LMFDB - Embedded newform 600.2.r.c.257.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(257,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))

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

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

chi := DirichletCharacter("600.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.r (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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			257.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	600.257
Dual form			600.2.r.c.593.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 + 1.00000i) q^{3} +(-0.414214 - 0.414214i) q^{7} +(1.00000 - 2.82843i) q^{9} +O(q^{10})$	$q+(-1.41421 + 1.00000i) q^{3} +(-0.414214 - 0.414214i) q^{7} +(1.00000 - 2.82843i) q^{9} +4.82843i q^{11} +(1.82843 - 1.82843i) q^{13} +(-3.82843 + 3.82843i) q^{17} +4.82843i q^{19} +(1.00000 + 0.171573i) q^{21} +(-1.58579 - 1.58579i) q^{23} +(1.41421 + 5.00000i) q^{27} -7.65685 q^{29} -5.65685 q^{31} +(-4.82843 - 6.82843i) q^{33} +(0.171573 + 0.171573i) q^{37} +(-0.757359 + 4.41421i) q^{39} +5.65685i q^{41} +(-2.41421 + 2.41421i) q^{43} +(-6.41421 + 6.41421i) q^{47} -6.65685i q^{49} +(1.58579 - 9.24264i) q^{51} +(3.00000 + 3.00000i) q^{53} +(-4.82843 - 6.82843i) q^{57} -4.00000 q^{59} +11.6569 q^{61} +(-1.58579 + 0.757359i) q^{63} +(4.07107 + 4.07107i) q^{67} +(3.82843 + 0.656854i) q^{69} +6.48528i q^{71} +(-6.65685 + 6.65685i) q^{73} +(2.00000 - 2.00000i) q^{77} -4.82843i q^{79} +(-7.00000 - 5.65685i) q^{81} +(5.24264 + 5.24264i) q^{83} +(10.8284 - 7.65685i) q^{87} +4.34315 q^{89} -1.51472 q^{91} +(8.00000 - 5.65685i) q^{93} +(-1.00000 - 1.00000i) q^{97} +(13.6569 + 4.82843i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^7 + 4 * q^9	$ 4 q + 4 q^{7} + 4 q^{9} - 4 q^{13} - 4 q^{17} + 4 q^{21} - 12 q^{23} - 8 q^{29} - 8 q^{33} + 12 q^{37} - 20 q^{39} - 4 q^{43} - 20 q^{47} + 12 q^{51} + 12 q^{53} - 8 q^{57} - 16 q^{59} + 24 q^{61} - 12 q^{63} - 12 q^{67} + 4 q^{69} - 4 q^{73} + 8 q^{77} - 28 q^{81} + 4 q^{83} + 32 q^{87} + 40 q^{89} - 40 q^{91} + 32 q^{93} - 4 q^{97} + 32 q^{99}+O(q^{100}) $ 4 * q + 4 * q^7 + 4 * q^9 - 4 * q^13 - 4 * q^17 + 4 * q^21 - 12 * q^23 - 8 * q^29 - 8 * q^33 + 12 * q^37 - 20 * q^39 - 4 * q^43 - 20 * q^47 + 12 * q^51 + 12 * q^53 - 8 * q^57 - 16 * q^59 + 24 * q^61 - 12 * q^63 - 12 * q^67 + 4 * q^69 - 4 * q^73 + 8 * q^77 - 28 * q^81 + 4 * q^83 + 32 * q^87 + 40 * q^89 - 40 * q^91 + 32 * q^93 - 4 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.41421	+	1.00000i	−0.816497	+	0.577350i
$3$	−1.41421	+	1.00000i	−0.816497	+	0.577350i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.414214	−	0.414214i	−0.156558	−	0.156558i	0.624482	−	0.781040i	$-0.285310\pi$
$7$	−0.414214	−	0.414214i	−0.156558	−	0.156558i	−0.781040	+	0.624482i	$0.785310\pi$
$8$		0			0
$9$	1.00000	−	2.82843i	0.333333	−	0.942809i
$10$		0			0
$11$			4.82843i			1.45583i	0.685670	+	0.727913i	$0.259509\pi$
$11$			4.82843i			1.45583i	−0.685670	+	0.727913i	$0.740491\pi$
$12$		0			0
$13$	1.82843	−	1.82843i	0.507114	−	0.507114i	−0.406525	−	0.913640i	$-0.633260\pi$
$13$	1.82843	−	1.82843i	0.507114	−	0.507114i	0.913640	+	0.406525i	$0.133260\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.82843	+	3.82843i	−0.928530	+	0.928530i	−0.997611	−	0.0690811i	$-0.977993\pi$
$17$	−3.82843	+	3.82843i	−0.928530	+	0.928530i	0.0690811	+	0.997611i	$0.477993\pi$
$18$		0			0
$19$			4.82843i			1.10772i	0.832611	+	0.553859i	$0.186845\pi$
$19$			4.82843i			1.10772i	−0.832611	+	0.553859i	$0.813155\pi$
$20$		0			0
$21$	1.00000	+	0.171573i	0.218218	+	0.0374403i
$22$		0			0
$23$	−1.58579	−	1.58579i	−0.330659	−	0.330659i	0.522178	−	0.852837i	$-0.325120\pi$
$23$	−1.58579	−	1.58579i	−0.330659	−	0.330659i	−0.852837	+	0.522178i	$0.825120\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.41421	+	5.00000i	0.272166	+	0.962250i
$28$		0			0
$29$	−7.65685			−1.42184			−0.710921	−	0.703272i	$-0.751722\pi$
$29$	−7.65685			−1.42184			−0.710921	+	0.703272i	$0.751722\pi$
$30$		0			0
$31$	−5.65685			−1.01600			−0.508001	−	0.861357i	$-0.669615\pi$
$31$	−5.65685			−1.01600			−0.508001	+	0.861357i	$0.669615\pi$
$32$		0			0
$33$	−4.82843	−	6.82843i	−0.840521	−	1.18868i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	0.171573	+	0.171573i	0.0282064	+	0.0282064i	0.721069	−	0.692863i	$-0.243651\pi$
$37$	0.171573	+	0.171573i	0.0282064	+	0.0282064i	−0.692863	+	0.721069i	$0.743651\pi$
$38$		0			0
$39$	−0.757359	+	4.41421i	−0.121275	+	0.706840i
$40$		0			0
$41$			5.65685i			0.883452i	0.897150	+	0.441726i	$0.145634\pi$
$41$			5.65685i			0.883452i	−0.897150	+	0.441726i	$0.854366\pi$
$42$		0			0
$43$	−2.41421	+	2.41421i	−0.368164	+	0.368164i	−0.866807	−	0.498643i	$-0.833832\pi$
$43$	−2.41421	+	2.41421i	−0.368164	+	0.368164i	0.498643	+	0.866807i	$0.333832\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.41421	+	6.41421i	−0.935609	+	0.935609i	−0.998049	−	0.0624395i	$-0.980112\pi$
$47$	−6.41421	+	6.41421i	−0.935609	+	0.935609i	0.0624395	+	0.998049i	$0.480112\pi$
$48$		0			0
$49$		−	6.65685i		−	0.950979i
$50$		0			0
$51$	1.58579	−	9.24264i	0.222055	−	1.29423i
$52$		0			0
$53$	3.00000	+	3.00000i	0.412082	+	0.412082i	0.882463	−	0.470381i	$-0.155884\pi$
$53$	3.00000	+	3.00000i	0.412082	+	0.412082i	−0.470381	+	0.882463i	$0.655884\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.82843	−	6.82843i	−0.639541	−	0.904447i
$58$		0			0
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$		0			0
$61$	11.6569			1.49251			0.746254	−	0.665662i	$-0.231851\pi$
$61$	11.6569			1.49251			0.746254	+	0.665662i	$0.231851\pi$
$62$		0			0
$63$	−1.58579	+	0.757359i	−0.199790	+	0.0954183i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.07107	+	4.07107i	0.497360	+	0.497360i	0.910615	−	0.413255i	$-0.135608\pi$
$67$	4.07107	+	4.07107i	0.497360	+	0.497360i	−0.413255	+	0.910615i	$0.635608\pi$
$68$		0			0
$69$	3.82843	+	0.656854i	0.460888	+	0.0790760i
$70$		0			0
$71$			6.48528i			0.769661i	0.922987	+	0.384831i	$0.125740\pi$
$71$			6.48528i			0.769661i	−0.922987	+	0.384831i	$0.874260\pi$
$72$		0			0
$73$	−6.65685	+	6.65685i	−0.779126	+	0.779126i	−0.979682	−	0.200556i	$-0.935725\pi$
$73$	−6.65685	+	6.65685i	−0.779126	+	0.779126i	0.200556	+	0.979682i	$0.435725\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.00000	−	2.00000i	0.227921	−	0.227921i
$78$		0			0
$79$		−	4.82843i		−	0.543240i	−0.962405	−	0.271620i	$-0.912441\pi$
$79$		−	4.82843i		−	0.543240i	0.962405	−	0.271620i	$-0.0875595\pi$
$80$		0			0
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$		0			0
$83$	5.24264	+	5.24264i	0.575455	+	0.575455i	0.933648	−	0.358193i	$-0.116607\pi$
$83$	5.24264	+	5.24264i	0.575455	+	0.575455i	−0.358193	+	0.933648i	$0.616607\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	10.8284	−	7.65685i	1.16093	−	0.820901i
$88$		0			0
$89$	4.34315			0.460373			0.230186	−	0.973147i	$-0.426066\pi$
$89$	4.34315			0.460373			0.230186	+	0.973147i	$0.426066\pi$
$90$		0			0
$91$	−1.51472			−0.158786
$92$		0			0
$93$	8.00000	−	5.65685i	0.829561	−	0.586588i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.00000	−	1.00000i	−0.101535	−	0.101535i	0.654515	−	0.756049i	$-0.272873\pi$
$97$	−1.00000	−	1.00000i	−0.101535	−	0.101535i	−0.756049	+	0.654515i	$0.772873\pi$
$98$		0			0
$99$	13.6569	+	4.82843i	1.37257	+	0.485275i
$100$		0			0
$101$		−	1.65685i		−	0.164863i	−0.996597	−	0.0824316i	$-0.973731\pi$
$101$		−	1.65685i		−	0.164863i	0.996597	−	0.0824316i	$-0.0262686\pi$
$102$		0			0
$103$	8.41421	−	8.41421i	0.829077	−	0.829077i	−0.158312	−	0.987389i	$-0.550605\pi$
$103$	8.41421	−	8.41421i	0.829077	−	0.829077i	0.987389	+	0.158312i	$0.0506052\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.4142	−	12.4142i	1.20013	−	1.20013i	0.226000	−	0.974127i	$-0.427435\pi$
$107$	12.4142	−	12.4142i	1.20013	−	1.20013i	0.974127	−	0.226000i	$-0.0725649\pi$
$108$		0			0
$109$			4.00000i			0.383131i	0.981480	+	0.191565i	$0.0613564\pi$
$109$			4.00000i			0.383131i	−0.981480	+	0.191565i	$0.938644\pi$
$110$		0			0
$111$	−0.414214	−	0.0710678i	−0.0393154	−	0.00674546i
$112$		0			0
$113$	7.48528	+	7.48528i	0.704156	+	0.704156i	0.965300	−	0.261144i	$-0.0840997\pi$
$113$	7.48528	+	7.48528i	0.704156	+	0.704156i	−0.261144	+	0.965300i	$0.584100\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.34315	−	7.00000i	−0.309074	−	0.647150i
$118$		0			0
$119$	3.17157			0.290738
$120$		0			0
$121$	−12.3137			−1.11943
$122$		0			0
$123$	−5.65685	−	8.00000i	−0.510061	−	0.721336i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.41421	−	8.41421i	−0.746641	−	0.746641i	0.227206	−	0.973847i	$-0.427041\pi$
$127$	−8.41421	−	8.41421i	−0.746641	−	0.746641i	−0.973847	+	0.227206i	$0.927041\pi$
$128$		0			0
$129$	1.00000	−	5.82843i	0.0880451	−	0.513164i
$130$		0			0
$131$		−	3.17157i		−	0.277102i	−0.990355	−	0.138551i	$-0.955756\pi$
$131$		−	3.17157i		−	0.277102i	0.990355	−	0.138551i	$-0.0442444\pi$
$132$		0			0
$133$	2.00000	−	2.00000i	0.173422	−	0.173422i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.17157	−	4.17157i	0.356402	−	0.356402i	−0.506083	−	0.862485i	$-0.668907\pi$
$137$	4.17157	−	4.17157i	0.356402	−	0.356402i	0.862485	+	0.506083i	$0.168907\pi$
$138$		0			0
$139$		−	3.17157i		−	0.269009i	−0.990913	−	0.134505i	$-0.957056\pi$
$139$		−	3.17157i		−	0.269009i	0.990913	−	0.134505i	$-0.0429443\pi$
$140$		0			0
$141$	2.65685	−	15.4853i	0.223747	−	1.30410i
$142$		0			0
$143$	8.82843	+	8.82843i	0.738270	+	0.738270i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	6.65685	+	9.41421i	0.549048	+	0.776471i
$148$		0			0
$149$	9.31371			0.763009			0.381504	−	0.924367i	$-0.375406\pi$
$149$	9.31371			0.763009			0.381504	+	0.924367i	$0.375406\pi$
$150$		0			0
$151$	−2.34315			−0.190682			−0.0953412	−	0.995445i	$-0.530394\pi$
$151$	−2.34315			−0.190682			−0.0953412	+	0.995445i	$0.530394\pi$
$152$		0			0
$153$	7.00000	+	14.6569i	0.565916	+	1.18494i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.4853	+	11.4853i	0.916625	+	0.916625i	0.996782	−	0.0801570i	$-0.0255422\pi$
$157$	11.4853	+	11.4853i	0.916625	+	0.916625i	−0.0801570	+	0.996782i	$0.525542\pi$
$158$		0			0
$159$	−7.24264	−	1.24264i	−0.574379	−	0.0985478i
$160$		0			0
$161$			1.31371i			0.103535i
$162$		0			0
$163$	−2.41421	+	2.41421i	−0.189096	+	0.189096i	−0.795305	−	0.606209i	$-0.792689\pi$
$163$	−2.41421	+	2.41421i	−0.189096	+	0.189096i	0.606209	+	0.795305i	$0.292689\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.757359	+	0.757359i	−0.0586062	+	0.0586062i	−0.735802	−	0.677196i	$-0.763195\pi$
$167$	−0.757359	+	0.757359i	−0.0586062	+	0.0586062i	0.677196	+	0.735802i	$0.263195\pi$
$168$		0			0
$169$			6.31371i			0.485670i
$170$		0			0
$171$	13.6569	+	4.82843i	1.04437	+	0.369239i
$172$		0			0
$173$	−10.6569	−	10.6569i	−0.810226	−	0.810226i	0.174442	−	0.984667i	$-0.444188\pi$
$173$	−10.6569	−	10.6569i	−0.810226	−	0.810226i	−0.984667	+	0.174442i	$0.944188\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.65685	−	4.00000i	0.425195	−	0.300658i
$178$		0			0
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	17.3137			1.28692			0.643459	−	0.765481i	$-0.277499\pi$
$181$	17.3137			1.28692			0.643459	+	0.765481i	$0.277499\pi$
$182$		0			0
$183$	−16.4853	+	11.6569i	−1.21863	+	0.861699i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−18.4853	−	18.4853i	−1.35178	−	1.35178i
$188$		0			0
$189$	1.48528	−	2.65685i	0.108038	−	0.193258i
$190$		0			0
$191$		−	24.1421i		−	1.74686i	−0.486946	−	0.873432i	$-0.661889\pi$
$191$		−	24.1421i		−	1.74686i	0.486946	−	0.873432i	$-0.338111\pi$
$192$		0			0
$193$	−3.34315	+	3.34315i	−0.240645	+	0.240645i	−0.817117	−	0.576472i	$-0.804429\pi$
$193$	−3.34315	+	3.34315i	−0.240645	+	0.240645i	0.576472	+	0.817117i	$0.304429\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.34315	+	3.34315i	−0.238189	+	0.238189i	−0.816100	−	0.577911i	$-0.803868\pi$
$197$	−3.34315	+	3.34315i	−0.238189	+	0.238189i	0.577911	+	0.816100i	$0.303868\pi$
$198$		0			0
$199$		−	1.51472i		−	0.107376i	−0.998558	−	0.0536878i	$-0.982902\pi$
$199$		−	1.51472i		−	0.107376i	0.998558	−	0.0536878i	$-0.0170976\pi$
$200$		0			0
$201$	−9.82843	−	1.68629i	−0.693244	−	0.118942i
$202$		0			0
$203$	3.17157	+	3.17157i	0.222601	+	0.222601i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.07107	+	2.89949i	−0.421968	+	0.201529i
$208$		0			0
$209$	−23.3137			−1.61264
$210$		0			0
$211$	−12.9706			−0.892930			−0.446465	−	0.894801i	$-0.647317\pi$
$211$	−12.9706			−0.892930			−0.446465	+	0.894801i	$0.647317\pi$
$212$		0			0
$213$	−6.48528	−	9.17157i	−0.444364	−	0.628426i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	2.34315	+	2.34315i	0.159063	+	0.159063i
$218$		0			0
$219$	2.75736	−	16.0711i	0.186325	−	1.08598i
$220$		0			0
$221$			14.0000i			0.941742i
$222$		0			0
$223$	8.41421	−	8.41421i	0.563457	−	0.563457i	−0.366830	−	0.930288i	$-0.619557\pi$
$223$	8.41421	−	8.41421i	0.563457	−	0.563457i	0.930288	+	0.366830i	$0.119557\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.8995	+	14.8995i	−0.988914	+	0.988914i	−0.999939	−	0.0110250i	$-0.996491\pi$
$227$	−14.8995	+	14.8995i	−0.988914	+	0.988914i	0.0110250	+	0.999939i	$0.496491\pi$
$228$		0			0
$229$			25.6569i			1.69545i	0.530434	+	0.847726i	$0.322029\pi$
$229$			25.6569i			1.69545i	−0.530434	+	0.847726i	$0.677971\pi$
$230$		0			0
$231$	−0.828427	+	4.82843i	−0.0545065	+	0.317687i
$232$		0			0
$233$	−6.17157	−	6.17157i	−0.404313	−	0.404313i	0.475437	−	0.879750i	$-0.342290\pi$
$233$	−6.17157	−	6.17157i	−0.404313	−	0.404313i	−0.879750	+	0.475437i	$0.842290\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	4.82843	+	6.82843i	0.313640	+	0.443554i
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	−11.6569			−0.750884			−0.375442	−	0.926846i	$-0.622509\pi$
$241$	−11.6569			−0.750884			−0.375442	+	0.926846i	$0.622509\pi$
$242$		0			0
$243$	15.5563	+	1.00000i	0.997940	+	0.0641500i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	8.82843	+	8.82843i	0.561739	+	0.561739i
$248$		0			0
$249$	−12.6569	−	2.17157i	−0.802096	−	0.137618i
$250$		0			0
$251$			9.51472i			0.600564i	0.953851	+	0.300282i	$0.0970807\pi$
$251$			9.51472i			0.600564i	−0.953851	+	0.300282i	$0.902919\pi$
$252$		0			0
$253$	7.65685	−	7.65685i	0.481382	−	0.481382i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.48528	−	7.48528i	0.466919	−	0.466919i	−0.433996	−	0.900915i	$-0.642897\pi$
$257$	7.48528	−	7.48528i	0.466919	−	0.466919i	0.900915	+	0.433996i	$0.142897\pi$
$258$		0			0
$259$		−	0.142136i		−	0.00883188i
$260$		0			0
$261$	−7.65685	+	21.6569i	−0.473947	+	1.34053i
$262$		0			0
$263$	−12.8995	−	12.8995i	−0.795417	−	0.795417i	0.186952	−	0.982369i	$-0.440139\pi$
$263$	−12.8995	−	12.8995i	−0.795417	−	0.795417i	−0.982369	+	0.186952i	$0.940139\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.14214	+	4.34315i	−0.375893	+	0.265796i
$268$		0			0
$269$	28.6274			1.74544			0.872722	−	0.488217i	$-0.162353\pi$
$269$	28.6274			1.74544			0.872722	+	0.488217i	$0.162353\pi$
$270$		0			0
$271$	21.6569			1.31556			0.657780	−	0.753210i	$-0.271496\pi$
$271$	21.6569			1.31556			0.657780	+	0.753210i	$0.271496\pi$
$272$		0			0
$273$	2.14214	−	1.51472i	0.129648	−	0.0916749i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.8284	+	13.8284i	0.830870	+	0.830870i	0.987636	−	0.156766i	$-0.0501069\pi$
$277$	13.8284	+	13.8284i	0.830870	+	0.830870i	−0.156766	+	0.987636i	$0.550107\pi$
$278$		0			0
$279$	−5.65685	+	16.0000i	−0.338667	+	0.957895i
$280$		0			0
$281$		−	5.65685i		−	0.337460i	−0.985662	−	0.168730i	$-0.946033\pi$
$281$		−	5.65685i		−	0.337460i	0.985662	−	0.168730i	$-0.0539665\pi$
$282$		0			0
$283$	3.24264	−	3.24264i	0.192755	−	0.192755i	−0.604130	−	0.796885i	$-0.706479\pi$
$283$	3.24264	−	3.24264i	0.192755	−	0.192755i	0.796885	+	0.604130i	$0.206479\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.34315	−	2.34315i	0.138312	−	0.138312i
$288$		0			0
$289$		−	12.3137i		−	0.724336i
$290$		0			0
$291$	2.41421	+	0.414214i	0.141524	+	0.0242816i
$292$		0			0
$293$	5.34315	+	5.34315i	0.312150	+	0.312150i	0.845742	−	0.533592i	$-0.179158\pi$
$293$	5.34315	+	5.34315i	0.312150	+	0.312150i	−0.533592	+	0.845742i	$0.679158\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−24.1421	+	6.82843i	−1.40087	+	0.396226i
$298$		0			0
$299$	−5.79899			−0.335364
$300$		0			0
$301$	2.00000			0.115278
$302$		0			0
$303$	1.65685	+	2.34315i	0.0951838	+	0.134610i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−12.8995	−	12.8995i	−0.736213	−	0.736213i	0.235630	−	0.971843i	$-0.424285\pi$
$307$	−12.8995	−	12.8995i	−0.736213	−	0.736213i	−0.971843	+	0.235630i	$0.924285\pi$
$308$		0			0
$309$	−3.48528	+	20.3137i	−0.198271	+	1.15561i
$310$		0			0
$311$			22.4853i			1.27502i	0.770441	+	0.637512i	$0.220036\pi$
$311$			22.4853i			1.27502i	−0.770441	+	0.637512i	$0.779964\pi$
$312$		0			0
$313$	−20.3137	+	20.3137i	−1.14820	+	1.14820i	−0.161292	+	0.986907i	$0.551566\pi$
$313$	−20.3137	+	20.3137i	−1.14820	+	1.14820i	−0.986907	+	0.161292i	$0.948434\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.65685	+	6.65685i	−0.373886	+	0.373886i	−0.868891	−	0.495004i	$-0.835166\pi$
$317$	−6.65685	+	6.65685i	−0.373886	+	0.373886i	0.495004	+	0.868891i	$0.335166\pi$
$318$		0			0
$319$		−	36.9706i		−	2.06995i
$320$		0			0
$321$	−5.14214	+	29.9706i	−0.287006	+	1.67279i
$322$		0			0
$323$	−18.4853	−	18.4853i	−1.02855	−	1.02855i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−4.00000	−	5.65685i	−0.221201	−	0.312825i
$328$		0			0
$329$	5.31371			0.292954
$330$		0			0
$331$	1.65685			0.0910689			0.0455345	−	0.998963i	$-0.485501\pi$
$331$	1.65685			0.0910689			0.0455345	+	0.998963i	$0.485501\pi$
$332$		0			0
$333$	0.656854	−	0.313708i	0.0359954	−	0.0171911i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.00000	−	1.00000i	−0.0544735	−	0.0544735i	0.679345	−	0.733819i	$-0.262264\pi$
$337$	−1.00000	−	1.00000i	−0.0544735	−	0.0544735i	−0.733819	+	0.679345i	$0.762264\pi$
$338$		0			0
$339$	−18.0711	−	3.10051i	−0.981486	−	0.168396i
$340$		0			0
$341$		−	27.3137i		−	1.47912i
$342$		0			0
$343$	−5.65685	+	5.65685i	−0.305441	+	0.305441i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.07107	−	2.07107i	0.111181	−	0.111181i	−0.649328	−	0.760509i	$-0.724950\pi$
$347$	2.07107	−	2.07107i	0.111181	−	0.111181i	0.760509	+	0.649328i	$0.224950\pi$
$348$		0			0
$349$			1.65685i			0.0886894i	0.999016	+	0.0443447i	$0.0141200\pi$
$349$			1.65685i			0.0886894i	−0.999016	+	0.0443447i	$0.985880\pi$
$350$		0			0
$351$	11.7279	+	6.55635i	0.625990	+	0.349952i
$352$		0			0
$353$	−1.48528	−	1.48528i	−0.0790536	−	0.0790536i	0.666474	−	0.745528i	$-0.267803\pi$
$353$	−1.48528	−	1.48528i	−0.0790536	−	0.0790536i	−0.745528	+	0.666474i	$0.767803\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.48528	+	3.17157i	−0.237386	+	0.167857i
$358$		0			0
$359$	−12.6863			−0.669557			−0.334778	−	0.942297i	$-0.608661\pi$
$359$	−12.6863			−0.669557			−0.334778	+	0.942297i	$0.608661\pi$
$360$		0			0
$361$	−4.31371			−0.227037
$362$		0			0
$363$	17.4142	−	12.3137i	0.914009	−	0.646302i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	13.2426	+	13.2426i	0.691260	+	0.691260i	0.962509	−	0.271249i	$-0.0874367\pi$
$367$	13.2426	+	13.2426i	0.691260	+	0.691260i	−0.271249	+	0.962509i	$0.587437\pi$
$368$		0			0
$369$	16.0000	+	5.65685i	0.832927	+	0.294484i
$370$		0			0
$371$		−	2.48528i		−	0.129029i
$372$		0			0
$373$	−17.4853	+	17.4853i	−0.905354	+	0.905354i	−0.995893	−	0.0905393i	$-0.971141\pi$
$373$	−17.4853	+	17.4853i	−0.905354	+	0.905354i	0.0905393	+	0.995893i	$0.471141\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−14.0000	+	14.0000i	−0.721037	+	0.721037i
$378$		0			0
$379$		−	9.79899i		−	0.503340i	−0.967813	−	0.251670i	$-0.919020\pi$
$379$		−	9.79899i		−	0.503340i	0.967813	−	0.251670i	$-0.0809798\pi$
$380$		0			0
$381$	20.3137	+	3.48528i	1.04070	+	0.178556i
$382$		0			0
$383$	−9.58579	−	9.58579i	−0.489811	−	0.489811i	0.418436	−	0.908246i	$-0.362579\pi$
$383$	−9.58579	−	9.58579i	−0.489811	−	0.489811i	−0.908246	+	0.418436i	$0.862579\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.41421	+	9.24264i	0.224387	+	0.469830i
$388$		0			0
$389$	−29.3137			−1.48626			−0.743132	−	0.669145i	$-0.766661\pi$
$389$	−29.3137			−1.48626			−0.743132	+	0.669145i	$0.766661\pi$
$390$		0			0
$391$	12.1421			0.614054
$392$		0			0
$393$	3.17157	+	4.48528i	0.159985	+	0.226253i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.17157	−	2.17157i	−0.108988	−	0.108988i	0.650510	−	0.759498i	$-0.274555\pi$
$397$	−2.17157	−	2.17157i	−0.108988	−	0.108988i	−0.759498	+	0.650510i	$0.774555\pi$
$398$		0			0
$399$	−0.828427	+	4.82843i	−0.0414732	+	0.241724i
$400$		0			0
$401$		−	16.0000i		−	0.799002i	−0.916733	−	0.399501i	$-0.869183\pi$
$401$		−	16.0000i		−	0.799002i	0.916733	−	0.399501i	$-0.130817\pi$
$402$		0			0
$403$	−10.3431	+	10.3431i	−0.515229	+	0.515229i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.828427	+	0.828427i	−0.0410636	+	0.0410636i
$408$		0			0
$409$			10.3431i			0.511436i	0.966751	+	0.255718i	$0.0823118\pi$
$409$			10.3431i			0.511436i	−0.966751	+	0.255718i	$0.917688\pi$
$410$		0			0
$411$	−1.72792	+	10.0711i	−0.0852321	+	0.496769i
$412$		0			0
$413$	1.65685	+	1.65685i	0.0815285	+	0.0815285i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	3.17157	+	4.48528i	0.155313	+	0.219645i
$418$		0			0
$419$	37.9411			1.85355			0.926773	−	0.375623i	$-0.122571\pi$
$419$	37.9411			1.85355			0.926773	+	0.375623i	$0.122571\pi$
$420$		0			0
$421$	−2.97056			−0.144776			−0.0723882	−	0.997377i	$-0.523062\pi$
$421$	−2.97056			−0.144776			−0.0723882	+	0.997377i	$0.523062\pi$
$422$		0			0
$423$	11.7279	+	24.5563i	0.570231	+	1.19397i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4.82843	−	4.82843i	−0.233664	−	0.233664i
$428$		0			0
$429$	−21.3137	−	3.65685i	−1.02904	−	0.176555i
$430$		0			0
$431$		−	8.14214i		−	0.392193i	−0.980585	−	0.196096i	$-0.937173\pi$
$431$		−	8.14214i		−	0.392193i	0.980585	−	0.196096i	$-0.0628266\pi$
$432$		0			0
$433$	15.0000	−	15.0000i	0.720854	−	0.720854i	−0.247925	−	0.968779i	$-0.579749\pi$
$433$	15.0000	−	15.0000i	0.720854	−	0.720854i	0.968779	+	0.247925i	$0.0797487\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	7.65685	−	7.65685i	0.366277	−	0.366277i
$438$		0			0
$439$			25.7990i			1.23132i	0.788012	+	0.615659i	$0.211110\pi$
$439$			25.7990i			1.23132i	−0.788012	+	0.615659i	$0.788890\pi$
$440$		0			0
$441$	−18.8284	−	6.65685i	−0.896592	−	0.316993i
$442$		0			0
$443$	−14.0711	−	14.0711i	−0.668537	−	0.668537i	0.288841	−	0.957377i	$-0.406730\pi$
$443$	−14.0711	−	14.0711i	−0.668537	−	0.668537i	−0.957377	+	0.288841i	$0.906730\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.1716	+	9.31371i	−0.622994	+	0.440523i
$448$		0			0
$449$	21.3137			1.00586			0.502928	−	0.864328i	$-0.332256\pi$
$449$	21.3137			1.00586			0.502928	+	0.864328i	$0.332256\pi$
$450$		0			0
$451$	−27.3137			−1.28615
$452$		0			0
$453$	3.31371	−	2.34315i	0.155692	−	0.110091i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.00000	−	1.00000i	−0.0467780	−	0.0467780i	0.683331	−	0.730109i	$-0.260531\pi$
$457$	−1.00000	−	1.00000i	−0.0467780	−	0.0467780i	−0.730109	+	0.683331i	$0.760531\pi$
$458$		0			0
$459$	−24.5563	−	13.7279i	−1.14619	−	0.640765i
$460$		0			0
$461$		−	4.97056i		−	0.231502i	−0.993278	−	0.115751i	$-0.963073\pi$
$461$		−	4.97056i		−	0.231502i	0.993278	−	0.115751i	$-0.0369275\pi$
$462$		0			0
$463$	24.4142	−	24.4142i	1.13462	−	1.13462i	0.145226	−	0.989398i	$-0.453609\pi$
$463$	24.4142	−	24.4142i	1.13462	−	1.13462i	0.989398	−	0.145226i	$-0.0463910\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	13.3848	−	13.3848i	0.619374	−	0.619374i	−0.325997	−	0.945371i	$-0.605700\pi$
$467$	13.3848	−	13.3848i	0.619374	−	0.619374i	0.945371	+	0.325997i	$0.105700\pi$
$468$		0			0
$469$		−	3.37258i		−	0.155731i
$470$		0			0
$471$	−27.7279	−	4.75736i	−1.27764	−	0.219208i
$472$		0			0
$473$	−11.6569	−	11.6569i	−0.535983	−	0.535983i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	11.4853	−	5.48528i	0.525875	−	0.251154i
$478$		0			0
$479$	−22.6274			−1.03387			−0.516937	−	0.856024i	$-0.672928\pi$
$479$	−22.6274			−1.03387			−0.516937	+	0.856024i	$0.672928\pi$
$480$		0			0
$481$	0.627417			0.0286078
$482$		0			0
$483$	−1.31371	−	1.85786i	−0.0597758	−	0.0845358i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	16.5563	+	16.5563i	0.750240	+	0.750240i	0.974524	−	0.224284i	$-0.0720043\pi$
$487$	16.5563	+	16.5563i	0.750240	+	0.750240i	−0.224284	+	0.974524i	$0.572004\pi$
$488$		0			0
$489$	1.00000	−	5.82843i	0.0452216	−	0.263571i
$490$		0			0
$491$		−	38.4853i		−	1.73682i	−0.495850	−	0.868408i	$-0.665143\pi$
$491$		−	38.4853i		−	1.73682i	0.495850	−	0.868408i	$-0.334857\pi$
$492$		0			0
$493$	29.3137	−	29.3137i	1.32022	−	1.32022i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.68629	−	2.68629i	0.120497	−	0.120497i
$498$		0			0
$499$			38.7696i			1.73556i	0.496945	+	0.867782i	$0.334455\pi$
$499$			38.7696i			1.73556i	−0.496945	+	0.867782i	$0.665545\pi$
$500$		0			0
$501$	0.313708	−	1.82843i	0.0140155	−	0.0816881i
$502$		0			0
$503$	20.0711	+	20.0711i	0.894925	+	0.894925i	0.994982	−	0.100057i	$-0.0319025\pi$
$503$	20.0711	+	20.0711i	0.894925	+	0.894925i	−0.100057	+	0.994982i	$0.531903\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.31371	−	8.92893i	−0.280402	−	0.396548i
$508$		0			0
$509$	−7.65685			−0.339384			−0.169692	−	0.985497i	$-0.554277\pi$
$509$	−7.65685			−0.339384			−0.169692	+	0.985497i	$0.554277\pi$
$510$		0			0
$511$	5.51472			0.243957
$512$		0			0
$513$	−24.1421	+	6.82843i	−1.06590	+	0.301482i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−30.9706	−	30.9706i	−1.36208	−	1.36208i
$518$		0			0
$519$	25.7279	+	4.41421i	1.12933	+	0.193762i
$520$		0			0
$521$			24.0000i			1.05146i	0.850652	+	0.525730i	$0.176208\pi$
$521$			24.0000i			1.05146i	−0.850652	+	0.525730i	$0.823792\pi$
$522$		0			0
$523$	−7.10051	+	7.10051i	−0.310483	+	0.310483i	−0.845097	−	0.534613i	$-0.820457\pi$
$523$	−7.10051	+	7.10051i	−0.310483	+	0.310483i	0.534613	+	0.845097i	$0.320457\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	21.6569	−	21.6569i	0.943387	−	0.943387i
$528$		0			0
$529$		−	17.9706i		−	0.781329i
$530$		0			0
$531$	−4.00000	+	11.3137i	−0.173585	+	0.490973i
$532$		0			0
$533$	10.3431	+	10.3431i	0.448011	+	0.448011i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	16.9706	−	12.0000i	0.732334	−	0.517838i
$538$		0			0
$539$	32.1421			1.38446
$540$		0			0
$541$	−6.68629			−0.287466			−0.143733	−	0.989616i	$-0.545911\pi$
$541$	−6.68629			−0.287466			−0.143733	+	0.989616i	$0.545911\pi$
$542$		0			0
$543$	−24.4853	+	17.3137i	−1.05076	+	0.743002i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	9.72792	+	9.72792i	0.415936	+	0.415936i	0.883800	−	0.467864i	$-0.154976\pi$
$547$	9.72792	+	9.72792i	0.415936	+	0.415936i	−0.467864	+	0.883800i	$0.654976\pi$
$548$		0			0
$549$	11.6569	−	32.9706i	0.497502	−	1.40715i
$550$		0			0
$551$		−	36.9706i		−	1.57500i
$552$		0			0
$553$	−2.00000	+	2.00000i	−0.0850487	+	0.0850487i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	29.6274	−	29.6274i	1.25535	−	1.25535i	0.302067	−	0.953287i	$-0.402323\pi$
$557$	29.6274	−	29.6274i	1.25535	−	1.25535i	0.953287	−	0.302067i	$-0.0976768\pi$
$558$		0			0
$559$			8.82843i			0.373403i
$560$		0			0
$561$	44.6274	+	7.65685i	1.88417	+	0.323273i
$562$		0			0
$563$	32.5563	+	32.5563i	1.37209	+	1.37209i	0.857346	+	0.514740i	$0.172112\pi$
$563$	32.5563	+	32.5563i	1.37209	+	1.37209i	0.514740	+	0.857346i	$0.327888\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.556349	+	5.24264i	0.0233645	+	0.220170i
$568$		0			0
$569$	22.6863			0.951059			0.475529	−	0.879700i	$-0.342257\pi$
$569$	22.6863			0.951059			0.475529	+	0.879700i	$0.342257\pi$
$570$		0			0
$571$	28.9706			1.21238			0.606190	−	0.795320i	$-0.292697\pi$
$571$	28.9706			1.21238			0.606190	+	0.795320i	$0.292697\pi$
$572$		0			0
$573$	24.1421	+	34.1421i	1.00855	+	1.42631i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−3.34315	−	3.34315i	−0.139177	−	0.139177i	0.634086	−	0.773263i	$-0.281377\pi$
$577$	−3.34315	−	3.34315i	−0.139177	−	0.139177i	−0.773263	+	0.634086i	$0.781377\pi$
$578$		0			0
$579$	1.38478	−	8.07107i	0.0575493	−	0.335422i
$580$		0			0
$581$		−	4.34315i		−	0.180184i
$582$		0			0
$583$	−14.4853	+	14.4853i	−0.599919	+	0.599919i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−20.5563	+	20.5563i	−0.848451	+	0.848451i	−0.989940	−	0.141489i	$-0.954811\pi$
$587$	−20.5563	+	20.5563i	−0.848451	+	0.848451i	0.141489	+	0.989940i	$0.454811\pi$
$588$		0			0
$589$		−	27.3137i		−	1.12544i
$590$		0			0
$591$	1.38478	−	8.07107i	0.0569621	−	0.331999i
$592$		0			0
$593$	−1.48528	−	1.48528i	−0.0609932	−	0.0609932i	0.675952	−	0.736945i	$-0.263733\pi$
$593$	−1.48528	−	1.48528i	−0.0609932	−	0.0609932i	−0.736945	+	0.675952i	$0.763733\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	1.51472	+	2.14214i	0.0619933	+	0.0876718i
$598$		0			0
$599$	25.9411			1.05993			0.529963	−	0.848021i	$-0.322206\pi$
$599$	25.9411			1.05993			0.529963	+	0.848021i	$0.322206\pi$
$600$		0			0
$601$	18.9706			0.773825			0.386913	−	0.922116i	$-0.373541\pi$
$601$	18.9706			0.773825			0.386913	+	0.922116i	$0.373541\pi$
$602$		0			0
$603$	15.5858	−	7.44365i	0.634702	−	0.303129i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−15.0416	−	15.0416i	−0.610521	−	0.610521i	0.332561	−	0.943082i	$-0.392087\pi$
$607$	−15.0416	−	15.0416i	−0.610521	−	0.610521i	−0.943082	+	0.332561i	$0.892087\pi$
$608$		0			0
$609$	−7.65685	−	1.31371i	−0.310271	−	0.0532342i
$610$		0			0
$611$			23.4558i			0.948922i
$612$		0			0
$613$	7.48528	−	7.48528i	0.302328	−	0.302328i	−0.539596	−	0.841924i	$-0.681423\pi$
$613$	7.48528	−	7.48528i	0.302328	−	0.302328i	0.841924	+	0.539596i	$0.181423\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	17.8284	−	17.8284i	0.717745	−	0.717745i	−0.250398	−	0.968143i	$-0.580561\pi$
$617$	17.8284	−	17.8284i	0.717745	−	0.717745i	0.968143	+	0.250398i	$0.0805614\pi$
$618$		0			0
$619$			8.14214i			0.327260i	0.986522	+	0.163630i	$0.0523203\pi$
$619$			8.14214i			0.327260i	−0.986522	+	0.163630i	$0.947680\pi$
$620$		0			0
$621$	5.68629	−	10.1716i	0.228183	−	0.408171i
$622$		0			0
$623$	−1.79899	−	1.79899i	−0.0720750	−	0.0720750i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	32.9706	−	23.3137i	1.31672	−	0.931060i
$628$		0			0
$629$	−1.31371			−0.0523810
$630$		0			0
$631$	−47.5980			−1.89485			−0.947423	−	0.319984i	$-0.896322\pi$
$631$	−47.5980			−1.89485			−0.947423	+	0.319984i	$0.896322\pi$
$632$		0			0
$633$	18.3431	−	12.9706i	0.729075	−	0.515534i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−12.1716	−	12.1716i	−0.482255	−	0.482255i
$638$		0			0
$639$	18.3431	+	6.48528i	0.725644	+	0.256554i
$640$		0			0
$641$		−	36.2843i		−	1.43314i	−0.697514	−	0.716571i	$-0.745710\pi$
$641$		−	36.2843i		−	1.43314i	0.697514	−	0.716571i	$-0.254290\pi$
$642$		0			0
$643$	−30.6985	+	30.6985i	−1.21063	+	1.21063i	−0.239810	+	0.970820i	$0.577085\pi$
$643$	−30.6985	+	30.6985i	−1.21063	+	1.21063i	−0.970820	+	0.239810i	$0.922915\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.2132	−	16.2132i	0.637407	−	0.637407i	−0.312508	−	0.949915i	$-0.601169\pi$
$647$	16.2132	−	16.2132i	0.637407	−	0.637407i	0.949915	+	0.312508i	$0.101169\pi$
$648$		0			0
$649$		−	19.3137i		−	0.758129i
$650$		0			0
$651$	−5.65685	−	0.970563i	−0.221710	−	0.0380394i
$652$		0			0
$653$	−15.3431	−	15.3431i	−0.600424	−	0.600424i	0.340001	−	0.940425i	$-0.389572\pi$
$653$	−15.3431	−	15.3431i	−0.600424	−	0.600424i	−0.940425	+	0.340001i	$0.889572\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	12.1716	+	25.4853i	0.474858	+	0.994276i
$658$		0			0
$659$	−34.6274			−1.34889			−0.674446	−	0.738324i	$-0.735618\pi$
$659$	−34.6274			−1.34889			−0.674446	+	0.738324i	$0.735618\pi$
$660$		0			0
$661$	3.65685			0.142235			0.0711176	−	0.997468i	$-0.477343\pi$
$661$	3.65685			0.142235			0.0711176	+	0.997468i	$0.477343\pi$
$662$		0			0
$663$	−14.0000	−	19.7990i	−0.543715	−	0.768929i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	12.1421	+	12.1421i	0.470145	+	0.470145i
$668$		0			0
$669$	−3.48528	+	20.3137i	−0.134749	+	0.785373i
$670$		0			0
$671$			56.2843i			2.17283i
$672$		0			0
$673$	26.3137	−	26.3137i	1.01432	−	1.01432i	0.0144229	−	0.999896i	$-0.495409\pi$
$673$	26.3137	−	26.3137i	1.01432	−	1.01432i	0.999896	−	0.0144229i	$-0.00459112\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.2843	+	21.2843i	−0.818021	+	0.818021i	−0.985821	−	0.167800i	$-0.946334\pi$
$677$	−21.2843	+	21.2843i	−0.818021	+	0.818021i	0.167800	+	0.985821i	$0.446334\pi$
$678$		0			0
$679$			0.828427i			0.0317921i
$680$		0			0
$681$	6.17157	−	35.9706i	0.236495	−	1.37839i
$682$		0			0
$683$	8.55635	+	8.55635i	0.327400	+	0.327400i	0.851597	−	0.524197i	$-0.175635\pi$
$683$	8.55635	+	8.55635i	0.327400	+	0.327400i	−0.524197	+	0.851597i	$0.675635\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−25.6569	−	36.2843i	−0.978870	−	1.38433i
$688$		0			0
$689$	10.9706			0.417945
$690$		0			0
$691$	−22.3431			−0.849973			−0.424987	−	0.905200i	$-0.639721\pi$
$691$	−22.3431			−0.849973			−0.424987	+	0.905200i	$0.639721\pi$
$692$		0			0
$693$	−3.65685	−	7.65685i	−0.138912	−	0.290860i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−21.6569	−	21.6569i	−0.820312	−	0.820312i
$698$		0			0
$699$	14.8995	+	2.55635i	0.563551	+	0.0966900i
$700$		0			0
$701$			4.00000i			0.151078i	0.997143	+	0.0755390i	$0.0240677\pi$
$701$			4.00000i			0.151078i	−0.997143	+	0.0755390i	$0.975932\pi$
$702$		0			0
$703$	−0.828427	+	0.828427i	−0.0312447	+	0.0312447i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.686292	+	0.686292i	−0.0258106	+	0.0258106i
$708$		0			0
$709$		−	24.2843i		−	0.912015i	−0.889976	−	0.456007i	$-0.849279\pi$
$709$		−	24.2843i		−	0.912015i	0.889976	−	0.456007i	$-0.150721\pi$
$710$		0			0
$711$	−13.6569	−	4.82843i	−0.512172	−	0.181080i
$712$		0			0
$713$	8.97056	+	8.97056i	0.335950	+	0.335950i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−22.6274	+	16.0000i	−0.845036	+	0.597531i
$718$		0			0
$719$	−16.0000			−0.596699			−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000			−0.596699			−0.298350	+	0.954457i	$0.596436\pi$
$720$		0			0
$721$	−6.97056			−0.259597
$722$		0			0
$723$	16.4853	−	11.6569i	0.613094	−	0.433523i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	21.2426	+	21.2426i	0.787846	+	0.787846i	0.981141	−	0.193295i	$-0.0619174\pi$
$727$	21.2426	+	21.2426i	0.787846	+	0.787846i	−0.193295	+	0.981141i	$0.561917\pi$
$728$		0			0
$729$	−23.0000	+	14.1421i	−0.851852	+	0.523783i
$730$		0			0
$731$		−	18.4853i		−	0.683703i
$732$		0			0
$733$	−23.1421	+	23.1421i	−0.854774	+	0.854774i	−0.990717	−	0.135942i	$-0.956594\pi$
$733$	−23.1421	+	23.1421i	−0.854774	+	0.854774i	0.135942	+	0.990717i	$0.456594\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−19.6569	+	19.6569i	−0.724070	+	0.724070i
$738$		0			0
$739$			52.8284i			1.94333i	0.236372	+	0.971663i	$0.424041\pi$
$739$			52.8284i			1.94333i	−0.236372	+	0.971663i	$0.575959\pi$
$740$		0			0
$741$	−21.3137	−	3.65685i	−0.782979	−	0.134338i
$742$		0			0
$743$	−0.615224	−	0.615224i	−0.0225704	−	0.0225704i	0.695732	−	0.718302i	$-0.255080\pi$
$743$	−0.615224	−	0.615224i	−0.0225704	−	0.0225704i	−0.718302	+	0.695732i	$0.755080\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	20.0711	−	9.58579i	0.734362	−	0.350726i
$748$		0			0
$749$	−10.2843			−0.375779
$750$		0			0
$751$	44.2843			1.61596			0.807978	−	0.589213i	$-0.200562\pi$
$751$	44.2843			1.61596			0.807978	+	0.589213i	$0.200562\pi$
$752$		0			0
$753$	−9.51472	−	13.4558i	−0.346736	−	0.490358i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	36.4558	+	36.4558i	1.32501	+	1.32501i	0.909663	+	0.415347i	$0.136340\pi$
$757$	36.4558	+	36.4558i	1.32501	+	1.32501i	0.415347	+	0.909663i	$0.363660\pi$
$758$		0			0
$759$	−3.17157	+	18.4853i	−0.115121	+	0.670973i
$760$		0			0
$761$			35.3137i			1.28012i	0.768325	+	0.640060i	$0.221091\pi$
$761$			35.3137i			1.28012i	−0.768325	+	0.640060i	$0.778909\pi$
$762$		0			0
$763$	1.65685	−	1.65685i	0.0599822	−	0.0599822i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.31371	+	7.31371i	−0.264083	+	0.264083i
$768$		0			0
$769$			17.9411i			0.646974i	0.946233	+	0.323487i	$0.104855\pi$
$769$			17.9411i			0.646974i	−0.946233	+	0.323487i	$0.895145\pi$
$770$		0			0
$771$	−3.10051	+	18.0711i	−0.111662	+	0.650814i
$772$		0			0
$773$	0.656854	+	0.656854i	0.0236254	+	0.0236254i	0.718821	−	0.695195i	$-0.244682\pi$
$773$	0.656854	+	0.656854i	0.0236254	+	0.0236254i	−0.695195	+	0.718821i	$0.744682\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.142136	+	0.201010i	0.00509909	+	0.00721120i
$778$		0			0
$779$	−27.3137			−0.978615
$780$		0			0
$781$	−31.3137			−1.12049
$782$		0			0
$783$	−10.8284	−	38.2843i	−0.386976	−	1.36817i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	30.4142	+	30.4142i	1.08415	+	1.08415i	0.996118	+	0.0880320i	$0.0280578\pi$
$787$	30.4142	+	30.4142i	1.08415	+	1.08415i	0.0880320	+	0.996118i	$0.471942\pi$
$788$		0			0
$789$	31.1421	+	5.34315i	1.10869	+	0.190221i
$790$		0			0
$791$		−	6.20101i		−	0.220483i
$792$		0			0
$793$	21.3137	−	21.3137i	0.756872	−	0.756872i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.65685	+	6.65685i	−0.235798	+	0.235798i	−0.815108	−	0.579310i	$-0.803322\pi$
$797$	−6.65685	+	6.65685i	−0.235798	+	0.235798i	0.579310	+	0.815108i	$0.303322\pi$
$798$		0			0
$799$		−	49.1127i		−	1.73748i
$800$		0			0
$801$	4.34315	−	12.2843i	0.153458	−	0.434043i
$802$		0			0
$803$	−32.1421	−	32.1421i	−1.13427	−	1.13427i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−40.4853	+	28.6274i	−1.42515	+	1.00773i
$808$		0			0
$809$	−43.6569			−1.53489			−0.767447	−	0.641113i	$-0.778473\pi$
$809$	−43.6569			−1.53489			−0.767447	+	0.641113i	$0.778473\pi$
$810$		0			0
$811$	22.3431			0.784574			0.392287	−	0.919843i	$-0.371684\pi$
$811$	22.3431			0.784574			0.392287	+	0.919843i	$0.371684\pi$
$812$		0			0
$813$	−30.6274	+	21.6569i	−1.07415	+	0.759539i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−11.6569	−	11.6569i	−0.407822	−	0.407822i
$818$		0			0
$819$	−1.51472	+	4.28427i	−0.0529286	+	0.149705i
$820$		0			0
$821$			29.9411i			1.04495i	0.852654	+	0.522476i	$0.174992\pi$
$821$			29.9411i			1.04495i	−0.852654	+	0.522476i	$0.825008\pi$
$822$		0			0
$823$	19.7279	−	19.7279i	0.687672	−	0.687672i	−0.274045	−	0.961717i	$-0.588362\pi$
$823$	19.7279	−	19.7279i	0.687672	−	0.687672i	0.961717	+	0.274045i	$0.0883617\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−37.5269	+	37.5269i	−1.30494	+	1.30494i	−0.379919	+	0.925020i	$0.624048\pi$
$827$	−37.5269	+	37.5269i	−1.30494	+	1.30494i	−0.925020	+	0.379919i	$0.875952\pi$
$828$		0			0
$829$		−	7.31371i		−	0.254016i	−0.991902	−	0.127008i	$-0.959463\pi$
$829$		−	7.31371i		−	0.254016i	0.991902	−	0.127008i	$-0.0405373\pi$
$830$		0			0
$831$	−33.3848	−	5.72792i	−1.15811	−	0.198699i
$832$		0			0
$833$	25.4853	+	25.4853i	0.883013	+	0.883013i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−8.00000	−	28.2843i	−0.276520	−	0.977647i
$838$		0			0
$839$	−35.3137			−1.21916			−0.609582	−	0.792723i	$-0.708663\pi$
$839$	−35.3137			−1.21916			−0.609582	+	0.792723i	$0.708663\pi$
$840$		0			0
$841$	29.6274			1.02164
$842$		0			0
$843$	5.65685	+	8.00000i	0.194832	+	0.275535i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.10051	+	5.10051i	0.175255	+	0.175255i
$848$		0			0
$849$	−1.34315	+	7.82843i	−0.0460966	+	0.268671i
$850$		0			0
$851$		−	0.544156i		−	0.0186534i
$852$		0			0
$853$	−26.4558	+	26.4558i	−0.905831	+	0.905831i	−0.995933	−	0.0901017i	$-0.971281\pi$
$853$	−26.4558	+	26.4558i	−0.905831	+	0.905831i	0.0901017	+	0.995933i	$0.471281\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.5147	+	16.5147i	−0.564132	+	0.564132i	−0.930479	−	0.366346i	$-0.880608\pi$
$857$	−16.5147	+	16.5147i	−0.564132	+	0.564132i	0.366346	+	0.930479i	$0.380608\pi$
$858$		0			0
$859$		−	32.4264i		−	1.10637i	−0.833057	−	0.553187i	$-0.813411\pi$
$859$		−	32.4264i		−	1.10637i	0.833057	−	0.553187i	$-0.186589\pi$
$860$		0			0
$861$	−0.970563	+	5.65685i	−0.0330767	+	0.192785i
$862$		0			0
$863$	6.41421	+	6.41421i	0.218342	+	0.218342i	0.807800	−	0.589457i	$-0.200658\pi$
$863$	6.41421	+	6.41421i	0.218342	+	0.218342i	−0.589457	+	0.807800i	$0.700658\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	12.3137	+	17.4142i	0.418195	+	0.591418i
$868$		0			0
$869$	23.3137			0.790863
$870$		0			0
$871$	14.8873			0.504437
$872$		0			0
$873$	−3.82843	+	1.82843i	−0.129573	+	0.0618829i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−38.4558	−	38.4558i	−1.29856	−	1.29856i	−0.929342	−	0.369219i	$-0.879625\pi$
$877$	−38.4558	−	38.4558i	−1.29856	−	1.29856i	−0.369219	−	0.929342i	$-0.620375\pi$
$878$		0			0
$879$	−12.8995	−	2.21320i	−0.435089	−	0.0746495i
$880$		0			0
$881$			24.9706i			0.841280i	0.907228	+	0.420640i	$0.138194\pi$
$881$			24.9706i			0.841280i	−0.907228	+	0.420640i	$0.861806\pi$
$882$		0			0
$883$	−34.4142	+	34.4142i	−1.15813	+	1.15813i	−0.173253	+	0.984877i	$0.555428\pi$
$883$	−34.4142	+	34.4142i	−1.15813	+	1.15813i	−0.984877	+	0.173253i	$0.944572\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−17.7279	+	17.7279i	−0.595245	+	0.595245i	−0.939044	−	0.343798i	$-0.888286\pi$
$887$	−17.7279	+	17.7279i	−0.595245	+	0.595245i	0.343798	+	0.939044i	$0.388286\pi$
$888$		0			0
$889$			6.97056i			0.233785i
$890$		0			0
$891$	27.3137	−	33.7990i	0.915044	−	1.13231i
$892$		0			0
$893$	−30.9706	−	30.9706i	−1.03639	−	1.03639i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	8.20101	−	5.79899i	0.273824	−	0.193623i
$898$		0			0
$899$	43.3137			1.44459
$900$		0			0
$901$	−22.9706			−0.765260
$902$		0			0
$903$	−2.82843	+	2.00000i	−0.0941242	+	0.0665558i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−25.5858	−	25.5858i	−0.849562	−	0.849562i	0.140516	−	0.990078i	$-0.455124\pi$
$907$	−25.5858	−	25.5858i	−0.849562	−	0.849562i	−0.990078	+	0.140516i	$0.955124\pi$
$908$		0			0
$909$	−4.68629	−	1.65685i	−0.155434	−	0.0549544i
$910$		0			0
$911$			35.1716i			1.16529i	0.812728	+	0.582643i	$0.197981\pi$
$911$			35.1716i			1.16529i	−0.812728	+	0.582643i	$0.802019\pi$
$912$		0			0
$913$	−25.3137	+	25.3137i	−0.837761	+	0.837761i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.31371	+	1.31371i	−0.0433825	+	0.0433825i
$918$		0			0
$919$			3.17157i			0.104621i	0.998631	+	0.0523103i	$0.0166585\pi$
$919$			3.17157i			0.104621i	−0.998631	+	0.0523103i	$0.983342\pi$
$920$		0			0
$921$	31.1421	+	5.34315i	1.02617	+	0.176063i
$922$		0			0
$923$	11.8579	+	11.8579i	0.390306	+	0.390306i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−15.3848	−	32.2132i	−0.505302	−	1.05802i
$928$		0			0
$929$	−55.9411			−1.83537			−0.917684	−	0.397310i	$-0.869944\pi$
$929$	−55.9411			−1.83537			−0.917684	+	0.397310i	$0.869944\pi$
$930$		0			0
$931$	32.1421			1.05342
$932$		0			0
$933$	−22.4853	−	31.7990i	−0.736135	−	1.04105i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	31.0000	+	31.0000i	1.01273	+	1.01273i	0.999918	+	0.0128079i	$0.00407699\pi$
$937$	31.0000	+	31.0000i	1.01273	+	1.01273i	0.0128079	+	0.999918i	$0.495923\pi$
$938$		0			0
$939$	8.41421	−	49.0416i	0.274587	−	1.60041i
$940$		0			0
$941$			35.5980i			1.16046i	0.814452	+	0.580230i	$0.197038\pi$
$941$			35.5980i			1.16046i	−0.814452	+	0.580230i	$0.802962\pi$
$942$		0			0
$943$	8.97056	−	8.97056i	0.292122	−	0.292122i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.7279	−	23.7279i	0.771054	−	0.771054i	−0.207237	−	0.978291i	$-0.566447\pi$
$947$	23.7279	−	23.7279i	0.771054	−	0.771054i	0.978291	+	0.207237i	$0.0664471\pi$
$948$		0			0
$949$			24.3431i			0.790212i
$950$		0			0
$951$	2.75736	−	16.0711i	0.0894135	−	0.521140i
$952$		0			0
$953$	−1.48528	−	1.48528i	−0.0481130	−	0.0481130i	0.682641	−	0.730754i	$-0.260831\pi$
$953$	−1.48528	−	1.48528i	−0.0481130	−	0.0481130i	−0.730754	+	0.682641i	$0.760831\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	36.9706	+	52.2843i	1.19509	+	1.69011i
$958$		0			0
$959$	−3.45584			−0.111595
$960$		0			0
$961$	1.00000			0.0322581
$962$		0			0
$963$	−22.6985	−	47.5269i	−0.731448	−	1.53153i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	15.5858	+	15.5858i	0.501205	+	0.501205i	0.911812	−	0.410607i	$-0.134683\pi$
$967$	15.5858	+	15.5858i	0.501205	+	0.501205i	−0.410607	+	0.911812i	$0.634683\pi$
$968$		0			0
$969$	44.6274	+	7.65685i	1.43364	+	0.245974i
$970$		0			0
$971$			25.5147i			0.818806i	0.912354	+	0.409403i	$0.134263\pi$
$971$			25.5147i			0.818806i	−0.912354	+	0.409403i	$0.865737\pi$
$972$		0			0
$973$	−1.31371	+	1.31371i	−0.0421156	+	0.0421156i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.14214	−	5.14214i	0.164511	−	0.164511i	−0.620050	−	0.784562i	$-0.712888\pi$
$977$	5.14214	−	5.14214i	0.164511	−	0.164511i	0.784562	+	0.620050i	$0.212888\pi$
$978$		0			0
$979$			20.9706i			0.670222i
$980$		0			0
$981$	11.3137	+	4.00000i	0.361219	+	0.127710i
$982$		0			0
$983$	26.6985	+	26.6985i	0.851549	+	0.851549i	0.990324	−	0.138775i	$-0.0443163\pi$
$983$	26.6985	+	26.6985i	0.851549	+	0.851549i	−0.138775	+	0.990324i	$0.544316\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−7.51472	+	5.31371i	−0.239196	+	0.169137i
$988$		0			0
$989$	7.65685			0.243474
$990$		0			0
$991$	−15.0294			−0.477426			−0.238713	−	0.971090i	$-0.576725\pi$
$991$	−15.0294			−0.477426			−0.238713	+	0.971090i	$0.576725\pi$
$992$		0			0
$993$	−2.34315	+	1.65685i	−0.0743575	+	0.0525787i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−8.79899	−	8.79899i	−0.278667	−	0.278667i	0.553910	−	0.832577i	$-0.313135\pi$
$997$	−8.79899	−	8.79899i	−0.278667	−	0.278667i	−0.832577	+	0.553910i	$0.813135\pi$
$998$		0			0
$999$	−0.615224	+	1.10051i	−0.0194648	+	0.0348184i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.r.c.257.1		4
3.2	odd	2		600.2.r.b.257.2		4
4.3	odd	2		1200.2.v.d.257.2		4
5.2	odd	4		120.2.r.c.113.2	yes	4
5.3	odd	4		600.2.r.b.593.1		4
5.4	even	2		120.2.r.b.17.2	✓	4
12.11	even	2		1200.2.v.j.257.1		4
15.2	even	4		120.2.r.b.113.2	yes	4
15.8	even	4	inner	600.2.r.c.593.1		4
15.14	odd	2		120.2.r.c.17.1	yes	4
20.3	even	4		1200.2.v.j.593.2		4
20.7	even	4		240.2.v.a.113.1		4
20.19	odd	2		240.2.v.c.17.1		4
40.19	odd	2		960.2.v.g.257.2		4
40.27	even	4		960.2.v.i.833.2		4
40.29	even	2		960.2.v.f.257.1		4
40.37	odd	4		960.2.v.a.833.1		4
60.23	odd	4		1200.2.v.d.593.2		4
60.47	odd	4		240.2.v.c.113.1		4
60.59	even	2		240.2.v.a.17.2		4
120.29	odd	2		960.2.v.a.257.2		4
120.59	even	2		960.2.v.i.257.1		4
120.77	even	4		960.2.v.f.833.1		4
120.107	odd	4		960.2.v.g.833.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.r.b.17.2	✓	4	5.4	even	2
120.2.r.b.113.2	yes	4	15.2	even	4
120.2.r.c.17.1	yes	4	15.14	odd	2
120.2.r.c.113.2	yes	4	5.2	odd	4
240.2.v.a.17.2		4	60.59	even	2
240.2.v.a.113.1		4	20.7	even	4
240.2.v.c.17.1		4	20.19	odd	2
240.2.v.c.113.1		4	60.47	odd	4
600.2.r.b.257.2		4	3.2	odd	2
600.2.r.b.593.1		4	5.3	odd	4
600.2.r.c.257.1		4	1.1	even	1	trivial
600.2.r.c.593.1		4	15.8	even	4	inner
960.2.v.a.257.2		4	120.29	odd	2
960.2.v.a.833.1		4	40.37	odd	4
960.2.v.f.257.1		4	40.29	even	2
960.2.v.f.833.1		4	120.77	even	4
960.2.v.g.257.2		4	40.19	odd	2
960.2.v.g.833.2		4	120.107	odd	4
960.2.v.i.257.1		4	120.59	even	2
960.2.v.i.833.2		4	40.27	even	4
1200.2.v.d.257.2		4	4.3	odd	2
1200.2.v.d.593.2		4	60.23	odd	4
1200.2.v.j.257.1		4	12.11	even	2
1200.2.v.j.593.2		4	20.3	even	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.r (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 1.00000i) q^{3} +(-0.414214 - 0.414214i) q^{7} +(1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(-1.41421 + 1.00000i) q^{3} +(-0.414214 - 0.414214i) q^{7} +(1.00000 - 2.82843i) q^{9} +4.82843i q^{11} +(1.82843 - 1.82843i) q^{13} +(-3.82843 + 3.82843i) q^{17} +4.82843i q^{19} +(1.00000 + 0.171573i) q^{21} +(-1.58579 - 1.58579i) q^{23} +(1.41421 + 5.00000i) q^{27} -7.65685 q^{29} -5.65685 q^{31} +(-4.82843 - 6.82843i) q^{33} +(0.171573 + 0.171573i) q^{37} +(-0.757359 + 4.41421i) q^{39} +5.65685i q^{41} +(-2.41421 + 2.41421i) q^{43} +(-6.41421 + 6.41421i) q^{47} -6.65685i q^{49} +(1.58579 - 9.24264i) q^{51} +(3.00000 + 3.00000i) q^{53} +(-4.82843 - 6.82843i) q^{57} -4.00000 q^{59} +11.6569 q^{61} +(-1.58579 + 0.757359i) q^{63} +(4.07107 + 4.07107i) q^{67} +(3.82843 + 0.656854i) q^{69} +6.48528i q^{71} +(-6.65685 + 6.65685i) q^{73} +(2.00000 - 2.00000i) q^{77} -4.82843i q^{79} +(-7.00000 - 5.65685i) q^{81} +(5.24264 + 5.24264i) q^{83} +(10.8284 - 7.65685i) q^{87} +4.34315 q^{89} -1.51472 q^{91} +(8.00000 - 5.65685i) q^{93} +(-1.00000 - 1.00000i) q^{97} +(13.6569 + 4.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^7 + 4 * q^9	\( 4 q + 4 q^{7} + 4 q^{9} - 4 q^{13} - 4 q^{17} + 4 q^{21} - 12 q^{23} - 8 q^{29} - 8 q^{33} + 12 q^{37} - 20 q^{39} - 4 q^{43} - 20 q^{47} + 12 q^{51} + 12 q^{53} - 8 q^{57} - 16 q^{59} + 24 q^{61} - 12 q^{63} - 12 q^{67} + 4 q^{69} - 4 q^{73} + 8 q^{77} - 28 q^{81} + 4 q^{83} + 32 q^{87} + 40 q^{89} - 40 q^{91} + 32 q^{93} - 4 q^{97} + 32 q^{99}+O(q^{100}) \) 4 * q + 4 * q^7 + 4 * q^9 - 4 * q^13 - 4 * q^17 + 4 * q^21 - 12 * q^23 - 8 * q^29 - 8 * q^33 + 12 * q^37 - 20 * q^39 - 4 * q^43 - 20 * q^47 + 12 * q^51 + 12 * q^53 - 8 * q^57 - 16 * q^59 + 24 * q^61 - 12 * q^63 - 12 * q^67 + 4 * q^69 - 4 * q^73 + 8 * q^77 - 28 * q^81 + 4 * q^83 + 32 * q^87 + 40 * q^89 - 40 * q^91 + 32 * q^93 - 4 * q^97 + 32 * q^99

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