LMFDB - Embedded newform 429.2.x.a.248.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(248,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9, 0]))

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

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

chi := DirichletCharacter("429.248");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.x (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			248.3
Character	$\chi$	$=$	429.248
Dual form			429.2.x.a.365.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.828482 - 2.54980i) q^{2} +(1.34014 - 1.09728i) q^{3} +(-4.19709 + 3.04936i) q^{4} +(2.56502 + 0.833425i) q^{5} +(-3.90813 - 2.50803i) q^{6} +(2.78275 + 3.83012i) q^{7} +(6.91450 + 5.02368i) q^{8} +(0.591966 - 2.94102i) q^{9} +O(q^{10})$	\(q+(-0.828482 - 2.54980i) q^{2} +(1.34014 - 1.09728i) q^{3} +(-4.19709 + 3.04936i) q^{4} +(2.56502 + 0.833425i) q^{5} +(-3.90813 - 2.50803i) q^{6} +(2.78275 + 3.83012i) q^{7} +(6.91450 + 5.02368i) q^{8} +(0.591966 - 2.94102i) q^{9} -7.23077i q^{10} +(-3.15751 - 1.01495i) q^{11} +(-2.27870 + 8.69195i) q^{12} +(0.951057 - 0.309017i) q^{13} +(7.46061 - 10.2687i) q^{14} +(4.35199 - 1.69763i) q^{15} +(3.87457 - 11.9247i) q^{16} +(0.622707 - 1.91649i) q^{17} +(-7.98945 + 0.927179i) q^{18} +(1.49966 - 2.06411i) q^{19} +(-13.3070 + 4.32371i) q^{20} +(7.93199 + 2.07947i) q^{21} +(0.0280078 + 8.89190i) q^{22} -1.65219i q^{23} +(14.7788 - 0.854674i) q^{24} +(1.83963 + 1.33657i) q^{25} +(-1.57587 - 2.16899i) q^{26} +(-2.43379 - 4.59093i) q^{27} +(-23.3589 - 7.58976i) q^{28} +(2.56908 - 1.86655i) q^{29} +(-7.93416 - 9.69026i) q^{30} +(-0.419363 - 1.29067i) q^{31} -16.5221 q^{32} +(-5.34520 + 2.10448i) q^{33} -5.40259 q^{34} +(3.94568 + 12.1435i) q^{35} +(6.48369 + 14.1488i) q^{36} +(-2.11663 + 1.53782i) q^{37} +(-6.50551 - 2.11377i) q^{38} +(0.935474 - 1.45770i) q^{39} +(13.5490 + 18.6485i) q^{40} +(8.73715 + 6.34791i) q^{41} +(-1.26927 - 21.9478i) q^{42} +8.47599i q^{43} +(16.3473 - 5.36855i) q^{44} +(3.96952 - 7.05040i) q^{45} +(-4.21277 + 1.36881i) q^{46} +(0.732957 - 1.00883i) q^{47} +(-7.89222 - 20.2323i) q^{48} +(-4.76305 + 14.6592i) q^{49} +(1.88389 - 5.79803i) q^{50} +(-1.26841 - 3.25166i) q^{51} +(-3.04936 + 4.19709i) q^{52} +(-6.86533 + 2.23068i) q^{53} +(-9.68963 + 10.0092i) q^{54} +(-7.25318 - 5.23492i) q^{55} +40.4630i q^{56} +(-0.255136 - 4.41174i) q^{57} +(-6.88777 - 5.00426i) q^{58} +(-3.97615 - 5.47270i) q^{59} +(-13.0890 + 20.3959i) q^{60} +(-0.891593 - 0.289696i) q^{61} +(-2.94351 + 2.13859i) q^{62} +(12.9118 - 5.91680i) q^{63} +(5.93911 + 18.2787i) q^{64} +2.69702 q^{65} +(9.79442 + 11.8857i) q^{66} +3.14422 q^{67} +(3.23053 + 9.94255i) q^{68} +(-1.81292 - 2.21418i) q^{69} +(27.6948 - 20.1214i) q^{70} +(-9.85531 - 3.20218i) q^{71} +(18.8679 - 17.3618i) q^{72} +(1.37666 + 1.89482i) q^{73} +(5.67472 + 4.12293i) q^{74} +(3.93196 - 0.227390i) q^{75} +13.2362i q^{76} +(-4.89916 - 14.9180i) q^{77} +(-4.49187 - 1.17760i) q^{78} +(-11.1922 + 3.63657i) q^{79} +(19.8767 - 27.3579i) q^{80} +(-8.29915 - 3.48197i) q^{81} +(8.94737 - 27.5372i) q^{82} +(-3.00150 + 9.23768i) q^{83} +(-39.6323 + 15.4598i) q^{84} +(3.19451 - 4.39686i) q^{85} +(21.6121 - 7.02220i) q^{86} +(1.39482 - 5.32044i) q^{87} +(-16.7338 - 22.8802i) q^{88} -11.5947i q^{89} +(-21.2658 - 4.28037i) q^{90} +(3.83012 + 2.78275i) q^{91} +(5.03814 + 6.93441i) q^{92} +(-1.97822 - 1.26952i) q^{93} +(-3.17956 - 1.03310i) q^{94} +(5.56694 - 4.04462i) q^{95} +(-22.1420 + 18.1293i) q^{96} +(-0.520822 - 1.60293i) q^{97} +41.3241 q^{98} +(-4.85413 + 8.68547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9}+O(q^{10}) $ 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9	$ 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9} - 20 q^{12} + 6 q^{15} - 28 q^{16} - 10 q^{18} - 60 q^{19} + 4 q^{22} + 30 q^{24} - 12 q^{25} + 30 q^{27} - 20 q^{28} + 12 q^{31} - 32 q^{33} + 56 q^{34} + 44 q^{36} + 60 q^{40} - 108 q^{42} - 40 q^{45} - 28 q^{48} - 24 q^{49} + 10 q^{51} + 20 q^{52} - 20 q^{55} + 50 q^{57} - 60 q^{58} + 36 q^{60} + 20 q^{61} - 30 q^{63} + 64 q^{64} - 30 q^{66} - 120 q^{67} - 16 q^{69} + 20 q^{70} + 150 q^{72} - 20 q^{73} + 18 q^{75} + 40 q^{78} - 160 q^{79} - 46 q^{81} + 88 q^{82} - 40 q^{85} + 72 q^{88} - 80 q^{90} + 8 q^{91} - 72 q^{93} - 120 q^{94} - 140 q^{96} - 88 q^{97} + 62 q^{99}+O(q^{100}) $ 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9 - 20 * q^12 + 6 * q^15 - 28 * q^16 - 10 * q^18 - 60 * q^19 + 4 * q^22 + 30 * q^24 - 12 * q^25 + 30 * q^27 - 20 * q^28 + 12 * q^31 - 32 * q^33 + 56 * q^34 + 44 * q^36 + 60 * q^40 - 108 * q^42 - 40 * q^45 - 28 * q^48 - 24 * q^49 + 10 * q^51 + 20 * q^52 - 20 * q^55 + 50 * q^57 - 60 * q^58 + 36 * q^60 + 20 * q^61 - 30 * q^63 + 64 * q^64 - 30 * q^66 - 120 * q^67 - 16 * q^69 + 20 * q^70 + 150 * q^72 - 20 * q^73 + 18 * q^75 + 40 * q^78 - 160 * q^79 - 46 * q^81 + 88 * q^82 - 40 * q^85 + 72 * q^88 - 80 * q^90 + 8 * q^91 - 72 * q^93 - 120 * q^94 - 140 * q^96 - 88 * q^97 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	−0.828482	−	2.54980i	−0.585825	−	1.80298i	−0.595932	−	0.803035i	$-0.703217\pi$
$2$	−0.828482	−	2.54980i	−0.585825	−	1.80298i	0.0101067	−	0.999949i	$-0.496783\pi$
$3$	1.34014	−	1.09728i	0.773732	−	0.633513i
$3$	1.34014	−	1.09728i	0.773732	−	0.633513i
$4$	−4.19709	+	3.04936i	−2.09854	+	1.52468i
$5$	2.56502	+	0.833425i	1.14711	+	0.372719i	0.820054	−	0.572286i	$-0.193943\pi$
$5$	2.56502	+	0.833425i	1.14711	+	0.372719i	0.327056	+	0.945005i	$0.393943\pi$
$6$	−3.90813	−	2.50803i	−1.59549	−	1.02390i
$7$	2.78275	+	3.83012i	1.05178	+	1.44765i	0.887256	+	0.461278i	$0.152609\pi$
$7$	2.78275	+	3.83012i	1.05178	+	1.44765i	0.164525	+	0.986373i	$0.447391\pi$
$8$	6.91450	+	5.02368i	2.44464	+	1.77614i
$9$	0.591966	−	2.94102i	0.197322	−	0.980339i
$10$		−	7.23077i		−	2.28657i
$11$	−3.15751	−	1.01495i	−0.952025	−	0.306020i
$11$	−3.15751	−	1.01495i	−0.952025	−	0.306020i
$12$	−2.27870	+	8.69195i	−0.657805	+	2.50915i
$13$	0.951057	−	0.309017i	0.263776	−	0.0857059i
$13$	0.951057	−	0.309017i	0.263776	−	0.0857059i
$14$	7.46061	−	10.2687i	1.99393	−	2.74441i
$15$	4.35199	−	1.69763i	1.12368	−	0.438325i
$16$	3.87457	−	11.9247i	0.968643	−	2.98118i
$17$	0.622707	−	1.91649i	0.151029	−	0.464818i	−0.846708	−	0.532057i	$-0.821419\pi$
$17$	0.622707	−	1.91649i	0.151029	−	0.464818i	0.997737	+	0.0672393i	$0.0214191\pi$
$18$	−7.98945	+	0.927179i	−1.88313	+	0.218538i
$19$	1.49966	−	2.06411i	0.344046	−	0.473539i	−0.601572	−	0.798819i	$-0.705459\pi$
$19$	1.49966	−	2.06411i	0.344046	−	0.473539i	0.945618	+	0.325280i	$0.105459\pi$
$20$	−13.3070	+	4.32371i	−2.97554	+	0.966811i
$21$	7.93199	+	2.07947i	1.73090	+	0.453777i
$22$	0.0280078	+	8.89190i	0.00597128	+	1.89576i
$23$		−	1.65219i		−	0.344506i	−0.985053	−	0.172253i	$-0.944895\pi$
$23$		−	1.65219i		−	0.344506i	0.985053	−	0.172253i	$-0.0551047\pi$
$24$	14.7788	−	0.854674i	3.01671	−	0.174460i
$25$	1.83963	+	1.33657i	0.367926	+	0.267314i
$26$	−1.57587	−	2.16899i	−0.309053	−	0.425375i
$27$	−2.43379	−	4.59093i	−0.468383	−	0.883526i
$28$	−23.3589	−	7.58976i	−4.41441	−	1.43433i
$29$	2.56908	−	1.86655i	0.477067	−	0.346609i	−0.323122	−	0.946357i	$-0.604732\pi$
$29$	2.56908	−	1.86655i	0.477067	−	0.346609i	0.800189	+	0.599748i	$0.204732\pi$
$30$	−7.93416	−	9.69026i	−1.44857	−	1.76919i
$31$	−0.419363	−	1.29067i	−0.0753197	−	0.231810i	0.906308	−	0.422619i	$-0.138889\pi$
$31$	−0.419363	−	1.29067i	−0.0753197	−	0.231810i	−0.981627	+	0.190808i	$0.938889\pi$
$32$	−16.5221			−2.92072
$33$	−5.34520	+	2.10448i	−0.930480	+	0.366343i
$34$	−5.40259			−0.926536
$35$	3.94568	+	12.1435i	0.666941	+	2.05263i
$36$	6.48369	+	14.1488i	1.08061	+	2.35814i
$37$	−2.11663	+	1.53782i	−0.347971	+	0.252816i	−0.748017	−	0.663679i	$-0.768994\pi$
$37$	−2.11663	+	1.53782i	−0.347971	+	0.252816i	0.400046	+	0.916495i	$0.368994\pi$
$38$	−6.50551	−	2.11377i	−1.05533	−	0.342899i
$39$	0.935474	−	1.45770i	0.149796	−	0.233419i
$40$	13.5490	+	18.6485i	2.14228	+	2.94859i
$41$	8.73715	+	6.34791i	1.36451	+	0.991378i	0.998143	+	0.0609087i	$0.0193999\pi$
$41$	8.73715	+	6.34791i	1.36451	+	0.991378i	0.366371	+	0.930469i	$0.380600\pi$
$42$	−1.26927	−	21.9478i	−0.195852	−	3.38662i
$43$			8.47599i			1.29258i	0.763093	+	0.646288i	$0.223680\pi$
$43$			8.47599i			1.29258i	−0.763093	+	0.646288i	$0.776320\pi$
$44$	16.3473	−	5.36855i	2.46445	−	0.809339i
$45$	3.96952	−	7.05040i	0.591741	−	1.05101i
$46$	−4.21277	+	1.36881i	−0.621140	+	0.201820i
$47$	0.732957	−	1.00883i	0.106913	−	0.147153i	−0.752208	−	0.658926i	$-0.771011\pi$
$47$	0.732957	−	1.00883i	0.106913	−	0.147153i	0.859121	+	0.511773i	$0.171011\pi$
$48$	−7.89222	−	20.2323i	−1.13914	−	2.92028i
$49$	−4.76305	+	14.6592i	−0.680435	+	2.09416i
$50$	1.88389	−	5.79803i	0.266423	−	0.819965i
$51$	−1.26841	−	3.25166i	−0.177613	−	0.455323i
$52$	−3.04936	+	4.19709i	−0.422870	+	0.582031i
$53$	−6.86533	+	2.23068i	−0.943025	+	0.306407i	−0.739878	−	0.672741i	$-0.765117\pi$
$53$	−6.86533	+	2.23068i	−0.943025	+	0.306407i	−0.203147	+	0.979148i	$0.565117\pi$
$54$	−9.68963	+	10.0092i	−1.31859	+	1.36208i
$55$	−7.25318	−	5.23492i	−0.978019	−	0.705876i
$56$			40.4630i			5.40710i
$57$	−0.255136	−	4.41174i	−0.0337936	−	0.584350i
$58$	−6.88777	−	5.00426i	−0.904409	−	0.657092i
$59$	−3.97615	−	5.47270i	−0.517650	−	0.712484i	0.467536	−	0.883974i	$-0.345142\pi$
$59$	−3.97615	−	5.47270i	−0.517650	−	0.712484i	−0.985186	+	0.171490i	$0.945142\pi$
$60$	−13.0890	+	20.3959i	−1.68978	+	2.63310i
$61$	−0.891593	−	0.289696i	−0.114157	−	0.0370918i	0.251382	−	0.967888i	$-0.419115\pi$
$61$	−0.891593	−	0.289696i	−0.114157	−	0.0370918i	−0.365538	+	0.930796i	$0.619115\pi$
$62$	−2.94351	+	2.13859i	−0.373826	+	0.271601i
$63$	12.9118	−	5.91680i	1.62673	−	0.745447i
$64$	5.93911	+	18.2787i	0.742389	+	2.28484i
$65$	2.69702			0.334524
$66$	9.79442	+	11.8857i	1.20561	+	1.46303i
$67$	3.14422			0.384127			0.192064	−	0.981382i	$-0.438482\pi$
$67$	3.14422			0.384127			0.192064	+	0.981382i	$0.438482\pi$
$68$	3.23053	+	9.94255i	0.391759	+	1.20571i
$69$	−1.81292	−	2.21418i	−0.218249	−	0.266556i
$70$	27.6948	−	20.1214i	3.31016	−	2.40497i
$71$	−9.85531	−	3.20218i	−1.16961	−	0.380029i	−0.341113	−	0.940022i	$-0.610804\pi$
$71$	−9.85531	−	3.20218i	−1.16961	−	0.380029i	−0.828497	+	0.559993i	$0.810804\pi$
$72$	18.8679	−	17.3618i	2.22360	−	2.04611i
$73$	1.37666	+	1.89482i	0.161126	+	0.221771i	0.881945	−	0.471352i	$-0.156234\pi$
$73$	1.37666	+	1.89482i	0.161126	+	0.221771i	−0.720819	+	0.693124i	$0.756234\pi$
$74$	5.67472	+	4.12293i	0.659673	+	0.479280i
$75$	3.93196	−	0.227390i	0.454023	−	0.0262567i
$76$			13.2362i			1.51830i
$77$	−4.89916	−	14.9180i	−0.558311	−	1.70007i
$78$	−4.49187	−	1.17760i	−0.508604	−	0.133337i
$79$	−11.1922	+	3.63657i	−1.25922	+	0.409147i	−0.861218	−	0.508236i	$-0.830298\pi$
$79$	−11.1922	+	3.63657i	−1.25922	+	0.409147i	−0.398006	+	0.917383i	$0.630298\pi$
$80$	19.8767	−	27.3579i	2.22228	−	3.05871i
$81$	−8.29915	−	3.48197i	−0.922128	−	0.386885i
$82$	8.94737	−	27.5372i	0.988071	−	3.04097i
$83$	−3.00150	+	9.23768i	−0.329458	+	1.01397i	0.639930	+	0.768433i	$0.278963\pi$
$83$	−3.00150	+	9.23768i	−0.329458	+	1.01397i	−0.969388	+	0.245534i	$0.921037\pi$
$84$	−39.6323	+	15.4598i	−4.32424	+	1.68680i
$85$	3.19451	−	4.39686i	0.346493	−	0.476907i
$86$	21.6121	−	7.02220i	2.33049	−	0.757224i
$87$	1.39482	−	5.32044i	0.149540	−	0.570411i
$88$	−16.7338	−	22.8802i	−1.78383	−	2.43904i
$89$		−	11.5947i		−	1.22903i	−0.788904	−	0.614516i	$-0.789351\pi$
$89$		−	11.5947i		−	1.22903i	0.788904	−	0.614516i	$-0.210649\pi$
$90$	−21.2658	−	4.28037i	−2.24161	−	0.451191i
$91$	3.83012	+	2.78275i	0.401506	+	0.291711i
$92$	5.03814	+	6.93441i	0.525262	+	0.722962i
$93$	−1.97822	−	1.26952i	−0.205132	−	0.131643i
$94$	−3.17956	−	1.03310i	−0.327946	−	0.106556i
$95$	5.56694	−	4.04462i	0.571156	−	0.414969i
$96$	−22.1420	+	18.1293i	−2.25986	+	1.85032i
$97$	−0.520822	−	1.60293i	−0.0528815	−	0.162753i	0.921128	−	0.389260i	$-0.127269\pi$
$97$	−0.520822	−	1.60293i	−0.0528815	−	0.162753i	−0.974009	+	0.226507i	$0.927269\pi$
$98$	41.3241			4.17436
$99$	−4.85413	+	8.68547i	−0.487859	+	0.872923i
$100$	−11.7968			−1.17968
$101$	2.89139	+	8.89880i	0.287704	+	0.885463i	0.985575	+	0.169239i	$0.0541311\pi$
$101$	2.89139	+	8.89880i	0.287704	+	0.885463i	−0.697870	+	0.716224i	$0.745869\pi$
$102$	−7.24024	+	5.92813i	−0.716890	+	0.586973i
$103$	0.708869	−	0.515024i	0.0698469	−	0.0507468i	−0.552314	−	0.833636i	$-0.686255\pi$
$103$	0.708869	−	0.515024i	0.0698469	−	0.0507468i	0.622161	+	0.782889i	$0.286255\pi$
$104$	8.12848	+	2.64110i	0.797063	+	0.258982i
$105$	18.6126	+	11.9446i	1.81640	+	1.16567i
$106$	11.3756	+	15.6572i	1.10490	+	1.52076i
$107$	−8.83622	−	6.41989i	−0.854230	−	0.620634i	0.0720793	−	0.997399i	$-0.477037\pi$
$107$	−8.83622	−	6.41989i	−0.854230	−	0.620634i	−0.926309	+	0.376765i	$0.877037\pi$
$108$	24.2142	+	11.8470i	2.33002	+	1.13998i
$109$		−	7.99407i		−	0.765693i	−0.923812	−	0.382847i	$-0.874944\pi$
$109$		−	7.99407i		−	0.765693i	0.923812	−	0.382847i	$-0.125056\pi$
$110$	−7.33889	+	22.8312i	−0.699736	+	2.17687i
$111$	−1.14917	+	4.38342i	−0.109074	+	0.416056i
$112$	56.4551	−	18.3434i	5.33450	−	1.73328i
$113$	−8.92823	+	12.2887i	−0.839898	+	1.15602i	0.146102	+	0.989270i	$0.453327\pi$
$113$	−8.92823	+	12.2887i	−0.839898	+	1.15602i	−0.985999	+	0.166750i	$0.946673\pi$
$114$	−11.0377	+	4.30560i	−1.03378	+	0.403256i
$115$	1.37698	−	4.23791i	0.128404	−	0.395187i
$116$	−5.09089	+	15.6681i	−0.472677	+	1.45475i
$117$	−0.345830	−	2.98000i	−0.0319720	−	0.275501i
$118$	−10.6601	+	14.6724i	−0.981345	+	1.35071i
$119$	9.07325	−	2.94808i	0.831743	−	0.270250i
$120$	38.6201	+	10.1247i	3.52552	+	0.924259i
$121$	8.93974	+	6.40945i	0.812704	+	0.582677i
$122$			2.51340i			0.227552i
$123$	18.6745	−	1.07997i	1.68382	−	0.0973772i
$124$	5.69581	+	4.13825i	0.511499	+	0.371625i
$125$	−4.32158	−	5.94815i	−0.386534	−	0.532019i
$126$	−25.7838	−	28.0205i	−2.29701	−	2.49626i
$127$	−3.57402	−	1.16127i	−0.317143	−	0.103046i	0.146120	−	0.989267i	$-0.453321\pi$
$127$	−3.57402	−	1.16127i	−0.317143	−	0.103046i	−0.463263	+	0.886221i	$0.653321\pi$
$128$	14.9534	−	10.8642i	1.32170	−	0.960273i
$129$	9.30051	+	11.3590i	0.818864	+	1.00011i
$130$	−2.23443	−	6.87687i	−0.195973	−	0.603141i
$131$	−5.35433			−0.467810			−0.233905	−	0.972259i	$-0.575150\pi$
$131$	−5.35433			−0.467810			−0.233905	+	0.972259i	$0.575150\pi$
$132$	16.0169	−	25.1321i	1.39410	−	2.18747i
$133$	12.0790			1.04738
$134$	−2.60493	−	8.01714i	−0.225031	−	0.692575i
$135$	−2.41652	−	13.8042i	−0.207981	−	1.18808i
$136$	13.9336	−	10.1233i	1.19479	−	0.868067i
$137$	5.04399	+	1.63889i	0.430937	+	0.140020i	0.516450	−	0.856317i	$-0.327253\pi$
$137$	5.04399	+	1.63889i	0.430937	+	0.140020i	−0.0855135	+	0.996337i	$0.527253\pi$
$138$	−4.14375	+	6.45699i	−0.352740	+	0.549655i
$139$	7.28089	+	10.0213i	0.617557	+	0.849995i	0.997172	−	0.0751499i	$-0.0239435\pi$
$139$	7.28089	+	10.0213i	0.617557	+	0.849995i	−0.379615	+	0.925145i	$0.623944\pi$
$140$	−53.5904	−	38.9357i	−4.52922	−	3.29067i
$141$	−0.124697	−	2.15623i	−0.0105014	−	0.181587i
$142$			27.7821i			2.33142i
$143$	−3.31661	+	0.0104467i	−0.277349	+	0.000873595i
$144$	−32.7771	−	18.4542i	−2.73143	−	1.53785i
$145$	8.14537	−	2.64659i	0.676436	−	0.219788i
$146$	3.69087	−	5.08004i	0.305458	−	0.420427i
$147$	9.70199	+	24.8717i	0.800206	+	2.05139i
$148$	4.19430	−	12.9087i	0.344769	−	1.06109i
$149$	5.05975	−	15.5723i	0.414511	−	1.27573i	−0.498177	−	0.867075i	$-0.665997\pi$
$149$	5.05975	−	15.5723i	0.414511	−	1.27573i	0.912688	−	0.408657i	$-0.134003\pi$
$150$	−3.83735	−	9.83734i	−0.313319	−	0.803215i
$151$	−12.5103	+	17.2190i	−1.01808	+	1.40126i	−0.104533	+	0.994521i	$0.533335\pi$
$151$	−12.5103	+	17.2190i	−1.01808	+	1.40126i	−0.913544	+	0.406741i	$0.866665\pi$
$152$	20.7388	−	6.73845i	1.68214	−	0.546561i
$153$	−5.26782	−	2.96589i	−0.425878	−	0.239778i
$154$	−33.9792	+	24.8512i	−2.73812	+	2.00257i
$155$		−	3.66009i		−	0.293985i
$156$	0.518786	+	8.97069i	0.0415361	+	0.718230i
$157$	−3.17978	−	2.31025i	−0.253774	−	0.184378i	0.453624	−	0.891193i	$-0.350131\pi$
$157$	−3.17978	−	2.31025i	−0.253774	−	0.184378i	−0.707398	+	0.706816i	$0.750131\pi$
$158$	18.5451	+	25.5251i	1.47537	+	2.03067i
$159$	−6.75285	+	10.5226i	−0.535536	+	0.834496i
$160$	−42.3795	−	13.7699i	−3.35039	−	1.08861i
$161$	6.32811	−	4.59764i	0.498725	−	0.362345i
$162$	−2.00264	+	24.0460i	−0.157342	+	1.88923i
$163$	6.24171	+	19.2100i	0.488889	+	1.50464i	0.826269	+	0.563276i	$0.190459\pi$
$163$	6.24171	+	19.2100i	0.488889	+	1.50464i	−0.337380	+	0.941368i	$0.609541\pi$
$164$	−56.0277			−4.37503
$165$	−15.4645	+	0.943209i	−1.20391	+	0.0734287i
$166$	26.0410			2.02117
$167$	−0.216874	−	0.667470i	−0.0167822	−	0.0516504i	0.942315	−	0.334728i	$-0.108645\pi$
$167$	−0.216874	−	0.667470i	−0.0167822	−	0.0516504i	−0.959097	+	0.283078i	$0.908645\pi$
$168$	44.3992	+	54.2262i	3.42547	+	4.18365i
$169$	0.809017	−	0.587785i	0.0622321	−	0.0452143i
$170$	−13.8577	−	4.50265i	−1.06284	−	0.345337i
$171$	−5.18282	−	5.63241i	−0.396340	−	0.430721i
$172$	−25.8464	−	35.5745i	−1.97077	−	2.71253i
$173$	−18.6398	−	13.5426i	−1.41715	−	1.02962i	−0.992233	−	0.124393i	$-0.960302\pi$
$173$	−18.6398	−	13.5426i	−1.41715	−	1.02962i	−0.424921	−	0.905230i	$-0.639698\pi$
$174$	−14.7217	+	0.851371i	−1.11605	+	0.0645423i
$175$			10.7654i			0.813785i
$176$	−24.3370	+	33.7199i	−1.83447	+	2.54173i
$177$	−11.3337	−	2.97126i	−0.851891	−	0.223334i
$178$	−29.5641	+	9.60597i	−2.21593	+	0.719998i
$179$	−6.05148	+	8.32914i	−0.452309	+	0.622549i	−0.972892	−	0.231262i	$-0.925715\pi$
$179$	−6.05148	+	8.32914i	−0.452309	+	0.622549i	0.520583	+	0.853811i	$0.325715\pi$
$180$	4.83880	+	41.6956i	0.360663	+	3.10781i
$181$	6.43840	−	19.8153i	0.478562	−	1.47286i	−0.362531	−	0.931972i	$-0.618087\pi$
$181$	6.43840	−	19.8153i	0.478562	−	1.47286i	0.841093	−	0.540891i	$-0.181913\pi$
$182$	3.92228	−	12.0715i	0.290738	−	0.894801i
$183$	−1.51274	+	0.590090i	−0.111825	+	0.0436207i
$184$	8.30010	−	11.4241i	0.611891	−	0.842196i
$185$	−6.71084	+	2.18048i	−0.493391	+	0.160312i
$186$	−1.59810	+	6.09586i	−0.117179	+	0.446970i
$187$	−3.91135	+	5.41933i	−0.286027	+	0.396301i
$188$			6.46919i			0.471814i
$189$	10.8112	−	22.0971i	0.786401	−	1.60733i
$190$	−14.9251	−	10.8437i	−1.08278	−	0.786685i
$191$	−1.18004	−	1.62419i	−0.0853848	−	0.117522i	0.764188	−	0.644994i	$-0.223140\pi$
$191$	−1.18004	−	1.62419i	−0.0853848	−	0.117522i	−0.849573	+	0.527472i	$0.823140\pi$
$192$	28.0160	+	17.9792i	2.02188	+	1.29754i
$193$	7.86391	+	2.55514i	0.566057	+	0.183923i	0.578045	−	0.816005i	$-0.303816\pi$
$193$	7.86391	+	2.55514i	0.566057	+	0.183923i	−0.0119879	+	0.999928i	$0.503816\pi$
$194$	−3.65566	+	2.65599i	−0.262461	+	0.190689i
$195$	3.61439	−	2.95938i	0.258832	−	0.211925i
$196$	−24.7101	−	76.0500i	−1.76501	−	5.43214i
$197$	−1.99374			−0.142048			−0.0710239	−	0.997475i	$-0.522627\pi$
$197$	−1.99374			−0.142048			−0.0710239	+	0.997475i	$0.522627\pi$
$198$	26.1678	+	5.18134i	1.85967	+	0.368222i
$199$	0.353143			0.0250337			0.0125168	−	0.999922i	$-0.496016\pi$
$199$	0.353143			0.0250337			0.0125168	+	0.999922i	$0.496016\pi$
$200$	6.00563	+	18.4834i	0.424662	+	1.30698i
$201$	4.21370	−	3.45008i	0.297211	−	0.243350i
$202$	20.2947	−	14.7450i	1.42793	−	1.03745i
$203$	14.2982	+	4.64578i	1.00354	+	0.326070i
$204$	15.2391	+	9.77965i	1.06695	+	0.684713i
$205$	17.1204	+	23.5643i	1.19574	+	1.64580i
$206$	−1.90049	−	1.38079i	−0.132414	−	0.0962042i
$207$	−4.85913	−	0.978044i	−0.337733	−	0.0679788i
$208$		−	12.5384i		−	0.869380i
$209$	−6.83017	+	4.99535i	−0.472453	+	0.345536i
$210$	15.0362	−	57.3544i	1.03759	−	3.95783i
$211$	−12.5108	+	4.06499i	−0.861277	+	0.279846i	−0.706162	−	0.708051i	$-0.749575\pi$
$211$	−12.5108	+	4.06499i	−0.861277	+	0.279846i	−0.155115	+	0.987896i	$0.549575\pi$
$212$	22.0122	−	30.2972i	1.51181	−	2.08082i
$213$	−16.7212	+	6.52262i	−1.14572	+	0.446922i
$214$	−9.04882	+	27.8494i	−0.618564	+	1.90375i
$215$	−7.06410	+	21.7411i	−0.481768	+	1.48273i
$216$	6.23493	−	43.9706i	0.424234	−	2.99182i
$217$	3.77643	−	5.19781i	0.256361	−	0.352850i
$218$	−20.3833	+	6.62294i	−1.38053	+	0.448562i
$219$	3.92406	+	1.02874i	0.265164	+	0.0695159i
$220$	46.4054	−	0.146168i	3.12865	−	0.00985464i
$221$		−	2.01512i		−	0.135552i
$222$	12.1289	−	0.701430i	0.814041	−	0.0470769i
$223$	−8.13660	−	5.91158i	−0.544867	−	0.395869i	0.281022	−	0.959701i	$-0.409326\pi$
$223$	−8.13660	−	5.91158i	−0.544867	−	0.395869i	−0.825889	+	0.563832i	$0.809326\pi$
$224$	−45.9768	−	63.2817i	−3.07196	−	4.22819i
$225$	5.01988	−	4.61918i	0.334658	−	0.307945i
$226$	38.7306	+	12.5843i	2.57632	+	0.837097i
$227$	7.03088	−	5.10823i	0.466656	−	0.339045i	−0.329481	−	0.944162i	$-0.606874\pi$
$227$	7.03088	−	5.10823i	0.466656	−	0.339045i	0.796137	+	0.605117i	$0.206874\pi$
$228$	14.5238	+	17.7385i	0.961864	+	1.17476i
$229$	−3.07694	−	9.46984i	−0.203330	−	0.625785i	−0.999778	−	0.0210779i	$-0.993290\pi$
$229$	−3.07694	−	9.46984i	−0.203330	−	0.625785i	0.796448	−	0.604707i	$-0.206710\pi$
$230$	−11.9466			−0.787738
$231$	−22.9348	−	14.6165i	−1.50900	−	0.961698i
$232$	27.1409			1.78189
$233$	4.23102	+	13.0217i	0.277184	+	0.853083i	0.988633	+	0.150346i	$0.0480389\pi$
$233$	4.23102	+	13.0217i	0.277184	+	0.853083i	−0.711450	+	0.702737i	$0.751961\pi$
$234$	−7.31190	+	3.35068i	−0.477994	+	0.219041i
$235$	2.72083	−	1.97680i	0.177487	−	0.128952i
$236$	33.3765	+	10.8447i	2.17262	+	0.705928i
$237$	−11.0089	+	17.1545i	−0.715102	+	1.11430i
$238$	−15.0340	−	20.6926i	−0.974512	−	1.34130i
$239$	−2.27647	−	1.65395i	−0.147253	−	0.106985i	0.511720	−	0.859152i	$-0.329009\pi$
$239$	−2.27647	−	1.65395i	−0.147253	−	0.106985i	−0.658972	+	0.752167i	$0.729009\pi$
$240$	−3.38160	−	58.4737i	−0.218282	−	3.77446i
$241$		−	26.3546i		−	1.69765i	−0.528675	−	0.848824i	$-0.677311\pi$
$241$		−	26.3546i		−	1.69765i	0.528675	−	0.848824i	$-0.322689\pi$
$242$	8.93643	−	28.1047i	0.574455	−	1.80664i
$243$	−14.9427	+	4.44014i	−0.958577	+	0.284835i
$244$	4.62548	−	1.50291i	0.296116	−	0.0962139i
$245$	−24.4346	+	33.6313i	−1.56107	+	2.14863i
$246$	−18.2251	−	46.7215i	−1.16199	−	2.97885i
$247$	0.788419	−	2.42650i	0.0501659	−	0.154395i
$248$	3.58420	−	11.0310i	0.227597	−	0.700472i
$249$	6.11385	+	15.6733i	0.387449	+	0.993254i
$250$	−11.5863	+	15.9471i	−0.732780	+	1.00858i
$251$	−16.1648	+	5.25226i	−1.02031	+	0.331520i	−0.770954	−	0.636891i	$-0.780220\pi$
$251$	−16.1648	+	5.25226i	−1.02031	+	0.331520i	−0.249359	+	0.968411i	$0.580220\pi$
$252$	−36.1493	+	64.2059i	−2.27719	+	4.04459i
$253$	−1.67690	+	5.21682i	−0.105426	+	0.327979i
$254$			10.0751i			0.632171i
$255$	−0.543479	−	9.39768i	−0.0340340	−	0.588506i
$256$	−8.99270	−	6.53358i	−0.562044	−	0.408349i
$257$	11.2698	+	15.5116i	0.702992	+	0.967586i	0.999920	+	0.0126857i	$0.00403809\pi$
$257$	11.2698	+	15.5116i	0.702992	+	0.967586i	−0.296927	+	0.954900i	$0.595962\pi$
$258$	21.2580	−	33.1252i	1.32347	−	2.06229i
$259$	−11.7801	−	3.82758i	−0.731978	−	0.237834i
$260$	−11.3196	+	8.22419i	−0.702013	+	0.510042i
$261$	−3.96874	−	8.66065i	−0.245659	−	0.536081i
$262$	4.43596	+	13.6525i	0.274055	+	0.843454i
$263$	9.17853			0.565972			0.282986	−	0.959124i	$-0.408675\pi$
$263$	9.17853			0.565972			0.282986	+	0.959124i	$0.408675\pi$
$264$	−47.5316	−	12.3011i	−2.92537	−	0.757082i
$265$	−19.4688			−1.19596
$266$	−10.0072	−	30.7990i	−0.613581	−	1.88841i
$267$	−12.7226	−	15.5385i	−0.778608	−	0.950941i
$268$	−13.1965	+	9.58785i	−0.806107	+	0.585671i
$269$	−11.2413	−	3.65252i	−0.685393	−	0.222698i	−0.0544382	−	0.998517i	$-0.517337\pi$
$269$	−11.2413	−	3.65252i	−0.685393	−	0.222698i	−0.630955	+	0.775819i	$0.717337\pi$
$270$	−33.1960	+	17.5982i	−2.02024	+	1.07099i
$271$	15.8932	+	21.8751i	0.965443	+	1.32882i	0.944316	+	0.329041i	$0.106725\pi$
$271$	15.8932	+	21.8751i	0.965443	+	1.32882i	0.0211268	+	0.999777i	$0.493275\pi$
$272$	−20.4409	−	14.8512i	−1.23941	−	0.900485i
$273$	8.18636	−	0.473427i	0.495461	−	0.0286531i
$274$		−	14.2190i		−	0.858999i
$275$	−4.45210	−	6.08738i	−0.268472	−	0.367083i
$276$	14.3608	+	3.76486i	0.864418	+	0.226618i
$277$	27.6904	−	8.99716i	1.66375	−	0.540587i	0.682101	−	0.731258i	$-0.261066\pi$
$277$	27.6904	−	8.99716i	1.66375	−	0.540587i	0.981654	+	0.190671i	$0.0610664\pi$
$278$	19.5202	−	26.8673i	1.17075	−	1.61139i
$279$	−4.04412	+	0.469322i	−0.242115	+	0.0280975i
$280$	−33.7229	+	103.788i	−2.01533	+	6.20254i
$281$	−2.26750	+	6.97866i	−0.135268	+	0.416312i	−0.995632	−	0.0933689i	$-0.970236\pi$
$281$	−2.26750	+	6.97866i	−0.135268	+	0.416312i	0.860364	+	0.509681i	$0.170236\pi$
$282$	−5.39466	+	2.10435i	−0.321247	+	0.125312i
$283$	11.8845	−	16.3577i	0.706463	−	0.972362i	−0.293403	−	0.955989i	$-0.594788\pi$
$283$	11.8845	−	16.3577i	0.706463	−	0.972362i	0.999866	−	0.0163737i	$-0.00521214\pi$
$284$	51.1282	−	16.6126i	3.03390	−	0.985774i
$285$	3.02243	−	11.5288i	0.179033	−	0.682909i
$286$	2.77439	+	8.44805i	0.164053	+	0.499544i
$287$			51.1290i			3.01805i
$288$	−9.78053	+	48.5917i	−0.576323	+	2.86330i
$289$	10.4681	+	7.60552i	0.615771	+	0.447384i
$290$	−13.4966	−	18.5765i	−0.792547	−	1.09085i
$291$	−2.45683	−	1.57666i	−0.144022	−	0.0924257i
$292$	−11.5560	−	3.75476i	−0.676261	−	0.219731i
$293$	−3.46625	+	2.51838i	−0.202501	+	0.147125i	−0.684414	−	0.729093i	$-0.739942\pi$
$293$	−3.46625	+	2.51838i	−0.202501	+	0.147125i	0.481914	+	0.876219i	$0.339942\pi$
$294$	55.3802	−	45.3440i	3.22984	−	2.64451i
$295$	−5.63780	−	17.3514i	−0.328246	−	1.01024i
$296$	−22.3609			−1.29970
$297$	3.02513	+	16.9661i	0.175536	+	0.984473i
$298$	−43.8982			−2.54296
$299$	−0.510556	−	1.57133i	−0.0295262	−	0.0908724i
$300$	−15.8094	+	12.9443i	−0.912755	+	0.747342i
$301$	−32.4641	+	23.5866i	−1.87120	+	1.35951i
$302$	54.2697	+	17.6333i	3.12287	+	1.01468i
$303$	13.6393	+	8.75300i	0.783559	+	0.502847i
$304$	−18.8033	−	25.8806i	−1.07844	−	1.48435i
$305$	−2.04551	−	1.48615i	−0.117126	−	0.0850967i
$306$	−3.19815	+	15.8891i	−0.182826	+	0.908319i
$307$		−	28.8866i		−	1.64865i	−0.566120	−	0.824323i	$-0.691556\pi$
$307$		−	28.8866i		−	1.64865i	0.566120	−	0.824323i	$-0.308444\pi$
$308$	66.0526	+	47.6729i	3.76370	+	2.71642i
$309$	0.384862	−	1.46803i	0.0218941	−	0.0835134i
$310$	−9.33250	+	3.03231i	−0.530051	+	0.172224i
$311$	6.61481	−	9.10451i	0.375092	−	0.516269i	−0.579184	−	0.815197i	$-0.696629\pi$
$311$	6.61481	−	9.10451i	0.375092	−	0.516269i	0.954276	+	0.298927i	$0.0966288\pi$
$312$	13.7914	−	5.37974i	0.780782	−	0.304568i
$313$	7.17406	−	22.0795i	0.405502	−	1.24801i	−0.514974	−	0.857206i	$-0.672198\pi$
$313$	7.17406	−	22.0795i	0.405502	−	1.24801i	0.920475	−	0.390800i	$-0.127802\pi$
$314$	−3.25628	+	10.0218i	−0.183763	+	0.565564i
$315$	38.0501	−	4.41573i	2.14388	−	0.248798i
$316$	35.8855	−	49.3922i	2.01872	−	2.77853i
$317$	27.5037	−	8.93649i	1.54476	−	0.501924i	0.592076	−	0.805882i	$-0.298308\pi$
$317$	27.5037	−	8.93649i	1.54476	−	0.501924i	0.952685	+	0.303958i	$0.0983083\pi$
$318$	32.4252	+	8.50066i	1.81831	+	0.476693i
$319$	−10.0064	+	3.28615i	−0.560249	+	0.183989i
$320$			51.8350i			2.89766i
$321$	−18.8862	+	1.09221i	−1.05412	+	0.0609613i
$322$	−16.9658	−	12.3264i	−0.945468	−	0.686923i
$323$	−3.02200	−	4.15943i	−0.168149	−	0.231437i
$324$	45.4500	−	10.6930i	2.52500	−	0.594056i
$325$	2.16262	+	0.702677i	0.119960	+	0.0389775i
$326$	43.8106	−	31.8303i	2.42645	−	1.76292i
$327$	−8.77171	−	10.7132i	−0.485077	−	0.592441i
$328$	28.5232	+	87.7853i	1.57493	+	4.84713i
$329$	5.90357			0.325474
$330$	15.2170	+	38.6499i	0.837669	+	2.12761i
$331$	−24.1402			−1.32687			−0.663433	−	0.748235i	$-0.730901\pi$
$331$	−24.1402			−1.32687			−0.663433	+	0.748235i	$0.730901\pi$
$332$	−15.5715	−	47.9240i	−0.854594	−	2.63017i
$333$	3.26978	+	7.13537i	0.179183	+	0.391016i
$334$	−1.52224	+	1.10597i	−0.0832933	+	0.0605162i
$335$	8.06497	+	2.62047i	0.440636	+	0.143171i
$336$	55.5301	−	86.5296i	3.02942	−	4.72058i
$337$	3.43955	+	4.73413i	0.187364	+	0.257885i	0.892357	−	0.451329i	$-0.149050\pi$
$337$	3.43955	+	4.73413i	0.187364	+	0.257885i	−0.704993	+	0.709214i	$0.749050\pi$
$338$	−2.16899	−	1.57587i	−0.117978	−	0.0857158i
$339$	1.51895	+	26.2653i	0.0824982	+	1.42654i
$340$			28.1952i			1.52910i
$341$	0.0141770	+	4.50092i	0.000767729	+	0.243739i
$342$	−10.0677	+	17.8815i	−0.544397	+	0.966923i
$343$	−37.8827	+	12.3088i	−2.04547	+	0.664614i
$344$	−42.5806	+	58.6072i	−2.29579	+	3.15989i
$345$	−2.80481	−	7.19033i	−0.151006	−	0.387114i
$346$	−19.0882	+	58.7475i	−1.02619	+	3.15829i
$347$	0.172266	−	0.530179i	0.00924771	−	0.0284615i	−0.946326	−	0.323213i	$-0.895237\pi$
$347$	0.172266	−	0.530179i	0.00924771	−	0.0284615i	0.955574	+	0.294752i	$0.0952369\pi$
$348$	10.3698	+	26.5837i	0.555878	+	1.42503i
$349$	2.65111	−	3.64894i	0.141911	−	0.195323i	−0.732145	−	0.681148i	$-0.761481\pi$
$349$	2.65111	−	3.64894i	0.141911	−	0.195323i	0.874056	+	0.485825i	$0.161481\pi$
$350$	27.4496	−	8.91890i	1.46724	−	0.476735i
$351$	−3.73335	−	3.61415i	−0.199271	−	0.192909i
$352$	52.1687	+	16.7691i	2.78060	+	0.893799i
$353$		−	19.1497i		−	1.01924i	−0.860400	−	0.509619i	$-0.829787\pi$
$353$		−	19.1497i		−	1.01924i	0.860400	−	0.509619i	$-0.170213\pi$
$354$	1.81360	+	31.3603i	0.0963918	+	1.66678i
$355$	−22.6103	−	16.4273i	−1.20003	−	0.871871i
$356$	35.3563	+	48.6638i	1.87388	+	2.57918i
$357$	8.92459	−	13.9067i	0.472339	−	0.736021i
$358$	26.2512	+	8.52954i	1.38742	+	0.450800i
$359$	16.8579	−	12.2480i	0.889725	−	0.646423i	−0.0460813	−	0.998938i	$-0.514673\pi$
$359$	16.8579	−	12.2480i	0.889725	−	0.646423i	0.935806	+	0.352515i	$0.114673\pi$
$360$	62.8662	−	28.8084i	3.31334	−	1.51834i
$361$	3.85977	+	11.8791i	0.203146	+	0.625218i
$362$	−55.8593			−2.93590
$363$	19.0135	−	1.21979i	0.997948	−	0.0640226i
$364$	−24.5610			−1.28734
$365$	1.95198	+	6.00758i	0.102171	+	0.314451i
$366$	2.75789	+	3.36831i	0.144157	+	0.176064i
$367$	−1.14880	+	0.834655i	−0.0599671	+	0.0435686i	−0.617365	−	0.786677i	$-0.711800\pi$
$367$	−1.14880	+	0.834655i	−0.0599671	+	0.0435686i	0.557398	+	0.830245i	$0.311800\pi$
$368$	−19.7019	−	6.40155i	−1.02703	−	0.333704i
$369$	23.8414	−	21.9384i	1.24113	−	1.14207i
$370$	11.1196	+	15.3048i	0.578081	+	0.795660i
$371$	−27.6483	−	20.0876i	−1.43543	−	1.04290i
$372$	12.1740	−	0.704036i	0.631192	−	0.0365026i
$373$			29.6715i			1.53633i	0.640251	+	0.768166i	$0.278830\pi$
$373$			29.6715i			1.53633i	−0.640251	+	0.768166i	$0.721170\pi$
$374$	17.0587	+	5.48337i	0.882085	+	0.283538i
$375$	−12.3183	−	3.22940i	−0.636115	−	0.166765i
$376$	10.1361	−	3.29340i	0.522727	−	0.169844i
$377$	1.86655	−	2.56908i	0.0961322	−	0.132315i
$378$	−65.3003	−	9.25944i	−3.35868	−	0.476254i
$379$	5.93274	−	18.2591i	0.304744	−	0.937907i	−0.675028	−	0.737792i	$-0.735869\pi$
$379$	5.93274	−	18.2591i	0.304744	−	0.937907i	0.979772	−	0.200115i	$-0.0641315\pi$
$380$	−11.0314	+	33.9512i	−0.565900	+	1.74166i
$381$	−6.06394	+	2.36542i	−0.310665	+	0.121184i
$382$	−3.16372	+	4.35448i	−0.161870	+	0.222795i
$383$	−0.0965525	+	0.0313718i	−0.00493360	+	0.00160303i	−0.311483	−	0.950252i	$-0.600826\pi$
$383$	−0.0965525	+	0.0313718i	−0.00493360	+	0.00160303i	0.306549	+	0.951855i	$0.400826\pi$
$384$	8.11854	−	30.9676i	0.414298	−	1.58031i
$385$	−0.133388	−	42.3481i	−0.00679809	−	2.15826i
$386$		−	22.1683i		−	1.12834i
$387$	24.9280	+	5.01750i	1.26716	+	0.255054i
$388$	7.07384	+	5.13945i	0.359120	+	0.260916i
$389$	2.86882	+	3.94859i	0.145455	+	0.200202i	0.875528	−	0.483168i	$-0.160514\pi$
$389$	2.86882	+	3.94859i	0.145455	+	0.200202i	−0.730073	+	0.683369i	$0.760514\pi$
$390$	−10.5403	−	6.76420i	−0.533728	−	0.342519i
$391$	−3.16642	−	1.02883i	−0.160133	−	0.0520303i
$392$	−106.577	+	77.4327i	−5.38295	+	3.91094i
$393$	−7.17556	+	5.87518i	−0.361959	+	0.296364i
$394$	1.65177	+	5.08364i	0.0832152	+	0.256110i
$395$	−31.7391			−1.59697
$396$	−6.11192	−	51.2557i	−0.307136	−	2.57569i
$397$	5.16938			0.259444			0.129722	−	0.991550i	$-0.458592\pi$
$397$	5.16938			0.259444			0.129722	+	0.991550i	$0.458592\pi$
$398$	−0.292573	−	0.900447i	−0.0146654	−	0.0451353i
$399$	16.1875	−	13.2540i	0.810391	−	0.663529i
$400$	23.0660	−	16.7584i	1.15330	−	0.837921i
$401$	0.397172	+	0.129049i	0.0198338	+	0.00644440i	0.318917	−	0.947783i	$-0.396681\pi$
$401$	0.397172	+	0.129049i	0.0198338	+	0.00644440i	−0.299083	+	0.954227i	$0.596681\pi$
$402$	−12.2880	−	7.88578i	−0.612869	−	0.393307i
$403$	−0.797675	−	1.09791i	−0.0397350	−	0.0546906i
$404$	−39.2711	−	28.5321i	−1.95381	−	1.41953i
$405$	−18.3855	−	15.8480i	−0.913583	−	0.787494i
$406$		−	40.3066i		−	2.00038i
$407$	8.24408	−	2.70740i	0.408644	−	0.134201i
$408$	7.56487	−	28.8557i	0.374517	−	1.42857i
$409$	−1.40169	+	0.455435i	−0.0693089	+	0.0225198i	−0.343466	−	0.939165i	$-0.611601\pi$
$409$	−1.40169	+	0.455435i	−0.0693089	+	0.0225198i	0.274157	+	0.961685i	$0.411601\pi$
$410$	45.9003	−	63.1763i	2.26685	−	3.12006i
$411$	8.55798	−	3.33830i	0.422134	−	0.164666i
$412$	−1.40469	+	4.32320i	−0.0692042	+	0.212989i
$413$	9.89649	−	30.4583i	0.486975	−	1.49875i
$414$	1.53188	+	13.2001i	0.0752878	+	0.648751i
$415$	−15.3978	+	21.1933i	−0.755849	+	1.04034i
$416$	−15.7134	+	5.10561i	−0.770415	+	0.250323i
$417$	20.7536	+	5.44080i	1.01631	+	0.266437i
$418$	18.3958	+	13.2770i	0.899770	+	0.649401i
$419$			21.5222i			1.05143i	0.850662	+	0.525713i	$0.176202\pi$
$419$			21.5222i			1.05143i	−0.850662	+	0.525713i	$0.823798\pi$
$420$	−114.542	+	6.62410i	−5.58908	+	0.323223i
$421$	19.8298	+	14.4072i	0.966446	+	0.702164i	0.954639	−	0.297766i	$-0.0962415\pi$
$421$	19.8298	+	14.4072i	0.966446	+	0.702164i	0.0118073	+	0.999930i	$0.496242\pi$
$422$	20.7299	+	28.5322i	1.00911	+	1.38893i
$423$	−2.53309	−	2.75283i	−0.123163	−	0.133847i
$424$	−58.6765	−	19.0652i	−2.84958	−	0.925886i
$425$	3.70708	−	2.69335i	0.179820	−	0.130647i
$426$	30.4846	+	37.2319i	1.47698	+	1.80389i
$427$	−1.37151	−	4.22106i	−0.0663719	−	0.204272i
$428$	56.6630			2.73891
$429$	−4.43327	+	3.65324i	−0.214040	+	0.176380i
$430$	61.2879			2.95557
$431$	−3.79465	−	11.6787i	−0.182782	−	0.562544i	0.817121	−	0.576466i	$-0.195569\pi$
$431$	−3.79465	−	11.6787i	−0.182782	−	0.562544i	−0.999903	+	0.0139213i	$0.995569\pi$
$432$	−64.1754	+	11.2343i	−3.08764	+	0.540512i
$433$	−6.26385	+	4.55096i	−0.301022	+	0.218705i	−0.728034	−	0.685541i	$-0.759566\pi$
$433$	−6.26385	+	4.55096i	−0.301022	+	0.218705i	0.427013	+	0.904246i	$0.359566\pi$
$434$	−16.3821	−	5.32287i	−0.786366	−	0.255506i
$435$	8.01192	−	12.4845i	0.384142	−	0.598588i
$436$	24.3768	+	33.5518i	1.16744	+	1.60684i
$437$	−3.41031	−	2.47773i	−0.163137	−	0.118526i
$438$	−0.627924	−	10.8579i	−0.0300034	−	0.518810i
$439$		−	38.8790i		−	1.85559i	−0.373089	−	0.927796i	$-0.621701\pi$
$439$		−	38.8790i		−	1.85559i	0.373089	−	0.927796i	$-0.378299\pi$
$440$	−23.8536	−	72.6345i	−1.13717	−	3.46271i
$441$	40.2932	+	22.6859i	1.91873	+	1.08028i
$442$	−5.13816	+	1.66949i	−0.244398	+	0.0794096i
$443$	−5.29820	+	7.29235i	−0.251725	+	0.346470i	−0.916115	−	0.400917i	$-0.868692\pi$
$443$	−5.29820	+	7.29235i	−0.251725	+	0.346470i	0.664389	+	0.747387i	$0.268692\pi$
$444$	−8.54348	−	21.9018i	−0.405456	−	1.03941i
$445$	9.66328	−	29.7405i	0.458083	−	1.40984i
$446$	−8.33236	+	25.6444i	−0.394549	+	1.21430i
$447$	−10.3063	−	26.4211i	−0.487473	−	1.24967i
$448$	−53.4826	+	73.6126i	−2.52682	+	3.47787i
$449$	26.8900	−	8.73708i	1.26902	−	0.412328i	0.404317	−	0.914619i	$-0.367509\pi$
$449$	26.8900	−	8.73708i	1.26902	−	0.412328i	0.864699	+	0.502291i	$0.167509\pi$
$450$	−15.9369	−	8.97280i	−0.751272	−	0.422982i
$451$	−21.1448	−	28.9114i	−0.995671	−	1.36138i
$452$		−	78.8020i		−	3.70653i
$453$	2.12837	+	36.8032i	0.0999997	+	1.72917i
$454$	−18.8500	−	13.6953i	−0.884672	−	0.642752i
$455$	7.50513	+	10.3299i	0.351846	+	0.484274i
$456$	20.3990	−	31.7867i	0.955272	−	1.48855i
$457$	−8.11283	−	2.63602i	−0.379502	−	0.123308i	0.113053	−	0.993589i	$-0.463937\pi$
$457$	−8.11283	−	2.63602i	−0.379502	−	0.123308i	−0.492555	+	0.870281i	$0.663937\pi$
$458$	−21.5971	+	15.6912i	−1.00916	+	0.733201i
$459$	−10.3140	+	1.80554i	−0.481418	+	0.0842753i
$460$	7.14361	+	21.9858i	0.333073	+	1.02509i
$461$	9.71386			0.452419			0.226210	−	0.974079i	$-0.427367\pi$
$461$	9.71386			0.452419			0.226210	+	0.974079i	$0.427367\pi$
$462$	−18.2683	+	70.5887i	−0.849917	+	3.28408i
$463$	33.8515			1.57321			0.786607	−	0.617453i	$-0.211836\pi$
$463$	33.8515			1.57321			0.786607	+	0.617453i	$0.211836\pi$
$464$	−12.3039	−	37.8676i	−0.571196	−	1.75796i
$465$	−4.01613	−	4.90504i	−0.186243	−	0.227466i
$466$	29.6976	−	21.5766i	1.37571	−	0.999515i
$467$	−23.0619	−	7.49326i	−1.06718	−	0.346747i	−0.277790	−	0.960642i	$-0.589602\pi$
$467$	−23.0619	−	7.49326i	−1.06718	−	0.346747i	−0.789388	+	0.613895i	$0.789602\pi$
$468$	10.5386	+	11.4528i	0.487146	+	0.529404i
$469$	8.74956	+	12.0427i	0.404017	+	0.556082i
$470$	−7.29460	−	5.29984i	−0.336475	−	0.244463i
$471$	−6.79634	+	0.393040i	−0.313159	+	0.0181103i
$472$		−	57.8158i		−	2.66119i
$473$	8.60273	−	26.7630i	0.395554	−	1.23057i
$474$	52.8612	+	13.8582i	2.42800	+	0.636530i
$475$	5.51765	−	1.79279i	0.253167	−	0.0822590i
$476$	−29.0915	+	40.0409i	−1.33340	+	1.83527i
$477$	2.49642	+	21.5115i	0.114303	+	0.984945i
$478$	−2.33124	+	7.17482i	−0.106629	+	0.328169i
$479$	−4.29847	+	13.2293i	−0.196402	+	0.604463i	0.803555	+	0.595230i	$0.202939\pi$
$479$	−4.29847	+	13.2293i	−0.196402	+	0.604463i	−0.999957	+	0.00923322i	$0.997061\pi$
$480$	−71.9039	+	28.0483i	−3.28195	+	1.28023i
$481$	−1.53782	+	2.11663i	−0.0701185	+	0.0965098i
$482$	−67.1991	+	21.8343i	−3.06083	+	0.994525i
$483$	3.43569	−	13.1052i	0.156329	−	0.596307i
$484$	−57.0656	+	0.359495i	−2.59389	+	0.0163407i
$485$		−	4.54560i		−	0.206405i
$486$	23.7013	+	34.4225i	1.07511	+	1.56143i
$487$	0.556028	+	0.403978i	0.0251960	+	0.0183060i	0.600312	−	0.799766i	$-0.295043\pi$
$487$	0.556028	+	0.403978i	0.0251960	+	0.0183060i	−0.575116	+	0.818072i	$0.695043\pi$
$488$	−4.70958	−	6.48218i	−0.213193	−	0.293434i
$489$	29.4435	+	18.8953i	1.33148	+	0.854474i
$490$	105.997	+	34.4405i	4.78845	+	1.55586i
$491$	−33.4018	+	24.2678i	−1.50740	+	1.09519i	−0.540086	+	0.841610i	$0.681608\pi$
$491$	−33.4018	+	24.2678i	−1.50740	+	1.09519i	−0.967314	+	0.253580i	$0.918392\pi$
$492$	−75.0851	+	61.4779i	−3.38510	+	2.77164i
$493$	−1.97744	−	6.08595i	−0.0890596	−	0.274097i
$494$	−6.84030			−0.307760
$495$	−19.6896	+	18.2328i	−0.884983	+	0.819505i
$496$	−17.0157			−0.764025
$497$	−15.1601	−	46.6579i	−0.680023	−	2.09289i
$498$	34.8986	−	28.5741i	1.56384	−	1.28044i
$499$	12.5467	−	9.11569i	0.561666	−	0.408074i	−0.270402	−	0.962747i	$-0.587157\pi$
$499$	12.5467	−	9.11569i	0.561666	−	0.408074i	0.832068	+	0.554673i	$0.187157\pi$
$500$	36.2761	+	11.7868i	1.62232	+	0.527123i
$501$	−1.02304	−	0.656534i	−0.0457061	−	0.0293318i
$502$	26.7845	+	36.8657i	1.19545	+	1.64540i
$503$	19.6475	+	14.2748i	0.876039	+	0.636480i	0.932201	−	0.361942i	$-0.117886\pi$
$503$	19.6475	+	14.2748i	0.876039	+	0.636480i	−0.0561613	+	0.998422i	$0.517886\pi$
$504$	119.002	+	23.9528i	5.30079	+	1.06694i
$505$			25.2353i			1.12296i
$506$	14.6912	−	0.0462743i	0.653102	−	0.00205714i
$507$	0.439235	−	1.67543i	0.0195071	−	0.0744085i
$508$	18.5416	−	6.02454i	0.822651	−	0.267296i
$509$	−5.88046	+	8.09375i	−0.260647	+	0.358749i	−0.919204	−	0.393781i	$-0.871167\pi$
$509$	−5.88046	+	8.09375i	−0.260647	+	0.358749i	0.658558	+	0.752530i	$0.271167\pi$
$510$	−23.5120	+	9.17157i	−1.04113	+	0.406124i
$511$	−3.42647	+	10.5456i	−0.151578	+	0.466509i
$512$	2.21428	−	6.81485i	0.0978582	−	0.301177i
$513$	−13.1260	−	1.86124i	−0.579529	−	0.0821759i
$514$	30.2147	−	41.5869i	1.33271	−	1.83432i
$515$	2.24749	−	0.730255i	0.0990364	−	0.0321789i
$516$	−73.6729	−	19.3143i	−3.24327	−	0.850263i
$517$	−3.33823	+	2.44147i	−0.146815	+	0.107376i
$518$			33.2080i			1.45907i
$519$	−39.8399	+	2.30399i	−1.74878	+	0.101134i
$520$	18.6485	+	13.5490i	0.817792	+	0.594161i
$521$	11.7443	+	16.1647i	0.514529	+	0.708188i	0.984675	−	0.174400i	$-0.0557987\pi$
$521$	11.7443	+	16.1647i	0.514529	+	0.708188i	−0.470146	+	0.882589i	$0.655799\pi$
$522$	−18.7949	+	17.2947i	−0.822632	+	0.756968i
$523$	24.9773	+	8.11563i	1.09218	+	0.354872i	0.799090	−	0.601212i	$-0.205315\pi$
$523$	24.9773	+	8.11563i	1.09218	+	0.354872i	0.293093	+	0.956084i	$0.405315\pi$
$524$	22.4726	−	16.3273i	0.981719	−	0.713261i
$525$	11.8126	+	14.4271i	0.515543	+	0.629651i
$526$	−7.60424	−	23.4034i	−0.331561	−	1.02044i
$527$	−2.73469			−0.119125
$528$	4.38496	+	71.8939i	0.190831	+	3.12878i
$529$	20.2703			0.881315
$530$	16.1295	+	49.6416i	0.700622	+	2.15629i
$531$	−18.4490	+	8.45426i	−0.800620	+	0.366884i
$532$	−50.6965	+	36.8331i	−2.19797	+	1.59692i
$533$	10.2711	+	3.33730i	0.444892	+	0.144554i
$534$	−29.0798	+	45.3134i	−1.25840	+	1.96090i
$535$	−17.3146	−	23.8315i	−0.748574	−	1.03032i
$536$	21.7407	+	15.7955i	0.939054	+	0.682263i
$537$	1.02953	+	17.8024i	0.0444276	+	0.768230i
$538$			31.6891i			1.36622i
$539$	29.9177	−	41.4522i	1.28865	−	1.78547i
$540$	52.2363	+	50.5686i	2.24789	+	2.17613i
$541$	−39.8069	+	12.9340i	−1.71143	+	0.556078i	−0.990571	−	0.137002i	$-0.956253\pi$
$541$	−39.8069	+	12.9340i	−1.71143	+	0.556078i	−0.720861	+	0.693080i	$0.756253\pi$
$542$	42.6100	−	58.6476i	1.83026	−	2.51913i
$543$	−13.1145	−	33.6201i	−0.562799	−	1.44278i
$544$	−10.2884	+	31.6645i	−0.441112	+	1.35760i
$545$	6.66246	−	20.5049i	0.285388	−	0.878335i
$546$	−7.98940	−	20.4814i	−0.341915	−	0.876523i
$547$	1.94968	−	2.68350i	0.0833623	−	0.114738i	−0.765299	−	0.643675i	$-0.777409\pi$
$547$	1.94968	−	2.68350i	0.0833623	−	0.114738i	0.848662	+	0.528936i	$0.177409\pi$
$548$	−26.1676	+	8.50238i	−1.11783	+	0.363204i
$549$	−1.37979	+	2.45070i	−0.0588882	+	0.104593i
$550$	−11.8331	+	16.3953i	−0.504567	+	0.699096i
$551$		−	8.10206i		−	0.345159i
$552$	−1.41209	−	24.4174i	−0.0601025	−	1.03927i
$553$	−45.0737	−	32.7479i	−1.91673	−	1.39258i
$554$	−45.8820	−	63.1511i	−1.94934	−	2.68303i
$555$	−6.60089	+	10.2858i	−0.280192	+	0.436608i
$556$	−61.1171	−	19.8581i	−2.59194	−	0.842173i
$557$	6.63023	−	4.81714i	0.280932	−	0.204109i	−0.438392	−	0.898784i	$-0.644452\pi$
$557$	6.63023	−	4.81714i	0.280932	−	0.204109i	0.719324	+	0.694675i	$0.244452\pi$
$558$	4.54715	+	9.92288i	0.192496	+	0.420069i
$559$	2.61923	+	8.06115i	0.110781	+	0.340950i
$560$	160.096			6.76529
$561$	0.704734	+	11.5545i	0.0297539	+	0.487832i
$562$	19.6728			0.829847
$563$	−1.08862	−	3.35043i	−0.0458799	−	0.141204i	0.925492	−	0.378766i	$-0.123652\pi$
$563$	−1.08862	−	3.35043i	−0.0458799	−	0.141204i	−0.971372	+	0.237562i	$0.923652\pi$
$564$	7.09849	+	8.66964i	0.298900	+	0.365058i
$565$	−33.1427	+	24.0796i	−1.39433	+	1.01304i
$566$	−51.5550	−	16.7512i	−2.16702	−	0.704107i
$567$	−9.75809	−	41.4762i	−0.409801	−	1.74184i
$568$	−52.0578	−	71.6514i	−2.18430	−	3.00643i
$569$	7.68520	+	5.58362i	0.322180	+	0.234078i	0.737105	−	0.675778i	$-0.236192\pi$
$569$	7.68520	+	5.58362i	0.322180	+	0.234078i	−0.414925	+	0.909856i	$0.636192\pi$
$570$	−31.9003	+	1.84483i	−1.33616	+	0.0772715i
$571$		−	4.76401i		−	0.199368i	−0.995019	−	0.0996838i	$-0.968217\pi$
$571$		−	4.76401i		−	0.199368i	0.995019	−	0.0996838i	$-0.0317831\pi$
$572$	13.8882	−	10.1574i	0.580696	−	0.424702i
$573$	−3.36361	−	0.881811i	−0.140517	−	0.0368382i
$574$	130.369	−	42.3595i	5.44150	−	1.76805i
$575$	2.20828	−	3.03943i	0.0920915	−	0.126753i
$576$	57.2737	−	6.64664i	2.38640	−	0.276943i
$577$	8.86569	−	27.2858i	0.369083	−	1.13592i	−0.578301	−	0.815823i	$-0.696284\pi$
$577$	8.86569	−	27.2858i	0.369083	−	1.13592i	0.947384	−	0.320098i	$-0.103716\pi$
$578$	10.7200	−	32.9927i	0.445892	−	1.37231i
$579$	13.3425	−	5.20464i	0.554494	−	0.216297i
$580$	−26.1164	+	35.9462i	−1.08443	+	1.49258i
$581$	−43.7339	+	14.2100i	−1.81439	+	0.589530i
$582$	−1.98475	+	7.57068i	−0.0822704	+	0.313815i
$583$	23.9414	−	0.0754107i	0.991551	−	0.00312319i
$584$			20.0176i			0.828335i
$585$	1.59654	−	7.93198i	0.0660090	−	0.327947i
$586$	9.29310	+	6.75183i	0.383894	+	0.278916i
$587$	13.1590	+	18.1118i	0.543128	+	0.747552i	0.989060	−	0.147515i	$-0.0471275\pi$
$587$	13.1590	+	18.1118i	0.543128	+	0.747552i	−0.445931	+	0.895067i	$0.647128\pi$
$588$	−116.563	−	74.8040i	−4.80698	−	3.08487i
$589$	−3.29297	−	1.06995i	−0.135685	−	0.0440866i
$590$	−39.5718	+	28.7506i	−1.62915	+	1.18364i
$591$	−2.67189	+	2.18768i	−0.109907	+	0.0899892i
$592$	10.1370	+	31.1985i	0.416629	+	1.28225i
$593$	6.83961			0.280869			0.140435	−	0.990090i	$-0.455150\pi$
$593$	6.83961			0.280869			0.140435	+	0.990090i	$0.455150\pi$
$594$	40.7540	−	21.7696i	1.67216	−	0.893218i
$595$	25.7300			1.05483
$596$	26.2494	+	80.7873i	1.07522	+	3.30918i
$597$	0.473263	−	0.387496i	0.0193694	−	0.0158592i
$598$	−3.58360	+	2.60364i	−0.146544	+	0.106471i
$599$	11.7563	+	3.81985i	0.480349	+	0.156075i	0.539176	−	0.842193i	$-0.318736\pi$
$599$	11.7563	+	3.81985i	0.480349	+	0.156075i	−0.0588266	+	0.998268i	$0.518736\pi$
$600$	28.3299	+	18.1806i	1.15656	+	0.742220i
$601$	−3.04222	−	4.18726i	−0.124095	−	0.170802i	0.742449	−	0.669902i	$-0.233664\pi$
$601$	−3.04222	−	4.18726i	−0.124095	−	0.170802i	−0.866544	+	0.499100i	$0.833664\pi$
$602$	87.0370	+	63.2361i	3.54736	+	2.57731i
$603$	1.86127	−	9.24719i	0.0757968	−	0.376575i
$604$		−	110.418i		−	4.49285i
$605$	17.5888	+	23.8909i	0.715086	+	0.971305i
$606$	11.0185	−	42.0293i	0.447596	−	1.70732i
$607$	−38.8772	+	12.6320i	−1.57798	+	0.512715i	−0.961534	−	0.274686i	$-0.911426\pi$
$607$	−38.8772	+	12.6320i	−1.57798	+	0.512715i	−0.616441	+	0.787401i	$0.711426\pi$
$608$	−24.7775	+	34.1034i	−1.00486	+	1.38307i
$609$	24.2594	−	9.46311i	0.983040	−	0.383465i
$610$	−2.09473	+	6.44690i	−0.0848129	+	0.261027i
$611$	0.385338	−	1.18595i	0.0155891	−	0.0479783i
$612$	31.1536	−	3.61539i	1.25931	−	0.146143i
$613$	−2.47720	+	3.40957i	−0.100053	+	0.137711i	−0.856108	−	0.516797i	$-0.827124\pi$
$613$	−2.47720	+	3.40957i	−0.100053	+	0.137711i	0.756055	+	0.654508i	$0.227124\pi$
$614$	−73.6552	+	23.9320i	−2.97248	+	0.965818i
$615$	48.8004	+	12.7936i	1.96782	+	0.515889i
$616$	41.0681	−	127.762i	1.65468	−	5.14770i
$617$			2.18020i			0.0877717i	0.999037	+	0.0438858i	$0.0139738\pi$
$617$			2.18020i			0.0877717i	−0.999037	+	0.0438858i	$0.986026\pi$
$618$	−4.06204	+	0.234913i	−0.163399	+	0.00944957i
$619$	13.6216	+	9.89670i	0.547500	+	0.397782i	0.826863	−	0.562404i	$-0.190123\pi$
$619$	13.6216	+	9.89670i	0.547500	+	0.397782i	−0.279363	+	0.960186i	$0.590123\pi$
$620$	11.1609	+	15.3617i	0.448234	+	0.616941i
$621$	−7.58512	+	4.02109i	−0.304380	+	0.161361i
$622$	−28.6950	−	9.32356i	−1.15056	−	0.373841i
$623$	44.4090	−	32.2650i	1.77921	−	1.29267i
$624$	−13.7581	−	16.8032i	−0.550764	−	0.672667i
$625$	−9.64099	−	29.6719i	−0.385639	−	1.18688i
$626$	−62.2419			−2.48769
$627$	−3.67212	+	14.1891i	−0.146650	+	0.566657i
$628$	20.3906			0.813673
$629$	1.62918	+	5.01411i	0.0649598	+	0.199926i
$630$	−42.7830	−	93.3619i	−1.70452	−	3.71963i
$631$	−31.2997	+	22.7405i	−1.24602	+	0.905286i	−0.997984	−	0.0634645i	$-0.979785\pi$
$631$	−31.2997	+	22.7405i	−1.24602	+	0.905286i	−0.248036	+	0.968751i	$0.579785\pi$
$632$	−95.6576	−	31.0810i	−3.80506	−	1.23634i
$633$	−12.3058	+	19.1755i	−0.489111	+	0.762156i
$634$	−45.5726	−	62.7253i	−1.80992	−	2.49114i
$635$	−8.19960	−	5.95736i	−0.325391	−	0.236411i
$636$	−3.74492	−	64.7561i	−0.148496	−	2.56775i
$637$			15.4135i			0.610707i
$638$	16.6691	+	22.7918i	0.659937	+	0.902335i
$639$	−15.2517	+	27.0890i	−0.603347	+	1.07163i
$640$	47.4101	−	15.4045i	1.87405	−	0.608916i
$641$	−23.1549	+	31.8700i	−0.914564	+	1.25879i	0.0510203	+	0.998698i	$0.483753\pi$
$641$	−23.1549	+	31.8700i	−0.914564	+	1.25879i	−0.965584	+	0.260091i	$0.916247\pi$
$642$	18.4318	+	47.2512i	0.727445	+	1.86486i
$643$	2.50399	−	7.70649i	0.0987477	−	0.303914i	−0.889465	−	0.457004i	$-0.848922\pi$
$643$	2.50399	−	7.70649i	0.0987477	−	0.303914i	0.988212	+	0.153090i	$0.0489224\pi$
$644$	−12.5398	+	38.5934i	−0.494136	+	1.52079i
$645$	14.3891	+	36.8874i	0.566569	+	1.45244i
$646$	−8.10205	+	11.1515i	−0.318771	+	0.438750i
$647$	−10.7460	+	3.49158i	−0.422468	+	0.137268i	−0.512533	−	0.858668i	$-0.671293\pi$
$647$	−10.7460	+	3.49158i	−0.422468	+	0.137268i	0.0900645	+	0.995936i	$0.471293\pi$
$648$	−39.8922	−	65.7683i	−1.56711	−	2.58362i
$649$	7.00019	+	21.3157i	0.274782	+	0.836714i
$650$		−	6.09641i		−	0.239121i
$651$	−0.642481	−	11.1096i	−0.0251808	−	0.435419i
$652$	−84.7753	−	61.5929i	−3.32006	−	2.41216i
$653$	−23.3707	−	32.1670i	−0.914567	−	1.25879i	−0.965583	−	0.260096i	$-0.916246\pi$
$653$	−23.3707	−	32.1670i	−0.914567	−	1.25879i	0.0510155	−	0.998698i	$-0.483754\pi$
$654$	−20.0494	+	31.2418i	−0.783992	+	1.22165i
$655$	−13.7339	−	4.46243i	−0.536630	−	0.174362i
$656$	109.550	−	79.5925i	4.27720	−	3.10757i
$657$	6.38762	−	2.92712i	0.249205	−	0.114198i
$658$	−4.89100	−	15.0530i	−0.190671	−	0.586825i
$659$	−35.4799			−1.38210			−0.691050	−	0.722807i	$-0.742852\pi$
$659$	−35.4799			−1.38210			−0.691050	+	0.722807i	$0.742852\pi$
$660$	62.0295	−	51.1155i	2.41449	−	1.98967i
$661$	14.3024			0.556299			0.278149	−	0.960538i	$-0.410279\pi$
$661$	14.3024			0.556299			0.278149	+	0.960538i	$0.410279\pi$
$662$	19.9997	+	61.5528i	0.777312	+	2.39232i
$663$	−2.21115	−	2.70055i	−0.0858738	−	0.104881i
$664$	−67.1610	+	48.7953i	−2.60635	+	1.89363i
$665$	30.9828	+	10.0669i	1.20146	+	0.390378i
$666$	15.4848	−	14.2488i	0.600025	−	0.552130i
$667$	−3.08390	−	4.24463i	−0.119409	−	0.164353i
$668$	2.94560	+	2.14010i	0.113969	+	0.0828030i
$669$	−17.3908	+	1.00573i	−0.672369	+	0.0388839i
$670$		−	22.7351i		−	0.878334i
$671$	2.52119	+	1.81964i	0.0973293	+	0.0702465i
$672$	−131.053	−	34.3572i	−5.05548	−	1.32536i
$673$	16.1796	−	5.25707i	0.623678	−	0.202645i	0.0199053	−	0.999802i	$-0.493664\pi$
$673$	16.1796	−	5.25707i	0.623678	−	0.202645i	0.603773	+	0.797157i	$0.293664\pi$
$674$	9.22151	−	12.6923i	0.355199	−	0.488890i
$675$	1.65883	−	11.6986i	0.0638484	−	0.450278i
$676$	−1.60314	+	4.93397i	−0.0616594	+	0.189768i
$677$	13.7183	−	42.2206i	0.527237	−	1.62267i	−0.232611	−	0.972570i	$-0.574727\pi$
$677$	13.7183	−	42.2206i	0.527237	−	1.62267i	0.759849	−	0.650100i	$-0.225273\pi$
$678$	65.7130	−	25.6334i	2.52369	−	0.984443i
$679$	4.69009	−	6.45536i	0.179989	−	0.247734i
$680$	44.1768	−	14.3539i	1.69410	−	0.550448i
$681$	3.81724	−	14.5606i	0.146277	−	0.557963i
$682$	11.4647	−	3.76508i	0.439007	−	0.144172i
$683$		−	7.37477i		−	0.282188i	−0.989996	−	0.141094i	$-0.954938\pi$
$683$		−	7.37477i		−	0.282188i	0.989996	−	0.141094i	$-0.0450620\pi$
$684$	38.9280	+	7.83541i	1.48845	+	0.299595i
$685$	11.5720	+	8.40757i	0.442144	+	0.321237i
$686$	62.7702	+	86.3958i	2.39658	+	3.29861i
$687$	−14.5146	−	9.31469i	−0.553766	−	0.355378i
$688$	101.074	+	32.8408i	3.85340	+	1.25204i
$689$	−5.84000	+	4.24301i	−0.222486	+	0.161646i
$690$	−16.0102	+	13.1088i	−0.609498	+	0.499042i
$691$	1.81891	+	5.59802i	0.0691944	+	0.212959i	0.979674	−	0.200595i	$-0.0642875\pi$
$691$	1.81891	+	5.59802i	0.0691944	+	0.212959i	−0.910480	+	0.413553i	$0.864287\pi$
$692$	119.529			4.54381
$693$	−46.7743	+	5.57754i	−1.77681	+	0.211873i
$694$	−1.49457			−0.0567332
$695$	10.3236	+	31.7729i	0.391597	+	1.20521i
$696$	36.3727	−	29.7811i	1.37870	−	1.12885i
$697$	17.6064	−	12.7918i	0.666891	−	0.484525i
$698$	−11.5005	−	3.73673i	−0.435299	−	0.141437i
$699$	19.9586	+	12.8084i	0.754905	+	0.484458i
$700$	−32.8275	−	45.1832i	−1.24076	−	1.70776i
$701$	−15.3653	−	11.1635i	−0.580339	−	0.421641i	0.258508	−	0.966009i	$-0.416769\pi$
$701$	−15.3653	−	11.1635i	−0.580339	−	0.421641i	−0.838846	+	0.544369i	$0.816769\pi$
$702$	−6.12238	+	12.5136i	−0.231074	+	0.472294i
$703$			6.67515i			0.251758i
$704$	−0.200778	−	63.7431i	−0.00756712	−	2.40241i
$705$	1.47720	−	5.63469i	0.0556347	−	0.212215i
$706$	−48.8281	+	15.8652i	−1.83767	+	0.597095i
$707$	−26.0375	+	35.8375i	−0.979240	+	1.34781i
$708$	56.6288	−	22.0898i	2.12824	−	0.830186i
$709$	5.64860	−	17.3846i	0.212137	−	0.652892i	−0.787207	−	0.616689i	$-0.788474\pi$
$709$	5.64860	−	17.3846i	0.212137	−	0.652892i	0.999344	−	0.0362031i	$-0.0115263\pi$
$710$	−23.1542	+	71.2615i	−0.868963	+	2.67439i
$711$	4.06980	+	35.0692i	0.152629	+	1.31520i
$712$	58.2479	−	80.1713i	2.18293	−	3.00455i
$713$	−2.13243	+	0.692869i	−0.0798602	+	0.0259481i
$714$	−42.8532	−	11.2345i	−1.60374	−	0.420441i
$715$	−8.51586	−	2.73735i	−0.318475	−	0.102371i
$716$		−	53.4113i		−	1.99607i
$717$	−4.86564	+	0.281386i	−0.181711	+	0.0105085i
$718$	−45.1964	−	32.8371i	−1.68671	−	1.22547i
$719$	−0.890195	−	1.22525i	−0.0331987	−	0.0456941i	0.792095	−	0.610398i	$-0.208990\pi$
$719$	−0.890195	−	1.22525i	−0.0331987	−	0.0456941i	−0.825294	+	0.564704i	$0.808990\pi$
$720$	−68.6937	−	74.6526i	−2.56006	−	2.78214i
$721$	3.94521	+	1.28188i	0.146927	+	0.0477396i
$722$	27.0918	−	19.6833i	1.00825	−	0.732537i
$723$	−28.9183	−	35.3189i	−1.07548	−	1.31353i
$724$	33.4017	+	102.800i	1.24136	+	3.82052i
$725$	7.22094			0.268179
$726$	−18.8625	−	47.4701i	−0.700055	−	1.76178i
$727$	23.1638			0.859098			0.429549	−	0.903043i	$-0.358672\pi$
$727$	23.1638			0.859098			0.429549	+	0.903043i	$0.358672\pi$
$728$	12.5038	+	38.4826i	0.463420	+	1.42626i
$729$	−15.1533	+	22.3467i	−0.561235	+	0.827657i
$730$	13.7010	−	9.95434i	0.507096	−	0.368427i
$731$	16.2442	+	5.27806i	0.600813	+	0.195216i
$732$	4.54970	−	7.08955i	0.168162	−	0.262037i
$733$	15.8488	+	21.8140i	0.585388	+	0.805717i	0.994273	−	0.106868i	$-0.0340823\pi$
$733$	15.8488	+	21.8140i	0.585388	+	0.805717i	−0.408885	+	0.912586i	$0.634082\pi$
$734$	3.07997	+	2.23773i	0.113684	+	0.0825961i
$735$	4.15704	+	71.8823i	0.153335	+	2.65142i
$736$			27.2977i			1.00621i
$737$	−9.92789	−	3.19123i	−0.365699	−	0.117551i
$738$	−75.6907	−	42.6154i	−2.78621	−	1.56870i
$739$	−4.50351	+	1.46328i	−0.165664	+	0.0538275i	−0.390675	−	0.920529i	$-0.627758\pi$
$739$	−4.50351	+	1.46328i	−0.165664	+	0.0538275i	0.225011	+	0.974356i	$0.427758\pi$
$740$	21.5169	−	29.6154i	0.790976	−	1.08869i
$741$	−1.60595	−	4.11698i	−0.0589961	−	0.151241i
$742$	−28.3135	+	87.1399i	−1.03942	+	3.19901i
$743$	−0.208530	+	0.641789i	−0.00765022	+	0.0235450i	−0.954809	−	0.297221i	$-0.903940\pi$
$743$	−0.208530	+	0.641789i	−0.00765022	+	0.0235450i	0.947159	+	0.320766i	$0.103940\pi$
$744$	−7.30077	−	18.7160i	−0.267659	−	0.686164i
$745$	25.9567	−	35.7263i	0.950979	−	1.30891i
$746$	75.6565	−	24.5823i	2.76998	−	0.900021i
$747$	25.3914	+	14.2959i	0.929022	+	0.523058i
$748$	−0.109212	−	34.6725i	−0.00399318	−	1.26775i
$749$		−	51.7088i		−	1.88940i
$750$	1.97116	+	34.0848i	0.0719766	+	1.24460i
$751$	31.9826	+	23.2367i	1.16706	+	0.847921i	0.990654	−	0.136396i	$-0.0435520\pi$
$751$	31.9826	+	23.2367i	1.16706	+	0.847921i	0.176409	+	0.984317i	$0.443552\pi$
$752$	−9.19009	−	12.6491i	−0.335128	−	0.461264i
$753$	−15.9000	+	24.7760i	−0.579427	+	0.902889i
$754$	−8.09706	−	2.63090i	−0.294878	−	0.0958116i
$755$	−46.4400	+	33.7406i	−1.69012	+	1.22795i
$756$	22.0065	+	125.711i	0.800369	+	4.57206i
$757$	−11.1578	−	34.3403i	−0.405538	−	1.24812i	−0.920445	−	0.390872i	$-0.872174\pi$
$757$	−11.1578	−	34.3403i	−0.405538	−	1.24812i	0.514907	−	0.857246i	$-0.327826\pi$
$758$	−51.4723			−1.86956
$759$	3.47701	+	8.83131i	0.126208	+	0.320556i
$760$	58.8114			2.13331
$761$	11.7560	+	36.1814i	0.426156	+	1.31157i	0.901883	+	0.431981i	$0.142185\pi$
$761$	11.7560	+	36.1814i	0.426156	+	1.31157i	−0.475726	+	0.879593i	$0.657815\pi$
$762$	11.0552	+	13.5021i	0.400489	+	0.489131i
$763$	30.6183	−	22.2455i	1.10846	−	0.805341i
$764$	9.90547	+	3.21848i	0.358367	+	0.116441i
$765$	−11.0402	−	11.9979i	−0.399159	−	0.433785i
$766$	0.159984	+	0.220199i	0.00578046	+	0.00795612i
$767$	−5.47270	−	3.97615i	−0.197608	−	0.143570i
$768$	−19.2207	+	1.11155i	−0.693566	+	0.0401097i
$769$			38.0757i			1.37305i	0.727108	+	0.686523i	$0.240864\pi$
$769$			38.0757i			1.37305i	−0.727108	+	0.686523i	$0.759136\pi$
$770$	−107.869	+	35.4247i	−3.88732	+	1.27662i
$771$	32.1237	+	8.42162i	1.15691	+	0.303297i
$772$	−40.7971	+	13.2558i	−1.46832	+	0.477086i
$773$	18.5016	−	25.4653i	0.665457	−	0.915923i	−0.334189	−	0.942506i	$-0.608462\pi$
$773$	18.5016	−	25.4653i	0.665457	−	0.915923i	0.999647	+	0.0265826i	$0.00846250\pi$
$774$	−7.85876	−	67.7185i	−0.282477	−	2.43409i
$775$	0.953593	−	2.93486i	0.0342541	−	0.105423i
$776$	4.45136	−	13.6999i	0.159795	−	0.491797i
$777$	−19.9869	+	7.79650i	−0.717026	+	0.279698i
$778$	7.69138	−	10.5863i	0.275749	−	0.379536i
$779$	26.2055	−	8.51470i	0.938911	−	0.305071i
$780$	−6.14570	+	23.4423i	−0.220051	+	0.839371i
$781$	27.8682	+	20.1136i	0.997201	+	0.719721i
$782$			8.92612i			0.319198i
$783$	−14.8218	−	7.25171i	−0.529688	−	0.259155i
$784$	156.351	+	113.596i	5.58398	+	4.05700i
$785$	−6.23078	−	8.57593i	−0.222386	−	0.306088i
$786$	20.9254	+	13.4288i	0.746384	+	0.478990i
$787$	−26.3853	−	8.57311i	−0.940535	−	0.305598i	−0.201672	−	0.979453i	$-0.564637\pi$
$787$	−26.3853	−	8.57311i	−0.940535	−	0.305598i	−0.738864	+	0.673855i	$0.764637\pi$
$788$	8.36789	−	6.07962i	0.298094	−	0.216578i
$789$	12.3005	−	10.0714i	0.437911	−	0.358551i
$790$	26.2952	+	80.9284i	0.935542	+	2.87930i
$791$	−71.9121			−2.55690
$792$	−77.1969	+	35.6701i	−2.74307	+	1.26748i
$793$	−0.937476			−0.0332908
$794$	−4.28274	−	13.1809i	−0.151989	−	0.467773i
$795$	−26.0910	+	21.3627i	−0.925351	+	0.757655i
$796$	−1.48217	+	1.07686i	−0.0525342	+	0.0381684i
$797$	−11.5559	−	3.75472i	−0.409329	−	0.132999i	0.0971123	−	0.995273i	$-0.469039\pi$
$797$	−11.5559	−	3.75472i	−0.409329	−	0.132999i	−0.506442	+	0.862274i	$0.669039\pi$
$798$	−47.2061	−	30.2944i	−1.67108	−	1.07241i
$799$	−1.47700	−	2.03291i	−0.0522524	−	0.0719192i
$800$	−30.3946	−	22.0829i	−1.07461	−	0.780750i
$801$	−34.1001	−	6.86365i	−1.20487	−	0.242515i
$802$		−	1.11963i		−	0.0395354i
$803$	−2.42368	−	7.38015i	−0.0855299	−	0.260440i
$804$	−7.16473	+	27.3294i	−0.252681	+	0.963832i
$805$	20.0635	−	6.51903i	0.707146	−	0.229766i
$806$	−2.13859	+	2.94351i	−0.0753285	+	0.103681i
$807$	−19.0728	+	7.43991i	−0.671393	+	0.261897i
$808$	−24.7121	+	76.0562i	−0.869370	+	2.67565i
$809$	−1.11555	+	3.43329i	−0.0392205	+	0.120708i	−0.968750	−	0.248040i	$-0.920214\pi$
$809$	−1.11555	+	3.43329i	−0.0392205	+	0.120708i	0.929529	+	0.368748i	$0.120214\pi$
$810$	−25.1773	+	60.0093i	−0.884640	+	2.10851i
$811$	12.1925	−	16.7816i	0.428137	−	0.589281i	−0.539387	−	0.842058i	$-0.681344\pi$
$811$	12.1925	−	16.7816i	0.428137	−	0.589281i	0.967524	+	0.252777i	$0.0813440\pi$
$812$	−74.1776	+	24.1018i	−2.60312	+	0.845806i
$813$	45.3022	+	11.8765i	1.58882	+	0.416528i
$814$	−13.7334	−	18.7778i	−0.481356	−	0.658160i
$815$			54.4760i			1.90821i
$816$	−43.6896	+	2.52662i	−1.52944	+	0.0884494i
$817$	17.4954	+	12.7111i	0.612085	+	0.444706i
$818$	2.32254	+	3.19670i	0.0812058	+	0.111770i
$819$	10.4514	−	9.61717i	0.365202	−	0.336051i
$820$	−143.712	−	46.6949i	−5.01864	−	1.63065i
$821$	−18.1406	+	13.1799i	−0.633110	+	0.459981i	−0.857476	−	0.514524i	$-0.827969\pi$
$821$	−18.1406	+	13.1799i	−0.633110	+	0.459981i	0.224366	+	0.974505i	$0.427969\pi$
$822$	−15.6022	−	19.0555i	−0.544187	−	0.664635i
$823$	−4.84051	−	14.8975i	−0.168729	−	0.519296i	0.830562	−	0.556926i	$-0.188019\pi$
$823$	−4.84051	−	14.8975i	−0.168729	−	0.519296i	−0.999292	+	0.0376299i	$0.988019\pi$
$824$	7.48879			0.260884
$825$	−12.6460	−	3.27277i	−0.440277	−	0.113943i
$826$	−85.8617			−2.98751
$827$	11.8109	+	36.3503i	0.410706	+	1.26402i	0.916036	+	0.401097i	$0.131371\pi$
$827$	11.8109	+	36.3503i	0.410706	+	1.26402i	−0.505329	+	0.862927i	$0.668629\pi$
$828$	23.3766	−	10.7123i	0.812393	−	0.372279i
$829$	−30.9134	+	22.4599i	−1.07367	+	0.780064i	−0.976568	−	0.215210i	$-0.930956\pi$
$829$	−30.9134	+	22.4599i	−1.07367	+	0.780064i	−0.0970988	+	0.995275i	$0.530956\pi$
$830$	66.7955	+	21.7032i	2.31851	+	0.753328i
$831$	27.2367	−	42.4415i	0.944832	−	1.47228i
$832$	11.2969	+	15.5488i	0.391648	+	0.539057i
$833$	25.1282	+	18.2567i	0.870640	+	0.632557i
$834$	−3.32096	−	57.4251i	−0.114996	−	1.98847i
$835$		−	1.89282i		−	0.0655037i
$836$	13.4342	−	41.7936i	0.464630	−	1.44546i
$837$	−4.90472	+	5.06647i	−0.169532	+	0.175123i
$838$	54.8773	−	17.8307i	1.89571	−	0.615952i
$839$	−16.0184	+	22.0474i	−0.553015	+	0.761160i	−0.990417	−	0.138106i	$-0.955899\pi$
$839$	−16.0184	+	22.0474i	−0.553015	+	0.761160i	0.437402	+	0.899266i	$0.355899\pi$
$840$	68.6911	+	176.095i	2.37007	+	6.07584i
$841$	−5.84530	+	17.9900i	−0.201562	+	0.620345i
$842$	20.3069	−	62.4983i	0.699823	−	2.15383i
$843$	4.61874	+	11.8405i	0.159078	+	0.407808i
$844$	40.1131	−	55.2110i	1.38075	−	1.90044i
$845$	2.56502	−	0.833425i	0.0882393	−	0.0286707i
$846$	−4.92055	+	8.73956i	−0.169172	+	0.300472i
$847$	0.328063	+	52.0762i	0.0112724	+	1.78936i
$848$			90.5099i			3.10812i
$849$	−2.02191	−	34.9622i	−0.0693917	−	1.19990i
$850$	−9.93877	−	7.22094i	−0.340897	−	0.247676i
$851$	2.54078	+	3.49708i	0.0870967	+	0.119878i
$852$	50.2905	−	78.3650i	1.72292	−	2.68474i
$853$	40.3971	+	13.1258i	1.38317	+	0.449419i	0.903710	−	0.428145i	$-0.140833\pi$
$853$	40.3971	+	13.1258i	1.38317	+	0.449419i	0.479460	+	0.877564i	$0.340833\pi$
$854$	−9.62662	+	6.99415i	−0.329416	+	0.239335i
$855$	−8.59984	−	18.7667i	−0.294108	−	0.641808i
$856$	−28.8466	−	88.7807i	−0.985956	−	3.03446i
$857$	31.4917			1.07573			0.537867	−	0.843029i	$-0.319230\pi$
$857$	31.4917			1.07573			0.537867	+	0.843029i	$0.319230\pi$
$858$	12.9879	+	8.27732i	0.443400	+	0.282583i
$859$	6.53487			0.222967			0.111484	−	0.993766i	$-0.464440\pi$
$859$	6.53487			0.222967			0.111484	+	0.993766i	$0.464440\pi$
$860$	−36.6477	−	112.790i	−1.24968	−	3.84611i
$861$	56.1027	+	68.5202i	1.91198	+	2.33516i
$862$	−26.6347	+	19.3512i	−0.907180	+	0.659105i
$863$	−13.2144	−	4.29362i	−0.449824	−	0.146157i	0.0753398	−	0.997158i	$-0.475996\pi$
$863$	−13.2144	−	4.29362i	−0.449824	−	0.146157i	−0.525164	+	0.851001i	$0.675996\pi$
$864$	40.2113	+	75.8518i	1.36802	+	2.58053i
$865$	−36.5246	−	50.2718i	−1.24187	−	1.70929i
$866$	16.7935	+	12.2012i	0.570668	+	0.414614i
$867$	22.3741	−	1.29392i	0.759865	−	0.0439439i
$868$			33.3314i			1.13134i
$869$	39.0305	−	0.122939i	1.32402	−	0.00417040i
$870$	−38.4709	−	10.0856i	−1.30428	−	0.341934i
$871$	2.99033	−	0.971616i	0.101323	−	0.0329220i
$872$	40.1596	−	55.2750i	1.35998	−	1.87185i
$873$	−5.02254	+	0.582868i	−0.169987	+	0.0197271i
$874$	−3.49236	+	10.7484i	−0.118131	+	0.363569i
$875$	10.7563	−	33.1044i	0.363628	−	1.11913i
$876$	−19.6066	+	7.64817i	−0.662447	+	0.258408i
$877$	6.64790	−	9.15005i	0.224484	−	0.308975i	−0.681888	−	0.731457i	$-0.738841\pi$
$877$	6.64790	−	9.15005i	0.224484	−	0.308975i	0.906372	+	0.422481i	$0.138841\pi$
$878$	−99.1337	+	32.2105i	−3.34560	+	1.08705i
$879$	−1.88191	+	7.17843i	−0.0634754	+	0.242122i
$880$	−90.5278	+	66.2090i	−3.05169	+	2.23190i
$881$		−	23.9859i		−	0.808105i	−0.914736	−	0.404052i	$-0.867601\pi$
$881$		−	23.9859i		−	0.808105i	0.914736	−	0.404052i	$-0.132399\pi$
$882$	24.4625	−	121.535i	0.823694	−	4.09229i
$883$	−6.44103	−	4.67968i	−0.216758	−	0.157484i	0.474108	−	0.880467i	$-0.342771\pi$
$883$	−6.44103	−	4.67968i	−0.216758	−	0.157484i	−0.690866	+	0.722983i	$0.742771\pi$
$884$	6.14483	+	8.45764i	0.206673	+	0.284461i
$885$	−26.5947	−	17.0671i	−0.893972	−	0.573704i
$886$	22.9835	+	7.46780i	0.772147	+	0.250886i
$887$	13.9297	−	10.1205i	0.467715	−	0.339815i	−0.328835	−	0.944387i	$-0.606656\pi$
$887$	13.9297	−	10.1205i	0.467715	−	0.339815i	0.796550	+	0.604573i	$0.206656\pi$
$888$	−29.9668	+	24.5361i	−1.00562	+	0.823378i
$889$	−5.49780	−	16.9205i	−0.184390	−	0.567495i
$890$	−83.8383			−2.81027
$891$	22.6706	+	19.4176i	0.759494	+	0.650514i
$892$	52.1766			1.74700
$893$	−0.983143	−	3.02580i	−0.0328996	−	0.101255i
$894$	−58.8299	+	48.1685i	−1.96757	+	1.61100i
$895$	−22.4639	+	16.3209i	−0.750884	+	0.545549i
$896$	83.2228	+	27.0407i	2.78028	+	0.903368i
$897$	−2.40840	−	1.54559i	−0.0804143	−	0.0516056i
$898$	−44.5557	−	61.3256i	−1.48684	−	2.04646i
$899$	−3.48647	−	2.53307i	−0.116280	−	0.0844825i
$900$	−6.98330	+	34.6945i	−0.232777	+	1.15648i
$901$			14.5464i			0.484611i
$902$	−56.2003	+	77.8677i	−1.87127	+	2.59271i
$903$	−17.6256	+	67.2315i	−0.586542	+	2.23732i
$904$	−123.469	+	40.1174i	−4.10650	+	1.33428i
$905$	33.0292	−	45.4608i	1.09793	−	1.51117i
$906$	92.0777	−	35.9177i	3.05908	−	1.19329i
$907$	9.80606	−	30.1799i	0.325605	−	1.00211i	−0.645562	−	0.763708i	$-0.723377\pi$
$907$	9.80606	−	30.1799i	0.325605	−	1.00211i	0.971167	−	0.238401i	$-0.0766232\pi$
$908$	−13.9324	+	42.8794i	−0.462362	+	1.42300i
$909$	27.8831	−	3.23585i	0.924824	−	0.107326i
$910$	20.1214	−	27.6948i	0.667018	−	0.918072i
$911$	−5.61768	+	1.82530i	−0.186122	+	0.0604747i	−0.400595	−	0.916255i	$-0.631197\pi$
$911$	−5.61768	+	1.82530i	−0.186122	+	0.0604747i	0.214473	+	0.976730i	$0.431197\pi$
$912$	−53.5973	−	14.0512i	−1.77478	−	0.465281i
$913$	18.8531	−	26.1217i	0.623946	−	0.864501i
$914$			22.8700i			0.756473i
$915$	−4.37200	+	0.252838i	−0.144534	+	0.00835855i
$916$	41.7912	+	30.3631i	1.38082	+	1.00322i
$917$	−14.8997	−	20.5077i	−0.492033	−	0.677225i
$918$	13.1488	+	24.8029i	0.433974	+	0.818618i
$919$	−27.9470	−	9.08052i	−0.921886	−	0.299539i	−0.190645	−	0.981659i	$-0.561058\pi$
$919$	−27.9470	−	9.08052i	−0.921886	−	0.299539i	−0.731240	+	0.682120i	$0.761058\pi$
$920$	30.8110	−	22.3855i	1.01581	−	0.738029i
$921$	−31.6966	−	38.7122i	−1.04444	−	1.27561i
$922$	−8.04775	−	24.7684i	−0.265039	−	0.815705i
$923$	−10.3625			−0.341085
$924$	140.830	−	8.58954i	4.63298	−	0.282575i
$925$	−5.94921			−0.195609
$926$	−28.0454	−	86.3148i	−0.921629	−	2.83648i
$927$	−1.09507	−	2.38967i	−0.0359667	−	0.0784871i
$928$	−42.4466	+	30.8393i	−1.39338	+	1.01235i
$929$	−39.4439	−	12.8161i	−1.29411	−	0.420482i	−0.420582	−	0.907254i	$-0.638174\pi$
$929$	−39.4439	−	12.8161i	−1.29411	−	0.420482i	−0.873529	+	0.486772i	$0.838174\pi$
$930$	−9.17960	+	14.3041i	−0.301011	+	0.469049i
$931$	23.1151	+	31.8152i	0.757567	+	1.04270i
$932$	−57.4660	−	41.7515i	−1.88236	−	1.36762i
$933$	−1.12537	−	19.4596i	−0.0368430	−	0.637079i
$934$			65.0114i			2.12724i
$935$	−14.5493	+	10.6409i	−0.475813	+	0.347993i
$936$	12.5793	−	22.3426i	0.411168	−	0.730289i
$937$	19.5508	−	6.35244i	0.638697	−	0.207525i	0.0282734	−	0.999600i	$-0.490999\pi$
$937$	19.5508	−	6.35244i	0.638697	−	0.207525i	0.610424	+	0.792075i	$0.290999\pi$
$938$	23.4578	−	32.2869i	0.765924	−	1.05420i
$939$	−14.6130	−	37.4616i	−0.476879	−	1.22251i
$940$	−5.39158	+	16.5936i	−0.175854	+	0.541223i
$941$	−7.14449	+	21.9885i	−0.232904	+	0.716804i	0.764489	+	0.644637i	$0.222991\pi$
$941$	−7.14449	+	21.9885i	−0.232904	+	0.716804i	−0.997393	+	0.0721670i	$0.977009\pi$
$942$	6.63282	+	17.0037i	0.216109	+	0.554011i
$943$	10.4880	−	14.4355i	0.341536	−	0.470084i
$944$	−80.6662	+	26.2100i	−2.62546	+	0.853064i
$945$	46.1473	−	47.6692i	1.50117	−	1.55068i
$946$	−75.3677	+	0.237394i	−2.45041	+	0.00771833i
$947$		−	13.7576i		−	0.447061i	−0.974697	−	0.223531i	$-0.928242\pi$
$947$		−	13.7576i		−	0.447061i	0.974697	−	0.223531i	$-0.0717583\pi$
$948$	−6.10517	−	105.569i	−0.198287	−	3.42872i
$949$	1.89482	+	1.37666i	0.0615083	+	0.0446884i
$950$	−9.14254	−	12.5836i	−0.296623	−	0.408267i
$951$	27.0531	−	42.1554i	0.877256	−	1.36698i
$952$	77.5472	+	25.1966i	2.51332	+	0.816626i
$953$	−15.6735	+	11.3875i	−0.507715	+	0.368877i	−0.811956	−	0.583718i	$-0.801597\pi$
$953$	−15.6735	+	11.3875i	−0.507715	+	0.368877i	0.304241	+	0.952595i	$0.401597\pi$
$954$	52.7819	−	24.1873i	1.70888	−	0.783093i
$955$	−1.67319	−	5.14954i	−0.0541431	−	0.166635i
$956$	14.5980			0.472135
$957$	−9.80415	+	15.3837i	−0.316923	+	0.497283i
$958$	37.2934			1.20489
$959$	7.75899	+	23.8797i	0.250551	+	0.771116i
$960$	56.8773	+	69.4663i	1.83571	+	2.24201i
$961$	23.5896	−	17.1388i	0.760954	−	0.552865i
$962$	6.67104	+	2.16755i	0.215083	+	0.0698846i
$963$	−24.1117	+	22.1871i	−0.776990	+	0.714970i
$964$	80.3647	+	110.613i	2.58837	+	3.56259i
$965$	18.0416	+	13.1080i	0.580778	+	0.421960i
$966$	−36.2621	+	2.09708i	−1.16671	+	0.0674724i
$967$			20.4595i			0.657933i	0.944342	+	0.328967i	$0.106700\pi$
$967$			20.4595i			0.657933i	−0.944342	+	0.328967i	$0.893300\pi$
$968$	29.6148	+	89.2285i	0.951857	+	2.86791i
$969$	−8.61395	−	2.25825i	−0.276720	−	0.0725456i
$970$	−11.5904	+	3.76595i	−0.372145	+	0.120917i
$971$	−3.54995	+	4.88609i	−0.113923	+	0.156802i	−0.862171	−	0.506618i	$-0.830896\pi$
$971$	−3.54995	+	4.88609i	−0.113923	+	0.156802i	0.748247	+	0.663420i	$0.230896\pi$
$972$	49.1764	−	64.2014i	1.57733	−	2.05926i
$973$	−18.1219	+	55.7735i	−0.580961	+	1.78801i
$974$	0.569406	−	1.75245i	0.0182449	−	0.0561522i
$975$	3.66925	−	1.43130i	0.117510	−	0.0458384i
$976$	−6.90908	+	9.50953i	−0.221154	+	0.304393i
$977$	−3.26120	+	1.05963i	−0.104335	+	0.0339005i	−0.360719	−	0.932674i	$-0.617469\pi$
$977$	−3.26120	+	1.05963i	−0.104335	+	0.0339005i	0.256384	+	0.966575i	$0.417469\pi$
$978$	23.7859	−	90.7295i	0.760588	−	2.90121i
$979$	−11.7680	+	36.6103i	−0.376108	+	1.17007i
$980$		−	215.664i		−	6.88912i
$981$	−23.5107	−	4.73222i	−0.750639	−	0.151088i
$982$	89.5509	+	65.0625i	2.85768	+	2.07623i
$983$	9.36146	+	12.8849i	0.298584	+	0.410966i	0.931779	−	0.363027i	$-0.118257\pi$
$983$	9.36146	+	12.8849i	0.298584	+	0.410966i	−0.633195	+	0.773993i	$0.718257\pi$
$984$	134.550	+	86.3470i	4.28929	+	2.75264i
$985$	−5.11397	−	1.66163i	−0.162945	−	0.0529439i
$986$	−13.8797	+	10.0842i	−0.442020	+	0.321146i
$987$	7.91163	−	6.47785i	0.251830	−	0.206192i
$988$	4.09023	+	12.5884i	0.130127	+	0.400491i
$989$	14.0040			0.445301
$990$	62.8026	+	35.0991i	1.99600	+	1.11552i
$991$	−1.15562			−0.0367096			−0.0183548	−	0.999832i	$-0.505843\pi$
$991$	−1.15562			−0.0367096			−0.0183548	+	0.999832i	$0.505843\pi$
$992$	6.92875	+	21.3245i	0.219988	+	0.677053i
$993$	−32.3514	+	26.4885i	−1.02664	+	0.840588i
$994$	−106.409	+	77.3105i	−3.37508	+	2.45214i
$995$	0.905819	+	0.294318i	0.0287164	+	0.00933052i
$996$	−73.4539	−	47.1388i	−2.32748	−	1.49365i
$997$	−26.7467	−	36.8137i	−0.847077	−	1.16590i	−0.984499	−	0.175389i	$-0.943882\pi$
$997$	−26.7467	−	36.8137i	−0.847077	−	1.16590i	0.137422	−	0.990513i	$-0.456118\pi$
$998$	−33.6379	−	24.4394i	−1.06479	−	0.773615i
$999$	12.2114	+	5.97456i	0.386353	+	0.189027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.x.a.248.3	✓	192
3.2	odd	2	inner	429.2.x.a.248.46	yes	192
11.2	odd	10	inner	429.2.x.a.365.46	yes	192
33.2	even	10	inner	429.2.x.a.365.3	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.x.a.248.3	✓	192	1.1	even	1	trivial
429.2.x.a.248.46	yes	192	3.2	odd	2	inner
429.2.x.a.365.3	yes	192	33.2	even	10	inner
429.2.x.a.365.46	yes	192	11.2	odd	10	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.828482 - 2.54980i) q^{2} +(1.34014 - 1.09728i) q^{3} +(-4.19709 + 3.04936i) q^{4} +(2.56502 + 0.833425i) q^{5} +(-3.90813 - 2.50803i) q^{6} +(2.78275 + 3.83012i) q^{7} +(6.91450 + 5.02368i) q^{8} +(0.591966 - 2.94102i) q^{9} +O(q^{10})\)	\(q+(-0.828482 - 2.54980i) q^{2} +(1.34014 - 1.09728i) q^{3} +(-4.19709 + 3.04936i) q^{4} +(2.56502 + 0.833425i) q^{5} +(-3.90813 - 2.50803i) q^{6} +(2.78275 + 3.83012i) q^{7} +(6.91450 + 5.02368i) q^{8} +(0.591966 - 2.94102i) q^{9} -7.23077i q^{10} +(-3.15751 - 1.01495i) q^{11} +(-2.27870 + 8.69195i) q^{12} +(0.951057 - 0.309017i) q^{13} +(7.46061 - 10.2687i) q^{14} +(4.35199 - 1.69763i) q^{15} +(3.87457 - 11.9247i) q^{16} +(0.622707 - 1.91649i) q^{17} +(-7.98945 + 0.927179i) q^{18} +(1.49966 - 2.06411i) q^{19} +(-13.3070 + 4.32371i) q^{20} +(7.93199 + 2.07947i) q^{21} +(0.0280078 + 8.89190i) q^{22} -1.65219i q^{23} +(14.7788 - 0.854674i) q^{24} +(1.83963 + 1.33657i) q^{25} +(-1.57587 - 2.16899i) q^{26} +(-2.43379 - 4.59093i) q^{27} +(-23.3589 - 7.58976i) q^{28} +(2.56908 - 1.86655i) q^{29} +(-7.93416 - 9.69026i) q^{30} +(-0.419363 - 1.29067i) q^{31} -16.5221 q^{32} +(-5.34520 + 2.10448i) q^{33} -5.40259 q^{34} +(3.94568 + 12.1435i) q^{35} +(6.48369 + 14.1488i) q^{36} +(-2.11663 + 1.53782i) q^{37} +(-6.50551 - 2.11377i) q^{38} +(0.935474 - 1.45770i) q^{39} +(13.5490 + 18.6485i) q^{40} +(8.73715 + 6.34791i) q^{41} +(-1.26927 - 21.9478i) q^{42} +8.47599i q^{43} +(16.3473 - 5.36855i) q^{44} +(3.96952 - 7.05040i) q^{45} +(-4.21277 + 1.36881i) q^{46} +(0.732957 - 1.00883i) q^{47} +(-7.89222 - 20.2323i) q^{48} +(-4.76305 + 14.6592i) q^{49} +(1.88389 - 5.79803i) q^{50} +(-1.26841 - 3.25166i) q^{51} +(-3.04936 + 4.19709i) q^{52} +(-6.86533 + 2.23068i) q^{53} +(-9.68963 + 10.0092i) q^{54} +(-7.25318 - 5.23492i) q^{55} +40.4630i q^{56} +(-0.255136 - 4.41174i) q^{57} +(-6.88777 - 5.00426i) q^{58} +(-3.97615 - 5.47270i) q^{59} +(-13.0890 + 20.3959i) q^{60} +(-0.891593 - 0.289696i) q^{61} +(-2.94351 + 2.13859i) q^{62} +(12.9118 - 5.91680i) q^{63} +(5.93911 + 18.2787i) q^{64} +2.69702 q^{65} +(9.79442 + 11.8857i) q^{66} +3.14422 q^{67} +(3.23053 + 9.94255i) q^{68} +(-1.81292 - 2.21418i) q^{69} +(27.6948 - 20.1214i) q^{70} +(-9.85531 - 3.20218i) q^{71} +(18.8679 - 17.3618i) q^{72} +(1.37666 + 1.89482i) q^{73} +(5.67472 + 4.12293i) q^{74} +(3.93196 - 0.227390i) q^{75} +13.2362i q^{76} +(-4.89916 - 14.9180i) q^{77} +(-4.49187 - 1.17760i) q^{78} +(-11.1922 + 3.63657i) q^{79} +(19.8767 - 27.3579i) q^{80} +(-8.29915 - 3.48197i) q^{81} +(8.94737 - 27.5372i) q^{82} +(-3.00150 + 9.23768i) q^{83} +(-39.6323 + 15.4598i) q^{84} +(3.19451 - 4.39686i) q^{85} +(21.6121 - 7.02220i) q^{86} +(1.39482 - 5.32044i) q^{87} +(-16.7338 - 22.8802i) q^{88} -11.5947i q^{89} +(-21.2658 - 4.28037i) q^{90} +(3.83012 + 2.78275i) q^{91} +(5.03814 + 6.93441i) q^{92} +(-1.97822 - 1.26952i) q^{93} +(-3.17956 - 1.03310i) q^{94} +(5.56694 - 4.04462i) q^{95} +(-22.1420 + 18.1293i) q^{96} +(-0.520822 - 1.60293i) q^{97} +41.3241 q^{98} +(-4.85413 + 8.68547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9}+O(q^{10}) \) 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9	\( 192 q + 6 q^{3} - 48 q^{4} - 10 q^{6} - 14 q^{9} - 20 q^{12} + 6 q^{15} - 28 q^{16} - 10 q^{18} - 60 q^{19} + 4 q^{22} + 30 q^{24} - 12 q^{25} + 30 q^{27} - 20 q^{28} + 12 q^{31} - 32 q^{33} + 56 q^{34} + 44 q^{36} + 60 q^{40} - 108 q^{42} - 40 q^{45} - 28 q^{48} - 24 q^{49} + 10 q^{51} + 20 q^{52} - 20 q^{55} + 50 q^{57} - 60 q^{58} + 36 q^{60} + 20 q^{61} - 30 q^{63} + 64 q^{64} - 30 q^{66} - 120 q^{67} - 16 q^{69} + 20 q^{70} + 150 q^{72} - 20 q^{73} + 18 q^{75} + 40 q^{78} - 160 q^{79} - 46 q^{81} + 88 q^{82} - 40 q^{85} + 72 q^{88} - 80 q^{90} + 8 q^{91} - 72 q^{93} - 120 q^{94} - 140 q^{96} - 88 q^{97} + 62 q^{99}+O(q^{100}) \) 192 * q + 6 * q^3 - 48 * q^4 - 10 * q^6 - 14 * q^9 - 20 * q^12 + 6 * q^15 - 28 * q^16 - 10 * q^18 - 60 * q^19 + 4 * q^22 + 30 * q^24 - 12 * q^25 + 30 * q^27 - 20 * q^28 + 12 * q^31 - 32 * q^33 + 56 * q^34 + 44 * q^36 + 60 * q^40 - 108 * q^42 - 40 * q^45 - 28 * q^48 - 24 * q^49 + 10 * q^51 + 20 * q^52 - 20 * q^55 + 50 * q^57 - 60 * q^58 + 36 * q^60 + 20 * q^61 - 30 * q^63 + 64 * q^64 - 30 * q^66 - 120 * q^67 - 16 * q^69 + 20 * q^70 + 150 * q^72 - 20 * q^73 + 18 * q^75 + 40 * q^78 - 160 * q^79 - 46 * q^81 + 88 * q^82 - 40 * q^85 + 72 * q^88 - 80 * q^90 + 8 * q^91 - 72 * q^93 - 120 * q^94 - 140 * q^96 - 88 * q^97 + 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more