LMFDB - Embedded newform 1512.2.j.c.323.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.10
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.c.323.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.985454 + 1.01434i) q^{2} +(-0.0577616 - 1.99917i) q^{4} +0.206991 q^{5} +1.00000i q^{7} +(2.08475 + 1.91150i) q^{8} +O(q^{10})$	\(q+(-0.985454 + 1.01434i) q^{2} +(-0.0577616 - 1.99917i) q^{4} +0.206991 q^{5} +1.00000i q^{7} +(2.08475 + 1.91150i) q^{8} +(-0.203980 + 0.209959i) q^{10} -6.42190i q^{11} +3.52336i q^{13} +(-1.01434 - 0.985454i) q^{14} +(-3.99333 + 0.230950i) q^{16} -3.90616i q^{17} -5.48691 q^{19} +(-0.0119562 - 0.413810i) q^{20} +(6.51397 + 6.32848i) q^{22} -0.880512 q^{23} -4.95715 q^{25} +(-3.57387 - 3.47211i) q^{26} +(1.99917 - 0.0577616i) q^{28} -3.20814 q^{29} +0.0631261i q^{31} +(3.70098 - 4.27817i) q^{32} +(3.96217 + 3.84934i) q^{34} +0.206991i q^{35} +9.91837i q^{37} +(5.40710 - 5.56558i) q^{38} +(0.431525 + 0.395663i) q^{40} +5.94221i q^{41} -1.13960 q^{43} +(-12.8384 + 0.370939i) q^{44} +(0.867704 - 0.893136i) q^{46} +6.81266 q^{47} -1.00000 q^{49} +(4.88505 - 5.02823i) q^{50} +(7.04378 - 0.203515i) q^{52} -12.6324 q^{53} -1.32928i q^{55} +(-1.91150 + 2.08475i) q^{56} +(3.16147 - 3.25414i) q^{58} +4.23338i q^{59} -12.3006i q^{61} +(-0.0640312 - 0.0622079i) q^{62} +(0.692368 + 7.96998i) q^{64} +0.729305i q^{65} -5.74666 q^{67} +(-7.80906 + 0.225626i) q^{68} +(-0.209959 - 0.203980i) q^{70} -10.1795 q^{71} +8.27618 q^{73} +(-10.0606 - 9.77409i) q^{74} +(0.316933 + 10.9692i) q^{76} +6.42190 q^{77} -4.86426i q^{79} +(-0.826584 + 0.0478047i) q^{80} +(-6.02741 - 5.85577i) q^{82} -7.51539i q^{83} -0.808542i q^{85} +(1.12302 - 1.15594i) q^{86} +(12.2754 - 13.3881i) q^{88} -4.44682i q^{89} -3.52336 q^{91} +(0.0508598 + 1.76029i) q^{92} +(-6.71356 + 6.91034i) q^{94} -1.13574 q^{95} -17.3929 q^{97} +(0.985454 - 1.01434i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) $ 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−0.985454	+	1.01434i	−0.696821	+	0.717245i
$2$	−0.985454	+	1.01434i	−0.696821	+	0.717245i
$3$		0			0
$3$		0			0
$4$	−0.0577616	−	1.99917i	−0.0288808	−	0.999583i
$5$	0.206991			0.0925694			0.0462847	−	0.998928i	$-0.485262\pi$
$5$	0.206991			0.0925694			0.0462847	+	0.998928i	$0.485262\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.08475	+	1.91150i	0.737071	+	0.675816i
$9$		0			0
$10$	−0.203980	+	0.209959i	−0.0645043	+	0.0663949i
$11$		−	6.42190i		−	1.93628i	−0.250418	−	0.968138i	$-0.580568\pi$
$11$		−	6.42190i		−	1.93628i	0.250418	−	0.968138i	$-0.419432\pi$
$12$		0			0
$13$			3.52336i			0.977204i	0.872507	+	0.488602i	$0.162493\pi$
$13$			3.52336i			0.977204i	−0.872507	+	0.488602i	$0.837507\pi$
$14$	−1.01434	−	0.985454i	−0.271093	−	0.263374i
$15$		0			0
$16$	−3.99333	+	0.230950i	−0.998332	+	0.0577375i
$17$		−	3.90616i		−	0.947383i	−0.880691	−	0.473692i	$-0.842921\pi$
$17$		−	3.90616i		−	0.947383i	0.880691	−	0.473692i	$-0.157079\pi$
$18$		0			0
$19$	−5.48691			−1.25878			−0.629392	−	0.777088i	$-0.716696\pi$
$19$	−5.48691			−1.25878			−0.629392	+	0.777088i	$0.716696\pi$
$20$	−0.0119562	−	0.413810i	−0.00267348	−	0.0925307i
$21$		0			0
$22$	6.51397	+	6.32848i	1.38878	+	1.34924i
$23$	−0.880512			−0.183599			−0.0917997	−	0.995777i	$-0.529262\pi$
$23$	−0.880512			−0.183599			−0.0917997	+	0.995777i	$0.529262\pi$
$24$		0			0
$25$	−4.95715			−0.991431
$26$	−3.57387	−	3.47211i	−0.700894	−	0.680936i
$27$		0			0
$28$	1.99917	−	0.0577616i	0.377807	−	0.0109159i
$29$	−3.20814			−0.595737			−0.297868	−	0.954607i	$-0.596276\pi$
$29$	−3.20814			−0.595737			−0.297868	+	0.954607i	$0.596276\pi$
$30$		0			0
$31$			0.0631261i			0.0113378i	0.999984	+	0.00566890i	$0.00180448\pi$
$31$			0.0631261i			0.0113378i	−0.999984	+	0.00566890i	$0.998196\pi$
$32$	3.70098	−	4.27817i	0.654247	−	0.756281i
$33$		0			0
$34$	3.96217	+	3.84934i	0.679506	+	0.660157i
$35$			0.206991i			0.0349879i
$36$		0			0
$37$			9.91837i			1.63057i	0.579060	+	0.815285i	$0.303420\pi$
$37$			9.91837i			1.63057i	−0.579060	+	0.815285i	$0.696580\pi$
$38$	5.40710	−	5.56558i	0.877147	−	0.902856i
$39$		0			0
$40$	0.431525	+	0.395663i	0.0682302	+	0.0625598i
$41$			5.94221i			0.928017i	0.885831	+	0.464009i	$0.153589\pi$
$41$			5.94221i			0.928017i	−0.885831	+	0.464009i	$0.846411\pi$
$42$		0			0
$43$	−1.13960			−0.173788			−0.0868938	−	0.996218i	$-0.527694\pi$
$43$	−1.13960			−0.173788			−0.0868938	+	0.996218i	$0.527694\pi$
$44$	−12.8384	+	0.370939i	−1.93547	+	0.0559212i
$45$		0			0
$46$	0.867704	−	0.893136i	0.127936	−	0.131686i
$47$	6.81266			0.993729			0.496864	−	0.867828i	$-0.334485\pi$
$47$	6.81266			0.993729			0.496864	+	0.867828i	$0.334485\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	4.88505	−	5.02823i	0.690850	−	0.711099i
$51$		0			0
$52$	7.04378	−	0.203515i	0.976796	−	0.0282224i
$53$	−12.6324			−1.73520			−0.867598	−	0.497265i	$-0.834338\pi$
$53$	−12.6324			−1.73520			−0.867598	+	0.497265i	$0.834338\pi$
$54$		0			0
$55$		−	1.32928i		−	0.179240i
$56$	−1.91150	+	2.08475i	−0.255434	+	0.278586i
$57$		0			0
$58$	3.16147	−	3.25414i	0.415122	−	0.427289i
$59$			4.23338i			0.551139i	0.961281	+	0.275570i	$0.0888664\pi$
$59$			4.23338i			0.551139i	−0.961281	+	0.275570i	$0.911134\pi$
$60$		0			0
$61$		−	12.3006i		−	1.57493i	−0.616359	−	0.787465i	$-0.711393\pi$
$61$		−	12.3006i		−	1.57493i	0.616359	−	0.787465i	$-0.288607\pi$
$62$	−0.0640312	−	0.0622079i	−0.00813197	−	0.00790041i
$63$		0			0
$64$	0.692368	+	7.96998i	0.0865460	+	0.996248i
$65$			0.729305i			0.0904591i
$66$		0			0
$67$	−5.74666			−0.702067			−0.351033	−	0.936363i	$-0.614170\pi$
$67$	−5.74666			−0.702067			−0.351033	+	0.936363i	$0.614170\pi$
$68$	−7.80906	+	0.225626i	−0.946988	+	0.0273612i
$69$		0			0
$70$	−0.209959	−	0.203980i	−0.0250949	−	0.0243803i
$71$	−10.1795			−1.20809			−0.604043	−	0.796952i	$-0.706444\pi$
$71$	−10.1795			−1.20809			−0.604043	+	0.796952i	$0.706444\pi$
$72$		0			0
$73$	8.27618			0.968653			0.484327	−	0.874887i	$-0.339065\pi$
$73$	8.27618			0.968653			0.484327	+	0.874887i	$0.339065\pi$
$74$	−10.0606	−	9.77409i	−1.16952	−	1.13622i
$75$		0			0
$76$	0.316933	+	10.9692i	0.0363547	+	1.25826i
$77$	6.42190			0.731843
$78$		0			0
$79$		−	4.86426i		−	0.547272i	−0.961833	−	0.273636i	$-0.911774\pi$
$79$		−	4.86426i		−	0.547272i	0.961833	−	0.273636i	$-0.0882264\pi$
$80$	−0.826584	+	0.0478047i	−0.0924149	+	0.00534472i
$81$		0			0
$82$	−6.02741	−	5.85577i	−0.665616	−	0.646662i
$83$		−	7.51539i		−	0.824921i	−0.910976	−	0.412460i	$-0.864669\pi$
$83$		−	7.51539i		−	0.824921i	0.910976	−	0.412460i	$-0.135331\pi$
$84$		0			0
$85$		−	0.808542i		−	0.0876987i
$86$	1.12302	−	1.15594i	0.121099	−	0.124648i
$87$		0			0
$88$	12.2754	−	13.3881i	1.30857	−	1.42717i
$89$		−	4.44682i		−	0.471362i	−0.971830	−	0.235681i	$-0.924268\pi$
$89$		−	4.44682i		−	0.471362i	0.971830	−	0.235681i	$-0.0757320\pi$
$90$		0			0
$91$	−3.52336			−0.369348
$92$	0.0508598	+	1.76029i	0.00530250	+	0.183523i
$93$		0			0
$94$	−6.71356	+	6.91034i	−0.692451	+	0.712747i
$95$	−1.13574			−0.116525
$96$		0			0
$97$	−17.3929			−1.76599			−0.882993	−	0.469387i	$-0.844475\pi$
$97$	−17.3929			−1.76599			−0.882993	+	0.469387i	$0.844475\pi$
$98$	0.985454	−	1.01434i	0.0995459	−	0.102464i
$99$		0			0
$100$	0.286333	+	9.91017i	0.0286333	+	0.991017i
$101$	−19.0273			−1.89329			−0.946643	−	0.322284i	$-0.895550\pi$
$101$	−19.0273			−1.89329			−0.946643	+	0.322284i	$0.895550\pi$
$102$		0			0
$103$			10.7903i			1.06320i	0.846995	+	0.531601i	$0.178409\pi$
$103$			10.7903i			1.06320i	−0.846995	+	0.531601i	$0.821591\pi$
$104$	−6.73488	+	7.34532i	−0.660410	+	0.720268i
$105$		0			0
$106$	12.4487	−	12.8135i	1.20912	−	1.24456i
$107$		−	4.97087i		−	0.480553i	−0.970705	−	0.240276i	$-0.922762\pi$
$107$		−	4.97087i		−	0.480553i	0.970705	−	0.240276i	$-0.0772380\pi$
$108$		0			0
$109$			2.84810i			0.272798i	0.990654	+	0.136399i	$0.0435530\pi$
$109$			2.84810i			0.272798i	−0.990654	+	0.136399i	$0.956447\pi$
$110$	1.34834	+	1.30994i	0.128559	+	0.124898i
$111$		0			0
$112$	−0.230950	−	3.99333i	−0.0218227	−	0.377334i
$113$			2.88561i			0.271455i	0.990746	+	0.135728i	$0.0433372\pi$
$113$			2.88561i			0.271455i	−0.990746	+	0.135728i	$0.956663\pi$
$114$		0			0
$115$	−0.182258			−0.0169957
$116$	0.185307	+	6.41360i	0.0172054	+	0.595488i
$117$		0			0
$118$	−4.29408	−	4.17180i	−0.395302	−	0.384045i
$119$	3.90616			0.358077
$120$		0			0
$121$	−30.2408			−2.74916
$122$	12.4770	+	12.1217i	1.12961	+	1.09744i
$123$		0			0
$124$	0.126200	−	0.00364627i	0.0113331	−	0.000327444i
$125$	−2.06105			−0.184345
$126$		0			0
$127$		−	7.23082i		−	0.641631i	−0.947142	−	0.320816i	$-0.896043\pi$
$127$		−	7.23082i		−	0.641631i	0.947142	−	0.320816i	$-0.103957\pi$
$128$	−8.76655	−	7.15175i	−0.774861	−	0.632132i
$129$		0			0
$130$	−0.739761	−	0.718696i	−0.0648813	−	0.0630338i
$131$		−	12.8026i		−	1.11857i	−0.828975	−	0.559286i	$-0.811076\pi$
$131$		−	12.8026i		−	1.11857i	0.828975	−	0.559286i	$-0.188924\pi$
$132$		0			0
$133$		−	5.48691i		−	0.475776i
$134$	5.66307	−	5.82906i	0.489215	−	0.503554i
$135$		0			0
$136$	7.46661	−	8.14337i	0.640257	−	0.698288i
$137$		−	0.363873i		−	0.0310878i	−0.999879	−	0.0155439i	$-0.995052\pi$
$137$		−	0.363873i		−	0.0310878i	0.999879	−	0.0155439i	$-0.00494798\pi$
$138$		0			0
$139$	−9.32338			−0.790799			−0.395399	−	0.918509i	$-0.629394\pi$
$139$	−9.32338			−0.790799			−0.395399	+	0.918509i	$0.629394\pi$
$140$	0.413810	−	0.0119562i	0.0349733	−	0.00101048i
$141$		0			0
$142$	10.0314	−	10.3255i	0.841819	−	0.866493i
$143$	22.6266			1.89214
$144$		0			0
$145$	−0.664057			−0.0551470
$146$	−8.15579	+	8.39484i	−0.674978	+	0.694762i
$147$		0			0
$148$	19.8285	−	0.572901i	1.62989	−	0.0470922i
$149$	−4.82519			−0.395295			−0.197648	−	0.980273i	$-0.563330\pi$
$149$	−4.82519			−0.395295			−0.197648	+	0.980273i	$0.563330\pi$
$150$		0			0
$151$			12.7969i			1.04140i	0.853740	+	0.520700i	$0.174329\pi$
$151$			12.7969i			1.04140i	−0.853740	+	0.520700i	$0.825671\pi$
$152$	−11.4388	−	10.4882i	−0.927813	−	0.850706i
$153$		0			0
$154$	−6.32848	+	6.51397i	−0.509964	+	0.524911i
$155$			0.0130666i			0.00104953i
$156$		0			0
$157$		−	15.5455i		−	1.24067i	−0.784337	−	0.620335i	$-0.786997\pi$
$157$		−	15.5455i		−	1.24067i	0.784337	−	0.620335i	$-0.213003\pi$
$158$	4.93400	+	4.79351i	0.392528	+	0.381351i
$159$		0			0
$160$	0.766071	−	0.885545i	0.0605632	−	0.0700085i
$161$		−	0.880512i		−	0.0693940i
$162$		0			0
$163$	18.4630			1.44613			0.723067	−	0.690778i	$-0.242732\pi$
$163$	18.4630			1.44613			0.723067	+	0.690778i	$0.242732\pi$
$164$	11.8795	−	0.343232i	0.927630	−	0.0268019i
$165$		0			0
$166$	7.62314	+	7.40607i	0.591670	+	0.574822i
$167$	12.5320			0.969754			0.484877	−	0.874582i	$-0.338864\pi$
$167$	12.5320			0.969754			0.484877	+	0.874582i	$0.338864\pi$
$168$		0			0
$169$	0.585951			0.0450731
$170$	0.820134	+	0.796781i	0.0629014	+	0.0611103i
$171$		0			0
$172$	0.0658252	+	2.27825i	0.00501912	+	0.173715i
$173$	5.49171			0.417527			0.208763	−	0.977966i	$-0.433056\pi$
$173$	5.49171			0.417527			0.208763	+	0.977966i	$0.433056\pi$
$174$		0			0
$175$		−	4.95715i		−	0.374726i
$176$	1.48314	+	25.6447i	0.111796	+	1.93305i
$177$		0			0
$178$	4.51058	+	4.38214i	0.338082	+	0.328455i
$179$		−	14.5830i		−	1.08998i	−0.838441	−	0.544992i	$-0.816533\pi$
$179$		−	14.5830i		−	1.08998i	0.838441	−	0.544992i	$-0.183467\pi$
$180$		0			0
$181$		−	17.2753i		−	1.28407i	−0.766677	−	0.642033i	$-0.778091\pi$
$181$		−	17.2753i		−	1.28407i	0.766677	−	0.642033i	$-0.221909\pi$
$182$	3.47211	−	3.57387i	0.257370	−	0.264913i
$183$		0			0
$184$	−1.83565	−	1.68309i	−0.135326	−	0.124079i
$185$			2.05302i			0.150941i
$186$		0			0
$187$	−25.0850			−1.83440
$188$	−0.393510	−	13.6196i	−0.0286997	−	0.993314i
$189$		0			0
$190$	1.11922	−	1.15203i	0.0811969	−	0.0835768i
$191$	−7.29828			−0.528085			−0.264042	−	0.964511i	$-0.585056\pi$
$191$	−7.29828			−0.528085			−0.264042	+	0.964511i	$0.585056\pi$
$192$		0			0
$193$	12.1106			0.871742			0.435871	−	0.900009i	$-0.356440\pi$
$193$	12.1106			0.871742			0.435871	+	0.900009i	$0.356440\pi$
$194$	17.1399	−	17.6423i	1.23058	−	1.26664i
$195$		0			0
$196$	0.0577616	+	1.99917i	0.00412583	+	0.142798i
$197$	−17.3925			−1.23917			−0.619584	−	0.784931i	$-0.712699\pi$
$197$	−17.3925			−1.23917			−0.619584	+	0.784931i	$0.712699\pi$
$198$		0			0
$199$			3.07583i			0.218040i	0.994040	+	0.109020i	$0.0347712\pi$
$199$			3.07583i			0.218040i	−0.994040	+	0.109020i	$0.965229\pi$
$200$	−10.3344	−	9.47558i	−0.730755	−	0.670025i
$201$		0			0
$202$	18.7505	−	19.3001i	1.31928	−	1.35795i
$203$		−	3.20814i		−	0.225167i
$204$		0			0
$205$			1.22999i			0.0859060i
$206$	−10.9450	−	10.6334i	−0.762576	−	0.740862i
$207$		0			0
$208$	−0.813720	−	14.0699i	−0.0564213	−	0.975573i
$209$			35.2364i			2.43735i
$210$		0			0
$211$	9.57154			0.658932			0.329466	−	0.944167i	$-0.393131\pi$
$211$	9.57154			0.658932			0.329466	+	0.944167i	$0.393131\pi$
$212$	0.729669	+	25.2543i	0.0501139	+	1.73447i
$213$		0			0
$214$	5.04214	+	4.89857i	0.344674	+	0.334859i
$215$	−0.235888			−0.0160874
$216$		0			0
$217$	−0.0631261			−0.00428528
$218$	−2.88893	−	2.80667i	−0.195663	−	0.190092i
$219$		0			0
$220$	−2.65745	+	0.0767812i	−0.179165	+	0.00517659i
$221$	13.7628			0.925786
$222$		0			0
$223$		−	26.5694i		−	1.77922i	−0.456722	−	0.889610i	$-0.650976\pi$
$223$		−	26.5694i		−	1.77922i	0.456722	−	0.889610i	$-0.349024\pi$
$224$	4.27817	+	3.70098i	0.285847	+	0.247282i
$225$		0			0
$226$	−2.92698	−	2.84363i	−0.194700	−	0.189156i
$227$		−	20.7345i		−	1.37620i	−0.725616	−	0.688100i	$-0.758445\pi$
$227$		−	20.7345i		−	1.37620i	0.725616	−	0.688100i	$-0.241555\pi$
$228$		0			0
$229$			19.2625i			1.27290i	0.771316	+	0.636452i	$0.219599\pi$
$229$			19.2625i			1.27290i	−0.771316	+	0.636452i	$0.780401\pi$
$230$	0.179607	−	0.184871i	0.0118429	−	0.0121901i
$231$		0			0
$232$	−6.68817	−	6.13235i	−0.439100	−	0.402608i
$233$			25.0038i			1.63805i	0.573756	+	0.819027i	$0.305486\pi$
$233$			25.0038i			1.63805i	−0.573756	+	0.819027i	$0.694514\pi$
$234$		0			0
$235$	1.41016			0.0919889
$236$	8.46323	−	0.244527i	0.550909	−	0.0159173i
$237$		0			0
$238$	−3.84934	+	3.96217i	−0.249516	+	0.256829i
$239$	15.0439			0.973107			0.486553	−	0.873651i	$-0.338254\pi$
$239$	15.0439			0.973107			0.486553	+	0.873651i	$0.338254\pi$
$240$		0			0
$241$	−3.23274			−0.208239			−0.104120	−	0.994565i	$-0.533203\pi$
$241$	−3.23274			−0.208239			−0.104120	+	0.994565i	$0.533203\pi$
$242$	29.8009	−	30.6744i	1.91567	−	1.97182i
$243$		0			0
$244$	−24.5909	+	0.710502i	−1.57427	+	0.0454853i
$245$	−0.206991			−0.0132242
$246$		0			0
$247$		−	19.3324i		−	1.23009i
$248$	−0.120665	+	0.131602i	−0.00766226	+	0.00835675i
$249$		0			0
$250$	2.03106	−	2.09060i	0.128456	−	0.132221i
$251$		−	10.4258i		−	0.658071i	−0.944318	−	0.329036i	$-0.893276\pi$
$251$		−	10.4258i		−	0.658071i	0.944318	−	0.329036i	$-0.106724\pi$
$252$		0			0
$253$			5.65456i			0.355499i
$254$	7.33449	+	7.12564i	0.460207	+	0.447102i
$255$		0			0
$256$	15.8933	−	1.84452i	0.993333	−	0.115282i
$257$			8.12452i			0.506794i	0.967362	+	0.253397i	$0.0815479\pi$
$257$			8.12452i			0.506794i	−0.967362	+	0.253397i	$0.918452\pi$
$258$		0			0
$259$	−9.91837			−0.616297
$260$	1.45800	−	0.0421258i	0.0904214	−	0.00261253i
$261$		0			0
$262$	12.9862	+	12.6164i	0.802290	+	0.779444i
$263$	14.7639			0.910382			0.455191	−	0.890394i	$-0.349571\pi$
$263$	14.7639			0.910382			0.455191	+	0.890394i	$0.349571\pi$
$264$		0			0
$265$	−2.61480			−0.160626
$266$	5.56558	+	5.40710i	0.341248	+	0.331530i
$267$		0			0
$268$	0.331937	+	11.4885i	0.0202762	+	0.701774i
$269$	26.8961			1.63989			0.819943	−	0.572445i	$-0.194005\pi$
$269$	26.8961			1.63989			0.819943	+	0.572445i	$0.194005\pi$
$270$		0			0
$271$			17.5914i			1.06860i	0.845295	+	0.534301i	$0.179425\pi$
$271$			17.5914i			1.06860i	−0.845295	+	0.534301i	$0.820575\pi$
$272$	0.902128	+	15.5986i	0.0546996	+	0.945803i
$273$		0			0
$274$	0.369090	+	0.358580i	0.0222976	+	0.0216626i
$275$			31.8343i			1.91968i
$276$		0			0
$277$			24.8383i			1.49239i	0.665729	+	0.746194i	$0.268121\pi$
$277$			24.8383i			1.49239i	−0.665729	+	0.746194i	$0.731879\pi$
$278$	9.18776	−	9.45706i	0.551045	−	0.567197i
$279$		0			0
$280$	−0.395663	+	0.431525i	−0.0236454	+	0.0257886i
$281$			4.13370i			0.246596i	0.992370	+	0.123298i	$0.0393471\pi$
$281$			4.13370i			0.246596i	−0.992370	+	0.123298i	$0.960653\pi$
$282$		0			0
$283$	−23.9297			−1.42247			−0.711236	−	0.702954i	$-0.751864\pi$
$283$	−23.9297			−1.42247			−0.711236	+	0.702954i	$0.751864\pi$
$284$	0.587985	+	20.3505i	0.0348905	+	1.20758i
$285$		0			0
$286$	−22.2975	+	22.9511i	−1.31848	+	1.35712i
$287$	−5.94221			−0.350758
$288$		0			0
$289$	1.74190			0.102465
$290$	0.654398	−	0.673578i	0.0384276	−	0.0395539i
$291$		0			0
$292$	−0.478045	−	16.5454i	−0.0279755	−	0.968249i
$293$	−12.0225			−0.702360			−0.351180	−	0.936308i	$-0.614219\pi$
$293$	−12.0225			−0.702360			−0.351180	+	0.936308i	$0.614219\pi$
$294$		0			0
$295$			0.876273i			0.0510186i
$296$	−18.9589	+	20.6773i	−1.10196	+	1.20184i
$297$		0			0
$298$	4.75501	−	4.89438i	0.275450	−	0.283524i
$299$		−	3.10236i		−	0.179414i
$300$		0			0
$301$		−	1.13960i		−	0.0656855i
$302$	−12.9804	−	12.6108i	−0.746939	−	0.725670i
$303$		0			0
$304$	21.9110	−	1.26720i	1.25668	−	0.0726790i
$305$		−	2.54612i		−	0.145790i
$306$		0			0
$307$	−5.82060			−0.332199			−0.166100	−	0.986109i	$-0.553117\pi$
$307$	−5.82060			−0.332199			−0.166100	+	0.986109i	$0.553117\pi$
$308$	−0.370939	−	12.8384i	−0.0211362	−	0.731538i
$309$		0			0
$310$	−0.0132539	−	0.0128765i	−0.000752772	−	0.000731336i
$311$	12.7884			0.725161			0.362580	−	0.931952i	$-0.381896\pi$
$311$	12.7884			0.725161			0.362580	+	0.931952i	$0.381896\pi$
$312$		0			0
$313$	1.74881			0.0988483			0.0494242	−	0.998778i	$-0.484261\pi$
$313$	1.74881			0.0988483			0.0494242	+	0.998778i	$0.484261\pi$
$314$	15.7684	+	15.3194i	0.889864	+	0.864525i
$315$		0			0
$316$	−9.72447	+	0.280968i	−0.547044	+	0.0158057i
$317$	−30.5938			−1.71832			−0.859159	−	0.511709i	$-0.829013\pi$
$317$	−30.5938			−1.71832			−0.859159	+	0.511709i	$0.829013\pi$
$318$		0			0
$319$			20.6024i			1.15351i
$320$	0.143314	+	1.64972i	0.00801151	+	0.0922220i
$321$		0			0
$322$	0.893136	+	0.867704i	0.0497725	+	0.0483552i
$323$			21.4328i			1.19255i
$324$		0			0
$325$		−	17.4658i		−	0.968830i
$326$	−18.1944	+	18.7277i	−1.00770	+	1.03723i
$327$		0			0
$328$	−11.3585	+	12.3880i	−0.627169	+	0.684014i
$329$			6.81266i			0.375594i
$330$		0			0
$331$	−20.7269			−1.13925			−0.569627	−	0.821904i	$-0.692912\pi$
$331$	−20.7269			−1.13925			−0.569627	+	0.821904i	$0.692912\pi$
$332$	−15.0245	+	0.434101i	−0.824577	+	0.0238244i
$333$		0			0
$334$	−12.3497	+	12.7117i	−0.675745	+	0.695551i
$335$	−1.18951			−0.0649899
$336$		0			0
$337$	19.9716			1.08792			0.543961	−	0.839110i	$-0.316924\pi$
$337$	19.9716			1.08792			0.543961	+	0.839110i	$0.316924\pi$
$338$	−0.577427	+	0.594352i	−0.0314079	+	0.0323285i
$339$		0			0
$340$	−1.61641	+	0.0467027i	−0.0876621	+	0.00253281i
$341$	0.405390			0.0219531
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−2.37578	−	2.17834i	−0.128094	−	0.117448i
$345$		0			0
$346$	−5.41182	+	5.57045i	−0.290942	+	0.299469i
$347$			10.6443i			0.571414i	0.958317	+	0.285707i	$0.0922284\pi$
$347$			10.6443i			0.571414i	−0.958317	+	0.285707i	$0.907772\pi$
$348$		0			0
$349$			21.1575i			1.13254i	0.824221	+	0.566268i	$0.191613\pi$
$349$			21.1575i			1.13254i	−0.824221	+	0.566268i	$0.808387\pi$
$350$	5.02823	+	4.88505i	0.268770	+	0.261117i
$351$		0			0
$352$	−27.4740	−	23.7673i	−1.46437	−	1.26680i
$353$			7.85498i			0.418079i	0.977907	+	0.209039i	$0.0670337\pi$
$353$			7.85498i			0.418079i	−0.977907	+	0.209039i	$0.932966\pi$
$354$		0			0
$355$	−2.10707			−0.111832
$356$	−8.88993	+	0.256855i	−0.471165	+	0.0136133i
$357$		0			0
$358$	14.7921	+	14.3709i	0.781785	+	0.759523i
$359$	−22.0102			−1.16165			−0.580826	−	0.814028i	$-0.697270\pi$
$359$	−22.0102			−1.16165			−0.580826	+	0.814028i	$0.697270\pi$
$360$		0			0
$361$	11.1062			0.584537
$362$	17.5230	+	17.0240i	0.920990	+	0.894764i
$363$		0			0
$364$	0.203515	+	7.04378i	0.0106671	+	0.369194i
$365$	1.71310			0.0896676
$366$		0			0
$367$		−	5.61196i		−	0.292942i	−0.989215	−	0.146471i	$-0.953209\pi$
$367$		−	5.61196i		−	0.292942i	0.989215	−	0.146471i	$-0.0467915\pi$
$368$	3.51617	−	0.203354i	0.183293	−	0.0106006i
$369$		0			0
$370$	−2.08245	−	2.02315i	−0.108262	−	0.105179i
$371$		−	12.6324i		−	0.655843i
$372$		0			0
$373$			21.5334i			1.11496i	0.830192	+	0.557478i	$0.188231\pi$
$373$			21.5334i			1.11496i	−0.830192	+	0.557478i	$0.811769\pi$
$374$	24.7201	−	25.4446i	1.27825	−	1.31571i
$375$		0			0
$376$	14.2027	+	13.0224i	0.732448	+	0.671578i
$377$		−	11.3034i		−	0.582156i
$378$		0			0
$379$	36.2973			1.86447			0.932233	−	0.361858i	$-0.117857\pi$
$379$	36.2973			1.86447			0.932233	+	0.361858i	$0.117857\pi$
$380$	0.0656024	+	2.27054i	0.00336533	+	0.116476i
$381$		0			0
$382$	7.19211	−	7.40292i	0.367981	−	0.378766i
$383$	−12.4362			−0.635462			−0.317731	−	0.948181i	$-0.602921\pi$
$383$	−12.4362			−0.635462			−0.317731	+	0.948181i	$0.602921\pi$
$384$		0			0
$385$	1.32928			0.0677463
$386$	−11.9345	+	12.2843i	−0.607448	+	0.625253i
$387$		0			0
$388$	1.00464	+	34.7714i	0.0510031	+	1.76525i
$389$	−5.47648			−0.277669			−0.138834	−	0.990316i	$-0.544336\pi$
$389$	−5.47648			−0.277669			−0.138834	+	0.990316i	$0.544336\pi$
$390$		0			0
$391$			3.43942i			0.173939i
$392$	−2.08475	−	1.91150i	−0.105296	−	0.0965451i
$393$		0			0
$394$	17.1396	−	17.6419i	0.863478	−	0.888787i
$395$		−	1.00686i		−	0.0506606i
$396$		0			0
$397$			9.58947i			0.481282i	0.970614	+	0.240641i	$0.0773576\pi$
$397$			9.58947i			0.481282i	−0.970614	+	0.240641i	$0.922642\pi$
$398$	−3.11993	−	3.03108i	−0.156388	−	0.151935i
$399$		0			0
$400$	19.7955	−	1.14486i	0.989777	−	0.0572428i
$401$			1.76702i			0.0882408i	0.999026	+	0.0441204i	$0.0140485\pi$
$401$			1.76702i			0.0882408i	−0.999026	+	0.0441204i	$0.985951\pi$
$402$		0			0
$403$	−0.222416			−0.0110793
$404$	1.09905	+	38.0387i	0.0546796	+	1.89250i
$405$		0			0
$406$	3.25414	+	3.16147i	0.161500	+	0.156901i
$407$	63.6948			3.15723
$408$		0			0
$409$	−5.87490			−0.290495			−0.145248	−	0.989395i	$-0.546398\pi$
$409$	−5.87490			−0.290495			−0.145248	+	0.989395i	$0.546398\pi$
$410$	−1.24762	−	1.21209i	−0.0616156	−	0.0598611i
$411$		0			0
$412$	21.5716	−	0.623266i	1.06276	−	0.0307061i
$413$	−4.23338			−0.208311
$414$		0			0
$415$		−	1.55562i		−	0.0763624i
$416$	15.0735	+	13.0399i	0.739041	+	0.639332i
$417$		0			0
$418$	−35.7416	−	34.7238i	−1.74818	−	1.69840i
$419$			18.9459i			0.925567i	0.886471	+	0.462783i	$0.153149\pi$
$419$			18.9459i			0.925567i	−0.886471	+	0.462783i	$0.846851\pi$
$420$		0			0
$421$		−	25.2598i		−	1.23109i	−0.788103	−	0.615544i	$-0.788936\pi$
$421$		−	25.2598i		−	1.23109i	0.788103	−	0.615544i	$-0.211064\pi$
$422$	−9.43231	+	9.70878i	−0.459158	+	0.472616i
$423$		0			0
$424$	−26.3355	−	24.1468i	−1.27896	−	1.17267i
$425$			19.3634i			0.939265i
$426$		0			0
$427$	12.3006			0.595268
$428$	−9.93760	+	0.287126i	−0.480352	+	0.0138787i
$429$		0			0
$430$	0.232456	−	0.239270i	0.0112100	−	0.0115386i
$431$	37.5774			1.81004			0.905020	−	0.425369i	$-0.139856\pi$
$431$	37.5774			1.81004			0.905020	+	0.425369i	$0.139856\pi$
$432$		0			0
$433$	21.1040			1.01419			0.507097	−	0.861889i	$-0.330719\pi$
$433$	21.1040			1.01419			0.507097	+	0.861889i	$0.330719\pi$
$434$	0.0622079	−	0.0640312i	0.00298607	−	0.00307360i
$435$		0			0
$436$	5.69382	−	0.164511i	0.272684	−	0.00787863i
$437$	4.83129			0.231112
$438$		0			0
$439$			2.88405i			0.137648i	0.997629	+	0.0688240i	$0.0219247\pi$
$439$			2.88405i			0.137648i	−0.997629	+	0.0688240i	$0.978075\pi$
$440$	2.54091	−	2.77121i	0.121133	−	0.132112i
$441$		0			0
$442$	−13.5626	+	13.9601i	−0.645107	+	0.664016i
$443$		−	34.5978i		−	1.64379i	−0.569640	−	0.821895i	$-0.692917\pi$
$443$		−	34.5978i		−	1.64379i	0.569640	−	0.821895i	$-0.307083\pi$
$444$		0			0
$445$		−	0.920453i		−	0.0436337i
$446$	26.9504	+	26.1829i	1.27614	+	1.23980i
$447$		0			0
$448$	−7.96998	+	0.692368i	−0.376546	+	0.0327113i
$449$		−	14.8661i		−	0.701575i	−0.936455	−	0.350787i	$-0.885914\pi$
$449$		−	14.8661i		−	0.701575i	0.936455	−	0.350787i	$-0.114086\pi$
$450$		0			0
$451$	38.1603			1.79690
$452$	5.76881	−	0.166677i	0.271342	−	0.00783985i
$453$		0			0
$454$	21.0318	+	20.4329i	0.987072	+	0.958965i
$455$	−0.729305			−0.0341903
$456$		0			0
$457$	11.0037			0.514730			0.257365	−	0.966314i	$-0.417146\pi$
$457$	11.0037			0.514730			0.257365	+	0.966314i	$0.417146\pi$
$458$	−19.5387	−	18.9823i	−0.912984	−	0.886987i
$459$		0			0
$460$	0.0105275	+	0.364365i	0.000490849	+	0.0169886i
$461$	−32.9687			−1.53551			−0.767753	−	0.640746i	$-0.778625\pi$
$461$	−32.9687			−1.53551			−0.767753	+	0.640746i	$0.778625\pi$
$462$		0			0
$463$		−	12.3348i		−	0.573245i	−0.958044	−	0.286622i	$-0.907468\pi$
$463$		−	12.3348i		−	0.573245i	0.958044	−	0.286622i	$-0.0925325\pi$
$464$	12.8112	−	0.740920i	0.594743	−	0.0343964i
$465$		0			0
$466$	−25.3623	−	24.6401i	−1.17489	−	1.14143i
$467$		−	33.5264i		−	1.55142i	−0.631091	−	0.775709i	$-0.717393\pi$
$467$		−	33.5264i		−	1.55142i	0.631091	−	0.775709i	$-0.282607\pi$
$468$		0			0
$469$		−	5.74666i		−	0.265356i
$470$	−1.38965	+	1.43038i	−0.0640998	+	0.0659785i
$471$		0			0
$472$	−8.09209	+	8.82554i	−0.372468	+	0.406228i
$473$			7.31840i			0.336501i
$474$		0			0
$475$	27.1995			1.24800
$476$	−0.225626	−	7.80906i	−0.0103416	−	0.357928i
$477$		0			0
$478$	−14.8250	+	15.2596i	−0.678081	+	0.697956i
$479$	9.65791			0.441281			0.220641	−	0.975355i	$-0.429185\pi$
$479$	9.65791			0.441281			0.220641	+	0.975355i	$0.429185\pi$
$480$		0			0
$481$	−34.9460			−1.59340
$482$	3.18572	−	3.27909i	0.145106	−	0.149359i
$483$		0			0
$484$	1.74676	+	60.4563i	0.0793980	+	2.74802i
$485$	−3.60019			−0.163476
$486$		0			0
$487$			25.1008i			1.13742i	0.822537	+	0.568712i	$0.192558\pi$
$487$			25.1008i			1.13742i	−0.822537	+	0.568712i	$0.807442\pi$
$488$	23.5125	−	25.6437i	1.06436	−	1.16083i
$489$		0			0
$490$	0.203980	−	0.209959i	0.00921490	−	0.00948499i
$491$			10.5524i			0.476224i	0.971238	+	0.238112i	$0.0765285\pi$
$491$			10.5524i			0.476224i	−0.971238	+	0.238112i	$0.923471\pi$
$492$		0			0
$493$			12.5315i			0.564391i
$494$	19.6095	+	19.0511i	0.882275	+	0.857151i
$495$		0			0
$496$	−0.0145790	−	0.252083i	−0.000654616	−	0.0113189i
$497$		−	10.1795i		−	0.456613i
$498$		0			0
$499$	−11.6619			−0.522059			−0.261029	−	0.965331i	$-0.584062\pi$
$499$	−11.6619			−0.522059			−0.261029	+	0.965331i	$0.584062\pi$
$500$	0.119049	+	4.12037i	0.00532405	+	0.184269i
$501$		0			0
$502$	10.5753	+	10.2742i	0.471998	+	0.458558i
$503$	−29.0202			−1.29394			−0.646972	−	0.762513i	$-0.723965\pi$
$503$	−29.0202			−1.29394			−0.646972	+	0.762513i	$0.723965\pi$
$504$		0			0
$505$	−3.93849			−0.175260
$506$	−5.73563	−	5.57230i	−0.254980	−	0.247719i
$507$		0			0
$508$	−14.4556	+	0.417664i	−0.641364	+	0.0185308i
$509$	22.0894			0.979096			0.489548	−	0.871976i	$-0.337162\pi$
$509$	22.0894			0.979096			0.489548	+	0.871976i	$0.337162\pi$
$510$		0			0
$511$			8.27618i			0.366116i
$512$	−13.7912	+	17.9389i	−0.609489	+	0.792794i
$513$		0			0
$514$	−8.24101	−	8.00634i	−0.363495	−	0.353145i
$515$			2.23350i			0.0984199i
$516$		0			0
$517$		−	43.7502i		−	1.92413i
$518$	9.77409	−	10.0606i	0.429449	−	0.442036i
$519$		0			0
$520$	−1.39406	+	1.52042i	−0.0611337	+	0.0666747i
$521$		−	14.5460i		−	0.637273i	−0.947877	−	0.318636i	$-0.896775\pi$
$521$		−	14.5460i		−	0.637273i	0.947877	−	0.318636i	$-0.103225\pi$
$522$		0			0
$523$	31.6350			1.38330			0.691651	−	0.722232i	$-0.256884\pi$
$523$	31.6350			1.38330			0.691651	+	0.722232i	$0.256884\pi$
$524$	−25.5946	+	0.739501i	−1.11810	+	0.0323052i
$525$		0			0
$526$	−14.5491	+	14.9756i	−0.634373	+	0.652967i
$527$	0.246581			0.0107412
$528$		0			0
$529$	−22.2247			−0.966291
$530$	2.57677	−	2.65229i	0.111928	−	0.115208i
$531$		0			0
$532$	−10.9692	+	0.316933i	−0.475577	+	0.0137408i
$533$	−20.9365			−0.906862
$534$		0			0
$535$		−	1.02893i		−	0.0444844i
$536$	−11.9804	−	10.9847i	−0.517473	−	0.474468i
$537$		0			0
$538$	−26.5049	+	27.2818i	−1.14271	+	1.17620i
$539$			6.42190i			0.276611i
$540$		0			0
$541$		−	22.7160i		−	0.976639i	−0.872665	−	0.488319i	$-0.837610\pi$
$541$		−	22.7160i		−	0.976639i	0.872665	−	0.488319i	$-0.162390\pi$
$542$	−17.8436	−	17.3355i	−0.766449	−	0.744624i
$543$		0			0
$544$	−16.7112	−	14.4566i	−0.716488	−	0.619822i
$545$			0.589532i			0.0252528i
$546$		0			0
$547$	−22.2601			−0.951774			−0.475887	−	0.879506i	$-0.657873\pi$
$547$	−22.2601			−0.951774			−0.475887	+	0.879506i	$0.657873\pi$
$548$	−0.727443	+	0.0210179i	−0.0310748	+	0.000897840i
$549$		0			0
$550$	−32.2908	−	31.3713i	−1.37688	−	1.33768i
$551$	17.6028			0.749904
$552$		0			0
$553$	4.86426			0.206849
$554$	−25.1944	−	24.4770i	−1.07041	−	1.03993i
$555$		0			0
$556$	0.538533	+	18.6390i	0.0228389	+	0.790469i
$557$	−2.99670			−0.126974			−0.0634872	−	0.997983i	$-0.520222\pi$
$557$	−2.99670			−0.126974			−0.0634872	+	0.997983i	$0.520222\pi$
$558$		0			0
$559$		−	4.01522i		−	0.169826i
$560$	−0.0478047	−	0.826584i	−0.00202012	−	0.0349296i
$561$		0			0
$562$	−4.19297	−	4.07357i	−0.176870	−	0.171833i
$563$		−	13.4913i		−	0.568589i	−0.958737	−	0.284295i	$-0.908241\pi$
$563$		−	13.4913i		−	0.568589i	0.958737	−	0.284295i	$-0.0917594\pi$
$564$		0			0
$565$			0.597296i			0.0251284i
$566$	23.5816	−	24.2728i	0.991208	−	1.02026i
$567$		0			0
$568$	−21.2217	−	19.4581i	−0.890444	−	0.816443i
$569$			40.7445i			1.70810i	0.520191	+	0.854050i	$0.325861\pi$
$569$			40.7445i			1.70810i	−0.520191	+	0.854050i	$0.674139\pi$
$570$		0			0
$571$	18.0110			0.753739			0.376869	−	0.926266i	$-0.377001\pi$
$571$	18.0110			0.753739			0.376869	+	0.926266i	$0.377001\pi$
$572$	−1.30695	−	45.2344i	−0.0546464	−	1.89135i
$573$		0			0
$574$	5.85577	−	6.02741i	0.244415	−	0.251579i
$575$	4.36483			0.182026
$576$		0			0
$577$	29.3495			1.22184			0.610919	−	0.791693i	$-0.290800\pi$
$577$	29.3495			1.22184			0.610919	+	0.791693i	$0.290800\pi$
$578$	−1.71656	+	1.76688i	−0.0713997	+	0.0734924i
$579$		0			0
$580$	0.0383570	+	1.32756i	0.00159269	+	0.0551240i
$581$	7.51539			0.311791
$582$		0			0
$583$			81.1242i			3.35982i
$584$	17.2538	+	15.8199i	0.713966	+	0.654631i
$585$		0			0
$586$	11.8476	−	12.1948i	0.489419	−	0.503764i
$587$		−	11.1732i		−	0.461168i	−0.973052	−	0.230584i	$-0.925936\pi$
$587$		−	11.1732i		−	0.461168i	0.973052	−	0.230584i	$-0.0740637\pi$
$588$		0			0
$589$		−	0.346368i		−	0.0142718i
$590$	−0.888837	−	0.863527i	−0.0365928	−	0.0355508i
$591$		0			0
$592$	−2.29065	−	39.6073i	−0.0941450	−	1.62785i
$593$			29.9792i			1.23110i	0.788099	+	0.615549i	$0.211066\pi$
$593$			29.9792i			1.23110i	−0.788099	+	0.615549i	$0.788934\pi$
$594$		0			0
$595$	0.808542			0.0331470
$596$	0.278711	+	9.64636i	0.0114164	+	0.395130i
$597$		0			0
$598$	3.14684	+	3.05723i	0.128684	+	0.125019i
$599$	6.38388			0.260838			0.130419	−	0.991459i	$-0.458368\pi$
$599$	6.38388			0.260838			0.130419	+	0.991459i	$0.458368\pi$
$600$		0			0
$601$	−23.5445			−0.960402			−0.480201	−	0.877159i	$-0.659436\pi$
$601$	−23.5445			−0.960402			−0.480201	+	0.877159i	$0.659436\pi$
$602$	1.15594	+	1.12302i	0.0471126	+	0.0457710i
$603$		0			0
$604$	25.5832	−	0.739172i	1.04097	−	0.0300765i
$605$	−6.25958			−0.254488
$606$		0			0
$607$		−	33.9599i		−	1.37839i	−0.724577	−	0.689194i	$-0.757965\pi$
$607$		−	33.9599i		−	1.37839i	0.724577	−	0.689194i	$-0.242035\pi$
$608$	−20.3069	+	23.4740i	−0.823555	+	0.951995i
$609$		0			0
$610$	2.58262	+	2.50908i	0.104567	+	0.101590i
$611$			24.0034i			0.971076i
$612$		0			0
$613$			20.6042i			0.832197i	0.909320	+	0.416098i	$0.136603\pi$
$613$			20.6042i			0.832197i	−0.909320	+	0.416098i	$0.863397\pi$
$614$	5.73593	−	5.90405i	0.231483	−	0.238268i
$615$		0			0
$616$	13.3881	+	12.2754i	0.539420	+	0.494591i
$617$		−	37.4489i		−	1.50764i	−0.657083	−	0.753818i	$-0.728210\pi$
$617$		−	37.4489i		−	1.50764i	0.657083	−	0.753818i	$-0.271790\pi$
$618$		0			0
$619$	14.2766			0.573825			0.286913	−	0.957957i	$-0.407371\pi$
$619$	14.2766			0.573825			0.286913	+	0.957957i	$0.407371\pi$
$620$	0.0261222		0.000754746i	0.00104909		3.03113e-5i
$621$		0			0
$622$	−12.6023	+	12.9717i	−0.505307	+	0.520118i
$623$	4.44682			0.178158
$624$		0			0
$625$	24.3592			0.974366
$626$	−1.72337	+	1.77388i	−0.0688796	+	0.0708985i
$627$		0			0
$628$	−31.0781	+	0.897936i	−1.24015	+	0.0358315i
$629$	38.7427			1.54477
$630$		0			0
$631$		−	7.00448i		−	0.278844i	−0.990233	−	0.139422i	$-0.955476\pi$
$631$		−	7.00448i		−	0.278844i	0.990233	−	0.139422i	$-0.0445244\pi$
$632$	9.29802	−	10.1408i	0.369855	−	0.403378i
$633$		0			0
$634$	30.1488	−	31.0324i	1.19736	−	1.23245i
$635$		−	1.49672i		−	0.0593954i
$636$		0			0
$637$		−	3.52336i		−	0.139601i
$638$	−20.8977	−	20.3027i	−0.827350	−	0.803790i
$639$		0			0
$640$	−1.81460	−	1.48035i	−0.0717284	−	0.0585160i
$641$		−	9.23092i		−	0.364599i	−0.983243	−	0.182300i	$-0.941646\pi$
$641$		−	9.23092i		−	0.364599i	0.983243	−	0.182300i	$-0.0583541\pi$
$642$		0			0
$643$	1.48603			0.0586031			0.0293016	−	0.999571i	$-0.490672\pi$
$643$	1.48603			0.0586031			0.0293016	+	0.999571i	$0.490672\pi$
$644$	−1.76029	+	0.0508598i	−0.0693651	+	0.00200416i
$645$		0			0
$646$	−21.7401	−	21.1210i	−0.855351	−	0.830995i
$647$	−16.2654			−0.639457			−0.319729	−	0.947509i	$-0.603592\pi$
$647$	−16.2654			−0.639457			−0.319729	+	0.947509i	$0.603592\pi$
$648$		0			0
$649$	27.1863			1.06716
$650$	17.7162	+	17.2118i	0.694888	+	0.675101i
$651$		0			0
$652$	−1.06645	−	36.9106i	−0.0417655	−	1.44553i
$653$	−6.92310			−0.270922			−0.135461	−	0.990783i	$-0.543252\pi$
$653$	−6.92310			−0.270922			−0.135461	+	0.990783i	$0.543252\pi$
$654$		0			0
$655$		−	2.65003i		−	0.103545i
$656$	−1.37235	−	23.7292i	−0.0535814	−	0.926469i
$657$		0			0
$658$	−6.91034	−	6.71356i	−0.269393	−	0.261722i
$659$			11.3057i			0.440407i	0.975454	+	0.220203i	$0.0706721\pi$
$659$			11.3057i			0.440407i	−0.975454	+	0.220203i	$0.929328\pi$
$660$		0			0
$661$		−	18.9877i		−	0.738536i	−0.929323	−	0.369268i	$-0.879608\pi$
$661$		−	18.9877i		−	0.738536i	0.929323	−	0.369268i	$-0.120392\pi$
$662$	20.4254	−	21.0241i	0.793856	−	0.817124i
$663$		0			0
$664$	14.3656	−	15.6677i	0.557495	−	0.608025i
$665$		−	1.13574i		−	0.0440422i
$666$		0			0
$667$	2.82481			0.109377
$668$	−0.723867	−	25.0535i	−0.0280073	−	0.969349i
$669$		0			0
$670$	1.17221	−	1.20656i	0.0452863	−	0.0466137i
$671$	−78.9932			−3.04950
$672$		0			0
$673$	17.6164			0.679061			0.339531	−	0.940595i	$-0.389732\pi$
$673$	17.6164			0.679061			0.339531	+	0.940595i	$0.389732\pi$
$674$	−19.6811	+	20.2580i	−0.758088	+	0.780307i
$675$		0			0
$676$	−0.0338455	−	1.17141i	−0.00130175	−	0.0450543i
$677$	7.42579			0.285396			0.142698	−	0.989766i	$-0.454422\pi$
$677$	7.42579			0.285396			0.142698	+	0.989766i	$0.454422\pi$
$678$		0			0
$679$		−	17.3929i		−	0.667480i
$680$	1.54552	−	1.68561i	0.0592681	−	0.0646401i
$681$		0			0
$682$	−0.399493	+	0.411202i	−0.0152974	+	0.0157457i
$683$			22.8832i			0.875600i	0.899072	+	0.437800i	$0.144242\pi$
$683$			22.8832i			0.875600i	−0.899072	+	0.437800i	$0.855758\pi$
$684$		0			0
$685$		−	0.0753186i		−	0.00287778i
$686$	1.01434	+	0.985454i	0.0387276	+	0.0376248i
$687$		0			0
$688$	4.55080	−	0.263191i	0.173498	−	0.0100341i
$689$		−	44.5086i		−	1.69564i
$690$		0			0
$691$	33.6439			1.27987			0.639936	−	0.768428i	$-0.278961\pi$
$691$	33.6439			1.27987			0.639936	+	0.768428i	$0.278961\pi$
$692$	−0.317210	−	10.9788i	−0.0120585	−	0.417353i
$693$		0			0
$694$	−10.7969	−	10.4894i	−0.409844	−	0.398173i
$695$	−1.92986			−0.0732038
$696$		0			0
$697$	23.2112			0.879188
$698$	−21.4609	−	20.8498i	−0.812306	−	0.789175i
$699$		0			0
$700$	−9.91017	+	0.286333i	−0.374569	+	0.0108224i
$701$	−35.4474			−1.33883			−0.669414	−	0.742890i	$-0.733455\pi$
$701$	−35.4474			−1.33883			−0.669414	+	0.742890i	$0.733455\pi$
$702$		0			0
$703$		−	54.4212i		−	2.05253i
$704$	51.1824	−	4.44632i	1.92901	−	0.167577i
$705$		0			0
$706$	−7.96760	−	7.74072i	−0.299865	−	0.291326i
$707$		−	19.0273i		−	0.715595i
$708$		0			0
$709$		−	8.71118i		−	0.327155i	−0.986530	−	0.163578i	$-0.947697\pi$
$709$		−	8.71118i		−	0.327155i	0.986530	−	0.163578i	$-0.0523034\pi$
$710$	2.07642	−	2.13728i	0.0779267	−	0.0802107i
$711$		0			0
$712$	8.50008	−	9.27051i	0.318554	−	0.347427i
$713$		−	0.0555833i		−	0.00208161i
$714$		0			0
$715$	4.68352			0.175154
$716$	−29.1538	+	0.842337i	−1.08953	+	0.0314796i
$717$		0			0
$718$	21.6900	−	22.3257i	0.809463	−	0.833189i
$719$	0.821108			0.0306222			0.0153111	−	0.999883i	$-0.495126\pi$
$719$	0.821108			0.0306222			0.0153111	+	0.999883i	$0.495126\pi$
$720$		0			0
$721$	−10.7903			−0.401853
$722$	−10.9446	+	11.2654i	−0.407318	+	0.419256i
$723$		0			0
$724$	−34.5363	+	0.997851i	−1.28353	+	0.0370848i
$725$	15.9032			0.590632
$726$		0			0
$727$		−	28.0509i		−	1.04035i	−0.854059	−	0.520176i	$-0.825866\pi$
$727$		−	28.0509i		−	1.04035i	0.854059	−	0.520176i	$-0.174134\pi$
$728$	−7.34532	−	6.73488i	−0.272236	−	0.249611i
$729$		0			0
$730$	−1.68818	+	1.73766i	−0.0624823	+	0.0643136i
$731$			4.45147i			0.164643i
$732$		0			0
$733$			21.9677i			0.811395i	0.914007	+	0.405697i	$0.132971\pi$
$733$			21.9677i			0.811395i	−0.914007	+	0.405697i	$0.867029\pi$
$734$	5.69242	+	5.53032i	0.210111	+	0.204128i
$735$		0			0
$736$	−3.25875	+	3.76698i	−0.120119	+	0.138853i
$737$			36.9045i			1.35939i
$738$		0			0
$739$	−18.6044			−0.684374			−0.342187	−	0.939632i	$-0.611168\pi$
$739$	−18.6044			−0.684374			−0.342187	+	0.939632i	$0.611168\pi$
$740$	4.10432	−	0.118586i	0.150878	−	0.00435929i
$741$		0			0
$742$	12.8135	+	12.4487i	0.470400	+	0.457005i
$743$	−29.0849			−1.06702			−0.533512	−	0.845793i	$-0.679128\pi$
$743$	−29.0849			−1.06702			−0.533512	+	0.845793i	$0.679128\pi$
$744$		0			0
$745$	−0.998774			−0.0365922
$746$	−21.8421	−	21.2201i	−0.799696	−	0.776925i
$747$		0			0
$748$	1.44895	+	50.1490i	0.0529788	+	1.83363i
$749$	4.97087			0.181632
$750$		0			0
$751$			14.4693i			0.527991i	0.964524	+	0.263995i	$0.0850403\pi$
$751$			14.4693i			0.527991i	−0.964524	+	0.263995i	$0.914960\pi$
$752$	−27.2052	+	1.57338i	−0.992071	+	0.0573754i
$753$		0			0
$754$	11.4655	+	11.1390i	0.417549	+	0.405659i
$755$			2.64886i			0.0964018i
$756$		0			0
$757$			13.6988i			0.497891i	0.968517	+	0.248946i	$0.0800840\pi$
$757$			13.6988i			0.497891i	−0.968517	+	0.248946i	$0.919916\pi$
$758$	−35.7693	+	36.8177i	−1.29920	+	1.33728i
$759$		0			0
$760$	−2.36774	−	2.17097i	−0.0858870	−	0.0787493i
$761$		−	46.5579i		−	1.68772i	−0.536562	−	0.843861i	$-0.680277\pi$
$761$		−	46.5579i		−	1.68772i	0.536562	−	0.843861i	$-0.319723\pi$
$762$		0			0
$763$	−2.84810			−0.103108
$764$	0.421560	+	14.5905i	0.0152515	+	0.527864i
$765$		0			0
$766$	12.2553	−	12.6145i	0.442804	−	0.455782i
$767$	−14.9157			−0.538575
$768$		0			0
$769$	50.6427			1.82622			0.913111	−	0.407711i	$-0.133673\pi$
$769$	50.6427			1.82622			0.913111	+	0.407711i	$0.133673\pi$
$770$	−1.30994	+	1.34834i	−0.0472070	+	0.0485907i
$771$		0			0
$772$	−0.699530	−	24.2112i	−0.0251766	−	0.871379i
$773$	6.66928			0.239877			0.119939	−	0.992781i	$-0.461730\pi$
$773$	6.66928			0.239877			0.119939	+	0.992781i	$0.461730\pi$
$774$		0			0
$775$		−	0.312926i		−	0.0112406i
$776$	−36.2599	−	33.2465i	−1.30166	−	1.19348i
$777$		0			0
$778$	5.39682	−	5.55500i	0.193485	−	0.199156i
$779$		−	32.6044i		−	1.16817i
$780$		0			0
$781$			65.3718i			2.33919i
$782$	−3.48873	−	3.38939i	−0.124757	−	0.121204i
$783$		0			0
$784$	3.99333	−	0.230950i	0.142619	−	0.00824822i
$785$		−	3.21779i		−	0.114848i
$786$		0			0
$787$	−0.759732			−0.0270815			−0.0135408	−	0.999908i	$-0.504310\pi$
$787$	−0.759732			−0.0270815			−0.0135408	+	0.999908i	$0.504310\pi$
$788$	1.00462	+	34.7706i	0.0357882	+	1.23865i
$789$		0			0
$790$	1.02130	+	0.992214i	0.0363361	+	0.0353014i
$791$	−2.88561			−0.102600
$792$		0			0
$793$	43.3394			1.53903
$794$	−9.72696	−	9.44998i	−0.345197	−	0.335367i
$795$		0			0
$796$	6.14909	−	0.177665i	0.217949	−	0.00629716i
$797$	26.1758			0.927194			0.463597	−	0.886046i	$-0.346559\pi$
$797$	26.1758			0.927194			0.463597	+	0.886046i	$0.346559\pi$
$798$		0			0
$799$		−	26.6114i		−	0.941442i
$800$	−18.3463	+	21.2076i	−0.648640	+	0.749801i
$801$		0			0
$802$	−1.79236	−	1.74132i	−0.0632903	−	0.0614880i
$803$		−	53.1488i		−	1.87558i
$804$		0			0
$805$		−	0.182258i		−	0.00642376i
$806$	0.219181	−	0.225605i	0.00772031	−	0.00794659i
$807$		0			0
$808$	−39.6672	−	36.3706i	−1.39549	−	1.27951i
$809$		−	14.6876i		−	0.516388i	−0.966093	−	0.258194i	$-0.916873\pi$
$809$		−	14.6876i		−	0.516388i	0.966093	−	0.258194i	$-0.0831273\pi$
$810$		0			0
$811$	−4.13912			−0.145344			−0.0726721	−	0.997356i	$-0.523153\pi$
$811$	−4.13912			−0.145344			−0.0726721	+	0.997356i	$0.523153\pi$
$812$	−6.41360	+	0.185307i	−0.225073	+	0.00650301i
$813$		0			0
$814$	−62.7682	+	64.6080i	−2.20003	+	2.26451i
$815$	3.82168			0.133868
$816$		0			0
$817$	6.25289			0.218761
$818$	5.78944	−	5.95913i	0.202423	−	0.208356i
$819$		0			0
$820$	2.45895	−	0.0710460i	0.0858701	−	0.00248103i
$821$	30.7760			1.07409			0.537045	−	0.843554i	$-0.319540\pi$
$821$	30.7760			1.07409			0.537045	+	0.843554i	$0.319540\pi$
$822$		0			0
$823$			28.3750i			0.989090i	0.869152	+	0.494545i	$0.164665\pi$
$823$			28.3750i			0.989090i	−0.869152	+	0.494545i	$0.835335\pi$
$824$	−20.6257	+	22.4951i	−0.718529	+	0.783655i
$825$		0			0
$826$	4.17180	−	4.29408i	0.145155	−	0.149410i
$827$			26.2522i			0.912880i	0.889754	+	0.456440i	$0.150876\pi$
$827$			26.2522i			0.912880i	−0.889754	+	0.456440i	$0.849124\pi$
$828$		0			0
$829$			8.40833i			0.292033i	0.989282	+	0.146017i	$0.0466453\pi$
$829$			8.40833i			0.292033i	−0.989282	+	0.146017i	$0.953355\pi$
$830$	1.57792	+	1.53299i	0.0547706	+	0.0532109i
$831$		0			0
$832$	−28.0811	+	2.43946i	−0.973537	+	0.0845731i
$833$			3.90616i			0.135340i
$834$		0			0
$835$	2.59401			0.0897695
$836$	70.4434	−	2.03531i	2.43634	−	0.0703927i
$837$		0			0
$838$	−19.2175	−	18.6703i	−0.663858	−	0.644954i
$839$	−10.3099			−0.355936			−0.177968	−	0.984036i	$-0.556952\pi$
$839$	−10.3099			−0.355936			−0.177968	+	0.984036i	$0.556952\pi$
$840$		0			0
$841$	−18.7078			−0.645098
$842$	25.6220	+	24.8924i	0.882991	+	0.857848i
$843$		0			0
$844$	−0.552868	−	19.1351i	−0.0190305	−	0.658657i
$845$	0.121287			0.00417239
$846$		0			0
$847$		−	30.2408i		−	1.03909i
$848$	50.4454	−	2.91746i	1.73230	−	0.100186i
$849$		0			0
$850$	−19.6411	−	19.0818i	−0.673683	−	0.654500i
$851$		−	8.73324i		−	0.299372i
$852$		0			0
$853$		−	42.6992i		−	1.46199i	−0.682382	−	0.730996i	$-0.739056\pi$
$853$		−	42.6992i		−	1.46199i	0.682382	−	0.730996i	$-0.260944\pi$
$854$	−12.1217	+	12.4770i	−0.414795	+	0.426953i
$855$		0			0
$856$	9.50180	−	10.3630i	0.324765	−	0.354201i
$857$		−	5.06990i		−	0.173185i	−0.996244	−	0.0865923i	$-0.972402\pi$
$857$		−	5.06990i		−	0.173185i	0.996244	−	0.0865923i	$-0.0275977\pi$
$858$		0			0
$859$	10.9220			0.372654			0.186327	−	0.982488i	$-0.440342\pi$
$859$	10.9220			0.372654			0.186327	+	0.982488i	$0.440342\pi$
$860$	0.0136252	+	0.471578i	0.000464617	+	0.0160807i
$861$		0			0
$862$	−37.0308	+	38.1162i	−1.26127	+	1.29824i
$863$	−38.1030			−1.29704			−0.648520	−	0.761197i	$-0.724612\pi$
$863$	−38.1030			−1.29704			−0.648520	+	0.761197i	$0.724612\pi$
$864$		0			0
$865$	1.13674			0.0386502
$866$	−20.7970	+	21.4066i	−0.706711	+	0.727425i
$867$		0			0
$868$	0.00364627	+	0.126200i	0.000123762	+	0.00428349i
$869$	−31.2378			−1.05967
$870$		0			0
$871$		−	20.2476i		−	0.686062i
$872$	−5.44413	+	5.93757i	−0.184361	+	0.201072i
$873$		0			0
$874$	−4.76101	+	4.90056i	−0.161044	+	0.165764i
$875$		−	2.06105i		−	0.0696760i
$876$		0			0
$877$		−	26.1674i		−	0.883610i	−0.897111	−	0.441805i	$-0.854338\pi$
$877$		−	26.1674i		−	0.883610i	0.897111	−	0.441805i	$-0.145662\pi$
$878$	−2.92540	−	2.84209i	−0.0987273	−	0.0959160i
$879$		0			0
$880$	0.306997	+	5.30824i	0.0103489	+	0.178941i
$881$		−	29.2903i		−	0.986817i	−0.869798	−	0.493408i	$-0.835751\pi$
$881$		−	29.2903i		−	0.986817i	0.869798	−	0.493408i	$-0.164249\pi$
$882$		0			0
$883$	−49.0887			−1.65197			−0.825983	−	0.563696i	$-0.809379\pi$
$883$	−49.0887			−1.65197			−0.825983	+	0.563696i	$0.809379\pi$
$884$	−0.794962	−	27.5141i	−0.0267375	−	0.925400i
$885$		0			0
$886$	35.0938	+	34.0945i	1.17900	+	1.14543i
$887$	−20.0617			−0.673606			−0.336803	−	0.941575i	$-0.609346\pi$
$887$	−20.0617			−0.673606			−0.336803	+	0.941575i	$0.609346\pi$
$888$		0			0
$889$	7.23082			0.242514
$890$	0.933651	+	0.907064i	0.0312960	+	0.0304049i
$891$		0			0
$892$	−53.1167	+	1.53469i	−1.77848	+	0.0513853i
$893$	−37.3805			−1.25089
$894$		0			0
$895$		−	3.01855i		−	0.100899i
$896$	7.15175	−	8.76655i	0.238923	−	0.292870i
$897$		0			0
$898$	15.0792	+	14.6499i	0.503201	+	0.488872i
$899$		−	0.202518i		−	0.00675434i
$900$		0			0
$901$			49.3443i			1.64390i
$902$	−37.6052	+	38.7074i	−1.25212	+	1.28882i
$903$		0			0
$904$	−5.51583	+	6.01577i	−0.183454	+	0.200082i
$905$		−	3.57585i		−	0.118865i
$906$		0			0
$907$	17.0142			0.564948			0.282474	−	0.959275i	$-0.408845\pi$
$907$	17.0142			0.564948			0.282474	+	0.959275i	$0.408845\pi$
$908$	−41.4518	+	1.19766i	−1.37563	+	0.0397457i
$909$		0			0
$910$	0.718696	−	0.739761i	0.0238245	−	0.0245228i
$911$	−8.54462			−0.283096			−0.141548	−	0.989931i	$-0.545208\pi$
$911$	−8.54462			−0.283096			−0.141548	+	0.989931i	$0.545208\pi$
$912$		0			0
$913$	−48.2631			−1.59727
$914$	−10.8436	+	11.1614i	−0.358675	+	0.369187i
$915$		0			0
$916$	38.5090	−	1.11264i	1.27237	−	0.0367625i
$917$	12.8026			0.422780
$918$		0			0
$919$			6.49841i			0.214363i	0.994239	+	0.107181i	$0.0341826\pi$
$919$			6.49841i			0.214363i	−0.994239	+	0.107181i	$0.965817\pi$
$920$	−0.379963	−	0.348386i	−0.0125270	−	0.0114859i
$921$		0			0
$922$	32.4891	−	33.4414i	1.06997	−	1.10133i
$923$		−	35.8660i		−	1.18055i
$924$		0			0
$925$		−	49.1669i		−	1.61660i
$926$	12.5116	+	12.1553i	0.411157	+	0.399449i
$927$		0			0
$928$	−11.8733	+	13.7250i	−0.389759	+	0.450544i
$929$			16.9216i			0.555181i	0.960699	+	0.277591i	$0.0895358\pi$
$929$			16.9216i			0.555181i	−0.960699	+	0.277591i	$0.910464\pi$
$930$		0			0
$931$	5.48691			0.179826
$932$	49.9867	−	1.44426i	1.63737	−	0.0473083i
$933$		0			0
$934$	34.0071	+	33.0387i	1.11275	+	1.08106i
$935$	−5.19237			−0.169809
$936$		0			0
$937$	14.4249			0.471240			0.235620	−	0.971845i	$-0.424288\pi$
$937$	14.4249			0.471240			0.235620	+	0.971845i	$0.424288\pi$
$938$	5.82906	+	5.66307i	0.190325	+	0.184906i
$939$		0			0
$940$	−0.0814532	−	2.81915i	−0.00265671	−	0.0919505i
$941$	−58.5364			−1.90823			−0.954116	−	0.299436i	$-0.903201\pi$
$941$	−58.5364			−1.90823			−0.954116	+	0.299436i	$0.903201\pi$
$942$		0			0
$943$		−	5.23218i		−	0.170383i
$944$	−0.977699	−	16.9053i	−0.0318214	−	0.550220i
$945$		0			0
$946$	−7.42333	−	7.21195i	−0.241353	−	0.234481i
$947$			15.3006i			0.497201i	0.968606	+	0.248601i	$0.0799707\pi$
$947$			15.3006i			0.497201i	−0.968606	+	0.248601i	$0.920029\pi$
$948$		0			0
$949$			29.1599i			0.946571i
$950$	−26.8038	+	27.5894i	−0.869631	+	0.895120i
$951$		0			0
$952$	8.14337	+	7.46661i	0.263928	+	0.241994i
$953$		−	14.9133i		−	0.483089i	−0.970390	−	0.241544i	$-0.922346\pi$
$953$		−	14.9133i		−	0.483089i	0.970390	−	0.241544i	$-0.0776539\pi$
$954$		0			0
$955$	−1.51068			−0.0488845
$956$	−0.868958	−	30.0752i	−0.0281041	−	0.972701i
$957$		0			0
$958$	−9.51743	+	9.79638i	−0.307494	+	0.316507i
$959$	0.363873			0.0117501
$960$		0			0
$961$	30.9960			0.999871
$962$	34.4376	−	35.4470i	1.11031	−	1.14286i
$963$		0			0
$964$	0.186729	+	6.46279i	0.00601412	+	0.208153i
$965$	2.50680			0.0806966
$966$		0			0
$967$			27.1896i			0.874358i	0.899375	+	0.437179i	$0.144022\pi$
$967$			27.1896i			0.874358i	−0.899375	+	0.437179i	$0.855978\pi$
$968$	−63.0445	−	57.8051i	−2.02633	−	1.85793i
$969$		0			0
$970$	3.54782	−	3.65181i	0.113914	−	0.117252i
$971$			35.0892i			1.12607i	0.826434	+	0.563034i	$0.190366\pi$
$971$			35.0892i			1.12607i	−0.826434	+	0.563034i	$0.809634\pi$
$972$		0			0
$973$		−	9.32338i		−	0.298894i
$974$	−25.4606	−	24.7356i	−0.815811	−	0.792581i
$975$		0			0
$976$	2.84082	+	49.1203i	0.0909326	+	1.57230i
$977$		−	32.0438i		−	1.02517i	−0.858636	−	0.512586i	$-0.828688\pi$
$977$		−	32.0438i		−	1.02517i	0.858636	−	0.512586i	$-0.171312\pi$
$978$		0			0
$979$	−28.5570			−0.912687
$980$	0.0119562	+	0.413810i	0.000381925	+	0.0132187i
$981$		0			0
$982$	−10.7037	−	10.3989i	−0.341569	−	0.331843i
$983$	43.5719			1.38973			0.694864	−	0.719142i	$-0.255465\pi$
$983$	43.5719			1.38973			0.694864	+	0.719142i	$0.255465\pi$
$984$		0			0
$985$	−3.60011			−0.114709
$986$	−12.7112	−	12.3492i	−0.404807	−	0.393280i
$987$		0			0
$988$	−38.6486	+	1.11667i	−1.22958	+	0.0355259i
$989$	1.00343			0.0319073
$990$		0			0
$991$			15.2929i			0.485794i	0.970052	+	0.242897i	$0.0780978\pi$
$991$			15.2929i			0.485794i	−0.970052	+	0.242897i	$0.921902\pi$
$992$	0.270065	+	0.233628i	0.00857456	+	0.00741771i
$993$		0			0
$994$	10.3255	+	10.0314i	0.327504	+	0.318178i
$995$			0.636670i			0.0201838i
$996$		0			0
$997$		−	29.8050i		−	0.943933i	−0.881616	−	0.471967i	$-0.843544\pi$
$997$		−	29.8050i		−	0.943933i	0.881616	−	0.471967i	$-0.156456\pi$
$998$	11.4923	−	11.8291i	0.363782	−	0.374444i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.c.323.10	yes	32
3.2	odd	2	inner	1512.2.j.c.323.23	yes	32
4.3	odd	2		6048.2.j.c.5615.19		32
8.3	odd	2	inner	1512.2.j.c.323.24	yes	32
8.5	even	2		6048.2.j.c.5615.13		32
12.11	even	2		6048.2.j.c.5615.14		32
24.5	odd	2		6048.2.j.c.5615.20		32
24.11	even	2	inner	1512.2.j.c.323.9	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.c.323.9	✓	32	24.11	even	2	inner
1512.2.j.c.323.10	yes	32	1.1	even	1	trivial
1512.2.j.c.323.23	yes	32	3.2	odd	2	inner
1512.2.j.c.323.24	yes	32	8.3	odd	2	inner
6048.2.j.c.5615.13		32	8.5	even	2
6048.2.j.c.5615.14		32	12.11	even	2
6048.2.j.c.5615.19		32	4.3	odd	2
6048.2.j.c.5615.20		32	24.5	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.985454 + 1.01434i) q^{2} +(-0.0577616 - 1.99917i) q^{4} +0.206991 q^{5} +1.00000i q^{7} +(2.08475 + 1.91150i) q^{8} +O(q^{10})\)	\(q+(-0.985454 + 1.01434i) q^{2} +(-0.0577616 - 1.99917i) q^{4} +0.206991 q^{5} +1.00000i q^{7} +(2.08475 + 1.91150i) q^{8} +(-0.203980 + 0.209959i) q^{10} -6.42190i q^{11} +3.52336i q^{13} +(-1.01434 - 0.985454i) q^{14} +(-3.99333 + 0.230950i) q^{16} -3.90616i q^{17} -5.48691 q^{19} +(-0.0119562 - 0.413810i) q^{20} +(6.51397 + 6.32848i) q^{22} -0.880512 q^{23} -4.95715 q^{25} +(-3.57387 - 3.47211i) q^{26} +(1.99917 - 0.0577616i) q^{28} -3.20814 q^{29} +0.0631261i q^{31} +(3.70098 - 4.27817i) q^{32} +(3.96217 + 3.84934i) q^{34} +0.206991i q^{35} +9.91837i q^{37} +(5.40710 - 5.56558i) q^{38} +(0.431525 + 0.395663i) q^{40} +5.94221i q^{41} -1.13960 q^{43} +(-12.8384 + 0.370939i) q^{44} +(0.867704 - 0.893136i) q^{46} +6.81266 q^{47} -1.00000 q^{49} +(4.88505 - 5.02823i) q^{50} +(7.04378 - 0.203515i) q^{52} -12.6324 q^{53} -1.32928i q^{55} +(-1.91150 + 2.08475i) q^{56} +(3.16147 - 3.25414i) q^{58} +4.23338i q^{59} -12.3006i q^{61} +(-0.0640312 - 0.0622079i) q^{62} +(0.692368 + 7.96998i) q^{64} +0.729305i q^{65} -5.74666 q^{67} +(-7.80906 + 0.225626i) q^{68} +(-0.209959 - 0.203980i) q^{70} -10.1795 q^{71} +8.27618 q^{73} +(-10.0606 - 9.77409i) q^{74} +(0.316933 + 10.9692i) q^{76} +6.42190 q^{77} -4.86426i q^{79} +(-0.826584 + 0.0478047i) q^{80} +(-6.02741 - 5.85577i) q^{82} -7.51539i q^{83} -0.808542i q^{85} +(1.12302 - 1.15594i) q^{86} +(12.2754 - 13.3881i) q^{88} -4.44682i q^{89} -3.52336 q^{91} +(0.0508598 + 1.76029i) q^{92} +(-6.71356 + 6.91034i) q^{94} -1.13574 q^{95} -17.3929 q^{97} +(0.985454 - 1.01434i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 8 q^{10} - 8 q^{16} - 64 q^{19} + 24 q^{22} - 16 q^{25} - 8 q^{28} + 8 q^{34} - 24 q^{40} - 48 q^{43} - 8 q^{46} - 32 q^{49} - 24 q^{52} - 96 q^{58} - 40 q^{64} + 16 q^{67} - 16 q^{70} - 16 q^{73} + 16 q^{76} + 24 q^{82} + 72 q^{88} + 16 q^{91} - 56 q^{94} + 64 q^{97}+O(q^{100}) \) 32 * q + 8 * q^4 - 8 * q^10 - 8 * q^16 - 64 * q^19 + 24 * q^22 - 16 * q^25 - 8 * q^28 + 8 * q^34 - 24 * q^40 - 48 * q^43 - 8 * q^46 - 32 * q^49 - 24 * q^52 - 96 * q^58 - 40 * q^64 + 16 * q^67 - 16 * q^70 - 16 * q^73 + 16 * q^76 + 24 * q^82 + 72 * q^88 + 16 * q^91 - 56 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

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