LMFDB - Embedded newform 245.4.j.e.214.7

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			214.7
Root			$2.31676 + 1.33758i$ of defining polynomial
Character	$\chi$	$=$	245.214
Dual form			245.4.j.e.79.7

$q$-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} +(4.78866 - 10.1029i) q^{5} +4.17779 q^{6} +22.1018i q^{8} +(-10.3901 - 17.9961i) q^{9} +(-1.51494 - 18.6675i) 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} +(-79.1375 - 96.7588i) q^{25} +(-38.1233 - 66.0315i) q^{26} -119.162i q^{27} +40.1708 q^{29} +(20.0060 - 42.2078i) 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} +(223.293 + 105.838i) q^{40} +169.556 q^{41} -147.428i q^{43} +(149.551 + 259.030i) q^{44} +(-231.568 + 18.7926i) 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} +(11.7143 + 144.347i) q^{60} +(-45.2290 - 78.3389i) q^{61} +83.0194i q^{62} -272.683 q^{64} +(-459.843 - 217.960i) 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} +(-50.2676 - 307.666i) q^{75} -650.149 q^{76} -190.156i q^{78} +(-12.6543 - 21.9179i) q^{79} +(-50.4425 + 4.09360i) 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} +(1394.94 - 113.204i) 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	−0.221118	−	0.975247i	$-0.570971\pi$
$2$	1.45073	−	0.837581i	0.512912	−	0.296130i	0.734030	+	0.679117i	$0.237637\pi$
$3$	2.15983	+	1.24698i	0.415660	+	0.239982i	0.693219	−	0.720727i	$-0.256192\pi$
$3$	2.15983	+	1.24698i	0.415660	+	0.239982i	−0.277559	+	0.960709i	$0.589525\pi$
$4$	−2.59692	+	4.49799i	−0.324615	+	0.562249i
$5$	4.78866	−	10.1029i	0.428311	−	0.903632i
$5$	4.78866	−	10.1029i	0.428311	−	0.903632i
$6$	4.17779			0.284263
$7$		0			0
$7$		0			0
$8$			22.1018i			0.976771i
$9$	−10.3901	−	17.9961i	−0.384818	−	0.666524i
$10$	−1.51494	−	18.6675i	−0.0479066	−	0.590319i
$11$	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	$-0.838626\pi$
$13$		−	45.5159i		−	0.971066i	0.874218	−	0.485533i	$-0.161374\pi$
$14$		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	0.945626	−	0.325255i	$-0.105450\pi$
$17$	79.6787	+	46.0025i	1.13676	+	0.656309i	0.191134	+	0.981564i	$0.438783\pi$
$18$	−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	0.274408	−	0.961613i	$-0.411518\pi$
$23$	137.262	−	79.2481i	1.24439	−	0.718451i	0.969986	+	0.243162i	$0.0781848\pi$
$24$	−27.5605	+	47.7362i	−0.234407	+	0.406005i
$25$	−79.1375	−	96.7588i	−0.633100	−	0.774070i
$26$	−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	$0.458948\pi$
$30$	20.0060	−	42.2078i	0.121753	−	0.256869i
$31$	−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	−0.873961	−	0.485997i	$-0.838457\pi$
$37$	−200.318	+	115.654i	−0.890056	+	0.513874i	−0.0160950	+	0.999870i	$0.505123\pi$
$38$	181.598	+	104.846i	0.775241	+	0.447586i
$39$	56.7575	−	98.3069i	0.233038	−	0.403633i
$40$	223.293	+	105.838i	0.882641	+	0.418361i
$41$	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	$-0.915808\pi$
$43$		−	147.428i		−	0.522849i	0.965224	−	0.261425i	$-0.0841923\pi$
$44$	149.551	+	259.030i	0.512402	+	0.887507i
$45$	−231.568	+	18.7926i	−0.767114	+	0.0622542i
$46$	132.753	−	229.936i	0.425509	−	0.737004i
$47$	58.0520	−	33.5164i	0.180165	−	0.104018i	−0.407205	−	0.913337i	$-0.633497\pi$
$47$	58.0520	−	33.5164i	0.180165	−	0.104018i	0.587370	+	0.809318i	$0.300163\pi$
$48$		−	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	0.167237	−	0.985917i	$-0.446516\pi$
$53$	−232.655	−	134.323i	−0.602974	−	0.348127i	−0.770211	+	0.637790i	$0.779849\pi$
$54$	−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	$0.252277\pi$
$60$	11.7143	+	144.347i	0.0252052	+	0.310585i
$61$	−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
$65$	−459.843	−	217.960i	−0.877485	−	0.415918i
$66$	120.295	−	208.358i	0.224353	−	0.388592i
$67$	−352.038	−	203.249i	−0.641914	−	0.370609i	0.143437	−	0.989659i	$-0.454184\pi$
$67$	−352.038	−	203.249i	−0.641914	−	0.370609i	−0.785351	+	0.619050i	$0.787518\pi$
$68$	−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	0.0702724	−	0.997528i	$-0.477613\pi$
$73$	−473.071	−	273.127i	−0.758476	−	0.437906i	−0.828748	+	0.559622i	$0.810946\pi$
$74$	−193.739	+	335.565i	−0.304347	+	0.527144i
$75$	−50.2676	−	307.666i	−0.0773920	−	0.473682i
$76$	−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	$0.839070\pi$
$80$	−50.4425	+	4.09360i	−0.0704956	+	0.00572098i
$81$	−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	$0.0800333\pi$
$83$			376.255i			0.497582i	−0.968557	+	0.248791i	$0.919967\pi$
$84$		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
$95$	1394.94	−	113.204i	1.50650	−	0.122258i
$96$	−229.940	−	398.267i	−0.244460	−	0.423416i
$97$			942.660i			0.986728i	0.869823	+	0.493364i	$0.164233\pi$
$97$			942.660i			0.986728i	−0.869823	+	0.493364i	$0.835767\pi$
$98$		0			0
$99$	−1196.69			−1.21487
$100$	640.733	−	104.685i	0.640733	−	0.104685i
$101$	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	−0.619463	−	0.785026i	$-0.712649\pi$
$103$	−260.645	+	150.484i	−0.249341	+	0.143957i	0.370121	+	0.928983i	$0.379316\pi$
$104$	1005.98			0.948509
$105$		0			0
$106$	−450.027			−0.412363
$107$	−1309.14	+	755.830i	−1.18279	+	0.682886i	−0.956659	−	0.291210i	$-0.905942\pi$
$107$	−1309.14	+	755.830i	−1.18279	+	0.682886i	−0.226135	+	0.974096i	$0.572609\pi$
$108$	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	$0.883707\pi$
$110$	−974.620	−	461.958i	−0.844785	−	0.400418i
$111$	−576.871			−0.493281
$112$		0			0
$113$			1045.27i			0.870182i	0.900387	+	0.435091i	$0.143284\pi$
$113$			1045.27i			0.870182i	−0.900387	+	0.435091i	$0.856716\pi$
$114$	261.482	+	452.900i	0.214825	+	0.372087i
$115$	−143.337	−	1766.23i	−0.116228	−	1.43219i
$116$	−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	$-0.970966\pi$
$127$		−	260.727i		−	0.182171i	0.995843	−	0.0910857i	$-0.0290337\pi$
$128$	881.951	−	509.195i	0.609017	−	0.351616i
$129$	183.840	−	318.419i	0.125474	−	0.217328i
$130$	−849.669	+	68.9539i	−0.573238	+	0.0465205i
$131$	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
$135$	−1203.88	−	570.625i	−0.767508	−	0.363790i
$136$	−1016.74	+	1761.04i	−0.641064	+	1.11036i
$137$	670.038	+	386.847i	0.417848	+	0.241245i	0.694156	−	0.719824i	$-0.255778\pi$
$137$	670.038	+	386.847i	0.417848	+	0.241245i	−0.276308	+	0.961069i	$0.589111\pi$
$138$	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
$145$	192.364	−	405.842i	0.110172	−	0.232437i
$146$	−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	$0.590449\pi$
$150$	−330.620	−	404.238i	−0.179967	−	0.220039i
$151$	−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	0.916817	−	0.399308i	$-0.130750\pi$
$157$	2025.07	+	1169.17i	1.02941	+	0.594333i	0.112597	+	0.993641i	$0.464083\pi$
$158$	−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	−0.749720	−	0.661755i	$-0.769812\pi$
$163$	−1147.66	+	662.602i	−0.551483	+	0.318399i	0.198237	+	0.980154i	$0.436478\pi$
$164$	−440.323	+	762.662i	−0.209655	+	0.363133i
$165$	−129.885	−	1600.48i	−0.0612822	−	0.755136i
$166$	315.144	+	545.845i	0.147349	+	0.255216i
$167$		−	2086.20i		−	0.966675i	−0.875434	−	0.483338i	$-0.839424\pi$
$167$		−	2086.20i		−	0.966675i	0.875434	−	0.483338i	$-0.160576\pi$
$168$		0			0
$169$	125.299			0.0570317
$170$	738.044	−	1557.09i	0.332973	−	0.702493i
$171$	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	−0.0883897	−	0.996086i	$-0.528172\pi$
$173$	1661.20	−	959.095i	0.730051	−	0.421495i	0.818441	+	0.574591i	$0.194839\pi$
$174$	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	$0.124741\pi$
$180$	516.833	−	1090.39i	0.214014	−	0.451517i
$181$	−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
$185$	209.184	+	2577.62i	0.0831324	+	1.02438i
$186$	−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	−0.335136	−	0.942170i	$-0.608782\pi$
$193$	−3535.61	−	2041.29i	−1.31865	−	0.761321i	−0.983511	+	0.180849i	$0.942116\pi$
$194$	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	$-0.788140\pi$
$197$		−	3414.89i		−	1.23503i	0.786559	−	0.617515i	$-0.211860\pi$
$198$	−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	$0.960147\pi$
$200$	2138.54	−	1749.08i	0.756089	−	0.618394i
$201$	−506.895	−	877.968i	−0.177879	−	0.308095i
$202$		−	1012.83i		−	0.352785i
$203$		0			0
$204$	−1191.76			−0.409020
$205$	811.946	−	1713.01i	0.276628	−	0.583619i
$206$	−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
$215$	−1489.45	−	705.981i	−0.472463	−	0.223942i
$216$	2633.69			0.829630
$217$		0			0
$218$			2960.16i			0.919667i
$219$	−681.169	−	1179.82i	−0.210179	−	0.364040i
$220$	3333.11	−	270.495i	1.02145	−	0.0828943i
$221$	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	$0.00872860\pi$
$223$			182.611i			0.0548365i	−0.999624	+	0.0274183i	$0.991271\pi$
$224$		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	0.0446271	−	0.999004i	$-0.485790\pi$
$227$	−2730.00	−	1576.17i	−0.798222	−	0.460854i	−0.842849	+	0.538150i	$0.819123\pi$
$228$	−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	−0.610133	−	0.792299i	$-0.708884\pi$
$233$	−814.635	+	470.330i	−0.229050	+	0.132242i	0.381084	+	0.924540i	$0.375551\pi$
$234$	−792.208	+	1372.14i	−0.221317	+	0.383333i
$235$	−60.6213	−	746.993i	−0.0168277	−	0.207355i
$236$	−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	$0.745975\pi$
$240$	−114.052	−	54.0593i	−0.0306751	−	0.0145396i
$241$	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
$250$	−1686.36	+	1623.88i	−0.426618	+	0.410814i
$251$	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
$255$	2557.00	−	207.511i	0.627944	−	0.0509601i
$256$	1943.71	−	3366.61i	0.474540	−	0.821927i
$257$	694.727	−	401.101i	0.168622	−	0.0973541i	−0.413314	−	0.910589i	$-0.635629\pi$
$257$	694.727	−	401.101i	0.168622	−	0.0973541i	0.581936	+	0.813235i	$0.302295\pi$
$258$		−	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	0.528852	−	0.848714i	$-0.322623\pi$
$263$	248.530	+	143.489i	0.0582701	+	0.0336423i	−0.470582	+	0.882356i	$0.655956\pi$
$264$	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	$0.0344288\pi$
$270$	−2224.46	+	180.523i	−0.501393	+	0.0406899i
$271$	−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
$275$	−7104.30	+	1160.73i	−1.55784	+	0.254525i
$276$	−1026.52	+	1777.98i	−0.223874	+	0.387760i
$277$	5705.97	+	3294.34i	1.23768	+	0.714578i	0.968620	−	0.248545i	$-0.0799523\pi$
$277$	5705.97	+	3294.34i	1.23768	+	0.714578i	0.269064	+	0.963122i	$0.413286\pi$
$278$	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	0.957132	−	0.289651i	$-0.0935391\pi$
$283$	5640.85	+	3256.75i	1.18485	+	0.684076i	0.227722	+	0.973726i	$0.426872\pi$
$284$	−859.013	+	1487.85i	−0.179483	+	0.310873i
$285$	3153.99	+	1494.96i	0.655532	+	0.310714i
$286$	−4390.89			−0.907828
$287$		0			0
$288$			3831.80i			0.783997i
$289$	1775.97	+	3076.07i	0.361483	+	0.626108i
$290$	−60.8564	−	749.889i	−0.0123228	−	0.151845i
$291$	−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	$0.0138249\pi$
$293$			435.520i			0.0868373i	−0.999057	+	0.0434186i	$0.986175\pi$
$294$		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
$305$	−1008.04	+	81.8060i	−0.189246	+	0.0153580i
$306$	−1601.35	−	2773.63i	−0.299161	−	0.518163i
$307$			4915.99i			0.913910i	0.889490	+	0.456955i	$0.151060\pi$
$307$			4915.99i			0.913910i	−0.889490	+	0.456955i	$0.848940\pi$
$308$		0			0
$309$	−750.601			−0.138188
$310$	838.738	+	397.552i	0.153668	+	0.0728368i
$311$	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	−0.678714	−	0.734403i	$-0.737462\pi$
$313$	−2115.66	+	1221.48i	−0.382059	+	0.220582i	0.296655	+	0.954985i	$0.404129\pi$
$314$	3917.11			0.703998
$315$		0			0
$316$	131.449			0.0234006
$317$	−1442.97	+	833.096i	−0.255662	+	0.147607i	−0.622354	−	0.782736i	$-0.713824\pi$
$317$	−1442.97	+	833.096i	−0.255662	+	0.147607i	0.366692	+	0.930342i	$0.380490\pi$
$318$	−971.983	−	561.175i	−0.171403	−	0.0989595i
$319$	1156.68	−	2003.43i	0.203014	−	0.351631i
$320$	−1305.78	+	2754.89i	−0.228111	+	0.481259i
$321$	−3770.02			−0.655521
$322$		0			0
$323$			11516.9i			1.98396i
$324$	−685.272	−	1186.93i	−0.117502	−	0.203520i
$325$	−4404.07	+	3602.02i	−0.751673	+	0.614782i
$326$	−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	$-0.669973\pi$
$337$		−	10650.5i		−	1.72157i	0.508970	−	0.860784i	$-0.330027\pi$
$338$	181.775	−	104.948i	0.0292522	−	0.0168888i
$339$	−1303.43	+	2257.60i	−0.208828	+	0.361700i
$340$	432.154	+	5325.12i	0.0689319	+	0.849397i
$341$	1427.00	+	2471.64i	0.226617	+	0.392513i
$342$		−	4357.43i		−	0.688956i
$343$		0			0
$344$	3258.42			0.510704
$345$	1892.88	−	3993.51i	0.295389	−	0.623198i
$346$	1606.64	−	2782.78i	0.249634	−	0.432380i
$347$	3480.67	+	2009.57i	0.538479	+	0.310891i	0.744462	−	0.667664i	$-0.232706\pi$
$347$	3480.67	+	2009.57i	0.538479	+	0.310891i	−0.205983	+	0.978556i	$0.566039\pi$
$348$	−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	0.294138	−	0.955763i	$-0.404967\pi$
$353$	−2563.42	−	1479.99i	−0.386507	−	0.223150i	−0.680646	+	0.732613i	$0.738301\pi$
$354$	−503.095	+	871.386i	−0.0755345	+	0.130830i
$355$	1584.00	−	3341.86i	0.236817	−	0.499627i
$356$	−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	$0.782338\pi$
$360$	−415.351	−	5118.07i	−0.0608081	−	0.749294i
$361$	−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	0.420892	−	0.907111i	$-0.361717\pi$
$367$	−1084.44	−	626.101i	−0.154243	−	0.0890523i	−0.575135	+	0.818058i	$0.695050\pi$
$368$	−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	−0.194024	−	0.980997i	$-0.562154\pi$
$373$	4023.57	−	2323.01i	0.558533	−	0.322469i	0.752556	+	0.658528i	$0.228821\pi$
$374$	4437.83	−	7686.55i	0.613569	−	1.06273i
$375$	−3349.03	−	965.458i	−0.461182	−	0.132949i
$376$	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	$0.530999\pi$
$380$	−3113.34	+	6568.39i	−0.420292	+	0.886714i
$381$	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	$0.676900\pi$
$383$	−11446.0	+	6608.36i	−1.52706	+	0.881649i	−0.999483	+	0.0321425i	$0.989767\pi$
$384$	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	$0.998015\pi$
$390$	−1921.13	−	910.592i	−0.249436	−	0.118230i
$391$	14582.5			1.88610
$392$		0			0
$393$			1804.44i			0.231607i
$394$	−2860.25	−	4954.09i	−0.365729	−	0.633461i
$395$	−282.032	+	22.8880i	−0.0359255	+	0.00291549i
$396$	3107.70	−	5382.69i	0.394363	−	0.683056i
$397$	3083.77	−	1780.41i	0.389848	−	0.225079i	−0.292246	−	0.956343i	$-0.594403\pi$
$397$	3083.77	−	1780.41i	0.389848	−	0.225079i	0.682094	+	0.731264i	$0.261069\pi$
$398$			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	$0.967260\pi$
$410$	−256.867	−	3165.19i	−0.0309409	−	0.381262i
$411$	964.780	+	1671.05i	0.115789	+	0.200552i
$412$		−	1563.17i		−	0.186922i
$413$		0			0
$414$	−5517.27			−0.654974
$415$	3801.27	+	1801.76i	0.449631	+	0.213120i
$416$	−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
$425$	−1854.43	−	11350.1i	−0.211654	−	1.29544i
$426$	1381.94			0.157172
$427$		0			0
$428$		−	7851.31i		−	0.886699i
$429$	−3268.55	−	5661.30i	−0.367849	−	0.637133i
$430$	−2752.11	+	223.344i	−0.308648	+	0.0250479i
$431$	−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	$0.289539\pi$
$433$			14222.8i			1.57853i	−0.614051	+	0.789267i	$0.710461\pi$
$434$		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	−0.303956	−	0.952686i	$-0.598308\pi$
$443$	3441.66	−	1987.04i	0.369116	−	0.213109i	0.673072	+	0.739577i	$0.264974\pi$
$444$	1498.09	−	2594.76i	0.160126	−	0.277347i
$445$	11438.3	−	928.263i	1.21849	−	0.0988852i
$446$	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	$0.204260\pi$
$450$	701.623	+	4294.33i	0.0734996	+	0.449859i
$451$	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	0.0601005	−	0.998192i	$-0.480858\pi$
$457$	9326.11	−	5384.43i	0.954611	−	0.551145i	0.894510	+	0.447048i	$0.147525\pi$
$458$	8722.32	+	5035.83i	0.889884	+	0.513775i
$459$	5481.75	−	9494.67i	0.557443	−	0.965519i
$460$	8316.74	+	3942.04i	0.842978	+	0.399562i
$461$	−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	$-0.864897\pi$
$463$		−	8205.35i		−	0.823618i	0.911270	−	0.411809i	$-0.135103\pi$
$464$	−90.9176	−	157.474i	−0.00909643	−	0.0157555i
$465$	111.777	+	1377.34i	0.0111474	+	0.137361i
$466$	−787.879	+	1364.65i	−0.0783214	+	0.135657i
$467$	145.170	−	83.8138i	0.0143847	−	0.00830501i	−0.492790	−	0.870148i	$-0.664023\pi$
$467$	145.170	−	83.8138i	0.0143847	−	0.00830501i	0.507175	+	0.861843i	$0.330690\pi$
$468$		−	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	$0.0642778\pi$
$480$	−5124.76	+	415.894i	−0.487317	+	0.0395476i
$481$	5264.08	+	9117.66i	0.499005	+	0.864302i
$482$		−	777.001i		−	0.0734262i
$483$		0			0
$484$	10311.7			0.968419
$485$	9523.60	+	4514.08i	0.891638	+	0.422626i
$486$	−3246.02	+	5622.28i	−0.302968	+	0.524757i
$487$	−17876.1	−	10320.8i	−1.66334	−	0.960327i	−0.971105	−	0.238651i	$-0.923295\pi$
$487$	−17876.1	−	10320.8i	−1.66334	−	0.960327i	−0.692231	−	0.721676i	$-0.743372\pi$
$488$	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
$495$	−5730.53	+	12090.0i	−0.520340	+	1.09779i
$496$	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	$-0.377839\pi$
$500$	2010.63	−	6974.57i	0.179836	−	0.623825i
$501$	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	$-0.667111\pi$
$503$		−	19523.7i		−	1.73065i	0.501209	−	0.865326i	$-0.332889\pi$
$504$		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
$515$	272.181	+	3353.89i	0.0232888	+	0.286971i
$516$	954.832	+	1653.82i	0.0814615	+	0.141095i
$517$		−	3860.28i		−	0.328385i
$518$		0			0
$519$	4783.89			0.404604
$520$	4817.32	−	10163.4i	0.406256	−	0.857102i
$521$	−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	−0.548634	−	0.836063i	$-0.684852\pi$
$523$	−1182.90	+	682.947i	−0.0988998	+	0.0570998i	0.449734	+	0.893162i	$0.351519\pi$
$524$	−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
$530$	−2155.03	+	4546.58i	−0.176619	+	0.372624i
$531$	5004.75			0.409016
$532$		0			0
$533$		−	7717.51i		−	0.627171i
$534$	2144.12	+	3713.72i	0.173755	+	0.300952i
$535$	1367.08	+	16845.5i	0.110474	+	1.36130i
$536$	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	$0.149117\pi$
$547$			11552.7i			0.903033i	−0.892263	+	0.451516i	$0.850883\pi$
$548$	−3480.06	+	2009.22i	−0.271279	+	0.156623i
$549$	−939.865	+	1627.89i	−0.0730646	+	0.126552i
$550$	−9334.24	+	7634.33i	−0.723661	+	0.591871i
$551$	2514.23	+	4354.78i	0.194392	+	0.336697i
$552$			8736.48i			0.673640i
$553$		0			0
$554$	11037.1			0.846430
$555$	−2762.44	+	5828.08i	−0.211277	+	0.445744i
$556$	−7668.60	+	13282.4i	−0.584930	+	1.01313i
$557$	−14208.2	−	8203.08i	−1.08082	−	0.624014i	−0.149706	−	0.988731i	$-0.547833\pi$
$557$	−14208.2	−	8203.08i	−1.08082	−	0.624014i	−0.931119	+	0.364717i	$0.881166\pi$
$558$	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	−0.0118502	−	0.999930i	$-0.503772\pi$
$563$	−11805.6	−	6815.95i	−0.883740	−	0.510227i	−0.871890	+	0.489702i	$0.837105\pi$
$564$	−434.145	+	751.961i	−0.0324127	+	0.0561405i
$565$	10560.2	+	5005.43i	0.786324	+	0.372708i
$566$	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	$0.869608\pi$
$570$	5827.75	−	472.944i	0.428241	−	0.0347534i
$571$	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	0.999845	−	0.0176156i	$-0.00560752\pi$
$577$	20575.4	+	11879.2i	1.48451	+	0.857083i	0.484667	+	0.874699i	$0.338941\pi$
$578$	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
$585$	855.364	+	10540.0i	0.0604529	+	0.744917i
$586$	364.783	+	631.823i	0.0257151	+	0.0445398i
$587$		−	596.893i		−	0.0419701i	−0.999780	−	0.0209850i	$-0.993320\pi$
$587$		−	596.893i		−	0.0419701i	0.999780	−	0.0209850i	$-0.00668023\pi$
$588$		0			0
$589$	−6203.66			−0.433985
$590$	4076.02	+	1931.99i	0.284419	+	0.134811i
$591$	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	0.215734	−	0.976452i	$-0.430785\pi$
$593$	16884.3	−	9748.16i	1.16923	−	0.675058i	0.953500	+	0.301394i	$0.0974521\pi$
$594$	−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	$0.125329\pi$
$600$	6799.97	−	1111.00i	0.462679	−	0.0755942i
$601$	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
$605$	−22124.5	+	1795.49i	−1.48676	+	0.120656i
$606$	1262.98	−	2187.55i	0.0846618	−	0.146639i
$607$	−16053.0	+	9268.21i	−1.07343	+	0.619745i	−0.929116	−	0.369787i	$-0.879431\pi$
$607$	−16053.0	+	9268.21i	−1.07343	+	0.619745i	−0.144313	+	0.989532i	$0.546097\pi$
$608$		−	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	0.437003	−	0.899460i	$-0.356040\pi$
$613$	−1873.62	−	1081.74i	−0.123450	−	0.0712738i	−0.560453	+	0.828186i	$0.689373\pi$
$614$	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	$-0.730431\pi$
$617$		−	22964.9i		−	1.49843i	0.662327	−	0.749215i	$-0.269569\pi$
$618$	−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	$0.181002\pi$
$620$	−2868.40	+	232.782i	−0.185803	+	0.0150786i
$621$	−9443.35	−	16356.4i	−0.610223	−	1.05694i
$622$		−	3067.41i		−	0.197736i
$623$		0			0
$624$	−513.831			−0.0329643
$625$	−3099.51	+	15314.5i	−0.198369	+	0.980127i
$626$	−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
$635$	−2634.10	−	1248.53i	−0.164616	−	0.0780259i
$636$	3479.84			0.216957
$637$		0			0
$638$		−	3875.25i		−	0.240474i
$639$	−3436.85	−	5952.80i	−0.212770	−	0.368528i
$640$	−920.985	−	11348.6i	−0.0568830	−	0.700928i
$641$	−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	$0.340328\pi$
$643$			28592.2i			1.75360i	−0.480851	+	0.876802i	$0.659672\pi$
$644$		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	0.0670835	−	0.997747i	$-0.478631\pi$
$647$	−12564.3	−	7253.97i	−0.763449	−	0.440778i	−0.830533	+	0.556970i	$0.811964\pi$
$648$	−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	−0.307235	−	0.951634i	$-0.599404\pi$
$653$	6062.05	−	3499.93i	0.363287	−	0.209744i	0.670522	+	0.741890i	$0.266070\pi$
$654$	−3691.26	+	6393.46i	−0.220703	+	0.382269i
$655$	8062.71	−	654.320i	0.480971	−	0.0390327i
$656$	−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	$0.569308\pi$
$660$	7536.26	+	3572.10i	0.444468	+	0.210672i
$661$	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
$670$	−3260.84	+	6879.58i	−0.188026	+	0.396688i
$671$	−5209.29			−0.299706
$672$		0			0
$673$		−	5400.26i		−	0.309309i	−0.987969	−	0.154654i	$-0.950574\pi$
$673$		−	5400.26i		−	0.309309i	0.987969	−	0.154654i	$-0.0494264\pi$
$674$	−8920.64	−	15451.0i	−0.509808	−	0.883013i
$675$	−11530.0	+	9430.17i	−0.657464	+	0.537730i
$676$	−325.390	+	563.593i	−0.0185133	+	0.0320660i
$677$	−5569.49	+	3215.55i	−0.316178	+	0.182546i	−0.649688	−	0.760201i	$-0.725100\pi$
$677$	−5569.49	+	3215.55i	−0.316178	+	0.182546i	0.333509	+	0.942747i	$0.391767\pi$
$678$			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	0.911881	−	0.410454i	$-0.134630\pi$
$683$	18070.3	+	10432.9i	1.01236	+	0.584486i	0.100477	+	0.994939i	$0.467963\pi$
$684$	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
$690$	−598.831	−	7378.96i	−0.0330393	−	0.407119i
$691$	−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
$695$	14140.7	−	29833.5i	0.771783	−	1.62827i
$696$	−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
$705$	800.554	−	1688.97i	0.0427668	−	0.0902276i
$706$	−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	$-0.376508\pi$
$710$	−501.115	−	6174.88i	−0.0264880	−	0.326393i
$711$	−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
$725$	−3179.02	−	3886.88i	−0.162849	−	0.199110i
$726$	−4147.25	−	7183.24i	−0.212009	−	0.367211i
$727$		−	35983.4i		−	1.83570i	−0.396931	−	0.917849i	$-0.629925\pi$
$727$		−	35983.4i		−	1.83570i	0.396931	−	0.917849i	$-0.370075\pi$
$728$		0			0
$729$	−2540.55			−0.129073
$730$	−4381.94	+	9244.82i	−0.222168	+	0.468721i
$731$	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	−0.531337	−	0.847161i	$-0.678310\pi$
$733$	−1257.04	+	725.752i	−0.0633422	+	0.0365706i	0.467994	+	0.883731i	$0.344977\pi$
$734$	−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	$0.213511\pi$
$740$	−12137.3	−	5752.95i	−0.602942	−	0.285788i
$741$	14209.5			0.704451
$742$		0			0
$743$			7438.65i			0.367292i	0.982992	+	0.183646i	$0.0587900\pi$
$743$			7438.65i			0.367292i	−0.982992	+	0.183646i	$0.941210\pi$
$744$	−1365.87	−	2365.76i	−0.0673056	−	0.116577i
$745$	28015.3	−	2273.55i	1.37772	−	0.111807i
$746$	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	$0.0786947\pi$
$757$			10193.8i			0.489432i	−0.969595	+	0.244716i	$0.921305\pi$
$758$	−2081.57	+	1201.79i	−0.0997439	+	0.0575872i
$759$	11381.8	−	19713.8i	0.544312	−	0.942776i
$760$	2502.02	+	30830.6i	0.119418	+	1.47151i
$761$	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
$765$	−19315.6	−	9155.34i	−0.912883	−	0.432696i
$766$	−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
$773$

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} +(4.78866 - 10.1029i) q^{5} +4.17779 q^{6} +22.1018i q^{8} +(-10.3901 - 17.9961i) q^{9} +(-1.51494 - 18.6675i) 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} +(-79.1375 - 96.7588i) q^{25} +(-38.1233 - 66.0315i) q^{26} -119.162i q^{27} +40.1708 q^{29} +(20.0060 - 42.2078i) 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} +(223.293 + 105.838i) q^{40} +169.556 q^{41} -147.428i q^{43} +(149.551 + 259.030i) q^{44} +(-231.568 + 18.7926i) 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} +(11.7143 + 144.347i) q^{60} +(-45.2290 - 78.3389i) q^{61} +83.0194i q^{62} -272.683 q^{64} +(-459.843 - 217.960i) 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} +(-50.2676 - 307.666i) q^{75} -650.149 q^{76} -190.156i q^{78} +(-12.6543 - 21.9179i) q^{79} +(-50.4425 + 4.09360i) 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} +(1394.94 - 113.204i) 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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