LMFDB - Embedded newform 320.3.r.a.111.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(111,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("320.111");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.r (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:	$8.71936845953$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			111.11
Character	$\chi$	$=$	320.111
Dual form			320.3.r.a.271.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40411 - 1.40411i) q^{3} +(-1.58114 + 1.58114i) q^{5} -0.552025 q^{7} +5.05693i q^{9} +O(q^{10})$	\(q+(1.40411 - 1.40411i) q^{3} +(-1.58114 + 1.58114i) q^{5} -0.552025 q^{7} +5.05693i q^{9} +(3.85004 + 3.85004i) q^{11} +(11.5784 + 11.5784i) q^{13} +4.44020i q^{15} +26.8154 q^{17} +(15.9405 - 15.9405i) q^{19} +(-0.775106 + 0.775106i) q^{21} -26.3746 q^{23} -5.00000i q^{25} +(19.7375 + 19.7375i) q^{27} +(12.3220 + 12.3220i) q^{29} -0.502877i q^{31} +10.8118 q^{33} +(0.872828 - 0.872828i) q^{35} +(4.19627 - 4.19627i) q^{37} +32.5147 q^{39} -47.8505i q^{41} +(3.50360 + 3.50360i) q^{43} +(-7.99571 - 7.99571i) q^{45} +32.9404i q^{47} -48.6953 q^{49} +(37.6519 - 37.6519i) q^{51} +(-25.8335 + 25.8335i) q^{53} -12.1749 q^{55} -44.7647i q^{57} +(62.5409 + 62.5409i) q^{59} +(60.5240 + 60.5240i) q^{61} -2.79155i q^{63} -36.6140 q^{65} +(31.3820 - 31.3820i) q^{67} +(-37.0329 + 37.0329i) q^{69} -93.4260 q^{71} -16.2092i q^{73} +(-7.02057 - 7.02057i) q^{75} +(-2.12532 - 2.12532i) q^{77} -94.3792i q^{79} +9.91509 q^{81} +(-100.652 + 100.652i) q^{83} +(-42.3989 + 42.3989i) q^{85} +34.6031 q^{87} -48.1573i q^{89} +(-6.39155 - 6.39155i) q^{91} +(-0.706097 - 0.706097i) q^{93} +50.4084i q^{95} +99.3742 q^{97} +(-19.4694 + 19.4694i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) $ 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/320\mathbb{Z}\right)^\times$.

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.40411	−	1.40411i	0.468038	−	0.468038i	−0.433240	−	0.901278i	$-0.642630\pi$
$3$	1.40411	−	1.40411i	0.468038	−	0.468038i	0.901278	+	0.433240i	$0.142630\pi$
$4$		0			0
$5$	−1.58114	+	1.58114i	−0.316228	+	0.316228i
$5$	−1.58114	+	1.58114i	−0.316228	+	0.316228i
$6$		0			0
$7$	−0.552025			−0.0788607			−0.0394304	−	0.999222i	$-0.512554\pi$
$7$	−0.552025			−0.0788607			−0.0394304	+	0.999222i	$0.512554\pi$
$8$		0			0
$9$			5.05693i			0.561881i
$10$		0			0
$11$	3.85004	+	3.85004i	0.350004	+	0.350004i	0.860111	−	0.510107i	$-0.170394\pi$
$11$	3.85004	+	3.85004i	0.350004	+	0.350004i	−0.510107	+	0.860111i	$0.670394\pi$
$12$		0			0
$13$	11.5784	+	11.5784i	0.890644	+	0.890644i	0.994584	−	0.103940i	$-0.0331449\pi$
$13$	11.5784	+	11.5784i	0.890644	+	0.890644i	−0.103940	+	0.994584i	$0.533145\pi$
$14$		0			0
$15$			4.44020i			0.296013i
$16$		0			0
$17$	26.8154			1.57738			0.788690	−	0.614792i	$-0.210760\pi$
$17$	26.8154			1.57738			0.788690	+	0.614792i	$0.210760\pi$
$18$		0			0
$19$	15.9405	−	15.9405i	0.838976	−	0.838976i	−0.149748	−	0.988724i	$-0.547846\pi$
$19$	15.9405	−	15.9405i	0.838976	−	0.838976i	0.988724	+	0.149748i	$0.0478463\pi$
$20$		0			0
$21$	−0.775106	+	0.775106i	−0.0369098	+	0.0369098i
$22$		0			0
$23$	−26.3746			−1.14672			−0.573360	−	0.819303i	$-0.694360\pi$
$23$	−26.3746			−1.14672			−0.573360	+	0.819303i	$0.694360\pi$
$24$		0			0
$25$		−	5.00000i		−	0.200000i
$26$		0			0
$27$	19.7375	+	19.7375i	0.731019	+	0.731019i
$28$		0			0
$29$	12.3220	+	12.3220i	0.424898	+	0.424898i	0.886886	−	0.461988i	$-0.152864\pi$
$29$	12.3220	+	12.3220i	0.424898	+	0.424898i	−0.461988	+	0.886886i	$0.652864\pi$
$30$		0			0
$31$		−	0.502877i		−	0.0162219i	−0.999967	−	0.00811093i	$-0.997418\pi$
$31$		−	0.502877i		−	0.0162219i	0.999967	−	0.00811093i	$-0.00258182\pi$
$32$		0			0
$33$	10.8118			0.327630
$34$		0			0
$35$	0.872828	−	0.872828i	0.0249380	−	0.0249380i
$36$		0			0
$37$	4.19627	−	4.19627i	0.113413	−	0.113413i	−0.648123	−	0.761536i	$-0.724446\pi$
$37$	4.19627	−	4.19627i	0.113413	−	0.113413i	0.761536	+	0.648123i	$0.224446\pi$
$38$		0			0
$39$	32.5147			0.833710
$40$		0			0
$41$		−	47.8505i		−	1.16709i	−0.812083	−	0.583543i	$-0.801666\pi$
$41$		−	47.8505i		−	1.16709i	0.812083	−	0.583543i	$-0.198334\pi$
$42$		0			0
$43$	3.50360	+	3.50360i	0.0814791	+	0.0814791i	0.746672	−	0.665193i	$-0.231651\pi$
$43$	3.50360	+	3.50360i	0.0814791	+	0.0814791i	−0.665193	+	0.746672i	$0.731651\pi$
$44$		0			0
$45$	−7.99571	−	7.99571i	−0.177682	−	0.177682i
$46$		0			0
$47$			32.9404i			0.700860i	0.936589	+	0.350430i	$0.113964\pi$
$47$			32.9404i			0.700860i	−0.936589	+	0.350430i	$0.886036\pi$
$48$		0			0
$49$	−48.6953			−0.993781
$50$		0			0
$51$	37.6519	−	37.6519i	0.738273	−	0.738273i
$52$		0			0
$53$	−25.8335	+	25.8335i	−0.487424	+	0.487424i	−0.907492	−	0.420069i	$-0.862006\pi$
$53$	−25.8335	+	25.8335i	−0.487424	+	0.487424i	0.420069	+	0.907492i	$0.362006\pi$
$54$		0			0
$55$	−12.1749			−0.221362
$56$		0			0
$57$		−	44.7647i		−	0.785345i
$58$		0			0
$59$	62.5409	+	62.5409i	1.06002	+	1.06002i	0.998080	+	0.0619352i	$0.0197272\pi$
$59$	62.5409	+	62.5409i	1.06002	+	1.06002i	0.0619352	+	0.998080i	$0.480273\pi$
$60$		0			0
$61$	60.5240	+	60.5240i	0.992197	+	0.992197i	0.999970	−	0.00777276i	$-0.00247417\pi$
$61$	60.5240	+	60.5240i	0.992197	+	0.992197i	−0.00777276	+	0.999970i	$0.502474\pi$
$62$		0			0
$63$		−	2.79155i		−	0.0443104i
$64$		0			0
$65$	−36.6140			−0.563293
$66$		0			0
$67$	31.3820	−	31.3820i	0.468388	−	0.468388i	−0.433004	−	0.901392i	$-0.642546\pi$
$67$	31.3820	−	31.3820i	0.468388	−	0.468388i	0.901392	+	0.433004i	$0.142546\pi$
$68$		0			0
$69$	−37.0329	+	37.0329i	−0.536709	+	0.536709i
$70$		0			0
$71$	−93.4260			−1.31586			−0.657930	−	0.753079i	$-0.728568\pi$
$71$	−93.4260			−1.31586			−0.657930	+	0.753079i	$0.728568\pi$
$72$		0			0
$73$		−	16.2092i		−	0.222044i	−0.993818	−	0.111022i	$-0.964588\pi$
$73$		−	16.2092i		−	0.222044i	0.993818	−	0.111022i	$-0.0354124\pi$
$74$		0			0
$75$	−7.02057	−	7.02057i	−0.0936076	−	0.0936076i
$76$		0			0
$77$	−2.12532	−	2.12532i	−0.0276016	−	0.0276016i
$78$		0			0
$79$		−	94.3792i		−	1.19467i	−0.801991	−	0.597337i	$-0.796226\pi$
$79$		−	94.3792i		−	1.19467i	0.801991	−	0.597337i	$-0.203774\pi$
$80$		0			0
$81$	9.91509			0.122408
$82$		0			0
$83$	−100.652	+	100.652i	−1.21267	+	1.21267i	−0.242529	+	0.970144i	$0.577977\pi$
$83$	−100.652	+	100.652i	−1.21267	+	1.21267i	−0.970144	+	0.242529i	$0.922023\pi$
$84$		0			0
$85$	−42.3989	+	42.3989i	−0.498811	+	0.498811i
$86$		0			0
$87$	34.6031			0.397737
$88$		0			0
$89$		−	48.1573i		−	0.541094i	−0.962707	−	0.270547i	$-0.912795\pi$
$89$		−	48.1573i		−	0.541094i	0.962707	−	0.270547i	$-0.0872045\pi$
$90$		0			0
$91$	−6.39155	−	6.39155i	−0.0702368	−	0.0702368i
$92$		0			0
$93$	−0.706097	−	0.706097i	−0.00759244	−	0.00759244i
$94$		0			0
$95$			50.4084i			0.530615i
$96$		0			0
$97$	99.3742			1.02448			0.512238	−	0.858843i	$-0.328817\pi$
$97$	99.3742			1.02448			0.512238	+	0.858843i	$0.328817\pi$
$98$		0			0
$99$	−19.4694	+	19.4694i	−0.196661	+	0.196661i
$100$		0			0
$101$	68.8291	−	68.8291i	0.681476	−	0.681476i	−0.278857	−	0.960333i	$-0.589955\pi$
$101$	68.8291	−	68.8291i	0.681476	−	0.681476i	0.960333	+	0.278857i	$0.0899555\pi$
$102$		0			0
$103$	−195.821			−1.90117			−0.950587	−	0.310459i	$-0.899517\pi$
$103$	−195.821			−1.90117			−0.950587	+	0.310459i	$0.899517\pi$
$104$		0			0
$105$		−	2.45110i		−	0.0233438i
$106$		0			0
$107$	−95.7648	−	95.7648i	−0.894998	−	0.894998i	0.0999902	−	0.994988i	$-0.468119\pi$
$107$	−95.7648	−	95.7648i	−0.894998	−	0.894998i	−0.994988	+	0.0999902i	$0.968119\pi$
$108$		0			0
$109$	−62.9871	−	62.9871i	−0.577863	−	0.577863i	0.356451	−	0.934314i	$-0.383987\pi$
$109$	−62.9871	−	62.9871i	−0.577863	−	0.577863i	−0.934314	+	0.356451i	$0.883987\pi$
$110$		0			0
$111$		−	11.7841i		−	0.106163i
$112$		0			0
$113$	−161.090			−1.42557			−0.712787	−	0.701381i	$-0.752567\pi$
$113$	−161.090			−1.42557			−0.712787	+	0.701381i	$0.752567\pi$
$114$		0			0
$115$	41.7019	−	41.7019i	0.362625	−	0.362625i
$116$		0			0
$117$	−58.5510	+	58.5510i	−0.500436	+	0.500436i
$118$		0			0
$119$	−14.8028			−0.124393
$120$		0			0
$121$		−	91.3543i		−	0.754994i
$122$		0			0
$123$	−67.1875	−	67.1875i	−0.546240	−	0.546240i
$124$		0			0
$125$	7.90569	+	7.90569i	0.0632456	+	0.0632456i
$126$		0			0
$127$		−	138.158i		−	1.08785i	−0.839132	−	0.543927i	$-0.816937\pi$
$127$		−	138.158i		−	1.08785i	0.839132	−	0.543927i	$-0.183063\pi$
$128$		0			0
$129$	9.83891			0.0762706
$130$		0			0
$131$	130.721	−	130.721i	0.997867	−	0.997867i	−0.00213065	−	0.999998i	$-0.500678\pi$
$131$	130.721	−	130.721i	0.997867	−	0.997867i	0.999998	+	0.00213065i	$0.000678207\pi$
$132$		0			0
$133$	−8.79958	+	8.79958i	−0.0661622	+	0.0661622i
$134$		0			0
$135$	−62.4155			−0.462337
$136$		0			0
$137$			208.693i			1.52331i	0.647984	+	0.761654i	$0.275612\pi$
$137$			208.693i			1.52331i	−0.647984	+	0.761654i	$0.724388\pi$
$138$		0			0
$139$	−38.5481	−	38.5481i	−0.277324	−	0.277324i	0.554716	−	0.832040i	$-0.312827\pi$
$139$	−38.5481	−	38.5481i	−0.277324	−	0.277324i	−0.832040	+	0.554716i	$0.812827\pi$
$140$		0			0
$141$	46.2521	+	46.2521i	0.328029	+	0.328029i
$142$		0			0
$143$			89.1545i			0.623458i
$144$		0			0
$145$	−38.9657			−0.268729
$146$		0			0
$147$	−68.3737	+	68.3737i	−0.465127	+	0.465127i
$148$		0			0
$149$	86.7897	−	86.7897i	0.582481	−	0.582481i	−0.353103	−	0.935584i	$-0.614874\pi$
$149$	86.7897	−	86.7897i	0.582481	−	0.582481i	0.935584	+	0.353103i	$0.114874\pi$
$150$		0			0
$151$	210.500			1.39404			0.697021	−	0.717051i	$-0.254509\pi$
$151$	210.500			1.39404			0.697021	+	0.717051i	$0.254509\pi$
$152$		0			0
$153$			135.604i			0.886300i
$154$		0			0
$155$	0.795119	+	0.795119i	0.00512980	+	0.00512980i
$156$		0			0
$157$	−198.050	−	198.050i	−1.26147	−	1.26147i	−0.950383	−	0.311082i	$-0.899309\pi$
$157$	−198.050	−	198.050i	−1.26147	−	1.26147i	−0.311082	−	0.950383i	$-0.600691\pi$
$158$		0			0
$159$			72.5462i			0.456266i
$160$		0			0
$161$	14.5594			0.0904312
$162$		0			0
$163$	−46.1173	+	46.1173i	−0.282928	+	0.282928i	−0.834276	−	0.551348i	$-0.814114\pi$
$163$	−46.1173	+	46.1173i	−0.282928	+	0.282928i	0.551348	+	0.834276i	$0.314114\pi$
$164$		0			0
$165$	−17.0950	+	17.0950i	−0.103606	+	0.103606i
$166$		0			0
$167$	157.682			0.944204			0.472102	−	0.881544i	$-0.343495\pi$
$167$	157.682			0.944204			0.472102	+	0.881544i	$0.343495\pi$
$168$		0			0
$169$			99.1173i			0.586493i
$170$		0			0
$171$	80.6102	+	80.6102i	0.471405	+	0.471405i
$172$		0			0
$173$	−102.122	−	102.122i	−0.590299	−	0.590299i	0.347413	−	0.937712i	$-0.387060\pi$
$173$	−102.122	−	102.122i	−0.590299	−	0.590299i	−0.937712	+	0.347413i	$0.887060\pi$
$174$		0			0
$175$			2.76013i			0.0157721i
$176$		0			0
$177$	175.629			0.992255
$178$		0			0
$179$	−142.850	+	142.850i	−0.798042	+	0.798042i	−0.982787	−	0.184744i	$-0.940854\pi$
$179$	−142.850	+	142.850i	−0.798042	+	0.798042i	0.184744	+	0.982787i	$0.440854\pi$
$180$		0			0
$181$	110.754	−	110.754i	0.611901	−	0.611901i	−0.331540	−	0.943441i	$-0.607568\pi$
$181$	110.754	−	110.754i	0.611901	−	0.611901i	0.943441	+	0.331540i	$0.107568\pi$
$182$		0			0
$183$	169.965			0.928772
$184$		0			0
$185$			13.2698i			0.0717285i
$186$		0			0
$187$	103.241	+	103.241i	0.552089	+	0.552089i
$188$		0			0
$189$	−10.8956	−	10.8956i	−0.0576487	−	0.0576487i
$190$		0			0
$191$			322.825i			1.69018i	0.534623	+	0.845091i	$0.320454\pi$
$191$			322.825i			1.69018i	−0.534623	+	0.845091i	$0.679546\pi$
$192$		0			0
$193$	−8.09410			−0.0419383			−0.0209692	−	0.999780i	$-0.506675\pi$
$193$	−8.09410			−0.0419383			−0.0209692	+	0.999780i	$0.506675\pi$
$194$		0			0
$195$	−51.4102	+	51.4102i	−0.263642	+	0.263642i
$196$		0			0
$197$	108.681	−	108.681i	0.551679	−	0.551679i	−0.375246	−	0.926925i	$-0.622442\pi$
$197$	108.681	−	108.681i	0.551679	−	0.551679i	0.926925	+	0.375246i	$0.122442\pi$
$198$		0			0
$199$	177.790			0.893418			0.446709	−	0.894679i	$-0.352596\pi$
$199$	177.790			0.893418			0.446709	+	0.894679i	$0.352596\pi$
$200$		0			0
$201$		−	88.1277i		−	0.438446i
$202$		0			0
$203$	−6.80208	−	6.80208i	−0.0335078	−	0.0335078i
$204$		0			0
$205$	75.6583	+	75.6583i	0.369065	+	0.369065i
$206$		0			0
$207$		−	133.374i		−	0.644321i
$208$		0			0
$209$	122.744			0.587290
$210$		0			0
$211$	218.999	−	218.999i	1.03791	−	1.03791i	0.0386558	−	0.999253i	$-0.487692\pi$
$211$	218.999	−	218.999i	1.03791	−	1.03791i	0.999253	−	0.0386558i	$-0.0123076\pi$
$212$		0			0
$213$	−131.181	+	131.181i	−0.615872	+	0.615872i
$214$		0			0
$215$	−11.0794			−0.0515319
$216$		0			0
$217$			0.277601i			0.00127927i
$218$		0			0
$219$	−22.7596	−	22.7596i	−0.103925	−	0.103925i
$220$		0			0
$221$	310.479	+	310.479i	1.40488	+	1.40488i
$222$		0			0
$223$		−	55.7557i		−	0.250025i	−0.992155	−	0.125013i	$-0.960103\pi$
$223$		−	55.7557i		−	0.250025i	0.992155	−	0.125013i	$-0.0398972\pi$
$224$		0			0
$225$	25.2847			0.112376
$226$		0			0
$227$	−135.477	+	135.477i	−0.596815	+	0.596815i	−0.939464	−	0.342649i	$-0.888676\pi$
$227$	−135.477	+	135.477i	−0.596815	+	0.596815i	0.342649	+	0.939464i	$0.388676\pi$
$228$		0			0
$229$	166.421	−	166.421i	0.726729	−	0.726729i	−0.243237	−	0.969967i	$-0.578209\pi$
$229$	166.421	−	166.421i	0.726729	−	0.726729i	0.969967	+	0.243237i	$0.0782094\pi$
$230$		0			0
$231$	−5.96838			−0.0258372
$232$		0			0
$233$			200.411i			0.860133i	0.902797	+	0.430066i	$0.141510\pi$
$233$			200.411i			0.860133i	−0.902797	+	0.430066i	$0.858490\pi$
$234$		0			0
$235$	−52.0834	−	52.0834i	−0.221631	−	0.221631i
$236$		0			0
$237$	−132.519	−	132.519i	−0.559152	−	0.559152i
$238$		0			0
$239$		−	197.050i		−	0.824476i	−0.911076	−	0.412238i	$-0.864747\pi$
$239$		−	197.050i		−	0.824476i	0.911076	−	0.412238i	$-0.135253\pi$
$240$		0			0
$241$	−134.564			−0.558356			−0.279178	−	0.960239i	$-0.590062\pi$
$241$	−134.564			−0.558356			−0.279178	+	0.960239i	$0.590062\pi$
$242$		0			0
$243$	−163.716	+	163.716i	−0.673728	+	0.673728i
$244$		0			0
$245$	76.9940	−	76.9940i	0.314261	−	0.314261i
$246$		0			0
$247$	369.131			1.49446
$248$		0			0
$249$			282.653i			1.13515i
$250$		0			0
$251$	−14.3088	−	14.3088i	−0.0570073	−	0.0570073i	0.678028	−	0.735036i	$-0.262835\pi$
$251$	−14.3088	−	14.3088i	−0.0570073	−	0.0570073i	−0.735036	+	0.678028i	$0.762835\pi$
$252$		0			0
$253$	−101.543	−	101.543i	−0.401357	−	0.401357i
$254$		0			0
$255$			119.066i			0.466925i
$256$		0			0
$257$	−37.3683			−0.145402			−0.0727009	−	0.997354i	$-0.523162\pi$
$257$	−37.3683			−0.145402			−0.0727009	+	0.997354i	$0.523162\pi$
$258$		0			0
$259$	−2.31645	+	2.31645i	−0.00894381	+	0.00894381i
$260$		0			0
$261$	−62.3117	+	62.3117i	−0.238742	+	0.238742i
$262$		0			0
$263$	160.717			0.611091			0.305546	−	0.952177i	$-0.401161\pi$
$263$	160.717			0.611091			0.305546	+	0.952177i	$0.401161\pi$
$264$		0			0
$265$		−	81.6926i		−	0.308274i
$266$		0			0
$267$	−67.6184	−	67.6184i	−0.253252	−	0.253252i
$268$		0			0
$269$	2.69578	+	2.69578i	0.0100215	+	0.0100215i	0.712100	−	0.702078i	$-0.247744\pi$
$269$	2.69578	+	2.69578i	0.0100215	+	0.0100215i	−0.702078	+	0.712100i	$0.747744\pi$
$270$		0			0
$271$		−	233.607i		−	0.862019i	−0.902347	−	0.431009i	$-0.858158\pi$
$271$		−	233.607i		−	0.862019i	0.902347	−	0.431009i	$-0.141842\pi$
$272$		0			0
$273$	−17.9489			−0.0657470
$274$		0			0
$275$	19.2502	−	19.2502i	0.0700008	−	0.0700008i
$276$		0			0
$277$	161.222	−	161.222i	0.582027	−	0.582027i	−0.353433	−	0.935460i	$-0.614986\pi$
$277$	161.222	−	161.222i	0.582027	−	0.582027i	0.935460	+	0.353433i	$0.114986\pi$
$278$		0			0
$279$	2.54302			0.00911475
$280$		0			0
$281$		−	120.862i		−	0.430114i	−0.976602	−	0.215057i	$-0.931006\pi$
$281$		−	120.862i		−	0.430114i	0.976602	−	0.215057i	$-0.0689936\pi$
$282$		0			0
$283$	148.621	+	148.621i	0.525163	+	0.525163i	0.919126	−	0.393963i	$-0.128896\pi$
$283$	148.621	+	148.621i	0.525163	+	0.525163i	−0.393963	+	0.919126i	$0.628896\pi$
$284$		0			0
$285$	70.7791	+	70.7791i	0.248348	+	0.248348i
$286$		0			0
$287$			26.4147i			0.0920372i
$288$		0			0
$289$	430.068			1.48812
$290$		0			0
$291$	139.533	−	139.533i	0.479494	−	0.479494i
$292$		0			0
$293$	−51.6844	+	51.6844i	−0.176397	+	0.176397i	−0.789783	−	0.613386i	$-0.789807\pi$
$293$	−51.6844	+	51.6844i	−0.176397	+	0.176397i	0.613386	+	0.789783i	$0.289807\pi$
$294$		0			0
$295$	−197.772			−0.670413
$296$		0			0
$297$			151.981i			0.511719i
$298$		0			0
$299$	−305.375	−	305.375i	−1.02132	−	1.02132i
$300$		0			0
$301$	−1.93408	−	1.93408i	−0.00642550	−	0.00642550i
$302$		0			0
$303$		−	193.288i		−	0.637913i
$304$		0			0
$305$	−191.394			−0.627521
$306$		0			0
$307$	−361.241	+	361.241i	−1.17668	+	1.17668i	−0.196095	+	0.980585i	$0.562826\pi$
$307$	−361.241	+	361.241i	−1.17668	+	1.17668i	−0.980585	+	0.196095i	$0.937174\pi$
$308$		0			0
$309$	−274.955	+	274.955i	−0.889821	+	0.889821i
$310$		0			0
$311$	−318.980			−1.02566			−0.512829	−	0.858491i	$-0.671402\pi$
$311$	−318.980			−1.02566			−0.512829	+	0.858491i	$0.671402\pi$
$312$		0			0
$313$		−	154.447i		−	0.493441i	−0.969087	−	0.246720i	$-0.920647\pi$
$313$		−	154.447i		−	0.493441i	0.969087	−	0.246720i	$-0.0793529\pi$
$314$		0			0
$315$	4.41383	+	4.41383i	0.0140122	+	0.0140122i
$316$		0			0
$317$	148.695	+	148.695i	0.469068	+	0.469068i	0.901613	−	0.432544i	$-0.142384\pi$
$317$	148.695	+	148.695i	0.469068	+	0.469068i	−0.432544	+	0.901613i	$0.642384\pi$
$318$		0			0
$319$			94.8808i			0.297432i
$320$		0			0
$321$	−268.929			−0.837786
$322$		0			0
$323$	427.453	−	427.453i	1.32338	−	1.32338i
$324$		0			0
$325$	57.8919	−	57.8919i	0.178129	−	0.178129i
$326$		0			0
$327$	−176.882			−0.540924
$328$		0			0
$329$		−	18.1839i		−	0.0552703i
$330$		0			0
$331$	−194.291	−	194.291i	−0.586981	−	0.586981i	0.349832	−	0.936813i	$-0.386239\pi$
$331$	−194.291	−	194.291i	−0.586981	−	0.586981i	−0.936813	+	0.349832i	$0.886239\pi$
$332$		0			0
$333$	21.2203	+	21.2203i	0.0637245	+	0.0637245i
$334$		0			0
$335$			99.2385i			0.296234i
$336$		0			0
$337$	97.7581			0.290083			0.145042	−	0.989426i	$-0.453668\pi$
$337$	97.7581			0.290083			0.145042	+	0.989426i	$0.453668\pi$
$338$		0			0
$339$	−226.188	+	226.188i	−0.667222	+	0.667222i
$340$		0			0
$341$	1.93610	−	1.93610i	0.00567771	−	0.00567771i
$342$		0			0
$343$	53.9302			0.157231
$344$		0			0
$345$		−	117.108i		−	0.339444i
$346$		0			0
$347$	221.087	+	221.087i	0.637137	+	0.637137i	0.949848	−	0.312711i	$-0.101237\pi$
$347$	221.087	+	221.087i	0.637137	+	0.637137i	−0.312711	+	0.949848i	$0.601237\pi$
$348$		0			0
$349$	−225.811	−	225.811i	−0.647022	−	0.647022i	0.305250	−	0.952272i	$-0.401260\pi$
$349$	−225.811	−	225.811i	−0.647022	−	0.647022i	−0.952272	+	0.305250i	$0.901260\pi$
$350$		0			0
$351$			457.057i			1.30216i
$352$		0			0
$353$	−203.790			−0.577308			−0.288654	−	0.957433i	$-0.593208\pi$
$353$	−203.790			−0.577308			−0.288654	+	0.957433i	$0.593208\pi$
$354$		0			0
$355$	147.720	−	147.720i	0.416111	−	0.416111i
$356$		0			0
$357$	−20.7848	+	20.7848i	−0.0582208	+	0.0582208i
$358$		0			0
$359$	−354.552			−0.987611			−0.493806	−	0.869572i	$-0.664395\pi$
$359$	−354.552			−0.987611			−0.493806	+	0.869572i	$0.664395\pi$
$360$		0			0
$361$		−	147.202i		−	0.407761i
$362$		0			0
$363$	−128.272	−	128.272i	−0.353366	−	0.353366i
$364$		0			0
$365$	25.6290	+	25.6290i	0.0702165	+	0.0702165i
$366$		0			0
$367$		−	488.199i		−	1.33024i	−0.746736	−	0.665121i	$-0.768380\pi$
$367$		−	488.199i		−	1.33024i	0.746736	−	0.665121i	$-0.231620\pi$
$368$		0			0
$369$	241.977			0.655763
$370$		0			0
$371$	14.2607	−	14.2607i	0.0384386	−	0.0384386i
$372$		0			0
$373$	5.45809	−	5.45809i	0.0146329	−	0.0146329i	−0.699752	−	0.714385i	$-0.746706\pi$
$373$	5.45809	−	5.45809i	0.0146329	−	0.0146329i	0.714385	+	0.699752i	$0.246706\pi$
$374$		0			0
$375$	22.2010			0.0592026
$376$		0			0
$377$			285.338i			0.756866i
$378$		0			0
$379$	109.881	+	109.881i	0.289924	+	0.289924i	0.837050	−	0.547126i	$-0.184278\pi$
$379$	109.881	+	109.881i	0.289924	+	0.289924i	−0.547126	+	0.837050i	$0.684278\pi$
$380$		0			0
$381$	−193.989	−	193.989i	−0.509157	−	0.509157i
$382$		0			0
$383$			477.564i			1.24690i	0.781862	+	0.623452i	$0.214270\pi$
$383$			477.564i			1.24690i	−0.781862	+	0.623452i	$0.785730\pi$
$384$		0			0
$385$	6.72085			0.0174568
$386$		0			0
$387$	−17.7175	+	17.7175i	−0.0457816	+	0.0457816i
$388$		0			0
$389$	−25.4984	+	25.4984i	−0.0655485	+	0.0655485i	−0.739121	−	0.673573i	$-0.764759\pi$
$389$	−25.4984	+	25.4984i	−0.0655485	+	0.0655485i	0.673573	+	0.739121i	$0.264759\pi$
$390$		0			0
$391$	−707.246			−1.80881
$392$		0			0
$393$		−	367.093i		−	0.934079i
$394$		0			0
$395$	149.227	+	149.227i	0.377789	+	0.377789i
$396$		0			0
$397$	−236.680	−	236.680i	−0.596172	−	0.596172i	0.343120	−	0.939292i	$-0.388516\pi$
$397$	−236.680	−	236.680i	−0.596172	−	0.596172i	−0.939292	+	0.343120i	$0.888516\pi$
$398$		0			0
$399$			24.7112i			0.0619329i
$400$		0			0
$401$	−768.463			−1.91637			−0.958183	−	0.286157i	$-0.907622\pi$
$401$	−768.463			−1.91637			−0.958183	+	0.286157i	$0.907622\pi$
$402$		0			0
$403$	5.82250	−	5.82250i	0.0144479	−	0.0144479i
$404$		0			0
$405$	−15.6771	+	15.6771i	−0.0387090	+	0.0387090i
$406$		0			0
$407$	32.3117			0.0793898
$408$		0			0
$409$		−	450.188i		−	1.10071i	−0.834932	−	0.550353i	$-0.814493\pi$
$409$		−	450.188i		−	1.10071i	0.834932	−	0.550353i	$-0.185507\pi$
$410$		0			0
$411$	293.029	+	293.029i	0.712966	+	0.712966i
$412$		0			0
$413$	−34.5241	−	34.5241i	−0.0835936	−	0.0835936i
$414$		0			0
$415$		−	318.289i		−	0.766962i
$416$		0			0
$417$	−108.252			−0.259596
$418$		0			0
$419$	447.047	−	447.047i	1.06694	−	1.06694i	0.0693451	−	0.997593i	$-0.477909\pi$
$419$	447.047	−	447.047i	1.06694	−	1.06694i	0.997593	−	0.0693451i	$-0.0220910\pi$
$420$		0			0
$421$	−552.100	+	552.100i	−1.31140	+	1.31140i	−0.391017	+	0.920383i	$0.627877\pi$
$421$	−552.100	+	552.100i	−1.31140	+	1.31140i	−0.920383	+	0.391017i	$0.872123\pi$
$422$		0			0
$423$	−166.577			−0.393800
$424$		0			0
$425$		−	134.077i		−	0.315476i
$426$		0			0
$427$	−33.4108	−	33.4108i	−0.0782454	−	0.0782454i
$428$		0			0
$429$	125.183	+	125.183i	0.291802	+	0.291802i
$430$		0			0
$431$			382.280i			0.886961i	0.896284	+	0.443481i	$0.146257\pi$
$431$			382.280i			0.886961i	−0.896284	+	0.443481i	$0.853743\pi$
$432$		0			0
$433$	783.797			1.81015			0.905077	−	0.425247i	$-0.139813\pi$
$433$	783.797			1.81015			0.905077	+	0.425247i	$0.139813\pi$
$434$		0			0
$435$	−54.7123	+	54.7123i	−0.125775	+	0.125775i
$436$		0			0
$437$	−420.425	+	420.425i	−0.962071	+	0.962071i
$438$		0			0
$439$	278.729			0.634918			0.317459	−	0.948272i	$-0.397170\pi$
$439$	278.729			0.634918			0.317459	+	0.948272i	$0.397170\pi$
$440$		0			0
$441$		−	246.249i		−	0.558387i
$442$		0			0
$443$	−2.34136	−	2.34136i	−0.00528524	−	0.00528524i	0.704459	−	0.709744i	$-0.251190\pi$
$443$	−2.34136	−	2.34136i	−0.00528524	−	0.00528524i	−0.709744	+	0.704459i	$0.751190\pi$
$444$		0			0
$445$	76.1434	+	76.1434i	0.171109	+	0.171109i
$446$		0			0
$447$		−	243.725i		−	0.545246i
$448$		0			0
$449$	−738.730			−1.64528			−0.822639	−	0.568564i	$-0.807499\pi$
$449$	−738.730			−1.64528			−0.822639	+	0.568564i	$0.807499\pi$
$450$		0			0
$451$	184.226	−	184.226i	0.408484	−	0.408484i
$452$		0			0
$453$	295.566	−	295.566i	0.652464	−	0.652464i
$454$		0			0
$455$	20.2119			0.0444217
$456$		0			0
$457$		−	449.865i		−	0.984387i	−0.870486	−	0.492193i	$-0.836195\pi$
$457$		−	449.865i		−	0.984387i	0.870486	−	0.492193i	$-0.163805\pi$
$458$		0			0
$459$	529.271	+	529.271i	1.15309	+	1.15309i
$460$		0			0
$461$	374.202	+	374.202i	0.811719	+	0.811719i	0.984892	−	0.173172i	$-0.0554018\pi$
$461$	374.202	+	374.202i	0.811719	+	0.811719i	−0.173172	+	0.984892i	$0.555402\pi$
$462$		0			0
$463$		−	428.003i		−	0.924412i	−0.886773	−	0.462206i	$-0.847058\pi$
$463$		−	428.003i		−	0.924412i	0.886773	−	0.462206i	$-0.152942\pi$
$464$		0			0
$465$	2.23288			0.00480188
$466$		0			0
$467$	91.7190	−	91.7190i	0.196401	−	0.196401i	−0.602054	−	0.798455i	$-0.705651\pi$
$467$	91.7190	−	91.7190i	0.196401	−	0.196401i	0.798455	+	0.602054i	$0.205651\pi$
$468$		0			0
$469$	−17.3236	+	17.3236i	−0.0369374	+	0.0369374i
$470$		0			0
$471$	−556.169			−1.18083
$472$		0			0
$473$			26.9780i			0.0570360i
$474$		0			0
$475$	−79.7027	−	79.7027i	−0.167795	−	0.167795i
$476$		0			0
$477$	−130.638	−	130.638i	−0.273874	−	0.273874i
$478$		0			0
$479$			201.917i			0.421538i	0.977536	+	0.210769i	$0.0675968\pi$
$479$			201.917i			0.421538i	−0.977536	+	0.210769i	$0.932403\pi$
$480$		0			0
$481$	97.1720			0.202021
$482$		0			0
$483$	20.4431	−	20.4431i	0.0423252	−	0.0423252i
$484$		0			0
$485$	−157.124	+	157.124i	−0.323968	+	0.323968i
$486$		0			0
$487$	−218.927			−0.449541			−0.224771	−	0.974412i	$-0.572163\pi$
$487$	−218.927			−0.449541			−0.224771	+	0.974412i	$0.572163\pi$
$488$		0			0
$489$			129.508i			0.264842i
$490$		0			0
$491$	−588.144	−	588.144i	−1.19785	−	1.19785i	−0.974809	−	0.223041i	$-0.928402\pi$
$491$	−588.144	−	588.144i	−1.19785	−	1.19785i	−0.223041	−	0.974809i	$-0.571598\pi$
$492$		0			0
$493$	330.421	+	330.421i	0.670225	+	0.670225i
$494$		0			0
$495$		−	61.5677i		−	0.124379i
$496$		0			0
$497$	51.5735			0.103770
$498$		0			0
$499$	−206.657	+	206.657i	−0.414143	+	0.414143i	−0.883179	−	0.469036i	$-0.844601\pi$
$499$	−206.657	+	206.657i	−0.414143	+	0.414143i	0.469036	+	0.883179i	$0.344601\pi$
$500$		0			0
$501$	221.404	−	221.404i	0.441923	−	0.441923i
$502$		0			0
$503$	252.446			0.501881			0.250940	−	0.968003i	$-0.419260\pi$
$503$	252.446			0.501881			0.250940	+	0.968003i	$0.419260\pi$
$504$		0			0
$505$			217.657i			0.431003i
$506$		0			0
$507$	139.172	+	139.172i	0.274501	+	0.274501i
$508$		0			0
$509$	−191.568	−	191.568i	−0.376361	−	0.376361i	0.493427	−	0.869787i	$-0.335744\pi$
$509$	−191.568	−	191.568i	−0.376361	−	0.376361i	−0.869787	+	0.493427i	$0.835744\pi$
$510$		0			0
$511$			8.94790i			0.0175106i
$512$		0			0
$513$	629.254			1.22662
$514$		0			0
$515$	309.620	−	309.620i	0.601204	−	0.601204i
$516$		0			0
$517$	−126.822	+	126.822i	−0.245304	+	0.245304i
$518$		0			0
$519$	−286.781			−0.552565
$520$		0			0
$521$		−	537.669i		−	1.03199i	−0.856590	−	0.515997i	$-0.827421\pi$
$521$		−	537.669i		−	1.03199i	0.856590	−	0.515997i	$-0.172579\pi$
$522$		0			0
$523$	209.551	+	209.551i	0.400671	+	0.400671i	0.878469	−	0.477799i	$-0.158565\pi$
$523$	209.551	+	209.551i	0.400671	+	0.400671i	−0.477799	+	0.878469i	$0.658565\pi$
$524$		0			0
$525$	3.87553	+	3.87553i	0.00738196	+	0.00738196i
$526$		0			0
$527$		−	13.4849i		−	0.0255880i
$528$		0			0
$529$	166.618			0.314968
$530$		0			0
$531$	−316.265	+	316.265i	−0.595603	+	0.595603i
$532$		0			0
$533$	554.031	−	554.031i	1.03946	−	1.03946i
$534$		0			0
$535$	302.835			0.566047
$536$		0			0
$537$			401.154i			0.747028i
$538$		0			0
$539$	−187.479	−	187.479i	−0.347827	−	0.347827i
$540$		0			0
$541$	594.135	+	594.135i	1.09822	+	1.09822i	0.994619	+	0.103597i	$0.0330354\pi$
$541$	594.135	+	594.135i	1.09822	+	1.09822i	0.103597	+	0.994619i	$0.466965\pi$
$542$		0			0
$543$		−	311.023i		−	0.572786i
$544$		0			0
$545$	199.183			0.365473
$546$		0			0
$547$	−192.678	+	192.678i	−0.352244	+	0.352244i	−0.860944	−	0.508700i	$-0.830126\pi$
$547$	−192.678	+	192.678i	−0.352244	+	0.352244i	0.508700	+	0.860944i	$0.330126\pi$
$548$		0			0
$549$	−306.066	+	306.066i	−0.557497	+	0.557497i
$550$		0			0
$551$	392.840			0.712958
$552$		0			0
$553$			52.0997i			0.0942128i
$554$		0			0
$555$	18.6323	+	18.6323i	0.0335717	+	0.0335717i
$556$		0			0
$557$	615.215	+	615.215i	1.10452	+	1.10452i	0.993859	+	0.110656i	$0.0352953\pi$
$557$	615.215	+	615.215i	1.10452	+	1.10452i	0.110656	+	0.993859i	$0.464705\pi$
$558$		0			0
$559$			81.1320i			0.145138i
$560$		0			0
$561$	289.923			0.516797
$562$		0			0
$563$	120.738	−	120.738i	0.214455	−	0.214455i	−0.591702	−	0.806157i	$-0.701544\pi$
$563$	120.738	−	120.738i	0.214455	−	0.214455i	0.806157	+	0.591702i	$0.201544\pi$
$564$		0			0
$565$	254.705	−	254.705i	0.450806	−	0.450806i
$566$		0			0
$567$	−5.47338			−0.00965322
$568$		0			0
$569$		−	111.750i		−	0.196397i	−0.995167	−	0.0981986i	$-0.968692\pi$
$569$		−	111.750i		−	0.196397i	0.995167	−	0.0981986i	$-0.0313080\pi$
$570$		0			0
$571$	480.097	+	480.097i	0.840800	+	0.840800i	0.988963	−	0.148163i	$-0.0473360\pi$
$571$	480.097	+	480.097i	0.840800	+	0.840800i	−0.148163	+	0.988963i	$0.547336\pi$
$572$		0			0
$573$	453.283	+	453.283i	0.791069	+	0.791069i
$574$		0			0
$575$			131.873i			0.229344i
$576$		0			0
$577$	−252.701			−0.437957			−0.218979	−	0.975730i	$-0.570273\pi$
$577$	−252.701			−0.437957			−0.218979	+	0.975730i	$0.570273\pi$
$578$		0			0
$579$	−11.3650	+	11.3650i	−0.0196287	+	0.0196287i
$580$		0			0
$581$	55.5624	−	55.5624i	0.0956323	−	0.0956323i
$582$		0			0
$583$	−198.920			−0.341201
$584$		0			0
$585$		−	185.155i		−	0.316504i
$586$		0			0
$587$	−224.296	−	224.296i	−0.382106	−	0.382106i	0.489755	−	0.871860i	$-0.337086\pi$
$587$	−224.296	−	224.296i	−0.382106	−	0.382106i	−0.871860	+	0.489755i	$0.837086\pi$
$588$		0			0
$589$	−8.01614	−	8.01614i	−0.0136097	−	0.0136097i
$590$		0			0
$591$		−	305.200i		−	0.516414i
$592$		0			0
$593$	−62.5277			−0.105443			−0.0527215	−	0.998609i	$-0.516790\pi$
$593$	−62.5277			−0.105443			−0.0527215	+	0.998609i	$0.516790\pi$
$594$		0			0
$595$	23.4053	−	23.4053i	0.0393366	−	0.0393366i
$596$		0			0
$597$	249.638	−	249.638i	0.418154	−	0.418154i
$598$		0			0
$599$	998.888			1.66759			0.833796	−	0.552073i	$-0.186163\pi$
$599$	998.888			1.66759			0.833796	+	0.552073i	$0.186163\pi$
$600$		0			0
$601$			1168.69i			1.94458i	0.233773	+	0.972291i	$0.424893\pi$
$601$			1168.69i			1.94458i	−0.233773	+	0.972291i	$0.575107\pi$
$602$		0			0
$603$	158.696	+	158.696i	0.263178	+	0.263178i
$604$		0			0
$605$	144.444	+	144.444i	0.238750	+	0.238750i
$606$		0			0
$607$			1099.01i			1.81056i	0.424814	+	0.905281i	$0.360339\pi$
$607$			1099.01i			1.81056i	−0.424814	+	0.905281i	$0.639661\pi$
$608$		0			0
$609$	−19.1018			−0.0313658
$610$		0			0
$611$	−381.396	+	381.396i	−0.624216	+	0.624216i
$612$		0			0
$613$	−34.0542	+	34.0542i	−0.0555533	+	0.0555533i	−0.734338	−	0.678784i	$-0.762507\pi$
$613$	−34.0542	+	34.0542i	−0.0555533	+	0.0555533i	0.678784	+	0.734338i	$0.262507\pi$
$614$		0			0
$615$	212.466			0.345473
$616$		0			0
$617$			639.802i			1.03696i	0.855091	+	0.518478i	$0.173501\pi$
$617$			639.802i			1.03696i	−0.855091	+	0.518478i	$0.826499\pi$
$618$		0			0
$619$	−20.8581	−	20.8581i	−0.0336964	−	0.0336964i	0.690058	−	0.723754i	$-0.257585\pi$
$619$	−20.8581	−	20.8581i	−0.0336964	−	0.0336964i	−0.723754	+	0.690058i	$0.757585\pi$
$620$		0			0
$621$	−520.569	−	520.569i	−0.838275	−	0.838275i
$622$		0			0
$623$			26.5841i			0.0426710i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	172.346	−	172.346i	0.274874	−	0.274874i
$628$		0			0
$629$	112.525	−	112.525i	0.178895	−	0.178895i
$630$		0			0
$631$	78.5385			0.124467			0.0622333	−	0.998062i	$-0.480178\pi$
$631$	78.5385			0.124467			0.0622333	+	0.998062i	$0.480178\pi$
$632$		0			0
$633$		−	614.998i		−	0.971561i
$634$		0			0
$635$	218.446	+	218.446i	0.344010	+	0.344010i
$636$		0			0
$637$	−563.812	−	563.812i	−0.885105	−	0.885105i
$638$		0			0
$639$		−	472.449i		−	0.739357i
$640$		0			0
$641$	208.610			0.325444			0.162722	−	0.986672i	$-0.447973\pi$
$641$	208.610			0.325444			0.162722	+	0.986672i	$0.447973\pi$
$642$		0			0
$643$	190.352	−	190.352i	0.296037	−	0.296037i	−0.543423	−	0.839459i	$-0.682872\pi$
$643$	190.352	−	190.352i	0.296037	−	0.296037i	0.839459	+	0.543423i	$0.182872\pi$
$644$		0			0
$645$	−15.5567	+	15.5567i	−0.0241189	+	0.0241189i
$646$		0			0
$647$	−189.805			−0.293362			−0.146681	−	0.989184i	$-0.546859\pi$
$647$	−189.805			−0.293362			−0.146681	+	0.989184i	$0.546859\pi$
$648$		0			0
$649$			481.570i			0.742019i
$650$		0			0
$651$	0.389783	+	0.389783i	0.000598745	+	0.000598745i
$652$		0			0
$653$	26.8792	+	26.8792i	0.0411627	+	0.0411627i	0.727389	−	0.686226i	$-0.240734\pi$
$653$	26.8792	+	26.8792i	0.0411627	+	0.0411627i	−0.686226	+	0.727389i	$0.740734\pi$
$654$		0			0
$655$			413.375i			0.631107i
$656$		0			0
$657$	81.9689			0.124762
$658$		0			0
$659$	325.678	−	325.678i	0.494200	−	0.494200i	−0.415427	−	0.909627i	$-0.636368\pi$
$659$	325.678	−	325.678i	0.494200	−	0.494200i	0.909627	+	0.415427i	$0.136368\pi$
$660$		0			0
$661$	−483.724	+	483.724i	−0.731807	+	0.731807i	−0.970978	−	0.239170i	$-0.923125\pi$
$661$	−483.724	+	483.724i	−0.731807	+	0.731807i	0.239170	+	0.970978i	$0.423125\pi$
$662$		0			0
$663$	871.896			1.31508
$664$		0			0
$665$		−	27.8267i		−	0.0418447i
$666$		0			0
$667$	−324.989	−	324.989i	−0.487239	−	0.487239i
$668$		0			0
$669$	−78.2873	−	78.2873i	−0.117021	−	0.117021i
$670$		0			0
$671$			466.040i			0.694546i
$672$		0			0
$673$	184.885			0.274717			0.137358	−	0.990521i	$-0.456139\pi$
$673$	184.885			0.274717			0.137358	+	0.990521i	$0.456139\pi$
$674$		0			0
$675$	98.6876	−	98.6876i	0.146204	−	0.146204i
$676$		0			0
$677$	113.519	−	113.519i	0.167679	−	0.167679i	−0.618279	−	0.785958i	$-0.712170\pi$
$677$	113.519	−	113.519i	0.167679	−	0.167679i	0.785958	+	0.618279i	$0.212170\pi$
$678$		0			0
$679$	−54.8571			−0.0807909
$680$		0			0
$681$			380.450i			0.558664i
$682$		0			0
$683$	−210.384	−	210.384i	−0.308029	−	0.308029i	0.536116	−	0.844144i	$-0.319891\pi$
$683$	−210.384	−	210.384i	−0.308029	−	0.308029i	−0.844144	+	0.536116i	$0.819891\pi$
$684$		0			0
$685$	−329.973	−	329.973i	−0.481712	−	0.481712i
$686$		0			0
$687$		−	467.348i		−	0.680274i
$688$		0			0
$689$	−598.219			−0.868242
$690$		0			0
$691$	−285.805	+	285.805i	−0.413611	+	0.413611i	−0.882994	−	0.469384i	$-0.844476\pi$
$691$	−285.805	+	285.805i	−0.413611	+	0.413611i	0.469384	+	0.882994i	$0.344476\pi$
$692$		0			0
$693$	10.7476	−	10.7476i	0.0155088	−	0.0155088i
$694$		0			0
$695$	121.900			0.175395
$696$		0			0
$697$		−	1283.13i		−	1.84094i
$698$		0			0
$699$	281.400	+	281.400i	0.402575	+	0.402575i
$700$		0			0
$701$	−681.310	−	681.310i	−0.971912	−	0.971912i	0.0277043	−	0.999616i	$-0.491180\pi$
$701$	−681.310	−	681.310i	−0.971912	−	0.971912i	−0.999616	+	0.0277043i	$0.991180\pi$
$702$		0			0
$703$		−	133.782i		−	0.190301i
$704$		0			0
$705$	−146.262			−0.207464
$706$		0			0
$707$	−37.9954	+	37.9954i	−0.0537417	+	0.0537417i
$708$		0			0
$709$	176.701	−	176.701i	0.249226	−	0.249226i	−0.571427	−	0.820653i	$-0.693610\pi$
$709$	176.701	−	176.701i	0.249226	−	0.249226i	0.820653	+	0.571427i	$0.193610\pi$
$710$		0			0
$711$	477.269			0.671264
$712$		0			0
$713$			13.2632i			0.0186019i
$714$		0			0
$715$	−140.966	−	140.966i	−0.197155	−	0.197155i
$716$		0			0
$717$	−276.680	−	276.680i	−0.385886	−	0.385886i
$718$		0			0
$719$		−	831.779i		−	1.15686i	−0.815734	−	0.578428i	$-0.803666\pi$
$719$		−	831.779i		−	1.15686i	0.815734	−	0.578428i	$-0.196334\pi$
$720$		0			0
$721$	108.098			0.149928
$722$		0			0
$723$	−188.943	+	188.943i	−0.261332	+	0.261332i
$724$		0			0
$725$	61.6102	−	61.6102i	0.0849796	−	0.0849796i
$726$		0			0
$727$	−271.929			−0.374043			−0.187021	−	0.982356i	$-0.559883\pi$
$727$	−271.929			−0.374043			−0.187021	+	0.982356i	$0.559883\pi$
$728$		0			0
$729$			548.987i			0.753069i
$730$		0			0
$731$	93.9506	+	93.9506i	0.128523	+	0.128523i
$732$		0			0
$733$	−729.816	−	729.816i	−0.995656	−	0.995656i	0.00433470	−	0.999991i	$-0.498620\pi$
$733$	−729.816	−	729.816i	−0.995656	−	0.995656i	−0.999991	+	0.00433470i	$0.998620\pi$
$734$		0			0
$735$		−	216.217i		−	0.294172i
$736$		0			0
$737$	241.644			0.327875
$738$		0			0
$739$	−520.294	+	520.294i	−0.704052	+	0.704052i	−0.965278	−	0.261226i	$-0.915873\pi$
$739$	−520.294	+	520.294i	−0.704052	+	0.704052i	0.261226	+	0.965278i	$0.415873\pi$
$740$		0			0
$741$	518.302	−	518.302i	0.699463	−	0.699463i
$742$		0			0
$743$	−669.227			−0.900709			−0.450355	−	0.892850i	$-0.648702\pi$
$743$	−669.227			−0.900709			−0.450355	+	0.892850i	$0.648702\pi$
$744$		0			0
$745$			274.453i			0.368393i
$746$		0			0
$747$	−508.990	−	508.990i	−0.681378	−	0.681378i
$748$		0			0
$749$	52.8646	+	52.8646i	0.0705802	+	0.0705802i
$750$		0			0
$751$		−	753.858i		−	1.00381i	−0.864924	−	0.501903i	$-0.832633\pi$
$751$		−	753.858i		−	1.00381i	0.864924	−	0.501903i	$-0.167367\pi$
$752$		0			0
$753$	−40.1825			−0.0533631
$754$		0			0
$755$	−332.830	+	332.830i	−0.440835	+	0.440835i
$756$		0			0
$757$	−300.693	+	300.693i	−0.397217	+	0.397217i	−0.877250	−	0.480033i	$-0.840625\pi$
$757$	−300.693	+	300.693i	−0.397217	+	0.397217i	0.480033	+	0.877250i	$0.340625\pi$
$758$		0			0
$759$	−285.157			−0.375700
$760$		0			0
$761$			537.167i			0.705870i	0.935648	+	0.352935i	$0.114816\pi$
$761$			537.167i			0.705870i	−0.935648	+	0.352935i	$0.885184\pi$
$762$		0			0
$763$	34.7705	+	34.7705i	0.0455707	+	0.0455707i
$764$		0			0
$765$	−214.408	−	214.408i	−0.280273	−	0.280273i
$766$		0			0
$767$			1448.24i			1.88819i
$768$		0			0
$769$	−1136.82			−1.47831			−0.739153	−	0.673538i	$-0.764774\pi$
$769$	−1136.82			−1.47831			−0.739153	+	0.673538i	$0.764774\pi$
$770$		0			0
$771$	−52.4693	+	52.4693i	−0.0680536	+	0.0680536i
$772$		0			0
$773$	238.427	−	238.427i	0.308443	−	0.308443i	−0.535862	−	0.844306i	$-0.680013\pi$
$773$	238.427	−	238.427i	0.308443	−	0.308443i	0.844306	+	0.535862i	$0.180013\pi$
$774$		0			0
$775$	−2.51439			−0.00324437
$776$		0			0
$777$			6.50511i			0.00837208i
$778$		0			0
$779$	−762.763	−	762.763i	−0.979156	−	0.979156i
$780$		0			0
$781$	−359.694	−	359.694i	−0.460556	−	0.460556i
$782$		0			0
$783$			486.413i			0.621218i
$784$		0			0
$785$	626.289			0.797821
$786$		0			0
$787$	−67.2311	+	67.2311i	−0.0854271	+	0.0854271i	−0.748529	−	0.663102i	$-0.769240\pi$
$787$	−67.2311	+	67.2311i	−0.0854271	+	0.0854271i	0.663102	+	0.748529i	$0.269240\pi$
$788$		0			0
$789$	225.665	−	225.665i	0.286014	−	0.286014i
$790$		0			0
$791$	88.9256			0.112422
$792$		0			0
$793$			1401.54i			1.76739i
$794$		0			0
$795$	−114.706	−	114.706i	−0.144284	−	0.144284i
$796$		0			0
$797$	−99.5829	−	99.5829i	−0.124947	−	0.124947i	0.641868	−	0.766815i	$-0.278160\pi$
$797$	−99.5829	−	99.5829i	−0.124947	−	0.124947i	−0.766815	+	0.641868i	$0.778160\pi$
$798$		0			0
$799$			883.312i			1.10552i
$800$		0			0
$801$	243.528			0.304030
$802$		0			0
$803$	62.4062	−	62.4062i	0.0777164	−	0.0777164i
$804$		0			0
$805$	−23.0205	+	23.0205i	−0.0285969	+	0.0285969i
$806$		0			0
$807$	7.57036			0.00938087
$808$		0			0
$809$		−	457.614i		−	0.565654i	−0.959171	−	0.282827i	$-0.908728\pi$
$809$		−	457.614i		−	0.565654i	0.959171	−	0.282827i	$-0.0912723\pi$
$810$		0			0
$811$	−784.487	−	784.487i	−0.967309	−	0.967309i	0.0321735	−	0.999482i	$-0.489757\pi$
$811$	−784.487	−	784.487i	−0.967309	−	0.967309i	−0.999482	+	0.0321735i	$0.989757\pi$
$812$		0			0
$813$	−328.011	−	328.011i	−0.403457	−	0.403457i
$814$		0			0
$815$		−	145.836i		−	0.178939i
$816$		0			0
$817$	111.699			0.136718
$818$		0			0
$819$	32.3216	−	32.3216i	0.0394647	−	0.0394647i
$820$		0			0
$821$	528.021	−	528.021i	0.643143	−	0.643143i	−0.308184	−	0.951327i	$-0.599721\pi$
$821$	528.021	−	528.021i	0.643143	−	0.643143i	0.951327	+	0.308184i	$0.0997211\pi$
$822$		0			0
$823$	714.122			0.867706			0.433853	−	0.900984i	$-0.357154\pi$
$823$	714.122			0.867706			0.433853	+	0.900984i	$0.357154\pi$
$824$		0			0
$825$		−	54.0590i		−	0.0655260i
$826$		0			0
$827$	−35.4554	−	35.4554i	−0.0428723	−	0.0428723i	0.685346	−	0.728218i	$-0.259651\pi$
$827$	−35.4554	−	35.4554i	−0.0428723	−	0.0428723i	−0.728218	+	0.685346i	$0.759651\pi$
$828$		0			0
$829$	687.047	+	687.047i	0.828765	+	0.828765i	0.987346	−	0.158581i	$-0.0506918\pi$
$829$	687.047	+	687.047i	0.828765	+	0.828765i	−0.158581	+	0.987346i	$0.550692\pi$
$830$		0			0
$831$		−	452.747i		−	0.544822i
$832$		0			0
$833$	−1305.79			−1.56757
$834$		0			0
$835$	−249.317	+	249.317i	−0.298583	+	0.298583i
$836$		0			0
$837$	9.92556	−	9.92556i	0.0118585	−	0.0118585i
$838$		0			0
$839$	−670.000			−0.798570			−0.399285	−	0.916827i	$-0.630742\pi$
$839$	−670.000			−0.798570			−0.399285	+	0.916827i	$0.630742\pi$
$840$		0			0
$841$		−	537.334i		−	0.638923i
$842$		0			0
$843$	−169.704	−	169.704i	−0.201309	−	0.201309i
$844$		0			0
$845$	−156.718	−	156.718i	−0.185465	−	0.185465i
$846$		0			0
$847$			50.4299i			0.0595394i
$848$		0			0
$849$	417.362			0.491592
$850$		0			0
$851$	−110.675	+	110.675i	−0.130053	+	0.130053i
$852$		0			0
$853$	−526.153	+	526.153i	−0.616826	+	0.616826i	−0.944716	−	0.327890i	$-0.893662\pi$
$853$	−526.153	+	526.153i	−0.616826	+	0.616826i	0.327890	+	0.944716i	$0.393662\pi$
$854$		0			0
$855$	−254.912			−0.298142
$856$		0			0
$857$		−	168.824i		−	0.196995i	−0.995137	−	0.0984973i	$-0.968596\pi$
$857$		−	168.824i		−	0.196995i	0.995137	−	0.0984973i	$-0.0314036\pi$
$858$		0			0
$859$	119.715	+	119.715i	0.139365	+	0.139365i	0.773348	−	0.633982i	$-0.218581\pi$
$859$	119.715	+	119.715i	0.139365	+	0.139365i	−0.633982	+	0.773348i	$0.718581\pi$
$860$		0			0
$861$	37.0892	+	37.0892i	0.0430769	+	0.0430769i
$862$		0			0
$863$		−	1095.61i		−	1.26953i	−0.772704	−	0.634767i	$-0.781096\pi$
$863$		−	1095.61i		−	1.26953i	0.772704	−	0.634767i	$-0.218904\pi$
$864$		0			0
$865$	322.938			0.373338
$866$		0			0
$867$	603.864	−	603.864i	0.696499	−	0.696499i
$868$		0			0
$869$	363.364	−	363.364i	0.418140	−	0.418140i
$870$		0			0
$871$	726.704			0.834333
$872$		0			0
$873$			502.528i			0.575634i
$874$		0			0
$875$	−4.36414	−	4.36414i	−0.00498759	−	0.00498759i
$876$		0			0
$877$	675.118	+	675.118i	0.769804	+	0.769804i	0.978072	−	0.208268i	$-0.0667825\pi$
$877$	675.118	+	675.118i	0.769804	+	0.769804i	−0.208268	+	0.978072i	$0.566783\pi$
$878$		0			0
$879$			145.141i			0.165121i
$880$		0			0
$881$	−496.966			−0.564093			−0.282046	−	0.959401i	$-0.591013\pi$
$881$	−496.966			−0.564093			−0.282046	+	0.959401i	$0.591013\pi$
$882$		0			0
$883$	−874.002	+	874.002i	−0.989809	+	0.989809i	−0.999949	−	0.0101392i	$-0.996773\pi$
$883$	−874.002	+	874.002i	−0.989809	+	0.989809i	0.0101392	+	0.999949i	$0.496773\pi$
$884$		0			0
$885$	−277.694	+	277.694i	−0.313778	+	0.313778i
$886$		0			0
$887$	378.524			0.426746			0.213373	−	0.976971i	$-0.431555\pi$
$887$	378.524			0.426746			0.213373	+	0.976971i	$0.431555\pi$
$888$		0			0
$889$			76.2664i			0.0857890i
$890$		0			0
$891$	38.1735	+	38.1735i	0.0428435	+	0.0428435i
$892$		0			0
$893$	525.088	+	525.088i	0.588004	+	0.588004i
$894$		0			0
$895$		−	451.730i		−	0.504726i
$896$		0			0
$897$	−857.561			−0.956033
$898$		0			0
$899$	6.19648	−	6.19648i	0.00689263	−	0.00689263i
$900$		0			0
$901$	−692.736	+	692.736i	−0.768852	+	0.768852i
$902$		0			0
$903$	−5.43132			−0.00601476
$904$		0			0
$905$			350.235i			0.387000i
$906$		0			0
$907$	848.525	+	848.525i	0.935529	+	0.935529i	0.998044	−	0.0625147i	$-0.0199120\pi$
$907$	848.525	+	848.525i	0.935529	+	0.935529i	−0.0625147	+	0.998044i	$0.519912\pi$
$908$		0			0
$909$	348.064	+	348.064i	0.382908	+	0.382908i
$910$		0			0
$911$		−	619.103i		−	0.679586i	−0.940500	−	0.339793i	$-0.889643\pi$
$911$		−	619.103i		−	0.679586i	0.940500	−	0.339793i	$-0.110357\pi$
$912$		0			0
$913$	−775.028			−0.848881
$914$		0			0
$915$	−268.739	+	268.739i	−0.293703	+	0.293703i
$916$		0			0
$917$	−72.1610	+	72.1610i	−0.0786925	+	0.0786925i
$918$		0			0
$919$	−367.125			−0.399484			−0.199742	−	0.979849i	$-0.564010\pi$
$919$	−367.125			−0.399484			−0.199742	+	0.979849i	$0.564010\pi$
$920$		0			0
$921$			1014.45i			1.10146i
$922$		0			0
$923$	−1081.72	−	1081.72i	−1.17196	−	1.17196i
$924$		0			0
$925$	−20.9814	−	20.9814i	−0.0226825	−	0.0226825i
$926$		0			0
$927$		−	990.253i		−	1.06823i
$928$		0			0
$929$	1834.08			1.97426			0.987128	−	0.159935i	$-0.0511284\pi$
$929$	1834.08			1.97426			0.987128	+	0.159935i	$0.0511284\pi$
$930$		0			0
$931$	−776.229	+	776.229i	−0.833758	+	0.833758i
$932$		0			0
$933$	−447.883	+	447.883i	−0.480047	+	0.480047i
$934$		0			0
$935$	−326.476			−0.349172
$936$		0			0
$937$			483.901i			0.516437i	0.966087	+	0.258218i	$0.0831354\pi$
$937$			483.901i			0.516437i	−0.966087	+	0.258218i	$0.916865\pi$
$938$		0			0
$939$	−216.861	−	216.861i	−0.230949	−	0.230949i
$940$		0			0
$941$	−922.531	−	922.531i	−0.980373	−	0.980373i	0.0194384	−	0.999811i	$-0.493812\pi$
$941$	−922.531	−	922.531i	−0.980373	−	0.980373i	−0.999811	+	0.0194384i	$0.993812\pi$
$942$		0			0
$943$			1262.04i			1.33832i
$944$		0			0
$945$	34.4549			0.0364603
$946$		0			0
$947$	700.392	−	700.392i	0.739590	−	0.739590i	−0.232908	−	0.972499i	$-0.574824\pi$
$947$	700.392	−	700.392i	0.739590	−	0.739590i	0.972499	+	0.232908i	$0.0748242\pi$
$948$		0			0
$949$	187.676	−	187.676i	0.197762	−	0.197762i
$950$		0			0
$951$	417.569			0.439084
$952$		0			0
$953$		−	1187.64i		−	1.24622i	−0.782135	−	0.623108i	$-0.785869\pi$
$953$		−	1187.64i		−	1.24622i	0.782135	−	0.623108i	$-0.214131\pi$
$954$		0			0
$955$	−510.431	−	510.431i	−0.534482	−	0.534482i
$956$		0			0
$957$	133.223	+	133.223i	0.139209	+	0.139209i
$958$		0			0
$959$		−	115.204i		−	0.120129i
$960$		0			0
$961$	960.747			0.999737
$962$		0			0
$963$	484.276	−	484.276i	0.502883	−	0.502883i
$964$		0			0
$965$	12.7979	−	12.7979i	0.0132621	−	0.0132621i
$966$		0			0
$967$	−204.631			−0.211615			−0.105807	−	0.994387i	$-0.533743\pi$
$967$	−204.631			−0.211615			−0.105807	+	0.994387i	$0.533743\pi$
$968$		0			0
$969$		−	1200.38i		−	1.23879i
$970$		0			0
$971$	413.965	+	413.965i	0.426329	+	0.426329i	0.887376	−	0.461047i	$-0.152526\pi$
$971$	413.965	+	413.965i	0.426329	+	0.426329i	−0.461047	+	0.887376i	$0.652526\pi$
$972$		0			0
$973$	21.2795	+	21.2795i	0.0218700	+	0.0218700i
$974$		0			0
$975$		−	162.573i		−	0.166742i
$976$		0			0
$977$	−109.324			−0.111898			−0.0559489	−	0.998434i	$-0.517818\pi$
$977$	−109.324			−0.111898			−0.0559489	+	0.998434i	$0.517818\pi$
$978$		0			0
$979$	185.408	−	185.408i	0.189385	−	0.189385i
$980$		0			0
$981$	318.521	−	318.521i	0.324690	−	0.324690i
$982$		0			0
$983$	−381.738			−0.388340			−0.194170	−	0.980968i	$-0.562201\pi$
$983$	−381.738			−0.388340			−0.194170	+	0.980968i	$0.562201\pi$
$984$		0			0
$985$			343.679i			0.348913i
$986$		0			0
$987$	−25.5323	−	25.5323i	−0.0258686	−	0.0258686i
$988$		0			0
$989$	−92.4060	−	92.4060i	−0.0934338	−	0.0934338i
$990$		0			0
$991$		−	990.060i		−	0.999051i	−0.866299	−	0.499525i	$-0.833508\pi$
$991$		−	990.060i		−	0.999051i	0.866299	−	0.499525i	$-0.166492\pi$
$992$		0			0
$993$	−545.612			−0.549458
$994$		0			0
$995$	−281.111	+	281.111i	−0.282524	+	0.282524i
$996$		0			0
$997$	700.591	−	700.591i	0.702699	−	0.702699i	−0.262290	−	0.964989i	$-0.584478\pi$
$997$	700.591	−	700.591i	0.702699	−	0.702699i	0.964989	+	0.262290i	$0.0844777\pi$
$998$		0			0
$999$	165.648			0.165814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.r.a.111.11		32
4.3	odd	2		80.3.r.a.51.10	yes	32
8.3	odd	2		640.3.r.a.351.11		32
8.5	even	2		640.3.r.b.351.6		32
16.3	odd	4		640.3.r.b.31.6		32
16.5	even	4		80.3.r.a.11.10	✓	32
16.11	odd	4	inner	320.3.r.a.271.11		32
16.13	even	4		640.3.r.a.31.11		32
20.3	even	4		400.3.k.h.99.15		32
20.7	even	4		400.3.k.g.99.2		32
20.19	odd	2		400.3.r.f.51.7		32
80.37	odd	4		400.3.k.h.299.15		32
80.53	odd	4		400.3.k.g.299.2		32
80.69	even	4		400.3.r.f.251.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.r.a.11.10	✓	32	16.5	even	4
80.3.r.a.51.10	yes	32	4.3	odd	2
320.3.r.a.111.11		32	1.1	even	1	trivial
320.3.r.a.271.11		32	16.11	odd	4	inner
400.3.k.g.99.2		32	20.7	even	4
400.3.k.g.299.2		32	80.53	odd	4
400.3.k.h.99.15		32	20.3	even	4
400.3.k.h.299.15		32	80.37	odd	4
400.3.r.f.51.7		32	20.19	odd	2
400.3.r.f.251.7		32	80.69	even	4
640.3.r.a.31.11		32	16.13	even	4
640.3.r.a.351.11		32	8.3	odd	2
640.3.r.b.31.6		32	16.3	odd	4
640.3.r.b.351.6		32	8.5	even	2

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:	\( N \)	\(=\)	\( 320 = 2^{6} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	320.r (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40411 - 1.40411i) q^{3} +(-1.58114 + 1.58114i) q^{5} -0.552025 q^{7} +5.05693i q^{9} +O(q^{10})\)	\(q+(1.40411 - 1.40411i) q^{3} +(-1.58114 + 1.58114i) q^{5} -0.552025 q^{7} +5.05693i q^{9} +(3.85004 + 3.85004i) q^{11} +(11.5784 + 11.5784i) q^{13} +4.44020i q^{15} +26.8154 q^{17} +(15.9405 - 15.9405i) q^{19} +(-0.775106 + 0.775106i) q^{21} -26.3746 q^{23} -5.00000i q^{25} +(19.7375 + 19.7375i) q^{27} +(12.3220 + 12.3220i) q^{29} -0.502877i q^{31} +10.8118 q^{33} +(0.872828 - 0.872828i) q^{35} +(4.19627 - 4.19627i) q^{37} +32.5147 q^{39} -47.8505i q^{41} +(3.50360 + 3.50360i) q^{43} +(-7.99571 - 7.99571i) q^{45} +32.9404i q^{47} -48.6953 q^{49} +(37.6519 - 37.6519i) q^{51} +(-25.8335 + 25.8335i) q^{53} -12.1749 q^{55} -44.7647i q^{57} +(62.5409 + 62.5409i) q^{59} +(60.5240 + 60.5240i) q^{61} -2.79155i q^{63} -36.6140 q^{65} +(31.3820 - 31.3820i) q^{67} +(-37.0329 + 37.0329i) q^{69} -93.4260 q^{71} -16.2092i q^{73} +(-7.02057 - 7.02057i) q^{75} +(-2.12532 - 2.12532i) q^{77} -94.3792i q^{79} +9.91509 q^{81} +(-100.652 + 100.652i) q^{83} +(-42.3989 + 42.3989i) q^{85} +34.6031 q^{87} -48.1573i q^{89} +(-6.39155 - 6.39155i) q^{91} +(-0.706097 - 0.706097i) q^{93} +50.4084i q^{95} +99.3742 q^{97} +(-19.4694 + 19.4694i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 32 q^{11} + 32 q^{19} + 128 q^{23} + 96 q^{27} + 32 q^{29} - 96 q^{37} - 384 q^{39} - 96 q^{43} + 224 q^{49} + 256 q^{51} - 160 q^{53} + 352 q^{59} - 32 q^{61} - 160 q^{67} + 96 q^{69} - 256 q^{71} + 224 q^{77} - 288 q^{81} + 480 q^{83} + 160 q^{85} + 384 q^{91} + 96 q^{93} - 608 q^{99}+O(q^{100}) \) 32 * q - 32 * q^11 + 32 * q^19 + 128 * q^23 + 96 * q^27 + 32 * q^29 - 96 * q^37 - 384 * q^39 - 96 * q^43 + 224 * q^49 + 256 * q^51 - 160 * q^53 + 352 * q^59 - 32 * q^61 - 160 * q^67 + 96 * q^69 - 256 * q^71 + 224 * q^77 - 288 * q^81 + 480 * q^83 + 160 * q^85 + 384 * q^91 + 96 * q^93 - 608 * q^99

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