LMFDB - Embedded newform 370.2.r.f.177.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(23,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.r (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			177.2
Character	$\chi$	$=$	370.177
Dual form			370.2.r.f.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.52625 + 0.676906i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.128227 + 2.23239i) q^{5} +(1.84934 - 1.84934i) q^{6} +(-3.97392 + 1.06481i) q^{7} +1.00000i q^{8} +(3.32566 - 1.92007i) q^{9} +(-1.22724 - 1.86919i) q^{10} +1.28194i q^{11} +(-0.676906 + 2.52625i) q^{12} +(0.274007 + 0.158198i) q^{13} +(2.90911 - 2.90911i) q^{14} +(-1.83505 - 5.55277i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.512303 + 0.887335i) q^{17} +(-1.92007 + 3.32566i) q^{18} +(-2.85215 + 0.764232i) q^{19} +(1.99742 + 1.00515i) q^{20} +(9.31834 - 5.37994i) q^{21} +(-0.640968 - 1.11019i) q^{22} -9.01738i q^{23} +(-0.676906 - 2.52625i) q^{24} +(-4.96712 + 0.572505i) q^{25} -0.316396 q^{26} +(-1.55370 + 1.55370i) q^{27} +(-1.06481 + 3.97392i) q^{28} +(5.62213 - 5.62213i) q^{29} +(4.36559 + 3.89132i) q^{30} +(0.661953 + 0.661953i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.867750 - 3.23849i) q^{33} +(-0.887335 - 0.512303i) q^{34} +(-2.88663 - 8.73480i) q^{35} -3.84014i q^{36} +(5.18181 + 3.18573i) q^{37} +(2.08792 - 2.08792i) q^{38} +(-0.799296 - 0.214171i) q^{39} +(-2.23239 + 0.128227i) q^{40} +(-9.70680 - 5.60422i) q^{41} +(-5.37994 + 9.31834i) q^{42} -5.24672i q^{43} +(1.11019 + 0.640968i) q^{44} +(4.71278 + 7.17795i) q^{45} +(4.50869 + 7.80928i) q^{46} +(2.65016 + 2.65016i) q^{47} +(1.84934 + 1.84934i) q^{48} +(8.59605 - 4.96293i) q^{49} +(4.01540 - 2.97936i) q^{50} +(-1.89485 - 1.89485i) q^{51} +(0.274007 - 0.158198i) q^{52} +(-6.83608 - 1.83172i) q^{53} +(0.568694 - 2.12239i) q^{54} +(-2.86178 + 0.164379i) q^{55} +(-1.06481 - 3.97392i) q^{56} +(6.68794 - 3.86128i) q^{57} +(-2.05784 + 7.67997i) q^{58} +(-2.26214 + 8.44244i) q^{59} +(-5.72637 - 1.18718i) q^{60} +(-7.25981 + 1.94526i) q^{61} +(-0.904244 - 0.242292i) q^{62} +(-11.1714 + 11.1714i) q^{63} -1.00000 q^{64} +(-0.318025 + 0.631976i) q^{65} +(2.37074 + 2.37074i) q^{66} +(-0.374556 - 1.39786i) q^{67} +1.02461 q^{68} +(6.10392 + 22.7802i) q^{69} +(6.86729 + 6.12124i) q^{70} +(-3.61602 + 6.26312i) q^{71} +(1.92007 + 3.32566i) q^{72} +(7.58180 + 7.58180i) q^{73} +(-6.08044 - 0.168023i) q^{74} +(12.1606 - 4.80856i) q^{75} +(-0.764232 + 2.85215i) q^{76} +(-1.36502 - 5.09431i) q^{77} +(0.799296 - 0.214171i) q^{78} +(-4.64055 + 1.24343i) q^{79} +(1.86919 - 1.22724i) q^{80} +(-2.88688 + 5.00023i) q^{81} +11.2084 q^{82} +(1.52707 + 0.409176i) q^{83} -10.7599i q^{84} +(-1.91518 + 1.25744i) q^{85} +(2.62336 + 4.54379i) q^{86} +(-10.3972 + 18.0086i) q^{87} -1.28194 q^{88} +(-1.06048 - 0.284155i) q^{89} +(-7.67036 - 3.85990i) q^{90} +(-1.25733 - 0.336902i) q^{91} +(-7.80928 - 4.50869i) q^{92} +(-2.12034 - 1.22418i) q^{93} +(-3.62018 - 0.970024i) q^{94} +(-2.07179 - 6.26912i) q^{95} +(-2.52625 - 0.676906i) q^{96} -11.2088 q^{97} +(-4.96293 + 8.59605i) q^{98} +(2.46140 + 4.26328i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{3} + 16 q^{4} + 6 q^{5} + 8 q^{6} + 2 q^{7} - 12 q^{9} + 6 q^{10} - 2 q^{12} + 12 q^{13} + 8 q^{14} - 8 q^{15} - 16 q^{16} - 6 q^{17} - 24 q^{18} - 2 q^{19} + 6 q^{20} - 54 q^{21} + 12 q^{22}+ \cdots + 26 q^{99}+O(q^{100}) $ 32 * q - 10 * q^3 + 16 * q^4 + 6 * q^5 + 8 * q^6 + 2 * q^7 - 12 * q^9 + 6 * q^10 - 2 * q^12 + 12 * q^13 + 8 * q^14 - 8 * q^15 - 16 * q^16 - 6 * q^17 - 24 * q^18 - 2 * q^19 + 6 * q^20 - 54 * q^21 + 12 * q^22 - 2 * q^24 - 14 * q^25 + 20 * q^26 - 40 * q^27 + 10 * q^28 - 6 * q^29 - 8 * q^30 - 4 * q^31 - 22 * q^33 + 12 * q^34 + 24 * q^37 - 26 * q^38 + 58 * q^39 + 18 * q^41 - 2 * q^42 - 6 * q^44 - 18 * q^45 + 6 * q^46 + 18 * q^47 + 8 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 + 12 * q^52 - 20 * q^54 + 42 * q^55 + 10 * q^56 + 36 * q^57 + 30 * q^58 - 42 * q^59 - 16 * q^60 - 46 * q^61 - 10 * q^62 - 32 * q^64 - 18 * q^65 + 4 * q^66 + 46 * q^67 - 12 * q^68 + 66 * q^69 + 12 * q^70 - 12 * q^71 + 24 * q^72 + 28 * q^73 - 16 * q^74 - 20 * q^75 - 28 * q^76 + 24 * q^77 - 58 * q^78 - 38 * q^79 + 56 * q^81 - 48 * q^82 + 12 * q^83 + 8 * q^85 - 16 * q^86 - 2 * q^87 + 24 * q^88 - 18 * q^89 + 52 * q^90 + 4 * q^91 - 12 * q^92 + 36 * q^93 - 30 * q^94 + 30 * q^95 - 10 * q^96 - 12 * q^97 - 16 * q^98 + 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−2.52625	+	0.676906i	−1.45853	+	0.390812i	−0.898982	−	0.437986i	$-0.855692\pi$
$3$	−2.52625	+	0.676906i	−1.45853	+	0.390812i	−0.559549	+	0.828798i	$0.689025\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.128227	+	2.23239i	0.0573449	+	0.998354i
$5$	0.128227	+	2.23239i	0.0573449	+	0.998354i
$6$	1.84934	−	1.84934i	0.754991	−	0.754991i
$7$	−3.97392	+	1.06481i	−1.50200	+	0.402460i	−0.913770	−	0.406233i	$-0.866842\pi$
$7$	−3.97392	+	1.06481i	−1.50200	+	0.402460i	−0.588231	+	0.808693i	$0.700176\pi$
$8$			1.00000i			0.353553i
$9$	3.32566	−	1.92007i	1.10855	−	0.640023i
$10$	−1.22724	−	1.86919i	−0.388088	−	0.591090i
$11$			1.28194i			0.386518i	0.981148	+	0.193259i	$0.0619058\pi$
$11$			1.28194i			0.386518i	−0.981148	+	0.193259i	$0.938094\pi$
$12$	−0.676906	+	2.52625i	−0.195406	+	0.729265i
$13$	0.274007	+	0.158198i	0.0759960	+	0.0438763i	0.537516	−	0.843253i	$-0.319363\pi$
$13$	0.274007	+	0.158198i	0.0759960	+	0.0438763i	−0.461521	+	0.887130i	$0.652696\pi$
$14$	2.90911	−	2.90911i	0.777493	−	0.777493i
$15$	−1.83505	−	5.55277i	−0.473808	−	1.43372i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.512303	+	0.887335i	0.124252	+	0.215210i	0.921440	−	0.388520i	$-0.127014\pi$
$17$	0.512303	+	0.887335i	0.124252	+	0.215210i	−0.797188	+	0.603730i	$0.793680\pi$
$18$	−1.92007	+	3.32566i	−0.452564	+	0.783865i
$19$	−2.85215	+	0.764232i	−0.654329	+	0.175327i	−0.570685	−	0.821169i	$-0.693322\pi$
$19$	−2.85215	+	0.764232i	−0.654329	+	0.175327i	−0.0836437	+	0.996496i	$0.526656\pi$
$20$	1.99742	+	1.00515i	0.446636	+	0.224758i
$21$	9.31834	−	5.37994i	2.03343	−	1.17400i
$22$	−0.640968	−	1.11019i	−0.136655	−	0.236693i
$23$		−	9.01738i		−	1.88025i	−0.340824	−	0.940127i	$-0.610706\pi$
$23$		−	9.01738i		−	1.88025i	0.340824	−	0.940127i	$-0.389294\pi$
$24$	−0.676906	−	2.52625i	−0.138173	−	0.515668i
$25$	−4.96712	+	0.572505i	−0.993423	+	0.114501i
$26$	−0.316396			−0.0620504
$27$	−1.55370	+	1.55370i	−0.299010	+	0.299010i
$28$	−1.06481	+	3.97392i	−0.201230	+	0.751000i
$29$	5.62213	−	5.62213i	1.04400	−	1.04400i	0.0450170	−	0.998986i	$-0.485666\pi$
$29$	5.62213	−	5.62213i	1.04400	−	1.04400i	0.998986	−	0.0450170i	$-0.0143342\pi$
$30$	4.36559	+	3.89132i	0.797043	+	0.710454i
$31$	0.661953	+	0.661953i	0.118890	+	0.118890i	0.764049	−	0.645159i	$-0.223209\pi$
$31$	0.661953	+	0.661953i	0.118890	+	0.118890i	−0.645159	+	0.764049i	$0.723209\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.867750	−	3.23849i	−0.151056	−	0.563748i
$34$	−0.887335	−	0.512303i	−0.152177	−	0.0878592i
$35$	−2.88663	−	8.73480i	−0.487930	−	1.47645i
$36$		−	3.84014i		−	0.640023i
$37$	5.18181	+	3.18573i	0.851884	+	0.523731i
$37$	5.18181	+	3.18573i	0.851884	+	0.523731i
$38$	2.08792	−	2.08792i	0.338706	−	0.338706i
$39$	−0.799296	−	0.214171i	−0.127990	−	0.0342948i
$40$	−2.23239	+	0.128227i	−0.352972	+	0.0202745i
$41$	−9.70680	−	5.60422i	−1.51595	−	0.875232i	−0.999825	−	0.0187171i	$-0.994042\pi$
$41$	−9.70680	−	5.60422i	−1.51595	−	0.875232i	−0.516122	−	0.856515i	$-0.672625\pi$
$42$	−5.37994	+	9.31834i	−0.830143	+	1.43785i
$43$		−	5.24672i		−	0.800117i	−0.916490	−	0.400059i	$-0.868990\pi$
$43$		−	5.24672i		−	0.800117i	0.916490	−	0.400059i	$-0.131010\pi$
$44$	1.11019	+	0.640968i	0.167367	+	0.0966295i
$45$	4.71278	+	7.17795i	0.702539	+	1.07003i
$46$	4.50869	+	7.80928i	0.664770	+	1.15142i
$47$	2.65016	+	2.65016i	0.386565	+	0.386565i	0.873460	−	0.486895i	$-0.161871\pi$
$47$	2.65016	+	2.65016i	0.386565	+	0.386565i	−0.486895	+	0.873460i	$0.661871\pi$
$48$	1.84934	+	1.84934i	0.266930	+	0.266930i
$49$	8.59605	−	4.96293i	1.22801	−	0.708990i
$50$	4.01540	−	2.97936i	0.567863	−	0.421345i
$51$	−1.89485	−	1.89485i	−0.265332	−	0.265332i
$52$	0.274007	−	0.158198i	0.0379980	−	0.0219381i
$53$	−6.83608	−	1.83172i	−0.939008	−	0.251606i	−0.243316	−	0.969947i	$-0.578235\pi$
$53$	−6.83608	−	1.83172i	−0.939008	−	0.251606i	−0.695692	+	0.718341i	$0.744902\pi$
$54$	0.568694	−	2.12239i	0.0773894	−	0.288821i
$55$	−2.86178	+	0.164379i	−0.385882	+	0.0221648i
$56$	−1.06481	−	3.97392i	−0.142291	−	0.531037i
$57$	6.68794	−	3.86128i	0.885839	−	0.511439i
$58$	−2.05784	+	7.67997i	−0.270208	+	1.00843i
$59$	−2.26214	+	8.44244i	−0.294506	+	1.09911i	0.647103	+	0.762403i	$0.275980\pi$
$59$	−2.26214	+	8.44244i	−0.294506	+	1.09911i	−0.941609	+	0.336709i	$0.890686\pi$
$60$	−5.72637	−	1.18718i	−0.739271	−	0.153265i
$61$	−7.25981	+	1.94526i	−0.929524	+	0.249065i	−0.691652	−	0.722231i	$-0.743117\pi$
$61$	−7.25981	+	1.94526i	−0.929524	+	0.249065i	−0.237872	+	0.971296i	$0.576450\pi$
$62$	−0.904244	−	0.242292i	−0.114839	−	0.0307711i
$63$	−11.1714	+	11.1714i	−1.40746	+	1.40746i
$64$	−1.00000			−0.125000
$65$	−0.318025	+	0.631976i	−0.0394461	+	0.0783870i
$66$	2.37074	+	2.37074i	0.291818	+	0.291818i
$67$	−0.374556	−	1.39786i	−0.0457593	−	0.170776i	0.939265	−	0.343194i	$-0.111509\pi$
$67$	−0.374556	−	1.39786i	−0.0457593	−	0.170776i	−0.985024	+	0.172418i	$0.944842\pi$
$68$	1.02461			0.124252
$69$	6.10392	+	22.7802i	0.734826	+	2.74241i
$70$	6.86729	+	6.12124i	0.820799	+	0.731628i
$71$	−3.61602	+	6.26312i	−0.429142	+	0.743296i	−0.996797	−	0.0799705i	$-0.974517\pi$
$71$	−3.61602	+	6.26312i	−0.429142	+	0.743296i	0.567655	+	0.823266i	$0.307851\pi$
$72$	1.92007	+	3.32566i	0.226282	+	0.391932i
$73$	7.58180	+	7.58180i	0.887382	+	0.887382i	0.994271	−	0.106889i	$-0.0340888\pi$
$73$	7.58180	+	7.58180i	0.887382	+	0.887382i	−0.106889	+	0.994271i	$0.534089\pi$
$74$	−6.08044	−	0.168023i	−0.706837	−	0.0195323i
$75$	12.1606	−	4.80856i	1.40419	−	0.555245i
$76$	−0.764232	+	2.85215i	−0.0876635	+	0.327165i
$77$	−1.36502	−	5.09431i	−0.155558	−	0.580550i
$78$	0.799296	−	0.214171i	0.0905025	−	0.0242501i
$79$	−4.64055	+	1.24343i	−0.522103	+	0.139897i	−0.510239	−	0.860033i	$-0.670443\pi$
$79$	−4.64055	+	1.24343i	−0.522103	+	0.139897i	−0.0118639	+	0.999930i	$0.503776\pi$
$80$	1.86919	−	1.22724i	0.208982	−	0.137210i
$81$	−2.88688	+	5.00023i	−0.320765	+	0.555581i
$82$	11.2084			1.23777
$83$	1.52707	+	0.409176i	0.167617	+	0.0449129i	0.341652	−	0.939827i	$-0.389014\pi$
$83$	1.52707	+	0.409176i	0.167617	+	0.0449129i	−0.174034	+	0.984740i	$0.555680\pi$
$84$		−	10.7599i		−	1.17400i
$85$	−1.91518	+	1.25744i	−0.207731	+	0.136388i
$86$	2.62336	+	4.54379i	0.282884	+	0.489970i
$87$	−10.3972	+	18.0086i	−1.11470	+	1.93072i
$88$	−1.28194			−0.136655
$89$	−1.06048	−	0.284155i	−0.112411	−	0.0301203i	0.202175	−	0.979349i	$-0.435199\pi$
$89$	−1.06048	−	0.284155i	−0.112411	−	0.0301203i	−0.314586	+	0.949229i	$0.601866\pi$
$90$	−7.67036	−	3.85990i	−0.808527	−	0.406869i
$91$	−1.25733	−	0.336902i	−0.131804	−	0.0353169i
$92$	−7.80928	−	4.50869i	−0.814174	−	0.470064i
$93$	−2.12034	−	1.22418i	−0.219869	−	0.126941i
$94$	−3.62018	−	0.970024i	−0.373393	−	0.100050i
$95$	−2.07179	−	6.26912i	−0.212561	−	0.643198i
$96$	−2.52625	−	0.676906i	−0.257834	−	0.0690865i
$97$	−11.2088			−1.13808			−0.569039	−	0.822311i	$-0.692684\pi$
$97$	−11.2088			−1.13808			−0.569039	+	0.822311i	$0.692684\pi$
$98$	−4.96293	+	8.59605i	−0.501332	+	0.868332i
$99$	2.46140	+	4.26328i	0.247380	+	0.428475i
$100$	−1.98775	+	4.58790i	−0.198775	+	0.458790i
$101$		−	17.5901i		−	1.75028i	−0.483868	−	0.875141i	$-0.660769\pi$
$101$		−	17.5901i		−	1.75028i	0.483868	−	0.875141i	$-0.339231\pi$
$102$	2.58841	+	0.693562i	0.256291	+	0.0686729i
$103$	−11.7069			−1.15352			−0.576759	−	0.816914i	$-0.695683\pi$
$103$	−11.7069			−1.15352			−0.576759	+	0.816914i	$0.695683\pi$
$104$	−0.158198	+	0.274007i	−0.0155126	+	0.0268686i
$105$	13.2050	+	20.1123i	1.28867	+	1.96276i
$106$	6.83608	−	1.83172i	0.663979	−	0.177913i
$107$	8.15032	−	2.18387i	0.787921	−	0.211123i	0.157647	−	0.987496i	$-0.449609\pi$
$107$	8.15032	−	2.18387i	0.787921	−	0.211123i	0.630274	+	0.776373i	$0.282943\pi$
$108$	0.568694	+	2.12239i	0.0547226	+	0.204227i
$109$	0.477608	−	1.78246i	0.0457466	−	0.170729i	−0.939273	−	0.343171i	$-0.888499\pi$
$109$	0.477608	−	1.78246i	0.0457466	−	0.170729i	0.985020	+	0.172442i	$0.0551658\pi$
$110$	2.39618	−	1.57325i	0.228467	−	0.150003i
$111$	−15.2470	−	4.54036i	−1.44718	−	0.430952i
$112$	2.90911	+	2.90911i	0.274885	+	0.274885i
$113$	−7.55141	−	13.0794i	−0.710377	−	1.23041i	−0.964716	−	0.263294i	$-0.915191\pi$
$113$	−7.55141	−	13.0794i	−0.710377	−	1.23041i	0.254339	−	0.967115i	$-0.418142\pi$
$114$	−3.86128	+	6.68794i	−0.361642	+	0.626383i
$115$	20.1303	−	1.15627i	1.87716	−	0.107823i
$116$	−2.05784	−	7.67997i	−0.191066	−	0.713067i
$117$	1.21501			0.112327
$118$	−2.26214	−	8.44244i	−0.208247	−	0.777189i
$119$	−2.98069	−	2.98069i	−0.273240	−	0.273240i
$120$	5.55277	−	1.83505i	0.506896	−	0.167517i
$121$	9.35664			0.850604
$122$	5.31455	−	5.31455i	0.481157	−	0.481157i
$123$	28.3153	+	7.58707i	2.55311	+	0.684103i
$124$	0.904244	−	0.242292i	0.0812035	−	0.0217584i
$125$	−1.91497	−	11.0151i	−0.171280	−	0.985222i
$126$	4.08901	−	15.2604i	0.364278	−	1.35950i
$127$	−2.85517	+	10.6556i	−0.253355	+	0.945536i	0.715642	+	0.698467i	$0.246134\pi$
$127$	−2.85517	+	10.6556i	−0.253355	+	0.945536i	−0.968998	+	0.247069i	$0.920533\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	3.55154	+	13.2545i	0.312695	+	1.16700i
$130$	−0.0405706	−	0.706320i	−0.00355828	−	0.0619483i
$131$	5.08374	−	18.9728i	0.444168	−	1.65766i	−0.273956	−	0.961742i	$-0.588332\pi$
$131$	5.08374	−	18.9728i	0.444168	−	1.65766i	0.718124	−	0.695915i	$-0.245001\pi$
$132$	−3.23849	−	0.867750i	−0.281874	−	0.0755280i
$133$	10.5205	−	6.07400i	0.912241	−	0.526682i
$134$	1.02331	+	1.02331i	0.0884003	+	0.0884003i
$135$	−3.66769	−	3.26923i	−0.315664	−	0.281371i
$136$	−0.887335	+	0.512303i	−0.0760883	+	0.0439296i
$137$	−4.87205	−	4.87205i	−0.416247	−	0.416247i	0.467661	−	0.883908i	$-0.345097\pi$
$137$	−4.87205	−	4.87205i	−0.416247	−	0.416247i	−0.883908	+	0.467661i	$0.845097\pi$
$138$	−16.6762	−	16.6762i	−1.41957	−	1.41957i
$139$	−2.69637	−	4.67024i	−0.228703	−	0.396125i	0.728721	−	0.684811i	$-0.240115\pi$
$139$	−2.69637	−	4.67024i	−0.228703	−	0.396125i	−0.957424	+	0.288686i	$0.906782\pi$
$140$	−9.00787	−	1.86750i	−0.761304	−	0.157833i
$141$	−8.48886	−	4.90105i	−0.714891	−	0.412742i
$142$		−	7.23203i		−	0.606899i
$143$	−0.202800	+	0.351260i	−0.0169590	+	0.0293738i
$144$	−3.32566	−	1.92007i	−0.277138	−	0.160006i
$145$	13.2717	+	11.8299i	1.10215	+	0.982417i
$146$	−10.3569	−	2.77513i	−0.857146	−	0.229671i
$147$	−18.3563	+	18.3563i	−1.51400	+	1.51400i
$148$	5.34983	−	2.89471i	0.439753	−	0.237944i
$149$			19.5916i			1.60500i	0.596650	+	0.802501i	$0.296498\pi$
$149$			19.5916i			1.60500i	−0.596650	+	0.802501i	$0.703502\pi$
$150$	−8.12714	+	10.2447i	−0.663578	+	0.836473i
$151$	−7.97563	−	4.60473i	−0.649048	−	0.374728i	0.139044	−	0.990286i	$-0.455597\pi$
$151$	−7.97563	−	4.60473i	−0.649048	−	0.374728i	−0.788091	+	0.615558i	$0.788931\pi$
$152$	−0.764232	−	2.85215i	−0.0619874	−	0.231340i
$153$	3.40749	+	1.96731i	0.275479	+	0.159048i
$154$	3.72929	+	3.72929i	0.300515	+	0.300515i
$155$	−1.39286	+	1.56262i	−0.111877	+	0.125512i
$156$	−0.585125	+	0.585125i	−0.0468475	+	0.0468475i
$157$	−6.27626	+	23.4233i	−0.500900	+	1.86939i	−0.00680694	+	0.999977i	$0.502167\pi$
$157$	−6.27626	+	23.4233i	−0.500900	+	1.86939i	−0.494093	+	0.869409i	$0.664500\pi$
$158$	3.39712	−	3.39712i	0.270260	−	0.270260i
$159$	18.5095			1.46790
$160$	−1.00515	+	1.99742i	−0.0794638	+	0.157910i
$161$	9.60179	+	35.8344i	0.756727	+	2.82414i
$162$		−	5.77376i		−	0.453630i
$163$	−5.99752	−	10.3880i	−0.469762	−	0.813652i	0.529640	−	0.848222i	$-0.322327\pi$
$163$	−5.99752	−	10.3880i	−0.469762	−	0.813652i	−0.999402	+	0.0345707i	$0.988994\pi$
$164$	−9.70680	+	5.60422i	−0.757973	+	0.437616i
$165$	7.11829	−	2.35242i	0.554158	−	0.183135i
$166$	−1.52707	+	0.409176i	−0.118523	+	0.0317582i
$167$	7.55214	−	13.0807i	0.584402	−	1.01221i	−0.410548	−	0.911839i	$-0.634662\pi$
$167$	7.55214	−	13.0807i	0.584402	−	1.01221i	0.994950	−	0.100375i	$-0.0320043\pi$
$168$	5.37994	+	9.31834i	0.415072	+	0.718925i
$169$	−6.44995	−	11.1716i	−0.496150	−	0.859357i
$170$	1.02988	−	2.04657i	0.0789881	−	0.156964i
$171$	−8.01790	+	8.01790i	−0.613144	+	0.613144i
$172$	−4.54379	−	2.62336i	−0.346461	−	0.200029i
$173$	1.48869	−	5.55587i	0.113183	−	0.422405i	−0.885961	−	0.463759i	$-0.846500\pi$
$173$	1.48869	−	5.55587i	0.113183	−	0.422405i	0.999145	+	0.0413538i	$0.0131671\pi$
$174$		−	20.7945i		−	1.57643i
$175$	19.1293	−	7.56412i	1.44604	−	0.571794i
$176$	1.11019	−	0.640968i	0.0836836	−	0.0483148i
$177$		−	22.8590i		−	1.71818i
$178$	1.06048	−	0.284155i	0.0794863	−	0.0212983i
$179$	12.3375	−	12.3375i	0.922149	−	0.922149i	−0.0750320	−	0.997181i	$-0.523906\pi$
$179$	12.3375	−	12.3375i	0.922149	−	0.922149i	0.997181	+	0.0750320i	$0.0239059\pi$
$180$	8.57268	−	0.492409i	0.638969	−	0.0367020i
$181$	3.76005	−	6.51260i	0.279483	−	0.484078i	−0.691774	−	0.722114i	$-0.743170\pi$
$181$	3.76005	−	6.51260i	0.279483	−	0.484078i	0.971256	+	0.238036i	$0.0765038\pi$
$182$	1.25733	−	0.336902i	0.0931998	−	0.0249728i
$183$	17.0233	−	9.82843i	1.25840	−	0.726538i
$184$	9.01738			0.664770
$185$	−6.44735	+	11.9763i	−0.474018	+	0.880515i
$186$	2.44835			0.179522
$187$	−1.13751	+	0.656739i	−0.0831826	+	0.0480255i
$188$	3.62018	−	0.970024i	0.264029	−	0.0707463i
$189$	4.51989	−	7.82867i	0.328773	−	0.569452i
$190$	4.92878	+	4.39332i	0.357571	+	0.318725i
$191$	−15.3950	+	15.3950i	−1.11394	+	1.11394i	−0.121331	+	0.992612i	$0.538716\pi$
$191$	−15.3950	+	15.3950i	−1.11394	+	1.11394i	−0.992612	+	0.121331i	$0.961284\pi$
$192$	2.52625	−	0.676906i	0.182316	−	0.0488515i
$193$			11.5000i			0.827787i	0.910325	+	0.413894i	$0.135831\pi$
$193$			11.5000i			0.827787i	−0.910325	+	0.413894i	$0.864169\pi$
$194$	9.70707	−	5.60438i	0.696927	−	0.402371i
$195$	0.375621	−	1.81180i	0.0268988	−	0.129746i
$196$		−	9.92586i		−	0.708990i
$197$	1.89451	−	7.07040i	0.134978	−	0.503745i	−0.865020	−	0.501738i	$-0.832694\pi$
$197$	1.89451	−	7.07040i	0.134978	−	0.503745i	0.999998	−	0.00200770i	$-0.000639070\pi$
$198$	−4.26328	−	2.46140i	−0.302978	−	0.174924i
$199$	−12.1172	+	12.1172i	−0.858964	+	0.858964i	−0.991216	−	0.132252i	$-0.957779\pi$
$199$	−12.1172	+	12.1172i	−0.858964	+	0.858964i	0.132252	+	0.991216i	$0.457779\pi$
$200$	−0.572505	−	4.96712i	−0.0404822	−	0.351228i
$201$	1.89245	+	3.27781i	0.133483	+	0.231199i
$202$	8.79506	+	15.2335i	0.618818	+	1.07182i
$203$	−16.3554	+	28.3284i	−1.14792	+	1.98826i
$204$	−2.58841	+	0.693562i	−0.181225	+	0.0485591i
$205$	11.2661	−	22.3879i	0.786860	−	1.56364i
$206$	10.1385	−	5.85347i	0.706383	−	0.407830i
$207$	−17.3140	−	29.9887i	−1.20341	−	2.08436i
$208$		−	0.316396i		−	0.0219381i
$209$	−0.979697	−	3.65628i	−0.0677670	−	0.252910i
$210$	−21.4920	−	10.8153i	−1.48309	−	0.746324i
$211$	−13.3691			−0.920364			−0.460182	−	0.887825i	$-0.652216\pi$
$211$	−13.3691			−0.920364			−0.460182	+	0.887825i	$0.652216\pi$
$212$	−5.00436	+	5.00436i	−0.343701	+	0.343701i
$213$	4.89541	−	18.2699i	0.335428	−	1.25183i
$214$	−5.96645	+	5.96645i	−0.407858	+	0.407858i
$215$	11.7127	−	0.672771i	0.798800	−	0.0458826i
$216$	−1.55370	−	1.55370i	−0.105716	−	0.105716i
$217$	−3.33540	−	1.92569i	−0.226422	−	0.130725i
$218$	0.477608	+	1.78246i	0.0323477	+	0.120723i
$219$	−24.2857	−	14.0213i	−1.64107	−	0.947474i
$220$	−1.28853	+	2.56056i	−0.0868729	+	0.172633i
$221$			0.324182i			0.0218068i
$222$	15.4744	−	3.69142i	1.03858	−	0.247752i
$223$	−1.68532	+	1.68532i	−0.112857	+	0.112857i	−0.761280	−	0.648423i	$-0.775429\pi$
$223$	−1.68532	+	1.68532i	−0.112857	+	0.112857i	0.648423	+	0.761280i	$0.275429\pi$
$224$	−3.97392	−	1.06481i	−0.265519	−	0.0711455i
$225$	−15.4197	+	11.4412i	−1.02798	+	0.762744i
$226$	13.0794	+	7.55141i	0.870030	+	0.502312i
$227$	8.05545	−	13.9524i	0.534659	−	0.926057i	−0.464521	−	0.885562i	$-0.653773\pi$
$227$	8.05545	−	13.9524i	0.534659	−	0.926057i	0.999180	−	0.0404943i	$-0.0128933\pi$
$228$		−	7.72257i		−	0.511439i
$229$	−15.8140	−	9.13024i	−1.04502	−	0.603343i	−0.123770	−	0.992311i	$-0.539498\pi$
$229$	−15.8140	−	9.13024i	−1.04502	−	0.603343i	−0.921251	+	0.388968i	$0.872832\pi$
$230$	−16.8552	+	11.0665i	−1.11140	+	0.729704i
$231$	6.89674	+	11.9455i	0.453772	+	0.785957i
$232$	5.62213	+	5.62213i	0.369111	+	0.369111i
$233$	−16.8682	−	16.8682i	−1.10507	−	1.10507i	−0.993788	−	0.111286i	$-0.964503\pi$
$233$	−16.8682	−	16.8682i	−1.10507	−	1.10507i	−0.111286	−	0.993788i	$-0.535497\pi$
$234$	−1.05223	+	0.607503i	−0.0687861	+	0.0397137i
$235$	−5.57635	+	6.25600i	−0.363761	+	0.408096i
$236$	6.18029	+	6.18029i	0.402303	+	0.402303i
$237$	10.8815	−	6.28244i	0.706830	−	0.408088i
$238$	4.07170	+	1.09101i	0.263929	+	0.0707196i
$239$	0.850999	−	3.17597i	0.0550465	−	0.205436i	−0.932925	−	0.360070i	$-0.882753\pi$
$239$	0.850999	−	3.17597i	0.0550465	−	0.205436i	0.987972	+	0.154633i	$0.0494196\pi$
$240$	−3.89132	+	4.36559i	−0.251183	+	0.281797i
$241$	−0.114824	−	0.428531i	−0.00739649	−	0.0276041i	0.962129	−	0.272595i	$-0.0878818\pi$
$241$	−0.114824	−	0.428531i	−0.00739649	−	0.0276041i	−0.969525	+	0.244991i	$0.921215\pi$
$242$	−8.10309	+	4.67832i	−0.520886	+	0.300734i
$243$	5.61438	−	20.9531i	0.360162	−	1.34414i
$244$	−1.94526	+	7.25981i	−0.124533	+	0.464762i
$245$	12.1814	+	18.5533i	0.778243	+	1.18533i
$246$	−28.3153	+	7.58707i	−1.80532	+	0.483734i
$247$	−0.902411	−	0.241800i	−0.0574191	−	0.0153854i
$248$	−0.661953	+	0.661953i	−0.0420340	+	0.0420340i
$249$	−4.13472			−0.262027
$250$	7.16598	+	8.58189i	0.453216	+	0.542766i
$251$	15.7017	+	15.7017i	0.991081	+	0.991081i	0.999961	−	0.00887934i	$-0.00282642\pi$
$251$	15.7017	+	15.7017i	0.991081	+	0.991081i	−0.00887934	+	0.999961i	$0.502826\pi$
$252$	4.08901	+	15.2604i	0.257583	+	0.961315i
$253$	11.5597			0.726752
$254$	−2.85517	−	10.6556i	−0.179149	−	0.668595i
$255$	3.98706	−	4.47300i	0.249680	−	0.280110i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.40494	+	14.5578i	0.524286	+	0.908089i	0.999600	+	0.0282735i	$0.00900092\pi$
$257$	8.40494	+	14.5578i	0.524286	+	0.908089i	−0.475315	+	0.879816i	$0.657666\pi$
$258$	−9.70298	−	9.70298i	−0.604081	−	0.604081i
$259$	−23.9843	−	7.14222i	−1.49031	−	0.443796i
$260$	0.388295	+	0.591405i	0.0240810	+	0.0366774i
$261$	7.90239	−	29.4921i	0.489146	−	1.82552i
$262$	5.08374	+	18.9728i	0.314074	+	1.17214i
$263$	−5.60128	+	1.50086i	−0.345390	+	0.0925470i	−0.427344	−	0.904089i	$-0.640551\pi$
$263$	−5.60128	+	1.50086i	−0.345390	+	0.0925470i	0.0819539	+	0.996636i	$0.473884\pi$
$264$	3.23849	−	0.867750i	0.199315	−	0.0534063i
$265$	3.21255	−	15.4957i	0.197345	−	0.951891i
$266$	−6.07400	+	10.5205i	−0.372421	+	0.645052i
$267$	2.87138			0.175726
$268$	−1.39786	−	0.374556i	−0.0853881	−	0.0228797i
$269$			20.6435i			1.25866i	0.777139	+	0.629329i	$0.216670\pi$
$269$			20.6435i			1.25866i	−0.777139	+	0.629329i	$0.783330\pi$
$270$	4.81093	+	0.997397i	0.292784	+	0.0606996i
$271$	2.00895	+	3.47961i	0.122035	+	0.211371i	0.920570	−	0.390577i	$-0.127725\pi$
$271$	2.00895	+	3.47961i	0.122035	+	0.211371i	−0.798535	+	0.601948i	$0.794391\pi$
$272$	0.512303	−	0.887335i	0.0310629	−	0.0538026i
$273$	3.40439			0.206043
$274$	6.65534	+	1.78329i	0.402064	+	0.107733i
$275$	−0.733915	−	6.36752i	−0.0442567	−	0.383976i
$276$	22.7802	+	6.10392i	1.37120	+	0.367413i
$277$	−16.7026	−	9.64325i	−1.00356	−	0.579407i	−0.0942619	−	0.995547i	$-0.530049\pi$
$277$	−16.7026	−	9.64325i	−1.00356	−	0.579407i	−0.909300	+	0.416141i	$0.863382\pi$
$278$	4.67024	+	2.69637i	0.280103	+	0.161717i
$279$	3.47242	+	0.930432i	0.207888	+	0.0557035i
$280$	8.73480	−	2.88663i	0.522004	−	0.172509i
$281$	−17.9274	−	4.80363i	−1.06946	−	0.286561i	−0.319188	−	0.947691i	$-0.603410\pi$
$281$	−17.9274	−	4.80363i	−1.06946	−	0.286561i	−0.750271	+	0.661131i	$0.770077\pi$
$282$	9.80209			0.583706
$283$	−12.0486	+	20.8688i	−0.716216	+	1.24052i	0.246273	+	0.969201i	$0.420794\pi$
$283$	−12.0486	+	20.8688i	−0.716216	+	1.24052i	−0.962489	+	0.271322i	$0.912539\pi$
$284$	3.61602	+	6.26312i	0.214571	+	0.371648i
$285$	9.47746	+	14.4350i	0.561396	+	0.855053i
$286$		−	0.405600i		−	0.0239836i
$287$	44.5415	+	11.9348i	2.62920	+	0.704492i
$288$	3.84014			0.226282
$289$	7.97509	−	13.8133i	0.469123	−	0.812545i
$290$	−17.4086	−	3.60912i	−1.02227	−	0.211935i
$291$	28.3161	−	7.58728i	1.65992	−	0.444774i
$292$	10.3569	−	2.77513i	0.606093	−	0.162402i
$293$	−2.24328	−	8.37202i	−0.131054	−	0.489099i	0.868929	−	0.494936i	$-0.164809\pi$
$293$	−2.24328	−	8.37202i	−0.131054	−	0.489099i	−0.999983	+	0.00583742i	$0.998142\pi$
$294$	6.71888	−	25.0752i	0.391853	−	1.46242i
$295$	−19.1369	−	3.96744i	−1.11419	−	0.230993i
$296$	−3.18573	+	5.18181i	−0.185167	+	0.301186i
$297$	−1.99174	−	1.99174i	−0.115573	−	0.115573i
$298$	−9.79578	−	16.9668i	−0.567454	−	0.982860i
$299$	1.42653	−	2.47083i	0.0824986	−	0.142892i
$300$	1.91598	−	12.9357i	0.110619	−	0.746843i
$301$	5.58675	+	20.8500i	0.322015	+	1.20178i
$302$	9.20947			0.529945
$303$	11.9069	+	44.4370i	0.684031	+	2.55284i
$304$	2.08792	+	2.08792i	0.119751	+	0.119751i
$305$	−5.27348	−	15.9573i	−0.301959	−	0.913711i
$306$	−3.93463			−0.224928
$307$	1.09942	−	1.09942i	0.0627473	−	0.0627473i	−0.675037	−	0.737784i	$-0.735872\pi$
$307$	1.09942	−	1.09942i	0.0627473	−	0.0627473i	0.737784	+	0.675037i	$0.235872\pi$
$308$	−5.09431	−	1.36502i	−0.290275	−	0.0777790i
$309$	29.5746	−	7.92450i	1.68244	−	0.450809i
$310$	0.424940	−	2.04969i	0.0241350	−	0.116415i
$311$	−6.59852	+	24.6260i	−0.374168	+	1.39641i	0.480389	+	0.877055i	$0.340495\pi$
$311$	−6.59852	+	24.6260i	−0.374168	+	1.39641i	−0.854557	+	0.519357i	$0.826171\pi$
$312$	0.214171	−	0.799296i	0.0121250	−	0.0452512i
$313$	−4.30971	+	2.48821i	−0.243599	+	0.140642i	−0.616830	−	0.787096i	$-0.711583\pi$
$313$	−4.30971	+	2.48821i	−0.243599	+	0.140642i	0.373231	+	0.927739i	$0.378250\pi$
$314$	−6.27626	−	23.4233i	−0.354190	−	1.32186i
$315$	−26.3713	−	23.5064i	−1.48586	−	1.32444i
$316$	−1.24343	+	4.64055i	−0.0699486	+	0.261052i
$317$	−22.7963	−	6.10824i	−1.28037	−	0.343073i	−0.446373	−	0.894847i	$-0.647284\pi$
$317$	−22.7963	−	6.10824i	−1.28037	−	0.343073i	−0.833994	+	0.551774i	$0.813951\pi$
$318$	−16.0297	+	9.25477i	−0.898903	+	0.518982i
$319$	7.20721	+	7.20721i	0.403526	+	0.403526i
$320$	−0.128227	−	2.23239i	−0.00716811	−	0.124794i
$321$	−19.1115	+	11.0340i	−1.06670	+	0.615858i
$322$	−26.2326	−	26.2326i	−1.46188	−	1.46188i
$323$	−2.13930	−	2.13930i	−0.119034	−	0.119034i
$324$	2.88688	+	5.00023i	0.160382	+	0.277790i
$325$	−1.45160	−	0.628918i	−0.0805200	−	0.0348861i
$326$	10.3880	+	5.99752i	0.575339	+	0.332172i
$327$			4.82623i			0.266891i
$328$	5.60422	−	9.70680i	0.309441	−	0.535968i
$329$	−13.3534	−	7.70960i	−0.736198	−	0.425044i
$330$	−4.98841	+	5.59640i	−0.274603	+	0.308072i
$331$	28.9715	+	7.76288i	1.59242	+	0.426687i	0.942741	−	0.333526i	$-0.108238\pi$
$331$	28.9715	+	7.76288i	1.59242	+	0.426687i	0.649675	+	0.760212i	$0.274905\pi$
$332$	1.11789	−	1.11789i	0.0613522	−	0.0613522i
$333$	23.3497	+	0.645231i	1.27956	+	0.0353584i
$334$			15.1043i			0.826469i
$335$	3.07255	−	1.01540i	0.167871	−	0.0554772i
$336$	−9.31834	−	5.37994i	−0.508357	−	0.293500i
$337$	−4.67605	−	17.4513i	−0.254721	−	0.950631i	−0.968246	−	0.250001i	$-0.919569\pi$
$337$	−4.67605	−	17.4513i	−0.254721	−	0.950631i	0.713525	−	0.700630i	$-0.247098\pi$
$338$	11.1716	+	6.44995i	0.607657	+	0.350831i
$339$	27.9303	+	27.9303i	1.51696	+	1.51696i
$340$	0.131382	+	2.28732i	0.00712520	+	0.124047i
$341$	−0.848581	+	0.848581i	−0.0459532	+	0.0459532i
$342$	2.93476	−	10.9527i	0.158693	−	0.592252i
$343$	−8.51166	+	8.51166i	−0.459587	+	0.459587i
$344$	5.24672			0.282884
$345$	−50.0715	+	16.5474i	−2.69576	+	0.890880i
$346$	1.48869	+	5.55587i	0.0800325	+	0.298686i
$347$			8.48949i			0.455739i	0.973692	+	0.227870i	$0.0731760\pi$
$347$			8.48949i			0.455739i	−0.973692	+	0.227870i	$0.926824\pi$
$348$	10.3972	+	18.0086i	0.557351	+	0.965360i
$349$	−9.23117	+	5.32962i	−0.494133	+	0.285288i	−0.726288	−	0.687391i	$-0.758756\pi$
$349$	−9.23117	+	5.32962i	−0.494133	+	0.285288i	0.232154	+	0.972679i	$0.425423\pi$
$350$	−12.7844	+	16.1154i	−0.683356	+	0.861403i
$351$	−0.671518	+	0.179933i	−0.0358430	+	0.00960409i
$352$	−0.640968	+	1.11019i	−0.0341637	+	0.0591733i
$353$	11.8748	+	20.5678i	0.632034	+	1.09472i	0.987135	+	0.159888i	$0.0511132\pi$
$353$	11.8748	+	20.5678i	0.632034	+	1.09472i	−0.355101	+	0.934828i	$0.615553\pi$
$354$	11.4295	+	19.7964i	0.607470	+	1.05217i
$355$	−14.4454	−	7.26925i	−0.766682	−	0.385812i
$356$	−0.776325	+	0.776325i	−0.0411451	+	0.0411451i
$357$	9.54762	+	5.51232i	0.505314	+	0.291743i
$358$	−4.51584	+	16.8534i	−0.238670	+	0.890728i
$359$		−	7.20698i		−	0.380370i	−0.981748	−	0.190185i	$-0.939091\pi$
$359$		−	7.20698i		−	0.380370i	0.981748	−	0.190185i	$-0.0609088\pi$
$360$	−7.17795	+	4.71278i	−0.378311	+	0.248385i
$361$	−8.90375	+	5.14058i	−0.468618	+	0.270557i
$362$			7.52011i			0.395248i
$363$	−23.6372	+	6.33357i	−1.24063	+	0.332426i
$364$	−0.920432	+	0.920432i	−0.0482438	+	0.0482438i
$365$	−15.9533	+	17.8977i	−0.835035	+	0.936809i
$366$	−9.82843	+	17.0233i	−0.513740	+	0.889824i
$367$	1.45490	−	0.389839i	0.0759452	−	0.0203494i	−0.220646	−	0.975354i	$-0.570817\pi$
$367$	1.45490	−	0.389839i	0.0759452	−	0.0203494i	0.296592	+	0.955004i	$0.404150\pi$
$368$	−7.80928	+	4.50869i	−0.407087	+	0.235032i
$369$	−43.0419			−2.24067
$370$	−0.404585	−	13.5955i	−0.0210334	−	0.706794i
$371$	29.1165			1.51165
$372$	−2.12034	+	1.22418i	−0.109934	+	0.0634706i
$373$	12.6458	−	3.38844i	0.654777	−	0.175447i	0.0838891	−	0.996475i	$-0.473266\pi$
$373$	12.6458	−	3.38844i	0.654777	−	0.175447i	0.570888	+	0.821028i	$0.306599\pi$
$374$	0.656739	−	1.13751i	0.0339592	−	0.0588190i
$375$	12.2939	+	26.5307i	0.634854	+	1.37004i
$376$	−2.65016	+	2.65016i	−0.136671	+	0.136671i
$377$	2.42992	−	0.651094i	0.125147	−	0.0335330i
$378$			9.03977i			0.464956i
$379$	−10.0980	+	5.83006i	−0.518697	+	0.299470i	−0.736401	−	0.676545i	$-0.763476\pi$
$379$	−10.0980	+	5.83006i	−0.518697	+	0.299470i	0.217704	+	0.976015i	$0.430143\pi$
$380$	−6.46511	−	1.34034i	−0.331653	−	0.0687580i
$381$		−	28.8515i		−	1.47811i
$382$	5.63496	−	21.0300i	0.288310	−	1.07599i
$383$	−16.3681	−	9.45011i	−0.836369	−	0.482878i	0.0196592	−	0.999807i	$-0.493742\pi$
$383$	−16.3681	−	9.45011i	−0.836369	−	0.482878i	−0.856028	+	0.516929i	$0.827075\pi$
$384$	−1.84934	+	1.84934i	−0.0943739	+	0.0943739i
$385$	11.1974	−	3.70047i	0.570675	−	0.188594i
$386$	−5.75000	−	9.95928i	−0.292667	−	0.506914i
$387$	−10.0741	−	17.4488i	−0.512093	−	0.886971i
$388$	−5.60438	+	9.70707i	−0.284519	+	0.492802i
$389$	27.5808	−	7.39025i	1.39840	−	0.374701i	0.520631	−	0.853782i	$-0.325697\pi$
$389$	27.5808	−	7.39025i	1.39840	−	0.374701i	0.877771	+	0.479081i	$0.159030\pi$
$390$	0.580604	+	1.75688i	0.0294000	+	0.0889629i
$391$	8.00143	−	4.61963i	0.404650	−	0.233625i
$392$	4.96293	+	8.59605i	0.250666	+	0.434166i
$393$			51.3711i			2.59133i
$394$	1.89451	+	7.07040i	0.0954440	+	0.356202i
$395$	−3.37087	−	10.2001i	−0.169607	−	0.513222i
$396$	4.92281			0.247380
$397$	−19.2370	+	19.2370i	−0.965477	+	0.965477i	−0.999424	−	0.0339463i	$-0.989192\pi$
$397$	−19.2370	+	19.2370i	−0.965477	+	0.965477i	0.0339463	+	0.999424i	$0.489192\pi$
$398$	4.43519	−	16.5524i	0.222316	−	0.829695i
$399$	−22.4658	+	22.4658i	−1.12470	+	1.12470i
$400$	2.97936	+	4.01540i	0.148968	+	0.200770i
$401$	−6.04888	−	6.04888i	−0.302067	−	0.302067i	0.539755	−	0.841822i	$-0.318517\pi$
$401$	−6.04888	−	6.04888i	−0.302067	−	0.302067i	−0.841822	+	0.539755i	$0.818517\pi$
$402$	−3.27781	−	1.89245i	−0.163482	−	0.0943866i
$403$	0.0766602	+	0.286100i	0.00381871	+	0.0142516i
$404$	−15.2335	−	8.79506i	−0.757894	−	0.437570i
$405$	−11.5326	−	5.80348i	−0.573061	−	0.288377i
$406$		−	32.7108i		−	1.62341i
$407$	−4.08390	+	6.64274i	−0.202432	+	0.329268i
$408$	1.89485	−	1.89485i	0.0938089	−	0.0938089i
$409$	19.7000	+	5.27859i	0.974100	+	0.261009i	0.710558	−	0.703639i	$-0.248443\pi$
$409$	19.7000	+	5.27859i	0.974100	+	0.261009i	0.263542	+	0.964648i	$0.415109\pi$
$410$	1.43723	+	25.0216i	0.0709795	+	1.23573i
$411$	15.6059	+	9.01008i	0.769783	+	0.444435i
$412$	−5.85347	+	10.1385i	−0.288380	+	0.499488i
$413$		−	35.9583i		−	1.76939i
$414$	29.9887	+	17.3140i	1.47386	+	0.850936i
$415$	−0.717629	+	3.46147i	−0.0352270	+	0.169917i
$416$	0.158198	+	0.274007i	0.00775630	+	0.0134343i
$417$	9.97301	+	9.97301i	0.488381	+	0.488381i
$418$	2.67658	+	2.67658i	0.130916	+	0.130916i
$419$	11.5211	−	6.65171i	0.562843	−	0.324957i	−0.191443	−	0.981504i	$-0.561317\pi$
$419$	11.5211	−	6.65171i	0.562843	−	0.324957i	0.754286	+	0.656546i	$0.227983\pi$
$420$	24.0203	−	1.37971i	1.17207	−	0.0673229i
$421$	−16.5257	−	16.5257i	−0.805413	−	0.805413i	0.178523	−	0.983936i	$-0.442868\pi$
$421$	−16.5257	−	16.5257i	−0.805413	−	0.805413i	−0.983936	+	0.178523i	$0.942868\pi$
$422$	11.5779	−	6.68453i	0.563606	−	0.325398i
$423$	13.9020	+	3.72502i	0.675937	+	0.181117i
$424$	1.83172	−	6.83608i	0.0889563	−	0.331989i
$425$	−3.05267	−	4.11420i	−0.148076	−	0.199568i
$426$	4.89541	+	18.2699i	0.237183	+	0.885180i
$427$	26.7786	−	15.4606i	1.29591	−	0.748192i
$428$	2.18387	−	8.15032i	0.105561	−	0.393960i
$429$	0.274553	−	1.02465i	0.0132555	−	0.0494704i
$430$	−9.80712	+	6.43899i	−0.472941	+	0.310516i
$431$	−6.77322	+	1.81488i	−0.326255	+	0.0874197i	−0.418229	−	0.908342i	$-0.637349\pi$
$431$	−6.77322	+	1.81488i	−0.326255	+	0.0874197i	0.0919741	+	0.995761i	$0.470682\pi$
$432$	2.12239	+	0.568694i	0.102114	+	0.0273613i
$433$	3.46329	−	3.46329i	0.166435	−	0.166435i	−0.618975	−	0.785410i	$-0.712452\pi$
$433$	3.46329	−	3.46329i	0.166435	−	0.166435i	0.785410	+	0.618975i	$0.212452\pi$
$434$	3.85139			0.184873
$435$	−41.5353	−	20.9015i	−1.99146	−	1.00215i
$436$	−1.30485	−	1.30485i	−0.0624910	−	0.0624910i
$437$	6.89138	+	25.7190i	0.329659	+	1.23030i
$438$	28.0427			1.33993
$439$	−3.93412	−	14.6823i	−0.187765	−	0.700749i	−0.994022	−	0.109183i	$-0.965177\pi$
$439$	−3.93412	−	14.6823i	−0.187765	−	0.700749i	0.806256	−	0.591566i	$-0.201490\pi$
$440$	−0.164379	−	2.86178i	−0.00783645	−	0.136430i
$441$	19.0583	−	33.0100i	0.907540	−	1.57190i
$442$	−0.162091	−	0.280749i	−0.00770987	−	0.0133539i
$443$	−0.683223	−	0.683223i	−0.0324609	−	0.0324609i	0.690690	−	0.723151i	$-0.257307\pi$
$443$	−0.683223	−	0.683223i	−0.0324609	−	0.0324609i	−0.723151	+	0.690690i	$0.757307\pi$
$444$	−11.5556	+	10.9341i	−0.548402	+	0.518909i
$445$	0.498361	−	2.40384i	0.0236246	−	0.113953i
$446$	0.616869	−	2.30219i	0.0292096	−	0.109012i
$447$	−13.2617	−	49.4932i	−0.627255	−	2.34095i
$448$	3.97392	−	1.06481i	0.187750	−	0.0503075i
$449$	22.3408	−	5.98619i	1.05433	−	0.282506i	0.310287	−	0.950643i	$-0.399575\pi$
$449$	22.3408	−	5.98619i	1.05433	−	0.282506i	0.744038	+	0.668137i	$0.232908\pi$
$450$	7.63325	−	17.6182i	0.359835	−	0.830528i
$451$	7.18425	−	12.4435i	0.338293	−	0.585941i
$452$	−15.1028			−0.710377
$453$	23.2654	+	6.23395i	1.09310	+	0.292896i
$454$			16.1109i			0.756122i
$455$	0.590871	−	2.85006i	0.0277005	−	0.133613i
$456$	3.86128	+	6.68794i	0.180821	+	0.313191i
$457$	0.227544	−	0.394118i	0.0106441	−	0.0184361i	−0.860654	−	0.509190i	$-0.829945\pi$
$457$	0.227544	−	0.394118i	0.0106441	−	0.0184361i	0.871298	+	0.490754i	$0.163278\pi$
$458$	18.2605			0.853256
$459$	−2.17462	−	0.582687i	−0.101502	−	0.0271975i
$460$	9.06379	−	18.0115i	0.422601	−	0.839790i
$461$	1.76440	+	0.472769i	0.0821762	+	0.0220191i	0.299673	−	0.954042i	$-0.403122\pi$
$461$	1.76440	+	0.472769i	0.0821762	+	0.0220191i	−0.217497	+	0.976061i	$0.569789\pi$
$462$	−11.9455	−	6.89674i	−0.555755	−	0.320865i
$463$	17.0754	+	9.85847i	0.793560	+	0.458162i	0.841214	−	0.540702i	$-0.181841\pi$
$463$	17.0754	+	9.85847i	0.793560	+	0.458162i	−0.0476546	+	0.998864i	$0.515175\pi$
$464$	−7.67997	−	2.05784i	−0.356534	−	0.0955329i
$465$	2.46095	−	4.89039i	0.114124	−	0.226786i
$466$	23.0424	+	6.17420i	1.06742	+	0.286014i
$467$	5.43514			0.251508			0.125754	−	0.992061i	$-0.459865\pi$
$467$	5.43514			0.251508			0.125754	+	0.992061i	$0.459865\pi$
$468$	0.607503	−	1.05223i	0.0280818	−	0.0486391i
$469$	2.97691	+	5.15617i	0.137461	+	0.238090i
$470$	1.70127	−	8.20603i	0.0784735	−	0.378516i
$471$		−	63.4216i		−	2.92231i
$472$	−8.44244	−	2.26214i	−0.388595	−	0.104124i
$473$	6.72595			0.309260
$474$	−6.28244	+	10.8815i	−0.288562	+	0.499804i
$475$	13.7295	−	5.42890i	0.629951	−	0.249095i
$476$	−4.07170	+	1.09101i	−0.186626	+	0.0500063i
$477$	−26.2515	+	7.03406i	−1.20197	+	0.322068i
$478$	0.850999	+	3.17597i	0.0389238	+	0.145265i
$479$	−1.75560	+	6.55198i	−0.0802154	+	0.299368i	−0.994365	−	0.106009i	$-0.966193\pi$
$479$	−1.75560	+	6.55198i	−0.0802154	+	0.299368i	0.914150	+	0.405376i	$0.132860\pi$
$480$	1.18718	−	5.72637i	0.0541873	−	0.261372i
$481$	0.915875	+	1.69267i	0.0417603	+	0.0771789i
$482$	0.313706	+	0.313706i	0.0142889	+	0.0142889i
$483$	−48.5130	−	84.0270i	−2.20742	−	3.82336i
$484$	4.67832	−	8.10309i	0.212651	−	0.368322i
$485$	−1.43727	−	25.0223i	−0.0652629	−	1.13620i
$486$	5.61438	+	20.9531i	0.254673	+	0.950454i
$487$	−6.62657			−0.300278			−0.150139	−	0.988665i	$-0.547972\pi$
$487$	−6.62657			−0.300278			−0.150139	+	0.988665i	$0.547972\pi$
$488$	−1.94526	−	7.25981i	−0.0880578	−	0.328636i
$489$	22.1829	+	22.1829i	1.00315	+	1.00315i
$490$	−19.8261	−	9.97694i	−0.895652	−	0.450712i
$491$	33.6405			1.51818			0.759088	−	0.650988i	$-0.225645\pi$
$491$	33.6405			1.51818			0.759088	+	0.650988i	$0.225645\pi$
$492$	20.7282	−	20.7282i	0.934502	−	0.934502i
$493$	7.86894	+	2.10848i	0.354399	+	0.0949610i
$494$	0.902411	−	0.241800i	0.0406014	−	0.0108791i
$495$	−9.20167	+	6.04148i	−0.413584	+	0.271544i
$496$	0.242292	−	0.904244i	0.0108792	−	0.0406018i
$497$	7.70073	−	28.7395i	0.345425	−	1.28914i
$498$	3.58077	−	2.06736i	0.160458	−	0.0926406i
$499$	3.85319	+	14.3803i	0.172492	+	0.643751i	0.996965	+	0.0778489i	$0.0248052\pi$
$499$	3.85319	+	14.3803i	0.172492	+	0.643751i	−0.824473	+	0.565902i	$0.808528\pi$
$500$	−10.4969	−	3.84915i	−0.469434	−	0.172139i
$501$	−10.2242	+	38.1572i	−0.456783	+	1.70474i
$502$	−21.4489	−	5.74721i	−0.957311	−	0.256511i
$503$	−3.97907	+	2.29732i	−0.177418	+	0.102432i	−0.586079	−	0.810254i	$-0.699329\pi$
$503$	−3.97907	+	2.29732i	−0.177418	+	0.102432i	0.408661	+	0.912686i	$0.365996\pi$
$504$	−11.1714	−	11.1714i	−0.497613	−	0.497613i
$505$	39.2680	−	2.25553i	1.74740	−	0.100370i
$506$	−10.0110	+	5.77985i	−0.445043	+	0.256946i
$507$	23.8563	+	23.8563i	1.05950	+	1.05950i
$508$	7.80047	+	7.80047i	0.346090	+	0.346090i
$509$	−9.21302	−	15.9574i	−0.408360	−	0.707300i	0.586346	−	0.810061i	$-0.300566\pi$
$509$	−9.21302	−	15.9574i	−0.408360	−	0.707300i	−0.994706	+	0.102760i	$0.967233\pi$
$510$	−1.21640	+	5.86727i	−0.0538629	+	0.259807i
$511$	−38.2026	−	22.0563i	−1.68998	−	0.975713i
$512$		−	1.00000i		−	0.0441942i
$513$	3.24400	−	5.61878i	0.143226	−	0.248075i
$514$	−14.5578	−	8.40494i	−0.642116	−	0.370726i
$515$	−1.50115	−	26.1344i	−0.0661484	−	1.15162i
$516$	13.2545	+	3.55154i	0.583498	+	0.156348i
$517$	−3.39733	+	3.39733i	−0.149414	+	0.149414i
$518$	24.3421	−	5.80680i	1.06953	−	0.255136i
$519$			15.0432i			0.660324i
$520$	−0.631976	−	0.318025i	−0.0277140	−	0.0139463i
$521$	18.6627	+	10.7749i	0.817629	+	0.472058i	0.849598	−	0.527430i	$-0.176844\pi$
$521$	18.6627	+	10.7749i	0.817629	+	0.472058i	−0.0319690	+	0.999489i	$0.510178\pi$
$522$	7.90239	+	29.4921i	0.345878	+	1.29084i
$523$	0.0940964	+	0.0543266i	0.00411455	+	0.00237554i	0.502056	−	0.864835i	$-0.332577\pi$
$523$	0.0940964	+	0.0543266i	0.00411455	+	0.00237554i	−0.497941	+	0.867211i	$0.665911\pi$
$524$	−13.8890	−	13.8890i	−0.606745	−	0.606745i
$525$	−43.2052	+	32.0576i	−1.88563	+	1.39911i
$526$	4.10042	−	4.10042i	0.178787	−	0.178787i
$527$	−0.248253	+	0.926494i	−0.0108141	+	0.0403587i
$528$	−2.37074	+	2.37074i	−0.103173	+	0.103173i
$529$	−58.3132			−2.53536
$530$	4.96569	+	15.0259i	0.215696	+	0.652684i
$531$	8.68694	+	32.4201i	0.376981	+	1.40691i
$532$		−	12.1480i		−	0.526682i
$533$	−1.77316	−	3.07119i	−0.0768039	−	0.133028i
$534$	−2.48669	+	1.43569i	−0.107610	+	0.0621284i
$535$	5.92034	+	17.9146i	0.255959	+	0.774517i
$536$	1.39786	−	0.374556i	0.0603785	−	0.0161784i
$537$	−22.8163	+	39.5190i	−0.984596	+	1.70537i
$538$	−10.3218	−	17.8778i	−0.445003	−	0.770768i
$539$	6.36216	+	11.0196i	0.274038	+	0.474647i
$540$	−4.66508	+	1.54169i	−0.200753	+	0.0663439i
$541$	−31.8709	+	31.8709i	−1.37024	+	1.37024i	−0.510155	+	0.860082i	$0.670412\pi$
$541$	−31.8709	+	31.8709i	−1.37024	+	1.37024i	−0.860082	+	0.510155i	$0.829588\pi$
$542$	−3.47961	−	2.00895i	−0.149462	−	0.0862919i
$543$	−5.09041	+	18.9977i	−0.218450	+	0.815268i
$544$			1.02461i			0.0439296i
$545$	4.04038	+	0.837648i	0.173071	+	0.0358809i
$546$	−2.94829	+	1.70219i	−0.126175	+	0.0728472i
$547$		−	19.5536i		−	0.836050i	−0.908435	−	0.418025i	$-0.862722\pi$
$547$		−	19.5536i		−	0.836050i	0.908435	−	0.418025i	$-0.137278\pi$
$548$	−6.65534	+	1.78329i	−0.284302	+	0.0761785i
$549$	−20.4086	+	20.4086i	−0.871018	+	0.871018i
$550$	3.81935	+	5.14748i	0.162858	+	0.219489i
$551$	−11.7386	+	20.3318i	−0.500080	+	0.866164i
$552$	−22.7802	+	6.10392i	−0.969588	+	0.259800i
$553$	17.1172	−	9.88261i	0.727896	−	0.420251i
$554$	19.2865			0.819405
$555$	8.18077	−	34.6194i	0.347254	−	1.46951i
$556$	−5.39273			−0.228703
$557$	27.9548	−	16.1397i	1.18448	−	0.683862i	0.227436	−	0.973793i	$-0.426966\pi$
$557$	27.9548	−	16.1397i	1.18448	−	0.683862i	0.957047	+	0.289931i	$0.0936325\pi$
$558$	−3.47242	+	0.930432i	−0.146999	+	0.0393883i
$559$	0.830021	−	1.43764i	0.0351062	−	0.0608057i
$560$	−6.12124	+	6.86729i	−0.258670	+	0.290196i
$561$	2.42907	−	2.42907i	0.102555	−	0.102555i
$562$	17.9274	−	4.80363i	0.756222	−	0.202629i
$563$			10.5166i			0.443221i	0.975135	+	0.221610i	$0.0711313\pi$
$563$			10.5166i			0.443221i	−0.975135	+	0.221610i	$0.928869\pi$
$564$	−8.48886	+	4.90105i	−0.357445	+	0.206371i
$565$	28.2301	−	18.5348i	1.18765	−	0.779766i
$566$		−	24.0972i		−	1.01288i
$567$	6.14795	−	22.9445i	0.258190	−	0.963577i
$568$	−6.26312	−	3.61602i	−0.262795	−	0.151725i
$569$	−17.6830	+	17.6830i	−0.741311	+	0.741311i	−0.972830	−	0.231520i	$-0.925630\pi$
$569$	−17.6830	+	17.6830i	−0.741311	+	0.741311i	0.231520	+	0.972830i	$0.425630\pi$
$570$	−15.4252	−	7.76231i	−0.646090	−	0.325127i
$571$	−12.0264	−	20.8303i	−0.503289	−	0.871723i	−0.999993	−	0.00380245i	$-0.998790\pi$
$571$	−12.0264	−	20.8303i	−0.503289	−	0.871723i	0.496703	−	0.867920i	$-0.334544\pi$
$572$	0.202800	+	0.351260i	0.00847949	+	0.0146869i
$573$	28.4706	−	49.3126i	1.18938	−	2.06006i
$574$	−44.5415	+	11.9348i	−1.85912	+	0.498151i
$575$	5.16250	+	44.7904i	0.215291	+	1.86789i
$576$	−3.32566	+	1.92007i	−0.138569	+	0.0800028i
$577$	−13.3636	−	23.1465i	−0.556336	−	0.963602i	−0.997798	−	0.0663223i	$-0.978873\pi$
$577$	−13.3636	−	23.1465i	−0.556336	−	0.963602i	0.441462	−	0.897280i	$-0.354460\pi$
$578$			15.9502i			0.663440i
$579$	−7.78442	−	29.0518i	−0.323509	−	1.20735i
$580$	16.8808	−	5.57868i	0.700937	−	0.231642i
$581$	−6.50413			−0.269837
$582$	−20.7288	+	20.7288i	−0.859238	+	0.859238i
$583$	2.34815	−	8.76342i	0.0972504	−	0.362944i
$584$	−7.58180	+	7.58180i	−0.313737	+	0.313737i
$585$	0.155797	+	2.71236i	0.00644139	+	0.112142i
$586$	6.12874	+	6.12874i	0.253176	+	0.253176i
$587$	19.9388	+	11.5117i	0.822961	+	0.475137i	0.851437	−	0.524458i	$-0.175732\pi$
$587$	19.9388	+	11.5117i	0.822961	+	0.475137i	−0.0284753	+	0.999594i	$0.509065\pi$
$588$	6.71888	+	25.0752i	0.277082	+	1.03408i
$589$	−2.39388	−	1.38211i	−0.0986380	−	0.0569487i
$590$	18.5567	−	6.13253i	0.763969	−	0.252472i
$591$			19.1440i			0.787479i
$592$	0.168023	−	6.08044i	0.00690570	−	0.249905i
$593$	−18.8196	+	18.8196i	−0.772828	+	0.772828i	−0.978600	−	0.205772i	$-0.934030\pi$
$593$	−18.8196	+	18.8196i	−0.772828	+	0.772828i	0.205772	+	0.978600i	$0.434030\pi$
$594$	2.72077	+	0.729028i	0.111635	+	0.0299124i
$595$	6.27186	−	7.03627i	0.257121	−	0.288459i
$596$	16.9668	+	9.79578i	0.694987	+	0.401251i
$597$	22.4088	−	38.8132i	0.917131	−	1.58852i
$598$			2.85307i			0.116671i
$599$	−26.6032	−	15.3593i	−1.08698	−	0.627566i	−0.154206	−	0.988039i	$-0.549282\pi$
$599$	−26.6032	−	15.3593i	−1.08698	−	0.627566i	−0.932770	+	0.360473i	$0.882615\pi$
$600$	4.80856	+	12.1606i	0.196309	+	0.496456i
$601$	−17.0654	−	29.5582i	−0.696112	−	1.20570i	−0.969804	−	0.243885i	$-0.921578\pi$
$601$	−17.0654	−	29.5582i	−0.696112	−	1.20570i	0.273692	−	0.961817i	$-0.411755\pi$
$602$	−15.2633	−	15.2633i	−0.622085	−	0.622085i
$603$	−3.92964	−	3.92964i	−0.160027	−	0.160027i
$604$	−7.97563	+	4.60473i	−0.324524	+	0.187364i
$605$	1.19977	+	20.8877i	0.0487778	+	0.849204i
$606$	−32.5301	−	32.5301i	−1.32145	−	1.32145i
$607$	−0.633692	+	0.365862i	−0.0257208	+	0.0148499i	−0.512805	−	0.858505i	$-0.671394\pi$
$607$	−0.633692	+	0.365862i	−0.0257208	+	0.0148499i	0.487084	+	0.873355i	$0.338060\pi$
$608$	−2.85215	−	0.764232i	−0.115670	−	0.0309937i
$609$	22.1422	−	82.6356i	0.897245	−	3.34857i
$610$	12.5456	+	11.1827i	0.507957	+	0.452773i
$611$	0.306912	+	1.14541i	0.0124163	+	0.0463384i
$612$	3.40749	−	1.96731i	0.137739	−	0.0795239i
$613$	−6.62436	+	24.7224i	−0.267555	+	0.998530i	0.693113	+	0.720829i	$0.256239\pi$
$613$	−6.62436	+	24.7224i	−0.267555	+	0.998530i	−0.960668	+	0.277700i	$0.910428\pi$
$614$	−0.402416	+	1.50184i	−0.0162402	+	0.0606092i
$615$	−13.3065	+	64.1836i	−0.536569	+	2.58813i
$616$	5.09431	−	1.36502i	0.205256	−	0.0549981i
$617$	−22.3165	−	5.97970i	−0.898430	−	0.240733i	−0.220088	−	0.975480i	$-0.570634\pi$
$617$	−22.3165	−	5.97970i	−0.898430	−	0.240733i	−0.678342	+	0.734747i	$0.737301\pi$
$618$	−21.6501	+	21.6501i	−0.870896	+	0.870896i
$619$	5.92880			0.238299			0.119149	−	0.992876i	$-0.461983\pi$
$619$	5.92880			0.238299			0.119149	+	0.992876i	$0.461983\pi$
$620$	0.656837	+	1.98756i	0.0263792	+	0.0798222i
$621$	14.0103	+	14.0103i	0.562214	+	0.562214i
$622$	−6.59852	−	24.6260i	−0.264576	−	0.987413i
$623$	4.51683			0.180963
$624$	0.214171	+	0.799296i	0.00857369	+	0.0319975i
$625$	24.3445	−	5.68740i	0.973779	−	0.227496i
$626$	2.48821	−	4.30971i	0.0994490	−	0.172251i
$627$	4.94992	+	8.57350i	0.197681	+	0.342393i
$628$	17.1471	+	17.1471i	0.684243	+	0.684243i
$629$	−0.172157	+	6.23005i	−0.00686436	+	0.248409i
$630$	34.5915	+	7.17146i	1.37816	+	0.285718i
$631$	−5.52933	+	20.6357i	−0.220119	+	0.821496i	0.764182	+	0.645000i	$0.223143\pi$
$631$	−5.52933	+	20.6357i	−0.220119	+	0.821496i	−0.984301	+	0.176495i	$0.943524\pi$
$632$	−1.24343	−	4.64055i	−0.0494611	−	0.184591i
$633$	33.7736	−	9.04960i	1.34238	−	0.359690i
$634$	22.7963	−	6.10824i	0.905356	−	0.242589i
$635$	−24.1536	−	5.00751i	−0.958508	−	0.198717i
$636$	9.25477	−	16.0297i	0.366976	−	0.635621i
$637$	3.14051			0.124431
$638$	−9.84523	−	2.63802i	−0.389776	−	0.104440i
$639$			27.7720i			1.09864i
$640$	1.22724	+	1.86919i	0.0485110	+	0.0738863i
$641$	3.77010	+	6.53000i	0.148910	+	0.257919i	0.930825	−	0.365466i	$-0.119090\pi$
$641$	3.77010	+	6.53000i	0.148910	+	0.257919i	−0.781915	+	0.623385i	$0.785757\pi$
$642$	11.0340	−	19.1115i	0.435477	−	0.754269i
$643$	13.3314			0.525738			0.262869	−	0.964832i	$-0.415331\pi$
$643$	13.3314			0.525738			0.262869	+	0.964832i	$0.415331\pi$
$644$	35.8344	+	9.60179i	1.41207	+	0.378363i
$645$	−29.1338	+	9.62800i	−1.14714	+	0.379102i
$646$	2.92233	+	0.783037i	0.114978	+	0.0308082i
$647$	−19.4591	−	11.2347i	−0.765016	−	0.441682i	0.0660780	−	0.997814i	$-0.478951\pi$
$647$	−19.4591	−	11.2347i	−0.765016	−	0.441682i	−0.831094	+	0.556132i	$0.812285\pi$
$648$	−5.00023	−	2.88688i	−0.196427	−	0.113407i
$649$	−10.8227	−	2.89992i	−0.424827	−	0.113832i
$650$	1.57158	−	0.181139i	0.0616423	−	0.00710484i
$651$	9.72957	+	2.60703i	0.381332	+	0.102178i
$652$	−11.9950			−0.469762
$653$	−6.37961	+	11.0498i	−0.249653	+	0.432412i	−0.963430	−	0.267962i	$-0.913650\pi$
$653$	−6.37961	+	11.0498i	−0.249653	+	0.432412i	0.713776	+	0.700374i	$0.246983\pi$
$654$	−2.41311	−	4.17964i	−0.0943603	−	0.163437i
$655$	43.0064	+	8.91605i	1.68040	+	0.348379i
$656$			11.2084i			0.437616i
$657$	39.7720	+	10.6569i	1.55165	+	0.415764i
$658$	15.4192			0.601103
$659$	21.1866	−	36.6963i	0.825314	−	1.42949i	−0.0763650	−	0.997080i	$-0.524331\pi$
$659$	21.1866	−	36.6963i	0.825314	−	1.42949i	0.901679	−	0.432406i	$-0.142335\pi$
$660$	1.52189	−	7.34083i	0.0592396	−	0.285741i
$661$	−5.22723	+	1.40063i	−0.203316	+	0.0544783i	−0.359040	−	0.933322i	$-0.616896\pi$
$661$	−5.22723	+	1.40063i	−0.203316	+	0.0544783i	0.155724	+	0.987801i	$0.450229\pi$
$662$	−28.9715	+	7.76288i	−1.12601	+	0.301713i
$663$	−0.219441	−	0.818963i	−0.00852236	−	0.0318059i
$664$	−0.409176	+	1.52707i	−0.0158791	+	0.0592616i
$665$	14.9085	+	22.7069i	0.578128	+	0.880537i
$666$	−20.5441	+	11.1161i	−0.796067	+	0.430739i
$667$	−50.6969	−	50.6969i	−1.96299	−	1.96299i
$668$	−7.55214	−	13.0807i	−0.292201	−	0.506107i
$669$	3.11673	−	5.39833i	0.120500	−	0.208712i
$670$	−2.15320	+	2.41563i	−0.0831855	+	0.0933241i
$671$	−2.49370	−	9.30661i	−0.0962682	−	0.359278i
$672$	10.7599			0.415072
$673$	7.13765	+	26.6381i	0.275136	+	1.02682i	0.955750	+	0.294180i	$0.0950465\pi$
$673$	7.13765	+	26.6381i	0.275136	+	1.02682i	−0.680614	+	0.732642i	$0.738287\pi$
$674$	12.7752	+	12.7752i	0.492083	+	0.492083i
$675$	6.82790	−	8.60691i	0.262806	−	0.331280i
$676$	−12.8999			−0.496150
$677$	−27.1242	+	27.1242i	−1.04247	+	1.04247i	−0.0434117	+	0.999057i	$0.513823\pi$
$677$	−27.1242	+	27.1242i	−1.04247	+	1.04247i	−0.999057	+	0.0434117i	$0.986177\pi$
$678$	−38.1535	−	10.2232i	−1.46528	−	0.392619i
$679$	44.5427	−	11.9352i	1.70939	−	0.458030i
$680$	−1.25744	−	1.91518i	−0.0482206	−	0.0734440i
$681$	−10.9056	+	40.7001i	−0.417902	+	1.55963i
$682$	0.310602	−	1.15918i	0.0118936	−	0.0443874i
$683$	−12.4838	+	7.20750i	−0.477678	+	0.275787i	−0.719448	−	0.694546i	$-0.755605\pi$
$683$	−12.4838	+	7.20750i	−0.477678	+	0.275787i	0.241771	+	0.970333i	$0.422272\pi$
$684$	2.93476	+	10.9527i	0.112213	+	0.418785i
$685$	10.2516	−	11.5010i	0.391692	−	0.439432i
$686$	3.11548	−	11.6271i	0.118950	−	0.443926i
$687$	46.1305	+	12.3606i	1.75999	+	0.471588i
$688$	−4.54379	+	2.62336i	−0.173230	+	0.100015i
$689$	−1.58336	−	1.58336i	−0.0603213	−	0.0603213i
$690$	35.0895	−	39.3662i	1.33583	−	1.49864i
$691$	11.9196	−	6.88177i	0.453442	−	0.261795i	−0.255841	−	0.966719i	$-0.582352\pi$
$691$	11.9196	−	6.88177i	0.453442	−	0.261795i	0.709283	+	0.704924i	$0.249019\pi$
$692$	−4.06718	−	4.06718i	−0.154611	−	0.154611i
$693$	−14.3210	−	14.3210i	−0.544010	−	0.544010i
$694$	−4.24474	−	7.35211i	−0.161128	−	0.279082i
$695$	10.0801	−	6.61819i	0.382358	−	0.251042i
$696$	−18.0086	−	10.3972i	−0.682612	−	0.394106i
$697$		−	11.4842i		−	0.434996i
$698$	5.32962	−	9.23117i	0.201729	−	0.349405i
$699$	54.0316	+	31.1951i	2.04366	+	1.17991i
$700$	3.01394	−	20.3485i	0.113916	−	0.769102i
$701$	15.4790	+	4.14760i	0.584635	+	0.156653i	0.539000	−	0.842306i	$-0.318802\pi$
$701$	15.4790	+	4.14760i	0.584635	+	0.156653i	0.0456352	+	0.998958i	$0.485469\pi$
$702$	0.491585	−	0.491585i	0.0185537	−	0.0185537i
$703$	−17.2139	−	5.12610i	−0.649236	−	0.193334i
$704$		−	1.28194i		−	0.0483148i
$705$	9.85253	−	19.5789i	0.371068	−	0.737383i
$706$	−20.5678	−	11.8748i	−0.774081	−	0.446916i
$707$	18.7301	+	69.9017i	0.704418	+	2.62892i
$708$	−19.7964	−	11.4295i	−0.743996	−	0.429546i
$709$	−11.2508	−	11.2508i	−0.422534	−	0.422534i	0.463541	−	0.886075i	$-0.346579\pi$
$709$	−11.2508	−	11.2508i	−0.422534	−	0.422534i	−0.886075	+	0.463541i	$0.846579\pi$
$710$	16.1447	−	0.927342i	0.605900	−	0.0348025i
$711$	−13.0454	+	13.0454i	−0.489241	+	0.489241i
$712$	0.284155	−	1.06048i	0.0106491	−	0.0397432i
$713$	5.96908	−	5.96908i	0.223544	−	0.223544i
$714$	−11.0246			−0.412587
$715$	−0.810152	−	0.407687i	−0.0302980	−	0.0152466i
$716$	−4.51584	−	16.8534i	−0.168765	−	0.629840i
$717$			8.59934i			0.321148i
$718$	3.60349	+	6.24143i	0.134481	+	0.232928i
$719$	−35.4007	+	20.4386i	−1.32022	+	0.762231i	−0.983764	−	0.179468i	$-0.942562\pi$
$719$	−35.4007	+	20.4386i	−1.32022	+	0.762231i	−0.336458	+	0.941698i	$0.609229\pi$
$720$	3.85990	−	7.67036i	0.143850	−	0.285857i
$721$	46.5224	−	12.4656i	1.73259	−	0.464245i
$722$	5.14058	−	8.90375i	0.191313	−	0.331363i
$723$	0.580150	+	1.00485i	0.0215760	+	0.0373708i
$724$	−3.76005	−	6.51260i	−0.139741	−	0.242039i
$725$	−24.7071	+	31.1445i	−0.917598	+	1.15668i
$726$	17.3036	−	17.3036i	0.642198	−	0.642198i
$727$	21.5146	+	12.4215i	0.797933	+	0.460687i	0.842748	−	0.538308i	$-0.180936\pi$
$727$	21.5146	+	12.4215i	0.797933	+	0.460687i	−0.0448149	+	0.998995i	$0.514270\pi$
$728$	0.336902	−	1.25733i	0.0124864	−	0.0465999i
$729$			39.4120i			1.45970i
$730$	4.86713	−	23.4765i	0.180141	−	0.868905i
$731$	4.65559	−	2.68791i	0.172193	−	0.0994159i
$732$		−	19.6569i		−	0.726538i
$733$	−20.1278	+	5.39322i	−0.743436	+	0.199203i	−0.610604	−	0.791936i	$-0.709073\pi$
$733$	−20.1278	+	5.39322i	−0.743436	+	0.199203i	−0.132831	+	0.991139i	$0.542407\pi$
$734$	−1.06506	+	1.06506i	−0.0393121	+	0.0393121i
$735$	−43.3322	−	38.6247i	−1.59833	−	1.42469i
$736$	4.50869	−	7.80928i	0.166193	−	0.287854i
$737$	1.79197	−	0.480157i	0.0660081	−	0.0176868i
$738$	37.2754	−	21.5210i	1.37213	−	0.792198i
$739$	5.96184			0.219310			0.109655	−	0.993970i	$-0.465025\pi$
$739$	5.96184			0.219310			0.109655	+	0.993970i	$0.465025\pi$
$740$	7.14811	+	11.5717i	0.262770	+	0.425385i
$741$	2.44339			0.0897602
$742$	−25.2156	+	14.5582i	−0.925694	+	0.534450i
$743$	16.3703	−	4.38642i	0.600569	−	0.160922i	0.0542899	−	0.998525i	$-0.482710\pi$
$743$	16.3703	−	4.38642i	0.600569	−	0.160922i	0.546279	+	0.837603i	$0.316044\pi$
$744$	1.22418	−	2.12034i	0.0448805	−	0.0777353i
$745$	−43.7360	+	2.51217i	−1.60236	+	0.0920387i
$746$	−9.25740	+	9.25740i	−0.338937	+	0.338937i
$747$	5.86414	−	1.57129i	0.214558	−	0.0574905i
$748$			1.31348i			0.0480255i
$749$	−30.0633	+	17.3571i	−1.09849	+	0.634213i
$750$	−23.9122	−	16.8293i	−0.873149	−	0.614519i
$751$		−	0.463178i		−	0.0169016i	−0.999964	−	0.00845080i	$-0.997310\pi$
$751$		−	0.463178i		−	0.0169016i	0.999964	−	0.00845080i	$-0.00269001\pi$
$752$	0.970024	−	3.62018i	0.0353731	−	0.132014i
$753$	−50.2949	−	29.0378i	−1.83285	−	1.05820i
$754$	−1.77882	+	1.77882i	−0.0647809	+	0.0647809i
$755$	9.25686	−	18.3952i	0.336892	−	0.669468i
$756$	−4.51989	−	7.82867i	−0.164387	−	0.284726i
$757$	26.8665	+	46.5341i	0.976480	+	1.69131i	0.674963	+	0.737851i	$0.264159\pi$
$757$	26.8665	+	46.5341i	0.976480	+	1.69131i	0.301516	+	0.953461i	$0.402507\pi$
$758$	5.83006	−	10.0980i	0.211757	−	0.366774i
$759$	−29.2027	+	7.82484i	−1.05999	+	0.284024i
$760$	6.26912	−	2.07179i	0.227405	−	0.0751516i
$761$	−17.6933	+	10.2152i	−0.641380	+	0.370301i	−0.785146	−	0.619311i	$-0.787412\pi$
$761$	−17.6933	+	10.2152i	−0.641380	+	0.370301i	0.143766	+	0.989612i	$0.454079\pi$
$762$	14.4257	+	24.9861i	0.522590	+	0.905152i
$763$			7.59191i			0.274846i
$764$	5.63496	+	21.0300i	0.203866	+	0.760837i
$765$	−3.95487	+	7.85909i	−0.142989	+	0.284146i
$766$	18.9002			0.682893
$767$	−1.95542	+	1.95542i	−0.0706062	+	0.0706062i
$768$	0.676906	−	2.52625i	0.0244258	−	0.0911582i
$769$	13.9242	−	13.9242i	0.502119	−	0.502119i	−0.409977	−	0.912096i	$-0.634463\pi$
$769$	13.9242	−	13.9242i	0.502119	−	0.502119i	0.912096	+	0.409977i	$0.134463\pi$
$770$	−7.84703	+	8.80343i	−0.282788	+	0.317254i
$771$	−31.0872	−	31.0872i	−1.11958	−	1.11958i
$772$	9.95928	+	5.75000i	0.358442	+	0.206947i
$773$	11.4911	+	42.8855i	0.413308	+	1.54249i	0.788201	+	0.615418i	$0.211013\pi$
$773$	11.4911	+	42.8855i	0.413308	+	1.54249i	−0.374893	+	0.927068i	$0.622321\pi$
$774$	17.4488	+	10.0741i	0.627183	+	0.362105i
$775$	−3.66697	−	2.90902i	−0.131721	−	0.104495i
$776$		−	11.2088i		−	0.402371i
$777$	65.4249	+	1.80791i	2.34710	+	0.0648584i
$778$	−20.1905	+	20.1905i	−0.723866	+	0.723866i
$779$	31.9682	+	8.56585i	1.14538	+	0.306904i
$780$	−1.38126	−	1.23120i	−0.0494569	−	0.0440840i
$781$	−8.02892	−	4.63550i	−0.287297	−	0.165871i
$782$	−4.61963	+	8.00143i	−0.165198	+	0.286131i
$783$			17.4702i			0.624334i
$784$	−8.59605	−	4.96293i	−0.307002	−	0.177248i
$785$	−53.0948	−	11.0076i	−1.89503	−	0.392876i
$786$	−25.6856	−	44.4887i	−0.916174	−	1.58686i
$787$	−25.0442	−	25.0442i	−0.892729	−	0.892729i	0.102050	−	0.994779i	$-0.467460\pi$
$787$	−25.0442	−	25.0442i	−0.892729	−	0.892729i	−0.994779	+	0.102050i	$0.967460\pi$
$788$	−5.17589	−	5.17589i	−0.184384	−	0.184384i
$789$	13.1343	−	7.58309i	0.467593	−	0.269965i
$790$	8.01930	+	7.14809i	0.285314	+	0.254318i
$791$	43.9358	+	43.9358i	1.56218	+	1.56218i
$792$	−4.26328	+	2.46140i	−0.151489	+	0.0874622i
$793$	−2.29698	−	0.615473i	−0.0815681	−	0.0218561i
$794$	7.04123	−	26.2782i	0.249884	−	0.932580i
$795$	2.37343	+	41.3205i	0.0841767	+	1.46549i
$796$	4.43519	+	16.5524i	0.157201	+	0.586683i
$797$	−9.78854	+	5.65142i	−0.346728	+	0.200183i	−0.663243	−	0.748404i	$-0.730820\pi$
$797$	−9.78854	+	5.65142i	−0.346728	+	0.200183i	0.316515	+	0.948587i	$0.397487\pi$
$798$	8.22306	−	30.6889i	0.291093	−	1.08637i
$799$	−0.993892	+	3.70926i	−0.0351614	+	0.131224i
$800$	−4.58790	−	1.98775i	−0.162207	−	0.0702777i
$801$	−4.07239	+	1.09119i	−0.143891	+	0.0385554i
$802$	8.26293	+	2.21404i	0.291774	+	0.0781806i
$803$	−9.71938	+	9.71938i	−0.342989	+	0.342989i
$804$	3.78489			0.133483
$805$	−78.7650	+	26.0299i	−2.77610	+	0.917432i
$806$	−0.209439	−	0.209439i	−0.00737719	−	0.00737719i
$807$	−13.9737	−	52.1507i	−0.491899	−	1.83579i
$808$	17.5901			0.618818
$809$	−2.84615	−	10.6220i	−0.100065	−	0.373449i	0.897673	−	0.440661i	$-0.145256\pi$
$809$	−2.84615	−	10.6220i	−0.100065	−	0.373449i	−0.997739	+	0.0672127i	$0.978589\pi$
$810$	12.8893	−	0.740353i	0.452883	−	0.0260133i
$811$	−0.191372	+	0.331467i	−0.00671999	+	0.0116394i	−0.869366	−	0.494169i	$-0.835472\pi$
$811$	−0.191372	+	0.331467i	−0.00671999	+	0.0116394i	0.862646	+	0.505808i	$0.168806\pi$
$812$	16.3554	+	28.3284i	0.573962	+	0.994132i
$813$	−7.43048	−	7.43048i	−0.260598	−	0.260598i
$814$	0.215395	−	7.79473i	0.00754958	−	0.273205i
$815$	22.4210	−	14.7208i	0.785374	−	0.515648i
$816$	−0.693562	+	2.58841i	−0.0242795	+	0.0906124i
$817$	4.00971	+	14.9645i	0.140282	+	0.523540i
$818$	−19.7000	+	5.27859i	−0.688793	+	0.184561i
$819$	−4.82833	+	1.29375i	−0.168716	+	0.0452072i
$820$	−13.7555	−	20.9507i	−0.480362	−	0.731631i
$821$	−4.93247	+	8.54328i	−0.172144	+	0.298163i	−0.939169	−	0.343455i	$-0.888403\pi$
$821$	−4.93247	+	8.54328i	−0.172144	+	0.298163i	0.767025	+	0.641617i	$0.221736\pi$
$822$	−18.0202			−0.628525
$823$	50.6354	+	13.5677i	1.76504	+	0.472941i	0.987729	−	0.156175i	$-0.0499164\pi$
$823$	50.6354	+	13.5677i	1.76504	+	0.472941i	0.777311	+	0.629116i	$0.216583\pi$
$824$		−	11.7069i		−	0.407830i
$825$	6.16427	+	15.5892i	0.214612	+	0.542745i
$826$	17.9792	+	31.1408i	0.625575	+	1.08353i
$827$	−15.1675	+	26.2708i	−0.527425	+	0.913527i	0.472064	+	0.881564i	$0.343509\pi$
$827$	−15.1675	+	26.2708i	−0.527425	+	0.913527i	−0.999489	+	0.0319627i	$0.989824\pi$
$828$	−34.6280			−1.20341
$829$	10.4459	+	2.79898i	0.362802	+	0.0972125i	0.435615	−	0.900133i	$-0.356531\pi$
$829$	10.4459	+	2.79898i	0.362802	+	0.0972125i	−0.0728130	+	0.997346i	$0.523198\pi$
$830$	−1.10925	−	3.35654i	−0.0385027	−	0.116507i
$831$	48.7225	+	13.0552i	1.69017	+	0.452878i
$832$	−0.274007	−	0.158198i	−0.00949949	−	0.00548454i
$833$	8.80756	+	5.08505i	0.305164	+	0.176186i
$834$	−13.6234	−	3.65038i	−0.471739	−	0.126402i
$835$	30.1696	+	15.1820i	1.04406	+	0.525395i
$836$	−3.65628	−	0.979697i	−0.126455	−	0.0338835i
$837$	−2.05695			−0.0710986
$838$	−6.65171	+	11.5211i	−0.229780	+	0.397990i
$839$	11.6320	+	20.1471i	0.401580	+	0.695556i	0.993917	−	0.110134i	$-0.0351280\pi$
$839$	11.6320	+	20.1471i	0.401580	+	0.695556i	−0.592337	+	0.805690i	$0.701795\pi$
$840$	−20.1123	+	13.2050i	−0.693940	+	0.455615i
$841$		−	34.2167i		−	1.17989i
$842$	22.5745	+	6.04882i	0.777969	+	0.208456i
$843$	48.5407			1.67183
$844$	−6.68453	+	11.5779i	−0.230091	+	0.398529i
$845$	24.1124	−	15.8313i	0.829491	−	0.544613i
$846$	−13.9020	+	3.72502i	−0.477960	+	0.128069i
$847$	−37.1826	+	9.96303i	−1.27761	+	0.342334i
$848$	1.83172	+	6.83608i	0.0629016	+	0.234752i
$849$	16.3116	−	60.8756i	0.559812	−	2.08925i
$850$	4.70079	+	2.03666i	0.161236	+	0.0698570i
$851$	28.7270	−	46.7263i	0.984748	−	1.60176i
$852$	−13.3745	−	13.3745i	−0.458203	−	0.458203i
$853$	−11.9490	−	20.6963i	−0.409126	−	0.708627i	0.585666	−	0.810553i	$-0.300833\pi$
$853$	−11.9490	−	20.6963i	−0.409126	−	0.708627i	−0.994792	+	0.101925i	$0.967500\pi$
$854$	−15.4606	+	26.7786i	−0.529052	+	0.916344i
$855$	−18.9272	−	16.8710i	−0.647296	−	0.576975i
$856$	2.18387	+	8.15032i	0.0746432	+	0.278572i
$857$	11.1858			0.382099			0.191049	−	0.981580i	$-0.438811\pi$
$857$	11.1858			0.382099			0.191049	+	0.981580i	$0.438811\pi$
$858$	0.274553	+	1.02465i	0.00937309	+	0.0349808i
$859$	22.0114	+	22.0114i	0.751018	+	0.751018i	0.974669	−	0.223651i	$-0.0717977\pi$
$859$	22.0114	+	22.0114i	0.751018	+	0.751018i	−0.223651	+	0.974669i	$0.571798\pi$
$860$	5.27372	−	10.4799i	0.179832	−	0.357361i
$861$	−120.602			−4.11009
$862$	4.95834	−	4.95834i	0.168882	−	0.168882i
$863$	−14.1094	−	3.78060i	−0.480289	−	0.128693i	0.0105483	−	0.999944i	$-0.496642\pi$
$863$	−14.1094	−	3.78060i	−0.480289	−	0.128693i	−0.490837	+	0.871251i	$0.663309\pi$
$864$	−2.12239	+	0.568694i	−0.0722053	+	0.0193473i
$865$	12.5938	+	2.61092i	0.428200	+	0.0887741i
$866$	−1.26765	+	4.73094i	−0.0430765	+	0.160764i
$867$	−10.7968	+	40.2941i	−0.366678	+	1.36846i
$868$	−3.33540	+	1.92569i	−0.113211	+	0.0653623i
$869$	−1.59400	−	5.94889i	−0.0540728	−	0.201802i
$870$	46.4214	−	2.66642i	1.57383	−	0.0904000i
$871$	0.118508	−	0.442279i	0.00401550	−	0.0149861i
$872$	1.78246	+	0.477608i	0.0603617	+	0.0161739i
$873$	−37.2765	+	21.5216i	−1.26162	+	0.728395i
$874$	−18.8276	−	18.8276i	−0.636853	−	0.636853i
$875$	19.3389	+	41.7341i	0.653776	+	1.41087i
$876$	−24.2857	+	14.0213i	−0.820537	+	0.473737i
$877$	15.8644	+	15.8644i	0.535702	+	0.535702i	0.922264	−	0.386562i	$-0.126337\pi$
$877$	15.8644	+	15.8644i	0.535702	+	0.535702i	−0.386562	+	0.922264i	$0.626337\pi$
$878$	10.7482	+	10.7482i	0.362735	+	0.362735i
$879$	11.3341	+	19.6313i	0.382291	+	0.662148i
$880$	1.57325	+	2.39618i	0.0530341	+	0.0807753i
$881$	8.88328	+	5.12876i	0.299285	+	0.172792i	0.642122	−	0.766603i	$-0.278054\pi$
$881$	8.88328	+	5.12876i	0.299285	+	0.172792i	−0.342836	+	0.939395i	$0.611388\pi$
$882$			38.1167i			1.28345i
$883$	−21.0638	+	36.4835i	−0.708853	+	1.22777i	0.256430	+	0.966563i	$0.417454\pi$
$883$	−21.0638	+	36.4835i	−0.708853	+	1.22777i	−0.965283	+	0.261206i	$0.915880\pi$
$884$	0.280749	+	0.162091i	0.00944263	+	0.00545170i
$885$	51.0301	−	2.93114i	1.71536	−	0.0985291i
$886$	0.933300	+	0.250077i	0.0313548	+	0.00840150i
$887$	24.3907	−	24.3907i	0.818960	−	0.818960i	−0.166997	−	0.985957i	$-0.553407\pi$
$887$	24.3907	−	24.3907i	0.818960	−	0.818960i	0.985957	+	0.166997i	$0.0534070\pi$
$888$	4.54036	−	15.2470i	0.152364	−	0.511655i
$889$		−	45.3849i		−	1.52216i
$890$	0.770326	+	2.33097i	0.0258214	+	0.0781342i
$891$	−6.40997	−	3.70080i	−0.214742	−	0.123981i
$892$	0.616869	+	2.30219i	0.0206543	+	0.0770829i
$893$	−9.58399	−	5.53332i	−0.320716	−	0.185165i
$894$	36.2315	+	36.2315i	1.21176	+	1.21176i
$895$	29.1241	+	25.9601i	0.973512	+	0.867751i
$896$	−2.90911	+	2.90911i	−0.0971866	+	0.0971866i
$897$	−1.93126	+	7.20756i	−0.0644829	+	0.240653i
$898$	−16.3546	+	16.3546i	−0.545759	+	0.545759i
$899$	7.44317			0.248244
$900$	2.19850	+	19.0744i	0.0732833	+	0.635813i
$901$	−1.87679	−	7.00429i	−0.0625251	−	0.233347i
$902$			14.3685i			0.478419i
$903$	−28.2271	−	48.8907i	−0.939338	−	1.62698i
$904$	13.0794	−	7.55141i	0.435015	−	0.251156i
$905$	15.0208	+	7.55881i	0.499308	+	0.251263i
$906$	−23.2654	+	6.23395i	−0.772941	+	0.207109i
$907$	−10.3734	+	17.9673i	−0.344443	+	0.596594i	−0.985252	−	0.171107i	$-0.945266\pi$
$907$	−10.3734	+	17.9673i	−0.344443	+	0.596594i	0.640809	+	0.767700i	$0.278599\pi$
$908$	−8.05545	−	13.9524i	−0.267330	−	0.463028i
$909$	−33.7742	−	58.4986i	−1.12022	−	1.94028i
$910$	0.913320	+	2.76366i	0.0302763	+	0.0916144i
$911$	35.2946	−	35.2946i	1.16936	−	1.16936i	0.187001	−	0.982360i	$-0.440123\pi$
$911$	35.2946	−	35.2946i	1.16936	−	1.16936i	0.982360	−	0.187001i	$-0.0598768\pi$
$912$	−6.68794	−	3.86128i	−0.221460	−	0.127860i
$913$	−0.524537	+	1.95760i	−0.0173596	+	0.0647871i
$914$			0.455088i			0.0150530i
$915$	24.1237	+	36.7424i	0.797505	+	1.21467i
$916$	−15.8140	+	9.13024i	−0.522510	+	0.301672i
$917$			80.8094i			2.66856i
$918$	2.17462	−	0.582687i	0.0717730	−	0.0192315i
$919$	−9.68968	+	9.68968i	−0.319633	+	0.319633i	−0.848626	−	0.528993i	$-0.822570\pi$
$919$	−9.68968	+	9.68968i	−0.319633	+	0.319633i	0.528993	+	0.848626i	$0.322570\pi$
$920$	1.15627	+	20.1303i	0.0381212	+	0.663676i
$921$	−2.03321	+	3.52162i	−0.0669965	+	0.116041i
$922$	−1.76440	+	0.472769i	−0.0581074	+	0.0155698i
$923$	−1.98163	+	1.14409i	−0.0652261	+	0.0376583i
$924$	13.7935			0.453772
$925$	−27.5625	−	12.8573i	−0.906249	−	0.422745i
$926$	−19.7169			−0.647939
$927$	−38.9332	+	22.4781i	−1.27874	+	0.738278i
$928$	7.67997	−	2.05784i	0.252107	−	0.0675520i
$929$	19.7848	−	34.2682i	0.649118	−	1.12430i	−0.334216	−	0.942496i	$-0.608472\pi$
$929$	19.7848	−	34.2682i	0.649118	−	1.12430i	0.983334	−	0.181808i	$-0.0581950\pi$
$930$	0.313945	+	5.46568i	0.0102947	+	0.179227i
$931$	−20.7244	+	20.7244i	−0.679216	+	0.679216i
$932$	−23.0424	+	6.17420i	−0.754780	+	0.202243i
$933$		−	66.6780i		−	2.18294i
$934$	−4.70697	+	2.71757i	−0.154017	+	0.0889215i
$935$	−1.61196	−	2.45514i	−0.0527166	−	0.0802917i
$936$			1.21501i			0.0397137i
$937$	−0.393853	+	1.46988i	−0.0128666	+	0.0480188i	−0.972061	−	0.234730i	$-0.924580\pi$
$937$	−0.393853	+	1.46988i	−0.0128666	+	0.0480188i	0.959194	+	0.282749i	$0.0912462\pi$
$938$	−5.15617	−	2.97691i	−0.168355	−	0.0971997i
$939$	9.20312	−	9.20312i	0.300333	−	0.300333i
$940$	2.62968	+	7.95726i	0.0857706	+	0.259537i
$941$	−26.0398	−	45.1023i	−0.848875	−	1.47029i	−0.882213	−	0.470850i	$-0.843947\pi$
$941$	−26.0398	−	45.1023i	−0.848875	−	1.47029i	0.0333387	−	0.999444i	$-0.489386\pi$
$942$	31.7108	+	54.9247i	1.03319	+	1.78954i
$943$	−50.5354	+	87.5299i	−1.64566	+	2.85037i
$944$	8.44244	−	2.26214i	0.274778	−	0.0736265i
$945$	18.0562	+	9.08629i	0.587368	+	0.295577i
$946$	−5.82485	+	3.36298i	−0.189382	+	0.109340i
$947$	−5.44950	−	9.43882i	−0.177085	−	0.306720i	0.763796	−	0.645458i	$-0.223333\pi$
$947$	−5.44950	−	9.43882i	−0.177085	−	0.306720i	−0.940881	+	0.338738i	$0.890000\pi$
$948$		−	12.5649i		−	0.408088i
$949$	0.878041	+	3.27689i	0.0285024	+	0.106373i
$950$	−9.17560	+	11.5663i	−0.297696	+	0.375260i
$951$	61.7238			2.00153
$952$	2.98069	−	2.98069i	0.0966048	−	0.0966048i
$953$	1.41345	−	5.27508i	0.0457862	−	0.170877i	−0.939247	−	0.343243i	$-0.888475\pi$
$953$	1.41345	−	5.27508i	0.0457862	−	0.170877i	0.985033	+	0.172366i	$0.0551413\pi$
$954$	19.2174	−	19.2174i	0.622187	−	0.622187i
$955$	−36.3417	−	32.3936i	−1.17599	−	1.04823i
$956$	−2.32497	−	2.32497i	−0.0751949	−	0.0751949i
$957$	−23.0858	−	13.3286i	−0.746258	−	0.430852i
$958$	−1.75560	−	6.55198i	−0.0567208	−	0.211685i
$959$	24.5489	+	14.1733i	0.792726	+	0.457681i
$960$	1.83505	+	5.55277i	0.0592260	+	0.179215i
$961$		−	30.1236i		−	0.971730i
$962$	−1.63950	−	1.00795i	−0.0528597	−	0.0324978i
$963$	22.9120	−	22.9120i	0.738328	−	0.738328i
$964$	−0.428531	−	0.114824i	−0.0138020	−	0.00369825i
$965$	−25.6724	+	1.47461i	−0.826425	+	0.0474694i
$966$	84.0270	+	48.5130i	2.70352	+	1.56088i
$967$	−5.17384	+	8.96135i	−0.166379	+	0.288178i	−0.937144	−	0.348942i	$-0.886541\pi$
$967$	−5.17384	+	8.96135i	−0.166379	+	0.288178i	0.770765	+	0.637120i	$0.219874\pi$
$968$			9.35664i			0.300734i
$969$	6.85250	+	3.95629i	0.220134	+	0.127094i
$970$	13.7559	+	20.9513i	0.441674	+	0.672706i
$971$	18.4005	+	31.8706i	0.590499	+	1.02277i	0.994165	+	0.107868i	$0.0344025\pi$
$971$	18.4005	+	31.8706i	0.590499	+	1.02277i	−0.403666	+	0.914907i	$0.632264\pi$
$972$	−15.3388	−	15.3388i	−0.491991	−	0.491991i
$973$	15.6881	+	15.6881i	0.502936	+	0.502936i
$974$	5.73878	−	3.31328i	0.183882	−	0.106164i
$975$	4.09281	+	0.606210i	0.131075	+	0.0194142i
$976$	5.31455	+	5.31455i	0.170115	+	0.170115i
$977$	−20.9252	+	12.0811i	−0.669455	+	0.386510i	−0.795870	−	0.605467i	$-0.792986\pi$
$977$	−20.9252	+	12.0811i	−0.669455	+	0.386510i	0.126415	+	0.991977i	$0.459653\pi$
$978$	−30.3025	−	8.11952i	−0.968966	−	0.259634i
$979$	0.364268	−	1.35947i	0.0116421	−	0.0434487i
$980$	22.1584	−	1.27276i	0.707823	−	0.0406570i
$981$	−1.83408	−	6.84488i	−0.0585577	−	0.218540i
$982$	−29.1335	+	16.8203i	−0.929689	+	0.536756i
$983$	8.28207	−	30.9091i	0.264157	−	0.985848i	−0.698607	−	0.715505i	$-0.746196\pi$
$983$	8.28207	−	30.9091i	0.264157	−	0.985848i	0.962764	−	0.270342i	$-0.0871368\pi$
$984$	−7.58707	+	28.3153i	−0.241867	+	0.902659i
$985$	16.0268	+	3.32266i	0.510657	+	0.105869i
$986$	−7.86894	+	2.10848i	−0.250598	+	0.0671476i
$987$	38.9527	+	10.4374i	1.23988	+	0.332225i
$988$	−0.660611	+	0.660611i	−0.0210168	+	0.0210168i
$989$	−47.3117			−1.50442
$990$	4.94814	−	9.83291i	0.157262	−	0.312510i
$991$	−8.81333	−	8.81333i	−0.279965	−	0.279965i	0.553130	−	0.833095i	$-0.313433\pi$
$991$	−8.81333	−	8.81333i	−0.279965	−	0.279965i	−0.833095	+	0.553130i	$0.813433\pi$
$992$	0.242292	+	0.904244i	0.00769276	+	0.0287098i
$993$	−78.4439			−2.48934
$994$	7.70073	+	28.7395i	0.244252	+	0.911562i
$995$	−28.6040	−	25.4965i	−0.906807	−	0.808293i
$996$	−2.06736	+	3.58077i	−0.0655068	+	0.113461i
$997$	28.5580	+	49.4638i	0.904440	+	1.56654i	0.821667	+	0.569967i	$0.193044\pi$
$997$	28.5580	+	49.4638i	0.904440	+	1.56654i	0.0827723	+	0.996568i	$0.473623\pi$
$998$	−10.5271	−	10.5271i	−0.333230	−	0.333230i
$999$	−13.0006	+	3.10130i	−0.411322	+	0.0981207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.f.177.2	yes	32
5.3	odd	4		370.2.q.f.103.2	yes	32
37.23	odd	12		370.2.q.f.97.2	✓	32
185.23	even	12	inner	370.2.r.f.23.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.f.97.2	✓	32	37.23	odd	12
370.2.q.f.103.2	yes	32	5.3	odd	4
370.2.r.f.23.2	yes	32	185.23	even	12	inner
370.2.r.f.177.2	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.52625 + 0.676906i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.128227 + 2.23239i) q^{5} +(1.84934 - 1.84934i) q^{6} +(-3.97392 + 1.06481i) q^{7} +1.00000i q^{8} +(3.32566 - 1.92007i) q^{9} +(-1.22724 - 1.86919i) q^{10} +1.28194i q^{11} +(-0.676906 + 2.52625i) q^{12} +(0.274007 + 0.158198i) q^{13} +(2.90911 - 2.90911i) q^{14} +(-1.83505 - 5.55277i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.512303 + 0.887335i) q^{17} +(-1.92007 + 3.32566i) q^{18} +(-2.85215 + 0.764232i) q^{19} +(1.99742 + 1.00515i) q^{20} +(9.31834 - 5.37994i) q^{21} +(-0.640968 - 1.11019i) q^{22} -9.01738i q^{23} +(-0.676906 - 2.52625i) q^{24} +(-4.96712 + 0.572505i) q^{25} -0.316396 q^{26} +(-1.55370 + 1.55370i) q^{27} +(-1.06481 + 3.97392i) q^{28} +(5.62213 - 5.62213i) q^{29} +(4.36559 + 3.89132i) q^{30} +(0.661953 + 0.661953i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.867750 - 3.23849i) q^{33} +(-0.887335 - 0.512303i) q^{34} +(-2.88663 - 8.73480i) q^{35} -3.84014i q^{36} +(5.18181 + 3.18573i) q^{37} +(2.08792 - 2.08792i) q^{38} +(-0.799296 - 0.214171i) q^{39} +(-2.23239 + 0.128227i) q^{40} +(-9.70680 - 5.60422i) q^{41} +(-5.37994 + 9.31834i) q^{42} -5.24672i q^{43} +(1.11019 + 0.640968i) q^{44} +(4.71278 + 7.17795i) q^{45} +(4.50869 + 7.80928i) q^{46} +(2.65016 + 2.65016i) q^{47} +(1.84934 + 1.84934i) q^{48} +(8.59605 - 4.96293i) q^{49} +(4.01540 - 2.97936i) q^{50} +(-1.89485 - 1.89485i) q^{51} +(0.274007 - 0.158198i) q^{52} +(-6.83608 - 1.83172i) q^{53} +(0.568694 - 2.12239i) q^{54} +(-2.86178 + 0.164379i) q^{55} +(-1.06481 - 3.97392i) q^{56} +(6.68794 - 3.86128i) q^{57} +(-2.05784 + 7.67997i) q^{58} +(-2.26214 + 8.44244i) q^{59} +(-5.72637 - 1.18718i) q^{60} +(-7.25981 + 1.94526i) q^{61} +(-0.904244 - 0.242292i) q^{62} +(-11.1714 + 11.1714i) q^{63} -1.00000 q^{64} +(-0.318025 + 0.631976i) q^{65} +(2.37074 + 2.37074i) q^{66} +(-0.374556 - 1.39786i) q^{67} +1.02461 q^{68} +(6.10392 + 22.7802i) q^{69} +(6.86729 + 6.12124i) q^{70} +(-3.61602 + 6.26312i) q^{71} +(1.92007 + 3.32566i) q^{72} +(7.58180 + 7.58180i) q^{73} +(-6.08044 - 0.168023i) q^{74} +(12.1606 - 4.80856i) q^{75} +(-0.764232 + 2.85215i) q^{76} +(-1.36502 - 5.09431i) q^{77} +(0.799296 - 0.214171i) q^{78} +(-4.64055 + 1.24343i) q^{79} +(1.86919 - 1.22724i) q^{80} +(-2.88688 + 5.00023i) q^{81} +11.2084 q^{82} +(1.52707 + 0.409176i) q^{83} -10.7599i q^{84} +(-1.91518 + 1.25744i) q^{85} +(2.62336 + 4.54379i) q^{86} +(-10.3972 + 18.0086i) q^{87} -1.28194 q^{88} +(-1.06048 - 0.284155i) q^{89} +(-7.67036 - 3.85990i) q^{90} +(-1.25733 - 0.336902i) q^{91} +(-7.80928 - 4.50869i) q^{92} +(-2.12034 - 1.22418i) q^{93} +(-3.62018 - 0.970024i) q^{94} +(-2.07179 - 6.26912i) q^{95} +(-2.52625 - 0.676906i) q^{96} -11.2088 q^{97} +(-4.96293 + 8.59605i) q^{98} +(2.46140 + 4.26328i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{3} + 16 q^{4} + 6 q^{5} + 8 q^{6} + 2 q^{7} - 12 q^{9} + 6 q^{10} - 2 q^{12} + 12 q^{13} + 8 q^{14} - 8 q^{15} - 16 q^{16} - 6 q^{17} - 24 q^{18} - 2 q^{19} + 6 q^{20} - 54 q^{21} + 12 q^{22}+ \cdots + 26 q^{99}+O(q^{100}) \) 32 * q - 10 * q^3 + 16 * q^4 + 6 * q^5 + 8 * q^6 + 2 * q^7 - 12 * q^9 + 6 * q^10 - 2 * q^12 + 12 * q^13 + 8 * q^14 - 8 * q^15 - 16 * q^16 - 6 * q^17 - 24 * q^18 - 2 * q^19 + 6 * q^20 - 54 * q^21 + 12 * q^22 - 2 * q^24 - 14 * q^25 + 20 * q^26 - 40 * q^27 + 10 * q^28 - 6 * q^29 - 8 * q^30 - 4 * q^31 - 22 * q^33 + 12 * q^34 + 24 * q^37 - 26 * q^38 + 58 * q^39 + 18 * q^41 - 2 * q^42 - 6 * q^44 - 18 * q^45 + 6 * q^46 + 18 * q^47 + 8 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 + 12 * q^52 - 20 * q^54 + 42 * q^55 + 10 * q^56 + 36 * q^57 + 30 * q^58 - 42 * q^59 - 16 * q^60 - 46 * q^61 - 10 * q^62 - 32 * q^64 - 18 * q^65 + 4 * q^66 + 46 * q^67 - 12 * q^68 + 66 * q^69 + 12 * q^70 - 12 * q^71 + 24 * q^72 + 28 * q^73 - 16 * q^74 - 20 * q^75 - 28 * q^76 + 24 * q^77 - 58 * q^78 - 38 * q^79 + 56 * q^81 - 48 * q^82 + 12 * q^83 + 8 * q^85 - 16 * q^86 - 2 * q^87 + 24 * q^88 - 18 * q^89 + 52 * q^90 + 4 * q^91 - 12 * q^92 + 36 * q^93 - 30 * q^94 + 30 * q^95 - 10 * q^96 - 12 * q^97 - 16 * q^98 + 26 * q^99

Introduction

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