LMFDB - Embedded newform 507.2.p.a.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

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

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			64.2
Character	$\chi$	$=$	507.64
Dual form			507.2.p.a.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.29315 - 0.278439i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(3.23914 + 0.798376i) q^{4} +(1.23177 + 2.34695i) q^{5} +(1.90109 - 1.31223i) q^{6} +(-4.14543 - 1.57215i) q^{7} +(-2.88578 - 1.09443i) q^{8} +(0.120537 - 0.992709i) q^{9} +(-2.17116 - 5.72488i) q^{10} +(6.17406 - 0.749667i) q^{11} +(-2.95395 + 1.55035i) q^{12} +(2.62810 + 2.46842i) q^{13} +(9.06835 + 4.75944i) q^{14} +(-2.47831 - 0.939898i) q^{15} +(0.404890 + 0.212503i) q^{16} +(1.47962 - 3.90143i) q^{17} +(-0.552818 + 2.24287i) q^{18} +0.489722i q^{19} +(2.11614 + 8.58550i) q^{20} +(4.14543 - 1.57215i) q^{21} -14.3668 q^{22} -1.28194 q^{23} +(2.88578 - 1.09443i) q^{24} +(-1.15057 + 1.66689i) q^{25} +(-5.33934 - 6.39222i) q^{26} +(0.568065 + 0.822984i) q^{27} +(-12.1724 - 8.40203i) q^{28} +(-0.454964 + 3.74697i) q^{29} +(5.42144 + 2.84539i) q^{30} +(0.411332 - 0.283922i) q^{31} +(4.21071 + 2.90644i) q^{32} +(-4.12423 + 4.65529i) q^{33} +(-4.47930 + 8.53459i) q^{34} +(-1.41646 - 11.6656i) q^{35} +(1.18299 - 3.11929i) q^{36} +(-8.92051 + 6.15739i) q^{37} +(0.136358 - 1.12301i) q^{38} +(-3.60403 - 0.104882i) q^{39} +(-0.986050 - 8.12085i) q^{40} +(6.97254 + 7.87037i) q^{41} +(-9.94385 + 2.45094i) q^{42} +(6.48106 - 9.38944i) q^{43} +(20.5972 + 2.50095i) q^{44} +(2.47831 - 0.939898i) q^{45} +(2.93969 + 0.356943i) q^{46} +(2.66609 + 10.8168i) q^{47} +(-0.443980 + 0.109431i) q^{48} +(9.47332 + 8.39263i) q^{49} +(3.10256 - 3.50207i) q^{50} +(1.47962 + 3.90143i) q^{51} +(6.54206 + 10.0938i) q^{52} +(-1.25757 + 3.31594i) q^{53} +(-1.07351 - 2.04540i) q^{54} +(9.36447 + 13.5668i) q^{55} +(10.2422 + 9.07376i) q^{56} +(-0.324746 - 0.366562i) q^{57} +(2.08660 - 8.46569i) q^{58} +(1.32370 + 2.52210i) q^{59} +(-7.27719 - 5.02308i) q^{60} +(2.54238 + 6.70371i) q^{61} +(-1.02230 + 0.536545i) q^{62} +(-2.06037 + 3.92570i) q^{63} +(-9.53107 - 8.44379i) q^{64} +(-2.55602 + 9.20854i) q^{65} +(10.7537 - 9.52695i) q^{66} +(-0.303840 - 1.23273i) q^{67} +(7.90749 - 11.4560i) q^{68} +(0.959549 - 0.850086i) q^{69} +27.1455i q^{70} +(-2.35869 - 2.66241i) q^{71} +(-1.43429 + 2.73282i) q^{72} +(9.08113 - 1.10265i) q^{73} +(22.1706 - 11.6360i) q^{74} +(-0.244138 - 2.01066i) q^{75} +(-0.390983 + 1.58628i) q^{76} +(-26.7727 - 6.59888i) q^{77} +(8.23538 + 1.24401i) q^{78} +(-2.27273 + 0.560178i) q^{79} +1.21201i q^{80} +(-0.970942 - 0.239316i) q^{81} +(-13.7977 - 19.9894i) q^{82} +(-7.19466 + 8.12109i) q^{83} +(14.6828 - 1.78281i) q^{84} +(10.9790 - 1.33309i) q^{85} +(-17.4764 + 19.7268i) q^{86} +(-2.14415 - 3.10634i) q^{87} +(-18.6374 - 4.59371i) q^{88} +1.64053i q^{89} +(-5.94485 + 1.46527i) q^{90} +(-7.01388 - 14.3644i) q^{91} +(-4.15240 - 1.02347i) q^{92} +(-0.119611 + 0.485282i) q^{93} +(-3.10194 - 25.5468i) q^{94} +(-1.14935 + 0.603227i) q^{95} +(-5.07909 + 0.616713i) q^{96} +(-6.19138 + 11.7967i) q^{97} +(-19.3869 - 21.8833i) q^{98} -6.21941i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{26}\right)$

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 $

$2$	−2.29315	−	0.278439i	−1.62150	−	0.196886i	−0.741196	−	0.671289i	$-0.765741\pi$
$2$	−2.29315	−	0.278439i	−1.62150	−	0.196886i	−0.880308	+	0.474402i	$0.842664\pi$
$3$	−0.748511	+	0.663123i	−0.432153	+	0.382854i
$3$	−0.748511	+	0.663123i	−0.432153	+	0.382854i
$4$	3.23914	+	0.798376i	1.61957	+	0.399188i
$5$	1.23177	+	2.34695i	0.550865	+	1.04959i	0.988612	+	0.150488i	$0.0480845\pi$
$5$	1.23177	+	2.34695i	0.550865	+	1.04959i	−0.437746	+	0.899099i	$0.644223\pi$
$6$	1.90109	−	1.31223i	0.776116	−	0.535714i
$7$	−4.14543	−	1.57215i	−1.56682	−	0.594218i	−0.589838	−	0.807521i	$-0.700808\pi$
$7$	−4.14543	−	1.57215i	−1.56682	−	0.594218i	−0.976986	+	0.213303i	$0.931578\pi$
$8$	−2.88578	−	1.09443i	−1.02028	−	0.386940i
$9$	0.120537	−	0.992709i	0.0401789	−	0.330903i
$10$	−2.17116	−	5.72488i	−0.686581	−	1.81037i
$11$	6.17406	−	0.749667i	1.86155	−	0.226033i	0.888866	−	0.458168i	$-0.151494\pi$
$11$	6.17406	−	0.749667i	1.86155	−	0.226033i	0.972684	+	0.232135i	$0.0745710\pi$
$12$	−2.95395	+	1.55035i	−0.852732	+	0.447548i
$13$	2.62810	+	2.46842i	0.728904	+	0.684615i
$13$	2.62810	+	2.46842i	0.728904	+	0.684615i
$14$	9.06835	+	4.75944i	2.42362	+	1.27201i
$15$	−2.47831	−	0.939898i	−0.639897	−	0.242681i
$16$	0.404890	+	0.212503i	0.101223	+	0.0531257i
$17$	1.47962	−	3.90143i	0.358860	−	0.946235i	−0.627053	−	0.778976i	$-0.715739\pi$
$17$	1.47962	−	3.90143i	0.358860	−	0.946235i	0.985913	−	0.167259i	$-0.0534916\pi$
$18$	−0.552818	+	2.24287i	−0.130300	+	0.528650i
$19$			0.489722i			0.112350i	0.998421	+	0.0561750i	$0.0178905\pi$
$19$			0.489722i			0.112350i	−0.998421	+	0.0561750i	$0.982110\pi$
$20$	2.11614	+	8.58550i	0.473183	+	1.91978i
$21$	4.14543	−	1.57215i	0.904606	−	0.343072i
$22$	−14.3668			−3.06301
$23$	−1.28194			−0.267304			−0.133652	−	0.991028i	$-0.542670\pi$
$23$	−1.28194			−0.267304			−0.133652	+	0.991028i	$0.542670\pi$
$24$	2.88578	−	1.09443i	0.589057	−	0.223400i
$25$	−1.15057	+	1.66689i	−0.230114	+	0.333378i
$26$	−5.33934	−	6.39222i	−1.04713	−	1.25362i
$27$	0.568065	+	0.822984i	0.109324	+	0.158383i
$28$	−12.1724	−	8.40203i	−2.30038	−	1.58783i
$29$	−0.454964	+	3.74697i	−0.0844847	+	0.695794i	0.887510	+	0.460789i	$0.152434\pi$
$29$	−0.454964	+	3.74697i	−0.0844847	+	0.695794i	−0.971994	+	0.235005i	$0.924489\pi$
$30$	5.42144	+	2.84539i	0.989814	+	0.519495i
$31$	0.411332	−	0.283922i	0.0738774	−	0.0509939i	−0.530554	−	0.847651i	$-0.678016\pi$
$31$	0.411332	−	0.283922i	0.0738774	−	0.0509939i	0.604431	+	0.796658i	$0.293401\pi$
$32$	4.21071	+	2.90644i	0.744355	+	0.513791i
$33$	−4.12423	+	4.65529i	−0.717936	+	0.810383i
$34$	−4.47930	+	8.53459i	−0.768193	+	1.46367i
$35$	−1.41646	−	11.6656i	−0.239426	−	1.97185i
$36$	1.18299	−	3.11929i	0.197165	−	0.519881i
$37$	−8.92051	+	6.15739i	−1.46652	+	1.01227i	−0.475336	+	0.879805i	$0.657673\pi$
$37$	−8.92051	+	6.15739i	−1.46652	+	1.01227i	−0.991188	+	0.132464i	$0.957711\pi$
$38$	0.136358	−	1.12301i	0.0221202	−	0.182176i
$39$	−3.60403	−	0.104882i	−0.577106	−	0.0167945i
$40$	−0.986050	−	8.12085i	−0.155908	−	1.28402i
$41$	6.97254	+	7.87037i	1.08893	+	1.22915i	0.971744	+	0.236036i	$0.0758482\pi$
$41$	6.97254	+	7.87037i	1.08893	+	1.22915i	0.117184	+	0.993110i	$0.462613\pi$
$42$	−9.94385	+	2.45094i	−1.53437	+	0.378188i
$43$	6.48106	−	9.38944i	0.988352	−	1.43188i	0.0882999	−	0.996094i	$-0.471857\pi$
$43$	6.48106	−	9.38944i	0.988352	−	1.43188i	0.900052	−	0.435782i	$-0.143528\pi$
$44$	20.5972	+	2.50095i	3.10514	+	0.377032i
$45$	2.47831	−	0.939898i	0.369444	−	0.140112i
$46$	2.93969	+	0.356943i	0.433434	+	0.0526284i
$47$	2.66609	+	10.8168i	0.388889	+	1.57779i	0.760462	+	0.649382i	$0.224972\pi$
$47$	2.66609	+	10.8168i	0.388889	+	1.57779i	−0.371573	+	0.928404i	$0.621182\pi$
$48$	−0.443980	+	0.109431i	−0.0640830	+	0.0157950i
$49$	9.47332	+	8.39263i	1.35333	+	1.19895i
$50$	3.10256	−	3.50207i	0.438769	−	0.495268i
$51$	1.47962	+	3.90143i	0.207188	+	0.546309i
$52$	6.54206	+	10.0938i	0.907221	+	1.39975i
$53$	−1.25757	+	3.31594i	−0.172741	+	0.455480i	−0.993228	−	0.116186i	$-0.962933\pi$
$53$	−1.25757	+	3.31594i	−0.172741	+	0.455480i	0.820487	+	0.571665i	$0.193702\pi$
$54$	−1.07351	−	2.04540i	−0.146086	−	0.278344i
$55$	9.36447	+	13.5668i	1.26270	+	1.82934i
$56$	10.2422	+	9.07376i	1.36867	+	1.21253i
$57$	−0.324746	−	0.366562i	−0.0430137	−	0.0485524i
$58$	2.08660	−	8.46569i	0.273985	−	1.11160i
$59$	1.32370	+	2.52210i	0.172331	+	0.328349i	0.956268	−	0.292491i	$-0.0944841\pi$
$59$	1.32370	+	2.52210i	0.172331	+	0.328349i	−0.783938	+	0.620840i	$0.786792\pi$
$60$	−7.27719	−	5.02308i	−0.939482	−	0.648477i
$61$	2.54238	+	6.70371i	0.325519	+	0.858322i	0.993468	+	0.114115i	$0.0364033\pi$
$61$	2.54238	+	6.70371i	0.325519	+	0.858322i	−0.667949	+	0.744207i	$0.732827\pi$
$62$	−1.02230	+	0.536545i	−0.129832	+	0.0681413i
$63$	−2.06037	+	3.92570i	−0.259582	+	0.494592i
$64$	−9.53107	−	8.44379i	−1.19138	−	1.05547i
$65$	−2.55602	+	9.20854i	−0.317035	+	1.14218i
$66$	10.7537	−	9.52695i	1.32369	−	1.17269i
$67$	−0.303840	−	1.23273i	−0.0371200	−	0.150602i	0.949457	−	0.313896i	$-0.101634\pi$
$67$	−0.303840	−	1.23273i	−0.0371200	−	0.150602i	−0.986577	+	0.163294i	$0.947788\pi$
$68$	7.90749	−	11.4560i	0.958924	−	1.38924i
$69$	0.959549	−	0.850086i	0.115516	−	0.102338i
$70$			27.1455i			3.24451i
$71$	−2.35869	−	2.66241i	−0.279925	−	0.315970i	0.591685	−	0.806169i	$-0.298463\pi$
$71$	−2.35869	−	2.66241i	−0.279925	−	0.315970i	−0.871611	+	0.490198i	$0.836924\pi$
$72$	−1.43429	+	2.73282i	−0.169033	+	0.322065i
$73$	9.08113	−	1.10265i	1.06287	−	0.129055i	0.429623	−	0.903008i	$-0.358647\pi$
$73$	9.08113	−	1.10265i	1.06287	−	0.129055i	0.633243	+	0.773953i	$0.281723\pi$
$74$	22.1706	−	11.6360i	2.57728	−	1.35266i
$75$	−0.244138	−	2.01066i	−0.0281906	−	0.232170i
$76$	−0.390983	+	1.58628i	−0.0448488	+	0.181959i
$77$	−26.7727	−	6.59888i	−3.05103	−	0.752012i
$78$	8.23538	+	1.24401i	0.932473	+	0.140857i
$79$	−2.27273	+	0.560178i	−0.255702	+	0.0630249i	−0.365083	−	0.930975i	$-0.618959\pi$
$79$	−2.27273	+	0.560178i	−0.255702	+	0.0630249i	0.109381	+	0.994000i	$0.465113\pi$
$80$			1.21201i			0.135507i
$81$	−0.970942	−	0.239316i	−0.107882	−	0.0265906i
$82$	−13.7977	−	19.9894i	−1.52370	−	2.20746i
$83$	−7.19466	+	8.12109i	−0.789717	+	0.891406i	−0.996205	−	0.0870432i	$-0.972258\pi$
$83$	−7.19466	+	8.12109i	−0.789717	+	0.891406i	0.206488	+	0.978449i	$0.433797\pi$
$84$	14.6828	−	1.78281i	1.60202	−	0.194521i
$85$	10.9790	−	1.33309i	1.19084	−	0.144594i
$86$	−17.4764	+	19.7268i	−1.88453	+	2.12720i
$87$	−2.14415	−	3.10634i	−0.229877	−	0.333035i
$88$	−18.6374	−	4.59371i	−1.98676	−	0.489691i
$89$			1.64053i			0.173895i	0.996213	+	0.0869477i	$0.0277113\pi$
$89$			1.64053i			0.173895i	−0.996213	+	0.0869477i	$0.972289\pi$
$90$	−5.94485	+	1.46527i	−0.626642	+	0.154453i
$91$	−7.01388	−	14.3644i	−0.735254	−	1.50580i
$92$	−4.15240	−	1.02347i	−0.432917	−	0.106704i
$93$	−0.119611	+	0.485282i	−0.0124031	+	0.0503214i
$94$	−3.10194	−	25.5468i	−0.319941	−	2.63495i
$95$	−1.14935	+	0.603227i	−0.117921	+	0.0618897i
$96$	−5.07909	+	0.616713i	−0.518382	+	0.0629430i
$97$	−6.19138	+	11.7967i	−0.628639	+	1.19777i	0.337883	+	0.941188i	$0.390289\pi$
$97$	−6.19138	+	11.7967i	−0.628639	+	1.19777i	−0.966522	+	0.256584i	$0.917403\pi$
$98$	−19.3869	−	21.8833i	−1.95838	−	2.21055i
$99$		−	6.21941i		−	0.625074i
$100$	−5.05767	+	4.48070i	−0.505767	+	0.448070i
$101$	1.76344	−	2.55478i	0.175468	−	0.254210i	−0.725375	−	0.688354i	$-0.758334\pi$
$101$	1.76344	−	2.55478i	0.175468	−	0.254210i	0.900844	+	0.434144i	$0.142949\pi$
$102$	−2.30668	−	9.35856i	−0.228395	−	0.926635i
$103$	1.21245	−	1.07414i	0.119466	−	0.105838i	−0.601274	−	0.799043i	$-0.705340\pi$
$103$	1.21245	−	1.07414i	0.119466	−	0.105838i	0.720741	+	0.693204i	$0.243802\pi$
$104$	−4.88260	−	9.99957i	−0.478779	−	0.980539i
$105$	8.79598	+	7.79256i	0.858400	+	0.760476i
$106$	3.80709	−	7.25381i	0.369778	−	0.704552i
$107$	8.21102	−	4.30948i	0.793789	−	0.416613i	−0.0185281	−	0.999828i	$-0.505898\pi$
$107$	8.21102	−	4.30948i	0.793789	−	0.416613i	0.812317	+	0.583216i	$0.198206\pi$
$108$	1.18299	+	3.11929i	0.113833	+	0.300154i
$109$	3.95005	+	2.72652i	0.378346	+	0.261154i	0.742027	−	0.670370i	$-0.233865\pi$
$109$	3.95005	+	2.72652i	0.378346	+	0.261154i	−0.363681	+	0.931524i	$0.618480\pi$
$110$	−17.6966	−	33.7181i	−1.68731	−	3.21490i
$111$	2.59400	−	10.5243i	0.246211	−	0.998919i
$112$	−1.34436	−	1.51746i	−0.127030	−	0.143387i
$113$	2.98059	+	2.64058i	0.280391	+	0.248404i	0.791583	−	0.611062i	$-0.209257\pi$
$113$	2.98059	+	2.64058i	0.280391	+	0.248404i	−0.511192	+	0.859467i	$0.670796\pi$
$114$	0.642627	+	0.931006i	0.0601875	+	0.0871967i
$115$	−1.57906	−	3.00865i	−0.147248	−	0.280558i
$116$	−4.46518	+	11.7737i	−0.414582	+	1.09316i
$117$	2.76720	−	2.31141i	0.255828	−	0.213690i
$118$	−2.33319	−	6.15212i	−0.214788	−	0.566349i
$119$	−12.2673	+	13.8469i	−1.12454	+	1.26934i
$120$	6.12319	+	5.42467i	0.558968	+	0.495203i
$121$	26.8767	−	6.62451i	2.44333	−	0.602228i
$122$	−3.96350	−	16.0805i	−0.358838	−	1.45586i
$123$	−10.4380	−	1.26741i	−0.941167	−	0.114278i
$124$	1.55904	−	0.591265i	0.140006	−	0.0530972i
$125$	7.82678	+	0.950344i	0.700049	+	0.0850013i
$126$	5.81780	−	8.42854i	0.518291	−	0.750874i
$127$	−4.34049	+	1.06983i	−0.385156	+	0.0949325i	−0.427139	−	0.904186i	$-0.640479\pi$
$127$	−4.34049	+	1.06983i	−0.385156	+	0.0949325i	0.0419831	+	0.999118i	$0.486632\pi$
$128$	12.7195	+	14.3574i	1.12426	+	1.26902i
$129$	1.37520	+	11.3258i	0.121080	+	0.997184i
$130$	8.42536	−	20.4049i	0.738953	−	1.78963i
$131$	−0.0176171	+	0.145090i	−0.00153921	+	0.0126765i	−0.993458	−	0.114196i	$-0.963571\pi$
$131$	−0.0176171	+	0.145090i	−0.00153921	+	0.0126765i	0.991919	+	0.126872i	$0.0404939\pi$
$132$	−17.0756	+	11.7865i	−1.48624	+	1.02588i
$133$	0.769918	−	2.03011i	0.0667604	−	0.176033i
$134$	0.353512	+	2.91144i	0.0305388	+	0.251510i
$135$	−1.23177	+	2.34695i	−0.106014	+	0.201993i
$136$	−8.53968	+	9.63931i	−0.732272	+	0.826564i
$137$	−6.22314	−	4.29552i	−0.531679	−	0.366991i	0.271773	−	0.962361i	$-0.412390\pi$
$137$	−6.22314	−	4.29552i	−0.531679	−	0.366991i	−0.803452	+	0.595370i	$0.797005\pi$
$138$	−2.43709	+	1.68220i	−0.207459	+	0.143199i
$139$	−20.1703	−	10.5862i	−1.71082	−	0.897908i	−0.975443	−	0.220251i	$-0.929312\pi$
$139$	−20.1703	−	10.5862i	−1.71082	−	0.897908i	−0.735378	−	0.677657i	$-0.762995\pi$
$140$	4.72544	−	38.9175i	0.399372	−	3.28913i
$141$	−9.16843	−	6.32851i	−0.772121	−	0.532957i
$142$	4.66752	+	6.76208i	0.391690	+	0.567461i
$143$	18.0766	+	13.2700i	1.51164	+	1.10969i
$144$	0.259758	−	0.376324i	0.0216465	−	0.0313603i
$145$	−9.35434	+	3.54763i	−0.776836	+	0.294615i
$146$	−21.1314			−1.74885
$147$	−12.6562			−1.04387
$148$	−33.8107	+	12.8227i	−2.77922	+	1.05402i
$149$	−1.65471	−	6.71344i	−0.135559	−	0.549986i	−0.998965	−	0.0454766i	$-0.985519\pi$
$149$	−1.65471	−	6.71344i	−0.135559	−	0.549986i	0.863406	−	0.504510i	$-0.168327\pi$
$150$			4.67872i			0.382016i
$151$	−0.662033	+	2.68597i	−0.0538755	+	0.218582i	−0.991709	−	0.128504i	$-0.958982\pi$
$151$	−0.662033	+	2.68597i	−0.0538755	+	0.218582i	0.937833	+	0.347086i	$0.112829\pi$
$152$	0.535967	−	1.41323i	0.0434727	−	0.114628i
$153$	−3.69463	−	1.93909i	−0.298694	−	0.156766i
$154$	59.5565	+	22.5868i	4.79920	+	1.82010i
$155$	1.17302	+	0.615647i	0.0942190	+	0.0494499i
$156$	−11.5902	−	3.21709i	−0.927959	−	0.257574i
$157$	−11.1684	+	5.86165i	−0.891339	+	0.467811i	−0.847236	−	0.531216i	$-0.821735\pi$
$157$	−11.1684	+	5.86165i	−0.891339	+	0.467811i	−0.0441029	+	0.999027i	$0.514043\pi$
$158$	5.36770	−	0.651756i	0.427031	−	0.0518509i
$159$	−1.25757	−	3.31594i	−0.0997319	−	0.262971i
$160$	−1.63463	+	13.4624i	−0.129229	+	1.06429i
$161$	5.31421	+	2.01541i	0.418818	+	0.158837i
$162$	2.15988	+	0.819136i	0.169696	+	0.0643574i
$163$	11.9607	−	8.25590i	0.936837	−	0.646652i	0.00134486	−	0.999999i	$-0.499572\pi$
$163$	11.9607	−	8.25590i	0.936837	−	0.646652i	0.935492	+	0.353347i	$0.114957\pi$
$164$	16.3015	+	31.0599i	1.27293	+	2.42537i
$165$	−16.0058	−	3.94509i	−1.24605	−	0.307124i
$166$	18.7597	−	16.6196i	1.45603	−	1.28993i
$167$	19.9192	+	2.41863i	1.54139	+	0.187159i	0.846670	−	0.532119i	$-0.178604\pi$
$167$	19.9192	+	2.41863i	1.54139	+	0.187159i	0.694723	+	0.719277i	$0.255527\pi$
$168$	−13.6834			−1.05570
$169$	0.813844	+	12.9745i	0.0626034	+	0.998038i
$170$	−25.5477			−1.95942
$171$	0.486152	+	0.0590295i	0.0371769	+	0.00451410i
$172$	28.4894	−	25.2394i	2.17229	−	1.92448i
$173$	−5.28969	−	1.30379i	−0.402167	−	0.0991254i	0.0330434	−	0.999454i	$-0.489480\pi$
$173$	−5.28969	−	1.30379i	−0.402167	−	0.0991254i	−0.435211	+	0.900329i	$0.643326\pi$
$174$	4.05194	+	7.72033i	0.307177	+	0.585277i
$175$	7.39022	−	5.10110i	0.558648	−	0.385607i
$176$	2.65912	+	1.00847i	0.200439	+	0.0760165i
$177$	−2.66326	−	1.01004i	−0.200183	−	0.0759194i
$178$	0.456787	−	3.76198i	0.0342376	−	0.281972i
$179$	−7.14705	−	18.8452i	−0.534196	−	1.40856i	−0.882115	−	0.471034i	$-0.843881\pi$
$179$	−7.14705	−	18.8452i	−0.534196	−	1.40856i	0.347919	−	0.937524i	$-0.386888\pi$
$180$	8.77798	−	1.06584i	0.654272	−	0.0794430i
$181$	0.609492	−	0.319886i	0.0453032	−	0.0237769i	−0.441919	−	0.897055i	$-0.645702\pi$
$181$	0.609492	−	0.319886i	0.0453032	−	0.0237769i	0.487223	+	0.873278i	$0.338010\pi$
$182$	12.0843	+	34.8927i	0.895746	+	2.58642i
$183$	−6.34838	−	3.33189i	−0.469286	−	0.246300i
$184$	3.69940	+	1.40300i	0.272724	+	0.103430i
$185$	−25.4391	−	13.3515i	−1.87032	−	0.981620i
$186$	0.409408	−	1.07952i	0.0300193	−	0.0791543i
$187$	6.21047	−	25.1969i	0.454155	−	1.84258i
$188$			37.1655i			2.71057i
$189$	−1.06101	−	4.30470i	−0.0771774	−	0.313121i
$190$	2.80360	−	1.06327i	0.203395	−	0.0771374i
$191$	11.6504			0.842992			0.421496	−	0.906830i	$-0.361505\pi$
$191$	11.6504			0.842992			0.421496	+	0.906830i	$0.361505\pi$
$192$	12.7334			0.918952
$193$	8.63663	−	3.27544i	0.621679	−	0.235772i	−0.0235969	−	0.999722i	$-0.507512\pi$
$193$	8.63663	−	3.27544i	0.621679	−	0.235772i	0.645275	+	0.763950i	$0.276743\pi$
$194$	17.4824	−	25.3277i	1.25517	−	1.81842i
$195$	−4.19319	−	8.58765i	−0.300280	−	0.614974i
$196$	23.9849	+	34.7482i	1.71321	+	2.48201i
$197$	−7.57319	−	5.22739i	−0.539567	−	0.372436i	0.266892	−	0.963727i	$-0.414003\pi$
$197$	−7.57319	−	5.22739i	−0.539567	−	0.372436i	−0.806459	+	0.591290i	$0.798619\pi$
$198$	−1.73173	+	14.2621i	−0.123068	+	1.01356i
$199$	−5.42561	−	2.84758i	−0.384611	−	0.201860i	0.261325	−	0.965251i	$-0.415841\pi$
$199$	−5.42561	−	2.84758i	−0.384611	−	0.201860i	−0.645936	+	0.763391i	$0.723533\pi$
$200$	5.14459	−	3.55105i	0.363777	−	0.251097i
$201$	1.04488	+	0.721227i	0.0737000	+	0.0508714i
$202$	−4.75518	+	5.36749i	−0.334573	+	0.377655i
$203$	7.77682	−	14.8175i	0.545826	−	1.03998i
$204$	1.67788	+	13.8186i	0.117475	+	0.967493i
$205$	−9.88276	+	26.0587i	−0.690242	+	1.82002i
$206$	−3.07942	+	2.12557i	−0.214553	+	0.148096i
$207$	−0.154521	+	1.27260i	−0.0107400	+	0.0884516i
$208$	0.539548	+	1.55792i	0.0374109	+	0.108022i
$209$	0.367129	+	3.02358i	0.0253948	+	0.209145i
$210$	−18.0008	−	20.3187i	−1.24217	−	1.40212i
$211$	3.57170	−	0.880344i	0.245886	−	0.0606054i	−0.114446	−	0.993429i	$-0.536509\pi$
$211$	3.57170	−	0.880344i	0.245886	−	0.0606054i	0.360332	+	0.932824i	$0.382663\pi$
$212$	−6.72082	+	9.73679i	−0.461588	+	0.668725i
$213$	3.53101	+	0.428743i	0.241941	+	0.0293770i
$214$	−20.0291	+	7.59602i	−1.36916	+	0.519253i
$215$	30.0197	+	3.64505i	2.04733	+	0.248590i
$216$	−0.738609	−	2.99665i	−0.0502560	−	0.203897i
$217$	−2.15151	+	0.530301i	−0.146054	+	0.0359992i
$218$	−8.29890	−	7.35218i	−0.562072	−	0.497953i
$219$	−6.06613	+	6.84724i	−0.409911	+	0.462694i
$220$	19.5014	+	51.4210i	1.31479	+	3.46681i
$221$	13.5189	−	6.60104i	0.909382	−	0.444034i
$222$	−8.87880	+	23.4115i	−0.595906	+	1.57128i
$223$	−5.30931	−	10.1160i	−0.355537	−	0.677420i	0.640344	−	0.768089i	$-0.278792\pi$
$223$	−5.30931	−	10.1160i	−0.355537	−	0.677420i	−0.995881	+	0.0906685i	$0.971100\pi$
$224$	−12.8858	−	18.6683i	−0.860969	−	1.24733i
$225$	1.51605	+	1.34310i	0.101070	+	0.0895402i
$226$	−6.09972	−	6.88516i	−0.405747	−	0.457994i
$227$	1.59726	−	6.48033i	0.106014	−	0.430115i	−0.893819	−	0.448429i	$-0.851984\pi$
$227$	1.59726	−	6.48033i	0.106014	−	0.430115i	0.999832	+	0.0183142i	$0.00582991\pi$
$228$	−0.759243	−	1.44662i	−0.0502821	−	0.0958045i
$229$	−15.8362	−	10.9309i	−1.04649	−	0.722337i	−0.0847743	−	0.996400i	$-0.527017\pi$
$229$	−15.8362	−	10.9309i	−1.04649	−	0.722337i	−0.961712	+	0.274063i	$0.911632\pi$
$230$	2.78331	+	7.33898i	0.183526	+	0.483918i
$231$	24.4155	−	12.8143i	1.60642	−	0.843116i
$232$	5.41372	−	10.3150i	0.355428	−	0.677211i
$233$	2.57408	+	2.28044i	0.168634	+	0.149396i	0.743219	−	0.669048i	$-0.233298\pi$
$233$	2.57408	+	2.28044i	0.168634	+	0.149396i	−0.574585	+	0.818445i	$0.694837\pi$
$234$	−6.98920	+	4.52991i	−0.456898	+	0.296129i
$235$	−22.1023	+	19.5810i	−1.44180	+	1.27732i
$236$	2.27406	+	9.22623i	0.148029	+	0.600576i
$237$	1.32970	−	1.92640i	0.0863731	−	0.125133i
$238$	31.9863	−	28.3374i	2.07336	−	1.83684i
$239$			18.7649i			1.21380i	0.794778	+	0.606900i	$0.207587\pi$
$239$			18.7649i			1.21380i	−0.794778	+	0.606900i	$0.792413\pi$
$240$	−0.803712	−	0.907203i	−0.0518794	−	0.0585597i
$241$	−4.29971	+	8.19240i	−0.276968	+	0.527719i	−0.983712	−	0.179750i	$-0.942471\pi$
$241$	−4.29971	+	8.19240i	−0.276968	+	0.527719i	0.706744	+	0.707469i	$0.250163\pi$
$242$	−63.4768	+	7.70748i	−4.08045	+	0.495456i
$243$	0.885456	−	0.464723i	0.0568020	−	0.0298120i
$244$	2.88305	+	23.7440i	0.184568	+	1.52006i
$245$	−8.02808	+	32.5712i	−0.512895	+	2.08090i
$246$	23.5831	+	5.81272i	1.50361	+	0.370606i
$247$	−1.20884	+	1.28704i	−0.0769165	+	0.0818924i
$248$	−1.49774	+	0.369161i	−0.0951068	+	0.0234417i
$249$		−	10.8497i		−	0.687570i
$250$	−17.6834	−	4.35857i	−1.11840	−	0.275660i
$251$	9.67594	+	14.0180i	0.610740	+	0.884810i	0.999330	−	0.0366012i	$-0.0116531\pi$
$251$	9.67594	+	14.0180i	0.610740	+	0.884810i	−0.388590	+	0.921411i	$0.627038\pi$
$252$	−9.80800	+	11.0709i	−0.617846	+	0.697404i
$253$	−7.91480	+	0.961031i	−0.497599	+	0.0604195i
$254$	10.2513	−	1.24473i	0.643223	−	0.0781014i
$255$	−7.33389	+	8.27825i	−0.459266	+	0.518404i
$256$	−10.7034	−	15.5066i	−0.668963	−	0.969160i
$257$	25.1609	+	6.20160i	1.56949	+	0.386845i	0.925671	−	0.378331i	$-0.123502\pi$
$257$	25.1609	+	6.20160i	1.56949	+	0.386845i	0.643822	+	0.765176i	$0.277348\pi$
$258$		−	26.3548i		−	1.64078i
$259$	46.6597	−	11.5006i	2.89929	−	0.714611i
$260$	−15.6312	+	27.7871i	−0.969404	+	1.72328i
$261$	3.66481	+	0.903294i	0.226846	+	0.0559125i
$262$	0.0807973	−	0.327808i	0.00499167	−	0.0202520i
$263$	0.151984	+	1.25170i	0.00937176	+	0.0771834i	0.996644	−	0.0818539i	$-0.0260841\pi$
$263$	0.151984	+	1.25170i	0.00937176	+	0.0771834i	−0.987273	+	0.159037i	$0.949161\pi$
$264$	16.9965	−	8.92045i	1.04606	−	0.549016i
$265$	−9.33139	+	1.13304i	−0.573222	+	0.0696018i
$266$	−2.33080	+	4.44097i	−0.142911	+	0.272294i
$267$	−1.08787	−	1.22795i	−0.0665766	−	0.0751494i
$268$		−	4.23556i		−	0.258728i
$269$	7.17496	−	6.35646i	0.437465	−	0.387560i	−0.415445	−	0.909618i	$-0.636374\pi$
$269$	7.17496	−	6.35646i	0.437465	−	0.387560i	0.852910	+	0.522058i	$0.174836\pi$
$270$	3.47813	−	5.03893i	0.211672	−	0.306660i
$271$	2.50142	+	10.1486i	0.151950	+	0.616486i	0.996689	+	0.0813076i	$0.0259096\pi$
$271$	2.50142	+	10.1486i	0.151950	+	0.616486i	−0.844739	+	0.535179i	$0.820244\pi$
$272$	1.42815	−	1.26523i	0.0865941	−	0.0767157i
$273$	14.7753	+	6.10086i	0.894244	+	0.369241i
$274$	13.0746	+	11.5831i	0.789864	+	0.699758i
$275$	−5.85409	+	11.1540i	−0.353015	+	0.672613i
$276$	3.78680	−	1.98747i	0.227939	−	0.119631i
$277$	−1.73115	−	4.56466i	−0.104014	−	0.274264i	0.872898	−	0.487902i	$-0.162238\pi$
$277$	−1.73115	−	4.56466i	−0.104014	−	0.274264i	−0.976913	+	0.213639i	$0.931469\pi$
$278$	43.3059	+	29.8919i	2.59732	+	1.79280i
$279$	−0.232271	−	0.442556i	−0.0139057	−	0.0264951i
$280$	−8.67962	+	35.2146i	−0.518707	+	2.10448i
$281$	−7.82553	−	8.83319i	−0.466832	−	0.526944i	0.467192	−	0.884156i	$-0.345266\pi$
$281$	−7.82553	−	8.83319i	−0.466832	−	0.526944i	−0.934023	+	0.357212i	$0.883727\pi$
$282$	19.2625	+	17.0651i	1.14707	+	1.01621i
$283$	12.9129	+	18.7075i	0.767592	+	1.11205i	0.990541	+	0.137218i	$0.0438162\pi$
$283$	12.9129	+	18.7075i	0.767592	+	1.11205i	−0.222949	+	0.974830i	$0.571568\pi$
$284$	−5.51453	−	10.5071i	−0.327227	−	0.623479i
$285$	0.460289	−	1.21368i	0.0272652	−	0.0718924i
$286$	−37.7574	−	35.4633i	−2.23264	−	2.09699i
$287$	−16.5307	−	43.5880i	−0.975778	−	2.57292i
$288$	3.39279	−	3.82967i	0.199922	−	0.225666i
$289$	−0.307197	−	0.272153i	−0.0180704	−	0.0160090i
$290$	22.4387	−	5.53065i	1.31765	−	0.324771i
$291$	−3.18834	−	12.9356i	−0.186904	−	0.758298i
$292$	30.2954	+	3.67852i	1.77290	+	0.215269i
$293$	19.7660	−	7.49625i	1.15474	−	0.437936i	0.298448	−	0.954426i	$-0.403531\pi$
$293$	19.7660	−	7.49625i	1.15474	−	0.437936i	0.856293	+	0.516490i	$0.172762\pi$
$294$	29.0227	+	3.52399i	1.69264	+	0.205523i
$295$	−4.28873	+	6.21330i	−0.249700	+	0.361752i
$296$	32.4814	−	8.00596i	1.88795	−	0.465337i
$297$	4.12423	+	4.65529i	0.239312	+	0.270128i
$298$	1.92523	+	15.8557i	0.111525	+	0.918495i
$299$	−3.36908	−	3.16437i	−0.194839	−	0.183000i
$300$	0.814463	−	6.70771i	0.0470230	−	0.387270i
$301$	−41.6284	+	28.7340i	−2.39942	+	1.65620i
$302$	2.26602	−	5.97502i	0.130395	−	0.343823i
$303$	0.374180	+	3.08165i	0.0214961	+	0.177036i
$304$	−0.104067	+	0.198284i	−0.00596867	+	0.0113724i
$305$	−12.6016	+	14.2243i	−0.721567	+	0.814480i
$306$	7.93244	+	5.47537i	0.453468	+	0.313006i
$307$	5.91474	−	4.08265i	0.337572	−	0.233009i	−0.387204	−	0.921994i	$-0.626559\pi$
$307$	5.91474	−	4.08265i	0.337572	−	0.233009i	0.724775	+	0.688985i	$0.241944\pi$
$308$	−81.4521	−	42.7494i	−4.64117	−	2.43587i
$309$	−0.195248	+	1.60801i	−0.0111073	+	0.0914765i
$310$	−2.51849	−	1.73839i	−0.143040	−	0.0987337i
$311$	−6.37780	−	9.23984i	−0.361652	−	0.523943i	0.599349	−	0.800488i	$-0.295426\pi$
$311$	−6.37780	−	9.23984i	−0.361652	−	0.523943i	−0.961001	+	0.276544i	$0.910811\pi$
$312$	10.2856	+	4.24702i	0.582309	+	0.240440i
$313$	15.0601	−	21.8184i	0.851249	−	1.23325i	−0.119424	−	0.992843i	$-0.538105\pi$
$313$	15.0601	−	21.8184i	0.851249	−	1.23325i	0.970673	−	0.240403i	$-0.0772797\pi$
$314$	27.2431	−	10.3319i	1.53742	−	0.583065i
$315$	−11.7513			−0.662111
$316$	−7.80892			−0.439286
$317$	6.35726	−	2.41099i	0.357060	−	0.135415i	−0.169551	−	0.985521i	$-0.554232\pi$
$317$	6.35726	−	2.41099i	0.357060	−	0.135415i	0.526611	+	0.850107i	$0.323463\pi$
$318$	1.96052	+	7.95412i	0.109940	+	0.446045i
$319$			23.4751i			1.31435i
$320$	8.07701	−	32.7697i	0.451519	−	1.83188i
$321$	−3.28833	+	8.67060i	−0.183536	+	0.483946i
$322$	−11.6251	−	6.10133i	−0.647842	−	0.340014i
$323$	1.91062	+	0.724601i	0.106310	+	0.0403179i
$324$	−2.95395	−	1.55035i	−0.164108	−	0.0861307i
$325$	−7.13840	+	1.54067i	−0.395967	+	0.0854610i
$326$	−29.7266	+	15.6017i	−1.64640	+	0.864099i
$327$	−4.76467	+	0.578536i	−0.263487	+	0.0319931i
$328$	−11.5076	−	30.3431i	−0.635402	−	1.67542i
$329$	5.95351	−	49.0316i	0.328228	−	2.70320i
$330$	35.6054	+	13.5033i	1.96001	+	0.743334i
$331$	−19.8462	−	7.52668i	−1.09085	−	0.413704i	−0.257401	−	0.966305i	$-0.582866\pi$
$331$	−19.8462	−	7.52668i	−1.09085	−	0.413704i	−0.833446	+	0.552601i	$0.813635\pi$
$332$	−29.7882	+	20.5613i	−1.63484	+	1.12845i
$333$	5.03724	+	9.59766i	0.276039	+	0.525949i
$334$	−45.0043	−	11.0926i	−2.46253	−	0.606958i
$335$	2.51889	−	2.23154i	0.137621	−	0.121922i
$336$	2.01253	+	0.244365i	0.109793	+	0.0133312i
$337$	4.23693			0.230800			0.115400	−	0.993319i	$-0.463185\pi$
$337$	4.23693			0.230800			0.115400	+	0.993319i	$0.463185\pi$
$338$	1.74634	−	29.9791i	0.0949884	−	1.63065i
$339$	−3.98203			−0.216274
$340$	36.6268	+	4.44730i	1.98637	+	0.241189i
$341$	2.32674	−	2.06131i	0.126000	−	0.111626i
$342$	−1.09838	−	0.270727i	−0.0593938	−	0.0146393i
$343$	−11.6539	−	22.2047i	−0.629252	−	1.19894i
$344$	−28.9790	+	20.0027i	−1.56244	+	1.07848i
$345$	3.17705	+	1.20490i	0.171047	+	0.0648695i
$346$	11.7670	+	4.46265i	0.632600	+	0.239913i
$347$	−2.25060	+	18.5353i	−0.120818	+	0.995030i	0.798631	+	0.601821i	$0.205558\pi$
$347$	−2.25060	+	18.5353i	−0.120818	+	0.995030i	−0.919449	+	0.393208i	$0.871365\pi$
$348$	−4.46518	−	11.7737i	−0.239359	−	0.631137i
$349$	17.4957	−	2.12436i	0.936524	−	0.113715i	0.361978	−	0.932187i	$-0.382102\pi$
$349$	17.4957	−	2.12436i	0.936524	−	0.113715i	0.574546	+	0.818472i	$0.305179\pi$
$350$	−18.3672	+	9.63987i	−0.981770	+	0.515273i
$351$	−0.538534	+	3.56511i	−0.0287448	+	0.190291i
$352$	28.1760	+	14.7879i	1.50179	+	0.788199i
$353$	−17.9296	−	6.79980i	−0.954297	−	0.361917i	−0.172192	−	0.985063i	$-0.555085\pi$
$353$	−17.9296	−	6.79980i	−0.954297	−	0.361917i	−0.782105	+	0.623146i	$0.785854\pi$
$354$	5.82603	+	3.05774i	0.309650	+	0.162517i
$355$	3.34317	−	8.81522i	0.177437	−	0.467863i
$356$	−1.30976	+	5.31389i	−0.0694170	+	0.281636i
$357$		−	18.4993i		−	0.979085i
$358$	11.1420	+	45.2050i	0.588875	+	2.38916i
$359$	6.58698	−	2.49811i	0.347647	−	0.131845i	−0.174600	−	0.984640i	$-0.555863\pi$
$359$	6.58698	−	2.49811i	0.347647	−	0.131845i	0.522247	+	0.852794i	$0.325094\pi$
$360$	−8.18050			−0.431150
$361$	18.7602			0.987377
$362$	−1.48673	+	0.563841i	−0.0781406	+	0.0296348i
$363$	−15.7246	+	22.7810i	−0.825328	+	1.19569i
$364$	−11.2507	−	52.1281i	−0.589698	−	2.73225i
$365$	13.7737	+	19.9547i	0.720950	+	1.04448i
$366$	13.6301	+	9.40817i	0.712456	+	0.491773i
$367$	2.35759	−	19.4165i	0.123065	−	1.01353i	−0.792083	−	0.610414i	$-0.791003\pi$
$367$	2.35759	−	19.4165i	0.123065	−	1.01353i	0.915148	−	0.403119i	$-0.132074\pi$
$368$	−0.519047	−	0.272417i	−0.0270572	−	0.0142007i
$369$	8.65344	−	5.97304i	0.450480	−	0.310944i
$370$	54.6182	+	37.7002i	2.83946	+	1.95994i
$371$	10.4263	−	11.7689i	0.541309	−	0.611011i
$372$	−0.774875	+	1.47640i	−0.0401754	+	0.0765478i
$373$	1.59014	+	13.0960i	0.0823344	+	0.678085i	0.974184	+	0.225754i	$0.0724844\pi$
$373$	1.59014	+	13.0960i	0.0823344	+	0.678085i	−0.891850	+	0.452331i	$0.850592\pi$
$374$	−21.2574	+	56.0511i	−1.09919	+	2.89833i
$375$	−6.48863	+	4.47878i	−0.335071	+	0.231283i
$376$	4.14445	−	34.1326i	0.213733	−	1.76025i
$377$	−10.4448	+	8.72437i	−0.537933	+	0.449328i
$378$	1.23447	+	10.1668i	0.0634943	+	0.522922i
$379$	18.3922	+	20.7604i	0.944741	+	1.06639i	0.997699	+	0.0677958i	$0.0215966\pi$
$379$	18.3922	+	20.7604i	0.944741	+	1.06639i	−0.0529579	+	0.998597i	$0.516865\pi$
$380$	−4.20451	+	1.03632i	−0.215687	+	0.0531621i
$381$	2.53947	−	3.67906i	0.130101	−	0.188484i
$382$	−26.7161	−	3.24392i	−1.36692	−	0.165974i
$383$	−15.2219	+	5.77290i	−0.777801	+	0.294981i	−0.711377	−	0.702810i	$-0.751928\pi$
$383$	−15.2219	+	5.77290i	−0.777801	+	0.294981i	−0.0664241	+	0.997791i	$0.521159\pi$
$384$	−19.0414	−	2.31204i	−0.971702	−	0.117986i
$385$	−17.4907	−	70.9624i	−0.891407	−	3.61658i
$386$	−20.7171	+	5.10632i	−1.05447	+	0.259905i
$387$	−8.53977	−	7.56558i	−0.434101	−	0.384580i
$388$	−29.4729	+	33.2681i	−1.49626	+	1.68893i
$389$	−1.11455	−	2.93882i	−0.0565098	−	0.149004i	0.903788	−	0.427979i	$-0.140774\pi$
$389$	−1.11455	−	2.93882i	−0.0565098	−	0.149004i	−0.960298	+	0.278975i	$0.910005\pi$
$390$	7.22449	+	20.8603i	0.365826	+	1.05630i
$391$	−1.89679	+	5.00141i	−0.0959246	+	0.252932i
$392$	−18.1527	−	34.5872i	−0.916852	−	1.74692i
$393$	−0.0830257	−	0.120283i	−0.00418809	−	0.00606750i
$394$	15.9110	+	14.0959i	0.801583	+	0.710141i
$395$	−4.11420	−	4.64397i	−0.207008	−	0.233663i
$396$	4.96543	−	20.1455i	0.249522	−	1.01235i
$397$	−10.4063	−	19.8275i	−0.522276	−	0.995113i	−0.993579	−	0.113142i	$-0.963908\pi$
$397$	−10.4063	−	19.8275i	−0.522276	−	0.995113i	0.471303	−	0.881971i	$-0.343784\pi$
$398$	11.6489	+	8.04064i	0.583906	+	0.403041i
$399$	0.769918	+	2.03011i	0.0385441	+	0.101633i
$400$	−0.820074	+	0.430408i	−0.0410037	+	0.0215204i
$401$	−2.79037	+	5.31661i	−0.139344	+	0.265499i	−0.945121	−	0.326721i	$-0.894056\pi$
$401$	−2.79037	+	5.31661i	−0.139344	+	0.265499i	0.805776	+	0.592220i	$0.201748\pi$
$402$	−2.19525	−	1.94482i	−0.109489	−	0.0969987i
$403$	1.78186	+	0.269162i	0.0887607	+	0.0134079i
$404$	7.75169	−	6.86740i	0.385661	−	0.341666i
$405$	−0.634318	−	2.57353i	−0.0315195	−	0.127880i
$406$	−21.9592	+	31.8134i	−1.08982	+	1.57887i
$407$	−50.4598	+	44.7035i	−2.50120	+	2.21587i
$408$		−	12.8780i		−	0.637555i
$409$	−17.6555	−	19.9289i	−0.873006	−	0.985420i	0.126973	−	0.991906i	$-0.459474\pi$
$409$	−17.6555	−	19.9289i	−0.873006	−	0.985420i	−0.999979	+	0.00648619i	$0.997935\pi$
$410$	29.9184	−	57.0048i	1.47757	−	2.81527i
$411$	7.50655	−	0.911460i	0.370271	−	0.0449590i
$412$	4.78487	−	2.51129i	0.235734	−	0.123723i
$413$	−1.52217	−	12.5362i	−0.0749012	−	0.616867i
$414$	0.708682	−	2.87524i	0.0348298	−	0.141310i
$415$	−27.9220	−	6.88215i	−1.37064	−	0.337831i
$416$	3.89186	+	18.0322i	0.190814	+	0.884101i
$417$	22.1176	−	5.45150i	1.08310	−	0.266961i
$418$		−	7.03574i		−	0.344130i
$419$	−20.5342	−	5.06122i	−1.00316	−	0.247257i	−0.296671	−	0.954980i	$-0.595876\pi$
$419$	−20.5342	−	5.06122i	−1.00316	−	0.247257i	−0.706490	+	0.707723i	$0.749723\pi$
$420$	22.2700	+	32.2637i	1.08667	+	1.57431i
$421$	9.50885	−	10.7333i	0.463433	−	0.523108i	−0.469609	−	0.882874i	$-0.655605\pi$
$421$	9.50885	−	10.7333i	0.463433	−	0.523108i	0.933042	+	0.359766i	$0.117144\pi$
$422$	−8.43557	+	1.02426i	−0.410637	+	0.0498604i
$423$	11.0592	−	1.34284i	0.537719	−	0.0652909i
$424$	7.25814	−	8.19275i	0.352486	−	0.397875i
$425$	4.80085	+	6.95523i	0.232875	+	0.337378i
$426$	−7.97778	−	1.96635i	−0.386525	−	0.0952698i
$427$		−	31.7868i		−	1.53827i
$428$	30.0372	−	7.40351i	1.45190	−	0.357862i
$429$	−22.3301	+	2.05427i	−1.07811	+	0.0991812i
$430$	−67.8248	−	16.7173i	−3.27080	−	0.806181i
$431$	6.30655	−	25.5867i	0.303776	−	1.23247i	−0.598435	−	0.801171i	$-0.704210\pi$
$431$	6.30655	−	25.5867i	0.303776	−	1.23247i	0.902211	−	0.431296i	$-0.141943\pi$
$432$	0.0551175	+	0.453933i	0.00265184	+	0.0218399i
$433$	−21.0448	+	11.0452i	−1.01135	+	0.530798i	−0.887161	−	0.461461i	$-0.847326\pi$
$433$	−21.0448	+	11.0452i	−1.01135	+	0.530798i	−0.124190	+	0.992258i	$0.539633\pi$
$434$	5.08141	−	0.616995i	0.243915	−	0.0296167i
$435$	4.64931	−	8.85852i	0.222917	−	0.424733i
$436$	10.6180	+	11.9852i	0.508509	+	0.573988i
$437$		−	0.627797i		−	0.0300316i
$438$	15.8171	−	14.0127i	0.755770	−	0.669554i
$439$	20.5571	−	29.7822i	0.981139	−	1.42142i	0.0756113	−	0.997137i	$-0.475909\pi$
$439$	20.5571	−	29.7822i	0.981139	−	1.42142i	0.905528	−	0.424288i	$-0.139475\pi$
$440$	−12.1759	−	49.3994i	−0.580462	−	2.35503i
$441$	9.47332	−	8.39263i	0.451111	−	0.399649i
$442$	−32.8390	+	11.3730i	−1.56199	+	0.540959i
$443$	−7.04404	−	6.24048i	−0.334672	−	0.296494i	0.479003	−	0.877813i	$-0.340998\pi$
$443$	−7.04404	−	6.24048i	−0.334672	−	0.296494i	−0.813676	+	0.581319i	$0.802537\pi$
$444$	16.8046	−	32.0186i	0.797513	−	1.51953i
$445$	−3.85023	+	2.02075i	−0.182518	+	0.0957930i
$446$	9.35835	+	24.6759i	0.443131	+	1.16844i
$447$	5.69041	+	3.92780i	0.269147	+	0.185779i
$448$	26.2354	+	49.9874i	1.23951	+	2.36168i
$449$	−8.65533	+	35.1161i	−0.408470	+	1.65723i	0.301853	+	0.953354i	$0.402395\pi$
$449$	−8.65533	+	35.1161i	−0.408470	+	1.65723i	−0.710324	+	0.703875i	$0.751451\pi$
$450$	−3.10256	−	3.50207i	−0.146256	−	0.165089i
$451$	48.9491	+	43.3651i	2.30492	+	2.04198i
$452$	7.54639	+	10.9328i	0.354952	+	0.514237i
$453$	−1.28559	−	2.44949i	−0.0604024	−	0.115087i
$454$	−5.46714	+	14.4157i	−0.256585	+	0.676560i
$455$	25.0730	−	34.1549i	1.17544	−	1.60121i
$456$	0.535967	+	1.41323i	0.0250990	+	0.0661805i
$457$	−18.3346	+	20.6955i	−0.857658	+	0.968096i	−0.999763	−	0.0217559i	$-0.993074\pi$
$457$	−18.3346	+	20.6955i	−0.857658	+	0.968096i	0.142105	+	0.989852i	$0.454613\pi$
$458$	33.2712	+	29.4758i	1.55466	+	1.37731i
$459$	4.05133	−	0.998563i	0.189100	−	0.0466089i
$460$	−2.71277	−	11.0061i	−0.126484	−	0.513164i
$461$	−15.5557	−	1.88881i	−0.724503	−	0.0879706i	−0.250027	−	0.968239i	$-0.580439\pi$
$461$	−15.5557	−	1.88881i	−0.724503	−	0.0879706i	−0.474476	+	0.880268i	$0.657363\pi$
$462$	−59.5565	+	22.5868i	−2.77082	+	1.05083i
$463$	−14.6400	−	1.77761i	−0.680377	−	0.0826127i	−0.226950	−	0.973906i	$-0.572875\pi$
$463$	−14.6400	−	1.77761i	−0.680377	−	0.0826127i	−0.453426	+	0.891294i	$0.649799\pi$
$464$	−0.980451	+	1.42043i	−0.0455163	+	0.0659418i
$465$	−1.28626	+	0.317036i	−0.0596491	+	0.0147022i
$466$	−5.26780	−	5.94611i	−0.244026	−	0.275448i
$467$	4.74917	+	39.1130i	0.219766	+	1.80993i	0.517936	+	0.855419i	$0.326700\pi$
$467$	4.74917	+	39.1130i	0.219766	+	1.80993i	−0.298171	+	0.954513i	$0.596376\pi$
$468$	10.8087	−	5.27770i	0.499633	−	0.243962i
$469$	−0.678490	+	5.58787i	−0.0313298	+	0.258024i
$470$	56.1361	−	38.7480i	2.58937	−	1.78731i
$471$	4.47271	−	11.7936i	0.206092	−	0.543419i
$472$	−1.05964	−	8.72690i	−0.0487738	−	0.401688i
$473$	32.9755	−	62.8296i	1.51622	−	2.88891i
$474$	−3.58558	+	4.04729i	−0.164691	+	0.185898i
$475$	−0.816313	−	0.563460i	−0.0374550	−	0.0258533i
$476$	−50.7905	+	35.0581i	−2.32798	+	1.60689i
$477$	3.14018	+	1.64810i	0.143779	+	0.0754611i
$478$	5.22488	−	43.0308i	0.238980	−	1.96818i
$479$	4.74030	+	3.27200i	0.216590	+	0.149501i	0.671420	−	0.741077i	$-0.265685\pi$
$479$	4.74030	+	3.27200i	0.216590	+	0.149501i	−0.454830	+	0.890578i	$0.650300\pi$
$480$	−7.70367	−	11.1607i	−0.351623	−	0.509414i
$481$	−38.6430	−	5.83730i	−1.76197	−	0.266158i
$482$	12.1410	−	17.5892i	0.553006	−	0.801168i
$483$	−5.31421	+	2.01541i	−0.241805	+	0.0917044i
$484$	92.3461			4.19755
$485$	−35.3126			−1.60346
$486$	−2.15988	+	0.819136i	−0.0979743	+	0.0371568i
$487$	−1.16091	−	4.71000i	−0.0526059	−	0.213430i	0.938757	−	0.344581i	$-0.111979\pi$
$487$	−1.16091	−	4.71000i	−0.0526059	−	0.213430i	−0.991362	+	0.131151i	$0.958133\pi$
$488$		−	22.1279i		−	1.00168i
$489$	−3.47807	+	14.1111i	−0.157284	+	0.638124i
$490$	27.4787	−	72.4554i	1.24136	−	3.27320i
$491$	−33.1873	−	17.4180i	−1.49772	−	0.786065i	−0.500882	−	0.865515i	$-0.666991\pi$
$491$	−33.1873	−	17.4180i	−1.49772	−	0.786065i	−0.996839	+	0.0794509i	$0.974683\pi$
$492$	−32.7984	−	12.4388i	−1.47867	−	0.560784i
$493$	13.9453	+	7.31908i	0.628067	+	0.329635i
$494$	3.13041	−	2.61479i	0.140844	−	0.117645i
$495$	14.5966	−	7.66090i	0.656069	−	0.344332i
$496$	0.226878	−	0.0275480i	0.0101871	−	0.00123694i
$497$	5.59207	+	14.7451i	0.250839	+	0.661407i
$498$	−3.02097	+	24.8800i	−0.135373	+	1.11490i
$499$	−10.7118	−	4.06244i	−0.479525	−	0.181860i	0.102986	−	0.994683i	$-0.467160\pi$
$499$	−10.7118	−	4.06244i	−0.479525	−	0.181860i	−0.582511	+	0.812823i	$0.697930\pi$
$500$	24.5933	+	9.32701i	1.09985	+	0.417117i
$501$	−16.5136	+	11.3985i	−0.737772	+	0.509247i
$502$	−18.2852	−	34.8396i	−0.816110	−	1.55497i
$503$	34.6569	+	8.54216i	1.54527	+	0.380876i	0.917569	−	0.397575i	$-0.130148\pi$
$503$	34.6569	+	8.54216i	1.54527	+	0.380876i	0.627705	+	0.778451i	$0.283994\pi$
$504$	10.2422	−	9.07376i	0.456222	−	0.404178i
$505$	8.16808	+	0.991785i	0.363475	+	0.0441338i
$506$	18.4174			0.818755
$507$	−9.21286	−	9.17187i	−0.409157	−	0.407337i
$508$	−14.9136			−0.661683
$509$	7.32961	+	0.889976i	0.324879	+	0.0394475i	0.281352	−	0.959605i	$-0.409217\pi$
$509$	7.32961	+	0.889976i	0.324879	+	0.0394475i	0.0435276	+	0.999052i	$0.486140\pi$
$510$	19.1227	−	16.9413i	0.846769	−	0.750172i
$511$	−39.3787	−	9.70597i	−1.74201	−	0.429367i
$512$	2.39896	+	4.57083i	0.106020	+	0.202004i
$513$	−0.403034	+	0.278194i	−0.0177944	+	0.0122826i
$514$	−55.9710	−	21.2270i	−2.46877	−	0.936282i
$515$	4.01441	+	1.52247i	0.176896	+	0.0670879i
$516$	−4.58779	+	37.7839i	−0.201966	+	1.66334i
$517$	24.5696	+	64.7846i	1.08057	+	2.84922i
$518$	−110.200	+	13.3807i	−4.84191	+	0.587915i
$519$	4.82396	−	2.53181i	0.211748	−	0.111134i
$520$	17.4542	−	23.7764i	0.765417	−	1.04266i
$521$	−2.35917	−	1.23819i	−0.103357	−	0.0542460i	0.412252	−	0.911070i	$-0.364742\pi$
$521$	−2.35917	−	1.23819i	−0.103357	−	0.0542460i	−0.515610	+	0.856824i	$0.672435\pi$
$522$	−8.15245	−	3.09182i	−0.356823	−	0.135325i
$523$	−3.85432	−	2.02290i	−0.168538	−	0.0884553i	0.378345	−	0.925665i	$-0.376493\pi$
$523$	−3.85432	−	2.02290i	−0.168538	−	0.0884553i	−0.546883	+	0.837209i	$0.684186\pi$
$524$	−0.172900	+	0.455901i	−0.00755318	+	0.0199161i
$525$	−2.14900	+	8.71885i	−0.0937902	+	0.380522i
$526$		−	2.91267i		−	0.126998i
$527$	−0.499087	−	2.02488i	−0.0217406	−	0.0882050i
$528$	−2.65912	+	1.00847i	−0.115723	+	0.0438881i
$529$	−21.3566			−0.928549
$530$	21.7138			0.943186
$531$	2.66326	−	1.01004i	0.115576	−	0.0438321i
$532$	4.11466	−	5.96112i	0.178393	−	0.258447i
$533$	−1.10280	+	37.8953i	−0.0477676	+	1.64143i
$534$	2.15274	+	3.11879i	0.0931583	+	0.134963i
$535$	20.2282	+	13.9625i	0.874542	+	0.603653i
$536$	−0.472320	+	3.88991i	−0.0204011	+	0.168018i
$537$	17.8463	+	9.36648i	0.770127	+	0.404194i
$538$	−18.2232	+	12.5785i	−0.785657	+	0.542300i
$539$	64.7806	+	44.7148i	2.79030	+	1.92600i
$540$	−5.86363	+	6.61867i	−0.252330	+	0.284822i
$541$	14.9882	−	28.5577i	0.644395	−	1.22779i	−0.315897	−	0.948794i	$-0.602305\pi$
$541$	14.9882	−	28.5577i	0.644395	−	1.22779i	0.960292	−	0.278998i	$-0.0900023\pi$
$542$	−2.91035	−	23.9689i	−0.125010	−	1.02955i
$543$	−0.244088	+	0.643606i	−0.0104748	+	0.0276198i
$544$	17.5695	−	12.1274i	0.753286	−	0.519956i
$545$	−1.53344	+	12.6290i	−0.0656854	+	0.540968i
$546$	−32.1834	−	18.1042i	−1.37732	−	0.774790i
$547$	−2.14904	−	17.6989i	−0.0918862	−	0.756751i	−0.963714	−	0.266938i	$-0.913988\pi$
$547$	−2.14904	−	17.6989i	−0.0918862	−	0.756751i	0.871827	−	0.489813i	$-0.162935\pi$
$548$	−16.7282	−	18.8822i	−0.714592	−	0.806608i
$549$	6.96129	−	1.71580i	0.297100	−	0.0732287i
$550$	16.5300	−	23.9479i	0.704843	−	1.02114i
$551$	−1.83497	−	0.222806i	−0.0781725	−	0.00949186i
$552$	−3.69940	+	1.40300i	−0.157457	+	0.0597156i
$553$	10.3021	+	1.25090i	0.438091	+	0.0531939i
$554$	2.69880	+	10.9495i	0.114661	+	0.465199i
$555$	27.8951	−	6.87553i	1.18408	−	0.291850i
$556$	−56.8826	−	50.3936i	−2.41236	−	2.13716i
$557$	14.5845	−	16.4625i	0.617964	−	0.697537i	−0.353308	−	0.935507i	$-0.614943\pi$
$557$	14.5845	−	16.4625i	0.617964	−	0.697537i	0.971273	+	0.237970i	$0.0764819\pi$
$558$	0.409408	+	1.07952i	0.0173316	+	0.0456998i
$559$	40.2099	−	8.67845i	1.70070	−	0.367059i
$560$	1.90547	−	5.02430i	0.0805207	−	0.212316i
$561$	12.0600	+	22.9784i	0.509174	+	0.970151i
$562$	15.4856	+	22.4348i	0.653222	+	0.946355i
$563$	−0.156927	−	0.139025i	−0.00661370	−	0.00585923i	0.659809	−	0.751433i	$-0.270637\pi$
$563$	−0.156927	−	0.139025i	−0.00661370	−	0.00585923i	−0.666423	+	0.745574i	$0.732175\pi$
$564$	−24.6453	−	27.8188i	−1.03775	−	1.17138i
$565$	−2.52588	+	10.2479i	−0.106264	+	0.431132i
$566$	−24.4023	−	46.4947i	−1.02571	−	1.95432i
$567$	3.64873	+	2.51853i	0.153232	+	0.105769i
$568$	3.89283	+	10.2646i	0.163340	+	0.430691i
$569$	4.17960	−	2.19362i	0.175218	−	0.0919615i	−0.374834	−	0.927092i	$-0.622300\pi$
$569$	4.17960	−	2.19362i	0.175218	−	0.0919615i	0.550052	+	0.835130i	$0.314608\pi$
$570$	−1.39345	+	2.65500i	−0.0583652	+	0.111206i
$571$	−13.6304	−	12.0755i	−0.570416	−	0.505345i	0.327889	−	0.944716i	$-0.393663\pi$
$571$	−13.6304	−	12.0755i	−0.570416	−	0.505345i	−0.898305	+	0.439372i	$0.855201\pi$
$572$	47.9581	+	57.4151i	2.00523	+	2.40065i
$573$	−8.72044	+	7.72563i	−0.364301	+	0.322743i
$574$	25.7709	+	104.557i	1.07566	+	4.36411i
$575$	1.47497	−	2.13686i	0.0615104	−	0.0891132i
$576$	−9.53107	+	8.44379i	−0.397128	+	0.351824i
$577$		−	2.30990i		−	0.0961623i	−0.998843	−	0.0480811i	$-0.984689\pi$
$577$		−	2.30990i		−	0.0961623i	0.998843	−	0.0480811i	$-0.0153106\pi$
$578$	0.628672	+	0.709624i	0.0261493	+	0.0295165i
$579$	−4.29259	+	8.17885i	−0.178394	+	0.339901i
$580$	−33.1324	+	4.02300i	−1.37575	+	0.167046i
$581$	42.5926	−	22.3543i	1.76704	−	0.927412i
$582$	3.70957	+	30.5511i	0.153767	+	1.26638i
$583$	−5.27847	+	21.4156i	−0.218612	+	0.886943i
$584$	−27.4129	−	6.75666i	−1.13435	−	0.279593i
$585$	8.83331	+	3.64735i	0.365212	+	0.150799i
$586$	−47.4137	+	11.6864i	−1.95864	+	0.482762i
$587$			6.81606i			0.281329i	0.990057	+	0.140665i	$0.0449239\pi$
$587$			6.81606i			0.281329i	−0.990057	+	0.140665i	$0.955076\pi$
$588$	−40.9953	−	10.1044i	−1.69062	−	0.416700i
$589$	0.139043	+	0.201438i	0.00572916	+	0.00830012i
$590$	11.5647	−	13.0539i	0.476113	−	0.537420i
$591$	9.13502	−	1.10919i	0.375764	−	0.0456261i
$592$	−4.92029	+	0.597431i	−0.202223	+	0.0245543i
$593$	11.5569	−	13.0450i	0.474583	−	0.535694i	−0.461655	−	0.887060i	$-0.652744\pi$
$593$	11.5569	−	13.0450i	0.474583	−	0.535694i	0.936238	+	0.351366i	$0.114283\pi$
$594$	−8.16128	−	11.8236i	−0.334861	−	0.485130i
$595$	−47.6085	−	11.7344i	−1.95176	−	0.481065i
$596$		−	23.0668i		−	0.944855i
$597$	5.94942	−	1.46640i	0.243494	−	0.0600158i
$598$	6.84473	+	8.19447i	0.279902	+	0.335097i
$599$	−16.3514	−	4.03025i	−0.668099	−	0.164672i	−0.109344	−	0.994004i	$-0.534875\pi$
$599$	−16.3514	−	4.03025i	−0.668099	−	0.164672i	−0.558756	+	0.829332i	$0.688721\pi$
$600$	−1.49600	+	6.06949i	−0.0610738	+	0.247786i
$601$	−1.51699	−	12.4935i	−0.0618793	−	0.509622i	−0.990389	−	0.138313i	$-0.955832\pi$
$601$	−1.51699	−	12.4935i	−0.0618793	−	0.509622i	0.928509	−	0.371309i	$-0.121091\pi$
$602$	103.461	−	54.3005i	4.21675	−	2.21312i
$603$	−1.26036	+	0.153036i	−0.0513260	+	0.00623210i
$604$	−4.28884	+	8.17169i	−0.174510	+	0.332502i
$605$	48.6533	+	54.9182i	1.97804	+	2.23274i
$606$		−	7.17089i		−	0.291297i
$607$	1.60156	−	1.41886i	0.0650054	−	0.0575897i	−0.629994	−	0.776600i	$-0.716943\pi$
$607$	1.60156	−	1.41886i	0.0650054	−	0.0575897i	0.695000	+	0.719010i	$0.255404\pi$
$608$	−1.42335	+	2.06208i	−0.0577244	+	0.0836283i
$609$	4.00478	+	16.2480i	0.162282	+	0.658404i
$610$	32.8580	−	29.1097i	1.33038	−	1.17862i
$611$	−19.6935	+	35.0086i	−0.796713	+	1.41629i
$612$	−10.4193	−	9.23070i	−0.421176	−	0.373129i
$613$	8.60739	−	16.4000i	0.347649	−	0.662390i	−0.647359	−	0.762185i	$-0.724126\pi$
$613$	8.60739	−	16.4000i	0.347649	−	0.662390i	0.995008	+	0.0997952i	$0.0318188\pi$
$614$	−14.7002	+	7.71524i	−0.593250	+	0.311362i
$615$	−9.88276	−	26.0587i	−0.398511	−	1.05079i
$616$	70.0380	+	48.3438i	2.82191	+	1.94783i
$617$	−10.7997	−	20.5771i	−0.434780	−	0.828405i	−0.999994	−	0.00346011i	$-0.998899\pi$
$617$	−10.7997	−	20.5771i	−0.434780	−	0.828405i	0.565214	−	0.824945i	$-0.308794\pi$
$618$	0.895466	−	3.63305i	0.0360209	−	0.146143i
$619$	4.53391	+	5.11773i	0.182233	+	0.205699i	0.832528	−	0.553983i	$-0.186893\pi$
$619$	4.53391	+	5.11773i	0.182233	+	0.205699i	−0.650294	+	0.759682i	$0.725354\pi$
$620$	3.30805	+	2.93067i	0.132854	+	0.117699i
$621$	−0.728227	−	1.05502i	−0.0292228	−	0.0423365i
$622$	12.0525	+	22.9642i	0.483263	+	0.920781i
$623$	2.57916	−	6.80068i	0.103332	−	0.272464i
$624$	−1.43695	−	0.808331i	−0.0575239	−	0.0323591i
$625$	11.0015	+	29.0087i	0.440061	+	1.16035i
$626$	−40.6103	+	45.8395i	−1.62311	+	1.83212i
$627$	−2.27980	−	2.01973i	−0.0910465	−	0.0806601i
$628$	−40.8560	+	10.0701i	−1.63033	+	0.401840i
$629$	10.8237	+	43.9133i	0.431568	+	1.75094i
$630$	26.9476	+	3.27203i	1.07362	+	0.130361i
$631$	−10.9813	+	4.16465i	−0.437158	+	0.165792i	−0.563358	−	0.826213i	$-0.690491\pi$
$631$	−10.9813	+	4.16465i	−0.437158	+	0.165792i	0.126200	+	0.992005i	$0.459722\pi$
$632$	7.17167	+	0.870798i	0.285274	+	0.0346385i
$633$	−2.08968	+	3.02742i	−0.0830572	+	0.120329i
$634$	−15.2495	+	3.75866i	−0.605635	+	0.149276i
$635$	−7.85734	−	8.86910i	−0.311809	−	0.351960i
$636$	−1.42608	−	11.7448i	−0.0565477	−	0.465712i
$637$	4.18036	+	45.4408i	0.165632	+	1.80043i
$638$	6.53638	−	53.8319i	0.258778	−	2.13123i
$639$	−2.92731	+	2.02058i	−0.115803	+	0.0799328i
$640$	−18.0284	+	47.5371i	−0.712636	+	1.87907i
$641$	5.90324	+	48.6175i	0.233164	+	1.92028i	0.368781	+	0.929516i	$0.379775\pi$
$641$	5.90324	+	48.6175i	0.233164	+	1.92028i	−0.135617	+	0.990761i	$0.543302\pi$
$642$	9.95487	−	18.9674i	0.392887	−	0.748584i
$643$	−14.3436	+	16.1905i	−0.565655	+	0.638493i	−0.959843	−	0.280537i	$-0.909487\pi$
$643$	−14.3436	+	16.1905i	−0.565655	+	0.638493i	0.394188	+	0.919030i	$0.371026\pi$
$644$	15.6044	+	10.7709i	0.614899	+	0.424434i
$645$	−24.8872	+	17.1784i	−0.979932	+	0.676398i
$646$	−4.17958	−	2.19361i	−0.164443	−	0.0863065i
$647$	4.78356	−	39.3962i	0.188061	−	1.54882i	−0.527063	−	0.849826i	$-0.676707\pi$
$647$	4.78356	−	39.3962i	0.188061	−	1.54882i	0.715125	−	0.698997i	$-0.246370\pi$
$648$	2.54001	+	1.75324i	0.0997809	+	0.0688738i
$649$	10.0633	+	14.5792i	0.395020	+	0.572285i
$650$	16.7984	−	1.54538i	0.658888	−	0.0606148i
$651$	1.25878	−	1.82365i	0.0493354	−	0.0714746i
$652$	45.3338	−	17.1928i	1.77541	−	0.673324i
$653$	−19.9326			−0.780022			−0.390011	−	0.920810i	$-0.627529\pi$
$653$	−19.9326			−0.780022			−0.390011	+	0.920810i	$0.627529\pi$
$654$	11.0872			0.433544
$655$	−0.362218	+	0.137371i	−0.0141530	+	0.00536754i
$656$	1.15064	+	4.66832i	0.0449249	+	0.182267i
$657$		−	9.14782i		−	0.356891i
$658$	−27.3046	+	110.779i	−1.06444	+	4.31862i
$659$	−11.4394	+	30.1633i	−0.445617	+	1.17500i	0.504586	+	0.863362i	$0.331645\pi$
$659$	−11.4394	+	30.1633i	−0.445617	+	1.17500i	−0.950202	+	0.311633i	$0.899124\pi$
$660$	−48.6955	−	25.5574i	−1.89547	−	0.994819i
$661$	−24.7253	−	9.37708i	−0.961704	−	0.364726i	−0.176733	−	0.984259i	$-0.556553\pi$
$661$	−24.7253	−	9.37708i	−0.961704	−	0.364726i	−0.784971	+	0.619533i	$0.787322\pi$
$662$	43.4147	+	22.7858i	1.68736	+	0.885595i
$663$	−5.74177	+	13.9057i	−0.222992	+	0.540051i
$664$	29.6502	−	15.5616i	1.15065	−	0.603907i
$665$	5.71292	−	0.693674i	0.221538	−	0.0268995i
$666$	−8.87880	−	23.4115i	−0.344047	−	0.907176i
$667$	0.583238	−	4.80340i	0.0225831	−	0.185988i
$668$	62.5900	+	23.7373i	2.42168	+	0.918423i
$669$	10.6822	+	4.05124i	0.413000	+	0.156630i
$670$	−6.39754	+	4.41590i	−0.247158	+	0.170601i
$671$	20.7224	+	39.4832i	0.799979	+	1.52423i
$672$	22.0245	+	5.42856i	0.849615	+	0.209411i
$673$	−7.38428	+	6.54190i	−0.284643	+	0.252172i	−0.793347	−	0.608770i	$-0.791663\pi$
$673$	−7.38428	+	6.54190i	−0.284643	+	0.252172i	0.508704	+	0.860942i	$0.330125\pi$
$674$	−9.71593	−	1.17973i	−0.374243	−	0.0454414i
$675$	−2.02542			−0.0779586
$676$	−7.72238	+	42.6760i	−0.297014	+	1.64138i
$677$	−1.20398			−0.0462728			−0.0231364	−	0.999732i	$-0.507365\pi$
$677$	−1.20398			−0.0462728			−0.0231364	+	0.999732i	$0.507365\pi$
$678$	9.13141	+	1.10875i	0.350690	+	0.0425814i
$679$	44.2121	−	39.1685i	1.69671	−	1.50315i
$680$	−33.1419	−	8.16874i	−1.27093	−	0.313257i
$681$	3.10169	+	5.90978i	0.118857	+	0.226463i
$682$	−5.90952	+	4.07905i	−0.226287	+	0.156195i
$683$	−22.3669	−	8.48265i	−0.855846	−	0.324580i	−0.112635	−	0.993636i	$-0.535929\pi$
$683$	−22.3669	−	8.48265i	−0.855846	−	0.324580i	−0.743211	+	0.669057i	$0.766698\pi$
$684$	1.52759	+	0.579337i	0.0584087	+	0.0221515i
$685$	2.41587	−	19.8965i	0.0923057	−	0.760206i
$686$	20.5415	+	54.1636i	0.784280	+	2.06798i
$687$	19.1021	−	2.31942i	0.728792	−	0.0884913i
$688$	4.61940	−	2.42445i	0.176113	−	0.0924312i
$689$	−11.4902	+	5.61043i	−0.437740	+	0.213740i
$690$	−6.94998	−	3.64763i	−0.264581	−	0.138863i
$691$	−17.1424	−	6.50127i	−0.652129	−	0.247320i	0.00627969	−	0.999980i	$-0.498001\pi$
$691$	−17.1424	−	6.50127i	−0.652129	−	0.247320i	−0.658409	+	0.752660i	$0.728770\pi$
$692$	−16.0931	−	8.44632i	−0.611769	−	0.321081i
$693$	−9.77786	+	25.7821i	−0.371430	+	0.979381i
$694$	10.3219	−	41.8777i	0.391815	−	1.58966i
$695$		−	60.3783i		−	2.29028i
$696$	2.78787	+	11.3108i	0.105674	+	0.428736i
$697$	41.0224	−	15.5577i	1.55383	−	0.589291i
$698$	−40.7118			−1.54097
$699$	−3.43894			−0.130072
$700$	28.0105	−	10.6230i	1.05870	−	0.401511i
$701$	−11.9875	+	17.3668i	−0.452760	+	0.655936i	−0.981191	−	0.193040i	$-0.938165\pi$
$701$	−11.9875	+	17.3668i	−0.452760	+	0.655936i	0.528431	+	0.848976i	$0.322781\pi$
$702$	2.22761	−	8.02538i	0.0840756	−	0.302899i
$703$	−3.01541	−	4.36857i	−0.113728	−	0.164764i
$704$	−65.1754	−	44.9873i	−2.45639	−	1.69552i
$705$	3.55926	−	29.3131i	0.134049	−	1.10400i
$706$	39.2220	+	20.5853i	1.47614	+	0.774738i
$707$	−11.3267	+	7.81826i	−0.425984	+	0.294036i
$708$	−7.82028	−	5.39795i	−0.293904	−	0.202867i
$709$	29.7595	−	33.5916i	1.11764	−	1.26156i	0.155850	−	0.987781i	$-0.450188\pi$
$709$	29.7595	−	33.5916i	1.11764	−	1.26156i	0.961793	−	0.273777i	$-0.0882731\pi$
$710$	−10.1209	+	19.2838i	−0.379831	+	0.723707i
$711$	0.282146	+	2.32368i	0.0105813	+	0.0871449i
$712$	1.79544	−	4.73419i	0.0672870	−	0.177421i
$713$	−0.527304	+	0.363972i	−0.0197477	+	0.0136309i
$714$	−5.15092	+	42.4217i	−0.192768	+	1.58759i
$715$	−8.87766	+	58.7703i	−0.332006	+	2.19788i
$716$	−8.10472	−	66.7483i	−0.302887	−	2.49450i
$717$	−12.4434	−	14.0457i	−0.464708	−	0.524547i
$718$	−15.8005	+	3.89448i	−0.589670	+	0.145341i
$719$	18.7612	−	27.1802i	0.699673	−	1.01365i	−0.298569	−	0.954388i	$-0.596509\pi$
$719$	18.7612	−	27.1802i	0.699673	−	1.01365i	0.998242	−	0.0592633i	$-0.0188752\pi$
$720$	1.20317	+	0.146092i	0.0448396	+	0.00544452i
$721$	−6.71484	+	2.54660i	−0.250074	+	0.0948405i
$722$	−43.0199	−	5.22357i	−1.60104	−	0.194401i
$723$	−2.21419	−	8.98334i	−0.0823467	−	0.334094i
$724$	2.22962	−	0.549552i	0.0828631	−	0.0204239i
$725$	−5.72231	−	5.06953i	−0.212521	−	0.188277i
$726$	42.4021	−	47.8621i	1.57369	−	1.77633i
$727$	−13.9577	−	36.8033i	−0.517661	−	1.36496i	−0.897952	−	0.440093i	$-0.854946\pi$
$727$	−13.9577	−	36.8033i	−0.517661	−	1.36496i	0.380291	−	0.924867i	$-0.375824\pi$
$728$	4.51963	+	49.1287i	0.167508	+	1.82083i
$729$	−0.354605	+	0.935016i	−0.0131335	+	0.0346302i
$730$	−26.0291	−	49.5943i	−0.963381	−	1.83557i
$731$	−27.0427	−	39.1782i	−1.00021	−	1.44906i
$732$	−17.9032	−	15.8609i	−0.661721	−	0.586234i
$733$	−4.85150	−	5.47621i	−0.179194	−	0.202268i	0.652050	−	0.758176i	$-0.273909\pi$
$733$	−4.85150	−	5.47621i	−0.179194	−	0.202268i	−0.831244	+	0.555908i	$0.812371\pi$
$734$	−10.8126	+	43.8685i	−0.399101	+	1.61922i
$735$	−15.5896	−	29.7035i	−0.575031	−	1.09563i
$736$	−5.39789	−	3.72589i	−0.198969	−	0.137338i
$737$	−2.80006	−	7.38316i	−0.103142	−	0.271962i
$738$	−21.5068	+	11.2876i	−0.791676	+	0.415503i
$739$	0.189359	−	0.360794i	0.00696569	−	0.0132720i	−0.881948	−	0.471346i	$-0.843768\pi$
$739$	0.189359	−	0.360794i	0.00696569	−	0.0132720i	0.888914	+	0.458074i	$0.151461\pi$
$740$	−71.7413	−	63.5572i	−2.63726	−	2.33641i
$741$	0.0513629	−	1.76497i	0.00188686	−	0.0648379i
$742$	−27.1861	+	24.0848i	−0.998034	+	0.884181i
$743$	−3.80994	−	15.4575i	−0.139773	−	0.567082i	−0.998505	−	0.0546572i	$-0.982593\pi$
$743$	−3.80994	−	15.4575i	−0.139773	−	0.567082i	0.858732	−	0.512425i	$-0.171253\pi$
$744$	0.876279	−	1.26951i	0.0321259	−	0.0465425i
$745$	13.7179	−	12.1530i	0.502583	−	0.445250i
$746$		−	30.4739i		−	1.11573i
$747$	7.19466	+	8.12109i	0.263239	+	0.297135i
$748$	40.2332	−	76.6579i	1.47107	−	2.80289i
$749$	−40.8133	+	4.95564i	−1.49129	+	0.181075i
$750$	16.1265	−	8.46383i	0.588856	−	0.309055i
$751$	0.357286	+	2.94252i	0.0130376	+	0.107374i	0.997775	−	0.0666733i	$-0.0212385\pi$
$751$	0.357286	+	2.94252i	0.0130376	+	0.107374i	−0.984737	+	0.174047i	$0.944315\pi$
$752$	−1.21912	+	4.94615i	−0.0444566	+	0.180368i
$753$	−16.5382	−	4.07630i	−0.602686	−	0.148549i
$754$	26.3806	−	17.0981i	0.960727	−	0.622675i
$755$	−7.11931	+	1.75475i	−0.259098	+	0.0638620i
$756$		−	14.7906i		−	0.537930i
$757$	16.9464	+	4.17691i	0.615927	+	0.151812i	0.534922	−	0.844901i	$-0.320341\pi$
$757$	16.9464	+	4.17691i	0.615927	+	0.151812i	0.0810050	+	0.996714i	$0.474187\pi$
$758$	−36.3955	−	52.7280i	−1.32194	−	1.91517i
$759$	5.28703	−	5.96783i	0.191907	−	0.216618i
$760$	3.97696	−	0.482891i	0.144260	−	0.0175163i
$761$	−36.5921	+	4.44308i	−1.32646	+	0.161062i	−0.752919	−	0.658113i	$-0.771355\pi$
$761$	−36.5921	+	4.44308i	−1.32646	+	0.161062i	−0.573543	+	0.819175i	$0.694432\pi$
$762$	−6.84779	+	7.72956i	−0.248069	+	0.280012i
$763$	−12.0881	−	17.5127i	−0.437620	−	0.634002i
$764$	37.7372	+	9.30139i	1.36528	+	0.336512i
$765$		−	11.0596i		−	0.399862i
$766$	36.5135	−	8.99977i	1.31929	−	0.325175i
$767$	−2.74677	+	9.89577i	−0.0991801	+	0.357315i
$768$	18.2944	+	4.50915i	0.660141	+	0.162710i
$769$	11.4607	−	46.4977i	0.413282	−	1.67675i	−0.283108	−	0.959088i	$-0.591365\pi$
$769$	11.4607	−	46.4977i	0.413282	−	1.67675i	0.696390	−	0.717663i	$-0.254788\pi$

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.29315 - 0.278439i) q^{2} +(-0.748511 + 0.663123i) q^{3} +(3.23914 + 0.798376i) q^{4} +(1.23177 + 2.34695i) q^{5} +(1.90109 - 1.31223i) q^{6} +(-4.14543 - 1.57215i) q^{7} +(-2.88578 - 1.09443i) q^{8} +(0.120537 - 0.992709i) q^{9} +(-2.17116 - 5.72488i) q^{10} +(6.17406 - 0.749667i) q^{11} +(-2.95395 + 1.55035i) q^{12} +(2.62810 + 2.46842i) q^{13} +(9.06835 + 4.75944i) q^{14} +(-2.47831 - 0.939898i) q^{15} +(0.404890 + 0.212503i) q^{16} +(1.47962 - 3.90143i) q^{17} +(-0.552818 + 2.24287i) q^{18} +0.489722i q^{19} +(2.11614 + 8.58550i) q^{20} +(4.14543 - 1.57215i) q^{21} -14.3668 q^{22} -1.28194 q^{23} +(2.88578 - 1.09443i) q^{24} +(-1.15057 + 1.66689i) q^{25} +(-5.33934 - 6.39222i) q^{26} +(0.568065 + 0.822984i) q^{27} +(-12.1724 - 8.40203i) q^{28} +(-0.454964 + 3.74697i) q^{29} +(5.42144 + 2.84539i) q^{30} +(0.411332 - 0.283922i) q^{31} +(4.21071 + 2.90644i) q^{32} +(-4.12423 + 4.65529i) q^{33} +(-4.47930 + 8.53459i) q^{34} +(-1.41646 - 11.6656i) q^{35} +(1.18299 - 3.11929i) q^{36} +(-8.92051 + 6.15739i) q^{37} +(0.136358 - 1.12301i) q^{38} +(-3.60403 - 0.104882i) q^{39} +(-0.986050 - 8.12085i) q^{40} +(6.97254 + 7.87037i) q^{41} +(-9.94385 + 2.45094i) q^{42} +(6.48106 - 9.38944i) q^{43} +(20.5972 + 2.50095i) q^{44} +(2.47831 - 0.939898i) q^{45} +(2.93969 + 0.356943i) q^{46} +(2.66609 + 10.8168i) q^{47} +(-0.443980 + 0.109431i) q^{48} +(9.47332 + 8.39263i) q^{49} +(3.10256 - 3.50207i) q^{50} +(1.47962 + 3.90143i) q^{51} +(6.54206 + 10.0938i) q^{52} +(-1.25757 + 3.31594i) q^{53} +(-1.07351 - 2.04540i) q^{54} +(9.36447 + 13.5668i) q^{55} +(10.2422 + 9.07376i) q^{56} +(-0.324746 - 0.366562i) q^{57} +(2.08660 - 8.46569i) q^{58} +(1.32370 + 2.52210i) q^{59} +(-7.27719 - 5.02308i) q^{60} +(2.54238 + 6.70371i) q^{61} +(-1.02230 + 0.536545i) q^{62} +(-2.06037 + 3.92570i) q^{63} +(-9.53107 - 8.44379i) q^{64} +(-2.55602 + 9.20854i) q^{65} +(10.7537 - 9.52695i) q^{66} +(-0.303840 - 1.23273i) q^{67} +(7.90749 - 11.4560i) q^{68} +(0.959549 - 0.850086i) q^{69} +27.1455i q^{70} +(-2.35869 - 2.66241i) q^{71} +(-1.43429 + 2.73282i) q^{72} +(9.08113 - 1.10265i) q^{73} +(22.1706 - 11.6360i) q^{74} +(-0.244138 - 2.01066i) q^{75} +(-0.390983 + 1.58628i) q^{76} +(-26.7727 - 6.59888i) q^{77} +(8.23538 + 1.24401i) q^{78} +(-2.27273 + 0.560178i) q^{79} +1.21201i q^{80} +(-0.970942 - 0.239316i) q^{81} +(-13.7977 - 19.9894i) q^{82} +(-7.19466 + 8.12109i) q^{83} +(14.6828 - 1.78281i) q^{84} +(10.9790 - 1.33309i) q^{85} +(-17.4764 + 19.7268i) q^{86} +(-2.14415 - 3.10634i) q^{87} +(-18.6374 - 4.59371i) q^{88} +1.64053i q^{89} +(-5.94485 + 1.46527i) q^{90} +(-7.01388 - 14.3644i) q^{91} +(-4.15240 - 1.02347i) q^{92} +(-0.119611 + 0.485282i) q^{93} +(-3.10194 - 25.5468i) q^{94} +(-1.14935 + 0.603227i) q^{95} +(-5.07909 + 0.616713i) q^{96} +(-6.19138 + 11.7967i) q^{97} +(-19.3869 - 21.8833i) q^{98} -6.21941i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31}+ \cdots - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

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