LMFDB - Embedded newform 1300.2.bb.g.549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1300,2,Mod(549,1300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1300, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1300.549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1300 = 2^{2} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1300.bb (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:	$10.3805522628$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 19 x^{18} + 238 x^{16} - 1699 x^{14} + 8746 x^{12} - 27082 x^{10} + 60616 x^{8} - 82792 x^{6} + \cdots + 6561 $ x^20 - 19x^18 + 238x^16 - 1699x^14 + 8746x^12 - 27082x^10 + 60616x^8 - 82792x^6 + 77845x^4 - 26082*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.1
Root			$-2.44987 + 1.41443i$ of defining polynomial
Character	$\chi$	$=$	1300.549
Dual form			1300.2.bb.g.1049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.44987 + 1.41443i) q^{3} +(-4.33228 - 2.50124i) q^{7} +(2.50124 - 4.33228i) q^{9} +O(q^{10})$	$q+(-2.44987 + 1.41443i) q^{3} +(-4.33228 - 2.50124i) q^{7} +(2.50124 - 4.33228i) q^{9} +(-3.09549 - 5.36155i) q^{11} +(-0.534272 + 3.56575i) q^{13} +(-0.292485 - 0.168866i) q^{17} +(-2.33237 + 4.03979i) q^{19} +14.1513 q^{21} +(2.61312 - 1.50869i) q^{23} +5.66475i q^{27} +(-3.74681 - 6.48966i) q^{29} +6.47624 q^{31} +(15.1671 + 8.75673i) q^{33} +(-3.30300 + 1.90699i) q^{37} +(-3.73461 - 9.49131i) q^{39} +(4.64905 + 8.05238i) q^{41} +(-1.27239 - 0.734613i) q^{43} +4.48412i q^{47} +(9.01241 + 15.6099i) q^{49} +0.955399 q^{51} -8.89084i q^{53} -13.1959i q^{57} +(-1.42188 + 2.46276i) q^{59} +(-2.07585 + 3.59548i) q^{61} +(-21.6721 + 12.5124i) q^{63} +(-3.42762 + 1.97894i) q^{67} +(-4.26787 + 7.39216i) q^{69} +(-4.91340 + 8.51027i) q^{71} -3.70935i q^{73} +30.9703i q^{77} -1.45186 q^{79} +(-0.508685 - 0.881068i) q^{81} -0.164117i q^{83} +(18.3584 + 10.5992i) q^{87} +(-2.33858 - 4.05054i) q^{89} +(11.2334 - 14.1115i) q^{91} +(-15.8660 + 9.16021i) q^{93} +(0.446768 + 0.257942i) q^{97} -30.9703 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 8 q^{9}+O(q^{10}) $ 20 * q + 8 * q^9	$ 20 q + 8 q^{9} - 14 q^{11} + 8 q^{19} + 16 q^{21} + 6 q^{29} + 32 q^{31} - 28 q^{39} + 20 q^{41} + 22 q^{49} + 16 q^{51} - 12 q^{59} - 18 q^{61} - 48 q^{69} + 10 q^{71} + 22 q^{81} - 44 q^{89} - 14 q^{91} - 112 q^{99}+O(q^{100}) $ 20 * q + 8 * q^9 - 14 * q^11 + 8 * q^19 + 16 * q^21 + 6 * q^29 + 32 * q^31 - 28 * q^39 + 20 * q^41 + 22 * q^49 + 16 * q^51 - 12 * q^59 - 18 * q^61 - 48 * q^69 + 10 * q^71 + 22 * q^81 - 44 * q^89 - 14 * q^91 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times$.

$n$	$301$	$651$	$677$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−2.44987	+	1.41443i	−1.41443	+	0.816623i	−0.995802	−	0.0915334i	$-0.970823\pi$
$3$	−2.44987	+	1.41443i	−1.41443	+	0.816623i	−0.418631	+	0.908157i	$0.637490\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−4.33228	−	2.50124i	−1.63745	−	0.945380i	−0.981708	−	0.190391i	$-0.939024\pi$
$7$	−4.33228	−	2.50124i	−1.63745	−	0.945380i	−0.655738	−	0.754989i	$-0.727642\pi$
$8$		0			0
$9$	2.50124	−	4.33228i	0.833747	−	1.44409i
$10$		0			0
$11$	−3.09549	−	5.36155i	−0.933326	−	1.61657i	−0.777592	−	0.628769i	$-0.783559\pi$
$11$	−3.09549	−	5.36155i	−0.933326	−	1.61657i	−0.155734	−	0.987799i	$-0.549774\pi$
$12$		0			0
$13$	−0.534272	+	3.56575i	−0.148180	+	0.988960i
$13$	−0.534272	+	3.56575i	−0.148180	+	0.988960i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.292485	−	0.168866i	−0.0709379	−	0.0409560i	0.464111	−	0.885777i	$-0.346374\pi$
$17$	−0.292485	−	0.168866i	−0.0709379	−	0.0409560i	−0.535049	+	0.844821i	$0.679707\pi$
$18$		0			0
$19$	−2.33237	+	4.03979i	−0.535083	+	0.926792i	0.464076	+	0.885795i	$0.346386\pi$
$19$	−2.33237	+	4.03979i	−0.535083	+	0.926792i	−0.999159	+	0.0409961i	$0.986947\pi$
$20$		0			0
$21$	14.1513			3.08808
$22$		0			0
$23$	2.61312	−	1.50869i	0.544873	−	0.314583i	−0.202179	−	0.979349i	$-0.564802\pi$
$23$	2.61312	−	1.50869i	0.544873	−	0.314583i	0.747052	+	0.664766i	$0.231469\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			5.66475i			1.09018i
$28$		0			0
$29$	−3.74681	−	6.48966i	−0.695765	−	1.20510i	−0.969922	−	0.243415i	$-0.921732\pi$
$29$	−3.74681	−	6.48966i	−0.695765	−	1.20510i	0.274158	−	0.961685i	$-0.411601\pi$
$30$		0			0
$31$	6.47624			1.16317			0.581584	−	0.813486i	$-0.302433\pi$
$31$	6.47624			1.16317			0.581584	+	0.813486i	$0.302433\pi$
$32$		0			0
$33$	15.1671	+	8.75673i	2.64025	+	1.52435i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.30300	+	1.90699i	−0.543010	+	0.313507i	−0.746298	−	0.665612i	$-0.768171\pi$
$37$	−3.30300	+	1.90699i	−0.543010	+	0.313507i	0.203288	+	0.979119i	$0.434837\pi$
$38$		0			0
$39$	−3.73461	−	9.49131i	−0.598017	−	1.51983i
$40$		0			0
$41$	4.64905	+	8.05238i	0.726059	+	1.25757i	0.958537	+	0.284969i	$0.0919834\pi$
$41$	4.64905	+	8.05238i	0.726059	+	1.25757i	−0.232478	+	0.972602i	$0.574683\pi$
$42$		0			0
$43$	−1.27239	−	0.734613i	−0.194037	−	0.112027i	0.399834	−	0.916588i	$-0.369068\pi$
$43$	−1.27239	−	0.734613i	−0.194037	−	0.112027i	−0.593871	+	0.804560i	$0.702401\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			4.48412i			0.654076i	0.945011	+	0.327038i	$0.106050\pi$
$47$			4.48412i			0.654076i	−0.945011	+	0.327038i	$0.893950\pi$
$48$		0			0
$49$	9.01241	+	15.6099i	1.28749	+	2.22999i
$50$		0			0
$51$	0.955399			0.133783
$52$		0			0
$53$		−	8.89084i		−	1.22125i	−0.791920	−	0.610625i	$-0.790918\pi$
$53$		−	8.89084i		−	1.22125i	0.791920	−	0.610625i	$-0.209082\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	13.1959i		−	1.74785i
$58$		0			0
$59$	−1.42188	+	2.46276i	−0.185113	+	0.320625i	−0.943614	−	0.331046i	$-0.892598\pi$
$59$	−1.42188	+	2.46276i	−0.185113	+	0.320625i	0.758502	+	0.651671i	$0.225932\pi$
$60$		0			0
$61$	−2.07585	+	3.59548i	−0.265786	+	0.460355i	−0.967769	−	0.251839i	$-0.918965\pi$
$61$	−2.07585	+	3.59548i	−0.265786	+	0.460355i	0.701983	+	0.712193i	$0.252298\pi$
$62$		0			0
$63$	−21.6721	+	12.5124i	−2.73043	+	1.57641i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.42762	+	1.97894i	−0.418751	+	0.241766i	−0.694543	−	0.719451i	$-0.744393\pi$
$67$	−3.42762	+	1.97894i	−0.418751	+	0.241766i	0.275792	+	0.961217i	$0.411060\pi$
$68$		0			0
$69$	−4.26787	+	7.39216i	−0.513791	+	0.889912i
$70$		0			0
$71$	−4.91340	+	8.51027i	−0.583114	+	1.00998i	0.411994	+	0.911187i	$0.364833\pi$
$71$	−4.91340	+	8.51027i	−0.583114	+	1.00998i	−0.995108	+	0.0987962i	$0.968501\pi$
$72$		0			0
$73$		−	3.70935i		−	0.434147i	−0.976155	−	0.217073i	$-0.930349\pi$
$73$		−	3.70935i		−	0.434147i	0.976155	−	0.217073i	$-0.0696511\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			30.9703i			3.52939i
$78$		0			0
$79$	−1.45186			−0.163347			−0.0816733	−	0.996659i	$-0.526026\pi$
$79$	−1.45186			−0.163347			−0.0816733	+	0.996659i	$0.526026\pi$
$80$		0			0
$81$	−0.508685	−	0.881068i	−0.0565206	−	0.0978965i
$82$		0			0
$83$		−	0.164117i		−	0.0180142i	−0.999959	−	0.00900710i	$-0.997133\pi$
$83$		−	0.164117i		−	0.0180142i	0.999959	−	0.00900710i	$-0.00286709\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	18.3584	+	10.5992i	1.96822	+	1.13635i
$88$		0			0
$89$	−2.33858	−	4.05054i	−0.247889	−	0.429356i	0.715051	−	0.699072i	$-0.246403\pi$
$89$	−2.33858	−	4.05054i	−0.247889	−	0.429356i	−0.962940	+	0.269716i	$0.913070\pi$
$90$		0			0
$91$	11.2334	−	14.1115i	1.17758	−	1.47928i
$92$		0			0
$93$	−15.8660	+	9.16021i	−1.64522	+	0.949870i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.446768	+	0.257942i	0.0453625	+	0.0261900i	0.522510	−	0.852633i	$-0.324996\pi$
$97$	0.446768	+	0.257942i	0.0453625	+	0.0261900i	−0.477147	+	0.878823i	$0.658329\pi$
$98$		0			0
$99$	−30.9703			−3.11263
$100$		0			0
$101$	0.762691	+	1.32102i	0.0758906	+	0.131446i	0.901473	−	0.432835i	$-0.142487\pi$
$101$	0.762691	+	1.32102i	0.0758906	+	0.131446i	−0.825583	+	0.564281i	$0.809153\pi$
$102$		0			0
$103$			10.5135i			1.03592i	0.855404	+	0.517961i	$0.173309\pi$
$103$			10.5135i			1.03592i	−0.855404	+	0.517961i	$0.826691\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.54562	−	5.51117i	0.922810	−	0.532784i	0.0382794	−	0.999267i	$-0.487812\pi$
$107$	9.54562	−	5.51117i	0.922810	−	0.532784i	0.884530	+	0.466483i	$0.154479\pi$
$108$		0			0
$109$	4.82887			0.462521			0.231261	−	0.972892i	$-0.425715\pi$
$109$	4.82887			0.462521			0.231261	+	0.972892i	$0.425715\pi$
$110$		0			0
$111$	5.39461	−	9.34374i	0.512034	−	0.886869i
$112$		0			0
$113$	12.5389	+	7.23936i	1.17956	+	0.681022i	0.955914	−	0.293647i	$-0.0948692\pi$
$113$	12.5389	+	7.23936i	1.17956	+	0.681022i	0.223651	+	0.974669i	$0.428202\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	14.1115	+	11.2334i	1.30460	+	1.03853i
$118$		0			0
$119$	0.844749	+	1.46315i	0.0774380	+	0.134127i
$120$		0			0
$121$	−13.6641	+	23.6670i	−1.24220	+	2.15155i
$122$		0			0
$123$	−22.7791	−	13.1515i	−2.05392	−	1.18583i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	15.7156	−	9.07340i	1.39453	−	0.805134i	0.400721	−	0.916200i	$-0.368760\pi$
$127$	15.7156	−	9.07340i	1.39453	−	0.805134i	0.993813	+	0.111066i	$0.0354264\pi$
$128$		0			0
$129$	4.15624			0.365937
$130$		0			0
$131$	5.02439			0.438983			0.219491	−	0.975614i	$-0.429560\pi$
$131$	5.02439			0.438983			0.219491	+	0.975614i	$0.429560\pi$
$132$		0			0
$133$	20.2090	−	11.6677i	1.75234	−	1.01171i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.01147	+	2.89337i	0.428159	+	0.247198i	0.698562	−	0.715550i	$-0.253824\pi$
$137$	5.01147	+	2.89337i	0.428159	+	0.247198i	−0.270403	+	0.962747i	$0.587157\pi$
$138$		0			0
$139$	5.26684	−	9.12243i	0.446727	−	0.773755i	−0.551443	−	0.834212i	$-0.685923\pi$
$139$	5.26684	−	9.12243i	0.446727	−	0.773755i	0.998171	+	0.0604577i	$0.0192560\pi$
$140$		0			0
$141$	−6.34248	−	10.9855i	−0.534133	−	0.925146i
$142$		0			0
$143$	20.7718	−	8.17322i	1.73702	−	0.683479i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−44.1584	−	25.4949i	−3.64213	−	2.10278i
$148$		0			0
$149$	5.14121	−	8.90483i	0.421184	−	0.729512i	−0.574871	−	0.818244i	$-0.694948\pi$
$149$	5.14121	−	8.90483i	0.421184	−	0.729512i	0.996056	+	0.0887314i	$0.0282813\pi$
$150$		0			0
$151$	7.45767			0.606897			0.303448	−	0.952848i	$-0.401862\pi$
$151$	7.45767			0.606897			0.303448	+	0.952848i	$0.401862\pi$
$152$		0			0
$153$	−1.46315	+	0.844749i	−0.118289	+	0.0682939i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			0.0351033i			0.00280155i	0.999999	+	0.00140077i	$0.000445880\pi$
$157$			0.0351033i			0.00280155i	−0.999999	+	0.00140077i	$0.999554\pi$
$158$		0			0
$159$	12.5755	+	21.7814i	0.997301	+	1.72738i
$160$		0			0
$161$	−15.0943			−1.18960
$162$		0			0
$163$	−8.20421	−	4.73670i	−0.642603	−	0.371007i	0.143014	−	0.989721i	$-0.454321\pi$
$163$	−8.20421	−	4.73670i	−0.642603	−	0.371007i	−0.785617	+	0.618714i	$0.787654\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.66536	+	4.42560i	−0.593163	+	0.342463i	−0.766347	−	0.642426i	$-0.777928\pi$
$167$	−7.66536	+	4.42560i	−0.593163	+	0.342463i	0.173184	+	0.984890i	$0.444594\pi$
$168$		0			0
$169$	−12.4291	−	3.81016i	−0.956085	−	0.293089i
$170$		0			0
$171$	11.6677	+	20.2090i	0.892248	+	1.54542i
$172$		0			0
$173$	10.0848	+	5.82245i	0.766731	+	0.442673i	0.831707	−	0.555214i	$-0.187364\pi$
$173$	10.0848	+	5.82245i	0.766731	+	0.442673i	−0.0649760	+	0.997887i	$0.520697\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		−	8.04460i		−	0.604669i
$178$		0			0
$179$	5.15029	+	8.92056i	0.384950	+	0.666754i	0.991762	−	0.128092i	$-0.0408852\pi$
$179$	5.15029	+	8.92056i	0.384950	+	0.666754i	−0.606812	+	0.794846i	$0.707552\pi$
$180$		0			0
$181$	−3.79624			−0.282173			−0.141086	−	0.989997i	$-0.545059\pi$
$181$	−3.79624			−0.282173			−0.141086	+	0.989997i	$0.545059\pi$
$182$		0			0
$183$		−	11.7446i		−	0.868188i
$184$		0			0
$185$		0			0
$186$		0			0
$187$			2.09089i			0.152901i
$188$		0			0
$189$	14.1689	−	24.5412i	1.03064	−	1.78511i
$190$		0			0
$191$	−7.59407	+	13.1533i	−0.549488	+	0.951741i	0.448822	+	0.893621i	$0.351844\pi$
$191$	−7.59407	+	13.1533i	−0.549488	+	0.951741i	−0.998310	+	0.0581194i	$0.981490\pi$
$192$		0			0
$193$	5.62185	−	3.24578i	0.404670	−	0.233636i	−0.283827	−	0.958875i	$-0.591604\pi$
$193$	5.62185	−	3.24578i	0.404670	−	0.233636i	0.688497	+	0.725239i	$0.258271\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.70177	+	5.02397i	−0.619975	+	0.357943i	−0.776859	−	0.629674i	$-0.783188\pi$
$197$	−8.70177	+	5.02397i	−0.619975	+	0.357943i	0.156884	+	0.987617i	$0.449855\pi$
$198$		0			0
$199$	−4.05582	+	7.02489i	−0.287510	+	0.497981i	−0.973215	−	0.229898i	$-0.926161\pi$
$199$	−4.05582	+	7.02489i	−0.287510	+	0.497981i	0.685705	+	0.727879i	$0.259494\pi$
$200$		0			0
$201$	5.59815	−	9.69629i	0.394863	−	0.683923i
$202$		0			0
$203$			37.4867i			2.63105i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	15.0943i		−	1.04913i
$208$		0			0
$209$	28.8794			1.99763
$210$		0			0
$211$	4.77262	+	8.26641i	0.328560	+	0.569083i	0.982226	−	0.187700i	$-0.0601032\pi$
$211$	4.77262	+	8.26641i	0.328560	+	0.569083i	−0.653666	+	0.756783i	$0.726770\pi$
$212$		0			0
$213$		−	27.7987i		−	1.90474i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−28.0569	−	16.1986i	−1.90462	−	1.09964i
$218$		0			0
$219$	5.24663	+	9.08742i	0.354534	+	0.614071i
$220$		0			0
$221$	0.758400	−	0.952706i	0.0510155	−	0.0640859i
$222$		0			0
$223$	10.8222	−	6.24823i	0.724711	−	0.418412i	−0.0917729	−	0.995780i	$-0.529253\pi$
$223$	10.8222	−	6.24823i	0.724711	−	0.418412i	0.816484	+	0.577368i	$0.195920\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−13.2893	−	7.67259i	−0.882043	−	0.509247i	−0.0107112	−	0.999943i	$-0.503410\pi$
$227$	−13.2893	−	7.67259i	−0.882043	−	0.509247i	−0.871331	+	0.490695i	$0.836743\pi$
$228$		0			0
$229$	−17.1968			−1.13640			−0.568198	−	0.822892i	$-0.692359\pi$
$229$	−17.1968			−1.13640			−0.568198	+	0.822892i	$0.692359\pi$
$230$		0			0
$231$	−43.8054	−	75.8731i	−2.88218	−	4.99209i
$232$		0			0
$233$		−	7.21495i		−	0.472667i	−0.971672	−	0.236333i	$-0.924054\pi$
$233$		−	7.21495i		−	0.472667i	0.971672	−	0.236333i	$-0.0759458\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.55686	−	2.05355i	0.231043	−	0.133393i
$238$		0			0
$239$	−1.02935			−0.0665830			−0.0332915	−	0.999446i	$-0.510599\pi$
$239$	−1.02935			−0.0665830			−0.0332915	+	0.999446i	$0.510599\pi$
$240$		0			0
$241$	12.1790	−	21.0947i	0.784519	−	1.35883i	−0.144768	−	0.989466i	$-0.546243\pi$
$241$	12.1790	−	21.0947i	0.784519	−	1.35883i	0.929286	−	0.369360i	$-0.120423\pi$
$242$		0			0
$243$	−12.2250	−	7.05812i	−0.784236	−	0.452779i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.1588	−	10.4750i	−0.837271	−	0.666509i
$248$		0			0
$249$	0.232133	+	0.402066i	0.0147108	+	0.0254799i
$250$		0			0
$251$	−6.28426	+	10.8847i	−0.396659	+	0.687034i	−0.993311	−	0.115466i	$-0.963164\pi$
$251$	−6.28426	+	10.8847i	−0.396659	+	0.687034i	0.596652	+	0.802500i	$0.296497\pi$
$252$		0			0
$253$	−16.1778	−	9.34025i	−1.01709	−	0.587216i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.3800	−	7.72493i	0.834620	−	0.481868i	−0.0208118	−	0.999783i	$-0.506625\pi$
$257$	13.3800	−	7.72493i	0.834620	−	0.481868i	0.855432	+	0.517915i	$0.173292\pi$
$258$		0			0
$259$	19.0793			1.18553
$260$		0			0
$261$	−37.4867			−2.32037
$262$		0			0
$263$	16.6997	−	9.64160i	1.02975	−	0.594527i	0.112837	−	0.993613i	$-0.464006\pi$
$263$	16.6997	−	9.64160i	1.02975	−	0.594527i	0.916913	+	0.399087i	$0.130673\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	11.4584	+	6.61552i	0.701244	+	0.404864i
$268$		0			0
$269$	4.46139	−	7.72735i	0.272016	−	0.471145i	−0.697362	−	0.716719i	$-0.745643\pi$
$269$	4.46139	−	7.72735i	0.272016	−	0.471145i	0.969378	+	0.245574i	$0.0789764\pi$
$270$		0			0
$271$	−2.59803	−	4.49992i	−0.157819	−	0.273351i	0.776263	−	0.630409i	$-0.217113\pi$
$271$	−2.59803	−	4.49992i	−0.157819	−	0.273351i	−0.934082	+	0.357059i	$0.883780\pi$
$272$		0			0
$273$	−7.56067	+	50.4601i	−0.457592	+	3.05399i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	15.9447	+	9.20566i	0.958022	+	0.553114i	0.895564	−	0.444933i	$-0.146773\pi$
$277$	15.9447	+	9.20566i	0.958022	+	0.553114i	0.0624585	+	0.998048i	$0.480106\pi$
$278$		0			0
$279$	16.1986	−	28.0569i	0.969787	−	1.67972i
$280$		0			0
$281$	27.7127			1.65320			0.826602	−	0.562787i	$-0.190271\pi$
$281$	27.7127			1.65320			0.826602	+	0.562787i	$0.190271\pi$
$282$		0			0
$283$	9.15759	−	5.28714i	0.544362	−	0.314288i	−0.202483	−	0.979286i	$-0.564901\pi$
$283$	9.15759	−	5.28714i	0.544362	−	0.314288i	0.746845	+	0.664998i	$0.231568\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	46.5135i		−	2.74561i
$288$		0			0
$289$	−8.44297	−	14.6237i	−0.496645	−	0.860215i
$290$		0			0
$291$	−1.45937			−0.0855495
$292$		0			0
$293$	−14.6898	−	8.48115i	−0.858187	−	0.495474i	0.00521804	−	0.999986i	$-0.498339\pi$
$293$	−14.6898	−	8.48115i	−0.858187	−	0.495474i	−0.863405	+	0.504512i	$0.831672\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	30.3718	−	17.5352i	1.76235	−	1.01749i
$298$		0			0
$299$	3.98347	+	10.1238i	0.230370	+	0.585473i
$300$		0			0
$301$	3.67489	+	6.36509i	0.211817	+	0.366878i
$302$		0			0
$303$	−3.73699	−	2.15755i	−0.214684	−	0.123948i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			25.7524i			1.46977i	0.678194	+	0.734883i	$0.262763\pi$
$307$			25.7524i			1.46977i	−0.678194	+	0.734883i	$0.737237\pi$
$308$		0			0
$309$	−14.8706	−	25.7566i	−0.845958	−	1.46524i
$310$		0			0
$311$	19.7222			1.11834			0.559171	−	0.829052i	$-0.311119\pi$
$311$	19.7222			1.11834			0.559171	+	0.829052i	$0.311119\pi$
$312$		0			0
$313$			8.08969i			0.457257i	0.973514	+	0.228628i	$0.0734240\pi$
$313$			8.08969i			0.457257i	−0.973514	+	0.228628i	$0.926576\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			1.11449i			0.0625959i	0.999510	+	0.0312979i	$0.00996407\pi$
$317$			1.11449i			0.0625959i	−0.999510	+	0.0312979i	$0.990036\pi$
$318$		0			0
$319$	−23.1964	+	40.1774i	−1.29875	+	2.24950i
$320$		0			0
$321$	−15.5903	+	27.0033i	−0.870168	+	1.50718i
$322$		0			0
$323$	1.36437	−	0.787718i	0.0759154	−	0.0438298i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−11.8301	+	6.83011i	−0.654205	+	0.377706i
$328$		0			0
$329$	11.2159	−	19.4264i	0.618350	−	1.07101i
$330$		0			0
$331$	−15.0647	+	26.0929i	−0.828034	+	1.43420i	0.0715451	+	0.997437i	$0.477207\pi$
$331$	−15.0647	+	26.0929i	−0.828034	+	1.43420i	−0.899579	+	0.436759i	$0.856126\pi$
$332$		0			0
$333$			19.0793i			1.04554i
$334$		0			0
$335$		0			0
$336$		0			0
$337$		−	19.1976i		−	1.04576i	−0.852407	−	0.522879i	$-0.824858\pi$
$337$		−	19.1976i		−	1.04576i	0.852407	−	0.522879i	$-0.175142\pi$
$338$		0			0
$339$	−40.9584			−2.22455
$340$		0			0
$341$	−20.0472	−	34.7227i	−1.08561	−	1.88034i
$342$		0			0
$343$		−	55.1514i		−	2.97790i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.09339	+	2.94067i	0.273427	+	0.157863i	0.630444	−	0.776235i	$-0.282873\pi$
$347$	5.09339	+	2.94067i	0.273427	+	0.157863i	−0.357017	+	0.934098i	$0.616206\pi$
$348$		0			0
$349$	−2.46427	−	4.26823i	−0.131909	−	0.228473i	0.792503	−	0.609868i	$-0.208777\pi$
$349$	−2.46427	−	4.26823i	−0.131909	−	0.228473i	−0.924412	+	0.381394i	$0.875444\pi$
$350$		0			0
$351$	−20.1991	−	3.02652i	−1.07815	−	0.161543i
$352$		0			0
$353$	9.27174	−	5.35304i	0.493485	−	0.284914i	−0.232534	−	0.972588i	$-0.574702\pi$
$353$	9.27174	−	5.35304i	0.493485	−	0.284914i	0.726019	+	0.687675i	$0.241368\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.13905	−	2.38968i	−0.219062	−	0.126475i
$358$		0			0
$359$	27.1191			1.43129			0.715647	−	0.698462i	$-0.246132\pi$
$359$	27.1191			1.43129			0.715647	+	0.698462i	$0.246132\pi$
$360$		0			0
$361$	−1.37994	−	2.39012i	−0.0726284	−	0.125796i
$362$		0			0
$363$		−	77.3081i		−	4.05762i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−24.2763	+	14.0159i	−1.26721	+	0.731625i	−0.974459	−	0.224564i	$-0.927904\pi$
$367$	−24.2763	+	14.0159i	−1.26721	+	0.731625i	−0.292752	+	0.956188i	$0.594571\pi$
$368$		0			0
$369$	46.5135			2.42140
$370$		0			0
$371$	−22.2381	+	38.5176i	−1.15455	+	1.99973i
$372$		0			0
$373$	18.2377	+	10.5296i	0.944314	+	0.545200i	0.891310	−	0.453394i	$-0.149787\pi$
$373$	18.2377	+	10.5296i	0.944314	+	0.545200i	0.0530042	+	0.998594i	$0.483120\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	25.1423	−	9.89292i	1.29489	−	0.509511i
$378$		0			0
$379$	3.12627	+	5.41485i	0.160585	+	0.278142i	0.935079	−	0.354440i	$-0.115328\pi$
$379$	3.12627	+	5.41485i	0.160585	+	0.278142i	−0.774493	+	0.632582i	$0.781995\pi$
$380$		0			0
$381$	−25.6674	+	44.4573i	−1.31498	+	2.27762i
$382$		0			0
$383$	−10.5677	−	6.10127i	−0.539985	−	0.311760i	0.205088	−	0.978744i	$-0.434252\pi$
$383$	−10.5677	−	6.10127i	−0.539985	−	0.311760i	−0.745073	+	0.666983i	$0.767585\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−6.36509	+	3.67489i	−0.323556	+	0.186805i
$388$		0			0
$389$	28.2139			1.43050			0.715250	−	0.698869i	$-0.246313\pi$
$389$	28.2139			1.43050			0.715250	+	0.698869i	$0.246313\pi$
$390$		0			0
$391$	−1.01906			−0.0515362
$392$		0			0
$393$	−12.3091	+	7.10666i	−0.620912	+	0.358483i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	24.5502	+	14.1740i	1.23214	+	0.711375i	0.967475	−	0.252967i	$-0.0814063\pi$
$397$	24.5502	+	14.1740i	1.23214	+	0.711375i	0.264662	+	0.964341i	$0.414740\pi$
$398$		0			0
$399$	−33.0062	+	57.1685i	−1.65238	+	2.86200i
$400$		0			0
$401$	−4.81419	−	8.33842i	−0.240409	−	0.416401i	0.720422	−	0.693536i	$-0.243948\pi$
$401$	−4.81419	−	8.33842i	−0.240409	−	0.416401i	−0.960831	+	0.277135i	$0.910615\pi$
$402$		0			0
$403$	−3.46008	+	23.0926i	−0.172359	+	1.15033i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	20.4488	+	11.8061i	1.01361	+	0.585208i
$408$		0			0
$409$	−14.0867	+	24.3988i	−0.696540	+	1.20644i	0.273118	+	0.961980i	$0.411945\pi$
$409$	−14.0867	+	24.3988i	−0.696540	+	1.20644i	−0.969659	+	0.244463i	$0.921388\pi$
$410$		0			0
$411$	−16.3699			−0.807469
$412$		0			0
$413$	12.3199	−	7.11291i	0.606224	−	0.350004i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			29.7984i			1.45923i
$418$		0			0
$419$	8.26993	+	14.3239i	0.404012	+	0.699770i	0.994206	−	0.107492i	$-0.0342819\pi$
$419$	8.26993	+	14.3239i	0.404012	+	0.699770i	−0.590194	+	0.807262i	$0.700949\pi$
$420$		0			0
$421$	−34.0033			−1.65722			−0.828610	−	0.559826i	$-0.810868\pi$
$421$	−34.0033			−1.65722			−0.828610	+	0.559826i	$0.810868\pi$
$422$		0			0
$423$	19.4264	+	11.2159i	0.944545	+	0.545333i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	17.9863	−	10.3844i	0.870420	−	0.502537i
$428$		0			0
$429$	−39.3277	+	49.4036i	−1.89876	+	2.38523i
$430$		0			0
$431$	14.1864	+	24.5716i	0.683337	+	1.18357i	0.973956	+	0.226736i	$0.0728054\pi$
$431$	14.1864	+	24.5716i	0.683337	+	1.18357i	−0.290619	+	0.956839i	$0.593861\pi$
$432$		0			0
$433$	−24.4356	−	14.1079i	−1.17430	−	0.677984i	−0.219613	−	0.975587i	$-0.570479\pi$
$433$	−24.4356	−	14.1079i	−1.17430	−	0.677984i	−0.954690	+	0.297603i	$0.903813\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$			14.0753i			0.673312i
$438$		0			0
$439$	−3.85259	−	6.67288i	−0.183874	−	0.318479i	0.759323	−	0.650714i	$-0.225531\pi$
$439$	−3.85259	−	6.67288i	−0.183874	−	0.318479i	−0.943197	+	0.332235i	$0.892197\pi$
$440$		0			0
$441$	90.1688			4.29375
$442$		0			0
$443$			38.0286i			1.80679i	0.428808	+	0.903396i	$0.358934\pi$
$443$			38.0286i			1.80679i	−0.428808	+	0.903396i	$0.641066\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			29.0876i			1.37579i
$448$		0			0
$449$	−5.29308	+	9.16788i	−0.249796	+	0.432659i	−0.963469	−	0.267820i	$-0.913697\pi$
$449$	−5.29308	+	9.16788i	−0.249796	+	0.432659i	0.713673	+	0.700479i	$0.247030\pi$
$450$		0			0
$451$	28.7822	−	49.8522i	1.35530	−	2.34745i
$452$		0			0
$453$	−18.2703	+	10.5484i	−0.858415	+	0.495606i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−36.0757	+	20.8283i	−1.68755	+	0.974306i	−0.731160	+	0.682206i	$0.761021\pi$
$457$	−36.0757	+	20.8283i	−1.68755	+	0.974306i	−0.956388	+	0.292100i	$0.905646\pi$
$458$		0			0
$459$	0.956584	−	1.65685i	0.0446495	−	0.0773352i
$460$		0			0
$461$	7.17712	−	12.4311i	0.334272	−	0.578976i	−0.649073	−	0.760726i	$-0.724843\pi$
$461$	7.17712	−	12.4311i	0.334272	−	0.578976i	0.983345	+	0.181750i	$0.0581763\pi$
$462$		0			0
$463$			6.50717i			0.302414i	0.988502	+	0.151207i	$0.0483160\pi$
$463$			6.50717i			0.302414i	−0.988502	+	0.151207i	$0.951684\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			25.6173i			1.18543i	0.805413	+	0.592714i	$0.201943\pi$
$467$			25.6173i			1.18543i	−0.805413	+	0.592714i	$0.798057\pi$
$468$		0			0
$469$	19.7992			0.914243
$470$		0			0
$471$	−0.0496512	−	0.0859985i	−0.00228781	−	0.00396260i
$472$		0			0
$473$			9.09596i			0.418233i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−38.5176	−	22.2381i	−1.76360	−	1.01821i
$478$		0			0
$479$	−17.4198	−	30.1720i	−0.795932	−	1.37859i	−0.922246	−	0.386604i	$-0.873648\pi$
$479$	−17.4198	−	30.1720i	−0.795932	−	1.37859i	0.126314	−	0.991990i	$-0.459685\pi$
$480$		0			0
$481$	−5.03514	−	12.7965i	−0.229582	−	0.583471i
$482$		0			0
$483$	36.9792	−	21.3499i	1.68261	−	0.971455i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.48256	+	3.16536i	0.248439	+	0.143436i	0.619049	−	0.785352i	$-0.287518\pi$
$487$	5.48256	+	3.16536i	0.248439	+	0.143436i	−0.370611	+	0.928788i	$0.620852\pi$
$488$		0			0
$489$	26.7990			1.21189
$490$		0			0
$491$	12.6931	+	21.9851i	0.572833	+	0.992175i	0.996273	+	0.0862515i	$0.0274889\pi$
$491$	12.6931	+	21.9851i	0.572833	+	0.992175i	−0.423441	+	0.905924i	$0.639178\pi$
$492$		0			0
$493$			2.53083i			0.113983i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	42.5724	−	24.5792i	1.90964	−	1.10253i
$498$		0			0
$499$	−8.12242			−0.363610			−0.181805	−	0.983335i	$-0.558194\pi$
$499$	−8.12242			−0.363610			−0.181805	+	0.983335i	$0.558194\pi$
$500$		0			0
$501$	12.5194	−	21.6843i	0.559327	−	0.968782i
$502$		0			0
$503$	13.0481	+	7.53334i	0.581787	+	0.335895i	0.761843	−	0.647761i	$-0.224295\pi$
$503$	13.0481	+	7.53334i	0.581787	+	0.335895i	−0.180056	+	0.983656i	$0.557628\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	35.8389	−	8.24575i	1.59166	−	0.366207i
$508$		0			0
$509$	−20.9514	−	36.2890i	−0.928656	−	1.60848i	−0.785573	−	0.618769i	$-0.787632\pi$
$509$	−20.9514	−	36.2890i	−0.928656	−	1.60848i	−0.143083	−	0.989711i	$-0.545702\pi$
$510$		0			0
$511$	−9.27797	+	16.0699i	−0.410433	+	0.710892i
$512$		0			0
$513$	−22.8844	−	13.2123i	−1.01037	−	0.583338i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	24.0418	−	13.8805i	1.05736	−	0.610466i
$518$		0			0
$519$	−32.9419			−1.44599
$520$		0			0
$521$	−27.8437			−1.21986			−0.609928	−	0.792457i	$-0.708802\pi$
$521$	−27.8437			−1.21986			−0.609928	+	0.792457i	$0.708802\pi$
$522$		0			0
$523$	−30.8015	+	17.7832i	−1.34685	+	0.777607i	−0.987803	−	0.155711i	$-0.950233\pi$
$523$	−30.8015	+	17.7832i	−1.34685	+	0.777607i	−0.359051	+	0.933318i	$0.616900\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.89420	−	1.09362i	−0.0825127	−	0.0476387i
$528$		0			0
$529$	−6.94774	+	12.0338i	−0.302076	+	0.523210i
$530$		0			0
$531$	7.11291	+	12.3199i	0.308674	+	0.534639i
$532$		0			0
$533$	−31.1966	+	12.2752i	−1.35128	+	0.531696i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−25.2351	−	14.5695i	−1.08897	−	0.628719i
$538$		0			0
$539$	55.7957	−	96.6409i	2.40329	−	4.16262i
$540$		0			0
$541$	−27.8180			−1.19599			−0.597995	−	0.801499i	$-0.704036\pi$
$541$	−27.8180			−1.19599			−0.597995	+	0.801499i	$0.704036\pi$
$542$		0			0
$543$	9.30030	−	5.36953i	0.399114	−	0.230429i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	24.9538i		−	1.06695i	−0.845817	−	0.533473i	$-0.820887\pi$
$547$		−	24.9538i		−	1.06695i	0.845817	−	0.533473i	$-0.179113\pi$
$548$		0			0
$549$	10.3844	+	17.9863i	0.443196	+	0.767638i
$550$		0			0
$551$	34.9558			1.48917
$552$		0			0
$553$	6.28984	+	3.63144i	0.267471	+	0.154425i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.48337	+	2.58848i	−0.189967	+	0.109677i	−0.591967	−	0.805962i	$-0.701648\pi$
$557$	−4.48337	+	2.58848i	−0.189967	+	0.109677i	0.402000	+	0.915640i	$0.368315\pi$
$558$		0			0
$559$	3.29925	−	4.14453i	0.139543	−	0.175295i
$560$		0			0
$561$	−2.95743	−	5.12242i	−0.124863	−	0.216269i
$562$		0			0
$563$	39.7273	+	22.9366i	1.67430	+	0.966660i	0.965183	+	0.261574i	$0.0842416\pi$
$563$	39.7273	+	22.9366i	1.67430	+	0.966660i	0.709122	+	0.705086i	$0.249092\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			5.08937i			0.213734i
$568$		0			0
$569$	−16.1491	−	27.9710i	−0.677005	−	1.17261i	−0.975879	−	0.218314i	$-0.929944\pi$
$569$	−16.1491	−	27.9710i	−0.677005	−	1.17261i	0.298874	−	0.954293i	$-0.403389\pi$
$570$		0			0
$571$	10.1241			0.423678			0.211839	−	0.977305i	$-0.432055\pi$
$571$	10.1241			0.423678			0.211839	+	0.977305i	$0.432055\pi$
$572$		0			0
$573$		−	42.9652i		−	1.79490i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			13.9748i			0.581780i	0.956757	+	0.290890i	$0.0939513\pi$
$577$			13.9748i			0.581780i	−0.956757	+	0.290890i	$0.906049\pi$
$578$		0			0
$579$	−9.18187	+	15.9035i	−0.381586	+	0.660926i
$580$		0			0
$581$	−0.410497	+	0.711001i	−0.0170303	+	0.0294973i
$582$		0			0
$583$	−47.6687	+	27.5215i	−1.97423	+	1.13982i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.9414	+	6.89437i	−0.492874	+	0.284561i	−0.725766	−	0.687942i	$-0.758514\pi$
$587$	−11.9414	+	6.89437i	−0.492874	+	0.284561i	0.232892	+	0.972503i	$0.425181\pi$
$588$		0			0
$589$	−15.1050	+	26.1627i	−0.622392	+	1.07801i
$590$		0			0
$591$	14.2121	−	24.6161i	0.584609	−	1.01257i
$592$		0			0
$593$			22.7491i			0.934193i	0.884206	+	0.467097i	$0.154700\pi$
$593$			22.7491i			0.934193i	−0.884206	+	0.467097i	$0.845300\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	22.9468i		−	0.939148i
$598$		0			0
$599$	0.331916			0.0135617			0.00678086	−	0.999977i	$-0.497842\pi$
$599$	0.331916			0.0135617			0.00678086	+	0.999977i	$0.497842\pi$
$600$		0			0
$601$	9.97424	+	17.2759i	0.406858	+	0.704698i	0.994536	−	0.104396i	$-0.0332911\pi$
$601$	9.97424	+	17.2759i	0.406858	+	0.704698i	−0.587678	+	0.809095i	$0.699958\pi$
$602$		0			0
$603$			19.7992i			0.806286i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−24.9085	−	14.3809i	−1.01101	−	0.583704i	−0.0995198	−	0.995036i	$-0.531731\pi$
$607$	−24.9085	−	14.3809i	−1.01101	−	0.583704i	−0.911486	+	0.411331i	$0.865064\pi$
$608$		0			0
$609$	−53.0224	−	91.8374i	−2.14857	−	3.72144i
$610$		0			0
$611$	−15.9892	−	2.39574i	−0.646855	−	0.0969212i
$612$		0			0
$613$	−9.98526	+	5.76499i	−0.403301	+	0.232846i	−0.687907	−	0.725799i	$-0.741470\pi$
$613$	−9.98526	+	5.76499i	−0.403301	+	0.232846i	0.284607	+	0.958644i	$0.408137\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	27.7981	+	16.0493i	1.11911	+	0.646119i	0.941174	−	0.337923i	$-0.109724\pi$
$617$	27.7981	+	16.0493i	1.11911	+	0.646119i	0.177937	+	0.984042i	$0.443058\pi$
$618$		0			0
$619$	0.651502			0.0261861			0.0130930	−	0.999914i	$-0.495832\pi$
$619$	0.651502			0.0261861			0.0130930	+	0.999914i	$0.495832\pi$
$620$		0			0
$621$	8.54632	+	14.8027i	0.342952	+	0.594010i
$622$		0			0
$623$			23.3974i			0.937397i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−70.7507	+	40.8480i	−2.82551	+	1.63131i
$628$		0			0
$629$	1.28810			0.0513600
$630$		0			0
$631$	11.8775	−	20.5724i	0.472834	−	0.818973i	−0.526683	−	0.850062i	$-0.676564\pi$
$631$	11.8775	−	20.5724i	0.472834	−	0.818973i	0.999517	+	0.0310895i	$0.00989769\pi$
$632$		0			0
$633$	−23.3846	−	13.5011i	−0.929453	−	0.536620i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−60.4762	+	23.7960i	−2.39615	+	0.942832i
$638$		0			0
$639$	24.5792	+	42.5724i	0.972339	+	1.68414i
$640$		0			0
$641$	14.7753	−	25.5916i	0.583590	−	1.01081i	−0.411460	−	0.911428i	$-0.634981\pi$
$641$	14.7753	−	25.5916i	0.583590	−	1.01081i	0.995050	−	0.0993791i	$-0.0316856\pi$
$642$		0			0
$643$	18.0577	+	10.4256i	0.712127	+	0.411147i	0.811848	−	0.583869i	$-0.198462\pi$
$643$	18.0577	+	10.4256i	0.712127	+	0.411147i	−0.0997211	+	0.995015i	$0.531795\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.348301	+	0.201092i	−0.0136931	+	0.00790574i	−0.506831	−	0.862045i	$-0.669183\pi$
$647$	−0.348301	+	0.201092i	−0.0136931	+	0.00790574i	0.493138	+	0.869951i	$0.335850\pi$
$648$		0			0
$649$	17.6056			0.691082
$650$		0			0
$651$	91.6476			3.59195
$652$		0			0
$653$	40.9220	−	23.6263i	1.60140	−	0.924570i	0.610194	−	0.792252i	$-0.291091\pi$
$653$	40.9220	−	23.6263i	1.60140	−	0.924570i	0.991207	−	0.132318i	$-0.0422419\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−16.0699	−	9.27797i	−0.626947	−	0.361968i
$658$		0			0
$659$	8.75246	−	15.1597i	0.340948	−	0.590539i	−0.643661	−	0.765310i	$-0.722585\pi$
$659$	8.75246	−	15.1597i	0.340948	−	0.590539i	0.984609	+	0.174772i	$0.0559188\pi$
$660$		0			0
$661$	4.70405	+	8.14766i	0.182966	+	0.316907i	0.942889	−	0.333106i	$-0.108097\pi$
$661$	4.70405	+	8.14766i	0.182966	+	0.316907i	−0.759923	+	0.650013i	$0.774763\pi$
$662$		0			0
$663$	−0.510443	+	3.40671i	−0.0198240	+	0.132306i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−19.5817	−	11.3055i	−0.758207	−	0.437751i
$668$		0			0
$669$	−17.6754	+	30.6147i	−0.683370	+	1.18363i
$670$		0			0
$671$	25.7032			0.992260
$672$		0			0
$673$	−16.2913	+	9.40580i	−0.627984	+	0.362567i	−0.779971	−	0.625816i	$-0.784766\pi$
$673$	−16.2913	+	9.40580i	−0.627984	+	0.362567i	0.151987	+	0.988383i	$0.451433\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			43.3999i			1.66800i	0.551768	+	0.833998i	$0.313953\pi$
$677$			43.3999i			1.66800i	−0.551768	+	0.833998i	$0.686047\pi$
$678$		0			0
$679$	−1.29035	−	2.23495i	−0.0495191	−	0.0857695i
$680$		0			0
$681$	43.4094			1.66345
$682$		0			0
$683$	−34.5459	−	19.9451i	−1.32186	−	0.763177i	−0.337836	−	0.941205i	$-0.609695\pi$
$683$	−34.5459	−	19.9451i	−1.32186	−	0.763177i	−0.984026	+	0.178027i	$0.943028\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	42.1299	−	24.3237i	1.60736	−	0.928008i
$688$		0			0
$689$	31.7025	+	4.75012i	1.20777	+	0.180965i
$690$		0			0
$691$	2.41303	+	4.17949i	0.0917961	+	0.158995i	0.908267	−	0.418391i	$-0.137406\pi$
$691$	2.41303	+	4.17949i	0.0917961	+	0.158995i	−0.816471	+	0.577387i	$0.804073\pi$
$692$		0			0
$693$	134.172	+	77.4641i	5.09676	+	2.94262i
$694$		0			0
$695$		0			0
$696$		0			0
$697$		−	3.14027i		−	0.118946i
$698$		0			0
$699$	10.2051	+	17.6757i	0.385991	+	0.668556i
$700$		0			0
$701$	−32.6358			−1.23264			−0.616319	−	0.787496i	$-0.711377\pi$
$701$	−32.6358			−1.23264			−0.616319	+	0.787496i	$0.711377\pi$
$702$		0			0
$703$		−	17.7912i		−	0.671009i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	7.63069i		−	0.286982i
$708$		0			0
$709$	9.85365	−	17.0670i	0.370061	−	0.640965i	−0.619513	−	0.784986i	$-0.712670\pi$
$709$	9.85365	−	17.0670i	0.370061	−	0.640965i	0.989575	+	0.144021i	$0.0460033\pi$
$710$		0			0
$711$	−3.63144	+	6.28984i	−0.136190	+	0.235888i
$712$		0			0
$713$	16.9232	−	9.77061i	0.633779	−	0.365912i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	2.52177	−	1.45594i	0.0941772	−	0.0543732i
$718$		0			0
$719$	−21.3564	+	36.9903i	−0.796458	+	1.37951i	0.125451	+	0.992100i	$0.459962\pi$
$719$	−21.3564	+	36.9903i	−0.796458	+	1.37951i	−0.921909	+	0.387406i	$0.873371\pi$
$720$		0			0
$721$	26.2967	−	45.5472i	0.979340	−	1.69627i
$722$		0			0
$723$			68.9055i			2.56262i
$724$		0			0
$725$		0			0
$726$		0			0
$727$		−	11.1831i		−	0.414757i	−0.978261	−	0.207379i	$-0.933507\pi$
$727$		−	11.1831i		−	0.414757i	0.978261	−	0.207379i	$-0.0664932\pi$
$728$		0			0
$729$	42.9851			1.59204
$730$		0			0
$731$	0.248103	+	0.429726i	0.00917641	+	0.0158940i
$732$		0			0
$733$			3.91032i			0.144431i	0.997389	+	0.0722156i	$0.0230070\pi$
$733$			3.91032i			0.144431i	−0.997389	+	0.0722156i	$0.976993\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	21.2204	+	12.2516i	0.781662	+	0.451293i
$738$		0			0
$739$	10.3101	+	17.8576i	0.379263	+	0.656903i	0.990955	−	0.134193i	$-0.0428441\pi$
$739$	10.3101	+	17.8576i	0.379263	+	0.656903i	−0.611692	+	0.791096i	$0.709511\pi$
$740$		0			0
$741$	47.0534	+	7.05022i	1.72855	+	0.258996i
$742$		0			0
$743$	−7.25716	+	4.18992i	−0.266239	+	0.153713i	−0.627177	−	0.778876i	$-0.715790\pi$
$743$	−7.25716	+	4.18992i	−0.266239	+	0.153713i	0.360938	+	0.932590i	$0.382457\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.711001	−	0.410497i	−0.0260142	−	0.0150193i
$748$		0			0
$749$	−55.1390			−2.01474
$750$		0			0
$751$	−7.39645	−	12.8110i	−0.269900	−	0.467481i	0.698935	−	0.715185i	$-0.253657\pi$
$751$	−7.39645	−	12.8110i	−0.269900	−	0.467481i	−0.968836	+	0.247703i	$0.920324\pi$
$752$		0			0
$753$		−	35.5547i		−	1.29568i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−2.78385	+	1.60726i	−0.101181	+	0.0584168i	−0.549737	−	0.835338i	$-0.685272\pi$
$757$	−2.78385	+	1.60726i	−0.101181	+	0.0584168i	0.448556	+	0.893755i	$0.351939\pi$
$758$		0			0
$759$	52.8446			1.91814
$760$		0			0
$761$	−20.3923	+	35.3205i	−0.739220	+	1.28037i	0.213627	+	0.976915i	$0.431472\pi$
$761$	−20.3923	+	35.3205i	−0.739220	+	1.28037i	−0.952847	+	0.303451i	$0.901861\pi$
$762$		0			0
$763$	−20.9200	−	12.0782i	−0.757354	−	0.437259i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.02193	−	6.38584i	−0.289655	−	0.230579i
$768$		0			0
$769$	3.52726	+	6.10940i	0.127196	+	0.220311i	0.922589	−	0.385783i	$-0.126069\pi$
$769$	3.52726	+	6.10940i	0.127196	+	0.220311i	−0.795393	+	0.606094i	$0.792735\pi$
$770$		0			0
$771$	−21.8528	+	37.8502i	−0.787009	+	1.36314i
$772$		0			0
$773$	−19.3372	−	11.1643i	−0.695510	−	0.401553i	0.110163	−	0.993914i	$-0.464863\pi$
$773$	−19.3372	−	11.1643i	−0.695510	−	0.401553i	−0.805673	+	0.592361i	$0.798196\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−46.7419	+	26.9864i	−1.67686	+	0.968133i
$778$		0			0
$779$	−43.3733			−1.55401
$780$		0			0
$781$	60.8376			2.17694
$782$		0			0
$783$	36.7623	−	21.2247i	1.31378	−	0.758510i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−30.3303	−	17.5112i	−1.08116	−	0.624207i	−0.149949	−	0.988694i	$-0.547911\pi$
$787$	−30.3303	−	17.5112i	−1.08116	−	0.624207i	−0.931208	+	0.364487i	$0.881244\pi$
$788$		0			0
$789$	−27.2748	+	47.2413i	−0.971008	+	1.68184i
$790$		0			0
$791$	−36.2148	−	62.7258i	−1.28765	−	2.23027i
$792$		0			0
$793$	−11.7115	−	9.32294i	−0.415888	−	0.331067i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−14.8430	−	8.56962i	−0.525767	−	0.303552i	0.213524	−	0.976938i	$-0.431506\pi$
$797$	−14.8430	−	8.56962i	−0.525767	−	0.303552i	−0.739291	+	0.673386i	$0.764839\pi$
$798$		0			0
$799$	0.757215	−	1.31154i	0.0267883	−	0.0463988i
$800$		0			0
$801$	−23.3974			−0.826706
$802$		0			0
$803$	−19.8879	+	11.4823i	−0.701827	+	0.405200i
$804$		0			0
$805$		0			0
$806$		0			0
$807$			25.2413i			0.888537i
$808$		0			0
$809$	21.9246	+	37.9745i	0.770827	+	1.33511i	0.937111	+	0.349033i	$0.113490\pi$
$809$	21.9246	+	37.9745i	0.770827	+	1.33511i	−0.166284	+	0.986078i	$0.553177\pi$
$810$		0			0
$811$	38.9513			1.36776			0.683882	−	0.729592i	$-0.260290\pi$
$811$	38.9513			1.36776			0.683882	+	0.729592i	$0.260290\pi$
$812$		0			0
$813$	12.7297	+	7.34947i	0.446449	+	0.257757i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	5.93537	−	3.42679i	0.207652	−	0.119888i
$818$		0			0
$819$	−33.0373	−	83.9623i	−1.15442	−	2.93388i
$820$		0			0
$821$	−9.30596	−	16.1184i	−0.324780	−	0.562536i	0.656687	−	0.754163i	$-0.271957\pi$
$821$	−9.30596	−	16.1184i	−0.324780	−	0.562536i	−0.981468	+	0.191627i	$0.938624\pi$
$822$		0			0
$823$	8.48349	+	4.89794i	0.295716	+	0.170732i	0.640517	−	0.767944i	$-0.278720\pi$
$823$	8.48349	+	4.89794i	0.295716	+	0.170732i	−0.344801	+	0.938676i	$0.612054\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			39.6991i			1.38047i	0.723584	+	0.690236i	$0.242494\pi$
$827$			39.6991i			1.38047i	−0.723584	+	0.690236i	$0.757506\pi$
$828$		0			0
$829$	−15.8405	−	27.4366i	−0.550164	−	0.952911i	−0.998262	−	0.0589273i	$-0.981232\pi$
$829$	−15.8405	−	27.4366i	−0.550164	−	0.952911i	0.448099	−	0.893984i	$-0.352101\pi$
$830$		0			0
$831$	−52.0831			−1.80674
$832$		0			0
$833$		−	6.08756i		−	0.210921i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			36.6863i			1.26806i
$838$		0			0
$839$	16.1325	−	27.9423i	0.556956	−	0.964677i	−0.440792	−	0.897609i	$-0.645302\pi$
$839$	16.1325	−	27.9423i	0.556956	−	0.964677i	0.997748	−	0.0670676i	$-0.0213643\pi$
$840$		0			0
$841$	−13.5771	+	23.5163i	−0.468177	+	0.810906i
$842$		0			0
$843$	−67.8926	+	39.1978i	−2.33835	+	1.35004i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	118.394	−	68.3546i	4.06806	−	2.34869i
$848$		0			0
$849$	−14.9566	+	25.9056i	−0.513309	+	0.889078i
$850$		0			0
$851$	−5.75409	+	9.96637i	−0.197248	+	0.341643i
$852$		0			0
$853$		−	17.3167i		−	0.592912i	−0.955047	−	0.296456i	$-0.904195\pi$
$853$		−	17.3167i		−	0.592912i	0.955047	−	0.296456i	$-0.0958048\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			40.9024i			1.39720i	0.715513	+	0.698600i	$0.246193\pi$
$857$			40.9024i			1.39720i	−0.715513	+	0.698600i	$0.753807\pi$
$858$		0			0
$859$	−2.14185			−0.0730789			−0.0365394	−	0.999332i	$-0.511633\pi$
$859$	−2.14185			−0.0730789			−0.0365394	+	0.999332i	$0.511633\pi$
$860$		0			0
$861$	65.7903	+	113.952i	2.24213	+	3.88348i
$862$		0			0
$863$			26.0760i			0.887638i	0.896116	+	0.443819i	$0.146377\pi$
$863$			26.0760i			0.887638i	−0.896116	+	0.443819i	$0.853623\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	41.3683	+	23.8840i	1.40494	+	0.811144i
$868$		0			0
$869$	4.49421	+	7.78420i	0.152456	+	0.264061i
$870$		0			0
$871$	−5.22512	−	13.2793i	−0.177046	−	0.449953i
$872$		0			0
$873$	2.23495	−	1.29035i	0.0756416	−	0.0436717i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	41.3881	+	23.8954i	1.39758	+	0.806890i	0.994138	−	0.108117i	$-0.0344821\pi$
$877$	41.3881	+	23.8954i	1.39758	+	0.806890i	0.403437	+	0.915007i	$0.367815\pi$
$878$		0			0
$879$	47.9841			1.61846
$880$		0			0
$881$	23.9463	+	41.4762i	0.806770	+	1.39737i	0.915089	+	0.403251i	$0.132120\pi$
$881$	23.9463	+	41.4762i	0.806770	+	1.39737i	−0.108319	+	0.994116i	$0.534547\pi$
$882$		0			0
$883$		−	35.3788i		−	1.19059i	−0.803507	−	0.595296i	$-0.797035\pi$
$883$		−	35.3788i		−	1.19059i	0.803507	−	0.595296i	$-0.202965\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.17211	+	4.14082i	−0.240816	+	0.139035i	−0.615552	−	0.788096i	$-0.711067\pi$
$887$	−7.17211	+	4.14082i	−0.240816	+	0.139035i	0.374736	+	0.927132i	$0.377733\pi$
$888$		0			0
$889$	−90.7791			−3.04463
$890$		0			0
$891$	−3.14926	+	5.45468i	−0.105504	+	0.182739i
$892$		0			0
$893$	−18.1149	−	10.4586i	−0.606192	−	0.349985i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−24.0784	−	19.1676i	−0.803954	−	0.639986i
$898$		0			0
$899$	−24.2652	−	42.0286i	−0.809291	−	1.40173i
$900$		0			0
$901$	−1.50136	+	2.60043i	−0.0500176	+	0.0866330i
$902$		0			0
$903$	−18.0060	−	10.3958i	−0.599202	−	0.345949i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	34.6327	−	19.9952i	1.14996	−	0.663929i	0.201082	−	0.979574i	$-0.435554\pi$
$907$	34.6327	−	19.9952i	1.14996	−	0.663929i	0.948877	+	0.315645i	$0.102221\pi$
$908$		0			0
$909$	7.63069			0.253094
$910$		0			0
$911$	−33.3447			−1.10476			−0.552380	−	0.833592i	$-0.686280\pi$
$911$	−33.3447			−1.10476			−0.552380	+	0.833592i	$0.686280\pi$
$912$		0			0
$913$	−0.879923	+	0.508024i	−0.0291212	+	0.0168131i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21.7670	−	12.5672i	−0.718811	−	0.415005i
$918$		0			0
$919$	27.3791	−	47.4220i	0.903154	−	1.56431i	0.0797777	−	0.996813i	$-0.474579\pi$
$919$	27.3791	−	47.4220i	0.903154	−	1.56431i	0.823376	−	0.567496i	$-0.192088\pi$
$920$		0			0
$921$	−36.4250	−	63.0900i	−1.20025	−	2.07889i
$922$		0			0
$923$	−27.7204	−	22.0668i	−0.912427	−	0.726336i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	45.5472	+	26.2967i	1.49597	+	0.863697i
$928$		0			0
$929$	−29.6237	+	51.3097i	−0.971921	+	1.68342i	−0.282177	+	0.959362i	$0.591057\pi$
$929$	−29.6237	+	51.3097i	−0.971921	+	1.68342i	−0.689744	+	0.724054i	$0.742277\pi$
$930$		0			0
$931$	−84.0812			−2.75565
$932$		0			0
$933$	−48.3168	+	27.8957i	−1.58182	+	0.913264i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			43.7040i			1.42775i	0.700274	+	0.713874i	$0.253061\pi$
$937$			43.7040i			1.42775i	−0.700274	+	0.713874i	$0.746939\pi$
$938$		0			0
$939$	−11.4423	−	19.8187i	−0.373406	−	0.646759i
$940$		0			0
$941$	−2.34191			−0.0763439			−0.0381720	−	0.999271i	$-0.512153\pi$
$941$	−2.34191			−0.0763439			−0.0381720	+	0.999271i	$0.512153\pi$
$942$		0			0
$943$	24.2970	+	14.0279i	0.791220	+	0.456811i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−12.5662	+	7.25510i	−0.408346	+	0.235759i	−0.690079	−	0.723734i	$-0.742424\pi$
$947$	−12.5662	+	7.25510i	−0.408346	+	0.235759i	0.281733	+	0.959493i	$0.409091\pi$
$948$		0			0
$949$	13.2266	+	1.98180i	0.429354	+	0.0643320i
$950$		0			0
$951$	−1.57637	−	2.73035i	−0.0511172	−	0.0885376i
$952$		0			0
$953$	28.9723	+	16.7272i	0.938505	+	0.541846i	0.889491	−	0.456952i	$-0.151059\pi$
$953$	28.9723	+	16.7272i	0.938505	+	0.541846i	0.0490137	+	0.998798i	$0.484392\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	131.239i		−	4.24236i
$958$		0			0
$959$	−14.4740	−	25.0698i	−0.467391	−	0.809545i
$960$		0			0
$961$	10.9417			0.352959
$962$		0			0
$963$		−	55.1390i		−	1.77683i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			2.89216i			0.0930056i	0.998918	+	0.0465028i	$0.0148076\pi$
$967$			2.89216i			0.0930056i	−0.998918	+	0.0465028i	$0.985192\pi$
$968$		0			0
$969$	−2.22835	+	3.85961i	−0.0715848	+	0.123989i
$970$		0			0
$971$	−22.2739	+	38.5795i	−0.714804	+	1.23808i	0.248231	+	0.968701i	$0.420151\pi$
$971$	−22.2739	+	38.5795i	−0.714804	+	1.23808i	−0.963035	+	0.269376i	$0.913183\pi$
$972$		0			0
$973$	−45.6348	+	26.3473i	−1.46298	+	0.844654i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.41096	+	3.12402i	−0.173112	+	0.0999462i	−0.584052	−	0.811716i	$-0.698534\pi$
$977$	−5.41096	+	3.12402i	−0.173112	+	0.0999462i	0.410940	+	0.911662i	$0.365200\pi$
$978$		0			0
$979$	−14.4781	+	25.0768i	−0.462722	+	0.801458i
$980$		0			0
$981$	12.0782	−	20.9200i	0.385626	−	0.667923i
$982$		0			0
$983$		−	46.2734i		−	1.47589i	−0.674860	−	0.737946i	$-0.735796\pi$
$983$		−	46.2734i		−	1.47589i	0.674860	−	0.737946i	$-0.264204\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			63.4563i			2.01984i
$988$		0			0
$989$	−4.43320			−0.140968
$990$		0			0
$991$	−24.0826	−	41.7122i	−0.765008	−	1.32503i	−0.940242	−	0.340506i	$-0.889402\pi$
$991$	−24.0826	−	41.7122i	−0.765008	−	1.32503i	0.175235	−	0.984527i	$-0.443932\pi$
$992$		0			0
$993$		−	85.2323i		−	2.70477i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	9.82165	+	5.67053i	0.311055	+	0.179588i	0.647398	−	0.762152i	$-0.275857\pi$
$997$	9.82165	+	5.67053i	0.311055	+	0.179588i	−0.336344	+	0.941739i	$0.609190\pi$
$998$		0			0
$999$	−10.8026	−	18.7107i	−0.341779	−	0.591979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1300.2.bb.g.549.1		20
5.2	odd	4		1300.2.i.h.601.5	yes	10
5.3	odd	4		1300.2.i.g.601.1	✓	10
5.4	even	2	inner	1300.2.bb.g.549.10		20
13.9	even	3	inner	1300.2.bb.g.1049.10		20
65.9	even	6	inner	1300.2.bb.g.1049.1		20
65.22	odd	12		1300.2.i.h.1101.5	yes	10
65.48	odd	12		1300.2.i.g.1101.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1300.2.i.g.601.1	✓	10	5.3	odd	4
1300.2.i.g.1101.1	yes	10	65.48	odd	12
1300.2.i.h.601.5	yes	10	5.2	odd	4
1300.2.i.h.1101.5	yes	10	65.22	odd	12
1300.2.bb.g.549.1		20	1.1	even	1	trivial
1300.2.bb.g.549.10		20	5.4	even	2	inner
1300.2.bb.g.1049.1		20	65.9	even	6	inner
1300.2.bb.g.1049.10		20	13.9	even	3	inner

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:	\( N \)	\(=\)	\( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1300.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.44987 + 1.41443i) q^{3} +(-4.33228 - 2.50124i) q^{7} +(2.50124 - 4.33228i) q^{9} +O(q^{10})\)	\(q+(-2.44987 + 1.41443i) q^{3} +(-4.33228 - 2.50124i) q^{7} +(2.50124 - 4.33228i) q^{9} +(-3.09549 - 5.36155i) q^{11} +(-0.534272 + 3.56575i) q^{13} +(-0.292485 - 0.168866i) q^{17} +(-2.33237 + 4.03979i) q^{19} +14.1513 q^{21} +(2.61312 - 1.50869i) q^{23} +5.66475i q^{27} +(-3.74681 - 6.48966i) q^{29} +6.47624 q^{31} +(15.1671 + 8.75673i) q^{33} +(-3.30300 + 1.90699i) q^{37} +(-3.73461 - 9.49131i) q^{39} +(4.64905 + 8.05238i) q^{41} +(-1.27239 - 0.734613i) q^{43} +4.48412i q^{47} +(9.01241 + 15.6099i) q^{49} +0.955399 q^{51} -8.89084i q^{53} -13.1959i q^{57} +(-1.42188 + 2.46276i) q^{59} +(-2.07585 + 3.59548i) q^{61} +(-21.6721 + 12.5124i) q^{63} +(-3.42762 + 1.97894i) q^{67} +(-4.26787 + 7.39216i) q^{69} +(-4.91340 + 8.51027i) q^{71} -3.70935i q^{73} +30.9703i q^{77} -1.45186 q^{79} +(-0.508685 - 0.881068i) q^{81} -0.164117i q^{83} +(18.3584 + 10.5992i) q^{87} +(-2.33858 - 4.05054i) q^{89} +(11.2334 - 14.1115i) q^{91} +(-15.8660 + 9.16021i) q^{93} +(0.446768 + 0.257942i) q^{97} -30.9703 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 8 q^{9}+O(q^{10}) \) 20 * q + 8 * q^9	\( 20 q + 8 q^{9} - 14 q^{11} + 8 q^{19} + 16 q^{21} + 6 q^{29} + 32 q^{31} - 28 q^{39} + 20 q^{41} + 22 q^{49} + 16 q^{51} - 12 q^{59} - 18 q^{61} - 48 q^{69} + 10 q^{71} + 22 q^{81} - 44 q^{89} - 14 q^{91} - 112 q^{99}+O(q^{100}) \) 20 * q + 8 * q^9 - 14 * q^11 + 8 * q^19 + 16 * q^21 + 6 * q^29 + 32 * q^31 - 28 * q^39 + 20 * q^41 + 22 * q^49 + 16 * q^51 - 12 * q^59 - 18 * q^61 - 48 * q^69 + 10 * q^71 + 22 * q^81 - 44 * q^89 - 14 * q^91 - 112 * q^99

Introduction

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