LMFDB - Embedded newform 750.2.o.a.229.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [750,2,Mod(19,750)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(750, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("750.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 750 = 2 \cdot 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	750.o (of order $50$, 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:	$5.98878015160$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.6
Character	$\chi$	$=$	750.229
Dual form			750.2.o.a.619.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.248690 - 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(2.06404 - 0.860088i) q^{5} +(0.425779 + 0.904827i) q^{6} +(1.97975 - 2.72489i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})$	\(q+(-0.248690 - 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(2.06404 - 0.860088i) q^{5} +(0.425779 + 0.904827i) q^{6} +(1.97975 - 2.72489i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-1.34637 - 1.78530i) q^{10} +(1.55701 - 0.399773i) q^{11} +(0.770513 - 0.637424i) q^{12} +(1.38553 + 3.49946i) q^{13} +(-3.13163 - 1.23990i) q^{14} +(-1.86631 + 1.23162i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-0.651889 + 1.18578i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(0.0105263 - 0.0551808i) q^{19} +(-1.39438 + 1.74806i) q^{20} +(-1.43409 + 3.04760i) q^{21} +(-0.774426 - 1.40868i) q^{22} +(4.41659 + 0.277868i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(3.52050 - 3.55051i) q^{25} +(3.04495 - 2.21228i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(-0.422142 + 3.34159i) q^{28} +(-7.10301 - 0.897319i) q^{29} +(1.65706 + 1.50139i) q^{30} +(0.591947 + 0.325426i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-1.45452 + 0.684446i) q^{33} +(1.31065 + 0.336517i) q^{34} +(1.74263 - 7.32704i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(-1.14675 - 0.727752i) q^{37} +(-0.0560650 + 0.00352731i) q^{38} +(-2.01673 - 3.17785i) q^{39} +(2.03991 + 0.915847i) q^{40} +(0.00918412 + 0.145977i) q^{41} +(3.30849 + 0.631129i) q^{42} +(11.7183 - 3.80750i) q^{43} +(-1.17183 + 1.10042i) q^{44} +(1.60247 - 1.55951i) q^{45} +(-0.829223 - 4.34694i) q^{46} +(8.03264 - 8.55389i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(-1.34251 - 4.13182i) q^{49} +(-4.31447 - 2.52692i) q^{50} +(0.418149 - 1.28693i) q^{51} +(-2.90003 - 2.39911i) q^{52} +(-4.77873 - 2.24870i) q^{53} +(0.728969 + 0.684547i) q^{54} +(2.86989 - 2.16431i) q^{55} +(3.34159 - 0.422142i) q^{56} +0.0561759i q^{57} +(0.897319 + 7.10301i) q^{58} +(-9.02755 - 10.9124i) q^{59} +(1.04213 - 1.97838i) q^{60} +(0.242919 - 3.86109i) q^{61} +(0.167991 - 0.654280i) q^{62} +(0.837626 - 3.26234i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(5.86964 + 6.03133i) q^{65} +(1.02467 + 1.23861i) q^{66} +(1.60186 + 12.6800i) q^{67} -1.35316i q^{68} +(-4.39043 + 0.554640i) q^{69} +(-7.53022 + 0.134278i) q^{70} +(-5.49260 - 5.15789i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-0.766351 - 0.633981i) q^{73} +(-0.419702 + 1.29171i) q^{74} +(-2.79284 + 4.14729i) q^{75} +(0.0173593 + 0.0534264i) q^{76} +(1.99316 - 5.03414i) q^{77} +(-2.57647 + 2.74367i) q^{78} +(0.467998 + 2.45333i) q^{79} +(0.379770 - 2.20358i) q^{80} +(0.728969 - 0.684547i) q^{81} +(0.139107 - 0.0451987i) q^{82} +(-7.91725 - 1.51030i) q^{83} +(-0.211488 - 3.36151i) q^{84} +(-0.325646 + 3.00818i) q^{85} +(-6.60210 - 10.4032i) q^{86} +(7.14534 - 0.449547i) q^{87} +(1.35727 + 0.861349i) q^{88} +(2.53372 - 3.06275i) q^{89} +(-1.90904 - 1.16429i) q^{90} +(12.2787 + 3.15262i) q^{91} +(-4.00415 + 1.88421i) q^{92} +(-0.642441 - 0.208742i) q^{93} +(-10.2828 - 5.65301i) q^{94} +(-0.0257337 - 0.122949i) q^{95} +(0.992115 + 0.125333i) q^{96} +(-0.668696 + 5.29327i) q^{97} +(-3.66815 + 2.32788i) q^{98} +(1.30051 - 0.944873i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) $ 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/750\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$2$	−0.248690	−	0.968583i	−0.175850	−	0.684892i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$3$	−0.982287	+	0.187381i	−0.567124	+	0.108185i
$4$	−0.876307	+	0.481754i	−0.438153	+	0.240877i
$5$	2.06404	−	0.860088i	0.923065	−	0.384643i
$5$	2.06404	−	0.860088i	0.923065	−	0.384643i
$6$	0.425779	+	0.904827i	0.173824	+	0.369394i
$7$	1.97975	−	2.72489i	0.748276	−	1.02991i	−0.249824	−	0.968291i	$-0.580373\pi$
$7$	1.97975	−	2.72489i	0.748276	−	1.02991i	0.998100	−	0.0616216i	$-0.0196272\pi$
$8$	0.684547	+	0.728969i	0.242024	+	0.257729i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	−1.34637	−	1.78530i	−0.425760	−	0.564560i
$11$	1.55701	−	0.399773i	0.469457	−	0.120536i	−0.00654834	−	0.999979i	$-0.502084\pi$
$11$	1.55701	−	0.399773i	0.469457	−	0.120536i	0.476005	+	0.879443i	$0.342084\pi$
$12$	0.770513	−	0.637424i	0.222428	−	0.184008i
$13$	1.38553	+	3.49946i	0.384278	+	0.970575i	0.985222	+	0.171284i	$0.0547915\pi$
$13$	1.38553	+	3.49946i	0.384278	+	0.970575i	−0.600944	+	0.799291i	$0.705208\pi$
$14$	−3.13163	−	1.23990i	−0.836963	−	0.331377i
$15$	−1.86631	+	1.23162i	−0.481880	+	0.318002i
$16$	0.535827	−	0.844328i	0.133957	−	0.211082i
$17$	−0.651889	+	1.18578i	−0.158106	+	0.287594i	−0.943481	−	0.331426i	$-0.892470\pi$
$17$	−0.651889	+	1.18578i	−0.158106	+	0.287594i	0.785375	+	0.619020i	$0.212470\pi$
$18$	−0.587785	−	0.809017i	−0.138542	−	0.190687i
$19$	0.0105263	−	0.0551808i	0.00241490	−	0.0126594i	−0.981059	−	0.193707i	$-0.937949\pi$
$19$	0.0105263	−	0.0551808i	0.00241490	−	0.0126594i	0.983474	+	0.181048i	$0.0579489\pi$
$20$	−1.39438	+	1.74806i	−0.311793	+	0.390878i
$21$	−1.43409	+	3.04760i	−0.312944	+	0.665040i
$22$	−0.774426	−	1.40868i	−0.165108	−	0.300331i
$23$	4.41659	+	0.277868i	0.920923	+	0.0579396i	0.516170	−	0.856486i	$-0.327357\pi$
$23$	4.41659	+	0.277868i	0.920923	+	0.0579396i	0.404753	+	0.914426i	$0.367357\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	3.52050	−	3.55051i	0.704099	−	0.710101i
$26$	3.04495	−	2.21228i	0.597164	−	0.433865i
$27$	−0.844328	+	0.535827i	−0.162491	+	0.103120i
$28$	−0.422142	+	3.34159i	−0.0797773	+	0.631502i
$29$	−7.10301	−	0.897319i	−1.31900	−	0.166628i	−0.565865	−	0.824498i	$-0.691458\pi$
$29$	−7.10301	−	0.897319i	−1.31900	−	0.166628i	−0.753132	+	0.657870i	$0.771458\pi$
$30$	1.65706	+	1.50139i	0.302536	+	0.274115i
$31$	0.591947	+	0.325426i	0.106317	+	0.0584482i	0.534025	−	0.845469i	$-0.320679\pi$
$31$	0.591947	+	0.325426i	0.106317	+	0.0584482i	−0.427708	+	0.903917i	$0.640679\pi$
$32$	−0.951057	−	0.309017i	−0.168125	−	0.0546270i
$33$	−1.45452	+	0.684446i	−0.253200	+	0.119147i
$34$	1.31065	+	0.336517i	0.224774	+	0.0577121i
$35$	1.74263	−	7.32704i	0.294558	−	1.23850i
$36$	−0.637424	+	0.770513i	−0.106237	+	0.128419i
$37$	−1.14675	−	0.727752i	−0.188525	−	0.119642i	0.438214	−	0.898870i	$-0.355611\pi$
$37$	−1.14675	−	0.727752i	−0.188525	−	0.119642i	−0.626740	+	0.779229i	$0.715611\pi$
$38$	−0.0560650	+	0.00352731i	−0.00909495	+	0.000572206i
$39$	−2.01673	−	3.17785i	−0.322934	−	0.508863i
$40$	2.03991	+	0.915847i	0.322538	+	0.144808i
$41$	0.00918412	+	0.145977i	0.00143432	+	0.0227978i	0.998679	−	0.0513875i	$-0.0163644\pi$
$41$	0.00918412	+	0.145977i	0.00143432	+	0.0227978i	−0.997244	+	0.0741853i	$0.976364\pi$
$42$	3.30849	+	0.631129i	0.510512	+	0.0973853i
$43$	11.7183	−	3.80750i	1.78702	−	0.580638i	0.787651	−	0.616122i	$-0.211297\pi$
$43$	11.7183	−	3.80750i	1.78702	−	0.580638i	0.999370	+	0.0354833i	$0.0112970\pi$
$44$	−1.17183	+	1.10042i	−0.176660	+	0.165894i
$45$	1.60247	−	1.55951i	0.238883	−	0.232478i
$46$	−0.829223	−	4.34694i	−0.122262	−	0.640921i
$47$	8.03264	−	8.55389i	1.17168	−	1.24771i	0.208748	−	0.977969i	$-0.433061\pi$
$47$	8.03264	−	8.55389i	1.17168	−	1.24771i	0.962932	−	0.269743i	$-0.0869389\pi$
$48$	−0.368125	+	0.929776i	−0.0531342	+	0.134202i
$49$	−1.34251	−	4.13182i	−0.191787	−	0.590261i
$50$	−4.31447	−	2.52692i	−0.610159	−	0.357360i
$51$	0.418149	−	1.28693i	0.0585525	−	0.180206i
$52$	−2.90003	−	2.39911i	−0.402162	−	0.332697i
$53$	−4.77873	−	2.24870i	−0.656409	−	0.308883i	0.0685772	−	0.997646i	$-0.478154\pi$
$53$	−4.77873	−	2.24870i	−0.656409	−	0.308883i	−0.724987	+	0.688763i	$0.758154\pi$
$54$	0.728969	+	0.684547i	0.0992001	+	0.0931551i
$55$	2.86989	−	2.16431i	0.386976	−	0.291836i
$56$	3.34159	−	0.422142i	0.446539	−	0.0564110i
$57$			0.0561759i			0.00744068i
$58$	0.897319	+	7.10301i	0.117824	+	0.932672i
$59$	−9.02755	−	10.9124i	−1.17529	−	1.42068i	−0.886155	−	0.463389i	$-0.846633\pi$
$59$	−9.02755	−	10.9124i	−1.17529	−	1.42068i	−0.289133	−	0.957289i	$-0.593367\pi$
$60$	1.04213	−	1.97838i	0.134538	−	0.255407i
$61$	0.242919	−	3.86109i	0.0311026	−	0.494362i	−0.951381	−	0.308015i	$-0.900335\pi$
$61$	0.242919	−	3.86109i	0.0311026	−	0.494362i	0.982484	−	0.186347i	$-0.0596647\pi$
$62$	0.167991	−	0.654280i	0.0213348	−	0.0830937i
$63$	0.837626	−	3.26234i	0.105531	−	0.411016i
$64$	−0.0627905	+	0.998027i	−0.00784881	+	0.124753i
$65$	5.86964	+	6.03133i	0.728039	+	0.748095i
$66$	1.02467	+	1.23861i	0.126128	+	0.152463i
$67$	1.60186	+	12.6800i	0.195698	+	1.54911i	0.717814	+	0.696234i	$0.245143\pi$
$67$	1.60186	+	12.6800i	0.195698	+	1.54911i	−0.522117	+	0.852874i	$0.674857\pi$
$68$		−	1.35316i		−	0.164094i
$69$	−4.39043	+	0.554640i	−0.528546	+	0.0667708i
$70$	−7.53022	+	0.134278i	−0.900034	+	0.0160493i
$71$	−5.49260	−	5.15789i	−0.651851	−	0.612129i	0.286389	−	0.958113i	$-0.407545\pi$
$71$	−5.49260	−	5.15789i	−0.651851	−	0.612129i	−0.938240	+	0.345984i	$0.887545\pi$
$72$	0.904827	+	0.425779i	0.106635	+	0.0501786i
$73$	−0.766351	−	0.633981i	−0.0896947	−	0.0742019i	0.591496	−	0.806308i	$-0.298538\pi$
$73$	−0.766351	−	0.633981i	−0.0896947	−	0.0742019i	−0.681191	+	0.732106i	$0.738538\pi$
$74$	−0.419702	+	1.29171i	−0.0487894	+	0.150158i
$75$	−2.79284	+	4.14729i	−0.322489	+	0.478888i
$76$	0.0173593	+	0.0534264i	0.00199125	+	0.00612843i
$77$	1.99316	−	5.03414i	0.227141	−	0.573694i
$78$	−2.57647	+	2.74367i	−0.291728	+	0.310659i
$79$	0.467998	+	2.45333i	0.0526538	+	0.276021i	0.998871	−	0.0475121i	$-0.0151293\pi$
$79$	0.467998	+	2.45333i	0.0526538	+	0.276021i	−0.946217	+	0.323533i	$0.895129\pi$
$80$	0.379770	−	2.20358i	0.0424596	−	0.246368i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	0.139107	−	0.0451987i	0.0153618	−	0.00499136i
$83$	−7.91725	−	1.51030i	−0.869031	−	0.165777i	−0.266464	−	0.963845i	$-0.585855\pi$
$83$	−7.91725	−	1.51030i	−0.869031	−	0.165777i	−0.602567	+	0.798068i	$0.705855\pi$
$84$	−0.211488	−	3.36151i	−0.0230752	−	0.366770i
$85$	−0.325646	+	3.00818i	−0.0353213	+	0.326283i
$86$	−6.60210	−	10.4032i	−0.711923	−	1.12181i
$87$	7.14534	−	0.449547i	0.766061	−	0.0481965i
$88$	1.35727	+	0.861349i	0.144685	+	0.0918202i
$89$	2.53372	−	3.06275i	0.268574	−	0.324651i	−0.618933	−	0.785443i	$-0.712435\pi$
$89$	2.53372	−	3.06275i	0.268574	−	0.324651i	0.887508	+	0.460793i	$0.152435\pi$
$90$	−1.90904	−	1.16429i	−0.201230	−	0.122727i
$91$	12.2787	+	3.15262i	1.28715	+	0.330485i
$92$	−4.00415	+	1.88421i	−0.417462	+	0.196443i
$93$	−0.642441	−	0.208742i	−0.0666180	−	0.0216455i
$94$	−10.2828	−	5.65301i	−1.06059	−	0.583063i
$95$	−0.0257337	−	0.122949i	−0.00264022	−	0.0126143i
$96$	0.992115	+	0.125333i	0.101257	+	0.0127918i
$97$	−0.668696	+	5.29327i	−0.0678958	+	0.537450i	0.921080	+	0.389373i	$0.127308\pi$
$97$	−0.668696	+	5.29327i	−0.0678958	+	0.537450i	−0.988976	+	0.148077i	$0.952692\pi$
$98$	−3.66815	+	2.32788i	−0.370539	+	0.235151i
$99$	1.30051	−	0.944873i	0.130706	−	0.0949633i
$100$	−1.37456	+	4.80735i	−0.137456	+	0.480735i
$101$	−3.60953	−	2.62248i	−0.359162	−	0.260946i	0.393540	−	0.919307i	$-0.371250\pi$
$101$	−3.60953	−	2.62248i	−0.359162	−	0.260946i	−0.752702	+	0.658361i	$0.771250\pi$
$102$	−1.35049	−	0.0849655i	−0.133718	−	0.00841284i
$103$	3.38623	+	6.15954i	0.333656	+	0.606917i	0.988914	−	0.148487i	$-0.0474404\pi$
$103$	3.38623	+	6.15954i	0.333656	+	0.606917i	−0.655259	+	0.755405i	$0.727440\pi$
$104$	−1.60253	+	3.40555i	−0.157141	+	0.333942i
$105$	−0.338813	+	7.52380i	−0.0330648	+	0.734247i
$106$	−0.989631	+	5.18783i	−0.0961215	+	0.503886i
$107$	3.99010	+	5.49190i	0.385738	+	0.530922i	0.957093	−	0.289780i	$-0.0935822\pi$
$107$	3.99010	+	5.49190i	0.385738	+	0.530922i	−0.571356	+	0.820703i	$0.693582\pi$
$108$	0.481754	−	0.876307i	0.0463568	−	0.0843226i
$109$	−5.37064	+	8.46278i	−0.514414	+	0.810587i	−0.997901	−	0.0647647i	$-0.979370\pi$
$109$	−5.37064	+	8.46278i	−0.514414	+	0.810587i	0.483486	+	0.875352i	$0.339370\pi$
$110$	−2.81003	−	2.24148i	−0.267926	−	0.213717i
$111$	1.26281	+	0.499981i	0.119861	+	0.0474561i
$112$	−1.23990	−	3.13163i	−0.117160	−	0.295911i
$113$	−8.99451	+	7.44090i	−0.846132	+	0.699981i	−0.955810	−	0.293986i	$-0.905018\pi$
$113$	−8.99451	+	7.44090i	−0.846132	+	0.699981i	0.109678	+	0.993967i	$0.465018\pi$
$114$	0.0544110	−	0.0139704i	0.00509606	−	0.00130845i
$115$	9.35500	−	3.22513i	0.872358	−	0.300745i
$116$	6.65671	−	2.63558i	0.618060	−	0.244707i
$117$	2.57647	+	2.74367i	0.238195	+	0.253652i
$118$	−8.32454	+	11.4577i	−0.766336	+	1.05477i
$119$	1.94055	+	4.12388i	0.177890	+	0.378035i
$120$	−2.17539	−	0.517385i	−0.198585	−	0.0472305i
$121$	−7.37491	+	4.05439i	−0.670446	+	0.368581i
$122$	−3.80020	+	0.724926i	−0.344054	+	0.0656317i
$123$	−0.0363749	−	0.141671i	−0.00327981	−	0.0127740i
$124$	−0.675502			−0.0606619
$125$	4.21269	−	10.3563i	0.376794	−	0.926297i
$126$	−3.36815			−0.300059
$127$	4.01350	+	15.6315i	0.356140	+	1.38707i	0.854206	+	0.519935i	$0.174044\pi$
$127$	4.01350	+	15.6315i	0.356140	+	1.38707i	−0.498065	+	0.867139i	$0.665956\pi$
$128$	0.982287	−	0.187381i	0.0868227	−	0.0165623i
$129$	−10.7973	+	5.93585i	−0.950646	+	0.522622i
$130$	4.38213	−	7.18516i	0.384338	−	0.630180i
$131$	3.84491	+	8.17085i	0.335931	+	0.713890i	0.999411	−	0.0343037i	$-0.0109213\pi$
$131$	3.84491	+	8.17085i	0.335931	+	0.713890i	−0.663480	+	0.748194i	$0.730921\pi$
$132$	0.944873	−	1.30051i	0.0822407	−	0.113195i
$133$	−0.129522	−	0.137927i	−0.0112310	−	0.0119598i
$134$	11.8833	−	4.70492i	1.02656	−	0.406443i
$135$	−1.28187	+	1.83216i	−0.110325	+	0.157687i
$136$	−1.31065	+	0.336517i	−0.112387	+	0.0288561i
$137$	2.66150	−	2.20179i	0.227388	−	0.188111i	−0.516753	−	0.856135i	$-0.672859\pi$
$137$	2.66150	−	2.20179i	0.227388	−	0.188111i	0.744140	+	0.668023i	$0.232859\pi$
$138$	1.62907	+	4.11456i	0.138676	+	0.350255i
$139$	−6.40970	−	2.53778i	−0.543664	−	0.215252i	0.0802083	−	0.996778i	$-0.474441\pi$
$139$	−6.40970	−	2.53778i	−0.543664	−	0.215252i	−0.623872	+	0.781526i	$0.714441\pi$
$140$	2.00275	+	7.26025i	0.169263	+	0.613603i
$141$	−6.28752	+	9.90754i	−0.529504	+	0.834365i
$142$	−3.62989	+	6.60275i	−0.304614	+	0.554091i
$143$	3.55628	+	4.89480i	0.297391	+	0.409324i
$144$	0.187381	−	0.982287i	0.0156151	−	0.0818573i
$145$	−15.4327	+	4.25712i	−1.28161	+	0.353534i
$146$	−0.423480	+	0.899940i	−0.0350474	+	0.0744795i
$147$	2.09296	+	3.80708i	0.172624	+	0.314002i
$148$	1.35551	+	0.0852812i	0.111422	+	0.00701007i
$149$	10.3745	+	7.53749i	0.849910	+	0.617495i	0.925121	−	0.379672i	$-0.123963\pi$
$149$	10.3745	+	7.53749i	0.849910	+	0.617495i	−0.0752115	+	0.997168i	$0.523963\pi$
$150$	4.71155	+	1.67371i	0.384696	+	0.136658i
$151$	14.7194	−	10.6942i	1.19784	−	0.870285i	0.203774	−	0.979018i	$-0.434679\pi$
$151$	14.7194	−	10.6942i	1.19784	−	0.870285i	0.994071	+	0.108733i	$0.0346794\pi$
$152$	0.0474309	−	0.0301005i	0.00384715	−	0.00244148i
$153$	−0.169596	+	1.34249i	−0.0137110	+	0.108534i
$154$	−5.37166	−	0.678599i	−0.432861	−	0.0546830i
$155$	1.50170	+	0.162564i	0.120619	+	0.0130574i
$156$	3.29821	+	1.81321i	0.264068	+	0.145173i
$157$	−6.35927	−	2.06625i	−0.507525	−	0.164905i	0.0440513	−	0.999029i	$-0.485973\pi$
$157$	−6.35927	−	2.06625i	−0.507525	−	0.164905i	−0.551576	+	0.834124i	$0.685973\pi$
$158$	2.25987	−	1.06341i	0.179785	−	0.0846006i
$159$	5.11545	+	1.31342i	0.405682	+	0.104161i
$160$	−2.22880	+	0.180170i	−0.176202	+	0.0142437i
$161$	9.50091	−	11.4846i	0.748777	−	0.905116i
$162$	−0.844328	−	0.535827i	−0.0663367	−	0.0420985i
$163$	−9.38527	+	0.590471i	−0.735111	+	0.0462493i	−0.425933	−	0.904755i	$-0.640054\pi$
$163$	−9.38527	+	0.590471i	−0.735111	+	0.0462493i	−0.309178	+	0.951004i	$0.600054\pi$
$164$	−0.0783733	−	0.123497i	−0.00611992	−	0.00964346i
$165$	−2.41350	+	2.66374i	−0.187891	+	0.207372i
$166$	0.506092	+	8.04411i	0.0392804	+	0.624344i
$167$	18.1169	+	3.45599i	1.40193	+	0.267433i	0.832235	−	0.554423i	$-0.187061\pi$
$167$	18.1169	+	3.45599i	1.40193	+	0.267433i	0.569696	+	0.821855i	$0.307061\pi$
$168$	−3.20330	+	1.04082i	−0.247140	+	0.0803007i
$169$	−0.849916	+	0.798124i	−0.0653781	+	0.0613941i
$170$	2.99466	−	0.432688i	0.229680	−	0.0331857i
$171$	−0.0105263	−	0.0551808i	−0.000804967	−	0.00421978i
$172$	−8.43453	+	8.98186i	−0.643127	+	0.684861i
$173$	−3.87126	+	9.77769i	−0.294327	+	0.743384i	0.705086	+	0.709122i	$0.250908\pi$
$173$	−3.87126	+	9.77769i	−0.294327	+	0.743384i	−0.999413	+	0.0342625i	$0.989092\pi$
$174$	−2.21240	−	6.80906i	−0.167721	−	0.516193i
$175$	−2.70505	−	16.6221i	−0.204482	−	1.25651i
$176$	0.496749	−	1.52884i	0.0374439	−	0.115240i
$177$	10.9124	+	9.02755i	0.820229	+	0.678553i
$178$	−3.59664	−	1.69245i	−0.269579	−	0.126854i
$179$	−12.5424	−	11.7781i	−0.937464	−	0.880337i	0.0555353	−	0.998457i	$-0.482313\pi$
$179$	−12.5424	−	11.7781i	−0.937464	−	0.880337i	−0.992999	+	0.118119i	$0.962313\pi$
$180$	−0.652957	+	2.13861i	−0.0486686	+	0.159402i
$181$	12.9291	−	1.63332i	0.961009	−	0.121404i	0.370852	−	0.928692i	$-0.379066\pi$
$181$	12.9291	−	1.63332i	0.961009	−	0.121404i	0.590157	+	0.807288i	$0.299066\pi$
$182$		−	12.6769i		−	0.939677i
$183$	0.484879	+	3.83822i	0.0358433	+	0.283729i
$184$	2.82081	+	3.40977i	0.207953	+	0.251372i
$185$	−2.99287	−	0.515798i	−0.220040	−	0.0379222i
$186$	−0.0424151	+	0.674169i	−0.00311003	+	0.0494325i
$187$	−0.540955	+	2.10688i	−0.0395586	+	0.154070i
$188$	−2.91819	+	11.3656i	−0.212831	+	0.828920i
$189$	−0.211488	+	3.36151i	−0.0153835	+	0.244514i
$190$	−0.112686	+	0.0555014i	−0.00817514	+	0.00402649i
$191$	−1.52333	−	1.84139i	−0.110224	−	0.133238i	0.712516	−	0.701656i	$-0.247556\pi$
$191$	−1.52333	−	1.84139i	−0.110224	−	0.133238i	−0.822740	+	0.568418i	$0.807556\pi$
$192$	−0.125333	−	0.992115i	−0.00904515	−	0.0715997i
$193$			4.26414i			0.306939i	0.988153	+	0.153470i	$0.0490447\pi$
$193$			4.26414i			0.306939i	−0.988153	+	0.153470i	$0.950955\pi$
$194$	5.29327	−	0.668696i	0.380035	−	0.0480096i
$195$	−6.89583	−	4.82464i	−0.493820	−	0.345500i
$196$	3.16697	+	2.97399i	0.226212	+	0.212428i
$197$	−5.70324	−	2.68374i	−0.406339	−	0.191209i	0.211737	−	0.977327i	$-0.432088\pi$
$197$	−5.70324	−	2.68374i	−0.406339	−	0.191209i	−0.618077	+	0.786118i	$0.712088\pi$
$198$	−1.23861	−	1.02467i	−0.0880243	−	0.0728200i
$199$	−2.40437	+	7.39990i	−0.170442	+	0.524565i	−0.999396	−	0.0347509i	$-0.988936\pi$
$199$	−2.40437	+	7.39990i	−0.170442	+	0.524565i	0.828954	+	0.559316i	$0.188936\pi$
$200$	4.99815	+	0.135842i	0.353423	+	0.00960548i
$201$	−3.94948	−	12.1552i	−0.278575	−	0.857365i
$202$	−1.64244	+	4.14832i	−0.115561	+	0.291875i
$203$	−16.5073	+	17.5785i	−1.15859	+	1.23377i
$204$	0.253556	+	1.32919i	0.0177525	+	0.0930619i
$205$	0.144510	+	0.293404i	0.0100930	+	0.0204922i
$206$	5.12390	−	4.81166i	0.356999	−	0.335245i
$207$	4.20873	−	1.36750i	0.292527	−	0.0950478i
$208$	3.69710	+	0.705259i	0.256348	+	0.0489009i
$209$	−0.00567021	−	0.0901253i	−0.000392216	−	0.00623410i
$210$	7.37168	−	1.54292i	0.508694	−	0.106472i
$211$	6.78771	+	10.6957i	0.467285	+	0.736324i	0.993476	−	0.114043i	$-0.0363802\pi$
$211$	6.78771	+	10.6957i	0.467285	+	0.736324i	−0.526191	+	0.850367i	$0.676380\pi$
$212$	5.27095	−	0.331620i	0.362011	−	0.0227758i
$213$	6.36180	+	4.03732i	0.435903	+	0.276633i
$214$	4.32707	−	5.23053i	0.295792	−	0.357551i
$215$	20.9122	−	17.9376i	1.42620	−	1.22333i
$216$	−0.968583	−	0.248690i	−0.0659037	−	0.0169212i
$217$	2.05866	−	0.968731i	0.139751	−	0.0657618i
$218$	9.53253	+	3.09731i	0.645624	+	0.209776i
$219$	0.871573	+	0.479152i	0.0588955	+	0.0323781i
$220$	−1.47224	+	3.27918i	−0.0992583	+	0.221082i
$221$	−5.05281	−	0.638318i	−0.339889	−	0.0429379i
$222$	0.170226	−	1.34748i	0.0114248	−	0.0904366i
$223$	20.0916	−	12.7505i	1.34543	−	0.853838i	0.348911	−	0.937156i	$-0.386552\pi$
$223$	20.0916	−	12.7505i	1.34543	−	0.853838i	0.996523	+	0.0833180i	$0.0265517\pi$
$224$	−2.72489	+	1.97975i	−0.182065	+	0.132278i
$225$	1.96625	−	4.59716i	0.131083	−	0.306477i
$226$	9.44398	+	6.86145i	0.628204	+	0.456417i
$227$	8.66482	+	0.545144i	0.575105	+	0.0361825i	0.347680	−	0.937613i	$-0.386970\pi$
$227$	8.66482	+	0.545144i	0.575105	+	0.0361825i	0.227424	+	0.973796i	$0.426970\pi$
$228$	−0.0270629	−	0.0492273i	−0.00179229	−	0.00326016i
$229$	−0.274137	+	0.582571i	−0.0181155	+	0.0384974i	−0.913680	−	0.406434i	$-0.866772\pi$
$229$	−0.274137	+	0.582571i	−0.0181155	+	0.0384974i	0.895565	+	0.444932i	$0.146772\pi$
$230$	−5.45030	−	8.25904i	−0.359382	−	0.544585i
$231$	−1.01455	+	5.31845i	−0.0667524	+	0.349928i
$232$	−4.20823	−	5.79213i	−0.276284	−	0.380272i
$233$	−5.17046	+	9.40503i	−0.338728	+	0.616144i	−0.989733	−	0.142930i	$-0.954348\pi$
$233$	−5.17046	+	9.40503i	−0.338728	+	0.616144i	0.651005	+	0.759074i	$0.274348\pi$
$234$	2.01673	−	3.17785i	0.131837	−	0.207743i
$235$	9.22256	−	24.5643i	0.601613	−	1.60240i
$236$	13.1680	+	5.21359i	0.857165	+	0.339375i
$237$	−0.919416	−	2.32218i	−0.0597225	−	0.150842i
$238$	3.51172	−	2.90515i	0.227631	−	0.188313i
$239$	−23.6831	+	6.08080i	−1.53194	+	0.393334i	−0.918180	−	0.396163i	$-0.870342\pi$
$239$	−23.6831	+	6.08080i	−1.53194	+	0.393334i	−0.613755	+	0.789497i	$0.710342\pi$
$240$	0.0398671	+	2.23571i	0.00257341	+	0.144315i
$241$	−19.5063	+	7.72307i	−1.25651	+	0.497487i	−0.899626	−	0.436662i	$-0.856160\pi$
$241$	−19.5063	+	7.72307i	−1.25651	+	0.497487i	−0.356883	+	0.934149i	$0.616160\pi$
$242$	5.76108	+	6.13492i	0.370336	+	0.394368i
$243$	−0.587785	+	0.809017i	−0.0377064	+	0.0518985i
$244$	1.64722	+	3.50052i	0.105453	+	0.224098i
$245$	−6.32473	−	7.37356i	−0.404072	−	0.471079i
$246$	−0.128174	+	0.0704642i	−0.00817207	+	0.00449263i
$247$	0.207688	−	0.0396185i	0.0132148	−	0.00252087i
$248$	0.167991	+	0.654280i	0.0106674	+	0.0415468i
$249$	8.06001			0.510783
$250$	−11.0786	−	1.50483i	−0.700673	−	0.0951735i
$251$	−23.6063			−1.49001			−0.745007	−	0.667057i	$-0.767554\pi$
$251$	−23.6063			−1.49001			−0.745007	+	0.667057i	$0.767554\pi$
$252$	0.837626	+	3.26234i	0.0527655	+	0.205508i
$253$	6.98777	−	1.33299i	0.439317	−	0.0838042i
$254$	14.1423	−	7.77481i	0.887369	−	0.487835i
$255$	−0.243798	−	3.01591i	−0.0152672	−	0.188864i
$256$	−0.425779	−	0.904827i	−0.0266112	−	0.0565517i
$257$	−11.5493	+	15.8963i	−0.720426	+	0.991582i	0.279083	+	0.960267i	$0.409970\pi$
$257$	−11.5493	+	15.8963i	−0.720426	+	0.991582i	−0.999510	+	0.0313150i	$0.990030\pi$
$258$	8.43453	+	8.98186i	0.525111	+	0.559186i
$259$	−4.25333	+	1.68401i	−0.264289	+	0.104640i
$260$	−8.04922	−	2.45758i	−0.499191	−	0.152412i
$261$	−6.93454	+	1.78049i	−0.429237	+	0.110209i
$262$	6.95795	−	5.75612i	0.429864	−	0.355614i
$263$	−6.22602	−	15.7251i	−0.383913	−	0.969653i	−0.985321	−	0.170711i	$-0.945394\pi$
$263$	−6.22602	−	15.7251i	−0.383913	−	0.969653i	0.601408	−	0.798942i	$-0.294606\pi$
$264$	−1.49463	−	0.591766i	−0.0919881	−	0.0364207i
$265$	−11.7976	−	0.531270i	−0.724718	−	0.0326357i
$266$	−0.101383	+	0.159754i	−0.00621620	+	0.00979517i
$267$	−1.91494	+	3.48327i	−0.117193	+	0.213173i
$268$	−7.51235	−	10.3399i	−0.458890	−	0.631608i
$269$	−5.93257	+	31.0996i	−0.361715	+	1.89618i	0.0760811	+	0.997102i	$0.475759\pi$
$269$	−5.93257	+	31.0996i	−0.361715	+	1.89618i	−0.437796	+	0.899074i	$0.644241\pi$
$270$	2.09339	+	0.785953i	0.127400	+	0.0478316i
$271$	−12.6839	+	26.9546i	−0.770490	+	1.63738i	6.33331e−5		1.00000i	$0.499980\pi$
$271$	−12.6839	+	26.9546i	−0.770490	+	1.63738i	−0.770554	+	0.637375i	$0.780020\pi$
$272$	0.651889	+	1.18578i	0.0395266	+	0.0718985i
$273$	−12.6519	−	0.795991i	−0.765729	−	0.0481756i
$274$	−2.79450	−	2.03033i	−0.168822	−	0.122656i
$275$	4.06206	−	6.93558i	0.244951	−	0.418231i
$276$	3.58016	−	2.60114i	0.215500	−	0.156570i
$277$	10.9517	−	6.95019i	0.658027	−	0.417596i	−0.164458	−	0.986384i	$-0.552587\pi$
$277$	10.9517	−	6.95019i	0.658027	−	0.417596i	0.822484	+	0.568788i	$0.192587\pi$
$278$	−0.864024	+	6.83945i	−0.0518207	+	0.410203i
$279$	0.670176	+	0.0846629i	0.0401224	+	0.00506863i
$280$	6.53410	−	3.74538i	0.390487	−	0.223829i
$281$	−11.8952	−	6.53943i	−0.709607	−	0.390110i	0.0856966	−	0.996321i	$-0.472688\pi$
$281$	−11.8952	−	6.53943i	−0.709607	−	0.390110i	−0.795303	+	0.606212i	$0.792688\pi$
$282$	11.1599	+	3.62608i	0.664564	+	0.215930i
$283$	4.23251	−	1.99167i	0.251597	−	0.118392i	−0.295846	−	0.955236i	$-0.595601\pi$
$283$	4.23251	−	1.99167i	0.251597	−	0.118392i	0.547442	+	0.836843i	$0.315601\pi$
$284$	7.29803	+	1.87382i	0.433059	+	0.111191i
$285$	0.0483162	+	0.115949i	0.00286200	+	0.00686823i
$286$	3.85661	−	4.66184i	0.228046	−	0.275660i
$287$	0.415955	+	0.263973i	0.0245531	+	0.0155818i
$288$	−0.998027	+	0.0627905i	−0.0588093	+	0.00369997i
$289$	8.12794	+	12.8076i	0.478114	+	0.753387i
$290$	7.96132	+	13.8891i	0.467505	+	0.815597i
$291$	−0.335009	−	5.32481i	−0.0196386	−	0.312146i
$292$	0.976982	+	0.186369i	0.0571735	+	0.0109064i
$293$	−6.62808	+	2.15359i	−0.387217	+	0.125814i	−0.496155	−	0.868234i	$-0.665255\pi$
$293$	−6.62808	+	2.15359i	−0.387217	+	0.125814i	0.108938	+	0.994049i	$0.465255\pi$
$294$	3.16697	−	2.97399i	0.184702	−	0.173446i
$295$	−28.0189	−	14.7592i	−1.63132	−	0.859313i
$296$	−0.254499	−	1.33413i	−0.0147924	−	0.0775446i
$297$	−1.10042	+	1.17183i	−0.0638528	+	0.0679963i
$298$	4.72066	−	11.9230i	0.273461	−	0.690683i
$299$	5.14695	+	15.8407i	0.297656	+	0.916090i
$300$	0.449411	−	4.97976i	0.0259467	−	0.287507i
$301$	12.8242	−	39.4690i	0.739177	−	2.27495i
$302$	−14.0188	−	11.5974i	−0.806692	−	0.667354i
$303$	4.03700	+	1.89967i	0.231920	+	0.109133i
$304$	−0.0409504	−	0.0384550i	−0.00234867	−	0.00220555i
$305$	−2.81948	−	8.17836i	−0.161443	−	0.468291i
$306$	1.34249	−	0.169596i	0.0767449	−	0.00969514i
$307$		−	9.99710i		−	0.570565i	−0.958444	−	0.285282i	$-0.907913\pi$
$307$		−	9.99710i		−	0.570565i	0.958444	−	0.285282i	$-0.0920874\pi$
$308$	0.678599	+	5.37166i	0.0386668	+	0.306079i
$309$	−4.48044	−	5.41592i	−0.254883	−	0.308101i
$310$	−0.216000	−	1.49495i	−0.0122680	−	0.0849072i
$311$	1.02076	−	16.2245i	0.0578819	−	0.920006i	−0.856753	−	0.515726i	$-0.827522\pi$
$311$	1.02076	−	16.2245i	0.0578819	−	0.920006i	0.914635	−	0.404280i	$-0.132478\pi$
$312$	0.936010	−	3.64552i	0.0529911	−	0.206387i
$313$	4.75412	−	18.5161i	0.268719	−	1.04659i	−0.680696	−	0.732566i	$-0.738323\pi$
$313$	4.75412	−	18.5161i	0.268719	−	1.04659i	0.949415	−	0.314025i	$-0.101677\pi$
$314$	−0.419851	+	6.67334i	−0.0236936	+	0.376598i
$315$	−1.07701	−	7.45402i	−0.0606825	−	0.419986i
$316$	−1.59201	−	1.92441i	−0.0895575	−	0.108256i
$317$	3.82359	+	30.2668i	0.214754	+	1.69995i	0.619072	+	0.785334i	$0.287509\pi$
$317$	3.82359	+	30.2668i	0.214754	+	1.69995i	−0.404318	+	0.914618i	$0.632491\pi$
$318$		−	5.28138i		−	0.296165i
$319$	−11.4182	+	1.44245i	−0.639296	+	0.0807619i
$320$	0.728789	+	2.11397i	0.0407405	+	0.118174i
$321$	−4.94851	−	4.64696i	−0.276199	−	0.259368i
$322$	−13.4866	−	6.34631i	−0.751579	−	0.353666i
$323$	0.0585704	+	0.0484537i	0.00325895	+	0.00269603i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	17.3026	+	7.40049i	0.959777	+	0.410505i
$326$	2.90594	+	8.94357i	0.160945	+	0.495339i
$327$	3.68975	−	9.31924i	0.204044	−	0.515355i
$328$	−0.100126	+	0.106623i	−0.00552853	+	0.00588729i
$329$	−7.40582	−	38.8226i	−0.408296	−	2.14036i
$330$	3.18027	+	1.67523i	0.175068	+	0.0922186i
$331$	5.44602	−	5.11415i	0.299340	−	0.281099i	−0.520293	−	0.853988i	$-0.674177\pi$
$331$	5.44602	−	5.11415i	0.299340	−	0.281099i	0.819633	+	0.572889i	$0.194177\pi$
$332$	7.66553	−	2.49068i	0.420701	−	0.136694i
$333$	−1.33413	−	0.254499i	−0.0731098	−	0.0139464i
$334$	−1.15809	−	18.4072i	−0.0633676	−	1.00720i
$335$	14.2122	+	24.7942i	0.776496	+	1.35465i
$336$	1.80475	+	2.84383i	0.0984570	+	0.155143i
$337$	−3.29686	+	0.207421i	−0.179591	+	0.0112989i	−0.152331	−	0.988329i	$-0.548678\pi$
$337$	−3.29686	+	0.207421i	−0.179591	+	0.0112989i	−0.0272598	+	0.999628i	$0.508678\pi$
$338$	0.984415	+	0.624729i	0.0535451	+	0.0339808i
$339$	7.44090	−	8.99451i	0.404134	−	0.488515i
$340$	−1.16383	−	2.79297i	−0.0631178	−	0.151470i
$341$	1.05176	+	0.270047i	0.0569563	+	0.0146239i
$342$	−0.0508295	+	0.0239185i	−0.00274854	+	0.00129337i
$343$	8.50651	+	2.76393i	0.459308	+	0.149238i
$344$	10.7973	+	5.93585i	0.582149	+	0.320039i
$345$	−8.58497	+	4.92095i	−0.462199	+	0.264935i
$346$	10.4333	+	1.31803i	0.560895	+	0.0708575i
$347$	−3.11303	+	24.6421i	−0.167116	+	1.32286i	0.655903	+	0.754845i	$0.272288\pi$
$347$	−3.11303	+	24.6421i	−0.167116	+	1.32286i	−0.823019	+	0.568014i	$0.807712\pi$
$348$	−6.04494	+	3.83624i	−0.324043	+	0.205644i
$349$	−26.8183	+	19.4846i	−1.43555	+	1.04299i	−0.446601	+	0.894733i	$0.647366\pi$
$349$	−26.8183	+	19.4846i	−1.43555	+	1.04299i	−0.988949	+	0.148255i	$0.952634\pi$
$350$	−15.4272	+	6.75381i	−0.824617	+	0.361006i
$351$	−3.04495	−	2.21228i	−0.162527	−	0.118083i
$352$	−1.60434	−	0.100937i	−0.0855117	−	0.00537994i
$353$	13.2290	+	24.0634i	0.704106	+	1.28076i	0.950237	+	0.311528i	$0.100841\pi$
$353$	13.2290	+	24.0634i	0.704106	+	1.28076i	−0.246131	+	0.969237i	$0.579159\pi$
$354$	6.03012	−	12.8147i	0.320497	−	0.681092i
$355$	−15.7732	−	5.92196i	−0.837153	−	0.314305i
$356$	−0.744830	+	3.90454i	−0.0394759	+	0.206940i
$357$	−2.67892	−	3.68721i	−0.141783	−	0.195148i
$358$	−8.28891	+	15.0775i	−0.438082	+	0.796869i
$359$	2.62397	−	4.13471i	0.138488	−	0.218222i	−0.768004	−	0.640445i	$-0.778750\pi$
$359$	2.62397	−	4.13471i	0.138488	−	0.218222i	0.906492	+	0.422223i	$0.138750\pi$
$360$	2.23380	+	0.100593i	0.117732	+	0.00530172i
$361$	17.6628	+	6.99320i	0.929622	+	0.368063i
$362$	−4.79733	−	12.1167i	−0.252142	−	0.636838i
$363$	6.48456	−	5.36449i	0.340351	−	0.281563i
$364$	−12.2787	+	3.15262i	−0.643577	+	0.165242i
$365$	−2.12706	−	0.649430i	−0.111335	−	0.0339927i
$366$	3.59705	−	1.42417i	0.188021	−	0.0744426i
$367$	−2.66244	−	2.83522i	−0.138978	−	0.147997i	0.655714	−	0.755010i	$-0.272368\pi$
$367$	−2.66244	−	2.83522i	−0.138978	−	0.147997i	−0.794692	+	0.607012i	$0.792368\pi$
$368$	2.60114	−	3.58016i	0.135594	−	0.186629i
$369$	0.0622771	+	0.132345i	0.00324201	+	0.00688963i
$370$	0.244704	+	3.02712i	0.0127216	+	0.157372i
$371$	−15.5882	+	8.56967i	−0.809297	+	0.444915i
$372$	0.663537	−	0.126577i	0.0344028	−	0.00656269i
$373$	−9.07335	−	35.3384i	−0.469800	−	1.82975i	−0.552951	−	0.833214i	$-0.686498\pi$
$373$	−9.07335	−	35.3384i	−0.469800	−	1.82975i	0.0831511	−	0.996537i	$-0.473502\pi$
$374$	2.17522			0.112478
$375$	−2.19749	+	10.9623i	−0.113478	+	0.566088i
$376$	11.7342			0.605147
$377$	−6.70133	−	26.1000i	−0.345136	−	1.34422i
$378$	3.30849	−	0.631129i	0.170171	−	0.0324618i
$379$	−28.6300	+	15.7395i	−1.47062	+	0.808482i	−0.997372	−	0.0724453i	$-0.976920\pi$
$379$	−28.6300	+	15.7395i	−1.47062	+	0.808482i	−0.473251	+	0.880927i	$0.656920\pi$
$380$	0.0817817	+	0.0953436i	0.00419531	+	0.00489102i
$381$	−6.87146	−	14.6026i	−0.352036	−	0.748114i
$382$	−1.40470	+	1.93341i	−0.0718708	+	0.0989217i
$383$	−22.7312	−	24.2063i	−1.16151	−	1.23688i	−0.966663	−	0.256050i	$-0.917579\pi$
$383$	−22.7312	−	24.2063i	−1.16151	−	1.23688i	−0.194848	−	0.980834i	$-0.562421\pi$
$384$	−0.929776	+	0.368125i	−0.0474475	+	0.0187858i
$385$	−0.215855	−	12.1049i	−0.0110010	−	0.616925i
$386$	4.13017	−	1.06045i	0.210220	−	0.0539754i
$387$	9.49375	−	7.85391i	0.482594	−	0.399237i
$388$	−1.96407	−	4.96068i	−0.0997106	−	0.251840i
$389$	25.3672	+	10.0436i	1.28617	+	0.509229i	0.908954	−	0.416897i	$-0.136882\pi$
$389$	25.3672	+	10.0436i	1.28617	+	0.509229i	0.377213	+	0.926126i	$0.376882\pi$
$390$	−2.95814	+	7.87902i	−0.149791	+	0.398970i
$391$	−3.20862	+	5.05597i	−0.162267	+	0.255691i
$392$	2.09296	−	3.80708i	0.105710	−	0.192286i
$393$	−5.30787	−	7.30565i	−0.267747	−	0.368521i
$394$	−1.18109	+	6.19148i	−0.0595024	+	0.311922i
$395$	3.07604	+	4.66124i	0.154773	+	0.234533i
$396$	−0.684446	+	1.45452i	−0.0343947	+	0.0730925i
$397$	14.3990	+	26.1918i	0.722667	+	1.31453i	0.940918	+	0.338634i	$0.109965\pi$
$397$	14.3990	+	26.1918i	0.722667	+	1.31453i	−0.218251	+	0.975893i	$0.570035\pi$
$398$	7.76536	+	0.488555i	0.389243	+	0.0244891i
$399$	0.153073	+	0.111214i	0.00766325	+	0.00556768i
$400$	−1.11142	−	4.87491i	−0.0555708	−	0.243746i
$401$	17.4924	−	12.7090i	0.873528	−	0.634656i	−0.0580030	−	0.998316i	$-0.518473\pi$
$401$	17.4924	−	12.7090i	0.873528	−	0.634656i	0.931531	+	0.363661i	$0.118473\pi$
$402$	−10.7912	+	6.84828i	−0.538215	+	0.341561i
$403$	−0.318651	+	2.52238i	−0.0158731	+	0.125649i
$404$	4.42645	+	0.559190i	0.220224	+	0.0278208i
$405$	0.915847	−	2.03991i	0.0455088	−	0.101364i
$406$	21.1314	+	11.6171i	1.04874	+	0.576547i
$407$	−2.07644	−	0.674678i	−0.102926	−	0.0334425i
$408$	1.22437	−	0.576147i	0.0606155	−	0.0285235i
$409$	10.2494	+	2.63160i	0.506800	+	0.130124i	0.493428	−	0.869786i	$-0.335743\pi$
$409$	10.2494	+	2.63160i	0.506800	+	0.130124i	0.0133718	+	0.999911i	$0.495743\pi$
$410$	0.248248	−	0.212936i	0.0122601	−	0.0105162i
$411$	−2.20179	+	2.66150i	−0.108606	+	0.131282i
$412$	−5.93476	−	3.76631i	−0.292385	−	0.185553i
$413$	−47.6075	+	2.99521i	−2.34261	+	0.147385i
$414$	−2.37121	−	3.73642i	−0.116538	−	0.183635i
$415$	−17.6405	+	3.69223i	−0.865937	+	0.181244i
$416$	−0.236329	−	3.75634i	−0.0115870	−	0.184170i
$417$	6.77170	+	1.29177i	0.331612	+	0.0632583i
$418$	−0.0858838	+	0.0279053i	−0.00420071	+	0.00136489i
$419$	12.5454	−	11.7810i	0.612885	−	0.575538i	−0.314680	−	0.949198i	$-0.601897\pi$
$419$	12.5454	−	11.7810i	0.612885	−	0.575538i	0.927566	+	0.373660i	$0.121897\pi$
$420$	−3.32771	−	6.75638i	−0.162376	−	0.329677i
$421$	3.56390	+	18.6826i	0.173694	+	0.910534i	0.957261	+	0.289227i	$0.0933982\pi$
$421$	3.56390	+	18.6826i	0.173694	+	0.910534i	−0.783567	+	0.621307i	$0.786602\pi$
$422$	8.67166	−	9.23438i	0.422130	−	0.449522i
$423$	4.31966	−	10.9102i	0.210029	−	0.530473i
$424$	−1.63204	−	5.02289i	−0.0792586	−	0.243933i
$425$	1.91515	+	6.48907i	0.0928986	+	0.314766i
$426$	2.32837	−	7.16597i	0.112810	−	0.347193i
$427$	−10.0401	−	8.30592i	−0.485876	−	0.401952i
$428$	−6.14230	−	2.89035i	−0.296899	−	0.139710i
$429$	−4.41048	−	4.14172i	−0.212940	−	0.199964i
$430$	−22.5747	−	15.7943i	−1.08865	−	0.761668i
$431$	29.8795	−	3.77466i	1.43924	−	0.181819i	0.633344	−	0.773871i	$-0.281682\pi$
$431$	29.8795	−	3.77466i	1.43924	−	0.181819i	0.805900	+	0.592052i	$0.201682\pi$
$432$			1.00000i			0.0481125i
$433$	−3.87878	−	30.7037i	−0.186402	−	1.47553i	−0.756524	−	0.653966i	$-0.773104\pi$
$433$	−3.87878	−	30.7037i	−0.186402	−	1.47553i	0.570122	−	0.821560i	$-0.306896\pi$
$434$	−1.45026	−	1.75307i	−0.0696149	−	0.0841500i
$435$	14.3616	−	7.07350i	0.688586	−	0.339149i
$436$	0.629355	−	10.0033i	0.0301407	−	0.479072i
$437$	0.0618234	−	0.240786i	0.00295742	−	0.0115184i
$438$	0.247347	−	0.963352i	0.0118187	−	0.0460307i
$439$	0.298671	−	4.74723i	0.0142548	−	0.226573i	−0.984449	−	0.175671i	$-0.943790\pi$
$439$	0.298671	−	4.74723i	0.0142548	−	0.226573i	0.998704	−	0.0509018i	$-0.0162096\pi$
$440$	3.54229	+	0.610486i	0.168872	+	0.0291038i
$441$	−2.76926	−	3.34746i	−0.131870	−	0.159403i
$442$	0.638318	+	5.05281i	0.0303617	+	0.240337i
$443$		−	10.4277i		−	0.495435i	−0.968832	−	0.247718i	$-0.920319\pi$
$443$		−	10.4277i		−	0.495435i	0.968832	−	0.247718i	$-0.0796805\pi$
$444$	−1.34748	+	0.170226i	−0.0639484	+	0.00807856i
$445$	2.59547	−	8.50085i	0.123037	−	0.402979i
$446$	−17.3465	−	16.2895i	−0.821382	−	0.771329i
$447$	−11.6031	−	5.46000i	−0.548807	−	0.258249i
$448$	2.59521	+	2.14694i	0.122612	+	0.101433i
$449$	−4.66498	+	14.3573i	−0.220154	+	0.677564i	0.778594	+	0.627529i	$0.215933\pi$
$449$	−4.66498	+	14.3573i	−0.220154	+	0.677564i	−0.998747	+	0.0500355i	$0.984067\pi$
$450$	−4.94172	−	0.761206i	−0.232955	−	0.0358836i
$451$	0.0726576	+	0.223617i	0.00342131	+	0.0105297i
$452$	4.29726	−	10.8536i	0.202126	−	0.510513i
$453$	−12.4547	+	13.2629i	−0.585175	+	0.623148i
$454$	−1.62684	−	8.52817i	−0.0763512	−	0.400247i
$455$	28.0552	−	4.05360i	1.31525	−	0.190036i
$456$	−0.0409504	+	0.0384550i	−0.00191768	+	0.00180082i
$457$	32.1628	−	10.4503i	1.50451	−	0.488845i	0.563182	−	0.826333i	$-0.309577\pi$
$457$	32.1628	−	10.4503i	1.50451	−	0.488845i	0.941330	+	0.337488i	$0.109577\pi$
$458$	0.632443	+	0.120645i	0.0295521	+	0.00563737i
$459$	−0.0849655	−	1.35049i	−0.00396585	−	0.0630354i
$460$	−6.64413	+	7.33301i	−0.309784	+	0.341903i
$461$	2.39384	+	3.77208i	0.111492	+	0.175683i	0.895492	−	0.445077i	$-0.146824\pi$
$461$	2.39384	+	3.77208i	0.111492	+	0.175683i	−0.784000	+	0.620761i	$0.786824\pi$
$462$	5.40367	−	0.339970i	0.251402	−	0.0158168i
$463$	−18.7301	−	11.8865i	−0.870460	−	0.552411i	0.0239225	−	0.999714i	$-0.492385\pi$
$463$	−18.7301	−	11.8865i	−0.870460	−	0.552411i	−0.894382	+	0.447303i	$0.852385\pi$
$464$	−4.56362	+	5.51647i	−0.211861	+	0.256095i
$465$	−1.50556	+	0.121705i	−0.0698186	+	0.00564395i
$466$	10.3954	+	2.66908i	0.481557	+	0.123643i
$467$	−14.6913	+	6.91319i	−0.679831	+	0.319904i	−0.734508	−	0.678600i	$-0.762587\pi$
$467$	−14.6913	+	6.91319i	−0.679831	+	0.319904i	0.0546772	+	0.998504i	$0.482587\pi$
$468$	−3.57955	−	1.16307i	−0.165465	−	0.0537628i
$469$	37.7229	+	20.7384i	1.74188	+	0.957608i
$470$	−26.0861	−	2.82392i	−1.20326	−	0.130258i
$471$	6.63381	+	0.838045i	0.305670	+	0.0386151i
$472$	1.77504	−	14.0509i	0.0817028	−	0.646744i
$473$	16.7234	−	10.6130i	0.768941	−	0.487985i
$474$	−2.02057	+	1.46803i	−0.0928081	+	0.0674290i
$475$	−0.158862	−	0.231638i	−0.00728910	−	0.0106283i
$476$	−3.68721	−	2.67892i	−0.169003	−	0.122788i
$477$	−5.27095	−	0.331620i	−0.241340	−	0.0151839i
$478$	11.7795	+	21.4269i	0.538783	+	0.980042i
$479$	11.9443	−	25.3830i	0.545750	−	1.15978i	−0.421705	−	0.906733i	$-0.638568\pi$
$479$	11.9443	−	25.3830i	0.545750	−	1.15978i	0.967455	−	0.253044i	$-0.0814317\pi$
$480$	2.15556	−	0.594614i	0.0983874	−	0.0271403i
$481$	0.957872	−	5.02134i	0.0436752	−	0.228954i
$482$	12.3314	+	16.9728i	0.561682	+	0.773089i
$483$	−7.18062	+	13.0615i	−0.326730	+	0.594319i
$484$	4.50946	−	7.10578i	0.204976	−	0.322990i
$485$	3.17247	+	11.5006i	0.144054	+	0.522217i
$486$	0.929776	+	0.368125i	0.0421755	+	0.0166985i
$487$	−8.11090	−	20.4858i	−0.367540	−	0.928299i	−0.989406	−	0.145176i	$-0.953625\pi$
$487$	−8.11090	−	20.4858i	−0.367540	−	0.928299i	0.621866	−	0.783124i	$-0.286375\pi$
$488$	2.98090	−	2.46602i	0.134939	−	0.111631i
$489$	9.10839	−	2.33864i	0.411896	−	0.105757i
$490$	−5.56901	+	7.95975i	−0.251582	+	0.359585i
$491$	−3.23333	+	1.28016i	−0.145918	+	0.0577730i	−0.439948	−	0.898023i	$-0.645003\pi$
$491$	−3.23333	+	1.28016i	−0.145918	+	0.0577730i	0.294030	+	0.955796i	$0.405003\pi$
$492$	0.100126	+	0.106623i	0.00451403	+	0.00480695i
$493$	5.69440	−	7.83767i	0.256463	−	0.352991i
$494$	−0.0900237	−	0.191310i	−0.00405036	−	0.00860745i
$495$	1.87162	−	3.06880i	0.0841230	−	0.137932i
$496$	0.591947	−	0.325426i	0.0265792	−	0.0146120i
$497$	−24.9287	+	4.75540i	−1.11820	+	0.213309i
$498$	−2.00444	−	7.80679i	−0.0898213	−	0.349831i
$499$	8.27576			0.370474			0.185237	−	0.982694i	$-0.440695\pi$
$499$	8.27576			0.370474			0.185237	+	0.982694i	$0.440695\pi$
$500$	1.29759	+	11.1048i	0.0580299	+	0.496621i
$501$	−18.4436			−0.824001
$502$	5.87064	+	22.8646i	0.262019	+	1.02050i
$503$	30.7540	−	5.86664i	1.37125	−	0.261581i	0.551442	−	0.834214i	$-0.314078\pi$
$503$	30.7540	−	5.86664i	1.37125	−	0.261581i	0.819812	+	0.572633i	$0.194078\pi$
$504$	2.95154	−	1.62262i	0.131472	−	0.0722773i
$505$	−9.70577	−	2.30838i	−0.431901	−	0.102721i
$506$	−3.02890	−	6.43673i	−0.134651	−	0.286148i
$507$	0.685308	−	0.943245i	0.0304356	−	0.0418910i
$508$	−11.0476	−	11.7645i	−0.490158	−	0.521965i
$509$	−5.56369	+	2.20282i	−0.246606	+	0.0976383i	−0.488176	−	0.872745i	$-0.662338\pi$
$509$	−5.56369	+	2.20282i	−0.246606	+	0.0976383i	0.241570	+	0.970383i	$0.422338\pi$
$510$	−2.86053	+	0.986167i	−0.126667	+	0.0436682i
$511$	−3.24472	+	0.833101i	−0.143538	+	0.0368542i
$512$	−0.770513	+	0.637424i	−0.0340522	+	0.0281704i
$513$	0.0206797	+	0.0522310i	0.000913032	+	0.00230606i
$514$	18.2691	+	7.23323i	0.805813	+	0.319044i
$515$	12.2871	+	9.80105i	0.541433	+	0.431886i
$516$	6.60210	−	10.4032i	0.290641	−	0.457977i
$517$	9.08730	−	16.5297i	0.399659	−	0.726977i
$518$	2.68887	+	3.70091i	0.118142	+	0.162609i
$519$	1.97053	−	10.3299i	0.0864969	−	0.453432i
$520$	−0.378609	+	8.40751i	−0.0166031	+	0.368694i
$521$	11.0531	−	23.4890i	0.484245	−	1.02907i	−0.502166	−	0.864771i	$-0.667463\pi$
$521$	11.0531	−	23.4890i	0.484245	−	1.02907i	0.986410	−	0.164301i	$-0.0525367\pi$
$522$	3.44910	+	6.27389i	0.150963	+	0.274601i
$523$	27.8688	+	1.75336i	1.21862	+	0.0766690i	0.659040	−	0.752108i	$-0.270963\pi$
$523$	27.8688	+	1.75336i	1.21862	+	0.0766690i	0.559579	+	0.828777i	$0.310963\pi$
$524$	−7.30565	−	5.30787i	−0.319149	−	0.231875i
$525$	5.77180	+	15.8208i	0.251902	+	0.690476i
$526$	−13.6827	+	9.94110i	−0.596596	+	0.433452i
$527$	−0.771767	+	0.489778i	−0.0336187	+	0.0213351i
$528$	−0.201475	+	1.59484i	−0.00876807	+	0.0694065i
$529$	−3.38957	−	0.428202i	−0.147373	−	0.0186175i
$530$	2.41935	+	11.5590i	0.105090	+	0.502093i
$531$	−12.4107	−	6.82286i	−0.538580	−	0.296087i
$532$	0.179948	+	0.0584688i	0.00780175	+	0.00253494i
$533$	−0.498117	+	0.234396i	−0.0215758	+	0.0101528i
$534$	3.85006	+	0.988528i	0.166609	+	0.0427778i
$535$	12.9592	+	7.90365i	0.560277	+	0.341705i
$536$	−8.14678	+	9.84776i	−0.351887	+	0.425358i
$537$	14.5273	+	9.21927i	0.626897	+	0.397841i
$538$	31.5979	−	1.98797i	1.36228	−	0.0857076i
$539$	−3.74210	−	5.89660i	−0.161183	−	0.253985i
$540$	0.240656	−	2.22308i	0.0103562	−	0.0956661i
$541$	0.149597	+	2.37778i	0.00643168	+	0.102229i	0.999933	−	0.0115938i	$-0.00369050\pi$
$541$	0.149597	+	2.37778i	0.00643168	+	0.102229i	−0.993501	+	0.113822i	$0.963691\pi$
$542$	29.2621	+	5.58205i	1.25692	+	0.239769i
$543$	−12.3940	+	4.02705i	−0.531877	+	0.172817i
$544$	0.986410	−	0.926300i	0.0422920	−	0.0397148i
$545$	−3.80647	+	22.0867i	−0.163051	+	0.946091i
$546$	2.37542	+	12.4524i	0.101659	+	0.532913i
$547$	−18.4867	+	19.6863i	−0.790433	+	0.841725i	−0.990422	−	0.138073i	$-0.955909\pi$
$547$	−18.4867	+	19.6863i	−0.790433	+	0.841725i	0.199989	+	0.979798i	$0.435909\pi$
$548$	−1.27157	+	3.21163i	−0.0543190	+	0.137194i
$549$	−1.19550	−	3.67937i	−0.0510227	−	0.157032i
$550$	−7.72788	−	2.20963i	−0.329518	−	0.0942191i
$551$	−0.124283	+	0.382505i	−0.00529465	+	0.0162953i
$552$	−3.40977	−	2.82081i	−0.145129	−	0.120062i
$553$	7.61158	+	3.58174i	0.323677	+	0.152311i
$554$	−9.45543	−	8.87924i	−0.401723	−	0.377243i
$555$	3.03651	−	0.0541469i	0.128893	−	0.00229841i
$556$	6.83945	−	0.864024i	0.290057	−	0.0366428i
$557$			24.0822i			1.02039i	0.860057	+	0.510197i	$0.170428\pi$
$557$			24.0822i			1.02039i	−0.860057	+	0.510197i	$0.829572\pi$
$558$	−0.0846629	−	0.670176i	−0.00358407	−	0.0283708i
$559$	29.5603	+	35.7322i	1.25027	+	1.51131i
$560$	−5.25268	−	5.39738i	−0.221966	−	0.228081i
$561$	0.136583	−	2.17093i	0.00576655	−	0.0916567i
$562$	−3.37577	+	13.1478i	−0.142398	+	0.554605i
$563$	−0.936879	+	3.64890i	−0.0394847	+	0.153783i	−0.985269	−	0.171014i	$-0.945296\pi$
$563$	−0.936879	+	3.64890i	−0.0394847	+	0.153783i	0.945784	+	0.324796i	$0.105296\pi$
$564$	0.736799	−	11.7111i	0.0310248	−	0.493125i
$565$	−12.1652	+	23.0944i	−0.511792	+	0.971587i
$566$	−2.98168	−	3.60423i	−0.125329	−	0.151497i
$567$	−0.422142	−	3.34159i	−0.0177283	−	0.140334i
$568$		−	7.53475i		−	0.316151i
$569$	31.6906	−	4.00346i	1.32854	−	0.167834i	0.571176	−	0.820827i	$-0.306487\pi$
$569$	31.6906	−	4.00346i	1.32854	−	0.167834i	0.757363	+	0.652994i	$0.226487\pi$
$570$	0.100291	−	0.0756336i	0.00420071	−	0.00316794i
$571$	1.14192	+	1.07234i	0.0477880	+	0.0448759i	0.708073	−	0.706139i	$-0.249565\pi$
$571$	1.14192	+	1.07234i	0.0477880	+	0.0448759i	−0.660285	+	0.751015i	$0.729565\pi$
$572$	−5.47448	−	2.57609i	−0.228899	−	0.107712i
$573$	1.84139	+	1.52333i	0.0769252	+	0.0636380i
$574$	0.152236	−	0.468535i	0.00635421	−	0.0195563i
$575$	16.5352	−	14.7029i	0.689564	−	0.613154i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−10.6726	+	26.9558i	−0.444304	+	1.12218i	0.519238	+	0.854629i	$0.326216\pi$
$577$	−10.6726	+	26.9558i	−0.444304	+	1.12218i	−0.963543	+	0.267555i	$0.913784\pi$
$578$	10.3839	−	11.0577i	0.431912	−	0.459940i
$579$	−0.799020	−	4.18861i	−0.0332061	−	0.174073i
$580$	11.4729	−	11.1653i	0.476385	−	0.463613i
$581$	−19.7896	+	18.5836i	−0.821010	+	0.770980i
$582$	−5.07421	+	1.64871i	−0.210333	+	0.0683413i
$583$	−8.33951	−	1.59085i	−0.345387	−	0.0658861i
$584$	−0.0624514	−	0.992636i	−0.00258426	−	0.0410756i
$585$	7.67773	+	3.44703i	0.317435	+	0.142517i
$586$	3.73427	+	5.88427i	0.154261	+	0.243077i
$587$	−15.5556	+	0.978672i	−0.642046	+	0.0403941i	−0.380477	−	0.924790i	$-0.624240\pi$
$587$	−15.5556	+	0.978672i	−0.642046	+	0.0403941i	−0.261570	+	0.965185i	$0.584240\pi$
$588$	−3.66815	−	2.32788i	−0.151272	−	0.0960000i
$589$	0.0241883	−	0.0292386i	0.000996661	−	0.00120476i
$590$	−7.32749	+	30.8091i	−0.301668	+	1.26839i
$591$	6.10511	+	1.56752i	0.251130	+	0.0644793i
$592$	−1.22892	+	0.578287i	−0.0505084	+	0.0237675i
$593$	−9.17203	−	2.98017i	−0.376650	−	0.122381i	0.114573	−	0.993415i	$-0.463450\pi$
$593$	−9.17203	−	2.98017i	−0.376650	−	0.122381i	−0.491223	+	0.871034i	$0.663450\pi$
$594$	1.40868	+	0.774426i	0.0577987	+	0.0317751i
$595$	7.55227	+	6.84279i	0.309613	+	0.280527i
$596$	−12.7224	−	1.60722i	−0.521131	−	0.0658342i
$597$	0.975183	−	7.71936i	0.0399116	−	0.315933i
$598$	14.0630	−	8.92466i	0.575080	−	0.364957i
$599$	−39.3378	+	28.5806i	−1.60730	+	1.16777i	−0.736052	+	0.676925i	$0.763312\pi$
$599$	−39.3378	+	28.5806i	−1.60730	+	1.16777i	−0.871247	+	0.490846i	$0.836688\pi$
$600$	−4.93508	+	0.803125i	−0.201474	+	0.0327874i
$601$	−33.9577	−	24.6717i	−1.38516	−	1.00638i	−0.996376	−	0.0850528i	$-0.972894\pi$
$601$	−33.9577	−	24.6717i	−1.38516	−	1.00638i	−0.388787	−	0.921328i	$-0.627106\pi$
$602$	−41.4182	−	2.60581i	−1.68808	−	0.106205i
$603$	6.15719	+	11.1999i	0.250740	+	0.456094i
$604$	−7.74668	+	16.4625i	−0.315208	+	0.669851i
$605$	−11.7349	+	14.7115i	−0.477093	+	0.598107i
$606$	0.836026	−	4.38260i	0.0339612	−	0.178031i
$607$	−20.2254	−	27.8379i	−0.820925	−	1.12991i	−0.989545	−	0.144225i	$-0.953931\pi$
$607$	−20.2254	−	27.8379i	−0.820925	−	1.12991i	0.168620	−	0.985681i	$-0.446069\pi$
$608$	−0.0270629	+	0.0492273i	−0.00109755	+	0.00199643i
$609$	12.9210	−	20.3603i	0.523587	−	0.825040i
$610$	−7.22024	+	4.76478i	−0.292339	+	0.192920i
$611$	41.0635	+	16.2582i	1.66125	+	0.657735i
$612$	−0.498131	−	1.25813i	−0.0201357	−	0.0508571i
$613$	23.7537	−	19.6508i	0.959405	−	0.793689i	−0.0191202	−	0.999817i	$-0.506087\pi$
$613$	23.7537	−	19.6508i	0.959405	−	0.793689i	0.978525	+	0.206129i	$0.0660865\pi$
$614$	−9.68302	+	2.48618i	−0.390775	+	0.100334i
$615$	−0.196929	−	0.261128i	−0.00794093	−	0.0105297i
$616$	5.03414	−	1.99316i	0.202831	−	0.0803066i
$617$	22.1363	+	23.5727i	0.891173	+	0.949003i	0.998979	−	0.0451690i	$-0.0143826\pi$
$617$	22.1363	+	23.5727i	0.891173	+	0.949003i	−0.107806	+	0.994172i	$0.534383\pi$
$618$	−4.13153	+	5.68656i	−0.166194	+	0.228747i
$619$	0.433789	+	0.921849i	0.0174355	+	0.0370523i	0.913355	−	0.407164i	$-0.133482\pi$
$619$	0.433789	+	0.921849i	0.0174355	+	0.0370523i	−0.895920	+	0.444216i	$0.853482\pi$
$620$	−1.39426	+	0.580992i	−0.0559949	+	0.0233332i
$621$	−3.87794	+	2.13192i	−0.155616	+	0.0855508i
$622$	−15.9686	+	3.04618i	−0.640283	+	0.122141i
$623$	−3.32951	−	12.9676i	−0.133394	−	0.519536i
$624$	−3.76376			−0.150671
$625$	−0.212206	−	24.9991i	−0.00848825	−	0.999964i
$626$	−19.1167			−0.764056
$627$	0.0224576	+	0.0874665i	0.000896869	+	0.00349307i
$628$	6.56810	−	1.25293i	0.262096	−	0.0499974i
$629$	1.61051	−	0.885386i	0.0642153	−	0.0353026i
$630$	−6.95199	+	2.89691i	−0.276974	+	0.115416i
$631$	9.94098	+	21.1257i	0.395744	+	0.840999i	0.999054	+	0.0434923i	$0.0138484\pi$
$631$	9.94098	+	21.1257i	0.395744	+	0.840999i	−0.603309	+	0.797507i	$0.706152\pi$
$632$	−1.46803	+	2.02057i	−0.0583952	+	0.0803742i
$633$	−8.67166	−	9.23438i	−0.344667	−	0.367034i
$634$	28.3650	−	11.2305i	1.12652	−	0.446020i
$635$	21.7285	+	28.8121i	0.862269	+	1.14337i
$636$	−5.11545	+	1.31342i	−0.202841	+	0.0520807i
$637$	12.5991	−	10.4228i	0.499193	−	0.412968i
$638$	4.23673	+	10.7008i	0.167734	+	0.423647i
$639$	−7.00563	−	2.77373i	−0.277139	−	0.109727i
$640$	1.86631	−	1.23162i	0.0737725	−	0.0486839i
$641$	−17.0083	+	26.8009i	−0.671789	+	1.05857i	0.321940	+	0.946760i	$0.395665\pi$
$641$	−17.0083	+	26.8009i	−0.671789	+	1.05857i	−0.993730	+	0.111810i	$0.964335\pi$
$642$	−3.27032	+	5.94869i	−0.129069	+	0.234776i
$643$	−13.5452	−	18.6434i	−0.534172	−	0.735224i	0.453587	−	0.891212i	$-0.350144\pi$
$643$	−13.5452	−	18.6434i	−0.534172	−	0.735224i	−0.987759	+	0.155988i	$0.950144\pi$
$644$	−2.79295	+	14.6412i	−0.110058	+	0.576942i
$645$	−17.1806	+	21.5384i	−0.676486	+	0.848074i
$646$	0.0323655	−	0.0687803i	0.00127340	−	0.00270612i
$647$	12.7240	+	23.1449i	0.500233	+	0.909921i	0.999065	+	0.0432225i	$0.0137624\pi$
$647$	12.7240	+	23.1449i	0.500233	+	0.909921i	−0.498832	+	0.866699i	$0.666238\pi$
$648$	0.998027	+	0.0627905i	0.0392062	+	0.00246664i
$649$	−18.4185	−	13.3818i	−0.722989	−	0.525283i
$650$	2.86500	−	18.5995i	0.112374	−	0.729531i
$651$	−1.84067	+	1.33733i	−0.0721416	+	0.0524140i
$652$	7.93992	−	5.03882i	0.310951	−	0.197336i
$653$	−0.0112217	+	0.0888287i	−0.000439138	+	0.00347614i	−0.992333	−	0.123595i	$-0.960558\pi$
$653$	−0.0112217	+	0.0888287i	−0.000439138	+	0.00347614i	0.991894	+	0.127071i	$0.0405576\pi$
$654$	−9.94406	−	1.25623i	−0.388844	−	0.0491224i
$655$	14.9637	+	13.5580i	0.584679	+	0.529754i
$656$	0.128174	+	0.0704642i	0.00500435	+	0.00275117i
$657$	−0.945920	−	0.307348i	−0.0369038	−	0.0119908i
$658$	−35.7612	+	16.8279i	−1.39412	+	0.656022i
$659$	29.9825	+	7.69821i	1.16795	+	0.299880i	0.782382	−	0.622798i	$-0.214004\pi$
$659$	29.9825	+	7.69821i	1.16795	+	0.299880i	0.385572	+	0.922678i	$0.374004\pi$
$660$	0.831703	−	3.49697i	0.0323740	−	0.136119i
$661$	−9.03681	+	10.9236i	−0.351491	+	0.424880i	−0.916394	−	0.400278i	$-0.868914\pi$
$661$	−9.03681	+	10.9236i	−0.351491	+	0.424880i	0.564903	+	0.825157i	$0.308914\pi$
$662$	−6.30785	−	4.00308i	−0.245162	−	0.155584i
$663$	5.08292	−	0.319790i	0.197404	−	0.0124196i
$664$	−4.31877	−	6.80529i	−0.167601	−	0.264097i
$665$	−0.385969	−	0.173287i	−0.0149672	−	0.00671976i
$666$	0.0852812	+	1.35551i	0.00330458	+	0.0525248i
$667$	−31.1218	−	5.93680i	−1.20504	−	0.229874i
$668$	−17.5409	+	5.69940i	−0.678679	+	0.220516i
$669$	−17.3465	+	16.2895i	−0.670655	+	0.629787i
$670$	20.4809	−	19.9318i	0.791245	−	0.770032i
$671$	−1.16533	−	6.10887i	−0.0449870	−	0.235830i
$672$	2.30566	−	2.45528i	0.0889428	−	0.0947144i
$673$	6.52437	−	16.4787i	0.251496	−	0.635206i	−0.748101	−	0.663584i	$-0.769034\pi$
$673$	6.52437	−	16.4787i	0.251496	−	0.635206i	0.999597	+	0.0283784i	$0.00903432\pi$
$674$	1.02080	+	3.14170i	0.0393197	+	0.121014i
$675$	−1.07000	+	4.88417i	−0.0411842	+	0.187992i
$676$	0.360288	−	1.10885i	0.0138572	−	0.0426481i
$677$	−20.5143	−	16.9709i	−0.788428	−	0.652244i	0.153467	−	0.988154i	$-0.450956\pi$
$677$	−20.5143	−	16.9709i	−0.788428	−	0.652244i	−0.941894	+	0.335910i	$0.890956\pi$
$678$	−10.5624	−	4.97029i	−0.405647	−	0.190883i
$679$	13.0997	+	12.3015i	0.502722	+	0.472088i
$680$	−2.41579	+	1.82185i	−0.0926412	+	0.0698649i
$681$	−8.61350	+	1.08814i	−0.330070	+	0.0416975i
$682$		−	1.08588i		−	0.0415805i
$683$	3.62153	+	28.6674i	0.138574	+	1.09693i	0.896015	+	0.444023i	$0.146449\pi$
$683$	3.62153	+	28.6674i	0.138574	+	1.09693i	−0.757442	+	0.652903i	$0.773551\pi$
$684$	0.0358078	+	0.0432843i	0.00136915	+	0.00165501i
$685$	3.59971	−	6.83370i	0.137538	−	0.261102i
$686$	0.561616	−	8.92663i	0.0214426	−	0.340820i
$687$	0.160118	−	0.623620i	0.00610890	−	0.0237926i
$688$	3.06419	−	11.9342i	0.116821	−	0.454988i
$689$	1.24814	−	19.8386i	0.0475504	−	0.755792i
$690$	6.90135	+	7.09146i	0.262730	+	0.269967i
$691$	−8.54678	−	10.3313i	−0.325135	−	0.393021i	0.582466	−	0.812855i	$-0.302088\pi$
$691$	−8.54678	−	10.3313i	−0.325135	−	0.393021i	−0.907601	+	0.419835i	$0.862088\pi$
$692$	−1.31803	−	10.4333i	−0.0501038	−	0.396613i
$693$		−	5.41436i		−	0.205674i
$694$	24.6421	−	3.11303i	0.935403	−	0.118169i
$695$	−15.4126	+	0.274836i	−0.584632	+	0.0104251i
$696$	5.21903	+	4.90099i	0.197827	+	0.185772i
$697$	−0.179084	−	0.0842707i	−0.00678330	−	0.00319198i
$698$	25.5419	+	21.1301i	0.966776	+	0.799787i
$699$	3.31655	−	10.2073i	0.125443	−	0.386075i
$700$	10.3782	+	13.2629i	0.392259	+	0.501290i
$701$	3.83036	+	11.7886i	0.144671	+	0.445251i	0.996969	−	0.0778061i	$-0.0247915\pi$
$701$	3.83036	+	11.7886i	0.144671	+	0.445251i	−0.852298	+	0.523057i	$0.824791\pi$
$702$	−1.38553	+	3.49946i	−0.0522936	+	0.132079i
$703$	−0.0522291	+	0.0556183i	−0.00196986	+	0.00209768i
$704$	0.301218	+	1.57904i	0.0113526	+	0.0595124i
$705$	−4.45631	+	25.8573i	−0.167834	+	0.973844i
$706$	20.0175	−	18.7977i	0.753368	−	0.707459i
$707$	−14.2920	+	4.64374i	−0.537504	+	0.174646i
$708$	−13.9117	−	2.65380i	−0.522834	−	0.0997359i
$709$	−0.0200868	−	0.319270i	−0.000754375	−	0.0119905i	0.997632	−	0.0687846i	$-0.0219121\pi$
$709$	−0.0200868	−	0.319270i	−0.000754375	−	0.0119905i	−0.998386	+	0.0567942i	$0.981912\pi$
$710$	−1.81329	+	16.7504i	−0.0680514	+	0.628629i
$711$	1.33826	+	2.10877i	0.0501888	+	0.0790849i
$712$	3.96710	−	0.249589i	0.148673	−	0.00935373i
$713$	2.52396	+	1.60176i	0.0945232	+	0.0599862i
$714$	−2.90515	+	3.51172i	−0.108723	+	0.131423i
$715$	11.5503	+	7.04433i	0.431955	+	0.263443i
$716$	16.6651	+	4.27888i	0.622806	+	0.159909i
$717$	22.1242	−	10.4109i	0.826244	−	0.388801i
$718$	−4.65737	−	1.51327i	−0.173811	−	0.0564747i
$719$	−15.6128	−	8.58321i	−0.582259	−	0.320100i	0.163261	−	0.986583i	$-0.447799\pi$
$719$	−15.6128	−	8.58321i	−0.582259	−	0.320100i	−0.745520	+	0.666483i	$0.767799\pi$
$720$	−0.458092	−	2.18864i	−0.0170721	−	0.0815659i
$721$	23.4880	+	2.96722i	0.874738	+	0.110505i
$722$	2.38094	−	18.8470i	0.0886093	−	0.701415i
$723$	17.7136	−	11.2414i	0.658775	−	0.418072i
$724$	−10.5430	+	7.65991i	−0.391826	+	0.284678i
$725$	−28.1921	+	22.0603i	−1.04703	+	0.819299i
$726$	−6.80860	−	4.94674i	−0.252691	−	0.183591i
$727$	−33.2687	−	2.09309i	−1.23387	−	0.0776283i	−0.567576	−	0.823321i	$-0.692119\pi$
$727$	−33.2687	−	2.09309i	−1.23387	−	0.0776283i	−0.666290	+	0.745693i	$0.732119\pi$
$728$	6.10716	+	11.1089i	0.226346	+	0.411723i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	−0.100050	+	2.22174i	−0.00370301	+	0.0822302i
$731$	−3.12415	+	16.3774i	−0.115551	+	0.605739i
$732$	−2.27398	−	3.12986i	−0.0840486	−	0.115683i
$733$	−12.5937	+	22.9078i	−0.465158	+	0.846120i	0.534841	+	0.844953i	$0.320372\pi$
$733$	−12.5937	+	22.9078i	−0.465158	+	0.846120i	−0.999999	+	0.00116723i	$0.999628\pi$
$734$	−2.08402	+	3.28389i	−0.0769225	+	0.121211i
$735$	7.59437	+	6.05782i	0.280122	+	0.223446i
$736$	−4.11456	−	1.62907i	−0.151665	−	0.0600483i
$737$	7.56323	+	19.1025i	0.278595	+	0.703651i
$738$	0.112700	−	0.0932335i	0.00414854	−	0.00343197i
$739$	28.3440	−	7.27750i	1.04265	−	0.267707i	0.311731	−	0.950170i	$-0.399091\pi$
$739$	28.3440	−	7.27750i	1.04265	−	0.267707i	0.730920	+	0.682463i	$0.239091\pi$
$740$	2.87116	−	0.989831i	0.105546	−	0.0363869i
$741$	−0.196585	+	0.0778336i	−0.00722174	+	0.00285929i
$742$	12.1771	+	12.9672i	0.447034	+	0.476043i
$743$	8.34427	−	11.4849i	0.306122	−	0.421340i	−0.628045	−	0.778177i	$-0.716145\pi$
$743$	8.34427	−	11.4849i	0.306122	−	0.421340i	0.934167	+	0.356837i	$0.116145\pi$
$744$	−0.287615	−	0.611213i	−0.0105445	−	0.0224081i
$745$	27.8962	+	6.63471i	1.02204	+	0.243077i
$746$	−31.9717	+	17.5766i	−1.17057	+	0.643524i
$747$	−7.91725	+	1.51030i	−0.289677	+	0.0552588i
$748$	−0.540955	−	2.10688i	−0.0197793	−	0.0770352i
$749$	22.8643			0.835442
$750$	11.1643	−	0.597753i	0.407664	−	0.0218269i
$751$	−25.5445			−0.932131			−0.466065	−	0.884750i	$-0.654329\pi$
$751$	−25.5445			−0.932131			−0.466065	+	0.884750i	$0.654329\pi$
$752$	−2.91819	−	11.3656i	−0.106415	−	0.414460i
$753$	23.1881	−	4.42337i	0.845022	−	0.161197i
$754$	−23.6134	+	12.9816i	−0.859951	+	0.472762i
$755$	21.1833	−	34.7333i	0.770940	−	1.26407i
$756$	−1.43409	−	3.04760i	−0.0521573	−	0.110840i
$757$	−23.5976	+	32.4794i	−0.857670	+	1.18048i	0.124450	+	0.992226i	$0.460284\pi$
$757$	−23.5976	+	32.4794i	−0.857670	+	1.18048i	−0.982120	+	0.188256i	$0.939716\pi$
$758$	22.3650	+	23.8163i	0.812332	+	0.865046i
$759$	−6.61422	+	2.61875i	−0.240081	+	0.0950548i
$760$	0.0720099	−	0.102923i	0.00261207	−	0.00373342i
$761$	−10.0929	+	2.59141i	−0.365866	+	0.0939384i	−0.427147	−	0.904182i	$-0.640481\pi$
$761$	−10.0929	+	2.59141i	−0.365866	+	0.0939384i	0.0612811	+	0.998121i	$0.480481\pi$
$762$	−12.4350	+	10.2871i	−0.450472	+	0.372662i
$763$	12.4276	+	31.3886i	0.449911	+	1.13634i
$764$	2.22200	+	0.879752i	0.0803891	+	0.0318283i
$765$	0.804606	+	2.91681i	0.0290906	+	0.105458i
$766$	−17.7928	+	28.0369i	−0.642879	+	1.01302i
$767$	25.6796	−	46.7111i	0.927238	−	1.68664i
$768$	0.587785	+	0.809017i	0.0212099	+	0.0291929i
$769$	0.826715	−	4.33379i	0.0298121	−	0.156281i	−0.964268	−	0.264928i	$-0.914652\pi$
$769$	0.826715	−	4.33379i	0.0298121	−	0.156281i	0.994080	+	0.108647i	$0.0346519\pi$
$770$	−11.6710	+	3.21945i	−0.420592	+	0.116021i
$771$	8.36608	−	17.7788i	0.301297	−	0.640289i
$772$	−2.05426	−	3.73669i	−0.0739346	−	0.134486i
$773$	−36.0084	−	2.26546i	−1.29513	−	0.0814828i	−0.599787	−	0.800160i	$-0.704748\pi$
$773$	−36.0084	−	2.26546i	−1.29513	−	0.0814828i	−0.695344	+	0.718677i	$0.744748\pi$
$774$	−9.96817	−	7.24230i	−0.358298	−	0.260319i
$775$	3.23937	−	0.956053i	0.116362	−	0.0343424i
$776$	−4.31638	+	3.13604i	−0.154949	+	0.112577i
$777$	3.86244	−	2.45118i	0.138564	−	0.0879356i
$778$	3.41948	−	27.0680i	0.122594	−	0.970433i
$779$	0.00815183	+	0.00102982i	0.000292070	+	3.68970e-5i
$780$	8.36715	+	0.905774i	0.299592	+	0.0324319i
$781$	−10.6140	−	5.83511i	−0.379799	−	0.208797i
$782$	5.69508	+	1.85044i	0.203656	+	0.0661717i
$783$	6.47808	−	3.04835i	0.231508	−	0.108939i
$784$	−4.20797	−	1.08042i	−0.150285	−	0.0385865i
$785$	−14.9029	+	1.20471i	−0.531908	+	0.0429980i
$786$	−5.75612	+	6.95795i	−0.205314	+	0.248182i
$787$	−33.2296	−	21.0882i	−1.18451	−	0.751712i	−0.210361	−	0.977624i	$-0.567464\pi$
$787$	−33.2296	−	21.0882i	−1.18451	−	0.751712i	−0.974148	+	0.225912i	$0.927464\pi$
$788$	6.29069	−	0.395777i	0.224097	−	0.0140990i
$789$	9.06233	+	14.2800i	0.322628	+	0.508380i
$790$	3.74982	−	4.13861i	0.133413	−	0.147245i
$791$	2.46878	+	39.2402i	0.0877799	+	1.39522i
$792$	1.57904	+	0.301218i	0.0561088	+	0.0107033i
$793$	13.8483	−	4.49958i	0.491767	−	0.159785i
$794$	21.7880	−	20.4603i	0.773227	−	0.726108i
$795$	11.6881	−	1.68878i	0.414536	−	0.0598949i
$796$	−1.45796	−	7.64290i	−0.0516761	−	0.270895i
$797$	−7.83847	+	8.34712i	−0.277653	+	0.295670i	−0.852647	−	0.522487i	$-0.825004\pi$
$797$	−7.83847	+	8.34712i	−0.277653	+	0.295670i	0.574994	+	0.818157i	$0.305004\pi$
$798$	0.0696525	−	0.175922i	0.00246567	−	0.00622757i
$799$	4.90665	+	15.1011i	0.173585	+	0.534240i
$800$	−4.44536	+	2.28884i	−0.157167	+	0.0809227i
$801$	1.22833	−	3.78040i	0.0434007	−	0.133574i
$802$	−16.6599	−	13.7822i	−0.588281	−	0.486668i
$803$	−1.44667	−	0.680749i	−0.0510517	−	0.0240231i
$804$	9.31679	+	8.74905i	0.328578	+	0.308555i
$805$	9.73244	−	31.8763i	0.343023	−	1.12349i
$806$	2.52238	−	0.318651i	0.0888472	−	0.0112240i
$807$		−	31.6604i		−	1.11450i
$808$	−0.559190	−	4.42645i	−0.0196722	−	0.155722i
$809$	−5.01148	−	6.05784i	−0.176194	−	0.212982i	0.675022	−	0.737798i	$-0.264134\pi$
$809$	−5.01148	−	6.05784i	−0.176194	−	0.212982i	−0.851216	+	0.524816i	$0.824134\pi$
$810$	−2.20358	−	0.379770i	−0.0774260	−	0.0133438i
$811$	−1.42628	+	22.6700i	−0.0500834	+	0.796053i	0.890181	+	0.455607i	$0.150578\pi$
$811$	−1.42628	+	22.6700i	−0.0500834	+	0.796053i	−0.940264	+	0.340446i	$0.889422\pi$
$812$	5.99696	−	23.3566i	0.210452	−	0.819656i
$813$	7.40842	−	28.8539i	0.259825	−	1.01195i
$814$	−0.137091	+	2.17899i	−0.00480503	+	0.0763737i
$815$	−18.8637	+	9.29092i	−0.660766	+	0.325447i
$816$	−0.862535	−	1.04263i	−0.0301948	−	0.0364992i
$817$	−0.0867508	−	0.686704i	−0.00303503	−	0.0240247i
$818$		−	10.5818i		−	0.369986i
$819$	12.5770	−	1.58884i	0.439475	−	0.0555186i
$820$	−0.267983	−	0.187493i	−0.00935838	−	0.00654756i
$821$	−30.3804	−	28.5291i	−1.06028	−	0.995671i	−0.0602851	−	0.998181i	$-0.519201\pi$
$821$	−30.3804	−	28.5291i	−1.06028	−	0.995671i	−0.999997	+	0.00251018i	$0.999201\pi$
$822$	3.12545	+	1.47072i	0.109013	+	0.0512974i
$823$	39.6759	+	32.8228i	1.38302	+	1.14413i	0.972668	+	0.232202i	$0.0745929\pi$
$823$	39.6759	+	32.8228i	1.38302	+	1.14413i	0.410349	+	0.911929i	$0.365407\pi$
$824$	−2.17207	+	6.68495i	−0.0756677	+	0.232881i
$825$	−2.69051	+	7.57389i	−0.0936715	+	0.263689i
$826$	14.7406	+	45.3670i	0.512892	+	1.57852i
$827$	5.55135	−	14.0211i	0.193039	−	0.487562i	−0.800729	−	0.599027i	$-0.795554\pi$
$827$	5.55135	−	14.0211i	0.193039	−	0.487562i	0.993768	+	0.111465i	$0.0355543\pi$
$828$	−3.02934	+	3.22592i	−0.105277	+	0.112109i
$829$	−4.51957	−	23.6924i	−0.156971	−	0.822871i	−0.970455	−	0.241283i	$-0.922432\pi$
$829$	−4.51957	−	23.6924i	−0.156971	−	0.822871i	0.813484	−	0.581588i	$-0.197568\pi$
$830$	7.96324	+	16.1681i	0.276408	+	0.561201i
$831$	−9.45543	+	8.87924i	−0.328005	+	0.308017i
$832$	−3.57955	+	1.16307i	−0.124099	+	0.0403221i
$833$	5.77461	+	1.10157i	0.200078	+	0.0381670i
$834$	−0.432866	−	6.88021i	−0.0149889	−	0.238242i
$835$	40.3665	−	8.44888i	1.39694	−	0.292385i
$836$	0.0483871	+	0.0762458i	0.00167350	+	0.00263702i
$837$	−0.674169	+	0.0424151i	−0.0233027	+	0.00146608i
$838$	−14.5308	−	9.22150i	−0.501957	−	0.318552i
$839$	−13.2946	+	16.0705i	−0.458982	+	0.554814i	−0.948335	−	0.317272i	$-0.897233\pi$
$839$	−13.2946	+	16.0705i	−0.458982	+	0.554814i	0.489352	+	0.872086i	$0.337233\pi$
$840$	−5.71654	+	4.90341i	−0.197240	+	0.169184i
$841$	21.5587	+	5.53534i	0.743404	+	0.190874i
$842$	17.2093	−	8.09810i	0.593073	−	0.279079i
$843$	12.9098	+	4.19466i	0.444639	+	0.144472i
$844$	−11.1008	−	6.10273i	−0.382106	−	0.210064i
$845$	−1.06780	+	2.37836i	−0.0367334	+	0.0818181i
$846$	−11.6417	−	1.47069i	−0.400250	−	0.0505633i
$847$	−3.55270	+	28.1225i	−0.122072	+	0.966301i
$848$	−4.45921	+	2.82990i	−0.153130	+	0.0971793i
$849$	−3.78434	+	2.74948i	−0.129878	+	0.0943620i
$850$	5.80893	−	3.46875i	0.199245	−	0.118977i
$851$	−4.86252	−	3.53283i	−0.166685	−	0.121104i
$852$	−7.51988	−	0.473111i	−0.257627	−	0.0162085i
$853$	20.8457	+	37.9182i	0.713743	+	1.29829i	0.945532	+	0.325528i	$0.105542\pi$
$853$	20.8457	+	37.9182i	0.713743	+	1.29829i	−0.231789	+	0.972766i	$0.574458\pi$
$854$	−5.54809	+	11.7903i	−0.189852	+	0.403456i
$855$	−0.0691871	−	0.104842i	−0.00236615	−	0.00358551i
$856$	−1.27201	+	6.66813i	−0.0434765	+	0.227912i
$857$	−26.4227	−	36.3678i	−0.902583	−	1.24230i	−0.969637	−	0.244550i	$-0.921360\pi$
$857$	−26.4227	−	36.3678i	−0.902583	−	1.24230i	0.0670532	−	0.997749i	$-0.478640\pi$
$858$	−2.91476	+	5.30192i	−0.0995081	+	0.181005i
$859$	−6.60992	+	10.4156i	−0.225528	+	0.355375i	−0.938183	−	0.346140i	$-0.887492\pi$
$859$	−6.60992	+	10.4156i	−0.225528	+	0.355375i	0.712655	+	0.701514i	$0.247492\pi$
$860$	−9.68399	+	25.7933i	−0.330221	+	0.879546i
$861$	−0.458051	−	0.181355i	−0.0156103	−	0.00618057i
$862$	−11.0868	−	28.0020i	−0.377618	−	0.953753i
$863$	−9.11050	+	7.53687i	−0.310125	+	0.256558i	−0.779445	−	0.626470i	$-0.784499\pi$
$863$	−9.11050	+	7.53687i	−0.310125	+	0.256558i	0.469320	+	0.883028i	$0.344499\pi$
$864$	0.968583	−	0.248690i	0.0329519	−	0.00846060i
$865$	0.419249	+	23.5111i	0.0142549	+	0.799403i
$866$	−28.7745	+	11.3926i	−0.977797	+	0.387137i
$867$	−10.3839	−	11.0577i	−0.352655	−	0.375539i
$868$	−1.33733	+	1.84067i	−0.0453918	+	0.0624765i
$869$	1.70945	+	3.63277i	0.0579892	+	0.123233i
$870$	−10.4229	−	12.1513i	−0.353368	−	0.411967i
$871$	−42.1537	+	23.1742i	−1.42832	+	0.785228i
$872$	−9.84556	+	1.87814i	−0.333413	+	0.0636019i
$873$	1.32685	+	5.16772i	0.0449069	+	0.174901i
$874$	−0.248596			−0.00840890
$875$	−19.8798	−	31.9820i	−0.672060	−	1.08119i
$876$	−0.994599			−0.0336044
$877$	−11.8764	−	46.2557i	−0.401039	−	1.56194i	−0.773439	−	0.633871i	$-0.781465\pi$
$877$	−11.8764	−	46.2557i	−0.401039	−	1.56194i	0.372400	−	0.928072i	$-0.378535\pi$
$878$	−4.67237	+	0.891302i	−0.157685	+	0.0300800i
$879$	6.10714	−	3.35743i	0.205989	−	0.113243i
$880$	−0.289626	−	3.58282i	−0.00976329	−	0.120777i
$881$	−4.41305	−	9.37821i	−0.148679	−	0.315960i	0.816589	−	0.577219i	$-0.195862\pi$
$881$	−4.41305	−	9.37821i	−0.148679	−	0.315960i	−0.965269	+	0.261259i	$0.915862\pi$
$882$	−2.55361	+	3.51474i	−0.0859845	+	0.118347i
$883$	−16.4354	−	17.5019i	−0.553095	−	0.588986i	0.390288	−	0.920693i	$-0.372376\pi$
$883$	−16.4354	−	17.5019i	−0.553095	−	0.588986i	−0.943383	+	0.331707i	$0.892376\pi$
$884$	4.73532	−	1.87485i	0.159266	−	0.0630579i
$885$	30.2882	+	9.24755i	1.01813	+	0.310853i
$886$	−10.1001	+	2.59326i	−0.339319	+	0.0871224i
$887$	43.0139	−	35.5842i	1.44427	−	1.19480i	0.499823	−	0.866127i	$-0.333398\pi$
$887$	43.0139	−	35.5842i	1.44427	−	1.19480i	0.944443	−	0.328674i	$-0.106602\pi$
$888$	0.499981	+	1.26281i	0.0167783	+	0.0423771i
$889$	50.5400	+	20.0102i	1.69506	+	0.671121i
$890$	−8.87925	−	0.399852i	−0.297633	−	0.0134031i
$891$	0.861349	−	1.35727i	0.0288563	−	0.0454702i
$892$	−11.4638	+	20.8526i	−0.383836	+	0.698196i
$893$	−0.387457	−	0.533288i	−0.0129657	−	0.0178458i
$894$	−2.40289	+	12.5964i	−0.0803648	+	0.421287i
$895$	−36.0182	−	13.5229i	−1.20396	−	0.452020i
$896$	1.43409	−	3.04760i	0.0479096	−	0.101813i
$897$	−8.02403	−	14.5957i	−0.267914	−	0.487335i
$898$	15.0664	+	0.947897i	0.502772	+	0.0316317i
$899$	−3.91260	−	2.84267i	−0.130492	−	0.0948083i
$900$	0.491664	+	4.97577i	0.0163888	+	0.165859i
$901$	5.78167	−	4.20063i	0.192615	−	0.139943i
$902$	0.198522	−	0.125986i	0.00661008	−	0.00419488i
$903$	−5.20135	+	41.1729i	−0.173090	+	1.37015i
$904$	−11.5813	−	1.46306i	−0.385190	−	0.0486608i
$905$	25.2813	−	14.4914i	0.840377	−	0.481709i
$906$	15.9436	+	8.76509i	0.529692	+	0.291201i
$907$	−15.1318	−	4.91662i	−0.502443	−	0.163254i	0.0468196	−	0.998903i	$-0.485091\pi$
$907$	−15.1318	−	4.91662i	−0.502443	−	0.163254i	−0.549263	+	0.835650i	$0.685091\pi$
$908$	−7.85567	+	3.69660i	−0.260699	+	0.122676i
$909$	−4.32146	−	1.10956i	−0.143334	−	0.0368018i
$910$	−10.9033	−	26.1657i	−0.361440	−	0.867383i
$911$	−7.59137	+	9.17638i	−0.251513	+	0.304027i	−0.881126	−	0.472882i	$-0.843214\pi$
$911$	−7.59137	+	9.17638i	−0.251513	+	0.304027i	0.629613	+	0.776909i	$0.283214\pi$
$912$	0.0474309	+	0.0301005i	0.00157059	+	0.000996728i
$913$	−12.9310	+	0.813551i	−0.427954	+	0.0269246i
$914$	−18.1206	−	28.5534i	−0.599375	−	0.944464i
$915$	4.30201	+	7.50518i	0.142220	+	0.248114i
$916$	−0.0404275	−	0.642577i	−0.00133576	−	0.0212313i
$917$	29.8766	+	5.69927i	0.986614	+	0.188207i
$918$	−1.28693	+	0.418149i	−0.0424750	+	0.0138010i
$919$	−34.1629	+	32.0811i	−1.12693	+	1.05826i	−0.129154	+	0.991625i	$0.541226\pi$
$919$	−34.1629	+	32.0811i	−1.12693	+	1.05826i	−0.997777	+	0.0666348i	$0.978774\pi$
$920$	8.75495	+	4.61175i	0.288642	+	0.152045i
$921$	1.87327	+	9.82003i	0.0617263	+	0.323581i
$922$	3.05825	−	3.25671i	0.100718	−	0.107254i
$923$	10.4396	−	26.3675i	0.343625	−	0.867898i
$924$	−1.67313	−	5.14936i	−0.0550419	−	0.169401i
$925$	−6.62103	+	1.50951i	−0.217698	+	0.0496324i
$926$	−6.85505	+	21.0977i	−0.225271	+	0.693312i
$927$	5.41592	+	4.48044i	0.177882	+	0.147157i
$928$	6.47808	+	3.04835i	0.212653	+	0.100067i
$929$	−20.0378	−	18.8168i	−0.657420	−	0.617359i	0.282290	−	0.959329i	$-0.408906\pi$
$929$	−20.0378	−	18.8168i	−0.657420	−	0.617359i	−0.939711	+	0.341970i	$0.888906\pi$
$930$	0.492299	+	1.42799i	0.0161431	+	0.0468257i
$931$	−0.242129	+	0.0305880i	−0.00793547	+	0.00100248i
$932$		−	10.7326i		−	0.351557i
$933$	2.03749	+	16.1284i	0.0667043	+	0.528019i
$934$	10.3496	+	12.5105i	0.338648	+	0.409355i
$935$	0.695553	+	4.81395i	0.0227470	+	0.157433i
$936$	−0.236329	+	3.75634i	−0.00772464	+	0.122780i
$937$	3.99190	−	15.5474i	0.130410	−	0.507912i	−0.869493	−	0.493945i	$-0.835554\pi$
$937$	3.99190	−	15.5474i	0.130410	−	0.507912i	0.999902	−	0.0139662i	$-0.00444574\pi$
$938$	10.7055	−	41.6952i	0.349547	−	1.36140i
$939$	−1.20035	+	19.0789i	−0.0391718	+	0.622618i
$940$	3.75216	+	25.9689i	0.122382	+	0.847011i
$941$	2.55985	+	3.09432i	0.0834486	+	0.100872i	0.810585	−	0.585621i	$-0.199149\pi$
$941$	2.55985	+	3.09432i	0.0834486	+	0.100872i	−0.727136	+	0.686493i	$0.759149\pi$
$942$	−0.838045	−	6.63381i	−0.0273050	−	0.216141i
$943$			0.647275i			0.0210782i
$944$	−14.0509	+	1.77504i	−0.457317	+	0.0577726i
$945$	2.45467	+	7.12017i	0.0798505	+	0.231619i
$946$	−14.4385	−	13.5586i	−0.469435	−	0.440829i
$947$	15.9274	+	7.49487i	0.517572	+	0.243551i	0.666779	−	0.745255i	$-0.267672\pi$
$947$	15.9274	+	7.49487i	0.517572	+	0.243551i	−0.149208	+	0.988806i	$0.547672\pi$
$948$	1.92441	+	1.59201i	0.0625019	+	0.0517061i
$949$	1.15678	−	3.56022i	0.0375508	−	0.115570i
$950$	−0.184853	+	0.211477i	−0.00599742	+	0.00686123i
$951$	−9.42729	−	29.0142i	−0.305701	−	0.940851i
$952$	−1.67778	+	4.23759i	−0.0543772	+	0.137341i
$953$	9.58252	−	10.2044i	0.310408	−	0.330551i	−0.554781	−	0.831996i	$-0.687198\pi$
$953$	9.58252	−	10.2044i	0.310408	−	0.330551i	0.865190	+	0.501445i	$0.167198\pi$
$954$	0.989631	+	5.18783i	0.0320405	+	0.167962i
$955$	−4.72797	−	2.49050i	−0.152993	−	0.0805906i
$956$	17.8242	−	16.7381i	0.576477	−	0.541348i
$957$	10.9457	−	3.55646i	0.353823	−	0.114964i
$958$	−27.5559	−	5.25658i	−0.890292	−	0.169832i
$959$	−0.730521	−	11.6113i	−0.0235898	−	0.374949i
$960$	−1.11200	−	1.93996i	−0.0358896	−	0.0626121i
$961$	−16.3661	−	25.7889i	−0.527940	−	0.831900i
$962$	−5.10180	+	0.320978i	−0.164489	+	0.0103487i
$963$	5.73161	+	3.63739i	0.184698	+	0.117213i
$964$	13.3728	−	16.1650i	0.430710	−	0.520639i
$965$	3.66753	+	8.80134i	0.118062	+	0.283325i
$966$	14.4369	+	3.70676i	0.464500	+	0.119263i
$967$	−41.2077	+	19.3909i	−1.32515	+	0.623568i	−0.952538	−	0.304420i	$-0.901538\pi$
$967$	−41.2077	+	19.3909i	−1.32515	+	0.623568i	−0.372611	+	0.927987i	$0.621538\pi$
$968$	−8.00399	−	2.60066i	−0.257258	−	0.0835882i
$969$	−0.0666123	−	0.0366204i	−0.00213990	−	0.00117642i
$970$	10.3504	−	5.93289i	0.332330	−	0.190494i
$971$	13.6871	+	1.72908i	0.439240	+	0.0554889i	0.341844	−	0.939757i	$-0.388949\pi$
$971$	13.6871	+	1.72908i	0.439240	+	0.0554889i	0.0973961	+	0.995246i	$0.468949\pi$
$972$	0.125333	−	0.992115i	0.00402007	−	0.0318221i
$973$	−19.6048	+	12.4416i	−0.628501	+	0.398859i
$974$	−17.8251	+	12.9507i	−0.571153	+	0.414967i
$975$	−18.3829	−	4.02721i	−0.588723	−	0.128974i
$976$	−3.12986	−	2.27398i	−0.100184	−	0.0727882i
$977$	17.6629	+	1.11126i	0.565088	+	0.0355523i	0.342766	−	0.939421i	$-0.388636\pi$
$977$	17.6629	+	1.11126i	0.565088	+	0.0355523i	0.222322	+	0.974973i	$0.428636\pi$
$978$	−4.53033	−	8.24064i	−0.144864	−	0.263507i
$979$	2.72064	−	5.78165i	0.0869519	−	0.184782i
$980$	9.09464	+	3.41454i	0.290518	+	0.109073i
$981$	−1.87814	+	9.84556i	−0.0599644	+	0.314344i
$982$	2.04404	+	2.81338i	0.0652280	+	0.0897786i
$983$	17.4211	−	31.6888i	0.555646	−	1.01072i	−0.438086	−	0.898933i	$-0.644344\pi$
$983$	17.4211	−	31.6888i	0.555646	−	1.01072i	0.993733	−	0.111784i	$-0.0356565\pi$
$984$	0.0783733	−	0.123497i	0.00249845	−	0.00393693i
$985$	−14.0800	−	0.634052i	−0.448625	−	0.0202026i
$986$	−9.00757	−	3.56635i	−0.286860	−	0.113576i
$987$	14.5493	+	36.7473i	0.463109	+	1.16968i
$988$	−0.162912	+	0.134772i	−0.00518291	+	0.00428768i
$989$	52.8128	−	13.5600i	1.67935	−	0.431184i
$990$	−3.43784	−	1.04964i	−0.109262	−	0.0333597i
$991$	−32.4385	+	12.8433i	−1.03044	+	0.407981i	−0.821658	−	0.569980i	$-0.806951\pi$
$991$	−32.4385	+	12.8433i	−1.03044	+	0.407981i	−0.208785	+	0.977962i	$0.566951\pi$
$992$	−0.462413	−	0.492420i	−0.0146816	−	0.0156344i
$993$	−4.39126	+	6.04405i	−0.139352	+	0.191802i
$994$	10.8055	+	22.9629i	0.342730	+	0.728338i
$995$	1.40185	+	17.3416i	0.0444417	+	0.549767i
$996$	−7.06304	+	3.88294i	−0.223801	+	0.123036i
$997$	−19.4605	+	3.71228i	−0.616320	+	0.117569i	−0.486081	−	0.873914i	$-0.661574\pi$
$997$	−19.4605	+	3.71228i	−0.616320	+	0.117569i	−0.130238	+	0.991483i	$0.541574\pi$
$998$	−2.05810	−	8.01576i	−0.0651479	−	0.253734i
$999$	1.35819			0.0429711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	750.2.o.a.229.6	✓	240
125.119	even	50	inner	750.2.o.a.619.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
750.2.o.a.229.6	✓	240	1.1	even	1	trivial
750.2.o.a.619.6	yes	240	125.119	even	50	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:	\( N \)	\(=\)	\( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	750.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248690 - 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(2.06404 - 0.860088i) q^{5} +(0.425779 + 0.904827i) q^{6} +(1.97975 - 2.72489i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +O(q^{10})\)	\(q+(-0.248690 - 0.968583i) q^{2} +(-0.982287 + 0.187381i) q^{3} +(-0.876307 + 0.481754i) q^{4} +(2.06404 - 0.860088i) q^{5} +(0.425779 + 0.904827i) q^{6} +(1.97975 - 2.72489i) q^{7} +(0.684547 + 0.728969i) q^{8} +(0.929776 - 0.368125i) q^{9} +(-1.34637 - 1.78530i) q^{10} +(1.55701 - 0.399773i) q^{11} +(0.770513 - 0.637424i) q^{12} +(1.38553 + 3.49946i) q^{13} +(-3.13163 - 1.23990i) q^{14} +(-1.86631 + 1.23162i) q^{15} +(0.535827 - 0.844328i) q^{16} +(-0.651889 + 1.18578i) q^{17} +(-0.587785 - 0.809017i) q^{18} +(0.0105263 - 0.0551808i) q^{19} +(-1.39438 + 1.74806i) q^{20} +(-1.43409 + 3.04760i) q^{21} +(-0.774426 - 1.40868i) q^{22} +(4.41659 + 0.277868i) q^{23} +(-0.809017 - 0.587785i) q^{24} +(3.52050 - 3.55051i) q^{25} +(3.04495 - 2.21228i) q^{26} +(-0.844328 + 0.535827i) q^{27} +(-0.422142 + 3.34159i) q^{28} +(-7.10301 - 0.897319i) q^{29} +(1.65706 + 1.50139i) q^{30} +(0.591947 + 0.325426i) q^{31} +(-0.951057 - 0.309017i) q^{32} +(-1.45452 + 0.684446i) q^{33} +(1.31065 + 0.336517i) q^{34} +(1.74263 - 7.32704i) q^{35} +(-0.637424 + 0.770513i) q^{36} +(-1.14675 - 0.727752i) q^{37} +(-0.0560650 + 0.00352731i) q^{38} +(-2.01673 - 3.17785i) q^{39} +(2.03991 + 0.915847i) q^{40} +(0.00918412 + 0.145977i) q^{41} +(3.30849 + 0.631129i) q^{42} +(11.7183 - 3.80750i) q^{43} +(-1.17183 + 1.10042i) q^{44} +(1.60247 - 1.55951i) q^{45} +(-0.829223 - 4.34694i) q^{46} +(8.03264 - 8.55389i) q^{47} +(-0.368125 + 0.929776i) q^{48} +(-1.34251 - 4.13182i) q^{49} +(-4.31447 - 2.52692i) q^{50} +(0.418149 - 1.28693i) q^{51} +(-2.90003 - 2.39911i) q^{52} +(-4.77873 - 2.24870i) q^{53} +(0.728969 + 0.684547i) q^{54} +(2.86989 - 2.16431i) q^{55} +(3.34159 - 0.422142i) q^{56} +0.0561759i q^{57} +(0.897319 + 7.10301i) q^{58} +(-9.02755 - 10.9124i) q^{59} +(1.04213 - 1.97838i) q^{60} +(0.242919 - 3.86109i) q^{61} +(0.167991 - 0.654280i) q^{62} +(0.837626 - 3.26234i) q^{63} +(-0.0627905 + 0.998027i) q^{64} +(5.86964 + 6.03133i) q^{65} +(1.02467 + 1.23861i) q^{66} +(1.60186 + 12.6800i) q^{67} -1.35316i q^{68} +(-4.39043 + 0.554640i) q^{69} +(-7.53022 + 0.134278i) q^{70} +(-5.49260 - 5.15789i) q^{71} +(0.904827 + 0.425779i) q^{72} +(-0.766351 - 0.633981i) q^{73} +(-0.419702 + 1.29171i) q^{74} +(-2.79284 + 4.14729i) q^{75} +(0.0173593 + 0.0534264i) q^{76} +(1.99316 - 5.03414i) q^{77} +(-2.57647 + 2.74367i) q^{78} +(0.467998 + 2.45333i) q^{79} +(0.379770 - 2.20358i) q^{80} +(0.728969 - 0.684547i) q^{81} +(0.139107 - 0.0451987i) q^{82} +(-7.91725 - 1.51030i) q^{83} +(-0.211488 - 3.36151i) q^{84} +(-0.325646 + 3.00818i) q^{85} +(-6.60210 - 10.4032i) q^{86} +(7.14534 - 0.449547i) q^{87} +(1.35727 + 0.861349i) q^{88} +(2.53372 - 3.06275i) q^{89} +(-1.90904 - 1.16429i) q^{90} +(12.2787 + 3.15262i) q^{91} +(-4.00415 + 1.88421i) q^{92} +(-0.642441 - 0.208742i) q^{93} +(-10.2828 - 5.65301i) q^{94} +(-0.0257337 - 0.122949i) q^{95} +(0.992115 + 0.125333i) q^{96} +(-0.668696 + 5.29327i) q^{97} +(-3.66815 + 2.32788i) q^{98} +(1.30051 - 0.944873i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 10 q^{11} + 20 q^{13} - 10 q^{17} + 10 q^{19} + 60 q^{23} - 60 q^{24} + 60 q^{25} + 10 q^{28} + 20 q^{29} + 10 q^{30} - 30 q^{31} - 10 q^{34} - 10 q^{35} + 20 q^{37} - 90 q^{38} - 20 q^{41} - 10 q^{42} - 10 q^{46} + 140 q^{47} + 50 q^{49} + 20 q^{50} + 10 q^{51} - 80 q^{52} + 30 q^{53} - 10 q^{55} - 30 q^{58} + 20 q^{59} + 40 q^{60} - 100 q^{61} - 10 q^{62} - 10 q^{63} - 20 q^{65} - 40 q^{66} - 10 q^{67} - 10 q^{69} + 10 q^{70} + 80 q^{71} + 20 q^{73} - 80 q^{75} + 10 q^{76} + 20 q^{77} + 140 q^{79} + 100 q^{82} - 70 q^{83} - 20 q^{85} + 20 q^{86} + 30 q^{87} - 10 q^{88} + 40 q^{89} + 10 q^{90} + 170 q^{91} + 120 q^{92} + 50 q^{93} - 30 q^{94} + 220 q^{95} - 60 q^{97} - 120 q^{98} - 20 q^{99}+O(q^{100}) \) 240 * q - 10 * q^11 + 20 * q^13 - 10 * q^17 + 10 * q^19 + 60 * q^23 - 60 * q^24 + 60 * q^25 + 10 * q^28 + 20 * q^29 + 10 * q^30 - 30 * q^31 - 10 * q^34 - 10 * q^35 + 20 * q^37 - 90 * q^38 - 20 * q^41 - 10 * q^42 - 10 * q^46 + 140 * q^47 + 50 * q^49 + 20 * q^50 + 10 * q^51 - 80 * q^52 + 30 * q^53 - 10 * q^55 - 30 * q^58 + 20 * q^59 + 40 * q^60 - 100 * q^61 - 10 * q^62 - 10 * q^63 - 20 * q^65 - 40 * q^66 - 10 * q^67 - 10 * q^69 + 10 * q^70 + 80 * q^71 + 20 * q^73 - 80 * q^75 + 10 * q^76 + 20 * q^77 + 140 * q^79 + 100 * q^82 - 70 * q^83 - 20 * q^85 + 20 * q^86 + 30 * q^87 - 10 * q^88 + 40 * q^89 + 10 * q^90 + 170 * q^91 + 120 * q^92 + 50 * q^93 - 30 * q^94 + 220 * q^95 - 60 * q^97 - 120 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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