LMFDB - Embedded newform 430.2.g.b.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(257,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("430.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.g (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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.1
Character	$\chi$	$=$	430.257
Dual form			430.2.g.b.343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-2.27071 - 2.27071i) q^{3} -1.00000i q^{4} +(-1.31680 + 1.80721i) q^{5} +3.21127 q^{6} +(-0.136059 + 0.136059i) q^{7} +(0.707107 + 0.707107i) q^{8} +7.31224i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.27071 - 2.27071i) q^{3} -1.00000i q^{4} +(-1.31680 + 1.80721i) q^{5} +3.21127 q^{6} +(-0.136059 + 0.136059i) q^{7} +(0.707107 + 0.707107i) q^{8} +7.31224i q^{9} +(-0.346772 - 2.20902i) q^{10} -0.331801 q^{11} +(-2.27071 + 2.27071i) q^{12} +(-0.227765 + 0.227765i) q^{13} -0.192416i q^{14} +(7.09374 - 1.11358i) q^{15} -1.00000 q^{16} +(-2.17935 - 2.17935i) q^{17} +(-5.17053 - 5.17053i) q^{18} +6.24824 q^{19} +(1.80721 + 1.31680i) q^{20} +0.617899 q^{21} +(0.234619 - 0.234619i) q^{22} +(1.18798 - 1.18798i) q^{23} -3.21127i q^{24} +(-1.53205 - 4.75950i) q^{25} -0.322108i q^{26} +(9.79184 - 9.79184i) q^{27} +(0.136059 + 0.136059i) q^{28} +0.0611545 q^{29} +(-4.22861 + 5.80345i) q^{30} +5.84403 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.753423 + 0.753423i) q^{33} +3.08206 q^{34} +(-0.0667245 - 0.425050i) q^{35} +7.31224 q^{36} +(6.41444 - 6.41444i) q^{37} +(-4.41818 + 4.41818i) q^{38} +1.03437 q^{39} +(-2.20902 + 0.346772i) q^{40} +3.48498 q^{41} +(-0.436921 + 0.436921i) q^{42} +(5.15004 - 4.05920i) q^{43} +0.331801i q^{44} +(-13.2148 - 9.62879i) q^{45} +1.68006i q^{46} +(5.80806 + 5.80806i) q^{47} +(2.27071 + 2.27071i) q^{48} +6.96298i q^{49} +(4.44880 + 2.28215i) q^{50} +9.89733i q^{51} +(0.227765 + 0.227765i) q^{52} +(-9.01382 + 9.01382i) q^{53} +13.8478i q^{54} +(0.436917 - 0.599636i) q^{55} -0.192416 q^{56} +(-14.1879 - 14.1879i) q^{57} +(-0.0432427 + 0.0432427i) q^{58} -5.56431i q^{59} +(-1.11358 - 7.09374i) q^{60} -1.13949i q^{61} +(-4.13235 + 4.13235i) q^{62} +(-0.994894 - 0.994894i) q^{63} +1.00000i q^{64} +(-0.111698 - 0.711541i) q^{65} -1.06550 q^{66} +(-8.76665 - 8.76665i) q^{67} +(-2.17935 + 2.17935i) q^{68} -5.39513 q^{69} +(0.347737 + 0.253374i) q^{70} +12.3226i q^{71} +(-5.17053 + 5.17053i) q^{72} +(8.28023 + 8.28023i) q^{73} +9.07139i q^{74} +(-7.32860 + 14.2863i) q^{75} -6.24824i q^{76} +(0.0451444 - 0.0451444i) q^{77} +(-0.731413 + 0.731413i) q^{78} -4.93159i q^{79} +(1.31680 - 1.80721i) q^{80} -22.5321 q^{81} +(-2.46426 + 2.46426i) q^{82} +(7.28759 - 7.28759i) q^{83} -0.617899i q^{84} +(6.80833 - 1.06877i) q^{85} +(-0.771338 + 6.51192i) q^{86} +(-0.138864 - 0.138864i) q^{87} +(-0.234619 - 0.234619i) q^{88} +10.6751 q^{89} +(16.1528 - 2.53568i) q^{90} -0.0619787i q^{91} +(-1.18798 - 1.18798i) q^{92} +(-13.2701 - 13.2701i) q^{93} -8.21384 q^{94} +(-8.22772 + 11.2919i) q^{95} -3.21127 q^{96} +(10.1638 + 10.1638i) q^{97} +(-4.92357 - 4.92357i) q^{98} -2.42621i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q+O(q^{10}) $ 40 * q	$ 40 q - 8 q^{10} + 16 q^{11} - 24 q^{13} + 8 q^{15} - 40 q^{16} - 12 q^{17} - 16 q^{21} + 44 q^{23} + 24 q^{25} + 32 q^{31} - 64 q^{35} + 48 q^{36} - 28 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} - 28 q^{47} + 24 q^{52} - 80 q^{53} + 24 q^{56} + 64 q^{57} + 12 q^{58} + 24 q^{67} - 12 q^{68} + 40 q^{78} - 120 q^{81} + 48 q^{83} + 28 q^{87} - 44 q^{92} - 16 q^{95} - 60 q^{97}+O(q^{100}) $ 40 * q - 8 * q^10 + 16 * q^11 - 24 * q^13 + 8 * q^15 - 40 * q^16 - 12 * q^17 - 16 * q^21 + 44 * q^23 + 24 * q^25 + 32 * q^31 - 64 * q^35 + 48 * q^36 - 28 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 - 28 * q^47 + 24 * q^52 - 80 * q^53 + 24 * q^56 + 64 * q^57 + 12 * q^58 + 24 * q^67 - 12 * q^68 + 40 * q^78 - 120 * q^81 + 48 * q^83 + 28 * q^87 - 44 * q^92 - 16 * q^95 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$	−2.27071	−	2.27071i	−1.31099	−	1.31099i	−0.920683	−	0.390312i	$-0.872367\pi$
$3$	−2.27071	−	2.27071i	−1.31099	−	1.31099i	−0.390312	−	0.920683i	$-0.627633\pi$
$4$		−	1.00000i		−	0.500000i
$5$	−1.31680	+	1.80721i	−0.588893	+	0.808211i
$5$	−1.31680	+	1.80721i	−0.588893	+	0.808211i
$6$	3.21127			1.31099
$7$	−0.136059	+	0.136059i	−0.0514254	+	0.0514254i	−0.732352	−	0.680926i	$-0.761577\pi$
$7$	−0.136059	+	0.136059i	−0.0514254	+	0.0514254i	0.680926	+	0.732352i	$0.261577\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			7.31224i			2.43741i
$10$	−0.346772	−	2.20902i	−0.109659	−	0.698552i
$11$	−0.331801			−0.100042			−0.0500209	−	0.998748i	$-0.515929\pi$
$11$	−0.331801			−0.100042			−0.0500209	+	0.998748i	$0.515929\pi$
$12$	−2.27071	+	2.27071i	−0.655497	+	0.655497i
$13$	−0.227765	+	0.227765i	−0.0631705	+	0.0631705i	−0.737986	−	0.674816i	$-0.764223\pi$
$13$	−0.227765	+	0.227765i	−0.0631705	+	0.0631705i	0.674816	+	0.737986i	$0.264223\pi$
$14$		−	0.192416i		−	0.0514254i
$15$	7.09374	−	1.11358i	1.83160	−	0.287525i
$16$	−1.00000			−0.250000
$17$	−2.17935	−	2.17935i	−0.528570	−	0.528570i	0.391576	−	0.920146i	$-0.371930\pi$
$17$	−2.17935	−	2.17935i	−0.528570	−	0.528570i	−0.920146	+	0.391576i	$0.871930\pi$
$18$	−5.17053	−	5.17053i	−1.21871	−	1.21871i
$19$	6.24824			1.43345			0.716723	−	0.697358i	$-0.245641\pi$
$19$	6.24824			1.43345			0.716723	+	0.697358i	$0.245641\pi$
$20$	1.80721	+	1.31680i	0.404105	+	0.294447i
$21$	0.617899			0.134837
$22$	0.234619	−	0.234619i	0.0500209	−	0.0500209i
$23$	1.18798	−	1.18798i	0.247712	−	0.247712i	−0.572319	−	0.820031i	$-0.693956\pi$
$23$	1.18798	−	1.18798i	0.247712	−	0.247712i	0.820031	+	0.572319i	$0.193956\pi$
$24$		−	3.21127i		−	0.655497i
$25$	−1.53205	−	4.75950i	−0.306410	−	0.951900i
$26$		−	0.322108i		−	0.0631705i
$27$	9.79184	−	9.79184i	1.88444	−	1.88444i
$28$	0.136059	+	0.136059i	0.0257127	+	0.0257127i
$29$	0.0611545			0.0113561			0.00567805	−	0.999984i	$-0.498193\pi$
$29$	0.0611545			0.0113561			0.00567805	+	0.999984i	$0.498193\pi$
$30$	−4.22861	+	5.80345i	−0.772036	+	1.05956i
$31$	5.84403			1.04962			0.524809	−	0.851220i	$-0.324137\pi$
$31$	5.84403			1.04962			0.524809	+	0.851220i	$0.324137\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.753423	+	0.753423i	0.131154	+	0.131154i
$34$	3.08206			0.528570
$35$	−0.0667245	−	0.425050i	−0.0112785	−	0.0718466i
$36$	7.31224			1.21871
$37$	6.41444	−	6.41444i	1.05453	−	1.05453i	0.0561032	−	0.998425i	$-0.482132\pi$
$37$	6.41444	−	6.41444i	1.05453	−	1.05453i	0.998425	−	0.0561032i	$-0.0178676\pi$
$38$	−4.41818	+	4.41818i	−0.716723	+	0.716723i
$39$	1.03437			0.165632
$40$	−2.20902	+	0.346772i	−0.349276	+	0.0548295i
$41$	3.48498			0.544263			0.272132	−	0.962260i	$-0.412271\pi$
$41$	3.48498			0.544263			0.272132	+	0.962260i	$0.412271\pi$
$42$	−0.436921	+	0.436921i	−0.0674184	+	0.0674184i
$43$	5.15004	−	4.05920i	0.785373	−	0.619022i
$43$	5.15004	−	4.05920i	0.785373	−	0.619022i
$44$			0.331801i			0.0500209i
$45$	−13.2148	−	9.62879i	−1.96994	−	1.43538i
$46$			1.68006i			0.247712i
$47$	5.80806	+	5.80806i	0.847193	+	0.847193i	0.989782	−	0.142589i	$-0.0455428\pi$
$47$	5.80806	+	5.80806i	0.847193	+	0.847193i	−0.142589	+	0.989782i	$0.545543\pi$
$48$	2.27071	+	2.27071i	0.327749	+	0.327749i
$49$			6.96298i			0.994711i
$50$	4.44880	+	2.28215i	0.629155	+	0.322745i
$51$			9.89733i			1.38590i
$52$	0.227765	+	0.227765i	0.0315853	+	0.0315853i
$53$	−9.01382	+	9.01382i	−1.23814	+	1.23814i	−0.277384	+	0.960759i	$0.589467\pi$
$53$	−9.01382	+	9.01382i	−1.23814	+	1.23814i	−0.960759	+	0.277384i	$0.910533\pi$
$54$			13.8478i			1.88444i
$55$	0.436917	−	0.599636i	0.0589139	−	0.0808548i
$56$	−0.192416			−0.0257127
$57$	−14.1879	−	14.1879i	−1.87924	−	1.87924i
$58$	−0.0432427	+	0.0432427i	−0.00567805	+	0.00567805i
$59$		−	5.56431i		−	0.724412i	−0.932098	−	0.362206i	$-0.882024\pi$
$59$		−	5.56431i		−	0.724412i	0.932098	−	0.362206i	$-0.117976\pi$
$60$	−1.11358	−	7.09374i	−0.143762	−	0.915798i
$61$		−	1.13949i		−	0.145896i	−0.997336	−	0.0729481i	$-0.976759\pi$
$61$		−	1.13949i		−	0.145896i	0.997336	−	0.0729481i	$-0.0232408\pi$
$62$	−4.13235	+	4.13235i	−0.524809	+	0.524809i
$63$	−0.994894	−	0.994894i	−0.125345	−	0.125345i
$64$			1.00000i			0.125000i
$65$	−0.111698	−	0.711541i	−0.0138544	−	0.0882558i
$66$	−1.06550			−0.131154
$67$	−8.76665	−	8.76665i	−1.07102	−	1.07102i	−0.997278	−	0.0737398i	$-0.976507\pi$
$67$	−8.76665	−	8.76665i	−1.07102	−	1.07102i	−0.0737398	−	0.997278i	$-0.523493\pi$
$68$	−2.17935	+	2.17935i	−0.264285	+	0.264285i
$69$	−5.39513			−0.649498
$70$	0.347737	+	0.253374i	0.0415625	+	0.0302840i
$71$			12.3226i			1.46243i	0.682148	+	0.731214i	$0.261046\pi$
$71$			12.3226i			1.46243i	−0.682148	+	0.731214i	$0.738954\pi$
$72$	−5.17053	+	5.17053i	−0.609353	+	0.609353i
$73$	8.28023	+	8.28023i	0.969128	+	0.969128i	0.999538	−	0.0304097i	$-0.00968122\pi$
$73$	8.28023	+	8.28023i	0.969128	+	0.969128i	−0.0304097	+	0.999538i	$0.509681\pi$
$74$			9.07139i			1.05453i
$75$	−7.32860	+	14.2863i	−0.846233	+	1.64964i
$76$		−	6.24824i		−	0.716723i
$77$	0.0451444	−	0.0451444i	0.00514468	−	0.00514468i
$78$	−0.731413	+	0.731413i	−0.0828162	+	0.0828162i
$79$		−	4.93159i		−	0.554847i	−0.960748	−	0.277424i	$-0.910519\pi$
$79$		−	4.93159i		−	0.554847i	0.960748	−	0.277424i	$-0.0894805\pi$
$80$	1.31680	−	1.80721i	0.147223	−	0.202053i
$81$	−22.5321			−2.50357
$82$	−2.46426	+	2.46426i	−0.272132	+	0.272132i
$83$	7.28759	−	7.28759i	0.799917	−	0.799917i	−0.183165	−	0.983082i	$-0.558634\pi$
$83$	7.28759	−	7.28759i	0.799917	−	0.799917i	0.983082	+	0.183165i	$0.0586344\pi$
$84$		−	0.617899i		−	0.0674184i
$85$	6.80833	−	1.06877i	0.738467	−	0.115925i
$86$	−0.771338	+	6.51192i	−0.0831756	+	0.702198i
$87$	−0.138864	−	0.138864i	−0.0148878	−	0.0148878i
$88$	−0.234619	−	0.234619i	−0.0250104	−	0.0250104i
$89$	10.6751			1.13155			0.565777	−	0.824558i	$-0.308576\pi$
$89$	10.6751			1.13155			0.565777	+	0.824558i	$0.308576\pi$
$90$	16.1528	−	2.53568i	1.70266	−	0.267284i
$91$		−	0.0619787i		−	0.00649713i
$92$	−1.18798	−	1.18798i	−0.123856	−	0.123856i
$93$	−13.2701	−	13.2701i	−1.37604	−	1.37604i
$94$	−8.21384			−0.847193
$95$	−8.22772	+	11.2919i	−0.844146	+	1.15853i
$96$	−3.21127			−0.327749
$97$	10.1638	+	10.1638i	1.03198	+	1.03198i	0.999471	+	0.0325073i	$0.0103492\pi$
$97$	10.1638	+	10.1638i	1.03198	+	1.03198i	0.0325073	+	0.999471i	$0.489651\pi$
$98$	−4.92357	−	4.92357i	−0.497355	−	0.497355i
$99$		−	2.42621i		−	0.243843i
$100$	−4.75950	+	1.53205i	−0.475950	+	0.153205i
$101$	10.8831			1.08290			0.541452	−	0.840732i	$-0.317875\pi$
$101$	10.8831			1.08290			0.541452	+	0.840732i	$0.317875\pi$
$102$	−6.99847	−	6.99847i	−0.692952	−	0.692952i
$103$	−3.28398	+	3.28398i	−0.323580	+	0.323580i	−0.850139	−	0.526558i	$-0.823482\pi$
$103$	−3.28398	+	3.28398i	−0.323580	+	0.323580i	0.526558	+	0.850139i	$0.323482\pi$
$104$	−0.322108			−0.0315853
$105$	−0.813653	+	1.11668i	−0.0794044	+	0.108977i
$106$		−	12.7475i		−	1.23814i
$107$	10.7097	+	10.7097i	1.03535	+	1.03535i	0.999352	+	0.0359938i	$0.0114597\pi$
$107$	10.7097	+	10.7097i	1.03535	+	1.03535i	0.0359938	+	0.999352i	$0.488540\pi$
$108$	−9.79184	−	9.79184i	−0.942220	−	0.942220i
$109$		−	11.9479i		−	1.14440i	−0.820113	−	0.572202i	$-0.806089\pi$
$109$		−	11.9479i		−	1.14440i	0.820113	−	0.572202i	$-0.193911\pi$
$110$	0.115059	+	0.732954i	0.0109705	+	0.0698844i
$111$	−29.1307			−2.76496
$112$	0.136059	−	0.136059i	0.0128563	−	0.0128563i
$113$	−3.59329	−	3.59329i	−0.338028	−	0.338028i	0.517597	−	0.855625i	$-0.326827\pi$
$113$	−3.59329	−	3.59329i	−0.338028	−	0.338028i	−0.855625	+	0.517597i	$0.826827\pi$
$114$	20.0648			1.87924
$115$	0.582599	+	3.71129i	0.0543276	+	0.346079i
$116$		−	0.0611545i		−	0.00567805i
$117$	−1.66547	−	1.66547i	−0.153973	−	0.153973i
$118$	3.93456	+	3.93456i	0.362206	+	0.362206i
$119$	0.593039			0.0543638
$120$	5.80345	+	4.22861i	0.529780	+	0.386018i
$121$	−10.8899			−0.989992
$122$	0.805738	+	0.805738i	0.0729481	+	0.0729481i
$123$	−7.91339	−	7.91339i	−0.713526	−	0.713526i
$124$		−	5.84403i		−	0.524809i
$125$	10.6188	+	3.49859i	0.949778	+	0.312923i
$126$	1.40699			0.125345
$127$	8.42719	+	8.42719i	0.747792	+	0.747792i	0.974064	−	0.226272i	$-0.0726537\pi$
$127$	8.42719	+	8.42719i	0.747792	+	0.747792i	−0.226272	+	0.974064i	$0.572654\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−20.9115	−	2.47697i	−1.84115	−	0.218085i
$130$	0.582118	+	0.424153i	0.0510551	+	0.0372007i
$131$		−	15.8182i		−	1.38204i	−0.722834	−	0.691022i	$-0.757161\pi$
$131$		−	15.8182i		−	1.38204i	0.722834	−	0.691022i	$-0.242839\pi$
$132$	0.753423	−	0.753423i	0.0655771	−	0.0655771i
$133$	−0.850128	+	0.850128i	−0.0737155	+	0.0737155i
$134$	12.3979			1.07102
$135$	4.80201	+	30.5899i	0.413291	+	2.63276i
$136$		−	3.08206i		−	0.264285i
$137$	−6.65703	+	6.65703i	−0.568748	+	0.568748i	−0.931778	−	0.363029i	$-0.881742\pi$
$137$	−6.65703	+	6.65703i	−0.568748	+	0.568748i	0.363029	+	0.931778i	$0.381742\pi$
$138$	3.81493	−	3.81493i	0.324749	−	0.324749i
$139$		−	17.1478i		−	1.45446i	−0.686394	−	0.727229i	$-0.740808\pi$
$139$		−	17.1478i		−	1.45446i	0.686394	−	0.727229i	$-0.259192\pi$
$140$	−0.425050	+	0.0667245i	−0.0359233	+	0.00563925i
$141$		−	26.3768i		−	2.22133i
$142$	−8.71342	−	8.71342i	−0.731214	−	0.731214i
$143$	0.0755725	−	0.0755725i	0.00631969	−	0.00631969i
$144$		−	7.31224i		−	0.609353i
$145$	−0.0805285	+	0.110519i	−0.00668753	+	0.00917812i
$146$	−11.7100			−0.969128
$147$	15.8109	−	15.8109i	1.30406	−	1.30406i
$148$	−6.41444	−	6.41444i	−0.527264	−	0.527264i
$149$	−5.64237			−0.462241			−0.231120	−	0.972925i	$-0.574239\pi$
$149$	−5.64237			−0.462241			−0.231120	+	0.972925i	$0.574239\pi$
$150$	−4.91982	−	15.2840i	−0.401702	−	1.24794i
$151$			8.47754i			0.689892i	0.938622	+	0.344946i	$0.112103\pi$
$151$			8.47754i			0.689892i	−0.938622	+	0.344946i	$0.887897\pi$
$152$	4.41818	+	4.41818i	0.358361	+	0.358361i
$153$	15.9359	−	15.9359i	1.28834	−	1.28834i
$154$			0.0638438i			0.00514468i
$155$	−7.69544	+	10.5614i	−0.618113	+	0.848313i
$156$		−	1.03437i		−	0.0828162i
$157$	−1.60147	+	1.60147i	−0.127811	+	0.127811i	−0.768119	−	0.640307i	$-0.778807\pi$
$157$	−1.60147	+	1.60147i	−0.127811	+	0.127811i	0.640307	+	0.768119i	$0.278807\pi$
$158$	3.48716	+	3.48716i	0.277424	+	0.277424i
$159$	40.9355			3.24640
$160$	0.346772	+	2.20902i	0.0274147	+	0.174638i
$161$			0.323271i			0.0254773i
$162$	15.9326	−	15.9326i	1.25178	−	1.25178i
$163$	−10.7173	−	10.7173i	−0.839442	−	0.839442i	0.149344	−	0.988785i	$-0.452284\pi$
$163$	−10.7173	−	10.7173i	−0.839442	−	0.839442i	−0.988785	+	0.149344i	$0.952284\pi$
$164$		−	3.48498i		−	0.272132i
$165$	−2.35371	+	0.369486i	−0.183236	+	0.0287645i
$166$			10.3062i			0.799917i
$167$	4.81188	+	4.81188i	0.372354	+	0.372354i	0.868334	−	0.495980i	$-0.165191\pi$
$167$	4.81188	+	4.81188i	0.372354	+	0.372354i	−0.495980	+	0.868334i	$0.665191\pi$
$168$	0.436921	+	0.436921i	0.0337092	+	0.0337092i
$169$			12.8962i			0.992019i
$170$	−4.05848	+	5.56995i	−0.311271	+	0.427196i
$171$			45.6887i			3.49390i
$172$	−4.05920	−	5.15004i	−0.309511	−	0.392687i
$173$	−9.67496	+	9.67496i	−0.735573	+	0.735573i	−0.971718	−	0.236145i	$-0.924116\pi$
$173$	−9.67496	+	9.67496i	−0.735573	+	0.735573i	0.236145	+	0.971718i	$0.424116\pi$
$174$	0.196383			0.0148878
$175$	0.856020	+	0.439123i	0.0647090	+	0.0331945i
$176$	0.331801			0.0250104
$177$	−12.6349	+	12.6349i	−0.949700	+	0.949700i
$178$	−7.54841	+	7.54841i	−0.565777	+	0.565777i
$179$	2.19297			0.163910			0.0819551	−	0.996636i	$-0.473884\pi$
$179$	2.19297			0.163910			0.0819551	+	0.996636i	$0.473884\pi$
$180$	−9.62879	+	13.2148i	−0.717688	+	0.984972i
$181$	12.4610			0.926217			0.463108	−	0.886302i	$-0.346734\pi$
$181$	12.4610			0.926217			0.463108	+	0.886302i	$0.346734\pi$
$182$	0.0438256	+	0.0438256i	0.00324857	+	0.00324857i
$183$	−2.58744	+	2.58744i	−0.191269	+	0.191269i
$184$	1.68006			0.123856
$185$	3.14571	+	20.0389i	0.231277	+	1.47329i
$186$	18.7667			1.37604
$187$	0.723110	+	0.723110i	0.0528790	+	0.0528790i
$188$	5.80806	−	5.80806i	0.423596	−	0.423596i
$189$			2.66453i			0.193816i
$190$	−2.16672	−	13.8025i	−0.157190	−	1.00134i
$191$		−	25.3921i		−	1.83731i	−0.395065	−	0.918653i	$-0.629278\pi$
$191$		−	25.3921i		−	1.83731i	0.395065	−	0.918653i	$-0.370722\pi$
$192$	2.27071	−	2.27071i	0.163874	−	0.163874i
$193$	6.98166	−	6.98166i	0.502551	−	0.502551i	−0.409679	−	0.912230i	$-0.634359\pi$
$193$	6.98166	−	6.98166i	0.502551	−	0.502551i	0.912230	+	0.409679i	$0.134359\pi$
$194$	−14.3738			−1.03198
$195$	−1.36207	+	1.86934i	−0.0975398	+	0.133866i
$196$	6.96298			0.497355
$197$	13.1418	+	13.1418i	0.936317	+	0.936317i	0.998090	−	0.0617736i	$-0.0196757\pi$
$197$	13.1418	+	13.1418i	0.936317	+	0.936317i	−0.0617736	+	0.998090i	$0.519676\pi$
$198$	1.71559	+	1.71559i	0.121922	+	0.121922i
$199$	−2.52666			−0.179110			−0.0895549	−	0.995982i	$-0.528544\pi$
$199$	−2.52666			−0.179110			−0.0895549	+	0.995982i	$0.528544\pi$
$200$	2.28215	−	4.44880i	0.161372	−	0.314577i
$201$			39.8130i			2.80820i
$202$	−7.69548	+	7.69548i	−0.541452	+	0.541452i
$203$	−0.00832060	+	0.00832060i	−0.000583991	+	0.000583991i
$204$	9.89733			0.692952
$205$	−4.58904	+	6.29811i	−0.320513	+	0.439879i
$206$		−	4.64425i		−	0.323580i
$207$	8.68682	+	8.68682i	0.603776	+	0.603776i
$208$	0.227765	−	0.227765i	0.0157926	−	0.0157926i
$209$	−2.07317			−0.143404
$210$	−0.214270	−	1.36495i	−0.0147861	−	0.0941905i
$211$			23.4480i			1.61423i	0.590397	+	0.807113i	$0.298971\pi$
$211$			23.4480i			1.61423i	−0.590397	+	0.807113i	$0.701029\pi$
$212$	9.01382	+	9.01382i	0.619071	+	0.619071i
$213$	27.9811	−	27.9811i	1.91723	−	1.91723i
$214$	−15.1458			−1.03535
$215$	0.554252	+	14.6524i	0.0377997	+	0.999285i
$216$	13.8478			0.942220
$217$	−0.795131	+	0.795131i	−0.0539770	+	0.0539770i
$218$	8.44846	+	8.44846i	0.572202	+	0.572202i
$219$		−	37.6040i		−	2.54104i
$220$	−0.599636	−	0.436917i	−0.0404274	−	0.0294570i
$221$	0.992756			0.0667800
$222$	20.5985	−	20.5985i	1.38248	−	1.38248i
$223$	12.1438	+	12.1438i	0.813210	+	0.813210i	0.985114	−	0.171903i	$-0.0549917\pi$
$223$	12.1438	+	12.1438i	0.813210	+	0.813210i	−0.171903	+	0.985114i	$0.554992\pi$
$224$			0.192416i			0.0128563i
$225$	34.8026	−	11.2027i	2.32017	−	0.746847i
$226$	5.08168			0.338028
$227$	8.71088	−	8.71088i	0.578162	−	0.578162i	−0.356235	−	0.934396i	$-0.615940\pi$
$227$	8.71088	−	8.71088i	0.578162	−	0.578162i	0.934396	+	0.356235i	$0.115940\pi$
$228$	−14.1879	+	14.1879i	−0.939620	+	0.939620i
$229$		−	9.95102i		−	0.657582i	−0.944403	−	0.328791i	$-0.893359\pi$
$229$		−	9.95102i		−	0.657582i	0.944403	−	0.328791i	$-0.106641\pi$
$230$	−3.03623	−	2.21232i	−0.200203	−	0.145876i
$231$	−0.205020			−0.0134893
$232$	0.0432427	+	0.0432427i	0.00283902	+	0.00283902i
$233$	−14.5338	−	14.5338i	−0.952142	−	0.952142i	0.0467643	−	0.998906i	$-0.485109\pi$
$233$	−14.5338	−	14.5338i	−0.952142	−	0.952142i	−0.998906	+	0.0467643i	$0.985109\pi$
$234$	2.35533			0.153973
$235$	−18.1445	+	2.84833i	−1.18362	+	0.185805i
$236$	−5.56431			−0.362206
$237$	−11.1982	+	11.1982i	−0.727402	+	0.727402i
$238$	−0.419342	+	0.419342i	−0.0271819	+	0.0271819i
$239$		−	6.34892i		−	0.410678i	−0.978691	−	0.205339i	$-0.934170\pi$
$239$		−	6.34892i		−	0.410678i	0.978691	−	0.205339i	$-0.0658296\pi$
$240$	−7.09374	+	1.11358i	−0.457899	+	0.0718811i
$241$		−	13.9058i		−	0.895748i	−0.894097	−	0.447874i	$-0.852181\pi$
$241$		−	13.9058i		−	0.895748i	0.894097	−	0.447874i	$-0.147819\pi$
$242$	7.70033	−	7.70033i	0.494996	−	0.494996i
$243$	21.7884	+	21.7884i	1.39772	+	1.39772i
$244$	−1.13949			−0.0729481
$245$	−12.5836	−	9.16888i	−0.803936	−	0.585778i
$246$	11.1912			0.713526
$247$	−1.42313	+	1.42313i	−0.0905515	+	0.0905515i
$248$	4.13235	+	4.13235i	0.262404	+	0.262404i
$249$	−33.0960			−2.09737
$250$	−9.98253	+	5.03478i	−0.631351	+	0.318428i
$251$	−15.4059			−0.972413			−0.486206	−	0.873844i	$-0.661620\pi$
$251$	−15.4059			−0.972413			−0.486206	+	0.873844i	$0.661620\pi$
$252$	−0.994894	+	0.994894i	−0.0626724	+	0.0626724i
$253$	−0.394174	+	0.394174i	−0.0247815	+	0.0247815i
$254$	−11.9179			−0.747792
$255$	−17.8866	−	13.0329i	−1.12010	−	0.816149i
$256$	1.00000			0.0625000
$257$	−2.52820	+	2.52820i	−0.157705	+	0.157705i	−0.781549	−	0.623844i	$-0.785570\pi$
$257$	−2.52820	+	2.52820i	−0.157705	+	0.157705i	0.623844	+	0.781549i	$0.285570\pi$
$258$	16.5381	−	13.0352i	1.02962	−	0.811535i
$259$			1.74548i			0.108459i
$260$	−0.711541	+	0.111698i	−0.0441279	+	0.00692721i
$261$			0.447176i			0.0276795i
$262$	11.1852	+	11.1852i	0.691022	+	0.691022i
$263$	−8.86096	−	8.86096i	−0.546390	−	0.546390i	0.379004	−	0.925395i	$-0.376266\pi$
$263$	−8.86096	−	8.86096i	−0.546390	−	0.546390i	−0.925395	+	0.379004i	$0.876266\pi$
$264$			1.06550i			0.0655771i
$265$	−4.42046	−	28.1593i	−0.271547	−	1.72981i
$266$		−	1.20226i		−	0.0737155i
$267$	−24.2400	−	24.2400i	−1.48346	−	1.48346i
$268$	−8.76665	+	8.76665i	−0.535509	+	0.535509i
$269$		−	3.37276i		−	0.205641i	−0.994700	−	0.102821i	$-0.967213\pi$
$269$		−	3.37276i		−	0.205641i	0.994700	−	0.102821i	$-0.0327867\pi$
$270$	−25.0259	−	18.2348i	−1.52303	−	1.10973i
$271$	14.3651			0.872620			0.436310	−	0.899796i	$-0.356285\pi$
$271$	14.3651			0.872620			0.436310	+	0.899796i	$0.356285\pi$
$272$	2.17935	+	2.17935i	0.132142	+	0.132142i
$273$	−0.140736	+	0.140736i	−0.00851770	+	0.00851770i
$274$		−	9.41446i		−	0.568748i
$275$	0.508336	+	1.57921i	0.0306538	+	0.0952297i
$276$			5.39513i			0.324749i
$277$	13.0716	−	13.0716i	0.785398	−	0.785398i	−0.195338	−	0.980736i	$-0.562580\pi$
$277$	13.0716	−	13.0716i	0.785398	−	0.785398i	0.980736	+	0.195338i	$0.0625803\pi$
$278$	12.1253	+	12.1253i	0.727229	+	0.727229i
$279$			42.7329i			2.55835i
$280$	0.253374	−	0.347737i	0.0151420	−	0.0207813i
$281$	−20.5868			−1.22810			−0.614052	−	0.789266i	$-0.710461\pi$
$281$	−20.5868			−1.22810			−0.614052	+	0.789266i	$0.710461\pi$
$282$	18.6512	+	18.6512i	1.11066	+	1.11066i
$283$	−11.0135	+	11.0135i	−0.654686	+	0.654686i	−0.954118	−	0.299432i	$-0.903203\pi$
$283$	−11.0135	+	11.0135i	−0.654686	+	0.654686i	0.299432	+	0.954118i	$0.403203\pi$
$284$	12.3226			0.731214
$285$	44.3234	−	6.95791i	2.62549	−	0.412151i
$286$			0.106876i			0.00631969i
$287$	−0.474162	+	0.474162i	−0.0279889	+	0.0279889i
$288$	5.17053	+	5.17053i	0.304677	+	0.304677i
$289$		−	7.50088i		−	0.441228i
$290$	−0.0212067	−	0.135091i	−0.00124530	−	0.00793282i
$291$		−	46.1581i		−	2.70584i
$292$	8.28023	−	8.28023i	0.484564	−	0.484564i
$293$	−5.20149	+	5.20149i	−0.303875	+	0.303875i	−0.842528	−	0.538653i	$-0.818933\pi$
$293$	−5.20149	+	5.20149i	−0.303875	+	0.303875i	0.538653	+	0.842528i	$0.318933\pi$
$294$			22.3600i			1.30406i
$295$	10.0559	+	7.32711i	0.585478	+	0.426601i
$296$	9.07139			0.527264
$297$	−3.24894	+	3.24894i	−0.188523	+	0.188523i
$298$	3.98976	−	3.98976i	0.231120	−	0.231120i
$299$			0.541161i			0.0312962i
$300$	14.2863	+	7.32860i	0.824818	+	0.423117i
$301$	−0.148418	+	1.25300i	−0.00855467	+	0.0722216i
$302$	−5.99452	−	5.99452i	−0.344946	−	0.344946i
$303$	−24.7122	−	24.7122i	−1.41968	−	1.41968i
$304$	−6.24824			−0.358361
$305$	2.05930	+	1.50048i	0.117915	+	0.0859173i
$306$			22.5368i			1.28834i
$307$	−20.0389	−	20.0389i	−1.14368	−	1.14368i	−0.987771	−	0.155911i	$-0.950169\pi$
$307$	−20.0389	−	20.0389i	−1.14368	−	1.14368i	−0.155911	−	0.987771i	$-0.549831\pi$
$308$	−0.0451444	−	0.0451444i	−0.00257234	−	0.00257234i
$309$	14.9139			0.848424
$310$	−2.02654	−	12.9095i	−0.115100	−	0.733213i
$311$	30.2370			1.71458			0.857290	−	0.514833i	$-0.172146\pi$
$311$	30.2370			1.71458			0.857290	+	0.514833i	$0.172146\pi$
$312$	0.731413	+	0.731413i	0.0414081	+	0.0414081i
$313$	5.27251	+	5.27251i	0.298020	+	0.298020i	0.840238	−	0.542218i	$-0.182415\pi$
$313$	5.27251	+	5.27251i	0.298020	+	0.298020i	−0.542218	+	0.840238i	$0.682415\pi$
$314$		−	2.26482i		−	0.127811i
$315$	3.10807	−	0.487906i	0.175120	−	0.0274904i
$316$	−4.93159			−0.277424
$317$	18.6979	+	18.6979i	1.05018	+	1.05018i	0.998673	+	0.0515074i	$0.0164026\pi$
$317$	18.6979	+	18.6979i	1.05018	+	1.05018i	0.0515074	+	0.998673i	$0.483597\pi$
$318$	−28.9458	+	28.9458i	−1.62320	+	1.62320i
$319$	−0.0202911			−0.00113608
$320$	−1.80721	−	1.31680i	−0.101026	−	0.0736116i
$321$		−	48.6372i		−	2.71467i
$322$	−0.228587	−	0.228587i	−0.0127387	−	0.0127387i
$323$	−13.6171	−	13.6171i	−0.757676	−	0.757676i
$324$			22.5321i			1.25178i
$325$	1.43299	+	0.735098i	0.0794881	+	0.0407759i
$326$	15.1565			0.839442
$327$	−27.1303	+	27.1303i	−1.50031	+	1.50031i
$328$	2.46426	+	2.46426i	0.136066	+	0.136066i
$329$	−1.58047			−0.0871344
$330$	1.40306	−	1.92559i	0.0772358	−	0.106000i
$331$		−	6.25818i		−	0.343981i	−0.985099	−	0.171990i	$-0.944980\pi$
$331$		−	6.25818i		−	0.343981i	0.985099	−	0.171990i	$-0.0550198\pi$
$332$	−7.28759	−	7.28759i	−0.399958	−	0.399958i
$333$	46.9039	+	46.9039i	2.57032	+	2.57032i
$334$	−6.80502			−0.372354
$335$	27.3872	−	4.29925i	1.49632	−	0.234893i
$336$	−0.617899			−0.0337092
$337$	−7.21962	−	7.21962i	−0.393278	−	0.393278i	0.482576	−	0.875854i	$-0.339701\pi$
$337$	−7.21962	−	7.21962i	−0.393278	−	0.393278i	−0.875854	+	0.482576i	$0.839701\pi$
$338$	−9.11902	−	9.11902i	−0.496009	−	0.496009i
$339$			16.3186i			0.886306i
$340$	−1.06877	−	6.80833i	−0.0579624	−	0.369233i
$341$	−1.93905			−0.105006
$342$	−32.3068	−	32.3068i	−1.74695	−	1.74695i
$343$	−1.89978	−	1.89978i	−0.102579	−	0.102579i
$344$	6.51192	+	0.771338i	0.351099	+	0.0415878i
$345$	7.10434	−	9.75016i	0.382485	−	0.524931i
$346$		−	13.6825i		−	0.735573i
$347$	−20.0067	+	20.0067i	−1.07402	+	1.07402i	−0.0769826	+	0.997032i	$0.524529\pi$
$347$	−20.0067	+	20.0067i	−1.07402	+	1.07402i	−0.997032	+	0.0769826i	$0.975471\pi$
$348$	−0.138864	+	0.138864i	−0.00744389	+	0.00744389i
$349$	−17.4644			−0.934848			−0.467424	−	0.884033i	$-0.654818\pi$
$349$	−17.4644			−0.934848			−0.467424	+	0.884033i	$0.654818\pi$
$350$	−0.915804	+	0.294791i	−0.0489518	+	0.0157572i
$351$			4.46047i			0.238082i
$352$	−0.234619	+	0.234619i	−0.0125052	+	0.0125052i
$353$	9.58097	−	9.58097i	0.509944	−	0.509944i	−0.404565	−	0.914509i	$-0.632577\pi$
$353$	9.58097	−	9.58097i	0.509944	−	0.509944i	0.914509	+	0.404565i	$0.132577\pi$
$354$		−	17.8685i		−	0.949700i
$355$	−22.2697	−	16.2265i	−1.18195	−	0.861214i
$356$		−	10.6751i		−	0.565777i
$357$	−1.34662	−	1.34662i	−0.0712706	−	0.0712706i
$358$	−1.55066	+	1.55066i	−0.0819551	+	0.0819551i
$359$		−	10.5021i		−	0.554280i	−0.960830	−	0.277140i	$-0.910613\pi$
$359$		−	10.5021i		−	0.554280i	0.960830	−	0.277140i	$-0.0893865\pi$
$360$	−2.53568	−	16.1528i	−0.133642	−	0.851330i
$361$	20.0406			1.05477
$362$	−8.81124	+	8.81124i	−0.463108	+	0.463108i
$363$	24.7278	+	24.7278i	1.29787	+	1.29787i
$364$	−0.0619787			−0.00324857
$365$	−25.8676	+	4.06071i	−1.35397	+	0.212547i
$366$		−	3.65919i		−	0.191269i
$367$	−15.2206	−	15.2206i	−0.794511	−	0.794511i	0.187713	−	0.982224i	$-0.439893\pi$
$367$	−15.2206	−	15.2206i	−0.794511	−	0.794511i	−0.982224	+	0.187713i	$0.939893\pi$
$368$	−1.18798	+	1.18798i	−0.0619279	+	0.0619279i
$369$			25.4830i			1.32659i
$370$	−16.3940	−	11.9453i	−0.852281	−	0.621004i
$371$		−	2.45282i		−	0.127344i
$372$	−13.2701	+	13.2701i	−0.688022	+	0.688022i
$373$	11.7798	+	11.7798i	0.609934	+	0.609934i	0.942929	−	0.332995i	$-0.108059\pi$
$373$	11.7798	+	11.7798i	0.609934	+	0.609934i	−0.332995	+	0.942929i	$0.608059\pi$
$374$	−1.02263			−0.0528790
$375$	−16.1680	−	32.0566i	−0.834914	−	1.65539i
$376$			8.21384i			0.423596i
$377$	−0.0139288	+	0.0139288i	−0.000717370	+	0.000717370i
$378$	−1.88411	−	1.88411i	−0.0969080	−	0.0969080i
$379$		−	12.4382i		−	0.638907i	−0.947602	−	0.319454i	$-0.896501\pi$
$379$		−	12.4382i		−	0.638907i	0.947602	−	0.319454i	$-0.103499\pi$
$380$	11.2919	+	8.22772i	0.579263	+	0.422073i
$381$		−	38.2714i		−	1.96070i
$382$	17.9549	+	17.9549i	0.918653	+	0.918653i
$383$	−24.9546	−	24.9546i	−1.27512	−	1.27512i	−0.943366	−	0.331753i	$-0.892360\pi$
$383$	−24.9546	−	24.9546i	−1.27512	−	1.27512i	−0.331753	−	0.943366i	$-0.607640\pi$
$384$			3.21127i			0.163874i
$385$	0.0221393	+	0.141032i	0.00112832	+	0.00718766i
$386$			9.87355i			0.502551i
$387$	29.6818	+	37.6583i	1.50881	+	1.91428i
$388$	10.1638	−	10.1638i	0.515989	−	0.515989i
$389$	13.5807			0.688567			0.344283	−	0.938866i	$-0.388122\pi$
$389$	13.5807			0.688567			0.344283	+	0.938866i	$0.388122\pi$
$390$	−0.358692	−	2.28495i	−0.0181631	−	0.115703i
$391$	−5.17806			−0.261866
$392$	−4.92357	+	4.92357i	−0.248678	+	0.248678i
$393$	−35.9185	+	35.9185i	−1.81185	+	1.81185i
$394$	−18.5854			−0.936317
$395$	8.91244	+	6.49394i	0.448434	+	0.326746i
$396$	−2.42621			−0.121922
$397$	11.5455	+	11.5455i	0.579451	+	0.579451i	0.934752	−	0.355301i	$-0.115622\pi$
$397$	11.5455	+	11.5455i	0.579451	+	0.579451i	−0.355301	+	0.934752i	$0.615622\pi$
$398$	1.78662	−	1.78662i	0.0895549	−	0.0895549i
$399$	3.86079			0.193281
$400$	1.53205	+	4.75950i	0.0766025	+	0.237975i
$401$	−5.45642			−0.272480			−0.136240	−	0.990676i	$-0.543502\pi$
$401$	−5.45642			−0.272480			−0.136240	+	0.990676i	$0.543502\pi$
$402$	−28.1521	−	28.1521i	−1.40410	−	1.40410i
$403$	−1.33106	+	1.33106i	−0.0663049	+	0.0663049i
$404$		−	10.8831i		−	0.541452i
$405$	29.6704	−	40.7204i	1.47433	−	2.02341i
$406$		−	0.0117671i		−	0.000583991i
$407$	−2.12832	+	2.12832i	−0.105497	+	0.105497i
$408$	−6.99847	+	6.99847i	−0.346476	+	0.346476i
$409$	−6.76815			−0.334663			−0.167332	−	0.985901i	$-0.553515\pi$
$409$	−6.76815			−0.334663			−0.167332	+	0.985901i	$0.553515\pi$
$410$	−1.20850	−	7.69838i	−0.0596833	−	0.380196i
$411$	30.2323			1.49125
$412$	3.28398	+	3.28398i	0.161790	+	0.161790i
$413$	0.757073	+	0.757073i	0.0372531	+	0.0372531i
$414$	−12.2850			−0.603776
$415$	3.57390	+	22.7666i	0.175436	+	1.11757i
$416$			0.322108i			0.0157926i
$417$	−38.9377	+	38.9377i	−1.90679	+	1.90679i
$418$	1.46596	−	1.46596i	0.0717022	−	0.0717022i
$419$	0.965048			0.0471457			0.0235728	−	0.999722i	$-0.492496\pi$
$419$	0.965048			0.0471457			0.0235728	+	0.999722i	$0.492496\pi$
$420$	1.11668	+	0.813653i	0.0544883	+	0.0397022i
$421$			33.6901i			1.64196i	0.570959	+	0.820979i	$0.306572\pi$
$421$			33.6901i			1.64196i	−0.570959	+	0.820979i	$0.693428\pi$
$422$	−16.5802	−	16.5802i	−0.807113	−	0.807113i
$423$	−42.4699	+	42.4699i	−2.06496	+	2.06496i
$424$	−12.7475			−0.619071
$425$	−7.03373	+	13.7115i	−0.341186	+	0.665104i
$426$			39.5713i			1.91723i
$427$	0.155037	+	0.155037i	0.00750277	+	0.00750277i
$428$	10.7097	−	10.7097i	0.517673	−	0.517673i
$429$	−0.343206			−0.0165702
$430$	−10.7527	−	9.96890i	−0.518542	−	0.480743i
$431$	9.40345			0.452948			0.226474	−	0.974017i	$-0.427280\pi$
$431$	9.40345			0.452948			0.226474	+	0.974017i	$0.427280\pi$
$432$	−9.79184	+	9.79184i	−0.471110	+	0.471110i
$433$	3.57975	+	3.57975i	0.172032	+	0.172032i	0.787871	−	0.615840i	$-0.211183\pi$
$433$	3.57975	+	3.57975i	0.172032	+	0.172032i	−0.615840	+	0.787871i	$0.711183\pi$
$434$		−	1.12448i		−	0.0539770i
$435$	0.433814	−	0.0681002i	0.0207998	−	0.00326516i
$436$	−11.9479			−0.572202
$437$	7.42281	−	7.42281i	0.355081	−	0.355081i
$438$	26.5900	+	26.5900i	1.27052	+	1.27052i
$439$		−	1.62440i		−	0.0775285i	−0.999248	−	0.0387643i	$-0.987658\pi$
$439$		−	1.62440i		−	0.0775285i	0.999248	−	0.0387643i	$-0.0123421\pi$
$440$	0.732954	−	0.115059i	0.0349422	−	0.00548524i
$441$	−50.9149			−2.42452
$442$	−0.701985	+	0.701985i	−0.0333900	+	0.0333900i
$443$	−10.3173	+	10.3173i	−0.490188	+	0.490188i	−0.908365	−	0.418178i	$-0.862669\pi$
$443$	−10.3173	+	10.3173i	−0.490188	+	0.490188i	0.418178	+	0.908365i	$0.362669\pi$
$444$			29.1307i			1.38248i
$445$	−14.0570	+	19.2921i	−0.666365	+	0.914535i
$446$	−17.1740			−0.813210
$447$	12.8122	+	12.8122i	0.605995	+	0.605995i
$448$	−0.136059	−	0.136059i	−0.00642817	−	0.00642817i
$449$	0.0835057			0.00394088			0.00197044	−	0.999998i	$-0.499373\pi$
$449$	0.0835057			0.00394088			0.00197044	+	0.999998i	$0.499373\pi$
$450$	−16.6876	+	32.5307i	−0.786662	+	1.53351i
$451$	−1.15632			−0.0544490
$452$	−3.59329	+	3.59329i	−0.169014	+	0.169014i
$453$	19.2500	−	19.2500i	0.904445	−	0.904445i
$454$			12.3190i			0.578162i
$455$	0.112009	+	0.0816138i	0.00525105	+	0.00382612i
$456$		−	20.0648i		−	0.939620i
$457$	13.3100	−	13.3100i	0.622614	−	0.622614i	−0.323585	−	0.946199i	$-0.604888\pi$
$457$	13.3100	−	13.3100i	0.622614	−	0.622614i	0.946199	+	0.323585i	$0.104888\pi$
$458$	7.03643	+	7.03643i	0.328791	+	0.328791i
$459$	−42.6796			−1.99212
$460$	3.71129	−	0.582599i	0.173040	−	0.0271638i
$461$	−38.2888			−1.78329			−0.891643	−	0.452740i	$-0.850447\pi$
$461$	−38.2888			−1.78329			−0.891643	+	0.452740i	$0.850447\pi$
$462$	0.144971	−	0.144971i	0.00674465	−	0.00674465i
$463$	1.06748	+	1.06748i	0.0496100	+	0.0496100i	0.731477	−	0.681867i	$-0.238832\pi$
$463$	1.06748	+	1.06748i	0.0496100	+	0.0496100i	−0.681867	+	0.731477i	$0.738832\pi$
$464$	−0.0611545			−0.00283902
$465$	41.4560	−	6.50778i	1.92248	−	0.301791i
$466$	20.5539			0.952142
$467$	17.4531	−	17.4531i	0.807633	−	0.807633i	−0.176642	−	0.984275i	$-0.556523\pi$
$467$	17.4531	−	17.4531i	0.807633	−	0.807633i	0.984275	+	0.176642i	$0.0565235\pi$
$468$	−1.66547	+	1.66547i	−0.0769863	+	0.0769863i
$469$	2.38556			0.110155
$470$	10.8160	−	14.8442i	0.498906	−	0.684710i
$471$	7.27295			0.335120
$472$	3.93456	−	3.93456i	0.181103	−	0.181103i
$473$	−1.70879	+	1.34685i	−0.0785701	+	0.0619281i
$474$		−	15.8367i		−	0.727402i
$475$	−9.57262	−	29.7385i	−0.439222	−	1.36450i
$476$		−	0.593039i		−	0.0271819i
$477$	−65.9112	−	65.9112i	−3.01787	−	3.01787i
$478$	4.48937	+	4.48937i	0.205339	+	0.205339i
$479$		−	25.1153i		−	1.14755i	−0.819015	−	0.573773i	$-0.805479\pi$
$479$		−	25.1153i		−	1.14755i	0.819015	−	0.573773i	$-0.194521\pi$
$480$	4.22861	−	5.80345i	0.193009	−	0.264890i
$481$			2.92197i			0.133230i
$482$	9.83285	+	9.83285i	0.447874	+	0.447874i
$483$	0.734055	−	0.734055i	0.0334006	−	0.0334006i
$484$			10.8899i			0.494996i
$485$	−31.7519	+	4.98443i	−1.44178	+	0.226331i
$486$	−30.8134			−1.39772
$487$	19.1898	+	19.1898i	0.869574	+	0.869574i	0.992425	−	0.122851i	$-0.0392038\pi$
$487$	19.1898	+	19.1898i	0.869574	+	0.869574i	−0.122851	+	0.992425i	$0.539204\pi$
$488$	0.805738	−	0.805738i	0.0364741	−	0.0364741i
$489$			48.6716i			2.20101i
$490$	15.3813	−	2.41457i	0.694857	−	0.109079i
$491$			6.17161i			0.278521i	0.990256	+	0.139260i	$0.0444725\pi$
$491$			6.17161i			0.278521i	−0.990256	+	0.139260i	$0.955527\pi$
$492$	−7.91339	+	7.91339i	−0.356763	+	0.356763i
$493$	−0.133277	−	0.133277i	−0.00600249	−	0.00600249i
$494$		−	2.01261i		−	0.0905515i
$495$	4.38468	+	3.19484i	0.197077	+	0.143597i
$496$	−5.84403			−0.262404
$497$	−1.67660	−	1.67660i	−0.0752059	−	0.0752059i
$498$	23.4024	−	23.4024i	1.04869	−	1.04869i
$499$	22.4749			1.00611			0.503056	−	0.864254i	$-0.332209\pi$
$499$	22.4749			1.00611			0.503056	+	0.864254i	$0.332209\pi$
$500$	3.49859	−	10.6188i	0.156462	−	0.474889i
$501$		−	21.8527i		−	0.976309i
$502$	10.8936	−	10.8936i	0.486206	−	0.486206i
$503$	25.5375	+	25.5375i	1.13866	+	1.13866i	0.988691	+	0.149970i	$0.0479177\pi$
$503$	25.5375	+	25.5375i	1.13866	+	1.13866i	0.149970	+	0.988691i	$0.452082\pi$
$504$		−	1.40699i		−	0.0626724i
$505$	−14.3309	+	19.6680i	−0.637715	+	0.875215i
$506$		−	0.557447i		−	0.0247815i
$507$	29.2836	−	29.2836i	1.30053	−	1.30053i
$508$	8.42719	−	8.42719i	0.373896	−	0.373896i
$509$			2.85645i			0.126610i	0.997994	+	0.0633049i	$0.0201640\pi$
$509$			2.85645i			0.126610i	−0.997994	+	0.0633049i	$0.979836\pi$
$510$	21.8634	−	3.43212i	0.968126	−	0.151977i
$511$	−2.25320			−0.0996755
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	61.1818	−	61.1818i	2.70124	−	2.70124i
$514$		−	3.57541i		−	0.157705i
$515$	−1.61050	−	10.2592i	−0.0709670	−	0.452076i
$516$	−2.47697	+	20.9115i	−0.109043	+	0.920577i
$517$	−1.92712	−	1.92712i	−0.0847546	−	0.0847546i
$518$	−1.23424	−	1.23424i	−0.0542295	−	0.0542295i
$519$	43.9380			1.92867
$520$	0.424153	−	0.582118i	0.0186003	−	0.0255275i
$521$			22.4314i			0.982738i	0.870952	+	0.491369i	$0.163503\pi$
$521$			22.4314i			0.982738i	−0.870952	+	0.491369i	$0.836497\pi$
$522$	−0.316201	−	0.316201i	−0.0138397	−	0.0138397i
$523$	16.0520	+	16.0520i	0.701906	+	0.701906i	0.964819	−	0.262913i	$-0.0846833\pi$
$523$	16.0520	+	16.0520i	0.701906	+	0.701906i	−0.262913	+	0.964819i	$0.584683\pi$
$524$	−15.8182			−0.691022
$525$	−0.946653	−	2.94089i	−0.0413153	−	0.128351i
$526$	12.5313			0.546390
$527$	−12.7362	−	12.7362i	−0.554796	−	0.554796i
$528$	−0.753423	−	0.753423i	−0.0327885	−	0.0327885i
$529$			20.1774i			0.877278i
$530$	23.0374	+	16.7859i	1.00068	+	0.729134i
$531$	40.6876			1.76569
$532$	0.850128	+	0.850128i	0.0368577	+	0.0368577i
$533$	−0.793756	+	0.793756i	−0.0343814	+	0.0343814i
$534$	34.2805			1.48346
$535$	−33.4573	+	5.25214i	−1.44649	+	0.227070i
$536$		−	12.3979i		−	0.535509i
$537$	−4.97960	−	4.97960i	−0.214885	−	0.214885i
$538$	2.38490	+	2.38490i	0.102821	+	0.102821i
$539$		−	2.31032i		−	0.0995126i
$540$	30.5899	−	4.80201i	1.31638	−	0.206646i
$541$	13.2089			0.567894			0.283947	−	0.958840i	$-0.408356\pi$
$541$	13.2089			0.567894			0.283947	+	0.958840i	$0.408356\pi$
$542$	−10.1577	+	10.1577i	−0.436310	+	0.436310i
$543$	−28.2952	−	28.2952i	−1.21426	−	1.21426i
$544$	−3.08206			−0.132142
$545$	21.5925	+	15.7331i	0.924920	+	0.673931i
$546$		−	0.199030i		−	0.00851770i
$547$	6.31769	+	6.31769i	0.270125	+	0.270125i	0.829150	−	0.559026i	$-0.188825\pi$
$547$	6.31769	+	6.31769i	0.270125	+	0.270125i	−0.559026	+	0.829150i	$0.688825\pi$
$548$	6.65703	+	6.65703i	0.284374	+	0.284374i
$549$	8.33219			0.355609
$550$	−1.47611	−	0.757220i	−0.0629418	−	0.0322880i
$551$	0.382108			0.0162783
$552$	−3.81493	−	3.81493i	−0.162374	−	0.162374i
$553$	0.670986	+	0.670986i	0.0285332	+	0.0285332i
$554$			18.4861i			0.785398i
$555$	38.3594	−	52.6454i	1.62827	−	2.23467i
$556$	−17.1478			−0.727229
$557$	13.6230	+	13.6230i	0.577227	+	0.577227i	0.934138	−	0.356911i	$-0.116170\pi$
$557$	13.6230	+	13.6230i	0.577227	+	0.577227i	−0.356911	+	0.934138i	$0.616170\pi$
$558$	−30.2167	−	30.2167i	−1.27918	−	1.27918i
$559$	−0.248454	+	2.09754i	−0.0105085	+	0.0887164i
$560$	0.0667245	+	0.425050i	0.00281963	+	0.0179616i
$561$		−	3.28394i		−	0.138648i
$562$	14.5570	−	14.5570i	0.614052	−	0.614052i
$563$	−11.9580	+	11.9580i	−0.503970	+	0.503970i	−0.912669	−	0.408699i	$-0.865983\pi$
$563$	−11.9580	+	11.9580i	−0.503970	+	0.503970i	0.408699	+	0.912669i	$0.365983\pi$
$564$	−26.3768			−1.11066
$565$	11.2255	−	1.76218i	0.472260	−	0.0741356i
$566$		−	15.5755i		−	0.654686i
$567$	3.06569	−	3.06569i	0.128747	−	0.128747i
$568$	−8.71342	+	8.71342i	−0.365607	+	0.365607i
$569$		−	12.1931i		−	0.511162i	−0.966788	−	0.255581i	$-0.917733\pi$
$569$		−	12.1931i		−	0.511162i	0.966788	−	0.255581i	$-0.0822668\pi$
$570$	−26.4214	+	36.2614i	−1.10667	+	1.51882i
$571$			19.6010i			0.820275i	0.912024	+	0.410138i	$0.134519\pi$
$571$			19.6010i			0.820275i	−0.912024	+	0.410138i	$0.865481\pi$
$572$	−0.0755725	−	0.0755725i	−0.00315984	−	0.00315984i
$573$	−57.6580	+	57.6580i	−2.40870	+	2.40870i
$574$		−	0.670567i		−	0.0279889i
$575$	−7.47426	−	3.83416i	−0.311698	−	0.159895i
$576$	−7.31224			−0.304677
$577$	16.1659	−	16.1659i	0.672995	−	0.672995i	−0.285410	−	0.958405i	$-0.592130\pi$
$577$	16.1659	−	16.1659i	0.672995	−	0.672995i	0.958405	+	0.285410i	$0.0921298\pi$
$578$	5.30393	+	5.30393i	0.220614	+	0.220614i
$579$	−31.7066			−1.31768
$580$	0.110519	+	0.0805285i	0.00458906	+	0.00334376i
$581$			1.98308i			0.0822720i
$582$	32.6387	+	32.6387i	1.35292	+	1.35292i
$583$	2.99079	−	2.99079i	0.123866	−	0.123866i
$584$			11.7100i			0.484564i
$585$	5.20296	−	0.816762i	0.215116	−	0.0337689i
$586$		−	7.35602i		−	0.303875i
$587$	11.1142	−	11.1142i	0.458732	−	0.458732i	−0.439507	−	0.898239i	$-0.644847\pi$
$587$	11.1142	−	11.1142i	0.458732	−	0.458732i	0.898239	+	0.439507i	$0.144847\pi$
$588$	−15.8109	−	15.8109i	−0.652030	−	0.652030i
$589$	36.5149			1.50457
$590$	−12.2917	+	1.92955i	−0.506039	+	0.0794382i
$591$		−	59.6825i		−	2.45501i
$592$	−6.41444	+	6.41444i	−0.263632	+	0.263632i
$593$	20.7067	+	20.7067i	0.850323	+	0.850323i	0.990173	−	0.139850i	$-0.0446619\pi$
$593$	20.7067	+	20.7067i	0.850323	+	0.850323i	−0.139850	+	0.990173i	$0.544662\pi$
$594$		−	4.59470i		−	0.188523i
$595$	−0.780916	+	1.07175i	−0.0320144	+	0.0439374i
$596$			5.64237i			0.231120i
$597$	5.73730	+	5.73730i	0.234812	+	0.234812i
$598$	−0.382659	−	0.382659i	−0.0156481	−	0.0156481i
$599$		−	18.8682i		−	0.770933i	−0.922722	−	0.385466i	$-0.874041\pi$
$599$		−	18.8682i		−	0.770933i	0.922722	−	0.385466i	$-0.125959\pi$
$600$	−15.2840	+	4.91982i	−0.623968	+	0.200851i
$601$			33.2843i			1.35770i	0.734279	+	0.678848i	$0.237521\pi$
$601$			33.2843i			1.35770i	−0.734279	+	0.678848i	$0.762479\pi$
$602$	−0.781055	−	0.990950i	−0.0318334	−	0.0403881i
$603$	64.1039	−	64.1039i	2.61051	−	2.61051i
$604$	8.47754			0.344946
$605$	14.3399	−	19.6804i	0.582999	−	0.800122i
$606$	34.9484			1.41968
$607$	9.46045	−	9.46045i	0.383988	−	0.383988i	−0.488549	−	0.872537i	$-0.662474\pi$
$607$	9.46045	−	9.46045i	0.383988	−	0.383988i	0.872537	+	0.488549i	$0.162474\pi$
$608$	4.41818	−	4.41818i	0.179181	−	0.179181i
$609$	0.0377873			0.00153122
$610$	−2.51714	+	0.395142i	−0.101916	+	0.0159988i
$611$	−2.64574			−0.107035
$612$	−15.9359	−	15.9359i	−0.644171	−	0.644171i
$613$	−0.754920	+	0.754920i	−0.0304909	+	0.0304909i	−0.722188	−	0.691697i	$-0.756863\pi$
$613$	−0.754920	+	0.754920i	−0.0304909	+	0.0304909i	0.691697	+	0.722188i	$0.256863\pi$
$614$	28.3393			1.14368
$615$	24.7216	−	3.88080i	0.996870	−	0.156489i
$616$	0.0638438			0.00257234
$617$	−13.7142	−	13.7142i	−0.552112	−	0.552112i	0.374938	−	0.927050i	$-0.377664\pi$
$617$	−13.7142	−	13.7142i	−0.552112	−	0.552112i	−0.927050	+	0.374938i	$0.877664\pi$
$618$	−10.5457	+	10.5457i	−0.424212	+	0.424212i
$619$			9.20775i			0.370091i	0.982730	+	0.185045i	$0.0592432\pi$
$619$			9.20775i			0.370091i	−0.982730	+	0.185045i	$0.940757\pi$
$620$	10.5614	+	7.69544i	0.424156	+	0.309056i
$621$		−	23.2651i		−	0.933596i
$622$	−21.3808	+	21.3808i	−0.857290	+	0.857290i
$623$	−1.45244	+	1.45244i	−0.0581906	+	0.0581906i
$624$	−1.03437			−0.0414081
$625$	−20.3056	+	14.5836i	−0.812226	+	0.583343i
$626$	−7.45645			−0.298020
$627$	4.70757	+	4.70757i	0.188002	+	0.188002i
$628$	1.60147	+	1.60147i	0.0639056	+	0.0639056i
$629$	−27.9586			−1.11478
$630$	−1.85273	+	2.54274i	−0.0738147	+	0.101305i
$631$		−	8.79639i		−	0.350179i	−0.984553	−	0.175089i	$-0.943979\pi$
$631$		−	8.79639i		−	0.350179i	0.984553	−	0.175089i	$-0.0560215\pi$
$632$	3.48716	−	3.48716i	0.138712	−	0.138712i
$633$	53.2435	−	53.2435i	2.11624	−	2.11624i
$634$	−26.4429			−1.05018
$635$	−26.3267	+	4.13278i	−1.04474	+	0.164004i
$636$		−	40.9355i		−	1.62320i
$637$	−1.58592	−	1.58592i	−0.0628364	−	0.0628364i
$638$	0.0143480	−	0.0143480i	0.000568042	−	0.000568042i
$639$	−90.1061			−3.56454
$640$	2.20902	−	0.346772i	0.0873190	−	0.0137074i
$641$			21.5612i			0.851617i	0.904813	+	0.425809i	$0.140010\pi$
$641$			21.5612i			0.851617i	−0.904813	+	0.425809i	$0.859990\pi$
$642$	34.3917	+	34.3917i	1.35733	+	1.35733i
$643$	−23.0884	+	23.0884i	−0.910519	+	0.910519i	−0.996313	−	0.0857940i	$-0.972657\pi$
$643$	−23.0884	+	23.0884i	−0.910519	+	0.910519i	0.0857940	+	0.996313i	$0.472657\pi$
$644$	0.323271			0.0127387
$645$	32.0128	−	34.5299i	1.26050	−	1.35961i
$646$	19.2575			0.757676
$647$	10.7376	−	10.7376i	0.422140	−	0.422140i	−0.463800	−	0.885940i	$-0.653514\pi$
$647$	10.7376	−	10.7376i	0.422140	−	0.422140i	0.885940	+	0.463800i	$0.153514\pi$
$648$	−15.9326	−	15.9326i	−0.625892	−	0.625892i
$649$			1.84624i			0.0724714i
$650$	−1.53307	+	0.493485i	−0.0601320	+	0.0193561i
$651$	3.61102			0.141527
$652$	−10.7173	+	10.7173i	−0.419721	+	0.419721i
$653$	−18.4112	−	18.4112i	−0.720485	−	0.720485i	0.248219	−	0.968704i	$-0.420155\pi$
$653$	−18.4112	−	18.4112i	−0.720485	−	0.720485i	−0.968704	+	0.248219i	$0.920155\pi$
$654$		−	38.3680i		−	1.50031i
$655$	28.5869	+	20.8295i	1.11698	+	0.813876i
$656$	−3.48498			−0.136066
$657$	−60.5470	+	60.5470i	−2.36216	+	2.36216i
$658$	1.11756	−	1.11756i	0.0435672	−	0.0435672i
$659$		−	22.8070i		−	0.888434i	−0.895919	−	0.444217i	$-0.853482\pi$
$659$		−	22.8070i		−	0.888434i	0.895919	−	0.444217i	$-0.146518\pi$
$660$	0.369486	+	2.35371i	0.0143822	+	0.0916180i
$661$	−32.3894			−1.25980			−0.629902	−	0.776675i	$-0.716905\pi$
$661$	−32.3894			−1.25980			−0.629902	+	0.776675i	$0.716905\pi$
$662$	4.42520	+	4.42520i	0.171990	+	0.171990i
$663$	−2.25426	−	2.25426i	−0.0875482	−	0.0875482i
$664$	10.3062			0.399958
$665$	−0.416911	−	2.65582i	−0.0161671	−	0.102988i
$666$	−66.3322			−2.57032
$667$	0.0726505	−	0.0726505i	0.00281304	−	0.00281304i
$668$	4.81188	−	4.81188i	0.186177	−	0.186177i
$669$		−	55.1502i		−	2.13223i
$670$	−16.3256	+	22.4057i	−0.630715	+	0.865608i
$671$			0.378083i			0.0145957i
$672$	0.436921	−	0.436921i	0.0168546	−	0.0168546i
$673$	0.956547	+	0.956547i	0.0368722	+	0.0368722i	0.725302	−	0.688430i	$-0.241700\pi$
$673$	0.956547	+	0.956547i	0.0368722	+	0.0368722i	−0.688430	+	0.725302i	$0.741700\pi$
$674$	10.2101			0.393278
$675$	−61.6058	−	31.6027i	−2.37121	−	1.21639i
$676$	12.8962			0.496009
$677$	−7.64071	+	7.64071i	−0.293656	+	0.293656i	−0.838523	−	0.544867i	$-0.816580\pi$
$677$	−7.64071	+	7.64071i	−0.293656	+	0.293656i	0.544867	+	0.838523i	$0.316580\pi$
$678$	−11.5390	−	11.5390i	−0.443153	−	0.443153i
$679$	−2.76575			−0.106140
$680$	5.56995	+	4.05848i	0.213598	+	0.155635i
$681$	−39.5598			−1.51593
$682$	1.37112	−	1.37112i	0.0525028	−	0.0525028i
$683$	25.9192	−	25.9192i	0.991771	−	0.991771i	−0.00819505	−	0.999966i	$-0.502609\pi$
$683$	25.9192	−	25.9192i	0.991771	−	0.991771i	0.999966	+	0.00819505i	$0.00260859\pi$
$684$	45.6887			1.74695
$685$	−3.26467	−	20.7967i	−0.124737	−	0.794600i
$686$	2.68670			0.102579
$687$	−22.5959	+	22.5959i	−0.862086	+	0.862086i
$688$	−5.15004	+	4.05920i	−0.196343	+	0.154756i
$689$		−	4.10605i		−	0.156428i
$690$	1.87088	+	11.9179i	0.0712232	+	0.453708i
$691$			19.7621i			0.751785i	0.926663	+	0.375892i	$0.122664\pi$
$691$			19.7621i			0.751785i	−0.926663	+	0.375892i	$0.877336\pi$
$692$	9.67496	+	9.67496i	0.367787	+	0.367787i
$693$	0.330107	+	0.330107i	0.0125397	+	0.0125397i
$694$		−	28.2937i		−	1.07402i
$695$	30.9898	+	22.5803i	1.17551	+	0.856521i
$696$		−	0.196383i		−	0.00744389i
$697$	−7.59499	−	7.59499i	−0.287681	−	0.287681i
$698$	12.3492	−	12.3492i	0.467424	−	0.467424i
$699$			66.0041i			2.49650i
$700$	0.439123	−	0.856020i	0.0165973	−	0.0323545i
$701$	−11.6408			−0.439667			−0.219833	−	0.975537i	$-0.570551\pi$
$701$	−11.6408			−0.439667			−0.219833	+	0.975537i	$0.570551\pi$
$702$	−3.15403	−	3.15403i	−0.119041	−	0.119041i
$703$	40.0790	−	40.0790i	1.51161	−	1.51161i
$704$		−	0.331801i		−	0.0125052i
$705$	47.6686	+	34.7331i	1.79530	+	1.30813i
$706$			13.5495i			0.509944i
$707$	−1.48073	+	1.48073i	−0.0556887	+	0.0556887i
$708$	12.6349	+	12.6349i	0.474850	+	0.474850i
$709$			40.3072i			1.51377i	0.653548	+	0.756885i	$0.273280\pi$
$709$			40.3072i			1.51377i	−0.653548	+	0.756885i	$0.726720\pi$
$710$	27.2209	−	4.27315i	1.02158	−	0.160368i
$711$	36.0610			1.35239
$712$	7.54841	+	7.54841i	0.282889	+	0.282889i
$713$	6.94261	−	6.94261i	0.260003	−	0.260003i
$714$	1.90441			0.0712706
$715$	0.0370615	+	0.236090i	0.00138602	+	0.00882926i
$716$		−	2.19297i		−	0.0819551i
$717$	−14.4166	+	14.4166i	−0.538396	+	0.538396i
$718$	7.42611	+	7.42611i	0.277140	+	0.277140i
$719$		−	12.5598i		−	0.468403i	−0.972188	−	0.234202i	$-0.924752\pi$
$719$		−	12.5598i		−	0.468403i	0.972188	−	0.234202i	$-0.0752476\pi$
$720$	13.2148	+	9.62879i	0.492486	+	0.358844i
$721$		−	0.893629i		−	0.0332805i
$722$	−14.1708	+	14.1708i	−0.527383	+	0.527383i
$723$	−31.5759	+	31.5759i	−1.17432	+	1.17432i
$724$		−	12.4610i		−	0.463108i
$725$	−0.0936917	−	0.291065i	−0.00347962	−	0.0108099i
$726$	−34.9704			−1.29787
$727$	−10.1508	+	10.1508i	−0.376473	+	0.376473i	−0.869828	−	0.493355i	$-0.835770\pi$
$727$	−10.1508	+	10.1508i	−0.376473	+	0.376473i	0.493355	+	0.869828i	$0.335770\pi$
$728$	0.0438256	−	0.0438256i	0.00162428	−	0.00162428i
$729$		−	31.3537i		−	1.16125i
$730$	15.4198	−	21.1625i	0.570713	−	0.783260i
$731$	−20.0701	−	2.37731i	−0.742321	−	0.0879281i
$732$	2.58744	+	2.58744i	0.0956346	+	0.0956346i
$733$	30.3984	+	30.3984i	1.12279	+	1.12279i	0.991320	+	0.131472i	$0.0419703\pi$
$733$	30.3984	+	30.3984i	1.12279	+	1.12279i	0.131472	+	0.991320i	$0.458030\pi$
$734$	21.5252			0.794511
$735$	7.75382	+	49.3935i	0.286004	+	1.82191i
$736$		−	1.68006i		−	0.0619279i
$737$	2.90878	+	2.90878i	0.107146	+	0.107146i
$738$	−18.0192	−	18.0192i	−0.663297	−	0.663297i
$739$	−35.1803			−1.29413			−0.647064	−	0.762435i	$-0.724003\pi$
$739$	−35.1803			−1.29413			−0.647064	+	0.762435i	$0.724003\pi$
$740$	20.0389	−	3.14571i	0.736643	−	0.115638i
$741$	6.46302			0.237425
$742$	1.73440	+	1.73440i	0.0636719	+	0.0636719i
$743$	−13.6504	−	13.6504i	−0.500785	−	0.500785i	0.410897	−	0.911682i	$-0.365216\pi$
$743$	−13.6504	−	13.6504i	−0.500785	−	0.500785i	−0.911682	+	0.410897i	$0.865216\pi$
$744$		−	18.7667i		−	0.688022i
$745$	7.42990	−	10.1970i	0.272210	−	0.373588i
$746$	−16.6591			−0.609934
$747$	53.2886	+	53.2886i	1.94973	+	1.94973i
$748$	0.723110	−	0.723110i	0.0264395	−	0.0264395i
$749$	−2.91430			−0.106486
$750$	34.1000	+	11.2349i	1.24515	+	0.410241i
$751$			6.32446i			0.230783i	0.993320	+	0.115391i	$0.0368122\pi$
$751$			6.32446i			0.230783i	−0.993320	+	0.115391i	$0.963188\pi$
$752$	−5.80806	−	5.80806i	−0.211798	−	0.211798i
$753$	34.9824	+	34.9824i	1.27483	+	1.27483i
$754$		−	0.0196983i		−	0.000717370i
$755$	−15.3207	−	11.1633i	−0.557578	−	0.406273i
$756$	2.66453			0.0969080
$757$	28.2087	−	28.2087i	1.02526	−	1.02526i	0.0255889	−	0.999673i	$-0.491854\pi$
$757$	28.2087	−	28.2087i	1.02526	−	1.02526i	0.999673	−	0.0255889i	$-0.00814609\pi$
$758$	8.79513	+	8.79513i	0.319454	+	0.319454i
$759$	1.79011			0.0649769
$760$	−13.8025	+	2.16672i	−0.500668	+	0.0785951i
$761$		−	9.03946i		−	0.327680i	−0.986487	−	0.163840i	$-0.947612\pi$
$761$		−	9.03946i		−	0.327680i	0.986487	−	0.163840i	$-0.0523881\pi$
$762$	27.0620	+	27.0620i	0.980352	+	0.980352i
$763$	1.62562	+	1.62562i	0.0588514	+	0.0588514i
$764$	−25.3921			−0.918653
$765$	7.81513	+	49.7841i	0.282557	+	1.79995i
$766$	35.2911			1.27512
$767$	1.26735	+	1.26735i	0.0457615	+	0.0457615i
$768$	−2.27071	−	2.27071i	−0.0819372	−	0.0819372i
$769$			51.2626i			1.84858i	0.381695	+	0.924288i	$0.375340\pi$
$769$			51.2626i			1.84858i	−0.381695	+	0.924288i	$0.624660\pi$
$770$	−0.115380	−	0.0840699i	−0.00415799	−	0.00302967i
$771$	11.4816			0.413500
$772$	−6.98166	−	6.98166i	−0.251275	−	0.251275i
$773$	−13.9764	−	13.9764i	−0.502698	−	0.502698i	0.409577	−	0.912275i	$-0.365676\pi$
$773$	−13.9764	−	13.9764i	−0.502698	−	0.502698i	−0.912275	+	0.409577i	$0.865676\pi$
$774$	−47.6167	−	5.64021i	−1.71155	−	0.202733i
$775$	−8.95334	−	27.8146i	−0.321613	−	0.999131i
$776$			14.3738i			0.515989i
$777$	3.96348	−	3.96348i	0.142189	−	0.142189i
$778$	−9.60297	+	9.60297i	−0.344283	+	0.344283i
$779$	21.7750			0.780172
$780$	1.86934	+	1.36207i	0.0669330	+	0.0487699i
$781$		−	4.08866i		−	0.146304i
$782$	3.66144	−	3.66144i	0.130933	−	0.130933i
$783$	0.598815	−	0.598815i	0.0213999	−	0.0213999i
$784$		−	6.96298i		−	0.248678i
$785$	−0.785377	−	5.00303i	−0.0280313	−	0.178566i
$786$		−	50.7965i		−	1.81185i
$787$	19.3461	+	19.3461i	0.689613	+	0.689613i	0.962146	−	0.272533i	$-0.0878615\pi$
$787$	19.3461	+	19.3461i	0.689613	+	0.689613i	−0.272533	+	0.962146i	$0.587861\pi$
$788$	13.1418	−	13.1418i	0.468158	−	0.468158i
$789$			40.2413i			1.43263i
$790$	−10.8940	+	1.71014i	−0.387590	+	0.0608440i
$791$	0.977796			0.0347664
$792$	1.71559	−	1.71559i	0.0609608	−	0.0609608i
$793$	0.259535	+	0.259535i	0.00921634	+	0.00921634i
$794$	−16.3278			−0.579451
$795$	−53.9041	+	73.9792i	−1.91178	+	2.62377i
$796$			2.52666i			0.0895549i
$797$	−16.9921	−	16.9921i	−0.601890	−	0.601890i	0.338924	−	0.940814i	$-0.389937\pi$
$797$	−16.9921	−	16.9921i	−0.601890	−	0.601890i	−0.940814	+	0.338924i	$0.889937\pi$
$798$	−2.72999	+	2.72999i	−0.0966405	+	0.0966405i
$799$		−	25.3156i		−	0.895601i
$800$	−4.44880	−	2.28215i	−0.157289	−	0.0806862i
$801$			78.0586i			2.75807i
$802$	3.85827	−	3.85827i	0.136240	−	0.136240i
$803$	−2.74739	−	2.74739i	−0.0969533	−	0.0969533i
$804$	39.8130			1.40410
$805$	−0.584220	−	0.425685i	−0.0205911	−	0.0150034i
$806$		−	1.88241i		−	0.0663049i
$807$	−7.65856	+	7.65856i	−0.269594	+	0.269594i
$808$	7.69548	+	7.69548i	0.270726	+	0.270726i
$809$		−	36.0439i		−	1.26724i	−0.773646	−	0.633618i	$-0.781569\pi$
$809$		−	36.0439i		−	1.26724i	0.773646	−	0.633618i	$-0.218431\pi$
$810$	7.81351	+	49.7738i	0.274539	+	1.74887i
$811$			36.7536i			1.29059i	0.763933	+	0.645296i	$0.223266\pi$
$811$			36.7536i			1.29059i	−0.763933	+	0.645296i	$0.776734\pi$
$812$	0.00832060	+	0.00832060i	0.000291996	+	0.000291996i
$813$	−32.6190	−	32.6190i	−1.14400	−	1.14400i
$814$		−	3.00990i		−	0.105497i
$815$	33.4810	−	5.25586i	1.17279	−	0.184105i
$816$		−	9.89733i		−	0.346476i
$817$	32.1787	−	25.3629i	1.12579	−	0.887335i
$818$	4.78580	−	4.78580i	0.167332	−	0.167332i
$819$	0.453203			0.0158362
$820$	6.29811	+	4.58904i	0.219940	+	0.160256i
$821$	47.4848			1.65723			0.828616	−	0.559817i	$-0.189129\pi$
$821$	47.4848			1.65723			0.828616	+	0.559817i	$0.189129\pi$
$822$	−21.3775	+	21.3775i	−0.745626	+	0.745626i
$823$	−16.4411	+	16.4411i	−0.573102	+	0.573102i	−0.932994	−	0.359892i	$-0.882814\pi$
$823$	−16.4411	+	16.4411i	−0.573102	+	0.573102i	0.359892	+	0.932994i	$0.382814\pi$
$824$	−4.64425			−0.161790
$825$	2.43164	−	4.74020i	0.0846587	−	0.165033i
$826$	−1.07066			−0.0372531
$827$	−29.1396	−	29.1396i	−1.01328	−	1.01328i	−0.999911	−	0.0133723i	$-0.995743\pi$
$827$	−29.1396	−	29.1396i	−1.01328	−	1.01328i	−0.0133723	−	0.999911i	$-0.504257\pi$
$828$	8.68682	−	8.68682i	0.301888	−	0.301888i
$829$	20.2192			0.702241			0.351120	−	0.936330i	$-0.385801\pi$
$829$	20.2192			0.702241			0.351120	+	0.936330i	$0.385801\pi$
$830$	−18.6255	−	13.5713i	−0.646501	−	0.471065i
$831$	−59.3637			−2.05931
$832$	−0.227765	−	0.227765i	−0.00789631	−	0.00789631i
$833$	15.1747	−	15.1747i	0.525774	−	0.525774i
$834$		−	55.0662i		−	1.90679i
$835$	−15.0324	+	2.35979i	−0.520218	+	0.0816640i
$836$			2.07317i			0.0717022i
$837$	57.2238	−	57.2238i	1.97794	−	1.97794i
$838$	−0.682392	+	0.682392i	−0.0235728	+	0.0235728i
$839$	1.68959			0.0583313			0.0291656	−	0.999575i	$-0.490715\pi$
$839$	1.68959			0.0583313			0.0291656	+	0.999575i	$0.490715\pi$
$840$	−1.36495	+	0.214270i	−0.0470952	+	0.00739303i
$841$	−28.9963			−0.999871
$842$	−23.8225	−	23.8225i	−0.820979	−	0.820979i
$843$	46.7466	+	46.7466i	1.61004	+	1.61004i
$844$	23.4480			0.807113
$845$	−23.3063	−	16.9818i	−0.801761	−	0.584193i
$846$		−	60.0615i		−	2.06496i
$847$	1.48167	−	1.48167i	0.0509107	−	0.0509107i
$848$	9.01382	−	9.01382i	0.309536	−	0.309536i
$849$	50.0170			1.71658
$850$	−4.72187	−	14.6691i	−0.161959	−	0.503145i
$851$		−	15.2405i		−	0.522438i
$852$	−27.9811	−	27.9811i	−0.958617	−	0.958617i
$853$	−34.4799	+	34.4799i	−1.18057	+	1.18057i	−0.200970	+	0.979597i	$0.564410\pi$
$853$	−34.4799	+	34.4799i	−1.18057	+	1.18057i	−0.979597	+	0.200970i	$0.935590\pi$
$854$	−0.219255			−0.00750277
$855$	−82.5692	−	60.1630i	−2.82381	−	2.05753i
$856$			15.1458i			0.517673i
$857$	−6.41954	−	6.41954i	−0.219287	−	0.219287i	0.588911	−	0.808198i	$-0.299557\pi$
$857$	−6.41954	−	6.41954i	−0.219287	−	0.219287i	−0.808198	+	0.588911i	$0.799557\pi$
$858$	0.242683	−	0.242683i	0.00828508	−	0.00828508i
$859$	−38.5050			−1.31377			−0.656886	−	0.753989i	$-0.728127\pi$
$859$	−38.5050			−1.31377			−0.656886	+	0.753989i	$0.728127\pi$
$860$	14.6524	−	0.554252i	0.499643	−	0.0188998i
$861$	2.15337			0.0733867
$862$	−6.64924	+	6.64924i	−0.226474	+	0.226474i
$863$	11.3527	+	11.3527i	0.386451	+	0.386451i	0.873420	−	0.486968i	$-0.161897\pi$
$863$	11.3527	+	11.3527i	0.386451	+	0.386451i	−0.486968	+	0.873420i	$0.661897\pi$
$864$		−	13.8478i		−	0.471110i
$865$	−4.74469	−	30.2248i	−0.161324	−	1.02767i
$866$	−5.06252			−0.172032
$867$	−17.0323	+	17.0323i	−0.578448	+	0.578448i
$868$	0.795131	+	0.795131i	0.0269885	+	0.0269885i
$869$			1.63631i			0.0555079i
$870$	−0.258599	+	0.354907i	−0.00876731	+	0.0120325i
$871$	3.99347			0.135313
$872$	8.44846	−	8.44846i	0.286101	−	0.286101i
$873$	−74.3202	+	74.3202i	−2.51536	+	2.51536i
$874$			10.4974i			0.355081i
$875$	−1.92080	+	0.968773i	−0.0649349	+	0.0327505i
$876$	−37.6040			−1.27052
$877$	−33.0290	−	33.0290i	−1.11531	−	1.11531i	−0.992420	−	0.122891i	$-0.960783\pi$
$877$	−33.0290	−	33.0290i	−1.11531	−	1.11531i	−0.122891	−	0.992420i	$-0.539217\pi$
$878$	1.14863	+	1.14863i	0.0387643	+	0.0387643i
$879$	23.6222			0.796756
$880$	−0.436917	+	0.599636i	−0.0147285	+	0.0202137i
$881$	43.9198			1.47970			0.739848	−	0.672774i	$-0.234897\pi$
$881$	43.9198			1.47970			0.739848	+	0.672774i	$0.234897\pi$
$882$	36.0023	−	36.0023i	1.21226	−	1.21226i
$883$	3.88203	−	3.88203i	0.130641	−	0.130641i	−0.638763	−	0.769404i	$-0.720554\pi$
$883$	3.88203	−	3.88203i	0.130641	−	0.130641i	0.769404	+	0.638763i	$0.220554\pi$
$884$		−	0.992756i		−	0.0333900i
$885$	−6.19629	−	39.4718i	−0.208286	−	1.32683i
$886$		−	14.5908i		−	0.490188i
$887$	5.51928	−	5.51928i	0.185319	−	0.185319i	−0.608350	−	0.793669i	$-0.708168\pi$
$887$	5.51928	−	5.51928i	0.185319	−	0.185319i	0.793669	+	0.608350i	$0.208168\pi$
$888$	−20.5985	−	20.5985i	−0.691240	−	0.691240i
$889$	−2.29319			−0.0769110
$890$	−3.70181	−	23.5814i	−0.124085	−	0.790450i
$891$	7.47618			0.250461
$892$	12.1438	−	12.1438i	0.406605	−	0.406605i
$893$	36.2902	+	36.2902i	1.21440	+	1.21440i
$894$	−18.1192			−0.605995
$895$	−2.88771	+	3.96317i	−0.0965256	+	0.132474i
$896$	0.192416			0.00642817
$897$	1.22882	−	1.22882i	0.0410291	−	0.0410291i
$898$	−0.0590474	+	0.0590474i	−0.00197044	+	0.00197044i
$899$	0.357388			0.0119196
$900$	−11.2027	−	34.8026i	−0.373424	−	1.16009i
$901$	39.2885			1.30889
$902$	0.817643	−	0.817643i	0.0272245	−	0.0272245i
$903$	3.18221	−	2.50818i	0.105897	−	0.0834669i
$904$		−	5.08168i		−	0.169014i
$905$	−16.4087	+	22.5197i	−0.545443	+	0.748579i
$906$			27.2236i			0.904445i
$907$	−21.3973	−	21.3973i	−0.710485	−	0.710485i	0.256152	−	0.966637i	$-0.417545\pi$
$907$	−21.3973	−	21.3973i	−0.710485	−	0.710485i	−0.966637	+	0.256152i	$0.917545\pi$
$908$	−8.71088	−	8.71088i	−0.289081	−	0.289081i
$909$			79.5795i			2.63948i
$910$	−0.136912	+	0.0214925i	−0.00453858	+	0.000712469i
$911$		−	15.5925i		−	0.516604i	−0.966064	−	0.258302i	$-0.916837\pi$
$911$		−	15.5925i		−	0.516604i	0.966064	−	0.258302i	$-0.0831629\pi$
$912$	14.1879	+	14.1879i	0.469810	+	0.469810i
$913$	−2.41803	+	2.41803i	−0.0800251	+	0.0800251i
$914$			18.8231i			0.622614i
$915$	−1.26891	−	8.08322i	−0.0419488	−	0.267223i
$916$	−9.95102			−0.328791
$917$	2.15220	+	2.15220i	0.0710721	+	0.0710721i
$918$	30.1791	−	30.1791i	0.996058	−	0.996058i
$919$			28.4754i			0.939318i	0.882848	+	0.469659i	$0.155623\pi$
$919$			28.4754i			0.939318i	−0.882848	+	0.469659i	$0.844377\pi$
$920$	−2.21232	+	3.03623i	−0.0729379	+	0.100102i
$921$			91.0051i			2.99872i
$922$	27.0742	−	27.0742i	0.891643	−	0.891643i
$923$	−2.80666	−	2.80666i	−0.0923823	−	0.0923823i
$924$			0.205020i			0.00674465i
$925$	−40.3568	−	20.7023i	−1.32692	−	0.680687i
$926$	−1.50964			−0.0496100
$927$	−24.0133	−	24.0133i	−0.788699	−	0.788699i
$928$	0.0432427	−	0.0432427i	0.00141951	−	0.00141951i
$929$	12.3775			0.406094			0.203047	−	0.979169i	$-0.434916\pi$
$929$	12.3775			0.406094			0.203047	+	0.979169i	$0.434916\pi$
$930$	−24.7121	+	33.9155i	−0.810342	+	1.11213i
$931$			43.5064i			1.42586i
$932$	−14.5338	+	14.5338i	−0.476071	+	0.476071i
$933$	−68.6593	−	68.6593i	−2.24781	−	2.24781i
$934$			24.6824i			0.807633i
$935$	−2.25901	+	0.354620i	−0.0738775	+	0.0115973i
$936$		−	2.35533i		−	0.0769863i
$937$	36.2005	−	36.2005i	1.18262	−	1.18262i	0.203554	−	0.979064i	$-0.434751\pi$
$937$	36.2005	−	36.2005i	1.18262	−	1.18262i	0.979064	−	0.203554i	$-0.0652491\pi$
$938$	−1.68685	+	1.68685i	−0.0550775	+	0.0550775i
$939$		−	23.9447i		−	0.781404i
$940$	2.84833	+	18.1445i	0.0929023	+	0.591808i
$941$	−6.17303			−0.201235			−0.100617	−	0.994925i	$-0.532082\pi$
$941$	−6.17303			−0.201235			−0.100617	+	0.994925i	$0.532082\pi$
$942$	−5.14275	+	5.14275i	−0.167560	+	0.167560i
$943$	4.14011	−	4.14011i	0.134820	−	0.134820i
$944$			5.56431i			0.181103i
$945$	−4.81538	−	3.50867i	−0.156644	−	0.114137i
$946$	0.255931	−	2.16066i	0.00832103	−	0.0702491i
$947$	7.41035	+	7.41035i	0.240804	+	0.240804i	0.817183	−	0.576379i	$-0.195535\pi$
$947$	7.41035	+	7.41035i	0.240804	+	0.240804i	−0.576379	+	0.817183i	$0.695535\pi$
$948$	11.1982	+	11.1982i	0.363701	+	0.363701i
$949$	−3.77189			−0.122441
$950$	27.7972	+	14.2594i	0.901859	+	0.462637i
$951$		−	84.9151i		−	2.75356i
$952$	0.419342	+	0.419342i	0.0135909	+	0.0135909i
$953$	−1.61402	−	1.61402i	−0.0522832	−	0.0522832i	0.680482	−	0.732765i	$-0.261771\pi$
$953$	−1.61402	−	1.61402i	−0.0522832	−	0.0522832i	−0.732765	+	0.680482i	$0.761771\pi$
$954$	93.2125			3.01787
$955$	45.8889	+	33.4364i	1.48493	+	1.08198i
$956$	−6.34892			−0.205339
$957$	0.0460752	+	0.0460752i	0.00148940	+	0.00148940i
$958$	17.7592	+	17.7592i	0.573773	+	0.573773i
$959$		−	1.81149i		−	0.0584962i
$960$	1.11358	+	7.09374i	0.0359406	+	0.228949i
$961$	3.15263			0.101698
$962$	−2.06614	−	2.06614i	−0.0666151	−	0.0666151i
$963$	−78.3119	+	78.3119i	−2.52357	+	2.52357i
$964$	−13.9058			−0.447874
$965$	3.42387	+	21.8108i	0.110218	+	0.702115i
$966$			1.03811i			0.0334006i
$967$	−17.7911	−	17.7911i	−0.572124	−	0.572124i	0.360598	−	0.932721i	$-0.382573\pi$
$967$	−17.7911	−	17.7911i	−0.572124	−	0.572124i	−0.932721	+	0.360598i	$0.882573\pi$
$968$	−7.70033	−	7.70033i	−0.247498	−	0.247498i
$969$			61.8409i			1.98662i
$970$	18.9275	−	25.9765i	0.607725	−	0.834057i
$971$	−32.8439			−1.05401			−0.527005	−	0.849862i	$-0.676685\pi$
$971$	−32.8439			−1.05401			−0.527005	+	0.849862i	$0.676685\pi$
$972$	21.7884	−	21.7884i	0.698862	−	0.698862i
$973$	2.33311	+	2.33311i	0.0747961	+	0.0747961i
$974$	−27.1385			−0.869574
$975$	−1.58471	−	4.92310i	−0.0507514	−	0.157665i
$976$			1.13949i			0.0364741i
$977$	27.7136	+	27.7136i	0.886636	+	0.886636i	0.994198	−	0.107563i	$-0.0343046\pi$
$977$	27.7136	+	27.7136i	0.886636	+	0.886636i	−0.107563	+	0.994198i	$0.534305\pi$
$978$	−34.4160	−	34.4160i	−1.10050	−	1.10050i
$979$	−3.54200			−0.113203
$980$	−9.16888	+	12.5836i	−0.292889	+	0.401968i
$981$	87.3661			2.78938
$982$	−4.36399	−	4.36399i	−0.139260	−	0.139260i
$983$	0.474888	+	0.474888i	0.0151466	+	0.0151466i	0.714640	−	0.699493i	$-0.246591\pi$
$983$	0.474888	+	0.474888i	0.0151466	+	0.0151466i	−0.699493	+	0.714640i	$0.746591\pi$
$984$		−	11.1912i		−	0.356763i
$985$	−41.0553	+	6.44488i	−1.30813	+	0.205351i
$986$	0.188482			0.00600249
$987$	3.58880	+	3.58880i	0.114233	+	0.114233i
$988$	1.42313	+	1.42313i	0.0452757	+	0.0452757i
$989$	1.29590	−	10.9404i	0.0412071	−	0.347885i
$990$	−5.35953	+	0.841341i	−0.170337	+	0.0267396i
$991$			10.3686i			0.329370i	0.986346	+	0.164685i	$0.0526608\pi$
$991$			10.3686i			0.329370i	−0.986346	+	0.164685i	$0.947339\pi$
$992$	4.13235	−	4.13235i	0.131202	−	0.131202i
$993$	−14.2105	+	14.2105i	−0.450957	+	0.450957i
$994$	2.37107			0.0752059
$995$	3.32711	−	4.56621i	0.105477	−	0.144759i
$996$			33.0960i			1.04869i
$997$	37.6261	−	37.6261i	1.19163	−	1.19163i	0.215022	−	0.976609i	$-0.431018\pi$
$997$	37.6261	−	37.6261i	1.19163	−	1.19163i	0.976609	−	0.215022i	$-0.0689822\pi$
$998$	−15.8921	+	15.8921i	−0.503056	+	0.503056i
$999$		−	125.618i		−	3.97439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.g.b.257.1	✓	40
5.3	odd	4	inner	430.2.g.b.343.20	yes	40
43.42	odd	2	inner	430.2.g.b.257.20	yes	40
215.128	even	4	inner	430.2.g.b.343.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.g.b.257.1	✓	40	1.1	even	1	trivial
430.2.g.b.257.20	yes	40	43.42	odd	2	inner
430.2.g.b.343.1	yes	40	215.128	even	4	inner
430.2.g.b.343.20	yes	40	5.3	odd	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.27071 - 2.27071i) q^{3} -1.00000i q^{4} +(-1.31680 + 1.80721i) q^{5} +3.21127 q^{6} +(-0.136059 + 0.136059i) q^{7} +(0.707107 + 0.707107i) q^{8} +7.31224i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-2.27071 - 2.27071i) q^{3} -1.00000i q^{4} +(-1.31680 + 1.80721i) q^{5} +3.21127 q^{6} +(-0.136059 + 0.136059i) q^{7} +(0.707107 + 0.707107i) q^{8} +7.31224i q^{9} +(-0.346772 - 2.20902i) q^{10} -0.331801 q^{11} +(-2.27071 + 2.27071i) q^{12} +(-0.227765 + 0.227765i) q^{13} -0.192416i q^{14} +(7.09374 - 1.11358i) q^{15} -1.00000 q^{16} +(-2.17935 - 2.17935i) q^{17} +(-5.17053 - 5.17053i) q^{18} +6.24824 q^{19} +(1.80721 + 1.31680i) q^{20} +0.617899 q^{21} +(0.234619 - 0.234619i) q^{22} +(1.18798 - 1.18798i) q^{23} -3.21127i q^{24} +(-1.53205 - 4.75950i) q^{25} -0.322108i q^{26} +(9.79184 - 9.79184i) q^{27} +(0.136059 + 0.136059i) q^{28} +0.0611545 q^{29} +(-4.22861 + 5.80345i) q^{30} +5.84403 q^{31} +(0.707107 - 0.707107i) q^{32} +(0.753423 + 0.753423i) q^{33} +3.08206 q^{34} +(-0.0667245 - 0.425050i) q^{35} +7.31224 q^{36} +(6.41444 - 6.41444i) q^{37} +(-4.41818 + 4.41818i) q^{38} +1.03437 q^{39} +(-2.20902 + 0.346772i) q^{40} +3.48498 q^{41} +(-0.436921 + 0.436921i) q^{42} +(5.15004 - 4.05920i) q^{43} +0.331801i q^{44} +(-13.2148 - 9.62879i) q^{45} +1.68006i q^{46} +(5.80806 + 5.80806i) q^{47} +(2.27071 + 2.27071i) q^{48} +6.96298i q^{49} +(4.44880 + 2.28215i) q^{50} +9.89733i q^{51} +(0.227765 + 0.227765i) q^{52} +(-9.01382 + 9.01382i) q^{53} +13.8478i q^{54} +(0.436917 - 0.599636i) q^{55} -0.192416 q^{56} +(-14.1879 - 14.1879i) q^{57} +(-0.0432427 + 0.0432427i) q^{58} -5.56431i q^{59} +(-1.11358 - 7.09374i) q^{60} -1.13949i q^{61} +(-4.13235 + 4.13235i) q^{62} +(-0.994894 - 0.994894i) q^{63} +1.00000i q^{64} +(-0.111698 - 0.711541i) q^{65} -1.06550 q^{66} +(-8.76665 - 8.76665i) q^{67} +(-2.17935 + 2.17935i) q^{68} -5.39513 q^{69} +(0.347737 + 0.253374i) q^{70} +12.3226i q^{71} +(-5.17053 + 5.17053i) q^{72} +(8.28023 + 8.28023i) q^{73} +9.07139i q^{74} +(-7.32860 + 14.2863i) q^{75} -6.24824i q^{76} +(0.0451444 - 0.0451444i) q^{77} +(-0.731413 + 0.731413i) q^{78} -4.93159i q^{79} +(1.31680 - 1.80721i) q^{80} -22.5321 q^{81} +(-2.46426 + 2.46426i) q^{82} +(7.28759 - 7.28759i) q^{83} -0.617899i q^{84} +(6.80833 - 1.06877i) q^{85} +(-0.771338 + 6.51192i) q^{86} +(-0.138864 - 0.138864i) q^{87} +(-0.234619 - 0.234619i) q^{88} +10.6751 q^{89} +(16.1528 - 2.53568i) q^{90} -0.0619787i q^{91} +(-1.18798 - 1.18798i) q^{92} +(-13.2701 - 13.2701i) q^{93} -8.21384 q^{94} +(-8.22772 + 11.2919i) q^{95} -3.21127 q^{96} +(10.1638 + 10.1638i) q^{97} +(-4.92357 - 4.92357i) q^{98} -2.42621i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q+O(q^{10}) \) 40 * q	\( 40 q - 8 q^{10} + 16 q^{11} - 24 q^{13} + 8 q^{15} - 40 q^{16} - 12 q^{17} - 16 q^{21} + 44 q^{23} + 24 q^{25} + 32 q^{31} - 64 q^{35} + 48 q^{36} - 28 q^{38} - 4 q^{40} + 8 q^{41} - 16 q^{43} - 28 q^{47} + 24 q^{52} - 80 q^{53} + 24 q^{56} + 64 q^{57} + 12 q^{58} + 24 q^{67} - 12 q^{68} + 40 q^{78} - 120 q^{81} + 48 q^{83} + 28 q^{87} - 44 q^{92} - 16 q^{95} - 60 q^{97}+O(q^{100}) \) 40 * q - 8 * q^10 + 16 * q^11 - 24 * q^13 + 8 * q^15 - 40 * q^16 - 12 * q^17 - 16 * q^21 + 44 * q^23 + 24 * q^25 + 32 * q^31 - 64 * q^35 + 48 * q^36 - 28 * q^38 - 4 * q^40 + 8 * q^41 - 16 * q^43 - 28 * q^47 + 24 * q^52 - 80 * q^53 + 24 * q^56 + 64 * q^57 + 12 * q^58 + 24 * q^67 - 12 * q^68 + 40 * q^78 - 120 * q^81 + 48 * q^83 + 28 * q^87 - 44 * q^92 - 16 * q^95 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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