LMFDB - Embedded newform 245.4.j.e.214.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(79,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("245.79");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 55 x^{18} + 2042 x^{16} - 41247 x^{14} + 600234 x^{12} - 4812047 x^{10} + 27547801 x^{8} + \cdots + 12960000 $ x^20 - 55x^18 + 2042x^16 - 41247x^14 + 600234x^12 - 4812047x^10 + 27547801x^8 - 79828440x^6 + 160801200x^4 - 48816000*x^2 + 12960000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2}\cdot 7^{8} $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.4
Root			$-2.31676 - 1.33758i$ of defining polynomial
Character	$\chi$	$=$	245.214
Dual form			245.4.j.e.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.45073 + 0.837581i) q^{2} +(-2.15983 - 1.24698i) q^{3} +(-2.59692 + 4.49799i) q^{4} +(-11.1437 - 0.904354i) q^{5} +4.17779 q^{6} -22.1018i q^{8} +(-10.3901 - 17.9961i) q^{9} +(16.9240 - 8.02178i) q^{10} +(28.7940 - 49.8727i) q^{11} +(11.2178 - 6.47661i) q^{12} +45.5159i q^{13} +(22.9408 + 15.8492i) q^{15} +(-2.26327 - 3.92011i) q^{16} +(-79.6787 - 46.0025i) q^{17} +(30.1465 + 17.4051i) q^{18} +(62.5885 + 108.407i) q^{19} +(33.0070 - 47.7757i) q^{20} +96.4692i q^{22} +(-137.262 + 79.2481i) q^{23} +(-27.5605 + 47.7362i) q^{24} +(123.364 + 20.1557i) q^{25} +(-38.1233 - 66.0315i) q^{26} +119.162i q^{27} +40.1708 q^{29} +(-46.5560 - 3.77820i) q^{30} +(-24.7795 + 42.9194i) q^{31} +(159.693 + 92.1986i) q^{32} +(-124.381 + 71.8111i) q^{33} +154.123 q^{34} +107.929 q^{36} +(200.318 - 115.654i) q^{37} +(-181.598 - 104.846i) q^{38} +(56.7575 - 98.3069i) q^{39} +(-19.9879 + 246.296i) q^{40} +169.556 q^{41} +147.428i q^{43} +(149.551 + 259.030i) q^{44} +(99.5091 + 209.940i) q^{45} +(132.753 - 229.936i) q^{46} +(-58.0520 + 33.5164i) q^{47} +11.2890i q^{48} +(-195.851 + 74.0870i) q^{50} +(114.729 + 198.716i) q^{51} +(-204.730 - 118.201i) q^{52} +(232.655 + 134.323i) q^{53} +(-99.8077 - 172.872i) q^{54} +(-365.974 + 529.726i) q^{55} -312.187i q^{57} +(-58.2771 + 33.6463i) q^{58} +(-120.421 + 208.576i) q^{59} +(-130.865 + 62.0285i) q^{60} +(-45.2290 - 78.3389i) q^{61} -83.0194i q^{62} -272.683 q^{64} +(41.1625 - 507.216i) q^{65} +(120.295 - 208.358i) q^{66} +(352.038 + 203.249i) q^{67} +(413.838 - 238.929i) q^{68} +395.283 q^{69} +330.782 q^{71} +(-397.747 + 229.640i) q^{72} +(473.071 + 273.127i) q^{73} +(-193.739 + 335.565i) q^{74} +(-241.313 - 197.366i) q^{75} -650.149 q^{76} +190.156i q^{78} +(-12.6543 - 21.9179i) q^{79} +(21.6761 + 45.7313i) q^{80} +(-131.940 + 228.526i) q^{81} +(-245.981 + 142.017i) q^{82} -376.255i q^{83} +(846.314 + 584.697i) q^{85} +(-123.483 - 213.878i) q^{86} +(-86.7623 - 50.0922i) q^{87} +(-1102.28 - 636.399i) q^{88} +(513.219 + 888.921i) q^{89} +(-320.203 - 221.220i) q^{90} -823.203i q^{92} +(107.039 - 61.7992i) q^{93} +(56.1453 - 97.2466i) q^{94} +(-599.430 - 1264.65i) q^{95} +(-229.940 - 398.267i) q^{96} -942.660i q^{97} -1196.69 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 36 q^{4} - 6 q^{5} + 24 q^{6} + 46 q^{9} + 16 q^{10} - 84 q^{11} + 16 q^{15} - 148 q^{16} - 72 q^{19} - 136 q^{20} - 72 q^{24} + 362 q^{25} + 620 q^{26} + 176 q^{29} - 52 q^{30} - 120 q^{31} + 1928 q^{34}+ \cdots - 10608 q^{99}+O(q^{100}) $ 20 * q + 36 * q^4 - 6 * q^5 + 24 * q^6 + 46 * q^9 + 16 * q^10 - 84 * q^11 + 16 * q^15 - 148 * q^16 - 72 * q^19 - 136 * q^20 - 72 * q^24 + 362 * q^25 + 620 * q^26 + 176 * q^29 - 52 * q^30 - 120 * q^31 + 1928 * q^34 - 840 * q^36 - 212 * q^39 - 1396 * q^40 - 1704 * q^41 + 1424 * q^44 + 510 * q^45 - 176 * q^46 + 3288 * q^50 - 1276 * q^51 + 996 * q^54 - 2272 * q^55 - 864 * q^59 + 1692 * q^60 + 884 * q^61 - 5448 * q^64 - 520 * q^65 - 1148 * q^66 + 9616 * q^69 + 1760 * q^71 - 3024 * q^74 - 720 * q^75 - 5344 * q^76 + 3580 * q^79 + 2316 * q^80 + 302 * q^81 + 3144 * q^85 - 2432 * q^86 + 1492 * q^89 - 15496 * q^90 - 1652 * q^94 + 1628 * q^95 - 4080 * q^96 - 10608 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−1.45073	+	0.837581i	−0.512912	+	0.296130i	−0.734030	−	0.679117i	$-0.762363\pi$
$2$	−1.45073	+	0.837581i	−0.512912	+	0.296130i	0.221118	+	0.975247i	$0.429029\pi$
$3$	−2.15983	−	1.24698i	−0.415660	−	0.239982i	0.277559	−	0.960709i	$-0.410475\pi$
$3$	−2.15983	−	1.24698i	−0.415660	−	0.239982i	−0.693219	+	0.720727i	$0.743808\pi$
$4$	−2.59692	+	4.49799i	−0.324615	+	0.562249i
$5$	−11.1437	−	0.904354i	−0.996723	−	0.0808879i
$5$	−11.1437	−	0.904354i	−0.996723	−	0.0808879i
$6$	4.17779			0.284263
$7$		0			0
$7$		0			0
$8$		−	22.1018i		−	0.976771i
$9$	−10.3901	−	17.9961i	−0.384818	−	0.666524i
$10$	16.9240	−	8.02178i	0.535184	−	0.253671i
$11$	28.7940	−	49.8727i	0.789247	−	1.36702i	−0.137182	−	0.990546i	$-0.543804\pi$
$11$	28.7940	−	49.8727i	0.789247	−	1.36702i	0.926429	−	0.376470i	$-0.122862\pi$
$12$	11.2178	−	6.47661i	0.269859	−	0.155803i
$13$			45.5159i			0.971066i	0.874218	+	0.485533i	$0.161374\pi$
$13$			45.5159i			0.971066i	−0.874218	+	0.485533i	$0.838626\pi$
$14$		0			0
$15$	22.9408	+	15.8492i	0.394887	+	0.272817i
$16$	−2.26327	−	3.92011i	−0.0353637	−	0.0612517i
$17$	−79.6787	−	46.0025i	−1.13676	−	0.656309i	−0.191134	−	0.981564i	$-0.561217\pi$
$17$	−79.6787	−	46.0025i	−1.13676	−	0.656309i	−0.945626	+	0.325255i	$0.894550\pi$
$18$	30.1465	+	17.4051i	0.394755	+	0.227912i
$19$	62.5885	+	108.407i	0.755726	+	1.30896i	0.945013	+	0.327034i	$0.106049\pi$
$19$	62.5885	+	108.407i	0.755726	+	1.30896i	−0.189286	+	0.981922i	$0.560617\pi$
$20$	33.0070	−	47.7757i	0.369030	−	0.534149i
$21$		0			0
$22$			96.4692i			0.934878i
$23$	−137.262	+	79.2481i	−1.24439	+	0.718451i	−0.969986	−	0.243162i	$-0.921815\pi$
$23$	−137.262	+	79.2481i	−1.24439	+	0.718451i	−0.274408	+	0.961613i	$0.588482\pi$
$24$	−27.5605	+	47.7362i	−0.234407	+	0.406005i
$25$	123.364	+	20.1557i	0.986914	+	0.161246i
$26$	−38.1233	−	66.0315i	−0.287561	−	0.498071i
$27$			119.162i			0.849360i
$28$		0			0
$29$	40.1708			0.257225			0.128613	−	0.991695i	$-0.458948\pi$
$29$	40.1708			0.257225			0.128613	+	0.991695i	$0.458948\pi$
$30$	−46.5560	−	3.77820i	−0.283331	−	0.0229934i
$31$	−24.7795	+	42.9194i	−0.143566	+	0.248663i	−0.928837	−	0.370489i	$-0.879190\pi$
$31$	−24.7795	+	42.9194i	−0.143566	+	0.248663i	0.785271	+	0.619152i	$0.212523\pi$
$32$	159.693	+	92.1986i	0.882185	+	0.509330i
$33$	−124.381	+	71.8111i	−0.656117	+	0.378809i
$34$	154.123			0.777410
$35$		0			0
$36$	107.929			0.499670
$37$	200.318	−	115.654i	0.890056	−	0.513874i	0.0160950	−	0.999870i	$-0.494877\pi$
$37$	200.318	−	115.654i	0.890056	−	0.513874i	0.873961	+	0.485997i	$0.161543\pi$
$38$	−181.598	−	104.846i	−0.775241	−	0.447586i
$39$	56.7575	−	98.3069i	0.233038	−	0.403633i
$40$	−19.9879	+	246.296i	−0.0790090	+	0.973570i
$41$	169.556			0.645859			0.322929	−	0.946423i	$-0.395332\pi$
$41$	169.556			0.645859			0.322929	+	0.946423i	$0.395332\pi$
$42$		0			0
$43$			147.428i			0.522849i	0.965224	+	0.261425i	$0.0841923\pi$
$43$			147.428i			0.522849i	−0.965224	+	0.261425i	$0.915808\pi$
$44$	149.551	+	259.030i	0.512402	+	0.887507i
$45$	99.5091	+	209.940i	0.329643	+	0.695467i
$46$	132.753	−	229.936i	0.425509	−	0.737004i
$47$	−58.0520	+	33.5164i	−0.180165	+	0.104018i	−0.587370	−	0.809318i	$-0.699837\pi$
$47$	−58.0520	+	33.5164i	−0.180165	+	0.104018i	0.407205	+	0.913337i	$0.366503\pi$
$48$			11.2890i			0.0339465i
$49$		0			0
$50$	−195.851	+	74.0870i	−0.553949	+	0.209550i
$51$	114.729	+	198.716i	0.315004	+	0.545603i
$52$	−204.730	−	118.201i	−0.545980	−	0.315222i
$53$	232.655	+	134.323i	0.602974	+	0.348127i	0.770211	−	0.637790i	$-0.220151\pi$
$53$	232.655	+	134.323i	0.602974	+	0.348127i	−0.167237	+	0.985917i	$0.553484\pi$
$54$	−99.8077	−	172.872i	−0.251521	−	0.435646i
$55$	−365.974	+	529.726i	−0.897236	+	1.29870i
$56$		0			0
$57$		−	312.187i		−	0.725441i
$58$	−58.2771	+	33.6463i	−0.131934	+	0.0761720i
$59$	−120.421	+	208.576i	−0.265721	+	0.460242i	−0.967752	−	0.251904i	$-0.918943\pi$
$59$	−120.421	+	208.576i	−0.265721	+	0.460242i	0.702031	+	0.712146i	$0.252277\pi$
$60$	−130.865	+	62.0285i	−0.281577	+	0.133464i
$61$	−45.2290	−	78.3389i	−0.0949340	−	0.164431i	0.814647	−	0.579957i	$-0.196931\pi$
$61$	−45.2290	−	78.3389i	−0.0949340	−	0.164431i	−0.909581	+	0.415527i	$0.863597\pi$
$62$		−	83.0194i		−	0.170056i
$63$		0			0
$64$	−272.683			−0.532583
$65$	41.1625	−	507.216i	0.0785475	−	0.967884i
$66$	120.295	−	208.358i	0.224353	−	0.388592i
$67$	352.038	+	203.249i	0.641914	+	0.370609i	0.785351	−	0.619050i	$-0.212482\pi$
$67$	352.038	+	203.249i	0.641914	+	0.370609i	−0.143437	+	0.989659i	$0.545816\pi$
$68$	413.838	−	238.929i	0.738018	−	0.426095i
$69$	395.283			0.689660
$70$		0			0
$71$	330.782			0.552910			0.276455	−	0.961027i	$-0.410840\pi$
$71$	330.782			0.552910			0.276455	+	0.961027i	$0.410840\pi$
$72$	−397.747	+	229.640i	−0.651041	+	0.375879i
$73$	473.071	+	273.127i	0.758476	+	0.437906i	0.828748	−	0.559622i	$-0.189054\pi$
$73$	473.071	+	273.127i	0.758476	+	0.437906i	−0.0702724	+	0.997528i	$0.522387\pi$
$74$	−193.739	+	335.565i	−0.304347	+	0.527144i
$75$	−241.313	−	197.366i	−0.371525	−	0.303865i
$76$	−650.149			−0.981279
$77$		0			0
$78$			190.156i			0.276038i
$79$	−12.6543	−	21.9179i	−0.0180218	−	0.0312147i	0.856874	−	0.515526i	$-0.172403\pi$
$79$	−12.6543	−	21.9179i	−0.0180218	−	0.0312147i	−0.874896	+	0.484311i	$0.839070\pi$
$80$	21.6761	+	45.7313i	0.0302933	+	0.0639114i
$81$	−131.940	+	228.526i	−0.180987	+	0.313479i
$82$	−245.981	+	142.017i	−0.331268	+	0.191258i
$83$		−	376.255i		−	0.497582i	−0.968557	−	0.248791i	$-0.919967\pi$
$83$		−	376.255i		−	0.497582i	0.968557	−	0.248791i	$-0.0800333\pi$
$84$		0			0
$85$	846.314	+	584.697i	1.07995	+	0.746109i
$86$	−123.483	−	213.878i	−0.154831	−	0.268175i
$87$	−86.7623	−	50.0922i	−0.106918	−	0.0617293i
$88$	−1102.28	−	636.399i	−1.33526	−	0.770914i
$89$	513.219	+	888.921i	0.611248	+	1.05871i	0.991030	+	0.133637i	$0.0426656\pi$
$89$	513.219	+	888.921i	0.611248	+	1.05871i	−0.379782	+	0.925076i	$0.624001\pi$
$90$	−320.203	−	221.220i	−0.375026	−	0.259096i
$91$		0			0
$92$		−	823.203i		−	0.932878i
$93$	107.039	−	61.7992i	0.119349	−	0.0689062i
$94$	56.1453	−	97.2466i	0.0616058	−	0.106704i
$95$	−599.430	−	1264.65i	−0.647371	−	1.36580i
$96$	−229.940	−	398.267i	−0.244460	−	0.423416i
$97$		−	942.660i		−	0.986728i	−0.869823	−	0.493364i	$-0.835767\pi$
$97$		−	942.660i		−	0.986728i	0.869823	−	0.493364i	$-0.164233\pi$
$98$		0			0
$99$	−1196.69			−1.21487
$100$	−411.027	+	502.549i	−0.411027	+	0.502549i
$101$	302.308	−	523.613i	0.297830	−	0.515856i	−0.677809	−	0.735238i	$-0.737071\pi$
$101$	302.308	−	523.613i	0.297830	−	0.515856i	0.975639	+	0.219381i	$0.0704039\pi$
$102$	−332.881	−	192.189i	−0.323139	−	0.186564i
$103$	260.645	−	150.484i	0.249341	−	0.143957i	−0.370121	−	0.928983i	$-0.620684\pi$
$103$	260.645	−	150.484i	0.249341	−	0.143957i	0.619463	+	0.785026i	$0.287351\pi$
$104$	1005.98			0.948509
$105$		0			0
$106$	−450.027			−0.412363
$107$	1309.14	−	755.830i	1.18279	−	0.682886i	0.226135	−	0.974096i	$-0.427391\pi$
$107$	1309.14	−	755.830i	1.18279	−	0.682886i	0.956659	+	0.291210i	$0.0940577\pi$
$108$	−535.989	−	309.453i	−0.477551	−	0.275714i
$109$	−883.545	+	1530.34i	−0.776406	+	1.34477i	0.157595	+	0.987504i	$0.449626\pi$
$109$	−883.545	+	1530.34i	−0.776406	+	1.34477i	−0.934001	+	0.357270i	$0.883707\pi$
$110$	87.2424	−	1075.02i	0.0756203	−	0.931814i
$111$	−576.871			−0.493281
$112$		0			0
$113$		−	1045.27i		−	0.870182i	−0.900387	−	0.435091i	$-0.856716\pi$
$113$		−	1045.27i		−	0.870182i	0.900387	−	0.435091i	$-0.143284\pi$
$114$	261.482	+	452.900i	0.214825	+	0.372087i
$115$	1601.27	−	758.984i	1.29843	−	0.615440i
$116$	−104.320	+	180.688i	−0.0834991	+	0.144625i
$117$	819.111	−	472.914i	0.647238	−	0.373683i
$118$		−	403.451i		−	0.314751i
$119$		0			0
$120$	350.297	−	507.034i	0.266480	−	0.385714i
$121$	−992.689	−	1719.39i	−0.745822	−	1.29180i
$122$	131.230	+	75.7658i	0.0973855	+	0.0562255i
$123$	−366.213	−	211.433i	−0.268458	−	0.154994i
$124$	−128.701	−	222.916i	−0.0932070	−	0.161439i
$125$	−1356.51	−	336.174i	−0.970638	−	0.240547i
$126$		0			0
$127$			260.727i			0.182171i	0.995843	+	0.0910857i	$0.0290337\pi$
$127$			260.727i			0.182171i	−0.995843	+	0.0910857i	$0.970966\pi$
$128$	−881.951	+	509.195i	−0.609017	+	0.351616i
$129$	183.840	−	318.419i	0.125474	−	0.217328i
$130$	365.119	+	770.312i	0.246331	+	0.519699i
$131$	361.761	+	626.588i	0.241276	+	0.417903i	0.961078	−	0.276277i	$-0.0891006\pi$
$131$	361.761	+	626.588i	0.241276	+	0.417903i	−0.719802	+	0.694180i	$0.755767\pi$
$132$		−	745.950i		−	0.491868i
$133$		0			0
$134$	−680.950			−0.438993
$135$	107.765	−	1327.90i	0.0687029	−	0.846577i
$136$	−1016.74	+	1761.04i	−0.641064	+	1.11036i
$137$	−670.038	−	386.847i	−0.417848	−	0.241245i	0.276308	−	0.961069i	$-0.410889\pi$
$137$	−670.038	−	386.847i	−0.417848	−	0.241245i	−0.694156	+	0.719824i	$0.744222\pi$
$138$	−573.451	+	331.082i	−0.353735	+	0.204229i
$139$	2952.97			1.80192			0.900961	−	0.433899i	$-0.142863\pi$
$139$	2952.97			1.80192			0.900961	+	0.433899i	$0.142863\pi$
$140$		0			0
$141$	167.177			0.0998499
$142$	−479.876	+	277.057i	−0.283594	+	0.163733i
$143$	2270.00	+	1310.59i	1.32746	+	0.766411i
$144$	−47.0312	+	81.4604i	−0.0272171	+	0.0471414i
$145$	−447.652	−	36.3287i	−0.256382	−	0.0208064i
$146$	−915.066			−0.518708
$147$		0			0
$148$			1201.37i			0.667244i
$149$	1257.00	+	2177.19i	0.691124	+	1.19706i	0.971470	+	0.237163i	$0.0762177\pi$
$149$	1257.00	+	2177.19i	0.691124	+	1.19706i	−0.280345	+	0.959899i	$0.590449\pi$
$150$	515.390	+	84.2063i	0.280543	+	0.0458361i
$151$	−50.5262	+	87.5140i	−0.0272302	+	0.0471642i	−0.879319	−	0.476233i	$-0.842002\pi$
$151$	−50.5262	+	87.5140i	−0.0272302	+	0.0471642i	0.852089	+	0.523397i	$0.175335\pi$
$152$	2395.98	−	1383.32i	1.27855	−	0.738171i
$153$			1911.88i			1.01024i
$154$		0			0
$155$	314.950	−	455.872i	0.163209	−	0.236235i
$156$	294.789	+	510.589i	0.151295	+	0.262050i
$157$	−2025.07	−	1169.17i	−1.02941	−	0.594333i	−0.112597	−	0.993641i	$-0.535917\pi$
$157$	−2025.07	−	1169.17i	−1.02941	−	0.594333i	−0.916817	+	0.399308i	$0.869250\pi$
$158$	36.7161	+	21.1980i	0.0184872	+	0.0106736i
$159$	−334.997	−	580.233i	−0.167088	−	0.289405i
$160$	−1696.19	−	1171.85i	−0.838096	−	0.579019i
$161$		0			0
$162$		−	442.040i		−	0.214383i
$163$	1147.66	−	662.602i	0.551483	−	0.318399i	−0.198237	−	0.980154i	$-0.563522\pi$
$163$	1147.66	−	662.602i	0.551483	−	0.318399i	0.749720	+	0.661755i	$0.230188\pi$
$164$	−440.323	+	762.662i	−0.209655	+	0.363133i
$165$	1451.00	−	687.758i	0.684608	−	0.324496i
$166$	315.144	+	545.845i	0.147349	+	0.255216i
$167$			2086.20i			0.966675i	0.875434	+	0.483338i	$0.160576\pi$
$167$			2086.20i			0.966675i	−0.875434	+	0.483338i	$0.839424\pi$
$168$		0			0
$169$	125.299			0.0570317
$170$	−1717.51	−	139.382i	−0.774863	−	0.0628831i
$171$	1300.60	−	2252.70i	0.581634	−	1.00742i
$172$	−663.129	−	382.858i	−0.293971	−	0.169724i
$173$	−1661.20	+	959.095i	−0.730051	+	0.421495i	−0.818441	−	0.574591i	$-0.805161\pi$
$173$	−1661.20	+	959.095i	−0.730051	+	0.421495i	0.0883897	+	0.996086i	$0.471828\pi$
$174$	167.825			0.0731195
$175$		0			0
$176$	−260.675			−0.111643
$177$	520.180	−	300.326i	0.220899	−	0.127536i
$178$	−1489.09	−	859.725i	−0.627032	−	0.362017i
$179$	314.523	−	544.770i	0.131333	−	0.227475i	−0.792858	−	0.609407i	$-0.791408\pi$
$179$	314.523	−	544.770i	0.131333	−	0.227475i	0.924191	+	0.381932i	$0.124741\pi$
$180$	−1202.72	−	97.6057i	−0.498032	−	0.0404172i
$181$	−2800.85			−1.15020			−0.575099	−	0.818084i	$-0.695036\pi$
$181$	−2800.85			−1.15020			−0.575099	+	0.818084i	$0.695036\pi$
$182$		0			0
$183$			225.599i			0.0911296i
$184$	1751.53	+	3033.73i	0.701762	+	1.21549i
$185$	−2336.88	+	1107.65i	−0.928705	+	0.440195i
$186$	−103.524	+	179.308i	−0.0408103	+	0.0706856i
$187$	−4588.54	+	2649.19i	−1.79437	+	1.03598i
$188$		−	348.157i		−	0.135063i
$189$		0			0
$190$	1928.86	+	1332.60i	0.736497	+	0.508827i
$191$	−370.127	−	641.080i	−0.140217	−	0.242863i	0.787361	−	0.616492i	$-0.211447\pi$
$191$	−370.127	−	641.080i	−0.140217	−	0.242863i	−0.927578	+	0.373629i	$0.878113\pi$
$192$	588.949	+	340.030i	0.221374	+	0.127810i
$193$	3535.61	+	2041.29i	1.31865	+	0.761321i	0.983511	−	0.180849i	$-0.0578844\pi$
$193$	3535.61	+	2041.29i	1.31865	+	0.761321i	0.335136	+	0.942170i	$0.391218\pi$
$194$	789.554	+	1367.55i	0.292199	+	0.506104i
$195$	−721.393	+	1044.17i	−0.264923	+	0.383461i
$196$		0			0
$197$			3414.89i			1.23503i	0.786559	+	0.617515i	$0.211860\pi$
$197$			3414.89i			1.23503i	−0.786559	+	0.617515i	$0.788140\pi$
$198$	1736.07	−	1002.32i	0.623118	−	0.359758i
$199$	−1696.22	+	2937.94i	−0.604231	+	1.04656i	0.387941	+	0.921684i	$0.373186\pi$
$199$	−1696.22	+	2937.94i	−0.604231	+	1.04656i	−0.992173	+	0.124875i	$0.960147\pi$
$200$	445.478	−	2726.57i	0.157500	−	0.963989i
$201$	−506.895	−	877.968i	−0.177879	−	0.308095i
$202$			1012.83i			0.352785i
$203$		0			0
$204$	−1191.76			−0.409020
$205$	−1889.48	−	153.339i	−0.643743	−	0.0522422i
$206$	−252.084	+	436.623i	−0.0852600	+	0.147675i
$207$	2852.32	+	1646.79i	0.957729	+	0.552945i
$208$	178.427	−	103.015i	0.0594794	−	0.0343404i
$209$	7208.70			2.38582
$210$		0			0
$211$	3398.04			1.10867			0.554337	−	0.832292i	$-0.312972\pi$
$211$	3398.04			1.10867			0.554337	+	0.832292i	$0.312972\pi$
$212$	−1208.37	+	697.653i	−0.391468	+	0.226014i
$213$	−714.434	−	412.479i	−0.229823	−	0.132688i
$214$	−1266.14	+	2193.02i	−0.404446	+	0.700521i
$215$	133.327	−	1642.89i	0.0422922	−	0.521136i
$216$	2633.69			0.829630
$217$		0			0
$218$		−	2960.16i		−	0.919667i
$219$	−681.169	−	1179.82i	−0.210179	−	0.364040i
$220$	−1432.30	−	3021.80i	−0.438935	−	0.926045i
$221$	2093.85	−	3626.65i	0.637319	−	1.10387i
$222$	836.886	−	483.176i	0.253010	−	0.146075i
$223$		−	182.611i		−	0.0548365i	−0.999624	−	0.0274183i	$-0.991271\pi$
$223$		−	182.611i		−	0.0548365i	0.999624	−	0.0274183i	$-0.00872860\pi$
$224$		0			0
$225$	−919.040	−	2429.50i	−0.272308	−	0.719852i
$226$	875.496	+	1516.40i	0.257687	+	0.446326i
$227$	2730.00	+	1576.17i	0.798222	+	0.460854i	0.842849	−	0.538150i	$-0.180877\pi$
$227$	2730.00	+	1576.17i	0.798222	+	0.460854i	−0.0446271	+	0.999004i	$0.514210\pi$
$228$	1404.21	+	810.723i	0.407878	+	0.235489i
$229$	3006.18	+	5206.85i	0.867483	+	1.50253i	0.864560	+	0.502529i	$0.167597\pi$
$229$	3006.18	+	5206.85i	0.867483	+	1.50253i	0.00292326	+	0.999996i	$0.499069\pi$
$230$	−1687.31	+	2442.28i	−0.483730	+	0.700170i
$231$		0			0
$232$		−	887.848i		−	0.251250i
$233$	814.635	−	470.330i	0.229050	−	0.132242i	−0.381084	−	0.924540i	$-0.624449\pi$
$233$	814.635	−	470.330i	0.229050	−	0.132242i	0.610133	+	0.792299i	$0.291116\pi$
$234$	−792.208	+	1372.14i	−0.221317	+	0.383333i
$235$	677.225	−	320.997i	0.187989	−	0.0891043i
$236$	−625.448	−	1083.31i	−0.172514	−	0.298802i
$237$			63.1188i			0.0172996i
$238$		0			0
$239$	−5158.82			−1.39622			−0.698109	−	0.715991i	$-0.745975\pi$
$239$	−5158.82			−1.39622			−0.698109	+	0.715991i	$0.745975\pi$
$240$	10.2093	−	125.802i	0.00274586	−	0.0338353i
$241$	231.918	−	401.694i	0.0619882	−	0.107367i	−0.833366	−	0.552722i	$-0.813589\pi$
$241$	231.918	−	401.694i	0.0619882	−	0.107367i	0.895354	+	0.445355i	$0.146923\pi$
$242$	2880.25	+	1662.92i	0.765081	+	0.441720i
$243$	3356.26	−	1937.74i	0.886025	−	0.511547i
$244$	469.823			0.123268
$245$		0			0
$246$	708.370			0.183594
$247$	−4934.23	+	2848.78i	−1.27108	+	0.733860i
$248$	948.596	+	547.672i	0.242887	+	0.140231i
$249$	−469.183	+	812.648i	−0.119411	+	0.206825i
$250$	2249.50	−	648.486i	0.569084	−	0.164055i
$251$	2290.25			0.575934			0.287967	−	0.957640i	$-0.407021\pi$
$251$	2290.25			0.575934			0.287967	+	0.957640i	$0.407021\pi$
$252$		0			0
$253$			9127.48i			2.26814i
$254$	−218.380	−	378.245i	−0.0539463	−	0.0934378i
$255$	−1098.79	−	2318.18i	−0.269839	−	0.569295i
$256$	1943.71	−	3366.61i	0.474540	−	0.821927i
$257$	−694.727	+	401.101i	−0.168622	+	0.0973541i	−0.581936	−	0.813235i	$-0.697705\pi$
$257$	−694.727	+	401.101i	−0.168622	+	0.0973541i	0.413314	+	0.910589i	$0.364371\pi$
$258$			615.922i			0.148627i
$259$		0			0
$260$	2174.56	+	1502.35i	0.518694	+	0.358352i
$261$	−417.378	−	722.920i	−0.0989849	−	0.171447i
$262$	−1049.64	−	606.008i	−0.247507	−	0.142898i
$263$	−248.530	−	143.489i	−0.0582701	−	0.0336423i	0.470582	−	0.882356i	$-0.344044\pi$
$263$	−248.530	−	143.489i	−0.0582701	−	0.0336423i	−0.528852	+	0.848714i	$0.677377\pi$
$264$	1587.16	+	2749.03i	0.370010	+	0.640876i
$265$	−2471.16	−	1707.26i	−0.572839	−	0.395760i
$266$		0			0
$267$		−	2559.90i		−	0.586753i
$268$	−1828.42	+	1055.64i	−0.416749	+	0.240610i
$269$	1780.61	−	3084.11i	0.403590	−	0.699039i	−0.590566	−	0.806989i	$-0.701095\pi$
$269$	1780.61	−	3084.11i	0.403590	−	0.699039i	0.994156	+	0.107951i	$0.0344288\pi$
$270$	955.890	+	2016.70i	0.215458	+	0.454564i
$271$	−964.403	−	1670.39i	−0.216175	−	0.374425i	0.737461	−	0.675390i	$-0.236025\pi$
$271$	−964.403	−	1670.39i	−0.216175	−	0.374425i	−0.953635	+	0.300965i	$0.902691\pi$
$272$			416.466i			0.0928380i
$273$		0			0
$274$	1296.06			0.285759
$275$	4557.37	−	5572.14i	0.999345	−	1.22187i
$276$	−1026.52	+	1777.98i	−0.223874	+	0.387760i
$277$	−5705.97	−	3294.34i	−1.23768	−	0.714578i	−0.269064	−	0.963122i	$-0.586714\pi$
$277$	−5705.97	−	3294.34i	−1.23768	−	0.714578i	−0.968620	+	0.248545i	$0.920048\pi$
$278$	−4283.96	+	2473.35i	−0.924227	+	0.533603i
$279$	1029.84			0.220986
$280$		0			0
$281$	815.552			0.173138			0.0865689	−	0.996246i	$-0.472410\pi$
$281$	815.552			0.173138			0.0865689	+	0.996246i	$0.472410\pi$
$282$	−242.529	+	140.024i	−0.0512142	+	0.0295685i
$283$	−5640.85	−	3256.75i	−1.18485	−	0.684076i	−0.227722	−	0.973726i	$-0.573128\pi$
$283$	−5640.85	−	3256.75i	−1.18485	−	0.684076i	−0.957132	+	0.289651i	$0.906461\pi$
$284$	−859.013	+	1487.85i	−0.179483	+	0.310873i
$285$	−282.327	+	3478.92i	−0.0586794	+	0.723064i
$286$	−4390.89			−0.907828
$287$		0			0
$288$		−	3831.80i		−	0.783997i
$289$	1775.97	+	3076.07i	0.361483	+	0.626108i
$290$	679.851	−	322.241i	0.137663	−	0.0652506i
$291$	−1175.48	+	2035.99i	−0.236796	+	0.410143i
$292$	−2457.05	+	1418.58i	−0.492425	+	0.284301i
$293$		−	435.520i		−	0.0868373i	−0.999057	−	0.0434186i	$-0.986175\pi$
$293$		−	435.520i		−	0.0868373i	0.999057	−	0.0434186i	$-0.0138249\pi$
$294$		0			0
$295$	1530.57	−	2215.40i	0.302078	−	0.437240i
$296$	−2556.15	−	4427.39i	−0.501937	−	0.869381i
$297$	5942.92	+	3431.15i	1.16109	+	0.670355i
$298$	−3647.15	−	2105.68i	−0.708971	−	0.409325i
$299$	−3607.05	−	6247.60i	−0.697663	−	1.20839i
$300$	1514.42	−	572.879i	0.291450	−	0.110251i
$301$		0			0
$302$		−	169.279i		−	0.0322547i
$303$	−1305.87	+	753.945i	−0.247592	+	0.142947i
$304$	283.310	−	490.707i	0.0534505	−	0.0925789i
$305$	433.172	+	913.888i	0.0813225	+	0.171571i
$306$	−1601.35	−	2773.63i	−0.299161	−	0.518163i
$307$		−	4915.99i		−	0.913910i	−0.889490	−	0.456955i	$-0.848940\pi$
$307$		−	4915.99i		−	0.913910i	0.889490	−	0.456955i	$-0.151060\pi$
$308$		0			0
$309$	−750.601			−0.138188
$310$	−75.0790	+	925.144i	−0.0137555	+	0.169499i
$311$	915.556	−	1585.79i	0.166934	−	0.289138i	−0.770407	−	0.637553i	$-0.779947\pi$
$311$	915.556	−	1585.79i	0.166934	−	0.289138i	0.937340	+	0.348415i	$0.113280\pi$
$312$	−2172.76	−	1254.44i	−0.394257	−	0.227625i
$313$	2115.66	−	1221.48i	0.382059	−	0.220582i	−0.296655	−	0.954985i	$-0.595871\pi$
$313$	2115.66	−	1221.48i	0.382059	−	0.220582i	0.678714	+	0.734403i	$0.262538\pi$
$314$	3917.11			0.703998
$315$		0			0
$316$	131.449			0.0234006
$317$	1442.97	−	833.096i	0.255662	−	0.147607i	−0.366692	−	0.930342i	$-0.619510\pi$
$317$	1442.97	−	833.096i	0.255662	−	0.147607i	0.622354	+	0.782736i	$0.286176\pi$
$318$	971.983	+	561.175i	0.171403	+	0.0989595i
$319$	1156.68	−	2003.43i	0.203014	−	0.351631i
$320$	3038.70	+	246.602i	0.530838	+	0.0430796i
$321$	−3770.02			−0.655521
$322$		0			0
$323$		−	11516.9i		−	1.98396i
$324$	−685.272	−	1186.93i	−0.117502	−	0.203520i
$325$	−917.406	+	5615.04i	−0.156580	+	0.958358i
$326$	−1109.97	+	1922.52i	−0.188575	+	0.326621i
$327$	3816.62	−	2203.53i	0.645442	−	0.372646i
$328$		−	3747.50i		−	0.630856i
$329$		0			0
$330$	−1528.96	+	2213.09i	−0.255051	+	0.369171i
$331$	2733.19	+	4734.02i	0.453866	+	0.786119i	0.998622	−	0.0524753i	$-0.0167111\pi$
$331$	2733.19	+	4734.02i	0.453866	+	0.786119i	−0.544756	+	0.838595i	$0.683378\pi$
$332$	1692.39	+	977.102i	0.279765	+	0.161522i
$333$	−4162.64	−	2403.30i	−0.685018	−	0.395496i
$334$	−1747.36	−	3026.51i	−0.286261	−	0.495819i
$335$	−3739.19	−	2583.31i	−0.609833	−	0.421318i
$336$		0			0
$337$			10650.5i			1.72157i	0.508970	+	0.860784i	$0.330027\pi$
$337$			10650.5i			1.72157i	−0.508970	+	0.860784i	$0.669973\pi$
$338$	−181.775	+	104.948i	−0.0292522	+	0.0168888i
$339$	−1303.43	+	2257.60i	−0.208828	+	0.361700i
$340$	−4827.77	+	2288.30i	−0.770066	+	0.365002i
$341$	1427.00	+	2471.64i	0.226617	+	0.392513i
$342$			4357.43i			0.688956i
$343$		0			0
$344$	3258.42			0.510704
$345$	−4404.92	−	357.476i	−0.687400	−	0.0557851i
$346$	1606.64	−	2782.78i	0.249634	−	0.432380i
$347$	−3480.67	−	2009.57i	−0.538479	−	0.310891i	0.205983	−	0.978556i	$-0.433961\pi$
$347$	−3480.67	−	2009.57i	−0.538479	−	0.310891i	−0.744462	+	0.667664i	$0.767294\pi$
$348$	450.629	−	260.171i	0.0694145	−	0.0400765i
$349$	−10544.9			−1.61735			−0.808674	−	0.588256i	$-0.799815\pi$
$349$	−10544.9			−1.61735			−0.808674	+	0.588256i	$0.799815\pi$
$350$		0			0
$351$	−5423.76			−0.824784
$352$	9196.38	−	5309.53i	1.39252	−	0.803974i
$353$	2563.42	+	1479.99i	0.386507	+	0.223150i	0.680646	−	0.732613i	$-0.261699\pi$
$353$	2563.42	+	1479.99i	0.386507	+	0.223150i	−0.294138	+	0.955763i	$0.595033\pi$
$354$	−503.095	+	871.386i	−0.0755345	+	0.130830i
$355$	−3686.14	−	299.144i	−0.551098	−	0.0447237i
$356$	−5331.14			−0.793680
$357$		0			0
$358$			1053.75i			0.155566i
$359$	1085.08	+	1879.42i	0.159523	+	0.276301i	0.934697	−	0.355447i	$-0.115671\pi$
$359$	1085.08	+	1879.42i	0.159523	+	0.276301i	−0.775174	+	0.631748i	$0.782338\pi$
$360$	4640.05	−	2199.33i	0.679312	−	0.321986i
$361$	−4405.15	+	7629.94i	−0.642244	+	1.11240i
$362$	4063.29	−	2345.94i	0.589949	−	0.340607i
$363$			4951.46i			0.715934i
$364$		0			0
$365$	−5024.76	−	3471.48i	−0.720569	−	0.497823i
$366$	−188.957	−	327.283i	−0.0269862	−	0.0467414i
$367$	1084.44	+	626.101i	0.154243	+	0.0890523i	0.575135	−	0.818058i	$-0.304950\pi$
$367$	1084.44	+	626.101i	0.154243	+	0.0890523i	−0.420892	+	0.907111i	$0.638283\pi$
$368$	621.322	+	358.720i	0.0880126	+	0.0508141i
$369$	−1761.70	−	3051.36i	−0.248538	−	0.430480i
$370$	2462.43	−	3564.23i	0.345989	−	0.500798i
$371$		0			0
$372$			641.949i			0.0894718i
$373$	−4023.57	+	2323.01i	−0.558533	+	0.322469i	−0.752556	−	0.658528i	$-0.771179\pi$
$373$	−4023.57	+	2323.01i	−0.558533	+	0.322469i	0.194024	+	0.980997i	$0.437846\pi$
$374$	4437.83	−	7686.55i	0.613569	−	1.06273i
$375$	2510.63	+	2417.62i	0.345729	+	0.332921i
$376$	740.772	+	1283.05i	0.101602	+	0.175980i
$377$			1828.41i			0.249783i
$378$		0			0
$379$	−1434.84			−0.194466			−0.0972331	−	0.995262i	$-0.530999\pi$
$379$	−1434.84			−0.194466			−0.0972331	+	0.995262i	$0.530999\pi$
$380$	7245.06	+	587.965i	0.978063	+	0.0793736i
$381$	325.121	−	563.126i	0.0437178	−	0.0757214i
$382$	1073.91	+	620.023i	0.143838	+	0.0830449i
$383$	11446.0	−	6608.36i	1.52706	−	0.881649i	0.527578	−	0.849507i	$-0.323100\pi$
$383$	11446.0	−	6608.36i	1.52706	−	0.881649i	0.999483	−	0.0321425i	$-0.0102330\pi$
$384$	2539.82			0.337526
$385$		0			0
$386$	−6838.97			−0.901799
$387$	2653.13	−	1531.79i	0.348492	−	0.201202i
$388$	4240.07	+	2448.01i	0.554787	+	0.320306i
$389$	−3877.50	+	6716.03i	−0.505391	+	0.875363i	0.494589	+	0.869127i	$0.335319\pi$
$389$	−3877.50	+	6716.03i	−0.505391	+	0.875363i	−0.999981	+	0.00623657i	$0.998015\pi$
$390$	171.968	−	2119.04i	0.0223281	−	0.275133i
$391$	14582.5			1.88610
$392$		0			0
$393$		−	1804.44i		−	0.231607i
$394$	−2860.25	−	4954.09i	−0.365729	−	0.633461i
$395$	121.194	+	255.691i	0.0154379	+	0.0325702i
$396$	3107.70	−	5382.69i	0.394363	−	0.683056i
$397$	−3083.77	+	1780.41i	−0.389848	+	0.225079i	−0.682094	−	0.731264i	$-0.738931\pi$
$397$	−3083.77	+	1780.41i	−0.389848	+	0.225079i	0.292246	+	0.956343i	$0.405597\pi$
$398$		−	5682.89i		−	0.715723i
$399$		0			0
$400$	−200.195	−	529.219i	−0.0250243	−	0.0661524i
$401$	2715.30	+	4703.04i	0.338144	+	0.585683i	0.984084	−	0.177706i	$-0.0568675\pi$
$401$	2715.30	+	4703.04i	0.338144	+	0.585683i	−0.645940	+	0.763389i	$0.723534\pi$
$402$	1470.74	+	849.132i	0.182472	+	0.105350i
$403$	−1953.52	−	1127.86i	−0.241468	−	0.139412i
$404$	1570.14	+	2719.56i	0.193360	+	0.334909i
$405$	1676.96	−	2427.31i	0.205751	−	0.297812i
$406$		0			0
$407$		−	13320.5i		−	1.62229i
$408$	4391.98	−	2535.71i	0.532929	−	0.307687i
$409$	−4849.39	+	8399.40i	−0.586277	+	1.01546i	0.408438	+	0.912786i	$0.366073\pi$
$409$	−4849.39	+	8399.40i	−0.586277	+	1.01546i	−0.994715	+	0.102675i	$0.967260\pi$
$410$	2869.57	−	1360.14i	0.345653	−	0.163836i
$411$	964.780	+	1671.05i	0.115789	+	0.200552i
$412$			1563.17i			0.186922i
$413$		0			0
$414$	−5517.27			−0.654974
$415$	−340.268	+	4192.87i	−0.0402484	+	0.495952i
$416$	−4196.51	+	7268.56i	−0.494593	+	0.856660i
$417$	−6377.91	−	3682.29i	−0.748988	−	0.432428i
$418$	−10457.9	+	6037.87i	−1.22371	+	0.706511i
$419$	−13830.9			−1.61261			−0.806307	−	0.591498i	$-0.798537\pi$
$419$	−13830.9			−1.61261			−0.806307	+	0.591498i	$0.798537\pi$
$420$		0			0
$421$	16703.0			1.93362			0.966810	−	0.255498i	$-0.0822393\pi$
$421$	16703.0			1.93362			0.966810	+	0.255498i	$0.0822393\pi$
$422$	−4929.64	+	2846.13i	−0.568652	+	0.328311i
$423$	1206.33	+	696.475i	0.138661	+	0.0800562i
$424$	2968.79	−	5142.10i	0.340041	−	0.588968i
$425$	−8902.30	−	7281.05i	−1.01606	−	0.831019i
$426$	1381.94			0.157172
$427$		0			0
$428$			7851.31i			0.886699i
$429$	−3268.55	−	5661.30i	−0.367849	−	0.637133i
$430$	1182.63	+	2495.07i	0.132632	+	0.279821i
$431$	−4087.04	+	7078.95i	−0.456765	+	0.791140i	−0.998788	−	0.0492238i	$-0.984325\pi$
$431$	−4087.04	+	7078.95i	−0.456765	+	0.791140i	0.542023	+	0.840364i	$0.317659\pi$
$432$	467.127	−	269.696i	0.0520247	−	0.0300365i
$433$		−	14222.8i		−	1.57853i	−0.614051	−	0.789267i	$-0.710461\pi$
$433$		−	14222.8i		−	1.57853i	0.614051	−	0.789267i	$-0.289539\pi$
$434$		0			0
$435$	921.552	+	636.677i	0.101575	+	0.0701755i
$436$	−4588.98	−	7948.35i	−0.504065	−	0.873066i
$437$	−17182.0	−	9920.05i	−1.88084	−	1.08590i
$438$	1976.39	+	1141.07i	0.215606	+	0.124480i
$439$	2768.69	+	4795.52i	0.301008	+	0.521361i	0.976365	−	0.216130i	$-0.0693436\pi$
$439$	2768.69	+	4795.52i	0.301008	+	0.521361i	−0.675357	+	0.737491i	$0.736010\pi$
$440$	11707.9	+	8088.70i	1.26853	+	0.876394i
$441$		0			0
$442$			7015.07i			0.754916i
$443$	−3441.66	+	1987.04i	−0.369116	+	0.213109i	−0.673072	−	0.739577i	$-0.735026\pi$
$443$	−3441.66	+	1987.04i	−0.369116	+	0.213109i	0.303956	+	0.952686i	$0.401692\pi$
$444$	1498.09	−	2594.76i	0.160126	−	0.277347i
$445$	−4915.26	−	10370.0i	−0.523608	−	1.10469i
$446$	152.952	+	264.920i	0.0162387	+	0.0281263i
$447$		−	6269.82i		−	0.663428i
$448$		0			0
$449$	15243.1			1.60216			0.801078	−	0.598559i	$-0.204260\pi$
$449$	15243.1			1.60216			0.801078	+	0.598559i	$0.204260\pi$
$450$	3368.18	+	2754.79i	0.352839	+	0.288582i
$451$	4882.20	−	8456.22i	0.509742	−	0.882900i
$452$	4701.60	+	2714.47i	0.489259	+	0.282474i
$453$	218.257	−	126.010i	0.0226371	−	0.0130695i
$454$	−5280.67			−0.545890
$455$		0			0
$456$	−6899.89			−0.708590
$457$	−9326.11	+	5384.43i	−0.954611	+	0.551145i	−0.894510	−	0.447048i	$-0.852475\pi$
$457$	−9326.11	+	5384.43i	−0.954611	+	0.551145i	−0.0601005	+	0.998192i	$0.519142\pi$
$458$	−8722.32	−	5035.83i	−0.889884	−	0.513775i
$459$	5481.75	−	9494.67i	0.557443	−	0.965519i
$460$	−744.467	+	9173.53i	−0.0754586	+	0.929822i
$461$	−332.605			−0.0336029			−0.0168015	−	0.999859i	$-0.505348\pi$
$461$	−332.605			−0.0336029			−0.0168015	+	0.999859i	$0.505348\pi$
$462$		0			0
$463$			8205.35i			0.823618i	0.911270	+	0.411809i	$0.135103\pi$
$463$			8205.35i			0.823618i	−0.911270	+	0.411809i	$0.864897\pi$
$464$	−90.9176	−	157.474i	−0.00909643	−	0.0157555i
$465$	−1248.70	+	591.870i	−0.124532	+	0.0590265i
$466$	−787.879	+	1364.65i	−0.0783214	+	0.135657i
$467$	−145.170	+	83.8138i	−0.0143847	+	0.00830501i	−0.507175	−	0.861843i	$-0.669310\pi$
$467$	−145.170	+	83.8138i	−0.0143847	+	0.00830501i	0.492790	+	0.870148i	$0.335977\pi$
$468$			4912.47i			0.485212i
$469$		0			0
$470$	−713.612	+	1032.91i	−0.0700351	+	0.101372i
$471$	2915.87	+	5050.44i	0.285258	+	0.494081i
$472$	4609.90	+	2661.53i	0.449551	+	0.259548i
$473$	7352.62	+	4245.04i	0.714744	+	0.412657i
$474$	−52.8671	−	91.5685i	−0.00512293	−	0.00887317i
$475$	5536.18	+	14635.0i	0.534773	+	1.41368i
$476$		0			0
$477$		−	5582.52i		−	0.535862i
$478$	7484.07	−	4320.93i	0.716137	−	0.413462i
$479$	3314.29	−	5740.52i	0.316146	−	0.547581i	−0.663535	−	0.748146i	$-0.730944\pi$
$479$	3314.29	−	5740.52i	0.316146	−	0.547581i	0.979680	+	0.200565i	$0.0642778\pi$
$480$	2202.21	+	4646.12i	0.209409	+	0.441803i
$481$	5264.08	+	9117.66i	0.499005	+	0.864302i
$482$			777.001i			0.0734262i
$483$		0			0
$484$	10311.7			0.968419
$485$	−852.498	+	10504.7i	−0.0798143	+	0.983494i
$486$	−3246.02	+	5622.28i	−0.302968	+	0.524757i
$487$	17876.1	+	10320.8i	1.66334	+	0.960327i	0.971105	+	0.238651i	$0.0767052\pi$
$487$	17876.1	+	10320.8i	1.66334	+	0.960327i	0.692231	+	0.721676i	$0.256628\pi$
$488$	−1731.43	+	999.642i	−0.160611	+	0.0927288i
$489$	−3305.01			−0.305640
$490$		0			0
$491$	−16710.8			−1.53594			−0.767972	−	0.640484i	$-0.778734\pi$
$491$	−16710.8			−1.53594			−0.767972	+	0.640484i	$0.778734\pi$
$492$	1902.05	−	1098.15i	0.174291	−	0.100627i
$493$	−3200.76	−	1847.96i	−0.292404	−	0.168819i
$494$	4772.16	−	8265.63i	0.434635	−	0.752810i
$495$	13335.5	+	1082.23i	1.21088	+	0.0982679i
$496$	224.331			0.0203080
$497$		0			0
$498$		−	1571.91i		−	0.141444i
$499$	−6864.35	−	11889.4i	−0.615812	−	1.06662i	−0.990241	−	0.139363i	$-0.955495\pi$
$499$	−6864.35	−	11889.4i	−0.615812	−	1.06662i	0.374429	−	0.927256i	$-0.377839\pi$
$500$	5034.84	−	5228.54i	0.450330	−	0.467655i
$501$	2601.45	−	4505.84i	0.231984	−	0.401809i
$502$	−3322.54	+	1918.27i	−0.295403	+	0.170551i
$503$			19523.7i			1.73065i	0.501209	+	0.865326i	$0.332889\pi$
$503$			19523.7i			1.73065i	−0.501209	+	0.865326i	$0.667111\pi$
$504$		0			0
$505$	−3842.37	+	5561.60i	−0.338580	+	0.490075i
$506$	−7645.00	−	13241.5i	−0.671664	−	1.16336i
$507$	−270.624	−	156.245i	−0.0237058	−	0.0136866i
$508$	−1172.75	−	677.086i	−0.102426	−	0.0591355i
$509$	−4344.08	−	7524.17i	−0.378287	−	0.655212i	0.612526	−	0.790450i	$-0.290153\pi$
$509$	−4344.08	−	7524.17i	−0.378287	−	0.655212i	−0.990813	+	0.135238i	$0.956820\pi$
$510$	3535.72	+	2442.74i	0.306989	+	0.212091i
$511$		0			0
$512$		−	1635.04i		−	0.141131i
$513$	−12917.9	+	7458.17i	−1.11177	+	0.641883i
$514$	671.909	−	1163.78i	0.0576588	−	0.0998680i
$515$	−3040.64	+	1441.23i	−0.260169	+	0.123317i
$516$	954.832	+	1653.82i	0.0814615	+	0.141095i
$517$			3860.28i			0.328385i
$518$		0			0
$519$	4783.89			0.404604
$520$	−11210.4	−	909.766i	−0.945401	−	0.0767229i
$521$	−3385.68	+	5864.17i	−0.284701	+	0.493117i	−0.972537	−	0.232750i	$-0.925228\pi$
$521$	−3385.68	+	5864.17i	−0.284701	+	0.493117i	0.687835	+	0.725867i	$0.258561\pi$
$522$	1211.01	+	699.176i	0.101541	+	0.0586247i
$523$	1182.90	−	682.947i	0.0988998	−	0.0570998i	−0.449734	−	0.893162i	$-0.648481\pi$
$523$	1182.90	−	682.947i	0.0988998	−	0.0570998i	0.548634	+	0.836063i	$0.315148\pi$
$524$	−3757.85			−0.313287
$525$		0			0
$526$	480.735			0.0398499
$527$	3948.80	−	2279.84i	0.326400	−	0.188447i
$528$	563.014	+	325.057i	0.0464054	+	0.0267922i
$529$	6477.02	−	11218.5i	0.532344	−	0.922046i
$530$	5014.97	+	406.984i	0.411012	+	0.0333552i
$531$	5004.75			0.409016
$532$		0			0
$533$			7717.51i			0.627171i
$534$	2144.12	+	3713.72i	0.173755	+	0.300952i
$535$	−15272.2	+	7238.82i	−1.23416	+	0.584975i
$536$	4492.17	−	7780.67i	0.362000	−	0.627003i
$537$	−1358.63	+	784.408i	−0.109180	+	0.0630348i
$538$			5965.62i			0.478060i
$539$		0			0
$540$	5693.05	+	3933.18i	0.453685	+	0.313439i
$541$	11625.0	+	20135.2i	0.923844	+	1.60014i	0.793410	+	0.608687i	$0.208303\pi$
$541$	11625.0	+	20135.2i	0.923844	+	1.60014i	0.130433	+	0.991457i	$0.458363\pi$
$542$	2798.18	+	1615.53i	0.221757	+	0.128031i
$543$	6049.37	+	3492.61i	0.478091	+	0.276026i
$544$	−8482.74	−	14692.5i	−0.668556	−	1.15797i
$545$	11229.9	−	16254.7i	0.882638	−	1.27757i
$546$		0			0
$547$		−	11552.7i		−	0.903033i	−0.892263	−	0.451516i	$-0.850883\pi$
$547$		−	11552.7i		−	0.903033i	0.892263	−	0.451516i	$-0.149117\pi$
$548$	3480.06	−	2009.22i	0.271279	−	0.156623i
$549$	−939.865	+	1627.89i	−0.0730646	+	0.126552i
$550$	−1944.41	+	11900.9i	−0.150745	+	0.922644i
$551$	2514.23	+	4354.78i	0.194392	+	0.336697i
$552$		−	8736.48i		−	0.673640i
$553$		0			0
$554$	11037.1			0.846430
$555$	6428.48	+	521.696i	0.491665	+	0.0399005i
$556$	−7668.60	+	13282.4i	−0.584930	+	1.01313i
$557$	14208.2	+	8203.08i	1.08082	+	0.624014i	0.931119	−	0.364717i	$-0.118834\pi$
$557$	14208.2	+	8203.08i	1.08082	+	0.624014i	0.149706	+	0.988731i	$0.452167\pi$
$558$	−1494.03	+	862.578i	−0.113346	+	0.0654406i
$559$	−6710.31			−0.507721
$560$		0			0
$561$	13214.0			0.994465
$562$	−1183.15	+	683.091i	−0.0888044	+	0.0512712i
$563$	11805.6	+	6815.95i	0.883740	+	0.510227i	0.871890	−	0.489702i	$-0.162895\pi$
$563$	11805.6	+	6815.95i	0.883740	+	0.510227i	0.0118502	+	0.999930i	$0.496228\pi$
$564$	−434.145	+	751.961i	−0.0324127	+	0.0561405i
$565$	−945.292	+	11648.2i	−0.0703872	+	0.867330i
$566$	10911.2			0.810300
$567$		0			0
$568$		−	7310.88i		−	0.540067i
$569$	−1543.41	−	2673.27i	−0.113714	−	0.196958i	0.803551	−	0.595236i	$-0.202941\pi$
$569$	−1543.41	−	2673.27i	−0.113714	−	0.196958i	−0.917265	+	0.398278i	$0.869608\pi$
$570$	−2504.29	−	5283.45i	−0.184023	−	0.388245i
$571$	1629.03	−	2821.57i	0.119392	−	0.206793i	−0.800135	−	0.599820i	$-0.795239\pi$
$571$	1629.03	−	2821.57i	0.119392	−	0.206793i	0.919527	+	0.393027i	$0.128572\pi$
$572$	−11790.0	+	6806.96i	−0.861827	+	0.497576i
$573$			1846.17i			0.134598i
$574$		0			0
$575$	−18530.5	+	7009.78i	−1.34396	+	0.508396i
$576$	2833.19	+	4907.24i	0.204948	+	0.354980i
$577$	−20575.4	−	11879.2i	−1.48451	−	0.857083i	−0.484667	−	0.874699i	$-0.661059\pi$
$577$	−20575.4	−	11879.2i	−1.48451	−	0.857083i	−0.999845	+	0.0176156i	$0.994392\pi$
$578$	−5152.91	−	2975.03i	−0.370818	−	0.214092i
$579$	−5090.89	−	8817.68i	−0.365406	−	0.632902i
$580$	1325.92	−	1919.19i	0.0949238	−	0.137397i
$581$		0			0
$582$		−	3938.23i		−	0.280490i
$583$	13398.1	−	7735.42i	0.951791	−	0.549517i
$584$	6036.61	−	10455.7i	0.427734	−	0.740857i
$585$	−9555.62	+	4529.25i	−0.675344	+	0.320105i
$586$	364.783	+	631.823i	0.0257151	+	0.0445398i
$587$			596.893i			0.0419701i	0.999780	+	0.0209850i	$0.00668023\pi$
$587$			596.893i			0.0419701i	−0.999780	+	0.0209850i	$0.993320\pi$
$588$		0			0
$589$	−6203.66			−0.433985
$590$	−364.862	+	4495.93i	−0.0254596	+	0.313720i
$591$	4258.30	−	7375.59i	0.296384	−	0.513353i
$592$	−906.749	−	523.512i	−0.0629513	−	0.0363449i
$593$	−16884.3	+	9748.16i	−1.16923	+	0.675058i	−0.953500	−	0.301394i	$-0.902548\pi$
$593$	−16884.3	+	9748.16i	−1.16923	+	0.675058i	−0.215734	+	0.976452i	$0.569215\pi$
$594$	−11495.5			−0.794047
$595$		0			0
$596$	−13057.3			−0.897396
$597$	7327.11	−	4230.31i	0.502310	−	0.290009i
$598$	10465.7	+	6042.40i	0.715679	+	0.413197i
$599$	1898.51	−	3288.31i	0.129501	−	0.224302i	−0.793983	−	0.607941i	$-0.791996\pi$
$599$	1898.51	−	3288.31i	0.129501	−	0.224302i	0.923483	+	0.383639i	$0.125329\pi$
$600$	−4362.14	+	5333.44i	−0.296806	+	0.362895i
$601$	5789.33			0.392931			0.196466	−	0.980511i	$-0.437054\pi$
$601$	5789.33			0.392931			0.196466	+	0.980511i	$0.437054\pi$
$602$		0			0
$603$		−	8447.09i		−	0.570468i
$604$	−262.425	−	454.533i	−0.0176787	−	0.0306203i
$605$	9507.30	+	20058.1i	0.638887	+	1.34790i
$606$	1262.98	−	2187.55i	0.0846618	−	0.146639i
$607$	16053.0	−	9268.21i	1.07343	−	0.619745i	0.144313	−	0.989532i	$-0.453903\pi$
$607$	16053.0	−	9268.21i	1.07343	−	0.619745i	0.929116	+	0.369787i	$0.120569\pi$
$608$			23082.3i			1.53966i
$609$		0			0
$610$	−1393.87	−	962.991i	−0.0925184	−	0.0639186i
$611$	−1525.53	−	2642.29i	−0.101009	−	0.174952i
$612$	−8599.62	−	4964.99i	−0.568005	−	0.327938i
$613$	1873.62	+	1081.74i	0.123450	+	0.0712738i	0.560453	−	0.828186i	$-0.310627\pi$
$613$	1873.62	+	1081.74i	0.123450	+	0.0712738i	−0.437003	+	0.899460i	$0.643960\pi$
$614$	4117.54	+	7131.79i	0.270636	+	0.468755i
$615$	3889.76	+	2687.34i	0.255041	+	0.176201i
$616$		0			0
$617$			22964.9i			1.49843i	0.662327	+	0.749215i	$0.269569\pi$
$617$			22964.9i			1.49843i	−0.662327	+	0.749215i	$0.730431\pi$
$618$	1088.92	−	628.689i	0.0708784	−	0.0409216i
$619$	−693.333	+	1200.89i	−0.0450200	+	0.0779770i	−0.887657	−	0.460505i	$-0.847668\pi$
$619$	−693.333	+	1200.89i	−0.0450200	+	0.0779770i	0.842637	+	0.538482i	$0.181002\pi$
$620$	1232.61	+	2600.50i	0.0798431	+	0.168450i
$621$	−9443.35	−	16356.4i	−0.610223	−	1.05694i
$622$			3067.41i			0.197736i
$623$		0			0
$624$	−513.831			−0.0329643
$625$	14812.5	+	4972.99i	0.948000	+	0.318271i
$626$	−2046.17	+	3544.08i	−0.130642	+	0.226278i
$627$	−15569.6	−	8989.11i	−0.991690	−	0.572552i
$628$	10517.9	−	6072.49i	0.668326	−	0.385858i
$629$	−21281.4			−1.34904
$630$		0			0
$631$	5969.39			0.376605			0.188303	−	0.982111i	$-0.439701\pi$
$631$	5969.39			0.376605			0.188303	+	0.982111i	$0.439701\pi$
$632$	−484.426	+	279.683i	−0.0304896	+	0.0176032i
$633$	−7339.19	−	4237.28i	−0.460832	−	0.266062i
$634$	−1395.57	+	2417.20i	−0.0874215	+	0.151418i
$635$	235.789	−	2905.46i	0.0147355	−	0.181574i
$636$	3479.84			0.216957
$637$		0			0
$638$			3875.25i			0.240474i
$639$	−3436.85	−	5952.80i	−0.212770	−	0.368528i
$640$	10288.7	−	4876.72i	0.635463	−	0.301202i
$641$	−15183.6	+	26298.7i	−0.935592	+	1.62049i	−0.162016	+	0.986788i	$0.551800\pi$
$641$	−15183.6	+	26298.7i	−0.935592	+	1.62049i	−0.773576	+	0.633704i	$0.781534\pi$
$642$	5469.29	−	3157.70i	0.336224	−	0.194119i
$643$		−	28592.2i		−	1.75360i	−0.480851	−	0.876802i	$-0.659672\pi$
$643$		−	28592.2i		−	1.75360i	0.480851	−	0.876802i	$-0.340328\pi$
$644$		0			0
$645$	−2336.62	+	3382.12i	−0.142642	+	0.206466i
$646$	9646.36	+	16708.0i	0.587509	+	1.01760i
$647$	12564.3	+	7253.97i	0.763449	+	0.440778i	0.830533	−	0.556970i	$-0.188036\pi$
$647$	12564.3	+	7253.97i	0.763449	+	0.440778i	−0.0670835	+	0.997747i	$0.521369\pi$
$648$	5050.84	+	2916.10i	0.306197	+	0.176783i
$649$	6934.83	+	12011.5i	0.419439	+	0.726489i
$650$	−3372.14	−	8914.33i	−0.203487	−	0.537921i
$651$		0			0
$652$			6882.89i			0.413428i
$653$	−6062.05	+	3499.93i	−0.363287	+	0.209744i	−0.670522	−	0.741890i	$-0.733930\pi$
$653$	−6062.05	+	3499.93i	−0.363287	+	0.209744i	0.307235	+	0.951634i	$0.400596\pi$
$654$	−3691.26	+	6393.46i	−0.220703	+	0.382269i
$655$	−3464.70	−	7309.68i	−0.206682	−	0.436050i
$656$	−383.752	−	664.678i	−0.0228399	−	0.0395599i
$657$		−	11351.3i		−	0.674056i
$658$		0			0
$659$	−7308.92			−0.432041			−0.216020	−	0.976389i	$-0.569308\pi$
$659$	−7308.92			−0.432041			−0.216020	+	0.976389i	$0.569308\pi$
$660$	−674.603	+	8312.64i	−0.0397862	+	0.490256i
$661$	15048.6	−	26065.0i	0.885512	−	1.53375i	0.0403854	−	0.999184i	$-0.487141\pi$
$661$	15048.6	−	26065.0i	0.885512	−	1.53375i	0.845126	−	0.534567i	$-0.179525\pi$
$662$	−7930.26	−	4578.54i	−0.465586	−	0.268806i
$663$	−9044.73	+	5221.98i	−0.529816	+	0.305890i
$664$	−8315.91			−0.486024
$665$		0			0
$666$	8051.83			0.468472
$667$	−5513.92	+	3183.46i	−0.320090	+	0.184804i
$668$	−9383.70	−	5417.68i	−0.543512	−	0.313797i
$669$	−227.713	+	394.410i	−0.0131598	+	0.0227934i
$670$	7588.31	+	615.820i	0.437555	+	0.0355093i
$671$	−5209.29			−0.299706
$672$		0			0
$673$			5400.26i			0.309309i	0.987969	+	0.154654i	$0.0494264\pi$
$673$			5400.26i			0.309309i	−0.987969	+	0.154654i	$0.950574\pi$
$674$	−8920.64	−	15451.0i	−0.509808	−	0.883013i
$675$	−2401.79	+	14700.3i	−0.136956	+	0.838245i
$676$	−325.390	+	563.593i	−0.0185133	+	0.0320660i
$677$	5569.49	−	3215.55i	0.316178	−	0.182546i	−0.333509	−	0.942747i	$-0.608233\pi$
$677$	5569.49	−	3215.55i	0.316178	−	0.182546i	0.649688	+	0.760201i	$0.274900\pi$
$678$		−	4366.91i		−	0.247360i
$679$		0			0
$680$	12922.9	−	18705.1i	0.728778	−	1.05486i
$681$	−3930.90	−	6808.51i	−0.221193	−	0.383117i
$682$	−4140.40	−	2390.46i	−0.232469	−	0.134216i
$683$	−18070.3	−	10432.9i	−1.01236	−	0.584486i	−0.100477	−	0.994939i	$-0.532037\pi$
$683$	−18070.3	−	10432.9i	−1.01236	−	0.584486i	−0.911881	+	0.410454i	$0.865370\pi$
$684$	6755.10	+	11700.2i	0.377613	+	0.654046i
$685$	7116.86	+	4916.86i	0.396965	+	0.274253i
$686$		0			0
$687$		−	14994.6i		−	0.832720i
$688$	577.933	−	333.669i	0.0320254	−	0.0184899i
$689$	−6113.86	+	10589.5i	−0.338054	+	0.585527i
$690$	6689.78	−	3170.88i	0.369095	−	0.174947i
$691$	−9225.13	−	15978.4i	−0.507873	−	0.879662i	−0.999958	−	0.00911505i	$-0.997099\pi$
$691$	−9225.13	−	15978.4i	−0.507873	−	0.879662i	0.492085	−	0.870547i	$-0.336235\pi$
$692$		−	9962.76i		−	0.547294i
$693$		0			0
$694$	6732.70			0.368256
$695$	−32907.0	−	2670.53i	−1.79602	−	0.145754i
$696$	−1107.13	+	1917.60i	−0.0602954	+	0.104435i
$697$	−13510.0	−	7800.01i	−0.734187	−	0.423883i
$698$	15297.8	−	8832.20i	0.829557	−	0.478945i
$699$	−2345.97			−0.126942
$700$		0			0
$701$	12639.3			0.680996			0.340498	−	0.940245i	$-0.389404\pi$
$701$	12639.3			0.680996			0.340498	+	0.940245i	$0.389404\pi$
$702$	7868.43	−	4542.84i	0.423041	−	0.244243i
$703$	25075.2	+	14477.2i	1.34528	+	0.776696i
$704$	−7851.63	+	13599.4i	−0.420340	+	0.728050i
$705$	−1862.97	−	151.187i	−0.0995228	−	0.00807665i
$706$	−4958.45			−0.264325
$707$		0			0
$708$			3119.69i			0.165600i
$709$	−11563.4	−	20028.4i	−0.612514	−	1.06091i	−0.990815	−	0.135223i	$-0.956825\pi$
$709$	−11563.4	−	20028.4i	−0.612514	−	1.06091i	0.378301	−	0.925683i	$-0.376508\pi$
$710$	5598.16	−	2653.46i	0.295909	−	0.140257i
$711$	−262.959	+	455.458i	−0.0138702	+	0.0240239i
$712$	19646.8	−	11343.1i	1.03412	−	0.597050i
$713$		−	7854.92i		−	0.412579i
$714$		0			0
$715$	−24111.0	−	16657.7i	−1.26112	−	0.871275i
$716$	1633.58	+	2829.44i	0.0852650	+	0.147683i
$717$	11142.2	+	6432.95i	0.580353	+	0.335067i
$718$	−3148.34	−	1817.69i	−0.163642	−	0.0944787i
$719$	−12046.6	−	20865.2i	−0.624841	−	1.08226i	−0.988572	−	0.150752i	$-0.951831\pi$
$719$	−12046.6	−	20865.2i	−0.624841	−	1.08226i	0.363731	−	0.931504i	$-0.381503\pi$
$720$	597.771	−	865.238i	0.0309411	−	0.0447854i
$721$		0			0
$722$		−	14758.7i		−	0.760750i
$723$	−1001.81	+	578.395i	−0.0515321	+	0.0297521i
$724$	7273.58	−	12598.2i	0.373371	−	0.646697i
$725$	4955.64	+	809.671i	0.253859	+	0.0414765i
$726$	−4147.25	−	7183.24i	−0.212009	−	0.367211i
$727$			35983.4i			1.83570i	0.396931	+	0.917849i	$0.370075\pi$
$727$			35983.4i			1.83570i	−0.396931	+	0.917849i	$0.629925\pi$
$728$		0			0
$729$	−2540.55			−0.129073
$730$	10197.2	+	827.543i	0.517008	+	0.0419572i
$731$	6782.05	−	11746.9i	0.343151	−	0.594355i
$732$	−1014.74	−	585.861i	−0.0512375	−	0.0295820i
$733$	1257.04	−	725.752i	0.0633422	−	0.0365706i	−0.467994	−	0.883731i	$-0.655023\pi$
$733$	1257.04	−	725.752i	0.0633422	−	0.0365706i	0.531337	+	0.847161i	$0.321690\pi$
$734$	−2097.64			−0.105484
$735$		0			0
$736$	−29226.3			−1.46371
$737$	20273.1	−	11704.7i	1.01326	−	0.585005i
$738$	5111.52	+	2951.14i	0.254956	+	0.147199i
$739$	−2945.83	+	5102.33i	−0.146636	+	0.253982i	−0.929982	−	0.367604i	$-0.880178\pi$
$739$	−2945.83	+	5102.33i	−0.146636	+	0.253982i	0.783346	+	0.621586i	$0.213511\pi$
$740$	1086.46	−	13387.7i	0.0539719	−	0.665057i
$741$	14209.5			0.704451
$742$		0			0
$743$		−	7438.65i		−	0.367292i	−0.982992	−	0.183646i	$-0.941210\pi$
$743$		−	7438.65i		−	0.367292i	0.982992	−	0.183646i	$-0.0587900\pi$
$744$	−1365.87	−	2365.76i	−0.0673056	−	0.116577i
$745$	−12038.7	−	25398.7i	−0.592032	−	1.24904i
$746$	3891.42	−	6740.13i	0.190985	−	0.330796i
$747$	−6771.14	+	3909.32i	−0.331651	+	0.191479i
$748$		−	27518.9i		−	1.34518i
$749$		0			0
$750$	−5667.20	−	1404.47i	−0.275916	−	0.0683784i
$751$	−10136.2	−	17556.4i	−0.492509	−	0.853051i	0.507454	−	0.861679i	$-0.330587\pi$
$751$	−10136.2	−	17556.4i	−0.492509	−	0.853051i	−0.999963	+	0.00862831i	$0.997253\pi$
$752$	262.775	+	151.713i	0.0127426	+	0.00735694i
$753$	−4946.56	−	2855.90i	−0.239393	−	0.138213i
$754$	−1531.44	−	2652.54i	−0.0739680	−	0.128116i
$755$	642.193	−	929.537i	0.0309560	−	0.0448070i
$756$		0			0
$757$		−	10193.8i		−	0.489432i	−0.969595	−	0.244716i	$-0.921305\pi$
$757$		−	10193.8i		−	0.489432i	0.969595	−	0.244716i	$-0.0786947\pi$
$758$	2081.57	−	1201.79i	0.0997439	−	0.0575872i
$759$	11381.8	−	19713.8i	0.544312	−	0.942776i
$760$	−27951.1	+	13248.5i	−1.33407	+	0.632333i
$761$	20558.8	+	35608.9i	0.979311	+	1.69622i	0.664906	+	0.746927i	$0.268472\pi$
$761$	20558.8	+	35608.9i	0.979311	+	1.69622i	0.314405	+	0.949289i	$0.398195\pi$
$762$			1089.26i			0.0517845i
$763$		0			0
$764$	3844.76			0.182066
$765$	1729.02	−	21305.4i	0.0817160	−	1.00693i
$766$	−11070.1	+	19173.9i	−0.522165	+	0.904416i
$767$	−9493.53	−	5481.09i	−0.446925	−	0.258032i
$768$	−8396.20	+	4847.55i	−0.394495	+	0.227762i
$769$	−11486.6			−0.538642			−0.269321	−	0.963050i	$-0.586799\pi$
$769$	−11486.6			−0.538642			−0.269321	+	0.963050i	$0.586799\pi$
$770$		0			0
$771$	2000.66			0.0934527
$772$	−18363.4	+	10602.1i	−0.856104	+	0.494272i
$773$	−18878.7	−	10899.6i	−0.878420	−	0.507156i	−0.00828254	−	0.999966i	$-0.502636\pi$
$773$	−18878.7	−	10899.6i	−0.878420	−	0.507156i	−0.870137	+	0.492810i	$0.835970\pi$
$774$	−2565.99	+	4444.42i	−0.119164	+	0.206397i
$775$	−3921.98	+	4795.27i	−0.181783	+	0.222260i
$776$	−20834.5			−0.963807
$777$		0			0
$778$		−	12990.9i		−	0.598645i
$779$	10612.3	+	18381.0i	0.488092	+	0.845401i
$780$	−2823.29	−	5956.45i	−0.129602	−	0.273430i
$781$	9524.54	−	16497.0i	0.436383	−	0.755837i
$782$	−21155.3	+	12214.0i	−0.967404	+	0.558531i
$783$			4786.83i			0.218477i
$784$		0			0
$785$	21509.4	+	14860.3i	0.977967	+	0.675652i
$786$	1511.36	+	2617.75i	0.0685858	+	0.118794i
$787$	20854.1	+	12040.1i	0.944560	+	0.545342i	0.891387	−	0.453243i	$-0.149733\pi$
$787$	20854.1	+	12040.1i	0.944560	+	0.545342i	0.0531734	+	0.998585i	$0.483066\pi$
$788$	−15360.1	−	8868.18i	−0.694394	−	0.400908i
$789$	357.856	+	619.825i	0.0161470	+	0.0279675i
$790$	−389.983	−	269.429i	−0.0175632	−	0.0121340i
$791$		0			0
$792$			26449.0i			1.18665i
$793$	3565.67	−	2058.64i	0.159673	−	0.0921872i
$794$	2982.48	−	5165.81i	0.133305	−	0.230891i
$795$	3208.38	+	6768.90i	0.143131	+	0.301972i
$796$	−8809.89	−	15259.2i	−0.392284	−	0.679456i
$797$		−	17194.3i		−	0.764184i	−0.924124	−	0.382092i	$-0.875204\pi$
$797$		−	17194.3i		−	0.764184i	0.924124	−	0.382092i	$-0.124796\pi$
$798$		0			0
$799$	6167.35			0.273073
$800$	17842.0	+	14592.7i	0.788514	+	0.644914i
$801$	10664.8	−	18471.9i	0.470438	−	0.814823i
$802$	−7878.36	−	4548.57i	−0.346876	−	0.200269i
$803$	27243.2	−	15728.9i	1.19725	−	0.691232i
$804$	5265.46			0.230968
$805$		0			0
$806$	3778.71			0.165136
$807$	−7691.65	+	4440.78i	−0.335513	+	0.193708i
$808$	−11572.8	−	6681.56i	−0.503873	−	0.290911i
$809$	16674.6	−	28881.2i	0.724656	−	1.25514i	−0.234460	−	0.972126i	$-0.575332\pi$
$809$	16674.6	−	28881.2i	0.724656	−	1.25514i	0.959115	−	0.283015i	$-0.0913346\pi$
$810$	−399.761	+	4925.97i	−0.0173410	+	0.213680i
$811$	4577.87			0.198213			0.0991066	−	0.995077i	$-0.468402\pi$
$811$	4577.87			0.198213			0.0991066	+	0.995077i	$0.468402\pi$
$812$		0			0
$813$			4810.37i			0.207512i
$814$	11157.0	+	19324.5i	0.480409	+	0.832093i
$815$	−13388.4	+	6345.95i	−0.575431	+	0.272747i
$816$	519.324	−	899.496i	0.0222794	−	0.0385891i
$817$	−15982.1	+	9227.29i	−0.684387	+	0.395131i
$818$		−	16247.0i		−	0.694455i
$819$		0			0
$820$	5596.55	−	8100.67i	0.238341	−	0.344985i
$821$	2916.26	+	5051.11i	0.123969	+	0.214720i	0.921329	−	0.388783i	$-0.127104\pi$
$821$	2916.26	+	5051.11i	0.123969	+	0.214720i	−0.797361	+	0.603503i	$0.793771\pi$
$822$	−2799.28	−	1616.16i	−0.118779	−	0.0685769i
$823$	32886.7	+	18987.1i	1.39290	+	0.804192i	0.993636	−	0.112642i	$-0.0359314\pi$
$823$	32886.7	+	18987.1i	1.39290	+	0.804192i	0.399267	+	0.916835i	$0.369265\pi$
$824$	−3325.96	−	5760.73i	−0.140613	−	0.243549i
$825$	−16791.5	+	6351.95i	−0.708613	+	0.268056i
$826$		0			0
$827$			15796.2i			0.664193i	0.943245	+	0.332096i	$0.107756\pi$
$827$			15796.2i			0.664193i	−0.943245	+	0.332096i	$0.892244\pi$
$828$	−14814.5	+	8553.14i	−0.621786	+	0.358988i
$829$	−6357.07	+	11010.8i	−0.266333	+	0.461302i	−0.967912	−	0.251289i	$-0.919145\pi$
$829$	−6357.07	+	11010.8i	−0.266333	+	0.461302i	0.701579	+	0.712592i	$0.252479\pi$
$830$	−3018.23	−	6367.74i	−0.126222	−	0.266298i
$831$	8215.97	+	14230.5i	0.342971	+	0.594043i
$832$		−	12411.4i		−	0.517173i
$833$		0			0
$834$	12336.9			0.512219
$835$	1886.66	−	23248.0i	0.0781923	−	0.963508i
$836$	−18720.4	+	32424.7i	−0.774471	+	1.34142i
$837$	−5114.36	−	2952.77i	−0.211204	−	0.121939i
$838$	20065.0	−	11584.5i	0.827128	−	0.477543i
$839$	42924.2			1.76628			0.883140	−	0.469109i	$-0.155425\pi$
$839$	42924.2			1.76628			0.883140	+	0.469109i	$0.155425\pi$
$840$		0			0
$841$	−22775.3			−0.933835
$842$	−24231.6	+	13990.1i	−0.991776	+	0.572602i
$843$	−1761.46	−	1016.98i	−0.0719665	−	0.0415499i
$844$	−8824.41	+	15284.3i	−0.359892	+	0.623351i
$845$	−1396.29	−	113.314i	−0.0568449	−	0.00461318i
$846$	−2333.42			−0.0948281
$847$		0			0
$848$		−	1216.04i		−	0.0492442i
$849$	8122.20	+	14068.1i	0.328331	+	0.568686i
$850$	19013.3	+	3106.47i	0.767237	+	0.125354i
$851$	−18330.7	+	31749.6i	−0.738386	+	1.27892i
$852$	3710.65	−	2142.35i	0.149208	−	0.0861450i
$853$			36172.5i			1.45196i	0.687716	+	0.725980i	$0.258613\pi$
$853$			36172.5i			1.45196i	−0.687716	+	0.725980i	$0.741387\pi$
$854$		0			0
$855$	−16530.7	+	23927.3i	−0.661216	+	0.957071i
$856$	−16705.2	−	28934.3i	−0.667024	−	1.15532i
$857$	27747.4	+	16020.0i	1.10599	+	0.638544i	0.937788	−	0.347209i	$-0.112871\pi$
$857$	27747.4	+	16020.0i	1.10599	+	0.638544i	0.168202	+	0.985753i	$0.446204\pi$
$858$	9483.59	+	5475.35i	0.377348	+	0.217862i
$859$	−3399.03	−	5887.30i	−0.135010	−	0.233844i	0.790591	−	0.612344i	$-0.209773\pi$
$859$	−3399.03	−	5887.30i	−0.135010	−	0.233844i	−0.925601	+	0.378500i	$0.876440\pi$
$860$	7043.47	+	4866.15i	0.279280	+	0.192947i
$861$		0			0
$862$		−	13692.9i		−	0.541046i
$863$	26136.0	−	15089.7i	1.03092	−	0.595200i	0.113670	−	0.993519i	$-0.463739\pi$
$863$	26136.0	−	15089.7i	1.03092	−	0.595200i	0.917247	+	0.398318i	$0.130406\pi$
$864$	−10986.6	+	19029.3i	−0.432604	+	0.749293i
$865$	19379.3	−	9185.56i	0.761753	−	0.361062i
$866$	11912.8	+	20633.5i	0.467450	+	0.809648i
$867$		−	8858.39i		−	0.346997i
$868$		0			0
$869$	−1457.47			−0.0568946
$870$	−1870.19	−	151.773i	−0.0728799	−	0.00591448i
$871$	−9251.07	+	16023.3i	−0.359886	+	0.623341i
$872$	33823.4	+	19527.9i	1.31354	+	0.758371i
$873$	−16964.2	+	9794.31i	−0.657678	+	0.379710i
$874$	33235.4			1.28627
$875$		0			0
$876$	7075.76			0.272908
$877$	−1472.69	+	850.256i	−0.0567037	+	0.0327379i	−0.528084	−	0.849192i	$-0.677089\pi$
$877$	−1472.69	+	850.256i	−0.0567037	+	0.0327379i	0.471380	+	0.881930i	$0.343756\pi$
$878$	−8033.27	−	4638.01i	−0.308781	−	0.178275i
$879$	−543.084	+	940.650i	−0.0208393	+	0.0360948i
$880$	2904.88	+	235.742i	0.111277	+	0.00903054i
$881$	1678.46			0.0641869			0.0320935	−	0.999485i	$-0.489783\pi$
$881$	1678.46			0.0641869			0.0320935	+	0.999485i	$0.489783\pi$
$882$		0			0
$883$		−	10285.8i		−	0.392009i	−0.980603	−	0.196005i	$-0.937203\pi$
$883$		−	10285.8i		−	0.392009i	0.980603	−	0.196005i	$-0.0627968\pi$
$884$	10875.1	+	18836.2i	0.413766	+	0.716664i
$885$	−6068.34	+	2876.32i	−0.230491	+	0.109250i
$886$	3328.62	−	5765.34i	0.126216	−	0.218612i
$887$	−10537.4	+	6083.77i	−0.398885	+	0.230296i	−0.686003	−	0.727599i	$-0.740636\pi$
$887$	−10537.4	+	6083.77i	−0.398885	+	0.230296i	0.287118	+	0.957895i	$0.407303\pi$
$888$			12749.9i			0.481823i
$889$		0			0
$890$	15816.4	+	10927.2i	0.595695	+	0.411550i
$891$	7598.14	+	13160.4i	0.285687	+	0.494824i
$892$	821.383	+	474.226i	0.0308318	+	0.0178007i
$893$	−7266.78	−	4195.48i	−0.272311	−	0.157219i
$894$	5251.49	+	9095.84i	0.196461	+	0.340280i
$895$	−3997.62	+	5786.31i	−0.149302	+	0.216106i
$896$		0			0
$897$			17991.7i			0.669705i
$898$	−22113.7	+	12767.4i	−0.821765	+	0.474446i
$899$	−995.414	+	1724.11i	−0.0369287	+	0.0639624i
$900$	13314.5	+	2175.38i	0.493131	+	0.0805696i
$901$	−12358.4	−	21405.4i	−0.456958	−	0.791475i
$902$			16356.9i			0.603799i
$903$		0			0
$904$	−23102.3			−0.849968
$905$	31211.9	+	2532.96i	1.14643	+	0.0930370i
$906$	−211.088	+	365.615i	−0.00774054	+	0.0134070i
$907$	43964.7	+	25383.0i	1.60951	+	0.929250i	0.989480	+	0.144670i	$0.0462120\pi$
$907$	43964.7	+	25383.0i	1.60951	+	0.929250i	0.620028	+	0.784580i	$0.287121\pi$
$908$	−14179.2	+	8186.34i	−0.518229	+	0.299200i
$909$	−12564.0			−0.458441
$910$		0			0
$911$	18451.1			0.671033			0.335517	−	0.942034i	$-0.391089\pi$
$911$	18451.1			0.671033			0.335517	+	0.942034i	$0.391089\pi$
$912$	−1223.81	+	706.564i	−0.0444345	+	0.0256543i
$913$	−18764.8	−	10833.9i	−0.680203	−	0.392715i
$914$	9019.80	−	15622.7i	0.326421	−	0.565377i
$915$	204.021	−	2514.00i	0.00737129	−	0.0908310i
$916$	−31227.1			−1.12639
$917$		0			0
$918$			18365.6i			0.660301i
$919$	196.930	+	341.093i	0.00706870	+	0.0122433i	0.869538	−	0.493866i	$-0.164417\pi$
$919$	196.930	+	341.093i	0.00706870	+	0.0122433i	−0.862469	+	0.506109i	$0.831083\pi$
$920$	−16774.9	−	35391.0i	−0.601144	−	1.26827i
$921$	−6130.15	+	10617.7i	−0.219322	+	0.379876i
$922$	482.520	−	278.583i	0.0172353	−	0.00995081i
$923$			15055.9i			0.536912i
$924$		0			0
$925$	27043.2	−	10230.0i	0.961269	−	0.363632i
$926$	−6872.64	−	11903.8i	−0.243898	−	0.422443i
$927$	−5416.25	−	3127.07i	−0.191902	−	0.110795i
$928$	6414.98	+	3703.69i	0.226920	+	0.131013i
$929$	13726.2	+	23774.4i	0.484759	+	0.839627i	0.999847	−	0.0175107i	$-0.00557410\pi$
$929$	13726.2	+	23774.4i	0.484759	+	0.839627i	−0.515088	+	0.857137i	$0.672241\pi$
$930$	1315.79	−	1904.54i	0.0463942	−	0.0671529i
$931$		0			0
$932$			4885.63i			0.171710i
$933$	−3954.90	+	2283.36i	−0.138775	+	0.0801221i
$934$	140.402	−	243.183i	0.00491872	−	0.00851947i
$935$	53529.1	−	25372.2i	1.87229	−	0.887443i
$936$	−10452.3	−	18103.8i	−0.365003	−	0.632204i
$937$			21608.3i			0.753375i	0.926340	+	0.376688i	$0.122937\pi$
$937$			21608.3i			0.753375i	−0.926340	+	0.376688i	$0.877063\pi$
$938$		0			0
$939$	−6092.64			−0.211742
$940$	−314.857	+	3879.75i	−0.0109250	+	0.134621i
$941$	8354.24	−	14470.0i	0.289416	−	0.501283i	−0.684255	−	0.729243i	$-0.739872\pi$
$941$	8354.24	−	14470.0i	0.289416	−	0.501283i	0.973670	+	0.227960i	$0.0732056\pi$
$942$	−8460.31	−	4884.56i	−0.292624	−	0.168947i
$943$	−23273.6	+	13437.0i	−0.803703	+	0.464018i
$944$	1090.19			0.0375874
$945$		0			0
$946$	−14222.2			−0.488800
$947$	12100.8	−	6986.39i	0.415230	−	0.239733i	−0.277805	−	0.960638i	$-0.589607\pi$
$947$	12100.8	−	6986.39i	0.415230	−	0.239733i	0.693034	+	0.720905i	$0.256273\pi$
$948$	−283.908	−	163.914i	−0.00972668	−	0.00561570i
$949$	−12431.7	+	21532.3i	−0.425236	+	0.736530i
$950$	−20289.5	−	16594.5i	−0.692925	−	0.566733i
$951$	−4155.42			−0.141692
$952$		0			0
$953$			11155.9i			0.379197i	0.981862	+	0.189598i	$0.0607186\pi$
$953$			11155.9i			0.379197i	−0.981862	+	0.189598i	$0.939281\pi$
$954$	4675.82	+	8098.75i	0.158685	+	0.274850i
$955$	3544.83	+	7478.73i	0.120113	+	0.253409i
$956$	13397.0	−	23204.3i	0.453233	−	0.785022i
$957$	−4996.47	+	2884.71i	−0.168770	+	0.0974394i
$958$			11104.0i			0.374481i
$959$		0			0
$960$	−6255.57	−	4321.81i	−0.210310	−	0.145298i
$961$	13667.5	+	23672.7i	0.458778	+	0.794627i
$962$	−15273.6	−	8818.19i	−0.511891	−	0.295540i
$963$	−27204.1	−	15706.3i	−0.910320	−	0.525574i
$964$	1204.54	+	2086.33i	0.0402445	+	0.0697056i
$965$	−37553.8	−	25944.9i	−1.25274	−	0.865489i
$966$		0			0
$967$		−	1212.55i		−	0.0403238i	−0.999797	−	0.0201619i	$-0.993582\pi$
$967$		−	1212.55i		−	0.0403238i	0.999797	−	0.0201619i	$-0.00641816\pi$
$968$	−38001.6	+	21940.2i	−1.26179	+	0.728497i
$969$	−14361.4	+	24874.7i	−0.476114	+	0.824653i
$970$	−7561.81	−	15953.6i	−0.250304	−	0.528081i
$971$	24416.1	+	42290.0i	0.806952	+	1.39768i	0.914965	+	0.403533i	$0.132218\pi$
$971$	24416.1	+	42290.0i	0.806952	+	1.39768i	−0.108013	+	0.994149i	$0.534449\pi$
$972$			20128.6i			0.664222i
$973$		0			0
$974$	−34578.0			−1.13753
$975$	8983.29	−	10983.6i	0.295072	−	0.360775i
$976$	−204.731	+	354.605i	−0.00671443	+	0.0116297i
$977$	−5143.49	−	2969.60i	−0.168429	−	0.0972424i	0.413416	−	0.910542i	$-0.364336\pi$
$977$	−5143.49	−	2969.60i	−0.168429	−	0.0972424i	−0.581845	+	0.813300i	$0.697669\pi$
$978$	4794.69	−	2768.21i	0.156766	−	0.0905089i
$979$	59110.5			1.92970
$980$		0			0
$981$	36720.4			1.19510
$982$	24242.9	−	13996.7i	0.787803	−	0.454838i
$983$	−18934.4	−	10931.8i	−0.614357	−	0.354699i	0.160312	−	0.987066i	$-0.448750\pi$
$983$	−18934.4	−	10931.8i	−0.614357	−	0.354699i	−0.774669	+	0.632367i	$0.782083\pi$
$984$	−4673.06	+	8093.97i	−0.151394	+	0.262222i
$985$	3088.27	−	38054.5i	0.0998989	−	1.23098i
$986$	6191.26			0.199970
$987$		0			0
$988$		−	29592.1i		−	0.952886i
$989$	−11683.4	−	20236.2i	−0.375642	−	0.650630i
$990$	−20252.8	+	9599.56i	−0.650177	+	0.308176i
$991$	22309.2	−	38640.7i	0.715113	−	1.23861i	−0.247804	−	0.968810i	$-0.579709\pi$
$991$	22309.2	−	38640.7i	0.715113	−	1.23861i	0.962916	−	0.269801i	$-0.0869579\pi$
$992$	−7914.21	+	4569.27i	−0.253303	+	0.146245i
$993$		−	13632.9i		−	0.435678i
$994$		0			0
$995$	21559.1	−	31205.6i	0.686905	−	0.994255i
$996$	−2436.86	−	4220.76i	−0.0775248	−	0.134277i
$997$	32843.1	+	18961.9i	1.04328	+	0.602338i	0.920761	−	0.390128i	$-0.127569\pi$
$997$	32843.1	+	18961.9i	1.04328	+	0.602338i	0.122519	+	0.992466i	$0.460903\pi$
$998$	19916.7	+	11498.9i	0.631714	+	0.364720i
$999$	13781.5	+	23870.3i	0.436464	+	0.755977i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.j.e.214.4		20
5.4	even	2	inner	245.4.j.e.214.7		20
7.2	even	3	inner	245.4.j.e.79.7		20
7.3	odd	6		245.4.b.d.99.4		10
7.4	even	3		35.4.b.a.29.4	✓	10
7.5	odd	6		245.4.j.f.79.7		20
7.6	odd	2		245.4.j.f.214.4		20
21.11	odd	6		315.4.d.c.64.7		10
28.11	odd	6		560.4.g.f.449.4		10
35.3	even	12		1225.4.a.bh.1.2		5
35.4	even	6		35.4.b.a.29.7	yes	10
35.9	even	6	inner	245.4.j.e.79.4		20
35.17	even	12		1225.4.a.be.1.4		5
35.18	odd	12		175.4.a.j.1.2		5
35.19	odd	6		245.4.j.f.79.4		20
35.24	odd	6		245.4.b.d.99.7		10
35.32	odd	12		175.4.a.i.1.4		5
35.34	odd	2		245.4.j.f.214.7		20
105.32	even	12		1575.4.a.bq.1.2		5
105.53	even	12		1575.4.a.bn.1.4		5
105.74	odd	6		315.4.d.c.64.4		10
140.39	odd	6		560.4.g.f.449.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.b.a.29.4	✓	10	7.4	even	3
35.4.b.a.29.7	yes	10	35.4	even	6
175.4.a.i.1.4		5	35.32	odd	12
175.4.a.j.1.2		5	35.18	odd	12
245.4.b.d.99.4		10	7.3	odd	6
245.4.b.d.99.7		10	35.24	odd	6
245.4.j.e.79.4		20	35.9	even	6	inner
245.4.j.e.79.7		20	7.2	even	3	inner
245.4.j.e.214.4		20	1.1	even	1	trivial
245.4.j.e.214.7		20	5.4	even	2	inner
245.4.j.f.79.4		20	35.19	odd	6
245.4.j.f.79.7		20	7.5	odd	6
245.4.j.f.214.4		20	7.6	odd	2
245.4.j.f.214.7		20	35.34	odd	2
315.4.d.c.64.4		10	105.74	odd	6
315.4.d.c.64.7		10	21.11	odd	6
560.4.g.f.449.4		10	28.11	odd	6
560.4.g.f.449.7		10	140.39	odd	6
1225.4.a.be.1.4		5	35.17	even	12
1225.4.a.bh.1.2		5	35.3	even	12
1575.4.a.bn.1.4		5	105.53	even	12
1575.4.a.bq.1.2		5	105.32	even	12

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.45073 + 0.837581i) q^{2} +(-2.15983 - 1.24698i) q^{3} +(-2.59692 + 4.49799i) q^{4} +(-11.1437 - 0.904354i) q^{5} +4.17779 q^{6} -22.1018i q^{8} +(-10.3901 - 17.9961i) q^{9} +(16.9240 - 8.02178i) q^{10} +(28.7940 - 49.8727i) q^{11} +(11.2178 - 6.47661i) q^{12} +45.5159i q^{13} +(22.9408 + 15.8492i) q^{15} +(-2.26327 - 3.92011i) q^{16} +(-79.6787 - 46.0025i) q^{17} +(30.1465 + 17.4051i) q^{18} +(62.5885 + 108.407i) q^{19} +(33.0070 - 47.7757i) q^{20} +96.4692i q^{22} +(-137.262 + 79.2481i) q^{23} +(-27.5605 + 47.7362i) q^{24} +(123.364 + 20.1557i) q^{25} +(-38.1233 - 66.0315i) q^{26} +119.162i q^{27} +40.1708 q^{29} +(-46.5560 - 3.77820i) q^{30} +(-24.7795 + 42.9194i) q^{31} +(159.693 + 92.1986i) q^{32} +(-124.381 + 71.8111i) q^{33} +154.123 q^{34} +107.929 q^{36} +(200.318 - 115.654i) q^{37} +(-181.598 - 104.846i) q^{38} +(56.7575 - 98.3069i) q^{39} +(-19.9879 + 246.296i) q^{40} +169.556 q^{41} +147.428i q^{43} +(149.551 + 259.030i) q^{44} +(99.5091 + 209.940i) q^{45} +(132.753 - 229.936i) q^{46} +(-58.0520 + 33.5164i) q^{47} +11.2890i q^{48} +(-195.851 + 74.0870i) q^{50} +(114.729 + 198.716i) q^{51} +(-204.730 - 118.201i) q^{52} +(232.655 + 134.323i) q^{53} +(-99.8077 - 172.872i) q^{54} +(-365.974 + 529.726i) q^{55} -312.187i q^{57} +(-58.2771 + 33.6463i) q^{58} +(-120.421 + 208.576i) q^{59} +(-130.865 + 62.0285i) q^{60} +(-45.2290 - 78.3389i) q^{61} -83.0194i q^{62} -272.683 q^{64} +(41.1625 - 507.216i) q^{65} +(120.295 - 208.358i) q^{66} +(352.038 + 203.249i) q^{67} +(413.838 - 238.929i) q^{68} +395.283 q^{69} +330.782 q^{71} +(-397.747 + 229.640i) q^{72} +(473.071 + 273.127i) q^{73} +(-193.739 + 335.565i) q^{74} +(-241.313 - 197.366i) q^{75} -650.149 q^{76} +190.156i q^{78} +(-12.6543 - 21.9179i) q^{79} +(21.6761 + 45.7313i) q^{80} +(-131.940 + 228.526i) q^{81} +(-245.981 + 142.017i) q^{82} -376.255i q^{83} +(846.314 + 584.697i) q^{85} +(-123.483 - 213.878i) q^{86} +(-86.7623 - 50.0922i) q^{87} +(-1102.28 - 636.399i) q^{88} +(513.219 + 888.921i) q^{89} +(-320.203 - 221.220i) q^{90} -823.203i q^{92} +(107.039 - 61.7992i) q^{93} +(56.1453 - 97.2466i) q^{94} +(-599.430 - 1264.65i) q^{95} +(-229.940 - 398.267i) q^{96} -942.660i q^{97} -1196.69 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 36 q^{4} - 6 q^{5} + 24 q^{6} + 46 q^{9} + 16 q^{10} - 84 q^{11} + 16 q^{15} - 148 q^{16} - 72 q^{19} - 136 q^{20} - 72 q^{24} + 362 q^{25} + 620 q^{26} + 176 q^{29} - 52 q^{30} - 120 q^{31} + 1928 q^{34}+ \cdots - 10608 q^{99}+O(q^{100}) \) 20 * q + 36 * q^4 - 6 * q^5 + 24 * q^6 + 46 * q^9 + 16 * q^10 - 84 * q^11 + 16 * q^15 - 148 * q^16 - 72 * q^19 - 136 * q^20 - 72 * q^24 + 362 * q^25 + 620 * q^26 + 176 * q^29 - 52 * q^30 - 120 * q^31 + 1928 * q^34 - 840 * q^36 - 212 * q^39 - 1396 * q^40 - 1704 * q^41 + 1424 * q^44 + 510 * q^45 - 176 * q^46 + 3288 * q^50 - 1276 * q^51 + 996 * q^54 - 2272 * q^55 - 864 * q^59 + 1692 * q^60 + 884 * q^61 - 5448 * q^64 - 520 * q^65 - 1148 * q^66 + 9616 * q^69 + 1760 * q^71 - 3024 * q^74 - 720 * q^75 - 5344 * q^76 + 3580 * q^79 + 2316 * q^80 + 302 * q^81 + 3144 * q^85 - 2432 * q^86 + 1492 * q^89 - 15496 * q^90 - 1652 * q^94 + 1628 * q^95 - 4080 * q^96 - 10608 * q^99

Introduction

L-functions

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