LMFDB - Embedded newform 900.3.u.c.749.4

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.4
Character	$\chi$	$=$	900.749
Dual form			900.3.u.c.149.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.920635 + 2.85525i) q^{3} +(1.02985 + 0.594587i) q^{7} +(-7.30486 - 5.25728i) q^{9} +O(q^{10})$	\(q+(-0.920635 + 2.85525i) q^{3} +(1.02985 + 0.594587i) q^{7} +(-7.30486 - 5.25728i) q^{9} +(3.63473 + 2.09851i) q^{11} +(12.3948 - 7.15614i) q^{13} -18.7074 q^{17} -33.8986 q^{19} +(-2.64581 + 2.39309i) q^{21} +(6.74989 + 11.6912i) q^{23} +(21.7359 - 16.0171i) q^{27} +(-30.6315 - 17.6851i) q^{29} +(4.97816 + 8.62242i) q^{31} +(-9.33802 + 8.44607i) q^{33} -19.3047i q^{37} +(9.02146 + 41.9784i) q^{39} +(-55.9648 + 32.3113i) q^{41} +(-35.9872 - 20.7772i) q^{43} +(33.6057 - 58.2068i) q^{47} +(-23.7929 - 41.2106i) q^{49} +(17.2227 - 53.4143i) q^{51} +30.0712 q^{53} +(31.2083 - 96.7889i) q^{57} +(-3.66554 + 2.11630i) q^{59} +(43.8210 - 75.9002i) q^{61} +(-4.39704 - 9.75761i) q^{63} +(-31.0106 + 17.9040i) q^{67} +(-39.5953 + 8.50932i) q^{69} +24.5173i q^{71} -11.9305i q^{73} +(2.49549 + 4.32232i) q^{77} +(-19.0858 + 33.0575i) q^{79} +(25.7220 + 76.8074i) q^{81} +(12.0489 - 20.8692i) q^{83} +(78.6957 - 71.1789i) q^{87} -44.4494i q^{89} +17.0198 q^{91} +(-29.2022 + 6.27576i) q^{93} +(-55.3688 - 31.9672i) q^{97} +(-15.5187 - 34.4381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 52 q^{9}+O(q^{10}) $ 24 * q - 52 * q^9	$ 24 q - 52 q^{9} + 96 q^{11} - 144 q^{19} - 256 q^{21} - 300 q^{29} - 24 q^{31} - 80 q^{39} + 180 q^{41} - 96 q^{49} - 288 q^{51} - 96 q^{59} - 156 q^{61} + 300 q^{69} - 240 q^{79} + 868 q^{81} + 240 q^{91} + 240 q^{99}+O(q^{100}) $ 24 * q - 52 * q^9 + 96 * q^11 - 144 * q^19 - 256 * q^21 - 300 * q^29 - 24 * q^31 - 80 * q^39 + 180 * q^41 - 96 * q^49 - 288 * q^51 - 96 * q^59 - 156 * q^61 + 300 * q^69 - 240 * q^79 + 868 * q^81 + 240 * q^91 + 240 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.920635	+	2.85525i	−0.306878	+	0.951749i
$3$	−0.920635	+	2.85525i	−0.306878	+	0.951749i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.02985	+	0.594587i	0.147122	+	0.0849410i	0.571754	−	0.820425i	$-0.306263\pi$
$7$	1.02985	+	0.594587i	0.147122	+	0.0849410i	−0.424632	+	0.905366i	$0.639596\pi$
$8$		0			0
$9$	−7.30486	−	5.25728i	−0.811651	−	0.584142i
$10$		0			0
$11$	3.63473	+	2.09851i	0.330430	+	0.190774i	0.656032	−	0.754733i	$-0.272234\pi$
$11$	3.63473	+	2.09851i	0.330430	+	0.190774i	−0.325602	+	0.945507i	$0.605567\pi$
$12$		0			0
$13$	12.3948	−	7.15614i	0.953447	−	0.550473i	0.0592967	−	0.998240i	$-0.481114\pi$
$13$	12.3948	−	7.15614i	0.953447	−	0.550473i	0.894150	+	0.447768i	$0.147781\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−18.7074			−1.10044			−0.550218	−	0.835021i	$-0.685455\pi$
$17$	−18.7074			−1.10044			−0.550218	+	0.835021i	$0.685455\pi$
$18$		0			0
$19$	−33.8986			−1.78414			−0.892069	−	0.451899i	$-0.850747\pi$
$19$	−33.8986			−1.78414			−0.892069	+	0.451899i	$0.850747\pi$
$20$		0			0
$21$	−2.64581	+	2.39309i	−0.125991	+	0.113957i
$22$		0			0
$23$	6.74989	+	11.6912i	0.293474	+	0.508311i	0.974629	−	0.223828i	$-0.0718554\pi$
$23$	6.74989	+	11.6912i	0.293474	+	0.508311i	−0.681155	+	0.732139i	$0.738522\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	21.7359	−	16.0171i	0.805035	−	0.593227i
$28$		0			0
$29$	−30.6315	−	17.6851i	−1.05626	−	0.609831i	−0.131863	−	0.991268i	$-0.542096\pi$
$29$	−30.6315	−	17.6851i	−1.05626	−	0.609831i	−0.924395	+	0.381437i	$0.875429\pi$
$30$		0			0
$31$	4.97816	+	8.62242i	0.160586	+	0.278143i	0.935079	−	0.354440i	$-0.115328\pi$
$31$	4.97816	+	8.62242i	0.160586	+	0.278143i	−0.774493	+	0.632582i	$0.781995\pi$
$32$		0			0
$33$	−9.33802	+	8.44607i	−0.282970	+	0.255942i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	19.3047i		−	0.521750i	−0.965373	−	0.260875i	$-0.915989\pi$
$37$		−	19.3047i		−	0.521750i	0.965373	−	0.260875i	$-0.0840110\pi$
$38$		0			0
$39$	9.02146	+	41.9784i	0.231319	+	1.07637i
$40$		0			0
$41$	−55.9648	+	32.3113i	−1.36499	+	0.788080i	−0.990284	−	0.139062i	$-0.955591\pi$
$41$	−55.9648	+	32.3113i	−1.36499	+	0.788080i	−0.374711	+	0.927142i	$0.622258\pi$
$42$		0			0
$43$	−35.9872	−	20.7772i	−0.836911	−	0.483191i	0.0193018	−	0.999814i	$-0.493856\pi$
$43$	−35.9872	−	20.7772i	−0.836911	−	0.483191i	−0.856213	+	0.516623i	$0.827189\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	33.6057	−	58.2068i	0.715015	−	1.23844i	−0.247939	−	0.968776i	$-0.579753\pi$
$47$	33.6057	−	58.2068i	0.715015	−	1.23844i	0.962954	−	0.269667i	$-0.0869135\pi$
$48$		0			0
$49$	−23.7929	−	41.2106i	−0.485570	−	0.841032i
$50$		0			0
$51$	17.2227	−	53.4143i	0.337700	−	1.04734i
$52$		0			0
$53$	30.0712			0.567382			0.283691	−	0.958916i	$-0.408441\pi$
$53$	30.0712			0.567382			0.283691	+	0.958916i	$0.408441\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	31.2083	−	96.7889i	0.547513	−	1.69805i
$58$		0			0
$59$	−3.66554	+	2.11630i	−0.0621278	+	0.0358695i	−0.530742	−	0.847533i	$-0.678087\pi$
$59$	−3.66554	+	2.11630i	−0.0621278	+	0.0358695i	0.468614	+	0.883403i	$0.344753\pi$
$60$		0			0
$61$	43.8210	−	75.9002i	0.718377	−	1.24427i	−0.243266	−	0.969960i	$-0.578219\pi$
$61$	43.8210	−	75.9002i	0.718377	−	1.24427i	0.961643	−	0.274305i	$-0.0884479\pi$
$62$		0			0
$63$	−4.39704	−	9.75761i	−0.0697942	−	0.154883i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−31.0106	+	17.9040i	−0.462845	+	0.267224i	−0.713240	−	0.700920i	$-0.752773\pi$
$67$	−31.0106	+	17.9040i	−0.462845	+	0.267224i	0.250395	+	0.968144i	$0.419440\pi$
$68$		0			0
$69$	−39.5953	+	8.50932i	−0.573845	+	0.123323i
$70$		0			0
$71$			24.5173i			0.345314i	0.984982	+	0.172657i	$0.0552352\pi$
$71$			24.5173i			0.345314i	−0.984982	+	0.172657i	$0.944765\pi$
$72$		0			0
$73$		−	11.9305i		−	0.163432i	−0.996656	−	0.0817159i	$-0.973960\pi$
$73$		−	11.9305i		−	0.163432i	0.996656	−	0.0817159i	$-0.0260400\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.49549	+	4.32232i	0.0324090	+	0.0561340i
$78$		0			0
$79$	−19.0858	+	33.0575i	−0.241592	+	0.418449i	−0.961168	−	0.275964i	$-0.911003\pi$
$79$	−19.0858	+	33.0575i	−0.241592	+	0.418449i	0.719576	+	0.694414i	$0.244336\pi$
$80$		0			0
$81$	25.7220	+	76.8074i	0.317556	+	0.948240i
$82$		0			0
$83$	12.0489	−	20.8692i	0.145167	−	0.251436i	−0.784268	−	0.620422i	$-0.786961\pi$
$83$	12.0489	−	20.8692i	0.145167	−	0.251436i	0.929435	+	0.368985i	$0.120295\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	78.6957	−	71.1789i	0.904548	−	0.818148i
$88$		0			0
$89$		−	44.4494i		−	0.499431i	−0.968319	−	0.249716i	$-0.919663\pi$
$89$		−	44.4494i		−	0.499431i	0.968319	−	0.249716i	$-0.0803371\pi$
$90$		0			0
$91$	17.0198			0.187031
$92$		0			0
$93$	−29.2022	+	6.27576i	−0.314002	+	0.0674813i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−55.3688	−	31.9672i	−0.570812	−	0.329558i	0.186662	−	0.982424i	$-0.440233\pi$
$97$	−55.3688	−	31.9672i	−0.570812	−	0.329558i	−0.757474	+	0.652866i	$0.773567\pi$
$98$		0			0
$99$	−15.5187	−	34.4381i	−0.156755	−	0.347860i
$100$		0			0
$101$	10.3591	+	5.98084i	0.102566	+	0.0592163i	0.550405	−	0.834898i	$-0.314473\pi$
$101$	10.3591	+	5.98084i	0.102566	+	0.0592163i	−0.447840	+	0.894114i	$0.647807\pi$
$102$		0			0
$103$	142.001	−	81.9841i	1.37865	−	0.795963i	0.386651	−	0.922226i	$-0.373632\pi$
$103$	142.001	−	81.9841i	1.37865	−	0.795963i	0.991997	+	0.126264i	$0.0402985\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	102.401			0.957019			0.478509	−	0.878082i	$-0.341177\pi$
$107$	102.401			0.957019			0.478509	+	0.878082i	$0.341177\pi$
$108$		0			0
$109$	56.4485			0.517876			0.258938	−	0.965894i	$-0.416627\pi$
$109$	56.4485			0.517876			0.258938	+	0.965894i	$0.416627\pi$
$110$		0			0
$111$	55.1198	+	17.7726i	0.496575	+	0.160114i
$112$		0			0
$113$	−86.2022	−	149.307i	−0.762852	−	1.32130i	−0.941375	−	0.337362i	$-0.890465\pi$
$113$	−86.2022	−	149.307i	−0.762852	−	1.32130i	0.178523	−	0.983936i	$-0.442868\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−128.164	−	12.8883i	−1.09542	−	0.110157i
$118$		0			0
$119$	−19.2659	−	11.1232i	−0.161899	−	0.0934722i
$120$		0			0
$121$	−51.6925	−	89.5341i	−0.427211	−	0.739951i
$122$		0			0
$123$	−40.7335	−	189.540i	−0.331167	−	1.54098i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	195.853i		−	1.54215i	−0.636746	−	0.771073i	$-0.719720\pi$
$127$		−	195.853i		−	1.54215i	0.636746	−	0.771073i	$-0.280280\pi$
$128$		0			0
$129$	92.4551	−	83.6240i	0.716706	−	0.648248i
$130$		0			0
$131$	−98.5249	+	56.8834i	−0.752099	+	0.434224i	−0.826452	−	0.563008i	$-0.809644\pi$
$131$	−98.5249	+	56.8834i	−0.752099	+	0.434224i	0.0743530	+	0.997232i	$0.476311\pi$
$132$		0			0
$133$	−34.9107	−	20.1557i	−0.262486	−	0.151546i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−90.5130	+	156.773i	−0.660679	+	1.14433i	0.319759	+	0.947499i	$0.396398\pi$
$137$	−90.5130	+	156.773i	−0.660679	+	1.14433i	−0.980438	+	0.196830i	$0.936935\pi$
$138$		0			0
$139$	−114.555	−	198.414i	−0.824134	−	1.42744i	−0.902579	−	0.430524i	$-0.858329\pi$
$139$	−114.555	−	198.414i	−0.824134	−	1.42744i	0.0784454	−	0.996918i	$-0.475004\pi$
$140$		0			0
$141$	135.256	+	149.540i	0.959263	+	1.06057i
$142$		0			0
$143$	60.0689			0.420063
$144$		0			0
$145$		0			0
$146$		0			0
$147$	139.571	−	29.9948i	0.949462	−	0.204046i
$148$		0			0
$149$	−233.844	+	135.010i	−1.56942	+	0.906107i	−0.573187	+	0.819425i	$0.694293\pi$
$149$	−233.844	+	135.010i	−1.56942	+	0.906107i	−0.996236	+	0.0866818i	$0.972374\pi$
$150$		0			0
$151$	81.5705	−	141.284i	0.540202	−	0.935658i	−0.458690	−	0.888596i	$-0.651681\pi$
$151$	81.5705	−	141.284i	0.540202	−	0.935658i	0.998892	−	0.0470612i	$-0.0149856\pi$
$152$		0			0
$153$	136.655	+	98.3501i	0.893171	+	0.642811i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−116.567	+	67.2998i	−0.742463	+	0.428661i	−0.822964	−	0.568094i	$-0.807681\pi$
$157$	−116.567	+	67.2998i	−0.742463	+	0.428661i	0.0805014	+	0.996754i	$0.474348\pi$
$158$		0			0
$159$	−27.6846	+	85.8607i	−0.174117	+	0.540005i
$160$		0			0
$161$			16.0536i			0.0997118i
$162$		0			0
$163$			159.658i			0.979500i	0.871863	+	0.489750i	$0.162912\pi$
$163$			159.658i			0.979500i	−0.871863	+	0.489750i	$0.837088\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	55.5770	+	96.2622i	0.332796	+	0.576420i	0.983059	−	0.183289i	$-0.0586745\pi$
$167$	55.5770	+	96.2622i	0.332796	+	0.576420i	−0.650263	+	0.759709i	$0.725341\pi$
$168$		0			0
$169$	17.9208	−	31.0397i	0.106040	−	0.183667i
$170$		0			0
$171$	247.625	+	178.215i	1.44810	+	1.04219i
$172$		0			0
$173$	−73.6755	+	127.610i	−0.425870	+	0.737629i	−0.996501	−	0.0835778i	$-0.973365\pi$
$173$	−73.6755	+	127.610i	−0.425870	+	0.737629i	0.570631	+	0.821207i	$0.306699\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.66793	−	12.4144i	−0.0150731	−	0.0701376i
$178$		0			0
$179$			253.022i			1.41353i	0.707449	+	0.706765i	$0.249846\pi$
$179$			253.022i			1.41353i	−0.707449	+	0.706765i	$0.750154\pi$
$180$		0			0
$181$	−212.017			−1.17136			−0.585682	−	0.810541i	$-0.699173\pi$
$181$	−212.017			−1.17136			−0.585682	+	0.810541i	$0.699173\pi$
$182$		0			0
$183$	176.371	+	194.996i	0.963773	+	1.06555i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−67.9963	−	39.2577i	−0.363617	−	0.209934i
$188$		0			0
$189$	31.9084	−	3.57142i	0.168828	−	0.0188964i
$190$		0			0
$191$	−287.027	−	165.715i	−1.50276	−	0.867619i	−0.999995	−	0.00319548i	$-0.998983\pi$
$191$	−287.027	−	165.715i	−1.50276	−	0.867619i	−0.502765	−	0.864423i	$-0.667684\pi$
$192$		0			0
$193$	−288.004	+	166.279i	−1.49225	+	0.861549i	−0.999961	−	0.00888358i	$-0.997172\pi$
$193$	−288.004	+	166.279i	−1.49225	+	0.861549i	−0.492287	+	0.870433i	$0.663839\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	321.219			1.63056			0.815278	−	0.579070i	$-0.196584\pi$
$197$	321.219			1.63056			0.815278	+	0.579070i	$0.196584\pi$
$198$		0			0
$199$	208.913			1.04981			0.524907	−	0.851160i	$-0.324100\pi$
$199$	208.913			1.04981			0.524907	+	0.851160i	$0.324100\pi$
$200$		0			0
$201$	−22.5708	−	105.026i	−0.112293	−	0.522518i
$202$		0			0
$203$	−21.0307	−	36.4262i	−0.103599	−	0.179439i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	12.1567	−	120.888i	0.0587278	−	0.584002i
$208$		0			0
$209$	−123.212	−	71.1366i	−0.589532	−	0.340366i
$210$		0			0
$211$	−110.304	−	191.053i	−0.522769	−	0.905463i	−0.999649	−	0.0264945i	$-0.991566\pi$
$211$	−110.304	−	191.053i	−0.522769	−	0.905463i	0.476880	−	0.878969i	$-0.341768\pi$
$212$		0			0
$213$	−70.0028	−	22.5715i	−0.328652	−	0.105969i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			11.8398i			0.0545613i
$218$		0			0
$219$	34.0646	+	10.9837i	0.155546	+	0.0501537i
$220$		0			0
$221$	−231.875	+	133.873i	−1.04921	+	0.605760i
$222$		0			0
$223$	248.767	+	143.626i	1.11555	+	0.644062i	0.940261	−	0.340455i	$-0.110581\pi$
$223$	248.767	+	143.626i	1.11555	+	0.644062i	0.175287	+	0.984517i	$0.443915\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−130.758	+	226.479i	−0.576024	+	0.997704i	0.419905	+	0.907568i	$0.362063\pi$
$227$	−130.758	+	226.479i	−0.576024	+	0.997704i	−0.995930	+	0.0901356i	$0.971270\pi$
$228$		0			0
$229$	99.2244	+	171.862i	0.433294	+	0.750488i	0.997155	−	0.0753822i	$-0.0240177\pi$
$229$	99.2244	+	171.862i	0.433294	+	0.750488i	−0.563860	+	0.825870i	$0.690684\pi$
$230$		0			0
$231$	−14.6387	+	3.14597i	−0.0633711	+	0.0136189i
$232$		0			0
$233$	−182.063			−0.781387			−0.390693	−	0.920521i	$-0.627765\pi$
$233$	−182.063			−0.781387			−0.390693	+	0.920521i	$0.627765\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−76.8163	−	84.9284i	−0.324119	−	0.358348i
$238$		0			0
$239$	210.133	−	121.320i	0.879218	−	0.507617i	0.00881748	−	0.999961i	$-0.497193\pi$
$239$	210.133	−	121.320i	0.879218	−	0.507617i	0.870400	+	0.492344i	$0.163860\pi$
$240$		0			0
$241$	158.882	−	275.192i	0.659263	−	1.14188i	−0.321544	−	0.946895i	$-0.604202\pi$
$241$	158.882	−	275.192i	0.659263	−	1.14188i	0.980807	−	0.194983i	$-0.0624650\pi$
$242$		0			0
$243$	−242.985	+	2.73105i	−0.999937	+	0.0112389i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−420.167	+	242.583i	−1.70108	+	0.982119i
$248$		0			0
$249$	48.4942	+	53.6154i	0.194756	+	0.215323i
$250$		0			0
$251$			64.0280i			0.255092i	0.991833	+	0.127546i	$0.0407100\pi$
$251$			64.0280i			0.255092i	−0.991833	+	0.127546i	$0.959290\pi$
$252$		0			0
$253$			56.6589i			0.223948i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	232.101	+	402.010i	0.903116	+	1.56424i	0.823426	+	0.567423i	$0.192060\pi$
$257$	232.101	+	402.010i	0.903116	+	1.56424i	0.0796896	+	0.996820i	$0.474607\pi$
$258$		0			0
$259$	11.4784	−	19.8811i	0.0443180	−	0.0767610i
$260$		0			0
$261$	130.783	+	290.225i	0.501085	+	1.11197i
$262$		0			0
$263$	−28.0482	+	48.5809i	−0.106647	+	0.184718i	−0.914410	−	0.404789i	$-0.867345\pi$
$263$	−28.0482	+	48.5809i	−0.106647	+	0.184718i	0.807763	+	0.589508i	$0.200678\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	126.914	+	40.9217i	0.475333	+	0.153265i
$268$		0			0
$269$		−	29.8910i		−	0.111119i	−0.998455	−	0.0555594i	$-0.982306\pi$
$269$		−	29.8910i		−	0.111119i	0.998455	−	0.0555594i	$-0.0176942\pi$
$270$		0			0
$271$	−166.826			−0.615594			−0.307797	−	0.951452i	$-0.599592\pi$
$271$	−166.826			−0.615594			−0.307797	+	0.951452i	$0.599592\pi$
$272$		0			0
$273$	−15.6690	+	48.5957i	−0.0573957	+	0.178006i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−170.443	−	98.4054i	−0.615318	−	0.355254i	0.159726	−	0.987161i	$-0.448939\pi$
$277$	−170.443	−	98.4054i	−0.615318	−	0.355254i	−0.775044	+	0.631907i	$0.782272\pi$
$278$		0			0
$279$	8.96574	−	89.1572i	0.0321353	−	0.319560i
$280$		0			0
$281$	288.196	+	166.390i	1.02561	+	0.592136i	0.915724	−	0.401808i	$-0.131618\pi$
$281$	288.196	+	166.390i	1.02561	+	0.592136i	0.109886	+	0.993944i	$0.464951\pi$
$282$		0			0
$283$	404.376	−	233.467i	1.42889	−	0.824971i	0.431858	−	0.901942i	$-0.357858\pi$
$283$	404.376	−	233.467i	1.42889	−	0.824971i	0.997033	+	0.0769712i	$0.0245249\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−76.8474			−0.267761
$288$		0			0
$289$	60.9675			0.210960
$290$		0			0
$291$	142.249	−	128.661i	0.488827	−	0.442135i
$292$		0			0
$293$	10.7616	+	18.6397i	0.0367291	+	0.0636167i	0.883806	−	0.467854i	$-0.154973\pi$
$293$	10.7616	+	18.6397i	0.0367291	+	0.0636167i	−0.847077	+	0.531471i	$0.821639\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	112.616	−	12.6048i	0.379179	−	0.0424405i
$298$		0			0
$299$	167.327	+	96.6064i	0.559623	+	0.323098i
$300$		0			0
$301$	−24.7077	−	42.7950i	−0.0820854	−	0.142176i
$302$		0			0
$303$	−26.6137	+	24.0717i	−0.0878342	+	0.0794445i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			452.833i			1.47503i	0.675332	+	0.737514i	$0.264000\pi$
$307$			452.833i			1.47503i	−0.675332	+	0.737514i	$0.736000\pi$
$308$		0			0
$309$	103.354	+	480.924i	0.334479	+	1.55639i
$310$		0			0
$311$	−488.695	+	282.148i	−1.57137	+	0.907229i	−0.575364	+	0.817897i	$0.695140\pi$
$311$	−488.695	+	282.148i	−1.57137	+	0.907229i	−0.996002	+	0.0893313i	$0.971527\pi$
$312$		0			0
$313$	−399.515	−	230.660i	−1.27641	−	0.736933i	−0.300220	−	0.953870i	$-0.597060\pi$
$313$	−399.515	−	230.660i	−1.27641	−	0.736933i	−0.976186	+	0.216937i	$0.930393\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−168.380	+	291.643i	−0.531167	+	0.920008i	0.468171	+	0.883638i	$0.344913\pi$
$317$	−168.380	+	291.643i	−0.531167	+	0.920008i	−0.999338	+	0.0363706i	$0.988420\pi$
$318$		0			0
$319$	−74.2247	−	128.561i	−0.232679	−	0.403012i
$320$		0			0
$321$	−94.2740	+	292.380i	−0.293688	+	0.910841i
$322$		0			0
$323$	634.156			1.96333
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−51.9684	+	161.174i	−0.158925	+	0.492888i
$328$		0			0
$329$	69.2180	−	39.9630i	0.210389	−	0.121468i
$330$		0			0
$331$	210.896	−	365.283i	0.637149	−	1.10357i	−0.348907	−	0.937158i	$-0.613447\pi$
$331$	210.896	−	365.283i	0.637149	−	1.10357i	0.986055	−	0.166417i	$-0.0532197\pi$
$332$		0			0
$333$	−101.490	+	141.019i	−0.304776	+	0.423479i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−102.557	+	59.2115i	−0.304325	+	0.175702i	−0.644384	−	0.764702i	$-0.722886\pi$
$337$	−102.557	+	59.2115i	−0.304325	+	0.175702i	0.340059	+	0.940404i	$0.389553\pi$
$338$		0			0
$339$	505.668	−	108.672i	1.49165	−	0.320565i
$340$		0			0
$341$			41.7869i			0.122542i
$342$		0			0
$343$		−	114.857i		−	0.334861i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	85.0001	+	147.224i	0.244957	+	0.424278i	0.962120	−	0.272628i	$-0.0878928\pi$
$347$	85.0001	+	147.224i	0.244957	+	0.424278i	−0.717163	+	0.696906i	$0.754559\pi$
$348$		0			0
$349$	310.127	−	537.156i	0.888617	−	1.53913i	0.0471063	−	0.998890i	$-0.485000\pi$
$349$	310.127	−	537.156i	0.888617	−	1.53913i	0.841511	−	0.540240i	$-0.181667\pi$
$350$		0			0
$351$	154.792	−	354.075i	0.441002	−	1.00876i
$352$		0			0
$353$	−204.704	+	354.557i	−0.579897	+	1.00441i	0.415593	+	0.909551i	$0.363574\pi$
$353$	−204.704	+	354.557i	−0.579897	+	1.00441i	−0.995491	+	0.0948611i	$0.969759\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	49.4963	−	44.7686i	0.138645	−	0.125402i
$358$		0			0
$359$			138.441i			0.385630i	0.981235	+	0.192815i	$0.0617618\pi$
$359$			138.441i			0.385630i	−0.981235	+	0.192815i	$0.938238\pi$
$360$		0			0
$361$	788.116			2.18315
$362$		0			0
$363$	303.232	−	65.1666i	0.835349	−	0.179522i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−68.4781	−	39.5358i	−0.186589	−	0.107727i	0.403796	−	0.914849i	$-0.367691\pi$
$367$	−68.4781	−	39.5358i	−0.186589	−	0.107727i	−0.590385	+	0.807122i	$0.701024\pi$
$368$		0			0
$369$	578.684	+	58.1931i	1.56825	+	0.157705i
$370$		0			0
$371$	30.9690	+	17.8800i	0.0834744	+	0.0481940i
$372$		0			0
$373$	−89.8672	+	51.8849i	−0.240931	+	0.139102i	−0.615605	−	0.788055i	$-0.711088\pi$
$373$	−89.8672	+	51.8849i	−0.240931	+	0.139102i	0.374674	+	0.927157i	$0.377755\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−506.228			−1.34278
$378$		0			0
$379$	−315.487			−0.832419			−0.416210	−	0.909269i	$-0.636642\pi$
$379$	−315.487			−0.832419			−0.416210	+	0.909269i	$0.636642\pi$
$380$		0			0
$381$	559.208	+	180.309i	1.46774	+	0.473252i
$382$		0			0
$383$	−207.092	−	358.695i	−0.540711	−	0.936540i	−0.998863	−	0.0476657i	$-0.984822\pi$
$383$	−207.092	−	358.695i	−0.540711	−	0.936540i	0.458152	−	0.888874i	$-0.348512\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	153.650	+	340.969i	0.397028	+	0.881058i
$388$		0			0
$389$	59.9057	+	34.5866i	0.153999	+	0.0889115i	0.575019	−	0.818140i	$-0.304994\pi$
$389$	59.9057	+	34.5866i	0.153999	+	0.0889115i	−0.421020	+	0.907051i	$0.638328\pi$
$390$		0			0
$391$	−126.273	−	218.711i	−0.322949	−	0.559364i
$392$		0			0
$393$	−71.7106	−	333.682i	−0.182470	−	0.849063i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			347.995i			0.876562i	0.898838	+	0.438281i	$0.144413\pi$
$397$			347.995i			0.876562i	−0.898838	+	0.438281i	$0.855587\pi$
$398$		0			0
$399$	89.6894	−	81.1225i	0.224785	−	0.203315i
$400$		0			0
$401$	−635.313	+	366.798i	−1.58432	+	0.914709i	−0.590104	+	0.807327i	$0.700913\pi$
$401$	−635.313	+	366.798i	−1.58432	+	0.914709i	−0.994218	+	0.107382i	$0.965753\pi$
$402$		0			0
$403$	123.407	+	71.2488i	0.306220	+	0.176796i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	40.5112	−	70.1675i	0.0995361	−	0.172402i
$408$		0			0
$409$	47.0727	+	81.5324i	0.115092	+	0.199346i	0.917817	−	0.397005i	$-0.129950\pi$
$409$	47.0727	+	81.5324i	0.115092	+	0.199346i	−0.802724	+	0.596350i	$0.796617\pi$
$410$		0			0
$411$	−364.296	−	402.768i	−0.886366	−	0.979970i
$412$		0			0
$413$	−5.03330			−0.0121872
$414$		0			0
$415$		0			0
$416$		0			0
$417$	671.985	−	144.414i	1.61147	−	0.346317i
$418$		0			0
$419$	90.6043	−	52.3104i	0.216239	−	0.124846i	−0.387968	−	0.921673i	$-0.626823\pi$
$419$	90.6043	−	52.3104i	0.216239	−	0.124846i	0.604208	+	0.796827i	$0.293490\pi$
$420$		0			0
$421$	−276.542	+	478.984i	−0.656868	+	1.13773i	0.324553	+	0.945867i	$0.394786\pi$
$421$	−276.542	+	478.984i	−0.656868	+	1.13773i	−0.981422	+	0.191862i	$0.938547\pi$
$422$		0			0
$423$	−551.494	+	248.518i	−1.30377	+	0.587513i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	90.2585	−	52.1108i	0.211378	−	0.122039i
$428$		0			0
$429$	−55.3016	+	171.512i	−0.128908	+	0.399794i
$430$		0			0
$431$		−	469.242i		−	1.08873i	−0.838849	−	0.544364i	$-0.816771\pi$
$431$		−	469.242i		−	1.08873i	0.838849	−	0.544364i	$-0.183229\pi$
$432$		0			0
$433$		−	426.644i		−	0.985321i	−0.870222	−	0.492660i	$-0.836024\pi$
$433$		−	426.644i		−	0.985321i	0.870222	−	0.492660i	$-0.163976\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−228.812	−	396.314i	−0.523598	−	0.906898i
$438$		0			0
$439$	−286.573	+	496.359i	−0.652786	+	1.13066i	0.329658	+	0.944100i	$0.393067\pi$
$439$	−286.573	+	496.359i	−0.652786	+	1.13066i	−0.982444	+	0.186558i	$0.940267\pi$
$440$		0			0
$441$	−42.8514	+	426.124i	−0.0971688	+	0.966267i
$442$		0			0
$443$	52.2986	−	90.5838i	0.118055	−	0.204478i	−0.800942	−	0.598743i	$-0.795667\pi$
$443$	52.2986	−	90.5838i	0.118055	−	0.204478i	0.918997	+	0.394264i	$0.129001\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−170.201	−	791.977i	−0.380764	−	1.77176i
$448$		0			0
$449$		−	401.878i		−	0.895051i	−0.894271	−	0.447526i	$-0.852305\pi$
$449$		−	401.878i		−	0.895051i	0.894271	−	0.447526i	$-0.147695\pi$
$450$		0			0
$451$	−271.222			−0.601379
$452$		0			0
$453$	328.305	+	362.975i	0.724735	+	0.801270i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−83.4142	−	48.1592i	−0.182526	−	0.105381i	0.405953	−	0.913894i	$-0.366940\pi$
$457$	−83.4142	−	48.1592i	−0.182526	−	0.105381i	−0.588479	+	0.808513i	$0.700273\pi$
$458$		0			0
$459$	−406.623	+	299.639i	−0.885890	+	0.652809i
$460$		0			0
$461$	−64.4588	−	37.2153i	−0.139824	−	0.0807274i	0.428456	−	0.903563i	$-0.359058\pi$
$461$	−64.4588	−	37.2153i	−0.139824	−	0.0807274i	−0.568280	+	0.822835i	$0.692391\pi$
$462$		0			0
$463$	−344.558	+	198.930i	−0.744185	+	0.429655i	−0.823589	−	0.567187i	$-0.808032\pi$
$463$	−344.558	+	198.930i	−0.744185	+	0.429655i	0.0794042	+	0.996843i	$0.474698\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	643.763			1.37851			0.689254	−	0.724520i	$-0.257938\pi$
$467$	643.763			1.37851			0.689254	+	0.724520i	$0.257938\pi$
$468$		0			0
$469$	−42.5819			−0.0907931
$470$		0			0
$471$	−84.8421	−	394.785i	−0.180132	−	0.838185i
$472$		0			0
$473$	−87.2024	−	151.039i	−0.184360	−	0.319321i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−219.666	−	158.093i	−0.460516	−	0.331432i
$478$		0			0
$479$	152.770	+	88.2019i	0.318936	+	0.184138i	0.650918	−	0.759148i	$-0.274384\pi$
$479$	152.770	+	88.2019i	0.318936	+	0.184138i	−0.331982	+	0.943286i	$0.607717\pi$
$480$		0			0
$481$	−138.148	−	239.279i	−0.287209	−	0.497461i
$482$		0			0
$483$	−45.8370	−	14.7795i	−0.0949006	−	0.0305994i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	494.859i		−	1.01614i	−0.861317	−	0.508069i	$-0.830360\pi$
$487$		−	494.859i		−	1.01614i	0.861317	−	0.508069i	$-0.169640\pi$
$488$		0			0
$489$	−455.864	−	146.987i	−0.932238	−	0.300587i
$490$		0			0
$491$	159.777	−	92.2472i	0.325411	−	0.187876i	−0.328391	−	0.944542i	$-0.606506\pi$
$491$	159.777	−	92.2472i	0.325411	−	0.187876i	0.653802	+	0.756666i	$0.273173\pi$
$492$		0			0
$493$	573.036	+	330.842i	1.16234	+	0.671080i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.5777	+	25.2492i	−0.0293313	+	0.0508033i
$498$		0			0
$499$	162.276	+	281.071i	0.325203	+	0.563269i	0.981553	−	0.191188i	$-0.0612339\pi$
$499$	162.276	+	281.071i	0.325203	+	0.563269i	−0.656350	+	0.754456i	$0.727901\pi$
$500$		0			0
$501$	−326.018	+	70.0636i	−0.650735	+	0.139848i
$502$		0			0
$503$	626.131			1.24479			0.622397	−	0.782702i	$-0.286159\pi$
$503$	626.131			1.24479			0.622397	+	0.782702i	$0.286159\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	72.1276	+	79.7446i	0.142263	+	0.157287i
$508$		0			0
$509$	−387.634	+	223.800i	−0.761559	+	0.439686i	−0.829855	−	0.557979i	$-0.811577\pi$
$509$	−387.634	+	223.800i	−0.761559	+	0.439686i	0.0682960	+	0.997665i	$0.478244\pi$
$510$		0			0
$511$	7.09374	−	12.2867i	0.0138821	−	0.0240444i
$512$		0			0
$513$	−736.818	+	542.959i	−1.43629	+	1.05840i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	244.295	−	141.044i	0.472524	−	0.272812i
$518$		0			0
$519$	−296.529	−	327.844i	−0.571347	−	0.631684i
$520$		0			0
$521$		−	181.821i		−	0.348984i	−0.984659	−	0.174492i	$-0.944172\pi$
$521$		−	181.821i		−	0.348984i	0.984659	−	0.174492i	$-0.0558284\pi$
$522$		0			0
$523$			293.719i			0.561604i	0.959766	+	0.280802i	$0.0906004\pi$
$523$			293.719i			0.561604i	−0.959766	+	0.280802i	$0.909400\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−93.1285	−	161.303i	−0.176714	−	0.306078i
$528$		0			0
$529$	173.378	−	300.299i	0.327746	−	0.567673i
$530$		0			0
$531$	37.9022	+	3.81149i	0.0713790	+	0.00717795i
$532$		0			0
$533$	−462.448	+	800.984i	−0.867633	+	1.50278i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−722.439	−	232.941i	−1.34532	−	0.433782i
$538$		0			0
$539$		−	199.719i		−	0.370536i
$540$		0			0
$541$	343.593			0.635107			0.317553	−	0.948240i	$-0.397139\pi$
$541$	343.593			0.635107			0.317553	+	0.948240i	$0.397139\pi$
$542$		0			0
$543$	195.190	−	605.360i	0.359466	−	1.11484i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	35.6434	+	20.5788i	0.0651617	+	0.0376211i	0.532227	−	0.846602i	$-0.321355\pi$
$547$	35.6434	+	20.5788i	0.0651617	+	0.0376211i	−0.467065	+	0.884223i	$0.654689\pi$
$548$		0			0
$549$	−719.135	+	324.061i	−1.30990	+	0.590275i
$550$		0			0
$551$	1038.36	+	599.500i	1.88451	+	1.08802i
$552$		0			0
$553$	−39.3111	+	22.6963i	−0.0710870	+	0.0410421i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	976.675			1.75346			0.876728	−	0.480986i	$-0.159721\pi$
$557$	976.675			1.75346			0.876728	+	0.480986i	$0.159721\pi$
$558$		0			0
$559$	−594.739			−1.06393
$560$		0			0
$561$	174.690	−	158.004i	0.311391	−	0.281647i
$562$		0			0
$563$	−221.313	−	383.325i	−0.393096	−	0.680862i	0.599760	−	0.800180i	$-0.295263\pi$
$563$	−221.313	−	383.325i	−0.393096	−	0.680862i	−0.992856	+	0.119318i	$0.961929\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−19.1788	+	94.3945i	−0.0338250	+	0.166481i
$568$		0			0
$569$	−681.591	−	393.517i	−1.19788	−	0.691594i	−0.237795	−	0.971315i	$-0.576425\pi$
$569$	−681.591	−	393.517i	−1.19788	−	0.691594i	−0.960081	+	0.279721i	$0.909758\pi$
$570$		0			0
$571$	3.41373	+	5.91275i	0.00597851	+	0.0103551i	0.868999	−	0.494814i	$-0.164764\pi$
$571$	3.41373	+	5.91275i	0.00597851	+	0.0103551i	−0.863021	+	0.505169i	$0.831430\pi$
$572$		0			0
$573$	737.405	−	666.970i	1.28692	−	1.16400i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	45.4328i		−	0.0787396i	−0.999225	−	0.0393698i	$-0.987465\pi$
$577$		−	45.4328i		−	0.0787396i	0.999225	−	0.0393698i	$-0.0125350\pi$
$578$		0			0
$579$	−209.621	−	975.404i	−0.362040	−	1.68464i
$580$		0			0
$581$	24.8171	−	14.3282i	0.0427145	−	0.0246612i
$582$		0			0
$583$	109.301	+	63.1048i	0.187480	+	0.108241i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−49.6244	+	85.9520i	−0.0845391	+	0.146426i	−0.905195	−	0.424997i	$-0.860275\pi$
$587$	−49.6244	+	85.9520i	−0.0845391	+	0.146426i	0.820656	+	0.571423i	$0.193608\pi$
$588$		0			0
$589$	−168.753	−	292.288i	−0.286507	−	0.496245i
$590$		0			0
$591$	−295.726	+	917.161i	−0.500382	+	1.55188i
$592$		0			0
$593$	226.897			0.382626			0.191313	−	0.981529i	$-0.438726\pi$
$593$	226.897			0.382626			0.191313	+	0.981529i	$0.438726\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−192.333	+	596.498i	−0.322165	+	0.999159i
$598$		0			0
$599$	−652.129	+	376.507i	−1.08870	+	0.628559i	−0.933229	−	0.359282i	$-0.883022\pi$
$599$	−652.129	+	376.507i	−1.08870	+	0.628559i	−0.155467	+	0.987841i	$0.549688\pi$
$600$		0			0
$601$	−342.525	+	593.270i	−0.569924	+	0.987138i	0.426648	+	0.904418i	$0.359694\pi$
$601$	−342.525	+	593.270i	−0.569924	+	0.987138i	−0.996573	+	0.0827206i	$0.973639\pi$
$602$		0			0
$603$	320.655	+	32.2454i	0.531766	+	0.0534749i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	787.174	−	454.475i	1.29683	−	0.748724i	0.316973	−	0.948435i	$-0.397334\pi$
$607$	787.174	−	454.475i	1.29683	−	0.748724i	0.979855	+	0.199711i	$0.0640003\pi$
$608$		0			0
$609$	123.367	−	26.5125i	0.202573	−	0.0435345i
$610$		0			0
$611$		−	961.949i		−	1.57438i
$612$		0			0
$613$		−	514.234i		−	0.838881i	−0.907783	−	0.419441i	$-0.862226\pi$
$613$		−	514.234i		−	0.838881i	0.907783	−	0.419441i	$-0.137774\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−575.133	−	996.159i	−0.932144	−	1.61452i	−0.779650	−	0.626216i	$-0.784603\pi$
$617$	−575.133	−	996.159i	−0.932144	−	1.61452i	−0.152494	−	0.988304i	$-0.548730\pi$
$618$		0			0
$619$	−69.9937	+	121.233i	−0.113076	+	0.195853i	−0.917009	−	0.398867i	$-0.869404\pi$
$619$	−69.9937	+	121.233i	−0.113076	+	0.195853i	0.803933	+	0.594719i	$0.202737\pi$
$620$		0			0
$621$	333.974	+	146.004i	0.537801	+	0.235112i
$622$		0			0
$623$	26.4290	−	45.7764i	0.0424222	−	0.0734774i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	316.546	−	286.310i	0.504858	−	0.456635i
$628$		0			0
$629$			361.142i			0.574153i
$630$		0			0
$631$	−369.971			−0.586325			−0.293163	−	0.956063i	$-0.594708\pi$
$631$	−369.971			−0.586325			−0.293163	+	0.956063i	$0.594708\pi$
$632$		0			0
$633$	647.053	−	139.056i	1.02220	−	0.219678i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−589.818	−	340.531i	−0.925930	−	0.534586i
$638$		0			0
$639$	128.894	−	179.095i	0.201712	−	0.280274i
$640$		0			0
$641$	67.0156	+	38.6914i	0.104548	+	0.0603611i	0.551363	−	0.834266i	$-0.314108\pi$
$641$	67.0156	+	38.6914i	0.104548	+	0.0603611i	−0.446814	+	0.894627i	$0.647441\pi$
$642$		0			0
$643$	−226.733	+	130.904i	−0.352617	+	0.203583i	−0.665837	−	0.746097i	$-0.731925\pi$
$643$	−226.733	+	130.904i	−0.352617	+	0.203583i	0.313220	+	0.949680i	$0.398592\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−617.428			−0.954293			−0.477147	−	0.878824i	$-0.658329\pi$
$647$	−617.428			−0.954293			−0.477147	+	0.878824i	$0.658329\pi$
$648$		0			0
$649$	−17.7643			−0.0273718
$650$		0			0
$651$	−33.8055	−	10.9001i	−0.0519286	−	0.0167437i
$652$		0			0
$653$	−337.239	−	584.115i	−0.516446	−	0.894510i	−0.999818	−	0.0190951i	$-0.993921\pi$
$653$	−337.239	−	584.115i	−0.516446	−	0.894510i	0.483372	−	0.875415i	$-0.339412\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−62.7221	+	87.1508i	−0.0954675	+	0.132650i
$658$		0			0
$659$	−332.973	−	192.242i	−0.505271	−	0.291718i	0.225617	−	0.974216i	$-0.427560\pi$
$659$	−332.973	−	192.242i	−0.505271	−	0.291718i	−0.730888	+	0.682498i	$0.760894\pi$
$660$		0			0
$661$	151.713	+	262.775i	0.229520	+	0.397541i	0.957666	−	0.287882i	$-0.0929509\pi$
$661$	151.713	+	262.775i	0.229520	+	0.397541i	−0.728146	+	0.685422i	$0.759618\pi$
$662$		0			0
$663$	−168.768	−	785.308i	−0.254552	−	1.18448i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	477.490i		−	0.715877i
$668$		0			0
$669$	−639.111	+	578.065i	−0.955323	+	0.864073i
$670$		0			0
$671$	318.554	−	183.918i	0.474746	−	0.274095i
$672$		0			0
$673$	−485.081	−	280.062i	−0.720775	−	0.416139i	0.0942631	−	0.995547i	$-0.469951\pi$
$673$	−485.081	−	280.062i	−0.720775	−	0.416139i	−0.815038	+	0.579408i	$0.803284\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	508.282	−	880.370i	0.750786	−	1.30040i	−0.196656	−	0.980472i	$-0.563008\pi$
$677$	508.282	−	880.370i	0.750786	−	1.30040i	0.947442	−	0.319927i	$-0.103658\pi$
$678$		0			0
$679$	−38.0145	−	65.8431i	−0.0559860	−	0.0969707i
$680$		0			0
$681$	−526.273	−	581.849i	−0.772794	−	0.854404i
$682$		0			0
$683$	88.7713			0.129973			0.0649863	−	0.997886i	$-0.479300\pi$
$683$	88.7713			0.129973			0.0649863	+	0.997886i	$0.479300\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−582.057	+	125.088i	−0.847245	+	0.182079i
$688$		0			0
$689$	372.727	−	215.194i	0.540968	−	0.312328i
$690$		0			0
$691$	−403.626	+	699.101i	−0.584119	+	1.01172i	0.410866	+	0.911696i	$0.365226\pi$
$691$	−403.626	+	699.101i	−0.584119	+	1.01172i	−0.994985	+	0.100027i	$0.968107\pi$
$692$		0			0
$693$	4.49442	−	44.6935i	0.00648546	−	0.0644927i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1046.96	−	604.460i	1.50209	−	0.867232i
$698$		0			0
$699$	167.614	−	519.835i	0.239791	−	0.743684i
$700$		0			0
$701$		−	201.018i		−	0.286758i	−0.989668	−	0.143379i	$-0.954203\pi$
$701$		−	201.018i		−	0.286758i	0.989668	−	0.143379i	$-0.0457968\pi$
$702$		0			0
$703$			654.404i			0.930874i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.11226	+	12.3188i	0.0100598	+	0.0174240i
$708$		0			0
$709$	195.660	−	338.894i	0.275967	−	0.477989i	−0.694412	−	0.719578i	$-0.744335\pi$
$709$	195.660	−	338.894i	0.275967	−	0.477989i	0.970379	+	0.241589i	$0.0776687\pi$
$710$		0			0
$711$	313.211	−	141.141i	0.440522	−	0.198511i
$712$		0			0
$713$	−67.2041	+	116.401i	−0.0942554	+	0.163255i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	152.944	+	711.674i	0.213311	+	0.992571i
$718$		0			0
$719$			1241.75i			1.72705i	0.504308	+	0.863524i	$0.331747\pi$
$719$			1241.75i			1.72705i	−0.504308	+	0.863524i	$0.668253\pi$
$720$		0			0
$721$	194.987			0.270439
$722$		0			0
$723$	639.469	+	707.000i	0.884467	+	0.977870i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	173.571	+	100.212i	0.238750	+	0.137843i	0.614602	−	0.788837i	$-0.289317\pi$
$727$	173.571	+	100.212i	0.238750	+	0.137843i	−0.375852	+	0.926680i	$0.622650\pi$
$728$		0			0
$729$	215.902	−	696.295i	0.296162	−	0.955138i
$730$		0			0
$731$	673.227	+	388.688i	0.920968	+	0.531721i
$732$		0			0
$733$	104.548	−	60.3607i	0.142630	−	0.0823475i	−0.426987	−	0.904258i	$-0.640425\pi$
$733$	104.548	−	60.3607i	0.142630	−	0.0823475i	0.569617	+	0.821910i	$0.307092\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−150.287			−0.203917
$738$		0			0
$739$	471.461			0.637972			0.318986	−	0.947759i	$-0.396658\pi$
$739$	471.461			0.637972			0.318986	+	0.947759i	$0.396658\pi$
$740$		0			0
$741$	−305.815	−	1423.01i	−0.412706	−	1.92039i
$742$		0			0
$743$	−651.339	−	1128.15i	−0.876634	−	1.51837i	−0.855012	−	0.518608i	$-0.826450\pi$
$743$	−651.339	−	1128.15i	−0.876634	−	1.51837i	−0.0216220	−	0.999766i	$-0.506883\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−197.731	+	89.1026i	−0.264700	+	0.119281i
$748$		0			0
$749$	105.458	+	60.8863i	0.140799	+	0.0812901i
$750$		0			0
$751$	439.726	+	761.629i	0.585521	+	1.01415i	0.994810	+	0.101748i	$0.0324435\pi$
$751$	439.726	+	761.629i	0.585521	+	1.01415i	−0.409289	+	0.912405i	$0.634223\pi$
$752$		0			0
$753$	−182.816	−	58.9464i	−0.242783	−	0.0782821i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	35.1814i		−	0.0464748i	−0.999730	−	0.0232374i	$-0.992603\pi$
$757$		−	35.1814i		−	0.0464748i	0.999730	−	0.0232374i	$-0.00739736\pi$
$758$		0			0
$759$	−161.775	−	52.1622i	−0.213142	−	0.0687248i
$760$		0			0
$761$	1102.94	−	636.785i	1.44933	−	0.836774i	0.450893	−	0.892578i	$-0.351106\pi$
$761$	1102.94	−	636.785i	1.44933	−	0.836774i	0.998442	+	0.0558046i	$0.0177724\pi$
$762$		0			0
$763$	58.1337	+	33.5635i	0.0761910	+	0.0439889i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−30.2891	+	52.4623i	−0.0394903	+	0.0683993i
$768$		0			0
$769$	379.742	+	657.733i	0.493813	+	0.855310i	0.999975	−	0.00712921i	$-0.00226932\pi$
$769$	379.742	+	657.733i	0.493813	+	0.855310i	−0.506161	+	0.862439i	$0.668936\pi$
$770$		0			0
$771$	−1361.52	+	292.600i	−1.76591	+	0.379507i
$772$		0			0
$773$	165.240			0.213765			0.106883	−	0.994272i	$-0.465913\pi$
$773$	165.240			0.213765			0.106883	+	0.994272i	$0.465913\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	46.1980	+	51.0767i	0.0594569	+	0.0657358i
$778$		0			0
$779$	1897.13	−	1095.31i	2.43534	−	1.40604i
$780$		0			0
$781$	−51.4497	+	89.1135i	−0.0658767	+	0.114102i
$782$		0			0
$783$	−949.069	+	106.227i	−1.21209	+	0.135666i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	498.401	−	287.752i	0.633293	−	0.365632i	−0.148733	−	0.988877i	$-0.547520\pi$
$787$	498.401	−	287.752i	0.633293	−	0.365632i	0.782026	+	0.623246i	$0.214186\pi$
$788$		0			0
$789$	−112.888	−	124.810i	−0.143078	−	0.158187i
$790$		0			0
$791$		−	205.019i		−	0.259190i
$792$		0			0
$793$		−	1254.36i		−	1.58179i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−303.808	−	526.210i	−0.381189	−	0.660238i	0.610044	−	0.792368i	$-0.291152\pi$
$797$	−303.808	−	526.210i	−0.381189	−	0.660238i	−0.991232	+	0.132129i	$0.957819\pi$
$798$		0			0
$799$	−628.676	+	1088.90i	−0.786828	+	1.36283i
$800$		0			0
$801$	−233.683	+	324.696i	−0.291739	+	0.405364i
$802$		0			0
$803$	25.0363	−	43.3642i	0.0311785	−	0.0540027i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	85.3460	+	27.5187i	0.105757	+	0.0341000i
$808$		0			0
$809$		−	962.401i		−	1.18962i	−0.803867	−	0.594809i	$-0.797228\pi$
$809$		−	962.401i		−	1.18962i	0.803867	−	0.594809i	$-0.202772\pi$
$810$		0			0
$811$	−140.096			−0.172745			−0.0863723	−	0.996263i	$-0.527527\pi$
$811$	−140.096			−0.172745			−0.0863723	+	0.996263i	$0.527527\pi$
$812$		0			0
$813$	153.586	−	476.329i	0.188913	−	0.585891i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1219.92	+	704.319i	1.49317	+	0.862079i
$818$		0			0
$819$	−124.327	−	89.4779i	−0.151804	−	0.109253i
$820$		0			0
$821$	−280.294	−	161.828i	−0.341406	−	0.197111i	0.319488	−	0.947590i	$-0.396489\pi$
$821$	−280.294	−	161.828i	−0.341406	−	0.197111i	−0.660894	+	0.750480i	$0.729823\pi$
$822$		0			0
$823$	167.327	−	96.6061i	0.203313	−	0.117383i	−0.394887	−	0.918730i	$-0.629216\pi$
$823$	167.327	−	96.6061i	0.203313	−	0.117383i	0.598200	+	0.801347i	$0.295883\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.7916			−0.0190951			−0.00954754	−	0.999954i	$-0.503039\pi$
$827$	−15.7916			−0.0190951			−0.00954754	+	0.999954i	$0.503039\pi$
$828$		0			0
$829$	265.576			0.320357			0.160178	−	0.987088i	$-0.448793\pi$
$829$	265.576			0.320357			0.160178	+	0.987088i	$0.448793\pi$
$830$		0			0
$831$	437.888	−	396.062i	0.526941	−	0.476609i
$832$		0			0
$833$	445.104	+	770.943i	0.534339	+	0.925502i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	246.312	+	107.681i	0.294279	+	0.128651i
$838$		0			0
$839$	761.943	+	439.908i	0.908156	+	0.524324i	0.879838	−	0.475275i	$-0.157651\pi$
$839$	761.943	+	439.908i	0.908156	+	0.524324i	0.0283189	+	0.999599i	$0.490985\pi$
$840$		0			0
$841$	205.025	+	355.114i	0.243787	+	0.422252i
$842$		0			0
$843$	−740.409	+	669.687i	−0.878303	+	0.794409i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	122.943i		−	0.145151i
$848$		0			0
$849$	294.322	+	1369.53i	0.346669	+	1.61311i
$850$		0			0
$851$	225.695	−	130.305i	0.265211	−	0.153120i
$852$		0			0
$853$	176.795	+	102.073i	0.207263	+	0.119663i	0.600039	−	0.799971i	$-0.295152\pi$
$853$	176.795	+	102.073i	0.207263	+	0.119663i	−0.392776	+	0.919634i	$0.628485\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−106.729	+	184.859i	−0.124537	+	0.215705i	−0.921552	−	0.388255i	$-0.873078\pi$
$857$	−106.729	+	184.859i	−0.124537	+	0.215705i	0.797015	+	0.603960i	$0.206411\pi$
$858$		0			0
$859$	323.677	+	560.625i	0.376806	+	0.652648i	0.990596	−	0.136822i	$-0.0436889\pi$
$859$	323.677	+	560.625i	0.376806	+	0.652648i	−0.613789	+	0.789470i	$0.710356\pi$
$860$		0			0
$861$	70.7485	−	219.418i	0.0821701	−	0.254841i
$862$		0			0
$863$	699.772			0.810859			0.405430	−	0.914126i	$-0.367122\pi$
$863$	699.772			0.810859			0.405430	+	0.914126i	$0.367122\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−56.1288	+	174.077i	−0.0647391	+	0.200781i
$868$		0			0
$869$	−138.743	+	80.1033i	−0.159658	+	0.0921787i
$870$		0			0
$871$	−256.247	+	443.833i	−0.294199	+	0.509567i
$872$		0			0
$873$	236.401	+	524.605i	0.270791	+	0.600922i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1234.05	+	712.480i	−1.40713	+	0.812406i	−0.995110	−	0.0987694i	$-0.968509\pi$
$877$	−1234.05	+	712.480i	−1.40713	+	0.812406i	−0.412018	+	0.911176i	$0.635176\pi$
$878$		0			0
$879$	−63.1285	+	13.5668i	−0.0718185	+	0.0154343i
$880$		0			0
$881$		−	1598.97i		−	1.81495i	−0.420102	−	0.907477i	$-0.638006\pi$
$881$		−	1598.97i		−	1.81495i	0.420102	−	0.907477i	$-0.361994\pi$
$882$		0			0
$883$			1117.03i			1.26504i	0.774542	+	0.632522i	$0.217980\pi$
$883$			1117.03i			1.26504i	−0.774542	+	0.632522i	$0.782020\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−583.003	−	1009.79i	−0.657275	−	1.13843i	−0.981318	−	0.192391i	$-0.938376\pi$
$887$	−583.003	−	1009.79i	−0.657275	−	1.13843i	0.324044	−	0.946042i	$-0.394958\pi$
$888$		0			0
$889$	116.451	−	201.700i	0.130992	−	0.226884i
$890$		0			0
$891$	−67.6887	+	333.152i	−0.0759693	+	0.373908i
$892$		0			0
$893$	−1139.19	+	1973.13i	−1.27569	+	2.20955i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−429.883	+	388.821i	−0.479245	+	0.433468i
$898$		0			0
$899$		−	352.157i		−	0.391721i
$900$		0			0
$901$	−562.555			−0.624367
$902$		0			0
$903$	144.937	−	31.1480i	0.160506	−	0.0344939i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1526.36	+	881.243i	1.68286	+	0.971602i	0.959742	+	0.280882i	$0.0906271\pi$
$907$	1526.36	+	881.243i	1.68286	+	0.971602i	0.723122	+	0.690720i	$0.242706\pi$
$908$		0			0
$909$	−44.2290	−	98.1500i	−0.0486568	−	0.107976i
$910$		0			0
$911$	1449.90	+	837.098i	1.59154	+	0.918878i	0.993043	+	0.117755i	$0.0375699\pi$
$911$	1449.90	+	837.098i	1.59154	+	0.918878i	0.598501	+	0.801122i	$0.295763\pi$
$912$		0			0
$913$	87.5885	−	50.5693i	0.0959349	−	0.0553880i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−135.289			−0.147534
$918$		0			0
$919$	−1136.29			−1.23644			−0.618221	−	0.786004i	$-0.712146\pi$
$919$	−1136.29			−1.23644			−0.618221	+	0.786004i	$0.712146\pi$
$920$		0			0
$921$	−1292.95	−	416.894i	−1.40386	−	0.452654i
$922$		0			0
$923$	175.449	+	303.887i	0.190086	+	0.329238i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1468.31	−	147.655i	−1.58394	−	0.159282i
$928$		0			0
$929$	−932.936	−	538.631i	−1.00424	−	0.579796i	−0.0947376	−	0.995502i	$-0.530201\pi$
$929$	−932.936	−	538.631i	−1.00424	−	0.579796i	−0.909499	+	0.415706i	$0.863535\pi$
$930$		0			0
$931$	806.548	+	1396.98i	0.866324	+	1.50052i
$932$		0			0
$933$	−355.693	−	1655.10i	−0.381235	−	1.77395i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			1063.87i			1.13540i	0.823234	+	0.567702i	$0.192167\pi$
$937$			1063.87i			1.13540i	−0.823234	+	0.567702i	$0.807833\pi$
$938$		0			0
$939$	1026.40	−	928.360i	1.09308	−	0.988668i
$940$		0			0
$941$	−994.783	+	574.338i	−1.05716	+	0.610349i	−0.924644	−	0.380833i	$-0.875637\pi$
$941$	−994.783	+	574.338i	−1.05716	+	0.610349i	−0.132511	+	0.991182i	$0.542304\pi$
$942$		0			0
$943$	−755.513	−	436.195i	−0.801180	−	0.462561i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	57.9461	−	100.366i	0.0611891	−	0.105983i	−0.833808	−	0.552054i	$-0.813844\pi$
$947$	57.9461	−	100.366i	0.0611891	−	0.105983i	0.894997	+	0.446072i	$0.147177\pi$
$948$		0			0
$949$	−85.3766	−	147.877i	−0.0899648	−	0.155824i
$950$		0			0
$951$	−677.695	−	749.263i	−0.712613	−	0.787868i
$952$		0			0
$953$	1854.05			1.94549			0.972744	−	0.231881i	$-0.0744879\pi$
$953$	1854.05			1.94549			0.972744	+	0.231881i	$0.0744879\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	435.407	−	93.5720i	0.454971	−	0.0977764i
$958$		0			0
$959$	−186.431	+	107.636i	−0.194401	+	0.112237i
$960$		0			0
$961$	430.936	−	746.403i	0.448424	−	0.776694i
$962$		0			0
$963$	−748.025	−	538.351i	−0.776766	−	0.559035i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−790.590	+	456.447i	−0.817569	+	0.472024i	−0.849578	−	0.527464i	$-0.823143\pi$
$967$	−790.590	+	456.447i	−0.817569	+	0.472024i	0.0320081	+	0.999488i	$0.489810\pi$
$968$		0			0
$969$	−583.826	+	1810.67i	−0.602504	+	1.86860i
$970$		0			0
$971$			1732.32i			1.78405i	0.451982	+	0.892027i	$0.350717\pi$
$971$			1732.32i			1.78405i	−0.451982	+	0.892027i	$0.649283\pi$
$972$		0			0
$973$		−	272.451i		−	0.280011i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−115.673	−	200.352i	−0.118396	−	0.205069i	0.800736	−	0.599018i	$-0.204442\pi$
$977$	−115.673	−	200.352i	−0.118396	−	0.205069i	−0.919132	+	0.393949i	$0.871109\pi$
$978$		0			0
$979$	93.2774	−	161.561i	0.0952783	−	0.165027i
$980$		0			0
$981$	−412.348	−	296.765i	−0.420335	−	0.302513i
$982$		0			0
$983$	389.601	−	674.808i	0.396338	−	0.686478i	−0.596933	−	0.802291i	$-0.703614\pi$
$983$	389.601	−	674.808i	0.396338	−	0.686478i	0.993271	+	0.115813i	$0.0369474\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	50.3798	+	234.426i	0.0510433	+	0.237513i
$988$		0			0
$989$		−	560.976i		−	0.567215i
$990$		0			0
$991$	222.470			0.224490			0.112245	−	0.993681i	$-0.464196\pi$
$991$	222.470			0.224490			0.112245	+	0.993681i	$0.464196\pi$
$992$		0			0
$993$	848.815	+	938.453i	0.854798	+	0.945069i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	392.676	+	226.712i	0.393858	+	0.227394i	0.683830	−	0.729641i	$-0.260313\pi$
$997$	392.676	+	226.712i	0.393858	+	0.227394i	−0.289972	+	0.957035i	$0.593646\pi$
$998$		0			0
$999$	−309.207	−	419.607i	−0.309516	−	0.420027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.c.749.4		24
3.2	odd	2		2700.3.u.c.2249.7		24
5.2	odd	4		900.3.p.c.101.5		12
5.3	odd	4		180.3.o.b.101.2	yes	12
5.4	even	2	inner	900.3.u.c.749.9		24
9.4	even	3		2700.3.u.c.449.6		24
9.5	odd	6	inner	900.3.u.c.149.9		24
15.2	even	4		2700.3.p.c.1601.3		12
15.8	even	4		540.3.o.b.521.5		12
15.14	odd	2		2700.3.u.c.2249.6		24
20.3	even	4		720.3.bs.b.641.5		12
45.4	even	6		2700.3.u.c.449.7		24
45.13	odd	12		540.3.o.b.341.5		12
45.14	odd	6	inner	900.3.u.c.149.4		24
45.22	odd	12		2700.3.p.c.2501.3		12
45.23	even	12		180.3.o.b.41.2	✓	12
45.32	even	12		900.3.p.c.401.5		12
45.38	even	12		1620.3.g.b.161.9		12
45.43	odd	12		1620.3.g.b.161.3		12
60.23	odd	4		2160.3.bs.b.1601.5		12
180.23	odd	12		720.3.bs.b.401.5		12
180.103	even	12		2160.3.bs.b.881.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.b.41.2	✓	12	45.23	even	12
180.3.o.b.101.2	yes	12	5.3	odd	4
540.3.o.b.341.5		12	45.13	odd	12
540.3.o.b.521.5		12	15.8	even	4
720.3.bs.b.401.5		12	180.23	odd	12
720.3.bs.b.641.5		12	20.3	even	4
900.3.p.c.101.5		12	5.2	odd	4
900.3.p.c.401.5		12	45.32	even	12
900.3.u.c.149.4		24	45.14	odd	6	inner
900.3.u.c.149.9		24	9.5	odd	6	inner
900.3.u.c.749.4		24	1.1	even	1	trivial
900.3.u.c.749.9		24	5.4	even	2	inner
1620.3.g.b.161.3		12	45.43	odd	12
1620.3.g.b.161.9		12	45.38	even	12
2160.3.bs.b.881.5		12	180.103	even	12
2160.3.bs.b.1601.5		12	60.23	odd	4
2700.3.p.c.1601.3		12	15.2	even	4
2700.3.p.c.2501.3		12	45.22	odd	12
2700.3.u.c.449.6		24	9.4	even	3
2700.3.u.c.449.7		24	45.4	even	6
2700.3.u.c.2249.6		24	15.14	odd	2
2700.3.u.c.2249.7		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.920635 + 2.85525i) q^{3} +(1.02985 + 0.594587i) q^{7} +(-7.30486 - 5.25728i) q^{9} +O(q^{10})\)	\(q+(-0.920635 + 2.85525i) q^{3} +(1.02985 + 0.594587i) q^{7} +(-7.30486 - 5.25728i) q^{9} +(3.63473 + 2.09851i) q^{11} +(12.3948 - 7.15614i) q^{13} -18.7074 q^{17} -33.8986 q^{19} +(-2.64581 + 2.39309i) q^{21} +(6.74989 + 11.6912i) q^{23} +(21.7359 - 16.0171i) q^{27} +(-30.6315 - 17.6851i) q^{29} +(4.97816 + 8.62242i) q^{31} +(-9.33802 + 8.44607i) q^{33} -19.3047i q^{37} +(9.02146 + 41.9784i) q^{39} +(-55.9648 + 32.3113i) q^{41} +(-35.9872 - 20.7772i) q^{43} +(33.6057 - 58.2068i) q^{47} +(-23.7929 - 41.2106i) q^{49} +(17.2227 - 53.4143i) q^{51} +30.0712 q^{53} +(31.2083 - 96.7889i) q^{57} +(-3.66554 + 2.11630i) q^{59} +(43.8210 - 75.9002i) q^{61} +(-4.39704 - 9.75761i) q^{63} +(-31.0106 + 17.9040i) q^{67} +(-39.5953 + 8.50932i) q^{69} +24.5173i q^{71} -11.9305i q^{73} +(2.49549 + 4.32232i) q^{77} +(-19.0858 + 33.0575i) q^{79} +(25.7220 + 76.8074i) q^{81} +(12.0489 - 20.8692i) q^{83} +(78.6957 - 71.1789i) q^{87} -44.4494i q^{89} +17.0198 q^{91} +(-29.2022 + 6.27576i) q^{93} +(-55.3688 - 31.9672i) q^{97} +(-15.5187 - 34.4381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 52 q^{9}+O(q^{10}) \) 24 * q - 52 * q^9	\( 24 q - 52 q^{9} + 96 q^{11} - 144 q^{19} - 256 q^{21} - 300 q^{29} - 24 q^{31} - 80 q^{39} + 180 q^{41} - 96 q^{49} - 288 q^{51} - 96 q^{59} - 156 q^{61} + 300 q^{69} - 240 q^{79} + 868 q^{81} + 240 q^{91} + 240 q^{99}+O(q^{100}) \) 24 * q - 52 * q^9 + 96 * q^11 - 144 * q^19 - 256 * q^21 - 300 * q^29 - 24 * q^31 - 80 * q^39 + 180 * q^41 - 96 * q^49 - 288 * q^51 - 96 * q^59 - 156 * q^61 + 300 * q^69 - 240 * q^79 + 868 * q^81 + 240 * q^91 + 240 * q^99

Introduction

L-functions

Modular forms

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Database

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