LMFDB - Embedded newform 320.3.h.g.319.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(319,320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(320, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("320.319");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.h (of order $2$, degree $1$, 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:	$6$
Coefficient field:	6.0.1827904.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 14x^{2} + 1 $ x^6 + 9x^4 + 14x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 160)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			319.6
Root			$2.65109i$ of defining polynomial
Character	$\chi$	$=$	320.319
Dual form			320.3.h.g.319.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.30219 q^{3} +(1.54778 + 4.75441i) q^{5} +0.206625 q^{7} +19.1132 q^{9} +O(q^{10})$	$q+5.30219 q^{3} +(1.54778 + 4.75441i) q^{5} +0.206625 q^{7} +19.1132 q^{9} -15.0176i q^{11} -11.6999i q^{13} +(8.20662 + 25.2087i) q^{15} +18.1911i q^{17} +19.3999i q^{19} +1.09556 q^{21} +27.2242 q^{23} +(-20.2087 + 14.7176i) q^{25} +53.6220 q^{27} -44.4175 q^{29} +20.3822i q^{31} -79.6262i q^{33} +(0.319810 + 0.982377i) q^{35} -18.1089i q^{37} -62.0352i q^{39} -32.3043 q^{41} -4.06244 q^{43} +(29.5830 + 90.8718i) q^{45} -5.37588 q^{47} -48.9573 q^{49} +96.4527i q^{51} -79.1703i q^{53} +(71.3999 - 23.2440i) q^{55} +102.862i q^{57} -83.3999i q^{59} +36.7486 q^{61} +3.94925 q^{63} +(55.6262 - 18.1089i) q^{65} -4.51518 q^{67} +144.348 q^{69} +41.6530i q^{71} -41.5910i q^{73} +(-107.151 + 78.0352i) q^{75} -3.10301i q^{77} -15.5473i q^{79} +112.295 q^{81} -50.9862 q^{83} +(-86.4880 + 28.1559i) q^{85} -235.510 q^{87} +10.8885 q^{89} -2.41749i q^{91} +108.070i q^{93} +(-92.2349 + 30.0268i) q^{95} +12.1559i q^{97} -287.035i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{3} + 2 q^{5} - 12 q^{7} + 18 q^{9}+O(q^{10}) $ 6 * q + 4 * q^3 + 2 * q^5 - 12 * q^7 + 18 * q^9	$ 6 q + 4 q^{3} + 2 q^{5} - 12 q^{7} + 18 q^{9} + 36 q^{15} - 8 q^{21} + 68 q^{23} - 10 q^{25} + 184 q^{27} - 44 q^{29} - 108 q^{35} - 68 q^{41} - 76 q^{43} + 6 q^{45} - 268 q^{47} - 62 q^{49} + 288 q^{55} + 100 q^{61} + 172 q^{63} + 308 q^{67} + 184 q^{69} - 284 q^{75} + 238 q^{81} - 204 q^{83} + 32 q^{85} - 584 q^{87} + 76 q^{89} + 32 q^{95}+O(q^{100}) $ 6 * q + 4 * q^3 + 2 * q^5 - 12 * q^7 + 18 * q^9 + 36 * q^15 - 8 * q^21 + 68 * q^23 - 10 * q^25 + 184 * q^27 - 44 * q^29 - 108 * q^35 - 68 * q^41 - 76 * q^43 + 6 * q^45 - 268 * q^47 - 62 * q^49 + 288 * q^55 + 100 * q^61 + 172 * q^63 + 308 * q^67 + 184 * q^69 - 284 * q^75 + 238 * q^81 - 204 * q^83 + 32 * q^85 - 584 * q^87 + 76 * q^89 + 32 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$257$	$261$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	5.30219			1.76740			0.883698	−	0.468058i	$-0.155046\pi$
$3$	5.30219			1.76740			0.883698	+	0.468058i	$0.155046\pi$
$4$		0			0
$5$	1.54778	+	4.75441i	0.309556	+	0.950881i
$5$	1.54778	+	4.75441i	0.309556	+	0.950881i
$6$		0			0
$7$	0.206625			0.0295178			0.0147589	−	0.999891i	$-0.495302\pi$
$7$	0.206625			0.0295178			0.0147589	+	0.999891i	$0.495302\pi$
$8$		0			0
$9$	19.1132			2.12369
$10$		0			0
$11$		−	15.0176i		−	1.36524i	−0.730774	−	0.682619i	$-0.760841\pi$
$11$		−	15.0176i		−	1.36524i	0.730774	−	0.682619i	$-0.239159\pi$
$12$		0			0
$13$		−	11.6999i		−	0.899995i	−0.893030	−	0.449998i	$-0.851425\pi$
$13$		−	11.6999i		−	0.899995i	0.893030	−	0.449998i	$-0.148575\pi$
$14$		0			0
$15$	8.20662	+	25.2087i	0.547108	+	1.68058i
$16$		0			0
$17$			18.1911i			1.07007i	0.844831	+	0.535033i	$0.179701\pi$
$17$			18.1911i			1.07007i	−0.844831	+	0.535033i	$0.820299\pi$
$18$		0			0
$19$			19.3999i			1.02105i	0.859864	+	0.510523i	$0.170548\pi$
$19$			19.3999i			1.02105i	−0.859864	+	0.510523i	$0.829452\pi$
$20$		0			0
$21$	1.09556			0.0521696
$22$		0			0
$23$	27.2242			1.18366			0.591831	−	0.806062i	$-0.298405\pi$
$23$	27.2242			1.18366			0.591831	+	0.806062i	$0.298405\pi$
$24$		0			0
$25$	−20.2087	+	14.7176i	−0.808350	+	0.588702i
$26$		0			0
$27$	53.6220			1.98600
$28$		0			0
$29$	−44.4175			−1.53164			−0.765819	−	0.643056i	$-0.777666\pi$
$29$	−44.4175			−1.53164			−0.765819	+	0.643056i	$0.777666\pi$
$30$		0			0
$31$			20.3822i			0.657492i	0.944418	+	0.328746i	$0.106626\pi$
$31$			20.3822i			0.657492i	−0.944418	+	0.328746i	$0.893374\pi$
$32$		0			0
$33$		−	79.6262i		−	2.41292i
$34$		0			0
$35$	0.319810	+	0.982377i	0.00913742	+	0.0280679i
$36$		0			0
$37$		−	18.1089i		−	0.489431i	−0.969595	−	0.244715i	$-0.921305\pi$
$37$		−	18.1089i		−	0.489431i	0.969595	−	0.244715i	$-0.0786945\pi$
$38$		0			0
$39$		−	62.0352i		−	1.59065i
$40$		0			0
$41$	−32.3043			−0.787910			−0.393955	−	0.919130i	$-0.628893\pi$
$41$	−32.3043			−0.787910			−0.393955	+	0.919130i	$0.628893\pi$
$42$		0			0
$43$	−4.06244			−0.0944753			−0.0472377	−	0.998884i	$-0.515042\pi$
$43$	−4.06244			−0.0944753			−0.0472377	+	0.998884i	$0.515042\pi$
$44$		0			0
$45$	29.5830	+	90.8718i	0.657401	+	2.01937i
$46$		0			0
$47$	−5.37588			−0.114380			−0.0571902	−	0.998363i	$-0.518214\pi$
$47$	−5.37588			−0.114380			−0.0571902	+	0.998363i	$0.518214\pi$
$48$		0			0
$49$	−48.9573			−0.999129
$50$		0			0
$51$			96.4527i			1.89123i
$52$		0			0
$53$		−	79.1703i		−	1.49378i	−0.664948	−	0.746890i	$-0.731546\pi$
$53$		−	79.1703i		−	1.49378i	0.664948	−	0.746890i	$-0.268454\pi$
$54$		0			0
$55$	71.3999	−	23.2440i	1.29818	−	0.422618i
$56$		0			0
$57$			102.862i			1.80459i
$58$		0			0
$59$		−	83.3999i		−	1.41356i	−0.707435	−	0.706779i	$-0.750148\pi$
$59$		−	83.3999i		−	1.41356i	0.707435	−	0.706779i	$-0.249852\pi$
$60$		0			0
$61$	36.7486			0.602435			0.301218	−	0.953555i	$-0.402607\pi$
$61$	36.7486			0.602435			0.301218	+	0.953555i	$0.402607\pi$
$62$		0			0
$63$	3.94925			0.0626866
$64$		0			0
$65$	55.6262	−	18.1089i	0.855788	−	0.278599i
$66$		0			0
$67$	−4.51518			−0.0673907			−0.0336954	−	0.999432i	$-0.510728\pi$
$67$	−4.51518			−0.0673907			−0.0336954	+	0.999432i	$0.510728\pi$
$68$		0			0
$69$	144.348			2.09200
$70$		0			0
$71$			41.6530i			0.586662i	0.956011	+	0.293331i	$0.0947638\pi$
$71$			41.6530i			0.586662i	−0.956011	+	0.293331i	$0.905236\pi$
$72$		0			0
$73$		−	41.5910i		−	0.569740i	−0.958566	−	0.284870i	$-0.908050\pi$
$73$		−	41.5910i		−	0.569740i	0.958566	−	0.284870i	$-0.0919504\pi$
$74$		0			0
$75$	−107.151	+	78.0352i	−1.42867	+	1.04047i
$76$		0			0
$77$		−	3.10301i		−	0.0402988i
$78$		0			0
$79$		−	15.5473i		−	0.196801i	−0.995147	−	0.0984004i	$-0.968627\pi$
$79$		−	15.5473i		−	0.196801i	0.995147	−	0.0984004i	$-0.0313726\pi$
$80$		0			0
$81$	112.295			1.38636
$82$		0			0
$83$	−50.9862			−0.614291			−0.307146	−	0.951663i	$-0.599374\pi$
$83$	−50.9862			−0.614291			−0.307146	+	0.951663i	$0.599374\pi$
$84$		0			0
$85$	−86.4880	+	28.1559i	−1.01751	+	0.331246i
$86$		0			0
$87$	−235.510			−2.70701
$88$		0			0
$89$	10.8885			0.122343			0.0611713	−	0.998127i	$-0.480516\pi$
$89$	10.8885			0.122343			0.0611713	+	0.998127i	$0.480516\pi$
$90$		0			0
$91$		−	2.41749i		−	0.0265659i
$92$		0			0
$93$			108.070i			1.16205i
$94$		0			0
$95$	−92.2349	+	30.0268i	−0.970893	+	0.316071i
$96$		0			0
$97$			12.1559i			0.125318i	0.998035	+	0.0626592i	$0.0199581\pi$
$97$			12.1559i			0.125318i	−0.998035	+	0.0626592i	$0.980042\pi$
$98$		0			0
$99$		−	287.035i		−	2.89934i
$100$		0			0
$101$	−127.723			−1.26459			−0.632294	−	0.774728i	$-0.717887\pi$
$101$	−127.723			−1.26459			−0.632294	+	0.774728i	$0.717887\pi$
$102$		0			0
$103$	−4.77575			−0.0463665			−0.0231833	−	0.999731i	$-0.507380\pi$
$103$	−4.77575			−0.0463665			−0.0231833	+	0.999731i	$0.507380\pi$
$104$		0			0
$105$	1.69569	+	5.20875i	0.0161494	+	0.0496071i
$106$		0			0
$107$	107.213			1.00199			0.500997	−	0.865449i	$-0.332967\pi$
$107$	107.213			1.00199			0.500997	+	0.865449i	$0.332967\pi$
$108$		0			0
$109$	−53.6689			−0.492376			−0.246188	−	0.969222i	$-0.579178\pi$
$109$	−53.6689			−0.492376			−0.246188	+	0.969222i	$0.579178\pi$
$110$		0			0
$111$		−	96.0170i		−	0.865018i
$112$		0			0
$113$		−	20.5063i		−	0.181471i	−0.995875	−	0.0907356i	$-0.971078\pi$
$113$		−	20.5063i		−	0.181471i	0.995875	−	0.0907356i	$-0.0289218\pi$
$114$		0			0
$115$	42.1372	+	129.435i	0.366410	+	1.12552i
$116$		0			0
$117$		−	223.623i		−	1.91131i
$118$		0			0
$119$			3.75873i			0.0315860i
$120$		0			0
$121$	−104.529			−0.863876
$122$		0			0
$123$	−171.283			−1.39255
$124$		0			0
$125$	−101.252	−	73.3010i	−0.810016	−	0.586408i
$126$		0			0
$127$	138.477			1.09037			0.545184	−	0.838316i	$-0.316460\pi$
$127$	138.477			1.09037			0.545184	+	0.838316i	$0.316460\pi$
$128$		0			0
$129$	−21.5398			−0.166975
$130$		0			0
$131$		−	219.105i		−	1.67256i	−0.548304	−	0.836279i	$-0.684726\pi$
$131$		−	219.105i		−	1.67256i	0.548304	−	0.836279i	$-0.315274\pi$
$132$		0			0
$133$			4.00849i			0.0301390i
$134$		0			0
$135$	82.9951	+	254.941i	0.614779	+	1.88845i
$136$		0			0
$137$			59.7821i			0.436366i	0.975908	+	0.218183i	$0.0700129\pi$
$137$			59.7821i			0.436366i	−0.975908	+	0.218183i	$0.929987\pi$
$138$		0			0
$139$			26.6524i			0.191744i	0.995394	+	0.0958718i	$0.0305639\pi$
$139$			26.6524i			0.191744i	−0.995394	+	0.0958718i	$0.969436\pi$
$140$		0			0
$141$	−28.5039			−0.202155
$142$		0			0
$143$	−175.705			−1.22871
$144$		0			0
$145$	−68.7486	−	211.179i	−0.474128	−	1.45641i
$146$		0			0
$147$	−259.581			−1.76586
$148$		0			0
$149$	−143.463			−0.962838			−0.481419	−	0.876490i	$-0.659879\pi$
$149$	−143.463			−0.962838			−0.481419	+	0.876490i	$0.659879\pi$
$150$		0			0
$151$			83.4937i			0.552939i	0.961023	+	0.276469i	$0.0891644\pi$
$151$			83.4937i			0.552939i	−0.961023	+	0.276469i	$0.910836\pi$
$152$		0			0
$153$			347.690i			2.27249i
$154$		0			0
$155$	−96.9055	+	31.5473i	−0.625197	+	0.203531i
$156$		0			0
$157$			169.673i			1.08072i	0.841434	+	0.540360i	$0.181712\pi$
$157$			169.673i			1.08072i	−0.841434	+	0.540360i	$0.818288\pi$
$158$		0			0
$159$		−	419.776i		−	2.64010i
$160$		0			0
$161$	5.62520			0.0349391
$162$		0			0
$163$	275.478			1.69005			0.845026	−	0.534726i	$-0.179585\pi$
$163$	275.478			1.69005			0.845026	+	0.534726i	$0.179585\pi$
$164$		0			0
$165$	378.575	−	123.244i	2.29440	−	0.746933i
$166$		0			0
$167$	−132.481			−0.793299			−0.396650	−	0.917970i	$-0.629827\pi$
$167$	−132.481			−0.793299			−0.396650	+	0.917970i	$0.629827\pi$
$168$		0			0
$169$	32.1115			0.190009
$170$		0			0
$171$			370.793i			2.16838i
$172$		0			0
$173$			272.614i			1.57580i	0.615801	+	0.787901i	$0.288832\pi$
$173$			272.614i			1.57580i	−0.615801	+	0.787901i	$0.711168\pi$
$174$		0			0
$175$	−4.17562	+	3.04101i	−0.0238607	+	0.0173772i
$176$		0			0
$177$		−	442.202i		−	2.49831i
$178$		0			0
$179$			157.523i			0.880014i	0.897994	+	0.440007i	$0.145024\pi$
$179$			157.523i			0.880014i	−0.897994	+	0.440007i	$0.854976\pi$
$180$		0			0
$181$	335.063			1.85118			0.925590	−	0.378529i	$-0.123570\pi$
$181$	335.063			1.85118			0.925590	+	0.378529i	$0.123570\pi$
$182$		0			0
$183$	194.848			1.06474
$184$		0			0
$185$	86.0972	−	28.0287i	0.465391	−	0.151506i
$186$		0			0
$187$	273.187			1.46090
$188$		0			0
$189$	11.0796			0.0586223
$190$		0			0
$191$			298.575i			1.56322i	0.623766	+	0.781611i	$0.285602\pi$
$191$			298.575i			1.56322i	−0.623766	+	0.781611i	$0.714398\pi$
$192$		0			0
$193$			191.915i			0.994376i	0.867643	+	0.497188i	$0.165634\pi$
$193$			191.915i			0.994376i	−0.867643	+	0.497188i	$0.834366\pi$
$194$		0			0
$195$	294.941	−	96.0170i	1.51252	−	0.492395i
$196$		0			0
$197$			59.2472i			0.300747i	0.988629	+	0.150374i	$0.0480477\pi$
$197$			59.2472i			0.300747i	−0.988629	+	0.150374i	$0.951952\pi$
$198$		0			0
$199$		−	309.100i		−	1.55327i	−0.629953	−	0.776633i	$-0.716926\pi$
$199$		−	309.100i		−	1.55327i	0.629953	−	0.776633i	$-0.283074\pi$
$200$		0			0
$201$	−23.9403			−0.119106
$202$		0			0
$203$	−9.17775			−0.0452106
$204$		0			0
$205$	−50.0000	−	153.588i	−0.243902	−	0.749209i
$206$		0			0
$207$	520.342			2.51373
$208$		0			0
$209$	291.340			1.39397
$210$		0			0
$211$			205.693i			0.974850i	0.873165	+	0.487425i	$0.162064\pi$
$211$			205.693i			0.974850i	−0.873165	+	0.487425i	$0.837936\pi$
$212$		0			0
$213$			220.852i			1.03686i
$214$		0			0
$215$	−6.28777	−	19.3145i	−0.0292454	−	0.0898348i
$216$		0			0
$217$			4.21147i			0.0194077i
$218$		0			0
$219$		−	220.523i		−	1.00696i
$220$		0			0
$221$	212.835			0.963054
$222$		0			0
$223$	228.723			1.02567			0.512833	−	0.858488i	$-0.328596\pi$
$223$	228.723			1.02567			0.512833	+	0.858488i	$0.328596\pi$
$224$		0			0
$225$	−386.254	+	281.299i	−1.71668	+	1.25022i
$226$		0			0
$227$	−282.403			−1.24407			−0.622033	−	0.782991i	$-0.713693\pi$
$227$	−282.403			−1.24407			−0.622033	+	0.782991i	$0.713693\pi$
$228$		0			0
$229$	−49.2525			−0.215076			−0.107538	−	0.994201i	$-0.534297\pi$
$229$	−49.2525			−0.215076			−0.107538	+	0.994201i	$0.534297\pi$
$230$		0			0
$231$		−	16.4527i		−	0.0712240i
$232$		0			0
$233$		−	124.273i		−	0.533363i	−0.963785	−	0.266681i	$-0.914073\pi$
$233$		−	124.273i		−	0.533363i	0.963785	−	0.266681i	$-0.0859271\pi$
$234$		0			0
$235$	−8.32069	−	25.5591i	−0.0354072	−	0.108762i
$236$		0			0
$237$		−	82.4345i		−	0.347825i
$238$		0			0
$239$			80.4527i			0.336622i	0.985734	+	0.168311i	$0.0538313\pi$
$239$			80.4527i			0.336622i	−0.985734	+	0.168311i	$0.946169\pi$
$240$		0			0
$241$	−1.20979			−0.00501988			−0.00250994	−	0.999997i	$-0.500799\pi$
$241$	−1.20979			−0.00501988			−0.00250994	+	0.999997i	$0.500799\pi$
$242$		0			0
$243$	112.812			0.464247
$244$		0			0
$245$	−75.7752	−	232.763i	−0.309287	−	0.950053i
$246$		0			0
$247$	226.977			0.918936
$248$		0			0
$249$	−270.338			−1.08570
$250$		0			0
$251$		−	211.853i		−	0.844034i	−0.906588	−	0.422017i	$-0.861322\pi$
$251$		−	211.853i		−	0.844034i	0.906588	−	0.422017i	$-0.138678\pi$
$252$		0			0
$253$		−	408.843i		−	1.61598i
$254$		0			0
$255$	−458.575	+	149.288i	−1.79834	+	0.585442i
$256$		0			0
$257$			182.646i			0.710685i	0.934736	+	0.355342i	$0.115636\pi$
$257$			182.646i			0.710685i	−0.934736	+	0.355342i	$0.884364\pi$
$258$		0			0
$259$		−	3.74175i		−	0.0144469i
$260$		0			0
$261$	−848.960			−3.25272
$262$		0			0
$263$	−74.6636			−0.283892			−0.141946	−	0.989874i	$-0.545336\pi$
$263$	−74.6636			−0.283892			−0.141946	+	0.989874i	$0.545336\pi$
$264$		0			0
$265$	376.408	−	122.538i	1.42041	−	0.462409i
$266$		0			0
$267$	57.7329			0.216228
$268$		0			0
$269$	184.089			0.684344			0.342172	−	0.939637i	$-0.388837\pi$
$269$	184.089			0.684344			0.342172	+	0.939637i	$0.388837\pi$
$270$		0			0
$271$			234.746i			0.866222i	0.901341	+	0.433111i	$0.142584\pi$
$271$			234.746i			0.866222i	−0.901341	+	0.433111i	$0.857416\pi$
$272$		0			0
$273$		−	12.8180i		−	0.0469524i
$274$		0			0
$275$	221.023	+	303.487i	0.803719	+	1.10359i
$276$		0			0
$277$			452.208i			1.63252i	0.577684	+	0.816260i	$0.303957\pi$
$277$			452.208i			1.63252i	−0.577684	+	0.816260i	$0.696043\pi$
$278$		0			0
$279$			389.570i			1.39631i
$280$		0			0
$281$	−196.110			−0.697900			−0.348950	−	0.937141i	$-0.613462\pi$
$281$	−196.110			−0.697900			−0.348950	+	0.937141i	$0.613462\pi$
$282$		0			0
$283$	418.449			1.47862			0.739309	−	0.673366i	$-0.235152\pi$
$283$	418.449			1.47862			0.739309	+	0.673366i	$0.235152\pi$
$284$		0			0
$285$	−489.046	+	159.207i	−1.71595	+	0.558623i
$286$		0			0
$287$	−6.67486			−0.0232574
$288$		0			0
$289$	−41.9170			−0.145042
$290$		0			0
$291$			64.4527i			0.221487i
$292$		0			0
$293$		−	286.666i		−	0.978383i	−0.872176	−	0.489191i	$-0.837292\pi$
$293$		−	286.666i		−	0.978383i	0.872176	−	0.489191i	$-0.162708\pi$
$294$		0			0
$295$	396.517	−	129.085i	1.34412	−	0.437575i
$296$		0			0
$297$		−	805.275i		−	2.71136i
$298$		0			0
$299$		−	318.522i		−	1.06529i
$300$		0			0
$301$	−0.839400			−0.00278870
$302$		0			0
$303$	−677.214			−2.23503
$304$		0			0
$305$	56.8787	+	174.718i	0.186488	+	0.572844i
$306$		0			0
$307$	−261.715			−0.852493			−0.426247	−	0.904607i	$-0.640164\pi$
$307$	−261.715			−0.852493			−0.426247	+	0.904607i	$0.640164\pi$
$308$		0			0
$309$	−25.3219			−0.0819480
$310$		0			0
$311$		−	578.904i		−	1.86143i	−0.365747	−	0.930714i	$-0.619187\pi$
$311$		−	578.904i		−	1.86143i	0.365747	−	0.930714i	$-0.380813\pi$
$312$		0			0
$313$			99.3124i			0.317292i	0.987336	+	0.158646i	$0.0507129\pi$
$313$			99.3124i			0.317292i	−0.987336	+	0.158646i	$0.949287\pi$
$314$		0			0
$315$	6.11258	+	18.7764i	0.0194050	+	0.0596075i
$316$		0			0
$317$			191.623i			0.604489i	0.953230	+	0.302245i	$0.0977359\pi$
$317$			191.623i			0.604489i	−0.953230	+	0.302245i	$0.902264\pi$
$318$		0			0
$319$			667.045i			2.09105i
$320$		0			0
$321$	568.466			1.77092
$322$		0			0
$323$	−352.905			−1.09259
$324$		0			0
$325$	172.194	+	236.441i	0.529829	+	0.727511i
$326$		0			0
$327$	−284.563			−0.870222
$328$		0			0
$329$	−1.11079			−0.00337626
$330$		0			0
$331$		−	530.187i		−	1.60177i	−0.598816	−	0.800886i	$-0.704362\pi$
$331$		−	530.187i		−	1.60177i	0.598816	−	0.800886i	$-0.295638\pi$
$332$		0			0
$333$		−	346.120i		−	1.03940i
$334$		0			0
$335$	−6.98851	−	21.4670i	−0.0208612	−	0.0640806i
$336$		0			0
$337$			487.427i			1.44637i	0.690653	+	0.723186i	$0.257323\pi$
$337$			487.427i			1.44637i	−0.690653	+	0.723186i	$0.742677\pi$
$338$		0			0
$339$		−	108.728i		−	0.320731i
$340$		0			0
$341$	306.093			0.897633
$342$		0			0
$343$	−20.2404			−0.0590099
$344$		0			0
$345$	223.419	+	686.289i	0.647592	+	1.98924i
$346$		0			0
$347$	−310.497			−0.894804			−0.447402	−	0.894333i	$-0.647651\pi$
$347$	−310.497			−0.894804			−0.447402	+	0.894333i	$0.647651\pi$
$348$		0			0
$349$	253.004			0.724941			0.362471	−	0.931995i	$-0.381933\pi$
$349$	253.004			0.724941			0.362471	+	0.931995i	$0.381933\pi$
$350$		0			0
$351$		−	627.374i		−	1.78739i
$352$		0			0
$353$		−	322.639i		−	0.913992i	−0.889469	−	0.456996i	$-0.848925\pi$
$353$		−	322.639i		−	0.913992i	0.889469	−	0.456996i	$-0.151075\pi$
$354$		0			0
$355$	−198.035	+	64.4697i	−0.557846	+	0.181605i
$356$		0			0
$357$			19.9295i			0.0558250i
$358$		0			0
$359$		−	254.975i		−	0.710236i	−0.934822	−	0.355118i	$-0.884441\pi$
$359$		−	254.975i		−	0.710236i	0.934822	−	0.355118i	$-0.115559\pi$
$360$		0			0
$361$	−15.3550			−0.0425347
$362$		0			0
$363$	−554.232			−1.52681
$364$		0			0
$365$	197.740	−	64.3738i	0.541755	−	0.176366i
$366$		0			0
$367$	207.935			0.566581			0.283291	−	0.959034i	$-0.408574\pi$
$367$	207.935			0.566581			0.283291	+	0.959034i	$0.408574\pi$
$368$		0			0
$369$	−617.438			−1.67327
$370$		0			0
$371$		−	16.3585i		−	0.0440931i
$372$		0			0
$373$		−	203.826i		−	0.546450i	−0.961950	−	0.273225i	$-0.911910\pi$
$373$		−	203.826i		−	0.546450i	0.961950	−	0.273225i	$-0.0880903\pi$
$374$		0			0
$375$	−536.857	−	388.656i	−1.43162	−	1.03642i
$376$		0			0
$377$			519.682i			1.37847i
$378$		0			0
$379$			454.099i			1.19815i	0.800692	+	0.599076i	$0.204465\pi$
$379$			454.099i			1.19815i	−0.800692	+	0.599076i	$0.795535\pi$
$380$		0			0
$381$	734.229			1.92711
$382$		0			0
$383$	541.569			1.41402			0.707009	−	0.707205i	$-0.250044\pi$
$383$	541.569			1.41402			0.707009	+	0.707205i	$0.250044\pi$
$384$		0			0
$385$	14.7530	−	4.80278i	0.0383194	−	0.0124748i
$386$		0			0
$387$	−77.6462			−0.200636
$388$		0			0
$389$	423.431			1.08851			0.544256	−	0.838919i	$-0.316812\pi$
$389$	423.431			1.08851			0.544256	+	0.838919i	$0.316812\pi$
$390$		0			0
$391$			495.240i			1.26660i
$392$		0			0
$393$		−	1161.74i		−	2.95607i
$394$		0			0
$395$	73.9180	−	24.0638i	0.187134	−	0.0609209i
$396$		0			0
$397$		−	11.7772i		−	0.0296654i	−0.999890	−	0.0148327i	$-0.995278\pi$
$397$		−	11.7772i		−	0.0296654i	0.999890	−	0.0148327i	$-0.00472157\pi$
$398$		0			0
$399$			21.2538i			0.0532676i
$400$		0			0
$401$	127.442			0.317809			0.158905	−	0.987294i	$-0.449204\pi$
$401$	127.442			0.317809			0.158905	+	0.987294i	$0.449204\pi$
$402$		0			0
$403$	238.471			0.591739
$404$		0			0
$405$	173.808	+	533.897i	0.429156	+	1.31826i
$406$		0			0
$407$	−271.953			−0.668190
$408$		0			0
$409$	608.012			1.48658			0.743290	−	0.668969i	$-0.233264\pi$
$409$	608.012			1.48658			0.743290	+	0.668969i	$0.233264\pi$
$410$		0			0
$411$			316.976i			0.771231i
$412$		0			0
$413$		−	17.2325i		−	0.0417251i
$414$		0			0
$415$	−78.9155	−	242.409i	−0.190158	−	0.584118i
$416$		0			0
$417$			141.316i			0.338887i
$418$		0			0
$419$			565.630i			1.34995i	0.737840	+	0.674976i	$0.235846\pi$
$419$			565.630i			1.34995i	−0.737840	+	0.674976i	$0.764154\pi$
$420$		0			0
$421$	−711.356			−1.68968			−0.844841	−	0.535018i	$-0.820305\pi$
$421$	−711.356			−1.68968			−0.844841	+	0.535018i	$0.820305\pi$
$422$		0			0
$423$	−102.750			−0.242908
$424$		0			0
$425$	−267.729	−	367.620i	−0.629950	−	0.864988i
$426$		0			0
$427$	7.59316			0.0177826
$428$		0			0
$429$	−931.622			−2.17161
$430$		0			0
$431$		−	309.254i		−	0.717526i	−0.933429	−	0.358763i	$-0.883199\pi$
$431$		−	309.254i		−	0.717526i	0.933429	−	0.358763i	$-0.116801\pi$
$432$		0			0
$433$			187.374i			0.432735i	0.976312	+	0.216368i	$0.0694210\pi$
$433$			187.374i			0.432735i	−0.976312	+	0.216368i	$0.930579\pi$
$434$		0			0
$435$	−364.518	−	1119.71i	−0.837972	−	2.57404i
$436$		0			0
$437$			528.147i			1.20857i
$438$		0			0
$439$		−	289.657i		−	0.659811i	−0.944014	−	0.329906i	$-0.892983\pi$
$439$		−	289.657i		−	0.659811i	0.944014	−	0.329906i	$-0.107017\pi$
$440$		0			0
$441$	−935.730			−2.12184
$442$		0			0
$443$	−295.516			−0.667079			−0.333539	−	0.942736i	$-0.608243\pi$
$443$	−295.516			−0.667079			−0.333539	+	0.942736i	$0.608243\pi$
$444$		0			0
$445$	16.8530	+	51.7683i	0.0378719	+	0.116333i
$446$		0			0
$447$	−760.667			−1.70172
$448$		0			0
$449$	−604.409			−1.34612			−0.673061	−	0.739587i	$-0.735021\pi$
$449$	−604.409			−1.34612			−0.673061	+	0.739587i	$0.735021\pi$
$450$		0			0
$451$			485.134i			1.07569i
$452$		0			0
$453$			442.699i			0.977262i
$454$		0			0
$455$	11.4937	−	3.74175i	0.0252610	−	0.00822363i
$456$		0			0
$457$		−	392.507i		−	0.858877i	−0.903096	−	0.429438i	$-0.858712\pi$
$457$		−	392.507i		−	0.858877i	0.903096	−	0.429438i	$-0.141288\pi$
$458$		0			0
$459$			975.444i			2.12515i
$460$		0			0
$461$	400.277			0.868279			0.434139	−	0.900846i	$-0.357053\pi$
$461$	400.277			0.868279			0.434139	+	0.900846i	$0.357053\pi$
$462$		0			0
$463$	−732.679			−1.58246			−0.791230	−	0.611518i	$-0.790559\pi$
$463$	−732.679			−1.58246			−0.791230	+	0.611518i	$0.790559\pi$
$464$		0			0
$465$	−513.811	+	167.269i	−1.10497	+	0.359719i
$466$		0			0
$467$	592.126			1.26794			0.633968	−	0.773360i	$-0.281425\pi$
$467$	592.126			1.26794			0.633968	+	0.773360i	$0.281425\pi$
$468$		0			0
$469$	−0.932947			−0.00198923
$470$		0			0
$471$			899.639i			1.91006i
$472$		0			0
$473$			61.0082i			0.128981i
$474$		0			0
$475$	−285.519	−	392.047i	−0.601092	−	0.825362i
$476$		0			0
$477$		−	1513.20i		−	3.17232i
$478$		0			0
$479$		−	309.151i		−	0.645409i	−0.946500	−	0.322705i	$-0.895408\pi$
$479$		−	309.151i		−	0.645409i	0.946500	−	0.322705i	$-0.104592\pi$
$480$		0			0
$481$	−211.873			−0.440485
$482$		0			0
$483$	29.8259			0.0617513
$484$		0			0
$485$	−57.7940	+	18.8146i	−0.119163	+	0.0387931i
$486$		0			0
$487$	570.769			1.17201			0.586005	−	0.810307i	$-0.300700\pi$
$487$	570.769			1.17201			0.586005	+	0.810307i	$0.300700\pi$
$488$		0			0
$489$	1460.64			2.98699
$490$		0			0
$491$		−	301.659i		−	0.614378i	−0.951649	−	0.307189i	$-0.900612\pi$
$491$		−	301.659i		−	0.614378i	0.951649	−	0.307189i	$-0.0993883\pi$
$492$		0			0
$493$		−	808.004i		−	1.63895i
$494$		0			0
$495$	1364.68	−	444.267i	2.75693	−	0.897509i
$496$		0			0
$497$			8.60653i			0.0173170i
$498$		0			0
$499$		−	517.758i		−	1.03759i	−0.854898	−	0.518795i	$-0.826381\pi$
$499$		−	517.758i		−	1.03759i	0.854898	−	0.518795i	$-0.173619\pi$
$500$		0			0
$501$	−702.439			−1.40207
$502$		0			0
$503$	406.671			0.808491			0.404246	−	0.914650i	$-0.367534\pi$
$503$	406.671			0.808491			0.404246	+	0.914650i	$0.367534\pi$
$504$		0			0
$505$	−197.688	−	607.249i	−0.391461	−	1.20247i
$506$		0			0
$507$	170.261			0.335821
$508$		0			0
$509$	−627.097			−1.23202			−0.616009	−	0.787739i	$-0.711252\pi$
$509$	−627.097			−1.23202			−0.616009	+	0.787739i	$0.711252\pi$
$510$		0			0
$511$		−	8.59372i		−	0.0168175i
$512$		0			0
$513$			1040.26i			2.02780i
$514$		0			0
$515$	−7.39182	−	22.7059i	−0.0143530	−	0.0440891i
$516$		0			0
$517$			80.7330i			0.156157i
$518$		0			0
$519$			1445.45i			2.78507i
$520$		0			0
$521$	−111.743			−0.214478			−0.107239	−	0.994233i	$-0.534201\pi$
$521$	−111.743			−0.214478			−0.107239	+	0.994233i	$0.534201\pi$
$522$		0			0
$523$	769.813			1.47192			0.735959	−	0.677027i	$-0.236732\pi$
$523$	769.813			1.47192			0.735959	+	0.677027i	$0.236732\pi$
$524$		0			0
$525$	−22.1399	+	16.1240i	−0.0421713	+	0.0307124i
$526$		0			0
$527$	−370.776			−0.703560
$528$		0			0
$529$	212.160			0.401058
$530$		0			0
$531$		−	1594.04i		−	3.00195i
$532$		0			0
$533$			377.958i			0.709115i
$534$		0			0
$535$	165.943	+	509.736i	0.310174	+	0.952778i
$536$		0			0
$537$			835.214i			1.55533i
$538$		0			0
$539$			735.222i			1.36405i
$540$		0			0
$541$	225.558			0.416927			0.208463	−	0.978030i	$-0.433154\pi$
$541$	225.558			0.416927			0.208463	+	0.978030i	$0.433154\pi$
$542$		0			0
$543$	1776.57			3.27177
$544$		0			0
$545$	−83.0678	−	255.164i	−0.152418	−	0.468191i
$546$		0			0
$547$	882.346			1.61306			0.806532	−	0.591190i	$-0.201342\pi$
$547$	882.346			1.61306			0.806532	+	0.591190i	$0.201342\pi$
$548$		0			0
$549$	702.382			1.27938
$550$		0			0
$551$		−	861.694i		−	1.56387i
$552$		0			0
$553$		−	3.21245i		−	0.00580913i
$554$		0			0
$555$	456.504	−	148.613i	0.822529	−	0.267772i
$556$		0			0
$557$			303.119i			0.544199i	0.962269	+	0.272100i	$0.0877180\pi$
$557$			303.119i			0.544199i	−0.962269	+	0.272100i	$0.912282\pi$
$558$		0			0
$559$			47.5303i			0.0850273i
$560$		0			0
$561$	1448.49			2.58198
$562$		0			0
$563$	−344.003			−0.611017			−0.305508	−	0.952189i	$-0.598826\pi$
$563$	−344.003			−0.611017			−0.305508	+	0.952189i	$0.598826\pi$
$564$		0			0
$565$	97.4950	−	31.7392i	0.172558	−	0.0561756i
$566$		0			0
$567$	23.2029			0.0409223
$568$		0			0
$569$	−228.925			−0.402329			−0.201165	−	0.979557i	$-0.564473\pi$
$569$	−228.925			−0.402329			−0.201165	+	0.979557i	$0.564473\pi$
$570$		0			0
$571$			371.169i			0.650033i	0.945708	+	0.325017i	$0.105370\pi$
$571$			371.169i			0.650033i	−0.945708	+	0.325017i	$0.894630\pi$
$572$		0			0
$573$			1583.10i			2.76283i
$574$		0			0
$575$	−550.168	+	400.674i	−0.956814	+	0.696825i
$576$		0			0
$577$			580.289i			1.00570i	0.864374	+	0.502850i	$0.167715\pi$
$577$			580.289i			1.00570i	−0.864374	+	0.502850i	$0.832285\pi$
$578$		0			0
$579$			1017.57i			1.75746i
$580$		0			0
$581$	−10.5350			−0.0181325
$582$		0			0
$583$	−1188.95			−2.03936
$584$		0			0
$585$	1063.19	−	346.120i	1.81743	−	0.591657i
$586$		0			0
$587$	65.0801			0.110869			0.0554345	−	0.998462i	$-0.482346\pi$
$587$	65.0801			0.110869			0.0554345	+	0.998462i	$0.482346\pi$
$588$		0			0
$589$	−395.413			−0.671329
$590$		0			0
$591$			314.140i			0.531539i
$592$		0			0
$593$		−	1002.90i		−	1.69124i	−0.533787	−	0.845619i	$-0.679232\pi$
$593$		−	1002.90i		−	1.69124i	0.533787	−	0.845619i	$-0.320768\pi$
$594$		0			0
$595$	−17.8705	+	5.81770i	−0.0300345	+	0.00977764i
$596$		0			0
$597$		−	1638.91i		−	2.74524i
$598$		0			0
$599$			888.567i			1.48342i	0.670722	+	0.741709i	$0.265984\pi$
$599$			888.567i			1.48342i	−0.670722	+	0.741709i	$0.734016\pi$
$600$		0			0
$601$	132.065			0.219742			0.109871	−	0.993946i	$-0.464956\pi$
$601$	132.065			0.219742			0.109871	+	0.993946i	$0.464956\pi$
$602$		0			0
$603$	−86.2995			−0.143117
$604$		0			0
$605$	−161.788	−	496.973i	−0.267418	−	0.821443i
$606$		0			0
$607$	−700.090			−1.15336			−0.576680	−	0.816970i	$-0.695652\pi$
$607$	−700.090			−1.15336			−0.576680	+	0.816970i	$0.695652\pi$
$608$		0			0
$609$	−48.6621			−0.0799050
$610$		0			0
$611$			62.8975i			0.102942i
$612$		0			0
$613$			727.420i			1.18666i	0.804961	+	0.593328i	$0.202186\pi$
$613$			727.420i			1.18666i	−0.804961	+	0.593328i	$0.797814\pi$
$614$		0			0
$615$	−265.109	−	814.351i	−0.431072	−	1.32415i
$616$		0			0
$617$		−	99.7137i		−	0.161611i	−0.996730	−	0.0808053i	$-0.974251\pi$
$617$		−	99.7137i		−	0.161611i	0.996730	−	0.0808053i	$-0.0257492\pi$
$618$		0			0
$619$		−	721.349i		−	1.16535i	−0.812707	−	0.582673i	$-0.802007\pi$
$619$		−	721.349i		−	1.16535i	0.812707	−	0.582673i	$-0.197993\pi$
$620$		0			0
$621$	1459.82			2.35075
$622$		0			0
$623$	2.24983			0.00361129
$624$		0			0
$625$	191.787	−	594.847i	0.306859	−	0.951755i
$626$		0			0
$627$	1544.74			2.46370
$628$		0			0
$629$	329.422			0.523723
$630$		0			0
$631$		−	796.856i		−	1.26285i	−0.775438	−	0.631423i	$-0.782471\pi$
$631$		−	796.856i		−	1.26285i	0.775438	−	0.631423i	$-0.217529\pi$
$632$		0			0
$633$			1090.62i			1.72295i
$634$		0			0
$635$	214.332	+	658.375i	0.337530	+	1.03681i
$636$		0			0
$637$			572.797i			0.899211i
$638$		0			0
$639$			796.121i			1.24589i
$640$		0			0
$641$	205.013			0.319833			0.159917	−	0.987131i	$-0.448877\pi$
$641$	205.013			0.319833			0.159917	+	0.987131i	$0.448877\pi$
$642$		0			0
$643$	−495.044			−0.769897			−0.384949	−	0.922938i	$-0.625781\pi$
$643$	−495.044			−0.769897			−0.384949	+	0.922938i	$0.625781\pi$
$644$		0			0
$645$	−33.3389	−	102.409i	−0.0516882	−	0.158774i
$646$		0			0
$647$	1121.84			1.73391			0.866953	−	0.498389i	$-0.166075\pi$
$647$	1121.84			1.73391			0.866953	+	0.498389i	$0.166075\pi$
$648$		0			0
$649$	−1252.47			−1.92984
$650$		0			0
$651$			22.3300i			0.0343011i
$652$		0			0
$653$			622.987i			0.954038i	0.878893	+	0.477019i	$0.158283\pi$
$653$			622.987i			0.954038i	−0.878893	+	0.477019i	$0.841717\pi$
$654$		0			0
$655$	1041.71	−	339.127i	1.59040	−	0.517751i
$656$		0			0
$657$		−	794.936i		−	1.20995i
$658$		0			0
$659$			264.030i			0.400653i	0.979729	+	0.200326i	$0.0642002\pi$
$659$			264.030i			0.400653i	−0.979729	+	0.200326i	$0.935800\pi$
$660$		0			0
$661$	−1285.15			−1.94425			−0.972124	−	0.234469i	$-0.924665\pi$
$661$	−1285.15			−1.94425			−0.972124	+	0.234469i	$0.924665\pi$
$662$		0			0
$663$	1128.49			1.70210
$664$		0			0
$665$	−19.0580	+	6.20427i	−0.0286586	+	0.00932972i
$666$		0			0
$667$	−1209.23			−1.81294
$668$		0			0
$669$	1212.73			1.81276
$670$		0			0
$671$		−	551.876i		−	0.822468i
$672$		0			0
$673$			1244.16i			1.84868i	0.381565	+	0.924342i	$0.375385\pi$
$673$			1244.16i			1.84868i	−0.381565	+	0.924342i	$0.624615\pi$
$674$		0			0
$675$	−1083.63	+	789.185i	−1.60538	+	1.16916i
$676$		0			0
$677$		−	963.335i		−	1.42295i	−0.702713	−	0.711473i	$-0.748028\pi$
$677$		−	963.335i		−	1.42295i	0.702713	−	0.711473i	$-0.251972\pi$
$678$		0			0
$679$			2.51170i			0.00369912i
$680$		0			0
$681$	−1497.35			−2.19876
$682$		0			0
$683$	770.819			1.12858			0.564289	−	0.825577i	$-0.309150\pi$
$683$	770.819			1.12858			0.564289	+	0.825577i	$0.309150\pi$
$684$		0			0
$685$	−284.228	+	92.5296i	−0.414932	+	0.135080i
$686$		0			0
$687$	−261.146			−0.380125
$688$		0			0
$689$	−926.287			−1.34439
$690$		0			0
$691$			408.765i			0.591555i	0.955257	+	0.295778i	$0.0955788\pi$
$691$			408.765i			0.591555i	−0.955257	+	0.295778i	$0.904421\pi$
$692$		0			0
$693$		−	59.3084i		−	0.0855821i
$694$		0			0
$695$	−126.716	+	41.2520i	−0.182325	+	0.0593554i
$696$		0			0
$697$		−	587.652i		−	0.843116i
$698$		0			0
$699$		−	658.921i		−	0.942663i
$700$		0			0
$701$	−1335.62			−1.90530			−0.952650	−	0.304068i	$-0.901655\pi$
$701$	−1335.62			−1.90530			−0.952650	+	0.304068i	$0.901655\pi$
$702$		0			0
$703$	351.311			0.499731
$704$		0			0
$705$	−44.1178	−	135.519i	−0.0625785	−	0.192226i
$706$		0			0
$707$	−26.3908			−0.0373279
$708$		0			0
$709$	−362.956			−0.511927			−0.255964	−	0.966686i	$-0.582393\pi$
$709$	−362.956			−0.511927			−0.255964	+	0.966686i	$0.582393\pi$
$710$		0			0
$711$		−	297.158i		−	0.417943i
$712$		0			0
$713$			554.891i			0.778249i
$714$		0			0
$715$	−271.953	−	835.374i	−0.380354	−	1.16836i
$716$		0			0
$717$			426.575i			0.594945i
$718$		0			0
$719$			648.098i			0.901388i	0.892679	+	0.450694i	$0.148823\pi$
$719$			648.098i			0.901388i	−0.892679	+	0.450694i	$0.851177\pi$
$720$		0			0
$721$	−0.986788			−0.00136864
$722$		0			0
$723$	−6.41453			−0.00887211
$724$		0			0
$725$	897.622	−	653.717i	1.23810	−	0.901679i
$726$		0			0
$727$	−431.123			−0.593017			−0.296508	−	0.955030i	$-0.595822\pi$
$727$	−431.123			−0.593017			−0.296508	+	0.955030i	$0.595822\pi$
$728$		0			0
$729$	−412.506			−0.565852
$730$		0			0
$731$		−	73.9003i		−	0.101095i
$732$		0			0
$733$		−	1464.87i		−	1.99846i	−0.0392126	−	0.999231i	$-0.512485\pi$
$733$		−	1464.87i		−	1.99846i	0.0392126	−	0.999231i	$-0.487515\pi$
$734$		0			0
$735$	−401.774	−	1234.15i	−0.546632	−	1.67912i
$736$		0			0
$737$			67.8073i			0.0920044i
$738$		0			0
$739$			99.1951i			0.134229i	0.997745	+	0.0671144i	$0.0213793\pi$
$739$			99.1951i			0.134229i	−0.997745	+	0.0671144i	$0.978621\pi$
$740$		0			0
$741$	1203.48			1.62412
$742$		0			0
$743$	−602.719			−0.811196			−0.405598	−	0.914052i	$-0.632937\pi$
$743$	−602.719			−0.811196			−0.405598	+	0.914052i	$0.632937\pi$
$744$		0			0
$745$	−222.049	−	682.081i	−0.298053	−	0.915545i
$746$		0			0
$747$	−974.508			−1.30456
$748$		0			0
$749$	22.1529			0.0295767
$750$		0			0
$751$			541.472i			0.721001i	0.932759	+	0.360501i	$0.117394\pi$
$751$			541.472i			0.721001i	−0.932759	+	0.360501i	$0.882606\pi$
$752$		0			0
$753$		−	1123.28i		−	1.49174i
$754$		0			0
$755$	−396.963	+	129.230i	−0.525779	+	0.171166i
$756$		0			0
$757$			1092.79i			1.44358i	0.692113	+	0.721789i	$0.256680\pi$
$757$			1092.79i			1.44358i	−0.692113	+	0.721789i	$0.743320\pi$
$758$		0			0
$759$		−	2167.76i		−	2.85608i
$760$		0			0
$761$	−18.7706			−0.0246657			−0.0123328	−	0.999924i	$-0.503926\pi$
$761$	−18.7706			−0.0246657			−0.0123328	+	0.999924i	$0.503926\pi$
$762$		0			0
$763$	−11.0893			−0.0145338
$764$		0			0
$765$	−1653.06	+	538.149i	−2.16086	+	0.703462i
$766$		0			0
$767$	−975.773			−1.27219
$768$		0			0
$769$	39.0830			0.0508231			0.0254116	−	0.999677i	$-0.491910\pi$
$769$	39.0830			0.0508231			0.0254116	+	0.999677i	$0.491910\pi$
$770$		0			0
$771$			968.423i			1.25606i
$772$		0			0
$773$		−	31.2171i		−	0.0403843i	−0.999796	−	0.0201922i	$-0.993572\pi$
$773$		−	31.2171i		−	0.0403843i	0.999796	−	0.0201922i	$-0.00642780\pi$
$774$		0			0
$775$	−299.977	−	411.900i	−0.387067	−	0.531484i
$776$		0			0
$777$		−	19.8395i		−	0.0255334i
$778$		0			0
$779$		−	626.699i		−	0.804492i
$780$		0			0
$781$	625.529			0.800933
$782$		0			0
$783$	−2381.75			−3.04183
$784$		0			0
$785$	−806.695	+	262.617i	−1.02764	+	0.334544i
$786$		0			0
$787$	−988.563			−1.25612			−0.628058	−	0.778167i	$-0.716150\pi$
$787$	−988.563			−1.25612			−0.628058	+	0.778167i	$0.716150\pi$
$788$		0			0
$789$	−395.880			−0.501750
$790$		0			0
$791$		−	4.23710i		−	0.00535663i
$792$		0			0
$793$		−	429.956i		−	0.542189i
$794$		0			0
$795$	1995.78	−	649.721i	2.51042	−	0.817259i
$796$		0			0
$797$		−	118.920i		−	0.149210i	−0.997213	−	0.0746048i	$-0.976230\pi$
$797$		−	118.920i		−	0.149210i	0.997213	−	0.0746048i	$-0.0237695\pi$
$798$		0			0
$799$		−	97.7933i		−	0.122395i
$800$		0			0
$801$	208.114			0.259818
$802$		0			0
$803$	−624.598			−0.777831
$804$		0			0
$805$	8.70658	+	26.7445i	0.0108156	+	0.0332230i
$806$		0			0
$807$	976.072			1.20951
$808$		0			0
$809$	1214.04			1.50067			0.750337	−	0.661056i	$-0.229891\pi$
$809$	1214.04			1.50067			0.750337	+	0.661056i	$0.229891\pi$
$810$		0			0
$811$			706.666i			0.871351i	0.900104	+	0.435676i	$0.143491\pi$
$811$			706.666i			0.871351i	−0.900104	+	0.435676i	$0.856509\pi$
$812$		0			0
$813$			1244.67i			1.53096i
$814$		0			0
$815$	426.380	+	1309.74i	0.523166	+	1.60704i
$816$		0			0
$817$		−	78.8108i		−	0.0964636i
$818$		0			0
$819$		−	46.2060i		−	0.0564176i
$820$		0			0
$821$	−991.775			−1.20801			−0.604004	−	0.796981i	$-0.706429\pi$
$821$	−991.775			−1.20801			−0.604004	+	0.796981i	$0.706429\pi$
$822$		0			0
$823$	−523.998			−0.636693			−0.318347	−	0.947974i	$-0.603128\pi$
$823$	−523.998			−0.636693			−0.318347	+	0.947974i	$0.603128\pi$
$824$		0			0
$825$	1171.90	+	1609.15i	1.42049	+	1.95048i
$826$		0			0
$827$	318.794			0.385483			0.192741	−	0.981250i	$-0.438262\pi$
$827$	318.794			0.385483			0.192741	+	0.981250i	$0.438262\pi$
$828$		0			0
$829$	1034.11			1.24742			0.623711	−	0.781655i	$-0.285624\pi$
$829$	1034.11			1.24742			0.623711	+	0.781655i	$0.285624\pi$
$830$		0			0
$831$			2397.69i			2.88531i
$832$		0			0
$833$		−	890.588i		−	1.06913i
$834$		0			0
$835$	−205.052	−	629.868i	−0.245571	−	0.754333i
$836$		0			0
$837$			1092.94i			1.30578i
$838$		0			0
$839$			445.284i			0.530732i	0.964148	+	0.265366i	$0.0854928\pi$
$839$			445.284i			0.530732i	−0.964148	+	0.265366i	$0.914507\pi$
$840$		0			0
$841$	1131.91			1.34591
$842$		0			0
$843$	−1039.81			−1.23346
$844$		0			0
$845$	49.7016	+	152.671i	0.0588184	+	0.180676i
$846$		0			0
$847$	−21.5983			−0.0254997
$848$		0			0
$849$	2218.69			2.61330
$850$		0			0
$851$		−	493.002i		−	0.579321i
$852$		0			0
$853$		−	1200.49i		−	1.40737i	−0.710513	−	0.703684i	$-0.751537\pi$
$853$		−	1200.49i		−	1.40737i	0.710513	−	0.703684i	$-0.248463\pi$
$854$		0			0
$855$	−1762.90	+	573.907i	−2.06187	+	0.671236i
$856$		0			0
$857$			1223.15i			1.42724i	0.700531	+	0.713622i	$0.252946\pi$
$857$			1223.15i			1.42724i	−0.700531	+	0.713622i	$0.747054\pi$
$858$		0			0
$859$			210.033i			0.244509i	0.992499	+	0.122254i	$0.0390124\pi$
$859$			210.033i			0.244509i	−0.992499	+	0.122254i	$0.960988\pi$
$860$		0			0
$861$	−35.3914			−0.0411050
$862$		0			0
$863$	1560.47			1.80819			0.904095	−	0.427333i	$-0.140547\pi$
$863$	1560.47			1.80819			0.904095	+	0.427333i	$0.140547\pi$
$864$		0			0
$865$	−1296.12	+	421.947i	−1.49840	+	0.487800i
$866$		0			0
$867$	−222.252			−0.256346
$868$		0			0
$869$	−233.483			−0.268680
$870$		0			0
$871$			52.8273i			0.0606513i
$872$		0			0
$873$			232.338i			0.266137i
$874$		0			0
$875$	−20.9211	−	15.1458i	−0.0239099	−	0.0173095i
$876$		0			0
$877$		−	1011.66i		−	1.15354i	−0.816906	−	0.576771i	$-0.804313\pi$
$877$		−	1011.66i		−	1.15354i	0.816906	−	0.576771i	$-0.195687\pi$
$878$		0			0
$879$		−	1519.96i		−	1.72919i
$880$		0			0
$881$	266.455			0.302446			0.151223	−	0.988500i	$-0.451679\pi$
$881$	266.455			0.302446			0.151223	+	0.988500i	$0.451679\pi$
$882$		0			0
$883$	−469.871			−0.532130			−0.266065	−	0.963955i	$-0.585724\pi$
$883$	−469.871			−0.532130			−0.266065	+	0.963955i	$0.585724\pi$
$884$		0			0
$885$	2102.41	−	684.431i	2.37560	−	0.773369i
$886$		0			0
$887$	764.559			0.861961			0.430980	−	0.902361i	$-0.358168\pi$
$887$	764.559			0.861961			0.430980	+	0.902361i	$0.358168\pi$
$888$		0			0
$889$	28.6127			0.0321853
$890$		0			0
$891$		−	1686.41i		−	1.89271i
$892$		0			0
$893$		−	104.291i		−	0.116788i
$894$		0			0
$895$	−748.926	+	243.810i	−0.836789	+	0.272414i
$896$		0			0
$897$		−	1688.86i		−	1.88279i
$898$		0			0
$899$		−	905.328i		−	1.00704i
$900$		0			0
$901$	1440.20			1.59844
$902$		0			0
$903$	−4.45065			−0.00492874
$904$		0			0
$905$	518.605	+	1593.03i	0.573044	+	1.76025i
$906$		0			0
$907$	−1333.20			−1.46990			−0.734948	−	0.678123i	$-0.762794\pi$
$907$	−1333.20			−1.46990			−0.734948	+	0.678123i	$0.762794\pi$
$908$		0			0
$909$	−2441.20			−2.68559
$910$		0			0
$911$		−	1496.11i		−	1.64227i	−0.570736	−	0.821134i	$-0.693342\pi$
$911$		−	1496.11i		−	1.64227i	0.570736	−	0.821134i	$-0.306658\pi$
$912$		0			0
$913$			765.691i			0.838654i
$914$		0			0
$915$	301.582	+	926.385i	0.329597	+	1.01244i
$916$		0			0
$917$		−	45.2725i		−	0.0493702i
$918$		0			0
$919$		−	564.228i		−	0.613959i	−0.951716	−	0.306980i	$-0.900682\pi$
$919$		−	564.228i		−	0.613959i	0.951716	−	0.306980i	$-0.0993183\pi$
$920$		0			0
$921$	−1387.66			−1.50669
$922$		0			0
$923$	487.337			0.527993
$924$		0			0
$925$	266.519	+	365.959i	0.288129	+	0.395631i
$926$		0			0
$927$	−91.2798			−0.0984680
$928$		0			0
$929$	1449.16			1.55991			0.779957	−	0.625833i	$-0.215241\pi$
$929$	1449.16			1.55991			0.779957	+	0.625833i	$0.215241\pi$
$930$		0			0
$931$		−	949.765i		−	1.02016i
$932$		0			0
$933$		−	3069.46i		−	3.28988i
$934$		0			0
$935$	422.834	+	1298.84i	0.452229	+	1.38914i
$936$		0			0
$937$			258.795i			0.276196i	0.990419	+	0.138098i	$0.0440989\pi$
$937$			258.795i			0.276196i	−0.990419	+	0.138098i	$0.955901\pi$
$938$		0			0
$939$			526.573i			0.560781i
$940$		0			0
$941$	−20.3444			−0.0216200			−0.0108100	−	0.999942i	$-0.503441\pi$
$941$	−20.3444			−0.0216200			−0.0108100	+	0.999942i	$0.503441\pi$
$942$		0			0
$943$	−879.461			−0.932620
$944$		0			0
$945$	17.1488	+	52.6770i	0.0181469	+	0.0557429i
$946$		0			0
$947$	613.539			0.647876			0.323938	−	0.946078i	$-0.394993\pi$
$947$	613.539			0.647876			0.323938	+	0.946078i	$0.394993\pi$
$948$		0			0
$949$	−486.612			−0.512763
$950$		0			0
$951$			1016.02i			1.06837i
$952$		0			0
$953$			81.6126i			0.0856376i	0.999083	+	0.0428188i	$0.0136338\pi$
$953$			81.6126i			0.0856376i	−0.999083	+	0.0428188i	$0.986366\pi$
$954$		0			0
$955$	−1419.55	+	462.129i	−1.48644	+	0.483905i
$956$		0			0
$957$			3536.80i			3.69571i
$958$		0			0
$959$			12.3525i			0.0128806i
$960$		0			0
$961$	545.564			0.567704
$962$		0			0
$963$	2049.19			2.12792
$964$		0			0
$965$	−912.440	+	297.042i	−0.945534	+	0.307815i
$966$		0			0
$967$	127.482			0.131833			0.0659165	−	0.997825i	$-0.479003\pi$
$967$	127.482			0.131833			0.0659165	+	0.997825i	$0.479003\pi$
$968$		0			0
$969$	−1871.17			−1.93103
$970$		0			0
$971$		−	1122.62i		−	1.15615i	−0.815983	−	0.578076i	$-0.803804\pi$
$971$		−	1122.62i		−	1.15615i	0.815983	−	0.578076i	$-0.196196\pi$
$972$		0			0
$973$			5.50703i			0.00565985i
$974$		0			0
$975$	913.007	+	1253.65i	0.936418	+	1.28580i
$976$		0			0
$977$		−	424.837i		−	0.434838i	−0.976078	−	0.217419i	$-0.930236\pi$
$977$		−	424.837i		−	0.434838i	0.976078	−	0.217419i	$-0.0697639\pi$
$978$		0			0
$979$		−	163.519i		−	0.167027i
$980$		0			0
$981$	−1025.78			−1.04565
$982$		0			0
$983$	−663.324			−0.674795			−0.337398	−	0.941362i	$-0.609547\pi$
$983$	−663.324			−0.674795			−0.337398	+	0.941362i	$0.609547\pi$
$984$		0			0
$985$	−281.685	+	91.7017i	−0.285975	+	0.0930982i
$986$		0			0
$987$	−5.88961			−0.00596719
$988$		0			0
$989$	−110.597			−0.111827
$990$		0			0
$991$		−	1771.36i		−	1.78745i	−0.448616	−	0.893724i	$-0.648083\pi$
$991$		−	1771.36i		−	1.78745i	0.448616	−	0.893724i	$-0.351917\pi$
$992$		0			0
$993$		−	2811.15i		−	2.83097i
$994$		0			0
$995$	1469.59	−	478.419i	1.47697	−	0.480823i
$996$		0			0
$997$			447.066i			0.448411i	0.974542	+	0.224205i	$0.0719786\pi$
$997$			447.066i			0.448411i	−0.974542	+	0.224205i	$0.928021\pi$
$998$		0			0
$999$		−	971.038i		−	0.972010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.h.g.319.6		6
4.3	odd	2		320.3.h.f.319.2		6
5.2	odd	4		1600.3.b.v.1151.1		6
5.3	odd	4		1600.3.b.w.1151.6		6
5.4	even	2		320.3.h.f.319.1		6
8.3	odd	2		160.3.h.b.159.5	yes	6
8.5	even	2		160.3.h.a.159.1	✓	6
16.3	odd	4		1280.3.e.h.639.1		6
16.5	even	4		1280.3.e.g.639.1		6
16.11	odd	4		1280.3.e.f.639.6		6
16.13	even	4		1280.3.e.i.639.6		6
20.3	even	4		1600.3.b.w.1151.1		6
20.7	even	4		1600.3.b.v.1151.6		6
20.19	odd	2	inner	320.3.h.g.319.5		6
24.5	odd	2		1440.3.j.a.1279.4		6
24.11	even	2		1440.3.j.b.1279.4		6
40.3	even	4		800.3.b.i.351.6		6
40.13	odd	4		800.3.b.i.351.1		6
40.19	odd	2		160.3.h.a.159.2	yes	6
40.27	even	4		800.3.b.h.351.1		6
40.29	even	2		160.3.h.b.159.6	yes	6
40.37	odd	4		800.3.b.h.351.6		6
80.19	odd	4		1280.3.e.g.639.6		6
80.29	even	4		1280.3.e.f.639.1		6
80.59	odd	4		1280.3.e.i.639.1		6
80.69	even	4		1280.3.e.h.639.6		6
120.29	odd	2		1440.3.j.b.1279.3		6
120.59	even	2		1440.3.j.a.1279.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.3.h.a.159.1	✓	6	8.5	even	2
160.3.h.a.159.2	yes	6	40.19	odd	2
160.3.h.b.159.5	yes	6	8.3	odd	2
160.3.h.b.159.6	yes	6	40.29	even	2
320.3.h.f.319.1		6	5.4	even	2
320.3.h.f.319.2		6	4.3	odd	2
320.3.h.g.319.5		6	20.19	odd	2	inner
320.3.h.g.319.6		6	1.1	even	1	trivial
800.3.b.h.351.1		6	40.27	even	4
800.3.b.h.351.6		6	40.37	odd	4
800.3.b.i.351.1		6	40.13	odd	4
800.3.b.i.351.6		6	40.3	even	4
1280.3.e.f.639.1		6	80.29	even	4
1280.3.e.f.639.6		6	16.11	odd	4
1280.3.e.g.639.1		6	16.5	even	4
1280.3.e.g.639.6		6	80.19	odd	4
1280.3.e.h.639.1		6	16.3	odd	4
1280.3.e.h.639.6		6	80.69	even	4
1280.3.e.i.639.1		6	80.59	odd	4
1280.3.e.i.639.6		6	16.13	even	4
1440.3.j.a.1279.3		6	120.59	even	2
1440.3.j.a.1279.4		6	24.5	odd	2
1440.3.j.b.1279.3		6	120.29	odd	2
1440.3.j.b.1279.4		6	24.11	even	2
1600.3.b.v.1151.1		6	5.2	odd	4
1600.3.b.v.1151.6		6	20.7	even	4
1600.3.b.w.1151.1		6	20.3	even	4
1600.3.b.w.1151.6		6	5.3	odd	4

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.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+5.30219 q^{3} +(1.54778 + 4.75441i) q^{5} +0.206625 q^{7} +19.1132 q^{9} +O(q^{10})\)	\(q+5.30219 q^{3} +(1.54778 + 4.75441i) q^{5} +0.206625 q^{7} +19.1132 q^{9} -15.0176i q^{11} -11.6999i q^{13} +(8.20662 + 25.2087i) q^{15} +18.1911i q^{17} +19.3999i q^{19} +1.09556 q^{21} +27.2242 q^{23} +(-20.2087 + 14.7176i) q^{25} +53.6220 q^{27} -44.4175 q^{29} +20.3822i q^{31} -79.6262i q^{33} +(0.319810 + 0.982377i) q^{35} -18.1089i q^{37} -62.0352i q^{39} -32.3043 q^{41} -4.06244 q^{43} +(29.5830 + 90.8718i) q^{45} -5.37588 q^{47} -48.9573 q^{49} +96.4527i q^{51} -79.1703i q^{53} +(71.3999 - 23.2440i) q^{55} +102.862i q^{57} -83.3999i q^{59} +36.7486 q^{61} +3.94925 q^{63} +(55.6262 - 18.1089i) q^{65} -4.51518 q^{67} +144.348 q^{69} +41.6530i q^{71} -41.5910i q^{73} +(-107.151 + 78.0352i) q^{75} -3.10301i q^{77} -15.5473i q^{79} +112.295 q^{81} -50.9862 q^{83} +(-86.4880 + 28.1559i) q^{85} -235.510 q^{87} +10.8885 q^{89} -2.41749i q^{91} +108.070i q^{93} +(-92.2349 + 30.0268i) q^{95} +12.1559i q^{97} -287.035i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{3} + 2 q^{5} - 12 q^{7} + 18 q^{9}+O(q^{10}) \) 6 * q + 4 * q^3 + 2 * q^5 - 12 * q^7 + 18 * q^9	\( 6 q + 4 q^{3} + 2 q^{5} - 12 q^{7} + 18 q^{9} + 36 q^{15} - 8 q^{21} + 68 q^{23} - 10 q^{25} + 184 q^{27} - 44 q^{29} - 108 q^{35} - 68 q^{41} - 76 q^{43} + 6 q^{45} - 268 q^{47} - 62 q^{49} + 288 q^{55} + 100 q^{61} + 172 q^{63} + 308 q^{67} + 184 q^{69} - 284 q^{75} + 238 q^{81} - 204 q^{83} + 32 q^{85} - 584 q^{87} + 76 q^{89} + 32 q^{95}+O(q^{100}) \) 6 * q + 4 * q^3 + 2 * q^5 - 12 * q^7 + 18 * q^9 + 36 * q^15 - 8 * q^21 + 68 * q^23 - 10 * q^25 + 184 * q^27 - 44 * q^29 - 108 * q^35 - 68 * q^41 - 76 * q^43 + 6 * q^45 - 268 * q^47 - 62 * q^49 + 288 * q^55 + 100 * q^61 + 172 * q^63 + 308 * q^67 + 184 * q^69 - 284 * q^75 + 238 * q^81 - 204 * q^83 + 32 * q^85 - 584 * q^87 + 76 * q^89 + 32 * q^95

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