LMFDB - Embedded newform 605.2.r.a.32.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(32,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 2]))

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

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

chi := DirichletCharacter("605.32");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.r (of order $44$, degree $20$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$64$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			32.6
Character	$\chi$	$=$	605.32
Dual form			605.2.r.a.208.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36166 - 1.81897i) q^{2} +(0.545918 - 0.545918i) q^{3} +(-0.891058 + 3.03466i) q^{4} +(-0.445983 - 2.19114i) q^{5} +(-1.73637 - 0.249652i) q^{6} +(-0.413052 + 1.89877i) q^{7} +(2.47545 - 0.923297i) q^{8} +2.40395i q^{9} +O(q^{10})$	\(q+(-1.36166 - 1.81897i) q^{2} +(0.545918 - 0.545918i) q^{3} +(-0.891058 + 3.03466i) q^{4} +(-0.445983 - 2.19114i) q^{5} +(-1.73637 - 0.249652i) q^{6} +(-0.413052 + 1.89877i) q^{7} +(2.47545 - 0.923297i) q^{8} +2.40395i q^{9} +(-3.37834 + 3.79483i) q^{10} +(3.16424 + 0.993785i) q^{11} +(1.17023 + 2.14312i) q^{12} +(3.40906 + 6.24322i) q^{13} +(4.01625 - 1.83416i) q^{14} +(-1.43965 - 0.952713i) q^{15} +(0.271211 + 0.174297i) q^{16} +(-0.330966 - 4.62751i) q^{17} +(4.37271 - 3.27337i) q^{18} +(2.48723 + 2.87042i) q^{19} +(7.04677 + 0.599025i) q^{20} +(0.811081 + 1.26207i) q^{21} +(-2.50096 - 7.10885i) q^{22} +(-7.45371 + 1.62145i) q^{23} +(0.847351 - 1.85544i) q^{24} +(-4.60220 + 1.95442i) q^{25} +(6.71424 - 14.7021i) q^{26} +(2.95011 + 2.95011i) q^{27} +(-5.39408 - 2.94539i) q^{28} +(4.54918 + 5.25003i) q^{29} +(0.227367 + 3.91596i) q^{30} +(0.115973 - 0.0340528i) q^{31} +(-0.429219 - 6.00127i) q^{32} +(2.26994 - 1.18489i) q^{33} +(-7.96663 + 6.90313i) q^{34} +(4.34469 + 0.0582364i) q^{35} +(-7.29517 - 2.14206i) q^{36} +(-1.18408 - 0.646554i) q^{37} +(1.83443 - 8.43274i) q^{38} +(5.26935 + 1.54722i) q^{39} +(-3.12708 - 5.01230i) q^{40} +(-2.96241 - 0.425931i) q^{41} +(1.19124 - 3.19384i) q^{42} +(4.29078 - 1.60038i) q^{43} +(-5.83532 + 8.71687i) q^{44} +(5.26739 - 1.07212i) q^{45} +(13.0988 + 11.3502i) q^{46} +(1.27449 - 1.70252i) q^{47} +(0.243211 - 0.0529073i) q^{48} +(2.93270 + 1.33932i) q^{49} +(9.82168 + 5.70999i) q^{50} +(-2.70692 - 2.34556i) q^{51} +(-21.9837 + 4.78227i) q^{52} +(-0.862651 + 3.96554i) q^{53} +(1.34910 - 9.38323i) q^{54} +(0.766328 - 7.37650i) q^{55} +(0.730637 + 5.08169i) q^{56} +(2.92484 + 0.209188i) q^{57} +(3.35520 - 15.4236i) q^{58} +(-7.09833 + 1.02059i) q^{59} +(4.17398 - 3.51994i) q^{60} +(0.326657 - 0.0469662i) q^{61} +(-0.219858 - 0.164583i) q^{62} +(-4.56454 - 0.992956i) q^{63} +(-9.84438 + 8.53020i) q^{64} +(12.1594 - 10.2541i) q^{65} +(-5.24617 - 2.51553i) q^{66} +(1.99713 - 1.49503i) q^{67} +(14.3378 + 3.11901i) q^{68} +(-3.18393 + 4.95430i) q^{69} +(-5.81008 - 7.98216i) q^{70} +(-4.07509 - 4.70290i) q^{71} +(2.21956 + 5.95086i) q^{72} +(-3.27485 - 15.0542i) q^{73} +(0.436250 + 3.03419i) q^{74} +(-1.44547 + 3.57938i) q^{75} +(-10.9270 + 4.99020i) q^{76} +(-3.19397 + 5.59767i) q^{77} +(-4.36074 - 11.6916i) q^{78} +(2.08409 + 4.56353i) q^{79} +(0.260953 - 0.671995i) q^{80} -3.99080 q^{81} +(3.25906 + 5.96852i) q^{82} +(2.49855 + 0.543525i) q^{83} +(-4.55267 + 1.33678i) q^{84} +(-9.99192 + 2.78898i) q^{85} +(-8.75364 - 5.62562i) q^{86} +(5.34957 + 0.382608i) q^{87} +(8.75048 - 0.461459i) q^{88} +(4.61374 + 3.99783i) q^{89} +(-9.12256 - 8.12135i) q^{90} +(-13.2626 + 3.89424i) q^{91} +(1.72111 - 24.0643i) q^{92} +(0.0447219 - 0.0819020i) q^{93} -4.83225 q^{94} +(5.18022 - 6.73003i) q^{95} +(-3.51052 - 3.04188i) q^{96} +(-1.02182 + 0.381120i) q^{97} +(-1.55717 - 7.15821i) q^{98} +(-2.38901 + 7.60666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 22 q^{2} - 40 q^{3} - 14 q^{5} - 44 q^{6} - 22 q^{7} - 22 q^{8}+O(q^{10}) $ 1280 * q - 22 * q^2 - 40 * q^3 - 14 * q^5 - 44 * q^6 - 22 * q^7 - 22 * q^8	$ 1280 q - 22 q^{2} - 40 q^{3} - 14 q^{5} - 44 q^{6} - 22 q^{7} - 22 q^{8} - 66 q^{10} - 48 q^{11} + 44 q^{12} - 66 q^{13} - 26 q^{15} + 80 q^{16} - 22 q^{17} - 44 q^{18} - 54 q^{20} - 44 q^{21} - 90 q^{22} - 34 q^{23} - 30 q^{25} - 12 q^{26} + 80 q^{27} - 22 q^{28} - 22 q^{30} - 52 q^{31} - 22 q^{32} - 62 q^{33} - 22 q^{35} + 216 q^{36} + 52 q^{37} + 70 q^{38} - 44 q^{41} + 44 q^{42} - 22 q^{43} + 104 q^{45} - 44 q^{46} - 18 q^{47} - 72 q^{48} + 88 q^{50} - 484 q^{51} - 22 q^{52} + 14 q^{53} + 140 q^{55} - 316 q^{56} + 44 q^{57} - 6 q^{58} + 34 q^{60} - 44 q^{61} - 22 q^{62} - 44 q^{63} - 22 q^{65} - 84 q^{66} - 138 q^{67} - 22 q^{68} - 126 q^{70} - 4 q^{71} + 220 q^{72} - 22 q^{73} - 66 q^{75} + 88 q^{76} - 22 q^{77} - 104 q^{78} - 324 q^{80} - 1056 q^{81} - 58 q^{82} - 22 q^{83} - 110 q^{85} - 52 q^{86} + 44 q^{87} - 2 q^{88} + 176 q^{90} + 104 q^{91} - 278 q^{92} - 128 q^{93} - 22 q^{95} - 44 q^{96} + 46 q^{97} - 22 q^{98}+O(q^{100}) $ 1280 * q - 22 * q^2 - 40 * q^3 - 14 * q^5 - 44 * q^6 - 22 * q^7 - 22 * q^8 - 66 * q^10 - 48 * q^11 + 44 * q^12 - 66 * q^13 - 26 * q^15 + 80 * q^16 - 22 * q^17 - 44 * q^18 - 54 * q^20 - 44 * q^21 - 90 * q^22 - 34 * q^23 - 30 * q^25 - 12 * q^26 + 80 * q^27 - 22 * q^28 - 22 * q^30 - 52 * q^31 - 22 * q^32 - 62 * q^33 - 22 * q^35 + 216 * q^36 + 52 * q^37 + 70 * q^38 - 44 * q^41 + 44 * q^42 - 22 * q^43 + 104 * q^45 - 44 * q^46 - 18 * q^47 - 72 * q^48 + 88 * q^50 - 484 * q^51 - 22 * q^52 + 14 * q^53 + 140 * q^55 - 316 * q^56 + 44 * q^57 - 6 * q^58 + 34 * q^60 - 44 * q^61 - 22 * q^62 - 44 * q^63 - 22 * q^65 - 84 * q^66 - 138 * q^67 - 22 * q^68 - 126 * q^70 - 4 * q^71 + 220 * q^72 - 22 * q^73 - 66 * q^75 + 88 * q^76 - 22 * q^77 - 104 * q^78 - 324 * q^80 - 1056 * q^81 - 58 * q^82 - 22 * q^83 - 110 * q^85 - 52 * q^86 + 44 * q^87 - 2 * q^88 + 176 * q^90 + 104 * q^91 - 278 * q^92 - 128 * q^93 - 22 * q^95 - 44 * q^96 + 46 * q^97 - 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{22}\right)$

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 $

$2$	−1.36166	−	1.81897i	−0.962842	−	1.28621i	−0.958165	−	0.286217i	$-0.907602\pi$
$2$	−1.36166	−	1.81897i	−0.962842	−	1.28621i	−0.00467668	−	0.999989i	$-0.501489\pi$
$3$	0.545918	−	0.545918i	0.315186	−	0.315186i	−0.531729	−	0.846915i	$-0.678457\pi$
$3$	0.545918	−	0.545918i	0.315186	−	0.315186i	0.846915	+	0.531729i	$0.178457\pi$
$4$	−0.891058	+	3.03466i	−0.445529	+	1.51733i
$5$	−0.445983	−	2.19114i	−0.199450	−	0.979908i
$5$	−0.445983	−	2.19114i	−0.199450	−	0.979908i
$6$	−1.73637	−	0.249652i	−0.708868	−	0.101920i
$7$	−0.413052	+	1.89877i	−0.156119	+	0.717668i	0.830816	+	0.556548i	$0.187874\pi$
$7$	−0.413052	+	1.89877i	−0.156119	+	0.717668i	−0.986935	+	0.161120i	$0.948489\pi$
$8$	2.47545	−	0.923297i	0.875205	−	0.326435i
$9$			2.40395i			0.801316i
$10$	−3.37834	+	3.79483i	−1.06832	+	1.20003i
$11$	3.16424	+	0.993785i	0.954053	+	0.299638i
$11$	3.16424	+	0.993785i	0.954053	+	0.299638i
$12$	1.17023	+	2.14312i	0.337817	+	0.618666i
$13$	3.40906	+	6.24322i	0.945502	+	1.73156i	0.616790	+	0.787127i	$0.288433\pi$
$13$	3.40906	+	6.24322i	0.945502	+	1.73156i	0.328712	+	0.944430i	$0.393386\pi$
$14$	4.01625	−	1.83416i	1.07339	−	0.490199i
$15$	−1.43965	−	0.952713i	−0.371717	−	0.245990i
$16$	0.271211	+	0.174297i	0.0678028	+	0.0435742i
$17$	−0.330966	−	4.62751i	−0.0802710	−	1.12234i	−0.864758	−	0.502190i	$-0.832528\pi$
$17$	−0.330966	−	4.62751i	−0.0802710	−	1.12234i	0.784487	−	0.620146i	$-0.212927\pi$
$18$	4.37271	−	3.27337i	1.03066	−	0.771540i
$19$	2.48723	+	2.87042i	0.570610	+	0.658519i	0.965559	−	0.260184i	$-0.0837833\pi$
$19$	2.48723	+	2.87042i	0.570610	+	0.658519i	−0.394949	+	0.918703i	$0.629238\pi$
$20$	7.04677	+	0.599025i	1.57571	+	0.133946i
$21$	0.811081	+	1.26207i	0.176992	+	0.275405i
$22$	−2.50096	−	7.10885i	−0.533206	−	1.51561i
$23$	−7.45371	+	1.62145i	−1.55421	+	0.338097i	−0.905970	−	0.423343i	$-0.860857\pi$
$23$	−7.45371	+	1.62145i	−1.55421	+	0.338097i	−0.648236	+	0.761440i	$0.724493\pi$
$24$	0.847351	−	1.85544i	0.172965	−	0.378740i
$25$	−4.60220	+	1.95442i	−0.920440	+	0.390885i
$26$	6.71424	−	14.7021i	1.31677	−	2.88333i
$27$	2.95011	+	2.95011i	0.567749	+	0.567749i
$28$	−5.39408	−	2.94539i	−1.01938	−	0.556626i
$29$	4.54918	+	5.25003i	0.844761	+	0.974906i	0.999916	−	0.0129840i	$-0.00413306\pi$
$29$	4.54918	+	5.25003i	0.844761	+	0.974906i	−0.155155	+	0.987890i	$0.549588\pi$
$30$	0.227367	+	3.91596i	0.0415114	+	0.714954i
$31$	0.115973	−	0.0340528i	0.0208294	−	0.00611607i	−0.271301	−	0.962494i	$-0.587454\pi$
$31$	0.115973	−	0.0340528i	0.0208294	−	0.00611607i	0.292131	+	0.956378i	$0.405636\pi$
$32$	−0.429219	−	6.00127i	−0.0758759	−	1.06088i
$33$	2.26994	−	1.18489i	0.395146	−	0.206263i
$34$	−7.96663	+	6.90313i	−1.36627	+	1.18388i
$35$	4.34469	+	0.0582364i	0.734387	+	0.00984374i
$36$	−7.29517	−	2.14206i	−1.21586	−	0.357009i
$37$	−1.18408	−	0.646554i	−0.194661	−	0.106293i	0.378963	−	0.925412i	$-0.376281\pi$
$37$	−1.18408	−	0.646554i	−0.194661	−	0.106293i	−0.573623	+	0.819119i	$0.694463\pi$
$38$	1.83443	−	8.43274i	0.297584	−	1.36797i
$39$	5.26935	+	1.54722i	0.843772	+	0.247754i
$40$	−3.12708	−	5.01230i	−0.494435	−	0.792514i
$41$	−2.96241	−	0.425931i	−0.462651	−	0.0665192i	−0.0929519	−	0.995671i	$-0.529630\pi$
$41$	−2.96241	−	0.425931i	−0.462651	−	0.0665192i	−0.369700	+	0.929151i	$0.620539\pi$
$42$	1.19124	−	3.19384i	0.183813	−	0.492820i
$43$	4.29078	−	1.60038i	0.654338	−	0.244055i	−0.000297758	−	1.00000i	$-0.500095\pi$
$43$	4.29078	−	1.60038i	0.654338	−	0.244055i	0.654636	+	0.755945i	$0.272822\pi$
$44$	−5.83532	+	8.71687i	−0.879708	+	1.31412i
$45$	5.26739	−	1.07212i	0.785216	−	0.159822i
$46$	13.0988	+	11.3502i	1.93132	+	1.67349i
$47$	1.27449	−	1.70252i	0.185903	−	0.248338i	−0.697901	−	0.716194i	$-0.745883\pi$
$47$	1.27449	−	1.70252i	0.185903	−	0.248338i	0.883805	+	0.467856i	$0.154974\pi$
$48$	0.243211	−	0.0529073i	0.0351045	−	0.00763651i
$49$	2.93270	+	1.33932i	0.418958	+	0.191332i
$50$	9.82168	+	5.70999i	1.38900	+	0.807515i
$51$	−2.70692	−	2.34556i	−0.379045	−	0.328444i
$52$	−21.9837	+	4.78227i	−3.04860	+	0.663182i
$53$	−0.862651	+	3.96554i	−0.118494	+	0.544709i	0.879177	+	0.476496i	$0.158093\pi$
$53$	−0.862651	+	3.96554i	−0.118494	+	0.544709i	−0.997671	+	0.0682129i	$0.978270\pi$
$54$	1.34910	−	9.38323i	0.183590	−	1.27690i
$55$	0.766328	−	7.37650i	0.103332	−	0.994647i
$56$	0.730637	+	5.08169i	0.0976355	+	0.679070i
$57$	2.92484	+	0.209188i	0.387404	+	0.0277077i
$58$	3.35520	−	15.4236i	0.440559	−	2.02522i
$59$	−7.09833	+	1.02059i	−0.924124	+	0.132869i	−0.587919	−	0.808920i	$-0.700053\pi$
$59$	−7.09833	+	1.02059i	−0.924124	+	0.132869i	−0.336205	+	0.941789i	$0.609143\pi$
$60$	4.17398	−	3.51994i	0.538858	−	0.454423i
$61$	0.326657	−	0.0469662i	0.0418241	−	0.00601340i	−0.121371	−	0.992607i	$-0.538729\pi$
$61$	0.326657	−	0.0469662i	0.0418241	−	0.00601340i	0.163195	+	0.986594i	$0.447820\pi$
$62$	−0.219858	−	0.164583i	−0.0279219	−	0.0209021i
$63$	−4.56454	−	0.992956i	−0.575079	−	0.125101i
$64$	−9.84438	+	8.53020i	−1.23055	+	1.06628i
$65$	12.1594	−	10.2541i	1.50819	−	1.27186i
$66$	−5.24617	−	2.51553i	−0.645759	−	0.309641i
$67$	1.99713	−	1.49503i	0.243988	−	0.182647i	−0.470284	−	0.882515i	$-0.655849\pi$
$67$	1.99713	−	1.49503i	0.243988	−	0.182647i	0.714273	+	0.699868i	$0.246758\pi$
$68$	14.3378	+	3.11901i	1.73872	+	0.378235i
$69$	−3.18393	+	4.95430i	−0.383300	+	0.596427i
$70$	−5.81008	−	7.98216i	−0.694437	−	0.954050i
$71$	−4.07509	−	4.70290i	−0.483624	−	0.558131i	0.460527	−	0.887646i	$-0.347660\pi$
$71$	−4.07509	−	4.70290i	−0.483624	−	0.558131i	−0.944151	+	0.329514i	$0.893115\pi$
$72$	2.21956	+	5.95086i	0.261577	+	0.701316i
$73$	−3.27485	−	15.0542i	−0.383292	−	1.76196i	−0.614360	−	0.789026i	$-0.710586\pi$
$73$	−3.27485	−	15.0542i	−0.383292	−	1.76196i	0.231068	−	0.972938i	$-0.425778\pi$
$74$	0.436250	+	3.03419i	0.0507130	+	0.352717i
$75$	−1.44547	+	3.57938i	−0.166908	+	0.413311i
$76$	−10.9270	+	4.99020i	−1.25341	+	0.572415i
$77$	−3.19397	+	5.59767i	−0.363986	+	0.637914i
$78$	−4.36074	−	11.6916i	−0.493756	−	1.32381i
$79$	2.08409	+	4.56353i	0.234479	+	0.513437i	0.989894	−	0.141809i	$-0.0452920\pi$
$79$	2.08409	+	4.56353i	0.234479	+	0.513437i	−0.755415	+	0.655247i	$0.772565\pi$
$80$	0.260953	−	0.671995i	0.0291755	−	0.0751314i
$81$	−3.99080			−0.443422
$82$	3.25906	+	5.96852i	0.359903	+	0.659113i
$83$	2.49855	+	0.543525i	0.274251	+	0.0596596i	0.347587	−	0.937648i	$-0.387001\pi$
$83$	2.49855	+	0.543525i	0.274251	+	0.0596596i	−0.0733364	+	0.997307i	$0.523365\pi$
$84$	−4.55267	+	1.33678i	−0.496737	+	0.145855i
$85$	−9.99192	+	2.78898i	−1.08378	+	0.302508i
$86$	−8.75364	−	5.62562i	−0.943929	−	0.606626i
$87$	5.34957	+	0.382608i	0.573534	+	0.0410199i
$88$	8.75048	−	0.461459i	0.932805	−	0.0491917i
$89$	4.61374	+	3.99783i	0.489056	+	0.423769i	0.864163	−	0.503212i	$-0.167849\pi$
$89$	4.61374	+	3.99783i	0.489056	+	0.423769i	−0.375107	+	0.926982i	$0.622394\pi$
$90$	−9.12256	−	8.12135i	−0.961602	−	0.856065i
$91$	−13.2626	+	3.89424i	−1.39029	+	0.408227i
$92$	1.72111	−	24.0643i	0.179438	−	2.50888i
$93$	0.0447219	−	0.0819020i	0.00463744	−	0.00849284i
$94$	−4.83225			−0.498409
$95$	5.18022	−	6.73003i	0.531480	−	0.690486i
$96$	−3.51052	−	3.04188i	−0.358291	−	0.310461i
$97$	−1.02182	+	0.381120i	−0.103750	+	0.0386969i	−0.400803	−	0.916164i	$-0.631269\pi$
$97$	−1.02182	+	0.381120i	−0.103750	+	0.0386969i	0.297053	+	0.954861i	$0.403996\pi$
$98$	−1.55717	−	7.15821i	−0.157298	−	0.723088i
$99$	−2.38901	+	7.60666i	−0.240104	+	0.764498i
$100$	−1.83019	−	15.7076i	−0.183019	−	1.57076i
$101$	5.36164	−	0.770888i	0.533503	−	0.0767062i	0.129702	−	0.991553i	$-0.458598\pi$
$101$	5.36164	−	0.770888i	0.533503	−	0.0767062i	0.403801	+	0.914847i	$0.367689\pi$
$102$	−0.580587	+	8.11767i	−0.0574867	+	0.803769i
$103$	−4.67306	−	6.24248i	−0.460450	−	0.615090i	0.508884	−	0.860835i	$-0.330058\pi$
$103$	−4.67306	−	6.24248i	−0.460450	−	0.615090i	−0.969334	+	0.245745i	$0.920967\pi$
$104$	14.2033	+	12.3072i	1.39275	+	1.20682i
$105$	2.40364	−	2.34005i	0.234571	−	0.228366i
$106$	8.38784	−	3.83060i	0.814699	−	0.372061i
$107$	16.4935	+	6.15176i	1.59449	+	0.594714i	0.980831	−	0.194859i	$-0.0624249\pi$
$107$	16.4935	+	6.15176i	1.59449	+	0.594714i	0.613657	+	0.789572i	$0.289698\pi$
$108$	−11.5813	+	6.32388i	−1.11441	+	0.608516i
$109$	19.3451	+	5.68023i	1.85292	+	0.544068i	0.999748	+	0.0224439i	$0.00714473\pi$
$109$	19.3451	+	5.68023i	1.85292	+	0.544068i	0.853176	+	0.521624i	$0.174673\pi$
$110$	−14.4611	+	8.65038i	−1.37881	+	0.824782i
$111$	−0.999374	+	0.293443i	−0.0948564	+	0.0278523i
$112$	−0.442974	+	0.442974i	−0.0418571	+	0.0418571i
$113$	4.20781	+	11.2816i	0.395837	+	1.06128i	0.970121	+	0.242624i	$0.0780080\pi$
$113$	4.20781	+	11.2816i	0.395837	+	1.06128i	−0.574283	+	0.818656i	$0.694719\pi$
$114$	−3.60214	−	5.60503i	−0.337371	−	0.524959i
$115$	6.87706	+	15.6090i	0.641289	+	1.45555i
$116$	−19.9857	+	9.12714i	−1.85562	+	0.847434i
$117$	−15.0084	+	8.19519i	−1.38752	+	0.757646i
$118$	11.5220	+	11.5220i	1.06068	+	1.06068i
$119$	8.92328	+	1.28297i	0.817996	+	0.117610i
$120$	−4.44344	−	1.02917i	−0.405628	−	0.0939500i
$121$	9.02478	+	6.28914i	0.820435	+	0.571740i
$122$	−0.530227	−	0.530227i	−0.0480045	−	0.0480045i
$123$	−1.84976	+	1.38471i	−0.166787	+	0.124855i
$124$			0.382283i			0.0343300i
$125$	6.33492	+	9.21243i	0.566612	+	0.823984i
$126$	4.40922	+	9.65484i	0.392804	+	0.860121i
$127$	−4.00263	−	5.34689i	−0.355176	−	0.474459i	0.586996	−	0.809590i	$-0.300310\pi$
$127$	−4.00263	−	5.34689i	−0.355176	−	0.474459i	−0.942172	+	0.335131i	$0.891220\pi$
$128$	17.1627	+	3.73352i	1.51698	+	0.330000i
$129$	1.46874	−	3.21609i	0.129315	−	0.283161i
$130$	−35.2089	−	8.15495i	−3.08802	−	0.715236i
$131$	0.160716	+	0.547347i	0.0140418	+	0.0478219i	0.966216	−	0.257734i	$-0.0829759\pi$
$131$	0.160716	+	0.547347i	0.0140418	+	0.0478219i	−0.952174	+	0.305556i	$0.901158\pi$
$132$	1.57309	+	7.94431i	0.136920	+	0.691463i
$133$	−6.47762	+	3.53705i	−0.561681	+	0.306701i
$134$	−5.43884	−	1.59699i	−0.469844	−	0.137959i
$135$	5.14841	−	7.77981i	0.443105	−	0.669580i
$136$	−5.09185	−	11.1496i	−0.436623	−	0.956071i
$137$	−2.72428	−	12.5233i	−0.232751	−	1.06994i	−0.934069	−	0.357092i	$-0.883768\pi$
$137$	−2.72428	−	12.5233i	−0.232751	−	1.06994i	0.701318	−	0.712848i	$-0.252595\pi$
$138$	13.3472	−	0.954608i	1.13619	−	0.0812616i
$139$	2.46328	−	17.1325i	0.208932	−	1.45316i	−0.567717	−	0.823224i	$-0.692173\pi$
$139$	2.46328	−	17.1325i	0.208932	−	1.45316i	0.776650	−	0.629933i	$-0.216918\pi$
$140$	−4.04810	+	13.1328i	−0.342127	+	1.10992i
$141$	−0.233669	−	1.62520i	−0.0196784	−	0.136867i
$142$	−3.00554	+	13.8162i	−0.252219	+	1.15943i
$143$	4.58264	+	23.1429i	0.383219	+	1.93531i
$144$	−0.419000	+	0.651977i	−0.0349167	+	0.0543314i
$145$	9.47470	−	12.3093i	0.786831	−	1.02223i
$146$	−22.9239	+	26.4556i	−1.89720	+	2.18948i
$147$	2.33218	−	0.869857i	0.192355	−	0.0717446i
$148$	3.01715	−	3.01715i	0.248009	−	0.248009i
$149$	−5.54059	+	1.62686i	−0.453902	+	0.133278i	−0.500689	−	0.865627i	$-0.666920\pi$
$149$	−5.54059	+	1.62686i	−0.453902	+	0.133278i	0.0467868	+	0.998905i	$0.485102\pi$
$150$	8.47902	−	2.24465i	0.692309	−	0.183275i
$151$	−0.436137	−	1.48535i	−0.0354923	−	0.120876i	0.939841	−	0.341611i	$-0.110973\pi$
$151$	−0.436137	−	1.48535i	−0.0354923	−	0.120876i	−0.975334	+	0.220735i	$0.929154\pi$
$152$	8.80727	+	4.80913i	0.714364	+	0.390072i
$153$	11.1243	−	0.795624i	0.899345	−	0.0643224i
$154$	14.5311	−	1.81242i	1.17095	−	0.146049i
$155$	−0.126337	−	0.238927i	−0.0101476	−	0.0191911i
$156$	−9.39059	+	14.6121i	−0.751849	+	1.16990i
$157$	−1.21355	−	2.22245i	−0.0968518	−	0.177371i	0.824761	−	0.565482i	$-0.191310\pi$
$157$	−1.21355	−	2.22245i	−0.0968518	−	0.177371i	−0.921613	+	0.388111i	$0.873128\pi$
$158$	5.46309	−	10.0049i	0.434620	−	0.795947i
$159$	1.69392	+	2.63580i	0.134337	+	0.209032i
$160$	−12.9582	+	3.61694i	−1.02444	+	0.285944i
$161$		−	14.8226i		−	1.16819i
$162$	5.43413	+	7.25914i	0.426945	+	0.570332i
$163$	−4.65862	−	1.73757i	−0.364891	−	0.136097i	0.160329	−	0.987064i	$-0.448744\pi$
$163$	−4.65862	−	1.73757i	−0.364891	−	0.136097i	−0.525220	+	0.850966i	$0.676017\pi$
$164$	3.93224	−	8.61040i	0.307056	−	0.672360i
$165$	−3.60861	−	4.44532i	−0.280930	−	0.346067i
$166$	−2.41352	−	5.28488i	−0.187326	−	0.410186i
$167$	1.52107	+	21.2673i	0.117704	+	1.64572i	0.622604	+	0.782537i	$0.286075\pi$
$167$	1.52107	+	21.2673i	0.117704	+	1.64572i	−0.504900	+	0.863178i	$0.668471\pi$
$168$	3.17306	+	2.37532i	0.244807	+	0.183260i
$169$	−20.3278	+	31.6307i	−1.56368	+	2.43313i
$170$	18.6787	+	14.3773i	1.43259	+	1.10269i
$171$	−6.90033	+	5.97917i	−0.527681	+	0.457238i
$172$	1.03328	+	14.4471i	0.0787867	+	1.10158i
$173$	4.35260	+	20.0086i	0.330922	+	1.52122i	0.778883	+	0.627170i	$0.215787\pi$
$173$	4.35260	+	20.0086i	0.330922	+	1.52122i	−0.447961	+	0.894053i	$0.647850\pi$
$174$	−6.58836	−	10.2517i	−0.499462	−	0.777178i
$175$	−1.81005	−	9.54580i	−0.136827	−	0.721595i
$176$	0.684962	+	0.821042i	0.0516310	+	0.0618884i
$177$	−3.31795	+	4.43226i	−0.249392	+	0.333149i
$178$	0.989568	−	13.8360i	0.0741712	−	1.03705i
$179$	−7.90259	−	12.2967i	−0.590667	−	0.919096i	−0.999978	−	0.00670100i	$-0.997867\pi$
$179$	−7.90259	−	12.2967i	−0.590667	−	0.919096i	0.409310	−	0.912395i	$-0.365769\pi$
$180$	−1.44002	+	16.9401i	−0.107333	+	1.26264i
$181$	0.275269	+	1.91454i	0.0204606	+	0.142307i	0.997491	−	0.0707933i	$-0.0225531\pi$
$181$	0.275269	+	1.91454i	0.0204606	+	0.142307i	−0.977030	+	0.213100i	$0.931644\pi$
$182$	25.1427	+	18.8216i	1.86370	+	1.39515i
$183$	0.152688	−	0.203968i	0.0112870	−	0.0150777i
$184$	−16.9542	+	10.8958i	−1.24988	+	0.803251i
$185$	−0.888614	+	2.88283i	−0.0653322	+	0.211950i
$186$	−0.209873	+	0.0301752i	−0.0153887	+	0.00221256i
$187$	3.55149	−	14.9714i	0.259711	−	1.09482i
$188$	4.03092	+	5.38468i	0.293985	+	0.392718i
$189$	−6.82014	+	4.38304i	−0.496092	+	0.318819i
$190$	−19.2954	−	0.258637i	−1.39984	−	0.0187635i
$191$	−6.33174	+	7.30722i	−0.458149	+	0.528732i	−0.937077	−	0.349122i	$-0.886480\pi$
$191$	−6.33174	+	7.30722i	−0.458149	+	0.528732i	0.478928	+	0.877854i	$0.341025\pi$
$192$	−0.717433	+	10.0310i	−0.0517762	+	0.723926i
$193$	−4.10298	+	1.53033i	−0.295339	+	0.110156i	−0.492766	−	0.870162i	$-0.664014\pi$
$193$	−4.10298	+	1.53033i	−0.295339	+	0.110156i	0.197427	+	0.980318i	$0.436741\pi$
$194$	2.08462	+	1.33971i	0.149667	+	0.0961854i
$195$	1.04014	−	12.2359i	0.0744859	−	0.876233i
$196$	−6.67760	+	7.70636i	−0.476971	+	0.550454i
$197$	12.4507	+	4.64388i	0.887076	+	0.330862i	0.751366	−	0.659886i	$-0.229395\pi$
$197$	12.4507	+	4.64388i	0.887076	+	0.330862i	0.135711	+	0.990748i	$0.456668\pi$
$198$	17.0893	−	6.01217i	1.21448	−	0.427267i
$199$	−8.83257	−	4.03370i	−0.626125	−	0.285942i	0.0769749	−	0.997033i	$-0.475474\pi$
$199$	−8.83257	−	4.03370i	−0.626125	−	0.285942i	−0.703099	+	0.711092i	$0.748201\pi$
$200$	−9.58802	+	9.08728i	−0.677975	+	0.642568i
$201$	0.274104	−	1.90644i	0.0193338	−	0.134470i
$202$	−8.70297	−	8.70297i	−0.612339	−	0.612339i
$203$	−11.8477	+	6.46931i	−0.831542	+	0.454056i
$204$	9.53001	−	6.12456i	0.667234	−	0.428805i
$205$	0.387912	+	6.68103i	0.0270929	+	0.466623i
$206$	−4.99174	+	17.0003i	−0.347791	+	1.18447i
$207$	−3.89789	−	17.9183i	−0.270922	−	1.24541i
$208$	−0.163599	+	2.28742i	−0.0113436	+	0.158604i
$209$	5.01760	+	11.5544i	0.347075	+	0.799238i
$210$	−7.52943	−	1.18578i	−0.519580	−	0.0818265i
$211$	4.64183	+	15.8086i	0.319557	+	1.08831i	0.950045	+	0.312112i	$0.101036\pi$
$211$	4.64183	+	15.8086i	0.319557	+	1.08831i	−0.630489	+	0.776198i	$0.717146\pi$
$212$	−11.2654	−	6.15138i	−0.773712	−	0.422479i
$213$	−4.79206	−	0.342735i	−0.328347	−	0.0234838i
$214$	−11.2688	−	38.3778i	−0.770316	−	2.62346i
$215$	−5.42027	−	8.68796i	−0.369659	−	0.592514i
$216$	10.0267	+	4.57904i	0.682231	+	0.311564i
$217$	0.0167555	+	0.234272i	0.00113744	+	0.0159034i
$218$	−16.0093	−	42.9227i	−1.08429	−	2.90709i
$219$	−10.0062	−	6.43058i	−0.676154	−	0.434538i
$220$	21.7024	+	8.89843i	1.46317	+	0.599932i
$221$	27.7623	−	17.8417i	1.86749	−	1.20016i
$222$	1.89457	+	1.41826i	0.127156	+	0.0951874i
$223$	6.59331	+	0.471563i	0.441521	+	0.0315782i	0.290330	−	0.956926i	$-0.406235\pi$
$223$	6.59331	+	0.471563i	0.441521	+	0.0315782i	0.151190	+	0.988505i	$0.451689\pi$
$224$	11.5723	+	1.66385i	0.773208	+	0.111171i
$225$	−4.69833	−	11.0634i	−0.313222	−	0.737563i
$226$	14.7912	−	23.0156i	0.983896	−	1.53097i
$227$	−25.7992	−	9.62260i	−1.71235	−	0.638674i	−0.714228	−	0.699913i	$-0.753222\pi$
$227$	−25.7992	−	9.62260i	−1.71235	−	0.638674i	−0.998123	+	0.0612387i	$0.980495\pi$
$228$	−3.24101	+	8.68949i	−0.214641	+	0.575476i
$229$	3.48570	−	11.8712i	0.230342	−	0.784472i	−0.760488	−	0.649352i	$-0.775040\pi$
$229$	3.48570	−	11.8712i	0.230342	−	0.784472i	0.990829	−	0.135119i	$-0.0431417\pi$
$230$	19.0280	−	33.7634i	1.25467	−	2.22629i
$231$	1.31223	+	4.79952i	0.0863383	+	0.315785i
$232$	16.1086	+	8.79597i	1.05758	+	0.577484i
$233$	−4.18861	−	4.18861i	−0.274405	−	0.274405i	0.556466	−	0.830871i	$-0.312157\pi$
$233$	−4.18861	−	4.18861i	−0.274405	−	0.274405i	−0.830871	+	0.556466i	$0.812157\pi$
$234$	35.3432	+	16.1407i	2.31045	+	1.05515i
$235$	−4.29885	−	2.03329i	−0.280426	−	0.132637i
$236$	3.22789	−	22.4504i	0.210117	−	1.46140i
$237$	3.62906	+	1.35357i	0.235733	+	0.0879238i
$238$	−9.81682	−	17.9782i	−0.636330	−	1.16535i
$239$	−17.1276			−1.10789			−0.553946	−	0.832553i	$-0.686879\pi$
$239$	−17.1276			−1.10789			−0.553946	+	0.832553i	$0.686879\pi$
$240$	−0.224395	−	0.509314i	−0.0144847	−	0.0328760i
$241$		−	26.7042i		−	1.72017i	−0.510150	−	0.860085i	$-0.670410\pi$
$241$		−	26.7042i		−	1.72017i	0.510150	−	0.860085i	$-0.329590\pi$
$242$	−0.848956	−	24.9795i	−0.0545730	−	1.60574i
$243$	−11.0290	+	11.0290i	−0.707510	+	0.707510i
$244$	−0.148544	+	1.03314i	−0.00950953	+	0.0661403i
$245$	1.62671	−	7.02328i	0.103926	−	0.448701i
$246$	5.03750	+	1.47914i	0.321179	+	0.0943068i
$247$	−9.44153	+	25.3137i	−0.600750	+	1.61067i
$248$	0.255646	−	0.191374i	0.0162335	−	0.0121523i
$249$	1.66072	−	1.06728i	0.105244	−	0.0676362i
$250$	8.13109	−	24.0673i	0.514256	−	1.52215i
$251$	19.2575			1.21552			0.607762	−	0.794119i	$-0.292067\pi$
$251$	19.2575			1.21552			0.607762	+	0.794119i	$0.292067\pi$
$252$	7.08056	−	12.9671i	0.446033	−	0.816849i
$253$	−25.1967	−	2.27672i	−1.58410	−	0.143136i
$254$	−4.27559	+	14.5613i	−0.268274	+	0.913659i
$255$	−3.93221	+	6.97732i	−0.246245	+	0.436937i
$256$	−5.75631	−	12.6046i	−0.359769	−	0.787785i
$257$	8.31522	−	22.2940i	0.518689	−	1.39066i	−0.368661	−	0.929564i	$-0.620184\pi$
$257$	8.31522	−	22.2940i	0.518689	−	1.39066i	0.887350	−	0.461096i	$-0.152544\pi$
$258$	−7.84990	+	1.70764i	−0.488713	+	0.106313i
$259$	1.71674	−	1.98123i	0.106673	−	0.123107i
$260$	20.2830	+	46.0367i	1.25790	+	2.85507i
$261$	−12.6208	+	10.9360i	−0.781207	+	0.676920i
$262$	0.776767	−	1.03764i	0.0479888	−	0.0641056i
$263$	−22.2361	−	4.83716i	−1.37113	−	0.298272i	−0.534100	−	0.845421i	$-0.679349\pi$
$263$	−22.2361	−	4.83716i	−1.37113	−	0.298272i	−0.837035	+	0.547149i	$0.815713\pi$
$264$	4.52513	−	5.02897i	0.278502	−	0.309511i
$265$	9.07379	+	0.121625i	0.557398	+	0.00747138i
$266$	15.2541	+	6.96632i	0.935290	+	0.427133i
$267$	4.70122	−	0.336238i	0.287710	−	0.0205774i
$268$	2.75737	+	7.39278i	0.168433	+	0.451586i
$269$		−	28.6231i		−	1.74518i	−0.488451	−	0.872592i	$-0.662438\pi$
$269$		−	28.6231i		−	1.74518i	0.488451	−	0.872592i	$-0.337562\pi$
$270$	−21.1617	+	1.22868i	−1.28786	+	0.0747752i
$271$	5.01407	−	4.34471i	0.304583	−	0.263923i	−0.489136	−	0.872208i	$-0.662688\pi$
$271$	5.01407	−	4.34471i	0.304583	−	0.263923i	0.793719	+	0.608285i	$0.208142\pi$
$272$	0.716798	−	1.31272i	0.0434623	−	0.0795952i
$273$	−5.11434	+	9.36621i	−0.309534	+	0.566869i
$274$	−19.0700	+	22.0079i	−1.15206	+	1.32955i
$275$	−16.5047	+	1.61066i	−0.995272	+	0.0971265i
$276$	−12.1976	−	14.0767i	−0.734207	−	0.847320i
$277$	12.2219	−	2.65870i	0.734341	−	0.159746i	0.170182	−	0.985413i	$-0.445564\pi$
$277$	12.2219	−	2.65870i	0.734341	−	0.159746i	0.564158	+	0.825667i	$0.309201\pi$
$278$	−34.5176	+	18.8480i	−2.07023	+	1.13043i
$279$	0.0818612	+	0.278794i	0.00490090	+	0.0166909i
$280$	10.8089	−	3.86728i	0.645952	−	0.231114i
$281$	−4.09149	+	13.9343i	−0.244078	+	0.831253i	0.742762	+	0.669555i	$0.233515\pi$
$281$	−4.09149	+	13.9343i	−0.244078	+	0.831253i	−0.986840	+	0.161698i	$0.948303\pi$
$282$	−2.63801	+	2.63801i	−0.157091	+	0.157091i
$283$	2.37540	−	1.77820i	0.141203	−	0.105703i	−0.526341	−	0.850273i	$-0.676437\pi$
$283$	2.37540	−	1.77820i	0.141203	−	0.105703i	0.667544	+	0.744570i	$0.267346\pi$
$284$	17.9029	−	8.17596i	1.06234	−	0.485154i
$285$	−0.846066	−	6.50202i	−0.0501166	−	0.385147i
$286$	35.8562	−	39.8485i	2.12022	−	2.35629i
$287$	2.03238	−	5.44902i	0.119967	−	0.321645i
$288$	14.4267	−	1.03182i	0.850103	−	0.0608006i
$289$	−4.47732	+	0.643741i	−0.263372	+	0.0378671i
$290$	−35.2916	−	0.473050i	−2.07240	−	0.0277785i
$291$	−0.349771	+	0.765892i	−0.0205039	+	0.0448974i
$292$	48.6026	+	3.47613i	2.84425	+	0.203425i
$293$	24.7062	−	1.76702i	1.44335	−	0.103231i	0.672430	−	0.740161i	$-0.265251\pi$
$293$	24.7062	−	1.76702i	1.44335	−	0.103231i	0.770921	+	0.636930i	$0.219796\pi$
$294$	−4.75788	−	3.05771i	−0.277485	−	0.178329i
$295$	5.40198	+	15.0983i	0.314516	+	0.879056i
$296$	−3.52809	−	0.507262i	−0.205066	−	0.0294840i
$297$	6.40307	+	12.2666i	0.371544	+	0.711782i
$298$	10.5036	+	7.86292i	0.608459	+	0.455487i
$299$	−35.5332	−	41.0075i	−2.05494	−	2.37153i
$300$	−9.57422	−	7.57594i	−0.552768	−	0.437397i
$301$	1.26644	+	8.80825i	0.0729961	+	0.507699i
$302$	−2.10793	+	2.81586i	−0.121298	+	0.162035i
$303$	2.50618	−	3.34786i	0.143976	−	0.192329i
$304$	0.174260	+	1.21200i	0.00999450	+	0.0695132i
$305$	−0.248593	−	0.694806i	−0.0142344	−	0.0397844i
$306$	−16.5947	−	19.1514i	−0.948658	−	1.09481i
$307$	1.70457	+	1.27602i	0.0972849	+	0.0728266i	0.646813	−	0.762649i	$-0.276101\pi$
$307$	1.70457	+	1.27602i	0.0972849	+	0.0728266i	−0.549528	+	0.835475i	$0.685192\pi$
$308$	−14.1411	−	14.6805i	−0.805761	−	0.836497i
$309$	−5.95899	−	0.856774i	−0.338995	−	0.0487402i
$310$	−0.262573	+	0.555140i	−0.0149131	+	0.0315299i
$311$	9.12982	+	5.86738i	0.517705	+	0.332709i	0.773263	−	0.634085i	$-0.218623\pi$
$311$	9.12982	+	5.86738i	0.517705	+	0.332709i	−0.255559	+	0.966794i	$0.582259\pi$
$312$	14.4726	−	1.03510i	0.819349	−	0.0586010i
$313$	6.80881	+	0.486976i	0.384857	+	0.0275255i	0.262427	−	0.964952i	$-0.415477\pi$
$313$	6.80881	+	0.486976i	0.384857	+	0.0275255i	0.122429	+	0.992477i	$0.460932\pi$
$314$	−2.39012	+	5.23364i	−0.134882	+	0.295351i
$315$	−0.139997	+	10.4444i	−0.00788794	+	0.588475i
$316$	−15.7058	+	2.25816i	−0.883522	+	0.127031i
$317$	2.49907	−	0.178737i	0.140362	−	0.0100389i	−0.000981468	−	1.00000i	$-0.500312\pi$
$317$	2.49907	−	0.178737i	0.140362	−	0.0100389i	0.141343	+	0.989961i	$0.454858\pi$
$318$	2.48788	−	6.67027i	0.139513	−	0.374050i
$319$	9.17727	+	21.1332i	0.513828	+	1.18323i
$320$	23.0813	+	17.7661i	1.29028	+	0.993155i
$321$	12.3625	−	5.64575i	0.690006	−	0.315115i
$322$	−26.9619	+	20.1834i	−1.50253	+	1.12478i
$323$	12.4597	−	12.4597i	0.693275	−	0.693275i
$324$	3.55603	−	12.1107i	0.197557	−	0.672819i
$325$	−27.8910	−	22.0698i	−1.54712	−	1.22421i
$326$	3.18287	+	10.8399i	0.176283	+	0.600365i
$327$	13.6618	−	7.45990i	0.755498	−	0.412533i
$328$	−7.72659	+	1.68082i	−0.426629	+	0.0928075i
$329$	2.70626	+	3.12319i	0.149201	+	0.172187i
$330$	−3.17218	+	12.6170i	−0.174623	+	0.694542i
$331$	13.6496	−	15.7525i	0.750250	−	0.865834i	−0.244343	−	0.969689i	$-0.578572\pi$
$331$	13.6496	−	15.7525i	0.750250	−	0.865834i	0.994592	+	0.103855i	$0.0331177\pi$
$332$	−3.87576	+	7.09793i	−0.212710	+	0.389550i
$333$	1.55428	−	2.84645i	0.0851741	−	0.155985i
$334$	36.6134	−	31.7257i	2.00340	−	1.73595i
$335$	−4.16652	−	3.70924i	−0.227641	−	0.202657i
$336$			0.483655i			0.0263856i
$337$	5.28528	+	14.1704i	0.287907	+	0.771910i	0.997718	+	0.0675171i	$0.0215077\pi$
$337$	5.28528	+	14.1704i	0.287907	+	0.771910i	−0.709811	+	0.704392i	$0.751220\pi$
$338$	85.2149	−	6.09469i	4.63508	−	0.331507i
$339$	8.45593	+	3.86169i	0.459263	+	0.209738i
$340$	0.439749	−	32.8072i	0.0238488	−	1.77922i
$341$	0.400808	+	0.00750136i	0.0217050	+	0.000406221i
$342$	20.2718	+	4.40987i	1.09618	+	0.238458i
$343$	−11.9060	+	15.9045i	−0.642861	+	0.858762i
$344$	9.14401	−	7.92333i	0.493012	−	0.427197i
$345$	12.2755	+	4.76691i	0.660893	+	0.256642i
$346$	30.4682	−	35.1622i	1.63798	−	1.89033i
$347$	−27.0413	+	5.88248i	−1.45165	+	0.315788i	−0.868142	−	0.496316i	$-0.834686\pi$
$347$	−27.0413	+	5.88248i	−1.45165	+	0.315788i	−0.583513	+	0.812104i	$0.698322\pi$
$348$	−5.92786	+	15.8932i	−0.317767	+	0.851965i
$349$	−4.25945	−	9.32689i	−0.228003	−	0.499257i	0.760708	−	0.649095i	$-0.224852\pi$
$349$	−4.25945	−	9.32689i	−0.228003	−	0.499257i	−0.988711	+	0.149838i	$0.952125\pi$
$350$	−14.8988	+	16.2906i	−0.796376	+	0.870769i
$351$	−8.36110	+	28.4753i	−0.446283	+	1.51990i
$352$	4.60582	−	19.4160i	0.245491	−	1.03488i
$353$	8.40583	−	15.3941i	0.447397	−	0.819347i	−0.552502	−	0.833511i	$-0.686327\pi$
$353$	8.40583	−	15.3941i	0.447397	−	0.819347i	0.999900	+	0.0141644i	$0.00450881\pi$
$354$	12.5801			0.668624
$355$	−8.48730	+	11.0265i	−0.450459	+	0.585226i
$356$	−16.2432	+	10.4389i	−0.860887	+	0.553259i
$357$	5.57178	−	4.17098i	0.294890	−	0.220752i
$358$	−11.6066	+	31.1185i	−0.613428	+	1.64466i
$359$	32.4977	+	9.54219i	1.71516	+	0.503618i	0.983937	−	0.178517i	$-0.0571299\pi$
$359$	32.4977	+	9.54219i	1.71516	+	0.503618i	0.731227	+	0.682134i	$0.238948\pi$
$360$	12.0493	−	7.51734i	0.635053	−	0.396199i
$361$	0.651005	−	4.52784i	0.0342634	−	0.238307i
$362$	3.10767	−	3.10767i	0.163335	−	0.163335i
$363$	8.36015	−	1.49343i	0.438794	−	0.0783850i
$364$		−	43.7174i		−	2.29142i
$365$	−31.5254	+	13.8896i	−1.65011	+	0.727014i
$366$	−0.578921			−0.0302607
$367$	1.42461	+	2.60898i	0.0743642	+	0.136188i	0.912216	−	0.409711i	$-0.134370\pi$
$367$	1.42461	+	2.60898i	0.0743642	+	0.136188i	−0.837851	+	0.545898i	$0.816188\pi$
$368$	−2.30414	−	0.859401i	−0.120112	−	0.0447994i
$369$	1.02392	−	7.12149i	0.0533029	−	0.370730i
$370$	6.45377	−	2.30908i	0.335516	−	0.120043i
$371$	−7.17334	−	3.27595i	−0.372421	−	0.170079i
$372$	0.208695	+	0.208695i	0.0108203	+	0.0108203i
$373$	−24.3412	−	13.2913i	−1.26034	−	0.688198i	−0.296590	−	0.955005i	$-0.595849\pi$
$373$	−24.3412	−	13.2913i	−1.26034	−	0.688198i	−0.963750	+	0.266807i	$0.914031\pi$
$374$	−32.0685	+	13.9260i	−1.65822	+	0.720096i
$375$	8.48758	+	1.57088i	0.438297	+	0.0811201i
$376$	1.58301	−	5.39123i	0.0816375	−	0.278032i
$377$	−17.2687	+	46.2992i	−0.889383	+	2.38453i
$378$	17.2593	+	6.43740i	0.887725	+	0.331104i
$379$	−5.03675	+	7.83734i	−0.258721	+	0.402577i	−0.946178	−	0.323648i	$-0.895091\pi$
$379$	−5.03675	+	7.83734i	−0.258721	+	0.402577i	0.687457	+	0.726225i	$0.258727\pi$
$380$	15.8075	+	21.7171i	0.810907	+	1.11406i
$381$	−5.10407	−	0.733854i	−0.261489	−	0.0375965i
$382$	21.9133	+	1.56727i	1.12118	+	0.0801886i
$383$	−18.7979	−	14.0719i	−0.960526	−	0.719041i	−0.000806226	−	1.00000i	$-0.500257\pi$
$383$	−18.7979	−	14.0719i	−0.960526	−	0.719041i	−0.959720	+	0.280959i	$0.909348\pi$
$384$	11.4076	−	7.33124i	0.582144	−	0.374121i
$385$	13.6897	+	4.50196i	0.697694	+	0.229441i
$386$	8.37051	+	5.37940i	0.426048	+	0.273804i
$387$	3.84722	+	10.3148i	0.195565	+	0.524331i
$388$	−0.246069	−	3.44049i	−0.0124922	−	0.174664i
$389$	−12.7825	−	5.83758i	−0.648099	−	0.295977i	0.0641116	−	0.997943i	$-0.479579\pi$
$389$	−12.7825	−	5.83758i	−0.648099	−	0.295977i	−0.712211	+	0.701966i	$0.752306\pi$
$390$	−23.6731	+	14.7692i	−1.19873	+	0.747870i
$391$	9.97022	+	33.9554i	0.504216	+	1.71720i
$392$	8.49637	+	0.607672i	0.429131	+	0.0306921i
$393$	0.386544	+	0.211069i	0.0194986	+	0.0106470i
$394$	−8.50661	−	28.9709i	−0.428557	−	1.45953i
$395$	9.06987	−	6.60180i	0.456355	−	0.332173i
$396$	−20.9549	−	14.0278i	−1.05302	−	0.704924i
$397$	0.0620783	−	0.867967i	0.00311562	−	0.0435620i	−0.995656	−	0.0931032i	$-0.970321\pi$
$397$	0.0620783	−	0.867967i	0.00311562	−	0.0435620i	0.998772	+	0.0495412i	$0.0157759\pi$
$398$	4.68981	+	21.5587i	0.235079	+	1.08064i
$399$	−1.60531	+	5.46719i	−0.0803661	+	0.273702i
$400$	−1.58882	−	0.272087i	−0.0794409	−	0.0136044i
$401$	1.84529	−	1.18590i	0.0921496	−	0.0592210i	−0.493755	−	0.869601i	$-0.664376\pi$
$401$	1.84529	−	1.18590i	0.0921496	−	0.0592210i	0.585904	+	0.810380i	$0.300740\pi$
$402$	−3.84099	+	2.09734i	−0.191571	+	0.104606i
$403$	0.607959	+	0.607959i	0.0302846	+	0.0302846i
$404$	−2.43815	+	16.9577i	−0.121302	+	0.843676i
$405$	1.77983	+	8.74441i	0.0884404	+	0.434513i
$406$	27.9000	+	12.7415i	1.38465	+	0.632350i
$407$	−3.10416	−	3.22257i	−0.153867	−	0.159737i
$408$	−8.86651	−	3.30704i	−0.438958	−	0.163723i
$409$	7.08662	−	8.17839i	0.350411	−	0.404395i	−0.552994	−	0.833186i	$-0.686515\pi$
$409$	7.08662	−	8.17839i	0.350411	−	0.404395i	0.903404	+	0.428790i	$0.141060\pi$
$410$	11.6244	−	9.80291i	0.574087	−	0.484131i
$411$	−8.32395	−	5.34948i	−0.410590	−	0.263870i
$412$	23.1078	−	8.61876i	1.13844	−	0.424616i
$413$	0.994123	−	13.8997i	0.0489176	−	0.683957i
$414$	−27.2853	+	31.4889i	−1.34100	+	1.54759i
$415$	0.0766318	−	5.71707i	0.00376170	−	0.280640i
$416$	36.0040	−	23.1384i	1.76524	−	1.13445i
$417$	−8.00818	−	10.6977i	−0.392162	−	0.523867i
$418$	14.1849	−	24.8601i	0.693806	−	1.21595i
$419$	−13.2263	+	1.90165i	−0.646147	+	0.0929019i	−0.457594	−	0.889161i	$-0.651289\pi$
$419$	−13.2263	+	1.90165i	−0.646147	+	0.0929019i	−0.188553	+	0.982063i	$0.560380\pi$
$420$	4.95949	+	9.37935i	0.241999	+	0.457666i
$421$	8.75272	−	5.62503i	0.426581	−	0.274147i	−0.309685	−	0.950839i	$-0.600224\pi$
$421$	8.75272	−	5.62503i	0.426581	−	0.274147i	0.736266	+	0.676692i	$0.236587\pi$
$422$	22.4348	−	29.9694i	1.09211	−	1.45889i
$423$	4.09276	+	3.06380i	0.198997	+	0.148967i
$424$	1.52592	+	10.6130i	0.0741052	+	0.515413i
$425$	10.5673	+	20.6499i	0.512588	+	1.00167i
$426$	5.90175	+	9.18330i	0.285941	+	0.444933i
$427$	−0.0457484	+	0.639646i	−0.00221392	+	0.0309547i
$428$	−33.3652	+	44.5707i	−1.61277	+	2.15441i
$429$	15.1359	+	10.1324i	0.730767	+	0.489196i
$430$	−8.42256	+	21.6894i	−0.406172	+	1.04596i
$431$	−12.3276	−	19.1821i	−0.593799	−	0.923970i	−0.999948	−	0.0101631i	$-0.996765\pi$
$431$	−12.3276	−	19.1821i	−0.593799	−	0.923970i	0.406149	−	0.913807i	$-0.366871\pi$
$432$	0.285908	+	1.31430i	0.0137558	+	0.0632342i
$433$	−2.40832	−	33.6727i	−0.115736	−	1.61820i	−0.641190	−	0.767383i	$-0.721559\pi$
$433$	−2.40832	−	33.6727i	−0.115736	−	1.61820i	0.525453	−	0.850822i	$-0.323896\pi$
$434$	0.403319	−	0.349478i	0.0193599	−	0.0167755i
$435$	−1.54747	−	11.8923i	−0.0741953	−	0.570192i
$436$	−34.4752	+	53.6444i	−1.65106	+	2.56910i
$437$	−23.1933	−	17.3623i	−1.10949	−	0.830552i
$438$	1.92802	+	26.9572i	0.0921242	+	1.28807i
$439$	1.39981	+	3.06515i	0.0668091	+	0.146292i	0.940091	−	0.340924i	$-0.110740\pi$
$439$	1.39981	+	3.06515i	0.0668091	+	0.146292i	−0.873282	+	0.487216i	$0.838013\pi$
$440$	−4.91369	−	18.9677i	−0.234251	−	0.904252i
$441$	−3.21966	+	7.05007i	−0.153317	+	0.335717i
$442$	−70.2564	−	26.2043i	−3.34176	−	1.24641i
$443$	−16.4421	−	21.9640i	−0.781186	−	1.04354i	−0.997735	−	0.0672706i	$-0.978571\pi$
$443$	−16.4421	−	21.9640i	−0.781186	−	1.04354i	0.216549	−	0.976272i	$-0.430520\pi$
$444$		−	3.29424i		−	0.156338i
$445$	6.70216	−	11.8923i	0.317713	−	0.563751i
$446$	−8.12011	−	12.6351i	−0.384499	−	0.598291i
$447$	−2.13657	+	3.91284i	−0.101056	+	0.185071i
$448$	−12.1307	−	22.2156i	−0.573120	−	1.04959i
$449$	15.5468	−	24.1912i	0.733696	−	1.14165i	−0.251103	−	0.967960i	$-0.580793\pi$
$449$	15.5468	−	24.1912i	0.733696	−	1.14165i	0.984800	−	0.173694i	$-0.0555703\pi$
$450$	−13.7265	+	23.6108i	−0.647074	+	1.11302i
$451$	−8.95050	−	4.29175i	−0.421462	−	0.202091i
$452$	−37.9851	+	2.71675i	−1.78667	+	0.127785i
$453$	−1.04897	−	0.572782i	−0.0492850	−	0.0269117i
$454$	17.6266	+	60.0307i	0.827257	+	2.81738i
$455$	14.4477	+	27.3234i	0.677319	+	1.28094i
$456$	7.43344	−	2.18266i	0.348103	−	0.102212i
$457$	8.02279	−	8.02279i	0.375290	−	0.375290i	−0.494109	−	0.869400i	$-0.664506\pi$
$457$	8.02279	−	8.02279i	0.375290	−	0.375290i	0.869400	+	0.494109i	$0.164506\pi$
$458$	−26.3397	+	9.82421i	−1.23077	+	0.459055i
$459$	12.6753	−	14.6281i	0.591631	−	0.682779i
$460$	−53.4959	+	6.96107i	−2.49426	+	0.324562i
$461$	11.0796	−	17.2402i	0.516027	−	0.802954i	−0.481259	−	0.876579i	$-0.659820\pi$
$461$	11.0796	−	17.2402i	0.516027	−	0.802954i	0.997286	+	0.0736245i	$0.0234566\pi$
$462$	6.94336	−	8.92223i	0.323034	−	0.415100i
$463$	−7.36128	+	33.8393i	−0.342108	+	1.57264i	0.409044	+	0.912515i	$0.365862\pi$
$463$	−7.36128	+	33.8393i	−0.342108	+	1.57264i	−0.751152	+	0.660129i	$0.770501\pi$
$464$	0.318724	+	2.21677i	0.0147964	+	0.102911i
$465$	−0.199404	−	0.0614650i	−0.00924714	−	0.00285037i
$466$	−1.91548	+	13.3224i	−0.0887327	+	0.617150i
$467$	−36.3065	+	2.59669i	−1.68006	+	0.120161i	−0.878498	−	0.477746i	$-0.841454\pi$
$467$	−36.3065	+	2.59669i	−1.68006	+	0.120161i	−0.801566	+	0.597907i	$0.795999\pi$
$468$	−11.4963	−	52.8477i	−0.531418	−	2.44289i
$469$	2.01381	+	4.40962i	0.0929890	+	0.203617i
$470$	2.15510	+	10.5881i	0.0994074	+	0.488395i
$471$	−1.87578	−	0.550777i	−0.0864312	−	0.0253785i
$472$	−16.6293	+	9.08028i	−0.765425	+	0.417954i
$473$	15.1675	−	0.799860i	0.697401	−	0.0367776i
$474$	−2.47946	−	8.44425i	−0.113885	−	0.387857i
$475$	−17.0567	−	8.34912i	−0.782617	−	0.383084i
$476$	−11.8446	+	25.9360i	−0.542894	+	1.18877i
$477$	−9.53295	−	2.07377i	−0.436484	−	0.0949512i
$478$	23.3220	+	31.1546i	1.06672	+	1.42498i
$479$	−8.62034	−	18.8759i	−0.393874	−	0.862463i	−0.997855	−	0.0654643i	$-0.979147\pi$
$479$	−8.62034	−	18.8759i	−0.393874	−	0.862463i	0.603981	−	0.796998i	$-0.293580\pi$
$480$	−5.09956	+	9.04867i	−0.232762	+	0.413013i
$481$		−	9.59658i		−	0.437566i
$482$	−48.5742	+	36.3622i	−2.21249	+	1.65625i
$483$	−8.09194	−	8.09194i	−0.368196	−	0.368196i
$484$	−27.1270	+	21.7832i	−1.23305	+	0.990145i
$485$	1.29080	+	2.06898i	0.0586124	+	0.0939477i
$486$	35.0792	+	5.04362i	1.59122	+	0.228783i
$487$	−10.6637	−	10.6637i	−0.483218	−	0.483218i	0.422940	−	0.906158i	$-0.360998\pi$
$487$	−10.6637	−	10.6637i	−0.483218	−	0.483218i	−0.906158	+	0.422940i	$0.860998\pi$
$488$	0.765261	−	0.417864i	0.0346417	−	0.0189158i
$489$	−3.49180	+	1.59465i	−0.157904	+	0.0721126i
$490$	−14.9902	+	6.60442i	−0.677187	+	0.298357i
$491$	−2.51942	−	3.92029i	−0.113700	−	0.176920i	0.779740	−	0.626104i	$-0.215351\pi$
$491$	−2.51942	−	3.92029i	−0.113700	−	0.176920i	−0.893440	+	0.449183i	$0.851715\pi$
$492$	−2.55389	−	6.84726i	−0.115138	−	0.308698i
$493$	22.7889	−	22.7889i	1.02636	−	1.02636i
$494$	58.9011	−	17.2949i	2.65009	−	0.778135i
$495$	17.7327	+	1.84221i	0.797026	+	0.0828013i
$496$	0.0373885	+	0.0109783i	0.00167879	+	0.000492939i
$497$	10.6130	−	5.79511i	0.476056	−	0.259946i
$498$	−4.20270	−	1.56752i	−0.188327	−	0.0702425i
$499$	−17.3117	+	7.90599i	−0.774978	+	0.353921i	−0.763328	−	0.646011i	$-0.776436\pi$
$499$	−17.3117	+	7.90599i	−0.774978	+	0.353921i	−0.0116506	+	0.999932i	$0.503709\pi$
$500$	−33.6014	+	11.0155i	−1.50270	+	0.492630i
$501$	12.4406	+	10.7798i	0.555805	+	0.481608i
$502$	−26.2223	−	35.0289i	−1.17036	−	1.56342i
$503$	−1.73029	+	24.1926i	−0.0771499	+	1.07870i	0.800481	+	0.599359i	$0.204578\pi$
$503$	−1.73029	+	24.1926i	−0.0771499	+	1.07870i	−0.877631	+	0.479338i	$0.840877\pi$
$504$	−12.2161	+	1.75641i	−0.544149	+	0.0782368i
$505$	−4.08032	−	11.4043i	−0.181572	−	0.507485i
$506$	30.1681	+	48.9321i	1.34114	+	2.17530i
$507$	6.17045	+	28.3651i	0.274039	+	1.25974i
$508$	19.7926	−	7.38225i	0.878153	−	0.327534i
$509$	26.3960	+	22.8722i	1.16998	+	1.01379i	0.999596	+	0.0284163i	$0.00904640\pi$
$509$	26.3960	+	22.8722i	1.16998	+	1.01379i	0.170384	+	0.985378i	$0.445499\pi$
$510$	18.0459	−	2.34819i	0.799086	−	0.103980i
$511$	29.9372			1.32434
$512$	1.74601	−	3.19757i	0.0771633	−	0.141314i
$513$	−1.13044	+	15.8057i	−0.0499103	+	0.697837i
$514$	−51.8746	+	15.2318i	−2.28809	+	0.671844i
$515$	−11.5940	+	13.0234i	−0.510895	+	0.573879i
$516$	8.45102	+	7.32285i	0.372036	+	0.322371i
$517$	5.72472	−	4.12060i	0.251773	−	0.181224i
$518$	−5.94142	−	0.424939i	−0.261051	−	0.0186707i
$519$	13.2992	+	8.54688i	0.583770	+	0.375166i
$520$	20.6325	−	36.6103i	0.904793	−	1.60547i
$521$	−37.9811	+	11.1523i	−1.66398	+	0.488590i	−0.972324	−	0.233635i	$-0.924938\pi$
$521$	−37.9811	+	11.1523i	−1.66398	+	0.488590i	−0.691659	+	0.722224i	$0.743120\pi$
$522$	37.0775	+	8.06571i	1.62284	+	0.353027i
$523$	3.13260	+	5.73694i	0.136979	+	0.250859i	0.937160	−	0.348900i	$-0.113445\pi$
$523$	3.13260	+	5.73694i	0.136979	+	0.250859i	−0.800181	+	0.599759i	$0.795263\pi$
$524$	−1.80422			−0.0788178
$525$	−6.19937	−	4.22308i	−0.270563	−	0.184311i
$526$	21.4794	+	47.0333i	0.936546	+	2.05075i
$527$	−0.195963	−	0.525397i	−0.00853628	−	0.0228866i
$528$	0.822155	+	0.0742882i	0.0357797	+	0.00323298i
$529$	32.0071	−	14.6172i	1.39161	−	0.635529i
$530$	−12.1342	−	16.6706i	−0.527077	−	0.724123i
$531$	−2.45343	−	17.0640i	−0.106470	−	0.740515i
$532$	−4.96182	−	22.8091i	−0.215122	−	0.988900i
$533$	−7.43986	−	19.9470i	−0.322256	−	0.864002i
$534$	−7.01308	−	8.09353i	−0.303486	−	0.350241i
$535$	6.12355	−	38.8832i	0.264744	−	1.68107i
$536$	3.56345	−	5.54483i	0.153918	−	0.239500i
$537$	−11.0271	−	2.39881i	−0.475856	−	0.103516i
$538$	−52.0646	+	38.9751i	−2.24466	+	1.68033i
$539$	7.94877	+	7.15241i	0.342378	+	0.308076i
$540$	19.0216	+	22.5560i	0.818559	+	0.970654i
$541$	−0.696760	+	0.603746i	−0.0299560	+	0.0259571i	−0.669710	−	0.742623i	$-0.733582\pi$
$541$	−0.696760	+	0.603746i	−0.0299560	+	0.0259571i	0.639754	+	0.768580i	$0.279036\pi$
$542$	−14.7304	−	3.20440i	−0.632724	−	0.137641i
$543$	1.19546	+	0.894908i	0.0513020	+	0.0384042i
$544$	−27.6289	+	3.97243i	−1.18458	+	0.170316i
$545$	3.81861	−	44.9211i	0.163571	−	1.92421i
$546$	24.0009	−	3.45080i	1.02714	−	0.147681i
$547$	1.41882	−	6.52222i	0.0606645	−	0.278870i	−0.936815	−	0.349825i	$-0.886241\pi$
$547$	1.41882	−	6.52222i	0.0606645	−	0.278870i	0.997480	+	0.0709549i	$0.0226047\pi$
$548$	40.4316	+	2.89172i	1.72715	+	0.123528i
$549$	0.112904	+	0.785266i	0.00481863	+	0.0335143i
$550$	25.4036	+	27.8284i	1.08321	+	1.18661i
$551$	−3.75492	+	26.1161i	−0.159965	+	1.11258i
$552$	−3.30740	+	15.2039i	−0.140772	+	0.647119i
$553$	−9.52594	+	2.07224i	−0.405084	+	0.0881207i
$554$	−21.4782	−	18.6109i	−0.912520	−	0.790703i
$555$	1.08868	+	2.05890i	0.0462118	+	0.0873954i
$556$	49.7963	+	22.7412i	2.11184	+	0.964443i
$557$	37.7603	−	8.21425i	1.59995	−	0.348049i	0.677914	−	0.735142i	$-0.262884\pi$
$557$	37.7603	−	8.21425i	1.59995	−	0.348049i	0.922041	+	0.387093i	$0.126521\pi$
$558$	0.395650	−	0.528526i	0.0167492	−	0.0223743i
$559$	24.6190	+	21.3325i	1.04127	+	0.902269i
$560$	1.16818	+	0.773060i	0.0493645	+	0.0326677i
$561$	−6.23435	−	10.1120i	−0.263215	−	0.426929i
$562$	30.9174	−	11.5316i	1.30417	−	0.486431i
$563$	−10.6529	+	28.5616i	−0.448967	+	1.20373i	0.493594	+	0.869693i	$0.335683\pi$
$563$	−10.6529	+	28.5616i	−0.448967	+	1.20373i	−0.942561	+	0.334035i	$0.891590\pi$
$564$	5.14015	+	0.739042i	0.216439	+	0.0311193i
$565$	22.8429	−	14.2513i	0.961007	−	0.599556i
$566$	−6.46898	−	1.89946i	−0.271912	−	0.0798404i
$567$	1.64841	−	7.57762i	0.0692267	−	0.318230i
$568$	−14.4299	−	7.87930i	−0.605464	−	0.330608i
$569$	−34.9832	−	10.2720i	−1.46657	−	0.430625i	−0.551590	−	0.834116i	$-0.685979\pi$
$569$	−34.9832	−	10.2720i	−1.46657	−	0.430625i	−0.914984	+	0.403491i	$0.867797\pi$
$570$	−10.6749	+	10.3925i	−0.447123	+	0.435295i
$571$	−14.5588	+	12.6153i	−0.609266	+	0.527932i	−0.903936	−	0.427667i	$-0.859336\pi$
$571$	−14.5588	+	12.6153i	−0.609266	+	0.527932i	0.294670	+	0.955599i	$0.404790\pi$
$572$	−74.3143	−	6.71489i	−3.10724	−	0.280764i
$573$	0.532531	+	7.44576i	0.0222468	+	0.311051i
$574$	−12.6790	+	3.72289i	−0.529212	+	0.155391i
$575$	31.1344	−	22.0300i	1.29840	−	0.918713i
$576$	−20.5062	−	23.6654i	−0.854423	−	0.986057i
$577$	28.7896	+	15.7203i	1.19852	+	0.654444i	0.949413	−	0.314031i	$-0.101679\pi$
$577$	28.7896	+	15.7203i	1.19852	+	0.654444i	0.249112	+	0.968475i	$0.419861\pi$
$578$	7.26755	+	7.26755i	0.302290	+	0.302290i
$579$	−1.40446	+	3.07533i	−0.0583672	+	0.127806i
$580$	28.9121	+	39.7208i	1.20051	+	1.64932i
$581$	−2.06406	+	4.51966i	−0.0856316	+	0.187507i
$582$	1.86940	−	0.406664i	0.0774893	−	0.0168568i
$583$	−6.67053	+	11.6906i	−0.276265	+	0.484176i
$584$	−22.0063	−	34.2424i	−0.910625	−	1.41696i
$585$	24.6503	+	29.2305i	1.01916	+	1.20853i
$586$	−36.8557	−	42.5337i	−1.52249	−	1.75705i
$587$	22.2598	−	16.6635i	0.918759	−	0.687775i	−0.0314107	−	0.999507i	$-0.510000\pi$
$587$	22.2598	−	16.6635i	0.918759	−	0.687775i	0.950170	+	0.311732i	$0.100909\pi$
$588$	0.561619	+	7.85246i	0.0231608	+	0.323830i
$589$	0.386198	+	0.248194i	0.0159130	+	0.0102267i
$590$	20.1076	−	30.3848i	0.827818	−	1.25092i
$591$	9.33225	−	4.26189i	0.383877	−	0.175311i
$592$	−0.208442	−	0.381733i	−0.00856692	−	0.0156891i
$593$	18.5660	+	34.0012i	0.762416	+	1.39626i	0.913124	+	0.407682i	$0.133663\pi$
$593$	18.5660	+	34.0012i	0.762416	+	1.39626i	−0.150708	+	0.988578i	$0.548155\pi$
$594$	13.5938	−	28.3500i	0.557760	−	1.16322i
$595$	−1.16845	−	20.1244i	−0.0479020	−	0.825018i
$596$		−	18.2634i		−	0.748100i
$597$	−7.02393	+	2.61979i	−0.287470	+	0.107221i
$598$	−26.2071	+	120.472i	−1.07169	+	4.92648i
$599$	23.3446	+	3.35644i	0.953833	+	0.137140i	0.601623	−	0.798780i	$-0.294521\pi$
$599$	23.3446	+	3.35644i	0.953833	+	0.137140i	0.352210	+	0.935921i	$0.385430\pi$
$600$	−0.273362	+	10.1952i	−0.0111600	+	0.416217i
$601$	4.84070	−	16.4859i	0.197456	−	0.672475i	−0.799922	−	0.600105i	$-0.795126\pi$
$601$	4.84070	−	16.4859i	0.197456	−	0.672475i	0.997378	−	0.0723699i	$-0.0230562\pi$
$602$	14.2975	−	14.2975i	0.582722	−	0.582722i
$603$	3.59398	+	4.80100i	0.146358	+	0.195512i
$604$	4.89615			0.199221
$605$	9.75550	−	22.5794i	0.396617	−	0.917984i
$606$	−9.50222			−0.386001
$607$	−0.0110616	−	0.0147765i	−0.000448975	−	0.000599760i	0.800317	−	0.599578i	$-0.204665\pi$
$607$	−0.0110616	−	0.0147765i	−0.000448975	−	0.000599760i	−0.800766	+	0.598978i	$0.795574\pi$
$608$	16.1586	−	16.1586i	0.655316	−	0.655316i
$609$	−2.93614	+	9.99956i	−0.118978	+	0.405203i
$610$	−0.925330	+	1.39827i	−0.0374655	+	0.0566145i
$611$	14.9740	+	2.15293i	0.605783	+	0.0870984i
$612$	−7.49792	+	34.4674i	−0.303086	+	1.39326i
$613$	−4.67706	+	1.74445i	−0.188905	+	0.0704578i	−0.442136	−	0.896948i	$-0.645779\pi$
$613$	−4.67706	+	1.74445i	−0.188905	+	0.0704578i	0.253232	+	0.967406i	$0.418507\pi$
$614$		−	4.83808i		−	0.195249i
$615$	3.85906	+	3.43553i	0.155612	+	0.138534i
$616$	−2.73820	+	16.8058i	−0.110325	+	0.677124i
$617$	19.0690	+	34.9222i	0.767689	+	1.40592i	0.909363	+	0.416003i	$0.136570\pi$
$617$	19.0690	+	34.9222i	0.767689	+	1.40592i	−0.141674	+	0.989913i	$0.545249\pi$
$618$	6.55570	+	12.0059i	0.263709	+	0.482947i
$619$	−25.0201	+	11.4263i	−1.00564	+	0.459261i	−0.848999	−	0.528394i	$-0.822794\pi$
$619$	−25.0201	+	11.4263i	−1.00564	+	0.459261i	−0.156643	+	0.987655i	$0.550067\pi$
$620$	0.837636	−	0.170492i	0.0336403	−	0.00684711i
$621$	−26.7728	−	17.2058i	−1.07435	−	0.690445i
$622$	−1.75916	−	24.5963i	−0.0705359	−	0.986221i
$623$	−9.49669	+	7.10913i	−0.380477	+	0.284821i
$624$	1.15943	+	1.33806i	0.0464144	+	0.0535651i
$625$	17.3605	−	17.9893i	0.694418	−	0.719572i
$626$	−8.38552	−	13.0481i	−0.335153	−	0.521508i
$627$	9.04698	+	3.56858i	0.361302	+	0.142515i
$628$	7.82573	−	1.70238i	0.312281	−	0.0679325i
$629$	−2.60005	+	5.69330i	−0.103671	+	0.227007i
$630$	19.1887	−	13.9671i	0.764495	−	0.556463i
$631$	2.45014	−	5.36505i	0.0975384	−	0.213579i	−0.854573	−	0.519332i	$-0.826181\pi$
$631$	2.45014	−	5.36505i	0.0975384	−	0.213579i	0.952111	+	0.305753i	$0.0989081\pi$
$632$	9.37258	+	9.37258i	0.372821	+	0.372821i
$633$	11.1643	+	6.09615i	0.443740	+	0.242300i
$634$	−3.72801	−	4.30235i	−0.148058	−	0.170868i
$635$	−9.93068	+	11.1549i	−0.394087	+	0.442670i
$636$	−9.50814	+	2.79184i	−0.377022	+	0.110704i
$637$	1.63608	+	22.8753i	0.0648237	+	0.906354i
$638$	25.9444	−	45.4695i	1.02715	−	1.80016i
$639$	11.3055	−	9.79629i	0.447239	−	0.387535i
$640$	0.526390	−	39.2710i	0.0208074	−	1.55232i
$641$	7.58017	+	2.22574i	0.299399	+	0.0879114i	0.427982	−	0.903787i	$-0.359225\pi$
$641$	7.58017	+	2.22574i	0.299399	+	0.0879114i	−0.128583	+	0.991699i	$0.541043\pi$
$642$	−27.1030	−	14.7993i	−1.06967	−	0.584084i
$643$	0.915992	−	4.21075i	0.0361232	−	0.166056i	−0.955551	−	0.294824i	$-0.904739\pi$
$643$	0.915992	−	4.21075i	0.0361232	−	0.166056i	0.991675	+	0.128769i	$0.0411025\pi$
$644$	44.9817	+	13.2078i	1.77253	+	0.520461i
$645$	−7.70194	−	1.78389i	−0.303264	−	0.0702407i
$646$	−39.6297	−	5.69789i	−1.55921	−	0.224180i
$647$	2.62974	−	7.05061i	0.103386	−	0.277188i	−0.874950	−	0.484214i	$-0.839106\pi$
$647$	2.62974	−	7.05061i	0.103386	−	0.277188i	0.978335	+	0.207026i	$0.0663784\pi$
$648$	−9.87905	+	3.68469i	−0.388086	+	0.144748i
$649$	−23.4750	−	3.82484i	−0.921476	−	0.150138i
$650$	−2.16607	+	80.7846i	−0.0849602	+	3.16863i
$651$	0.137041	+	0.118746i	0.00537105	+	0.00465404i
$652$	9.42405	−	12.5891i	0.369074	−	0.493025i
$653$	−5.09167	+	1.10763i	−0.199252	+	0.0433447i	−0.311084	−	0.950382i	$-0.600692\pi$
$653$	−5.09167	+	1.10763i	−0.199252	+	0.0433447i	0.111831	+	0.993727i	$0.464328\pi$
$654$	−32.1721	−	14.6925i	−1.25803	−	0.574522i
$655$	1.12764	−	0.596258i	0.0440605	−	0.0232977i
$656$	−0.729201	−	0.631857i	−0.0284705	−	0.0246699i
$657$	36.1896	−	7.87256i	1.41189	−	0.307138i
$658$	1.99597	−	9.17534i	0.0778111	−	0.357692i
$659$	5.16459	−	35.9205i	0.201184	−	1.39927i	−0.599594	−	0.800304i	$-0.704671\pi$
$659$	5.16459	−	35.9205i	0.201184	−	1.39927i	0.800778	−	0.598961i	$-0.204420\pi$
$660$	16.7055	−	6.98989i	0.650262	−	0.272081i
$661$	2.96826	+	20.6447i	0.115452	+	0.802987i	0.962463	+	0.271412i	$0.0874905\pi$
$661$	2.96826	+	20.6447i	0.115452	+	0.802987i	−0.847011	+	0.531575i	$0.821600\pi$
$662$	−47.2394	−	3.37863i	−1.83601	−	0.131314i
$663$	5.41580	−	24.8960i	0.210332	−	0.966882i
$664$	6.68687	−	0.961427i	0.259501	−	0.0373106i
$665$	10.6391	+	12.6159i	0.412566	+	0.489224i
$666$	−7.29402	+	1.04872i	−0.282638	+	0.0406372i
$667$	−42.4209	−	31.7559i	−1.64254	−	1.22959i
$668$	−65.8946	−	14.3345i	−2.54954	−	0.554618i
$669$	3.85684	−	3.34197i	0.149114	−	0.129208i
$670$	−1.07359	+	12.6295i	−0.0414766	+	0.487920i
$671$	1.08029	+	0.176015i	0.0417043	+	0.00679498i
$672$	7.22587	−	5.40922i	0.278744	−	0.208665i
$673$	−15.5362	−	3.37970i	−0.598878	−	0.130278i	−0.0971003	−	0.995275i	$-0.530957\pi$
$673$	−15.5362	−	3.37970i	−0.598878	−	0.130278i	−0.501778	+	0.864997i	$0.667320\pi$
$674$	18.5787	−	28.9090i	0.715625	−	1.11353i
$675$	−19.3428	−	7.81123i	−0.744504	−	0.300655i
$676$	−77.8752	−	89.8728i	−2.99520	−	3.45665i
$677$	12.5354	+	33.6088i	0.481776	+	1.29169i	0.919680	+	0.392669i	$0.128448\pi$
$677$	12.5354	+	33.6088i	0.481776	+	1.29169i	−0.437904	+	0.899022i	$0.644279\pi$
$678$	−4.48983	−	20.6394i	−0.172431	−	0.792651i
$679$	−0.301594	−	2.09763i	−0.0115741	−	0.0804996i
$680$	−22.1595	+	16.1295i	−0.849777	+	0.618538i
$681$	−19.3374	+	8.83109i	−0.741010	+	0.338408i
$682$	−0.532121	−	0.739272i	−0.0203760	−	0.0283082i
$683$	−13.4172	−	35.9730i	−0.513396	−	1.37647i	−0.892472	−	0.451103i	$-0.851031\pi$
$683$	−13.4172	−	35.9730i	−0.513396	−	1.37647i	0.379076	−	0.925366i	$-0.376242\pi$
$684$	−11.9962	−	26.2680i	−0.458685	−	1.00438i
$685$	−26.2254	+	11.5545i	−1.00202	+	0.441474i
$686$	45.1417			1.72352
$687$	−4.57780	−	8.38362i	−0.174654	−	0.319855i
$688$	1.44265	+	0.313829i	0.0550004	+	0.0119646i
$689$	−27.6986	+	8.13303i	−1.05523	+	0.309844i
$690$	−8.04429	−	28.8198i	−0.306241	−	1.09715i
$691$	−7.05368	−	4.53312i	−0.268334	−	0.172448i	0.399554	−	0.916710i	$-0.369165\pi$
$691$	−7.05368	−	4.53312i	−0.268334	−	0.172448i	−0.667888	+	0.744262i	$0.732802\pi$
$692$	−64.5977	−	4.62012i	−2.45563	−	0.175630i
$693$	−13.4565	−	7.67812i	−0.511171	−	0.291668i
$694$	47.5213	+	41.1774i	1.80388	+	1.56307i
$695$	−38.6382	+	2.24340i	−1.46563	+	0.0850971i
$696$	13.5959	−	3.99211i	0.515350	−	0.151320i
$697$	−0.990540	+	13.8496i	−0.0375194	+	0.524590i
$698$	−11.1654	+	20.4479i	−0.422616	+	0.773964i
$699$	−4.57328			−0.172977
$700$	30.5812	+	3.01295i	1.15586	+	0.113879i
$701$	3.58336	+	3.10500i	0.135342	+	0.117274i	0.719901	−	0.694077i	$-0.244187\pi$
$701$	3.58336	+	3.10500i	0.135342	+	0.117274i	−0.584559	+	0.811351i	$0.698733\pi$
$702$	63.1807	−	23.5652i	2.38460	−	0.889411i
$703$	−1.08919	−	5.00692i	−0.0410795	−	0.188839i
$704$	−39.6271	+	17.2084i	−1.49350	+	0.648565i
$705$	−3.45683	+	1.23681i	−0.130192	+	0.0465811i
$706$	−39.4474	+	5.67168i	−1.48462	+	0.213456i
$707$	−0.750899	+	10.4989i	−0.0282405	+	0.394853i
$708$	−10.4939	−	14.0183i	−0.394387	−	0.526839i
$709$	−1.94533	−	1.68563i	−0.0730582	−	0.0633053i	0.617566	−	0.786519i	$-0.288119\pi$
$709$	−1.94533	−	1.68563i	−0.0730582	−	0.0633053i	−0.690624	+	0.723214i	$0.742664\pi$
$710$	31.6137	+	0.423751i	1.18644	+	0.0159031i
$711$	−10.9705	+	5.01005i	−0.411425	+	0.187892i
$712$	15.1123	+	5.63660i	0.566358	+	0.211240i
$713$	−0.809216	+	0.441865i	−0.0303054	+	0.0165480i
$714$	−15.1738	−	4.45542i	−0.567865	−	0.166740i
$715$	48.6656	−	20.3625i	1.81999	−	0.761516i
$716$	44.3579	−	13.0247i	1.65773	−	0.486754i
$717$	−9.35027	+	9.35027i	−0.349192	+	0.349192i
$718$	−26.8940	−	72.1056i	−1.00368	−	2.69096i
$719$	−4.33648	−	6.74769i	−0.161723	−	0.251646i	0.750929	−	0.660383i	$-0.229606\pi$
$719$	−4.33648	−	6.74769i	−0.161723	−	0.251646i	−0.912653	+	0.408736i	$0.865970\pi$
$720$	1.61544	+	0.627318i	0.0602039	+	0.0233788i
$721$	13.7833	−	6.29460i	0.513315	−	0.234423i
$722$	−9.12245	+	4.98124i	−0.339503	+	0.185382i
$723$	−14.5783	−	14.5783i	−0.542174	−	0.542174i
$724$	−6.05527	−	0.870616i	−0.225042	−	0.0323562i
$725$	−31.1970	−	15.2707i	−1.15863	−	0.567138i
$726$	−14.1002	−	13.1733i	−0.523308	−	0.488907i
$727$	−5.51767	−	5.51767i	−0.204639	−	0.204639i	0.597345	−	0.801984i	$-0.296222\pi$
$727$	−5.51767	−	5.51767i	−0.204639	−	0.204639i	−0.801984	+	0.597345i	$0.796222\pi$
$728$	−29.2353	+	21.8853i	−1.08353	+	0.811123i
$729$			0.0694503i			0.00257223i
$730$	68.1917	+	38.4308i	2.52389	+	1.42239i
$731$	−8.82586	−	19.3259i	−0.326436	−	0.714796i
$732$	0.482919	+	0.645105i	0.0178492	+	0.0238438i
$733$	28.6447	+	6.23127i	1.05802	+	0.230157i	0.707728	−	0.706485i	$-0.249720\pi$
$733$	28.6447	+	6.23127i	1.05802	+	0.230157i	0.350287	+	0.936642i	$0.386084\pi$
$734$	2.80582	−	6.14388i	0.103565	−	0.226775i
$735$	−2.94609	−	4.72219i	−0.108668	−	0.174180i
$736$	12.9301	+	44.0357i	0.476608	+	1.62318i
$737$	7.80514	−	2.74592i	0.287506	−	0.101147i
$738$	−14.3480	+	7.83460i	−0.528157	+	0.288396i
$739$	24.2491	+	7.12018i	0.892018	+	0.261920i	0.695454	−	0.718571i	$-0.255203\pi$
$739$	24.2491	+	7.12018i	0.892018	+	0.261920i	0.196564	+	0.980491i	$0.437022\pi$
$740$	−7.95661	−	5.26541i	−0.292491	−	0.193560i
$741$	8.66492	+	18.9735i	0.318314	+	0.697010i
$742$	3.80881	+	17.5088i	0.139826	+	0.642769i
$743$	−19.2846	+	1.37926i	−0.707483	+	0.0506002i	−0.420444	−	0.907319i	$-0.638126\pi$
$743$	−19.2846	+	1.37926i	−0.707483	+	0.0506002i	−0.287039	+	0.957919i	$0.592671\pi$
$744$	0.0350871	−	0.244036i	0.00128636	−	0.00894680i
$745$	6.03569	+	11.4147i	0.221131	+	0.418200i
$746$	8.96806	+	62.3742i	0.328344	+	2.28368i
$747$	−1.30661	+	6.00637i	−0.0478062	+	0.219762i
$748$	42.2687	+	24.1180i	1.54550	+	0.881842i
$749$	−18.4935	+	28.7764i	−0.675737	+	1.05147i
$750$	−8.69984	−	17.5777i	−0.317673	−	0.641845i
$751$	−19.4976	+	22.5014i	−0.711478	+	0.821089i	−0.990255	−	0.139267i	$-0.955526\pi$
$751$	−19.4976	+	22.5014i	−0.711478	+	0.821089i	0.278777	+	0.960356i	$0.410071\pi$
$752$	0.642399	−	0.239602i	0.0234259	−	0.00873740i
$753$	10.5130	−	10.5130i	0.383116	−	0.383116i
$754$	107.731	−	31.6327i	3.92333	−	1.15199i
$755$	−3.06009	+	1.61808i	−0.111368	+	0.0588878i
$756$	−7.22391	−	24.6024i	−0.262731	−	0.894780i
$757$	34.0795	+	18.6088i	1.23864	+	0.676349i	0.958905	−	0.283728i	$-0.0915712\pi$
$757$	34.0795	+	18.6088i	1.23864	+	0.676349i	0.279736	+	0.960077i	$0.409753\pi$
$758$	21.1143	−	1.51012i	0.766904	−	0.0548501i
$759$	−14.9982	+	12.5124i	−0.544401	+	0.454172i
$760$	6.60960	−	21.4428i	0.239755	−	0.777811i
$761$	27.7877	−	43.2385i	1.00730	−	1.56739i	0.197828	−	0.980237i	$-0.436611\pi$
$761$	27.7877	−	43.2385i	1.00730	−	1.56739i	0.809474	−	0.587156i	$-0.199752\pi$
$762$	5.61517	+	10.2834i	0.203416	+	0.372529i
$763$	−18.7760	+	34.3857i	−0.679737	+	1.24484i
$764$	−16.5330	−	25.7259i	−0.598143	−	0.930729i
$765$	−6.70457	−	24.0200i	−0.242404	−	0.868446i
$766$			53.3539i			1.92776i
$767$	−30.5703	−	40.8372i	−1.10383	−	1.47455i
$768$	−10.0235	−	3.73859i	−0.361693	−	0.134905i
$769$	−12.2442	+	26.8111i	−0.441538	+	0.966833i	0.549776	+	0.835312i	$0.314713\pi$
$769$	−12.2442	+	26.8111i	−0.441538	+	0.966833i	−0.991313	+	0.131520i	$0.958014\pi$
$770$	−10.4519	−	31.0314i	−0.376660	−	1.11829i
$771$	−7.63125	−	16.7101i	−0.274833	−	0.601800i
$772$	−0.988053	−	13.8148i	−0.0355608	−	0.497205i
$773$	30.2726	+	22.6618i	1.08883	+	0.815087i	0.983780	−	0.179380i	$-0.0574093\pi$
$773$	30.2726	+	22.6618i	1.08883	+	0.815087i	0.105048	+	0.994467i	$0.466500\pi$
$774$	13.5237	−	21.0433i	0.486099	−	0.756385i
$775$	−0.467178	+	0.383379i	−0.0167815	+	0.0137714i
$776$	−2.17759	+	1.88689i	−0.0781709	+	0.0677355i
$777$	−0.144387	−	2.01879i	−0.00517984	−	0.0724237i
$778$	6.78711	+	31.1998i	0.243330	+	1.11857i
$779$	−6.14561	−	9.56275i	−0.220189	−	0.342621i
$780$	36.2051	+	14.0594i	1.29635	+	0.503407i
$781$	−8.22086	−	18.9308i	−0.294166	−	0.677399i
$782$	48.1878	−	64.3714i	1.72319	−	2.30192i
$783$	−2.06760	+	28.9088i	−0.0738898	+	1.03312i
$784$	0.561943	+	0.874400i	0.0200694	+	0.0312286i
$785$	−4.32848	+	3.65023i	−0.154490	+	0.130282i
$786$	−0.142415	−	0.990518i	−0.00507977	−	0.0353306i
$787$	24.5130	+	18.3502i	0.873796	+	0.654115i	0.939060	−	0.343753i	$-0.111698\pi$
$787$	24.5130	+	18.3502i	0.873796	+	0.654115i	−0.0652646	+	0.997868i	$0.520789\pi$
$788$	−25.1869	+	33.6458i	−0.897246	+	1.19858i
$789$	−14.7798	+	9.49838i	−0.526174	+	0.338151i
$790$	−24.3586	−	7.50838i	−0.866640	−	0.267136i
$791$	−23.1591	+	3.32978i	−0.823444	+	0.118393i
$792$	1.10932	+	21.0357i	0.0394181	+	0.747471i
$793$	1.40681	+	1.87928i	0.0499574	+	0.0667352i
$794$	−1.66334	+	1.06896i	−0.0590296	+	0.0379360i
$795$	5.01994	−	4.88715i	0.178039	−	0.173329i
$796$	20.1113	−	23.2096i	0.712825	−	0.822644i
$797$	2.00917	−	28.0918i	0.0711683	−	0.995063i	−0.828923	−	0.559362i	$-0.811046\pi$
$797$	2.00917	−	28.0918i	0.0711683	−	0.995063i	0.900092	−	0.435701i	$-0.143499\pi$
$798$	12.1305	−	4.52446i	0.429417	−	0.160164i
$799$	−8.30022	−	5.33423i	−0.293641	−	0.188711i
$800$	13.7044	+	26.7801i	0.484523	+	0.946821i
$801$	−9.61058	+	11.0912i	−0.339573	+	0.391888i
$802$	−4.66978	−	1.74174i	−0.164896	−	0.0615030i
$803$	4.59828	−	50.8896i	0.162270	−	1.79586i
$804$	5.54115	+	2.53056i	0.195421	+	0.0892459i
$805$	−32.4785	+	6.61064i	−1.14472	+	0.232994i
$806$	0.278023	−	1.93369i	0.00979295	−	0.0681114i
$807$	−15.6259	−	15.6259i	−0.550057	−	0.550057i
$808$	12.5607	−	6.85868i	0.441885	−	0.241288i
$809$	−9.94373	+	6.39045i	−0.349603	+	0.224676i	−0.703642	−	0.710554i	$-0.748444\pi$
$809$	−9.94373	+	6.39045i	−0.349603	+	0.224676i	0.354039	+	0.935230i	$0.384808\pi$
$810$	13.4823	−	15.1444i	0.473719	−	0.532120i
$811$	14.7858	−	50.3557i	0.519198	−	1.76823i	−0.113188	−	0.993574i	$-0.536106\pi$
$811$	14.7858	−	50.3557i	0.519198	−	1.76823i	0.632386	−	0.774653i	$-0.282076\pi$
$812$	−9.07523	−	41.7182i	−0.318478	−	1.46402i
$813$	0.365412	−	5.10913i	0.0128156	−	0.179185i
$814$	−1.63493	+	10.0344i	−0.0573043	+	0.351706i
$815$	−1.72961	+	10.9826i	−0.0605854	+	0.384704i
$816$	−0.325323	−	1.10795i	−0.0113886	−	0.0387860i
$817$	15.2659	+	8.33582i	0.534087	+	0.291633i
$818$	−24.5258	−	1.75412i	−0.857526	−	0.0613314i
$819$	−9.36155	−	31.8825i	−0.327119	−	1.11406i
$820$	−20.6203	−	4.77600i	−0.720093	−	0.166785i
$821$	−18.2177	−	8.31974i	−0.635802	−	0.290361i	0.0713190	−	0.997454i	$-0.477279\pi$
$821$	−18.2177	−	8.31974i	−0.635802	−	0.290361i	−0.707121	+	0.707093i	$0.750006\pi$
$822$	1.60388	+	22.4252i	0.0559418	+	0.782168i
$823$	14.4772	+	38.8150i	0.504645	+	1.35300i	0.900566	+	0.434720i	$0.143153\pi$
$823$	14.4772	+	38.8150i	0.504645	+	1.35300i	−0.395921	+	0.918285i	$0.629575\pi$
$824$	−17.3316	−	11.1384i	−0.603775	−	0.388023i
$825$	−8.13094	+	9.88951i	−0.283083	+	0.344309i
$826$	−26.6367	+	17.1184i	−0.926810	+	0.595625i
$827$	32.7691	+	24.5306i	1.13949	+	0.853014i	0.990728	−	0.135859i	$-0.0433794\pi$
$827$	32.7691	+	24.5306i	1.13949	+	0.853014i	0.148765	+	0.988873i	$0.452470\pi$
$828$	57.8493	+	4.13746i	2.01040	+	0.143787i
$829$	−21.2682	−	3.05791i	−0.738676	−	0.106206i	−0.237302	−	0.971436i	$-0.576263\pi$
$829$	−21.2682	−	3.05791i	−0.738676	−	0.106206i	−0.501375	+	0.865230i	$0.667172\pi$
$830$	−10.5035	+	7.64533i	−0.364583	+	0.265373i
$831$	5.22070	−	8.12357i	0.181104	−	0.281804i
$832$	−86.8160	−	32.3807i	−3.00980	−	1.12260i
$833$	5.22709	−	14.0144i	0.181108	−	0.485570i
$834$	−8.55430	+	29.1333i	−0.296211	+	1.00880i
$835$	45.9213	−	12.8177i	1.58917	−	0.443576i
$836$	−39.5348	+	4.93106i	−1.36734	+	0.170544i
$837$	0.442594	+	0.241675i	0.0152983	+	0.00835349i
$838$	21.4688	+	21.4688i	0.741628	+	0.741628i
$839$	5.10800	+	2.33274i	0.176348	+	0.0805353i	0.501633	−	0.865081i	$-0.332733\pi$
$839$	5.10800	+	2.33274i	0.176348	+	0.0805353i	−0.325285	+	0.945616i	$0.605460\pi$
$840$	3.78953	−	8.01197i	0.130751	−	0.276439i
$841$	−2.74068	+	19.0618i	−0.0945060	+	0.657304i
$842$	−22.1500	−	8.26153i	−0.763340	−	0.284711i
$843$	5.37339	+	9.84063i	0.185069	+	0.338929i
$844$	−52.1100			−1.79370
$845$	78.3731	+	30.4343i	2.69612	+	1.04697i
$846$		−	11.6165i		−	0.399383i
$847$	−15.6693	+	14.5382i	−0.538405	+	0.499540i
$848$	−0.925142	+	0.925142i	−0.0317695	+	0.0317695i
$849$	0.326021	−	2.26752i	0.0111890	−	0.0778212i
$850$	23.1724	−	47.3397i	0.794806	−	1.62374i
$851$	9.87411	+	2.89930i	0.338480	+	0.0993867i
$852$	5.31009	−	14.2369i	0.181921	−	0.487748i
$853$	−30.6535	+	22.9469i	−1.04956	+	0.785689i	−0.977335	−	0.211700i	$-0.932100\pi$
$853$	−30.6535	+	22.9469i	−1.04956	+	0.785689i	−0.0722223	+	0.997389i	$0.523009\pi$
$854$	1.22579	−	0.787768i	0.0419457	−	0.0269569i
$855$	16.1786	+	12.4530i	0.553297	+	0.425883i
$856$	46.5089			1.58964
$857$	2.98751	−	5.47121i	0.102051	−	0.186893i	−0.821665	−	0.569971i	$-0.806954\pi$
$857$	2.98751	−	5.47121i	0.102051	−	0.186893i	0.923716	+	0.383078i	$0.125136\pi$
$858$	−2.17947	−	41.3286i	−0.0744060	−	1.41093i
$859$	8.55437	−	29.1335i	0.291871	−	0.994023i	−0.674800	−	0.738001i	$-0.735770\pi$
$859$	8.55437	−	29.1335i	0.291871	−	0.994023i	0.966671	−	0.256022i	$-0.0824118\pi$
$860$	31.1948	−	8.70722i	1.06373	−	0.296914i
$861$	−1.86520	−	4.08423i	−0.0635660	−	0.139190i
$862$	−18.1056	+	48.5431i	−0.616681	+	1.65339i
$863$	−53.0854	+	11.5480i	−1.80705	+	0.393099i	−0.984470	−	0.175555i	$-0.943828\pi$
$863$	−53.0854	+	11.5480i	−1.80705	+	0.393099i	−0.822577	+	0.568654i	$0.807464\pi$
$864$	16.4382	−	18.9707i	0.559238	−	0.645395i
$865$	41.9004	−	18.4606i	1.42466	−	0.627680i
$866$	−57.9702	+	50.2315i	−1.96991	+	1.70694i
$867$	−2.09282	+	2.79568i	−0.0710759	+	0.0949463i
$868$	−0.725868	−	0.157903i	−0.0246376	−	0.00535957i
$869$	2.05940	+	16.5112i	0.0698603	+	0.560105i
$870$	−19.5246	+	19.0081i	−0.661945	+	0.644435i
$871$	16.1422	+	7.37188i	0.546956	+	0.249786i
$872$	53.1324	−	3.80011i	1.79929	−	0.128688i
$873$	−0.916192	−	2.45641i	−0.0310084	−	0.0831368i
$874$			65.8296i			2.22672i
$875$	−20.1089	+	8.22335i	−0.679806	+	0.278000i
$876$	28.4307	−	24.6354i	0.960585	−	0.832351i
$877$	−4.93935	+	9.04574i	−0.166790	+	0.305453i	−0.947684	−	0.319211i	$-0.896582\pi$
$877$	−4.93935	+	9.04574i	−0.166790	+	0.305453i	0.780894	+	0.624664i	$0.214764\pi$
$878$	3.66935	−	6.71991i	0.123834	−	0.226786i
$879$	12.5229	−	14.4522i	0.422387	−	0.487461i
$880$	1.49354	−	1.86702i	0.0503471	−	0.0629372i
$881$	−0.246774	−	0.284792i	−0.00831402	−	0.00959489i	0.751577	−	0.659645i	$-0.229293\pi$
$881$	−0.246774	−	0.284792i	−0.00831402	−	0.00959489i	−0.759891	+	0.650050i	$0.774748\pi$
$882$	17.2079	−	3.74336i	0.579422	−	0.126045i
$883$	13.6605	−	7.45918i	0.459711	−	0.251021i	−0.232666	−	0.972557i	$-0.574745\pi$
$883$	13.6605	−	7.45918i	0.459711	−	0.251021i	0.692378	+	0.721535i	$0.256563\pi$
$884$	29.4059	+	100.147i	0.989026	+	3.36831i
$885$	11.1915	+	5.29338i	0.376197	+	0.177935i
$886$	−17.5633	+	59.8152i	−0.590052	+	2.00953i
$887$	2.05288	−	2.05288i	0.0689289	−	0.0689289i	−0.671802	−	0.740731i	$-0.734479\pi$
$887$	2.05288	−	2.05288i	0.0689289	−	0.0689289i	0.740731	+	0.671802i	$0.234479\pi$
$888$	−2.20297	+	1.64912i	−0.0739268	+	0.0553409i
$889$	11.8058	−	5.39153i	0.395954	−	0.180826i
$890$	−30.7579	+	4.00232i	−1.03101	+	0.134158i
$891$	−12.6278	−	3.96600i	−0.423048	−	0.132866i
$892$	−7.30606	+	19.5883i	−0.244625	+	0.655865i
$893$	8.05688	−	0.576239i	0.269613	−	0.0192831i
$894$	10.0266	−	1.44161i	0.335341	−	0.0482147i
$895$	−23.4193	+	22.7998i	−0.782821	+	0.762113i
$896$	−14.1782	+	31.0459i	−0.473660	+	1.03717i
$897$	−41.7850	−	2.98852i	−1.39516	−	0.0997838i
$898$	−65.1725	+	4.66123i	−2.17484	+	0.155547i
$899$	0.706361	+	0.453951i	0.0235585	+	0.0151401i
$900$	37.7603	−	4.39969i	1.25868	−	0.146656i
$901$	18.6361	+	2.67946i	0.620858	+	0.0892659i
$902$	4.38100	+	22.1246i	0.145871	+	0.736669i
$903$	5.49995	+	4.11721i	0.183027	+	0.137012i
$904$	20.8325	+	24.0419i	0.692877	+	0.799623i
$905$	4.07226	−	1.45701i	0.135367	−	0.0484325i
$906$	0.386474	+	2.68799i	0.0128397	+	0.0893023i
$907$	1.15583	−	1.54400i	0.0383786	−	0.0512678i	−0.780941	−	0.624604i	$-0.785260\pi$
$907$	1.15583	−	1.54400i	0.0383786	−	0.0512678i	0.819320	+	0.573336i	$0.194351\pi$
$908$	52.1899	−	69.7175i	1.73198	−	2.31366i
$909$	1.85317	+	12.8891i	0.0614659	+	0.427504i
$910$	30.0275	−	63.4852i	0.995402	−	2.10451i
$911$	−16.1813	−	18.6743i	−0.536112	−	0.618706i	0.421479	−	0.906838i	$-0.361511\pi$
$911$	−16.1813	−	18.6743i	−0.536112	−	0.618706i	−0.957591	+	0.288132i	$0.906966\pi$
$912$	0.756787	+	0.566524i	0.0250597	+	0.0187595i
$913$	7.36584	+	4.20286i	0.243774	+	0.139094i
$914$	−25.5176	−	3.66887i	−0.844046	−	0.121356i
$915$	−0.515018	−	0.243596i	−0.0170260	−	0.00805302i
$916$	32.9192	+	21.1559i	1.08768	+	0.699009i
$917$	−1.10567	+	0.0790791i	−0.0365125	+	0.00261142i
$918$	−43.8675	−	3.13746i	−1.44784	−	0.103552i
$919$	8.93432	−	19.5634i	0.294716	−	0.645338i	−0.703121	−	0.711070i	$-0.748211\pi$
$919$	8.93432	−	19.5634i	0.294716	−	0.645338i	0.997837	+	0.0657320i	$0.0209382\pi$
$920$	31.4356	+	32.2898i	1.03640	+	1.06456i
$921$	1.62716	−	0.233950i	0.0536168	−	0.00770893i
$922$	−46.4460	+	3.32188i	−1.52962	+	0.109400i
$923$	15.4690	−	41.4741i	0.509170	−	1.36514i
$924$	−15.7342	−	0.294475i	−0.517617	−	0.00968750i
$925$	6.71299	+	0.661385i	0.220722	+	0.0217462i
$926$	71.5762	−	32.6878i	2.35214	−	1.07419i
$927$	15.0066	−	11.2338i	0.492881	−	0.368966i
$928$	29.5542	−	29.5542i	0.970166	−	0.970166i
$929$	−3.70723	+	12.6257i	−0.121630	+	0.414235i	−0.997687	−	0.0679730i	$-0.978347\pi$
$929$	−3.70723	+	12.6257i	−0.121630	+	0.414235i	0.876057	+	0.482208i	$0.160165\pi$
$930$	0.159718	+	0.446404i	0.00523736	+	0.0146382i
$931$	3.44990	+	11.7493i	0.113066	+	0.385067i
$932$	16.4433	−	8.97873i	0.538619	−	0.294108i
$933$	8.18725	−	1.78103i	0.268038	−	0.0583082i
$934$	54.1605	+	62.5046i	1.77219	+	2.04521i
$935$	−34.3884	−	1.10482i	−1.12462	−	0.0361315i
$936$	−29.5859	+	34.1440i	−0.967047	+	1.11603i
$937$	−3.92343	+	7.18522i	−0.128173	+	0.234731i	−0.933883	−	0.357579i	$-0.883602\pi$
$937$	−3.92343	+	7.18522i	−0.128173	+	0.234731i	0.805710	+	0.592310i	$0.201784\pi$
$938$	5.27884	−	9.66748i	0.172360	−	0.315654i
$939$	3.98290	−	3.45120i	0.129977	−	0.112626i
$940$	10.0009	−	11.2338i	0.326193	−	0.366406i
$941$			6.89549i			0.224786i	0.993664	+	0.112393i	$0.0358516\pi$
$941$			6.89549i			0.224786i	−0.993664	+	0.112393i	$0.964148\pi$
$942$	1.55233	+	4.16195i	0.0505776	+	0.135604i
$943$	22.7716	−	1.62866i	0.741545	−	0.0530364i
$944$	−2.10303	−	0.960422i	−0.0684478	−	0.0312591i
$945$	12.6455	+	12.9891i	0.411359	+	0.422536i
$946$	−22.1079	−	26.5000i	−0.718791	−	0.861591i
$947$	5.28957	+	1.15068i	0.171888	+	0.0373919i	0.297685	−	0.954664i	$-0.403785\pi$
$947$	5.28957	+	1.15068i	0.171888	+	0.0373919i	−0.125798	+	0.992056i	$0.540149\pi$
$948$	−7.34133	+	9.80687i	−0.238435	+	0.318512i
$949$	82.8227	−	71.7663i	2.68854	−	2.32963i
$950$	8.03873	+	42.3944i	0.260811	+	1.37546i
$951$	1.26671	−	1.46186i	0.0410760	−	0.0474042i
$952$	23.2738	−	5.06289i	0.754307	−	0.164089i
$953$	14.7774	−	39.6197i	0.478687	−	1.28341i	−0.443364	−	0.896342i	$-0.646215\pi$
$953$	14.7774	−	39.6197i	0.478687	−	1.28341i	0.922051	−	0.387068i	$-0.126512\pi$
$954$	9.20855	+	20.1639i	0.298138	+	0.652831i
$955$	18.8350	+	10.6148i	0.609486	+	0.343488i
$956$	15.2617	−	51.9765i	0.493598	−	1.68104i
$957$	16.5471	+	6.52698i	0.534890	+	0.210987i
$958$	−22.5967	+	41.3828i	−0.730067	+	1.33702i
$959$	24.9042			0.804199
$960$	22.2993	−	2.90167i	0.719708	−	0.0936509i
$961$	−26.0666	+	16.7520i	−0.840857	+	0.540386i
$962$	−17.4559	+	13.0673i	−0.562801	+	0.421307i
$963$	−14.7885	+	39.6495i	−0.476553	+	1.27769i
$964$	81.0384	+	23.7950i	2.61007	+	0.766386i
$965$	5.18304	+	8.30771i	0.166848	+	0.267435i
$966$	−3.70049	+	25.7375i	−0.119061	+	0.828091i
$967$	1.64447	−	1.64447i	0.0528827	−	0.0528827i	−0.680171	−	0.733054i	$-0.738094\pi$
$967$	1.64447	−	1.64447i	0.0528827	−	0.0528827i	0.733054	+	0.680171i	$0.238094\pi$
$968$	28.1472	+	7.23594i	0.904685	+	0.232572i
$969$		−	13.6039i		−	0.437021i
$970$	2.00578	−	5.16519i	0.0644017	−	0.165844i
$971$	23.8522			0.765454			0.382727	−	0.923862i	$-0.374985\pi$
$971$	23.8522			0.765454			0.382727	+	0.923862i	$0.374985\pi$
$972$	−23.6418	−	43.2967i	−0.758311	−	1.38874i
$973$	31.5132	+	11.7538i	1.01027	+	0.376810i
$974$	−4.87657	+	33.9173i	−0.156255	+	1.08678i
$975$	−27.2745	+	3.17793i	−0.873484	+	0.101775i
$976$	0.0967791	+	0.0441975i	0.00309782	+	0.00141473i
$977$	12.1389	+	12.1389i	0.388357	+	0.388357i	0.874101	−	0.485744i	$-0.161451\pi$
$977$	12.1389	+	12.1389i	0.388357	+	0.388357i	−0.485744	+	0.874101i	$0.661451\pi$
$978$	7.65527	+	4.18009i	0.244789	+	0.133665i
$979$	10.6260	+	17.2352i	0.339608	+	0.550838i
$980$	19.8638	+	11.1947i	0.634526	+	0.357600i
$981$	−13.6550	+	46.5046i	−0.435970	+	1.48478i
$982$	−3.70029	+	9.92087i	−0.118081	+	0.316588i
$983$	32.1550	+	11.9932i	1.02558	+	0.382523i	0.805272	−	0.592906i	$-0.202019\pi$
$983$	32.1550	+	11.9932i	1.02558	+	0.382523i	0.220313	+	0.975429i	$0.429292\pi$
$984$	−3.30050	+	5.13567i	−0.105216	+	0.163719i
$985$	4.62258	−	29.3524i	0.147288	−	0.935244i
$986$	−72.4832	−	10.4215i	−2.30834	−	0.331889i
$987$	3.18240	+	0.227610i	0.101297	+	0.00724490i
$988$	−68.4057	−	51.2079i	−2.17628	−	1.62914i
$989$	−29.3873	+	18.8861i	−0.934461	+	0.600542i
$990$	−20.7951	−	34.7637i	−0.660910	−	1.10486i
$991$	−0.780280	−	0.501456i	−0.0247864	−	0.0159293i	0.528189	−	0.849127i	$-0.322871\pi$
$991$	−0.780280	−	0.501456i	−0.0247864	−	0.0159293i	−0.552975	+	0.833198i	$0.686508\pi$
$992$	−0.254138	−	0.681370i	−0.00806889	−	0.0216335i
$993$	−1.14800	−	16.0511i	−0.0364307	−	0.509367i
$994$	−24.9924	−	11.4136i	−0.792711	−	0.362019i
$995$	−4.89923	+	21.1524i	−0.155316	+	0.670575i
$996$	1.75904	+	5.99074i	0.0557373	+	0.189824i
$997$	−37.7330	−	2.69872i	−1.19502	−	0.0854693i	−0.540386	−	0.841418i	$-0.681722\pi$
$997$	−37.7330	−	2.69872i	−1.19502	−	0.0854693i	−0.654631	+	0.755948i	$0.727176\pi$
$998$	37.9535	+	20.7242i	1.20140	+	0.656012i
$999$	−1.58575	−	5.40056i	−0.0501709	−	0.170866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.r.a.32.6	✓	1280
5.3	odd	4	inner	605.2.r.a.153.6	yes	1280
121.87	odd	22	inner	605.2.r.a.87.6	yes	1280
605.208	even	44	inner	605.2.r.a.208.6	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.r.a.32.6	✓	1280	1.1	even	1	trivial
605.2.r.a.87.6	yes	1280	121.87	odd	22	inner
605.2.r.a.153.6	yes	1280	5.3	odd	4	inner
605.2.r.a.208.6	yes	1280	605.208	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.r (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36166 - 1.81897i) q^{2} +(0.545918 - 0.545918i) q^{3} +(-0.891058 + 3.03466i) q^{4} +(-0.445983 - 2.19114i) q^{5} +(-1.73637 - 0.249652i) q^{6} +(-0.413052 + 1.89877i) q^{7} +(2.47545 - 0.923297i) q^{8} +2.40395i q^{9} +O(q^{10})\)	\(q+(-1.36166 - 1.81897i) q^{2} +(0.545918 - 0.545918i) q^{3} +(-0.891058 + 3.03466i) q^{4} +(-0.445983 - 2.19114i) q^{5} +(-1.73637 - 0.249652i) q^{6} +(-0.413052 + 1.89877i) q^{7} +(2.47545 - 0.923297i) q^{8} +2.40395i q^{9} +(-3.37834 + 3.79483i) q^{10} +(3.16424 + 0.993785i) q^{11} +(1.17023 + 2.14312i) q^{12} +(3.40906 + 6.24322i) q^{13} +(4.01625 - 1.83416i) q^{14} +(-1.43965 - 0.952713i) q^{15} +(0.271211 + 0.174297i) q^{16} +(-0.330966 - 4.62751i) q^{17} +(4.37271 - 3.27337i) q^{18} +(2.48723 + 2.87042i) q^{19} +(7.04677 + 0.599025i) q^{20} +(0.811081 + 1.26207i) q^{21} +(-2.50096 - 7.10885i) q^{22} +(-7.45371 + 1.62145i) q^{23} +(0.847351 - 1.85544i) q^{24} +(-4.60220 + 1.95442i) q^{25} +(6.71424 - 14.7021i) q^{26} +(2.95011 + 2.95011i) q^{27} +(-5.39408 - 2.94539i) q^{28} +(4.54918 + 5.25003i) q^{29} +(0.227367 + 3.91596i) q^{30} +(0.115973 - 0.0340528i) q^{31} +(-0.429219 - 6.00127i) q^{32} +(2.26994 - 1.18489i) q^{33} +(-7.96663 + 6.90313i) q^{34} +(4.34469 + 0.0582364i) q^{35} +(-7.29517 - 2.14206i) q^{36} +(-1.18408 - 0.646554i) q^{37} +(1.83443 - 8.43274i) q^{38} +(5.26935 + 1.54722i) q^{39} +(-3.12708 - 5.01230i) q^{40} +(-2.96241 - 0.425931i) q^{41} +(1.19124 - 3.19384i) q^{42} +(4.29078 - 1.60038i) q^{43} +(-5.83532 + 8.71687i) q^{44} +(5.26739 - 1.07212i) q^{45} +(13.0988 + 11.3502i) q^{46} +(1.27449 - 1.70252i) q^{47} +(0.243211 - 0.0529073i) q^{48} +(2.93270 + 1.33932i) q^{49} +(9.82168 + 5.70999i) q^{50} +(-2.70692 - 2.34556i) q^{51} +(-21.9837 + 4.78227i) q^{52} +(-0.862651 + 3.96554i) q^{53} +(1.34910 - 9.38323i) q^{54} +(0.766328 - 7.37650i) q^{55} +(0.730637 + 5.08169i) q^{56} +(2.92484 + 0.209188i) q^{57} +(3.35520 - 15.4236i) q^{58} +(-7.09833 + 1.02059i) q^{59} +(4.17398 - 3.51994i) q^{60} +(0.326657 - 0.0469662i) q^{61} +(-0.219858 - 0.164583i) q^{62} +(-4.56454 - 0.992956i) q^{63} +(-9.84438 + 8.53020i) q^{64} +(12.1594 - 10.2541i) q^{65} +(-5.24617 - 2.51553i) q^{66} +(1.99713 - 1.49503i) q^{67} +(14.3378 + 3.11901i) q^{68} +(-3.18393 + 4.95430i) q^{69} +(-5.81008 - 7.98216i) q^{70} +(-4.07509 - 4.70290i) q^{71} +(2.21956 + 5.95086i) q^{72} +(-3.27485 - 15.0542i) q^{73} +(0.436250 + 3.03419i) q^{74} +(-1.44547 + 3.57938i) q^{75} +(-10.9270 + 4.99020i) q^{76} +(-3.19397 + 5.59767i) q^{77} +(-4.36074 - 11.6916i) q^{78} +(2.08409 + 4.56353i) q^{79} +(0.260953 - 0.671995i) q^{80} -3.99080 q^{81} +(3.25906 + 5.96852i) q^{82} +(2.49855 + 0.543525i) q^{83} +(-4.55267 + 1.33678i) q^{84} +(-9.99192 + 2.78898i) q^{85} +(-8.75364 - 5.62562i) q^{86} +(5.34957 + 0.382608i) q^{87} +(8.75048 - 0.461459i) q^{88} +(4.61374 + 3.99783i) q^{89} +(-9.12256 - 8.12135i) q^{90} +(-13.2626 + 3.89424i) q^{91} +(1.72111 - 24.0643i) q^{92} +(0.0447219 - 0.0819020i) q^{93} -4.83225 q^{94} +(5.18022 - 6.73003i) q^{95} +(-3.51052 - 3.04188i) q^{96} +(-1.02182 + 0.381120i) q^{97} +(-1.55717 - 7.15821i) q^{98} +(-2.38901 + 7.60666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 22 q^{2} - 40 q^{3} - 14 q^{5} - 44 q^{6} - 22 q^{7} - 22 q^{8}+O(q^{10}) \) 1280 * q - 22 * q^2 - 40 * q^3 - 14 * q^5 - 44 * q^6 - 22 * q^7 - 22 * q^8	\( 1280 q - 22 q^{2} - 40 q^{3} - 14 q^{5} - 44 q^{6} - 22 q^{7} - 22 q^{8} - 66 q^{10} - 48 q^{11} + 44 q^{12} - 66 q^{13} - 26 q^{15} + 80 q^{16} - 22 q^{17} - 44 q^{18} - 54 q^{20} - 44 q^{21} - 90 q^{22} - 34 q^{23} - 30 q^{25} - 12 q^{26} + 80 q^{27} - 22 q^{28} - 22 q^{30} - 52 q^{31} - 22 q^{32} - 62 q^{33} - 22 q^{35} + 216 q^{36} + 52 q^{37} + 70 q^{38} - 44 q^{41} + 44 q^{42} - 22 q^{43} + 104 q^{45} - 44 q^{46} - 18 q^{47} - 72 q^{48} + 88 q^{50} - 484 q^{51} - 22 q^{52} + 14 q^{53} + 140 q^{55} - 316 q^{56} + 44 q^{57} - 6 q^{58} + 34 q^{60} - 44 q^{61} - 22 q^{62} - 44 q^{63} - 22 q^{65} - 84 q^{66} - 138 q^{67} - 22 q^{68} - 126 q^{70} - 4 q^{71} + 220 q^{72} - 22 q^{73} - 66 q^{75} + 88 q^{76} - 22 q^{77} - 104 q^{78} - 324 q^{80} - 1056 q^{81} - 58 q^{82} - 22 q^{83} - 110 q^{85} - 52 q^{86} + 44 q^{87} - 2 q^{88} + 176 q^{90} + 104 q^{91} - 278 q^{92} - 128 q^{93} - 22 q^{95} - 44 q^{96} + 46 q^{97} - 22 q^{98}+O(q^{100}) \) 1280 * q - 22 * q^2 - 40 * q^3 - 14 * q^5 - 44 * q^6 - 22 * q^7 - 22 * q^8 - 66 * q^10 - 48 * q^11 + 44 * q^12 - 66 * q^13 - 26 * q^15 + 80 * q^16 - 22 * q^17 - 44 * q^18 - 54 * q^20 - 44 * q^21 - 90 * q^22 - 34 * q^23 - 30 * q^25 - 12 * q^26 + 80 * q^27 - 22 * q^28 - 22 * q^30 - 52 * q^31 - 22 * q^32 - 62 * q^33 - 22 * q^35 + 216 * q^36 + 52 * q^37 + 70 * q^38 - 44 * q^41 + 44 * q^42 - 22 * q^43 + 104 * q^45 - 44 * q^46 - 18 * q^47 - 72 * q^48 + 88 * q^50 - 484 * q^51 - 22 * q^52 + 14 * q^53 + 140 * q^55 - 316 * q^56 + 44 * q^57 - 6 * q^58 + 34 * q^60 - 44 * q^61 - 22 * q^62 - 44 * q^63 - 22 * q^65 - 84 * q^66 - 138 * q^67 - 22 * q^68 - 126 * q^70 - 4 * q^71 + 220 * q^72 - 22 * q^73 - 66 * q^75 + 88 * q^76 - 22 * q^77 - 104 * q^78 - 324 * q^80 - 1056 * q^81 - 58 * q^82 - 22 * q^83 - 110 * q^85 - 52 * q^86 + 44 * q^87 - 2 * q^88 + 176 * q^90 + 104 * q^91 - 278 * q^92 - 128 * q^93 - 22 * q^95 - 44 * q^96 + 46 * q^97 - 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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