LMFDB - Embedded newform 390.2.t.a.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(307,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("390.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.t (of order $4$, degree $2$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6x^{10} - 24x^{9} + 18x^{8} + 40x^{7} - 82x^{6} + 12x^{5} + 228x^{4} - 284x^{3} + 124x^{2} - 16x + 2 $ x^12 + 6x^10 - 24x^9 + 18x^8 + 40x^7 - 82x^6 + 12x^5 + 228x^4 - 284x^3 + 124x^2 - 16x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Root			$0.0572576 - 0.138232i$ of defining polynomial
Character	$\chi$	$=$	390.307
Dual form			390.2.t.a.343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.20289 + 0.383740i) q^{5} +(0.707107 + 0.707107i) q^{6} +1.52873 q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.20289 + 0.383740i) q^{5} +(0.707107 + 0.707107i) q^{6} +1.52873 q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.383740 + 2.20289i) q^{10} +(2.70115 - 2.70115i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.17182 + 1.71451i) q^{13} -1.52873i q^{14} +(1.28634 - 1.82903i) q^{15} +1.00000 q^{16} +(4.03439 - 4.03439i) q^{17} -1.00000 q^{18} +(1.06701 - 1.06701i) q^{19} +(2.20289 - 0.383740i) q^{20} +(-1.08097 + 1.08097i) q^{21} +(-2.70115 - 2.70115i) q^{22} +(-0.485915 - 0.485915i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(4.70549 - 1.69068i) q^{25} +(1.71451 - 3.17182i) q^{26} +(0.707107 + 0.707107i) q^{27} -1.52873 q^{28} +2.28429i q^{29} +(-1.82903 - 1.28634i) q^{30} +(1.00000 + 1.00000i) q^{31} -1.00000i q^{32} +3.82000i q^{33} +(-4.03439 - 4.03439i) q^{34} +(-3.36763 + 0.586634i) q^{35} +1.00000i q^{36} +7.96284 q^{37} +(-1.06701 - 1.06701i) q^{38} +(-3.45516 + 1.03047i) q^{39} +(-0.383740 - 2.20289i) q^{40} +(-8.22579 - 8.22579i) q^{41} +(1.08097 + 1.08097i) q^{42} +(5.76210 + 5.76210i) q^{43} +(-2.70115 + 2.70115i) q^{44} +(0.383740 + 2.20289i) q^{45} +(-0.485915 + 0.485915i) q^{46} +2.92343 q^{47} +(-0.707107 + 0.707107i) q^{48} -4.66299 q^{49} +(-1.69068 - 4.70549i) q^{50} +5.70549i q^{51} +(-3.17182 - 1.71451i) q^{52} +(-3.69068 + 3.69068i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-4.91381 + 6.98689i) q^{55} +1.52873i q^{56} +1.50898i q^{57} +2.28429 q^{58} +(-4.50044 - 4.50044i) q^{59} +(-1.28634 + 1.82903i) q^{60} -2.43047 q^{61} +(1.00000 - 1.00000i) q^{62} -1.52873i q^{63} -1.00000 q^{64} +(-7.64511 - 2.55973i) q^{65} +3.82000 q^{66} +3.79906i q^{67} +(-4.03439 + 4.03439i) q^{68} +0.687188 q^{69} +(0.586634 + 3.36763i) q^{70} +(10.7079 + 10.7079i) q^{71} +1.00000 q^{72} -10.3127i q^{73} -7.96284i q^{74} +(-2.13179 + 4.52277i) q^{75} +(-1.06701 + 1.06701i) q^{76} +(4.12932 - 4.12932i) q^{77} +(1.03047 + 3.45516i) q^{78} -1.53731i q^{79} +(-2.20289 + 0.383740i) q^{80} -1.00000 q^{81} +(-8.22579 + 8.22579i) q^{82} +7.72020 q^{83} +(1.08097 - 1.08097i) q^{84} +(-7.33918 + 10.4355i) q^{85} +(5.76210 - 5.76210i) q^{86} +(-1.61524 - 1.61524i) q^{87} +(2.70115 + 2.70115i) q^{88} +(-7.21676 - 7.21676i) q^{89} +(2.20289 - 0.383740i) q^{90} +(4.84885 + 2.62102i) q^{91} +(0.485915 + 0.485915i) q^{92} -1.41421 q^{93} -2.92343i q^{94} +(-1.94106 + 2.75997i) q^{95} +(0.707107 + 0.707107i) q^{96} +6.36597i q^{97} +4.66299i q^{98} +(-2.70115 - 2.70115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 4 q^{5}+O(q^{10}) $ 12 * q - 12 * q^4 - 4 * q^5	$ 12 q - 12 q^{4} - 4 q^{5} + 4 q^{11} + 20 q^{13} - 4 q^{15} + 12 q^{16} + 8 q^{17} - 12 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{25} - 4 q^{26} + 4 q^{30} + 12 q^{31} - 8 q^{34} + 12 q^{35} - 16 q^{37} + 4 q^{38} - 12 q^{39} + 8 q^{41} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{47} - 20 q^{49} + 8 q^{50} - 20 q^{52} - 16 q^{53} - 12 q^{55} - 40 q^{58} + 20 q^{59} + 4 q^{60} + 16 q^{61} + 12 q^{62} - 12 q^{64} - 32 q^{65} - 16 q^{66} - 8 q^{68} - 32 q^{69} - 20 q^{70} - 32 q^{71} + 12 q^{72} + 4 q^{76} + 16 q^{77} - 4 q^{80} - 12 q^{81} + 8 q^{82} + 32 q^{83} + 8 q^{84} + 12 q^{85} + 16 q^{86} + 20 q^{87} + 4 q^{88} + 16 q^{89} + 4 q^{90} - 28 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^11 + 20 * q^13 - 4 * q^15 + 12 * q^16 + 8 * q^17 - 12 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^25 - 4 * q^26 + 4 * q^30 + 12 * q^31 - 8 * q^34 + 12 * q^35 - 16 * q^37 + 4 * q^38 - 12 * q^39 + 8 * q^41 + 8 * q^42 + 16 * q^43 - 4 * q^44 + 32 * q^47 - 20 * q^49 + 8 * q^50 - 20 * q^52 - 16 * q^53 - 12 * q^55 - 40 * q^58 + 20 * q^59 + 4 * q^60 + 16 * q^61 + 12 * q^62 - 12 * q^64 - 32 * q^65 - 16 * q^66 - 8 * q^68 - 32 * q^69 - 20 * q^70 - 32 * q^71 + 12 * q^72 + 4 * q^76 + 16 * q^77 - 4 * q^80 - 12 * q^81 + 8 * q^82 + 32 * q^83 + 8 * q^84 + 12 * q^85 + 16 * q^86 + 20 * q^87 + 4 * q^88 + 16 * q^89 + 4 * q^90 - 28 * q^91 - 8 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	−2.20289	+	0.383740i	−0.985164	+	0.171614i
$5$	−2.20289	+	0.383740i	−0.985164	+	0.171614i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	1.52873			0.577805			0.288903	−	0.957359i	$-0.406710\pi$
$7$	1.52873			0.577805			0.288903	+	0.957359i	$0.406710\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	0.383740	+	2.20289i	0.121349	+	0.696616i
$11$	2.70115	−	2.70115i	0.814427	−	0.814427i	−0.170867	−	0.985294i	$-0.554657\pi$
$11$	2.70115	−	2.70115i	0.814427	−	0.814427i	0.985294	+	0.170867i	$0.0546568\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	3.17182	+	1.71451i	0.879705	+	0.475520i
$13$	3.17182	+	1.71451i	0.879705	+	0.475520i
$14$		−	1.52873i		−	0.408570i
$15$	1.28634	−	1.82903i	0.332131	−	0.472253i
$16$	1.00000			0.250000
$17$	4.03439	−	4.03439i	0.978483	−	0.978483i	−0.0212904	−	0.999773i	$-0.506777\pi$
$17$	4.03439	−	4.03439i	0.978483	−	0.978483i	0.999773	+	0.0212904i	$0.00677744\pi$
$18$	−1.00000			−0.235702
$19$	1.06701	−	1.06701i	0.244790	−	0.244790i	−0.574039	−	0.818828i	$-0.694624\pi$
$19$	1.06701	−	1.06701i	0.244790	−	0.244790i	0.818828	+	0.574039i	$0.194624\pi$
$20$	2.20289	−	0.383740i	0.492582	−	0.0858069i
$21$	−1.08097	+	1.08097i	−0.235888	+	0.235888i
$22$	−2.70115	−	2.70115i	−0.575887	−	0.575887i
$23$	−0.485915	−	0.485915i	−0.101320	−	0.101320i	0.654630	−	0.755950i	$-0.272825\pi$
$23$	−0.485915	−	0.485915i	−0.101320	−	0.101320i	−0.755950	+	0.654630i	$0.772825\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	4.70549	−	1.69068i	0.941097	−	0.338136i
$26$	1.71451	−	3.17182i	0.336243	−	0.622045i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−1.52873			−0.288903
$29$			2.28429i			0.424183i	0.977250	+	0.212091i	$0.0680275\pi$
$29$			2.28429i			0.424183i	−0.977250	+	0.212091i	$0.931973\pi$
$30$	−1.82903	−	1.28634i	−0.333933	−	0.234852i
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	0.791184	−	0.611578i	$-0.209465\pi$
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	−0.611578	+	0.791184i	$0.709465\pi$
$32$		−	1.00000i		−	0.176777i
$33$			3.82000i			0.664977i
$34$	−4.03439	−	4.03439i	−0.691892	−	0.691892i
$35$	−3.36763	+	0.586634i	−0.569233	+	0.0991593i
$36$			1.00000i			0.166667i
$37$	7.96284			1.30908			0.654541	−	0.756026i	$-0.272862\pi$
$37$	7.96284			1.30908			0.654541	+	0.756026i	$0.272862\pi$
$38$	−1.06701	−	1.06701i	−0.173092	−	0.173092i
$39$	−3.45516	+	1.03047i	−0.553268	+	0.165008i
$40$	−0.383740	−	2.20289i	−0.0606746	−	0.348308i
$41$	−8.22579	−	8.22579i	−1.28465	−	1.28465i	−0.937990	−	0.346663i	$-0.887315\pi$
$41$	−8.22579	−	8.22579i	−1.28465	−	1.28465i	−0.346663	−	0.937990i	$-0.612685\pi$
$42$	1.08097	+	1.08097i	0.166798	+	0.166798i
$43$	5.76210	+	5.76210i	0.878711	+	0.878711i	0.993401	−	0.114690i	$-0.0365874\pi$
$43$	5.76210	+	5.76210i	0.878711	+	0.878711i	−0.114690	+	0.993401i	$0.536587\pi$
$44$	−2.70115	+	2.70115i	−0.407214	+	0.407214i
$45$	0.383740	+	2.20289i	0.0572046	+	0.328388i
$46$	−0.485915	+	0.485915i	−0.0716443	+	0.0716443i
$47$	2.92343			0.426426			0.213213	−	0.977006i	$-0.431607\pi$
$47$	2.92343			0.426426			0.213213	+	0.977006i	$0.431607\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	−4.66299			−0.666141
$50$	−1.69068	−	4.70549i	−0.239098	−	0.665456i
$51$			5.70549i			0.798928i
$52$	−3.17182	−	1.71451i	−0.439852	−	0.237760i
$53$	−3.69068	+	3.69068i	−0.506954	+	0.506954i	−0.913590	−	0.406636i	$-0.866702\pi$
$53$	−3.69068	+	3.69068i	−0.506954	+	0.506954i	0.406636	+	0.913590i	$0.366702\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	−4.91381	+	6.98689i	−0.662578	+	0.942112i
$56$			1.52873i			0.204285i
$57$			1.50898i			0.199870i
$58$	2.28429			0.299943
$59$	−4.50044	−	4.50044i	−0.585908	−	0.585908i	0.350613	−	0.936521i	$-0.385973\pi$
$59$	−4.50044	−	4.50044i	−0.585908	−	0.585908i	−0.936521	+	0.350613i	$0.885973\pi$
$60$	−1.28634	+	1.82903i	−0.166065	+	0.236126i
$61$	−2.43047			−0.311190			−0.155595	−	0.987821i	$-0.549729\pi$
$61$	−2.43047			−0.311190			−0.155595	+	0.987821i	$0.549729\pi$
$62$	1.00000	−	1.00000i	0.127000	−	0.127000i
$63$		−	1.52873i		−	0.192602i
$64$	−1.00000			−0.125000
$65$	−7.64511	−	2.55973i	−0.948260	−	0.317496i
$66$	3.82000			0.470210
$67$			3.79906i			0.464129i	0.972700	+	0.232064i	$0.0745480\pi$
$67$			3.79906i			0.464129i	−0.972700	+	0.232064i	$0.925452\pi$
$68$	−4.03439	+	4.03439i	−0.489241	+	0.489241i
$69$	0.687188			0.0827277
$70$	0.586634	+	3.36763i	0.0701162	+	0.402509i
$71$	10.7079	+	10.7079i	1.27080	+	1.27080i	0.945670	+	0.325128i	$0.105407\pi$
$71$	10.7079	+	10.7079i	1.27080	+	1.27080i	0.325128	+	0.945670i	$0.394593\pi$
$72$	1.00000			0.117851
$73$		−	10.3127i		−	1.20701i	−0.797358	−	0.603506i	$-0.793770\pi$
$73$		−	10.3127i		−	1.20701i	0.797358	−	0.603506i	$-0.206230\pi$
$74$		−	7.96284i		−	0.925661i
$75$	−2.13179	+	4.52277i	−0.246158	+	0.522245i
$76$	−1.06701	+	1.06701i	−0.122395	+	0.122395i
$77$	4.12932	−	4.12932i	0.470580	−	0.470580i
$78$	1.03047	+	3.45516i	0.116678	+	0.391220i
$79$		−	1.53731i		−	0.172961i	−0.996254	−	0.0864803i	$-0.972438\pi$
$79$		−	1.53731i		−	0.172961i	0.996254	−	0.0864803i	$-0.0275620\pi$
$80$	−2.20289	+	0.383740i	−0.246291	+	0.0429034i
$81$	−1.00000			−0.111111
$82$	−8.22579	+	8.22579i	−0.908387	+	0.908387i
$83$	7.72020			0.847402			0.423701	−	0.905802i	$-0.360731\pi$
$83$	7.72020			0.847402			0.423701	+	0.905802i	$0.360731\pi$
$84$	1.08097	−	1.08097i	0.117944	−	0.117944i
$85$	−7.33918	+	10.4355i	−0.796045	+	1.13189i
$86$	5.76210	−	5.76210i	0.621343	−	0.621343i
$87$	−1.61524	−	1.61524i	−0.173172	−	0.173172i
$88$	2.70115	+	2.70115i	0.287944	+	0.287944i
$89$	−7.21676	−	7.21676i	−0.764976	−	0.764976i	0.212242	−	0.977217i	$-0.431924\pi$
$89$	−7.21676	−	7.21676i	−0.764976	−	0.764976i	−0.977217	+	0.212242i	$0.931924\pi$
$90$	2.20289	−	0.383740i	0.232205	−	0.0404498i
$91$	4.84885	+	2.62102i	0.508298	+	0.274758i
$92$	0.485915	+	0.485915i	0.0506602	+	0.0506602i
$93$	−1.41421			−0.146647
$94$		−	2.92343i		−	0.301529i
$95$	−1.94106	+	2.75997i	−0.199149	+	0.283167i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$			6.36597i			0.646366i	0.946336	+	0.323183i	$0.104753\pi$
$97$			6.36597i			0.646366i	−0.946336	+	0.323183i	$0.895247\pi$
$98$			4.66299i			0.471033i
$99$	−2.70115	−	2.70115i	−0.271476	−	0.271476i
$100$	−4.70549	+	1.69068i	−0.470549	+	0.169068i
$101$		−	10.5668i		−	1.05143i	−0.850660	−	0.525717i	$-0.823797\pi$
$101$		−	10.5668i		−	1.05143i	0.850660	−	0.525717i	$-0.176203\pi$
$102$	5.70549			0.564927
$103$	−4.86744	−	4.86744i	−0.479603	−	0.479603i	0.425402	−	0.905005i	$-0.360133\pi$
$103$	−4.86744	−	4.86744i	−0.479603	−	0.479603i	−0.905005	+	0.425402i	$0.860133\pi$
$104$	−1.71451	+	3.17182i	−0.168122	+	0.311023i
$105$	1.96646	−	2.79609i	0.191907	−	0.272870i
$106$	3.69068	+	3.69068i	0.358470	+	0.358470i
$107$	13.0918	+	13.0918i	1.26563	+	1.26563i	0.948323	+	0.317307i	$0.102779\pi$
$107$	13.0918	+	13.0918i	1.26563	+	1.26563i	0.317307	+	0.948323i	$0.397221\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−0.124070	+	0.124070i	−0.0118838	+	0.0118838i	−0.713024	−	0.701140i	$-0.752675\pi$
$109$	−0.124070	+	0.124070i	−0.0118838	+	0.0118838i	0.701140	+	0.713024i	$0.252675\pi$
$110$	6.98689	+	4.91381i	0.666173	+	0.468513i
$111$	−5.63058	+	5.63058i	−0.534431	+	0.534431i
$112$	1.52873			0.144451
$113$	−3.69674	+	3.69674i	−0.347760	+	0.347760i	−0.859275	−	0.511514i	$-0.829085\pi$
$113$	−3.69674	+	3.69674i	−0.347760	+	0.347760i	0.511514	+	0.859275i	$0.329085\pi$
$114$	1.50898			0.141329
$115$	1.25688	+	0.883955i	0.117205	+	0.0824292i
$116$		−	2.28429i		−	0.212091i
$117$	1.71451	−	3.17182i	0.158507	−	0.293235i
$118$	−4.50044	+	4.50044i	−0.414299	+	0.414299i
$119$	6.16749	−	6.16749i	0.565372	−	0.565372i
$120$	1.82903	+	1.28634i	0.166967	+	0.117426i
$121$		−	3.59242i		−	0.326583i
$122$			2.43047i			0.220044i
$123$	11.6330			1.04891
$124$	−1.00000	−	1.00000i	−0.0898027	−	0.0898027i
$125$	−9.71691	+	5.53007i	−0.869107	+	0.494624i
$126$	−1.52873			−0.136190
$127$	−10.2359	+	10.2359i	−0.908290	+	0.908290i	−0.996134	−	0.0878440i	$-0.972002\pi$
$127$	−10.2359	+	10.2359i	−0.908290	+	0.908290i	0.0878440	+	0.996134i	$0.472002\pi$
$128$			1.00000i			0.0883883i
$129$	−8.14884			−0.717465
$130$	−2.55973	+	7.64511i	−0.224503	+	0.670521i
$131$	−11.8485			−1.03521			−0.517606	−	0.855619i	$-0.673177\pi$
$131$	−11.8485			−1.03521			−0.517606	+	0.855619i	$0.673177\pi$
$132$		−	3.82000i		−	0.332489i
$133$	1.63117	−	1.63117i	0.141441	−	0.141441i
$134$	3.79906			0.328189
$135$	−1.82903	−	1.28634i	−0.157418	−	0.110710i
$136$	4.03439	+	4.03439i	0.345946	+	0.345946i
$137$	−11.9361			−1.01977			−0.509886	−	0.860242i	$-0.670312\pi$
$137$	−11.9361			−1.01977			−0.509886	+	0.860242i	$0.670312\pi$
$138$		−	0.687188i		−	0.0584973i
$139$			20.0448i			1.70018i	0.526639	+	0.850089i	$0.323452\pi$
$139$			20.0448i			1.70018i	−0.526639	+	0.850089i	$0.676548\pi$
$140$	3.36763	−	0.586634i	0.284616	−	0.0495797i
$141$	−2.06718	+	2.06718i	−0.174088	+	0.174088i
$142$	10.7079	−	10.7079i	0.898590	−	0.898590i
$143$	13.1987	−	3.93641i	1.10373	−	0.329179i
$144$		−	1.00000i		−	0.0833333i
$145$	−0.876575	−	5.03206i	−0.0727956	−	0.417890i
$146$	−10.3127			−0.853486
$147$	3.29723	−	3.29723i	0.271951	−	0.271951i
$148$	−7.96284			−0.654541
$149$	3.91078	−	3.91078i	0.320383	−	0.320383i	−0.528531	−	0.848914i	$-0.677257\pi$
$149$	3.91078	−	3.91078i	0.320383	−	0.320383i	0.848914	+	0.528531i	$0.177257\pi$
$150$	4.52277	+	2.13179i	0.369283	+	0.174060i
$151$	16.6941	−	16.6941i	1.35854	−	1.35854i	0.482830	−	0.875714i	$-0.339609\pi$
$151$	16.6941	−	16.6941i	1.35854	−	1.35854i	0.875714	−	0.482830i	$-0.160391\pi$
$152$	1.06701	+	1.06701i	0.0865462	+	0.0865462i
$153$	−4.03439	−	4.03439i	−0.326161	−	0.326161i
$154$	−4.12932	−	4.12932i	−0.332750	−	0.332750i
$155$	−2.58663	−	1.81915i	−0.207763	−	0.146118i
$156$	3.45516	−	1.03047i	0.276634	−	0.0825039i
$157$	−9.39497	−	9.39497i	−0.749800	−	0.749800i	0.224642	−	0.974441i	$-0.427879\pi$
$157$	−9.39497	−	9.39497i	−0.749800	−	0.749800i	−0.974441	+	0.224642i	$0.927879\pi$
$158$	−1.53731			−0.122302
$159$		−	5.21941i		−	0.413926i
$160$	0.383740	+	2.20289i	0.0303373	+	0.174154i
$161$	−0.742832	−	0.742832i	−0.0585434	−	0.0585434i
$162$			1.00000i			0.0785674i
$163$		−	14.0308i		−	1.09898i	−0.835501	−	0.549489i	$-0.814822\pi$
$163$		−	14.0308i		−	1.09898i	0.835501	−	0.549489i	$-0.185178\pi$
$164$	8.22579	+	8.22579i	0.642326	+	0.642326i
$165$	−1.46589	−	8.41506i	−0.114119	−	0.655112i
$166$		−	7.72020i		−	0.599204i
$167$	14.4217			1.11599			0.557993	−	0.829845i	$-0.311571\pi$
$167$	14.4217			1.11599			0.557993	+	0.829845i	$0.311571\pi$
$168$	−1.08097	−	1.08097i	−0.0833990	−	0.0833990i
$169$	7.12090	+	10.8762i	0.547762	+	0.836635i
$170$	10.4355	+	7.33918i	0.800365	+	0.562889i
$171$	−1.06701	−	1.06701i	−0.0815965	−	0.0815965i
$172$	−5.76210	−	5.76210i	−0.439356	−	0.439356i
$173$	12.0153	+	12.0153i	0.913507	+	0.913507i	0.996546	−	0.0830394i	$-0.0264627\pi$
$173$	12.0153	+	12.0153i	0.913507	+	0.913507i	−0.0830394	+	0.996546i	$0.526463\pi$
$174$	−1.61524	+	1.61524i	−0.122451	+	0.122451i
$175$	7.19341	−	2.58459i	0.543771	−	0.195376i
$176$	2.70115	−	2.70115i	0.203607	−	0.203607i
$177$	6.36459			0.478392
$178$	−7.21676	+	7.21676i	−0.540919	+	0.540919i
$179$	−10.2606			−0.766913			−0.383456	−	0.923559i	$-0.625266\pi$
$179$	−10.2606			−0.766913			−0.383456	+	0.923559i	$0.625266\pi$
$180$	−0.383740	−	2.20289i	−0.0286023	−	0.164194i
$181$		−	22.4534i		−	1.66895i	−0.551046	−	0.834475i	$-0.685771\pi$
$181$		−	22.4534i		−	1.66895i	0.551046	−	0.834475i	$-0.314229\pi$
$182$	2.62102	−	4.84885i	0.194283	−	0.359421i
$183$	1.71860	−	1.71860i	0.127043	−	0.127043i
$184$	0.485915	−	0.485915i	0.0358221	−	0.0358221i
$185$	−17.5413	+	3.05566i	−1.28966	+	0.224657i
$186$			1.41421i			0.103695i
$187$		−	21.7950i		−	1.59381i
$188$	−2.92343			−0.213213
$189$	1.08097	+	1.08097i	0.0786293	+	0.0786293i
$190$	2.75997	+	1.94106i	0.200229	+	0.140819i
$191$	−12.2203			−0.884229			−0.442115	−	0.896959i	$-0.645772\pi$
$191$	−12.2203			−0.884229			−0.442115	+	0.896959i	$0.645772\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$		−	24.1428i		−	1.73783i	−0.494958	−	0.868917i	$-0.664817\pi$
$193$		−	24.1428i		−	1.73783i	0.494958	−	0.868917i	$-0.335183\pi$
$194$	6.36597			0.457050
$195$	7.21592	−	3.59591i	0.516743	−	0.257508i
$196$	4.66299			0.333071
$197$			3.53326i			0.251735i	0.992047	+	0.125867i	$0.0401714\pi$
$197$			3.53326i			0.251735i	−0.992047	+	0.125867i	$0.959829\pi$
$198$	−2.70115	+	2.70115i	−0.191962	+	0.191962i
$199$	−12.1781			−0.863284			−0.431642	−	0.902045i	$-0.642066\pi$
$199$	−12.1781			−0.863284			−0.431642	+	0.902045i	$0.642066\pi$
$200$	1.69068	+	4.70549i	0.119549	+	0.332728i
$201$	−2.68634	−	2.68634i	−0.189480	−	0.189480i
$202$	−10.5668			−0.743476
$203$			3.49207i			0.245095i
$204$		−	5.70549i		−	0.399464i
$205$	21.2771	+	14.9640i	1.48606	+	1.04513i
$206$	−4.86744	+	4.86744i	−0.339130	+	0.339130i
$207$	−0.485915	+	0.485915i	−0.0337734	+	0.0337734i
$208$	3.17182	+	1.71451i	0.219926	+	0.118880i
$209$		−	5.76432i		−	0.398726i
$210$	−2.79609	−	1.96646i	−0.192948	−	0.135699i
$211$	−14.2670			−0.982180			−0.491090	−	0.871109i	$-0.663401\pi$
$211$	−14.2670			−0.982180			−0.491090	+	0.871109i	$0.663401\pi$
$212$	3.69068	−	3.69068i	0.253477	−	0.253477i
$213$	−15.1433			−1.03760
$214$	13.0918	−	13.0918i	0.894935	−	0.894935i
$215$	−14.9044	−	10.4821i	−1.01647	−	0.714876i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	1.52873	+	1.52873i	0.103777	+	0.103777i
$218$	0.124070	+	0.124070i	0.00840311	+	0.00840311i
$219$	7.29219	+	7.29219i	0.492761	+	0.492761i
$220$	4.91381	−	6.98689i	0.331289	−	0.471056i
$221$	19.7134	−	5.87935i	1.32606	−	0.395488i
$222$	5.63058	+	5.63058i	0.377900	+	0.377900i
$223$	−11.9632			−0.801112			−0.400556	−	0.916272i	$-0.631183\pi$
$223$	−11.9632			−0.801112			−0.400556	+	0.916272i	$0.631183\pi$
$224$		−	1.52873i		−	0.102142i
$225$	−1.69068	−	4.70549i	−0.112712	−	0.313699i
$226$	3.69674	+	3.69674i	0.245904	+	0.245904i
$227$			22.2944i			1.47973i	0.672756	+	0.739864i	$0.265110\pi$
$227$			22.2944i			1.47973i	−0.672756	+	0.739864i	$0.734890\pi$
$228$		−	1.50898i		−	0.0999349i
$229$	5.97023	+	5.97023i	0.394524	+	0.394524i	0.876296	−	0.481772i	$-0.160007\pi$
$229$	5.97023	+	5.97023i	0.394524	+	0.394524i	−0.481772	+	0.876296i	$0.660007\pi$
$230$	0.883955	−	1.25688i	0.0582862	−	0.0828765i
$231$			5.83975i			0.384227i
$232$	−2.28429			−0.149971
$233$	−13.3554	−	13.3554i	−0.874943	−	0.874943i	0.118063	−	0.993006i	$-0.462332\pi$
$233$	−13.3554	−	13.3554i	−0.874943	−	0.874943i	−0.993006	+	0.118063i	$0.962332\pi$
$234$	−3.17182	−	1.71451i	−0.207348	−	0.112081i
$235$	−6.44001	+	1.12184i	−0.420100	+	0.0731806i
$236$	4.50044	+	4.50044i	0.292954	+	0.292954i
$237$	1.08704	+	1.08704i	0.0706108	+	0.0706108i
$238$	−6.16749	−	6.16749i	−0.399779	−	0.399779i
$239$	9.78834	−	9.78834i	0.633155	−	0.633155i	−0.315703	−	0.948858i	$-0.602240\pi$
$239$	9.78834	−	9.78834i	0.633155	−	0.633155i	0.948858	+	0.315703i	$0.102240\pi$
$240$	1.28634	−	1.82903i	0.0830327	−	0.118063i
$241$	−4.18100	+	4.18100i	−0.269322	+	0.269322i	−0.828827	−	0.559505i	$-0.810991\pi$
$241$	−4.18100	+	4.18100i	−0.269322	+	0.269322i	0.559505	+	0.828827i	$0.310991\pi$
$242$	−3.59242			−0.230929
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	2.43047			0.155595
$245$	10.2721	−	1.78938i	0.656259	−	0.114319i
$246$		−	11.6330i		−	0.741695i
$247$	5.21378	−	1.55497i	0.331745	−	0.0989402i
$248$	−1.00000	+	1.00000i	−0.0635001	+	0.0635001i
$249$	−5.45901	+	5.45901i	−0.345950	+	0.345950i
$250$	5.53007	+	9.71691i	0.349752	+	0.614551i
$251$			16.6015i			1.04788i	0.851755	+	0.523940i	$0.175538\pi$
$251$			16.6015i			1.04788i	−0.851755	+	0.523940i	$0.824462\pi$
$252$			1.52873i			0.0963009i
$253$	−2.62506			−0.165036
$254$	10.2359	+	10.2359i	0.642258	+	0.642258i
$255$	−2.18942	−	12.5686i	−0.137107	−	0.787075i
$256$	1.00000			0.0625000
$257$	−11.6326	+	11.6326i	−0.725624	+	0.725624i	−0.969745	−	0.244121i	$-0.921501\pi$
$257$	−11.6326	+	11.6326i	−0.725624	+	0.725624i	0.244121	+	0.969745i	$0.421501\pi$
$258$			8.14884i			0.507324i
$259$	12.1730			0.756395
$260$	7.64511	+	2.55973i	0.474130	+	0.158748i
$261$	2.28429			0.141394
$262$			11.8485i			0.732005i
$263$	1.07114	−	1.07114i	0.0660491	−	0.0660491i	−0.673311	−	0.739360i	$-0.735128\pi$
$263$	1.07114	−	1.07114i	0.0660491	−	0.0660491i	0.739360	+	0.673311i	$0.235128\pi$
$264$	−3.82000			−0.235105
$265$	6.71391	−	9.54643i	0.412432	−	0.586433i
$266$	−1.63117	−	1.63117i	−0.100014	−	0.100014i
$267$	10.2060			0.624600
$268$		−	3.79906i		−	0.232064i
$269$			16.8729i			1.02876i	0.857562	+	0.514380i	$0.171978\pi$
$269$			16.8729i			1.02876i	−0.857562	+	0.514380i	$0.828022\pi$
$270$	−1.28634	+	1.82903i	−0.0782839	+	0.111311i
$271$	4.55193	−	4.55193i	0.276510	−	0.276510i	−0.555204	−	0.831714i	$-0.687360\pi$
$271$	4.55193	−	4.55193i	0.276510	−	0.276510i	0.831714	+	0.555204i	$0.187360\pi$
$272$	4.03439	−	4.03439i	0.244621	−	0.244621i
$273$	−5.28200	+	1.57531i	−0.319681	+	0.0953424i
$274$			11.9361i			0.721087i
$275$	8.14345	−	17.2770i	0.491069	−	1.04184i
$276$	−0.687188			−0.0413638
$277$	3.22540	−	3.22540i	0.193796	−	0.193796i	−0.603538	−	0.797334i	$-0.706243\pi$
$277$	3.22540	−	3.22540i	0.193796	−	0.193796i	0.797334	+	0.603538i	$0.206243\pi$
$278$	20.0448			1.20221
$279$	1.00000	−	1.00000i	0.0598684	−	0.0598684i
$280$	−0.586634	−	3.36763i	−0.0350581	−	0.201254i
$281$	4.05048	−	4.05048i	0.241631	−	0.241631i	−0.575894	−	0.817525i	$-0.695346\pi$
$281$	4.05048	−	4.05048i	0.241631	−	0.241631i	0.817525	+	0.575894i	$0.195346\pi$
$282$	2.06718	+	2.06718i	0.123099	+	0.123099i
$283$	14.1280	+	14.1280i	0.839825	+	0.839825i	0.988836	−	0.149010i	$-0.0476088\pi$
$283$	14.1280	+	14.1280i	0.839825	+	0.839825i	−0.149010	+	0.988836i	$0.547609\pi$
$284$	−10.7079	−	10.7079i	−0.635399	−	0.635399i
$285$	−0.579058	−	3.32413i	−0.0343004	−	0.196905i
$286$	−3.93641	−	13.1987i	−0.232765	−	0.780456i
$287$	−12.5750	−	12.5750i	−0.742279	−	0.742279i
$288$	−1.00000			−0.0589256
$289$		−	15.5526i		−	0.914858i
$290$	−5.03206	+	0.876575i	−0.295493	+	0.0514743i
$291$	−4.50142	−	4.50142i	−0.263878	−	0.263878i
$292$			10.3127i			0.603506i
$293$			29.4674i			1.72150i	0.509027	+	0.860751i	$0.330005\pi$
$293$			29.4674i			1.72150i	−0.509027	+	0.860751i	$0.669995\pi$
$294$	−3.29723	−	3.29723i	−0.192298	−	0.192298i
$295$	11.6410	+	8.18700i	0.677765	+	0.476666i
$296$			7.96284i			0.462831i
$297$	3.82000			0.221659
$298$	−3.91078	−	3.91078i	−0.226545	−	0.226545i
$299$	−0.708129	−	2.37434i	−0.0409522	−	0.137312i
$300$	2.13179	−	4.52277i	0.123079	−	0.261122i
$301$	8.80868	+	8.80868i	0.507724	+	0.507724i
$302$	−16.6941	−	16.6941i	−0.960636	−	0.960636i
$303$	7.47184	+	7.47184i	0.429246	+	0.429246i
$304$	1.06701	−	1.06701i	0.0611974	−	0.0611974i
$305$	5.35407	−	0.932668i	0.306573	−	0.0534044i
$306$	−4.03439	+	4.03439i	−0.230631	+	0.230631i
$307$	−20.8097			−1.18767			−0.593835	−	0.804587i	$-0.702387\pi$
$307$	−20.8097			−1.18767			−0.593835	+	0.804587i	$0.702387\pi$
$308$	−4.12932	+	4.12932i	−0.235290	+	0.235290i
$309$	6.88359			0.391594
$310$	−1.81915	+	2.58663i	−0.103321	+	0.146911i
$311$			31.1763i			1.76785i	0.467631	+	0.883924i	$0.345108\pi$
$311$			31.1763i			1.76785i	−0.467631	+	0.883924i	$0.654892\pi$
$312$	−1.03047	−	3.45516i	−0.0583391	−	0.195610i
$313$	10.7473	−	10.7473i	0.607475	−	0.607475i	−0.334811	−	0.942285i	$-0.608672\pi$
$313$	10.7473	−	10.7473i	0.607475	−	0.607475i	0.942285	+	0.334811i	$0.108672\pi$
$314$	−9.39497	+	9.39497i	−0.530189	+	0.530189i
$315$	0.586634	+	3.36763i	0.0330531	+	0.189744i
$316$			1.53731i			0.0864803i
$317$			19.2205i			1.07953i	0.841816	+	0.539764i	$0.181487\pi$
$317$			19.2205i			1.07953i	−0.841816	+	0.539764i	$0.818513\pi$
$318$	−5.21941			−0.292690
$319$	6.17022	+	6.17022i	0.345466	+	0.345466i
$320$	2.20289	−	0.383740i	0.123146	−	0.0214517i
$321$	−18.5146			−1.03338
$322$	−0.742832	+	0.742832i	−0.0413964	+	0.0413964i
$323$		−	8.60949i		−	0.479045i
$324$	1.00000			0.0555556
$325$	17.8237	+	2.70509i	0.988678	+	0.150051i
$326$	−14.0308			−0.777095
$327$		−	0.175462i		−	0.00970308i
$328$	8.22579	−	8.22579i	0.454193	−	0.454193i
$329$	4.46913			0.246391
$330$	−8.41506	+	1.46589i	−0.463234	+	0.0806945i
$331$	12.9738	+	12.9738i	0.713107	+	0.713107i	0.967184	−	0.254077i	$-0.0817717\pi$
$331$	12.9738	+	12.9738i	0.713107	+	0.713107i	−0.254077	+	0.967184i	$0.581772\pi$
$332$	−7.72020			−0.423701
$333$		−	7.96284i		−	0.436361i
$334$		−	14.4217i		−	0.789122i
$335$	−1.45785	−	8.36892i	−0.0796509	−	0.457243i
$336$	−1.08097	+	1.08097i	−0.0589720	+	0.0589720i
$337$	−19.7453	+	19.7453i	−1.07560	+	1.07560i	−0.0786992	+	0.996898i	$0.525077\pi$
$337$	−19.7453	+	19.7453i	−1.07560	+	1.07560i	−0.996898	+	0.0786992i	$0.974923\pi$
$338$	10.8762	−	7.12090i	0.591590	−	0.387326i
$339$		−	5.22798i		−	0.283945i
$340$	7.33918	−	10.4355i	0.398023	−	0.565944i
$341$	5.40230			0.292551
$342$	−1.06701	+	1.06701i	−0.0576974	+	0.0576974i
$343$	−17.8295			−0.962705
$344$	−5.76210	+	5.76210i	−0.310671	+	0.310671i
$345$	−1.51380	+	0.263701i	−0.0815004	+	0.0141972i
$346$	12.0153	−	12.0153i	0.645947	−	0.645947i
$347$	−0.843939	−	0.843939i	−0.0453050	−	0.0453050i	0.684091	−	0.729396i	$-0.260199\pi$
$347$	−0.843939	−	0.843939i	−0.0453050	−	0.0453050i	−0.729396	+	0.684091i	$0.760199\pi$
$348$	1.61524	+	1.61524i	0.0865859	+	0.0865859i
$349$	17.0343	+	17.0343i	0.911828	+	0.911828i	0.996416	−	0.0845883i	$-0.0269575\pi$
$349$	17.0343	+	17.0343i	0.911828	+	0.911828i	−0.0845883	+	0.996416i	$0.526958\pi$
$350$	−2.58459	−	7.19341i	−0.138152	−	0.384504i
$351$	1.03047	+	3.45516i	0.0550026	+	0.184423i
$352$	−2.70115	−	2.70115i	−0.143972	−	0.143972i
$353$	−6.51257			−0.346629			−0.173314	−	0.984867i	$-0.555448\pi$
$353$	−6.51257			−0.346629			−0.173314	+	0.984867i	$0.555448\pi$
$354$		−	6.36459i		−	0.338274i
$355$	−27.6975	−	19.4794i	−1.47003	−	1.03386i
$356$	7.21676	+	7.21676i	0.382488	+	0.382488i
$357$			8.72214i			0.461625i
$358$			10.2606i			0.542289i
$359$	17.5895	+	17.5895i	0.928337	+	0.928337i	0.997599	−	0.0692614i	$-0.0220643\pi$
$359$	17.5895	+	17.5895i	0.928337	+	0.928337i	−0.0692614	+	0.997599i	$0.522064\pi$
$360$	−2.20289	+	0.383740i	−0.116103	+	0.0202249i
$361$			16.7230i			0.880156i
$362$	−22.4534			−1.18013
$363$	2.54022	+	2.54022i	0.133327	+	0.133327i
$364$	−4.84885	−	2.62102i	−0.254149	−	0.137379i
$365$	3.95740	+	22.7178i	0.207140	+	1.18911i
$366$	−1.71860	−	1.71860i	−0.0898327	−	0.0898327i
$367$	−10.9276	−	10.9276i	−0.570418	−	0.570418i	0.361827	−	0.932245i	$-0.382153\pi$
$367$	−10.9276	−	10.9276i	−0.570418	−	0.570418i	−0.932245	+	0.361827i	$0.882153\pi$
$368$	−0.485915	−	0.485915i	−0.0253301	−	0.0253301i
$369$	−8.22579	+	8.22579i	−0.428218	+	0.428218i
$370$	3.05566	+	17.5413i	0.158856	+	0.911929i
$371$	−5.64204	+	5.64204i	−0.292920	+	0.292920i
$372$	1.41421			0.0733236
$373$	6.56604	−	6.56604i	0.339977	−	0.339977i	−0.516382	−	0.856359i	$-0.672721\pi$
$373$	6.56604	−	6.56604i	0.339977	−	0.339977i	0.856359	+	0.516382i	$0.172721\pi$
$374$	−21.7950			−1.12699
$375$	2.96054	−	10.7812i	0.152882	−	0.556741i
$376$			2.92343i			0.150764i
$377$	−3.91645	+	7.24537i	−0.201707	+	0.373156i
$378$	1.08097	−	1.08097i	0.0555993	−	0.0555993i
$379$	−23.1557	+	23.1557i	−1.18943	+	1.18943i	−0.212203	+	0.977226i	$0.568064\pi$
$379$	−23.1557	+	23.1557i	−1.18943	+	1.18943i	−0.977226	+	0.212203i	$0.931936\pi$
$380$	1.94106	−	2.75997i	0.0995743	−	0.141584i
$381$		−	14.4758i		−	0.741616i
$382$			12.2203i			0.625244i
$383$	1.38206			0.0706198			0.0353099	−	0.999376i	$-0.488758\pi$
$383$	1.38206			0.0706198			0.0353099	+	0.999376i	$0.488758\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	−7.51188	+	10.6811i	−0.382841	+	0.544357i
$386$	−24.1428			−1.22883
$387$	5.76210	−	5.76210i	0.292904	−	0.292904i
$388$		−	6.36597i		−	0.323183i
$389$	−19.6760			−0.997614			−0.498807	−	0.866713i	$-0.666228\pi$
$389$	−19.6760			−0.997614			−0.498807	+	0.866713i	$0.666228\pi$
$390$	−3.59591	−	7.21592i	−0.182086	−	0.365392i
$391$	−3.92074			−0.198280
$392$		−	4.66299i		−	0.235516i
$393$	8.37818	−	8.37818i	0.422624	−	0.422624i
$394$	3.53326			0.178003
$395$	0.589926	+	3.38652i	0.0296824	+	0.170395i
$396$	2.70115	+	2.70115i	0.135738	+	0.135738i
$397$	−35.9373			−1.80364			−0.901819	−	0.432113i	$-0.857768\pi$
$397$	−35.9373			−1.80364			−0.901819	+	0.432113i	$0.857768\pi$
$398$			12.1781i			0.610434i
$399$			2.30683i			0.115486i
$400$	4.70549	−	1.69068i	0.235274	−	0.0845339i
$401$	−1.64796	+	1.64796i	−0.0822953	+	0.0822953i	−0.747056	−	0.664761i	$-0.768533\pi$
$401$	−1.64796	+	1.64796i	−0.0822953	+	0.0822953i	0.664761	+	0.747056i	$0.268533\pi$
$402$	−2.68634	+	2.68634i	−0.133982	+	0.133982i
$403$	1.45731	+	4.88633i	0.0725938	+	0.243406i
$404$			10.5668i			0.525717i
$405$	2.20289	−	0.383740i	0.109463	−	0.0190682i
$406$	3.49207			0.173308
$407$	21.5088	−	21.5088i	1.06615	−	1.06615i
$408$	−5.70549			−0.282464
$409$	12.3833	−	12.3833i	0.612314	−	0.612314i	−0.331234	−	0.943548i	$-0.607465\pi$
$409$	12.3833	−	12.3833i	0.612314	−	0.612314i	0.943548	+	0.331234i	$0.107465\pi$
$410$	14.9640	−	21.2771i	0.739018	−	1.05080i
$411$	8.44011	−	8.44011i	0.416320	−	0.416320i
$412$	4.86744	+	4.86744i	0.239801	+	0.239801i
$413$	−6.87996	−	6.87996i	−0.338540	−	0.338540i
$414$	0.485915	+	0.485915i	0.0238814	+	0.0238814i
$415$	−17.0068	+	2.96255i	−0.834830	+	0.145426i
$416$	1.71451	−	3.17182i	0.0840608	−	0.155511i
$417$	−14.1738	−	14.1738i	−0.694095	−	0.694095i
$418$	−5.76432			−0.281942
$419$		−	8.21451i		−	0.401305i	−0.979662	−	0.200652i	$-0.935694\pi$
$419$		−	8.21451i		−	0.401305i	0.979662	−	0.200652i	$-0.0643062\pi$
$420$	−1.96646	+	2.79609i	−0.0959534	+	0.136435i
$421$	−10.9922	−	10.9922i	−0.535725	−	0.535725i	0.386545	−	0.922270i	$-0.373668\pi$
$421$	−10.9922	−	10.9922i	−0.535725	−	0.535725i	−0.922270	+	0.386545i	$0.873668\pi$
$422$			14.2670i			0.694506i
$423$		−	2.92343i		−	0.142142i
$424$	−3.69068	−	3.69068i	−0.179235	−	0.179235i
$425$	12.1629	−	25.8046i	0.589988	−	1.25171i
$426$			15.1433i			0.733696i
$427$	−3.71553			−0.179807
$428$	−13.0918	−	13.0918i	−0.632815	−	0.632815i
$429$	−6.54944	+	12.1164i	−0.316210	+	0.584984i
$430$	−10.4821	+	14.9044i	−0.505494	+	0.718756i
$431$	15.4246	+	15.4246i	0.742976	+	0.742976i	0.973150	−	0.230174i	$-0.0739294\pi$
$431$	15.4246	+	15.4246i	0.742976	+	0.742976i	−0.230174	+	0.973150i	$0.573929\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	−3.28016	−	3.28016i	−0.157634	−	0.157634i	0.623883	−	0.781518i	$-0.285554\pi$
$433$	−3.28016	−	3.28016i	−0.157634	−	0.157634i	−0.781518	+	0.623883i	$0.785554\pi$
$434$	1.52873	−	1.52873i	0.0733813	−	0.0733813i
$435$	4.17804	+	2.93837i	0.200321	+	0.140884i
$436$	0.124070	−	0.124070i	0.00594190	−	0.00594190i
$437$	−1.03696			−0.0496043
$438$	7.29219	−	7.29219i	0.348434	−	0.348434i
$439$	12.4347			0.593477			0.296739	−	0.954959i	$-0.404101\pi$
$439$	12.4347			0.593477			0.296739	+	0.954959i	$0.404101\pi$
$440$	−6.98689	−	4.91381i	−0.333087	−	0.234257i
$441$			4.66299i			0.222047i
$442$	−5.87935	−	19.7134i	−0.279652	−	0.937669i
$443$	−12.5904	+	12.5904i	−0.598187	+	0.598187i	−0.939830	−	0.341643i	$-0.889017\pi$
$443$	−12.5904	+	12.5904i	−0.598187	+	0.598187i	0.341643	+	0.939830i	$0.389017\pi$
$444$	5.63058	−	5.63058i	0.267215	−	0.267215i
$445$	18.6671	+	13.1284i	0.884907	+	0.622346i
$446$			11.9632i			0.566472i
$447$			5.53068i			0.261592i
$448$	−1.52873			−0.0722256
$449$	15.4853	+	15.4853i	0.730796	+	0.730796i	0.970777	−	0.239982i	$-0.0771414\pi$
$449$	15.4853	+	15.4853i	0.730796	+	0.730796i	−0.239982	+	0.970777i	$0.577141\pi$
$450$	−4.70549	+	1.69068i	−0.221819	+	0.0796993i
$451$	−44.4382			−2.09251
$452$	3.69674	−	3.69674i	0.173880	−	0.173880i
$453$			23.6090i			1.10925i
$454$	22.2944			1.04633
$455$	−11.6873	−	3.91314i	−0.547909	−	0.183451i
$456$	−1.50898			−0.0706646
$457$		−	15.3846i		−	0.719660i	−0.933018	−	0.359830i	$-0.882835\pi$
$457$		−	15.3846i		−	0.719660i	0.933018	−	0.359830i	$-0.117165\pi$
$458$	5.97023	−	5.97023i	0.278971	−	0.278971i
$459$	5.70549			0.266309
$460$	−1.25688	−	0.883955i	−0.0586026	−	0.0412146i
$461$	−26.1557	−	26.1557i	−1.21819	−	1.21819i	−0.968265	−	0.249925i	$-0.919594\pi$
$461$	−26.1557	−	26.1557i	−1.21819	−	1.21819i	−0.249925	−	0.968265i	$-0.580406\pi$
$462$	5.83975			0.271690
$463$		−	5.65611i		−	0.262862i	−0.991325	−	0.131431i	$-0.958043\pi$
$463$		−	5.65611i		−	0.262862i	0.991325	−	0.131431i	$-0.0419571\pi$
$464$			2.28429i			0.106046i
$465$	3.11536	−	0.542690i	0.144472	−	0.0251667i
$466$	−13.3554	+	13.3554i	−0.618678	+	0.618678i
$467$	23.4369	−	23.4369i	1.08453	−	1.08453i	0.0884497	−	0.996081i	$-0.471809\pi$
$467$	23.4369	−	23.4369i	1.08453	−	1.08453i	0.996081	−	0.0884497i	$-0.0281913\pi$
$468$	−1.71451	+	3.17182i	−0.0792533	+	0.146617i
$469$			5.80773i			0.268176i
$470$	1.12184	+	6.44001i	0.0517465	+	0.297056i
$471$	13.2865			0.612209
$472$	4.50044	−	4.50044i	0.207150	−	0.207150i
$473$	31.1286			1.43129
$474$	1.08704	−	1.08704i	0.0499294	−	0.0499294i
$475$	3.21684	−	6.82479i	0.147599	−	0.313143i
$476$	−6.16749	+	6.16749i	−0.282686	+	0.282686i
$477$	3.69068	+	3.69068i	0.168985	+	0.168985i
$478$	−9.78834	−	9.78834i	−0.447708	−	0.447708i
$479$	−3.55522	−	3.55522i	−0.162442	−	0.162442i	0.621206	−	0.783648i	$-0.286643\pi$
$479$	−3.55522	−	3.55522i	−0.162442	−	0.162442i	−0.783648	+	0.621206i	$0.786643\pi$
$480$	−1.82903	−	1.28634i	−0.0834833	−	0.0587130i
$481$	25.2567	+	13.6524i	1.15161	+	0.622495i
$482$	4.18100	+	4.18100i	0.190439	+	0.190439i
$483$	1.05052			0.0478005
$484$			3.59242i			0.163292i
$485$	−2.44288	−	14.0236i	−0.110925	−	0.636777i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$			6.62780i			0.300334i	0.988661	+	0.150167i	$0.0479812\pi$
$487$			6.62780i			0.300334i	−0.988661	+	0.150167i	$0.952019\pi$
$488$		−	2.43047i		−	0.110022i
$489$	9.92129	+	9.92129i	0.448656	+	0.448656i
$490$	−1.78938	−	10.2721i	−0.0808357	−	0.464045i
$491$		−	15.5268i		−	0.700713i	−0.936616	−	0.350357i	$-0.886060\pi$
$491$		−	15.5268i		−	0.700713i	0.936616	−	0.350357i	$-0.113940\pi$
$492$	−11.6330			−0.524457
$493$	9.21573	+	9.21573i	0.415056	+	0.415056i
$494$	−1.55497	−	5.21378i	−0.0699613	−	0.234579i
$495$	6.98689	+	4.91381i	0.314037	+	0.220859i
$496$	1.00000	+	1.00000i	0.0449013	+	0.0449013i
$497$	16.3695	+	16.3695i	0.734274	+	0.734274i
$498$	5.45901	+	5.45901i	0.244624	+	0.244624i
$499$	3.06206	−	3.06206i	0.137077	−	0.137077i	−0.635239	−	0.772316i	$-0.719098\pi$
$499$	3.06206	−	3.06206i	0.137077	−	0.137077i	0.772316	+	0.635239i	$0.219098\pi$
$500$	9.71691	−	5.53007i	0.434553	−	0.247312i
$501$	−10.1977	+	10.1977i	−0.455600	+	0.455600i
$502$	16.6015			0.740963
$503$	−21.0989	+	21.0989i	−0.940753	+	0.940753i	−0.998340	−	0.0575878i	$-0.981659\pi$
$503$	−21.0989	+	21.0989i	−0.940753	+	0.940753i	0.0575878	+	0.998340i	$0.481659\pi$
$504$	1.52873			0.0680950
$505$	4.05489	+	23.2775i	0.180440	+	1.03583i
$506$			2.62506i			0.116698i
$507$	−12.7259	−	2.65543i	−0.565177	−	0.117932i
$508$	10.2359	−	10.2359i	0.454145	−	0.454145i
$509$	23.9745	−	23.9745i	1.06265	−	1.06265i	0.0647506	−	0.997901i	$-0.479375\pi$
$509$	23.9745	−	23.9745i	1.06265	−	1.06265i	0.997901	−	0.0647506i	$-0.0206252\pi$
$510$	−12.5686	+	2.18942i	−0.556546	+	0.0969493i
$511$		−	15.7653i		−	0.697418i
$512$		−	1.00000i		−	0.0441942i
$513$	1.50898			0.0666233
$514$	11.6326	+	11.6326i	0.513094	+	0.513094i
$515$	12.5903	+	8.85462i	0.554794	+	0.390181i
$516$	8.14884			0.358732
$517$	7.89663	−	7.89663i	0.347293	−	0.347293i
$518$		−	12.1730i		−	0.534852i
$519$	−16.9922			−0.745875
$520$	2.55973	−	7.64511i	0.112252	−	0.335260i
$521$	−17.4440			−0.764238			−0.382119	−	0.924113i	$-0.624806\pi$
$521$	−17.4440			−0.764238			−0.382119	+	0.924113i	$0.624806\pi$
$522$		−	2.28429i		−	0.0999808i
$523$	20.2159	−	20.2159i	0.883980	−	0.883980i	−0.109957	−	0.993936i	$-0.535071\pi$
$523$	20.2159	−	20.2159i	0.883980	−	0.883980i	0.993936	+	0.109957i	$0.0350712\pi$
$524$	11.8485			0.517606
$525$	−3.25893	+	6.91409i	−0.142231	+	0.301756i
$526$	−1.07114	−	1.07114i	−0.0467038	−	0.0467038i
$527$	8.06878			0.351481
$528$			3.82000i			0.166244i
$529$		−	22.5278i		−	0.979468i
$530$	−9.54643	−	6.71391i	−0.414671	−	0.291634i
$531$	−4.50044	+	4.50044i	−0.195303	+	0.195303i
$532$	−1.63117	+	1.63117i	−0.0707203	+	0.0707203i
$533$	−11.9875	−	40.1940i	−0.519237	−	1.74099i
$534$		−	10.2060i		−	0.441659i
$535$	−33.8636	−	23.8160i	−1.46405	−	1.02965i
$536$	−3.79906			−0.164094
$537$	7.25534	−	7.25534i	0.313091	−	0.313091i
$538$	16.8729			0.727443
$539$	−12.5954	+	12.5954i	−0.542524	+	0.542524i
$540$	1.82903	+	1.28634i	0.0787088	+	0.0553551i
$541$	−0.554543	+	0.554543i	−0.0238417	+	0.0238417i	−0.718927	−	0.695085i	$-0.755367\pi$
$541$	−0.554543	+	0.554543i	−0.0238417	+	0.0238417i	0.695085	+	0.718927i	$0.255367\pi$
$542$	−4.55193	−	4.55193i	−0.195522	−	0.195522i
$543$	15.8770	+	15.8770i	0.681346	+	0.681346i
$544$	−4.03439	−	4.03439i	−0.172973	−	0.172973i
$545$	0.225703	−	0.320925i	0.00966807	−	0.0137469i
$546$	1.57531	+	5.28200i	0.0674172	+	0.226049i
$547$	−9.17919	−	9.17919i	−0.392474	−	0.392474i	0.483095	−	0.875568i	$-0.339513\pi$
$547$	−9.17919	−	9.17919i	−0.392474	−	0.392474i	−0.875568	+	0.483095i	$0.839513\pi$
$548$	11.9361			0.509886
$549$			2.43047i			0.103730i
$550$	−17.2770	−	8.14345i	−0.736694	−	0.347238i
$551$	2.43737	+	2.43737i	0.103835	+	0.103835i
$552$			0.687188i			0.0292487i
$553$		−	2.35013i		−	0.0999375i
$554$	−3.22540	−	3.22540i	−0.137034	−	0.137034i
$555$	10.2429	−	14.5642i	0.434787	−	0.618218i
$556$		−	20.0448i		−	0.850089i
$557$	37.1733			1.57508			0.787541	−	0.616262i	$-0.211354\pi$
$557$	37.1733			1.57508			0.787541	+	0.616262i	$0.211354\pi$
$558$	−1.00000	−	1.00000i	−0.0423334	−	0.0423334i
$559$	8.39716	+	28.1555i	0.355162	+	1.19085i
$560$	−3.36763	+	0.586634i	−0.142308	+	0.0247898i
$561$	15.4114	+	15.4114i	0.650669	+	0.650669i
$562$	−4.05048	−	4.05048i	−0.170859	−	0.170859i
$563$	19.8005	+	19.8005i	0.834493	+	0.834493i	0.988128	−	0.153635i	$-0.0490979\pi$
$563$	19.8005	+	19.8005i	0.834493	+	0.834493i	−0.153635	+	0.988128i	$0.549098\pi$
$564$	2.06718	−	2.06718i	0.0870439	−	0.0870439i
$565$	6.72495	−	9.56212i	0.282921	−	0.402282i
$566$	14.1280	−	14.1280i	0.593846	−	0.593846i
$567$	−1.52873			−0.0642006
$568$	−10.7079	+	10.7079i	−0.449295	+	0.449295i
$569$	−22.5105			−0.943689			−0.471844	−	0.881682i	$-0.656412\pi$
$569$	−22.5105			−0.943689			−0.471844	+	0.881682i	$0.656412\pi$
$570$	−3.32413	+	0.579058i	−0.139233	+	0.0242541i
$571$			17.9308i			0.750379i	0.926948	+	0.375190i	$0.122422\pi$
$571$			17.9308i			0.750379i	−0.926948	+	0.375190i	$0.877578\pi$
$572$	−13.1987	+	3.93641i	−0.551866	+	0.164590i
$573$	8.64105	−	8.64105i	0.360985	−	0.360985i
$574$	−12.5750	+	12.5750i	−0.524870	+	0.524870i
$575$	−3.10799	−	1.46494i	−0.129612	−	0.0610923i
$576$			1.00000i			0.0416667i
$577$			12.5758i			0.523535i	0.965131	+	0.261768i	$0.0843054\pi$
$577$			12.5758i			0.523535i	−0.965131	+	0.261768i	$0.915695\pi$
$578$	−15.5526			−0.646902
$579$	17.0715	+	17.0715i	0.709467	+	0.709467i
$580$	0.876575	+	5.03206i	0.0363978	+	0.208945i
$581$	11.8021			0.489633
$582$	−4.50142	+	4.50142i	−0.186590	+	0.186590i
$583$			19.9381i			0.825754i
$584$	10.3127			0.426743
$585$	−2.55973	+	7.64511i	−0.105832	+	0.316087i
$586$	29.4674			1.21729
$587$		−	9.73305i		−	0.401726i	−0.979619	−	0.200863i	$-0.935625\pi$
$587$		−	9.73305i		−	0.401726i	0.979619	−	0.200863i	$-0.0643746\pi$
$588$	−3.29723	+	3.29723i	−0.135976	+	0.135976i
$589$	2.13403			0.0879310
$590$	8.18700	−	11.6410i	0.337053	−	0.479252i
$591$	−2.49840	−	2.49840i	−0.102770	−	0.102770i
$592$	7.96284			0.327271
$593$		−	29.3940i		−	1.20707i	−0.797337	−	0.603534i	$-0.793759\pi$
$593$		−	29.3940i		−	1.20707i	0.797337	−	0.603534i	$-0.206241\pi$
$594$		−	3.82000i		−	0.156737i
$595$	−11.2196	+	15.9530i	−0.459959	+	0.654010i
$596$	−3.91078	+	3.91078i	−0.160192	+	0.160192i
$597$	8.61123	−	8.61123i	0.352434	−	0.352434i
$598$	−2.37434	+	0.708129i	−0.0970941	+	0.0289575i
$599$			7.65108i			0.312615i	0.987708	+	0.156307i	$0.0499590\pi$
$599$			7.65108i			0.312615i	−0.987708	+	0.156307i	$0.950041\pi$
$600$	−4.52277	−	2.13179i	−0.184641	−	0.0870301i
$601$	−8.65440			−0.353020			−0.176510	−	0.984299i	$-0.556481\pi$
$601$	−8.65440			−0.353020			−0.176510	+	0.984299i	$0.556481\pi$
$602$	8.80868	−	8.80868i	0.359015	−	0.359015i
$603$	3.79906			0.154710
$604$	−16.6941	+	16.6941i	−0.679272	+	0.679272i
$605$	1.37855	+	7.91372i	0.0560462	+	0.321738i
$606$	7.47184	−	7.47184i	0.303523	−	0.303523i
$607$	19.6391	+	19.6391i	0.797125	+	0.797125i	0.982641	−	0.185516i	$-0.0593958\pi$
$607$	19.6391	+	19.6391i	0.797125	+	0.797125i	−0.185516	+	0.982641i	$0.559396\pi$
$608$	−1.06701	−	1.06701i	−0.0432731	−	0.0432731i
$609$	−2.46926	−	2.46926i	−0.100060	−	0.100060i
$610$	−0.932668	−	5.35407i	−0.0377626	−	0.216780i
$611$	9.27260	+	5.01226i	0.375129	+	0.202774i
$612$	4.03439	+	4.03439i	0.163080	+	0.163080i
$613$	5.05853			0.204312			0.102156	−	0.994768i	$-0.467426\pi$
$613$	5.05853			0.204312			0.102156	+	0.994768i	$0.467426\pi$
$614$			20.8097i			0.839810i
$615$	−25.6263	+	4.46406i	−1.03335	+	0.180008i
$616$	4.12932	+	4.12932i	0.166375	+	0.166375i
$617$		−	3.30694i		−	0.133132i	−0.997782	−	0.0665662i	$-0.978796\pi$
$617$		−	3.30694i		−	0.133132i	0.997782	−	0.0665662i	$-0.0212044\pi$
$618$		−	6.88359i		−	0.276899i
$619$	−2.89470	−	2.89470i	−0.116348	−	0.116348i	0.646536	−	0.762884i	$-0.276217\pi$
$619$	−2.89470	−	2.89470i	−0.116348	−	0.116348i	−0.762884	+	0.646536i	$0.776217\pi$
$620$	2.58663	+	1.81915i	0.103882	+	0.0730590i
$621$		−	0.687188i		−	0.0275759i
$622$	31.1763			1.25006
$623$	−11.0325	−	11.0325i	−0.442007	−	0.442007i
$624$	−3.45516	+	1.03047i	−0.138317	+	0.0412520i
$625$	19.2832	−	15.9109i	0.771329	−	0.636437i
$626$	−10.7473	−	10.7473i	−0.429549	−	0.429549i
$627$	4.07599	+	4.07599i	0.162779	+	0.162779i
$628$	9.39497	+	9.39497i	0.374900	+	0.374900i
$629$	32.1252	−	32.1252i	1.28092	−	1.28092i
$630$	3.36763	−	0.586634i	0.134170	−	0.0233721i
$631$	6.05694	−	6.05694i	0.241123	−	0.241123i	−0.576192	−	0.817315i	$-0.695462\pi$
$631$	6.05694	−	6.05694i	0.241123	−	0.241123i	0.817315	+	0.576192i	$0.195462\pi$
$632$	1.53731			0.0611508
$633$	10.0883	−	10.0883i	0.400973	−	0.400973i
$634$	19.2205			0.763342
$635$	18.6207	−	26.4766i	0.738940	−	1.05069i
$636$			5.21941i			0.206963i
$637$	−14.7902	−	7.99475i	−0.586008	−	0.316763i
$638$	6.17022	−	6.17022i	0.244281	−	0.244281i
$639$	10.7079	−	10.7079i	0.423599	−	0.423599i
$640$	−0.383740	−	2.20289i	−0.0151687	−	0.0870770i
$641$		−	6.88364i		−	0.271887i	−0.990717	−	0.135944i	$-0.956593\pi$
$641$		−	6.88364i		−	0.271887i	0.990717	−	0.135944i	$-0.0434066\pi$
$642$			18.5146i			0.730712i
$643$	−44.0145			−1.73576			−0.867882	−	0.496771i	$-0.834519\pi$
$643$	−44.0145			−1.73576			−0.867882	+	0.496771i	$0.834519\pi$
$644$	0.742832	+	0.742832i	0.0292717	+	0.0292717i
$645$	17.9510	−	3.12703i	0.706821	−	0.123127i
$646$	−8.60949			−0.338736
$647$	6.25687	−	6.25687i	0.245983	−	0.245983i	−0.573337	−	0.819320i	$-0.694351\pi$
$647$	6.25687	−	6.25687i	0.245983	−	0.245983i	0.819320	+	0.573337i	$0.194351\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−24.3127			−0.954358
$650$	2.70509	−	17.8237i	0.106102	−	0.699101i
$651$	−2.16195			−0.0847335
$652$			14.0308i			0.549489i
$653$	−29.1179	+	29.1179i	−1.13947	+	1.13947i	−0.150926	+	0.988545i	$0.548226\pi$
$653$	−29.1179	+	29.1179i	−1.13947	+	1.13947i	−0.988545	+	0.150926i	$0.951774\pi$
$654$	−0.175462			−0.00686111
$655$	26.1011	−	4.54676i	1.01985	−	0.177657i
$656$	−8.22579	−	8.22579i	−0.321163	−	0.321163i
$657$	−10.3127			−0.402337
$658$		−	4.46913i		−	0.174225i
$659$		−	41.2913i		−	1.60848i	−0.594304	−	0.804241i	$-0.702572\pi$
$659$		−	41.2913i		−	1.60848i	0.594304	−	0.804241i	$-0.297428\pi$
$660$	1.46589	+	8.41506i	0.0570596	+	0.327556i
$661$	−27.4575	+	27.4575i	−1.06797	+	1.06797i	−0.0704594	+	0.997515i	$0.522447\pi$
$661$	−27.4575	+	27.4575i	−1.06797	+	1.06797i	−0.997515	+	0.0704594i	$0.977553\pi$
$662$	12.9738	−	12.9738i	0.504243	−	0.504243i
$663$	−9.78212	+	18.0968i	−0.379906	+	0.702821i
$664$			7.72020i			0.299602i
$665$	−2.96736	+	4.21925i	−0.115069	+	0.163615i
$666$	−7.96284			−0.308554
$667$	1.10997	−	1.10997i	0.0429783	−	0.0429783i
$668$	−14.4217			−0.557993
$669$	8.45923	−	8.45923i	0.327053	−	0.327053i
$670$	−8.36892	+	1.45785i	−0.323320	+	0.0563217i
$671$	−6.56506	+	6.56506i	−0.253441	+	0.253441i
$672$	1.08097	+	1.08097i	0.0416995	+	0.0416995i
$673$	27.6552	+	27.6552i	1.06603	+	1.06603i	0.997660	+	0.0683689i	$0.0217795\pi$
$673$	27.6552	+	27.6552i	1.06603	+	1.06603i	0.0683689	+	0.997660i	$0.478221\pi$
$674$	19.7453	+	19.7453i	0.760562	+	0.760562i
$675$	4.52277	+	2.13179i	0.174082	+	0.0820527i
$676$	−7.12090	−	10.8762i	−0.273881	−	0.418317i
$677$	−16.1493	−	16.1493i	−0.620669	−	0.620669i	0.325033	−	0.945703i	$-0.394624\pi$
$677$	−16.1493	−	16.1493i	−0.620669	−	0.620669i	−0.945703	+	0.325033i	$0.894624\pi$
$678$	−5.22798			−0.200780
$679$			9.73184i			0.373474i
$680$	−10.4355	−	7.33918i	−0.400183	−	0.281445i
$681$	−15.7645	−	15.7645i	−0.604096	−	0.604096i
$682$		−	5.40230i		−	0.206865i
$683$		−	45.8440i		−	1.75417i	−0.480333	−	0.877086i	$-0.659484\pi$
$683$		−	45.8440i		−	1.75417i	0.480333	−	0.877086i	$-0.340516\pi$
$684$	1.06701	+	1.06701i	0.0407983	+	0.0407983i
$685$	26.2940	−	4.58037i	1.00464	−	0.175007i
$686$			17.8295i			0.680735i
$687$	−8.44318			−0.322128
$688$	5.76210	+	5.76210i	0.219678	+	0.219678i
$689$	−18.0339	+	5.37846i	−0.687036	+	0.204903i
$690$	0.263701	+	1.51380i	0.0100389	+	0.0576295i
$691$	−17.8144	−	17.8144i	−0.677692	−	0.677692i	0.281786	−	0.959477i	$-0.409073\pi$
$691$	−17.8144	−	17.8144i	−0.677692	−	0.677692i	−0.959477	+	0.281786i	$0.909073\pi$
$692$	−12.0153	−	12.0153i	−0.456753	−	0.456753i
$693$	−4.12932	−	4.12932i	−0.156860	−	0.156860i
$694$	−0.843939	+	0.843939i	−0.0320355	+	0.0320355i
$695$	−7.69200	−	44.1566i	−0.291774	−	1.67496i
$696$	1.61524	−	1.61524i	0.0612255	−	0.0612255i
$697$	−66.3721			−2.51402
$698$	17.0343	−	17.0343i	0.644760	−	0.644760i
$699$	18.8874			0.714388
$700$	−7.19341	+	2.58459i	−0.271885	+	0.0976882i
$701$			21.1219i			0.797763i	0.917003	+	0.398881i	$0.130601\pi$
$701$			21.1219i			0.797763i	−0.917003	+	0.398881i	$0.869399\pi$
$702$	3.45516	−	1.03047i	0.130407	−	0.0388927i
$703$	8.49645	−	8.49645i	0.320450	−	0.320450i
$704$	−2.70115	+	2.70115i	−0.101803	+	0.101803i
$705$	3.76052	−	5.34704i	0.141629	−	0.201381i
$706$			6.51257i			0.245104i
$707$		−	16.1537i		−	0.607523i
$708$	−6.36459			−0.239196
$709$	9.51410	+	9.51410i	0.357310	+	0.357310i	0.862820	−	0.505511i	$-0.168696\pi$
$709$	9.51410	+	9.51410i	0.357310	+	0.357310i	−0.505511	+	0.862820i	$0.668696\pi$
$710$	−19.4794	+	27.6975i	−0.731048	+	1.03947i
$711$	−1.53731			−0.0576535
$712$	7.21676	−	7.21676i	0.270460	−	0.270460i
$713$		−	0.971830i		−	0.0363953i
$714$	8.72214			0.326418
$715$	−27.5648	+	13.7364i	−1.03087	+	0.513711i
$716$	10.2606			0.383456
$717$			13.8428i			0.516969i
$718$	17.5895	−	17.5895i	0.656433	−	0.656433i
$719$	−33.0993			−1.23440			−0.617198	−	0.786808i	$-0.711732\pi$
$719$	−33.0993			−1.23440			−0.617198	+	0.786808i	$0.711732\pi$
$720$	0.383740	+	2.20289i	0.0143011	+	0.0820970i
$721$	−7.44099	−	7.44099i	−0.277117	−	0.277117i
$722$	16.7230			0.622364
$723$		−	5.91283i		−	0.219901i
$724$			22.4534i			0.834475i
$725$	3.86200	+	10.7487i	0.143431	+	0.399197i
$726$	2.54022	−	2.54022i	0.0942765	−	0.0942765i
$727$	3.32729	−	3.32729i	0.123402	−	0.123402i	−0.642708	−	0.766111i	$-0.722189\pi$
$727$	3.32729	−	3.32729i	0.123402	−	0.123402i	0.766111	+	0.642708i	$0.222189\pi$
$728$	−2.62102	+	4.84885i	−0.0971416	+	0.179710i
$729$			1.00000i			0.0370370i
$730$	22.7178	−	3.95740i	0.840824	−	0.146470i
$731$	46.4931			1.71961
$732$	−1.71860	+	1.71860i	−0.0635213	+	0.0635213i
$733$	−33.4623			−1.23596			−0.617980	−	0.786194i	$-0.712049\pi$
$733$	−33.4623			−1.23596			−0.617980	+	0.786194i	$0.712049\pi$
$734$	−10.9276	+	10.9276i	−0.403346	+	0.403346i
$735$	−5.99817	+	8.52873i	−0.221246	+	0.314587i
$736$	−0.485915	+	0.485915i	−0.0179111	+	0.0179111i
$737$	10.2618	+	10.2618i	0.377999	+	0.377999i
$738$	8.22579	+	8.22579i	0.302796	+	0.302796i
$739$	−34.2147	−	34.2147i	−1.25861	−	1.25861i	−0.951758	−	0.306850i	$-0.900725\pi$
$739$	−34.2147	−	34.2147i	−1.25861	−	1.25861i	−0.306850	−	0.951758i	$-0.599275\pi$
$740$	17.5413	−	3.05566i	0.644831	−	0.112328i
$741$	−2.58717	+	4.78623i	−0.0950421	+	0.175826i
$742$	5.64204	+	5.64204i	0.207126	+	0.207126i
$743$	−39.0384			−1.43218			−0.716091	−	0.698007i	$-0.754070\pi$
$743$	−39.0384			−1.43218			−0.716091	+	0.698007i	$0.754070\pi$
$744$		−	1.41421i		−	0.0518476i
$745$	−7.11431	+	10.1158i	−0.260648	+	0.370613i
$746$	−6.56604	−	6.56604i	−0.240400	−	0.240400i
$747$		−	7.72020i		−	0.282467i
$748$			21.7950i			0.796903i
$749$	20.0138	+	20.0138i	0.731287	+	0.731287i
$750$	−10.7812	−	2.96054i	−0.393675	−	0.108104i
$751$		−	4.17727i		−	0.152431i	−0.997091	−	0.0762154i	$-0.975716\pi$
$751$		−	4.17727i		−	0.152431i	0.997091	−	0.0762154i	$-0.0242837\pi$
$752$	2.92343			0.106607
$753$	−11.7391	−	11.7391i	−0.427795	−	0.427795i
$754$	7.24537	+	3.91645i	0.263861	+	0.142629i
$755$	−30.3691	+	43.1815i	−1.10524	+	1.57153i
$756$	−1.08097	−	1.08097i	−0.0393147	−	0.0393147i
$757$	12.0444	+	12.0444i	0.437763	+	0.437763i	0.891258	−	0.453496i	$-0.149823\pi$
$757$	12.0444	+	12.0444i	0.437763	+	0.437763i	−0.453496	+	0.891258i	$0.649823\pi$
$758$	23.1557	+	23.1557i	0.841053	+	0.841053i
$759$	1.85620	−	1.85620i	0.0673757	−	0.0673757i
$760$	−2.75997	−	1.94106i	−0.100115	−	0.0704097i
$761$	15.0242	−	15.0242i	0.544628	−	0.544628i	−0.380254	−	0.924882i	$-0.624163\pi$
$761$	15.0242	−	15.0242i	0.544628	−	0.544628i	0.924882	+	0.380254i	$0.124163\pi$
$762$	−14.4758			−0.524402
$763$	−0.189670	+	0.189670i	−0.00686652	+	0.00686652i
$764$	12.2203			0.442115
$765$	10.4355	+	7.33918i	0.377296	+	0.265348i
$766$		−	1.38206i		−	0.0499358i
$767$	−6.55854	−	21.9907i	−0.236815	−	0.794037i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	17.0100	−	17.0100i	0.613397	−	0.613397i	−0.330432	−	0.943830i	$-0.607195\pi$
$769$	17.0100	−	17.0100i	0.613397	−	0.613397i	0.943830	+	0.330432i	$0.107195\pi$
$770$	10.6811	+	7.51188i	0.384918	+	0.270709i
$771$		−	16.4510i		−	0.592470i
$772$			24.1428i			0.868917i
$773$	−20.2751			−0.729246			−0.364623	−	0.931155i	$-0.618802\pi$
$773$	−20.2751			−0.729246			−0.364623	+	0.931155i	$0.618802\pi$
$774$	−5.76210	−	5.76210i	−0.207114	−	0.207114i
$775$	6.39616	+	3.01481i	0.229757	+	0.108295i
$776$	−6.36597			−0.228525
$777$	−8.60763	+	8.60763i	−0.308797	+	0.308797i
$778$			19.6760i			0.705420i
$779$	−17.5540			−0.628939
$780$	−7.21592	+	3.59591i	−0.258371	+	0.128754i
$781$	57.8475			2.06994
$782$			3.92074i			0.140205i
$783$	−1.61524	+	1.61524i	−0.0577240	+	0.0577240i
$784$	−4.66299			−0.166535
$785$	24.3013	+	17.0909i	0.867352	+	0.610000i
$786$	−8.37818	−	8.37818i	−0.298840	−	0.298840i
$787$	20.9508			0.746815			0.373408	−	0.927667i	$-0.378189\pi$
$787$	20.9508			0.746815			0.373408	+	0.927667i	$0.378189\pi$
$788$		−	3.53326i		−	0.125867i
$789$			1.51482i			0.0539289i
$790$	3.38652	−	0.589926i	0.120487	−	0.0209886i
$791$	−5.65132	+	5.65132i	−0.200938	+	0.200938i
$792$	2.70115	−	2.70115i	0.0959812	−	0.0959812i
$793$	−7.70901	−	4.16707i	−0.273755	−	0.147977i
$794$			35.9373i			1.27537i
$795$	2.00290	+	11.4978i	0.0710354	+	0.407785i
$796$	12.1781			0.431642
$797$	−20.7876	+	20.7876i	−0.736334	+	0.736334i	−0.971866	−	0.235532i	$-0.924317\pi$
$797$	−20.7876	+	20.7876i	−0.736334	+	0.736334i	0.235532	+	0.971866i	$0.424317\pi$
$798$	2.30683			0.0816608
$799$	11.7943	−	11.7943i	0.417251	−	0.417251i
$800$	−1.69068	−	4.70549i	−0.0597745	−	0.166364i
$801$	−7.21676	+	7.21676i	−0.254992	+	0.254992i
$802$	1.64796	+	1.64796i	0.0581916	+	0.0581916i
$803$	−27.8562	−	27.8562i	−0.983023	−	0.983023i
$804$	2.68634	+	2.68634i	0.0947399	+	0.0947399i
$805$	1.92144	+	1.35133i	0.0677217	+	0.0476280i
$806$	4.88633	−	1.45731i	0.172114	−	0.0513315i
$807$	−11.9310	−	11.9310i	−0.419990	−	0.419990i
$808$	10.5668			0.371738
$809$		−	33.1948i		−	1.16707i	−0.812090	−	0.583533i	$-0.801670\pi$
$809$		−	33.1948i		−	1.16707i	0.812090	−	0.583533i	$-0.198330\pi$
$810$	−0.383740	−	2.20289i	−0.0134833	−	0.0774018i
$811$	−18.7578	−	18.7578i	−0.658674	−	0.658674i	0.296392	−	0.955066i	$-0.404217\pi$
$811$	−18.7578	−	18.7578i	−0.658674	−	0.658674i	−0.955066	+	0.296392i	$0.904217\pi$
$812$		−	3.49207i		−	0.122547i
$813$			6.43741i			0.225770i
$814$	−21.5088	−	21.5088i	−0.753884	−	0.753884i
$815$	5.38419	+	30.9084i	0.188600	+	1.08267i
$816$			5.70549i			0.199732i
$817$	12.2965			0.430199
$818$	−12.3833	−	12.3833i	−0.432971	−	0.432971i
$819$	2.62102	−	4.84885i	0.0915860	−	0.169433i
$820$	−21.2771	−	14.9640i	−0.743029	−	0.522565i
$821$	35.9136	+	35.9136i	1.25339	+	1.25339i	0.954189	+	0.299203i	$0.0967208\pi$
$821$	35.9136	+	35.9136i	1.25339	+	1.25339i	0.299203	+	0.954189i	$0.403279\pi$
$822$	−8.44011	−	8.44011i	−0.294383	−	0.294383i
$823$	19.7562	+	19.7562i	0.688659	+	0.688659i	0.961936	−	0.273276i	$-0.0881073\pi$
$823$	19.7562	+	19.7562i	0.688659	+	0.688659i	−0.273276	+	0.961936i	$0.588107\pi$
$824$	4.86744	−	4.86744i	0.169565	−	0.169565i
$825$	6.45839	+	17.9750i	0.224852	+	0.625808i
$826$	−6.87996	+	6.87996i	−0.239384	+	0.239384i
$827$	−25.7405			−0.895086			−0.447543	−	0.894262i	$-0.647701\pi$
$827$	−25.7405			−0.895086			−0.447543	+	0.894262i	$0.647701\pi$
$828$	0.485915	−	0.485915i	0.0168867	−	0.0168867i
$829$	−20.1531			−0.699946			−0.349973	−	0.936760i	$-0.613809\pi$
$829$	−20.1531			−0.699946			−0.349973	+	0.936760i	$0.613809\pi$
$830$	2.96255	+	17.0068i	0.102832	+	0.590314i
$831$			4.56141i			0.158234i
$832$	−3.17182	−	1.71451i	−0.109963	−	0.0594400i
$833$	−18.8123	+	18.8123i	−0.651808	+	0.651808i
$834$	−14.1738	+	14.1738i	−0.490799	+	0.490799i
$835$	−31.7695	+	5.53419i	−1.09943	+	0.191519i
$836$			5.76432i			0.199363i
$837$			1.41421i			0.0488824i
$838$	−8.21451			−0.283765
$839$	−39.6805	−	39.6805i	−1.36992	−	1.36992i	−0.860539	−	0.509384i	$-0.829873\pi$
$839$	−39.6805	−	39.6805i	−1.36992	−	1.36992i	−0.509384	−	0.860539i	$-0.670127\pi$
$840$	2.79609	+	1.96646i	0.0964741	+	0.0678493i
$841$	23.7820			0.820069
$842$	−10.9922	+	10.9922i	−0.378815	+	0.378815i
$843$			5.72824i			0.197291i
$844$	14.2670			0.491090
$845$	−19.8602	−	21.2267i	−0.683213	−	0.730219i
$846$	−2.92343			−0.100510
$847$		−	5.49183i		−	0.188702i
$848$	−3.69068	+	3.69068i	−0.126738	+	0.126738i
$849$	−19.9801			−0.685714
$850$	−25.8046	−	12.1629i	−0.885091	−	0.417185i
$851$	−3.86927	−	3.86927i	−0.132637	−	0.132637i
$852$	15.1433			0.518801
$853$			1.09187i			0.0373849i	0.999825	+	0.0186924i	$0.00595034\pi$
$853$			1.09187i			0.0373849i	−0.999825	+	0.0186924i	$0.994050\pi$
$854$			3.71553i			0.127143i
$855$	2.75997	+	1.94106i	0.0943890	+	0.0663829i
$856$	−13.0918	+	13.0918i	−0.447468	+	0.447468i
$857$	−22.5338	+	22.5338i	−0.769740	+	0.769740i	−0.978061	−	0.208321i	$-0.933200\pi$
$857$	−22.5338	+	22.5338i	−0.769740	+	0.769740i	0.208321	+	0.978061i	$0.433200\pi$
$858$	12.1164	+	6.54944i	0.413646	+	0.223594i
$859$		−	23.9381i		−	0.816758i	−0.912812	−	0.408379i	$-0.866094\pi$
$859$		−	23.9381i		−	0.816758i	0.912812	−	0.408379i	$-0.133906\pi$
$860$	14.9044	+	10.4821i	0.508237	+	0.357438i
$861$	17.7837			0.606068
$862$	15.4246	−	15.4246i	0.525363	−	0.525363i
$863$	36.6009			1.24591			0.622955	−	0.782258i	$-0.285932\pi$
$863$	36.6009			1.24591			0.622955	+	0.782258i	$0.285932\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−31.0792	−	21.8577i	−1.05672	−	0.743184i
$866$	−3.28016	+	3.28016i	−0.111464	+	0.111464i
$867$	10.9973	+	10.9973i	0.373489	+	0.373489i
$868$	−1.52873	−	1.52873i	−0.0518884	−	0.0518884i
$869$	−4.15250	−	4.15250i	−0.140864	−	0.140864i
$870$	2.93837	−	4.17804i	0.0996201	−	0.141649i
$871$	−6.51353	+	12.0499i	−0.220703	+	0.408296i
$872$	−0.124070	−	0.124070i	−0.00420156	−	0.00420156i
$873$	6.36597			0.215455
$874$			1.03696i			0.0350755i
$875$	−14.8545	+	8.45397i	−0.502174	+	0.285796i
$876$	−7.29219	−	7.29219i	−0.246380	−	0.246380i
$877$			27.6527i			0.933765i	0.884319	+	0.466883i	$0.154623\pi$
$877$			27.6527i			0.933765i	−0.884319	+	0.466883i	$0.845377\pi$
$878$		−	12.4347i		−	0.419652i
$879$	−20.8366	−	20.8366i	−0.702800	−	0.702800i
$880$	−4.91381	+	6.98689i	−0.165644	+	0.235528i
$881$		−	42.6267i		−	1.43613i	−0.695976	−	0.718065i	$-0.745028\pi$
$881$		−	42.6267i		−	1.43613i	0.695976	−	0.718065i	$-0.254972\pi$
$882$	4.66299			0.157011
$883$	32.2845	+	32.2845i	1.08646	+	1.08646i	0.995890	+	0.0905713i	$0.0288693\pi$
$883$	32.2845	+	32.2845i	1.08646	+	1.08646i	0.0905713	+	0.995890i	$0.471131\pi$
$884$	−19.7134	+	5.87935i	−0.663032	+	0.197744i
$885$	−14.0205	+	2.44235i	−0.471294	+	0.0820986i
$886$	12.5904	+	12.5904i	0.422982	+	0.422982i
$887$	−14.7620	−	14.7620i	−0.495658	−	0.495658i	0.414425	−	0.910083i	$-0.363983\pi$
$887$	−14.7620	−	14.7620i	−0.495658	−	0.495658i	−0.910083	+	0.414425i	$0.863983\pi$
$888$	−5.63058	−	5.63058i	−0.188950	−	0.188950i
$889$	−15.6479	+	15.6479i	−0.524815	+	0.524815i
$890$	13.1284	−	18.6671i	0.440065	−	0.625724i
$891$	−2.70115	+	2.70115i	−0.0904919	+	0.0904919i
$892$	11.9632			0.400556
$893$	3.11934	−	3.11934i	0.104385	−	0.104385i
$894$	5.53068			0.184973
$895$	22.6030	−	3.93740i	0.755535	−	0.131613i
$896$			1.52873i			0.0510712i
$897$	2.17964	+	1.17819i	0.0727760	+	0.0393387i
$898$	15.4853	−	15.4853i	0.516751	−	0.516751i
$899$	−2.28429	+	2.28429i	−0.0761855	+	0.0761855i
$900$	1.69068	+	4.70549i	0.0563559	+	0.156850i
$901$			29.7793i			0.992091i
$902$			44.4382i			1.47963i
$903$	−12.4574			−0.414555
$904$	−3.69674	−	3.69674i	−0.122952	−	0.122952i
$905$	8.61627	+	49.4625i	0.286415	+	1.64419i
$906$	23.6090			0.784356
$907$	21.1516	−	21.1516i	0.702328	−	0.702328i	−0.262581	−	0.964910i	$-0.584574\pi$
$907$	21.1516	−	21.1516i	0.702328	−	0.702328i	0.964910	+	0.262581i	$0.0845738\pi$
$908$		−	22.2944i		−	0.739864i
$909$	−10.5668			−0.350478
$910$	−3.91314	+	11.6873i	−0.129719	+	0.387430i
$911$	9.72304			0.322139			0.161069	−	0.986943i	$-0.448506\pi$
$911$	9.72304			0.322139			0.161069	+	0.986943i	$0.448506\pi$
$912$			1.50898i			0.0499674i
$913$	20.8534	−	20.8534i	0.690147	−	0.690147i
$914$	−15.3846			−0.508876
$915$	−3.12640	+	4.44539i	−0.103356	+	0.146960i
$916$	−5.97023	−	5.97023i	−0.197262	−	0.197262i
$917$	−18.1132			−0.598151
$918$		−	5.70549i		−	0.188309i
$919$		−	8.88839i		−	0.293201i	−0.989196	−	0.146600i	$-0.953167\pi$
$919$		−	8.88839i		−	0.293201i	0.989196	−	0.146600i	$-0.0468331\pi$
$920$	−0.883955	+	1.25688i	−0.0291431	+	0.0414383i
$921$	14.7147	−	14.7147i	0.484865	−	0.484865i
$922$	−26.1557	+	26.1557i	−0.861391	+	0.861391i
$923$	15.6048	+	52.3225i	0.513637	+	1.72222i
$924$		−	5.83975i		−	0.192114i
$925$	37.4690	−	13.4626i	1.23197	−	0.442647i
$926$	−5.65611			−0.185871
$927$	−4.86744	+	4.86744i	−0.159868	+	0.159868i
$928$	2.28429			0.0749856
$929$	−2.93787	+	2.93787i	−0.0963885	+	0.0963885i	−0.753657	−	0.657268i	$-0.771712\pi$
$929$	−2.93787	+	2.93787i	−0.0963885	+	0.0963885i	0.657268	+	0.753657i	$0.271712\pi$
$930$	−0.542690	−	3.11536i	−0.0177955	−	0.102157i
$931$	−4.97547	+	4.97547i	−0.163064	+	0.163064i
$932$	13.3554	+	13.3554i	0.437472	+	0.437472i
$933$	−22.0450	−	22.0450i	−0.721721	−	0.721721i
$934$	−23.4369	−	23.4369i	−0.766879	−	0.766879i
$935$	8.36360	+	48.0120i	0.273519	+	1.57016i
$936$	3.17182	+	1.71451i	0.103674	+	0.0560406i
$937$	8.97253	+	8.97253i	0.293120	+	0.293120i	0.838311	−	0.545192i	$-0.183543\pi$
$937$	8.97253	+	8.97253i	0.293120	+	0.293120i	−0.545192	+	0.838311i	$0.683543\pi$
$938$	5.80773			0.189629
$939$			15.1990i			0.496001i
$940$	6.44001	−	1.12184i	0.210050	−	0.0365903i
$941$	−17.2320	−	17.2320i	−0.561746	−	0.561746i	0.368057	−	0.929803i	$-0.380023\pi$
$941$	−17.2320	−	17.2320i	−0.561746	−	0.561746i	−0.929803	+	0.368057i	$0.880023\pi$
$942$		−	13.2865i		−	0.432897i
$943$			7.99407i			0.260323i
$944$	−4.50044	−	4.50044i	−0.146477	−	0.146477i
$945$	−2.79609	−	1.96646i	−0.0909567	−	0.0639689i
$946$		−	31.1286i		−	1.01208i
$947$	12.7574			0.414559			0.207280	−	0.978282i	$-0.433539\pi$
$947$	12.7574			0.414559			0.207280	+	0.978282i	$0.433539\pi$
$948$	−1.08704	−	1.08704i	−0.0353054	−	0.0353054i
$949$	17.6813	−	32.7101i	0.573958	−	1.06181i
$950$	−6.82479	−	3.21684i	−0.221425	−	0.104368i
$951$	−13.5909	−	13.5909i	−0.440716	−	0.440716i
$952$	6.16749	+	6.16749i	0.199889	+	0.199889i
$953$	26.8078	+	26.8078i	0.868391	+	0.868391i	0.992294	−	0.123904i	$-0.0395414\pi$
$953$	26.8078	+	26.8078i	0.868391	+	0.868391i	−0.123904	+	0.992294i	$0.539541\pi$
$954$	3.69068	−	3.69068i	0.119490	−	0.119490i
$955$	26.9200	−	4.68941i	0.871111	−	0.151746i
$956$	−9.78834	+	9.78834i	−0.316578	+	0.316578i
$957$	−8.72601			−0.282072
$958$	−3.55522	+	3.55522i	−0.114864	+	0.114864i
$959$	−18.2471			−0.589229
$960$	−1.28634	+	1.82903i	−0.0415163	+	0.0590316i
$961$		−	29.0000i		−	0.935484i
$962$	13.6524	−	25.2567i	0.440170	−	0.814309i
$963$	13.0918	−	13.0918i	0.421877	−	0.421877i
$964$	4.18100	−	4.18100i	0.134661	−	0.134661i
$965$	9.26454	+	53.1839i	0.298236	+	1.71205i
$966$		−	1.05052i		−	0.0338000i
$967$		−	31.5490i		−	1.01455i	−0.861785	−	0.507275i	$-0.830653\pi$
$967$		−	31.5490i		−	1.01455i	0.861785	−	0.507275i	$-0.169347\pi$
$968$	3.59242			0.115465
$969$	6.08783	+	6.08783i	0.195569	+	0.195569i
$970$	−14.0236	+	2.44288i	−0.450269	+	0.0784361i
$971$	0.406721			0.0130523			0.00652616	−	0.999979i	$-0.497923\pi$
$971$	0.406721			0.0130523			0.00652616	+	0.999979i	$0.497923\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$			30.6431i			0.982372i
$974$	6.62780			0.212368
$975$	−14.5160	+	10.6904i	−0.464884	+	0.342368i
$976$	−2.43047			−0.0777974
$977$			50.8543i			1.62697i	0.581584	+	0.813486i	$0.302433\pi$
$977$			50.8543i			1.62697i	−0.581584	+	0.813486i	$0.697567\pi$
$978$	9.92129	−	9.92129i	0.317248	−	0.317248i
$979$	−38.9871			−1.24603
$980$	−10.2721	+	1.78938i	−0.328129	+	0.0571595i
$981$	0.124070	+	0.124070i	0.00396127	+	0.00396127i
$982$	−15.5268			−0.495479
$983$			22.0015i			0.701738i	0.936425	+	0.350869i	$0.114114\pi$
$983$			22.0015i			0.701738i	−0.936425	+	0.350869i	$0.885886\pi$
$984$			11.6330i			0.370847i
$985$	−1.35585	−	7.78341i	−0.0432011	−	0.248000i
$986$	9.21573	−	9.21573i	0.293489	−	0.293489i
$987$	−3.16016	+	3.16016i	−0.100589	+	0.100589i
$988$	−5.21378	+	1.55497i	−0.165872	+	0.0494701i
$989$		−	5.59978i		−	0.178063i
$990$	4.91381	−	6.98689i	0.156171	−	0.222058i
$991$	5.60675			0.178104			0.0890521	−	0.996027i	$-0.471616\pi$
$991$	5.60675			0.178104			0.0890521	+	0.996027i	$0.471616\pi$
$992$	1.00000	−	1.00000i	0.0317500	−	0.0317500i
$993$	−18.3478			−0.582249
$994$	16.3695	−	16.3695i	0.519210	−	0.519210i
$995$	26.8271	−	4.67323i	0.850477	−	0.148151i
$996$	5.45901	−	5.45901i	0.172975	−	0.172975i
$997$	37.6139	+	37.6139i	1.19124	+	1.19124i	0.976718	+	0.214526i	$0.0688206\pi$
$997$	37.6139	+	37.6139i	1.19124	+	1.19124i	0.214526	+	0.976718i	$0.431179\pi$
$998$	−3.06206	−	3.06206i	−0.0969278	−	0.0969278i
$999$	5.63058	+	5.63058i	0.178144	+	0.178144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.t.a.307.1	yes	12
3.2	odd	2		1170.2.w.f.307.5		12
5.2	odd	4		1950.2.j.c.1243.5		12
5.3	odd	4		390.2.j.a.73.2	✓	12
5.4	even	2		1950.2.t.b.307.5		12
13.5	odd	4		390.2.j.a.187.2	yes	12
15.8	even	4		1170.2.m.f.73.3		12
39.5	even	4		1170.2.m.f.577.3		12
65.18	even	4	inner	390.2.t.a.343.1	yes	12
65.44	odd	4		1950.2.j.c.1357.5		12
65.57	even	4		1950.2.t.b.343.5		12
195.83	odd	4		1170.2.w.f.343.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.j.a.73.2	✓	12	5.3	odd	4
390.2.j.a.187.2	yes	12	13.5	odd	4
390.2.t.a.307.1	yes	12	1.1	even	1	trivial
390.2.t.a.343.1	yes	12	65.18	even	4	inner
1170.2.m.f.73.3		12	15.8	even	4
1170.2.m.f.577.3		12	39.5	even	4
1170.2.w.f.307.5		12	3.2	odd	2
1170.2.w.f.343.5		12	195.83	odd	4
1950.2.j.c.1243.5		12	5.2	odd	4
1950.2.j.c.1357.5		12	65.44	odd	4
1950.2.t.b.307.5		12	5.4	even	2
1950.2.t.b.343.5		12	65.57	even	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.20289 + 0.383740i) q^{5} +(0.707107 + 0.707107i) q^{6} +1.52873 q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(-2.20289 + 0.383740i) q^{5} +(0.707107 + 0.707107i) q^{6} +1.52873 q^{7} +1.00000i q^{8} -1.00000i q^{9} +(0.383740 + 2.20289i) q^{10} +(2.70115 - 2.70115i) q^{11} +(0.707107 - 0.707107i) q^{12} +(3.17182 + 1.71451i) q^{13} -1.52873i q^{14} +(1.28634 - 1.82903i) q^{15} +1.00000 q^{16} +(4.03439 - 4.03439i) q^{17} -1.00000 q^{18} +(1.06701 - 1.06701i) q^{19} +(2.20289 - 0.383740i) q^{20} +(-1.08097 + 1.08097i) q^{21} +(-2.70115 - 2.70115i) q^{22} +(-0.485915 - 0.485915i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(4.70549 - 1.69068i) q^{25} +(1.71451 - 3.17182i) q^{26} +(0.707107 + 0.707107i) q^{27} -1.52873 q^{28} +2.28429i q^{29} +(-1.82903 - 1.28634i) q^{30} +(1.00000 + 1.00000i) q^{31} -1.00000i q^{32} +3.82000i q^{33} +(-4.03439 - 4.03439i) q^{34} +(-3.36763 + 0.586634i) q^{35} +1.00000i q^{36} +7.96284 q^{37} +(-1.06701 - 1.06701i) q^{38} +(-3.45516 + 1.03047i) q^{39} +(-0.383740 - 2.20289i) q^{40} +(-8.22579 - 8.22579i) q^{41} +(1.08097 + 1.08097i) q^{42} +(5.76210 + 5.76210i) q^{43} +(-2.70115 + 2.70115i) q^{44} +(0.383740 + 2.20289i) q^{45} +(-0.485915 + 0.485915i) q^{46} +2.92343 q^{47} +(-0.707107 + 0.707107i) q^{48} -4.66299 q^{49} +(-1.69068 - 4.70549i) q^{50} +5.70549i q^{51} +(-3.17182 - 1.71451i) q^{52} +(-3.69068 + 3.69068i) q^{53} +(0.707107 - 0.707107i) q^{54} +(-4.91381 + 6.98689i) q^{55} +1.52873i q^{56} +1.50898i q^{57} +2.28429 q^{58} +(-4.50044 - 4.50044i) q^{59} +(-1.28634 + 1.82903i) q^{60} -2.43047 q^{61} +(1.00000 - 1.00000i) q^{62} -1.52873i q^{63} -1.00000 q^{64} +(-7.64511 - 2.55973i) q^{65} +3.82000 q^{66} +3.79906i q^{67} +(-4.03439 + 4.03439i) q^{68} +0.687188 q^{69} +(0.586634 + 3.36763i) q^{70} +(10.7079 + 10.7079i) q^{71} +1.00000 q^{72} -10.3127i q^{73} -7.96284i q^{74} +(-2.13179 + 4.52277i) q^{75} +(-1.06701 + 1.06701i) q^{76} +(4.12932 - 4.12932i) q^{77} +(1.03047 + 3.45516i) q^{78} -1.53731i q^{79} +(-2.20289 + 0.383740i) q^{80} -1.00000 q^{81} +(-8.22579 + 8.22579i) q^{82} +7.72020 q^{83} +(1.08097 - 1.08097i) q^{84} +(-7.33918 + 10.4355i) q^{85} +(5.76210 - 5.76210i) q^{86} +(-1.61524 - 1.61524i) q^{87} +(2.70115 + 2.70115i) q^{88} +(-7.21676 - 7.21676i) q^{89} +(2.20289 - 0.383740i) q^{90} +(4.84885 + 2.62102i) q^{91} +(0.485915 + 0.485915i) q^{92} -1.41421 q^{93} -2.92343i q^{94} +(-1.94106 + 2.75997i) q^{95} +(0.707107 + 0.707107i) q^{96} +6.36597i q^{97} +4.66299i q^{98} +(-2.70115 - 2.70115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 4 q^{5}+O(q^{10}) \) 12 * q - 12 * q^4 - 4 * q^5	\( 12 q - 12 q^{4} - 4 q^{5} + 4 q^{11} + 20 q^{13} - 4 q^{15} + 12 q^{16} + 8 q^{17} - 12 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{25} - 4 q^{26} + 4 q^{30} + 12 q^{31} - 8 q^{34} + 12 q^{35} - 16 q^{37} + 4 q^{38} - 12 q^{39} + 8 q^{41} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{47} - 20 q^{49} + 8 q^{50} - 20 q^{52} - 16 q^{53} - 12 q^{55} - 40 q^{58} + 20 q^{59} + 4 q^{60} + 16 q^{61} + 12 q^{62} - 12 q^{64} - 32 q^{65} - 16 q^{66} - 8 q^{68} - 32 q^{69} - 20 q^{70} - 32 q^{71} + 12 q^{72} + 4 q^{76} + 16 q^{77} - 4 q^{80} - 12 q^{81} + 8 q^{82} + 32 q^{83} + 8 q^{84} + 12 q^{85} + 16 q^{86} + 20 q^{87} + 4 q^{88} + 16 q^{89} + 4 q^{90} - 28 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^11 + 20 * q^13 - 4 * q^15 + 12 * q^16 + 8 * q^17 - 12 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^25 - 4 * q^26 + 4 * q^30 + 12 * q^31 - 8 * q^34 + 12 * q^35 - 16 * q^37 + 4 * q^38 - 12 * q^39 + 8 * q^41 + 8 * q^42 + 16 * q^43 - 4 * q^44 + 32 * q^47 - 20 * q^49 + 8 * q^50 - 20 * q^52 - 16 * q^53 - 12 * q^55 - 40 * q^58 + 20 * q^59 + 4 * q^60 + 16 * q^61 + 12 * q^62 - 12 * q^64 - 32 * q^65 - 16 * q^66 - 8 * q^68 - 32 * q^69 - 20 * q^70 - 32 * q^71 + 12 * q^72 + 4 * q^76 + 16 * q^77 - 4 * q^80 - 12 * q^81 + 8 * q^82 + 32 * q^83 + 8 * q^84 + 12 * q^85 + 16 * q^86 + 20 * q^87 + 4 * q^88 + 16 * q^89 + 4 * q^90 - 28 * q^91 - 8 * q^95 - 4 * q^99

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