LMFDB - Embedded newform 1216.2.m.a.303.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(303,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1216.303");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.m (of order $4$, 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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 304)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			303.1
Character	$\chi$	$=$	1216.303
Dual form			1216.2.m.a.911.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.33030 - 2.33030i) q^{3} +(1.33252 - 1.33252i) q^{5} -2.39899 q^{7} +7.86060i q^{9} +(2.97334 + 2.97334i) q^{11} +(2.73192 - 2.73192i) q^{13} -6.21034 q^{15} +2.34440 q^{17} +(3.47263 + 2.63455i) q^{19} +(5.59038 + 5.59038i) q^{21} +5.58224 q^{23} +1.44878i q^{25} +(11.3267 - 11.3267i) q^{27} +(-1.09806 + 1.09806i) q^{29} +5.96193 q^{31} -13.8576i q^{33} +(-3.19671 + 3.19671i) q^{35} +(3.00913 + 3.00913i) q^{37} -12.7324 q^{39} -11.6084 q^{41} +(-1.11788 - 1.11788i) q^{43} +(10.4744 + 10.4744i) q^{45} +0.270003i q^{47} -1.24483 q^{49} +(-5.46317 - 5.46317i) q^{51} +(-1.45983 - 1.45983i) q^{53} +7.92408 q^{55} +(-1.95299 - 14.2316i) q^{57} +(-0.797173 + 0.797173i) q^{59} +(9.29825 + 9.29825i) q^{61} -18.8575i q^{63} -7.28068i q^{65} +(0.276174 + 0.276174i) q^{67} +(-13.0083 - 13.0083i) q^{69} +0.225827i q^{71} -13.2848i q^{73} +(3.37610 - 3.37610i) q^{75} +(-7.13304 - 7.13304i) q^{77} -7.28534 q^{79} -29.2072 q^{81} +(3.66221 - 3.66221i) q^{83} +(3.12397 - 3.12397i) q^{85} +5.11762 q^{87} +11.2392 q^{89} +(-6.55386 + 6.55386i) q^{91} +(-13.8931 - 13.8931i) q^{93} +(8.13793 - 1.11677i) q^{95} +3.27963i q^{97} +(-23.3723 + 23.3723i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 4 q^{5} + 8 q^{7} + 4 q^{11} - 8 q^{17} - 6 q^{19} + 8 q^{23} + 8 q^{39} + 4 q^{43} + 4 q^{45} + 44 q^{49} + 8 q^{55} + 28 q^{61} - 32 q^{77} - 52 q^{81} - 36 q^{83} - 56 q^{85} + 120 q^{87} - 16 q^{93}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q - 4 * q^5 + 8 * q^7 + 4 * q^11 - 8 * q^17 - 6 * q^19 + 8 * q^23 + 8 * q^39 + 4 * q^43 + 4 * q^45 + 44 * q^49 + 8 * q^55 + 28 * q^61 - 32 * q^77 - 52 * q^81 - 36 * q^83 - 56 * q^85 + 120 * q^87 - 16 * q^93 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.33030	−	2.33030i	−1.34540	−	1.34540i	−0.890588	−	0.454812i	$-0.849706\pi$
$3$	−2.33030	−	2.33030i	−1.34540	−	1.34540i	−0.454812	−	0.890588i	$-0.650294\pi$
$4$		0			0
$5$	1.33252	−	1.33252i	0.595921	−	0.595921i	−0.343304	−	0.939224i	$-0.611546\pi$
$5$	1.33252	−	1.33252i	0.595921	−	0.595921i	0.939224	+	0.343304i	$0.111546\pi$
$6$		0			0
$7$	−2.39899			−0.906734			−0.453367	−	0.891324i	$-0.649777\pi$
$7$	−2.39899			−0.906734			−0.453367	+	0.891324i	$0.649777\pi$
$8$		0			0
$9$			7.86060i			2.62020i
$10$		0			0
$11$	2.97334	+	2.97334i	0.896497	+	0.896497i	0.995124	−	0.0986273i	$-0.0314452\pi$
$11$	2.97334	+	2.97334i	0.896497	+	0.896497i	−0.0986273	+	0.995124i	$0.531445\pi$
$12$		0			0
$13$	2.73192	−	2.73192i	0.757699	−	0.757699i	−0.218205	−	0.975903i	$-0.570020\pi$
$13$	2.73192	−	2.73192i	0.757699	−	0.757699i	0.975903	+	0.218205i	$0.0700200\pi$
$14$		0			0
$15$	−6.21034			−1.60350
$16$		0			0
$17$	2.34440			0.568602			0.284301	−	0.958735i	$-0.408239\pi$
$17$	2.34440			0.568602			0.284301	+	0.958735i	$0.408239\pi$
$18$		0			0
$19$	3.47263	+	2.63455i	0.796676	+	0.604406i
$19$	3.47263	+	2.63455i	0.796676	+	0.604406i
$20$		0			0
$21$	5.59038	+	5.59038i	1.21992	+	1.21992i
$22$		0			0
$23$	5.58224			1.16398			0.581989	−	0.813197i	$-0.302275\pi$
$23$	5.58224			1.16398			0.581989	+	0.813197i	$0.302275\pi$
$24$		0			0
$25$			1.44878i			0.289757i
$26$		0			0
$27$	11.3267	−	11.3267i	2.17982	−	2.17982i
$28$		0			0
$29$	−1.09806	+	1.09806i	−0.203905	+	0.203905i	−0.801671	−	0.597766i	$-0.796055\pi$
$29$	−1.09806	+	1.09806i	−0.203905	+	0.203905i	0.597766	+	0.801671i	$0.296055\pi$
$30$		0			0
$31$	5.96193			1.07079			0.535397	−	0.844601i	$-0.320162\pi$
$31$	5.96193			1.07079			0.535397	+	0.844601i	$0.320162\pi$
$32$		0			0
$33$		−	13.8576i		−	2.41229i
$34$		0			0
$35$	−3.19671	+	3.19671i	−0.540342	+	0.540342i
$36$		0			0
$37$	3.00913	+	3.00913i	0.494698	+	0.494698i	0.909783	−	0.415085i	$-0.136248\pi$
$37$	3.00913	+	3.00913i	0.494698	+	0.494698i	−0.415085	+	0.909783i	$0.636248\pi$
$38$		0			0
$39$	−12.7324			−2.03881
$40$		0			0
$41$	−11.6084			−1.81293			−0.906463	−	0.422286i	$-0.861228\pi$
$41$	−11.6084			−1.81293			−0.906463	+	0.422286i	$0.861228\pi$
$42$		0			0
$43$	−1.11788	−	1.11788i	−0.170475	−	0.170475i	0.616713	−	0.787188i	$-0.288464\pi$
$43$	−1.11788	−	1.11788i	−0.170475	−	0.170475i	−0.787188	+	0.616713i	$0.788464\pi$
$44$		0			0
$45$	10.4744	+	10.4744i	1.56143	+	1.56143i
$46$		0			0
$47$			0.270003i			0.0393840i	0.999806	+	0.0196920i	$0.00626856\pi$
$47$			0.270003i			0.0393840i	−0.999806	+	0.0196920i	$0.993731\pi$
$48$		0			0
$49$	−1.24483			−0.177833
$50$		0			0
$51$	−5.46317	−	5.46317i	−0.764996	−	0.764996i
$52$		0			0
$53$	−1.45983	−	1.45983i	−0.200523	−	0.200523i	0.599701	−	0.800224i	$-0.295286\pi$
$53$	−1.45983	−	1.45983i	−0.200523	−	0.200523i	−0.800224	+	0.599701i	$0.795286\pi$
$54$		0			0
$55$	7.92408			1.06848
$56$		0			0
$57$	−1.95299	−	14.2316i	−0.258680	−	1.88502i
$58$		0			0
$59$	−0.797173	+	0.797173i	−0.103783	+	0.103783i	−0.757092	−	0.653309i	$-0.773380\pi$
$59$	−0.797173	+	0.797173i	−0.103783	+	0.103783i	0.653309	+	0.757092i	$0.273380\pi$
$60$		0			0
$61$	9.29825	+	9.29825i	1.19052	+	1.19052i	0.976922	+	0.213597i	$0.0685178\pi$
$61$	9.29825	+	9.29825i	1.19052	+	1.19052i	0.213597	+	0.976922i	$0.431482\pi$
$62$		0			0
$63$		−	18.8575i		−	2.37582i
$64$		0			0
$65$		−	7.28068i		−	0.903057i
$66$		0			0
$67$	0.276174	+	0.276174i	0.0337400	+	0.0337400i	0.723776	−	0.690036i	$-0.242405\pi$
$67$	0.276174	+	0.276174i	0.0337400	+	0.0337400i	−0.690036	+	0.723776i	$0.742405\pi$
$68$		0			0
$69$	−13.0083	−	13.0083i	−1.56602	−	1.56602i
$70$		0			0
$71$			0.225827i			0.0268008i	0.999910	+	0.0134004i	$0.00426560\pi$
$71$			0.225827i			0.0268008i	−0.999910	+	0.0134004i	$0.995734\pi$
$72$		0			0
$73$		−	13.2848i		−	1.55487i	−0.628966	−	0.777433i	$-0.716522\pi$
$73$		−	13.2848i		−	1.55487i	0.628966	−	0.777433i	$-0.283478\pi$
$74$		0			0
$75$	3.37610	−	3.37610i	0.389838	−	0.389838i
$76$		0			0
$77$	−7.13304	−	7.13304i	−0.812885	−	0.812885i
$78$		0			0
$79$	−7.28534			−0.819665			−0.409832	−	0.912161i	$-0.634413\pi$
$79$	−7.28534			−0.819665			−0.409832	+	0.912161i	$0.634413\pi$
$80$		0			0
$81$	−29.2072			−3.24525
$82$		0			0
$83$	3.66221	−	3.66221i	0.401980	−	0.401980i	−0.476950	−	0.878930i	$-0.658258\pi$
$83$	3.66221	−	3.66221i	0.401980	−	0.401980i	0.878930	+	0.476950i	$0.158258\pi$
$84$		0			0
$85$	3.12397	−	3.12397i	0.338842	−	0.338842i
$86$		0			0
$87$	5.11762			0.548666
$88$		0			0
$89$	11.2392			1.19135			0.595677	−	0.803224i	$-0.296884\pi$
$89$	11.2392			1.19135			0.595677	+	0.803224i	$0.296884\pi$
$90$		0			0
$91$	−6.55386	+	6.55386i	−0.687031	+	0.687031i
$92$		0			0
$93$	−13.8931	−	13.8931i	−1.44064	−	1.44064i
$94$		0			0
$95$	8.13793	−	1.11677i	0.834934	−	0.114578i
$96$		0			0
$97$			3.27963i			0.332996i	0.986042	+	0.166498i	$0.0532459\pi$
$97$			3.27963i			0.332996i	−0.986042	+	0.166498i	$0.946754\pi$
$98$		0			0
$99$	−23.3723	+	23.3723i	−2.34900	+	2.34900i
$100$		0			0
$101$	7.70237	−	7.70237i	0.766414	−	0.766414i	−0.211059	−	0.977473i	$-0.567691\pi$
$101$	7.70237	−	7.70237i	0.766414	−	0.766414i	0.977473	+	0.211059i	$0.0676913\pi$
$102$		0			0
$103$			2.67310i			0.263388i	0.991290	+	0.131694i	$0.0420417\pi$
$103$			2.67310i			0.263388i	−0.991290	+	0.131694i	$0.957958\pi$
$104$		0			0
$105$	14.8986			1.45395
$106$		0			0
$107$	−2.80581	+	2.80581i	−0.271248	+	0.271248i	−0.829602	−	0.558355i	$-0.811433\pi$
$107$	−2.80581	+	2.80581i	−0.271248	+	0.271248i	0.558355	+	0.829602i	$0.311433\pi$
$108$		0			0
$109$	11.5264	−	11.5264i	1.10403	−	1.10403i	0.110110	−	0.993919i	$-0.464880\pi$
$109$	11.5264	−	11.5264i	1.10403	−	1.10403i	0.993919	−	0.110110i	$-0.0351203\pi$
$110$		0			0
$111$		−	14.0244i		−	1.33113i
$112$		0			0
$113$			4.74600i			0.446466i	0.974765	+	0.223233i	$0.0716611\pi$
$113$			4.74600i			0.446466i	−0.974765	+	0.223233i	$0.928339\pi$
$114$		0			0
$115$	7.43845	−	7.43845i	0.693639	−	0.693639i
$116$		0			0
$117$	21.4745	+	21.4745i	1.98532	+	1.98532i
$118$		0			0
$119$	−5.62421			−0.515571
$120$		0			0
$121$			6.68156i			0.607414i
$122$		0			0
$123$	27.0510	+	27.0510i	2.43911	+	2.43911i
$124$		0			0
$125$	8.59313	+	8.59313i	0.768593	+	0.768593i
$126$		0			0
$127$	0.202697			0.0179864			0.00899322	−	0.999960i	$-0.497137\pi$
$127$	0.202697			0.0179864			0.00899322	+	0.999960i	$0.497137\pi$
$128$		0			0
$129$			5.21000i			0.458715i
$130$		0			0
$131$	5.99216	−	5.99216i	0.523537	−	0.523537i	−0.395101	−	0.918638i	$-0.629290\pi$
$131$	5.99216	−	5.99216i	0.523537	−	0.523537i	0.918638	+	0.395101i	$0.129290\pi$
$132$		0			0
$133$	−8.33082	−	6.32026i	−0.722374	−	0.548036i
$134$		0			0
$135$		−	30.1860i		−	2.59800i
$136$		0			0
$137$			8.24092i			0.704069i	0.935987	+	0.352035i	$0.114510\pi$
$137$			8.24092i			0.704069i	−0.935987	+	0.352035i	$0.885490\pi$
$138$		0			0
$139$	−13.2949	−	13.2949i	−1.12766	−	1.12766i	−0.990556	−	0.137106i	$-0.956220\pi$
$139$	−13.2949	−	13.2949i	−1.12766	−	1.12766i	−0.137106	−	0.990556i	$-0.543780\pi$
$140$		0			0
$141$	0.629188	−	0.629188i	0.0529872	−	0.0529872i
$142$		0			0
$143$	16.2459			1.35855
$144$		0			0
$145$			2.92637i			0.243022i
$146$		0			0
$147$	2.90082	+	2.90082i	0.239256	+	0.239256i
$148$		0			0
$149$	8.75170	−	8.75170i	0.716967	−	0.716967i	−0.251016	−	0.967983i	$-0.580765\pi$
$149$	8.75170	−	8.75170i	0.716967	−	0.716967i	0.967983	+	0.251016i	$0.0807647\pi$
$150$		0			0
$151$			19.9711i			1.62523i	0.582803	+	0.812614i	$0.301956\pi$
$151$			19.9711i			1.62523i	−0.582803	+	0.812614i	$0.698044\pi$
$152$		0			0
$153$			18.4284i			1.48985i
$154$		0			0
$155$	7.94438	−	7.94438i	0.638108	−	0.638108i
$156$		0			0
$157$	−3.17405	−	3.17405i	−0.253317	−	0.253317i	0.569012	−	0.822329i	$-0.307326\pi$
$157$	−3.17405	−	3.17405i	−0.253317	−	0.253317i	−0.822329	+	0.569012i	$0.807326\pi$
$158$		0			0
$159$			6.80368i			0.539567i
$160$		0			0
$161$	−13.3918			−1.05542
$162$		0			0
$163$	6.37132	−	6.37132i	0.499040	−	0.499040i	−0.412099	−	0.911139i	$-0.635204\pi$
$163$	6.37132	−	6.37132i	0.499040	−	0.499040i	0.911139	+	0.412099i	$0.135204\pi$
$164$		0			0
$165$	−18.4655	−	18.4655i	−1.43754	−	1.43754i
$166$		0			0
$167$			9.04774i			0.700135i	0.936725	+	0.350067i	$0.113841\pi$
$167$			9.04774i			0.700135i	−0.936725	+	0.350067i	$0.886159\pi$
$168$		0			0
$169$		−	1.92678i		−	0.148214i
$170$		0			0
$171$	−20.7091	+	27.2970i	−1.58366	+	2.08745i
$172$		0			0
$173$	−0.0273170	+	0.0273170i	−0.00207688	+	0.00207688i	−0.708144	−	0.706068i	$-0.750467\pi$
$173$	−0.0273170	+	0.0273170i	−0.00207688	+	0.00207688i	0.706068	+	0.708144i	$0.250467\pi$
$174$		0			0
$175$		−	3.47562i		−	0.262732i
$176$		0			0
$177$	3.71531			0.279260
$178$		0			0
$179$	−2.17615	−	2.17615i	−0.162653	−	0.162653i	0.621088	−	0.783741i	$-0.286691\pi$
$179$	−2.17615	−	2.17615i	−0.162653	−	0.162653i	−0.783741	+	0.621088i	$0.786691\pi$
$180$		0			0
$181$	−4.89736	−	4.89736i	−0.364018	−	0.364018i	0.501272	−	0.865290i	$-0.332866\pi$
$181$	−4.89736	−	4.89736i	−0.364018	−	0.364018i	−0.865290	+	0.501272i	$0.832866\pi$
$182$		0			0
$183$		−	43.3354i		−	3.20345i
$184$		0			0
$185$	8.01945			0.589602
$186$		0			0
$187$	6.97072	+	6.97072i	0.509750	+	0.509750i
$188$		0			0
$189$	−27.1726	+	27.1726i	−1.97651	+	1.97651i
$190$		0			0
$191$		−	16.3442i		−	1.18262i	−0.806444	−	0.591311i	$-0.798611\pi$
$191$		−	16.3442i		−	1.18262i	0.806444	−	0.591311i	$-0.201389\pi$
$192$		0			0
$193$		−	2.52445i		−	0.181714i	−0.995864	−	0.0908568i	$-0.971039\pi$
$193$		−	2.52445i		−	0.181714i	0.995864	−	0.0908568i	$-0.0289606\pi$
$194$		0			0
$195$	−16.9662	+	16.9662i	−1.21497	+	1.21497i
$196$		0			0
$197$	10.2745	−	10.2745i	0.732029	−	0.732029i	−0.238993	−	0.971021i	$-0.576817\pi$
$197$	10.2745	−	10.2745i	0.732029	−	0.732029i	0.971021	+	0.238993i	$0.0768171\pi$
$198$		0			0
$199$	19.9560			1.41465			0.707323	−	0.706891i	$-0.249903\pi$
$199$	19.9560			1.41465			0.707323	+	0.706891i	$0.249903\pi$
$200$		0			0
$201$		−	1.28714i		−	0.0907876i
$202$		0			0
$203$	2.63424	−	2.63424i	0.184887	−	0.184887i
$204$		0			0
$205$	−15.4684	+	15.4684i	−1.08036	+	1.08036i
$206$		0			0
$207$			43.8798i			3.04985i
$208$		0			0
$209$	2.49192	+	18.1587i	0.172370	+	1.25607i
$210$		0			0
$211$	−11.7475	−	11.7475i	−0.808734	−	0.808734i	0.175708	−	0.984442i	$-0.443778\pi$
$211$	−11.7475	−	11.7475i	−0.808734	−	0.808734i	−0.984442	+	0.175708i	$0.943778\pi$
$212$		0			0
$213$	0.526245	−	0.526245i	0.0360577	−	0.0360577i
$214$		0			0
$215$	−2.97920			−0.203180
$216$		0			0
$217$	−14.3026			−0.970925
$218$		0			0
$219$	−30.9575	+	30.9575i	−2.09192	+	2.09192i
$220$		0			0
$221$	6.40473	−	6.40473i	0.430829	−	0.430829i
$222$		0			0
$223$	5.60143			0.375100			0.187550	−	0.982255i	$-0.439945\pi$
$223$	5.60143			0.375100			0.187550	+	0.982255i	$0.439945\pi$
$224$		0			0
$225$	−11.3883			−0.759220
$226$		0			0
$227$	−1.37469	−	1.37469i	−0.0912411	−	0.0912411i	0.660013	−	0.751254i	$-0.270551\pi$
$227$	−1.37469	−	1.37469i	−0.0912411	−	0.0912411i	−0.751254	+	0.660013i	$0.770551\pi$
$228$		0			0
$229$	−17.9610	+	17.9610i	−1.18690	+	1.18690i	−0.208979	+	0.977920i	$0.567014\pi$
$229$	−17.9610	+	17.9610i	−1.18690	+	1.18690i	−0.977920	+	0.208979i	$0.932986\pi$
$230$		0			0
$231$			33.2442i			2.18731i
$232$		0			0
$233$		−	1.79953i		−	0.117891i	−0.998261	−	0.0589456i	$-0.981226\pi$
$233$		−	1.79953i		−	0.117891i	0.998261	−	0.0589456i	$-0.0187739\pi$
$234$		0			0
$235$	0.359784	+	0.359784i	0.0234697	+	0.0234697i
$236$		0			0
$237$	16.9770	+	16.9770i	1.10278	+	1.10278i
$238$		0			0
$239$			15.5816i			1.00789i	0.863735	+	0.503947i	$0.168119\pi$
$239$			15.5816i			1.00789i	−0.863735	+	0.503947i	$0.831881\pi$
$240$		0			0
$241$			19.0529i			1.22730i	0.789577	+	0.613651i	$0.210300\pi$
$241$			19.0529i			1.22730i	−0.789577	+	0.613651i	$0.789700\pi$
$242$		0			0
$243$	34.0816	+	34.0816i	2.18634	+	2.18634i
$244$		0			0
$245$	−1.65876	+	1.65876i	−0.105974	+	0.105974i
$246$		0			0
$247$	16.6843	−	2.28958i	1.06160	−	0.145683i
$248$		0			0
$249$	−17.0681			−1.08165
$250$		0			0
$251$	12.1046	+	12.1046i	0.764036	+	0.764036i	0.977049	−	0.213013i	$-0.0683278\pi$
$251$	12.1046	+	12.1046i	0.764036	+	0.764036i	−0.213013	+	0.977049i	$0.568328\pi$
$252$		0			0
$253$	16.5979	+	16.5979i	1.04350	+	1.04350i
$254$		0			0
$255$	−14.5596			−0.911755
$256$		0			0
$257$			23.8066i			1.48502i	0.669838	+	0.742508i	$0.266364\pi$
$257$			23.8066i			1.48502i	−0.669838	+	0.742508i	$0.733636\pi$
$258$		0			0
$259$	−7.21889	−	7.21889i	−0.448560	−	0.448560i
$260$		0			0
$261$	−8.63140	−	8.63140i	−0.534271	−	0.534271i
$262$		0			0
$263$	−14.7026			−0.906602			−0.453301	−	0.891358i	$-0.649754\pi$
$263$	−14.7026			−0.906602			−0.453301	+	0.891358i	$0.649754\pi$
$264$		0			0
$265$	−3.89050			−0.238992
$266$		0			0
$267$	−26.1907	−	26.1907i	−1.60285	−	1.60285i
$268$		0			0
$269$	22.6486	−	22.6486i	1.38091	−	1.38091i	0.537903	−	0.843007i	$-0.319217\pi$
$269$	22.6486	−	22.6486i	1.38091	−	1.38091i	0.843007	−	0.537903i	$-0.180783\pi$
$270$		0			0
$271$		−	23.6407i		−	1.43607i	−0.696007	−	0.718035i	$-0.745042\pi$
$271$		−	23.6407i		−	1.43607i	0.696007	−	0.718035i	$-0.254958\pi$
$272$		0			0
$273$	30.5449			1.84866
$274$		0			0
$275$	−4.30773	+	4.30773i	−0.259766	+	0.259766i
$276$		0			0
$277$	−11.3244	+	11.3244i	−0.680416	+	0.680416i	−0.960094	−	0.279678i	$-0.909772\pi$
$277$	−11.3244	+	11.3244i	−0.680416	+	0.680416i	0.279678	+	0.960094i	$0.409772\pi$
$278$		0			0
$279$			46.8643i			2.80569i
$280$		0			0
$281$	−13.3448			−0.796083			−0.398042	−	0.917367i	$-0.630310\pi$
$281$	−13.3448			−0.796083			−0.398042	+	0.917367i	$0.630310\pi$
$282$		0			0
$283$	−6.55442	−	6.55442i	−0.389620	−	0.389620i	0.484932	−	0.874552i	$-0.338844\pi$
$283$	−6.55442	−	6.55442i	−0.389620	−	0.389620i	−0.874552	+	0.484932i	$0.838844\pi$
$284$		0			0
$285$	−21.5662	−	16.3614i	−1.27747	−	0.969167i
$286$		0			0
$287$	27.8484			1.64384
$288$		0			0
$289$	−11.5038			−0.676692
$290$		0			0
$291$	7.64252	−	7.64252i	0.448012	−	0.448012i
$292$		0			0
$293$	15.0537	+	15.0537i	0.879448	+	0.879448i	0.993477	−	0.114029i	$-0.0363757\pi$
$293$	15.0537	+	15.0537i	0.879448	+	0.879448i	−0.114029	+	0.993477i	$0.536376\pi$
$294$		0			0
$295$			2.12450i			0.123693i
$296$		0			0
$297$	67.3561			3.90840
$298$		0			0
$299$	15.2502	−	15.2502i	0.881944	−	0.881944i
$300$		0			0
$301$	2.68179	+	2.68179i	0.154576	+	0.154576i
$302$		0			0
$303$	−35.8977			−2.06227
$304$		0			0
$305$	24.7802			1.41891
$306$		0			0
$307$	−6.30108	−	6.30108i	−0.359621	−	0.359621i	0.504052	−	0.863673i	$-0.331842\pi$
$307$	−6.30108	−	6.30108i	−0.359621	−	0.359621i	−0.863673	+	0.504052i	$0.831842\pi$
$308$		0			0
$309$	6.22913	−	6.22913i	0.354363	−	0.354363i
$310$		0			0
$311$	−2.98954			−0.169521			−0.0847605	−	0.996401i	$-0.527013\pi$
$311$	−2.98954			−0.169521			−0.0847605	+	0.996401i	$0.527013\pi$
$312$		0			0
$313$		−	19.5677i		−	1.10603i	−0.833171	−	0.553015i	$-0.813477\pi$
$313$		−	19.5677i		−	1.10603i	0.833171	−	0.553015i	$-0.186523\pi$
$314$		0			0
$315$	−25.1280	−	25.1280i	−1.41580	−	1.41580i
$316$		0			0
$317$	4.52149	−	4.52149i	0.253952	−	0.253952i	−0.568637	−	0.822589i	$-0.692529\pi$
$317$	4.52149	−	4.52149i	0.253952	−	0.253952i	0.822589	+	0.568637i	$0.192529\pi$
$318$		0			0
$319$	−6.52982			−0.365600
$320$		0			0
$321$	13.0768			0.729873
$322$		0			0
$323$	8.14125	+	6.17644i	0.452991	+	0.343666i
$324$		0			0
$325$	3.95796	+	3.95796i	0.219548	+	0.219548i
$326$		0			0
$327$	−53.7200			−2.97072
$328$		0			0
$329$		−	0.647735i		−	0.0357108i
$330$		0			0
$331$	2.04624	−	2.04624i	0.112472	−	0.112472i	−0.648631	−	0.761103i	$-0.724658\pi$
$331$	2.04624	−	2.04624i	0.112472	−	0.112472i	0.761103	+	0.648631i	$0.224658\pi$
$332$		0			0
$333$	−23.6536	+	23.6536i	−1.29621	+	1.29621i
$334$		0			0
$335$	0.736014			0.0402128
$336$		0			0
$337$		−	18.1089i		−	0.986454i	−0.869901	−	0.493227i	$-0.835817\pi$
$337$		−	18.1089i		−	0.986454i	0.869901	−	0.493227i	$-0.164183\pi$
$338$		0			0
$339$	11.0596	−	11.0596i	0.600676	−	0.600676i
$340$		0			0
$341$	17.7269	+	17.7269i	0.959963	+	0.959963i
$342$		0			0
$343$	19.7793			1.06798
$344$		0			0
$345$	−34.6676			−1.86644
$346$		0			0
$347$	13.2006	+	13.2006i	0.708646	+	0.708646i	0.966250	−	0.257605i	$-0.0829332\pi$
$347$	13.2006	+	13.2006i	0.708646	+	0.708646i	−0.257605	+	0.966250i	$0.582933\pi$
$348$		0			0
$349$	−1.46513	−	1.46513i	−0.0784265	−	0.0784265i	0.666805	−	0.745232i	$-0.267661\pi$
$349$	−1.46513	−	1.46513i	−0.0784265	−	0.0784265i	−0.745232	+	0.666805i	$0.767661\pi$
$350$		0			0
$351$		−	61.8870i		−	3.30329i
$352$		0			0
$353$	12.5708			0.669077			0.334538	−	0.942382i	$-0.391420\pi$
$353$	12.5708			0.669077			0.334538	+	0.942382i	$0.391420\pi$
$354$		0			0
$355$	0.300919	+	0.300919i	0.0159711	+	0.0159711i
$356$		0			0
$357$	13.1061	+	13.1061i	0.693648	+	0.693648i
$358$		0			0
$359$	−28.1715			−1.48684			−0.743418	−	0.668827i	$-0.766797\pi$
$359$	−28.1715			−1.48684			−0.743418	+	0.668827i	$0.766797\pi$
$360$		0			0
$361$	5.11834	+	18.2976i	0.269386	+	0.963032i
$362$		0			0
$363$	15.5700	−	15.5700i	0.817215	−	0.817215i
$364$		0			0
$365$	−17.7022	−	17.7022i	−0.926577	−	0.926577i
$366$		0			0
$367$			31.5789i			1.64840i	0.566297	+	0.824201i	$0.308376\pi$
$367$			31.5789i			1.64840i	−0.566297	+	0.824201i	$0.691624\pi$
$368$		0			0
$369$		−	91.2488i		−	4.75023i
$370$		0			0
$371$	3.50212	+	3.50212i	0.181821	+	0.181821i
$372$		0			0
$373$	−9.32220	−	9.32220i	−0.482685	−	0.482685i	0.423303	−	0.905988i	$-0.360871\pi$
$373$	−9.32220	−	9.32220i	−0.482685	−	0.482685i	−0.905988	+	0.423303i	$0.860871\pi$
$374$		0			0
$375$		−	40.0491i		−	2.06813i
$376$		0			0
$377$			5.99962i			0.308996i
$378$		0			0
$379$	6.70381	−	6.70381i	0.344352	−	0.344352i	−0.513649	−	0.858001i	$-0.671707\pi$
$379$	6.70381	−	6.70381i	0.344352	−	0.344352i	0.858001	+	0.513649i	$0.171707\pi$
$380$		0			0
$381$	−0.472345	−	0.472345i	−0.0241989	−	0.0241989i
$382$		0			0
$383$	−23.6297			−1.20742			−0.603712	−	0.797203i	$-0.706312\pi$
$383$	−23.6297			−1.20742			−0.603712	+	0.797203i	$0.706312\pi$
$384$		0			0
$385$	−19.0098			−0.968830
$386$		0			0
$387$	8.78722	−	8.78722i	0.446680	−	0.446680i
$388$		0			0
$389$	4.44506	−	4.44506i	0.225374	−	0.225374i	−0.585383	−	0.810757i	$-0.699056\pi$
$389$	4.44506	−	4.44506i	0.225374	−	0.225374i	0.810757	+	0.585383i	$0.199056\pi$
$390$		0			0
$391$	13.0870			0.661840
$392$		0			0
$393$	−27.9271			−1.40873
$394$		0			0
$395$	−9.70786	+	9.70786i	−0.488456	+	0.488456i
$396$		0			0
$397$	−9.43095	−	9.43095i	−0.473326	−	0.473326i	0.429664	−	0.902989i	$-0.358632\pi$
$397$	−9.43095	−	9.43095i	−0.473326	−	0.473326i	−0.902989	+	0.429664i	$0.858632\pi$
$398$		0			0
$399$	4.68522	+	34.1414i	0.234554	+	1.70921i
$400$		0			0
$401$		−	1.35978i		−	0.0679041i	−0.999423	−	0.0339521i	$-0.989191\pi$
$401$		−	1.35978i		−	0.0679041i	0.999423	−	0.0339521i	$-0.0108094\pi$
$402$		0			0
$403$	16.2875	−	16.2875i	0.811339	−	0.811339i
$404$		0			0
$405$	−38.9192	+	38.9192i	−1.93391	+	1.93391i
$406$		0			0
$407$			17.8944i			0.886991i
$408$		0			0
$409$	−29.3461			−1.45107			−0.725535	−	0.688185i	$-0.758408\pi$
$409$	−29.3461			−1.45107			−0.725535	+	0.688185i	$0.758408\pi$
$410$		0			0
$411$	19.2038	−	19.2038i	0.947254	−	0.947254i
$412$		0			0
$413$	1.91241	−	1.91241i	0.0941037	−	0.0941037i
$414$		0			0
$415$		−	9.75995i		−	0.479097i
$416$		0			0
$417$			61.9624i			3.03431i
$418$		0			0
$419$	−9.29373	+	9.29373i	−0.454028	+	0.454028i	−0.896689	−	0.442661i	$-0.854035\pi$
$419$	−9.29373	+	9.29373i	−0.454028	+	0.454028i	0.442661	+	0.896689i	$0.354035\pi$
$420$		0			0
$421$	2.81150	+	2.81150i	0.137024	+	0.137024i	0.772292	−	0.635268i	$-0.219110\pi$
$421$	2.81150	+	2.81150i	0.137024	+	0.137024i	−0.635268	+	0.772292i	$0.719110\pi$
$422$		0			0
$423$	−2.12238			−0.103194
$424$		0			0
$425$			3.39653i			0.164756i
$426$		0			0
$427$	−22.3064	−	22.3064i	−1.07948	−	1.07948i
$428$		0			0
$429$	−37.8578	−	37.8578i	−1.82779	−	1.82779i
$430$		0			0
$431$	36.4166			1.75413			0.877063	−	0.480376i	$-0.159500\pi$
$431$	36.4166			1.75413			0.877063	+	0.480376i	$0.159500\pi$
$432$		0			0
$433$		−	4.74856i		−	0.228201i	−0.993469	−	0.114101i	$-0.963601\pi$
$433$		−	4.74856i		−	0.228201i	0.993469	−	0.114101i	$-0.0363986\pi$
$434$		0			0
$435$	6.81933	−	6.81933i	0.326962	−	0.326962i
$436$		0			0
$437$	19.3851	+	14.7067i	0.927314	+	0.703515i
$438$		0			0
$439$			6.45592i			0.308124i	0.988061	+	0.154062i	$0.0492356\pi$
$439$			6.45592i			0.308124i	−0.988061	+	0.154062i	$0.950764\pi$
$440$		0			0
$441$		−	9.78510i		−	0.465957i
$442$		0			0
$443$	1.87841	+	1.87841i	0.0892461	+	0.0892461i	0.750320	−	0.661074i	$-0.229899\pi$
$443$	1.87841	+	1.87841i	0.0892461	+	0.0892461i	−0.661074	+	0.750320i	$0.729899\pi$
$444$		0			0
$445$	14.9765	−	14.9765i	0.709952	−	0.709952i
$446$		0			0
$447$	−40.7882			−1.92921
$448$		0			0
$449$			25.3294i			1.19537i	0.801732	+	0.597683i	$0.203912\pi$
$449$			25.3294i			1.19537i	−0.801732	+	0.597683i	$0.796088\pi$
$450$		0			0
$451$	−34.5157	−	34.5157i	−1.62528	−	1.62528i
$452$		0			0
$453$	46.5387	−	46.5387i	2.18658	−	2.18658i
$454$		0			0
$455$			17.4663i			0.818833i
$456$		0			0
$457$		−	23.2446i		−	1.08734i	−0.839300	−	0.543668i	$-0.817035\pi$
$457$		−	23.2446i		−	1.08734i	0.839300	−	0.543668i	$-0.182965\pi$
$458$		0			0
$459$	26.5543	−	26.5543i	1.23945	−	1.23945i
$460$		0			0
$461$	24.3080	+	24.3080i	1.13213	+	1.13213i	0.989822	+	0.142313i	$0.0454539\pi$
$461$	24.3080	+	24.3080i	1.13213	+	1.13213i	0.142313	+	0.989822i	$0.454546\pi$
$462$		0			0
$463$		−	31.0847i		−	1.44463i	−0.691564	−	0.722315i	$-0.743078\pi$
$463$		−	31.0847i		−	1.44463i	0.691564	−	0.722315i	$-0.256922\pi$
$464$		0			0
$465$	−37.0256			−1.71702
$466$		0			0
$467$	15.3866	−	15.3866i	0.712005	−	0.712005i	−0.254949	−	0.966954i	$-0.582059\pi$
$467$	15.3866	−	15.3866i	0.712005	−	0.712005i	0.966954	+	0.254949i	$0.0820588\pi$
$468$		0			0
$469$	−0.662539	−	0.662539i	−0.0305932	−	0.0305932i
$470$		0			0
$471$			14.7930i			0.681624i
$472$		0			0
$473$		−	6.64770i		−	0.305662i
$474$		0			0
$475$	−3.81688	+	5.03109i	−0.175131	+	0.230842i
$476$		0			0
$477$	11.4751	−	11.4751i	0.525410	−	0.525410i
$478$		0			0
$479$		−	3.19320i		−	0.145901i	−0.997336	−	0.0729505i	$-0.976758\pi$
$479$		−	3.19320i		−	0.145901i	0.997336	−	0.0729505i	$-0.0232415\pi$
$480$		0			0
$481$	16.4414			0.749664
$482$		0			0
$483$	31.2068	+	31.2068i	1.41996	+	1.41996i
$484$		0			0
$485$	4.37017	+	4.37017i	0.198439	+	0.198439i
$486$		0			0
$487$		−	22.1580i		−	1.00407i	−0.864846	−	0.502037i	$-0.832584\pi$
$487$		−	22.1580i		−	1.00407i	0.864846	−	0.502037i	$-0.167416\pi$
$488$		0			0
$489$	−29.6942			−1.34282
$490$		0			0
$491$	20.0830	+	20.0830i	0.906333	+	0.906333i	0.995974	−	0.0896416i	$-0.0285722\pi$
$491$	20.0830	+	20.0830i	0.906333	+	0.906333i	−0.0896416	+	0.995974i	$0.528572\pi$
$492$		0			0
$493$	−2.57430	+	2.57430i	−0.115940	+	0.115940i
$494$		0			0
$495$			62.2880i			2.79964i
$496$		0			0
$497$		−	0.541758i		−	0.0243012i
$498$		0			0
$499$	−21.2194	+	21.2194i	−0.949912	+	0.949912i	−0.998804	−	0.0488919i	$-0.984431\pi$
$499$	−21.2194	+	21.2194i	−0.949912	+	0.949912i	0.0488919	+	0.998804i	$0.484431\pi$
$500$		0			0
$501$	21.0839	−	21.0839i	0.941961	−	0.941961i
$502$		0			0
$503$	15.4238			0.687714			0.343857	−	0.939022i	$-0.388266\pi$
$503$	15.4238			0.687714			0.343857	+	0.939022i	$0.388266\pi$
$504$		0			0
$505$		−	20.5271i		−	0.913444i
$506$		0			0
$507$	−4.48998	+	4.48998i	−0.199407	+	0.199407i
$508$		0			0
$509$	9.94323	−	9.94323i	0.440726	−	0.440726i	−0.451530	−	0.892256i	$-0.649122\pi$
$509$	9.94323	−	9.94323i	0.440726	−	0.440726i	0.892256	+	0.451530i	$0.149122\pi$
$510$		0			0
$511$			31.8701i			1.40985i
$512$		0			0
$513$	69.1739	−	9.49271i	3.05410	−	0.419113i
$514$		0			0
$515$	3.56196	+	3.56196i	0.156959	+	0.156959i
$516$		0			0
$517$	−0.802812	+	0.802812i	−0.0353076	+	0.0353076i
$518$		0			0
$519$	0.127314			0.00558846
$520$		0			0
$521$	29.1422			1.27674			0.638371	−	0.769729i	$-0.279609\pi$
$521$	29.1422			1.27674			0.638371	+	0.769729i	$0.279609\pi$
$522$		0			0
$523$	13.4425	−	13.4425i	0.587801	−	0.587801i	−0.349235	−	0.937035i	$-0.613558\pi$
$523$	13.4425	−	13.4425i	0.587801	−	0.587801i	0.937035	+	0.349235i	$0.113558\pi$
$524$		0			0
$525$	−8.09924	+	8.09924i	−0.353480	+	0.353480i
$526$		0			0
$527$	13.9772			0.608855
$528$		0			0
$529$	8.16142			0.354844
$530$		0			0
$531$	−6.26626	−	6.26626i	−0.271933	−	0.271933i
$532$		0			0
$533$	−31.7132	+	31.7132i	−1.37365	+	1.37365i
$534$		0			0
$535$			7.47759i			0.323284i
$536$		0			0
$537$			10.1422i			0.437667i
$538$		0			0
$539$	−3.70131	−	3.70131i	−0.159426	−	0.159426i
$540$		0			0
$541$	9.25234	+	9.25234i	0.397789	+	0.397789i	0.877453	−	0.479663i	$-0.159241\pi$
$541$	9.25234	+	9.25234i	0.397789	+	0.397789i	−0.479663	+	0.877453i	$0.659241\pi$
$542$		0			0
$543$			22.8246i			0.979499i
$544$		0			0
$545$		−	30.7183i		−	1.31583i
$546$		0			0
$547$	−15.1431	−	15.1431i	−0.647473	−	0.647473i	0.304909	−	0.952381i	$-0.401374\pi$
$547$	−15.1431	−	15.1431i	−0.647473	−	0.647473i	−0.952381	+	0.304909i	$0.901374\pi$
$548$		0			0
$549$	−73.0898	+	73.0898i	−3.11940	+	3.11940i
$550$		0			0
$551$	−6.70604	+	0.920268i	−0.285687	+	0.0392047i
$552$		0			0
$553$	17.4775			0.743218
$554$		0			0
$555$	−18.6877	−	18.6877i	−0.793250	−	0.793250i
$556$		0			0
$557$	−13.4125	−	13.4125i	−0.568307	−	0.568307i	0.363347	−	0.931654i	$-0.381634\pi$
$557$	−13.4125	−	13.4125i	−0.568307	−	0.568307i	−0.931654	+	0.363347i	$0.881634\pi$
$558$		0			0
$559$	−6.10793			−0.258338
$560$		0			0
$561$		−	32.4878i		−	1.37163i
$562$		0			0
$563$	−2.35825	−	2.35825i	−0.0993885	−	0.0993885i	0.655664	−	0.755053i	$-0.272389\pi$
$563$	−2.35825	−	2.35825i	−0.0993885	−	0.0993885i	−0.755053	+	0.655664i	$0.772389\pi$
$564$		0			0
$565$	6.32414	+	6.32414i	0.266059	+	0.266059i
$566$		0			0
$567$	70.0679			2.94258
$568$		0			0
$569$	24.1782			1.01360			0.506802	−	0.862062i	$-0.330828\pi$
$569$	24.1782			1.01360			0.506802	+	0.862062i	$0.330828\pi$
$570$		0			0
$571$	15.9271	+	15.9271i	0.666528	+	0.666528i	0.956911	−	0.290383i	$-0.0937827\pi$
$571$	15.9271	+	15.9271i	0.666528	+	0.666528i	−0.290383	+	0.956911i	$0.593783\pi$
$572$		0			0
$573$	−38.0868	+	38.0868i	−1.59110	+	1.59110i
$574$		0			0
$575$			8.08745i			0.337270i
$576$		0			0
$577$	−9.78296			−0.407270			−0.203635	−	0.979047i	$-0.565276\pi$
$577$	−9.78296			−0.407270			−0.203635	+	0.979047i	$0.565276\pi$
$578$		0			0
$579$	−5.88272	+	5.88272i	−0.244478	+	0.244478i
$580$		0			0
$581$	−8.78563	+	8.78563i	−0.364489	+	0.364489i
$582$		0			0
$583$		−	8.68115i		−	0.359536i
$584$		0			0
$585$	57.2305			2.36619
$586$		0			0
$587$	−12.6453	−	12.6453i	−0.521928	−	0.521928i	0.396225	−	0.918153i	$-0.370320\pi$
$587$	−12.6453	−	12.6453i	−0.521928	−	0.521928i	−0.918153	+	0.396225i	$0.870320\pi$
$588$		0			0
$589$	20.7036	+	15.7070i	0.853076	+	0.647194i
$590$		0			0
$591$	−47.8854			−1.96974
$592$		0			0
$593$	−41.0325			−1.68500			−0.842502	−	0.538693i	$-0.818918\pi$
$593$	−41.0325			−1.68500			−0.842502	+	0.538693i	$0.818918\pi$
$594$		0			0
$595$	−7.49437	+	7.49437i	−0.307239	+	0.307239i
$596$		0			0
$597$	−46.5036	−	46.5036i	−1.90326	−	1.90326i
$598$		0			0
$599$		−	14.8233i		−	0.605664i	−0.953044	−	0.302832i	$-0.902068\pi$
$599$		−	14.8233i		−	0.605664i	0.953044	−	0.302832i	$-0.0979320\pi$
$600$		0			0
$601$	−28.0014			−1.14220			−0.571099	−	0.820881i	$-0.693483\pi$
$601$	−28.0014			−1.14220			−0.571099	+	0.820881i	$0.693483\pi$
$602$		0			0
$603$	−2.17089	+	2.17089i	−0.0884055	+	0.0884055i
$604$		0			0
$605$	8.90331	+	8.90331i	0.361971	+	0.361971i
$606$		0			0
$607$	21.8986			0.888837			0.444418	−	0.895819i	$-0.353410\pi$
$607$	21.8986			0.888837			0.444418	+	0.895819i	$0.353410\pi$
$608$		0			0
$609$	−12.2771			−0.497494
$610$		0			0
$611$	0.737627	+	0.737627i	0.0298412	+	0.0298412i
$612$		0			0
$613$	2.68844	−	2.68844i	0.108585	−	0.108585i	−0.650727	−	0.759312i	$-0.725536\pi$
$613$	2.68844	−	2.68844i	0.108585	−	0.108585i	0.759312	+	0.650727i	$0.225536\pi$
$614$		0			0
$615$	72.0920			2.90703
$616$		0			0
$617$			11.0704i			0.445676i	0.974856	+	0.222838i	$0.0715320\pi$
$617$			11.0704i			0.445676i	−0.974856	+	0.222838i	$0.928468\pi$
$618$		0			0
$619$	−19.2885	−	19.2885i	−0.775270	−	0.775270i	0.203752	−	0.979022i	$-0.434686\pi$
$619$	−19.2885	−	19.2885i	−0.775270	−	0.775270i	−0.979022	+	0.203752i	$0.934686\pi$
$620$		0			0
$621$	63.2281	−	63.2281i	2.53726	−	2.53726i
$622$		0			0
$623$	−26.9628			−1.08024
$624$		0			0
$625$	15.6571			0.626285
$626$		0			0
$627$	36.5084	−	48.1222i	1.45801	−	1.92182i
$628$		0			0
$629$	7.05462	+	7.05462i	0.281286	+	0.281286i
$630$		0			0
$631$	9.40185			0.374282			0.187141	−	0.982333i	$-0.440078\pi$
$631$	9.40185			0.374282			0.187141	+	0.982333i	$0.440078\pi$
$632$		0			0
$633$			54.7506i			2.17614i
$634$		0			0
$635$	0.270098	−	0.270098i	0.0107185	−	0.0107185i
$636$		0			0
$637$	−3.40077	+	3.40077i	−0.134744	+	0.134744i
$638$		0			0
$639$	−1.77514			−0.0702233
$640$		0			0
$641$			2.24937i			0.0888449i	0.999013	+	0.0444224i	$0.0141448\pi$
$641$			2.24937i			0.0888449i	−0.999013	+	0.0444224i	$0.985855\pi$
$642$		0			0
$643$	−29.5495	+	29.5495i	−1.16532	+	1.16532i	−0.182025	+	0.983294i	$0.558265\pi$
$643$	−29.5495	+	29.5495i	−1.16532	+	1.16532i	−0.983294	+	0.182025i	$0.941735\pi$
$644$		0			0
$645$	6.94243	+	6.94243i	0.273358	+	0.273358i
$646$		0			0
$647$	8.30973			0.326689			0.163345	−	0.986569i	$-0.447772\pi$
$647$	8.30973			0.326689			0.163345	+	0.986569i	$0.447772\pi$
$648$		0			0
$649$	−4.74054			−0.186083
$650$		0			0
$651$	33.3294	+	33.3294i	1.30628	+	1.30628i
$652$		0			0
$653$	−21.7566	−	21.7566i	−0.851401	−	0.851401i	0.138905	−	0.990306i	$-0.455642\pi$
$653$	−21.7566	−	21.7566i	−0.851401	−	0.851401i	−0.990306	+	0.138905i	$0.955642\pi$
$654$		0			0
$655$		−	15.9693i		−	0.623974i
$656$		0			0
$657$	104.426			4.07406
$658$		0			0
$659$	−16.8631	−	16.8631i	−0.656892	−	0.656892i	0.297751	−	0.954643i	$-0.403763\pi$
$659$	−16.8631	−	16.8631i	−0.656892	−	0.656892i	−0.954643	+	0.297751i	$0.903763\pi$
$660$		0			0
$661$	−30.4953	−	30.4953i	−1.18613	−	1.18613i	−0.978129	−	0.208001i	$-0.933304\pi$
$661$	−30.4953	−	30.4953i	−1.18613	−	1.18613i	−0.208001	−	0.978129i	$-0.566696\pi$
$662$		0			0
$663$	−29.8499			−1.15927
$664$		0			0
$665$	−19.5229	+	2.67911i	−0.757064	+	0.103892i
$666$		0			0
$667$	−6.12963	+	6.12963i	−0.237340	+	0.237340i
$668$		0			0
$669$	−13.0530	−	13.0530i	−0.504659	−	0.504659i
$670$		0			0
$671$			55.2938i			2.13459i
$672$		0			0
$673$			30.5918i			1.17923i	0.807685	+	0.589614i	$0.200720\pi$
$673$			30.5918i			1.17923i	−0.807685	+	0.589614i	$0.799280\pi$
$674$		0			0
$675$	16.4099	+	16.4099i	0.631616	+	0.631616i
$676$		0			0
$677$	−21.7266	−	21.7266i	−0.835021	−	0.835021i	0.153178	−	0.988199i	$-0.451049\pi$
$677$	−21.7266	−	21.7266i	−0.835021	−	0.835021i	−0.988199	+	0.153178i	$0.951049\pi$
$678$		0			0
$679$		−	7.86781i		−	0.301939i
$680$		0			0
$681$			6.40686i			0.245512i
$682$		0			0
$683$	−33.2404	+	33.2404i	−1.27191	+	1.27191i	−0.326824	+	0.945085i	$0.605979\pi$
$683$	−33.2404	+	33.2404i	−1.27191	+	1.27191i	−0.945085	+	0.326824i	$0.894021\pi$
$684$		0			0
$685$	10.9812	+	10.9812i	0.419570	+	0.419570i
$686$		0			0
$687$	83.7092			3.19371
$688$		0			0
$689$	−7.97627			−0.303872
$690$		0			0
$691$	−6.33177	+	6.33177i	−0.240872	+	0.240872i	−0.817211	−	0.576339i	$-0.804481\pi$
$691$	−6.33177	+	6.33177i	−0.240872	+	0.240872i	0.576339	+	0.817211i	$0.304481\pi$
$692$		0			0
$693$	56.0699	−	56.0699i	2.12992	−	2.12992i
$694$		0			0
$695$	−35.4316			−1.34400
$696$		0			0
$697$	−27.2147			−1.03083
$698$		0			0
$699$	−4.19345	+	4.19345i	−0.158611	+	0.158611i
$700$		0			0
$701$	−8.55890	−	8.55890i	−0.323265	−	0.323265i	0.526753	−	0.850018i	$-0.323409\pi$
$701$	−8.55890	−	8.55890i	−0.323265	−	0.323265i	−0.850018	+	0.526753i	$0.823409\pi$
$702$		0			0
$703$	2.52191	+	18.3773i	0.0951156	+	0.693113i
$704$		0			0
$705$		−	1.67681i		−	0.0631523i
$706$		0			0
$707$	−18.4779	+	18.4779i	−0.694934	+	0.694934i
$708$		0			0
$709$	−11.8005	+	11.8005i	−0.443178	+	0.443178i	−0.893079	−	0.449901i	$-0.851459\pi$
$709$	−11.8005	+	11.8005i	−0.443178	+	0.443178i	0.449901	+	0.893079i	$0.351459\pi$
$710$		0			0
$711$		−	57.2671i		−	2.14769i
$712$		0			0
$713$	33.2809			1.24638
$714$		0			0
$715$	21.6480	−	21.6480i	0.809588	−	0.809588i
$716$		0			0
$717$	36.3099	−	36.3099i	1.35602	−	1.35602i
$718$		0			0
$719$		−	16.7274i		−	0.623826i	−0.950111	−	0.311913i	$-0.899030\pi$
$719$		−	16.7274i		−	0.623826i	0.950111	−	0.311913i	$-0.100970\pi$
$720$		0			0
$721$		−	6.41275i		−	0.238823i
$722$		0			0
$723$	44.3989	−	44.3989i	1.65121	−	1.65121i
$724$		0			0
$725$	−1.59085	−	1.59085i	−0.0590827	−	0.0590827i
$726$		0			0
$727$	−34.2209			−1.26918			−0.634592	−	0.772848i	$-0.718832\pi$
$727$	−34.2209			−1.26918			−0.634592	+	0.772848i	$0.718832\pi$
$728$		0			0
$729$		−	71.2191i		−	2.63774i
$730$		0			0
$731$	−2.62077	−	2.62077i	−0.0969326	−	0.0969326i
$732$		0			0
$733$	−29.4292	−	29.4292i	−1.08699	−	1.08699i	−0.995837	−	0.0911546i	$-0.970944\pi$
$733$	−29.4292	−	29.4292i	−1.08699	−	1.08699i	−0.0911546	−	0.995837i	$-0.529056\pi$
$734$		0			0
$735$	7.73081			0.285155
$736$		0			0
$737$			1.64232i			0.0604956i
$738$		0			0
$739$	−28.5250	+	28.5250i	−1.04931	+	1.04931i	−0.0505889	+	0.998720i	$0.516110\pi$
$739$	−28.5250	+	28.5250i	−1.04931	+	1.04931i	−0.998720	+	0.0505889i	$0.983890\pi$
$740$		0			0
$741$	−44.2149	−	33.5441i	−1.62428	−	1.23227i
$742$		0			0
$743$			2.63098i			0.0965214i	0.998835	+	0.0482607i	$0.0153678\pi$
$743$			2.63098i			0.0965214i	−0.998835	+	0.0482607i	$0.984632\pi$
$744$		0			0
$745$		−	23.3236i		−	0.854511i
$746$		0			0
$747$	28.7872	+	28.7872i	1.05327	+	1.05327i
$748$		0			0
$749$	6.73112	−	6.73112i	0.245950	−	0.245950i
$750$		0			0
$751$	36.9118			1.34693			0.673466	−	0.739218i	$-0.264805\pi$
$751$	36.9118			1.34693			0.673466	+	0.739218i	$0.264805\pi$
$752$		0			0
$753$		−	56.4147i		−	2.05587i
$754$		0			0
$755$	26.6119	+	26.6119i	0.968507	+	0.968507i
$756$		0			0
$757$	−10.6159	+	10.6159i	−0.385843	+	0.385843i	−0.873202	−	0.487359i	$-0.837960\pi$
$757$	−10.6159	+	10.6159i	−0.385843	+	0.385843i	0.487359	+	0.873202i	$0.337960\pi$
$758$		0			0
$759$		−	77.3563i		−	2.80786i
$760$		0			0
$761$			1.24281i			0.0450517i	0.999746	+	0.0225259i	$0.00717081\pi$
$761$			1.24281i			0.0450517i	−0.999746	+	0.0225259i	$0.992829\pi$
$762$		0			0
$763$	−27.6518	+	27.6518i	−1.00106	+	1.00106i
$764$		0			0
$765$	24.5562	+	24.5562i	0.887832	+	0.887832i
$766$		0			0
$767$			4.35563i			0.157273i
$768$		0			0
$769$	−8.10047			−0.292110			−0.146055	−	0.989276i	$-0.546658\pi$
$769$	−8.10047			−0.292110			−0.146055	+	0.989276i	$0.546658\pi$
$770$		0			0
$771$	55.4765	−	55.4765i	1.99794	−	1.99794i
$772$		0			0
$773$	−1.50351	−	1.50351i	−0.0540776	−	0.0540776i	0.679551	−	0.733628i	$-0.262175\pi$
$773$	−1.50351	−	1.50351i	−0.0540776	−	0.0540776i	−0.733628	+	0.679551i	$0.762175\pi$
$774$		0			0
$775$			8.63753i			0.310269i
$776$		0			0
$777$			33.6443i			1.20698i
$778$		0			0
$779$	−40.3116	−	30.5828i	−1.44431	−	1.09574i
$780$		0			0
$781$	−0.671462	+	0.671462i	−0.0240268	+	0.0240268i
$782$		0			0
$783$			24.8747i			0.888948i
$784$		0			0
$785$	−8.45896			−0.301913
$786$		0			0
$787$	20.6706	+	20.6706i	0.736828	+	0.736828i	0.971963	−	0.235135i	$-0.0755531\pi$
$787$	20.6706	+	20.6706i	0.736828	+	0.736828i	−0.235135	+	0.971963i	$0.575553\pi$
$788$		0			0
$789$	34.2615	+	34.2615i	1.21974	+	1.21974i
$790$		0			0
$791$		−	11.3856i		−	0.404826i
$792$		0			0
$793$	50.8042			1.80411
$794$		0			0
$795$	9.06604	+	9.06604i	0.321539	+	0.321539i
$796$		0			0
$797$	−4.73425	+	4.73425i	−0.167696	+	0.167696i	−0.785966	−	0.618270i	$-0.787834\pi$
$797$	−4.73425	+	4.73425i	−0.167696	+	0.167696i	0.618270	+	0.785966i	$0.287834\pi$
$798$		0			0
$799$			0.632996i			0.0223938i
$800$		0			0
$801$			88.3469i			3.12158i
$802$		0			0
$803$	39.5002	−	39.5002i	1.39393	−	1.39393i
$804$		0			0
$805$	−17.8448	+	17.8448i	−0.628946	+	0.628946i
$806$		0			0
$807$	−105.556			−3.71575
$808$		0			0
$809$			34.1881i			1.20199i	0.799253	+	0.600995i	$0.205229\pi$
$809$			34.1881i			1.20199i	−0.799253	+	0.600995i	$0.794771\pi$
$810$		0			0
$811$	4.94468	−	4.94468i	0.173631	−	0.173631i	−0.614942	−	0.788573i	$-0.710820\pi$
$811$	4.94468	−	4.94468i	0.173631	−	0.173631i	0.788573	+	0.614942i	$0.210820\pi$
$812$		0			0
$813$	−55.0899	+	55.0899i	−1.93209	+	1.93209i
$814$		0			0
$815$		−	16.9798i		−	0.594777i
$816$		0			0
$817$	−0.936882	−	6.82711i	−0.0327773	−	0.238850i
$818$		0			0
$819$	−51.5173	−	51.5173i	−1.80016	−	1.80016i
$820$		0			0
$821$	1.33689	−	1.33689i	0.0466578	−	0.0466578i	−0.683393	−	0.730051i	$-0.739496\pi$
$821$	1.33689	−	1.33689i	0.0466578	−	0.0466578i	0.730051	+	0.683393i	$0.239496\pi$
$822$		0			0
$823$	−16.6744			−0.581233			−0.290616	−	0.956840i	$-0.593860\pi$
$823$	−16.6744			−0.581233			−0.290616	+	0.956840i	$0.593860\pi$
$824$		0			0
$825$	20.0766			0.698978
$826$		0			0
$827$	24.6269	−	24.6269i	0.856362	−	0.856362i	−0.134546	−	0.990907i	$-0.542957\pi$
$827$	24.6269	−	24.6269i	0.856362	−	0.856362i	0.990907	+	0.134546i	$0.0429575\pi$
$828$		0			0
$829$	−24.5347	+	24.5347i	−0.852125	+	0.852125i	−0.990395	−	0.138270i	$-0.955846\pi$
$829$	−24.5347	+	24.5347i	−0.852125	+	0.852125i	0.138270	+	0.990395i	$0.455846\pi$
$830$		0			0
$831$	52.7784			1.83086
$832$		0			0
$833$	−2.91838			−0.101116
$834$		0			0
$835$	12.0563	+	12.0563i	0.417225	+	0.417225i
$836$		0			0
$837$	67.5287	−	67.5287i	2.33413	−	2.33413i
$838$		0			0
$839$		−	43.1844i		−	1.49089i	−0.666566	−	0.745446i	$-0.732237\pi$
$839$		−	43.1844i		−	1.49089i	0.666566	−	0.745446i	$-0.267763\pi$
$840$		0			0
$841$			26.5885i			0.916846i
$842$		0			0
$843$	31.0974	+	31.0974i	1.07105	+	1.07105i
$844$		0			0
$845$	−2.56748	−	2.56748i	−0.0883239	−	0.0883239i
$846$		0			0
$847$		−	16.0290i		−	0.550763i
$848$		0			0
$849$			30.5476i			1.04839i
$850$		0			0
$851$	16.7977	+	16.7977i	0.575818	+	0.575818i
$852$		0			0
$853$	−14.1512	+	14.1512i	−0.484529	+	0.484529i	−0.906575	−	0.422046i	$-0.861312\pi$
$853$	−14.1512	+	14.1512i	−0.484529	+	0.484529i	0.422046	+	0.906575i	$0.361312\pi$
$854$		0			0
$855$	8.77845	+	63.9690i	0.300217	+	2.18769i
$856$		0			0
$857$	12.0528			0.411716			0.205858	−	0.978582i	$-0.434001\pi$
$857$	12.0528			0.411716			0.205858	+	0.978582i	$0.434001\pi$
$858$		0			0
$859$	9.28621	+	9.28621i	0.316841	+	0.316841i	0.847553	−	0.530711i	$-0.178075\pi$
$859$	9.28621	+	9.28621i	0.316841	+	0.316841i	−0.530711	+	0.847553i	$0.678075\pi$
$860$		0			0
$861$	−64.8952	−	64.8952i	−2.21162	−	2.21162i
$862$		0			0
$863$	1.23001			0.0418700			0.0209350	−	0.999781i	$-0.493336\pi$
$863$	1.23001			0.0418700			0.0209350	+	0.999781i	$0.493336\pi$
$864$		0			0
$865$			0.0728010i			0.00247531i
$866$		0			0
$867$	26.8072	+	26.8072i	0.910421	+	0.910421i
$868$		0			0
$869$	−21.6618	−	21.6618i	−0.734827	−	0.734827i
$870$		0			0
$871$	1.50897			0.0511295
$872$		0			0
$873$	−25.7798			−0.872515
$874$		0			0
$875$	−20.6149	−	20.6149i	−0.696910	−	0.696910i
$876$		0			0
$877$	28.8338	−	28.8338i	0.973649	−	0.973649i	−0.0260127	−	0.999662i	$-0.508281\pi$
$877$	28.8338	−	28.8338i	0.973649	−	0.973649i	0.999662	+	0.0260127i	$0.00828103\pi$
$878$		0			0
$879$		−	70.1594i		−	2.36642i
$880$		0			0
$881$	−39.7413			−1.33892			−0.669460	−	0.742848i	$-0.733474\pi$
$881$	−39.7413			−1.33892			−0.669460	+	0.742848i	$0.733474\pi$
$882$		0			0
$883$	−27.2693	+	27.2693i	−0.917684	+	0.917684i	−0.996861	−	0.0791763i	$-0.974771\pi$
$883$	−27.2693	+	27.2693i	−0.917684	+	0.917684i	0.0791763	+	0.996861i	$0.474771\pi$
$884$		0			0
$885$	4.95072	−	4.95072i	0.166417	−	0.166417i
$886$		0			0
$887$			40.9715i			1.37569i	0.725858	+	0.687844i	$0.241443\pi$
$887$			40.9715i			1.37569i	−0.725858	+	0.687844i	$0.758557\pi$
$888$		0			0
$889$	−0.486269			−0.0163089
$890$		0			0
$891$	−86.8431	−	86.8431i	−2.90935	−	2.90935i
$892$		0			0
$893$	−0.711335	+	0.937621i	−0.0238039	+	0.0313763i
$894$		0			0
$895$	−5.79953			−0.193857
$896$		0			0
$897$	−71.0753			−2.37313
$898$		0			0
$899$	−6.54655	+	6.54655i	−0.218340	+	0.218340i
$900$		0			0
$901$	−3.42243	−	3.42243i	−0.114018	−	0.114018i
$902$		0			0
$903$		−	12.4988i		−	0.415933i
$904$		0			0
$905$	−13.0517			−0.433852
$906$		0			0
$907$	−23.3335	+	23.3335i	−0.774775	+	0.774775i	−0.978937	−	0.204162i	$-0.934553\pi$
$907$	−23.3335	+	23.3335i	−0.774775	+	0.774775i	0.204162	+	0.978937i	$0.434553\pi$
$908$		0			0
$909$	60.5452	+	60.5452i	2.00816	+	2.00816i
$910$		0			0
$911$	10.3255			0.342100			0.171050	−	0.985262i	$-0.445284\pi$
$911$	10.3255			0.342100			0.171050	+	0.985262i	$0.445284\pi$
$912$		0			0
$913$	21.7781			0.720748
$914$		0			0
$915$	−57.7453	−	57.7453i	−1.90900	−	1.90900i
$916$		0			0
$917$	−14.3751	+	14.3751i	−0.474709	+	0.474709i
$918$		0			0
$919$	−18.4954			−0.610108			−0.305054	−	0.952335i	$-0.598675\pi$
$919$	−18.4954			−0.610108			−0.305054	+	0.952335i	$0.598675\pi$
$920$		0			0
$921$			29.3668i			0.967669i
$922$		0			0
$923$	0.616942	+	0.616942i	0.0203069	+	0.0203069i
$924$		0			0
$925$	−4.35958	+	4.35958i	−0.143342	+	0.143342i
$926$		0			0
$927$	−21.0122			−0.690130
$928$		0			0
$929$	41.8953			1.37454			0.687270	−	0.726402i	$-0.258809\pi$
$929$	41.8953			1.37454			0.687270	+	0.726402i	$0.258809\pi$
$930$		0			0
$931$	−4.32283	−	3.27956i	−0.141675	−	0.107483i
$932$		0			0
$933$	6.96652	+	6.96652i	0.228074	+	0.228074i
$934$		0			0
$935$	18.5773			0.607541
$936$		0			0
$937$		−	51.1111i		−	1.66973i	−0.550458	−	0.834863i	$-0.685547\pi$
$937$		−	51.1111i		−	1.66973i	0.550458	−	0.834863i	$-0.314453\pi$
$938$		0			0
$939$	−45.5985	+	45.5985i	−1.48805	+	1.48805i
$940$		0			0
$941$	19.1950	−	19.1950i	0.625738	−	0.625738i	−0.321255	−	0.946993i	$-0.604105\pi$
$941$	19.1950	−	19.1950i	0.625738	−	0.625738i	0.946993	+	0.321255i	$0.104105\pi$
$942$		0			0
$943$	−64.8008			−2.11020
$944$		0			0
$945$			72.4160i			2.35569i
$946$		0			0
$947$	−7.49703	+	7.49703i	−0.243621	+	0.243621i	−0.818346	−	0.574726i	$-0.805109\pi$
$947$	−7.49703	+	7.49703i	−0.243621	+	0.243621i	0.574726	+	0.818346i	$0.305109\pi$
$948$		0			0
$949$	−36.2930	−	36.2930i	−1.17812	−	1.17812i
$950$		0			0
$951$	−21.0729			−0.683335
$952$		0			0
$953$	57.0862			1.84920			0.924602	−	0.380935i	$-0.124398\pi$
$953$	57.0862			1.84920			0.924602	+	0.380935i	$0.124398\pi$
$954$		0			0
$955$	−21.7789	−	21.7789i	−0.704749	−	0.704749i
$956$		0			0
$957$	15.2164	+	15.2164i	0.491878	+	0.491878i
$958$		0			0
$959$		−	19.7699i		−	0.638404i
$960$		0			0
$961$	4.54455			0.146598
$962$		0			0
$963$	−22.0553	−	22.0553i	−0.710723	−	0.710723i
$964$		0			0
$965$	−3.36388	−	3.36388i	−0.108287	−	0.108287i
$966$		0			0
$967$	35.4312			1.13939			0.569695	−	0.821856i	$-0.307061\pi$
$967$	35.4312			1.13939			0.569695	+	0.821856i	$0.307061\pi$
$968$		0			0
$969$	−4.57860	−	33.3645i	−0.147086	−	1.07182i
$970$		0			0
$971$	21.0434	−	21.0434i	0.675316	−	0.675316i	−0.283621	−	0.958937i	$-0.591536\pi$
$971$	21.0434	−	21.0434i	0.675316	−	0.675316i	0.958937	+	0.283621i	$0.0915356\pi$
$972$		0			0
$973$	31.8945	+	31.8945i	1.02249	+	1.02249i
$974$		0			0
$975$		−	18.4465i		−	0.590760i
$976$		0			0
$977$		−	28.4135i		−	0.909027i	−0.890740	−	0.454514i	$-0.849813\pi$
$977$		−	28.4135i		−	0.909027i	0.890740	−	0.454514i	$-0.150187\pi$
$978$		0			0
$979$	33.4180	+	33.4180i	1.06805	+	1.06805i
$980$		0			0
$981$	90.6044	+	90.6044i	2.89278	+	2.89278i
$982$		0			0
$983$			45.7243i			1.45838i	0.684312	+	0.729190i	$0.260103\pi$
$983$			45.7243i			1.45838i	−0.684312	+	0.729190i	$0.739897\pi$
$984$		0			0
$985$		−	27.3820i		−	0.872463i
$986$		0			0
$987$	−1.50942	+	1.50942i	−0.0480453	+	0.0480453i
$988$		0			0
$989$	−6.24029	−	6.24029i	−0.198430	−	0.198430i
$990$		0			0
$991$	−26.3265			−0.836289			−0.418145	−	0.908380i	$-0.637319\pi$
$991$	−26.3265			−0.836289			−0.418145	+	0.908380i	$0.637319\pi$
$992$		0			0
$993$	−9.53672			−0.302639
$994$		0			0
$995$	26.5918	−	26.5918i	0.843017	−	0.843017i
$996$		0			0
$997$	12.8909	−	12.8909i	0.408258	−	0.408258i	−0.472873	−	0.881131i	$-0.656783\pi$
$997$	12.8909	−	12.8909i	0.408258	−	0.408258i	0.881131	+	0.472873i	$0.156783\pi$
$998$		0			0
$999$	68.1668			2.15670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.m.a.303.1		76
4.3	odd	2		304.2.m.a.227.3	yes	76
16.5	even	4		304.2.m.a.75.36	yes	76
16.11	odd	4	inner	1216.2.m.a.911.38		76
19.18	odd	2	inner	1216.2.m.a.303.38		76
76.75	even	2		304.2.m.a.227.36	yes	76
304.37	odd	4		304.2.m.a.75.3	✓	76
304.75	even	4	inner	1216.2.m.a.911.1		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
304.2.m.a.75.3	✓	76	304.37	odd	4
304.2.m.a.75.36	yes	76	16.5	even	4
304.2.m.a.227.3	yes	76	4.3	odd	2
304.2.m.a.227.36	yes	76	76.75	even	2
1216.2.m.a.303.1		76	1.1	even	1	trivial
1216.2.m.a.303.38		76	19.18	odd	2	inner
1216.2.m.a.911.1		76	304.75	even	4	inner
1216.2.m.a.911.38		76	16.11	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.m (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.33030 - 2.33030i) q^{3} +(1.33252 - 1.33252i) q^{5} -2.39899 q^{7} +7.86060i q^{9} +(2.97334 + 2.97334i) q^{11} +(2.73192 - 2.73192i) q^{13} -6.21034 q^{15} +2.34440 q^{17} +(3.47263 + 2.63455i) q^{19} +(5.59038 + 5.59038i) q^{21} +5.58224 q^{23} +1.44878i q^{25} +(11.3267 - 11.3267i) q^{27} +(-1.09806 + 1.09806i) q^{29} +5.96193 q^{31} -13.8576i q^{33} +(-3.19671 + 3.19671i) q^{35} +(3.00913 + 3.00913i) q^{37} -12.7324 q^{39} -11.6084 q^{41} +(-1.11788 - 1.11788i) q^{43} +(10.4744 + 10.4744i) q^{45} +0.270003i q^{47} -1.24483 q^{49} +(-5.46317 - 5.46317i) q^{51} +(-1.45983 - 1.45983i) q^{53} +7.92408 q^{55} +(-1.95299 - 14.2316i) q^{57} +(-0.797173 + 0.797173i) q^{59} +(9.29825 + 9.29825i) q^{61} -18.8575i q^{63} -7.28068i q^{65} +(0.276174 + 0.276174i) q^{67} +(-13.0083 - 13.0083i) q^{69} +0.225827i q^{71} -13.2848i q^{73} +(3.37610 - 3.37610i) q^{75} +(-7.13304 - 7.13304i) q^{77} -7.28534 q^{79} -29.2072 q^{81} +(3.66221 - 3.66221i) q^{83} +(3.12397 - 3.12397i) q^{85} +5.11762 q^{87} +11.2392 q^{89} +(-6.55386 + 6.55386i) q^{91} +(-13.8931 - 13.8931i) q^{93} +(8.13793 - 1.11677i) q^{95} +3.27963i q^{97} +(-23.3723 + 23.3723i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 4 q^{5} + 8 q^{7} + 4 q^{11} - 8 q^{17} - 6 q^{19} + 8 q^{23} + 8 q^{39} + 4 q^{43} + 4 q^{45} + 44 q^{49} + 8 q^{55} + 28 q^{61} - 32 q^{77} - 52 q^{81} - 36 q^{83} - 56 q^{85} + 120 q^{87} - 16 q^{93}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q - 4 * q^5 + 8 * q^7 + 4 * q^11 - 8 * q^17 - 6 * q^19 + 8 * q^23 + 8 * q^39 + 4 * q^43 + 4 * q^45 + 44 * q^49 + 8 * q^55 + 28 * q^61 - 32 * q^77 - 52 * q^81 - 36 * q^83 - 56 * q^85 + 120 * q^87 - 16 * q^93 - 76 * q^99

Introduction

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