LMFDB - Embedded newform 930.2.k.b.247.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(247,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("930.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.k (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			247.14
Character	$\chi$	$=$	930.247
Dual form			930.2.k.b.433.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(0.975733 - 2.01195i) q^{5} +1.00000i q^{6} +(-3.17444 - 3.17444i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(0.975733 - 2.01195i) q^{5} +1.00000i q^{6} +(-3.17444 - 3.17444i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(2.11261 - 0.732717i) q^{10} -5.75420i q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.935765 + 0.935765i) q^{13} -4.48934i q^{14} +(2.11261 - 0.732717i) q^{15} -1.00000 q^{16} +(-2.02169 + 2.02169i) q^{17} +(-0.707107 + 0.707107i) q^{18} -6.40480i q^{19} +(2.01195 + 0.975733i) q^{20} -4.48934i q^{21} +(4.06883 - 4.06883i) q^{22} +(4.01969 + 4.01969i) q^{23} -1.00000 q^{24} +(-3.09589 - 3.92625i) q^{25} +1.32337i q^{26} +(-0.707107 + 0.707107i) q^{27} +(3.17444 - 3.17444i) q^{28} +4.54385 q^{29} +(2.01195 + 0.975733i) q^{30} +(-3.66929 - 4.18764i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.06883 - 4.06883i) q^{33} -2.85910 q^{34} +(-9.48423 + 3.28942i) q^{35} -1.00000 q^{36} +(3.68930 - 3.68930i) q^{37} +(4.52888 - 4.52888i) q^{38} +1.32337i q^{39} +(0.732717 + 2.11261i) q^{40} +0.446315 q^{41} +(3.17444 - 3.17444i) q^{42} +(8.48801 + 8.48801i) q^{43} +5.75420 q^{44} +(2.01195 + 0.975733i) q^{45} +5.68470i q^{46} +(-7.10601 - 7.10601i) q^{47} +(-0.707107 - 0.707107i) q^{48} +13.1542i q^{49} +(0.587153 - 4.96541i) q^{50} -2.85910 q^{51} +(-0.935765 + 0.935765i) q^{52} +(-2.35521 - 2.35521i) q^{53} -1.00000 q^{54} +(-11.5772 - 5.61456i) q^{55} +4.48934 q^{56} +(4.52888 - 4.52888i) q^{57} +(3.21299 + 3.21299i) q^{58} +1.60002i q^{59} +(0.732717 + 2.11261i) q^{60} +12.4957i q^{61} +(0.366530 - 5.55569i) q^{62} +(3.17444 - 3.17444i) q^{63} -1.00000i q^{64} +(2.79577 - 0.969657i) q^{65} +5.75420 q^{66} +(6.43017 + 6.43017i) q^{67} +(-2.02169 - 2.02169i) q^{68} +5.68470i q^{69} +(-9.03233 - 4.38040i) q^{70} +3.97623 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-3.59966 - 3.59966i) q^{73} +5.21746 q^{74} +(0.587153 - 4.96541i) q^{75} +6.40480 q^{76} +(-18.2664 + 18.2664i) q^{77} +(-0.935765 + 0.935765i) q^{78} -3.68040 q^{79} +(-0.975733 + 2.01195i) q^{80} -1.00000 q^{81} +(0.315592 + 0.315592i) q^{82} +(2.02091 + 2.02091i) q^{83} +4.48934 q^{84} +(2.09491 + 6.04016i) q^{85} +12.0039i q^{86} +(3.21299 + 3.21299i) q^{87} +(4.06883 + 4.06883i) q^{88} -14.0364 q^{89} +(0.732717 + 2.11261i) q^{90} -5.94107i q^{91} +(-4.01969 + 4.01969i) q^{92} +(0.366530 - 5.55569i) q^{93} -10.0494i q^{94} +(-12.8861 - 6.24937i) q^{95} -1.00000i q^{96} +(13.2779 + 13.2779i) q^{97} +(-9.30141 + 9.30141i) q^{98} +5.75420 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7}+O(q^{10}) $ 32 * q - 4 * q^7	$ 32 q - 4 q^{7} + 4 q^{10} + 4 q^{15} - 32 q^{16} + 8 q^{17} - 4 q^{22} - 32 q^{24} + 8 q^{25} + 4 q^{28} + 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} + 4 q^{37} + 16 q^{38} - 16 q^{41} + 4 q^{42} - 16 q^{43} - 8 q^{44} - 8 q^{47} - 16 q^{50} - 24 q^{53} - 32 q^{54} - 28 q^{55} + 16 q^{57} + 20 q^{58} - 8 q^{62} + 4 q^{63} + 56 q^{65} - 8 q^{66} + 32 q^{67} + 8 q^{68} - 28 q^{70} + 16 q^{71} - 20 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 40 q^{77} - 56 q^{79} - 32 q^{81} + 16 q^{82} + 72 q^{83} - 32 q^{85} + 20 q^{87} - 4 q^{88} - 64 q^{89} - 8 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 + 4 * q^15 - 32 * q^16 + 8 * q^17 - 4 * q^22 - 32 * q^24 + 8 * q^25 + 4 * q^28 + 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 + 4 * q^37 + 16 * q^38 - 16 * q^41 + 4 * q^42 - 16 * q^43 - 8 * q^44 - 8 * q^47 - 16 * q^50 - 24 * q^53 - 32 * q^54 - 28 * q^55 + 16 * q^57 + 20 * q^58 - 8 * q^62 + 4 * q^63 + 56 * q^65 - 8 * q^66 + 32 * q^67 + 8 * q^68 - 28 * q^70 + 16 * q^71 - 20 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 40 * q^77 - 56 * q^79 - 32 * q^81 + 16 * q^82 + 72 * q^83 - 32 * q^85 + 20 * q^87 - 4 * q^88 - 64 * q^89 - 8 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$			1.00000i			0.500000i
$5$	0.975733	−	2.01195i	0.436361	−	0.899772i
$5$	0.975733	−	2.01195i	0.436361	−	0.899772i
$6$			1.00000i			0.408248i
$7$	−3.17444	−	3.17444i	−1.19983	−	1.19983i	−0.974218	−	0.225609i	$-0.927563\pi$
$7$	−3.17444	−	3.17444i	−1.19983	−	1.19983i	−0.225609	−	0.974218i	$-0.572437\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	2.11261	−	0.732717i	0.668066	−	0.231705i
$11$		−	5.75420i		−	1.73496i	−0.497475	−	0.867478i	$-0.665740\pi$
$11$		−	5.75420i		−	1.73496i	0.497475	−	0.867478i	$-0.334260\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	0.935765	+	0.935765i	0.259535	+	0.259535i	0.824865	−	0.565330i	$-0.191251\pi$
$13$	0.935765	+	0.935765i	0.259535	+	0.259535i	−0.565330	+	0.824865i	$0.691251\pi$
$14$		−	4.48934i		−	1.19983i
$15$	2.11261	−	0.732717i	0.545474	−	0.189187i
$16$	−1.00000			−0.250000
$17$	−2.02169	+	2.02169i	−0.490331	+	0.490331i	−0.908410	−	0.418080i	$-0.862703\pi$
$17$	−2.02169	+	2.02169i	−0.490331	+	0.490331i	0.418080	+	0.908410i	$0.362703\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$		−	6.40480i		−	1.46936i	−0.678413	−	0.734681i	$-0.737332\pi$
$19$		−	6.40480i		−	1.46936i	0.678413	−	0.734681i	$-0.262668\pi$
$20$	2.01195	+	0.975733i	0.449886	+	0.218180i
$21$		−	4.48934i		−	0.979654i
$22$	4.06883	−	4.06883i	0.867478	−	0.867478i
$23$	4.01969	+	4.01969i	0.838163	+	0.838163i	0.988617	−	0.150454i	$-0.0480735\pi$
$23$	4.01969	+	4.01969i	0.838163	+	0.838163i	−0.150454	+	0.988617i	$0.548074\pi$
$24$	−1.00000			−0.204124
$25$	−3.09589	−	3.92625i	−0.619178	−	0.785250i
$26$			1.32337i			0.259535i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	3.17444	−	3.17444i	0.599913	−	0.599913i
$29$	4.54385			0.843771			0.421886	−	0.906649i	$-0.361368\pi$
$29$	4.54385			0.843771			0.421886	+	0.906649i	$0.361368\pi$
$30$	2.01195	+	0.975733i	0.367330	+	0.178144i
$31$	−3.66929	−	4.18764i	−0.659024	−	0.752122i
$31$	−3.66929	−	4.18764i	−0.659024	−	0.752122i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	4.06883	−	4.06883i	0.708293	−	0.708293i
$34$	−2.85910			−0.490331
$35$	−9.48423	+	3.28942i	−1.60313	+	0.556013i
$36$	−1.00000			−0.166667
$37$	3.68930	−	3.68930i	0.606517	−	0.606517i	−0.335517	−	0.942034i	$-0.608911\pi$
$37$	3.68930	−	3.68930i	0.606517	−	0.606517i	0.942034	+	0.335517i	$0.108911\pi$
$38$	4.52888	−	4.52888i	0.734681	−	0.734681i
$39$			1.32337i			0.211909i
$40$	0.732717	+	2.11261i	0.115853	+	0.334033i
$41$	0.446315			0.0697027			0.0348513	−	0.999393i	$-0.488904\pi$
$41$	0.446315			0.0697027			0.0348513	+	0.999393i	$0.488904\pi$
$42$	3.17444	−	3.17444i	0.489827	−	0.489827i
$43$	8.48801	+	8.48801i	1.29441	+	1.29441i	0.932032	+	0.362377i	$0.118035\pi$
$43$	8.48801	+	8.48801i	1.29441	+	1.29441i	0.362377	+	0.932032i	$0.381965\pi$
$44$	5.75420			0.867478
$45$	2.01195	+	0.975733i	0.299924	+	0.145454i
$46$			5.68470i			0.838163i
$47$	−7.10601	−	7.10601i	−1.03652	−	1.03652i	−0.999307	−	0.0372106i	$-0.988153\pi$
$47$	−7.10601	−	7.10601i	−1.03652	−	1.03652i	−0.0372106	−	0.999307i	$-0.511847\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$			13.1542i			1.87917i
$50$	0.587153	−	4.96541i	0.0830360	−	0.702214i
$51$	−2.85910			−0.400353
$52$	−0.935765	+	0.935765i	−0.129767	+	0.129767i
$53$	−2.35521	−	2.35521i	−0.323512	−	0.323512i	0.526600	−	0.850113i	$-0.323466\pi$
$53$	−2.35521	−	2.35521i	−0.323512	−	0.323512i	−0.850113	+	0.526600i	$0.823466\pi$
$54$	−1.00000			−0.136083
$55$	−11.5772	−	5.61456i	−1.56106	−	0.757067i
$56$	4.48934			0.599913
$57$	4.52888	−	4.52888i	0.599865	−	0.599865i
$58$	3.21299	+	3.21299i	0.421886	+	0.421886i
$59$			1.60002i			0.208304i	0.994561	+	0.104152i	$0.0332129\pi$
$59$			1.60002i			0.208304i	−0.994561	+	0.104152i	$0.966787\pi$
$60$	0.732717	+	2.11261i	0.0945934	+	0.272737i
$61$			12.4957i			1.59991i	0.600062	+	0.799954i	$0.295143\pi$
$61$			12.4957i			1.59991i	−0.600062	+	0.799954i	$0.704857\pi$
$62$	0.366530	−	5.55569i	0.0465493	−	0.705573i
$63$	3.17444	−	3.17444i	0.399942	−	0.399942i
$64$		−	1.00000i		−	0.125000i
$65$	2.79577	−	0.969657i	0.346773	−	0.120271i
$66$	5.75420			0.708293
$67$	6.43017	+	6.43017i	0.785570	+	0.785570i	0.980765	−	0.195194i	$-0.0625337\pi$
$67$	6.43017	+	6.43017i	0.785570	+	0.785570i	−0.195194	+	0.980765i	$0.562534\pi$
$68$	−2.02169	−	2.02169i	−0.245165	−	0.245165i
$69$			5.68470i			0.684357i
$70$	−9.03233	−	4.38040i	−1.07957	−	0.523557i
$71$	3.97623			0.471892			0.235946	−	0.971766i	$-0.424181\pi$
$71$	3.97623			0.471892			0.235946	+	0.971766i	$0.424181\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−3.59966	−	3.59966i	−0.421308	−	0.421308i	0.464346	−	0.885654i	$-0.346290\pi$
$73$	−3.59966	−	3.59966i	−0.421308	−	0.421308i	−0.885654	+	0.464346i	$0.846290\pi$
$74$	5.21746			0.606517
$75$	0.587153	−	4.96541i	0.0677986	−	0.573356i
$76$	6.40480			0.734681
$77$	−18.2664	+	18.2664i	−2.08165	+	2.08165i
$78$	−0.935765	+	0.935765i	−0.105955	+	0.105955i
$79$	−3.68040			−0.414077			−0.207038	−	0.978333i	$-0.566383\pi$
$79$	−3.68040			−0.414077			−0.207038	+	0.978333i	$0.566383\pi$
$80$	−0.975733	+	2.01195i	−0.109090	+	0.224943i
$81$	−1.00000			−0.111111
$82$	0.315592	+	0.315592i	0.0348513	+	0.0348513i
$83$	2.02091	+	2.02091i	0.221824	+	0.221824i	0.809266	−	0.587442i	$-0.199865\pi$
$83$	2.02091	+	2.02091i	0.221824	+	0.221824i	−0.587442	+	0.809266i	$0.699865\pi$
$84$	4.48934			0.489827
$85$	2.09491	+	6.04016i	0.227225	+	0.655147i
$86$			12.0039i			1.29441i
$87$	3.21299	+	3.21299i	0.344468	+	0.344468i
$88$	4.06883	+	4.06883i	0.433739	+	0.433739i
$89$	−14.0364			−1.48785			−0.743926	−	0.668262i	$-0.767039\pi$
$89$	−14.0364			−1.48785			−0.743926	+	0.668262i	$0.767039\pi$
$90$	0.732717	+	2.11261i	0.0772352	+	0.222689i
$91$		−	5.94107i		−	0.622793i
$92$	−4.01969	+	4.01969i	−0.419082	+	0.419082i
$93$	0.366530	−	5.55569i	0.0380074	−	0.576098i
$94$		−	10.0494i		−	1.03652i
$95$	−12.8861	−	6.24937i	−1.32209	−	0.641172i
$96$		−	1.00000i		−	0.102062i
$97$	13.2779	+	13.2779i	1.34816	+	1.34816i	0.887655	+	0.460509i	$0.152333\pi$
$97$	13.2779	+	13.2779i	1.34816	+	1.34816i	0.460509	+	0.887655i	$0.347667\pi$
$98$	−9.30141	+	9.30141i	−0.939584	+	0.939584i
$99$	5.75420			0.578319
$100$	3.92625	−	3.09589i	0.392625	−	0.309589i
$101$	6.81329			0.677947			0.338974	−	0.940796i	$-0.389920\pi$
$101$	6.81329			0.677947			0.338974	+	0.940796i	$0.389920\pi$
$102$	−2.02169	−	2.02169i	−0.200177	−	0.200177i
$103$	8.28090	−	8.28090i	0.815942	−	0.815942i	−0.169576	−	0.985517i	$-0.554240\pi$
$103$	8.28090	−	8.28090i	0.815942	−	0.815942i	0.985517	+	0.169576i	$0.0542397\pi$
$104$	−1.32337			−0.129767
$105$	−9.03233	−	4.38040i	−0.881465	−	0.427483i
$106$		−	3.33076i		−	0.323512i
$107$	2.33284	+	2.33284i	0.225524	+	0.225524i	0.810820	−	0.585296i	$-0.199022\pi$
$107$	2.33284	+	2.33284i	0.225524	+	0.225524i	−0.585296	+	0.810820i	$0.699022\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	0.609335i		−	0.0583637i	−0.999574	−	0.0291819i	$-0.990710\pi$
$109$		−	0.609335i		−	0.0583637i	0.999574	−	0.0291819i	$-0.00929019\pi$
$110$	−4.21620	−	12.1564i	−0.401999	−	1.15907i
$111$	5.21746			0.495219
$112$	3.17444	+	3.17444i	0.299957	+	0.299957i
$113$	11.7755	−	11.7755i	1.10774	−	1.10774i	0.114298	−	0.993447i	$-0.463538\pi$
$113$	11.7755	−	11.7755i	1.10774	−	1.10774i	0.993447	−	0.114298i	$-0.0364619\pi$
$114$	6.40480			0.599865
$115$	12.0096	−	4.16527i	1.11990	−	0.388414i
$116$			4.54385i			0.421886i
$117$	−0.935765	+	0.935765i	−0.0865115	+	0.0865115i
$118$	−1.13138	+	1.13138i	−0.104152	+	0.104152i
$119$	12.8355			1.17662
$120$	−0.975733	+	2.01195i	−0.0890718	+	0.183665i
$121$	−22.1108			−2.01007
$122$	−8.83578	+	8.83578i	−0.799954	+	0.799954i
$123$	0.315592	+	0.315592i	0.0284560	+	0.0284560i
$124$	4.18764	−	3.66929i	0.376061	−	0.329512i
$125$	−10.9202	+	2.39781i	−0.976731	+	0.214467i
$126$	4.48934			0.399942
$127$	13.6442	−	13.6442i	1.21072	−	1.21072i	0.239934	−	0.970789i	$-0.422874\pi$
$127$	13.6442	−	13.6442i	1.21072	−	1.21072i	0.970789	−	0.239934i	$-0.0771257\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$			12.0039i			1.05688i
$130$	2.66256	+	1.29126i	0.233522	+	0.113251i
$131$	−3.44698			−0.301164			−0.150582	−	0.988598i	$-0.548115\pi$
$131$	−3.44698			−0.301164			−0.150582	+	0.988598i	$0.548115\pi$
$132$	4.06883	+	4.06883i	0.354146	+	0.354146i
$133$	−20.3317	+	20.3317i	−1.76298	+	1.76298i
$134$			9.09363i			0.785570i
$135$	0.732717	+	2.11261i	0.0630622	+	0.181825i
$136$		−	2.85910i		−	0.245165i
$137$	−12.6143	+	12.6143i	−1.07772	+	1.07772i	−0.0810026	+	0.996714i	$0.525812\pi$
$137$	−12.6143	+	12.6143i	−1.07772	+	1.07772i	−0.996714	+	0.0810026i	$0.974188\pi$
$138$	−4.01969	+	4.01969i	−0.342179	+	0.342179i
$139$	14.9718			1.26989			0.634945	−	0.772558i	$-0.281023\pi$
$139$	14.9718			1.26989			0.634945	+	0.772558i	$0.281023\pi$
$140$	−3.28942	−	9.48423i	−0.278006	−	0.801564i
$141$		−	10.0494i		−	0.846313i
$142$	2.81162	+	2.81162i	0.235946	+	0.235946i
$143$	5.38458	−	5.38458i	0.450281	−	0.450281i
$144$		−	1.00000i		−	0.0833333i
$145$	4.43358	−	9.14200i	0.368189	−	0.759201i
$146$		−	5.09069i		−	0.421308i
$147$	−9.30141	+	9.30141i	−0.767167	+	0.767167i
$148$	3.68930	+	3.68930i	0.303259	+	0.303259i
$149$		−	17.5610i		−	1.43865i	−0.694673	−	0.719326i	$-0.744451\pi$
$149$		−	17.5610i		−	1.43865i	0.694673	−	0.719326i	$-0.255549\pi$
$150$	3.92625	−	3.09589i	0.320577	−	0.252779i
$151$		−	5.34465i		−	0.434941i	−0.976067	−	0.217471i	$-0.930219\pi$
$151$		−	5.34465i		−	0.434941i	0.976067	−	0.217471i	$-0.0697807\pi$
$152$	4.52888	+	4.52888i	0.367341	+	0.367341i
$153$	−2.02169	−	2.02169i	−0.163444	−	0.163444i
$154$	−25.8326			−2.08165
$155$	−12.0056	+	3.29641i	−0.964310	+	0.264774i
$156$	−1.32337			−0.105955
$157$	6.12504	+	6.12504i	0.488831	+	0.488831i	0.907937	−	0.419106i	$-0.137656\pi$
$157$	6.12504	+	6.12504i	0.488831	+	0.488831i	−0.419106	+	0.907937i	$0.637656\pi$
$158$	−2.60243	−	2.60243i	−0.207038	−	0.207038i
$159$		−	3.33076i		−	0.264147i
$160$	−2.11261	+	0.732717i	−0.167017	+	0.0579264i
$161$		−	25.5205i		−	2.01130i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−1.66259	+	1.66259i	−0.130224	+	0.130224i	−0.769215	−	0.638990i	$-0.779352\pi$
$163$	−1.66259	+	1.66259i	−0.130224	+	0.130224i	0.638990	+	0.769215i	$0.279352\pi$
$164$			0.446315i			0.0348513i
$165$	−4.21620	−	12.1564i	−0.328231	−	0.946373i
$166$			2.85800i			0.221824i
$167$	−4.99910	+	4.99910i	−0.386842	+	0.386842i	−0.873560	−	0.486717i	$-0.838194\pi$
$167$	−4.99910	+	4.99910i	−0.386842	+	0.386842i	0.486717	+	0.873560i	$0.338194\pi$
$168$	3.17444	+	3.17444i	0.244914	+	0.244914i
$169$		−	11.2487i		−	0.865284i
$170$	−2.78971	+	5.75236i	−0.213961	+	0.441186i
$171$	6.40480			0.489787
$172$	−8.48801	+	8.48801i	−0.647204	+	0.647204i
$173$	−0.324997	+	0.324997i	−0.0247090	+	0.0247090i	−0.719353	−	0.694644i	$-0.755562\pi$
$173$	−0.324997	+	0.324997i	−0.0247090	+	0.0247090i	0.694644	+	0.719353i	$0.255562\pi$
$174$			4.54385i			0.344468i
$175$	−2.63593	+	22.2914i	−0.199258	+	1.68507i
$176$			5.75420i			0.433739i
$177$	−1.13138	+	1.13138i	−0.0850399	+	0.0850399i
$178$	−9.92521	−	9.92521i	−0.743926	−	0.743926i
$179$	−22.2632			−1.66403			−0.832014	−	0.554754i	$-0.812812\pi$
$179$	−22.2632			−1.66403			−0.832014	+	0.554754i	$0.812812\pi$
$180$	−0.975733	+	2.01195i	−0.0727268	+	0.149962i
$181$			10.5173i			0.781742i	0.920446	+	0.390871i	$0.127826\pi$
$181$			10.5173i			0.781742i	−0.920446	+	0.390871i	$0.872174\pi$
$182$	4.20097	−	4.20097i	0.311397	−	0.311397i
$183$	−8.83578	+	8.83578i	−0.653159	+	0.653159i
$184$	−5.68470			−0.419082
$185$	−3.82292	−	11.0225i	−0.281067	−	0.810388i
$186$	4.18764	−	3.66929i	0.307053	−	0.269045i
$187$	11.6332	+	11.6332i	0.850703	+	0.850703i
$188$	7.10601	−	7.10601i	0.518259	−	0.518259i
$189$	4.48934			0.326551
$190$	−4.69291	−	13.5309i	−0.340459	−	0.981631i
$191$	−7.55134			−0.546396			−0.273198	−	0.961958i	$-0.588081\pi$
$191$	−7.55134			−0.546396			−0.273198	+	0.961958i	$0.588081\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	−11.7035	+	11.7035i	−0.842438	+	0.842438i	−0.989175	−	0.146737i	$-0.953123\pi$
$193$	−11.7035	+	11.7035i	−0.842438	+	0.842438i	0.146737	+	0.989175i	$0.453123\pi$
$194$			18.7778i			1.34816i
$195$	2.66256	+	1.29126i	0.190670	+	0.0924688i
$196$	−13.1542			−0.939584
$197$	−1.68004	+	1.68004i	−0.119698	+	0.119698i	−0.764418	−	0.644721i	$-0.776974\pi$
$197$	−1.68004	+	1.68004i	−0.119698	+	0.119698i	0.644721	+	0.764418i	$0.276974\pi$
$198$	4.06883	+	4.06883i	0.289159	+	0.289159i
$199$	−12.1116			−0.858572			−0.429286	−	0.903169i	$-0.641235\pi$
$199$	−12.1116			−0.858572			−0.429286	+	0.903169i	$0.641235\pi$
$200$	4.96541	+	0.587153i	0.351107	+	0.0415180i
$201$			9.09363i			0.641416i
$202$	4.81772	+	4.81772i	0.338974	+	0.338974i
$203$	−14.4242	−	14.4242i	−1.01238	−	1.01238i
$204$		−	2.85910i		−	0.200177i
$205$	0.435484	−	0.897964i	0.0304155	−	0.0627165i
$206$	11.7110			0.815942
$207$	−4.01969	+	4.01969i	−0.279388	+	0.279388i
$208$	−0.935765	−	0.935765i	−0.0648836	−	0.0648836i
$209$	−36.8545			−2.54928
$210$	−3.28942	−	9.48423i	−0.226991	−	0.654474i
$211$	22.4254			1.54383			0.771914	−	0.635727i	$-0.219300\pi$
$211$	22.4254			1.54383			0.771914	+	0.635727i	$0.219300\pi$
$212$	2.35521	−	2.35521i	0.161756	−	0.161756i
$213$	2.81162	+	2.81162i	0.192649	+	0.192649i
$214$			3.29913i			0.225524i
$215$	25.3595	−	8.79543i	1.72950	−	0.599843i
$216$		−	1.00000i		−	0.0680414i
$217$	−1.64548	+	24.9414i	−0.111702	+	1.69313i
$218$	0.430865	−	0.430865i	0.0291819	−	0.0291819i
$219$		−	5.09069i		−	0.343997i
$220$	5.61456	−	11.5772i	0.378533	−	0.780532i
$221$	−3.78365			−0.254516
$222$	3.68930	+	3.68930i	0.247610	+	0.247610i
$223$	5.17394	+	5.17394i	0.346472	+	0.346472i	0.858794	−	0.512321i	$-0.171214\pi$
$223$	5.17394	+	5.17394i	0.346472	+	0.346472i	−0.512321	+	0.858794i	$0.671214\pi$
$224$			4.48934i			0.299957i
$225$	3.92625	−	3.09589i	0.261750	−	0.206393i
$226$	16.6531			1.10774
$227$	−0.547026	−	0.547026i	−0.0363074	−	0.0363074i	0.688720	−	0.725027i	$-0.258173\pi$
$227$	−0.547026	−	0.547026i	−0.0363074	−	0.0363074i	−0.725027	+	0.688720i	$0.758173\pi$
$228$	4.52888	+	4.52888i	0.299932	+	0.299932i
$229$	24.8830			1.64431			0.822157	−	0.569261i	$-0.192771\pi$
$229$	24.8830			1.64431			0.822157	+	0.569261i	$0.192771\pi$
$230$	11.4373	+	5.54674i	0.754155	+	0.365742i
$231$	−25.8326			−1.69966
$232$	−3.21299	+	3.21299i	−0.210943	+	0.210943i
$233$	1.81314	−	1.81314i	0.118783	−	0.118783i	−0.645217	−	0.763999i	$-0.723233\pi$
$233$	1.81314	−	1.81314i	0.118783	−	0.118783i	0.763999	+	0.645217i	$0.223233\pi$
$234$	−1.32337			−0.0865115
$235$	−21.2305	+	7.36338i	−1.38493	+	0.480334i
$236$	−1.60002			−0.104152
$237$	−2.60243	−	2.60243i	−0.169046	−	0.169046i
$238$	9.07604	+	9.07604i	0.588312	+	0.588312i
$239$	17.7715			1.14954			0.574770	−	0.818315i	$-0.305091\pi$
$239$	17.7715			1.14954			0.574770	+	0.818315i	$0.305091\pi$
$240$	−2.11261	+	0.732717i	−0.136368	+	0.0472967i
$241$			12.1437i			0.782246i	0.920338	+	0.391123i	$0.127913\pi$
$241$			12.1437i			0.782246i	−0.920338	+	0.391123i	$0.872087\pi$
$242$	−15.6347	−	15.6347i	−1.00504	−	1.00504i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−12.4957			−0.799954
$245$	26.4656	+	12.8350i	1.69082	+	0.819996i
$246$			0.446315i			0.0284560i
$247$	5.99339	−	5.99339i	0.381350	−	0.381350i
$248$	5.55569	+	0.366530i	0.352786	+	0.0232747i
$249$			2.85800i			0.181118i
$250$	−9.41725	−	6.02623i	−0.595599	−	0.381132i
$251$		−	4.66645i		−	0.294544i	−0.989096	−	0.147272i	$-0.952951\pi$
$251$		−	4.66645i		−	0.294544i	0.989096	−	0.147272i	$-0.0470492\pi$
$252$	3.17444	+	3.17444i	0.199971	+	0.199971i
$253$	23.1301	−	23.1301i	1.45418	−	1.45418i
$254$	19.2957			1.21072
$255$	−2.78971	+	5.75236i	−0.174699	+	0.360227i
$256$	1.00000			0.0625000
$257$	−7.50472	−	7.50472i	−0.468131	−	0.468131i	0.433177	−	0.901309i	$-0.357392\pi$
$257$	−7.50472	−	7.50472i	−0.468131	−	0.468131i	−0.901309	+	0.433177i	$0.857392\pi$
$258$	−8.48801	+	8.48801i	−0.528440	+	0.528440i
$259$	−23.4230			−1.45543
$260$	0.969657	+	2.79577i	0.0601356	+	0.173386i
$261$			4.54385i			0.281257i
$262$	−2.43738	−	2.43738i	−0.150582	−	0.150582i
$263$	16.2702	+	16.2702i	1.00327	+	1.00327i	0.999995	+	0.00327042i	$0.00104101\pi$
$263$	16.2702	+	16.2702i	1.00327	+	1.00327i	0.00327042	+	0.999995i	$0.498959\pi$
$264$			5.75420i			0.354146i
$265$	−7.03661	+	2.44051i	−0.432255	+	0.149919i
$266$	−28.7533			−1.76298
$267$	−9.92521	−	9.92521i	−0.607413	−	0.607413i
$268$	−6.43017	+	6.43017i	−0.392785	+	0.392785i
$269$	0.358834			0.0218785			0.0109392	−	0.999940i	$-0.496518\pi$
$269$	0.358834			0.0218785			0.0109392	+	0.999940i	$0.496518\pi$
$270$	−0.975733	+	2.01195i	−0.0593812	+	0.122443i
$271$		−	8.83562i		−	0.536726i	−0.963318	−	0.268363i	$-0.913517\pi$
$271$		−	8.83562i		−	0.536726i	0.963318	−	0.268363i	$-0.0864826\pi$
$272$	2.02169	−	2.02169i	0.122583	−	0.122583i
$273$	4.20097	−	4.20097i	0.254254	−	0.254254i
$274$	−17.8394			−1.07772
$275$	−22.5924	+	17.8144i	−1.36237	+	1.07425i
$276$	−5.68470			−0.342179
$277$	11.8790	−	11.8790i	0.713739	−	0.713739i	−0.253577	−	0.967315i	$-0.581607\pi$
$277$	11.8790	−	11.8790i	0.713739	−	0.713739i	0.967315	+	0.253577i	$0.0816070\pi$
$278$	10.5866	+	10.5866i	0.634945	+	0.634945i
$279$	4.18764	−	3.66929i	0.250707	−	0.219675i
$280$	4.38040	−	9.03233i	0.261779	−	0.539785i
$281$	−12.4610			−0.743363			−0.371682	−	0.928360i	$-0.621219\pi$
$281$	−12.4610			−0.743363			−0.371682	+	0.928360i	$0.621219\pi$
$282$	7.10601	−	7.10601i	0.423157	−	0.423157i
$283$	8.45015	−	8.45015i	0.502310	−	0.502310i	−0.409845	−	0.912155i	$-0.634417\pi$
$283$	8.45015	−	8.45015i	0.502310	−	0.502310i	0.912155	+	0.409845i	$0.134417\pi$
$284$			3.97623i			0.235946i
$285$	−4.69291	−	13.5309i	−0.277984	−	0.801499i
$286$	7.61494			0.450281
$287$	−1.41680	−	1.41680i	−0.0836311	−	0.0836311i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$			8.82557i			0.519151i
$290$	9.59938	−	3.32935i	0.563695	−	0.195506i
$291$			18.7778i			1.10077i
$292$	3.59966	−	3.59966i	0.210654	−	0.210654i
$293$	−1.12792	+	1.12792i	−0.0658940	+	0.0658940i	−0.739286	−	0.673392i	$-0.764837\pi$
$293$	−1.12792	+	1.12792i	−0.0658940	+	0.0658940i	0.673392	+	0.739286i	$0.264837\pi$
$294$	−13.1542			−0.767167
$295$	3.21915	+	1.56119i	0.187426	+	0.0908958i
$296$			5.21746i			0.303259i
$297$	4.06883	+	4.06883i	0.236098	+	0.236098i
$298$	12.4175	−	12.4175i	0.719326	−	0.719326i
$299$			7.52297i			0.435065i
$300$	4.96541	+	0.587153i	0.286678	+	0.0338993i
$301$		−	53.8894i		−	3.10613i
$302$	3.77924	−	3.77924i	0.217471	−	0.217471i
$303$	4.81772	+	4.81772i	0.276771	+	0.276771i
$304$			6.40480i			0.367341i
$305$	25.1407	+	12.1924i	1.43955	+	0.698137i
$306$		−	2.85910i		−	0.163444i
$307$	−12.4779	−	12.4779i	−0.712149	−	0.712149i	0.254836	−	0.966984i	$-0.417979\pi$
$307$	−12.4779	−	12.4779i	−0.712149	−	0.712149i	−0.966984	+	0.254836i	$0.917979\pi$
$308$	−18.2664	−	18.2664i	−1.04082	−	1.04082i
$309$	11.7110			0.666214
$310$	−10.8201	−	6.15830i	−0.614542	−	0.349768i
$311$	−8.22180			−0.466216			−0.233108	−	0.972451i	$-0.574889\pi$
$311$	−8.22180			−0.466216			−0.233108	+	0.972451i	$0.574889\pi$
$312$	−0.935765	−	0.935765i	−0.0529773	−	0.0529773i
$313$	15.1092	+	15.1092i	0.854024	+	0.854024i	0.990626	−	0.136602i	$-0.0436181\pi$
$313$	15.1092	+	15.1092i	0.854024	+	0.854024i	−0.136602	+	0.990626i	$0.543618\pi$
$314$			8.66211i			0.488831i
$315$	−3.28942	−	9.48423i	−0.185338	−	0.534376i
$316$		−	3.68040i		−	0.207038i
$317$	3.69067	+	3.69067i	0.207288	+	0.207288i	0.803114	−	0.595825i	$-0.203175\pi$
$317$	3.69067	+	3.69067i	0.207288	+	0.207288i	−0.595825	+	0.803114i	$0.703175\pi$
$318$	2.35521	−	2.35521i	0.132073	−	0.132073i
$319$		−	26.1462i		−	1.46391i
$320$	−2.01195	−	0.975733i	−0.112471	−	0.0545451i
$321$			3.29913i			0.184140i
$322$	18.0458	−	18.0458i	1.00565	−	1.00565i
$323$	12.9485	+	12.9485i	0.720474	+	0.720474i
$324$		−	1.00000i		−	0.0555556i
$325$	0.777022	−	6.57108i	0.0431014	−	0.364498i
$326$	−2.35126			−0.130224
$327$	0.430865	−	0.430865i	0.0238269	−	0.0238269i
$328$	−0.315592	+	0.315592i	−0.0174257	+	0.0174257i
$329$			45.1152i			2.48728i
$330$	5.61456	−	11.5772i	0.309071	−	0.637302i
$331$		−	8.27276i		−	0.454712i	−0.973812	−	0.227356i	$-0.926992\pi$
$331$		−	8.27276i		−	0.454712i	0.973812	−	0.227356i	$-0.0730081\pi$
$332$	−2.02091	+	2.02091i	−0.110912	+	0.110912i
$333$	3.68930	+	3.68930i	0.202172	+	0.202172i
$334$	−7.06980			−0.386842
$335$	19.2113	−	6.66306i	1.04963	−	0.364042i
$336$			4.48934i			0.244914i
$337$	−16.5142	+	16.5142i	−0.899587	+	0.899587i	−0.995399	−	0.0958121i	$-0.969455\pi$
$337$	−16.5142	+	16.5142i	−0.899587	+	0.899587i	0.0958121	+	0.995399i	$0.469455\pi$
$338$	7.95402	−	7.95402i	0.432642	−	0.432642i
$339$	16.6531			0.904470
$340$	−6.04016	+	2.09491i	−0.327574	+	0.113612i
$341$	−24.0965	+	21.1138i	−1.30490	+	1.14338i
$342$	4.52888	+	4.52888i	0.244894	+	0.244894i
$343$	19.5361	−	19.5361i	1.05485	−	1.05485i
$344$	−12.0039			−0.647204
$345$	11.4373	+	5.54674i	0.615765	+	0.298627i
$346$	−0.459615			−0.0247090
$347$	0.990250	−	0.990250i	0.0531594	−	0.0531594i	−0.680027	−	0.733187i	$-0.738032\pi$
$347$	0.990250	−	0.990250i	0.0531594	−	0.0531594i	0.733187	+	0.680027i	$0.238032\pi$
$348$	−3.21299	+	3.21299i	−0.172234	+	0.172234i
$349$			13.4586i			0.720421i	0.932871	+	0.360210i	$0.117295\pi$
$349$			13.4586i			0.720421i	−0.932871	+	0.360210i	$0.882705\pi$
$350$	−17.6263	+	13.8985i	−0.942164	+	0.742907i
$351$	−1.32337			−0.0706364
$352$	−4.06883	+	4.06883i	−0.216870	+	0.216870i
$353$	−0.172644	−	0.172644i	−0.00918890	−	0.00918890i	0.702497	−	0.711686i	$-0.252068\pi$
$353$	−0.172644	−	0.172644i	−0.00918890	−	0.00918890i	−0.711686	+	0.702497i	$0.752068\pi$
$354$	−1.60002			−0.0850399
$355$	3.87974	−	7.99998i	0.205915	−	0.424595i
$356$		−	14.0364i		−	0.743926i
$357$	9.07604	+	9.07604i	0.480355	+	0.480355i
$358$	−15.7424	−	15.7424i	−0.832014	−	0.832014i
$359$		−	23.8905i		−	1.26089i	−0.776233	−	0.630446i	$-0.782872\pi$
$359$		−	23.8905i		−	1.26089i	0.776233	−	0.630446i	$-0.217128\pi$
$360$	−2.11261	+	0.732717i	−0.111344	+	0.0386176i
$361$	−22.0215			−1.15902
$362$	−7.43682	+	7.43682i	−0.390871	+	0.390871i
$363$	−15.6347	−	15.6347i	−0.820609	−	0.820609i
$364$	5.94107			0.311397
$365$	−10.7546	+	3.73003i	−0.562924	+	0.195239i
$366$	−12.4957			−0.653159
$367$	−10.6324	+	10.6324i	−0.555006	+	0.555006i	−0.927881	−	0.372875i	$-0.878372\pi$
$367$	−10.6324	+	10.6324i	−0.555006	+	0.555006i	0.372875	+	0.927881i	$0.378372\pi$
$368$	−4.01969	−	4.01969i	−0.209541	−	0.209541i
$369$			0.446315i			0.0232342i
$370$	5.09085	−	10.4973i	0.264660	−	0.545727i
$371$			14.9529i			0.776318i
$372$	5.55569	+	0.366530i	0.288049	+	0.0190037i
$373$	12.5473	−	12.5473i	0.649676	−	0.649676i	−0.303239	−	0.952915i	$-0.598068\pi$
$373$	12.5473	−	12.5473i	0.649676	−	0.649676i	0.952915	+	0.303239i	$0.0980679\pi$
$374$			16.4518i			0.850703i
$375$	−9.41725	−	6.02623i	−0.486305	−	0.311193i
$376$	10.0494			0.518259
$377$	4.25197	+	4.25197i	0.218988	+	0.218988i
$378$	3.17444	+	3.17444i	0.163276	+	0.163276i
$379$			29.0814i			1.49381i	0.664931	+	0.746905i	$0.268461\pi$
$379$			29.0814i			1.49381i	−0.664931	+	0.746905i	$0.731539\pi$
$380$	6.24937	−	12.8861i	0.320586	−	0.661045i
$381$	19.2957			0.988551
$382$	−5.33960	−	5.33960i	−0.273198	−	0.273198i
$383$	1.30000	+	1.30000i	0.0664271	+	0.0664271i	0.739540	−	0.673113i	$-0.235043\pi$
$383$	1.30000	+	1.30000i	0.0664271	+	0.0664271i	−0.673113	+	0.739540i	$0.735043\pi$
$384$	1.00000			0.0510310
$385$	18.9280	+	54.5742i	0.964658	+	2.78136i
$386$	−16.5513			−0.842438
$387$	−8.48801	+	8.48801i	−0.431470	+	0.431470i
$388$	−13.2779	+	13.2779i	−0.674082	+	0.674082i
$389$	22.3781			1.13461			0.567307	−	0.823506i	$-0.307985\pi$
$389$	22.3781			1.13461			0.567307	+	0.823506i	$0.307985\pi$
$390$	0.969657	+	2.79577i	0.0491005	+	0.141569i
$391$	−16.2531			−0.821954
$392$	−9.30141	−	9.30141i	−0.469792	−	0.469792i
$393$	−2.43738	−	2.43738i	−0.122950	−	0.122950i
$394$	−2.37593			−0.119698
$395$	−3.59108	+	7.40478i	−0.180687	+	0.372575i
$396$			5.75420i			0.289159i
$397$	2.85699	+	2.85699i	0.143388	+	0.143388i	0.775157	−	0.631769i	$-0.217671\pi$
$397$	2.85699	+	2.85699i	0.143388	+	0.143388i	−0.631769	+	0.775157i	$0.717671\pi$
$398$	−8.56423	−	8.56423i	−0.429286	−	0.429286i
$399$	−28.7533			−1.43947
$400$	3.09589	+	3.92625i	0.154795	+	0.196313i
$401$			9.26468i			0.462656i	0.972876	+	0.231328i	$0.0743070\pi$
$401$			9.26468i			0.462656i	−0.972876	+	0.231328i	$0.925693\pi$
$402$	−6.43017	+	6.43017i	−0.320708	+	0.320708i
$403$	0.485055	−	7.35224i	0.0241623	−	0.366241i
$404$			6.81329i			0.338974i
$405$	−0.975733	+	2.01195i	−0.0484845	+	0.0999746i
$406$		−	20.3989i		−	1.01238i
$407$	−21.2290	−	21.2290i	−1.05228	−	1.05228i
$408$	2.02169	−	2.02169i	0.100088	−	0.100088i
$409$	−7.58950			−0.375277			−0.187638	−	0.982238i	$-0.560083\pi$
$409$	−7.58950			−0.375277			−0.187638	+	0.982238i	$0.560083\pi$
$410$	0.942890	−	0.327023i	0.0465660	−	0.0161505i
$411$	−17.8394			−0.879952
$412$	8.28090	+	8.28090i	0.407971	+	0.407971i
$413$	5.07916	−	5.07916i	0.249929	−	0.249929i
$414$	−5.68470			−0.279388
$415$	6.03784	−	2.09410i	0.296386	−	0.102795i
$416$		−	1.32337i		−	0.0648836i
$417$	10.5866	+	10.5866i	0.518430	+	0.518430i
$418$	−26.0601	−	26.0601i	−1.27464	−	1.27464i
$419$		−	20.0760i		−	0.980778i	−0.871504	−	0.490389i	$-0.836855\pi$
$419$		−	20.0760i		−	0.980778i	0.871504	−	0.490389i	$-0.163145\pi$
$420$	4.38040	−	9.03233i	0.213741	−	0.440733i
$421$	14.6844			0.715673			0.357837	−	0.933784i	$-0.383514\pi$
$421$	14.6844			0.715673			0.357837	+	0.933784i	$0.383514\pi$
$422$	15.8571	+	15.8571i	0.771914	+	0.771914i
$423$	7.10601	−	7.10601i	0.345506	−	0.345506i
$424$	3.33076			0.161756
$425$	14.1966	+	1.67873i	0.688635	+	0.0814302i
$426$			3.97623i			0.192649i
$427$	39.6668	−	39.6668i	1.91961	−	1.91961i
$428$	−2.33284	+	2.33284i	−0.112762	+	0.112762i
$429$	7.61494			0.367653
$430$	24.1512	+	11.7125i	1.16467	+	0.564829i
$431$	30.7325			1.48033			0.740166	−	0.672424i	$-0.234747\pi$
$431$	30.7325			1.48033			0.740166	+	0.672424i	$0.234747\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	1.29610	+	1.29610i	0.0622864	+	0.0622864i	0.737564	−	0.675277i	$-0.235976\pi$
$433$	1.29610	+	1.29610i	0.0622864	+	0.0622864i	−0.675277	+	0.737564i	$0.735976\pi$
$434$	−18.7997	+	16.4727i	−0.902416	+	0.790714i
$435$	9.59938	−	3.32935i	0.460255	−	0.159630i
$436$	0.609335			0.0291819
$437$	25.7453	−	25.7453i	1.23156	−	1.23156i
$438$	3.59966	−	3.59966i	0.171998	−	0.171998i
$439$		−	14.3261i		−	0.683748i	−0.939746	−	0.341874i	$-0.888938\pi$
$439$		−	14.3261i		−	0.683748i	0.939746	−	0.341874i	$-0.111062\pi$
$440$	12.1564	−	4.21620i	0.579533	−	0.200999i
$441$	−13.1542			−0.626390
$442$	−2.67544	−	2.67544i	−0.127258	−	0.127258i
$443$	−20.0006	+	20.0006i	−0.950255	+	0.950255i	−0.998820	−	0.0485648i	$-0.984535\pi$
$443$	−20.0006	+	20.0006i	−0.950255	+	0.950255i	0.0485648	+	0.998820i	$0.484535\pi$
$444$			5.21746i			0.247610i
$445$	−13.6957	+	28.2405i	−0.649241	+	1.33873i
$446$			7.31705i			0.346472i
$447$	12.4175	−	12.4175i	0.587327	−	0.587327i
$448$	−3.17444	+	3.17444i	−0.149978	+	0.149978i
$449$	−7.96541			−0.375911			−0.187955	−	0.982178i	$-0.560186\pi$
$449$	−7.96541			−0.375911			−0.187955	+	0.982178i	$0.560186\pi$
$450$	4.96541	+	0.587153i	0.234071	+	0.0276787i
$451$		−	2.56818i		−	0.120931i
$452$	11.7755	+	11.7755i	0.553872	+	0.553872i
$453$	3.77924	−	3.77924i	0.177564	−	0.177564i
$454$		−	0.773612i		−	0.0363074i
$455$	−11.9531	−	5.79689i	−0.560372	−	0.271763i
$456$			6.40480i			0.299932i
$457$	10.1006	−	10.1006i	0.472486	−	0.472486i	−0.430232	−	0.902718i	$-0.641568\pi$
$457$	10.1006	−	10.1006i	0.472486	−	0.472486i	0.902718	+	0.430232i	$0.141568\pi$
$458$	17.5949	+	17.5949i	0.822157	+	0.822157i
$459$		−	2.85910i		−	0.133451i
$460$	4.16527	+	12.0096i	0.194207	+	0.559948i
$461$		−	19.4667i		−	0.906653i	−0.891345	−	0.453326i	$-0.850237\pi$
$461$		−	19.4667i		−	0.906653i	0.891345	−	0.453326i	$-0.149763\pi$
$462$	−18.2664	−	18.2664i	−0.849829	−	0.849829i
$463$	26.7435	+	26.7435i	1.24287	+	1.24287i	0.958803	+	0.284071i	$0.0916853\pi$
$463$	26.7435	+	26.7435i	1.24287	+	1.24287i	0.284071	+	0.958803i	$0.408315\pi$
$464$	−4.54385			−0.210943
$465$	−10.8201	−	6.15830i	−0.501772	−	0.285585i
$466$	2.56416			0.118783
$467$	24.0329	+	24.0329i	1.11211	+	1.11211i	0.992865	+	0.119247i	$0.0380479\pi$
$467$	24.0329	+	24.0329i	1.11211	+	1.11211i	0.119247	+	0.992865i	$0.461952\pi$
$468$	−0.935765	−	0.935765i	−0.0432558	−	0.0432558i
$469$		−	40.8244i		−	1.88510i
$470$	−20.2189	−	9.80554i	−0.932630	−	0.452296i
$471$			8.66211i			0.399129i
$472$	−1.13138	−	1.13138i	−0.0520761	−	0.0520761i
$473$	48.8417	−	48.8417i	2.24574	−	2.24574i
$474$		−	3.68040i		−	0.169046i
$475$	−25.1469	+	19.8286i	−1.15382	+	0.909797i
$476$			12.8355i			0.588312i
$477$	2.35521	−	2.35521i	0.107837	−	0.107837i
$478$	12.5663	+	12.5663i	0.574770	+	0.574770i
$479$		−	2.67248i		−	0.122109i	−0.998134	−	0.0610543i	$-0.980554\pi$
$479$		−	2.67248i		−	0.122109i	0.998134	−	0.0610543i	$-0.0194463\pi$
$480$	−2.01195	−	0.975733i	−0.0918326	−	0.0445359i
$481$	6.90464			0.314825
$482$	−8.58691	+	8.58691i	−0.391123	+	0.391123i
$483$	18.0458	−	18.0458i	0.821110	−	0.821110i
$484$		−	22.1108i		−	1.00504i
$485$	39.6701	−	13.7588i	1.80133	−	0.624754i
$486$		−	1.00000i		−	0.0453609i
$487$	10.7650	−	10.7650i	0.487808	−	0.487808i	−0.419806	−	0.907614i	$-0.637902\pi$
$487$	10.7650	−	10.7650i	0.487808	−	0.487808i	0.907614	+	0.419806i	$0.137902\pi$
$488$	−8.83578	−	8.83578i	−0.399977	−	0.399977i
$489$	−2.35126			−0.106328
$490$	9.63829	+	27.7897i	0.435414	+	1.25541i
$491$		−	16.9940i		−	0.766927i	−0.923556	−	0.383464i	$-0.874731\pi$
$491$		−	16.9940i		−	0.766927i	0.923556	−	0.383464i	$-0.125269\pi$
$492$	−0.315592	+	0.315592i	−0.0142280	+	0.0142280i
$493$	−9.18623	+	9.18623i	−0.413727	+	0.413727i
$494$	8.47593			0.381350
$495$	5.61456	−	11.5772i	0.252356	−	0.520355i
$496$	3.66929	+	4.18764i	0.164756	+	0.188031i
$497$	−12.6223	−	12.6223i	−0.566188	−	0.566188i
$498$	−2.02091	+	2.02091i	−0.0905591	+	0.0905591i
$499$	−26.3911			−1.18143			−0.590713	−	0.806882i	$-0.701154\pi$
$499$	−26.3911			−1.18143			−0.590713	+	0.806882i	$0.701154\pi$
$500$	−2.39781	−	10.9202i	−0.107233	−	0.488366i
$501$	−7.06980			−0.315855
$502$	3.29968	−	3.29968i	0.147272	−	0.147272i
$503$	7.19276	−	7.19276i	0.320709	−	0.320709i	−0.528330	−	0.849039i	$-0.677182\pi$
$503$	7.19276	−	7.19276i	0.320709	−	0.320709i	0.849039	+	0.528330i	$0.177182\pi$
$504$			4.48934i			0.199971i
$505$	6.64794	−	13.7080i	0.295830	−	0.609998i
$506$	32.7109			1.45418
$507$	7.95402	−	7.95402i	0.353251	−	0.353251i
$508$	13.6442	+	13.6442i	0.605362	+	0.605362i
$509$	1.79112			0.0793898			0.0396949	−	0.999212i	$-0.487361\pi$
$509$	1.79112			0.0793898			0.0396949	+	0.999212i	$0.487361\pi$
$510$	−6.04016	+	2.09491i	−0.267463	+	0.0927641i
$511$			22.8538i			1.01099i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	4.52888	+	4.52888i	0.199955	+	0.199955i
$514$		−	10.6133i		−	0.468131i
$515$	−8.58082	−	24.7407i	−0.378116	−	1.09021i
$516$	−12.0039			−0.528440
$517$	−40.8894	+	40.8894i	−1.79831	+	1.79831i
$518$	−16.5625	−	16.5625i	−0.727716	−	0.727716i
$519$	−0.459615			−0.0201748
$520$	−1.29126	+	2.66256i	−0.0566254	+	0.116761i
$521$	−9.73843			−0.426648			−0.213324	−	0.976981i	$-0.568429\pi$
$521$	−9.73843			−0.426648			−0.213324	+	0.976981i	$0.568429\pi$
$522$	−3.21299	+	3.21299i	−0.140629	+	0.140629i
$523$	−7.84855	−	7.84855i	−0.343193	−	0.343193i	0.514373	−	0.857566i	$-0.328025\pi$
$523$	−7.84855	−	7.84855i	−0.343193	−	0.343193i	−0.857566	+	0.514373i	$0.828025\pi$
$524$		−	3.44698i		−	0.150582i
$525$	−17.6263	+	13.8985i	−0.769274	+	0.606581i
$526$			23.0096i			1.00327i
$527$	15.8842	+	1.04794i	0.691928	+	0.0456492i
$528$	−4.06883	+	4.06883i	−0.177073	+	0.177073i
$529$			9.31579i			0.405035i
$530$	−6.70133	−	3.24993i	−0.291087	−	0.141168i
$531$	−1.60002			−0.0694348
$532$	−20.3317	−	20.3317i	−0.881490	−	0.881490i
$533$	0.417646	+	0.417646i	0.0180903	+	0.0180903i
$534$		−	14.0364i		−	0.607413i
$535$	6.96978	−	2.41733i	0.301330	−	0.104510i
$536$	−9.09363			−0.392785
$537$	−15.7424	−	15.7424i	−0.679337	−	0.679337i
$538$	0.253734	+	0.253734i	0.0109392	+	0.0109392i
$539$	75.6918			3.26028
$540$	−2.11261	+	0.732717i	−0.0909123	+	0.0315311i
$541$	41.4181			1.78070			0.890351	−	0.455274i	$-0.150459\pi$
$541$	41.4181			1.78070			0.890351	+	0.455274i	$0.150459\pi$
$542$	6.24773	−	6.24773i	0.268363	−	0.268363i
$543$	−7.43682	+	7.43682i	−0.319145	+	0.319145i
$544$	2.85910			0.122583
$545$	−1.22595	−	0.594548i	−0.0525140	−	0.0254676i
$546$	5.94107			0.254254
$547$	−18.0344	−	18.0344i	−0.771096	−	0.771096i	0.207203	−	0.978298i	$-0.433564\pi$
$547$	−18.0344	−	18.0344i	−0.771096	−	0.771096i	−0.978298	+	0.207203i	$0.933564\pi$
$548$	−12.6143	−	12.6143i	−0.538858	−	0.538858i
$549$	−12.4957			−0.533302
$550$	−28.5719	−	3.37859i	−1.21831	−	0.144064i
$551$		−	29.1024i		−	1.23981i
$552$	−4.01969	−	4.01969i	−0.171089	−	0.171089i
$553$	11.6832	+	11.6832i	0.496821	+	0.496821i
$554$	16.7994			0.713739
$555$	5.09085	−	10.4973i	0.216094	−	0.445584i
$556$			14.9718i			0.634945i
$557$	6.21840	−	6.21840i	0.263482	−	0.263482i	−0.562985	−	0.826467i	$-0.690347\pi$
$557$	6.21840	−	6.21840i	0.263482	−	0.263482i	0.826467	+	0.562985i	$0.190347\pi$
$558$	5.55569	+	0.366530i	0.235191	+	0.0155164i
$559$			15.8856i			0.671888i
$560$	9.48423	−	3.28942i	0.400782	−	0.139003i
$561$			16.4518i			0.694596i
$562$	−8.81128	−	8.81128i	−0.371682	−	0.371682i
$563$	−4.07024	+	4.07024i	−0.171540	+	0.171540i	−0.787656	−	0.616116i	$-0.788705\pi$
$563$	−4.07024	+	4.07024i	−0.171540	+	0.171540i	0.616116	+	0.787656i	$0.288705\pi$
$564$	10.0494			0.423157
$565$	−12.2020	−	35.1814i	−0.513341	−	1.48009i
$566$	11.9503			0.502310
$567$	3.17444	+	3.17444i	0.133314	+	0.133314i
$568$	−2.81162	+	2.81162i	−0.117973	+	0.117973i
$569$	24.3688			1.02159			0.510796	−	0.859702i	$-0.329351\pi$
$569$	24.3688			1.02159			0.510796	+	0.859702i	$0.329351\pi$
$570$	6.24937	−	12.8861i	0.261757	−	0.539741i
$571$		−	31.8356i		−	1.33228i	−0.745827	−	0.666140i	$-0.767945\pi$
$571$		−	31.8356i		−	1.33228i	0.745827	−	0.666140i	$-0.232055\pi$
$572$	5.38458	+	5.38458i	0.225141	+	0.225141i
$573$	−5.33960	−	5.33960i	−0.223065	−	0.223065i
$574$		−	2.00366i		−	0.0836311i
$575$	3.33779	−	28.2268i	0.139195	−	1.17714i
$576$	1.00000			0.0416667
$577$	20.4752	+	20.4752i	0.852393	+	0.852393i	0.990427	−	0.138035i	$-0.0440785\pi$
$577$	20.4752	+	20.4752i	0.852393	+	0.852393i	−0.138035	+	0.990427i	$0.544079\pi$
$578$	−6.24062	+	6.24062i	−0.259576	+	0.259576i
$579$	−16.5513			−0.687848
$580$	9.14200	+	4.43358i	0.379601	+	0.184094i
$581$		−	12.8305i		−	0.532300i
$582$	−13.2779	+	13.2779i	−0.550386	+	0.550386i
$583$	−13.5523	+	13.5523i	−0.561280	+	0.561280i
$584$	5.09069			0.210654
$585$	0.969657	+	2.79577i	0.0400904	+	0.115591i
$586$	−1.59512			−0.0658940
$587$	−32.8470	+	32.8470i	−1.35574	+	1.35574i	−0.476643	+	0.879097i	$0.658147\pi$
$587$	−32.8470	+	32.8470i	−1.35574	+	1.35574i	−0.879097	+	0.476643i	$0.841853\pi$
$588$	−9.30141	−	9.30141i	−0.383584	−	0.383584i
$589$	−26.8210	+	23.5011i	−1.10514	+	0.968344i
$590$	1.17236	+	3.38021i	0.0482652	+	0.139161i
$591$	−2.37593			−0.0977329
$592$	−3.68930	+	3.68930i	−0.151629	+	0.151629i
$593$	−3.51335	+	3.51335i	−0.144276	+	0.144276i	−0.775555	−	0.631279i	$-0.782530\pi$
$593$	−3.51335	+	3.51335i	−0.144276	+	0.144276i	0.631279	+	0.775555i	$0.282530\pi$
$594$			5.75420i			0.236098i
$595$	12.5240	−	25.8243i	0.513433	−	1.05869i
$596$	17.5610			0.719326
$597$	−8.56423	−	8.56423i	−0.350511	−	0.350511i
$598$	−5.31954	+	5.31954i	−0.217532	+	0.217532i
$599$			21.7185i			0.887393i	0.896177	+	0.443697i	$0.146333\pi$
$599$			21.7185i			0.887393i	−0.896177	+	0.443697i	$0.853667\pi$
$600$	3.09589	+	3.92625i	0.126389	+	0.160289i
$601$		−	11.3848i		−	0.464397i	−0.972668	−	0.232199i	$-0.925408\pi$
$601$		−	11.3848i		−	0.464397i	0.972668	−	0.232199i	$-0.0745919\pi$
$602$	38.1055	−	38.1055i	1.55307	−	1.55307i
$603$	−6.43017	+	6.43017i	−0.261857	+	0.261857i
$604$	5.34465			0.217471
$605$	−21.5742	+	44.4858i	−0.877117	+	1.80861i
$606$			6.81329i			0.276771i
$607$	−10.6748	−	10.6748i	−0.433279	−	0.433279i	0.456464	−	0.889742i	$-0.349116\pi$
$607$	−10.6748	−	10.6748i	−0.433279	−	0.433279i	−0.889742	+	0.456464i	$0.849116\pi$
$608$	−4.52888	+	4.52888i	−0.183670	+	0.183670i
$609$		−	20.3989i		−	0.826604i
$610$	9.15579	+	26.3985i	0.370707	+	1.06884i
$611$		−	13.2991i		−	0.538025i
$612$	2.02169	−	2.02169i	0.0817218	−	0.0817218i
$613$	7.86031	+	7.86031i	0.317475	+	0.317475i	0.847796	−	0.530322i	$-0.177929\pi$
$613$	7.86031	+	7.86031i	0.317475	+	0.317475i	−0.530322	+	0.847796i	$0.677929\pi$
$614$		−	17.6464i		−	0.712149i
$615$	0.942890	−	0.327023i	0.0380210	−	0.0131868i
$616$		−	25.8326i		−	1.04082i
$617$	1.34957	+	1.34957i	0.0543315	+	0.0543315i	0.733750	−	0.679419i	$-0.237768\pi$
$617$	1.34957	+	1.34957i	0.0543315	+	0.0543315i	−0.679419	+	0.733750i	$0.737768\pi$
$618$	8.28090	+	8.28090i	0.333107	+	0.333107i
$619$	30.1323			1.21112			0.605560	−	0.795799i	$-0.292949\pi$
$619$	30.1323			1.21112			0.605560	+	0.795799i	$0.292949\pi$
$620$	−3.29641	−	12.0056i	−0.132387	−	0.482155i
$621$	−5.68470			−0.228119
$622$	−5.81369	−	5.81369i	−0.233108	−	0.233108i
$623$	44.5577	+	44.5577i	1.78517	+	1.78517i
$624$		−	1.32337i		−	0.0529773i
$625$	−5.83090	+	24.3105i	−0.233236	+	0.972420i
$626$			21.3677i			0.854024i
$627$	−26.0601	−	26.0601i	−1.04074	−	1.04074i
$628$	−6.12504	+	6.12504i	−0.244416	+	0.244416i
$629$			14.9172i			0.594788i
$630$	4.38040	−	9.03233i	0.174519	−	0.359857i
$631$			31.9401i			1.27151i	0.771889	+	0.635757i	$0.219312\pi$
$631$			31.9401i			1.27151i	−0.771889	+	0.635757i	$0.780688\pi$
$632$	2.60243	−	2.60243i	0.103519	−	0.103519i
$633$	15.8571	+	15.8571i	0.630265	+	0.630265i
$634$			5.21939i			0.207288i
$635$	−14.1383	−	40.7644i	−0.561062	−	1.61769i
$636$	3.33076			0.132073
$637$	−12.3092	+	12.3092i	−0.487709	+	0.487709i
$638$	18.4882	−	18.4882i	0.731953	−	0.731953i
$639$			3.97623i			0.157297i
$640$	−0.732717	−	2.11261i	−0.0289632	−	0.0835083i
$641$		−	5.01134i		−	0.197936i	−0.995091	−	0.0989680i	$-0.968446\pi$
$641$		−	5.01134i		−	0.197936i	0.995091	−	0.0989680i	$-0.0315541\pi$
$642$	−2.33284	+	2.33284i	−0.0920698	+	0.0920698i
$643$	1.86693	+	1.86693i	0.0736247	+	0.0736247i	0.742960	−	0.669336i	$-0.233421\pi$
$643$	1.86693	+	1.86693i	0.0736247	+	0.0736247i	−0.669336	+	0.742960i	$0.733421\pi$
$644$	25.5205			1.00565
$645$	24.1512	+	11.7125i	0.950951	+	0.461181i
$646$			18.3119i			0.720474i
$647$	−28.8008	+	28.8008i	−1.13228	+	1.13228i	−0.142479	+	0.989798i	$0.545507\pi$
$647$	−28.8008	+	28.8008i	−1.13228	+	1.13228i	−0.989798	+	0.142479i	$0.954493\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	9.20681			0.361399
$650$	5.19589	−	4.09702i	0.203800	−	0.160698i
$651$	−18.7997	+	16.4727i	−0.736820	+	0.645615i
$652$	−1.66259	−	1.66259i	−0.0651121	−	0.0651121i
$653$	−21.9337	+	21.9337i	−0.858331	+	0.858331i	−0.991141	−	0.132811i	$-0.957600\pi$
$653$	−21.9337	+	21.9337i	−0.858331	+	0.858331i	0.132811	+	0.991141i	$0.457600\pi$
$654$	0.609335			0.0238269
$655$	−3.36333	+	6.93515i	−0.131416	+	0.270979i
$656$	−0.446315			−0.0174257
$657$	3.59966	−	3.59966i	0.140436	−	0.140436i
$658$	−31.9013	+	31.9013i	−1.24364	+	1.24364i
$659$		−	12.6114i		−	0.491270i	−0.969362	−	0.245635i	$-0.921004\pi$
$659$		−	12.6114i		−	0.491270i	0.969362	−	0.245635i	$-0.0789964\pi$
$660$	12.1564	−	4.21620i	0.473187	−	0.164115i
$661$	−25.7340			−1.00093			−0.500467	−	0.865755i	$-0.666838\pi$
$661$	−25.7340			−1.00093			−0.500467	+	0.865755i	$0.666838\pi$
$662$	5.84973	−	5.84973i	0.227356	−	0.227356i
$663$	−2.67544	−	2.67544i	−0.103906	−	0.103906i
$664$	−2.85800			−0.110912
$665$	21.0681	+	60.7446i	0.816984	+	2.35558i
$666$			5.21746i			0.202172i
$667$	18.2649	+	18.2649i	0.707218	+	0.707218i
$668$	−4.99910	−	4.99910i	−0.193421	−	0.193421i
$669$			7.31705i			0.282894i
$670$	18.2959	+	8.87295i	0.706834	+	0.342792i
$671$	71.9026			2.77577
$672$	−3.17444	+	3.17444i	−0.122457	+	0.122457i
$673$	13.5406	+	13.5406i	0.521953	+	0.521953i	0.918161	−	0.396208i	$-0.129674\pi$
$673$	13.5406	+	13.5406i	0.521953	+	0.521953i	−0.396208	+	0.918161i	$0.629674\pi$
$674$	−23.3546			−0.899587
$675$	4.96541	+	0.587153i	0.191119	+	0.0225995i
$676$	11.2487			0.432642
$677$	3.75171	−	3.75171i	0.144190	−	0.144190i	−0.631327	−	0.775517i	$-0.717489\pi$
$677$	3.75171	−	3.75171i	0.144190	−	0.144190i	0.775517	+	0.631327i	$0.217489\pi$
$678$	11.7755	+	11.7755i	0.452235	+	0.452235i
$679$		−	84.2997i		−	3.23513i
$680$	−5.75236	−	2.78971i	−0.220593	−	0.106981i
$681$		−	0.773612i		−	0.0296449i
$682$	−31.9685	−	2.10909i	−1.22414	−	0.0807611i
$683$	−16.4852	+	16.4852i	−0.630790	+	0.630790i	−0.948266	−	0.317476i	$-0.897165\pi$
$683$	−16.4852	+	16.4852i	−0.630790	+	0.630790i	0.317476	+	0.948266i	$0.397165\pi$
$684$			6.40480i			0.244894i
$685$	13.0712	+	37.6877i	0.499426	+	1.43997i
$686$	27.6282			1.05485
$687$	17.5949	+	17.5949i	0.671288	+	0.671288i
$688$	−8.48801	−	8.48801i	−0.323602	−	0.323602i
$689$		−	4.40784i		−	0.167925i
$690$	4.16527	+	12.0096i	0.158569	+	0.457196i
$691$	−4.97695			−0.189332			−0.0946660	−	0.995509i	$-0.530178\pi$
$691$	−4.97695			−0.189332			−0.0946660	+	0.995509i	$0.530178\pi$
$692$	−0.324997	−	0.324997i	−0.0123545	−	0.0123545i
$693$	−18.2664	−	18.2664i	−0.693882	−	0.693882i
$694$	1.40042			0.0531594
$695$	14.6084	−	30.1225i	0.554130	−	1.14261i
$696$	−4.54385			−0.172234
$697$	−0.902309	+	0.902309i	−0.0341774	+	0.0341774i
$698$	−9.51664	+	9.51664i	−0.360210	+	0.360210i
$699$	2.56416			0.0969856
$700$	−22.2914	−	2.63593i	−0.842536	−	0.0996288i
$701$	34.2586			1.29393			0.646965	−	0.762519i	$-0.276038\pi$
$701$	34.2586			1.29393			0.646965	+	0.762519i	$0.276038\pi$
$702$	−0.935765	−	0.935765i	−0.0353182	−	0.0353182i
$703$	−23.6292	−	23.6292i	−0.891194	−	0.891194i
$704$	−5.75420			−0.216870
$705$	−20.2189	−	9.80554i	−0.761489	−	0.369298i
$706$		−	0.244155i		−	0.00918890i
$707$	−21.6284	−	21.6284i	−0.813419	−	0.813419i
$708$	−1.13138	−	1.13138i	−0.0425199	−	0.0425199i
$709$	−43.3435			−1.62780			−0.813899	−	0.581007i	$-0.802659\pi$
$709$	−43.3435			−1.62780			−0.813899	+	0.581007i	$0.802659\pi$
$710$	8.40023	−	2.91345i	0.315255	−	0.109340i
$711$		−	3.68040i		−	0.138026i
$712$	9.92521	−	9.92521i	0.371963	−	0.371963i
$713$	2.08361	−	31.5824i	0.0780319	−	1.18277i
$714$			12.8355i			0.480355i
$715$	−5.57960	−	16.0874i	−0.208665	−	0.601635i
$716$		−	22.2632i		−	0.832014i
$717$	12.5663	+	12.5663i	0.469298	+	0.469298i
$718$	16.8931	−	16.8931i	0.630446	−	0.630446i
$719$	−10.0856			−0.376131			−0.188065	−	0.982157i	$-0.560222\pi$
$719$	−10.0856			−0.376131			−0.188065	+	0.982157i	$0.560222\pi$
$720$	−2.01195	−	0.975733i	−0.0749810	−	0.0363634i
$721$	−52.5745			−1.95798
$722$	−15.5715	−	15.5715i	−0.579512	−	0.579512i
$723$	−8.58691	+	8.58691i	−0.319351	+	0.319351i
$724$	−10.5173			−0.390871
$725$	−14.0673	−	17.8403i	−0.522445	−	0.662572i
$726$		−	22.1108i		−	0.820609i
$727$	−26.1870	−	26.1870i	−0.971224	−	0.971224i	0.0283737	−	0.999597i	$-0.490967\pi$
$727$	−26.1870	−	26.1870i	−0.971224	−	0.971224i	−0.999597	+	0.0283737i	$0.990967\pi$
$728$	4.20097	+	4.20097i	0.155698	+	0.155698i
$729$		−	1.00000i		−	0.0370370i
$730$	−10.2422	−	4.96715i	−0.379081	−	0.183842i
$731$	−34.3202			−1.26938
$732$	−8.83578	−	8.83578i	−0.326580	−	0.326580i
$733$	−10.3909	+	10.3909i	−0.383797	+	0.383797i	−0.872468	−	0.488671i	$-0.837482\pi$
$733$	−10.3909	+	10.3909i	−0.383797	+	0.383797i	0.488671	+	0.872468i	$0.337482\pi$
$734$	−15.0365			−0.555006
$735$	9.63829	+	27.7897i	0.355514	+	1.02504i
$736$		−	5.68470i		−	0.209541i
$737$	37.0005	−	37.0005i	1.36293	−	1.36293i
$738$	−0.315592	+	0.315592i	−0.0116171	+	0.0116171i
$739$	4.10111			0.150862			0.0754308	−	0.997151i	$-0.475967\pi$
$739$	4.10111			0.150862			0.0754308	+	0.997151i	$0.475967\pi$
$740$	11.0225	−	3.82292i	0.405194	−	0.140533i
$741$	8.47593			0.311371
$742$	−10.5733	+	10.5733i	−0.388159	+	0.388159i
$743$	−33.2805	−	33.2805i	−1.22094	−	1.22094i	−0.967297	−	0.253646i	$-0.918370\pi$
$743$	−33.2805	−	33.2805i	−1.22094	−	1.22094i	−0.253646	−	0.967297i	$-0.581630\pi$
$744$	3.66929	+	4.18764i	0.134523	+	0.153526i
$745$	−35.3318	−	17.1348i	−1.29446	−	0.627771i
$746$	17.7446			0.649676
$747$	−2.02091	+	2.02091i	−0.0739412	+	0.0739412i
$748$	−11.6332	+	11.6332i	−0.425351	+	0.425351i
$749$		−	14.8109i		−	0.541179i
$750$	−2.39781	−	10.9202i	−0.0875557	−	0.398749i
$751$	6.70955			0.244835			0.122417	−	0.992479i	$-0.460935\pi$
$751$	6.70955			0.244835			0.122417	+	0.992479i	$0.460935\pi$
$752$	7.10601	+	7.10601i	0.259130	+	0.259130i
$753$	3.29968	−	3.29968i	0.120247	−	0.120247i
$754$			6.01320i			0.218988i
$755$	−10.7532	−	5.21495i	−0.391348	−	0.189791i
$756$			4.48934i			0.163276i
$757$	38.4333	−	38.4333i	1.39688	−	1.39688i	0.588084	−	0.808800i	$-0.299883\pi$
$757$	38.4333	−	38.4333i	1.39688	−	1.39688i	0.808800	−	0.588084i	$-0.200117\pi$
$758$	−20.5636	+	20.5636i	−0.746905	+	0.746905i
$759$	32.7109			1.18733
$760$	13.5309	−	4.69291i	0.490816	−	0.170230i
$761$			40.4126i			1.46496i	0.680791	+	0.732478i	$0.261636\pi$
$761$			40.4126i			1.46496i	−0.680791	+	0.732478i	$0.738364\pi$
$762$	13.6442	+	13.6442i	0.494276	+	0.494276i
$763$	−1.93430	+	1.93430i	−0.0700263	+	0.0700263i
$764$		−	7.55134i		−	0.273198i
$765$	−6.04016	+	2.09491i	−0.218382	+	0.0757416i
$766$			1.83848i			0.0664271i
$767$	−1.49724	+	1.49724i	−0.0540622	+	0.0540622i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$		−	10.5247i		−	0.379530i	−0.981830	−	0.189765i	$-0.939227\pi$
$769$		−	10.5247i		−	0.379530i	0.981830	−	0.189765i	$-0.0607727\pi$
$770$	−25.2057	+	51.9738i	−0.908349	+	1.87301i
$771$		−	10.6133i		−	0.382228i
$772$	−11.7035	−	11.7035i	−0.421219	−	0.421219i
$773$	24.5081	+	24.5081i	0.881495	+	0.881495i	0.993687	−	0.112192i	$-0.0357871\pi$
$773$	24.5081	+	24.5081i	0.881495	+	0.881495i	−0.112192	+	0.993687i	$0.535787\pi$
$774$	−12.0039			−0.431470
$775$	−5.08201	+	27.3710i	−0.182551	+	0.983196i
$776$	−18.7778			−0.674082
$777$	−16.5625	−	16.5625i	−0.594178	−	0.594178i
$778$	15.8237	+	15.8237i	0.567307	+	0.567307i
$779$		−	2.85856i		−	0.102418i
$780$	−1.29126	+	2.66256i	−0.0462344	+	0.0953349i
$781$		−	22.8800i		−	0.818711i
$782$	−11.4927	−	11.4927i	−0.410977	−	0.410977i
$783$	−3.21299	+	3.21299i	−0.114823	+	0.114823i
$784$		−	13.1542i		−	0.469792i
$785$	18.2997	−	6.34688i	0.653143	−	0.226530i
$786$		−	3.44698i		−	0.122950i
$787$	−7.16045	+	7.16045i	−0.255243	+	0.255243i	−0.823116	−	0.567873i	$-0.807766\pi$
$787$	−7.16045	+	7.16045i	−0.255243	+	0.255243i	0.567873	+	0.823116i	$0.307766\pi$
$788$	−1.68004	−	1.68004i	−0.0598489	−	0.0598489i
$789$			23.0096i			0.819163i
$790$	−7.77525	+	2.69669i	−0.276631	+	0.0959439i
$791$	−74.7612			−2.65820
$792$	−4.06883	+	4.06883i	−0.144580	+	0.144580i
$793$	−11.6930	+	11.6930i	−0.415231	+	0.415231i
$794$			4.04040i			0.143388i
$795$	−6.70133	−	3.24993i	−0.237672	−	0.115263i
$796$		−	12.1116i		−	0.429286i
$797$	−15.3953	+	15.3953i	−0.545330	+	0.545330i	−0.925087	−	0.379756i	$-0.876008\pi$
$797$	−15.3953	+	15.3953i	−0.545330	+	0.545330i	0.379756	+	0.925087i	$0.376008\pi$
$798$	−20.3317	−	20.3317i	−0.719734	−	0.719734i
$799$	28.7322			1.01647
$800$	−0.587153	+	4.96541i	−0.0207590	+	0.175554i
$801$		−	14.0364i		−	0.495951i
$802$	−6.55111	+	6.55111i	−0.231328	+	0.231328i
$803$	−20.7132	+	20.7132i	−0.730952	+	0.730952i
$804$	−9.09363			−0.320708
$805$	−51.3461	−	24.9012i	−1.80971	−	0.877653i
$806$	5.54180	−	4.85583i	0.195202	−	0.171039i
$807$	0.253734	+	0.253734i	0.00893185	+	0.00893185i
$808$	−4.81772	+	4.81772i	−0.169487	+	0.169487i
$809$	−10.1397			−0.356492			−0.178246	−	0.983986i	$-0.557042\pi$
$809$	−10.1397			−0.356492			−0.178246	+	0.983986i	$0.557042\pi$
$810$	−2.11261	+	0.732717i	−0.0742296	+	0.0257451i
$811$	7.86073			0.276027			0.138014	−	0.990430i	$-0.455928\pi$
$811$	7.86073			0.276027			0.138014	+	0.990430i	$0.455928\pi$
$812$	14.4242	−	14.4242i	0.506190	−	0.506190i
$813$	6.24773	−	6.24773i	0.219117	−	0.219117i
$814$		−	30.0223i		−	1.05228i
$815$	1.72281	+	4.96729i	0.0603473	+	0.173997i
$816$	2.85910			0.100088
$817$	54.3640	−	54.3640i	1.90196	−	1.90196i
$818$	−5.36659	−	5.36659i	−0.187638	−	0.187638i
$819$	5.94107			0.207598
$820$	0.897964	+	0.435484i	0.0313583	+	0.0152078i
$821$			22.7883i			0.795319i	0.917533	+	0.397659i	$0.130177\pi$
$821$			22.7883i			0.795319i	−0.917533	+	0.397659i	$0.869823\pi$
$822$	−12.6143	−	12.6143i	−0.439976	−	0.439976i
$823$	−7.92094	−	7.92094i	−0.276106	−	0.276106i	0.555446	−	0.831553i	$-0.312548\pi$
$823$	−7.92094	−	7.92094i	−0.276106	−	0.276106i	−0.831553	+	0.555446i	$0.812548\pi$
$824$			11.7110i			0.407971i
$825$	−28.5719	−	3.37859i	−0.994747	−	0.117628i
$826$	7.18302			0.249929
$827$	−18.4274	+	18.4274i	−0.640785	+	0.640785i	−0.950748	−	0.309964i	$-0.899683\pi$
$827$	−18.4274	+	18.4274i	−0.640785	+	0.640785i	0.309964	+	0.950748i	$0.399683\pi$
$828$	−4.01969	−	4.01969i	−0.139694	−	0.139694i
$829$	−17.1554			−0.595833			−0.297916	−	0.954592i	$-0.596292\pi$
$829$	−17.1554			−0.595833			−0.297916	+	0.954592i	$0.596292\pi$
$830$	5.75015	+	2.78864i	0.199591	+	0.0967951i
$831$	16.7994			0.582765
$832$	0.935765	−	0.935765i	0.0324418	−	0.0324418i
$833$	−26.5936	−	26.5936i	−0.921414	−	0.921414i
$834$			14.9718i			0.518430i
$835$	5.18016	+	14.9357i	0.179267	+	0.516873i
$836$		−	36.8545i		−	1.27464i
$837$	5.55569	+	0.366530i	0.192033	+	0.0126691i
$838$	14.1959	−	14.1959i	0.490389	−	0.490389i
$839$			6.32869i			0.218490i	0.994015	+	0.109245i	$0.0348434\pi$
$839$			6.32869i			0.218490i	−0.994015	+	0.109245i	$0.965157\pi$
$840$	9.48423	−	3.28942i	0.327237	−	0.113496i
$841$	−8.35345			−0.288050
$842$	10.3834	+	10.3834i	0.357837	+	0.357837i
$843$	−8.81128	−	8.81128i	−0.303477	−	0.303477i
$844$			22.4254i			0.771914i
$845$	−22.6318	−	10.9757i	−0.778558	−	0.377576i
$846$	10.0494			0.345506
$847$	70.1895	+	70.1895i	2.41174	+	2.41174i
$848$	2.35521	+	2.35521i	0.0808781	+	0.0808781i
$849$	11.9503			0.410134
$850$	8.85145	+	11.2255i	0.303602	+	0.385032i
$851$	29.6597			1.01672
$852$	−2.81162	+	2.81162i	−0.0963245	+	0.0963245i
$853$	−0.469338	+	0.469338i	−0.0160698	+	0.0160698i	−0.715096	−	0.699026i	$-0.753617\pi$
$853$	−0.469338	+	0.469338i	−0.0160698	+	0.0160698i	0.699026	+	0.715096i	$0.253617\pi$
$854$	56.0973			1.91961
$855$	6.24937	−	12.8861i	0.213724	−	0.440697i
$856$	−3.29913			−0.112762
$857$	21.3954	+	21.3954i	0.730853	+	0.730853i	0.970789	−	0.239936i	$-0.0771263\pi$
$857$	21.3954	+	21.3954i	0.730853	+	0.730853i	−0.239936	+	0.970789i	$0.577126\pi$
$858$	5.38458	+	5.38458i	0.183827	+	0.183827i
$859$	−28.3097			−0.965913			−0.482956	−	0.875644i	$-0.660437\pi$
$859$	−28.3097			−0.965913			−0.482956	+	0.875644i	$0.660437\pi$
$860$	8.79543	+	25.3595i	0.299922	+	0.864751i
$861$		−	2.00366i		−	0.0682845i
$862$	21.7312	+	21.7312i	0.740166	+	0.740166i
$863$	−6.38952	−	6.38952i	−0.217502	−	0.217502i	0.589943	−	0.807445i	$-0.299150\pi$
$863$	−6.38952	−	6.38952i	−0.217502	−	0.217502i	−0.807445	+	0.589943i	$0.799150\pi$
$864$	1.00000			0.0340207
$865$	0.336767	+	0.970987i	0.0114504	+	0.0330145i
$866$			1.83296i			0.0622864i
$867$	−6.24062	+	6.24062i	−0.211943	+	0.211943i
$868$	−24.9414	−	1.64548i	−0.846565	−	0.0558511i
$869$			21.1777i			0.718405i
$870$	9.14200	+	4.43358i	0.309943	+	0.150312i
$871$			12.0343i			0.407765i
$872$	0.430865	+	0.430865i	0.0145909	+	0.0145909i
$873$	−13.2779	+	13.2779i	−0.449388	+	0.449388i
$874$	36.4094			1.23156
$875$	42.2772	+	27.0538i	1.42923	+	0.914585i
$876$	5.09069			0.171998
$877$	−9.08096	−	9.08096i	−0.306642	−	0.306642i	0.536963	−	0.843606i	$-0.319571\pi$
$877$	−9.08096	−	9.08096i	−0.306642	−	0.306642i	−0.843606	+	0.536963i	$0.819571\pi$
$878$	10.1301	−	10.1301i	0.341874	−	0.341874i
$879$	−1.59512			−0.0538022
$880$	11.5772	+	5.61456i	0.390266	+	0.189267i
$881$		−	6.47345i		−	0.218096i	−0.994036	−	0.109048i	$-0.965220\pi$
$881$		−	6.47345i		−	0.218096i	0.994036	−	0.109048i	$-0.0347802\pi$
$882$	−9.30141	−	9.30141i	−0.313195	−	0.313195i
$883$	8.19927	+	8.19927i	0.275927	+	0.275927i	0.831481	−	0.555553i	$-0.187494\pi$
$883$	8.19927	+	8.19927i	0.275927	+	0.275927i	−0.555553	+	0.831481i	$0.687494\pi$
$884$		−	3.78365i		−	0.127258i
$885$	1.17236	+	3.38021i	0.0394084	+	0.113625i
$886$	−28.2851			−0.950255
$887$	−12.3726	−	12.3726i	−0.415432	−	0.415432i	0.468194	−	0.883626i	$-0.344905\pi$
$887$	−12.3726	−	12.3726i	−0.415432	−	0.415432i	−0.883626	+	0.468194i	$0.844905\pi$
$888$	−3.68930	+	3.68930i	−0.123805	+	0.123805i
$889$	−86.6252			−2.90532
$890$	−29.6534	+	10.2847i	−0.993984	+	0.344744i
$891$			5.75420i			0.192773i
$892$	−5.17394	+	5.17394i	−0.173236	+	0.173236i
$893$	−45.5126	+	45.5126i	−1.52302	+	1.52302i
$894$	17.5610			0.587327
$895$	−21.7229	+	44.7924i	−0.726117	+	1.49725i
$896$	−4.48934			−0.149978
$897$	−5.31954	+	5.31954i	−0.177614	+	0.177614i
$898$	−5.63239	−	5.63239i	−0.187955	−	0.187955i
$899$	−16.6727	−	19.0280i	−0.556065	−	0.634619i
$900$	3.09589	+	3.92625i	0.103196	+	0.130875i
$901$	9.52297			0.317256
$902$	1.81598	−	1.81598i	0.0604656	−	0.0604656i
$903$	38.1055	−	38.1055i	1.26807	−	1.26807i
$904$			16.6531i			0.553872i
$905$	21.1602	+	10.2620i	0.703389	+	0.341121i
$906$	5.34465			0.177564
$907$	23.0265	+	23.0265i	0.764584	+	0.764584i	0.977147	−	0.212564i	$-0.0681813\pi$
$907$	23.0265	+	23.0265i	0.764584	+	0.764584i	−0.212564	+	0.977147i	$0.568181\pi$
$908$	0.547026	−	0.547026i	0.0181537	−	0.0181537i
$909$			6.81329i			0.225982i
$910$	−4.35312	−	12.5512i	−0.144305	−	0.416067i
$911$			60.0455i			1.98939i	0.102845	+	0.994697i	$0.467205\pi$
$911$			60.0455i			1.98939i	−0.102845	+	0.994697i	$0.532795\pi$
$912$	−4.52888	+	4.52888i	−0.149966	+	0.149966i
$913$	11.6287	−	11.6287i	0.384854	−	0.384854i
$914$	14.2844			0.472486
$915$	9.15579	+	26.3985i	0.302681	+	0.872708i
$916$			24.8830i			0.822157i
$917$	10.9422	+	10.9422i	0.361345	+	0.361345i
$918$	2.02169	−	2.02169i	0.0667256	−	0.0667256i
$919$		−	23.9004i		−	0.788402i	−0.919024	−	0.394201i	$-0.871021\pi$
$919$		−	23.9004i		−	0.788402i	0.919024	−	0.394201i	$-0.128979\pi$
$920$	−5.54674	+	11.4373i	−0.182871	+	0.377078i
$921$		−	17.6464i		−	0.581467i
$922$	13.7650	−	13.7650i	0.453326	−	0.453326i
$923$	3.72082	+	3.72082i	0.122472	+	0.122472i
$924$		−	25.8326i		−	0.849829i
$925$	−25.9068	−	3.06345i	−0.851811	−	0.100726i
$926$			37.8210i			1.24287i
$927$	8.28090	+	8.28090i	0.271981	+	0.271981i
$928$	−3.21299	−	3.21299i	−0.105471	−	0.105471i
$929$	−5.77852			−0.189587			−0.0947935	−	0.995497i	$-0.530219\pi$
$929$	−5.77852			−0.189587			−0.0947935	+	0.995497i	$0.530219\pi$
$930$	−3.29641	−	12.0056i	−0.108094	−	0.393678i
$931$	84.2499			2.76118
$932$	1.81314	+	1.81314i	0.0593913	+	0.0593913i
$933$	−5.81369	−	5.81369i	−0.190332	−	0.190332i
$934$			33.9877i			1.11211i
$935$	34.7563	−	12.0545i	1.13665	−	0.394225i
$936$		−	1.32337i		−	0.0432558i
$937$	−23.4129	−	23.4129i	−0.764867	−	0.764867i	0.212331	−	0.977198i	$-0.431895\pi$
$937$	−23.4129	−	23.4129i	−0.764867	−	0.764867i	−0.977198	+	0.212331i	$0.931895\pi$
$938$	28.8672	−	28.8672i	0.942548	−	0.942548i
$939$			21.3677i			0.697308i
$940$	−7.36338	−	21.2305i	−0.240167	−	0.692463i
$941$		−	37.3115i		−	1.21632i	−0.793814	−	0.608161i	$-0.791908\pi$
$941$		−	37.3115i		−	1.21632i	0.793814	−	0.608161i	$-0.208092\pi$
$942$	−6.12504	+	6.12504i	−0.199565	+	0.199565i
$943$	1.79405	+	1.79405i	0.0584222	+	0.0584222i
$944$		−	1.60002i		−	0.0520761i
$945$	4.38040	−	9.03233i	0.142494	−	0.293822i
$946$	69.0726			2.24574
$947$	−17.1945	+	17.1945i	−0.558745	+	0.558745i	−0.928950	−	0.370205i	$-0.879287\pi$
$947$	−17.1945	+	17.1945i	−0.558745	+	0.558745i	0.370205	+	0.928950i	$0.379287\pi$
$948$	2.60243	−	2.60243i	0.0845231	−	0.0845231i
$949$		−	6.73687i		−	0.218688i
$950$	−31.8024	−	3.76060i	−1.03181	−	0.122010i
$951$			5.21939i			0.169250i
$952$	−9.07604	+	9.07604i	−0.294156	+	0.294156i
$953$	15.7711	+	15.7711i	0.510876	+	0.510876i	0.914795	−	0.403919i	$-0.132352\pi$
$953$	15.7711	+	15.7711i	0.510876	+	0.510876i	−0.403919	+	0.914795i	$0.632352\pi$
$954$	3.33076			0.107837
$955$	−7.36809	+	15.1929i	−0.238426	+	0.491632i
$956$			17.7715i			0.574770i
$957$	18.4882	−	18.4882i	0.597637	−	0.597637i
$958$	1.88973	−	1.88973i	0.0610543	−	0.0610543i
$959$	80.0871			2.58615
$960$	−0.732717	−	2.11261i	−0.0236483	−	0.0681842i
$961$	−4.07265	+	30.7313i	−0.131376	+	0.991333i
$962$	4.88232	+	4.88232i	0.157412	+	0.157412i
$963$	−2.33284	+	2.33284i	−0.0751746	+	0.0751746i
$964$	−12.1437			−0.391123
$965$	12.1274	+	34.9664i	0.390395	+	1.12561i
$966$	25.5205			0.821110
$967$	−19.3408	+	19.3408i	−0.621959	+	0.621959i	−0.946032	−	0.324073i	$-0.894948\pi$
$967$	−19.3408	+	19.3408i	−0.621959	+	0.621959i	0.324073	+	0.946032i	$0.394948\pi$
$968$	15.6347	−	15.6347i	0.502518	−	0.502518i
$969$			18.3119i			0.588264i
$970$	37.7799	+	18.3221i	1.21304	+	0.588286i
$971$	−47.2709			−1.51700			−0.758498	−	0.651676i	$-0.774066\pi$
$971$	−47.2709			−1.51700			−0.758498	+	0.651676i	$0.774066\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	−47.5270	−	47.5270i	−1.52365	−	1.52365i
$974$	15.2240			0.487808
$975$	5.19589	−	4.09702i	0.166402	−	0.131210i
$976$		−	12.4957i		−	0.399977i
$977$	−27.1454	−	27.1454i	−0.868457	−	0.868457i	0.123845	−	0.992302i	$-0.460478\pi$
$977$	−27.1454	−	27.1454i	−0.868457	−	0.868457i	−0.992302	+	0.123845i	$0.960478\pi$
$978$	−1.66259	−	1.66259i	−0.0531638	−	0.0531638i
$979$			80.7681i			2.58136i
$980$	−12.8350	+	26.4656i	−0.409998	+	0.845411i
$981$	0.609335			0.0194546
$982$	12.0166	−	12.0166i	0.383464	−	0.383464i
$983$	−20.9743	−	20.9743i	−0.668976	−	0.668976i	0.288503	−	0.957479i	$-0.406843\pi$
$983$	−20.9743	−	20.9743i	−0.668976	−	0.668976i	−0.957479	+	0.288503i	$0.906843\pi$
$984$	−0.446315			−0.0142280
$985$	1.74089	+	5.01943i	0.0554693	+	0.159932i
$986$	−12.9913			−0.413727
$987$	−31.9013	+	31.9013i	−1.01543	+	1.01543i
$988$	5.99339	+	5.99339i	0.190675	+	0.190675i
$989$			68.2383i			2.16985i
$990$	12.1564	−	4.21620i	0.386355	−	0.134000i
$991$		−	44.7720i		−	1.42223i	−0.703077	−	0.711114i	$-0.748191\pi$
$991$		−	44.7720i		−	1.42223i	0.703077	−	0.711114i	$-0.251809\pi$
$992$	−0.366530	+	5.55569i	−0.0116373	+	0.176393i
$993$	5.84973	−	5.84973i	0.185635	−	0.185635i
$994$		−	17.8506i		−	0.566188i
$995$	−11.8177	+	24.3680i	−0.374647	+	0.772519i
$996$	−2.85800			−0.0905591
$997$	−15.6560	−	15.6560i	−0.495829	−	0.495829i	0.414308	−	0.910137i	$-0.364024\pi$
$997$	−15.6560	−	15.6560i	−0.495829	−	0.495829i	−0.910137	+	0.414308i	$0.864024\pi$
$998$	−18.6613	−	18.6613i	−0.590713	−	0.590713i
$999$			5.21746i			0.165073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.k.b.247.14	yes	32
5.3	odd	4		930.2.k.a.433.14	yes	32
31.30	odd	2		930.2.k.a.247.14	✓	32
155.123	even	4	inner	930.2.k.b.433.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.k.a.247.14	✓	32	31.30	odd	2
930.2.k.a.433.14	yes	32	5.3	odd	4
930.2.k.b.247.14	yes	32	1.1	even	1	trivial
930.2.k.b.433.14	yes	32	155.123	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(0.975733 - 2.01195i) q^{5} +1.00000i q^{6} +(-3.17444 - 3.17444i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(0.975733 - 2.01195i) q^{5} +1.00000i q^{6} +(-3.17444 - 3.17444i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(2.11261 - 0.732717i) q^{10} -5.75420i q^{11} +(-0.707107 + 0.707107i) q^{12} +(0.935765 + 0.935765i) q^{13} -4.48934i q^{14} +(2.11261 - 0.732717i) q^{15} -1.00000 q^{16} +(-2.02169 + 2.02169i) q^{17} +(-0.707107 + 0.707107i) q^{18} -6.40480i q^{19} +(2.01195 + 0.975733i) q^{20} -4.48934i q^{21} +(4.06883 - 4.06883i) q^{22} +(4.01969 + 4.01969i) q^{23} -1.00000 q^{24} +(-3.09589 - 3.92625i) q^{25} +1.32337i q^{26} +(-0.707107 + 0.707107i) q^{27} +(3.17444 - 3.17444i) q^{28} +4.54385 q^{29} +(2.01195 + 0.975733i) q^{30} +(-3.66929 - 4.18764i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.06883 - 4.06883i) q^{33} -2.85910 q^{34} +(-9.48423 + 3.28942i) q^{35} -1.00000 q^{36} +(3.68930 - 3.68930i) q^{37} +(4.52888 - 4.52888i) q^{38} +1.32337i q^{39} +(0.732717 + 2.11261i) q^{40} +0.446315 q^{41} +(3.17444 - 3.17444i) q^{42} +(8.48801 + 8.48801i) q^{43} +5.75420 q^{44} +(2.01195 + 0.975733i) q^{45} +5.68470i q^{46} +(-7.10601 - 7.10601i) q^{47} +(-0.707107 - 0.707107i) q^{48} +13.1542i q^{49} +(0.587153 - 4.96541i) q^{50} -2.85910 q^{51} +(-0.935765 + 0.935765i) q^{52} +(-2.35521 - 2.35521i) q^{53} -1.00000 q^{54} +(-11.5772 - 5.61456i) q^{55} +4.48934 q^{56} +(4.52888 - 4.52888i) q^{57} +(3.21299 + 3.21299i) q^{58} +1.60002i q^{59} +(0.732717 + 2.11261i) q^{60} +12.4957i q^{61} +(0.366530 - 5.55569i) q^{62} +(3.17444 - 3.17444i) q^{63} -1.00000i q^{64} +(2.79577 - 0.969657i) q^{65} +5.75420 q^{66} +(6.43017 + 6.43017i) q^{67} +(-2.02169 - 2.02169i) q^{68} +5.68470i q^{69} +(-9.03233 - 4.38040i) q^{70} +3.97623 q^{71} +(-0.707107 - 0.707107i) q^{72} +(-3.59966 - 3.59966i) q^{73} +5.21746 q^{74} +(0.587153 - 4.96541i) q^{75} +6.40480 q^{76} +(-18.2664 + 18.2664i) q^{77} +(-0.935765 + 0.935765i) q^{78} -3.68040 q^{79} +(-0.975733 + 2.01195i) q^{80} -1.00000 q^{81} +(0.315592 + 0.315592i) q^{82} +(2.02091 + 2.02091i) q^{83} +4.48934 q^{84} +(2.09491 + 6.04016i) q^{85} +12.0039i q^{86} +(3.21299 + 3.21299i) q^{87} +(4.06883 + 4.06883i) q^{88} -14.0364 q^{89} +(0.732717 + 2.11261i) q^{90} -5.94107i q^{91} +(-4.01969 + 4.01969i) q^{92} +(0.366530 - 5.55569i) q^{93} -10.0494i q^{94} +(-12.8861 - 6.24937i) q^{95} -1.00000i q^{96} +(13.2779 + 13.2779i) q^{97} +(-9.30141 + 9.30141i) q^{98} +5.75420 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7}+O(q^{10}) \) 32 * q - 4 * q^7	\( 32 q - 4 q^{7} + 4 q^{10} + 4 q^{15} - 32 q^{16} + 8 q^{17} - 4 q^{22} - 32 q^{24} + 8 q^{25} + 4 q^{28} + 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} + 4 q^{37} + 16 q^{38} - 16 q^{41} + 4 q^{42} - 16 q^{43} - 8 q^{44} - 8 q^{47} - 16 q^{50} - 24 q^{53} - 32 q^{54} - 28 q^{55} + 16 q^{57} + 20 q^{58} - 8 q^{62} + 4 q^{63} + 56 q^{65} - 8 q^{66} + 32 q^{67} + 8 q^{68} - 28 q^{70} + 16 q^{71} - 20 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 40 q^{77} - 56 q^{79} - 32 q^{81} + 16 q^{82} + 72 q^{83} - 32 q^{85} + 20 q^{87} - 4 q^{88} - 64 q^{89} - 8 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 + 4 * q^15 - 32 * q^16 + 8 * q^17 - 4 * q^22 - 32 * q^24 + 8 * q^25 + 4 * q^28 + 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 + 4 * q^37 + 16 * q^38 - 16 * q^41 + 4 * q^42 - 16 * q^43 - 8 * q^44 - 8 * q^47 - 16 * q^50 - 24 * q^53 - 32 * q^54 - 28 * q^55 + 16 * q^57 + 20 * q^58 - 8 * q^62 + 4 * q^63 + 56 * q^65 - 8 * q^66 + 32 * q^67 + 8 * q^68 - 28 * q^70 + 16 * q^71 - 20 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 40 * q^77 - 56 * q^79 - 32 * q^81 + 16 * q^82 + 72 * q^83 - 32 * q^85 + 20 * q^87 - 4 * q^88 - 64 * q^89 - 8 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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