LMFDB - Embedded newform 756.2.i.b.613.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(37,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			613.7
Root			$-0.674693 - 1.59524i$ of defining polynomial
Character	$\chi$	$=$	756.613
Dual form			756.2.i.b.37.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.07260 - 3.58985i) q^{5} +(2.19013 - 1.48437i) q^{7} +(0.434429 + 0.752453i) q^{11} +(2.86231 + 4.95766i) q^{13} +(1.44613 - 2.50478i) q^{17} +(-2.00703 - 3.47627i) q^{19} +(-2.91488 + 5.04873i) q^{23} +(-6.09133 - 10.5505i) q^{25} +(0.900417 - 1.55957i) q^{29} -2.96091 q^{31} +(-0.789399 - 10.9387i) q^{35} +(-2.64925 - 4.58864i) q^{37} +(5.89325 + 10.2074i) q^{41} +(-2.00703 + 3.47627i) q^{43} -2.34436 q^{47} +(2.59331 - 6.50190i) q^{49} +(1.09116 - 1.88995i) q^{53} +3.60159 q^{55} +3.05430 q^{59} +5.63318 q^{61} +23.7297 q^{65} -2.51078 q^{67} +1.09143 q^{71} +(0.723285 - 1.25277i) q^{73} +(2.06837 + 1.00312i) q^{77} -2.12928 q^{79} +(-2.18784 + 3.78946i) q^{83} +(-5.99451 - 10.3828i) q^{85} +(-5.83373 - 10.1043i) q^{89} +(13.6278 + 6.60919i) q^{91} -16.6391 q^{95} +(-3.98779 + 6.90706i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{5} + 6 q^{7} - 2 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} + 2 q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} - 6 q^{47} - 4 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots - 18 q^{97}+O(q^{100}) $ 14 * q + 2 * q^5 + 6 * q^7 - 2 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 - 11 * q^23 - 9 * q^25 - q^29 + 2 * q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 - 6 * q^47 - 4 * q^49 + 15 * q^53 - 28 * q^55 - 28 * q^59 + 20 * q^61 + 30 * q^65 - 12 * q^67 - 2 * q^71 + 21 * q^73 + 47 * q^77 + 20 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 - 56 * q^95 - 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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			0
$3$		0			0
$4$		0			0
$5$	2.07260	−	3.58985i	0.926894	−	1.60543i	0.138409	−	0.990375i	$-0.455801\pi$
$5$	2.07260	−	3.58985i	0.926894	−	1.60543i	0.788486	−	0.615053i	$-0.210865\pi$
$6$		0			0
$7$	2.19013	−	1.48437i	0.827790	−	0.561038i
$7$	2.19013	−	1.48437i	0.827790	−	0.561038i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.434429	+	0.752453i	0.130985	+	0.226873i	0.924057	−	0.382256i	$-0.124853\pi$
$11$	0.434429	+	0.752453i	0.130985	+	0.226873i	−0.793071	+	0.609129i	$0.791519\pi$
$12$		0			0
$13$	2.86231	+	4.95766i	0.793861	+	1.37501i	0.923560	+	0.383455i	$0.125266\pi$
$13$	2.86231	+	4.95766i	0.793861	+	1.37501i	−0.129698	+	0.991554i	$0.541401\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.44613	−	2.50478i	0.350739	−	0.607498i	−0.635640	−	0.771986i	$-0.719264\pi$
$17$	1.44613	−	2.50478i	0.350739	−	0.607498i	0.986379	+	0.164488i	$0.0525971\pi$
$18$		0			0
$19$	−2.00703	−	3.47627i	−0.460444	−	0.797512i	0.538539	−	0.842600i	$-0.318976\pi$
$19$	−2.00703	−	3.47627i	−0.460444	−	0.797512i	−0.998983	+	0.0450884i	$0.985643\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.91488	+	5.04873i	−0.607795	+	1.05273i	0.383808	+	0.923413i	$0.374613\pi$
$23$	−2.91488	+	5.04873i	−0.607795	+	1.05273i	−0.991603	+	0.129319i	$0.958721\pi$
$24$		0			0
$25$	−6.09133	−	10.5505i	−1.21827	−	2.11010i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.900417	−	1.55957i	0.167203	−	0.289604i	−0.770232	−	0.637763i	$-0.779860\pi$
$29$	0.900417	−	1.55957i	0.167203	−	0.289604i	0.937435	+	0.348159i	$0.113193\pi$
$30$		0			0
$31$	−2.96091			−0.531795			−0.265898	−	0.964001i	$-0.585668\pi$
$31$	−2.96091			−0.531795			−0.265898	+	0.964001i	$0.585668\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.789399	−	10.9387i	−0.133433	−	1.84898i
$36$		0			0
$37$	−2.64925	−	4.58864i	−0.435535	−	0.754368i	0.561804	−	0.827270i	$-0.310107\pi$
$37$	−2.64925	−	4.58864i	−0.435535	−	0.754368i	−0.997339	+	0.0729017i	$0.976774\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.89325	+	10.2074i	0.920371	+	1.59413i	0.798842	+	0.601541i	$0.205446\pi$
$41$	5.89325	+	10.2074i	0.920371	+	1.59413i	0.121528	+	0.992588i	$0.461220\pi$
$42$		0			0
$43$	−2.00703	+	3.47627i	−0.306069	+	0.530127i	−0.977499	−	0.210941i	$-0.932347\pi$
$43$	−2.00703	+	3.47627i	−0.306069	+	0.530127i	0.671430	+	0.741068i	$0.265680\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.34436			−0.341961			−0.170980	−	0.985274i	$-0.554693\pi$
$47$	−2.34436			−0.341961			−0.170980	+	0.985274i	$0.554693\pi$
$48$		0			0
$49$	2.59331	−	6.50190i	0.370472	−	0.928844i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.09116	−	1.88995i	0.149883	−	0.259605i	−0.781301	−	0.624154i	$-0.785444\pi$
$53$	1.09116	−	1.88995i	0.149883	−	0.259605i	0.931184	+	0.364549i	$0.118777\pi$
$54$		0			0
$55$	3.60159			0.485638
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.05430			0.397636			0.198818	−	0.980036i	$-0.436290\pi$
$59$	3.05430			0.397636			0.198818	+	0.980036i	$0.436290\pi$
$60$		0			0
$61$	5.63318			0.721255			0.360628	−	0.932710i	$-0.382563\pi$
$61$	5.63318			0.721255			0.360628	+	0.932710i	$0.382563\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	23.7297			2.94330
$66$		0			0
$67$	−2.51078			−0.306740			−0.153370	−	0.988169i	$-0.549013\pi$
$67$	−2.51078			−0.306740			−0.153370	+	0.988169i	$0.549013\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	1.09143			0.129529			0.0647647	−	0.997901i	$-0.479370\pi$
$71$	1.09143			0.129529			0.0647647	+	0.997901i	$0.479370\pi$
$72$		0			0
$73$	0.723285	−	1.25277i	0.0846541	−	0.146625i	−0.820590	−	0.571518i	$-0.806355\pi$
$73$	0.723285	−	1.25277i	0.0846541	−	0.146625i	0.905244	+	0.424893i	$0.139688\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.06837	+	1.00312i	0.235713	+	0.114316i
$78$		0			0
$79$	−2.12928			−0.239563			−0.119781	−	0.992800i	$-0.538219\pi$
$79$	−2.12928			−0.239563			−0.119781	+	0.992800i	$0.538219\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.18784	+	3.78946i	−0.240147	+	0.415947i	−0.960756	−	0.277395i	$-0.910529\pi$
$83$	−2.18784	+	3.78946i	−0.240147	+	0.415947i	0.720609	+	0.693342i	$0.243862\pi$
$84$		0			0
$85$	−5.99451	−	10.3828i	−0.650196	−	1.12617i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.83373	−	10.1043i	−0.618374	−	1.07105i	−0.989783	−	0.142585i	$-0.954459\pi$
$89$	−5.83373	−	10.1043i	−0.618374	−	1.07105i	0.371409	−	0.928469i	$-0.378875\pi$
$90$		0			0
$91$	13.6278	+	6.60919i	1.42858	+	0.692831i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−16.6391			−1.70713
$96$		0			0
$97$	−3.98779	+	6.90706i	−0.404899	+	0.701306i	−0.994310	−	0.106528i	$-0.966027\pi$
$97$	−3.98779	+	6.90706i	−0.404899	+	0.701306i	0.589411	+	0.807834i	$0.299360\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.88185	−	3.25946i	−0.187251	−	0.324329i	0.757082	−	0.653320i	$-0.226624\pi$
$101$	−1.88185	−	3.25946i	−0.187251	−	0.324329i	−0.944333	+	0.328992i	$0.893291\pi$
$102$		0			0
$103$	−5.42778	+	9.40119i	−0.534815	+	0.926327i	0.464357	+	0.885648i	$0.346285\pi$
$103$	−5.42778	+	9.40119i	−0.534815	+	0.926327i	−0.999172	+	0.0406786i	$0.987048\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.82343	+	8.35442i	0.466298	+	0.807653i	0.999259	−	0.0384875i	$-0.0122540\pi$
$107$	4.82343	+	8.35442i	0.466298	+	0.807653i	−0.532961	+	0.846140i	$0.678921\pi$
$108$		0			0
$109$	−5.86131	+	10.1521i	−0.561412	+	0.972394i	0.435962	+	0.899965i	$0.356408\pi$
$109$	−5.86131	+	10.1521i	−0.561412	+	0.972394i	−0.997374	+	0.0724288i	$0.976925\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.88981	−	5.00530i	−0.271851	−	0.470859i	0.697485	−	0.716599i	$-0.254302\pi$
$113$	−2.88981	−	5.00530i	−0.271851	−	0.470859i	−0.969336	+	0.245740i	$0.920969\pi$
$114$		0			0
$115$	12.0828	+	20.9280i	1.12672	+	1.95154i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.550795	−	7.63237i	−0.0504913	−	0.699659i
$120$		0			0
$121$	5.12254	−	8.87250i	0.465686	−	0.806591i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−29.7736			−2.66303
$126$		0			0
$127$	6.47468			0.574535			0.287268	−	0.957850i	$-0.407253\pi$
$127$	6.47468			0.574535			0.287268	+	0.957850i	$0.407253\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.86514	+	15.3549i	−0.774551	+	1.34156i	0.160495	+	0.987037i	$0.448691\pi$
$131$	−8.86514	+	15.3549i	−0.774551	+	1.34156i	−0.935046	+	0.354525i	$0.884643\pi$
$132$		0			0
$133$	−9.55571	−	4.63431i	−0.828585	−	0.401846i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.36116	+	2.35760i	0.116292	+	0.201423i	0.918295	−	0.395896i	$-0.129566\pi$
$137$	1.36116	+	2.35760i	0.116292	+	0.201423i	−0.802004	+	0.597319i	$0.796233\pi$
$138$		0			0
$139$	8.65431	+	14.9897i	0.734049	+	1.27141i	0.955139	+	0.296157i	$0.0957051\pi$
$139$	8.65431	+	14.9897i	0.734049	+	1.27141i	−0.221090	+	0.975253i	$0.570962\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.48694	+	4.30751i	−0.207968	+	0.360212i
$144$		0			0
$145$	−3.73241	−	6.46472i	−0.309959	−	0.536865i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.42343	+	5.92955i	−0.280458	+	0.485767i	−0.971498	−	0.237049i	$-0.923820\pi$
$149$	−3.42343	+	5.92955i	−0.280458	+	0.485767i	0.691040	+	0.722817i	$0.257153\pi$
$150$		0			0
$151$	−4.64083	−	8.03816i	−0.377666	−	0.654136i	0.613057	−	0.790039i	$-0.289940\pi$
$151$	−4.64083	−	8.03816i	−0.377666	−	0.654136i	−0.990722	+	0.135903i	$0.956606\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.13678	+	10.6292i	−0.492918	+	0.853759i
$156$		0			0
$157$	13.6768			1.09153			0.545764	−	0.837939i	$-0.316240\pi$
$157$	13.6768			1.09153			0.545764	+	0.837939i	$0.316240\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.11020	+	15.3841i	0.0874963	+	1.21244i
$162$		0			0
$163$	−1.65003	−	2.85793i	−0.129240	−	0.223850i	0.794142	−	0.607732i	$-0.207920\pi$
$163$	−1.65003	−	2.85793i	−0.129240	−	0.223850i	−0.923382	+	0.383882i	$0.874587\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.96228	−	10.3270i	−0.461375	−	0.799125i	0.537655	−	0.843165i	$-0.319310\pi$
$167$	−5.96228	−	10.3270i	−0.461375	−	0.799125i	−0.999030	+	0.0440399i	$0.985977\pi$
$168$		0			0
$169$	−9.88562	+	17.1224i	−0.760432	+	1.31711i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.63389			0.732451			0.366225	−	0.930526i	$-0.380650\pi$
$173$	9.63389			0.732451			0.366225	+	0.930526i	$0.380650\pi$
$174$		0			0
$175$	−29.0016	−	14.0651i	−2.19231	−	1.06322i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.5285	−	19.9680i	0.861682	−	1.49248i	−0.00862183	−	0.999963i	$-0.502744\pi$
$179$	11.5285	−	19.9680i	0.861682	−	1.49248i	0.870304	−	0.492515i	$-0.163922\pi$
$180$		0			0
$181$	−11.8325			−0.879504			−0.439752	−	0.898119i	$-0.644934\pi$
$181$	−11.8325			−0.879504			−0.439752	+	0.898119i	$0.644934\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−21.9634			−1.61478
$186$		0			0
$187$	2.51297			0.183767
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.28508			0.454772			0.227386	−	0.973805i	$-0.426982\pi$
$191$	6.28508			0.454772			0.227386	+	0.973805i	$0.426982\pi$
$192$		0			0
$193$	13.7312			0.988392			0.494196	−	0.869351i	$-0.335463\pi$
$193$	13.7312			0.988392			0.494196	+	0.869351i	$0.335463\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.161495			0.0115061			0.00575303	−	0.999983i	$-0.498169\pi$
$197$	0.161495			0.0115061			0.00575303	+	0.999983i	$0.498169\pi$
$198$		0			0
$199$	−12.4140	+	21.5016i	−0.880003	+	1.52421i	−0.0286672	+	0.999589i	$0.509126\pi$
$199$	−12.4140	+	21.5016i	−0.880003	+	1.52421i	−0.851336	+	0.524621i	$0.824207\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.342945	−	4.75220i	−0.0240700	−	0.333539i
$204$		0			0
$205$	48.8573			3.41235
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.74382	−	3.02039i	0.120623	−	0.208925i
$210$		0			0
$211$	9.44607	+	16.3611i	0.650295	+	1.12634i	0.983051	+	0.183331i	$0.0586879\pi$
$211$	9.44607	+	16.3611i	0.650295	+	1.12634i	−0.332757	+	0.943013i	$0.607979\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.31953	+	14.4098i	0.567387	+	0.982743i
$216$		0			0
$217$	−6.48477	+	4.39508i	−0.440215	+	0.298357i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	16.5571			1.11375
$222$		0			0
$223$	7.04717	−	12.2061i	0.471914	−	0.817378i	−0.527570	−	0.849512i	$-0.676897\pi$
$223$	7.04717	−	12.2061i	0.471914	−	0.817378i	0.999484	+	0.0321333i	$0.0102301\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.9891	+	22.4978i	0.862118	+	1.49323i	0.869881	+	0.493262i	$0.164196\pi$
$227$	12.9891	+	22.4978i	0.862118	+	1.49323i	−0.00776306	+	0.999970i	$0.502471\pi$
$228$		0			0
$229$	−12.4579	+	21.5777i	−0.823239	+	1.42589i	0.0800190	+	0.996793i	$0.474502\pi$
$229$	−12.4579	+	21.5777i	−0.823239	+	1.42589i	−0.903258	+	0.429098i	$0.858831\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.05923	+	5.29874i	0.200417	+	0.347132i	0.948663	−	0.316289i	$-0.102437\pi$
$233$	3.05923	+	5.29874i	0.200417	+	0.347132i	−0.748246	+	0.663421i	$0.769104\pi$
$234$		0			0
$235$	−4.85893	+	8.41591i	−0.316961	+	0.548993i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.71988	+	13.3712i	0.499357	+	0.864912i	1.00000		0.000742080i	$-0.000236211\pi$
$239$	7.71988	+	13.3712i	0.499357	+	0.864912i	−0.500643	+	0.865654i	$0.666903\pi$
$240$		0			0
$241$	−4.92259	−	8.52617i	−0.317092	−	0.549219i	0.662788	−	0.748807i	$-0.269373\pi$
$241$	−4.92259	−	8.52617i	−0.317092	−	0.549219i	−0.979880	+	0.199588i	$0.936040\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−17.9660	−	22.7854i	−1.14780	−	1.45571i
$246$		0			0
$247$	11.4895	−	19.9003i	0.731057	−	1.26623i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−26.8843			−1.69692			−0.848461	−	0.529258i	$-0.822470\pi$
$251$	−26.8843			−1.69692			−0.848461	+	0.529258i	$0.822470\pi$
$252$		0			0
$253$	−5.06524			−0.318449
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.50636	−	9.53729i	0.343477	−	0.594920i	−0.641599	−	0.767040i	$-0.721729\pi$
$257$	5.50636	−	9.53729i	0.343477	−	0.594920i	0.985076	+	0.172121i	$0.0550619\pi$
$258$		0			0
$259$	−12.6134	−	6.11724i	−0.783761	−	0.380107i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.65547	−	6.33146i	−0.225406	−	0.390415i	0.731035	−	0.682340i	$-0.239038\pi$
$263$	−3.65547	−	6.33146i	−0.225406	−	0.390415i	−0.956441	+	0.291925i	$0.905704\pi$
$264$		0			0
$265$	−4.52309	−	7.83423i	−0.277851	−	0.481253i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.08048	−	3.60349i	0.126849	−	0.219709i	−0.795605	−	0.605815i	$-0.792847\pi$
$269$	2.08048	−	3.60349i	0.126849	−	0.219709i	0.922454	+	0.386107i	$0.126180\pi$
$270$		0			0
$271$	−4.18300	−	7.24516i	−0.254099	−	0.440112i	0.710551	−	0.703645i	$-0.248446\pi$
$271$	−4.18300	−	7.24516i	−0.254099	−	0.440112i	−0.964650	+	0.263533i	$0.915112\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.29250	−	9.16689i	0.319150	−	0.552784i
$276$		0			0
$277$	1.39928	+	2.42362i	0.0840745	+	0.145621i	0.904996	−	0.425419i	$-0.139873\pi$
$277$	1.39928	+	2.42362i	0.0840745	+	0.145621i	−0.820922	+	0.571040i	$0.806540\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.44314	−	9.42779i	0.324710	−	0.562415i	−0.656743	−	0.754114i	$-0.728067\pi$
$281$	5.44314	−	9.42779i	0.324710	−	0.562415i	0.981454	+	0.191699i	$0.0613998\pi$
$282$		0			0
$283$	−2.02424			−0.120328			−0.0601642	−	0.998188i	$-0.519162\pi$
$283$	−2.02424			−0.120328			−0.0601642	+	0.998188i	$0.519162\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	28.0585	+	13.6078i	1.65624	+	0.803241i
$288$		0			0
$289$	4.31739	+	7.47794i	0.253964	+	0.439879i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.65448	+	16.7220i	0.564021	+	0.976912i	0.997140	+	0.0755757i	$0.0240795\pi$
$293$	9.65448	+	16.7220i	0.564021	+	0.976912i	−0.433120	+	0.901336i	$0.642587\pi$
$294$		0			0
$295$	6.33035	−	10.9645i	0.368567	−	0.638377i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−33.3732			−1.93002
$300$		0			0
$301$	0.764425	+	10.5926i	0.0440607	+	0.610550i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	11.6753	−	20.2223i	0.668527	−	1.15792i
$306$		0			0
$307$	−13.1378			−0.749813			−0.374907	−	0.927063i	$-0.622325\pi$
$307$	−13.1378			−0.749813			−0.374907	+	0.927063i	$0.622325\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	13.5321			0.767336			0.383668	−	0.923471i	$-0.374661\pi$
$311$	13.5321			0.767336			0.383668	+	0.923471i	$0.374661\pi$
$312$		0			0
$313$	−25.2000			−1.42439			−0.712194	−	0.701983i	$-0.752298\pi$
$313$	−25.2000			−1.42439			−0.712194	+	0.701983i	$0.752298\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.2978			0.690711			0.345356	−	0.938472i	$-0.387758\pi$
$317$	12.2978			0.690711			0.345356	+	0.938472i	$0.387758\pi$
$318$		0			0
$319$	1.56467			0.0876047
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−11.6097			−0.645982
$324$		0			0
$325$	34.8705	−	60.3975i	1.93427	−	3.35025i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.13445	+	3.47990i	−0.283072	+	0.191853i
$330$		0			0
$331$	−19.9257			−1.09522			−0.547608	−	0.836735i	$-0.684461\pi$
$331$	−19.9257			−1.09522			−0.547608	+	0.836735i	$0.684461\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.20383	+	9.01330i	−0.284316	+	0.492449i
$336$		0			0
$337$	−0.966380	−	1.67382i	−0.0526421	−	0.0911788i	0.838504	−	0.544896i	$-0.183431\pi$
$337$	−0.966380	−	1.67382i	−0.0526421	−	0.0911788i	−0.891146	+	0.453717i	$0.850098\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.28631	−	2.22795i	−0.0696574	−	0.120650i
$342$		0			0
$343$	−3.97155	−	18.0894i	−0.214444	−	0.976736i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.9648			−0.910720			−0.455360	−	0.890307i	$-0.650489\pi$
$347$	−16.9648			−0.910720			−0.455360	+	0.890307i	$0.650489\pi$
$348$		0			0
$349$	−6.25767	+	10.8386i	−0.334966	+	0.580177i	−0.983478	−	0.181027i	$-0.942058\pi$
$349$	−6.25767	+	10.8386i	−0.334966	+	0.580177i	0.648513	+	0.761204i	$0.275391\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	16.1929	+	28.0468i	0.861859	+	1.49278i	0.870133	+	0.492817i	$0.164033\pi$
$353$	16.1929	+	28.0468i	0.861859	+	1.49278i	−0.00827416	+	0.999966i	$0.502634\pi$
$354$		0			0
$355$	2.26211	−	3.91808i	0.120060	−	0.207950i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.98559	−	15.5635i	−0.474242	−	0.821410i	0.525323	−	0.850903i	$-0.323944\pi$
$359$	−8.98559	−	15.5635i	−0.474242	−	0.821410i	−0.999565	+	0.0294922i	$0.990611\pi$
$360$		0			0
$361$	1.44368	−	2.50052i	0.0759830	−	0.131606i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.99816	−	5.19297i	−0.156931	−	0.271812i
$366$		0			0
$367$	−4.08420	−	7.07404i	−0.213194	−	0.369262i	0.739519	−	0.673136i	$-0.235053\pi$
$367$	−4.08420	−	7.07404i	−0.213194	−	0.369262i	−0.952712	+	0.303874i	$0.901720\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.415596	−	5.75892i	−0.0215767	−	0.298988i
$372$		0			0
$373$	2.58080	−	4.47008i	0.133629	−	0.231452i	−0.791444	−	0.611242i	$-0.790670\pi$
$373$	2.58080	−	4.47008i	0.133629	−	0.231452i	0.925073	+	0.379790i	$0.124004\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	10.3091			0.530945
$378$		0			0
$379$	21.0017			1.07878			0.539392	−	0.842055i	$-0.318654\pi$
$379$	21.0017			1.07878			0.539392	+	0.842055i	$0.318654\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	14.7794	−	25.5988i	0.755194	−	1.30804i	−0.190083	−	0.981768i	$-0.560876\pi$
$383$	14.7794	−	25.5988i	0.755194	−	1.30804i	0.945278	−	0.326267i	$-0.105791\pi$
$384$		0			0
$385$	7.88794	−	5.34608i	0.402006	−	0.272462i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.26895	−	14.3222i	−0.419252	−	0.726166i	0.576612	−	0.817018i	$-0.304374\pi$
$389$	−8.26895	−	14.3222i	−0.419252	−	0.726166i	−0.995864	+	0.0908518i	$0.971041\pi$
$390$		0			0
$391$	8.43063	+	14.6023i	0.426355	+	0.738469i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.41315	+	7.64379i	−0.222049	+	0.384601i
$396$		0			0
$397$	15.4394	+	26.7418i	0.774881	+	1.34213i	0.934861	+	0.355014i	$0.115524\pi$
$397$	15.4394	+	26.7418i	0.774881	+	1.34213i	−0.159980	+	0.987120i	$0.551143\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.31614	−	9.20782i	0.265475	−	0.459817i	−0.702213	−	0.711967i	$-0.747804\pi$
$401$	5.31614	−	9.20782i	0.265475	−	0.459817i	0.967688	+	0.252150i	$0.0811378\pi$
$402$		0			0
$403$	−8.47504	−	14.6792i	−0.422172	−	0.731223i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.30183	−	3.98688i	0.114097	−	0.197622i
$408$		0			0
$409$	−14.7956			−0.731598			−0.365799	−	0.930694i	$-0.619204\pi$
$409$	−14.7956			−0.731598			−0.365799	+	0.930694i	$0.619204\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.68931	−	4.53371i	0.329159	−	0.223089i
$414$		0			0
$415$	9.06904	+	15.7080i	0.445182	+	0.771078i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.56134	+	2.70432i	0.0762765	+	0.132115i	0.901641	−	0.432486i	$-0.142363\pi$
$419$	1.56134	+	2.70432i	0.0762765	+	0.132115i	−0.825364	+	0.564601i	$0.809030\pi$
$420$		0			0
$421$	−0.644580	+	1.11645i	−0.0314149	+	0.0544122i	−0.881305	−	0.472547i	$-0.843335\pi$
$421$	−0.644580	+	1.11645i	−0.0314149	+	0.0544122i	0.849891	+	0.526959i	$0.176668\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−35.2355			−1.70917
$426$		0			0
$427$	12.3374	−	8.36171i	0.597048	−	0.404652i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.5916	−	20.0773i	0.558350	−	0.967090i	−0.439285	−	0.898348i	$-0.644768\pi$
$431$	11.5916	−	20.0773i	0.558350	−	0.967090i	0.997634	−	0.0687421i	$-0.0218986\pi$
$432$		0			0
$433$	35.6437			1.71293			0.856464	−	0.516207i	$-0.172657\pi$
$433$	35.6437			1.71293			0.856464	+	0.516207i	$0.172657\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	23.4010			1.11942
$438$		0			0
$439$	16.0124			0.764230			0.382115	−	0.924115i	$-0.375196\pi$
$439$	16.0124			0.764230			0.382115	+	0.924115i	$0.375196\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.3556			−0.682054			−0.341027	−	0.940054i	$-0.610775\pi$
$443$	−14.3556			−0.682054			−0.341027	+	0.940054i	$0.610775\pi$
$444$		0			0
$445$	−48.3639			−2.29267
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−5.72475			−0.270168			−0.135084	−	0.990834i	$-0.543130\pi$
$449$	−5.72475			−0.270168			−0.135084	+	0.990834i	$0.543130\pi$
$450$		0			0
$451$	−5.12040	+	8.86879i	−0.241110	+	0.417615i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	51.9710	−	35.2235i	2.43644	−	1.65131i
$456$		0			0
$457$	14.6635			0.685930			0.342965	−	0.939348i	$-0.388569\pi$
$457$	14.6635			0.685930			0.342965	+	0.939348i	$0.388569\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.9720	−	22.4681i	0.604164	−	1.04644i	−0.388018	−	0.921652i	$-0.626840\pi$
$461$	12.9720	−	22.4681i	0.604164	−	1.04644i	0.992183	−	0.124792i	$-0.0398263\pi$
$462$		0			0
$463$	−6.46277	−	11.1939i	−0.300351	−	0.520223i	0.675865	−	0.737026i	$-0.263770\pi$
$463$	−6.46277	−	11.1939i	−0.300351	−	0.520223i	−0.976215	+	0.216803i	$0.930437\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.3104	+	28.2504i	0.754755	+	1.30727i	0.945496	+	0.325633i	$0.105577\pi$
$467$	16.3104	+	28.2504i	0.754755	+	1.30727i	−0.190741	+	0.981640i	$0.561089\pi$
$468$		0			0
$469$	−5.49892	+	3.72692i	−0.253916	+	0.172093i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.48765			−0.160362
$474$		0			0
$475$	−24.4509	+	42.3503i	−1.12189	+	1.94316i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.6739	−	21.9518i	−0.579084	−	1.00300i	−0.995585	−	0.0938679i	$-0.970077\pi$
$479$	−12.6739	−	21.9518i	−0.579084	−	1.00300i	0.416500	−	0.909136i	$-0.363256\pi$
$480$		0			0
$481$	15.1660	−	26.2682i	0.691509	−	1.19773i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	16.5302	+	28.6311i	0.750597	+	1.30007i
$486$		0			0
$487$	17.7383	−	30.7236i	0.803799	−	1.39222i	−0.113299	−	0.993561i	$-0.536142\pi$
$487$	17.7383	−	30.7236i	0.803799	−	1.39222i	0.917099	−	0.398660i	$-0.130525\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−13.2554	−	22.9590i	−0.598208	−	1.03613i	−0.993085	−	0.117393i	$-0.962546\pi$
$491$	−13.2554	−	22.9590i	−0.598208	−	1.03613i	0.394877	−	0.918734i	$-0.370787\pi$
$492$		0			0
$493$	−2.60425	−	4.51069i	−0.117289	−	0.203151i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.39038	−	1.62009i	0.107223	−	0.0726710i
$498$		0			0
$499$	3.00130	−	5.19841i	0.134357	−	0.232713i	−0.790995	−	0.611823i	$-0.790437\pi$
$499$	3.00130	−	5.19841i	0.134357	−	0.232713i	0.925352	+	0.379110i	$0.123770\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	22.9460			1.02311			0.511556	−	0.859250i	$-0.329069\pi$
$503$	22.9460			1.02311			0.511556	+	0.859250i	$0.329069\pi$
$504$		0			0
$505$	−15.6013			−0.694248
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.9348	−	25.8679i	0.661975	−	1.14657i	−0.318121	−	0.948050i	$-0.603052\pi$
$509$	14.9348	−	25.8679i	0.661975	−	1.14657i	0.980096	−	0.198524i	$-0.0636147\pi$
$510$		0			0
$511$	−0.275480	−	3.81734i	−0.0121865	−	0.168869i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	22.4992	+	38.9698i	0.991434	+	1.71721i
$516$		0			0
$517$	−1.01846	−	1.76402i	−0.0447918	−	0.0775817i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−15.5980	+	27.0166i	−0.683362	+	1.18362i	0.290587	+	0.956849i	$0.406149\pi$
$521$	−15.5980	+	27.0166i	−0.683362	+	1.18362i	−0.973949	+	0.226769i	$0.927184\pi$
$522$		0			0
$523$	−3.07911	−	5.33318i	−0.134640	−	0.233203i	0.790820	−	0.612049i	$-0.209654\pi$
$523$	−3.07911	−	5.33318i	−0.134640	−	0.233203i	−0.925460	+	0.378846i	$0.876321\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.28187	+	7.41642i	−0.186521	+	0.323064i
$528$		0			0
$529$	−5.49310	−	9.51433i	−0.238830	−	0.413666i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−33.7366	+	58.4335i	−1.46129	+	2.53103i
$534$		0			0
$535$	39.9881			1.72884
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.01899	−	0.873275i	0.259256	−	0.0376146i
$540$		0			0
$541$	−13.5137	−	23.4064i	−0.580999	−	1.00632i	−0.995361	−	0.0962083i	$-0.969329\pi$
$541$	−13.5137	−	23.4064i	−0.580999	−	1.00632i	0.414362	−	0.910112i	$-0.364005\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	24.2963	+	42.0824i	1.04074	+	1.80261i
$546$		0			0
$547$	14.9426	−	25.8814i	0.638900	−	1.10661i	−0.346775	−	0.937948i	$-0.612723\pi$
$547$	14.9426	−	25.8814i	0.638900	−	1.10661i	0.985675	−	0.168658i	$-0.0539434\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.22865			−0.307951
$552$		0			0
$553$	−4.66339	+	3.16064i	−0.198308	+	0.134404i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−10.6650	+	18.4722i	−0.451889	+	0.782694i	−0.998503	−	0.0546900i	$-0.982583\pi$
$557$	−10.6650	+	18.4722i	−0.451889	+	0.782694i	0.546615	+	0.837384i	$0.315916\pi$
$558$		0			0
$559$	−22.9789			−0.971905
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−31.4635			−1.32603			−0.663014	−	0.748607i	$-0.730723\pi$
$563$	−31.4635			−1.32603			−0.663014	+	0.748607i	$0.730723\pi$
$564$		0			0
$565$	−23.9577			−1.00791
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−29.3391			−1.22996			−0.614980	−	0.788543i	$-0.710836\pi$
$569$	−29.3391			−1.22996			−0.614980	+	0.788543i	$0.710836\pi$
$570$		0			0
$571$	−27.4947			−1.15062			−0.575308	−	0.817937i	$-0.695118\pi$
$571$	−27.4947			−1.15062			−0.575308	+	0.817937i	$0.695118\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	71.0221			2.96183
$576$		0			0
$577$	−20.2293	+	35.0381i	−0.842156	+	1.45866i	0.0459122	+	0.998945i	$0.485381\pi$
$577$	−20.2293	+	35.0381i	−0.842156	+	1.45866i	−0.888068	+	0.459712i	$0.847953\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.833292	+	11.5470i	0.0345708	+	0.479048i
$582$		0			0
$583$	1.89613			0.0785299
$584$		0			0
$585$		0			0
$586$		0			0
$587$	13.6559	−	23.6528i	0.563641	−	0.976255i	−0.433533	−	0.901137i	$-0.642733\pi$
$587$	13.6559	−	23.6528i	0.563641	−	0.976255i	0.997175	−	0.0751177i	$-0.0239333\pi$
$588$		0			0
$589$	5.94263	+	10.2929i	0.244862	+	0.424113i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.2898	−	24.7507i	−0.586813	−	1.01639i	−0.994647	−	0.103334i	$-0.967049\pi$
$593$	−14.2898	−	24.7507i	−0.586813	−	1.01639i	0.407833	−	0.913056i	$-0.366284\pi$
$594$		0			0
$595$	−28.5406	−	13.8416i	−1.17005	−	0.567449i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−39.9838			−1.63370			−0.816848	−	0.576854i	$-0.804280\pi$
$599$	−39.9838			−1.63370			−0.816848	+	0.576854i	$0.804280\pi$
$600$		0			0
$601$	−12.6948	+	21.9880i	−0.517831	+	0.896910i	0.481954	+	0.876196i	$0.339927\pi$
$601$	−12.6948	+	21.9880i	−0.517831	+	0.896910i	−0.999785	+	0.0207133i	$0.993406\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−21.2340	−	36.7783i	−0.863283	−	1.49525i
$606$		0			0
$607$	18.6469	−	32.2975i	0.756856	−	1.31091i	−0.187590	−	0.982247i	$-0.560068\pi$
$607$	18.6469	−	32.2975i	0.756856	−	1.31091i	0.944446	−	0.328666i	$-0.106599\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.71029	−	11.6226i	−0.271469	−	0.470199i
$612$		0			0
$613$	−11.7319	+	20.3203i	−0.473848	+	0.820729i	−0.999552	−	0.0299390i	$-0.990469\pi$
$613$	−11.7319	+	20.3203i	−0.473848	+	0.820729i	0.525704	+	0.850668i	$0.323802\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.56888	−	11.3776i	−0.264453	−	0.458047i	0.702967	−	0.711223i	$-0.251858\pi$
$617$	−6.56888	−	11.3776i	−0.264453	−	0.458047i	−0.967420	+	0.253176i	$0.918525\pi$
$618$		0			0
$619$	−10.7776	−	18.6674i	−0.433190	−	0.750308i	0.563956	−	0.825805i	$-0.309279\pi$
$619$	−10.7776	−	18.6674i	−0.433190	−	0.750308i	−0.997146	+	0.0754975i	$0.975946\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−27.7751	−	13.4703i	−1.11279	−	0.539677i
$624$		0			0
$625$	−31.2520	+	54.1300i	−1.25008	+	2.16520i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−15.3247			−0.611036
$630$		0			0
$631$	−6.15223			−0.244916			−0.122458	−	0.992474i	$-0.539078\pi$
$631$	−6.15223			−0.244916			−0.122458	+	0.992474i	$0.539078\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	13.4194	−	23.2431i	0.532533	−	0.922375i
$636$		0			0
$637$	39.6571	−	5.75372i	1.57127	−	0.227971i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.23682	−	3.87429i	−0.0883491	−	0.153025i	0.818464	−	0.574557i	$-0.194826\pi$
$641$	−2.23682	−	3.87429i	−0.0883491	−	0.153025i	−0.906813	+	0.421532i	$0.861492\pi$
$642$		0			0
$643$	8.98009	+	15.5540i	0.354140	+	0.613389i	0.986970	−	0.160902i	$-0.0514402\pi$
$643$	8.98009	+	15.5540i	0.354140	+	0.613389i	−0.632830	+	0.774291i	$0.718107\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.02992	+	10.4441i	−0.237061	+	0.410601i	−0.959870	−	0.280447i	$-0.909517\pi$
$647$	−6.02992	+	10.4441i	−0.237061	+	0.410601i	0.722809	+	0.691048i	$0.242851\pi$
$648$		0			0
$649$	1.32688	+	2.29822i	0.0520845	+	0.0902131i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−24.1366	+	41.8059i	−0.944540	+	1.63599i	−0.187870	+	0.982194i	$0.560158\pi$
$653$	−24.1366	+	41.8059i	−0.944540	+	1.63599i	−0.756670	+	0.653797i	$0.773175\pi$
$654$		0			0
$655$	36.7478	+	63.6490i	1.43585	+	2.48697i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14.5795	+	25.2525i	−0.567937	+	0.983696i	0.428832	+	0.903384i	$0.358925\pi$
$659$	−14.5795	+	25.2525i	−0.567937	+	0.983696i	−0.996770	+	0.0803122i	$0.974408\pi$
$660$		0			0
$661$	−14.5486			−0.565873			−0.282937	−	0.959139i	$-0.591309\pi$
$661$	−14.5486			−0.565873			−0.282937	+	0.959139i	$0.591309\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−36.4416	+	24.6985i	−1.41315	+	0.957766i
$666$		0			0
$667$	5.24922	+	9.09192i	0.203251	+	0.352040i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.44722	+	4.23871i	0.0944738	+	0.163633i
$672$		0			0
$673$	11.6825	−	20.2348i	0.450329	−	0.779993i	−0.548077	−	0.836428i	$-0.684640\pi$
$673$	11.6825	−	20.2348i	0.450329	−	0.779993i	0.998406	+	0.0564349i	$0.0179733\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.7175			0.680939			0.340469	−	0.940256i	$-0.389414\pi$
$677$	17.7175			0.680939			0.340469	+	0.940256i	$0.389414\pi$
$678$		0			0
$679$	1.51885	+	21.0467i	0.0582880	+	0.807698i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−21.7769	+	37.7186i	−0.833269	+	1.44326i	0.0621637	+	0.998066i	$0.480200\pi$
$683$	−21.7769	+	37.7186i	−0.833269	+	1.44326i	−0.895432	+	0.445198i	$0.853133\pi$
$684$		0			0
$685$	11.2846			0.431161
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.4930			0.475945
$690$		0			0
$691$	23.5344			0.895291			0.447645	−	0.894211i	$-0.352263\pi$
$691$	23.5344			0.895291			0.447645	+	0.894211i	$0.352263\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	71.7476			2.72154
$696$		0			0
$697$	34.0897			1.29124
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−45.1804			−1.70644			−0.853219	−	0.521552i	$-0.825353\pi$
$701$	−45.1804			−1.70644			−0.853219	+	0.521552i	$0.825353\pi$
$702$		0			0
$703$	−10.6343	+	18.4191i	−0.401079	+	0.694689i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.95973	−	4.34527i	−0.336965	−	0.163421i
$708$		0			0
$709$	−27.0127			−1.01448			−0.507242	−	0.861804i	$-0.669335\pi$
$709$	−27.0127			−1.01448			−0.507242	+	0.861804i	$0.669335\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.63071	−	14.9488i	0.323223	−	0.559838i
$714$		0			0
$715$	10.3089	+	17.8555i	0.385529	+	0.667757i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	11.2096	+	19.4156i	0.418048	+	0.724080i	0.995743	−	0.0921724i	$-0.0293811\pi$
$719$	11.2096	+	19.4156i	0.418048	+	0.724080i	−0.577695	+	0.816253i	$0.696048\pi$
$720$		0			0
$721$	2.06730	+	28.6466i	0.0769902	+	1.06686i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−21.9389			−0.814792
$726$		0			0
$727$	21.9820	−	38.0740i	0.815268	−	1.41208i	−0.0938680	−	0.995585i	$-0.529923\pi$
$727$	21.9820	−	38.0740i	0.815268	−	1.41208i	0.909136	−	0.416500i	$-0.136744\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.80486	+	10.0543i	0.214701	+	0.371872i
$732$		0			0
$733$	−0.433386	+	0.750646i	−0.0160075	+	0.0277257i	−0.873918	−	0.486073i	$-0.838429\pi$
$733$	−0.433386	+	0.750646i	−0.0160075	+	0.0277257i	0.857911	+	0.513799i	$0.171762\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.09075	−	1.88924i	−0.0401785	−	0.0695911i
$738$		0			0
$739$	13.0442	−	22.5932i	0.479838	−	0.831103i	−0.519895	−	0.854230i	$-0.674029\pi$
$739$	13.0442	−	22.5932i	0.479838	−	0.831103i	0.999733	+	0.0231270i	$0.00736222\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−22.5842	−	39.1170i	−0.828533	−	1.43506i	−0.899189	−	0.437561i	$-0.855842\pi$
$743$	−22.5842	−	39.1170i	−0.828533	−	1.43506i	0.0706551	−	0.997501i	$-0.477491\pi$
$744$		0			0
$745$	14.1908	+	24.5791i	0.519910	+	0.900510i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	22.9650	+	11.1375i	0.839121	+	0.406955i
$750$		0			0
$751$	10.2994	−	17.8391i	0.375831	−	0.650958i	−0.614620	−	0.788823i	$-0.710691\pi$
$751$	10.2994	−	17.8391i	0.375831	−	0.650958i	0.990451	+	0.137865i	$0.0440241\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−38.4743			−1.40022
$756$		0			0
$757$	−39.0856			−1.42059			−0.710294	−	0.703905i	$-0.751438\pi$
$757$	−39.0856			−1.42059			−0.710294	+	0.703905i	$0.751438\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.4436	+	25.0171i	−0.523581	+	0.906868i	0.476043	+	0.879422i	$0.342071\pi$
$761$	−14.4436	+	25.0171i	−0.523581	+	0.906868i	−0.999623	+	0.0274459i	$0.991263\pi$
$762$		0			0
$763$	2.23242	+	30.9347i	0.0808191	+	1.11991i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.74236	+	15.1422i	0.315668	+	0.546753i
$768$		0			0
$769$	−11.1407	−	19.2962i	−0.401742	−	0.695838i	0.592194	−	0.805796i	$-0.298262\pi$
$769$	−11.1407	−	19.2962i	−0.401742	−	0.695838i	−0.993936	+	0.109957i	$0.964929\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	21.3593	−	36.9955i	0.768242	−	1.33063i	−0.170273	−	0.985397i	$-0.554465\pi$
$773$	21.3593	−	36.9955i	0.768242	−	1.33063i	0.938515	−	0.345238i	$-0.112202\pi$
$774$		0			0
$775$	18.0359	+	31.2391i	0.647868	+	1.12214i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	23.6558	−	40.9731i	0.847558	−	1.46801i
$780$		0			0
$781$	0.474151	+	0.821254i	0.0169665	+	0.0293868i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	28.3465	−	49.0976i	1.01173	−	1.75237i
$786$		0			0
$787$	−0.286769			−0.0102222			−0.00511110	−	0.999987i	$-0.501627\pi$
$787$	−0.286769			−0.0102222			−0.00511110	+	0.999987i	$0.501627\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−13.7588	−	6.67270i	−0.489205	−	0.237254i
$792$		0			0
$793$	16.1239	+	27.9274i	0.572577	+	0.991732i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.457746	+	0.792840i	0.0162142	+	0.0280838i	0.874019	−	0.485892i	$-0.161505\pi$
$797$	0.457746	+	0.792840i	0.0162142	+	0.0280838i	−0.857804	+	0.513976i	$0.828172\pi$
$798$		0			0
$799$	−3.39026	+	5.87211i	−0.119939	+	0.207740i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.25687			0.0443538
$804$		0			0
$805$	57.5276	+	27.8996i	2.02758	+	0.983333i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	14.3721	−	24.8932i	0.505297	−	0.875199i	−0.494685	−	0.869073i	$-0.664716\pi$
$809$	14.3721	−	24.8932i	0.505297	−	0.875199i	0.999981	−	0.00612685i	$-0.00195025\pi$
$810$		0			0
$811$	14.3005			0.502157			0.251079	−	0.967967i	$-0.419215\pi$
$811$	14.3005			0.502157			0.251079	+	0.967967i	$0.419215\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−13.6794			−0.479167
$816$		0			0
$817$	16.1126			0.563710
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−35.6250			−1.24332			−0.621660	−	0.783287i	$-0.713542\pi$
$821$	−35.6250			−1.24332			−0.621660	+	0.783287i	$0.713542\pi$
$822$		0			0
$823$	−22.4313			−0.781907			−0.390953	−	0.920411i	$-0.627855\pi$
$823$	−22.4313			−0.781907			−0.390953	+	0.920411i	$0.627855\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	26.6728			0.927505			0.463753	−	0.885965i	$-0.346503\pi$
$827$	26.6728			0.927505			0.463753	+	0.885965i	$0.346503\pi$
$828$		0			0
$829$	−16.0078	+	27.7263i	−0.555973	+	0.962973i	0.441854	+	0.897087i	$0.354321\pi$
$829$	−16.0078	+	27.7263i	−0.555973	+	0.962973i	−0.997827	+	0.0658866i	$0.979012\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−12.5356	−	15.8983i	−0.434331	−	0.550843i
$834$		0			0
$835$	−49.4297			−1.71058
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9.10375	+	15.7682i	−0.314296	+	0.544377i	−0.979288	−	0.202474i	$-0.935102\pi$
$839$	−9.10375	+	15.7682i	−0.314296	+	0.544377i	0.664991	+	0.746851i	$0.268435\pi$
$840$		0			0
$841$	12.8785	+	22.3062i	0.444086	+	0.769180i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	40.9778	+	70.9757i	1.40968	+	2.44164i
$846$		0			0
$847$	−1.95104	−	27.0356i	−0.0670386	−	0.928956i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	30.8891			1.05886
$852$		0			0
$853$	20.9242	−	36.2419i	0.716432	−	1.24090i	−0.245972	−	0.969277i	$-0.579107\pi$
$853$	20.9242	−	36.2419i	0.716432	−	1.24090i	0.962404	−	0.271621i	$-0.0875596\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.85704	+	13.6088i	0.268391	+	0.464867i	0.968447	−	0.249221i	$-0.0801746\pi$
$857$	7.85704	+	13.6088i	0.268391	+	0.464867i	−0.700055	+	0.714089i	$0.746841\pi$
$858$		0			0
$859$	−12.1023	+	20.9618i	−0.412924	+	0.715206i	−0.995208	−	0.0977797i	$-0.968826\pi$
$859$	−12.1023	+	20.9618i	−0.412924	+	0.715206i	0.582284	+	0.812986i	$0.302159\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−26.0542	−	45.1272i	−0.886896	−	1.53615i	−0.843525	−	0.537090i	$-0.819523\pi$
$863$	−26.0542	−	45.1272i	−0.886896	−	1.53615i	−0.0433714	−	0.999059i	$-0.513810\pi$
$864$		0			0
$865$	19.9672	−	34.5842i	0.678904	−	1.17590i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.925022	−	1.60219i	−0.0313792	−	0.0543504i
$870$		0			0
$871$	−7.18662	−	12.4476i	−0.243509	−	0.421770i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−65.2078	+	44.1949i	−2.20443	+	1.49406i
$876$		0			0
$877$	6.98841	−	12.1043i	0.235982	−	0.408733i	−0.723576	−	0.690245i	$-0.757503\pi$
$877$	6.98841	−	12.1043i	0.235982	−	0.408733i	0.959558	+	0.281512i	$0.0908360\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−28.1210			−0.947421			−0.473710	−	0.880681i	$-0.657086\pi$
$881$	−28.1210			−0.947421			−0.473710	+	0.880681i	$0.657086\pi$
$882$		0			0
$883$	−35.1633			−1.18334			−0.591670	−	0.806180i	$-0.701531\pi$
$883$	−35.1633			−1.18334			−0.591670	+	0.806180i	$0.701531\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.4610	+	23.3151i	−0.451975	+	0.782844i	−0.998509	−	0.0545932i	$-0.982614\pi$
$887$	−13.4610	+	23.3151i	−0.451975	+	0.782844i	0.546533	+	0.837437i	$0.315947\pi$
$888$		0			0
$889$	14.1804	−	9.61081i	0.475594	−	0.322336i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.70520	+	8.14965i	0.157454	+	0.272718i
$894$		0			0
$895$	−47.7880	−	82.7713i	−1.59738	−	2.76674i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.66605	+	4.61774i	−0.0889179	+	0.154010i
$900$		0			0
$901$	−3.15594	−	5.46625i	−0.105140	−	0.182107i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−24.5241	+	42.4769i	−0.815207	+	1.41198i
$906$		0			0
$907$	22.3571	+	38.7236i	0.742355	+	1.28580i	0.951420	+	0.307895i	$0.0996246\pi$
$907$	22.3571	+	38.7236i	0.742355	+	1.28580i	−0.209065	+	0.977902i	$0.567042\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	13.7822	−	23.8715i	0.456626	−	0.790899i	−0.542154	−	0.840279i	$-0.682391\pi$
$911$	13.7822	−	23.8715i	0.456626	−	0.790899i	0.998780	+	0.0493800i	$0.0157246\pi$
$912$		0			0
$913$	−3.80185			−0.125823
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.37650	+	46.7882i	0.111502	+	1.54508i
$918$		0			0
$919$	−21.3836	−	37.0376i	−0.705381	−	1.22176i	−0.966554	−	0.256464i	$-0.917442\pi$
$919$	−21.3836	−	37.0376i	−0.705381	−	1.22176i	0.261173	−	0.965292i	$-0.415891\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.12402	+	5.41096i	0.102828	+	0.178104i
$924$		0			0
$925$	−32.2750	+	55.9019i	−1.06119	+	1.83804i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−47.9497			−1.57318			−0.786589	−	0.617477i	$-0.788155\pi$
$929$	−47.9497			−1.57318			−0.786589	+	0.617477i	$0.788155\pi$
$930$		0			0
$931$	−27.8072	+	4.03446i	−0.911346	+	0.132224i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.20838	−	9.02118i	0.170332	−	0.295024i
$936$		0			0
$937$	33.9136			1.10791			0.553955	−	0.832547i	$-0.313118\pi$
$937$	33.9136			1.10791			0.553955	+	0.832547i	$0.313118\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	8.54790			0.278654			0.139327	−	0.990246i	$-0.455506\pi$
$941$	8.54790			0.278654			0.139327	+	0.990246i	$0.455506\pi$
$942$		0			0
$943$	−68.7125			−2.23759
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.823127			−0.0267480			−0.0133740	−	0.999911i	$-0.504257\pi$
$947$	−0.823127			−0.0267480			−0.0133740	+	0.999911i	$0.504257\pi$
$948$		0			0
$949$	8.28106			0.268815
$950$		0			0
$951$		0			0
$952$		0			0
$953$	44.6726			1.44709			0.723544	−	0.690278i	$-0.242512\pi$
$953$	44.6726			1.44709			0.723544	+	0.690278i	$0.242512\pi$
$954$		0			0
$955$	13.0264	−	22.5625i	0.421526	−	0.730104i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.48065	+	3.14298i	0.209271	+	0.101492i
$960$		0			0
$961$	−22.2330			−0.717194
$962$		0			0
$963$		0			0
$964$		0			0
$965$	28.4592	−	49.2928i	0.916135	−	1.58679i
$966$		0			0
$967$	−18.2289	−	31.5735i	−0.586203	−	1.01533i	−0.994724	−	0.102585i	$-0.967289\pi$
$967$	−18.2289	−	31.5735i	−0.586203	−	1.01533i	0.408521	−	0.912749i	$-0.366045\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−8.63674	−	14.9593i	−0.277166	−	0.480066i	0.693513	−	0.720444i	$-0.256062\pi$
$971$	−8.63674	−	14.9593i	−0.277166	−	0.480066i	−0.970679	+	0.240378i	$0.922729\pi$
$972$		0			0
$973$	41.2043	+	19.9832i	1.32095	+	0.640631i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−9.03550			−0.289071			−0.144536	−	0.989500i	$-0.546169\pi$
$977$	−9.03550			−0.289071			−0.144536	+	0.989500i	$0.546169\pi$
$978$		0			0
$979$	5.06868	−	8.77921i	0.161996	−	0.280585i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11.4286	−	19.7950i	−0.364517	−	0.631362i	0.624182	−	0.781279i	$-0.285432\pi$
$983$	−11.4286	−	19.7950i	−0.364517	−	0.631362i	−0.988698	+	0.149918i	$0.952099\pi$
$984$		0			0
$985$	0.334715	−	0.579743i	0.0106649	−	0.0184722i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−11.7005	−	20.2659i	−0.372055	−	0.644417i
$990$		0			0
$991$	−4.37884	+	7.58437i	−0.139098	+	0.240925i	−0.927156	−	0.374677i	$-0.877754\pi$
$991$	−4.37884	+	7.58437i	−0.139098	+	0.240925i	0.788057	+	0.615602i	$0.211087\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	51.4584	+	89.1285i	1.63134	+	2.82556i
$996$		0			0
$997$	−3.46535	−	6.00216i	−0.109749	−	0.190090i	0.805920	−	0.592025i	$-0.201671\pi$
$997$	−3.46535	−	6.00216i	−0.109749	−	0.190090i	−0.915668	+	0.401934i	$0.868338\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.i.b.613.7		14
3.2	odd	2		252.2.i.b.25.7	✓	14
4.3	odd	2		3024.2.q.j.2881.7		14
7.2	even	3		756.2.l.b.289.1		14
7.3	odd	6		5292.2.j.g.3529.1		14
7.4	even	3		5292.2.j.h.3529.7		14
7.5	odd	6		5292.2.l.i.3313.7		14
7.6	odd	2		5292.2.i.i.2125.1		14
9.2	odd	6		2268.2.k.e.1621.1		14
9.4	even	3		756.2.l.b.361.1		14
9.5	odd	6		252.2.l.b.193.3	yes	14
9.7	even	3		2268.2.k.f.1621.7		14
12.11	even	2		1008.2.q.j.529.1		14
21.2	odd	6		252.2.l.b.205.3	yes	14
21.5	even	6		1764.2.l.i.961.5		14
21.11	odd	6		1764.2.j.g.1177.3		14
21.17	even	6		1764.2.j.h.1177.5		14
21.20	even	2		1764.2.i.i.1537.1		14
28.23	odd	6		3024.2.t.j.289.1		14
36.23	even	6		1008.2.t.j.193.5		14
36.31	odd	6		3024.2.t.j.1873.1		14
63.2	odd	6		2268.2.k.e.1297.1		14
63.4	even	3		5292.2.j.h.1765.7		14
63.5	even	6		1764.2.i.i.373.1		14
63.13	odd	6		5292.2.l.i.361.7		14
63.16	even	3		2268.2.k.f.1297.7		14
63.23	odd	6		252.2.i.b.121.7	yes	14
63.31	odd	6		5292.2.j.g.1765.1		14
63.32	odd	6		1764.2.j.g.589.3		14
63.40	odd	6		5292.2.i.i.1549.1		14
63.41	even	6		1764.2.l.i.949.5		14
63.58	even	3	inner	756.2.i.b.37.7		14
63.59	even	6		1764.2.j.h.589.5		14
84.23	even	6		1008.2.t.j.961.5		14
252.23	even	6		1008.2.q.j.625.1		14
252.247	odd	6		3024.2.q.j.2305.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.7	✓	14	3.2	odd	2
252.2.i.b.121.7	yes	14	63.23	odd	6
252.2.l.b.193.3	yes	14	9.5	odd	6
252.2.l.b.205.3	yes	14	21.2	odd	6
756.2.i.b.37.7		14	63.58	even	3	inner
756.2.i.b.613.7		14	1.1	even	1	trivial
756.2.l.b.289.1		14	7.2	even	3
756.2.l.b.361.1		14	9.4	even	3
1008.2.q.j.529.1		14	12.11	even	2
1008.2.q.j.625.1		14	252.23	even	6
1008.2.t.j.193.5		14	36.23	even	6
1008.2.t.j.961.5		14	84.23	even	6
1764.2.i.i.373.1		14	63.5	even	6
1764.2.i.i.1537.1		14	21.20	even	2
1764.2.j.g.589.3		14	63.32	odd	6
1764.2.j.g.1177.3		14	21.11	odd	6
1764.2.j.h.589.5		14	63.59	even	6
1764.2.j.h.1177.5		14	21.17	even	6
1764.2.l.i.949.5		14	63.41	even	6
1764.2.l.i.961.5		14	21.5	even	6
2268.2.k.e.1297.1		14	63.2	odd	6
2268.2.k.e.1621.1		14	9.2	odd	6
2268.2.k.f.1297.7		14	63.16	even	3
2268.2.k.f.1621.7		14	9.7	even	3
3024.2.q.j.2305.7		14	252.247	odd	6
3024.2.q.j.2881.7		14	4.3	odd	2
3024.2.t.j.289.1		14	28.23	odd	6
3024.2.t.j.1873.1		14	36.31	odd	6
5292.2.i.i.1549.1		14	63.40	odd	6
5292.2.i.i.2125.1		14	7.6	odd	2
5292.2.j.g.1765.1		14	63.31	odd	6
5292.2.j.g.3529.1		14	7.3	odd	6
5292.2.j.h.1765.7		14	63.4	even	3
5292.2.j.h.3529.7		14	7.4	even	3
5292.2.l.i.361.7		14	63.13	odd	6
5292.2.l.i.3313.7		14	7.5	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.07260 - 3.58985i) q^{5} +(2.19013 - 1.48437i) q^{7} +(0.434429 + 0.752453i) q^{11} +(2.86231 + 4.95766i) q^{13} +(1.44613 - 2.50478i) q^{17} +(-2.00703 - 3.47627i) q^{19} +(-2.91488 + 5.04873i) q^{23} +(-6.09133 - 10.5505i) q^{25} +(0.900417 - 1.55957i) q^{29} -2.96091 q^{31} +(-0.789399 - 10.9387i) q^{35} +(-2.64925 - 4.58864i) q^{37} +(5.89325 + 10.2074i) q^{41} +(-2.00703 + 3.47627i) q^{43} -2.34436 q^{47} +(2.59331 - 6.50190i) q^{49} +(1.09116 - 1.88995i) q^{53} +3.60159 q^{55} +3.05430 q^{59} +5.63318 q^{61} +23.7297 q^{65} -2.51078 q^{67} +1.09143 q^{71} +(0.723285 - 1.25277i) q^{73} +(2.06837 + 1.00312i) q^{77} -2.12928 q^{79} +(-2.18784 + 3.78946i) q^{83} +(-5.99451 - 10.3828i) q^{85} +(-5.83373 - 10.1043i) q^{89} +(13.6278 + 6.60919i) q^{91} -16.6391 q^{95} +(-3.98779 + 6.90706i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{5} + 6 q^{7} - 2 q^{11} + 2 q^{13} - 2 q^{17} + 7 q^{19} - 11 q^{23} - 9 q^{25} - q^{29} + 2 q^{31} + 19 q^{35} + 10 q^{37} + 33 q^{41} + 7 q^{43} - 6 q^{47} - 4 q^{49} + 15 q^{53} - 28 q^{55}+ \cdots - 18 q^{97}+O(q^{100}) \) 14 * q + 2 * q^5 + 6 * q^7 - 2 * q^11 + 2 * q^13 - 2 * q^17 + 7 * q^19 - 11 * q^23 - 9 * q^25 - q^29 + 2 * q^31 + 19 * q^35 + 10 * q^37 + 33 * q^41 + 7 * q^43 - 6 * q^47 - 4 * q^49 + 15 * q^53 - 28 * q^55 - 28 * q^59 + 20 * q^61 + 30 * q^65 - 12 * q^67 - 2 * q^71 + 21 * q^73 + 47 * q^77 + 20 * q^79 + 25 * q^83 + 8 * q^85 + 6 * q^89 + 2 * q^91 - 56 * q^95 - 18 * q^97

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