LMFDB - Embedded newform 525.2.bc.e.82.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.6
Character	$\chi$	$=$	525.82
Dual form			525.2.bc.e.493.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.969545 - 0.259789i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.859523 + 0.496246i) q^{4} +1.00375i q^{6} +(-2.42328 + 1.06195i) q^{7} +(-2.12394 + 2.12394i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.969545 - 0.259789i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.859523 + 0.496246i) q^{4} +1.00375i q^{6} +(-2.42328 + 1.06195i) q^{7} +(-2.12394 + 2.12394i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.78283 - 3.08796i) q^{11} +(-0.256876 - 0.958673i) q^{12} +(-2.78368 - 2.78368i) q^{13} +(-2.07359 + 1.65915i) q^{14} +(-0.514988 + 0.891986i) q^{16} +(0.506489 + 0.135713i) q^{17} +(-0.969545 - 0.259789i) q^{18} +(-2.06188 + 3.57128i) q^{19} +(-0.398574 - 2.61556i) q^{21} +(-2.53075 - 2.53075i) q^{22} +(-0.668338 - 2.49427i) q^{23} +(-1.50185 - 2.60128i) q^{24} +(-3.42207 - 1.97574i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.55587 - 2.11531i) q^{28} +6.14396i q^{29} +(-1.71173 + 0.988266i) q^{31} +(1.28726 - 4.80410i) q^{32} +(3.44417 - 0.922863i) q^{33} +0.526321 q^{34} +0.992492 q^{36} +(-0.152803 + 0.0409435i) q^{37} +(-1.07131 + 3.99817i) q^{38} +(3.40930 - 1.96836i) q^{39} +8.28475i q^{41} +(-1.06593 - 2.43236i) q^{42} +(-9.01253 + 9.01253i) q^{43} +(3.06477 + 1.76945i) q^{44} +(-1.29597 - 2.24468i) q^{46} +(1.39091 + 5.19095i) q^{47} +(-0.728304 - 0.728304i) q^{48} +(4.74453 - 5.14679i) q^{49} +(-0.262178 + 0.454106i) q^{51} +(3.77403 + 1.01125i) q^{52} +(-5.55200 - 1.48765i) q^{53} +(0.501874 - 0.869271i) q^{54} +(2.89138 - 7.40241i) q^{56} +(-2.91594 - 2.91594i) q^{57} +(1.59613 + 5.95685i) q^{58} +(1.30044 + 2.25243i) q^{59} +(8.67653 + 5.00940i) q^{61} +(-1.40286 + 1.40286i) q^{62} +(2.62959 + 0.291963i) q^{63} -7.05216i q^{64} +(3.09953 - 1.78951i) q^{66} +(1.42661 - 5.32418i) q^{67} +(-0.502686 + 0.134694i) q^{68} +2.58226 q^{69} -7.23274 q^{71} +(2.90136 - 0.777416i) q^{72} +(3.98240 - 14.8625i) q^{73} +(-0.137513 + 0.0793931i) q^{74} -4.09280i q^{76} +(7.59955 + 5.58969i) q^{77} +(2.79411 - 2.79411i) q^{78} +(-13.1146 - 7.57171i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.15229 + 8.03244i) q^{82} +(9.42372 + 9.42372i) q^{83} +(1.64054 + 2.05034i) q^{84} +(-6.39670 + 11.0794i) q^{86} +(-5.93461 - 1.59017i) q^{87} +(10.3453 + 2.77201i) q^{88} +(-5.52672 + 9.57257i) q^{89} +(9.70175 + 3.78950i) q^{91} +(1.81222 + 1.81222i) q^{92} +(-0.511564 - 1.90918i) q^{93} +(2.69710 + 4.67152i) q^{94} +(4.30724 + 2.48679i) q^{96} +(-2.48828 + 2.48828i) q^{97} +(3.26295 - 6.22262i) q^{98} +3.56567i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) $ 32 * q - 8 * q^7 + 24 * q^8	$ 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) $ 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.969545	−	0.259789i	0.685572	−	0.183698i	0.100813	−	0.994905i	$-0.467856\pi$
$2$	0.969545	−	0.259789i	0.685572	−	0.183698i	0.584759	+	0.811207i	$0.301189\pi$
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$	−0.859523	+	0.496246i	−0.429762	+	0.248123i
$5$		0			0
$5$		0			0
$6$			1.00375i			0.409778i
$7$	−2.42328	+	1.06195i	−0.915912	+	0.401379i
$7$	−2.42328	+	1.06195i	−0.915912	+	0.401379i
$8$	−2.12394	+	2.12394i	−0.750926	+	0.750926i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	−1.78283	−	3.08796i	−0.537545	−	0.931054i	−0.999036	−	0.0439095i	$-0.986019\pi$
$11$	−1.78283	−	3.08796i	−0.537545	−	0.931054i	0.461491	−	0.887145i	$-0.347315\pi$
$12$	−0.256876	−	0.958673i	−0.0741536	−	0.276745i
$13$	−2.78368	−	2.78368i	−0.772054	−	0.772054i	0.206411	−	0.978465i	$-0.433822\pi$
$13$	−2.78368	−	2.78368i	−0.772054	−	0.772054i	−0.978465	+	0.206411i	$0.933822\pi$
$14$	−2.07359	+	1.65915i	−0.554191	+	0.443426i
$15$		0			0
$16$	−0.514988	+	0.891986i	−0.128747	+	0.222997i
$17$	0.506489	+	0.135713i	0.122842	+	0.0329153i	0.319716	−	0.947513i	$-0.396412\pi$
$17$	0.506489	+	0.135713i	0.122842	+	0.0329153i	−0.196874	+	0.980429i	$0.563079\pi$
$18$	−0.969545	−	0.259789i	−0.228524	−	0.0612328i
$19$	−2.06188	+	3.57128i	−0.473028	+	0.819308i	−0.999523	−	0.0308699i	$-0.990172\pi$
$19$	−2.06188	+	3.57128i	−0.473028	+	0.819308i	0.526496	+	0.850178i	$0.323506\pi$
$20$		0			0
$21$	−0.398574	−	2.61556i	−0.0869761	−	0.570761i
$22$	−2.53075	−	2.53075i	−0.539559	−	0.539559i
$23$	−0.668338	−	2.49427i	−0.139358	−	0.520092i	−0.999942	−	0.0107826i	$-0.996568\pi$
$23$	−0.668338	−	2.49427i	−0.139358	−	0.520092i	0.860584	−	0.509309i	$-0.170099\pi$
$24$	−1.50185	−	2.60128i	−0.306564	−	0.530985i
$25$		0			0
$26$	−3.42207	−	1.97574i	−0.671124	−	0.387474i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.55587	−	2.11531i	0.294032	−	0.399756i
$29$			6.14396i			1.14091i	0.821331	+	0.570453i	$0.193232\pi$
$29$			6.14396i			1.14091i	−0.821331	+	0.570453i	$0.806768\pi$
$30$		0			0
$31$	−1.71173	+	0.988266i	−0.307435	+	0.177498i	−0.645778	−	0.763525i	$-0.723467\pi$
$31$	−1.71173	+	0.988266i	−0.307435	+	0.177498i	0.338343	+	0.941023i	$0.390134\pi$
$32$	1.28726	−	4.80410i	0.227557	−	0.849253i
$33$	3.44417	−	0.922863i	0.599553	−	0.160650i
$34$	0.526321			0.0902633
$35$		0			0
$36$	0.992492			0.165415
$37$	−0.152803	+	0.0409435i	−0.0251207	+	0.00673106i	−0.271357	−	0.962479i	$-0.587473\pi$
$37$	−0.152803	+	0.0409435i	−0.0251207	+	0.00673106i	0.246237	+	0.969210i	$0.420806\pi$
$38$	−1.07131	+	3.99817i	−0.173789	+	0.648589i
$39$	3.40930	−	1.96836i	0.545925	−	0.315190i
$40$		0			0
$41$			8.28475i			1.29386i	0.762549	+	0.646930i	$0.223948\pi$
$41$			8.28475i			1.29386i	−0.762549	+	0.646930i	$0.776052\pi$
$42$	−1.06593	−	2.43236i	−0.164476	−	0.375321i
$43$	−9.01253	+	9.01253i	−1.37440	+	1.37440i	−0.520594	+	0.853805i	$0.674289\pi$
$43$	−9.01253	+	9.01253i	−1.37440	+	1.37440i	−0.853805	+	0.520594i	$0.825711\pi$
$44$	3.06477	+	1.76945i	0.462032	+	0.266754i
$45$		0			0
$46$	−1.29597	−	2.24468i	−0.191080	−	0.330960i
$47$	1.39091	+	5.19095i	0.202885	+	0.757178i	0.990084	+	0.140478i	$0.0448640\pi$
$47$	1.39091	+	5.19095i	0.202885	+	0.757178i	−0.787198	+	0.616700i	$0.788469\pi$
$48$	−0.728304	−	0.728304i	−0.105122	−	0.105122i
$49$	4.74453	−	5.14679i	0.677790	−	0.735256i
$50$		0			0
$51$	−0.262178	+	0.454106i	−0.0367123	+	0.0635875i
$52$	3.77403	+	1.01125i	0.523363	+	0.140235i
$53$	−5.55200	−	1.48765i	−0.762626	−	0.204345i	−0.143514	−	0.989648i	$-0.545840\pi$
$53$	−5.55200	−	1.48765i	−0.762626	−	0.204345i	−0.619111	+	0.785303i	$0.712507\pi$
$54$	0.501874	−	0.869271i	0.0682963	−	0.118293i
$55$		0			0
$56$	2.89138	−	7.40241i	0.386376	−	0.989188i
$57$	−2.91594	−	2.91594i	−0.386225	−	0.386225i
$58$	1.59613	+	5.95685i	0.209583	+	0.782173i
$59$	1.30044	+	2.25243i	0.169303	+	0.293242i	0.938175	−	0.346161i	$-0.112515\pi$
$59$	1.30044	+	2.25243i	0.169303	+	0.293242i	−0.768872	+	0.639403i	$0.779182\pi$
$60$		0			0
$61$	8.67653	+	5.00940i	1.11092	+	0.641387i	0.939066	−	0.343736i	$-0.111692\pi$
$61$	8.67653	+	5.00940i	1.11092	+	0.641387i	0.171849	+	0.985123i	$0.445026\pi$
$62$	−1.40286	+	1.40286i	−0.178163	+	0.178163i
$63$	2.62959	+	0.291963i	0.331298	+	0.0367838i
$64$		−	7.05216i		−	0.881521i
$65$		0			0
$66$	3.09953	−	1.78951i	0.381526	−	0.220274i
$67$	1.42661	−	5.32418i	0.174288	−	0.650452i	−0.822384	−	0.568933i	$-0.807356\pi$
$67$	1.42661	−	5.32418i	0.174288	−	0.650452i	0.996672	−	0.0815189i	$-0.0259771\pi$
$68$	−0.502686	+	0.134694i	−0.0609596	+	0.0163341i
$69$	2.58226			0.310868
$70$		0			0
$71$	−7.23274			−0.858369			−0.429184	−	0.903217i	$-0.641199\pi$
$71$	−7.23274			−0.858369			−0.429184	+	0.903217i	$0.641199\pi$
$72$	2.90136	−	0.777416i	0.341928	−	0.0916194i
$73$	3.98240	−	14.8625i	0.466105	−	1.73953i	−0.187096	−	0.982342i	$-0.559908\pi$
$73$	3.98240	−	14.8625i	0.466105	−	1.73953i	0.653201	−	0.757185i	$-0.273426\pi$
$74$	−0.137513	+	0.0793931i	−0.0159855	+	0.00922926i
$75$		0			0
$76$		−	4.09280i		−	0.469476i
$77$	7.59955	+	5.58969i	0.866049	+	0.637005i
$78$	2.79411	−	2.79411i	0.316371	−	0.316371i
$79$	−13.1146	−	7.57171i	−1.47551	−	0.851884i	−0.475888	−	0.879506i	$-0.657873\pi$
$79$	−13.1146	−	7.57171i	−1.47551	−	0.851884i	−0.999618	+	0.0276214i	$0.991207\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	2.15229	+	8.03244i	0.237680	+	0.887035i
$83$	9.42372	+	9.42372i	1.03439	+	1.03439i	0.999387	+	0.0350007i	$0.0111434\pi$
$83$	9.42372	+	9.42372i	1.03439	+	1.03439i	0.0350007	+	0.999387i	$0.488857\pi$
$84$	1.64054	+	2.05034i	0.178998	+	0.223710i
$85$		0			0
$86$	−6.39670	+	11.0794i	−0.689774	+	1.19472i
$87$	−5.93461	−	1.59017i	−0.636257	−	0.170485i
$88$	10.3453	+	2.77201i	1.10281	+	0.295497i
$89$	−5.52672	+	9.57257i	−0.585831	+	1.01469i	0.408940	+	0.912561i	$0.365899\pi$
$89$	−5.52672	+	9.57257i	−0.585831	+	1.01469i	−0.994771	+	0.102128i	$0.967435\pi$
$90$		0			0
$91$	9.70175	+	3.78950i	1.01702	+	0.397247i
$92$	1.81222	+	1.81222i	0.188937	+	0.188937i
$93$	−0.511564	−	1.90918i	−0.0530467	−	0.197973i
$94$	2.69710	+	4.67152i	0.278185	+	0.481830i
$95$		0			0
$96$	4.30724	+	2.48679i	0.439606	+	0.253807i
$97$	−2.48828	+	2.48828i	−0.252647	+	0.252647i	−0.822055	−	0.569408i	$-0.807172\pi$
$97$	−2.48828	+	2.48828i	−0.252647	+	0.252647i	0.569408	+	0.822055i	$0.307172\pi$
$98$	3.26295	−	6.22262i	0.329608	−	0.628580i
$99$			3.56567i			0.358363i
$100$		0			0
$101$	0.739502	−	0.426952i	0.0735832	−	0.0424833i	−0.462757	−	0.886485i	$-0.653140\pi$
$101$	0.739502	−	0.426952i	0.0735832	−	0.0424833i	0.536340	+	0.844002i	$0.319806\pi$
$102$	−0.136222	+	0.508387i	−0.0134880	+	0.0503378i
$103$	5.86357	−	1.57114i	0.577755	−	0.154809i	0.0419040	−	0.999122i	$-0.486658\pi$
$103$	5.86357	−	1.57114i	0.577755	−	0.154809i	0.535851	+	0.844313i	$0.319991\pi$
$104$	11.8247			1.15951
$105$		0			0
$106$	−5.76939			−0.560373
$107$	−11.2984	+	3.02740i	−1.09226	+	0.292670i	−0.759608	−	0.650381i	$-0.774609\pi$
$107$	−11.2984	+	3.02740i	−1.09226	+	0.292670i	−0.332650	+	0.943051i	$0.607943\pi$
$108$	−0.256876	+	0.958673i	−0.0247179	+	0.0922484i
$109$	10.8565	−	6.26802i	1.03987	−	0.600367i	0.120071	−	0.992765i	$-0.461688\pi$
$109$	10.8565	−	6.26802i	1.03987	−	0.600367i	0.919796	+	0.392398i	$0.128354\pi$
$110$		0			0
$111$		−	0.158193i		−	0.0150151i
$112$	0.300715	−	2.70842i	0.0284149	−	0.255922i
$113$	7.25767	−	7.25767i	0.682744	−	0.682744i	−0.277874	−	0.960618i	$-0.589630\pi$
$113$	7.25767	−	7.25767i	0.682744	−	0.682744i	0.960618	+	0.277874i	$0.0896296\pi$
$114$	−3.58466	−	2.06961i	−0.335734	−	0.193836i
$115$		0			0
$116$	−3.04892	−	5.28088i	−0.283085	−	0.490317i
$117$	1.01890	+	3.80258i	0.0941971	+	0.351549i
$118$	1.84600	+	1.84600i	0.169938	+	0.169938i
$119$	−1.37148	+	0.208995i	−0.125724	+	0.0191585i
$120$		0			0
$121$	−0.856990	+	1.48435i	−0.0779082	+	0.134941i
$122$	9.71367	+	2.60277i	0.879435	+	0.235644i
$123$	−8.00245	−	2.14425i	−0.721557	−	0.193341i
$124$	0.980846	−	1.69887i	0.0880825	−	0.152563i
$125$		0			0
$126$	2.62536	−	0.400068i	0.233885	−	0.0356409i
$127$	1.06249	+	1.06249i	0.0942804	+	0.0942804i	0.752674	−	0.658393i	$-0.228764\pi$
$127$	1.06249	+	1.06249i	0.0942804	+	0.0942804i	−0.658393	+	0.752674i	$0.728764\pi$
$128$	0.742437	+	2.77081i	0.0656228	+	0.244908i
$129$	−6.37282	−	11.0381i	−0.561096	−	0.971846i
$130$		0			0
$131$	10.3808	+	5.99337i	0.906976	+	0.523643i	0.879457	−	0.475979i	$-0.157906\pi$
$131$	10.3808	+	5.99337i	0.906976	+	0.523643i	0.0275190	+	0.999621i	$0.491239\pi$
$132$	−2.50238	+	2.50238i	−0.217804	+	0.217804i
$133$	1.20398	−	10.8438i	0.104399	−	0.940277i
$134$		−	5.53265i		−	0.477948i
$135$		0			0
$136$	−1.36400	+	0.787505i	−0.116962	+	0.0675280i
$137$	−1.63597	+	6.10553i	−0.139770	+	0.521630i	0.860162	+	0.510021i	$0.170362\pi$
$137$	−1.63597	+	6.10553i	−0.139770	+	0.521630i	−0.999933	+	0.0116098i	$0.996304\pi$
$138$	2.50362	−	0.670842i	0.213122	−	0.0571059i
$139$	−5.07872			−0.430772			−0.215386	−	0.976529i	$-0.569101\pi$
$139$	−5.07872			−0.430772			−0.215386	+	0.976529i	$0.569101\pi$
$140$		0			0
$141$	−5.37407			−0.452578
$142$	−7.01247	+	1.87899i	−0.588474	+	0.157681i
$143$	−3.63305	+	13.5587i	−0.303811	+	1.13384i
$144$	0.891986	−	0.514988i	0.0743322	−	0.0429157i
$145$		0			0
$146$		−	15.4445i		−	1.27819i
$147$	3.74344	+	5.91495i	0.308754	+	0.487857i
$148$	0.111020	−	0.111020i	0.00912577	−	0.00912577i
$149$	−13.1991	−	7.62048i	−1.08131	−	0.624294i	−0.150060	−	0.988677i	$-0.547947\pi$
$149$	−13.1991	−	7.62048i	−1.08131	−	0.624294i	−0.931249	+	0.364383i	$0.881280\pi$
$150$		0			0
$151$	−7.46500	−	12.9298i	−0.607493	−	1.05221i	−0.991652	−	0.128942i	$-0.958842\pi$
$151$	−7.46500	−	12.9298i	−0.607493	−	1.05221i	0.384159	−	0.923267i	$-0.374491\pi$
$152$	−3.20588	−	11.9645i	−0.260031	−	0.970449i
$153$	−0.370776	−	0.370776i	−0.0299754	−	0.0299754i
$154$	8.82025	+	3.44518i	0.710756	+	0.277621i
$155$		0			0
$156$	−1.95358	+	3.38370i	−0.156412	+	0.270913i
$157$	−6.36897	−	1.70656i	−0.508299	−	0.136198i	−0.00445019	−	0.999990i	$-0.501417\pi$
$157$	−6.36897	−	1.70656i	−0.508299	−	0.136198i	−0.503849	+	0.863792i	$0.668083\pi$
$158$	−14.6822	−	3.93409i	−1.16806	−	0.312980i
$159$	2.87393	−	4.97779i	0.227917	−	0.394764i
$160$		0			0
$161$	4.26836	+	5.33457i	0.336394	+	0.420423i
$162$	0.709756	+	0.709756i	0.0557637	+	0.0557637i
$163$	−0.361835	−	1.35039i	−0.0283411	−	0.105770i	0.950306	−	0.311316i	$-0.100770\pi$
$163$	−0.361835	−	1.35039i	−0.0283411	−	0.105770i	−0.978648	+	0.205546i	$0.934103\pi$
$164$	−4.11127	−	7.12093i	−0.321036	−	0.556051i
$165$		0			0
$166$	11.5849	+	6.68855i	0.899163	+	0.519132i
$167$	−4.18179	+	4.18179i	−0.323597	+	0.323597i	−0.850145	−	0.526548i	$-0.823486\pi$
$167$	−4.18179	+	4.18179i	−0.323597	+	0.323597i	0.526548	+	0.850145i	$0.323486\pi$
$168$	6.40183	+	4.70874i	0.493912	+	0.363287i
$169$			2.49776i			0.192135i
$170$		0			0
$171$	3.57128	−	2.06188i	0.273103	−	0.157676i
$172$	3.27405	−	12.2189i	0.249644	−	0.931683i
$173$	2.31263	−	0.619668i	0.175826	−	0.0471125i	−0.169832	−	0.985473i	$-0.554322\pi$
$173$	2.31263	−	0.619668i	0.175826	−	0.0471125i	0.345658	+	0.938361i	$0.387656\pi$
$174$	−6.16698			−0.467518
$175$		0			0
$176$	3.67255			0.276829
$177$	−2.51226	+	0.673159i	−0.188833	+	0.0505977i
$178$	−2.87156	+	10.7168i	−0.215233	+	0.803259i
$179$	−1.63071	+	0.941493i	−0.121885	+	0.0703705i	−0.559703	−	0.828693i	$-0.689085\pi$
$179$	−1.63071	+	0.941493i	−0.121885	+	0.0703705i	0.437818	+	0.899064i	$0.355751\pi$
$180$		0			0
$181$		−	17.7439i		−	1.31889i	−0.751751	−	0.659447i	$-0.770791\pi$
$181$		−	17.7439i		−	1.31889i	0.751751	−	0.659447i	$-0.229209\pi$
$182$	10.3908	+	1.15368i	0.770214	+	0.0855166i
$183$	−7.08436	+	7.08436i	−0.523691	+	0.523691i
$184$	6.71719	+	3.87817i	0.495198	+	0.285903i
$185$		0			0
$186$	−0.991969	−	1.71814i	−0.0727347	−	0.125980i
$187$	−0.483908	−	1.80597i	−0.0353869	−	0.132066i
$188$	−3.77151	−	3.77151i	−0.275066	−	0.275066i
$189$	−0.962603	+	2.46443i	−0.0700191	+	0.179261i
$190$		0			0
$191$	−5.37301	+	9.30633i	−0.388778	+	0.673382i	−0.992285	−	0.123975i	$-0.960436\pi$
$191$	−5.37301	+	9.30633i	−0.388778	+	0.673382i	0.603508	+	0.797357i	$0.293769\pi$
$192$	6.81187	+	1.82523i	0.491604	+	0.131725i
$193$	−3.11109	−	0.833614i	−0.223941	−	0.0600049i	0.145104	−	0.989416i	$-0.453648\pi$
$193$	−3.11109	−	0.833614i	−0.223941	−	0.0600049i	−0.369045	+	0.929412i	$0.620315\pi$
$194$	−1.76607	+	3.05893i	−0.126797	+	0.219618i
$195$		0			0
$196$	−1.52396	+	6.77824i	−0.108854	+	0.484160i
$197$	10.9317	+	10.9317i	0.778852	+	0.778852i	0.979636	−	0.200784i	$-0.0643489\pi$
$197$	10.9317	+	10.9317i	0.778852	+	0.778852i	−0.200784	+	0.979636i	$0.564349\pi$
$198$	0.926321	+	3.45708i	0.0658307	+	0.245684i
$199$	6.19974	+	10.7383i	0.439488	+	0.761215i	0.997650	−	0.0685166i	$-0.0218266\pi$
$199$	6.19974	+	10.7383i	0.439488	+	0.761215i	−0.558162	+	0.829732i	$0.688493\pi$
$200$		0			0
$201$	4.77353	+	2.75600i	0.336699	+	0.194393i
$202$	0.606063	−	0.606063i	0.0426425	−	0.0426425i
$203$	−6.52458	−	14.8885i	−0.457935	−	1.04497i
$204$		−	0.520419i		−	0.0364366i
$205$		0			0
$206$	5.27683	−	3.04658i	0.367654	−	0.212265i
$207$	−0.668338	+	2.49427i	−0.0464527	+	0.173364i
$208$	3.91657	−	1.04944i	0.271565	−	0.0727657i
$209$	14.7040			1.01709
$210$		0			0
$211$	−13.4216			−0.923982			−0.461991	−	0.886885i	$-0.652865\pi$
$211$	−13.4216			−0.923982			−0.461991	+	0.886885i	$0.652865\pi$
$212$	5.51031	−	1.47648i	0.378450	−	0.101405i
$213$	1.87197	−	6.98629i	0.128265	−	0.478693i
$214$	−10.1678	+	5.87040i	−0.695058	+	0.401292i
$215$		0			0
$216$			3.00370i			0.204376i
$217$	3.09850	−	4.21261i	0.210340	−	0.285970i
$218$	8.89753	−	8.89753i	0.602617	−	0.602617i
$219$	13.3254	+	7.69341i	0.900445	+	0.519872i
$220$		0			0
$221$	−1.03212	−	1.78769i	−0.0694280	−	0.120253i
$222$	−0.0410969	−	0.153376i	−0.00275824	−	0.0102939i
$223$	1.60905	+	1.60905i	0.107750	+	0.107750i	0.758927	−	0.651176i	$-0.225724\pi$
$223$	1.60905	+	1.60905i	0.107750	+	0.107750i	−0.651176	+	0.758927i	$0.725724\pi$
$224$	1.98234	+	13.0087i	0.132451	+	0.869178i
$225$		0			0
$226$	5.15118	−	8.92210i	0.342651	−	0.593489i
$227$	−24.9026	−	6.67262i	−1.65284	−	0.442878i	−0.692435	−	0.721480i	$-0.743462\pi$
$227$	−24.9026	−	6.67262i	−1.65284	−	0.442878i	−0.960407	+	0.278603i	$0.910129\pi$
$228$	3.95334	+	1.05929i	0.261816	+	0.0701534i
$229$	0.669566	−	1.15972i	0.0442462	−	0.0766366i	−0.843054	−	0.537829i	$-0.819245\pi$
$229$	0.669566	−	1.15972i	0.0442462	−	0.0766366i	0.887300	+	0.461192i	$0.152578\pi$
$230$		0			0
$231$	−7.36614	+	5.89388i	−0.484656	+	0.387789i
$232$	−13.0494	−	13.0494i	−0.856736	−	0.856736i
$233$	5.55413	+	20.7283i	0.363863	+	1.35796i	0.868956	+	0.494890i	$0.164792\pi$
$233$	5.55413	+	20.7283i	0.363863	+	1.35796i	−0.505093	+	0.863065i	$0.668542\pi$
$234$	1.97574	+	3.42207i	0.129158	+	0.223708i
$235$		0			0
$236$	−2.23552	−	1.29068i	−0.145520	−	0.0840161i
$237$	10.7080	−	10.7080i	0.695561	−	0.695561i
$238$	−1.27542	+	0.558926i	−0.0826732	+	0.0362298i
$239$		−	12.8433i		−	0.830767i	−0.909646	−	0.415384i	$-0.863647\pi$
$239$		−	12.8433i		−	0.830767i	0.909646	−	0.415384i	$-0.136353\pi$
$240$		0			0
$241$	−22.0766	+	12.7459i	−1.42208	+	0.821036i	−0.996476	−	0.0838747i	$-0.973270\pi$
$241$	−22.0766	+	12.7459i	−1.42208	+	0.821036i	−0.425601	+	0.904911i	$0.639937\pi$
$242$	−0.445273	+	1.66178i	−0.0286232	+	0.106823i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−9.94357			−0.636572
$245$		0			0
$246$	−8.31579			−0.530196
$247$	15.6809	−	4.20169i	0.997753	−	0.267347i
$248$	1.53659	−	5.73462i	0.0975734	−	0.364149i
$249$	−11.5417	+	6.66358i	−0.731423	+	0.422287i
$250$		0			0
$251$			12.0858i			0.762849i	0.924400	+	0.381425i	$0.124566\pi$
$251$			12.0858i			0.762849i	−0.924400	+	0.381425i	$0.875434\pi$
$252$	−2.40508	+	1.05398i	−0.151506	+	0.0663942i
$253$	−6.51067	+	6.51067i	−0.409322	+	0.409322i
$254$	1.30615	+	0.754106i	0.0819552	+	0.0473168i
$255$		0			0
$256$	8.49182	+	14.7083i	0.530739	+	0.919266i
$257$	−2.68228	−	10.0104i	−0.167316	−	0.624431i	−0.997733	−	0.0672896i	$-0.978565\pi$
$257$	−2.68228	−	10.0104i	−0.167316	−	0.624431i	0.830418	−	0.557141i	$-0.188102\pi$
$258$	−9.04630	−	9.04630i	−0.563198	−	0.563198i
$259$	0.326804	−	0.261486i	0.0203066	−	0.0162480i
$260$		0			0
$261$	3.07198	−	5.32083i	0.190151	−	0.329351i
$262$	11.6217	+	3.11402i	0.717990	+	0.192385i
$263$	−7.68155	−	2.05827i	−0.473665	−	0.126918i	0.0140863	−	0.999901i	$-0.495516\pi$
$263$	−7.68155	−	2.05827i	−0.473665	−	0.126918i	−0.487751	+	0.872983i	$0.662183\pi$
$264$	−5.35511	+	9.27532i	−0.329584	+	0.570856i
$265$		0			0
$266$	−1.64978	−	10.8263i	−0.101155	−	0.663806i
$267$	−7.81597	−	7.81597i	−0.478329	−	0.478329i
$268$	1.41590	+	5.28421i	0.0864898	+	0.322784i
$269$	0.857638	+	1.48547i	0.0522911	+	0.0905709i	0.890986	−	0.454030i	$-0.150014\pi$
$269$	0.857638	+	1.48547i	0.0522911	+	0.0905709i	−0.838695	+	0.544601i	$0.816681\pi$
$270$		0			0
$271$	−10.0645	−	5.81076i	−0.611377	−	0.352979i	0.162127	−	0.986770i	$-0.448164\pi$
$271$	−10.0645	−	5.81076i	−0.611377	−	0.352979i	−0.773504	+	0.633791i	$0.781498\pi$
$272$	−0.381890	+	0.381890i	−0.0231555	+	0.0231555i
$273$	−6.17137	+	8.39038i	−0.373508	+	0.507809i
$274$			6.34459i			0.383291i
$275$		0			0
$276$	−2.21951	+	1.28144i	−0.133599	+	0.0771334i
$277$	−2.36709	+	8.83410i	−0.142225	+	0.530790i	0.857639	+	0.514253i	$0.171931\pi$
$277$	−2.36709	+	8.83410i	−0.142225	+	0.530790i	−0.999863	+	0.0165369i	$0.994736\pi$
$278$	−4.92405	+	1.31940i	−0.295325	+	0.0791321i
$279$	1.97653			0.118332
$280$		0			0
$281$	15.0644			0.898669			0.449334	−	0.893364i	$-0.351661\pi$
$281$	15.0644			0.898669			0.449334	+	0.893364i	$0.351661\pi$
$282$	−5.21040	+	1.39612i	−0.310275	+	0.0831379i
$283$	−4.14461	+	15.4679i	−0.246371	+	0.919470i	0.726318	+	0.687359i	$0.241230\pi$
$283$	−4.14461	+	15.4679i	−0.246371	+	0.919470i	−0.972689	+	0.232111i	$0.925437\pi$
$284$	6.21671	−	3.58922i	0.368894	−	0.212981i
$285$		0			0
$286$			14.0896i			0.833137i
$287$	−8.79798	−	20.0762i	−0.519329	−	1.18506i
$288$	−3.51685	+	3.51685i	−0.207232	+	0.207232i
$289$	−14.4843	−	8.36253i	−0.852019	−	0.491913i
$290$		0			0
$291$	−1.75948	−	3.04751i	−0.103143	−	0.178648i
$292$	3.95250	+	14.7509i	0.231302	+	0.863233i
$293$	6.20477	+	6.20477i	0.362487	+	0.362487i	0.864728	−	0.502241i	$-0.167491\pi$
$293$	6.20477	+	6.20477i	0.362487	+	0.362487i	−0.502241	+	0.864728i	$0.667491\pi$
$294$	5.16608	+	4.76231i	0.301292	+	0.277743i
$295$		0			0
$296$	0.237583	−	0.411506i	0.0138092	−	0.0239183i
$297$	−3.44417	−	0.922863i	−0.199851	−	0.0535499i
$298$	−14.7768	−	3.95943i	−0.855997	−	0.229364i
$299$	−5.08282	+	8.80370i	−0.293947	+	0.509131i
$300$		0			0
$301$	12.2690	−	31.4107i	0.707173	−	1.81048i
$302$	−10.5967	−	10.5967i	−0.609769	−	0.609769i
$303$	0.221006	+	0.824807i	0.0126965	+	0.0473839i
$304$	−2.12369	−	3.67834i	−0.121802	−	0.210967i
$305$		0			0
$306$	−0.455807	−	0.263160i	−0.0260568	−	0.0150439i
$307$	6.26397	−	6.26397i	0.357504	−	0.357504i	−0.505388	−	0.862892i	$-0.668651\pi$
$307$	6.26397	−	6.26397i	0.357504	−	0.357504i	0.862892	+	0.505388i	$0.168651\pi$
$308$	−9.30585	−	1.03322i	−0.530250	−	0.0588735i
$309$			6.07042i			0.345334i
$310$		0			0
$311$	−5.78463	+	3.33976i	−0.328016	+	0.189380i	−0.654960	−	0.755664i	$-0.727315\pi$
$311$	−5.78463	+	3.33976i	−0.328016	+	0.189380i	0.326944	+	0.945044i	$0.393981\pi$
$312$	−3.06047	+	11.4218i	−0.173265	+	0.646633i
$313$	1.79143	−	0.480011i	0.101257	−	0.0271318i	−0.207835	−	0.978164i	$-0.566642\pi$
$313$	1.79143	−	0.480011i	0.101257	−	0.0271318i	0.309092	+	0.951032i	$0.399975\pi$
$314$	−6.61835			−0.373495
$315$		0			0
$316$	15.0297			0.845488
$317$	−1.66619	+	0.446453i	−0.0935824	+	0.0250753i	−0.305306	−	0.952254i	$-0.598759\pi$
$317$	−1.66619	+	0.446453i	−0.0935824	+	0.0250753i	0.211724	+	0.977329i	$0.432092\pi$
$318$	1.49323	−	5.57280i	0.0837361	−	0.312507i
$319$	18.9723	−	10.9537i	1.06224	−	0.613287i
$320$		0			0
$321$		−	11.6970i		−	0.652861i
$322$	5.52423	+	4.06323i	0.307853	+	0.226435i
$323$	−1.52899	+	1.52899i	−0.0850752	+	0.0850752i
$324$	−0.859523	−	0.496246i	−0.0477513	−	0.0275692i
$325$		0			0
$326$	−0.701630	−	1.21526i	−0.0388597	−	0.0673070i
$327$	3.24457	+	12.1089i	0.179425	+	0.669623i
$328$	−17.5963	−	17.5963i	−0.971594	−	0.971594i
$329$	−8.88309	−	11.1020i	−0.489741	−	0.612075i
$330$		0			0
$331$	−13.0089	+	22.5320i	−0.715032	+	1.23847i	0.247915	+	0.968782i	$0.420255\pi$
$331$	−13.0089	+	22.5320i	−0.715032	+	1.23847i	−0.962947	+	0.269690i	$0.913079\pi$
$332$	−12.7764	−	3.42342i	−0.701196	−	0.187885i
$333$	0.152803	+	0.0409435i	0.00837356	+	0.00224369i
$334$	−2.96806	+	5.14082i	−0.162405	+	0.281293i
$335$		0			0
$336$	2.53830	+	0.991459i	0.138476	+	0.0540885i
$337$	14.7150	+	14.7150i	0.801579	+	0.801579i	0.983342	−	0.181763i	$-0.0581805\pi$
$337$	14.7150	+	14.7150i	0.801579	+	0.801579i	−0.181763	+	0.983342i	$0.558180\pi$
$338$	0.648890	+	2.42169i	0.0352950	+	0.131723i
$339$	5.13195	+	8.88879i	0.278729	+	0.482773i
$340$		0			0
$341$	6.10345	+	3.52383i	0.330520	+	0.190826i
$342$	2.92686	−	2.92686i	0.158267	−	0.158267i
$343$	−6.03166	+	17.5105i	−0.325679	+	0.945480i
$344$		−	38.2842i		−	2.06414i
$345$		0			0
$346$	2.08122	−	1.20159i	0.111887	−	0.0645980i
$347$	3.31515	−	12.3723i	0.177967	−	0.664181i	−0.818060	−	0.575132i	$-0.804951\pi$
$347$	3.31515	−	12.3723i	0.177967	−	0.664181i	0.996027	−	0.0890489i	$-0.0283827\pi$
$348$	5.89005	−	1.57823i	0.315740	−	0.0846023i
$349$	−12.7510			−0.682546			−0.341273	−	0.939964i	$-0.610858\pi$
$349$	−12.7510			−0.682546			−0.341273	+	0.939964i	$0.610858\pi$
$350$		0			0
$351$	−3.93672			−0.210127
$352$	−17.1298	+	4.58992i	−0.913023	+	0.244644i
$353$	4.46786	−	16.6743i	0.237800	−	0.887483i	−0.739066	−	0.673633i	$-0.764733\pi$
$353$	4.46786	−	16.6743i	0.237800	−	0.887483i	0.976866	−	0.213850i	$-0.0686004\pi$
$354$	−2.26087	+	1.30532i	−0.120164	+	0.0693768i
$355$		0			0
$356$		−	10.9705i		−	0.581433i
$357$	0.153092	−	1.37884i	0.00810250	−	0.0729761i
$358$	−1.33646	+	1.33646i	−0.0706342	+	0.0706342i
$359$	6.50719	+	3.75693i	0.343437	+	0.198283i	0.661791	−	0.749689i	$-0.269797\pi$
$359$	6.50719	+	3.75693i	0.343437	+	0.198283i	−0.318354	+	0.947972i	$0.603130\pi$
$360$		0			0
$361$	0.997305	+	1.72738i	0.0524897	+	0.0909149i
$362$	−4.60967	−	17.2035i	−0.242279	−	0.904197i
$363$	−1.21197	−	1.21197i	−0.0636118	−	0.0636118i
$364$	−10.2194	+	1.55729i	−0.535642	+	0.0816244i
$365$		0			0
$366$	−5.02817	+	8.70904i	−0.262826	+	0.455229i
$367$	6.65407	+	1.78295i	0.347340	+	0.0930693i	0.428271	−	0.903650i	$-0.359123\pi$
$367$	6.65407	+	1.78295i	0.347340	+	0.0930693i	−0.0809315	+	0.996720i	$0.525790\pi$
$368$	2.56904	+	0.688373i	0.133921	+	0.0358839i
$369$	4.14237	−	7.17480i	0.215643	−	0.373505i
$370$		0			0
$371$	15.0338	−	2.29095i	0.780518	−	0.118940i
$372$	1.38713	+	1.38713i	0.0719191	+	0.0719191i
$373$	−1.74301	−	6.50499i	−0.0902494	−	0.336816i	0.906007	−	0.423263i	$-0.139115\pi$
$373$	−1.74301	−	6.50499i	−0.0902494	−	0.336816i	−0.996256	+	0.0864472i	$0.972449\pi$
$374$	−0.938342	−	1.62526i	−0.0485205	−	0.0840400i
$375$		0			0
$376$	−13.9795	−	8.07106i	−0.720937	−	0.416233i
$377$	17.1028	−	17.1028i	0.880840	−	0.880840i
$378$	−0.293057	+	2.63945i	−0.0150732	+	0.135758i
$379$			37.6021i			1.93149i	0.259496	+	0.965744i	$0.416444\pi$
$379$			37.6021i			1.93149i	−0.259496	+	0.965744i	$0.583556\pi$
$380$		0			0
$381$	−1.30127	+	0.751291i	−0.0666663	+	0.0384898i
$382$	−2.79170	+	10.4188i	−0.142836	+	0.533070i
$383$	14.9343	−	4.00163i	0.763106	−	0.204474i	0.143782	−	0.989609i	$-0.454073\pi$
$383$	14.9343	−	4.00163i	0.763106	−	0.204474i	0.619324	+	0.785136i	$0.287407\pi$
$384$	−2.86856			−0.146385
$385$		0			0
$386$	−3.23291			−0.164551
$387$	12.3113	−	3.29882i	0.625821	−	0.167688i
$388$	0.903935	−	3.37353i	0.0458904	−	0.171265i
$389$	−16.0657	+	9.27555i	−0.814565	+	0.470289i	−0.848539	−	0.529134i	$-0.822517\pi$
$389$	−16.0657	+	9.27555i	−0.814565	+	0.470289i	0.0339739	+	0.999423i	$0.489184\pi$
$390$		0			0
$391$		−	1.35402i		−	0.0684759i
$392$	0.854385	+	21.0086i	0.0431530	+	1.06109i
$393$	−8.47590	+	8.47590i	−0.427553	+	0.427553i
$394$	13.4387	+	7.75885i	0.677033	+	0.390885i
$395$		0			0
$396$	−1.76945	−	3.06477i	−0.0889181	−	0.154011i
$397$	1.17781	+	4.39567i	0.0591128	+	0.220612i	0.989163	−	0.146820i	$-0.0469037\pi$
$397$	1.17781	+	4.39567i	0.0591128	+	0.220612i	−0.930050	+	0.367432i	$0.880237\pi$
$398$	8.80061	+	8.80061i	0.441135	+	0.441135i
$399$	10.1627	+	3.96954i	0.508771	+	0.198726i
$400$		0			0
$401$	11.1701	−	19.3471i	0.557806	−	0.966148i	−0.439873	−	0.898060i	$-0.644977\pi$
$401$	11.1701	−	19.3471i	0.557806	−	0.966148i	0.997679	−	0.0680885i	$-0.0216900\pi$
$402$	5.34413	+	1.43196i	0.266541	+	0.0714195i
$403$	7.51592	+	2.01388i	0.374395	+	0.100319i
$404$	−0.423746	+	0.733949i	−0.0210821	+	0.0365153i
$405$		0			0
$406$	−10.1937	−	12.7401i	−0.505907	−	0.632279i
$407$	0.398854	+	0.398854i	0.0197705	+	0.0197705i
$408$	−0.407643	−	1.52134i	−0.0201813	−	0.0753177i
$409$	−3.04693	−	5.27744i	−0.150661	−	0.260953i	0.780810	−	0.624769i	$-0.214807\pi$
$409$	−3.04693	−	5.27744i	−0.150661	−	0.260953i	−0.931471	+	0.363816i	$0.881474\pi$
$410$		0			0
$411$	−5.47407	−	3.16045i	−0.270016	−	0.155894i
$412$	−4.26020	+	4.26020i	−0.209885	+	0.209885i
$413$	−5.54331	−	4.07726i	−0.272768	−	0.200629i
$414$			2.59194i			0.127387i
$415$		0			0
$416$	−16.9564	+	9.78978i	−0.831356	+	0.479984i
$417$	1.31447	−	4.90567i	0.0643699	−	0.240232i
$418$	14.2561	−	3.81992i	0.697291	−	0.186839i
$419$	23.3177			1.13914			0.569572	−	0.821942i	$-0.307109\pi$
$419$	23.3177			1.13914			0.569572	+	0.821942i	$0.307109\pi$
$420$		0			0
$421$	−0.0119079			−0.000580356			−0.000290178	−	1.00000i	$-0.500092\pi$
$421$	−0.0119079			−0.000580356			−0.000290178		1.00000i	$0.500092\pi$
$422$	−13.0129	+	3.48679i	−0.633456	+	0.169734i
$423$	1.39091	−	5.19095i	0.0676284	−	0.252393i
$424$	14.9518	−	8.63243i	0.726124	−	0.419228i
$425$		0			0
$426$		−	7.25985i		−	0.351741i
$427$	−26.3453	−	2.92511i	−1.27494	−	0.141556i
$428$	8.20890	−	8.20890i	0.396792	−	0.396792i
$429$	−12.1564	−	7.01851i	−0.586918	−	0.338857i
$430$		0			0
$431$	−9.44866	−	16.3656i	−0.455126	−	0.788301i	0.543569	−	0.839364i	$-0.317072\pi$
$431$	−9.44866	−	16.3656i	−0.455126	−	0.788301i	−0.998695	+	0.0510628i	$0.983739\pi$
$432$	0.266578	+	0.994881i	0.0128257	+	0.0478662i
$433$	−18.7716	−	18.7716i	−0.902105	−	0.902105i	0.0935133	−	0.995618i	$-0.470190\pi$
$433$	−18.7716	−	18.7716i	−0.902105	−	0.902105i	−0.995618	+	0.0935133i	$0.970190\pi$
$434$	1.90974	−	4.88927i	0.0916707	−	0.234692i
$435$		0			0
$436$	−6.22096	+	10.7750i	−0.297930	+	0.516029i
$437$	10.2858	+	2.75607i	0.492035	+	0.131840i
$438$	14.9182	+	3.99732i	0.712820	+	0.190999i
$439$	−3.40990	+	5.90612i	−0.162746	+	0.281884i	−0.935852	−	0.352392i	$-0.885368\pi$
$439$	−3.40990	+	5.90612i	−0.162746	+	0.281884i	0.773107	+	0.634276i	$0.218702\pi$
$440$		0			0
$441$	−6.68228	+	2.08499i	−0.318204	+	0.0992852i
$442$	−1.46511	−	1.46511i	−0.0696881	−	0.0696881i
$443$	−1.78571	−	6.66435i	−0.0848415	−	0.316633i	0.910443	−	0.413635i	$-0.135741\pi$
$443$	−1.78571	−	6.66435i	−0.0848415	−	0.316633i	−0.995284	+	0.0970026i	$0.969074\pi$
$444$	0.0785028	+	0.135971i	0.00372558	+	0.00645289i
$445$		0			0
$446$	1.97807	+	1.14204i	0.0936641	+	0.0540770i
$447$	10.7770	−	10.7770i	0.509734	−	0.509734i
$448$	7.48904	+	17.0893i	0.353824	+	0.807395i
$449$		−	27.2653i		−	1.28673i	−0.765560	−	0.643365i	$-0.777538\pi$
$449$		−	27.2653i		−	1.28673i	0.765560	−	0.643365i	$-0.222462\pi$
$450$		0			0
$451$	25.5830	−	14.7703i	1.20465	−	0.695508i
$452$	−2.63655	+	9.83972i	−0.124013	+	0.462822i
$453$	14.4213	−	3.86417i	0.677570	−	0.181554i
$454$	−25.8776			−1.21450
$455$		0			0
$456$	12.3866			0.580054
$457$	−16.7691	+	4.49326i	−0.784425	+	0.210186i	−0.628735	−	0.777620i	$-0.716427\pi$
$457$	−16.7691	+	4.49326i	−0.784425	+	0.210186i	−0.155690	+	0.987806i	$0.549760\pi$
$458$	0.347892	−	1.29835i	0.0162559	−	0.0606679i
$459$	0.454106	−	0.262178i	0.0211958	−	0.0122374i
$460$		0			0
$461$			41.8808i			1.95058i	0.220920	+	0.975292i	$0.429094\pi$
$461$			41.8808i			1.95058i	−0.220920	+	0.975292i	$0.570906\pi$
$462$	−5.61064	+	7.62803i	−0.261031	+	0.354888i
$463$	15.4654	−	15.4654i	0.718740	−	0.718740i	−0.249607	−	0.968347i	$-0.580302\pi$
$463$	15.4654	−	15.4654i	0.718740	−	0.718740i	0.968347	+	0.249607i	$0.0803016\pi$
$464$	−5.48033	−	3.16407i	−0.254418	−	0.146888i
$465$		0			0
$466$	10.7700	+	18.6541i	0.498909	+	0.864135i
$467$	8.68477	+	32.4120i	0.401883	+	1.49985i	0.809732	+	0.586800i	$0.199612\pi$
$467$	8.68477	+	32.4120i	0.401883	+	1.49985i	−0.407849	+	0.913049i	$0.633721\pi$
$468$	−2.76278	−	2.76278i	−0.127710	−	0.127710i
$469$	2.19694	+	14.4169i	0.101445	+	0.665713i
$470$		0			0
$471$	3.29682	−	5.71026i	0.151910	−	0.263115i
$472$	−7.54610	−	2.02197i	−0.347337	−	0.0930688i
$473$	43.8982	+	11.7625i	2.01844	+	0.540839i
$474$	7.60009	−	13.1637i	0.349083	−	0.604630i
$475$		0			0
$476$	1.07511	−	0.860229i	0.0492775	−	0.0394285i
$477$	4.06435	+	4.06435i	0.186094	+	0.186094i
$478$	−3.33656	−	12.4522i	−0.152611	−	0.569551i
$479$	−8.19191	−	14.1888i	−0.374298	−	0.648303i	0.615924	−	0.787806i	$-0.288783\pi$
$479$	−8.19191	−	14.1888i	−0.374298	−	0.648303i	−0.990222	+	0.139503i	$0.955450\pi$
$480$		0			0
$481$	0.539329	+	0.311381i	0.0245913	+	0.0141978i
$482$	−18.0930	+	18.0930i	−0.824113	+	0.824113i
$483$	−6.25753	+	2.74223i	−0.284727	+	0.124776i
$484$		−	1.70111i		−	0.0773232i
$485$		0			0
$486$	−0.869271	+	0.501874i	−0.0394309	+	0.0227654i
$487$	1.13179	−	4.22392i	0.0512865	−	0.191404i	−0.935530	−	0.353248i	$-0.885077\pi$
$487$	1.13179	−	4.22392i	0.0512865	−	0.191404i	0.986816	+	0.161844i	$0.0517440\pi$
$488$	−29.0681	+	7.78877i	−1.31585	+	0.352581i
$489$	1.39802			0.0632208
$490$		0			0
$491$	33.8633			1.52823			0.764116	−	0.645079i	$-0.223176\pi$
$491$	33.8633			1.52823			0.764116	+	0.645079i	$0.223176\pi$
$492$	7.94237	−	2.12815i	0.358070	−	0.0959445i
$493$	−0.833817	+	3.11185i	−0.0375532	+	0.140151i
$494$	14.1118	−	8.14746i	0.634920	−	0.366571i
$495$		0			0
$496$		−	2.03578i		−	0.0914093i
$497$	17.5269	−	7.68081i	0.786190	−	0.344531i
$498$	−9.45904	+	9.45904i	−0.423870	+	0.423870i
$499$	15.2390	+	8.79824i	0.682192	+	0.393864i	0.800680	−	0.599092i	$-0.204472\pi$
$499$	15.2390	+	8.79824i	0.682192	+	0.393864i	−0.118489	+	0.992955i	$0.537805\pi$
$500$		0			0
$501$	−2.95698	−	5.12163i	−0.132108	−	0.228818i
$502$	3.13976	+	11.7177i	0.140134	+	0.522988i
$503$	9.37063	+	9.37063i	0.417816	+	0.417816i	0.884450	−	0.466635i	$-0.154534\pi$
$503$	9.37063	+	9.37063i	0.417816	+	0.417816i	−0.466635	+	0.884450i	$0.654534\pi$
$504$	−6.20521	+	4.96499i	−0.276402	+	0.221158i
$505$		0			0
$506$	−4.62099	+	8.00379i	−0.205428	+	0.355812i
$507$	−2.41265	−	0.646467i	−0.107150	−	0.0287106i
$508$	−1.44049	−	0.385977i	−0.0639112	−	0.0171250i
$509$	13.8907	−	24.0594i	0.615695	−	1.06641i	−0.374567	−	0.927200i	$-0.622209\pi$
$509$	13.8907	−	24.0594i	0.615695	−	1.06641i	0.990262	−	0.139215i	$-0.0444580\pi$
$510$		0			0
$511$	6.13279	+	40.2451i	0.271299	+	1.78034i
$512$	7.99749	+	7.99749i	0.353442	+	0.353442i
$513$	1.06731	+	3.98325i	0.0471228	+	0.175865i
$514$	−5.20118	−	9.00870i	−0.229414	−	0.397357i
$515$		0			0
$516$	10.9552	+	6.32497i	0.482275	+	0.278441i
$517$	13.5497	−	13.5497i	0.595914	−	0.595914i
$518$	0.248920	−	0.338423i	0.0109369	−	0.0148695i
$519$			2.39421i			0.105094i
$520$		0			0
$521$	15.2942	−	8.83010i	0.670050	−	0.386854i	−0.126045	−	0.992024i	$-0.540228\pi$
$521$	15.2942	−	8.83010i	0.670050	−	0.386854i	0.796096	+	0.605171i	$0.206895\pi$
$522$	1.59613	−	5.95685i	0.0698608	−	0.260724i
$523$	−4.04661	+	1.08429i	−0.176946	+	0.0474125i	−0.346204	−	0.938159i	$-0.612530\pi$
$523$	−4.04661	+	1.08429i	−0.176946	+	0.0474125i	0.169258	+	0.985572i	$0.445863\pi$
$524$	−11.8967			−0.519711
$525$		0			0
$526$	−7.98233			−0.348046
$527$	−1.00109	+	0.268242i	−0.0436082	+	0.0116848i
$528$	−0.950527	+	3.54742i	−0.0413664	+	0.154381i
$529$	14.1439	−	8.16597i	0.614951	−	0.355042i
$530$		0			0
$531$		−	2.60089i		−	0.112869i
$532$	4.34634	+	9.91797i	0.188438	+	0.429999i
$533$	23.0621	−	23.0621i	0.998930	−	0.998930i
$534$	−9.60844	−	5.54743i	−0.415798	−	0.240061i
$535$		0			0
$536$	8.27821	+	14.3383i	0.357564	+	0.619319i
$537$	−0.487353	−	1.81883i	−0.0210308	−	0.0784881i
$538$	1.21743	+	1.21743i	0.0524871	+	0.0524871i
$539$	−24.3518	−	5.47503i	−1.04891	−	0.235826i
$540$		0			0
$541$	9.49606	−	16.4477i	0.408267	−	0.707140i	−0.586428	−	0.810001i	$-0.699466\pi$
$541$	9.49606	−	16.4477i	0.408267	−	0.707140i	0.994696	+	0.102861i	$0.0327998\pi$
$542$	−11.2676	−	3.01914i	−0.483984	−	0.129683i
$543$	17.1393	+	4.59246i	0.735517	+	0.197081i
$544$	1.30396	−	2.25853i	0.0559069	−	0.0968336i
$545$		0			0
$546$	−3.80370	+	9.73811i	−0.162783	+	0.416753i
$547$	4.10986	+	4.10986i	0.175725	+	0.175725i	0.789489	−	0.613764i	$-0.210345\pi$
$547$	4.10986	+	4.10986i	0.175725	+	0.175725i	−0.613764	+	0.789489i	$0.710345\pi$
$548$	−1.62369	−	6.05969i	−0.0693605	−	0.258857i
$549$	−5.00940	−	8.67653i	−0.213796	−	0.370305i
$550$		0			0
$551$	−21.9418	−	12.6681i	−0.934752	−	0.539680i
$552$	−5.48457	+	5.48457i	−0.233439	+	0.233439i
$553$	39.8210	+	4.42131i	1.69336	+	0.188013i
$554$			9.18001i			0.390021i
$555$		0			0
$556$	4.36528	−	2.52029i	0.185129	−	0.106884i
$557$	7.31412	−	27.2967i	0.309909	−	1.15660i	−0.618727	−	0.785606i	$-0.712351\pi$
$557$	7.31412	−	27.2967i	0.309909	−	1.15660i	0.928637	−	0.370991i	$-0.120982\pi$
$558$	1.91634	−	0.513481i	0.0811250	−	0.0217374i
$559$	50.1760			2.12222
$560$		0			0
$561$	1.86968			0.0789379
$562$	14.6057	−	3.91357i	0.616102	−	0.165084i
$563$	−6.40394	+	23.8998i	−0.269894	+	1.00726i	0.689292	+	0.724483i	$0.257922\pi$
$563$	−6.40394	+	23.8998i	−0.269894	+	1.00726i	−0.959186	+	0.282775i	$0.908745\pi$
$564$	4.61914	−	2.66686i	0.194501	−	0.112295i
$565$		0			0
$566$			16.0735i			0.675621i
$567$	−2.13131	−	1.56764i	−0.0895067	−	0.0658348i
$568$	15.3619	−	15.3619i	0.644572	−	0.644572i
$569$	31.0893	+	17.9494i	1.30333	+	0.752479i	0.980974	−	0.194140i	$-0.0621914\pi$
$569$	31.0893	+	17.9494i	1.30333	+	0.752479i	0.322357	+	0.946618i	$0.395525\pi$
$570$		0			0
$571$	3.51101	+	6.08125i	0.146931	+	0.254492i	0.930092	−	0.367327i	$-0.119727\pi$
$571$	3.51101	+	6.08125i	0.146931	+	0.254492i	−0.783161	+	0.621820i	$0.786394\pi$
$572$	−3.60577	−	13.4569i	−0.150765	−	0.562662i
$573$	−7.59859	−	7.59859i	−0.317436	−	0.317436i
$574$	−13.7456	−	17.1792i	−0.573731	−	0.717046i
$575$		0			0
$576$	−3.52608	+	6.10735i	−0.146920	+	0.254473i
$577$	24.1765	+	6.47806i	1.00648	+	0.269685i	0.724157	−	0.689635i	$-0.242229\pi$
$577$	24.1765	+	6.47806i	1.00648	+	0.269685i	0.282321	+	0.959320i	$0.408896\pi$
$578$	−16.2157	−	4.34498i	−0.674484	−	0.180727i
$579$	1.61042	−	2.78933i	0.0669267	−	0.115921i
$580$		0			0
$581$	−32.8438	−	12.8288i	−1.36259	−	0.532227i
$582$	−2.49760	−	2.49760i	−0.103529	−	0.103529i
$583$	5.30448	+	19.7966i	0.219689	+	0.819891i
$584$	23.1087	+	40.0255i	0.956246	+	1.65627i
$585$		0			0
$586$	7.62774	+	4.40388i	0.315099	+	0.181923i
$587$	−22.0509	+	22.0509i	−0.910139	+	0.910139i	−0.996283	−	0.0861436i	$-0.972546\pi$
$587$	−22.0509	+	22.0509i	−0.910139	+	0.910139i	0.0861436	+	0.996283i	$0.472546\pi$
$588$	−6.15285	−	3.22637i	−0.253739	−	0.133053i
$589$		−	8.15074i		−	0.335845i
$590$		0			0
$591$	−13.3885	+	7.72988i	−0.550731	+	0.317965i
$592$	0.0421708	−	0.157384i	0.00173321	−	0.00646843i
$593$	−41.6575	+	11.1621i	−1.71067	+	0.458372i	−0.975588	−	0.219609i	$-0.929522\pi$
$593$	−41.6575	+	11.1621i	−1.71067	+	0.458372i	−0.735079	+	0.677981i	$0.762855\pi$
$594$	−3.57903			−0.146849
$595$		0			0
$596$	15.1265			0.619607
$597$	−11.9770	+	3.20922i	−0.490185	+	0.131345i
$598$	−2.64092	+	9.85604i	−0.107995	+	0.403043i
$599$	−23.6940	+	13.6797i	−0.968111	+	0.558939i	−0.898660	−	0.438646i	$-0.855458\pi$
$599$	−23.6940	+	13.6797i	−0.968111	+	0.558939i	−0.0694514	+	0.997585i	$0.522125\pi$
$600$		0			0
$601$		−	7.61565i		−	0.310649i	−0.987864	−	0.155324i	$-0.950358\pi$
$601$		−	7.61565i		−	0.310649i	0.987864	−	0.155324i	$-0.0496423\pi$
$602$	3.73520	−	33.6414i	0.152235	−	1.37112i
$603$	−3.89757	+	3.89757i	−0.158721	+	0.158721i
$604$	12.8327	+	7.40895i	0.522154	+	0.301466i
$605$		0			0
$606$	0.428551	+	0.742273i	0.0174087	+	0.0301528i
$607$	−4.02590	−	15.0249i	−0.163406	−	0.609840i	−0.998238	−	0.0593354i	$-0.981102\pi$
$607$	−4.02590	−	15.0249i	−0.163406	−	0.609840i	0.834832	−	0.550505i	$-0.185565\pi$
$608$	14.5026	+	14.5026i	0.588159	+	0.588159i
$609$	16.0699	−	2.44883i	0.651184	−	0.0992314i
$610$		0			0
$611$	10.5781	−	18.3218i	0.427944	−	0.741221i
$612$	0.502686	+	0.134694i	0.0203199	+	0.00544469i
$613$	3.28737	+	0.880848i	0.132776	+	0.0355771i	0.324595	−	0.945853i	$-0.394772\pi$
$613$	3.28737	+	0.880848i	0.132776	+	0.0355771i	−0.191819	+	0.981430i	$0.561439\pi$
$614$	4.44590	−	7.70052i	0.179422	−	0.310768i
$615$		0			0
$616$	−28.0132	+	4.26882i	−1.12868	+	0.171996i
$617$	19.3906	+	19.3906i	0.780637	+	0.780637i	0.979938	−	0.199301i	$-0.0638671\pi$
$617$	19.3906	+	19.3906i	0.780637	+	0.780637i	−0.199301	+	0.979938i	$0.563867\pi$
$618$	1.57703	+	5.88554i	0.0634373	+	0.236751i
$619$	−15.4314	−	26.7280i	−0.620240	−	1.07429i	−0.989441	−	0.144938i	$-0.953702\pi$
$619$	−15.4314	−	26.7280i	−0.620240	−	1.07429i	0.369200	−	0.929350i	$-0.379632\pi$
$620$		0			0
$621$	−2.23630	−	1.29113i	−0.0897397	−	0.0518113i
$622$	−4.74083	+	4.74083i	−0.190090	+	0.190090i
$623$	3.22719	−	29.0661i	0.129295	−	1.16451i
$624$			4.05473i			0.162319i
$625$		0			0
$626$	1.61217	−	0.930785i	0.0644351	−	0.0372016i
$627$	−3.80566	+	14.2029i	−0.151984	+	0.567210i
$628$	6.32115	−	1.69375i	0.252241	−	0.0675879i
$629$	−0.0829496			−0.00330742
$630$		0			0
$631$	−19.0017			−0.756446			−0.378223	−	0.925714i	$-0.623465\pi$
$631$	−19.0017			−0.756446			−0.378223	+	0.925714i	$0.623465\pi$
$632$	43.9365	−	11.7727i	1.74770	−	0.468295i
$633$	3.47377	−	12.9643i	0.138070	−	0.515284i
$634$	−1.49946	+	0.865713i	−0.0595512	+	0.0343819i
$635$		0			0
$636$			5.70470i			0.226206i
$637$	−27.5343	+	1.11978i	−1.09095	+	0.0443671i
$638$	15.5489	−	15.5489i	0.615585	−	0.615585i
$639$	6.26374	+	3.61637i	0.247790	+	0.143061i
$640$		0			0
$641$	8.84861	+	15.3262i	0.349499	+	0.605350i	0.986161	−	0.165793i	$-0.0530185\pi$
$641$	8.84861	+	15.3262i	0.349499	+	0.605350i	−0.636661	+	0.771143i	$0.719685\pi$
$642$	−3.03874	−	11.3407i	−0.119930	−	0.447583i
$643$	−1.20751	−	1.20751i	−0.0476194	−	0.0476194i	0.682896	−	0.730516i	$-0.260720\pi$
$643$	−1.20751	−	1.20751i	−0.0476194	−	0.0476194i	−0.730516	+	0.682896i	$0.760720\pi$
$644$	−6.31601	−	2.46703i	−0.248886	−	0.0972145i
$645$		0			0
$646$	−1.08521	+	1.87964i	−0.0426970	+	0.0739534i
$647$	−3.64972	−	0.977939i	−0.143485	−	0.0384468i	0.186362	−	0.982481i	$-0.440330\pi$
$647$	−3.64972	−	0.977939i	−0.143485	−	0.0384468i	−0.329847	+	0.944034i	$0.606997\pi$
$648$	−2.90136	−	0.777416i	−0.113976	−	0.0305398i
$649$	4.63695	−	8.03143i	0.182016	−	0.315261i
$650$		0			0
$651$	3.26712	+	4.08322i	0.128048	+	0.160034i
$652$	0.981129	+	0.981129i	0.0384240	+	0.0384240i
$653$	−2.33731	−	8.72296i	−0.0914660	−	0.341356i	0.904994	−	0.425424i	$-0.139875\pi$
$653$	−2.33731	−	8.72296i	−0.0914660	−	0.341356i	−0.996460	+	0.0840686i	$0.973209\pi$
$654$	6.29151	+	10.8972i	0.246017	+	0.426115i
$655$		0			0
$656$	−7.38988	−	4.26655i	−0.288526	−	0.166581i
$657$	−10.8801	+	10.8801i	−0.424474	+	0.424474i
$658$	−11.4967	−	8.45619i	−0.448190	−	0.329657i
$659$			40.3378i			1.57134i	0.618648	+	0.785668i	$0.287681\pi$
$659$			40.3378i			1.57134i	−0.618648	+	0.785668i	$0.712319\pi$
$660$		0			0
$661$	23.8392	−	13.7636i	0.927238	−	0.535341i	0.0413010	−	0.999147i	$-0.486850\pi$
$661$	23.8392	−	13.7636i	0.927238	−	0.535341i	0.885937	+	0.463806i	$0.153516\pi$
$662$	−6.75912	+	25.2254i	−0.262701	+	0.980412i
$663$	1.99390	−	0.534265i	0.0774368	−	0.0207491i
$664$	−40.0308			−1.55350
$665$		0			0
$666$	0.158786			0.00615284
$667$	15.3247	−	4.10624i	0.593375	−	0.158994i
$668$	1.51915	−	5.66955i	0.0587777	−	0.219361i
$669$	−1.97068	+	1.13777i	−0.0761909	+	0.0439889i
$670$		0			0
$671$		−	35.7237i		−	1.37910i
$672$	−13.0785	−	1.45210i	−0.504513	−	0.0560159i
$673$	−22.5966	+	22.5966i	−0.871035	+	0.871035i	−0.992585	−	0.121550i	$-0.961213\pi$
$673$	−22.5966	+	22.5966i	−0.871035	+	0.871035i	0.121550	+	0.992585i	$0.461213\pi$
$674$	18.0897	+	10.4441i	0.696789	+	0.402291i
$675$		0			0
$676$	−1.23950	−	2.14688i	−0.0476732	−	0.0825723i
$677$	−2.39472	−	8.93720i	−0.0920364	−	0.343484i	0.904517	−	0.426437i	$-0.140232\pi$
$677$	−2.39472	−	8.93720i	−0.0920364	−	0.343484i	−0.996553	+	0.0829529i	$0.973565\pi$
$678$	7.28486	+	7.28486i	0.279774	+	0.279774i
$679$	3.38736	−	8.67221i	0.129995	−	0.332809i
$680$		0			0
$681$	12.8905	−	22.3270i	0.493966	−	0.855574i
$682$	6.83302	+	1.83090i	0.261650	+	0.0701089i
$683$	4.49527	+	1.20450i	0.172007	+	0.0460891i	0.343794	−	0.939045i	$-0.388288\pi$
$683$	4.49527	+	1.20450i	0.172007	+	0.0460891i	−0.171788	+	0.985134i	$0.554954\pi$
$684$	−2.04640	+	3.54447i	−0.0782460	+	0.135526i
$685$		0			0
$686$	−1.29893	+	18.5442i	−0.0495933	+	0.708022i
$687$	0.946910	+	0.946910i	0.0361269	+	0.0361269i
$688$	−3.39770	−	12.6804i	−0.129536	−	0.483436i
$689$	11.3138	+	19.5961i	0.431023	+	0.746554i
$690$		0			0
$691$	−6.52332	−	3.76624i	−0.248159	−	0.143275i	0.370762	−	0.928728i	$-0.379097\pi$
$691$	−6.52332	−	3.76624i	−0.248159	−	0.143275i	−0.618921	+	0.785453i	$0.712430\pi$
$692$	−1.68025	+	1.68025i	−0.0638736	+	0.0638736i
$693$	−3.78656	−	8.64059i	−0.143839	−	0.328229i
$694$		−	12.8568i		−	0.488036i
$695$		0			0
$696$	15.9822	−	9.22732i	0.605804	−	0.349761i
$697$	−1.12435	+	4.19613i	−0.0425878	+	0.158940i
$698$	−12.3627	+	3.31257i	−0.467934	+	0.125383i
$699$	−21.4595			−0.811673
$700$		0			0
$701$	−45.2736			−1.70996			−0.854981	−	0.518660i	$-0.826431\pi$
$701$	−45.2736			−1.70996			−0.854981	+	0.518660i	$0.826431\pi$
$702$	−3.81683	+	1.02272i	−0.144057	+	0.0385999i
$703$	0.168841	−	0.630123i	0.00636796	−	0.0237655i
$704$	−21.7768	+	12.5728i	−0.820744	+	0.473857i
$705$		0			0
$706$		−	17.3272i		−	0.652117i
$707$	−1.33862	+	1.81993i	−0.0503438	+	0.0684457i
$708$	1.82530	−	1.82530i	0.0685988	−	0.0685988i
$709$	−27.8909	−	16.1028i	−1.04747	−	0.604754i	−0.125527	−	0.992090i	$-0.540062\pi$
$709$	−27.8909	−	16.1028i	−1.04747	−	0.604754i	−0.921939	+	0.387336i	$0.873395\pi$
$710$		0			0
$711$	7.57171	+	13.1146i	0.283961	+	0.491836i
$712$	−8.59313	−	32.0700i	−0.322041	−	1.20187i
$713$	3.60902	+	3.60902i	0.135159	+	0.135159i
$714$	−0.209778	−	1.37662i	−0.00785074	−	0.0515188i
$715$		0			0
$716$	0.934424	−	1.61847i	0.0349211	−	0.0604851i
$717$	12.4057	+	3.32410i	0.463300	+	0.124141i
$718$	7.28503	+	1.95202i	0.271875	+	0.0728486i
$719$	−14.8623	+	25.7422i	−0.554270	+	0.960023i	0.443690	+	0.896180i	$0.353669\pi$
$719$	−14.8623	+	25.7422i	−0.554270	+	0.960023i	−0.997960	+	0.0638430i	$0.979664\pi$
$720$		0			0
$721$	−12.5406	+	10.0341i	−0.467036	+	0.373690i
$722$	1.41569	+	1.41569i	0.0526864	+	0.0526864i
$723$	−6.59777	−	24.6232i	−0.245374	−	0.915747i
$724$	8.80534	+	15.2513i	0.327248	+	0.566810i
$725$		0			0
$726$	−1.48991	−	0.860202i	−0.0552958	−	0.0319251i
$727$	8.03461	−	8.03461i	0.297987	−	0.297987i	−0.542238	−	0.840225i	$-0.682423\pi$
$727$	8.03461	−	8.03461i	0.297987	−	0.297987i	0.840225	+	0.542238i	$0.182423\pi$
$728$	−28.6546	+	12.5573i	−1.06201	+	0.465404i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−5.78787	+	3.34163i	−0.214072	+	0.123595i
$732$	2.57358	−	9.60475i	0.0951224	−	0.355002i
$733$	−29.0188	+	7.77556i	−1.07183	+	0.287197i	−0.751246	−	0.660022i	$-0.770547\pi$
$733$	−29.0188	+	7.77556i	−1.07183	+	0.287197i	−0.320587	+	0.947219i	$0.603880\pi$
$734$	6.91461			0.255223
$735$		0			0
$736$	−12.8431			−0.473401
$737$	−18.9843	+	5.08682i	−0.699294	+	0.187375i
$738$	2.15229	−	8.03244i	0.0792267	−	0.295678i
$739$	−35.8813	+	20.7161i	−1.31992	+	0.762054i	−0.983715	−	0.179736i	$-0.942476\pi$
$739$	−35.8813	+	20.7161i	−1.31992	+	0.762054i	−0.336202	+	0.941790i	$0.609142\pi$
$740$		0			0
$741$			16.2341i			0.596374i
$742$	13.9808	−	6.12680i	0.513252	−	0.224922i
$743$	−10.5103	+	10.5103i	−0.385585	+	0.385585i	−0.873109	−	0.487525i	$-0.837900\pi$
$743$	−10.5103	+	10.5103i	−0.385585	+	0.385585i	0.487525	+	0.873109i	$0.337900\pi$
$744$	5.14152	+	2.96846i	0.188497	+	0.108829i
$745$		0			0
$746$	−3.37985	−	5.85407i	−0.123745	−	0.214333i
$747$	−3.44932	−	12.8730i	−0.126204	−	0.471000i
$748$	1.31214	+	1.31214i	0.0479764	+	0.0479764i
$749$	24.1642	−	19.3346i	0.882941	−	0.706469i
$750$		0			0
$751$	21.0235	−	36.4138i	0.767159	−	1.32876i	−0.171938	−	0.985108i	$-0.555003\pi$
$751$	21.0235	−	36.4138i	0.767159	−	1.32876i	0.939097	−	0.343651i	$-0.111664\pi$
$752$	−5.34656	−	1.43261i	−0.194969	−	0.0522418i
$753$	−11.6740	−	3.12804i	−0.425424	−	0.113992i
$754$	12.1388	−	21.0251i	0.442071	−	0.765689i
$755$		0			0
$756$	−0.395582	−	2.59592i	−0.0143872	−	0.0944126i
$757$	−12.0838	−	12.0838i	−0.439193	−	0.439193i	0.452547	−	0.891740i	$-0.350515\pi$
$757$	−12.0838	−	12.0838i	−0.439193	−	0.439193i	−0.891740	+	0.452547i	$0.850515\pi$
$758$	9.76860	+	36.4569i	0.354811	+	1.32417i
$759$	−4.60374	−	7.97391i	−0.167105	−	0.289435i
$760$		0			0
$761$	−12.6620	−	7.31041i	−0.458997	−	0.265002i	0.252625	−	0.967564i	$-0.418706\pi$
$761$	−12.6620	−	7.31041i	−0.458997	−	0.265002i	−0.711623	+	0.702562i	$0.752039\pi$
$762$	−1.06647	+	1.06647i	−0.0386340	+	0.0386340i
$763$	−19.6520	+	26.7182i	−0.711451	+	0.967264i
$764$		−	10.6653i		−	0.385858i
$765$		0			0
$766$	13.4399	−	7.75952i	0.485603	−	0.280363i
$767$	2.65004	−	9.89008i	0.0956874	−	0.357110i
$768$	−16.4049	+	4.39569i	−0.591962	+	0.158616i
$769$	5.95109			0.214602			0.107301	−	0.994227i	$-0.465779\pi$
$769$	5.95109			0.214602			0.107301	+	0.994227i	$0.465779\pi$
$770$		0			0
$771$	10.3635			0.373233
$772$	3.08773	−	0.827355i	0.111130	−	0.0297772i
$773$	−1.22902	+	4.58677i	−0.0442049	+	0.164975i	−0.984500	−	0.175386i	$-0.943883\pi$
$773$	−1.22902	+	4.58677i	−0.0442049	+	0.164975i	0.940295	+	0.340361i	$0.110549\pi$
$774$	11.0794	−	6.39670i	0.398241	−	0.229925i
$775$		0			0
$776$		−	10.5699i		−	0.379438i
$777$	0.167993	+	0.383346i	0.00602673	+	0.0137525i
$778$	−13.1668	+	13.1668i	−0.472051	+	0.472051i
$779$	−29.5872	−	17.0822i	−1.06007	−	0.612032i
$780$		0			0
$781$	12.8948	+	22.3344i	0.461411	+	0.799188i
$782$	−0.351760	−	1.31279i	−0.0125789	−	0.0469452i
$783$	4.34444	+	4.34444i	0.155258	+	0.155258i
$784$	2.14749	+	6.88259i	0.0766961	+	0.245807i
$785$		0			0
$786$	−6.01582	+	10.4197i	−0.214577	+	0.371659i
$787$	−15.9097	−	4.26300i	−0.567120	−	0.151959i	−0.0361447	−	0.999347i	$-0.511508\pi$
$787$	−15.9097	−	4.26300i	−0.567120	−	0.151959i	−0.530976	+	0.847387i	$0.678174\pi$
$788$	−14.8209	−	3.97124i	−0.527971	−	0.141470i
$789$	3.97626	−	6.88709i	0.141559	−	0.245187i
$790$		0			0
$791$	−9.88005	+	25.2946i	−0.351294	+	0.899373i
$792$	−7.57326	−	7.57326i	−0.269104	−	0.269104i
$793$	−10.2081	−	38.0972i	−0.362501	−	1.35287i
$794$	2.28389	+	3.95581i	0.0810522	+	0.140387i
$795$		0			0
$796$	−10.6576	−	6.15319i	−0.377750	−	0.218094i
$797$	−33.5483	+	33.5483i	−1.18834	+	1.18834i	−0.210818	+	0.977525i	$0.567613\pi$
$797$	−33.5483	+	33.5483i	−1.18834	+	1.18834i	−0.977525	+	0.210818i	$0.932387\pi$
$798$	10.8844	+	1.20849i	0.385305	+	0.0427803i
$799$			2.81792i			0.0996910i
$800$		0			0
$801$	9.57257	−	5.52672i	0.338230	−	0.195277i
$802$	5.80371	−	21.6598i	0.204936	−	0.764832i
$803$	−52.9948	+	14.1999i	−1.87015	+	0.501104i
$804$	−5.47061			−0.192934
$805$		0			0
$806$	7.81021			0.275103
$807$	−1.65683	+	0.443946i	−0.0583232	+	0.0156276i
$808$	−0.663838	+	2.47748i	−0.0233537	+	0.0871573i
$809$	−5.58195	+	3.22274i	−0.196251	+	0.113306i	−0.594906	−	0.803796i	$-0.702811\pi$
$809$	−5.58195	+	3.22274i	−0.196251	+	0.113306i	0.398655	+	0.917101i	$0.369477\pi$
$810$		0			0
$811$			0.116404i			0.00408751i	0.999998	+	0.00204375i	$0.000650547\pi$
$811$			0.116404i			0.00408751i	−0.999998	+	0.00204375i	$0.999349\pi$
$812$	12.9964	+	9.55922i	0.456084	+	0.335463i
$813$	8.21766	−	8.21766i	0.288206	−	0.288206i
$814$	0.490325	+	0.283089i	0.0171859	+	0.00992227i
$815$		0			0
$816$	−0.270037	−	0.467718i	−0.00945319	−	0.0163734i
$817$	−13.6035	−	50.7690i	−0.475927	−	1.77618i
$818$	−4.32516	−	4.32516i	−0.151226	−	0.151226i
$819$	−6.50722	−	8.13268i	−0.227381	−	0.284179i
$820$		0			0
$821$	0.698986	−	1.21068i	0.0243948	−	0.0422530i	−0.853570	−	0.520978i	$-0.825567\pi$
$821$	0.698986	−	1.21068i	0.0243948	−	0.0422530i	0.877965	+	0.478725i	$0.158901\pi$
$822$	−6.12841	−	1.64210i	−0.213753	−	0.0572749i
$823$	−15.7573	−	4.22216i	−0.549265	−	0.147175i	−0.0264952	−	0.999649i	$-0.508435\pi$
$823$	−15.7573	−	4.22216i	−0.549265	−	0.147175i	−0.522770	+	0.852474i	$0.675101\pi$
$824$	−9.11687	+	15.7909i	−0.317601	+	0.550101i
$825$		0			0
$826$	−6.43371	−	2.51300i	−0.223858	−	0.0874386i
$827$	29.7712	+	29.7712i	1.03524	+	1.03524i	0.999356	+	0.0358886i	$0.0114262\pi$
$827$	29.7712	+	29.7712i	1.03524	+	1.03524i	0.0358886	+	0.999356i	$0.488574\pi$
$828$	−0.663320	−	2.47554i	−0.0230520	−	0.0860311i
$829$	3.31772	+	5.74647i	0.115229	+	0.199583i	0.917871	−	0.396878i	$-0.129906\pi$
$829$	3.31772	+	5.74647i	0.115229	+	0.199583i	−0.802642	+	0.596461i	$0.796573\pi$
$830$		0			0
$831$	−7.92044	−	4.57287i	−0.274757	−	0.158631i
$832$	−19.6310	+	19.6310i	−0.680582	+	0.680582i
$833$	3.10154	−	1.96290i	0.107462	−	0.0680104i
$834$		−	5.09775i		−	0.176521i
$835$		0			0
$836$	−12.6384	+	7.29677i	−0.437108	+	0.252364i
$837$	−0.511564	+	1.90918i	−0.0176822	+	0.0659910i
$838$	22.6076	−	6.05768i	0.780965	−	0.209259i
$839$	−18.1682			−0.627234			−0.313617	−	0.949550i	$-0.601541\pi$
$839$	−18.1682			−0.627234			−0.313617	+	0.949550i	$0.601541\pi$
$840$		0			0
$841$	−8.74827			−0.301664
$842$	−0.0115453	+	0.00309354i	−0.000397876	+	0.000106610i
$843$	−3.89896	+	14.5511i	−0.134287	+	0.501167i
$844$	11.5362	−	6.66042i	0.397092	−	0.229261i
$845$		0			0
$846$		−	5.39421i		−	0.185457i
$847$	0.500418	−	4.50707i	0.0171946	−	0.154865i
$848$	4.18618	−	4.18618i	0.143754	−	0.143754i
$849$	−13.8681	−	8.00677i	−0.475953	−	0.274791i
$850$		0			0
$851$	0.204248	+	0.353768i	0.00700154	+	0.0121270i
$852$	1.85792	+	6.93384i	0.0636512	+	0.237549i
$853$	34.0703	+	34.0703i	1.16654	+	1.16654i	0.983014	+	0.183530i	$0.0587523\pi$
$853$	34.0703	+	34.0703i	1.16654	+	1.16654i	0.183530	+	0.983014i	$0.441248\pi$
$854$	−26.3029	+	4.00820i	−0.900067	+	0.137158i
$855$		0			0
$856$	17.5671	−	30.4271i	0.600432	−	1.03998i
$857$	35.5991	+	9.53874i	1.21604	+	0.325837i	0.809129	−	0.587631i	$-0.199939\pi$
$857$	35.5991	+	9.53874i	1.21604	+	0.325837i	0.406911	+	0.913468i	$0.366606\pi$
$858$	−13.6095	−	3.64666i	−0.464622	−	0.124495i
$859$	6.11471	−	10.5910i	0.208631	−	0.361360i	−0.742652	−	0.669677i	$-0.766433\pi$
$859$	6.11471	−	10.5910i	0.208631	−	0.361360i	0.951284	+	0.308317i	$0.0997658\pi$
$860$		0			0
$861$	21.6692	−	3.30209i	0.738486	−	0.112535i
$862$	−13.4125	−	13.4125i	−0.456831	−	0.456831i
$863$	−10.7526	−	40.1292i	−0.366022	−	1.36601i	−0.866030	−	0.499993i	$-0.833336\pi$
$863$	−10.7526	−	40.1292i	−0.366022	−	1.36601i	0.500007	−	0.866021i	$-0.333331\pi$
$864$	−2.48679	−	4.30724i	−0.0846022	−	0.146535i
$865$		0			0
$866$	−23.0765	−	13.3233i	−0.784173	−	0.452743i
$867$	11.8264	−	11.8264i	0.401645	−	0.401645i
$868$	−0.572740	+	5.15845i	−0.0194401	+	0.175089i
$869$			53.9964i			1.83170i
$870$		0			0
$871$	−18.7920	+	10.8496i	−0.636744	+	0.367624i
$872$	−9.74572	+	36.3715i	−0.330032	+	1.23169i
$873$	3.39905	−	0.910774i	0.115041	−	0.0308250i
$874$	10.6885			0.361545
$875$		0			0
$876$	−15.2713			−0.515969
$877$	2.41873	−	0.648098i	0.0816748	−	0.0218847i	−0.217750	−	0.976005i	$-0.569872\pi$
$877$	2.41873	−	0.648098i	0.0816748	−	0.0218847i	0.299425	+	0.954120i	$0.403205\pi$
$878$	−1.77171	+	6.61211i	−0.0597923	+	0.223148i
$879$	−7.59927	+	4.38744i	−0.256317	+	0.147985i
$880$		0			0
$881$			48.7030i			1.64084i	0.571758	+	0.820422i	$0.306262\pi$
$881$			48.7030i			1.64084i	−0.571758	+	0.820422i	$0.693738\pi$
$882$	−5.93711	+	3.75747i	−0.199913	+	0.126521i
$883$	5.87749	−	5.87749i	0.197793	−	0.197793i	−0.601260	−	0.799053i	$-0.705334\pi$
$883$	5.87749	−	5.87749i	0.197793	−	0.197793i	0.799053	+	0.601260i	$0.205334\pi$
$884$	1.77426	+	1.02437i	0.0596749	+	0.0344533i
$885$		0			0
$886$	−3.46265	−	5.99748i	−0.116330	−	0.201489i
$887$	−2.50907	−	9.36397i	−0.0842463	−	0.314411i	0.910924	−	0.412574i	$-0.135370\pi$
$887$	−2.50907	−	9.36397i	−0.0842463	−	0.314411i	−0.995170	+	0.0981626i	$0.968703\pi$
$888$	0.335993	+	0.335993i	0.0112752	+	0.0112752i
$889$	−3.70300	−	1.44639i	−0.124195	−	0.0485104i
$890$		0			0
$891$	1.78283	−	3.08796i	0.0597272	−	0.103450i
$892$	−2.18151	−	0.584533i	−0.0730422	−	0.0195716i
$893$	−21.4062	−	5.73578i	−0.716332	−	0.191941i
$894$	7.64903	−	13.2485i	0.255822	−	0.443097i
$895$		0			0
$896$	−4.74159	−	5.92601i	−0.158406	−	0.197974i
$897$	−7.18819	−	7.18819i	−0.240007	−	0.240007i
$898$	−7.08322	−	26.4350i	−0.236370	−	0.882146i
$899$	−6.07187	−	10.5168i	−0.202508	−	0.350754i
$900$		0			0
$901$	−2.61013	−	1.50696i	−0.0869561	−	0.0502041i
$902$	20.9667	−	20.9667i	0.698114	−	0.698114i
$903$	27.1650	+	19.9806i	0.903993	+	0.664914i
$904$			30.8297i			1.02538i
$905$		0			0
$906$	12.9782	−	7.49297i	0.431172	−	0.248937i
$907$	−8.54407	+	31.8869i	−0.283701	+	1.05879i	0.666082	+	0.745878i	$0.267970\pi$
$907$	−8.54407	+	31.8869i	−0.283701	+	1.05879i	−0.949783	+	0.312909i	$0.898697\pi$
$908$	24.7156	−	6.62252i	0.820216	−	0.219776i
$909$	−0.853903			−0.0283222
$910$		0			0
$911$	33.1445			1.09813			0.549064	−	0.835781i	$-0.314984\pi$
$911$	33.1445			1.09813			0.549064	+	0.835781i	$0.314984\pi$
$912$	4.10265	−	1.09930i	0.135852	−	0.0364015i
$913$	12.2991	−	45.9010i	0.407042	−	1.51910i
$914$	−15.0911	+	8.71284i	−0.499169	+	0.288195i
$915$		0			0
$916$			1.32908i			0.0439140i
$917$	−31.5202	−	3.49968i	−1.04089	−	0.115570i
$918$	0.372165	−	0.372165i	0.0122833	−	0.0122833i
$919$	27.8600	+	16.0850i	0.919015	+	0.530594i	0.883321	−	0.468769i	$-0.155302\pi$
$919$	27.8600	+	16.0850i	0.919015	+	0.530594i	0.0356945	+	0.999363i	$0.488636\pi$
$920$		0			0
$921$	4.42930	+	7.67177i	0.145950	+	0.252793i
$922$	10.8802	+	40.6053i	0.358319	+	1.33727i
$923$	20.1336	+	20.1336i	0.662707	+	0.662707i
$924$	3.40655	−	8.72134i	0.112067	−	0.286911i
$925$		0			0
$926$	10.9767	−	19.0122i	0.360716	−	0.624779i
$927$	−5.86357	−	1.57114i	−0.192585	−	0.0516030i
$928$	29.5162	+	7.90885i	0.968918	+	0.259621i
$929$	−20.2533	+	35.0798i	−0.664490	+	1.15093i	0.314934	+	0.949114i	$0.398018\pi$
$929$	−20.2533	+	35.0798i	−0.664490	+	1.15093i	−0.979423	+	0.201816i	$0.935316\pi$
$930$		0			0
$931$	8.59799	+	27.5561i	0.281788	+	0.903115i
$932$	−15.0602	−	15.0602i	−0.493314	−	0.493314i
$933$	−1.72878	−	6.45191i	−0.0565979	−	0.211226i
$934$	16.8406	+	29.1687i	0.551040	+	0.954429i
$935$		0			0
$936$	−10.2405	−	5.91237i	−0.334722	−	0.193252i
$937$	10.0291	−	10.0291i	0.327637	−	0.327637i	−0.524050	−	0.851687i	$-0.675580\pi$
$937$	10.0291	−	10.0291i	0.327637	−	0.327637i	0.851687	+	0.524050i	$0.175580\pi$
$938$	5.87540	+	13.4071i	0.191838	+	0.437759i
$939$			1.85462i			0.0605232i
$940$		0			0
$941$	−32.3581	+	18.6820i	−1.05485	+	0.609015i	−0.924002	−	0.382388i	$-0.875102\pi$
$941$	−32.3581	+	18.6820i	−1.05485	+	0.609015i	−0.130843	+	0.991403i	$0.541768\pi$
$942$	1.71296	−	6.39284i	0.0558111	−	0.208290i
$943$	20.6644	−	5.53701i	0.672926	−	0.180310i
$944$	−2.67885			−0.0871893
$945$		0			0
$946$	45.6170			1.48314
$947$	1.86785	−	0.500489i	0.0606970	−	0.0162637i	−0.228343	−	0.973581i	$-0.573331\pi$
$947$	1.86785	−	0.500489i	0.0606970	−	0.0162637i	0.289040	+	0.957317i	$0.406664\pi$
$948$	−3.88998	+	14.5176i	−0.126341	+	0.471510i
$949$	−52.4582	+	30.2868i	−1.70287	+	0.983150i
$950$		0			0
$951$		−	1.72496i		−	0.0559358i
$952$	2.46905	−	3.35684i	0.0800225	−	0.108796i
$953$	−14.5970	+	14.5970i	−0.472845	+	0.472845i	−0.902834	−	0.429989i	$-0.858517\pi$
$953$	−14.5970	+	14.5970i	−0.472845	+	0.472845i	0.429989	+	0.902834i	$0.358517\pi$
$954$	4.99644	+	2.88470i	0.161766	+	0.0933955i
$955$		0			0
$956$	6.37346	+	11.0392i	0.206132	+	0.357032i
$957$	5.67003	+	21.1608i	0.183286	+	0.684033i
$958$	−11.6285	−	11.6285i	−0.375700	−	0.375700i
$959$	−2.51935	−	16.5327i	−0.0813541	−	0.533869i
$960$		0			0
$961$	−13.5467	+	23.4635i	−0.436989	+	0.756887i
$962$	0.603797	+	0.161787i	0.0194672	+	0.00521622i
$963$	11.2984	+	3.02740i	0.364086	+	0.0975565i
$964$	12.6502	−	21.9108i	0.407436	−	0.705700i
$965$		0			0
$966$	−5.35456	+	4.28435i	−0.172280	+	0.137847i
$967$	−34.5723	−	34.5723i	−1.11177	−	1.11177i	−0.992911	−	0.118858i	$-0.962077\pi$
$967$	−34.5723	−	34.5723i	−1.11177	−	1.11177i	−0.118858	−	0.992911i	$-0.537923\pi$
$968$	−1.33248	−	4.97287i	−0.0428274	−	0.159834i
$969$	−1.08116	−	1.87262i	−0.0347318	−	0.0601573i
$970$		0			0
$971$	−2.45937	−	1.41992i	−0.0789251	−	0.0455674i	0.460018	−	0.887910i	$-0.347843\pi$
$971$	−2.45937	−	1.41992i	−0.0789251	−	0.0455674i	−0.538943	+	0.842342i	$0.681176\pi$
$972$	0.701798	−	0.701798i	0.0225102	−	0.0225102i
$973$	12.3071	−	5.39334i	0.394549	−	0.172903i
$974$		−	4.38930i		−	0.140642i
$975$		0			0
$976$	−8.93662	+	5.15956i	−0.286054	+	0.165154i
$977$	9.66661	−	36.0763i	0.309262	−	1.15418i	−0.619951	−	0.784640i	$-0.712848\pi$
$977$	9.66661	−	36.0763i	0.309262	−	1.15418i	0.929214	−	0.369543i	$-0.120486\pi$
$978$	1.35545	−	0.363191i	0.0433424	−	0.0116136i
$979$	39.4129			1.25964
$980$		0			0
$981$	−12.5360			−0.400245
$982$	32.8320	−	8.79732i	1.04771	−	0.280734i
$983$	−8.29834	+	30.9698i	−0.264676	+	0.987784i	0.697772	+	0.716320i	$0.254175\pi$
$983$	−8.29834	+	30.9698i	−0.264676	+	0.987784i	−0.962448	+	0.271465i	$0.912492\pi$
$984$	21.5510	−	12.4425i	0.687021	−	0.396651i
$985$		0			0
$986$			3.23369i			0.102982i
$987$	13.0228	−	5.70699i	0.414522	−	0.181655i
$988$	−11.3930	+	11.3930i	−0.362461	+	0.362461i
$989$	28.5031	+	16.4563i	0.906346	+	0.523279i
$990$		0			0
$991$	−20.9999	−	36.3729i	−0.667084	−	1.15542i	−0.978716	−	0.205221i	$-0.934209\pi$
$991$	−20.9999	−	36.3729i	−0.667084	−	1.15542i	0.311632	−	0.950203i	$-0.399125\pi$
$992$	2.54430	+	9.49546i	0.0807817	+	0.301481i
$993$	−18.3973	−	18.3973i	−0.583821	−	0.583821i
$994$	14.9978	−	12.0002i	0.475700	−	0.380623i
$995$		0			0
$996$	6.61355	−	11.4550i	0.209558	−	0.362966i
$997$	−21.2023	−	5.68114i	−0.671484	−	0.179924i	−0.0930609	−	0.995660i	$-0.529665\pi$
$997$	−21.2023	−	5.68114i	−0.671484	−	0.179924i	−0.578423	+	0.815737i	$0.696332\pi$
$998$	17.0606	+	4.57137i	0.540044	+	0.144704i
$999$	−0.0790967	+	0.136999i	−0.00250251	+	0.00433447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.e.82.6		32
5.2	odd	4		105.2.u.a.103.6	yes	32
5.3	odd	4	inner	525.2.bc.e.418.3		32
5.4	even	2		105.2.u.a.82.3	yes	32
7.3	odd	6	inner	525.2.bc.e.157.3		32
15.2	even	4		315.2.bz.d.208.3		32
15.14	odd	2		315.2.bz.d.82.6		32
35.2	odd	12		735.2.m.c.538.11		32
35.3	even	12	inner	525.2.bc.e.493.6		32
35.4	even	6		735.2.v.b.472.6		32
35.9	even	6		735.2.m.c.97.12		32
35.12	even	12		735.2.m.c.538.12		32
35.17	even	12		105.2.u.a.73.3	yes	32
35.19	odd	6		735.2.m.c.97.11		32
35.24	odd	6		105.2.u.a.52.6	✓	32
35.27	even	4		735.2.v.b.313.6		32
35.32	odd	12		735.2.v.b.178.3		32
35.34	odd	2		735.2.v.b.607.3		32
105.17	odd	12		315.2.bz.d.73.6		32
105.59	even	6		315.2.bz.d.262.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.u.a.52.6	✓	32	35.24	odd	6
105.2.u.a.73.3	yes	32	35.17	even	12
105.2.u.a.82.3	yes	32	5.4	even	2
105.2.u.a.103.6	yes	32	5.2	odd	4
315.2.bz.d.73.6		32	105.17	odd	12
315.2.bz.d.82.6		32	15.14	odd	2
315.2.bz.d.208.3		32	15.2	even	4
315.2.bz.d.262.3		32	105.59	even	6
525.2.bc.e.82.6		32	1.1	even	1	trivial
525.2.bc.e.157.3		32	7.3	odd	6	inner
525.2.bc.e.418.3		32	5.3	odd	4	inner
525.2.bc.e.493.6		32	35.3	even	12	inner
735.2.m.c.97.11		32	35.19	odd	6
735.2.m.c.97.12		32	35.9	even	6
735.2.m.c.538.11		32	35.2	odd	12
735.2.m.c.538.12		32	35.12	even	12
735.2.v.b.178.3		32	35.32	odd	12
735.2.v.b.313.6		32	35.27	even	4
735.2.v.b.472.6		32	35.4	even	6
735.2.v.b.607.3		32	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.969545 - 0.259789i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.859523 + 0.496246i) q^{4} +1.00375i q^{6} +(-2.42328 + 1.06195i) q^{7} +(-2.12394 + 2.12394i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.969545 - 0.259789i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-0.859523 + 0.496246i) q^{4} +1.00375i q^{6} +(-2.42328 + 1.06195i) q^{7} +(-2.12394 + 2.12394i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.78283 - 3.08796i) q^{11} +(-0.256876 - 0.958673i) q^{12} +(-2.78368 - 2.78368i) q^{13} +(-2.07359 + 1.65915i) q^{14} +(-0.514988 + 0.891986i) q^{16} +(0.506489 + 0.135713i) q^{17} +(-0.969545 - 0.259789i) q^{18} +(-2.06188 + 3.57128i) q^{19} +(-0.398574 - 2.61556i) q^{21} +(-2.53075 - 2.53075i) q^{22} +(-0.668338 - 2.49427i) q^{23} +(-1.50185 - 2.60128i) q^{24} +(-3.42207 - 1.97574i) q^{26} +(0.707107 - 0.707107i) q^{27} +(1.55587 - 2.11531i) q^{28} +6.14396i q^{29} +(-1.71173 + 0.988266i) q^{31} +(1.28726 - 4.80410i) q^{32} +(3.44417 - 0.922863i) q^{33} +0.526321 q^{34} +0.992492 q^{36} +(-0.152803 + 0.0409435i) q^{37} +(-1.07131 + 3.99817i) q^{38} +(3.40930 - 1.96836i) q^{39} +8.28475i q^{41} +(-1.06593 - 2.43236i) q^{42} +(-9.01253 + 9.01253i) q^{43} +(3.06477 + 1.76945i) q^{44} +(-1.29597 - 2.24468i) q^{46} +(1.39091 + 5.19095i) q^{47} +(-0.728304 - 0.728304i) q^{48} +(4.74453 - 5.14679i) q^{49} +(-0.262178 + 0.454106i) q^{51} +(3.77403 + 1.01125i) q^{52} +(-5.55200 - 1.48765i) q^{53} +(0.501874 - 0.869271i) q^{54} +(2.89138 - 7.40241i) q^{56} +(-2.91594 - 2.91594i) q^{57} +(1.59613 + 5.95685i) q^{58} +(1.30044 + 2.25243i) q^{59} +(8.67653 + 5.00940i) q^{61} +(-1.40286 + 1.40286i) q^{62} +(2.62959 + 0.291963i) q^{63} -7.05216i q^{64} +(3.09953 - 1.78951i) q^{66} +(1.42661 - 5.32418i) q^{67} +(-0.502686 + 0.134694i) q^{68} +2.58226 q^{69} -7.23274 q^{71} +(2.90136 - 0.777416i) q^{72} +(3.98240 - 14.8625i) q^{73} +(-0.137513 + 0.0793931i) q^{74} -4.09280i q^{76} +(7.59955 + 5.58969i) q^{77} +(2.79411 - 2.79411i) q^{78} +(-13.1146 - 7.57171i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.15229 + 8.03244i) q^{82} +(9.42372 + 9.42372i) q^{83} +(1.64054 + 2.05034i) q^{84} +(-6.39670 + 11.0794i) q^{86} +(-5.93461 - 1.59017i) q^{87} +(10.3453 + 2.77201i) q^{88} +(-5.52672 + 9.57257i) q^{89} +(9.70175 + 3.78950i) q^{91} +(1.81222 + 1.81222i) q^{92} +(-0.511564 - 1.90918i) q^{93} +(2.69710 + 4.67152i) q^{94} +(4.30724 + 2.48679i) q^{96} +(-2.48828 + 2.48828i) q^{97} +(3.26295 - 6.22262i) q^{98} +3.56567i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{7} + 24 q^{8}+O(q^{10}) \) 32 * q - 8 * q^7 + 24 * q^8	\( 32 q - 8 q^{7} + 24 q^{8} - 8 q^{11} - 8 q^{21} + 8 q^{22} + 8 q^{23} + 24 q^{26} + 24 q^{28} + 24 q^{31} - 24 q^{32} + 36 q^{33} - 32 q^{36} - 4 q^{37} - 12 q^{38} - 16 q^{42} - 40 q^{43} - 40 q^{46} + 60 q^{47} - 8 q^{51} + 108 q^{52} + 24 q^{53} - 48 q^{56} - 16 q^{57} - 4 q^{58} - 24 q^{61} - 4 q^{63} + 72 q^{66} - 8 q^{67} - 132 q^{68} - 16 q^{71} - 12 q^{72} - 36 q^{73} - 60 q^{77} - 80 q^{78} + 16 q^{81} - 12 q^{82} - 16 q^{86} + 24 q^{87} + 32 q^{88} - 24 q^{91} + 56 q^{92} + 24 q^{93} + 72 q^{98}+O(q^{100}) \) 32 * q - 8 * q^7 + 24 * q^8 - 8 * q^11 - 8 * q^21 + 8 * q^22 + 8 * q^23 + 24 * q^26 + 24 * q^28 + 24 * q^31 - 24 * q^32 + 36 * q^33 - 32 * q^36 - 4 * q^37 - 12 * q^38 - 16 * q^42 - 40 * q^43 - 40 * q^46 + 60 * q^47 - 8 * q^51 + 108 * q^52 + 24 * q^53 - 48 * q^56 - 16 * q^57 - 4 * q^58 - 24 * q^61 - 4 * q^63 + 72 * q^66 - 8 * q^67 - 132 * q^68 - 16 * q^71 - 12 * q^72 - 36 * q^73 - 60 * q^77 - 80 * q^78 + 16 * q^81 - 12 * q^82 - 16 * q^86 + 24 * q^87 + 32 * q^88 - 24 * q^91 + 56 * q^92 + 24 * q^93 + 72 * q^98

Introduction

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