LMFDB - Embedded newform 144.2.k.c.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,2,Mod(37,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 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("144.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.629407744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 2x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 2x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.1
Root			$-1.38255 + 0.297594i$ of defining polynomial
Character	$\chi$	$=$	144.109
Dual form			144.2.k.c.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38255 + 0.297594i) q^{2} +(1.82288 - 0.822876i) q^{4} +(0.595188 - 0.595188i) q^{5} -1.64575i q^{7} +(-2.27533 + 1.68014i) q^{8} +O(q^{10})$	\(q+(-1.38255 + 0.297594i) q^{2} +(1.82288 - 0.822876i) q^{4} +(0.595188 - 0.595188i) q^{5} -1.64575i q^{7} +(-2.27533 + 1.68014i) q^{8} +(-0.645751 + 1.00000i) q^{10} +(3.36028 - 3.36028i) q^{11} +(2.64575 + 2.64575i) q^{13} +(0.489766 + 2.27533i) q^{14} +(2.64575 - 3.00000i) q^{16} +5.53019 q^{17} +(-3.64575 - 3.64575i) q^{19} +(0.595188 - 1.57472i) q^{20} +(-3.64575 + 5.64575i) q^{22} +4.33981i q^{23} +4.29150i q^{25} +(-4.44524 - 2.87052i) q^{26} +(-1.35425 - 3.00000i) q^{28} +(-6.12538 - 6.12538i) q^{29} -5.64575 q^{31} +(-2.76510 + 4.93500i) q^{32} +(-7.64575 + 1.64575i) q^{34} +(-0.979531 - 0.979531i) q^{35} +(-0.645751 + 0.645751i) q^{37} +(6.12538 + 3.95547i) q^{38} +(-0.354249 + 2.35425i) q^{40} +7.91094i q^{41} +(-0.354249 + 0.354249i) q^{43} +(3.36028 - 8.89047i) q^{44} +(-1.29150 - 6.00000i) q^{46} -9.10132 q^{47} +4.29150 q^{49} +(-1.27713 - 5.93321i) q^{50} +(7.00000 + 2.64575i) q^{52} +(-4.93500 + 4.93500i) q^{53} -4.00000i q^{55} +(2.76510 + 3.74463i) q^{56} +(10.2915 + 6.64575i) q^{58} +(4.33981 - 4.33981i) q^{59} +(-0.645751 - 0.645751i) q^{61} +(7.80552 - 1.68014i) q^{62} +(2.35425 - 7.64575i) q^{64} +3.14944 q^{65} +(4.00000 + 4.00000i) q^{67} +(10.0808 - 4.55066i) q^{68} +(1.64575 + 1.06275i) q^{70} +13.4411i q^{71} -3.29150i q^{73} +(0.700610 - 1.08495i) q^{74} +(-9.64575 - 3.64575i) q^{76} +(-5.53019 - 5.53019i) q^{77} +9.64575 q^{79} +(-0.210845 - 3.36028i) q^{80} +(-2.35425 - 10.9373i) q^{82} +(-3.36028 - 3.36028i) q^{83} +(3.29150 - 3.29150i) q^{85} +(0.384343 - 0.595188i) q^{86} +(-2.00000 + 13.2915i) q^{88} +2.38075i q^{89} +(4.35425 - 4.35425i) q^{91} +(3.57113 + 7.91094i) q^{92} +(12.5830 - 2.70850i) q^{94} -4.33981 q^{95} -10.5830 q^{97} +(-5.93321 + 1.27713i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} + 16 q^{10} - 8 q^{19} - 8 q^{22} - 32 q^{28} - 24 q^{31} - 40 q^{34} + 16 q^{37} - 24 q^{40} - 24 q^{43} + 32 q^{46} - 8 q^{49} + 56 q^{52} + 40 q^{58} + 16 q^{61} + 40 q^{64} + 32 q^{67} - 8 q^{70} - 56 q^{76} + 56 q^{79} - 40 q^{82} - 16 q^{85} - 16 q^{88} + 56 q^{91} + 16 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 + 16 * q^10 - 8 * q^19 - 8 * q^22 - 32 * q^28 - 24 * q^31 - 40 * q^34 + 16 * q^37 - 24 * q^40 - 24 * q^43 + 32 * q^46 - 8 * q^49 + 56 * q^52 + 40 * q^58 + 16 * q^61 + 40 * q^64 + 32 * q^67 - 8 * q^70 - 56 * q^76 + 56 * q^79 - 40 * q^82 - 16 * q^85 - 16 * q^88 + 56 * q^91 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.38255	+	0.297594i	−0.977609	+	0.210431i
$2$	−1.38255	+	0.297594i	−0.977609	+	0.210431i
$3$		0			0
$3$		0			0
$4$	1.82288	−	0.822876i	0.911438	−	0.411438i
$5$	0.595188	−	0.595188i	0.266176	−	0.266176i	−0.561381	−	0.827557i	$-0.689730\pi$
$5$	0.595188	−	0.595188i	0.266176	−	0.266176i	0.827557	+	0.561381i	$0.189730\pi$
$6$		0			0
$7$		−	1.64575i		−	0.622036i	−0.950404	−	0.311018i	$-0.899330\pi$
$7$		−	1.64575i		−	0.622036i	0.950404	−	0.311018i	$-0.100670\pi$
$8$	−2.27533	+	1.68014i	−0.804450	+	0.594020i
$9$		0			0
$10$	−0.645751	+	1.00000i	−0.204204	+	0.316228i
$11$	3.36028	−	3.36028i	1.01316	−	1.01316i	0.0132513	−	0.999912i	$-0.495782\pi$
$11$	3.36028	−	3.36028i	1.01316	−	1.01316i	0.999912	−	0.0132513i	$-0.00421814\pi$
$12$		0			0
$13$	2.64575	+	2.64575i	0.733799	+	0.733799i	0.971370	−	0.237571i	$-0.0763512\pi$
$13$	2.64575	+	2.64575i	0.733799	+	0.733799i	−0.237571	+	0.971370i	$0.576351\pi$
$14$	0.489766	+	2.27533i	0.130895	+	0.608107i
$15$		0			0
$16$	2.64575	−	3.00000i	0.661438	−	0.750000i
$17$	5.53019			1.34127			0.670634	−	0.741788i	$-0.266022\pi$
$17$	5.53019			1.34127			0.670634	+	0.741788i	$0.266022\pi$
$18$		0			0
$19$	−3.64575	−	3.64575i	−0.836393	−	0.836393i	0.151989	−	0.988382i	$-0.451432\pi$
$19$	−3.64575	−	3.64575i	−0.836393	−	0.836393i	−0.988382	+	0.151989i	$0.951432\pi$
$20$	0.595188	−	1.57472i	0.133088	−	0.352118i
$21$		0			0
$22$	−3.64575	+	5.64575i	−0.777277	+	1.20368i
$23$			4.33981i			0.904914i	0.891786	+	0.452457i	$0.149452\pi$
$23$			4.33981i			0.904914i	−0.891786	+	0.452457i	$0.850548\pi$
$24$		0			0
$25$			4.29150i			0.858301i
$26$	−4.44524	−	2.87052i	−0.871783	−	0.562955i
$27$		0			0
$28$	−1.35425	−	3.00000i	−0.255929	−	0.566947i
$29$	−6.12538	−	6.12538i	−1.13745	−	1.13745i	−0.988905	−	0.148549i	$-0.952540\pi$
$29$	−6.12538	−	6.12538i	−1.13745	−	1.13745i	−0.148549	−	0.988905i	$-0.547460\pi$
$30$		0			0
$31$	−5.64575			−1.01401			−0.507003	−	0.861944i	$-0.669247\pi$
$31$	−5.64575			−1.01401			−0.507003	+	0.861944i	$0.669247\pi$
$32$	−2.76510	+	4.93500i	−0.488804	+	0.872393i
$33$		0			0
$34$	−7.64575	+	1.64575i	−1.31124	+	0.282244i
$35$	−0.979531	−	0.979531i	−0.165571	−	0.165571i
$36$		0			0
$37$	−0.645751	+	0.645751i	−0.106161	+	0.106161i	−0.758192	−	0.652031i	$-0.773917\pi$
$37$	−0.645751	+	0.645751i	−0.106161	+	0.106161i	0.652031	+	0.758192i	$0.273917\pi$
$38$	6.12538	+	3.95547i	0.993668	+	0.641662i
$39$		0			0
$40$	−0.354249	+	2.35425i	−0.0560116	+	0.372239i
$41$			7.91094i			1.23548i	0.786382	+	0.617741i	$0.211952\pi$
$41$			7.91094i			1.23548i	−0.786382	+	0.617741i	$0.788048\pi$
$42$		0			0
$43$	−0.354249	+	0.354249i	−0.0540224	+	0.0540224i	−0.733602	−	0.679579i	$-0.762162\pi$
$43$	−0.354249	+	0.354249i	−0.0540224	+	0.0540224i	0.679579	+	0.733602i	$0.262162\pi$
$44$	3.36028	−	8.89047i	0.506582	−	1.34029i
$45$		0			0
$46$	−1.29150	−	6.00000i	−0.190422	−	0.884652i
$47$	−9.10132			−1.32756			−0.663782	−	0.747926i	$-0.731050\pi$
$47$	−9.10132			−1.32756			−0.663782	+	0.747926i	$0.731050\pi$
$48$		0			0
$49$	4.29150			0.613072
$50$	−1.27713	−	5.93321i	−0.180613	−	0.839082i
$51$		0			0
$52$	7.00000	+	2.64575i	0.970725	+	0.366900i
$53$	−4.93500	+	4.93500i	−0.677875	+	0.677875i	−0.959519	−	0.281644i	$-0.909120\pi$
$53$	−4.93500	+	4.93500i	−0.677875	+	0.677875i	0.281644	+	0.959519i	$0.409120\pi$
$54$		0			0
$55$		−	4.00000i		−	0.539360i
$56$	2.76510	+	3.74463i	0.369501	+	0.500397i
$57$		0			0
$58$	10.2915	+	6.64575i	1.35134	+	0.872630i
$59$	4.33981	−	4.33981i	0.564996	−	0.564996i	−0.365727	−	0.930722i	$-0.619179\pi$
$59$	4.33981	−	4.33981i	0.564996	−	0.564996i	0.930722	+	0.365727i	$0.119179\pi$
$60$		0			0
$61$	−0.645751	−	0.645751i	−0.0826800	−	0.0826800i	0.664557	−	0.747237i	$-0.268620\pi$
$61$	−0.645751	−	0.645751i	−0.0826800	−	0.0826800i	−0.747237	+	0.664557i	$0.768620\pi$
$62$	7.80552	−	1.68014i	0.991302	−	0.213378i
$63$		0			0
$64$	2.35425	−	7.64575i	0.294281	−	0.955719i
$65$	3.14944			0.390640
$66$		0			0
$67$	4.00000	+	4.00000i	0.488678	+	0.488678i	0.907889	−	0.419211i	$-0.137693\pi$
$67$	4.00000	+	4.00000i	0.488678	+	0.488678i	−0.419211	+	0.907889i	$0.637693\pi$
$68$	10.0808	−	4.55066i	1.22248	−	0.551848i
$69$		0			0
$70$	1.64575	+	1.06275i	0.196705	+	0.127022i
$71$			13.4411i			1.59517i	0.603207	+	0.797584i	$0.293889\pi$
$71$			13.4411i			1.59517i	−0.603207	+	0.797584i	$0.706111\pi$
$72$		0			0
$73$		−	3.29150i		−	0.385241i	−0.981273	−	0.192621i	$-0.938301\pi$
$73$		−	3.29150i		−	0.385241i	0.981273	−	0.192621i	$-0.0616987\pi$
$74$	0.700610	−	1.08495i	0.0814443	−	0.126123i
$75$		0			0
$76$	−9.64575	−	3.64575i	−1.10644	−	0.418196i
$77$	−5.53019	−	5.53019i	−0.630224	−	0.630224i
$78$		0			0
$79$	9.64575			1.08523			0.542616	−	0.839981i	$-0.317434\pi$
$79$	9.64575			1.08523			0.542616	+	0.839981i	$0.317434\pi$
$80$	−0.210845	−	3.36028i	−0.0235731	−	0.375691i
$81$		0			0
$82$	−2.35425	−	10.9373i	−0.259983	−	1.20782i
$83$	−3.36028	−	3.36028i	−0.368839	−	0.368839i	0.498215	−	0.867054i	$-0.333989\pi$
$83$	−3.36028	−	3.36028i	−0.368839	−	0.368839i	−0.867054	+	0.498215i	$0.833989\pi$
$84$		0			0
$85$	3.29150	−	3.29150i	0.357014	−	0.357014i
$86$	0.384343	−	0.595188i	0.0414448	−	0.0641808i
$87$		0			0
$88$	−2.00000	+	13.2915i	−0.213201	+	1.41688i
$89$			2.38075i			0.252359i	0.992007	+	0.126180i	$0.0402716\pi$
$89$			2.38075i			0.252359i	−0.992007	+	0.126180i	$0.959728\pi$
$90$		0			0
$91$	4.35425	−	4.35425i	0.456449	−	0.456449i
$92$	3.57113	+	7.91094i	0.372316	+	0.824773i
$93$		0			0
$94$	12.5830	−	2.70850i	1.29784	−	0.279360i
$95$	−4.33981			−0.445256
$96$		0			0
$97$	−10.5830			−1.07454			−0.537271	−	0.843410i	$-0.680545\pi$
$97$	−10.5830			−1.07454			−0.537271	+	0.843410i	$0.680545\pi$
$98$	−5.93321	+	1.27713i	−0.599344	+	0.129009i
$99$		0			0
$100$	3.53137	+	7.82288i	0.353137	+	0.782288i
$101$	0.595188	−	0.595188i	0.0592234	−	0.0592234i	−0.676875	−	0.736098i	$-0.736666\pi$
$101$	0.595188	−	0.595188i	0.0592234	−	0.0592234i	0.736098	+	0.676875i	$0.236666\pi$
$102$		0			0
$103$			16.9373i			1.66888i	0.551101	+	0.834439i	$0.314208\pi$
$103$			16.9373i			1.66888i	−0.551101	+	0.834439i	$0.685792\pi$
$104$	−10.4652	−	1.57472i	−1.02620	−	0.154414i
$105$		0			0
$106$	5.35425	−	8.29150i	0.520051	−	0.805342i
$107$	2.38075	−	2.38075i	0.230156	−	0.230156i	−0.582602	−	0.812758i	$-0.697965\pi$
$107$	2.38075	−	2.38075i	0.230156	−	0.230156i	0.812758	+	0.582602i	$0.197965\pi$
$108$		0			0
$109$	−6.64575	−	6.64575i	−0.636548	−	0.636548i	0.313155	−	0.949702i	$-0.398614\pi$
$109$	−6.64575	−	6.64575i	−0.636548	−	0.636548i	−0.949702	+	0.313155i	$0.898614\pi$
$110$	1.19038	+	5.53019i	0.113498	+	0.527283i
$111$		0			0
$112$	−4.93725	−	4.35425i	−0.466527	−	0.411438i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	2.58301	+	2.58301i	0.240866	+	0.240866i
$116$	−16.2062	−	6.12538i	−1.50471	−	0.568727i
$117$		0			0
$118$	−4.70850	+	7.29150i	−0.433452	+	0.671237i
$119$		−	9.10132i		−	0.834316i
$120$		0			0
$121$		−	11.5830i		−	1.05300i
$122$	1.08495	+	0.700610i	0.0982271	+	0.0634303i
$123$		0			0
$124$	−10.2915	+	4.64575i	−0.924204	+	0.417201i
$125$	5.53019	+	5.53019i	0.494635	+	0.494635i
$126$		0			0
$127$	0.937254			0.0831678			0.0415839	−	0.999135i	$-0.486760\pi$
$127$	0.937254			0.0831678			0.0415839	+	0.999135i	$0.486760\pi$
$128$	−0.979531	+	11.2712i	−0.0865792	+	0.996245i
$129$		0			0
$130$	−4.35425	+	0.937254i	−0.381893	+	0.0822026i
$131$	6.72057	+	6.72057i	0.587179	+	0.587179i	0.936866	−	0.349688i	$-0.113712\pi$
$131$	6.72057	+	6.72057i	0.587179	+	0.587179i	−0.349688	+	0.936866i	$0.613712\pi$
$132$		0			0
$133$	−6.00000	+	6.00000i	−0.520266	+	0.520266i
$134$	−6.72057	−	4.33981i	−0.580568	−	0.374903i
$135$		0			0
$136$	−12.5830	+	9.29150i	−1.07898	+	0.796740i
$137$		−	10.2917i		−	0.879279i	−0.898174	−	0.439639i	$-0.855106\pi$
$137$		−	10.2917i		−	0.879279i	0.898174	−	0.439639i	$-0.144894\pi$
$138$		0			0
$139$	−14.5830	+	14.5830i	−1.23691	+	1.23691i	−0.275659	+	0.961256i	$0.588896\pi$
$139$	−14.5830	+	14.5830i	−1.23691	+	1.23691i	−0.961256	+	0.275659i	$0.911104\pi$
$140$	−2.59160	−	0.979531i	−0.219030	−	0.0827855i
$141$		0			0
$142$	−4.00000	−	18.5830i	−0.335673	−	1.55945i
$143$	17.7809			1.48692
$144$		0			0
$145$	−7.29150			−0.605526
$146$	0.979531	+	4.55066i	0.0810666	+	0.376615i
$147$		0			0
$148$	−0.645751	+	1.70850i	−0.0530804	+	0.140438i
$149$	11.6556	−	11.6556i	0.954861	−	0.954861i	−0.0441630	−	0.999024i	$-0.514062\pi$
$149$	11.6556	−	11.6556i	0.954861	−	0.954861i	0.999024	+	0.0441630i	$0.0140621\pi$
$150$		0			0
$151$		−	10.3542i		−	0.842617i	−0.906917	−	0.421308i	$-0.861571\pi$
$151$		−	10.3542i		−	0.842617i	0.906917	−	0.421308i	$-0.138429\pi$
$152$	14.4207	+	2.16991i	1.16967	+	0.176003i
$153$		0			0
$154$	9.29150	+	6.00000i	0.748731	+	0.483494i
$155$	−3.36028	+	3.36028i	−0.269904	+	0.269904i
$156$		0			0
$157$	−6.64575	−	6.64575i	−0.530389	−	0.530389i	0.390299	−	0.920688i	$-0.372372\pi$
$157$	−6.64575	−	6.64575i	−0.530389	−	0.530389i	−0.920688	+	0.390299i	$0.872372\pi$
$158$	−13.3357	+	2.87052i	−1.06093	+	0.228366i
$159$		0			0
$160$	1.29150	+	4.58301i	0.102102	+	0.362318i
$161$	7.14226			0.562889
$162$		0			0
$163$	11.6458	+	11.6458i	0.912166	+	0.912166i	0.996442	−	0.0842767i	$-0.0268580\pi$
$163$	11.6458	+	11.6458i	0.912166	+	0.912166i	−0.0842767	+	0.996442i	$0.526858\pi$
$164$	6.50972	+	14.4207i	0.508324	+	1.12606i
$165$		0			0
$166$	5.64575	+	3.64575i	0.438195	+	0.282965i
$167$		−	17.7809i		−	1.37593i	−0.725743	−	0.687965i	$-0.758504\pi$
$167$		−	17.7809i		−	1.37593i	0.725743	−	0.687965i	$-0.241496\pi$
$168$		0			0
$169$			1.00000i			0.0769231i
$170$	−3.57113	+	5.53019i	−0.273893	+	0.424146i
$171$		0			0
$172$	−0.354249	+	0.937254i	−0.0270112	+	0.0714649i
$173$	4.93500	+	4.93500i	0.375201	+	0.375201i	0.869367	−	0.494166i	$-0.164527\pi$
$173$	4.93500	+	4.93500i	0.375201	+	0.375201i	−0.494166	+	0.869367i	$0.664527\pi$
$174$		0			0
$175$	7.06275			0.533893
$176$	−1.19038	−	18.9713i	−0.0897280	−	1.43002i
$177$		0			0
$178$	−0.708497	−	3.29150i	−0.0531041	−	0.246709i
$179$	−2.38075	−	2.38075i	−0.177946	−	0.177946i	0.612514	−	0.790460i	$-0.290158\pi$
$179$	−2.38075	−	2.38075i	−0.177946	−	0.177946i	−0.790460	+	0.612514i	$0.790158\pi$
$180$		0			0
$181$	−0.645751	+	0.645751i	−0.0479983	+	0.0479983i	−0.730699	−	0.682700i	$-0.760805\pi$
$181$	−0.645751	+	0.645751i	−0.0479983	+	0.0479983i	0.682700	+	0.730699i	$0.260805\pi$
$182$	−4.72416	+	7.31575i	−0.350178	+	0.542280i
$183$		0			0
$184$	−7.29150	−	9.87451i	−0.537537	−	0.727958i
$185$			0.768687i			0.0565150i
$186$		0			0
$187$	18.5830	−	18.5830i	1.35892	−	1.35892i
$188$	−16.5906	+	7.48925i	−1.20999	+	0.546210i
$189$		0			0
$190$	6.00000	−	1.29150i	0.435286	−	0.0936954i
$191$	9.10132			0.658548			0.329274	−	0.944234i	$-0.393196\pi$
$191$	9.10132			0.658548			0.329274	+	0.944234i	$0.393196\pi$
$192$		0			0
$193$	11.8745			0.854746			0.427373	−	0.904075i	$-0.359439\pi$
$193$	11.8745			0.854746			0.427373	+	0.904075i	$0.359439\pi$
$194$	14.6315	−	3.14944i	1.05048	−	0.226117i
$195$		0			0
$196$	7.82288	−	3.53137i	0.558777	−	0.252241i
$197$	−8.50613	+	8.50613i	−0.606037	+	0.606037i	−0.941908	−	0.335871i	$-0.890969\pi$
$197$	−8.50613	+	8.50613i	−0.606037	+	0.606037i	0.335871	+	0.941908i	$0.390969\pi$
$198$		0			0
$199$			13.6458i			0.967322i	0.875256	+	0.483661i	$0.160693\pi$
$199$			13.6458i			0.967322i	−0.875256	+	0.483661i	$0.839307\pi$
$200$	−7.21033	−	9.76458i	−0.509847	−	0.690460i
$201$		0			0
$202$	−0.645751	+	1.00000i	−0.0454349	+	0.0703598i
$203$	−10.0808	+	10.0808i	−0.707537	+	0.707537i
$204$		0			0
$205$	4.70850	+	4.70850i	0.328856	+	0.328856i
$206$	−5.04042	−	23.4166i	−0.351183	−	1.63151i
$207$		0			0
$208$	14.9373	−	0.937254i	1.03571	−	0.0649869i
$209$	−24.5015			−1.69481
$210$		0			0
$211$	−14.5830	−	14.5830i	−1.00394	−	1.00394i	−0.999992	−	0.00394326i	$-0.998745\pi$
$211$	−14.5830	−	14.5830i	−1.00394	−	1.00394i	−0.00394326	−	0.999992i	$-0.501255\pi$
$212$	−4.93500	+	13.0568i	−0.338937	+	0.896744i
$213$		0			0
$214$	−2.58301	+	4.00000i	−0.176571	+	0.273434i
$215$			0.421689i			0.0287590i
$216$		0			0
$217$			9.29150i			0.630748i
$218$	11.1658	+	7.21033i	0.756244	+	0.488345i
$219$		0			0
$220$	−3.29150	−	7.29150i	−0.221913	−	0.491593i
$221$	14.6315	+	14.6315i	0.984222	+	0.984222i
$222$		0			0
$223$	−14.3542			−0.961232			−0.480616	−	0.876931i	$-0.659587\pi$
$223$	−14.3542			−0.961232			−0.480616	+	0.876931i	$0.659587\pi$
$224$	8.12179	+	4.55066i	0.542660	+	0.304054i
$225$		0			0
$226$		0			0
$227$	−1.40122	−	1.40122i	−0.0930023	−	0.0930023i	0.659075	−	0.752077i	$-0.270948\pi$
$227$	−1.40122	−	1.40122i	−0.0930023	−	0.0930023i	−0.752077	+	0.659075i	$0.770948\pi$
$228$		0			0
$229$	17.9373	−	17.9373i	1.18533	−	1.18533i	0.206982	−	0.978345i	$-0.433636\pi$
$229$	17.9373	−	17.9373i	1.18533	−	1.18533i	0.978345	−	0.206982i	$-0.0663643\pi$
$230$	−4.33981	−	2.80244i	−0.286159	−	0.184787i
$231$		0			0
$232$	24.2288	+	3.64575i	1.59070	+	0.239355i
$233$		−	19.7400i		−	1.29321i	−0.762825	−	0.646606i	$-0.776188\pi$
$233$		−	19.7400i		−	1.29321i	0.762825	−	0.646606i	$-0.223812\pi$
$234$		0			0
$235$	−5.41699	+	5.41699i	−0.353366	+	0.353366i
$236$	4.33981	−	11.4821i	0.282498	−	0.747419i
$237$		0			0
$238$	2.70850	+	12.5830i	0.175566	+	0.815635i
$239$	−13.0194			−0.842158			−0.421079	−	0.907024i	$-0.638348\pi$
$239$	−13.0194			−0.842158			−0.421079	+	0.907024i	$0.638348\pi$
$240$		0			0
$241$	−1.29150			−0.0831930			−0.0415965	−	0.999134i	$-0.513244\pi$
$241$	−1.29150			−0.0831930			−0.0415965	+	0.999134i	$0.513244\pi$
$242$	3.44703	+	16.0141i	0.221584	+	1.02942i
$243$		0			0
$244$	−1.70850	−	0.645751i	−0.109375	−	0.0413400i
$245$	2.55425	−	2.55425i	0.163185	−	0.163185i
$246$		0			0
$247$		−	19.2915i		−	1.22749i
$248$	12.8459	−	9.48566i	0.815718	−	0.602340i
$249$		0			0
$250$	−9.29150	−	6.00000i	−0.587646	−	0.379473i
$251$	−18.7605	+	18.7605i	−1.18415	+	1.18415i	−0.205492	+	0.978659i	$0.565879\pi$
$251$	−18.7605	+	18.7605i	−1.18415	+	1.18415i	−0.978659	+	0.205492i	$0.934121\pi$
$252$		0			0
$253$	14.5830	+	14.5830i	0.916826	+	0.916826i
$254$	−1.29580	+	0.278921i	−0.0813056	+	0.0175011i
$255$		0			0
$256$	−2.00000	−	15.8745i	−0.125000	−	0.992157i
$257$	−29.2630			−1.82538			−0.912688	−	0.408656i	$-0.865998\pi$
$257$	−29.2630			−1.82538			−0.912688	+	0.408656i	$0.865998\pi$
$258$		0			0
$259$	1.06275	+	1.06275i	0.0660358	+	0.0660358i
$260$	5.74103	−	2.59160i	0.356044	−	0.160724i
$261$		0			0
$262$	−11.2915	−	7.29150i	−0.697591	−	0.450471i
$263$		−	8.67963i		−	0.535209i	−0.963529	−	0.267604i	$-0.913768\pi$
$263$		−	8.67963i		−	0.535209i	0.963529	−	0.267604i	$-0.0862320\pi$
$264$		0			0
$265$			5.87451i			0.360868i
$266$	6.50972	−	10.0808i	0.399137	−	0.618097i
$267$		0			0
$268$	10.5830	+	4.00000i	0.646460	+	0.244339i
$269$	10.4652	+	10.4652i	0.638074	+	0.638074i	0.950080	−	0.312006i	$-0.101001\pi$
$269$	10.4652	+	10.4652i	0.638074	+	0.638074i	−0.312006	+	0.950080i	$0.601001\pi$
$270$		0			0
$271$	6.35425			0.385993			0.192997	−	0.981199i	$-0.438179\pi$
$271$	6.35425			0.385993			0.192997	+	0.981199i	$0.438179\pi$
$272$	14.6315	−	16.5906i	0.887166	−	1.00595i
$273$		0			0
$274$	3.06275	+	14.2288i	0.185027	+	0.859591i
$275$	14.4207	+	14.4207i	0.869599	+	0.869599i
$276$		0			0
$277$	−16.5203	+	16.5203i	−0.992606	+	0.992606i	−0.999973	−	0.00736669i	$-0.997655\pi$
$277$	−16.5203	+	16.5203i	−0.992606	+	0.992606i	0.00736669	+	0.999973i	$0.497655\pi$
$278$	15.8219	−	24.5015i	0.948934	−	1.46950i
$279$		0			0
$280$	3.87451	+	0.583005i	0.231546	+	0.0348412i
$281$			2.38075i			0.142024i	0.997475	+	0.0710119i	$0.0226228\pi$
$281$			2.38075i			0.142024i	−0.997475	+	0.0710119i	$0.977377\pi$
$282$		0			0
$283$	−2.58301	+	2.58301i	−0.153544	+	0.153544i	−0.779699	−	0.626155i	$-0.784628\pi$
$283$	−2.58301	+	2.58301i	−0.153544	+	0.153544i	0.626155	+	0.779699i	$0.284628\pi$
$284$	11.0604	+	24.5015i	0.656313	+	1.45390i
$285$		0			0
$286$	−24.5830	+	5.29150i	−1.45362	+	0.312893i
$287$	13.0194			0.768513
$288$		0			0
$289$	13.5830			0.799000
$290$	10.0808	−	2.16991i	0.591968	−	0.127421i
$291$		0			0
$292$	−2.70850	−	6.00000i	−0.158503	−	0.351123i
$293$	2.55425	−	2.55425i	0.149221	−	0.149221i	−0.628549	−	0.777770i	$-0.716351\pi$
$293$	2.55425	−	2.55425i	0.149221	−	0.149221i	0.777770	+	0.628549i	$0.216351\pi$
$294$		0			0
$295$		−	5.16601i		−	0.300777i
$296$	0.384343	−	2.55425i	0.0223395	−	0.148463i
$297$		0			0
$298$	−12.6458	+	19.5830i	−0.732549	+	1.13441i
$299$	−11.4821	+	11.4821i	−0.664025	+	0.664025i
$300$		0			0
$301$	0.583005	+	0.583005i	0.0336039	+	0.0336039i
$302$	3.08136	+	14.3152i	0.177312	+	0.823750i
$303$		0			0
$304$	−20.5830	+	1.29150i	−1.18052	+	0.0740728i
$305$	−0.768687			−0.0440149
$306$		0			0
$307$	−20.0000	−	20.0000i	−1.14146	−	1.14146i	−0.988183	−	0.153277i	$-0.951017\pi$
$307$	−20.0000	−	20.0000i	−1.14146	−	1.14146i	−0.153277	−	0.988183i	$-0.548983\pi$
$308$	−14.6315	−	5.53019i	−0.833708	−	0.315112i
$309$		0			0
$310$	3.64575	−	5.64575i	0.207065	−	0.320657i
$311$		−	8.67963i		−	0.492177i	−0.969247	−	0.246088i	$-0.920855\pi$
$311$		−	8.67963i		−	0.492177i	0.969247	−	0.246088i	$-0.0791453\pi$
$312$		0			0
$313$			9.29150i			0.525187i	0.964907	+	0.262593i	$0.0845778\pi$
$313$			9.29150i			0.525187i	−0.964907	+	0.262593i	$0.915422\pi$
$314$	11.1658	+	7.21033i	0.630123	+	0.406903i
$315$		0			0
$316$	17.5830	−	7.93725i	0.989121	−	0.446505i
$317$	−0.595188	−	0.595188i	−0.0334291	−	0.0334291i	0.690195	−	0.723624i	$-0.257525\pi$
$317$	−0.595188	−	0.595188i	−0.0334291	−	0.0334291i	−0.723624	+	0.690195i	$0.757525\pi$
$318$		0			0
$319$	−41.1660			−2.30485
$320$	−3.14944	−	5.95188i	−0.176059	−	0.332720i
$321$		0			0
$322$	−9.87451	+	2.12549i	−0.550285	+	0.118449i
$323$	−20.1617	−	20.1617i	−1.12183	−	1.12183i
$324$		0			0
$325$	−11.3542	+	11.3542i	−0.629820	+	0.629820i
$326$	−19.5665	−	12.6351i	−1.08369	−	0.699793i
$327$		0			0
$328$	−13.2915	−	18.0000i	−0.733900	−	0.993884i
$329$			14.9785i			0.825792i
$330$		0			0
$331$	−8.00000	+	8.00000i	−0.439720	+	0.439720i	−0.891918	−	0.452198i	$-0.850640\pi$
$331$	−8.00000	+	8.00000i	−0.439720	+	0.439720i	0.452198	+	0.891918i	$0.350640\pi$
$332$	−8.89047	−	3.36028i	−0.487928	−	0.184419i
$333$		0			0
$334$	5.29150	+	24.5830i	0.289538	+	1.34512i
$335$	4.76150			0.260149
$336$		0			0
$337$	4.70850			0.256488			0.128244	−	0.991743i	$-0.459066\pi$
$337$	4.70850			0.256488			0.128244	+	0.991743i	$0.459066\pi$
$338$	−0.297594	−	1.38255i	−0.0161870	−	0.0752007i
$339$		0			0
$340$	3.29150	−	8.70850i	0.178507	−	0.472285i
$341$	−18.9713	+	18.9713i	−1.02735	+	1.02735i
$342$		0			0
$343$		−	18.5830i		−	1.00339i
$344$	0.210845	−	1.40122i	0.0113680	−	0.0755487i
$345$		0			0
$346$	−8.29150	−	5.35425i	−0.445754	−	0.287846i
$347$	3.36028	−	3.36028i	0.180389	−	0.180389i	−0.611136	−	0.791526i	$-0.709287\pi$
$347$	3.36028	−	3.36028i	0.180389	−	0.180389i	0.791526	+	0.611136i	$0.209287\pi$
$348$		0			0
$349$	3.22876	+	3.22876i	0.172831	+	0.172831i	0.788222	−	0.615391i	$-0.211002\pi$
$349$	3.22876	+	3.22876i	0.172831	+	0.172831i	−0.615391	+	0.788222i	$0.711002\pi$
$350$	−9.76458	+	2.10183i	−0.521939	+	0.112348i
$351$		0			0
$352$	7.29150	+	25.8745i	0.388638	+	1.37912i
$353$	7.14226			0.380144			0.190072	−	0.981770i	$-0.439128\pi$
$353$	7.14226			0.380144			0.190072	+	0.981770i	$0.439128\pi$
$354$		0			0
$355$	8.00000	+	8.00000i	0.424596	+	0.424596i
$356$	1.95906	+	4.33981i	0.103830	+	0.230010i
$357$		0			0
$358$	4.00000	+	2.58301i	0.211407	+	0.136516i
$359$		−	4.76150i		−	0.251303i	−0.992074	−	0.125651i	$-0.959898\pi$
$359$		−	4.76150i		−	0.251303i	0.992074	−	0.125651i	$-0.0401020\pi$
$360$		0			0
$361$			7.58301i			0.399106i
$362$	0.700610	−	1.08495i	0.0368233	−	0.0570239i
$363$		0			0
$364$	4.35425	−	11.5203i	0.228225	−	0.603826i
$365$	−1.95906	−	1.95906i	−0.102542	−	0.102542i
$366$		0			0
$367$	34.8118			1.81716			0.908580	−	0.417712i	$-0.137168\pi$
$367$	34.8118			1.81716			0.908580	+	0.417712i	$0.137168\pi$
$368$	13.0194	+	11.4821i	0.678685	+	0.598544i
$369$		0			0
$370$	−0.228757	−	1.06275i	−0.0118925	−	0.0552495i
$371$	8.12179	+	8.12179i	0.421662	+	0.421662i
$372$		0			0
$373$	11.9373	−	11.9373i	0.618088	−	0.618088i	−0.326953	−	0.945041i	$-0.606022\pi$
$373$	11.9373	−	11.9373i	0.618088	−	0.618088i	0.945041	+	0.326953i	$0.106022\pi$
$374$	−20.1617	+	31.2221i	−1.04254	+	1.61446i
$375$		0			0
$376$	20.7085	−	15.2915i	1.06796	−	0.788599i
$377$		−	32.4125i		−	1.66933i
$378$		0			0
$379$	8.35425	−	8.35425i	0.429129	−	0.429129i	−0.459203	−	0.888332i	$-0.651865\pi$
$379$	8.35425	−	8.35425i	0.429129	−	0.429129i	0.888332	+	0.459203i	$0.151865\pi$
$380$	−7.91094	+	3.57113i	−0.405823	+	0.183195i
$381$		0			0
$382$	−12.5830	+	2.70850i	−0.643803	+	0.138579i
$383$	−9.10132			−0.465056			−0.232528	−	0.972590i	$-0.574700\pi$
$383$	−9.10132			−0.465056			−0.232528	+	0.972590i	$0.574700\pi$
$384$		0			0
$385$	−6.58301			−0.335501
$386$	−16.4171	+	3.53378i	−0.835607	+	0.179865i
$387$		0			0
$388$	−19.2915	+	8.70850i	−0.979378	+	0.442107i
$389$	20.7569	−	20.7569i	1.05242	−	1.05242i	0.0538679	−	0.998548i	$-0.482845\pi$
$389$	20.7569	−	20.7569i	1.05242	−	1.05242i	0.998548	−	0.0538679i	$-0.0171550\pi$
$390$		0			0
$391$			24.0000i			1.21373i
$392$	−9.76458	+	7.21033i	−0.493186	+	0.364177i
$393$		0			0
$394$	9.22876	−	14.2915i	0.464938	−	0.719996i
$395$	5.74103	−	5.74103i	0.288863	−	0.288863i
$396$		0			0
$397$	8.06275	+	8.06275i	0.404658	+	0.404658i	0.879871	−	0.475213i	$-0.157629\pi$
$397$	8.06275	+	8.06275i	0.404658	+	0.404658i	−0.475213	+	0.879871i	$0.657629\pi$
$398$	−4.06089	−	18.8659i	−0.203554	−	0.945662i
$399$		0			0
$400$	12.8745	+	11.3542i	0.643725	+	0.567712i
$401$	16.5906			0.828494			0.414247	−	0.910165i	$-0.364045\pi$
$401$	16.5906			0.828494			0.414247	+	0.910165i	$0.364045\pi$
$402$		0			0
$403$	−14.9373	−	14.9373i	−0.744078	−	0.744078i
$404$	0.595188	−	1.57472i	0.0296117	−	0.0783452i
$405$		0			0
$406$	10.9373	−	16.9373i	0.542807	−	0.840582i
$407$			4.33981i			0.215117i
$408$		0			0
$409$		−	25.1660i		−	1.24438i	−0.782867	−	0.622190i	$-0.786243\pi$
$409$		−	25.1660i		−	1.24438i	0.782867	−	0.622190i	$-0.213757\pi$
$410$	−7.91094	−	5.10850i	−0.390694	−	0.252291i
$411$		0			0
$412$	13.9373	+	30.8745i	0.686639	+	1.52108i
$413$	−7.14226	−	7.14226i	−0.351447	−	0.351447i
$414$		0			0
$415$	−4.00000			−0.196352
$416$	−20.3725	+	5.74103i	−0.998846	+	0.281477i
$417$		0			0
$418$	33.8745	−	7.29150i	1.65686	−	0.356639i
$419$	18.7605	+	18.7605i	0.916509	+	0.916509i	0.996774	−	0.0802643i	$-0.0255764\pi$
$419$	18.7605	+	18.7605i	0.916509	+	0.916509i	−0.0802643	+	0.996774i	$0.525576\pi$
$420$		0			0
$421$	11.3542	−	11.3542i	0.553372	−	0.553372i	−0.374040	−	0.927412i	$-0.622028\pi$
$421$	11.3542	−	11.3542i	0.553372	−	0.553372i	0.927412	+	0.374040i	$0.122028\pi$
$422$	24.5015	+	15.8219i	1.19271	+	0.770197i
$423$		0			0
$424$	2.93725	−	19.5203i	0.142646	−	0.947988i
$425$			23.7328i			1.15121i
$426$		0			0
$427$	−1.06275	+	1.06275i	−0.0514299	+	0.0514299i
$428$	2.38075	−	6.29888i	0.115078	−	0.304468i
$429$		0			0
$430$	−0.125492	−	0.583005i	−0.00605177	−	0.0281150i
$431$	31.2221			1.50391			0.751957	−	0.659212i	$-0.229110\pi$
$431$	31.2221			1.50391			0.751957	+	0.659212i	$0.229110\pi$
$432$		0			0
$433$	−4.00000			−0.192228			−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000			−0.192228			−0.0961139	+	0.995370i	$0.530641\pi$
$434$	−2.76510	−	12.8459i	−0.132729	−	0.616625i
$435$		0			0
$436$	−17.5830	−	6.64575i	−0.842073	−	0.318274i
$437$	15.8219	−	15.8219i	0.756863	−	0.756863i
$438$		0			0
$439$		−	0.479741i		−	0.0228968i	−0.999934	−	0.0114484i	$-0.996356\pi$
$439$		−	0.479741i		−	0.0228968i	0.999934	−	0.0114484i	$-0.00364422\pi$
$440$	6.72057	+	9.10132i	0.320390	+	0.433888i
$441$		0			0
$442$	−24.5830	−	15.8745i	−1.16929	−	0.755073i
$443$	21.5629	−	21.5629i	1.02449	−	1.02449i	0.0247926	−	0.999693i	$-0.492107\pi$
$443$	21.5629	−	21.5629i	1.02449	−	1.02449i	0.999693	−	0.0247926i	$-0.00789253\pi$
$444$		0			0
$445$	1.41699	+	1.41699i	0.0671720	+	0.0671720i
$446$	19.8454	−	4.27174i	0.939708	−	0.202273i
$447$		0			0
$448$	−12.5830	−	3.87451i	−0.594491	−	0.183053i
$449$	9.44832			0.445894			0.222947	−	0.974831i	$-0.428432\pi$
$449$	9.44832			0.445894			0.222947	+	0.974831i	$0.428432\pi$
$450$		0			0
$451$	26.5830	+	26.5830i	1.25174	+	1.25174i
$452$		0			0
$453$		0			0
$454$	2.35425	+	1.52026i	0.110490	+	0.0713493i
$455$		−	5.18319i		−	0.242992i
$456$		0			0
$457$			5.41699i			0.253396i	0.991941	+	0.126698i	$0.0404380\pi$
$457$			5.41699i			0.253396i	−0.991941	+	0.126698i	$0.959562\pi$
$458$	−19.4611	+	30.1371i	−0.909357	+	1.40822i
$459$		0			0
$460$	6.83399	+	2.58301i	0.318636	+	0.120433i
$461$	8.50613	+	8.50613i	0.396170	+	0.396170i	0.876880	−	0.480710i	$-0.159621\pi$
$461$	8.50613	+	8.50613i	0.396170	+	0.396170i	−0.480710	+	0.876880i	$0.659621\pi$
$462$		0			0
$463$	15.0627			0.700025			0.350013	−	0.936745i	$-0.386177\pi$
$463$	15.0627			0.700025			0.350013	+	0.936745i	$0.386177\pi$
$464$	−34.5824	+	2.16991i	−1.60545	+	0.100735i
$465$		0			0
$466$	5.87451	+	27.2915i	0.272131	+	1.26425i
$467$	−25.4810	−	25.4810i	−1.17912	−	1.17912i	−0.979968	−	0.199154i	$-0.936181\pi$
$467$	−25.4810	−	25.4810i	−1.17912	−	1.17912i	−0.199154	−	0.979968i	$-0.563819\pi$
$468$		0			0
$469$	6.58301	−	6.58301i	0.303975	−	0.303975i
$470$	5.87719	−	9.10132i	0.271094	−	0.419812i
$471$		0			0
$472$	−2.58301	+	17.1660i	−0.118892	+	0.790130i
$473$			2.38075i			0.109467i
$474$		0			0
$475$	15.6458	−	15.6458i	0.717876	−	0.717876i
$476$	−7.48925	−	16.5906i	−0.343269	−	0.760428i
$477$		0			0
$478$	18.0000	−	3.87451i	0.823301	−	0.177216i
$479$	−22.1208			−1.01072			−0.505362	−	0.862908i	$-0.668641\pi$
$479$	−22.1208			−1.01072			−0.505362	+	0.862908i	$0.668641\pi$
$480$		0			0
$481$	−3.41699			−0.155802
$482$	1.78556	−	0.384343i	0.0813302	−	0.0175064i
$483$		0			0
$484$	−9.53137	−	21.1144i	−0.433244	−	0.959744i
$485$	−6.29888	+	6.29888i	−0.286017	+	0.286017i
$486$		0			0
$487$			8.22876i			0.372881i	0.982466	+	0.186440i	$0.0596951\pi$
$487$			8.22876i			0.372881i	−0.982466	+	0.186440i	$0.940305\pi$
$488$	2.55425	+	0.384343i	0.115625	+	0.0173984i
$489$		0			0
$490$	−2.77124	+	4.29150i	−0.125192	+	0.193870i
$491$	15.4002	−	15.4002i	0.695001	−	0.695001i	−0.268327	−	0.963328i	$-0.586471\pi$
$491$	15.4002	−	15.4002i	0.695001	−	0.695001i	0.963328	+	0.268327i	$0.0864707\pi$
$492$		0			0
$493$	−33.8745	−	33.8745i	−1.52563	−	1.52563i
$494$	5.74103	+	26.6714i	0.258301	+	1.20000i
$495$		0			0
$496$	−14.9373	+	16.9373i	−0.670703	+	0.760505i
$497$	22.1208			0.992252
$498$		0			0
$499$	10.5830	+	10.5830i	0.473760	+	0.473760i	0.903129	−	0.429369i	$-0.141264\pi$
$499$	10.5830	+	10.5830i	0.473760	+	0.473760i	−0.429369	+	0.903129i	$0.641264\pi$
$500$	14.6315	+	5.53019i	0.654341	+	0.247318i
$501$		0			0
$502$	20.3542	−	31.5203i	0.908455	−	1.40682i
$503$			31.6438i			1.41093i	0.708747	+	0.705463i	$0.249261\pi$
$503$			31.6438i			1.41093i	−0.708747	+	0.705463i	$0.750739\pi$
$504$		0			0
$505$		−	0.708497i		−	0.0315277i
$506$	−24.5015	−	15.8219i	−1.08923	−	0.703369i
$507$		0			0
$508$	1.70850	−	0.771243i	0.0758023	−	0.0342184i
$509$	−24.6750	−	24.6750i	−1.09370	−	1.09370i	−0.995130	−	0.0985706i	$-0.968573\pi$
$509$	−24.6750	−	24.6750i	−1.09370	−	1.09370i	−0.0985706	−	0.995130i	$-0.531427\pi$
$510$		0			0
$511$	−5.41699			−0.239634
$512$	7.48925	+	21.3521i	0.330981	+	0.943637i
$513$		0			0
$514$	40.4575	−	8.70850i	1.78450	−	0.384115i
$515$	10.0808	+	10.0808i	0.444215	+	0.444215i
$516$		0			0
$517$	−30.5830	+	30.5830i	−1.34504	+	1.34504i
$518$	−1.78556	−	1.15303i	−0.0784532	−	0.0506612i
$519$		0			0
$520$	−7.16601	+	5.29150i	−0.314250	+	0.232048i
$521$		−	14.2098i		−	0.622543i	−0.950321	−	0.311272i	$-0.899245\pi$
$521$		−	14.2098i		−	0.622543i	0.950321	−	0.311272i	$-0.100755\pi$
$522$		0			0
$523$	−18.9373	+	18.9373i	−0.828068	+	0.828068i	−0.987249	−	0.159181i	$-0.949115\pi$
$523$	−18.9373	+	18.9373i	−0.828068	+	0.828068i	0.159181	+	0.987249i	$0.449115\pi$
$524$	17.7809	+	6.72057i	0.776764	+	0.293589i
$525$		0			0
$526$	2.58301	+	12.0000i	0.112624	+	0.523225i
$527$	−31.2221			−1.36006
$528$		0			0
$529$	4.16601			0.181131
$530$	−1.74822	−	8.12179i	−0.0759377	−	0.352788i
$531$		0			0
$532$	−6.00000	+	15.8745i	−0.260133	+	0.688247i
$533$	−20.9304	+	20.9304i	−0.906596	+	0.906596i
$534$		0			0
$535$		−	2.83399i		−	0.122524i
$536$	−15.8219	−	2.38075i	−0.683401	−	0.102833i
$537$		0			0
$538$	−17.5830	−	11.3542i	−0.758057	−	0.489516i
$539$	14.4207	−	14.4207i	0.621142	−	0.621142i
$540$		0			0
$541$	−28.5203	−	28.5203i	−1.22618	−	1.22618i	−0.965397	−	0.260785i	$-0.916019\pi$
$541$	−28.5203	−	28.5203i	−1.22618	−	1.22618i	−0.260785	−	0.965397i	$-0.583981\pi$
$542$	−8.78505	+	1.89099i	−0.377350	+	0.0812248i
$543$		0			0
$544$	−15.2915	+	27.2915i	−0.655618	+	1.17011i
$545$	−7.91094			−0.338868
$546$		0			0
$547$	14.9373	+	14.9373i	0.638671	+	0.638671i	0.950228	−	0.311557i	$-0.100850\pi$
$547$	14.9373	+	14.9373i	0.638671	+	0.638671i	−0.311557	+	0.950228i	$0.600850\pi$
$548$	−8.46878	−	18.7605i	−0.361769	−	0.801408i
$549$		0			0
$550$	−24.2288	−	15.6458i	−1.03312	−	0.667137i
$551$			44.6632i			1.90272i
$552$		0			0
$553$		−	15.8745i		−	0.675053i
$554$	17.9237	−	27.7564i	0.761506	−	1.17926i
$555$		0			0
$556$	−14.5830	+	38.5830i	−0.618457	+	1.63628i
$557$	−18.7978	−	18.7978i	−0.796489	−	0.796489i	0.186051	−	0.982540i	$-0.440431\pi$
$557$	−18.7978	−	18.7978i	−0.796489	−	0.796489i	−0.982540	+	0.186051i	$0.940431\pi$
$558$		0			0
$559$	−1.87451			−0.0792832
$560$	−5.53019	+	0.346998i	−0.233693	+	0.0146633i
$561$		0			0
$562$	−0.708497	−	3.29150i	−0.0298862	−	0.138844i
$563$	−5.31935	−	5.31935i	−0.224184	−	0.224184i	0.586074	−	0.810258i	$-0.300673\pi$
$563$	−5.31935	−	5.31935i	−0.224184	−	0.224184i	−0.810258	+	0.586074i	$0.800673\pi$
$564$		0			0
$565$		0			0
$566$	2.80244	−	4.33981i	0.117795	−	0.182416i
$567$		0			0
$568$	−22.5830	−	30.5830i	−0.947562	−	1.28323i
$569$			41.0921i			1.72267i	0.508038	+	0.861335i	$0.330371\pi$
$569$			41.0921i			1.72267i	−0.508038	+	0.861335i	$0.669629\pi$
$570$		0			0
$571$	4.00000	−	4.00000i	0.167395	−	0.167395i	−0.618438	−	0.785833i	$-0.712234\pi$
$571$	4.00000	−	4.00000i	0.167395	−	0.167395i	0.785833	+	0.618438i	$0.212234\pi$
$572$	32.4125	−	14.6315i	1.35523	−	0.611774i
$573$		0			0
$574$	−18.0000	+	3.87451i	−0.751305	+	0.161719i
$575$	−18.6243			−0.776688
$576$		0			0
$577$	−39.0405			−1.62528			−0.812639	−	0.582767i	$-0.801970\pi$
$577$	−39.0405			−1.62528			−0.812639	+	0.582767i	$0.801970\pi$
$578$	−18.7792	+	4.04222i	−0.781110	+	0.168134i
$579$		0			0
$580$	−13.2915	+	6.00000i	−0.551900	+	0.249136i
$581$	−5.53019	+	5.53019i	−0.229431	+	0.229431i
$582$		0			0
$583$			33.1660i			1.37360i
$584$	5.53019	+	7.48925i	0.228841	+	0.309907i
$585$		0			0
$586$	−2.77124	+	4.29150i	−0.114479	+	0.177280i
$587$	−4.76150	+	4.76150i	−0.196528	+	0.196528i	−0.798510	−	0.601982i	$-0.794378\pi$
$587$	−4.76150	+	4.76150i	−0.196528	+	0.196528i	0.601982	+	0.798510i	$0.294378\pi$
$588$		0			0
$589$	20.5830	+	20.5830i	0.848108	+	0.848108i
$590$	1.53737	+	7.14226i	0.0632927	+	0.294042i
$591$		0			0
$592$	0.228757	+	3.64575i	0.00940184	+	0.149839i
$593$	22.1208			0.908391			0.454195	−	0.890902i	$-0.349927\pi$
$593$	22.1208			0.908391			0.454195	+	0.890902i	$0.349927\pi$
$594$		0			0
$595$	−5.41699	−	5.41699i	−0.222075	−	0.222075i
$596$	11.6556	−	30.8377i	0.477431	−	1.26316i
$597$		0			0
$598$	12.4575	−	19.2915i	0.509426	−	0.788888i
$599$		−	13.8628i		−	0.566420i	−0.959058	−	0.283210i	$-0.908601\pi$
$599$		−	13.8628i		−	0.566420i	0.959058	−	0.283210i	$-0.0913993\pi$
$600$		0			0
$601$		−	3.29150i		−	0.134263i	−0.997744	−	0.0671316i	$-0.978615\pi$
$601$		−	3.29150i		−	0.134263i	0.997744	−	0.0671316i	$-0.0213847\pi$
$602$	−0.979531	−	0.632534i	−0.0399227	−	0.0257801i
$603$		0			0
$604$	−8.52026	−	18.8745i	−0.346684	−	0.767993i
$605$	−6.89407	−	6.89407i	−0.280284	−	0.280284i
$606$		0			0
$607$	14.1033			0.572434			0.286217	−	0.958165i	$-0.407602\pi$
$607$	14.1033			0.572434			0.286217	+	0.958165i	$0.407602\pi$
$608$	28.0726	−	7.91094i	1.13850	−	0.320831i
$609$		0			0
$610$	1.06275	−	0.228757i	0.0430293	−	0.00926208i
$611$	−24.0798	−	24.0798i	−0.974165	−	0.974165i
$612$		0			0
$613$	26.6458	−	26.6458i	1.07621	−	1.07621i	0.0793662	−	0.996846i	$-0.474710\pi$
$613$	26.6458	−	26.6458i	1.07621	−	1.07621i	0.996846	−	0.0793662i	$-0.0252897\pi$
$614$	33.6028	+	21.6991i	1.35610	+	0.875703i
$615$		0			0
$616$	21.8745	+	3.29150i	0.881349	+	0.132618i
$617$			31.6438i			1.27393i	0.770893	+	0.636965i	$0.219810\pi$
$617$			31.6438i			1.27393i	−0.770893	+	0.636965i	$0.780190\pi$
$618$		0			0
$619$	−21.1660	+	21.1660i	−0.850734	+	0.850734i	−0.990224	−	0.139490i	$-0.955454\pi$
$619$	−21.1660	+	21.1660i	−0.850734	+	0.850734i	0.139490	+	0.990224i	$0.455454\pi$
$620$	−3.36028	+	8.89047i	−0.134952	+	0.357050i
$621$		0			0
$622$	2.58301	+	12.0000i	0.103569	+	0.481156i
$623$	3.91813			0.156976
$624$		0			0
$625$	−14.8745			−0.594980
$626$	−2.76510	−	12.8459i	−0.110515	−	0.513427i
$627$		0			0
$628$	−17.5830	−	6.64575i	−0.701638	−	0.265194i
$629$	−3.57113	+	3.57113i	−0.142390	+	0.142390i
$630$		0			0
$631$		−	8.22876i		−	0.327582i	−0.986495	−	0.163791i	$-0.947628\pi$
$631$		−	8.22876i		−	0.327582i	0.986495	−	0.163791i	$-0.0523722\pi$
$632$	−21.9473	+	16.2062i	−0.873015	+	0.644649i
$633$		0			0
$634$	1.00000	+	0.645751i	0.0397151	+	0.0256461i
$635$	0.557842	−	0.557842i	0.0221373	−	0.0221373i
$636$		0			0
$637$	11.3542	+	11.3542i	0.449872	+	0.449872i
$638$	56.9140	−	12.2508i	2.25325	−	0.485012i
$639$		0			0
$640$	6.12549	+	7.29150i	0.242131	+	0.288222i
$641$	16.5906			0.655288			0.327644	−	0.944801i	$-0.393745\pi$
$641$	16.5906			0.655288			0.327644	+	0.944801i	$0.393745\pi$
$642$		0			0
$643$	−3.64575	−	3.64575i	−0.143774	−	0.143774i	0.631556	−	0.775330i	$-0.282417\pi$
$643$	−3.64575	−	3.64575i	−0.143774	−	0.143774i	−0.775330	+	0.631556i	$0.782417\pi$
$644$	13.0194	−	5.87719i	0.513038	−	0.231594i
$645$		0			0
$646$	33.8745	+	21.8745i	1.33277	+	0.860641i
$647$			4.33981i			0.170616i	0.996355	+	0.0853079i	$0.0271874\pi$
$647$			4.33981i			0.170616i	−0.996355	+	0.0853079i	$0.972813\pi$
$648$		0			0
$649$		−	29.1660i		−	1.14487i
$650$	12.3188	−	19.0767i	0.483184	−	0.748252i
$651$		0			0
$652$	30.8118	+	11.6458i	1.20668	+	0.456083i
$653$	−20.7569	−	20.7569i	−0.812280	−	0.812280i	0.172696	−	0.984975i	$-0.444752\pi$
$653$	−20.7569	−	20.7569i	−0.812280	−	0.812280i	−0.984975	+	0.172696i	$0.944752\pi$
$654$		0			0
$655$	8.00000			0.312586
$656$	23.7328	+	20.9304i	0.926611	+	0.817194i
$657$		0			0
$658$	−4.45751	−	20.7085i	−0.173772	−	0.807301i
$659$	24.9232	+	24.9232i	0.970870	+	0.970870i	0.999588	−	0.0287175i	$-0.00914231\pi$
$659$	24.9232	+	24.9232i	0.970870	+	0.970870i	−0.0287175	+	0.999588i	$0.509142\pi$
$660$		0			0
$661$	−2.77124	+	2.77124i	−0.107789	+	0.107789i	−0.758944	−	0.651155i	$-0.774285\pi$
$661$	−2.77124	+	2.77124i	−0.107789	+	0.107789i	0.651155	+	0.758944i	$0.274285\pi$
$662$	8.67963	−	13.4411i	0.337343	−	0.522404i
$663$		0			0
$664$	13.2915	+	2.00000i	0.515810	+	0.0776151i
$665$			7.14226i			0.276965i
$666$		0			0
$667$	26.5830	−	26.5830i	1.02930	−	1.02930i
$668$	−14.6315	−	32.4125i	−0.566110	−	1.25408i
$669$		0			0
$670$	−6.58301	+	1.41699i	−0.254324	+	0.0547433i
$671$	−4.33981			−0.167537
$672$		0			0
$673$	20.0000			0.770943			0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000			0.770943			0.385472	+	0.922720i	$0.374039\pi$
$674$	−6.50972	+	1.40122i	−0.250745	+	0.0539730i
$675$		0			0
$676$	0.822876	+	1.82288i	0.0316491	+	0.0701106i
$677$	−14.0363	+	14.0363i	−0.539460	+	0.539460i	−0.923370	−	0.383911i	$-0.874577\pi$
$677$	−14.0363	+	14.0363i	−0.539460	+	0.539460i	0.383911	+	0.923370i	$0.374577\pi$
$678$		0			0
$679$			17.4170i			0.668403i
$680$	−1.95906	+	13.0194i	−0.0751266	+	0.499273i
$681$		0			0
$682$	20.5830	−	31.8745i	0.788164	−	1.22054i
$683$	−0.557842	+	0.557842i	−0.0213452	+	0.0213452i	−0.717699	−	0.696354i	$-0.754805\pi$
$683$	−0.557842	+	0.557842i	−0.0213452	+	0.0213452i	0.696354	+	0.717699i	$0.254805\pi$
$684$		0			0
$685$	−6.12549	−	6.12549i	−0.234043	−	0.234043i
$686$	5.53019	+	25.6919i	0.211144	+	0.980921i
$687$		0			0
$688$	0.125492	+	2.00000i	0.00478434	+	0.0762493i
$689$	−26.1136			−0.994848
$690$		0			0
$691$	−3.64575	−	3.64575i	−0.138691	−	0.138691i	0.634353	−	0.773044i	$-0.281267\pi$
$691$	−3.64575	−	3.64575i	−0.138691	−	0.138691i	−0.773044	+	0.634353i	$0.781267\pi$
$692$	13.0568	+	4.93500i	0.496345	+	0.187601i
$693$		0			0
$694$	−3.64575	+	5.64575i	−0.138391	+	0.214310i
$695$			17.3593i			0.658474i
$696$		0			0
$697$			43.7490i			1.65711i
$698$	−5.42477	−	3.50305i	−0.205330	−	0.132592i
$699$		0			0
$700$	12.8745	−	5.81176i	0.486611	−	0.219664i
$701$	−4.16632	−	4.16632i	−0.157360	−	0.157360i	0.624036	−	0.781396i	$-0.285492\pi$
$701$	−4.16632	−	4.16632i	−0.157360	−	0.157360i	−0.781396	+	0.624036i	$0.785492\pi$
$702$		0			0
$703$	4.70850			0.177584
$704$	−17.7809	−	33.6028i	−0.670145	−	1.26645i
$705$		0			0
$706$	−9.87451	+	2.12549i	−0.371632	+	0.0799940i
$707$	−0.979531	−	0.979531i	−0.0368391	−	0.0368391i
$708$		0			0
$709$	−8.77124	+	8.77124i	−0.329411	+	0.329411i	−0.852362	−	0.522951i	$-0.824831\pi$
$709$	−8.77124	+	8.77124i	−0.329411	+	0.329411i	0.522951	+	0.852362i	$0.324831\pi$
$710$	−13.4411	−	8.67963i	−0.504437	−	0.325741i
$711$		0			0
$712$	−4.00000	−	5.41699i	−0.149906	−	0.203010i
$713$		−	24.5015i		−	0.917589i
$714$		0			0
$715$	10.5830	−	10.5830i	0.395782	−	0.395782i
$716$	−6.29888	−	2.38075i	−0.235400	−	0.0889729i
$717$		0			0
$718$	1.41699	+	6.58301i	0.0528818	+	0.245676i
$719$	−40.3234			−1.50381			−0.751904	−	0.659272i	$-0.770865\pi$
$719$	−40.3234			−1.50381			−0.751904	+	0.659272i	$0.770865\pi$
$720$		0			0
$721$	27.8745			1.03810
$722$	−2.25666	−	10.4839i	−0.0839841	−	0.390169i
$723$		0			0
$724$	−0.645751	+	1.70850i	−0.0239992	+	0.0634958i
$725$	26.2871	−	26.2871i	0.976278	−	0.976278i
$726$		0			0
$727$		−	33.3948i		−	1.23854i	−0.785177	−	0.619272i	$-0.787428\pi$
$727$		−	33.3948i		−	1.23854i	0.785177	−	0.619272i	$-0.212572\pi$
$728$	−2.59160	+	17.2231i	−0.0960510	+	0.638331i
$729$		0			0
$730$	3.29150	+	2.12549i	0.121824	+	0.0786680i
$731$	−1.95906	+	1.95906i	−0.0724586	+	0.0724586i
$732$		0			0
$733$	−12.6458	−	12.6458i	−0.467081	−	0.467081i	0.433886	−	0.900968i	$-0.357142\pi$
$733$	−12.6458	−	12.6458i	−0.467081	−	0.467081i	−0.900968	+	0.433886i	$0.857142\pi$
$734$	−48.1289	+	10.3598i	−1.77647	+	0.382386i
$735$		0			0
$736$	−21.4170	−	12.0000i	−0.789441	−	0.442326i
$737$	26.8823			0.990221
$738$		0			0
$739$	−9.16601	−	9.16601i	−0.337177	−	0.337177i	0.518127	−	0.855304i	$-0.326630\pi$
$739$	−9.16601	−	9.16601i	−0.337177	−	0.337177i	−0.855304	+	0.518127i	$0.826630\pi$
$740$	0.632534	+	1.40122i	0.0232524	+	0.0515099i
$741$		0			0
$742$	−13.6458	−	8.81176i	−0.500951	−	0.323490i
$743$			22.5425i			0.827002i	0.910504	+	0.413501i	$0.135694\pi$
$743$			22.5425i			0.827002i	−0.910504	+	0.413501i	$0.864306\pi$
$744$		0			0
$745$		−	13.8745i		−	0.508323i
$746$	−12.9514	+	20.0563i	−0.474183	+	0.734312i
$747$		0			0
$748$	18.5830	−	49.1660i	0.679462	−	1.79769i
$749$	−3.91813	−	3.91813i	−0.143165	−	0.143165i
$750$		0			0
$751$	12.9373			0.472087			0.236044	−	0.971742i	$-0.424149\pi$
$751$	12.9373			0.472087			0.236044	+	0.971742i	$0.424149\pi$
$752$	−24.0798	+	27.3040i	−0.878101	+	0.995673i
$753$		0			0
$754$	9.64575	+	44.8118i	0.351278	+	1.63195i
$755$	−6.16272	−	6.16272i	−0.224284	−	0.224284i
$756$		0			0
$757$	−7.22876	+	7.22876i	−0.262734	+	0.262734i	−0.826164	−	0.563430i	$-0.809481\pi$
$757$	−7.22876	+	7.22876i	−0.262734	+	0.262734i	0.563430	+	0.826164i	$0.309481\pi$
$758$	−9.06397	+	14.0363i	−0.329218	+	0.509822i
$759$		0			0
$760$	9.87451	−	7.29150i	0.358186	−	0.264491i
$761$			7.91094i			0.286771i	0.989667	+	0.143386i	$0.0457989\pi$
$761$			7.91094i			0.286771i	−0.989667	+	0.143386i	$0.954201\pi$
$762$		0			0
$763$	−10.9373	+	10.9373i	−0.395955	+	0.395955i
$764$	16.5906	−	7.48925i	0.600226	−	0.270952i
$765$		0			0
$766$	12.5830	−	2.70850i	0.454642	−	0.0978620i
$767$	22.9641			0.829187
$768$		0			0
$769$	17.2915			0.623548			0.311774	−	0.950156i	$-0.399077\pi$
$769$	17.2915			0.623548			0.311774	+	0.950156i	$0.399077\pi$
$770$	9.10132	−	1.95906i	0.327989	−	0.0705997i
$771$		0			0
$772$	21.6458	−	9.77124i	0.779048	−	0.351675i
$773$	−21.5256	+	21.5256i	−0.774221	+	0.774221i	−0.978841	−	0.204620i	$-0.934404\pi$
$773$	−21.5256	+	21.5256i	−0.774221	+	0.774221i	0.204620	+	0.978841i	$0.434404\pi$
$774$		0			0
$775$		−	24.2288i		−	0.870323i
$776$	24.0798	−	17.7809i	0.864415	−	0.638299i
$777$		0			0
$778$	−22.5203	+	34.8745i	−0.807390	+	1.25031i
$779$	28.8413	−	28.8413i	1.03335	−	1.03335i
$780$		0			0
$781$	45.1660	+	45.1660i	1.61617	+	1.61617i
$782$	−7.14226	−	33.1811i	−0.255407	−	1.18656i
$783$		0			0
$784$	11.3542	−	12.8745i	0.405509	−	0.459804i
$785$	−7.91094			−0.282354
$786$		0			0
$787$	6.22876	+	6.22876i	0.222031	+	0.222031i	0.809353	−	0.587322i	$-0.199818\pi$
$787$	6.22876	+	6.22876i	0.222031	+	0.222031i	−0.587322	+	0.809353i	$0.699818\pi$
$788$	−8.50613	+	22.5051i	−0.303018	+	0.801711i
$789$		0			0
$790$	−6.22876	+	9.64575i	−0.221609	+	0.343180i
$791$		0			0
$792$		0			0
$793$		−	3.41699i		−	0.121341i
$794$	−13.5466	−	8.74771i	−0.480749	−	0.310444i
$795$		0			0
$796$	11.2288	+	24.8745i	0.397993	+	0.881654i
$797$	21.5256	+	21.5256i	0.762475	+	0.762475i	0.976769	−	0.214294i	$-0.0687451\pi$
$797$	21.5256	+	21.5256i	0.762475	+	0.762475i	−0.214294	+	0.976769i	$0.568745\pi$
$798$		0			0
$799$	−50.3320			−1.78062
$800$	−21.1786	−	11.8664i	−0.748776	−	0.419541i
$801$		0			0
$802$	−22.9373	+	4.93725i	−0.809943	+	0.174340i
$803$	−11.0604	−	11.0604i	−0.390312	−	0.390312i
$804$		0			0
$805$	4.25098	−	4.25098i	0.149828	−	0.149828i
$806$	25.0967	+	16.2062i	0.883994	+	0.570840i
$807$		0			0
$808$	−0.354249	+	2.35425i	−0.0124624	+	0.0828222i
$809$		−	17.4339i		−	0.612945i	−0.951880	−	0.306473i	$-0.900851\pi$
$809$		−	17.4339i		−	0.612945i	0.951880	−	0.306473i	$-0.0991488\pi$
$810$		0			0
$811$	−15.6458	+	15.6458i	−0.549397	+	0.549397i	−0.926266	−	0.376870i	$-0.877000\pi$
$811$	−15.6458	+	15.6458i	−0.549397	+	0.549397i	0.376870	+	0.926266i	$0.377000\pi$
$812$	−10.0808	+	26.6714i	−0.353768	+	0.935983i
$813$		0			0
$814$	−1.29150	−	6.00000i	−0.0452671	−	0.210300i
$815$	13.8628			0.485593
$816$		0			0
$817$	2.58301			0.0903679
$818$	7.48925	+	34.7932i	0.261856	+	1.21652i
$819$		0			0
$820$	12.4575	+	4.70850i	0.435035	+	0.164428i
$821$	7.73744	−	7.73744i	0.270039	−	0.270039i	−0.559077	−	0.829116i	$-0.688844\pi$
$821$	7.73744	−	7.73744i	0.270039	−	0.270039i	0.829116	+	0.559077i	$0.188844\pi$
$822$		0			0
$823$		−	32.2288i		−	1.12342i	−0.827333	−	0.561712i	$-0.810143\pi$
$823$		−	32.2288i		−	1.12342i	0.827333	−	0.561712i	$-0.189857\pi$
$824$	−28.4570	−	38.5378i	−0.991346	−	1.34253i
$825$		0			0
$826$	12.0000	+	7.74902i	0.417533	+	0.269623i
$827$	4.33981	−	4.33981i	0.150910	−	0.150910i	−0.627614	−	0.778524i	$-0.715968\pi$
$827$	4.33981	−	4.33981i	0.150910	−	0.150910i	0.778524	+	0.627614i	$0.215968\pi$
$828$		0			0
$829$	14.6458	+	14.6458i	0.508668	+	0.508668i	0.914117	−	0.405449i	$-0.132885\pi$
$829$	14.6458	+	14.6458i	0.508668	+	0.508668i	−0.405449	+	0.914117i	$0.632885\pi$
$830$	5.53019	−	1.19038i	0.191956	−	0.0413186i
$831$		0			0
$832$	26.4575	−	14.0000i	0.917249	−	0.485363i
$833$	23.7328			0.822294
$834$		0			0
$835$	−10.5830	−	10.5830i	−0.366240	−	0.366240i
$836$	−44.6632	+	20.1617i	−1.54471	+	0.697307i
$837$		0			0
$838$	−31.5203	−	20.3542i	−1.08885	−	0.703126i
$839$		−	52.9212i		−	1.82704i	−0.406793	−	0.913521i	$-0.633353\pi$
$839$		−	52.9212i		−	1.82704i	0.406793	−	0.913521i	$-0.366647\pi$
$840$		0			0
$841$			46.0405i			1.58760i
$842$	−12.3188	+	19.0767i	−0.424535	+	0.657428i
$843$		0			0
$844$	−38.5830	−	14.5830i	−1.32808	−	0.501968i
$845$	0.595188	+	0.595188i	0.0204751	+	0.0204751i
$846$		0			0
$847$	−19.0627			−0.655004
$848$	1.74822	+	27.8618i	0.0600341	+	0.956778i
$849$		0			0
$850$	−7.06275	−	32.8118i	−0.242250	−	1.12543i
$851$	−2.80244	−	2.80244i	−0.0960664	−	0.0960664i
$852$		0			0
$853$	11.9373	−	11.9373i	0.408724	−	0.408724i	−0.472570	−	0.881293i	$-0.656673\pi$
$853$	11.9373	−	11.9373i	0.408724	−	0.408724i	0.881293	+	0.472570i	$0.156673\pi$
$854$	1.15303	−	1.78556i	0.0394559	−	0.0611007i
$855$		0			0
$856$	−1.41699	+	9.41699i	−0.0484319	+	0.321866i
$857$		−	10.2917i		−	0.351558i	−0.984430	−	0.175779i	$-0.943756\pi$
$857$		−	10.2917i		−	0.351558i	0.984430	−	0.175779i	$-0.0562443\pi$
$858$		0			0
$859$	−5.77124	+	5.77124i	−0.196912	+	0.196912i	−0.798675	−	0.601763i	$-0.794465\pi$
$859$	−5.77124	+	5.77124i	−0.196912	+	0.196912i	0.601763	+	0.798675i	$0.294465\pi$
$860$	0.346998	+	0.768687i	0.0118325	+	0.0262120i
$861$		0			0
$862$	−43.1660	+	9.29150i	−1.47024	+	0.316470i
$863$	53.3428			1.81581			0.907906	−	0.419174i	$-0.137680\pi$
$863$	53.3428			1.81581			0.907906	+	0.419174i	$0.137680\pi$
$864$		0			0
$865$	5.87451			0.199739
$866$	5.53019	−	1.19038i	0.187924	−	0.0404506i
$867$		0			0
$868$	7.64575	+	16.9373i	0.259514	+	0.574888i
$869$	32.4125	−	32.4125i	1.09952	−	1.09952i
$870$		0			0
$871$			21.1660i			0.717183i
$872$	26.2871	+	3.95547i	0.890193	+	0.133949i
$873$		0			0
$874$	−17.1660	+	26.5830i	−0.580649	+	0.899184i
$875$	9.10132	−	9.10132i	0.307681	−	0.307681i
$876$		0			0
$877$	−21.9373	−	21.9373i	−0.740768	−	0.740768i	0.231957	−	0.972726i	$-0.425487\pi$
$877$	−21.9373	−	21.9373i	−0.740768	−	0.740768i	−0.972726	+	0.231957i	$0.925487\pi$
$878$	0.142768	+	0.663265i	0.00481819	+	0.0223841i
$879$		0			0
$880$	−12.0000	−	10.5830i	−0.404520	−	0.356753i
$881$	−14.9785			−0.504639			−0.252319	−	0.967644i	$-0.581193\pi$
$881$	−14.9785			−0.504639			−0.252319	+	0.967644i	$0.581193\pi$
$882$		0			0
$883$	−35.3948	−	35.3948i	−1.19113	−	1.19113i	−0.976751	−	0.214378i	$-0.931228\pi$
$883$	−35.3948	−	35.3948i	−1.19113	−	1.19113i	−0.214378	−	0.976751i	$-0.568772\pi$
$884$	38.7113	+	14.6315i	1.30200	+	0.492111i
$885$		0			0
$886$	−23.3948	+	36.2288i	−0.785963	+	1.21713i
$887$		−	4.76150i		−	0.159876i	−0.996800	−	0.0799378i	$-0.974528\pi$
$887$		−	4.76150i		−	0.159876i	0.996800	−	0.0799378i	$-0.0254722\pi$
$888$		0			0
$889$		−	1.54249i		−	0.0517333i
$890$	−2.38075	−	1.53737i	−0.0798030	−	0.0515329i
$891$		0			0
$892$	−26.1660	+	11.8118i	−0.876103	+	0.395487i
$893$	33.1811	+	33.1811i	1.11036	+	1.11036i
$894$		0			0
$895$	−2.83399			−0.0947298
$896$	18.5496	+	1.61206i	0.619700	+	0.0538553i
$897$		0			0
$898$	−13.0627	+	2.81176i	−0.435909	+	0.0938297i
$899$	34.5824	+	34.5824i	1.15339	+	1.15339i
$900$		0			0
$901$	−27.2915	+	27.2915i	−0.909212	+	0.909212i
$902$	−44.6632	−	28.8413i	−1.48712	−	0.960311i
$903$		0			0
$904$		0			0
$905$			0.768687i			0.0255520i
$906$		0			0
$907$	16.1033	−	16.1033i	0.534700	−	0.534700i	−0.387267	−	0.921967i	$-0.626581\pi$
$907$	16.1033	−	16.1033i	0.534700	−	0.534700i	0.921967	+	0.387267i	$0.126581\pi$
$908$	−3.70728	−	1.40122i	−0.123030	−	0.0465011i
$909$		0			0
$910$	1.54249	+	7.16601i	0.0511329	+	0.237551i
$911$	−5.18319			−0.171727			−0.0858634	−	0.996307i	$-0.527365\pi$
$911$	−5.18319			−0.171727			−0.0858634	+	0.996307i	$0.527365\pi$
$912$		0			0
$913$	−22.5830			−0.747388
$914$	−1.61206	−	7.48925i	−0.0533224	−	0.247722i
$915$		0			0
$916$	17.9373	−	47.4575i	0.592664	−	1.56804i
$917$	11.0604	−	11.0604i	0.365246	−	0.365246i
$918$		0			0
$919$			42.1033i			1.38886i	0.719561	+	0.694429i	$0.244343\pi$
$919$			42.1033i			1.38886i	−0.719561	+	0.694429i	$0.755657\pi$
$920$	−10.2170	−	1.53737i	−0.336845	−	0.0506857i
$921$		0			0
$922$	−14.2915	−	9.22876i	−0.470666	−	0.303933i
$923$	−35.5619	+	35.5619i	−1.17053	+	1.17053i
$924$		0			0
$925$	−2.77124	−	2.77124i	−0.0911179	−	0.0911179i
$926$	−20.8250	+	4.48258i	−0.684351	+	0.147307i
$927$		0			0
$928$	47.1660	−	13.2915i	1.54830	−	0.436315i
$929$	−23.7328			−0.778649			−0.389324	−	0.921101i	$-0.627291\pi$
$929$	−23.7328			−0.778649			−0.389324	+	0.921101i	$0.627291\pi$
$930$		0			0
$931$	−15.6458	−	15.6458i	−0.512769	−	0.512769i
$932$	−16.2436	−	35.9836i	−0.532076	−	1.17868i
$933$		0			0
$934$	42.8118	+	27.6458i	1.40084	+	0.904597i
$935$		−	22.1208i		−	0.723426i
$936$		0			0
$937$			31.1660i			1.01815i	0.860722	+	0.509075i	$0.170012\pi$
$937$			31.1660i			1.01815i	−0.860722	+	0.509075i	$0.829988\pi$
$938$	−7.14226	+	11.0604i	−0.233203	+	0.361134i
$939$		0			0
$940$	−5.41699	+	14.3320i	−0.176683	+	0.467459i
$941$	12.4243	+	12.4243i	0.405019	+	0.405019i	0.879997	−	0.474978i	$-0.157544\pi$
$941$	12.4243	+	12.4243i	0.405019	+	0.405019i	−0.474978	+	0.879997i	$0.657544\pi$
$942$		0			0
$943$	−34.3320			−1.11800
$944$	−1.53737	−	24.5015i	−0.0500372	−	0.797456i
$945$		0			0
$946$	−0.708497	−	3.29150i	−0.0230352	−	0.107016i
$947$	−2.38075	−	2.38075i	−0.0773640	−	0.0773640i	0.667366	−	0.744730i	$-0.267422\pi$
$947$	−2.38075	−	2.38075i	−0.0773640	−	0.0773640i	−0.744730	+	0.667366i	$0.767422\pi$
$948$		0			0
$949$	8.70850	−	8.70850i	0.282690	−	0.282690i
$950$	−16.9749	+	26.2871i	−0.550739	+	0.852865i
$951$		0			0
$952$	15.2915	+	20.7085i	0.495600	+	0.671166i
$953$		−	25.2702i		−	0.818582i	−0.912404	−	0.409291i	$-0.865776\pi$
$953$		−	25.2702i		−	0.818582i	0.912404	−	0.409291i	$-0.134224\pi$
$954$		0			0
$955$	5.41699	−	5.41699i	0.175290	−	0.175290i
$956$	−23.7328	+	10.7134i	−0.767574	+	0.346496i
$957$		0			0
$958$	30.5830	−	6.58301i	0.988092	−	0.212687i
$959$	−16.9376			−0.546943
$960$		0			0
$961$	0.874508			0.0282099
$962$	4.72416	−	1.01688i	0.152313	−	0.0327854i
$963$		0			0
$964$	−2.35425	+	1.06275i	−0.0758252	+	0.0342287i
$965$	7.06756	−	7.06756i	0.227513	−	0.227513i
$966$		0			0
$967$		−	45.3948i		−	1.45980i	−0.683555	−	0.729899i	$-0.739567\pi$
$967$		−	45.3948i		−	1.45980i	0.683555	−	0.729899i	$-0.260433\pi$
$968$	19.4611	+	26.3552i	0.625503	+	0.847087i
$969$		0			0
$970$	6.83399	−	10.5830i	0.219426	−	0.339800i
$971$	−20.7195	+	20.7195i	−0.664922	+	0.664922i	−0.956536	−	0.291614i	$-0.905808\pi$
$971$	−20.7195	+	20.7195i	−0.664922	+	0.664922i	0.291614	+	0.956536i	$0.405808\pi$
$972$		0			0
$973$	24.0000	+	24.0000i	0.769405	+	0.769405i
$974$	−2.44883	−	11.3766i	−0.0784655	−	0.364531i
$975$		0			0
$976$	−3.64575	+	0.228757i	−0.116698	+	0.00732232i
$977$	−20.5087			−0.656131			−0.328066	−	0.944655i	$-0.606397\pi$
$977$	−20.5087			−0.656131			−0.328066	+	0.944655i	$0.606397\pi$
$978$		0			0
$979$	8.00000	+	8.00000i	0.255681	+	0.255681i
$980$	2.55425	−	6.75791i	0.0815925	−	0.215874i
$981$		0			0
$982$	−16.7085	+	25.8745i	−0.533190	+	0.825689i
$983$		−	26.8823i		−	0.857411i	−0.903444	−	0.428706i	$-0.858970\pi$
$983$		−	26.8823i		−	0.857411i	0.903444	−	0.428706i	$-0.141030\pi$
$984$		0			0
$985$			10.1255i			0.322625i
$986$	56.9140	+	36.7523i	1.81251	+	1.17043i
$987$		0			0
$988$	−15.8745	−	35.1660i	−0.505035	−	1.11878i
$989$	−1.53737	−	1.53737i	−0.0488856	−	0.0488856i
$990$		0			0
$991$	3.06275			0.0972913			0.0486457	−	0.998816i	$-0.484509\pi$
$991$	3.06275			0.0972913			0.0486457	+	0.998816i	$0.484509\pi$
$992$	15.6110	−	27.8618i	0.495651	−	0.884613i
$993$		0			0
$994$	−30.5830	+	6.58301i	−0.970034	+	0.208800i
$995$	8.12179	+	8.12179i	0.257478	+	0.257478i
$996$		0			0
$997$	36.5203	−	36.5203i	1.15661	−	1.15661i	0.171408	−	0.985200i	$-0.445168\pi$
$997$	36.5203	−	36.5203i	1.15661	−	1.15661i	0.985200	−	0.171408i	$-0.0548317\pi$
$998$	−17.7809	−	11.4821i	−0.562846	−	0.363459i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.k.c.109.1	yes	8
3.2	odd	2	inner	144.2.k.c.109.4	yes	8
4.3	odd	2		576.2.k.c.145.3		8
8.3	odd	2		1152.2.k.d.289.2		8
8.5	even	2		1152.2.k.e.289.2		8
12.11	even	2		576.2.k.c.145.2		8
16.3	odd	4		1152.2.k.d.865.2		8
16.5	even	4	inner	144.2.k.c.37.1	✓	8
16.11	odd	4		576.2.k.c.433.3		8
16.13	even	4		1152.2.k.e.865.2		8
24.5	odd	2		1152.2.k.e.289.3		8
24.11	even	2		1152.2.k.d.289.3		8
32.5	even	8		9216.2.a.bq.1.6		8
32.11	odd	8		9216.2.a.bt.1.3		8
32.21	even	8		9216.2.a.bq.1.3		8
32.27	odd	8		9216.2.a.bt.1.6		8
48.5	odd	4	inner	144.2.k.c.37.4	yes	8
48.11	even	4		576.2.k.c.433.2		8
48.29	odd	4		1152.2.k.e.865.3		8
48.35	even	4		1152.2.k.d.865.3		8
96.5	odd	8		9216.2.a.bq.1.4		8
96.11	even	8		9216.2.a.bt.1.5		8
96.53	odd	8		9216.2.a.bq.1.5		8
96.59	even	8		9216.2.a.bt.1.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.k.c.37.1	✓	8	16.5	even	4	inner
144.2.k.c.37.4	yes	8	48.5	odd	4	inner
144.2.k.c.109.1	yes	8	1.1	even	1	trivial
144.2.k.c.109.4	yes	8	3.2	odd	2	inner
576.2.k.c.145.2		8	12.11	even	2
576.2.k.c.145.3		8	4.3	odd	2
576.2.k.c.433.2		8	48.11	even	4
576.2.k.c.433.3		8	16.11	odd	4
1152.2.k.d.289.2		8	8.3	odd	2
1152.2.k.d.289.3		8	24.11	even	2
1152.2.k.d.865.2		8	16.3	odd	4
1152.2.k.d.865.3		8	48.35	even	4
1152.2.k.e.289.2		8	8.5	even	2
1152.2.k.e.289.3		8	24.5	odd	2
1152.2.k.e.865.2		8	16.13	even	4
1152.2.k.e.865.3		8	48.29	odd	4
9216.2.a.bq.1.3		8	32.21	even	8
9216.2.a.bq.1.4		8	96.5	odd	8
9216.2.a.bq.1.5		8	96.53	odd	8
9216.2.a.bq.1.6		8	32.5	even	8
9216.2.a.bt.1.3		8	32.11	odd	8
9216.2.a.bt.1.4		8	96.59	even	8
9216.2.a.bt.1.5		8	96.11	even	8
9216.2.a.bt.1.6		8	32.27	odd	8

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38255 + 0.297594i) q^{2} +(1.82288 - 0.822876i) q^{4} +(0.595188 - 0.595188i) q^{5} -1.64575i q^{7} +(-2.27533 + 1.68014i) q^{8} +O(q^{10})\)	\(q+(-1.38255 + 0.297594i) q^{2} +(1.82288 - 0.822876i) q^{4} +(0.595188 - 0.595188i) q^{5} -1.64575i q^{7} +(-2.27533 + 1.68014i) q^{8} +(-0.645751 + 1.00000i) q^{10} +(3.36028 - 3.36028i) q^{11} +(2.64575 + 2.64575i) q^{13} +(0.489766 + 2.27533i) q^{14} +(2.64575 - 3.00000i) q^{16} +5.53019 q^{17} +(-3.64575 - 3.64575i) q^{19} +(0.595188 - 1.57472i) q^{20} +(-3.64575 + 5.64575i) q^{22} +4.33981i q^{23} +4.29150i q^{25} +(-4.44524 - 2.87052i) q^{26} +(-1.35425 - 3.00000i) q^{28} +(-6.12538 - 6.12538i) q^{29} -5.64575 q^{31} +(-2.76510 + 4.93500i) q^{32} +(-7.64575 + 1.64575i) q^{34} +(-0.979531 - 0.979531i) q^{35} +(-0.645751 + 0.645751i) q^{37} +(6.12538 + 3.95547i) q^{38} +(-0.354249 + 2.35425i) q^{40} +7.91094i q^{41} +(-0.354249 + 0.354249i) q^{43} +(3.36028 - 8.89047i) q^{44} +(-1.29150 - 6.00000i) q^{46} -9.10132 q^{47} +4.29150 q^{49} +(-1.27713 - 5.93321i) q^{50} +(7.00000 + 2.64575i) q^{52} +(-4.93500 + 4.93500i) q^{53} -4.00000i q^{55} +(2.76510 + 3.74463i) q^{56} +(10.2915 + 6.64575i) q^{58} +(4.33981 - 4.33981i) q^{59} +(-0.645751 - 0.645751i) q^{61} +(7.80552 - 1.68014i) q^{62} +(2.35425 - 7.64575i) q^{64} +3.14944 q^{65} +(4.00000 + 4.00000i) q^{67} +(10.0808 - 4.55066i) q^{68} +(1.64575 + 1.06275i) q^{70} +13.4411i q^{71} -3.29150i q^{73} +(0.700610 - 1.08495i) q^{74} +(-9.64575 - 3.64575i) q^{76} +(-5.53019 - 5.53019i) q^{77} +9.64575 q^{79} +(-0.210845 - 3.36028i) q^{80} +(-2.35425 - 10.9373i) q^{82} +(-3.36028 - 3.36028i) q^{83} +(3.29150 - 3.29150i) q^{85} +(0.384343 - 0.595188i) q^{86} +(-2.00000 + 13.2915i) q^{88} +2.38075i q^{89} +(4.35425 - 4.35425i) q^{91} +(3.57113 + 7.91094i) q^{92} +(12.5830 - 2.70850i) q^{94} -4.33981 q^{95} -10.5830 q^{97} +(-5.93321 + 1.27713i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} + 16 q^{10} - 8 q^{19} - 8 q^{22} - 32 q^{28} - 24 q^{31} - 40 q^{34} + 16 q^{37} - 24 q^{40} - 24 q^{43} + 32 q^{46} - 8 q^{49} + 56 q^{52} + 40 q^{58} + 16 q^{61} + 40 q^{64} + 32 q^{67} - 8 q^{70} - 56 q^{76} + 56 q^{79} - 40 q^{82} - 16 q^{85} - 16 q^{88} + 56 q^{91} + 16 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 + 16 * q^10 - 8 * q^19 - 8 * q^22 - 32 * q^28 - 24 * q^31 - 40 * q^34 + 16 * q^37 - 24 * q^40 - 24 * q^43 + 32 * q^46 - 8 * q^49 + 56 * q^52 + 40 * q^58 + 16 * q^61 + 40 * q^64 + 32 * q^67 - 8 * q^70 - 56 * q^76 + 56 * q^79 - 40 * q^82 - 16 * q^85 - 16 * q^88 + 56 * q^91 + 16 * q^94

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