LMFDB - Embedded newform 315.2.bh.c.169.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(169,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 0]))

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

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

chi := DirichletCharacter("315.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bh (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			169.4
Character	$\chi$	$=$	315.169
Dual form			315.2.bh.c.274.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08930 - 1.20626i) q^{2} +(-1.72484 - 0.157901i) q^{3} +(1.91013 + 3.30844i) q^{4} +(-0.387093 - 2.20231i) q^{5} +(3.41324 + 2.41051i) q^{6} +(0.866025 + 0.500000i) q^{7} -4.39141i q^{8} +(2.95013 + 0.544707i) q^{9} +O(q^{10})$	\(q+(-2.08930 - 1.20626i) q^{2} +(-1.72484 - 0.157901i) q^{3} +(1.91013 + 3.30844i) q^{4} +(-0.387093 - 2.20231i) q^{5} +(3.41324 + 2.41051i) q^{6} +(0.866025 + 0.500000i) q^{7} -4.39141i q^{8} +(2.95013 + 0.544707i) q^{9} +(-1.84780 + 5.06823i) q^{10} +(0.772957 - 1.33880i) q^{11} +(-2.77226 - 6.00813i) q^{12} +(4.59231 - 2.65137i) q^{13} +(-1.20626 - 2.08930i) q^{14} +(0.319927 + 3.85975i) q^{15} +(-1.47692 + 2.55811i) q^{16} +0.119594i q^{17} +(-5.50667 - 4.69669i) q^{18} -3.86313 q^{19} +(6.54680 - 5.48736i) q^{20} +(-1.41480 - 0.999165i) q^{21} +(-3.22988 + 1.86477i) q^{22} +(0.821601 - 0.474351i) q^{23} +(-0.693406 + 7.57447i) q^{24} +(-4.70032 + 1.70500i) q^{25} -12.7930 q^{26} +(-5.00250 - 1.40536i) q^{27} +3.82026i q^{28} +(0.937813 - 1.62434i) q^{29} +(3.98744 - 8.45010i) q^{30} +(-4.76891 - 8.25999i) q^{31} +(-1.43466 + 0.828299i) q^{32} +(-1.54462 + 2.18716i) q^{33} +(0.144261 - 0.249868i) q^{34} +(0.765921 - 2.10080i) q^{35} +(3.83301 + 10.8008i) q^{36} +5.45362i q^{37} +(8.07125 + 4.65994i) q^{38} +(-8.33964 + 3.84806i) q^{39} +(-9.67123 + 1.69988i) q^{40} +(1.23962 + 2.14708i) q^{41} +(1.75070 + 3.79418i) q^{42} +(-2.24441 - 1.29581i) q^{43} +5.90579 q^{44} +(0.0576347 - 6.70796i) q^{45} -2.28876 q^{46} +(-10.4293 - 6.02134i) q^{47} +(2.95138 - 4.17911i) q^{48} +(0.500000 + 0.866025i) q^{49} +(11.8771 + 2.10755i) q^{50} +(0.0188839 - 0.206280i) q^{51} +(17.5438 + 10.1289i) q^{52} -9.28531i q^{53} +(8.75651 + 8.97054i) q^{54} +(-3.24766 - 1.18405i) q^{55} +(2.19570 - 3.80307i) q^{56} +(6.66327 + 0.609991i) q^{57} +(-3.91875 + 2.26249i) q^{58} +(5.04844 + 8.74416i) q^{59} +(-12.1586 + 8.43107i) q^{60} +(6.46811 - 11.2031i) q^{61} +23.0102i q^{62} +(2.28254 + 1.94680i) q^{63} +9.90427 q^{64} +(-7.61678 - 9.08735i) q^{65} +(5.86548 - 2.70643i) q^{66} +(10.6942 - 6.17433i) q^{67} +(-0.395669 + 0.228439i) q^{68} +(-1.49203 + 0.688448i) q^{69} +(-4.13436 + 3.46531i) q^{70} -3.95838 q^{71} +(2.39203 - 12.9552i) q^{72} -13.8513i q^{73} +(6.57849 - 11.3943i) q^{74} +(8.37651 - 2.19866i) q^{75} +(-7.37907 - 12.7809i) q^{76} +(1.33880 - 0.772957i) q^{77} +(22.0658 + 2.02002i) q^{78} +(-2.74306 + 4.75112i) q^{79} +(6.20544 + 2.26241i) q^{80} +(8.40659 + 3.21392i) q^{81} -5.98122i q^{82} +(1.34560 + 0.776885i) q^{83} +(0.603221 - 6.58932i) q^{84} +(0.263382 - 0.0462939i) q^{85} +(3.12617 + 5.41468i) q^{86} +(-1.87406 + 2.65364i) q^{87} +(-5.87922 - 3.39437i) q^{88} -9.89616 q^{89} +(-8.21196 + 13.9454i) q^{90} +5.30274 q^{91} +(3.13872 + 1.81214i) q^{92} +(6.92133 + 15.0002i) q^{93} +(14.5266 + 25.1608i) q^{94} +(1.49539 + 8.50780i) q^{95} +(2.60534 - 1.20215i) q^{96} +(4.51862 + 2.60883i) q^{97} -2.41252i q^{98} +(3.00958 - 3.52861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.08930	−	1.20626i	−1.47736	−	0.852955i	−0.477688	−	0.878529i	$-0.658525\pi$
$2$	−2.08930	−	1.20626i	−1.47736	−	0.852955i	−0.999673	+	0.0255745i	$0.991858\pi$
$3$	−1.72484	−	0.157901i	−0.995836	−	0.0911640i
$3$	−1.72484	−	0.157901i	−0.995836	−	0.0911640i
$4$	1.91013	+	3.30844i	0.955064	+	1.65422i
$5$	−0.387093	−	2.20231i	−0.173113	−	0.984902i
$5$	−0.387093	−	2.20231i	−0.173113	−	0.984902i
$6$	3.41324	+	2.41051i	1.39345	+	0.984085i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	4.39141i		−	1.55260i
$9$	2.95013	+	0.544707i	0.983378	+	0.181569i
$10$	−1.84780	+	5.06823i	−0.584326	+	1.60271i
$11$	0.772957	−	1.33880i	0.233055	−	0.403664i	−0.725650	−	0.688064i	$-0.758461\pi$
$11$	0.772957	−	1.33880i	0.233055	−	0.403664i	0.958706	+	0.284400i	$0.0917944\pi$
$12$	−2.77226	−	6.00813i	−0.800282	−	1.73440i
$13$	4.59231	−	2.65137i	1.27368	−	0.735358i	0.297999	−	0.954566i	$-0.403681\pi$
$13$	4.59231	−	2.65137i	1.27368	−	0.735358i	0.975678	+	0.219208i	$0.0703475\pi$
$14$	−1.20626	−	2.08930i	−0.322387	−	0.558390i
$15$	0.319927	+	3.85975i	0.0826048	+	0.996582i
$16$	−1.47692	+	2.55811i	−0.369231	+	0.639526i
$17$			0.119594i			0.0290057i	0.999895	+	0.0145029i	$0.00461657\pi$
$17$			0.119594i			0.0290057i	−0.999895	+	0.0145029i	$0.995383\pi$
$18$	−5.50667	−	4.69669i	−1.29793	−	1.10702i
$19$	−3.86313			−0.886263			−0.443131	−	0.896457i	$-0.646132\pi$
$19$	−3.86313			−0.886263			−0.443131	+	0.896457i	$0.646132\pi$
$20$	6.54680	−	5.48736i	1.46391	−	1.22701i
$21$	−1.41480	−	0.999165i	−0.308735	−	0.218036i
$22$	−3.22988	+	1.86477i	−0.688614	+	0.397571i
$23$	0.821601	−	0.474351i	0.171316	−	0.0989091i	−0.411890	−	0.911233i	$-0.635131\pi$
$23$	0.821601	−	0.474351i	0.171316	−	0.0989091i	0.583206	+	0.812324i	$0.301798\pi$
$24$	−0.693406	+	7.57447i	−0.141541	+	1.54613i
$25$	−4.70032	+	1.70500i	−0.940064	+	0.340999i
$26$	−12.7930			−2.50891
$27$	−5.00250	−	1.40536i	−0.962731	−	0.270462i
$28$			3.82026i			0.721961i
$29$	0.937813	−	1.62434i	0.174147	−	0.301632i	−0.765718	−	0.643176i	$-0.777616\pi$
$29$	0.937813	−	1.62434i	0.174147	−	0.301632i	0.939866	+	0.341544i	$0.110950\pi$
$30$	3.98744	−	8.45010i	0.728003	−	1.54277i
$31$	−4.76891	−	8.25999i	−0.856521	−	1.48354i	−0.875227	−	0.483712i	$-0.839288\pi$
$31$	−4.76891	−	8.25999i	−0.856521	−	1.48354i	0.0187064	−	0.999825i	$-0.494045\pi$
$32$	−1.43466	+	0.828299i	−0.253614	+	0.146424i
$33$	−1.54462	+	2.18716i	−0.268884	+	0.380736i
$34$	0.144261	−	0.249868i	0.0247406	−	0.0428520i
$35$	0.765921	−	2.10080i	0.129464	−	0.355100i
$36$	3.83301	+	10.8008i	0.638834	+	1.80013i
$37$			5.45362i			0.896570i	0.893891	+	0.448285i	$0.147965\pi$
$37$			5.45362i			0.896570i	−0.893891	+	0.448285i	$0.852035\pi$
$38$	8.07125	+	4.65994i	1.30933	+	0.755942i
$39$	−8.33964	+	3.84806i	−1.33541	+	0.616182i
$40$	−9.67123	+	1.69988i	−1.52916	+	0.268775i
$41$	1.23962	+	2.14708i	0.193596	+	0.335318i	0.946439	−	0.322882i	$-0.104652\pi$
$41$	1.23962	+	2.14708i	0.193596	+	0.335318i	−0.752843	+	0.658200i	$0.771318\pi$
$42$	1.75070	+	3.79418i	0.270139	+	0.585455i
$43$	−2.24441	−	1.29581i	−0.342269	−	0.197609i	0.319006	−	0.947753i	$-0.396651\pi$
$43$	−2.24441	−	1.29581i	−0.342269	−	0.197609i	−0.661275	+	0.750144i	$0.729984\pi$
$44$	5.90579			0.890331
$45$	0.0576347	−	6.70796i	0.00859167	−	0.999963i
$46$	−2.28876			−0.337460
$47$	−10.4293	−	6.02134i	−1.52126	−	0.878303i	−0.999685	−	0.0251000i	$-0.992010\pi$
$47$	−10.4293	−	6.02134i	−1.52126	−	0.878303i	−0.521580	−	0.853203i	$-0.674657\pi$
$48$	2.95138	−	4.17911i	0.425995	−	0.603203i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	11.8771	+	2.10755i	1.67967	+	0.298053i
$51$	0.0188839	−	0.206280i	0.00264428	−	0.0288850i
$52$	17.5438	+	10.1289i	2.43289	+	1.40463i
$53$		−	9.28531i		−	1.27544i	−0.770270	−	0.637718i	$-0.779879\pi$
$53$		−	9.28531i		−	1.27544i	0.770270	−	0.637718i	$-0.220121\pi$
$54$	8.75651	+	8.97054i	1.19161	+	1.22074i
$55$	−3.24766	−	1.18405i	−0.437914	−	0.159657i
$56$	2.19570	−	3.80307i	0.293413	−	0.508206i
$57$	6.66327	+	0.609991i	0.882572	+	0.0807953i
$58$	−3.91875	+	2.26249i	−0.514557	+	0.297080i
$59$	5.04844	+	8.74416i	0.657251	+	1.13839i	0.981324	+	0.192361i	$0.0616144\pi$
$59$	5.04844	+	8.74416i	0.657251	+	1.13839i	−0.324073	+	0.946032i	$0.605052\pi$
$60$	−12.1586	+	8.43107i	−1.56967	+	1.08845i
$61$	6.46811	−	11.2031i	0.828157	−	1.43441i	−0.0713253	−	0.997453i	$-0.522723\pi$
$61$	6.46811	−	11.2031i	0.828157	−	1.43441i	0.899482	−	0.436957i	$-0.143944\pi$
$62$			23.0102i			2.92229i
$63$	2.28254	+	1.94680i	0.287573	+	0.245273i
$64$	9.90427			1.23803
$65$	−7.61678	−	9.08735i	−0.944746	−	1.12715i
$66$	5.86548	−	2.70643i	0.721990	−	0.333139i
$67$	10.6942	−	6.17433i	1.30651	−	0.754314i	0.324998	−	0.945715i	$-0.394636\pi$
$67$	10.6942	−	6.17433i	1.30651	−	0.754314i	0.981512	+	0.191400i	$0.0613029\pi$
$68$	−0.395669	+	0.228439i	−0.0479819	+	0.0277023i
$69$	−1.49203	+	0.688448i	−0.179619	+	0.0828794i
$70$	−4.13436	+	3.46531i	−0.494150	+	0.414184i
$71$	−3.95838			−0.469773			−0.234887	−	0.972023i	$-0.575472\pi$
$71$	−3.95838			−0.469773			−0.234887	+	0.972023i	$0.575472\pi$
$72$	2.39203	−	12.9552i	0.281903	−	1.52679i
$73$		−	13.8513i		−	1.62118i	−0.585617	−	0.810588i	$-0.699148\pi$
$73$		−	13.8513i		−	1.62118i	0.585617	−	0.810588i	$-0.300852\pi$
$74$	6.57849	−	11.3943i	0.764734	−	1.32456i
$75$	8.37651	−	2.19866i	0.967236	−	0.253879i
$76$	−7.37907	−	12.7809i	−0.846438	−	1.46607i
$77$	1.33880	−	0.772957i	0.152571	−	0.0880866i
$78$	22.0658	+	2.02002i	2.49846	+	0.228722i
$79$	−2.74306	+	4.75112i	−0.308618	+	0.534542i	−0.978060	−	0.208322i	$-0.933200\pi$
$79$	−2.74306	+	4.75112i	−0.308618	+	0.534542i	0.669442	+	0.742864i	$0.266533\pi$
$80$	6.20544	+	2.26241i	0.693789	+	0.252945i
$81$	8.40659	+	3.21392i	0.934065	+	0.357102i
$82$		−	5.98122i		−	0.660515i
$83$	1.34560	+	0.776885i	0.147699	+	0.0852742i	0.572028	−	0.820234i	$-0.306157\pi$
$83$	1.34560	+	0.776885i	0.147699	+	0.0852742i	−0.424329	+	0.905508i	$0.639490\pi$
$84$	0.603221	−	6.58932i	0.0658168	−	0.718954i
$85$	0.263382	−	0.0462939i	0.0285678	−	0.00502128i
$86$	3.12617	+	5.41468i	0.337104	+	0.583880i
$87$	−1.87406	+	2.65364i	−0.200920	+	0.284500i
$88$	−5.87922	−	3.39437i	−0.626727	−	0.361841i
$89$	−9.89616			−1.04899			−0.524495	−	0.851413i	$-0.675746\pi$
$89$	−9.89616			−1.04899			−0.524495	+	0.851413i	$0.675746\pi$
$90$	−8.21196	+	13.9454i	−0.865616	+	1.46998i
$91$	5.30274			0.555878
$92$	3.13872	+	1.81214i	0.327235	+	0.188929i
$93$	6.92133	+	15.0002i	0.717709	+	1.55544i
$94$	14.5266	+	25.1608i	1.49830	+	2.59514i
$95$	1.49539	+	8.50780i	0.153424	+	0.872882i
$96$	2.60534	−	1.20215i	0.265906	−	0.122694i
$97$	4.51862	+	2.60883i	0.458797	+	0.264886i	0.711538	−	0.702647i	$-0.247999\pi$
$97$	4.51862	+	2.60883i	0.458797	+	0.264886i	−0.252741	+	0.967534i	$0.581332\pi$
$98$		−	2.41252i		−	0.243701i
$99$	3.00958	−	3.52861i	0.302474	−	0.354638i
$100$	−14.6191	−	12.2940i	−1.46191	−	1.22940i
$101$	7.19224	−	12.4573i	0.715655	−	1.23955i	−0.247052	−	0.969002i	$-0.579462\pi$
$101$	7.19224	−	12.4573i	0.715655	−	1.23955i	0.962707	−	0.270548i	$-0.0872049\pi$
$102$	−0.288282	+	0.408202i	−0.0285441	+	0.0404181i
$103$	−7.85934	+	4.53759i	−0.774404	+	0.447102i	−0.834443	−	0.551094i	$-0.814211\pi$
$103$	−7.85934	+	4.53759i	−0.774404	+	0.447102i	0.0600396	+	0.998196i	$0.480877\pi$
$104$	−11.6432	−	20.1667i	−1.14171	−	1.97751i
$105$	−1.65281	+	3.50260i	−0.161298	+	0.341819i
$106$	−11.2005	+	19.3998i	−1.08789	+	1.88428i
$107$			12.5115i			1.20953i	0.796404	+	0.604765i	$0.206733\pi$
$107$			12.5115i			1.20953i	−0.796404	+	0.604765i	$0.793267\pi$
$108$	−4.90586	−	19.2349i	−0.472067	−	1.85088i
$109$	−19.7832			−1.89489			−0.947443	−	0.319923i	$-0.896343\pi$
$109$	−19.7832			−1.89489			−0.947443	+	0.319923i	$0.896343\pi$
$110$	5.35707	+	6.39136i	0.510777	+	0.609392i
$111$	0.861131	−	9.40661i	0.0817349	−	0.892836i
$112$	−2.55811	+	1.47692i	−0.241718	+	0.139556i
$113$	−8.68672	+	5.01528i	−0.817178	+	0.471798i	−0.849442	−	0.527682i	$-0.823061\pi$
$113$	−8.68672	+	5.01528i	−0.817178	+	0.471798i	0.0322645	+	0.999479i	$0.489728\pi$
$114$	−13.1858	−	9.31210i	−1.23496	−	0.872158i
$115$	−1.36270	−	1.62580i	−0.127073	−	0.151607i
$116$	7.16537			0.665288
$117$	14.9921	−	5.32044i	1.38602	−	0.491875i
$118$		−	24.3590i		−	2.24242i
$119$	−0.0597969	+	0.103571i	−0.00548157	+	0.00949436i
$120$	16.9497	−	1.40493i	1.54729	−	0.128252i
$121$	4.30508	+	7.45661i	0.391370	+	0.677874i
$122$	−27.0277	+	15.6045i	−2.44697	+	1.41276i
$123$	−1.79912	−	3.89911i	−0.162221	−	0.351571i
$124$	18.2184	−	31.5553i	1.63606	−	2.83375i
$125$	5.57439	+	9.69155i	0.498588	+	0.866839i
$126$	−2.42057	−	6.82079i	−0.215642	−	0.607644i
$127$			1.71207i			0.151922i	0.997111	+	0.0759609i	$0.0242024\pi$
$127$			1.71207i			0.151922i	−0.997111	+	0.0759609i	$0.975798\pi$
$128$	−17.8237	−	10.2905i	−1.57541	−	0.909563i
$129$	3.66663	+	2.58946i	0.322829	+	0.227989i
$130$	4.95207	+	28.1741i	0.434325	+	2.47103i
$131$	1.83103	+	3.17144i	0.159978	+	0.277090i	0.934861	−	0.355015i	$-0.115524\pi$
$131$	1.83103	+	3.17144i	0.159978	+	0.277090i	−0.774882	+	0.632105i	$0.782191\pi$
$132$	−10.1865	−	0.932528i	−0.886624	−	0.0811662i
$133$	−3.34557	−	1.93156i	−0.290098	−	0.167488i
$134$	−29.7914			−2.57358
$135$	−1.15860	+	11.5610i	−0.0997166	+	0.995016i
$136$	0.525185			0.0450342
$137$	0.215321	+	0.124316i	0.0183961	+	0.0106210i	0.509170	−	0.860666i	$-0.329952\pi$
$137$	0.215321	+	0.124316i	0.0183961	+	0.0106210i	−0.490774	+	0.871287i	$0.663286\pi$
$138$	3.94775	+	0.361398i	0.336055	+	0.0307642i
$139$	−5.94576	−	10.2984i	−0.504313	−	0.873495i	−0.999988	−	0.00498708i	$-0.998413\pi$
$139$	−5.94576	−	10.2984i	−0.504313	−	0.873495i	0.495675	−	0.868508i	$-0.334921\pi$
$140$	8.41338	−	1.47879i	0.711060	−	0.124981i
$141$	17.0380	+	12.0326i	1.43486	+	1.01333i
$142$	8.27026	+	4.77484i	0.694025	+	0.400695i
$143$		−	8.19758i		−	0.685516i
$144$	−5.75054	+	6.74227i	−0.479211	+	0.561855i
$145$	−3.94032	−	1.43658i	−0.327225	−	0.119302i
$146$	−16.7083	+	28.9396i	−1.38279	+	2.39506i
$147$	−0.725673	−	1.57270i	−0.0598525	−	0.129714i
$148$	−18.0430	+	10.4171i	−1.48312	+	0.856282i
$149$	−1.47843	−	2.56072i	−0.121118	−	0.209783i	0.799091	−	0.601210i	$-0.205315\pi$
$149$	−1.47843	−	2.56072i	−0.121118	−	0.209783i	−0.920209	+	0.391428i	$0.871981\pi$
$150$	−20.1532	−	5.51058i	−1.64550	−	0.449937i
$151$	−4.12661	+	7.14749i	−0.335818	+	0.581655i	−0.983642	−	0.180136i	$-0.942346\pi$
$151$	−4.12661	+	7.14749i	−0.335818	+	0.581655i	0.647823	+	0.761791i	$0.275680\pi$
$152$			16.9646i			1.37601i
$153$	−0.0651435	+	0.352818i	−0.00526654	+	0.0285236i
$154$	−3.72955			−0.300536
$155$	−16.3450	+	13.7000i	−1.31286	+	1.10041i
$156$	−28.6608	−	20.2409i	−2.29470	−	1.62057i
$157$	14.6109	−	8.43560i	1.16608	−	0.673234i	0.213323	−	0.976982i	$-0.431571\pi$
$157$	14.6109	−	8.43560i	1.16608	−	0.673234i	0.952753	+	0.303747i	$0.0982379\pi$
$158$	11.4622	−	6.61768i	0.911881	−	0.526475i
$159$	−1.46616	+	16.0157i	−0.116274	+	1.27012i
$160$	2.37952	+	2.83893i	0.188117	+	0.224437i
$161$	0.948703			0.0747682
$162$	−13.6871	−	16.8554i	−1.07536	−	1.32428i
$163$			4.17172i			0.326754i	0.986564	+	0.163377i	$0.0522387\pi$
$163$			4.17172i			0.326754i	−0.986564	+	0.163377i	$0.947761\pi$
$164$	−4.73566	+	8.20241i	−0.369793	+	0.640501i
$165$	5.41472	+	2.55510i	0.421536	+	0.198914i
$166$	−1.87425	−	3.24630i	−0.145470	−	0.251962i
$167$	9.60249	−	5.54400i	0.743063	−	0.429007i	−0.0801191	−	0.996785i	$-0.525530\pi$
$167$	9.60249	−	5.54400i	0.743063	−	0.429007i	0.823182	+	0.567778i	$0.192197\pi$
$168$	−4.38774	+	6.21298i	−0.338522	+	0.479342i
$169$	7.55953	−	13.0935i	0.581502	−	1.00719i
$170$	−0.606128	−	0.220985i	−0.0464879	−	0.0169488i
$171$	−11.3968	−	2.10427i	−0.871532	−	0.160918i
$172$		−	9.90066i		−	0.754918i
$173$	7.66488	+	4.42532i	0.582750	+	0.336451i	0.762225	−	0.647312i	$-0.224107\pi$
$173$	7.66488	+	4.42532i	0.582750	+	0.336451i	−0.179476	+	0.983762i	$0.557440\pi$
$174$	7.11646	−	3.28366i	0.539498	−	0.248934i
$175$	−4.92309	−	0.873589i	−0.372151	−	0.0660371i
$176$	2.28320	+	3.95461i	0.172102	+	0.298090i
$177$	−7.32704	−	15.8794i	−0.550734	−	1.19357i
$178$	20.6761	+	11.9373i	1.54974	+	0.894742i
$179$	17.9738			1.34342			0.671711	−	0.740814i	$-0.265560\pi$
$179$	17.9738			1.34342			0.671711	+	0.740814i	$0.265560\pi$
$180$	22.3030	−	12.6224i	1.66236	−	0.940816i
$181$	5.90943			0.439245			0.219622	−	0.975585i	$-0.429517\pi$
$181$	5.90943			0.439245			0.219622	+	0.975585i	$0.429517\pi$
$182$	−11.0790	−	6.39649i	−0.821233	−	0.474139i
$183$	−12.9254	+	18.3022i	−0.955475	+	1.35294i
$184$	−2.08307	−	3.60798i	−0.153566	−	0.265984i
$185$	12.0106	−	2.11106i	0.883033	−	0.155208i
$186$	3.63332	−	39.6888i	0.266408	−	2.91013i
$187$	0.160112	+	0.0924408i	0.0117086	+	0.00675994i
$188$		−	46.0061i		−	3.35534i
$189$	−3.62961	−	3.71832i	−0.264015	−	0.270468i
$190$	7.13830	−	19.5792i	0.517866	−	1.42043i
$191$	6.63906	−	11.4992i	0.480385	−	0.832052i	−0.519362	−	0.854555i	$-0.673830\pi$
$191$	6.63906	−	11.4992i	0.480385	−	0.832052i	0.999747	+	0.0225029i	$0.00716352\pi$
$192$	−17.0833	−	1.56389i	−1.23288	−	0.112864i
$193$	6.28075	−	3.62619i	0.452098	−	0.261019i	−0.256618	−	0.966513i	$-0.582608\pi$
$193$	6.28075	−	3.62619i	0.452098	−	0.261019i	0.708716	+	0.705494i	$0.249275\pi$
$194$	−6.29385	−	10.9013i	−0.451872	−	0.782666i
$195$	11.7028	+	16.8769i	0.838056	+	1.20858i
$196$	−1.91013	+	3.30844i	−0.136438	+	0.236317i
$197$		−	6.35610i		−	0.452854i	−0.974028	−	0.226427i	$-0.927296\pi$
$197$		−	6.35610i		−	0.452854i	0.974028	−	0.226427i	$-0.0727044\pi$
$198$	−10.5443	+	3.74200i	−0.749354	+	0.265932i
$199$	12.5194			0.887474			0.443737	−	0.896157i	$-0.353652\pi$
$199$	12.5194			0.887474			0.443737	+	0.896157i	$0.353652\pi$
$200$	7.48733	+	20.6410i	0.529434	+	1.45954i
$201$	−19.4208	+	8.96109i	−1.36984	+	0.632066i
$202$	−30.0536	+	17.3514i	−2.11456	+	1.22084i
$203$	1.62434	−	0.937813i	0.114006	−	0.0658216i
$204$	0.718535	−	0.331545i	0.0503075	−	0.0232128i
$205$	4.24869	−	3.56115i	0.296742	−	0.248721i
$206$	21.8941			1.52543
$207$	2.68221	−	0.951869i	0.186427	−	0.0661595i
$208$			15.6635i			1.08607i
$209$	−2.98603	+	5.17196i	−0.206548	+	0.357752i
$210$	7.67827	−	5.32428i	0.529851	−	0.367411i
$211$	−4.96811	−	8.60503i	−0.342019	−	0.592394i	0.642788	−	0.766044i	$-0.277777\pi$
$211$	−4.96811	−	8.60503i	−0.342019	−	0.592394i	−0.984808	+	0.173649i	$0.944444\pi$
$212$	30.7199	−	17.7361i	2.10985	−	1.21812i
$213$	6.82756	+	0.625031i	0.467817	+	0.0428264i
$214$	15.0921	−	26.1403i	1.03167	−	1.78691i
$215$	−1.98498	+	5.44448i	−0.135374	+	0.371310i
$216$	−6.17150	+	21.9680i	−0.419918	+	1.49473i
$217$		−	9.53781i		−	0.647469i
$218$	41.3331	+	23.8637i	2.79943	+	1.61625i
$219$	−2.18714	+	23.8913i	−0.147793	+	1.61442i
$220$	−2.28609	−	13.0064i	−0.154128	−	0.876889i
$221$	0.317087	+	0.549211i	0.0213296	+	0.0369439i
$222$	−13.1460	+	18.6145i	−0.882301	+	1.24933i
$223$	−13.5440	−	7.81962i	−0.906972	−	0.523641i	−0.0275166	−	0.999621i	$-0.508760\pi$
$223$	−13.5440	−	7.81962i	−0.906972	−	0.523641i	−0.879456	+	0.475981i	$0.842093\pi$
$224$	−1.65660			−0.110686
$225$	−14.7953	+	2.46967i	−0.986353	+	0.164645i
$226$	24.1989			1.60969
$227$	−17.9435	−	10.3597i	−1.19095	−	0.687596i	−0.232429	−	0.972613i	$-0.574667\pi$
$227$	−17.9435	−	10.3597i	−1.19095	−	0.687596i	−0.958522	+	0.285017i	$0.908001\pi$
$228$	10.7096	+	23.2102i	0.709260	+	1.53713i
$229$	−1.29668	−	2.24592i	−0.0856871	−	0.148414i	0.819997	−	0.572368i	$-0.193975\pi$
$229$	−1.29668	−	2.24592i	−0.0856871	−	0.148414i	−0.905684	+	0.423954i	$0.860642\pi$
$230$	0.885965	+	5.04056i	0.0584188	+	0.332365i
$231$	−2.43127	+	1.12183i	−0.159966	+	0.0738109i
$232$	−7.13313	−	4.11832i	−0.468313	−	0.270381i
$233$			16.4535i			1.07790i	0.842337	+	0.538952i	$0.181179\pi$
$233$			16.4535i			1.07790i	−0.842337	+	0.538952i	$0.818821\pi$
$234$	−37.7410	−	6.96842i	−2.46721	−	0.455540i
$235$	−9.22374	+	25.2993i	−0.601691	+	1.65034i
$236$	−19.2864	+	33.4049i	−1.25543	+	2.17448i
$237$	5.48154	−	7.76178i	0.356064	−	0.504182i
$238$	0.249868	−	0.144261i	0.0161965	−	0.00935106i
$239$	0.310745	+	0.538226i	0.0201004	+	0.0348149i	0.875901	−	0.482492i	$-0.160268\pi$
$239$	0.310745	+	0.538226i	0.0201004	+	0.0348149i	−0.855800	+	0.517306i	$0.826935\pi$
$240$	−10.3461	−	4.88214i	−0.667841	−	0.315141i
$241$	−9.31597	+	16.1357i	−0.600095	+	1.03939i	0.392712	+	0.919662i	$0.371537\pi$
$241$	−9.31597	+	16.1357i	−0.600095	+	1.03939i	−0.992806	+	0.119733i	$0.961796\pi$
$242$		−	20.7722i		−	1.33529i
$243$	−13.9925	−	6.87089i	−0.897621	−	0.440768i
$244$	49.4197			3.16377
$245$	1.71371	−	1.43639i	0.109485	−	0.0917674i
$246$	−0.944439	+	10.3166i	−0.0602152	+	0.657764i
$247$	−17.7407	+	10.2426i	−1.12881	+	0.651720i
$248$	−36.2730	+	20.9422i	−2.30333	+	1.32983i
$249$	−2.19828	−	1.55247i	−0.139310	−	0.0983840i
$250$	0.0439477	−	26.9728i	0.00277949	−	1.70591i
$251$	26.0256			1.64272			0.821361	−	0.570409i	$-0.193215\pi$
$251$	26.0256			1.64272			0.821361	+	0.570409i	$0.193215\pi$
$252$	−2.08092	+	11.2703i	−0.131086	+	0.709960i
$253$		−	1.46661i		−	0.0922051i
$254$	2.06521	−	3.57704i	0.129583	−	0.224443i
$255$	−0.461602	+	0.0382613i	−0.0289066	+	0.00239601i
$256$	14.9218	+	25.8454i	0.932615	+	1.61534i
$257$	−2.27275	+	1.31217i	−0.141770	+	0.0818509i	−0.569207	−	0.822194i	$-0.692750\pi$
$257$	−2.27275	+	1.31217i	−0.141770	+	0.0818509i	0.427437	+	0.904045i	$0.359416\pi$
$258$	−4.53715	−	9.83308i	−0.282471	−	0.612181i
$259$	−2.72681	+	4.72297i	−0.169436	+	0.293471i
$260$	15.5159	−	42.5577i	0.962255	−	2.63931i
$261$	3.65146	−	4.28119i	0.226020	−	0.264999i
$262$		−	8.83481i		−	0.545816i
$263$	14.9593	+	8.63677i	0.922431	+	0.532566i	0.884410	−	0.466711i	$-0.154561\pi$
$263$	14.9593	+	8.63677i	0.922431	+	0.532566i	0.0380214	+	0.999277i	$0.487894\pi$
$264$	9.60473	+	6.78307i	0.591130	+	0.417469i
$265$	−20.4491	+	3.59428i	−1.25618	+	0.220795i
$266$	4.65994	+	8.07125i	0.285719	+	0.494880i
$267$	17.0693	+	1.56261i	1.04462	+	0.0956302i
$268$	40.8548	+	23.5875i	2.49560	+	1.44084i
$269$	−17.7322			−1.08115			−0.540577	−	0.841295i	$-0.681794\pi$
$269$	−17.7322			−1.08115			−0.540577	+	0.841295i	$0.681794\pi$
$270$	16.3663	−	22.7570i	0.996021	−	1.38494i
$271$	9.03211			0.548662			0.274331	−	0.961635i	$-0.411544\pi$
$271$	9.03211			0.548662			0.274331	+	0.961635i	$0.411544\pi$
$272$	−0.305933	−	0.176631i	−0.0185499	−	0.0107098i
$273$	−9.14637	−	0.837307i	−0.553563	−	0.0506761i
$274$	−0.299915	−	0.519467i	−0.0181185	−	0.0313822i
$275$	−1.35049	+	7.61068i	−0.0814378	+	0.458941i
$276$	−5.12765	−	3.62126i	−0.308649	−	0.217974i
$277$	12.4493	+	7.18760i	0.748005	+	0.431861i	0.824973	−	0.565173i	$-0.191190\pi$
$277$	12.4493	+	7.18760i	0.748005	+	0.431861i	−0.0769677	+	0.997034i	$0.524524\pi$
$278$			28.6885i			1.72062i
$279$	−9.56964	−	26.9657i	−0.572920	−	1.61440i
$280$	−9.22547	−	3.36347i	−0.551327	−	0.201006i
$281$	13.9293	−	24.1262i	0.830950	−	1.43925i	−0.0663360	−	0.997797i	$-0.521131\pi$
$281$	13.9293	−	24.1262i	0.830950	−	1.43925i	0.897286	−	0.441450i	$-0.145536\pi$
$282$	−21.0831	−	45.6921i	−1.25548	−	2.72093i
$283$	−10.8714	+	6.27658i	−0.646235	+	0.373104i	−0.787012	−	0.616937i	$-0.788373\pi$
$283$	−10.8714	+	6.27658i	−0.646235	+	0.373104i	0.140777	+	0.990041i	$0.455040\pi$
$284$	−7.56101	−	13.0961i	−0.448663	−	0.777108i
$285$	−1.23592	−	14.9107i	−0.0732095	−	0.883234i
$286$	−9.88842	+	17.1272i	−0.584714	+	1.01275i
$287$			2.47924i			0.146345i
$288$	−4.68361	+	1.66213i	−0.275984	+	0.0979418i
$289$	16.9857			0.999159
$290$	6.49963	+	7.75450i	0.381671	+	0.455360i
$291$	−7.38196	−	5.21330i	−0.432738	−	0.305609i
$292$	45.8263	−	26.4578i	2.68178	−	1.54833i
$293$	15.7854	−	9.11369i	0.922192	−	0.532428i	0.0378582	−	0.999283i	$-0.487946\pi$
$293$	15.7854	−	9.11369i	0.922192	−	0.532428i	0.884334	+	0.466855i	$0.154613\pi$
$294$	−0.380939	+	4.16121i	−0.0222168	+	0.242687i
$295$	17.3031	−	14.5030i	1.00743	−	0.844399i
$296$	23.9491			1.39201
$297$	−5.74821	+	5.61106i	−0.333545	+	0.325587i
$298$			7.13351i			0.413233i
$299$	2.51536	−	4.35673i	0.145467	−	0.251956i
$300$	23.2743	+	23.5134i	1.34374	+	1.35755i
$301$	−1.29581	−	2.24441i	−0.0746893	−	0.129366i
$302$	17.2435	−	9.95552i	0.992250	−	0.572876i
$303$	−14.3725	+	20.3512i	−0.825677	+	1.16915i
$304$	5.70554	−	9.88229i	0.327235	−	0.566788i
$305$	−27.1764	−	9.90813i	−1.55612	−	0.567338i
$306$	0.561694	−	0.658563i	0.0321099	−	0.0376476i
$307$			29.9086i			1.70697i	0.521115	+	0.853486i	$0.325516\pi$
$307$			29.9086i			1.70697i	−0.521115	+	0.853486i	$0.674484\pi$
$308$	5.11456	+	2.95289i	0.291429	+	0.168257i
$309$	14.2726	−	6.58562i	0.811939	−	0.374643i
$310$	50.6755	−	8.90708i	2.87817	−	0.505888i
$311$	4.60688	+	7.97935i	0.261232	+	0.452468i	0.966570	−	0.256404i	$-0.0825378\pi$
$311$	4.60688	+	7.97935i	0.261232	+	0.452468i	−0.705337	+	0.708872i	$0.749204\pi$
$312$	16.8984	+	36.6228i	0.956682	+	2.07336i
$313$	9.96920	+	5.75572i	0.563493	+	0.325333i	0.754546	−	0.656247i	$-0.227857\pi$
$313$	9.96920	+	5.75572i	0.563493	+	0.325333i	−0.191054	+	0.981580i	$0.561190\pi$
$314$	−40.7021			−2.29695
$315$	3.40389	−	5.78044i	0.191788	−	0.325691i
$316$	−20.9584			−1.17900
$317$	23.8823	+	13.7885i	1.34137	+	0.774438i	0.987008	−	0.160672i	$-0.0513661\pi$
$317$	23.8823	+	13.7885i	1.34137	+	0.774438i	0.354358	+	0.935110i	$0.384699\pi$
$318$	22.3823	−	31.6930i	1.25514	−	1.77726i
$319$	−1.44978	−	2.51109i	−0.0811720	−	0.140594i
$320$	−3.83387	−	21.8122i	−0.214320	−	1.21934i
$321$	1.97557	−	21.5803i	0.110266	−	1.20449i
$322$	−1.98213	−	1.14438i	−0.110460	−	0.0637739i
$323$		−	0.462006i		−	0.0257067i
$324$	5.42462	+	33.9517i	0.301368	+	1.88620i
$325$	−17.0647	+	20.2922i	−0.946581	+	1.12561i
$326$	5.03218	−	8.71598i	0.278706	−	0.482734i
$327$	34.1228	+	3.12378i	1.88700	+	0.172746i
$328$	9.42872	−	5.44367i	0.520614	−	0.300577i
$329$	−6.02134	−	10.4293i	−0.331967	−	0.574984i
$330$	−8.23089	−	11.8699i	−0.453095	−	0.653419i
$331$	0.00838703	−	0.0145268i	0.000460993	−	0.000798463i	−0.865795	−	0.500399i	$-0.833187\pi$
$331$	0.00838703	−	0.0145268i	0.000460993	−	0.000798463i	0.866256	+	0.499601i	$0.166520\pi$
$332$			5.93580i			0.325769i
$333$	−2.97062	+	16.0889i	−0.162789	+	0.881667i
$334$	−26.7500			−1.46370
$335$	−17.7374	−	21.1620i	−0.969100	−	1.15620i
$336$	4.64553	−	2.14353i	0.253434	−	0.116939i
$337$	−1.36437	+	0.787719i	−0.0743220	+	0.0429098i	−0.536700	−	0.843773i	$-0.680329\pi$
$337$	−1.36437	+	0.787719i	−0.0743220	+	0.0429098i	0.462378	+	0.886683i	$0.346996\pi$
$338$	−31.5883	+	18.2375i	−1.71818	+	0.991990i
$339$	15.7751	−	7.27891i	0.856786	−	0.395336i
$340$	0.656254	+	0.782957i	0.0355904	+	0.0424618i
$341$	−14.7446			−0.798467
$342$	21.2730	+	18.1439i	1.15031	+	0.981111i
$343$			1.00000i			0.0539949i
$344$	−5.69043	+	9.85611i	−0.306807	+	0.531406i
$345$	2.09373	+	3.01941i	0.112723	+	0.162560i
$346$	−10.6762	−	18.4917i	−0.573955	−	0.994119i
$347$	8.52635	−	4.92269i	0.457718	−	0.264264i	−0.253366	−	0.967370i	$-0.581538\pi$
$347$	8.52635	−	4.92269i	0.457718	−	0.264264i	0.711084	+	0.703107i	$0.248204\pi$
$348$	−12.3591	−	1.13142i	−0.662518	−	0.0606503i
$349$	−16.4814	+	28.5466i	−0.882229	+	1.52807i	−0.0333729	+	0.999443i	$0.510625\pi$
$349$	−16.4814	+	28.5466i	−0.882229	+	1.52807i	−0.848857	+	0.528623i	$0.822708\pi$
$350$	9.23206	+	7.76372i	0.493475	+	0.414989i
$351$	−26.6991	+	6.80963i	−1.42509	+	0.363471i
$352$			2.56096i			0.136500i
$353$	11.9454	+	6.89669i	0.635791	+	0.367074i	0.782991	−	0.622033i	$-0.213693\pi$
$353$	11.9454	+	6.89669i	0.635791	+	0.367074i	−0.147201	+	0.989107i	$0.547026\pi$
$354$	−3.84630	+	42.0153i	−0.204428	+	2.23309i
$355$	1.53226	+	8.71757i	0.0813240	+	0.462680i
$356$	−18.9029	−	32.7408i	−1.00185	−	1.73526i
$357$	0.119494	−	0.169202i	0.00632429	−	0.00895510i
$358$	−37.5526	−	21.6810i	−1.98472	−	1.14588i
$359$	5.26401			0.277824			0.138912	−	0.990305i	$-0.455640\pi$
$359$	5.26401			0.277824			0.138912	+	0.990305i	$0.455640\pi$
$360$	−29.4574	−	0.253097i	−1.55254	−	0.0133394i
$361$	−4.07623			−0.214538
$362$	−12.3466	−	7.12832i	−0.648923	−	0.374656i
$363$	−6.24815	−	13.5412i	−0.327943	−	0.710730i
$364$	10.1289	+	17.5438i	0.530899	+	0.919545i
$365$	−30.5049	+	5.36175i	−1.59670	+	0.280647i
$366$	49.0824	−	22.6475i	2.56558	−	1.18380i
$367$	−16.8659	−	9.73756i	−0.880395	−	0.508296i	−0.00960636	−	0.999954i	$-0.503058\pi$
$367$	−16.8659	−	9.73756i	−0.880395	−	0.508296i	−0.870789	+	0.491658i	$0.836391\pi$
$368$			2.80232i			0.146081i
$369$	2.48751	+	7.00942i	0.129495	+	0.364896i
$370$	−27.6402	−	10.0772i	−1.43694	−	0.523889i
$371$	4.64266	−	8.04131i	0.241035	−	0.417484i
$372$	−36.4065	+	51.5510i	−1.88759	+	2.67280i
$373$	19.9237	−	11.5029i	1.03161	−	0.595599i	0.114163	−	0.993462i	$-0.463581\pi$
$373$	19.9237	−	11.5029i	1.03161	−	0.595599i	0.917445	+	0.397863i	$0.130248\pi$
$374$	−0.223015	−	0.386274i	−0.0115318	−	0.0199737i
$375$	−8.08461	−	17.5966i	−0.417488	−	0.908683i
$376$	−26.4421	+	45.7991i	−1.36365	+	2.36191i
$377$		−	9.94596i		−	0.512243i
$378$	3.09809	+	12.1470i	0.159349	+	0.624772i
$379$	24.7091			1.26922			0.634611	−	0.772832i	$-0.281161\pi$
$379$	24.7091			1.26922			0.634611	+	0.772832i	$0.281161\pi$
$380$	−25.2912	+	21.1984i	−1.29741	+	1.08745i
$381$	0.270338	−	2.95305i	0.0138498	−	0.151289i
$382$	−27.7420	+	16.0169i	−1.41941	+	0.819494i
$383$	1.89259	−	1.09269i	0.0967068	−	0.0558337i	−0.450867	−	0.892591i	$-0.648885\pi$
$383$	1.89259	−	1.09269i	0.0967068	−	0.0558337i	0.547573	+	0.836758i	$0.315552\pi$
$384$	29.1182	+	20.5639i	1.48593	+	1.04940i
$385$	−2.22053	−	2.64924i	−0.113169	−	0.135018i
$386$	−17.4965			−0.890550
$387$	−5.91547	−	5.04536i	−0.300700	−	0.256470i
$388$			19.9328i			1.01193i
$389$	2.99857	−	5.19367i	0.152033	−	0.263330i	−0.779941	−	0.625852i	$-0.784751\pi$
$389$	2.99857	−	5.19367i	0.152033	−	0.263330i	0.931975	+	0.362523i	$0.118085\pi$
$390$	−4.09282	−	49.3776i	−0.207248	−	2.50033i
$391$	0.0567294	+	0.0982583i	0.00286893	+	0.00496913i
$392$	3.80307	−	2.19570i	0.192084	−	0.110900i
$393$	−2.65746	−	5.75935i	−0.134051	−	0.290521i
$394$	−7.66712	+	13.2798i	−0.386264	+	0.669028i
$395$	11.5252	+	4.20193i	0.579898	+	0.211422i
$396$	17.4229	+	3.21692i	0.875532	+	0.161656i
$397$			10.4576i			0.524852i	0.964952	+	0.262426i	$0.0845225\pi$
$397$			10.4576i			0.524852i	−0.964952	+	0.262426i	$0.915478\pi$
$398$	−26.1567	−	15.1016i	−1.31112	−	0.756975i
$399$	5.46557	+	3.85991i	0.273621	+	0.193237i
$400$	2.58045	−	14.5421i	0.129022	−	0.727103i
$401$	−7.19922	−	12.4694i	−0.359512	−	0.622693i	0.628367	−	0.777917i	$-0.283724\pi$
$401$	−7.19922	−	12.4694i	−0.359512	−	0.622693i	−0.987879	+	0.155224i	$0.950390\pi$
$402$	51.3853	+	4.70408i	2.56287	+	0.234618i
$403$	−43.8006	−	25.2883i	−2.18186	−	1.25970i
$404$	54.9524			2.73398
$405$	3.82390	−	19.7580i	0.190011	−	0.981782i
$406$	−4.52499			−0.224571
$407$	7.30131	+	4.21541i	0.361913	+	0.208950i
$408$	−0.905859	−	0.0829270i	−0.0448467	−	0.00410550i
$409$	−12.6156	−	21.8508i	−0.623801	−	1.08045i	−0.988771	−	0.149436i	$-0.952254\pi$
$409$	−12.6156	−	21.8508i	−0.623801	−	1.08045i	0.364971	−	0.931019i	$-0.381079\pi$
$410$	−13.1725	+	2.31529i	−0.650542	+	0.114344i
$411$	−0.351765	−	0.248424i	−0.0173513	−	0.0122539i
$412$	−30.0247	−	17.3348i	−1.47921	−	0.854023i
$413$			10.0969i			0.496835i
$414$	−6.75216	−	1.24671i	−0.331851	−	0.0612722i
$415$	1.19007	−	3.26416i	0.0584180	−	0.160231i
$416$	−4.39226	+	7.60761i	−0.215348	+	0.372994i
$417$	8.62936	+	18.7018i	0.422581	+	0.915833i
$418$	12.4775	−	7.20387i	0.610293	−	0.352353i
$419$	7.70993	+	13.3540i	0.376655	+	0.652386i	0.990573	−	0.136984i	$-0.0437409\pi$
$419$	7.70993	+	13.3540i	0.376655	+	0.652386i	−0.613918	+	0.789370i	$0.710408\pi$
$420$	−14.7452	+	1.22220i	−0.719493	+	0.0596374i
$421$	−5.54687	+	9.60746i	−0.270338	+	0.468239i	−0.968948	−	0.247263i	$-0.920469\pi$
$421$	−5.54687	+	9.60746i	−0.270338	+	0.468239i	0.698611	+	0.715502i	$0.253802\pi$
$422$			23.9714i			1.16691i
$423$	−27.4879	−	23.4447i	−1.33651	−	1.13992i
$424$	−40.7756			−1.98024
$425$	−0.203907	−	0.562129i	−0.00989093	−	0.0272672i
$426$	−13.5109	−	9.54170i	−0.654606	−	0.462297i
$427$	11.2031	−	6.46811i	0.542156	−	0.313014i
$428$	−41.3935	+	23.8985i	−2.00083	+	1.15518i
$429$	−1.29440	+	14.1395i	−0.0624944	+	0.682662i
$430$	10.7147	−	8.98077i	0.516708	−	0.433091i
$431$	−2.28735			−0.110178			−0.0550889	−	0.998481i	$-0.517544\pi$
$431$	−2.28735			−0.110178			−0.0550889	+	0.998481i	$0.517544\pi$
$432$	10.9834	−	10.7213i	0.528437	−	0.515829i
$433$			17.7079i			0.850985i	0.904962	+	0.425493i	$0.139899\pi$
$433$			17.7079i			0.850985i	−0.904962	+	0.425493i	$0.860101\pi$
$434$	−11.5051	+	19.9274i	−0.552262	+	0.956545i
$435$	6.56957	+	3.10005i	0.314987	+	0.148636i
$436$	−37.7884	−	65.4515i	−1.80974	−	3.13456i
$437$	−3.17395	+	1.83248i	−0.151831	+	0.0876594i
$438$	33.3887	−	47.2779i	1.59537	−	2.25903i
$439$	1.67033	−	2.89310i	0.0797206	−	0.138080i	−0.823409	−	0.567449i	$-0.807931\pi$
$439$	1.67033	−	2.89310i	0.0797206	−	0.138080i	0.903129	+	0.429369i	$0.141264\pi$
$440$	−5.19964	+	14.2618i	−0.247883	+	0.679904i
$441$	1.00334	+	2.82724i	0.0477780	+	0.134631i
$442$		−	1.52996i		−	0.0727727i
$443$	14.3225	+	8.26909i	0.680482	+	0.392876i	0.800036	−	0.599951i	$-0.204813\pi$
$443$	14.3225	+	8.26909i	0.680482	+	0.392876i	−0.119555	+	0.992828i	$0.538147\pi$
$444$	32.7661	−	15.1188i	1.55501	−	0.717508i
$445$	3.83073	+	21.7944i	0.181594	+	1.03315i
$446$	18.8650	+	32.6751i	0.893284	+	1.54721i
$447$	2.14572	+	4.65028i	0.101489	+	0.219951i
$448$	8.57735	+	4.95213i	0.405242	+	0.233966i
$449$	5.77859			0.272708			0.136354	−	0.990660i	$-0.456461\pi$
$449$	5.77859			0.272708			0.136354	+	0.990660i	$0.456461\pi$
$450$	33.8909	+	12.6871i	1.59763	+	0.598074i
$451$	3.83269			0.180474
$452$	−33.1855	−	19.1597i	−1.56091	−	0.901194i
$453$	8.24632	−	11.6767i	0.387446	−	0.548618i
$454$	24.9929	+	43.2891i	1.17298	+	2.03166i
$455$	−2.05265	−	11.6783i	−0.0962299	−	0.547486i
$456$	2.67872	−	29.2611i	0.125442	−	1.37028i
$457$	−17.0344	−	9.83480i	−0.796834	−	0.460053i	0.0455286	−	0.998963i	$-0.485503\pi$
$457$	−17.0344	−	9.83480i	−0.796834	−	0.460053i	−0.842363	+	0.538910i	$0.818836\pi$
$458$			6.25654i			0.292349i
$459$	0.168072	−	0.598267i	0.00784494	−	0.0279247i
$460$	2.77592	−	7.61391i	0.129428	−	0.355000i
$461$	1.40062	−	2.42594i	0.0652332	−	0.112987i	−0.831564	−	0.555429i	$-0.812554\pi$
$461$	1.40062	−	2.42594i	0.0652332	−	0.112987i	0.896797	+	0.442441i	$0.145888\pi$
$462$	6.43287	+	0.588899i	0.299284	+	0.0273980i
$463$	5.36641	−	3.09830i	0.249398	−	0.143990i	−0.370091	−	0.928996i	$-0.620673\pi$
$463$	5.36641	−	3.09830i	0.249398	−	0.143990i	0.619489	+	0.785006i	$0.287340\pi$
$464$	2.77015	+	4.79805i	0.128601	+	0.222744i
$465$	30.3558	−	21.0494i	1.40771	−	0.976141i
$466$	19.8472	−	34.3763i	0.919403	−	1.59245i
$467$		−	0.404744i		−	0.0187293i	−0.999956	−	0.00936466i	$-0.997019\pi$
$467$		−	0.404744i		−	0.0187293i	0.999956	−	0.00936466i	$-0.00298091\pi$
$468$	46.2393	+	39.4379i	2.13741	+	1.82302i
$469$	12.3487			0.570208
$470$	49.7887	−	41.7316i	2.29658	−	1.92494i
$471$	−26.5334	+	12.2430i	−1.22260	+	0.564127i
$472$	38.3992	−	22.1698i	1.76746	−	1.02045i
$473$	−3.46966	+	2.00321i	−0.159535	+	0.0921078i
$474$	−20.8153	+	9.60455i	−0.956079	+	0.441152i
$475$	18.1579	−	6.58662i	0.833143	−	0.302215i
$476$	−0.456879			−0.0209410
$477$	5.05777	−	27.3929i	0.231579	−	1.25424i
$478$		−	1.49936i		−	0.0685789i
$479$	−0.237048	+	0.410579i	−0.0108310	+	0.0187599i	−0.871390	−	0.490591i	$-0.836781\pi$
$479$	−0.237048	+	0.410579i	−0.0108310	+	0.0187599i	0.860559	+	0.509351i	$0.170114\pi$
$480$	−3.65601	−	5.27242i	−0.166873	−	0.240652i
$481$	14.4596	+	25.0447i	0.659300	+	1.14194i
$482$	38.9278	−	22.4750i	1.77311	−	1.02371i
$483$	−1.63636	−	0.149801i	−0.0744569	−	0.00681618i
$484$	−16.4465	+	28.4862i	−0.747568	+	1.29483i
$485$	3.99631	−	10.9613i	0.181463	−	0.497725i
$486$	20.9466	+	31.2340i	0.950155	+	1.41680i
$487$		−	31.8090i		−	1.44140i	−0.693245	−	0.720702i	$-0.743820\pi$
$487$		−	31.8090i		−	1.44140i	0.693245	−	0.720702i	$-0.256180\pi$
$488$	−49.1974	−	28.4041i	−2.22706	−	1.28579i
$489$	0.658717	−	7.19554i	0.0297882	−	0.325393i
$490$	−5.31311	+	0.933870i	−0.240022	+	0.0421880i
$491$	−1.04351	−	1.80740i	−0.0470927	−	0.0815670i	0.841518	−	0.540229i	$-0.181662\pi$
$491$	−1.04351	−	1.80740i	−0.0470927	−	0.0815670i	−0.888611	+	0.458662i	$0.848329\pi$
$492$	9.46342	−	13.4001i	0.426644	−	0.604122i
$493$	0.194261	+	0.112157i	0.00874907	+	0.00505128i
$494$	49.4209			2.22355
$495$	−8.93607	−	5.26212i	−0.401646	−	0.236515i
$496$	28.1732			1.26501
$497$	−3.42806	−	1.97919i	−0.153769	−	0.0887788i
$498$	2.72019	+	5.89529i	0.121895	+	0.264174i
$499$	−15.4523	−	26.7642i	−0.691740	−	1.19813i	−0.971267	−	0.237991i	$-0.923511\pi$
$499$	−15.4523	−	26.7642i	−0.691740	−	1.19813i	0.279528	−	0.960138i	$-0.409822\pi$
$500$	−21.4161	+	36.9546i	−0.957758	+	1.65266i
$501$	−17.4381	+	8.04626i	−0.779079	+	0.359480i
$502$	−54.3754	−	31.3937i	−2.42689	−	1.40117i
$503$		−	5.33051i		−	0.237676i	−0.992914	−	0.118838i	$-0.962083\pi$
$503$		−	5.33051i		−	0.237676i	0.992914	−	0.118838i	$-0.0379169\pi$
$504$	8.54918	−	10.0236i	0.380811	−	0.446485i
$505$	−30.2189	−	11.0174i	−1.34472	−	0.490267i
$506$	−1.76912	+	3.06420i	−0.0786468	+	0.136220i
$507$	−15.1064	+	21.3905i	−0.670900	+	0.949985i
$508$	−5.66429	+	3.27028i	−0.251312	+	0.145095i
$509$	3.11555	+	5.39629i	0.138094	+	0.239186i	0.926775	−	0.375616i	$-0.122569\pi$
$509$	3.11555	+	5.39629i	0.138094	+	0.239186i	−0.788681	+	0.614803i	$0.789236\pi$
$510$	1.01058	+	0.476872i	0.0447492	+	0.0211163i
$511$	6.92566	−	11.9956i	0.306373	−	0.530654i
$512$		−	30.8364i		−	1.36279i
$513$	19.3253	+	5.42909i	0.853232	+	0.239700i
$514$	6.33128			0.279261
$515$	13.0355	+	15.5522i	0.574411	+	0.685312i
$516$	−1.56332	+	17.0770i	−0.0688214	+	0.751774i
$517$	−16.1227	+	9.30847i	−0.709078	+	0.409386i
$518$	11.3943	−	6.57849i	0.500636	−	0.289042i
$519$	−12.5219	−	8.84325i	−0.549651	−	0.388176i
$520$	−39.9062	+	33.4484i	−1.75000	+	1.46681i
$521$	13.8782			0.608016			0.304008	−	0.952670i	$-0.401675\pi$
$521$	13.8782			0.608016			0.304008	+	0.952670i	$0.401675\pi$
$522$	−12.7932	+	4.54009i	−0.559945	+	0.198714i
$523$		−	6.40689i		−	0.280154i	−0.990141	−	0.140077i	$-0.955265\pi$
$523$		−	6.40689i		−	0.280154i	0.990141	−	0.140077i	$-0.0447349\pi$
$524$	−6.99501	+	12.1157i	−0.305579	+	0.529278i
$525$	8.35360	+	2.28416i	0.364581	+	0.0996889i
$526$	−20.8364	−	36.0897i	−0.908510	−	1.57358i
$527$	0.987843	−	0.570331i	0.0430311	−	0.0248440i
$528$	−3.31371	−	7.18158i	−0.144211	−	0.312538i
$529$	−11.0500	+	19.1391i	−0.480434	+	0.832136i
$530$	47.0600	+	17.1574i	2.04416	+	0.745270i
$531$	10.1306	+	28.5464i	0.439630	+	1.23881i
$532$		−	14.7581i		−	0.639847i
$533$	11.3854	+	6.57338i	0.493158	+	0.284725i
$534$	−33.7780	−	23.8548i	−1.46172	−	1.03230i
$535$	27.5541	−	4.84311i	1.19127	−	0.209386i
$536$	−27.1140	−	46.9628i	−1.17115	−	2.02848i
$537$	−31.0018	−	2.83807i	−1.33783	−	0.122472i
$538$	37.0480	+	21.3897i	1.59725	+	0.922175i
$539$	1.54591			0.0665872
$540$	−40.4621	+	18.2499i	−1.74121	+	0.785351i
$541$	16.8193			0.723120			0.361560	−	0.932349i	$-0.382244\pi$
$541$	16.8193			0.723120			0.361560	+	0.932349i	$0.382244\pi$
$542$	−18.8708	−	10.8951i	−0.810571	−	0.467984i
$543$	−10.1928	−	0.933104i	−0.437416	−	0.0400433i
$544$	−0.0990594	−	0.171576i	−0.00424714	−	0.00735626i
$545$	7.65794	+	43.5687i	0.328030	+	1.86628i
$546$	18.0995	+	12.7823i	0.774589	+	0.547032i
$547$	−1.33794	−	0.772461i	−0.0572063	−	0.0330281i	0.471124	−	0.882067i	$-0.343848\pi$
$547$	−1.33794	−	0.772461i	−0.0572063	−	0.0330281i	−0.528330	+	0.849039i	$0.677182\pi$
$548$			0.949837i			0.0405750i
$549$	25.1842	−	29.5274i	1.07484	−	1.26020i
$550$	12.0021	−	14.2720i	0.511769	−	0.608559i
$551$	−3.62289	+	6.27503i	−0.154340	+	0.267325i
$552$	3.02325	+	6.55210i	0.128678	+	0.278876i
$553$	−4.75112	+	2.74306i	−0.202038	+	0.116647i
$554$	−17.3402	−	30.0342i	−0.736716	−	1.27603i
$555$	−21.0496	+	1.74476i	−0.893506	+	0.0740609i
$556$	22.7143	−	39.3424i	0.963302	−	1.66849i
$557$		−	9.22101i		−	0.390707i	−0.980733	−	0.195353i	$-0.937415\pi$
$557$		−	9.22101i		−	0.390707i	0.980733	−	0.195353i	$-0.0625854\pi$
$558$	−12.5338	+	67.8831i	−0.530598	+	2.87372i
$559$	−13.7427			−0.581254
$560$	4.24286	+	5.06203i	0.179294	+	0.213910i
$561$	−0.261571	−	0.184727i	−0.0110435	−	0.00779919i
$562$	−58.2049	+	33.6046i	−2.45523	+	1.41753i
$563$	16.4126	−	9.47581i	0.691708	−	0.399358i	−0.112544	−	0.993647i	$-0.535900\pi$
$563$	16.4126	−	9.47581i	0.691708	−	0.399358i	0.804252	+	0.594289i	$0.202566\pi$
$564$	−7.26440	+	79.3531i	−0.305886	+	3.34137i
$565$	14.4078	+	17.1894i	0.606139	+	0.723165i
$566$	30.2848			1.27296
$567$	5.67336	+	6.98663i	0.238259	+	0.293411i
$568$			17.3828i			0.729368i
$569$	−1.74156	+	3.01646i	−0.0730098	+	0.126457i	−0.900219	−	0.435437i	$-0.856594\pi$
$569$	−1.74156	+	3.01646i	−0.0730098	+	0.126457i	0.827209	+	0.561894i	$0.189927\pi$
$570$	−15.4040	+	32.6438i	−0.645202	+	1.36730i
$571$	−0.916022	−	1.58660i	−0.0383343	−	0.0663970i	0.846222	−	0.532831i	$-0.178872\pi$
$571$	−0.916022	−	1.58660i	−0.0383343	−	0.0663970i	−0.884556	+	0.466434i	$0.845539\pi$
$572$	27.1212	−	15.6584i	1.13399	−	0.654712i
$573$	−13.2670	+	18.7859i	−0.554238	+	0.784793i
$574$	2.99061	−	5.17989i	0.124826	−	0.216204i
$575$	−3.05302	+	3.63043i	−0.127320	+	0.151399i
$576$	29.2189	+	5.39492i	1.21746	+	0.224788i
$577$			27.2971i			1.13639i	0.822894	+	0.568196i	$0.192358\pi$
$577$			27.2971i			1.13639i	−0.822894	+	0.568196i	$0.807642\pi$
$578$	−35.4883	−	20.4892i	−1.47612	−	0.852237i
$579$	−11.4059	+	5.26286i	−0.474011	+	0.218717i
$580$	−2.77367	−	15.7803i	−0.115170	−	0.655243i
$581$	0.776885	+	1.34560i	0.0322306	+	0.0558251i
$582$	9.13456	+	19.7967i	0.378640	+	0.820601i
$583$	−12.4312	−	7.17715i	−0.514847	−	0.297247i
$584$	−60.8268			−2.51703
$585$	−17.5206	−	30.9578i	−0.724388	−	1.27995i
$586$	−43.9740			−1.81655
$587$	10.0138	+	5.78149i	0.413315	+	0.238628i	0.692213	−	0.721693i	$-0.256636\pi$
$587$	10.0138	+	5.78149i	0.413315	+	0.238628i	−0.278898	+	0.960321i	$0.589969\pi$
$588$	3.81707	−	5.40491i	0.157413	−	0.222895i
$589$	18.4229	+	31.9094i	0.759102	+	1.31480i
$590$	−53.6459	+	9.42918i	−2.20857	+	0.388193i
$591$	−1.00363	+	10.9633i	−0.0412840	+	0.450968i
$592$	−13.9509	−	8.05458i	−0.573380	−	0.331041i
$593$		−	4.75476i		−	0.195255i	−0.995223	−	0.0976273i	$-0.968875\pi$
$593$		−	4.75476i		−	0.195255i	0.995223	−	0.0976273i	$-0.0311253\pi$
$594$	18.7782	−	4.78938i	0.770477	−	0.196511i
$595$	0.251243	+	0.0915994i	0.0102999	+	0.00375521i
$596$	5.64800	−	9.78262i	0.231351	−	0.400712i
$597$	−21.5939	−	1.97682i	−0.883778	−	0.0809057i
$598$	−10.5107	+	6.06836i	−0.429815	+	0.248154i
$599$	20.0466	+	34.7218i	0.819082	+	1.41869i	0.906359	+	0.422508i	$0.138850\pi$
$599$	20.0466	+	34.7218i	0.819082	+	1.41869i	−0.0872767	+	0.996184i	$0.527816\pi$
$600$	−9.65520	−	36.7847i	−0.394172	−	1.50173i
$601$	−12.4892	+	21.6319i	−0.509443	+	0.882382i	0.490497	+	0.871443i	$0.336815\pi$
$601$	−12.4892	+	21.6319i	−0.509443	+	0.882382i	−0.999940	+	0.0109389i	$0.996518\pi$
$602$			6.25234i			0.254826i
$603$	34.9127	−	12.3899i	1.42175	−	0.504555i
$604$	−31.5294			−1.28291
$605$	14.7553	−	12.3675i	0.599888	−	0.502810i
$606$	54.5773	−	25.1829i	2.21705	−	1.02299i
$607$	12.5744	−	7.25983i	0.510379	−	0.294667i	−0.222611	−	0.974907i	$-0.571458\pi$
$607$	12.5744	−	7.25983i	0.510379	−	0.294667i	0.732989	+	0.680240i	$0.238125\pi$
$608$	5.54226	−	3.19983i	0.224769	−	0.129770i
$609$	−2.94980	+	1.36109i	−0.119532	+	0.0551542i
$610$	44.8281	+	53.4830i	1.81504	+	2.16546i
$611$	−63.8592			−2.58347
$612$	−1.29171	+	0.458404i	−0.0522142	+	0.0185299i
$613$			21.5125i			0.868880i	0.900701	+	0.434440i	$0.143054\pi$
$613$			21.5125i			0.868880i	−0.900701	+	0.434440i	$0.856946\pi$
$614$	36.0775	−	62.4881i	1.45597	−	2.52182i
$615$	−7.89061	+	5.47153i	−0.318180	+	0.220633i
$616$	−3.39437	−	5.87922i	−0.136763	−	0.236880i
$617$	8.03363	−	4.63822i	0.323422	−	0.186728i	−0.329495	−	0.944157i	$-0.606878\pi$
$617$	8.03363	−	4.63822i	0.323422	−	0.186728i	0.652917	+	0.757430i	$0.273545\pi$
$618$	−37.7637	−	3.45709i	−1.51908	−	0.139065i
$619$	2.66624	−	4.61805i	0.107165	−	0.185615i	−0.807456	−	0.589928i	$-0.799156\pi$
$619$	2.66624	−	4.61805i	0.107165	−	0.185615i	0.914621	+	0.404313i	$0.132489\pi$
$620$	−76.5466	−	27.9078i	−3.07419	−	1.12080i
$621$	−4.77669	+	1.21830i	−0.191682	+	0.0488886i
$622$		−	22.2284i		−	0.891277i
$623$	−8.57032	−	4.94808i	−0.343363	−	0.198241i
$624$	2.47327	−	27.0170i	0.0990102	−	1.08154i
$625$	19.1860	−	16.0280i	0.767439	−	0.641122i
$626$	−13.8858	−	24.0509i	−0.554988	−	0.961267i
$627$	5.96708	−	8.44930i	0.238302	−	0.337433i
$628$	55.8173	+	32.2262i	2.22735	+	1.28596i
$629$	−0.652219			−0.0260057
$630$	−14.0845	+	7.97113i	−0.561139	+	0.317577i
$631$	27.7499			1.10470			0.552352	−	0.833611i	$-0.313730\pi$
$631$	27.7499			1.10470			0.552352	+	0.833611i	$0.313730\pi$
$632$	20.8641	+	12.0459i	0.829928	+	0.479159i
$633$	7.21045	+	15.6267i	0.286590	+	0.621108i
$634$	−33.2650	−	57.6166i	−1.32112	−	2.28825i
$635$	3.77051	−	0.662731i	0.149628	−	0.0262997i
$636$	−55.7874	+	25.7413i	−2.21211	+	1.02071i
$637$	4.59231	+	2.65137i	0.181954	+	0.105051i
$638$			6.99524i			0.276944i
$639$	−11.6778	−	2.15615i	−0.461965	−	0.0852962i
$640$	−15.7635	+	43.2367i	−0.623106	+	1.70908i
$641$	−21.8099	+	37.7758i	−0.861437	+	1.49205i	0.00910444	+	0.999959i	$0.497102\pi$
$641$	−21.8099	+	37.7758i	−0.861437	+	1.49205i	−0.870542	+	0.492095i	$0.836231\pi$
$642$	−30.1590	+	42.7047i	−1.19028	+	1.68542i
$643$	27.6545	−	15.9663i	1.09059	−	0.629650i	0.156853	−	0.987622i	$-0.449865\pi$
$643$	27.6545	−	15.9663i	1.09059	−	0.629650i	0.933732	+	0.357972i	$0.116532\pi$
$644$	1.81214	+	3.13872i	0.0714085	+	0.123683i
$645$	4.28345	−	9.07742i	0.168661	−	0.357423i
$646$	−0.557300	+	0.965271i	−0.0219267	+	0.0379781i
$647$			16.1251i			0.633941i	0.948435	+	0.316971i	$0.102666\pi$
$647$			16.1251i			0.633941i	−0.948435	+	0.316971i	$0.897334\pi$
$648$	14.1136	−	36.9167i	0.554435	−	1.45023i
$649$	15.6089			0.612704
$650$	60.1310	−	21.8120i	2.35853	−	0.855536i
$651$	−1.50603	+	16.4512i	−0.0590259	+	0.644773i
$652$	−13.8019	+	7.96851i	−0.540523	+	0.312071i
$653$	18.1194	−	10.4612i	0.709065	−	0.409379i	−0.101649	−	0.994820i	$-0.532412\pi$
$653$	18.1194	−	10.4612i	0.709065	−	0.409379i	0.810715	+	0.585441i	$0.199079\pi$
$654$	−67.5249	−	47.6875i	−2.64043	−	1.86473i
$655$	6.27571	−	5.26014i	0.245212	−	0.205531i
$656$	−7.32329			−0.285926
$657$	7.54491	−	40.8633i	0.294355	−	1.59423i
$658$			29.0532i			1.13261i
$659$	7.75751	−	13.4364i	0.302190	−	0.523408i	−0.674442	−	0.738328i	$-0.735616\pi$
$659$	7.75751	−	13.4364i	0.302190	−	0.523408i	0.976632	+	0.214920i	$0.0689491\pi$
$660$	1.88942	+	22.7948i	0.0735456	+	0.887288i
$661$	7.95891	+	13.7852i	0.309566	+	0.536184i	0.978267	−	0.207347i	$-0.0664829\pi$
$661$	7.95891	+	13.7852i	0.309566	+	0.536184i	−0.668702	+	0.743531i	$0.733150\pi$
$662$	−0.0350461	+	0.0202339i	−0.00136211	+	0.000786412i
$663$	−0.460203	−	0.997369i	−0.0178728	−	0.0387346i
$664$	3.41162	−	5.90909i	0.132396	−	0.229317i
$665$	−2.95885	+	8.11567i	−0.114739	+	0.314712i
$666$	25.6140	−	30.0313i	0.992521	−	1.16369i
$667$		−	1.77941i		−	0.0688991i
$668$	36.6840	+	21.1795i	1.41934	+	0.819459i
$669$	22.1265	+	15.6262i	0.855458	+	0.604144i
$670$	11.5320	+	65.6098i	0.445522	+	2.53473i
$671$	−9.99915	−	17.3190i	−0.386013	−	0.668594i
$672$	2.85736	+	0.261578i	0.110225	+	0.0100906i
$673$	2.38399	+	1.37640i	0.0918962	+	0.0530563i	0.545244	−	0.838277i	$-0.316437\pi$
$673$	2.38399	+	1.37640i	0.0918962	+	0.0530563i	−0.453348	+	0.891334i	$0.649770\pi$
$674$	3.80078			0.146401
$675$	25.9095	−	1.92360i	0.997255	−	0.0740394i
$676$	57.7587			2.22149
$677$	−35.7539	−	20.6425i	−1.37413	−	0.793357i	−0.382689	−	0.923877i	$-0.625002\pi$
$677$	−35.7539	−	20.6425i	−1.37413	−	0.793357i	−0.991446	+	0.130520i	$0.958335\pi$
$678$	−41.7392	−	3.82103i	−1.60299	−	0.146746i
$679$	2.60883	+	4.51862i	0.100118	+	0.173409i
$680$	−0.203295	−	1.15662i	−0.00779602	−	0.0443543i
$681$	29.3138	+	20.7021i	1.12331	+	0.793305i
$682$	30.8060	+	17.7859i	1.17962	+	0.681056i
$683$			12.6392i			0.483625i	0.970323	+	0.241813i	$0.0777419\pi$
$683$			12.6392i			0.483625i	−0.970323	+	0.241813i	$0.922258\pi$
$684$	−14.8074	−	41.7249i	−0.566175	−	1.59539i
$685$	0.190432	−	0.522326i	0.00727604	−	0.0199570i
$686$	1.20626	−	2.08930i	0.0460552	−	0.0797700i
$687$	1.88193	+	4.07859i	0.0718003	+	0.155608i
$688$	6.62964	−	3.82762i	0.252753	−	0.145927i
$689$	−24.6188	−	42.6410i	−0.937901	−	1.62449i
$690$	−0.732238	−	8.83405i	−0.0278758	−	0.336307i
$691$	−7.41057	+	12.8355i	−0.281911	+	0.488285i	−0.971855	−	0.235578i	$-0.924302\pi$
$691$	−7.41057	+	12.8355i	−0.281911	+	0.488285i	0.689944	+	0.723863i	$0.257635\pi$
$692$			33.8117i			1.28533i
$693$	4.37068	−	1.55107i	0.166028	−	0.0589204i
$694$	−23.7522			−0.901620
$695$	−20.3786	+	17.0808i	−0.773004	+	0.647912i
$696$	11.6532	+	8.22976i	0.441714	+	0.311948i
$697$	−0.256778	+	0.148251i	−0.00972615	+	0.00561540i
$698$	68.8693	−	39.7617i	2.60674	−	1.50500i
$699$	2.59802	−	28.3796i	0.0982660	−	1.07341i
$700$	−6.51352	−	17.9564i	−0.246188	−	0.678689i
$701$	−43.4728			−1.64194			−0.820972	−	0.570969i	$-0.806568\pi$
$701$	−43.4728			−1.64194			−0.820972	+	0.570969i	$0.806568\pi$
$702$	63.9968	+	17.9787i	2.41540	+	0.678563i
$703$		−	21.0680i		−	0.794596i
$704$	7.65557	−	13.2598i	0.288530	−	0.499749i
$705$	19.9042	−	42.1807i	0.749637	−	1.58862i
$706$	−16.6384	−	28.8186i	−0.626195	−	1.08460i
$707$	12.4573	−	7.19224i	0.468506	−	0.270492i
$708$	38.5405	−	54.5728i	1.44844	−	2.05097i
$709$	17.9868	−	31.1541i	0.675510	−	1.17002i	−0.300810	−	0.953684i	$-0.597257\pi$
$709$	17.9868	−	31.1541i	0.675510	−	1.17002i	0.976320	−	0.216333i	$-0.0694097\pi$
$710$	7.31430	−	20.0620i	0.274501	−	0.752912i
$711$	−10.6804	+	12.5223i	−0.400545	+	0.469622i
$712$			43.4580i			1.62866i
$713$	−7.83627	−	4.52427i	−0.293471	−	0.169435i
$714$	−0.453760	+	0.209373i	−0.0169816	+	0.00783558i
$715$	−18.0536	+	3.17323i	−0.675166	+	0.118672i
$716$	34.3322	+	59.4651i	1.28305	+	2.22231i
$717$	−0.450998	−	0.977419i	−0.0168428	−	0.0365024i
$718$	−10.9981	−	6.34976i	−0.410446	−	0.236971i
$719$	14.0091			0.522452			0.261226	−	0.965278i	$-0.415873\pi$
$719$	14.0091			0.522452			0.261226	+	0.965278i	$0.415873\pi$
$720$	17.0745	+	10.0546i	0.636330	+	0.374712i
$721$	−9.07518			−0.337977
$722$	8.51648	+	4.91699i	0.316951	+	0.182992i
$723$	18.6164	−	26.3605i	0.692351	−	0.980359i
$724$	11.2878	+	19.5510i	0.419507	+	0.726607i
$725$	−1.63853	+	9.23388i	−0.0608533	+	0.342938i
$726$	−3.27994	+	35.8286i	−0.121730	+	1.32973i
$727$	14.7661	+	8.52524i	0.547646	+	0.316184i	0.748172	−	0.663505i	$-0.230932\pi$
$727$	14.7661	+	8.52524i	0.547646	+	0.316184i	−0.200526	+	0.979688i	$0.564265\pi$
$728$		−	23.2865i		−	0.863055i
$729$	23.0499	+	14.0606i	0.853701	+	0.520763i
$730$	70.2017	+	25.5945i	2.59828	+	0.947295i
$731$	0.154971	−	0.268417i	0.00573180	−	0.00992777i
$732$	−85.2410	−	7.80341i	−3.15060	−	0.288422i
$733$	−9.16171	+	5.28951i	−0.338395	+	0.195373i	−0.659562	−	0.751650i	$-0.729258\pi$
$733$	−9.16171	+	5.28951i	−0.338395	+	0.195373i	0.321167	+	0.947023i	$0.395925\pi$
$734$	23.4921	+	40.6894i	0.867108	+	1.50187i
$735$	−3.18268	+	2.20694i	−0.117395	+	0.0814041i
$736$	−0.785810	+	1.36106i	−0.0289653	+	0.0501694i
$737$		−	19.0900i		−	0.703188i
$738$	3.25801	−	17.6454i	0.119929	−	0.649536i
$739$	−18.5498			−0.682365			−0.341182	−	0.939997i	$-0.610827\pi$
$739$	−18.5498			−0.682365			−0.341182	+	0.939997i	$0.610827\pi$
$740$	29.9260	+	35.7038i	1.10010	+	1.31250i
$741$	32.2171	−	14.8655i	1.18353	−	0.546099i
$742$	−19.3998	+	11.2005i	−0.712190	+	0.411183i
$743$	−9.11146	+	5.26051i	−0.334267	+	0.192989i	−0.657734	−	0.753250i	$-0.728485\pi$
$743$	−9.11146	+	5.26051i	−0.334267	+	0.192989i	0.323467	+	0.946239i	$0.395152\pi$
$744$	65.8718	−	30.3944i	2.41498	−	1.11431i
$745$	−5.06721	+	4.24720i	−0.185648	+	0.155606i
$746$	−55.5021			−2.03208
$747$	3.54654	+	3.02487i	0.129761	+	0.110674i
$748$			0.706295i			0.0258247i
$749$	−6.25574	+	10.8353i	−0.228580	+	0.395912i
$750$	−4.33482	+	46.5167i	−0.158285	+	1.69855i
$751$	16.1856	+	28.0343i	0.590622	+	1.02299i	0.994149	+	0.108019i	$0.0344509\pi$
$751$	16.1856	+	28.0343i	0.590622	+	1.02299i	−0.403527	+	0.914968i	$0.632216\pi$
$752$	30.8064	−	17.7861i	1.12340	−	0.648592i
$753$	−44.8900	−	4.10946i	−1.63588	−	0.149757i
$754$	−11.9974	+	20.7801i	−0.436920	+	0.756768i
$755$	17.3384	+	6.32131i	0.631007	+	0.230056i
$756$	5.36883	−	19.1108i	0.195263	−	0.695054i
$757$			12.2052i			0.443606i	0.975091	+	0.221803i	$0.0711942\pi$
$757$			12.2052i			0.443606i	−0.975091	+	0.221803i	$0.928806\pi$
$758$	−51.6248	−	29.8056i	−1.87510	−	1.08259i
$759$	−0.231579	+	2.52967i	−0.00840579	+	0.0918212i
$760$	37.3612	−	6.56687i	1.35523	−	0.238205i
$761$	−9.33925	−	16.1761i	−0.338548	−	0.586382i	0.645612	−	0.763665i	$-0.276602\pi$
$761$	−9.33925	−	16.1761i	−0.338548	−	0.586382i	−0.984160	+	0.177284i	$0.943269\pi$
$762$	−4.12696	+	5.84372i	−0.149504	+	0.211696i
$763$	−17.1328	−	9.89160i	−0.620247	−	0.358100i
$764$	50.7258			1.83519
$765$	0.802230	+	0.00689275i	0.0290047	+	0.000249208i
$766$	−5.27226			−0.190495
$767$	46.3680	+	26.7706i	1.67425	+	0.966630i
$768$	−21.6568	−	46.9353i	−0.781471	−	1.69363i
$769$	1.19205	+	2.06469i	0.0429863	+	0.0744545i	0.886718	−	0.462311i	$-0.152979\pi$
$769$	1.19205	+	2.06469i	0.0429863	+	0.0744545i	−0.843732	+	0.536765i	$0.819646\pi$
$770$	1.44368	+	8.21362i	0.0520267	+	0.295998i
$771$	4.12731	−	1.90441i	0.148641	−	0.0685858i
$772$	23.9941	+	13.8530i	0.863566	+	0.498580i
$773$			37.0954i			1.33423i	0.744956	+	0.667114i	$0.232471\pi$
$773$			37.0954i			1.33423i	−0.744956	+	0.667114i	$0.767529\pi$
$774$	6.27321	+	17.6769i	0.225486	+	0.635383i
$775$	36.4986	+	30.6936i	1.31107	+	1.10255i
$776$	11.4564	−	19.8431i	0.411262	−	0.712326i
$777$	5.44907	−	7.71580i	0.195484	−	0.276803i
$778$	−12.5298	+	7.23410i	−0.449216	+	0.259355i
$779$	−4.78881	−	8.29447i	−0.171577	−	0.297180i
$780$	−33.4823	+	70.9551i	−1.19886	+	2.54060i
$781$	−3.05966	+	5.29948i	−0.109483	+	0.189630i
$782$		−	0.273722i		−	0.00978828i
$783$	−6.97418	+	6.80779i	−0.249237	+	0.243290i
$784$	−2.95385			−0.105494
$785$	−24.2336	−	28.9123i	−0.864933	−	1.03192i
$786$	−1.39502	+	15.2386i	−0.0497588	+	0.543544i
$787$	−20.3576	+	11.7535i	−0.725672	+	0.418967i	−0.816837	−	0.576869i	$-0.804274\pi$
$787$	−20.3576	+	11.7535i	−0.725672	+	0.418967i	0.0911650	+	0.995836i	$0.470941\pi$
$788$	21.0288	−	12.1410i	0.749119	−	0.432504i
$789$	−24.4387	−	17.2591i	−0.870039	−	0.614441i
$790$	−19.0111	−	22.6816i	−0.676385	−	0.806973i
$791$	−10.0306			−0.356646
$792$	−15.4955	−	13.2163i	−0.550610	−	0.469620i
$793$		−	68.5975i		−	2.43597i
$794$	12.6146	−	21.8491i	0.447675	−	0.775395i
$795$	35.8389	−	2.97062i	1.27108	−	0.105357i
$796$	23.9136	+	41.4195i	0.847594	+	1.46808i
$797$	17.5130	−	10.1111i	0.620341	−	0.358154i	−0.156661	−	0.987652i	$-0.550073\pi$
$797$	17.5130	−	10.1111i	0.620341	−	0.358154i	0.777002	+	0.629499i	$0.216740\pi$
$798$	−6.76319	−	14.6574i	−0.239414	−	0.518867i
$799$	0.720114	−	1.24727i	0.0254758	−	0.0441254i
$800$	5.33109	−	6.33935i	0.188483	−	0.224130i
$801$	−29.1950	−	5.39050i	−1.03155	−	0.190464i
$802$			34.7366i			1.22659i
$803$	−18.5442	−	10.7065i	−0.654410	−	0.377824i
$804$	−66.7434	−	47.1356i	−2.35386	−	1.66235i
$805$	−0.367236	−	2.08934i	−0.0129434	−	0.0736394i
$806$	61.0085	+	105.670i	2.14893	+	3.72206i
$807$	30.5852	+	2.79993i	1.07665	+	0.0985623i
$808$	−54.7052	−	31.5840i	−1.92452	−	1.11112i
$809$	−32.0104			−1.12543			−0.562713	−	0.826652i	$-0.690242\pi$
$809$	−32.0104			−1.12543			−0.562713	+	0.826652i	$0.690242\pi$
$810$	−31.8226	+	36.6678i	−1.11813	+	1.28838i
$811$	−46.4283			−1.63032			−0.815159	−	0.579238i	$-0.803350\pi$
$811$	−46.4283			−1.63032			−0.815159	+	0.579238i	$0.803350\pi$
$812$	6.20539	+	3.58269i	0.217767	+	0.125728i
$813$	−15.5789	−	1.42618i	−0.546377	−	0.0500182i
$814$	−10.1698	−	17.6146i	−0.356450	−	0.617390i
$815$	9.18740	−	1.61484i	0.321821	−	0.0565655i
$816$	0.499795	+	0.352966i	0.0174963	+	0.0123563i
$817$	8.67045	+	5.00588i	0.303340	+	0.175134i
$818$			60.8707i			2.12830i
$819$	15.6438	+	2.88844i	0.546639	+	0.100930i
$820$	19.8974	+	7.25429i	0.694847	+	0.253331i
$821$	12.1846	−	21.1044i	0.425246	−	0.736547i	−0.571198	−	0.820812i	$-0.693521\pi$
$821$	12.1846	−	21.1044i	0.425246	−	0.736547i	0.996443	+	0.0842655i	$0.0268544\pi$
$822$	0.435280	+	0.943354i	0.0151821	+	0.0329032i
$823$	26.6381	−	15.3795i	0.928544	−	0.536095i	0.0421935	−	0.999109i	$-0.486565\pi$
$823$	26.6381	−	15.3795i	0.928544	−	0.536095i	0.886351	+	0.463014i	$0.153232\pi$
$824$	19.9264	+	34.5136i	0.694169	+	1.20234i
$825$	3.53111	−	12.9139i	0.122938	−	0.449606i
$826$	12.1795	−	21.0955i	0.423778	−	0.734005i
$827$		−	49.8329i		−	1.73286i	−0.499300	−	0.866429i	$-0.666409\pi$
$827$		−	49.8329i		−	1.73286i	0.499300	−	0.866429i	$-0.333591\pi$
$828$	8.27257	+	7.05575i	0.287492	+	0.245204i
$829$	−4.74199			−0.164696			−0.0823481	−	0.996604i	$-0.526242\pi$
$829$	−4.74199			−0.164696			−0.0823481	+	0.996604i	$0.526242\pi$
$830$	−6.42384	+	5.38430i	−0.222975	+	0.186892i
$831$	−20.3381	−	14.3632i	−0.705520	−	0.498254i
$832$	45.4835	−	26.2599i	1.57686	−	0.910398i
$833$	−0.103571	+	0.0597969i	−0.00358853	+	0.00207184i
$834$	4.52994	−	49.4831i	0.156859	−	1.71346i
$835$	−15.9266	−	19.0016i	−0.551164	−	0.657577i
$836$	−22.8148			−0.789067
$837$	12.2482	+	48.0226i	0.423359	+	1.65990i
$838$		−	37.2008i		−	1.28508i
$839$	−14.4239	+	24.9828i	−0.497967	+	0.862504i	−0.999997	−	0.00234629i	$-0.999253\pi$
$839$	−14.4239	+	24.9828i	−0.497967	+	0.862504i	0.502031	+	0.864850i	$0.332586\pi$
$840$	15.3813	+	7.25815i	0.530707	+	0.250430i
$841$	12.7410	+	22.0681i	0.439345	+	0.760968i
$842$	23.1782	−	13.3819i	0.798773	−	0.461172i
$843$	−27.8353	+	39.4143i	−0.958697	+	1.35750i
$844$	18.9795	−	32.8734i	0.653300	−	1.13155i
$845$	−31.7621	−	11.5800i	−1.09265	−	0.398364i
$846$	29.1502	+	82.1405i	1.00220	+	2.82405i
$847$			8.61015i			0.295848i
$848$	23.7528	+	13.7137i	0.815674	+	0.470930i
$849$	19.7424	−	9.10949i	0.677558	−	0.312637i
$850$	−0.252050	+	1.42042i	−0.00864524	+	0.0487201i
$851$	2.58693	+	4.48070i	0.0886789	+	0.153596i
$852$	10.9736	+	23.7825i	0.375951	+	0.814774i
$853$	0.958443	+	0.553357i	0.0328165	+	0.0189466i	0.516318	−	0.856397i	$-0.327302\pi$
$853$	0.958443	+	0.553357i	0.0328165	+	0.0189466i	−0.483502	+	0.875343i	$0.660635\pi$
$854$	−31.2089			−1.06795
$855$	−0.222650	+	25.9137i	−0.00761448	+	0.886230i
$856$	54.9430			1.87791
$857$	−17.8522	−	10.3070i	−0.609820	−	0.352080i	0.163075	−	0.986614i	$-0.447859\pi$
$857$	−17.8522	−	10.3070i	−0.609820	−	0.352080i	−0.772895	+	0.634534i	$0.781192\pi$
$858$	19.7603	−	27.9803i	0.674606	−	0.955233i
$859$	−9.62216	−	16.6661i	−0.328304	−	0.568639i	0.653871	−	0.756606i	$-0.273144\pi$
$859$	−9.62216	−	16.6661i	−0.328304	−	0.568639i	−0.982175	+	0.187966i	$0.939810\pi$
$860$	−21.8043	+	3.83248i	−0.743520	+	0.130686i
$861$	0.391474	−	4.27629i	0.0133414	−	0.145735i
$862$	4.77897	+	2.75914i	0.162772	+	0.0939767i
$863$		−	24.3260i		−	0.828068i	−0.910261	−	0.414034i	$-0.864119\pi$
$863$		−	24.3260i		−	0.828068i	0.910261	−	0.414034i	$-0.135881\pi$
$864$	8.34092	−	2.12736i	0.283764	−	0.0723741i
$865$	6.77889	−	18.5934i	0.230489	−	0.632196i
$866$	21.3603	−	36.9971i	0.725852	−	1.25721i
$867$	−29.2976	−	2.68205i	−0.994998	−	0.0910873i
$868$	31.5553	−	18.2184i	1.07106	−	0.618374i
$869$	4.24053	+	7.34482i	0.143850	+	0.249156i
$870$	−9.98636	−	14.4016i	−0.338569	−	0.488259i
$871$	32.7409	−	56.7088i	1.10938	−	1.92151i
$872$			86.8761i			2.94199i
$873$	11.9095	+	10.1577i	0.403076	+	0.343787i
$874$	8.84180			0.299078
$875$	−0.0182165	+	11.1803i	−0.000615830	+	0.377964i
$876$	−83.2206	+	38.3994i	−2.81176	+	1.29740i
$877$	4.06263	−	2.34556i	0.137185	−	0.0792039i	−0.429837	−	0.902907i	$-0.641429\pi$
$877$	4.06263	−	2.34556i	0.137185	−	0.0792039i	0.567022	+	0.823703i	$0.308096\pi$
$878$	−6.97966	+	4.02971i	−0.235552	+	0.135996i
$879$	−28.6663	+	13.2271i	−0.966890	+	0.446140i
$880$	7.82546	−	6.55910i	0.263796	−	0.221107i
$881$	41.8077			1.40854			0.704269	−	0.709934i	$-0.251275\pi$
$881$	41.8077			1.40854			0.704269	+	0.709934i	$0.251275\pi$
$882$	1.31412	−	7.11726i	0.0442486	−	0.239651i
$883$			2.12840i			0.0716262i	0.999359	+	0.0358131i	$0.0114021\pi$
$883$			2.12840i			0.0716262i	−0.999359	+	0.0358131i	$0.988598\pi$
$884$	−1.21135	+	2.09813i	−0.0407423	+	0.0705677i
$885$	−32.1351	+	22.2832i	−1.08021	+	0.749042i
$886$	−19.9493	−	34.5533i	−0.670211	−	1.16084i
$887$	−45.6784	+	26.3724i	−1.53373	+	0.885500i	−0.534545	+	0.845140i	$0.679517\pi$
$887$	−45.6784	+	26.3724i	−1.53373	+	0.885500i	−0.999185	+	0.0403597i	$0.987150\pi$
$888$	−41.3083	−	3.78158i	−1.38621	−	0.126901i
$889$	−0.856036	+	1.48270i	−0.0287105	+	0.0497281i
$890$	18.2861	−	50.1560i	0.612952	−	1.68123i
$891$	10.8007	−	8.77053i	0.361838	−	0.293824i
$892$		−	59.7459i		−	2.00044i
$893$	40.2896	+	23.2612i	1.34824	+	0.778407i
$894$	1.12639	−	12.3041i	0.0376720	−	0.411512i
$895$	−6.95752	−	39.5837i	−0.232564	−	1.32314i
$896$	−10.2905	−	17.8237i	−0.343782	−	0.595449i
$897$	−5.02652	+	7.11749i	−0.167831	+	0.237646i
$898$	−12.0732	−	6.97048i	−0.402889	−	0.232608i
$899$	−17.8894			−0.596644
$900$	−36.4317	−	44.2319i	−1.21439	−	1.47440i
$901$	1.11046			0.0369949
$902$	−8.00766	−	4.62322i	−0.266626	−	0.153936i
$903$	1.88067	+	4.07585i	0.0625848	+	0.135636i
$904$	22.0241	+	38.1469i	0.732512	+	1.26875i
$905$	−2.28750	−	13.0144i	−0.0760391	−	0.432613i
$906$	−31.3142	+	14.4489i	−1.04034	+	0.480033i
$907$	0.736727	+	0.425350i	0.0244626	+	0.0141235i	0.512181	−	0.858877i	$-0.328838\pi$
$907$	0.736727	+	0.425350i	0.0244626	+	0.0141235i	−0.487719	+	0.873001i	$0.662171\pi$
$908$		−	79.1533i		−	2.62679i
$909$	28.0037	−	32.8331i	0.928823	−	1.08901i
$910$	−9.79841	+	26.8755i	−0.324814	+	0.890914i
$911$	−17.8317	+	30.8854i	−0.590790	+	1.02328i	0.403336	+	0.915052i	$0.367851\pi$
$911$	−17.8317	+	30.8854i	−0.590790	+	1.02328i	−0.994126	+	0.108227i	$0.965483\pi$
$912$	−11.4016	+	16.1444i	−0.377543	+	0.534596i
$913$	2.08019	−	1.20100i	0.0688442	−	0.0397472i
$914$	23.7267	+	41.0958i	0.784808	+	1.35933i
$915$	45.3105	+	21.3811i	1.49792	+	0.706838i
$916$	4.95366	−	8.57999i	0.163673	−	0.283491i
$917$			3.66207i			0.120932i
$918$	−1.07282	+	1.04722i	−0.0354083	+	0.0345635i
$919$	16.6854			0.550401			0.275201	−	0.961387i	$-0.411256\pi$
$919$	16.6854			0.550401			0.275201	+	0.961387i	$0.411256\pi$
$920$	−7.13954	+	5.98418i	−0.235384	+	0.197293i
$921$	4.72259	−	51.5875i	0.155615	−	1.69986i
$922$	−5.85263	+	3.37902i	−0.192746	+	0.111282i
$923$	−18.1781	+	10.4951i	−0.598339	+	0.345451i
$924$	−8.35553	−	5.90086i	−0.274877	−	0.194124i
$925$	−9.29840	−	25.6338i	−0.305730	−	0.842833i
$926$	−14.9494			−0.491268
$927$	−25.6578	+	9.10547i	−0.842712	+	0.299063i
$928$			3.10716i			0.101997i
$929$	−12.4944	+	21.6409i	−0.409928	+	0.710016i	−0.994881	−	0.101051i	$-0.967779\pi$
$929$	−12.4944	+	21.6409i	−0.409928	+	0.710016i	0.584953	+	0.811067i	$0.301113\pi$
$930$	−88.8134	+	7.36157i	−2.91231	+	0.241395i
$931$	−1.93156	−	3.34557i	−0.0633045	−	0.109647i
$932$	−54.4353	+	31.4283i	−1.78309	+	1.02947i
$933$	−6.68618	−	14.4905i	−0.218896	−	0.474398i
$934$	−0.488227	+	0.845633i	−0.0159753	+	0.0276700i
$935$	0.141605	−	0.388399i	0.00463097	−	0.0127020i
$936$	−23.3642	−	65.8366i	−0.763683	−	2.15194i
$937$		−	33.7654i		−	1.10307i	−0.834153	−	0.551533i	$-0.814043\pi$
$937$		−	33.7654i		−	1.10307i	0.834153	−	0.551533i	$-0.185957\pi$
$938$	−25.8001	−	14.8957i	−0.842403	−	0.486362i
$939$	−16.2864	−	11.5018i	−0.531487	−	0.375348i
$940$	−101.320	+	17.8086i	−3.30468	+	0.580854i
$941$	17.8282	+	30.8794i	0.581183	+	1.00664i	0.995339	+	0.0964333i	$0.0307435\pi$
$941$	17.8282	+	30.8794i	0.581183	+	1.00664i	−0.414156	+	0.910206i	$0.635923\pi$
$942$	70.2046	+	6.42690i	2.28739	+	0.209400i
$943$	2.03694	+	1.17603i	0.0663320	+	0.0382968i
$944$	−29.8246			−0.970710
$945$	−6.78390	+	9.43285i	−0.220680	+	0.306851i
$946$	9.66558			0.314255
$947$	−29.5751	−	17.0752i	−0.961060	−	0.554868i	−0.0645611	−	0.997914i	$-0.520565\pi$
$947$	−29.5751	−	17.0752i	−0.961060	−	0.554868i	−0.896499	+	0.443045i	$0.853898\pi$
$948$	36.1498	+	3.30934i	1.17409	+	0.107482i
$949$	−36.7250	−	63.6096i	−1.19214	−	2.06485i
$950$	−45.8826	−	8.14175i	−1.48863	−	0.264153i
$951$	−39.0160	−	27.5539i	−1.26518	−	0.893498i
$952$	0.454823	+	0.262592i	0.0147409	+	0.00851067i
$953$			1.88107i			0.0609337i	0.999536	+	0.0304669i	$0.00969940\pi$
$953$			1.88107i			0.0609337i	−0.999536	+	0.0304669i	$0.990301\pi$
$954$	−43.6102	+	51.1311i	−1.41193	+	1.65543i
$955$	−27.8947	−	10.1700i	−0.902650	−	0.329093i
$956$	−1.18712	+	2.05616i	−0.0383943	+	0.0665010i
$957$	2.10413	+	4.56014i	0.0680168	+	0.147409i
$958$	0.990531	−	0.571884i	0.0320026	−	0.0184767i
$959$	0.124316	+	0.215321i	0.00401437	+	0.00695309i
$960$	3.16864	+	38.2280i	0.102268	+	1.23380i
$961$	−29.9849	+	51.9354i	−0.967255	+	1.67534i
$962$		−	69.7680i		−	2.24941i
$963$	−6.81509	+	36.9105i	−0.219613	+	1.18943i
$964$	−71.1788			−2.29251
$965$	−10.4172	−	12.4285i	−0.335343	−	0.400087i
$966$	3.23815	+	2.28685i	0.104186	+	0.0735783i
$967$	43.7558	−	25.2624i	1.40709	−	0.812385i	0.411985	−	0.911191i	$-0.364836\pi$
$967$	43.7558	−	25.2624i	1.40709	−	0.812385i	0.995107	+	0.0988058i	$0.0315023\pi$
$968$	32.7450	−	18.9053i	1.05246	−	0.607640i
$969$	−0.0729511	+	0.796886i	−0.00234353	+	0.0255997i
$970$	−21.5716	+	18.0808i	−0.692624	+	0.580540i
$971$	43.4008			1.39280			0.696399	−	0.717655i	$-0.254784\pi$
$971$	43.4008			1.39280			0.696399	+	0.717655i	$0.254784\pi$
$972$	−3.99560	−	59.4177i	−0.128159	−	1.90582i
$973$		−	11.8915i		−	0.381225i
$974$	−38.3699	+	66.4587i	−1.22945	+	2.12947i
$975$	32.6380	−	32.3061i	1.04525	−	1.03462i
$976$	19.1058	+	33.0922i	0.611562	+	1.05926i
$977$	−32.5476	+	18.7914i	−1.04129	+	0.601190i	−0.920199	−	0.391452i	$-0.871973\pi$
$977$	−32.5476	+	18.7914i	−1.04129	+	0.601190i	−0.121092	+	0.992641i	$0.538640\pi$
$978$	−10.0559	+	14.2391i	−0.321554	+	0.455316i
$979$	−7.64930	+	13.2490i	−0.244473	+	0.423439i
$980$	8.02560	+	2.92602i	0.256368	+	0.0934681i
$981$	−58.3631	−	10.7760i	−1.86339	−	0.344052i
$982$			5.03496i			0.160672i
$983$	−11.0692	−	6.39078i	−0.353051	−	0.203834i	0.312977	−	0.949761i	$-0.398674\pi$
$983$	−11.0692	−	6.39078i	−0.353051	−	0.203834i	−0.666028	+	0.745926i	$0.732007\pi$
$984$	−17.1226	+	7.90065i	−0.545848	+	0.251864i
$985$	−13.9981	+	2.46040i	−0.446016	+	0.0783950i
$986$	−0.270580	−	0.468658i	−0.00861702	−	0.0149251i
$987$	8.73905	+	18.9396i	0.278167	+	0.602853i
$988$	−67.7740	−	39.1293i	−2.15618	−	1.24487i
$989$	−2.45868			−0.0781814
$990$	12.3227	+	21.7734i	0.391640	+	0.692004i
$991$	49.4365			1.57040			0.785201	−	0.619241i	$-0.212560\pi$
$991$	49.4365			1.57040			0.785201	+	0.619241i	$0.212560\pi$
$992$	13.6835	+	7.90016i	0.434451	+	0.250830i
$993$	−0.0167601	+	0.0237320i	−0.000531864	+	0.000753112i
$994$	4.77484	+	8.27026i	0.151449	+	0.262317i
$995$	−4.84616	−	27.5715i	−0.153633	−	0.874075i
$996$	0.937267	−	10.2383i	0.0296984	−	0.324413i
$997$	−15.5487	−	8.97703i	−0.492432	−	0.284305i	0.233151	−	0.972441i	$-0.425096\pi$
$997$	−15.5487	−	8.97703i	−0.492432	−	0.284305i	−0.725583	+	0.688135i	$0.758430\pi$
$998$			74.5580i			2.36009i
$999$	7.66430	−	27.2817i	0.242488	−	0.863155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bh.c.169.4	✓	64
3.2	odd	2		945.2.bh.c.694.29		64
5.4	even	2	inner	315.2.bh.c.169.29	yes	64
9.4	even	3	inner	315.2.bh.c.274.29	yes	64
9.5	odd	6		945.2.bh.c.64.4		64
15.14	odd	2		945.2.bh.c.694.4		64
45.4	even	6	inner	315.2.bh.c.274.4	yes	64
45.14	odd	6		945.2.bh.c.64.29		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bh.c.169.4	✓	64	1.1	even	1	trivial
315.2.bh.c.169.29	yes	64	5.4	even	2	inner
315.2.bh.c.274.4	yes	64	45.4	even	6	inner
315.2.bh.c.274.29	yes	64	9.4	even	3	inner
945.2.bh.c.64.4		64	9.5	odd	6
945.2.bh.c.64.29		64	45.14	odd	6
945.2.bh.c.694.4		64	15.14	odd	2
945.2.bh.c.694.29		64	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08930 - 1.20626i) q^{2} +(-1.72484 - 0.157901i) q^{3} +(1.91013 + 3.30844i) q^{4} +(-0.387093 - 2.20231i) q^{5} +(3.41324 + 2.41051i) q^{6} +(0.866025 + 0.500000i) q^{7} -4.39141i q^{8} +(2.95013 + 0.544707i) q^{9} +O(q^{10})\)	\(q+(-2.08930 - 1.20626i) q^{2} +(-1.72484 - 0.157901i) q^{3} +(1.91013 + 3.30844i) q^{4} +(-0.387093 - 2.20231i) q^{5} +(3.41324 + 2.41051i) q^{6} +(0.866025 + 0.500000i) q^{7} -4.39141i q^{8} +(2.95013 + 0.544707i) q^{9} +(-1.84780 + 5.06823i) q^{10} +(0.772957 - 1.33880i) q^{11} +(-2.77226 - 6.00813i) q^{12} +(4.59231 - 2.65137i) q^{13} +(-1.20626 - 2.08930i) q^{14} +(0.319927 + 3.85975i) q^{15} +(-1.47692 + 2.55811i) q^{16} +0.119594i q^{17} +(-5.50667 - 4.69669i) q^{18} -3.86313 q^{19} +(6.54680 - 5.48736i) q^{20} +(-1.41480 - 0.999165i) q^{21} +(-3.22988 + 1.86477i) q^{22} +(0.821601 - 0.474351i) q^{23} +(-0.693406 + 7.57447i) q^{24} +(-4.70032 + 1.70500i) q^{25} -12.7930 q^{26} +(-5.00250 - 1.40536i) q^{27} +3.82026i q^{28} +(0.937813 - 1.62434i) q^{29} +(3.98744 - 8.45010i) q^{30} +(-4.76891 - 8.25999i) q^{31} +(-1.43466 + 0.828299i) q^{32} +(-1.54462 + 2.18716i) q^{33} +(0.144261 - 0.249868i) q^{34} +(0.765921 - 2.10080i) q^{35} +(3.83301 + 10.8008i) q^{36} +5.45362i q^{37} +(8.07125 + 4.65994i) q^{38} +(-8.33964 + 3.84806i) q^{39} +(-9.67123 + 1.69988i) q^{40} +(1.23962 + 2.14708i) q^{41} +(1.75070 + 3.79418i) q^{42} +(-2.24441 - 1.29581i) q^{43} +5.90579 q^{44} +(0.0576347 - 6.70796i) q^{45} -2.28876 q^{46} +(-10.4293 - 6.02134i) q^{47} +(2.95138 - 4.17911i) q^{48} +(0.500000 + 0.866025i) q^{49} +(11.8771 + 2.10755i) q^{50} +(0.0188839 - 0.206280i) q^{51} +(17.5438 + 10.1289i) q^{52} -9.28531i q^{53} +(8.75651 + 8.97054i) q^{54} +(-3.24766 - 1.18405i) q^{55} +(2.19570 - 3.80307i) q^{56} +(6.66327 + 0.609991i) q^{57} +(-3.91875 + 2.26249i) q^{58} +(5.04844 + 8.74416i) q^{59} +(-12.1586 + 8.43107i) q^{60} +(6.46811 - 11.2031i) q^{61} +23.0102i q^{62} +(2.28254 + 1.94680i) q^{63} +9.90427 q^{64} +(-7.61678 - 9.08735i) q^{65} +(5.86548 - 2.70643i) q^{66} +(10.6942 - 6.17433i) q^{67} +(-0.395669 + 0.228439i) q^{68} +(-1.49203 + 0.688448i) q^{69} +(-4.13436 + 3.46531i) q^{70} -3.95838 q^{71} +(2.39203 - 12.9552i) q^{72} -13.8513i q^{73} +(6.57849 - 11.3943i) q^{74} +(8.37651 - 2.19866i) q^{75} +(-7.37907 - 12.7809i) q^{76} +(1.33880 - 0.772957i) q^{77} +(22.0658 + 2.02002i) q^{78} +(-2.74306 + 4.75112i) q^{79} +(6.20544 + 2.26241i) q^{80} +(8.40659 + 3.21392i) q^{81} -5.98122i q^{82} +(1.34560 + 0.776885i) q^{83} +(0.603221 - 6.58932i) q^{84} +(0.263382 - 0.0462939i) q^{85} +(3.12617 + 5.41468i) q^{86} +(-1.87406 + 2.65364i) q^{87} +(-5.87922 - 3.39437i) q^{88} -9.89616 q^{89} +(-8.21196 + 13.9454i) q^{90} +5.30274 q^{91} +(3.13872 + 1.81214i) q^{92} +(6.92133 + 15.0002i) q^{93} +(14.5266 + 25.1608i) q^{94} +(1.49539 + 8.50780i) q^{95} +(2.60534 - 1.20215i) q^{96} +(4.51862 + 2.60883i) q^{97} -2.41252i q^{98} +(3.00958 - 3.52861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

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