LMFDB - Embedded newform 936.2.q.d.625.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [936,2,Mod(313,936)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(936, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("936.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - 6 x^{11} + 29 x^{10} - 90 x^{9} + 217 x^{8} - 394 x^{7} + 555 x^{6} - 598 x^{5} + 483 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 29x^10 - 90x^9 + 217x^8 - 394x^7 + 555x^6 - 598x^5 + 483x^4 - 282x^3 + 112x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			625.5
Root			$0.500000 - 0.667413i$ of defining polynomial
Character	$\chi$	$=$	936.625
Dual form			936.2.q.d.313.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.409577 + 1.68293i) q^{3} +(-1.87385 + 3.24560i) q^{5} +(0.175717 + 0.304350i) q^{7} +(-2.66449 + 1.37858i) q^{9} +(1.64765 + 2.85382i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-6.22960 - 1.82423i) q^{15} +3.88461 q^{17} -4.45847 q^{19} +(-0.440230 + 0.420374i) q^{21} +(2.33425 - 4.04304i) q^{23} +(-4.52263 - 7.83342i) q^{25} +(-3.41136 - 3.91952i) q^{27} +(2.22269 + 3.84982i) q^{29} +(-0.391033 + 0.677289i) q^{31} +(-4.12793 + 3.94174i) q^{33} -1.31707 q^{35} -11.4322 q^{37} +(-1.66225 - 0.486760i) q^{39} +(3.42133 - 5.92592i) q^{41} +(4.77046 + 8.26268i) q^{43} +(0.518544 - 11.2311i) q^{45} +(1.03306 + 1.78931i) q^{47} +(3.43825 - 5.95522i) q^{49} +(1.59105 + 6.53751i) q^{51} -2.97755 q^{53} -12.3498 q^{55} +(-1.82609 - 7.50328i) q^{57} +(-0.470310 + 0.814600i) q^{59} +(-7.20988 - 12.4879i) q^{61} +(-0.887767 - 0.568700i) q^{63} +(-1.87385 - 3.24560i) q^{65} +(-2.12749 + 3.68491i) q^{67} +(7.76020 + 2.27244i) q^{69} -5.25904 q^{71} +7.09427 q^{73} +(11.3307 - 10.8196i) q^{75} +(-0.579040 + 1.00293i) q^{77} +(7.10680 + 12.3093i) q^{79} +(5.19905 - 7.34642i) q^{81} +(6.27717 + 10.8724i) q^{83} +(-7.27917 + 12.6079i) q^{85} +(-5.56861 + 5.31743i) q^{87} -5.56256 q^{89} -0.351433 q^{91} +(-1.29999 - 0.380678i) q^{93} +(8.35450 - 14.4704i) q^{95} +(0.853296 + 1.47795i) q^{97} +(-8.32437 - 5.33256i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} - q^{5} + 2 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - 2 q^{15} + 12 q^{17} - 14 q^{19} - 24 q^{21} + 19 q^{23} + 5 q^{25} - 7 q^{27} - 2 q^{29} + 8 q^{31} - 9 q^{33} + 2 q^{35} - 34 q^{37}+ \cdots - 39 q^{99}+O(q^{100}) $ 12 * q - 4 * q^3 - q^5 + 2 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - 2 * q^15 + 12 * q^17 - 14 * q^19 - 24 * q^21 + 19 * q^23 + 5 * q^25 - 7 * q^27 - 2 * q^29 + 8 * q^31 - 9 * q^33 + 2 * q^35 - 34 * q^37 - q^39 - 2 * q^41 + 15 * q^43 + 10 * q^45 - 9 * q^47 + 12 * q^49 + 4 * q^51 + 32 * q^53 - 10 * q^55 - 14 * q^57 + 5 * q^59 + 6 * q^61 + 18 * q^63 - q^65 + 8 * q^67 + 15 * q^69 - 42 * q^71 - 2 * q^73 + 10 * q^75 + 3 * q^77 + 34 * q^79 + 62 * q^81 + 44 * q^83 + 7 * q^85 - 21 * q^87 + 22 * q^89 - 4 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 - 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.409577	+	1.68293i	0.236469	+	0.971639i
$3$	0.409577	+	1.68293i	0.236469	+	0.971639i
$4$		0			0
$5$	−1.87385	+	3.24560i	−0.838011	+	1.45148i	0.0535439	+	0.998565i	$0.482948\pi$
$5$	−1.87385	+	3.24560i	−0.838011	+	1.45148i	−0.891555	+	0.452912i	$0.850385\pi$
$6$		0			0
$7$	0.175717	+	0.304350i	0.0664147	+	0.115034i	0.897321	−	0.441379i	$-0.145511\pi$
$7$	0.175717	+	0.304350i	0.0664147	+	0.115034i	−0.830906	+	0.556413i	$0.812177\pi$
$8$		0			0
$9$	−2.66449	+	1.37858i	−0.888164	+	0.459526i
$10$		0			0
$11$	1.64765	+	2.85382i	0.496786	+	0.860458i	0.999993	−	0.00370733i	$-0.00118008\pi$
$11$	1.64765	+	2.85382i	0.496786	+	0.860458i	−0.503207	+	0.864166i	$0.667847\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$		0			0
$15$	−6.22960	−	1.82423i	−1.60848	−	0.471014i
$16$		0			0
$17$	3.88461			0.942155			0.471078	−	0.882092i	$-0.343865\pi$
$17$	3.88461			0.942155			0.471078	+	0.882092i	$0.343865\pi$
$18$		0			0
$19$	−4.45847			−1.02284			−0.511421	−	0.859330i	$-0.670881\pi$
$19$	−4.45847			−1.02284			−0.511421	+	0.859330i	$0.670881\pi$
$20$		0			0
$21$	−0.440230	+	0.420374i	−0.0960661	+	0.0917330i
$22$		0			0
$23$	2.33425	−	4.04304i	0.486725	−	0.843032i	−0.513159	−	0.858294i	$-0.671525\pi$
$23$	2.33425	−	4.04304i	0.486725	−	0.843032i	0.999884	+	0.0152616i	$0.00485811\pi$
$24$		0			0
$25$	−4.52263	−	7.83342i	−0.904525	−	1.56668i
$26$		0			0
$27$	−3.41136	−	3.91952i	−0.656517	−	0.754311i
$28$		0			0
$29$	2.22269	+	3.84982i	0.412744	+	0.714894i	0.995189	−	0.0979767i	$-0.0312371\pi$
$29$	2.22269	+	3.84982i	0.412744	+	0.714894i	−0.582445	+	0.812870i	$0.697904\pi$
$30$		0			0
$31$	−0.391033	+	0.677289i	−0.0702316	+	0.121645i	−0.899003	−	0.437943i	$-0.855707\pi$
$31$	−0.391033	+	0.677289i	−0.0702316	+	0.121645i	0.828771	+	0.559588i	$0.189041\pi$
$32$		0			0
$33$	−4.12793	+	3.94174i	−0.718580	+	0.686169i
$34$		0			0
$35$	−1.31707			−0.222625
$36$		0			0
$37$	−11.4322			−1.87944			−0.939721	−	0.341943i	$-0.888915\pi$
$37$	−11.4322			−1.87944			−0.939721	+	0.341943i	$0.888915\pi$
$38$		0			0
$39$	−1.66225	−	0.486760i	−0.266173	−	0.0779439i
$40$		0			0
$41$	3.42133	−	5.92592i	0.534322	−	0.925473i	−0.464874	−	0.885377i	$-0.653900\pi$
$41$	3.42133	−	5.92592i	0.534322	−	0.925473i	0.999196	−	0.0400958i	$-0.0127663\pi$
$42$		0			0
$43$	4.77046	+	8.26268i	0.727488	+	1.26005i	0.957942	+	0.286963i	$0.0926457\pi$
$43$	4.77046	+	8.26268i	0.727488	+	1.26005i	−0.230453	+	0.973083i	$0.574021\pi$
$44$		0			0
$45$	0.518544	−	11.2311i	0.0773000	−	1.67424i
$46$		0			0
$47$	1.03306	+	1.78931i	0.150687	+	0.260998i	0.931480	−	0.363792i	$-0.118518\pi$
$47$	1.03306	+	1.78931i	0.150687	+	0.260998i	−0.780793	+	0.624790i	$0.785185\pi$
$48$		0			0
$49$	3.43825	−	5.95522i	0.491178	−	0.850746i
$50$		0			0
$51$	1.59105	+	6.53751i	0.222791	+	0.915435i
$52$		0			0
$53$	−2.97755			−0.408998			−0.204499	−	0.978867i	$-0.565557\pi$
$53$	−2.97755			−0.408998			−0.204499	+	0.978867i	$0.565557\pi$
$54$		0			0
$55$	−12.3498			−1.66525
$56$		0			0
$57$	−1.82609	−	7.50328i	−0.241871	−	0.993833i
$58$		0			0
$59$	−0.470310	+	0.814600i	−0.0612291	+	0.106052i	−0.895015	−	0.446036i	$-0.852835\pi$
$59$	−0.470310	+	0.814600i	−0.0612291	+	0.106052i	0.833786	+	0.552088i	$0.186169\pi$
$60$		0			0
$61$	−7.20988	−	12.4879i	−0.923130	−	1.59891i	−0.794541	−	0.607211i	$-0.792288\pi$
$61$	−7.20988	−	12.4879i	−0.923130	−	1.59891i	−0.128590	−	0.991698i	$-0.541045\pi$
$62$		0			0
$63$	−0.887767	−	0.568700i	−0.111848	−	0.0716495i
$64$		0			0
$65$	−1.87385	−	3.24560i	−0.232422	−	0.402568i
$66$		0			0
$67$	−2.12749	+	3.68491i	−0.259914	+	0.450184i	−0.966219	−	0.257724i	$-0.917027\pi$
$67$	−2.12749	+	3.68491i	−0.259914	+	0.450184i	0.706305	+	0.707908i	$0.250361\pi$
$68$		0			0
$69$	7.76020	+	2.27244i	0.934218	+	0.273569i
$70$		0			0
$71$	−5.25904			−0.624133			−0.312067	−	0.950060i	$-0.601021\pi$
$71$	−5.25904			−0.624133			−0.312067	+	0.950060i	$0.601021\pi$
$72$		0			0
$73$	7.09427			0.830322			0.415161	−	0.909748i	$-0.363725\pi$
$73$	7.09427			0.830322			0.415161	+	0.909748i	$0.363725\pi$
$74$		0			0
$75$	11.3307	−	10.8196i	1.30836	−	1.24935i
$76$		0			0
$77$	−0.579040	+	1.00293i	−0.0659878	+	0.114294i
$78$		0			0
$79$	7.10680	+	12.3093i	0.799577	+	1.38491i	0.919892	+	0.392172i	$0.128276\pi$
$79$	7.10680	+	12.3093i	0.799577	+	1.38491i	−0.120315	+	0.992736i	$0.538390\pi$
$80$		0			0
$81$	5.19905	−	7.34642i	0.577672	−	0.816269i
$82$		0			0
$83$	6.27717	+	10.8724i	0.689009	+	1.19340i	0.972159	+	0.234323i	$0.0752874\pi$
$83$	6.27717	+	10.8724i	0.689009	+	1.19340i	−0.283149	+	0.959076i	$0.591379\pi$
$84$		0			0
$85$	−7.27917	+	12.6079i	−0.789537	+	1.36752i
$86$		0			0
$87$	−5.56861	+	5.31743i	−0.597017	+	0.570089i
$88$		0			0
$89$	−5.56256			−0.589631			−0.294815	−	0.955554i	$-0.595258\pi$
$89$	−5.56256			−0.589631			−0.294815	+	0.955554i	$0.595258\pi$
$90$		0			0
$91$	−0.351433			−0.0368402
$92$		0			0
$93$	−1.29999	−	0.380678i	−0.134802	−	0.0394745i
$94$		0			0
$95$	8.35450	−	14.4704i	0.857153	−	1.48463i
$96$		0			0
$97$	0.853296	+	1.47795i	0.0866391	+	0.150063i	0.906088	−	0.423088i	$-0.139054\pi$
$97$	0.853296	+	1.47795i	0.0866391	+	0.150063i	−0.819449	+	0.573152i	$0.805721\pi$
$98$		0			0
$99$	−8.32437	−	5.33256i	−0.836630	−	0.535943i
$100$		0			0
$101$	1.31437	+	2.27655i	0.130784	+	0.226525i	0.923979	−	0.382443i	$-0.124917\pi$
$101$	1.31437	+	2.27655i	0.130784	+	0.226525i	−0.793195	+	0.608968i	$0.791584\pi$
$102$		0			0
$103$	−6.78217	+	11.7471i	−0.668267	+	1.15747i	0.310121	+	0.950697i	$0.399630\pi$
$103$	−6.78217	+	11.7471i	−0.668267	+	1.15747i	−0.978388	+	0.206776i	$0.933703\pi$
$104$		0			0
$105$	−0.539441	−	2.21653i	−0.0526440	−	0.216311i
$106$		0			0
$107$	3.58218			0.346302			0.173151	−	0.984895i	$-0.444605\pi$
$107$	3.58218			0.346302			0.173151	+	0.984895i	$0.444605\pi$
$108$		0			0
$109$	11.1068			1.06384			0.531918	−	0.846796i	$-0.321472\pi$
$109$	11.1068			1.06384			0.531918	+	0.846796i	$0.321472\pi$
$110$		0			0
$111$	−4.68237	−	19.2396i	−0.444431	−	1.82614i
$112$		0			0
$113$	−1.03347	+	1.79003i	−0.0972210	+	0.168392i	−0.910533	−	0.413436i	$-0.864329\pi$
$113$	−1.03347	+	1.79003i	−0.0972210	+	0.168392i	0.813312	+	0.581827i	$0.197662\pi$
$114$		0			0
$115$	8.74807	+	15.1521i	0.815762	+	1.41294i
$116$		0			0
$117$	0.138363	−	2.99681i	0.0127917	−	0.277055i
$118$		0			0
$119$	0.682590	+	1.18228i	0.0625730	+	0.108380i
$120$		0			0
$121$	0.0704825	−	0.122079i	0.00640750	−	0.0110981i
$122$		0			0
$123$	11.3742	+	3.33073i	1.02558	+	0.300322i
$124$		0			0
$125$	15.1604			1.35599
$126$		0			0
$127$	−15.0773			−1.33789			−0.668945	−	0.743312i	$-0.733254\pi$
$127$	−15.0773			−1.33789			−0.668945	+	0.743312i	$0.733254\pi$
$128$		0			0
$129$	−11.9516	+	11.4125i	−1.05228	+	1.00482i
$130$		0			0
$131$	−6.82003	+	11.8126i	−0.595869	+	1.03207i	0.397555	+	0.917578i	$0.369859\pi$
$131$	−6.82003	+	11.8126i	−0.595869	+	1.03207i	−0.993424	+	0.114496i	$0.963475\pi$
$132$		0			0
$133$	−0.783427	−	1.35694i	−0.0679317	−	0.117661i
$134$		0			0
$135$	19.1136	−	3.72734i	1.64503	−	0.320799i
$136$		0			0
$137$	3.11762	+	5.39988i	0.266356	+	0.461343i	0.967918	−	0.251266i	$-0.0808468\pi$
$137$	3.11762	+	5.39988i	0.266356	+	0.461343i	−0.701562	+	0.712609i	$0.747513\pi$
$138$		0			0
$139$	−0.835988	+	1.44797i	−0.0709076	+	0.122816i	−0.899299	−	0.437334i	$-0.855923\pi$
$139$	−0.835988	+	1.44797i	−0.0709076	+	0.122816i	0.828392	+	0.560149i	$0.189256\pi$
$140$		0			0
$141$	−2.58817	+	2.47143i	−0.217963	+	0.208132i
$142$		0			0
$143$	−3.29530			−0.275567
$144$		0			0
$145$	−16.6600			−1.38354
$146$		0			0
$147$	11.4304	+	3.34720i	0.942766	+	0.276072i
$148$		0			0
$149$	−8.29479	+	14.3670i	−0.679536	+	1.17699i	0.295585	+	0.955316i	$0.404485\pi$
$149$	−8.29479	+	14.3670i	−0.679536	+	1.17699i	−0.975121	+	0.221674i	$0.928848\pi$
$150$		0			0
$151$	7.79995	+	13.5099i	0.634751	+	1.09942i	0.986568	+	0.163352i	$0.0522305\pi$
$151$	7.79995	+	13.5099i	0.634751	+	1.09942i	−0.351817	+	0.936069i	$0.614436\pi$
$152$		0			0
$153$	−10.3505	+	5.35523i	−0.836789	+	0.432945i
$154$		0			0
$155$	−1.46547	−	2.53828i	−0.117710	−	0.203879i
$156$		0			0
$157$	8.17650	−	14.1621i	0.652556	−	1.13026i	−0.329945	−	0.944000i	$-0.607030\pi$
$157$	8.17650	−	14.1621i	0.652556	−	1.13026i	0.982501	−	0.186259i	$-0.0596365\pi$
$158$		0			0
$159$	−1.21954	−	5.01101i	−0.0967156	−	0.397399i
$160$		0			0
$161$	1.64067			0.129303
$162$		0			0
$163$	5.60740			0.439206			0.219603	−	0.975589i	$-0.429524\pi$
$163$	5.60740			0.439206			0.219603	+	0.975589i	$0.429524\pi$
$164$		0			0
$165$	−5.05820	−	20.7838i	−0.393780	−	1.61802i
$166$		0			0
$167$	2.36444	−	4.09532i	0.182966	−	0.316906i	−0.759924	−	0.650012i	$-0.774764\pi$
$167$	2.36444	−	4.09532i	0.182966	−	0.316906i	0.942889	+	0.333107i	$0.108097\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$		0			0
$171$	11.8796	−	6.14634i	0.908452	−	0.470022i
$172$		0			0
$173$	8.39746	+	14.5448i	0.638447	+	1.10582i	0.985774	+	0.168078i	$0.0537562\pi$
$173$	8.39746	+	14.5448i	0.638447	+	1.10582i	−0.347327	+	0.937744i	$0.612910\pi$
$174$		0			0
$175$	1.58940	−	2.75293i	0.120148	−	0.208102i
$176$		0			0
$177$	−1.56354	−	0.457856i	−0.117523	−	0.0344145i
$178$		0			0
$179$	11.7878			0.881062			0.440531	−	0.897737i	$-0.354790\pi$
$179$	11.7878			0.881062			0.440531	+	0.897737i	$0.354790\pi$
$180$		0			0
$181$	−26.0931			−1.93948			−0.969742	−	0.244132i	$-0.921497\pi$
$181$	−26.0931			−1.93948			−0.969742	+	0.244132i	$0.921497\pi$
$182$		0			0
$183$	18.0632	−	17.2485i	1.33527	−	1.27504i
$184$		0			0
$185$	21.4222	−	37.1044i	1.57499	−	2.72797i
$186$		0			0
$187$	6.40048	+	11.0860i	0.468050	+	0.810686i
$188$		0			0
$189$	0.593472	−	1.72697i	0.0431688	−	0.125619i
$190$		0			0
$191$	7.91958	+	13.7171i	0.573041	+	0.992535i	0.996251	+	0.0865042i	$0.0275696\pi$
$191$	7.91958	+	13.7171i	0.573041	+	0.992535i	−0.423211	+	0.906031i	$0.639097\pi$
$192$		0			0
$193$	−5.53722	+	9.59074i	−0.398578	+	0.690357i	−0.993551	−	0.113389i	$-0.963829\pi$
$193$	−5.53722	+	9.59074i	−0.398578	+	0.690357i	0.594973	+	0.803746i	$0.297163\pi$
$194$		0			0
$195$	4.69463	−	4.48288i	0.336189	−	0.321026i
$196$		0			0
$197$	8.36629			0.596073			0.298037	−	0.954554i	$-0.403668\pi$
$197$	8.36629			0.596073			0.298037	+	0.954554i	$0.403668\pi$
$198$		0			0
$199$	2.63356			0.186688			0.0933441	−	0.995634i	$-0.470244\pi$
$199$	2.63356			0.186688			0.0933441	+	0.995634i	$0.470244\pi$
$200$		0			0
$201$	−7.07281	−	2.07115i	−0.498878	−	0.146088i
$202$		0			0
$203$	−0.781129	+	1.35296i	−0.0548245	+	0.0949589i
$204$		0			0
$205$	12.8221	+	22.2086i	0.895535	+	1.55111i
$206$		0			0
$207$	−0.645949	+	13.9906i	−0.0448966	+	0.972414i
$208$		0			0
$209$	−7.34600	−	12.7236i	−0.508134	−	0.880113i
$210$		0			0
$211$	12.1778	−	21.0925i	0.838351	−	1.45207i	−0.0529214	−	0.998599i	$-0.516853\pi$
$211$	12.1778	−	21.0925i	0.838351	−	1.45207i	0.891273	−	0.453468i	$-0.149813\pi$
$212$		0			0
$213$	−2.15398	−	8.85059i	−0.147589	−	0.606432i
$214$		0			0
$215$	−35.7565			−2.43857
$216$		0			0
$217$	−0.274844			−0.0186576
$218$		0			0
$219$	2.90565	+	11.9392i	0.196346	+	0.806773i
$220$		0			0
$221$	−1.94230	+	3.36417i	−0.130653	+	0.226298i
$222$		0			0
$223$	−12.8601	−	22.2744i	−0.861178	−	1.49160i	−0.870793	−	0.491651i	$-0.836394\pi$
$223$	−12.8601	−	22.2744i	−0.861178	−	1.49160i	0.00961429	−	0.999954i	$-0.496940\pi$
$224$		0			0
$225$	22.8495	+	14.6373i	1.52330	+	0.975820i
$226$		0			0
$227$	−11.1762	−	19.3577i	−0.741788	−	1.28481i	−0.951681	−	0.307090i	$-0.900645\pi$
$227$	−11.1762	−	19.3577i	−0.741788	−	1.28481i	0.209893	−	0.977724i	$-0.432689\pi$
$228$		0			0
$229$	−2.42023	+	4.19196i	−0.159933	+	0.277012i	−0.934844	−	0.355058i	$-0.884461\pi$
$229$	−2.42023	+	4.19196i	−0.159933	+	0.277012i	0.774911	+	0.632070i	$0.217795\pi$
$230$		0			0
$231$	−1.92502	−	0.563707i	−0.126657	−	0.0370892i
$232$		0			0
$233$	25.0840			1.64331			0.821655	−	0.569986i	$-0.193051\pi$
$233$	25.0840			1.64331			0.821655	+	0.569986i	$0.193051\pi$
$234$		0			0
$235$	−7.74321			−0.505111
$236$		0			0
$237$	−17.8049	+	17.0018i	−1.15656	+	1.10439i
$238$		0			0
$239$	−12.3092	+	21.3202i	−0.796217	+	1.37909i	0.125846	+	0.992050i	$0.459836\pi$
$239$	−12.3092	+	21.3202i	−0.796217	+	1.37909i	−0.922063	+	0.387039i	$0.873498\pi$
$240$		0			0
$241$	10.0909	+	17.4780i	0.650015	+	1.12586i	0.983119	+	0.182968i	$0.0585706\pi$
$241$	10.0909	+	17.4780i	0.650015	+	1.12586i	−0.333104	+	0.942890i	$0.608096\pi$
$242$		0			0
$243$	14.4929	+	5.74070i	0.929721	+	0.368266i
$244$		0			0
$245$	12.8855	+	22.3184i	0.823226	+	1.42587i
$246$		0			0
$247$	2.22923	−	3.86114i	0.141843	−	0.245679i
$248$		0			0
$249$	−15.7265	+	15.0171i	−0.996623	+	0.951671i
$250$		0			0
$251$	26.3117			1.66078			0.830391	−	0.557181i	$-0.188117\pi$
$251$	26.3117			1.66078			0.830391	+	0.557181i	$0.188117\pi$
$252$		0			0
$253$	15.3841			0.967192
$254$		0			0
$255$	−24.1996	−	7.08641i	−1.51543	−	0.443768i
$256$		0			0
$257$	4.52109	−	7.83076i	0.282018	−	0.488470i	−0.689864	−	0.723939i	$-0.742330\pi$
$257$	4.52109	−	7.83076i	0.282018	−	0.488470i	0.971882	+	0.235470i	$0.0756629\pi$
$258$		0			0
$259$	−2.00883	−	3.47939i	−0.124823	−	0.216199i
$260$		0			0
$261$	−11.2296	−	7.19366i	−0.695097	−	0.445276i
$262$		0			0
$263$	0.953008	+	1.65066i	0.0587650	+	0.101784i	0.893911	−	0.448244i	$-0.147950\pi$
$263$	0.953008	+	1.65066i	0.0587650	+	0.101784i	−0.835146	+	0.550028i	$0.814617\pi$
$264$		0			0
$265$	5.57949	−	9.66396i	0.342745	−	0.593652i
$266$		0			0
$267$	−2.27830	−	9.36139i	−0.139430	−	0.572908i
$268$		0			0
$269$	13.5293			0.824896			0.412448	−	0.910981i	$-0.364674\pi$
$269$	13.5293			0.824896			0.412448	+	0.910981i	$0.364674\pi$
$270$		0			0
$271$	8.66113			0.526126			0.263063	−	0.964779i	$-0.415267\pi$
$271$	8.66113			0.526126			0.263063	+	0.964779i	$0.415267\pi$
$272$		0			0
$273$	−0.143939	−	0.591437i	−0.00871159	−	0.0357954i
$274$		0			0
$275$	14.9034	−	25.8135i	0.898711	−	1.55661i
$276$		0			0
$277$	−12.7451	−	22.0752i	−0.765779	−	1.32637i	−0.939834	−	0.341633i	$-0.889020\pi$
$277$	−12.7451	−	22.0752i	−0.765779	−	1.32637i	0.174054	−	0.984736i	$-0.444313\pi$
$278$		0			0
$279$	0.108209	−	2.34370i	0.00647832	−	0.140314i
$280$		0			0
$281$	11.3596	+	19.6755i	0.677659	+	1.17374i	0.975684	+	0.219182i	$0.0703389\pi$
$281$	11.3596	+	19.6755i	0.677659	+	1.17374i	−0.298025	+	0.954558i	$0.596328\pi$
$282$		0			0
$283$	−0.405631	+	0.702573i	−0.0241122	+	0.0417636i	−0.877830	−	0.478973i	$-0.841009\pi$
$283$	−0.405631	+	0.702573i	−0.0241122	+	0.0417636i	0.853717	+	0.520736i	$0.174343\pi$
$284$		0			0
$285$	27.7745	+	8.13327i	1.64522	+	0.481773i
$286$		0			0
$287$	2.40474			0.141947
$288$		0			0
$289$	−1.90983			−0.112343
$290$		0			0
$291$	−2.13780	+	2.04137i	−0.125320	+	0.119667i
$292$		0			0
$293$	−8.22954	+	14.2540i	−0.480775	+	0.832726i	−0.999757	−	0.0220590i	$-0.992978\pi$
$293$	−8.22954	+	14.2540i	−0.480775	+	0.832726i	0.518982	+	0.854785i	$0.326311\pi$
$294$		0			0
$295$	−1.76258	−	3.05288i	−0.102621	−	0.177745i
$296$		0			0
$297$	5.56485	−	16.1934i	0.322905	−	0.939637i
$298$		0			0
$299$	2.33425	+	4.04304i	0.134993	+	0.233815i
$300$		0			0
$301$	−1.67650	+	2.90378i	−0.0966318	+	0.167371i
$302$		0			0
$303$	−3.29294	+	3.14441i	−0.189174	+	0.180642i
$304$		0			0
$305$	54.0409			3.09437
$306$		0			0
$307$	−1.61680			−0.0922754			−0.0461377	−	0.998935i	$-0.514691\pi$
$307$	−1.61680			−0.0922754			−0.0461377	+	0.998935i	$0.514691\pi$
$308$		0			0
$309$	−22.5473	−	6.60258i	−1.28267	−	0.375607i
$310$		0			0
$311$	−14.8865	+	25.7842i	−0.844136	+	1.46209i	0.0422326	+	0.999108i	$0.486553\pi$
$311$	−14.8865	+	25.7842i	−0.844136	+	1.46209i	−0.886369	+	0.462979i	$0.846780\pi$
$312$		0			0
$313$	−1.00615	−	1.74270i	−0.0568707	−	0.0985030i	0.836188	−	0.548442i	$-0.184779\pi$
$313$	−1.00615	−	1.74270i	−0.0568707	−	0.0985030i	−0.893059	+	0.449939i	$0.851446\pi$
$314$		0			0
$315$	3.50932	−	1.81568i	0.197728	−	0.102302i
$316$		0			0
$317$	−6.51655	−	11.2870i	−0.366006	−	0.633941i	0.622931	−	0.782277i	$-0.285942\pi$
$317$	−6.51655	−	11.2870i	−0.366006	−	0.633941i	−0.988937	+	0.148336i	$0.952608\pi$
$318$		0			0
$319$	−7.32446	+	12.6863i	−0.410091	+	0.710298i
$320$		0			0
$321$	1.46718	+	6.02855i	0.0818900	+	0.336481i
$322$		0			0
$323$	−17.3194			−0.963676
$324$		0			0
$325$	9.04525			0.501740
$326$		0			0
$327$	4.54908	+	18.6919i	0.251565	+	1.03366i
$328$		0			0
$329$	−0.363052	+	0.628825i	−0.0200157	+	0.0346682i
$330$		0			0
$331$	−1.21081	−	2.09718i	−0.0665520	−	0.115271i	0.830829	−	0.556527i	$-0.187866\pi$
$331$	−1.21081	−	2.09718i	−0.0665520	−	0.115271i	−0.897381	+	0.441256i	$0.854533\pi$
$332$		0			0
$333$	30.4610	−	15.7602i	1.66925	−	0.863652i
$334$		0			0
$335$	−7.97318	−	13.8099i	−0.435621	−	0.754518i
$336$		0			0
$337$	15.5590	−	26.9490i	0.847552	−	1.46800i	−0.0358338	−	0.999358i	$-0.511409\pi$
$337$	15.5590	−	26.9490i	0.847552	−	1.46800i	0.883386	−	0.468646i	$-0.155258\pi$
$338$		0			0
$339$	−3.43578	−	1.00611i	−0.186606	−	0.0546442i
$340$		0			0
$341$	−2.57715			−0.139560
$342$		0			0
$343$	4.87666			0.263315
$344$		0			0
$345$	−21.9169	+	20.9283i	−1.17997	+	1.12674i
$346$		0			0
$347$	9.88032	−	17.1132i	0.530403	−	0.918686i	−0.468967	−	0.883215i	$-0.655374\pi$
$347$	9.88032	−	17.1132i	0.530403	−	0.918686i	0.999371	−	0.0354701i	$-0.0112928\pi$
$348$		0			0
$349$	−2.46951	−	4.27732i	−0.132190	−	0.228960i	0.792330	−	0.610092i	$-0.208868\pi$
$349$	−2.46951	−	4.27732i	−0.132190	−	0.228960i	−0.924521	+	0.381132i	$0.875534\pi$
$350$		0			0
$351$	5.10008	−	0.994568i	0.272222	−	0.0530861i
$352$		0			0
$353$	−4.03380	−	6.98675i	−0.214698	−	0.371867i	0.738481	−	0.674274i	$-0.235543\pi$
$353$	−4.03380	−	6.98675i	−0.214698	−	0.371867i	−0.953179	+	0.302407i	$0.902210\pi$
$354$		0			0
$355$	9.85466	−	17.0688i	0.523031	−	0.905916i
$356$		0			0
$357$	−1.71012	+	1.63299i	−0.0905092	+	0.0864268i
$358$		0			0
$359$	−5.70600			−0.301151			−0.150576	−	0.988598i	$-0.548113\pi$
$359$	−5.70600			−0.301151			−0.150576	+	0.988598i	$0.548113\pi$
$360$		0			0
$361$	0.877919			0.0462063
$362$		0			0
$363$	0.234319	+	0.0686161i	0.0122985	+	0.00360141i
$364$		0			0
$365$	−13.2936	+	23.0252i	−0.695819	+	1.20519i
$366$		0			0
$367$	5.24676	+	9.08766i	0.273879	+	0.474372i	0.969852	−	0.243696i	$-0.0783600\pi$
$367$	5.24676	+	9.08766i	0.273879	+	0.474372i	−0.695973	+	0.718068i	$0.745027\pi$
$368$		0			0
$369$	−0.946773	+	20.5061i	−0.0492870	+	1.06751i
$370$		0			0
$371$	−0.523206	−	0.906219i	−0.0271635	−	0.0470486i
$372$		0			0
$373$	14.4631	−	25.0508i	0.748870	−	1.29708i	−0.199494	−	0.979899i	$-0.563930\pi$
$373$	14.4631	−	25.0508i	0.748870	−	1.29708i	0.948365	−	0.317182i	$-0.102737\pi$
$374$		0			0
$375$	6.20935	+	25.5139i	0.320650	+	1.31753i
$376$		0			0
$377$	−4.44539			−0.228949
$378$		0			0
$379$	−35.6342			−1.83040			−0.915202	−	0.402995i	$-0.867969\pi$
$379$	−35.6342			−1.83040			−0.915202	+	0.402995i	$0.867969\pi$
$380$		0			0
$381$	−6.17530	−	25.3739i	−0.316370	−	1.29995i
$382$		0			0
$383$	10.3651	−	17.9529i	0.529632	−	0.917350i	−0.469770	−	0.882789i	$-0.655663\pi$
$383$	10.3651	−	17.9529i	0.529632	−	0.917350i	0.999403	−	0.0345616i	$-0.0110035\pi$
$384$		0			0
$385$	−2.17007	−	3.75867i	−0.110597	−	0.191560i
$386$		0			0
$387$	−24.1016	−	15.4394i	−1.22515	−	0.784829i
$388$		0			0
$389$	−10.0822	−	17.4629i	−0.511189	−	0.885405i	−0.999916	−	0.0129685i	$-0.995872\pi$
$389$	−10.0822	−	17.4629i	−0.511189	−	0.885405i	0.488727	−	0.872437i	$-0.337461\pi$
$390$		0			0
$391$	9.06764	−	15.7056i	0.458570	−	0.794267i
$392$		0			0
$393$	−22.6731	−	6.63943i	−1.14371	−	0.334915i
$394$		0			0
$395$	−53.2683			−2.68022
$396$		0			0
$397$	−2.27323			−0.114090			−0.0570450	−	0.998372i	$-0.518168\pi$
$397$	−2.27323			−0.114090			−0.0570450	+	0.998372i	$0.518168\pi$
$398$		0			0
$399$	1.96275	−	1.87422i	0.0982604	−	0.0938284i
$400$		0			0
$401$	−13.0963	+	22.6835i	−0.653999	+	1.13276i	0.328144	+	0.944628i	$0.393577\pi$
$401$	−13.0963	+	22.6835i	−0.653999	+	1.13276i	−0.982144	+	0.188132i	$0.939757\pi$
$402$		0			0
$403$	−0.391033	−	0.677289i	−0.0194787	−	0.0337382i
$404$		0			0
$405$	14.1013	+	30.6401i	0.700701	+	1.52252i
$406$		0			0
$407$	−18.8363	−	32.6254i	−0.933680	−	1.61718i
$408$		0			0
$409$	−4.03259	+	6.98464i	−0.199399	+	0.345368i	−0.948334	−	0.317275i	$-0.897232\pi$
$409$	−4.03259	+	6.98464i	−0.199399	+	0.345368i	0.748935	+	0.662643i	$0.230566\pi$
$410$		0			0
$411$	−7.81070	+	7.45840i	−0.385274	+	0.367896i
$412$		0			0
$413$	−0.330565			−0.0162660
$414$		0			0
$415$	−47.0499			−2.30959
$416$		0			0
$417$	−2.77924	−	0.813851i	−0.136100	−	0.0398544i
$418$		0			0
$419$	−8.74243	+	15.1423i	−0.427096	+	0.739751i	−0.996614	−	0.0822277i	$-0.973797\pi$
$419$	−8.74243	+	15.1423i	−0.427096	+	0.739751i	0.569518	+	0.821979i	$0.307130\pi$
$420$		0			0
$421$	10.0221	+	17.3588i	0.488447	+	0.846015i	0.999912	−	0.0132894i	$-0.00423028\pi$
$421$	10.0221	+	17.3588i	0.488447	+	0.846015i	−0.511465	+	0.859304i	$0.670897\pi$
$422$		0			0
$423$	−5.21929	−	3.34346i	−0.253771	−	0.162565i
$424$		0			0
$425$	−17.5686	−	30.4298i	−0.852204	−	1.47606i
$426$		0			0
$427$	2.53379	−	4.38866i	0.122619	−	0.212382i
$428$		0			0
$429$	−1.34968	−	5.54576i	−0.0651632	−	0.267752i
$430$		0			0
$431$	8.01436			0.386038			0.193019	−	0.981195i	$-0.438172\pi$
$431$	8.01436			0.386038			0.193019	+	0.981195i	$0.438172\pi$
$432$		0			0
$433$	−25.8390			−1.24174			−0.620872	−	0.783912i	$-0.713221\pi$
$433$	−25.8390			−1.24174			−0.620872	+	0.783912i	$0.713221\pi$
$434$		0			0
$435$	−6.82355	−	28.0376i	−0.327164	−	1.34430i
$436$		0			0
$437$	−10.4072	+	18.0258i	−0.497843	+	0.862289i
$438$		0			0
$439$	−1.22088	−	2.11463i	−0.0582697	−	0.100926i	0.835419	−	0.549613i	$-0.185225\pi$
$439$	−1.22088	−	2.11463i	−0.0582697	−	0.100926i	−0.893689	+	0.448687i	$0.851892\pi$
$440$		0			0
$441$	−0.951454	+	20.6075i	−0.0453074	+	0.981311i
$442$		0			0
$443$	8.70678	+	15.0806i	0.413672	+	0.716500i	0.995288	−	0.0969631i	$-0.0309129\pi$
$443$	8.70678	+	15.0806i	0.413672	+	0.716500i	−0.581616	+	0.813463i	$0.697580\pi$
$444$		0			0
$445$	10.4234	−	18.0539i	0.494117	−	0.855836i
$446$		0			0
$447$	−27.5760	−	8.07514i	−1.30430	−	0.381941i
$448$		0			0
$449$	18.3826			0.867528			0.433764	−	0.901026i	$-0.357185\pi$
$449$	18.3826			0.867528			0.433764	+	0.901026i	$0.357185\pi$
$450$		0			0
$451$	22.5486			1.06177
$452$		0			0
$453$	−19.5415	+	18.6601i	−0.918141	+	0.876728i
$454$		0			0
$455$	0.658534	−	1.14061i	0.0308725	−	0.0534728i
$456$		0			0
$457$	7.96425	+	13.7945i	0.372552	+	0.645279i	0.989957	−	0.141366i	$-0.0451495\pi$
$457$	7.96425	+	13.7945i	0.372552	+	0.645279i	−0.617405	+	0.786645i	$0.711816\pi$
$458$		0			0
$459$	−13.2518	−	15.2258i	−0.618541	−	0.710678i
$460$		0			0
$461$	−13.8147	−	23.9277i	−0.643414	−	1.11443i	−0.984665	−	0.174454i	$-0.944184\pi$
$461$	−13.8147	−	23.9277i	−0.643414	−	1.11443i	0.341251	−	0.939972i	$-0.389149\pi$
$462$		0			0
$463$	−10.0645	+	17.4323i	−0.467739	+	0.810148i	−0.999320	−	0.0368592i	$-0.988265\pi$
$463$	−10.0645	+	17.4323i	−0.467739	+	0.810148i	0.531581	+	0.847007i	$0.321598\pi$
$464$		0			0
$465$	3.67151	−	3.50591i	0.170262	−	0.162583i
$466$		0			0
$467$	−1.34267			−0.0621315			−0.0310657	−	0.999517i	$-0.509890\pi$
$467$	−1.34267			−0.0621315			−0.0310657	+	0.999517i	$0.509890\pi$
$468$		0			0
$469$	−1.49534			−0.0690483
$470$		0			0
$471$	27.1827	+	7.95998i	1.25251	+	0.366777i
$472$		0			0
$473$	−15.7201	+	27.2280i	−0.722812	+	1.25195i
$474$		0			0
$475$	20.1640	+	34.9250i	0.925187	+	1.60247i
$476$		0			0
$477$	7.93367	−	4.10479i	0.363258	−	0.187945i
$478$		0			0
$479$	5.17811	+	8.96875i	0.236594	+	0.409793i	0.959735	−	0.280908i	$-0.0906355\pi$
$479$	5.17811	+	8.96875i	0.236594	+	0.409793i	−0.723141	+	0.690701i	$0.757302\pi$
$480$		0			0
$481$	5.71610	−	9.90057i	0.260632	−	0.451427i
$482$		0			0
$483$	0.671980	+	2.76112i	0.0305761	+	0.125636i
$484$		0			0
$485$	−6.39579			−0.290418
$486$		0			0
$487$	40.8998			1.85335			0.926674	−	0.375867i	$-0.122655\pi$
$487$	40.8998			1.85335			0.926674	+	0.375867i	$0.122655\pi$
$488$		0			0
$489$	2.29666	+	9.43685i	0.103859	+	0.426749i
$490$		0			0
$491$	−8.00358	+	13.8626i	−0.361197	+	0.625611i	−0.988158	−	0.153439i	$-0.950965\pi$
$491$	−8.00358	+	13.8626i	−0.361197	+	0.625611i	0.626961	+	0.779050i	$0.284298\pi$
$492$		0			0
$493$	8.63429	+	14.9550i	0.388869	+	0.673541i
$494$		0			0
$495$	32.9060	−	17.0252i	1.47901	−	0.765225i
$496$		0			0
$497$	−0.924102	−	1.60059i	−0.0414516	−	0.0717963i
$498$		0			0
$499$	1.18119	−	2.04589i	0.0528775	−	0.0915866i	−0.838375	−	0.545094i	$-0.816494\pi$
$499$	1.18119	−	2.04589i	0.0528775	−	0.0915866i	0.891253	+	0.453507i	$0.149827\pi$
$500$		0			0
$501$	7.86055	+	2.30182i	0.351184	+	0.102838i
$502$		0			0
$503$	−25.8661			−1.15331			−0.576655	−	0.816988i	$-0.695642\pi$
$503$	−25.8661			−1.15331			−0.576655	+	0.816988i	$0.695642\pi$
$504$		0			0
$505$	−9.85171			−0.438395
$506$		0			0
$507$	1.25267	−	1.19617i	0.0556330	−	0.0531237i
$508$		0			0
$509$	10.3604	−	17.9447i	0.459217	−	0.795387i	−0.539703	−	0.841855i	$-0.681463\pi$
$509$	10.3604	−	17.9447i	0.459217	−	0.795387i	0.998920	+	0.0464688i	$0.0147968\pi$
$510$		0			0
$511$	1.24658	+	2.15914i	0.0551456	+	0.0955149i
$512$		0			0
$513$	15.2094	+	17.4750i	0.671513	+	0.771541i
$514$		0			0
$515$	−25.4175	−	44.0245i	−1.12003	−	1.93995i
$516$		0			0
$517$	−3.40425	+	5.89634i	−0.149719	+	0.259321i
$518$		0			0
$519$	−21.0385	+	20.0895i	−0.923487	+	0.881833i
$520$		0			0
$521$	−39.8677			−1.74664			−0.873318	−	0.487150i	$-0.838036\pi$
$521$	−39.8677			−1.74664			−0.873318	+	0.487150i	$0.838036\pi$
$522$		0			0
$523$	−12.3303			−0.539167			−0.269583	−	0.962977i	$-0.586886\pi$
$523$	−12.3303			−0.539167			−0.269583	+	0.962977i	$0.586886\pi$
$524$		0			0
$525$	5.28396	+	1.54731i	0.230611	+	0.0675303i
$526$		0			0
$527$	−1.51901	+	2.63100i	−0.0661691	+	0.114608i
$528$		0			0
$529$	0.602551	+	1.04365i	0.0261979	+	0.0453760i
$530$		0			0
$531$	0.130147	−	2.81885i	0.00564790	−	0.122328i
$532$		0			0
$533$	3.42133	+	5.92592i	0.148194	+	0.256680i
$534$		0			0
$535$	−6.71247	+	11.6263i	−0.290205	+	0.502650i
$536$		0			0
$537$	4.82802	+	19.8380i	0.208344	+	0.856074i
$538$		0			0
$539$	22.6601			0.976042
$540$		0			0
$541$	22.9129			0.985104			0.492552	−	0.870283i	$-0.336064\pi$
$541$	22.9129			0.985104			0.492552	+	0.870283i	$0.336064\pi$
$542$		0			0
$543$	−10.6871	−	43.9128i	−0.458629	−	1.88448i
$544$		0			0
$545$	−20.8124	+	36.0482i	−0.891506	+	1.54413i
$546$		0			0
$547$	3.74712	+	6.49020i	0.160215	+	0.277501i	0.934946	−	0.354791i	$-0.115448\pi$
$547$	3.74712	+	6.49020i	0.160215	+	0.277501i	−0.774731	+	0.632291i	$0.782115\pi$
$548$		0			0
$549$	36.4262	+	23.3345i	1.55463	+	0.995892i
$550$		0			0
$551$	−9.90981	−	17.1643i	−0.422172	−	0.731223i
$552$		0			0
$553$	−2.49757	+	4.32591i	−0.106207	+	0.183956i
$554$		0			0
$555$	71.2180	+	20.8550i	3.02304	+	0.885243i
$556$		0			0
$557$	−26.2053			−1.11036			−0.555178	−	0.831732i	$-0.687350\pi$
$557$	−26.2053			−1.11036			−0.555178	+	0.831732i	$0.687350\pi$
$558$		0			0
$559$	−9.54092			−0.403538
$560$		0			0
$561$	−16.0354	+	15.3121i	−0.677014	+	0.646478i
$562$		0			0
$563$	13.0128	−	22.5388i	0.548424	−	0.949898i	−0.449959	−	0.893049i	$-0.648561\pi$
$563$	13.0128	−	22.5388i	0.548424	−	0.949898i	0.998383	−	0.0568489i	$-0.0181053\pi$
$564$		0			0
$565$	−3.87315	−	6.70849i	−0.162945	−	0.282228i
$566$		0			0
$567$	3.14945	+	0.291442i	0.132264	+	0.0122394i
$568$		0			0
$569$	−14.9250	−	25.8509i	−0.625689	−	1.08373i	−0.988407	−	0.151827i	$-0.951484\pi$
$569$	−14.9250	−	25.8509i	−0.625689	−	1.08373i	0.362718	−	0.931899i	$-0.381849\pi$
$570$		0			0
$571$	−4.48711	+	7.77190i	−0.187780	+	0.325244i	−0.944510	−	0.328484i	$-0.893462\pi$
$571$	−4.48711	+	7.77190i	−0.187780	+	0.325244i	0.756730	+	0.653727i	$0.226796\pi$
$572$		0			0
$573$	−19.8412	+	18.9463i	−0.828879	+	0.791493i
$574$		0			0
$575$	−42.2278			−1.76102
$576$		0			0
$577$	−32.4990			−1.35295			−0.676476	−	0.736465i	$-0.736494\pi$
$577$	−32.4990			−1.35295			−0.676476	+	0.736465i	$0.736494\pi$
$578$		0			0
$579$	−18.4084	−	5.39059i	−0.765029	−	0.224025i
$580$		0			0
$581$	−2.20601	+	3.82092i	−0.0915207	+	0.158518i
$582$		0			0
$583$	−4.90597	−	8.49739i	−0.203185	−	0.351926i
$584$		0			0
$585$	9.46718	+	6.06464i	0.391420	+	0.250742i
$586$		0			0
$587$	7.11365	+	12.3212i	0.293612	+	0.508550i	0.974661	−	0.223687i	$-0.0718094\pi$
$587$	7.11365	+	12.3212i	0.293612	+	0.508550i	−0.681049	+	0.732238i	$0.738476\pi$
$588$		0			0
$589$	1.74341	−	3.01967i	0.0718359	−	0.124423i
$590$		0			0
$591$	3.42664	+	14.0799i	0.140953	+	0.579168i
$592$		0			0
$593$	−14.7975			−0.607662			−0.303831	−	0.952726i	$-0.598266\pi$
$593$	−14.7975			−0.607662			−0.303831	+	0.952726i	$0.598266\pi$
$594$		0			0
$595$	−5.11629			−0.209747
$596$		0			0
$597$	1.07865	+	4.43209i	0.0441461	+	0.181393i
$598$		0			0
$599$	−0.671811	+	1.16361i	−0.0274495	+	0.0475438i	−0.879424	−	0.476040i	$-0.842072\pi$
$599$	−0.671811	+	1.16361i	−0.0274495	+	0.0475438i	0.851974	+	0.523584i	$0.175405\pi$
$600$		0			0
$601$	−14.3597	−	24.8718i	−0.585746	−	1.01454i	−0.994782	−	0.102024i	$-0.967468\pi$
$601$	−14.3597	−	24.8718i	−0.585746	−	1.01454i	0.409036	−	0.912518i	$-0.365865\pi$
$602$		0			0
$603$	0.588732	−	12.7513i	0.0239750	−	0.519274i
$604$		0			0
$605$	0.264147	+	0.457517i	0.0107391	+	0.0186007i
$606$		0			0
$607$	1.56230	−	2.70598i	0.0634118	−	0.109832i	−0.832577	−	0.553910i	$-0.813135\pi$
$607$	1.56230	−	2.70598i	0.0634118	−	0.109832i	0.895988	+	0.444078i	$0.146469\pi$
$608$		0			0
$609$	−2.59686	−	0.760445i	−0.105230	−	0.0308148i
$610$		0			0
$611$	−2.06612			−0.0835864
$612$		0			0
$613$	19.6800			0.794867			0.397433	−	0.917631i	$-0.369901\pi$
$613$	19.6800			0.794867			0.397433	+	0.917631i	$0.369901\pi$
$614$		0			0
$615$	−32.1238	+	30.6748i	−1.29535	+	1.23693i
$616$		0			0
$617$	−5.02955	+	8.71143i	−0.202482	+	0.350709i	−0.949328	−	0.314288i	$-0.898234\pi$
$617$	−5.02955	+	8.71143i	−0.202482	+	0.350709i	0.746846	+	0.664998i	$0.231567\pi$
$618$		0			0
$619$	21.2803	+	36.8585i	0.855326	+	1.48147i	0.876342	+	0.481689i	$0.159976\pi$
$619$	21.2803	+	36.8585i	0.855326	+	1.48147i	−0.0210164	+	0.999779i	$0.506690\pi$
$620$		0			0
$621$	−23.8097	+	4.64314i	−0.955452	+	0.186323i
$622$		0			0
$623$	−0.977436	−	1.69297i	−0.0391601	−	0.0678273i
$624$		0			0
$625$	−5.79518	+	10.0375i	−0.231807	+	0.401502i
$626$		0			0
$627$	18.4042	−	17.5741i	0.734994	−	0.701842i
$628$		0			0
$629$	−44.4096			−1.77073
$630$		0			0
$631$	20.2946			0.807916			0.403958	−	0.914778i	$-0.367634\pi$
$631$	20.2946			0.807916			0.403958	+	0.914778i	$0.367634\pi$
$632$		0			0
$633$	40.4849	+	11.8553i	1.60913	+	0.471205i
$634$		0			0
$635$	28.2525	−	48.9348i	1.12117	−	1.94192i
$636$		0			0
$637$	3.43825	+	5.95522i	0.136228	+	0.235954i
$638$		0			0
$639$	14.0127	−	7.25000i	0.554333	−	0.286805i
$640$		0			0
$641$	−1.74579	−	3.02380i	−0.0689546	−	0.119433i	0.829487	−	0.558526i	$-0.188633\pi$
$641$	−1.74579	−	3.02380i	−0.0689546	−	0.119433i	−0.898441	+	0.439094i	$0.855300\pi$
$642$		0			0
$643$	17.5279	−	30.3592i	0.691233	−	1.19725i	−0.280202	−	0.959941i	$-0.590401\pi$
$643$	17.5279	−	30.3592i	0.691233	−	1.19725i	0.971434	−	0.237309i	$-0.0762654\pi$
$644$		0			0
$645$	−14.6450	−	60.1756i	−0.576648	−	2.36941i
$646$		0			0
$647$	44.6001			1.75341			0.876705	−	0.481028i	$-0.159736\pi$
$647$	44.6001			1.75341			0.876705	+	0.481028i	$0.159736\pi$
$648$		0			0
$649$	−3.09963			−0.121671
$650$		0			0
$651$	−0.112570	−	0.462543i	−0.00441196	−	0.0181285i
$652$		0			0
$653$	5.89687	−	10.2137i	0.230762	−	0.399692i	−0.727270	−	0.686351i	$-0.759211\pi$
$653$	5.89687	−	10.2137i	0.230762	−	0.399692i	0.958033	+	0.286659i	$0.0925447\pi$
$654$		0			0
$655$	−25.5594	−	44.2702i	−0.998689	−	1.72978i
$656$		0			0
$657$	−18.9026	+	9.78001i	−0.737462	+	0.381554i
$658$		0			0
$659$	9.08369	+	15.7334i	0.353850	+	0.612887i	0.986920	−	0.161208i	$-0.0515389\pi$
$659$	9.08369	+	15.7334i	0.353850	+	0.612887i	−0.633070	+	0.774094i	$0.718206\pi$
$660$		0			0
$661$	−2.10078	+	3.63866i	−0.0817108	+	0.141527i	−0.903985	−	0.427564i	$-0.859372\pi$
$661$	−2.10078	+	3.63866i	−0.0817108	+	0.141527i	0.822274	+	0.569092i	$0.192705\pi$
$662$		0			0
$663$	−6.45718	−	1.89087i	−0.250776	−	0.0734353i
$664$		0			0
$665$	5.87210			0.227710
$666$		0			0
$667$	20.7533			0.803571
$668$		0			0
$669$	32.2190	−	30.7658i	1.24566	−	1.18947i
$670$		0			0
$671$	23.7588	−	41.1514i	0.917196	−	1.58863i
$672$		0			0
$673$	22.2315	+	38.5061i	0.856961	+	1.48430i	0.874814	+	0.484459i	$0.160983\pi$
$673$	22.2315	+	38.5061i	0.856961	+	1.48430i	−0.0178535	+	0.999841i	$0.505683\pi$
$674$		0			0
$675$	−15.2749	+	44.4491i	−0.587931	+	1.71085i
$676$		0			0
$677$	−3.74338	−	6.48372i	−0.143870	−	0.249189i	0.785081	−	0.619393i	$-0.212621\pi$
$677$	−3.74338	−	6.48372i	−0.143870	−	0.249189i	−0.928951	+	0.370204i	$0.879288\pi$
$678$		0			0
$679$	−0.299877	+	0.519402i	−0.0115082	+	0.0199328i
$680$		0			0
$681$	28.0001	−	26.7371i	1.07297	−	1.02457i
$682$		0			0
$683$	38.6166			1.47762			0.738811	−	0.673912i	$-0.235387\pi$
$683$	38.6166			1.47762			0.738811	+	0.673912i	$0.235387\pi$
$684$		0			0
$685$	−23.3678			−0.892839
$686$		0			0
$687$	−8.04603	−	2.35614i	−0.306975	−	0.0898923i
$688$		0			0
$689$	1.48878	−	2.57864i	0.0567179	−	0.0982382i
$690$		0			0
$691$	−10.2047	−	17.6751i	−0.388206	−	0.672393i	0.604002	−	0.796983i	$-0.293572\pi$
$691$	−10.2047	−	17.6751i	−0.388206	−	0.672393i	−0.992208	+	0.124590i	$0.960239\pi$
$692$		0			0
$693$	0.160236	−	3.47054i	0.00608686	−	0.131835i
$694$		0			0
$695$	−3.13303	−	5.42657i	−0.118843	−	0.205842i
$696$		0			0
$697$	13.2905	−	23.0199i	0.503414	−	0.871939i
$698$		0			0
$699$	10.2738	+	42.2146i	0.388592	+	1.59670i
$700$		0			0
$701$	−19.9987			−0.755341			−0.377670	−	0.925940i	$-0.623275\pi$
$701$	−19.9987			−0.755341			−0.377670	+	0.925940i	$0.623275\pi$
$702$		0			0
$703$	50.9701			1.92237
$704$		0			0
$705$	−3.17144	−	13.0313i	−0.119443	−	0.490786i
$706$		0			0
$707$	−0.461913	+	0.800057i	−0.0173720	+	0.0300892i
$708$		0			0
$709$	6.60484	+	11.4399i	0.248050	+	0.429635i	0.962985	−	0.269556i	$-0.0868769\pi$
$709$	6.60484	+	11.4399i	0.248050	+	0.429635i	−0.714935	+	0.699191i	$0.753544\pi$
$710$		0			0
$711$	−35.9054	−	23.0009i	−1.34656	−	0.862600i
$712$		0			0
$713$	1.82554	+	3.16192i	0.0683669	+	0.118415i
$714$		0			0
$715$	6.17491	−	10.6953i	0.230928	−	0.399980i
$716$		0			0
$717$	−40.9219	−	11.9833i	−1.52826	−	0.447523i
$718$		0			0
$719$	−36.4662			−1.35996			−0.679979	−	0.733231i	$-0.738011\pi$
$719$	−36.4662			−1.35996			−0.679979	+	0.733231i	$0.738011\pi$
$720$		0			0
$721$	−4.76696			−0.177531
$722$		0			0
$723$	−25.2812	+	24.1409i	−0.940219	+	0.897811i
$724$		0			0
$725$	20.1048	−	34.8226i	0.746675	−	1.29328i
$726$		0			0
$727$	−20.5827	−	35.6503i	−0.763371	−	1.32220i	−0.941103	−	0.338119i	$-0.890209\pi$
$727$	−20.5827	−	35.6503i	−0.763371	−	1.32220i	0.177732	−	0.984079i	$-0.443124\pi$
$728$		0			0
$729$	−3.72521	+	26.7418i	−0.137971	+	0.990436i
$730$		0			0
$731$	18.5314	+	32.0972i	0.685407	+	1.18716i
$732$		0			0
$733$	14.7514	−	25.5503i	0.544857	−	0.943720i	−0.453759	−	0.891125i	$-0.649917\pi$
$733$	14.7514	−	25.5503i	0.544857	−	0.943720i	0.998616	−	0.0525958i	$-0.0167495\pi$
$734$		0			0
$735$	−32.2826	+	30.8265i	−1.19076	+	1.13705i
$736$		0			0
$737$	−14.0214			−0.516486
$738$		0			0
$739$	44.3622			1.63189			0.815945	−	0.578129i	$-0.196217\pi$
$739$	44.3622			1.63189			0.815945	+	0.578129i	$0.196217\pi$
$740$		0			0
$741$	7.41107	+	2.17020i	0.272253	+	0.0797244i
$742$		0			0
$743$	5.07949	−	8.79794i	0.186349	−	0.322765i	−0.757682	−	0.652624i	$-0.773668\pi$
$743$	5.07949	−	8.79794i	0.186349	−	0.322765i	0.944030	+	0.329859i	$0.107001\pi$
$744$		0			0
$745$	−31.0864	−	53.8432i	−1.13892	−	1.97266i
$746$		0			0
$747$	−31.7139	−	20.3158i	−1.16035	−	0.743317i
$748$		0			0
$749$	0.629449	+	1.09024i	0.0229996	+	0.0398364i
$750$		0			0
$751$	−3.81481	+	6.60744i	−0.139204	+	0.241109i	−0.927196	−	0.374577i	$-0.877788\pi$
$751$	−3.81481	+	6.60744i	−0.139204	+	0.241109i	0.787991	+	0.615686i	$0.211121\pi$
$752$		0			0
$753$	10.7767	+	44.2808i	0.392724	+	1.61368i
$754$		0			0
$755$	−58.4637			−2.12771
$756$		0			0
$757$	49.6248			1.80364			0.901822	−	0.432107i	$-0.142230\pi$
$757$	49.6248			1.80364			0.901822	+	0.432107i	$0.142230\pi$
$758$		0			0
$759$	6.30099	+	25.8904i	0.228711	+	0.939762i
$760$		0			0
$761$	9.85989	−	17.0778i	0.357421	−	0.619071i	−0.630108	−	0.776507i	$-0.716990\pi$
$761$	9.85989	−	17.0778i	0.357421	−	0.619071i	0.987529	+	0.157436i	$0.0503229\pi$
$762$		0			0
$763$	1.95165	+	3.38035i	0.0706543	+	0.122377i
$764$		0			0
$765$	2.01434	−	43.6285i	0.0728286	−	1.57739i
$766$		0			0
$767$	−0.470310	−	0.814600i	−0.0169819	−	0.0294135i
$768$		0			0
$769$	25.6736	−	44.4679i	0.925812	−	1.60355i	0.135563	−	0.990769i	$-0.456716\pi$
$769$	25.6736	−	44.4679i	0.925812	−	1.60355i	0.790250	−	0.612785i	$-0.209951\pi$
$770$		0			0
$771$	15.0303	+	4.40137i	0.541305	+	0.158512i
$772$		0			0
$773$	−1.28424			−0.0461910			−0.0230955	−	0.999733i	$-0.507352\pi$
$773$	−1.28424			−0.0461910			−0.0230955	+	0.999733i	$0.507352\pi$
$774$		0			0
$775$	7.07399			0.254105
$776$		0			0
$777$	5.03280	−	4.80579i	0.180551	−	0.172407i
$778$		0			0
$779$	−15.2539	+	26.4205i	−0.546527	+	0.946613i
$780$		0			0
$781$	−8.66507	−	15.0083i	−0.310061	−	0.537041i
$782$		0			0
$783$	7.50701	−	21.8450i	0.268279	−	0.780677i
$784$		0			0
$785$	30.6431	+	53.0753i	1.09370	+	1.89434i
$786$		0			0
$787$	0.0130933	−	0.0226783i	0.000466726	−	0.000808392i	−0.865792	−	0.500404i	$-0.833185\pi$
$787$	0.0130933	−	0.0226783i	0.000466726	−	0.000808392i	0.866259	+	0.499596i	$0.166518\pi$
$788$		0			0
$789$	−2.38761	+	2.27992i	−0.0850011	+	0.0811671i
$790$		0			0
$791$	−0.726395			−0.0258276
$792$		0			0
$793$	14.4198			0.512061
$794$		0			0
$795$	18.5490	+	5.43174i	0.657864	+	0.192644i
$796$		0			0
$797$	7.48668	−	12.9673i	0.265192	−	0.459326i	−0.702422	−	0.711761i	$-0.747898\pi$
$797$	7.48668	−	12.9673i	0.265192	−	0.459326i	0.967614	+	0.252435i	$0.0812314\pi$
$798$		0			0
$799$	4.01304	+	6.95078i	0.141971	+	0.245901i
$800$		0			0
$801$	14.8214	−	7.66843i	0.523689	−	0.270951i
$802$		0			0
$803$	11.6889	+	20.2458i	0.412492	+	0.714458i
$804$		0			0
$805$	−3.07436	+	5.32496i	−0.108357	+	0.187680i
$806$		0			0
$807$	5.54129	+	22.7688i	0.195063	+	0.801501i
$808$		0			0
$809$	41.1952			1.44834			0.724172	−	0.689619i	$-0.242222\pi$
$809$	41.1952			1.44834			0.724172	+	0.689619i	$0.242222\pi$
$810$		0			0
$811$	−49.0285			−1.72162			−0.860811	−	0.508924i	$-0.830043\pi$
$811$	−49.0285			−1.72162			−0.860811	+	0.508924i	$0.830043\pi$
$812$		0			0
$813$	3.54740	+	14.5761i	0.124413	+	0.511205i
$814$		0			0
$815$	−10.5074	+	18.1994i	−0.368059	+	0.637497i
$816$		0			0
$817$	−21.2689	−	36.8389i	−0.744106	−	1.28883i
$818$		0			0
$819$	0.936392	−	0.484478i	0.0327202	−	0.0169290i
$820$		0			0
$821$	4.88998	+	8.46969i	0.170661	+	0.295594i	0.938651	−	0.344868i	$-0.112076\pi$
$821$	4.88998	+	8.46969i	0.170661	+	0.295594i	−0.767990	+	0.640462i	$0.778743\pi$
$822$		0			0
$823$	17.6004	−	30.4848i	0.613512	−	1.06263i	−0.377132	−	0.926159i	$-0.623090\pi$
$823$	17.6004	−	30.4848i	0.613512	−	1.06263i	0.990644	−	0.136474i	$-0.0435769\pi$
$824$		0			0
$825$	49.5464	+	14.5088i	1.72498	+	0.505131i
$826$		0			0
$827$	−4.45020			−0.154749			−0.0773743	−	0.997002i	$-0.524654\pi$
$827$	−4.45020			−0.154749			−0.0773743	+	0.997002i	$0.524654\pi$
$828$		0			0
$829$	31.8398			1.10584			0.552921	−	0.833234i	$-0.313513\pi$
$829$	31.8398			1.10584			0.552921	+	0.833234i	$0.313513\pi$
$830$		0			0
$831$	31.9308	−	30.4906i	1.10767	−	1.05771i
$832$		0			0
$833$	13.3562	−	23.1337i	0.462766	−	0.801535i
$834$		0			0
$835$	8.86120	+	15.3480i	0.306654	+	0.531141i
$836$		0			0
$837$	3.98860	−	0.777818i	0.137866	−	0.0268853i
$838$		0			0
$839$	27.0849	+	46.9125i	0.935076	+	1.61960i	0.774499	+	0.632576i	$0.218002\pi$
$839$	27.0849	+	46.9125i	0.935076	+	1.61960i	0.160577	+	0.987023i	$0.448664\pi$
$840$		0			0
$841$	4.61926	−	8.00079i	0.159285	−	0.275889i
$842$		0			0
$843$	−28.4598	+	27.1761i	−0.980206	+	0.935994i
$844$		0			0
$845$	3.74770			0.128925
$846$		0			0
$847$	0.0495398			0.00170221
$848$		0			0
$849$	−1.34852	−	0.394889i	−0.0462810	−	0.0135526i
$850$		0			0
$851$	−26.6856	+	46.2208i	−0.914771	+	1.58443i
$852$		0			0
$853$	20.3524	+	35.2514i	0.696853	+	1.20699i	0.969552	+	0.244886i	$0.0787504\pi$
$853$	20.3524	+	35.2514i	0.696853	+	1.20699i	−0.272699	+	0.962099i	$0.587916\pi$
$854$		0			0
$855$	−2.31191	+	50.0736i	−0.0790657	+	1.71248i
$856$		0			0
$857$	−1.30175	−	2.25470i	−0.0444669	−	0.0770189i	0.842935	−	0.538015i	$-0.180826\pi$
$857$	−1.30175	−	2.25470i	−0.0444669	−	0.0770189i	−0.887402	+	0.460996i	$0.847492\pi$
$858$		0			0
$859$	8.22618	−	14.2482i	0.280674	−	0.486141i	−0.690877	−	0.722972i	$-0.742776\pi$
$859$	8.22618	−	14.2482i	0.280674	−	0.486141i	0.971551	+	0.236831i	$0.0761088\pi$
$860$		0			0
$861$	0.984926	+	4.04700i	0.0335662	+	0.137921i
$862$		0			0
$863$	18.2597			0.621566			0.310783	−	0.950481i	$-0.399409\pi$
$863$	18.2597			0.621566			0.310783	+	0.950481i	$0.399409\pi$
$864$		0			0
$865$	−62.9423			−2.14010
$866$		0			0
$867$	−0.782224	−	3.21411i	−0.0265657	−	0.109157i
$868$		0			0
$869$	−23.4191	+	40.5630i	−0.794437	+	1.37601i
$870$		0			0
$871$	−2.12749	−	3.68491i	−0.0720871	−	0.124859i
$872$		0			0
$873$	−4.31107	−	2.76166i	−0.145908	−	0.0934680i
$874$		0			0
$875$	2.66394	+	4.61407i	0.0900575	+	0.155984i
$876$		0			0
$877$	21.3370	−	36.9567i	0.720498	−	1.24794i	−0.240302	−	0.970698i	$-0.577246\pi$
$877$	21.3370	−	36.9567i	0.720498	−	1.24794i	0.960800	−	0.277242i	$-0.0894203\pi$
$878$		0			0
$879$	−27.3590	−	8.01162i	−0.922798	−	0.270225i
$880$		0			0
$881$	26.5618			0.894890			0.447445	−	0.894311i	$-0.352334\pi$
$881$	26.5618			0.894890			0.447445	+	0.894311i	$0.352334\pi$
$882$		0			0
$883$	47.3009			1.59180			0.795900	−	0.605428i	$-0.206998\pi$
$883$	47.3009			1.59180			0.795900	+	0.605428i	$0.206998\pi$
$884$		0			0
$885$	4.41586	−	4.21668i	0.148437	−	0.141742i
$886$		0			0
$887$	21.3381	−	36.9587i	0.716464	−	1.24095i	−0.245928	−	0.969288i	$-0.579093\pi$
$887$	21.3381	−	36.9587i	0.716464	−	1.24095i	0.962392	−	0.271664i	$-0.0875738\pi$
$888$		0			0
$889$	−2.64933	−	4.58877i	−0.0888556	−	0.153902i
$890$		0			0
$891$	29.5316	+	2.73278i	0.989345	+	0.0915517i
$892$		0			0
$893$	−4.60587	−	7.97760i	−0.154130	−	0.266960i
$894$		0			0
$895$	−22.0886	+	38.2585i	−0.738340	+	1.27884i
$896$		0			0
$897$	−5.84809	+	5.58431i	−0.195262	+	0.186455i
$898$		0			0
$899$	−3.47659			−0.115951
$900$		0			0
$901$	−11.5666			−0.385340
$902$		0			0
$903$	−5.57351	−	1.63210i	−0.185475	−	0.0543130i
$904$		0			0
$905$	48.8945	−	84.6878i	1.62531	−	2.81512i
$906$		0			0
$907$	20.1924	+	34.9742i	0.670477	+	1.16130i	0.977769	+	0.209685i	$0.0672438\pi$
$907$	20.1924	+	34.9742i	0.670477	+	1.16130i	−0.307292	+	0.951615i	$0.599423\pi$
$908$		0			0
$909$	−6.64053	−	4.25390i	−0.220252	−	0.141093i
$910$		0			0
$911$	26.6453	+	46.1511i	0.882799	+	1.52905i	0.848215	+	0.529651i	$0.177677\pi$
$911$	26.6453	+	46.1511i	0.882799	+	1.52905i	0.0345838	+	0.999402i	$0.488989\pi$
$912$		0			0
$913$	−20.6852	+	35.8278i	−0.684580	+	1.18573i
$914$		0			0
$915$	22.1339	+	90.9470i	0.731725	+	3.00661i
$916$		0			0
$917$	−4.79357			−0.158298
$918$		0			0
$919$	−5.72441			−0.188831			−0.0944155	−	0.995533i	$-0.530098\pi$
$919$	−5.72441			−0.188831			−0.0944155	+	0.995533i	$0.530098\pi$
$920$		0			0
$921$	−0.662203	−	2.72095i	−0.0218203	−	0.0896584i
$922$		0			0
$923$	2.62952	−	4.55446i	0.0865517	−	0.149912i
$924$		0			0
$925$	51.7036	+	89.5532i	1.70000	+	2.94449i
$926$		0			0
$927$	1.87681	−	40.6497i	0.0616424	−	1.33511i
$928$		0			0
$929$	−2.36266	−	4.09225i	−0.0775165	−	0.134262i	0.824661	−	0.565627i	$-0.191366\pi$
$929$	−2.36266	−	4.09225i	−0.0775165	−	0.134262i	−0.902178	+	0.431364i	$0.858032\pi$
$930$		0			0
$931$	−15.3293	+	26.5511i	−0.502398	+	0.870179i
$932$		0			0
$933$	−49.4901	−	14.4923i	−1.62023	−	0.474457i
$934$		0			0
$935$	−47.9742			−1.56892
$936$		0			0
$937$	−1.19269			−0.0389635			−0.0194818	−	0.999810i	$-0.506202\pi$
$937$	−1.19269			−0.0389635			−0.0194818	+	0.999810i	$0.506202\pi$
$938$		0			0
$939$	2.52074	−	2.40704i	0.0822612	−	0.0785508i
$940$		0			0
$941$	−21.2736	+	36.8470i	−0.693500	+	1.20118i	0.277184	+	0.960817i	$0.410599\pi$
$941$	−21.2736	+	36.8470i	−0.693500	+	1.20118i	−0.970684	+	0.240360i	$0.922734\pi$
$942$		0			0
$943$	−15.9725	−	27.6651i	−0.520135	−	0.900901i
$944$		0			0
$945$	4.49299	+	5.16227i	0.146157	+	0.167929i
$946$		0			0
$947$	9.57469	+	16.5839i	0.311136	+	0.538903i	0.978609	−	0.205731i	$-0.0659573\pi$
$947$	9.57469	+	16.5839i	0.311136	+	0.538903i	−0.667473	+	0.744634i	$0.732624\pi$
$948$		0			0
$949$	−3.54714	+	6.14382i	−0.115145	+	0.199437i
$950$		0			0
$951$	16.3262	−	15.5898i	0.529413	−	0.505533i
$952$		0			0
$953$	42.6090			1.38024			0.690120	−	0.723695i	$-0.257558\pi$
$953$	42.6090			1.38024			0.690120	+	0.723695i	$0.257558\pi$
$954$		0			0
$955$	−59.3604			−1.92086
$956$		0			0
$957$	−24.3501	−	7.13050i	−0.787127	−	0.230496i
$958$		0			0
$959$	−1.09564	+	1.89770i	−0.0353800	+	0.0612799i
$960$		0			0
$961$	15.1942	+	26.3171i	0.490135	+	0.848939i
$962$		0			0
$963$	−9.54469	+	4.93831i	−0.307573	+	0.159135i
$964$		0			0
$965$	−20.7518	−	35.9432i	−0.668025	−	1.15705i
$966$		0			0
$967$	11.2242	−	19.4409i	0.360947	−	0.625178i	−0.627170	−	0.778882i	$-0.715787\pi$
$967$	11.2242	−	19.4409i	0.360947	−	0.625178i	0.988117	+	0.153704i	$0.0491203\pi$
$968$		0			0
$969$	−7.09362	−	29.1473i	−0.227880	−	0.936345i
$970$		0			0
$971$	36.1977			1.16164			0.580820	−	0.814032i	$-0.302732\pi$
$971$	36.1977			1.16164			0.580820	+	0.814032i	$0.302732\pi$
$972$		0			0
$973$	−0.587588			−0.0188372
$974$		0			0
$975$	3.70473	+	15.2225i	0.118646	+	0.487511i
$976$		0			0
$977$	2.56406	−	4.44108i	0.0820316	−	0.142083i	−0.822091	−	0.569356i	$-0.807193\pi$
$977$	2.56406	−	4.44108i	0.0820316	−	0.142083i	0.904122	+	0.427273i	$0.140526\pi$
$978$		0			0
$979$	−9.16517	−	15.8745i	−0.292920	−	0.507353i
$980$		0			0
$981$	−29.5939	+	15.3115i	−0.944861	+	0.488860i
$982$		0			0
$983$	12.7722	+	22.1221i	0.407369	+	0.705584i	0.994594	−	0.103840i	$-0.0331129\pi$
$983$	12.7722	+	22.1221i	0.407369	+	0.705584i	−0.587225	+	0.809424i	$0.699780\pi$
$984$		0			0
$985$	−15.6772	+	27.1536i	−0.499516	+	0.865187i
$986$		0			0
$987$	−1.20697	−	0.353439i	−0.0384181	−	0.0112501i
$988$		0			0
$989$	44.5418			1.41635
$990$		0			0
$991$	−6.62586			−0.210477			−0.105239	−	0.994447i	$-0.533561\pi$
$991$	−6.62586			−0.210477			−0.105239	+	0.994447i	$0.533561\pi$
$992$		0			0
$993$	3.03348	−	2.89666i	0.0962647	−	0.0919227i
$994$		0			0
$995$	−4.93490	+	8.54749i	−0.156447	+	0.270974i
$996$		0			0
$997$	9.46041	+	16.3859i	0.299614	+	0.518947i	0.976048	−	0.217557i	$-0.0698088\pi$
$997$	9.46041	+	16.3859i	0.299614	+	0.518947i	−0.676434	+	0.736504i	$0.736475\pi$
$998$		0			0
$999$	38.9994	+	44.8087i	1.23389	+	1.41768i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.q.d.625.5	yes	12
3.2	odd	2		2808.2.q.d.1873.6		12
9.2	odd	6		2808.2.q.d.937.6		12
9.4	even	3		8424.2.a.v.1.6		6
9.5	odd	6		8424.2.a.u.1.1		6
9.7	even	3	inner	936.2.q.d.313.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.q.d.313.5	✓	12	9.7	even	3	inner
936.2.q.d.625.5	yes	12	1.1	even	1	trivial
2808.2.q.d.937.6		12	9.2	odd	6
2808.2.q.d.1873.6		12	3.2	odd	2
8424.2.a.u.1.1		6	9.5	odd	6
8424.2.a.v.1.6		6	9.4	even	3

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.409577 + 1.68293i) q^{3} +(-1.87385 + 3.24560i) q^{5} +(0.175717 + 0.304350i) q^{7} +(-2.66449 + 1.37858i) q^{9} +(1.64765 + 2.85382i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(-6.22960 - 1.82423i) q^{15} +3.88461 q^{17} -4.45847 q^{19} +(-0.440230 + 0.420374i) q^{21} +(2.33425 - 4.04304i) q^{23} +(-4.52263 - 7.83342i) q^{25} +(-3.41136 - 3.91952i) q^{27} +(2.22269 + 3.84982i) q^{29} +(-0.391033 + 0.677289i) q^{31} +(-4.12793 + 3.94174i) q^{33} -1.31707 q^{35} -11.4322 q^{37} +(-1.66225 - 0.486760i) q^{39} +(3.42133 - 5.92592i) q^{41} +(4.77046 + 8.26268i) q^{43} +(0.518544 - 11.2311i) q^{45} +(1.03306 + 1.78931i) q^{47} +(3.43825 - 5.95522i) q^{49} +(1.59105 + 6.53751i) q^{51} -2.97755 q^{53} -12.3498 q^{55} +(-1.82609 - 7.50328i) q^{57} +(-0.470310 + 0.814600i) q^{59} +(-7.20988 - 12.4879i) q^{61} +(-0.887767 - 0.568700i) q^{63} +(-1.87385 - 3.24560i) q^{65} +(-2.12749 + 3.68491i) q^{67} +(7.76020 + 2.27244i) q^{69} -5.25904 q^{71} +7.09427 q^{73} +(11.3307 - 10.8196i) q^{75} +(-0.579040 + 1.00293i) q^{77} +(7.10680 + 12.3093i) q^{79} +(5.19905 - 7.34642i) q^{81} +(6.27717 + 10.8724i) q^{83} +(-7.27917 + 12.6079i) q^{85} +(-5.56861 + 5.31743i) q^{87} -5.56256 q^{89} -0.351433 q^{91} +(-1.29999 - 0.380678i) q^{93} +(8.35450 - 14.4704i) q^{95} +(0.853296 + 1.47795i) q^{97} +(-8.32437 - 5.33256i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} - q^{5} + 2 q^{7} + 2 q^{9} - q^{11} - 6 q^{13} - 2 q^{15} + 12 q^{17} - 14 q^{19} - 24 q^{21} + 19 q^{23} + 5 q^{25} - 7 q^{27} - 2 q^{29} + 8 q^{31} - 9 q^{33} + 2 q^{35} - 34 q^{37}+ \cdots - 39 q^{99}+O(q^{100}) \) 12 * q - 4 * q^3 - q^5 + 2 * q^7 + 2 * q^9 - q^11 - 6 * q^13 - 2 * q^15 + 12 * q^17 - 14 * q^19 - 24 * q^21 + 19 * q^23 + 5 * q^25 - 7 * q^27 - 2 * q^29 + 8 * q^31 - 9 * q^33 + 2 * q^35 - 34 * q^37 - q^39 - 2 * q^41 + 15 * q^43 + 10 * q^45 - 9 * q^47 + 12 * q^49 + 4 * q^51 + 32 * q^53 - 10 * q^55 - 14 * q^57 + 5 * q^59 + 6 * q^61 + 18 * q^63 - q^65 + 8 * q^67 + 15 * q^69 - 42 * q^71 - 2 * q^73 + 10 * q^75 + 3 * q^77 + 34 * q^79 + 62 * q^81 + 44 * q^83 + 7 * q^85 - 21 * q^87 + 22 * q^89 - 4 * q^91 - 18 * q^93 + 6 * q^95 + 12 * q^97 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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