LMFDB - Embedded newform 1900.2.s.c.349.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(49,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1900.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.s (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:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.3
Root			$-1.90412 - 1.09935i$ of defining polynomial
Character	$\chi$	$=$	1900.349
Dual form			1900.2.s.c.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.315621 + 0.182224i) q^{3} -0.635552i q^{7} +(-1.43359 + 2.48305i) q^{9} +O(q^{10})$	\(q+(-0.315621 + 0.182224i) q^{3} -0.635552i q^{7} +(-1.43359 + 2.48305i) q^{9} +1.63555 q^{11} +(0.866025 + 0.500000i) q^{13} +(5.71237 - 3.29804i) q^{17} +(-0.0466721 - 4.35865i) q^{19} +(0.115813 + 0.200594i) q^{21} +(-0.750998 - 0.433589i) q^{23} -2.13828i q^{27} +(-4.54940 + 7.87979i) q^{29} -1.86718 q^{31} +(-0.516215 + 0.298037i) q^{33} -0.635552i q^{37} -0.364448 q^{39} +(-0.953328 - 1.65121i) q^{41} +(3.42991 - 1.98026i) q^{43} +(7.87979 + 4.54940i) q^{47} +6.59607 q^{49} +(-1.20196 + 2.08186i) q^{51} +(8.54523 + 4.93359i) q^{53} +(0.808981 + 1.36718i) q^{57} +(4.54940 + 7.87979i) q^{59} +(-1.13555 + 1.96683i) q^{61} +(1.57811 + 0.911120i) q^{63} +(10.7935 + 6.23163i) q^{67} +0.316041 q^{69} +(-1.25136 - 2.16743i) q^{71} +(-0.349810 + 0.201963i) q^{73} -1.03948i q^{77} +(5.36445 + 9.29150i) q^{79} +(-3.91112 - 6.77426i) q^{81} -15.8672i q^{83} -3.31604i q^{87} +(0.271104 - 0.469566i) q^{89} +(0.317776 - 0.550404i) q^{91} +(0.589321 - 0.340245i) q^{93} +(6.38253 - 3.68495i) q^{97} +(-2.34471 + 4.06116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{9}+O(q^{10}) $ 12 * q + 16 * q^9	$ 12 q + 16 q^{9} + 20 q^{11} - 32 q^{21} + 12 q^{29} + 44 q^{31} - 4 q^{39} - 12 q^{41} + 12 q^{49} - 48 q^{51} - 12 q^{59} - 14 q^{61} - 60 q^{69} + 18 q^{71} + 64 q^{79} - 46 q^{81} + 4 q^{89} + 4 q^{91} + 6 q^{99}+O(q^{100}) $ 12 * q + 16 * q^9 + 20 * q^11 - 32 * q^21 + 12 * q^29 + 44 * q^31 - 4 * q^39 - 12 * q^41 + 12 * q^49 - 48 * q^51 - 12 * q^59 - 14 * q^61 - 60 * q^69 + 18 * q^71 + 64 * q^79 - 46 * q^81 + 4 * q^89 + 4 * q^91 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.315621	+	0.182224i	−0.182224	+	0.105207i	−0.588337	−	0.808616i	$-0.700217\pi$
$3$	−0.315621	+	0.182224i	−0.182224	+	0.105207i	0.406113	+	0.913823i	$0.366884\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	0.635552i		−	0.240216i	−0.992761	−	0.120108i	$-0.961676\pi$
$7$		−	0.635552i		−	0.240216i	0.992761	−	0.120108i	$-0.0383241\pi$
$8$		0			0
$9$	−1.43359	+	2.48305i	−0.477863	+	0.827683i
$10$		0			0
$11$	1.63555			0.493137			0.246569	−	0.969125i	$-0.420697\pi$
$11$	1.63555			0.493137			0.246569	+	0.969125i	$0.420697\pi$
$12$		0			0
$13$	0.866025	+	0.500000i	0.240192	+	0.138675i	0.615265	−	0.788320i	$-0.289049\pi$
$13$	0.866025	+	0.500000i	0.240192	+	0.138675i	−0.375073	+	0.926995i	$0.622382\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.71237	−	3.29804i	1.38545	−	0.799891i	0.392654	−	0.919686i	$-0.371557\pi$
$17$	5.71237	−	3.29804i	1.38545	−	0.799891i	0.992799	+	0.119795i	$0.0382237\pi$
$18$		0			0
$19$	−0.0466721	−	4.35865i	−0.0107073	−	0.999943i
$19$	−0.0466721	−	4.35865i	−0.0107073	−	0.999943i
$20$		0			0
$21$	0.115813	+	0.200594i	0.0252724	+	0.0437731i
$22$		0			0
$23$	−0.750998	−	0.433589i	−0.156594	−	0.0904095i	0.419655	−	0.907684i	$-0.362151\pi$
$23$	−0.750998	−	0.433589i	−0.156594	−	0.0904095i	−0.576249	+	0.817274i	$0.695484\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	2.13828i		−	0.411512i
$28$		0			0
$29$	−4.54940	+	7.87979i	−0.844803	+	1.46324i	0.0409898	+	0.999160i	$0.486949\pi$
$29$	−4.54940	+	7.87979i	−0.844803	+	1.46324i	−0.885792	+	0.464082i	$0.846384\pi$
$30$		0			0
$31$	−1.86718			−0.335355			−0.167677	−	0.985842i	$-0.553627\pi$
$31$	−1.86718			−0.335355			−0.167677	+	0.985842i	$0.553627\pi$
$32$		0			0
$33$	−0.516215	+	0.298037i	−0.0898615	+	0.0518816i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	0.635552i		−	0.104484i	−0.998634	−	0.0522420i	$-0.983363\pi$
$37$		−	0.635552i		−	0.104484i	0.998634	−	0.0522420i	$-0.0166367\pi$
$38$		0			0
$39$	−0.364448			−0.0583584
$40$		0			0
$41$	−0.953328	−	1.65121i	−0.148885	−	0.257876i	0.781931	−	0.623365i	$-0.214235\pi$
$41$	−0.953328	−	1.65121i	−0.148885	−	0.257876i	−0.930816	+	0.365489i	$0.880902\pi$
$42$		0			0
$43$	3.42991	−	1.98026i	0.523057	−	0.301987i	−0.215128	−	0.976586i	$-0.569017\pi$
$43$	3.42991	−	1.98026i	0.523057	−	0.301987i	0.738184	+	0.674599i	$0.235683\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.87979	+	4.54940i	1.14939	+	0.663598i	0.948738	−	0.316065i	$-0.102362\pi$
$47$	7.87979	+	4.54940i	1.14939	+	0.663598i	0.200649	+	0.979663i	$0.435695\pi$
$48$		0			0
$49$	6.59607			0.942296
$50$		0			0
$51$	−1.20196	+	2.08186i	−0.168309	+	0.291519i
$52$		0			0
$53$	8.54523	+	4.93359i	1.17378	+	0.677681i	0.954567	−	0.297997i	$-0.0963186\pi$
$53$	8.54523	+	4.93359i	1.17378	+	0.677681i	0.219210	+	0.975678i	$0.429652\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.808981	+	1.36718i	0.107152	+	0.181087i
$58$		0			0
$59$	4.54940	+	7.87979i	0.592282	+	1.02586i	0.993924	+	0.110065i	$0.0351060\pi$
$59$	4.54940	+	7.87979i	0.592282	+	1.02586i	−0.401643	+	0.915796i	$0.631561\pi$
$60$		0			0
$61$	−1.13555	+	1.96683i	−0.145393	+	0.251827i	−0.929519	−	0.368773i	$-0.879778\pi$
$61$	−1.13555	+	1.96683i	−0.145393	+	0.251827i	0.784127	+	0.620601i	$0.213111\pi$
$62$		0			0
$63$	1.57811	+	0.911120i	0.198823	+	0.114790i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	10.7935	+	6.23163i	1.31863	+	0.761314i	0.983509	−	0.180859i	$-0.0578878\pi$
$67$	10.7935	+	6.23163i	1.31863	+	0.761314i	0.335126	+	0.942173i	$0.391221\pi$
$68$		0			0
$69$	0.316041			0.0380469
$70$		0			0
$71$	−1.25136	−	2.16743i	−0.148510	−	0.257226i	0.782167	−	0.623069i	$-0.214114\pi$
$71$	−1.25136	−	2.16743i	−0.148510	−	0.257226i	−0.930677	+	0.365842i	$0.880781\pi$
$72$		0			0
$73$	−0.349810	+	0.201963i	−0.0409422	+	0.0236380i	−0.520331	−	0.853964i	$-0.674192\pi$
$73$	−0.349810	+	0.201963i	−0.0409422	+	0.0236380i	0.479389	+	0.877602i	$0.340858\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	1.03948i		−	0.118460i
$78$		0			0
$79$	5.36445	+	9.29150i	0.603548	+	1.04538i	0.992279	+	0.124024i	$0.0395800\pi$
$79$	5.36445	+	9.29150i	0.603548	+	1.04538i	−0.388732	+	0.921351i	$0.627087\pi$
$80$		0			0
$81$	−3.91112	−	6.77426i	−0.434569	−	0.752695i
$82$		0			0
$83$		−	15.8672i		−	1.74165i	−0.491594	−	0.870825i	$-0.663586\pi$
$83$		−	15.8672i		−	1.74165i	0.491594	−	0.870825i	$-0.336414\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	3.31604i		−	0.355517i
$88$		0			0
$89$	0.271104	−	0.469566i	0.0287370	−	0.0497739i	−0.851299	−	0.524680i	$-0.824185\pi$
$89$	0.271104	−	0.469566i	0.0287370	−	0.0497739i	0.880036	+	0.474907i	$0.157518\pi$
$90$		0			0
$91$	0.317776	−	0.550404i	0.0333120	−	0.0576980i
$92$		0			0
$93$	0.589321	−	0.340245i	0.0611097	−	0.0352817i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.38253	−	3.68495i	0.648047	−	0.374150i	−0.139660	−	0.990199i	$-0.544601\pi$
$97$	6.38253	−	3.68495i	0.648047	−	0.374150i	0.787708	+	0.616049i	$0.211268\pi$
$98$		0			0
$99$	−2.34471	+	4.06116i	−0.235652	+	0.408161i
$100$		0			0
$101$	4.66248	−	8.07566i	0.463935	−	0.803558i	−0.535218	−	0.844714i	$-0.679771\pi$
$101$	4.66248	−	8.07566i	0.463935	−	0.803558i	0.999153	+	0.0411556i	$0.0131039\pi$
$102$		0			0
$103$		−	10.8672i		−	1.07077i	−0.844607	−	0.535387i	$-0.820166\pi$
$103$		−	10.8672i		−	1.07077i	0.844607	−	0.535387i	$-0.179834\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	11.3304i		−	1.09535i	−0.836690	−	0.547677i	$-0.815512\pi$
$107$		−	11.3304i		−	1.09535i	0.836690	−	0.547677i	$-0.184488\pi$
$108$		0			0
$109$	6.61581	+	11.4589i	0.633680	+	1.09757i	0.986793	+	0.161985i	$0.0517897\pi$
$109$	6.61581	+	11.4589i	0.633680	+	1.09757i	−0.353113	+	0.935581i	$0.614877\pi$
$110$		0			0
$111$	0.115813	+	0.200594i	0.0109925	+	0.0190395i
$112$		0			0
$113$			7.09334i			0.667286i	0.942700	+	0.333643i	$0.108278\pi$
$113$			7.09334i			0.667286i	−0.942700	+	0.333643i	$0.891722\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.48305	+	1.43359i	−0.229558	+	0.132535i
$118$		0			0
$119$	−2.09607	−	3.63051i	−0.192147	−	0.332808i
$120$		0			0
$121$	−8.32497			−0.756815
$122$		0			0
$123$	0.601781	+	0.347439i	0.0542608	+	0.0313275i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	14.0959	+	8.13828i	1.25081	+	0.722156i	0.971270	−	0.237978i	$-0.0764847\pi$
$127$	14.0959	+	8.13828i	1.25081	+	0.722156i	0.279540	+	0.960134i	$0.409818\pi$
$128$		0			0
$129$	−0.721702	+	1.25002i	−0.0635423	+	0.110059i
$130$		0			0
$131$	5.31778	+	9.21066i	0.464616	+	0.804739i	0.999184	−	0.0403866i	$-0.0128590\pi$
$131$	5.31778	+	9.21066i	0.464616	+	0.804739i	−0.534568	+	0.845126i	$0.679526\pi$
$132$		0			0
$133$	−2.77015	+	0.0296625i	−0.240202	+	0.00257207i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.02873	+	1.74864i	0.258761	+	0.149396i	0.623769	−	0.781608i	$-0.285600\pi$
$137$	3.02873	+	1.74864i	0.258761	+	0.149396i	−0.365008	+	0.931004i	$0.618934\pi$
$138$		0			0
$139$	0.367178	−	0.635970i	0.0311436	−	0.0539423i	−0.850034	−	0.526729i	$-0.823418\pi$
$139$	0.367178	−	0.635970i	0.0311436	−	0.0539423i	0.881177	+	0.472786i	$0.156752\pi$
$140$		0			0
$141$	−3.31604			−0.279261
$142$		0			0
$143$	1.41643	+	0.817776i	0.118448	+	0.0683859i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.08186	+	1.20196i	−0.171709	+	0.0991362i
$148$		0			0
$149$	5.06914	+	8.78001i	0.415280	+	0.719286i	0.995458	−	0.0952036i	$-0.0303502\pi$
$149$	5.06914	+	8.78001i	0.415280	+	0.719286i	−0.580178	+	0.814490i	$0.697017\pi$
$150$		0			0
$151$	2.81331			0.228944			0.114472	−	0.993426i	$-0.463482\pi$
$151$	2.81331			0.228944			0.114472	+	0.993426i	$0.463482\pi$
$152$		0			0
$153$			18.9121i			1.52895i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.831836	+	0.480261i	−0.0663878	+	0.0383290i	−0.532826	−	0.846225i	$-0.678870\pi$
$157$	−0.831836	+	0.480261i	−0.0663878	+	0.0383290i	0.466439	+	0.884554i	$0.345537\pi$
$158$		0			0
$159$	−3.59607			−0.285187
$160$		0			0
$161$	−0.275568	+	0.477298i	−0.0217178	+	0.0376164i
$162$		0			0
$163$			3.13828i			0.245809i	0.992418	+	0.122905i	$0.0392209\pi$
$163$			3.13828i			0.245809i	−0.992418	+	0.122905i	$0.960779\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−9.21066	−	5.31778i	−0.712742	−	0.411502i	0.0993334	−	0.995054i	$-0.468329\pi$
$167$	−9.21066	−	5.31778i	−0.712742	−	0.411502i	−0.812076	+	0.583552i	$0.801662\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$	10.8896	+	6.13262i	0.832752	+	0.468973i
$172$		0			0
$173$	10.7127	−	6.18495i	0.814468	−	0.470233i	−0.0340371	−	0.999421i	$-0.510836\pi$
$173$	10.7127	−	6.18495i	0.814468	−	0.470233i	0.848505	+	0.529187i	$0.177503\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−2.87178	−	1.65802i	−0.215856	−	0.124624i
$178$		0			0
$179$	0.324970			0.0242894			0.0121447	−	0.999926i	$-0.496134\pi$
$179$	0.324970			0.0242894			0.0121447	+	0.999926i	$0.496134\pi$
$180$		0			0
$181$	−4.40666	+	7.63255i	−0.327544	+	0.567323i	−0.982024	−	0.188756i	$-0.939554\pi$
$181$	−4.40666	+	7.63255i	−0.327544	+	0.567323i	0.654480	+	0.756079i	$0.272888\pi$
$182$		0			0
$183$		−	0.827699i		−	0.0611853i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	9.34287	−	5.39411i	0.683219	−	0.394456i
$188$		0			0
$189$	−1.35899			−0.0988519
$190$		0			0
$191$	25.1921			1.82284			0.911420	−	0.411478i	$-0.134987\pi$
$191$	25.1921			1.82284			0.911420	+	0.411478i	$0.134987\pi$
$192$		0			0
$193$	−16.3442	+	9.43632i	−1.17648	+	0.679241i	−0.955198	−	0.295969i	$-0.904358\pi$
$193$	−16.3442	+	9.43632i	−1.17648	+	0.679241i	−0.221282	+	0.975210i	$0.571024\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			7.36445i			0.524695i	0.964973	+	0.262348i	$0.0844967\pi$
$197$			7.36445i			0.524695i	−0.964973	+	0.262348i	$0.915503\pi$
$198$		0			0
$199$	1.38419	−	2.39748i	0.0981224	−	0.169953i	−0.812785	−	0.582564i	$-0.802050\pi$
$199$	1.38419	−	2.39748i	0.0981224	−	0.169953i	0.910907	+	0.412611i	$0.135383\pi$
$200$		0			0
$201$	−4.54221			−0.320383
$202$		0			0
$203$	5.00802	+	2.89138i	0.351494	+	0.202935i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.15324	−	1.24318i	0.149661	−	0.0864067i
$208$		0			0
$209$	−0.0763346	−	7.12880i	−0.00528018	−	0.493109i
$210$		0			0
$211$	−8.46325	−	14.6588i	−0.582634	−	1.00915i	−0.995166	−	0.0982088i	$-0.968689\pi$
$211$	−8.46325	−	14.6588i	−0.582634	−	1.00915i	0.412532	−	0.910943i	$-0.364645\pi$
$212$		0			0
$213$	0.789915	+	0.456057i	0.0541241	+	0.0312485i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			1.18669i			0.0805577i
$218$		0			0
$219$	0.0736051	−	0.127488i	0.00497377	−	0.00861482i
$220$		0			0
$221$	6.59607			0.443700
$222$		0			0
$223$	7.48334	−	4.32051i	0.501121	−	0.289322i	−0.228055	−	0.973648i	$-0.573237\pi$
$223$	7.48334	−	4.32051i	0.501121	−	0.289322i	0.729176	+	0.684326i	$0.239903\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	20.9265i		−	1.38894i	−0.719521	−	0.694470i	$-0.755639\pi$
$227$		−	20.9265i		−	1.38894i	0.719521	−	0.694470i	$-0.244361\pi$
$228$		0			0
$229$	−22.3754			−1.47861			−0.739303	−	0.673373i	$-0.764845\pi$
$229$	−22.3754			−1.47861			−0.739303	+	0.673373i	$0.764845\pi$
$230$		0			0
$231$	0.189418	+	0.328081i	0.0124628	+	0.0215862i
$232$		0			0
$233$	−16.6598	+	9.61854i	−1.09142	+	0.630132i	−0.933954	−	0.357393i	$-0.883666\pi$
$233$	−16.6598	+	9.61854i	−1.09142	+	0.630132i	−0.157466	+	0.987524i	$0.550332\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−3.38627	−	1.95506i	−0.219962	−	0.126995i
$238$		0			0
$239$	2.13282			0.137961			0.0689804	−	0.997618i	$-0.478025\pi$
$239$	2.13282			0.137961			0.0689804	+	0.997618i	$0.478025\pi$
$240$		0			0
$241$	−12.2316	+	21.1858i	−0.787908	+	1.36470i	0.139338	+	0.990245i	$0.455503\pi$
$241$	−12.2316	+	21.1858i	−0.787908	+	1.36470i	−0.927246	+	0.374452i	$0.877831\pi$
$242$		0			0
$243$	8.02428	+	4.63282i	0.514758	+	0.297196i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.13891	−	3.79804i	0.136095	−	0.241663i
$248$		0			0
$249$	2.89138	+	5.00802i	0.183234	+	0.317370i
$250$		0			0
$251$	−1.64002	+	2.84059i	−0.103517	+	0.179297i	−0.913131	−	0.407666i	$-0.866343\pi$
$251$	−1.64002	+	2.84059i	−0.103517	+	0.179297i	0.809614	+	0.586962i	$0.199676\pi$
$252$		0			0
$253$	−1.22830	−	0.709157i	−0.0772223	−	0.0445843i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.61258	−	3.81778i	−0.412482	−	0.238146i	0.279374	−	0.960182i	$-0.409873\pi$
$257$	−6.61258	−	3.81778i	−0.412482	−	0.238146i	−0.691855	+	0.722036i	$0.743206\pi$
$258$		0			0
$259$	−0.403926			−0.0250988
$260$		0			0
$261$	−13.0439	−	22.5928i	−0.807400	−	1.39846i
$262$		0			0
$263$	12.7556	−	7.36445i	0.786544	−	0.454111i	−0.0522005	−	0.998637i	$-0.516624\pi$
$263$	12.7556	−	7.36445i	0.786544	−	0.454111i	0.838744	+	0.544525i	$0.183290\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			0.197607i			0.0120933i
$268$		0			0
$269$	−6.73163	−	11.6595i	−0.410434	−	0.710893i	0.584503	−	0.811392i	$-0.301290\pi$
$269$	−6.73163	−	11.6595i	−0.410434	−	0.710893i	−0.994937	+	0.100498i	$0.967956\pi$
$270$		0			0
$271$	−1.93086	−	3.34435i	−0.117291	−	0.203155i	0.801402	−	0.598126i	$-0.204088\pi$
$271$	−1.93086	−	3.34435i	−0.117291	−	0.203155i	−0.918693	+	0.394971i	$0.870754\pi$
$272$		0			0
$273$			0.231626i			0.0140186i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			24.2766i			1.45864i	0.684174	+	0.729319i	$0.260163\pi$
$277$			24.2766i			1.45864i	−0.684174	+	0.729319i	$0.739837\pi$
$278$		0			0
$279$	2.67676	−	4.63629i	0.160254	−	0.277568i
$280$		0			0
$281$	−0.248635	+	0.430649i	−0.0148323	+	0.0256904i	−0.873346	−	0.487100i	$-0.838055\pi$
$281$	−0.248635	+	0.430649i	−0.0148323	+	0.0256904i	0.858514	+	0.512790i	$0.171388\pi$
$282$		0			0
$283$	−13.1273	+	7.57906i	−0.780338	+	0.450529i	−0.836550	−	0.547890i	$-0.815431\pi$
$283$	−13.1273	+	7.57906i	−0.780338	+	0.450529i	0.0562118	+	0.998419i	$0.482098\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.04943	+	0.605889i	−0.0619460	+	0.0357645i
$288$		0			0
$289$	13.2541	−	22.9568i	0.779653	−	1.35040i
$290$		0			0
$291$	−1.34297	+	2.32610i	−0.0787265	+	0.136358i
$292$		0			0
$293$		−	13.4094i		−	0.783385i	−0.920096	−	0.391692i	$-0.871890\pi$
$293$		−	13.4094i		−	0.783385i	0.920096	−	0.391692i	$-0.128110\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	3.49727i		−	0.202932i
$298$		0			0
$299$	−0.433589	−	0.750998i	−0.0250751	−	0.0434313i
$300$		0			0
$301$	−1.25856	−	2.17989i	−0.0725421	−	0.125647i
$302$		0			0
$303$			3.39847i			0.195237i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−27.8917	+	16.1033i	−1.59186	+	0.919062i	−0.598875	+	0.800843i	$0.704385\pi$
$307$	−27.8917	+	16.1033i	−1.59186	+	0.919062i	−0.992988	+	0.118219i	$0.962281\pi$
$308$		0			0
$309$	1.98026	+	3.42991i	0.112653	+	0.195121i
$310$		0			0
$311$	12.3699			0.701433			0.350717	−	0.936482i	$-0.385938\pi$
$311$	12.3699			0.701433			0.350717	+	0.936482i	$0.385938\pi$
$312$		0			0
$313$	−21.4672	−	12.3941i	−1.21340	−	0.700557i	−0.249901	−	0.968271i	$-0.580398\pi$
$313$	−21.4672	−	12.3941i	−1.21340	−	0.700557i	−0.963498	+	0.267715i	$0.913732\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.33115	+	3.65529i	0.355593	+	0.205302i	0.667146	−	0.744927i	$-0.267516\pi$
$317$	6.33115	+	3.65529i	0.355593	+	0.205302i	−0.311553	+	0.950229i	$0.600849\pi$
$318$		0			0
$319$	−7.44078	+	12.8878i	−0.416604	+	0.721579i
$320$		0			0
$321$	2.06468	+	3.57612i	0.115239	+	0.199600i
$322$		0			0
$323$	−14.6416	−	24.7443i	−0.814680	−	1.37681i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−4.17618	−	2.41112i	−0.230943	−	0.133335i
$328$		0			0
$329$	2.89138	−	5.00802i	0.159407	−	0.276101i
$330$		0			0
$331$	18.4722			1.01532			0.507661	−	0.861557i	$-0.330510\pi$
$331$	18.4722			1.01532			0.507661	+	0.861557i	$0.330510\pi$
$332$		0			0
$333$	1.57811	+	0.911120i	0.0864797	+	0.0499291i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−26.3819	+	15.2316i	−1.43712	+	0.829720i	−0.997648	−	0.0685388i	$-0.978166\pi$
$337$	−26.3819	+	15.2316i	−1.43712	+	0.829720i	−0.439468	+	0.898258i	$0.644833\pi$
$338$		0			0
$339$	−1.29258	−	2.23881i	−0.0702032	−	0.121595i
$340$		0			0
$341$	−3.05387			−0.165376
$342$		0			0
$343$		−	8.64101i		−	0.466571i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−20.1970	+	11.6608i	−1.08423	+	0.625982i	−0.932035	−	0.362368i	$-0.881968\pi$
$347$	−20.1970	+	11.6608i	−1.08423	+	0.625982i	−0.152197	+	0.988350i	$0.548635\pi$
$348$		0			0
$349$	17.6894			0.946893			0.473446	−	0.880823i	$-0.343010\pi$
$349$	17.6894			0.946893			0.473446	+	0.880823i	$0.343010\pi$
$350$		0			0
$351$	1.06914	−	1.85181i	0.0570665	−	0.0988421i
$352$		0			0
$353$		−	7.13828i		−	0.379932i	−0.981791	−	0.189966i	$-0.939162\pi$
$353$		−	7.13828i		−	0.379932i	0.981791	−	0.189966i	$-0.0608378\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.32313	+	0.763910i	0.0700275	+	0.0404304i
$358$		0			0
$359$	−15.0719	−	26.1052i	−0.795463	−	1.37778i	−0.922545	−	0.385890i	$-0.873894\pi$
$359$	−15.0719	−	26.1052i	−0.795463	−	1.37778i	0.127082	−	0.991892i	$-0.459439\pi$
$360$		0			0
$361$	−18.9956	+	0.406855i	−0.999771	+	0.0214134i
$362$		0			0
$363$	2.62754	−	1.51701i	0.137910	−	0.0796224i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−26.1566	−	15.1015i	−1.36536	−	0.788294i	−0.375033	−	0.927012i	$-0.622369\pi$
$367$	−26.1566	−	15.1015i	−1.36536	−	0.788294i	−0.990332	+	0.138718i	$0.955702\pi$
$368$		0			0
$369$	5.46672			0.284586
$370$		0			0
$371$	3.13555	−	5.43094i	0.162790	−	0.281960i
$372$		0			0
$373$			29.0449i			1.50389i	0.659226	+	0.751945i	$0.270884\pi$
$373$			29.0449i			1.50389i	−0.659226	+	0.751945i	$0.729116\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.87979	+	4.54940i	−0.405830	+	0.234306i
$378$		0			0
$379$	−2.76837			−0.142202			−0.0711009	−	0.997469i	$-0.522651\pi$
$379$	−2.76837			−0.142202			−0.0711009	+	0.997469i	$0.522651\pi$
$380$		0			0
$381$	−5.93196			−0.303904
$382$		0			0
$383$	23.0453	−	13.3052i	1.17756	−	0.679866i	0.222112	−	0.975021i	$-0.428705\pi$
$383$	23.0453	−	13.3052i	1.17756	−	0.679866i	0.955449	+	0.295156i	$0.0953715\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			11.3555i			0.577233i
$388$		0			0
$389$	−2.77830	+	4.81215i	−0.140865	+	0.243986i	−0.927823	−	0.373021i	$-0.878322\pi$
$389$	−2.77830	+	4.81215i	−0.140865	+	0.243986i	0.786957	+	0.617007i	$0.211655\pi$
$390$		0			0
$391$	−5.71997			−0.289271
$392$		0			0
$393$	−3.35681	−	1.93805i	−0.169328	−	0.0977618i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.35083	+	1.35725i	−0.117985	+	0.0681186i	−0.557831	−	0.829955i	$-0.688366\pi$
$397$	−2.35083	+	1.35725i	−0.117985	+	0.0681186i	0.439846	+	0.898073i	$0.355033\pi$
$398$		0			0
$399$	0.868912	−	0.514150i	0.0435000	−	0.0257397i
$400$		0			0
$401$	8.94078	+	15.4859i	0.446481	+	0.773328i	0.998154	−	0.0607322i	$-0.0193436\pi$
$401$	8.94078	+	15.4859i	0.446481	+	0.773328i	−0.551673	+	0.834061i	$0.686010\pi$
$402$		0			0
$403$	−1.61702	−	0.933589i	−0.0805497	−	0.0465054i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	1.03948i		−	0.0515250i
$408$		0			0
$409$	13.1625	−	22.7981i	0.650843	−	1.12729i	−0.332076	−	0.943253i	$-0.607749\pi$
$409$	13.1625	−	22.7981i	0.650843	−	1.12729i	0.982919	−	0.184040i	$-0.0589177\pi$
$410$		0			0
$411$	−1.27457			−0.0628701
$412$		0			0
$413$	5.00802	−	2.89138i	0.246428	−	0.142276i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			0.267634i			0.0131061i
$418$		0			0
$419$	−15.3250			−0.748674			−0.374337	−	0.927293i	$-0.622130\pi$
$419$	−15.3250			−0.748674			−0.374337	+	0.927293i	$0.622130\pi$
$420$		0			0
$421$	−10.9166	−	18.9081i	−0.532042	−	0.921523i	−0.999300	−	0.0374023i	$-0.988092\pi$
$421$	−10.9166	−	18.9081i	−0.532042	−	0.921523i	0.467259	−	0.884121i	$-0.345242\pi$
$422$		0			0
$423$	−22.5928	+	13.0439i	−1.09850	+	0.634218i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	1.25002	+	0.721702i	0.0604929	+	0.0349256i
$428$		0			0
$429$	−0.596074			−0.0287787
$430$		0			0
$431$	−11.6427	+	20.1658i	−0.560811	+	0.971354i	0.436615	+	0.899649i	$0.356177\pi$
$431$	−11.6427	+	20.1658i	−0.560811	+	0.971354i	−0.997426	+	0.0717050i	$0.977156\pi$
$432$		0			0
$433$	3.37854	+	1.95060i	0.162362	+	0.0937398i	0.578979	−	0.815342i	$-0.303451\pi$
$433$	3.37854	+	1.95060i	0.162362	+	0.0937398i	−0.416617	+	0.909082i	$0.636784\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.85481	+	3.29357i	−0.0887276	+	0.157553i
$438$		0			0
$439$	−9.73882	−	16.8681i	−0.464808	−	0.805072i	0.534384	−	0.845242i	$-0.320543\pi$
$439$	−9.73882	−	16.8681i	−0.464808	−	0.805072i	−0.999193	+	0.0401697i	$0.987210\pi$
$440$		0			0
$441$	−9.45606	+	16.3784i	−0.450288	+	0.779922i
$442$		0			0
$443$	−1.65121	−	0.953328i	−0.0784515	−	0.0452940i	0.460261	−	0.887784i	$-0.347756\pi$
$443$	−1.65121	−	0.953328i	−0.0784515	−	0.0452940i	−0.538713	+	0.842490i	$0.681089\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−3.19986	−	1.84744i	−0.151348	−	0.0873808i
$448$		0			0
$449$	8.05933			0.380343			0.190172	−	0.981751i	$-0.439096\pi$
$449$	8.05933			0.380343			0.190172	+	0.981751i	$0.439096\pi$
$450$		0			0
$451$	−1.55922	−	2.70064i	−0.0734207	−	0.127168i
$452$		0			0
$453$	−0.887941	+	0.512653i	−0.0417191	+	0.0240865i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	11.3250i		−	0.529760i	−0.964281	−	0.264880i	$-0.914668\pi$
$457$		−	11.3250i		−	0.529760i	0.964281	−	0.264880i	$-0.0853323\pi$
$458$		0			0
$459$	−7.05213	−	12.2146i	−0.329165	−	0.570131i
$460$		0			0
$461$	−10.0521	−	17.4108i	−0.468174	−	0.810902i	0.531164	−	0.847269i	$-0.321755\pi$
$461$	−10.0521	−	17.4108i	−0.468174	−	0.810902i	−0.999338	+	0.0363671i	$0.988421\pi$
$462$		0			0
$463$			1.33043i			0.0618303i	0.999522	+	0.0309151i	$0.00984216\pi$
$463$			1.33043i			0.0618303i	−0.999522	+	0.0309151i	$0.990158\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	10.0844i		−	0.466651i	−0.972399	−	0.233326i	$-0.925039\pi$
$467$		−	10.0844i		−	0.466651i	0.972399	−	0.233326i	$-0.0749608\pi$
$468$		0			0
$469$	3.96052	−	6.85982i	0.182880	−	0.316757i
$470$		0			0
$471$	0.175030	−	0.303161i	0.00806496	−	0.0139689i
$472$		0			0
$473$	5.60980	−	3.23882i	0.257939	−	0.148921i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−24.5007	+	14.1455i	−1.12181	+	0.647677i
$478$		0			0
$479$	4.44078	−	7.69166i	0.202905	−	0.351441i	−0.746559	−	0.665320i	$-0.768295\pi$
$479$	4.44078	−	7.69166i	0.202905	−	0.351441i	0.949463	+	0.313879i	$0.101629\pi$
$480$		0			0
$481$	0.317776	−	0.550404i	0.0144893	−	0.0250963i
$482$		0			0
$483$		−	0.200861i		−	0.00913947i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	5.32497i		−	0.241297i	−0.992695	−	0.120649i	$-0.961503\pi$
$487$		−	5.32497i		−	0.241297i	0.992695	−	0.120649i	$-0.0384975\pi$
$488$		0			0
$489$	−0.571870	−	0.990508i	−0.0258609	−	0.0447923i
$490$		0			0
$491$	9.70469	+	16.8090i	0.437967	+	0.758580i	0.997533	−	0.0702054i	$-0.0223655\pi$
$491$	9.70469	+	16.8090i	0.437967	+	0.758580i	−0.559566	+	0.828786i	$0.689032\pi$
$492$		0			0
$493$			60.0164i			2.70300i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.37751	+	0.795307i	−0.0617899	+	0.0356744i
$498$		0			0
$499$	5.79357	+	10.0348i	0.259356	+	0.449218i	0.966070	−	0.258282i	$-0.0831564\pi$
$499$	5.79357	+	10.0348i	0.259356	+	0.449218i	−0.706714	+	0.707500i	$0.749823\pi$
$500$		0			0
$501$	3.87611			0.173172
$502$		0			0
$503$	−30.4012	−	17.5521i	−1.35552	−	0.782611i	−0.366505	−	0.930416i	$-0.619446\pi$
$503$	−30.4012	−	17.5521i	−1.35552	−	0.782611i	−0.989017	+	0.147805i	$0.952779\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.78746	+	2.18669i	0.168207	+	0.0971142i
$508$		0			0
$509$	−7.93359	+	13.7414i	−0.351650	+	0.609076i	−0.986539	−	0.163528i	$-0.947713\pi$
$509$	−7.93359	+	13.7414i	−0.351650	+	0.609076i	0.634889	+	0.772604i	$0.281046\pi$
$510$		0			0
$511$	0.128358	+	0.222323i	0.00567823	+	0.00983498i
$512$		0			0
$513$	−9.32002	+	0.0997981i	−0.411489	+	0.00440619i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	12.8878	+	7.44078i	0.566805	+	0.327245i
$518$		0			0
$519$	−2.25409	+	3.90421i	−0.0989438	+	0.171376i
$520$		0			0
$521$	36.6949			1.60763			0.803816	−	0.594878i	$-0.202800\pi$
$521$	36.6949			1.60763			0.803816	+	0.594878i	$0.202800\pi$
$522$		0			0
$523$	26.8687	+	15.5127i	1.17489	+	0.678321i	0.954826	−	0.297165i	$-0.0960412\pi$
$523$	26.8687	+	15.5127i	1.17489	+	0.678321i	0.220060	+	0.975486i	$0.429375\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−10.6660	+	6.15802i	−0.464618	+	0.268248i
$528$		0			0
$529$	−11.1240	−	19.2673i	−0.483652	−	0.837710i
$530$		0			0
$531$	−26.0879			−1.13212
$532$		0			0
$533$		−	1.90666i		−	0.0825864i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.102567	+	0.0592173i	−0.00442611	+	0.00255542i
$538$		0			0
$539$	10.7882			0.464682
$540$		0			0
$541$	3.79357	−	6.57066i	0.163098	−	0.282495i	−0.772880	−	0.634552i	$-0.781185\pi$
$541$	3.79357	−	6.57066i	0.163098	−	0.282495i	0.935978	+	0.352058i	$0.114518\pi$
$542$		0			0
$543$		−	3.21199i		−	0.137840i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−26.6587	−	15.3914i	−1.13984	−	0.658088i	−0.193450	−	0.981110i	$-0.561968\pi$
$547$	−26.6587	−	15.3914i	−1.13984	−	0.658088i	−0.946391	+	0.323022i	$0.895301\pi$
$548$		0			0
$549$	−3.25583	−	5.63926i	−0.138955	−	0.240678i
$550$		0			0
$551$	34.5576	+	19.4615i	1.47220	+	0.829087i
$552$		0			0
$553$	5.90523	−	3.40939i	0.251116	−	0.144982i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	26.9106	+	15.5369i	1.14024	+	0.658318i	0.946490	−	0.322733i	$-0.104602\pi$
$557$	26.9106	+	15.5369i	1.14024	+	0.658318i	0.193750	+	0.981051i	$0.437935\pi$
$558$		0			0
$559$	3.96052			0.167512
$560$		0			0
$561$	−1.96587	+	3.40499i	−0.0829992	+	0.143759i
$562$		0			0
$563$		−	23.2766i		−	0.980990i	−0.871444	−	0.490495i	$-0.836816\pi$
$563$		−	23.2766i		−	0.980990i	0.871444	−	0.490495i	$-0.163184\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−4.30539	+	2.48572i	−0.180810	+	0.104390i
$568$		0			0
$569$	−24.1976			−1.01442			−0.507208	−	0.861824i	$-0.669322\pi$
$569$	−24.1976			−1.01442			−0.507208	+	0.861824i	$0.669322\pi$
$570$		0			0
$571$	29.8475			1.24908			0.624540	−	0.780992i	$-0.285286\pi$
$571$	29.8475			1.24908			0.624540	+	0.780992i	$0.285286\pi$
$572$		0			0
$573$	−7.95118	+	4.59061i	−0.332165	+	0.191776i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	33.7882i		−	1.40662i	−0.710882	−	0.703311i	$-0.751704\pi$
$577$		−	33.7882i		−	1.40662i	0.710882	−	0.703311i	$-0.248296\pi$
$578$		0			0
$579$	3.43905	−	5.95661i	0.142922	−	0.247548i
$580$		0			0
$581$	−10.0844			−0.418372
$582$		0			0
$583$	13.9762	+	8.06914i	0.578833	+	0.334190i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	26.5825	−	15.3474i	1.09718	−	0.633457i	0.161700	−	0.986840i	$-0.448302\pi$
$587$	26.5825	−	15.3474i	1.09718	−	0.633457i	0.935479	+	0.353383i	$0.114969\pi$
$588$		0			0
$589$	0.0871451	+	8.13837i	0.00359075	+	0.335336i
$590$		0			0
$591$	−1.34198	−	2.32438i	−0.0552017	−	0.0956121i
$592$		0			0
$593$	−6.05745	−	3.49727i	−0.248750	−	0.143616i	0.370442	−	0.928856i	$-0.379206\pi$
$593$	−6.05745	−	3.49727i	−0.248750	−	0.143616i	−0.619192	+	0.785240i	$0.712540\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			1.00893i			0.0412927i
$598$		0			0
$599$	−2.26837	+	3.92894i	−0.0926833	+	0.160532i	−0.908639	−	0.417582i	$-0.862878\pi$
$599$	−2.26837	+	3.92894i	−0.0926833	+	0.160532i	0.815956	+	0.578114i	$0.196211\pi$
$600$		0			0
$601$	16.0790			0.655874			0.327937	−	0.944700i	$-0.393647\pi$
$601$	16.0790			0.655874			0.327937	+	0.944700i	$0.393647\pi$
$602$		0			0
$603$	−30.9469	+	17.8672i	−1.26025	+	0.727608i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			34.0702i			1.38287i	0.722439	+	0.691434i	$0.243021\pi$
$607$			34.0702i			1.38287i	−0.722439	+	0.691434i	$0.756979\pi$
$608$		0			0
$609$	−2.10752			−0.0854009
$610$		0			0
$611$	4.54940	+	7.87979i	0.184049	+	0.318782i
$612$		0			0
$613$	−34.1544	+	19.7191i	−1.37949	+	0.796446i	−0.992097	−	0.125471i	$-0.959956\pi$
$613$	−34.1544	+	19.7191i	−1.37949	+	0.796446i	−0.387388	+	0.921917i	$0.626623\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−33.9928	−	19.6257i	−1.36850	−	0.790102i	−0.377761	−	0.925903i	$-0.623306\pi$
$617$	−33.9928	−	19.6257i	−1.36850	−	0.790102i	−0.990736	+	0.135801i	$0.956639\pi$
$618$		0			0
$619$	−24.3644			−0.979290			−0.489645	−	0.871922i	$-0.662874\pi$
$619$	−24.3644			−0.979290			−0.489645	+	0.871922i	$0.662874\pi$
$620$		0			0
$621$	−0.927135	+	1.60584i	−0.0372046	+	0.0644403i
$622$		0			0
$623$	−0.298433	−	0.172301i	−0.0119565	−	0.00690308i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.32313	+	2.23609i	0.0528408	+	0.0893008i
$628$		0			0
$629$	−2.09607	−	3.63051i	−0.0835759	−	0.144758i
$630$		0			0
$631$	17.6949	−	30.6484i	0.704422	−	1.22009i	−0.262478	−	0.964938i	$-0.584540\pi$
$631$	17.6949	−	30.6484i	0.704422	−	1.22009i	0.966900	−	0.255157i	$-0.0821270\pi$
$632$		0			0
$633$	5.34236	+	3.08442i	0.212340	+	0.122595i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	5.71237	+	3.29804i	0.226332	+	0.130673i
$638$		0			0
$639$	7.17577			0.283869
$640$		0			0
$641$	−17.8546	−	30.9251i	−0.705216	−	1.22147i	−0.966614	−	0.256238i	$-0.917517\pi$
$641$	−17.8546	−	30.9251i	−0.705216	−	1.22147i	0.261398	−	0.965231i	$-0.415816\pi$
$642$		0			0
$643$	18.2816	−	10.5549i	0.720954	−	0.416243i	−0.0941496	−	0.995558i	$-0.530013\pi$
$643$	18.2816	−	10.5549i	0.720954	−	0.416243i	0.815104	+	0.579315i	$0.196680\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	43.7058i		−	1.71825i	−0.511764	−	0.859126i	$-0.671008\pi$
$647$		−	43.7058i		−	1.71825i	0.511764	−	0.859126i	$-0.328992\pi$
$648$		0			0
$649$	7.44078	+	12.8878i	0.292076	+	0.505891i
$650$		0			0
$651$	−0.216243	−	0.374544i	−0.00847524	−	0.0146795i
$652$		0			0
$653$		−	24.1887i		−	0.946576i	−0.880908	−	0.473288i	$-0.843067\pi$
$653$		−	24.1887i		−	0.946576i	0.880908	−	0.473288i	$-0.156933\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	1.15813i		−	0.0451829i
$658$		0			0
$659$	16.9956	−	29.4373i	0.662056	−	1.14672i	−0.318018	−	0.948085i	$-0.603017\pi$
$659$	16.9956	−	29.4373i	0.662056	−	1.14672i	0.980074	−	0.198630i	$-0.0636494\pi$
$660$		0			0
$661$	−2.27830	+	3.94613i	−0.0886155	+	0.153487i	−0.906926	−	0.421290i	$-0.861578\pi$
$661$	−2.27830	+	3.94613i	−0.0886155	+	0.153487i	0.818311	+	0.574776i	$0.194911\pi$
$662$		0			0
$663$	−2.08186	+	1.20196i	−0.0808528	+	0.0466804i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	6.83318	−	3.94514i	0.264582	−	0.152756i
$668$		0			0
$669$	−1.57460	+	2.72729i	−0.0608775	+	0.105443i
$670$		0			0
$671$	−1.85725	+	3.21686i	−0.0716985	+	0.124185i
$672$		0			0
$673$		−	22.7487i		−	0.876900i	−0.898756	−	0.438450i	$-0.855528\pi$
$673$		−	22.7487i		−	0.876900i	0.898756	−	0.438450i	$-0.144472\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			15.6949i			0.603203i	0.953434	+	0.301602i	$0.0975212\pi$
$677$			15.6949i			0.603203i	−0.953434	+	0.301602i	$0.902479\pi$
$678$		0			0
$679$	−2.34198	−	4.05643i	−0.0898769	−	0.155671i
$680$		0			0
$681$	3.81331	+	6.60485i	0.146126	+	0.253098i
$682$		0			0
$683$		−	8.82770i		−	0.337783i	−0.985635	−	0.168891i	$-0.945981\pi$
$683$		−	8.82770i		−	0.337783i	0.985635	−	0.168891i	$-0.0540187\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	7.06214	−	4.07733i	0.269438	−	0.155560i
$688$		0			0
$689$	4.93359	+	8.54523i	0.187955	+	0.325547i
$690$		0			0
$691$	−23.0198			−0.875716			−0.437858	−	0.899044i	$-0.644263\pi$
$691$	−23.0198			−0.875716			−0.437858	+	0.899044i	$0.644263\pi$
$692$		0			0
$693$	2.58107	+	1.49018i	0.0980469	+	0.0566074i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−10.8915	−	6.28822i	−0.412546	−	0.238183i
$698$		0			0
$699$	3.50546	−	6.07163i	0.132589	−	0.229650i
$700$		0			0
$701$	4.95606	+	8.58414i	0.187188	+	0.324219i	0.944312	−	0.329053i	$-0.106729\pi$
$701$	4.95606	+	8.58414i	0.187188	+	0.324219i	−0.757124	+	0.653271i	$0.773396\pi$
$702$		0			0
$703$	−2.77015	+	0.0296625i	−0.104478	+	0.00111874i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.13250	−	2.96325i	−0.193028	−	0.111445i
$708$		0			0
$709$	−18.0521	+	31.2672i	−0.677962	+	1.17426i	0.297632	+	0.954681i	$0.403803\pi$
$709$	−18.0521	+	31.2672i	−0.677962	+	1.17426i	−0.975594	+	0.219584i	$0.929530\pi$
$710$		0			0
$711$	−30.7617			−1.15365
$712$		0			0
$713$	1.40225	+	0.809587i	0.0525145	+	0.0303193i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.673164	+	0.388651i	−0.0251398	+	0.0145145i
$718$		0			0
$719$	−9.50546	−	16.4639i	−0.354494	−	0.614001i	0.632537	−	0.774530i	$-0.282013\pi$
$719$	−9.50546	−	16.4639i	−0.354494	−	0.614001i	−0.987031	+	0.160529i	$0.948680\pi$
$720$		0			0
$721$	−6.90666			−0.257217
$722$		0			0
$723$		−	8.91558i		−	0.331574i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.50024	−	1.44351i	0.0927286	−	0.0535369i	−0.452919	−	0.891552i	$-0.649617\pi$
$727$	2.50024	−	1.44351i	0.0927286	−	0.0535369i	0.545647	+	0.838015i	$0.316284\pi$
$728$		0			0
$729$	20.0899			0.744069
$730$		0			0
$731$	13.0619	−	22.6240i	0.483114	−	0.836777i
$732$		0			0
$733$			44.9463i			1.66013i	0.557666	+	0.830066i	$0.311697\pi$
$733$			44.9463i			1.66013i	−0.557666	+	0.830066i	$0.688303\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	17.6533	+	10.1921i	0.650268	+	0.375433i
$738$		0			0
$739$	25.4956	+	44.1597i	0.937872	+	1.62444i	0.769430	+	0.638731i	$0.220540\pi$
$739$	25.4956	+	44.1597i	0.937872	+	1.62444i	0.168442	+	0.985711i	$0.446126\pi$
$740$		0			0
$741$	0.0170096	+	1.58850i	0.000624862	+	0.0583550i
$742$		0			0
$743$	16.3472	−	9.43805i	0.599720	−	0.346249i	−0.169211	−	0.985580i	$-0.554122\pi$
$743$	16.3472	−	9.43805i	0.599720	−	0.346249i	0.768931	+	0.639331i	$0.220789\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	39.3990	+	22.7470i	1.44153	+	0.832270i
$748$		0			0
$749$	−7.20108			−0.263122
$750$		0			0
$751$	−13.0127	+	22.5386i	−0.474838	+	0.822444i	−0.999585	−	0.0288143i	$-0.990827\pi$
$751$	−13.0127	+	22.5386i	−0.474838	+	0.822444i	0.524746	+	0.851259i	$0.324160\pi$
$752$		0			0
$753$		−	1.19540i		−	0.0435629i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	10.3192	−	5.95779i	0.375058	−	0.216540i	−0.300608	−	0.953748i	$-0.597190\pi$
$757$	10.3192	−	5.95779i	0.375058	−	0.216540i	0.675666	+	0.737208i	$0.263856\pi$
$758$		0			0
$759$	0.516902			0.0187623
$760$		0			0
$761$	−2.39500			−0.0868186			−0.0434093	−	0.999057i	$-0.513822\pi$
$761$	−2.39500			−0.0868186			−0.0434093	+	0.999057i	$0.513822\pi$
$762$		0			0
$763$	7.28274	−	4.20469i	0.263653	−	0.152220i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			9.09880i			0.328539i
$768$		0			0
$769$	2.66248	−	4.61156i	0.0960117	−	0.166297i	−0.814019	−	0.580839i	$-0.802725\pi$
$769$	2.66248	−	4.61156i	0.0960117	−	0.166297i	0.910030	+	0.414542i	$0.136058\pi$
$770$		0			0
$771$	2.78276			0.100219
$772$		0			0
$773$	21.2153	+	12.2486i	0.763060	+	0.440553i	0.830393	−	0.557178i	$-0.188116\pi$
$773$	21.2153	+	12.2486i	0.763060	+	0.440553i	−0.0673334	+	0.997731i	$0.521449\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.127488	−	0.0736051i	0.00457360	−	0.00264057i
$778$		0			0
$779$	−7.15256	+	4.23229i	−0.256267	+	0.151637i
$780$		0			0
$781$	−2.04667	−	3.54494i	−0.0732357	−	0.126848i
$782$		0			0
$783$	16.8492	+	9.72790i	0.602142	+	0.347647i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			20.5171i			0.731356i	0.930741	+	0.365678i	$0.119163\pi$
$787$			20.5171i			0.731356i	−0.930741	+	0.365678i	$0.880837\pi$
$788$		0			0
$789$	−2.68396	+	4.64875i	−0.0955515	+	0.165500i
$790$		0			0
$791$	4.50819			0.160293
$792$		0			0
$793$	−1.96683	+	1.13555i	−0.0698443	+	0.0403246i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			23.0144i			0.815211i	0.913158	+	0.407606i	$0.133636\pi$
$797$			23.0144i			0.815211i	−0.913158	+	0.407606i	$0.866364\pi$
$798$		0			0
$799$	60.0164			2.12323
$800$		0			0
$801$	0.777303	+	1.34633i	0.0274647	+	0.0475702i
$802$		0			0
$803$	−0.572133	+	0.330321i	−0.0201901	+	0.0116568i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.24929	+	2.45333i	0.149582	+	0.0863612i
$808$		0			0
$809$	28.3195			0.995661			0.497830	−	0.867274i	$-0.334130\pi$
$809$	28.3195			0.995661			0.497830	+	0.867274i	$0.334130\pi$
$810$		0			0
$811$	−19.7766	+	34.2540i	−0.694449	+	1.20282i	0.275917	+	0.961181i	$0.411019\pi$
$811$	−19.7766	+	34.2540i	−0.694449	+	1.20282i	−0.970366	+	0.241640i	$0.922315\pi$
$812$		0			0
$813$	1.21884	+	0.703698i	0.0427466	+	0.0246798i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−8.79134	−	14.8574i	−0.307570	−	0.519793i
$818$		0			0
$819$	0.911120	+	1.57811i	0.0318371	+	0.0551435i
$820$		0			0
$821$	−15.4013	+	26.6758i	−0.537509	+	0.930993i	0.461528	+	0.887126i	$0.347301\pi$
$821$	−15.4013	+	26.6758i	−0.537509	+	0.930993i	−0.999037	+	0.0438677i	$0.986032\pi$
$822$		0			0
$823$	13.8564	+	8.00000i	0.483004	+	0.278862i	0.721668	−	0.692240i	$-0.243376\pi$
$823$	13.8564	+	8.00000i	0.483004	+	0.278862i	−0.238664	+	0.971102i	$0.576709\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	17.5678	+	10.1427i	0.610891	+	0.352698i	0.773314	−	0.634023i	$-0.218598\pi$
$827$	17.5678	+	10.1427i	0.610891	+	0.352698i	−0.162423	+	0.986721i	$0.551931\pi$
$828$		0			0
$829$	−44.0792			−1.53093			−0.765466	−	0.643476i	$-0.777492\pi$
$829$	−44.0792			−1.53093			−0.765466	+	0.643476i	$0.777492\pi$
$830$		0			0
$831$	−4.42377	−	7.66220i	−0.153459	−	0.265799i
$832$		0			0
$833$	37.6792	−	21.7541i	1.30551	−	0.753735i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			3.99255i			0.138003i
$838$		0			0
$839$	26.9534	+	46.6847i	0.930536	+	1.61174i	0.782407	+	0.622767i	$0.213992\pi$
$839$	26.9534	+	46.6847i	0.930536	+	1.61174i	0.148129	+	0.988968i	$0.452675\pi$
$840$		0			0
$841$	−26.8941	−	46.5820i	−0.927383	−	1.60627i
$842$		0			0
$843$		−	0.181229i		−	0.00624187i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			5.29095i			0.181799i
$848$		0			0
$849$	2.76218	−	4.78423i	0.0947976	−	0.164194i
$850$		0			0
$851$	−0.275568	+	0.477298i	−0.00944636	+	0.0163616i
$852$		0			0
$853$	23.4388	−	13.5324i	0.802529	−	0.463340i	−0.0418258	−	0.999125i	$-0.513317\pi$
$853$	23.4388	−	13.5324i	0.802529	−	0.463340i	0.844355	+	0.535785i	$0.179984\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.90424	−	1.67676i	0.0992070	−	0.0572772i	−0.449576	−	0.893242i	$-0.648425\pi$
$857$	2.90424	−	1.67676i	0.0992070	−	0.0572772i	0.548783	+	0.835965i	$0.315091\pi$
$858$		0			0
$859$	−26.8529	+	46.5106i	−0.916209	+	1.58692i	−0.111088	+	0.993811i	$0.535433\pi$
$859$	−26.8529	+	46.5106i	−0.916209	+	1.58692i	−0.805121	+	0.593110i	$0.797900\pi$
$860$		0			0
$861$	0.220815	−	0.382463i	0.00752536	−	0.0130343i
$862$		0			0
$863$		−	39.1527i		−	1.33277i	−0.745607	−	0.666386i	$-0.767840\pi$
$863$		−	39.1527i		−	1.33277i	0.745607	−	0.666386i	$-0.232160\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			9.66086i			0.328100i
$868$		0			0
$869$	8.77383	+	15.1967i	0.297632	+	0.515514i
$870$		0			0
$871$	6.23163	+	10.7935i	0.211151	+	0.365724i
$872$		0			0
$873$			21.1308i			0.715170i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.6793	−	14.8260i	0.867129	−	0.500637i	0.000735993	−	1.00000i	$-0.499766\pi$
$877$	25.6793	−	14.8260i	0.867129	−	0.500637i	0.866393	+	0.499362i	$0.166432\pi$
$878$		0			0
$879$	2.44351	+	4.23229i	0.0824176	+	0.142752i
$880$		0			0
$881$	43.2820			1.45821			0.729104	−	0.684403i	$-0.239937\pi$
$881$	43.2820			1.45821			0.729104	+	0.684403i	$0.239937\pi$
$882$		0			0
$883$	−49.3340	−	28.4830i	−1.66022	−	0.958529i	−0.972608	−	0.232451i	$-0.925325\pi$
$883$	−49.3340	−	28.4830i	−1.66022	−	0.958529i	−0.687613	−	0.726078i	$-0.741341\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	17.5211	+	10.1158i	0.588301	+	0.339656i	0.764425	−	0.644712i	$-0.223023\pi$
$887$	17.5211	+	10.1158i	0.588301	+	0.339656i	−0.176124	+	0.984368i	$0.556356\pi$
$888$		0			0
$889$	5.17230	−	8.95869i	0.173473	−	0.300465i
$890$		0			0
$891$	−6.39684	−	11.0797i	−0.214302	−	0.371182i
$892$		0			0
$893$	19.4615	−	34.5576i	0.651254	−	1.15643i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.273700	+	0.158021i	0.00913857	+	0.00527615i
$898$		0			0
$899$	8.49454	−	14.7130i	0.283309	−	0.490705i
$900$		0			0
$901$	65.0846			2.16828
$902$		0			0
$903$	0.794456	+	0.458679i	0.0264378	+	0.0152639i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	8.66025	−	5.00000i	0.287559	−	0.166022i	−0.349281	−	0.937018i	$-0.613574\pi$
$907$	8.66025	−	5.00000i	0.287559	−	0.166022i	0.636841	+	0.770996i	$0.280241\pi$
$908$		0			0
$909$	13.3682	+	23.1544i	0.443394	+	0.767981i
$910$		0			0
$911$	−55.0109			−1.82259			−0.911297	−	0.411751i	$-0.864917\pi$
$911$	−55.0109			−1.82259			−0.911297	+	0.411751i	$0.864917\pi$
$912$		0			0
$913$		−	25.9516i		−	0.858872i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.85385	−	3.37972i	0.193311	−	0.111608i
$918$		0			0
$919$	−48.6159			−1.60369			−0.801846	−	0.597531i	$-0.796148\pi$
$919$	−48.6159			−1.60369			−0.801846	+	0.597531i	$0.796148\pi$
$920$		0			0
$921$	5.86880	−	10.1651i	0.193384	−	0.334950i
$922$		0			0
$923$		−	2.50273i		−	0.0823783i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	26.9837	+	15.5791i	0.886262	+	0.511684i
$928$		0			0
$929$	5.66075	+	9.80471i	0.185723	+	0.321682i	0.943820	−	0.330460i	$-0.107204\pi$
$929$	5.66075	+	9.80471i	0.185723	+	0.321682i	−0.758097	+	0.652142i	$0.773871\pi$
$930$		0			0
$931$	−0.307853	−	28.7500i	−0.0100895	−	0.942242i
$932$		0			0
$933$	−3.90421	+	2.25409i	−0.127818	+	0.0737957i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−9.09090	−	5.24864i	−0.296987	−	0.171465i	0.344102	−	0.938932i	$-0.388184\pi$
$937$	−9.09090	−	5.24864i	−0.296987	−	0.171465i	−0.641088	+	0.767467i	$0.721517\pi$
$938$		0			0
$939$	9.03402			0.294814
$940$		0			0
$941$	1.40939	−	2.44113i	0.0459447	−	0.0795785i	−0.842139	−	0.539261i	$-0.818704\pi$
$941$	1.40939	−	2.44113i	0.0459447	−	0.0795785i	0.888083	+	0.459683i	$0.152037\pi$
$942$		0			0
$943$			1.65341i			0.0538424i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	39.4160	−	22.7568i	1.28085	−	0.739497i	0.303844	−	0.952722i	$-0.401730\pi$
$947$	39.4160	−	22.7568i	1.28085	−	0.739497i	0.977003	+	0.213224i	$0.0683966\pi$
$948$		0			0
$949$	−0.403926			−0.0131120
$950$		0			0
$951$	−2.66433			−0.0863967
$952$		0			0
$953$	−17.9440	+	10.3600i	−0.581264	+	0.335593i	−0.761635	−	0.648006i	$-0.775603\pi$
$953$	−17.9440	+	10.3600i	−0.581264	+	0.335593i	0.180372	+	0.983599i	$0.442270\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	5.42356i		−	0.175319i
$958$		0			0
$959$	1.11135	−	1.92491i	0.0358873	−	0.0621587i
$960$		0			0
$961$	−27.5136			−0.887537
$962$		0			0
$963$	28.1340	+	16.2432i	0.906606	+	0.523429i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	11.6642	−	6.73436i	0.375097	−	0.216562i	−0.300586	−	0.953755i	$-0.597182\pi$
$967$	11.6642	−	6.73436i	0.375097	−	0.216562i	0.675683	+	0.737192i	$0.263849\pi$
$968$		0			0
$969$	9.13020	+	5.14177i	0.293304	+	0.165177i
$970$		0			0
$971$	23.5252	+	40.7468i	0.754960	+	1.30763i	0.945394	+	0.325928i	$0.105677\pi$
$971$	23.5252	+	40.7468i	0.754960	+	1.30763i	−0.190435	+	0.981700i	$0.560990\pi$
$972$		0			0
$973$	−0.404192	−	0.233360i	−0.0129578	−	0.00748119i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	43.0648i		−	1.37776i	−0.724873	−	0.688882i	$-0.758102\pi$
$977$		−	43.0648i		−	1.37776i	0.724873	−	0.688882i	$-0.241898\pi$
$978$		0			0
$979$	0.443404	−	0.767999i	0.0141713	−	0.0245454i
$980$		0			0
$981$	−37.9374			−1.21125
$982$		0			0
$983$	−46.8339	+	27.0396i	−1.49377	+	0.862429i	−0.999974	−	0.00714884i	$-0.997724\pi$
$983$	−46.8339	+	27.0396i	−1.49377	+	0.862429i	−0.493796	+	0.869578i	$0.664391\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			2.10752i			0.0670830i
$988$		0			0
$989$	−3.43448			−0.109210
$990$		0			0
$991$	−20.6356	−	35.7418i	−0.655510	−	1.13538i	−0.981766	−	0.190095i	$-0.939120\pi$
$991$	−20.6356	−	35.7418i	−0.655510	−	1.13538i	0.326256	−	0.945282i	$-0.394213\pi$
$992$		0			0
$993$	−5.83021	+	3.36608i	−0.185016	+	0.106819i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−0.943859	−	0.544937i	−0.0298923	−	0.0172583i	0.484979	−	0.874526i	$-0.338827\pi$
$997$	−0.943859	−	0.544937i	−0.0298923	−	0.0172583i	−0.514872	+	0.857267i	$0.672160\pi$
$998$		0			0
$999$	−1.35899			−0.0429965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.s.c.349.3		12
5.2	odd	4		380.2.i.b.121.2	✓	6
5.3	odd	4		1900.2.i.c.501.2		6
5.4	even	2	inner	1900.2.s.c.349.4		12
15.2	even	4		3420.2.t.v.1261.2		6
19.11	even	3	inner	1900.2.s.c.49.4		12
20.7	even	4		1520.2.q.i.881.2		6
95.7	odd	12		7220.2.a.n.1.2		3
95.12	even	12		7220.2.a.o.1.2		3
95.49	even	6	inner	1900.2.s.c.49.3		12
95.68	odd	12		1900.2.i.c.201.2		6
95.87	odd	12		380.2.i.b.201.2	yes	6
285.182	even	12		3420.2.t.v.3241.2		6
380.87	even	12		1520.2.q.i.961.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.b.121.2	✓	6	5.2	odd	4
380.2.i.b.201.2	yes	6	95.87	odd	12
1520.2.q.i.881.2		6	20.7	even	4
1520.2.q.i.961.2		6	380.87	even	12
1900.2.i.c.201.2		6	95.68	odd	12
1900.2.i.c.501.2		6	5.3	odd	4
1900.2.s.c.49.3		12	95.49	even	6	inner
1900.2.s.c.49.4		12	19.11	even	3	inner
1900.2.s.c.349.3		12	1.1	even	1	trivial
1900.2.s.c.349.4		12	5.4	even	2	inner
3420.2.t.v.1261.2		6	15.2	even	4
3420.2.t.v.3241.2		6	285.182	even	12
7220.2.a.n.1.2		3	95.7	odd	12
7220.2.a.o.1.2		3	95.12	even	12

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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.315621 + 0.182224i) q^{3} -0.635552i q^{7} +(-1.43359 + 2.48305i) q^{9} +O(q^{10})\)	\(q+(-0.315621 + 0.182224i) q^{3} -0.635552i q^{7} +(-1.43359 + 2.48305i) q^{9} +1.63555 q^{11} +(0.866025 + 0.500000i) q^{13} +(5.71237 - 3.29804i) q^{17} +(-0.0466721 - 4.35865i) q^{19} +(0.115813 + 0.200594i) q^{21} +(-0.750998 - 0.433589i) q^{23} -2.13828i q^{27} +(-4.54940 + 7.87979i) q^{29} -1.86718 q^{31} +(-0.516215 + 0.298037i) q^{33} -0.635552i q^{37} -0.364448 q^{39} +(-0.953328 - 1.65121i) q^{41} +(3.42991 - 1.98026i) q^{43} +(7.87979 + 4.54940i) q^{47} +6.59607 q^{49} +(-1.20196 + 2.08186i) q^{51} +(8.54523 + 4.93359i) q^{53} +(0.808981 + 1.36718i) q^{57} +(4.54940 + 7.87979i) q^{59} +(-1.13555 + 1.96683i) q^{61} +(1.57811 + 0.911120i) q^{63} +(10.7935 + 6.23163i) q^{67} +0.316041 q^{69} +(-1.25136 - 2.16743i) q^{71} +(-0.349810 + 0.201963i) q^{73} -1.03948i q^{77} +(5.36445 + 9.29150i) q^{79} +(-3.91112 - 6.77426i) q^{81} -15.8672i q^{83} -3.31604i q^{87} +(0.271104 - 0.469566i) q^{89} +(0.317776 - 0.550404i) q^{91} +(0.589321 - 0.340245i) q^{93} +(6.38253 - 3.68495i) q^{97} +(-2.34471 + 4.06116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{9}+O(q^{10}) \) 12 * q + 16 * q^9	\( 12 q + 16 q^{9} + 20 q^{11} - 32 q^{21} + 12 q^{29} + 44 q^{31} - 4 q^{39} - 12 q^{41} + 12 q^{49} - 48 q^{51} - 12 q^{59} - 14 q^{61} - 60 q^{69} + 18 q^{71} + 64 q^{79} - 46 q^{81} + 4 q^{89} + 4 q^{91} + 6 q^{99}+O(q^{100}) \) 12 * q + 16 * q^9 + 20 * q^11 - 32 * q^21 + 12 * q^29 + 44 * q^31 - 4 * q^39 - 12 * q^41 + 12 * q^49 - 48 * q^51 - 12 * q^59 - 14 * q^61 - 60 * q^69 + 18 * q^71 + 64 * q^79 - 46 * q^81 + 4 * q^89 + 4 * q^91 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more