LMFDB - Embedded newform 425.2.j.d.149.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(149,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("425.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.j (of order $4$, degree $2$, not 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:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 119x^{8} + 364x^{6} + 519x^{4} + 278x^{2} + 1 $ x^12 + 18x^10 + 119x^8 + 364x^6 + 519x^4 + 278*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			149.4
Root			$-1.21647i$ of defining polynomial
Character	$\chi$	$=$	425.149
Dual form			425.2.j.d.174.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.21647 q^{2} +(2.23861 - 2.23861i) q^{3} -0.520205 q^{4} +(2.72320 - 2.72320i) q^{6} +(0.679950 + 0.679950i) q^{7} -3.06575 q^{8} -7.02277i q^{9} +(2.22126 - 2.22126i) q^{11} +(-1.16454 + 1.16454i) q^{12} +2.02534i q^{13} +(0.827137 + 0.827137i) q^{14} -2.68898 q^{16} +(-2.07407 - 3.56346i) q^{17} -8.54297i q^{18} +5.28609i q^{19} +3.04429 q^{21} +(2.70209 - 2.70209i) q^{22} +(6.01797 + 6.01797i) q^{23} +(-6.86302 + 6.86302i) q^{24} +2.46376i q^{26} +(-9.00542 - 9.00542i) q^{27} +(-0.353714 - 0.353714i) q^{28} +(0.857606 + 0.857606i) q^{29} +(3.97529 + 3.97529i) q^{31} +2.86045 q^{32} -9.94509i q^{33} +(-2.52305 - 4.33483i) q^{34} +3.65328i q^{36} +(-5.84955 + 5.84955i) q^{37} +6.43037i q^{38} +(4.53395 + 4.53395i) q^{39} +(-1.04325 + 1.04325i) q^{41} +3.70328 q^{42} -7.01089 q^{43} +(-1.15551 + 1.15551i) q^{44} +(7.32067 + 7.32067i) q^{46} -10.9275i q^{47} +(-6.01957 + 6.01957i) q^{48} -6.07534i q^{49} +(-12.6202 - 3.33415i) q^{51} -1.05359i q^{52} -5.24568 q^{53} +(-10.9548 - 10.9548i) q^{54} +(-2.08456 - 2.08456i) q^{56} +(11.8335 + 11.8335i) q^{57} +(1.04325 + 1.04325i) q^{58} +13.8346i q^{59} +(2.70557 - 2.70557i) q^{61} +(4.83581 + 4.83581i) q^{62} +(4.77513 - 4.77513i) q^{63} +8.85759 q^{64} -12.0979i q^{66} +2.37336i q^{67} +(1.07894 + 1.85373i) q^{68} +26.9438 q^{69} +(2.82261 + 2.82261i) q^{71} +21.5300i q^{72} +(-5.51272 + 5.51272i) q^{73} +(-7.11579 + 7.11579i) q^{74} -2.74985i q^{76} +3.02069 q^{77} +(5.51540 + 5.51540i) q^{78} +(4.74215 - 4.74215i) q^{79} -19.2510 q^{81} +(-1.26908 + 1.26908i) q^{82} -0.171341 q^{83} -1.58365 q^{84} -8.52853 q^{86} +3.83969 q^{87} +(-6.80983 + 6.80983i) q^{88} -1.32080 q^{89} +(-1.37713 + 1.37713i) q^{91} +(-3.13058 - 3.13058i) q^{92} +17.7982 q^{93} -13.2930i q^{94} +(6.40343 - 6.40343i) q^{96} +(1.33838 - 1.33838i) q^{97} -7.39045i q^{98} +(-15.5994 - 15.5994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{6} + 12 q^{8} - 4 q^{11} - 4 q^{12} - 14 q^{14} + 4 q^{16} - 10 q^{17} + 8 q^{21} + 10 q^{22} + 12 q^{23} + 8 q^{24} - 22 q^{27} - 34 q^{28} + 6 q^{29} - 6 q^{31}+ \cdots - 30 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^6 + 12 * q^8 - 4 * q^11 - 4 * q^12 - 14 * q^14 + 4 * q^16 - 10 * q^17 + 8 * q^21 + 10 * q^22 + 12 * q^23 + 8 * q^24 - 22 * q^27 - 34 * q^28 + 6 * q^29 - 6 * q^31 + 48 * q^32 - 30 * q^34 + 18 * q^37 - 16 * q^39 + 6 * q^41 - 56 * q^42 + 16 * q^43 - 32 * q^44 + 30 * q^46 + 10 * q^48 - 40 * q^51 - 48 * q^53 - 16 * q^54 - 56 * q^56 + 18 * q^57 - 6 * q^58 - 8 * q^61 + 22 * q^62 + 30 * q^63 + 44 * q^64 - 18 * q^68 + 72 * q^69 - 20 * q^71 + 18 * q^73 + 26 * q^74 - 24 * q^77 + 38 * q^78 + 14 * q^79 - 8 * q^81 - 10 * q^82 - 52 * q^83 - 36 * q^84 + 84 * q^86 + 48 * q^87 - 66 * q^88 + 24 * q^89 + 12 * q^91 + 32 * q^92 + 60 * q^93 + 22 * q^96 - 52 * q^97 - 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	1.21647			0.860173			0.430086	−	0.902788i	$-0.358483\pi$
$2$	1.21647			0.860173			0.430086	+	0.902788i	$0.358483\pi$
$3$	2.23861	−	2.23861i	1.29246	−	1.29246i	0.359204	−	0.933259i	$-0.383048\pi$
$3$	2.23861	−	2.23861i	1.29246	−	1.29246i	0.933259	−	0.359204i	$-0.116952\pi$
$4$	−0.520205			−0.260103
$5$		0			0
$5$		0			0
$6$	2.72320	−	2.72320i	1.11174	−	1.11174i
$7$	0.679950	+	0.679950i	0.256997	+	0.256997i	0.823832	−	0.566835i	$-0.191832\pi$
$7$	0.679950	+	0.679950i	0.256997	+	0.256997i	−0.566835	+	0.823832i	$0.691832\pi$
$8$	−3.06575			−1.08391
$9$		−	7.02277i		−	2.34092i
$10$		0			0
$11$	2.22126	−	2.22126i	0.669736	−	0.669736i	−0.287919	−	0.957655i	$-0.592963\pi$
$11$	2.22126	−	2.22126i	0.669736	−	0.669736i	0.957655	+	0.287919i	$0.0929634\pi$
$12$	−1.16454	+	1.16454i	−0.336173	+	0.336173i
$13$			2.02534i			0.561728i	0.959748	+	0.280864i	$0.0906210\pi$
$13$			2.02534i			0.561728i	−0.959748	+	0.280864i	$0.909379\pi$
$14$	0.827137	+	0.827137i	0.221062	+	0.221062i
$15$		0			0
$16$	−2.68898			−0.672244
$17$	−2.07407	−	3.56346i	−0.503037	−	0.864265i
$17$	−2.07407	−	3.56346i	−0.503037	−	0.864265i
$18$		−	8.54297i		−	2.01360i
$19$			5.28609i			1.21271i	0.795193	+	0.606357i	$0.207370\pi$
$19$			5.28609i			1.21271i	−0.795193	+	0.606357i	$0.792630\pi$
$20$		0			0
$21$	3.04429			0.664318
$22$	2.70209	−	2.70209i	0.576088	−	0.576088i
$23$	6.01797	+	6.01797i	1.25483	+	1.25483i	0.953527	+	0.301307i	$0.0974230\pi$
$23$	6.01797	+	6.01797i	1.25483	+	1.25483i	0.301307	+	0.953527i	$0.402577\pi$
$24$	−6.86302	+	6.86302i	−1.40091	+	1.40091i
$25$		0			0
$26$			2.46376i			0.483183i
$27$	−9.00542	−	9.00542i	−1.73309	−	1.73309i
$28$	−0.353714	−	0.353714i	−0.0668456	−	0.0668456i
$29$	0.857606	+	0.857606i	0.159253	+	0.159253i	0.782236	−	0.622982i	$-0.214079\pi$
$29$	0.857606	+	0.857606i	0.159253	+	0.159253i	−0.622982	+	0.782236i	$0.714079\pi$
$30$		0			0
$31$	3.97529	+	3.97529i	0.713982	+	0.713982i	0.967366	−	0.253384i	$-0.0815435\pi$
$31$	3.97529	+	3.97529i	0.713982	+	0.713982i	−0.253384	+	0.967366i	$0.581543\pi$
$32$	2.86045			0.505660
$33$		−	9.94509i		−	1.73122i
$34$	−2.52305	−	4.33483i	−0.432699	−	0.743417i
$35$		0			0
$36$			3.65328i			0.608880i
$37$	−5.84955	+	5.84955i	−0.961660	+	0.961660i	−0.999292	−	0.0376315i	$-0.988019\pi$
$37$	−5.84955	+	5.84955i	−0.961660	+	0.961660i	0.0376315	+	0.999292i	$0.488019\pi$
$38$			6.43037i			1.04314i
$39$	4.53395	+	4.53395i	0.726013	+	0.726013i
$40$		0			0
$41$	−1.04325	+	1.04325i	−0.162928	+	0.162928i	−0.783863	−	0.620934i	$-0.786753\pi$
$41$	−1.04325	+	1.04325i	−0.162928	+	0.162928i	0.620934	+	0.783863i	$0.286753\pi$
$42$	3.70328			0.571428
$43$	−7.01089			−1.06915			−0.534576	−	0.845121i	$-0.679529\pi$
$43$	−7.01089			−1.06915			−0.534576	+	0.845121i	$0.679529\pi$
$44$	−1.15551	+	1.15551i	−0.174200	+	0.174200i
$45$		0			0
$46$	7.32067	+	7.32067i	1.07937	+	1.07937i
$47$		−	10.9275i		−	1.59394i	−0.604019	−	0.796970i	$-0.706435\pi$
$47$		−	10.9275i		−	1.59394i	0.604019	−	0.796970i	$-0.293565\pi$
$48$	−6.01957	+	6.01957i	−0.868851	+	0.868851i
$49$		−	6.07534i		−	0.867905i
$50$		0			0
$51$	−12.6202	−	3.33415i	−1.76719	−	0.466874i
$52$		−	1.05359i		−	0.146107i
$53$	−5.24568			−0.720550			−0.360275	−	0.932846i	$-0.617317\pi$
$53$	−5.24568			−0.720550			−0.360275	+	0.932846i	$0.617317\pi$
$54$	−10.9548	−	10.9548i	−1.49076	−	1.49076i
$55$		0			0
$56$	−2.08456	−	2.08456i	−0.278561	−	0.278561i
$57$	11.8335	+	11.8335i	1.56739	+	1.56739i
$58$	1.04325	+	1.04325i	0.136985	+	0.136985i
$59$			13.8346i			1.80111i	0.434747	+	0.900553i	$0.356838\pi$
$59$			13.8346i			1.80111i	−0.434747	+	0.900553i	$0.643162\pi$
$60$		0			0
$61$	2.70557	−	2.70557i	0.346412	−	0.346412i	−0.512359	−	0.858771i	$-0.671228\pi$
$61$	2.70557	−	2.70557i	0.346412	−	0.346412i	0.858771	+	0.512359i	$0.171228\pi$
$62$	4.83581	+	4.83581i	0.614148	+	0.614148i
$63$	4.77513	−	4.77513i	0.601610	−	0.601610i
$64$	8.85759			1.10720
$65$		0			0
$66$		−	12.0979i		−	1.48915i
$67$			2.37336i			0.289953i	0.989435	+	0.144976i	$0.0463106\pi$
$67$			2.37336i			0.289953i	−0.989435	+	0.144976i	$0.953689\pi$
$68$	1.07894	+	1.85373i	0.130841	+	0.224798i
$69$	26.9438			3.24366
$70$		0			0
$71$	2.82261	+	2.82261i	0.334983	+	0.334983i	0.854475	−	0.519492i	$-0.173879\pi$
$71$	2.82261	+	2.82261i	0.334983	+	0.334983i	−0.519492	+	0.854475i	$0.673879\pi$
$72$			21.5300i			2.53734i
$73$	−5.51272	+	5.51272i	−0.645215	+	0.645215i	−0.951833	−	0.306618i	$-0.900803\pi$
$73$	−5.51272	+	5.51272i	−0.645215	+	0.645215i	0.306618	+	0.951833i	$0.400803\pi$
$74$	−7.11579	+	7.11579i	−0.827194	+	0.827194i
$75$		0			0
$76$		−	2.74985i		−	0.315430i
$77$	3.02069			0.344240
$78$	5.51540	+	5.51540i	0.624496	+	0.624496i
$79$	4.74215	−	4.74215i	0.533534	−	0.533534i	−0.388089	−	0.921622i	$-0.626865\pi$
$79$	4.74215	−	4.74215i	0.533534	−	0.533534i	0.921622	+	0.388089i	$0.126865\pi$
$80$		0			0
$81$	−19.2510			−2.13900
$82$	−1.26908	+	1.26908i	−0.140147	+	0.140147i
$83$	−0.171341			−0.0188071			−0.00940355	−	0.999956i	$-0.502993\pi$
$83$	−0.171341			−0.0188071			−0.00940355	+	0.999956i	$0.502993\pi$
$84$	−1.58365			−0.172791
$85$		0			0
$86$	−8.52853			−0.919655
$87$	3.83969			0.411658
$88$	−6.80983	+	6.80983i	−0.725930	+	0.725930i
$89$	−1.32080			−0.140004			−0.0700020	−	0.997547i	$-0.522301\pi$
$89$	−1.32080			−0.140004			−0.0700020	+	0.997547i	$0.522301\pi$
$90$		0			0
$91$	−1.37713	+	1.37713i	−0.144362	+	0.144362i
$92$	−3.13058	−	3.13058i	−0.326386	−	0.326386i
$93$	17.7982			1.84559
$94$		−	13.2930i		−	1.37106i
$95$		0			0
$96$	6.40343	−	6.40343i	0.653547	−	0.653547i
$97$	1.33838	−	1.33838i	0.135892	−	0.135892i	−0.635889	−	0.771781i	$-0.719366\pi$
$97$	1.33838	−	1.33838i	0.135892	−	0.135892i	0.771781	+	0.635889i	$0.219366\pi$
$98$		−	7.39045i		−	0.746548i
$99$	−15.5994	−	15.5994i	−1.56780	−	1.56780i
$100$		0			0
$101$	4.43204			0.441004			0.220502	−	0.975386i	$-0.429230\pi$
$101$	4.43204			0.441004			0.220502	+	0.975386i	$0.429230\pi$
$102$	−15.3521	−	4.05588i	−1.52009	−	0.401592i
$103$		−	15.4586i		−	1.52318i	−0.648057	−	0.761591i	$-0.724418\pi$
$103$		−	15.4586i		−	1.52318i	0.648057	−	0.761591i	$-0.275582\pi$
$104$		−	6.20918i		−	0.608860i
$105$		0			0
$106$	−6.38121			−0.619798
$107$	−0.692094	+	0.692094i	−0.0669072	+	0.0669072i	−0.739769	−	0.672861i	$-0.765065\pi$
$107$	−0.692094	+	0.692094i	−0.0669072	+	0.0669072i	0.672861	+	0.739769i	$0.265065\pi$
$108$	4.68467	+	4.68467i	0.450782	+	0.450782i
$109$	3.51917	−	3.51917i	0.337075	−	0.337075i	−0.518190	−	0.855265i	$-0.673394\pi$
$109$	3.51917	−	3.51917i	0.337075	−	0.337075i	0.855265	+	0.518190i	$0.173394\pi$
$110$		0			0
$111$			26.1897i			2.48582i
$112$	−1.82837	−	1.82837i	−0.172765	−	0.172765i
$113$	−3.07762	−	3.07762i	−0.289519	−	0.289519i	0.547371	−	0.836890i	$-0.315629\pi$
$113$	−3.07762	−	3.07762i	−0.289519	−	0.289519i	−0.836890	+	0.547371i	$0.815629\pi$
$114$	14.3951	+	14.3951i	1.34822	+	1.34822i
$115$		0			0
$116$	−0.446131	−	0.446131i	−0.0414222	−	0.0414222i
$117$	14.2235			1.31496
$118$			16.8293i			1.54926i
$119$	1.01270	−	3.83324i	0.0928345	−	0.351392i
$120$		0			0
$121$			1.13199i			0.102909i
$122$	3.29124	−	3.29124i	0.297974	−	0.297974i
$123$			4.67087i			0.421158i
$124$	−2.06796	−	2.06796i	−0.185709	−	0.185709i
$125$		0			0
$126$	5.80879	−	5.80879i	0.517488	−	0.517488i
$127$	−20.0499			−1.77914			−0.889572	−	0.456795i	$-0.848997\pi$
$127$	−20.0499			−1.77914			−0.889572	+	0.456795i	$0.848997\pi$
$128$	5.05409			0.446722
$129$	−15.6947	+	15.6947i	−1.38184	+	1.38184i
$130$		0			0
$131$	−11.3827	−	11.3827i	−0.994508	−	0.994508i	0.00547746	−	0.999985i	$-0.498256\pi$
$131$	−11.3827	−	11.3827i	−0.994508	−	0.994508i	−0.999985	+	0.00547746i	$0.998256\pi$
$132$			5.17349i			0.450294i
$133$	−3.59428	+	3.59428i	−0.311664	+	0.311664i
$134$			2.88712i			0.249409i
$135$		0			0
$136$	6.35859	+	10.9247i	0.545245	+	0.936782i
$137$		−	4.53005i		−	0.387028i	−0.981098	−	0.193514i	$-0.938011\pi$
$137$		−	4.53005i		−	0.387028i	0.981098	−	0.193514i	$-0.0619885\pi$
$138$	32.7763			2.79010
$139$	0.678975	+	0.678975i	0.0575899	+	0.0575899i	0.735315	−	0.677725i	$-0.237034\pi$
$139$	0.678975	+	0.678975i	0.0575899	+	0.0575899i	−0.677725	+	0.735315i	$0.737034\pi$
$140$		0			0
$141$	−24.4624	−	24.4624i	−2.06011	−	2.06011i
$142$	3.43362	+	3.43362i	0.288143	+	0.288143i
$143$	4.49881	+	4.49881i	0.376209	+	0.376209i
$144$			18.8841i			1.57367i
$145$		0			0
$146$	−6.70605	+	6.70605i	−0.554996	+	0.554996i
$147$	−13.6003	−	13.6003i	−1.12174	−	1.12174i
$148$	3.04297	−	3.04297i	0.250130	−	0.250130i
$149$	1.68439			0.137990			0.0689952	−	0.997617i	$-0.478021\pi$
$149$	1.68439			0.137990			0.0689952	+	0.997617i	$0.478021\pi$
$150$		0			0
$151$			7.30864i			0.594769i	0.954758	+	0.297384i	$0.0961142\pi$
$151$			7.30864i			0.594769i	−0.954758	+	0.297384i	$0.903886\pi$
$152$		−	16.2058i		−	1.31447i
$153$	−25.0253	+	14.5657i	−2.02318	+	1.17757i
$154$	3.67458			0.296106
$155$		0			0
$156$	−2.35858	−	2.35858i	−0.188838	−	0.188838i
$157$			7.30709i			0.583169i	0.956545	+	0.291585i	$0.0941825\pi$
$157$			7.30709i			0.583169i	−0.956545	+	0.291585i	$0.905818\pi$
$158$	5.76867	−	5.76867i	0.458931	−	0.458931i
$159$	−11.7431	+	11.7431i	−0.931285	+	0.931285i
$160$		0			0
$161$			8.18384i			0.644977i
$162$	−23.4182			−1.83991
$163$	−15.4004	−	15.4004i	−1.20626	−	1.20626i	−0.972231	−	0.234025i	$-0.924810\pi$
$163$	−15.4004	−	15.4004i	−1.20626	−	1.20626i	−0.234025	−	0.972231i	$-0.575190\pi$
$164$	0.542704	−	0.542704i	0.0423781	−	0.0423781i
$165$		0			0
$166$	−0.208431			−0.0161774
$167$	−6.15592	+	6.15592i	−0.476360	+	0.476360i	−0.903965	−	0.427606i	$-0.859357\pi$
$167$	−6.15592	+	6.15592i	−0.476360	+	0.476360i	0.427606	+	0.903965i	$0.359357\pi$
$168$	−9.33302			−0.720058
$169$	8.89800			0.684462
$170$		0			0
$171$	37.1230			2.83887
$172$	3.64710			0.278089
$173$	−5.08754	+	5.08754i	−0.386798	+	0.386798i	−0.873544	−	0.486745i	$-0.838184\pi$
$173$	−5.08754	+	5.08754i	−0.386798	+	0.386798i	0.486745	+	0.873544i	$0.338184\pi$
$174$	4.67087			0.354097
$175$		0			0
$176$	−5.97292	+	5.97292i	−0.450226	+	0.450226i
$177$	30.9702	+	30.9702i	2.32786	+	2.32786i
$178$	−1.60671			−0.120428
$179$		−	9.93729i		−	0.742748i	−0.928483	−	0.371374i	$-0.878887\pi$
$179$		−	9.93729i		−	0.742748i	0.928483	−	0.371374i	$-0.121113\pi$
$180$		0			0
$181$	0.985498	−	0.985498i	0.0732515	−	0.0732515i	−0.669532	−	0.742783i	$-0.733505\pi$
$181$	0.985498	−	0.985498i	0.0732515	−	0.0732515i	0.742783	+	0.669532i	$0.233505\pi$
$182$	−1.67523	+	1.67523i	−0.124177	+	0.124177i
$183$		−	12.1134i		−	0.895450i
$184$	−18.4496	−	18.4496i	−1.36012	−	1.36012i
$185$		0			0
$186$	21.6510			1.58753
$187$	−12.5224	−	3.30831i	−0.915731	−	0.241927i
$188$			5.68454i			0.414588i
$189$		−	12.2465i		−	0.890799i
$190$		0			0
$191$	4.39578			0.318068			0.159034	−	0.987273i	$-0.449162\pi$
$191$	4.39578			0.318068			0.159034	+	0.987273i	$0.449162\pi$
$192$	19.8287	−	19.8287i	1.43101	−	1.43101i
$193$	−7.54658	−	7.54658i	−0.543215	−	0.543215i	0.381255	−	0.924470i	$-0.375492\pi$
$193$	−7.54658	−	7.54658i	−0.543215	−	0.543215i	−0.924470	+	0.381255i	$0.875492\pi$
$194$	1.62810	−	1.62810i	0.116891	−	0.116891i
$195$		0			0
$196$			3.16042i			0.225744i
$197$	−3.37366	−	3.37366i	−0.240364	−	0.240364i	0.576637	−	0.817001i	$-0.304365\pi$
$197$	−3.37366	−	3.37366i	−0.240364	−	0.240364i	−0.817001	+	0.576637i	$0.804365\pi$
$198$	−18.9762	−	18.9762i	−1.34858	−	1.34858i
$199$	−13.0268	−	13.0268i	−0.923445	−	0.923445i	0.0738262	−	0.997271i	$-0.476479\pi$
$199$	−13.0268	−	13.0268i	−0.923445	−	0.923445i	−0.997271	+	0.0738262i	$0.976479\pi$
$200$		0			0
$201$	5.31304	+	5.31304i	0.374753	+	0.374753i
$202$	5.39143			0.379340
$203$			1.16626i			0.0818553i
$204$	6.56512	+	1.73444i	0.459650	+	0.121435i
$205$		0			0
$206$		−	18.8049i		−	1.31020i
$207$	42.2628	−	42.2628i	2.93747	−	2.93747i
$208$		−	5.44609i		−	0.377618i
$209$	11.7418	+	11.7418i	0.812197	+	0.812197i
$210$		0			0
$211$	14.5044	−	14.5044i	0.998523	−	0.998523i	−0.00147578	−	0.999999i	$-0.500470\pi$
$211$	14.5044	−	14.5044i	0.998523	−	0.998523i	0.999999	+	0.00147578i	$0.000469756\pi$
$212$	2.72883			0.187417
$213$	12.6375			0.865905
$214$	−0.841910	+	0.841910i	−0.0575518	+	0.0575518i
$215$		0			0
$216$	27.6084	+	27.6084i	1.87851	+	1.87851i
$217$			5.40599i			0.366982i
$218$	4.28096	−	4.28096i	0.289943	−	0.289943i
$219$			24.6817i			1.66783i
$220$		0			0
$221$	7.21720	−	4.20070i	0.485482	−	0.282570i
$222$			31.8590i			2.13824i
$223$	−16.2801			−1.09019			−0.545097	−	0.838373i	$-0.683507\pi$
$223$	−16.2801			−1.09019			−0.545097	+	0.838373i	$0.683507\pi$
$224$	1.94496	+	1.94496i	0.129953	+	0.129953i
$225$		0			0
$226$	−3.74383	−	3.74383i	−0.249036	−	0.249036i
$227$	10.4633	+	10.4633i	0.694477	+	0.694477i	0.963214	−	0.268737i	$-0.0866062\pi$
$227$	10.4633	+	10.4633i	0.694477	+	0.694477i	−0.268737	+	0.963214i	$0.586606\pi$
$228$	−6.15586	−	6.15586i	−0.407682	−	0.407682i
$229$		−	13.4006i		−	0.885534i	−0.896637	−	0.442767i	$-0.853997\pi$
$229$		−	13.4006i		−	0.885534i	0.896637	−	0.442767i	$-0.146003\pi$
$230$		0			0
$231$	6.76216	−	6.76216i	0.444917	−	0.444917i
$232$	−2.62921	−	2.62921i	−0.172616	−	0.172616i
$233$	17.4785	−	17.4785i	1.14505	−	1.14505i	0.157541	−	0.987512i	$-0.449643\pi$
$233$	17.4785	−	17.4785i	1.14505	−	1.14505i	0.987512	−	0.157541i	$-0.0503567\pi$
$234$	17.3024			1.13109
$235$		0			0
$236$		−	7.19681i		−	0.468472i
$237$		−	21.2317i		−	1.37914i
$238$	1.23192	−	4.66301i	0.0798537	−	0.302258i
$239$	−1.28352			−0.0830243			−0.0415121	−	0.999138i	$-0.513218\pi$
$239$	−1.28352			−0.0830243			−0.0415121	+	0.999138i	$0.513218\pi$
$240$		0			0
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	0.355091	−	0.934832i	$-0.384450\pi$
$241$	−9.00000	−	9.00000i	−0.579741	−	0.579741i	−0.934832	+	0.355091i	$0.884450\pi$
$242$			1.37703i			0.0885191i
$243$	−16.0792	+	16.0792i	−1.03148	+	1.03148i
$244$	−1.40745	+	1.40745i	−0.0901028	+	0.0901028i
$245$		0			0
$246$			5.68196i			0.362268i
$247$	−10.7061			−0.681215
$248$	−12.1872	−	12.1872i	−0.773890	−	0.773890i
$249$	−0.383566	+	0.383566i	−0.0243075	+	0.0243075i
$250$		0			0
$251$	15.1133			0.953943			0.476972	−	0.878919i	$-0.341734\pi$
$251$	15.1133			0.953943			0.476972	+	0.878919i	$0.341734\pi$
$252$	−2.48405	+	2.48405i	−0.156480	+	0.156480i
$253$	26.7350			1.68081
$254$	−24.3901			−1.53037
$255$		0			0
$256$	−11.5670			−0.722941
$257$	0.247858			0.0154609			0.00773047	−	0.999970i	$-0.497539\pi$
$257$	0.247858			0.0154609			0.00773047	+	0.999970i	$0.497539\pi$
$258$	−19.0921	+	19.0921i	−1.18862	+	1.18862i
$259$	−7.95480			−0.494287
$260$		0			0
$261$	6.02277	−	6.02277i	0.372800	−	0.372800i
$262$	−13.8466	−	13.8466i	−0.855448	−	0.855448i
$263$	12.6190			0.778120			0.389060	−	0.921212i	$-0.372800\pi$
$263$	12.6190			0.778120			0.389060	+	0.921212i	$0.372800\pi$
$264$			30.4891i			1.87648i
$265$		0			0
$266$	−4.37233	+	4.37233i	−0.268085	+	0.268085i
$267$	−2.95675	+	2.95675i	−0.180950	+	0.180950i
$268$		−	1.23464i		−	0.0754174i
$269$	10.1203	+	10.1203i	0.617046	+	0.617046i	0.944773	−	0.327727i	$-0.106283\pi$
$269$	10.1203	+	10.1203i	0.617046	+	0.617046i	−0.327727	+	0.944773i	$0.606283\pi$
$270$		0			0
$271$	−18.9859			−1.15331			−0.576656	−	0.816987i	$-0.695643\pi$
$271$	−18.9859			−1.15331			−0.576656	+	0.816987i	$0.695643\pi$
$272$	5.57713	+	9.58205i	0.338163	+	0.580997i
$273$			6.16571i			0.373166i
$274$		−	5.51066i		−	0.332911i
$275$		0			0
$276$	−14.0163			−0.843683
$277$	−10.4399	+	10.4399i	−0.627275	+	0.627275i	−0.947382	−	0.320106i	$-0.896281\pi$
$277$	−10.4399	+	10.4399i	−0.627275	+	0.627275i	0.320106	+	0.947382i	$0.396281\pi$
$278$	0.825952	+	0.825952i	0.0495373	+	0.0495373i
$279$	27.9175	−	27.9175i	1.67138	−	1.67138i
$280$		0			0
$281$			23.7227i			1.41518i	0.706624	+	0.707589i	$0.250217\pi$
$281$			23.7227i			1.41518i	−0.706624	+	0.707589i	$0.749783\pi$
$282$	−29.7578	−	29.7578i	−1.77205	−	1.77205i
$283$	18.6754	+	18.6754i	1.11013	+	1.11013i	0.993132	+	0.117003i	$0.0373288\pi$
$283$	18.6754	+	18.6754i	1.11013	+	1.11013i	0.117003	+	0.993132i	$0.462671\pi$
$284$	−1.46834	−	1.46834i	−0.0871299	−	0.0871299i
$285$		0			0
$286$	5.47266	+	5.47266i	0.323605	+	0.323605i
$287$	−1.41872			−0.0837442
$288$		−	20.0882i		−	1.18371i
$289$	−8.39643	+	14.7817i	−0.493908	+	0.869514i
$290$		0			0
$291$		−	5.99223i		−	0.351271i
$292$	2.86775	−	2.86775i	0.167822	−	0.167822i
$293$			11.0287i			0.644306i	0.946688	+	0.322153i	$0.104407\pi$
$293$			11.0287i			0.644306i	−0.946688	+	0.322153i	$0.895593\pi$
$294$	−16.5444	−	16.5444i	−0.964887	−	0.964887i
$295$		0			0
$296$	17.9333	−	17.9333i	1.04235	−	1.04235i
$297$	−40.0068			−2.32143
$298$	2.04900			0.118696
$299$	−12.1884	+	12.1884i	−0.704876	+	0.704876i
$300$		0			0
$301$	−4.76706	−	4.76706i	−0.274769	−	0.274769i
$302$			8.89073i			0.511604i
$303$	9.92162	−	9.92162i	0.569982	−	0.569982i
$304$		−	14.2142i		−	0.815239i
$305$		0			0
$306$	−30.4425	+	17.7188i	−1.74028	+	1.01291i
$307$			5.11998i			0.292213i	0.989269	+	0.146106i	$0.0466742\pi$
$307$			5.11998i			0.292213i	−0.989269	+	0.146106i	$0.953326\pi$
$308$	−1.57138			−0.0895377
$309$	−34.6059	−	34.6059i	−1.96866	−	1.96866i
$310$		0			0
$311$	−1.28347	−	1.28347i	−0.0727789	−	0.0727789i	0.669780	−	0.742559i	$-0.266388\pi$
$311$	−1.28347	−	1.28347i	−0.0727789	−	0.0727789i	−0.742559	+	0.669780i	$0.766388\pi$
$312$	−13.8999	−	13.8999i	−0.786930	−	0.786930i
$313$	−11.4417	−	11.4417i	−0.646721	−	0.646721i	0.305478	−	0.952199i	$-0.401184\pi$
$313$	−11.4417	−	11.4417i	−0.646721	−	0.646721i	−0.952199	+	0.305478i	$0.901184\pi$
$314$			8.88884i			0.501626i
$315$		0			0
$316$	−2.46689	+	2.46689i	−0.138773	+	0.138773i
$317$	8.07082	+	8.07082i	0.453303	+	0.453303i	0.896449	−	0.443147i	$-0.146138\pi$
$317$	8.07082	+	8.07082i	0.453303	+	0.453303i	−0.443147	+	0.896449i	$0.646138\pi$
$318$	−14.2850	+	14.2850i	−0.801066	+	0.801066i
$319$	3.80993			0.213315
$320$		0			0
$321$			3.09866i			0.172950i
$322$			9.95538i			0.554792i
$323$	18.8368	−	10.9638i	1.04811	−	0.610040i
$324$	10.0145			0.556359
$325$		0			0
$326$	−18.7341	−	18.7341i	−1.03759	−	1.03759i
$327$		−	15.7561i		−	0.871314i
$328$	3.19834	−	3.19834i	0.176599	−	0.176599i
$329$	7.43015	−	7.43015i	0.409638	−	0.409638i
$330$		0			0
$331$			8.46764i			0.465423i	0.972546	+	0.232712i	$0.0747599\pi$
$331$			8.46764i			0.465423i	−0.972546	+	0.232712i	$0.925240\pi$
$332$	0.0891324			0.00489178
$333$	41.0800	+	41.0800i	2.25117	+	2.25117i
$334$	−7.48848	+	7.48848i	−0.409752	+	0.409752i
$335$		0			0
$336$	−8.18602			−0.446584
$337$	1.92994	−	1.92994i	0.105131	−	0.105131i	−0.652585	−	0.757716i	$-0.726315\pi$
$337$	1.92994	−	1.92994i	0.105131	−	0.105131i	0.757716	+	0.652585i	$0.226315\pi$
$338$	10.8241			0.588755
$339$	−13.7792			−0.748384
$340$		0			0
$341$	17.6603			0.956359
$342$	45.1590			2.44192
$343$	8.89057	−	8.89057i	0.480046	−	0.480046i
$344$	21.4936			1.15886
$345$		0			0
$346$	−6.18883	+	6.18883i	−0.332713	+	0.332713i
$347$	9.34214	+	9.34214i	0.501512	+	0.501512i	0.911908	−	0.410395i	$-0.134609\pi$
$347$	9.34214	+	9.34214i	0.501512	+	0.501512i	−0.410395	+	0.911908i	$0.634609\pi$
$348$	−1.99743			−0.107073
$349$			27.0950i			1.45036i	0.688558	+	0.725181i	$0.258244\pi$
$349$			27.0950i			1.45036i	−0.688558	+	0.725181i	$0.741756\pi$
$350$		0			0
$351$	18.2390	−	18.2390i	0.973527	−	0.973527i
$352$	6.35380	−	6.35380i	0.338659	−	0.338659i
$353$			27.4302i			1.45996i	0.683468	+	0.729980i	$0.260471\pi$
$353$			27.4302i			1.45996i	−0.683468	+	0.729980i	$0.739529\pi$
$354$	37.6743	+	37.6743i	2.00236	+	2.00236i
$355$		0			0
$356$	0.687085			0.0364154
$357$	−6.31408	−	10.8482i	−0.334176	−	0.574147i
$358$		−	12.0884i		−	0.638892i
$359$			3.45103i			0.182138i	0.995845	+	0.0910692i	$0.0290284\pi$
$359$			3.45103i			0.182138i	−0.995845	+	0.0910692i	$0.970972\pi$
$360$		0			0
$361$	−8.94280			−0.470674
$362$	1.19883	−	1.19883i	0.0630090	−	0.0630090i
$363$	2.53410	+	2.53410i	0.133006	+	0.133006i
$364$	0.716390	−	0.716390i	0.0375490	−	0.0375490i
$365$		0			0
$366$		−	14.7356i		−	0.770242i
$367$	1.01764	+	1.01764i	0.0531203	+	0.0531203i	0.733168	−	0.680048i	$-0.238041\pi$
$367$	1.01764	+	1.01764i	0.0531203	+	0.0531203i	−0.680048	+	0.733168i	$0.738041\pi$
$368$	−16.1822	−	16.1822i	−0.843555	−	0.843555i
$369$	7.32651	+	7.32651i	0.381403	+	0.381403i
$370$		0			0
$371$	−3.56680	−	3.56680i	−0.185179	−	0.185179i
$372$	−9.25874			−0.480043
$373$			16.8892i			0.874490i	0.899342	+	0.437245i	$0.144046\pi$
$373$			16.8892i			0.874490i	−0.899342	+	0.437245i	$0.855954\pi$
$374$	−15.2331	−	4.02445i	−0.787687	−	0.208099i
$375$		0			0
$376$			33.5010i			1.72768i
$377$	−1.73694	+	1.73694i	−0.0894571	+	0.0894571i
$378$		−	14.8974i		−	0.766241i
$379$	−21.9472	−	21.9472i	−1.12735	−	1.12735i	−0.990606	−	0.136748i	$-0.956335\pi$
$379$	−21.9472	−	21.9472i	−1.12735	−	1.12735i	−0.136748	−	0.990606i	$-0.543665\pi$
$380$		0			0
$381$	−44.8840	+	44.8840i	−2.29948	+	2.29948i
$382$	5.34733			0.273593
$383$	31.3111			1.59992			0.799961	−	0.600052i	$-0.204853\pi$
$383$	31.3111			1.59992			0.799961	+	0.600052i	$0.204853\pi$
$384$	11.3141	−	11.3141i	0.577372	−	0.577372i
$385$		0			0
$386$	−9.18018	−	9.18018i	−0.467259	−	0.467259i
$387$			49.2359i			2.50280i
$388$	−0.696232	+	0.696232i	−0.0353458	+	0.0353458i
$389$		−	28.2233i		−	1.43098i	−0.698624	−	0.715489i	$-0.746204\pi$
$389$		−	28.2233i		−	1.43098i	0.698624	−	0.715489i	$-0.253796\pi$
$390$		0			0
$391$	8.96306	−	33.9265i	0.453281	−	1.71574i
$392$			18.6255i			0.940728i
$393$	−50.9627			−2.57073
$394$	−4.10396	−	4.10396i	−0.206754	−	0.206754i
$395$		0			0
$396$	8.11489	+	8.11489i	0.407789	+	0.407789i
$397$	−8.15876	−	8.15876i	−0.409476	−	0.409476i	0.472080	−	0.881556i	$-0.343503\pi$
$397$	−8.15876	−	8.15876i	−0.409476	−	0.409476i	−0.881556	+	0.472080i	$0.843503\pi$
$398$	−15.8467	−	15.8467i	−0.794322	−	0.794322i
$399$			16.0924i			0.805627i
$400$		0			0
$401$	−0.0456362	+	0.0456362i	−0.00227896	+	0.00227896i	−0.708245	−	0.705966i	$-0.750513\pi$
$401$	−0.0456362	+	0.0456362i	−0.00227896	+	0.00227896i	0.705966	+	0.708245i	$0.250513\pi$
$402$	6.46315	+	6.46315i	0.322352	+	0.322352i
$403$	−8.05130	+	8.05130i	−0.401064	+	0.401064i
$404$	−2.30557			−0.114706
$405$		0			0
$406$			1.41872i			0.0704097i
$407$			25.9868i			1.28812i
$408$	38.6905	+	10.2217i	1.91547	+	0.506048i
$409$	−5.13414			−0.253867			−0.126933	−	0.991911i	$-0.540513\pi$
$409$	−5.13414			−0.253867			−0.126933	+	0.991911i	$0.540513\pi$
$410$		0			0
$411$	−10.1410	−	10.1410i	−0.500220	−	0.500220i
$412$			8.04166i			0.396184i
$413$	−9.40680	+	9.40680i	−0.462879	+	0.462879i
$414$	51.4114	−	51.4114i	2.52673	−	2.52673i
$415$		0			0
$416$			5.79337i			0.284043i
$417$	3.03993			0.148866
$418$	14.2835	+	14.2835i	0.698630	+	0.698630i
$419$	12.9683	−	12.9683i	0.633544	−	0.633544i	−0.315411	−	0.948955i	$-0.602142\pi$
$419$	12.9683	−	12.9683i	0.633544	−	0.633544i	0.948955	+	0.315411i	$0.102142\pi$
$420$		0			0
$421$	16.0749			0.783441			0.391721	−	0.920084i	$-0.371880\pi$
$421$	16.0749			0.783441			0.391721	+	0.920084i	$0.371880\pi$
$422$	17.6441	−	17.6441i	0.858902	−	0.858902i
$423$	−76.7413			−3.73129
$424$	16.0820			0.781009
$425$		0			0
$426$	15.3731			0.744828
$427$	3.67930			0.178054
$428$	0.360031	−	0.360031i	0.0174027	−	0.0174027i
$429$	20.1422			0.972473
$430$		0			0
$431$	9.69615	−	9.69615i	0.467047	−	0.467047i	−0.433909	−	0.900956i	$-0.642866\pi$
$431$	9.69615	−	9.69615i	0.467047	−	0.467047i	0.900956	+	0.433909i	$0.142866\pi$
$432$	24.2153	+	24.2153i	1.16506	+	1.16506i
$433$	−24.9519			−1.19911			−0.599555	−	0.800334i	$-0.704656\pi$
$433$	−24.9519			−1.19911			−0.599555	+	0.800334i	$0.704656\pi$
$434$			6.57621i			0.315668i
$435$		0			0
$436$	−1.83069	+	1.83069i	−0.0876741	+	0.0876741i
$437$	−31.8116	+	31.8116i	−1.52175	+	1.52175i
$438$			30.0245i			1.43463i
$439$	6.47186	+	6.47186i	0.308885	+	0.308885i	0.844477	−	0.535592i	$-0.179911\pi$
$439$	6.47186	+	6.47186i	0.308885	+	0.308885i	−0.535592	+	0.844477i	$0.679911\pi$
$440$		0			0
$441$	−42.6657			−2.03170
$442$	8.77950	−	5.11002i	0.417598	−	0.243059i
$443$		−	28.9501i		−	1.37546i	−0.725967	−	0.687730i	$-0.758607\pi$
$443$		−	28.9501i		−	1.37546i	0.725967	−	0.687730i	$-0.241393\pi$
$444$		−	13.6240i		−	0.646569i
$445$		0			0
$446$	−19.8042			−0.937755
$447$	3.77069	−	3.77069i	0.178348	−	0.178348i
$448$	6.02272	+	6.02272i	0.284547	+	0.284547i
$449$	−16.8659	+	16.8659i	−0.795953	+	0.795953i	−0.982455	−	0.186502i	$-0.940285\pi$
$449$	−16.8659	+	16.8659i	−0.795953	+	0.795953i	0.186502	+	0.982455i	$0.440285\pi$
$450$		0			0
$451$			4.63466i			0.218238i
$452$	1.60100	+	1.60100i	0.0753045	+	0.0753045i
$453$	16.3612	+	16.3612i	0.768717	+	0.768717i
$454$	12.7283	+	12.7283i	0.597370	+	0.597370i
$455$		0			0
$456$	−36.2786	−	36.2786i	−1.69890	−	1.69890i
$457$	6.99557			0.327239			0.163620	−	0.986524i	$-0.447683\pi$
$457$	6.99557			0.327239			0.163620	+	0.986524i	$0.447683\pi$
$458$		−	16.3014i		−	0.761713i
$459$	−13.4125	+	50.7683i	−0.626042	+	2.36966i
$460$		0			0
$461$		−	4.25687i		−	0.198262i	−0.995074	−	0.0991311i	$-0.968394\pi$
$461$		−	4.25687i		−	0.198262i	0.995074	−	0.0991311i	$-0.0316063\pi$
$462$	8.22595	−	8.22595i	0.382706	−	0.382706i
$463$		−	3.53171i		−	0.164133i	−0.996627	−	0.0820663i	$-0.973848\pi$
$463$		−	3.53171i		−	0.164133i	0.996627	−	0.0820663i	$-0.0261519\pi$
$464$	−2.30608	−	2.30608i	−0.107057	−	0.107057i
$465$		0			0
$466$	21.2620	−	21.2620i	0.984944	−	0.984944i
$467$	16.7312			0.774226			0.387113	−	0.922032i	$-0.373472\pi$
$467$	16.7312			0.774226			0.387113	+	0.922032i	$0.373472\pi$
$468$	−7.39913			−0.342025
$469$	−1.61377	+	1.61377i	−0.0745169	+	0.0745169i
$470$		0			0
$471$	16.3577	+	16.3577i	0.753725	+	0.753725i
$472$		−	42.4133i		−	1.95223i
$473$	−15.5730	+	15.5730i	−0.716049	+	0.716049i
$474$		−	25.8276i		−	1.18630i
$475$		0			0
$476$	−0.526814	+	1.99407i	−0.0241465	+	0.0913981i
$477$			36.8392i			1.68675i
$478$	−1.56137			−0.0714152
$479$	18.2107	+	18.2107i	0.832067	+	0.832067i	0.987799	−	0.155733i	$-0.0497738\pi$
$479$	18.2107	+	18.2107i	0.832067	+	0.832067i	−0.155733	+	0.987799i	$0.549774\pi$
$480$		0			0
$481$	−11.8473	−	11.8473i	−0.540191	−	0.540191i
$482$	−10.9482	−	10.9482i	−0.498677	−	0.498677i
$483$	18.3204	+	18.3204i	0.833609	+	0.833609i
$484$		−	0.588869i		−	0.0267668i
$485$		0			0
$486$	−19.5598	+	19.5598i	−0.887252	+	0.887252i
$487$	22.0660	+	22.0660i	0.999907	+	0.999907i	1.00000		9.30234e-5i	$-2.96103e-5\pi$
$487$	22.0660	+	22.0660i	0.999907	+	0.999907i	−9.30234e−5		1.00000i	$0.500030\pi$
$488$	−8.29459	+	8.29459i	−0.375478	+	0.375478i
$489$	−68.9512			−3.11808
$490$		0			0
$491$			30.6676i			1.38401i	0.721893	+	0.692005i	$0.243272\pi$
$491$			30.6676i			1.38401i	−0.721893	+	0.692005i	$0.756728\pi$
$492$		−	2.42981i		−	0.109544i
$493$	1.27730	−	4.83478i	0.0575268	−	0.217748i
$494$	−13.0237			−0.585963
$495$		0			0
$496$	−10.6894	−	10.6894i	−0.479970	−	0.479970i
$497$			3.83847i			0.172179i
$498$	−0.466595	+	0.466595i	−0.0209086	+	0.0209086i
$499$	17.9340	−	17.9340i	0.802837	−	0.802837i	−0.180701	−	0.983538i	$-0.557837\pi$
$499$	17.9340	−	17.9340i	0.802837	−	0.802837i	0.983538	+	0.180701i	$0.0578366\pi$
$500$		0			0
$501$			27.5614i			1.23135i
$502$	18.3849			0.820556
$503$	−19.0780	−	19.0780i	−0.850647	−	0.850647i	0.139566	−	0.990213i	$-0.455429\pi$
$503$	−19.0780	−	19.0780i	−0.850647	−	0.850647i	−0.990213	+	0.139566i	$0.955429\pi$
$504$	−14.6394	+	14.6394i	−0.652089	+	0.652089i
$505$		0			0
$506$	32.5223			1.44579
$507$	19.9192	−	19.9192i	0.884642	−	0.884642i
$508$	10.4301			0.462760
$509$	32.5718			1.44372			0.721859	−	0.692040i	$-0.243288\pi$
$509$	32.5718			1.44372			0.721859	+	0.692040i	$0.243288\pi$
$510$		0			0
$511$	−7.49675			−0.331637
$512$	−24.1791			−1.06858
$513$	47.6035	−	47.6035i	2.10175	−	2.10175i
$514$	0.301511			0.0132991
$515$		0			0
$516$	8.16445	−	8.16445i	0.359420	−	0.359420i
$517$	−24.2728	−	24.2728i	−1.06752	−	1.06752i
$518$	−9.67676			−0.425173
$519$			22.7780i			0.999845i
$520$		0			0
$521$	−22.4613	+	22.4613i	−0.984048	+	0.984048i	−0.999875	−	0.0158266i	$-0.994962\pi$
$521$	−22.4613	+	22.4613i	−0.984048	+	0.984048i	0.0158266	+	0.999875i	$0.494962\pi$
$522$	7.32651	−	7.32651i	0.320672	−	0.320672i
$523$		−	4.04111i		−	0.176705i	−0.996089	−	0.0883527i	$-0.971840\pi$
$523$		−	4.04111i		−	0.176705i	0.996089	−	0.0883527i	$-0.0281602\pi$
$524$	5.92132	+	5.92132i	0.258674	+	0.258674i
$525$		0			0
$526$	15.3506			0.669318
$527$	5.92072	−	22.4108i	0.257910	−	0.976229i
$528$			26.7421i			1.16380i
$529$			49.4320i			2.14922i
$530$		0			0
$531$	97.1569			4.21625
$532$	1.86976	−	1.86976i	0.0810645	−	0.0810645i
$533$	−2.11294	−	2.11294i	−0.0915214	−	0.0915214i
$534$	−3.59679	+	3.59679i	−0.155648	+	0.155648i
$535$		0			0
$536$		−	7.27614i		−	0.314281i
$537$	−22.2457	−	22.2457i	−0.959975	−	0.959975i
$538$	12.3110	+	12.3110i	0.530766	+	0.530766i
$539$	−13.4949	−	13.4949i	−0.581267	−	0.581267i
$540$		0			0
$541$	25.3445	+	25.3445i	1.08965	+	1.08965i	0.995564	+	0.0940826i	$0.0299918\pi$
$541$	25.3445	+	25.3445i	1.08965	+	1.08965i	0.0940826	+	0.995564i	$0.470008\pi$
$542$	−23.0957			−0.992047
$543$		−	4.41230i		−	0.189350i
$544$	−5.93278	−	10.1931i	−0.254366	−	0.437024i
$545$		0			0
$546$			7.50039i			0.320987i
$547$	11.4397	−	11.4397i	0.489125	−	0.489125i	−0.418905	−	0.908030i	$-0.637586\pi$
$547$	11.4397	−	11.4397i	0.489125	−	0.489125i	0.908030	+	0.418905i	$0.137586\pi$
$548$			2.35656i			0.100667i
$549$	−19.0006	−	19.0006i	−0.810925	−	0.810925i
$550$		0			0
$551$	−4.53339	+	4.53339i	−0.193129	+	0.193129i
$552$	−82.6030			−3.51582
$553$	6.44885			0.274233
$554$	−12.6999	+	12.6999i	−0.539565	+	0.539565i
$555$		0			0
$556$	−0.353207	−	0.353207i	−0.0149793	−	0.0149793i
$557$		−	15.9925i		−	0.677622i	−0.940854	−	0.338811i	$-0.889975\pi$
$557$		−	15.9925i		−	0.677622i	0.940854	−	0.338811i	$-0.110025\pi$
$558$	33.9608	−	33.9608i	1.43767	−	1.43767i
$559$		−	14.1994i		−	0.600572i
$560$		0			0
$561$	−35.4389	+	20.6268i	−1.49623	+	0.870866i
$562$			28.8579i			1.21730i
$563$	−11.0267			−0.464721			−0.232361	−	0.972630i	$-0.574645\pi$
$563$	−11.0267			−0.464721			−0.232361	+	0.972630i	$0.574645\pi$
$564$	12.7255	+	12.7255i	0.535840	+	0.535840i
$565$		0			0
$566$	22.7180	+	22.7180i	0.954908	+	0.954908i
$567$	−13.0897	−	13.0897i	−0.549715	−	0.549715i
$568$	−8.65342	−	8.65342i	−0.363090	−	0.363090i
$569$		−	45.7921i		−	1.91970i	−0.280506	−	0.959852i	$-0.590502\pi$
$569$		−	45.7921i		−	1.91970i	0.280506	−	0.959852i	$-0.409498\pi$
$570$		0			0
$571$	−19.8850	+	19.8850i	−0.832160	+	0.832160i	−0.987812	−	0.155652i	$-0.950252\pi$
$571$	−19.8850	+	19.8850i	−0.832160	+	0.832160i	0.155652	+	0.987812i	$0.450252\pi$
$572$	−2.34030	−	2.34030i	−0.0978530	−	0.0978530i
$573$	9.84045	−	9.84045i	0.411091	−	0.411091i
$574$	−1.72582			−0.0720344
$575$		0			0
$576$		−	62.2048i		−	2.59187i
$577$		−	19.7460i		−	0.822036i	−0.911627	−	0.411018i	$-0.865173\pi$
$577$		−	19.7460i		−	0.822036i	0.911627	−	0.411018i	$-0.134827\pi$
$578$	−10.2140	+	17.9815i	−0.424846	+	0.747933i
$579$	−33.7877			−1.40417
$580$		0			0
$581$	−0.116503	−	0.116503i	−0.00483337	−	0.00483337i
$582$		−	7.28935i		−	0.302153i
$583$	−11.6520	+	11.6520i	−0.482578	+	0.482578i
$584$	16.9006	−	16.9006i	0.699353	−	0.699353i
$585$		0			0
$586$			13.4161i			0.554215i
$587$	4.39220			0.181285			0.0906427	−	0.995883i	$-0.471108\pi$
$587$	4.39220			0.181285			0.0906427	+	0.995883i	$0.471108\pi$
$588$	7.07496	+	7.07496i	0.291766	+	0.291766i
$589$	−21.0137	+	21.0137i	−0.865856	+	0.865856i
$590$		0			0
$591$	−15.1047			−0.621322
$592$	15.7293	−	15.7293i	0.646470	−	0.646470i
$593$	10.5967			0.435153			0.217576	−	0.976043i	$-0.430185\pi$
$593$	10.5967			0.435153			0.217576	+	0.976043i	$0.430185\pi$
$594$	−48.6670			−1.99683
$595$		0			0
$596$	−0.876228			−0.0358917
$597$	−58.3239			−2.38704
$598$	−14.8268	+	14.8268i	−0.606315	+	0.606315i
$599$	18.0402			0.737103			0.368551	−	0.929607i	$-0.379854\pi$
$599$	18.0402			0.737103			0.368551	+	0.929607i	$0.379854\pi$
$600$		0			0
$601$	−28.9823	+	28.9823i	−1.18221	+	1.18221i	−0.203041	+	0.979170i	$0.565083\pi$
$601$	−28.9823	+	28.9823i	−1.18221	+	1.18221i	−0.979170	+	0.203041i	$0.934917\pi$
$602$	−5.79897	−	5.79897i	−0.236348	−	0.236348i
$603$	16.6676			0.678757
$604$		−	3.80199i		−	0.154701i
$605$		0			0
$606$	12.0693	−	12.0693i	0.490283	−	0.490283i
$607$	−31.3128	+	31.3128i	−1.27095	+	1.27095i	−0.325356	+	0.945591i	$0.605484\pi$
$607$	−31.3128	+	31.3128i	−1.27095	+	1.27095i	−0.945591	+	0.325356i	$0.894516\pi$
$608$			15.1206i			0.613221i
$609$	2.61080	+	2.61080i	0.105795	+	0.105795i
$610$		0			0
$611$	22.1319			0.895361
$612$	13.0183	−	7.57718i	0.526234	−	0.306289i
$613$			36.5738i			1.47720i	0.674142	+	0.738602i	$0.264514\pi$
$613$			36.5738i			1.47720i	−0.674142	+	0.738602i	$0.735486\pi$
$614$			6.22830i			0.251354i
$615$		0			0
$616$	−9.26069			−0.373124
$617$	22.6074	−	22.6074i	0.910140	−	0.910140i	−0.0861430	−	0.996283i	$-0.527454\pi$
$617$	22.6074	−	22.6074i	0.910140	−	0.910140i	0.996283	+	0.0861430i	$0.0274542\pi$
$618$	−42.0969	−	42.0969i	−1.69339	−	1.69339i
$619$	9.87497	−	9.87497i	0.396909	−	0.396909i	−0.480233	−	0.877141i	$-0.659448\pi$
$619$	9.87497	−	9.87497i	0.396909	−	0.396909i	0.877141	+	0.480233i	$0.159448\pi$
$620$		0			0
$621$		−	108.389i		−	4.34949i
$622$	−1.56130	−	1.56130i	−0.0626024	−	0.0626024i
$623$	−0.898075	−	0.898075i	−0.0359806	−	0.0359806i
$624$	−12.1917	−	12.1917i	−0.488058	−	0.488058i
$625$		0			0
$626$	−13.9184	−	13.9184i	−0.556292	−	0.556292i
$627$	52.5707			2.09947
$628$		−	3.80119i		−	0.151684i
$629$	32.9770	+	8.71221i	1.31488	+	0.347379i
$630$		0			0
$631$		−	37.1093i		−	1.47730i	−0.674090	−	0.738649i	$-0.735464\pi$
$631$		−	37.1093i		−	1.47730i	0.674090	−	0.738649i	$-0.264536\pi$
$632$	−14.5382	+	14.5382i	−0.578300	+	0.578300i
$633$		−	64.9394i		−	2.58111i
$634$	9.81790	+	9.81790i	0.389919	+	0.389919i
$635$		0			0
$636$	6.10880	−	6.10880i	0.242230	−	0.242230i
$637$	12.3046			0.487527
$638$	4.63466			0.183488
$639$	19.8226	−	19.8226i	0.784168	−	0.784168i
$640$		0			0
$641$	−1.90323	−	1.90323i	−0.0751730	−	0.0751730i	0.668521	−	0.743694i	$-0.266928\pi$
$641$	−1.90323	−	1.90323i	−0.0751730	−	0.0751730i	−0.743694	+	0.668521i	$0.766928\pi$
$642$			3.76942i			0.148767i
$643$	19.7734	−	19.7734i	0.779788	−	0.779788i	−0.200007	−	0.979795i	$-0.564096\pi$
$643$	19.7734	−	19.7734i	0.779788	−	0.779788i	0.979795	+	0.200007i	$0.0640964\pi$
$644$		−	4.25728i		−	0.167760i
$645$		0			0
$646$	22.9143	−	13.3371i	0.901552	−	0.524739i
$647$			4.31955i			0.169819i	0.996389	+	0.0849096i	$0.0270601\pi$
$647$			4.31955i			0.169819i	−0.996389	+	0.0849096i	$0.972940\pi$
$648$	59.0186			2.31847
$649$	30.7302	+	30.7302i	1.20626	+	1.20626i
$650$		0			0
$651$	12.1019	+	12.1019i	0.474311	+	0.474311i
$652$	8.01139	+	8.01139i	0.313750	+	0.313750i
$653$	−5.90260	−	5.90260i	−0.230987	−	0.230987i	0.582118	−	0.813104i	$-0.302224\pi$
$653$	−5.90260	−	5.90260i	−0.230987	−	0.230987i	−0.813104	+	0.582118i	$0.802224\pi$
$654$		−	19.1668i		−	0.749481i
$655$		0			0
$656$	2.80527	−	2.80527i	0.109528	−	0.109528i
$657$	38.7146	+	38.7146i	1.51040	+	1.51040i
$658$	9.03854	−	9.03854i	0.352359	−	0.352359i
$659$	−4.31764			−0.168192			−0.0840958	−	0.996458i	$-0.526800\pi$
$659$	−4.31764			−0.168192			−0.0840958	+	0.996458i	$0.526800\pi$
$660$		0			0
$661$		−	32.6701i		−	1.27072i	−0.772216	−	0.635360i	$-0.780852\pi$
$661$		−	32.6701i		−	1.27072i	0.772216	−	0.635360i	$-0.219148\pi$
$662$			10.3006i			0.400345i
$663$	6.75278	−	25.5603i	0.262256	−	0.992678i
$664$	0.525288			0.0203851
$665$		0			0
$666$	49.9726	+	49.9726i	1.93640	+	1.93640i
$667$			10.3221i			0.399673i
$668$	3.20234	−	3.20234i	0.123902	−	0.123902i
$669$	−36.4447	+	36.4447i	−1.40903	+	1.40903i
$670$		0			0
$671$		−	12.0195i		−	0.464009i
$672$	8.70802			0.335919
$673$	−0.921112	−	0.921112i	−0.0355063	−	0.0355063i	0.689131	−	0.724637i	$-0.257993\pi$
$673$	−0.921112	−	0.921112i	−0.0355063	−	0.0355063i	−0.724637	+	0.689131i	$0.757993\pi$
$674$	2.34771	−	2.34771i	0.0904306	−	0.0904306i
$675$		0			0
$676$	−4.62879			−0.178030
$677$	17.5174	−	17.5174i	0.673250	−	0.673250i	−0.285214	−	0.958464i	$-0.592065\pi$
$677$	17.5174	−	17.5174i	0.673250	−	0.673250i	0.958464	+	0.285214i	$0.0920647\pi$
$678$	−16.7620			−0.643740
$679$	1.82006			0.0698476
$680$		0			0
$681$	46.8467			1.79517
$682$	21.4832			0.822634
$683$	−14.6591	+	14.6591i	−0.560913	+	0.560913i	−0.929567	−	0.368654i	$-0.879819\pi$
$683$	−14.6591	+	14.6591i	−0.560913	+	0.560913i	0.368654	+	0.929567i	$0.379819\pi$
$684$	−19.3116			−0.738397
$685$		0			0
$686$	10.8151	−	10.8151i	0.412922	−	0.412922i
$687$	−29.9987	−	29.9987i	−1.14452	−	1.14452i
$688$	18.8521			0.718730
$689$		−	10.6243i		−	0.404753i
$690$		0			0
$691$	1.95620	−	1.95620i	0.0744174	−	0.0744174i	−0.668918	−	0.743336i	$-0.733242\pi$
$691$	1.95620	−	1.95620i	0.0744174	−	0.0744174i	0.743336	+	0.668918i	$0.233242\pi$
$692$	2.64656	−	2.64656i	0.100607	−	0.100607i
$693$		−	21.2136i		−	0.805839i
$694$	11.3644	+	11.3644i	0.431387	+	0.431387i
$695$		0			0
$696$	−11.7715			−0.446199
$697$	5.88136	+	1.55380i	0.222772	+	0.0588543i
$698$			32.9602i			1.24756i
$699$		−	78.2551i		−	2.95988i
$700$		0			0
$701$	34.0966			1.28781			0.643906	−	0.765105i	$-0.277313\pi$
$701$	34.0966			1.28781			0.643906	+	0.765105i	$0.277313\pi$
$702$	22.1872	−	22.1872i	0.837401	−	0.837401i
$703$	−30.9213	−	30.9213i	−1.16622	−	1.16622i
$704$	19.6750	−	19.6750i	0.741531	−	0.741531i
$705$		0			0
$706$			33.3679i			1.25582i
$707$	3.01356	+	3.01356i	0.113337	+	0.113337i
$708$	−16.1109	−	16.1109i	−0.605483	−	0.605483i
$709$	17.1425	+	17.1425i	0.643801	+	0.643801i	0.951488	−	0.307687i	$-0.0995549\pi$
$709$	17.1425	+	17.1425i	0.643801	+	0.643801i	−0.307687	+	0.951488i	$0.599555\pi$
$710$		0			0
$711$	−33.3030	−	33.3030i	−1.24896	−	1.24896i
$712$	4.04923			0.151751
$713$			47.8463i			1.79186i
$714$	−7.68088	−	13.1965i	−0.287450	−	0.493866i
$715$		0			0
$716$			5.16943i			0.193191i
$717$	−2.87331	+	2.87331i	−0.107306	+	0.107306i
$718$			4.19807i			0.156670i
$719$	−20.5856	−	20.5856i	−0.767715	−	0.767715i	0.209989	−	0.977704i	$-0.432657\pi$
$719$	−20.5856	−	20.5856i	−0.767715	−	0.767715i	−0.977704	+	0.209989i	$0.932657\pi$
$720$		0			0
$721$	10.5111	−	10.5111i	0.391453	−	0.391453i
$722$	−10.8786			−0.404861
$723$	−40.2950			−1.49859
$724$	−0.512661	+	0.512661i	−0.0190529	+	0.0190529i
$725$		0			0
$726$	3.08265	+	3.08265i	0.114408	+	0.114408i
$727$		−	47.0608i		−	1.74539i	−0.488265	−	0.872695i	$-0.662370\pi$
$727$		−	47.0608i		−	1.74539i	0.488265	−	0.872695i	$-0.337630\pi$
$728$	4.22193	−	4.22193i	0.156475	−	0.156475i
$729$			14.2373i			0.527306i
$730$		0			0
$731$	14.5411	+	24.9830i	0.537823	+	0.924030i
$732$			6.30147i			0.232909i
$733$	20.8419			0.769812			0.384906	−	0.922956i	$-0.374234\pi$
$733$	20.8419			0.769812			0.384906	+	0.922956i	$0.374234\pi$
$734$	1.23792	+	1.23792i	0.0456926	+	0.0456926i
$735$		0			0
$736$	17.2141	+	17.2141i	0.634520	+	0.634520i
$737$	5.27186	+	5.27186i	0.194192	+	0.194192i
$738$	8.91246	+	8.91246i	0.328072	+	0.328072i
$739$			5.26172i			0.193556i	0.995306	+	0.0967778i	$0.0308536\pi$
$739$			5.26172i			0.193556i	−0.995306	+	0.0967778i	$0.969146\pi$
$740$		0			0
$741$	−23.9669	+	23.9669i	−0.880445	+	0.880445i
$742$	−4.33890	−	4.33890i	−0.159286	−	0.159286i
$743$	−5.95166	+	5.95166i	−0.218345	+	0.218345i	−0.807801	−	0.589456i	$-0.799342\pi$
$743$	−5.95166	+	5.95166i	−0.218345	+	0.218345i	0.589456	+	0.807801i	$0.299342\pi$
$744$	−54.5650			−2.00045
$745$		0			0
$746$			20.5452i			0.752213i
$747$			1.20329i			0.0440260i
$748$	6.51423	+	1.72100i	0.238184	+	0.0629259i
$749$	−0.941178			−0.0343899
$750$		0			0
$751$	−14.1448	−	14.1448i	−0.516152	−	0.516152i	0.400253	−	0.916405i	$-0.368922\pi$
$751$	−14.1448	−	14.1448i	−0.516152	−	0.516152i	−0.916405	+	0.400253i	$0.868922\pi$
$752$			29.3838i			1.07152i
$753$	33.8328	−	33.8328i	1.23294	−	1.23294i
$754$	−2.11294	+	2.11294i	−0.0769486	+	0.0769486i
$755$		0			0
$756$			6.37068i			0.231699i
$757$	30.7146			1.11634			0.558170	−	0.829727i	$-0.311504\pi$
$757$	30.7146			1.11634			0.558170	+	0.829727i	$0.311504\pi$
$758$	−26.6981	−	26.6981i	−0.969719	−	0.969719i
$759$	59.8493	−	59.8493i	2.17239	−	2.17239i
$760$		0			0
$761$	24.4465			0.886186			0.443093	−	0.896476i	$-0.353881\pi$
$761$	24.4465			0.886186			0.443093	+	0.896476i	$0.353881\pi$
$762$	−54.6000	+	54.6000i	−1.97795	+	1.97795i
$763$	4.78572			0.173255
$764$	−2.28671			−0.0827302
$765$		0			0
$766$	38.0890			1.37621
$767$	−28.0197			−1.01173
$768$	−25.8941	+	25.8941i	−0.934374	+	0.934374i
$769$	24.2567			0.874719			0.437359	−	0.899287i	$-0.355914\pi$
$769$	24.2567			0.874719			0.437359	+	0.899287i	$0.355914\pi$
$770$		0			0
$771$	0.554857	−	0.554857i	0.0199827	−	0.0199827i
$772$	3.92577	+	3.92577i	0.141292	+	0.141292i
$773$	−18.9396			−0.681209			−0.340604	−	0.940207i	$-0.610632\pi$
$773$	−18.9396			−0.681209			−0.340604	+	0.940207i	$0.610632\pi$
$774$			59.8939i			2.15284i
$775$		0			0
$776$	−4.10314	+	4.10314i	−0.147294	+	0.147294i
$777$	−17.8077	+	17.8077i	−0.638848	+	0.638848i
$778$		−	34.3328i		−	1.23089i
$779$	−5.51472	−	5.51472i	−0.197585	−	0.197585i
$780$		0			0
$781$	12.5395			0.448699
$782$	10.9033	−	41.2705i	0.389900	−	1.47583i
$783$		−	15.4462i		−	0.552002i
$784$			16.3364i			0.583444i
$785$		0			0
$786$	−61.9945			−2.21127
$787$	−30.8634	+	30.8634i	−1.10016	+	1.10016i	−0.105769	+	0.994391i	$0.533730\pi$
$787$	−30.8634	+	30.8634i	−1.10016	+	1.10016i	−0.994391	+	0.105769i	$0.966270\pi$
$788$	1.75500	+	1.75500i	0.0625192	+	0.0625192i
$789$	28.2490	−	28.2490i	1.00569	−	1.00569i
$790$		0			0
$791$		−	4.18526i		−	0.148811i
$792$	47.8239	+	47.8239i	1.69935	+	1.69935i
$793$	5.47969	+	5.47969i	0.194589	+	0.194589i
$794$	−9.92487	−	9.92487i	−0.352220	−	0.352220i
$795$		0			0
$796$	6.77661	+	6.77661i	0.240190	+	0.240190i
$797$	21.7263			0.769585			0.384792	−	0.923003i	$-0.374273\pi$
$797$	21.7263			0.769585			0.384792	+	0.923003i	$0.374273\pi$
$798$			19.5759i			0.692979i
$799$	−38.9397	+	22.6644i	−1.37759	+	0.801811i
$800$		0			0
$801$			9.27564i			0.327739i
$802$	−0.0555149	+	0.0555149i	−0.00196030	+	0.00196030i
$803$			24.4904i			0.864247i
$804$	−2.76387	−	2.76387i	−0.0974743	−	0.0974743i
$805$		0			0
$806$	−9.79415	+	9.79415i	−0.344984	+	0.344984i
$807$	45.3109			1.59502
$808$	−13.5875			−0.478007
$809$	−31.5971	+	31.5971i	−1.11090	+	1.11090i	−0.117867	+	0.993029i	$0.537606\pi$
$809$	−31.5971	+	31.5971i	−1.11090	+	1.11090i	−0.993029	+	0.117867i	$0.962394\pi$
$810$		0			0
$811$	−27.5170	−	27.5170i	−0.966251	−	0.966251i	0.0331973	−	0.999449i	$-0.489431\pi$
$811$	−27.5170	−	27.5170i	−0.966251	−	0.966251i	−0.999449	+	0.0331973i	$0.989431\pi$
$812$		−	0.606694i		−	0.0212908i
$813$	−42.5021	+	42.5021i	−1.49061	+	1.49061i
$814$			31.6121i			1.10800i
$815$		0			0
$816$	33.9355	+	8.96544i	1.18798	+	0.313853i
$817$		−	37.0602i		−	1.29657i
$818$	−6.24552			−0.218369
$819$	9.67126	+	9.67126i	0.337941	+	0.337941i
$820$		0			0
$821$	−12.8847	−	12.8847i	−0.449679	−	0.449679i	0.445569	−	0.895248i	$-0.353002\pi$
$821$	−12.8847	−	12.8847i	−0.449679	−	0.449679i	−0.895248	+	0.445569i	$0.853002\pi$
$822$	−12.3362	−	12.3362i	−0.430275	−	0.430275i
$823$	14.5848	+	14.5848i	0.508395	+	0.508395i	0.914034	−	0.405639i	$-0.132951\pi$
$823$	14.5848	+	14.5848i	0.508395	+	0.508395i	−0.405639	+	0.914034i	$0.632951\pi$
$824$			47.3923i			1.65099i
$825$		0			0
$826$	−11.4431	+	11.4431i	−0.398156	+	0.398156i
$827$	−36.7846	−	36.7846i	−1.27912	−	1.27912i	−0.941158	−	0.337966i	$-0.890261\pi$
$827$	−36.7846	−	36.7846i	−1.27912	−	1.27912i	−0.337966	−	0.941158i	$-0.609739\pi$
$828$	−21.9854	+	21.9854i	−0.764044	+	0.764044i
$829$	10.2614			0.356395			0.178197	−	0.983995i	$-0.442973\pi$
$829$	10.2614			0.356395			0.178197	+	0.983995i	$0.442973\pi$
$830$		0			0
$831$			46.7419i			1.62146i
$832$			17.9396i			0.621945i
$833$	−21.6492	+	12.6007i	−0.750100	+	0.436588i
$834$	3.69797			0.128050
$835$		0			0
$836$	−6.10815	−	6.10815i	−0.211255	−	0.211255i
$837$		−	71.5982i		−	2.47480i
$838$	15.7755	−	15.7755i	0.544957	−	0.544957i
$839$	−23.4767	+	23.4767i	−0.810504	+	0.810504i	−0.984709	−	0.174205i	$-0.944264\pi$
$839$	−23.4767	+	23.4767i	−0.810504	+	0.810504i	0.174205	+	0.984709i	$0.444264\pi$
$840$		0			0
$841$		−	27.5290i		−	0.949277i
$842$	19.5546			0.673895
$843$	53.1059	+	53.1059i	1.82907	+	1.82907i
$844$	−7.54526	+	7.54526i	−0.259719	+	0.259719i
$845$		0			0
$846$	−93.3534			−3.20955
$847$	−0.769699	+	0.769699i	−0.0264472	+	0.0264472i
$848$	14.1055			0.484385
$849$	83.6138			2.86962
$850$		0			0
$851$	−70.4049			−2.41345
$852$	−6.57408			−0.225224
$853$	−12.2943	+	12.2943i	−0.420950	+	0.420950i	−0.885531	−	0.464581i	$-0.846205\pi$
$853$	−12.2943	+	12.2943i	−0.420950	+	0.420950i	0.464581	+	0.885531i	$0.346205\pi$
$854$	4.47575			0.153157
$855$		0			0
$856$	2.12179	−	2.12179i	0.0725211	−	0.0725211i
$857$	−5.16808	−	5.16808i	−0.176538	−	0.176538i	0.613307	−	0.789845i	$-0.289839\pi$
$857$	−5.16808	−	5.16808i	−0.176538	−	0.176538i	−0.789845	+	0.613307i	$0.789839\pi$
$858$	24.5023			0.836495
$859$			3.45616i			0.117923i	0.998260	+	0.0589613i	$0.0187789\pi$
$859$			3.45616i			0.117923i	−0.998260	+	0.0589613i	$0.981221\pi$
$860$		0			0
$861$	−3.17595	+	3.17595i	−0.108236	+	0.108236i
$862$	11.7951	−	11.7951i	0.401741	−	0.401741i
$863$		−	4.15372i		−	0.141394i	−0.997498	−	0.0706971i	$-0.977478\pi$
$863$		−	4.15372i		−	0.141394i	0.997498	−	0.0706971i	$-0.0225224\pi$
$864$	−25.7595	−	25.7595i	−0.876356	−	0.876356i
$865$		0			0
$866$	−30.3531			−1.03144
$867$	14.2942	+	51.8869i	0.485458	+	1.76217i
$868$		−	2.81222i		−	0.0954531i
$869$		−	21.0671i		−	0.714653i
$870$		0			0
$871$	−4.80687			−0.162874
$872$	−10.7889	+	10.7889i	−0.365358	+	0.365358i
$873$	−9.39913	−	9.39913i	−0.318112	−	0.318112i
$874$	−38.6978	+	38.6978i	−1.30897	+	1.30897i
$875$		0			0
$876$		−	12.8395i		−	0.433808i
$877$	6.06412	+	6.06412i	0.204771	+	0.204771i	0.802040	−	0.597270i	$-0.203748\pi$
$877$	6.06412	+	6.06412i	0.204771	+	0.204771i	−0.597270	+	0.802040i	$0.703748\pi$
$878$	7.87282	+	7.87282i	0.265695	+	0.265695i
$879$	24.6891	+	24.6891i	0.832742	+	0.832742i
$880$		0			0
$881$	8.93223	+	8.93223i	0.300935	+	0.300935i	0.841379	−	0.540445i	$-0.181744\pi$
$881$	8.93223	+	8.93223i	0.300935	+	0.300935i	−0.540445	+	0.841379i	$0.681744\pi$
$882$	−51.9014			−1.74761
$883$			35.6843i			1.20087i	0.799673	+	0.600436i	$0.205006\pi$
$883$			35.6843i			1.20087i	−0.799673	+	0.600436i	$0.794994\pi$
$884$	−3.75443	+	2.18523i	−0.126275	+	0.0734972i
$885$		0			0
$886$		−	35.2169i		−	1.18313i
$887$	−15.7269	+	15.7269i	−0.528058	+	0.528058i	−0.919993	−	0.391935i	$-0.871806\pi$
$887$	−15.7269	+	15.7269i	−0.528058	+	0.528058i	0.391935	+	0.919993i	$0.371806\pi$
$888$		−	80.2912i		−	2.69440i
$889$	−13.6330	−	13.6330i	−0.457235	−	0.457235i
$890$		0			0
$891$	−42.7614	+	42.7614i	−1.43256	+	1.43256i
$892$	8.46897			0.283562
$893$	57.7638			1.93299
$894$	4.58693	−	4.58693i	0.153410	−	0.153410i
$895$		0			0
$896$	3.43653	+	3.43653i	0.114806	+	0.114806i
$897$			54.5704i			1.82205i
$898$	−20.5169	+	20.5169i	−0.684657	+	0.684657i
$899$			6.81846i			0.227408i
$900$		0			0
$901$	10.8799	+	18.6928i	0.362463	+	0.622746i
$902$			5.63792i			0.187722i
$903$	−21.3432			−0.710257
$904$	9.43522	+	9.43522i	0.313811	+	0.313811i
$905$		0			0
$906$	19.9029	+	19.9029i	0.661229	+	0.661229i
$907$	6.27061	+	6.27061i	0.208212	+	0.208212i	0.803507	−	0.595295i	$-0.202965\pi$
$907$	6.27061	+	6.27061i	0.208212	+	0.208212i	−0.595295	+	0.803507i	$0.702965\pi$
$908$	−5.44309	−	5.44309i	−0.180635	−	0.180635i
$909$		−	31.1252i		−	1.03236i
$910$		0			0
$911$	−3.48594	+	3.48594i	−0.115494	+	0.115494i	−0.762492	−	0.646998i	$-0.776024\pi$
$911$	−3.48594	+	3.48594i	−0.115494	+	0.115494i	0.646998	+	0.762492i	$0.276024\pi$
$912$	−31.8200	−	31.8200i	−1.05367	−	1.05367i
$913$	−0.380593	+	0.380593i	−0.0125958	+	0.0125958i
$914$	8.50989			0.281482
$915$		0			0
$916$			6.97105i			0.230330i
$917$		−	15.4793i		−	0.511171i
$918$	−16.3159	+	61.7580i	−0.538504	+	2.03832i
$919$	39.8706			1.31521			0.657606	−	0.753362i	$-0.271569\pi$
$919$	39.8706			1.31521			0.657606	+	0.753362i	$0.271569\pi$
$920$		0			0
$921$	11.4617	+	11.4617i	0.377674	+	0.377674i
$922$		−	5.17835i		−	0.170540i
$923$	−5.71675	+	5.71675i	−0.188169	+	0.188169i
$924$	−3.51771	+	3.51771i	−0.115724	+	0.115724i
$925$		0			0
$926$		−	4.29622i		−	0.141182i
$927$	−108.562			−3.56565
$928$	2.45314	+	2.45314i	0.0805281	+	0.0805281i
$929$	−1.16727	+	1.16727i	−0.0382967	+	0.0382967i	−0.725996	−	0.687699i	$-0.758621\pi$
$929$	−1.16727	+	1.16727i	−0.0382967	+	0.0382967i	0.687699	+	0.725996i	$0.258621\pi$
$930$		0			0
$931$	32.1148			1.05252
$932$	−9.09240	+	9.09240i	−0.297832	+	0.297832i
$933$	−5.74638			−0.188128
$934$	20.3529			0.665969
$935$		0			0
$936$	−43.6056			−1.42529
$937$	35.6142			1.16346			0.581732	−	0.813380i	$-0.302375\pi$
$937$	35.6142			1.16346			0.581732	+	0.813380i	$0.302375\pi$
$938$	−1.96310	+	1.96310i	−0.0640974	+	0.0640974i
$939$	−51.2269			−1.67173
$940$		0			0
$941$	−20.7529	+	20.7529i	−0.676526	+	0.676526i	−0.959212	−	0.282686i	$-0.908774\pi$
$941$	−20.7529	+	20.7529i	−0.676526	+	0.676526i	0.282686	+	0.959212i	$0.408774\pi$
$942$	19.8987	+	19.8987i	0.648334	+	0.648334i
$943$	−12.5565			−0.408896
$944$		−	37.2008i		−	1.21078i
$945$		0			0
$946$	−18.9441	+	18.9441i	−0.615926	+	0.615926i
$947$	16.8899	−	16.8899i	0.548848	−	0.548848i	−0.377259	−	0.926108i	$-0.623133\pi$
$947$	16.8899	−	16.8899i	0.548848	−	0.548848i	0.926108	+	0.377259i	$0.123133\pi$
$948$			11.0448i			0.358719i
$949$	−11.1651	−	11.1651i	−0.362435	−	0.362435i
$950$		0			0
$951$	36.1349			1.17175
$952$	−3.10470	+	11.7517i	−0.100624	+	0.380876i
$953$		−	21.4293i		−	0.694163i	−0.937835	−	0.347081i	$-0.887173\pi$
$953$		−	21.4293i		−	0.694163i	0.937835	−	0.347081i	$-0.112827\pi$
$954$			44.8137i			1.45090i
$955$		0			0
$956$	0.667696			0.0215948
$957$	8.52897	−	8.52897i	0.275702	−	0.275702i
$958$	22.1527	+	22.1527i	0.715721	+	0.715721i
$959$	3.08021	−	3.08021i	0.0994650	−	0.0994650i
$960$		0			0
$961$			0.605790i			0.0195416i
$962$	−14.4119	−	14.4119i	−0.464658	−	0.464658i
$963$	4.86041	+	4.86041i	0.156625	+	0.156625i
$964$	4.68185	+	4.68185i	0.150792	+	0.150792i
$965$		0			0
$966$	22.2862	+	22.2862i	0.717048	+	0.717048i
$967$	29.8258			0.959133			0.479567	−	0.877505i	$-0.340794\pi$
$967$	29.8258			0.959133			0.479567	+	0.877505i	$0.340794\pi$
$968$		−	3.47041i		−	0.111543i
$969$	17.6246	−	66.7118i	0.566184	−	2.14309i
$970$		0			0
$971$		−	7.71562i		−	0.247606i	−0.992307	−	0.123803i	$-0.960491\pi$
$971$		−	7.71562i		−	0.247606i	0.992307	−	0.123803i	$-0.0395091\pi$
$972$	8.36449	−	8.36449i	0.268291	−	0.268291i
$973$			0.923338i			0.0296009i
$974$	26.8426	+	26.8426i	0.860093	+	0.860093i
$975$		0			0
$976$	−7.27520	+	7.27520i	−0.232874	+	0.232874i
$977$	13.5920			0.434846			0.217423	−	0.976077i	$-0.430235\pi$
$977$	13.5920			0.434846			0.217423	+	0.976077i	$0.430235\pi$
$978$	−83.8769			−2.68209
$979$	−2.93383	+	2.93383i	−0.0937657	+	0.0937657i
$980$		0			0
$981$	−24.7143	−	24.7143i	−0.789067	−	0.789067i
$982$			37.3062i			1.19049i
$983$	17.4851	−	17.4851i	0.557689	−	0.557689i	−0.370960	−	0.928649i	$-0.620971\pi$
$983$	17.4851	−	17.4851i	0.557689	−	0.557689i	0.928649	+	0.370960i	$0.120971\pi$
$984$		−	14.3197i		−	0.456495i
$985$		0			0
$986$	1.55380	−	5.88136i	0.0494830	−	0.187301i
$987$		−	33.2665i		−	1.05888i
$988$	5.56939			0.177186
$989$	−42.1914	−	42.1914i	−1.34161	−	1.34161i
$990$		0			0
$991$	−20.9616	−	20.9616i	−0.665868	−	0.665868i	0.290889	−	0.956757i	$-0.406049\pi$
$991$	−20.9616	−	20.9616i	−0.665868	−	0.665868i	−0.956757	+	0.290889i	$0.906049\pi$
$992$	11.3711	+	11.3711i	0.361032	+	0.361032i
$993$	18.9558	+	18.9558i	0.601543	+	0.601543i
$994$			4.66938i			0.148104i
$995$		0			0
$996$	0.199533	−	0.199533i	0.00632244	−	0.00632244i
$997$	29.2994	+	29.2994i	0.927923	+	0.927923i	0.997572	−	0.0696488i	$-0.0221879\pi$
$997$	29.2994	+	29.2994i	0.927923	+	0.927923i	−0.0696488	+	0.997572i	$0.522188\pi$
$998$	21.8162	−	21.8162i	0.690579	−	0.690579i
$999$	105.355			3.33329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.j.d.149.4		12
5.2	odd	4		425.2.e.c.251.4	✓	12
5.3	odd	4		425.2.e.e.251.3	yes	12
5.4	even	2		425.2.j.a.149.3		12
17.4	even	4		425.2.j.a.174.3		12
85.2	odd	8		7225.2.a.bm.1.5		12
85.4	even	4	inner	425.2.j.d.174.4		12
85.32	odd	8		7225.2.a.bm.1.6		12
85.38	odd	4		425.2.e.e.276.4	yes	12
85.53	odd	8		7225.2.a.br.1.8		12
85.72	odd	4		425.2.e.c.276.3	yes	12
85.83	odd	8		7225.2.a.br.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.e.c.251.4	✓	12	5.2	odd	4
425.2.e.c.276.3	yes	12	85.72	odd	4
425.2.e.e.251.3	yes	12	5.3	odd	4
425.2.e.e.276.4	yes	12	85.38	odd	4
425.2.j.a.149.3		12	5.4	even	2
425.2.j.a.174.3		12	17.4	even	4
425.2.j.d.149.4		12	1.1	even	1	trivial
425.2.j.d.174.4		12	85.4	even	4	inner
7225.2.a.bm.1.5		12	85.2	odd	8
7225.2.a.bm.1.6		12	85.32	odd	8
7225.2.a.br.1.7		12	85.83	odd	8
7225.2.a.br.1.8		12	85.53	odd	8

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.21647 q^{2} +(2.23861 - 2.23861i) q^{3} -0.520205 q^{4} +(2.72320 - 2.72320i) q^{6} +(0.679950 + 0.679950i) q^{7} -3.06575 q^{8} -7.02277i q^{9} +(2.22126 - 2.22126i) q^{11} +(-1.16454 + 1.16454i) q^{12} +2.02534i q^{13} +(0.827137 + 0.827137i) q^{14} -2.68898 q^{16} +(-2.07407 - 3.56346i) q^{17} -8.54297i q^{18} +5.28609i q^{19} +3.04429 q^{21} +(2.70209 - 2.70209i) q^{22} +(6.01797 + 6.01797i) q^{23} +(-6.86302 + 6.86302i) q^{24} +2.46376i q^{26} +(-9.00542 - 9.00542i) q^{27} +(-0.353714 - 0.353714i) q^{28} +(0.857606 + 0.857606i) q^{29} +(3.97529 + 3.97529i) q^{31} +2.86045 q^{32} -9.94509i q^{33} +(-2.52305 - 4.33483i) q^{34} +3.65328i q^{36} +(-5.84955 + 5.84955i) q^{37} +6.43037i q^{38} +(4.53395 + 4.53395i) q^{39} +(-1.04325 + 1.04325i) q^{41} +3.70328 q^{42} -7.01089 q^{43} +(-1.15551 + 1.15551i) q^{44} +(7.32067 + 7.32067i) q^{46} -10.9275i q^{47} +(-6.01957 + 6.01957i) q^{48} -6.07534i q^{49} +(-12.6202 - 3.33415i) q^{51} -1.05359i q^{52} -5.24568 q^{53} +(-10.9548 - 10.9548i) q^{54} +(-2.08456 - 2.08456i) q^{56} +(11.8335 + 11.8335i) q^{57} +(1.04325 + 1.04325i) q^{58} +13.8346i q^{59} +(2.70557 - 2.70557i) q^{61} +(4.83581 + 4.83581i) q^{62} +(4.77513 - 4.77513i) q^{63} +8.85759 q^{64} -12.0979i q^{66} +2.37336i q^{67} +(1.07894 + 1.85373i) q^{68} +26.9438 q^{69} +(2.82261 + 2.82261i) q^{71} +21.5300i q^{72} +(-5.51272 + 5.51272i) q^{73} +(-7.11579 + 7.11579i) q^{74} -2.74985i q^{76} +3.02069 q^{77} +(5.51540 + 5.51540i) q^{78} +(4.74215 - 4.74215i) q^{79} -19.2510 q^{81} +(-1.26908 + 1.26908i) q^{82} -0.171341 q^{83} -1.58365 q^{84} -8.52853 q^{86} +3.83969 q^{87} +(-6.80983 + 6.80983i) q^{88} -1.32080 q^{89} +(-1.37713 + 1.37713i) q^{91} +(-3.13058 - 3.13058i) q^{92} +17.7982 q^{93} -13.2930i q^{94} +(6.40343 - 6.40343i) q^{96} +(1.33838 - 1.33838i) q^{97} -7.39045i q^{98} +(-15.5994 - 15.5994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 2 q^{3} + 12 q^{4} + 6 q^{6} + 12 q^{8} - 4 q^{11} - 4 q^{12} - 14 q^{14} + 4 q^{16} - 10 q^{17} + 8 q^{21} + 10 q^{22} + 12 q^{23} + 8 q^{24} - 22 q^{27} - 34 q^{28} + 6 q^{29} - 6 q^{31}+ \cdots - 30 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + 2 * q^3 + 12 * q^4 + 6 * q^6 + 12 * q^8 - 4 * q^11 - 4 * q^12 - 14 * q^14 + 4 * q^16 - 10 * q^17 + 8 * q^21 + 10 * q^22 + 12 * q^23 + 8 * q^24 - 22 * q^27 - 34 * q^28 + 6 * q^29 - 6 * q^31 + 48 * q^32 - 30 * q^34 + 18 * q^37 - 16 * q^39 + 6 * q^41 - 56 * q^42 + 16 * q^43 - 32 * q^44 + 30 * q^46 + 10 * q^48 - 40 * q^51 - 48 * q^53 - 16 * q^54 - 56 * q^56 + 18 * q^57 - 6 * q^58 - 8 * q^61 + 22 * q^62 + 30 * q^63 + 44 * q^64 - 18 * q^68 + 72 * q^69 - 20 * q^71 + 18 * q^73 + 26 * q^74 - 24 * q^77 + 38 * q^78 + 14 * q^79 - 8 * q^81 - 10 * q^82 - 52 * q^83 - 36 * q^84 + 84 * q^86 + 48 * q^87 - 66 * q^88 + 24 * q^89 + 12 * q^91 + 32 * q^92 + 60 * q^93 + 22 * q^96 - 52 * q^97 - 30 * q^99

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