LMFDB - Embedded newform 1512.2.j.c.323.23

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			323.23
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.c.323.24

$q$-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	$-0.514738\pi$
$5$	−0.206991			−0.0925694			−0.0462847	+	0.998928i	$0.514738\pi$
$6$		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	$0.419432\pi$
$11$			6.42190i			1.93628i	−0.250418	+	0.968138i	$0.580568\pi$
$12$		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	$0.157079\pi$
$17$			3.90616i			0.947383i	−0.880691	+	0.473692i	$0.842921\pi$
$18$		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	$-0.470738\pi$
$23$	0.880512			0.183599			0.0917997	+	0.995777i	$0.470738\pi$
$24$		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	$-0.403724\pi$
$29$	3.20814			0.595737			0.297868	+	0.954607i	$0.403724\pi$
$30$		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	$-0.846411\pi$
$41$		−	5.94221i		−	0.928017i	0.885831	−	0.464009i	$-0.153589\pi$
$42$		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	$-0.665515\pi$
$47$	−6.81266			−0.993729			−0.496864	+	0.867828i	$0.665515\pi$
$48$		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	$-0.165662\pi$
$53$	12.6324			1.73520			0.867598	+	0.497265i	$0.165662\pi$
$54$		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	$-0.911134\pi$
$59$		−	4.23338i		−	0.551139i	0.961281	−	0.275570i	$-0.0888664\pi$
$60$		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	$-0.293556\pi$
$71$	10.1795			1.20809			0.604043	+	0.796952i	$0.293556\pi$
$72$		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	$0.135331\pi$
$83$			7.51539i			0.824921i	−0.910976	+	0.412460i	$0.864669\pi$
$84$		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	$0.0757320\pi$
$89$			4.44682i			0.471362i	−0.971830	+	0.235681i	$0.924268\pi$
$90$		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	$-0.104450\pi$
$101$	19.0273			1.89329			0.946643	+	0.322284i	$0.104450\pi$
$102$		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	$0.0772380\pi$
$107$			4.97087i			0.480553i	−0.970705	+	0.240276i	$0.922762\pi$
$108$		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	$-0.956663\pi$
$113$		−	2.88561i		−	0.271455i	0.990746	−	0.135728i	$-0.0433372\pi$
$114$		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	$0.188924\pi$
$131$			12.8026i			1.11857i	−0.828975	+	0.559286i	$0.811076\pi$
$132$		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	$0.00494798\pi$
$137$			0.363873i			0.0310878i	−0.999879	+	0.0155439i	$0.995052\pi$
$138$		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	$-0.436670\pi$
$149$	4.82519			0.395295			0.197648	+	0.980273i	$0.436670\pi$
$150$		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	$-0.661136\pi$
$167$	−12.5320			−0.969754			−0.484877	+	0.874582i	$0.661136\pi$
$168$		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	$-0.566944\pi$
$173$	−5.49171			−0.417527			−0.208763	+	0.977966i	$0.566944\pi$
$174$		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	$0.183467\pi$
$179$			14.5830i			1.08998i	−0.838441	+	0.544992i	$0.816533\pi$
$180$		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	$-0.414944\pi$
$191$	7.29828			0.528085			0.264042	+	0.964511i	$0.414944\pi$
$192$		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	$-0.287301\pi$
$197$	17.3925			1.23917			0.619584	+	0.784931i	$0.287301\pi$
$198$		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	$0.241555\pi$
$227$			20.7345i			1.37620i	−0.725616	+	0.688100i	$0.758445\pi$
$228$		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	$-0.694514\pi$
$233$		−	25.0038i		−	1.63805i	0.573756	−	0.819027i	$-0.305486\pi$
$234$		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	$-0.661746\pi$
$239$	−15.0439			−0.973107			−0.486553	+	0.873651i	$0.661746\pi$
$240$		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	$0.106724\pi$
$251$			10.4258i			0.658071i	−0.944318	+	0.329036i	$0.893276\pi$
$252$		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	$-0.918452\pi$
$257$		−	8.12452i		−	0.506794i	0.967362	−	0.253397i	$-0.0815479\pi$
$258$		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	$-0.650429\pi$
$263$	−14.7639			−0.910382			−0.455191	+	0.890394i	$0.650429\pi$
$264$		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	$-0.805995\pi$
$269$	−26.8961			−1.63989			−0.819943	+	0.572445i	$0.805995\pi$
$270$		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	$-0.960653\pi$
$281$		−	4.13370i		−	0.246596i	0.992370	−	0.123298i	$-0.0393471\pi$
$282$		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	$-0.385781\pi$
$293$	12.0225			0.702360			0.351180	+	0.936308i	$0.385781\pi$
$294$		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	$-0.618104\pi$
$311$	−12.7884			−0.725161			−0.362580	+	0.931952i	$0.618104\pi$
$312$		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	$-0.170987\pi$
$317$	30.5938			1.71832			0.859159	+	0.511709i	$0.170987\pi$
$318$		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	$-0.907772\pi$
$347$		−	10.6443i		−	0.571414i	0.958317	−	0.285707i	$-0.0922284\pi$
$348$		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	$-0.932966\pi$
$353$		−	7.85498i		−	0.418079i	0.977907	−	0.209039i	$-0.0670337\pi$
$354$		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	$-0.302730\pi$
$359$	22.0102			1.16165			0.580826	+	0.814028i	$0.302730\pi$
$360$		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	$-0.397079\pi$
$383$	12.4362			0.635462			0.317731	+	0.948181i	$0.397079\pi$
$384$		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	$-0.455664\pi$
$389$	5.47648			0.277669			0.138834	+	0.990316i	$0.455664\pi$
$390$		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	$-0.985951\pi$
$401$		−	1.76702i		−	0.0882408i	0.999026	−	0.0441204i	$-0.0140485\pi$
$402$		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	$-0.846851\pi$
$419$		−	18.9459i		−	0.925567i	0.886471	−	0.462783i	$-0.153149\pi$
$420$		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	$-0.860144\pi$
$431$	−37.5774			−1.81004			−0.905020	+	0.425369i	$0.860144\pi$
$432$		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	$0.307083\pi$
$443$			34.5978i			1.64379i	−0.569640	+	0.821895i	$0.692917\pi$
$444$		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	$0.114086\pi$
$449$			14.8661i			0.701575i	−0.936455	+	0.350787i	$0.885914\pi$
$450$		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	$-0.221375\pi$
$461$	32.9687			1.53551			0.767753	+	0.640746i	$0.221375\pi$
$462$		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	$0.282607\pi$
$467$			33.5264i			1.55142i	−0.631091	+	0.775709i	$0.717393\pi$
$468$		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	$-0.570815\pi$
$479$	−9.65791			−0.441281			−0.220641	+	0.975355i	$0.570815\pi$
$480$		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	$-0.923471\pi$
$491$		−	10.5524i		−	0.476224i	0.971238	−	0.238112i	$-0.0765285\pi$
$492$		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	$-0.276035\pi$
$503$	29.0202			1.29394			0.646972	+	0.762513i	$0.276035\pi$
$504$		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	$-0.662838\pi$
$509$	−22.0894			−0.979096			−0.489548	+	0.871976i	$0.662838\pi$
$510$		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	$0.103225\pi$
$521$			14.5460i			0.637273i	−0.947877	+	0.318636i	$0.896775\pi$
$522$		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	$-0.479778\pi$
$557$	2.99670			0.126974			0.0634872	+	0.997983i	$0.479778\pi$
$558$		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	$0.0917594\pi$
$563$			13.4913i			0.568589i	−0.958737	+	0.284295i	$0.908241\pi$
$564$		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	$-0.674139\pi$
$569$		−	40.7445i		−	1.70810i	0.520191	−	0.854050i	$-0.325861\pi$
$570$		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	$0.0740637\pi$
$587$			11.1732i			0.461168i	−0.973052	+	0.230584i	$0.925936\pi$
$588$		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	$-0.788934\pi$
$593$		−	29.9792i		−	1.23110i	0.788099	−	0.615549i	$-0.211066\pi$
$594$		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	$-0.541632\pi$
$599$	−6.38388			−0.260838			−0.130419	+	0.991459i	$0.541632\pi$
$600$		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	$0.271790\pi$
$617$			37.4489i			1.50764i	−0.657083	+	0.753818i	$0.728210\pi$
$618$		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	$0.0583541\pi$
$641$			9.23092i			0.364599i	−0.983243	+	0.182300i	$0.941646\pi$
$642$		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	$-0.396408\pi$
$647$	16.2654			0.639457			0.319729	+	0.947509i	$0.396408\pi$
$648$		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	$-0.456748\pi$
$653$	6.92310			0.270922			0.135461	+	0.990783i	$0.456748\pi$
$654$		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	$-0.929328\pi$
$659$		−	11.3057i		−	0.440407i	0.975454	−	0.220203i	$-0.0706721\pi$
$660$		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	$-0.545578\pi$
$677$	−7.42579			−0.285396			−0.142698	+	0.989766i	$0.545578\pi$
$678$		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	$-0.855758\pi$
$683$		−	22.8832i		−	0.875600i	0.899072	−	0.437800i	$-0.144242\pi$
$684$		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	$-0.266545\pi$
$701$	35.4474			1.33883			0.669414	+	0.742890i	$0.266545\pi$
$702$		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	$-0.504874\pi$
$719$	−0.821108			−0.0306222			−0.0153111	+	0.999883i	$0.504874\pi$
$720$		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	$-0.320872\pi$
$743$	29.0849			1.06702			0.533512	+	0.845793i	$0.320872\pi$
$744$		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	$0.319723\pi$
$761$			46.5579i			1.68772i	−0.536562	+	0.843861i	$0.680277\pi$
$762$		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	$-0.538270\pi$
$773$	−6.66928			−0.239877			−0.119939	+	0.992781i	$0.538270\pi$
$774$		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	$-0.653441\pi$
$797$	−26.1758			−0.927194			−0.463597	+	0.886046i	$0.653441\pi$
$798$		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	$0.0831273\pi$
$809$			14.6876i			0.516388i	−0.966093	+	0.258194i	$0.916873\pi$
$810$		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	$-0.680460\pi$
$821$	−30.7760			−1.07409			−0.537045	+	0.843554i	$0.680460\pi$
$822$		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	$-0.849124\pi$
$827$		−	26.2522i		−	0.912880i	0.889754	−	0.456440i	$-0.150876\pi$
$828$		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	$-0.443048\pi$
$839$	10.3099			0.355936			0.177968	+	0.984036i	$0.443048\pi$
$840$		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	$0.0275977\pi$
$857$			5.06990i			0.173185i	−0.996244	+	0.0865923i	$0.972402\pi$
$858$		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	$-0.275388\pi$
$863$	38.1030			1.29704			0.648520	+	0.761197i	$0.275388\pi$
$864$		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	$0.164249\pi$
$881$			29.2903i			0.986817i	−0.869798	+	0.493408i	$0.835751\pi$
$882$		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	$-0.390654\pi$
$887$	20.0617			0.673606			0.336803	+	0.941575i	$0.390654\pi$
$888$		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	$-0.454792\pi$
$911$	8.54462			0.283096			0.141548	+	0.989931i	$0.454792\pi$
$912$		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	$-0.910464\pi$
$929$		−	16.9216i		−	0.555181i	0.960699	−	0.277591i	$-0.0895358\pi$
$930$		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	$-0.0967986\pi$
$941$	58.5364			1.90823			0.954116	+	0.299436i	$0.0967986\pi$
$942$		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	$-0.920029\pi$
$947$		−	15.3006i		−	0.497201i	0.968606	−	0.248601i	$-0.0799707\pi$
$948$		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	$0.0776539\pi$
$953$			14.9133i			0.483089i	−0.970390	+	0.241544i	$0.922346\pi$
$954$		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	$-0.809634\pi$
$971$		−	35.0892i		−	1.12607i	0.826434	−	0.563034i	$-0.190366\pi$
$972$		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	$0.171312\pi$
$977$			32.0438i			1.02517i	−0.858636	+	0.512586i	$0.828688\pi$
$978$		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	$-0.744535\pi$
$983$	−43.5719			−1.38973			−0.694864	+	0.719142i	$0.744535\pi$
$984$		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.323.23	yes	32
3.2	odd	2	inner	1512.2.j.c.323.10	yes	32
4.3	odd	2		6048.2.j.c.5615.14		32
8.3	odd	2	inner	1512.2.j.c.323.9	✓	32
8.5	even	2		6048.2.j.c.5615.20		32
12.11	even	2		6048.2.j.c.5615.19		32
24.5	odd	2		6048.2.j.c.5615.13		32
24.11	even	2	inner	1512.2.j.c.323.24	yes	32

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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more