LMFDB - Embedded newform 630.4.m.a.323.4

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			323.4
Root			$-4.87117 + 11.7600i$ of defining polynomial
Character	$\chi$	$=$	630.323
Dual form			630.4.m.a.197.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41421 - 1.41421i) q^{2} +4.00000i q^{4} +(2.20200 + 10.9614i) q^{5} +(-4.94975 + 4.94975i) q^{7} +(5.65685 - 5.65685i) q^{8} +(12.3876 - 18.6158i) q^{10} -11.1562i q^{11} +(-13.2513 - 13.2513i) q^{13} +14.0000 q^{14} -16.0000 q^{16} +(-64.0454 - 64.0454i) q^{17} -24.3466i q^{19} +(-43.8454 + 8.80800i) q^{20} +(-15.7773 + 15.7773i) q^{22} +(-34.3522 + 34.3522i) q^{23} +(-115.302 + 48.2738i) q^{25} +37.4803i q^{26} +(-19.7990 - 19.7990i) q^{28} -100.235 q^{29} +255.547 q^{31} +(22.6274 + 22.6274i) q^{32} +181.148i q^{34} +(-65.1553 - 43.3566i) q^{35} +(269.852 - 269.852i) q^{37} +(-34.4312 + 34.4312i) q^{38} +(74.4632 + 49.5504i) q^{40} -209.816i q^{41} +(131.973 + 131.973i) q^{43} +44.6248 q^{44} +97.1626 q^{46} +(-101.411 - 101.411i) q^{47} -49.0000i q^{49} +(231.332 + 94.7928i) q^{50} +(53.0052 - 53.0052i) q^{52} +(-88.7497 + 88.7497i) q^{53} +(122.287 - 24.5660i) q^{55} +56.0000i q^{56} +(141.754 + 141.754i) q^{58} +130.691 q^{59} +926.587 q^{61} +(-361.398 - 361.398i) q^{62} -64.0000i q^{64} +(116.073 - 174.431i) q^{65} +(234.513 - 234.513i) q^{67} +(256.182 - 256.182i) q^{68} +(30.8280 + 153.459i) q^{70} +35.1316i q^{71} +(509.130 + 509.130i) q^{73} -763.257 q^{74} +97.3862 q^{76} +(55.2204 + 55.2204i) q^{77} -577.709i q^{79} +(-35.2320 - 175.382i) q^{80} +(-296.724 + 296.724i) q^{82} +(87.0751 - 87.0751i) q^{83} +(560.996 - 843.052i) q^{85} -373.275i q^{86} +(-63.1091 - 63.1091i) q^{88} -130.731 q^{89} +131.181 q^{91} +(-137.409 - 137.409i) q^{92} +286.833i q^{94} +(266.871 - 53.6111i) q^{95} +(-948.039 + 948.039i) q^{97} +(-69.2965 + 69.2965i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.20200	+	10.9614i	0.196953	+	0.980413i
$5$	2.20200	+	10.9614i	0.196953	+	0.980413i
$6$		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
$10$	12.3876	−	18.6158i	0.391730	−	0.588683i
$11$		−	11.1562i		−	0.305793i	−0.988242	−	0.152897i	$-0.951140\pi$
$11$		−	11.1562i		−	0.305793i	0.988242	−	0.152897i	$-0.0488601\pi$
$12$		0			0
$13$	−13.2513	−	13.2513i	−0.282711	−	0.282711i	0.551478	−	0.834189i	$-0.314064\pi$
$13$	−13.2513	−	13.2513i	−0.282711	−	0.282711i	−0.834189	+	0.551478i	$0.814064\pi$
$14$	14.0000			0.267261
$15$		0			0
$16$	−16.0000			−0.250000
$17$	−64.0454	−	64.0454i	−0.913723	−	0.913723i	0.0828395	−	0.996563i	$-0.473601\pi$
$17$	−64.0454	−	64.0454i	−0.913723	−	0.913723i	−0.996563	+	0.0828395i	$0.973601\pi$
$18$		0			0
$19$		−	24.3466i		−	0.293973i	−0.989139	−	0.146986i	$-0.953043\pi$
$19$		−	24.3466i		−	0.293973i	0.989139	−	0.146986i	$-0.0469574\pi$
$20$	−43.8454	+	8.80800i	−0.490206	+	0.0984764i
$21$		0			0
$22$	−15.7773	+	15.7773i	−0.152897	+	0.152897i
$23$	−34.3522	+	34.3522i	−0.311431	+	0.311431i	−0.845464	−	0.534033i	$-0.820676\pi$
$23$	−34.3522	+	34.3522i	−0.311431	+	0.311431i	0.534033	+	0.845464i	$0.320676\pi$
$24$		0			0
$25$	−115.302	+	48.2738i	−0.922419	+	0.386190i
$26$			37.4803i			0.282711i
$27$		0			0
$28$	−19.7990	−	19.7990i	−0.133631	−	0.133631i
$29$	−100.235			−0.641833			−0.320917	−	0.947107i	$-0.603991\pi$
$29$	−100.235			−0.641833			−0.320917	+	0.947107i	$0.603991\pi$
$30$		0			0
$31$	255.547			1.48057			0.740283	−	0.672296i	$-0.234692\pi$
$31$	255.547			1.48057			0.740283	+	0.672296i	$0.234692\pi$
$32$	22.6274	+	22.6274i	0.125000	+	0.125000i
$33$		0			0
$34$			181.148i			0.913723i
$35$	−65.1553	−	43.3566i	−0.314664	−	0.209389i
$36$		0			0
$37$	269.852	−	269.852i	1.19901	−	1.19901i	0.224548	−	0.974463i	$-0.427910\pi$
$37$	269.852	−	269.852i	1.19901	−	1.19901i	0.974463	−	0.224548i	$-0.0720904\pi$
$38$	−34.4312	+	34.4312i	−0.146986	+	0.146986i
$39$		0			0
$40$	74.4632	+	49.5504i	0.294341	+	0.195865i
$41$		−	209.816i		−	0.799212i	−0.916687	−	0.399606i	$-0.869147\pi$
$41$		−	209.816i		−	0.799212i	0.916687	−	0.399606i	$-0.130853\pi$
$42$		0			0
$43$	131.973	+	131.973i	0.468038	+	0.468038i	0.901278	−	0.433240i	$-0.142630\pi$
$43$	131.973	+	131.973i	0.468038	+	0.468038i	−0.433240	+	0.901278i	$0.642630\pi$
$44$	44.6248			0.152897
$45$		0			0
$46$	97.1626			0.311431
$47$	−101.411	−	101.411i	−0.314730	−	0.314730i	0.532009	−	0.846739i	$-0.321437\pi$
$47$	−101.411	−	101.411i	−0.314730	−	0.314730i	−0.846739	+	0.532009i	$0.821437\pi$
$48$		0			0
$49$		−	49.0000i		−	0.142857i
$50$	231.332	+	94.7928i	0.654305	+	0.268114i
$51$		0			0
$52$	53.0052	−	53.0052i	0.141356	−	0.141356i
$53$	−88.7497	+	88.7497i	−0.230013	+	0.230013i	−0.812698	−	0.582685i	$-0.802002\pi$
$53$	−88.7497	+	88.7497i	−0.230013	+	0.230013i	0.582685	+	0.812698i	$0.302002\pi$
$54$		0			0
$55$	122.287	−	24.5660i	0.299803	−	0.0602268i
$56$			56.0000i			0.133631i
$57$		0			0
$58$	141.754	+	141.754i	0.320917	+	0.320917i
$59$	130.691			0.288382			0.144191	−	0.989550i	$-0.453942\pi$
$59$	130.691			0.288382			0.144191	+	0.989550i	$0.453942\pi$
$60$		0			0
$61$	926.587			1.94487			0.972437	−	0.233167i	$-0.0749087\pi$
$61$	926.587			1.94487			0.972437	+	0.233167i	$0.0749087\pi$
$62$	−361.398	−	361.398i	−0.740283	−	0.740283i
$63$		0			0
$64$		−	64.0000i		−	0.125000i
$65$	116.073	−	174.431i	0.221493	−	0.332855i
$66$		0			0
$67$	234.513	−	234.513i	0.427616	−	0.427616i	−0.460200	−	0.887815i	$-0.652222\pi$
$67$	234.513	−	234.513i	0.427616	−	0.427616i	0.887815	+	0.460200i	$0.152222\pi$
$68$	256.182	−	256.182i	0.456862	−	0.456862i
$69$		0			0
$70$	30.8280	+	153.459i	0.0526379	+	0.262026i
$71$			35.1316i			0.0587233i	0.999569	+	0.0293617i	$0.00934745\pi$
$71$			35.1316i			0.0587233i	−0.999569	+	0.0293617i	$0.990653\pi$
$72$		0			0
$73$	509.130	+	509.130i	0.816289	+	0.816289i	0.985568	−	0.169279i	$-0.0541438\pi$
$73$	509.130	+	509.130i	0.816289	+	0.816289i	−0.169279	+	0.985568i	$0.554144\pi$
$74$	−763.257			−1.19901
$75$		0			0
$76$	97.3862			0.146986
$77$	55.2204	+	55.2204i	0.0817266	+	0.0817266i
$78$		0			0
$79$		−	577.709i		−	0.822751i	−0.911466	−	0.411375i	$-0.865049\pi$
$79$		−	577.709i		−	0.822751i	0.911466	−	0.411375i	$-0.134951\pi$
$80$	−35.2320	−	175.382i	−0.0492382	−	0.245103i
$81$		0			0
$82$	−296.724	+	296.724i	−0.399606	+	0.399606i
$83$	87.0751	−	87.0751i	0.115153	−	0.115153i	−0.647182	−	0.762335i	$-0.724053\pi$
$83$	87.0751	−	87.0751i	0.115153	−	0.115153i	0.762335	+	0.647182i	$0.224053\pi$
$84$		0			0
$85$	560.996	−	843.052i	0.715866	−	1.07579i
$86$		−	373.275i		−	0.468038i
$87$		0			0
$88$	−63.1091	−	63.1091i	−0.0764483	−	0.0764483i
$89$	−130.731			−0.155702			−0.0778508	−	0.996965i	$-0.524806\pi$
$89$	−130.731			−0.155702			−0.0778508	+	0.996965i	$0.524806\pi$
$90$		0			0
$91$	131.181			0.151116
$92$	−137.409	−	137.409i	−0.155716	−	0.155716i
$93$		0			0
$94$			286.833i			0.314730i
$95$	266.871	−	53.6111i	0.288215	−	0.0578988i
$96$		0			0
$97$	−948.039	+	948.039i	−0.992358	+	0.992358i	−0.999971	−	0.00761270i	$-0.997577\pi$
$97$	−948.039	+	948.039i	−0.992358	+	0.992358i	0.00761270	+	0.999971i	$0.497577\pi$
$98$	−69.2965	+	69.2965i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	−193.095	−	461.210i	−0.193095	−	0.461210i
$101$		−	1264.05i		−	1.24532i	−0.782492	−	0.622661i	$-0.786052\pi$
$101$		−	1264.05i		−	1.24532i	0.782492	−	0.622661i	$-0.213948\pi$
$102$		0			0
$103$	−1276.13	−	1276.13i	−1.22079	−	1.22079i	−0.967352	−	0.253437i	$-0.918439\pi$
$103$	−1276.13	−	1276.13i	−1.22079	−	1.22079i	−0.253437	−	0.967352i	$-0.581561\pi$
$104$	−149.921			−0.141356
$105$		0			0
$106$	251.022			0.230013
$107$	−863.617	−	863.617i	−0.780271	−	0.780271i	0.199606	−	0.979876i	$-0.436034\pi$
$107$	−863.617	−	863.617i	−0.780271	−	0.780271i	−0.979876	+	0.199606i	$0.936034\pi$
$108$		0			0
$109$			595.503i			0.523292i	0.965164	+	0.261646i	$0.0842653\pi$
$109$			595.503i			0.523292i	−0.965164	+	0.261646i	$0.915735\pi$
$110$	−207.682	−	138.199i	−0.180015	−	0.119788i
$111$		0			0
$112$	79.1960	−	79.1960i	0.0668153	−	0.0668153i
$113$	1045.53	−	1045.53i	0.870401	−	0.870401i	−0.122115	−	0.992516i	$-0.538968\pi$
$113$	1045.53	−	1045.53i	0.870401	−	0.870401i	0.992516	+	0.122115i	$0.0389676\pi$
$114$		0			0
$115$	−452.190	−	300.903i	−0.366669	−	0.243994i
$116$		−	400.940i		−	0.320917i
$117$		0			0
$118$	−184.825	−	184.825i	−0.144191	−	0.144191i
$119$	634.017			0.488406
$120$		0			0
$121$	1206.54			0.906491
$122$	−1310.39	−	1310.39i	−0.972437	−	0.972437i
$123$		0			0
$124$			1022.19i			0.740283i
$125$	−783.042	−	1157.57i	−0.560299	−	0.828290i
$126$		0			0
$127$	1574.42	−	1574.42i	1.10006	−	1.10006i	0.105657	−	0.994403i	$-0.466305\pi$
$127$	1574.42	−	1574.42i	1.10006	−	1.10006i	0.994403	−	0.105657i	$-0.0336945\pi$
$128$	−90.5097	+	90.5097i	−0.0625000	+	0.0625000i
$129$		0			0
$130$	−410.835	+	82.5317i	−0.277174	+	0.0556808i
$131$		−	280.821i		−	0.187294i	−0.995605	−	0.0936469i	$-0.970148\pi$
$131$		−	280.821i		−	0.187294i	0.995605	−	0.0936469i	$-0.0298525\pi$
$132$		0			0
$133$	120.509	+	120.509i	0.0785675	+	0.0785675i
$134$	−663.302			−0.427616
$135$		0			0
$136$	−724.591			−0.456862
$137$	252.477	+	252.477i	0.157450	+	0.157450i	0.781436	−	0.623986i	$-0.214488\pi$
$137$	252.477	+	252.477i	0.157450	+	0.157450i	−0.623986	+	0.781436i	$0.714488\pi$
$138$		0			0
$139$			264.069i			0.161137i	0.996749	+	0.0805684i	$0.0256736\pi$
$139$			264.069i			0.161137i	−0.996749	+	0.0805684i	$0.974326\pi$
$140$	173.426	−	260.621i	0.104694	−	0.157332i
$141$		0			0
$142$	49.6836	−	49.6836i	0.0293617	−	0.0293617i
$143$	−147.834	+	147.834i	−0.0864512	+	0.0864512i
$144$		0			0
$145$	−220.717	−	1098.71i	−0.126411	−	0.629261i
$146$		−	1440.04i		−	0.816289i
$147$		0			0
$148$	1079.41	+	1079.41i	0.599505	+	0.599505i
$149$	2198.50			1.20878			0.604389	−	0.796690i	$-0.293417\pi$
$149$	2198.50			1.20878			0.604389	+	0.796690i	$0.293417\pi$
$150$		0			0
$151$	−765.951			−0.412796			−0.206398	−	0.978468i	$-0.566174\pi$
$151$	−765.951			−0.412796			−0.206398	+	0.978468i	$0.566174\pi$
$152$	−137.725	−	137.725i	−0.0734932	−	0.0734932i
$153$		0			0
$154$		−	156.187i		−	0.0817266i
$155$	562.714	+	2801.14i	0.291602	+	1.45157i
$156$		0			0
$157$	726.741	−	726.741i	0.369429	−	0.369429i	−0.497840	−	0.867269i	$-0.665873\pi$
$157$	726.741	−	726.741i	0.369429	−	0.369429i	0.867269	+	0.497840i	$0.165873\pi$
$158$	−817.003	+	817.003i	−0.411375	+	0.411375i
$159$		0			0
$160$	−198.201	+	297.853i	−0.0979325	+	0.147171i
$161$		−	340.069i		−	0.166467i
$162$		0			0
$163$	−2180.21	−	2180.21i	−1.04765	−	1.04765i	−0.998806	−	0.0488469i	$-0.984445\pi$
$163$	−2180.21	−	2180.21i	−1.04765	−	1.04765i	−0.0488469	−	0.998806i	$-0.515555\pi$
$164$	839.262			0.399606
$165$		0			0
$166$	−246.285			−0.115153
$167$	−2005.42	−	2005.42i	−0.929247	−	0.929247i	0.0684103	−	0.997657i	$-0.478207\pi$
$167$	−2005.42	−	2005.42i	−0.929247	−	0.929247i	−0.997657	+	0.0684103i	$0.978207\pi$
$168$		0			0
$169$		−	1845.81i		−	0.840149i
$170$	−1985.62	+	398.888i	−0.895826	+	0.179960i
$171$		0			0
$172$	−527.891	+	527.891i	−0.234019	+	0.234019i
$173$	−548.219	+	548.219i	−0.240927	+	0.240927i	−0.817233	−	0.576307i	$-0.804493\pi$
$173$	−548.219	+	548.219i	−0.240927	+	0.240927i	0.576307	+	0.817233i	$0.304493\pi$
$174$		0			0
$175$	331.775	−	809.661i	0.143313	−	0.349741i
$176$			178.499i			0.0764483i
$177$		0			0
$178$	184.881	+	184.881i	0.0778508	+	0.0778508i
$179$	567.116			0.236806			0.118403	−	0.992966i	$-0.462223\pi$
$179$	567.116			0.236806			0.118403	+	0.992966i	$0.462223\pi$
$180$		0			0
$181$	1630.60			0.669622			0.334811	−	0.942285i	$-0.391328\pi$
$181$	1630.60			0.669622			0.334811	+	0.942285i	$0.391328\pi$
$182$	−185.518	−	185.518i	−0.0755578	−	0.0755578i
$183$		0			0
$184$			388.650i			0.155716i
$185$	3552.16	+	2363.73i	1.41167	+	0.939377i
$186$		0			0
$187$	−714.504	+	714.504i	−0.279410	+	0.279410i
$188$	405.643	−	405.643i	0.157365	−	0.157365i
$189$		0			0
$190$	−453.230	−	301.595i	−0.173057	−	0.115158i
$191$			746.332i			0.282737i	0.989957	+	0.141368i	$0.0451502\pi$
$191$			746.332i			0.282737i	−0.989957	+	0.141368i	$0.954850\pi$
$192$		0			0
$193$	−794.631	−	794.631i	−0.296367	−	0.296367i	0.543222	−	0.839589i	$-0.317204\pi$
$193$	−794.631	−	794.631i	−0.296367	−	0.296367i	−0.839589	+	0.543222i	$0.817204\pi$
$194$	2681.46			0.992358
$195$		0			0
$196$	196.000			0.0714286
$197$	−1274.65	−	1274.65i	−0.460990	−	0.460990i	0.437990	−	0.898980i	$-0.355691\pi$
$197$	−1274.65	−	1274.65i	−0.460990	−	0.460990i	−0.898980	+	0.437990i	$0.855691\pi$
$198$		0			0
$199$			2325.26i			0.828309i	0.910207	+	0.414155i	$0.135923\pi$
$199$			2325.26i			0.828309i	−0.910207	+	0.414155i	$0.864077\pi$
$200$	−379.171	+	925.327i	−0.134057	+	0.327152i
$201$		0			0
$202$	−1787.63	+	1787.63i	−0.622661	+	0.622661i
$203$	496.138	−	496.138i	0.171537	−	0.171537i
$204$		0			0
$205$	2299.86	−	462.014i	0.783558	−	0.157407i
$206$			3609.45i			1.22079i
$207$		0			0
$208$	212.021	+	212.021i	0.0706778	+	0.0706778i
$209$	−271.615			−0.0898949
$210$		0			0
$211$	4052.63			1.32225			0.661125	−	0.750276i	$-0.270079\pi$
$211$	4052.63			1.32225			0.661125	+	0.750276i	$0.270079\pi$
$212$	−354.999	−	354.999i	−0.115007	−	0.115007i
$213$		0			0
$214$			2442.68i			0.780271i
$215$	−1155.99	+	1737.20i	−0.366689	+	0.551052i
$216$		0			0
$217$	−1264.89	+	1264.89i	−0.395698	+	0.395698i
$218$	842.168	−	842.168i	0.261646	−	0.261646i
$219$		0			0
$220$	98.2639	+	489.148i	0.0301134	+	0.149902i
$221$			1697.37i			0.516640i
$222$		0			0
$223$	−2347.66	−	2347.66i	−0.704982	−	0.704982i	0.260494	−	0.965476i	$-0.416115\pi$
$223$	−2347.66	−	2347.66i	−0.704982	−	0.704982i	−0.965476	+	0.260494i	$0.916115\pi$
$224$	−224.000			−0.0668153
$225$		0			0
$226$	−2957.21			−0.870401
$227$	2784.65	+	2784.65i	0.814202	+	0.814202i	0.985261	−	0.171059i	$-0.0547189\pi$
$227$	2784.65	+	2784.65i	0.814202	+	0.814202i	−0.171059	+	0.985261i	$0.554719\pi$
$228$		0			0
$229$			520.541i			0.150211i	0.997176	+	0.0751054i	$0.0239293\pi$
$229$			520.541i			0.150211i	−0.997176	+	0.0751054i	$0.976071\pi$
$230$	213.952	+	1065.03i	0.0613373	+	0.305331i
$231$		0			0
$232$	−567.014	+	567.014i	−0.160458	+	0.160458i
$233$	−1571.50	+	1571.50i	−0.441854	+	0.441854i	−0.892635	−	0.450780i	$-0.851146\pi$
$233$	−1571.50	+	1571.50i	−0.441854	+	0.441854i	0.450780	+	0.892635i	$0.351146\pi$
$234$		0			0
$235$	888.293	−	1334.91i	0.246578	−	0.370552i
$236$			522.764i			0.144191i
$237$		0			0
$238$	−896.636	−	896.636i	−0.244203	−	0.244203i
$239$	1384.19			0.374626			0.187313	−	0.982300i	$-0.440022\pi$
$239$	1384.19			0.374626			0.187313	+	0.982300i	$0.440022\pi$
$240$		0			0
$241$	3182.15			0.850542			0.425271	−	0.905066i	$-0.360179\pi$
$241$	3182.15			0.850542			0.425271	+	0.905066i	$0.360179\pi$
$242$	−1706.30	−	1706.30i	−0.453245	−	0.453245i
$243$		0			0
$244$			3706.35i			0.972437i
$245$	537.106	−	107.898i	0.140059	−	0.0281361i
$246$		0			0
$247$	−322.623	+	322.623i	−0.0831094	+	0.0831094i
$248$	1445.59	−	1445.59i	0.370141	−	0.370141i
$249$		0			0
$250$	−529.664	+	2744.44i	−0.133996	+	0.694295i
$251$		−	2486.77i		−	0.625354i	−0.949860	−	0.312677i	$-0.898774\pi$
$251$		−	2486.77i		−	0.625354i	0.949860	−	0.312677i	$-0.101226\pi$
$252$		0			0
$253$	383.240	+	383.240i	0.0952336	+	0.0952336i
$254$	−4453.14			−1.10006
$255$		0			0
$256$	256.000			0.0625000
$257$	2405.54	+	2405.54i	0.583866	+	0.583866i	0.935963	−	0.352098i	$-0.114531\pi$
$257$	2405.54	+	2405.54i	0.583866	+	0.583866i	−0.352098	+	0.935963i	$0.614531\pi$
$258$		0			0
$259$			2671.40i			0.640898i
$260$	697.726	+	464.291i	0.166427	+	0.110747i
$261$		0			0
$262$	−397.141	+	397.141i	−0.0936469	+	0.0936469i
$263$	3431.00	−	3431.00i	0.804428	−	0.804428i	−0.179357	−	0.983784i	$-0.557402\pi$
$263$	3431.00	−	3431.00i	0.804428	−	0.804428i	0.983784	+	0.179357i	$0.0574016\pi$
$264$		0			0
$265$	−1168.24	−	777.390i	−0.270810	−	0.180206i
$266$		−	340.852i		−	0.0785675i
$267$		0			0
$268$	938.050	+	938.050i	0.213808	+	0.213808i
$269$	954.486			0.216342			0.108171	−	0.994132i	$-0.465501\pi$
$269$	954.486			0.216342			0.108171	+	0.994132i	$0.465501\pi$
$270$		0			0
$271$	−6647.95			−1.49016			−0.745082	−	0.666973i	$-0.767589\pi$
$271$	−6647.95			−1.49016			−0.745082	+	0.666973i	$0.767589\pi$
$272$	1024.73	+	1024.73i	0.228431	+	0.228431i
$273$		0			0
$274$		−	714.114i		−	0.157450i
$275$	538.552	+	1286.34i	0.118094	+	0.282069i
$276$		0			0
$277$	−886.468	+	886.468i	−0.192284	+	0.192284i	−0.796682	−	0.604398i	$-0.793414\pi$
$277$	−886.468	+	886.468i	−0.192284	+	0.192284i	0.604398	+	0.796682i	$0.293414\pi$
$278$	373.450	−	373.450i	0.0805684	−	0.0805684i
$279$		0			0
$280$	−613.836	+	123.312i	−0.131013	+	0.0263189i
$281$			6975.17i			1.48080i	0.672169	+	0.740398i	$0.265363\pi$
$281$			6975.17i			1.48080i	−0.672169	+	0.740398i	$0.734637\pi$
$282$		0			0
$283$	−2865.87	−	2865.87i	−0.601974	−	0.601974i	0.338862	−	0.940836i	$-0.389958\pi$
$283$	−2865.87	−	2865.87i	−0.601974	−	0.601974i	−0.940836	+	0.338862i	$0.889958\pi$
$284$	−140.526			−0.0293617
$285$		0			0
$286$	418.138			0.0864512
$287$	1038.53	+	1038.53i	0.213598	+	0.213598i
$288$		0			0
$289$			3290.63i			0.669781i
$290$	−1241.67	+	1865.95i	−0.251425	+	0.377836i
$291$		0			0
$292$	−2036.52	+	2036.52i	−0.408145	+	0.408145i
$293$	−3734.87	+	3734.87i	−0.744688	+	0.744688i	−0.973476	−	0.228788i	$-0.926524\pi$
$293$	−3734.87	+	3734.87i	−0.744688	+	0.744688i	0.228788	+	0.973476i	$0.426524\pi$
$294$		0			0
$295$	287.781	+	1432.55i	0.0567976	+	0.282733i
$296$		−	3053.03i		−	0.599505i
$297$		0			0
$298$	−3109.14	−	3109.14i	−0.604389	−	0.604389i
$299$	910.421			0.176090
$300$		0			0
$301$	−1306.46			−0.250177
$302$	1083.22	+	1083.22i	0.206398	+	0.206398i
$303$		0			0
$304$			389.545i			0.0734932i
$305$	2040.34	+	10156.6i	0.383048	+	1.90678i
$306$		0			0
$307$	1810.71	−	1810.71i	0.336621	−	0.336621i	−0.518473	−	0.855094i	$-0.673499\pi$
$307$	1810.71	−	1810.71i	0.336621	−	0.336621i	0.855094	+	0.518473i	$0.173499\pi$
$308$	−220.882	+	220.882i	−0.0408633	+	0.0408633i
$309$		0			0
$310$	3165.61	−	4757.20i	0.579982	−	0.871584i
$311$			5454.29i			0.994484i	0.867612	+	0.497242i	$0.165654\pi$
$311$			5454.29i			0.994484i	−0.867612	+	0.497242i	$0.834346\pi$
$312$		0			0
$313$	−1449.71	−	1449.71i	−0.261797	−	0.261797i	0.563987	−	0.825784i	$-0.309267\pi$
$313$	−1449.71	−	1449.71i	−0.261797	−	0.261797i	−0.825784	+	0.563987i	$0.809267\pi$
$314$	−2055.54			−0.369429
$315$		0			0
$316$	2310.83			0.411375
$317$	−5878.12	−	5878.12i	−1.04148	−	1.04148i	−0.999102	−	0.0423754i	$-0.986507\pi$
$317$	−5878.12	−	5878.12i	−1.04148	−	1.04148i	−0.0423754	−	0.999102i	$-0.513493\pi$
$318$		0			0
$319$			1118.24i			0.196268i
$320$	701.526	−	140.928i	0.122552	−	0.0246191i
$321$		0			0
$322$	−480.930	+	480.930i	−0.0832335	+	0.0832335i
$323$	−1559.29	+	1559.29i	−0.268610	+	0.268610i
$324$		0			0
$325$	2167.60	+	888.216i	0.369959	+	0.151598i
$326$			6166.57i			1.04765i
$327$		0			0
$328$	−1186.90	−	1186.90i	−0.199803	−	0.199803i
$329$	1003.92			0.168230
$330$		0			0
$331$	−1074.33			−0.178400			−0.0892001	−	0.996014i	$-0.528431\pi$
$331$	−1074.33			−0.178400			−0.0892001	+	0.996014i	$0.528431\pi$
$332$	348.300	+	348.300i	0.0575767	+	0.0575767i
$333$		0			0
$334$			5672.19i			0.929247i
$335$	3086.97	+	2054.18i	0.503460	+	0.335020i
$336$		0			0
$337$	1465.54	−	1465.54i	0.236894	−	0.236894i	−0.578669	−	0.815563i	$-0.696428\pi$
$337$	1465.54	−	1465.54i	0.236894	−	0.236894i	0.815563	+	0.578669i	$0.196428\pi$
$338$	−2610.36	+	2610.36i	−0.420074	+	0.420074i
$339$		0			0
$340$	3372.21	+	2243.99i	0.537893	+	0.357933i
$341$		−	2850.93i		−	0.452747i
$342$		0			0
$343$	242.538	+	242.538i	0.0381802	+	0.0381802i
$344$	1493.10			0.234019
$345$		0			0
$346$	1550.60			0.240927
$347$	7444.95	+	7444.95i	1.15177	+	1.15177i	0.986197	+	0.165578i	$0.0529490\pi$
$347$	7444.95	+	7444.95i	1.15177	+	1.15177i	0.165578	+	0.986197i	$0.447051\pi$
$348$		0			0
$349$			1705.27i			0.261550i	0.991412	+	0.130775i	$0.0417465\pi$
$349$			1705.27i			0.261550i	−0.991412	+	0.130775i	$0.958254\pi$
$350$	−1614.23	+	675.833i	−0.246527	+	0.103214i
$351$		0			0
$352$	252.436	−	252.436i	0.0382241	−	0.0382241i
$353$	1279.17	−	1279.17i	0.192871	−	0.192871i	−0.604065	−	0.796935i	$-0.706453\pi$
$353$	1279.17	−	1279.17i	0.192871	−	0.192871i	0.796935	+	0.604065i	$0.206453\pi$
$354$		0			0
$355$	−385.090	+	77.3598i	−0.0575731	+	0.0115657i
$356$		−	522.923i		−	0.0778508i
$357$		0			0
$358$	−802.024	−	802.024i	−0.118403	−	0.118403i
$359$	−10602.6			−1.55872			−0.779362	−	0.626574i	$-0.784457\pi$
$359$	−10602.6			−1.55872			−0.779362	+	0.626574i	$0.784457\pi$
$360$		0			0
$361$	6266.25			0.913580
$362$	−2306.02	−	2306.02i	−0.334811	−	0.334811i
$363$		0			0
$364$			524.724i			0.0755578i
$365$	−4459.65	+	6701.85i	−0.639530	+	0.961071i
$366$		0			0
$367$	−3185.68	+	3185.68i	−0.453110	+	0.453110i	−0.896385	−	0.443275i	$-0.853816\pi$
$367$	−3185.68	+	3185.68i	−0.453110	+	0.453110i	0.443275	+	0.896385i	$0.353816\pi$
$368$	549.635	−	549.635i	0.0778578	−	0.0778578i
$369$		0			0
$370$	−1680.69	−	8366.32i	−0.236149	−	1.17553i
$371$		−	878.577i		−	0.122947i
$372$		0			0
$373$	−7344.99	−	7344.99i	−1.01959	−	1.01959i	−0.999804	−	0.0197908i	$-0.993700\pi$
$373$	−7344.99	−	7344.99i	−1.01959	−	1.01959i	−0.0197908	−	0.999804i	$-0.506300\pi$
$374$	2020.92			0.279410
$375$		0			0
$376$	−1147.33			−0.157365
$377$	1328.24	+	1328.24i	0.181453	+	0.181453i
$378$		0			0
$379$			473.320i			0.0641499i	0.999485	+	0.0320749i	$0.0102115\pi$
$379$			473.320i			0.0641499i	−0.999485	+	0.0320749i	$0.989788\pi$
$380$	214.445	+	1067.48i	0.0289494	+	0.144107i
$381$		0			0
$382$	1055.47	−	1055.47i	0.141368	−	0.141368i
$383$	4292.11	−	4292.11i	0.572628	−	0.572628i	−0.360234	−	0.932862i	$-0.617303\pi$
$383$	4292.11	−	4292.11i	0.572628	−	0.572628i	0.932862	+	0.360234i	$0.117303\pi$
$384$		0			0
$385$	−483.695	+	726.886i	−0.0640296	+	0.0962221i
$386$			2247.56i			0.296367i
$387$		0			0
$388$	−3792.16	−	3792.16i	−0.496179	−	0.496179i
$389$	6713.73			0.875063			0.437532	−	0.899203i	$-0.355853\pi$
$389$	6713.73			0.875063			0.437532	+	0.899203i	$0.355853\pi$
$390$		0			0
$391$	4400.20			0.569124
$392$	−277.186	−	277.186i	−0.0357143	−	0.0357143i
$393$		0			0
$394$			3605.26i			0.460990i
$395$	6332.47	−	1272.11i	0.806635	−	0.162043i
$396$		0			0
$397$	−4327.63	+	4327.63i	−0.547097	+	0.547097i	−0.925600	−	0.378503i	$-0.876439\pi$
$397$	−4327.63	+	4327.63i	−0.547097	+	0.547097i	0.378503	+	0.925600i	$0.376439\pi$
$398$	3288.42	−	3288.42i	0.414155	−	0.414155i
$399$		0			0
$400$	1844.84	−	772.381i	0.230605	−	0.0965476i
$401$		−	10695.5i		−	1.33194i	−0.745977	−	0.665972i	$-0.768017\pi$
$401$		−	10695.5i		−	1.33194i	0.745977	−	0.665972i	$-0.231983\pi$
$402$		0			0
$403$	−3386.32	−	3386.32i	−0.418573	−	0.418573i
$404$	5056.19			0.622661
$405$		0			0
$406$	−1403.29			−0.171537
$407$	−3010.53	−	3010.53i	−0.366649	−	0.366649i
$408$		0			0
$409$			12106.0i			1.46358i	0.681530	+	0.731790i	$0.261315\pi$
$409$			12106.0i			1.46358i	−0.681530	+	0.731790i	$0.738685\pi$
$410$	−3905.88	−	2599.11i	−0.470482	−	0.313075i
$411$		0			0
$412$	5104.54	−	5104.54i	0.610394	−	0.610394i
$413$	−646.887	+	646.887i	−0.0770732	+	0.0770732i
$414$		0			0
$415$	1146.20	+	762.721i	0.135578	+	0.0902181i
$416$		−	599.685i		−	0.0706778i
$417$		0			0
$418$	384.122	+	384.122i	0.0449474	+	0.0449474i
$419$	−13263.1			−1.54641			−0.773207	−	0.634154i	$-0.781348\pi$
$419$	−13263.1			−1.54641			−0.773207	+	0.634154i	$0.781348\pi$
$420$		0			0
$421$	9762.69			1.13018			0.565089	−	0.825030i	$-0.308842\pi$
$421$	9762.69			1.13018			0.565089	+	0.825030i	$0.308842\pi$
$422$	−5731.29	−	5731.29i	−0.661125	−	0.661125i
$423$		0			0
$424$			1004.09i			0.115007i
$425$	10476.3	+	4292.88i	1.19571	+	0.489965i
$426$		0			0
$427$	−4586.37	+	4586.37i	−0.519789	+	0.519789i
$428$	3454.47	−	3454.47i	0.390135	−	0.390135i
$429$		0			0
$430$	4091.60	−	821.952i	0.458871	−	0.0921815i
$431$		−	12237.2i		−	1.36762i	−0.729659	−	0.683811i	$-0.760321\pi$
$431$		−	12237.2i		−	1.36762i	0.729659	−	0.683811i	$-0.239679\pi$
$432$		0			0
$433$	−7799.19	−	7799.19i	−0.865601	−	0.865601i	0.126381	−	0.991982i	$-0.459664\pi$
$433$	−7799.19	−	7799.19i	−0.865601	−	0.865601i	−0.991982	+	0.126381i	$0.959664\pi$
$434$	3577.65			0.395698
$435$		0			0
$436$	−2382.01			−0.261646
$437$	836.357	+	836.357i	0.0915524	+	0.0915524i
$438$		0			0
$439$			11028.7i			1.19903i	0.800365	+	0.599513i	$0.204639\pi$
$439$			11028.7i			1.19903i	−0.800365	+	0.599513i	$0.795361\pi$
$440$	552.794	−	830.727i	0.0598942	−	0.0900076i
$441$		0			0
$442$	2400.44	−	2400.44i	0.258320	−	0.258320i
$443$	6642.85	−	6642.85i	0.712441	−	0.712441i	−0.254605	−	0.967045i	$-0.581945\pi$
$443$	6642.85	−	6642.85i	0.712441	−	0.712441i	0.967045	+	0.254605i	$0.0819453\pi$
$444$		0			0
$445$	−287.869	−	1432.99i	−0.0306659	−	0.152652i
$446$			6640.19i			0.704982i
$447$		0			0
$448$	316.784	+	316.784i	0.0334077	+	0.0334077i
$449$	−9379.79			−0.985879			−0.492940	−	0.870064i	$-0.664078\pi$
$449$	−9379.79			−0.985879			−0.492940	+	0.870064i	$0.664078\pi$
$450$		0			0
$451$	−2340.75			−0.244393
$452$	4182.13	+	4182.13i	0.435201	+	0.435201i
$453$		0			0
$454$		−	7876.18i		−	0.814202i
$455$	288.861	+	1437.92i	0.0297626	+	0.148156i
$456$		0			0
$457$	−1475.37	+	1475.37i	−0.151017	+	0.151017i	−0.778572	−	0.627555i	$-0.784056\pi$
$457$	−1475.37	+	1475.37i	−0.151017	+	0.151017i	0.627555	+	0.778572i	$0.284056\pi$
$458$	736.156	−	736.156i	0.0751054	−	0.0751054i
$459$		0			0
$460$	1203.61	−	1808.76i	0.121997	−	0.183334i
$461$			4695.56i			0.474391i	0.971462	+	0.237195i	$0.0762281\pi$
$461$			4695.56i			0.474391i	−0.971462	+	0.237195i	$0.923772\pi$
$462$		0			0
$463$	−11226.8	−	11226.8i	−1.12690	−	1.12690i	−0.990679	−	0.136219i	$-0.956505\pi$
$463$	−11226.8	−	11226.8i	−1.12690	−	1.12690i	−0.136219	−	0.990679i	$-0.543495\pi$
$464$	1603.76			0.160458
$465$		0			0
$466$	4444.86			0.441854
$467$	−9068.66	−	9068.66i	−0.898603	−	0.898603i	0.0967097	−	0.995313i	$-0.469168\pi$
$467$	−9068.66	−	9068.66i	−0.898603	−	0.898603i	−0.995313	+	0.0967097i	$0.969168\pi$
$468$		0			0
$469$			2321.56i			0.228570i
$470$	−3144.08	+	631.607i	−0.308565	+	0.0619869i
$471$		0			0
$472$	739.300	−	739.300i	0.0720954	−	0.0720954i
$473$	1472.31	−	1472.31i	0.143123	−	0.143123i
$474$		0			0
$475$	1175.30	+	2807.22i	0.113529	+	0.271166i
$476$			2536.07i			0.244203i
$477$		0			0
$478$	−1957.54	−	1957.54i	−0.187313	−	0.187313i
$479$	6196.56			0.591082			0.295541	−	0.955330i	$-0.404500\pi$
$479$	6196.56			0.591082			0.295541	+	0.955330i	$0.404500\pi$
$480$		0			0
$481$	−7151.78			−0.677948
$482$	−4500.25	−	4500.25i	−0.425271	−	0.425271i
$483$		0			0
$484$			4826.16i			0.453245i
$485$	−12479.4	−	8304.20i	−1.16837	−	0.777473i
$486$		0			0
$487$	−1520.50	+	1520.50i	−0.141479	+	0.141479i	−0.774299	−	0.632820i	$-0.781897\pi$
$487$	−1520.50	+	1520.50i	−0.141479	+	0.141479i	0.632820	+	0.774299i	$0.281897\pi$
$488$	5241.57	−	5241.57i	0.486218	−	0.486218i
$489$		0			0
$490$	−912.174	−	606.992i	−0.0840976	−	0.0559614i
$491$		−	11019.6i		−	1.01285i	−0.862285	−	0.506423i	$-0.830967\pi$
$491$		−	11019.6i		−	1.01285i	0.862285	−	0.506423i	$-0.169033\pi$
$492$		0			0
$493$	6419.59	+	6419.59i	0.586458	+	0.586458i
$494$	912.517			0.0831094
$495$		0			0
$496$	−4088.75			−0.370141
$497$	−173.893	−	173.893i	−0.0156945	−	0.0156945i
$498$		0			0
$499$		−	22048.8i		−	1.97803i	−0.147800	−	0.989017i	$-0.547219\pi$
$499$		−	22048.8i		−	1.97803i	0.147800	−	0.989017i	$-0.452781\pi$
$500$	4630.28	−	3132.17i	0.414145	−	0.280150i
$501$		0			0
$502$	−3516.83	+	3516.83i	−0.312677	+	0.312677i
$503$	12595.9	−	12595.9i	1.11655	−	1.11655i	0.124307	−	0.992244i	$-0.460329\pi$
$503$	12595.9	−	12595.9i	1.11655	−	1.11655i	0.992244	−	0.124307i	$-0.0396709\pi$
$504$		0			0
$505$	13855.7	−	2783.44i	1.22093	−	0.245270i
$506$		−	1083.97i		−	0.0952336i
$507$		0			0
$508$	6297.70	+	6297.70i	0.550030	+	0.550030i
$509$	−16575.0			−1.44337			−0.721685	−	0.692222i	$-0.756632\pi$
$509$	−16575.0			−1.44337			−0.721685	+	0.692222i	$0.756632\pi$
$510$		0			0
$511$	−5040.13			−0.436325
$512$	−362.039	−	362.039i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	6803.89i		−	0.583866i
$515$	11178.1	−	16798.2i	0.956439	−	1.43731i
$516$		0			0
$517$	−1131.36	+	1131.36i	−0.0962421	+	0.0962421i
$518$	3777.93	−	3777.93i	0.320449	−	0.320449i
$519$		0			0
$520$	−330.127	−	1643.34i	−0.0278404	−	0.138587i
$521$			6016.40i			0.505918i	0.967477	+	0.252959i	$0.0814038\pi$
$521$			6016.40i			0.505918i	−0.967477	+	0.252959i	$0.918596\pi$
$522$		0			0
$523$	−2484.66	−	2484.66i	−0.207737	−	0.207737i	0.595568	−	0.803305i	$-0.296927\pi$
$523$	−2484.66	−	2484.66i	−0.207737	−	0.207737i	−0.803305	+	0.595568i	$0.796927\pi$
$524$	1123.29			0.0936469
$525$		0			0
$526$	−9704.33			−0.804428
$527$	−16366.6	−	16366.6i	−1.35283	−	1.35283i
$528$		0			0
$529$			9806.86i			0.806021i
$530$	552.751	+	2751.54i	0.0453018	+	0.225508i
$531$		0			0
$532$	−482.037	+	482.037i	−0.0392838	+	0.0392838i
$533$	−2780.33	+	2780.33i	−0.225946	+	0.225946i
$534$		0			0
$535$	7564.72	−	11368.1i	0.611311	−	0.918664i
$536$		−	2653.21i		−	0.213808i
$537$		0			0
$538$	−1349.85	−	1349.85i	−0.108171	−	0.108171i
$539$	−546.654			−0.0436847
$540$		0			0
$541$	21734.4			1.72724			0.863620	−	0.504144i	$-0.168192\pi$
$541$	21734.4			1.72724			0.863620	+	0.504144i	$0.168192\pi$
$542$	9401.62	+	9401.62i	0.745082	+	0.745082i
$543$		0			0
$544$		−	2898.37i		−	0.228431i
$545$	−6527.52	+	1311.30i	−0.513042	+	0.103064i
$546$		0			0
$547$	−11992.9	+	11992.9i	−0.937437	+	0.937437i	−0.998155	−	0.0607183i	$-0.980661\pi$
$547$	−11992.9	+	11992.9i	−0.937437	+	0.937437i	0.0607183	+	0.998155i	$0.480661\pi$
$548$	−1009.91	+	1009.91i	−0.0787248	+	0.0787248i
$549$		0			0
$550$	1057.53	−	2580.78i	0.0819875	−	0.200082i
$551$			2440.38i			0.188681i
$552$		0			0
$553$	2859.51	+	2859.51i	0.219889	+	0.219889i
$554$	2507.31			0.192284
$555$		0			0
$556$	−1056.28			−0.0805684
$557$	−845.158	−	845.158i	−0.0642917	−	0.0642917i	0.674230	−	0.738522i	$-0.264476\pi$
$557$	−845.158	−	845.158i	−0.0642917	−	0.0642917i	−0.738522	+	0.674230i	$0.764476\pi$
$558$		0			0
$559$		−	3497.62i		−	0.264639i
$560$	1042.48	+	693.705i	0.0786661	+	0.0523471i
$561$		0			0
$562$	9864.38	−	9864.38i	0.740398	−	0.740398i
$563$	−7506.71	+	7506.71i	−0.561936	+	0.561936i	−0.929857	−	0.367921i	$-0.880070\pi$
$563$	−7506.71	+	7506.71i	−0.561936	+	0.561936i	0.367921	+	0.929857i	$0.380070\pi$
$564$		0			0
$565$	13762.7	+	9158.18i	1.02478	+	0.681925i
$566$			8105.92i			0.601974i
$567$		0			0
$568$	198.734	+	198.734i	0.0146808	+	0.0146808i
$569$	−26291.3			−1.93707			−0.968533	−	0.248885i	$-0.919936\pi$
$569$	−26291.3			−1.93707			−0.968533	+	0.248885i	$0.919936\pi$
$570$		0			0
$571$	7621.82			0.558604			0.279302	−	0.960203i	$-0.409897\pi$
$571$	7621.82			0.558604			0.279302	+	0.960203i	$0.409897\pi$
$572$	−591.337	−	591.337i	−0.0432256	−	0.0432256i
$573$		0			0
$574$		−	2937.42i		−	0.213598i
$575$	2302.58	−	5619.20i	0.166998	−	0.407542i
$576$		0			0
$577$	−3844.11	+	3844.11i	−0.277352	+	0.277352i	−0.832051	−	0.554699i	$-0.812833\pi$
$577$	−3844.11	+	3844.11i	−0.277352	+	0.277352i	0.554699	+	0.832051i	$0.312833\pi$
$578$	4653.66	−	4653.66i	0.334891	−	0.334891i
$579$		0			0
$580$	4394.84	−	882.869i	0.314631	−	0.0632054i
$581$			861.999i			0.0615521i
$582$		0			0
$583$	990.110	+	990.110i	0.0703365	+	0.0703365i
$584$	5760.15			0.408145
$585$		0			0
$586$	10563.8			0.744688
$587$	−17141.5	−	17141.5i	−1.20529	−	1.20529i	−0.972536	−	0.232751i	$-0.925227\pi$
$587$	−17141.5	−	17141.5i	−1.20529	−	1.20529i	−0.232751	−	0.972536i	$-0.574773\pi$
$588$		0			0
$589$		−	6221.68i		−	0.435246i
$590$	1618.95	−	2432.91i	0.112968	−	0.169765i
$591$		0			0
$592$	−4317.63	+	4317.63i	−0.299753	+	0.299753i
$593$	18789.8	−	18789.8i	1.30119	−	1.30119i	0.373602	−	0.927589i	$-0.378122\pi$
$593$	18789.8	−	18789.8i	1.30119	−	1.30119i	0.927589	−	0.373602i	$-0.121878\pi$
$594$		0			0
$595$	1396.11	+	6949.69i	0.0961929	+	0.478839i
$596$			8793.99i			0.604389i
$597$		0			0
$598$	−1287.53	−	1287.53i	−0.0880452	−	0.0880452i
$599$	−4068.85			−0.277544			−0.138772	−	0.990324i	$-0.544315\pi$
$599$	−4068.85			−0.277544			−0.138772	+	0.990324i	$0.544315\pi$
$600$		0			0
$601$	21141.3			1.43489			0.717447	−	0.696613i	$-0.245311\pi$
$601$	21141.3			1.43489			0.717447	+	0.696613i	$0.245311\pi$
$602$	1847.62	+	1847.62i	0.125088	+	0.125088i
$603$		0			0
$604$		−	3063.80i		−	0.206398i
$605$	2656.80	+	13225.3i	0.178536	+	0.888735i
$606$		0			0
$607$	−4688.80	+	4688.80i	−0.313530	+	0.313530i	−0.846275	−	0.532746i	$-0.821160\pi$
$607$	−4688.80	+	4688.80i	−0.313530	+	0.313530i	0.532746	+	0.846275i	$0.321160\pi$
$608$	550.900	−	550.900i	0.0367466	−	0.0367466i
$609$		0			0
$610$	11478.2	−	17249.1i	0.761865	−	1.14491i
$611$			2687.65i			0.177955i
$612$		0			0
$613$	−9592.65	−	9592.65i	−0.632045	−	0.632045i	0.316536	−	0.948581i	$-0.397480\pi$
$613$	−9592.65	−	9592.65i	−0.632045	−	0.632045i	−0.948581	+	0.316536i	$0.897480\pi$
$614$	−5121.47			−0.336621
$615$		0			0
$616$	624.748			0.0408633
$617$	−1440.20	−	1440.20i	−0.0939715	−	0.0939715i	0.658558	−	0.752530i	$-0.271167\pi$
$617$	−1440.20	−	1440.20i	−0.0939715	−	0.0939715i	−0.752530	+	0.658558i	$0.771167\pi$
$618$		0			0
$619$			27476.0i			1.78409i	0.451942	+	0.892047i	$0.350731\pi$
$619$			27476.0i			1.78409i	−0.451942	+	0.892047i	$0.649269\pi$
$620$	−11204.5	+	2250.86i	−0.725783	+	0.145801i
$621$		0			0
$622$	7713.54	−	7713.54i	0.497242	−	0.497242i
$623$	647.084	−	647.084i	0.0416130	−	0.0416130i
$624$		0			0
$625$	10964.3	−	11132.2i	0.701714	−	0.712459i
$626$			4100.40i			0.261797i
$627$		0			0
$628$	2906.97	+	2906.97i	0.184714	+	0.184714i
$629$	−34565.6			−2.19113
$630$		0			0
$631$	8466.11			0.534121			0.267061	−	0.963680i	$-0.413948\pi$
$631$	8466.11			0.534121			0.267061	+	0.963680i	$0.413948\pi$
$632$	−3268.01	−	3268.01i	−0.205688	−	0.205688i
$633$		0			0
$634$			16625.8i			1.04148i
$635$	20724.7	+	13790.9i	1.29517	+	0.861853i
$636$		0			0
$637$	−649.313	+	649.313i	−0.0403873	+	0.0403873i
$638$	1581.43	−	1581.43i	0.0981340	−	0.0981340i
$639$		0			0
$640$	−1191.41	−	792.806i	−0.0735854	−	0.0489663i
$641$			10985.9i			0.676937i	0.940978	+	0.338469i	$0.109909\pi$
$641$			10985.9i			0.676937i	−0.940978	+	0.338469i	$0.890091\pi$
$642$		0			0
$643$	−3316.64	−	3316.64i	−0.203414	−	0.203414i	0.598047	−	0.801461i	$-0.295944\pi$
$643$	−3316.64	−	3316.64i	−0.203414	−	0.203414i	−0.801461	+	0.598047i	$0.795944\pi$
$644$	1360.28			0.0832335
$645$		0			0
$646$	4410.33			0.268610
$647$	4424.11	+	4424.11i	0.268825	+	0.268825i	0.828627	−	0.559802i	$-0.189123\pi$
$647$	4424.11	+	4424.11i	0.268825	+	0.268825i	−0.559802	+	0.828627i	$0.689123\pi$
$648$		0			0
$649$		−	1458.02i		−	0.0881851i
$650$	−1809.32	−	4321.57i	−0.109180	−	0.260778i
$651$		0			0
$652$	8720.85	−	8720.85i	0.523827	−	0.523827i
$653$	−10798.5	+	10798.5i	−0.647135	+	0.647135i	−0.952300	−	0.305165i	$-0.901288\pi$
$653$	−10798.5	+	10798.5i	−0.647135	+	0.647135i	0.305165	+	0.952300i	$0.401288\pi$
$654$		0			0
$655$	3078.18	−	618.369i	0.183625	−	0.0368880i
$656$			3357.05i			0.199803i
$657$		0			0
$658$	−1419.75	−	1419.75i	−0.0841150	−	0.0841150i
$659$	−9904.31			−0.585459			−0.292729	−	0.956195i	$-0.594563\pi$
$659$	−9904.31			−0.585459			−0.292729	+	0.956195i	$0.594563\pi$
$660$		0			0
$661$	−11545.5			−0.679378			−0.339689	−	0.940538i	$-0.610322\pi$
$661$	−11545.5			−0.679378			−0.339689	+	0.940538i	$0.610322\pi$
$662$	1519.33	+	1519.33i	0.0892001	+	0.0892001i
$663$		0			0
$664$		−	985.142i		−	0.0575767i
$665$	−1055.58	+	1586.31i	−0.0615545	+	0.0925027i
$666$		0			0
$667$	3443.29	−	3443.29i	0.199887	−	0.199887i
$668$	8021.69	−	8021.69i	0.464623	−	0.464623i
$669$		0			0
$670$	−1460.59	−	7270.68i	−0.0842202	−	0.419240i
$671$		−	10337.2i		−	0.594729i
$672$		0			0
$673$	19870.9	+	19870.9i	1.13814	+	1.13814i	0.988784	+	0.149352i	$0.0477189\pi$
$673$	19870.9	+	19870.9i	1.13814	+	1.13814i	0.149352	+	0.988784i	$0.452281\pi$
$674$	−4145.18			−0.236894
$675$		0			0
$676$	7383.23			0.420074
$677$	12685.1	+	12685.1i	0.720131	+	0.720131i	0.968632	−	0.248501i	$-0.0799379\pi$
$677$	12685.1	+	12685.1i	0.720131	+	0.720131i	−0.248501	+	0.968632i	$0.579938\pi$
$678$		0			0
$679$		−	9385.11i		−	0.530438i
$680$	−1595.55	−	7942.50i	−0.0899802	−	0.447913i
$681$		0			0
$682$	−4031.83	+	4031.83i	−0.226373	+	0.226373i
$683$	1163.64	−	1163.64i	0.0651910	−	0.0651910i	−0.673760	−	0.738951i	$-0.735322\pi$
$683$	1163.64	−	1163.64i	0.0651910	−	0.0651910i	0.738951	+	0.673760i	$0.235322\pi$
$684$		0			0
$685$	−2211.54	+	3323.45i	−0.123355	+	0.185376i
$686$		−	686.000i		−	0.0381802i
$687$		0			0
$688$	−2111.56	−	2111.56i	−0.117010	−	0.117010i
$689$	2352.10			0.130055
$690$		0			0
$691$	−5447.87			−0.299923			−0.149961	−	0.988692i	$-0.547915\pi$
$691$	−5447.87			−0.299923			−0.149961	+	0.988692i	$0.547915\pi$
$692$	−2192.87	−	2192.87i	−0.120463	−	0.120463i
$693$		0			0
$694$		−	21057.5i		−	1.15177i
$695$	−2894.55	+	581.480i	−0.157981	+	0.0317364i
$696$		0			0
$697$	−13437.7	+	13437.7i	−0.730259	+	0.730259i
$698$	2411.61	−	2411.61i	0.130775	−	0.130775i
$699$		0			0
$700$	3238.64	+	1327.10i	0.174870	+	0.0716566i
$701$		−	24663.2i		−	1.32884i	−0.747360	−	0.664419i	$-0.768679\pi$
$701$		−	24663.2i		−	1.32884i	0.747360	−	0.664419i	$-0.231321\pi$
$702$		0			0
$703$	−6569.97	−	6569.97i	−0.352477	−	0.352477i
$704$	−713.997			−0.0382241
$705$		0			0
$706$	−3618.04			−0.192871
$707$	6256.72	+	6256.72i	0.332826	+	0.332826i
$708$		0			0
$709$		−	12637.3i		−	0.669401i	−0.942325	−	0.334700i	$-0.891365\pi$
$709$		−	12637.3i		−	0.669401i	0.942325	−	0.334700i	$-0.108635\pi$
$710$	654.003	+	435.196i	0.0345694	+	0.0230037i
$711$		0			0
$712$	−739.525	+	739.525i	−0.0389254	+	0.0389254i
$713$	−8778.58	+	8778.58i	−0.461095	+	0.461095i
$714$		0			0
$715$	−1945.99	−	1294.93i	−0.101785	−	0.0677310i
$716$			2268.47i			0.118403i
$717$		0			0
$718$	14994.3	+	14994.3i	0.779362	+	0.779362i
$719$	32882.4			1.70557			0.852787	−	0.522260i	$-0.174911\pi$
$719$	32882.4			1.70557			0.852787	+	0.522260i	$0.174911\pi$
$720$		0			0
$721$	12633.1			0.652539
$722$	−8861.81	−	8861.81i	−0.456790	−	0.456790i
$723$		0			0
$724$			6522.40i			0.334811i
$725$	11557.3	−	4838.72i	0.592039	−	0.247870i
$726$		0			0
$727$	−7994.87	+	7994.87i	−0.407859	+	0.407859i	−0.880991	−	0.473132i	$-0.843123\pi$
$727$	−7994.87	+	7994.87i	−0.407859	+	0.407859i	0.473132	+	0.880991i	$0.343123\pi$
$728$	742.072	−	742.072i	0.0377789	−	0.0377789i
$729$		0			0
$730$	15784.7	−	3170.96i	0.800301	−	0.160771i
$731$		−	16904.5i		−	0.855315i
$732$		0			0
$733$	15704.5	+	15704.5i	0.791351	+	0.791351i	0.981714	−	0.190363i	$-0.0609664\pi$
$733$	15704.5	+	15704.5i	0.791351	+	0.791351i	−0.190363	+	0.981714i	$0.560966\pi$
$734$	9010.47			0.453110
$735$		0			0
$736$	−1554.60			−0.0778578
$737$	−2616.27	−	2616.27i	−0.130762	−	0.130762i
$738$		0			0
$739$		−	14876.6i		−	0.740522i	−0.928928	−	0.370261i	$-0.879268\pi$
$739$		−	14876.6i		−	0.740522i	0.928928	−	0.370261i	$-0.120732\pi$
$740$	−9454.91	+	14208.6i	−0.469689	+	0.705837i
$741$		0			0
$742$	−1242.50	+	1242.50i	−0.0614737	+	0.0614737i
$743$	−8266.54	+	8266.54i	−0.408170	+	0.408170i	−0.881100	−	0.472930i	$-0.843196\pi$
$743$	−8266.54	+	8266.54i	−0.408170	+	0.408170i	0.472930	+	0.881100i	$0.343196\pi$
$744$		0			0
$745$	4841.09	+	24098.5i	0.238072	+	1.18510i
$746$			20774.8i			1.01959i
$747$		0			0
$748$	−2858.02	−	2858.02i	−0.139705	−	0.139705i
$749$	8549.37			0.417072
$750$		0			0
$751$	−15772.3			−0.766362			−0.383181	−	0.923673i	$-0.625171\pi$
$751$	−15772.3			−0.766362			−0.383181	+	0.923673i	$0.625171\pi$
$752$	1622.57	+	1622.57i	0.0786824	+	0.0786824i
$753$		0			0
$754$		−	3756.84i		−	0.181453i
$755$	−1686.62	−	8395.86i	−0.0813014	−	0.404711i
$756$		0			0
$757$	−4591.71	+	4591.71i	−0.220460	+	0.220460i	−0.808692	−	0.588232i	$-0.799824\pi$
$757$	−4591.71	+	4591.71i	−0.220460	+	0.220460i	0.588232	+	0.808692i	$0.299824\pi$
$758$	669.375	−	669.375i	0.0320749	−	0.0320749i
$759$		0			0
$760$	1206.38	−	1812.92i	0.0575790	−	0.0865284i
$761$			21849.6i			1.04080i	0.853923	+	0.520399i	$0.174217\pi$
$761$			21849.6i			1.04080i	−0.853923	+	0.520399i	$0.825783\pi$
$762$		0			0
$763$	−2947.59	−	2947.59i	−0.139856	−	0.139856i
$764$	−2985.33			−0.141368
$765$		0			0
$766$	−12139.9			−0.572628
$767$	−1731.82	−	1731.82i	−0.0815287	−	0.0815287i
$768$		0			0
$769$			24303.2i			1.13965i	0.821765	+	0.569827i	$0.192990\pi$
$769$			24303.2i			1.13965i	−0.821765	+	0.569827i	$0.807010\pi$
$770$	1712.02	−	343.924i	0.0801259	−	0.0160963i
$771$		0			0
$772$	3178.53	−	3178.53i	0.148183	−	0.148183i
$773$	−15121.1	+	15121.1i	−0.703580	+	0.703580i	−0.965177	−	0.261598i	$-0.915751\pi$
$773$	−15121.1	+	15121.1i	−0.703580	+	0.703580i	0.261598	+	0.965177i	$0.415751\pi$
$774$		0			0
$775$	−29465.1	+	12336.2i	−1.36570	+	0.571780i
$776$			10725.8i			0.496179i
$777$		0			0
$778$	−9494.65	−	9494.65i	−0.437532	−	0.437532i
$779$	−5108.29			−0.234947
$780$		0			0
$781$	391.936			0.0179572
$782$	−6222.82	−	6222.82i	−0.284562	−	0.284562i
$783$		0			0
$784$			784.000i			0.0357143i
$785$	9566.35	+	6365.78i	0.434953	+	0.289433i
$786$		0			0
$787$	−25166.4	+	25166.4i	−1.13988	+	1.13988i	−0.151406	+	0.988472i	$0.548380\pi$
$787$	−25166.4	+	25166.4i	−1.13988	+	1.13988i	−0.988472	+	0.151406i	$0.951620\pi$
$788$	5098.60	−	5098.60i	0.230495	−	0.230495i
$789$		0			0
$790$	−10754.5	−	7156.42i	−0.484339	−	0.322296i
$791$			10350.2i			0.465249i
$792$		0			0
$793$	−12278.5	−	12278.5i	−0.549838	−	0.549838i
$794$	12240.4			0.547097
$795$		0			0
$796$	−9301.05			−0.414155
$797$	9173.02	+	9173.02i	0.407685	+	0.407685i	0.880931	−	0.473245i	$-0.156918\pi$
$797$	9173.02	+	9173.02i	0.407685	+	0.407685i	−0.473245	+	0.880931i	$0.656918\pi$
$798$		0			0
$799$			12989.8i			0.575152i
$800$	−3701.31	−	1516.68i	−0.163576	−	0.0670286i
$801$		0			0
$802$	−15125.8	+	15125.8i	−0.665972	+	0.665972i
$803$	5679.96	−	5679.96i	0.249616	−	0.249616i
$804$		0			0
$805$	3727.62	−	748.832i	0.163206	−	0.0327862i
$806$			9577.97i			0.418573i
$807$		0			0
$808$	−7150.54	−	7150.54i	−0.311331	−	0.311331i
$809$	11657.9			0.506640			0.253320	−	0.967383i	$-0.418477\pi$
$809$	11657.9			0.506640			0.253320	+	0.967383i	$0.418477\pi$
$810$		0			0
$811$	3256.76			0.141012			0.0705058	−	0.997511i	$-0.477539\pi$
$811$	3256.76			0.141012			0.0705058	+	0.997511i	$0.477539\pi$
$812$	1984.55	+	1984.55i	0.0857685	+	0.0857685i
$813$		0			0
$814$			8515.05i			0.366649i
$815$	19097.2	−	28698.9i	0.820794	−	1.23347i
$816$		0			0
$817$	3213.08	−	3213.08i	0.137591	−	0.137591i
$818$	17120.5	−	17120.5i	0.731790	−	0.731790i
$819$		0			0
$820$	1848.06	+	9199.45i	0.0787035	+	0.391779i
$821$		−	33602.8i		−	1.42844i	−0.699922	−	0.714219i	$-0.746782\pi$
$821$		−	33602.8i		−	1.42844i	0.699922	−	0.714219i	$-0.253218\pi$
$822$		0			0
$823$	−30124.8	−	30124.8i	−1.27592	−	1.27592i	−0.942930	−	0.332992i	$-0.891942\pi$
$823$	−30124.8	−	30124.8i	−1.27592	−	1.27592i	−0.332992	−	0.942930i	$-0.608058\pi$
$824$	−14437.8			−0.610394
$825$		0			0
$826$	1829.67			0.0770732
$827$	15779.9	+	15779.9i	0.663508	+	0.663508i	0.956205	−	0.292698i	$-0.0945529\pi$
$827$	15779.9	+	15779.9i	0.663508	+	0.663508i	−0.292698	+	0.956205i	$0.594553\pi$
$828$		0			0
$829$			10880.8i			0.455858i	0.973678	+	0.227929i	$0.0731955\pi$
$829$			10880.8i			0.455858i	−0.973678	+	0.227929i	$0.926805\pi$
$830$	−542.321	−	2699.62i	−0.0226798	−	0.112898i
$831$		0			0
$832$	−848.083	+	848.083i	−0.0353389	+	0.0353389i
$833$	−3138.23	+	3138.23i	−0.130532	+	0.130532i
$834$		0			0
$835$	17566.2	−	26398.1i	0.728028	−	1.09406i
$836$		−	1086.46i		−	0.0449474i
$837$		0			0
$838$	18756.9	+	18756.9i	0.773207	+	0.773207i
$839$	−41921.6			−1.72502			−0.862511	−	0.506038i	$-0.831110\pi$
$839$	−41921.6			−1.72502			−0.862511	+	0.506038i	$0.831110\pi$
$840$		0			0
$841$	−14342.0			−0.588050
$842$	−13806.5	−	13806.5i	−0.565089	−	0.565089i
$843$		0			0
$844$			16210.5i			0.661125i
$845$	20232.5	−	4064.47i	0.823693	−	0.165470i
$846$		0			0
$847$	−5972.06	+	5972.06i	−0.242270	+	0.242270i
$848$	1420.00	−	1420.00i	0.0575033	−	0.0575033i
$849$		0			0
$850$	−8744.69	−	20886.8i	−0.352871	−	0.842836i
$851$			18540.0i			0.746819i
$852$		0			0
$853$	15664.8	+	15664.8i	0.628783	+	0.628783i	0.947762	−	0.318979i	$-0.103340\pi$
$853$	15664.8	+	15664.8i	0.628783	+	0.628783i	−0.318979	+	0.947762i	$0.603340\pi$
$854$	12972.2			0.519789
$855$		0			0
$856$	−9770.71			−0.390135
$857$	18769.7	+	18769.7i	0.748144	+	0.748144i	0.974131	−	0.225986i	$-0.0725604\pi$
$857$	18769.7	+	18769.7i	0.748144	+	0.748144i	−0.225986	+	0.974131i	$0.572560\pi$
$858$		0			0
$859$		−	45678.3i		−	1.81435i	−0.420757	−	0.907174i	$-0.638235\pi$
$859$		−	45678.3i		−	1.81435i	0.420757	−	0.907174i	$-0.361765\pi$
$860$	−6948.81	−	4623.98i	−0.275526	−	0.183345i
$861$		0			0
$862$	−17306.0	+	17306.0i	−0.683811	+	0.683811i
$863$	−28253.7	+	28253.7i	−1.11445	+	1.11445i	−0.121904	+	0.992542i	$0.538900\pi$
$863$	−28253.7	+	28253.7i	−1.11445	+	1.11445i	−0.992542	+	0.121904i	$0.961100\pi$
$864$		0			0
$865$	−7216.39	−	4802.04i	−0.283659	−	0.188756i
$866$			22059.4i			0.865601i
$867$		0			0
$868$	−5059.57	−	5059.57i	−0.197849	−	0.197849i
$869$	−6445.04			−0.251591
$870$		0			0
$871$	−6215.19			−0.241784
$872$	3368.67	+	3368.67i	0.130823	+	0.130823i
$873$		0			0
$874$		−	2365.57i		−	0.0915524i
$875$	9605.54	+	1853.83i	0.371116	+	0.0716237i
$876$		0			0
$877$	16236.5	−	16236.5i	0.625163	−	0.625163i	−0.321684	−	0.946847i	$-0.604249\pi$
$877$	16236.5	−	16236.5i	0.625163	−	0.625163i	0.946847	+	0.321684i	$0.104249\pi$
$878$	15597.0	−	15597.0i	0.599513	−	0.599513i
$879$		0			0
$880$	−1956.59	+	393.056i	−0.0749509	+	0.0150567i
$881$			26937.3i			1.03013i	0.857152	+	0.515064i	$0.172232\pi$
$881$			26937.3i			1.03013i	−0.857152	+	0.515064i	$0.827768\pi$
$882$		0			0
$883$	−31344.0	−	31344.0i	−1.19458	−	1.19458i	−0.975768	−	0.218807i	$-0.929783\pi$
$883$	−31344.0	−	31344.0i	−1.19458	−	1.19458i	−0.218807	−	0.975768i	$-0.570217\pi$
$884$	−6789.48			−0.258320
$885$		0			0
$886$	−18788.8			−0.712441
$887$	30884.9	+	30884.9i	1.16913	+	1.16913i	0.982415	+	0.186710i	$0.0597826\pi$
$887$	30884.9	+	30884.9i	1.16913	+	1.16913i	0.186710	+	0.982415i	$0.440217\pi$
$888$		0			0
$889$			15586.0i			0.588007i
$890$	−1619.44	+	2433.66i	−0.0609930	+	0.0916588i
$891$		0			0
$892$	9390.64	−	9390.64i	0.352491	−	0.352491i
$893$	−2469.01	+	2469.01i	−0.0925220	+	0.0925220i
$894$		0			0
$895$	1248.79	+	6216.36i	0.0466396	+	0.232168i
$896$		−	896.000i		−	0.0334077i
$897$		0			0
$898$	13265.0	+	13265.0i	0.492940	+	0.492940i
$899$	−25614.7			−0.950276
$900$		0			0
$901$	11368.0			0.420337
$902$	3310.31	+	3310.31i	0.122197	+	0.122197i
$903$		0			0
$904$		−	11828.8i		−	0.435201i
$905$	3590.58	+	17873.6i	0.131884	+	0.656506i
$906$		0			0
$907$	−16176.9	+	16176.9i	−0.592222	+	0.592222i	−0.938231	−	0.346009i	$-0.887537\pi$
$907$	−16176.9	+	16176.9i	−0.592222	+	0.592222i	0.346009	+	0.938231i	$0.387537\pi$
$908$	−11138.6	+	11138.6i	−0.407101	+	0.407101i
$909$		0			0
$910$	1625.02	−	2442.04i	0.0591965	−	0.0889591i
$911$			27877.8i			1.01387i	0.861985	+	0.506934i	$0.169221\pi$
$911$			27877.8i			1.01387i	−0.861985	+	0.506934i	$0.830779\pi$
$912$		0			0
$913$	−971.428	−	971.428i	−0.0352131	−	0.0352131i
$914$	4172.97			0.151017
$915$		0			0
$916$	−2082.16			−0.0751054
$917$	1389.99	+	1389.99i	0.0500564	+	0.0500564i
$918$		0			0
$919$		−	42951.1i		−	1.54170i	−0.637014	−	0.770852i	$-0.719831\pi$
$919$		−	42951.1i		−	1.54170i	0.637014	−	0.770852i	$-0.280169\pi$
$920$	−4260.13	+	855.808i	−0.152666	+	0.0306687i
$921$		0			0
$922$	6640.53	−	6640.53i	0.237195	−	0.237195i
$923$	465.539	−	465.539i	0.0166017	−	0.0166017i
$924$		0			0
$925$	−18087.8	+	44141.4i	−0.642944	+	1.56904i
$926$			31754.2i			1.12690i
$927$		0			0
$928$	−2268.06	−	2268.06i	−0.0802291	−	0.0802291i
$929$	11071.3			0.390999			0.195499	−	0.980704i	$-0.437367\pi$
$929$	11071.3			0.390999			0.195499	+	0.980704i	$0.437367\pi$
$930$		0			0
$931$	−1192.98			−0.0419961
$932$	−6285.98	−	6285.98i	−0.220927	−	0.220927i
$933$		0			0
$934$			25650.0i			0.898603i
$935$	−9405.27	−	6258.59i	−0.328968	−	0.218907i
$936$		0			0
$937$	14724.1	−	14724.1i	0.513356	−	0.513356i	−0.402197	−	0.915553i	$-0.631753\pi$
$937$	14724.1	−	14724.1i	0.513356	−	0.513356i	0.915553	+	0.402197i	$0.131753\pi$
$938$	3283.18	−	3283.18i	0.114285	−	0.114285i
$939$		0			0
$940$	5339.63	+	3553.17i	0.185276	+	0.123289i
$941$			350.679i			0.0121486i	0.999982	+	0.00607429i	$0.00193352\pi$
$941$			350.679i			0.0121486i	−0.999982	+	0.00607429i	$0.998066\pi$
$942$		0			0
$943$	7207.62	+	7207.62i	0.248900	+	0.248900i
$944$	−2091.06			−0.0720954
$945$		0			0
$946$	−4164.34			−0.143123
$947$	12754.6	+	12754.6i	0.437664	+	0.437664i	0.891225	−	0.453561i	$-0.149847\pi$
$947$	12754.6	+	12754.6i	0.437664	+	0.437664i	−0.453561	+	0.891225i	$0.649847\pi$
$948$		0			0
$949$		−	13493.3i		−	0.461549i
$950$	2307.88	−	5632.13i	0.0788184	−	0.192348i
$951$		0			0
$952$	3586.54	−	3586.54i	0.122101	−	0.122101i
$953$	33245.6	−	33245.6i	1.13004	−	1.13004i	0.139874	−	0.990169i	$-0.455330\pi$
$953$	33245.6	−	33245.6i	1.13004	−	1.13004i	0.990169	−	0.139874i	$-0.0446696\pi$
$954$		0			0
$955$	−8180.81	+	1643.42i	−0.277199	+	0.0556858i
$956$			5536.75i			0.187313i
$957$		0			0
$958$	−8763.26	−	8763.26i	−0.295541	−	0.295541i
$959$	−2499.40			−0.0841604
$960$		0			0
$961$	35513.1			1.19208
$962$	10114.1	+	10114.1i	0.338974	+	0.338974i
$963$		0			0
$964$			12728.6i			0.425271i
$965$	6960.45	−	10460.0i	0.232192	−	0.348932i
$966$		0			0
$967$	4645.67	−	4645.67i	0.154493	−	0.154493i	−0.625628	−	0.780121i	$-0.715157\pi$
$967$	4645.67	−	4645.67i	0.154493	−	0.154493i	0.780121	+	0.625628i	$0.215157\pi$
$968$	6825.22	−	6825.22i	0.226623	−	0.226623i
$969$		0			0
$970$	5904.57	+	29392.4i	0.195448	+	0.972921i
$971$		−	25155.4i		−	0.831384i	−0.909505	−	0.415692i	$-0.863539\pi$
$971$		−	25155.4i		−	0.831384i	0.909505	−	0.415692i	$-0.136461\pi$
$972$		0			0
$973$	−1307.07	−	1307.07i	−0.0430656	−	0.0430656i
$974$	4300.62			0.141479
$975$		0			0
$976$	−14825.4			−0.486218
$977$	28348.0	+	28348.0i	0.928285	+	0.928285i	0.997595	−	0.0693105i	$-0.0220799\pi$
$977$	28348.0	+	28348.0i	0.928285	+	0.928285i	−0.0693105	+	0.997595i	$0.522080\pi$
$978$		0			0
$979$			1458.46i			0.0476125i
$980$	431.592	+	2148.42i	0.0140681	+	0.0700295i
$981$		0			0
$982$	−15584.1	+	15584.1i	−0.506423	+	0.506423i
$983$	21336.6	−	21336.6i	0.692299	−	0.692299i	−0.270438	−	0.962737i	$-0.587169\pi$
$983$	21336.6	−	21336.6i	0.692299	−	0.692299i	0.962737	+	0.270438i	$0.0871685\pi$
$984$		0			0
$985$	11165.1	−	16778.7i	0.361167	−	0.542754i
$986$		−	18157.3i		−	0.586458i
$987$		0			0
$988$	−1290.49	−	1290.49i	−0.0415547	−	0.0415547i
$989$	−9067.10			−0.291524
$990$		0			0
$991$	−26409.0			−0.846529			−0.423265	−	0.906006i	$-0.639116\pi$
$991$	−26409.0			−0.846529			−0.423265	+	0.906006i	$0.639116\pi$
$992$	5782.36	+	5782.36i	0.185071	+	0.185071i
$993$		0			0
$994$			491.843i			0.0156945i
$995$	−25488.0	+	5120.23i	−0.812085	+	0.163138i
$996$		0			0
$997$	10650.8	−	10650.8i	0.338330	−	0.338330i	−0.517409	−	0.855738i	$-0.673103\pi$
$997$	10650.8	−	10650.8i	0.338330	−	0.338330i	0.855738	+	0.517409i	$0.173103\pi$
$998$	−31181.7	+	31181.7i	−0.989017	+	0.989017i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.m.a.323.4	yes	16
3.2	odd	2		630.4.m.b.323.5	yes	16
5.2	odd	4		630.4.m.b.197.5	yes	16
15.2	even	4	inner	630.4.m.a.197.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.4.m.a.197.4	✓	16	15.2	even	4	inner
630.4.m.a.323.4	yes	16	1.1	even	1	trivial
630.4.m.b.197.5	yes	16	5.2	odd	4
630.4.m.b.323.5	yes	16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41421 - 1.41421i) q^{2} +4.00000i q^{4} +(2.20200 + 10.9614i) q^{5} +(-4.94975 + 4.94975i) q^{7} +(5.65685 - 5.65685i) q^{8} +(12.3876 - 18.6158i) q^{10} -11.1562i q^{11} +(-13.2513 - 13.2513i) q^{13} +14.0000 q^{14} -16.0000 q^{16} +(-64.0454 - 64.0454i) q^{17} -24.3466i q^{19} +(-43.8454 + 8.80800i) q^{20} +(-15.7773 + 15.7773i) q^{22} +(-34.3522 + 34.3522i) q^{23} +(-115.302 + 48.2738i) q^{25} +37.4803i q^{26} +(-19.7990 - 19.7990i) q^{28} -100.235 q^{29} +255.547 q^{31} +(22.6274 + 22.6274i) q^{32} +181.148i q^{34} +(-65.1553 - 43.3566i) q^{35} +(269.852 - 269.852i) q^{37} +(-34.4312 + 34.4312i) q^{38} +(74.4632 + 49.5504i) q^{40} -209.816i q^{41} +(131.973 + 131.973i) q^{43} +44.6248 q^{44} +97.1626 q^{46} +(-101.411 - 101.411i) q^{47} -49.0000i q^{49} +(231.332 + 94.7928i) q^{50} +(53.0052 - 53.0052i) q^{52} +(-88.7497 + 88.7497i) q^{53} +(122.287 - 24.5660i) q^{55} +56.0000i q^{56} +(141.754 + 141.754i) q^{58} +130.691 q^{59} +926.587 q^{61} +(-361.398 - 361.398i) q^{62} -64.0000i q^{64} +(116.073 - 174.431i) q^{65} +(234.513 - 234.513i) q^{67} +(256.182 - 256.182i) q^{68} +(30.8280 + 153.459i) q^{70} +35.1316i q^{71} +(509.130 + 509.130i) q^{73} -763.257 q^{74} +97.3862 q^{76} +(55.2204 + 55.2204i) q^{77} -577.709i q^{79} +(-35.2320 - 175.382i) q^{80} +(-296.724 + 296.724i) q^{82} +(87.0751 - 87.0751i) q^{83} +(560.996 - 843.052i) q^{85} -373.275i q^{86} +(-63.1091 - 63.1091i) q^{88} -130.731 q^{89} +131.181 q^{91} +(-137.409 - 137.409i) q^{92} +286.833i q^{94} +(266.871 - 53.6111i) q^{95} +(-948.039 + 948.039i) q^{97} +(-69.2965 + 69.2965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 44 q^{5} - 24 q^{10} - 212 q^{13} + 224 q^{14} - 256 q^{16} + 32 q^{17} + 32 q^{20} + 72 q^{22} - 128 q^{23} - 268 q^{25} + 232 q^{29} - 200 q^{31} + 112 q^{35} + 900 q^{37} - 368 q^{38} - 128 q^{40}+ \cdots - 2668 q^{97}+O(q^{100}) \) 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

Properties

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