LMFDB - Embedded newform 1900.2.s.c.349.1

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			349.1
Root			$-0.617942 - 0.356769i$ of defining polynomial
Character	$\chi$	$=$	1900.349
Dual form			1900.2.s.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77509 + 1.60220i) q^{3} +2.20440i q^{7} +(3.63409 - 6.29444i) q^{9} +O(q^{10})$	\(q+(-2.77509 + 1.60220i) q^{3} +2.20440i q^{7} +(3.63409 - 6.29444i) q^{9} -1.20440 q^{11} +(0.866025 + 0.500000i) q^{13} +(1.85383 - 1.07031i) q^{17} +(-4.30660 + 0.673184i) q^{19} +(-3.53189 - 6.11742i) q^{21} +(8.02649 + 4.63409i) q^{23} +13.6770i q^{27} +(4.16599 - 7.21570i) q^{29} +8.26819 q^{31} +(3.34233 - 1.92969i) q^{33} +2.20440i q^{37} -3.20440 q^{39} +(3.30660 + 5.72720i) q^{41} +(2.03084 - 1.17251i) q^{43} +(-7.21570 - 4.16599i) q^{47} +2.14061 q^{49} +(-3.42969 + 5.94040i) q^{51} +(-0.232259 - 0.134095i) q^{53} +(10.8726 - 8.76819i) q^{57} +(-4.16599 - 7.21570i) q^{59} +(1.70440 - 2.95211i) q^{61} +(13.8755 + 8.01100i) q^{63} +(-1.84253 - 1.06379i) q^{67} -29.6990 q^{69} +(5.23630 + 9.06953i) q^{71} +(-4.20835 + 2.42969i) q^{73} -2.65498i q^{77} +(8.20440 + 14.2104i) q^{79} +(-11.0110 - 19.0716i) q^{81} -5.73181i q^{83} +26.6990i q^{87} +(-5.40880 + 9.36832i) q^{89} +(-1.10220 + 1.90907i) q^{91} +(-22.9450 + 13.2473i) q^{93} +(-13.6319 + 7.87039i) q^{97} +(-4.37691 + 7.58103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.77509	+	1.60220i	−1.60220	+	0.925031i	−0.611155	+	0.791511i	$0.709295\pi$
$3$	−2.77509	+	1.60220i	−1.60220	+	0.925031i	−0.991046	+	0.133520i	$0.957372\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			2.20440i			0.833185i	0.909093	+	0.416593i	$0.136776\pi$
$7$			2.20440i			0.833185i	−0.909093	+	0.416593i	$0.863224\pi$
$8$		0			0
$9$	3.63409	−	6.29444i	1.21136	−	2.09815i
$10$		0			0
$11$	−1.20440			−0.363141			−0.181570	−	0.983378i	$-0.558118\pi$
$11$	−1.20440			−0.363141			−0.181570	+	0.983378i	$0.558118\pi$
$12$		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
$17$	1.85383	−	1.07031i	0.449619	−	0.259588i	−0.258050	−	0.966131i	$-0.583080\pi$
$17$	1.85383	−	1.07031i	0.449619	−	0.259588i	0.707669	+	0.706544i	$0.249747\pi$
$18$		0			0
$19$	−4.30660	+	0.673184i	−0.988002	+	0.154439i
$19$	−4.30660	+	0.673184i	−0.988002	+	0.154439i
$20$		0			0
$21$	−3.53189	−	6.11742i	−0.770722	−	1.33493i
$22$		0			0
$23$	8.02649	+	4.63409i	1.67364	+	0.966276i	0.965574	+	0.260127i	$0.0837645\pi$
$23$	8.02649	+	4.63409i	1.67364	+	0.966276i	0.708064	+	0.706148i	$0.249569\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			13.6770i			2.63214i
$28$		0			0
$29$	4.16599	−	7.21570i	0.773605	−	1.33992i	−0.161971	−	0.986796i	$-0.551785\pi$
$29$	4.16599	−	7.21570i	0.773605	−	1.33992i	0.935575	−	0.353127i	$-0.114882\pi$
$30$		0			0
$31$	8.26819			1.48501			0.742505	−	0.669840i	$-0.233637\pi$
$31$	8.26819			1.48501			0.742505	+	0.669840i	$0.233637\pi$
$32$		0			0
$33$	3.34233	−	1.92969i	0.581824	−	0.335916i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			2.20440i			0.362401i	0.983446	+	0.181201i	$0.0579984\pi$
$37$			2.20440i			0.362401i	−0.983446	+	0.181201i	$0.942002\pi$
$38$		0			0
$39$	−3.20440			−0.513115
$40$		0			0
$41$	3.30660	+	5.72720i	0.516405	+	0.894439i	0.999819	+	0.0190471i	$0.00606323\pi$
$41$	3.30660	+	5.72720i	0.516405	+	0.894439i	−0.483414	+	0.875392i	$0.660603\pi$
$42$		0			0
$43$	2.03084	−	1.17251i	0.309701	−	0.178806i	−0.337092	−	0.941472i	$-0.609443\pi$
$43$	2.03084	−	1.17251i	0.309701	−	0.178806i	0.646793	+	0.762666i	$0.276110\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.21570	−	4.16599i	−1.05252	−	0.607672i	−0.129165	−	0.991623i	$-0.541230\pi$
$47$	−7.21570	−	4.16599i	−1.05252	−	0.607672i	−0.923353	+	0.383951i	$0.874563\pi$
$48$		0			0
$49$	2.14061			0.305802
$50$		0			0
$51$	−3.42969	+	5.94040i	−0.480253	+	0.831823i
$52$		0			0
$53$	−0.232259	−	0.134095i	−0.0319032	−	0.0184193i	0.483964	−	0.875088i	$-0.339197\pi$
$53$	−0.232259	−	0.134095i	−0.0319032	−	0.0184193i	−0.515867	+	0.856669i	$0.672530\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	10.8726	−	8.76819i	1.44012	−	1.16138i
$58$		0			0
$59$	−4.16599	−	7.21570i	−0.542366	−	0.939405i	−0.998768	−	0.0496310i	$-0.984195\pi$
$59$	−4.16599	−	7.21570i	−0.542366	−	0.939405i	0.456402	−	0.889774i	$-0.349138\pi$
$60$		0			0
$61$	1.70440	−	2.95211i	0.218226	−	0.377979i	−0.736040	−	0.676939i	$-0.763306\pi$
$61$	1.70440	−	2.95211i	0.218226	−	0.377979i	0.954266	+	0.298960i	$0.0966396\pi$
$62$		0			0
$63$	13.8755	+	8.01100i	1.74814	+	1.00929i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.84253	−	1.06379i	−0.225101	−	0.129962i	0.383209	−	0.923662i	$-0.374819\pi$
$67$	−1.84253	−	1.06379i	−0.225101	−	0.129962i	−0.608310	+	0.793699i	$0.708152\pi$
$68$		0			0
$69$	−29.6990			−3.57534
$70$		0			0
$71$	5.23630	+	9.06953i	0.621434	+	1.07636i	0.989219	+	0.146444i	$0.0467829\pi$
$71$	5.23630	+	9.06953i	0.621434	+	1.07636i	−0.367785	+	0.929911i	$0.619884\pi$
$72$		0			0
$73$	−4.20835	+	2.42969i	−0.492550	+	0.284374i	−0.725632	−	0.688083i	$-0.758452\pi$
$73$	−4.20835	+	2.42969i	−0.492550	+	0.284374i	0.233082	+	0.972457i	$0.425119\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	2.65498i		−	0.302564i
$78$		0			0
$79$	8.20440	+	14.2104i	0.923067	+	1.59880i	0.794640	+	0.607080i	$0.207659\pi$
$79$	8.20440	+	14.2104i	0.923067	+	1.59880i	0.128427	+	0.991719i	$0.459007\pi$
$80$		0			0
$81$	−11.0110	−	19.0716i	−1.22344	−	2.11907i
$82$		0			0
$83$		−	5.73181i		−	0.629148i	−0.949233	−	0.314574i	$-0.898138\pi$
$83$		−	5.73181i		−	0.629148i	0.949233	−	0.314574i	$-0.101862\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			26.6990i			2.86243i
$88$		0			0
$89$	−5.40880	+	9.36832i	−0.573332	+	0.993040i	0.422889	+	0.906182i	$0.361016\pi$
$89$	−5.40880	+	9.36832i	−0.573332	+	0.993040i	−0.996221	+	0.0868585i	$0.972317\pi$
$90$		0			0
$91$	−1.10220	+	1.90907i	−0.115542	+	0.200125i
$92$		0			0
$93$	−22.9450	+	13.2473i	−2.37929	+	1.37368i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−13.6319	+	7.87039i	−1.38411	+	0.799117i	−0.992643	−	0.121075i	$-0.961366\pi$
$97$	−13.6319	+	7.87039i	−1.38411	+	0.799117i	−0.391468	+	0.920192i	$0.628033\pi$
$98$		0			0
$99$	−4.37691	+	7.58103i	−0.439896	+	0.761922i
$100$		0			0
$101$	5.27471	−	9.13606i	0.524853	−	0.909072i	−0.474728	−	0.880133i	$-0.657454\pi$
$101$	5.27471	−	9.13606i	0.524853	−	0.909072i	0.999581	−	0.0289397i	$-0.00921308\pi$
$102$		0			0
$103$		−	0.731811i		−	0.0721075i	−0.999350	−	0.0360537i	$-0.988521\pi$
$103$		−	0.731811i		−	0.0721075i	0.999350	−	0.0360537i	$-0.0114787\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			13.3958i			1.29502i	0.762058	+	0.647509i	$0.224189\pi$
$107$			13.3958i			1.29502i	−0.762058	+	0.647509i	$0.775811\pi$
$108$		0			0
$109$	2.96811	+	5.14091i	0.284293	+	0.492410i	0.972437	−	0.233164i	$-0.0749078\pi$
$109$	2.96811	+	5.14091i	0.284293	+	0.492410i	−0.688144	+	0.725574i	$0.741574\pi$
$110$		0			0
$111$	−3.53189	−	6.11742i	−0.335233	−	0.580640i
$112$		0			0
$113$			15.6132i			1.46877i	0.678735	+	0.734383i	$0.262529\pi$
$113$			15.6132i			1.46877i	−0.678735	+	0.734383i	$0.737471\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.29444	−	3.63409i	0.581921	−	0.335972i
$118$		0			0
$119$	2.35939	+	4.08658i	0.216285	+	0.374616i
$120$		0			0
$121$	−9.54942			−0.868129
$122$		0			0
$123$	−18.3523	−	10.5957i	−1.65477	−	0.955380i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−13.2969	−	7.67699i	−1.17991	−	0.681223i	−0.223918	−	0.974608i	$-0.571885\pi$
$127$	−13.2969	−	7.67699i	−1.17991	−	0.681223i	−0.955994	+	0.293385i	$0.905218\pi$
$128$		0			0
$129$	−3.75719	+	6.50764i	−0.330802	+	0.572965i
$130$		0			0
$131$	3.89780	+	6.75119i	0.340552	+	0.589854i	0.984535	−	0.175186i	$-0.0560526\pi$
$131$	3.89780	+	6.75119i	0.340552	+	0.589854i	−0.643983	+	0.765040i	$0.722719\pi$
$132$		0			0
$133$	−1.48397	−	9.49348i	−0.128676	−	0.823189i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.2657	+	8.23630i	1.21880	+	0.703674i	0.964661	−	0.263494i	$-0.0848748\pi$
$137$	14.2657	+	8.23630i	1.21880	+	0.703674i	0.254138	+	0.967168i	$0.418208\pi$
$138$		0			0
$139$	−9.76819	+	16.9190i	−0.828527	+	1.43505i	0.0706667	+	0.997500i	$0.477487\pi$
$139$	−9.76819	+	16.9190i	−0.828527	+	1.43505i	−0.899194	+	0.437551i	$0.855846\pi$
$140$		0			0
$141$	26.6990			2.24846
$142$		0			0
$143$	−1.04304	−	0.602201i	−0.0872236	−	0.0503586i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.94040	+	3.42969i	−0.489956	+	0.282876i
$148$		0			0
$149$	−2.83850	−	4.91642i	−0.232539	−	0.402769i	0.726016	−	0.687678i	$-0.241370\pi$
$149$	−2.83850	−	4.91642i	−0.232539	−	0.402769i	−0.958555	+	0.284909i	$0.908037\pi$
$150$		0			0
$151$	−14.2264			−1.15773			−0.578864	−	0.815424i	$-0.696504\pi$
$151$	−14.2264			−1.15773			−0.578864	+	0.815424i	$0.696504\pi$
$152$		0			0
$153$		−	15.5584i		−	1.25782i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.567233	−	0.327492i	0.0452701	−	0.0261367i	−0.477194	−	0.878798i	$-0.658346\pi$
$157$	0.567233	−	0.327492i	0.0452701	−	0.0261367i	0.522464	+	0.852661i	$0.325013\pi$
$158$		0			0
$159$	0.859386			0.0681538
$160$		0			0
$161$	−10.2154	+	17.6936i	−0.805087	+	1.39445i
$162$		0			0
$163$		−	12.6770i		−	0.992939i	−0.868054	−	0.496469i	$-0.834630\pi$
$163$		−	12.6770i		−	0.992939i	0.868054	−	0.496469i	$-0.165370\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.75119	−	3.89780i	−0.522422	−	0.301621i	0.215503	−	0.976503i	$-0.430861\pi$
$167$	−6.75119	−	3.89780i	−0.522422	−	0.301621i	−0.737925	+	0.674882i	$0.764194\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$	−11.4133	+	29.5540i	−0.872796	+	2.26005i
$172$		0			0
$173$	−9.30179	+	5.37039i	−0.707202	+	0.408303i	−0.810024	−	0.586397i	$-0.800546\pi$
$173$	−9.30179	+	5.37039i	−0.707202	+	0.408303i	0.102822	+	0.994700i	$0.467213\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	23.1220	+	13.3495i	1.73796	+	1.00341i
$178$		0			0
$179$	1.54942			0.115809			0.0579044	−	0.998322i	$-0.481558\pi$
$179$	1.54942			0.115809			0.0579044	+	0.998322i	$0.481558\pi$
$180$		0			0
$181$	4.11320	−	7.12428i	0.305732	−	0.529544i	−0.671692	−	0.740831i	$-0.734432\pi$
$181$	4.11320	−	7.12428i	0.305732	−	0.529544i	0.977424	+	0.211287i	$0.0677655\pi$
$182$		0			0
$183$			10.9232i			0.807464i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.23275	+	1.28908i	−0.163275	+	0.0942668i
$188$		0			0
$189$	−30.1496			−2.19306
$190$		0			0
$191$	16.2812			1.17807			0.589034	−	0.808108i	$-0.299508\pi$
$191$	16.2812			1.17807			0.589034	+	0.808108i	$0.299508\pi$
$192$		0			0
$193$	14.9072	−	8.60669i	1.07304	−	0.619523i	0.144033	−	0.989573i	$-0.453993\pi$
$193$	14.9072	−	8.60669i	1.07304	−	0.619523i	0.929012	+	0.370050i	$0.120659\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			10.2044i			0.727034i	0.931588	+	0.363517i	$0.118424\pi$
$197$			10.2044i			0.727034i	−0.931588	+	0.363517i	$0.881576\pi$
$198$		0			0
$199$	5.03189	−	8.71550i	0.356701	−	0.617825i	−0.630706	−	0.776022i	$-0.717235\pi$
$199$	5.03189	−	8.71550i	0.356701	−	0.617825i	0.987408	+	0.158197i	$0.0505680\pi$
$200$		0			0
$201$	6.81761			0.480877
$202$		0			0
$203$	15.9063	+	9.18351i	1.11640	+	0.644556i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	58.3380	−	33.6815i	4.05477	−	2.34102i
$208$		0			0
$209$	5.18688	−	0.810784i	0.358784	−	0.0560831i
$210$		0			0
$211$	6.12758	+	10.6133i	0.421840	+	0.730648i	0.996119	−	0.0880113i	$-0.0280512\pi$
$211$	6.12758	+	10.6133i	0.421840	+	0.730648i	−0.574280	+	0.818659i	$0.694718\pi$
$212$		0			0
$213$	−29.0624	−	16.7792i	−1.99132	−	1.14969i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			18.2264i			1.23729i
$218$		0			0
$219$	7.78571	−	13.4852i	0.526110	−	0.911249i
$220$		0			0
$221$	2.14061			0.143993
$222$		0			0
$223$	−17.4501	+	10.0748i	−1.16854	+	0.674658i	−0.953336	−	0.301911i	$-0.902376\pi$
$223$	−17.4501	+	10.0748i	−1.16854	+	0.674658i	−0.215206	+	0.976569i	$0.569042\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			8.25515i			0.547914i	0.961742	+	0.273957i	$0.0883325\pi$
$227$			8.25515i			0.547914i	−0.961742	+	0.273957i	$0.911667\pi$
$228$		0			0
$229$	26.6860			1.76346			0.881729	−	0.471756i	$-0.156380\pi$
$229$	26.6860			1.76346			0.881729	+	0.471756i	$0.156380\pi$
$230$		0			0
$231$	4.25382	+	7.36783i	0.279881	+	0.484768i
$232$		0			0
$233$	12.1321	−	7.00448i	0.794802	−	0.458879i	−0.0468485	−	0.998902i	$-0.514918\pi$
$233$	12.1321	−	7.00448i	0.794802	−	0.458879i	0.841650	+	0.540023i	$0.181584\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−45.5360	−	26.2902i	−2.95788	−	1.70773i
$238$		0			0
$239$	12.2682			0.793563			0.396782	−	0.917913i	$-0.370127\pi$
$239$	12.2682			0.793563			0.396782	+	0.917913i	$0.370127\pi$
$240$		0			0
$241$	−4.93621	+	8.54977i	−0.317969	+	0.550739i	−0.980064	−	0.198681i	$-0.936334\pi$
$241$	−4.93621	+	8.54977i	−0.317969	+	0.550739i	0.662095	+	0.749420i	$0.269668\pi$
$242$		0			0
$243$	25.5793	+	14.7682i	1.64091	+	0.947380i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−4.06622	−	1.57031i	−0.258727	−	0.0999162i
$248$		0			0
$249$	9.18351	+	15.9063i	0.581981	+	1.00802i
$250$		0			0
$251$	−14.4198	+	24.9758i	−0.910170	+	1.57646i	−0.0963474	+	0.995348i	$0.530716\pi$
$251$	−14.4198	+	24.9758i	−0.910170	+	1.57646i	−0.813823	+	0.581113i	$0.802617\pi$
$252$		0			0
$253$	−9.66711	−	5.58131i	−0.607766	−	0.350894i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.15311	−	2.39780i	−0.259064	−	0.149571i	0.364844	−	0.931069i	$-0.381122\pi$
$257$	−4.15311	−	2.39780i	−0.259064	−	0.149571i	−0.623907	+	0.781498i	$0.714456\pi$
$258$		0			0
$259$	−4.85939			−0.301948
$260$		0			0
$261$	−30.2792	−	52.4451i	−1.87424	−	3.24627i
$262$		0			0
$263$	17.6745	−	10.2044i	1.08986	−	0.629230i	0.156320	−	0.987706i	$-0.450037\pi$
$263$	17.6745	−	10.2044i	1.08986	−	0.629230i	0.933539	+	0.358476i	$0.116704\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	34.6640i		−	2.12140i
$268$		0			0
$269$	0.563788	+	0.976509i	0.0343747	+	0.0595388i	0.882701	−	0.469935i	$-0.155723\pi$
$269$	0.563788	+	0.976509i	0.0343747	+	0.0595388i	−0.848326	+	0.529474i	$0.822389\pi$
$270$		0			0
$271$	−9.83850	−	17.0408i	−0.597646	−	1.03515i	−0.993168	−	0.116697i	$-0.962769\pi$
$271$	−9.83850	−	17.0408i	−0.597646	−	1.03515i	0.395522	−	0.918457i	$-0.370564\pi$
$272$		0			0
$273$		−	7.06379i		−	0.427520i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		−	7.35398i		−	0.441858i	−0.975290	−	0.220929i	$-0.929091\pi$
$277$		−	7.35398i		−	0.441858i	0.975290	−	0.220929i	$-0.0709089\pi$
$278$		0			0
$279$	30.0474	−	52.0436i	1.79889	−	3.11577i
$280$		0			0
$281$	−6.73630	+	11.6676i	−0.401854	+	0.696031i	−0.993950	−	0.109836i	$-0.964967\pi$
$281$	−6.73630	+	11.6676i	−0.401854	+	0.696031i	0.592096	+	0.805867i	$0.298301\pi$
$282$		0			0
$283$	18.4627	−	10.6595i	1.09750	−	0.633640i	0.161934	−	0.986802i	$-0.448227\pi$
$283$	18.4627	−	10.6595i	1.09750	−	0.633640i	0.935562	+	0.353162i	$0.114894\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−12.6251	+	7.28908i	−0.745233	+	0.430261i
$288$		0			0
$289$	−6.20889	+	10.7541i	−0.365229	+	0.632594i
$290$		0			0
$291$	25.2199	−	43.6821i	1.47842	−	2.56069i
$292$		0			0
$293$			8.08580i			0.472377i	0.971707	+	0.236189i	$0.0758983\pi$
$293$			8.08580i			0.472377i	−0.971707	+	0.236189i	$0.924102\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	16.4726i		−	0.955837i
$298$		0			0
$299$	4.63409	+	8.02649i	0.267997	+	0.464184i
$300$		0			0
$301$	2.58468	+	4.47679i	0.148978	+	0.258038i
$302$		0			0
$303$			33.8046i			1.94202i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−24.7549	+	14.2922i	−1.41284	+	0.815701i	−0.995655	−	0.0931229i	$-0.970315\pi$
$307$	−24.7549	+	14.2922i	−1.41284	+	0.815701i	−0.417180	+	0.908824i	$0.636982\pi$
$308$		0			0
$309$	1.17251	+	2.03084i	0.0667016	+	0.115531i
$310$		0			0
$311$	−10.7408			−0.609054			−0.304527	−	0.952504i	$-0.598498\pi$
$311$	−10.7408			−0.609054			−0.304527	+	0.952504i	$0.598498\pi$
$312$		0			0
$313$	−9.89160	−	5.71092i	−0.559107	−	0.322800i	0.193680	−	0.981065i	$-0.437958\pi$
$313$	−9.89160	−	5.71092i	−0.559107	−	0.322800i	−0.752787	+	0.658264i	$0.771291\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.81128	+	1.62309i	0.157897	+	0.0911619i	0.576867	−	0.816838i	$-0.304275\pi$
$317$	2.81128	+	1.62309i	0.157897	+	0.0911619i	−0.418970	+	0.908000i	$0.637609\pi$
$318$		0			0
$319$	−5.01752	+	8.69060i	−0.280927	+	0.486580i
$320$		0			0
$321$	−21.4627	−	37.1745i	−1.19793	−	2.07488i
$322$		0			0
$323$	−7.26318	+	5.85735i	−0.404134	+	0.325912i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−16.4735	−	9.51100i	−0.910989	−	0.525960i
$328$		0			0
$329$	9.18351	−	15.9063i	0.506303	−	0.876943i
$330$		0			0
$331$	35.1208			1.93042			0.965208	−	0.261483i	$-0.0842116\pi$
$331$	35.1208			1.93042			0.965208	+	0.261483i	$0.0842116\pi$
$332$		0			0
$333$	13.8755	+	8.01100i	0.760371	+	0.439000i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−13.7459	+	7.93621i	−0.748788	+	0.432313i	−0.825256	−	0.564759i	$-0.808969\pi$
$337$	−13.7459	+	7.93621i	−0.748788	+	0.432313i	0.0764677	+	0.997072i	$0.475636\pi$
$338$		0			0
$339$	−25.0155	−	43.3281i	−1.35865	−	2.35326i
$340$		0			0
$341$	−9.95822			−0.539268
$342$		0			0
$343$			20.1496i			1.08798i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	28.2707	−	16.3221i	1.51765	−	0.876216i	0.517866	−	0.855462i	$-0.326727\pi$
$347$	28.2707	−	16.3221i	1.51765	−	0.876216i	0.999785	−	0.0207537i	$-0.00660660\pi$
$348$		0			0
$349$	21.7538			1.16446			0.582228	−	0.813026i	$-0.302181\pi$
$349$	21.7538			1.16446			0.582228	+	0.813026i	$0.302181\pi$
$350$		0			0
$351$	−6.83850	+	11.8446i	−0.365012	+	0.632219i
$352$		0			0
$353$			8.67699i			0.461830i	0.972974	+	0.230915i	$0.0741719\pi$
$353$			8.67699i			0.461830i	−0.972974	+	0.230915i	$0.925828\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−13.0950	−	7.56042i	−0.693063	−	0.400140i
$358$		0			0
$359$	5.81109	+	10.0651i	0.306697	+	0.531216i	0.977638	−	0.210296i	$-0.0674427\pi$
$359$	5.81109	+	10.0651i	0.306697	+	0.531216i	−0.670940	+	0.741511i	$0.734109\pi$
$360$		0			0
$361$	18.0936	−	5.79827i	0.952297	−	0.305172i
$362$		0			0
$363$	26.5005	−	15.3001i	1.39092	−	0.803046i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	26.5083	+	15.3046i	1.38372	+	0.798892i	0.992598	−	0.121446i	$-0.0387532\pi$
$367$	26.5083	+	15.3046i	1.38372	+	0.798892i	0.391123	+	0.920338i	$0.372087\pi$
$368$		0			0
$369$	48.0660			2.50222
$370$		0			0
$371$	0.295598	−	0.511992i	0.0153467	−	0.0265813i
$372$		0			0
$373$			4.70980i			0.243864i	0.992538	+	0.121932i	$0.0389090\pi$
$373$			4.70980i			0.243864i	−0.992538	+	0.121932i	$0.961091\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	7.21570	−	4.16599i	0.371628	−	0.214559i
$378$		0			0
$379$	−10.0638			−0.516942			−0.258471	−	0.966019i	$-0.583219\pi$
$379$	−10.0638			−0.516942			−0.258471	+	0.966019i	$0.583219\pi$
$380$		0			0
$381$	49.2003			2.52061
$382$		0			0
$383$	23.7671	−	13.7219i	1.21444	−	0.701158i	0.250717	−	0.968060i	$-0.419334\pi$
$383$	23.7671	−	13.7219i	1.21444	−	0.701158i	0.963723	+	0.266903i	$0.0860003\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	17.0440i		−	0.866396i
$388$		0			0
$389$	0.257185	−	0.445458i	0.0130398	−	0.0225856i	−0.859432	−	0.511250i	$-0.829183\pi$
$389$	0.257185	−	0.445458i	0.0130398	−	0.0225856i	0.872472	+	0.488665i	$0.162516\pi$
$390$		0			0
$391$	19.8396			1.00333
$392$		0			0
$393$	−21.6335	−	12.4901i	−1.09127	−	0.630043i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.68950	+	1.55278i	−0.134982	+	0.0779320i	−0.565970	−	0.824426i	$-0.691498\pi$
$397$	−2.68950	+	1.55278i	−0.134982	+	0.0779320i	0.430988	+	0.902358i	$0.358165\pi$
$398$		0			0
$399$	19.3286	+	23.9677i	0.967641	+	1.19988i
$400$		0			0
$401$	6.51752	+	11.2887i	0.325470	+	0.563730i	0.981607	−	0.190911i	$-0.0611443\pi$
$401$	6.51752	+	11.2887i	0.325470	+	0.563730i	−0.656138	+	0.754641i	$0.727811\pi$
$402$		0			0
$403$	7.16046	+	4.13409i	0.356688	+	0.205934i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	2.65498i		−	0.131603i
$408$		0			0
$409$	13.7747	−	23.8585i	0.681115	−	1.17973i	−0.293525	−	0.955951i	$-0.594828\pi$
$409$	13.7747	−	23.8585i	0.681115	−	1.17973i	0.974641	−	0.223775i	$-0.0718382\pi$
$410$		0			0
$411$	−52.7848			−2.60368
$412$		0			0
$413$	15.9063	−	9.18351i	0.782698	−	0.451891i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	62.6024i		−	3.06565i
$418$		0			0
$419$	−16.5494			−0.808492			−0.404246	−	0.914650i	$-0.632466\pi$
$419$	−16.5494			−0.808492			−0.404246	+	0.914650i	$0.632466\pi$
$420$		0			0
$421$	7.93418	+	13.7424i	0.386688	+	0.669764i	0.992002	−	0.126223i	$-0.0402856\pi$
$421$	7.93418	+	13.7424i	0.386688	+	0.669764i	−0.605314	+	0.795987i	$0.706952\pi$
$422$		0			0
$423$	−52.4451	+	30.2792i	−2.54997	+	1.47222i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.50764	+	3.75719i	0.314927	+	0.181823i
$428$		0			0
$429$	3.85939			0.186333
$430$		0			0
$431$	−11.4472	+	19.8272i	−0.551393	+	0.955041i	0.446781	+	0.894643i	$0.352570\pi$
$431$	−11.4472	+	19.8272i	−0.551393	+	0.955041i	−0.998174	+	0.0603975i	$0.980763\pi$
$432$		0			0
$433$	18.4740	+	10.6660i	0.887805	+	0.512575i	0.873224	−	0.487319i	$-0.162025\pi$
$433$	18.4740	+	10.6660i	0.887805	+	0.512575i	0.0145814	+	0.999894i	$0.495358\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−37.6865	−	14.5539i	−1.80279	−	0.696208i
$438$		0			0
$439$	−5.08783	−	8.81238i	−0.242829	−	0.420592i	0.718690	−	0.695331i	$-0.244742\pi$
$439$	−5.08783	−	8.81238i	−0.242829	−	0.420592i	−0.961519	+	0.274739i	$0.911409\pi$
$440$		0			0
$441$	7.77919	−	13.4740i	0.370438	−	0.641617i
$442$		0			0
$443$	5.72720	+	3.30660i	0.272108	+	0.157101i	0.629845	−	0.776721i	$-0.283118\pi$
$443$	5.72720	+	3.30660i	0.272108	+	0.157101i	−0.357737	+	0.933822i	$0.616452\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	15.7542	+	9.09568i	0.745147	+	0.430211i
$448$		0			0
$449$	−10.9870			−0.518507			−0.259253	−	0.965809i	$-0.583476\pi$
$449$	−10.9870			−0.518507			−0.259253	+	0.965809i	$0.583476\pi$
$450$		0			0
$451$	−3.98248	−	6.89785i	−0.187528	−	0.324807i
$452$		0			0
$453$	39.4796	−	22.7936i	1.85491	−	1.07094i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	12.5494i		−	0.587037i	−0.955953	−	0.293518i	$-0.905174\pi$
$457$		−	12.5494i		−	0.587037i	0.955953	−	0.293518i	$-0.0948262\pi$
$458$		0			0
$459$	14.6386	+	25.3548i	0.683270	+	1.18346i
$460$		0			0
$461$	11.6386	+	20.1586i	0.542063	+	0.938880i	0.998785	+	0.0492710i	$0.0156898\pi$
$461$	11.6386	+	20.1586i	0.542063	+	0.938880i	−0.456723	+	0.889609i	$0.650977\pi$
$462$		0			0
$463$		−	23.3958i		−	1.08729i	−0.839314	−	0.543647i	$-0.817043\pi$
$463$		−	23.3958i		−	1.08729i	0.839314	−	0.543647i	$-0.182957\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			12.6352i			0.584688i	0.956313	+	0.292344i	$0.0944352\pi$
$467$			12.6352i			0.584688i	−0.956313	+	0.292344i	$0.905565\pi$
$468$		0			0
$469$	2.34502	−	4.06169i	0.108283	−	0.187551i
$470$		0			0
$471$	−1.04942	+	1.81764i	−0.0483546	+	0.0837526i
$472$		0			0
$473$	−2.44595	+	1.41217i	−0.112465	+	0.0649316i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.68810	+	0.974625i	−0.0772928	+	0.0446250i
$478$		0			0
$479$	2.01752	−	3.49445i	0.0921830	−	0.159666i	−0.816246	−	0.577704i	$-0.803949\pi$
$479$	2.01752	−	3.49445i	0.0921830	−	0.159666i	0.908429	+	0.418038i	$0.137282\pi$
$480$		0			0
$481$	−1.10220	+	1.90907i	−0.0502560	+	0.0870460i
$482$		0			0
$483$		−	65.4685i		−	2.97892i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	6.54942i		−	0.296782i	−0.988929	−	0.148391i	$-0.952591\pi$
$487$		−	6.54942i		−	0.296782i	0.988929	−	0.148391i	$-0.0474095\pi$
$488$		0			0
$489$	20.3111	+	35.1798i	0.918499	+	1.59089i
$490$		0			0
$491$	−1.04290	−	1.80635i	−0.0470653	−	0.0815195i	0.841533	−	0.540206i	$-0.181654\pi$
$491$	−1.04290	−	1.80635i	−0.0470653	−	0.0815195i	−0.888598	+	0.458686i	$0.848320\pi$
$492$		0			0
$493$		−	17.8355i		−	0.803273i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−19.9929	+	11.5429i	−0.896803	+	0.517770i
$498$		0			0
$499$	−12.0539	−	20.8780i	−0.539607	−	0.934626i	−0.998925	−	0.0463546i	$-0.985240\pi$
$499$	−12.0539	−	20.8780i	−0.539607	−	0.934626i	0.459318	−	0.888272i	$-0.348094\pi$
$500$		0			0
$501$	24.9802			1.11603
$502$		0			0
$503$	7.16823	+	4.13858i	0.319616	+	0.184530i	0.651221	−	0.758888i	$-0.274257\pi$
$503$	7.16823	+	4.13858i	0.319616	+	0.184530i	−0.331606	+	0.943418i	$0.607590\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	33.3011	+	19.2264i	1.47895	+	0.853875i
$508$		0			0
$509$	−2.86591	+	4.96389i	−0.127029	+	0.220021i	−0.922524	−	0.385939i	$-0.873877\pi$
$509$	−2.86591	+	4.96389i	−0.127029	+	0.220021i	0.795495	+	0.605960i	$0.207211\pi$
$510$		0			0
$511$	−5.35602	−	9.27690i	−0.236936	−	0.410386i
$512$		0			0
$513$	−9.20713	−	58.9014i	−0.406505	−	2.60056i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	8.69060	+	5.01752i	0.382212	+	0.220670i
$518$		0			0
$519$	17.2089	−	29.8067i	0.755386	−	1.30837i
$520$		0			0
$521$	14.8086			0.648778			0.324389	−	0.945924i	$-0.394841\pi$
$521$	14.8086			0.648778			0.324389	+	0.945924i	$0.394841\pi$
$522$		0			0
$523$	−13.4988	−	7.79356i	−0.590263	−	0.340789i	0.174938	−	0.984579i	$-0.444027\pi$
$523$	−13.4988	−	7.79356i	−0.590263	−	0.340789i	−0.765202	+	0.643791i	$0.777361\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	15.3278	−	8.84950i	0.667689	−	0.385490i
$528$		0			0
$529$	31.4497	+	54.4724i	1.36738	+	2.36837i
$530$		0			0
$531$	−60.5584			−2.62801
$532$		0			0
$533$			6.61320i			0.286450i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.29978	+	2.48248i	−0.185549	+	0.107127i
$538$		0			0
$539$	−2.57816			−0.111049
$540$		0			0
$541$	−14.0539	+	24.3421i	−0.604224	+	1.04655i	0.387949	+	0.921681i	$0.373184\pi$
$541$	−14.0539	+	24.3421i	−0.604224	+	1.04655i	−0.992174	+	0.124867i	$0.960150\pi$
$542$		0			0
$543$			26.3607i			1.13125i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−37.5569	−	21.6835i	−1.60582	−	0.927120i	−0.990292	−	0.139004i	$-0.955610\pi$
$547$	−37.5569	−	21.6835i	−1.60582	−	0.927120i	−0.615527	−	0.788116i	$-0.711057\pi$
$548$		0			0
$549$	−12.3879	−	21.4565i	−0.528703	−	0.915741i
$550$		0			0
$551$	−13.0838	+	33.8796i	−0.557387	+	1.44332i
$552$		0			0
$553$	−31.3255	+	18.0858i	−1.33210	+	0.769086i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.9963	+	8.65814i	0.635415	+	0.366857i	0.782846	−	0.622215i	$-0.213767\pi$
$557$	14.9963	+	8.65814i	0.635415	+	0.366857i	−0.147431	+	0.989072i	$0.547100\pi$
$558$		0			0
$559$	2.34502			0.0991836
$560$		0			0
$561$	4.13073	−	7.15463i	0.174399	−	0.302069i
$562$		0			0
$563$			8.35398i			0.352078i	0.984383	+	0.176039i	$0.0563286\pi$
$563$			8.35398i			0.352078i	−0.984383	+	0.176039i	$0.943671\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	42.0415	−	24.2727i	1.76558	−	1.01936i
$568$		0			0
$569$	10.6640			0.447056			0.223528	−	0.974697i	$-0.428243\pi$
$569$	10.6640			0.447056			0.223528	+	0.974697i	$0.428243\pi$
$570$		0			0
$571$	−2.56512			−0.107347			−0.0536735	−	0.998559i	$-0.517093\pi$
$571$	−2.56512			−0.107347			−0.0536735	+	0.998559i	$0.517093\pi$
$572$		0			0
$573$	−45.1819	+	26.0858i	−1.88750	+	1.08975i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	20.4218i		−	0.850172i	−0.905153	−	0.425086i	$-0.860244\pi$
$577$		−	20.4218i		−	0.850172i	0.905153	−	0.425086i	$-0.139756\pi$
$578$		0			0
$579$	−27.5793	+	47.7687i	−1.14616	+	1.98520i
$580$		0			0
$581$	12.6352			0.524197
$582$		0			0
$583$	0.279733	+	0.161504i	0.0115853	+	0.00668880i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	7.62850	−	4.40432i	0.314862	−	0.181786i	−0.334238	−	0.942489i	$-0.608479\pi$
$587$	7.62850	−	4.40432i	0.314862	−	0.181786i	0.649100	+	0.760703i	$0.275146\pi$
$588$		0			0
$589$	−35.6078	+	5.56601i	−1.46719	+	0.229343i
$590$		0			0
$591$	−16.3495	−	28.3182i	−0.672529	−	1.16485i
$592$		0			0
$593$	−28.5314	−	16.4726i	−1.17164	−	0.676448i	−0.217576	−	0.976043i	$-0.569815\pi$
$593$	−28.5314	−	16.4726i	−1.17164	−	0.676448i	−0.954066	+	0.299595i	$0.903148\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			32.2484i			1.31984i
$598$		0			0
$599$	−9.56379	+	16.5650i	−0.390766	+	0.676826i	−0.992551	−	0.121832i	$-0.961123\pi$
$599$	−9.56379	+	16.5650i	−0.390766	+	0.676826i	0.601785	+	0.798658i	$0.294456\pi$
$600$		0			0
$601$	19.3100			0.787670			0.393835	−	0.919181i	$-0.371148\pi$
$601$	19.3100			0.787670			0.393835	+	0.919181i	$0.371148\pi$
$602$		0			0
$603$	−13.3919	+	7.73181i	−0.545360	+	0.314864i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	36.8773i		−	1.49680i	−0.663245	−	0.748402i	$-0.730821\pi$
$607$		−	36.8773i		−	1.49680i	0.663245	−	0.748402i	$-0.269179\pi$
$608$		0			0
$609$	−58.8553			−2.38494
$610$		0			0
$611$	−4.16599	−	7.21570i	−0.168538	−	0.291916i
$612$		0			0
$613$	−24.6996	+	14.2603i	−0.997609	+	0.575970i	−0.907540	−	0.419966i	$-0.862042\pi$
$613$	−24.6996	+	14.2603i	−0.997609	+	0.575970i	−0.0900688	+	0.995936i	$0.528709\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.78112	−	5.64713i	−0.393773	−	0.227345i	0.290021	−	0.957020i	$-0.406338\pi$
$617$	−9.78112	−	5.64713i	−0.393773	−	0.227345i	−0.683794	+	0.729675i	$0.739671\pi$
$618$		0			0
$619$	−27.2044			−1.09344			−0.546719	−	0.837316i	$-0.684123\pi$
$619$	−27.2044			−1.09344			−0.546719	+	0.837316i	$0.684123\pi$
$620$		0			0
$621$	−63.3805	+	109.778i	−2.54337	+	4.40525i
$622$		0			0
$623$	−20.6515	−	11.9232i	−0.827387	−	0.477692i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−13.0950	+	10.5604i	−0.522965	+	0.421743i
$628$		0			0
$629$	2.35939	+	4.08658i	0.0940749	+	0.162942i
$630$		0			0
$631$	−4.19136	+	7.25965i	−0.166856	+	0.289002i	−0.937313	−	0.348490i	$-0.886695\pi$
$631$	−4.19136	+	7.25965i	−0.166856	+	0.289002i	0.770457	+	0.637492i	$0.220028\pi$
$632$		0			0
$633$	−34.0092	−	19.6352i	−1.35174	−	0.780430i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.85383	+	1.07031i	0.0734513	+	0.0424071i
$638$		0			0
$639$	76.1168			3.01113
$640$		0			0
$641$	−9.55594	−	16.5514i	−0.377437	−	0.653740i	0.613252	−	0.789888i	$-0.289861\pi$
$641$	−9.55594	−	16.5514i	−0.377437	−	0.653740i	−0.990689	+	0.136148i	$0.956528\pi$
$642$		0			0
$643$	−41.7618	+	24.1112i	−1.64692	+	0.950852i	−0.668638	+	0.743588i	$0.733123\pi$
$643$	−41.7618	+	24.1112i	−1.64692	+	0.950852i	−0.978285	+	0.207264i	$0.933544\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			30.0817i			1.18263i	0.806439	+	0.591317i	$0.201392\pi$
$647$			30.0817i			1.18263i	−0.806439	+	0.591317i	$0.798608\pi$
$648$		0			0
$649$	5.01752	+	8.69060i	0.196955	+	0.341136i
$650$		0			0
$651$	−29.2024	−	50.5800i	−1.14453	−	1.98239i
$652$		0			0
$653$			41.9124i			1.64016i	0.572250	+	0.820079i	$0.306071\pi$
$653$			41.9124i			1.64016i	−0.572250	+	0.820079i	$0.693929\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			35.3189i			1.37792i
$658$		0			0
$659$	−20.0936	+	34.8032i	−0.782737	+	1.35574i	0.147604	+	0.989047i	$0.452844\pi$
$659$	−20.0936	+	34.8032i	−0.782737	+	1.35574i	−0.930341	+	0.366694i	$0.880489\pi$
$660$		0			0
$661$	0.757185	−	1.31148i	0.0294511	−	0.0510108i	−0.850924	−	0.525289i	$-0.823957\pi$
$661$	0.757185	−	1.31148i	0.0294511	−	0.0510108i	0.880375	+	0.474278i	$0.157291\pi$
$662$		0			0
$663$	−5.94040	+	3.42969i	−0.230706	+	0.133198i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	66.8765	−	38.6112i	2.58947	−	1.49503i
$668$		0			0
$669$	32.2837	−	55.9170i	1.24816	−	2.16187i
$670$		0			0
$671$	−2.05278	+	3.55553i	−0.0792468	+	0.137260i
$672$		0			0
$673$		−	7.76686i		−	0.299390i	−0.988732	−	0.149695i	$-0.952171\pi$
$673$		−	7.76686i		−	0.299390i	0.988732	−	0.149695i	$-0.0478292\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	6.19136i		−	0.237953i	−0.992897	−	0.118977i	$-0.962039\pi$
$677$		−	6.19136i		−	0.237953i	0.992897	−	0.118977i	$-0.0379614\pi$
$678$		0			0
$679$	−17.3495	−	30.0502i	−0.665813	−	1.15322i
$680$		0			0
$681$	−13.2264	−	22.9088i	−0.506837	−	0.877868i
$682$		0			0
$683$			2.92317i			0.111852i	0.998435	+	0.0559261i	$0.0178111\pi$
$683$			2.92317i			0.111852i	−0.998435	+	0.0559261i	$0.982189\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−74.0560	+	42.7563i	−2.82541	+	1.63125i
$688$		0			0
$689$	−0.134095	−	0.232259i	−0.00510860	−	0.00884835i
$690$		0			0
$691$	−2.35805			−0.0897046			−0.0448523	−	0.998994i	$-0.514282\pi$
$691$	−2.35805			−0.0897046			−0.0448523	+	0.998994i	$0.514282\pi$
$692$		0			0
$693$	−16.7116	−	9.64847i	−0.634822	−	0.366515i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	12.2597	+	7.07816i	0.464370	+	0.268104i
$698$		0			0
$699$	−22.4452	+	38.8762i	−0.848955	+	1.47043i
$700$		0			0
$701$	−12.2792	−	21.2682i	−0.463779	−	0.803288i	0.535367	−	0.844620i	$-0.320173\pi$
$701$	−12.2792	−	21.2682i	−0.463779	−	0.803288i	−0.999145	+	0.0413314i	$0.986840\pi$
$702$		0			0
$703$	−1.48397	−	9.49348i	−0.0559689	−	0.358053i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	20.1396	+	11.6276i	0.757426	+	0.437300i
$708$		0			0
$709$	3.63858	−	6.30220i	0.136650	−	0.236684i	−0.789577	−	0.613652i	$-0.789700\pi$
$709$	3.63858	−	6.30220i	0.136650	−	0.236684i	0.926226	+	0.376968i	$0.123033\pi$
$710$		0			0
$711$	119.262			4.47269
$712$		0			0
$713$	66.3645	+	38.3156i	2.48537	+	1.43493i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−34.0454	+	19.6561i	−1.27145	+	0.734071i
$718$		0			0
$719$	16.4452	+	28.4839i	0.613302	+	1.06227i	0.990680	+	0.136211i	$0.0434924\pi$
$719$	16.4452	+	28.4839i	0.613302	+	1.06227i	−0.377378	+	0.926059i	$0.623174\pi$
$720$		0			0
$721$	1.61320			0.0600789
$722$		0			0
$723$		−	31.6352i		−	1.17653i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−24.1709	+	13.9551i	−0.896449	+	0.517565i	−0.876046	−	0.482227i	$-0.839828\pi$
$727$	−24.1709	+	13.9551i	−0.896449	+	0.517565i	−0.0204023	+	0.999792i	$0.506495\pi$
$728$		0			0
$729$	−28.5804			−1.05853
$730$		0			0
$731$	2.50989	−	4.34725i	0.0928315	−	0.160789i
$732$		0			0
$733$		−	4.89710i		−	0.180878i	−0.995902	−	0.0904392i	$-0.971173\pi$
$733$		−	4.89710i		−	0.180878i	0.995902	−	0.0904392i	$-0.0288271\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.21915	+	1.28123i	0.0817435	+	0.0471946i
$738$		0			0
$739$	−11.5936	−	20.0808i	−0.426479	−	0.738684i	0.570078	−	0.821591i	$-0.306913\pi$
$739$	−11.5936	−	20.0808i	−0.426479	−	0.738684i	−0.996557	+	0.0829069i	$0.973580\pi$
$740$		0			0
$741$	13.8001	−	2.15715i	0.506959	−	0.0792449i
$742$		0			0
$743$	34.6239	−	19.9901i	1.27023	−	0.733366i	0.295197	−	0.955436i	$-0.404615\pi$
$743$	34.6239	−	19.9901i	1.27023	−	0.733366i	0.975031	+	0.222070i	$0.0712815\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−36.0785	−	20.8299i	−1.32004	−	0.762128i
$748$		0			0
$749$	−29.5296			−1.07899
$750$		0			0
$751$	10.2936	−	17.8290i	0.375617	−	0.650589i	−0.614802	−	0.788682i	$-0.710764\pi$
$751$	10.2936	−	17.8290i	0.375617	−	0.650589i	0.990419	+	0.138093i	$0.0440973\pi$
$752$		0			0
$753$		−	92.4137i		−	3.36774i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	29.9950	−	17.3176i	1.09019	−	0.629419i	0.156560	−	0.987668i	$-0.449960\pi$
$757$	29.9950	−	17.3176i	1.09019	−	0.629419i	0.933626	+	0.358249i	$0.116626\pi$
$758$		0			0
$759$	35.7695			1.29835
$760$		0			0
$761$	24.3890			0.884102			0.442051	−	0.896990i	$-0.354251\pi$
$761$	24.3890			0.884102			0.442051	+	0.896990i	$0.354251\pi$
$762$		0			0
$763$	−11.3326	+	6.54290i	−0.410269	+	0.236869i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	8.33198i		−	0.300850i
$768$		0			0
$769$	3.27471	−	5.67196i	0.118089	−	0.204536i	−0.800921	−	0.598770i	$-0.795657\pi$
$769$	3.27471	−	5.67196i	0.118089	−	0.204536i	0.919010	+	0.394233i	$0.128990\pi$
$770$		0			0
$771$	15.3670			0.553430
$772$		0			0
$773$	32.4522	+	18.7363i	1.16723	+	0.673898i	0.953025	−	0.302892i	$-0.0979522\pi$
$773$	32.4522	+	18.7363i	1.16723	+	0.673898i	0.214200	+	0.976790i	$0.431286\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	13.4852	−	7.78571i	0.483781	−	0.279311i
$778$		0			0
$779$	−18.0957	−	22.4388i	−0.648345	−	0.803955i
$780$		0			0
$781$	−6.30660	−	10.9234i	−0.225668	−	0.390868i
$782$		0			0
$783$	98.6891	+	56.9782i	3.52686	+	2.03623i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			12.8306i			0.457363i	0.973501	+	0.228682i	$0.0734415\pi$
$787$			12.8306i			0.457363i	−0.973501	+	0.228682i	$0.926559\pi$
$788$		0			0
$789$	−32.6990	+	56.6363i	−1.16412	+	2.01631i
$790$		0			0
$791$	−34.4178			−1.22376
$792$		0			0
$793$	2.95211	−	1.70440i	0.104833	−	0.0605251i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			28.3032i			1.00255i	0.865287	+	0.501276i	$0.167136\pi$
$797$			28.3032i			1.00255i	−0.865287	+	0.501276i	$0.832864\pi$
$798$		0			0
$799$	−17.8355			−0.630976
$800$		0			0
$801$	39.3122	+	68.0907i	1.38903	+	2.40587i
$802$		0			0
$803$	5.06855	−	2.92633i	0.178865	−	0.103268i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.12913	−	1.80660i	−0.110150	−	0.0635954i
$808$		0			0
$809$	55.4946			1.95109			0.975543	−	0.219808i	$-0.0705432\pi$
$809$	55.4946			1.95109			0.975543	+	0.219808i	$0.0705432\pi$
$810$		0			0
$811$	11.8540	−	20.5317i	0.416250	−	0.720966i	−0.579309	−	0.815108i	$-0.696678\pi$
$811$	11.8540	−	20.5317i	0.416250	−	0.720966i	0.995559	+	0.0941424i	$0.0300109\pi$
$812$		0			0
$813$	54.6055	+	31.5265i	1.91510	+	1.10568i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−7.95672	+	6.41665i	−0.278370	+	0.224490i
$818$		0			0
$819$	8.01100	+	13.8755i	0.279927	+	0.484848i
$820$		0			0
$821$	−11.3625	+	19.6805i	−0.396555	+	0.686854i	−0.993298	−	0.115578i	$-0.963128\pi$
$821$	−11.3625	+	19.6805i	−0.396555	+	0.686854i	0.596743	+	0.802432i	$0.296461\pi$
$822$		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
$827$	17.2291	+	9.94722i	0.599114	+	0.345899i	0.768693	−	0.639618i	$-0.220907\pi$
$827$	17.2291	+	9.94722i	0.599114	+	0.345899i	−0.169579	+	0.985517i	$0.554241\pi$
$828$		0			0
$829$	−4.37109			−0.151814			−0.0759071	−	0.997115i	$-0.524185\pi$
$829$	−4.37109			−0.151814			−0.0759071	+	0.997115i	$0.524185\pi$
$830$		0			0
$831$	11.7826	+	20.4080i	0.408732	+	0.707945i
$832$		0			0
$833$	3.96833	−	2.29111i	0.137494	−	0.0793824i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			113.084i			3.90875i
$838$		0			0
$839$	1.22396	+	2.11996i	0.0422558	+	0.0731891i	0.886380	−	0.462959i	$-0.153212\pi$
$839$	1.22396	+	2.11996i	0.0422558	+	0.0731891i	−0.844124	+	0.536148i	$0.819879\pi$
$840$		0			0
$841$	−20.2109	−	35.0063i	−0.696928	−	1.20712i
$842$		0			0
$843$		−	43.1716i		−	1.48691i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		−	21.0507i		−	0.723312i
$848$		0			0
$849$	−34.1572	+	59.1620i	−1.17227	+	2.03044i
$850$		0			0
$851$	−10.2154	+	17.6936i	−0.350180	+	0.606529i
$852$		0			0
$853$	−15.5297	+	8.96607i	−0.531727	+	0.306992i	−0.741719	−	0.670711i	$-0.765989\pi$
$853$	−15.5297	+	8.96607i	−0.531727	+	0.306992i	0.209993	+	0.977703i	$0.432656\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	50.3115	−	29.0474i	1.71861	−	0.992240i	0.797135	−	0.603801i	$-0.206348\pi$
$857$	50.3115	−	29.0474i	1.71861	−	0.992240i	0.921475	−	0.388438i	$-0.126985\pi$
$858$		0			0
$859$	10.0409	−	17.3913i	0.342590	−	0.593383i	−0.642323	−	0.766434i	$-0.722029\pi$
$859$	10.0409	−	17.3913i	0.342590	−	0.593383i	0.984913	+	0.173051i	$0.0553626\pi$
$860$		0			0
$861$	23.3571	−	40.4557i	0.796009	−	1.37873i
$862$		0			0
$863$		−	28.6262i		−	0.974449i	−0.873277	−	0.487224i	$-0.838009\pi$
$863$		−	28.6262i		−	0.974449i	0.873277	−	0.487224i	$-0.161991\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	39.7915i		−	1.35139i
$868$		0			0
$869$	−9.88139	−	17.1151i	−0.335203	−	0.580589i
$870$		0			0
$871$	−1.06379	−	1.84253i	−0.0360451	−	0.0624319i
$872$		0			0
$873$			114.407i			3.87209i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−44.2019	+	25.5200i	−1.49259	+	0.861748i	−0.999964	−	0.00849182i	$-0.997297\pi$
$877$	−44.2019	+	25.5200i	−1.49259	+	0.861748i	−0.492628	+	0.870240i	$0.663964\pi$
$878$		0			0
$879$	−12.9551	−	22.4388i	−0.436964	−	0.756843i
$880$		0			0
$881$	−14.2992			−0.481751			−0.240876	−	0.970556i	$-0.577435\pi$
$881$	−14.2992			−0.481751			−0.240876	+	0.970556i	$0.577435\pi$
$882$		0			0
$883$	−25.4610	−	14.6999i	−0.856831	−	0.494692i	0.00611882	−	0.999981i	$-0.498052\pi$
$883$	−25.4610	−	14.6999i	−0.856831	−	0.494692i	−0.862950	+	0.505290i	$0.831386\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11.2031	+	6.46811i	0.376163	+	0.217178i	0.676147	−	0.736766i	$-0.263648\pi$
$887$	11.2031	+	6.46811i	0.376163	+	0.217178i	−0.299985	+	0.953944i	$0.596982\pi$
$888$		0			0
$889$	16.9232	−	29.3118i	0.567585	−	0.983086i
$890$		0			0
$891$	13.2617	+	22.9699i	0.444283	+	0.769520i
$892$		0			0
$893$	33.8796	+	13.0838i	1.13374	+	0.437831i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−25.7201	−	14.8495i	−0.858769	−	0.495810i
$898$		0			0
$899$	34.4452	−	59.6608i	1.14881	−	1.98980i
$900$		0			0
$901$	−0.574090			−0.0191257
$902$		0			0
$903$	−14.3454	−	8.28235i	−0.477386	−	0.275619i
$904$		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
$909$	−38.3376	−	66.4026i	−1.27158	−	2.20244i
$910$		0			0
$911$	−3.10964			−0.103027			−0.0515134	−	0.998672i	$-0.516404\pi$
$911$	−3.10964			−0.103027			−0.0515134	+	0.998672i	$0.516404\pi$
$912$		0			0
$913$			6.90340i			0.228469i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−14.8823	+	8.59231i	−0.491458	+	0.283743i
$918$		0			0
$919$	−23.4987			−0.775150			−0.387575	−	0.921838i	$-0.626687\pi$
$919$	−23.4987			−0.775150			−0.387575	+	0.921838i	$0.626687\pi$
$920$		0			0
$921$	45.7980	−	79.3245i	1.50910	−	2.61383i
$922$		0			0
$923$			10.4726i			0.344710i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−4.60634	−	2.65947i	−0.151292	−	0.0873484i
$928$		0			0
$929$	−22.3221	−	38.6630i	−0.732364	−	1.26849i	−0.955870	−	0.293789i	$-0.905084\pi$
$929$	−22.3221	−	38.6630i	−0.732364	−	1.26849i	0.223506	−	0.974703i	$-0.428250\pi$
$930$		0			0
$931$	−9.21877	+	1.44103i	−0.302133	+	0.0472277i
$932$		0			0
$933$	29.8067	−	17.2089i	0.975826	−	0.563394i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−20.3279	−	11.7363i	−0.664082	−	0.383408i	0.129748	−	0.991547i	$-0.458583\pi$
$937$	−20.3279	−	11.7363i	−0.664082	−	0.383408i	−0.793831	+	0.608139i	$0.791916\pi$
$938$		0			0
$939$	36.6002			1.19440
$940$		0			0
$941$	−20.0858	+	34.7896i	−0.654778	+	1.13411i	0.327171	+	0.944965i	$0.393905\pi$
$941$	−20.0858	+	34.7896i	−0.654778	+	1.13411i	−0.981949	+	0.189144i	$0.939429\pi$
$942$		0			0
$943$			61.2924i			1.99596i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−16.7688	+	9.68148i	−0.544913	+	0.314606i	−0.747068	−	0.664748i	$-0.768539\pi$
$947$	−16.7688	+	9.68148i	−0.544913	+	0.314606i	0.202155	+	0.979354i	$0.435206\pi$
$948$		0			0
$949$	−4.85939			−0.157742
$950$		0			0
$951$	−10.4021			−0.337310
$952$		0			0
$953$	4.19123	−	2.41981i	0.135767	−	0.0783852i	−0.430578	−	0.902553i	$-0.641690\pi$
$953$	4.19123	−	2.41981i	0.135767	−	0.0783852i	0.566345	+	0.824168i	$0.308357\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	32.1563i		−	1.03947i
$958$		0			0
$959$	−18.1561	+	31.4473i	−0.586291	+	1.01549i
$960$		0			0
$961$	37.3630			1.20526
$962$		0			0
$963$	84.3188	+	48.6815i	2.71714	+	1.56874i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−23.4457	+	13.5364i	−0.753963	+	0.435301i	−0.827124	−	0.562020i	$-0.810025\pi$
$967$	−23.4457	+	13.5364i	−0.753963	+	0.435301i	0.0731612	+	0.997320i	$0.476691\pi$
$968$		0			0
$969$	10.7713	−	27.8918i	0.346025	−	0.896013i
$970$		0			0
$971$	−1.61769	−	2.80192i	−0.0519141	−	0.0899179i	0.838901	−	0.544285i	$-0.183199\pi$
$971$	−1.61769	−	2.80192i	−0.0519141	−	0.0899179i	−0.890815	+	0.454367i	$0.849866\pi$
$972$		0			0
$973$	−37.2963	−	21.5330i	−1.19566	−	0.690317i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			1.93214i			0.0618147i	0.999522	+	0.0309074i	$0.00983969\pi$
$977$			1.93214i			0.0618147i	−0.999522	+	0.0309074i	$0.990160\pi$
$978$		0			0
$979$	6.51437	−	11.2832i	0.208200	−	0.360613i
$980$		0			0
$981$	43.1455			1.37753
$982$		0			0
$983$	−12.4457	+	7.18555i	−0.396957	+	0.229183i	−0.685170	−	0.728383i	$-0.740272\pi$
$983$	−12.4457	+	7.18555i	−0.396957	+	0.229183i	0.288213	+	0.957566i	$0.406939\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			58.8553i			1.87339i
$988$		0			0
$989$	21.7340			0.691102
$990$		0			0
$991$	−17.7956	−	30.8229i	−0.565296	−	0.979121i	−0.997022	−	0.0771164i	$-0.975429\pi$
$991$	−17.7956	−	30.8229i	−0.565296	−	0.979121i	0.431726	−	0.902005i	$-0.357905\pi$
$992$		0			0
$993$	−97.4636	+	56.2706i	−3.09291	+	1.78569i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	41.2058	+	23.7902i	1.30500	+	0.753443i	0.981257	−	0.192702i	$-0.0617249\pi$
$997$	41.2058	+	23.7902i	1.30500	+	0.753443i	0.323744	+	0.946145i	$0.395058\pi$
$998$		0			0
$999$	−30.1496			−0.953891

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.s.c.349.1		12
5.2	odd	4		380.2.i.b.121.3	✓	6
5.3	odd	4		1900.2.i.c.501.1		6
5.4	even	2	inner	1900.2.s.c.349.6		12
15.2	even	4		3420.2.t.v.1261.1		6
19.11	even	3	inner	1900.2.s.c.49.6		12
20.7	even	4		1520.2.q.i.881.1		6
95.7	odd	12		7220.2.a.n.1.1		3
95.12	even	12		7220.2.a.o.1.3		3
95.49	even	6	inner	1900.2.s.c.49.1		12
95.68	odd	12		1900.2.i.c.201.1		6
95.87	odd	12		380.2.i.b.201.3	yes	6
285.182	even	12		3420.2.t.v.3241.1		6
380.87	even	12		1520.2.q.i.961.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.b.121.3	✓	6	5.2	odd	4
380.2.i.b.201.3	yes	6	95.87	odd	12
1520.2.q.i.881.1		6	20.7	even	4
1520.2.q.i.961.1		6	380.87	even	12
1900.2.i.c.201.1		6	95.68	odd	12
1900.2.i.c.501.1		6	5.3	odd	4
1900.2.s.c.49.1		12	95.49	even	6	inner
1900.2.s.c.49.6		12	19.11	even	3	inner
1900.2.s.c.349.1		12	1.1	even	1	trivial
1900.2.s.c.349.6		12	5.4	even	2	inner
3420.2.t.v.1261.1		6	15.2	even	4
3420.2.t.v.3241.1		6	285.182	even	12
7220.2.a.n.1.1		3	95.7	odd	12
7220.2.a.o.1.3		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)

\(f(q)\)	\(=\)	\(q+(-2.77509 + 1.60220i) q^{3} +2.20440i q^{7} +(3.63409 - 6.29444i) q^{9} +O(q^{10})\)	\(q+(-2.77509 + 1.60220i) q^{3} +2.20440i q^{7} +(3.63409 - 6.29444i) q^{9} -1.20440 q^{11} +(0.866025 + 0.500000i) q^{13} +(1.85383 - 1.07031i) q^{17} +(-4.30660 + 0.673184i) q^{19} +(-3.53189 - 6.11742i) q^{21} +(8.02649 + 4.63409i) q^{23} +13.6770i q^{27} +(4.16599 - 7.21570i) q^{29} +8.26819 q^{31} +(3.34233 - 1.92969i) q^{33} +2.20440i q^{37} -3.20440 q^{39} +(3.30660 + 5.72720i) q^{41} +(2.03084 - 1.17251i) q^{43} +(-7.21570 - 4.16599i) q^{47} +2.14061 q^{49} +(-3.42969 + 5.94040i) q^{51} +(-0.232259 - 0.134095i) q^{53} +(10.8726 - 8.76819i) q^{57} +(-4.16599 - 7.21570i) q^{59} +(1.70440 - 2.95211i) q^{61} +(13.8755 + 8.01100i) q^{63} +(-1.84253 - 1.06379i) q^{67} -29.6990 q^{69} +(5.23630 + 9.06953i) q^{71} +(-4.20835 + 2.42969i) q^{73} -2.65498i q^{77} +(8.20440 + 14.2104i) q^{79} +(-11.0110 - 19.0716i) q^{81} -5.73181i q^{83} +26.6990i q^{87} +(-5.40880 + 9.36832i) q^{89} +(-1.10220 + 1.90907i) q^{91} +(-22.9450 + 13.2473i) q^{93} +(-13.6319 + 7.87039i) q^{97} +(-4.37691 + 7.58103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{9}+O(q^{10}) \) 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

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