LMFDB - Embedded newform 460.2.w.a.3.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			3.8
Character	$\chi$	$=$	460.3
Dual form			460.2.w.a.307.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32376 - 0.497658i) q^{2} +(0.189809 + 0.508896i) q^{3} +(1.50467 + 1.31756i) q^{4} +(0.243658 + 2.22275i) q^{5} +(0.00199564 - 0.768116i) q^{6} +(3.80918 + 0.828636i) q^{7} +(-1.33613 - 2.49294i) q^{8} +(2.04430 - 1.77140i) q^{9} +O(q^{10})$	\(q+(-1.32376 - 0.497658i) q^{2} +(0.189809 + 0.508896i) q^{3} +(1.50467 + 1.31756i) q^{4} +(0.243658 + 2.22275i) q^{5} +(0.00199564 - 0.768116i) q^{6} +(3.80918 + 0.828636i) q^{7} +(-1.33613 - 2.49294i) q^{8} +(2.04430 - 1.77140i) q^{9} +(0.783626 - 3.06365i) q^{10} +(0.0624757 + 0.00898264i) q^{11} +(-0.384901 + 1.01581i) q^{12} +(-0.512301 - 2.35501i) q^{13} +(-4.63005 - 2.99258i) q^{14} +(-1.08490 + 0.545894i) q^{15} +(0.528083 + 3.96499i) q^{16} +(-4.72182 + 2.57831i) q^{17} +(-3.58771 + 1.32754i) q^{18} +(5.44205 - 1.59793i) q^{19} +(-2.56198 + 3.66555i) q^{20} +(0.301325 + 2.09576i) q^{21} +(-0.0782324 - 0.0429824i) q^{22} +(2.34983 + 4.18071i) q^{23} +(1.01504 - 1.15313i) q^{24} +(-4.88126 + 1.08318i) q^{25} +(-0.493826 + 3.37241i) q^{26} +(2.71960 + 1.48501i) q^{27} +(4.63979 + 6.26564i) q^{28} +(-0.311991 + 1.06254i) q^{29} +(1.70782 - 0.182722i) q^{30} +(0.772599 - 0.352834i) q^{31} +(1.27415 - 5.51149i) q^{32} +(0.00728718 + 0.0334986i) q^{33} +(7.53366 - 1.06321i) q^{34} +(-0.913717 + 8.66876i) q^{35} +(5.40992 + 0.0281112i) q^{36} +(-3.84395 - 0.274925i) q^{37} +(-7.99918 - 0.593005i) q^{38} +(1.10122 - 0.707709i) q^{39} +(5.21563 - 3.57731i) q^{40} +(3.22621 - 3.72324i) q^{41} +(0.644090 - 2.92424i) q^{42} +(-2.83078 - 7.58962i) q^{43} +(0.0821703 + 0.0958312i) q^{44} +(4.43549 + 4.11236i) q^{45} +(-1.03004 - 6.70366i) q^{46} +(6.75585 + 6.75585i) q^{47} +(-1.91753 + 1.02133i) q^{48} +(7.45577 + 3.40494i) q^{49} +(7.00067 + 0.995327i) q^{50} +(-2.20833 - 1.91353i) q^{51} +(2.33201 - 4.21850i) q^{52} +(-11.1228 - 2.41962i) q^{53} +(-2.86106 - 3.31922i) q^{54} +(-0.00474351 + 0.141057i) q^{55} +(-3.02382 - 10.6032i) q^{56} +(1.84613 + 2.46614i) q^{57} +(0.941784 - 1.25129i) q^{58} +(2.01191 + 1.29298i) q^{59} +(-2.35167 - 0.608030i) q^{60} +(4.62019 + 10.1168i) q^{61} +(-1.19832 + 0.0825772i) q^{62} +(9.25494 - 5.05358i) q^{63} +(-4.42951 + 6.66179i) q^{64} +(5.10978 - 1.71253i) q^{65} +(0.00702439 - 0.0479706i) q^{66} +(-7.43571 + 9.93294i) q^{67} +(-10.5019 - 2.34176i) q^{68} +(-1.68153 + 1.98935i) q^{69} +(5.52362 - 11.0206i) q^{70} +(10.1162 - 1.45448i) q^{71} +(-7.14744 - 2.72950i) q^{72} +(4.62577 + 2.52586i) q^{73} +(4.95165 + 2.27691i) q^{74} +(-1.47773 - 2.27846i) q^{75} +(10.2939 + 4.76585i) q^{76} +(0.230537 + 0.0859860i) q^{77} +(-1.80994 + 0.388806i) q^{78} +(-0.464003 - 0.298197i) q^{79} +(-8.68452 + 2.13990i) q^{80} +(0.915369 - 6.36653i) q^{81} +(-6.12362 + 3.32313i) q^{82} +(-16.0313 - 1.14658i) q^{83} +(-2.30789 + 3.55044i) q^{84} +(-6.88145 - 9.86721i) q^{85} +(-0.0297628 + 11.4556i) q^{86} +(-0.599943 + 0.0429088i) q^{87} +(-0.0610825 - 0.167750i) q^{88} +(-4.39167 - 2.00561i) q^{89} +(-3.82496 - 7.65113i) q^{90} -9.39515i q^{91} +(-1.97261 + 9.38663i) q^{92} +(0.326202 + 0.326202i) q^{93} +(-5.58101 - 12.3052i) q^{94} +(4.87780 + 11.7070i) q^{95} +(3.04662 - 0.397716i) q^{96} +(0.0286355 + 0.400377i) q^{97} +(-8.17514 - 8.21773i) q^{98} +(0.143631 - 0.0923059i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−1.32376	−	0.497658i	−0.936039	−	0.351897i
$2$	−1.32376	−	0.497658i	−0.936039	−	0.351897i
$3$	0.189809	+	0.508896i	0.109586	+	0.293812i	0.980154	−	0.198236i	$-0.0635213\pi$
$3$	0.189809	+	0.508896i	0.109586	+	0.293812i	−0.870568	+	0.492048i	$0.836249\pi$
$4$	1.50467	+	1.31756i	0.752337	+	0.658779i
$5$	0.243658	+	2.22275i	0.108967	+	0.994045i
$5$	0.243658	+	2.22275i	0.108967	+	0.994045i
$6$	0.00199564	−	0.768116i	0.000814718	−	0.313582i
$7$	3.80918	+	0.828636i	1.43973	+	0.313195i	0.863607	−	0.504166i	$-0.168200\pi$
$7$	3.80918	+	0.828636i	1.43973	+	0.313195i	0.576127	+	0.817360i	$0.304564\pi$
$8$	−1.33613	−	2.49294i	−0.472394	−	0.881388i
$9$	2.04430	−	1.77140i	0.681433	−	0.590465i
$10$	0.783626	−	3.06365i	0.247804	−	0.968810i
$11$	0.0624757	+	0.00898264i	0.0188371	+	0.00270837i	0.151727	−	0.988422i	$-0.451517\pi$
$11$	0.0624757	+	0.00898264i	0.0188371	+	0.00270837i	−0.132890	+	0.991131i	$0.542426\pi$
$12$	−0.384901	+	1.01581i	−0.111111	+	0.293238i
$13$	−0.512301	−	2.35501i	−0.142087	−	0.653162i	−0.992000	−	0.126239i	$-0.959709\pi$
$13$	−0.512301	−	2.35501i	−0.142087	−	0.653162i	0.849913	−	0.526923i	$-0.176654\pi$
$14$	−4.63005	−	2.99258i	−1.23743	−	0.799801i
$15$	−1.08490	+	0.545894i	−0.280121	+	0.140949i
$16$	0.528083	+	3.96499i	0.132021	+	0.991247i
$17$	−4.72182	+	2.57831i	−1.14521	+	0.625331i	−0.935812	−	0.352500i	$-0.885332\pi$
$17$	−4.72182	+	2.57831i	−1.14521	+	0.625331i	−0.209397	+	0.977831i	$0.567150\pi$
$18$	−3.58771	+	1.32754i	−0.845631	+	0.312904i
$19$	5.44205	−	1.59793i	1.24849	−	0.366590i	0.410292	−	0.911954i	$-0.365427\pi$
$19$	5.44205	−	1.59793i	1.24849	−	0.366590i	0.838199	+	0.545364i	$0.183609\pi$
$20$	−2.56198	+	3.66555i	−0.572876	+	0.819642i
$21$	0.301325	+	2.09576i	0.0657544	+	0.457332i
$22$	−0.0782324	−	0.0429824i	−0.0166792	−	0.00916387i
$23$	2.34983	+	4.18071i	0.489972	+	0.871738i
$23$	2.34983	+	4.18071i	0.489972	+	0.871738i
$24$	1.01504	−	1.15313i	0.207194	−	0.235382i
$25$	−4.88126	+	1.08318i	−0.976252	+	0.216636i
$26$	−0.493826	+	3.37241i	−0.0968473	+	0.661384i
$27$	2.71960	+	1.48501i	0.523386	+	0.285791i
$28$	4.63979	+	6.26564i	0.876838	+	1.18409i
$29$	−0.311991	+	1.06254i	−0.0579353	+	0.197309i	−0.983375	−	0.181585i	$-0.941877\pi$
$29$	−0.311991	+	1.06254i	−0.0579353	+	0.197309i	0.925440	+	0.378894i	$0.123696\pi$
$30$	1.70782	−	0.182722i	0.311803	−	0.0333602i
$31$	0.772599	−	0.352834i	0.138763	−	0.0633709i	−0.344823	−	0.938668i	$-0.612061\pi$
$31$	0.772599	−	0.352834i	0.138763	−	0.0633709i	0.483586	+	0.875297i	$0.339334\pi$
$32$	1.27415	−	5.51149i	0.225241	−	0.974303i
$33$	0.00728718	+	0.0334986i	0.00126854	+	0.00583136i
$34$	7.53366	−	1.06321i	1.29201	−	0.182338i
$35$	−0.913717	+	8.66876i	−0.154446	+	1.46529i
$36$	5.40992	+	0.0281112i	0.901654	+	0.00468521i
$37$	−3.84395	−	0.274925i	−0.631942	−	0.0451974i	−0.248306	−	0.968682i	$-0.579874\pi$
$37$	−3.84395	−	0.274925i	−0.631942	−	0.0451974i	−0.383636	+	0.923484i	$0.625328\pi$
$38$	−7.99918	−	0.593005i	−1.29764	−	0.0961982i
$39$	1.10122	−	0.707709i	0.176336	−	0.113324i
$40$	5.21563	−	3.57731i	0.824664	−	0.565623i
$41$	3.22621	−	3.72324i	0.503849	−	0.581473i	−0.445664	−	0.895200i	$-0.647032\pi$
$41$	3.22621	−	3.72324i	0.503849	−	0.581473i	0.949513	+	0.313727i	$0.101578\pi$
$42$	0.644090	−	2.92424i	0.0993852	−	0.451219i
$43$	−2.83078	−	7.58962i	−0.431690	−	1.15741i	−0.952715	−	0.303865i	$-0.901723\pi$
$43$	−2.83078	−	7.58962i	−0.431690	−	1.15741i	0.521025	−	0.853541i	$-0.325550\pi$
$44$	0.0821703	+	0.0958312i	0.0123876	+	0.0144471i
$45$	4.43549	+	4.11236i	0.661203	+	0.613034i
$46$	−1.03004	−	6.70366i	−0.151871	−	0.988400i
$47$	6.75585	+	6.75585i	0.985442	+	0.985442i	0.999896	−	0.0144531i	$-0.00460071\pi$
$47$	6.75585	+	6.75585i	0.985442	+	0.985442i	−0.0144531	+	0.999896i	$0.504601\pi$
$48$	−1.91753	+	1.02133i	−0.276772	+	0.147416i
$49$	7.45577	+	3.40494i	1.06511	+	0.486419i
$50$	7.00067	+	0.995327i	0.990044	+	0.140760i
$51$	−2.20833	−	1.91353i	−0.309228	−	0.267948i
$52$	2.33201	−	4.21850i	0.323392	−	0.585001i
$53$	−11.1228	−	2.41962i	−1.52784	−	0.332360i	−0.631372	−	0.775480i	$-0.717508\pi$
$53$	−11.1228	−	2.41962i	−1.52784	−	0.332360i	−0.896463	+	0.443120i	$0.853872\pi$
$54$	−2.86106	−	3.31922i	−0.389341	−	0.451689i
$55$	−0.00474351	+	0.141057i	−0.000639615	+	0.0190201i
$56$	−3.02382	−	10.6032i	−0.404075	−	1.41691i
$57$	1.84613	+	2.46614i	0.244526	+	0.326648i
$58$	0.941784	−	1.25129i	0.123662	−	0.164302i
$59$	2.01191	+	1.29298i	0.261929	+	0.168332i	0.665014	−	0.746831i	$-0.268426\pi$
$59$	2.01191	+	1.29298i	0.261929	+	0.168332i	−0.403085	+	0.915163i	$0.632062\pi$
$60$	−2.35167	−	0.608030i	−0.303599	−	0.0784963i
$61$	4.62019	+	10.1168i	0.591555	+	1.29533i	0.934498	+	0.355969i	$0.115849\pi$
$61$	4.62019	+	10.1168i	0.591555	+	1.29533i	−0.342943	+	0.939356i	$0.611424\pi$
$62$	−1.19832	+	0.0825772i	−0.152187	+	0.0104873i
$63$	9.25494	−	5.05358i	1.16601	−	0.636691i
$64$	−4.42951	+	6.66179i	−0.553689	+	0.832724i
$65$	5.10978	−	1.71253i	0.633790	−	0.212414i
$66$	0.00702439	−	0.0479706i	0.000864642	−	0.00590477i
$67$	−7.43571	+	9.93294i	−0.908416	+	1.21350i	0.0680176	+	0.997684i	$0.478333\pi$
$67$	−7.43571	+	9.93294i	−0.908416	+	1.21350i	−0.976434	+	0.215818i	$0.930758\pi$
$68$	−10.5019	−	2.34176i	−1.27354	−	0.283980i
$69$	−1.68153	+	1.98935i	−0.202433	+	0.239490i
$70$	5.52362	−	11.0206i	0.660199	−	1.31722i
$71$	10.1162	−	1.45448i	1.20057	−	0.172616i	0.487127	−	0.873331i	$-0.338045\pi$
$71$	10.1162	−	1.45448i	1.20057	−	0.172616i	0.713441	+	0.700715i	$0.247136\pi$
$72$	−7.14744	−	2.72950i	−0.842334	−	0.321675i
$73$	4.62577	+	2.52586i	0.541405	+	0.295629i	0.726587	−	0.687075i	$-0.241106\pi$
$73$	4.62577	+	2.52586i	0.541405	+	0.295629i	−0.185182	+	0.982704i	$0.559287\pi$
$74$	4.95165	+	2.27691i	0.575618	+	0.264685i
$75$	−1.47773	−	2.27846i	−0.170634	−	0.263094i
$76$	10.2939	+	4.76585i	1.18079	+	0.546680i
$77$	0.230537	+	0.0859860i	0.0262722	+	0.00979902i
$78$	−1.80994	+	0.388806i	−0.204935	+	0.0440237i
$79$	−0.464003	−	0.298197i	−0.0522044	−	0.0335497i	0.514278	−	0.857623i	$-0.328060\pi$
$79$	−0.464003	−	0.298197i	−0.0522044	−	0.0335497i	−0.566483	+	0.824074i	$0.691696\pi$
$80$	−8.68452	+	2.13990i	−0.970959	+	0.239248i
$81$	0.915369	−	6.36653i	0.101708	−	0.707392i
$82$	−6.12362	+	3.32313i	−0.676241	+	0.366978i
$83$	−16.0313	−	1.14658i	−1.75966	−	0.125853i	−0.846223	−	0.532830i	$-0.821129\pi$
$83$	−16.0313	−	1.14658i	−1.75966	−	0.125853i	−0.913439	+	0.406976i	$0.866583\pi$
$84$	−2.30789	+	3.55044i	−0.251811	+	0.387385i
$85$	−6.88145	−	9.86721i	−0.746398	−	1.07025i
$86$	−0.0297628	+	11.4556i	−0.00320940	+	1.23529i
$87$	−0.599943	+	0.0429088i	−0.0643207	+	0.00460031i
$88$	−0.0610825	−	0.167750i	−0.00651141	−	0.0178822i
$89$	−4.39167	−	2.00561i	−0.465516	−	0.212594i	0.168827	−	0.985646i	$-0.446002\pi$
$89$	−4.39167	−	2.00561i	−0.465516	−	0.212594i	−0.634343	+	0.773052i	$0.718729\pi$
$90$	−3.82496	−	7.65113i	−0.403187	−	0.806500i
$91$		−	9.39515i		−	0.984880i
$92$	−1.97261	+	9.38663i	−0.205658	+	0.978624i
$93$	0.326202	+	0.326202i	0.0338256	+	0.0338256i
$94$	−5.58101	−	12.3052i	−0.575638	−	1.26919i
$95$	4.87780	+	11.7070i	0.500452	+	1.20111i
$96$	3.04662	−	0.397716i	0.310945	−	0.0405917i
$97$	0.0286355	+	0.400377i	0.00290750	+	0.0406521i	0.998699	−	0.0509983i	$-0.0162403\pi$
$97$	0.0286355	+	0.400377i	0.00290750	+	0.0406521i	−0.995791	+	0.0916504i	$0.970786\pi$
$98$	−8.17514	−	8.21773i	−0.825814	−	0.830117i
$99$	0.143631	−	0.0923059i	0.0144354	−	0.00927709i
$100$	−8.77186	−	4.80151i	−0.877186	−	0.480151i
$101$	−2.82523	−	3.26049i	−0.281121	−	0.324431i	0.597575	−	0.801813i	$-0.296131\pi$
$101$	−2.82523	−	3.26049i	−0.281121	−	0.324431i	−0.878696	+	0.477383i	$0.841586\pi$
$102$	1.97101	+	3.63205i	0.195160	+	0.359626i
$103$	−7.03780	−	9.40140i	−0.693455	−	0.926348i	0.306217	−	0.951962i	$-0.400937\pi$
$103$	−7.03780	−	9.40140i	−0.693455	−	0.926348i	−0.999672	+	0.0256140i	$0.991846\pi$
$104$	−5.18640	+	4.42373i	−0.508568	+	0.433783i
$105$	−4.58493	+	1.18042i	−0.447444	+	0.115197i
$106$	13.5198	+	8.73834i	1.31316	+	0.848743i
$107$	−0.762008	+	2.04302i	−0.0736661	+	0.197506i	−0.968564	−	0.248764i	$-0.919975\pi$
$107$	−0.762008	+	2.04302i	−0.0736661	+	0.197506i	0.894898	+	0.446271i	$0.147248\pi$
$108$	2.13551	+	5.81768i	0.205490	+	0.559807i
$109$	1.28938	−	4.39123i	0.123500	−	0.420604i	−0.874412	−	0.485184i	$-0.838753\pi$
$109$	1.28938	−	4.39123i	0.123500	−	0.420604i	0.997913	+	0.0645802i	$0.0205708\pi$
$110$	0.0764772	−	0.184364i	0.00729182	−	0.0175784i
$111$	−0.589707	−	2.00836i	−0.0559725	−	0.190625i
$112$	−1.27397	+	15.5409i	−0.120379	+	1.46848i
$113$	3.83408	−	5.12173i	0.360680	−	0.481812i	−0.583093	−	0.812405i	$-0.698158\pi$
$113$	3.83408	−	5.12173i	0.360680	−	0.481812i	0.943773	+	0.330593i	$0.107249\pi$
$114$	−1.21653	−	4.18331i	−0.113939	−	0.391803i
$115$	−8.72013	+	6.24174i	−0.813156	+	0.582046i
$116$	−1.86941	+	1.18772i	−0.173570	+	0.110277i
$117$	−5.21895	−	3.90686i	−0.482492	−	0.361189i
$118$	−2.01983	−	2.71284i	−0.185940	−	0.249737i
$119$	−20.1227	+	5.90856i	−1.84465	+	0.541637i
$120$	2.81045	+	1.97521i	0.256558	+	0.180311i
$121$	−10.5506	−	3.09794i	−0.959145	−	0.281631i
$122$	−1.08131	−	15.6915i	−0.0978971	−	1.42064i
$123$	2.50711	+	0.935103i	0.226058	+	0.0843154i
$124$	1.62739	+	0.487044i	0.146144	+	0.0437378i
$125$	−3.59700	−	10.5859i	−0.321726	−	0.946833i
$126$	−14.7663	+	2.08393i	−1.31548	+	0.185651i
$127$	15.3459	−	11.4878i	1.36173	−	1.01937i	0.365660	−	0.930748i	$-0.380843\pi$
$127$	15.3459	−	11.4878i	1.36173	−	1.01937i	0.996065	−	0.0886265i	$-0.0282478\pi$
$128$	9.17889	−	6.61422i	0.811307	−	0.584620i
$129$	3.32502	−	2.88115i	0.292752	−	0.253671i
$130$	−7.61636	−	0.275939i	−0.667999	−	0.0242014i
$131$	−8.52051	−	13.2582i	−0.744440	−	1.15837i	−0.982344	−	0.187083i	$-0.940097\pi$
$131$	−8.52051	−	13.2582i	−0.744440	−	1.15837i	0.237904	−	0.971289i	$-0.423540\pi$
$132$	−0.0331715	+	0.0600058i	−0.00288721	+	0.00522283i
$133$	22.0538	−	1.57732i	1.91231	−	0.136771i
$134$	14.7863	−	9.44838i	1.27734	−	0.816215i
$135$	−2.63816	+	6.40682i	−0.227057	+	0.551412i
$136$	12.7365	+	8.32625i	1.09215	+	0.713970i
$137$	2.06035	−	2.06035i	0.176028	−	0.176028i	−0.613594	−	0.789622i	$-0.710277\pi$
$137$	2.06035	−	2.06035i	0.176028	−	0.176028i	0.789622	+	0.613594i	$0.210277\pi$
$138$	3.21596	−	1.79659i	0.273760	−	0.152936i
$139$	−2.48706			−0.210950			−0.105475	−	0.994422i	$-0.533636\pi$
$139$	−2.48706			−0.210950			−0.105475	+	0.994422i	$0.533636\pi$
$140$	−12.7964	+	11.8398i	−1.08150	+	1.00064i
$141$	−2.15571	+	4.72035i	−0.181544	+	0.397525i
$142$	−14.1152	−	3.10900i	−1.18452	−	0.260902i
$143$	−0.0108521	−	0.151732i	−0.000907500	−	0.0126885i
$144$	8.10313	+	7.17018i	0.675260	+	0.597515i
$145$	−2.43779	−	0.434582i	−0.202448	−	0.0360901i
$146$	−4.86638	−	5.64568i	−0.402745	−	0.467239i
$147$	−0.317591	+	4.44050i	−0.0261945	+	0.366246i
$148$	−5.42167	−	5.47831i	−0.445658	−	0.450314i
$149$	−20.6337	−	2.96667i	−1.69038	−	0.243039i	−0.771118	−	0.636693i	$-0.780302\pi$
$149$	−20.6337	−	2.96667i	−1.69038	−	0.243039i	−0.919259	+	0.393653i	$0.871211\pi$
$150$	0.822268	+	3.75154i	0.0671379	+	0.306312i
$151$	0.471253	−	0.733284i	0.0383500	−	0.0596738i	−0.821549	−	0.570138i	$-0.806890\pi$
$151$	0.471253	−	0.733284i	0.0383500	−	0.0596738i	0.859899	+	0.510464i	$0.170526\pi$
$152$	−11.2548	−	11.4317i	−0.912887	−	0.927230i
$153$	−5.08561	+	13.6350i	−0.411147	+	1.10233i
$154$	−0.262384	−	0.228554i	−0.0211435	−	0.0184174i
$155$	0.972512	+	1.63133i	0.0781141	+	0.131031i
$156$	2.58942	+	0.386046i	0.207319	+	0.0309084i
$157$	−4.53017	+	8.29638i	−0.361547	+	0.662123i	−0.993619	−	0.112786i	$-0.964023\pi$
$157$	−4.53017	+	8.29638i	−0.361547	+	0.662123i	0.632073	+	0.774909i	$0.282204\pi$
$158$	0.465828	+	0.625655i	0.0370593	+	0.0497744i
$159$	−0.879869	−	6.11962i	−0.0697781	−	0.485318i
$160$	12.5611	+	1.48921i	0.993045	+	0.117732i
$161$	5.48662	+	17.8722i	0.432406	+	1.40853i
$162$	−4.38008	+	7.97221i	−0.344132	+	0.626356i
$163$	−2.69513	−	2.01755i	−0.211099	−	0.158027i	0.488496	−	0.872566i	$-0.337546\pi$
$163$	−2.69513	−	2.01755i	−0.211099	−	0.158027i	−0.699595	+	0.714539i	$0.746636\pi$
$164$	9.75998	−	1.35155i	0.762126	−	0.105538i
$165$	−0.0726836	+	0.0243598i	−0.00565841	+	0.00189641i
$166$	20.6509	+	9.49589i	1.60282	+	0.737024i
$167$	−1.93245	−	3.53901i	−0.149537	−	0.273857i	0.792163	−	0.610309i	$-0.208955\pi$
$167$	−1.93245	−	3.53901i	−0.149537	−	0.273857i	−0.941701	+	0.336452i	$0.890773\pi$
$168$	4.82199	−	3.55139i	0.372025	−	0.273996i
$169$	6.54161	−	2.98745i	0.503200	−	0.229804i
$170$	4.19888	+	16.4864i	0.322039	+	1.26445i
$171$	8.29461	−	12.9067i	0.634305	−	0.986998i
$172$	5.74036	−	15.1496i	0.437698	−	1.15515i
$173$	18.9466	−	14.1833i	1.44048	−	1.07833i	0.458645	−	0.888620i	$-0.348335\pi$
$173$	18.9466	−	14.1833i	1.44048	−	1.07833i	0.981840	−	0.189713i	$-0.0607558\pi$
$174$	0.815534	+	0.241766i	0.0618255	+	0.0183282i
$175$	−19.4912	+	0.0812454i	−1.47339	+	0.00614158i
$176$	−0.00262374	+	0.252459i	−0.000197772	+	0.0190298i
$177$	−0.276114	+	1.26927i	−0.0207540	+	0.0954045i
$178$	4.81540	+	4.84049i	0.360929	+	0.362810i
$179$	−8.42523	+	9.72324i	−0.629731	+	0.726749i	−0.977524	−	0.210823i	$-0.932386\pi$
$179$	−8.42523	+	9.72324i	−0.629731	+	0.726749i	0.347793	+	0.937571i	$0.386931\pi$
$180$	1.25569	+	12.0318i	0.0935933	+	0.896795i
$181$	5.63021	−	12.3284i	0.418491	−	0.916366i	−0.576565	−	0.817051i	$-0.695607\pi$
$181$	5.63021	−	12.3284i	0.418491	−	0.916366i	0.995056	−	0.0993155i	$-0.0316653\pi$
$182$	−4.67557	+	12.4369i	−0.346576	+	0.921885i
$183$	−4.27146	+	4.27146i	−0.315755	+	0.315755i
$184$	7.28258	−	11.4439i	0.536879	−	0.843659i
$185$	−0.325519	−	8.61115i	−0.0239326	−	0.633104i
$186$	−0.269476	−	0.594149i	−0.0197589	−	0.0435651i
$187$	−0.318159	+	0.118667i	−0.0232661	+	0.00867779i
$188$	1.26412	+	19.0666i	0.0921957	+	1.39057i
$189$	9.12889	+	7.91023i	0.664029	+	0.575384i
$190$	−0.630958	−	17.9247i	−0.0457745	−	1.30039i
$191$	1.59369	+	2.47983i	0.115315	+	0.179434i	0.894114	−	0.447840i	$-0.147807\pi$
$191$	1.59369	+	2.47983i	0.115315	+	0.179434i	−0.778798	+	0.627275i	$0.784170\pi$
$192$	−4.23092	−	0.989696i	−0.305340	−	0.0714252i
$193$	−0.0530168	+	0.741272i	−0.00381623	+	0.0533579i	−0.999003	−	0.0446347i	$-0.985788\pi$
$193$	−0.0530168	+	0.741272i	−0.00381623	+	0.0533579i	0.995187	+	0.0979926i	$0.0312422\pi$
$194$	0.161344	−	0.544253i	0.0115838	−	0.0390751i
$195$	1.84138	+	2.27529i	0.131864	+	0.162937i
$196$	6.73230	+	14.9467i	0.480878	+	1.06762i
$197$	22.8311	−	4.96661i	1.62665	−	0.353856i	0.695511	−	0.718516i	$-0.255178\pi$
$197$	22.8311	−	4.96661i	1.62665	−	0.353856i	0.931141	+	0.364659i	$0.118814\pi$
$198$	−0.236069	+	0.0507117i	−0.0167767	+	0.00360393i
$199$	−3.83872	−	8.40563i	−0.272120	−	0.595859i	0.723398	−	0.690431i	$-0.242579\pi$
$199$	−3.83872	−	8.40563i	−0.272120	−	0.595859i	−0.995518	+	0.0945718i	$0.969852\pi$
$200$	9.22231	+	10.7214i	0.652116	+	0.758119i
$201$	−6.46620	−	1.89865i	−0.456091	−	0.133920i
$202$	2.11731	+	5.72210i	0.148974	+	0.402605i
$203$	−2.06889	+	3.78889i	−0.145208	+	0.265928i
$204$	−0.801631	−	5.78884i	−0.0561254	−	0.405300i
$205$	9.06194	+	6.26387i	0.632913	+	0.437487i
$206$	4.63767	+	15.9476i	0.323122	+	1.11112i
$207$	12.2094	+	4.38415i	0.848615	+	0.304720i
$208$	9.06704	−	3.27491i	0.628686	−	0.227074i
$209$	0.354349	−	0.0509477i	0.0245108	−	0.00352413i
$210$	6.65679	+	0.719140i	0.459362	+	0.0496254i
$211$	3.04644	+	10.3752i	0.209726	+	0.714261i	0.995416	+	0.0956404i	$0.0304899\pi$
$211$	3.04644	+	10.3752i	0.209726	+	0.714261i	−0.785690	+	0.618620i	$0.787692\pi$
$212$	−13.5482	−	18.2957i	−0.930494	−	1.25655i
$213$	2.66032	+	4.87201i	0.182282	+	0.333824i
$214$	2.02544	−	2.32525i	0.138456	−	0.158951i
$215$	16.1801	−	8.14140i	1.10347	−	0.555239i
$216$	0.0683102	−	8.76396i	0.00464792	−	0.596312i
$217$	3.23534	−	0.703804i	0.219629	−	0.0477773i
$218$	−3.89216	+	5.17126i	−0.263610	+	0.350242i
$219$	−0.407391	+	2.83347i	−0.0275289	+	0.191468i
$220$	−0.192988	+	0.205994i	−0.0130112	+	0.0138881i
$221$	8.49092	+	9.79905i	0.571161	+	0.659155i
$222$	−0.218845	+	2.95205i	−0.0146879	+	0.198129i
$223$	3.56731	−	16.3986i	0.238885	−	1.09813i	−0.688853	−	0.724901i	$-0.741885\pi$
$223$	3.56731	−	16.3986i	0.238885	−	1.09813i	0.927737	−	0.373233i	$-0.121751\pi$
$224$	9.42049	−	19.9384i	0.629433	−	1.33219i
$225$	−8.06002	+	10.8610i	−0.537335	+	0.724067i
$226$	−7.62427	+	4.87188i	−0.507159	+	0.324073i
$227$	12.8324	−	4.78624i	0.851716	−	0.317674i	0.114577	−	0.993414i	$-0.463449\pi$
$227$	12.8324	−	4.78624i	0.851716	−	0.317674i	0.737139	+	0.675741i	$0.236176\pi$
$228$	−0.471460	+	6.14311i	−0.0312232	+	0.406837i
$229$		−	3.00502i		−	0.198578i	−0.995059	−	0.0992888i	$-0.968343\pi$
$229$		−	3.00502i		−	0.198578i	0.995059	−	0.0992888i	$-0.0316568\pi$
$230$	14.6496	−	3.92292i	0.965966	−	0.258670i
$231$			0.133641i			0.00879291i
$232$	3.06572	−	0.641923i	0.201274	−	0.0421443i
$233$	−24.1829	+	9.01976i	−1.58427	+	0.590904i	−0.978774	−	0.204941i	$-0.934300\pi$
$233$	−24.1829	+	9.01976i	−1.58427	+	0.590904i	−0.605501	+	0.795845i	$0.707027\pi$
$234$	4.96435	+	7.76899i	0.324530	+	0.507874i
$235$	−13.3705	+	16.6627i	−0.872194	+	1.08696i
$236$	1.32370	+	4.59633i	0.0861655	+	0.299195i
$237$	0.0636795	−	0.292730i	0.00413643	−	0.0190148i
$238$	29.5781	+	2.19272i	1.91726	+	0.142133i
$239$	−17.7274	−	20.4585i	−1.14669	−	1.32335i	−0.938508	−	0.345257i	$-0.887792\pi$
$239$	−17.7274	−	20.4585i	−1.14669	−	1.32335i	−0.208179	−	0.978091i	$-0.566754\pi$
$240$	−2.73738	−	4.01335i	−0.176697	−	0.259061i
$241$	−1.47981	+	10.2923i	−0.0953232	+	0.662988i	0.885000	+	0.465590i	$0.154158\pi$
$241$	−1.47981	+	10.2923i	−0.0953232	+	0.662988i	−0.980324	+	0.197397i	$0.936751\pi$
$242$	12.4247	+	9.35151i	0.798692	+	0.601138i
$243$	12.4971	−	2.71857i	0.801688	−	0.174397i
$244$	−6.37760	+	21.3099i	−0.408284	+	1.36422i
$245$	−5.75167	+	17.4020i	−0.367461	+	1.11177i
$246$	−2.85344	−	2.48553i	−0.181929	−	0.158472i
$247$	−6.55110	−	11.9974i	−0.416836	−	0.763379i
$248$	−1.91189	−	1.45461i	−0.121405	−	0.0923678i
$249$	−2.45938	−	8.37589i	−0.155857	−	0.530801i
$250$	−0.506598	+	15.8033i	−0.0320401	+	0.999487i
$251$	0.737035	−	0.105970i	0.0465212	−	0.00668874i	−0.119015	−	0.992892i	$-0.537974\pi$
$251$	0.737035	−	0.105970i	0.0465212	−	0.00668874i	0.165536	+	0.986204i	$0.447065\pi$
$252$	20.5841	+	4.58993i	1.29667	+	0.289139i
$253$	0.109253	+	0.282300i	0.00686868	+	0.0177481i
$254$	−26.0312	+	7.57004i	−1.63334	+	0.474987i
$255$	3.71523	−	5.37482i	0.232657	−	0.336585i
$256$	−15.4423	+	4.18768i	−0.965141	+	0.261730i
$257$	−4.59330	+	8.41201i	−0.286522	+	0.524727i	−0.980809	−	0.194972i	$-0.937538\pi$
$257$	−4.59330	+	8.41201i	−0.286522	+	0.524727i	0.694286	+	0.719699i	$0.255720\pi$
$258$	−5.83535	+	2.15922i	−0.363293	+	0.134427i
$259$	−14.4145	−	4.23248i	−0.895673	−	0.262993i
$260$	9.94490	+	4.15562i	0.616757	+	0.257721i
$261$	1.24438	+	2.72482i	0.0770254	+	0.168662i
$262$	4.68106	+	21.7909i	0.289197	+	1.34625i
$263$	26.8909	−	5.84976i	1.65816	−	0.360711i	0.716584	−	0.697501i	$-0.245705\pi$
$263$	26.8909	−	5.84976i	1.65816	−	0.360711i	0.941580	+	0.336790i	$0.109341\pi$
$264$	0.0737735	−	0.0629251i	0.00454044	−	0.00387277i
$265$	2.66806	−	25.3128i	0.163897	−	1.55495i
$266$	−29.9789	−	8.88727i	−1.83812	−	0.544913i
$267$	0.187070	−	2.61558i	0.0114485	−	0.160071i
$268$	−24.2755	+	5.14886i	−1.48286	+	0.314517i
$269$	−1.22342	−	1.90368i	−0.0745934	−	0.116070i	0.801953	−	0.597388i	$-0.203795\pi$
$269$	−1.22342	−	1.90368i	−0.0745934	−	0.116070i	−0.876546	+	0.481318i	$0.840158\pi$
$270$	6.68070	−	7.16818i	0.406574	−	0.436242i
$271$	−0.495142	−	0.429043i	−0.0300777	−	0.0260625i	0.639692	−	0.768631i	$-0.279062\pi$
$271$	−0.495142	−	0.429043i	−0.0300777	−	0.0260625i	−0.669770	+	0.742569i	$0.733607\pi$
$272$	−12.7165	−	17.3604i	−0.771049	−	1.05263i
$273$	4.78116	−	1.78328i	0.289369	−	0.107929i
$274$	−3.75276	+	1.70206i	−0.226713	+	0.102825i
$275$	−0.314690	+	0.0238259i	−0.0189765	+	0.00143676i
$276$	−5.15124	+	0.777811i	−0.310068	+	0.0468187i
$277$	−13.4896	+	13.4896i	−0.810514	+	0.810514i	−0.984711	−	0.174197i	$-0.944267\pi$
$277$	−13.4896	+	13.4896i	−0.810514	+	0.810514i	0.174197	+	0.984711i	$0.444267\pi$
$278$	3.29227	+	1.23771i	0.197457	+	0.0742326i
$279$	0.954415	−	2.08988i	0.0571393	−	0.125118i
$280$	22.8316	−	9.30476i	1.36445	−	0.556066i
$281$	4.46939	−	5.15795i	0.266621	−	0.307697i	−0.606614	−	0.794997i	$-0.707472\pi$
$281$	4.46939	−	5.15795i	0.266621	−	0.307697i	0.873235	+	0.487299i	$0.162018\pi$
$282$	5.20276	−	5.17580i	0.309820	−	0.308214i
$283$	2.86332	−	13.1625i	0.170207	−	0.782428i	−0.810311	−	0.586000i	$-0.800702\pi$
$283$	2.86332	−	13.1625i	0.170207	−	0.782428i	0.980518	−	0.196429i	$-0.0629344\pi$
$284$	17.1379	+	11.1401i	1.01695	+	0.661044i
$285$	−5.03179	+	4.70438i	−0.298058	+	0.278663i
$286$	−0.0611453	+	0.206258i	−0.00361560	+	0.0121963i
$287$	15.3744	−	11.5091i	0.907523	−	0.679363i
$288$	−7.15828	−	13.5242i	−0.421806	−	0.796920i
$289$	6.45699	−	10.0473i	0.379823	−	0.591016i
$290$	3.01077	+	1.78847i	0.176799	+	0.105022i
$291$	−0.198315	+	0.0905675i	−0.0116254	+	0.00530916i
$292$	3.63230	+	9.89531i	0.212564	+	0.579079i
$293$	−11.6152	−	21.2717i	−0.678568	−	1.24270i	−0.959157	−	0.282876i	$-0.908712\pi$
$293$	−11.6152	−	21.2717i	−0.678568	−	1.24270i	0.280589	−	0.959828i	$-0.409470\pi$
$294$	2.63026	−	5.72010i	0.153400	−	0.333603i
$295$	−2.38375	+	4.78703i	−0.138788	+	0.278712i
$296$	4.45066	+	9.95009i	0.258689	+	0.578337i
$297$	0.156569	+	0.117206i	0.00908506	+	0.00680099i
$298$	25.8376	+	14.1957i	1.49673	+	0.822333i
$299$	8.64178	−	7.67564i	0.499767	−	0.443894i
$300$	0.778497	−	5.37534i	0.0449465	−	0.310345i
$301$	−4.49392	−	31.2559i	−0.259025	−	1.80156i
$302$	−0.988750	+	0.736168i	−0.0568962	+	0.0423617i
$303$	1.12300	−	2.05662i	0.0645145	−	0.118150i
$304$	9.20962	+	20.7338i	0.528208	+	1.18917i
$305$	−21.3614	+	12.7346i	−1.22315	+	0.729180i
$306$	13.5177	−	15.5186i	0.772756	−	0.887140i
$307$	−3.26703	+	8.75924i	−0.186459	+	0.499916i	−0.996222	−	0.0868408i	$-0.972323\pi$
$307$	−3.26703	+	8.75924i	−0.186459	+	0.499916i	0.809763	+	0.586757i	$0.199596\pi$
$308$	0.233592	+	0.433127i	0.0133101	+	0.0246797i
$309$	3.44851	−	5.36598i	0.196179	−	0.305260i
$310$	−0.475530	−	2.64346i	−0.0270083	−	0.150138i
$311$	8.46585	+	1.21721i	0.480054	+	0.0690214i	0.378094	−	0.925767i	$-0.376580\pi$
$311$	8.46585	+	1.21721i	0.480054	+	0.0690214i	0.101960	+	0.994788i	$0.467489\pi$
$312$	−3.23564	−	1.79968i	−0.183182	−	0.101887i
$313$	−1.76666	+	24.7011i	−0.0998572	+	1.39619i	0.662515	+	0.749048i	$0.269489\pi$
$313$	−1.76666	+	24.7011i	−0.0998572	+	1.39619i	−0.762373	+	0.647138i	$0.775966\pi$
$314$	10.1256	−	8.72793i	0.571421	−	0.492546i
$315$	13.4879	+	19.3401i	0.759957	+	1.08969i
$316$	−0.305282	−	1.06004i	−0.0171734	−	0.0596319i
$317$	−1.61728	−	22.6125i	−0.0908353	−	1.27004i	−0.814611	−	0.580008i	$-0.803050\pi$
$317$	−1.61728	−	22.6125i	−0.0908353	−	1.27004i	0.723776	−	0.690035i	$-0.242405\pi$
$318$	−1.88074	+	8.53877i	−0.105467	+	0.478831i
$319$	−0.0290363	+	0.0635806i	−0.00162572	+	0.00355983i
$320$	−15.8868	−	8.22251i	−0.888099	−	0.459652i
$321$	−1.18432			−0.0661024
$322$	1.63129	−	26.3889i	0.0909083	−	1.47060i
$323$	−21.5764	+	21.5764i	−1.20054	+	1.20054i
$324$	9.76561	−	8.37350i	0.542534	−	0.465194i
$325$	5.05158	+	10.9405i	0.280211	+	0.606870i
$326$	2.56365	+	4.01200i	0.141988	+	0.222204i
$327$	2.47942	−	0.177331i	0.137112	−	0.00980645i
$328$	−13.5925	−	3.06801i	−0.750518	−	0.169402i
$329$	20.1361	+	31.3324i	1.11014	+	1.72741i
$330$	0.108338	+	0.00392507i	0.00596383	+	0.000216068i
$331$	−19.8792	+	17.2254i	−1.09266	+	0.946794i	−0.998809	−	0.0487924i	$-0.984463\pi$
$331$	−19.8792	+	17.2254i	−1.09266	+	0.946794i	−0.0938496	+	0.995586i	$0.529917\pi$
$332$	−22.6112	−	22.8474i	−1.24095	−	1.25391i
$333$	−8.34520	+	6.24714i	−0.457314	+	0.342341i
$334$	0.796876	+	5.64650i	0.0436031	+	0.308963i
$335$	−23.8902	−	14.1075i	−1.30526	−	0.770775i
$336$	−8.15053	+	2.30148i	−0.444648	+	0.125556i
$337$	17.9241	+	6.68535i	0.976389	+	0.364174i	0.786472	−	0.617626i	$-0.211905\pi$
$337$	17.9241	+	6.68535i	0.976389	+	0.364174i	0.189917	+	0.981800i	$0.439178\pi$
$338$	−10.1462	+	0.699182i	−0.551882	+	0.0380305i
$339$	3.33417	+	0.979002i	0.181087	+	0.0531721i
$340$	2.64629	−	23.9136i	0.143515	−	1.29690i
$341$	0.0514380	−	0.0151036i	0.00278552	−	0.000817903i
$342$	−17.4032	+	12.9574i	−0.941056	+	0.700658i
$343$	3.73384	+	2.79512i	0.201608	+	0.150922i
$344$	−15.1382	+	17.1977i	−0.816196	+	0.927237i
$345$	−4.83156	−	3.25291i	−0.260122	−	0.175131i
$346$	−32.1391	+	9.34627i	−1.72781	+	0.502459i
$347$	−7.44089	+	9.93987i	−0.399448	+	0.533600i	−0.954498	−	0.298217i	$-0.903608\pi$
$347$	−7.44089	+	9.93987i	−0.399448	+	0.533600i	0.555050	+	0.831817i	$0.312699\pi$
$348$	−0.959254	−	0.725896i	−0.0514214	−	0.0389121i
$349$	−3.29890	−	11.2350i	−0.176586	−	0.601396i	−0.999450	−	0.0331582i	$-0.989443\pi$
$349$	−3.29890	−	11.2350i	−0.176586	−	0.601396i	0.822864	−	0.568238i	$-0.192375\pi$
$350$	25.8420	+	9.59238i	1.38131	+	0.512734i
$351$	2.10396	−	7.16544i	0.112301	−	0.382463i
$352$	0.129111	−	0.332889i	0.00688166	−	0.0177430i
$353$	0.360763	−	0.967242i	0.0192015	−	0.0514811i	−0.926995	−	0.375073i	$-0.877618\pi$
$353$	0.360763	−	0.967242i	0.0192015	−	0.0514811i	0.946197	+	0.323592i	$0.104890\pi$
$354$	0.997173	−	1.54280i	0.0529991	−	0.0819991i
$355$	5.69784	+	22.1313i	0.302410	+	1.17461i
$356$	−3.96552	−	8.80406i	−0.210172	−	0.466614i
$357$	−6.82631	−	9.11888i	−0.361287	−	0.482622i
$358$	15.9918	−	8.67833i	0.845194	−	0.458664i
$359$	24.0759	+	27.7850i	1.27068	+	1.46644i	0.818496	+	0.574512i	$0.194808\pi$
$359$	24.0759	+	27.7850i	1.27068	+	1.46644i	0.452180	+	0.891927i	$0.350646\pi$
$360$	4.32548	−	16.5521i	0.227973	−	0.872370i
$361$	11.0787	−	7.11983i	0.583088	−	0.374728i
$362$	−13.5884	+	13.5180i	−0.714190	+	0.710489i
$363$	−0.426066	−	5.95718i	−0.0223627	−	0.312671i
$364$	12.3787	−	14.1366i	0.648818	−	0.740961i
$365$	−4.48726	+	10.8974i	−0.234874	+	0.570395i
$366$	7.78010	−	3.52865i	0.406672	−	0.184446i
$367$	14.9391	+	14.9391i	0.779812	+	0.779812i	0.979799	−	0.199987i	$-0.0640898\pi$
$367$	14.9391	+	14.9391i	0.779812	+	0.779812i	−0.199987	+	0.979799i	$0.564090\pi$
$368$	−15.3356	+	11.5248i	−0.799421	+	0.600771i
$369$		−	13.3263i		−	0.693741i
$370$	−3.85450	+	11.5611i	−0.200386	+	0.601032i
$371$	−40.3638	−	18.4335i	−2.09558	−	0.957020i
$372$	0.0610374	+	0.920617i	0.00316464	+	0.0477318i
$373$	12.8839	−	0.921478i	0.667105	−	0.0477123i	0.266320	−	0.963885i	$-0.414192\pi$
$373$	12.8839	−	0.921478i	0.667105	−	0.0477123i	0.400785	+	0.916172i	$0.368738\pi$
$374$	0.480221	+	0.00124766i	0.0248316	+	6.45151e-5i
$375$	4.70439	−	3.83980i	0.242934	−	0.198286i
$376$	7.81524	−	25.8686i	0.403040	−	1.33407i
$377$	2.66213	+	0.190399i	0.137107	+	0.00980607i
$378$	−8.14786	−	15.0143i	−0.419080	−	0.772252i
$379$	−3.18508	+	22.1527i	−0.163607	+	1.13791i	0.728158	+	0.685409i	$0.240377\pi$
$379$	−3.18508	+	22.1527i	−0.163607	+	1.13791i	−0.891765	+	0.452500i	$0.850532\pi$
$380$	−8.08513	+	24.0420i	−0.414758	+	1.23333i
$381$	8.75886	+	5.62898i	0.448730	+	0.288381i
$382$	−0.875554	−	4.07581i	−0.0447972	−	0.208536i
$383$	−15.4817	−	5.77439i	−0.791080	−	0.295057i	−0.0787426	−	0.996895i	$-0.525091\pi$
$383$	−15.4817	−	5.77439i	−0.791080	−	0.295057i	−0.712337	+	0.701838i	$0.752363\pi$
$384$	5.10819	+	3.41567i	0.260676	+	0.174305i
$385$	−0.134953	+	0.533379i	−0.00687786	+	0.0271835i
$386$	0.439081	−	0.954881i	0.0223486	−	0.0486021i
$387$	−19.2312	−	10.5010i	−0.977576	−	0.533797i
$388$	−0.484433	+	0.640166i	−0.0245934	+	0.0324995i
$389$	−10.8830	+	1.56474i	−0.551791	+	0.0793355i	−0.412570	−	0.910926i	$-0.635369\pi$
$389$	−10.8830	+	1.56474i	−0.551791	+	0.0793355i	−0.139221	+	0.990261i	$0.544460\pi$
$390$	−1.30523	−	3.92832i	−0.0660927	−	0.198918i
$391$	−21.8746	−	13.6820i	−1.10625	−	0.691927i
$392$	−1.47358	−	23.1362i	−0.0744270	−	1.16856i
$393$	5.12977	−	6.85257i	0.258763	−	0.345667i
$394$	−32.6946	−	4.78751i	−1.64713	−	0.241191i
$395$	0.549759	−	1.10402i	0.0276614	−	0.0555494i
$396$	0.337736	+	0.0503517i	0.0169719	+	0.00253027i
$397$	−17.0793	+	9.32602i	−0.857187	+	0.468059i	−0.846815	−	0.531887i	$-0.821483\pi$
$397$	−17.0793	+	9.32602i	−0.857187	+	0.468059i	−0.0103712	+	0.999946i	$0.503301\pi$
$398$	0.898413	+	13.0374i	0.0450334	+	0.653505i
$399$	4.98870	+	10.9237i	0.249747	+	0.546870i
$400$	−6.87252	−	18.7821i	−0.343626	−	0.939107i
$401$	−12.5189	−	8.04540i	−0.625164	−	0.401768i	0.189352	−	0.981909i	$-0.439361\pi$
$401$	−12.5189	−	8.04540i	−0.625164	−	0.401768i	−0.814516	+	0.580141i	$0.802997\pi$
$402$	7.61481	+	5.73131i	0.379792	+	0.285852i
$403$	−1.22673	−	1.63872i	−0.0611078	−	0.0816304i
$404$	0.0448351	−	8.62837i	0.00223063	−	0.429277i
$405$	14.3743	+	0.483384i	0.714263	+	0.0240195i
$406$	4.62428	−	3.98598i	0.229499	−	0.197821i
$407$	−0.237684	−	0.0517050i	−0.0117816	−	0.00256292i
$408$	−1.81970	+	8.06197i	−0.0900885	+	0.399127i
$409$	−9.39133	−	8.13763i	−0.464371	−	0.402380i	0.391004	−	0.920389i	$-0.372128\pi$
$409$	−9.39133	−	8.13763i	−0.464371	−	0.402380i	−0.855375	+	0.518009i	$0.826673\pi$
$410$	−8.87856	−	12.8016i	−0.438481	−	0.632226i
$411$	1.43958	+	0.657434i	0.0710092	+	0.0324288i
$412$	1.79730	−	23.4188i	0.0885466	−	1.15376i
$413$	6.59233	+	6.59233i	0.324387	+	0.324387i
$414$	−13.9805	−	11.8797i	−0.687106	−	0.583855i
$415$	−1.35758	−	35.9129i	−0.0666411	−	1.76290i
$416$	−13.6324	−	0.177101i	−0.668381	−	0.00868308i
$417$	−0.472065	−	1.26566i	−0.0231171	−	0.0619794i
$418$	−0.494427	−	0.108902i	−0.0241832	−	0.00532658i
$419$	6.30370	−	7.27486i	0.307956	−	0.355400i	−0.580583	−	0.814201i	$-0.697175\pi$
$419$	6.30370	−	7.27486i	0.307956	−	0.355400i	0.888539	+	0.458801i	$0.151721\pi$
$420$	−8.45410	−	4.26477i	−0.412518	−	0.208100i
$421$	−12.1002	+	7.77631i	−0.589726	+	0.378994i	−0.801206	−	0.598388i	$-0.795808\pi$
$421$	−12.1002	+	7.77631i	−0.589726	+	0.378994i	0.211480	+	0.977382i	$0.432172\pi$
$422$	1.13056	−	15.2504i	0.0550349	−	0.742378i
$423$	25.7783	+	1.84370i	1.25338	+	0.0896437i
$424$	8.82956	+	30.9614i	0.428801	+	1.50362i
$425$	20.2556	−	17.7000i	0.982543	−	0.858575i
$426$	−1.09702	−	7.77329i	−0.0531510	−	0.376617i
$427$	9.21598	+	42.3652i	0.445993	+	2.05020i
$428$	−3.83837	+	2.07009i	−0.185535	+	0.100062i
$429$	0.0751563	−	0.0343227i	0.00362858	−	0.00165712i
$430$	−25.4702	+	2.72509i	−1.22828	+	0.131415i
$431$	−4.82538	+	16.4337i	−0.232430	+	0.791585i	0.757841	+	0.652439i	$0.226254\pi$
$431$	−4.82538	+	16.4337i	−0.232430	+	0.791585i	−0.990272	+	0.139147i	$0.955564\pi$
$432$	−4.45188	+	11.5674i	−0.214191	+	0.556535i
$433$	−15.5611	−	8.49703i	−0.747821	−	0.408341i	0.0596723	−	0.998218i	$-0.480994\pi$
$433$	−15.5611	−	8.49703i	−0.747821	−	0.408341i	−0.807493	+	0.589877i	$0.799176\pi$
$434$	−4.63306	−	0.678424i	−0.222394	−	0.0325654i
$435$	−0.241557	−	1.32307i	−0.0115818	−	0.0634364i
$436$	7.72580	−	4.90853i	0.369999	−	0.235076i
$437$	19.4683	+	18.9968i	0.931297	+	0.908738i
$438$	1.94938	−	3.54808i	0.0931451	−	0.169534i
$439$	3.09138	+	21.5010i	0.147544	+	1.02619i	0.920224	+	0.391393i	$0.128007\pi$
$439$	3.09138	+	21.5010i	0.147544	+	1.02619i	−0.772680	+	0.634796i	$0.781084\pi$
$440$	0.357984	−	0.176645i	0.0170662	−	0.00842121i
$441$	21.2733	−	6.24641i	1.01302	−	0.297448i
$442$	−6.36336	−	17.1971i	−0.302674	−	0.817985i
$443$	25.3749	−	13.8557i	1.20560	−	0.658305i	0.254462	−	0.967083i	$-0.418102\pi$
$443$	25.3749	−	13.8557i	1.20560	−	0.658305i	0.951134	+	0.308778i	$0.0999200\pi$
$444$	1.75881	−	3.79890i	0.0834695	−	0.180288i
$445$	3.38790	−	10.2503i	0.160602	−	0.485909i
$446$	−12.8832	+	19.9326i	−0.610036	+	0.943834i
$447$	−2.40672	−	11.0635i	−0.113834	−	0.523286i
$448$	−22.3930	+	21.7055i	−1.05797	+	1.02549i
$449$	−26.4207	−	3.79873i	−1.24687	−	0.179273i	−0.512897	−	0.858450i	$-0.671428\pi$
$449$	−26.4207	−	3.79873i	−1.24687	−	0.179273i	−0.733975	+	0.679177i	$0.762337\pi$
$450$	16.0746	−	10.3662i	0.757763	−	0.488668i
$451$	0.235004	−	0.203632i	0.0110659	−	0.00958866i
$452$	12.5172	−	2.65491i	0.588761	−	0.124877i
$453$	0.462614	+	0.100635i	0.0217355	+	0.00472826i
$454$	−19.3689	−	0.0503224i	−0.909028	−	0.00236175i
$455$	20.8831	−	2.28920i	0.979015	−	0.107319i
$456$	3.68127	−	7.89737i	0.172391	−	0.369828i
$457$	−13.3808	−	35.8753i	−0.625927	−	1.67818i	−0.729864	−	0.683592i	$-0.760417\pi$
$457$	−13.3808	−	35.8753i	−0.625927	−	1.67818i	0.103937	−	0.994584i	$-0.466856\pi$
$458$	−1.49547	+	3.97793i	−0.0698789	+	0.185876i
$459$	−16.6702			−0.778100
$460$	−21.3448	−	2.09749i	−0.995206	−	0.0977960i
$461$	27.7540			1.29263			0.646317	−	0.763069i	$-0.276309\pi$
$461$	27.7540			1.29263			0.646317	+	0.763069i	$0.276309\pi$
$462$	0.0665073	−	0.176908i	0.00309420	−	0.00823050i
$463$	−0.852414	−	2.28541i	−0.0396151	−	0.106212i	0.915636	−	0.402008i	$-0.131688\pi$
$463$	−0.852414	−	2.28541i	−0.0396151	−	0.106212i	−0.955251	+	0.295796i	$0.904415\pi$
$464$	−4.37773	−	0.675929i	−0.203231	−	0.0313792i
$465$	−0.645584	+	0.804548i	−0.0299383	+	0.0373100i
$466$	36.5011	+	0.0948335i	1.69088	+	0.00439308i
$467$	1.27626	+	0.277633i	0.0590582	+	0.0128473i	0.241997	−	0.970277i	$-0.422197\pi$
$467$	1.27626	+	0.277633i	0.0590582	+	0.0128473i	−0.182939	+	0.983124i	$0.558561\pi$
$468$	−2.70530	−	12.7548i	−0.125053	−	0.589591i
$469$	−36.5547	+	31.6748i	−1.68794	+	1.46261i
$470$	25.9916	−	15.4035i	1.19890	−	0.710510i
$471$	−5.08186	−	0.730661i	−0.234160	−	0.0336671i
$472$	0.535139	−	6.74317i	0.0246318	−	0.310380i
$473$	−0.108680	−	0.499594i	−0.00499712	−	0.0229714i
$474$	−0.229975	+	0.355813i	−0.0105631	+	0.0163430i
$475$	−24.8332	+	13.6946i	−1.13943	+	0.628353i
$476$	−38.0630	−	17.6224i	−1.74461	−	0.807720i
$477$	−27.0245	+	14.7565i	−1.23737	+	0.675652i
$478$	13.2854	+	35.9042i	0.607661	+	1.64222i
$479$	36.9076	−	10.8370i	1.68635	−	0.495157i	0.708721	−	0.705489i	$-0.249273\pi$
$479$	36.9076	−	10.8370i	1.68635	−	0.495157i	0.977630	+	0.210332i	$0.0674543\pi$
$480$	1.62636	+	6.67498i	0.0742328	+	0.304670i
$481$	1.32181	+	9.19339i	0.0602693	+	0.419182i
$482$	7.08098	−	12.8881i	0.322530	−	0.587038i
$483$	−8.05370	+	6.18442i	−0.366456	+	0.281401i
$484$	−11.7935	−	18.5624i	−0.536068	−	0.843746i
$485$	−0.882962	+	0.161205i	−0.0400932	+	0.00731993i
$486$	−17.8960	−	2.62054i	−0.811780	−	0.118870i
$487$	4.95990	+	2.70831i	0.224755	+	0.122725i	0.587682	−	0.809092i	$-0.300041\pi$
$487$	4.95990	+	2.70831i	0.224755	+	0.122725i	−0.362927	+	0.931818i	$0.618223\pi$
$488$	19.0474	−	25.0353i	0.862237	−	1.13329i
$489$	0.515165	−	1.75449i	0.0232966	−	0.0793409i
$490$	16.2741	−	20.1736i	0.735187	−	0.911352i
$491$	3.24287	−	1.48097i	0.146349	−	0.0668352i	−0.340894	−	0.940102i	$-0.610730\pi$
$491$	3.24287	−	1.48097i	0.146349	−	0.0668352i	0.487243	+	0.873266i	$0.338003\pi$
$492$	2.54033	+	4.71028i	0.114527	+	0.212356i
$493$	−1.26640	−	5.82155i	−0.0570358	−	0.262189i
$494$	2.70145	+	19.1419i	0.121544	+	0.861236i
$495$	0.240170	+	0.296765i	0.0107948	+	0.0133386i
$496$	1.80698	+	2.87702i	0.0811357	+	0.129182i
$497$	39.7395	+	2.84223i	1.78256	+	0.127491i
$498$	−0.912699	+	12.3116i	−0.0408990	+	0.551696i
$499$	−17.1435	+	11.0175i	−0.767448	+	0.493209i	−0.864847	−	0.502036i	$-0.832584\pi$
$499$	−17.1435	+	11.0175i	−0.767448	+	0.493209i	0.0973981	+	0.995246i	$0.468948\pi$
$500$	8.53524	−	20.6676i	0.381707	−	0.924283i
$501$	1.43420	−	1.65515i	0.0640752	−	0.0739467i
$502$	−1.02839	−	0.226513i	−0.0458994	−	0.0101098i
$503$	13.6359	+	36.5593i	0.607996	+	1.63010i	0.766133	+	0.642683i	$0.222179\pi$
$503$	13.6359	+	36.5593i	0.607996	+	1.63010i	−0.158137	+	0.987417i	$0.550549\pi$
$504$	−24.9641	−	16.3198i	−1.11199	−	0.726941i
$505$	6.55887	−	7.07423i	0.291866	−	0.314799i
$506$	−0.00413576	−	0.428068i	−0.000183857	−	0.0190299i
$507$	2.76196	+	2.76196i	0.122663	+	0.122663i
$508$	38.2263	+	2.93372i	1.69602	+	0.130163i
$509$	4.55707	+	2.08115i	0.201989	+	0.0922452i	0.513841	−	0.857885i	$-0.328222\pi$
$509$	4.55707	+	2.08115i	0.201989	+	0.0922452i	−0.311852	+	0.950131i	$0.600949\pi$
$510$	−7.59289	+	5.26606i	−0.336219	+	0.233185i
$511$	15.5273	+	13.4545i	0.686889	+	0.595193i
$512$	22.5259	+	2.14148i	0.995511	+	0.0946408i
$513$	17.1731	+	3.73578i	0.758211	+	0.164939i
$514$	10.2667	−	8.84957i	0.452846	−	0.390338i
$515$	19.1822	−	17.9340i	0.845268	−	0.790267i
$516$	8.79915	+	0.0457225i	0.387361	+	0.00201282i
$517$	0.361391	+	0.482762i	0.0158940	+	0.0212318i
$518$	16.9750	+	12.7763i	0.745838	+	0.561357i
$519$	10.8140	+	6.94976i	0.474684	+	0.305061i
$520$	−11.0966	−	10.4502i	−0.486617	−	0.458271i
$521$	−10.2165	−	22.3710i	−0.447594	−	0.980093i	−0.990142	−	0.140068i	$-0.955268\pi$
$521$	−10.2165	−	22.3710i	−0.447594	−	0.980093i	0.542548	−	0.840025i	$-0.317460\pi$
$522$	−0.291235	−	4.22628i	−0.0127470	−	0.184979i
$523$	24.8273	−	13.5567i	1.08562	−	0.592795i	0.166211	−	0.986090i	$-0.446847\pi$
$523$	24.8273	−	13.5567i	1.08562	−	0.592795i	0.919412	+	0.393295i	$0.128665\pi$
$524$	4.64782	−	31.1755i	0.203041	−	1.36191i
$525$	−3.74093	−	9.90356i	−0.163268	−	0.432227i
$526$	−38.5082	−	5.63880i	−1.67904	−	0.245863i
$527$	−2.73835	+	3.65801i	−0.119285	+	0.159346i
$528$	−0.128973	+	0.0465836i	−0.00561285	+	0.00202729i
$529$	−11.9566	+	19.6479i	−0.519854	+	0.854255i
$530$	−16.1290	+	32.1803i	−0.700598	+	1.39782i
$531$	6.40334	−	0.920661i	0.277881	−	0.0399533i
$532$	35.2620	+	26.6838i	1.52880	+	1.15689i
$533$	−10.4211	−	5.69033i	−0.451386	−	0.246475i
$534$	−1.54930	+	3.36931i	−0.0670449	+	0.145804i
$535$	−4.72680	−	1.19596i	−0.204358	−	0.0517057i
$536$	34.6973	+	5.26507i	1.49870	+	0.227416i
$537$	−6.54730	−	2.44202i	−0.282537	−	0.105381i
$538$	0.672133	+	3.12886i	0.0289777	+	0.134895i
$539$	0.435219	+	0.279698i	0.0187462	+	0.0120474i
$540$	−12.4109	+	6.16424i	−0.534082	+	0.265267i
$541$	−2.20600	+	15.3431i	−0.0948434	+	0.659650i	0.885832	+	0.464007i	$0.153589\pi$
$541$	−2.20600	+	15.3431i	−0.0948434	+	0.659650i	−0.980675	+	0.195643i	$0.937320\pi$
$542$	0.441932	+	0.814361i	0.0189826	+	0.0349798i
$543$	7.34257	+	0.525151i	0.315100	+	0.0225364i
$544$	8.19400	+	29.3094i	0.351315	+	1.25663i
$545$	10.0748	+	1.79602i	0.431557	+	0.0769330i
$546$	−7.21657	−	0.0187494i	−0.308840	−	0.000802399i
$547$	17.2196	−	1.23157i	0.736258	−	0.0526582i	0.301826	−	0.953363i	$-0.402404\pi$
$547$	17.2196	−	1.23157i	0.736258	−	0.0526582i	0.434432	+	0.900705i	$0.356949\pi$
$548$	5.81480	−	0.385524i	0.248396	−	0.0164688i
$549$	27.3659	+	12.4976i	1.16795	+	0.533385i
$550$	0.428431	+	0.125068i	0.0182683	+	0.00533292i
$551$			6.28095i			0.267578i
$552$	7.20608	+	1.53392i	0.306711	+	0.0652881i
$553$	−1.52037	−	1.52037i	−0.0646528	−	0.0646528i
$554$	24.5702	−	11.1438i	1.04389	−	0.473454i
$555$	4.32040	−	1.80013i	0.183391	−	0.0764111i
$556$	−3.74221	−	3.27685i	−0.158705	−	0.138969i
$557$	2.06818	+	28.9169i	0.0876315	+	1.22525i	0.830964	+	0.556326i	$0.187789\pi$
$557$	2.06818	+	28.9169i	0.0876315	+	1.22525i	−0.743333	+	0.668922i	$0.766756\pi$
$558$	−2.30346	+	2.29152i	−0.0975132	+	0.0970078i
$559$	−16.4234	+	10.5547i	−0.694636	+	0.446415i
$560$	−34.8541	+	0.954950i	−1.47285	+	0.0403540i
$561$	−0.120778	−	0.139386i	−0.00509927	−	0.00588487i
$562$	−8.48329	+	4.60365i	−0.357846	+	0.194193i
$563$	−21.3130	−	28.4708i	−0.898236	−	1.19990i	−0.979141	−	0.203181i	$-0.934872\pi$
$563$	−21.3130	−	28.4708i	−0.898236	−	1.19990i	0.0809051	−	0.996722i	$-0.474219\pi$
$564$	−9.46297	+	4.26231i	−0.398463	+	0.179476i
$565$	12.3186	+	7.27427i	0.518245	+	0.306031i
$566$	−10.3408	+	15.9990i	−0.434655	+	0.672488i
$567$	8.76234	−	23.4927i	0.367984	−	0.986602i
$568$	−17.1425	−	23.2756i	−0.719282	−	0.976623i
$569$	−4.45255	+	15.1640i	−0.186661	+	0.635708i	0.811985	+	0.583678i	$0.198387\pi$
$569$	−4.45255	+	15.1640i	−0.186661	+	0.635708i	−0.998646	+	0.0520293i	$0.983431\pi$
$570$	9.00205	−	3.72335i	0.377054	−	0.155954i
$571$	−1.43381	−	4.88312i	−0.0600032	−	0.204352i	0.924036	−	0.382307i	$-0.124870\pi$
$571$	−1.43381	−	4.88312i	−0.0600032	−	0.204352i	−0.984039	+	0.177955i	$0.943052\pi$
$572$	0.183587	−	0.242606i	0.00767618	−	0.0101439i
$573$	−0.959481	+	1.28172i	−0.0400829	+	0.0535445i
$574$	−26.0796	+	7.58413i	−1.08854	+	0.316555i
$575$	−15.9986	−	17.8618i	−0.667187	−	0.744890i
$576$	2.74543	+	21.4651i	0.114393	+	0.894380i
$577$	−16.2675	−	12.1777i	−0.677225	−	0.506964i	0.204417	−	0.978884i	$-0.434470\pi$
$577$	−16.2675	−	12.1777i	−0.677225	−	0.506964i	−0.881641	+	0.471920i	$0.843561\pi$
$578$	−13.5476	+	10.0868i	−0.563506	+	0.419555i
$579$	−0.387294	+	0.113720i	−0.0160954	+	0.00472603i
$580$	−3.09549	−	3.86584i	−0.128533	−	0.160520i
$581$	−60.1159	−	17.6516i	−2.49403	−	0.732312i
$582$	0.307593	−	0.0211964i	0.0127501	−	0.000878619i
$583$	−0.673170	−	0.251079i	−0.0278799	−	0.0103986i
$584$	0.116189	−	14.9066i	0.00480793	−	0.616841i
$585$	7.41234	−	12.5524i	0.306462	−	0.518977i
$586$	4.78972	+	33.9389i	0.197861	+	1.40200i
$587$	5.31370	−	3.97779i	0.219320	−	0.164181i	−0.483969	−	0.875085i	$-0.660805\pi$
$587$	5.31370	−	3.97779i	0.219320	−	0.164181i	0.703289	+	0.710904i	$0.251714\pi$
$588$	−6.32849	+	6.26306i	−0.260982	+	0.258284i
$589$	3.64071	−	3.15470i	0.150013	−	0.129987i
$590$	5.53782	−	5.15058i	0.227988	−	0.212046i
$591$	6.86104	+	10.6760i	0.282225	+	0.439151i
$592$	−0.939852	−	15.3864i	−0.0386277	−	0.632378i
$593$	14.7010	−	1.05143i	0.603696	−	0.0431772i	0.233854	−	0.972272i	$-0.424866\pi$
$593$	14.7010	−	1.05143i	0.603696	−	0.0431772i	0.369842	+	0.929095i	$0.379412\pi$
$594$	−0.148931	−	0.233071i	−0.00611072	−	0.00956300i
$595$	−18.0363	−	43.2881i	−0.739417	−	1.77464i
$596$	−27.1382	−	31.6499i	−1.11162	−	1.29643i
$597$	3.54897	−	3.54897i	0.145250	−	0.145250i
$598$	−15.2595	+	5.86004i	−0.624006	+	0.239635i
$599$	42.4486			1.73440			0.867201	−	0.497958i	$-0.165917\pi$
$599$	42.4486			1.73440			0.867201	+	0.497958i	$0.165917\pi$
$600$	−3.70562	+	6.72822i	−0.151281	+	0.274678i
$601$	−17.6718	+	38.6957i	−0.720846	+	1.57843i	0.0918695	+	0.995771i	$0.470716\pi$
$601$	−17.6718	+	38.6957i	−0.720846	+	1.57843i	−0.812715	+	0.582661i	$0.802012\pi$
$602$	−9.60588	+	43.6117i	−0.391506	+	1.77748i
$603$	2.39436	+	33.4775i	0.0975058	+	1.36331i
$604$	1.67523	−	0.482450i	0.0681640	−	0.0196306i
$605$	4.31521	−	24.2062i	0.175438	−	0.984123i
$606$	−2.51007	+	2.16360i	−0.101965	+	0.0878901i
$607$	0.0639438	−	0.894052i	0.00259540	−	0.0362884i	−0.995989	−	0.0894716i	$-0.971482\pi$
$607$	0.0639438	−	0.894052i	0.00259540	−	0.0362884i	0.998585	+	0.0531832i	$0.0169367\pi$
$608$	−1.87297	−	32.0298i	−0.0759590	−	1.29898i
$609$	−2.32085	−	0.333687i	−0.0940454	−	0.0135217i
$610$	34.6148	−	6.22684i	1.40151	−	0.252117i
$611$	12.4491	−	19.3711i	0.503635	−	0.783672i
$612$	−25.6171	+	13.8157i	−1.03551	+	0.558467i
$613$	−13.1763	+	35.3270i	−0.532185	+	1.42684i	0.341283	+	0.939960i	$0.389138\pi$
$613$	−13.1763	+	35.3270i	−0.532185	+	1.42684i	−0.873468	+	0.486882i	$0.838134\pi$
$614$	8.68386	−	9.96926i	0.350452	−	0.402326i
$615$	−1.46763	+	5.80053i	−0.0591804	+	0.233900i
$616$	−0.0936702	−	0.689605i	−0.00377408	−	0.0277850i
$617$	−11.4771	+	21.0187i	−0.462050	+	0.846182i	0.537945	+	0.842980i	$0.319201\pi$
$617$	−11.4771	+	21.0187i	−0.462050	+	0.846182i	−0.999995	+	0.00320162i	$0.998981\pi$
$618$	−7.23541	+	5.38709i	−0.291051	+	0.216700i
$619$	−0.704437	−	4.89947i	−0.0283137	−	0.196926i	0.970755	−	0.240072i	$-0.0771711\pi$
$619$	−0.704437	−	4.89947i	−0.0283137	−	0.196926i	−0.999069	+	0.0431459i	$0.986262\pi$
$620$	−0.686052	+	3.73595i	−0.0275525	+	0.150039i
$621$	0.182174	+	14.8594i	0.00731038	+	0.596285i
$622$	−10.6010	−	5.82438i	−0.425061	−	0.233537i
$623$	−15.0667	−	11.2788i	−0.603635	−	0.451876i
$624$	3.38759	+	3.99258i	0.135612	+	0.159831i
$625$	22.6534	−	10.5746i	0.906137	−	0.422984i
$626$	14.6313	−	31.8191i	0.584785	−	1.27175i
$627$	0.0931856	+	0.170657i	0.00372147	+	0.00681537i
$628$	−17.7474	+	6.51458i	−0.708197	+	0.259960i
$629$	18.8593	−	8.61275i	0.751969	−	0.343413i
$630$	−8.22997	−	32.3140i	−0.327890	−	1.28742i
$631$	−24.8434	+	38.6572i	−0.989002	+	1.53892i	−0.154441	+	0.988002i	$0.549358\pi$
$631$	−24.8434	+	38.6572i	−0.989002	+	1.53892i	−0.834561	+	0.550915i	$0.814279\pi$
$632$	−0.123418	+	1.55516i	−0.00490930	+	0.0618610i
$633$	−4.70168	+	3.51963i	−0.186875	+	0.139893i
$634$	−9.11239	+	30.7383i	−0.361899	+	1.22077i
$635$	29.2736	+	31.3110i	1.16169	+	1.24254i
$636$	6.73904	−	10.3673i	0.267220	−	0.411091i
$637$	4.19906	−	19.3027i	0.166373	−	0.764803i
$638$	0.0700784	−	0.0697152i	0.00277443	−	0.00276005i
$639$	18.1040	−	20.8931i	0.716184	−	0.826520i
$640$	16.9383	+	18.7908i	0.669545	+	0.742772i
$641$	10.6176	−	23.2492i	0.419368	−	0.918288i	−0.575566	−	0.817756i	$-0.695218\pi$
$641$	10.6176	−	23.2492i	0.419368	−	0.918288i	0.994934	−	0.100533i	$-0.0320547\pi$
$642$	1.56776	+	0.589387i	0.0618744	+	0.0232613i
$643$	−15.4705	+	15.4705i	−0.610096	+	0.610096i	−0.942971	−	0.332875i	$-0.891981\pi$
$643$	−15.4705	+	15.4705i	−0.610096	+	0.610096i	0.332875	+	0.942971i	$0.391981\pi$
$644$	−15.2921	+	34.1208i	−0.602593	+	1.34455i
$645$	7.21425	+	6.68869i	0.284061	+	0.263367i
$646$	39.2996	−	17.8243i	1.54622	−	0.701286i
$647$	−21.6977	+	8.09283i	−0.853026	+	0.318162i	−0.737669	−	0.675162i	$-0.764074\pi$
$647$	−21.6977	+	8.09283i	−0.853026	+	0.318162i	−0.115356	+	0.993324i	$0.536801\pi$
$648$	−17.0944	+	6.22456i	−0.671533	+	0.244524i
$649$	0.114081	+	0.0988520i	0.00447808	+	0.00388028i
$650$	−1.24244	−	16.9965i	−0.0487326	−	0.666659i
$651$	0.972258	+	1.51286i	0.0381058	+	0.0592938i
$652$	−1.39705	−	6.58675i	−0.0547128	−	0.257957i
$653$	−0.272303	+	3.80730i	−0.0106560	+	0.148991i	0.989338	+	0.145635i	$0.0465227\pi$
$653$	−0.272303	+	3.80730i	−0.0106560	+	0.148991i	−0.999994	+	0.00335555i	$0.998932\pi$
$654$	−3.37040	−	0.999158i	−0.131793	−	0.0390702i
$655$	27.3936	−	22.1694i	1.07035	−	0.866232i
$656$	16.4663	+	10.8257i	0.642902	+	0.422672i
$657$	13.9308	−	3.03045i	0.543490	−	0.118229i
$658$	−11.0625	−	51.4974i	−0.431262	−	2.00758i
$659$	10.5684	+	23.1417i	0.411688	+	0.901471i	0.995950	+	0.0899062i	$0.0286567\pi$
$659$	10.5684	+	23.1417i	0.411688	+	0.901471i	−0.584262	+	0.811565i	$0.698616\pi$
$660$	−0.141460	−	0.0591113i	−0.00550634	−	0.00230090i
$661$	−18.2470	−	5.35780i	−0.709726	−	0.208394i	−0.0931069	−	0.995656i	$-0.529680\pi$
$661$	−18.2470	−	5.35780i	−0.709726	−	0.208394i	−0.616619	+	0.787262i	$0.711498\pi$
$662$	34.8876	−	12.9092i	1.35594	−	0.501732i
$663$	−3.37505	+	6.18094i	−0.131076	+	0.240048i
$664$	18.5615	+	41.4970i	0.720327	+	1.61040i
$665$	8.87958	+	48.6359i	0.344335	+	1.88602i
$666$	14.1560	−	4.11665i	0.548533	−	0.159517i
$667$	−5.17531	+	1.19245i	−0.200389	+	0.0461718i
$668$	1.75515	−	7.87117i	0.0679089	−	0.304545i
$669$	9.02232	−	1.29721i	0.348823	−	0.0501532i
$670$	24.6042	+	30.5641i	0.950543	+	1.18079i
$671$	0.197774	+	0.673556i	0.00763498	+	0.0260023i
$672$	11.9347	+	1.00957i	0.460391	+	0.0389450i
$673$	−12.4841	−	22.8629i	−0.481226	−	0.881300i	−0.999657	−	0.0261806i	$-0.991666\pi$
$673$	−12.4841	−	22.8629i	−0.481226	−	0.881300i	0.518431	−	0.855119i	$-0.326516\pi$
$674$	−20.4002	−	17.7699i	−0.785786	−	0.684470i
$675$	−14.8836	−	4.30291i	−0.572870	−	0.165619i
$676$	13.7791	+	4.12381i	0.529966	+	0.158608i
$677$	26.3950	−	5.74188i	1.01444	−	0.220678i	0.325536	−	0.945530i	$-0.394455\pi$
$677$	26.3950	−	5.74188i	1.01444	−	0.220678i	0.688905	+	0.724851i	$0.258092\pi$
$678$	−3.92643	−	2.95524i	−0.150794	−	0.113495i
$679$	−0.222689	+	1.54884i	−0.00854602	+	0.0594389i
$680$	−15.4038	+	30.3389i	−0.590711	+	1.16344i
$681$	4.87140	+	5.62189i	0.186672	+	0.215431i
$682$	−0.0756079	−	0.00560506i	−0.00289518	−	0.000214629i
$683$	−6.04091	+	27.7696i	−0.231149	+	1.06257i	0.704517	+	0.709687i	$0.251164\pi$
$683$	−6.04091	+	27.7696i	−0.231149	+	1.06257i	−0.935666	+	0.352888i	$0.885200\pi$
$684$	29.4860	−	8.49169i	1.12742	−	0.324688i
$685$	5.08168	+	4.07764i	0.194161	+	0.155798i
$686$	−3.55169	−	5.55824i	−0.135604	−	0.212215i
$687$	1.52925	−	0.570379i	0.0583444	−	0.0217613i
$688$	28.5979	−	15.2320i	1.09028	−	0.580713i
$689$			27.4339i			1.04515i
$690$	4.77698	+	6.71052i	0.181856	+	0.255465i
$691$		−	11.0623i		−	0.420829i	−0.977612	−	0.210415i	$-0.932519\pi$
$691$		−	11.0623i		−	0.420829i	0.977612	−	0.210415i	$-0.0674814\pi$
$692$	47.1957	+	3.62209i	1.79411	+	0.137691i
$693$	0.623603	−	0.232592i	0.0236887	−	0.00883544i
$694$	14.7966	−	9.45497i	0.561671	−	0.358906i
$695$	−0.605992	−	5.52812i	−0.0229866	−	0.209694i
$696$	0.908572	+	1.43829i	0.0344393	+	0.0545183i
$697$	−5.63390	+	25.8986i	−0.213399	+	0.980980i
$698$	−1.22425	+	16.5142i	−0.0463385	+	0.625070i
$699$	−9.18025	−	10.5946i	−0.347229	−	0.400723i
$700$	−29.4349	−	25.5585i	−1.11253	−	0.966020i
$701$	3.36551	−	23.4076i	0.127114	−	0.884094i	−0.822073	−	0.569382i	$-0.807183\pi$
$701$	3.36551	−	23.4076i	0.127114	−	0.884094i	0.949187	−	0.314713i	$-0.101908\pi$
$702$	−6.35108	+	8.43826i	−0.239706	+	0.318482i
$703$	−21.3583	+	4.64621i	−0.805543	+	0.175235i
$704$	−0.336577	+	0.376411i	−0.0126852	+	0.0141865i
$705$	−11.0174	−	3.64146i	−0.414940	−	0.137145i
$706$	−0.958918	+	1.10086i	−0.0360894	+	0.0414313i
$707$	−8.06004	−	14.7609i	−0.303129	−	0.555139i
$708$	−2.08780	+	1.54605i	−0.0784645	+	0.0581040i
$709$	−6.36674	−	21.6831i	−0.239108	−	0.814327i	−0.988372	−	0.152055i	$-0.951411\pi$
$709$	−6.36674	−	21.6831i	−0.239108	−	0.814327i	0.749264	−	0.662271i	$-0.230407\pi$
$710$	3.47127	−	32.1321i	0.130274	−	1.20590i
$711$	−1.47679	+	0.212330i	−0.0553838	+	0.00796299i
$712$	0.867982	+	13.6279i	0.0325290	+	0.510728i
$713$	3.29057	+	2.40091i	0.123233	+	0.0899148i
$714$	4.49830	+	15.4684i	0.168345	+	0.578889i
$715$	0.334620	−	0.0610924i	0.0125141	−	0.00228473i
$716$	−25.4881	+	3.52956i	−0.952537	+	0.131906i
$717$	7.04643	−	12.9046i	0.263154	−	0.481930i
$718$	−18.0432	−	48.7622i	−0.673366	−	1.81979i
$719$	3.59391	+	1.05527i	0.134030	+	0.0393549i	0.348060	−	0.937472i	$-0.386841\pi$
$719$	3.59391	+	1.05527i	0.134030	+	0.0393549i	−0.214029	+	0.976827i	$0.568659\pi$
$720$	−13.9632	+	19.7583i	−0.520376	+	0.736349i
$721$	−19.0179	−	41.6434i	−0.708264	−	1.55088i
$722$	−18.2087	+	3.91155i	−0.677659	+	0.145573i
$723$	−5.51861	+	1.20050i	−0.205239	+	0.0446471i
$724$	24.7151	−	11.1322i	0.918529	−	0.413723i
$725$	0.371981	−	5.52450i	0.0138150	−	0.205175i
$726$	−2.40063	+	8.09790i	−0.0890957	+	0.300541i
$727$	3.05347	−	42.6930i	0.113247	−	1.58340i	−0.550109	−	0.835093i	$-0.685414\pi$
$727$	3.05347	−	42.6930i	0.113247	−	1.58340i	0.663356	−	0.748304i	$-0.269132\pi$
$728$	−23.4216	+	12.5532i	−0.868061	+	0.465251i
$729$	−6.67668	−	10.3891i	−0.247285	−	0.384782i
$730$	11.3632	−	12.1924i	0.420571	−	0.451260i
$731$	32.9348	+	28.5382i	1.21814	+	1.05552i
$732$	−12.0550	+	0.799256i	−0.445567	+	0.0295413i
$733$	−46.8553	+	17.4761i	−1.73064	+	0.645495i	−0.999332	−	0.0365525i	$-0.988362\pi$
$733$	−46.8553	+	17.4761i	−1.73064	+	0.645495i	−0.731308	+	0.682048i	$0.761090\pi$
$734$	−12.3412	−	27.2102i	−0.455521	−	1.00435i
$735$	−9.94752	+	0.376037i	−0.366920	+	0.0138703i
$736$	26.0360	−	7.62418i	0.959699	−	0.281031i
$737$	−0.553775	+	0.553775i	−0.0203986	+	0.0203986i
$738$	−6.63195	+	17.6408i	−0.244125	+	0.649368i
$739$	8.20058	−	17.9568i	0.301663	−	0.660550i	−0.696723	−	0.717340i	$-0.745359\pi$
$739$	8.20058	−	17.9568i	0.301663	−	0.660550i	0.998386	+	0.0567901i	$0.0180866\pi$
$740$	10.8559	−	13.3859i	0.399070	−	0.492074i
$741$	4.86200	−	5.61105i	0.178610	−	0.206127i
$742$	44.2583	+	44.4889i	1.62477	+	1.63324i
$743$	−10.5515	+	48.5044i	−0.387096	+	1.77945i	0.210436	+	0.977608i	$0.432512\pi$
$743$	−10.5515	+	48.5044i	−0.387096	+	1.77945i	−0.597532	+	0.801845i	$0.703852\pi$
$744$	0.377353	−	1.24905i	0.0138344	−	0.0457924i
$745$	1.56663	−	46.5864i	0.0573968	−	1.70679i
$746$	−17.5138	−	5.19198i	−0.641226	−	0.190092i
$747$	−34.8038	+	26.0538i	−1.27340	+	0.953259i
$748$	−0.635075	−	0.240637i	−0.0232207	−	0.00879857i
$749$	−4.59554	+	7.15081i	−0.167918	+	0.261285i
$750$	−8.13839	+	2.74179i	−0.297172	+	0.100116i
$751$	−32.8603	+	15.0068i	−1.19909	+	0.547606i	−0.911957	−	0.410285i	$-0.865429\pi$
$751$	−32.8603	+	15.0068i	−1.19909	+	0.547606i	−0.287133	+	0.957891i	$0.592702\pi$
$752$	−23.2192	+	30.3545i	−0.846718	+	1.10692i
$753$	0.193823	+	0.354961i	0.00706331	+	0.0129355i
$754$	−3.42927	−	1.57687i	−0.124887	−	0.0574264i
$755$	1.74473	+	0.868809i	0.0634974	+	0.0316192i
$756$	3.31381	+	23.9301i	0.120522	+	0.870331i
$757$	38.5699	+	28.8731i	1.40185	+	1.04941i	0.990438	+	0.137960i	$0.0440545\pi$
$757$	38.5699	+	28.8731i	1.40185	+	1.04941i	0.411410	+	0.911450i	$0.365036\pi$
$758$	15.2408	−	27.7398i	0.553569	−	1.00755i
$759$	−0.122924	+	0.109181i	−0.00446187	+	0.00396304i
$760$	22.6674	−	27.8021i	0.822234	−	1.00849i
$761$	5.01423	+	34.8747i	0.181766	+	1.26421i	0.852586	+	0.522587i	$0.175033\pi$
$761$	5.01423	+	34.8747i	0.181766	+	1.26421i	−0.670820	+	0.741620i	$0.734058\pi$
$762$	−8.79331	−	11.8103i	−0.318548	−	0.427843i
$763$	8.55022	−	15.6586i	0.309539	−	0.566878i
$764$	−0.869337	+	5.83111i	−0.0314515	+	0.210962i
$765$	−31.5465	−	7.98176i	−1.14057	−	0.288581i
$766$	17.6204	+	15.3485i	0.636651	+	0.554564i
$767$	2.01427	−	5.40047i	0.0727311	−	0.195000i
$768$	−5.06217	−	7.06365i	−0.182665	−	0.254888i
$769$	4.35615	−	6.77830i	0.157087	−	0.244432i	−0.753785	−	0.657121i	$-0.771774\pi$
$769$	4.35615	−	6.77830i	0.157087	−	0.244432i	0.910872	+	0.412689i	$0.135410\pi$
$770$	0.444086	−	0.638904i	0.0160038	−	0.0230245i
$771$	−5.15269	−	0.740845i	−0.185570	−	0.0266809i
$772$	−1.05644	+	1.04552i	−0.0380222	+	0.0376291i
$773$	−0.554381	+	7.75127i	−0.0199397	+	0.278794i	0.977694	+	0.210036i	$0.0673581\pi$
$773$	−0.554381	+	7.75127i	−0.0199397	+	0.278794i	−0.997633	+	0.0687577i	$0.978096\pi$
$774$	20.2315	+	23.4714i	0.727207	+	0.843661i
$775$	−3.38907	+	2.55914i	−0.121739	+	0.0919270i
$776$	0.959856	−	0.606343i	0.0344568	−	0.0217664i
$777$	−0.582102	−	8.13884i	−0.0208828	−	0.291979i
$778$	15.1852	+	3.34468i	0.544415	+	0.119913i
$779$	11.6077	−	25.4173i	0.415889	−	0.910670i
$780$	−0.227152	+	5.84970i	−0.00813336	+	0.209453i
$781$	0.645079			0.0230827
$782$	22.1477	+	28.9977i	0.792001	+	1.03695i
$783$	−2.42638	+	2.42638i	−0.0867117	+	0.0867117i
$784$	−9.56326	+	31.3601i	−0.341545	+	1.12000i
$785$	−19.5446	−	8.04796i	−0.697577	−	0.287244i
$786$	−10.2008	+	6.51828i	−0.363851	+	0.232499i
$787$	5.34720	−	0.382439i	0.190607	−	0.0136325i	0.0242908	−	0.999705i	$-0.492267\pi$
$787$	5.34720	−	0.382439i	0.190607	−	0.0136325i	0.166316	+	0.986072i	$0.446813\pi$
$788$	40.8972	+	22.6082i	1.45690	+	0.805385i
$789$	8.08104	+	12.5743i	0.287693	+	0.447659i
$790$	−1.27717	+	1.18787i	−0.0454398	+	0.0422624i
$791$	18.8488	−	16.3325i	0.670184	−	0.580718i
$792$	−0.422023	−	0.234730i	−0.0149959	−	0.00834078i
$793$	21.4582	−	16.0634i	0.762005	−	0.570430i
$794$	27.2501	−	3.84573i	0.967069	−	0.136480i
$795$	13.3880	−	3.44682i	0.474824	−	0.122246i
$796$	5.29888	−	17.7055i	0.187814	−	0.627553i
$797$	−20.6246	−	7.69259i	−0.730562	−	0.272486i	−0.0434689	−	0.999055i	$-0.513841\pi$
$797$	−20.6246	−	7.69259i	−0.730562	−	0.272486i	−0.687093	+	0.726569i	$0.741114\pi$
$798$	−1.16755	−	16.9430i	−0.0413309	−	0.599777i
$799$	−49.3186	−	14.4812i	−1.74477	−	0.512309i
$800$	−0.249526	+	28.2832i	−0.00882206	+	0.999961i
$801$	−12.5306	+	3.67932i	−0.442747	+	0.130002i
$802$	12.5681	+	16.8803i	0.443796	+	0.596064i
$803$	0.266309	+	0.199356i	0.00939783	+	0.00703513i
$804$	−7.22794	−	11.3764i	−0.254910	−	0.401216i
$805$	−38.3886	+	16.5501i	−1.35302	+	0.583314i
$806$	0.808372	+	2.77976i	0.0284737	+	0.0979129i
$807$	0.736561	−	0.983930i	0.0259282	−	0.0346360i
$808$	−4.35333	+	11.3996i	−0.153150	+	0.401035i
$809$	2.57023	+	8.75341i	0.0903646	+	0.307753i	0.992256	−	0.124209i	$-0.0396394\pi$
$809$	2.57023	+	8.75341i	0.0903646	+	0.307753i	−0.901891	+	0.431963i	$0.857821\pi$
$810$	−18.7875	−	7.79335i	−0.660125	−	0.273830i
$811$	7.15494	−	24.3675i	0.251244	−	0.855658i	−0.733208	−	0.680004i	$-0.761978\pi$
$811$	7.15494	−	24.3675i	0.251244	−	0.855658i	0.984452	−	0.175654i	$-0.0562039\pi$
$812$	−8.10509	+	2.97516i	−0.284433	+	0.104408i
$813$	0.124356	−	0.333412i	0.00436137	−	0.0116933i
$814$	0.288905	+	0.186730i	0.0101261	+	0.00654489i
$815$	3.82783	−	6.48221i	0.134083	−	0.227062i
$816$	6.42094	−	9.76651i	0.224778	−	0.341896i
$817$	−27.5329	−	36.7797i	−0.963255	−	1.28676i
$818$	8.38209	+	15.4459i	0.293073	+	0.540054i
$819$	−16.6425	−	19.2065i	−0.581537	−	0.671130i
$820$	5.38225	+	21.3647i	0.187956	+	0.746088i
$821$	6.05548	−	3.89162i	0.211338	−	0.135818i	−0.430690	−	0.902500i	$-0.641730\pi$
$821$	6.05548	−	3.89162i	0.211338	−	0.135818i	0.642028	+	0.766681i	$0.278093\pi$
$822$	−1.57848	−	1.58670i	−0.0550558	−	0.0553426i
$823$	1.42877	+	19.9769i	0.0498039	+	0.696350i	0.959613	+	0.281323i	$0.0907732\pi$
$823$	1.42877	+	19.9769i	0.0498039	+	0.696350i	−0.909809	+	0.415027i	$0.863772\pi$
$824$	−14.0337	+	30.1063i	−0.488888	+	1.04880i
$825$	−0.0718557	−	0.155622i	−0.00250170	−	0.00541807i
$826$	−5.44593	−	12.0074i	−0.189488	−	0.417790i
$827$	4.38288	+	4.38288i	0.152408	+	0.152408i	0.779192	−	0.626785i	$-0.215629\pi$
$827$	4.38288	+	4.38288i	0.152408	+	0.152408i	−0.626785	+	0.779192i	$0.715629\pi$
$828$	12.5948	+	22.6834i	0.437701	+	0.788301i
$829$		−	8.37513i		−	0.290880i	−0.989367	−	0.145440i	$-0.953540\pi$
$829$		−	8.37513i		−	0.290880i	0.989367	−	0.145440i	$-0.0464598\pi$
$830$	−16.0752	+	48.2157i	−0.557980	+	1.67359i
$831$	−9.42528	−	4.30438i	−0.326959	−	0.149317i
$832$	17.9578	+	7.01869i	0.622575	+	0.243329i
$833$	−43.9837	+	3.14578i	−1.52395	+	0.108995i
$834$	−0.00496328	+	1.91035i	−0.000171864	+	0.0661500i
$835$	7.39550	−	5.15766i	0.255932	−	0.178488i
$836$	0.600306	+	0.390216i	0.0207620	+	0.0134959i
$837$	2.62512	+	0.187752i	0.0907374	+	0.00648966i
$838$	−11.9650	+	6.49307i	−0.413323	+	0.224299i
$839$	0.718504	−	4.99730i	0.0248055	−	0.172526i	−0.973653	−	0.228036i	$-0.926769\pi$
$839$	0.718504	−	4.99730i	0.0248055	−	0.172526i	0.998458	+	0.0555103i	$0.0176786\pi$
$840$	9.06879	+	9.85278i	0.312903	+	0.339953i
$841$	23.3647	+	15.0156i	0.805679	+	0.517778i
$842$	19.8876	−	4.27221i	0.685373	−	0.147230i
$843$	3.47319	+	1.29543i	0.119623	+	0.0446171i
$844$	−9.08607	+	19.6252i	−0.312755	+	0.675527i
$845$	8.23428	+	13.8125i	0.283268	+	0.475163i
$846$	−33.2067	−	15.2694i	−1.14167	−	0.524972i
$847$	−37.6220	−	20.5432i	−1.29271	−	0.705872i
$848$	3.71999	−	45.3796i	0.127745	−	1.55834i
$849$	7.24182	−	1.04122i	0.248539	−	0.0357345i
$850$	−35.6221	+	13.3501i	−1.22183	+	0.457905i
$851$	−7.88324	−	16.7165i	−0.270234	−	0.573034i
$852$	−2.41624	+	10.8359i	−0.0827791	+	0.371232i
$853$	26.7156	−	35.6879i	0.914726	−	1.22193i	−0.0599252	−	0.998203i	$-0.519086\pi$
$853$	26.7156	−	35.6879i	0.914726	−	1.22193i	0.974652	−	0.223728i	$-0.0718229\pi$
$854$	8.88363	−	60.6677i	0.303992	−	2.07601i
$855$	30.7094	+	15.2921i	1.05024	+	0.522977i
$856$	6.11128	−	0.830105i	0.208879	−	0.0283724i
$857$	−33.4154	+	18.2462i	−1.14145	+	0.623278i	−0.934813	−	0.355140i	$-0.884433\pi$
$857$	−33.4154	+	18.2462i	−1.14145	+	0.623278i	−0.206635	+	0.978418i	$0.566251\pi$
$858$	−0.116570	+	0.00803288i	−0.00397963	+	0.000274238i
$859$	−1.08774	−	2.38183i	−0.0371133	−	0.0812669i	0.890167	−	0.455634i	$-0.150587\pi$
$859$	−1.08774	−	2.38183i	−0.0371133	−	0.0812669i	−0.927281	+	0.374367i	$0.877860\pi$
$860$	35.0725	+	9.06808i	1.19596	+	0.309219i
$861$	8.77516	+	5.63945i	0.299057	+	0.192192i
$862$	14.5660	−	19.3529i	0.496121	−	0.659163i
$863$	13.6889	+	18.2862i	0.465975	+	0.622470i	0.970550	−	0.240898i	$-0.0774419\pi$
$863$	13.6889	+	18.2862i	0.465975	+	0.622470i	−0.504576	+	0.863368i	$0.668351\pi$
$864$	11.6498	−	13.0969i	0.396335	−	0.445565i
$865$	36.1424	+	38.6578i	1.22888	+	1.31440i
$866$	16.3706	+	18.9921i	0.556295	+	0.645379i
$867$	6.33861	+	1.37888i	0.215271	+	0.0468292i
$868$	5.79543	+	3.20375i	0.196710	+	0.108742i
$869$	−0.0263103	−	0.0227980i	−0.000892516	−	0.000773369i
$870$	−0.338674	+	1.87164i	−0.0114821	+	0.0634545i
$871$	27.2015	+	12.4225i	0.921687	+	0.420920i
$872$	−12.6699	+	2.65291i	−0.429056	+	0.0898388i
$873$	0.767766	+	0.767766i	0.0259849	+	0.0259849i
$874$	−16.3175	−	34.8357i	−0.551947	−	1.17833i
$875$	−4.92976	−	43.3042i	−0.166656	−	1.46395i
$876$	−4.34624	+	3.72668i	−0.146846	+	0.125913i
$877$	6.03747	+	16.1871i	0.203871	+	0.546599i	0.998140	−	0.0609676i	$-0.0194186\pi$
$877$	6.03747	+	16.1871i	0.203871	+	0.546599i	−0.794269	+	0.607566i	$0.792146\pi$
$878$	6.60792	−	30.0006i	0.223006	−	1.01247i
$879$	8.62041	−	9.94848i	0.290759	−	0.335554i
$880$	−0.561793	+	0.0556816i	−0.0189380	+	0.00187703i
$881$	19.4133	−	12.4762i	0.654051	−	0.420333i	−0.171094	−	0.985255i	$-0.554730\pi$
$881$	19.4133	−	12.4762i	0.654051	−	0.420333i	0.825144	+	0.564922i	$0.191094\pi$
$882$	−31.2693	−	2.31810i	−1.05289	−	0.0780544i
$883$	−8.96479	−	0.641174i	−0.301689	−	0.0215772i	−0.0803259	−	0.996769i	$-0.525596\pi$
$883$	−8.96479	−	0.641174i	−0.301689	−	0.0215772i	−0.221363	+	0.975191i	$0.571051\pi$
$884$	−0.134747	+	25.9316i	−0.00453203	+	0.872176i
$885$	−2.88856	−	0.304464i	−0.0970979	−	0.0102344i
$886$	−40.4856	+	5.71363i	−1.36014	+	0.191953i
$887$	−3.72140	−	17.1070i	−0.124952	−	0.574396i	−0.996464	−	0.0840215i	$-0.973224\pi$
$887$	−3.72140	−	17.1070i	−0.124952	−	0.574396i	0.871512	−	0.490375i	$-0.163140\pi$
$888$	−4.21879	+	4.15353i	−0.141573	+	0.139383i
$889$	67.9743	−	31.0428i	2.27978	−	1.04114i
$890$	−9.58590	+	11.8829i	−0.321320	+	0.398315i
$891$	0.114377	−	0.389531i	0.00383176	−	0.0130498i
$892$	26.9738	−	19.9745i	0.903150	−	0.668795i
$893$	47.5610	+	25.9703i	1.59157	+	0.869063i
$894$	−2.31993	+	15.8431i	−0.0775900	+	0.529874i
$895$	−23.6652	−	16.3581i	−0.791041	−	0.546790i
$896$	40.4448	−	17.5888i	1.35117	−	0.587600i
$897$	5.54639	+	2.94087i	0.185189	+	0.0981929i
$898$	33.0842	+	18.1771i	1.10403	+	0.606578i
$899$	0.133858	+	0.931001i	0.00446441	+	0.0310506i
$900$	−26.4377	+	5.72271i	−0.881256	+	0.190757i
$901$	58.7584	−	17.2530i	1.95752	−	0.574781i
$902$	−0.412428	+	0.152608i	−0.0137323	+	0.00508130i
$903$	15.0530	−	8.21957i	0.500933	−	0.273530i
$904$	−17.8910	−	2.71483i	−0.595046	−	0.0902940i
$905$	28.7749	+	9.51065i	0.956512	+	0.316145i
$906$	−0.562307	−	0.363440i	−0.0186814	−	0.0120745i
$907$	−5.17838	−	23.8046i	−0.171945	−	0.790420i	−0.979631	−	0.200807i	$-0.935644\pi$
$907$	−5.17838	−	23.8046i	−0.171945	−	0.790420i	0.807686	−	0.589614i	$-0.200720\pi$
$908$	25.6147	+	9.70570i	0.850054	+	0.322095i
$909$	−11.5512	−	1.66082i	−0.383130	−	0.0550858i
$910$	−28.7834	−	7.36229i	−0.954161	−	0.244058i
$911$	−15.3992	+	13.3435i	−0.510197	+	0.442089i	−0.871525	−	0.490350i	$-0.836869\pi$
$911$	−15.3992	+	13.3435i	−0.510197	+	0.442089i	0.361328	+	0.932439i	$0.382323\pi$
$912$	−8.80330	+	8.62220i	−0.291506	+	0.285510i
$913$	−0.991265	−	0.215637i	−0.0328061	−	0.00713653i
$914$	−0.140685	+	54.1493i	−0.00465346	+	1.79110i
$915$	−10.5352	−	8.45362i	−0.348282	−	0.279468i
$916$	3.95929	−	4.52158i	0.130819	−	0.149397i
$917$	−21.4699	−	57.5631i	−0.709000	−	1.90090i
$918$	22.0674	+	8.29608i	0.728332	+	0.273811i
$919$	−31.7321			−1.04675			−0.523373	−	0.852104i	$-0.675327\pi$
$919$	−31.7321			−1.04675			−0.523373	+	0.852104i	$0.675327\pi$
$920$	27.2115	+	13.3990i	0.897138	+	0.441751i
$921$	−5.07766			−0.167314
$922$	−36.7396	−	13.8120i	−1.20995	−	0.454874i
$923$	−8.60784	−	23.0785i	−0.283331	−	0.759639i
$924$	−0.176079	+	0.201085i	−0.00579258	+	0.00661522i
$925$	19.0611	−	2.82172i	0.626727	−	0.0927777i
$926$	−0.00896226	+	3.44954i	−0.000294518	+	0.113359i
$927$	−31.0410	−	6.75256i	−1.01952	−	0.221783i
$928$	5.45868	+	3.07338i	0.179190	+	0.100889i
$929$	16.5302	−	14.3235i	0.542337	−	0.469937i	−0.340086	−	0.940394i	$-0.610456\pi$
$929$	16.5302	−	14.3235i	0.542337	−	0.469937i	0.882423	+	0.470457i	$0.155911\pi$
$930$	1.25499	−	0.743747i	0.0411527	−	0.0243884i
$931$	46.0155	+	6.61603i	1.50810	+	0.216832i
$932$	−48.2714	−	18.2906i	−1.58118	−	0.599128i
$933$	0.987459	+	4.53928i	0.0323280	+	0.148609i
$934$	−1.55129	−	1.00266i	−0.0507598	−	0.0328080i
$935$	−0.341289	−	0.678274i	−0.0111614	−	0.0221819i
$936$	−2.76636	+	18.2306i	−0.0904214	+	0.595886i
$937$	0.528230	−	0.288435i	0.0172565	−	0.00942278i	−0.470598	−	0.882348i	$-0.655962\pi$
$937$	0.528230	−	0.288435i	0.0172565	−	0.00942278i	0.487854	+	0.872925i	$0.337780\pi$
$938$	64.1528	−	23.7381i	2.09466	−	0.775076i
$939$	−12.9056	+	3.78943i	−0.421159	+	0.123663i
$940$	−42.0723	+	7.45556i	−1.37225	+	0.243173i
$941$	4.44332	+	30.9039i	0.144848	+	1.00744i	0.924488	+	0.381212i	$0.124493\pi$
$941$	4.44332	+	30.9039i	0.144848	+	1.00744i	−0.779640	+	0.626228i	$0.784598\pi$
$942$	6.36354	+	3.49625i	0.207335	+	0.113914i
$943$	23.1468	+	4.73887i	0.753764	+	0.154319i
$944$	−4.06419	+	8.66002i	−0.132278	+	0.281860i
$945$	−15.3582	+	22.2186i	−0.499601	+	0.722773i
$946$	−0.104761	+	0.715428i	−0.00340607	+	0.0232606i
$947$	−40.9695	−	22.3710i	−1.33133	−	0.726961i	−0.353317	−	0.935504i	$-0.614946\pi$
$947$	−40.9695	−	22.3710i	−1.33133	−	0.726961i	−0.978013	+	0.208543i	$0.933128\pi$
$948$	0.481505	−	0.356561i	0.0156386	−	0.0115806i
$949$	3.57864	−	12.1877i	0.116167	−	0.395630i
$950$	39.6884	−	5.76995i	1.28766	−	0.187202i
$951$	11.2004	−	5.11507i	0.363199	−	0.165867i
$952$	41.6163	+	42.2701i	1.34879	+	1.36998i
$953$	2.59082	+	11.9098i	0.0839250	+	0.385797i	0.999880	−	0.0154837i	$-0.00492883\pi$
$953$	2.59082	+	11.9098i	0.0839250	+	0.385797i	−0.915955	+	0.401281i	$0.868565\pi$
$954$	43.1175	−	6.08507i	1.39598	−	0.197011i
$955$	−5.12373	+	4.14661i	−0.165800	+	0.134181i
$956$	0.281325	−	54.1401i	0.00909870	−	1.75102i
$957$	−0.0378673	−	0.00270832i	−0.00122408	−	8.75476e-5i
$958$	−54.2499	−	4.02172i	−1.75273	−	0.129936i
$959$	9.55554	−	6.14097i	0.308564	−	0.198302i
$960$	1.16895	−	9.64544i	0.0377278	−	0.311305i
$961$	−19.8283	+	22.8830i	−0.639621	+	0.738163i
$962$	2.82541	−	12.8276i	0.0910947	−	0.413580i
$963$	2.06123	+	5.52637i	0.0664222	+	0.178085i
$964$	−15.7874	+	13.5369i	−0.508477	+	0.435993i
$965$	−1.66058	+	0.0627734i	−0.0534560	+	0.00202075i
$966$	13.7389	−	4.17869i	0.442041	−	0.134447i
$967$	−14.4387	−	14.4387i	−0.464318	−	0.464318i	0.435750	−	0.900068i	$-0.356483\pi$
$967$	−14.4387	−	14.4387i	−0.464318	−	0.464318i	−0.900068	+	0.435750i	$0.856483\pi$
$968$	6.37401	+	30.4413i	0.204869	+	0.978419i
$969$	−15.0755	−	6.88477i	−0.484296	−	0.221171i
$970$	1.24905	+	0.226017i	0.0401047	+	0.00725697i
$971$	−9.05502	−	7.84622i	−0.290589	−	0.251797i	0.497350	−	0.867550i	$-0.334307\pi$
$971$	−9.05502	−	7.84622i	−0.290589	−	0.251797i	−0.787939	+	0.615753i	$0.788852\pi$
$972$	22.3859	+	12.3751i	0.718028	+	0.396930i
$973$	−9.47365	−	2.06087i	−0.303711	−	0.0660684i
$974$	−5.21790	−	6.05348i	−0.167192	−	0.193966i
$975$	−4.60875	+	4.64733i	−0.147598	+	0.148834i
$976$	−37.6732	+	23.6615i	−1.20589	+	0.757387i
$977$	−8.55845	−	11.4327i	−0.273809	−	0.365766i	0.642467	−	0.766313i	$-0.277911\pi$
$977$	−8.55845	−	11.4327i	−0.273809	−	0.365766i	−0.916276	+	0.400547i	$0.868820\pi$
$978$	−1.55509	+	2.06615i	−0.0497263	+	0.0660681i
$979$	−0.256357	−	0.164750i	−0.00819319	−	0.00526544i
$980$	−31.5825	+	18.6061i	−1.00887	+	0.594351i
$981$	−5.14273	−	11.2610i	−0.164195	−	0.359536i
$982$	−5.02980	+	0.346606i	−0.160507	+	0.0110606i
$983$	−5.17644	+	2.82655i	−0.165103	+	0.0901530i	−0.559676	−	0.828712i	$-0.689074\pi$
$983$	−5.17644	+	2.82655i	−0.165103	+	0.0901530i	0.394573	+	0.918865i	$0.370893\pi$
$984$	−1.01867	−	7.49949i	−0.0324739	−	0.239075i
$985$	16.6025	+	49.5379i	0.529001	+	1.57841i
$986$	−1.22073	+	8.33655i	−0.0388760	+	0.265490i
$987$	−12.1229	+	16.1943i	−0.385877	+	0.515472i
$988$	5.95006	−	26.6837i	0.189297	−	0.848921i
$989$	25.0781	−	29.6689i	0.797438	−	0.943418i
$990$	−0.170240	−	0.512367i	−0.00541058	−	0.0162841i
$991$	24.9672	−	3.58974i	0.793108	−	0.114032i	0.266160	−	0.963929i	$-0.414245\pi$
$991$	24.9672	−	3.58974i	0.793108	−	0.114032i	0.526949	+	0.849897i	$0.323336\pi$
$992$	−0.960232	−	4.70773i	−0.0304874	−	0.149471i
$993$	−12.5392	−	6.84691i	−0.397919	−	0.217280i
$994$	−51.1910	−	23.5391i	−1.62368	−	0.746615i
$995$	17.7483	−	10.5806i	0.562659	−	0.335428i
$996$	7.33515	−	15.8434i	0.232423	−	0.502016i
$997$	49.9489	+	18.6300i	1.58190	+	0.590017i	0.978286	−	0.207261i	$-0.0664551\pi$
$997$	49.9489	+	18.6300i	1.58190	+	0.590017i	0.603612	+	0.797279i	$0.293728\pi$
$998$	28.1768	−	6.05286i	0.891920	−	0.191600i
$999$	−10.0457	−	6.45600i	−0.317833	−	0.204259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.3.8	✓	1360
4.3	odd	2	inner	460.2.w.a.3.21	yes	1360
5.2	odd	4	inner	460.2.w.a.187.42	yes	1360
20.7	even	4	inner	460.2.w.a.187.55	yes	1360
23.8	even	11	inner	460.2.w.a.123.55	yes	1360
92.31	odd	22	inner	460.2.w.a.123.42	yes	1360
115.77	odd	44	inner	460.2.w.a.307.21	yes	1360
460.307	even	44	inner	460.2.w.a.307.8	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.3.8	✓	1360	1.1	even	1	trivial
460.2.w.a.3.21	yes	1360	4.3	odd	2	inner
460.2.w.a.123.42	yes	1360	92.31	odd	22	inner
460.2.w.a.123.55	yes	1360	23.8	even	11	inner
460.2.w.a.187.42	yes	1360	5.2	odd	4	inner
460.2.w.a.187.55	yes	1360	20.7	even	4	inner
460.2.w.a.307.8	yes	1360	460.307	even	44	inner
460.2.w.a.307.21	yes	1360	115.77	odd	44	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32376 - 0.497658i) q^{2} +(0.189809 + 0.508896i) q^{3} +(1.50467 + 1.31756i) q^{4} +(0.243658 + 2.22275i) q^{5} +(0.00199564 - 0.768116i) q^{6} +(3.80918 + 0.828636i) q^{7} +(-1.33613 - 2.49294i) q^{8} +(2.04430 - 1.77140i) q^{9} +O(q^{10})\)	\(q+(-1.32376 - 0.497658i) q^{2} +(0.189809 + 0.508896i) q^{3} +(1.50467 + 1.31756i) q^{4} +(0.243658 + 2.22275i) q^{5} +(0.00199564 - 0.768116i) q^{6} +(3.80918 + 0.828636i) q^{7} +(-1.33613 - 2.49294i) q^{8} +(2.04430 - 1.77140i) q^{9} +(0.783626 - 3.06365i) q^{10} +(0.0624757 + 0.00898264i) q^{11} +(-0.384901 + 1.01581i) q^{12} +(-0.512301 - 2.35501i) q^{13} +(-4.63005 - 2.99258i) q^{14} +(-1.08490 + 0.545894i) q^{15} +(0.528083 + 3.96499i) q^{16} +(-4.72182 + 2.57831i) q^{17} +(-3.58771 + 1.32754i) q^{18} +(5.44205 - 1.59793i) q^{19} +(-2.56198 + 3.66555i) q^{20} +(0.301325 + 2.09576i) q^{21} +(-0.0782324 - 0.0429824i) q^{22} +(2.34983 + 4.18071i) q^{23} +(1.01504 - 1.15313i) q^{24} +(-4.88126 + 1.08318i) q^{25} +(-0.493826 + 3.37241i) q^{26} +(2.71960 + 1.48501i) q^{27} +(4.63979 + 6.26564i) q^{28} +(-0.311991 + 1.06254i) q^{29} +(1.70782 - 0.182722i) q^{30} +(0.772599 - 0.352834i) q^{31} +(1.27415 - 5.51149i) q^{32} +(0.00728718 + 0.0334986i) q^{33} +(7.53366 - 1.06321i) q^{34} +(-0.913717 + 8.66876i) q^{35} +(5.40992 + 0.0281112i) q^{36} +(-3.84395 - 0.274925i) q^{37} +(-7.99918 - 0.593005i) q^{38} +(1.10122 - 0.707709i) q^{39} +(5.21563 - 3.57731i) q^{40} +(3.22621 - 3.72324i) q^{41} +(0.644090 - 2.92424i) q^{42} +(-2.83078 - 7.58962i) q^{43} +(0.0821703 + 0.0958312i) q^{44} +(4.43549 + 4.11236i) q^{45} +(-1.03004 - 6.70366i) q^{46} +(6.75585 + 6.75585i) q^{47} +(-1.91753 + 1.02133i) q^{48} +(7.45577 + 3.40494i) q^{49} +(7.00067 + 0.995327i) q^{50} +(-2.20833 - 1.91353i) q^{51} +(2.33201 - 4.21850i) q^{52} +(-11.1228 - 2.41962i) q^{53} +(-2.86106 - 3.31922i) q^{54} +(-0.00474351 + 0.141057i) q^{55} +(-3.02382 - 10.6032i) q^{56} +(1.84613 + 2.46614i) q^{57} +(0.941784 - 1.25129i) q^{58} +(2.01191 + 1.29298i) q^{59} +(-2.35167 - 0.608030i) q^{60} +(4.62019 + 10.1168i) q^{61} +(-1.19832 + 0.0825772i) q^{62} +(9.25494 - 5.05358i) q^{63} +(-4.42951 + 6.66179i) q^{64} +(5.10978 - 1.71253i) q^{65} +(0.00702439 - 0.0479706i) q^{66} +(-7.43571 + 9.93294i) q^{67} +(-10.5019 - 2.34176i) q^{68} +(-1.68153 + 1.98935i) q^{69} +(5.52362 - 11.0206i) q^{70} +(10.1162 - 1.45448i) q^{71} +(-7.14744 - 2.72950i) q^{72} +(4.62577 + 2.52586i) q^{73} +(4.95165 + 2.27691i) q^{74} +(-1.47773 - 2.27846i) q^{75} +(10.2939 + 4.76585i) q^{76} +(0.230537 + 0.0859860i) q^{77} +(-1.80994 + 0.388806i) q^{78} +(-0.464003 - 0.298197i) q^{79} +(-8.68452 + 2.13990i) q^{80} +(0.915369 - 6.36653i) q^{81} +(-6.12362 + 3.32313i) q^{82} +(-16.0313 - 1.14658i) q^{83} +(-2.30789 + 3.55044i) q^{84} +(-6.88145 - 9.86721i) q^{85} +(-0.0297628 + 11.4556i) q^{86} +(-0.599943 + 0.0429088i) q^{87} +(-0.0610825 - 0.167750i) q^{88} +(-4.39167 - 2.00561i) q^{89} +(-3.82496 - 7.65113i) q^{90} -9.39515i q^{91} +(-1.97261 + 9.38663i) q^{92} +(0.326202 + 0.326202i) q^{93} +(-5.58101 - 12.3052i) q^{94} +(4.87780 + 11.7070i) q^{95} +(3.04662 - 0.397716i) q^{96} +(0.0286355 + 0.400377i) q^{97} +(-8.17514 - 8.21773i) q^{98} +(0.143631 - 0.0923059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

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