LMFDB - Embedded newform 320.3.t.a.17.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [320,3,Mod(17,320)]

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([0, 3, 1]))

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

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

chi := DirichletCharacter("320.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 320 = 2^{6} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	320.t (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:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.13
Character	$\chi$	$=$	320.17
Dual form			320.3.t.a.113.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24645 q^{3} +(1.50036 + 4.76958i) q^{5} +(-3.62600 + 3.62600i) q^{7} -7.44635 q^{9} +O(q^{10})$	\(q+1.24645 q^{3} +(1.50036 + 4.76958i) q^{5} +(-3.62600 + 3.62600i) q^{7} -7.44635 q^{9} +(-9.10832 + 9.10832i) q^{11} -9.59167 q^{13} +(1.87013 + 5.94507i) q^{15} +(-14.5630 - 14.5630i) q^{17} +(10.1736 - 10.1736i) q^{19} +(-4.51965 + 4.51965i) q^{21} +(20.9529 + 20.9529i) q^{23} +(-20.4978 + 14.3122i) q^{25} -20.4996 q^{27} +(15.9714 - 15.9714i) q^{29} -22.3264 q^{31} +(-11.3531 + 11.3531i) q^{33} +(-22.7348 - 11.8542i) q^{35} +28.7135 q^{37} -11.9556 q^{39} +71.4731i q^{41} +18.1083i q^{43} +(-11.1722 - 35.5160i) q^{45} +(52.4024 + 52.4024i) q^{47} +22.7042i q^{49} +(-18.1521 - 18.1521i) q^{51} +24.3168i q^{53} +(-57.1086 - 29.7771i) q^{55} +(12.6810 - 12.6810i) q^{57} +(-48.9777 - 48.9777i) q^{59} +(42.1700 + 42.1700i) q^{61} +(27.0005 - 27.0005i) q^{63} +(-14.3909 - 45.7483i) q^{65} -73.7087i q^{67} +(26.1169 + 26.1169i) q^{69} +28.6304i q^{71} +(-9.24608 - 9.24608i) q^{73} +(-25.5496 + 17.8395i) q^{75} -66.0535i q^{77} +85.8203i q^{79} +41.4653 q^{81} +71.8998 q^{83} +(47.6097 - 91.3092i) q^{85} +(19.9076 - 19.9076i) q^{87} -124.642 q^{89} +(34.7794 - 34.7794i) q^{91} -27.8289 q^{93} +(63.7881 + 33.2599i) q^{95} +(19.5684 + 19.5684i) q^{97} +(67.8237 - 67.8237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	$ 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) $ 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 380 * q^95 - 4 * q^97 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	1.24645			0.415485			0.207742	−	0.978184i	$-0.433388\pi$
$3$	1.24645			0.415485			0.207742	+	0.978184i	$0.433388\pi$
$4$		0			0
$5$	1.50036	+	4.76958i	0.300072	+	0.953917i
$5$	1.50036	+	4.76958i	0.300072	+	0.953917i
$6$		0			0
$7$	−3.62600	+	3.62600i	−0.518000	+	0.518000i	−0.916966	−	0.398966i	$-0.869369\pi$
$7$	−3.62600	+	3.62600i	−0.518000	+	0.518000i	0.398966	+	0.916966i	$0.369369\pi$
$8$		0			0
$9$	−7.44635			−0.827372
$10$		0			0
$11$	−9.10832	+	9.10832i	−0.828029	+	0.828029i	−0.987244	−	0.159215i	$-0.949104\pi$
$11$	−9.10832	+	9.10832i	−0.828029	+	0.828029i	0.159215	+	0.987244i	$0.449104\pi$
$12$		0			0
$13$	−9.59167			−0.737821			−0.368910	−	0.929465i	$-0.620269\pi$
$13$	−9.59167			−0.737821			−0.368910	+	0.929465i	$0.620269\pi$
$14$		0			0
$15$	1.87013	+	5.94507i	0.124675	+	0.396338i
$16$		0			0
$17$	−14.5630	−	14.5630i	−0.856648	−	0.856648i	0.134294	−	0.990942i	$-0.457123\pi$
$17$	−14.5630	−	14.5630i	−0.856648	−	0.856648i	−0.990942	+	0.134294i	$0.957123\pi$
$18$		0			0
$19$	10.1736	−	10.1736i	0.535454	−	0.535454i	−0.386736	−	0.922190i	$-0.626398\pi$
$19$	10.1736	−	10.1736i	0.535454	−	0.535454i	0.922190	+	0.386736i	$0.126398\pi$
$20$		0			0
$21$	−4.51965	+	4.51965i	−0.215221	+	0.215221i
$22$		0			0
$23$	20.9529	+	20.9529i	0.910996	+	0.910996i	0.996351	−	0.0853546i	$-0.0272023\pi$
$23$	20.9529	+	20.9529i	0.910996	+	0.910996i	−0.0853546	+	0.996351i	$0.527202\pi$
$24$		0			0
$25$	−20.4978	+	14.3122i	−0.819914	+	0.572487i
$26$		0			0
$27$	−20.4996			−0.759246
$28$		0			0
$29$	15.9714	−	15.9714i	0.550737	−	0.550737i	−0.375916	−	0.926654i	$-0.622672\pi$
$29$	15.9714	−	15.9714i	0.550737	−	0.550737i	0.926654	+	0.375916i	$0.122672\pi$
$30$		0			0
$31$	−22.3264			−0.720208			−0.360104	−	0.932912i	$-0.617259\pi$
$31$	−22.3264			−0.720208			−0.360104	+	0.932912i	$0.617259\pi$
$32$		0			0
$33$	−11.3531	+	11.3531i	−0.344034	+	0.344034i
$34$		0			0
$35$	−22.7348	−	11.8542i	−0.649566	−	0.338692i
$36$		0			0
$37$	28.7135			0.776041			0.388020	−	0.921651i	$-0.373159\pi$
$37$	28.7135			0.776041			0.388020	+	0.921651i	$0.373159\pi$
$38$		0			0
$39$	−11.9556			−0.306553
$40$		0			0
$41$			71.4731i			1.74325i	0.490177	+	0.871623i	$0.336932\pi$
$41$			71.4731i			1.74325i	−0.490177	+	0.871623i	$0.663068\pi$
$42$		0			0
$43$			18.1083i			0.421123i	0.977581	+	0.210561i	$0.0675292\pi$
$43$			18.1083i			0.421123i	−0.977581	+	0.210561i	$0.932471\pi$
$44$		0			0
$45$	−11.1722	−	35.5160i	−0.248271	−	0.789244i
$46$		0			0
$47$	52.4024	+	52.4024i	1.11495	+	1.11495i	0.992472	+	0.122474i	$0.0390827\pi$
$47$	52.4024	+	52.4024i	1.11495	+	1.11495i	0.122474	+	0.992472i	$0.460917\pi$
$48$		0			0
$49$			22.7042i			0.463352i
$50$		0			0
$51$	−18.1521	−	18.1521i	−0.355924	−	0.355924i
$52$		0			0
$53$			24.3168i			0.458808i	0.973331	+	0.229404i	$0.0736776\pi$
$53$			24.3168i			0.458808i	−0.973331	+	0.229404i	$0.926322\pi$
$54$		0			0
$55$	−57.1086	−	29.7771i	−1.03834	−	0.541402i
$56$		0			0
$57$	12.6810	−	12.6810i	0.222473	−	0.222473i
$58$		0			0
$59$	−48.9777	−	48.9777i	−0.830131	−	0.830131i	0.157403	−	0.987534i	$-0.449688\pi$
$59$	−48.9777	−	48.9777i	−0.830131	−	0.830131i	−0.987534	+	0.157403i	$0.949688\pi$
$60$		0			0
$61$	42.1700	+	42.1700i	0.691311	+	0.691311i	0.962520	−	0.271209i	$-0.0874235\pi$
$61$	42.1700	+	42.1700i	0.691311	+	0.691311i	−0.271209	+	0.962520i	$0.587424\pi$
$62$		0			0
$63$	27.0005	−	27.0005i	0.428579	−	0.428579i
$64$		0			0
$65$	−14.3909	−	45.7483i	−0.221399	−	0.703819i
$66$		0			0
$67$		−	73.7087i		−	1.10013i	−0.835122	−	0.550065i	$-0.814603\pi$
$67$		−	73.7087i		−	1.10013i	0.835122	−	0.550065i	$-0.185397\pi$
$68$		0			0
$69$	26.1169	+	26.1169i	0.378505	+	0.378505i
$70$		0			0
$71$			28.6304i			0.403244i	0.979463	+	0.201622i	$0.0646213\pi$
$71$			28.6304i			0.403244i	−0.979463	+	0.201622i	$0.935379\pi$
$72$		0			0
$73$	−9.24608	−	9.24608i	−0.126659	−	0.126659i	0.640936	−	0.767594i	$-0.278546\pi$
$73$	−9.24608	−	9.24608i	−0.126659	−	0.126659i	−0.767594	+	0.640936i	$0.778546\pi$
$74$		0			0
$75$	−25.5496	+	17.8395i	−0.340662	+	0.237860i
$76$		0			0
$77$		−	66.0535i		−	0.857838i
$78$		0			0
$79$			85.8203i			1.08633i	0.839625	+	0.543166i	$0.182775\pi$
$79$			85.8203i			1.08633i	−0.839625	+	0.543166i	$0.817225\pi$
$80$		0			0
$81$	41.4653			0.511917
$82$		0			0
$83$	71.8998			0.866263			0.433131	−	0.901331i	$-0.357409\pi$
$83$	71.8998			0.866263			0.433131	+	0.901331i	$0.357409\pi$
$84$		0			0
$85$	47.6097	−	91.3092i	0.560115	−	1.07423i
$86$		0			0
$87$	19.9076	−	19.9076i	0.228823	−	0.228823i
$88$		0			0
$89$	−124.642			−1.40047			−0.700233	−	0.713914i	$-0.746921\pi$
$89$	−124.642			−1.40047			−0.700233	+	0.713914i	$0.746921\pi$
$90$		0			0
$91$	34.7794	−	34.7794i	0.382191	−	0.382191i
$92$		0			0
$93$	−27.8289			−0.299236
$94$		0			0
$95$	63.7881	+	33.2599i	0.671454	+	0.350104i
$96$		0			0
$97$	19.5684	+	19.5684i	0.201736	+	0.201736i	0.800743	−	0.599008i	$-0.204438\pi$
$97$	19.5684	+	19.5684i	0.201736	+	0.201736i	−0.599008	+	0.800743i	$0.704438\pi$
$98$		0			0
$99$	67.8237	−	67.8237i	0.685088	−	0.685088i
$100$		0			0
$101$	52.5412	−	52.5412i	0.520210	−	0.520210i	−0.397425	−	0.917635i	$-0.630096\pi$
$101$	52.5412	−	52.5412i	0.520210	−	0.520210i	0.917635	+	0.397425i	$0.130096\pi$
$102$		0			0
$103$	−21.9304	−	21.9304i	−0.212916	−	0.212916i	0.592589	−	0.805505i	$-0.298106\pi$
$103$	−21.9304	−	21.9304i	−0.212916	−	0.212916i	−0.805505	+	0.592589i	$0.798106\pi$
$104$		0			0
$105$	−28.3379	−	14.7757i	−0.269885	−	0.140721i
$106$		0			0
$107$	172.582			1.61291			0.806456	−	0.591294i	$-0.201383\pi$
$107$	172.582			1.61291			0.806456	+	0.591294i	$0.201383\pi$
$108$		0			0
$109$	−33.6276	+	33.6276i	−0.308510	+	0.308510i	−0.844331	−	0.535821i	$-0.820002\pi$
$109$	−33.6276	+	33.6276i	−0.308510	+	0.308510i	0.535821	+	0.844331i	$0.320002\pi$
$110$		0			0
$111$	35.7901			0.322433
$112$		0			0
$113$	33.7854	−	33.7854i	0.298986	−	0.298986i	−0.541631	−	0.840617i	$-0.682193\pi$
$113$	33.7854	−	33.7854i	0.298986	−	0.298986i	0.840617	+	0.541631i	$0.182193\pi$
$114$		0			0
$115$	−68.4997	+	131.374i	−0.595650	+	1.14238i
$116$		0			0
$117$	71.4229			0.610452
$118$		0			0
$119$	105.611			0.887487
$120$		0			0
$121$		−	44.9229i		−	0.371264i
$122$		0			0
$123$			89.0880i			0.724292i
$124$		0			0
$125$	−99.0172	−	76.2928i	−0.792138	−	0.610342i
$126$		0			0
$127$	−104.424	−	104.424i	−0.822234	−	0.822234i	0.164194	−	0.986428i	$-0.447498\pi$
$127$	−104.424	−	104.424i	−0.822234	−	0.822234i	−0.986428	+	0.164194i	$0.947498\pi$
$128$		0			0
$129$			22.5711i			0.174970i
$130$		0			0
$131$	21.2047	+	21.2047i	0.161868	+	0.161868i	0.783394	−	0.621526i	$-0.213487\pi$
$131$	21.2047	+	21.2047i	0.161868	+	0.161868i	−0.621526	+	0.783394i	$0.713487\pi$
$132$		0			0
$133$			73.7792i			0.554731i
$134$		0			0
$135$	−30.7568	−	97.7747i	−0.227828	−	0.724257i
$136$		0			0
$137$	192.446	−	192.446i	1.40471	−	1.40471i	0.620531	−	0.784182i	$-0.286917\pi$
$137$	192.446	−	192.446i	1.40471	−	1.40471i	0.784182	−	0.620531i	$-0.213083\pi$
$138$		0			0
$139$	−100.158	−	100.158i	−0.720563	−	0.720563i	0.248157	−	0.968720i	$-0.420175\pi$
$139$	−100.158	−	100.158i	−0.720563	−	0.720563i	−0.968720	+	0.248157i	$0.920175\pi$
$140$		0			0
$141$	65.3173	+	65.3173i	0.463243	+	0.463243i
$142$		0			0
$143$	87.3640	−	87.3640i	0.610937	−	0.610937i
$144$		0			0
$145$	100.140	+	52.2140i	0.690618	+	0.360097i
$146$		0			0
$147$			28.2998i			0.192516i
$148$		0			0
$149$	−96.2282	−	96.2282i	−0.645827	−	0.645827i	0.306155	−	0.951982i	$-0.400957\pi$
$149$	−96.2282	−	96.2282i	−0.645827	−	0.645827i	−0.951982	+	0.306155i	$0.900957\pi$
$150$		0			0
$151$			153.137i			1.01415i	0.861902	+	0.507075i	$0.169273\pi$
$151$			153.137i			1.01415i	−0.861902	+	0.507075i	$0.830727\pi$
$152$		0			0
$153$	108.441	+	108.441i	0.708767	+	0.708767i
$154$		0			0
$155$	−33.4977	−	106.488i	−0.216114	−	0.687018i
$156$		0			0
$157$			125.408i			0.798778i	0.916782	+	0.399389i	$0.130778\pi$
$157$			125.408i			0.798778i	−0.916782	+	0.399389i	$0.869222\pi$
$158$		0			0
$159$			30.3098i			0.190628i
$160$		0			0
$161$	−151.951			−0.943792
$162$		0			0
$163$	−170.310			−1.04485			−0.522424	−	0.852686i	$-0.674972\pi$
$163$	−170.310			−1.04485			−0.522424	+	0.852686i	$0.674972\pi$
$164$		0			0
$165$	−71.1833	−	37.1158i	−0.431414	−	0.224945i
$166$		0			0
$167$	100.234	−	100.234i	0.600206	−	0.600206i	−0.340161	−	0.940367i	$-0.610482\pi$
$167$	100.234	−	100.234i	0.600206	−	0.600206i	0.940367	+	0.340161i	$0.110482\pi$
$168$		0			0
$169$	−76.9999			−0.455621
$170$		0			0
$171$	−75.7565	+	75.7565i	−0.443020	+	0.443020i
$172$		0			0
$173$	230.629			1.33312			0.666559	−	0.745452i	$-0.267766\pi$
$173$	230.629			1.33312			0.666559	+	0.745452i	$0.267766\pi$
$174$		0			0
$175$	22.4292	−	126.221i	0.128167	−	0.721264i
$176$		0			0
$177$	−61.0485	−	61.0485i	−0.344907	−	0.344907i
$178$		0			0
$179$	−141.787	+	141.787i	−0.792106	+	0.792106i	−0.981836	−	0.189731i	$-0.939239\pi$
$179$	−141.787	+	141.787i	−0.792106	+	0.792106i	0.189731	+	0.981836i	$0.439239\pi$
$180$		0			0
$181$	−222.974	+	222.974i	−1.23190	+	1.23190i	−0.268665	+	0.963234i	$0.586582\pi$
$181$	−222.974	+	222.974i	−1.23190	+	1.23190i	−0.963234	+	0.268665i	$0.913418\pi$
$182$		0			0
$183$	52.5630	+	52.5630i	0.287229	+	0.287229i
$184$		0			0
$185$	43.0806	+	136.951i	0.232868	+	0.740278i
$186$		0			0
$187$	265.289			1.41866
$188$		0			0
$189$	74.3317	−	74.3317i	0.393289	−	0.393289i
$190$		0			0
$191$	−360.691			−1.88843			−0.944217	−	0.329325i	$-0.893179\pi$
$191$	−360.691			−1.88843			−0.944217	+	0.329325i	$0.893179\pi$
$192$		0			0
$193$	24.2248	−	24.2248i	0.125517	−	0.125517i	−0.641558	−	0.767075i	$-0.721712\pi$
$193$	24.2248	−	24.2248i	0.125517	−	0.125517i	0.767075	+	0.641558i	$0.221712\pi$
$194$		0			0
$195$	−17.9377	−	57.0231i	−0.0919880	−	0.292426i
$196$		0			0
$197$	−169.208			−0.858922			−0.429461	−	0.903085i	$-0.641296\pi$
$197$	−169.208			−0.858922			−0.429461	+	0.903085i	$0.641296\pi$
$198$		0			0
$199$	−176.493			−0.886899			−0.443450	−	0.896299i	$-0.646245\pi$
$199$	−176.493			−0.886899			−0.443450	+	0.896299i	$0.646245\pi$
$200$		0			0
$201$		−	91.8746i		−	0.457087i
$202$		0			0
$203$			115.824i			0.570564i
$204$		0			0
$205$	−340.897	+	107.235i	−1.66291	+	0.523099i
$206$		0			0
$207$	−156.023	−	156.023i	−0.753733	−	0.753733i
$208$		0			0
$209$			185.329i			0.886744i
$210$		0			0
$211$	242.205	+	242.205i	1.14789	+	1.14789i	0.986967	+	0.160925i	$0.0514478\pi$
$211$	242.205	+	242.205i	1.14789	+	1.14789i	0.160925	+	0.986967i	$0.448552\pi$
$212$		0			0
$213$			35.6864i			0.167542i
$214$		0			0
$215$	−86.3689	+	27.1689i	−0.401716	+	0.126367i
$216$		0			0
$217$	80.9557	−	80.9557i	0.373068	−	0.373068i
$218$		0			0
$219$	−11.5248	−	11.5248i	−0.0526248	−	0.0526248i
$220$		0			0
$221$	139.684	+	139.684i	0.632052	+	0.632052i
$222$		0			0
$223$	−112.186	+	112.186i	−0.503076	+	0.503076i	−0.912392	−	0.409316i	$-0.865767\pi$
$223$	−112.186	+	112.186i	−0.503076	+	0.503076i	0.409316	+	0.912392i	$0.365767\pi$
$224$		0			0
$225$	152.634	−	106.573i	0.678374	−	0.473660i
$226$		0			0
$227$			3.50408i			0.0154365i	0.999970	+	0.00771824i	$0.00245682\pi$
$227$			3.50408i			0.0154365i	−0.999970	+	0.00771824i	$0.997543\pi$
$228$		0			0
$229$	12.5594	+	12.5594i	0.0548445	+	0.0548445i	0.733997	−	0.679153i	$-0.237653\pi$
$229$	12.5594	+	12.5594i	0.0548445	+	0.0548445i	−0.679153	+	0.733997i	$0.737653\pi$
$230$		0			0
$231$		−	82.3327i		−	0.356419i
$232$		0			0
$233$	137.748	+	137.748i	0.591192	+	0.591192i	0.937953	−	0.346761i	$-0.112719\pi$
$233$	137.748	+	137.748i	0.591192	+	0.591192i	−0.346761	+	0.937953i	$0.612719\pi$
$234$		0			0
$235$	−171.315	+	328.560i	−0.729001	+	1.39813i
$236$		0			0
$237$			106.971i			0.451355i
$238$		0			0
$239$			93.2096i			0.389998i	0.980803	+	0.194999i	$0.0624704\pi$
$239$			93.2096i			0.389998i	−0.980803	+	0.194999i	$0.937530\pi$
$240$		0			0
$241$	−180.914			−0.750682			−0.375341	−	0.926887i	$-0.622474\pi$
$241$	−180.914			−0.750682			−0.375341	+	0.926887i	$0.622474\pi$
$242$		0			0
$243$	236.181			0.971939
$244$		0			0
$245$	−108.290	+	34.0645i	−0.441999	+	0.139039i
$246$		0			0
$247$	−97.5821	+	97.5821i	−0.395069	+	0.395069i
$248$		0			0
$249$	89.6199			0.359919
$250$		0			0
$251$	218.622	−	218.622i	0.871005	−	0.871005i	−0.121577	−	0.992582i	$-0.538795\pi$
$251$	218.622	−	218.622i	0.871005	−	0.871005i	0.992582	+	0.121577i	$0.0387950\pi$
$252$		0			0
$253$	−381.692			−1.50866
$254$		0			0
$255$	59.3434	−	113.813i	0.232719	−	0.446325i
$256$		0			0
$257$	−97.0001	−	97.0001i	−0.377432	−	0.377432i	0.492743	−	0.870175i	$-0.335994\pi$
$257$	−97.0001	−	97.0001i	−0.377432	−	0.377432i	−0.870175	+	0.492743i	$0.835994\pi$
$258$		0			0
$259$	−104.115	+	104.115i	−0.401989	+	0.401989i
$260$		0			0
$261$	−118.929	+	118.929i	−0.455665	+	0.455665i
$262$		0			0
$263$	62.4735	+	62.4735i	0.237542	+	0.237542i	0.815831	−	0.578290i	$-0.196280\pi$
$263$	62.4735	+	62.4735i	0.237542	+	0.237542i	−0.578290	+	0.815831i	$0.696280\pi$
$264$		0			0
$265$	−115.981	+	36.4839i	−0.437664	+	0.137675i
$266$		0			0
$267$	−155.360			−0.581873
$268$		0			0
$269$	315.384	−	315.384i	1.17243	−	1.17243i	0.190804	−	0.981628i	$-0.438891\pi$
$269$	315.384	−	315.384i	1.17243	−	1.17243i	0.981628	−	0.190804i	$-0.0611095\pi$
$270$		0			0
$271$	113.916			0.420354			0.210177	−	0.977663i	$-0.432596\pi$
$271$	113.916			0.420354			0.210177	+	0.977663i	$0.432596\pi$
$272$		0			0
$273$	43.3509	−	43.3509i	0.158795	−	0.158795i
$274$		0			0
$275$	56.3410	−	317.061i	0.204876	−	1.15295i
$276$		0			0
$277$	−26.5970			−0.0960179			−0.0480089	−	0.998847i	$-0.515288\pi$
$277$	−26.5970			−0.0960179			−0.0480089	+	0.998847i	$0.515288\pi$
$278$		0			0
$279$	166.251			0.595880
$280$		0			0
$281$		−	335.487i		−	1.19390i	−0.802278	−	0.596951i	$-0.796379\pi$
$281$		−	335.487i		−	1.19390i	0.802278	−	0.596951i	$-0.203621\pi$
$282$		0			0
$283$			165.652i			0.585342i	0.956213	+	0.292671i	$0.0945441\pi$
$283$			165.652i			0.585342i	−0.956213	+	0.292671i	$0.905456\pi$
$284$		0			0
$285$	79.5090	+	41.4569i	0.278979	+	0.145463i
$286$		0			0
$287$	−259.161	−	259.161i	−0.903001	−	0.903001i
$288$		0			0
$289$			135.163i			0.467690i
$290$		0			0
$291$	24.3911	+	24.3911i	0.0838182	+	0.0838182i
$292$		0			0
$293$		−	331.620i		−	1.13181i	−0.824471	−	0.565905i	$-0.808527\pi$
$293$		−	331.620i		−	1.13181i	0.824471	−	0.565905i	$-0.191473\pi$
$294$		0			0
$295$	160.119	−	307.088i	0.542777	−	1.04097i
$296$		0			0
$297$	186.717	−	186.717i	0.628677	−	0.628677i
$298$		0			0
$299$	−200.973	−	200.973i	−0.672152	−	0.672152i
$300$		0			0
$301$	−65.6606	−	65.6606i	−0.218142	−	0.218142i
$302$		0			0
$303$	65.4902	−	65.4902i	0.216139	−	0.216139i
$304$		0			0
$305$	−137.863	+	264.403i	−0.452010	+	0.866896i
$306$		0			0
$307$			164.676i			0.536404i	0.963363	+	0.268202i	$0.0864295\pi$
$307$			164.676i			0.536404i	−0.963363	+	0.268202i	$0.913570\pi$
$308$		0			0
$309$	−27.3352	−	27.3352i	−0.0884635	−	0.0884635i
$310$		0			0
$311$			573.207i			1.84311i	0.388250	+	0.921554i	$0.373080\pi$
$311$			573.207i			1.84311i	−0.388250	+	0.921554i	$0.626920\pi$
$312$		0			0
$313$	14.3002	+	14.3002i	0.0456875	+	0.0456875i	0.729581	−	0.683894i	$-0.239715\pi$
$313$	14.3002	+	14.3002i	0.0456875	+	0.0456875i	−0.683894	+	0.729581i	$0.739715\pi$
$314$		0			0
$315$	169.291	+	88.2706i	0.537433	+	0.280224i
$316$		0			0
$317$			297.136i			0.937338i	0.883374	+	0.468669i	$0.155266\pi$
$317$			297.136i			0.937338i	−0.883374	+	0.468669i	$0.844734\pi$
$318$		0			0
$319$			290.945i			0.912053i
$320$		0			0
$321$	215.115			0.670140
$322$		0			0
$323$	−296.318			−0.917392
$324$		0			0
$325$	196.609	−	137.278i	0.604949	−	0.422393i
$326$		0			0
$327$	−41.9152	+	41.9152i	−0.128181	+	0.128181i
$328$		0			0
$329$	−380.023			−1.15508
$330$		0			0
$331$	114.533	−	114.533i	0.346020	−	0.346020i	−0.512605	−	0.858625i	$-0.671319\pi$
$331$	114.533	−	114.533i	0.346020	−	0.346020i	0.858625	+	0.512605i	$0.171319\pi$
$332$		0			0
$333$	−213.811			−0.642075
$334$		0			0
$335$	351.560	−	110.590i	1.04943	−	0.330118i
$336$		0			0
$337$	128.010	+	128.010i	0.379850	+	0.379850i	0.871048	−	0.491198i	$-0.163441\pi$
$337$	128.010	+	128.010i	0.379850	+	0.379850i	−0.491198	+	0.871048i	$0.663441\pi$
$338$		0			0
$339$	42.1120	−	42.1120i	0.124224	−	0.124224i
$340$		0			0
$341$	203.356	−	203.356i	0.596353	−	0.596353i
$342$		0			0
$343$	−260.000	−	260.000i	−0.758016	−	0.758016i
$344$		0			0
$345$	−85.3818	+	163.751i	−0.247484	+	0.474641i
$346$		0			0
$347$	402.112			1.15882			0.579412	−	0.815035i	$-0.303282\pi$
$347$	402.112			1.15882			0.579412	+	0.815035i	$0.303282\pi$
$348$		0			0
$349$	183.939	−	183.939i	0.527047	−	0.527047i	−0.392644	−	0.919691i	$-0.628439\pi$
$349$	183.939	−	183.939i	0.527047	−	0.527047i	0.919691	+	0.392644i	$0.128439\pi$
$350$		0			0
$351$	196.626			0.560187
$352$		0			0
$353$	−24.3150	+	24.3150i	−0.0688810	+	0.0688810i	−0.740708	−	0.671827i	$-0.765510\pi$
$353$	−24.3150	+	24.3150i	−0.0688810	+	0.0688810i	0.671827	+	0.740708i	$0.265510\pi$
$354$		0			0
$355$	−136.555	+	42.9558i	−0.384661	+	0.121002i
$356$		0			0
$357$	131.639			0.368737
$358$		0			0
$359$	574.715			1.60088			0.800439	−	0.599414i	$-0.204600\pi$
$359$	574.715			1.60088			0.800439	+	0.599414i	$0.204600\pi$
$360$		0			0
$361$			153.994i			0.426577i
$362$		0			0
$363$		−	55.9944i		−	0.154254i
$364$		0			0
$365$	30.2275	−	57.9724i	0.0828151	−	0.158829i
$366$		0			0
$367$	380.075	+	380.075i	1.03563	+	1.03563i	0.999341	+	0.0362850i	$0.0115524\pi$
$367$	380.075	+	380.075i	1.03563	+	1.03563i	0.0362850	+	0.999341i	$0.488448\pi$
$368$		0			0
$369$		−	532.214i		−	1.44231i
$370$		0			0
$371$	−88.1727	−	88.1727i	−0.237662	−	0.237662i
$372$		0			0
$373$		−	1.18922i		−	0.00318825i	−0.999999	−	0.00159413i	$-0.999493\pi$
$373$		−	1.18922i		−	0.00318825i	0.999999	−	0.00159413i	$-0.000507426\pi$
$374$		0			0
$375$	−123.421	−	95.0955i	−0.329121	−	0.253588i
$376$		0			0
$377$	−153.192	+	153.192i	−0.406345	+	0.406345i
$378$		0			0
$379$	−241.146	−	241.146i	−0.636269	−	0.636269i	0.313364	−	0.949633i	$-0.398544\pi$
$379$	−241.146	−	241.146i	−0.636269	−	0.636269i	−0.949633	+	0.313364i	$0.898544\pi$
$380$		0			0
$381$	−130.159	−	130.159i	−0.341626	−	0.341626i
$382$		0			0
$383$	−18.5247	+	18.5247i	−0.0483675	+	0.0483675i	−0.730877	−	0.682509i	$-0.760889\pi$
$383$	−18.5247	+	18.5247i	−0.0483675	+	0.0483675i	0.682509	+	0.730877i	$0.260889\pi$
$384$		0			0
$385$	315.048	−	99.1040i	0.818306	−	0.257413i
$386$		0			0
$387$		−	134.841i		−	0.348425i
$388$		0			0
$389$	420.008	+	420.008i	1.07971	+	1.07971i	0.996535	+	0.0831763i	$0.0265065\pi$
$389$	420.008	+	420.008i	1.07971	+	1.07971i	0.0831763	+	0.996535i	$0.473494\pi$
$390$		0			0
$391$		−	610.275i		−	1.56081i
$392$		0			0
$393$	26.4307	+	26.4307i	0.0672537	+	0.0672537i
$394$		0			0
$395$	−409.327	+	128.761i	−1.03627	+	0.325978i
$396$		0			0
$397$			146.340i			0.368615i	0.982869	+	0.184307i	$0.0590042\pi$
$397$			146.340i			0.368615i	−0.982869	+	0.184307i	$0.940996\pi$
$398$		0			0
$399$			91.9625i			0.230482i
$400$		0			0
$401$	−132.278			−0.329871			−0.164936	−	0.986304i	$-0.552742\pi$
$401$	−132.278			−0.329871			−0.164936	+	0.986304i	$0.552742\pi$
$402$		0			0
$403$	214.148			0.531384
$404$		0			0
$405$	62.2128	+	197.772i	0.153612	+	0.488326i
$406$		0			0
$407$	−261.532	+	261.532i	−0.642584	+	0.642584i
$408$		0			0
$409$	−306.287			−0.748867			−0.374433	−	0.927254i	$-0.622163\pi$
$409$	−306.287			−0.748867			−0.374433	+	0.927254i	$0.622163\pi$
$410$		0			0
$411$	239.875	−	239.875i	0.583637	−	0.583637i
$412$		0			0
$413$	355.187			0.860016
$414$		0			0
$415$	107.876	+	342.932i	0.259941	+	0.826343i
$416$		0			0
$417$	−124.843	−	124.843i	−0.299383	−	0.299383i
$418$		0			0
$419$	347.061	−	347.061i	0.828309	−	0.828309i	−0.158974	−	0.987283i	$-0.550819\pi$
$419$	347.061	−	347.061i	0.828309	−	0.828309i	0.987283	+	0.158974i	$0.0508186\pi$
$420$		0			0
$421$	303.635	−	303.635i	0.721222	−	0.721222i	−0.247632	−	0.968854i	$-0.579652\pi$
$421$	303.635	−	303.635i	0.721222	−	0.721222i	0.968854	+	0.247632i	$0.0796523\pi$
$422$		0			0
$423$	−390.207	−	390.207i	−0.922475	−	0.922475i
$424$		0			0
$425$	506.939	+	90.0819i	1.19280	+	0.211957i
$426$		0			0
$427$	−305.817			−0.716198
$428$		0			0
$429$	108.895	−	108.895i	0.253835	−	0.253835i
$430$		0			0
$431$	−131.782			−0.305760			−0.152880	−	0.988245i	$-0.548855\pi$
$431$	−131.782			−0.305760			−0.152880	+	0.988245i	$0.548855\pi$
$432$		0			0
$433$	322.889	−	322.889i	0.745701	−	0.745701i	−0.227967	−	0.973669i	$-0.573208\pi$
$433$	322.889	−	322.889i	0.745701	−	0.745701i	0.973669	+	0.227967i	$0.0732080\pi$
$434$		0			0
$435$	124.820	+	65.0824i	0.286941	+	0.149615i
$436$		0			0
$437$	426.335			0.975594
$438$		0			0
$439$	−423.768			−0.965304			−0.482652	−	0.875812i	$-0.660326\pi$
$439$	−423.768			−0.965304			−0.482652	+	0.875812i	$0.660326\pi$
$440$		0			0
$441$		−	169.064i		−	0.383364i
$442$		0			0
$443$		−	758.450i		−	1.71208i	−0.516912	−	0.856038i	$-0.672919\pi$
$443$		−	758.450i		−	1.71208i	0.516912	−	0.856038i	$-0.327081\pi$
$444$		0			0
$445$	−187.007	−	594.488i	−0.420241	−	1.33593i
$446$		0			0
$447$	−119.944	−	119.944i	−0.268331	−	0.268331i
$448$		0			0
$449$			516.303i			1.14989i	0.818191	+	0.574947i	$0.194977\pi$
$449$			516.303i			1.14989i	−0.818191	+	0.574947i	$0.805023\pi$
$450$		0			0
$451$	−650.999	−	650.999i	−1.44346	−	1.44346i
$452$		0			0
$453$			190.878i			0.421364i
$454$		0			0
$455$	218.065	+	113.702i	0.479263	+	0.249894i
$456$		0			0
$457$	−612.830	+	612.830i	−1.34099	+	1.34099i	−0.445905	+	0.895080i	$0.647118\pi$
$457$	−612.830	+	612.830i	−1.34099	+	1.34099i	−0.895080	+	0.445905i	$0.852882\pi$
$458$		0			0
$459$	298.536	+	298.536i	0.650406	+	0.650406i
$460$		0			0
$461$	193.692	+	193.692i	0.420156	+	0.420156i	0.885257	−	0.465102i	$-0.153982\pi$
$461$	193.692	+	193.692i	0.420156	+	0.420156i	−0.465102	+	0.885257i	$0.653982\pi$
$462$		0			0
$463$	159.340	−	159.340i	0.344146	−	0.344146i	−0.513777	−	0.857924i	$-0.671754\pi$
$463$	159.340	−	159.340i	0.344146	−	0.344146i	0.857924	+	0.513777i	$0.171754\pi$
$464$		0			0
$465$	−41.7534	−	132.732i	−0.0897922	−	0.285446i
$466$		0			0
$467$			190.782i			0.408528i	0.978916	+	0.204264i	$0.0654801\pi$
$467$			190.782i			0.408528i	−0.978916	+	0.204264i	$0.934520\pi$
$468$		0			0
$469$	267.268	+	267.268i	0.569867	+	0.569867i
$470$		0			0
$471$			156.316i			0.331880i
$472$		0			0
$473$	−164.936	−	164.936i	−0.348702	−	0.348702i
$474$		0			0
$475$	−62.9307	+	354.144i	−0.132486	+	0.745567i
$476$		0			0
$477$		−	181.071i		−	0.379605i
$478$		0			0
$479$			246.542i			0.514701i	0.966318	+	0.257350i	$0.0828494\pi$
$479$			246.542i			0.514701i	−0.966318	+	0.257350i	$0.917151\pi$
$480$		0			0
$481$	−275.410			−0.572579
$482$		0			0
$483$	−189.399			−0.392131
$484$		0			0
$485$	−63.9734	+	122.693i	−0.131904	+	0.252974i
$486$		0			0
$487$	−118.580	+	118.580i	−0.243491	+	0.243491i	−0.818293	−	0.574802i	$-0.805079\pi$
$487$	−118.580	+	118.580i	−0.243491	+	0.243491i	0.574802	+	0.818293i	$0.305079\pi$
$488$		0			0
$489$	−212.284			−0.434118
$490$		0			0
$491$	−273.453	+	273.453i	−0.556930	+	0.556930i	−0.928432	−	0.371502i	$-0.878843\pi$
$491$	−273.453	+	273.453i	−0.556930	+	0.556930i	0.371502	+	0.928432i	$0.378843\pi$
$492$		0			0
$493$	−465.183			−0.943576
$494$		0			0
$495$	425.251	+	221.731i	0.859093	+	0.447941i
$496$		0			0
$497$	−103.814	−	103.814i	−0.208881	−	0.208881i
$498$		0			0
$499$	458.148	−	458.148i	0.918133	−	0.918133i	−0.0787603	−	0.996894i	$-0.525096\pi$
$499$	458.148	−	458.148i	0.918133	−	0.918133i	0.996894	+	0.0787603i	$0.0250962\pi$
$500$		0			0
$501$	124.938	−	124.938i	0.249377	−	0.249377i
$502$		0			0
$503$	424.905	+	424.905i	0.844742	+	0.844742i	0.989471	−	0.144729i	$-0.0462311\pi$
$503$	424.905	+	424.905i	0.844742	+	0.844742i	−0.144729	+	0.989471i	$0.546231\pi$
$504$		0			0
$505$	329.430	+	171.769i	0.652337	+	0.340137i
$506$		0			0
$507$	−95.9769			−0.189304
$508$		0			0
$509$	36.5107	−	36.5107i	0.0717303	−	0.0717303i	−0.670331	−	0.742062i	$-0.733848\pi$
$509$	36.5107	−	36.5107i	0.0717303	−	0.0717303i	0.742062	+	0.670331i	$0.233848\pi$
$510$		0			0
$511$	67.0526			0.131218
$512$		0			0
$513$	−208.556	+	208.556i	−0.406541	+	0.406541i
$514$		0			0
$515$	71.6953	−	137.502i	0.139214	−	0.266995i
$516$		0			0
$517$	−954.596			−1.84641
$518$		0			0
$519$	287.469			0.553891
$520$		0			0
$521$		−	220.060i		−	0.422381i	−0.977445	−	0.211190i	$-0.932266\pi$
$521$		−	220.060i		−	0.422381i	0.977445	−	0.211190i	$-0.0677340\pi$
$522$		0			0
$523$			558.669i			1.06820i	0.845421	+	0.534100i	$0.179350\pi$
$523$			558.669i			1.06820i	−0.845421	+	0.534100i	$0.820650\pi$
$524$		0			0
$525$	27.9570	−	157.329i	0.0532515	−	0.299674i
$526$		0			0
$527$	325.140	+	325.140i	0.616964	+	0.616964i
$528$		0			0
$529$			349.049i			0.659828i
$530$		0			0
$531$	364.705	+	364.705i	0.686827	+	0.686827i
$532$		0			0
$533$		−	685.546i		−	1.28620i
$534$		0			0
$535$	258.934	+	823.142i	0.483989	+	1.53858i
$536$		0			0
$537$	−176.731	+	176.731i	−0.329108	+	0.329108i
$538$		0			0
$539$	−206.797	−	206.797i	−0.383669	−	0.383669i
$540$		0			0
$541$	304.353	+	304.353i	0.562575	+	0.562575i	0.930038	−	0.367463i	$-0.119774\pi$
$541$	304.353	+	304.353i	0.562575	+	0.562575i	−0.367463	+	0.930038i	$0.619774\pi$
$542$		0			0
$543$	−277.927	+	277.927i	−0.511835	+	0.511835i
$544$		0			0
$545$	−210.843	−	109.936i	−0.386868	−	0.201718i
$546$		0			0
$547$			72.4546i			0.132458i	0.997804	+	0.0662290i	$0.0210968\pi$
$547$			72.4546i			0.132458i	−0.997804	+	0.0662290i	$0.978903\pi$
$548$		0			0
$549$	−314.012	−	314.012i	−0.571972	−	0.571972i
$550$		0			0
$551$		−	324.974i		−	0.589790i
$552$		0			0
$553$	−311.184	−	311.184i	−0.562721	−	0.562721i
$554$		0			0
$555$	53.6980	+	170.704i	0.0967532	+	0.307574i
$556$		0			0
$557$			219.766i			0.394553i	0.980348	+	0.197276i	$0.0632096\pi$
$557$			219.766i			0.394553i	−0.980348	+	0.197276i	$0.936790\pi$
$558$		0			0
$559$		−	173.689i		−	0.310713i
$560$		0			0
$561$	330.671			0.589431
$562$		0			0
$563$	−102.644			−0.182316			−0.0911581	−	0.995836i	$-0.529057\pi$
$563$	−102.644			−0.182316			−0.0911581	+	0.995836i	$0.529057\pi$
$564$		0			0
$565$	211.833	+	110.452i	0.374925	+	0.195491i
$566$		0			0
$567$	−150.353	+	150.353i	−0.265173	+	0.265173i
$568$		0			0
$569$	146.493			0.257457			0.128729	−	0.991680i	$-0.458910\pi$
$569$	146.493			0.257457			0.128729	+	0.991680i	$0.458910\pi$
$570$		0			0
$571$	−163.098	+	163.098i	−0.285635	+	0.285635i	−0.835351	−	0.549716i	$-0.814736\pi$
$571$	−163.098	+	163.098i	−0.285635	+	0.285635i	0.549716	+	0.835351i	$0.314736\pi$
$572$		0			0
$573$	−449.585			−0.784616
$574$		0			0
$575$	−729.371	−	129.608i	−1.26847	−	0.225405i
$576$		0			0
$577$	−298.200	−	298.200i	−0.516811	−	0.516811i	0.399794	−	0.916605i	$-0.369082\pi$
$577$	−298.200	−	298.200i	−0.516811	−	0.516811i	−0.916605	+	0.399794i	$0.869082\pi$
$578$		0			0
$579$	30.1951	−	30.1951i	0.0521504	−	0.0521504i
$580$		0			0
$581$	−260.709	+	260.709i	−0.448724	+	0.448724i
$582$		0			0
$583$	−221.485	−	221.485i	−0.379906	−	0.379906i
$584$		0			0
$585$	107.160	+	340.658i	0.183180	+	0.582321i
$586$		0			0
$587$	−738.236			−1.25764			−0.628821	−	0.777550i	$-0.716462\pi$
$587$	−738.236			−1.25764			−0.628821	+	0.777550i	$0.716462\pi$
$588$		0			0
$589$	−227.141	+	227.141i	−0.385639	+	0.385639i
$590$		0			0
$591$	−210.910			−0.356869
$592$		0			0
$593$	−632.549	+	632.549i	−1.06669	+	1.06669i	−0.0690814	+	0.997611i	$0.522007\pi$
$593$	−632.549	+	632.549i	−1.06669	+	1.06669i	−0.997611	+	0.0690814i	$0.977993\pi$
$594$		0			0
$595$	158.454	+	503.720i	0.266310	+	0.846589i
$596$		0			0
$597$	−219.990			−0.368493
$598$		0			0
$599$	419.874			0.700958			0.350479	−	0.936571i	$-0.386019\pi$
$599$	419.874			0.700958			0.350479	+	0.936571i	$0.386019\pi$
$600$		0			0
$601$			230.628i			0.383741i	0.981420	+	0.191871i	$0.0614554\pi$
$601$			230.628i			0.383741i	−0.981420	+	0.191871i	$0.938545\pi$
$602$		0			0
$603$			548.861i			0.910217i
$604$		0			0
$605$	214.264	−	67.4005i	0.354155	−	0.111406i
$606$		0			0
$607$	−641.727	−	641.727i	−1.05721	−	1.05721i	−0.998261	−	0.0589500i	$-0.981225\pi$
$607$	−641.727	−	641.727i	−1.05721	−	1.05721i	−0.0589500	−	0.998261i	$-0.518775\pi$
$608$		0			0
$609$			144.370i			0.237061i
$610$		0			0
$611$	−502.627	−	502.627i	−0.822630	−	0.822630i
$612$		0			0
$613$			724.254i			1.18149i	0.806858	+	0.590746i	$0.201166\pi$
$613$			724.254i			1.18149i	−0.806858	+	0.590746i	$0.798834\pi$
$614$		0			0
$615$	−424.912	+	133.664i	−0.690914	+	0.217340i
$616$		0			0
$617$	−102.268	+	102.268i	−0.165750	+	0.165750i	−0.785108	−	0.619358i	$-0.787393\pi$
$617$	−102.268	+	102.268i	−0.165750	+	0.165750i	0.619358	+	0.785108i	$0.287393\pi$
$618$		0			0
$619$	−1.61045	−	1.61045i	−0.00260170	−	0.00260170i	0.705805	−	0.708406i	$-0.250586\pi$
$619$	−1.61045	−	1.61045i	−0.00260170	−	0.00260170i	−0.708406	+	0.705805i	$0.750586\pi$
$620$		0			0
$621$	−429.527	−	429.527i	−0.691670	−	0.691670i
$622$		0			0
$623$	451.950	−	451.950i	0.725442	−	0.725442i
$624$		0			0
$625$	215.323	−	586.738i	0.344517	−	0.938780i
$626$		0			0
$627$			231.005i			0.368429i
$628$		0			0
$629$	−418.155	−	418.155i	−0.664794	−	0.664794i
$630$		0			0
$631$		−	333.003i		−	0.527738i	−0.964559	−	0.263869i	$-0.915001\pi$
$631$		−	333.003i		−	0.527738i	0.964559	−	0.263869i	$-0.0849987\pi$
$632$		0			0
$633$	301.898	+	301.898i	0.476932	+	0.476932i
$634$		0			0
$635$	341.385	−	654.731i	0.537614	−	1.03107i
$636$		0			0
$637$		−	217.772i		−	0.341871i
$638$		0			0
$639$		−	213.192i		−	0.333633i
$640$		0			0
$641$	90.2646			0.140818			0.0704092	−	0.997518i	$-0.477570\pi$
$641$	90.2646			0.140818			0.0704092	+	0.997518i	$0.477570\pi$
$642$		0			0
$643$	177.970			0.276781			0.138391	−	0.990378i	$-0.455807\pi$
$643$	177.970			0.276781			0.138391	+	0.990378i	$0.455807\pi$
$644$		0			0
$645$	−107.655	+	33.8648i	−0.166907	+	0.0525036i
$646$		0			0
$647$	−591.289	+	591.289i	−0.913893	+	0.913893i	−0.996576	−	0.0826827i	$-0.973651\pi$
$647$	−591.289	+	591.289i	−0.913893	+	0.913893i	0.0826827	+	0.996576i	$0.473651\pi$
$648$		0			0
$649$	892.209			1.37474
$650$		0			0
$651$	100.908	−	100.908i	0.155004	−	0.155004i
$652$		0			0
$653$	390.593			0.598152			0.299076	−	0.954229i	$-0.403322\pi$
$653$	390.593			0.598152			0.299076	+	0.954229i	$0.403322\pi$
$654$		0			0
$655$	−69.3230	+	132.952i	−0.105837	+	0.202981i
$656$		0			0
$657$	68.8496	+	68.8496i	0.104794	+	0.104794i
$658$		0			0
$659$	−766.873	+	766.873i	−1.16369	+	1.16369i	−0.180032	+	0.983661i	$0.557620\pi$
$659$	−766.873	+	766.873i	−1.16369	+	1.16369i	−0.983661	+	0.180032i	$0.942380\pi$
$660$		0			0
$661$	−48.7607	+	48.7607i	−0.0737680	+	0.0737680i	−0.743028	−	0.669260i	$-0.766611\pi$
$661$	−48.7607	+	48.7607i	−0.0737680	+	0.0737680i	0.669260	+	0.743028i	$0.266611\pi$
$662$		0			0
$663$	174.109	+	174.109i	0.262608	+	0.262608i
$664$		0			0
$665$	−351.896	+	110.695i	−0.529167	+	0.166459i
$666$		0			0
$667$	669.294			1.00344
$668$		0			0
$669$	−139.835	+	139.835i	−0.209021	+	0.209021i
$670$		0			0
$671$	−768.195			−1.14485
$672$		0			0
$673$	290.185	−	290.185i	0.431181	−	0.431181i	−0.457849	−	0.889030i	$-0.651380\pi$
$673$	290.185	−	290.185i	0.431181	−	0.431181i	0.889030	+	0.457849i	$0.151380\pi$
$674$		0			0
$675$	420.198	−	293.394i	0.622516	−	0.434658i
$676$		0			0
$677$	407.637			0.602123			0.301061	−	0.953605i	$-0.402659\pi$
$677$	407.637			0.602123			0.301061	+	0.953605i	$0.402659\pi$
$678$		0			0
$679$	−141.910			−0.208998
$680$		0			0
$681$			4.36768i			0.00641362i
$682$		0			0
$683$		−	684.730i		−	1.00253i	−0.865293	−	0.501267i	$-0.832868\pi$
$683$		−	684.730i		−	1.00253i	0.865293	−	0.501267i	$-0.167132\pi$
$684$		0			0
$685$	1206.62	+	629.148i	1.76149	+	0.918464i
$686$		0			0
$687$	15.6547	+	15.6547i	0.0227871	+	0.0227871i
$688$		0			0
$689$		−	233.239i		−	0.338518i
$690$		0			0
$691$	405.351	+	405.351i	0.586616	+	0.586616i	0.936713	−	0.350098i	$-0.113852\pi$
$691$	405.351	+	405.351i	0.586616	+	0.586616i	−0.350098	+	0.936713i	$0.613852\pi$
$692$		0			0
$693$			491.858i			0.709751i
$694$		0			0
$695$	327.440	−	627.986i	0.471136	−	0.903577i
$696$		0			0
$697$	1040.86	−	1040.86i	1.49335	−	1.49335i
$698$		0			0
$699$	171.696	+	171.696i	0.245631	+	0.245631i
$700$		0			0
$701$	87.8312	+	87.8312i	0.125294	+	0.125294i	0.766973	−	0.641679i	$-0.221762\pi$
$701$	87.8312	+	87.8312i	0.125294	+	0.125294i	−0.641679	+	0.766973i	$0.721762\pi$
$702$		0			0
$703$	292.121	−	292.121i	0.415535	−	0.415535i
$704$		0			0
$705$	−213.537	+	409.536i	−0.302889	+	0.580901i
$706$		0			0
$707$			381.029i			0.538938i
$708$		0			0
$709$	286.699	+	286.699i	0.404370	+	0.404370i	0.879770	−	0.475400i	$-0.157696\pi$
$709$	286.699	+	286.699i	0.404370	+	0.404370i	−0.475400	+	0.879770i	$0.657696\pi$
$710$		0			0
$711$		−	639.048i		−	0.898802i
$712$		0			0
$713$	−467.804	−	467.804i	−0.656107	−	0.656107i
$714$		0			0
$715$	547.767	+	285.612i	0.766108	+	0.399458i
$716$		0			0
$717$			116.182i			0.162038i
$718$		0			0
$719$			170.890i			0.237677i	0.992914	+	0.118839i	$0.0379171\pi$
$719$			170.890i			0.237677i	−0.992914	+	0.118839i	$0.962083\pi$
$720$		0			0
$721$	159.039			0.220581
$722$		0			0
$723$	−225.502			−0.311897
$724$		0			0
$725$	−98.7936	+	555.964i	−0.136267	+	0.766847i
$726$		0			0
$727$	510.540	−	510.540i	0.702256	−	0.702256i	−0.262638	−	0.964894i	$-0.584593\pi$
$727$	510.540	−	510.540i	0.702256	−	0.702256i	0.964894	+	0.262638i	$0.0845926\pi$
$728$		0			0
$729$	−78.7983			−0.108091
$730$		0			0
$731$	263.711	−	263.711i	0.360754	−	0.360754i
$732$		0			0
$733$	0.0813496			0.000110982			5.54908e−5	−	1.00000i	$-0.499982\pi$
$733$	0.0813496			0.000110982			5.54908e−5		1.00000i	$0.499982\pi$
$734$		0			0
$735$	−134.978	+	42.4599i	−0.183644	+	0.0577686i
$736$		0			0
$737$	671.362	+	671.362i	0.910939	+	0.910939i
$738$		0			0
$739$	−37.3702	+	37.3702i	−0.0505685	+	0.0505685i	−0.731939	−	0.681370i	$-0.761384\pi$
$739$	−37.3702	+	37.3702i	−0.0505685	+	0.0505685i	0.681370	+	0.731939i	$0.261384\pi$
$740$		0			0
$741$	−121.632	+	121.632i	−0.164145	+	0.164145i
$742$		0			0
$743$	−217.733	−	217.733i	−0.293046	−	0.293046i	0.545236	−	0.838282i	$-0.316440\pi$
$743$	−217.733	−	217.733i	−0.293046	−	0.293046i	−0.838282	+	0.545236i	$0.816440\pi$
$744$		0			0
$745$	314.591	−	603.345i	0.422270	−	0.809859i
$746$		0			0
$747$	−535.391			−0.716722
$748$		0			0
$749$	−625.781	+	625.781i	−0.835488	+	0.835488i
$750$		0			0
$751$	321.722			0.428391			0.214196	−	0.976791i	$-0.431287\pi$
$751$	321.722			0.428391			0.214196	+	0.976791i	$0.431287\pi$
$752$		0			0
$753$	272.503	−	272.503i	0.361890	−	0.361890i
$754$		0			0
$755$	−730.398	+	229.760i	−0.967414	+	0.304318i
$756$		0			0
$757$	−794.309			−1.04929			−0.524643	−	0.851322i	$-0.675801\pi$
$757$	−794.309			−1.04929			−0.524643	+	0.851322i	$0.675801\pi$
$758$		0			0
$759$	−475.761			−0.626826
$760$		0			0
$761$		−	413.877i		−	0.543859i	−0.962317	−	0.271929i	$-0.912338\pi$
$761$		−	413.877i		−	0.543859i	0.962317	−	0.271929i	$-0.0876617\pi$
$762$		0			0
$763$		−	243.867i		−	0.319616i
$764$		0			0
$765$	−354.519	+	679.921i	−0.463423	+	0.888785i
$766$		0			0
$767$	469.778	+	469.778i	0.612488	+	0.612488i
$768$		0			0
$769$		−	1059.37i		−	1.37760i	−0.724952	−	0.688799i	$-0.758138\pi$
$769$		−	1059.37i		−	1.37760i	0.724952	−	0.688799i	$-0.241862\pi$
$770$		0			0
$771$	−120.906	−	120.906i	−0.156817	−	0.156817i
$772$		0			0
$773$		−	1328.27i		−	1.71833i	−0.511700	−	0.859164i	$-0.670984\pi$
$773$		−	1328.27i		−	1.71833i	0.511700	−	0.859164i	$-0.329016\pi$
$774$		0			0
$775$	457.644	−	319.540i	0.590508	−	0.412310i
$776$		0			0
$777$	−129.775	+	129.775i	−0.167020	+	0.167020i
$778$		0			0
$779$	727.141	+	727.141i	0.933429	+	0.933429i
$780$		0			0
$781$	−260.774	−	260.774i	−0.333898	−	0.333898i
$782$		0			0
$783$	−327.407	+	327.407i	−0.418145	+	0.418145i
$784$		0			0
$785$	−598.144	+	188.157i	−0.761967	+	0.239691i
$786$		0			0
$787$		−	126.631i		−	0.160903i	−0.996759	−	0.0804515i	$-0.974364\pi$
$787$		−	126.631i		−	0.160903i	0.996759	−	0.0804515i	$-0.0256362\pi$
$788$		0			0
$789$	77.8703	+	77.8703i	0.0986950	+	0.0986950i
$790$		0			0
$791$			245.012i			0.309750i
$792$		0			0
$793$	−404.480	−	404.480i	−0.510064	−	0.510064i
$794$		0			0
$795$	−144.565	+	45.4756i	−0.181843	+	0.0572020i
$796$		0			0
$797$			123.005i			0.154335i	0.997018	+	0.0771677i	$0.0245877\pi$
$797$			123.005i			0.154335i	−0.997018	+	0.0771677i	$0.975412\pi$
$798$		0			0
$799$		−	1526.27i		−	1.91023i
$800$		0			0
$801$	928.124			1.15871
$802$		0			0
$803$	168.433			0.209754
$804$		0			0
$805$	−227.980	−	724.741i	−0.283205	−	0.900299i
$806$		0			0
$807$	393.112	−	393.112i	0.487128	−	0.487128i
$808$		0			0
$809$	1294.86			1.60057			0.800285	−	0.599620i	$-0.204682\pi$
$809$	1294.86			1.60057			0.800285	+	0.599620i	$0.204682\pi$
$810$		0			0
$811$	596.423	−	596.423i	0.735416	−	0.735416i	−0.236271	−	0.971687i	$-0.575925\pi$
$811$	596.423	−	596.423i	0.735416	−	0.735416i	0.971687	+	0.236271i	$0.0759253\pi$
$812$		0			0
$813$	141.991			0.174651
$814$		0			0
$815$	−255.526	−	812.308i	−0.313529	−	0.996697i
$816$		0			0
$817$	184.227	+	184.227i	0.225492	+	0.225492i
$818$		0			0
$819$	−258.980	+	258.980i	−0.316214	+	0.316214i
$820$		0			0
$821$	113.969	−	113.969i	0.138817	−	0.138817i	−0.634284	−	0.773100i	$-0.718705\pi$
$821$	113.969	−	113.969i	0.138817	−	0.138817i	0.773100	+	0.634284i	$0.218705\pi$
$822$		0			0
$823$	704.375	+	704.375i	0.855862	+	0.855862i	0.990848	−	0.134985i	$-0.0430987\pi$
$823$	704.375	+	704.375i	0.855862	+	0.855862i	−0.134985	+	0.990848i	$0.543099\pi$
$824$		0			0
$825$	70.2265	−	395.202i	0.0851231	−	0.479033i
$826$		0			0
$827$	307.918			0.372331			0.186166	−	0.982518i	$-0.440394\pi$
$827$	307.918			0.372331			0.186166	+	0.982518i	$0.440394\pi$
$828$		0			0
$829$	151.064	−	151.064i	0.182224	−	0.182224i	−0.610100	−	0.792324i	$-0.708871\pi$
$829$	151.064	−	151.064i	0.182224	−	0.182224i	0.792324	+	0.610100i	$0.208871\pi$
$830$		0			0
$831$	−33.1519			−0.0398940
$832$		0			0
$833$	330.642	−	330.642i	0.396929	−	0.396929i
$834$		0			0
$835$	628.464	+	327.689i	0.752652	+	0.392442i
$836$		0			0
$837$	457.684			0.546815
$838$		0			0
$839$	−131.699			−0.156972			−0.0784859	−	0.996915i	$-0.525009\pi$
$839$	−131.699			−0.156972			−0.0784859	+	0.996915i	$0.525009\pi$
$840$		0			0
$841$			330.830i			0.393377i
$842$		0			0
$843$		−	418.169i		−	0.496048i
$844$		0			0
$845$	−115.528	−	367.257i	−0.136719	−	0.434624i
$846$		0			0
$847$	162.890	+	162.890i	0.192315	+	0.192315i
$848$		0			0
$849$			206.478i			0.243201i
$850$		0			0
$851$	601.632	+	601.632i	0.706970	+	0.706970i
$852$		0			0
$853$		−	125.517i		−	0.147147i	−0.997290	−	0.0735737i	$-0.976560\pi$
$853$		−	125.517i		−	0.147147i	0.997290	−	0.0735737i	$-0.0234404\pi$
$854$		0			0
$855$	−474.989	−	247.665i	−0.555542	−	0.289666i
$856$		0			0
$857$	−146.932	+	146.932i	−0.171449	+	0.171449i	−0.787616	−	0.616167i	$-0.788685\pi$
$857$	−146.932	+	146.932i	−0.171449	+	0.171449i	0.616167	+	0.787616i	$0.288685\pi$
$858$		0			0
$859$	117.232	+	117.232i	0.136475	+	0.136475i	0.772044	−	0.635569i	$-0.219234\pi$
$859$	117.232	+	117.232i	0.136475	+	0.136475i	−0.635569	+	0.772044i	$0.719234\pi$
$860$		0			0
$861$	−323.033	−	323.033i	−0.375183	−	0.375183i
$862$		0			0
$863$	164.801	−	164.801i	0.190963	−	0.190963i	−0.605149	−	0.796112i	$-0.706886\pi$
$863$	164.801	−	164.801i	0.190963	−	0.190963i	0.796112	+	0.605149i	$0.206886\pi$
$864$		0			0
$865$	346.027	+	1100.01i	0.400031	+	1.27168i
$866$		0			0
$867$			168.474i			0.194318i
$868$		0			0
$869$	−781.679	−	781.679i	−0.899515	−	0.899515i
$870$		0			0
$871$			706.989i			0.811698i
$872$		0			0
$873$	−145.713	−	145.713i	−0.166911	−	0.166911i
$874$		0			0
$875$	635.674	−	82.3990i	0.726485	−	0.0941703i
$876$		0			0
$877$		−	362.710i		−	0.413580i	−0.978385	−	0.206790i	$-0.933698\pi$
$877$		−	362.710i		−	0.413580i	0.978385	−	0.206790i	$-0.0663017\pi$
$878$		0			0
$879$		−	413.350i		−	0.470250i
$880$		0			0
$881$	−900.515			−1.02215			−0.511075	−	0.859536i	$-0.670753\pi$
$881$	−900.515			−1.02215			−0.511075	+	0.859536i	$0.670753\pi$
$882$		0			0
$883$	374.768			0.424426			0.212213	−	0.977223i	$-0.431933\pi$
$883$	374.768			0.424426			0.212213	+	0.977223i	$0.431933\pi$
$884$		0			0
$885$	199.581	−	382.771i	0.225516	−	0.432509i
$886$		0			0
$887$	493.146	−	493.146i	0.555971	−	0.555971i	−0.372187	−	0.928158i	$-0.621392\pi$
$887$	493.146	−	493.146i	0.555971	−	0.555971i	0.928158	+	0.372187i	$0.121392\pi$
$888$		0			0
$889$	757.281			0.851835
$890$		0			0
$891$	−377.679	+	377.679i	−0.423882	+	0.423882i
$892$		0			0
$893$	1066.25			1.19401
$894$		0			0
$895$	−888.996	−	463.533i	−0.993291	−	0.517914i
$896$		0			0
$897$	−250.504	−	250.504i	−0.279269	−	0.279269i
$898$		0			0
$899$	−356.584	+	356.584i	−0.396645	+	0.396645i
$900$		0			0
$901$	354.126	−	354.126i	0.393036	−	0.393036i
$902$		0			0
$903$	−81.8430	−	81.8430i	−0.0906345	−	0.0906345i
$904$		0			0
$905$	−1398.03	−	728.951i	−1.54479	−	0.805470i
$906$		0			0
$907$	−107.286			−0.118286			−0.0591432	−	0.998250i	$-0.518837\pi$
$907$	−107.286			−0.118286			−0.0591432	+	0.998250i	$0.518837\pi$
$908$		0			0
$909$	−391.240	+	391.240i	−0.430407	+	0.430407i
$910$		0			0
$911$	1193.83			1.31047			0.655233	−	0.755427i	$-0.272570\pi$
$911$	1193.83			1.31047			0.655233	+	0.755427i	$0.272570\pi$
$912$		0			0
$913$	−654.886	+	654.886i	−0.717291	+	0.717291i
$914$		0			0
$915$	−171.840	+	329.567i	−0.187803	+	0.360182i
$916$		0			0
$917$	−153.777			−0.167695
$918$		0			0
$919$	−1001.83			−1.09013			−0.545064	−	0.838394i	$-0.683495\pi$
$919$	−1001.83			−1.09013			−0.545064	+	0.838394i	$0.683495\pi$
$920$		0			0
$921$			205.261i			0.222868i
$922$		0			0
$923$		−	274.613i		−	0.297522i
$924$		0			0
$925$	−588.565	+	410.953i	−0.636287	+	0.444273i
$926$		0			0
$927$	163.301	+	163.301i	0.176161	+	0.176161i
$928$		0			0
$929$			527.162i			0.567451i	0.958905	+	0.283726i	$0.0915705\pi$
$929$			527.162i			0.567451i	−0.958905	+	0.283726i	$0.908429\pi$
$930$		0			0
$931$	230.985	+	230.985i	0.248104	+	0.248104i
$932$		0			0
$933$			714.476i			0.765784i
$934$		0			0
$935$	398.029	+	1265.32i	0.425699	+	1.35328i
$936$		0			0
$937$	129.020	−	129.020i	0.137694	−	0.137694i	−0.634900	−	0.772594i	$-0.718959\pi$
$937$	129.020	−	129.020i	0.137694	−	0.137694i	0.772594	+	0.634900i	$0.218959\pi$
$938$		0			0
$939$	17.8245	+	17.8245i	0.0189825	+	0.0189825i
$940$		0			0
$941$	−381.136	−	381.136i	−0.405033	−	0.405033i	0.474969	−	0.880002i	$-0.342459\pi$
$941$	−381.136	−	381.136i	−0.405033	−	0.405033i	−0.880002	+	0.474969i	$0.842459\pi$
$942$		0			0
$943$	−1497.57	+	1497.57i	−1.58809	+	1.58809i
$944$		0			0
$945$	466.055	+	243.007i	0.493180	+	0.257150i
$946$		0			0
$947$		−	1038.55i		−	1.09667i	−0.836259	−	0.548334i	$-0.815262\pi$
$947$		−	1038.55i		−	1.09667i	0.836259	−	0.548334i	$-0.184738\pi$
$948$		0			0
$949$	88.6854	+	88.6854i	0.0934514	+	0.0934514i
$950$		0			0
$951$			370.367i			0.389450i
$952$		0			0
$953$	871.876	+	871.876i	0.914875	+	0.914875i	0.996651	−	0.0817757i	$-0.0260591\pi$
$953$	871.876	+	871.876i	0.914875	+	0.914875i	−0.0817757	+	0.996651i	$0.526059\pi$
$954$		0			0
$955$	−541.166	−	1720.34i	−0.566666	−	1.80141i
$956$		0			0
$957$			362.650i			0.378944i
$958$		0			0
$959$			1395.62i			1.45528i
$960$		0			0
$961$	−462.530			−0.481300
$962$		0			0
$963$	−1285.10			−1.33448
$964$		0			0
$965$	151.888	+	79.1962i	0.157397	+	0.0820686i
$966$		0			0
$967$	866.285	−	866.285i	0.895848	−	0.895848i	−0.0992181	−	0.995066i	$-0.531634\pi$
$967$	866.285	−	866.285i	0.895848	−	0.895848i	0.995066	+	0.0992181i	$0.0316342\pi$
$968$		0			0
$969$	−369.346			−0.381162
$970$		0			0
$971$	−1165.60	+	1165.60i	−1.20041	+	1.20041i	−0.226371	+	0.974041i	$0.572686\pi$
$971$	−1165.60	+	1165.60i	−1.20041	+	1.20041i	−0.974041	+	0.226371i	$0.927314\pi$
$972$		0			0
$973$	726.347			0.746503
$974$		0			0
$975$	245.064	−	171.110i	0.251347	−	0.175498i
$976$		0			0
$977$	765.976	+	765.976i	0.784008	+	0.784008i	0.980504	−	0.196497i	$-0.0629565\pi$
$977$	765.976	+	765.976i	0.784008	+	0.784008i	−0.196497	+	0.980504i	$0.562957\pi$
$978$		0			0
$979$	1135.27	−	1135.27i	1.15963	−	1.15963i
$980$		0			0
$981$	250.403	−	250.403i	0.255252	−	0.255252i
$982$		0			0
$983$	−212.053	−	212.053i	−0.215720	−	0.215720i	0.590972	−	0.806692i	$-0.298744\pi$
$983$	−212.053	−	212.053i	−0.215720	−	0.215720i	−0.806692	+	0.590972i	$0.798744\pi$
$984$		0			0
$985$	−253.872	−	807.050i	−0.257738	−	0.819340i
$986$		0			0
$987$	−473.681			−0.479920
$988$		0			0
$989$	−379.421	+	379.421i	−0.383641	+	0.383641i
$990$		0			0
$991$	1530.97			1.54487			0.772435	−	0.635094i	$-0.219039\pi$
$991$	1530.97			1.54487			0.772435	+	0.635094i	$0.219039\pi$
$992$		0			0
$993$	142.760	−	142.760i	0.143766	−	0.143766i
$994$		0			0
$995$	−264.803	−	841.798i	−0.266133	−	0.846028i
$996$		0			0
$997$	834.620			0.837131			0.418565	−	0.908187i	$-0.362533\pi$
$997$	834.620			0.837131			0.418565	+	0.908187i	$0.362533\pi$
$998$		0			0
$999$	−588.616			−0.589206

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	320.3.t.a.17.13		44
4.3	odd	2		80.3.t.a.77.21	yes	44
5.3	odd	4		320.3.i.a.273.13		44
8.3	odd	2		640.3.t.b.417.13		44
8.5	even	2		640.3.t.a.417.10		44
16.3	odd	4		640.3.i.b.97.10		44
16.5	even	4		320.3.i.a.177.10		44
16.11	odd	4		80.3.i.a.37.13	yes	44
16.13	even	4		640.3.i.a.97.13		44
20.3	even	4		80.3.i.a.13.13	✓	44
20.7	even	4		400.3.i.b.93.10		44
20.19	odd	2		400.3.t.b.157.2		44
40.3	even	4		640.3.i.b.33.13		44
40.13	odd	4		640.3.i.a.33.10		44
80.3	even	4		640.3.t.b.353.13		44
80.13	odd	4		640.3.t.a.353.10		44
80.27	even	4		400.3.t.b.293.2		44
80.43	even	4		80.3.t.a.53.21	yes	44
80.53	odd	4	inner	320.3.t.a.113.13		44
80.59	odd	4		400.3.i.b.357.10		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.3.i.a.13.13	✓	44	20.3	even	4
80.3.i.a.37.13	yes	44	16.11	odd	4
80.3.t.a.53.21	yes	44	80.43	even	4
80.3.t.a.77.21	yes	44	4.3	odd	2
320.3.i.a.177.10		44	16.5	even	4
320.3.i.a.273.13		44	5.3	odd	4
320.3.t.a.17.13		44	1.1	even	1	trivial
320.3.t.a.113.13		44	80.53	odd	4	inner
400.3.i.b.93.10		44	20.7	even	4
400.3.i.b.357.10		44	80.59	odd	4
400.3.t.b.157.2		44	20.19	odd	2
400.3.t.b.293.2		44	80.27	even	4
640.3.i.a.33.10		44	40.13	odd	4
640.3.i.a.97.13		44	16.13	even	4
640.3.i.b.33.13		44	40.3	even	4
640.3.i.b.97.10		44	16.3	odd	4
640.3.t.a.353.10		44	80.13	odd	4
640.3.t.a.417.10		44	8.5	even	2
640.3.t.b.353.13		44	80.3	even	4
640.3.t.b.417.13		44	8.3	odd	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.t (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.24645 q^{3} +(1.50036 + 4.76958i) q^{5} +(-3.62600 + 3.62600i) q^{7} -7.44635 q^{9} +O(q^{10})\)	\(q+1.24645 q^{3} +(1.50036 + 4.76958i) q^{5} +(-3.62600 + 3.62600i) q^{7} -7.44635 q^{9} +(-9.10832 + 9.10832i) q^{11} -9.59167 q^{13} +(1.87013 + 5.94507i) q^{15} +(-14.5630 - 14.5630i) q^{17} +(10.1736 - 10.1736i) q^{19} +(-4.51965 + 4.51965i) q^{21} +(20.9529 + 20.9529i) q^{23} +(-20.4978 + 14.3122i) q^{25} -20.4996 q^{27} +(15.9714 - 15.9714i) q^{29} -22.3264 q^{31} +(-11.3531 + 11.3531i) q^{33} +(-22.7348 - 11.8542i) q^{35} +28.7135 q^{37} -11.9556 q^{39} +71.4731i q^{41} +18.1083i q^{43} +(-11.1722 - 35.5160i) q^{45} +(52.4024 + 52.4024i) q^{47} +22.7042i q^{49} +(-18.1521 - 18.1521i) q^{51} +24.3168i q^{53} +(-57.1086 - 29.7771i) q^{55} +(12.6810 - 12.6810i) q^{57} +(-48.9777 - 48.9777i) q^{59} +(42.1700 + 42.1700i) q^{61} +(27.0005 - 27.0005i) q^{63} +(-14.3909 - 45.7483i) q^{65} -73.7087i q^{67} +(26.1169 + 26.1169i) q^{69} +28.6304i q^{71} +(-9.24608 - 9.24608i) q^{73} +(-25.5496 + 17.8395i) q^{75} -66.0535i q^{77} +85.8203i q^{79} +41.4653 q^{81} +71.8998 q^{83} +(47.6097 - 91.3092i) q^{85} +(19.9076 - 19.9076i) q^{87} -124.642 q^{89} +(34.7794 - 34.7794i) q^{91} -27.8289 q^{93} +(63.7881 + 33.2599i) q^{95} +(19.5684 + 19.5684i) q^{97} +(67.8237 - 67.8237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9}+O(q^{10}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9	\( 44 q + 4 q^{3} - 2 q^{5} + 108 q^{9} + 4 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 32 q^{19} - 4 q^{21} + 40 q^{27} + 8 q^{31} - 4 q^{33} + 4 q^{35} - 4 q^{37} + 72 q^{39} - 70 q^{45} + 4 q^{47} + 100 q^{51} - 36 q^{57} + 64 q^{59} - 36 q^{61} + 200 q^{63} - 4 q^{65} + 60 q^{69} - 48 q^{73} + 324 q^{75} + 100 q^{81} - 156 q^{83} - 52 q^{85} + 36 q^{87} - 188 q^{91} - 40 q^{93} - 380 q^{95} - 4 q^{97} - 92 q^{99}+O(q^{100}) \) 44 * q + 4 * q^3 - 2 * q^5 + 108 * q^9 + 4 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 32 * q^19 - 4 * q^21 + 40 * q^27 + 8 * q^31 - 4 * q^33 + 4 * q^35 - 4 * q^37 + 72 * q^39 - 70 * q^45 + 4 * q^47 + 100 * q^51 - 36 * q^57 + 64 * q^59 - 36 * q^61 + 200 * q^63 - 4 * q^65 + 60 * q^69 - 48 * q^73 + 324 * q^75 + 100 * q^81 - 156 * q^83 - 52 * q^85 + 36 * q^87 - 188 * q^91 - 40 * q^93 - 380 * q^95 - 4 * q^97 - 92 * q^99

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