LMFDB - Embedded newform 1900.2.i.f.201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(201,1900)]

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, 0, 4]))

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

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

chi := DirichletCharacter("1900.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + \cdots + 9 $ x^12 - 3x^11 + 15x^10 - 16x^9 + 79x^8 - 65x^7 + 298x^6 + 13x^5 + 233x^4 + 14x^3 + 145x^2 + 33*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.2
Root			$1.28913 - 2.23284i$ of defining polynomial
Character	$\chi$	$=$	1900.201
Dual form			1900.2.i.f.501.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.789132 + 1.36682i) q^{3} +1.39989 q^{7} +(0.254541 + 0.440878i) q^{9} +O(q^{10})$	\(q+(-0.789132 + 1.36682i) q^{3} +1.39989 q^{7} +(0.254541 + 0.440878i) q^{9} -4.67848 q^{11} +(-0.696425 - 1.20624i) q^{13} +(2.17388 - 3.76528i) q^{17} +(-0.608224 - 4.31626i) q^{19} +(-1.10470 + 1.91340i) q^{21} +(-1.64183 - 2.84373i) q^{23} -5.53826 q^{27} +(-1.19642 - 2.07227i) q^{29} -3.94001 q^{31} +(3.69194 - 6.39463i) q^{33} +11.3570 q^{37} +2.19828 q^{39} +(-5.99312 + 10.3804i) q^{41} +(3.68032 - 6.37450i) q^{43} +(-1.48093 - 2.56504i) q^{47} -5.04030 q^{49} +(3.43096 + 5.94260i) q^{51} +(-3.81219 - 6.60291i) q^{53} +(6.37950 + 2.57476i) q^{57} +(5.34285 - 9.25409i) q^{59} +(0.146691 + 0.254076i) q^{61} +(0.356331 + 0.617183i) q^{63} +(-3.77020 - 6.53018i) q^{67} +5.18249 q^{69} +(-0.0920970 + 0.159517i) q^{71} +(0.919287 - 1.59225i) q^{73} -6.54938 q^{77} +(-0.875405 + 1.51625i) q^{79} +(3.60679 - 6.24715i) q^{81} +2.49503 q^{83} +3.77655 q^{87} +(1.02719 + 1.77915i) q^{89} +(-0.974921 - 1.68861i) q^{91} +(3.10919 - 5.38527i) q^{93} +(-0.261586 + 0.453081i) q^{97} +(-1.19087 - 2.06264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{3} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^3 - 3 * q^9	$ 12 q + 3 q^{3} - 3 q^{9} + 2 q^{11} + 7 q^{13} - q^{17} + q^{21} - 2 q^{23} - 24 q^{27} + q^{29} + 2 q^{31} + 10 q^{33} + 20 q^{37} + 36 q^{39} - 7 q^{41} + 19 q^{43} - 14 q^{47} + 8 q^{49} + 11 q^{51} + 6 q^{53} - 28 q^{57} - 5 q^{61} - 11 q^{63} + 14 q^{67} - 14 q^{69} + 8 q^{71} - 9 q^{73} + 2 q^{77} + q^{79} + 2 q^{81} - 26 q^{83} + 30 q^{87} - 8 q^{89} + 3 q^{91} + 9 q^{93} - 11 q^{97} - 18 q^{99}+O(q^{100}) $ 12 * q + 3 * q^3 - 3 * q^9 + 2 * q^11 + 7 * q^13 - q^17 + q^21 - 2 * q^23 - 24 * q^27 + q^29 + 2 * q^31 + 10 * q^33 + 20 * q^37 + 36 * q^39 - 7 * q^41 + 19 * q^43 - 14 * q^47 + 8 * q^49 + 11 * q^51 + 6 * q^53 - 28 * q^57 - 5 * q^61 - 11 * q^63 + 14 * q^67 - 14 * q^69 + 8 * q^71 - 9 * q^73 + 2 * q^77 + q^79 + 2 * q^81 - 26 * q^83 + 30 * q^87 - 8 * q^89 + 3 * q^91 + 9 * q^93 - 11 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$	$951$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.789132	+	1.36682i	−0.455606	+	0.789132i	−0.998723	−	0.0505248i	$-0.983911\pi$
$3$	−0.789132	+	1.36682i	−0.455606	+	0.789132i	0.543117	+	0.839657i	$0.317244\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.39989			0.529110			0.264555	−	0.964371i	$-0.414775\pi$
$7$	1.39989			0.529110			0.264555	+	0.964371i	$0.414775\pi$
$8$		0			0
$9$	0.254541	+	0.440878i	0.0848470	+	0.146959i
$10$		0			0
$11$	−4.67848			−1.41061			−0.705307	−	0.708902i	$-0.749191\pi$
$11$	−4.67848			−1.41061			−0.705307	+	0.708902i	$0.749191\pi$
$12$		0			0
$13$	−0.696425	−	1.20624i	−0.193153	−	0.334552i	0.753140	−	0.657860i	$-0.228538\pi$
$13$	−0.696425	−	1.20624i	−0.193153	−	0.334552i	−0.946294	+	0.323308i	$0.895205\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.17388	−	3.76528i	0.527244	−	0.913214i	−0.472252	−	0.881464i	$-0.656559\pi$
$17$	2.17388	−	3.76528i	0.527244	−	0.913214i	0.999496	−	0.0317500i	$-0.0101080\pi$
$18$		0			0
$19$	−0.608224	−	4.31626i	−0.139536	−	0.990217i
$19$	−0.608224	−	4.31626i	−0.139536	−	0.990217i
$20$		0			0
$21$	−1.10470	+	1.91340i	−0.241066	+	0.417538i
$22$		0			0
$23$	−1.64183	−	2.84373i	−0.342345	−	0.592960i	0.642522	−	0.766267i	$-0.277888\pi$
$23$	−1.64183	−	2.84373i	−0.342345	−	0.592960i	−0.984868	+	0.173307i	$0.944555\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.53826			−1.06584
$28$		0			0
$29$	−1.19642	−	2.07227i	−0.222170	−	0.384811i	0.733296	−	0.679909i	$-0.237981\pi$
$29$	−1.19642	−	2.07227i	−0.222170	−	0.384811i	−0.955467	+	0.295099i	$0.904647\pi$
$30$		0			0
$31$	−3.94001			−0.707647			−0.353823	−	0.935312i	$-0.615119\pi$
$31$	−3.94001			−0.707647			−0.353823	+	0.935312i	$0.615119\pi$
$32$		0			0
$33$	3.69194	−	6.39463i	0.642684	−	1.11316i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	11.3570			1.86707			0.933536	−	0.358483i	$-0.116706\pi$
$37$	11.3570			1.86707			0.933536	+	0.358483i	$0.116706\pi$
$38$		0			0
$39$	2.19828			0.352007
$40$		0			0
$41$	−5.99312	+	10.3804i	−0.935968	+	1.62114i	−0.163070	+	0.986614i	$0.552140\pi$
$41$	−5.99312	+	10.3804i	−0.935968	+	1.62114i	−0.772898	+	0.634530i	$0.781194\pi$
$42$		0			0
$43$	3.68032	−	6.37450i	0.561243	−	0.972102i	−0.436145	−	0.899876i	$-0.643657\pi$
$43$	3.68032	−	6.37450i	0.561243	−	0.972102i	0.997388	−	0.0722255i	$-0.0230101\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.48093	−	2.56504i	−0.216015	−	0.374149i	0.737571	−	0.675270i	$-0.235973\pi$
$47$	−1.48093	−	2.56504i	−0.216015	−	0.374149i	−0.953586	+	0.301120i	$0.902639\pi$
$48$		0			0
$49$	−5.04030			−0.720042
$50$		0			0
$51$	3.43096	+	5.94260i	0.480431	+	0.832131i
$52$		0			0
$53$	−3.81219	−	6.60291i	−0.523645	−	0.906979i	−0.999621	−	0.0275214i	$-0.991239\pi$
$53$	−3.81219	−	6.60291i	−0.523645	−	0.906979i	0.475976	−	0.879458i	$-0.342095\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	6.37950	+	2.57476i	0.844985	+	0.341036i
$58$		0			0
$59$	5.34285	−	9.25409i	0.695580	−	1.20478i	−0.274405	−	0.961614i	$-0.588481\pi$
$59$	5.34285	−	9.25409i	0.695580	−	1.20478i	0.969985	−	0.243166i	$-0.0781859\pi$
$60$		0			0
$61$	0.146691	+	0.254076i	0.0187818	+	0.0325311i	0.875264	−	0.483646i	$-0.160688\pi$
$61$	0.146691	+	0.254076i	0.0187818	+	0.0325311i	−0.856482	+	0.516177i	$0.827355\pi$
$62$		0			0
$63$	0.356331	+	0.617183i	0.0448934	+	0.0777577i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.77020	−	6.53018i	−0.460604	−	0.797789i	0.538388	−	0.842697i	$-0.319034\pi$
$67$	−3.77020	−	6.53018i	−0.460604	−	0.797789i	−0.998991	+	0.0449086i	$0.985700\pi$
$68$		0			0
$69$	5.18249			0.623898
$70$		0			0
$71$	−0.0920970	+	0.159517i	−0.0109299	+	0.0189311i	−0.871439	−	0.490505i	$-0.836812\pi$
$71$	−0.0920970	+	0.159517i	−0.0109299	+	0.0189311i	0.860509	+	0.509436i	$0.170146\pi$
$72$		0			0
$73$	0.919287	−	1.59225i	0.107594	−	0.186359i	−0.807201	−	0.590277i	$-0.799019\pi$
$73$	0.919287	−	1.59225i	0.107594	−	0.186359i	0.914795	+	0.403918i	$0.132352\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.54938			−0.746371
$78$		0			0
$79$	−0.875405	+	1.51625i	−0.0984907	+	0.170591i	−0.911060	−	0.412273i	$-0.864735\pi$
$79$	−0.875405	+	1.51625i	−0.0984907	+	0.170591i	0.812569	+	0.582864i	$0.198068\pi$
$80$		0			0
$81$	3.60679	−	6.24715i	0.400755	−	0.694128i
$82$		0			0
$83$	2.49503			0.273866			0.136933	−	0.990580i	$-0.456276\pi$
$83$	2.49503			0.273866			0.136933	+	0.990580i	$0.456276\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.77655			0.404888
$88$		0			0
$89$	1.02719	+	1.77915i	0.108882	+	0.188590i	0.915318	−	0.402733i	$-0.131940\pi$
$89$	1.02719	+	1.77915i	0.108882	+	0.188590i	−0.806435	+	0.591322i	$0.798606\pi$
$90$		0			0
$91$	−0.974921	−	1.68861i	−0.102199	−	0.177015i
$92$		0			0
$93$	3.10919	−	5.38527i	0.322408	−	0.558427i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.261586	+	0.453081i	−0.0265601	+	0.0460034i	−0.879000	−	0.476822i	$-0.841789\pi$
$97$	−0.261586	+	0.453081i	−0.0265601	+	0.0460034i	0.852440	+	0.522825i	$0.175122\pi$
$98$		0			0
$99$	−1.19087	−	2.06264i	−0.119686	−	0.207303i
$100$		0			0
$101$	1.61367	+	2.79497i	0.160567	+	0.278110i	0.935072	−	0.354458i	$-0.115335\pi$
$101$	1.61367	+	2.79497i	0.160567	+	0.278110i	−0.774505	+	0.632567i	$0.782001\pi$
$102$		0			0
$103$	13.4295			1.32325			0.661624	−	0.749835i	$-0.269867\pi$
$103$	13.4295			1.32325			0.661624	+	0.749835i	$0.269867\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−14.8197			−1.43268			−0.716339	−	0.697752i	$-0.754184\pi$
$107$	−14.8197			−1.43268			−0.716339	+	0.697752i	$0.754184\pi$
$108$		0			0
$109$	−0.591723	+	1.02489i	−0.0566768	+	0.0981671i	−0.892972	−	0.450113i	$-0.851384\pi$
$109$	−0.591723	+	1.02489i	−0.0566768	+	0.0981671i	0.836295	+	0.548280i	$0.184717\pi$
$110$		0			0
$111$	−8.96214	+	15.5229i	−0.850649	+	1.47337i
$112$		0			0
$113$	5.57115			0.524090			0.262045	−	0.965056i	$-0.415603\pi$
$113$	5.57115			0.524090			0.262045	+	0.965056i	$0.415603\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.354537	−	0.614077i	0.0327770	−	0.0567714i
$118$		0			0
$119$	3.04321	−	5.27099i	0.278970	−	0.483191i
$120$		0			0
$121$	10.8882			0.989834
$122$		0			0
$123$	−9.45873	−	16.3830i	−0.852865	−	1.47721i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.68102	−	2.91161i	−0.149166	−	0.258363i	0.781753	−	0.623588i	$-0.214326\pi$
$127$	−1.68102	−	2.91161i	−0.149166	−	0.258363i	−0.930920	+	0.365224i	$0.880992\pi$
$128$		0			0
$129$	5.80851	+	10.0606i	0.511411	+	0.885790i
$130$		0			0
$131$	3.73438	−	6.46814i	0.326275	−	0.565124i	−0.655495	−	0.755200i	$-0.727540\pi$
$131$	3.73438	−	6.46814i	0.326275	−	0.565124i	0.981769	+	0.190075i	$0.0608733\pi$
$132$		0			0
$133$	−0.851450	−	6.04230i	−0.0738300	−	0.523934i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.40898	+	4.17247i	0.205813	+	0.356478i	0.950391	−	0.311057i	$-0.100683\pi$
$137$	2.40898	+	4.17247i	0.205813	+	0.356478i	−0.744579	+	0.667535i	$0.767350\pi$
$138$		0			0
$139$	−10.7854	−	18.6809i	−0.914807	−	1.58449i	−0.807183	−	0.590301i	$-0.799009\pi$
$139$	−10.7854	−	18.6809i	−0.914807	−	1.58449i	−0.107624	−	0.994192i	$-0.534324\pi$
$140$		0			0
$141$	4.67458			0.393671
$142$		0			0
$143$	3.25821	+	5.64338i	0.272465	+	0.471923i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.97746	−	6.88916i	0.328055	−	0.568208i
$148$		0			0
$149$	11.6341	−	20.1508i	0.953102	−	1.65082i	0.214450	−	0.976735i	$-0.431204\pi$
$149$	11.6341	−	20.1508i	0.953102	−	1.65082i	0.738652	−	0.674087i	$-0.235463\pi$
$150$		0			0
$151$	10.2567			0.834682			0.417341	−	0.908750i	$-0.362962\pi$
$151$	10.2567			0.834682			0.417341	+	0.908750i	$0.362962\pi$
$152$		0			0
$153$	2.21337			0.178940
$154$		0			0
$155$		0			0
$156$		0			0
$157$	11.2392	−	19.4669i	0.896988	−	1.55363i	0.0656625	−	0.997842i	$-0.479084\pi$
$157$	11.2392	−	19.4669i	0.896988	−	1.55363i	0.831325	−	0.555786i	$-0.187583\pi$
$158$		0			0
$159$	12.0333			0.954302
$160$		0			0
$161$	−2.29839	−	3.98093i	−0.181138	−	0.313741i
$162$		0			0
$163$	7.27491			0.569815			0.284907	−	0.958555i	$-0.408037\pi$
$163$	7.27491			0.569815			0.284907	+	0.958555i	$0.408037\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.41834	−	5.92075i	−0.264519	−	0.458161i	0.702918	−	0.711271i	$-0.251880\pi$
$167$	−3.41834	−	5.92075i	−0.264519	−	0.458161i	−0.967438	+	0.253110i	$0.918547\pi$
$168$		0			0
$169$	5.52999	−	9.57822i	0.425383	−	0.736786i
$170$		0			0
$171$	1.74812	−	1.36682i	0.133682	−	0.104523i
$172$		0			0
$173$	3.58985	−	6.21780i	0.272931	−	0.472731i	−0.696680	−	0.717382i	$-0.745340\pi$
$173$	3.58985	−	6.21780i	0.272931	−	0.472731i	0.969611	+	0.244651i	$0.0786735\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.43243	+	14.6054i	0.633820	+	1.09781i
$178$		0			0
$179$	−3.47867			−0.260008			−0.130004	−	0.991513i	$-0.541499\pi$
$179$	−3.47867			−0.260008			−0.130004	+	0.991513i	$0.541499\pi$
$180$		0			0
$181$	9.22373	+	15.9760i	0.685594	+	1.18748i	0.973250	+	0.229750i	$0.0737909\pi$
$181$	9.22373	+	15.9760i	0.685594	+	1.18748i	−0.287655	+	0.957734i	$0.592876\pi$
$182$		0			0
$183$	−0.463034			−0.0342284
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−10.1705	+	17.6158i	−0.743739	+	1.28819i
$188$		0			0
$189$	−7.75298			−0.563946
$190$		0			0
$191$	−25.1007			−1.81622			−0.908112	−	0.418727i	$-0.862477\pi$
$191$	−25.1007			−1.81622			−0.908112	+	0.418727i	$0.862477\pi$
$192$		0			0
$193$	5.65851	−	9.80083i	0.407309	−	0.705479i	−0.587279	−	0.809385i	$-0.699801\pi$
$193$	5.65851	−	9.80083i	0.407309	−	0.705479i	0.994587	+	0.103906i	$0.0331340\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−10.1926			−0.726195			−0.363098	−	0.931751i	$-0.618281\pi$
$197$	−10.1926			−0.726195			−0.363098	+	0.931751i	$0.618281\pi$
$198$		0			0
$199$	10.2142	+	17.6916i	0.724068	+	1.25412i	0.959357	+	0.282197i	$0.0910632\pi$
$199$	10.2142	+	17.6916i	0.724068	+	1.25412i	−0.235289	+	0.971926i	$0.575604\pi$
$200$		0			0
$201$	11.9008			0.839414
$202$		0			0
$203$	−1.67487	−	2.90096i	−0.117553	−	0.203607i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.835827	−	1.44769i	0.0580940	−	0.100622i
$208$		0			0
$209$	2.84556	+	20.1935i	0.196832	+	1.39681i
$210$		0			0
$211$	−0.0585254	+	0.101369i	−0.00402905	+	0.00697853i	−0.868033	−	0.496507i	$-0.834616\pi$
$211$	−0.0585254	+	0.101369i	−0.00402905	+	0.00697853i	0.864004	+	0.503485i	$0.167949\pi$
$212$		0			0
$213$	−0.145353	−	0.251759i	−0.00995945	−	0.0172503i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.51560			−0.374423
$218$		0			0
$219$	1.45088	+	2.51299i	0.0980412	+	0.169812i
$220$		0			0
$221$	−6.05578			−0.407356
$222$		0			0
$223$	−6.80869	+	11.7930i	−0.455944	+	0.789718i	−0.998742	−	0.0501456i	$-0.984031\pi$
$223$	−6.80869	+	11.7930i	−0.455944	+	0.789718i	0.542798	+	0.839863i	$0.317365\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.84713			0.388088			0.194044	−	0.980993i	$-0.437840\pi$
$227$	5.84713			0.388088			0.194044	+	0.980993i	$0.437840\pi$
$228$		0			0
$229$	−23.9558			−1.58305			−0.791523	−	0.611140i	$-0.790711\pi$
$229$	−23.9558			−1.58305			−0.791523	+	0.611140i	$0.790711\pi$
$230$		0			0
$231$	5.16832	−	8.95180i	0.340051	−	0.588985i
$232$		0			0
$233$	−9.84858	+	17.0582i	−0.645202	+	1.11752i	0.339053	+	0.940767i	$0.389893\pi$
$233$	−9.84858	+	17.0582i	−0.645202	+	1.11752i	−0.984255	+	0.176755i	$0.943440\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.38162	−	2.39304i	−0.0897459	−	0.155444i
$238$		0			0
$239$	−18.6424			−1.20587			−0.602937	−	0.797789i	$-0.706003\pi$
$239$	−18.6424			−1.20587			−0.602937	+	0.797789i	$0.706003\pi$
$240$		0			0
$241$	−3.57780	−	6.19693i	−0.230466	−	0.399179i	0.727479	−	0.686130i	$-0.240692\pi$
$241$	−3.57780	−	6.19693i	−0.230466	−	0.399179i	−0.957945	+	0.286951i	$0.907358\pi$
$242$		0			0
$243$	−2.61491	−	4.52916i	−0.167747	−	0.290546i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.78287	+	3.73961i	−0.304327	+	0.237946i
$248$		0			0
$249$	−1.96891	+	3.41025i	−0.124775	+	0.216116i
$250$		0			0
$251$	−3.67103	−	6.35840i	−0.231713	−	0.401339i	0.726599	−	0.687062i	$-0.241100\pi$
$251$	−3.67103	−	6.35840i	−0.231713	−	0.401339i	−0.958312	+	0.285723i	$0.907766\pi$
$252$		0			0
$253$	7.68127	+	13.3044i	0.482917	+	0.836438i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.57010	−	7.91565i	−0.285075	−	0.493764i	0.687552	−	0.726135i	$-0.258685\pi$
$257$	−4.57010	−	7.91565i	−0.285075	−	0.493764i	−0.972627	+	0.232370i	$0.925352\pi$
$258$		0			0
$259$	15.8985			0.987887
$260$		0			0
$261$	0.609078	−	1.05495i	0.0377010	−	0.0653001i
$262$		0			0
$263$	−11.9226	+	20.6505i	−0.735177	+	1.27336i	0.219469	+	0.975619i	$0.429568\pi$
$263$	−11.9226	+	20.6505i	−0.735177	+	1.27336i	−0.954646	+	0.297744i	$0.903766\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−3.24236			−0.198429
$268$		0			0
$269$	−7.56760	+	13.1075i	−0.461405	+	0.799176i	−0.999031	−	0.0440068i	$-0.985988\pi$
$269$	−7.56760	+	13.1075i	−0.461405	+	0.799176i	0.537627	+	0.843183i	$0.319321\pi$
$270$		0			0
$271$	−0.744750	+	1.28994i	−0.0452403	+	0.0783586i	−0.887759	−	0.460309i	$-0.847739\pi$
$271$	−0.744750	+	1.28994i	−0.0452403	+	0.0783586i	0.842519	+	0.538667i	$0.181072\pi$
$272$		0			0
$273$	3.07737			0.186251
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.8346			0.831241			0.415621	−	0.909538i	$-0.363564\pi$
$277$	13.8346			0.831241			0.415621	+	0.909538i	$0.363564\pi$
$278$		0			0
$279$	−1.00289	−	1.73706i	−0.0600417	−	0.103995i
$280$		0			0
$281$	−0.437342	−	0.757498i	−0.0260896	−	0.0451885i	0.852686	−	0.522424i	$-0.174972\pi$
$281$	−0.437342	−	0.757498i	−0.0260896	−	0.0451885i	−0.878775	+	0.477236i	$0.841639\pi$
$282$		0			0
$283$	−6.52975	+	11.3099i	−0.388153	+	0.672301i	−0.992201	−	0.124647i	$-0.960220\pi$
$283$	−6.52975	+	11.3099i	−0.388153	+	0.672301i	0.604048	+	0.796948i	$0.293554\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.38974	+	14.5314i	−0.495230	+	0.857764i
$288$		0			0
$289$	−0.951541	−	1.64812i	−0.0559730	−	0.0969481i
$290$		0			0
$291$	−0.412852	−	0.715081i	−0.0242018	−	0.0419188i
$292$		0			0
$293$	−13.4807			−0.787548			−0.393774	−	0.919207i	$-0.628831\pi$
$293$	−13.4807			−0.787548			−0.393774	+	0.919207i	$0.628831\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	25.9106			1.50349
$298$		0			0
$299$	−2.28682	+	3.96089i	−0.132250	+	0.229064i
$300$		0			0
$301$	5.15206	−	8.92362i	0.296960	−	0.514349i
$302$		0			0
$303$	−5.09361			−0.292620
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−11.9744	+	20.7403i	−0.683418	+	1.18371i	0.290514	+	0.956871i	$0.406174\pi$
$307$	−11.9744	+	20.7403i	−0.683418	+	1.18371i	−0.973931	+	0.226843i	$0.927159\pi$
$308$		0			0
$309$	−10.5977	+	18.3557i	−0.602880	+	1.04422i
$310$		0			0
$311$	−20.8129			−1.18019			−0.590095	−	0.807334i	$-0.700910\pi$
$311$	−20.8129			−1.18019			−0.590095	+	0.807334i	$0.700910\pi$
$312$		0			0
$313$	5.34701	+	9.26130i	0.302231	+	0.523479i	0.976641	−	0.214878i	$-0.0689353\pi$
$313$	5.34701	+	9.26130i	0.302231	+	0.523479i	−0.674410	+	0.738357i	$0.735602\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.6592	+	25.3905i	0.823343	+	1.42607i	0.903179	+	0.429264i	$0.141227\pi$
$317$	14.6592	+	25.3905i	0.823343	+	1.42607i	−0.0798355	+	0.996808i	$0.525439\pi$
$318$		0			0
$319$	5.59745	+	9.69507i	0.313397	+	0.542819i
$320$		0			0
$321$	11.6947	−	20.2559i	0.652736	−	1.13057i
$322$		0			0
$323$	−17.5741	−	7.09291i	−0.977849	−	0.394660i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.933895	−	1.61755i	−0.0516445	−	0.0894509i
$328$		0			0
$329$	−2.07314	−	3.59078i	−0.114296	−	0.197966i
$330$		0			0
$331$	−29.8654			−1.64155			−0.820777	−	0.571249i	$-0.806459\pi$
$331$	−29.8654			−1.64155			−0.820777	+	0.571249i	$0.806459\pi$
$332$		0			0
$333$	2.89081	+	5.00703i	0.158416	+	0.274384i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	9.86326	−	17.0837i	0.537286	−	0.930607i	−0.461763	−	0.887003i	$-0.652783\pi$
$337$	9.86326	−	17.0837i	0.537286	−	0.930607i	0.999049	−	0.0436035i	$-0.0138838\pi$
$338$		0			0
$339$	−4.39637	+	7.61474i	−0.238778	+	0.413576i
$340$		0			0
$341$	18.4333			0.998217
$342$		0			0
$343$	−16.8551			−0.910092
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.92364	−	15.4562i	0.479046	−	0.829732i	−0.520665	−	0.853761i	$-0.674316\pi$
$347$	8.92364	−	15.4562i	0.479046	−	0.829732i	0.999711	+	0.0240287i	$0.00764932\pi$
$348$		0			0
$349$	−16.4218			−0.879040			−0.439520	−	0.898233i	$-0.644851\pi$
$349$	−16.4218			−0.879040			−0.439520	+	0.898233i	$0.644851\pi$
$350$		0			0
$351$	3.85698	+	6.68049i	0.205870	+	0.356578i
$352$		0			0
$353$	18.9506			1.00864			0.504319	−	0.863517i	$-0.331743\pi$
$353$	18.9506			1.00864			0.504319	+	0.863517i	$0.331743\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4.80299	+	8.31902i	0.254201	+	0.440289i
$358$		0			0
$359$	13.9335	−	24.1335i	0.735380	−	1.27371i	−0.219177	−	0.975685i	$-0.570337\pi$
$359$	13.9335	−	24.1335i	0.735380	−	1.27371i	0.954557	−	0.298030i	$-0.0963295\pi$
$360$		0			0
$361$	−18.2601	+	5.25050i	−0.961059	+	0.276342i
$362$		0			0
$363$	−8.59221	+	14.8821i	−0.450974	+	0.781110i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−13.2265	−	22.9090i	−0.690418	−	1.19584i	−0.971701	−	0.236214i	$-0.924093\pi$
$367$	−13.2265	−	22.9090i	−0.690418	−	1.19584i	0.281283	−	0.959625i	$-0.409240\pi$
$368$		0			0
$369$	−6.10198			−0.317656
$370$		0			0
$371$	−5.33667	−	9.24338i	−0.277066	−	0.479892i
$372$		0			0
$373$	−29.3566			−1.52003			−0.760013	−	0.649908i	$-0.774807\pi$
$373$	−29.3566			−1.52003			−0.760013	+	0.649908i	$0.774807\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.66644	+	2.88636i	−0.0858260	+	0.148655i
$378$		0			0
$379$	7.49172			0.384824			0.192412	−	0.981314i	$-0.438369\pi$
$379$	7.49172			0.384824			0.192412	+	0.981314i	$0.438369\pi$
$380$		0			0
$381$	5.30618			0.271844
$382$		0			0
$383$	−3.44220	+	5.96207i	−0.175888	+	0.304648i	−0.940468	−	0.339881i	$-0.889613\pi$
$383$	−3.44220	+	5.96207i	−0.175888	+	0.304648i	0.764580	+	0.644529i	$0.222946\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.74717			0.190479
$388$		0			0
$389$	10.1533	+	17.5861i	0.514794	+	0.891650i	0.999853	+	0.0171681i	$0.00546505\pi$
$389$	10.1533	+	17.5861i	0.514794	+	0.891650i	−0.485058	+	0.874482i	$0.661202\pi$
$390$		0			0
$391$	−14.2766			−0.721999
$392$		0			0
$393$	5.89384	+	10.2084i	0.297305	+	0.514948i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.89768	−	8.48303i	0.245808	−	0.425751i	−0.716551	−	0.697535i	$-0.754280\pi$
$397$	4.89768	−	8.48303i	0.245808	−	0.425751i	0.962358	+	0.271784i	$0.0876135\pi$
$398$		0			0
$399$	8.93063	+	3.60440i	0.447091	+	0.180446i
$400$		0			0
$401$	1.78057	−	3.08404i	0.0889174	−	0.154009i	−0.818136	−	0.575024i	$-0.804993\pi$
$401$	1.78057	−	3.08404i	0.0889174	−	0.154009i	0.907054	+	0.421015i	$0.138326\pi$
$402$		0			0
$403$	2.74392	+	4.75261i	0.136684	+	0.236744i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−53.1333			−2.63372
$408$		0			0
$409$	−10.9468	−	18.9604i	−0.541285	−	0.937533i	−0.998831	−	0.0483469i	$-0.984605\pi$
$409$	−10.9468	−	18.9604i	−0.541285	−	0.937533i	0.457546	−	0.889186i	$-0.348729\pi$
$410$		0			0
$411$	−7.60400			−0.375078
$412$		0			0
$413$	7.47943	−	12.9547i	0.368039	−	0.637462i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	34.0445			1.66717
$418$		0			0
$419$	25.6000			1.25064			0.625322	−	0.780367i	$-0.284968\pi$
$419$	25.6000			1.25064			0.625322	+	0.780367i	$0.284968\pi$
$420$		0			0
$421$	5.61245	−	9.72105i	0.273534	−	0.473775i	−0.696230	−	0.717819i	$-0.745141\pi$
$421$	5.61245	−	9.72105i	0.273534	−	0.473775i	0.969764	+	0.244044i	$0.0784740\pi$
$422$		0			0
$423$	0.753913	−	1.30582i	0.0366565	−	0.0634909i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.205352	+	0.355680i	0.00993766	+	0.0172125i
$428$		0			0
$429$	−10.2846			−0.496547
$430$		0			0
$431$	13.4540	+	23.3030i	0.648057	+	1.12247i	0.983586	+	0.180438i	$0.0577515\pi$
$431$	13.4540	+	23.3030i	0.648057	+	1.12247i	−0.335529	+	0.942030i	$0.608915\pi$
$432$		0			0
$433$	15.5168	+	26.8758i	0.745688	+	1.29157i	0.949873	+	0.312637i	$0.101212\pi$
$433$	15.5168	+	26.8758i	0.745688	+	1.29157i	−0.204185	+	0.978932i	$0.565454\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.2757	+	8.81619i	−0.539389	+	0.421736i
$438$		0			0
$439$	−11.4195	+	19.7791i	−0.545022	+	0.944005i	0.453584	+	0.891214i	$0.350145\pi$
$439$	−11.4195	+	19.7791i	−0.545022	+	0.944005i	−0.998606	+	0.0527915i	$0.983188\pi$
$440$		0			0
$441$	−1.28296	−	2.22216i	−0.0610934	−	0.105817i
$442$		0			0
$443$	12.7905	+	22.1538i	0.607696	+	1.05256i	0.991619	+	0.129196i	$0.0412396\pi$
$443$	12.7905	+	22.1538i	0.607696	+	1.05256i	−0.383923	+	0.923365i	$0.625427\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	18.3617	+	31.8034i	0.868478	+	1.50425i
$448$		0			0
$449$	−29.7102			−1.40211			−0.701055	−	0.713107i	$-0.747287\pi$
$449$	−29.7102			−1.40211			−0.701055	+	0.713107i	$0.747287\pi$
$450$		0			0
$451$	28.0387	−	48.5644i	1.32029	−	2.28681i
$452$		0			0
$453$	−8.09393	+	14.0191i	−0.380286	+	0.658674i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−13.9693			−0.653458			−0.326729	−	0.945118i	$-0.605946\pi$
$457$	−13.9693			−0.653458			−0.326729	+	0.945118i	$0.605946\pi$
$458$		0			0
$459$	−12.0395	+	20.8531i	−0.561957	+	0.973338i
$460$		0			0
$461$	10.7999	−	18.7060i	0.503001	−	0.871224i	−0.496993	−	0.867755i	$-0.665562\pi$
$461$	10.7999	−	18.7060i	0.503001	−	0.871224i	0.999994	−	0.00346920i	$-0.00110428\pi$
$462$		0			0
$463$	−14.4002			−0.669233			−0.334617	−	0.942354i	$-0.608607\pi$
$463$	−14.4002			−0.669233			−0.334617	+	0.942354i	$0.608607\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−34.9770			−1.61854			−0.809271	−	0.587435i	$-0.800138\pi$
$467$	−34.9770			−1.61854			−0.809271	+	0.587435i	$0.800138\pi$
$468$		0			0
$469$	−5.27789	−	9.14157i	−0.243710	−	0.422118i
$470$		0			0
$471$	17.7385	+	30.7239i	0.817345	+	1.41568i
$472$		0			0
$473$	−17.2183	+	29.8230i	−0.791698	+	1.37126i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.94072	−	3.36142i	0.0888594	−	0.153909i
$478$		0			0
$479$	9.14007	+	15.8311i	0.417620	+	0.723340i	0.995700	−	0.0926410i	$-0.0295309\pi$
$479$	9.14007	+	15.8311i	0.417620	+	0.723340i	−0.578079	+	0.815981i	$0.696198\pi$
$480$		0			0
$481$	−7.90927	−	13.6993i	−0.360632	−	0.624632i
$482$		0			0
$483$	7.25493			0.330111
$484$		0			0
$485$		0			0
$486$		0			0
$487$	19.3488			0.876780			0.438390	−	0.898785i	$-0.355549\pi$
$487$	19.3488			0.876780			0.438390	+	0.898785i	$0.355549\pi$
$488$		0			0
$489$	−5.74086	+	9.94347i	−0.259611	+	0.449659i
$490$		0			0
$491$	6.23725	−	10.8032i	0.281483	−	0.487543i	−0.690267	−	0.723554i	$-0.742507\pi$
$491$	6.23725	−	10.8032i	0.281483	−	0.487543i	0.971750	+	0.236012i	$0.0758404\pi$
$492$		0			0
$493$	−10.4036			−0.468552
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.128926	+	0.223306i	−0.00578312	+	0.0100167i
$498$		0			0
$499$	−6.58105	+	11.3987i	−0.294608	+	0.510276i	−0.974894	−	0.222671i	$-0.928522\pi$
$499$	−6.58105	+	11.3987i	−0.294608	+	0.510276i	0.680286	+	0.732947i	$0.261856\pi$
$500$		0			0
$501$	10.7901			0.482066
$502$		0			0
$503$	−9.87656	−	17.1067i	−0.440374	−	0.762750i	0.557343	−	0.830282i	$-0.311821\pi$
$503$	−9.87656	−	17.1067i	−0.440374	−	0.762750i	−0.997717	+	0.0675323i	$0.978487\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	8.72778	+	15.1170i	0.387614	+	0.671368i
$508$		0			0
$509$	−5.63237	−	9.75556i	−0.249651	−	0.432407i	0.713778	−	0.700372i	$-0.246982\pi$
$509$	−5.63237	−	9.75556i	−0.249651	−	0.432407i	−0.963429	+	0.267964i	$0.913649\pi$
$510$		0			0
$511$	1.28690	−	2.22898i	0.0569293	−	0.0986044i
$512$		0			0
$513$	3.36850	+	23.9045i	0.148723	+	1.05541i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.92848	+	12.0005i	0.304714	+	0.527781i
$518$		0			0
$519$	5.66573	+	9.81333i	0.248698	+	0.430758i
$520$		0			0
$521$	−13.2410			−0.580098			−0.290049	−	0.957012i	$-0.593672\pi$
$521$	−13.2410			−0.580098			−0.290049	+	0.957012i	$0.593672\pi$
$522$		0			0
$523$	2.74503	+	4.75453i	0.120032	+	0.207901i	0.919780	−	0.392434i	$-0.128367\pi$
$523$	2.74503	+	4.75453i	0.120032	+	0.207901i	−0.799748	+	0.600336i	$0.795034\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.56512	+	14.8352i	−0.373103	+	0.646233i
$528$		0			0
$529$	6.10878	−	10.5807i	0.265599	−	0.460031i
$530$		0			0
$531$	5.43990			0.236072
$532$		0			0
$533$	16.6950			0.723142
$534$		0			0
$535$		0			0
$536$		0			0
$537$	2.74513	−	4.75470i	0.118461	−	0.205181i
$538$		0			0
$539$	23.5809			1.01570
$540$		0			0
$541$	−0.888663	−	1.53921i	−0.0382066	−	0.0661758i	0.846290	−	0.532723i	$-0.178831\pi$
$541$	−0.888663	−	1.53921i	−0.0382066	−	0.0661758i	−0.884496	+	0.466547i	$0.845498\pi$
$542$		0			0
$543$	−29.1150			−1.24944
$544$		0			0
$545$		0			0
$546$		0			0
$547$	19.5968	+	33.9427i	0.837899	+	1.45128i	0.891648	+	0.452730i	$0.149550\pi$
$547$	19.5968	+	33.9427i	0.837899	+	1.45128i	−0.0537486	+	0.998554i	$0.517117\pi$
$548$		0			0
$549$	−0.0746777	+	0.129346i	−0.00318717	+	0.00552033i
$550$		0			0
$551$	−8.21675	+	6.42448i	−0.350045	+	0.273692i
$552$		0			0
$553$	−1.22547	+	2.12258i	−0.0521125	+	0.0902615i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−22.3691	−	38.7443i	−0.947807	−	1.64165i	−0.750031	−	0.661403i	$-0.769961\pi$
$557$	−22.3691	−	38.7443i	−0.947807	−	1.64165i	−0.197777	−	0.980247i	$-0.563372\pi$
$558$		0			0
$559$	−10.2523			−0.433624
$560$		0			0
$561$	−16.0517	−	27.8023i	−0.677703	−	1.17382i
$562$		0			0
$563$	16.3322			0.688318			0.344159	−	0.938911i	$-0.388164\pi$
$563$	16.3322			0.688318			0.344159	+	0.938911i	$0.388164\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	5.04913	−	8.74535i	0.212044	−	0.367270i
$568$		0			0
$569$	27.0171			1.13261			0.566307	−	0.824194i	$-0.308372\pi$
$569$	27.0171			1.13261			0.566307	+	0.824194i	$0.308372\pi$
$570$		0			0
$571$	34.0260			1.42395			0.711973	−	0.702207i	$-0.247802\pi$
$571$	34.0260			1.42395			0.711973	+	0.702207i	$0.247802\pi$
$572$		0			0
$573$	19.8078	−	34.3081i	0.827482	−	1.43324i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−7.96551			−0.331608			−0.165804	−	0.986159i	$-0.553022\pi$
$577$	−7.96551			−0.331608			−0.165804	+	0.986159i	$0.553022\pi$
$578$		0			0
$579$	8.93063	+	15.4683i	0.371144	+	0.642841i
$580$		0			0
$581$	3.49278			0.144905
$582$		0			0
$583$	17.8353	+	30.8916i	0.738661	+	1.27940i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.4543	+	19.8395i	−0.472771	+	0.818864i	−0.999514	−	0.0311607i	$-0.990080\pi$
$587$	−11.4543	+	19.8395i	−0.472771	+	0.818864i	0.526743	+	0.850025i	$0.323413\pi$
$588$		0			0
$589$	2.39641	+	17.0061i	0.0987423	+	0.700724i
$590$		0			0
$591$	8.04334	−	13.9315i	0.330859	−	0.573064i
$592$		0			0
$593$	−1.51758	−	2.62852i	−0.0623194	−	0.107940i	0.833182	−	0.552998i	$-0.186516\pi$
$593$	−1.51758	−	2.62852i	−0.0623194	−	0.107940i	−0.895502	+	0.445058i	$0.853183\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−32.2415			−1.31956
$598$		0			0
$599$	0.0457108	+	0.0791734i	0.00186769	+	0.00323494i	0.866958	−	0.498382i	$-0.166072\pi$
$599$	0.0457108	+	0.0791734i	0.00186769	+	0.00323494i	−0.865090	+	0.501617i	$0.832739\pi$
$600$		0			0
$601$	27.2190			1.11029			0.555144	−	0.831754i	$-0.312663\pi$
$601$	27.2190			1.11029			0.555144	+	0.831754i	$0.312663\pi$
$602$		0			0
$603$	1.91934	−	3.32440i	0.0781617	−	0.135380i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	22.9612			0.931965			0.465983	−	0.884794i	$-0.345701\pi$
$607$	22.9612			0.931965			0.465983	+	0.884794i	$0.345701\pi$
$608$		0			0
$609$	5.28677			0.214231
$610$		0			0
$611$	−2.06271	+	3.57271i	−0.0834482	+	0.144536i
$612$		0			0
$613$	11.7101	−	20.2825i	0.472967	−	0.819202i	−0.526555	−	0.850141i	$-0.676516\pi$
$613$	11.7101	−	20.2825i	0.472967	−	0.819202i	0.999521	+	0.0309391i	$0.00984979\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.4969	−	23.3773i	−0.543365	−	0.941136i	−0.998708	−	0.0508196i	$-0.983817\pi$
$617$	−13.4969	−	23.3773i	−0.543365	−	0.941136i	0.455343	−	0.890316i	$-0.349517\pi$
$618$		0			0
$619$	−8.52401			−0.342609			−0.171304	−	0.985218i	$-0.554798\pi$
$619$	−8.52401			−0.342609			−0.171304	+	0.985218i	$0.554798\pi$
$620$		0			0
$621$	9.09288	+	15.7493i	0.364885	+	0.631999i
$622$		0			0
$623$	1.43796	+	2.49062i	0.0576107	+	0.0997847i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−29.8464	−	12.0460i	−1.19195	−	0.481070i
$628$		0			0
$629$	24.6887	−	42.7621i	0.984403	−	1.70504i
$630$		0			0
$631$	−0.243045	−	0.420966i	−0.00967547	−	0.0167584i	0.861147	−	0.508356i	$-0.169747\pi$
$631$	−0.243045	−	0.420966i	−0.00967547	−	0.0167584i	−0.870823	+	0.491597i	$0.836413\pi$
$632$		0			0
$633$	−0.0923685	−	0.159987i	−0.00367132	−	0.00635891i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.51019	+	6.07982i	0.139079	+	0.240891i
$638$		0			0
$639$	−0.0937698			−0.00370948
$640$		0			0
$641$	−4.40147	+	7.62356i	−0.173847	+	0.301113i	−0.939762	−	0.341830i	$-0.888953\pi$
$641$	−4.40147	+	7.62356i	−0.173847	+	0.301113i	0.765914	+	0.642943i	$0.222287\pi$
$642$		0			0
$643$	14.0490	−	24.3336i	0.554039	−	0.959623i	−0.443939	−	0.896057i	$-0.646419\pi$
$643$	14.0490	−	24.3336i	0.554039	−	0.959623i	0.997978	−	0.0635663i	$-0.0202474\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−22.9675			−0.902946			−0.451473	−	0.892285i	$-0.649101\pi$
$647$	−22.9675			−0.902946			−0.451473	+	0.892285i	$0.649101\pi$
$648$		0			0
$649$	−24.9964	+	43.2951i	−0.981195	+	1.69948i
$650$		0			0
$651$	4.35254	−	7.53881i	0.170589	−	0.295469i
$652$		0			0
$653$	−47.8297			−1.87172			−0.935860	−	0.352372i	$-0.885375\pi$
$653$	−47.8297			−1.87172			−0.935860	+	0.352372i	$0.885375\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.935985			0.0365162
$658$		0			0
$659$	2.61520	+	4.52966i	0.101874	+	0.176451i	0.912457	−	0.409173i	$-0.134183\pi$
$659$	2.61520	+	4.52966i	0.101874	+	0.176451i	−0.810583	+	0.585624i	$0.800850\pi$
$660$		0			0
$661$	15.6767	+	27.1529i	0.609754	+	1.05613i	0.991281	+	0.131767i	$0.0420652\pi$
$661$	15.6767	+	27.1529i	0.609754	+	1.05613i	−0.381527	+	0.924358i	$0.624602\pi$
$662$		0			0
$663$	4.77881	−	8.27715i	0.185594	−	0.321458i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.92865	+	6.80463i	−0.152118	+	0.263476i
$668$		0			0
$669$	−10.7459	−	18.6125i	−0.415461	−	0.719600i
$670$		0			0
$671$	−0.686290	−	1.18869i	−0.0264939	−	0.0458888i
$672$		0			0
$673$	28.6781			1.10546			0.552729	−	0.833361i	$-0.313586\pi$
$673$	28.6781			1.10546			0.552729	+	0.833361i	$0.313586\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−17.1600			−0.659513			−0.329757	−	0.944066i	$-0.606967\pi$
$677$	−17.1600			−0.659513			−0.329757	+	0.944066i	$0.606967\pi$
$678$		0			0
$679$	−0.366193	+	0.634265i	−0.0140532	+	0.0243409i
$680$		0			0
$681$	−4.61416	+	7.99195i	−0.176815	+	0.306252i
$682$		0			0
$683$	0.150796			0.00577004			0.00288502	−	0.999996i	$-0.499082\pi$
$683$	0.150796			0.00577004			0.00288502	+	0.999996i	$0.499082\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	18.9043	−	32.7432i	0.721244	−	1.24923i
$688$		0			0
$689$	−5.30981	+	9.19686i	−0.202288	+	0.350372i
$690$		0			0
$691$	−33.0669			−1.25792			−0.628962	−	0.777436i	$-0.716520\pi$
$691$	−33.0669			−1.25792			−0.628962	+	0.777436i	$0.716520\pi$
$692$		0			0
$693$	−1.66709	−	2.88748i	−0.0633273	−	0.109686i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	26.0567	+	45.1315i	0.986968	+	1.70948i
$698$		0			0
$699$	−15.5437	−	26.9224i	−0.587915	−	1.01830i
$700$		0			0
$701$	−19.7648	+	34.2336i	−0.746505	+	1.29298i	0.202984	+	0.979182i	$0.434936\pi$
$701$	−19.7648	+	34.2336i	−0.746505	+	1.29298i	−0.949488	+	0.313802i	$0.898397\pi$
$702$		0			0
$703$	−6.90758	−	49.0195i	−0.260524	−	1.84881i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.25897	+	3.91266i	0.0849575	+	0.147151i
$708$		0			0
$709$	−19.2276	−	33.3032i	−0.722108	−	1.25073i	−0.960153	−	0.279474i	$-0.909840\pi$
$709$	−19.2276	−	33.3032i	−0.722108	−	1.25073i	0.238045	−	0.971254i	$-0.423493\pi$
$710$		0			0
$711$	−0.891306			−0.0334266
$712$		0			0
$713$	6.46883	+	11.2043i	0.242260	+	0.419606i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	14.7113	−	25.4807i	0.549403	−	0.951593i
$718$		0			0
$719$	13.7416	−	23.8011i	0.512475	−	0.887633i	−0.487420	−	0.873167i	$-0.662062\pi$
$719$	13.7416	−	23.8011i	0.512475	−	0.887633i	0.999895	−	0.0144653i	$-0.00460462\pi$
$720$		0			0
$721$	18.7999			0.700145
$722$		0			0
$723$	11.2934			0.420007
$724$		0			0
$725$		0			0
$726$		0			0
$727$	24.6371	−	42.6727i	0.913739	−	1.58264i	0.105003	−	0.994472i	$-0.466515\pi$
$727$	24.6371	−	42.6727i	0.913739	−	1.58264i	0.808737	−	0.588171i	$-0.200152\pi$
$728$		0			0
$729$	29.8948			1.10722
$730$		0			0
$731$	−16.0012	−	27.7148i	−0.591825	−	1.02507i
$732$		0			0
$733$	39.6606			1.46490			0.732449	−	0.680821i	$-0.238377\pi$
$733$	39.6606			1.46490			0.732449	+	0.680821i	$0.238377\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	17.6388	+	30.5513i	0.649734	+	1.12537i
$738$		0			0
$739$	16.9817	−	29.4131i	0.624680	−	1.08198i	−0.363922	−	0.931429i	$-0.618563\pi$
$739$	16.9817	−	29.4131i	0.624680	−	1.08198i	0.988603	−	0.150549i	$-0.0481040\pi$
$740$		0			0
$741$	−1.33705	−	9.48836i	−0.0491177	−	0.348563i
$742$		0			0
$743$	1.41651	−	2.45347i	0.0519668	−	0.0900091i	−0.838872	−	0.544329i	$-0.816784\pi$
$743$	1.41651	−	2.45347i	0.0519668	−	0.0900091i	0.890839	+	0.454320i	$0.150118\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.635088	+	1.10001i	0.0232367	+	0.0402471i
$748$		0			0
$749$	−20.7461			−0.758045
$750$		0			0
$751$	16.9289	+	29.3217i	0.617743	+	1.06996i	0.989897	+	0.141792i	$0.0452863\pi$
$751$	16.9289	+	29.3217i	0.617743	+	1.06996i	−0.372153	+	0.928171i	$0.621380\pi$
$752$		0			0
$753$	11.5877			0.422279
$754$		0			0
$755$		0			0
$756$		0			0
$757$	11.2423	−	19.4722i	0.408608	−	0.707729i	−0.586126	−	0.810220i	$-0.699348\pi$
$757$	11.2423	−	19.4722i	0.408608	−	0.707729i	0.994734	+	0.102490i	$0.0326811\pi$
$758$		0			0
$759$	−24.2462			−0.880080
$760$		0			0
$761$	−27.7383			−1.00551			−0.502755	−	0.864429i	$-0.667680\pi$
$761$	−27.7383			−1.00551			−0.502755	+	0.864429i	$0.667680\pi$
$762$		0			0
$763$	−0.828350	+	1.43474i	−0.0299883	+	0.0519412i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−14.8836			−0.537415
$768$		0			0
$769$	25.2036	+	43.6539i	0.908865	+	1.57420i	0.815643	+	0.578556i	$0.196383\pi$
$769$	25.2036	+	43.6539i	0.908865	+	1.57420i	0.0932225	+	0.995645i	$0.470283\pi$
$770$		0			0
$771$	14.4257			0.519527
$772$		0			0
$773$	−19.5558	−	33.8717i	−0.703374	−	1.21828i	−0.967275	−	0.253730i	$-0.918343\pi$
$773$	−19.5558	−	33.8717i	−0.703374	−	1.21828i	0.263901	−	0.964550i	$-0.414991\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−12.5461	+	21.7304i	−0.450087	+	0.779574i
$778$		0			0
$779$	48.4496	+	19.5542i	1.73589	+	0.700603i
$780$		0			0
$781$	0.430874	−	0.746295i	0.0154179	−	0.0267046i
$782$		0			0
$783$	6.62611	+	11.4768i	0.236798	+	0.410146i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	10.6415			0.379328			0.189664	−	0.981849i	$-0.439260\pi$
$787$	10.6415			0.379328			0.189664	+	0.981849i	$0.439260\pi$
$788$		0			0
$789$	−18.8170	−	32.5919i	−0.669901	−	1.16030i
$790$		0			0
$791$	7.79902			0.277301
$792$		0			0
$793$	0.204318	−	0.353890i	0.00725555	−	0.0125670i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.1004			−0.570304			−0.285152	−	0.958482i	$-0.592044\pi$
$797$	−16.1004			−0.570304			−0.285152	+	0.958482i	$0.592044\pi$
$798$		0			0
$799$	−12.8774			−0.455571
$800$		0			0
$801$	−0.522926	+	0.905734i	−0.0184767	+	0.0320025i
$802$		0			0
$803$	−4.30086	+	7.44932i	−0.151774	+	0.262881i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−11.9437	−	20.6870i	−0.420437	−	0.728218i
$808$		0			0
$809$	21.1658			0.744151			0.372075	−	0.928202i	$-0.378646\pi$
$809$	21.1658			0.744151			0.372075	+	0.928202i	$0.378646\pi$
$810$		0			0
$811$	20.6707	+	35.8028i	0.725848	+	1.25721i	0.958624	+	0.284675i	$0.0918857\pi$
$811$	20.6707	+	35.8028i	0.725848	+	1.25721i	−0.232776	+	0.972530i	$0.574781\pi$
$812$		0			0
$813$	−1.17541	−	2.03587i	−0.0412235	−	0.0714012i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−29.7524	−	12.0081i	−1.04091	−	0.420109i
$818$		0			0
$819$	0.496315	−	0.859642i	0.0173426	−	0.0300383i
$820$		0			0
$821$	2.98387	+	5.16822i	0.104138	+	0.180372i	0.913386	−	0.407095i	$-0.133458\pi$
$821$	2.98387	+	5.16822i	0.104138	+	0.180372i	−0.809248	+	0.587467i	$0.800125\pi$
$822$		0			0
$823$	−15.4868	−	26.8239i	−0.539835	−	0.935022i	−0.998912	−	0.0466254i	$-0.985153\pi$
$823$	−15.4868	−	26.8239i	−0.539835	−	0.935022i	0.459077	−	0.888396i	$-0.348180\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.0562	+	22.6140i	0.454009	+	0.786367i	0.998631	−	0.0523152i	$-0.0166601\pi$
$827$	13.0562	+	22.6140i	0.454009	+	0.786367i	−0.544622	+	0.838682i	$0.683327\pi$
$828$		0			0
$829$	2.68227			0.0931591			0.0465795	−	0.998915i	$-0.485168\pi$
$829$	2.68227			0.0931591			0.0465795	+	0.998915i	$0.485168\pi$
$830$		0			0
$831$	−10.9173	+	18.9094i	−0.378718	+	0.655959i
$832$		0			0
$833$	−10.9570	+	18.9781i	−0.379638	+	0.657553i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	21.8208			0.754237
$838$		0			0
$839$	−5.25063	+	9.09436i	−0.181272	+	0.313972i	−0.942314	−	0.334730i	$-0.891355\pi$
$839$	−5.25063	+	9.09436i	−0.181272	+	0.313972i	0.761042	+	0.648703i	$0.224688\pi$
$840$		0			0
$841$	11.6371	−	20.1561i	0.401281	−	0.695038i
$842$		0			0
$843$	1.38048			0.0475463
$844$		0			0
$845$		0			0
$846$		0			0
$847$	15.2423			0.523731
$848$		0			0
$849$	−10.3057	−	17.8499i	−0.353690	−	0.612608i
$850$		0			0
$851$	−18.6462	−	32.2962i	−0.639184	−	1.10710i
$852$		0			0
$853$	−19.8508	+	34.3826i	−0.679678	+	1.17724i	0.295400	+	0.955374i	$0.404547\pi$
$853$	−19.8508	+	34.3826i	−0.679678	+	1.17724i	−0.975078	+	0.221863i	$0.928786\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.03975	−	15.6573i	0.308792	−	0.534843i	−0.669306	−	0.742986i	$-0.733409\pi$
$857$	9.03975	−	15.6573i	0.308792	−	0.534843i	0.978098	+	0.208143i	$0.0667420\pi$
$858$		0			0
$859$	−13.4851	−	23.3569i	−0.460105	−	0.796926i	0.538860	−	0.842395i	$-0.318855\pi$
$859$	−13.4851	−	23.3569i	−0.460105	−	0.796926i	−0.998966	+	0.0454693i	$0.985522\pi$
$860$		0			0
$861$	−13.2412	−	22.9345i	−0.451260	−	0.781605i
$862$		0			0
$863$	−18.3734			−0.625438			−0.312719	−	0.949846i	$-0.601240\pi$
$863$	−18.3734			−0.625438			−0.312719	+	0.949846i	$0.601240\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	3.00357			0.102006
$868$		0			0
$869$	4.09556	−	7.09373i	0.138933	−	0.240638i
$870$		0			0
$871$	−5.25132	+	9.09556i	−0.177934	+	0.308191i
$872$		0			0
$873$	−0.266338			−0.00901416
$874$		0			0
$875$		0			0
$876$		0			0
$877$	23.6617	−	40.9832i	0.798998	−	1.38391i	−0.121271	−	0.992619i	$-0.538697\pi$
$877$	23.6617	−	40.9832i	0.798998	−	1.38391i	0.920269	−	0.391286i	$-0.127970\pi$
$878$		0			0
$879$	10.6380	−	18.4256i	0.358811	−	0.621480i
$880$		0			0
$881$	−15.8395			−0.533646			−0.266823	−	0.963745i	$-0.585974\pi$
$881$	−15.8395			−0.533646			−0.266823	+	0.963745i	$0.585974\pi$
$882$		0			0
$883$	−21.3443	−	36.9695i	−0.718294	−	1.24412i	−0.961675	−	0.274191i	$-0.911590\pi$
$883$	−21.3443	−	36.9695i	−0.718294	−	1.24412i	0.243381	−	0.969931i	$-0.421743\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.9515	+	20.7006i	0.401293	+	0.695059i	0.993882	−	0.110445i	$-0.0352277\pi$
$887$	11.9515	+	20.7006i	0.401293	+	0.695059i	−0.592589	+	0.805505i	$0.701894\pi$
$888$		0			0
$889$	−2.35325	−	4.07594i	−0.0789254	−	0.136703i
$890$		0			0
$891$	−16.8743	+	29.2272i	−0.565311	+	0.979147i
$892$		0			0
$893$	−10.1706	+	7.95217i	−0.340347	+	0.266109i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−3.60921	−	6.25134i	−0.120508	−	0.208726i
$898$		0			0
$899$	4.71393	+	8.16476i	0.157218	+	0.272310i
$900$		0			0
$901$	−33.1490			−1.10435
$902$		0			0
$903$	8.13131	+	14.0838i	0.270593	+	0.468681i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	18.2637	−	31.6336i	0.606435	−	1.05038i	−0.385387	−	0.922755i	$-0.625932\pi$
$907$	18.2637	−	31.6336i	0.606435	−	1.05038i	0.991823	−	0.127622i	$-0.0407345\pi$
$908$		0			0
$909$	−0.821493	+	1.42287i	−0.0272472	+	0.0471935i
$910$		0			0
$911$	−25.1950			−0.834749			−0.417374	−	0.908735i	$-0.637050\pi$
$911$	−25.1950			−0.834749			−0.417374	+	0.908735i	$0.637050\pi$
$912$		0			0
$913$	−11.6730			−0.386319
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.22774	−	9.05472i	0.172635	−	0.299013i
$918$		0			0
$919$	8.16199			0.269239			0.134620	−	0.990897i	$-0.457019\pi$
$919$	8.16199			0.269239			0.134620	+	0.990897i	$0.457019\pi$
$920$		0			0
$921$	−18.8988	−	32.7338i	−0.622738	−	1.07861i
$922$		0			0
$923$	0.256554			0.00844459
$924$		0			0
$925$		0			0
$926$		0			0
$927$	3.41836	+	5.92078i	0.112274	+	0.194464i
$928$		0			0
$929$	6.01835	−	10.4241i	0.197456	−	0.342003i	−0.750247	−	0.661158i	$-0.770065\pi$
$929$	6.01835	−	10.4241i	0.197456	−	0.342003i	0.947703	+	0.319154i	$0.103399\pi$
$930$		0			0
$931$	3.06563	+	21.7552i	0.100472	+	0.712998i
$932$		0			0
$933$	16.4241	−	28.4474i	0.537701	−	0.931326i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	17.5593	+	30.4135i	0.573636	+	0.993567i	0.996188	+	0.0872286i	$0.0278011\pi$
$937$	17.5593	+	30.4135i	0.573636	+	0.993567i	−0.422552	+	0.906339i	$0.638866\pi$
$938$		0			0
$939$	−16.8780			−0.550793
$940$		0			0
$941$	29.8189	+	51.6478i	0.972067	+	1.68367i	0.689292	+	0.724483i	$0.257922\pi$
$941$	29.8189	+	51.6478i	0.972067	+	1.68367i	0.282775	+	0.959186i	$0.408745\pi$
$942$		0			0
$943$	39.3588			1.28170
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.07831	+	8.79590i	−0.165023	+	0.285828i	−0.936663	−	0.350231i	$-0.886103\pi$
$947$	−5.07831	+	8.79590i	−0.165023	+	0.285828i	0.771640	+	0.636059i	$0.219437\pi$
$948$		0			0
$949$	−2.56086			−0.0831289
$950$		0			0
$951$	−46.2722			−1.50048
$952$		0			0
$953$	24.8376	−	43.0199i	0.804568	−	1.39355i	−0.112015	−	0.993707i	$-0.535730\pi$
$953$	24.8376	−	43.0199i	0.804568	−	1.39355i	0.916583	−	0.399846i	$-0.130936\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−17.6685			−0.571142
$958$		0			0
$959$	3.37231	+	5.84102i	0.108898	+	0.188616i
$960$		0			0
$961$	−15.4763			−0.499236
$962$		0			0
$963$	−3.77223	−	6.53370i	−0.121558	−	0.210545i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	17.9740	−	31.1319i	0.578005	−	1.00113i	−0.417703	−	0.908584i	$-0.637165\pi$
$967$	17.9740	−	31.1319i	0.578005	−	1.00113i	0.995708	−	0.0925508i	$-0.0295021\pi$
$968$		0			0
$969$	23.5630	−	18.4233i	0.756952	−	0.591843i
$970$		0			0
$971$	−19.8394	+	34.3628i	−0.636676	+	1.10276i	0.349481	+	0.936943i	$0.386358\pi$
$971$	−19.8394	+	34.3628i	−0.636676	+	1.10276i	−0.986157	+	0.165812i	$0.946975\pi$
$972$		0			0
$973$	−15.0984	−	26.1513i	−0.484034	−	0.838372i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−34.3337			−1.09843			−0.549216	−	0.835681i	$-0.685074\pi$
$977$	−34.3337			−1.09843			−0.549216	+	0.835681i	$0.685074\pi$
$978$		0			0
$979$	−4.80570	−	8.32372i	−0.153591	−	0.266027i
$980$		0			0
$981$	−0.602471			−0.0192354
$982$		0			0
$983$	3.03255	−	5.25253i	0.0967234	−	0.167530i	−0.813603	−	0.581421i	$-0.802497\pi$
$983$	3.03255	−	5.25253i	0.0967234	−	0.167530i	0.910327	+	0.413891i	$0.135830\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	6.54392			0.208295
$988$		0			0
$989$	−24.1698			−0.768556
$990$		0			0
$991$	13.7694	−	23.8493i	0.437400	−	0.757599i	−0.560088	−	0.828433i	$-0.689233\pi$
$991$	13.7694	−	23.8493i	0.437400	−	0.757599i	0.997488	+	0.0708340i	$0.0225661\pi$
$992$		0			0
$993$	23.5678	−	40.8206i	0.747901	−	1.29540i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.15784	−	3.73748i	−0.0683394	−	0.118367i	0.829831	−	0.558015i	$-0.188437\pi$
$997$	−2.15784	−	3.73748i	−0.0683394	−	0.118367i	−0.898170	+	0.439647i	$0.855103\pi$
$998$		0			0
$999$	−62.8978			−1.99000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.f.201.2	yes	12
5.2	odd	4		1900.2.s.e.49.9		24
5.3	odd	4		1900.2.s.e.49.4		24
5.4	even	2		1900.2.i.e.201.5	✓	12
19.7	even	3	inner	1900.2.i.f.501.2	yes	12
95.7	odd	12		1900.2.s.e.349.4		24
95.64	even	6		1900.2.i.e.501.5	yes	12
95.83	odd	12		1900.2.s.e.349.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.2.i.e.201.5	✓	12	5.4	even	2
1900.2.i.e.501.5	yes	12	95.64	even	6
1900.2.i.f.201.2	yes	12	1.1	even	1	trivial
1900.2.i.f.501.2	yes	12	19.7	even	3	inner
1900.2.s.e.49.4		24	5.3	odd	4
1900.2.s.e.49.9		24	5.2	odd	4
1900.2.s.e.349.4		24	95.7	odd	12
1900.2.s.e.349.9		24	95.83	odd	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.789132 + 1.36682i) q^{3} +1.39989 q^{7} +(0.254541 + 0.440878i) q^{9} +O(q^{10})\)	\(q+(-0.789132 + 1.36682i) q^{3} +1.39989 q^{7} +(0.254541 + 0.440878i) q^{9} -4.67848 q^{11} +(-0.696425 - 1.20624i) q^{13} +(2.17388 - 3.76528i) q^{17} +(-0.608224 - 4.31626i) q^{19} +(-1.10470 + 1.91340i) q^{21} +(-1.64183 - 2.84373i) q^{23} -5.53826 q^{27} +(-1.19642 - 2.07227i) q^{29} -3.94001 q^{31} +(3.69194 - 6.39463i) q^{33} +11.3570 q^{37} +2.19828 q^{39} +(-5.99312 + 10.3804i) q^{41} +(3.68032 - 6.37450i) q^{43} +(-1.48093 - 2.56504i) q^{47} -5.04030 q^{49} +(3.43096 + 5.94260i) q^{51} +(-3.81219 - 6.60291i) q^{53} +(6.37950 + 2.57476i) q^{57} +(5.34285 - 9.25409i) q^{59} +(0.146691 + 0.254076i) q^{61} +(0.356331 + 0.617183i) q^{63} +(-3.77020 - 6.53018i) q^{67} +5.18249 q^{69} +(-0.0920970 + 0.159517i) q^{71} +(0.919287 - 1.59225i) q^{73} -6.54938 q^{77} +(-0.875405 + 1.51625i) q^{79} +(3.60679 - 6.24715i) q^{81} +2.49503 q^{83} +3.77655 q^{87} +(1.02719 + 1.77915i) q^{89} +(-0.974921 - 1.68861i) q^{91} +(3.10919 - 5.38527i) q^{93} +(-0.261586 + 0.453081i) q^{97} +(-1.19087 - 2.06264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{3} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^3 - 3 * q^9	\( 12 q + 3 q^{3} - 3 q^{9} + 2 q^{11} + 7 q^{13} - q^{17} + q^{21} - 2 q^{23} - 24 q^{27} + q^{29} + 2 q^{31} + 10 q^{33} + 20 q^{37} + 36 q^{39} - 7 q^{41} + 19 q^{43} - 14 q^{47} + 8 q^{49} + 11 q^{51} + 6 q^{53} - 28 q^{57} - 5 q^{61} - 11 q^{63} + 14 q^{67} - 14 q^{69} + 8 q^{71} - 9 q^{73} + 2 q^{77} + q^{79} + 2 q^{81} - 26 q^{83} + 30 q^{87} - 8 q^{89} + 3 q^{91} + 9 q^{93} - 11 q^{97} - 18 q^{99}+O(q^{100}) \) 12 * q + 3 * q^3 - 3 * q^9 + 2 * q^11 + 7 * q^13 - q^17 + q^21 - 2 * q^23 - 24 * q^27 + q^29 + 2 * q^31 + 10 * q^33 + 20 * q^37 + 36 * q^39 - 7 * q^41 + 19 * q^43 - 14 * q^47 + 8 * q^49 + 11 * q^51 + 6 * q^53 - 28 * q^57 - 5 * q^61 - 11 * q^63 + 14 * q^67 - 14 * q^69 + 8 * q^71 - 9 * q^73 + 2 * q^77 + q^79 + 2 * q^81 - 26 * q^83 + 30 * q^87 - 8 * q^89 + 3 * q^91 + 9 * q^93 - 11 * q^97 - 18 * q^99

Introduction

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