LMFDB - Embedded newform 1400.2.bh.i.249.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(249,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("1400.249");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.bh (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:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.32905425960566784.37
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 36x^{10} + 432x^{8} + 2040x^{6} + 3780x^{4} + 2592x^{2} + 576 $ x^12 + 36x^10 + 432x^8 + 2040x^6 + 3780x^4 + 2592*x^2 + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.4
Root			$3.37523i$ of defining polynomial
Character	$\chi$	$=$	1400.249
Dual form			1400.2.bh.i.849.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.611171 + 0.352860i) q^{3} +(2.56539 + 0.647140i) q^{7} +(-1.25098 - 2.16676i) q^{9} +O(q^{10})$	$q+(0.611171 + 0.352860i) q^{3} +(2.56539 + 0.647140i) q^{7} +(-1.25098 - 2.16676i) q^{9} +(2.25098 - 3.89881i) q^{11} -5.09052i q^{13} +(-1.73205 - 1.00000i) q^{17} +(-1.54526 - 2.67647i) q^{19} +(1.33954 + 1.30074i) q^{21} +(-5.01969 + 2.89812i) q^{23} -3.88284i q^{27} -9.50196 q^{29} +(-2.70572 + 4.68644i) q^{31} +(2.75147 - 1.58856i) q^{33} +(6.14057 - 3.54526i) q^{37} +(1.79624 - 3.11118i) q^{39} -6.59248 q^{41} -4.70572i q^{43} +(8.74204 - 5.04722i) q^{47} +(6.16242 + 3.32033i) q^{49} +(-0.705720 - 1.22234i) q^{51} +(8.58526 + 4.95670i) q^{53} -2.18104i q^{57} +(4.00000 - 6.92820i) q^{59} +(4.45670 + 7.71923i) q^{61} +(-1.80705 - 6.36814i) q^{63} +(0.101463 + 0.0585795i) q^{67} -4.09052 q^{69} +(7.08499 + 4.09052i) q^{73} +(8.29771 - 8.54526i) q^{77} +(-7.09052 - 12.2811i) q^{79} +(-2.38284 + 4.12720i) q^{81} +10.7057i q^{83} +(-5.80732 - 3.35286i) q^{87} +(2.04526 + 3.54249i) q^{89} +(3.29428 - 13.0592i) q^{91} +(-3.30732 + 1.90948i) q^{93} -2.00000i q^{97} -11.2637 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{9}+O(q^{10}) $ 12 * q + 18 * q^9	$ 12 q + 18 q^{9} - 6 q^{11} + 6 q^{19} - 48 q^{29} - 24 q^{31} - 36 q^{39} + 36 q^{41} + 24 q^{49} + 48 q^{59} + 12 q^{61} - 36 q^{79} - 54 q^{81} + 48 q^{91} - 252 q^{99}+O(q^{100}) $ 12 * q + 18 * q^9 - 6 * q^11 + 6 * q^19 - 48 * q^29 - 24 * q^31 - 36 * q^39 + 36 * q^41 + 24 * q^49 + 48 * q^59 + 12 * q^61 - 36 * q^79 - 54 * q^81 + 48 * q^91 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.611171	+	0.352860i	0.352860	+	0.203724i	0.665944	−	0.746002i	$-0.268029\pi$
$3$	0.611171	+	0.352860i	0.352860	+	0.203724i	−0.313084	+	0.949725i	$0.601362\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.56539	+	0.647140i	0.969625	+	0.244596i
$7$	2.56539	+	0.647140i	0.969625	+	0.244596i
$8$		0			0
$9$	−1.25098	−	2.16676i	−0.416993	−	0.722254i
$10$		0			0
$11$	2.25098	−	3.89881i	0.678696	−	1.17554i	−0.296678	−	0.954978i	$-0.595879\pi$
$11$	2.25098	−	3.89881i	0.678696	−	1.17554i	0.975374	−	0.220558i	$-0.0707879\pi$
$12$		0			0
$13$		−	5.09052i		−	1.41186i	−0.708283	−	0.705928i	$-0.750530\pi$
$13$		−	5.09052i		−	1.41186i	0.708283	−	0.705928i	$-0.249470\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	−1.73205	−	1.00000i	−0.420084	−	0.242536i	−0.695113	+	0.718900i	$0.744646\pi$
$18$		0			0
$19$	−1.54526	−	2.67647i	−0.354507	−	0.614024i	0.632526	−	0.774539i	$-0.282018\pi$
$19$	−1.54526	−	2.67647i	−0.354507	−	0.614024i	−0.987033	+	0.160515i	$0.948685\pi$
$20$		0			0
$21$	1.33954	+	1.30074i	0.292312	+	0.283844i
$22$		0			0
$23$	−5.01969	+	2.89812i	−1.04668	+	0.604300i	−0.921717	−	0.387862i	$-0.873214\pi$
$23$	−5.01969	+	2.89812i	−1.04668	+	0.604300i	−0.124960	+	0.992162i	$0.539880\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	3.88284i		−	0.747253i
$28$		0			0
$29$	−9.50196			−1.76447			−0.882235	−	0.470810i	$-0.843962\pi$
$29$	−9.50196			−1.76447			−0.882235	+	0.470810i	$0.843962\pi$
$30$		0			0
$31$	−2.70572	+	4.68644i	−0.485962	+	0.841710i	−0.999870	−	0.0161350i	$-0.994864\pi$
$31$	−2.70572	+	4.68644i	−0.485962	+	0.841710i	0.513908	+	0.857845i	$0.328197\pi$
$32$		0			0
$33$	2.75147	−	1.58856i	0.478969	−	0.276533i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.14057	−	3.54526i	1.00950	−	0.582837i	0.0984573	−	0.995141i	$-0.468609\pi$
$37$	6.14057	−	3.54526i	1.00950	−	0.582837i	0.911046	+	0.412304i	$0.135276\pi$
$38$		0			0
$39$	1.79624	−	3.11118i	0.287629	−	0.498187i
$40$		0			0
$41$	−6.59248			−1.02957			−0.514786	−	0.857319i	$-0.672129\pi$
$41$	−6.59248			−1.02957			−0.514786	+	0.857319i	$0.672129\pi$
$42$		0			0
$43$		−	4.70572i		−	0.717616i	−0.933411	−	0.358808i	$-0.883183\pi$
$43$		−	4.70572i		−	0.717616i	0.933411	−	0.358808i	$-0.116817\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.74204	−	5.04722i	1.27516	−	0.736213i	0.299204	−	0.954189i	$-0.403279\pi$
$47$	8.74204	−	5.04722i	1.27516	−	0.736213i	0.975954	+	0.217977i	$0.0699456\pi$
$48$		0			0
$49$	6.16242	+	3.32033i	0.880346	+	0.474333i
$50$		0			0
$51$	−0.705720	−	1.22234i	−0.0988205	−	0.171162i
$52$		0			0
$53$	8.58526	+	4.95670i	1.17928	+	0.680855i	0.955847	−	0.293865i	$-0.0949417\pi$
$53$	8.58526	+	4.95670i	1.17928	+	0.680855i	0.223429	+	0.974720i	$0.428275\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	2.18104i		−	0.288886i
$58$		0			0
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	−0.478953	−	0.877841i	$-0.658984\pi$
$59$	4.00000	−	6.92820i	0.520756	−	0.901975i	0.999709	−	0.0241347i	$-0.00768307\pi$
$60$		0			0
$61$	4.45670	+	7.71923i	0.570622	+	0.988346i	0.996502	+	0.0835666i	$0.0266311\pi$
$61$	4.45670	+	7.71923i	0.570622	+	0.988346i	−0.425880	+	0.904780i	$0.640036\pi$
$62$		0			0
$63$	−1.80705	−	6.36814i	−0.227667	−	0.802310i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.101463	+	0.0585795i	0.0123956	+	0.00715662i	0.506185	−	0.862425i	$-0.331055\pi$
$67$	0.101463	+	0.0585795i	0.0123956	+	0.00715662i	−0.493789	+	0.869582i	$0.664389\pi$
$68$		0			0
$69$	−4.09052			−0.492441
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	7.08499	+	4.09052i	0.829235	+	0.478759i	0.853591	−	0.520944i	$-0.174420\pi$
$73$	7.08499	+	4.09052i	0.829235	+	0.478759i	−0.0243555	+	0.999703i	$0.507753\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.29771	−	8.54526i	0.945612	−	0.973823i
$78$		0			0
$79$	−7.09052	−	12.2811i	−0.797746	−	1.38174i	−0.921081	−	0.389371i	$-0.872692\pi$
$79$	−7.09052	−	12.2811i	−0.797746	−	1.38174i	0.123335	−	0.992365i	$-0.460641\pi$
$80$		0			0
$81$	−2.38284	+	4.12720i	−0.264760	+	0.458578i
$82$		0			0
$83$			10.7057i			1.17511i	0.809186	+	0.587553i	$0.199909\pi$
$83$			10.7057i			1.17511i	−0.809186	+	0.587553i	$0.800091\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−5.80732	−	3.35286i	−0.622610	−	0.359464i
$88$		0			0
$89$	2.04526	+	3.54249i	0.216797	+	0.375504i	0.953827	−	0.300356i	$-0.0971056\pi$
$89$	2.04526	+	3.54249i	0.216797	+	0.375504i	−0.737030	+	0.675860i	$0.763772\pi$
$90$		0			0
$91$	3.29428	−	13.0592i	0.345334	−	1.36897i
$92$		0			0
$93$	−3.30732	+	1.90948i	−0.342953	+	0.198004i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	2.00000i		−	0.203069i	−0.994832	−	0.101535i	$-0.967625\pi$
$97$		−	2.00000i		−	0.203069i	0.994832	−	0.101535i	$-0.0323753\pi$
$98$		0			0
$99$	−11.2637			−1.13205
$100$		0			0
$101$	1.66046	−	2.87600i	0.165222	−	0.286173i	−0.771512	−	0.636215i	$-0.780499\pi$
$101$	1.66046	−	2.87600i	0.165222	−	0.286173i	0.936734	+	0.350042i	$0.113833\pi$
$102$		0			0
$103$	9.42821	−	5.44338i	0.928989	−	0.536352i	0.0424975	−	0.999097i	$-0.486469\pi$
$103$	9.42821	−	5.44338i	0.928989	−	0.536352i	0.886492	+	0.462744i	$0.153135\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.36264	−	1.94142i	0.325079	−	0.187684i	−0.328575	−	0.944478i	$-0.606569\pi$
$107$	3.36264	−	1.94142i	0.325079	−	0.187684i	0.653654	+	0.756794i	$0.273235\pi$
$108$		0			0
$109$	−5.13578	+	8.89543i	−0.491919	+	0.852028i	−0.999957	−	0.00930661i	$-0.997038\pi$
$109$	−5.13578	+	8.89543i	−0.491919	+	0.852028i	0.508038	+	0.861335i	$0.330371\pi$
$110$		0			0
$111$	5.00392			0.474951
$112$		0			0
$113$		−	2.82288i		−	0.265554i	−0.991146	−	0.132777i	$-0.957611\pi$
$113$		−	2.82288i		−	0.265554i	0.991146	−	0.132777i	$-0.0423894\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−11.0299	+	6.36814i	−1.01972	+	0.588735i
$118$		0			0
$119$	−3.79624	−	3.68627i	−0.348001	−	0.337919i
$120$		0			0
$121$	−4.63382	−	8.02601i	−0.421256	−	0.729638i
$122$		0			0
$123$	−4.02913	−	2.32622i	−0.363295	−	0.209748i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	1.73236i		−	0.153722i	−0.997042	−	0.0768610i	$-0.975510\pi$
$127$		−	1.73236i		−	0.153722i	0.997042	−	0.0768610i	$-0.0244898\pi$
$128$		0			0
$129$	1.66046	−	2.87600i	0.146195	−	0.253218i
$130$		0			0
$131$	6.36814	+	11.0299i	0.556387	+	0.963690i	0.997794	+	0.0663835i	$0.0211461\pi$
$131$	6.36814	+	11.0299i	0.556387	+	0.963690i	−0.441407	+	0.897307i	$0.645521\pi$
$132$		0			0
$133$	−2.23214	−	7.86618i	−0.193551	−	0.682084i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	0.344668	−	0.938725i	$-0.387992\pi$
$137$	−3.46410	−	2.00000i	−0.295958	−	0.170872i	−0.640626	+	0.767853i	$0.721325\pi$
$138$		0			0
$139$	1.41144			0.119717			0.0598584	−	0.998207i	$-0.480935\pi$
$139$	1.41144			0.119717			0.0598584	+	0.998207i	$0.480935\pi$
$140$		0			0
$141$	7.12384			0.599936
$142$		0			0
$143$	−19.8470	−	11.4587i	−1.65969	−	0.958221i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.59468	+	4.20376i	0.214006	+	0.346720i
$148$		0			0
$149$	11.5472	+	20.0004i	0.945985	+	1.63849i	0.753767	+	0.657142i	$0.228235\pi$
$149$	11.5472	+	20.0004i	0.945985	+	1.63849i	0.192218	+	0.981352i	$0.438432\pi$
$150$		0			0
$151$	0.203760	−	0.352922i	0.0165817	−	0.0287204i	−0.857615	−	0.514291i	$-0.828055\pi$
$151$	0.203760	−	0.352922i	0.0165817	−	0.0287204i	0.874197	+	0.485571i	$0.161388\pi$
$152$		0			0
$153$			5.00392i			0.404543i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	12.2061	+	7.04722i	0.974156	+	0.562429i	0.900501	−	0.434854i	$-0.143200\pi$
$157$	12.2061	+	7.04722i	0.974156	+	0.562429i	0.0736555	+	0.997284i	$0.476533\pi$
$158$		0			0
$159$	3.49804	+	6.05878i	0.277413	+	0.480493i
$160$		0			0
$161$	−14.7529	+	4.18636i	−1.16269	+	0.329931i
$162$		0			0
$163$	14.0132	−	8.09052i	1.09760	−	0.633698i	0.162009	−	0.986789i	$-0.448203\pi$
$163$	14.0132	−	8.09052i	1.09760	−	0.633698i	0.935589	+	0.353091i	$0.114869\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			7.79624i			0.603291i	0.953420	+	0.301646i	$0.0975359\pi$
$167$			7.79624i			0.603291i	−0.953420	+	0.301646i	$0.902464\pi$
$168$		0			0
$169$	−12.9134			−0.993338
$170$		0			0
$171$	−3.86618	+	6.69642i	−0.295654	+	0.512088i
$172$		0			0
$173$	7.71584	−	4.45474i	0.586624	−	0.338688i	−0.177137	−	0.984186i	$-0.556684\pi$
$173$	7.71584	−	4.45474i	0.586624	−	0.338688i	0.763762	+	0.645499i	$0.223350\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.88937	−	2.82288i	0.367507	−	0.212181i
$178$		0			0
$179$	0.839541	−	1.45413i	0.0627502	−	0.108687i	−0.832944	−	0.553358i	$-0.813346\pi$
$179$	0.839541	−	1.45413i	0.0627502	−	0.108687i	0.895694	+	0.444671i	$0.146680\pi$
$180$		0			0
$181$	12.5059			0.929555			0.464777	−	0.885428i	$-0.346134\pi$
$181$	12.5059			0.929555			0.464777	+	0.885428i	$0.346134\pi$
$182$		0			0
$183$			6.29036i			0.464997i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.79762	+	4.50196i	−0.570219	+	0.329216i
$188$		0			0
$189$	2.51274	−	9.96099i	0.182775	−	0.724555i
$190$		0			0
$191$	−3.29428	−	5.70586i	−0.238366	−	0.412862i	0.721880	−	0.692019i	$-0.243278\pi$
$191$	−3.29428	−	5.70586i	−0.238366	−	0.412862i	−0.960245	+	0.279157i	$0.909945\pi$
$192$		0			0
$193$	15.4385	+	8.91340i	1.11128	+	0.641601i	0.939162	−	0.343475i	$-0.111604\pi$
$193$	15.4385	+	8.91340i	1.11128	+	0.641601i	0.172123	+	0.985075i	$0.444937\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.09052i			0.362685i	0.983420	+	0.181342i	$0.0580442\pi$
$197$			5.09052i			0.362685i	−0.983420	+	0.181342i	$0.941956\pi$
$198$		0			0
$199$	12.1810	−	21.0982i	0.863491	−	1.49561i	−0.00504654	−	0.999987i	$-0.501606\pi$
$199$	12.1810	−	21.0982i	0.863491	−	1.49561i	0.868538	−	0.495623i	$-0.165060\pi$
$200$		0			0
$201$	0.0413407	+	0.0716041i	0.00291595	+	0.00505057i
$202$		0			0
$203$	−24.3762	−	6.14910i	−1.71087	−	0.431582i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	12.5591	+	7.25098i	0.872915	+	0.503978i
$208$		0			0
$209$	−13.9134			−0.962410
$210$		0			0
$211$	−8.26764			−0.569168			−0.284584	−	0.958651i	$-0.591855\pi$
$211$	−8.26764			−0.569168			−0.284584	+	0.958651i	$0.591855\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−9.97400	+	10.2716i	−0.677079	+	0.697279i
$218$		0			0
$219$	2.88676	+	5.00002i	0.195069	+	0.337870i
$220$		0			0
$221$	−5.09052	+	8.81704i	−0.342425	+	0.593098i
$222$		0			0
$223$			17.8268i			1.19377i	0.802327	+	0.596885i	$0.203595\pi$
$223$			17.8268i			1.19377i	−0.802327	+	0.596885i	$0.796405\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.64030	−	2.67908i	−0.307988	−	0.177817i	0.338038	−	0.941133i	$-0.390237\pi$
$227$	−4.64030	−	2.67908i	−0.307988	−	0.177817i	−0.646026	+	0.763316i	$0.723570\pi$
$228$		0			0
$229$	12.0905	+	20.9414i	0.798964	+	1.38385i	0.920291	+	0.391234i	$0.127952\pi$
$229$	12.0905	+	20.9414i	0.798964	+	1.38385i	−0.121327	+	0.992613i	$0.538715\pi$
$230$		0			0
$231$	8.08660	−	2.29469i	0.532059	−	0.150979i
$232$		0			0
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.914461	−	0.404674i	$-0.867385\pi$
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.106773	+	0.994283i	$0.534052\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	10.0078i		−	0.650079i
$238$		0			0
$239$	12.7696			0.825997			0.412998	−	0.910732i	$-0.364481\pi$
$239$	12.7696			0.825997			0.412998	+	0.910732i	$0.364481\pi$
$240$		0			0
$241$	11.0472	−	19.1343i	0.711614	−	1.23255i	−0.252637	−	0.967561i	$-0.581298\pi$
$241$	11.0472	−	19.1343i	0.711614	−	1.23255i	0.964251	−	0.264990i	$-0.0853688\pi$
$242$		0			0
$243$	−13.0006	+	7.50588i	−0.833987	+	0.481502i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.6246	+	7.86618i	−0.866914	+	0.500513i
$248$		0			0
$249$	−3.77762	+	6.54303i	−0.239397	+	0.414647i
$250$		0			0
$251$	−13.5059			−0.852484			−0.426242	−	0.904609i	$-0.640163\pi$
$251$	−13.5059			−0.852484			−0.426242	+	0.904609i	$0.640163\pi$
$252$		0			0
$253$			26.0944i			1.64054i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.1700	+	8.18104i	−0.883899	+	0.510319i	−0.871942	−	0.489609i	$-0.837139\pi$
$257$	−14.1700	+	8.18104i	−0.883899	+	0.510319i	−0.0119570	+	0.999929i	$0.503806\pi$
$258$		0			0
$259$	18.0472	−	5.12115i	1.12140	−	0.318213i
$260$		0			0
$261$	11.8868	+	20.5885i	0.735772	+	1.27439i
$262$		0			0
$263$	7.89230	+	4.55662i	0.486660	+	0.280973i	0.723188	−	0.690651i	$-0.242676\pi$
$263$	7.89230	+	4.55662i	0.486660	+	0.280973i	−0.236528	+	0.971625i	$0.576009\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			2.88676i			0.176667i
$268$		0			0
$269$	4.45670	−	7.71923i	0.271730	−	0.470650i	−0.697575	−	0.716512i	$-0.745738\pi$
$269$	4.45670	−	7.71923i	0.271730	−	0.470650i	0.969305	+	0.245862i	$0.0790710\pi$
$270$		0			0
$271$	−8.18104	−	14.1700i	−0.496963	−	0.860765i	0.503031	−	0.864268i	$-0.332218\pi$
$271$	−8.18104	−	14.1700i	−0.496963	−	0.860765i	−0.999994	+	0.00350346i	$0.998885\pi$
$272$		0			0
$273$	6.62142	−	6.81896i	0.400747	−	0.412702i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−9.67967	−	5.58856i	−0.581595	−	0.335784i	0.180172	−	0.983635i	$-0.442335\pi$
$277$	−9.67967	−	5.58856i	−0.581595	−	0.335784i	−0.761767	+	0.647851i	$0.775668\pi$
$278$		0			0
$279$	13.5392			0.810571
$280$		0			0
$281$	−28.2755			−1.68677			−0.843387	−	0.537307i	$-0.819442\pi$
$281$	−28.2755			−1.68677			−0.843387	+	0.537307i	$0.819442\pi$
$282$		0			0
$283$	−11.1049	−	6.41144i	−0.660120	−	0.381121i	0.132203	−	0.991223i	$-0.457795\pi$
$283$	−11.1049	−	6.41144i	−0.660120	−	0.381121i	−0.792323	+	0.610102i	$0.791128\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−16.9123	−	4.26626i	−0.998299	−	0.251829i
$288$		0			0
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$		0			0
$291$	0.705720	−	1.22234i	0.0413700	−	0.0716550i
$292$		0			0
$293$		−	8.90948i		−	0.520497i	−0.965542	−	0.260249i	$-0.916195\pi$
$293$		−	8.90948i		−	0.520497i	0.965542	−	0.260249i	$-0.0838045\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−15.1385	−	8.74020i	−0.878423	−	0.507158i
$298$		0			0
$299$	14.7529	+	25.5528i	0.853185	+	1.47776i
$300$		0			0
$301$	3.04526	−	12.0720i	0.175526	−	0.695818i
$302$		0			0
$303$	2.02965	−	1.17182i	0.116600	−	0.0673192i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	9.12108i		−	0.520567i	−0.965532	−	0.260284i	$-0.916184\pi$
$307$		−	9.12108i		−	0.520567i	0.965532	−	0.260284i	$-0.0838161\pi$
$308$		0			0
$309$	7.68300			0.437071
$310$		0			0
$311$	6.58856	−	11.4117i	0.373603	−	0.647099i	−0.616514	−	0.787344i	$-0.711456\pi$
$311$	6.58856	−	11.4117i	0.373603	−	0.647099i	0.990117	+	0.140245i	$0.0447889\pi$
$312$		0			0
$313$	15.1894	−	8.76960i	0.858555	−	0.495687i	−0.00497286	−	0.999988i	$-0.501583\pi$
$313$	15.1894	−	8.76960i	0.858555	−	0.495687i	0.863528	+	0.504300i	$0.168250\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.4185	+	6.59248i	−0.641327	+	0.370271i	−0.785126	−	0.619336i	$-0.787402\pi$
$317$	−11.4185	+	6.59248i	−0.641327	+	0.370271i	0.143798	+	0.989607i	$0.454068\pi$
$318$		0			0
$319$	−21.3887	+	37.0464i	−1.19754	+	2.07420i
$320$		0			0
$321$	2.74020			0.152943
$322$		0			0
$323$			6.18104i			0.343922i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.27768	+	3.62442i	−0.347157	+	0.200431i
$328$		0			0
$329$	25.6930	−	7.29075i	1.41650	−	0.401952i
$330$		0			0
$331$	−4.25098	−	7.36291i	−0.233655	−	0.404702i	0.725226	−	0.688511i	$-0.241735\pi$
$331$	−4.25098	−	7.36291i	−0.233655	−	0.404702i	−0.958881	+	0.283809i	$0.908402\pi$
$332$		0			0
$333$	−15.3635	−	8.87010i	−0.841913	−	0.486078i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			28.1889i			1.53555i	0.640722	+	0.767773i	$0.278635\pi$
$337$			28.1889i			1.53555i	−0.640722	+	0.767773i	$0.721365\pi$
$338$		0			0
$339$	0.996080	−	1.72526i	0.0540997	−	0.0937034i
$340$		0			0
$341$	12.1810	+	21.0982i	0.659640	+	1.14253i
$342$		0			0
$343$	13.6603	+	12.5059i	0.737585	+	0.675254i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.34322	−	1.35286i	−0.125791	−	0.0726253i	0.435784	−	0.900051i	$-0.356471\pi$
$347$	−2.34322	−	1.35286i	−0.125791	−	0.0726253i	−0.561575	+	0.827426i	$0.689804\pi$
$348$		0			0
$349$	13.6830			0.732434			0.366217	−	0.930529i	$-0.380653\pi$
$349$	13.6830			0.732434			0.366217	+	0.930529i	$0.380653\pi$
$350$		0			0
$351$	−19.7657			−1.05501
$352$		0			0
$353$	−17.6341	−	10.1810i	−0.938567	−	0.541882i	−0.0490565	−	0.998796i	$-0.515621\pi$
$353$	−17.6341	−	10.1810i	−0.938567	−	0.541882i	−0.889511	+	0.456914i	$0.848955\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−1.01942	−	3.59248i	−0.0539533	−	0.190134i
$358$		0			0
$359$	−9.20768	−	15.9482i	−0.485963	−	0.841712i	0.513907	−	0.857846i	$-0.328198\pi$
$359$	−9.20768	−	15.9482i	−0.485963	−	0.841712i	−0.999870	+	0.0161337i	$0.994864\pi$
$360$		0			0
$361$	4.72434	−	8.18280i	0.248650	−	0.430674i
$362$		0			0
$363$		−	6.54036i		−	0.343280i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	22.1902	+	12.8115i	1.15832	+	0.668756i	0.950901	−	0.309496i	$-0.100160\pi$
$367$	22.1902	+	12.8115i	1.15832	+	0.668756i	0.207419	+	0.978252i	$0.433494\pi$
$368$		0			0
$369$	8.24706	+	14.2843i	0.429325	+	0.743612i
$370$		0			0
$371$	18.8168	+	18.2717i	0.976921	+	0.948620i
$372$		0			0
$373$	−24.4123	+	14.0944i	−1.26402	+	0.729782i	−0.973850	−	0.227193i	$-0.927045\pi$
$373$	−24.4123	+	14.0944i	−1.26402	+	0.729782i	−0.290170	+	0.956975i	$0.593712\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			48.3699i			2.49118i
$378$		0			0
$379$	−21.7402			−1.11672			−0.558359	−	0.829599i	$-0.688569\pi$
$379$	−21.7402			−1.11672			−0.558359	+	0.829599i	$0.688569\pi$
$380$		0			0
$381$	0.611280	−	1.05877i	0.0313168	−	0.0542423i
$382$		0			0
$383$	17.5038	−	10.1058i	0.894400	−	0.516382i	0.0190210	−	0.999819i	$-0.493945\pi$
$383$	17.5038	−	10.1058i	0.894400	−	0.516382i	0.875379	+	0.483437i	$0.160612\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−10.1962	+	5.88676i	−0.518300	+	0.299241i
$388$		0			0
$389$	6.91340	−	11.9744i	0.350523	−	0.607124i	−0.635818	−	0.771839i	$-0.719337\pi$
$389$	6.91340	−	11.9744i	0.350523	−	0.607124i	0.986341	+	0.164715i	$0.0526704\pi$
$390$		0			0
$391$	11.5925			0.586257
$392$		0			0
$393$			8.98824i			0.453397i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	31.4973	−	18.1850i	1.58080	−	0.912677i	0.586061	−	0.810267i	$-0.300678\pi$
$397$	31.4973	−	18.1850i	1.58080	−	0.912677i	0.994742	−	0.102410i	$-0.0326553\pi$
$398$		0			0
$399$	1.41144	−	5.59521i	0.0706603	−	0.280111i
$400$		0			0
$401$	3.40948	+	5.90539i	0.170261	+	0.294901i	0.938511	−	0.345249i	$-0.112205\pi$
$401$	3.40948	+	5.90539i	0.170261	+	0.294901i	−0.768250	+	0.640150i	$0.778872\pi$
$402$		0			0
$403$	23.8564	+	13.7735i	1.18837	+	0.686108i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	31.9212i		−	1.58228i
$408$		0			0
$409$	−8.93202	+	15.4707i	−0.441660	+	0.764978i	−0.997813	−	0.0661025i	$-0.978944\pi$
$409$	−8.93202	+	15.4707i	−0.441660	+	0.764978i	0.556153	+	0.831080i	$0.312277\pi$
$410$		0			0
$411$	−1.41144	−	2.44468i	−0.0696212	−	0.120587i
$412$		0			0
$413$	14.7451	−	15.1850i	0.725557	−	0.747203i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.862631	+	0.498040i	0.0422432	+	0.0243891i
$418$		0			0
$419$	−18.4487			−0.901277			−0.450639	−	0.892706i	$-0.648804\pi$
$419$	−18.4487			−0.901277			−0.450639	+	0.892706i	$0.648804\pi$
$420$		0			0
$421$	−10.7324			−0.523063			−0.261532	−	0.965195i	$-0.584228\pi$
$421$	−10.7324			−0.523063			−0.261532	+	0.965195i	$0.584228\pi$
$422$		0			0
$423$	−21.8722	−	12.6279i	−1.06346	−	0.613992i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	6.43773	+	22.6869i	0.311544	+	1.09790i
$428$		0			0
$429$	−8.08660	−	14.0064i	−0.390425	−	0.676236i
$430$		0			0
$431$	−3.29428	+	5.70586i	−0.158680	+	0.274842i	−0.934393	−	0.356244i	$-0.884057\pi$
$431$	−3.29428	+	5.70586i	−0.158680	+	0.274842i	0.775713	+	0.631086i	$0.217390\pi$
$432$		0			0
$433$		−	5.17712i		−	0.248797i	−0.992232	−	0.124398i	$-0.960300\pi$
$433$		−	5.17712i		−	0.248797i	0.992232	−	0.124398i	$-0.0397001\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.5135	+	8.95670i	0.742109	+	0.428457i
$438$		0			0
$439$	15.5059	+	26.8570i	0.740055	+	1.28181i	0.952470	+	0.304634i	$0.0985340\pi$
$439$	15.5059	+	26.8570i	0.740055	+	1.28181i	−0.212414	+	0.977180i	$0.568133\pi$
$440$		0			0
$441$	−0.514702	−	17.5062i	−0.0245096	−	0.833626i
$442$		0			0
$443$	−4.22527	+	2.43946i	−0.200749	+	0.115902i	−0.597005	−	0.802238i	$-0.703643\pi$
$443$	−4.22527	+	2.43946i	−0.200749	+	0.115902i	0.396256	+	0.918140i	$0.370309\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			16.2982i			0.770878i
$448$		0			0
$449$	−27.7696			−1.31053			−0.655264	−	0.755400i	$-0.727443\pi$
$449$	−27.7696			−1.31053			−0.655264	+	0.755400i	$0.727443\pi$
$450$		0			0
$451$	−14.8395	+	25.7028i	−0.698767	+	1.21030i
$452$		0			0
$453$	0.249064	−	0.143797i	0.0117021	−	0.00675619i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−21.6540	+	12.5020i	−1.01293	+	0.584817i	−0.912049	−	0.410081i	$-0.865500\pi$
$457$	−21.6540	+	12.5020i	−1.01293	+	0.584817i	−0.100884	+	0.994898i	$0.532167\pi$
$458$		0			0
$459$	−3.88284	+	6.72528i	−0.181236	+	0.313909i
$460$		0			0
$461$	−4.00784			−0.186664			−0.0933318	−	0.995635i	$-0.529752\pi$
$461$	−4.00784			−0.186664			−0.0933318	+	0.995635i	$0.529752\pi$
$462$		0			0
$463$			36.8002i			1.71025i	0.518423	+	0.855124i	$0.326519\pi$
$463$			36.8002i			1.71025i	−0.518423	+	0.855124i	$0.673481\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.3302	+	11.7377i	−0.940771	+	0.543154i	−0.890202	−	0.455566i	$-0.849437\pi$
$467$	−20.3302	+	11.7377i	−0.940771	+	0.543154i	−0.0505688	+	0.998721i	$0.516103\pi$
$468$		0			0
$469$	0.222382	+	0.215939i	0.0102686	+	0.00997116i
$470$		0			0
$471$	4.97336	+	8.61411i	0.229160	+	0.396917i
$472$		0			0
$473$	−18.3467	−	10.5925i	−0.843583	−	0.487043i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	24.8029i		−	1.13565i
$478$		0			0
$479$	−18.8868	+	32.7128i	−0.862958	+	1.49469i	0.00610232	+	0.999981i	$0.498058\pi$
$479$	−18.8868	+	32.7128i	−0.862958	+	1.49469i	−0.869060	+	0.494706i	$0.835276\pi$
$480$		0			0
$481$	−18.0472	−	31.2587i	−0.822882	−	1.42527i
$482$		0			0
$483$	−10.4938	−	2.64714i	−0.477483	−	0.120449i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.34615	+	3.08660i	0.242257	+	0.139867i	0.616214	−	0.787579i	$-0.288666\pi$
$487$	5.34615	+	3.08660i	0.242257	+	0.139867i	−0.373957	+	0.927446i	$0.621999\pi$
$488$		0			0
$489$	11.4193			0.516398
$490$		0			0
$491$	39.7814			1.79531			0.897654	−	0.440701i	$-0.145270\pi$
$491$	39.7814			1.79531			0.897654	+	0.440701i	$0.145270\pi$
$492$		0			0
$493$	16.4579	+	9.50196i	0.741226	+	0.427947i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.88284	+	3.26118i	0.0842875	+	0.145990i	0.905087	−	0.425226i	$-0.139805\pi$
$499$	1.88284	+	3.26118i	0.0842875	+	0.145990i	−0.820800	+	0.571216i	$0.806472\pi$
$500$		0			0
$501$	−2.75098	+	4.76484i	−0.122905	+	0.212877i
$502$		0			0
$503$		−	18.7057i		−	0.834047i	−0.908896	−	0.417023i	$-0.863073\pi$
$503$		−	18.7057i		−	0.834047i	0.908896	−	0.417023i	$-0.136927\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.89230	−	4.55662i	−0.350509	−	0.202367i
$508$		0			0
$509$	6.16242	+	10.6736i	0.273144	+	0.473100i	0.969665	−	0.244437i	$-0.0786030\pi$
$509$	6.16242	+	10.6736i	0.273144	+	0.473100i	−0.696521	+	0.717537i	$0.745270\pi$
$510$		0			0
$511$	15.5286	+	15.0787i	0.686945	+	0.667045i
$512$		0			0
$513$	−10.3923	+	6.00000i	−0.458831	+	0.264906i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		−	45.4448i		−	1.99866i
$518$		0			0
$519$	6.28759			0.275995
$520$		0			0
$521$	14.7796	−	25.5990i	0.647505	−	1.12151i	−0.336212	−	0.941786i	$-0.609146\pi$
$521$	14.7796	−	25.5990i	0.647505	−	1.12151i	0.983717	−	0.179725i	$-0.0575209\pi$
$522$		0			0
$523$	37.2425	−	21.5020i	1.62850	−	0.940215i	0.643959	−	0.765060i	$-0.277291\pi$
$523$	37.2425	−	21.5020i	1.62850	−	0.940215i	0.984541	−	0.175155i	$-0.0560428\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	9.37289	−	5.41144i	0.408289	−	0.235726i
$528$		0			0
$529$	5.29820	−	9.17675i	0.230357	−	0.398989i
$530$		0			0
$531$	−20.0157			−0.868606
$532$		0			0
$533$			33.5592i			1.45361i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	1.02621	−	0.592480i	0.0442841	−	0.0255674i
$538$		0			0
$539$	26.8168	−	16.5521i	1.15508	−	0.712950i
$540$		0			0
$541$	2.48334	+	4.30127i	0.106767	+	0.184926i	0.914459	−	0.404679i	$-0.132617\pi$
$541$	2.48334	+	4.30127i	0.106767	+	0.184926i	−0.807692	+	0.589605i	$0.799283\pi$
$542$		0			0
$543$	7.64323	+	4.41282i	0.328003	+	0.189372i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	22.1250i		−	0.945997i	−0.881063	−	0.472998i	$-0.843172\pi$
$547$		−	22.1250i		−	0.945997i	0.881063	−	0.472998i	$-0.156828\pi$
$548$		0			0
$549$	11.1505	−	19.3132i	0.475891	−	0.824267i
$550$		0			0
$551$	14.6830	+	25.4317i	0.625517	+	1.08343i
$552$		0			0
$553$	−10.2423	−	36.0944i	−0.435547	−	1.53489i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.81437	−	2.77958i	−0.203991	−	0.117775i	0.394524	−	0.918885i	$-0.370909\pi$
$557$	−4.81437	−	2.77958i	−0.203991	−	0.117775i	−0.598516	+	0.801111i	$0.704243\pi$
$558$		0			0
$559$	−23.9546			−1.01317
$560$		0			0
$561$	−6.35424			−0.268276
$562$		0			0
$563$	8.21266	+	4.74158i	0.346122	+	0.199834i	0.662976	−	0.748641i	$-0.269293\pi$
$563$	8.21266	+	4.74158i	0.346122	+	0.199834i	−0.316854	+	0.948474i	$0.602626\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−8.78379	+	9.04584i	−0.368884	+	0.379889i
$568$		0			0
$569$	−17.1417	−	29.6902i	−0.718616	−	1.24468i	−0.961548	−	0.274636i	$-0.911443\pi$
$569$	−17.1417	−	29.6902i	−0.718616	−	1.24468i	0.242933	−	0.970043i	$-0.421891\pi$
$570$		0			0
$571$	15.7735	−	27.3205i	0.660101	−	1.14333i	−0.320487	−	0.947253i	$-0.603847\pi$
$571$	15.7735	−	27.3205i	0.660101	−	1.14333i	0.980589	−	0.196076i	$-0.0628200\pi$
$572$		0			0
$573$		−	4.64968i		−	0.194243i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	9.21610	+	5.32092i	0.383671	+	0.221513i	0.679414	−	0.733755i	$-0.262234\pi$
$577$	9.21610	+	5.32092i	0.383671	+	0.221513i	−0.295743	+	0.955268i	$0.595567\pi$
$578$		0			0
$579$	6.29036	+	10.8952i	0.261418	+	0.452790i
$580$		0			0
$581$	−6.92810	+	27.4643i	−0.287426	+	1.13941i
$582$		0			0
$583$	38.6505	−	22.3149i	1.60074	−	0.924187i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			6.64184i			0.274138i	0.990562	+	0.137069i	$0.0437682\pi$
$587$			6.64184i			0.274138i	−0.990562	+	0.137069i	$0.956232\pi$
$588$		0			0
$589$	16.7242			0.689107
$590$		0			0
$591$	−1.79624	+	3.11118i	−0.0738874	+	0.127977i
$592$		0			0
$593$	−11.7253	+	6.76960i	−0.481500	+	0.277994i	−0.721041	−	0.692892i	$-0.756336\pi$
$593$	−11.7253	+	6.76960i	−0.481500	+	0.277994i	0.239541	+	0.970886i	$0.423003\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	14.8894	−	8.59640i	0.609383	−	0.351827i
$598$		0			0
$599$	13.0905	−	22.6734i	0.534864	−	0.926412i	−0.464306	−	0.885675i	$-0.653696\pi$
$599$	13.0905	−	22.6734i	0.534864	−	0.926412i	0.999170	−	0.0407369i	$-0.0129706\pi$
$600$		0			0
$601$	−36.0078			−1.46879			−0.734395	−	0.678722i	$-0.762534\pi$
$601$	−36.0078			−1.46879			−0.734395	+	0.678722i	$0.762534\pi$
$602$		0			0
$603$		−	0.293127i		−	0.0119371i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	20.5620	−	11.8715i	0.834586	−	0.481849i	−0.0208341	−	0.999783i	$-0.506632\pi$
$607$	20.5620	−	11.8715i	0.834586	−	0.481849i	0.855420	+	0.517934i	$0.173299\pi$
$608$		0			0
$609$	−12.7283	−	12.3595i	−0.515775	−	0.500834i
$610$		0			0
$611$	−25.6930	−	44.5015i	−1.03943	−	1.80034i
$612$		0			0
$613$	−8.27847	−	4.77958i	−0.334364	−	0.193045i	0.323413	−	0.946258i	$-0.395170\pi$
$613$	−8.27847	−	4.77958i	−0.334364	−	0.193045i	−0.657777	+	0.753213i	$0.728503\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	19.8268i		−	0.798197i	−0.916908	−	0.399098i	$-0.869323\pi$
$617$		−	19.8268i		−	0.798197i	0.916908	−	0.399098i	$-0.130677\pi$
$618$		0			0
$619$	13.5758	−	23.5140i	0.545658	−	0.945108i	−0.452907	−	0.891558i	$-0.649613\pi$
$619$	13.5758	−	23.5140i	0.545658	−	0.945108i	0.998565	−	0.0535500i	$-0.0170536\pi$
$620$		0			0
$621$	11.2529	+	19.4907i	0.451565	+	0.782133i
$622$		0			0
$623$	2.95439	+	10.4114i	0.118365	+	0.417126i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−8.50347	−	4.90948i	−0.339596	−	0.196066i
$628$		0			0
$629$	−14.1810			−0.565435
$630$		0			0
$631$	−49.7735			−1.98145			−0.990726	−	0.135873i	$-0.956616\pi$
$631$	−49.7735			−1.98145			−0.990726	+	0.135873i	$0.956616\pi$
$632$		0			0
$633$	−5.05294	−	2.91732i	−0.200836	−	0.115953i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	16.9022	−	31.3699i	0.669690	−	1.24292i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.1152	+	17.5200i	−0.399526	+	0.692000i	−0.993667	−	0.112361i	$-0.964159\pi$
$641$	−10.1152	+	17.5200i	−0.399526	+	0.692000i	0.594141	+	0.804361i	$0.297492\pi$
$642$		0			0
$643$			25.1850i			0.993198i	0.867980	+	0.496599i	$0.165418\pi$
$643$			25.1850i			0.993198i	−0.867980	+	0.496599i	$0.834582\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−16.9479	−	9.78488i	−0.666291	−	0.384683i	0.128379	−	0.991725i	$-0.459023\pi$
$647$	−16.9479	−	9.78488i	−0.666291	−	0.384683i	−0.794670	+	0.607042i	$0.792356\pi$
$648$		0			0
$649$	−18.0078	−	31.1905i	−0.706870	−	1.22433i
$650$		0			0
$651$	−9.72024	+	2.75826i	−0.380966	+	0.108105i
$652$		0			0
$653$	−15.8202	+	9.13382i	−0.619094	+	0.357434i	−0.776516	−	0.630097i	$-0.783015\pi$
$653$	−15.8202	+	9.13382i	−0.619094	+	0.357434i	0.157422	+	0.987531i	$0.449682\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	20.4686i		−	0.798558i
$658$		0			0
$659$	−46.0078			−1.79221			−0.896105	−	0.443841i	$-0.853615\pi$
$659$	−46.0078			−1.79221			−0.896105	+	0.443841i	$0.853615\pi$
$660$		0			0
$661$	24.2302	−	41.9680i	0.942446	−	1.63236i	0.181661	−	0.983361i	$-0.441853\pi$
$661$	24.2302	−	41.9680i	0.942446	−	1.63236i	0.760785	−	0.649004i	$-0.224814\pi$
$662$		0			0
$663$	−6.22236	+	3.59248i	−0.241656	+	0.139520i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	47.6969	−	27.5378i	1.84683	−	1.06627i
$668$		0			0
$669$	−6.29036	+	10.8952i	−0.243199	+	0.421234i
$670$		0			0
$671$	40.1278			1.54912
$672$		0			0
$673$			15.0118i			0.578661i	0.957229	+	0.289330i	$0.0934326\pi$
$673$			15.0118i			0.578661i	−0.957229	+	0.289330i	$0.906567\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.85320	−	3.95670i	0.263390	−	0.152068i	−0.362490	−	0.931988i	$-0.618073\pi$
$677$	6.85320	−	3.95670i	0.263390	−	0.152068i	0.625880	+	0.779919i	$0.284740\pi$
$678$		0			0
$679$	1.29428	−	5.13077i	0.0496699	−	0.196901i
$680$		0			0
$681$	−1.89068	−	3.27475i	−0.0724510	−	0.125489i
$682$		0			0
$683$	25.7293	+	14.8548i	0.984504	+	0.568404i	0.903627	−	0.428320i	$-0.140894\pi$
$683$	25.7293	+	14.8548i	0.984504	+	0.568404i	0.0808774	+	0.996724i	$0.474228\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$			17.0650i			0.651072i
$688$		0			0
$689$	25.2322	−	43.7034i	0.961270	−	1.66497i
$690$		0			0
$691$	10.8868	+	18.8564i	0.414152	+	0.717332i	0.995339	−	0.0964378i	$-0.0307449\pi$
$691$	10.8868	+	18.8564i	0.414152	+	0.717332i	−0.581187	+	0.813770i	$0.697412\pi$
$692$		0			0
$693$	−28.8958	−	7.28921i	−1.09766	−	0.276894i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	11.4185	+	6.59248i	0.432507	+	0.249708i
$698$		0			0
$699$	−12.7030			−0.480470
$700$		0			0
$701$	24.0905			0.909886			0.454943	−	0.890520i	$-0.349660\pi$
$701$	24.0905			0.909886			0.454943	+	0.890520i	$0.349660\pi$
$702$		0			0
$703$	−18.9776	−	10.9567i	−0.715752	−	0.413240i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.12090	−	6.30350i	0.230200	−	0.237068i
$708$		0			0
$709$	−12.0186	−	20.8169i	−0.451369	−	0.781794i	0.547103	−	0.837066i	$-0.315731\pi$
$709$	−12.0186	−	20.8169i	−0.451369	−	0.781794i	−0.998471	+	0.0552719i	$0.982397\pi$
$710$		0			0
$711$	−17.7402	+	30.7269i	−0.665309	+	1.15235i
$712$		0			0
$713$		−	31.3660i		−	1.17467i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	7.80441	+	4.50588i	0.291461	+	0.168275i
$718$		0			0
$719$	−0.117159	−	0.202925i	−0.00436929	−	0.00756783i	0.863832	−	0.503779i	$-0.168057\pi$
$719$	−0.117159	−	0.202925i	−0.00436929	−	0.00756783i	−0.868202	+	0.496211i	$0.834724\pi$
$720$		0			0
$721$	27.7096	−	7.86300i	1.03196	−	0.292833i
$722$		0			0
$723$	13.5035	−	7.79624i	0.502200	−	0.289945i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			9.44200i			0.350184i	0.984552	+	0.175092i	$0.0560223\pi$
$727$			9.44200i			0.350184i	−0.984552	+	0.175092i	$0.943978\pi$
$728$		0			0
$729$	3.70295			0.137146
$730$		0			0
$731$	−4.70572	+	8.15055i	−0.174047	+	0.301459i
$732$		0			0
$733$	24.8931	−	14.3721i	0.919449	−	0.530844i	0.0359897	−	0.999352i	$-0.488542\pi$
$733$	24.8931	−	14.3721i	0.919449	−	0.530844i	0.883459	+	0.468508i	$0.155208\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.456781	−	0.263722i	0.0168257	−	0.00971434i
$738$		0			0
$739$	−13.0739	+	22.6446i	−0.480930	+	0.832995i	−0.999761	−	0.0218823i	$-0.993034\pi$
$739$	−13.0739	+	22.6446i	−0.480930	+	0.832995i	0.518831	+	0.854877i	$0.326367\pi$
$740$		0			0
$741$	−11.1026			−0.407865
$742$		0			0
$743$		−	32.7547i		−	1.20165i	−0.799379	−	0.600827i	$-0.794838\pi$
$743$		−	32.7547i		−	1.20165i	0.799379	−	0.600827i	$-0.205162\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	23.1967	−	13.3926i	0.848724	−	0.490011i
$748$		0			0
$749$	9.88284	−	2.80440i	0.361111	−	0.102470i
$750$		0			0
$751$	−13.0905	−	22.6734i	−0.477680	−	0.827366i	0.521993	−	0.852950i	$-0.325189\pi$
$751$	−13.0905	−	22.6734i	−0.477680	−	0.827366i	−0.999673	+	0.0255841i	$0.991855\pi$
$752$		0			0
$753$	−8.25440	−	4.76568i	−0.300807	−	0.173671i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			16.8229i			0.611438i	0.952122	+	0.305719i	$0.0988968\pi$
$757$			16.8229i			0.611438i	−0.952122	+	0.305719i	$0.901103\pi$
$758$		0			0
$759$	−9.20768	+	15.9482i	−0.334218	+	0.578882i
$760$		0			0
$761$	2.95278	+	5.11436i	0.107038	+	0.185396i	0.914569	−	0.404430i	$-0.132530\pi$
$761$	2.95278	+	5.11436i	0.107038	+	0.185396i	−0.807531	+	0.589825i	$0.799197\pi$
$762$		0			0
$763$	−18.9319	+	19.4967i	−0.685379	+	0.705826i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−35.2682	−	20.3621i	−1.27346	−	0.735232i
$768$		0			0
$769$	−0.275481			−0.00993410			−0.00496705	−	0.999988i	$-0.501581\pi$
$769$	−0.275481			−0.00993410			−0.00496705	+	0.999988i	$0.501581\pi$
$770$		0			0
$771$	−11.5470			−0.415857
$772$		0			0
$773$	6.38964	+	3.68906i	0.229819	+	0.132686i	0.610489	−	0.792025i	$-0.290973\pi$
$773$	6.38964	+	3.68906i	0.229819	+	0.132686i	−0.380669	+	0.924711i	$0.624306\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	12.8370	+	3.23824i	0.460524	+	0.116171i
$778$		0			0
$779$	10.1871	+	17.6446i	0.364991	+	0.632182i
$780$		0			0
$781$		0			0
$782$		0			0
$783$			36.8946i			1.31851i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	16.1603	+	9.33014i	0.576052	+	0.332584i	0.759563	−	0.650434i	$-0.225413\pi$
$787$	16.1603	+	9.33014i	0.576052	+	0.332584i	−0.183511	+	0.983018i	$0.558746\pi$
$788$		0			0
$789$	3.21570	+	5.56975i	0.114482	+	0.198288i
$790$		0			0
$791$	1.82680	−	7.24178i	0.0649535	−	0.257488i
$792$		0			0
$793$	39.2949	−	22.6869i	1.39540	−	0.805636i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			9.81896i			0.347805i	0.984763	+	0.173903i	$0.0556378\pi$
$797$			9.81896i			0.347805i	−0.984763	+	0.173903i	$0.944362\pi$
$798$		0			0
$799$	−20.1889			−0.714231
$800$		0			0
$801$	5.11716	−	8.86318i	0.180806	−	0.313165i
$802$		0			0
$803$	31.8963	−	18.4154i	1.12560	−	0.649864i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.44761	−	3.14518i	0.191765	−	0.110716i
$808$		0			0
$809$	−16.0020	+	27.7162i	−0.562599	+	0.974450i	0.434670	+	0.900590i	$0.356865\pi$
$809$	−16.0020	+	27.7162i	−0.562599	+	0.974450i	−0.997269	+	0.0738600i	$0.976468\pi$
$810$		0			0
$811$	43.5137			1.52797			0.763987	−	0.645232i	$-0.223239\pi$
$811$	43.5137			1.52797			0.763987	+	0.645232i	$0.223239\pi$
$812$		0			0
$813$		−	11.5470i		−	0.404972i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−12.5947	+	7.27156i	−0.440633	+	0.254400i
$818$		0			0
$819$	−32.4171	+	9.19882i	−1.13275	+	0.321433i
$820$		0			0
$821$	17.3621	+	30.0720i	0.605941	+	1.04952i	0.991902	+	0.127005i	$0.0405365\pi$
$821$	17.3621	+	30.0720i	0.605941	+	1.04952i	−0.385961	+	0.922515i	$0.626130\pi$
$822$		0			0
$823$	−20.1802	−	11.6511i	−0.703439	−	0.406130i	0.105188	−	0.994452i	$-0.466455\pi$
$823$	−20.1802	−	11.6511i	−0.703439	−	0.406130i	−0.808627	+	0.588322i	$0.799789\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			11.2943i			0.392741i	0.980530	+	0.196370i	$0.0629155\pi$
$827$			11.2943i			0.392741i	−0.980530	+	0.196370i	$0.937085\pi$
$828$		0			0
$829$	10.0039	−	17.3273i	0.347450	−	0.601802i	−0.638345	−	0.769750i	$-0.720381\pi$
$829$	10.0039	−	17.3273i	0.347450	−	0.601802i	0.985796	+	0.167948i	$0.0537141\pi$
$830$		0			0
$831$	−3.94396	−	6.83113i	−0.136814	−	0.236969i
$832$		0			0
$833$	−7.35329	−	11.9134i	−0.254777	−	0.412775i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	18.1967	+	10.5059i	0.628971	+	0.363136i
$838$		0			0
$839$	−13.5846			−0.468994			−0.234497	−	0.972117i	$-0.575344\pi$
$839$	−13.5846			−0.468994			−0.234497	+	0.972117i	$0.575344\pi$
$840$		0			0
$841$	61.2872			2.11335
$842$		0			0
$843$	−17.2812	−	9.97728i	−0.595195	−	0.343636i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−6.69359	−	23.5886i	−0.229994	−	0.810513i
$848$		0			0
$849$	−4.52468	−	7.83697i	−0.155287	−	0.268964i
$850$		0			0
$851$	−20.5492	+	35.5922i	−0.704417	+	1.22009i
$852$		0			0
$853$			29.6336i			1.01464i	0.861759	+	0.507318i	$0.169363\pi$
$853$			29.6336i			1.01464i	−0.861759	+	0.507318i	$0.830637\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.3079	+	9.41536i	0.557067	+	0.321623i	0.751967	−	0.659200i	$-0.229105\pi$
$857$	16.3079	+	9.41536i	0.557067	+	0.321623i	−0.194901	+	0.980823i	$0.562438\pi$
$858$		0			0
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$		0			0
$861$	−8.83090	−	8.57507i	−0.300956	−	0.292238i
$862$		0			0
$863$	−17.1970	+	9.92868i	−0.585392	+	0.337976i	−0.763273	−	0.646076i	$-0.776409\pi$
$863$	−17.1970	+	9.92868i	−0.585392	+	0.337976i	0.177881	+	0.984052i	$0.443076\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	9.17436i		−	0.311577i
$868$		0			0
$869$	−63.8425			−2.16571
$870$		0			0
$871$	0.298200	−	0.516497i	0.0101041	−	0.0175008i
$872$		0			0
$873$	−4.33352	+	2.50196i	−0.146667	+	0.0846785i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−11.7358	+	6.77566i	−0.396289	+	0.228798i	−0.684882	−	0.728654i	$-0.740146\pi$
$877$	−11.7358	+	6.77566i	−0.396289	+	0.228798i	0.288592	+	0.957452i	$0.406813\pi$
$878$		0			0
$879$	3.14380	−	5.44522i	0.106038	−	0.183663i
$880$		0			0
$881$	−47.5964			−1.60356			−0.801782	−	0.597617i	$-0.796114\pi$
$881$	−47.5964			−1.60356			−0.801782	+	0.597617i	$0.796114\pi$
$882$		0			0
$883$		−	36.6497i		−	1.23336i	−0.787214	−	0.616680i	$-0.788477\pi$
$883$		−	36.6497i		−	1.23336i	0.787214	−	0.616680i	$-0.211523\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	39.9454	−	23.0625i	1.34124	−	0.774363i	0.354247	−	0.935152i	$-0.384737\pi$
$887$	39.9454	−	23.0625i	1.34124	−	0.774363i	0.986989	+	0.160789i	$0.0514038\pi$
$888$		0			0
$889$	1.12108	−	4.44417i	0.0375998	−	0.149053i
$890$		0			0
$891$	10.7275	+	18.5805i	0.359383	+	0.622470i
$892$		0			0
$893$	−27.0175	−	15.5985i	−0.904105	−	0.521985i
$894$		0			0
$895$		0			0
$896$		0			0
$897$			20.8229i			0.695256i
$898$		0			0
$899$	25.7096	−	44.5304i	0.857464	−	1.48517i
$900$		0			0
$901$	−9.91340	−	17.1705i	−0.330263	−	0.572033i
$902$		0			0
$903$	6.12090	−	6.30350i	0.203691	−	0.209767i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	4.38884	+	2.53390i	0.145729	+	0.0841368i	0.571092	−	0.820886i	$-0.306520\pi$
$907$	4.38884	+	2.53390i	0.145729	+	0.0841368i	−0.425363	+	0.905023i	$0.639853\pi$
$908$		0			0
$909$	−8.30881			−0.275586
$910$		0			0
$911$	−2.41536			−0.0800244			−0.0400122	−	0.999199i	$-0.512740\pi$
$911$	−2.41536			−0.0800244			−0.0400122	+	0.999199i	$0.512740\pi$
$912$		0			0
$913$	41.7396	+	24.0984i	1.38138	+	0.797539i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	9.19882	+	32.4171i	0.303772	+	1.07051i
$918$		0			0
$919$	18.2755	+	31.6541i	0.602852	+	1.04417i	0.992387	+	0.123159i	$0.0393026\pi$
$919$	18.2755	+	31.6541i	0.602852	+	1.04417i	−0.389534	+	0.921012i	$0.627364\pi$
$920$		0			0
$921$	3.21846	−	5.57454i	0.106052	−	0.183687i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−23.5890	−	13.6191i	−0.774765	−	0.447311i
$928$		0			0
$929$	−8.11520	−	14.0559i	−0.266251	−	0.461160i	0.701640	−	0.712532i	$-0.252452\pi$
$929$	−8.11520	−	14.0559i	−0.266251	−	0.461160i	−0.967891	+	0.251372i	$0.919118\pi$
$930$		0			0
$931$	−0.635781	−	21.6243i	−0.0208369	−	0.708708i
$932$		0			0
$933$	8.05348	−	4.64968i	0.263659	−	0.152224i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	44.1889i		−	1.44359i	−0.692108	−	0.721794i	$-0.743318\pi$
$937$		−	44.1889i		−	1.44359i	0.692108	−	0.721794i	$-0.256682\pi$
$938$		0			0
$939$	12.3778			0.403933
$940$		0			0
$941$	−11.7363	+	20.3278i	−0.382592	+	0.662668i	−0.991432	−	0.130625i	$-0.958302\pi$
$941$	−11.7363	+	20.3278i	−0.382592	+	0.662668i	0.608840	+	0.793293i	$0.291635\pi$
$942$		0			0
$943$	33.0922	−	19.1058i	1.07763	−	0.622170i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	48.5595	−	28.0359i	1.57797	−	0.911043i	0.582831	−	0.812594i	$-0.301945\pi$
$947$	48.5595	−	28.0359i	1.57797	−	0.911043i	0.995142	−	0.0984495i	$-0.0313883\pi$
$948$		0			0
$949$	20.8229	−	36.0663i	0.675939	−	1.17076i
$950$		0			0
$951$	−9.30489			−0.301732
$952$		0			0
$953$			22.7163i			0.735854i	0.929855	+	0.367927i	$0.119932\pi$
$953$			22.7163i			0.735854i	−0.929855	+	0.367927i	$0.880068\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−26.1443	+	15.0944i	−0.845126	+	0.487934i
$958$		0			0
$959$	−7.59248	−	7.37253i	−0.245174	−	0.238072i
$960$		0			0
$961$	0.858162	+	1.48638i	0.0276827	+	0.0479478i
$962$		0			0
$963$	−8.41319	−	4.85736i	−0.271111	−	0.156526i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			10.9400i			0.351808i	0.984407	+	0.175904i	$0.0562848\pi$
$967$			10.9400i			0.351808i	−0.984407	+	0.175904i	$0.943715\pi$
$968$		0			0
$969$	−2.18104	+	3.77767i	−0.0700651	+	0.121356i
$970$		0			0
$971$	−12.8701	−	22.2917i	−0.413021	−	0.715374i	0.582197	−	0.813048i	$-0.302193\pi$
$971$	−12.8701	−	22.2917i	−0.413021	−	0.715374i	−0.995218	+	0.0976739i	$0.968860\pi$
$972$		0			0
$973$	3.62089	+	0.913399i	0.116080	+	0.0292822i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−14.5690	−	8.41144i	−0.466105	−	0.269106i	0.248503	−	0.968631i	$-0.420061\pi$
$977$	−14.5690	−	8.41144i	−0.466105	−	0.269106i	−0.714608	+	0.699525i	$0.753395\pi$
$978$		0			0
$979$	18.4154			0.588557
$980$		0			0
$981$	25.6990			0.820507
$982$		0			0
$983$	−38.0922	−	21.9926i	−1.21495	−	0.701454i	−0.251119	−	0.967956i	$-0.580799\pi$
$983$	−38.0922	−	21.9926i	−1.21495	−	0.701454i	−0.963834	+	0.266502i	$0.914132\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	18.2754	+	4.61013i	0.581713	+	0.146742i
$988$		0			0
$989$	13.6377	+	23.6213i	0.433655	+	0.751112i
$990$		0			0
$991$	22.1172	−	38.3080i	0.702575	−	1.21690i	−0.264985	−	0.964253i	$-0.585367\pi$
$991$	22.1172	−	38.3080i	0.702575	−	1.21690i	0.967560	−	0.252643i	$-0.0812997\pi$
$992$		0			0
$993$		−	6.00000i		−	0.190404i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−29.6152	−	17.0984i	−0.937924	−	0.541510i	−0.0486148	−	0.998818i	$-0.515481\pi$
$997$	−29.6152	−	17.0984i	−0.937924	−	0.541510i	−0.889309	+	0.457307i	$0.848814\pi$
$998$		0			0
$999$	−13.7657	−	23.8429i	−0.435527	−	0.754355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.bh.i.249.4		12
5.2	odd	4		1400.2.q.j.1201.2		6
5.3	odd	4		280.2.q.e.81.2	✓	6
5.4	even	2	inner	1400.2.bh.i.249.3		12
7.2	even	3	inner	1400.2.bh.i.849.3		12
15.8	even	4		2520.2.bi.q.361.2		6
20.3	even	4		560.2.q.l.81.2		6
35.2	odd	12		1400.2.q.j.401.2		6
35.3	even	12		1960.2.a.v.1.2		3
35.9	even	6	inner	1400.2.bh.i.849.4		12
35.13	even	4		1960.2.q.w.361.2		6
35.17	even	12		9800.2.a.cf.1.2		3
35.18	odd	12		1960.2.a.w.1.2		3
35.23	odd	12		280.2.q.e.121.2	yes	6
35.32	odd	12		9800.2.a.ce.1.2		3
35.33	even	12		1960.2.q.w.961.2		6
105.23	even	12		2520.2.bi.q.1801.2		6
140.3	odd	12		3920.2.a.cb.1.2		3
140.23	even	12		560.2.q.l.401.2		6
140.123	even	12		3920.2.a.cc.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.q.e.81.2	✓	6	5.3	odd	4
280.2.q.e.121.2	yes	6	35.23	odd	12
560.2.q.l.81.2		6	20.3	even	4
560.2.q.l.401.2		6	140.23	even	12
1400.2.q.j.401.2		6	35.2	odd	12
1400.2.q.j.1201.2		6	5.2	odd	4
1400.2.bh.i.249.3		12	5.4	even	2	inner
1400.2.bh.i.249.4		12	1.1	even	1	trivial
1400.2.bh.i.849.3		12	7.2	even	3	inner
1400.2.bh.i.849.4		12	35.9	even	6	inner
1960.2.a.v.1.2		3	35.3	even	12
1960.2.a.w.1.2		3	35.18	odd	12
1960.2.q.w.361.2		6	35.13	even	4
1960.2.q.w.961.2		6	35.33	even	12
2520.2.bi.q.361.2		6	15.8	even	4
2520.2.bi.q.1801.2		6	105.23	even	12
3920.2.a.cb.1.2		3	140.3	odd	12
3920.2.a.cc.1.2		3	140.123	even	12
9800.2.a.ce.1.2		3	35.32	odd	12
9800.2.a.cf.1.2		3	35.17	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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.611171 + 0.352860i) q^{3} +(2.56539 + 0.647140i) q^{7} +(-1.25098 - 2.16676i) q^{9} +O(q^{10})\)	\(q+(0.611171 + 0.352860i) q^{3} +(2.56539 + 0.647140i) q^{7} +(-1.25098 - 2.16676i) q^{9} +(2.25098 - 3.89881i) q^{11} -5.09052i q^{13} +(-1.73205 - 1.00000i) q^{17} +(-1.54526 - 2.67647i) q^{19} +(1.33954 + 1.30074i) q^{21} +(-5.01969 + 2.89812i) q^{23} -3.88284i q^{27} -9.50196 q^{29} +(-2.70572 + 4.68644i) q^{31} +(2.75147 - 1.58856i) q^{33} +(6.14057 - 3.54526i) q^{37} +(1.79624 - 3.11118i) q^{39} -6.59248 q^{41} -4.70572i q^{43} +(8.74204 - 5.04722i) q^{47} +(6.16242 + 3.32033i) q^{49} +(-0.705720 - 1.22234i) q^{51} +(8.58526 + 4.95670i) q^{53} -2.18104i q^{57} +(4.00000 - 6.92820i) q^{59} +(4.45670 + 7.71923i) q^{61} +(-1.80705 - 6.36814i) q^{63} +(0.101463 + 0.0585795i) q^{67} -4.09052 q^{69} +(7.08499 + 4.09052i) q^{73} +(8.29771 - 8.54526i) q^{77} +(-7.09052 - 12.2811i) q^{79} +(-2.38284 + 4.12720i) q^{81} +10.7057i q^{83} +(-5.80732 - 3.35286i) q^{87} +(2.04526 + 3.54249i) q^{89} +(3.29428 - 13.0592i) q^{91} +(-3.30732 + 1.90948i) q^{93} -2.00000i q^{97} -11.2637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{9}+O(q^{10}) \) 12 * q + 18 * q^9	\( 12 q + 18 q^{9} - 6 q^{11} + 6 q^{19} - 48 q^{29} - 24 q^{31} - 36 q^{39} + 36 q^{41} + 24 q^{49} + 48 q^{59} + 12 q^{61} - 36 q^{79} - 54 q^{81} + 48 q^{91} - 252 q^{99}+O(q^{100}) \) 12 * q + 18 * q^9 - 6 * q^11 + 6 * q^19 - 48 * q^29 - 24 * q^31 - 36 * q^39 + 36 * q^41 + 24 * q^49 + 48 * q^59 + 12 * q^61 - 36 * q^79 - 54 * q^81 + 48 * q^91 - 252 * q^99

Introduction

L-functions

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