.906179	−	0.420016i
$401$	−2.42720	−	1.40135i	−0.121209	−	0.0699799i	0.438170	−	0.898892i	$-0.355627\pi$
$401$	−2.42720	−	1.40135i	−0.121209	−	0.0699799i	−0.559379	+	0.828912i	$0.688960\pi$
$402$	0.0691402	−	0.150058i	0.00344840	−	0.00748423i
$403$	−5.01754	+	18.7257i	−0.249941	+	0.932793i
$404$	−12.8191			−0.637775
$405$	−19.8976	+	3.01403i	−0.988721	+	0.149768i
$406$	0.420398			0.0208640
$407$	2.40365	−	8.97056i	0.119145	−	0.444654i
$408$	0.419715	−	0.910929i	0.0207790	−	0.0450977i
$409$	−11.8194	−	6.82391i	−0.584430	−	0.337421i	0.178462	−	0.983947i	$-0.442888\pi$
$409$	−11.8194	−	6.82391i	−0.584430	−	0.337421i	−0.762892	+	0.646526i	$0.776221\pi$
$410$	0.0987746	+	0.0512741i	0.00487813	+	0.00253225i
$411$	−8.81949	−	7.33200i	−0.435033	−	0.361661i
$412$	10.2425	+	2.74447i	0.504613	+	0.135211i
$413$	−7.06878	+	7.06878i	−0.347832	+	0.347832i
$414$	−0.0126299	−	0.0147753i	−0.000620726	−	0.000726168i
$415$	−0.805630	−	17.9762i	−0.0395468	−	0.882419i
$416$	0.886847	−	0.512021i	0.0434812	−	0.0251039i
$417$	−29.6216	+	20.9437i	−1.45058	+	1.02562i
$418$	−0.199625	+	0.0534892i	−0.00976396	+	0.00261624i
$419$	−14.4028	+	24.9464i	−0.703624	+	1.21871i	0.263562	+	0.964643i	$0.415103\pi$
$419$	−14.4028	+	24.9464i	−0.703624	+	1.21871i	−0.967186	+	0.254070i	$0.918231\pi$
$420$	15.2310	+	19.6159i	0.743195	+	0.957157i
$421$	−9.81986	−	17.0085i	−0.478591	−	0.828943i	0.521108	−	0.853491i	$-0.325519\pi$
$421$	−9.81986	−	17.0085i	−0.478591	−	0.828943i	−0.999699	+	0.0245475i	$0.992186\pi$
$422$	−0.400445	−	0.400445i	−0.0194933	−	0.0194933i
$423$	−31.4565	+	15.0200i	−1.52947	+	0.730297i
$424$		−	0.692847i		−	0.0336476i
$425$	25.0729	+	4.36142i	1.21621	+	0.211560i
$426$	−0.296205	+	0.356298i	−0.0143512	+	0.0172627i
$427$	−5.75539	−	21.4794i	−0.278523	−	1.03946i
$428$	5.41274	+	20.2006i	0.261635	+	0.976434i
$429$	1.80032	+	4.87687i	0.0869201	+	0.235457i
$430$	−0.0886961	+	0.402277i	−0.00427731	+	0.0193995i
$431$			23.0868i			1.11205i	0.831165	+	0.556025i	$0.187674\pi$
$431$			23.0868i			1.11205i	−0.831165	+	0.556025i	$0.812326\pi$
$432$	−14.8790	−	14.4765i	−0.715865	−	0.696499i
$433$	−4.93579	−	4.93579i	−0.237199	−	0.237199i	0.578490	−	0.815689i	$-0.303642\pi$
$433$	−4.93579	−	4.93579i	−0.237199	−	0.237199i	−0.815689	+	0.578490i	$0.803642\pi$
$434$	0.294681	+	0.510402i	0.0141451	+	0.0245001i
$435$	−6.92292	−	16.4465i	−0.331929	−	0.788551i
$436$	−16.0917	+	27.8716i	−0.770651	+	1.33481i
$437$	1.59823	−	0.428245i	0.0764538	−	0.0204857i
$438$	0.00752353	+	0.0816924i	0.000359488	+	0.00390342i
$439$	29.3931	−	16.9701i	1.40286	−	0.809939i	0.408171	−	0.912905i	$-0.366167\pi$
$439$	29.3931	−	16.9701i	1.40286	−	0.809939i	0.994685	+	0.102966i	$0.0328333\pi$
$440$	−0.254139	+	0.0113896i	−0.0121156	+	0.000542976i
$441$	−1.80145	−	9.69734i	−0.0857832	−	0.461778i
$442$	−0.307300	+	0.307300i	−0.0146168	+	0.0146168i
$443$	1.60494	+	0.430042i	0.0762530	+	0.0204319i	0.296744	−	0.954957i	$-0.404099\pi$
$443$	1.60494	+	0.430042i	0.0762530	+	0.0204319i	−0.220491	+	0.975389i	$0.570766\pi$
$444$	5.43940	−	31.6948i	0.258143	−	1.50417i
$445$	4.74760	+	14.9972i	0.225058	+	0.710933i
$446$	−0.273109	−	0.157679i	−0.0129321	−	0.00746633i
$447$	2.30342	+	3.25783i	0.108948	+	0.154090i
$448$	−6.62508	+	24.7251i	−0.313006	+	1.16815i
$449$	21.4074			1.01028			0.505138	−	0.863039i	$-0.331442\pi$
$449$	21.4074			1.01028			0.505138	+	0.863039i	$0.331442\pi$
$450$	−0.209115	+	0.371966i	−0.00985776	+	0.0175347i
$451$	−1.74953			−0.0823823
$452$	−3.00395	+	11.2109i	−0.141294	+	0.527316i
$453$	−4.81118	+	0.443089i	−0.226049	+	0.0208182i
$454$	−0.577852	−	0.333623i	−0.0271199	−	0.0156577i
$455$	−6.49672	−	20.5224i	−0.304571	−	0.962105i
$456$	−1.34295	+	0.495758i	−0.0628896	+	0.0232160i
$457$	−5.99463	−	1.60626i	−0.280417	−	0.0751375i	0.115869	−	0.993264i	$-0.463035\pi$
$457$	−5.99463	−	1.60626i	−0.280417	−	0.0751375i	−0.396286	+	0.918127i	$0.629701\pi$
$458$	−0.257312	+	0.257312i	−0.0120234	+	0.0120234i
$459$	23.0836	+	12.9086i	1.07745	+	0.602522i
$460$	1.01714	−	0.0455843i	0.0474242	−	0.00212538i
$461$	10.3969	−	6.00263i	0.484230	−	0.279571i	−0.237947	−	0.971278i	$-0.576475\pi$
$461$	10.3969	−	6.00263i	0.484230	−	0.279571i	0.722178	+	0.691708i	$0.243141\pi$
$462$	0.143538	+	0.0661357i	0.00667797	+	0.00307691i
$463$	−30.6581	+	8.21481i	−1.42480	+	0.381775i	−0.887185	−	0.461414i	$-0.847342\pi$
$463$	−30.6581	+	8.21481i	−1.42480	+	0.381775i	−0.537618	+	0.843189i	$0.680676\pi$
$464$	9.20352	−	15.9410i	0.427263	−	0.740041i
$465$	15.1149	−	19.9334i	0.700939	−	0.924388i
$466$	0.0922566	+	0.159793i	0.00427371	+	0.00740228i
$467$	−7.68283	−	7.68283i	−0.355519	−	0.355519i	0.506639	−	0.862158i	$-0.330888\pi$
$467$	−7.68283	−	7.68283i	−0.355519	−	0.355519i	−0.862158	+	0.506639i	$0.830888\pi$
$468$	7.75637	+	16.2443i	0.358538	+	0.750891i
$469$		−	10.7551i		−	0.496625i
$470$	−0.159145	+	0.721795i	−0.00734081	+	0.0332939i
$471$	4.34268	+	0.745283i	0.200100	+	0.0343408i
$472$	−0.0917733	−	0.342503i	−0.00422421	−	0.0157650i
$473$	−1.67608	−	6.25522i	−0.0770663	−	0.287615i
$474$	−0.359422	−	0.0616834i	−0.0165088	−	0.00283321i
$475$	−20.9030	−	29.7066i	−0.959097	−	1.36303i
$476$		−	32.6378i		−	1.49595i
$477$	18.2142	+	1.42590i	0.833972	+	0.0652877i
$478$	0.0578336	+	0.0578336i	0.00264525	+	0.00264525i
$479$	−18.7658	−	32.5033i	−0.857432	−	1.48512i	−0.874370	−	0.485259i	$-0.838725\pi$
$479$	−18.7658	−	32.5033i	−0.857432	−	1.48512i	0.0169383	−	0.999857i	$-0.494608\pi$
$480$	−1.30911	+	0.179976i	−0.0597524	+	0.00821473i
$481$	−13.9370	+	24.1395i	−0.635470	+	1.10067i
$482$	−0.0599715	+	0.0160693i	−0.00273163	+	0.000731937i
$483$	−1.14919	−	0.529495i	−0.0522899	−	0.0240929i
$484$	1.73135	−	0.999595i	0.0786977	−	0.0454362i
$485$	0.903190	+	20.1531i	0.0410118	+	0.915107i
$486$	−0.333106	+	0.292737i	−0.0151100	+	0.0132788i
$487$	−1.70686	+	1.70686i	−0.0773451	+	0.0773451i	−0.744721	−	0.667376i	$-0.767417\pi$
$487$	−1.70686	+	1.70686i	−0.0773451	+	0.0773451i	0.667376	+	0.744721i	$0.267417\pi$
$488$	0.761874	+	0.204144i	0.0344884	+	0.00924114i
$489$	−35.2787	+	13.0233i	−1.59536	+	0.588934i
$490$	−0.185619	−	0.0963551i	−0.00838540	−	0.00435288i
$491$	2.08785	+	1.20542i	0.0942235	+	0.0544000i	0.546371	−	0.837543i	$-0.316009\pi$
$491$	2.08785	+	1.20542i	0.0942235	+	0.0544000i	−0.452148	+	0.891943i	$0.649342\pi$
$492$	−6.03258	+	0.555575i	−0.271970	+	0.0250473i
$493$	−6.06952	+	22.6518i	−0.273358	+	1.02018i
$494$	0.620286			0.0279080
$495$	0.223607	−	6.70448i	0.0100504	−	0.301344i
$496$	25.8051			1.15868
$497$	−7.80635	+	29.1337i	−0.350163	+	1.30683i
$498$	−0.228914	−	0.323763i	−0.0102579	−	0.0145082i
$499$	17.3958	+	10.0435i	0.778744	+	0.449608i	0.835985	−	0.548753i	$-0.184897\pi$
$499$	17.3958	+	10.0435i	0.778744	+	0.449608i	−0.0572413	+	0.998360i	$0.518230\pi$
$500$	−8.62499	−	20.6205i	−0.385721	−	0.922177i
$501$	−4.28323	+	24.9579i	−0.191361	+	1.11504i
$502$	−0.565346	−	0.151484i	−0.0252326	−	0.00676106i
$503$	−6.67948	+	6.67948i	−0.297823	+	0.297823i	−0.840161	−	0.542338i	$-0.817539\pi$
$503$	−6.67948	+	6.67948i	−0.297823	+	0.297823i	0.542338	+	0.840161i	$0.317539\pi$
$504$	1.03208	+	0.364998i	0.0459724	+	0.0162583i
$505$	−10.5822	−	9.67442i	−0.470904	−	0.430506i
$506$	0.00561119	−	0.00323962i	0.000249448	−	0.000144019i
$507$	0.634048	+	6.88466i	0.0281591	+	0.305759i
$508$	4.04242	−	1.08316i	0.179353	−	0.0480575i
$509$	3.24681	−	5.62364i	0.143912	−	0.249264i	−0.785054	−	0.619427i	$-0.787365\pi$
$509$	3.24681	−	5.62364i	0.143912	−	0.249264i	0.928967	+	0.370163i	$0.120698\pi$
$510$	0.516867	−	0.217568i	0.0228873	−	0.00963405i
$511$	2.67015	+	4.62484i	0.118121	+	0.204591i
$512$	−1.60665	−	1.60665i	−0.0710045	−	0.0710045i
$513$	−10.2691	−	36.3251i	−0.453392	−	1.60379i
$514$		−	0.455133i		−	0.0200751i
$515$	6.38404	+	9.99547i	0.281314	+	0.440453i
$516$	−7.76570	−	21.0364i	−0.341866	−	0.926077i
$517$	−3.00735	−	11.2236i	−0.132263	−	0.493612i
$518$	0.219322	+	0.818519i	0.00963644	+	0.0359637i
$519$	−18.0069	+	21.6601i	−0.790415	+	0.950771i
$520$	0.745625	+	0.164399i	0.0326978	+	0.00720938i
$521$			35.3245i			1.54759i	0.633434	+	0.773797i	$0.281645\pi$
$521$			35.3245i			1.54759i	−0.633434	+	0.773797i	$0.718355\pi$
$522$	−0.324145	−	0.222581i	−0.0141874	−	0.00974211i
$523$	16.0303	+	16.0303i	0.700955	+	0.700955i	0.964615	−	0.263661i	$-0.0849300\pi$
$523$	16.0303	+	16.0303i	0.700955	+	0.700955i	−0.263661	+	0.964615i	$0.584930\pi$
$524$	−5.56496	−	9.63879i	−0.243106	−	0.421072i
$525$	−2.23061	+	27.6876i	−0.0973519	+	1.20839i
$526$	0.225236	−	0.390120i	0.00982075	−	0.0170100i
$527$	−31.7558	+	8.50894i	−1.38330	+	0.370655i
$528$	5.65016	−	3.99490i	0.245892	−	0.173856i
$529$	19.8737	−	11.4741i	0.864072	−	0.498872i
$530$	0.261389	−	0.285917i	0.0113540	−	0.0124194i
$531$	9.19291	−	1.70774i	0.398938	−	0.0741097i
$532$	−32.9398	+	32.9398i	−1.42812	+	1.42812i
$533$	5.07210	+	1.35906i	0.219697	+	0.0588676i
$534$	0.266553	+	0.221597i	0.0115349	+	0.00958943i
$535$	−10.7769	+	20.7607i	−0.465926	+	0.897561i
$536$	0.330374	+	0.190742i	0.0142700	+	0.00823879i
$537$	17.0726	−	37.0535i	0.736736	−	1.59898i
$538$	0.113925	−	0.425173i	0.00491164	−	0.0183305i
$539$	3.28775			0.141613
$540$	−1.35803	−	23.1888i	−0.0584403	−	0.997886i
$541$	39.5238			1.69926			0.849630	−	0.527378i	$-0.176825\pi$
$541$	39.5238			1.69926			0.849630	+	0.527378i	$0.176825\pi$
$542$	0.0811539	−	0.302870i	0.00348586	−	0.0130094i
$543$	−2.77969	+	6.03289i	−0.119288	+	0.258896i
$544$	1.50395	+	0.868306i	0.0644813	+	0.0372283i
$545$	−34.3181	+	10.8640i	−1.47003	+	0.465362i
$546$	−0.364757	−	0.303237i	−0.0156102	−	0.0129774i
$547$	16.9192	+	4.53350i	0.723414	+	0.193838i	0.601695	−	0.798726i	$-0.294492\pi$
$547$	16.9192	+	4.53350i	0.723414	+	0.193838i	0.121720	+	0.992565i	$0.461159\pi$
$548$	9.36074	−	9.36074i	0.399871	−	0.399871i
$549$	−6.93468	+	19.6087i	−0.295965	+	0.836880i
$550$	−0.109172	−	0.0911780i	−0.00465511	−	0.00388784i
$551$	28.9870	−	16.7356i	1.23489	−	0.712963i
$552$	0.0366459	−	0.0259101i	0.00155975	−	0.00110281i
$553$	−22.9299	+	6.14404i	−0.975078	+	0.261271i
$554$	0.239107	−	0.414146i	0.0101587	−	0.0175954i
$555$	28.4099	−	22.0592i	1.20593	−	0.936359i
$556$	−20.9365	−	36.2631i	−0.887907	−	1.53790i
$557$	25.8166	+	25.8166i	1.09388	+	1.09388i	0.995110	+	0.0987730i	$0.0314918\pi$
$557$	25.8166	+	25.8166i	1.09388	+	1.09388i	0.0987730	+	0.995110i	$0.468508\pi$
$558$	0.0430225	−	0.549561i	0.00182129	−	0.0232648i
$559$			19.4366i			0.822082i
$560$	−24.1483	+	15.4234i	−1.02045	+	0.651756i
$561$	−5.63584	+	6.77921i	−0.237945	+	0.286219i
$562$	0.181875	+	0.678767i	0.00767194	+	0.0286321i
$563$	−1.84627	−	6.89036i	−0.0778108	−	0.290394i	0.916045	−	0.401075i	$-0.131363\pi$
$563$	−1.84627	−	6.89036i	−0.0778108	−	0.290394i	−0.993856	+	0.110681i	$0.964697\pi$
$564$	−13.9338	−	37.7451i	−0.586718	−	1.58935i
$565$	−10.9405	+	6.98761i	−0.460270	+	0.293971i
$566$			0.849643i			0.0357132i
$567$	−11.7195	+	26.3811i	−0.492171	+	1.10790i
$568$	−0.756481	−	0.756481i	−0.0317412	−	0.0317412i
$569$	−9.19967	−	15.9343i	−0.385670	−	0.668000i	0.606192	−	0.795319i	$-0.292696\pi$
$569$	−9.19967	−	15.9343i	−0.385670	−	0.668000i	−0.991862	+	0.127318i	$0.959363\pi$
$570$	−0.741229	−	0.302069i	−0.0310467	−	0.0126523i
$571$	22.3140	−	38.6489i	0.933810	−	1.61741i	0.157069	−	0.987588i	$-0.449795\pi$
$571$	22.3140	−	38.6489i	0.933810	−	1.61741i	0.776741	−	0.629820i	$-0.216871\pi$
$572$	−5.79589	+	1.55300i	−0.242338	+	0.0649343i
$573$	−3.38948	−	36.8039i	−0.141598	−	1.53750i
$574$	0.138249	−	0.0798181i	0.00577040	−	0.00333154i
$575$	0.874053	+	0.729989i	0.0364505	+	0.0304426i
$576$	18.1990	−	15.5565i	0.758292	−	0.648186i
$577$	−8.48653	+	8.48653i	−0.353299	+	0.353299i	−0.861335	−	0.508037i	$-0.830371\pi$
$577$	−8.48653	+	8.48653i	−0.353299	+	0.353299i	0.508037	+	0.861335i	$0.330371\pi$
$578$	−0.244745	−	0.0655793i	−0.0101801	−	0.00272774i
$579$	4.51216	−	26.2918i	0.187519	−	1.09265i
$580$	19.6360	−	6.21610i	0.815339	−	0.258109i
$581$	−22.3532	−	12.9056i	−0.927368	−	0.535416i
$582$	0.256635	+	0.362970i	0.0106379	+	0.0150456i
$583$	−1.57620	+	5.88248i	−0.0652797	+	0.243627i
$584$	−0.189421			−0.00783828
$585$	−5.85640	+	19.2634i	−0.242133	+	0.796442i
$586$	−0.579323			−0.0239316
$587$	3.07768	−	11.4861i	0.127029	−	0.474080i	−0.872874	−	0.487945i	$-0.837747\pi$
$587$	3.07768	−	11.4861i	0.127029	−	0.474080i	0.999904	+	0.0138645i	$0.00441336\pi$
$588$	11.3365	−	1.04405i	0.467510	−	0.0430557i
$589$	40.6372	+	23.4619i	1.67443	+	0.966731i
$590$	0.0913430	−	0.175963i	0.00376053	−	0.00724430i
$591$	28.2123	−	10.4147i	1.16050	−	0.428403i
$592$	35.8387	+	9.60295i	1.47296	+	0.394679i
$593$	−27.6174	+	27.6174i	−1.13411	+	1.13411i	−0.144622	+	0.989487i	$0.546197\pi$
$593$	−27.6174	+	27.6174i	−1.13411	+	1.13411i	−0.989487	+	0.144622i	$0.953803\pi$
$594$	−0.0756578	−	0.126990i	−0.00310428	−	0.00521046i
$595$	24.6313	−	26.9427i	1.00979	−	1.10454i
$596$	−3.98828	+	2.30263i	−0.163366	+	0.0943195i
$597$	17.2439	+	7.94522i	0.705746	+	0.325176i
$598$	−0.0187841	+	0.00503318i	−0.000768138	+	0.000205822i
$599$	8.55530	−	14.8182i	0.349560	−	0.605456i	−0.636611	−	0.771185i	$-0.719664\pi$
$599$	8.55530	−	14.8182i	0.349560	−	0.605456i	0.986171	+	0.165729i	$0.0529977\pi$
$600$	−0.810947	−	0.559560i	−0.0331068	−	0.0228439i
$601$	15.0104	+	25.9988i	0.612288	+	1.06051i	0.990854	+	0.134939i	$0.0430840\pi$
$601$	15.0104	+	25.9988i	0.612288	+	1.06051i	−0.378566	+	0.925574i	$0.623583\pi$
$602$	0.417824	+	0.417824i	0.0170292	+	0.0170292i
$603$	−5.69432	+	8.29264i	−0.231891	+	0.337703i
$604$		−	5.57672i		−	0.226914i
$605$	2.18362	+	0.481456i	0.0887768	+	0.0195740i
$606$	−0.311394	−	0.0534409i	−0.0126495	−	0.00217089i
$607$	7.37827	+	27.5361i	0.299475	+	1.11765i	0.937598	+	0.347721i	$0.113044\pi$
$607$	7.37827	+	27.5361i	0.299475	+	1.11765i	−0.638123	+	0.769934i	$0.720289\pi$
$608$	−0.641525	−	2.39420i	−0.0260173	−	0.0970977i
$609$	−25.2272	−	4.32945i	−1.02226	−	0.175438i
$610$	0.237385	+	0.371674i	0.00961145	+	0.0150486i
$611$			34.8746i			1.41088i
$612$	−17.2802	+	25.1652i	−0.698511	+	1.01724i
$613$	−15.6053	−	15.6053i	−0.630291	−	0.630291i	0.317850	−	0.948141i	$-0.397039\pi$
$613$	−15.6053	−	15.6053i	−0.630291	−	0.630291i	−0.948141	+	0.317850i	$0.897039\pi$
$614$	−0.192531	−	0.333474i	−0.00776994	−	0.0134579i
$615$	−5.39921	−	4.09408i	−0.217717	−	0.165089i
$616$	−0.182453	+	0.316018i	−0.00735125	+	0.0127327i
$617$	−17.8825	+	4.79160i	−0.719922	+	0.192903i	−0.600137	−	0.799897i	$-0.704887\pi$
$617$	−17.8825	+	4.79160i	−0.719922	+	0.192903i	−0.119785	+	0.992800i	$0.538221\pi$
$618$	0.237364	+	0.109367i	0.00954817	+	0.00439937i
$619$	−25.4965	+	14.7204i	−1.02479	+	0.591663i	−0.915488	−	0.402345i	$-0.868195\pi$
$619$	−25.4965	+	14.7204i	−1.02479	+	0.591663i	−0.109303	+	0.994009i	$0.534862\pi$
$620$	21.3109	+	19.4826i	0.855865	+	0.782442i
$621$	0.605731	+	1.01671i	0.0243072	+	0.0407990i
$622$	−0.594139	+	0.594139i	−0.0238228	+	0.0238228i
$623$	21.7955	+	5.84008i	0.873218	+	0.233978i
$624$	−19.4838	+	7.19253i	−0.779976	+	0.287932i
$625$	8.44205	−	23.5315i	0.337682	−	0.941260i
$626$	0.545757	+	0.315093i	0.0218128	+	0.0125936i
$627$	12.5299	−	1.15395i	0.500396	−	0.0460844i
$628$	−1.31629	+	4.91245i	−0.0525255	+	0.196028i
$629$	−47.2697			−1.88477
$630$	0.288206	+	0.539993i	0.0114824	+	0.0215138i
$631$	0.564520			0.0224732			0.0112366	−	0.999937i	$-0.496423\pi$
$631$	0.564520			0.0224732			0.0112366	+	0.999937i	$0.496423\pi$
$632$	0.217929	−	0.813323i	0.00866876	−	0.0323522i
$633$	19.9059	+	28.1538i	0.791188	+	1.11901i
$634$	−0.217782	−	0.125736i	−0.00864921	−	0.00499362i
$635$	4.15448	+	2.15660i	0.164866	+	0.0855822i
$636$	−3.56691	+	20.7839i	−0.141437	+	0.824137i
$637$	−9.53156	−	2.55398i	−0.377654	−	0.101192i
$638$	0.0926799	−	0.0926799i	0.00366923	−	0.00366923i
$639$	21.4440	−	18.3302i	0.848310	−	0.725133i
$640$	−0.0910428	−	2.03146i	−0.00359878	−	0.0803006i
$641$	−1.08228	+	0.624855i	−0.0427475	+	0.0246803i	−0.521221	−	0.853421i	$-0.674523\pi$
$641$	−1.08228	+	0.624855i	−0.0427475	+	0.0246803i	0.478474	+	0.878102i	$0.341190\pi$
$642$	0.0472697	+	0.513266i	0.00186558	+	0.0202570i
$643$	9.62115	−	2.57798i	0.379421	−	0.101666i	−0.0640676	−	0.997946i	$-0.520407\pi$
$643$	9.62115	−	2.57798i	0.379421	−	0.101666i	0.443489	+	0.896280i	$0.353741\pi$
$644$	0.730230	−	1.26480i	0.0287751	−	0.0498399i
$645$	9.46530	−	23.2264i	0.372696	−	0.914537i
$646$	0.525953	+	0.910978i	0.0206933	+	0.0358419i
$647$	−28.0800	−	28.0800i	−1.10394	−	1.10394i	−0.993931	−	0.110008i	$-0.964912\pi$
$647$	−28.0800	−	28.0800i	−1.10394	−	1.10394i	−0.110008	−	0.993931i	$-0.535088\pi$
$648$	−0.602528	−	0.827866i	−0.0236695	−	0.0325216i
$649$			3.11673i			0.122342i
$650$	0.245674	+	0.349142i	0.00963613	+	0.0136945i
$651$	−12.4268	−	33.6629i	−0.487045	−	1.31935i
$652$	−11.2343	−	41.9268i	−0.439968	−	1.64198i
$653$	3.08328	+	11.5069i	0.120658	+	0.450301i	0.999648	−	0.0265390i	$-0.00844861\pi$
$653$	3.08328	+	11.5069i	0.120658	+	0.450301i	−0.878990	+	0.476840i	$0.841782\pi$
$654$	−0.507081	+	0.609956i	−0.0198284	+	0.0238512i
$655$	2.68037	−	12.1567i	0.104731	−	0.475001i
$656$		−	6.98964i		−	0.272899i
$657$	0.389834	−	4.97967i	0.0152089	−	0.194275i
$658$	0.749690	+	0.749690i	0.0292260	+	0.0292260i
$659$	−10.5233	−	18.2269i	−0.409930	−	0.710019i	0.584952	−	0.811068i	$-0.301113\pi$
$659$	−10.5233	−	18.2269i	−0.409930	−	0.710019i	−0.994881	+	0.101049i	$0.967780\pi$
$660$	7.68225	+	0.966689i	0.299031	+	0.0376283i
$661$	−9.04860	+	15.6726i	−0.351950	+	0.609595i	−0.986591	−	0.163212i	$-0.947815\pi$
$661$	−9.04860	+	15.6726i	−0.351950	+	0.609595i	0.634641	+	0.772807i	$0.281148\pi$
$662$	0.0296550	−	0.00794603i	0.00115257	−	0.000308831i
$663$	21.6052	−	15.2757i	0.839075	−	0.593260i
$664$	0.792869	−	0.457763i	0.0307693	−	0.0177647i
$665$	−52.0512	+	2.33274i	−2.01846	+	0.0904599i
$666$	0.264261	−	0.747234i	0.0102399	−	0.0289547i
$667$	−0.742013	+	0.742013i	−0.0287309	+	0.0287309i
$668$	−28.2324	−	7.56486i	−1.09235	−	0.292693i
$669$	14.7648	+	12.2746i	0.570841	+	0.474563i
$670$	0.0643748	+	0.203353i	0.00248701	+	0.00785620i
$671$	−6.00411	−	3.46648i	−0.231786	−	0.133822i
$672$	−0.793201	+	1.72152i	−0.0305984	+	0.0664092i
$673$	3.18300	−	11.8791i	0.122696	−	0.457906i	−0.877052	−	0.480396i	$-0.840493\pi$
$673$	3.18300	−	11.8791i	0.122696	−	0.457906i	0.999747	+	0.0224904i	$0.00715951\pi$
$674$	−0.0925204			−0.00356375
$675$	16.3792	−	20.1673i	0.630436	−	0.776241i
$676$	−7.98013			−0.306928
$677$	−6.19250	+	23.1107i	−0.237997	+	0.888218i	0.738778	+	0.673949i	$0.235403\pi$
$677$	−6.19250	+	23.1107i	−0.237997	+	0.888218i	−0.976775	+	0.214268i	$0.931263\pi$
$678$	−0.119706	+	0.259805i	−0.00459730	+	0.00997775i
$679$	25.0602	+	14.4685i	0.961721	+	0.555250i
$680$	0.390787	+	1.23445i	0.0149860	+	0.0473391i
$681$	31.2399	+	25.9710i	1.19711	+	0.995210i
$682$	0.177486	+	0.0475574i	0.00679631	+	0.00182107i
$683$	2.35896	−	2.35896i	0.0902632	−	0.0902632i	−0.660533	−	0.750797i	$-0.729670\pi$
$683$	2.35896	−	2.35896i	0.0902632	−	0.0902632i	0.750797	+	0.660533i	$0.229670\pi$
$684$	42.8380	−	7.95790i	1.63795	−	0.304278i
$685$	14.7918	−	0.662913i	0.565164	−	0.0253286i
$686$	0.293344	−	0.169362i	0.0111999	−	0.00646628i
$687$	18.0907	−	12.7909i	0.690203	−	0.488001i
$688$	24.9905	−	6.69619i	0.952755	−	0.255290i
$689$	9.13920	−	15.8296i	0.348176	−	0.603058i
$690$	0.0248977	+	0.00313298i	0.000947838	+	0.000119270i
$691$	6.41886	+	11.1178i	0.244185	+	0.422941i	0.961902	−	0.273394i	$-0.0881462\pi$
$691$	6.41886	+	11.1178i	0.244185	+	0.422941i	−0.717717	+	0.696335i	$0.754813\pi$
$692$	−22.9893	−	22.9893i	−0.873924	−	0.873924i
$693$	−7.93229	−	5.44688i	−0.301323	−	0.206910i
$694$			0.664130i			0.0252100i
$695$	10.0841	−	45.7360i	0.382512	−	1.73486i
$696$	0.580396	−	0.698144i	0.0219999	−	0.0264631i
$697$	2.30476	+	8.60147i	0.0872989	+	0.325804i
$698$	0.197932	+	0.738694i	0.00749185	+	0.0279600i
$699$	−3.89050	−	10.5389i	−0.147152	−	0.398620i
$700$	−31.5872	−	5.49459i	−1.19388	−	0.207676i
$701$		−	25.8725i		−	0.977189i	−0.872511	−	0.488595i	$-0.837510\pi$
$701$		−	25.8725i		−	0.977189i	0.872511	−	0.488595i	$-0.162490\pi$
$702$	0.120693	+	0.426931i	0.00455527	+	0.0161135i
$703$	47.7070	+	47.7070i	1.79930	+	1.79930i
$704$	3.99029	+	6.91139i	0.150390	+	0.260483i
$705$	16.9833	−	41.6744i	0.639629	−	1.56955i
$706$	−0.375109	+	0.649707i	−0.0141174	+	0.0244521i
$707$	−19.8659	+	5.32304i	−0.747133	+	0.200194i
$708$	0.989737	+	10.7468i	0.0371966	+	0.403890i
$709$	9.51442	−	5.49315i	0.357321	−	0.206300i	−0.310584	−	0.950546i	$-0.600525\pi$
$709$	9.51442	−	5.49315i	0.357321	−	0.206300i	0.667905	+	0.744246i	$0.267191\pi$
$710$	−0.0267810	−	0.597572i	−0.00100507	−	0.0224265i
$711$	20.9329	+	7.40298i	0.785045	+	0.277633i
$712$	−0.565938	+	0.565938i	−0.0212094	+	0.0212094i
$713$	−1.42099	−	0.380753i	−0.0532165	−	0.0142593i
$714$	0.136062	−	0.792818i	0.00509200	−	0.0296705i
$715$	−5.95657	−	3.09207i	−0.222763	−	0.115637i
$716$	40.7810	+	23.5449i	1.52406	+	0.879914i
$717$	−2.87488	−	4.06607i	−0.107364	−	0.151850i
$718$	−0.157814	+	0.588970i	−0.00588957	+	0.0219802i
$719$	−45.6020			−1.70067			−0.850334	−	0.526244i	$-0.823600\pi$
$719$	−45.6020			−1.70067			−0.850334	+	0.526244i	$0.823600\pi$
$720$	26.7854	+	0.893340i	0.998231	+	0.0332928i
$721$	17.0125			0.633580
$722$	0.248692	−	0.928132i	0.00925537	−	0.0345415i
$723$	3.76425	−	0.346672i	0.139994	−	0.0128929i
$724$	−6.63978	−	3.83348i	−0.246766	−	0.142470i
$725$	20.9008	+	9.68758i	0.776236	+	0.359788i
$726$	0.0462241	−	0.0170638i	0.00171554	−	0.000633298i
$727$	−30.7841	−	8.24857i	−1.14172	−	0.305923i	−0.362077	−	0.932148i	$-0.617932\pi$
$727$	−30.7841	−	8.24857i	−1.14172	−	0.305923i	−0.779642	+	0.626226i	$0.784599\pi$
$728$	0.774441	−	0.774441i	0.0287027	−	0.0287027i
$729$	23.0037	−	14.1360i	0.851991	−	0.523557i
$730$	−0.0781681	−	0.0714622i	−0.00289313	−	0.00264493i
$731$	−28.5454	+	16.4807i	−1.05579	+	0.609561i
$732$	−21.8036	−	10.0461i	−0.805885	−	0.371316i
$733$	44.8415	−	12.0153i	1.65626	−	0.443794i	0.694904	−	0.719102i	$-0.255447\pi$
$733$	44.8415	−	12.0153i	1.65626	−	0.443794i	0.961356	+	0.275308i	$0.0887800\pi$
$734$	0.175610	−	0.304166i	0.00648190	−	0.0112270i
$735$	10.1463	+	7.69365i	0.374251	+	0.283785i
$736$	0.0388545	+	0.0672980i	0.00143220	+	0.00248064i
$737$	−2.37104	−	2.37104i	−0.0873385	−	0.0873385i
$738$	−0.148856	−	0.0116532i	−0.00547946	−	0.000428960i
$739$			38.1714i			1.40416i	0.712099	+	0.702079i	$0.247745\pi$
$739$			38.1714i			1.40416i	−0.712099	+	0.702079i	$0.752255\pi$
$740$	22.3469	+	34.9885i	0.821487	+	1.28620i
$741$	−37.2221	−	6.38799i	−1.36739	−	0.234669i
$742$	−0.143821	−	0.536747i	−0.00527983	−	0.0197046i
$743$	−7.86627	−	29.3573i	−0.288585	−	1.07702i	−0.946179	−	0.323643i	$-0.895092\pi$
$743$	−7.86627	−	29.3573i	−0.288585	−	1.07702i	0.657594	−	0.753373i	$-0.271574\pi$
$744$	1.25444	+	0.215285i	0.0459901	+	0.00789275i
$745$	−5.03011	−	1.10906i	−0.184289	−	0.0406330i
$746$			0.430406i			0.0157583i
$747$	10.4024	+	21.7858i	0.380602	+	0.797100i
$748$	−7.19525	−	7.19525i	−0.263085	−	0.263085i
$749$	16.7763	+	29.0575i	0.612994	+	1.06174i
$750$	−0.123549	−	0.536857i	−0.00451138	−	0.0196032i
$751$	13.3968	−	23.2039i	0.488855	−	0.846721i	−0.511063	−	0.859543i	$-0.670748\pi$
$751$	13.3968	−	23.2039i	0.488855	−	0.846721i	0.999918	+	0.0128219i	$0.00408146\pi$
$752$	44.8398	−	12.0148i	1.63514	−	0.438134i
$753$	32.3652	+	14.9124i	1.17945	+	0.543439i
$754$	−0.340685	+	0.196695i	−0.0124070	+	0.00716320i
$755$	4.20868	−	4.60362i	0.153170	−	0.167543i
$756$	−29.0811	−	16.2625i	−1.05767	−	0.591461i
$757$	−11.4087	+	11.4087i	−0.414657	+	0.414657i	−0.883357	−	0.468700i	$-0.844722\pi$
$757$	−11.4087	+	11.4087i	−0.414657	+	0.414657i	0.468700	+	0.883357i	$0.344722\pi$
$758$	0.118107	+	0.0316467i	0.00428984	+	0.00114946i
$759$	−0.370079	+	0.136616i	−0.0134330	+	0.00495886i
$760$	0.851470	−	1.64027i	0.0308861	−	0.0594990i
$761$	25.7323	+	14.8565i	0.932795	+	0.538549i	0.887694	−	0.460433i	$-0.152306\pi$
$761$	25.7323	+	14.8565i	0.932795	+	0.538549i	0.0451005	+	0.998982i	$0.485639\pi$
$762$	0.102711	−	0.00945929i	0.00372084	−	0.000342674i
$763$	−13.3639	+	49.8747i	−0.483806	+	1.80559i
$764$	42.6600			1.54338
$765$	−33.2567	+	7.73283i	−1.20240	+	0.279581i
$766$	1.06605			0.0385180
$767$	2.42112	−	9.03576i	0.0874217	−	0.326262i
$768$	15.9343	+	22.5366i	0.574980	+	0.813220i
$769$	−24.3067	−	14.0335i	−0.876523	−	0.506061i	−0.00701246	−	0.999975i	$-0.502232\pi$
$769$	−24.3067	−	14.0335i	−0.876523	−	0.506061i	−0.869510	+	0.493915i	$0.835565\pi$
$770$	−0.194516	+	0.0615774i	−0.00700987	+	0.00221910i
$771$	−4.68717	+	27.3116i	−0.168804	+	0.983602i
$772$	29.7414	+	7.96918i	1.07042	+	0.286817i
$773$	−7.97067	+	7.97067i	−0.286685	+	0.286685i	−0.835768	−	0.549083i	$-0.814977\pi$
$773$	−7.97067	+	7.97067i	−0.286685	+	0.286685i	0.549083	+	0.835768i	$0.314977\pi$
$774$	−0.100942	−	0.543378i	−0.00362828	−	0.0195313i
$775$	2.88893	+	32.1661i	0.103774	+	1.15544i
$776$	−0.888884	+	0.513198i	−0.0319091	+	0.0184227i
$777$	−4.73154	−	51.3763i	−0.169743	−	1.84311i
$778$	−0.710771	+	0.190451i	−0.0254824	+	0.00682798i
$779$	6.35496	−	11.0071i	0.227690	−	0.394371i
$780$	−21.5208	−	8.77024i	−0.770568	−	0.314025i
$781$	4.70177	+	8.14371i	0.168243	+	0.291405i
$782$	−0.0233193	−	0.0233193i	−0.000833898	−	0.000833898i
$783$	17.1590	+	16.6948i	0.613213	+	0.596624i
$784$			13.1350i			0.469108i
$785$	−4.79396	+	3.06187i	−0.171104	+	0.109283i
$786$	−0.0949979	−	0.257339i	−0.00338846	−	0.00917898i
$787$	−3.22168	−	12.0235i	−0.114840	−	0.428590i	0.884435	−	0.466664i	$-0.154544\pi$
$787$	−3.22168	−	12.0235i	−0.114840	−	0.428590i	−0.999275	+	0.0380742i	$0.987878\pi$
$788$	8.98400	+	33.5287i	0.320042	+	1.19441i
$789$	−17.5336	+	21.0907i	−0.624211	+	0.750849i
$790$	0.396773	−	0.253416i	0.0141165	−	0.00901613i
$791$			18.6210i			0.662085i
$792$	0.307996	−	0.147063i	0.0109442	−	0.00522566i
$793$	14.7138	+	14.7138i	0.522503	+	0.522503i
$794$	−0.128077	−	0.221835i	−0.00454527	−	0.00787265i
$795$	−18.6299	+	14.4654i	−0.660734	+	0.513034i
$796$	−10.9573	+	18.9786i	−0.388371	+	0.672678i
$797$	31.1970	−	8.35922i	1.10506	−	0.296099i	0.340234	−	0.940341i	$-0.389494\pi$
$797$	31.1970	−	8.35922i	1.10506	−	0.296099i	0.764821	+	0.644242i	$0.222827\pi$
$798$	−0.937473	+	0.662832i	−0.0331862	+	0.0234640i
$799$	−51.2183	+	29.5709i	−1.81197	+	1.04614i
$800$	1.09355	−	1.30936i	0.0386627	−	0.0462928i
$801$	−13.7132	−	16.0426i	−0.484532	−	0.566839i
$802$	0.0563780	−	0.0563780i	0.00199078	−	0.00199078i
$803$	1.60824	+	0.430926i	0.0567534	+	0.0152070i
$804$	−8.92855	−	7.42267i	−0.314886	−	0.261778i
$805$	1.55733	−	0.493001i	0.0548888	−	0.0173760i
$806$	−0.477611	−	0.275749i	−0.0168231	−	0.00971283i
$807$	−11.2150	+	24.3405i	−0.394787	+	0.856825i
$808$	0.188808	−	0.704642i	0.00664225	−	0.0247892i
$809$	1.79619			0.0631505			0.0315753	−	0.999501i	$-0.489948\pi$
$809$	1.79619			0.0631505			0.0315753	+	0.999501i	$0.489948\pi$
$810$	0.0636820	−	0.568949i	0.00223756	−	0.0199908i
$811$	−31.1802			−1.09488			−0.547442	−	0.836844i	$-0.684398\pi$
$811$	−31.1802			−1.09488			−0.547442	+	0.836844i	$0.684398\pi$
$812$	7.64649	−	28.5371i	0.268339	−	1.00146i
$813$	−7.98897	+	17.3389i	−0.280185	+	0.608100i
$814$	0.228800	+	0.132098i	0.00801943	+	0.00463002i
$815$	22.3677	−	43.0892i	0.783506	−	1.50935i
$816$	−27.0839	−	22.5160i	−0.948127	−	0.788217i
$817$	45.4427	+	12.1763i	1.58984	+	0.425996i
$818$	0.274535	−	0.274535i	0.00959888	−	0.00959888i
$819$	18.7654	+	21.9531i	0.655717	+	0.767102i
$820$	5.27713	−	5.77232i	0.184285	−	0.201578i
$821$	5.30733	−	3.06419i	0.185227	−	0.106941i	−0.404519	−	0.914530i	$-0.632561\pi$
$821$	5.30733	−	3.06419i	0.185227	−	0.106941i	0.589746	+	0.807589i	$0.299228\pi$
$822$	0.266409	−	0.188362i	0.00929207	−	0.00656987i
$823$	−16.5999	+	4.44794i	−0.578637	+	0.155045i	−0.536255	−	0.844056i	$-0.680161\pi$
$823$	−16.5999	+	4.44794i	−0.578637	+	0.155045i	−0.0423825	+	0.999101i	$0.513495\pi$
$824$	−0.301717	+	0.522589i	−0.0105108	+	0.0182053i
$825$	5.61219	+	6.59570i	0.195391	+	0.229633i
$826$	−0.142193	−	0.246286i	−0.00494753	−	0.00856937i
$827$	13.3792	+	13.3792i	0.465240	+	0.465240i	0.900369	−	0.435128i	$-0.143297\pi$
$827$	13.3792	+	13.3792i	0.465240	+	0.465240i	−0.435128	+	0.900369i	$0.643297\pi$
$828$	−1.23269	+	0.588588i	−0.0428389	+	0.0204549i
$829$		−	46.0040i		−	1.59778i	−0.601474	−	0.798892i	$-0.705420\pi$
$829$		−	46.0040i		−	1.59778i	0.601474	−	0.798892i	$-0.294580\pi$
$830$	0.499892	+	0.110219i	0.0173515	+	0.00382575i
$831$	−18.6134	+	22.3896i	−0.645691	+	0.776686i
$832$	−6.19944	−	23.1366i	−0.214927	−	0.802119i
$833$	−4.33113	−	16.1640i	−0.150065	−	0.560050i
$834$	−0.357402	−	0.968163i	−0.0123758	−	0.0335247i
$835$	−17.5969	−	27.5515i	−0.608967	−	0.953458i
$836$			14.5236i			0.502310i
$837$	−8.24132	+	32.5349i	−0.284862	+	1.12457i
$838$	−0.579444	−	0.579444i	−0.0200166	−	0.0200166i
$839$	−4.56651	−	7.90943i	−0.157653	−	0.273064i	0.776369	−	0.630279i	$-0.217060\pi$
$839$	−4.56651	−	7.90943i	−0.157653	−	0.273064i	−0.934022	+	0.357215i	$0.883726\pi$
$840$	−1.30258	+	0.548302i	−0.0449433	+	0.0189182i
$841$	3.88615	−	6.73100i	0.134005	−	0.232104i
$842$	0.539670	−	0.144604i	0.0185982	−	0.00498339i
$843$	−3.92369	−	42.6044i	−0.135139	−	1.46737i
$844$	−34.4662	+	19.8991i	−1.18638	+	0.684954i
$845$	−6.58764	−	6.02250i	−0.226622	−	0.207180i
$846$	−0.181117	−	0.974968i	−0.00622694	−	0.0335201i
$847$	2.26801	−	2.26801i	0.0779298	−	0.0779298i
$848$	−23.5013	−	6.29717i	−0.807039	−	0.216246i
$849$	8.75001	−	50.9853i	0.300300	−	1.74981i
$850$	−0.304453	+	0.656852i	−0.0104426	+	0.0225298i
$851$	−1.83182	−	1.05760i	−0.0627938	−	0.0362540i
$852$	18.7983	+	26.5873i	0.644020	+	0.910867i
$853$	7.46361	−	27.8546i	0.255549	−	0.953722i	−0.712235	−	0.701941i	$-0.752317\pi$
$853$	7.46361	−	27.8546i	0.255549	−	0.953722i	0.967784	−	0.251781i	$-0.0810163\pi$
$854$	0.632597			0.0216470
$855$	41.3687	+	25.7600i	1.41478	+	0.880974i
$856$	−1.19011			−0.0406772
$857$	−4.32792	+	16.1520i	−0.147839	+	0.551743i	0.851774	+	0.523910i	$0.175527\pi$
$857$	−4.32792	+	16.1520i	−0.147839	+	0.551743i	−0.999613	+	0.0278327i	$0.991139\pi$
$858$	−0.147264	+	0.0135624i	−0.00502752	+	0.000463014i
$859$	−27.0868	−	15.6386i	−0.924191	−	0.533582i	−0.0392215	−	0.999231i	$-0.512488\pi$
$859$	−27.0868	−	15.6386i	−0.924191	−	0.533582i	−0.884970	+	0.465648i	$0.845821\pi$
$860$	25.6938	+	13.3377i	0.876150	+	0.454811i
$861$	−9.11803	+	3.36596i	−0.310742	+	0.114712i
$862$	−0.634390	−	0.169984i	−0.0216074	−	0.00578969i
$863$	−27.1480	+	27.1480i	−0.924130	+	0.924130i	−0.997318	−	0.0731879i	$-0.976683\pi$
$863$	−27.1480	+	27.1480i	−0.924130	+	0.924130i	0.0731879	+	0.997318i	$0.476683\pi$
$864$	1.52306	−	0.907404i	0.0518154	−	0.0308705i
$865$	−1.62807	−	36.3276i	−0.0553561	−	1.23518i
$866$	0.171969	−	0.0992866i	0.00584376	−	0.00337389i
$867$	14.0113	+	6.45577i	0.475848	+	0.219250i
$868$	40.0065	−	10.7197i	1.35791	−	0.363851i
$869$	−3.70056	+	6.40956i	−0.125533	+	0.217430i
$870$	0.502899	−	0.0691383i	0.0170499	−	0.00234401i
$871$	5.03207	+	8.71580i	0.170505	+	0.295323i
$872$	−1.29504	−	1.29504i	−0.0438556	−	0.0438556i
$873$	−11.6621	−	24.4240i	−0.394701	−	0.826628i
$874$			0.0470701i			0.00159217i
$875$	−21.9287	−	28.3743i	−0.741326	−	0.959226i
$876$	5.68222	+	0.975172i	0.191984	+	0.0329480i
$877$	3.84160	+	14.3370i	0.129722	+	0.484128i	0.999964	−	0.00849635i	$-0.00270451\pi$
$877$	3.84160	+	14.3370i	0.129722	+	0.484128i	−0.870242	+	0.492624i	$0.836038\pi$
$878$	0.249897	+	0.932626i	0.00843360	+	0.0314746i
$879$	34.7640	+	5.96613i	1.17256	+	0.201233i
$880$	−1.92349	+	8.72388i	−0.0648407	+	0.294082i
$881$		−	43.3440i		−	1.46030i	−0.683289	−	0.730148i	$-0.739451\pi$
$881$		−	43.3440i		−	1.46030i	0.683289	−	0.730148i	$-0.260549\pi$
$882$	0.279732	+	0.0218989i	0.00941907	+	0.000737374i
$883$	−11.7828	−	11.7828i	−0.396524	−	0.396524i	0.480481	−	0.877005i	$-0.340462\pi$
$883$	−11.7828	−	11.7828i	−0.396524	−	0.396524i	−0.877005	+	0.480481i	$0.840462\pi$
$884$	15.2705	+	26.4493i	0.513602	+	0.889585i
$885$	−7.29345	+	9.61850i	−0.245167	+	0.323322i
$886$	−0.0236338	+	0.0409350i	−0.000793994	+	0.00137524i
$887$	1.59865	−	0.428358i	0.0536775	−	0.0143828i	−0.231880	−	0.972744i	$-0.574488\pi$
$887$	1.59865	−	0.428358i	0.0536775	−	0.0143828i	0.285558	+	0.958361i	$0.407821\pi$
$888$	1.66209	+	0.765815i	0.0557760	+	0.0256991i
$889$	5.81479	−	3.35717i	0.195022	−	0.112596i
$890$	−0.447055	+	0.0200354i	−0.0149853	+	0.000671587i
$891$	3.23227	+	8.39955i	0.108285	+	0.281396i
$892$	−15.6709	+	15.6709i	−0.524702	+	0.524702i
$893$	81.5365	+	21.8476i	2.72852	+	0.731103i
$894$	−0.106480	+	0.0393076i	−0.00356123	+	0.00131464i
$895$	15.8959	+	50.2133i	0.531341	+	1.67845i
$896$	−2.52610	−	1.45844i	−0.0843911	−	0.0487232i
$897$	1.17903	−	0.108583i	0.0393666	−	0.00362550i
$898$	−0.157619	+	0.588242i	−0.00525981	+	0.0196299i
$899$	−29.7594			−0.992531
$900$	21.4460	+	20.9605i	0.714865	+	0.698684i
$901$	30.9973			1.03267
$902$	0.0128815	−	0.0480745i	0.000428908	−	0.00160071i
$903$	−20.7698	−	29.3757i	−0.691175	−	0.977561i
$904$	−0.571997	−	0.330243i	−0.0190243	−	0.0109837i
$905$	−2.58810	−	8.17552i	−0.0860313	−	0.271763i
$906$	0.0232485	−	0.135466i	0.000772380	−	0.00450057i
$907$	−11.2088	−	3.00340i	−0.372183	−	0.0997261i	0.0678789	−	0.997694i	$-0.478377\pi$
$907$	−11.2088	−	3.00340i	−0.372183	−	0.0997261i	−0.440062	+	0.897967i	$0.645044\pi$
$908$	−33.1571	+	33.1571i	−1.10036	+	1.10036i
$909$	18.1357	+	6.41375i	0.601524	+	0.212731i
$910$	0.611759	−	0.0274168i	0.0202796	−	0.000908859i
$911$	−22.0149	+	12.7103i	−0.729388	+	0.421112i	−0.818198	−	0.574936i	$-0.805027\pi$
$911$	−22.0149	+	12.7103i	−0.729388	+	0.421112i	0.0888105	+	0.996049i	$0.471693\pi$
$912$	4.61020	+	50.0588i	0.152659	+	1.65761i
$913$	−7.77308	+	2.08279i	−0.257252	+	0.0689303i
$914$	0.0882750	−	0.152897i	0.00291988	−	0.00505738i
$915$	−10.4173	−	24.7481i	−0.344386	−	0.818146i
$916$	12.7865	+	22.1468i	0.422477	+	0.731752i
$917$	−12.6265	−	12.6265i	−0.416964	−	0.416964i
$918$	−0.524670	+	0.539258i	−0.0173167	+	0.0177982i
$919$		−	0.140888i		−	0.00464747i	−0.999997	−	0.00232373i	$-0.999260\pi$
$919$		−	0.140888i		−	0.00464747i	0.999997	−	0.00232373i	$-0.000739668\pi$
$920$	−0.0124754	+	0.0565814i	−0.000411300	+	0.00186543i
$921$	8.11914	+	21.9939i	0.267535	+	0.724722i
$922$	0.0883929	+	0.329887i	0.00291106	+	0.0108642i
$923$	−7.30483	−	27.2620i	−0.240441	−	0.897339i
$924$	7.10013	−	8.54057i	0.233577	−	0.280964i
$925$	−7.95787	+	45.7481i	−0.261653	+	1.50419i
$926$		−	0.902923i		−	0.0296719i
$927$	−13.1174	−	9.00733i	−0.430831	−	0.295840i
$928$	1.11156	+	1.11156i	0.0364887	+	0.0364887i
$929$	−7.76864	−	13.4557i	−0.254881	−	0.441467i	0.709982	−	0.704220i	$-0.248703\pi$
$929$	−7.76864	−	13.4557i	−0.254881	−	0.441467i	−0.964863	+	0.262753i	$0.915370\pi$
$930$	0.436450	+	0.562102i	0.0143118	+	0.0184321i
$931$	−11.9423	+	20.6847i	−0.391395	+	0.677915i
$932$	12.5250	−	3.35605i	0.410269	−	0.109931i
$933$	41.7717	−	29.5343i	1.36755	−	0.966910i
$934$	0.267680	−	0.154545i	0.00875876	−	0.00505687i
$935$	−0.509557	−	11.3699i	−0.0166643	−	0.371835i
$936$	−1.00716	+	0.187097i	−0.0329200	+	0.00611545i
$937$	−3.96712	+	3.96712i	−0.129600	+	0.129600i	−0.768931	−	0.639331i	$-0.779211\pi$
$937$	−3.96712	+	3.96712i	−0.129600	+	0.129600i	0.639331	+	0.768931i	$0.279211\pi$
$938$	0.295534	+	0.0791881i	0.00964953	+	0.00258558i
$939$	−29.5047	−	24.5285i	−0.962851	−	0.800457i
$940$	46.1016	+	23.9314i	1.50367	+	0.780557i
$941$	−7.10353	−	4.10123i	−0.231569	−	0.133696i	0.379727	−	0.925099i	$-0.376018\pi$
$941$	−7.10353	−	4.10123i	−0.231569	−	0.133696i	−0.611295	+	0.791402i	$0.709351\pi$
$942$	−0.0524537	+	0.113843i	−0.00170903	+	0.00370920i
$943$	−0.103132	+	0.384894i	−0.00335844	+	0.0125339i
$944$	−12.4518			−0.405271
$945$	−11.7335	−	35.3719i	−0.381691	−	1.15065i
$946$	0.184225			0.00598967
$947$	−3.47481	+	12.9682i	−0.112916	+	0.421409i	−0.999123	−	0.0418819i	$-0.986665\pi$
$947$	−3.47481	+	12.9682i	−0.112916	+	0.421409i	0.886206	+	0.463290i	$0.153331\pi$
$948$	−10.7245	+	23.2760i	−0.348317	+	0.755969i
$949$	−4.32771	−	2.49861i	−0.140484	−	0.0811082i
$950$	0.970197	−	0.355659i	0.0314774	−	0.0115391i
$951$	11.7737	+	9.78798i	0.381789	+	0.317397i
$952$	1.79404	+	0.480712i	0.0581452	+	0.0155799i
$953$	12.1659	−	12.1659i	0.394091	−	0.394091i	−0.482052	−	0.876143i	$-0.660108\pi$
$953$	12.1659	−	12.1659i	0.394091	−	0.394091i	0.876143	+	0.482052i	$0.160108\pi$
$954$	−0.173290	+	0.490001i	−0.00561048	+	0.0158644i
$955$	35.2161	+	32.1950i	1.13957	+	1.04180i
$956$	4.97773	−	2.87389i	0.160991	−	0.0929483i
$957$	−6.51599	+	4.60707i	−0.210632	+	0.148925i
$958$	1.03131	−	0.276339i	0.0333202	−	0.00892812i
$959$	10.6194	−	18.3934i	0.342919	−	0.593953i
$960$	−3.85893	+	30.6668i	−0.124547	+	0.989768i
$961$	−5.36002	−	9.28383i	−0.172904	−	0.299478i
$962$	−0.560702	−	0.560702i	−0.0180777	−	0.0180777i
$963$	2.44929	−	31.2868i	0.0789274	−	1.00820i
$964$			4.36321i			0.140530i
$965$	18.5374	+	29.0240i	0.596741	+	0.934317i
$966$	0.0230110	−	0.0276794i	0.000740368	−	0.000890571i
$967$	−0.828536	−	3.09214i	−0.0266439	−	0.0994365i	0.951323	−	0.308194i	$-0.0997247\pi$
$967$	−0.828536	−	3.09214i	−0.0266439	−	0.0994365i	−0.977967	+	0.208758i	$0.933058\pi$
$968$	0.0294454	+	0.109892i	0.000946411	+	0.00353205i
$969$	−22.1797	−	60.0823i	−0.712514	−	1.93012i
$970$	−0.560428	−	0.123566i	−0.0179943	−	0.00396747i
$971$		−	54.7305i		−	1.75639i	−0.478307	−	0.878193i	$-0.658749\pi$
$971$		−	54.7305i		−	1.75639i	0.478307	−	0.878193i	$-0.341251\pi$
$972$	13.8125	+	27.9361i	0.443037	+	0.896052i
$973$	−47.5035	−	47.5035i	−1.52289	−	1.52289i
$974$	−0.0343346	−	0.0594692i	−0.00110015	−	0.00190552i
$975$	−11.1468	−	23.4813i	−0.356982	−	0.752005i
$976$	13.8491	−	23.9873i	0.443298	−	0.767815i
$977$	14.1042	−	3.77921i	0.451233	−	0.120908i	−0.0260431	−	0.999661i	$-0.508291\pi$
$977$	14.1042	−	3.77921i	0.451233	−	0.120908i	0.477276	+	0.878753i	$0.341624\pi$
$978$	−0.0981092	−	1.06530i	−0.00313719	−	0.0340644i
$979$	6.09247	−	3.51749i	0.194716	−	0.112419i
$980$	−9.91685	+	10.8474i	−0.316782	+	0.346509i
$981$	36.7105	−	31.3800i	1.17207	−	1.00189i
$982$	−0.0484957	+	0.0484957i	−0.00154756	+	0.00154756i
$983$	−53.4896	−	14.3325i	−1.70605	−	0.457135i	−0.731601	−	0.681733i	$-0.761226\pi$
$983$	−53.4896	−	14.3325i	−1.70605	−	0.457135i	−0.974452	+	0.224598i	$0.927893\pi$
$984$	0.0583129	−	0.339782i	0.00185895	−	0.0108319i
$985$	−17.8874	+	34.4583i	−0.569939	+	1.09793i
$986$	−0.577748	−	0.333563i	−0.0183992	−	0.0106228i
$987$	−37.2666	−	52.7079i	−1.18621	−	1.67771i
$988$	11.2822	−	42.1057i	0.358934	−	1.33956i
$989$	−1.47494			−0.0469003
$990$	0.182583	+	0.0555084i	0.00580285	+	0.00176417i
$991$	−30.3795			−0.965038			−0.482519	−	0.875885i	$-0.660278\pi$
$991$	−30.3795			−0.965038			−0.482519	+	0.875885i	$0.660278\pi$
$992$	−0.570380	+	2.12869i	−0.0181096	+	0.0675859i
$993$	−1.86137	+	0.171424i	−0.0590686	+	0.00543998i
$994$	−0.743073	−	0.429014i	−0.0235689	−	0.0136075i
$995$	−23.3682	+	7.39760i	−0.740822	+	0.234520i
$996$	−26.1410	+	9.65008i	−0.828310	+	0.305775i
$997$	−17.9471	−	4.80890i	−0.568389	−	0.152299i	−0.0368314	−	0.999321i	$-0.511726\pi$
$997$	−17.9471	−	4.80890i	−0.568389	−	0.152299i	−0.531558	+	0.847022i	$0.678393\pi$
$998$	−0.404062	+	0.404062i	−0.0127904	+	0.0127904i
$999$	−23.5531	+	42.1184i	−0.745187	+	1.33257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.bc.d.23.17	yes	116
5.2	odd	4		495.2.bc.c.122.17	✓	116
9.2	odd	6		495.2.bc.c.353.17	yes	116
45.2	even	12	inner	495.2.bc.d.452.17	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.bc.c.122.17	✓	116	5.2	odd	4
495.2.bc.c.353.17	yes	116	9.2	odd	6
495.2.bc.d.23.17	yes	116	1.1	even	1	trivial
495.2.bc.d.452.17	yes	116	45.2	even	12	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00736284 + 0.0274785i) q^{2} +(0.724814 - 1.57310i) q^{3} +(1.73135 + 0.999595i) q^{4} +(0.674857 + 2.13180i) q^{5} +(0.0378897 + 0.0314993i) q^{6} +(3.09816 + 0.830150i) q^{7} +(-0.0804463 + 0.0804463i) q^{8} +(-1.94929 - 2.28041i) q^{9} +O(q^{10})\)	\(q+(-0.00736284 + 0.0274785i) q^{2} +(0.724814 - 1.57310i) q^{3} +(1.73135 + 0.999595i) q^{4} +(0.674857 + 2.13180i) q^{5} +(0.0378897 + 0.0314993i) q^{6} +(3.09816 + 0.830150i) q^{7} +(-0.0804463 + 0.0804463i) q^{8} +(-1.94929 - 2.28041i) q^{9} +(-0.0635475 + 0.00284797i) q^{10} +(0.866025 - 0.500000i) q^{11} +(2.82737 - 1.99907i) q^{12} +(-2.89912 + 0.776816i) q^{13} +(-0.0456225 + 0.0790205i) q^{14} +(3.84268 + 0.483540i) q^{15} +(1.99757 + 3.45990i) q^{16} +(-3.59908 - 3.59908i) q^{17} +(0.0770146 - 0.0367732i) q^{18} +7.26476i q^{19} +(-0.962522 + 4.36547i) q^{20} +(3.55150 - 4.27201i) q^{21} +(0.00736284 + 0.0274785i) q^{22} +(-0.0589483 - 0.219998i) q^{23} +(0.0682415 + 0.184859i) q^{24} +(-4.08914 + 2.87732i) q^{25} -0.0853829i q^{26} +(-5.00019 + 1.41355i) q^{27} +(4.53419 + 4.53419i) q^{28} +(-2.30368 - 3.99009i) q^{29} +(-0.0415800 + 0.102031i) q^{30} +(3.22955 - 5.59375i) q^{31} +(-0.329564 + 0.0883064i) q^{32} +(-0.158842 - 1.72475i) q^{33} +(0.125397 - 0.0723979i) q^{34} +(0.321104 + 7.16489i) q^{35} +(-1.09541 - 5.89669i) q^{36} +(6.56691 - 6.56691i) q^{37} +(-0.199625 - 0.0534892i) q^{38} +(-0.879312 + 5.12365i) q^{39} +(-0.225785 - 0.117206i) q^{40} +(-1.51514 - 0.874766i) q^{41} +(0.0912393 + 0.129044i) q^{42} +(1.67608 - 6.25522i) q^{43} +1.99919 q^{44} +(3.54589 - 5.69444i) q^{45} +0.00647924 q^{46} +(3.00735 - 11.2236i) q^{47} +(6.89063 - 0.634599i) q^{48} +(2.84727 + 1.64387i) q^{49} +(-0.0489568 - 0.133549i) q^{50} +(-8.27039 + 3.05305i) q^{51} +(-5.79589 - 1.55300i) q^{52} +(-4.30627 + 4.30627i) q^{53} +(-0.00202667 - 0.147805i) q^{54} +(1.65034 + 1.50876i) q^{55} +(-0.316018 + 0.182453i) q^{56} +(11.4282 + 5.26560i) q^{57} +(0.126603 - 0.0339232i) q^{58} +(-1.55836 + 2.69917i) q^{59} +(6.16968 + 4.67830i) q^{60} +(-3.46648 - 6.00411i) q^{61} +(0.129929 + 0.129929i) q^{62} +(-4.14613 - 8.68328i) q^{63} +7.98058i q^{64} +(-3.61251 - 5.65609i) q^{65} +(0.0485631 + 0.00833432i) q^{66} +(-0.867862 - 3.23891i) q^{67} +(-2.63365 - 9.82890i) q^{68} +(-0.388806 - 0.0667262i) q^{69} +(-0.199245 - 0.0439305i) q^{70} +9.40355i q^{71} +(0.340264 + 0.0266376i) q^{72} +(1.17731 + 1.17731i) q^{73} +(0.132098 + 0.228800i) q^{74} +(1.56245 + 8.51814i) q^{75} +(-7.26182 + 12.5778i) q^{76} +(3.09816 - 0.830150i) q^{77} +(-0.134316 - 0.0618868i) q^{78} +(-6.40956 + 3.70056i) q^{79} +(-6.02773 + 6.59336i) q^{80} +(-1.40055 + 8.89036i) q^{81} +(0.0351930 - 0.0351930i) q^{82} +(-7.77308 - 2.08279i) q^{83} +(10.4192 - 3.84629i) q^{84} +(5.24365 - 10.1014i) q^{85} +(0.159543 + 0.0921124i) q^{86} +(-7.94654 + 0.731843i) q^{87} +(-0.0294454 + 0.109892i) q^{88} +7.03497 q^{89} +(0.130367 + 0.139363i) q^{90} -9.62680 q^{91} +(0.117849 - 0.439818i) q^{92} +(-6.45870 - 9.13484i) q^{93} +(0.286264 + 0.165275i) q^{94} +(-15.4870 + 4.90267i) q^{95} +(-0.0999579 + 0.582443i) q^{96} +(8.71439 + 2.33501i) q^{97} +(-0.0661352 + 0.0661352i) q^{98} +(-2.82834 - 1.00025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 2 q^{2} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 10 q^{7} + 2 q^{8} + 16 q^{9}+O(q^{10}) \) 116 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 10 * q^7 + 2 * q^8 + 16 * q^9	\( 116 q - 2 q^{2} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 10 q^{7} + 2 q^{8} + 16 q^{9} + 6 q^{10} - 8 q^{12} + 12 q^{13} - 10 q^{14} + 20 q^{15} + 62 q^{16} - 8 q^{17} - 54 q^{18} + 6 q^{20} - 10 q^{21} + 2 q^{22} - 14 q^{23} - 62 q^{24} - 12 q^{25} + 30 q^{27} + 18 q^{28} - 2 q^{29} - 18 q^{30} - 2 q^{31} - 48 q^{32} + 4 q^{33} - 24 q^{34} + 2 q^{35} + 24 q^{36} - 14 q^{37} - 6 q^{38} + 4 q^{39} + 98 q^{40} + 6 q^{41} - 44 q^{42} + 26 q^{43} - 120 q^{44} - 18 q^{45} - 44 q^{46} - 2 q^{47} - 20 q^{48} - 18 q^{49} - 20 q^{50} - 8 q^{51} + 102 q^{52} - 44 q^{53} + 28 q^{54} + 2 q^{55} + 42 q^{56} - 48 q^{57} - 16 q^{58} + 22 q^{59} - 8 q^{60} - 10 q^{61} - 16 q^{62} - 26 q^{63} - 108 q^{65} + 6 q^{66} - 36 q^{67} - 72 q^{68} - 76 q^{69} - 134 q^{70} + 30 q^{72} + 12 q^{73} - 8 q^{74} + 20 q^{75} - 6 q^{76} - 10 q^{77} + 210 q^{78} - 6 q^{79} + 4 q^{80} + 44 q^{81} - 50 q^{82} + 24 q^{83} + 222 q^{84} + 54 q^{85} + 90 q^{86} - 32 q^{87} - 4 q^{88} + 8 q^{89} - 74 q^{90} + 72 q^{91} + 18 q^{92} - 98 q^{93} + 42 q^{94} + 54 q^{95} + 68 q^{96} + 18 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 116 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 10 * q^7 + 2 * q^8 + 16 * q^9 + 6 * q^10 - 8 * q^12 + 12 * q^13 - 10 * q^14 + 20 * q^15 + 62 * q^16 - 8 * q^17 - 54 * q^18 + 6 * q^20 - 10 * q^21 + 2 * q^22 - 14 * q^23 - 62 * q^24 - 12 * q^25 + 30 * q^27 + 18 * q^28 - 2 * q^29 - 18 * q^30 - 2 * q^31 - 48 * q^32 + 4 * q^33 - 24 * q^34 + 2 * q^35 + 24 * q^36 - 14 * q^37 - 6 * q^38 + 4 * q^39 + 98 * q^40 + 6 * q^41 - 44 * q^42 + 26 * q^43 - 120 * q^44 - 18 * q^45 - 44 * q^46 - 2 * q^47 - 20 * q^48 - 18 * q^49 - 20 * q^50 - 8 * q^51 + 102 * q^52 - 44 * q^53 + 28 * q^54 + 2 * q^55 + 42 * q^56 - 48 * q^57 - 16 * q^58 + 22 * q^59 - 8 * q^60 - 10 * q^61 - 16 * q^62 - 26 * q^63 - 108 * q^65 + 6 * q^66 - 36 * q^67 - 72 * q^68 - 76 * q^69 - 134 * q^70 + 30 * q^72 + 12 * q^73 - 8 * q^74 + 20 * q^75 - 6 * q^76 - 10 * q^77 + 210 * q^78 - 6 * q^79 + 4 * q^80 + 44 * q^81 - 50 * q^82 + 24 * q^83 + 222 * q^84 + 54 * q^85 + 90 * q^86 - 32 * q^87 - 4 * q^88 + 8 * q^89 - 74 * q^90 + 72 * q^91 + 18 * q^92 - 98 * q^93 + 42 * q^94 + 54 * q^95 + 68 * q^96 + 18 * q^97 + 16 * q^98 - 4 * q^99

Introduction

L-functions

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