LMFDB - Embedded newform 144.2.k.c.37.4

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			37.4
Root			$1.38255 + 0.297594i$ of defining polynomial
Character	$\chi$	$=$	144.37
Dual form			144.2.k.c.109.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38255 + 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} +(-0.595188 - 0.595188i) q^{5} +1.64575i q^{7} +(2.27533 + 1.68014i) q^{8} +O(q^{10})$	\(q+(1.38255 + 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} +(-0.595188 - 0.595188i) q^{5} +1.64575i q^{7} +(2.27533 + 1.68014i) q^{8} +(-0.645751 - 1.00000i) q^{10} +(-3.36028 - 3.36028i) q^{11} +(2.64575 - 2.64575i) q^{13} +(-0.489766 + 2.27533i) q^{14} +(2.64575 + 3.00000i) q^{16} -5.53019 q^{17} +(-3.64575 + 3.64575i) q^{19} +(-0.595188 - 1.57472i) q^{20} +(-3.64575 - 5.64575i) q^{22} +4.33981i q^{23} -4.29150i q^{25} +(4.44524 - 2.87052i) q^{26} +(-1.35425 + 3.00000i) q^{28} +(6.12538 - 6.12538i) q^{29} -5.64575 q^{31} +(2.76510 + 4.93500i) q^{32} +(-7.64575 - 1.64575i) q^{34} +(0.979531 - 0.979531i) q^{35} +(-0.645751 - 0.645751i) q^{37} +(-6.12538 + 3.95547i) q^{38} +(-0.354249 - 2.35425i) q^{40} +7.91094i q^{41} +(-0.354249 - 0.354249i) q^{43} +(-3.36028 - 8.89047i) q^{44} +(-1.29150 + 6.00000i) q^{46} +9.10132 q^{47} +4.29150 q^{49} +(1.27713 - 5.93321i) q^{50} +(7.00000 - 2.64575i) q^{52} +(4.93500 + 4.93500i) q^{53} +4.00000i q^{55} +(-2.76510 + 3.74463i) q^{56} +(10.2915 - 6.64575i) q^{58} +(-4.33981 - 4.33981i) q^{59} +(-0.645751 + 0.645751i) q^{61} +(-7.80552 - 1.68014i) q^{62} +(2.35425 + 7.64575i) q^{64} -3.14944 q^{65} +(4.00000 - 4.00000i) q^{67} +(-10.0808 - 4.55066i) q^{68} +(1.64575 - 1.06275i) q^{70} +13.4411i q^{71} +3.29150i q^{73} +(-0.700610 - 1.08495i) q^{74} +(-9.64575 + 3.64575i) q^{76} +(5.53019 - 5.53019i) q^{77} +9.64575 q^{79} +(0.210845 - 3.36028i) q^{80} +(-2.35425 + 10.9373i) q^{82} +(3.36028 - 3.36028i) q^{83} +(3.29150 + 3.29150i) q^{85} +(-0.384343 - 0.595188i) q^{86} +(-2.00000 - 13.2915i) q^{88} +2.38075i q^{89} +(4.35425 + 4.35425i) q^{91} +(-3.57113 + 7.91094i) q^{92} +(12.5830 + 2.70850i) q^{94} +4.33981 q^{95} -10.5830 q^{97} +(5.93321 + 1.27713i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

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

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	$-0.310270\pi$
$5$	−0.595188	−	0.595188i	−0.266176	−	0.266176i	−0.827557	+	0.561381i	$0.810270\pi$
$6$		0			0
$7$			1.64575i			0.622036i	0.950404	+	0.311018i	$0.100670\pi$
$7$			1.64575i			0.622036i	−0.950404	+	0.311018i	$0.899330\pi$
$8$	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	−0.999912	−	0.0132513i	$-0.995782\pi$
$11$	−3.36028	−	3.36028i	−1.01316	−	1.01316i	−0.0132513	−	0.999912i	$-0.504218\pi$
$12$		0			0
$13$	2.64575	−	2.64575i	0.733799	−	0.733799i	−0.237571	−	0.971370i	$-0.576351\pi$
$13$	2.64575	−	2.64575i	0.733799	−	0.733799i	0.971370	+	0.237571i	$0.0763512\pi$
$14$	−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	$-0.733978\pi$
$17$	−5.53019			−1.34127			−0.670634	+	0.741788i	$0.733978\pi$
$18$		0			0
$19$	−3.64575	+	3.64575i	−0.836393	+	0.836393i	−0.988382	−	0.151989i	$-0.951432\pi$
$19$	−3.64575	+	3.64575i	−0.836393	+	0.836393i	0.151989	+	0.988382i	$0.451432\pi$
$20$	−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	0.148549	−	0.988905i	$-0.452540\pi$
$29$	6.12538	−	6.12538i	1.13745	−	1.13745i	0.988905	−	0.148549i	$-0.0474603\pi$
$30$		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	0.652031	−	0.758192i	$-0.273917\pi$
$37$	−0.645751	−	0.645751i	−0.106161	−	0.106161i	−0.758192	+	0.652031i	$0.773917\pi$
$38$	−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	0.679579	−	0.733602i	$-0.262162\pi$
$43$	−0.354249	−	0.354249i	−0.0540224	−	0.0540224i	−0.733602	+	0.679579i	$0.762162\pi$
$44$	−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	$-0.268950\pi$
$47$	9.10132			1.32756			0.663782	+	0.747926i	$0.268950\pi$
$48$		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	$-0.0908798\pi$
$53$	4.93500	+	4.93500i	0.677875	+	0.677875i	−0.281644	+	0.959519i	$0.590880\pi$
$54$		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	$-0.380821\pi$
$59$	−4.33981	−	4.33981i	−0.564996	−	0.564996i	−0.930722	+	0.365727i	$0.880821\pi$
$60$		0			0
$61$	−0.645751	+	0.645751i	−0.0826800	+	0.0826800i	−0.747237	−	0.664557i	$-0.768620\pi$
$61$	−0.645751	+	0.645751i	−0.0826800	+	0.0826800i	0.664557	+	0.747237i	$0.268620\pi$
$62$	−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	−0.419211	−	0.907889i	$-0.637693\pi$
$67$	4.00000	−	4.00000i	0.488678	−	0.488678i	0.907889	+	0.419211i	$0.137693\pi$
$68$	−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	$0.0616987\pi$
$73$			3.29150i			0.385241i	−0.981273	+	0.192621i	$0.938301\pi$
$74$	−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	$-0.666011\pi$
$83$	3.36028	−	3.36028i	0.368839	−	0.368839i	0.867054	+	0.498215i	$0.166011\pi$
$84$		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	$-0.263334\pi$
$101$	−0.595188	−	0.595188i	−0.0592234	−	0.0592234i	−0.736098	+	0.676875i	$0.763334\pi$
$102$		0			0
$103$		−	16.9373i		−	1.66888i	−0.551101	−	0.834439i	$-0.685792\pi$
$103$		−	16.9373i		−	1.66888i	0.551101	−	0.834439i	$-0.314208\pi$
$104$	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	$-0.302035\pi$
$107$	−2.38075	−	2.38075i	−0.230156	−	0.230156i	−0.812758	+	0.582602i	$0.802035\pi$
$108$		0			0
$109$	−6.64575	+	6.64575i	−0.636548	+	0.636548i	−0.949702	−	0.313155i	$-0.898614\pi$
$109$	−6.64575	+	6.64575i	−0.636548	+	0.636548i	0.313155	+	0.949702i	$0.398614\pi$
$110$	−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	$-0.886288\pi$
$131$	−6.72057	+	6.72057i	−0.587179	+	0.587179i	0.349688	+	0.936866i	$0.386288\pi$
$132$		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	−0.961256	−	0.275659i	$-0.911104\pi$
$139$	−14.5830	−	14.5830i	−1.23691	−	1.23691i	−0.275659	−	0.961256i	$-0.588896\pi$
$140$	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	$-0.485938\pi$
$149$	−11.6556	−	11.6556i	−0.954861	−	0.954861i	−0.999024	+	0.0441630i	$0.985938\pi$
$150$		0			0
$151$			10.3542i			0.842617i	0.906917	+	0.421308i	$0.138429\pi$
$151$			10.3542i			0.842617i	−0.906917	+	0.421308i	$0.861571\pi$
$152$	−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	−0.920688	−	0.390299i	$-0.872372\pi$
$157$	−6.64575	+	6.64575i	−0.530389	+	0.530389i	0.390299	+	0.920688i	$0.372372\pi$
$158$	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	−0.0842767	−	0.996442i	$-0.526858\pi$
$163$	11.6458	−	11.6458i	0.912166	−	0.912166i	0.996442	+	0.0842767i	$0.0268580\pi$
$164$	−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	$-0.835473\pi$
$173$	−4.93500	+	4.93500i	−0.375201	+	0.375201i	0.494166	+	0.869367i	$0.335473\pi$
$174$		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	$-0.709842\pi$
$179$	2.38075	−	2.38075i	0.177946	−	0.177946i	0.790460	+	0.612514i	$0.209842\pi$
$180$		0			0
$181$	−0.645751	−	0.645751i	−0.0479983	−	0.0479983i	0.682700	−	0.730699i	$-0.260805\pi$
$181$	−0.645751	−	0.645751i	−0.0479983	−	0.0479983i	−0.730699	+	0.682700i	$0.760805\pi$
$182$	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	$-0.606804\pi$
$191$	−9.10132			−0.658548			−0.329274	+	0.944234i	$0.606804\pi$
$192$		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	$-0.109031\pi$
$197$	8.50613	+	8.50613i	0.606037	+	0.606037i	−0.335871	+	0.941908i	$0.609031\pi$
$198$		0			0
$199$		−	13.6458i		−	0.967322i	−0.875256	−	0.483661i	$-0.839307\pi$
$199$		−	13.6458i		−	0.967322i	0.875256	−	0.483661i	$-0.160693\pi$
$200$	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	−0.00394326	+	0.999992i	$0.501255\pi$
$211$	−14.5830	+	14.5830i	−1.00394	+	1.00394i	−0.999992	+	0.00394326i	$0.998745\pi$
$212$	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	$-0.729052\pi$
$227$	1.40122	−	1.40122i	0.0930023	−	0.0930023i	0.752077	+	0.659075i	$0.229052\pi$
$228$		0			0
$229$	17.9373	+	17.9373i	1.18533	+	1.18533i	0.978345	+	0.206982i	$0.0663643\pi$
$229$	17.9373	+	17.9373i	1.18533	+	1.18533i	0.206982	+	0.978345i	$0.433636\pi$
$230$	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	$-0.361652\pi$
$239$	13.0194			0.842158			0.421079	+	0.907024i	$0.361652\pi$
$240$		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	0.978659	+	0.205492i	$0.0658795\pi$
$251$	18.7605	+	18.7605i	1.18415	+	1.18415i	0.205492	+	0.978659i	$0.434121\pi$
$252$		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	$-0.134002\pi$
$257$	29.2630			1.82538			0.912688	+	0.408656i	$0.134002\pi$
$258$		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	$-0.898999\pi$
$269$	−10.4652	+	10.4652i	−0.638074	+	0.638074i	0.312006	+	0.950080i	$0.398999\pi$
$270$		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	0.00736669	−	0.999973i	$-0.497655\pi$
$277$	−16.5203	−	16.5203i	−0.992606	−	0.992606i	−0.999973	+	0.00736669i	$0.997655\pi$
$278$	−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	0.626155	−	0.779699i	$-0.284628\pi$
$283$	−2.58301	−	2.58301i	−0.153544	−	0.153544i	−0.779699	+	0.626155i	$0.784628\pi$
$284$	−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	$-0.283649\pi$
$293$	−2.55425	−	2.55425i	−0.149221	−	0.149221i	−0.777770	+	0.628549i	$0.783649\pi$
$294$		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	−0.153277	+	0.988183i	$0.548983\pi$
$307$	−20.0000	+	20.0000i	−1.14146	+	1.14146i	−0.988183	+	0.153277i	$0.951017\pi$
$308$	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	$-0.915422\pi$
$313$		−	9.29150i		−	0.525187i	0.964907	−	0.262593i	$-0.0845778\pi$
$314$	−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	$-0.742475\pi$
$317$	0.595188	−	0.595188i	0.0334291	−	0.0334291i	0.723624	+	0.690195i	$0.242475\pi$
$318$		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	0.452198	−	0.891918i	$-0.350640\pi$
$331$	−8.00000	−	8.00000i	−0.439720	−	0.439720i	−0.891918	+	0.452198i	$0.850640\pi$
$332$	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	$-0.290713\pi$
$347$	−3.36028	−	3.36028i	−0.180389	−	0.180389i	−0.791526	+	0.611136i	$0.790713\pi$
$348$		0			0
$349$	3.22876	−	3.22876i	0.172831	−	0.172831i	−0.615391	−	0.788222i	$-0.711002\pi$
$349$	3.22876	−	3.22876i	0.172831	−	0.172831i	0.788222	+	0.615391i	$0.211002\pi$
$350$	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	$-0.560872\pi$
$353$	−7.14226			−0.380144			−0.190072	+	0.981770i	$0.560872\pi$
$354$		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	0.945041	−	0.326953i	$-0.106022\pi$
$373$	11.9373	+	11.9373i	0.618088	+	0.618088i	−0.326953	+	0.945041i	$0.606022\pi$
$374$	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	0.888332	−	0.459203i	$-0.151865\pi$
$379$	8.35425	+	8.35425i	0.429129	+	0.429129i	−0.459203	+	0.888332i	$0.651865\pi$
$380$	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	$-0.425300\pi$
$383$	9.10132			0.465056			0.232528	+	0.972590i	$0.425300\pi$
$384$		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	−0.998548	−	0.0538679i	$-0.982845\pi$
$389$	−20.7569	−	20.7569i	−1.05242	−	1.05242i	−0.0538679	−	0.998548i	$-0.517155\pi$
$390$		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	−0.475213	−	0.879871i	$-0.657629\pi$
$397$	8.06275	−	8.06275i	0.404658	−	0.404658i	0.879871	+	0.475213i	$0.157629\pi$
$398$	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	$-0.635955\pi$
$401$	−16.5906			−0.828494			−0.414247	+	0.910165i	$0.635955\pi$
$402$		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	$0.213757\pi$
$409$			25.1660i			1.24438i	−0.782867	+	0.622190i	$0.786243\pi$
$410$	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	$-0.974424\pi$
$419$	−18.7605	+	18.7605i	−0.916509	+	0.916509i	0.0802643	+	0.996774i	$0.474424\pi$
$420$		0			0
$421$	11.3542	+	11.3542i	0.553372	+	0.553372i	0.927412	−	0.374040i	$-0.122028\pi$
$421$	11.3542	+	11.3542i	0.553372	+	0.553372i	−0.374040	+	0.927412i	$0.622028\pi$
$422$	−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	$-0.770890\pi$
$431$	−31.2221			−1.50391			−0.751957	+	0.659212i	$0.770890\pi$
$432$		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	$0.00364422\pi$
$439$			0.479741i			0.0228968i	−0.999934	+	0.0114484i	$0.996356\pi$
$440$	−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	−0.999693	−	0.0247926i	$-0.992107\pi$
$443$	−21.5629	−	21.5629i	−1.02449	−	1.02449i	−0.0247926	−	0.999693i	$-0.507893\pi$
$444$		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	$-0.571568\pi$
$449$	−9.44832			−0.445894			−0.222947	+	0.974831i	$0.571568\pi$
$450$		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	$-0.959562\pi$
$457$		−	5.41699i		−	0.253396i	0.991941	−	0.126698i	$-0.0404380\pi$
$458$	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	$-0.840379\pi$
$461$	−8.50613	+	8.50613i	−0.396170	+	0.396170i	0.480710	+	0.876880i	$0.340379\pi$
$462$		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	0.199154	−	0.979968i	$-0.436181\pi$
$467$	25.4810	−	25.4810i	1.17912	−	1.17912i	0.979968	−	0.199154i	$-0.0638194\pi$
$468$		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	$-0.331359\pi$
$479$	22.1208			1.01072			0.505362	+	0.862908i	$0.331359\pi$
$480$		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	$-0.940305\pi$
$487$		−	8.22876i		−	0.372881i	0.982466	−	0.186440i	$-0.0596951\pi$
$488$	−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	$-0.413529\pi$
$491$	−15.4002	−	15.4002i	−0.695001	−	0.695001i	−0.963328	+	0.268327i	$0.913529\pi$
$492$		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	−0.429369	−	0.903129i	$-0.641264\pi$
$499$	10.5830	−	10.5830i	0.473760	−	0.473760i	0.903129	+	0.429369i	$0.141264\pi$
$500$	−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	0.0985706	−	0.995130i	$-0.468573\pi$
$509$	24.6750	−	24.6750i	1.09370	−	1.09370i	0.995130	−	0.0985706i	$-0.0314270\pi$
$510$		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	0.159181	−	0.987249i	$-0.449115\pi$
$523$	−18.9373	−	18.9373i	−0.828068	−	0.828068i	−0.987249	+	0.159181i	$0.949115\pi$
$524$	−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	−0.260785	+	0.965397i	$0.583981\pi$
$541$	−28.5203	+	28.5203i	−1.22618	+	1.22618i	−0.965397	+	0.260785i	$0.916019\pi$
$542$	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	−0.311557	−	0.950228i	$-0.600850\pi$
$547$	14.9373	−	14.9373i	0.638671	−	0.638671i	0.950228	+	0.311557i	$0.100850\pi$
$548$	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	$-0.559569\pi$
$557$	18.7978	−	18.7978i	0.796489	−	0.796489i	0.982540	+	0.186051i	$0.0595689\pi$
$558$		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	$-0.699327\pi$
$563$	5.31935	−	5.31935i	0.224184	−	0.224184i	0.810258	+	0.586074i	$0.199327\pi$
$564$		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	0.785833	−	0.618438i	$-0.212234\pi$
$571$	4.00000	+	4.00000i	0.167395	+	0.167395i	−0.618438	+	0.785833i	$0.712234\pi$
$572$	−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	$-0.205622\pi$
$587$	4.76150	+	4.76150i	0.196528	+	0.196528i	−0.601982	+	0.798510i	$0.705622\pi$
$588$		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	$-0.650073\pi$
$593$	−22.1208			−0.908391			−0.454195	+	0.890902i	$0.650073\pi$
$594$		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	$0.0213847\pi$
$601$			3.29150i			0.134263i	−0.997744	+	0.0671316i	$0.978615\pi$
$602$	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	0.996846	+	0.0793662i	$0.0252897\pi$
$613$	26.6458	+	26.6458i	1.07621	+	1.07621i	0.0793662	+	0.996846i	$0.474710\pi$
$614$	−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	0.139490	−	0.990224i	$-0.455454\pi$
$619$	−21.1660	−	21.1660i	−0.850734	−	0.850734i	−0.990224	+	0.139490i	$0.955454\pi$
$620$	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	$0.0523722\pi$
$631$			8.22876i			0.327582i	−0.986495	+	0.163791i	$0.947628\pi$
$632$	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	$-0.606255\pi$
$641$	−16.5906			−0.655288			−0.327644	+	0.944801i	$0.606255\pi$
$642$		0			0
$643$	−3.64575	+	3.64575i	−0.143774	+	0.143774i	−0.775330	−	0.631556i	$-0.782417\pi$
$643$	−3.64575	+	3.64575i	−0.143774	+	0.143774i	0.631556	+	0.775330i	$0.282417\pi$
$644$	−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	$-0.555248\pi$
$653$	20.7569	−	20.7569i	0.812280	−	0.812280i	0.984975	+	0.172696i	$0.0552477\pi$
$654$		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	$-0.990858\pi$
$659$	−24.9232	+	24.9232i	−0.970870	+	0.970870i	0.0287175	+	0.999588i	$0.490858\pi$
$660$		0			0
$661$	−2.77124	−	2.77124i	−0.107789	−	0.107789i	0.651155	−	0.758944i	$-0.274285\pi$
$661$	−2.77124	−	2.77124i	−0.107789	−	0.107789i	−0.758944	+	0.651155i	$0.774285\pi$
$662$	−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	$-0.125423\pi$
$677$	14.0363	+	14.0363i	0.539460	+	0.539460i	−0.383911	+	0.923370i	$0.625423\pi$
$678$		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	$-0.245195\pi$
$683$	0.557842	+	0.557842i	0.0213452	+	0.0213452i	−0.696354	+	0.717699i	$0.745195\pi$
$684$		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	−0.773044	−	0.634353i	$-0.781267\pi$
$691$	−3.64575	+	3.64575i	−0.138691	+	0.138691i	0.634353	+	0.773044i	$0.281267\pi$
$692$	−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	$-0.714508\pi$
$701$	4.16632	−	4.16632i	0.157360	−	0.157360i	0.781396	+	0.624036i	$0.214508\pi$
$702$		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	0.522951	−	0.852362i	$-0.324831\pi$
$709$	−8.77124	−	8.77124i	−0.329411	−	0.329411i	−0.852362	+	0.522951i	$0.824831\pi$
$710$	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	$-0.229135\pi$
$719$	40.3234			1.50381			0.751904	+	0.659272i	$0.229135\pi$
$720$		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	$0.212572\pi$
$727$			33.3948i			1.23854i	−0.785177	+	0.619272i	$0.787428\pi$
$728$	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	−0.900968	−	0.433886i	$-0.857142\pi$
$733$	−12.6458	+	12.6458i	−0.467081	+	0.467081i	0.433886	+	0.900968i	$0.357142\pi$
$734$	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	−0.855304	−	0.518127i	$-0.826630\pi$
$739$	−9.16601	+	9.16601i	−0.337177	+	0.337177i	0.518127	+	0.855304i	$0.326630\pi$
$740$	−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	0.563430	−	0.826164i	$-0.309481\pi$
$757$	−7.22876	−	7.22876i	−0.262734	−	0.262734i	−0.826164	+	0.563430i	$0.809481\pi$
$758$	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	$-0.0655960\pi$
$773$	21.5256	+	21.5256i	0.774221	+	0.774221i	−0.204620	+	0.978841i	$0.565596\pi$
$774$		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	−0.587322	−	0.809353i	$-0.699818\pi$
$787$	6.22876	−	6.22876i	0.222031	−	0.222031i	0.809353	+	0.587322i	$0.199818\pi$
$788$	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	$-0.931255\pi$
$797$	−21.5256	+	21.5256i	−0.762475	+	0.762475i	0.214294	+	0.976769i	$0.431255\pi$
$798$		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	0.376870	−	0.926266i	$-0.377000\pi$
$811$	−15.6458	−	15.6458i	−0.549397	−	0.549397i	−0.926266	+	0.376870i	$0.877000\pi$
$812$	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	$-0.311156\pi$
$821$	−7.73744	−	7.73744i	−0.270039	−	0.270039i	−0.829116	+	0.559077i	$0.811156\pi$
$822$		0			0
$823$			32.2288i			1.12342i	0.827333	+	0.561712i	$0.189857\pi$
$823$			32.2288i			1.12342i	−0.827333	+	0.561712i	$0.810143\pi$
$824$	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	$-0.284032\pi$
$827$	−4.33981	−	4.33981i	−0.150910	−	0.150910i	−0.778524	+	0.627614i	$0.784032\pi$
$828$		0			0
$829$	14.6458	−	14.6458i	0.508668	−	0.508668i	−0.405449	−	0.914117i	$-0.632885\pi$
$829$	14.6458	−	14.6458i	0.508668	−	0.508668i	0.914117	+	0.405449i	$0.132885\pi$
$830$	−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	0.881293	−	0.472570i	$-0.156673\pi$
$853$	11.9373	+	11.9373i	0.408724	+	0.408724i	−0.472570	+	0.881293i	$0.656673\pi$
$854$	−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	0.601763	−	0.798675i	$-0.294465\pi$
$859$	−5.77124	−	5.77124i	−0.196912	−	0.196912i	−0.798675	+	0.601763i	$0.794465\pi$
$860$	−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	$-0.862320\pi$
$863$	−53.3428			−1.81581			−0.907906	+	0.419174i	$0.862320\pi$
$864$		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	−0.972726	−	0.231957i	$-0.925487\pi$
$877$	−21.9373	+	21.9373i	−0.740768	+	0.740768i	0.231957	+	0.972726i	$0.425487\pi$
$878$	−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	$-0.418807\pi$
$881$	14.9785			0.504639			0.252319	+	0.967644i	$0.418807\pi$
$882$		0			0
$883$	−35.3948	+	35.3948i	−1.19113	+	1.19113i	−0.214378	+	0.976751i	$0.568772\pi$
$883$	−35.3948	+	35.3948i	−1.19113	+	1.19113i	−0.976751	+	0.214378i	$0.931228\pi$
$884$	−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	0.921967	−	0.387267i	$-0.126581\pi$
$907$	16.1033	+	16.1033i	0.534700	+	0.534700i	−0.387267	+	0.921967i	$0.626581\pi$
$908$	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	$-0.472635\pi$
$911$	5.18319			0.171727			0.0858634	+	0.996307i	$0.472635\pi$
$912$		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	$-0.755657\pi$
$919$		−	42.1033i		−	1.38886i	0.719561	−	0.694429i	$-0.244343\pi$
$920$	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	$-0.372709\pi$
$929$	23.7328			0.778649			0.389324	+	0.921101i	$0.372709\pi$
$930$		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	$-0.829988\pi$
$937$		−	31.1660i		−	1.01815i	0.860722	−	0.509075i	$-0.170012\pi$
$938$	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	$-0.842456\pi$
$941$	−12.4243	+	12.4243i	−0.405019	+	0.405019i	0.474978	+	0.879997i	$0.342456\pi$
$942$		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	$-0.732578\pi$
$947$	2.38075	−	2.38075i	0.0773640	−	0.0773640i	0.744730	+	0.667366i	$0.232578\pi$
$948$		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	$0.260433\pi$
$967$			45.3948i			1.45980i	−0.683555	+	0.729899i	$0.739567\pi$
$968$	−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	$-0.0941924\pi$
$971$	20.7195	+	20.7195i	0.664922	+	0.664922i	−0.291614	+	0.956536i	$0.594192\pi$
$972$		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	$-0.393603\pi$
$977$	20.5087			0.656131			0.328066	+	0.944655i	$0.393603\pi$
$978$		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	0.985200	+	0.171408i	$0.0548317\pi$
$997$	36.5203	+	36.5203i	1.15661	+	1.15661i	0.171408	+	0.985200i	$0.445168\pi$
$998$	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.37.4	yes	8
3.2	odd	2	inner	144.2.k.c.37.1	✓	8
4.3	odd	2		576.2.k.c.433.2		8
8.3	odd	2		1152.2.k.d.865.3		8
8.5	even	2		1152.2.k.e.865.3		8
12.11	even	2		576.2.k.c.433.3		8
16.3	odd	4		576.2.k.c.145.2		8
16.5	even	4		1152.2.k.e.289.3		8
16.11	odd	4		1152.2.k.d.289.3		8
16.13	even	4	inner	144.2.k.c.109.4	yes	8
24.5	odd	2		1152.2.k.e.865.2		8
24.11	even	2		1152.2.k.d.865.2		8
32.3	odd	8		9216.2.a.bt.1.5		8
32.13	even	8		9216.2.a.bq.1.4		8
32.19	odd	8		9216.2.a.bt.1.4		8
32.29	even	8		9216.2.a.bq.1.5		8
48.5	odd	4		1152.2.k.e.289.2		8
48.11	even	4		1152.2.k.d.289.2		8
48.29	odd	4	inner	144.2.k.c.109.1	yes	8
48.35	even	4		576.2.k.c.145.3		8
96.29	odd	8		9216.2.a.bq.1.3		8
96.35	even	8		9216.2.a.bt.1.3		8
96.77	odd	8		9216.2.a.bq.1.6		8
96.83	even	8		9216.2.a.bt.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.k.c.37.1	✓	8	3.2	odd	2	inner
144.2.k.c.37.4	yes	8	1.1	even	1	trivial
144.2.k.c.109.1	yes	8	48.29	odd	4	inner
144.2.k.c.109.4	yes	8	16.13	even	4	inner
576.2.k.c.145.2		8	16.3	odd	4
576.2.k.c.145.3		8	48.35	even	4
576.2.k.c.433.2		8	4.3	odd	2
576.2.k.c.433.3		8	12.11	even	2
1152.2.k.d.289.2		8	48.11	even	4
1152.2.k.d.289.3		8	16.11	odd	4
1152.2.k.d.865.2		8	24.11	even	2
1152.2.k.d.865.3		8	8.3	odd	2
1152.2.k.e.289.2		8	48.5	odd	4
1152.2.k.e.289.3		8	16.5	even	4
1152.2.k.e.865.2		8	24.5	odd	2
1152.2.k.e.865.3		8	8.5	even	2
9216.2.a.bq.1.3		8	96.29	odd	8
9216.2.a.bq.1.4		8	32.13	even	8
9216.2.a.bq.1.5		8	32.29	even	8
9216.2.a.bq.1.6		8	96.77	odd	8
9216.2.a.bt.1.3		8	96.35	even	8
9216.2.a.bt.1.4		8	32.19	odd	8
9216.2.a.bt.1.5		8	32.3	odd	8
9216.2.a.bt.1.6		8	96.83	even	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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