LMFDB - Embedded newform 630.4.m.b.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,4,Mod(197,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("630.197");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	630.m (of order $4$, degree $2$, 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:	$37.1712033036$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} - 62 x^{14} + 184 x^{13} + 5442 x^{12} + 68448 x^{11} + 1829094 x^{10} + \cdots + 101023536964 $ x^16 - 8x^15 - 62x^14 + 184x^13 + 5442x^12 + 68448x^11 + 1829094x^10 - 45903568x^9 + 994701932x^8 - 9338829780x^7 + 56019913036x^6 - 164275655480x^5 - 103469892238x^4 + 1441603925160x^3 + 2253271661956x^2 + 418235574120*x + 101023536964
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.2
Root			$-13.4677 + 5.57851i$ of defining polynomial
Character	$\chi$	$=$	630.323
Dual form			630.4.m.b.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 1.41421i) q^{2} +4.00000i q^{4} +(2.41767 + 10.9158i) q^{5} +(4.94975 - 4.94975i) q^{7} +(5.65685 - 5.65685i) q^{8} +(12.0182 - 18.8564i) q^{10} +40.3451i q^{11} +(-4.00250 - 4.00250i) q^{13} -14.0000 q^{14} -16.0000 q^{16} +(24.2848 + 24.2848i) q^{17} +88.7246i q^{19} +(-43.6632 + 9.67066i) q^{20} +(57.0566 - 57.0566i) q^{22} +(100.543 - 100.543i) q^{23} +(-113.310 + 52.7816i) q^{25} +11.3208i q^{26} +(19.7990 + 19.7990i) q^{28} +131.171 q^{29} -127.843 q^{31} +(22.6274 + 22.6274i) q^{32} -68.6879i q^{34} +(65.9973 + 42.0637i) q^{35} +(11.9075 - 11.9075i) q^{37} +(125.476 - 125.476i) q^{38} +(75.4255 + 48.0728i) q^{40} +78.8741i q^{41} +(-154.322 - 154.322i) q^{43} -161.381 q^{44} -284.378 q^{46} +(-12.9636 - 12.9636i) q^{47} -49.0000i q^{49} +(234.889 + 85.5998i) q^{50} +(16.0100 - 16.0100i) q^{52} +(-196.358 + 196.358i) q^{53} +(-440.400 + 97.5411i) q^{55} -56.0000i q^{56} +(-185.504 - 185.504i) q^{58} -102.561 q^{59} -670.777 q^{61} +(180.798 + 180.798i) q^{62} -64.0000i q^{64} +(34.0138 - 53.3672i) q^{65} +(-559.907 + 559.907i) q^{67} +(-97.1393 + 97.1393i) q^{68} +(-33.8473 - 152.821i) q^{70} +688.906i q^{71} +(40.3519 + 40.3519i) q^{73} -33.6795 q^{74} -354.898 q^{76} +(199.698 + 199.698i) q^{77} -194.895i q^{79} +(-38.6827 - 174.653i) q^{80} +(111.545 - 111.545i) q^{82} +(283.254 - 283.254i) q^{83} +(-206.376 + 323.801i) q^{85} +436.488i q^{86} +(228.227 + 228.227i) q^{88} +21.4027 q^{89} -39.6227 q^{91} +(402.171 + 402.171i) q^{92} +36.6666i q^{94} +(-968.501 + 214.506i) q^{95} +(-348.520 + 348.520i) q^{97} +(-69.2965 + 69.2965i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 44 q^{5} - 24 q^{10} - 212 q^{13} - 224 q^{14} - 256 q^{16} - 32 q^{17} - 32 q^{20} + 72 q^{22} + 128 q^{23} - 268 q^{25} - 232 q^{29} - 200 q^{31} - 112 q^{35} + 900 q^{37} + 368 q^{38} - 128 q^{40}+ \cdots - 2668 q^{97}+O(q^{100}) $ 16 * q + 44 * q^5 - 24 * q^10 - 212 * q^13 - 224 * q^14 - 256 * q^16 - 32 * q^17 - 32 * q^20 + 72 * q^22 + 128 * q^23 - 268 * q^25 - 232 * q^29 - 200 * q^31 - 112 * q^35 + 900 * q^37 + 368 * q^38 - 128 * q^40 - 908 * q^43 - 352 * q^44 + 208 * q^46 + 604 * q^47 - 896 * q^50 + 848 * q^52 + 440 * q^53 - 1232 * q^55 + 536 * q^58 - 224 * q^59 + 1200 * q^61 + 1304 * q^62 - 1936 * q^65 + 652 * q^67 + 128 * q^68 - 616 * q^70 - 2148 * q^73 - 1328 * q^74 + 252 * q^77 - 704 * q^80 + 616 * q^82 + 2624 * q^83 - 1712 * q^85 + 288 * q^88 - 2400 * q^89 + 512 * q^92 - 4200 * q^95 - 2668 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$2$	−1.41421	−	1.41421i	−0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$			4.00000i			0.500000i
$5$	2.41767	+	10.9158i	0.216243	+	0.976340i
$5$	2.41767	+	10.9158i	0.216243	+	0.976340i
$6$		0			0
$7$	4.94975	−	4.94975i	0.267261	−	0.267261i
$7$	4.94975	−	4.94975i	0.267261	−	0.267261i
$8$	5.65685	−	5.65685i	0.250000	−	0.250000i
$9$		0			0
$10$	12.0182	−	18.8564i	0.380049	−	0.596291i
$11$			40.3451i			1.10587i	0.833226	+	0.552933i	$0.186491\pi$
$11$			40.3451i			1.10587i	−0.833226	+	0.552933i	$0.813509\pi$
$12$		0			0
$13$	−4.00250	−	4.00250i	−0.0853918	−	0.0853918i	0.663121	−	0.748513i	$-0.269232\pi$
$13$	−4.00250	−	4.00250i	−0.0853918	−	0.0853918i	−0.748513	+	0.663121i	$0.769232\pi$
$14$	−14.0000			−0.267261
$15$		0			0
$16$	−16.0000			−0.250000
$17$	24.2848	+	24.2848i	0.346467	+	0.346467i	0.858792	−	0.512325i	$-0.171216\pi$
$17$	24.2848	+	24.2848i	0.346467	+	0.346467i	−0.512325	+	0.858792i	$0.671216\pi$
$18$		0			0
$19$			88.7246i			1.07131i	0.844438	+	0.535653i	$0.179935\pi$
$19$			88.7246i			1.07131i	−0.844438	+	0.535653i	$0.820065\pi$
$20$	−43.6632	+	9.67066i	−0.488170	+	0.108121i
$21$		0			0
$22$	57.0566	−	57.0566i	0.552933	−	0.552933i
$23$	100.543	−	100.543i	0.911505	−	0.911505i	−0.0848860	−	0.996391i	$-0.527053\pi$
$23$	100.543	−	100.543i	0.911505	−	0.911505i	0.996391	+	0.0848860i	$0.0270526\pi$
$24$		0			0
$25$	−113.310	+	52.7816i	−0.906478	+	0.422253i
$26$			11.3208i			0.0853918i
$27$		0			0
$28$	19.7990	+	19.7990i	0.133631	+	0.133631i
$29$	131.171			0.839927			0.419963	−	0.907541i	$-0.362043\pi$
$29$	131.171			0.839927			0.419963	+	0.907541i	$0.362043\pi$
$30$		0			0
$31$	−127.843			−0.740689			−0.370344	−	0.928895i	$-0.620760\pi$
$31$	−127.843			−0.740689			−0.370344	+	0.928895i	$0.620760\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$		0			0
$34$		−	68.6879i		−	0.346467i
$35$	65.9973	+	42.0637i	0.318731	+	0.203144i
$36$		0			0
$37$	11.9075	−	11.9075i	0.0529075	−	0.0529075i	−0.680158	−	0.733066i	$-0.738089\pi$
$37$	11.9075	−	11.9075i	0.0529075	−	0.0529075i	0.733066	+	0.680158i	$0.238089\pi$
$38$	125.476	−	125.476i	0.535653	−	0.535653i
$39$		0			0
$40$	75.4255	+	48.0728i	0.298146	+	0.190024i
$41$			78.8741i			0.300441i	0.988653	+	0.150220i	$0.0479983\pi$
$41$			78.8741i			0.300441i	−0.988653	+	0.150220i	$0.952002\pi$
$42$		0			0
$43$	−154.322	−	154.322i	−0.547298	−	0.547298i	0.378360	−	0.925658i	$-0.376488\pi$
$43$	−154.322	−	154.322i	−0.547298	−	0.547298i	−0.925658	+	0.378360i	$0.876488\pi$
$44$	−161.381			−0.552933
$45$		0			0
$46$	−284.378			−0.911505
$47$	−12.9636	−	12.9636i	−0.0402326	−	0.0402326i	0.686704	−	0.726937i	$-0.259057\pi$
$47$	−12.9636	−	12.9636i	−0.0402326	−	0.0402326i	−0.726937	+	0.686704i	$0.759057\pi$
$48$		0			0
$49$		−	49.0000i		−	0.142857i
$50$	234.889	+	85.5998i	0.664365	+	0.242113i
$51$		0			0
$52$	16.0100	−	16.0100i	0.0426959	−	0.0426959i
$53$	−196.358	+	196.358i	−0.508903	+	0.508903i	−0.914190	−	0.405286i	$-0.867172\pi$
$53$	−196.358	+	196.358i	−0.508903	+	0.508903i	0.405286	+	0.914190i	$0.367172\pi$
$54$		0			0
$55$	−440.400	+	97.5411i	−1.07970	+	0.239135i
$56$		−	56.0000i		−	0.133631i
$57$		0			0
$58$	−185.504	−	185.504i	−0.419963	−	0.419963i
$59$	−102.561			−0.226309			−0.113155	−	0.993577i	$-0.536096\pi$
$59$	−102.561			−0.226309			−0.113155	+	0.993577i	$0.536096\pi$
$60$		0			0
$61$	−670.777			−1.40794			−0.703969	−	0.710231i	$-0.748591\pi$
$61$	−670.777			−1.40794			−0.703969	+	0.710231i	$0.748591\pi$
$62$	180.798	+	180.798i	0.370344	+	0.370344i
$63$		0			0
$64$		−	64.0000i		−	0.125000i
$65$	34.0138	−	53.3672i	0.0649061	−	0.101837i
$66$		0			0
$67$	−559.907	+	559.907i	−1.02095	+	1.02095i	−0.0211725	+	0.999776i	$0.506740\pi$
$67$	−559.907	+	559.907i	−1.02095	+	1.02095i	−0.999776	+	0.0211725i	$0.993260\pi$
$68$	−97.1393	+	97.1393i	−0.173233	+	0.173233i
$69$		0			0
$70$	−33.8473	−	152.821i	−0.0577933	−	0.260938i
$71$			688.906i			1.15152i	0.817618	+	0.575761i	$0.195294\pi$
$71$			688.906i			1.15152i	−0.817618	+	0.575761i	$0.804706\pi$
$72$		0			0
$73$	40.3519	+	40.3519i	0.0646963	+	0.0646963i	0.738715	−	0.674018i	$-0.235433\pi$
$73$	40.3519	+	40.3519i	0.0646963	+	0.0646963i	−0.674018	+	0.738715i	$0.735433\pi$
$74$	−33.6795			−0.0529075
$75$		0			0
$76$	−354.898			−0.535653
$77$	199.698	+	199.698i	0.295555	+	0.295555i
$78$		0			0
$79$		−	194.895i		−	0.277562i	−0.990323	−	0.138781i	$-0.955682\pi$
$79$		−	194.895i		−	0.277562i	0.990323	−	0.138781i	$-0.0443184\pi$
$80$	−38.6827	−	174.653i	−0.0540607	−	0.244085i
$81$		0			0
$82$	111.545	−	111.545i	0.150220	−	0.150220i
$83$	283.254	−	283.254i	0.374592	−	0.374592i	−0.494555	−	0.869146i	$-0.664669\pi$
$83$	283.254	−	283.254i	0.374592	−	0.374592i	0.869146	+	0.494555i	$0.164669\pi$
$84$		0			0
$85$	−206.376	+	323.801i	−0.263348	+	0.413190i
$86$			436.488i			0.547298i
$87$		0			0
$88$	228.227	+	228.227i	0.276466	+	0.276466i
$89$	21.4027			0.0254908			0.0127454	−	0.999919i	$-0.495943\pi$
$89$	21.4027			0.0254908			0.0127454	+	0.999919i	$0.495943\pi$
$90$		0			0
$91$	−39.6227			−0.0456439
$92$	402.171	+	402.171i	0.455752	+	0.455752i
$93$		0			0
$94$			36.6666i			0.0402326i
$95$	−968.501	+	214.506i	−1.04596	+	0.231662i
$96$		0			0
$97$	−348.520	+	348.520i	−0.364813	+	0.364813i	−0.865581	−	0.500769i	$-0.833051\pi$
$97$	−348.520	+	348.520i	−0.364813	+	0.364813i	0.500769	+	0.865581i	$0.333051\pi$
$98$	−69.2965	+	69.2965i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	−211.126	−	453.239i	−0.211126	−	0.453239i
$101$			471.820i			0.464830i	0.972617	+	0.232415i	$0.0746628\pi$
$101$			471.820i			0.464830i	−0.972617	+	0.232415i	$0.925337\pi$
$102$		0			0
$103$	−184.571	−	184.571i	−0.176567	−	0.176567i	0.613291	−	0.789857i	$-0.289845\pi$
$103$	−184.571	−	184.571i	−0.176567	−	0.176567i	−0.789857	+	0.613291i	$0.789845\pi$
$104$	−45.2831			−0.0426959
$105$		0			0
$106$	555.385			0.508903
$107$	1424.75	+	1424.75i	1.28725	+	1.28725i	0.936452	+	0.350797i	$0.114089\pi$
$107$	1424.75	+	1424.75i	1.28725	+	1.28725i	0.350797	+	0.936452i	$0.385911\pi$
$108$		0			0
$109$			226.862i			0.199352i	0.995020	+	0.0996761i	$0.0317807\pi$
$109$			226.862i			0.199352i	−0.995020	+	0.0996761i	$0.968219\pi$
$110$	760.763	+	484.875i	0.659418	+	0.420282i
$111$		0			0
$112$	−79.1960	+	79.1960i	−0.0668153	+	0.0668153i
$113$	−1027.24	+	1027.24i	−0.855173	+	0.855173i	−0.990765	−	0.135592i	$-0.956706\pi$
$113$	−1027.24	+	1027.24i	−0.855173	+	0.855173i	0.135592	+	0.990765i	$0.456706\pi$
$114$		0			0
$115$	1340.58	+	854.426i	1.08704	+	0.692832i
$116$			524.685i			0.419963i
$117$		0			0
$118$	145.043	+	145.043i	0.113155	+	0.113155i
$119$	240.408			0.185194
$120$		0			0
$121$	−296.730			−0.222937
$122$	948.622	+	948.622i	0.703969	+	0.703969i
$123$		0			0
$124$		−	511.374i		−	0.370344i
$125$	−850.099	−	1109.26i	−0.608281	−	0.793722i
$126$		0			0
$127$	1226.36	−	1226.36i	0.856862	−	0.856862i	−0.134105	−	0.990967i	$-0.542816\pi$
$127$	1226.36	−	1226.36i	0.856862	−	0.856862i	0.990967	+	0.134105i	$0.0428159\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−123.576	+	27.3699i	−0.0833714	+	0.0184654i
$131$			1245.84i			0.830915i	0.909613	+	0.415457i	$0.136378\pi$
$131$			1245.84i			0.830915i	−0.909613	+	0.415457i	$0.863622\pi$
$132$		0			0
$133$	439.164	+	439.164i	0.286319	+	0.286319i
$134$	1583.66			1.02095
$135$		0			0
$136$	274.752			0.173233
$137$	1415.10	+	1415.10i	0.882482	+	0.882482i	0.993786	−	0.111305i	$-0.0355030\pi$
$137$	1415.10	+	1415.10i	0.882482	+	0.882482i	−0.111305	+	0.993786i	$0.535503\pi$
$138$		0			0
$139$			2947.20i			1.79840i	0.437536	+	0.899201i	$0.355851\pi$
$139$			2947.20i			1.79840i	−0.437536	+	0.899201i	$0.644149\pi$
$140$	−168.255	+	263.989i	−0.101572	+	0.159366i
$141$		0			0
$142$	974.260	−	974.260i	0.575761	−	0.575761i
$143$	161.481	−	161.481i	0.0944319	−	0.0944319i
$144$		0			0
$145$	317.128	+	1431.84i	0.181628	+	0.820054i
$146$		−	114.132i		−	0.0646963i
$147$		0			0
$148$	47.6300	+	47.6300i	0.0264538	+	0.0264538i
$149$	−2507.52			−1.37869			−0.689344	−	0.724434i	$-0.742101\pi$
$149$	−2507.52			−1.37869			−0.689344	+	0.724434i	$0.742101\pi$
$150$		0			0
$151$	−1584.70			−0.854049			−0.427025	−	0.904240i	$-0.640438\pi$
$151$	−1584.70			−0.854049			−0.427025	+	0.904240i	$0.640438\pi$
$152$	501.902	+	501.902i	0.267827	+	0.267827i
$153$		0			0
$154$		−	564.832i		−	0.295555i
$155$	−309.083	−	1395.51i	−0.160168	−	0.723164i
$156$		0			0
$157$	−1845.14	+	1845.14i	−0.937950	+	0.937950i	−0.998184	−	0.0602346i	$-0.980815\pi$
$157$	−1845.14	+	1845.14i	−0.937950	+	0.937950i	0.0602346	+	0.998184i	$0.480815\pi$
$158$	−275.623	+	275.623i	−0.138781	+	0.138781i
$159$		0			0
$160$	−192.291	+	301.702i	−0.0950121	+	0.149073i
$161$		−	995.322i		−	0.487220i
$162$		0			0
$163$	312.292	+	312.292i	0.150065	+	0.150065i	0.778147	−	0.628082i	$-0.216160\pi$
$163$	312.292	+	312.292i	0.150065	+	0.150065i	−0.628082	+	0.778147i	$0.716160\pi$
$164$	−315.496			−0.150220
$165$		0			0
$166$	−801.162			−0.374592
$167$	−2181.85	−	2181.85i	−1.01100	−	1.01100i	−0.999939	−	0.0110606i	$-0.996479\pi$
$167$	−2181.85	−	2181.85i	−1.01100	−	1.01100i	−0.0110606	−	0.999939i	$-0.503521\pi$
$168$		0			0
$169$		−	2164.96i		−	0.985416i
$170$	749.784	−	166.064i	0.338269	−	0.0749209i
$171$		0			0
$172$	617.287	−	617.287i	0.273649	−	0.273649i
$173$	−1213.15	+	1213.15i	−0.533145	+	0.533145i	−0.921507	−	0.388362i	$-0.873041\pi$
$173$	−1213.15	+	1213.15i	−0.533145	+	0.533145i	0.388362	+	0.921507i	$0.373041\pi$
$174$		0			0
$175$	−299.599	+	822.110i	−0.129415	+	0.355118i
$176$		−	645.522i		−	0.276466i
$177$		0			0
$178$	−30.2679	−	30.2679i	−0.0127454	−	0.0127454i
$179$	1173.65			0.490072			0.245036	−	0.969514i	$-0.421200\pi$
$179$	1173.65			0.490072			0.245036	+	0.969514i	$0.421200\pi$
$180$		0			0
$181$	−3434.97			−1.41060			−0.705301	−	0.708908i	$-0.749188\pi$
$181$	−3434.97			−1.41060			−0.705301	+	0.708908i	$0.749188\pi$
$182$	56.0350	+	56.0350i	0.0228219	+	0.0228219i
$183$		0			0
$184$		−	1137.51i		−	0.455752i
$185$	158.768	+	101.192i	0.0630966	+	0.0402149i
$186$		0			0
$187$	−979.775	+	979.775i	−0.383146	+	0.383146i
$188$	51.8543	−	51.8543i	0.0201163	−	0.0201163i
$189$		0			0
$190$	1673.02	+	1066.31i	0.638810	+	0.407148i
$191$		−	2813.63i		−	1.06590i	−0.846147	−	0.532950i	$-0.821083\pi$
$191$		−	2813.63i		−	1.06590i	0.846147	−	0.532950i	$-0.178917\pi$
$192$		0			0
$193$	572.110	+	572.110i	0.213375	+	0.213375i	0.805700	−	0.592324i	$-0.201790\pi$
$193$	572.110	+	572.110i	0.213375	+	0.213375i	−0.592324	+	0.805700i	$0.701790\pi$
$194$	985.763			0.364813
$195$		0			0
$196$	196.000			0.0714286
$197$	1716.48	+	1716.48i	0.620781	+	0.620781i	0.945731	−	0.324950i	$-0.105347\pi$
$197$	1716.48	+	1716.48i	0.620781	+	0.620781i	−0.324950	+	0.945731i	$0.605347\pi$
$198$		0			0
$199$		−	171.950i		−	0.0612523i	−0.999531	−	0.0306262i	$-0.990250\pi$
$199$		−	171.950i		−	0.0612523i	0.999531	−	0.0306262i	$-0.00975014\pi$
$200$	−342.399	+	939.555i	−0.121056	+	0.332183i
$201$		0			0
$202$	667.254	−	667.254i	0.232415	−	0.232415i
$203$	649.264	−	649.264i	0.224480	−	0.224480i
$204$		0			0
$205$	−860.974	+	190.691i	−0.293332	+	0.0649681i
$206$			522.047i			0.176567i
$207$		0			0
$208$	64.0400	+	64.0400i	0.0213480	+	0.0213480i
$209$	−3579.61			−1.18472
$210$		0			0
$211$	4091.72			1.33500			0.667502	−	0.744608i	$-0.267364\pi$
$211$	4091.72			1.33500			0.667502	+	0.744608i	$0.267364\pi$
$212$	−785.433	−	785.433i	−0.254452	−	0.254452i
$213$		0			0
$214$		−	4029.80i		−	1.28725i
$215$	1311.45	−	2057.64i	0.416000	−	0.652698i
$216$		0			0
$217$	−632.793	+	632.793i	−0.197957	+	0.197957i
$218$	320.831	−	320.831i	0.0996761	−	0.0996761i
$219$		0			0
$220$	−390.164	−	1761.60i	−0.119568	−	0.539850i
$221$		−	194.400i		−	0.0591709i
$222$		0			0
$223$	2894.39	+	2894.39i	0.869160	+	0.869160i	0.992379	−	0.123220i	$-0.0393220\pi$
$223$	2894.39	+	2894.39i	0.869160	+	0.869160i	−0.123220	+	0.992379i	$0.539322\pi$
$224$	224.000			0.0668153
$225$		0			0
$226$	2905.47			0.855173
$227$	−294.719	−	294.719i	−0.0861725	−	0.0861725i	0.662707	−	0.748879i	$-0.269408\pi$
$227$	−294.719	−	294.719i	−0.0861725	−	0.0861725i	−0.748879	+	0.662707i	$0.769408\pi$
$228$		0			0
$229$		−	5417.69i		−	1.56337i	−0.623675	−	0.781683i	$-0.714361\pi$
$229$		−	5417.69i		−	1.56337i	0.623675	−	0.781683i	$-0.285639\pi$
$230$	−687.531	−	3104.21i	−0.197106	−	0.889938i
$231$		0			0
$232$	742.016	−	742.016i	0.209982	−	0.209982i
$233$	−1056.45	+	1056.45i	−0.297039	+	0.297039i	−0.839853	−	0.542814i	$-0.817359\pi$
$233$	−1056.45	+	1056.45i	−0.297039	+	0.297039i	0.542814	+	0.839853i	$0.317359\pi$
$234$		0			0
$235$	110.166	−	172.850i	0.0305807	−	0.0479807i
$236$		−	410.242i		−	0.113155i
$237$		0			0
$238$	−339.988	−	339.988i	−0.0925972	−	0.0925972i
$239$	−3947.63			−1.06841			−0.534207	−	0.845354i	$-0.679390\pi$
$239$	−3947.63			−1.06841			−0.534207	+	0.845354i	$0.679390\pi$
$240$		0			0
$241$	−3423.18			−0.914965			−0.457482	−	0.889219i	$-0.651249\pi$
$241$	−3423.18			−0.914965			−0.457482	+	0.889219i	$0.651249\pi$
$242$	419.639	+	419.639i	0.111469	+	0.111469i
$243$		0			0
$244$		−	2683.11i		−	0.703969i
$245$	534.875	−	118.466i	0.139477	−	0.0308918i
$246$		0			0
$247$	355.120	−	355.120i	0.0914808	−	0.0914808i
$248$	−723.191	+	723.191i	−0.185172	+	0.185172i
$249$		0			0
$250$	−366.509	+	2770.95i	−0.0927203	+	0.701001i
$251$			1277.32i			0.321210i	0.987019	+	0.160605i	$0.0513445\pi$
$251$			1277.32i			0.321210i	−0.987019	+	0.160605i	$0.948655\pi$
$252$		0			0
$253$	4056.41	+	4056.41i	1.00800	+	1.00800i
$254$	−3468.66			−0.856862
$255$		0			0
$256$	256.000			0.0625000
$257$	−2863.31	−	2863.31i	−0.694975	−	0.694975i	0.268348	−	0.963322i	$-0.413522\pi$
$257$	−2863.31	−	2863.31i	−0.694975	−	0.694975i	−0.963322	+	0.268348i	$0.913522\pi$
$258$		0			0
$259$		−	117.878i		−	0.0282803i
$260$	213.469	+	136.055i	0.0509184	+	0.0324530i
$261$		0			0
$262$	1761.89	−	1761.89i	0.415457	−	0.415457i
$263$	750.238	−	750.238i	0.175900	−	0.175900i	−0.613666	−	0.789566i	$-0.710306\pi$
$263$	750.238	−	750.238i	0.175900	−	0.175900i	0.789566	+	0.613666i	$0.210306\pi$
$264$		0			0
$265$	−2618.14	−	1668.68i	−0.606909	−	0.386816i
$266$		−	1242.14i		−	0.286319i
$267$		0			0
$268$	−2239.63	−	2239.63i	−0.510474	−	0.510474i
$269$	7027.41			1.59282			0.796410	−	0.604757i	$-0.206730\pi$
$269$	7027.41			1.59282			0.796410	+	0.604757i	$0.206730\pi$
$270$		0			0
$271$	−4337.40			−0.972246			−0.486123	−	0.873891i	$-0.661589\pi$
$271$	−4337.40			−0.972246			−0.486123	+	0.873891i	$0.661589\pi$
$272$	−388.557	−	388.557i	−0.0866167	−	0.0866167i
$273$		0			0
$274$		−	4002.50i		−	0.882482i
$275$	−2129.48	−	4571.50i	−0.466954	−	1.00244i
$276$		0			0
$277$	2073.14	−	2073.14i	0.449685	−	0.449685i	−0.445565	−	0.895250i	$-0.646997\pi$
$277$	2073.14	−	2073.14i	0.449685	−	0.449685i	0.895250	+	0.445565i	$0.146997\pi$
$278$	4167.96	−	4167.96i	0.899201	−	0.899201i
$279$		0			0
$280$	611.285	−	135.389i	0.130469	−	0.0288966i
$281$		−	2805.05i		−	0.595498i	−0.954644	−	0.297749i	$-0.903764\pi$
$281$		−	2805.05i		−	0.595498i	0.954644	−	0.297749i	$-0.0962359\pi$
$282$		0			0
$283$	6499.81	+	6499.81i	1.36528	+	1.36528i	0.867042	+	0.498235i	$0.166018\pi$
$283$	6499.81	+	6499.81i	1.36528	+	1.36528i	0.498235	+	0.867042i	$0.333982\pi$
$284$	−2755.62			−0.575761
$285$		0			0
$286$	−456.738			−0.0944319
$287$	390.407	+	390.407i	0.0802961	+	0.0802961i
$288$		0			0
$289$		−	3733.49i		−	0.759921i
$290$	1576.44	−	2473.41i	0.319213	−	0.500841i
$291$		0			0
$292$	−161.408	+	161.408i	−0.0323482	+	0.0323482i
$293$	4804.81	−	4804.81i	0.958021	−	0.958021i	−0.0411325	−	0.999154i	$-0.513097\pi$
$293$	4804.81	−	4804.81i	0.958021	−	0.958021i	0.999154	+	0.0411325i	$0.0130966\pi$
$294$		0			0
$295$	−247.957	−	1119.53i	−0.0489377	−	0.220955i
$296$		−	134.718i		−	0.0264538i
$297$		0			0
$298$	3546.18	+	3546.18i	0.689344	+	0.689344i
$299$	−804.845			−0.155670
$300$		0			0
$301$	−1527.71			−0.292543
$302$	2241.11	+	2241.11i	0.427025	+	0.427025i
$303$		0			0
$304$		−	1419.59i		−	0.267827i
$305$	−1621.72	−	7322.08i	−0.304456	−	1.37463i
$306$		0			0
$307$	4340.43	−	4340.43i	0.806911	−	0.806911i	−0.177255	−	0.984165i	$-0.556722\pi$
$307$	4340.43	−	4340.43i	0.806911	−	0.806911i	0.984165	+	0.177255i	$0.0567216\pi$
$308$	−798.793	+	798.793i	−0.147777	+	0.147777i
$309$		0			0
$310$	−1536.45	+	2410.66i	−0.281498	+	0.441666i
$311$			1602.95i			0.292266i	0.989265	+	0.146133i	$0.0466828\pi$
$311$			1602.95i			0.292266i	−0.989265	+	0.146133i	$0.953317\pi$
$312$		0			0
$313$	1409.87	+	1409.87i	0.254602	+	0.254602i	0.822854	−	0.568252i	$-0.192380\pi$
$313$	1409.87	+	1409.87i	0.254602	+	0.254602i	−0.568252	+	0.822854i	$0.692380\pi$
$314$	5218.84			0.937950
$315$		0			0
$316$	779.579			0.138781
$317$	−7511.16	−	7511.16i	−1.33082	−	1.33082i	−0.904641	−	0.426175i	$-0.859861\pi$
$317$	−7511.16	−	7511.16i	−1.33082	−	1.33082i	−0.426175	−	0.904641i	$-0.640139\pi$
$318$		0			0
$319$			5292.12i			0.928846i
$320$	698.612	−	154.731i	0.122042	−	0.0270303i
$321$		0			0
$322$	−1407.60	+	1407.60i	−0.243610	+	0.243610i
$323$	−2154.66	+	2154.66i	−0.371172	+	0.371172i
$324$		0			0
$325$	664.781	+	242.264i	0.113463	+	0.0413489i
$326$		−	883.294i		−	0.150065i
$327$		0			0
$328$	446.179	+	446.179i	0.0751101	+	0.0751101i
$329$	−128.333			−0.0215052
$330$		0			0
$331$	−2550.38			−0.423509			−0.211754	−	0.977323i	$-0.567918\pi$
$331$	−2550.38			−0.423509			−0.211754	+	0.977323i	$0.567918\pi$
$332$	1133.01	+	1133.01i	0.187296	+	0.187296i
$333$		0			0
$334$			6171.21i			1.01100i
$335$	−7465.51	−	4758.17i	−1.21756	−	0.776020i
$336$		0			0
$337$	1093.33	−	1093.33i	0.176729	−	0.176729i	−0.613199	−	0.789928i	$-0.710118\pi$
$337$	1093.33	−	1093.33i	0.176729	−	0.176729i	0.789928	+	0.613199i	$0.210118\pi$
$338$	−3061.72	+	3061.72i	−0.492708	+	0.492708i
$339$		0			0
$340$	−1295.20	−	825.504i	−0.206595	−	0.131674i
$341$		−	5157.86i		−	0.819102i
$342$		0			0
$343$	−242.538	−	242.538i	−0.0381802	−	0.0381802i
$344$	−1745.95			−0.273649
$345$		0			0
$346$	3431.30			0.533145
$347$	5694.51	+	5694.51i	0.880972	+	0.880972i	0.993633	−	0.112662i	$-0.0359376\pi$
$347$	5694.51	+	5694.51i	0.880972	+	0.880972i	−0.112662	+	0.993633i	$0.535938\pi$
$348$		0			0
$349$		−	9393.06i		−	1.44068i	−0.693619	−	0.720342i	$-0.743985\pi$
$349$		−	9393.06i		−	1.44068i	0.693619	−	0.720342i	$-0.256015\pi$
$350$	1586.34	−	738.942i	0.242267	−	0.112852i
$351$		0			0
$352$	−912.906	+	912.906i	−0.138233	+	0.138233i
$353$	−534.035	+	534.035i	−0.0805207	+	0.0805207i	−0.746220	−	0.665699i	$-0.768133\pi$
$353$	−534.035	+	534.035i	−0.0805207	+	0.0805207i	0.665699	+	0.746220i	$0.268133\pi$
$354$		0			0
$355$	−7519.96	+	1665.54i	−1.12428	+	0.249008i
$356$			85.6106i			0.0127454i
$357$		0			0
$358$	−1659.79	−	1659.79i	−0.245036	−	0.245036i
$359$	−3069.61			−0.451275			−0.225638	−	0.974211i	$-0.572447\pi$
$359$	−3069.61			−0.451275			−0.225638	+	0.974211i	$0.572447\pi$
$360$		0			0
$361$	−1013.05			−0.147697
$362$	4857.78	+	4857.78i	0.705301	+	0.705301i
$363$		0			0
$364$		−	158.491i		−	0.0228219i
$365$	−342.916	+	538.031i	−0.0491755	+	0.0771557i
$366$		0			0
$367$	8419.72	−	8419.72i	1.19756	−	1.19756i	0.222669	−	0.974894i	$-0.428523\pi$
$367$	8419.72	−	8419.72i	1.19756	−	1.19756i	0.974894	−	0.222669i	$-0.0714769\pi$
$368$	−1608.68	+	1608.68i	−0.227876	+	0.227876i
$369$		0			0
$370$	−81.4257	−	367.639i	−0.0114409	−	0.0516557i
$371$			1943.85i			0.272020i
$372$		0			0
$373$	2521.54	+	2521.54i	0.350027	+	0.350027i	0.860120	−	0.510092i	$-0.170389\pi$
$373$	2521.54	+	2521.54i	0.350027	+	0.350027i	−0.510092	+	0.860120i	$0.670389\pi$
$374$	2771.22			0.383146
$375$		0			0
$376$	−146.666			−0.0201163
$377$	−525.013	−	525.013i	−0.0717229	−	0.0717229i
$378$		0			0
$379$		−	7021.86i		−	0.951685i	−0.879530	−	0.475843i	$-0.842143\pi$
$379$		−	7021.86i		−	0.951685i	0.879530	−	0.475843i	$-0.157857\pi$
$380$	−858.026	−	3874.00i	−0.115831	−	0.522979i
$381$		0			0
$382$	−3979.07	+	3979.07i	−0.532950	+	0.532950i
$383$	−2600.78	+	2600.78i	−0.346981	+	0.346981i	−0.858984	−	0.512003i	$-0.828904\pi$
$383$	−2600.78	+	2600.78i	−0.346981	+	0.346981i	0.512003	+	0.858984i	$0.328904\pi$
$384$		0			0
$385$	−1697.06	+	2662.67i	−0.224650	+	0.352473i
$386$		−	1618.17i		−	0.213375i
$387$		0			0
$388$	−1394.08	−	1394.08i	−0.182406	−	0.182406i
$389$	11198.4			1.45959			0.729794	−	0.683668i	$-0.239616\pi$
$389$	11198.4			1.45959			0.729794	+	0.683668i	$0.239616\pi$
$390$		0			0
$391$	4883.33			0.631612
$392$	−277.186	−	277.186i	−0.0357143	−	0.0357143i
$393$		0			0
$394$		−	4854.93i		−	0.620781i
$395$	2127.44	−	471.191i	0.270995	−	0.0600207i
$396$		0			0
$397$	−7834.36	+	7834.36i	−0.990416	+	0.990416i	−0.999955	−	0.00953870i	$-0.996964\pi$
$397$	−7834.36	+	7834.36i	−0.990416	+	0.990416i	0.00953870	+	0.999955i	$0.496964\pi$
$398$	−243.174	+	243.174i	−0.0306262	+	0.0306262i
$399$		0			0
$400$	1812.96	−	844.505i	0.226620	−	0.105563i
$401$		−	15372.7i		−	1.91440i	−0.289422	−	0.957201i	$-0.593463\pi$
$401$		−	15372.7i		−	1.91440i	0.289422	−	0.957201i	$-0.406537\pi$
$402$		0			0
$403$	511.693	+	511.693i	0.0632488	+	0.0632488i
$404$	−1887.28			−0.232415
$405$		0			0
$406$	−1836.40			−0.224480
$407$	480.409	+	480.409i	0.0585086	+	0.0585086i
$408$		0			0
$409$			2650.95i			0.320491i	0.987077	+	0.160246i	$0.0512287\pi$
$409$			2650.95i			0.320491i	−0.987077	+	0.160246i	$0.948771\pi$
$410$	1487.28	+	947.924i	0.179150	+	0.114182i
$411$		0			0
$412$	738.286	−	738.286i	0.0882833	−	0.0882833i
$413$	−507.649	+	507.649i	−0.0604837	+	0.0604837i
$414$		0			0
$415$	3776.75	+	2407.13i	0.446731	+	0.284726i
$416$		−	181.133i		−	0.0213480i
$417$		0			0
$418$	5062.33	+	5062.33i	0.592360	+	0.592360i
$419$	−4280.02			−0.499028			−0.249514	−	0.968371i	$-0.580271\pi$
$419$	−4280.02			−0.499028			−0.249514	+	0.968371i	$0.580271\pi$
$420$		0			0
$421$	2639.09			0.305514			0.152757	−	0.988264i	$-0.451185\pi$
$421$	2639.09			0.305514			0.152757	+	0.988264i	$0.451185\pi$
$422$	−5786.57	−	5786.57i	−0.667502	−	0.667502i
$423$		0			0
$424$			2221.54i			0.254452i
$425$	−4033.50	−	1469.92i	−0.460361	−	0.167768i
$426$		0			0
$427$	−3320.18	+	3320.18i	−0.376287	+	0.376287i
$428$	−5698.99	+	5698.99i	−0.643624	+	0.643624i
$429$		0			0
$430$	−4764.61	+	1055.28i	−0.534349	+	0.118349i
$431$			14510.6i			1.62169i	0.585258	+	0.810847i	$0.300993\pi$
$431$			14510.6i			1.62169i	−0.585258	+	0.810847i	$0.699007\pi$
$432$		0			0
$433$	80.2055	+	80.2055i	0.00890168	+	0.00890168i	0.711544	−	0.702642i	$-0.247996\pi$
$433$	80.2055	+	80.2055i	0.00890168	+	0.00890168i	−0.702642	+	0.711544i	$0.747996\pi$
$434$	1789.81			0.197957
$435$		0			0
$436$	−907.446			−0.0996761
$437$	8920.61	+	8920.61i	0.976501	+	0.976501i
$438$		0			0
$439$			1131.71i			0.123038i	0.998106	+	0.0615190i	$0.0195945\pi$
$439$			1131.71i			0.123038i	−0.998106	+	0.0615190i	$0.980406\pi$
$440$	−1939.50	+	3043.05i	−0.210141	+	0.329709i
$441$		0			0
$442$	−274.923	+	274.923i	−0.0295854	+	0.0295854i
$443$	−12391.3	+	12391.3i	−1.32896	+	1.32896i	−0.422681	+	0.906278i	$0.638911\pi$
$443$	−12391.3	+	12391.3i	−1.32896	+	1.32896i	−0.906278	+	0.422681i	$0.861089\pi$
$444$		0			0
$445$	51.7445	+	233.627i	0.00551219	+	0.0248876i
$446$		−	8186.57i		−	0.869160i
$447$		0			0
$448$	−316.784	−	316.784i	−0.0334077	−	0.0334077i
$449$	1970.09			0.207070			0.103535	−	0.994626i	$-0.466985\pi$
$449$	1970.09			0.207070			0.103535	+	0.994626i	$0.466985\pi$
$450$		0			0
$451$	−3182.19			−0.332247
$452$	−4108.96	−	4108.96i	−0.427586	−	0.427586i
$453$		0			0
$454$			833.590i			0.0861725i
$455$	−95.7946	−	432.514i	−0.00987015	−	0.0445639i
$456$		0			0
$457$	10123.8	−	10123.8i	1.03627	−	1.03627i	0.0369484	−	0.999317i	$-0.488236\pi$
$457$	10123.8	−	10123.8i	1.03627	−	1.03627i	0.999317	−	0.0369484i	$-0.0117637\pi$
$458$	−7661.77	+	7661.77i	−0.781683	+	0.781683i
$459$		0			0
$460$	−3417.71	+	5362.34i	−0.346416	+	0.543522i
$461$			15485.6i			1.56450i	0.622963	+	0.782252i	$0.285929\pi$
$461$			15485.6i			1.56450i	−0.622963	+	0.782252i	$0.714071\pi$
$462$		0			0
$463$	8726.03	+	8726.03i	0.875881	+	0.875881i	0.993105	−	0.117224i	$-0.0373996\pi$
$463$	8726.03	+	8726.03i	0.875881	+	0.875881i	−0.117224	+	0.993105i	$0.537400\pi$
$464$	−2098.74			−0.209982
$465$		0			0
$466$	2988.08			0.297039
$467$	7409.34	+	7409.34i	0.734183	+	0.734183i	0.971446	−	0.237262i	$-0.0762501\pi$
$467$	7409.34	+	7409.34i	0.734183	+	0.734183i	−0.237262	+	0.971446i	$0.576250\pi$
$468$		0			0
$469$			5542.80i			0.545720i
$470$	−400.245	+	88.6475i	−0.0392807	+	0.00870001i
$471$		0			0
$472$	−580.170	+	580.170i	−0.0565773	+	0.0565773i
$473$	6226.13	−	6226.13i	0.605238	−	0.605238i
$474$		0			0
$475$	−4683.02	−	10053.4i	−0.452362	−	0.971116i
$476$			961.630i			0.0925972i
$477$		0			0
$478$	5582.79	+	5582.79i	0.534207	+	0.534207i
$479$	11356.0			1.08323			0.541617	−	0.840625i	$-0.317812\pi$
$479$	11356.0			1.08323			0.541617	+	0.840625i	$0.317812\pi$
$480$		0			0
$481$	−95.3195			−0.00903575
$482$	4841.11	+	4841.11i	0.457482	+	0.457482i
$483$		0			0
$484$		−	1186.92i		−	0.111469i
$485$	−4646.98	−	2961.77i	−0.435069	−	0.277293i
$486$		0			0
$487$	7953.48	−	7953.48i	0.740054	−	0.740054i	−0.232534	−	0.972588i	$-0.574702\pi$
$487$	7953.48	−	7953.48i	0.740054	−	0.740054i	0.972588	+	0.232534i	$0.0747016\pi$
$488$	−3794.49	+	3794.49i	−0.351985	+	0.351985i
$489$		0			0
$490$	−923.963	−	588.891i	−0.0851844	−	0.0542926i
$491$			10105.6i			0.928837i	0.885616	+	0.464418i	$0.153737\pi$
$491$			10105.6i			0.928837i	−0.885616	+	0.464418i	$0.846263\pi$
$492$		0			0
$493$	3185.47	+	3185.47i	0.291007	+	0.291007i
$494$	−1004.43			−0.0914808
$495$		0			0
$496$	2045.49			0.185172
$497$	3409.91	+	3409.91i	0.307757	+	0.307757i
$498$		0			0
$499$		−	16871.6i		−	1.51358i	−0.653660	−	0.756788i	$-0.726767\pi$
$499$		−	16871.6i		−	1.51358i	0.653660	−	0.756788i	$-0.273233\pi$
$500$	4437.04	−	3400.39i	0.396861	−	0.304141i
$501$		0			0
$502$	1806.40	−	1806.40i	0.160605	−	0.160605i
$503$	−7926.80	+	7926.80i	−0.702661	+	0.702661i	−0.964981	−	0.262320i	$-0.915512\pi$
$503$	−7926.80	+	7926.80i	−0.702661	+	0.702661i	0.262320	+	0.964981i	$0.415512\pi$
$504$		0			0
$505$	−5150.30	+	1140.70i	−0.453832	+	0.100516i
$506$		−	11473.3i		−	1.00800i
$507$		0			0
$508$	4905.42	+	4905.42i	0.428431	+	0.428431i
$509$	18856.8			1.64207			0.821036	−	0.570877i	$-0.193397\pi$
$509$	18856.8			1.64207			0.821036	+	0.570877i	$0.193397\pi$
$510$		0			0
$511$	399.463			0.0345816
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			8098.67i			0.694975i
$515$	1568.51	−	2460.98i	0.134208	−	0.210570i
$516$		0			0
$517$	523.018	−	523.018i	0.0444918	−	0.0444918i
$518$	−166.705	+	166.705i	−0.0141401	+	0.0141401i
$519$		0			0
$520$	−109.479	−	494.302i	−0.00923268	−	0.0416857i
$521$			21317.6i			1.79259i	0.443457	+	0.896296i	$0.353752\pi$
$521$			21317.6i			1.79259i	−0.443457	+	0.896296i	$0.646248\pi$
$522$		0			0
$523$	11839.2	+	11839.2i	0.989848	+	0.989848i	0.999949	−	0.0101011i	$-0.00321533\pi$
$523$	11839.2	+	11839.2i	0.989848	+	0.989848i	−0.0101011	+	0.999949i	$0.503215\pi$
$524$	−4983.37			−0.415457
$525$		0			0
$526$	−2121.99			−0.175900
$527$	−3104.66	−	3104.66i	−0.256624	−	0.256624i
$528$		0			0
$529$		−	8050.68i		−	0.661681i
$530$	1342.74	+	6062.48i	0.110047	+	0.496863i
$531$		0			0
$532$	−1756.66	+	1756.66i	−0.143159	+	0.143159i
$533$	315.694	−	315.694i	0.0256552	−	0.0256552i
$534$		0			0
$535$	−12107.7	+	18996.8i	−0.978434	+	1.53515i
$536$			6334.63i			0.510474i
$537$		0			0
$538$	−9938.26	−	9938.26i	−0.796410	−	0.796410i
$539$	1976.91			0.157981
$540$		0			0
$541$	−20518.6			−1.63062			−0.815309	−	0.579026i	$-0.803433\pi$
$541$	−20518.6			−1.63062			−0.815309	+	0.579026i	$0.803433\pi$
$542$	6134.02	+	6134.02i	0.486123	+	0.486123i
$543$		0			0
$544$			1099.01i			0.0866167i
$545$	−2476.38	+	548.475i	−0.194636	+	0.0431085i
$546$		0			0
$547$	2597.59	−	2597.59i	0.203044	−	0.203044i	−0.598259	−	0.801303i	$-0.704141\pi$
$547$	2597.59	−	2597.59i	0.203044	−	0.203044i	0.801303	+	0.598259i	$0.204141\pi$
$548$	−5660.39	+	5660.39i	−0.441241	+	0.441241i
$549$		0			0
$550$	−3453.54	+	9476.61i	−0.267744	+	0.734698i
$551$			11638.1i			0.899819i
$552$		0			0
$553$	−964.680	−	964.680i	−0.0741815	−	0.0741815i
$554$	−5863.72			−0.449685
$555$		0			0
$556$	−11788.8			−0.899201
$557$	12709.7	+	12709.7i	0.966838	+	0.966838i	0.999468	−	0.0326300i	$-0.0103883\pi$
$557$	12709.7	+	12709.7i	0.966838	+	0.966838i	−0.0326300	+	0.999468i	$0.510388\pi$
$558$		0			0
$559$			1235.35i			0.0934696i
$560$	−1055.96	−	673.019i	−0.0796828	−	0.0507861i
$561$		0			0
$562$	−3966.93	+	3966.93i	−0.297749	+	0.297749i
$563$	−5831.66	+	5831.66i	−0.436546	+	0.436546i	−0.890848	−	0.454302i	$-0.849889\pi$
$563$	−5831.66	+	5831.66i	−0.436546	+	0.436546i	0.454302	+	0.890848i	$0.349889\pi$
$564$		0			0
$565$	−13696.7	−	8729.63i	−1.01986	−	0.650014i
$566$		−	18384.2i		−	1.36528i
$567$		0			0
$568$	3897.04	+	3897.04i	0.287880	+	0.287880i
$569$	3671.47			0.270502			0.135251	−	0.990811i	$-0.456816\pi$
$569$	3671.47			0.270502			0.135251	+	0.990811i	$0.456816\pi$
$570$		0			0
$571$	6892.33			0.505140			0.252570	−	0.967579i	$-0.418724\pi$
$571$	6892.33			0.505140			0.252570	+	0.967579i	$0.418724\pi$
$572$	645.926	+	645.926i	0.0472159	+	0.0472159i
$573$		0			0
$574$		−	1104.24i		−	0.0802961i
$575$	−6085.67	+	16699.3i	−0.441374	+	1.21114i
$576$		0			0
$577$	−2678.84	+	2678.84i	−0.193278	+	0.193278i	−0.797111	−	0.603833i	$-0.793639\pi$
$577$	−2678.84	+	2678.84i	−0.193278	+	0.193278i	0.603833	+	0.797111i	$0.293639\pi$
$578$	−5279.96	+	5279.96i	−0.379961	+	0.379961i
$579$		0			0
$580$	−5727.36	+	1268.51i	−0.410027	+	0.0908140i
$581$		−	2804.07i		−	0.200228i
$582$		0			0
$583$	−7922.10	−	7922.10i	−0.562779	−	0.562779i
$584$	456.530			0.0323482
$585$		0			0
$586$	−13590.1			−0.958021
$587$	−6205.42	−	6205.42i	−0.436329	−	0.436329i	0.454446	−	0.890774i	$-0.349837\pi$
$587$	−6205.42	−	6205.42i	−0.436329	−	0.436329i	−0.890774	+	0.454446i	$0.849837\pi$
$588$		0			0
$589$		−	11342.9i		−	0.793504i
$590$	−1232.59	+	1933.92i	−0.0860085	+	0.134946i
$591$		0			0
$592$	−190.520	+	190.520i	−0.0132269	+	0.0132269i
$593$	18830.2	−	18830.2i	1.30398	−	1.30398i	0.378302	−	0.925682i	$-0.376508\pi$
$593$	18830.2	−	18830.2i	1.30398	−	1.30398i	0.925682	−	0.378302i	$-0.123492\pi$
$594$		0			0
$595$	581.225	+	2624.24i	0.0400469	+	0.180813i
$596$		−	10030.1i		−	0.689344i
$597$		0			0
$598$	1138.22	+	1138.22i	0.0778351	+	0.0778351i
$599$	26032.7			1.77574			0.887868	−	0.460099i	$-0.152186\pi$
$599$	26032.7			1.77574			0.887868	+	0.460099i	$0.152186\pi$
$600$		0			0
$601$	−14414.1			−0.978308			−0.489154	−	0.872197i	$-0.662694\pi$
$601$	−14414.1			−0.978308			−0.489154	+	0.872197i	$0.662694\pi$
$602$	2160.50	+	2160.50i	0.146272	+	0.146272i
$603$		0			0
$604$		−	6338.82i		−	0.427025i
$605$	−717.393	−	3239.04i	−0.0482086	−	0.217663i
$606$		0			0
$607$	1947.35	−	1947.35i	0.130215	−	0.130215i	−0.638995	−	0.769211i	$-0.720650\pi$
$607$	1947.35	−	1947.35i	0.130215	−	0.130215i	0.769211	+	0.638995i	$0.220650\pi$
$608$	−2007.61	+	2007.61i	−0.133913	+	0.133913i
$609$		0			0
$610$	−8061.53	+	12648.4i	−0.535085	+	0.839541i
$611$			103.774i			0.00687108i
$612$		0			0
$613$	−11137.1	−	11137.1i	−0.733804	−	0.733804i	0.237567	−	0.971371i	$-0.423650\pi$
$613$	−11137.1	−	11137.1i	−0.733804	−	0.733804i	−0.971371	+	0.237567i	$0.923650\pi$
$614$	−12276.6			−0.806911
$615$		0			0
$616$	2259.33			0.147777
$617$	−11483.9	−	11483.9i	−0.749308	−	0.749308i	0.225041	−	0.974349i	$-0.427748\pi$
$617$	−11483.9	−	11483.9i	−0.749308	−	0.749308i	−0.974349	+	0.225041i	$0.927748\pi$
$618$		0			0
$619$			15622.6i			1.01442i	0.861823	+	0.507209i	$0.169323\pi$
$619$			15622.6i			1.01442i	−0.861823	+	0.507209i	$0.830677\pi$
$620$	5582.06	−	1236.33i	0.361582	−	0.0800842i
$621$		0			0
$622$	2266.91	−	2266.91i	0.146133	−	0.146133i
$623$	105.938	−	105.938i	0.00681269	−	0.00681269i
$624$		0			0
$625$	10053.2	−	11961.3i	0.643406	−	0.765525i
$626$		−	3987.71i		−	0.254602i
$627$		0			0
$628$	−7380.55	−	7380.55i	−0.468975	−	0.468975i
$629$	578.343			0.0366614
$630$		0			0
$631$	−4708.65			−0.297066			−0.148533	−	0.988907i	$-0.547455\pi$
$631$	−4708.65			−0.297066			−0.148533	+	0.988907i	$0.547455\pi$
$632$	−1102.49	−	1102.49i	−0.0693905	−	0.0693905i
$633$		0			0
$634$			21244.8i			1.33082i
$635$	16351.6	+	10421.7i	1.02188	+	0.651298i
$636$		0			0
$637$	−196.123	+	196.123i	−0.0121988	+	0.0121988i
$638$	7484.19	−	7484.19i	0.464423	−	0.464423i
$639$		0			0
$640$	−1206.81	−	769.164i	−0.0745364	−	0.0475061i
$641$		−	26907.3i		−	1.65799i	−0.559254	−	0.828996i	$-0.688912\pi$
$641$		−	26907.3i		−	1.65799i	0.559254	−	0.828996i	$-0.311088\pi$
$642$		0			0
$643$	14530.0	+	14530.0i	0.891148	+	0.891148i	0.994631	−	0.103484i	$-0.0329989\pi$
$643$	14530.0	+	14530.0i	0.891148	+	0.891148i	−0.103484	+	0.994631i	$0.532999\pi$
$644$	3981.29			0.243610
$645$		0			0
$646$	6094.30			0.371172
$647$	10879.1	+	10879.1i	0.661056	+	0.661056i	0.955629	−	0.294573i	$-0.0951775\pi$
$647$	10879.1	+	10879.1i	0.661056	+	0.661056i	−0.294573	+	0.955629i	$0.595178\pi$
$648$		0			0
$649$		−	4137.82i		−	0.250267i
$650$	−597.529	−	1282.76i	−0.0360569	−	0.0774059i
$651$		0			0
$652$	−1249.17	+	1249.17i	−0.0750324	+	0.0750324i
$653$	−592.509	+	592.509i	−0.0355079	+	0.0355079i	−0.724638	−	0.689130i	$-0.757993\pi$
$653$	−592.509	+	592.509i	−0.0355079	+	0.0355079i	0.689130	+	0.724638i	$0.257993\pi$
$654$		0			0
$655$	−13599.4	+	3012.03i	−0.811255	+	0.179679i
$656$		−	1261.99i		−	0.0751101i
$657$		0			0
$658$	181.490	+	181.490i	0.0107526	+	0.0107526i
$659$	10388.9			0.614106			0.307053	−	0.951692i	$-0.400657\pi$
$659$	10388.9			0.614106			0.307053	+	0.951692i	$0.400657\pi$
$660$		0			0
$661$	−18643.0			−1.09702			−0.548508	−	0.836145i	$-0.684804\pi$
$661$	−18643.0			−1.09702			−0.548508	+	0.836145i	$0.684804\pi$
$662$	3606.78	+	3606.78i	0.211754	+	0.211754i
$663$		0			0
$664$		−	3204.65i		−	0.187296i
$665$	−3732.08	+	5855.59i	−0.217630	+	0.341459i
$666$		0			0
$667$	13188.3	−	13188.3i	0.765597	−	0.765597i
$668$	8727.41	−	8727.41i	0.505500	−	0.505500i
$669$		0			0
$670$	3828.75	+	17286.9i	0.220773	+	0.996792i
$671$		−	27062.6i		−	1.55699i
$672$		0			0
$673$	−8073.74	−	8073.74i	−0.462436	−	0.462436i	0.437017	−	0.899453i	$-0.356035\pi$
$673$	−8073.74	−	8073.74i	−0.462436	−	0.462436i	−0.899453	+	0.437017i	$0.856035\pi$
$674$	−3092.42			−0.176729
$675$		0			0
$676$	8659.84			0.492708
$677$	12054.0	+	12054.0i	0.684305	+	0.684305i	0.960967	−	0.276663i	$-0.0892284\pi$
$677$	12054.0	+	12054.0i	0.684305	+	0.684305i	−0.276663	+	0.960967i	$0.589228\pi$
$678$		0			0
$679$			3450.17i			0.195001i
$680$	664.257	+	2999.14i	0.0374605	+	0.169135i
$681$		0			0
$682$	−7294.31	+	7294.31i	−0.409551	+	0.409551i
$683$	−2125.94	+	2125.94i	−0.119102	+	0.119102i	−0.764146	−	0.645044i	$-0.776839\pi$
$683$	−2125.94	+	2125.94i	−0.119102	+	0.119102i	0.645044	+	0.764146i	$0.276839\pi$
$684$		0			0
$685$	−12025.7	+	18868.2i	−0.670772	+	1.05243i
$686$			686.000i			0.0381802i
$687$		0			0
$688$	2469.15	+	2469.15i	0.136825	+	0.136825i
$689$	1571.85			0.0869124
$690$		0			0
$691$	−13023.7			−0.716998			−0.358499	−	0.933530i	$-0.616711\pi$
$691$	−13023.7			−0.716998			−0.358499	+	0.933530i	$0.616711\pi$
$692$	−4852.60	−	4852.60i	−0.266572	−	0.266572i
$693$		0			0
$694$		−	16106.5i		−	0.880972i
$695$	−32171.0	+	7125.34i	−1.75585	+	0.388891i
$696$		0			0
$697$	−1915.44	+	1915.44i	−0.104093	+	0.104093i
$698$	−13283.8	+	13283.8i	−0.720342	+	0.720342i
$699$		0			0
$700$	−3288.44	−	1198.40i	−0.177559	−	0.0647074i
$701$		−	1567.72i		−	0.0844679i	−0.999108	−	0.0422340i	$-0.986553\pi$
$701$		−	1567.72i		−	0.0844679i	0.999108	−	0.0422340i	$-0.0134475\pi$
$702$		0			0
$703$	1056.49	+	1056.49i	0.0566802	+	0.0566802i
$704$	2582.09			0.138233
$705$		0			0
$706$	1510.48			0.0805207
$707$	2335.39	+	2335.39i	0.124231	+	0.124231i
$708$		0			0
$709$		−	24185.3i		−	1.28110i	−0.767918	−	0.640548i	$-0.778707\pi$
$709$		−	24185.3i		−	1.28110i	0.767918	−	0.640548i	$-0.221293\pi$
$710$	12990.3	+	8279.40i	0.686642	+	0.437634i
$711$		0			0
$712$	121.072	−	121.072i	0.00637269	−	0.00637269i
$713$	−12853.7	+	12853.7i	−0.675141	+	0.675141i
$714$		0			0
$715$	2153.11	+	1372.29i	0.112618	+	0.0717774i
$716$			4694.61i			0.245036i
$717$		0			0
$718$	4341.08	+	4341.08i	0.225638	+	0.225638i
$719$	31466.9			1.63215			0.816076	−	0.577944i	$-0.196145\pi$
$719$	31466.9			1.63215			0.816076	+	0.577944i	$0.196145\pi$
$720$		0			0
$721$	−1827.16			−0.0943788
$722$	1432.67	+	1432.67i	0.0738485	+	0.0738485i
$723$		0			0
$724$		−	13739.9i		−	0.705301i
$725$	−14863.0	+	6923.42i	−0.761375	+	0.354661i
$726$		0			0
$727$	23692.9	−	23692.9i	1.20870	−	1.20870i	0.237247	−	0.971449i	$-0.423755\pi$
$727$	23692.9	−	23692.9i	1.20870	−	1.20870i	0.971449	−	0.237247i	$-0.0762449\pi$
$728$	−224.140	+	224.140i	−0.0114110	+	0.0114110i
$729$		0			0
$730$	1245.85	−	275.934i	0.0631656	−	0.0139901i
$731$		−	7495.35i		−	0.379242i
$732$		0			0
$733$	11853.3	+	11853.3i	0.597286	+	0.597286i	0.939589	−	0.342304i	$-0.111207\pi$
$733$	11853.3	+	11853.3i	0.597286	+	0.597286i	−0.342304	+	0.939589i	$0.611207\pi$
$734$	−23814.6			−1.19756
$735$		0			0
$736$	4550.04			0.227876
$737$	−22589.5	−	22589.5i	−1.12903	−	1.12903i
$738$		0			0
$739$		−	3369.40i		−	0.167720i	−0.996478	−	0.0838601i	$-0.973275\pi$
$739$		−	3369.40i		−	0.167720i	0.996478	−	0.0838601i	$-0.0267249\pi$
$740$	−404.766	+	635.073i	−0.0201074	+	0.0315483i
$741$		0			0
$742$	2749.02	−	2749.02i	0.136010	−	0.136010i
$743$	1801.92	−	1801.92i	0.0889716	−	0.0889716i	−0.661220	−	0.750192i	$-0.729961\pi$
$743$	1801.92	−	1801.92i	0.0889716	−	0.0889716i	0.750192	+	0.661220i	$0.229961\pi$
$744$		0			0
$745$	−6062.36	−	27371.7i	−0.298131	−	1.34607i
$746$		−	7131.98i		−	0.350027i
$747$		0			0
$748$	−3919.10	−	3919.10i	−0.191573	−	0.191573i
$749$	14104.3			0.688063
$750$		0			0
$751$	30070.1			1.46108			0.730542	−	0.682868i	$-0.239268\pi$
$751$	30070.1			1.46108			0.730542	+	0.682868i	$0.239268\pi$
$752$	207.417	+	207.417i	0.0100582	+	0.0100582i
$753$		0			0
$754$			1484.96i			0.0717229i
$755$	−3831.29	−	17298.3i	−0.184682	−	0.833842i
$756$		0			0
$757$	11817.8	−	11817.8i	0.567403	−	0.567403i	−0.363997	−	0.931400i	$-0.618588\pi$
$757$	11817.8	−	11817.8i	0.567403	−	0.567403i	0.931400	+	0.363997i	$0.118588\pi$
$758$	−9930.41	+	9930.41i	−0.475843	+	0.475843i
$759$		0			0
$760$	−4265.24	+	6692.10i	−0.203574	+	0.319405i
$761$			21917.9i			1.04405i	0.852930	+	0.522025i	$0.174823\pi$
$761$			21917.9i			1.04405i	−0.852930	+	0.522025i	$0.825177\pi$
$762$		0			0
$763$	1122.91	+	1122.91i	0.0532791	+	0.0532791i
$764$	11254.5			0.532950
$765$		0			0
$766$	7356.12			0.346981
$767$	410.499	+	410.499i	0.0193250	+	0.0193250i
$768$		0			0
$769$			25770.5i			1.20846i	0.796809	+	0.604231i	$0.206520\pi$
$769$			25770.5i			1.20846i	−0.796809	+	0.604231i	$0.793480\pi$
$770$	6165.60	−	1365.57i	0.288562	−	0.0639116i
$771$		0			0
$772$	−2288.44	+	2288.44i	−0.106688	+	0.106688i
$773$	−307.986	+	307.986i	−0.0143305	+	0.0143305i	−0.714236	−	0.699905i	$-0.753226\pi$
$773$	−307.986	+	307.986i	−0.0143305	+	0.0143305i	0.699905	+	0.714236i	$0.253226\pi$
$774$		0			0
$775$	14485.9	−	6747.77i	0.671418	−	0.312758i
$776$			3943.05i			0.182406i
$777$		0			0
$778$	−15836.9	−	15836.9i	−0.729794	−	0.729794i
$779$	−6998.07			−0.321864
$780$		0			0
$781$	−27794.0			−1.27343
$782$	−6906.07	−	6906.07i	−0.315806	−	0.315806i
$783$		0			0
$784$			784.000i			0.0357143i
$785$	−24602.1	−	15680.3i	−1.11858	−	0.712933i
$786$		0			0
$787$	811.853	−	811.853i	0.0367718	−	0.0367718i	−0.688482	−	0.725254i	$-0.741722\pi$
$787$	811.853	−	811.853i	0.0367718	−	0.0367718i	0.725254	+	0.688482i	$0.241722\pi$
$788$	−6865.91	+	6865.91i	−0.310391	+	0.310391i
$789$		0			0
$790$	−3675.01	−	2342.28i	−0.165508	−	0.105487i
$791$			10169.1i			0.457109i
$792$		0			0
$793$	2684.79	+	2684.79i	0.120226	+	0.120226i
$794$	22158.9			0.990416
$795$		0			0
$796$	687.800			0.0306262
$797$	−6554.94	−	6554.94i	−0.291327	−	0.291327i	0.546277	−	0.837605i	$-0.316045\pi$
$797$	−6554.94	−	6554.94i	−0.291327	−	0.291327i	−0.837605	+	0.546277i	$0.816045\pi$
$798$		0			0
$799$		−	629.637i		−	0.0278785i
$800$	−3758.22	−	1369.60i	−0.166091	−	0.0605282i
$801$		0			0
$802$	−21740.3	+	21740.3i	−0.957201	+	0.957201i
$803$	−1628.00	+	1628.00i	−0.0715454	+	0.0715454i
$804$		0			0
$805$	10864.7	−	2406.36i	0.475692	−	0.105358i
$806$		−	1447.29i		−	0.0632488i
$807$		0			0
$808$	2669.02	+	2669.02i	0.116208	+	0.116208i
$809$	−4231.33			−0.183888			−0.0919442	−	0.995764i	$-0.529308\pi$
$809$	−4231.33			−0.183888			−0.0919442	+	0.995764i	$0.529308\pi$
$810$		0			0
$811$	35734.6			1.54724			0.773620	−	0.633650i	$-0.218444\pi$
$811$	35734.6			1.54724			0.773620	+	0.633650i	$0.218444\pi$
$812$	2597.06	+	2597.06i	0.112240	+	0.112240i
$813$		0			0
$814$		−	1358.80i		−	0.0585086i
$815$	−2653.90	+	4163.93i	−0.114064	+	0.178965i
$816$		0			0
$817$	13692.1	−	13692.1i	0.586324	−	0.586324i
$818$	3749.01	−	3749.01i	0.160246	−	0.160246i
$819$		0			0
$820$	−762.765	−	3443.90i	−0.0324840	−	0.146666i
$821$		−	13153.2i		−	0.559135i	−0.960126	−	0.279568i	$-0.909809\pi$
$821$		−	13153.2i		−	0.559135i	0.960126	−	0.279568i	$-0.0901911\pi$
$822$		0			0
$823$	−4956.95	−	4956.95i	−0.209950	−	0.209950i	0.594296	−	0.804246i	$-0.297431\pi$
$823$	−4956.95	−	4956.95i	−0.209950	−	0.209950i	−0.804246	+	0.594296i	$0.797431\pi$
$824$	−2088.19			−0.0882833
$825$		0			0
$826$	1435.85			0.0604837
$827$	−25407.4	−	25407.4i	−1.06832	−	1.06832i	−0.997488	−	0.0708322i	$-0.977435\pi$
$827$	−25407.4	−	25407.4i	−1.06832	−	1.06832i	−0.0708322	−	0.997488i	$-0.522565\pi$
$828$		0			0
$829$			43198.8i			1.80984i	0.425584	+	0.904919i	$0.360069\pi$
$829$			43198.8i			1.80984i	−0.425584	+	0.904919i	$0.639931\pi$
$830$	−1936.94	−	8745.33i	−0.0810027	−	0.365729i
$831$		0			0
$832$	−256.160	+	256.160i	−0.0106740	+	0.0106740i
$833$	1189.96	−	1189.96i	0.0494953	−	0.0494953i
$834$		0			0
$835$	18541.7	−	29091.7i	0.768458	−	1.20570i
$836$		−	14318.4i		−	0.592360i
$837$		0			0
$838$	6052.86	+	6052.86i	0.249514	+	0.249514i
$839$	−13633.2			−0.560990			−0.280495	−	0.959855i	$-0.590499\pi$
$839$	−13633.2			−0.560990			−0.280495	+	0.959855i	$0.590499\pi$
$840$		0			0
$841$	−7183.12			−0.294523
$842$	−3732.23	−	3732.23i	−0.152757	−	0.152757i
$843$		0			0
$844$			16366.9i			0.667502i
$845$	23632.3	−	5234.15i	0.962101	−	0.213089i
$846$		0			0
$847$	−1468.74	+	1468.74i	−0.0595825	+	0.0595825i
$848$	3141.73	−	3141.73i	0.127226	−	0.127226i
$849$		0			0
$850$	3625.45	+	7783.01i	0.146297	+	0.314065i
$851$		−	2394.42i		−	0.0964509i
$852$		0			0
$853$	−16506.9	−	16506.9i	−0.662585	−	0.662585i	0.293404	−	0.955989i	$-0.405212\pi$
$853$	−16506.9	−	16506.9i	−0.662585	−	0.662585i	−0.955989	+	0.293404i	$0.905212\pi$
$854$	9390.88			0.376287
$855$		0			0
$856$	16119.2			0.643624
$857$	8639.90	+	8639.90i	0.344380	+	0.344380i	0.858011	−	0.513631i	$-0.171700\pi$
$857$	8639.90	+	8639.90i	0.344380	+	0.344380i	−0.513631	+	0.858011i	$0.671700\pi$
$858$		0			0
$859$			22833.4i			0.906945i	0.891270	+	0.453473i	$0.149815\pi$
$859$			22833.4i			0.906945i	−0.891270	+	0.453473i	$0.850185\pi$
$860$	8230.58	+	5245.79i	0.326349	+	0.208000i
$861$		0			0
$862$	20521.1	−	20521.1i	0.810847	−	0.810847i
$863$	−381.699	+	381.699i	−0.0150558	+	0.0150558i	−0.714595	−	0.699539i	$-0.753389\pi$
$863$	−381.699	+	381.699i	−0.0150558	+	0.0150558i	0.699539	+	0.714595i	$0.253389\pi$
$864$		0			0
$865$	−16175.5	−	10309.5i	−0.635819	−	0.405242i
$866$		−	226.855i		−	0.00890168i
$867$		0			0
$868$	−2531.17	−	2531.17i	−0.0989787	−	0.0989787i
$869$	7863.06			0.306946
$870$		0			0
$871$	4482.06			0.174361
$872$	1283.32	+	1283.32i	0.0498381	+	0.0498381i
$873$		0			0
$874$		−	25231.3i		−	0.976501i
$875$	−9698.33	−	1282.78i	−0.374701	−	0.0495611i
$876$		0			0
$877$	28593.5	−	28593.5i	1.10095	−	1.10095i	0.106655	−	0.994296i	$-0.465986\pi$
$877$	28593.5	−	28593.5i	1.10095	−	1.10095i	0.994296	−	0.106655i	$-0.0340139\pi$
$878$	1600.48	−	1600.48i	0.0615190	−	0.0615190i
$879$		0			0
$880$	7046.40	−	1560.66i	0.269925	−	0.0597838i
$881$			10417.9i			0.398397i	0.979959	+	0.199199i	$0.0638339\pi$
$881$			10417.9i			0.398397i	−0.979959	+	0.199199i	$0.936166\pi$
$882$		0			0
$883$	32942.7	+	32942.7i	1.25550	+	1.25550i	0.953217	+	0.302288i	$0.0977506\pi$
$883$	32942.7	+	32942.7i	1.25550	+	1.25550i	0.302288	+	0.953217i	$0.402249\pi$
$884$	777.601			0.0295854
$885$		0			0
$886$	35047.9			1.32896
$887$	−19572.3	−	19572.3i	−0.740893	−	0.740893i	0.231857	−	0.972750i	$-0.425520\pi$
$887$	−19572.3	−	19572.3i	−0.740893	−	0.740893i	−0.972750	+	0.231857i	$0.925520\pi$
$888$		0			0
$889$		−	12140.3i		−	0.458012i
$890$	257.221	−	403.577i	0.00968772	−	0.0151999i
$891$		0			0
$892$	−11577.6	+	11577.6i	−0.434580	+	0.434580i
$893$	1150.19	−	1150.19i	0.0431015	−	0.0431015i
$894$		0			0
$895$	2837.50	+	12811.4i	0.105974	+	0.478476i
$896$			896.000i			0.0334077i
$897$		0			0
$898$	−2786.13	−	2786.13i	−0.103535	−	0.103535i
$899$	−16769.4			−0.622124
$900$		0			0
$901$	−9537.06			−0.352636
$902$	4500.29	+	4500.29i	0.166123	+	0.166123i
$903$		0			0
$904$			11621.9i			0.427586i
$905$	−8304.60	−	37495.4i	−0.305032	−	1.37723i
$906$		0			0
$907$	−4361.42	+	4361.42i	−0.159668	+	0.159668i	−0.782419	−	0.622752i	$-0.786015\pi$
$907$	−4361.42	+	4361.42i	−0.159668	+	0.159668i	0.622752	+	0.782419i	$0.286015\pi$
$908$	1178.87	−	1178.87i	0.0430863	−	0.0430863i
$909$		0			0
$910$	−476.194	+	747.141i	−0.0173469	+	0.0272170i
$911$			9322.91i			0.339058i	0.985525	+	0.169529i	$0.0542246\pi$
$911$			9322.91i			0.339058i	−0.985525	+	0.169529i	$0.945775\pi$
$912$		0			0
$913$	11427.9	+	11427.9i	0.414248	+	0.414248i
$914$	−28634.6			−1.03627
$915$		0			0
$916$	21670.8			0.781683
$917$	6166.61	+	6166.61i	0.222071	+	0.222071i
$918$		0			0
$919$			27816.4i			0.998453i	0.866472	+	0.499226i	$0.166382\pi$
$919$			27816.4i			0.998453i	−0.866472	+	0.499226i	$0.833618\pi$
$920$	12416.9	−	2750.12i	0.444969	−	0.0985531i
$921$		0			0
$922$	21899.9	−	21899.9i	0.782252	−	0.782252i
$923$	2757.35	−	2757.35i	0.0983306	−	0.0983306i
$924$		0			0
$925$	−720.739	+	1977.73i	−0.0256192	+	0.0702999i
$926$		−	24680.9i		−	0.875881i
$927$		0			0
$928$	2968.07	+	2968.07i	0.104991	+	0.104991i
$929$	9230.43			0.325986			0.162993	−	0.986627i	$-0.447885\pi$
$929$	9230.43			0.325986			0.162993	+	0.986627i	$0.447885\pi$
$930$		0			0
$931$	4347.51			0.153044
$932$	−4225.78	−	4225.78i	−0.148519	−	0.148519i
$933$		0			0
$934$		−	20956.8i		−	0.734183i
$935$	−13063.8	−	8326.27i	−0.456933	−	0.291228i
$936$		0			0
$937$	−8192.12	+	8192.12i	−0.285619	+	0.285619i	−0.835345	−	0.549726i	$-0.814732\pi$
$937$	−8192.12	+	8192.12i	−0.285619	+	0.285619i	0.549726	+	0.835345i	$0.314732\pi$
$938$	7838.70	−	7838.70i	0.272860	−	0.272860i
$939$		0			0
$940$	691.399	+	440.666i	0.0239904	+	0.0152903i
$941$		−	53096.5i		−	1.83942i	−0.392596	−	0.919711i	$-0.628423\pi$
$941$		−	53096.5i		−	1.83942i	0.392596	−	0.919711i	$-0.371577\pi$
$942$		0			0
$943$	7930.22	+	7930.22i	0.273853	+	0.273853i
$944$	1640.97			0.0565773
$945$		0			0
$946$	−17610.1			−0.605238
$947$	2923.75	+	2923.75i	0.100326	+	0.100326i	0.755488	−	0.655162i	$-0.227400\pi$
$947$	2923.75	+	2923.75i	0.100326	+	0.100326i	−0.655162	+	0.755488i	$0.727400\pi$
$948$		0			0
$949$		−	323.017i		−	0.0110491i
$950$	−7594.81	+	20840.4i	−0.259377	+	0.711739i
$951$		0			0
$952$	1359.95	−	1359.95i	0.0462986	−	0.0462986i
$953$	18049.1	−	18049.1i	0.613503	−	0.613503i	−0.330354	−	0.943857i	$-0.607168\pi$
$953$	18049.1	−	18049.1i	0.613503	−	0.613503i	0.943857	+	0.330354i	$0.107168\pi$
$954$		0			0
$955$	30713.0	−	6802.41i	1.04068	−	0.230493i
$956$		−	15790.5i		−	0.534207i
$957$		0			0
$958$	−16059.8	−	16059.8i	−0.541617	−	0.541617i
$959$	14008.8			0.471706
$960$		0			0
$961$	−13447.1			−0.451380
$962$	134.802	+	134.802i	0.00451787	+	0.00451787i
$963$		0			0
$964$		−	13692.7i		−	0.457482i
$965$	−4861.88	+	7628.22i	−0.162186	+	0.254467i
$966$		0			0
$967$	−31317.7	+	31317.7i	−1.04148	+	1.04148i	−0.0423748	+	0.999102i	$0.513492\pi$
$967$	−31317.7	+	31317.7i	−1.04148	+	1.04148i	−0.999102	+	0.0423748i	$0.986508\pi$
$968$	−1678.56	+	1678.56i	−0.0557344	+	0.0557344i
$969$		0			0
$970$	2383.25	+	10760.4i	0.0788881	+	0.356181i
$971$			19092.3i			0.630999i	0.948926	+	0.315499i	$0.102172\pi$
$971$			19092.3i			0.630999i	−0.948926	+	0.315499i	$0.897828\pi$
$972$		0			0
$973$	14587.9	+	14587.9i	0.480643	+	0.480643i
$974$	−22495.8			−0.740054
$975$		0			0
$976$	10732.4			0.351985
$977$	8060.23	+	8060.23i	0.263940	+	0.263940i	0.826653	−	0.562712i	$-0.190242\pi$
$977$	8060.23	+	8060.23i	0.263940	+	0.263940i	−0.562712	+	0.826653i	$0.690242\pi$
$978$		0			0
$979$			863.493i			0.0281893i
$980$	473.863	+	2139.50i	0.0154459	+	0.0697385i
$981$		0			0
$982$	14291.5	−	14291.5i	0.464418	−	0.464418i
$983$	5529.57	−	5529.57i	0.179416	−	0.179416i	−0.611685	−	0.791101i	$-0.709508\pi$
$983$	5529.57	−	5529.57i	0.179416	−	0.179416i	0.791101	+	0.611685i	$0.209508\pi$
$984$		0			0
$985$	−14586.9	+	22886.6i	−0.471854	+	0.740333i
$986$		−	9009.87i		−	0.291007i
$987$		0			0
$988$	1420.48	+	1420.48i	0.0457404	+	0.0457404i
$989$	−31031.8			−0.997730
$990$		0			0
$991$	5089.64			0.163146			0.0815731	−	0.996667i	$-0.474006\pi$
$991$	5089.64			0.163146			0.0815731	+	0.996667i	$0.474006\pi$
$992$	−2892.77	−	2892.77i	−0.0925861	−	0.0925861i
$993$		0			0
$994$		−	9644.68i		−	0.307757i
$995$	1876.97	−	415.718i	0.0598031	−	0.0132454i
$996$		0			0
$997$	−22287.5	+	22287.5i	−0.707977	+	0.707977i	−0.966110	−	0.258132i	$-0.916893\pi$
$997$	−22287.5	+	22287.5i	−0.707977	+	0.707977i	0.258132	+	0.966110i	$0.416893\pi$
$998$	−23860.0	+	23860.0i	−0.756788	+	0.756788i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.m.b.323.2	yes	16
3.2	odd	2		630.4.m.a.323.7	yes	16
5.2	odd	4		630.4.m.a.197.7	✓	16
15.2	even	4	inner	630.4.m.b.197.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.4.m.a.197.7	✓	16	5.2	odd	4
630.4.m.a.323.7	yes	16	3.2	odd	2
630.4.m.b.197.2	yes	16	15.2	even	4	inner
630.4.m.b.323.2	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +4.00000i q^{4} +(2.41767 + 10.9158i) q^{5} +(4.94975 - 4.94975i) q^{7} +(5.65685 - 5.65685i) q^{8} +(12.0182 - 18.8564i) q^{10} +40.3451i q^{11} +(-4.00250 - 4.00250i) q^{13} -14.0000 q^{14} -16.0000 q^{16} +(24.2848 + 24.2848i) q^{17} +88.7246i q^{19} +(-43.6632 + 9.67066i) q^{20} +(57.0566 - 57.0566i) q^{22} +(100.543 - 100.543i) q^{23} +(-113.310 + 52.7816i) q^{25} +11.3208i q^{26} +(19.7990 + 19.7990i) q^{28} +131.171 q^{29} -127.843 q^{31} +(22.6274 + 22.6274i) q^{32} -68.6879i q^{34} +(65.9973 + 42.0637i) q^{35} +(11.9075 - 11.9075i) q^{37} +(125.476 - 125.476i) q^{38} +(75.4255 + 48.0728i) q^{40} +78.8741i q^{41} +(-154.322 - 154.322i) q^{43} -161.381 q^{44} -284.378 q^{46} +(-12.9636 - 12.9636i) q^{47} -49.0000i q^{49} +(234.889 + 85.5998i) q^{50} +(16.0100 - 16.0100i) q^{52} +(-196.358 + 196.358i) q^{53} +(-440.400 + 97.5411i) q^{55} -56.0000i q^{56} +(-185.504 - 185.504i) q^{58} -102.561 q^{59} -670.777 q^{61} +(180.798 + 180.798i) q^{62} -64.0000i q^{64} +(34.0138 - 53.3672i) q^{65} +(-559.907 + 559.907i) q^{67} +(-97.1393 + 97.1393i) q^{68} +(-33.8473 - 152.821i) q^{70} +688.906i q^{71} +(40.3519 + 40.3519i) q^{73} -33.6795 q^{74} -354.898 q^{76} +(199.698 + 199.698i) q^{77} -194.895i q^{79} +(-38.6827 - 174.653i) q^{80} +(111.545 - 111.545i) q^{82} +(283.254 - 283.254i) q^{83} +(-206.376 + 323.801i) q^{85} +436.488i q^{86} +(228.227 + 228.227i) q^{88} +21.4027 q^{89} -39.6227 q^{91} +(402.171 + 402.171i) q^{92} +36.6666i q^{94} +(-968.501 + 214.506i) q^{95} +(-348.520 + 348.520i) q^{97} +(-69.2965 + 69.2965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 44 q^{5} - 24 q^{10} - 212 q^{13} - 224 q^{14} - 256 q^{16} - 32 q^{17} - 32 q^{20} + 72 q^{22} + 128 q^{23} - 268 q^{25} - 232 q^{29} - 200 q^{31} - 112 q^{35} + 900 q^{37} + 368 q^{38} - 128 q^{40}+ \cdots - 2668 q^{97}+O(q^{100}) \) 16 * q + 44 * q^5 - 24 * q^10 - 212 * q^13 - 224 * q^14 - 256 * q^16 - 32 * q^17 - 32 * q^20 + 72 * q^22 + 128 * q^23 - 268 * q^25 - 232 * q^29 - 200 * q^31 - 112 * q^35 + 900 * q^37 + 368 * q^38 - 128 * q^40 - 908 * q^43 - 352 * q^44 + 208 * q^46 + 604 * q^47 - 896 * q^50 + 848 * q^52 + 440 * q^53 - 1232 * q^55 + 536 * q^58 - 224 * q^59 + 1200 * q^61 + 1304 * q^62 - 1936 * q^65 + 652 * q^67 + 128 * q^68 - 616 * q^70 - 2148 * q^73 - 1328 * q^74 + 252 * q^77 - 704 * q^80 + 616 * q^82 + 2624 * q^83 - 1712 * q^85 + 288 * q^88 - 2400 * q^89 + 512 * q^92 - 4200 * q^95 - 2668 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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