LMFDB - Embedded newform 900.3.u.a.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.149");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.u (of order $6$, degree $2$, not 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.303595776.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.1
Root			$-0.396143 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	900.149
Dual form			900.3.u.a.749.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.92048 - 0.686141i) q^{3} +(-7.89542 + 4.55842i) q^{7} +(8.05842 + 4.00772i) q^{9} +O(q^{10})$	\(q+(-2.92048 - 0.686141i) q^{3} +(-7.89542 + 4.55842i) q^{7} +(8.05842 + 4.00772i) q^{9} +(-0.383156 + 0.221215i) q^{11} +(9.62747 + 5.55842i) q^{13} -8.01544 q^{17} +8.11684 q^{19} +(26.1861 - 7.89542i) q^{21} +(-11.8020 + 20.4416i) q^{23} +(-20.7846 - 17.2337i) q^{27} +(45.9090 - 26.5055i) q^{29} +(-14.6753 + 25.4183i) q^{31} +(1.27078 - 0.383156i) q^{33} -18.4674i q^{37} +(-24.3030 - 22.8391i) q^{39} +(-38.9674 - 22.4978i) q^{41} +(19.9186 - 11.5000i) q^{43} +(4.22894 + 7.32473i) q^{47} +(17.0584 - 29.5461i) q^{49} +(23.4090 + 5.49972i) q^{51} -60.5841 q^{53} +(-23.7051 - 5.56930i) q^{57} +(-65.9674 - 38.0863i) q^{59} +(-2.67527 - 4.63370i) q^{61} +(-81.8935 + 5.09105i) q^{63} +(-95.0039 - 54.8505i) q^{67} +(48.4932 - 51.6014i) q^{69} +16.0309i q^{71} -4.35053i q^{73} +(2.01678 - 3.49317i) q^{77} +(0.792110 + 1.37197i) q^{79} +(48.8763 + 64.5918i) q^{81} +(-4.22894 - 7.32473i) q^{83} +(-152.263 + 45.9090i) q^{87} -64.1236i q^{89} -101.351 q^{91} +(60.2994 - 64.1644i) q^{93} +(-99.7953 + 57.6168i) q^{97} +(-3.97420 + 0.247063i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 30 q^{9}+O(q^{10}) $ 8 * q + 30 * q^9	$ 8 q + 30 q^{9} - 72 q^{11} - 4 q^{19} + 198 q^{21} + 126 q^{29} - 14 q^{31} - 114 q^{39} - 36 q^{41} + 102 q^{49} - 54 q^{51} - 252 q^{59} + 82 q^{61} - 198 q^{69} - 166 q^{79} - 126 q^{81} - 604 q^{91} - 342 q^{99}+O(q^{100}) $ 8 * q + 30 * q^9 - 72 * q^11 - 4 * q^19 + 198 * q^21 + 126 * q^29 - 14 * q^31 - 114 * q^39 - 36 * q^41 + 102 * q^49 - 54 * q^51 - 252 * q^59 + 82 * q^61 - 198 * q^69 - 166 * q^79 - 126 * q^81 - 604 * q^91 - 342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−2.92048	−	0.686141i	−0.973494	−	0.228714i
$3$	−2.92048	−	0.686141i	−0.973494	−	0.228714i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−7.89542	+	4.55842i	−1.12792	+	0.651203i	−0.943410	−	0.331628i	$-0.892402\pi$
$7$	−7.89542	+	4.55842i	−1.12792	+	0.651203i	−0.184507	+	0.982831i	$0.559069\pi$
$8$		0			0
$9$	8.05842	+	4.00772i	0.895380	+	0.445302i
$10$		0			0
$11$	−0.383156	+	0.221215i	−0.0348324	+	0.0201105i	−0.517315	−	0.855795i	$-0.673068\pi$
$11$	−0.383156	+	0.221215i	−0.0348324	+	0.0201105i	0.482483	+	0.875906i	$0.339735\pi$
$12$		0			0
$13$	9.62747	+	5.55842i	0.740575	+	0.427571i	0.822278	−	0.569086i	$-0.192703\pi$
$13$	9.62747	+	5.55842i	0.740575	+	0.427571i	−0.0817036	+	0.996657i	$0.526036\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−8.01544			−0.471497			−0.235748	−	0.971814i	$-0.575754\pi$
$17$	−8.01544			−0.471497			−0.235748	+	0.971814i	$0.575754\pi$
$18$		0			0
$19$	8.11684			0.427202			0.213601	−	0.976921i	$-0.431481\pi$
$19$	8.11684			0.427202			0.213601	+	0.976921i	$0.431481\pi$
$20$		0			0
$21$	26.1861	−	7.89542i	1.24696	−	0.375972i
$22$		0			0
$23$	−11.8020	+	20.4416i	−0.513128	+	0.888764i	0.486756	+	0.873538i	$0.338180\pi$
$23$	−11.8020	+	20.4416i	−0.513128	+	0.888764i	−0.999884	+	0.0152262i	$0.995153\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−20.7846	−	17.2337i	−0.769800	−	0.638285i
$28$		0			0
$29$	45.9090	−	26.5055i	1.58307	−	0.913984i	0.588659	−	0.808381i	$-0.299656\pi$
$29$	45.9090	−	26.5055i	1.58307	−	0.913984i	0.994408	−	0.105603i	$-0.0336772\pi$
$30$		0			0
$31$	−14.6753	+	25.4183i	−0.473396	+	0.819945i	−0.999536	−	0.0304523i	$-0.990305\pi$
$31$	−14.6753	+	25.4183i	−0.473396	+	0.819945i	0.526141	+	0.850398i	$0.323639\pi$
$32$		0			0
$33$	1.27078	−	0.383156i	0.0385086	−	0.0116108i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	18.4674i		−	0.499118i	−0.968360	−	0.249559i	$-0.919714\pi$
$37$		−	18.4674i		−	0.499118i	0.968360	−	0.249559i	$-0.0802857\pi$
$38$		0			0
$39$	−24.3030	−	22.8391i	−0.623153	−	0.585617i
$40$		0			0
$41$	−38.9674	−	22.4978i	−0.950424	−	0.548727i	−0.0572112	−	0.998362i	$-0.518221\pi$
$41$	−38.9674	−	22.4978i	−0.950424	−	0.548727i	−0.893213	+	0.449635i	$0.851554\pi$
$42$		0			0
$43$	19.9186	−	11.5000i	0.463223	−	0.267442i	−0.250176	−	0.968200i	$-0.580488\pi$
$43$	19.9186	−	11.5000i	0.463223	−	0.267442i	0.713398	+	0.700759i	$0.247155\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.22894	+	7.32473i	0.0899774	+	0.155845i	0.907501	−	0.420049i	$-0.137987\pi$
$47$	4.22894	+	7.32473i	0.0899774	+	0.155845i	−0.817524	+	0.575895i	$0.804654\pi$
$48$		0			0
$49$	17.0584	−	29.5461i	0.348131	−	0.602981i
$50$		0			0
$51$	23.4090	+	5.49972i	0.458999	+	0.107838i
$52$		0			0
$53$	−60.5841			−1.14310			−0.571548	−	0.820569i	$-0.693657\pi$
$53$	−60.5841			−1.14310			−0.571548	+	0.820569i	$0.693657\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−23.7051	−	5.56930i	−0.415879	−	0.0977070i
$58$		0			0
$59$	−65.9674	−	38.0863i	−1.11809	−	0.645530i	−0.177178	−	0.984179i	$-0.556697\pi$
$59$	−65.9674	−	38.0863i	−1.11809	−	0.645530i	−0.940913	+	0.338649i	$0.890030\pi$
$60$		0			0
$61$	−2.67527	−	4.63370i	−0.0438568	−	0.0759622i	0.843264	−	0.537500i	$-0.180631\pi$
$61$	−2.67527	−	4.63370i	−0.0438568	−	0.0759622i	−0.887121	+	0.461538i	$0.847298\pi$
$62$		0			0
$63$	−81.8935	+	5.09105i	−1.29990	+	0.0808103i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−95.0039	−	54.8505i	−1.41797	−	0.818665i	−0.421848	−	0.906666i	$-0.638619\pi$
$67$	−95.0039	−	54.8505i	−1.41797	−	0.818665i	−0.996120	+	0.0880017i	$0.971952\pi$
$68$		0			0
$69$	48.4932	−	51.6014i	0.702800	−	0.747847i
$70$		0			0
$71$			16.0309i			0.225787i	0.993607	+	0.112894i	$0.0360119\pi$
$71$			16.0309i			0.225787i	−0.993607	+	0.112894i	$0.963988\pi$
$72$		0			0
$73$		−	4.35053i		−	0.0595963i	−0.999556	−	0.0297982i	$-0.990514\pi$
$73$		−	4.35053i		−	0.0595963i	0.999556	−	0.0297982i	$-0.00948645\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.01678	−	3.49317i	0.0261920	−	0.0453659i
$78$		0			0
$79$	0.792110	+	1.37197i	0.0100267	+	0.0173668i	0.870995	−	0.491291i	$-0.163475\pi$
$79$	0.792110	+	1.37197i	0.0100267	+	0.0173668i	−0.860969	+	0.508658i	$0.830142\pi$
$80$		0			0
$81$	48.8763	+	64.5918i	0.603411	+	0.797430i
$82$		0			0
$83$	−4.22894	−	7.32473i	−0.0509511	−	0.0882498i	0.839425	−	0.543475i	$-0.182892\pi$
$83$	−4.22894	−	7.32473i	−0.0509511	−	0.0882498i	−0.890376	+	0.455226i	$0.849559\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−152.263	+	45.9090i	−1.75015	+	0.527689i
$88$		0			0
$89$		−	64.1236i		−	0.720489i	−0.932858	−	0.360245i	$-0.882693\pi$
$89$		−	64.1236i		−	0.720489i	0.932858	−	0.360245i	$-0.117307\pi$
$90$		0			0
$91$	−101.351			−1.11374
$92$		0			0
$93$	60.2994	−	64.1644i	0.648380	−	0.689940i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−99.7953	+	57.6168i	−1.02882	+	0.593988i	−0.916646	−	0.399701i	$-0.869114\pi$
$97$	−99.7953	+	57.6168i	−1.02882	+	0.593988i	−0.112172	+	0.993689i	$0.535781\pi$
$98$		0			0
$99$	−3.97420	+	0.247063i	−0.0401435	+	0.00249558i
$100$		0			0
$101$	114.558	−	66.1403i	1.13424	−	0.654855i	0.189244	−	0.981930i	$-0.439396\pi$
$101$	114.558	−	66.1403i	1.13424	−	0.654855i	0.944998	+	0.327075i	$0.106063\pi$
$102$		0			0
$103$	−108.557	−	62.6753i	−1.05395	−	0.608498i	−0.130197	−	0.991488i	$-0.541561\pi$
$103$	−108.557	−	62.6753i	−1.05395	−	0.608498i	−0.923752	+	0.382990i	$0.874894\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	36.5378			0.341475			0.170737	−	0.985317i	$-0.445385\pi$
$107$	36.5378			0.341475			0.170737	+	0.985317i	$0.445385\pi$
$108$		0			0
$109$	−134.701			−1.23579			−0.617895	−	0.786261i	$-0.712014\pi$
$109$	−134.701			−1.23579			−0.617895	+	0.786261i	$0.712014\pi$
$110$		0			0
$111$	−12.6712	+	53.9336i	−0.114155	+	0.485889i
$112$		0			0
$113$	95.1051	−	164.727i	0.841638	−	1.45776i	−0.0468711	−	0.998901i	$-0.514925\pi$
$113$	95.1051	−	164.727i	0.841638	−	1.45776i	0.888509	−	0.458859i	$-0.151742\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	55.3056	+	83.3763i	0.472697	+	0.712618i
$118$		0			0
$119$	63.2853	−	36.5378i	0.531809	−	0.307040i
$120$		0			0
$121$	−60.4021	+	104.620i	−0.499191	+	0.864624i
$122$		0			0
$123$	98.3668	+	92.4416i	0.799730	+	0.751558i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	184.103i		−	1.44963i	−0.688943	−	0.724816i	$-0.741925\pi$
$127$		−	184.103i		−	1.44963i	0.688943	−	0.724816i	$-0.258075\pi$
$128$		0			0
$129$	−66.0625	+	19.9186i	−0.512112	+	0.154408i
$130$		0			0
$131$	−109.194	−	63.0433i	−0.833544	−	0.481247i	0.0215207	−	0.999768i	$-0.493149\pi$
$131$	−109.194	−	63.0433i	−0.833544	−	0.481247i	−0.855064	+	0.518522i	$0.826483\pi$
$132$		0			0
$133$	−64.0859	+	37.0000i	−0.481849	+	0.278195i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−62.1326	−	107.617i	−0.453523	−	0.785524i	0.545079	−	0.838385i	$-0.316500\pi$
$137$	−62.1326	−	107.617i	−0.453523	−	0.785524i	−0.998602	+	0.0528602i	$0.983166\pi$
$138$		0			0
$139$	13.3832	−	23.1803i	0.0962817	−	0.166765i	−0.813861	−	0.581059i	$-0.802638\pi$
$139$	13.3832	−	23.1803i	0.0962817	−	0.166765i	0.910143	+	0.414295i	$0.135972\pi$
$140$		0			0
$141$	−7.32473	−	24.2934i	−0.0519485	−	0.172294i
$142$		0			0
$143$	−4.91843			−0.0343946
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−70.0916	+	74.5842i	−0.476813	+	0.507376i
$148$		0			0
$149$	−69.8437	−	40.3243i	−0.468750	−	0.270633i	0.246966	−	0.969024i	$-0.420566\pi$
$149$	−69.8437	−	40.3243i	−0.468750	−	0.270633i	−0.715716	+	0.698391i	$0.753900\pi$
$150$		0			0
$151$	−49.9742	−	86.5579i	−0.330955	−	0.573231i	0.651744	−	0.758439i	$-0.274037\pi$
$151$	−49.9742	−	86.5579i	−0.330955	−	0.573231i	−0.982699	+	0.185208i	$0.940704\pi$
$152$		0			0
$153$	−64.5918	−	32.1237i	−0.422169	−	0.209959i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−60.1487	−	34.7269i	−0.383113	−	0.221190i	0.296059	−	0.955170i	$-0.404327\pi$
$157$	−60.1487	−	34.7269i	−0.383113	−	0.221190i	−0.679172	+	0.733979i	$0.737661\pi$
$158$		0			0
$159$	176.935	+	41.5692i	1.11280	+	0.261442i
$160$		0			0
$161$		−	215.193i		−	1.33660i
$162$		0			0
$163$			162.467i			0.996732i	0.866967	+	0.498366i	$0.166066\pi$
$163$			162.467i			0.996732i	−0.866967	+	0.498366i	$0.833934\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	48.3397	−	83.7269i	0.289459	−	0.501358i	−0.684221	−	0.729274i	$-0.739858\pi$
$167$	48.3397	−	83.7269i	0.289459	−	0.501358i	0.973681	+	0.227916i	$0.0731911\pi$
$168$		0			0
$169$	−22.7079	−	39.3312i	−0.134366	−	0.232729i
$170$		0			0
$171$	65.4090	+	32.5301i	0.382509	+	0.190234i
$172$		0			0
$173$	−14.0141	−	24.2731i	−0.0810064	−	0.140307i	0.822676	−	0.568510i	$-0.192480\pi$
$173$	−14.0141	−	24.2731i	−0.0810064	−	0.140307i	−0.903682	+	0.428203i	$0.859147\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	166.524	+	156.493i	0.940813	+	0.884142i
$178$		0			0
$179$			35.6012i			0.198889i	0.995043	+	0.0994447i	$0.0317067\pi$
$179$			35.6012i			0.198889i	−0.995043	+	0.0994447i	$0.968293\pi$
$180$		0			0
$181$	−19.6358			−0.108485			−0.0542426	−	0.998528i	$-0.517274\pi$
$181$	−19.6358			−0.108485			−0.0542426	+	0.998528i	$0.517274\pi$
$182$		0			0
$183$	4.63370	+	15.3682i	0.0253207	+	0.0839794i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.07117	−	1.77314i	0.0164233	−	0.00948202i
$188$		0			0
$189$	242.662	+	41.3222i	1.28392	+	0.218636i
$190$		0			0
$191$	188.662	−	108.924i	0.987757	−	0.570282i	0.0831540	−	0.996537i	$-0.473501\pi$
$191$	188.662	−	108.924i	0.987757	−	0.570282i	0.904603	+	0.426255i	$0.140167\pi$
$192$		0			0
$193$	42.4352	+	24.5000i	0.219872	+	0.126943i	0.605891	−	0.795548i	$-0.292817\pi$
$193$	42.4352	+	24.5000i	0.219872	+	0.126943i	−0.386019	+	0.922491i	$0.626150\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	359.965			1.82723			0.913617	−	0.406575i	$-0.133277\pi$
$197$	359.965			1.82723			0.913617	+	0.406575i	$0.133277\pi$
$198$		0			0
$199$	61.0652			0.306861			0.153430	−	0.988159i	$-0.450968\pi$
$199$	61.0652			0.306861			0.153430	+	0.988159i	$0.450968\pi$
$200$		0			0
$201$	239.822	+	225.376i	1.19314	+	1.12127i
$202$		0			0
$203$	−241.647	+	418.545i	−1.19038	+	2.06180i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−177.029	+	117.428i	−0.855214	+	0.567285i
$208$		0			0
$209$	−3.11002	+	1.79557i	−0.0148805	+	0.00859124i
$210$		0			0
$211$	−193.493	+	335.140i	−0.917029	+	1.58834i	−0.113126	+	0.993581i	$0.536087\pi$
$211$	−193.493	+	335.140i	−0.917029	+	1.58834i	−0.803903	+	0.594761i	$0.797247\pi$
$212$		0			0
$213$	10.9994	−	46.8179i	0.0516406	−	0.219802i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	267.584i		−	1.23311i
$218$		0			0
$219$	−2.98508	+	12.7056i	−0.0136305	+	0.0580167i
$220$		0			0
$221$	−77.1684	−	44.5532i	−0.349178	−	0.201598i
$222$		0			0
$223$	88.9864	−	51.3763i	0.399042	−	0.230387i	−0.287028	−	0.957922i	$-0.592667\pi$
$223$	88.9864	−	51.3763i	0.399042	−	0.230387i	0.686071	+	0.727535i	$0.259334\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	169.482	+	293.552i	0.746617	+	1.29318i	0.949435	+	0.313962i	$0.101657\pi$
$227$	169.482	+	293.552i	0.746617	+	1.29318i	−0.202818	+	0.979216i	$0.565010\pi$
$228$		0			0
$229$	−148.376	+	256.995i	−0.647932	+	1.12225i	0.335685	+	0.941974i	$0.391032\pi$
$229$	−148.376	+	256.995i	−0.647932	+	1.12225i	−0.983616	+	0.180276i	$0.942301\pi$
$230$		0			0
$231$	−8.28679	+	8.81795i	−0.0358736	+	0.0381729i
$232$		0			0
$233$	346.537			1.48728			0.743642	−	0.668578i	$-0.233097\pi$
$233$	346.537			1.48728			0.743642	+	0.668578i	$0.233097\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.37197	−	4.55033i	−0.00578892	−	0.0191997i
$238$		0			0
$239$	140.026	+	80.8439i	0.585882	+	0.338259i	0.763468	−	0.645846i	$-0.223495\pi$
$239$	140.026	+	80.8439i	0.585882	+	0.338259i	−0.177586	+	0.984105i	$0.556829\pi$
$240$		0			0
$241$	162.370	+	281.232i	0.673732	+	1.16694i	0.976838	+	0.213982i	$0.0686433\pi$
$241$	162.370	+	281.232i	0.673732	+	1.16694i	−0.303105	+	0.952957i	$0.598023\pi$
$242$		0			0
$243$	−98.4233	−	222.175i	−0.405034	−	0.914302i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	78.1447	+	45.1168i	0.316375	+	0.182659i
$248$		0			0
$249$	7.32473	+	24.2934i	0.0294166	+	0.0975638i
$250$		0			0
$251$		−	384.012i		−	1.52993i	−0.644074	−	0.764963i	$-0.722757\pi$
$251$		−	384.012i		−	1.52993i	0.644074	−	0.764963i	$-0.277243\pi$
$252$		0			0
$253$		−	10.4431i		−	0.0412770i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.46694	+	11.2011i	−0.0251632	+	0.0435839i	−0.878333	−	0.478050i	$-0.841344\pi$
$257$	−6.46694	+	11.2011i	−0.0251632	+	0.0435839i	0.853170	+	0.521634i	$0.174677\pi$
$258$		0			0
$259$	84.1821	+	145.808i	0.325027	+	0.562964i
$260$		0			0
$261$	476.181	−	29.6026i	1.82445	−	0.113420i
$262$		0			0
$263$	−24.7358	−	42.8437i	−0.0940526	−	0.162904i	0.815160	−	0.579236i	$-0.196649\pi$
$263$	−24.7358	−	42.8437i	−0.0940526	−	0.162904i	−0.909213	+	0.416332i	$0.863316\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−43.9978	+	187.272i	−0.164786	+	0.701392i
$268$		0			0
$269$		−	21.4434i		−	0.0797154i	−0.999205	−	0.0398577i	$-0.987310\pi$
$269$		−	21.4434i		−	0.0797154i	0.999205	−	0.0398577i	$-0.0126905\pi$
$270$		0			0
$271$	−326.907			−1.20630			−0.603150	−	0.797628i	$-0.706088\pi$
$271$	−326.907			−1.20630			−0.603150	+	0.797628i	$0.706088\pi$
$272$		0			0
$273$	295.992	+	69.5407i	1.08422	+	0.254728i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	413.487	−	238.727i	1.49273	−	0.861830i	0.492768	−	0.870161i	$-0.335985\pi$
$277$	413.487	−	238.727i	1.49273	−	0.861830i	0.999965	+	0.00833105i	$0.00265189\pi$
$278$		0			0
$279$	−220.129	+	146.017i	−0.788993	+	0.523359i
$280$		0			0
$281$	−103.064	+	59.5039i	−0.366775	+	0.211758i	−0.672049	−	0.740507i	$-0.734585\pi$
$281$	−103.064	+	59.5039i	−0.366775	+	0.211758i	0.305274	+	0.952265i	$0.401252\pi$
$282$		0			0
$283$	338.920	+	195.675i	1.19760	+	0.691432i	0.960018	−	0.279937i	$-0.0903135\pi$
$283$	338.920	+	195.675i	1.19760	+	0.691432i	0.237577	+	0.971369i	$0.423647\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	410.218			1.42933
$288$		0			0
$289$	−224.753			−0.777691
$290$		0			0
$291$	330.984	−	99.7953i	1.13740	−	0.342939i
$292$		0			0
$293$	−35.8483	+	62.0910i	−0.122349	+	0.211915i	−0.920694	−	0.390286i	$-0.872376\pi$
$293$	−35.8483	+	62.0910i	−0.122349	+	0.211915i	0.798345	+	0.602201i	$0.205709\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	11.7761	+	2.00532i	0.0396502	+	0.00675192i
$298$		0			0
$299$	−227.246	+	131.200i	−0.760020	+	0.438797i
$300$		0			0
$301$	−104.844	+	181.595i	−0.348318	+	0.603304i
$302$		0			0
$303$	−379.947	+	114.558i	−1.25395	+	0.378081i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			172.351i			0.561402i	0.959795	+	0.280701i	$0.0905670\pi$
$307$			172.351i			0.561402i	−0.959795	+	0.280701i	$0.909433\pi$
$308$		0			0
$309$	274.034	+	257.527i	0.886841	+	0.833421i
$310$		0			0
$311$	−524.246	−	302.673i	−1.68568	−	0.973227i	−0.957763	−	0.287559i	$-0.907156\pi$
$311$	−524.246	−	302.673i	−1.68568	−	0.973227i	−0.727915	−	0.685667i	$-0.759511\pi$
$312$		0			0
$313$	283.595	−	163.734i	0.906055	−	0.523111i	0.0268949	−	0.999638i	$-0.491438\pi$
$313$	283.595	−	163.734i	0.906055	−	0.523111i	0.879160	+	0.476527i	$0.158105\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	34.5210	+	59.7921i	0.108899	+	0.188619i	0.915325	−	0.402717i	$-0.131934\pi$
$317$	34.5210	+	59.7921i	0.108899	+	0.188619i	−0.806425	+	0.591336i	$0.798601\pi$
$318$		0			0
$319$	−11.7269	+	20.3115i	−0.0367613	+	0.0636725i
$320$		0			0
$321$	−106.708	−	25.0701i	−0.332423	−	0.0780999i
$322$		0			0
$323$	−65.0601			−0.201424
$324$		0			0
$325$		0			0
$326$		0			0
$327$	393.392	+	92.4239i	1.20303	+	0.282642i
$328$		0			0
$329$	−66.7785	−	38.5546i	−0.202974	−	0.117187i
$330$		0			0
$331$	−254.895	−	441.492i	−0.770076	−	1.33381i	−0.937521	−	0.347930i	$-0.886885\pi$
$331$	−254.895	−	441.492i	−0.770076	−	1.33381i	0.167444	−	0.985882i	$-0.446449\pi$
$332$		0			0
$333$	74.0121	−	148.818i	0.222259	−	0.446901i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−292.232	−	168.720i	−0.867156	−	0.500653i	−0.000754096	−	1.00000i	$-0.500240\pi$
$337$	−292.232	−	168.720i	−0.867156	−	0.500653i	−0.866402	+	0.499347i	$0.833573\pi$
$338$		0			0
$339$	−390.778	+	415.826i	−1.15274	+	1.22663i
$340$		0			0
$341$		−	12.9856i		−	0.0380808i
$342$		0			0
$343$		−	135.687i		−	0.395590i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	107.622	−	186.407i	0.310151	−	0.537197i	−0.668244	−	0.743942i	$-0.732954\pi$
$347$	107.622	−	186.407i	0.310151	−	0.537197i	0.978395	+	0.206745i	$0.0662871\pi$
$348$		0			0
$349$	181.012	+	313.522i	0.518659	+	0.898345i	0.999765	+	0.0216818i	$0.00690207\pi$
$349$	181.012	+	313.522i	0.518659	+	0.898345i	−0.481105	+	0.876663i	$0.659765\pi$
$350$		0			0
$351$	−104.311	−	281.446i	−0.297183	−	0.801842i
$352$		0			0
$353$	−292.420	−	506.486i	−0.828385	−	1.43481i	−0.899304	−	0.437323i	$-0.855926\pi$
$353$	−292.420	−	506.486i	−0.828385	−	1.43481i	0.0709189	−	0.997482i	$-0.477407\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−209.894	+	63.2853i	−0.587937	+	0.177270i
$358$		0			0
$359$		−	393.693i		−	1.09664i	−0.836269	−	0.548319i	$-0.815268\pi$
$359$		−	393.693i		−	1.09664i	0.836269	−	0.548319i	$-0.184732\pi$
$360$		0			0
$361$	−295.117			−0.817498
$362$		0			0
$363$	248.187	−	264.095i	0.683711	−	0.727535i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−329.831	+	190.428i	−0.898722	+	0.518877i	−0.876785	−	0.480882i	$-0.840316\pi$
$367$	−329.831	+	190.428i	−0.898722	+	0.518877i	−0.0219364	+	0.999759i	$0.506983\pi$
$368$		0			0
$369$	−223.851	−	337.467i	−0.606641	−	0.914546i
$370$		0			0
$371$	478.337	−	276.168i	1.28932	−	0.744388i
$372$		0			0
$373$	−115.080	−	66.4416i	−0.308526	−	0.178128i	0.337741	−	0.941239i	$-0.390337\pi$
$373$	−115.080	−	66.4416i	−0.308526	−	0.178128i	−0.646267	+	0.763112i	$0.723671\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	589.316			1.56317
$378$		0			0
$379$	−507.622			−1.33937			−0.669686	−	0.742644i	$-0.733571\pi$
$379$	−507.622			−1.33937			−0.669686	+	0.742644i	$0.733571\pi$
$380$		0			0
$381$	−126.321	+	537.670i	−0.331550	+	1.41121i
$382$		0			0
$383$	−165.968	+	287.466i	−0.433338	+	0.750564i	−0.997158	−	0.0753339i	$-0.975998\pi$
$383$	−165.968	+	287.466i	−0.433338	+	0.750564i	0.563820	+	0.825898i	$0.309331\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	206.601	−	12.8437i	0.533853	−	0.0331879i
$388$		0			0
$389$	−296.662	+	171.278i	−0.762626	+	0.440302i	−0.830238	−	0.557409i	$-0.811795\pi$
$389$	−296.662	+	171.278i	−0.762626	+	0.440302i	0.0676116	+	0.997712i	$0.478462\pi$
$390$		0			0
$391$	94.5979	−	163.848i	0.241938	−	0.419049i
$392$		0			0
$393$	275.643	+	259.039i	0.701382	+	0.659133i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			24.8043i			0.0624792i	0.999512	+	0.0312396i	$0.00994550\pi$
$397$			24.8043i			0.0624792i	−0.999512	+	0.0312396i	$0.990055\pi$
$398$		0			0
$399$	212.549	−	64.0859i	0.532704	−	0.160616i
$400$		0			0
$401$	52.0842	+	30.0708i	0.129886	+	0.0749896i	0.563535	−	0.826092i	$-0.309441\pi$
$401$	52.0842	+	30.0708i	0.129886	+	0.0749896i	−0.433649	+	0.901082i	$0.642774\pi$
$402$		0			0
$403$	−282.571	+	163.143i	−0.701170	+	0.404820i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.08526	+	7.07589i	0.0100375	+	0.0173855i
$408$		0			0
$409$	−240.720	+	416.939i	−0.588558	+	1.01941i	0.405864	+	0.913933i	$0.366971\pi$
$409$	−240.720	+	416.939i	−0.588558	+	1.01941i	−0.994422	+	0.105478i	$0.966363\pi$
$410$		0			0
$411$	107.617	+	356.925i	0.261841	+	0.868430i
$412$		0			0
$413$	694.453			1.68149
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−54.9902	+	58.5149i	−0.131871	+	0.140324i
$418$		0			0
$419$	479.531	+	276.857i	1.14447	+	0.660758i	0.947533	−	0.319659i	$-0.103568\pi$
$419$	479.531	+	276.857i	1.14447	+	0.660758i	0.196933	+	0.980417i	$0.436902\pi$
$420$		0			0
$421$	190.947	+	330.730i	0.453556	+	0.785581i	0.998604	−	0.0528233i	$-0.0168220\pi$
$421$	190.947	+	330.730i	0.453556	+	0.785581i	−0.545048	+	0.838405i	$0.683489\pi$
$422$		0			0
$423$	4.72306	+	75.9742i	0.0111656	+	0.179608i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	42.2447	+	24.3900i	0.0989337	+	0.0571194i
$428$		0			0
$429$	14.3642	+	3.37474i	0.0334829	+	0.00786652i
$430$		0			0
$431$			821.321i			1.90562i	0.303570	+	0.952809i	$0.401821\pi$
$431$			821.321i			1.90562i	−0.303570	+	0.952809i	$0.598179\pi$
$432$		0			0
$433$		−	199.155i		−	0.459942i	−0.973198	−	0.229971i	$-0.926137\pi$
$433$		−	199.155i		−	0.459942i	0.973198	−	0.229971i	$-0.0738631\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−95.7946	+	165.921i	−0.219210	+	0.379682i
$438$		0			0
$439$	−240.830	−	417.130i	−0.548588	−	0.950182i	−0.998372	−	0.0570445i	$-0.981832\pi$
$439$	−240.830	−	417.130i	−0.548588	−	0.950182i	0.449784	−	0.893137i	$-0.351501\pi$
$440$		0			0
$441$	255.876	−	169.729i	0.580218	−	0.384873i
$442$		0			0
$443$	−270.143	−	467.902i	−0.609805	−	1.05621i	−0.991272	−	0.131830i	$-0.957915\pi$
$443$	−270.143	−	467.902i	−0.609805	−	1.05621i	0.381468	−	0.924382i	$-0.375419\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	176.309	+	165.689i	0.394428	+	0.370669i
$448$		0			0
$449$		−	300.318i		−	0.668859i	−0.942421	−	0.334429i	$-0.891456\pi$
$449$		−	300.318i		−	0.668859i	0.942421	−	0.334429i	$-0.108544\pi$
$450$		0			0
$451$	19.9074			0.0441407
$452$		0			0
$453$	86.5579	+	287.080i	0.191077	+	0.633731i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−134.841	+	77.8505i	−0.295057	+	0.170351i	−0.640220	−	0.768191i	$-0.721157\pi$
$457$	−134.841	+	77.8505i	−0.295057	+	0.170351i	0.345163	+	0.938543i	$0.387824\pi$
$458$		0			0
$459$	166.598	+	138.136i	0.362958	+	0.300949i
$460$		0			0
$461$	261.143	−	150.771i	0.566470	−	0.327052i	−0.189268	−	0.981925i	$-0.560612\pi$
$461$	261.143	−	150.771i	0.566470	−	0.327052i	0.755738	+	0.654874i	$0.227278\pi$
$462$		0			0
$463$	−206.790	−	119.390i	−0.446630	−	0.257862i	0.259776	−	0.965669i	$-0.416351\pi$
$463$	−206.790	−	119.390i	−0.446630	−	0.257862i	−0.706406	+	0.707807i	$0.749685\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−423.152			−0.906107			−0.453054	−	0.891483i	$-0.649665\pi$
$467$	−423.152			−0.906107			−0.453054	+	0.891483i	$0.649665\pi$
$468$		0			0
$469$	1000.13			2.13247
$470$		0			0
$471$	151.836	+	142.690i	0.322369	+	0.302950i
$472$		0			0
$473$	−5.08795	+	8.81259i	−0.0107568	+	0.0186313i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−488.212	−	242.804i	−1.02351	−	0.509024i
$478$		0			0
$479$	379.284	−	218.980i	0.791824	−	0.457160i	−0.0487802	−	0.998810i	$-0.515533\pi$
$479$	379.284	−	218.980i	0.791824	−	0.457160i	0.840604	+	0.541650i	$0.182200\pi$
$480$		0			0
$481$	102.649	−	177.794i	0.213408	−	0.369634i
$482$		0			0
$483$	−147.653	+	628.467i	−0.305699	+	1.30117i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	401.945i		−	0.825350i	−0.910878	−	0.412675i	$-0.864595\pi$
$487$		−	401.945i		−	0.825350i	0.910878	−	0.412675i	$-0.135405\pi$
$488$		0			0
$489$	111.475	−	474.483i	0.227966	−	0.970313i
$490$		0			0
$491$	−241.084	−	139.190i	−0.491007	−	0.283483i	0.233985	−	0.972240i	$-0.424823\pi$
$491$	−241.084	−	139.190i	−0.491007	−	0.283483i	−0.724992	+	0.688757i	$0.758157\pi$
$492$		0			0
$493$	−367.981	+	212.454i	−0.746411	+	0.430941i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−73.0756	−	126.571i	−0.147033	−	0.254669i
$498$		0			0
$499$	272.655	−	472.252i	0.546402	−	0.946397i	−0.452115	−	0.891960i	$-0.649330\pi$
$499$	272.655	−	472.252i	0.546402	−	0.946397i	0.998517	−	0.0544369i	$-0.0173364\pi$
$500$		0			0
$501$	−198.624	+	211.355i	−0.396454	+	0.421866i
$502$		0			0
$503$	306.460			0.609264			0.304632	−	0.952470i	$-0.401466\pi$
$503$	306.460			0.609264			0.304632	+	0.952470i	$0.401466\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	39.3312	+	130.447i	0.0775764	+	0.257292i
$508$		0			0
$509$	−480.208	−	277.248i	−0.943434	−	0.544692i	−0.0523989	−	0.998626i	$-0.516687\pi$
$509$	−480.208	−	277.248i	−0.943434	−	0.544692i	−0.891035	+	0.453934i	$0.850020\pi$
$510$		0			0
$511$	19.8316	+	34.3493i	0.0388093	+	0.0672197i
$512$		0			0
$513$	−168.705	−	139.883i	−0.328860	−	0.272677i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−3.24069	−	1.87101i	−0.00626825	−	0.00361898i
$518$		0			0
$519$	24.2731	+	80.5049i	0.0467691	+	0.155115i
$520$		0			0
$521$			154.167i			0.295905i	0.988994	+	0.147953i	$0.0472683\pi$
$521$			154.167i			0.295905i	−0.988994	+	0.147953i	$0.952732\pi$
$522$		0			0
$523$			480.598i			0.918925i	0.888197	+	0.459463i	$0.151958\pi$
$523$			480.598i			0.918925i	−0.888197	+	0.459463i	$0.848042\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	117.629	−	203.739i	0.223204	−	0.386602i
$528$		0			0
$529$	−14.0721	−	24.3735i	−0.0266013	−	0.0460748i
$530$		0			0
$531$	−378.954	−	571.294i	−0.713660	−	1.07588i
$532$		0			0
$533$	−250.105	−	433.194i	−0.469240	−	0.812747i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	24.4274	−	103.973i	0.0454887	−	0.193618i
$538$		0			0
$539$			15.0943i			0.0280043i
$540$		0			0
$541$	−300.543			−0.555533			−0.277766	−	0.960649i	$-0.589594\pi$
$541$	−300.543			−0.555533			−0.277766	+	0.960649i	$0.589594\pi$
$542$		0			0
$543$	57.3460	+	13.4729i	0.105610	+	0.0248120i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	87.6473	−	50.6032i	0.160233	−	0.0925104i	−0.417739	−	0.908567i	$-0.637178\pi$
$547$	87.6473	−	50.6032i	0.160233	−	0.0925104i	0.577972	+	0.816056i	$0.303844\pi$
$548$		0			0
$549$	−2.98785	−	48.0620i	−0.00544236	−	0.0875446i
$550$		0			0
$551$	372.636	−	215.141i	0.676290	−	0.390456i
$552$		0			0
$553$	−12.5081	−	7.22154i	−0.0226186	−	0.0130588i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−433.041			−0.777452			−0.388726	−	0.921353i	$-0.627085\pi$
$557$	−433.041			−0.777452			−0.388726	+	0.921353i	$0.627085\pi$
$558$		0			0
$559$	255.687			0.457401
$560$		0			0
$561$	−10.1859	+	3.07117i	−0.0181567	+	0.00547445i
$562$		0			0
$563$	−520.886	+	902.201i	−0.925197	+	1.60249i	−0.133954	+	0.990988i	$0.542767\pi$
$563$	−520.886	+	902.201i	−0.925197	+	1.60249i	−0.791244	+	0.611501i	$0.790566\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−680.336	−	287.181i	−1.19989	−	0.506491i
$568$		0			0
$569$	−257.445	+	148.636i	−0.452452	+	0.261223i	−0.708865	−	0.705344i	$-0.750793\pi$
$569$	−257.445	+	148.636i	−0.452452	+	0.261223i	0.256413	+	0.966567i	$0.417459\pi$
$570$		0			0
$571$	339.524	−	588.073i	0.594613	−	1.02990i	−0.398988	−	0.916956i	$-0.630638\pi$
$571$	339.524	−	588.073i	0.594613	−	1.02990i	0.993601	−	0.112945i	$-0.0360282\pi$
$572$		0			0
$573$	−625.720	+	188.662i	−1.09201	+	0.329252i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			148.351i			0.257107i	0.991703	+	0.128553i	$0.0410333\pi$
$577$			148.351i			0.257107i	−0.991703	+	0.128553i	$0.958967\pi$
$578$		0			0
$579$	−107.121	−	100.668i	−0.185010	−	0.173866i
$580$		0			0
$581$	66.7785	+	38.5546i	0.114937	+	0.0663590i
$582$		0			0
$583$	23.2132	−	13.4021i	0.0398168	−	0.0229882i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−263.559	−	456.497i	−0.448993	−	0.777678i	0.549328	−	0.835607i	$-0.314884\pi$
$587$	−263.559	−	456.497i	−0.448993	−	0.777678i	−0.998321	+	0.0579287i	$0.981550\pi$
$588$		0			0
$589$	−119.117	+	206.316i	−0.202236	+	0.350283i
$590$		0			0
$591$	−1051.27	−	246.987i	−1.77880	−	0.417913i
$592$		0			0
$593$	473.848			0.799069			0.399534	−	0.916718i	$-0.369172\pi$
$593$	473.848			0.799069			0.399534	+	0.916718i	$0.369172\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−178.340	−	41.8993i	−0.298727	−	0.0701832i
$598$		0			0
$599$	601.414	+	347.227i	1.00403	+	0.579677i	0.909438	−	0.415839i	$-0.136512\pi$
$599$	601.414	+	347.227i	1.00403	+	0.579677i	0.0945922	+	0.995516i	$0.469845\pi$
$600$		0			0
$601$	−93.3559	−	161.697i	−0.155334	−	0.269047i	0.777846	−	0.628454i	$-0.216312\pi$
$601$	−93.3559	−	161.697i	−0.155334	−	0.269047i	−0.933181	+	0.359408i	$0.882979\pi$
$602$		0			0
$603$	−545.756	−	822.758i	−0.905068	−	1.36444i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−712.209	−	411.194i	−1.17333	−	0.677420i	−0.218865	−	0.975755i	$-0.570236\pi$
$607$	−712.209	−	411.194i	−1.17333	−	0.677420i	−0.954461	+	0.298335i	$0.903569\pi$
$608$		0			0
$609$	992.906	−	1056.55i	1.63039	−	1.73489i
$610$		0			0
$611$			94.0249i			0.153887i
$612$		0			0
$613$		−	482.206i		−	0.786634i	−0.919403	−	0.393317i	$-0.871328\pi$
$613$		−	482.206i		−	0.786634i	0.919403	−	0.393317i	$-0.128672\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−344.052	+	595.916i	−0.557621	+	0.965828i	0.440073	+	0.897962i	$0.354952\pi$
$617$	−344.052	+	595.916i	−0.557621	+	0.965828i	−0.997694	+	0.0678661i	$0.978381\pi$
$618$		0			0
$619$	−380.253	−	658.617i	−0.614302	−	1.06400i	−0.990507	−	0.137465i	$-0.956105\pi$
$619$	−380.253	−	658.617i	−0.614302	−	1.06400i	0.376205	−	0.926536i	$-0.377229\pi$
$620$		0			0
$621$	597.583	−	221.479i	0.962291	−	0.356649i
$622$		0			0
$623$	292.302	+	506.282i	0.469185	+	0.812652i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	10.3148	−	3.11002i	0.0164510	−	0.00496016i
$628$		0			0
$629$			148.024i			0.235333i
$630$		0			0
$631$	1008.08			1.59758			0.798792	−	0.601607i	$-0.205473\pi$
$631$	1008.08			1.59758			0.798792	+	0.601607i	$0.205473\pi$
$632$		0			0
$633$	795.046	−	846.007i	1.25600	−	1.33650i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	328.459	−	189.636i	0.515634	−	0.297701i
$638$		0			0
$639$	−64.2473	+	129.184i	−0.100544	+	0.202165i
$640$		0			0
$641$	−488.095	+	281.802i	−0.761458	+	0.439628i	−0.829819	−	0.558032i	$-0.811556\pi$
$641$	−488.095	+	281.802i	−0.761458	+	0.439628i	0.0683607	+	0.997661i	$0.478223\pi$
$642$		0			0
$643$	499.697	+	288.500i	0.777133	+	0.448678i	0.835413	−	0.549622i	$-0.185228\pi$
$643$	499.697	+	288.500i	0.777133	+	0.448678i	−0.0582801	+	0.998300i	$0.518562\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1024.52			−1.58349			−0.791744	−	0.610853i	$-0.790827\pi$
$647$	−1024.52			−1.58349			−0.791744	+	0.610853i	$0.790827\pi$
$648$		0			0
$649$	33.7011			0.0519277
$650$		0			0
$651$	−183.600	+	781.475i	−0.282028	+	1.20042i
$652$		0			0
$653$	−199.697	+	345.885i	−0.305814	+	0.529686i	−0.977442	−	0.211203i	$-0.932262\pi$
$653$	−199.697	+	345.885i	−0.305814	+	0.529686i	0.671628	+	0.740888i	$0.265595\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	17.4357	−	35.0584i	0.0265384	−	0.0533614i
$658$		0			0
$659$	646.308	−	373.146i	0.980741	−	0.566231i	0.0782470	−	0.996934i	$-0.475068\pi$
$659$	646.308	−	373.146i	0.980741	−	0.566231i	0.902494	+	0.430703i	$0.141734\pi$
$660$		0			0
$661$	−475.624	+	823.804i	−0.719552	+	1.24630i	0.241626	+	0.970369i	$0.422319\pi$
$661$	−475.624	+	823.804i	−0.719552	+	1.24630i	−0.961178	+	0.275931i	$0.911014\pi$
$662$		0			0
$663$	194.799	+	183.065i	0.293815	+	0.276117i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			1251.27i			1.87596i
$668$		0			0
$669$	−295.135	+	88.9864i	−0.441158	+	0.133014i
$670$		0			0
$671$	2.05009	+	1.18362i	0.00305527	+	0.00176396i
$672$		0			0
$673$	−298.113	+	172.115i	−0.442961	+	0.255743i	−0.704853	−	0.709354i	$-0.748987\pi$
$673$	−298.113	+	172.115i	−0.442961	+	0.255743i	0.261892	+	0.965097i	$0.415654\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−492.832	−	853.610i	−0.727965	−	1.26087i	−0.957742	−	0.287628i	$-0.907133\pi$
$677$	−492.832	−	853.610i	−0.727965	−	1.26087i	0.229778	−	0.973243i	$-0.426200\pi$
$678$		0			0
$679$	525.284	−	909.818i	0.773614	−	1.33994i
$680$		0			0
$681$	−293.552	−	973.600i	−0.431060	−	1.42966i
$682$		0			0
$683$	−166.658			−0.244009			−0.122004	−	0.992530i	$-0.538932\pi$
$683$	−166.658			−0.244009			−0.122004	+	0.992530i	$0.538932\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	609.665	−	648.743i	0.887431	−	0.944313i
$688$		0			0
$689$	−583.272	−	336.752i	−0.846548	−	0.488755i
$690$		0			0
$691$	449.077	+	777.825i	0.649895	+	1.12565i	0.983148	+	0.182813i	$0.0585204\pi$
$691$	449.077	+	777.825i	0.649895	+	1.12565i	−0.333253	+	0.942838i	$0.608146\pi$
$692$		0			0
$693$	30.2518	−	20.0668i	0.0436534	−	0.0289564i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	312.341	+	180.330i	0.448122	+	0.258723i
$698$		0			0
$699$	−1012.06	−	237.773i	−1.44786	−	0.340162i
$700$		0			0
$701$			730.549i			1.04215i	0.853510	+	0.521076i	$0.174469\pi$
$701$			730.549i			1.04215i	−0.853510	+	0.521076i	$0.825531\pi$
$702$		0			0
$703$		−	149.897i		−	0.213224i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−602.991	+	1044.41i	−0.852887	+	1.47724i
$708$		0			0
$709$	−114.961	−	199.118i	−0.162145	−	0.280843i	0.773493	−	0.633805i	$-0.218508\pi$
$709$	−114.961	−	199.118i	−0.162145	−	0.280843i	−0.935638	+	0.352962i	$0.885174\pi$
$710$		0			0
$711$	0.884663	+	14.2305i	0.00124425	+	0.0200148i
$712$		0			0
$713$	−346.394	−	599.971i	−0.485825	−	0.841474i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−353.472	−	332.181i	−0.492988	−	0.463292i
$718$		0			0
$719$			907.095i			1.26161i	0.775943	+	0.630803i	$0.217275\pi$
$719$			907.095i			1.26161i	−0.775943	+	0.630803i	$0.782725\pi$
$720$		0			0
$721$	1142.80			1.58502
$722$		0			0
$723$	−281.232	−	932.742i	−0.388980	−	1.29010i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−186.838	+	107.871i	−0.256999	+	0.148378i	−0.622965	−	0.782250i	$-0.714072\pi$
$727$	−186.838	+	107.871i	−0.256999	+	0.148378i	0.365966	+	0.930628i	$0.380739\pi$
$728$		0			0
$729$	135.000	+	716.391i	0.185185	+	0.982704i
$730$		0			0
$731$	−159.656	+	92.1776i	−0.218408	+	0.126098i
$732$		0			0
$733$	−544.963	−	314.634i	−0.743469	−	0.429242i	0.0798604	−	0.996806i	$-0.474553\pi$
$733$	−544.963	−	314.634i	−0.743469	−	0.429242i	−0.823329	+	0.567564i	$0.807886\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	48.5351			0.0658549
$738$		0			0
$739$	−547.649			−0.741068			−0.370534	−	0.928819i	$-0.620825\pi$
$739$	−547.649			−0.741068			−0.370534	+	0.928819i	$0.620825\pi$
$740$		0			0
$741$	−197.264	−	185.381i	−0.266213	−	0.250177i
$742$		0			0
$743$	267.072	−	462.583i	0.359451	−	0.622588i	−0.628418	−	0.777876i	$-0.716297\pi$
$743$	267.072	−	462.583i	0.359451	−	0.622588i	0.987869	+	0.155288i	$0.0496306\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.72306	−	75.9742i	−0.00632271	−	0.101706i
$748$		0			0
$749$	−288.481	+	166.555i	−0.385155	+	0.222369i
$750$		0			0
$751$	225.545	−	390.655i	0.300326	−	0.520180i	−0.675884	−	0.737008i	$-0.736238\pi$
$751$	225.545	−	390.655i	0.300326	−	0.520180i	0.976210	+	0.216828i	$0.0695712\pi$
$752$		0			0
$753$	−263.486	+	1121.50i	−0.349915	+	1.48937i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			352.391i			0.465511i	0.972535	+	0.232755i	$0.0747741\pi$
$757$			352.391i			0.465511i	−0.972535	+	0.232755i	$0.925226\pi$
$758$		0			0
$759$	−7.16543	+	30.4988i	−0.00944061	+	0.0401829i
$760$		0			0
$761$	−929.923	−	536.891i	−1.22197	−	0.705507i	−0.256636	−	0.966508i	$-0.582614\pi$
$761$	−929.923	−	536.891i	−1.22197	−	0.705507i	−0.965339	+	0.261001i	$0.915947\pi$
$762$		0			0
$763$	1063.52	−	614.024i	1.39387	−	0.804750i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−423.399	−	733.349i	−0.552020	−	0.956126i
$768$		0			0
$769$	177.988	−	308.284i	0.231454	−	0.400889i	−0.726782	−	0.686868i	$-0.758985\pi$
$769$	177.988	−	308.284i	0.231454	−	0.400889i	0.958236	+	0.285978i	$0.0923185\pi$
$770$		0			0
$771$	26.5721	−	28.2753i	0.0344644	−	0.0366735i
$772$		0			0
$773$	−370.790			−0.479677			−0.239838	−	0.970813i	$-0.577094\pi$
$773$	−370.790			−0.479677			−0.239838	+	0.970813i	$0.577094\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−145.808	−	483.589i	−0.187655	−	0.622380i
$778$		0			0
$779$	−316.292	−	182.611i	−0.406023	−	0.234418i
$780$		0			0
$781$	−3.54628	−	6.14233i	−0.00454069	−	0.00786470i
$782$		0			0
$783$	−1410.99	−	240.273i	−1.80203	−	0.306862i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	998.581	+	576.531i	1.26885	+	0.732568i	0.974769	−	0.223214i	$-0.0716549\pi$
$787$	998.581	+	576.531i	1.26885	+	0.732568i	0.294076	+	0.955782i	$0.404988\pi$
$788$		0			0
$789$	42.8437	+	142.096i	0.0543013	+	0.180097i
$790$		0			0
$791$			1734.12i			2.19231i
$792$		0			0
$793$		−	59.4810i		−	0.0750076i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−439.873	+	761.882i	−0.551910	+	0.955937i	0.446226	+	0.894920i	$0.352768\pi$
$797$	−439.873	+	761.882i	−0.551910	+	0.955937i	−0.998137	+	0.0610167i	$0.980566\pi$
$798$		0			0
$799$	−33.8968	−	58.7110i	−0.0424240	−	0.0734806i
$800$		0			0
$801$	256.989	−	516.735i	0.320836	−	0.645112i
$802$		0			0
$803$	0.962404	+	1.66693i	0.00119851	+	0.00207588i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−14.7132	+	62.6252i	−0.0182320	+	0.0776025i
$808$		0			0
$809$		−	884.508i		−	1.09334i	−0.837350	−	0.546668i	$-0.815896\pi$
$809$		−	884.508i		−	1.09334i	0.837350	−	0.546668i	$-0.184104\pi$
$810$		0			0
$811$	−961.464			−1.18553			−0.592765	−	0.805376i	$-0.701964\pi$
$811$	−961.464			−1.18553			−0.592765	+	0.805376i	$0.701964\pi$
$812$		0			0
$813$	954.727	+	224.304i	1.17433	+	0.275897i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	161.676	−	93.3437i	0.197890	−	0.114252i
$818$		0			0
$819$	−816.725	−	406.185i	−0.997223	−	0.495952i
$820$		0			0
$821$	778.064	−	449.215i	0.947702	−	0.547156i	0.0553360	−	0.998468i	$-0.482377\pi$
$821$	778.064	−	449.215i	0.947702	−	0.547156i	0.892366	+	0.451312i	$0.149044\pi$
$822$		0			0
$823$	−187.219	−	108.091i	−0.227484	−	0.131338i	0.381927	−	0.924193i	$-0.375261\pi$
$823$	−187.219	−	108.091i	−0.227484	−	0.131338i	−0.609411	+	0.792855i	$0.708594\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	113.883			0.137706			0.0688528	−	0.997627i	$-0.478066\pi$
$827$	113.883			0.137706			0.0688528	+	0.997627i	$0.478066\pi$
$828$		0			0
$829$	−101.326			−0.122227			−0.0611135	−	0.998131i	$-0.519465\pi$
$829$	−101.326			−0.122227			−0.0611135	+	0.998131i	$0.519465\pi$
$830$		0			0
$831$	−1371.38	+	413.487i	−1.65028	+	0.497578i
$832$		0			0
$833$	−136.731	+	236.825i	−0.164143	+	0.284303i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	743.071	−	275.401i	0.887779	−	0.329033i
$838$		0			0
$839$	−60.4689	+	34.9117i	−0.0720726	+	0.0416111i	−0.535603	−	0.844470i	$-0.679916\pi$
$839$	−60.4689	+	34.9117i	−0.0720726	+	0.0416111i	0.463531	+	0.886081i	$0.346582\pi$
$840$		0			0
$841$	984.588	−	1705.36i	1.17073	−	2.02777i
$842$		0			0
$843$	341.824	−	103.064i	0.405485	−	0.122258i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	1101.35i		−	1.30030i
$848$		0			0
$849$	−855.547	−	804.012i	−1.00771	−	0.947011i
$850$		0			0
$851$	377.502	+	217.951i	0.443598	+	0.256112i
$852$		0			0
$853$	−993.028	+	573.325i	−1.16416	+	0.672127i	−0.952297	−	0.305172i	$-0.901286\pi$
$853$	−993.028	+	573.325i	−1.16416	+	0.672127i	−0.211862	+	0.977300i	$0.567953\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−125.788	−	217.871i	−0.146777	−	0.254225i	0.783258	−	0.621697i	$-0.213557\pi$
$857$	−125.788	−	217.871i	−0.146777	−	0.254225i	−0.930035	+	0.367472i	$0.880223\pi$
$858$		0			0
$859$	−244.266	+	423.082i	−0.284361	+	0.492528i	−0.972454	−	0.233095i	$-0.925115\pi$
$859$	−244.266	+	423.082i	−0.284361	+	0.492528i	0.688093	+	0.725623i	$0.258448\pi$
$860$		0			0
$861$	−1198.03	−	281.467i	−1.39145	−	0.326908i
$862$		0			0
$863$	596.889			0.691644			0.345822	−	0.938300i	$-0.387600\pi$
$863$	596.889			0.691644			0.345822	+	0.938300i	$0.387600\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	656.386	+	154.212i	0.757077	+	0.177868i
$868$		0			0
$869$	−0.607003	−	0.350454i	−0.000698508	−	0.000403284i
$870$		0			0
$871$	−609.765	−	1056.14i	−0.700074	−	1.21256i
$872$		0			0
$873$	−1035.10	+	64.3490i	−1.18569	+	0.0737102i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	620.434	+	358.208i	0.707451	+	0.408447i	0.810116	−	0.586269i	$-0.199404\pi$
$877$	620.434	+	358.208i	0.707451	+	0.408447i	−0.102666	+	0.994716i	$0.532737\pi$
$878$		0			0
$879$	147.297	−	156.739i	0.167574	−	0.178315i
$880$		0			0
$881$			1200.86i			1.36306i	0.731790	+	0.681531i	$0.238685\pi$
$881$			1200.86i			1.36306i	−0.731790	+	0.681531i	$0.761315\pi$
$882$		0			0
$883$			22.8938i			0.0259273i	0.999916	+	0.0129636i	$0.00412657\pi$
$883$			22.8938i			0.0259273i	−0.999916	+	0.0129636i	$0.995873\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	301.294	−	521.857i	0.339678	−	0.588340i	−0.644694	−	0.764441i	$-0.723015\pi$
$887$	301.294	−	521.857i	0.339678	−	0.588340i	0.984372	+	0.176101i	$0.0563485\pi$
$888$		0			0
$889$	839.220	+	1453.57i	0.944005	+	1.63506i
$890$		0			0
$891$	−33.0160	−	13.9366i	−0.0370549	−	0.0156415i
$892$		0			0
$893$	34.3256	+	59.4537i	0.0384385	+	0.0665775i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	753.689	−	227.246i	0.840233	−	0.253340i
$898$		0			0
$899$			1555.90i			1.73071i
$900$		0			0
$901$	485.609			0.538966
$902$		0			0
$903$	430.794	−	458.406i	0.477069	−	0.507648i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−366.281	+	211.473i	−0.403838	+	0.233156i	−0.688139	−	0.725579i	$-0.741572\pi$
$907$	−366.281	+	211.473i	−0.403838	+	0.233156i	0.284300	+	0.958735i	$0.408239\pi$
$908$		0			0
$909$	1188.23	−	73.8684i	1.30719	−	0.0812634i
$910$		0			0
$911$	125.376	−	72.3861i	0.137625	−	0.0794578i	−0.429607	−	0.903016i	$-0.641348\pi$
$911$	125.376	−	72.3861i	0.137625	−	0.0794578i	0.567232	+	0.823558i	$0.308014\pi$
$912$		0			0
$913$	3.24069	+	1.87101i	0.00354949	+	0.00204930i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1149.51			1.25356
$918$		0			0
$919$	869.093			0.945694			0.472847	−	0.881145i	$-0.343226\pi$
$919$	869.093			0.945694			0.472847	+	0.881145i	$0.343226\pi$
$920$		0			0
$921$	118.257	−	503.347i	0.128400	−	0.546522i
$922$		0			0
$923$	−89.1064	+	154.337i	−0.0965400	+	0.167212i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−623.611	−	940.129i	−0.672720	−	1.01416i
$928$		0			0
$929$	−82.2838	+	47.5066i	−0.0885724	+	0.0511373i	−0.543632	−	0.839324i	$-0.682951\pi$
$929$	−82.2838	+	47.5066i	−0.0885724	+	0.0511373i	0.455060	+	0.890461i	$0.349618\pi$
$930$		0			0
$931$	138.461	−	239.821i	0.148722	−	0.257595i
$932$		0			0
$933$	1323.37	+	1243.66i	1.41841	+	1.33297i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			1555.55i			1.66014i	0.557657	+	0.830071i	$0.311700\pi$
$937$			1555.55i			1.66014i	−0.557657	+	0.830071i	$0.688300\pi$
$938$		0			0
$939$	−940.578	+	283.595i	−1.00168	+	0.302018i
$940$		0			0
$941$	335.246	+	193.554i	0.356265	+	0.205690i	0.667441	−	0.744662i	$-0.267389\pi$
$941$	335.246	+	193.554i	0.356265	+	0.205690i	−0.311176	+	0.950352i	$0.600723\pi$
$942$		0			0
$943$	919.782	−	531.036i	0.975379	−	0.563135i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	484.894	+	839.861i	0.512032	+	0.886865i	0.999903	+	0.0139492i	$0.00444033\pi$
$947$	484.894	+	839.861i	0.512032	+	0.886865i	−0.487871	+	0.872916i	$0.662226\pi$
$948$		0			0
$949$	24.1821	−	41.8846i	0.0254817	−	0.0441355i
$950$		0			0
$951$	−59.7921	−	198.308i	−0.0628729	−	0.208526i
$952$		0			0
$953$	1294.65			1.35850			0.679248	−	0.733909i	$-0.262306\pi$
$953$	1294.65			1.35850			0.679248	+	0.733909i	$0.262306\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	48.1846	−	51.2731i	0.0503497	−	0.0535769i
$958$		0			0
$959$	981.126	+	566.453i	1.02307	+	0.590671i
$960$		0			0
$961$	49.7731	+	86.2096i	0.0517931	+	0.0897082i
$962$		0			0
$963$	294.437	+	146.433i	0.305750	+	0.152059i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	713.668	+	412.036i	0.738023	+	0.426098i	0.821350	−	0.570425i	$-0.193221\pi$
$967$	713.668	+	412.036i	0.738023	+	0.426098i	−0.0833272	+	0.996522i	$0.526555\pi$
$968$		0			0
$969$	190.007	+	44.6404i	0.196085	+	0.0460685i
$970$		0			0
$971$			1518.35i			1.56370i	0.623469	+	0.781848i	$0.285723\pi$
$971$			1518.35i			1.56370i	−0.623469	+	0.781848i	$0.714277\pi$
$972$		0			0
$973$			244.024i			0.250796i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−185.616	+	321.497i	−0.189986	+	0.329065i	−0.945245	−	0.326361i	$-0.894178\pi$
$977$	−185.616	+	321.497i	−0.189986	+	0.329065i	0.755259	+	0.655426i	$0.227511\pi$
$978$		0			0
$979$	14.1851	+	24.5693i	0.0144894	+	0.0250963i
$980$		0			0
$981$	−1085.48	−	539.844i	−1.10650	−	0.550300i
$982$		0			0
$983$	−466.522	−	808.039i	−0.474590	−	0.822014i	0.524987	−	0.851110i	$-0.324070\pi$
$983$	−466.522	−	808.039i	−0.474590	−	0.822014i	−0.999577	+	0.0290967i	$0.990737\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	168.571	+	158.417i	0.170792	+	0.160504i
$988$		0			0
$989$			542.890i			0.548928i
$990$		0			0
$991$	1615.53			1.63020			0.815099	−	0.579321i	$-0.196682\pi$
$991$	1615.53			1.63020			0.815099	+	0.579321i	$0.196682\pi$
$992$		0			0
$993$	441.492	+	1464.26i	0.444604	+	1.47458i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−899.586	+	519.376i	−0.902293	+	0.520939i	−0.877943	−	0.478764i	$-0.841085\pi$
$997$	−899.586	+	519.376i	−0.902293	+	0.520939i	−0.0243496	+	0.999704i	$0.507751\pi$
$998$		0			0
$999$	−318.261	+	383.837i	−0.318580	+	0.384221i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.a.149.1		8
3.2	odd	2		2700.3.u.b.449.1		8
5.2	odd	4		36.3.g.a.5.1	✓	4
5.3	odd	4		900.3.p.a.401.2		4
5.4	even	2	inner	900.3.u.a.149.4		8
9.2	odd	6	inner	900.3.u.a.749.4		8
9.7	even	3		2700.3.u.b.2249.4		8
15.2	even	4		108.3.g.a.17.1		4
15.8	even	4		2700.3.p.b.2501.2		4
15.14	odd	2		2700.3.u.b.449.4		8
20.7	even	4		144.3.q.b.113.2		4
40.27	even	4		576.3.q.g.257.1		4
40.37	odd	4		576.3.q.d.257.2		4
45.2	even	12		36.3.g.a.29.1	yes	4
45.7	odd	12		108.3.g.a.89.1		4
45.22	odd	12		324.3.c.b.161.1		4
45.29	odd	6	inner	900.3.u.a.749.1		8
45.32	even	12		324.3.c.b.161.4		4
45.34	even	6		2700.3.u.b.2249.1		8
45.38	even	12		900.3.p.a.101.2		4
45.43	odd	12		2700.3.p.b.1601.2		4
60.47	odd	4		432.3.q.b.17.1		4
120.77	even	4		1728.3.q.g.449.2		4
120.107	odd	4		1728.3.q.h.449.2		4
180.7	even	12		432.3.q.b.305.1		4
180.47	odd	12		144.3.q.b.65.2		4
180.67	even	12		1296.3.e.e.161.1		4
180.167	odd	12		1296.3.e.e.161.4		4
360.187	even	12		1728.3.q.h.1601.2		4
360.227	odd	12		576.3.q.g.65.1		4
360.277	odd	12		1728.3.q.g.1601.2		4
360.317	even	12		576.3.q.d.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.g.a.5.1	✓	4	5.2	odd	4
36.3.g.a.29.1	yes	4	45.2	even	12
108.3.g.a.17.1		4	15.2	even	4
108.3.g.a.89.1		4	45.7	odd	12
144.3.q.b.65.2		4	180.47	odd	12
144.3.q.b.113.2		4	20.7	even	4
324.3.c.b.161.1		4	45.22	odd	12
324.3.c.b.161.4		4	45.32	even	12
432.3.q.b.17.1		4	60.47	odd	4
432.3.q.b.305.1		4	180.7	even	12
576.3.q.d.65.2		4	360.317	even	12
576.3.q.d.257.2		4	40.37	odd	4
576.3.q.g.65.1		4	360.227	odd	12
576.3.q.g.257.1		4	40.27	even	4
900.3.p.a.101.2		4	45.38	even	12
900.3.p.a.401.2		4	5.3	odd	4
900.3.u.a.149.1		8	1.1	even	1	trivial
900.3.u.a.149.4		8	5.4	even	2	inner
900.3.u.a.749.1		8	45.29	odd	6	inner
900.3.u.a.749.4		8	9.2	odd	6	inner
1296.3.e.e.161.1		4	180.67	even	12
1296.3.e.e.161.4		4	180.167	odd	12
1728.3.q.g.449.2		4	120.77	even	4
1728.3.q.g.1601.2		4	360.277	odd	12
1728.3.q.h.449.2		4	120.107	odd	4
1728.3.q.h.1601.2		4	360.187	even	12
2700.3.p.b.1601.2		4	45.43	odd	12
2700.3.p.b.2501.2		4	15.8	even	4
2700.3.u.b.449.1		8	3.2	odd	2
2700.3.u.b.449.4		8	15.14	odd	2
2700.3.u.b.2249.1		8	45.34	even	6
2700.3.u.b.2249.4		8	9.7	even	3

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.92048 - 0.686141i) q^{3} +(-7.89542 + 4.55842i) q^{7} +(8.05842 + 4.00772i) q^{9} +O(q^{10})\)	\(q+(-2.92048 - 0.686141i) q^{3} +(-7.89542 + 4.55842i) q^{7} +(8.05842 + 4.00772i) q^{9} +(-0.383156 + 0.221215i) q^{11} +(9.62747 + 5.55842i) q^{13} -8.01544 q^{17} +8.11684 q^{19} +(26.1861 - 7.89542i) q^{21} +(-11.8020 + 20.4416i) q^{23} +(-20.7846 - 17.2337i) q^{27} +(45.9090 - 26.5055i) q^{29} +(-14.6753 + 25.4183i) q^{31} +(1.27078 - 0.383156i) q^{33} -18.4674i q^{37} +(-24.3030 - 22.8391i) q^{39} +(-38.9674 - 22.4978i) q^{41} +(19.9186 - 11.5000i) q^{43} +(4.22894 + 7.32473i) q^{47} +(17.0584 - 29.5461i) q^{49} +(23.4090 + 5.49972i) q^{51} -60.5841 q^{53} +(-23.7051 - 5.56930i) q^{57} +(-65.9674 - 38.0863i) q^{59} +(-2.67527 - 4.63370i) q^{61} +(-81.8935 + 5.09105i) q^{63} +(-95.0039 - 54.8505i) q^{67} +(48.4932 - 51.6014i) q^{69} +16.0309i q^{71} -4.35053i q^{73} +(2.01678 - 3.49317i) q^{77} +(0.792110 + 1.37197i) q^{79} +(48.8763 + 64.5918i) q^{81} +(-4.22894 - 7.32473i) q^{83} +(-152.263 + 45.9090i) q^{87} -64.1236i q^{89} -101.351 q^{91} +(60.2994 - 64.1644i) q^{93} +(-99.7953 + 57.6168i) q^{97} +(-3.97420 + 0.247063i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 30 q^{9}+O(q^{10}) \) 8 * q + 30 * q^9	\( 8 q + 30 q^{9} - 72 q^{11} - 4 q^{19} + 198 q^{21} + 126 q^{29} - 14 q^{31} - 114 q^{39} - 36 q^{41} + 102 q^{49} - 54 q^{51} - 252 q^{59} + 82 q^{61} - 198 q^{69} - 166 q^{79} - 126 q^{81} - 604 q^{91} - 342 q^{99}+O(q^{100}) \) 8 * q + 30 * q^9 - 72 * q^11 - 4 * q^19 + 198 * q^21 + 126 * q^29 - 14 * q^31 - 114 * q^39 - 36 * q^41 + 102 * q^49 - 54 * q^51 - 252 * q^59 + 82 * q^61 - 198 * q^69 - 166 * q^79 - 126 * q^81 - 604 * q^91 - 342 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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