LMFDB - Embedded newform 980.2.g.a.391.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(391,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("980.391");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.g (of order $2$, degree $1$, 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.10
Character	$\chi$	$=$	980.391
Dual form			980.2.g.a.391.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.976830 - 1.02265i) q^{2} +1.11294 q^{3} +(-0.0916073 + 1.99790i) q^{4} -1.00000i q^{5} +(-1.08715 - 1.13814i) q^{6} +(2.13263 - 1.85793i) q^{8} -1.76137 q^{9} +(-1.02265 + 0.976830i) q^{10} -1.71377i q^{11} +(-0.101953 + 2.22354i) q^{12} +2.45950i q^{13} -1.11294i q^{15} +(-3.98322 - 0.366045i) q^{16} -6.21892i q^{17} +(1.72056 + 1.80126i) q^{18} -0.216513 q^{19} +(1.99790 + 0.0916073i) q^{20} +(-1.75258 + 1.67406i) q^{22} -6.56656i q^{23} +(2.37348 - 2.06776i) q^{24} -1.00000 q^{25} +(2.51519 - 2.40251i) q^{26} -5.29911 q^{27} -2.47123 q^{29} +(-1.13814 + 1.08715i) q^{30} +0.163826 q^{31} +(3.51659 + 4.43098i) q^{32} -1.90732i q^{33} +(-6.35975 + 6.07482i) q^{34} +(0.161354 - 3.51904i) q^{36} +7.69679 q^{37} +(0.211496 + 0.221416i) q^{38} +2.73727i q^{39} +(-1.85793 - 2.13263i) q^{40} -8.34130i q^{41} -1.89449i q^{43} +(3.42394 + 0.156994i) q^{44} +1.76137i q^{45} +(-6.71527 + 6.41442i) q^{46} -11.7045 q^{47} +(-4.43307 - 0.407385i) q^{48} +(0.976830 + 1.02265i) q^{50} -6.92127i q^{51} +(-4.91383 - 0.225308i) q^{52} +13.0276 q^{53} +(5.17633 + 5.41911i) q^{54} -1.71377 q^{55} -0.240965 q^{57} +(2.41397 + 2.52720i) q^{58} -4.28758 q^{59} +(2.22354 + 0.101953i) q^{60} -7.00039i q^{61} +(-0.160030 - 0.167536i) q^{62} +(1.09621 - 7.92454i) q^{64} +2.45950 q^{65} +(-1.95051 + 1.86313i) q^{66} -5.17415i q^{67} +(12.4248 + 0.569698i) q^{68} -7.30818i q^{69} -5.04201i q^{71} +(-3.75635 + 3.27250i) q^{72} +7.61517i q^{73} +(-7.51846 - 7.87109i) q^{74} -1.11294 q^{75} +(0.0198341 - 0.432571i) q^{76} +(2.79925 - 2.67384i) q^{78} -15.9493i q^{79} +(-0.366045 + 3.98322i) q^{80} -0.613471 q^{81} +(-8.53020 + 8.14803i) q^{82} -5.47827 q^{83} -6.21892 q^{85} +(-1.93739 + 1.85060i) q^{86} -2.75033 q^{87} +(-3.18406 - 3.65483i) q^{88} +1.78368i q^{89} +(1.80126 - 1.72056i) q^{90} +(13.1193 + 0.601545i) q^{92} +0.182328 q^{93} +(11.4333 + 11.9696i) q^{94} +0.216513i q^{95} +(3.91375 + 4.93141i) q^{96} +10.5305i q^{97} +3.01858i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60}+ \cdots + 16 q^{93}+O(q^{100}) $ 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.976830	−	1.02265i	−0.690723	−	0.723120i
$2$	−0.976830	−	1.02265i	−0.690723	−	0.723120i
$3$	1.11294			0.642555			0.321278	−	0.946985i	$-0.395888\pi$
$3$	1.11294			0.642555			0.321278	+	0.946985i	$0.395888\pi$
$4$	−0.0916073	+	1.99790i	−0.0458036	+	0.998950i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.08715	−	1.13814i	−0.443827	−	0.464644i
$7$		0			0
$7$		0			0
$8$	2.13263	−	1.85793i	0.753998	−	0.656876i
$9$	−1.76137			−0.587123
$10$	−1.02265	+	0.976830i	−0.323389	+	0.308901i
$11$		−	1.71377i		−	0.516721i	−0.966049	−	0.258360i	$-0.916818\pi$
$11$		−	1.71377i		−	0.516721i	0.966049	−	0.258360i	$-0.0831822\pi$
$12$	−0.101953	+	2.22354i	−0.0294314	+	0.641881i
$13$			2.45950i			0.682142i	0.940038	+	0.341071i	$0.110790\pi$
$13$			2.45950i			0.682142i	−0.940038	+	0.341071i	$0.889210\pi$
$14$		0			0
$15$		−	1.11294i		−	0.287359i
$16$	−3.98322	−	0.366045i	−0.995804	−	0.0915112i
$17$		−	6.21892i		−	1.50831i	−0.656697	−	0.754155i	$-0.728047\pi$
$17$		−	6.21892i		−	1.50831i	0.656697	−	0.754155i	$-0.271953\pi$
$18$	1.72056	+	1.80126i	0.405539	+	0.424560i
$19$	−0.216513			−0.0496714			−0.0248357	−	0.999692i	$-0.507906\pi$
$19$	−0.216513			−0.0496714			−0.0248357	+	0.999692i	$0.507906\pi$
$20$	1.99790	+	0.0916073i	0.446744	+	0.0204840i
$21$		0			0
$22$	−1.75258	+	1.67406i	−0.373651	+	0.356911i
$23$		−	6.56656i		−	1.36922i	−0.728908	−	0.684612i	$-0.759972\pi$
$23$		−	6.56656i		−	1.36922i	0.728908	−	0.684612i	$-0.240028\pi$
$24$	2.37348	−	2.06776i	0.484485	−	0.422079i
$25$	−1.00000			−0.200000
$26$	2.51519	−	2.40251i	0.493270	−	0.471171i
$27$	−5.29911			−1.01981
$28$		0			0
$29$	−2.47123			−0.458896			−0.229448	−	0.973321i	$-0.573692\pi$
$29$	−2.47123			−0.458896			−0.229448	+	0.973321i	$0.573692\pi$
$30$	−1.13814	+	1.08715i	−0.207795	+	0.198486i
$31$	0.163826			0.0294241			0.0147120	−	0.999892i	$-0.495317\pi$
$31$	0.163826			0.0294241			0.0147120	+	0.999892i	$0.495317\pi$
$32$	3.51659	+	4.43098i	0.621651	+	0.783294i
$33$		−	1.90732i		−	0.332022i
$34$	−6.35975	+	6.07482i	−1.09069	+	1.04182i
$35$		0			0
$36$	0.161354	−	3.51904i	0.0268924	−	0.586507i
$37$	7.69679			1.26535			0.632673	−	0.774419i	$-0.281958\pi$
$37$	7.69679			1.26535			0.632673	+	0.774419i	$0.281958\pi$
$38$	0.211496	+	0.221416i	0.0343092	+	0.0359184i
$39$			2.73727i			0.438313i
$40$	−1.85793	−	2.13263i	−0.293764	−	0.337198i
$41$		−	8.34130i		−	1.30269i	−0.758781	−	0.651346i	$-0.774205\pi$
$41$		−	8.34130i		−	1.30269i	0.758781	−	0.651346i	$-0.225795\pi$
$42$		0			0
$43$		−	1.89449i		−	0.288907i	−0.989512	−	0.144454i	$-0.953858\pi$
$43$		−	1.89449i		−	0.288907i	0.989512	−	0.144454i	$-0.0461425\pi$
$44$	3.42394	+	0.156994i	0.516179	+	0.0236677i
$45$			1.76137i			0.262569i
$46$	−6.71527	+	6.41442i	−0.990112	+	0.945754i
$47$	−11.7045			−1.70728			−0.853639	−	0.520865i	$-0.825609\pi$
$47$	−11.7045			−1.70728			−0.853639	+	0.520865i	$0.825609\pi$
$48$	−4.43307	−	0.407385i	−0.639859	−	0.0588010i
$49$		0			0
$50$	0.976830	+	1.02265i	0.138145	+	0.144624i
$51$		−	6.92127i		−	0.969172i
$52$	−4.91383	−	0.225308i	−0.681426	−	0.0312446i
$53$	13.0276			1.78949			0.894743	−	0.446582i	$-0.147359\pi$
$53$	13.0276			1.78949			0.894743	+	0.446582i	$0.147359\pi$
$54$	5.17633	+	5.41911i	0.704409	+	0.737447i
$55$	−1.71377			−0.231085
$56$		0			0
$57$	−0.240965			−0.0319166
$58$	2.41397	+	2.52720i	0.316970	+	0.331837i
$59$	−4.28758			−0.558195			−0.279098	−	0.960263i	$-0.590035\pi$
$59$	−4.28758			−0.558195			−0.279098	+	0.960263i	$0.590035\pi$
$60$	2.22354	+	0.101953i	0.287058	+	0.0131621i
$61$		−	7.00039i		−	0.896308i	−0.893956	−	0.448154i	$-0.852082\pi$
$61$		−	7.00039i		−	0.896308i	0.893956	−	0.448154i	$-0.147918\pi$
$62$	−0.160030	−	0.167536i	−0.0203239	−	0.0212771i
$63$		0			0
$64$	1.09621	−	7.92454i	0.137027	−	0.990567i
$65$	2.45950			0.305063
$66$	−1.95051	+	1.86313i	−0.240091	+	0.229335i
$67$		−	5.17415i		−	0.632124i	−0.948739	−	0.316062i	$-0.897639\pi$
$67$		−	5.17415i		−	0.632124i	0.948739	−	0.316062i	$-0.102361\pi$
$68$	12.4248	+	0.569698i	1.50673	+	0.0690861i
$69$		−	7.30818i		−	0.879801i
$70$		0			0
$71$		−	5.04201i		−	0.598376i	−0.954194	−	0.299188i	$-0.903284\pi$
$71$		−	5.04201i		−	0.598376i	0.954194	−	0.299188i	$-0.0967158\pi$
$72$	−3.75635	+	3.27250i	−0.442690	+	0.385667i
$73$			7.61517i			0.891288i	0.895210	+	0.445644i	$0.147025\pi$
$73$			7.61517i			0.891288i	−0.895210	+	0.445644i	$0.852975\pi$
$74$	−7.51846	−	7.87109i	−0.874003	−	0.914996i
$75$	−1.11294			−0.128511
$76$	0.0198341	−	0.432571i	0.00227513	−	0.0496193i
$77$		0			0
$78$	2.79925	−	2.67384i	0.316953	−	0.302753i
$79$		−	15.9493i		−	1.79443i	−0.441592	−	0.897216i	$-0.645586\pi$
$79$		−	15.9493i		−	1.79443i	0.441592	−	0.897216i	$-0.354414\pi$
$80$	−0.366045	+	3.98322i	−0.0409250	+	0.445337i
$81$	−0.613471			−0.0681635
$82$	−8.53020	+	8.14803i	−0.942002	+	0.899800i
$83$	−5.47827			−0.601318			−0.300659	−	0.953732i	$-0.597207\pi$
$83$	−5.47827			−0.601318			−0.300659	+	0.953732i	$0.597207\pi$
$84$		0			0
$85$	−6.21892			−0.674536
$86$	−1.93739	+	1.85060i	−0.208915	+	0.199555i
$87$	−2.75033			−0.294866
$88$	−3.18406	−	3.65483i	−0.339422	−	0.389607i
$89$			1.78368i			0.189069i	0.995522	+	0.0945347i	$0.0301363\pi$
$89$			1.78368i			0.189069i	−0.995522	+	0.0945347i	$0.969864\pi$
$90$	1.80126	−	1.72056i	0.189869	−	0.181363i
$91$		0			0
$92$	13.1193	+	0.601545i	1.36779	+	0.0627154i
$93$	0.182328			0.0189066
$94$	11.4333	+	11.9696i	1.17926	+	1.23457i
$95$			0.216513i			0.0222137i
$96$	3.91375	+	4.93141i	0.399445	+	0.503310i
$97$			10.5305i			1.06921i	0.845101	+	0.534606i	$0.179540\pi$
$97$			10.5305i			1.06921i	−0.845101	+	0.534606i	$0.820460\pi$
$98$		0			0
$99$			3.01858i			0.303379i
$100$	0.0916073	−	1.99790i	0.00916073	−	0.199790i
$101$		−	0.449771i		−	0.0447539i	−0.999750	−	0.0223769i	$-0.992877\pi$
$101$		−	0.449771i		−	0.0447539i	0.999750	−	0.0223769i	$-0.00712339\pi$
$102$	−7.07800	+	6.76090i	−0.700827	+	0.669429i
$103$	−9.28196			−0.914579			−0.457289	−	0.889318i	$-0.651180\pi$
$103$	−9.28196			−0.914579			−0.457289	+	0.889318i	$0.651180\pi$
$104$	4.56957	+	5.24519i	0.448083	+	0.514334i
$105$		0			0
$106$	−12.7258	−	13.3227i	−1.23604	−	1.29401i
$107$			18.5240i			1.79078i	0.445278	+	0.895392i	$0.353105\pi$
$107$			18.5240i			1.79078i	−0.445278	+	0.895392i	$0.646895\pi$
$108$	0.485437	−	10.5871i	0.0467112	−	1.01874i
$109$	−6.97114			−0.667714			−0.333857	−	0.942624i	$-0.608350\pi$
$109$	−6.97114			−0.667714			−0.333857	+	0.942624i	$0.608350\pi$
$110$	1.67406	+	1.75258i	0.159615	+	0.167102i
$111$	8.56605			0.813054
$112$		0			0
$113$	0.333646			0.0313868			0.0156934	−	0.999877i	$-0.495004\pi$
$113$	0.333646			0.0313868			0.0156934	+	0.999877i	$0.495004\pi$
$114$	0.235382	+	0.246422i	0.0220455	+	0.0230795i
$115$	−6.56656			−0.612335
$116$	0.226383	−	4.93728i	0.0210191	−	0.458415i
$117$		−	4.33208i		−	0.400501i
$118$	4.18824	+	4.38467i	0.385558	+	0.403642i
$119$		0			0
$120$	−2.06776	−	2.37348i	−0.188760	−	0.216668i
$121$	8.06299			0.732999
$122$	−7.15891	+	6.83819i	−0.648138	+	0.619100i
$123$		−	9.28335i		−	0.837052i
$124$	−0.0150077	+	0.327309i	−0.00134773	+	0.0293932i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			15.8806i			1.40918i	0.709616	+	0.704589i	$0.248869\pi$
$127$			15.8806i			1.40918i	−0.709616	+	0.704589i	$0.751131\pi$
$128$	−9.17481	+	6.61989i	−0.810946	+	0.585121i
$129$		−	2.10845i		−	0.185639i
$130$	−2.40251	−	2.51519i	−0.210714	−	0.220597i
$131$	3.20657			0.280159			0.140080	−	0.990140i	$-0.455264\pi$
$131$	3.20657			0.280159			0.140080	+	0.990140i	$0.455264\pi$
$132$	3.81063	+	0.174724i	0.331673	+	0.0152078i
$133$		0			0
$134$	−5.29133	+	5.05427i	−0.457101	+	0.436622i
$135$			5.29911i			0.456075i
$136$	−11.5543	−	13.2626i	−0.990773	−	1.13726i
$137$	1.30357			0.111372			0.0556859	−	0.998448i	$-0.482265\pi$
$137$	1.30357			0.111372			0.0556859	+	0.998448i	$0.482265\pi$
$138$	−7.47368	+	7.13885i	−0.636201	+	0.607699i
$139$	−20.8813			−1.77113			−0.885563	−	0.464519i	$-0.846227\pi$
$139$	−20.8813			−1.77113			−0.885563	+	0.464519i	$0.846227\pi$
$140$		0			0
$141$	−13.0264			−1.09702
$142$	−5.15619	+	4.92518i	−0.432697	+	0.413312i
$143$	4.21501			0.352477
$144$	7.01591	+	0.644740i	0.584660	+	0.0537283i
$145$			2.47123i			0.205225i
$146$	7.78762	−	7.43873i	0.644508	−	0.615633i
$147$		0			0
$148$	−0.705083	+	15.3774i	−0.0579574	+	1.26402i
$149$	9.73494			0.797517			0.398759	−	0.917056i	$-0.369441\pi$
$149$	9.73494			0.797517			0.398759	+	0.917056i	$0.369441\pi$
$150$	1.08715	+	1.13814i	0.0887655	+	0.0929288i
$151$		−	14.9372i		−	1.21557i	−0.794102	−	0.607784i	$-0.792059\pi$
$151$		−	14.9372i		−	1.21557i	0.794102	−	0.607784i	$-0.207941\pi$
$152$	−0.461741	+	0.402265i	−0.0374521	+	0.0326280i
$153$			10.9538i			0.885563i
$154$		0			0
$155$		−	0.163826i		−	0.0131588i
$156$	−5.46879	−	0.250754i	−0.437853	−	0.0200764i
$157$			8.22463i			0.656397i	0.944609	+	0.328198i	$0.106441\pi$
$157$			8.22463i			0.656397i	−0.944609	+	0.328198i	$0.893559\pi$
$158$	−16.3104	+	15.5797i	−1.29759	+	1.23946i
$159$	14.4990			1.14984
$160$	4.43098	−	3.51659i	0.350300	−	0.278011i
$161$		0			0
$162$	0.599257	+	0.627364i	0.0470821	+	0.0492903i
$163$		−	11.9866i		−	0.938863i	−0.882969	−	0.469431i	$-0.844459\pi$
$163$		−	11.9866i		−	0.938863i	0.882969	−	0.469431i	$-0.155541\pi$
$164$	16.6651	+	0.764124i	1.30133	+	0.0596681i
$165$	−1.90732			−0.148485
$166$	5.35133	+	5.60232i	0.415344	+	0.434825i
$167$	14.8103			1.14606			0.573029	−	0.819535i	$-0.305768\pi$
$167$	14.8103			1.14606			0.573029	+	0.819535i	$0.305768\pi$
$168$		0			0
$169$	6.95088			0.534683
$170$	6.07482	+	6.35975i	0.465918	+	0.487770i
$171$	0.381359			0.0291632
$172$	3.78501	+	0.173549i	0.288604	+	0.0132330i
$173$		−	15.6209i		−	1.18763i	−0.804600	−	0.593817i	$-0.797620\pi$
$173$		−	15.6209i		−	1.18763i	0.804600	−	0.593817i	$-0.202380\pi$
$174$	2.68660	+	2.81261i	0.203671	+	0.213224i
$175$		0			0
$176$	−0.627316	+	6.82631i	−0.0472857	+	0.514553i
$177$	−4.77181			−0.358671
$178$	1.82407	−	1.74235i	0.136720	−	0.130595i
$179$			6.38903i			0.477538i	0.971076	+	0.238769i	$0.0767439\pi$
$179$			6.38903i			0.477538i	−0.971076	+	0.238769i	$0.923256\pi$
$180$	−3.51904	−	0.161354i	−0.262294	−	0.0120266i
$181$		−	1.18770i		−	0.0882808i	−0.999025	−	0.0441404i	$-0.985945\pi$
$181$		−	1.18770i		−	0.0882808i	0.999025	−	0.0441404i	$-0.0140549\pi$
$182$		0			0
$183$		−	7.79100i		−	0.575927i
$184$	−12.2002	−	14.0040i	−0.899411	−	1.03239i
$185$		−	7.69679i		−	0.565880i
$186$	−0.178104	−	0.186457i	−0.0130592	−	0.0136717i
$187$	−10.6578			−0.779375
$188$	1.07222	−	23.3844i	0.0781996	−	1.70549i
$189$		0			0
$190$	0.221416	−	0.211496i	0.0160632	−	0.0153435i
$191$			10.5610i			0.764166i	0.924128	+	0.382083i	$0.124793\pi$
$191$			10.5610i			0.764166i	−0.924128	+	0.382083i	$0.875207\pi$
$192$	1.22002	−	8.81952i	0.0880471	−	0.636494i
$193$	5.40807			0.389281			0.194641	−	0.980875i	$-0.437646\pi$
$193$	5.40807			0.389281			0.194641	+	0.980875i	$0.437646\pi$
$194$	10.7690	−	10.2865i	0.773168	−	0.738529i
$195$	2.73727			0.196020
$196$		0			0
$197$	17.9504			1.27892			0.639458	−	0.768826i	$-0.279159\pi$
$197$	17.9504			1.27892			0.639458	+	0.768826i	$0.279159\pi$
$198$	3.08694	−	2.94864i	0.219379	−	0.209551i
$199$	7.65076			0.542348			0.271174	−	0.962530i	$-0.412588\pi$
$199$	7.65076			0.542348			0.271174	+	0.962530i	$0.412588\pi$
$200$	−2.13263	+	1.85793i	−0.150800	+	0.131375i
$201$		−	5.75851i		−	0.406174i
$202$	−0.459956	+	0.439349i	−0.0323624	+	0.0309125i
$203$		0			0
$204$	13.8280	+	0.634039i	0.968154	+	0.0443916i
$205$	−8.34130			−0.582582
$206$	9.06689	+	9.49215i	0.631720	+	0.661350i
$207$			11.5661i			0.803903i
$208$	0.900285	−	9.79671i	0.0624236	−	0.679279i
$209$			0.371053i			0.0256662i
$210$		0			0
$211$			15.5710i			1.07195i	0.844234	+	0.535975i	$0.180056\pi$
$211$			15.5710i			1.07195i	−0.844234	+	0.535975i	$0.819944\pi$
$212$	−1.19343	+	26.0279i	−0.0819649	+	1.78761i
$213$		−	5.61144i		−	0.384490i
$214$	18.9435	−	18.0948i	1.29495	−	1.23694i
$215$	−1.89449			−0.129203
$216$	−11.3010	+	9.84536i	−0.768938	+	0.669892i
$217$		0			0
$218$	6.80962	+	7.12900i	0.461205	+	0.482837i
$219$			8.47521i			0.572702i
$220$	0.156994	−	3.42394i	0.0105845	−	0.230842i
$221$	15.2954			1.02888
$222$	−8.36758	−	8.76004i	−0.561595	−	0.587935i
$223$	11.4678			0.767938			0.383969	−	0.923346i	$-0.374557\pi$
$223$	11.4678			0.767938			0.383969	+	0.923346i	$0.374557\pi$
$224$		0			0
$225$	1.76137			0.117425
$226$	−0.325915	−	0.341202i	−0.0216796	−	0.0226964i
$227$	−8.95435			−0.594321			−0.297161	−	0.954828i	$-0.596040\pi$
$227$	−8.95435			−0.594321			−0.297161	+	0.954828i	$0.596040\pi$
$228$	0.0220742	−	0.481424i	0.00146190	−	0.0318831i
$229$			2.40675i			0.159042i	0.996833	+	0.0795212i	$0.0253391\pi$
$229$			2.40675i			0.159042i	−0.996833	+	0.0795212i	$0.974661\pi$
$230$	6.41442	+	6.71527i	0.422954	+	0.442792i
$231$		0			0
$232$	−5.27022	+	4.59137i	−0.346007	+	0.301438i
$233$	−2.56075			−0.167761			−0.0838803	−	0.996476i	$-0.526731\pi$
$233$	−2.56075			−0.167761			−0.0838803	+	0.996476i	$0.526731\pi$
$234$	−4.43018	+	4.23171i	−0.289610	+	0.276635i
$235$			11.7045i			0.763518i
$236$	0.392774	−	8.56616i	0.0255674	−	0.557610i
$237$		−	17.7505i		−	1.15302i
$238$		0			0
$239$			6.31200i			0.408289i	0.978941	+	0.204145i	$0.0654413\pi$
$239$			6.31200i			0.408289i	−0.978941	+	0.204145i	$0.934559\pi$
$240$	−0.407385	+	4.43307i	−0.0262966	+	0.286154i
$241$			9.62616i			0.620076i	0.950724	+	0.310038i	$0.100342\pi$
$241$			9.62616i			0.620076i	−0.950724	+	0.310038i	$0.899658\pi$
$242$	−7.87617	−	8.24558i	−0.506300	−	0.530046i
$243$	15.2146			0.976015
$244$	13.9861	+	0.641286i	0.895367	+	0.0410542i
$245$		0			0
$246$	−9.49358	+	9.06825i	−0.605288	+	0.578171i
$247$		−	0.532512i		−	0.0338829i
$248$	0.349380	−	0.304377i	0.0221857	−	0.0193280i
$249$	−6.09697			−0.386380
$250$	1.02265	−	0.976830i	0.0646778	−	0.0617801i
$251$	24.9508			1.57488			0.787440	−	0.616391i	$-0.211406\pi$
$251$	24.9508			1.57488			0.787440	+	0.616391i	$0.211406\pi$
$252$		0			0
$253$	−11.2536			−0.707506
$254$	16.2402	−	15.5127i	1.01900	−	0.973351i
$255$	−6.92127			−0.433427
$256$	15.7320	+	2.91607i	0.983251	+	0.182254i
$257$			16.9763i			1.05895i	0.848325	+	0.529475i	$0.177611\pi$
$257$			16.9763i			1.05895i	−0.848325	+	0.529475i	$0.822389\pi$
$258$	−2.15620	+	2.05960i	−0.134239	+	0.128225i
$259$		0			0
$260$	−0.225308	+	4.91383i	−0.0139730	+	0.304743i
$261$	4.35275			0.269429
$262$	−3.13227	−	3.27918i	−0.193512	−	0.202589i
$263$		−	15.0335i		−	0.927005i	−0.886096	−	0.463503i	$-0.846592\pi$
$263$		−	15.0335i		−	0.927005i	0.886096	−	0.463503i	$-0.153408\pi$
$264$	−3.54366	−	4.06760i	−0.218097	−	0.250344i
$265$		−	13.0276i		−	0.800282i
$266$		0			0
$267$			1.98512i			0.121487i
$268$	10.3374	+	0.473990i	0.631460	+	0.0289536i
$269$		−	31.4313i		−	1.91640i	−0.286097	−	0.958201i	$-0.592358\pi$
$269$		−	31.4313i		−	1.91640i	0.286097	−	0.958201i	$-0.407642\pi$
$270$	5.41911	−	5.17633i	0.329796	−	0.315021i
$271$	−3.31771			−0.201536			−0.100768	−	0.994910i	$-0.532130\pi$
$271$	−3.31771			−0.201536			−0.100768	+	0.994910i	$0.532130\pi$
$272$	−2.27640	+	24.7713i	−0.138027	+	1.50198i
$273$		0			0
$274$	−1.27337	−	1.33309i	−0.0769270	−	0.0805351i
$275$			1.71377i			0.103344i
$276$	14.6010	+	0.669483i	0.878878	+	0.0402981i
$277$	14.7459			0.885994			0.442997	−	0.896523i	$-0.353915\pi$
$277$	14.7459			0.885994			0.442997	+	0.896523i	$0.353915\pi$
$278$	20.3974	+	21.3541i	1.22336	+	1.28074i
$279$	−0.288558			−0.0172755
$280$		0			0
$281$	20.5438			1.22554			0.612769	−	0.790262i	$-0.290056\pi$
$281$	20.5438			1.22554			0.612769	+	0.790262i	$0.290056\pi$
$282$	12.7246	+	13.3214i	0.757737	+	0.793277i
$283$	27.8362			1.65469			0.827346	−	0.561692i	$-0.189849\pi$
$283$	27.8362			1.65469			0.827346	+	0.561692i	$0.189849\pi$
$284$	10.0734	+	0.461885i	0.597748	+	0.0274078i
$285$			0.240965i			0.0142735i
$286$	−4.11735	−	4.31046i	−0.243464	−	0.254883i
$287$		0			0
$288$	−6.19401	−	7.80459i	−0.364986	−	0.459890i
$289$	−21.6749			−1.27500
$290$	2.52720	−	2.41397i	0.148402	−	0.141753i
$291$			11.7198i			0.687027i
$292$	−15.2144	−	0.697605i	−0.890353	−	0.0408243i
$293$			4.28428i			0.250290i	0.992138	+	0.125145i	$0.0399396\pi$
$293$			4.28428i			0.250290i	−0.992138	+	0.125145i	$0.960060\pi$
$294$		0			0
$295$			4.28758i			0.249633i
$296$	16.4144	−	14.3001i	0.954068	−	0.831176i
$297$			9.08145i			0.526959i
$298$	−9.50938	−	9.95539i	−0.550864	−	0.576700i
$299$	16.1504			0.934004
$300$	0.101953	−	2.22354i	0.00588627	−	0.128376i
$301$		0			0
$302$	−15.2754	+	14.5911i	−0.879001	+	0.839621i
$303$		−	0.500567i		−	0.0287568i
$304$	0.862416	+	0.0792533i	0.0494630	+	0.00454549i
$305$	−7.00039			−0.400841
$306$	11.2019	−	10.7000i	0.640368	−	0.611679i
$307$	14.3171			0.817117			0.408559	−	0.912732i	$-0.366032\pi$
$307$	14.3171			0.817117			0.408559	+	0.912732i	$0.366032\pi$
$308$		0			0
$309$	−10.3302			−0.587667
$310$	−0.167536	+	0.160030i	−0.00951541	+	0.00908911i
$311$	25.6631			1.45522			0.727609	−	0.685992i	$-0.240631\pi$
$311$	25.6631			1.45522			0.727609	+	0.685992i	$0.240631\pi$
$312$	5.08564	+	5.83757i	0.287918	+	0.330488i
$313$			32.5054i			1.83731i	0.395059	+	0.918656i	$0.370724\pi$
$313$			32.5054i			1.83731i	−0.395059	+	0.918656i	$0.629276\pi$
$314$	8.41088	−	8.03406i	0.474653	−	0.453388i
$315$		0			0
$316$	31.8650	+	1.46107i	1.79255	+	0.0821915i
$317$	2.92067			0.164041			0.0820205	−	0.996631i	$-0.473863\pi$
$317$	2.92067			0.164041			0.0820205	+	0.996631i	$0.473863\pi$
$318$	−14.1630	−	14.8273i	−0.794223	−	0.831474i
$319$			4.23512i			0.237121i
$320$	−7.92454	−	1.09621i	−0.442995	−	0.0612801i
$321$			20.6161i			1.15068i
$322$		0			0
$323$			1.34647i			0.0749198i
$324$	0.0561984	−	1.22565i	0.00312214	−	0.0680919i
$325$		−	2.45950i		−	0.136428i
$326$	−12.2580	+	11.7089i	−0.678910	+	0.648494i
$327$	−7.75845			−0.429043
$328$	−15.4975	−	17.7889i	−0.855708	−	0.982228i
$329$		0			0
$330$	1.86313	+	1.95051i	0.102562	+	0.107372i
$331$		−	3.94866i		−	0.217038i	−0.994094	−	0.108519i	$-0.965389\pi$
$331$		−	3.94866i		−	0.217038i	0.994094	−	0.108519i	$-0.0346108\pi$
$332$	0.501849	−	10.9450i	0.0275425	−	0.600687i
$333$	−13.5569			−0.742913
$334$	−14.4672	−	15.1457i	−0.791609	−	0.828737i
$335$	−5.17415			−0.282694
$336$		0			0
$337$	−10.0467			−0.547280			−0.273640	−	0.961832i	$-0.588228\pi$
$337$	−10.0467			−0.547280			−0.273640	+	0.961832i	$0.588228\pi$
$338$	−6.78982	−	7.10828i	−0.369318	−	0.386640i
$339$	0.371327			0.0201677
$340$	0.569698	−	12.4248i	0.0308962	−	0.673828i
$341$		−	0.280760i		−	0.0152040i
$342$	−0.372522	−	0.389995i	−0.0201437	−	0.0210885i
$343$		0			0
$344$	−3.51983	−	4.04025i	−0.189776	−	0.217836i
$345$	−7.30818			−0.393459
$346$	−15.9746	+	15.2589i	−0.858801	+	0.820326i
$347$		−	0.0201100i		−	0.00107956i	−1.00000		0.000539780i	$-0.999828\pi$
$347$		−	0.0201100i		−	0.00107956i	1.00000		0.000539780i	$-0.000171817\pi$
$348$	0.251950	−	5.49489i	0.0135060	−	0.294557i
$349$		−	5.60366i		−	0.299957i	−0.988689	−	0.149978i	$-0.952080\pi$
$349$		−	5.60366i		−	0.299957i	0.988689	−	0.149978i	$-0.0479204\pi$
$350$		0			0
$351$		−	13.0331i		−	0.695657i
$352$	7.59368	−	6.02662i	0.404744	−	0.321220i
$353$			25.4844i			1.35640i	0.734880	+	0.678198i	$0.237239\pi$
$353$			25.4844i			1.35640i	−0.734880	+	0.678198i	$0.762761\pi$
$354$	4.66125	+	4.87987i	0.247742	+	0.259362i
$355$	−5.04201			−0.267602
$356$	−3.56361	−	0.163398i	−0.188871	−	0.00866007i
$357$		0			0
$358$	6.53371	−	6.24099i	0.345317	−	0.329847i
$359$			19.3484i			1.02117i	0.859827	+	0.510586i	$0.170572\pi$
$359$			19.3484i			1.02117i	−0.859827	+	0.510586i	$0.829428\pi$
$360$	3.27250	+	3.75635i	0.172476	+	0.197977i
$361$	−18.9531			−0.997533
$362$	−1.21459	+	1.16018i	−0.0638375	+	0.0609776i
$363$	8.97361			0.470993
$364$		0			0
$365$	7.61517			0.398596
$366$	−7.96743	+	7.61048i	−0.416464	+	0.397806i
$367$	−17.2951			−0.902799			−0.451399	−	0.892322i	$-0.649075\pi$
$367$	−17.2951			−0.902799			−0.451399	+	0.892322i	$0.649075\pi$
$368$	−2.40366	+	26.1560i	−0.125299	+	1.36348i
$369$			14.6921i			0.764841i
$370$	−7.87109	+	7.51846i	−0.409199	+	0.390866i
$371$		0			0
$372$	−0.0167026	+	0.364274i	−0.000865990	+	0.0188867i
$373$	11.1097			0.575237			0.287618	−	0.957745i	$-0.407137\pi$
$373$	11.1097			0.575237			0.287618	+	0.957745i	$0.407137\pi$
$374$	10.4108	+	10.8991i	0.538332	+	0.563581i
$375$			1.11294i			0.0574719i
$376$	−24.9614	+	21.7461i	−1.28728	+	1.12147i
$377$		−	6.07799i		−	0.313032i
$378$		0			0
$379$		−	14.3198i		−	0.735558i	−0.929913	−	0.367779i	$-0.880118\pi$
$379$		−	14.3198i		−	0.735558i	0.929913	−	0.367779i	$-0.119882\pi$
$380$	−0.432571	−	0.0198341i	−0.0221904	−	0.00101747i
$381$			17.6741i			0.905474i
$382$	10.8001	−	10.3163i	0.552583	−	0.527827i
$383$	10.4539			0.534167			0.267084	−	0.963673i	$-0.413940\pi$
$383$	10.4539			0.534167			0.267084	+	0.963673i	$0.413940\pi$
$384$	−10.2110	+	7.36753i	−0.521077	+	0.375972i
$385$		0			0
$386$	−5.28276	−	5.53054i	−0.268886	−	0.281497i
$387$			3.33690i			0.169624i
$388$	−21.0389	−	0.964672i	−1.06809	−	0.0489738i
$389$	−30.1257			−1.52744			−0.763718	−	0.645550i	$-0.776628\pi$
$389$	−30.1257			−1.52744			−0.763718	+	0.645550i	$0.776628\pi$
$390$	−2.67384	−	2.79925i	−0.135395	−	0.141746i
$391$	−40.8369			−2.06521
$392$		0			0
$393$	3.56871			0.180018
$394$	−17.5345	−	18.3569i	−0.883377	−	0.924809i
$395$	−15.9493			−0.802494
$396$	−6.03082	−	0.276524i	−0.303060	−	0.0138959i
$397$		−	13.4379i		−	0.674429i	−0.941428	−	0.337215i	$-0.890515\pi$
$397$		−	13.4379i		−	0.674429i	0.941428	−	0.337215i	$-0.109485\pi$
$398$	−7.47349	−	7.82401i	−0.374612	−	0.392182i
$399$		0			0
$400$	3.98322	+	0.366045i	0.199161	+	0.0183022i
$401$	−28.8847			−1.44243			−0.721216	−	0.692710i	$-0.756416\pi$
$401$	−28.8847			−1.44243			−0.721216	+	0.692710i	$0.756416\pi$
$402$	−5.88892	+	5.62509i	−0.293712	+	0.280554i
$403$			0.402930i			0.0200714i
$404$	0.898597	+	0.0412023i	0.0447069	+	0.00204989i
$405$			0.613471i			0.0304836i
$406$		0			0
$407$		−	13.1905i		−	0.653830i
$408$	−12.8592	−	14.7605i	−0.636626	−	0.730754i
$409$		−	25.9031i		−	1.28083i	−0.768030	−	0.640413i	$-0.778763\pi$
$409$		−	25.9031i		−	1.28083i	0.768030	−	0.640413i	$-0.221237\pi$
$410$	8.14803	+	8.53020i	0.402403	+	0.421276i
$411$	1.45080			0.0715625
$412$	0.850295	−	18.5444i	0.0418910	−	0.913619i
$413$		0			0
$414$	11.8281	−	11.2982i	0.581318	−	0.555274i
$415$			5.47827i			0.268917i
$416$	−10.8980	+	8.64904i	−0.534318	+	0.424054i
$417$	−23.2396			−1.13805
$418$	0.379455	−	0.362455i	0.0185598	−	0.0177283i
$419$	−28.1022			−1.37288			−0.686441	−	0.727185i	$-0.740828\pi$
$419$	−28.1022			−1.37288			−0.686441	+	0.727185i	$0.740828\pi$
$420$		0			0
$421$	15.6269			0.761608			0.380804	−	0.924656i	$-0.375647\pi$
$421$	15.6269			0.761608			0.380804	+	0.924656i	$0.375647\pi$
$422$	15.9236	−	15.2102i	0.775148	−	0.740420i
$423$	20.6160			1.00238
$424$	27.7831	−	24.2044i	1.34927	−	1.17547i
$425$			6.21892i			0.301662i
$426$	−5.73851	+	5.48142i	−0.278032	+	0.265576i
$427$		0			0
$428$	−37.0092	−	1.69694i	−1.78890	−	0.0820245i
$429$	4.69104			0.226486
$430$	1.85060	+	1.93739i	0.0892437	+	0.0934294i
$431$		−	19.9499i		−	0.960953i	−0.877008	−	0.480477i	$-0.840464\pi$
$431$		−	19.9499i		−	0.960953i	0.877008	−	0.480477i	$-0.159536\pi$
$432$	21.1075	+	1.93971i	1.01553	+	0.0933243i
$433$			11.8294i			0.568487i	0.958752	+	0.284243i	$0.0917424\pi$
$433$			11.8294i			0.568487i	−0.958752	+	0.284243i	$0.908258\pi$
$434$		0			0
$435$			2.75033i			0.131868i
$436$	0.638607	−	13.9276i	0.0305837	−	0.667013i
$437$			1.42174i			0.0680112i
$438$	8.66714	−	8.27884i	0.414132	−	0.395578i
$439$	27.8949			1.33135			0.665675	−	0.746242i	$-0.268144\pi$
$439$	27.8949			1.33135			0.665675	+	0.746242i	$0.268144\pi$
$440$	−3.65483	+	3.18406i	−0.174237	+	0.151794i
$441$		0			0
$442$	−14.9410	−	15.6418i	−0.710671	−	0.744003i
$443$			19.1991i			0.912177i	0.889934	+	0.456088i	$0.150750\pi$
$443$			19.1991i			0.912177i	−0.889934	+	0.456088i	$0.849250\pi$
$444$	−0.784713	+	17.1141i	−0.0372408	+	0.812201i
$445$	1.78368			0.0845544
$446$	−11.2021	−	11.7275i	−0.530433	−	0.555311i
$447$	10.8344			0.512449
$448$		0			0
$449$	−4.94035			−0.233150			−0.116575	−	0.993182i	$-0.537191\pi$
$449$	−4.94035			−0.233150			−0.116575	+	0.993182i	$0.537191\pi$
$450$	−1.72056	−	1.80126i	−0.0811079	−	0.0849120i
$451$	−14.2951			−0.673129
$452$	−0.0305644	+	0.666592i	−0.00143763	+	0.0313538i
$453$		−	16.6241i		−	0.781070i
$454$	8.74688	+	9.15713i	0.410511	+	0.429765i
$455$		0			0
$456$	−0.513889	+	0.447696i	−0.0240651	+	0.0209653i
$457$	−26.1243			−1.22204			−0.611022	−	0.791614i	$-0.709241\pi$
$457$	−26.1243			−1.22204			−0.611022	+	0.791614i	$0.709241\pi$
$458$	2.46125	−	2.35098i	0.115007	−	0.109854i
$459$			32.9547i			1.53819i
$460$	0.601545	−	13.1193i	0.0280472	−	0.611693i
$461$			13.3894i			0.623609i	0.950146	+	0.311804i	$0.100933\pi$
$461$			13.3894i			0.623609i	−0.950146	+	0.311804i	$0.899067\pi$
$462$		0			0
$463$		−	16.4019i		−	0.762259i	−0.924522	−	0.381130i	$-0.875535\pi$
$463$		−	16.4019i		−	0.762259i	0.924522	−	0.381130i	$-0.124465\pi$
$464$	9.84346	+	0.904582i	0.456971	+	0.0419941i
$465$		−	0.182328i		−	0.00845528i
$466$	2.50142	+	2.61874i	0.115876	+	0.121311i
$467$	11.9333			0.552206			0.276103	−	0.961128i	$-0.410957\pi$
$467$	11.9333			0.552206			0.276103	+	0.961128i	$0.410957\pi$
$468$	8.65507	+	0.396850i	0.400081	+	0.0183444i
$469$		0			0
$470$	11.9696	−	11.4333i	0.552115	−	0.527379i
$471$			9.15350i			0.421771i
$472$	−9.14382	+	7.96601i	−0.420878	+	0.366665i
$473$	−3.24672			−0.149285
$474$	−18.1525	+	17.3393i	−0.833772	+	0.796418i
$475$	0.216513			0.00993428
$476$		0			0
$477$	−22.9465			−1.05065
$478$	6.45494	−	6.16575i	0.295242	−	0.282015i
$479$	−37.1777			−1.69869			−0.849347	−	0.527834i	$-0.823004\pi$
$479$	−37.1777			−1.69869			−0.849347	+	0.527834i	$0.823004\pi$
$480$	4.93141	−	3.91375i	0.225087	−	0.178637i
$481$			18.9302i			0.863145i
$482$	9.84415	−	9.40312i	0.448389	−	0.428300i
$483$		0			0
$484$	−0.738629	+	16.1091i	−0.0335741	+	0.732230i
$485$	10.5305			0.478166
$486$	−14.8620	−	15.5591i	−0.674156	−	0.705776i
$487$		−	0.978376i		−	0.0443344i	−0.999754	−	0.0221672i	$-0.992943\pi$
$487$		−	0.978376i		−	0.0443344i	0.999754	−	0.0221672i	$-0.00705662\pi$
$488$	−13.0062	−	14.9292i	−0.588763	−	0.675814i
$489$		−	13.3403i		−	0.603271i
$490$		0			0
$491$		−	18.4167i		−	0.831132i	−0.909563	−	0.415566i	$-0.863583\pi$
$491$		−	18.4167i		−	0.831132i	0.909563	−	0.415566i	$-0.136417\pi$
$492$	18.5472	+	0.850423i	0.836173	+	0.0383400i
$493$			15.3684i			0.692158i
$494$	−0.544571	+	0.520174i	−0.0245014	+	0.0234037i
$495$	3.01858			0.135675
$496$	−0.652555	−	0.0599677i	−0.0293006	−	0.00269263i
$497$		0			0
$498$	5.95570	+	6.23504i	0.266881	+	0.279399i
$499$		−	19.5338i		−	0.874451i	−0.899352	−	0.437226i	$-0.855961\pi$
$499$		−	19.5338i		−	0.874451i	0.899352	−	0.437226i	$-0.144039\pi$
$500$	−1.99790	−	0.0916073i	−0.0893488	−	0.00409680i
$501$	16.4830			0.736406
$502$	−24.3727	−	25.5158i	−1.08781	−	1.13883i
$503$	−11.7007			−0.521707			−0.260853	−	0.965378i	$-0.584004\pi$
$503$	−11.7007			−0.521707			−0.260853	+	0.965378i	$0.584004\pi$
$504$		0			0
$505$	−0.449771			−0.0200145
$506$	10.9928	+	11.5084i	0.488691	+	0.511612i
$507$	7.73590			0.343563
$508$	−31.7279	−	1.45478i	−1.40770	−	0.0645455i
$509$			2.14293i			0.0949838i	0.998872	+	0.0474919i	$0.0151228\pi$
$509$			2.14293i			0.0949838i	−0.998872	+	0.0474919i	$0.984877\pi$
$510$	6.76090	+	7.07800i	0.299378	+	0.313419i
$511$		0			0
$512$	−12.3854	−	18.9368i	−0.547363	−	0.836896i
$513$	1.14732			0.0506556
$514$	17.3607	−	16.5829i	0.765748	−	0.731441i
$515$			9.28196i			0.409012i
$516$	4.21248	+	0.193150i	0.185444	+	0.00850294i
$517$			20.0588i			0.882186i
$518$		0			0
$519$		−	17.3851i		−	0.763120i
$520$	5.24519	−	4.56957i	0.230017	−	0.200389i
$521$		−	13.6715i		−	0.598960i	−0.954103	−	0.299480i	$-0.903187\pi$
$521$		−	13.6715i		−	0.598960i	0.954103	−	0.299480i	$-0.0968131\pi$
$522$	−4.25190	−	4.45132i	−0.186101	−	0.194829i
$523$	−37.5656			−1.64263			−0.821316	−	0.570474i	$-0.806759\pi$
$523$	−37.5656			−1.64263			−0.821316	+	0.570474i	$0.806759\pi$
$524$	−0.293745	+	6.40640i	−0.0128323	+	0.279865i
$525$		0			0
$526$	−15.3739	+	14.6852i	−0.670336	+	0.640304i
$527$		−	1.01882i		−	0.0443806i
$528$	−0.698164	+	7.59726i	−0.0303837	+	0.330628i
$529$	−20.1198			−0.874773
$530$	−13.3227	+	12.7258i	−0.578700	+	0.552773i
$531$	7.55201			0.327729
$532$		0			0
$533$	20.5154			0.888621
$534$	2.03008	−	1.93913i	0.0878499	−	0.0839142i
$535$	18.5240			0.800863
$536$	−9.61320	−	11.0346i	−0.415227	−	0.476620i
$537$			7.11059i			0.306845i
$538$	−32.1431	+	30.7030i	−1.38579	+	1.32370i
$539$		0			0
$540$	−10.5871	−	0.485437i	−0.455596	−	0.0208899i
$541$	26.6104			1.14407			0.572034	−	0.820230i	$-0.306154\pi$
$541$	26.6104			1.14407			0.572034	+	0.820230i	$0.306154\pi$
$542$	3.24083	+	3.39284i	0.139206	+	0.145735i
$543$		−	1.32183i		−	0.0567253i
$544$	27.5559	−	21.8694i	1.18145	−	0.937642i
$545$			6.97114i			0.298611i
$546$		0			0
$547$		−	24.0582i		−	1.02865i	−0.857594	−	0.514327i	$-0.828042\pi$
$547$		−	24.0582i		−	1.02865i	0.857594	−	0.514327i	$-0.171958\pi$
$548$	−0.119417	+	2.60441i	−0.00510123	+	0.111255i
$549$			12.3303i			0.526243i
$550$	1.75258	−	1.67406i	0.0747302	−	0.0713822i
$551$	0.535053			0.0227940
$552$	−13.5781	−	15.5856i	−0.577921	−	0.663369i
$553$		0			0
$554$	−14.4042	−	15.0798i	−0.611976	−	0.640679i
$555$		−	8.56605i		−	0.363609i
$556$	1.91288	−	41.7187i	0.0811240	−	1.76927i
$557$	26.7419			1.13309			0.566546	−	0.824030i	$-0.308279\pi$
$557$	26.7419			1.13309			0.566546	+	0.824030i	$0.308279\pi$
$558$	0.281872	+	0.295093i	0.0119326	+	0.0124923i
$559$	4.65950			0.197076
$560$		0			0
$561$	−11.8615			−0.500791
$562$	−20.0678	−	21.0090i	−0.846507	−	0.886210i
$563$	−17.4713			−0.736329			−0.368165	−	0.929761i	$-0.620014\pi$
$563$	−17.4713			−0.736329			−0.368165	+	0.929761i	$0.620014\pi$
$564$	1.19331	−	26.0254i	0.0502475	−	1.09587i
$565$		−	0.333646i		−	0.0140366i
$566$	−27.1913	−	28.4666i	−1.14293	−	1.19654i
$567$		0			0
$568$	−9.36768	−	10.7527i	−0.393059	−	0.451175i
$569$	−20.3584			−0.853468			−0.426734	−	0.904377i	$-0.640336\pi$
$569$	−20.3584			−0.853468			−0.426734	+	0.904377i	$0.640336\pi$
$570$	0.246422	−	0.235382i	0.0103215	−	0.00985906i
$571$			22.2550i			0.931342i	0.884958	+	0.465671i	$0.154187\pi$
$571$			22.2550i			0.931342i	−0.884958	+	0.465671i	$0.845813\pi$
$572$	−0.386126	+	8.42117i	−0.0161447	+	0.352107i
$573$			11.7537i			0.491019i
$574$		0			0
$575$			6.56656i			0.273845i
$576$	−1.93083	+	13.9580i	−0.0804515	+	0.581585i
$577$		−	0.971128i		−	0.0404286i	−0.999796	−	0.0202143i	$-0.993565\pi$
$577$		−	0.971128i		−	0.0404286i	0.999796	−	0.0202143i	$-0.00643485\pi$
$578$	21.1727	+	22.1658i	0.880669	+	0.921975i
$579$	6.01885			0.250135
$580$	−4.93728	−	0.226383i	−0.205009	−	0.00940004i
$581$		0			0
$582$	11.9852	−	11.4483i	0.496803	−	0.474546i
$583$		−	22.3264i		−	0.924664i
$584$	14.1484	+	16.2403i	0.585466	+	0.672030i
$585$	−4.33208			−0.179110
$586$	4.38130	−	4.18501i	0.180990	−	0.172881i
$587$	−17.6042			−0.726602			−0.363301	−	0.931672i	$-0.618350\pi$
$587$	−17.6042			−0.726602			−0.363301	+	0.931672i	$0.618350\pi$
$588$		0			0
$589$	−0.0354704			−0.00146153
$590$	4.38467	−	4.18824i	0.180514	−	0.172427i
$591$	19.9777			0.821774
$592$	−30.6580	−	2.81737i	−1.26004	−	0.115793i
$593$		−	22.3772i		−	0.918922i	−0.888198	−	0.459461i	$-0.848043\pi$
$593$		−	22.3772i		−	0.918922i	0.888198	−	0.459461i	$-0.151957\pi$
$594$	9.28710	−	8.87103i	0.381054	−	0.363983i
$595$		0			0
$596$	−0.891792	+	19.4494i	−0.0365292	+	0.796680i
$597$	8.51482			0.348488
$598$	−15.7762	−	16.5162i	−0.645138	−	0.675397i
$599$			18.3668i			0.750446i	0.926935	+	0.375223i	$0.122434\pi$
$599$			18.3668i			0.750446i	−0.926935	+	0.375223i	$0.877566\pi$
$600$	−2.37348	+	2.06776i	−0.0968971	+	0.0844159i
$601$			11.9668i			0.488136i	0.969758	+	0.244068i	$0.0784820\pi$
$601$			11.9668i			0.488136i	−0.969758	+	0.244068i	$0.921518\pi$
$602$		0			0
$603$			9.11360i			0.371134i
$604$	29.8430	+	1.36835i	1.21429	+	0.0556775i
$605$		−	8.06299i		−	0.327807i
$606$	−0.511902	+	0.488969i	−0.0207946	+	0.0198630i
$607$	16.3726			0.664542			0.332271	−	0.943184i	$-0.392185\pi$
$607$	16.3726			0.664542			0.332271	+	0.943184i	$0.392185\pi$
$608$	−0.761386	−	0.959363i	−0.0308783	−	0.0389073i
$609$		0			0
$610$	6.83819	+	7.15891i	0.276870	+	0.289856i
$611$		−	28.7872i		−	1.16461i
$612$	−21.8846	−	1.00345i	−0.884634	−	0.0405620i
$613$	45.7436			1.84757			0.923783	−	0.382916i	$-0.125080\pi$
$613$	45.7436			1.84757			0.923783	+	0.382916i	$0.125080\pi$
$614$	−13.9853	−	14.6413i	−0.564402	−	0.590873i
$615$	−9.28335			−0.374341
$616$		0			0
$617$	3.88479			0.156396			0.0781979	−	0.996938i	$-0.475083\pi$
$617$	3.88479			0.156396			0.0781979	+	0.996938i	$0.475083\pi$
$618$	10.0909	+	10.5642i	0.405915	+	0.424954i
$619$	−20.4330			−0.821272			−0.410636	−	0.911799i	$-0.634693\pi$
$619$	−20.4330			−0.821272			−0.410636	+	0.911799i	$0.634693\pi$
$620$	0.327309	+	0.0150077i	0.0131450	+	0.000602723i
$621$			34.7969i			1.39635i
$622$	−25.0684	−	26.2442i	−1.00515	−	1.05230i
$623$		0			0
$624$	1.00196	−	10.9031i	0.0401106	−	0.436474i
$625$	1.00000			0.0400000
$626$	33.2414	−	31.7522i	1.32860	−	1.26907i
$627$			0.412959i			0.0164920i
$628$	−16.4320	−	0.753436i	−0.655708	−	0.0300654i
$629$		−	47.8657i		−	1.90853i
$630$		0			0
$631$			23.7070i			0.943762i	0.881662	+	0.471881i	$0.156425\pi$
$631$			23.7070i			0.943762i	−0.881662	+	0.471881i	$0.843575\pi$
$632$	−29.6326	−	34.0139i	−1.17872	−	1.35300i
$633$			17.3295i			0.688786i
$634$	−2.85299	−	2.98681i	−0.113307	−	0.118621i
$635$	15.8806			0.630203
$636$	−1.32821	+	28.9675i	−0.0526670	+	1.14864i
$637$		0			0
$638$	4.33103	−	4.13700i	0.171467	−	0.163785i
$639$			8.88084i			0.351320i
$640$	6.61989	+	9.17481i	0.261674	+	0.362666i
$641$	14.3937			0.568515			0.284258	−	0.958748i	$-0.408253\pi$
$641$	14.3937			0.568515			0.284258	+	0.958748i	$0.408253\pi$
$642$	21.0829	−	20.1384i	0.832077	−	0.794799i
$643$	47.6127			1.87766			0.938830	−	0.344380i	$-0.111911\pi$
$643$	47.6127			1.87766			0.938830	+	0.344380i	$0.111911\pi$
$644$		0			0
$645$	−2.10845			−0.0830202
$646$	1.37697	−	1.31528i	0.0541760	−	0.0517488i
$647$	−0.0108286			−0.000425715			−0.000212858	−	1.00000i	$-0.500068\pi$
$647$	−0.0108286			−0.000425715			−0.000212858		1.00000i	$0.500068\pi$
$648$	−1.30831	+	1.13978i	−0.0513951	+	0.0447750i
$649$			7.34792i			0.288431i
$650$	−2.51519	+	2.40251i	−0.0986540	+	0.0942342i
$651$		0			0
$652$	23.9480	+	1.09806i	0.937877	+	0.0430033i
$653$	−10.6223			−0.415681			−0.207841	−	0.978163i	$-0.566644\pi$
$653$	−10.6223			−0.415681			−0.207841	+	0.978163i	$0.566644\pi$
$654$	7.57868	+	7.93414i	0.296350	+	0.310249i
$655$		−	3.20657i		−	0.125291i
$656$	−3.05329	+	33.2252i	−0.119211	+	1.29723i
$657$		−	13.4131i		−	0.523296i
$658$		0			0
$659$		−	13.3688i		−	0.520773i	−0.965505	−	0.260386i	$-0.916150\pi$
$659$		−	13.3688i		−	0.520773i	0.965505	−	0.260386i	$-0.0838499\pi$
$660$	0.174724	−	3.81063i	0.00680114	−	0.148329i
$661$		−	7.50536i		−	0.291925i	−0.989290	−	0.145962i	$-0.953372\pi$
$661$		−	7.50536i		−	0.291925i	0.989290	−	0.145962i	$-0.0466278\pi$
$662$	−4.03808	+	3.85717i	−0.156944	+	0.149913i
$663$	17.0228			0.661112
$664$	−11.6831	+	10.1782i	−0.453393	+	0.394992i
$665$		0			0
$666$	13.2428	+	13.8639i	0.513147	+	0.537215i
$667$			16.2275i			0.628332i
$668$	−1.35674	+	29.5896i	−0.0524937	+	1.14486i
$669$	12.7629			0.493443
$670$	5.05427	+	5.29133i	0.195263	+	0.204422i
$671$	−11.9970			−0.463141
$672$		0			0
$673$	19.9107			0.767501			0.383751	−	0.923437i	$-0.374632\pi$
$673$	19.9107			0.767501			0.383751	+	0.923437i	$0.374632\pi$
$674$	9.81395	+	10.2742i	0.378019	+	0.395749i
$675$	5.29911			0.203963
$676$	−0.636751	+	13.8872i	−0.0244904	+	0.534122i
$677$		−	26.0053i		−	0.999466i	−0.866180	−	0.499733i	$-0.833431\pi$
$677$		−	26.0053i		−	0.999466i	0.866180	−	0.499733i	$-0.166569\pi$
$678$	−0.362724	−	0.379736i	−0.0139303	−	0.0145837i
$679$		0			0
$680$	−13.2626	+	11.5543i	−0.508599	+	0.443087i
$681$	−9.96564			−0.381884
$682$	−0.287118	+	0.274255i	−0.0109943	+	0.0105018i
$683$		−	14.8200i		−	0.567071i	−0.958962	−	0.283536i	$-0.908493\pi$
$683$		−	14.8200i		−	0.567071i	0.958962	−	0.283536i	$-0.0915074\pi$
$684$	−0.0349352	+	0.761917i	−0.00133578	+	0.0291326i
$685$		−	1.30357i		−	0.0498070i
$686$		0			0
$687$			2.67856i			0.102194i
$688$	−0.693469	+	7.54617i	−0.0264383	+	0.287695i
$689$			32.0415i			1.22068i
$690$	7.13885	+	7.47368i	0.271771	+	0.284518i
$691$	−26.4910			−1.00776			−0.503882	−	0.863773i	$-0.668095\pi$
$691$	−26.4910			−1.00776			−0.503882	+	0.863773i	$0.668095\pi$
$692$	31.2090	+	1.43099i	1.18639	+	0.0543980i
$693$		0			0
$694$	−0.0205654	+	0.0196440i	−0.000780651	+	0.000745677i
$695$			20.8813i			0.792072i
$696$	−5.86543	+	5.10991i	−0.222329	+	0.193691i
$697$	−51.8739			−1.96486
$698$	−5.73055	+	5.47382i	−0.216905	+	0.207187i
$699$	−2.84996			−0.107795
$700$		0			0
$701$	−0.713553			−0.0269505			−0.0134753	−	0.999909i	$-0.504289\pi$
$701$	−0.713553			−0.0269505			−0.0134753	+	0.999909i	$0.504289\pi$
$702$	−13.3283	+	12.7312i	−0.503043	+	0.480507i
$703$	−1.66645			−0.0628515
$704$	−13.5808	−	1.87866i	−0.511847	−	0.0708045i
$705$			13.0264i			0.490602i
$706$	26.0615	−	24.8939i	0.980836	−	0.936893i
$707$		0			0
$708$	0.437133	−	9.53361i	0.0164285	−	0.358295i
$709$	−19.1317			−0.718505			−0.359253	−	0.933240i	$-0.616968\pi$
$709$	−19.1317			−0.718505			−0.359253	+	0.933240i	$0.616968\pi$
$710$	4.92518	+	5.15619i	0.184839	+	0.193508i
$711$			28.0925i			1.05355i
$712$	3.31394	+	3.80392i	0.124195	+	0.142558i
$713$		−	1.07578i		−	0.0402881i
$714$		0			0
$715$		−	4.21501i		−	0.157632i
$716$	−12.7646	−	0.585282i	−0.477037	−	0.0218730i
$717$			7.02486i			0.262348i
$718$	19.7866	−	18.9001i	0.738429	−	0.705347i
$719$	−40.0572			−1.49388			−0.746941	−	0.664890i	$-0.768478\pi$
$719$	−40.0572			−1.49388			−0.746941	+	0.664890i	$0.768478\pi$
$720$	0.644740	−	7.01591i	0.0240280	−	0.261468i
$721$		0			0
$722$	18.5140	+	19.3823i	0.689019	+	0.721335i
$723$			10.7133i			0.398433i
$724$	2.37290	+	0.108802i	0.0881881	+	0.00404358i
$725$	2.47123			0.0917793
$726$	−8.76569	−	9.17682i	−0.325325	−	0.340584i
$727$	−14.4074			−0.534341			−0.267171	−	0.963649i	$-0.586089\pi$
$727$	−14.4074			−0.534341			−0.267171	+	0.963649i	$0.586089\pi$
$728$		0			0
$729$	18.7733			0.695307
$730$	−7.43873	−	7.78762i	−0.275320	−	0.288233i
$731$	−11.7817			−0.435762
$732$	15.5656	+	0.713712i	0.575322	+	0.0263796i
$733$		−	0.774526i		−	0.0286078i	−0.999898	−	0.0143039i	$-0.995447\pi$
$733$		−	0.774526i		−	0.0286078i	0.999898	−	0.0143039i	$-0.00455322\pi$
$734$	16.8944	+	17.6868i	0.623584	+	0.652831i
$735$		0			0
$736$	29.0963	−	23.0919i	1.07250	−	0.851179i
$737$	−8.86731			−0.326631
$738$	15.0248	−	14.3517i	0.553071	−	0.528293i
$739$			8.19740i			0.301546i	0.988568	+	0.150773i	$0.0481763\pi$
$739$			8.19740i			0.301546i	−0.988568	+	0.150773i	$0.951824\pi$
$740$	15.3774	+	0.705083i	0.565286	+	0.0259194i
$741$		−	0.592653i		−	0.0217716i
$742$		0			0
$743$			8.66498i			0.317887i	0.987288	+	0.158944i	$0.0508088\pi$
$743$			8.66498i			0.317887i	−0.987288	+	0.158944i	$0.949191\pi$
$744$	0.388839	−	0.338753i	0.0142555	−	0.0124193i
$745$		−	9.73494i		−	0.356661i
$746$	−10.8523	−	11.3613i	−0.397329	−	0.415965i
$747$	9.64925			0.353048
$748$	0.976331	−	21.2932i	0.0356982	−	0.778557i
$749$		0			0
$750$	1.13814	−	1.08715i	0.0415590	−	0.0396971i
$751$			7.77354i			0.283661i	0.989891	+	0.141830i	$0.0452987\pi$
$751$			7.77354i			0.283661i	−0.989891	+	0.141830i	$0.954701\pi$
$752$	46.6216	+	4.28437i	1.70011	+	0.156235i
$753$	27.7687			1.01195
$754$	−6.21563	+	5.93716i	−0.226360	+	0.216219i
$755$	−14.9372			−0.543619
$756$		0			0
$757$	−5.10767			−0.185641			−0.0928206	−	0.995683i	$-0.529588\pi$
$757$	−5.10767			−0.185641			−0.0928206	+	0.995683i	$0.529588\pi$
$758$	−14.6441	+	13.9880i	−0.531896	+	0.508066i
$759$	−12.5245			−0.454612
$760$	0.402265	+	0.461741i	0.0145917	+	0.0167491i
$761$			4.80634i			0.174230i	0.996198	+	0.0871149i	$0.0277647\pi$
$761$			4.80634i			0.174230i	−0.996198	+	0.0871149i	$0.972235\pi$
$762$	18.0744	−	17.2646i	0.654766	−	0.625432i
$763$		0			0
$764$	−21.0998	−	0.967463i	−0.763364	−	0.0350016i
$765$	10.9538			0.396036
$766$	−10.2116	−	10.6906i	−0.368961	−	0.386267i
$767$		−	10.5453i		−	0.380768i
$768$	17.5088	+	3.24540i	0.631793	+	0.117108i
$769$			24.7841i			0.893738i	0.894600	+	0.446869i	$0.147461\pi$
$769$			24.7841i			0.893738i	−0.894600	+	0.446869i	$0.852539\pi$
$770$		0			0
$771$			18.8935i			0.680434i
$772$	−0.495419	+	10.8048i	−0.0178305	+	0.388873i
$773$		−	25.3120i		−	0.910410i	−0.890387	−	0.455205i	$-0.849566\pi$
$773$		−	25.3120i		−	0.910410i	0.890387	−	0.455205i	$-0.150434\pi$
$774$	3.41247	−	3.25958i	0.122659	−	0.117163i
$775$	−0.163826			−0.00588481
$776$	19.5649	+	22.4577i	0.702340	+	0.806184i
$777$		0			0
$778$	29.4277	+	30.8080i	1.05504	+	1.10452i
$779$			1.80600i			0.0647066i
$780$	−0.250754	+	5.46879i	−0.00897842	+	0.195814i
$781$	−8.64084			−0.309193
$782$	39.8907	+	41.7617i	1.42649	+	1.49340i
$783$	13.0953			0.467989
$784$		0			0
$785$	8.22463			0.293549
$786$	−3.48602	−	3.64953i	−0.124342	−	0.130174i
$787$	49.8985			1.77869			0.889345	−	0.457236i	$-0.151161\pi$
$787$	49.8985			1.77869			0.889345	+	0.457236i	$0.151161\pi$
$788$	−1.64439	+	35.8632i	−0.0585790	+	1.27757i
$789$		−	16.7313i		−	0.595652i
$790$	15.5797	+	16.3104i	0.554301	+	0.580299i
$791$		0			0
$792$	5.60830	+	6.43751i	0.199282	+	0.228747i
$793$	17.2174			0.611409
$794$	−13.7422	+	13.1266i	−0.487693	+	0.465844i
$795$		−	14.4990i		−	0.514225i
$796$	−0.700865	+	15.2855i	−0.0248415	+	0.541779i
$797$			38.2770i			1.35584i	0.735135	+	0.677921i	$0.237119\pi$
$797$			38.2770i			1.35584i	−0.735135	+	0.677921i	$0.762881\pi$
$798$		0			0
$799$			72.7894i			2.57510i
$800$	−3.51659	−	4.43098i	−0.124330	−	0.156659i
$801$		−	3.14171i		−	0.111007i
$802$	28.2154	+	29.5388i	0.996321	+	1.04305i
$803$	13.0506			0.460547
$804$	11.5049	+	0.527522i	0.405748	+	0.0186043i
$805$		0			0
$806$	0.412054	−	0.393594i	0.0145140	−	0.0138638i
$807$		−	34.9811i		−	1.23139i
$808$	−0.835641	−	0.959194i	−0.0293978	−	0.0337443i
$809$	9.80301			0.344655			0.172328	−	0.985040i	$-0.444871\pi$
$809$	9.80301			0.344655			0.172328	+	0.985040i	$0.444871\pi$
$810$	0.627364	−	0.599257i	0.0220433	−	0.0210557i
$811$	4.75188			0.166861			0.0834305	−	0.996514i	$-0.473412\pi$
$811$	4.75188			0.166861			0.0834305	+	0.996514i	$0.473412\pi$
$812$		0			0
$813$	−3.69240			−0.129498
$814$	−13.4892	+	12.8849i	−0.472797	+	0.451616i
$815$	−11.9866			−0.419872
$816$	−2.53349	+	27.5689i	−0.0886900	+	0.965105i
$817$			0.410182i			0.0143504i
$818$	−26.4897	+	25.3029i	−0.926191	+	0.884696i
$819$		0			0
$820$	0.764124	−	16.6651i	0.0266844	−	0.581970i
$821$	15.6564			0.546414			0.273207	−	0.961955i	$-0.411916\pi$
$821$	15.6564			0.546414			0.273207	+	0.961955i	$0.411916\pi$
$822$	−1.41718	−	1.48365i	−0.0494299	−	0.0517482i
$823$		−	19.7970i		−	0.690079i	−0.938588	−	0.345039i	$-0.887866\pi$
$823$		−	19.7970i		−	0.690079i	0.938588	−	0.345039i	$-0.112134\pi$
$824$	−19.7950	+	17.2452i	−0.689591	+	0.600765i
$825$			1.90732i			0.0664043i
$826$		0			0
$827$		−	13.0808i		−	0.454863i	−0.973794	−	0.227431i	$-0.926967\pi$
$827$		−	13.0808i		−	0.454863i	0.973794	−	0.227431i	$-0.0730327\pi$
$828$	−23.1080	−	1.05954i	−0.803059	−	0.0368217i
$829$		−	25.0676i		−	0.870633i	−0.900278	−	0.435316i	$-0.856637\pi$
$829$		−	25.0676i		−	0.870633i	0.900278	−	0.435316i	$-0.143363\pi$
$830$	5.60232	−	5.35133i	0.194459	−	0.185747i
$831$	16.4112			0.569300
$832$	19.4904	+	2.69613i	0.675707	+	0.0934715i
$833$		0			0
$834$	22.7011	+	23.7658i	0.786074	+	0.822943i
$835$		−	14.8103i		−	0.512533i
$836$	−0.741326	−	0.0339911i	−0.0256393	−	0.00117561i
$837$	−0.868133			−0.0300071
$838$	27.4511	+	28.7386i	0.948281	+	0.992758i
$839$	32.1347			1.10941			0.554707	−	0.832046i	$-0.312830\pi$
$839$	32.1347			1.10941			0.554707	+	0.832046i	$0.312830\pi$
$840$		0			0
$841$	−22.8930			−0.789414
$842$	−15.2648	−	15.9808i	−0.526060	−	0.550734i
$843$	22.8639			0.787476
$844$	−31.1092	−	1.42641i	−1.07082	−	0.0490992i
$845$		−	6.95088i		−	0.239117i
$846$	−20.1383	−	21.0828i	−0.692368	−	0.724842i
$847$		0			0
$848$	−51.8919	−	4.76870i	−1.78198	−	0.163758i
$849$	30.9800			1.06323
$850$	6.35975	−	6.07482i	0.218138	−	0.208365i
$851$		−	50.5415i		−	1.73254i
$852$	11.2111	+	0.514049i	0.384086	+	0.0176110i
$853$		−	45.8238i		−	1.56898i	−0.620142	−	0.784489i	$-0.712925\pi$
$853$		−	45.8238i		−	1.56898i	0.620142	−	0.784489i	$-0.287075\pi$
$854$		0			0
$855$		−	0.381359i		−	0.0130422i
$856$	34.4163	+	39.5049i	1.17632	+	1.35025i
$857$		−	37.3257i		−	1.27502i	−0.770441	−	0.637512i	$-0.779964\pi$
$857$		−	37.3257i		−	1.27502i	0.770441	−	0.637512i	$-0.220036\pi$
$858$	−4.58235	−	4.79727i	−0.156439	−	0.163776i
$859$	−13.2521			−0.452156			−0.226078	−	0.974109i	$-0.572590\pi$
$859$	−13.2521			−0.452156			−0.226078	+	0.974109i	$0.572590\pi$
$860$	0.173549	−	3.78501i	0.00591798	−	0.129068i
$861$		0			0
$862$	−20.4017	+	19.4877i	−0.694884	+	0.663752i
$863$			7.93414i			0.270081i	0.990840	+	0.135041i	$0.0431165\pi$
$863$			7.93414i			0.270081i	−0.990840	+	0.135041i	$0.956884\pi$
$864$	−18.6348	−	23.4802i	−0.633969	−	0.798814i
$865$	−15.6209			−0.531126
$866$	12.0973	−	11.5554i	0.411084	−	0.392667i
$867$	−24.1229			−0.819255
$868$		0			0
$869$	−27.3334			−0.927221
$870$	2.81261	−	2.68660i	0.0953565	−	0.0910844i
$871$	12.7258			0.431198
$872$	−14.8669	+	12.9519i	−0.503455	+	0.438606i
$873$		−	18.5481i		−	0.627759i
$874$	1.45394	−	1.38880i	0.0491803	−	0.0469769i
$875$		0			0
$876$	−16.9326	−	0.776391i	−0.572101	−	0.0262318i
$877$	51.7540			1.74761			0.873803	−	0.486279i	$-0.161646\pi$
$877$	51.7540			1.74761			0.873803	+	0.486279i	$0.161646\pi$
$878$	−27.2486	−	28.5266i	−0.919594	−	0.962726i
$879$			4.76813i			0.160825i
$880$	6.82631	+	0.627316i	0.230115	+	0.0211468i
$881$			7.69261i			0.259171i	0.991568	+	0.129585i	$0.0413646\pi$
$881$			7.69261i			0.259171i	−0.991568	+	0.129585i	$0.958635\pi$
$882$		0			0
$883$			35.2766i			1.18715i	0.804778	+	0.593575i	$0.202284\pi$
$883$			35.2766i			1.18715i	−0.804778	+	0.593575i	$0.797716\pi$
$884$	−1.40117	+	30.5587i	−0.0471265	+	1.02780i
$885$			4.77181i			0.160403i
$886$	19.6339	−	18.7543i	0.659613	−	0.630062i
$887$	11.6261			0.390366			0.195183	−	0.980767i	$-0.437470\pi$
$887$	11.6261			0.390366			0.195183	+	0.980767i	$0.437470\pi$
$888$	18.2682	−	15.9151i	0.613041	−	0.534076i
$889$		0			0
$890$	−1.74235	−	1.82407i	−0.0584036	−	0.0611429i
$891$			1.05135i			0.0352215i
$892$	−1.05053	+	22.9115i	−0.0351744	+	0.767132i
$893$	2.53417			0.0848029
$894$	−10.5833	−	11.0797i	−0.353960	−	0.370562i
$895$	6.38903			0.213562
$896$		0			0
$897$	17.9744			0.600149
$898$	4.82588	+	5.05223i	0.161042	+	0.168595i
$899$	−0.404853			−0.0135026
$900$	−0.161354	+	3.51904i	−0.00537848	+	0.117301i
$901$		−	81.0179i		−	2.69910i
$902$	13.9638	+	14.6188i	0.464945	+	0.486752i
$903$		0			0
$904$	0.711543	−	0.619890i	0.0236656	−	0.0206172i
$905$	−1.18770			−0.0394804
$906$	−17.0006	+	16.2389i	−0.564807	+	0.539503i
$907$		−	23.1775i		−	0.769596i	−0.923001	−	0.384798i	$-0.874271\pi$
$907$		−	23.1775i		−	0.769596i	0.923001	−	0.384798i	$-0.125729\pi$
$908$	0.820284	−	17.8899i	0.0272221	−	0.593697i
$909$			0.792212i			0.0262760i
$910$		0			0
$911$		−	43.0818i		−	1.42737i	−0.700469	−	0.713683i	$-0.747026\pi$
$911$		−	43.0818i		−	1.42737i	0.700469	−	0.713683i	$-0.252974\pi$
$912$	0.959816	+	0.0882040i	0.0317827	+	0.00292073i
$913$			9.38848i			0.310713i
$914$	25.5190	+	26.7159i	0.844094	+	0.883684i
$915$	−7.79100			−0.257562
$916$	−4.80845	−	0.220476i	−0.158876	−	0.00728473i
$917$		0			0
$918$	33.7010	−	32.1911i	1.11230	−	1.06247i
$919$			20.9526i			0.691162i	0.938389	+	0.345581i	$0.112318\pi$
$919$			20.9526i			0.691162i	−0.938389	+	0.345581i	$0.887682\pi$
$920$	−14.0040	+	12.2002i	−0.461700	+	0.402229i
$921$	15.9340			0.525043
$922$	13.6927	−	13.0792i	0.450944	−	0.430741i
$923$	12.4008			0.408177
$924$		0			0
$925$	−7.69679			−0.253069
$926$	−16.7733	+	16.0218i	−0.551205	+	0.526510i
$927$	16.3490			0.536970
$928$	−8.69031	−	10.9500i	−0.285274	−	0.359451i
$929$			10.2775i			0.337194i	0.985685	+	0.168597i	$0.0539237\pi$
$929$			10.2775i			0.337194i	−0.985685	+	0.168597i	$0.946076\pi$
$930$	−0.186457	+	0.178104i	−0.00611418	+	0.00584025i
$931$		0			0
$932$	0.234584	−	5.11613i	0.00768405	−	0.167585i
$933$	28.5614			0.935058
$934$	−11.6568	−	12.2035i	−0.381421	−	0.399311i
$935$			10.6578i			0.348547i
$936$	−8.04869	−	9.23872i	−0.263080	−	0.301977i
$937$		−	38.3992i		−	1.25445i	−0.778839	−	0.627224i	$-0.784191\pi$
$937$		−	38.3992i		−	1.25445i	0.778839	−	0.627224i	$-0.215809\pi$
$938$		0			0
$939$			36.1764i			1.18057i
$940$	−23.3844	−	1.07222i	−0.762717	−	0.0349719i
$941$		−	15.3449i		−	0.500229i	−0.968216	−	0.250115i	$-0.919532\pi$
$941$		−	15.3449i		−	0.500229i	0.968216	−	0.250115i	$-0.0804683\pi$
$942$	9.36078	−	8.94141i	0.304991	−	0.291327i
$943$	−54.7737			−1.78368
$944$	17.0784	+	1.56945i	0.555853	+	0.0510811i
$945$		0			0
$946$	3.17150	+	3.32025i	0.103114	+	0.107951i
$947$		−	26.6228i		−	0.865123i	−0.901604	−	0.432562i	$-0.857610\pi$
$947$		−	26.6228i		−	0.865123i	0.901604	−	0.432562i	$-0.142390\pi$
$948$	35.4638	+	1.62608i	1.15181	+	0.0528126i
$949$	−18.7295			−0.607985
$950$	−0.211496	−	0.221416i	−0.00686183	−	0.00718367i
$951$	3.25052			0.105405
$952$		0			0
$953$	5.39146			0.174646			0.0873232	−	0.996180i	$-0.472169\pi$
$953$	5.39146			0.174646			0.0873232	+	0.996180i	$0.472169\pi$
$954$	22.4148	+	23.4661i	0.725707	+	0.759744i
$955$	10.5610			0.341745
$956$	−12.6107	−	0.578225i	−0.407861	−	0.0187011i
$957$			4.71343i			0.152364i
$958$	36.3163	+	38.0197i	1.17333	+	1.22836i
$959$		0			0
$960$	−8.81952	−	1.22002i	−0.284649	−	0.0393759i
$961$	−30.9732			−0.999134
$962$	19.3589	−	18.4916i	0.624157	−	0.596194i
$963$		−	32.6276i		−	1.05141i
$964$	−19.2321	−	0.881827i	−0.619425	−	0.0284017i
$965$		−	5.40807i		−	0.174092i
$966$		0			0
$967$		−	6.14901i		−	0.197739i	−0.995100	−	0.0988694i	$-0.968477\pi$
$967$		−	6.14901i		−	0.197739i	0.995100	−	0.0988694i	$-0.0315226\pi$
$968$	17.1954	−	14.9805i	0.552680	−	0.481490i
$969$			1.49854i			0.0481401i
$970$	−10.2865	−	10.7690i	−0.330280	−	0.345771i
$971$	−31.3632			−1.00649			−0.503247	−	0.864143i	$-0.667861\pi$
$971$	−31.3632			−1.00649			−0.503247	+	0.864143i	$0.667861\pi$
$972$	−1.39377	+	30.3972i	−0.0447051	+	0.974991i
$973$		0			0
$974$	−1.00053	+	0.955707i	−0.0320591	+	0.0306228i
$975$		−	2.73727i		−	0.0876627i
$976$	−2.56245	+	27.8841i	−0.0820221	+	0.892547i
$977$	39.3113			1.25768			0.628841	−	0.777534i	$-0.283530\pi$
$977$	39.3113			1.25768			0.628841	+	0.777534i	$0.283530\pi$
$978$	−13.6424	+	13.0312i	−0.436237	+	0.416693i
$979$	3.05681			0.0976961
$980$		0			0
$981$	12.2787			0.392030
$982$	−18.8337	+	17.9899i	−0.601008	+	0.574082i
$983$	−30.4856			−0.972341			−0.486170	−	0.873864i	$-0.661607\pi$
$983$	−30.4856			−0.972341			−0.486170	+	0.873864i	$0.661607\pi$
$984$	−17.2478	−	19.7979i	−0.549840	−	0.631135i
$985$		−	17.9504i		−	0.571949i
$986$	15.7164	−	15.0123i	0.500513	−	0.478089i
$987$		0			0
$988$	1.06391	+	0.0487820i	0.0338474	+	0.00155196i
$989$	−12.4403			−0.395579
$990$	−2.94864	−	3.08694i	−0.0937139	−	0.0981093i
$991$		−	13.1486i		−	0.417679i	−0.977950	−	0.208840i	$-0.933031\pi$
$991$		−	13.1486i		−	0.417679i	0.977950	−	0.208840i	$-0.0669687\pi$
$992$	0.576110	+	0.725911i	0.0182915	+	0.0230477i
$993$		−	4.39461i		−	0.139459i
$994$		0			0
$995$		−	7.65076i		−	0.242545i
$996$	0.558527	−	12.1811i	0.0176976	−	0.385974i
$997$			11.3190i			0.358476i	0.983806	+	0.179238i	$0.0573632\pi$
$997$			11.3190i			0.358476i	−0.983806	+	0.179238i	$0.942637\pi$
$998$	−19.9761	+	19.0812i	−0.632333	+	0.604004i
$999$	−40.7861			−1.29042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.g.a.391.10		32
4.3	odd	2	inner	980.2.g.a.391.11		32
7.2	even	3		980.2.o.f.31.7		32
7.3	odd	6		980.2.o.f.411.15		32
7.4	even	3		140.2.o.a.131.15	yes	32
7.5	odd	6		140.2.o.a.31.7	✓	32
7.6	odd	2	inner	980.2.g.a.391.9		32
28.3	even	6		980.2.o.f.411.7		32
28.11	odd	6		140.2.o.a.131.7	yes	32
28.19	even	6		140.2.o.a.31.15	yes	32
28.23	odd	6		980.2.o.f.31.15		32
28.27	even	2	inner	980.2.g.a.391.12		32
35.4	even	6		700.2.p.c.551.2		32
35.12	even	12		700.2.t.d.199.2		32
35.18	odd	12		700.2.t.d.299.7		32
35.19	odd	6		700.2.p.c.451.10		32
35.32	odd	12		700.2.t.c.299.10		32
35.33	even	12		700.2.t.c.199.15		32
140.19	even	6		700.2.p.c.451.2		32
140.39	odd	6		700.2.p.c.551.10		32
140.47	odd	12		700.2.t.d.199.7		32
140.67	even	12		700.2.t.c.299.15		32
140.103	odd	12		700.2.t.c.199.10		32
140.123	even	12		700.2.t.d.299.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.7	✓	32	7.5	odd	6
140.2.o.a.31.15	yes	32	28.19	even	6
140.2.o.a.131.7	yes	32	28.11	odd	6
140.2.o.a.131.15	yes	32	7.4	even	3
700.2.p.c.451.2		32	140.19	even	6
700.2.p.c.451.10		32	35.19	odd	6
700.2.p.c.551.2		32	35.4	even	6
700.2.p.c.551.10		32	140.39	odd	6
700.2.t.c.199.10		32	140.103	odd	12
700.2.t.c.199.15		32	35.33	even	12
700.2.t.c.299.10		32	35.32	odd	12
700.2.t.c.299.15		32	140.67	even	12
700.2.t.d.199.2		32	35.12	even	12
700.2.t.d.199.7		32	140.47	odd	12
700.2.t.d.299.2		32	140.123	even	12
700.2.t.d.299.7		32	35.18	odd	12
980.2.g.a.391.9		32	7.6	odd	2	inner
980.2.g.a.391.10		32	1.1	even	1	trivial
980.2.g.a.391.11		32	4.3	odd	2	inner
980.2.g.a.391.12		32	28.27	even	2	inner
980.2.o.f.31.7		32	7.2	even	3
980.2.o.f.31.15		32	28.23	odd	6
980.2.o.f.411.7		32	28.3	even	6
980.2.o.f.411.15		32	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.976830 - 1.02265i) q^{2} +1.11294 q^{3} +(-0.0916073 + 1.99790i) q^{4} -1.00000i q^{5} +(-1.08715 - 1.13814i) q^{6} +(2.13263 - 1.85793i) q^{8} -1.76137 q^{9} +(-1.02265 + 0.976830i) q^{10} -1.71377i q^{11} +(-0.101953 + 2.22354i) q^{12} +2.45950i q^{13} -1.11294i q^{15} +(-3.98322 - 0.366045i) q^{16} -6.21892i q^{17} +(1.72056 + 1.80126i) q^{18} -0.216513 q^{19} +(1.99790 + 0.0916073i) q^{20} +(-1.75258 + 1.67406i) q^{22} -6.56656i q^{23} +(2.37348 - 2.06776i) q^{24} -1.00000 q^{25} +(2.51519 - 2.40251i) q^{26} -5.29911 q^{27} -2.47123 q^{29} +(-1.13814 + 1.08715i) q^{30} +0.163826 q^{31} +(3.51659 + 4.43098i) q^{32} -1.90732i q^{33} +(-6.35975 + 6.07482i) q^{34} +(0.161354 - 3.51904i) q^{36} +7.69679 q^{37} +(0.211496 + 0.221416i) q^{38} +2.73727i q^{39} +(-1.85793 - 2.13263i) q^{40} -8.34130i q^{41} -1.89449i q^{43} +(3.42394 + 0.156994i) q^{44} +1.76137i q^{45} +(-6.71527 + 6.41442i) q^{46} -11.7045 q^{47} +(-4.43307 - 0.407385i) q^{48} +(0.976830 + 1.02265i) q^{50} -6.92127i q^{51} +(-4.91383 - 0.225308i) q^{52} +13.0276 q^{53} +(5.17633 + 5.41911i) q^{54} -1.71377 q^{55} -0.240965 q^{57} +(2.41397 + 2.52720i) q^{58} -4.28758 q^{59} +(2.22354 + 0.101953i) q^{60} -7.00039i q^{61} +(-0.160030 - 0.167536i) q^{62} +(1.09621 - 7.92454i) q^{64} +2.45950 q^{65} +(-1.95051 + 1.86313i) q^{66} -5.17415i q^{67} +(12.4248 + 0.569698i) q^{68} -7.30818i q^{69} -5.04201i q^{71} +(-3.75635 + 3.27250i) q^{72} +7.61517i q^{73} +(-7.51846 - 7.87109i) q^{74} -1.11294 q^{75} +(0.0198341 - 0.432571i) q^{76} +(2.79925 - 2.67384i) q^{78} -15.9493i q^{79} +(-0.366045 + 3.98322i) q^{80} -0.613471 q^{81} +(-8.53020 + 8.14803i) q^{82} -5.47827 q^{83} -6.21892 q^{85} +(-1.93739 + 1.85060i) q^{86} -2.75033 q^{87} +(-3.18406 - 3.65483i) q^{88} +1.78368i q^{89} +(1.80126 - 1.72056i) q^{90} +(13.1193 + 0.601545i) q^{92} +0.182328 q^{93} +(11.4333 + 11.9696i) q^{94} +0.216513i q^{95} +(3.91375 + 4.93141i) q^{96} +10.5305i q^{97} +3.01858i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60}+ \cdots + 16 q^{93}+O(q^{100}) \) 32 * q - 4 * q^2 + 4 * q^4 - 4 * q^8 + 32 * q^9 + 28 * q^16 - 8 * q^22 - 32 * q^25 - 40 * q^29 - 4 * q^32 + 60 * q^36 - 16 * q^37 + 36 * q^44 - 4 * q^46 + 4 * q^50 + 16 * q^53 + 48 * q^57 - 4 * q^58 - 28 * q^60 + 4 * q^64 - 8 * q^65 - 8 * q^72 - 76 * q^74 + 120 * q^78 + 72 * q^81 - 56 * q^86 - 8 * q^88 - 4 * q^92 + 16 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more