LMFDB - Embedded newform 930.2.bg.d.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 21x^{14} + 167x^{12} + 653x^{10} + 1350x^{8} + 1472x^{6} + 777x^{4} + 149x^{2} + 1 $ x^16 + 21x^14 + 167x^12 + 653x^10 + 1350x^8 + 1472x^6 + 777x^4 + 149*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			751.1
Root			$2.86648i$ of defining polynomial
Character	$\chi$	$=$	930.751
Dual form			930.2.bg.d.691.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.461080 - 0.205286i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.461080 - 0.205286i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.978148 + 0.207912i) q^{10} +(0.111410 + 1.05999i) q^{11} +(0.669131 - 0.743145i) q^{12} +(1.28441 + 1.42648i) q^{13} +(0.0527571 - 0.501950i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.267253 + 2.54274i) q^{17} +(0.669131 + 0.743145i) q^{18} +(0.589263 - 0.654443i) q^{19} +(0.104528 + 0.994522i) q^{20} +(0.493686 + 0.104936i) q^{21} +(-0.973686 + 0.433513i) q^{22} +(3.27538 + 2.37971i) q^{23} +(0.913545 + 0.406737i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.959760 + 1.66235i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.493686 - 0.104936i) q^{28} +(0.692835 + 2.13233i) q^{29} -1.00000 q^{30} +(1.71067 + 5.29845i) q^{31} +1.00000 q^{32} +(-0.329360 - 1.01367i) q^{33} +(-2.50088 + 0.531578i) q^{34} +(-0.408323 + 0.296664i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.79593 + 8.30680i) q^{37} +(0.804504 + 0.358188i) q^{38} +(-1.55293 - 1.12827i) q^{39} +(-0.913545 + 0.406737i) q^{40} +(4.07758 + 0.866716i) q^{41} +(0.0527571 + 0.501950i) q^{42} +(-2.75002 + 3.05421i) q^{43} +(-0.713181 - 0.792068i) q^{44} +(0.104528 - 0.994522i) q^{45} +(-1.25109 + 3.85044i) q^{46} +(-2.99894 + 9.22979i) q^{47} +(-0.104528 + 0.994522i) q^{48} +(-4.51346 - 5.01271i) q^{49} +(0.669131 - 0.743145i) q^{50} +(-0.267253 - 2.54274i) q^{51} +(-1.87757 - 0.399091i) q^{52} +(-0.919436 + 0.409359i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(0.973686 + 0.433513i) q^{55} +(0.252358 + 0.437096i) q^{56} +(-0.440320 + 0.762656i) q^{57} +(-1.81387 + 1.31785i) q^{58} +(-9.41829 + 2.00192i) q^{59} +(-0.309017 - 0.951057i) q^{60} +11.2837 q^{61} +(-4.51050 + 3.26425i) q^{62} -0.504715 q^{63} +(0.309017 + 0.951057i) q^{64} +(1.87757 - 0.399091i) q^{65} +(0.862276 - 0.626480i) q^{66} +(1.13972 - 1.97406i) q^{67} +(-1.27837 - 2.21421i) q^{68} +(-3.69858 - 1.64671i) q^{69} +(-0.408323 - 0.296664i) q^{70} +(-8.17500 + 3.63974i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(0.0271610 + 0.258420i) q^{73} +(-6.41821 + 7.12815i) q^{74} +(0.669131 + 0.743145i) q^{75} +(-0.0920519 + 0.875815i) q^{76} +(0.166233 - 0.511613i) q^{77} +(0.593165 - 1.82557i) q^{78} +(0.784025 - 7.45950i) q^{79} +(-0.669131 - 0.743145i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.435745 + 4.14584i) q^{82} +(-0.771873 - 0.164067i) q^{83} +(-0.461080 + 0.205286i) q^{84} +(2.06845 + 1.50282i) q^{85} +(-3.75453 - 1.67162i) q^{86} +(-1.12103 - 1.94168i) q^{87} +(0.532916 - 0.923038i) q^{88} +(4.82338 - 3.50439i) q^{89} +(0.978148 - 0.207912i) q^{90} +(-0.299379 - 0.921395i) q^{91} -4.04860 q^{92} +(-2.77490 - 4.82700i) q^{93} -9.70477 q^{94} +(-0.272133 - 0.837538i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(7.01736 - 5.09841i) q^{97} +(3.37263 - 5.84157i) q^{98} +(0.532916 + 0.923038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{14}{15}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$3$	−0.978148	+	0.207912i	−0.564734	+	0.120038i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.461080	−	0.205286i	−0.174272	−	0.0775909i	0.317746	−	0.948176i	$-0.397074\pi$
$7$	−0.461080	−	0.205286i	−0.174272	−	0.0775909i	−0.492018	+	0.870585i	$0.663741\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	0.913545	−	0.406737i	0.304515	−	0.135579i
$10$	0.978148	+	0.207912i	0.309317	+	0.0657474i
$11$	0.111410	+	1.05999i	0.0335913	+	0.319600i	0.998395	+	0.0566297i	$0.0180355\pi$
$11$	0.111410	+	1.05999i	0.0335913	+	0.319600i	−0.964804	+	0.262970i	$0.915298\pi$
$12$	0.669131	−	0.743145i	0.193161	−	0.214527i
$13$	1.28441	+	1.42648i	0.356231	+	0.395635i	0.894448	−	0.447171i	$-0.147569\pi$
$13$	1.28441	+	1.42648i	0.356231	+	0.395635i	−0.538217	+	0.842806i	$0.680902\pi$
$14$	0.0527571	−	0.501950i	0.0140999	−	0.134152i
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.267253	+	2.54274i	−0.0648184	+	0.616706i	0.913102	+	0.407730i	$0.133680\pi$
$17$	−0.267253	+	2.54274i	−0.0648184	+	0.616706i	−0.977921	+	0.208976i	$0.932987\pi$
$18$	0.669131	+	0.743145i	0.157716	+	0.175161i
$19$	0.589263	−	0.654443i	0.135186	−	0.150139i	−0.671750	−	0.740778i	$-0.734457\pi$
$19$	0.589263	−	0.654443i	0.135186	−	0.150139i	0.806937	+	0.590638i	$0.201124\pi$
$20$	0.104528	+	0.994522i	0.0233733	+	0.222382i
$21$	0.493686	+	0.104936i	0.107731	+	0.0228990i
$22$	−0.973686	+	0.433513i	−0.207591	+	0.0924253i
$23$	3.27538	+	2.37971i	0.682965	+	0.496203i	0.874340	−	0.485314i	$-0.161295\pi$
$23$	3.27538	+	2.37971i	0.682965	+	0.496203i	−0.191375	+	0.981517i	$0.561295\pi$
$24$	0.913545	+	0.406737i	0.186477	+	0.0830248i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.959760	+	1.66235i	−0.188225	+	0.326014i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	0.493686	−	0.104936i	0.0932979	−	0.0198311i
$29$	0.692835	+	2.13233i	0.128656	+	0.395963i	0.994549	−	0.104266i	$-0.0332492\pi$
$29$	0.692835	+	2.13233i	0.128656	+	0.395963i	−0.865893	+	0.500229i	$0.833249\pi$
$30$	−1.00000			−0.182574
$31$	1.71067	+	5.29845i	0.307245	+	0.951630i
$31$	1.71067	+	5.29845i	0.307245	+	0.951630i
$32$	1.00000			0.176777
$33$	−0.329360	−	1.01367i	−0.0573343	−	0.176457i
$34$	−2.50088	+	0.531578i	−0.428897	+	0.0911649i
$35$	−0.408323	+	0.296664i	−0.0690192	+	0.0501454i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.79593	+	8.30680i	0.788447	+	1.36563i	0.926918	+	0.375263i	$0.122448\pi$
$37$	4.79593	+	8.30680i	0.788447	+	1.36563i	−0.138472	+	0.990366i	$0.544219\pi$
$38$	0.804504	+	0.358188i	0.130508	+	0.0581058i
$39$	−1.55293	−	1.12827i	−0.248667	−	0.180667i
$40$	−0.913545	+	0.406737i	−0.144444	+	0.0643107i
$41$	4.07758	+	0.866716i	0.636811	+	0.135358i	0.514993	−	0.857194i	$-0.327794\pi$
$41$	4.07758	+	0.866716i	0.636811	+	0.135358i	0.121817	+	0.992553i	$0.461128\pi$
$42$	0.0527571	+	0.501950i	0.00814060	+	0.0774526i
$43$	−2.75002	+	3.05421i	−0.419374	+	0.465762i	−0.915400	−	0.402546i	$-0.868125\pi$
$43$	−2.75002	+	3.05421i	−0.419374	+	0.465762i	0.496026	+	0.868308i	$0.334792\pi$
$44$	−0.713181	−	0.792068i	−0.107516	−	0.119409i
$45$	0.104528	−	0.994522i	0.0155822	−	0.148255i
$46$	−1.25109	+	3.85044i	−0.184462	+	0.567717i
$47$	−2.99894	+	9.22979i	−0.437440	+	1.34630i	0.453125	+	0.891447i	$0.350309\pi$
$47$	−2.99894	+	9.22979i	−0.437440	+	1.34630i	−0.890565	+	0.454856i	$0.849691\pi$
$48$	−0.104528	+	0.994522i	−0.0150874	+	0.143547i
$49$	−4.51346	−	5.01271i	−0.644780	−	0.716101i
$50$	0.669131	−	0.743145i	0.0946294	−	0.105097i
$51$	−0.267253	−	2.54274i	−0.0374229	−	0.356055i
$52$	−1.87757	−	0.399091i	−0.260373	−	0.0553439i
$53$	−0.919436	+	0.409359i	−0.126294	+	0.0562298i	−0.468911	−	0.883245i	$-0.655353\pi$
$53$	−0.919436	+	0.409359i	−0.126294	+	0.0562298i	0.342617	+	0.939475i	$0.388687\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	0.973686	+	0.433513i	0.131292	+	0.0584549i
$56$	0.252358	+	0.437096i	0.0337227	+	0.0584095i
$57$	−0.440320	+	0.762656i	−0.0583218	+	0.101016i
$58$	−1.81387	+	1.31785i	−0.238172	+	0.173042i
$59$	−9.41829	+	2.00192i	−1.22616	+	0.260628i	−0.775083	−	0.631859i	$-0.782292\pi$
$59$	−9.41829	+	2.00192i	−1.22616	+	0.260628i	−0.451074	+	0.892487i	$0.648959\pi$
$60$	−0.309017	−	0.951057i	−0.0398939	−	0.122781i
$61$	11.2837			1.44474			0.722368	−	0.691509i	$-0.243054\pi$
$61$	11.2837			1.44474			0.722368	+	0.691509i	$0.243054\pi$
$62$	−4.51050	+	3.26425i	−0.572835	+	0.414561i
$63$	−0.504715			−0.0635882
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	1.87757	−	0.399091i	0.232884	−	0.0495011i
$66$	0.862276	−	0.626480i	0.106139	−	0.0771144i
$67$	1.13972	−	1.97406i	0.139240	−	0.241170i	−0.787969	−	0.615714i	$-0.788868\pi$
$67$	1.13972	−	1.97406i	0.139240	−	0.241170i	0.927209	+	0.374544i	$0.122201\pi$
$68$	−1.27837	−	2.21421i	−0.155026	−	0.268512i
$69$	−3.69858	−	1.64671i	−0.445256	−	0.198241i
$70$	−0.408323	−	0.296664i	−0.0488040	−	0.0354582i
$71$	−8.17500	+	3.63974i	−0.970194	+	0.431958i	−0.829753	−	0.558131i	$-0.811519\pi$
$71$	−8.17500	+	3.63974i	−0.970194	+	0.431958i	−0.140441	+	0.990089i	$0.544852\pi$
$72$	−0.978148	−	0.207912i	−0.115276	−	0.0245026i
$73$	0.0271610	+	0.258420i	0.00317896	+	0.0302458i	0.995996	−	0.0893935i	$-0.0284929\pi$
$73$	0.0271610	+	0.258420i	0.00317896	+	0.0302458i	−0.992817	+	0.119639i	$0.961826\pi$
$74$	−6.41821	+	7.12815i	−0.746102	+	0.828630i
$75$	0.669131	+	0.743145i	0.0772645	+	0.0858110i
$76$	−0.0920519	+	0.875815i	−0.0105591	+	0.100463i
$77$	0.166233	−	0.511613i	0.0189440	−	0.0583037i
$78$	0.593165	−	1.82557i	0.0671627	−	0.206705i
$79$	0.784025	−	7.45950i	0.0882097	−	0.839260i	−0.857552	−	0.514398i	$-0.828016\pi$
$79$	0.784025	−	7.45950i	0.0882097	−	0.839260i	0.945761	−	0.324862i	$-0.105318\pi$
$80$	−0.669131	−	0.743145i	−0.0748111	−	0.0830861i
$81$	0.669131	−	0.743145i	0.0743478	−	0.0825716i
$82$	0.435745	+	4.14584i	0.0481200	+	0.457831i
$83$	−0.771873	−	0.164067i	−0.0847240	−	0.0180086i	0.165355	−	0.986234i	$-0.447123\pi$
$83$	−0.771873	−	0.164067i	−0.0847240	−	0.0180086i	−0.250079	+	0.968226i	$0.580456\pi$
$84$	−0.461080	+	0.205286i	−0.0503080	+	0.0223986i
$85$	2.06845	+	1.50282i	0.224355	+	0.163004i
$86$	−3.75453	−	1.67162i	−0.404861	−	0.180256i
$87$	−1.12103	−	1.94168i	−0.120187	−	0.208170i
$88$	0.532916	−	0.923038i	0.0568090	−	0.0983961i
$89$	4.82338	−	3.50439i	0.511277	−	0.371464i	−0.302031	−	0.953298i	$-0.597665\pi$
$89$	4.82338	−	3.50439i	0.511277	−	0.371464i	0.813308	+	0.581834i	$0.197665\pi$
$90$	0.978148	−	0.207912i	0.103106	−	0.0219158i
$91$	−0.299379	−	0.921395i	−0.0313835	−	0.0965884i
$92$	−4.04860			−0.422095
$93$	−2.77490	−	4.82700i	−0.287743	−	0.500537i
$94$	−9.70477			−1.00097
$95$	−0.272133	−	0.837538i	−0.0279202	−	0.0859296i
$96$	−0.978148	+	0.207912i	−0.0998318	+	0.0212199i
$97$	7.01736	−	5.09841i	0.712505	−	0.517665i	−0.171476	−	0.985188i	$-0.554854\pi$
$97$	7.01736	−	5.09841i	0.712505	−	0.517665i	0.883981	+	0.467523i	$0.154854\pi$
$98$	3.37263	−	5.84157i	0.340687	−	0.590088i
$99$	0.532916	+	0.923038i	0.0535601	+	0.0927688i
$100$	0.913545	+	0.406737i	0.0913545	+	0.0406737i
$101$	2.93695	+	2.13382i	0.292237	+	0.212323i	0.724237	−	0.689551i	$-0.242192\pi$
$101$	2.93695	+	2.13382i	0.292237	+	0.212323i	−0.432000	+	0.901874i	$0.642192\pi$
$102$	2.33571	−	1.03992i	0.231269	−	0.102968i
$103$	−3.59237	−	0.763582i	−0.353967	−	0.0752380i	0.0274966	−	0.999622i	$-0.491246\pi$
$103$	−3.59237	−	0.763582i	−0.353967	−	0.0752380i	−0.381463	+	0.924384i	$0.624580\pi$
$104$	−0.200645	−	1.90901i	−0.0196748	−	0.187193i
$105$	0.337720	−	0.375077i	0.0329581	−	0.0366037i
$106$	−0.673445	−	0.747937i	−0.0654108	−	0.0726460i
$107$	−1.81444	+	17.2632i	−0.175408	+	1.66890i	0.453378	+	0.891319i	$0.350219\pi$
$107$	−1.81444	+	17.2632i	−0.175408	+	1.66890i	−0.628786	+	0.777579i	$0.716448\pi$
$108$	0.309017	−	0.951057i	0.0297352	−	0.0915155i
$109$	1.87670	−	5.77590i	0.179756	−	0.553231i	−0.820063	−	0.572273i	$-0.806062\pi$
$109$	1.87670	−	5.77590i	0.179756	−	0.553231i	0.999819	+	0.0190421i	$0.00606165\pi$
$110$	−0.111410	+	1.05999i	−0.0106225	+	0.101066i
$111$	−6.41821	−	7.12815i	−0.609190	−	0.676574i
$112$	−0.337720	+	0.375077i	−0.0319116	+	0.0354414i
$113$	0.965814	+	9.18911i	0.0908562	+	0.864439i	0.941118	+	0.338078i	$0.109777\pi$
$113$	0.965814	+	9.18911i	0.0908562	+	0.864439i	−0.850262	+	0.526360i	$0.823556\pi$
$114$	−0.861395	−	0.183095i	−0.0806771	−	0.0171484i
$115$	3.69858	−	1.64671i	0.344894	−	0.153557i
$116$	−1.81387	−	1.31785i	−0.168413	−	0.122359i
$117$	1.75357	+	0.780740i	0.162118	+	0.0721794i
$118$	−4.81435	−	8.33870i	−0.443197	−	0.767640i
$119$	0.645215	−	1.11755i	0.0591468	−	0.102445i
$120$	0.809017	−	0.587785i	0.0738528	−	0.0536572i
$121$	9.64845	−	2.05084i	0.877132	−	0.186440i
$122$	3.48687	+	10.7315i	0.315686	+	0.971582i
$123$	−4.16867			−0.375877
$124$	−4.49831	−	3.28103i	−0.403960	−	0.294646i
$125$	−1.00000			−0.0894427
$126$	−0.155966	−	0.480013i	−0.0138945	−	0.0427629i
$127$	1.65331	−	0.351422i	0.146707	−	0.0311836i	−0.133973	−	0.990985i	$-0.542773\pi$
$127$	1.65331	−	0.351422i	0.146707	−	0.0311836i	0.280680	+	0.959801i	$0.409440\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	2.05492	−	3.55923i	0.180926	−	0.313372i
$130$	0.959760	+	1.66235i	0.0841766	+	0.145798i
$131$	3.48702	+	1.55252i	0.304662	+	0.135644i	0.553373	−	0.832933i	$-0.313340\pi$
$131$	3.48702	+	1.55252i	0.304662	+	0.135644i	−0.248711	+	0.968578i	$0.580007\pi$
$132$	0.862276	+	0.626480i	0.0750515	+	0.0545281i
$133$	−0.406046	+	0.180783i	−0.0352086	+	0.0156759i
$134$	2.22964	+	0.473924i	0.192611	+	0.0409408i
$135$	0.104528	+	0.994522i	0.00899638	+	0.0855948i
$136$	1.71080	−	1.90003i	0.146700	−	0.162927i
$137$	−0.100000	−	0.111061i	−0.00854358	−	0.00948861i	0.738858	−	0.673861i	$-0.235365\pi$
$137$	−0.100000	−	0.111061i	−0.00854358	−	0.00948861i	−0.747401	+	0.664373i	$0.768699\pi$
$138$	0.423194	−	4.02642i	0.0360246	−	0.342751i
$139$	3.37890	−	10.3992i	0.286595	−	0.882048i	−0.699321	−	0.714807i	$-0.746514\pi$
$139$	3.37890	−	10.3992i	0.286595	−	0.882048i	0.985916	−	0.167241i	$-0.0534857\pi$
$140$	0.155966	−	0.480013i	0.0131815	−	0.0405685i
$141$	1.01442	−	9.65161i	0.0854300	−	0.812812i
$142$	−5.98781	−	6.65014i	−0.502486	−	0.558068i
$143$	−1.36897	+	1.52039i	−0.114479	+	0.127141i
$144$	−0.104528	−	0.994522i	−0.00871071	−	0.0828768i
$145$	2.19307	+	0.466151i	0.182124	+	0.0387117i
$146$	−0.237379	+	0.105688i	−0.0196456	+	0.00874679i
$147$	5.45703	+	3.96477i	0.450088	+	0.327008i
$148$	−8.76261	−	3.90136i	−0.720282	−	0.320690i
$149$	−1.56358	−	2.70819i	−0.128093	−	0.221864i	0.794845	−	0.606813i	$-0.207552\pi$
$149$	−1.56358	−	2.70819i	−0.128093	−	0.221864i	−0.922938	+	0.384949i	$0.874219\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	13.4837	−	9.79650i	1.09729	−	0.797227i	0.116674	−	0.993170i	$-0.462777\pi$
$151$	13.4837	−	9.79650i	1.09729	−	0.797227i	0.980615	+	0.195943i	$0.0627767\pi$
$152$	−0.861395	+	0.183095i	−0.0698684	+	0.0148510i
$153$	0.790079	+	2.43161i	0.0638741	+	0.196584i
$154$	0.537942			0.0433486
$155$	5.44393	+	1.16775i	0.437267	+	0.0937956i
$156$	1.91952			0.153685
$157$	2.29856	+	7.07425i	0.183445	+	0.564586i	0.999918	−	0.0127974i	$-0.00407366\pi$
$157$	2.29856	+	7.07425i	0.183445	+	0.564586i	−0.816473	+	0.577384i	$0.804074\pi$
$158$	7.33669	−	1.55946i	0.583675	−	0.124064i
$159$	0.814233	−	0.591575i	0.0645729	−	0.0469150i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−1.02169	−	1.76963i	−0.0805208	−	0.139466i
$162$	0.913545	+	0.406737i	0.0717749	+	0.0319562i
$163$	5.06115	+	3.67714i	0.396420	+	0.288016i	0.768081	−	0.640352i	$-0.221212\pi$
$163$	5.06115	+	3.67714i	0.396420	+	0.288016i	−0.371661	+	0.928368i	$0.621212\pi$
$164$	−3.80827	+	1.69555i	−0.297376	+	0.132400i
$165$	−1.04254	−	0.221599i	−0.0811617	−	0.0172515i
$166$	−0.0824852	−	0.784794i	−0.00640209	−	0.0609118i
$167$	5.94465	−	6.60220i	0.460011	−	0.510894i	−0.467856	−	0.883804i	$-0.654974\pi$
$167$	5.94465	−	6.60220i	0.460011	−	0.510894i	0.927867	+	0.372911i	$0.121640\pi$
$168$	−0.337720	−	0.375077i	−0.0260557	−	0.0289378i
$169$	0.973729	−	9.26441i	0.0749022	−	0.712647i
$170$	−0.790079	+	2.43161i	−0.0605963	+	0.186496i
$171$	0.272133	−	0.837538i	0.0208105	−	0.0640481i
$172$	0.429595	−	4.08733i	0.0327563	−	0.311656i
$173$	−10.3140	−	11.4548i	−0.784158	−	0.870896i	0.210125	−	0.977675i	$-0.432613\pi$
$173$	−10.3140	−	11.4548i	−0.784158	−	0.870896i	−0.994283	+	0.106779i	$0.965946\pi$
$174$	1.50023	−	1.66618i	0.113732	−	0.126313i
$175$	0.0527571	+	0.501950i	0.00398806	+	0.0379439i
$176$	1.04254	+	0.221599i	0.0785845	+	0.0167036i
$177$	8.79626	−	3.91635i	0.661167	−	0.294371i
$178$	4.82338	+	3.50439i	0.361527	+	0.262665i
$179$	−11.7488	−	5.23088i	−0.878143	−	0.390974i	−0.0823932	−	0.996600i	$-0.526256\pi$
$179$	−11.7488	−	5.23088i	−0.878143	−	0.390974i	−0.795750	+	0.605625i	$0.792923\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	5.48915	−	9.50749i	0.408006	−	0.706686i	−0.586661	−	0.809833i	$-0.699558\pi$
$181$	5.48915	−	9.50749i	0.408006	−	0.706686i	0.994666	+	0.103147i	$0.0328911\pi$
$182$	0.783785	−	0.569453i	0.0580980	−	0.0422107i
$183$	−11.0372	+	2.34602i	−0.815891	+	0.173423i
$184$	−1.25109	−	3.85044i	−0.0922312	−	0.283859i
$185$	9.59187			0.705208
$186$	3.73326	−	4.13071i	0.273736	−	0.302878i
$187$	−2.72506			−0.199276
$188$	−2.99894	−	9.22979i	−0.218720	−	0.673151i
$189$	0.493686	−	0.104936i	0.0359104	−	0.00763299i
$190$	0.712452	−	0.517627i	0.0516867	−	0.0375526i
$191$	−2.90351	+	5.02903i	−0.210091	+	0.363888i	−0.951743	−	0.306897i	$-0.900709\pi$
$191$	−2.90351	+	5.02903i	−0.210091	+	0.363888i	0.741652	+	0.670785i	$0.234043\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	9.40849	+	4.18893i	0.677238	+	0.301526i	0.716382	−	0.697708i	$-0.245797\pi$
$193$	9.40849	+	4.18893i	0.677238	+	0.301526i	−0.0391447	+	0.999234i	$0.512463\pi$
$194$	7.01736	+	5.09841i	0.503817	+	0.366044i
$195$	−1.75357	+	0.780740i	−0.125576	+	0.0559099i
$196$	6.59786	+	1.40242i	0.471276	+	0.100173i
$197$	−0.160245	−	1.52463i	−0.0114170	−	0.108626i	0.987329	−	0.158685i	$-0.0507255\pi$
$197$	−0.160245	−	1.52463i	−0.0114170	−	0.108626i	−0.998746	+	0.0500596i	$0.984059\pi$
$198$	−0.713181	+	0.792068i	−0.0506836	+	0.0562898i
$199$	−10.7569	−	11.9467i	−0.762535	−	0.846881i	0.229439	−	0.973323i	$-0.426311\pi$
$199$	−10.7569	−	11.9467i	−0.762535	−	0.846881i	−0.991974	+	0.126442i	$0.959644\pi$
$200$	−0.104528	+	0.994522i	−0.00739128	+	0.0703233i
$201$	−0.704389	+	2.16789i	−0.0496837	+	0.152911i
$202$	−1.12181	+	3.45259i	−0.0789305	+	0.242923i
$203$	0.118285	−	1.12540i	0.00830196	−	0.0789879i
$204$	1.71080	+	1.90003i	0.119780	+	0.133029i
$205$	2.78939	−	3.09793i	0.194819	−	0.216369i
$206$	−0.383894	−	3.65251i	−0.0267472	−	0.254482i
$207$	3.96013	+	0.841751i	0.275248	+	0.0585057i
$208$	1.75357	−	0.780740i	0.121588	−	0.0541345i
$209$	0.759355	+	0.551703i	0.0525257	+	0.0381621i
$210$	0.461080	+	0.205286i	0.0318176	+	0.0141661i
$211$	3.95374	+	6.84809i	0.272187	+	0.471442i	0.969422	−	0.245401i	$-0.0789197\pi$
$211$	3.95374	+	6.84809i	0.272187	+	0.471442i	−0.697235	+	0.716843i	$0.745586\pi$
$212$	0.503224	−	0.871609i	0.0345616	−	0.0598624i
$213$	7.23961	−	5.25988i	0.496050	−	0.360401i
$214$	−16.9790	+	3.60899i	−1.16066	+	0.246706i
$215$	1.27001	+	3.90869i	0.0866140	+	0.266570i
$216$	1.00000			0.0680414
$217$	0.298945	−	2.79419i	0.0202937	−	0.189682i
$218$	6.07314			0.411325
$219$	−0.0802960	−	0.247126i	−0.00542590	−	0.0166992i
$220$	−1.04254	+	0.221599i	−0.0702881	+	0.0149402i
$221$	−3.97044	+	2.88469i	−0.267081	+	0.194045i
$222$	4.79593	−	8.30680i	0.321882	−	0.557516i
$223$	−10.1218	−	17.5315i	−0.677806	−	1.17399i	−0.975640	−	0.219376i	$-0.929598\pi$
$223$	−10.1218	−	17.5315i	−0.677806	−	1.17399i	0.297835	−	0.954617i	$-0.403736\pi$
$224$	−0.461080	−	0.205286i	−0.0308072	−	0.0137163i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	−8.44091	+	3.75813i	−0.561481	+	0.249987i
$227$	21.5102	+	4.57213i	1.42768	+	0.303463i	0.855984	−	0.517002i	$-0.172952\pi$
$227$	21.5102	+	4.57213i	1.42768	+	0.303463i	0.571697	+	0.820465i	$0.306285\pi$
$228$	−0.0920519	−	0.875815i	−0.00609629	−	0.0580023i
$229$	6.02740	−	6.69411i	0.398302	−	0.442359i	−0.510316	−	0.859987i	$-0.670472\pi$
$229$	6.02740	−	6.69411i	0.398302	−	0.442359i	0.908618	+	0.417628i	$0.137138\pi$
$230$	2.70904	+	3.00869i	0.178629	+	0.198387i
$231$	−0.0562302	+	0.534995i	−0.00369968	+	0.0352001i
$232$	0.692835	−	2.13233i	0.0454869	−	0.139994i
$233$	−2.40151	+	7.39110i	−0.157328	+	0.484207i	−0.998389	−	0.0567334i	$-0.981931\pi$
$233$	−2.40151	+	7.39110i	−0.157328	+	0.484207i	0.841061	+	0.540940i	$0.181931\pi$
$234$	−0.200645	+	1.90901i	−0.0131165	+	0.124796i
$235$	6.49376	+	7.21205i	0.423606	+	0.470462i
$236$	6.44286	−	7.15552i	0.419394	−	0.465785i
$237$	0.784025	+	7.45950i	0.0509279	+	0.484547i
$238$	1.26223	+	0.268296i	0.0818183	+	0.0173910i
$239$	2.29146	−	1.02022i	0.148222	−	0.0659928i	−0.331285	−	0.943531i	$-0.607482\pi$
$239$	2.29146	−	1.02022i	0.148222	−	0.0659928i	0.479507	+	0.877538i	$0.340815\pi$
$240$	0.809017	+	0.587785i	0.0522218	+	0.0379414i
$241$	−13.9276	−	6.20099i	−0.897158	−	0.399441i	−0.0942538	−	0.995548i	$-0.530047\pi$
$241$	−13.9276	−	6.20099i	−0.897158	−	0.399441i	−0.802905	+	0.596108i	$0.796713\pi$
$242$	4.93200	+	8.54248i	0.317041	+	0.549131i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−9.12874	+	6.63242i	−0.584408	+	0.424597i
$245$	−6.59786	+	1.40242i	−0.421522	+	0.0895973i
$246$	−1.28819	−	3.96464i	−0.0821320	−	0.252776i
$247$	1.69041			0.107558
$248$	1.73039	−	5.29204i	0.109880	−	0.336045i
$249$	0.789117			0.0500082
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−21.6710	+	4.60630i	−1.36786	+	0.290747i	−0.832569	−	0.553921i	$-0.813131\pi$
$251$	−21.6710	+	4.60630i	−1.36786	+	0.290747i	−0.535289	+	0.844669i	$0.679797\pi$
$252$	0.408323	−	0.296664i	0.0257220	−	0.0186881i
$253$	−2.15756	+	3.73701i	−0.135645	+	0.234944i
$254$	0.845122	+	1.46379i	0.0530277	+	0.0918466i
$255$	−2.33571	−	1.03992i	−0.146268	−	0.0651225i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	12.5156	−	5.57232i	0.780704	−	0.347592i	0.0226163	−	0.999744i	$-0.492800\pi$
$257$	12.5156	−	5.57232i	0.780704	−	0.347592i	0.758088	+	0.652152i	$0.226134\pi$
$258$	4.02003	+	0.854484i	0.250276	+	0.0531978i
$259$	−0.506039	−	4.81464i	−0.0314438	−	0.299167i
$260$	−1.28441	+	1.42648i	−0.0796557	+	0.0884667i
$261$	1.50023	+	1.66618i	0.0928621	+	0.103134i
$262$	−0.398987	+	3.79611i	−0.0246495	+	0.234524i
$263$	−4.56839	+	14.0601i	−0.281699	+	0.866981i	0.705669	+	0.708541i	$0.250646\pi$
$263$	−4.56839	+	14.0601i	−0.281699	+	0.866981i	−0.987369	+	0.158440i	$0.949354\pi$
$264$	−0.329360	+	1.01367i	−0.0202707	+	0.0623869i
$265$	−0.105202	+	1.00093i	−0.00646254	+	0.0614869i
$266$	−0.297410	−	0.330307i	−0.0182354	−	0.0202524i
$267$	−3.98937	+	4.43064i	−0.244145	+	0.271151i
$268$	0.238267	+	2.26696i	0.0145545	+	0.138477i
$269$	−2.10674	−	0.447800i	−0.128450	−	0.0273029i	0.143238	−	0.989688i	$-0.454249\pi$
$269$	−2.10674	−	0.447800i	−0.128450	−	0.0273029i	−0.271688	+	0.962385i	$0.587582\pi$
$270$	−0.913545	+	0.406737i	−0.0555966	+	0.0247532i
$271$	13.2400	+	9.61939i	0.804270	+	0.584336i	0.912164	−	0.409826i	$-0.134411\pi$
$271$	13.2400	+	9.61939i	0.804270	+	0.584336i	−0.107894	+	0.994162i	$0.534411\pi$
$272$	2.33571	+	1.03992i	0.141623	+	0.0630546i
$273$	0.484406	+	0.839016i	0.0293176	+	0.0507795i
$274$	0.0747238	−	0.129426i	0.00451423	−	0.00781888i
$275$	0.862276	−	0.626480i	0.0519972	−	0.0377782i
$276$	3.96013	−	0.841751i	0.238372	−	0.0506674i
$277$	−3.22735	−	9.93276i	−0.193913	−	0.596801i	−0.999988	−	0.00498810i	$-0.998412\pi$
$277$	−3.22735	−	9.93276i	−0.193913	−	0.596801i	0.806075	−	0.591813i	$-0.201588\pi$
$278$	10.9344			0.655799
$279$	3.71785	+	4.14459i	0.222582	+	0.248130i
$280$	0.504715			0.0301625
$281$	−6.79900	−	20.9252i	−0.405595	−	1.24829i	−0.920398	−	0.390983i	$-0.872135\pi$
$281$	−6.79900	−	20.9252i	−0.405595	−	1.24829i	0.514803	−	0.857308i	$-0.327865\pi$
$282$	9.49270	−	2.01774i	0.565282	−	0.120154i
$283$	−0.743807	+	0.540407i	−0.0442147	+	0.0321239i	−0.609673	−	0.792653i	$-0.708699\pi$
$283$	−0.743807	+	0.540407i	−0.0442147	+	0.0321239i	0.565458	+	0.824777i	$0.308699\pi$
$284$	4.47432	−	7.74976i	0.265502	−	0.459863i
$285$	0.440320	+	0.762656i	0.0260823	+	0.0451759i
$286$	−1.86901	−	0.832137i	−0.110517	−	0.0492053i
$287$	−1.70217	−	1.23670i	−0.100476	−	0.0729999i
$288$	0.913545	−	0.406737i	0.0538312	−	0.0239672i
$289$	10.2344	+	2.17539i	0.602023	+	0.127964i
$290$	0.234359	+	2.22978i	0.0137621	+	0.130937i
$291$	−5.80399	+	6.44599i	−0.340236	+	0.377870i
$292$	−0.173869	−	0.193101i	−0.0101749	−	0.0113004i
$293$	−0.633195	+	6.02444i	−0.0369916	+	0.351952i	0.960333	+	0.278855i	$0.0899549\pi$
$293$	−0.633195	+	6.02444i	−0.0369916	+	0.351952i	−0.997325	+	0.0730968i	$0.976712\pi$
$294$	−2.08440	+	6.41513i	−0.121565	+	0.374138i
$295$	−2.97543	+	9.15744i	−0.173236	+	0.533167i
$296$	1.00262	−	9.53932i	0.0582763	−	0.554462i
$297$	−0.713181	−	0.792068i	−0.0413829	−	0.0459604i
$298$	2.09247	−	2.32393i	0.121214	−	0.134621i
$299$	0.812329	+	7.72879i	0.0469782	+	0.446968i
$300$	−0.978148	−	0.207912i	−0.0564734	−	0.0120038i
$301$	1.89497	−	0.843693i	0.109224	−	0.0486297i
$302$	13.4837	+	9.79650i	0.775901	+	0.563725i
$303$	−3.31641	−	1.47656i	−0.190523	−	0.0848263i
$304$	−0.440320	−	0.762656i	−0.0252541	−	0.0437413i
$305$	5.64187	−	9.77201i	0.323053	−	0.559544i
$306$	−2.06845	+	1.50282i	−0.118246	+	0.0859105i
$307$	−28.5743	+	6.07366i	−1.63082	+	0.346642i	−0.930246	−	0.366936i	$-0.880407\pi$
$307$	−28.5743	+	6.07366i	−1.63082	+	0.346642i	−0.700576	+	0.713578i	$0.747073\pi$
$308$	0.166233	+	0.511613i	0.00947201	+	0.0291519i
$309$	3.67263			0.208928
$310$	0.571674	+	5.53834i	0.0324689	+	0.314556i
$311$	−16.6755			−0.945579			−0.472789	−	0.881175i	$-0.656753\pi$
$311$	−16.6755			−0.945579			−0.472789	+	0.881175i	$0.656753\pi$
$312$	0.593165	+	1.82557i	0.0335813	+	0.103353i
$313$	−27.0192	+	5.74311i	−1.52722	+	0.324620i	−0.893542	−	0.448981i	$-0.851787\pi$
$313$	−27.0192	+	5.74311i	−1.52722	+	0.324620i	−0.633674	+	0.773600i	$0.718454\pi$
$314$	−6.01771	+	4.37212i	−0.339599	+	0.246733i
$315$	−0.252358	+	0.437096i	−0.0142187	+	0.0246276i
$316$	3.75030	+	6.49570i	0.210971	+	0.365412i
$317$	6.52737	+	2.90617i	0.366614	+	0.163227i	0.581771	−	0.813352i	$-0.302360\pi$
$317$	6.52737	+	2.90617i	0.366614	+	0.163227i	−0.215158	+	0.976579i	$0.569027\pi$
$318$	0.814233	+	0.591575i	0.0456599	+	0.0331739i
$319$	−2.18306	+	0.971963i	−0.122228	+	0.0544195i
$320$	0.978148	+	0.207912i	0.0546801	+	0.0116226i
$321$	−1.81444	−	17.2632i	−0.101272	−	0.963538i
$322$	1.36729	−	1.51853i	0.0761963	−	0.0846246i
$323$	1.50660	+	1.67325i	0.0838293	+	0.0931019i
$324$	−0.104528	+	0.994522i	−0.00580714	+	0.0552512i
$325$	0.593165	−	1.82557i	0.0329029	−	0.101265i
$326$	−1.93319	+	5.94974i	−0.107069	+	0.329526i
$327$	−0.634816	+	6.03987i	−0.0351054	+	0.334006i
$328$	−2.78939	−	3.09793i	−0.154018	−	0.171054i
$329$	3.27750	−	3.64003i	0.180694	−	0.200682i
$330$	−0.111410	−	1.05999i	−0.00613291	−	0.0583507i
$331$	8.59690	+	1.82733i	0.472528	+	0.100439i	0.438020	−	0.898965i	$-0.355680\pi$
$331$	8.59690	+	1.82733i	0.472528	+	0.100439i	0.0345087	+	0.999404i	$0.489013\pi$
$332$	0.720894	−	0.320963i	0.0395642	−	0.0176151i
$333$	7.75998	+	5.63796i	0.425244	+	0.308958i
$334$	8.11606	+	3.61350i	0.444091	+	0.197722i
$335$	−1.13972	−	1.97406i	−0.0622698	−	0.107854i
$336$	0.252358	−	0.437096i	0.0137672	−	0.0238456i
$337$	−6.37269	+	4.63003i	−0.347143	+	0.252214i	−0.747669	−	0.664071i	$-0.768827\pi$
$337$	−6.37269	+	4.63003i	−0.347143	+	0.252214i	0.400527	+	0.916285i	$0.368827\pi$
$338$	9.11187	−	1.93679i	0.495621	−	0.105347i
$339$	−2.85523	−	8.78750i	−0.155075	−	0.477271i
$340$	−2.55675			−0.138659
$341$	−5.42574	+	2.40360i	−0.293820	+	0.130162i
$342$	0.880640			0.0476195
$343$	2.14379	+	6.59790i	0.115754	+	0.356253i
$344$	4.02003	−	0.854484i	0.216745	−	0.0460707i
$345$	−3.27538	+	2.37971i	−0.176341	+	0.128119i
$346$	7.70701	−	13.3489i	0.414331	−	0.717643i
$347$	3.29994	+	5.71567i	0.177150	+	0.306833i	0.940903	−	0.338675i	$-0.109979\pi$
$347$	3.29994	+	5.71567i	0.177150	+	0.306833i	−0.763753	+	0.645509i	$0.776645\pi$
$348$	2.04823	+	0.911929i	0.109796	+	0.0488845i
$349$	−11.4181	−	8.29577i	−0.611199	−	0.444062i	0.238637	−	0.971109i	$-0.423299\pi$
$349$	−11.4181	−	8.29577i	−0.611199	−	0.444062i	−0.849837	+	0.527046i	$0.823299\pi$
$350$	−0.461080	+	0.205286i	−0.0246458	+	0.0109730i
$351$	−1.87757	−	0.399091i	−0.100218	−	0.0213019i
$352$	0.111410	+	1.05999i	0.00593816	+	0.0564978i
$353$	16.8455	−	18.7088i	0.896596	−	0.995771i	−0.103403	−	0.994639i	$-0.532973\pi$
$353$	16.8455	−	18.7088i	0.896596	−	0.995771i	0.999999	−	0.00113111i	$-0.000360043\pi$
$354$	6.44286	+	7.15552i	0.342434	+	0.380312i
$355$	−0.935388	+	8.89963i	−0.0496453	+	0.472343i
$356$	−1.84237	+	5.67022i	−0.0976452	+	0.300521i
$357$	−0.398765	+	1.22727i	−0.0211049	+	0.0649541i
$358$	1.34430	−	12.7902i	0.0710485	−	0.675981i
$359$	−4.81254	−	5.34486i	−0.253996	−	0.282091i	0.602639	−	0.798014i	$-0.294116\pi$
$359$	−4.81254	−	5.34486i	−0.253996	−	0.282091i	−0.856635	+	0.515923i	$0.827449\pi$
$360$	−0.669131	+	0.743145i	−0.0352663	+	0.0391672i
$361$	1.90498	+	18.1246i	0.100262	+	0.953928i
$362$	10.7384	+	2.28252i	0.564398	+	0.119966i
$363$	−9.01121	+	4.01205i	−0.472966	+	0.210578i
$364$	0.783785	+	0.569453i	0.0410815	+	0.0298475i
$365$	0.237379	+	0.105688i	0.0124250	+	0.00553195i
$366$	−5.64187	−	9.77201i	−0.294905	−	0.510791i
$367$	7.50288	−	12.9954i	0.391647	−	0.678353i	−0.601020	−	0.799234i	$-0.705239\pi$
$367$	7.50288	−	12.9954i	0.391647	−	0.678353i	0.992667	+	0.120881i	$0.0385720\pi$
$368$	3.27538	−	2.37971i	0.170741	−	0.124051i
$369$	4.07758	−	0.866716i	0.212270	−	0.0451194i
$370$	2.96405	+	9.12241i	0.154094	+	0.474251i
$371$	0.507970			0.0263725
$372$	5.08218	+	2.27408i	0.263499	+	0.117906i
$373$	−16.9266			−0.876428			−0.438214	−	0.898871i	$-0.644389\pi$
$373$	−16.9266			−0.876428			−0.438214	+	0.898871i	$0.644389\pi$
$374$	−0.842091	−	2.59169i	−0.0435435	−	0.134013i
$375$	0.978148	−	0.207912i	0.0505113	−	0.0107365i
$376$	7.85133	−	5.70432i	0.404901	−	0.294178i
$377$	−2.15184	+	3.72710i	−0.110826	+	0.191955i
$378$	0.252358	+	0.437096i	0.0129799	+	0.0224818i
$379$	−17.9314	−	7.98355i	−0.921072	−	0.410088i	−0.109264	−	0.994013i	$-0.534849\pi$
$379$	−17.9314	−	7.98355i	−0.921072	−	0.410088i	−0.811807	+	0.583925i	$0.801516\pi$
$380$	0.712452	+	0.517627i	0.0365480	+	0.0265537i
$381$	−1.54412	+	0.687484i	−0.0791074	+	0.0352209i
$382$	−5.68013	−	1.20735i	−0.290621	−	0.0617734i
$383$	−2.36503	−	22.5017i	−0.120847	−	1.14978i	−0.871949	−	0.489598i	$-0.837144\pi$
$383$	−2.36503	−	22.5017i	−0.120847	−	1.14978i	0.751101	−	0.660187i	$-0.229523\pi$
$384$	0.669131	−	0.743145i	0.0341464	−	0.0379235i
$385$	−0.359953	−	0.399769i	−0.0183449	−	0.0203741i
$386$	−1.07653	+	10.2425i	−0.0547937	+	0.521327i
$387$	−1.27001	+	3.90869i	−0.0645582	+	0.198690i
$388$	−2.68039	+	8.24940i	−0.136076	+	0.418800i
$389$	0.269023	−	2.55959i	0.0136400	−	0.129776i	−0.985583	−	0.169194i	$-0.945884\pi$
$389$	0.269023	−	2.55959i	0.0136400	−	0.129776i	0.999223	+	0.0394176i	$0.0125503\pi$
$390$	−1.28441	−	1.42648i	−0.0650386	−	0.0722327i
$391$	−6.92634	+	7.69247i	−0.350280	+	0.389025i
$392$	0.705072	+	6.70831i	0.0356115	+	0.338821i
$393$	−3.73361	−	0.793602i	−0.188335	−	0.0400319i
$394$	1.40049	−	0.623540i	0.0705559	−	0.0314135i
$395$	−6.06811	−	4.40874i	−0.305320	−	0.221828i
$396$	−0.973686	−	0.433513i	−0.0489296	−	0.0217848i
$397$	3.21063	+	5.56097i	0.161137	+	0.279097i	0.935277	−	0.353918i	$-0.115151\pi$
$397$	3.21063	+	5.56097i	0.161137	+	0.279097i	−0.774140	+	0.633015i	$0.781817\pi$
$398$	8.03795	−	13.9221i	0.402906	−	0.697854i
$399$	0.359586	−	0.261254i	0.0180018	−	0.0130791i
$400$	−0.978148	+	0.207912i	−0.0489074	+	0.0103956i
$401$	−3.26204	−	10.0395i	−0.162899	−	0.501351i	0.835977	−	0.548765i	$-0.184902\pi$
$401$	−3.26204	−	10.0395i	−0.162899	−	0.501351i	−0.998875	+	0.0474144i	$0.984902\pi$
$402$	−2.27945			−0.113689
$403$	−5.36095	+	9.24562i	−0.267048	+	0.460557i
$404$	−3.63027			−0.180612
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	1.10687	−	0.235274i	0.0549333	−	0.0116764i
$407$	−8.27084	+	6.00912i	−0.409970	+	0.297861i
$408$	−1.27837	+	2.21421i	−0.0632890	+	0.109620i
$409$	9.63076	+	16.6810i	0.476210	+	0.824820i	0.999628	−	0.0272555i	$-0.00867678\pi$
$409$	9.63076	+	16.6810i	0.476210	+	0.824820i	−0.523418	+	0.852076i	$0.675343\pi$
$410$	3.80827	+	1.69555i	0.188077	+	0.0837374i
$411$	0.120906	+	0.0878432i	0.00596384	+	0.00433298i
$412$	3.35511	−	1.49379i	0.165294	−	0.0735938i
$413$	4.75356	+	1.01040i	0.233907	+	0.0497185i
$414$	0.423194	+	4.02642i	0.0207988	+	0.197888i
$415$	−0.528022	+	0.586428i	−0.0259196	+	0.0287866i
$416$	1.28441	+	1.42648i	0.0629734	+	0.0699390i
$417$	−1.14295	+	10.8745i	−0.0559706	+	0.532525i
$418$	−0.290048	+	0.892675i	−0.0141867	+	0.0436622i
$419$	0.868628	−	2.67336i	0.0424353	−	0.130602i	−0.927594	−	0.373589i	$-0.878127\pi$
$419$	0.868628	−	2.67336i	0.0424353	−	0.130602i	0.970030	+	0.242987i	$0.0781271\pi$
$420$	−0.0527571	+	0.501950i	−0.00257428	+	0.0244927i
$421$	−3.33125	−	3.69973i	−0.162355	−	0.180314i	0.656478	−	0.754345i	$-0.272045\pi$
$421$	−3.33125	−	3.69973i	−0.162355	−	0.180314i	−0.818833	+	0.574031i	$0.805379\pi$
$422$	−5.29114	+	5.87641i	−0.257569	+	0.286059i
$423$	1.01442	+	9.65161i	0.0493230	+	0.469277i
$424$	0.984455	+	0.209252i	0.0478093	+	0.0101622i
$425$	2.33571	−	1.03992i	0.113298	−	0.0504437i
$426$	7.23961	+	5.25988i	0.350760	+	0.254842i
$427$	−5.20271	−	2.31640i	−0.251777	−	0.112098i
$428$	−8.67915	−	15.0327i	−0.419522	−	0.726634i
$429$	1.02294	−	1.77179i	0.0493882	−	0.0855428i
$430$	−3.32493	+	2.41570i	−0.160342	+	0.116496i
$431$	−3.70289	+	0.787073i	−0.178362	+	0.0379120i	−0.296227	−	0.955118i	$-0.595728\pi$
$431$	−3.70289	+	0.787073i	−0.178362	+	0.0379120i	0.117865	+	0.993030i	$0.462395\pi$
$432$	0.309017	+	0.951057i	0.0148676	+	0.0457577i
$433$	14.1918			0.682015			0.341008	−	0.940061i	$-0.389232\pi$
$433$	14.1918			0.682015			0.341008	+	0.940061i	$0.389232\pi$
$434$	2.74981	−	0.579139i	0.131995	−	0.0277996i
$435$	−2.24206			−0.107499
$436$	1.87670	+	5.77590i	0.0898779	+	0.276616i
$437$	3.48744	−	0.741279i	0.166827	−	0.0354602i
$438$	0.210218	−	0.152732i	0.0100446	−	0.00729782i
$439$	12.3687	−	21.4232i	0.590325	−	1.02247i	−0.403863	−	0.914819i	$-0.632333\pi$
$439$	12.3687	−	21.4232i	0.590325	−	1.02247i	0.994188	−	0.107654i	$-0.0343338\pi$
$440$	−0.532916	−	0.923038i	−0.0254058	−	0.0440041i
$441$	−6.16210	−	2.74355i	−0.293434	−	0.130645i
$442$	−3.97044	−	2.88469i	−0.188855	−	0.137211i
$443$	−1.13462	+	0.505165i	−0.0539073	+	0.0240011i	−0.433513	−	0.901147i	$-0.642726\pi$
$443$	−1.13462	+	0.505165i	−0.0539073	+	0.0240011i	0.379606	+	0.925148i	$0.376060\pi$
$444$	9.38226	+	1.99426i	0.445262	+	0.0946435i
$445$	−0.623201	−	5.92936i	−0.0295426	−	0.281079i
$446$	13.5456	−	15.0439i	0.641403	−	0.712350i
$447$	2.09247	+	2.32393i	0.0989705	+	0.109918i
$448$	0.0527571	−	0.501950i	0.00249254	−	0.0237149i
$449$	−4.62447	+	14.2327i	−0.218242	+	0.671681i	0.780665	+	0.624950i	$0.214880\pi$
$449$	−4.62447	+	14.2327i	−0.218242	+	0.671681i	−0.998907	+	0.0467313i	$0.985120\pi$
$450$	0.309017	−	0.951057i	0.0145672	−	0.0448332i
$451$	−0.464431	+	4.41877i	−0.0218692	+	0.208072i
$452$	−6.18258	−	6.86645i	−0.290804	−	0.322971i
$453$	−11.1523	+	12.3858i	−0.523979	+	0.581938i
$454$	2.29866	+	21.8703i	0.107881	+	1.02642i
$455$	−0.947641	−	0.201427i	−0.0444261	−	0.00944306i
$456$	0.804504	−	0.358188i	0.0376744	−	0.0167737i
$457$	−5.16778	−	3.75462i	−0.241739	−	0.175633i	0.460319	−	0.887754i	$-0.347735\pi$
$457$	−5.16778	−	3.75462i	−0.241739	−	0.175633i	−0.702058	+	0.712120i	$0.747735\pi$
$458$	8.22904	+	3.66381i	0.384518	+	0.171198i
$459$	−1.27837	−	2.21421i	−0.0596694	−	0.103350i
$460$	−2.02430	+	3.50619i	−0.0943834	+	0.163477i
$461$	−25.5244	+	18.5446i	−1.18879	+	0.863706i	−0.993136	−	0.116967i	$-0.962683\pi$
$461$	−25.5244	+	18.5446i	−1.18879	+	0.863706i	−0.195653	+	0.980673i	$0.562683\pi$
$462$	−0.526186	+	0.111844i	−0.0244804	+	0.00520347i
$463$	−2.05258	−	6.31720i	−0.0953916	−	0.293585i	0.891964	−	0.452107i	$-0.149327\pi$
$463$	−2.05258	−	6.31720i	−0.0953916	−	0.293585i	−0.987356	+	0.158521i	$0.949327\pi$
$464$	2.24206			0.104085
$465$	−5.56775	−	0.0103712i	−0.258198	−	0.000480954i
$466$	−7.77146			−0.360006
$467$	−1.84412	−	5.67563i	−0.0853358	−	0.262637i	0.899279	−	0.437375i	$-0.144092\pi$
$467$	−1.84412	−	5.67563i	−0.0853358	−	0.262637i	−0.984615	+	0.174739i	$0.944092\pi$
$468$	−1.87757	+	0.399091i	−0.0867909	+	0.0184480i
$469$	−0.930752	+	0.676231i	−0.0429782	+	0.0312255i
$470$	−4.85239	+	8.40458i	−0.223824	+	0.387674i
$471$	−3.71915	−	6.44176i	−0.171369	−	0.296821i
$472$	8.79626	+	3.91635i	0.404881	+	0.180264i
$473$	−3.54382	−	2.57473i	−0.162945	−	0.118386i
$474$	−6.85213	+	3.05077i	−0.314729	+	0.140126i
$475$	−0.861395	−	0.183095i	−0.0395235	−	0.00840099i
$476$	0.134887	+	1.28336i	0.00618252	+	0.0588228i
$477$	−0.673445	+	0.747937i	−0.0308349	+	0.0342457i
$478$	1.67839	+	1.86404i	0.0767678	+	0.0852593i
$479$	0.780743	−	7.42827i	0.0356730	−	0.339406i	−0.962100	−	0.272699i	$-0.912084\pi$
$479$	0.780743	−	7.42827i	0.0356730	−	0.339406i	0.997773	−	0.0667078i	$-0.0212495\pi$
$480$	−0.309017	+	0.951057i	−0.0141046	+	0.0434096i
$481$	−5.68956	+	17.5107i	−0.259421	+	0.798417i
$482$	1.59361	−	15.1622i	0.0725870	−	0.690619i
$483$	1.36729	+	1.51853i	0.0622140	+	0.0690957i
$484$	−6.60031	+	7.33038i	−0.300014	+	0.333199i
$485$	−0.906673	−	8.62641i	−0.0411699	−	0.391705i
$486$	−0.978148	−	0.207912i	−0.0443697	−	0.00943107i
$487$	13.4318	−	5.98020i	0.608651	−	0.270989i	−0.0791794	−	0.996860i	$-0.525230\pi$
$487$	13.4318	−	5.98020i	0.608651	−	0.270989i	0.687830	+	0.725872i	$0.258563\pi$
$488$	−9.12874	−	6.63242i	−0.413239	−	0.300235i
$489$	−5.71508	−	2.54452i	−0.258445	−	0.115067i
$490$	−3.37263	−	5.84157i	−0.152360	−	0.263895i
$491$	−15.9787	+	27.6759i	−0.721109	+	1.24900i	0.239447	+	0.970909i	$0.423034\pi$
$491$	−15.9787	+	27.6759i	−0.721109	+	1.24900i	−0.960556	+	0.278087i	$0.910299\pi$
$492$	3.37253	−	2.45028i	0.152045	−	0.110467i
$493$	−5.60712	+	1.19183i	−0.252532	+	0.0536774i
$494$	0.522364	+	1.60767i	0.0235023	+	0.0723326i
$495$	1.06583			0.0479056
$496$	5.56775	+	0.0103712i	0.250000	+	0.000465682i
$497$	4.51652			0.202594
$498$	0.243850	+	0.750495i	0.0109272	+	0.0336305i
$499$	−18.1957	+	3.86762i	−0.814553	+	0.173138i	−0.596308	−	0.802756i	$-0.703366\pi$
$499$	−18.1957	+	3.86762i	−0.814553	+	0.173138i	−0.218244	+	0.975894i	$0.570033\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	−4.44207	+	7.69389i	−0.198457	+	0.343738i
$502$	−11.0775	−	19.1869i	−0.494415	−	0.856352i
$503$	−23.6615	−	10.5348i	−1.05501	−	0.469723i	−0.195430	−	0.980718i	$-0.562610\pi$
$503$	−23.6615	−	10.5348i	−1.05501	−	0.469723i	−0.859584	+	0.510995i	$0.829277\pi$
$504$	0.408323	+	0.296664i	0.0181882	+	0.0132145i
$505$	3.31641	−	1.47656i	0.147578	−	0.0657062i
$506$	−4.22083	−	0.897165i	−0.187639	−	0.0398838i
$507$	0.973729	+	9.26441i	0.0432448	+	0.411447i
$508$	−1.13099	+	1.25610i	−0.0501798	+	0.0557303i
$509$	13.4069	+	14.8899i	0.594250	+	0.659981i	0.962986	−	0.269553i	$-0.0868759\pi$
$509$	13.4069	+	14.8899i	0.594250	+	0.659981i	−0.368736	+	0.929534i	$0.620209\pi$
$510$	0.267253	−	2.54274i	0.0118342	−	0.112595i
$511$	0.0405266	−	0.124728i	0.00179279	−	0.00551765i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−0.0920519	+	0.875815i	−0.00406419	+	0.0386682i
$514$	9.16714	+	10.1811i	0.404345	+	0.449071i
$515$	−2.45747	+	2.72929i	−0.108289	+	0.120267i
$516$	0.429595	+	4.08733i	0.0189119	+	0.179934i
$517$	−10.1176	−	2.15057i	−0.444973	−	0.0945818i
$518$	4.42262	−	1.96908i	0.194319	−	0.0865163i
$519$	12.4702	+	9.06013i	0.547381	+	0.397696i
$520$	−1.75357	−	0.780740i	−0.0768991	−	0.0342377i
$521$	−15.2530	−	26.4190i	−0.668246	−	1.15744i	−0.978394	−	0.206748i	$-0.933712\pi$
$521$	−15.2530	−	26.4190i	−0.668246	−	1.15744i	0.310148	−	0.950688i	$-0.399621\pi$
$522$	−1.12103	+	1.94168i	−0.0490662	+	0.0849851i
$523$	8.29085	−	6.02365i	0.362534	−	0.263396i	−0.391575	−	0.920146i	$-0.628069\pi$
$523$	8.29085	−	6.02365i	0.362534	−	0.263396i	0.754108	+	0.656750i	$0.228069\pi$
$524$	−3.73361	+	0.793602i	−0.163103	+	0.0346687i
$525$	−0.155966	−	0.480013i	−0.00680690	−	0.0209495i
$526$	−14.7836			−0.644597
$527$	−13.9298	+	2.93376i	−0.606791	+	0.127797i
$528$	−1.06583			−0.0463844
$529$	−2.04225	−	6.28540i	−0.0887935	−	0.273278i
$530$	−0.984455	+	0.209252i	−0.0427620	+	0.00908934i
$531$	−7.78978	+	5.65961i	−0.338048	+	0.245606i
$532$	0.222236	−	0.384924i	0.00963516	−	0.0166886i
$533$	4.00093	+	6.92981i	0.173299	+	0.300163i
$534$	−5.44658	−	2.42497i	−0.235696	−	0.104939i
$535$	14.0432	+	10.2030i	0.607139	+	0.441112i
$536$	−2.08238	+	0.927136i	−0.0899451	+	0.0400462i
$537$	12.5796	+	2.67387i	0.542849	+	0.115386i
$538$	−0.225133	−	2.14200i	−0.00970619	−	0.0923483i
$539$	4.81059	−	5.34270i	0.207207	−	0.230127i
$540$	−0.669131	−	0.743145i	−0.0287948	−	0.0319799i
$541$	−3.51153	+	33.4100i	−0.150972	+	1.43641i	0.612451	+	0.790509i	$0.290184\pi$
$541$	−3.51153	+	33.4100i	−0.150972	+	1.43641i	−0.763423	+	0.645898i	$0.776483\pi$
$542$	−5.05721	+	15.5645i	−0.217226	+	0.668552i
$543$	−3.39248	+	10.4410i	−0.145585	+	0.448066i
$544$	−0.267253	+	2.54274i	−0.0114584	+	0.109019i
$545$	−4.06373	−	4.51323i	−0.174071	−	0.193325i
$546$	−0.648262	+	0.719967i	−0.0277430	+	0.0308118i
$547$	3.78410	+	36.0033i	0.161797	+	1.53939i	0.710694	+	0.703501i	$0.248381\pi$
$547$	3.78410	+	36.0033i	0.161797	+	1.53939i	−0.548897	+	0.835890i	$0.684952\pi$
$548$	0.146182	+	0.0310719i	0.00624458	+	0.00132733i
$549$	10.3082	−	4.58951i	0.439944	−	0.195876i
$550$	0.862276	+	0.626480i	0.0367676	+	0.0267132i
$551$	1.80375	+	0.803081i	0.0768423	+	0.0342124i
$552$	2.02430	+	3.50619i	0.0861599	+	0.149233i
$553$	−1.89283	+	3.27848i	−0.0804914	+	0.139415i
$554$	8.44931	−	6.13878i	0.358977	−	0.260812i
$555$	−9.38226	+	1.99426i	−0.398255	+	0.0846517i
$556$	3.37890	+	10.3992i	0.143297	+	0.441024i
$557$	12.4171			0.526128			0.263064	−	0.964778i	$-0.415267\pi$
$557$	12.4171			0.526128			0.263064	+	0.964778i	$0.415267\pi$
$558$	−2.79286	+	4.81663i	−0.118231	+	0.203904i
$559$	−7.88892			−0.333666
$560$	0.155966	+	0.480013i	0.00659075	+	0.0202842i
$561$	2.66552	−	0.566573i	0.112538	−	0.0239207i
$562$	17.8000	−	12.9325i	0.750849	−	0.545524i
$563$	−13.5801	+	23.5214i	−0.572332	+	0.991308i	0.423994	+	0.905665i	$0.360628\pi$
$563$	−13.5801	+	23.5214i	−0.572332	+	0.991308i	−0.996326	+	0.0856430i	$0.972706\pi$
$564$	4.85239	+	8.40458i	0.204322	+	0.353897i
$565$	8.44091	+	3.75813i	0.355112	+	0.158106i
$566$	−0.743807	−	0.540407i	−0.0312645	−	0.0227150i
$567$	−0.461080	+	0.205286i	−0.0193636	+	0.00862121i
$568$	8.75310	+	1.86053i	0.367272	+	0.0780660i
$569$	−1.47609	−	14.0440i	−0.0618807	−	0.588756i	−0.980896	−	0.194534i	$-0.937681\pi$
$569$	−1.47609	−	14.0440i	−0.0618807	−	0.588756i	0.919015	−	0.394222i	$-0.128986\pi$
$570$	−0.589263	+	0.654443i	−0.0246815	+	0.0274116i
$571$	11.3330	+	12.5865i	0.474270	+	0.526730i	0.932047	−	0.362337i	$-0.118021\pi$
$571$	11.3330	+	12.5865i	0.474270	+	0.526730i	−0.457777	+	0.889067i	$0.651354\pi$
$572$	0.213853	−	2.03468i	0.00894166	−	0.0850742i
$573$	1.79447	−	5.52281i	0.0749651	−	0.230719i
$574$	0.650170	−	2.00102i	0.0271376	−	0.0835208i
$575$	0.423194	−	4.02642i	0.0176484	−	0.167913i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	−12.1843	+	13.5321i	−0.507240	+	0.563347i	−0.941315	−	0.337530i	$-0.890409\pi$
$577$	−12.1843	+	13.5321i	−0.507240	+	0.563347i	0.434075	+	0.900877i	$0.357075\pi$
$578$	1.09368	+	10.4057i	0.0454913	+	0.432821i
$579$	−10.0738	−	2.14126i	−0.418654	−	0.0889875i
$580$	−2.04823	+	0.911929i	−0.0850479	+	0.0378658i
$581$	0.322215	+	0.234103i	0.0133677	+	0.00971222i
$582$	−7.92403	−	3.52801i	−0.328462	−	0.146241i
$583$	−0.536352	−	0.928989i	−0.0222134	−	0.0384748i
$584$	0.129922	−	0.225031i	0.00537620	−	0.00931185i
$585$	1.55293	−	1.12827i	0.0642055	−	0.0466481i
$586$	−5.92525	+	1.25945i	−0.244770	+	0.0520275i
$587$	−7.02382	−	21.6171i	−0.289904	−	0.892232i	−0.984886	−	0.173205i	$-0.944588\pi$
$587$	−7.02382	−	21.6171i	−0.289904	−	0.892232i	0.694982	−	0.719027i	$-0.255412\pi$
$588$	−6.74526			−0.278170
$589$	4.47557	+	2.00265i	0.184413	+	0.0825177i
$590$	−9.62870			−0.396407
$591$	0.473733	+	1.45800i	0.0194868	+	0.0599741i
$592$	9.38226	−	1.99426i	0.385609	−	0.0819636i
$593$	27.6610	−	20.0969i	1.13590	−	0.825280i	0.149358	−	0.988783i	$-0.452279\pi$
$593$	27.6610	−	20.0969i	1.13590	−	0.825280i	0.986543	+	0.163503i	$0.0522792\pi$
$594$	0.532916	−	0.923038i	0.0218658	−	0.0378727i
$595$	−0.645215	−	1.11755i	−0.0264512	−	0.0458149i
$596$	2.85679	+	1.27193i	0.117019	+	0.0521001i
$597$	13.0057	+	9.44918i	0.532287	+	0.386729i
$598$	−7.09950	+	3.16090i	−0.290320	+	0.129259i
$599$	36.3297	+	7.72211i	1.48439	+	0.315517i	0.877619	−	0.479359i	$-0.159131\pi$
$599$	36.3297	+	7.72211i	1.48439	+	0.315517i	0.606771	+	0.794876i	$0.292464\pi$
$600$	−0.104528	−	0.994522i	−0.00426736	−	0.0406012i
$601$	3.54171	−	3.93346i	0.144469	−	0.160449i	−0.666567	−	0.745445i	$-0.732237\pi$
$601$	3.54171	−	3.93346i	0.144469	−	0.160449i	0.811036	+	0.584996i	$0.198904\pi$
$602$	1.38798	+	1.54150i	0.0565697	+	0.0628270i
$603$	0.238267	−	2.26696i	0.00970300	−	0.0923178i
$604$	−5.15032	+	15.8511i	−0.209564	+	0.644971i
$605$	3.04814	−	9.38122i	0.123925	−	0.381401i
$606$	0.379466	−	3.61038i	0.0154148	−	0.146662i
$607$	−17.9184	−	19.9004i	−0.727285	−	0.807732i	0.260182	−	0.965560i	$-0.416218\pi$
$607$	−17.9184	−	19.9004i	−0.727285	−	0.807732i	−0.987467	+	0.157828i	$0.949551\pi$
$608$	0.589263	−	0.654443i	0.0238978	−	0.0265412i
$609$	0.118285	+	1.12540i	0.00479314	+	0.0456037i
$610$	11.0372	+	2.34602i	0.446882	+	0.0949877i
$611$	−17.0180	+	7.57690i	−0.688474	+	0.306529i
$612$	−2.06845	−	1.50282i	−0.0836123	−	0.0607479i
$613$	−30.9649	−	13.7865i	−1.25066	−	0.556830i	−0.328818	−	0.944393i	$-0.606650\pi$
$613$	−30.9649	−	13.7865i	−1.25066	−	0.556830i	−0.921843	+	0.387563i	$0.873317\pi$
$614$	−14.6063	−	25.2989i	−0.589464	−	1.02098i
$615$	−2.08434	+	3.61018i	−0.0840486	+	0.145576i
$616$	−0.435204	+	0.316194i	−0.0175349	+	0.0127398i
$617$	−10.4831	+	2.22825i	−0.422033	+	0.0897058i	−0.414032	−	0.910262i	$-0.635880\pi$
$617$	−10.4831	+	2.22825i	−0.422033	+	0.0897058i	−0.00800031	+	0.999968i	$0.502547\pi$
$618$	1.13490	+	3.49288i	0.0456525	+	0.140504i
$619$	42.4657			1.70684			0.853420	−	0.521225i	$-0.174525\pi$
$619$	42.4657			1.70684			0.853420	+	0.521225i	$0.174525\pi$
$620$	−5.09062	+	2.25514i	−0.204444	+	0.0905684i
$621$	−4.04860			−0.162465
$622$	−5.15300	−	15.8593i	−0.206617	−	0.635900i
$623$	−2.94337	+	0.625632i	−0.117923	+	0.0250654i
$624$	−1.55293	+	1.12827i	−0.0621668	+	0.0451668i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.8114	−	23.9221i	−0.552015	−	0.956118i
$627$	−0.857466	−	0.381769i	−0.0342439	−	0.0152464i
$628$	−6.01771	−	4.37212i	−0.240133	−	0.174467i
$629$	−22.4038	+	9.97481i	−0.893297	+	0.397722i
$630$	−0.493686	−	0.104936i	−0.0196689	−	0.00418076i
$631$	3.09666	+	29.4628i	0.123276	+	1.17289i	0.864853	+	0.502026i	$0.167412\pi$
$631$	3.09666	+	29.4628i	0.123276	+	1.17289i	−0.741577	+	0.670868i	$0.765922\pi$
$632$	−5.01888	+	5.57403i	−0.199640	+	0.221723i
$633$	−5.29114	−	5.87641i	−0.210304	−	0.233566i
$634$	−0.746866	+	7.10595i	−0.0296618	+	0.282213i
$635$	0.522314	−	1.60752i	0.0207274	−	0.0637924i
$636$	−0.311010	+	0.957189i	−0.0123323	+	0.0379550i
$637$	1.35340	−	12.8767i	0.0536237	−	0.510195i
$638$	−1.59900	−	1.77586i	−0.0633048	−	0.0703072i
$639$	−5.98781	+	6.65014i	−0.236874	+	0.263076i
$640$	0.104528	+	0.994522i	0.00413185	+	0.0393119i
$641$	30.2300	+	6.42559i	1.19401	+	0.253795i	0.761701	−	0.647928i	$-0.224364\pi$
$641$	30.2300	+	6.42559i	1.19401	+	0.253795i	0.432312	+	0.901724i	$0.357698\pi$
$642$	15.8576	−	7.06026i	0.625849	−	0.278646i
$643$	30.0569	+	21.8376i	1.18533	+	0.861191i	0.992763	−	0.120093i	$-0.0383194\pi$
$643$	30.0569	+	21.8376i	1.18533	+	0.861191i	0.192565	+	0.981284i	$0.438319\pi$
$644$	1.86673	+	0.831121i	0.0735594	+	0.0327508i
$645$	−2.05492	−	3.55923i	−0.0809124	−	0.140144i
$646$	−1.12579	+	1.94992i	−0.0442935	+	0.0767186i
$647$	17.9864	−	13.0679i	0.707119	−	0.513752i	−0.175124	−	0.984546i	$-0.556033\pi$
$647$	17.9864	−	13.0679i	0.707119	−	0.513752i	0.882243	+	0.470794i	$0.156033\pi$
$648$	−0.978148	+	0.207912i	−0.0384253	+	0.00816754i
$649$	−3.17131	−	9.76029i	−0.124485	−	0.383125i
$650$	1.91952			0.0752898
$651$	0.288533	+	2.79528i	0.0113085	+	0.109556i
$652$	−6.25593			−0.245001
$653$	−1.19070	−	3.66459i	−0.0465955	−	0.143406i	0.925052	−	0.379841i	$-0.124021\pi$
$653$	−1.19070	−	3.66459i	−0.0465955	−	0.143406i	−0.971647	+	0.236434i	$0.924021\pi$
$654$	−5.94043	+	1.26268i	−0.232289	+	0.0493746i
$655$	3.08803	−	2.24359i	0.120659	−	0.0876642i
$656$	2.08434	−	3.61018i	0.0813797	−	0.140954i
$657$	0.129922	+	0.225031i	0.00506873	+	0.00877929i
$658$	4.47468	+	1.99226i	0.174441	+	0.0776662i
$659$	20.6044	+	14.9700i	0.802634	+	0.583148i	0.911686	−	0.410888i	$-0.134781\pi$
$659$	20.6044	+	14.9700i	0.802634	+	0.583148i	−0.109052	+	0.994036i	$0.534781\pi$
$660$	0.973686	−	0.433513i	0.0379007	−	0.0168745i
$661$	39.9028	+	8.48161i	1.55204	+	0.329896i	0.902588	−	0.430505i	$-0.141665\pi$
$661$	39.9028	+	8.48161i	1.55204	+	0.329896i	0.649453	+	0.760402i	$0.274998\pi$
$662$	0.918696	+	8.74081i	0.0357061	+	0.339721i
$663$	3.28391	−	3.64716i	0.127537	−	0.141644i
$664$	0.528022	+	0.586428i	0.0204912	+	0.0227578i
$665$	−0.0464600	+	0.442037i	−0.00180164	+	0.0171415i
$666$	−2.96405	+	9.12241i	−0.114855	+	0.353486i
$667$	−2.80501	+	8.63294i	−0.108610	+	0.334269i
$668$	−0.928645	+	8.83547i	−0.0359304	+	0.341855i
$669$	13.5456	+	15.0439i	0.523703	+	0.581632i
$670$	1.52525	−	1.69396i	0.0589255	−	0.0654434i
$671$	1.25712	+	11.9607i	0.0485306	+	0.461737i
$672$	0.493686	+	0.104936i	0.0190444	+	0.00404800i
$673$	6.67609	−	2.97239i	0.257344	−	0.114577i	−0.274010	−	0.961727i	$-0.588350\pi$
$673$	6.67609	−	2.97239i	0.257344	−	0.114577i	0.531354	+	0.847150i	$0.321683\pi$
$674$	−6.37269	−	4.63003i	−0.245467	−	0.178342i
$675$	0.913545	+	0.406737i	0.0351624	+	0.0156553i
$676$	4.65772	+	8.06741i	0.179143	+	0.310285i
$677$	20.9423	−	36.2731i	0.804878	−	1.39409i	−0.111495	−	0.993765i	$-0.535564\pi$
$677$	20.9423	−	36.2731i	0.804878	−	1.39409i	0.916373	−	0.400325i	$-0.131103\pi$
$678$	7.47509	−	5.43097i	0.287079	−	0.208575i
$679$	−4.28220	+	0.910209i	−0.164336	+	0.0349306i
$680$	−0.790079	−	2.43161i	−0.0302981	−	0.0932481i
$681$	−21.9907			−0.842687
$682$	−3.96260	−	4.41743i	−0.151736	−	0.169152i
$683$	18.0458			0.690505			0.345253	−	0.938510i	$-0.387793\pi$
$683$	18.0458			0.690505			0.345253	+	0.938510i	$0.387793\pi$
$684$	0.272133	+	0.837538i	0.0104052	+	0.0320241i
$685$	−0.146182	+	0.0310719i	−0.00558532	+	0.00118720i
$686$	−5.61251	+	4.07773i	−0.214287	+	0.155688i
$687$	−4.50390	+	7.80099i	−0.171835	+	0.297626i
$688$	2.05492	+	3.55923i	0.0783431	+	0.135694i
$689$	−1.76488	−	0.785774i	−0.0672364	−	0.0299356i
$690$	−3.27538	−	2.37971i	−0.124692	−	0.0905938i
$691$	4.52697	−	2.01554i	0.172214	−	0.0766746i	−0.318819	−	0.947816i	$-0.603286\pi$
$691$	4.52697	−	2.01554i	0.172214	−	0.0766746i	0.491033	+	0.871141i	$0.336619\pi$
$692$	15.0772	+	3.20475i	0.573148	+	0.121826i
$693$	−0.0562302	−	0.534995i	−0.00213601	−	0.0203228i
$694$	−4.41619	+	4.90467i	−0.167636	+	0.186179i
$695$	−7.31651	−	8.12581i	−0.277531	−	0.308230i
$696$	−0.234359	+	2.22978i	−0.00888337	+	0.0845196i
$697$	−3.29358	+	10.1366i	−0.124753	+	0.383951i
$698$	4.36134	−	13.4228i	0.165079	−	0.508062i
$699$	0.812339	−	7.72889i	0.0307255	−	0.292333i
$700$	−0.337720	−	0.375077i	−0.0127646	−	0.0141766i
$701$	−0.710260	+	0.788824i	−0.0268261	+	0.0297935i	−0.756409	−	0.654099i	$-0.773048\pi$
$701$	−0.710260	+	0.788824i	−0.0268261	+	0.0297935i	0.729582	+	0.683893i	$0.239714\pi$
$702$	−0.200645	−	1.90901i	−0.00757284	−	0.0720508i
$703$	8.26239	+	1.75623i	0.311622	+	0.0662373i
$704$	−0.973686	+	0.433513i	−0.0366972	+	0.0163386i
$705$	−7.85133	−	5.70432i	−0.295698	−	0.214837i
$706$	22.9987	+	10.2397i	0.865568	+	0.385376i
$707$	−0.916125	−	1.58678i	−0.0344544	−	0.0596768i
$708$	−4.81435	+	8.33870i	−0.180934	+	0.313388i
$709$	−19.4117	+	14.1035i	−0.729023	+	0.529667i	−0.889254	−	0.457413i	$-0.848776\pi$
$709$	−19.4117	+	14.1035i	−0.729023	+	0.529667i	0.160231	+	0.987080i	$0.448776\pi$
$710$	−8.75310	+	1.86053i	−0.328498	+	0.0698244i
$711$	−2.31781	−	7.13349i	−0.0869247	−	0.267527i
$712$	−5.96202			−0.223436
$713$	−7.00567	+	21.4254i	−0.262364	+	0.802386i
$714$	−1.29043			−0.0482931
$715$	0.632214	+	1.94575i	0.0236435	+	0.0727671i
$716$	12.5796	−	2.67387i	0.470121	−	0.0999273i
$717$	−2.02927	+	1.47435i	−0.0757845	+	0.0550606i
$718$	3.59611	−	6.22865i	0.134206	−	0.232451i
$719$	1.22986	+	2.13018i	0.0458660	+	0.0794422i	0.888047	−	0.459753i	$-0.152062\pi$
$719$	1.22986	+	2.13018i	0.0458660	+	0.0794422i	−0.842181	+	0.539195i	$0.818729\pi$
$720$	−0.913545	−	0.406737i	−0.0340458	−	0.0151582i
$721$	1.49962	+	1.08954i	0.0558487	+	0.0405765i
$722$	−16.6489	+	7.41256i	−0.619607	+	0.275867i
$723$	14.9126	+	3.16976i	0.554604	+	0.117885i
$724$	1.14755	+	10.9182i	0.0426482	+	0.405770i
$725$	1.50023	−	1.66618i	0.0557172	−	0.0618803i
$726$	−6.60031	−	7.33038i	−0.244960	−	0.272056i
$727$	4.43124	−	42.1604i	0.164346	−	1.56364i	−0.532504	−	0.846427i	$-0.678749\pi$
$727$	4.43124	−	42.1604i	0.164346	−	1.56364i	0.696850	−	0.717217i	$-0.254584\pi$
$728$	−0.299379	+	0.921395i	−0.0110957	+	0.0341492i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−0.0271610	+	0.258420i	−0.00100527	+	0.00956455i
$731$	−7.03111	−	7.80884i	−0.260055	−	0.288820i
$732$	7.55030	−	8.38546i	0.279067	−	0.309935i
$733$	3.97248	+	37.7956i	0.146727	+	1.39601i	0.781785	+	0.623548i	$0.214309\pi$
$733$	3.97248	+	37.7956i	0.146727	+	1.39601i	−0.635058	+	0.772464i	$0.719024\pi$
$734$	14.6779	+	3.11987i	0.541769	+	0.115157i
$735$	6.16210	−	2.74355i	0.227293	−	0.101197i
$736$	3.27538	+	2.37971i	0.120732	+	0.0877171i
$737$	2.21947	+	0.988171i	0.0817552	+	0.0363997i
$738$	2.08434	+	3.61018i	0.0767255	+	0.132892i
$739$	11.6260	−	20.1368i	0.427668	−	0.740743i	−0.568997	−	0.822339i	$-0.692669\pi$
$739$	11.6260	−	20.1368i	0.427668	−	0.740743i	0.996665	+	0.0815965i	$0.0260019\pi$
$740$	−7.75998	+	5.63796i	−0.285263	+	0.207255i
$741$	−1.65347	+	0.351455i	−0.0607416	+	0.0129110i
$742$	0.156971	+	0.483108i	0.00576260	+	0.0177355i
$743$	−4.65333			−0.170714			−0.0853570	−	0.996350i	$-0.527203\pi$
$743$	−4.65333			−0.170714			−0.0853570	+	0.996350i	$0.527203\pi$
$744$	−0.592303	+	5.53617i	−0.0217149	+	0.202966i
$745$	−3.12715			−0.114570
$746$	−5.23062	−	16.0982i	−0.191507	−	0.589397i
$747$	−0.771873	+	0.164067i	−0.0282413	+	0.00600288i
$748$	2.20462	−	1.60175i	0.0806090	−	0.0585659i
$749$	4.38050	−	7.58725i	0.160060	−	0.277232i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	1.87845	+	0.836339i	0.0685456	+	0.0305185i	0.440723	−	0.897643i	$-0.354722\pi$
$751$	1.87845	+	0.836339i	0.0685456	+	0.0305185i	−0.372178	+	0.928162i	$0.621389\pi$
$752$	7.85133	+	5.70432i	0.286308	+	0.208015i
$753$	20.2397	−	9.01129i	0.737575	−	0.328390i
$754$	−4.20964	−	0.894786i	−0.153306	−	0.0325862i
$755$	−1.74215	−	16.5755i	−0.0634035	−	0.603244i
$756$	−0.337720	+	0.375077i	−0.0122828	+	0.0136414i
$757$	15.9143	+	17.6747i	0.578416	+	0.642396i	0.959354	−	0.282204i	$-0.0910655\pi$
$757$	15.9143	+	17.6747i	0.578416	+	0.642396i	−0.380938	+	0.924601i	$0.624399\pi$
$758$	2.05172	−	19.5208i	0.0745217	−	0.709027i
$759$	1.33345	−	4.10393i	0.0484011	−	0.148963i
$760$	−0.272133	+	0.837538i	−0.00987129	+	0.0303807i
$761$	3.85927	−	36.7185i	0.139898	−	1.33104i	−0.669073	−	0.743197i	$-0.733309\pi$
$761$	3.85927	−	36.7185i	0.139898	−	1.33104i	0.808971	−	0.587848i	$-0.200025\pi$
$762$	−1.13099	−	1.25610i	−0.0409716	−	0.0455036i
$763$	−2.05103	+	2.27789i	−0.0742521	+	0.0824653i
$764$	−0.607000	−	5.77522i	−0.0219605	−	0.208940i
$765$	2.50088	+	0.531578i	0.0904194	+	0.0192192i
$766$	20.6696	−	9.20269i	0.746822	−	0.332507i
$767$	−14.9527	−	10.8637i	−0.539909	−	0.392267i
$768$	0.913545	+	0.406737i	0.0329647	+	0.0146768i
$769$	1.49734	+	2.59346i	0.0539953	+	0.0935227i	0.891760	−	0.452509i	$-0.149471\pi$
$769$	1.49734	+	2.59346i	0.0539953	+	0.0935227i	−0.837764	+	0.546032i	$0.816138\pi$
$770$	0.268971	−	0.465871i	0.00969304	−	0.0167888i
$771$	−11.0836	+	8.05270i	−0.399166	+	0.290011i
$772$	−10.0738	+	2.14126i	−0.362565	+	0.0770655i
$773$	13.0666	+	40.2150i	0.469974	+	1.44643i	0.852617	+	0.522536i	$0.175014\pi$
$773$	13.0666	+	40.2150i	0.469974	+	1.44643i	−0.382643	+	0.923896i	$0.624986\pi$
$774$	−4.10984			−0.147725
$775$	3.73326	−	4.13071i	0.134103	−	0.148379i
$776$	−8.67393			−0.311376
$777$	1.49600	+	4.60422i	0.0536688	+	0.165175i
$778$	2.51744	−	0.535099i	0.0902548	−	0.0191842i
$779$	2.96998	−	2.15782i	0.106411	−	0.0773118i
$780$	0.959760	−	1.66235i	0.0343649	−	0.0595218i
$781$	−4.76888	−	8.25994i	−0.170644	−	0.295564i
$782$	−9.45633	−	4.21023i	−0.338158	−	0.150558i
$783$	−1.81387	−	1.31785i	−0.0648223	−	0.0470962i
$784$	−6.16210	+	2.74355i	−0.220075	+	0.0979838i
$785$	7.27576	+	1.54651i	0.259683	+	0.0551973i
$786$	−0.398987	−	3.79611i	−0.0142314	−	0.135403i
$787$	13.1611	−	14.6168i	0.469141	−	0.521034i	−0.461414	−	0.887185i	$-0.652658\pi$
$787$	13.1611	−	14.6168i	0.469141	−	0.521034i	0.930556	+	0.366151i	$0.119325\pi$
$788$	1.02580	+	1.13926i	0.0365426	+	0.0405846i
$789$	1.54531	−	14.7026i	0.0550145	−	0.523428i
$790$	2.31781	−	7.13349i	0.0824640	−	0.253798i
$791$	1.44108	−	4.43519i	0.0512389	−	0.157697i
$792$	0.111410	−	1.05999i	0.00395877	−	0.0376652i
$793$	14.4930	+	16.0961i	0.514660	+	0.571588i
$794$	−4.29666	+	4.77192i	−0.152483	+	0.169349i
$795$	−0.105202	−	1.00093i	−0.00373115	−	0.0354995i
$796$	15.7246	+	3.34237i	0.557344	+	0.118467i
$797$	−0.496801	+	0.221190i	−0.0175976	+	0.00783495i	−0.415517	−	0.909586i	$-0.636399\pi$
$797$	−0.496801	+	0.221190i	−0.0175976	+	0.00783495i	0.397919	+	0.917421i	$0.369733\pi$
$798$	0.359586	+	0.261254i	0.0127292	+	0.00924830i
$799$	−22.6675	−	10.0922i	−0.801918	−	0.357037i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	2.98101	−	5.16326i	0.105329	−	0.182435i
$802$	8.54014	−	6.20478i	0.301563	−	0.219098i
$803$	−0.270897	+	0.0575810i	−0.00955976	+	0.00203199i
$804$	−0.704389	−	2.16789i	−0.0248419	−	0.0764554i
$805$	−2.04339			−0.0720200
$806$	−10.4497	−	2.24151i	−0.368076	−	0.0789539i
$807$	2.15380			0.0758174
$808$	−1.12181	−	3.45259i	−0.0394653	−	0.121462i
$809$	−23.5502	+	5.00574i	−0.827979	+	0.175992i	−0.602361	−	0.798223i	$-0.705773\pi$
$809$	−23.5502	+	5.00574i	−0.827979	+	0.175992i	−0.225618	+	0.974216i	$0.572440\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	0.420409	−	0.728170i	0.0147626	−	0.0255695i	−0.858550	−	0.512730i	$-0.828634\pi$
$811$	0.420409	−	0.728170i	0.0147626	−	0.0255695i	0.873312	+	0.487161i	$0.161967\pi$
$812$	0.565802	+	0.979997i	0.0198557	+	0.0343912i
$813$	−14.9506	−	6.65644i	−0.524341	−	0.233452i
$814$	−8.27084	−	6.00912i	−0.289893	−	0.210619i
$815$	5.71508	−	2.54452i	0.200190	−	0.0891305i
$816$	−2.50088	−	0.531578i	−0.0875482	−	0.0186090i
$817$	0.378319	+	3.59946i	0.0132357	+	0.125929i
$818$	−12.8885	+	14.3141i	−0.450635	+	0.500481i
$819$	−0.648262	−	0.719967i	−0.0226521	−	0.0251577i
$820$	−0.435745	+	4.14584i	−0.0152169	+	0.144779i
$821$	6.56805	−	20.2144i	0.229226	−	0.705487i	−0.768609	−	0.639719i	$-0.779051\pi$
$821$	6.56805	−	20.2144i	0.229226	−	0.705487i	0.997835	−	0.0657671i	$-0.0209494\pi$
$822$	−0.0461819	+	0.142133i	−0.00161078	+	0.00495746i
$823$	5.15435	−	49.0404i	0.179669	−	1.70944i	−0.418622	−	0.908161i	$-0.637487\pi$
$823$	5.15435	−	49.0404i	0.179669	−	1.70944i	0.598291	−	0.801279i	$-0.295847\pi$
$824$	2.45747	+	2.72929i	0.0856099	+	0.0950794i
$825$	−0.713181	+	0.792068i	−0.0248298	+	0.0275763i
$826$	0.507983	+	4.83313i	0.0176750	+	0.168166i
$827$	−13.0933	−	2.78307i	−0.455300	−	0.0967770i	−0.0254475	−	0.999676i	$-0.508101\pi$
$827$	−13.0933	−	2.78307i	−0.455300	−	0.0967770i	−0.429852	+	0.902899i	$0.641434\pi$
$828$	−3.69858	+	1.64671i	−0.128534	+	0.0572272i
$829$	21.1414	+	15.3601i	0.734272	+	0.533480i	0.890912	−	0.454176i	$-0.150066\pi$
$829$	21.1414	+	15.3601i	0.734272	+	0.533480i	−0.156640	+	0.987656i	$0.550066\pi$
$830$	−0.720894	−	0.320963i	−0.0250226	−	0.0111408i
$831$	5.22196	+	9.04470i	0.181148	+	0.313757i
$832$	−0.959760	+	1.66235i	−0.0332737	+	0.0576318i
$833$	13.9523	−	10.1369i	0.483417	−	0.351223i
$834$	−10.6954	+	2.27338i	−0.370352	+	0.0787207i
$835$	−2.74535	−	8.44932i	−0.0950068	−	0.292401i
$836$	−0.938614			−0.0324626
$837$	−4.49831	−	3.28103i	−0.155484	−	0.113409i
$838$	2.81094			0.0971023
$839$	−13.3065	−	40.9531i	−0.459390	−	1.41386i	−0.865903	−	0.500212i	$-0.833256\pi$
$839$	−13.3065	−	40.9531i	−0.459390	−	1.41386i	0.406513	−	0.913645i	$-0.366744\pi$
$840$	−0.493686	+	0.104936i	−0.0170338	+	0.00362064i
$841$	19.3947	−	14.0911i	0.668782	−	0.485899i
$842$	2.48924	−	4.31148i	0.0857847	−	0.148584i
$843$	11.0010	+	19.0543i	0.378895	+	0.656266i
$844$	−7.22385	−	3.21627i	−0.248655	−	0.110708i
$845$	−7.53635	−	5.47548i	−0.259258	−	0.188362i
$846$	−8.86575	+	3.94729i	−0.304811	+	0.135711i
$847$	−4.86972	−	1.03509i	−0.167326	−	0.0355662i
$848$	0.105202	+	1.00093i	0.00361267	+	0.0343722i
$849$	0.615196	−	0.683244i	0.0211135	−	0.0234489i
$850$	1.71080	+	1.90003i	0.0586799	+	0.0651707i
$851$	−4.05922	+	38.6209i	−0.139148	+	1.32391i
$852$	−2.76528	+	8.51067i	−0.0947371	+	0.291571i
$853$	7.79682	−	23.9962i	0.266958	−	0.821613i	−0.724278	−	0.689508i	$-0.757827\pi$
$853$	7.79682	−	23.9962i	0.266958	−	0.821613i	0.991236	−	0.132104i	$-0.0421734\pi$
$854$	0.595298	−	5.66388i	0.0203707	−	0.193814i
$855$	−0.589263	−	0.654443i	−0.0201524	−	0.0223815i
$856$	11.6150	−	12.8997i	0.396991	−	0.440904i
$857$	−4.52536	−	43.0560i	−0.154583	−	1.47076i	−0.746834	−	0.665010i	$-0.768427\pi$
$857$	−4.52536	−	43.0560i	−0.154583	−	1.47076i	0.592251	−	0.805754i	$-0.298239\pi$
$858$	2.00118	+	0.425364i	0.0683191	+	0.0145217i
$859$	20.7984	−	9.26004i	0.709632	−	0.315948i	−0.0199891	−	0.999800i	$-0.506363\pi$
$859$	20.7984	−	9.26004i	0.709632	−	0.315948i	0.729621	+	0.683852i	$0.239696\pi$
$860$	−3.32493	−	2.41570i	−0.113379	−	0.0823748i
$861$	1.92209	+	0.855771i	0.0655048	+	0.0291646i
$862$	−1.89281	−	3.27844i	−0.0644693	−	0.111664i
$863$	14.5028	−	25.1196i	0.493681	−	0.855081i	−0.506292	−	0.862362i	$-0.668984\pi$
$863$	14.5028	−	25.1196i	0.493681	−	0.855081i	0.999973	+	0.00728118i	$0.00231769\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−15.0772	+	3.20475i	−0.512639	+	0.108965i
$866$	4.38551	+	13.4972i	0.149026	+	0.458654i
$867$	−10.4630			−0.355343
$868$	1.40053	+	2.43626i	0.0475372	+	0.0826921i
$869$	7.99437			0.271190
$870$	−0.692835	−	2.13233i	−0.0234893	−	0.0722927i
$871$	4.27984	−	0.909707i	0.145017	−	0.0308243i
$872$	−4.91328	+	3.56970i	−0.166385	+	0.120885i
$873$	4.33697	−	7.51184i	0.146784	−	0.254237i
$874$	1.78268	+	3.08769i	0.0603000	+	0.104443i
$875$	0.461080	+	0.205286i	0.0155874	+	0.00693994i
$876$	0.210218	+	0.152732i	0.00710260	+	0.00516034i
$877$	−36.3831	+	16.1988i	−1.22857	+	0.546995i	−0.915340	−	0.402682i	$-0.868078\pi$
$877$	−36.3831	+	16.1988i	−1.22857	+	0.546995i	−0.313231	+	0.949677i	$0.601411\pi$
$878$	24.1968	+	5.14319i	0.816603	+	0.173574i
$879$	−0.633195	−	6.02444i	−0.0213571	−	0.203199i
$880$	0.713181	−	0.792068i	0.0240413	−	0.0267006i
$881$	−12.6947	−	14.0988i	−0.427694	−	0.475002i	0.490325	−	0.871540i	$-0.336878\pi$
$881$	−12.6947	−	14.0988i	−0.427694	−	0.475002i	−0.918018	+	0.396538i	$0.870212\pi$
$882$	0.705072	−	6.70831i	0.0237410	−	0.225881i
$883$	−4.78390	+	14.7233i	−0.160991	+	0.495479i	−0.998719	−	0.0506090i	$-0.983884\pi$
$883$	−4.78390	+	14.7233i	−0.160991	+	0.495479i	0.837728	+	0.546088i	$0.183884\pi$
$884$	1.51657	−	4.66753i	0.0510079	−	0.156986i
$885$	1.00647	−	9.57596i	0.0338322	−	0.321892i
$886$	−0.831056	−	0.922982i	−0.0279199	−	0.0310082i
$887$	14.0746	−	15.6314i	0.472577	−	0.524850i	−0.458979	−	0.888447i	$-0.651785\pi$
$887$	14.0746	−	15.6314i	0.472577	−	0.524850i	0.931556	+	0.363597i	$0.118451\pi$
$888$	1.00262	+	9.53932i	0.0336458	+	0.320119i
$889$	−0.834450	−	0.177368i	−0.0279866	−	0.00594873i
$890$	5.44658	−	2.42497i	0.182570	−	0.0812853i
$891$	0.862276	+	0.626480i	0.0288873	+	0.0209879i
$892$	18.4934	+	8.23381i	0.619206	+	0.275688i
$893$	4.27320	+	7.40140i	0.142997	+	0.247679i
$894$	−1.56358	+	2.70819i	−0.0522938	+	0.0905755i
$895$	−10.4045	+	7.55928i	−0.347783	+	0.252679i
$896$	0.493686	−	0.104936i	0.0164929	−	0.00350567i
$897$	−2.40148	−	7.39101i	−0.0801832	−	0.246779i
$898$	−14.9651			−0.499392
$899$	−10.1128	+	7.31866i	−0.337282	+	0.244091i
$900$	1.00000			0.0333333
$901$	−0.795173	−	2.44729i	−0.0264911	−	0.0815311i
$902$	−4.34601	+	0.923774i	−0.144706	+	0.0307583i
$903$	−1.67814	+	1.21924i	−0.0558451	+	0.0405738i
$904$	4.61986	−	8.00184i	0.153654	−	0.266137i
$905$	−5.48915	−	9.50749i	−0.182466	−	0.316040i
$906$	−15.2259	−	6.77900i	−0.505846	−	0.225217i
$907$	−46.9038	−	34.0776i	−1.55742	−	1.13153i	−0.938088	−	0.346397i	$-0.887405\pi$
$907$	−46.9038	−	34.0776i	−1.55742	−	1.13153i	−0.619328	−	0.785132i	$-0.712595\pi$
$908$	−20.0895	+	8.94444i	−0.666694	+	0.296832i
$909$	3.55094	+	0.754775i	0.117777	+	0.0250343i
$910$	−0.101268	−	0.963504i	−0.00335701	−	0.0319399i
$911$	17.7565	−	19.7206i	0.588298	−	0.653371i	−0.373339	−	0.927695i	$-0.621787\pi$
$911$	17.7565	−	19.7206i	0.588298	−	0.653371i	0.961637	+	0.274324i	$0.0884539\pi$
$912$	0.589263	+	0.654443i	0.0195124	+	0.0216708i
$913$	0.0879153	−	0.836458i	0.00290957	−	0.0276827i
$914$	1.97392	−	6.07510i	0.0652914	−	0.200946i
$915$	−3.48687	+	10.7315i	−0.115272	+	0.354772i
$916$	−0.941573	+	8.95846i	−0.0311104	+	0.295996i
$917$	−1.28908	−	1.43167i	−0.0425693	−	0.0472780i
$918$	1.71080	−	1.90003i	0.0564648	−	0.0627105i
$919$	4.83895	+	46.0395i	0.159622	+	1.51870i	0.722041	+	0.691851i	$0.243204\pi$
$919$	4.83895	+	46.0395i	0.159622	+	1.51870i	−0.562419	+	0.826853i	$0.690129\pi$
$920$	−3.96013	−	0.841751i	−0.130561	−	0.0277517i
$921$	26.6871	−	11.8819i	0.879370	−	0.391521i
$922$	−25.5244	−	18.5446i	−0.840601	−	0.610732i
$923$	−15.6921	−	6.98656i	−0.516511	−	0.229966i
$924$	−0.268971	−	0.465871i	−0.00884849	−	0.0153260i
$925$	4.79593	−	8.30680i	0.157689	−	0.273126i
$926$	5.37373	−	3.90424i	0.176592	−	0.128301i
$927$	−3.59237	+	0.763582i	−0.117989	+	0.0250793i
$928$	0.692835	+	2.13233i	0.0227434	+	0.0699971i
$929$	52.4160			1.71971			0.859856	−	0.510537i	$-0.170553\pi$
$929$	52.4160			1.71971			0.859856	+	0.510537i	$0.170553\pi$
$930$	−1.71067	−	5.29845i	−0.0560950	−	0.173743i
$931$	−5.94014			−0.194680
$932$	−2.40151	−	7.39110i	−0.0786642	−	0.242103i
$933$	16.3111	−	3.46702i	0.534000	−	0.113505i
$934$	4.82798	−	3.50773i	0.157976	−	0.114776i
$935$	−1.36253	+	2.35998i	−0.0445596	+	0.0771794i
$936$	−0.959760	−	1.66235i	−0.0313708	−	0.0543357i
$937$	−26.9766	−	12.0108i	−0.881288	−	0.392375i	−0.0843500	−	0.996436i	$-0.526881\pi$
$937$	−26.9766	−	12.0108i	−0.881288	−	0.392375i	−0.796938	+	0.604062i	$0.793548\pi$
$938$	−0.930752	−	0.676231i	−0.0303901	−	0.0220797i
$939$	25.2347	−	11.2352i	0.823503	−	0.366647i
$940$	−9.49270	−	2.01774i	−0.309618	−	0.0658113i
$941$	−5.91015	−	56.2313i	−0.192665	−	1.83309i	−0.482363	−	0.875971i	$-0.660221\pi$
$941$	−5.91015	−	56.2313i	−0.192665	−	1.83309i	0.289698	−	0.957118i	$-0.406445\pi$
$942$	4.97720	−	5.52774i	0.162166	−	0.180103i
$943$	11.2931	+	12.5423i	0.367754	+	0.408432i
$944$	−1.00647	+	9.57596i	−0.0327579	+	0.311671i
$945$	0.155966	−	0.480013i	0.00507356	−	0.0156148i
$946$	1.35362	−	4.16601i	0.0440099	−	0.135449i
$947$	2.30595	−	21.9396i	0.0749333	−	0.712943i	−0.890974	−	0.454054i	$-0.849977\pi$
$947$	2.30595	−	21.9396i	0.0749333	−	0.712943i	0.965907	−	0.258888i	$-0.0833561\pi$
$948$	−5.01888	−	5.57403i	−0.163005	−	0.181036i
$949$	−0.333745	+	0.370662i	−0.0108338	+	0.0120322i
$950$	−0.0920519	−	0.875815i	−0.00298656	−	0.0284152i
$951$	−6.98896	−	1.48555i	−0.226632	−	0.0481722i
$952$	−1.17887	+	0.524865i	−0.0382073	+	0.0170110i
$953$	32.9103	+	23.9107i	1.06607	+	0.774544i	0.975202	−	0.221319i	$-0.0710361\pi$
$953$	32.9103	+	23.9107i	1.06607	+	0.774544i	0.0908674	+	0.995863i	$0.471036\pi$
$954$	−0.919436	−	0.409359i	−0.0297678	−	0.0132535i
$955$	2.90351	+	5.02903i	0.0939555	+	0.162736i
$956$	−1.25416	+	2.17226i	−0.0405624	+	0.0702561i
$957$	1.93328	−	1.40461i	0.0624940	−	0.0454045i
$958$	7.30597	−	1.55293i	0.236045	−	0.0501729i
$959$	0.0233087	+	0.0717368i	0.000752677	+	0.00231650i
$960$	−1.00000			−0.0322749
$961$	−25.1472	+	18.1278i	−0.811201	+	0.584767i
$962$	−18.4118			−0.593620
$963$	5.36401	+	16.5087i	0.172853	+	0.531986i
$964$	14.9126	−	3.16976i	0.480301	−	0.102091i
$965$	8.33196	−	6.05352i	0.268215	−	0.194870i
$966$	−1.02169	+	1.76963i	−0.0328725	+	0.0569368i
$967$	−5.12117	−	8.87014i	−0.164686	−	0.285244i	0.771858	−	0.635795i	$-0.219328\pi$
$967$	−5.12117	−	8.87014i	−0.164686	−	0.285244i	−0.936544	+	0.350551i	$0.885994\pi$
$968$	−9.01121	−	4.01205i	−0.289631	−	0.128952i
$969$	−1.82156	−	1.32344i	−0.0585170	−	0.0425151i
$970$	7.92403	−	3.52801i	0.254425	−	0.113277i
$971$	41.5371	+	8.82899i	1.33299	+	0.283336i	0.818671	−	0.574263i	$-0.194711\pi$
$971$	41.5371	+	8.82899i	1.33299	+	0.283336i	0.514319	+	0.857599i	$0.328045\pi$
$972$	−0.104528	−	0.994522i	−0.00335275	−	0.0318993i
$973$	−3.69276	+	4.10122i	−0.118384	+	0.131479i
$974$	9.83815	+	10.9264i	0.315235	+	0.350104i
$975$	−0.200645	+	1.90901i	−0.00642577	+	0.0611371i
$976$	3.48687	−	10.7315i	0.111612	−	0.343506i
$977$	−9.35480	+	28.7911i	−0.299287	+	0.921110i	0.682461	+	0.730922i	$0.260910\pi$
$977$	−9.35480	+	28.7911i	−0.299287	+	0.921110i	−0.981748	+	0.190188i	$0.939090\pi$
$978$	0.653923	−	6.22166i	0.0209101	−	0.198947i
$979$	4.25200	+	4.72232i	0.135894	+	0.150926i
$980$	4.51346	−	5.01271i	0.144177	−	0.160125i
$981$	−0.634816	−	6.03987i	−0.0202681	−	0.192838i
$982$	−31.2591	−	6.64432i	−0.997517	−	0.212029i
$983$	−17.7096	+	7.88482i	−0.564848	+	0.251487i	−0.669236	−	0.743050i	$-0.733378\pi$
$983$	−17.7096	+	7.88482i	−0.564848	+	0.251487i	0.104388	+	0.994537i	$0.466712\pi$
$984$	3.37253	+	2.45028i	0.107512	+	0.0781122i
$985$	−1.40049	−	0.623540i	−0.0446235	−	0.0198676i
$986$	−2.86619	−	4.96440i	−0.0912782	−	0.158099i
$987$	−2.44907	+	4.24192i	−0.0779549	+	0.135022i
$988$	−1.36757	+	0.993596i	−0.0435081	+	0.0316105i
$989$	−16.2755	+	3.45946i	−0.517530	+	0.110004i
$990$	0.329360	+	1.01367i	0.0104678	+	0.0322164i
$991$	37.2609			1.18363			0.591816	−	0.806073i	$-0.298411\pi$
$991$	37.2609			1.18363			0.591816	+	0.806073i	$0.298411\pi$
$992$	1.71067	+	5.29845i	0.0543137	+	0.168226i
$993$	−8.78896			−0.278909
$994$	1.39568	+	4.29547i	0.0442683	+	0.136244i
$995$	−15.7246	+	3.34237i	−0.498504	+	0.105960i
$996$	−0.638409	+	0.463831i	−0.0202288	+	0.0146971i
$997$	−2.33752	+	4.04870i	−0.0740299	+	0.128224i	−0.900664	−	0.434516i	$-0.856919\pi$
$997$	−2.33752	+	4.04870i	−0.0740299	+	0.128224i	0.826634	+	0.562740i	$0.190253\pi$
$998$	−9.30111	−	16.1100i	−0.294422	−	0.509953i
$999$	−8.76261	−	3.90136i	−0.277237	−	0.123434i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.d.751.1	yes	16
31.9	even	15	inner	930.2.bg.d.691.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.d.691.1	✓	16	31.9	even	15	inner
930.2.bg.d.751.1	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.461080 - 0.205286i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.978148 + 0.207912i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.461080 - 0.205286i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.978148 + 0.207912i) q^{10} +(0.111410 + 1.05999i) q^{11} +(0.669131 - 0.743145i) q^{12} +(1.28441 + 1.42648i) q^{13} +(0.0527571 - 0.501950i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.267253 + 2.54274i) q^{17} +(0.669131 + 0.743145i) q^{18} +(0.589263 - 0.654443i) q^{19} +(0.104528 + 0.994522i) q^{20} +(0.493686 + 0.104936i) q^{21} +(-0.973686 + 0.433513i) q^{22} +(3.27538 + 2.37971i) q^{23} +(0.913545 + 0.406737i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.959760 + 1.66235i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.493686 - 0.104936i) q^{28} +(0.692835 + 2.13233i) q^{29} -1.00000 q^{30} +(1.71067 + 5.29845i) q^{31} +1.00000 q^{32} +(-0.329360 - 1.01367i) q^{33} +(-2.50088 + 0.531578i) q^{34} +(-0.408323 + 0.296664i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.79593 + 8.30680i) q^{37} +(0.804504 + 0.358188i) q^{38} +(-1.55293 - 1.12827i) q^{39} +(-0.913545 + 0.406737i) q^{40} +(4.07758 + 0.866716i) q^{41} +(0.0527571 + 0.501950i) q^{42} +(-2.75002 + 3.05421i) q^{43} +(-0.713181 - 0.792068i) q^{44} +(0.104528 - 0.994522i) q^{45} +(-1.25109 + 3.85044i) q^{46} +(-2.99894 + 9.22979i) q^{47} +(-0.104528 + 0.994522i) q^{48} +(-4.51346 - 5.01271i) q^{49} +(0.669131 - 0.743145i) q^{50} +(-0.267253 - 2.54274i) q^{51} +(-1.87757 - 0.399091i) q^{52} +(-0.919436 + 0.409359i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(0.973686 + 0.433513i) q^{55} +(0.252358 + 0.437096i) q^{56} +(-0.440320 + 0.762656i) q^{57} +(-1.81387 + 1.31785i) q^{58} +(-9.41829 + 2.00192i) q^{59} +(-0.309017 - 0.951057i) q^{60} +11.2837 q^{61} +(-4.51050 + 3.26425i) q^{62} -0.504715 q^{63} +(0.309017 + 0.951057i) q^{64} +(1.87757 - 0.399091i) q^{65} +(0.862276 - 0.626480i) q^{66} +(1.13972 - 1.97406i) q^{67} +(-1.27837 - 2.21421i) q^{68} +(-3.69858 - 1.64671i) q^{69} +(-0.408323 - 0.296664i) q^{70} +(-8.17500 + 3.63974i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(0.0271610 + 0.258420i) q^{73} +(-6.41821 + 7.12815i) q^{74} +(0.669131 + 0.743145i) q^{75} +(-0.0920519 + 0.875815i) q^{76} +(0.166233 - 0.511613i) q^{77} +(0.593165 - 1.82557i) q^{78} +(0.784025 - 7.45950i) q^{79} +(-0.669131 - 0.743145i) q^{80} +(0.669131 - 0.743145i) q^{81} +(0.435745 + 4.14584i) q^{82} +(-0.771873 - 0.164067i) q^{83} +(-0.461080 + 0.205286i) q^{84} +(2.06845 + 1.50282i) q^{85} +(-3.75453 - 1.67162i) q^{86} +(-1.12103 - 1.94168i) q^{87} +(0.532916 - 0.923038i) q^{88} +(4.82338 - 3.50439i) q^{89} +(0.978148 - 0.207912i) q^{90} +(-0.299379 - 0.921395i) q^{91} -4.04860 q^{92} +(-2.77490 - 4.82700i) q^{93} -9.70477 q^{94} +(-0.272133 - 0.837538i) q^{95} +(-0.978148 + 0.207912i) q^{96} +(7.01736 - 5.09841i) q^{97} +(3.37263 - 5.84157i) q^{98} +(0.532916 + 0.923038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 8 q^{5} - 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} + 2 q^{12} - 20 q^{13} - 4 q^{14} + 4 q^{15} - 4 q^{16} - 12 q^{17} + 2 q^{18} - 7 q^{19} - 2 q^{20} - 4 q^{21} + 11 q^{22} + 11 q^{23} + 2 q^{24} - 8 q^{25} + 5 q^{26} - 4 q^{27} - 4 q^{28} + 23 q^{29} - 16 q^{30} - 17 q^{31} + 16 q^{32} - 2 q^{33} - 2 q^{34} + 7 q^{35} - 8 q^{36} + 17 q^{37} - 2 q^{38} - 5 q^{39} - 2 q^{40} + 8 q^{41} - 4 q^{42} + 32 q^{43} + q^{44} - 2 q^{45} + 11 q^{46} - 7 q^{47} + 2 q^{48} - q^{49} + 2 q^{50} - 12 q^{51} + 10 q^{52} + 54 q^{53} - 4 q^{54} - 11 q^{55} + q^{56} + 18 q^{57} - 22 q^{58} - 38 q^{59} + 4 q^{60} - 28 q^{61} - 27 q^{62} - 2 q^{63} - 4 q^{64} - 10 q^{65} - 7 q^{66} + q^{67} - 2 q^{68} - 13 q^{69} + 7 q^{70} - 11 q^{71} + 2 q^{72} + 53 q^{73} + 2 q^{74} + 2 q^{75} - 2 q^{76} + 44 q^{77} + 10 q^{78} + 48 q^{79} - 2 q^{80} + 2 q^{81} + 8 q^{82} + 56 q^{83} + 11 q^{84} - 24 q^{85} - 13 q^{86} + q^{87} - 9 q^{88} - 43 q^{89} - 2 q^{90} - 50 q^{91} - 44 q^{92} - 22 q^{93} - 72 q^{94} - 14 q^{95} + 2 q^{96} + 17 q^{97} + 29 q^{98} - 9 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 8 * q^5 - 8 * q^6 + 11 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 + 2 * q^12 - 20 * q^13 - 4 * q^14 + 4 * q^15 - 4 * q^16 - 12 * q^17 + 2 * q^18 - 7 * q^19 - 2 * q^20 - 4 * q^21 + 11 * q^22 + 11 * q^23 + 2 * q^24 - 8 * q^25 + 5 * q^26 - 4 * q^27 - 4 * q^28 + 23 * q^29 - 16 * q^30 - 17 * q^31 + 16 * q^32 - 2 * q^33 - 2 * q^34 + 7 * q^35 - 8 * q^36 + 17 * q^37 - 2 * q^38 - 5 * q^39 - 2 * q^40 + 8 * q^41 - 4 * q^42 + 32 * q^43 + q^44 - 2 * q^45 + 11 * q^46 - 7 * q^47 + 2 * q^48 - q^49 + 2 * q^50 - 12 * q^51 + 10 * q^52 + 54 * q^53 - 4 * q^54 - 11 * q^55 + q^56 + 18 * q^57 - 22 * q^58 - 38 * q^59 + 4 * q^60 - 28 * q^61 - 27 * q^62 - 2 * q^63 - 4 * q^64 - 10 * q^65 - 7 * q^66 + q^67 - 2 * q^68 - 13 * q^69 + 7 * q^70 - 11 * q^71 + 2 * q^72 + 53 * q^73 + 2 * q^74 + 2 * q^75 - 2 * q^76 + 44 * q^77 + 10 * q^78 + 48 * q^79 - 2 * q^80 + 2 * q^81 + 8 * q^82 + 56 * q^83 + 11 * q^84 - 24 * q^85 - 13 * q^86 + q^87 - 9 * q^88 - 43 * q^89 - 2 * q^90 - 50 * q^91 - 44 * q^92 - 22 * q^93 - 72 * q^94 - 14 * q^95 + 2 * q^96 + 17 * q^97 + 29 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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