LMFDB - Embedded newform 1050.3.c.b.449.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,3,Mod(449,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1050.449");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.c (of order $2$, degree $1$, 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:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			449.27
Character	$\chi$	$=$	1050.449
Dual form			1050.3.c.b.449.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(0.577861 - 2.94382i) q^{3} +2.00000 q^{4} +(0.817218 - 4.16319i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-8.33215 - 3.40224i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(0.577861 - 2.94382i) q^{3} +2.00000 q^{4} +(0.817218 - 4.16319i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-8.33215 - 3.40224i) q^{9} +14.2674i q^{11} +(1.15572 - 5.88764i) q^{12} +17.9044i q^{13} +3.74166i q^{14} +4.00000 q^{16} -13.7434 q^{17} +(-11.7834 - 4.81149i) q^{18} +33.2895 q^{19} +(7.78862 + 1.52888i) q^{21} +20.1772i q^{22} +41.7116 q^{23} +(1.63444 - 8.32638i) q^{24} +25.3207i q^{26} +(-14.8304 + 22.5623i) q^{27} +5.29150i q^{28} +35.8465i q^{29} -0.0811935 q^{31} +5.65685 q^{32} +(42.0008 + 8.24459i) q^{33} -19.4362 q^{34} +(-16.6643 - 6.80447i) q^{36} -63.4244i q^{37} +47.0785 q^{38} +(52.7074 + 10.3463i) q^{39} +46.9306i q^{41} +(11.0148 + 2.16216i) q^{42} +10.1137i q^{43} +28.5349i q^{44} +58.9891 q^{46} +44.1704 q^{47} +(2.31144 - 11.7753i) q^{48} -7.00000 q^{49} +(-7.94180 + 40.4582i) q^{51} +35.8089i q^{52} -87.8765 q^{53} +(-20.9733 + 31.9080i) q^{54} +7.48331i q^{56} +(19.2367 - 97.9983i) q^{57} +50.6946i q^{58} -91.1530i q^{59} +38.5147 q^{61} -0.114825 q^{62} +(9.00147 - 22.0448i) q^{63} +8.00000 q^{64} +(59.3980 + 11.6596i) q^{66} -29.0894i q^{67} -27.4869 q^{68} +(24.1035 - 122.791i) q^{69} +27.3041i q^{71} +(-23.5669 - 9.62298i) q^{72} -47.0278i q^{73} -89.6956i q^{74} +66.5790 q^{76} -37.7481 q^{77} +(74.5396 + 14.6318i) q^{78} -117.994 q^{79} +(57.8496 + 56.6959i) q^{81} +66.3698i q^{82} +90.9832 q^{83} +(15.5772 + 3.05775i) q^{84} +14.3030i q^{86} +(105.526 + 20.7143i) q^{87} +40.3544i q^{88} +102.875i q^{89} -47.3707 q^{91} +83.4232 q^{92} +(-0.0469185 + 0.239019i) q^{93} +62.4663 q^{94} +(3.26887 - 16.6528i) q^{96} +25.1998i q^{97} -9.89949 q^{98} +(48.5412 - 118.878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	$ 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) $ 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.41421			0.707107
$2$	1.41421			0.707107
$3$	0.577861	−	2.94382i	0.192620	−	0.981273i
$3$	0.577861	−	2.94382i	0.192620	−	0.981273i
$4$	2.00000			0.500000
$5$		0			0
$5$		0			0
$6$	0.817218	−	4.16319i	0.136203	−	0.693865i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	2.82843			0.353553
$9$	−8.33215	−	3.40224i	−0.925795	−	0.378026i
$10$		0			0
$11$			14.2674i			1.29704i	0.761198	+	0.648520i	$0.224612\pi$
$11$			14.2674i			1.29704i	−0.761198	+	0.648520i	$0.775388\pi$
$12$	1.15572	−	5.88764i	0.0963101	−	0.490637i
$13$			17.9044i			1.37726i	0.725111	+	0.688632i	$0.241789\pi$
$13$			17.9044i			1.37726i	−0.725111	+	0.688632i	$0.758211\pi$
$14$			3.74166i			0.267261i
$15$		0			0
$16$	4.00000			0.250000
$17$	−13.7434			−0.808438			−0.404219	−	0.914662i	$-0.632457\pi$
$17$	−13.7434			−0.808438			−0.404219	+	0.914662i	$0.632457\pi$
$18$	−11.7834	−	4.81149i	−0.654636	−	0.267305i
$19$	33.2895			1.75208			0.876039	−	0.482240i	$-0.160177\pi$
$19$	33.2895			1.75208			0.876039	+	0.482240i	$0.160177\pi$
$20$		0			0
$21$	7.78862	+	1.52888i	0.370886	+	0.0728036i
$22$			20.1772i			0.917145i
$23$	41.7116			1.81355			0.906774	−	0.421618i	$-0.138538\pi$
$23$	41.7116			1.81355			0.906774	+	0.421618i	$0.138538\pi$
$24$	1.63444	−	8.32638i	0.0681015	−	0.346933i
$25$		0			0
$26$			25.3207i			0.973873i
$27$	−14.8304	+	22.5623i	−0.549274	+	0.835642i
$28$			5.29150i			0.188982i
$29$			35.8465i			1.23609i	0.786145	+	0.618043i	$0.212074\pi$
$29$			35.8465i			1.23609i	−0.786145	+	0.618043i	$0.787926\pi$
$30$		0			0
$31$	−0.0811935			−0.00261915			−0.00130957	−	0.999999i	$-0.500417\pi$
$31$	−0.0811935			−0.00261915			−0.00130957	+	0.999999i	$0.500417\pi$
$32$	5.65685			0.176777
$33$	42.0008	+	8.24459i	1.27275	+	0.249836i
$34$	−19.4362			−0.571652
$35$		0			0
$36$	−16.6643	−	6.80447i	−0.462897	−	0.189013i
$37$		−	63.4244i		−	1.71417i	−0.515173	−	0.857086i	$-0.672272\pi$
$37$		−	63.4244i		−	1.71417i	0.515173	−	0.857086i	$-0.327728\pi$
$38$	47.0785			1.23891
$39$	52.7074	+	10.3463i	1.35147	+	0.265289i
$40$		0			0
$41$			46.9306i			1.14465i	0.820028	+	0.572324i	$0.193958\pi$
$41$			46.9306i			1.14465i	−0.820028	+	0.572324i	$0.806042\pi$
$42$	11.0148	+	2.16216i	0.262256	+	0.0514799i
$43$			10.1137i			0.235203i	0.993061	+	0.117602i	$0.0375206\pi$
$43$			10.1137i			0.235203i	−0.993061	+	0.117602i	$0.962479\pi$
$44$			28.5349i			0.648520i
$45$		0			0
$46$	58.9891			1.28237
$47$	44.1704			0.939795			0.469898	−	0.882721i	$-0.344291\pi$
$47$	44.1704			0.939795			0.469898	+	0.882721i	$0.344291\pi$
$48$	2.31144	−	11.7753i	0.0481551	−	0.245318i
$49$	−7.00000			−0.142857
$50$		0			0
$51$	−7.94180	+	40.4582i	−0.155722	+	0.793299i
$52$			35.8089i			0.688632i
$53$	−87.8765			−1.65805			−0.829023	−	0.559214i	$-0.811103\pi$
$53$	−87.8765			−1.65805			−0.829023	+	0.559214i	$0.811103\pi$
$54$	−20.9733	+	31.9080i	−0.388395	+	0.590888i
$55$		0			0
$56$			7.48331i			0.133631i
$57$	19.2367	−	97.9983i	0.337486	−	1.71927i
$58$			50.6946i			0.874044i
$59$		−	91.1530i		−	1.54497i	−0.635035	−	0.772483i	$-0.719014\pi$
$59$		−	91.1530i		−	1.54497i	0.635035	−	0.772483i	$-0.280986\pi$
$60$		0			0
$61$	38.5147			0.631388			0.315694	−	0.948861i	$-0.397763\pi$
$61$	38.5147			0.631388			0.315694	+	0.948861i	$0.397763\pi$
$62$	−0.114825			−0.00185202
$63$	9.00147	−	22.0448i	0.142880	−	0.349918i
$64$	8.00000			0.125000
$65$		0			0
$66$	59.3980	+	11.6596i	0.899970	+	0.176661i
$67$		−	29.0894i		−	0.434170i	−0.976153	−	0.217085i	$-0.930345\pi$
$67$		−	29.0894i		−	0.434170i	0.976153	−	0.217085i	$-0.0696549\pi$
$68$	−27.4869			−0.404219
$69$	24.1035	−	122.791i	0.349326	−	1.77959i
$70$		0			0
$71$			27.3041i			0.384565i	0.981340	+	0.192283i	$0.0615891\pi$
$71$			27.3041i			0.384565i	−0.981340	+	0.192283i	$0.938411\pi$
$72$	−23.5669	−	9.62298i	−0.327318	−	0.133652i
$73$		−	47.0278i		−	0.644216i	−0.946703	−	0.322108i	$-0.895609\pi$
$73$		−	47.0278i		−	0.644216i	0.946703	−	0.322108i	$-0.104391\pi$
$74$		−	89.6956i		−	1.21210i
$75$		0			0
$76$	66.5790			0.876039
$77$	−37.7481			−0.490235
$78$	74.5396	+	14.6318i	0.955636	+	0.187588i
$79$	−117.994			−1.49359			−0.746795	−	0.665054i	$-0.768408\pi$
$79$	−117.994			−1.49359			−0.746795	+	0.665054i	$0.768408\pi$
$80$		0			0
$81$	57.8496	+	56.6959i	0.714192	+	0.699949i
$82$			66.3698i			0.809388i
$83$	90.9832			1.09618			0.548092	−	0.836418i	$-0.315354\pi$
$83$	90.9832			1.09618			0.548092	+	0.836418i	$0.315354\pi$
$84$	15.5772	+	3.05775i	0.185443	+	0.0364018i
$85$		0			0
$86$			14.3030i			0.166314i
$87$	105.526	+	20.7143i	1.21294	+	0.238095i
$88$			40.3544i			0.458573i
$89$			102.875i			1.15590i	0.816072	+	0.577951i	$0.196147\pi$
$89$			102.875i			1.15590i	−0.816072	+	0.577951i	$0.803853\pi$
$90$		0			0
$91$	−47.3707			−0.520557
$92$	83.4232			0.906774
$93$	−0.0469185	+	0.239019i	−0.000504500	+	0.00257010i
$94$	62.4663			0.664535
$95$		0			0
$96$	3.26887	−	16.6528i	0.0340508	−	0.173466i
$97$			25.1998i			0.259792i	0.991528	+	0.129896i	$0.0414644\pi$
$97$			25.1998i			0.259792i	−0.991528	+	0.129896i	$0.958536\pi$
$98$	−9.89949			−0.101015
$99$	48.5412	−	118.878i	0.490315	−	1.20079i
$100$		0			0
$101$			152.332i			1.50824i	0.656737	+	0.754120i	$0.271936\pi$
$101$			152.332i			1.50824i	−0.656737	+	0.754120i	$0.728064\pi$
$102$	−11.2314	+	57.2166i	−0.110112	+	0.560947i
$103$			28.9987i			0.281541i	0.990042	+	0.140770i	$0.0449579\pi$
$103$			28.9987i			0.281541i	−0.990042	+	0.140770i	$0.955042\pi$
$104$			50.6414i			0.486937i
$105$		0			0
$106$	−124.276			−1.17242
$107$	20.7173			0.193620			0.0968100	−	0.995303i	$-0.469136\pi$
$107$	20.7173			0.193620			0.0968100	+	0.995303i	$0.469136\pi$
$108$	−29.6608	+	45.1247i	−0.274637	+	0.417821i
$109$	−161.082			−1.47782			−0.738911	−	0.673804i	$-0.764659\pi$
$109$	−161.082			−1.47782			−0.738911	+	0.673804i	$0.764659\pi$
$110$		0			0
$111$	−186.710	−	36.6505i	−1.68207	−	0.330184i
$112$			10.5830i			0.0944911i
$113$	75.1337			0.664900			0.332450	−	0.943121i	$-0.392125\pi$
$113$	75.1337			0.664900			0.332450	+	0.943121i	$0.392125\pi$
$114$	27.2048	−	138.591i	0.238639	−	1.21571i
$115$		0			0
$116$			71.6930i			0.618043i
$117$	60.9151	−	149.183i	0.520642	−	1.27506i
$118$		−	128.910i		−	1.09246i
$119$		−	36.3617i		−	0.305561i
$120$		0			0
$121$	−82.5597			−0.682311
$122$	54.4680			0.446459
$123$	138.155	+	27.1193i	1.12321	+	0.220482i
$124$	−0.162387			−0.00130957
$125$		0			0
$126$	12.7300	−	31.1761i	0.101032	−	0.247429i
$127$		−	73.3212i		−	0.577332i	−0.957430	−	0.288666i	$-0.906788\pi$
$127$		−	73.3212i		−	0.577332i	0.957430	−	0.288666i	$-0.0932117\pi$
$128$	11.3137			0.0883883
$129$	29.7730	+	5.84433i	0.230799	+	0.0453049i
$130$		0			0
$131$			127.227i			0.971198i	0.874182	+	0.485599i	$0.161399\pi$
$131$			127.227i			0.971198i	−0.874182	+	0.485599i	$0.838601\pi$
$132$	84.0015	+	16.4892i	0.636375	+	0.124918i
$133$			88.0757i			0.662223i
$134$		−	41.1386i		−	0.307005i
$135$		0			0
$136$	−38.8723			−0.285826
$137$	207.394			1.51382			0.756912	−	0.653517i	$-0.226707\pi$
$137$	207.394			1.51382			0.756912	+	0.653517i	$0.226707\pi$
$138$	34.0875	−	173.653i	0.247011	−	1.25836i
$139$	41.6001			0.299281			0.149641	−	0.988740i	$-0.452188\pi$
$139$	41.6001			0.299281			0.149641	+	0.988740i	$0.452188\pi$
$140$		0			0
$141$	25.5243	−	130.030i	0.181024	−	0.922196i
$142$			38.6139i			0.271929i
$143$	−255.450			−1.78637
$144$	−33.3286	−	13.6089i	−0.231449	−	0.0945066i
$145$		0			0
$146$		−	66.5073i		−	0.455529i
$147$	−4.04503	+	20.6067i	−0.0275172	+	0.140182i
$148$		−	126.849i		−	0.857086i
$149$		−	128.509i		−	0.862474i	−0.902239	−	0.431237i	$-0.858077\pi$
$149$		−	128.509i		−	0.862474i	0.902239	−	0.431237i	$-0.141923\pi$
$150$		0			0
$151$	114.468			0.758065			0.379032	−	0.925383i	$-0.376257\pi$
$151$	114.468			0.758065			0.379032	+	0.925383i	$0.376257\pi$
$152$	94.1569			0.619453
$153$	114.513	+	46.7585i	0.748448	+	0.305611i
$154$	−53.3839			−0.346648
$155$		0			0
$156$	105.415	+	20.6925i	0.675736	+	0.132645i
$157$		−	2.25663i		−	0.0143734i	−0.999974	−	0.00718671i	$-0.997712\pi$
$157$		−	2.25663i		−	0.0143734i	0.999974	−	0.00718671i	$-0.00228762\pi$
$158$	−166.868			−1.05613
$159$	−50.7804	+	258.692i	−0.319373	+	1.62700i
$160$		0			0
$161$			110.358i			0.685456i
$162$	81.8117	+	80.1801i	0.505010	+	0.494939i
$163$		−	37.2963i		−	0.228812i	−0.993434	−	0.114406i	$-0.963504\pi$
$163$		−	37.2963i		−	0.228812i	0.993434	−	0.114406i	$-0.0364964\pi$
$164$			93.8611i			0.572324i
$165$		0			0
$166$	128.670			0.775119
$167$	52.9627			0.317142			0.158571	−	0.987348i	$-0.449311\pi$
$167$	52.9627			0.317142			0.158571	+	0.987348i	$0.449311\pi$
$168$	22.0295	+	4.32431i	0.131128	+	0.0257400i
$169$	−151.569			−0.896857
$170$		0			0
$171$	−277.373	−	113.259i	−1.62207	−	0.662332i
$172$			20.2275i			0.117602i
$173$	116.414			0.672914			0.336457	−	0.941699i	$-0.390771\pi$
$173$	116.414			0.672914			0.336457	+	0.941699i	$0.390771\pi$
$174$	149.236	+	29.2944i	0.857676	+	0.168359i
$175$		0			0
$176$			57.0697i			0.324260i
$177$	−268.338	−	52.6738i	−1.51603	−	0.297592i
$178$			145.488i			0.817346i
$179$		−	11.4416i		−	0.0639194i	−0.999489	−	0.0319597i	$-0.989825\pi$
$179$		−	11.4416i		−	0.0639194i	0.999489	−	0.0319597i	$-0.0101748\pi$
$180$		0			0
$181$	194.805			1.07627			0.538135	−	0.842858i	$-0.319129\pi$
$181$	194.805			1.07627			0.538135	+	0.842858i	$0.319129\pi$
$182$	−66.9923			−0.368089
$183$	22.2561	−	113.380i	0.121618	−	0.619564i
$184$	117.978			0.641186
$185$		0			0
$186$	−0.0663528	+	0.338024i	−0.000356736	+	0.00181733i
$187$		−	196.084i		−	1.04858i
$188$	88.3407			0.469898
$189$	−59.6944	−	39.2375i	−0.315843	−	0.207606i
$190$		0			0
$191$			192.124i			1.00589i	0.864320	+	0.502943i	$0.167749\pi$
$191$			192.124i			1.00589i	−0.864320	+	0.502943i	$0.832251\pi$
$192$	4.62289	−	23.5506i	0.0240775	−	0.122659i
$193$		−	284.882i		−	1.47607i	−0.674761	−	0.738037i	$-0.735753\pi$
$193$		−	284.882i		−	1.47607i	0.674761	−	0.738037i	$-0.264247\pi$
$194$			35.6379i			0.183701i
$195$		0			0
$196$	−14.0000			−0.0714286
$197$	171.732			0.871734			0.435867	−	0.900011i	$-0.356442\pi$
$197$	171.732			0.871734			0.435867	+	0.900011i	$0.356442\pi$
$198$	68.6476	−	168.120i	0.346705	−	0.849089i
$199$	−348.035			−1.74892			−0.874459	−	0.485100i	$-0.838783\pi$
$199$	−348.035			−1.74892			−0.874459	+	0.485100i	$0.838783\pi$
$200$		0			0
$201$	−85.6339	−	16.8096i	−0.426040	−	0.0836299i
$202$			215.430i			1.06649i
$203$	−94.8409			−0.467196
$204$	−15.8836	+	80.9165i	−0.0778608	+	0.396649i
$205$		0			0
$206$			41.0103i			0.199079i
$207$	−347.547	−	141.913i	−1.67897	−	0.685568i
$208$			71.6177i			0.344316i
$209$			474.956i			2.27252i
$210$		0			0
$211$	−102.763			−0.487031			−0.243515	−	0.969897i	$-0.578301\pi$
$211$	−102.763			−0.487031			−0.243515	+	0.969897i	$0.578301\pi$
$212$	−175.753			−0.829023
$213$	80.3785	+	15.7780i	0.377364	+	0.0740751i
$214$	29.2987			0.136910
$215$		0			0
$216$	−41.9467	+	63.8159i	−0.194198	+	0.295444i
$217$		−	0.214818i		−	0.000989944i
$218$	−227.805			−1.04498
$219$	−138.441	−	27.1755i	−0.632152	−	0.124089i
$220$		0			0
$221$		−	246.069i		−	1.11343i
$222$	−264.048	−	51.8316i	−1.18940	−	0.233476i
$223$			115.243i			0.516784i	0.966040	+	0.258392i	$0.0831925\pi$
$223$			115.243i			0.516784i	−0.966040	+	0.258392i	$0.916807\pi$
$224$			14.9666i			0.0668153i
$225$		0			0
$226$	106.255			0.470155
$227$	−2.80189			−0.0123431			−0.00617157	−	0.999981i	$-0.501964\pi$
$227$	−2.80189			−0.0123431			−0.00617157	+	0.999981i	$0.501964\pi$
$228$	38.4734	−	195.997i	0.168743	−	0.859634i
$229$	109.965			0.480197			0.240098	−	0.970749i	$-0.422820\pi$
$229$	109.965			0.480197			0.240098	+	0.970749i	$0.422820\pi$
$230$		0			0
$231$	−21.8131	+	111.124i	−0.0944292	+	0.481054i
$232$			101.389i			0.437022i
$233$	−199.489			−0.856177			−0.428089	−	0.903737i	$-0.640813\pi$
$233$	−199.489			−0.856177			−0.428089	+	0.903737i	$0.640813\pi$
$234$	86.1470	−	210.976i	0.368150	−	0.901607i
$235$		0			0
$236$		−	182.306i		−	0.772483i
$237$	−68.1839	+	347.352i	−0.287696	+	1.46562i
$238$		−	51.4233i		−	0.216064i
$239$		−	16.8335i		−	0.0704329i	−0.999380	−	0.0352165i	$-0.988788\pi$
$239$		−	16.8335i		−	0.0704329i	0.999380	−	0.0352165i	$-0.0112121\pi$
$240$		0			0
$241$	−29.6944			−0.123213			−0.0616066	−	0.998101i	$-0.519622\pi$
$241$	−29.6944			−0.123213			−0.0616066	+	0.998101i	$0.519622\pi$
$242$	−116.757			−0.482467
$243$	200.332	−	137.536i	0.824410	−	0.565993i
$244$	77.0293			0.315694
$245$		0			0
$246$	195.381	+	38.3525i	0.794231	+	0.155905i
$247$			596.030i			2.41308i
$248$	−0.229650			−0.000926008
$249$	52.5756	−	267.838i	0.211147	−	1.07566i
$250$		0			0
$251$			239.487i			0.954133i	0.878867	+	0.477067i	$0.158300\pi$
$251$			239.487i			0.954133i	−0.878867	+	0.477067i	$0.841700\pi$
$252$	18.0029	−	44.0896i	0.0714402	−	0.174959i
$253$			595.117i			2.35224i
$254$		−	103.692i		−	0.408235i
$255$		0			0
$256$	16.0000			0.0625000
$257$	−192.966			−0.750841			−0.375421	−	0.926855i	$-0.622502\pi$
$257$	−192.966			−0.750841			−0.375421	+	0.926855i	$0.622502\pi$
$258$	42.1054	+	8.26513i	0.163199	+	0.0320354i
$259$	167.805			0.647896
$260$		0			0
$261$	121.958	−	298.678i	0.467273	−	1.14436i
$262$			179.926i			0.686741i
$263$	−244.184			−0.928457			−0.464228	−	0.885716i	$-0.653668\pi$
$263$	−244.184			−0.928457			−0.464228	+	0.885716i	$0.653668\pi$
$264$	118.796	+	23.3192i	0.449985	+	0.0883304i
$265$		0			0
$266$			124.558i			0.468263i
$267$	302.846	+	59.4476i	1.13426	+	0.222650i
$268$		−	58.1788i		−	0.217085i
$269$			60.6343i			0.225406i	0.993629	+	0.112703i	$0.0359509\pi$
$269$			60.6343i			0.225406i	−0.993629	+	0.112703i	$0.964049\pi$
$270$		0			0
$271$	−271.747			−1.00276			−0.501378	−	0.865228i	$-0.667173\pi$
$271$	−271.747			−1.00276			−0.501378	+	0.865228i	$0.667173\pi$
$272$	−54.9738			−0.202110
$273$	−27.3737	+	139.451i	−0.100270	+	0.510809i
$274$	293.299			1.07044
$275$		0			0
$276$	48.2070	−	245.583i	0.174663	−	0.889793i
$277$		−	465.627i		−	1.68096i	−0.541839	−	0.840482i	$-0.682272\pi$
$277$		−	465.627i		−	1.68096i	0.541839	−	0.840482i	$-0.317728\pi$
$278$	58.8314			0.211624
$279$	0.676517	+	0.276240i	0.00242479	+	0.000990106i
$280$		0			0
$281$		−	499.505i		−	1.77760i	−0.458296	−	0.888800i	$-0.651540\pi$
$281$		−	499.505i		−	1.77760i	0.458296	−	0.888800i	$-0.348460\pi$
$282$	36.0968	−	183.890i	0.128003	−	0.652091i
$283$			90.9224i			0.321280i	0.987013	+	0.160640i	$0.0513559\pi$
$283$			90.9224i			0.321280i	−0.987013	+	0.160640i	$0.948644\pi$
$284$			54.6083i			0.192283i
$285$		0			0
$286$	−361.261			−1.26315
$287$	−124.167			−0.432636
$288$	−47.1338	−	19.2460i	−0.163659	−	0.0668262i
$289$	−100.118			−0.346428
$290$		0			0
$291$	74.1838	+	14.5620i	0.254927	+	0.0500412i
$292$		−	94.0555i		−	0.322108i
$293$	−90.2424			−0.307995			−0.153997	−	0.988071i	$-0.549215\pi$
$293$	−90.2424			−0.307995			−0.153997	+	0.988071i	$0.549215\pi$
$294$	−5.72053	+	29.1423i	−0.0194576	+	0.0991236i
$295$		0			0
$296$		−	179.391i		−	0.606052i
$297$	−321.907	−	211.592i	−1.08386	−	0.712430i
$298$		−	181.739i		−	0.609861i
$299$			746.823i			2.49773i
$300$		0			0
$301$	−26.7584			−0.0888984
$302$	161.882			0.536033
$303$	448.439	+	88.0268i	1.48000	+	0.290518i
$304$	133.158			0.438020
$305$		0			0
$306$	161.945	+	66.1264i	0.529233	+	0.216099i
$307$		−	538.749i		−	1.75488i	−0.479683	−	0.877442i	$-0.659248\pi$
$307$		−	538.749i		−	1.75488i	0.479683	−	0.877442i	$-0.340752\pi$
$308$	−75.4962			−0.245117
$309$	85.3669	+	16.7572i	0.276268	+	0.0542304i
$310$		0			0
$311$		−	62.9946i		−	0.202555i	−0.994858	−	0.101277i	$-0.967707\pi$
$311$		−	62.9946i		−	0.202555i	0.994858	−	0.101277i	$-0.0322930\pi$
$312$	149.079	+	29.2637i	0.477818	+	0.0937938i
$313$		−	432.883i		−	1.38301i	−0.722370	−	0.691507i	$-0.756947\pi$
$313$		−	432.883i		−	1.38301i	0.722370	−	0.691507i	$-0.243053\pi$
$314$		−	3.19135i		−	0.0101635i
$315$		0			0
$316$	−235.987			−0.746795
$317$	−333.665			−1.05257			−0.526285	−	0.850308i	$-0.676415\pi$
$317$	−333.665			−1.05257			−0.526285	+	0.850308i	$0.676415\pi$
$318$	−71.8143	+	365.846i	−0.225831	+	1.15046i
$319$	−511.437			−1.60325
$320$		0			0
$321$	11.9717	−	60.9881i	0.0372951	−	0.189994i
$322$			156.070i			0.484691i
$323$	−457.512			−1.41645
$324$	115.699	+	113.392i	0.357096	+	0.349975i
$325$		0			0
$326$		−	52.7450i		−	0.161794i
$327$	−93.0832	+	474.198i	−0.284658	+	1.45015i
$328$			132.740i			0.404694i
$329$			116.864i			0.355209i
$330$		0			0
$331$	195.468			0.590538			0.295269	−	0.955414i	$-0.404591\pi$
$331$	195.468			0.590538			0.295269	+	0.955414i	$0.404591\pi$
$332$	181.966			0.548092
$333$	−215.785	+	528.462i	−0.648002	+	1.58697i
$334$	74.9006			0.224253
$335$		0			0
$336$	31.1545	+	6.11550i	0.0927216	+	0.0182009i
$337$		−	67.6092i		−	0.200621i	−0.994956	−	0.100310i	$-0.968016\pi$
$337$		−	67.6092i		−	0.200621i	0.994956	−	0.100310i	$-0.0319836\pi$
$338$	−214.351			−0.634174
$339$	43.4168	−	221.180i	0.128073	−	0.652449i
$340$		0			0
$341$		−	1.15842i		−	0.00339714i
$342$	−392.265	−	160.172i	−1.14697	−	0.468339i
$343$		−	18.5203i		−	0.0539949i
$344$			28.6060i			0.0831569i
$345$		0			0
$346$	164.634			0.475822
$347$	−182.062			−0.524675			−0.262338	−	0.964976i	$-0.584493\pi$
$347$	−182.062			−0.524675			−0.262338	+	0.964976i	$0.584493\pi$
$348$	211.051	+	41.4285i	0.606469	+	0.119048i
$349$	86.1666			0.246896			0.123448	−	0.992351i	$-0.460605\pi$
$349$	86.1666			0.246896			0.123448	+	0.992351i	$0.460605\pi$
$350$		0			0
$351$	−403.966	−	265.530i	−1.15090	−	0.756495i
$352$			80.7088i			0.229286i
$353$	−400.345			−1.13412			−0.567060	−	0.823676i	$-0.691919\pi$
$353$	−400.345			−1.13412			−0.567060	+	0.823676i	$0.691919\pi$
$354$	−379.487	−	74.4920i	−1.07200	−	0.210429i
$355$		0			0
$356$			205.750i			0.577951i
$357$	−107.042	−	21.0120i	−0.299839	−	0.0588572i
$358$		−	16.1808i		−	0.0451979i
$359$		−	68.2498i		−	0.190111i	−0.995472	−	0.0950554i	$-0.969697\pi$
$359$		−	68.2498i		−	0.190111i	0.995472	−	0.0950554i	$-0.0303028\pi$
$360$		0			0
$361$	747.190			2.06978
$362$	275.496			0.761038
$363$	−47.7080	+	243.041i	−0.131427	+	0.669534i
$364$	−94.7414			−0.260279
$365$		0			0
$366$	31.4749	−	160.344i	0.0859970	−	0.438098i
$367$			217.412i			0.592403i	0.955125	+	0.296202i	$0.0957200\pi$
$367$			217.412i			0.592403i	−0.955125	+	0.296202i	$0.904280\pi$
$368$	166.846			0.453387
$369$	159.669	−	391.033i	0.432707	−	1.05971i
$370$		0			0
$371$		−	232.499i		−	0.626683i
$372$	−0.0938371	+	0.478038i	−0.000252250	+	0.00128505i
$373$		−	62.8851i		−	0.168593i	−0.996441	−	0.0842964i	$-0.973136\pi$
$373$		−	62.8851i		−	0.168593i	0.996441	−	0.0842964i	$-0.0268643\pi$
$374$		−	277.304i		−	0.741455i
$375$		0			0
$376$	124.933			0.332268
$377$	−641.811			−1.70242
$378$	−84.4206	−	55.4903i	−0.223335	−	0.146800i
$379$	225.628			0.595324			0.297662	−	0.954671i	$-0.403793\pi$
$379$	225.628			0.595324			0.297662	+	0.954671i	$0.403793\pi$
$380$		0			0
$381$	−215.844	−	42.3694i	−0.566521	−	0.111206i
$382$			271.705i			0.711268i
$383$	−245.742			−0.641624			−0.320812	−	0.947143i	$-0.603956\pi$
$383$	−245.742			−0.641624			−0.320812	+	0.947143i	$0.603956\pi$
$384$	6.53775	−	33.3055i	0.0170254	−	0.0867331i
$385$		0			0
$386$		−	402.884i		−	1.04374i
$387$	34.4093	−	84.2692i	0.0889129	−	0.217750i
$388$			50.3997i			0.129896i
$389$		−	407.237i		−	1.04688i	−0.852062	−	0.523441i	$-0.824648\pi$
$389$		−	407.237i		−	1.04688i	0.852062	−	0.523441i	$-0.175352\pi$
$390$		0			0
$391$	−573.261			−1.46614
$392$	−19.7990			−0.0505076
$393$	374.533	+	73.5195i	0.953011	+	0.187072i
$394$	242.865			0.616409
$395$		0			0
$396$	97.0824	−	237.757i	0.245157	−	0.600396i
$397$		−	330.458i		−	0.832388i	−0.909276	−	0.416194i	$-0.863364\pi$
$397$		−	330.458i		−	0.832388i	0.909276	−	0.416194i	$-0.136636\pi$
$398$	−492.195			−1.23667
$399$	259.279	+	50.8955i	0.649822	+	0.127558i
$400$		0			0
$401$			267.184i			0.666294i	0.942875	+	0.333147i	$0.108110\pi$
$401$			267.184i			0.666294i	−0.942875	+	0.333147i	$0.891890\pi$
$402$	−121.105	−	23.7724i	−0.301255	−	0.0591353i
$403$		−	1.45372i		−	0.00360726i
$404$			304.665i			0.754120i
$405$		0			0
$406$	−134.125			−0.330358
$407$	904.903			2.22335
$408$	−22.4628	+	114.433i	−0.0550559	+	0.280473i
$409$	654.773			1.60091			0.800456	−	0.599392i	$-0.204591\pi$
$409$	654.773			1.60091			0.800456	+	0.599392i	$0.204591\pi$
$410$		0			0
$411$	119.845	−	610.530i	0.291593	−	1.48548i
$412$			57.9974i			0.140770i
$413$	241.168			0.583943
$414$	−491.506	−	200.695i	−1.18721	−	0.484770i
$415$		0			0
$416$			101.283i			0.243468i
$417$	24.0390	−	122.463i	0.0576476	−	0.293676i
$418$			671.689i			1.60691i
$419$			71.4321i			0.170482i	0.996360	+	0.0852411i	$0.0271661\pi$
$419$			71.4321i			0.170482i	−0.996360	+	0.0852411i	$0.972834\pi$
$420$		0			0
$421$	306.425			0.727851			0.363926	−	0.931428i	$-0.381436\pi$
$421$	306.425			0.727851			0.363926	+	0.931428i	$0.381436\pi$
$422$	−145.329			−0.344383
$423$	−368.034	−	150.278i	−0.870057	−	0.355267i
$424$	−248.552			−0.586208
$425$		0			0
$426$	113.672	+	22.3135i	0.266837	+	0.0523790i
$427$			101.900i			0.238642i
$428$	41.4347			0.0968100
$429$	−147.615	+	752.000i	−0.344090	+	1.75291i
$430$		0			0
$431$		−	472.801i		−	1.09698i	−0.836155	−	0.548492i	$-0.815202\pi$
$431$		−	472.801i		−	1.09698i	0.836155	−	0.548492i	$-0.184798\pi$
$432$	−59.3216	+	90.2494i	−0.137318	+	0.208911i
$433$			378.058i			0.873114i	0.899677	+	0.436557i	$0.143802\pi$
$433$			378.058i			0.873114i	−0.899677	+	0.436557i	$0.856198\pi$
$434$		−	0.303798i		−	0.000699996i
$435$		0			0
$436$	−322.165			−0.738911
$437$	1388.56			3.17748
$438$	−195.786	−	38.4320i	−0.446999	−	0.0877442i
$439$	121.193			0.276066			0.138033	−	0.990428i	$-0.455922\pi$
$439$	121.193			0.276066			0.138033	+	0.990428i	$0.455922\pi$
$440$		0			0
$441$	58.3251	+	23.8157i	0.132256	+	0.0540037i
$442$		−	347.994i		−	0.787316i
$443$	−408.418			−0.921936			−0.460968	−	0.887417i	$-0.652498\pi$
$443$	−408.418			−0.921936			−0.460968	+	0.887417i	$0.652498\pi$
$444$	−373.420	−	73.3009i	−0.841036	−	0.165092i
$445$		0			0
$446$			162.978i			0.365421i
$447$	−378.306	−	74.2601i	−0.846323	−	0.166130i
$448$			21.1660i			0.0472456i
$449$		−	473.545i		−	1.05467i	−0.849659	−	0.527333i	$-0.823192\pi$
$449$		−	473.545i		−	1.05467i	0.849659	−	0.527333i	$-0.176808\pi$
$450$		0			0
$451$	−669.579			−1.48465
$452$	150.267			0.332450
$453$	66.1464	−	336.973i	0.146019	−	0.743869i
$454$	−3.96247			−0.00872791
$455$		0			0
$456$	54.4096	−	277.181i	0.119319	−	0.607853i
$457$		−	897.706i		−	1.96435i	−0.187981	−	0.982173i	$-0.560194\pi$
$457$		−	897.706i		−	1.96435i	0.187981	−	0.982173i	$-0.439806\pi$
$458$	155.514			0.339551
$459$	203.821	−	310.084i	0.444054	−	0.675565i
$460$		0			0
$461$		−	429.768i		−	0.932253i	−0.884718	−	0.466126i	$-0.845649\pi$
$461$		−	429.768i		−	0.932253i	0.884718	−	0.466126i	$-0.154351\pi$
$462$	−30.8484	+	157.152i	−0.0667715	+	0.340157i
$463$		−	86.6076i		−	0.187057i	−0.995617	−	0.0935287i	$-0.970185\pi$
$463$		−	86.6076i		−	0.187057i	0.995617	−	0.0935287i	$-0.0298147\pi$
$464$			143.386i			0.309021i
$465$		0			0
$466$	−282.120			−0.605409
$467$	−907.883			−1.94408			−0.972038	−	0.234826i	$-0.924548\pi$
$467$	−907.883			−1.94408			−0.972038	+	0.234826i	$0.924548\pi$
$468$	121.830	−	298.365i	0.260321	−	0.637532i
$469$	76.9633			0.164101
$470$		0			0
$471$	−6.64310	−	1.30402i	−0.0141043	−	0.00276861i
$472$		−	257.820i		−	0.546228i
$473$	−144.297			−0.305068
$474$	−96.4266	+	491.230i	−0.203432	+	1.03635i
$475$		0			0
$476$		−	72.7235i		−	0.152780i
$477$	732.200	+	298.976i	1.53501	+	0.626785i
$478$		−	23.8061i		−	0.0498036i
$479$			79.1123i			0.165161i	0.996584	+	0.0825807i	$0.0263162\pi$
$479$			79.1123i			0.165161i	−0.996584	+	0.0825807i	$0.973684\pi$
$480$		0			0
$481$	1135.58			2.36087
$482$	−41.9942			−0.0871249
$483$	324.876	+	63.7718i	0.672620	+	0.132033i
$484$	−165.119			−0.341156
$485$		0			0
$486$	283.312	−	194.506i	0.582946	−	0.400218i
$487$			16.5695i			0.0340236i	0.999855	+	0.0170118i	$0.00541529\pi$
$487$			16.5695i			0.0340236i	−0.999855	+	0.0170118i	$0.994585\pi$
$488$	108.936			0.223229
$489$	−109.794	−	21.5521i	−0.224527	−	0.0440738i
$490$		0			0
$491$		−	401.794i		−	0.818317i	−0.912463	−	0.409159i	$-0.865822\pi$
$491$		−	401.794i		−	0.818317i	0.912463	−	0.409159i	$-0.134178\pi$
$492$	276.310	+	54.2386i	0.561606	+	0.110241i
$493$		−	492.654i		−	0.999299i
$494$			842.913i			1.70630i
$495$		0			0
$496$	−0.324774			−0.000654786
$497$	−72.2400			−0.145352
$498$	74.3532	−	378.781i	0.149304	−	0.760603i
$499$	−376.051			−0.753609			−0.376804	−	0.926293i	$-0.622977\pi$
$499$	−376.051			−0.753609			−0.376804	+	0.926293i	$0.622977\pi$
$500$		0			0
$501$	30.6051	−	155.913i	0.0610880	−	0.311203i
$502$			338.686i			0.674674i
$503$	639.290			1.27096			0.635478	−	0.772119i	$-0.280803\pi$
$503$	639.290			1.27096			0.635478	+	0.772119i	$0.280803\pi$
$504$	25.4600	−	62.3521i	0.0505159	−	0.123715i
$505$		0			0
$506$			841.623i			1.66329i
$507$	−87.5857	+	446.192i	−0.172753	+	0.880062i
$508$		−	146.642i		−	0.288666i
$509$			199.998i			0.392923i	0.980512	+	0.196461i	$0.0629450\pi$
$509$			199.998i			0.392923i	−0.980512	+	0.196461i	$0.937055\pi$
$510$		0			0
$511$	124.424			0.243491
$512$	22.6274			0.0441942
$513$	−493.696	+	751.089i	−0.962371	+	1.46411i
$514$	−272.895			−0.530925
$515$		0			0
$516$	59.5460	+	11.6887i	0.115399	+	0.0226524i
$517$			630.198i			1.21895i
$518$	237.312			0.458132
$519$	67.2711	−	342.702i	0.129617	−	0.660313i
$520$		0			0
$521$			17.5409i			0.0336678i	0.999858	+	0.0168339i	$0.00535865\pi$
$521$			17.5409i			0.0336678i	−0.999858	+	0.0168339i	$0.994641\pi$
$522$	172.475	−	422.395i	0.330412	−	0.809186i
$523$		−	556.462i		−	1.06398i	−0.846751	−	0.531990i	$-0.821444\pi$
$523$		−	556.462i		−	1.06398i	0.846751	−	0.531990i	$-0.178556\pi$
$524$			254.454i			0.485599i
$525$		0			0
$526$	−345.329			−0.656518
$527$	1.11588			0.00211742
$528$	168.003	+	32.9784i	0.318188	+	0.0624590i
$529$	1210.86			2.28895
$530$		0			0
$531$	−310.124	+	759.501i	−0.584038	+	1.43032i
$532$			176.151i			0.331112i
$533$	−840.265			−1.57648
$534$	428.289	+	84.0715i	0.802040	+	0.157437i
$535$		0			0
$536$		−	82.2772i		−	0.153502i
$537$	−33.6819	−	6.61164i	−0.0627224	−	0.0123122i
$538$			85.7498i			0.159386i
$539$		−	99.8720i		−	0.185291i
$540$		0			0
$541$	301.519			0.557336			0.278668	−	0.960387i	$-0.410107\pi$
$541$	301.519			0.557336			0.278668	+	0.960387i	$0.410107\pi$
$542$	−384.308			−0.709056
$543$	112.570	−	573.471i	0.207311	−	1.05612i
$544$	−77.7447			−0.142913
$545$		0			0
$546$	−38.7122	+	197.213i	−0.0709015	+	0.361196i
$547$		−	89.9582i		−	0.164457i	−0.996613	−	0.0822287i	$-0.973796\pi$
$547$		−	89.9582i		−	0.164457i	0.996613	−	0.0822287i	$-0.0262038\pi$
$548$	414.788			0.756912
$549$	−320.910	−	131.036i	−0.584536	−	0.238681i
$550$		0			0
$551$			1193.31i			2.16572i
$552$	68.1750	−	347.307i	0.123505	−	0.629179i
$553$		−	312.182i		−	0.564524i
$554$		−	658.496i		−	1.18862i
$555$		0			0
$556$	83.2001			0.149641
$557$	−496.569			−0.891507			−0.445753	−	0.895156i	$-0.647064\pi$
$557$	−496.569			−0.891507			−0.445753	+	0.895156i	$0.647064\pi$
$558$	0.956739	+	0.390662i	0.00171459	+	0.000700111i
$559$	−181.081			−0.323937
$560$		0			0
$561$	−577.235	−	113.309i	−1.02894	−	0.201977i
$562$		−	706.407i		−	1.25695i
$563$	846.707			1.50392			0.751960	−	0.659208i	$-0.229108\pi$
$563$	846.707			1.50392			0.751960	+	0.659208i	$0.229108\pi$
$564$	51.0486	−	260.059i	0.0905118	−	0.461098i
$565$		0			0
$566$			128.584i			0.227180i
$567$	−150.003	+	153.056i	−0.264556	+	0.269939i
$568$			77.2278i			0.135964i
$569$			406.419i			0.714270i	0.934053	+	0.357135i	$0.116246\pi$
$569$			406.419i			0.714270i	−0.934053	+	0.357135i	$0.883754\pi$
$570$		0			0
$571$	−679.669			−1.19031			−0.595157	−	0.803610i	$-0.702910\pi$
$571$	−679.669			−1.19031			−0.595157	+	0.803610i	$0.702910\pi$
$572$	−510.901			−0.893183
$573$	565.579	+	111.021i	0.987049	+	0.193754i
$574$	−175.598			−0.305920
$575$		0			0
$576$	−66.6572	−	27.2179i	−0.115724	−	0.0472533i
$577$			103.056i			0.178606i	0.996005	+	0.0893030i	$0.0284639\pi$
$577$			103.056i			0.178606i	−0.996005	+	0.0893030i	$0.971536\pi$
$578$	−141.588			−0.244961
$579$	−838.642	−	164.622i	−1.44843	−	0.284322i
$580$		0			0
$581$			240.719i			0.414318i
$582$	104.912	+	20.5938i	0.180261	+	0.0353845i
$583$		−	1253.77i		−	2.15055i
$584$		−	133.015i		−	0.227765i
$585$		0			0
$586$	−127.622			−0.217785
$587$	−205.505			−0.350093			−0.175047	−	0.984560i	$-0.556008\pi$
$587$	−205.505			−0.350093			−0.175047	+	0.984560i	$0.556008\pi$
$588$	−8.09005	+	41.2135i	−0.0137586	+	0.0700910i
$589$	−2.70289			−0.00458895
$590$		0			0
$591$	99.2369	−	505.547i	0.167914	−	0.855409i
$592$		−	253.698i		−	0.428543i
$593$	432.614			0.729534			0.364767	−	0.931099i	$-0.381149\pi$
$593$	432.614			0.729534			0.364767	+	0.931099i	$0.381149\pi$
$594$	−455.245	−	299.236i	−0.766406	−	0.503764i
$595$		0			0
$596$		−	257.017i		−	0.431237i
$597$	−201.116	+	1024.55i	−0.336877	+	1.71617i
$598$			1056.17i			1.76616i
$599$			630.716i			1.05295i	0.850191	+	0.526474i	$0.176486\pi$
$599$			630.716i			1.05295i	−0.850191	+	0.526474i	$0.823514\pi$
$600$		0			0
$601$	283.127			0.471093			0.235547	−	0.971863i	$-0.424312\pi$
$601$	283.127			0.471093			0.235547	+	0.971863i	$0.424312\pi$
$602$	−37.8421			−0.0628607
$603$	−98.9690	+	242.377i	−0.164128	+	0.401952i
$604$	228.936			0.379032
$605$		0			0
$606$	634.188	+	124.489i	1.04652	+	0.205427i
$607$			285.181i			0.469820i	0.972017	+	0.234910i	$0.0754795\pi$
$607$			285.181i			0.469820i	−0.972017	+	0.234910i	$0.924521\pi$
$608$	188.314			0.309727
$609$	−54.8048	+	279.194i	−0.0899915	+	0.458447i
$610$		0			0
$611$			790.846i			1.29435i
$612$	229.025	+	93.5169i	0.374224	+	0.152805i
$613$			14.0972i			0.0229970i	0.999934	+	0.0114985i	$0.00366017\pi$
$613$			14.0972i			0.0229970i	−0.999934	+	0.0114985i	$0.996340\pi$
$614$		−	761.906i		−	1.24089i
$615$		0			0
$616$	−106.768			−0.173324
$617$	177.382			0.287491			0.143745	−	0.989615i	$-0.454085\pi$
$617$	177.382			0.287491			0.143745	+	0.989615i	$0.454085\pi$
$618$	120.727	+	23.6983i	0.195351	+	0.0383467i
$619$	−288.349			−0.465830			−0.232915	−	0.972497i	$-0.574826\pi$
$619$	−288.349			−0.465830			−0.232915	+	0.972497i	$0.574826\pi$
$620$		0			0
$621$	−618.599	+	941.111i	−0.996134	+	1.51548i
$622$		−	89.0878i		−	0.143228i
$623$	−272.182			−0.436890
$624$	210.830	+	41.3851i	0.337868	+	0.0663223i
$625$		0			0
$626$		−	612.189i		−	0.977938i
$627$	1398.18	+	274.458i	2.22996	+	0.437732i
$628$		−	4.51325i		−	0.00718671i
$629$			871.670i			1.38580i
$630$		0			0
$631$	794.689			1.25941			0.629706	−	0.776834i	$-0.283175\pi$
$631$	794.689			1.25941			0.629706	+	0.776834i	$0.283175\pi$
$632$	−333.736			−0.528064
$633$	−59.3830	+	302.517i	−0.0938119	+	0.477910i
$634$	−471.873			−0.744279
$635$		0			0
$636$	−101.561	+	517.385i	−0.159687	+	0.813498i
$637$		−	125.331i		−	0.196752i
$638$	−723.281			−1.13367
$639$	92.8951	−	227.502i	0.145376	−	0.356029i
$640$		0			0
$641$			1151.75i			1.79680i	0.439181	+	0.898399i	$0.355269\pi$
$641$			1151.75i			1.79680i	−0.439181	+	0.898399i	$0.644731\pi$
$642$	16.9306	−	86.2502i	0.0263716	−	0.134346i
$643$		−	528.134i		−	0.821359i	−0.911780	−	0.410679i	$-0.865292\pi$
$643$		−	528.134i		−	0.821359i	0.911780	−	0.410679i	$-0.134708\pi$
$644$			220.717i			0.342728i
$645$		0			0
$646$	−647.020			−1.00158
$647$	605.917			0.936503			0.468251	−	0.883595i	$-0.344884\pi$
$647$	605.917			0.936503			0.468251	+	0.883595i	$0.344884\pi$
$648$	163.623	+	160.360i	0.252505	+	0.247470i
$649$	1300.52			2.00388
$650$		0			0
$651$	−0.632385	−	0.124135i	−0.000971406	−	0.000190683i
$652$		−	74.5927i		−	0.114406i
$653$	500.560			0.766554			0.383277	−	0.923633i	$-0.374795\pi$
$653$	500.560			0.766554			0.383277	+	0.923633i	$0.374795\pi$
$654$	−131.640	+	670.617i	−0.201284	+	1.02541i
$655$		0			0
$656$			187.722i			0.286162i
$657$	−160.000	+	391.843i	−0.243531	+	0.596412i
$658$			165.270i			0.251171i
$659$		−	1168.36i		−	1.77293i	−0.462796	−	0.886465i	$-0.653154\pi$
$659$		−	1168.36i		−	1.77293i	0.462796	−	0.886465i	$-0.346846\pi$
$660$		0			0
$661$	−890.409			−1.34706			−0.673531	−	0.739159i	$-0.735223\pi$
$661$	−890.409			−1.34706			−0.673531	+	0.739159i	$0.735223\pi$
$662$	276.434			0.417574
$663$	−724.382	−	142.193i	−1.09258	−	0.214470i
$664$	257.339			0.387559
$665$		0			0
$666$	−305.166	+	747.358i	−0.458207	+	1.12216i
$667$			1495.21i			2.24170i
$668$	105.925			0.158571
$669$	339.254	+	66.5942i	0.507106	+	0.0995430i
$670$		0			0
$671$			549.506i			0.818935i
$672$	44.0591	+	8.64863i	0.0655641	+	0.0128700i
$673$			402.432i			0.597968i	0.954258	+	0.298984i	$0.0966477\pi$
$673$			402.432i			0.597968i	−0.954258	+	0.298984i	$0.903352\pi$
$674$		−	95.6139i		−	0.141860i
$675$		0			0
$676$	−303.138			−0.448429
$677$	−1055.94			−1.55973			−0.779865	−	0.625948i	$-0.784712\pi$
$677$	−1055.94			−1.55973			−0.779865	+	0.625948i	$0.784712\pi$
$678$	61.4006	−	312.796i	0.0905614	−	0.461351i
$679$	−66.6725			−0.0981922
$680$		0			0
$681$	−1.61910	+	8.24826i	−0.00237754	+	0.0121120i
$682$		−	1.63826i		−	0.00240214i
$683$	0.617425			0.000903990			0.000451995	−	1.00000i	$-0.499856\pi$
$683$	0.617425			0.000903990			0.000451995		1.00000i	$0.499856\pi$
$684$	−554.746	−	226.517i	−0.811033	−	0.331166i
$685$		0			0
$686$		−	26.1916i		−	0.0381802i
$687$	63.5445	−	323.717i	0.0924957	−	0.471205i
$688$			40.4549i			0.0588008i
$689$		−	1573.38i		−	2.28357i
$690$		0			0
$691$	499.521			0.722896			0.361448	−	0.932392i	$-0.382282\pi$
$691$	499.521			0.722896			0.361448	+	0.932392i	$0.382282\pi$
$692$	232.828			0.336457
$693$	314.523	+	128.428i	0.453857	+	0.185322i
$694$	−257.475			−0.371001
$695$		0			0
$696$	298.471	+	58.5888i	0.428838	+	0.0841793i
$697$		−	644.988i		−	0.925377i
$698$	121.858			0.174582
$699$	−115.277	+	587.261i	−0.164917	+	0.840144i
$700$		0			0
$701$		−	142.009i		−	0.202581i	−0.994857	−	0.101291i	$-0.967703\pi$
$701$		−	142.009i		−	0.202581i	0.994857	−	0.101291i	$-0.0322972\pi$
$702$	−571.294	−	375.516i	−0.813810	−	0.534923i
$703$		−	2111.37i		−	3.00337i
$704$			114.139i			0.162130i
$705$		0			0
$706$	−566.173			−0.801944
$707$	−403.033			−0.570061
$708$	−536.676	−	105.348i	−0.758017	−	0.148796i
$709$	−926.335			−1.30654			−0.653268	−	0.757126i	$-0.726603\pi$
$709$	−926.335			−1.30654			−0.653268	+	0.757126i	$0.726603\pi$
$710$		0			0
$711$	983.141	+	401.442i	1.38276	+	0.564616i
$712$			290.975i			0.408673i
$713$	−3.38671			−0.00474995
$714$	−151.381	−	29.7155i	−0.212018	−	0.0416183i
$715$		0			0
$716$		−	22.8832i		−	0.0319597i
$717$	−49.5547	−	9.72740i	−0.0691140	−	0.0135668i
$718$		−	96.5197i		−	0.134429i
$719$		−	1233.69i		−	1.71584i	−0.513779	−	0.857922i	$-0.671755\pi$
$719$		−	1233.69i		−	1.71584i	0.513779	−	0.857922i	$-0.328245\pi$
$720$		0			0
$721$	−76.7233			−0.106412
$722$	1056.69			1.46356
$723$	−17.1592	+	87.4150i	−0.0237334	+	0.120906i
$724$	389.610			0.538135
$725$		0			0
$726$	−67.4693	+	343.712i	−0.0929329	+	0.473432i
$727$			977.663i			1.34479i	0.740192	+	0.672395i	$0.234735\pi$
$727$			977.663i			1.34479i	−0.740192	+	0.672395i	$0.765265\pi$
$728$	−133.985			−0.184045
$729$	−289.119	−	669.217i	−0.396596	−	0.917993i
$730$		0			0
$731$		−	138.998i		−	0.190147i
$732$	44.5122	−	226.761i	0.0608091	−	0.309782i
$733$			1128.84i			1.54003i	0.638025	+	0.770015i	$0.279751\pi$
$733$			1128.84i			1.54003i	−0.638025	+	0.770015i	$0.720249\pi$
$734$			307.467i			0.418892i
$735$		0			0
$736$	235.956			0.320593
$737$	415.031			0.563136
$738$	225.806	−	553.004i	0.305970	−	0.749327i
$739$	−656.955			−0.888979			−0.444489	−	0.895784i	$-0.646615\pi$
$739$	−656.955			−0.888979			−0.444489	+	0.895784i	$0.646615\pi$
$740$		0			0
$741$	1754.60	+	344.422i	2.36789	+	0.464807i
$742$		−	328.804i		−	0.443132i
$743$	446.332			0.600716			0.300358	−	0.953827i	$-0.402894\pi$
$743$	446.332			0.600716			0.300358	+	0.953827i	$0.402894\pi$
$744$	−0.132706	+	0.676048i	−0.000178368	+	0.000908667i
$745$		0			0
$746$		−	88.9330i		−	0.119213i
$747$	−758.086	−	309.546i	−1.01484	−	0.414386i
$748$		−	392.167i		−	0.524288i
$749$			54.8129i			0.0731815i
$750$		0			0
$751$	1413.22			1.88179			0.940895	−	0.338698i	$-0.109986\pi$
$751$	1413.22			1.88179			0.940895	+	0.338698i	$0.109986\pi$
$752$	176.681			0.234949
$753$	705.008	+	138.390i	0.936266	+	0.183785i
$754$	−907.658			−1.20379
$755$		0			0
$756$	−119.389	−	78.4751i	−0.157922	−	0.103803i
$757$		−	35.0203i		−	0.0462620i	−0.999732	−	0.0231310i	$-0.992637\pi$
$757$		−	35.0203i		−	0.0462620i	0.999732	−	0.0231310i	$-0.00736348\pi$
$758$	319.086			0.420957
$759$	1751.92	+	343.895i	2.30819	+	0.453090i
$760$		0			0
$761$			350.361i			0.460395i	0.973144	+	0.230198i	$0.0739373\pi$
$761$			350.361i			0.460395i	−0.973144	+	0.230198i	$0.926063\pi$
$762$	−305.250	−	59.9194i	−0.400591	−	0.0786344i
$763$		−	426.184i		−	0.558564i
$764$			384.248i			0.502943i
$765$		0			0
$766$	−347.531			−0.453696
$767$	1632.04			2.12783
$768$	9.24577	−	47.1011i	0.0120388	−	0.0613296i
$769$	512.826			0.666874			0.333437	−	0.942772i	$-0.391792\pi$
$769$	512.826			0.666874			0.333437	+	0.942772i	$0.391792\pi$
$770$		0			0
$771$	−111.508	+	568.058i	−0.144627	+	0.736780i
$772$		−	569.764i		−	0.738037i
$773$	1212.50			1.56856			0.784279	−	0.620408i	$-0.213033\pi$
$773$	1212.50			1.56856			0.784279	+	0.620408i	$0.213033\pi$
$774$	48.6621	−	119.175i	0.0628709	−	0.153972i
$775$		0			0
$776$			71.2759i			0.0918504i
$777$	96.9680	−	493.988i	0.124798	−	0.635764i
$778$		−	575.920i		−	0.740257i
$779$			1562.29i			2.00551i
$780$		0			0
$781$	−389.560			−0.498797
$782$	−810.714			−1.03672
$783$	−808.781	−	531.617i	−1.03293	−	0.678949i
$784$	−28.0000			−0.0357143
$785$		0			0
$786$	529.670	+	103.972i	0.673881	+	0.132280i
$787$		−	1421.34i		−	1.80603i	−0.429611	−	0.903014i	$-0.641349\pi$
$787$		−	1421.34i		−	1.80603i	0.429611	−	0.903014i	$-0.358651\pi$
$788$	343.463			0.435867
$789$	−141.104	+	718.834i	−0.178840	+	0.911070i
$790$		0			0
$791$			198.785i			0.251309i
$792$	137.295	−	336.239i	0.173353	−	0.424544i
$793$			689.583i			0.869588i
$794$		−	467.338i		−	0.588587i
$795$		0			0
$796$	−696.069			−0.874459
$797$	879.246			1.10319			0.551597	−	0.834110i	$-0.314018\pi$
$797$	879.246			1.10319			0.551597	+	0.834110i	$0.314018\pi$
$798$	366.676	+	71.9771i	0.459494	+	0.0901969i
$799$	−607.053			−0.759766
$800$		0			0
$801$	350.006	−	857.172i	0.436961	−	1.07013i
$802$			377.855i			0.471141i
$803$	670.966			0.835573
$804$	−171.268	−	33.6192i	−0.213020	−	0.0418150i
$805$		0			0
$806$		−	2.05588i		−	0.00255072i
$807$	178.496	+	35.0382i	0.221185	+	0.0434178i
$808$			430.861i			0.533243i
$809$			178.159i			0.220221i	0.993919	+	0.110110i	$0.0351205\pi$
$809$			178.159i			0.220221i	−0.993919	+	0.110110i	$0.964880\pi$
$810$		0			0
$811$	1376.56			1.69736			0.848682	−	0.528904i	$-0.177397\pi$
$811$	1376.56			1.69736			0.848682	+	0.528904i	$0.177397\pi$
$812$	−189.682			−0.233598
$813$	−157.032	+	799.974i	−0.193151	+	0.983978i
$814$	1279.73			1.57215
$815$		0			0
$816$	−31.7672	+	161.833i	−0.0389304	+	0.198325i
$817$			336.681i			0.412094i
$818$	925.988			1.13202
$819$	394.700	+	161.166i	0.481929	+	0.196784i
$820$		0			0
$821$		−	501.707i		−	0.611093i	−0.952177	−	0.305546i	$-0.901161\pi$
$821$		−	501.707i		−	0.611093i	0.952177	−	0.305546i	$-0.0988391\pi$
$822$	169.486	−	863.420i	0.206188	−	1.05039i
$823$		−	449.336i		−	0.545973i	−0.962018	−	0.272986i	$-0.911989\pi$
$823$		−	449.336i		−	0.545973i	0.962018	−	0.272986i	$-0.0880114\pi$
$824$			82.0207i			0.0995396i
$825$		0			0
$826$	341.063			0.412910
$827$	816.523			0.987331			0.493665	−	0.869652i	$-0.335657\pi$
$827$	816.523			0.987331			0.493665	+	0.869652i	$0.335657\pi$
$828$	−695.095	−	283.825i	−0.839486	−	0.342784i
$829$	−788.741			−0.951436			−0.475718	−	0.879598i	$-0.657812\pi$
$829$	−788.741			−0.951436			−0.475718	+	0.879598i	$0.657812\pi$
$830$		0			0
$831$	−1370.72	−	269.068i	−1.64949	−	0.323788i
$832$			143.235i			0.172158i
$833$	96.2041			0.115491
$834$	33.9963	−	173.189i	0.0407630	−	0.207661i
$835$		0			0
$836$			949.911i			1.13626i
$837$	1.20413	−	1.83192i	0.00143863	−	0.00218867i
$838$			101.020i			0.120549i
$839$		−	355.122i		−	0.423268i	−0.977349	−	0.211634i	$-0.932121\pi$
$839$		−	355.122i		−	0.423268i	0.977349	−	0.211634i	$-0.0678786\pi$
$840$		0			0
$841$	−443.970			−0.527907
$842$	433.351			0.514669
$843$	−1470.45	−	288.645i	−1.74431	−	0.342402i
$844$	−205.527			−0.243515
$845$		0			0
$846$	−520.479	−	212.525i	−0.615224	−	0.251212i
$847$		−	218.432i		−	0.257889i
$848$	−351.506			−0.414512
$849$	267.659	+	52.5405i	0.315264	+	0.0618851i
$850$		0			0
$851$		−	2645.53i		−	3.10873i
$852$	160.757	+	31.5560i	0.188682	+	0.0370375i
$853$			1434.04i			1.68118i	0.541674	+	0.840589i	$0.317791\pi$
$853$			1434.04i			1.68118i	−0.541674	+	0.840589i	$0.682209\pi$
$854$			144.109i			0.168746i
$855$		0			0
$856$	58.5975			0.0684550
$857$	877.050			1.02340			0.511698	−	0.859165i	$-0.329017\pi$
$857$	877.050			1.02340			0.511698	+	0.859165i	$0.329017\pi$
$858$	−208.759	+	1063.49i	−0.243309	+	1.23950i
$859$	−640.688			−0.745854			−0.372927	−	0.927861i	$-0.621646\pi$
$859$	−640.688			−0.745854			−0.372927	+	0.927861i	$0.621646\pi$
$860$		0			0
$861$	−71.7510	+	365.524i	−0.0833345	+	0.424534i
$862$		−	668.641i		−	0.775686i
$863$	1386.76			1.60691			0.803453	−	0.595369i	$-0.202994\pi$
$863$	1386.76			1.60691			0.803453	+	0.595369i	$0.202994\pi$
$864$	−83.8934	+	127.632i	−0.0970988	+	0.147722i
$865$		0			0
$866$			534.655i			0.617385i
$867$	−57.8541	+	294.728i	−0.0667290	+	0.339940i
$868$		−	0.429636i		−	0.000494972i
$869$		−	1683.47i		−	1.93725i
$870$		0			0
$871$	520.829			0.597967
$872$	−455.610			−0.522489
$873$	85.7358	−	209.969i	0.0982082	−	0.240514i
$874$	1963.72			2.24682
$875$		0			0
$876$	−276.883	−	54.3510i	−0.316076	−	0.0620445i
$877$			146.885i			0.167485i	0.996487	+	0.0837427i	$0.0266874\pi$
$877$			146.885i			0.167485i	−0.996487	+	0.0837427i	$0.973313\pi$
$878$	171.393			0.195208
$879$	−52.1475	+	265.657i	−0.0593260	+	0.302227i
$880$		0			0
$881$			193.140i			0.219228i	0.993974	+	0.109614i	$0.0349614\pi$
$881$			193.140i			0.219228i	−0.993974	+	0.109614i	$0.965039\pi$
$882$	82.4841	+	33.6804i	0.0935194	+	0.0381864i
$883$		−	480.906i		−	0.544627i	−0.962209	−	0.272313i	$-0.912211\pi$
$883$		−	480.906i		−	0.544627i	0.962209	−	0.272313i	$-0.0877888\pi$
$884$		−	492.137i		−	0.556717i
$885$		0			0
$886$	−577.590			−0.651907
$887$	−180.862			−0.203903			−0.101952	−	0.994789i	$-0.532509\pi$
$887$	−180.862			−0.203903			−0.101952	+	0.994789i	$0.532509\pi$
$888$	−528.096	−	103.663i	−0.594702	−	0.116738i
$889$	193.990			0.218211
$890$		0			0
$891$	−808.905	+	825.365i	−0.907862	+	0.926336i
$892$			230.485i			0.258392i
$893$	1470.41			1.64659
$894$	−535.006	−	105.020i	−0.598440	−	0.117472i
$895$		0			0
$896$			29.9333i			0.0334077i
$897$	2198.51	+	431.559i	2.45096	+	0.481114i
$898$		−	669.693i		−	0.745761i
$899$		−	2.91050i		−	0.00323749i
$900$		0			0
$901$	1207.73			1.34043
$902$	−946.927			−1.04981
$903$	−15.4626	+	78.7720i	−0.0171236	+	0.0872336i
$904$	212.510			0.235078
$905$		0			0
$906$	93.5452	−	476.551i	0.103251	−	0.525995i
$907$			1106.96i			1.22046i	0.792224	+	0.610231i	$0.208923\pi$
$907$			1106.96i			1.22046i	−0.792224	+	0.610231i	$0.791077\pi$
$908$	−5.60378			−0.00617157
$909$	518.270	−	1269.26i	0.570154	−	1.39632i
$910$		0			0
$911$		−	1437.60i		−	1.57805i	−0.614364	−	0.789023i	$-0.710587\pi$
$911$		−	1437.60i		−	1.57805i	0.614364	−	0.789023i	$-0.289413\pi$
$912$	76.9468	−	391.993i	0.0843715	−	0.429817i
$913$			1298.10i			1.42179i
$914$		−	1269.55i		−	1.38900i
$915$		0			0
$916$	219.930			0.240098
$917$	−336.611			−0.367079
$918$	288.246	−	438.526i	0.313994	−	0.477697i
$919$	−683.039			−0.743242			−0.371621	−	0.928385i	$-0.621198\pi$
$919$	−683.039			−0.743242			−0.371621	+	0.928385i	$0.621198\pi$
$920$		0			0
$921$	−1585.98	−	311.322i	−1.72202	−	0.338026i
$922$		−	607.784i		−	0.659202i
$923$	−488.865			−0.529648
$924$	−43.6263	+	222.247i	−0.0472146	+	0.240527i
$925$		0			0
$926$		−	122.482i		−	0.132270i
$927$	98.6604	−	241.621i	0.106430	−	0.260649i
$928$			202.778i			0.218511i
$929$		−	1314.60i		−	1.41507i	−0.706680	−	0.707533i	$-0.749808\pi$
$929$		−	1314.60i		−	1.41507i	0.706680	−	0.707533i	$-0.250192\pi$
$930$		0			0
$931$	−233.026			−0.250297
$932$	−398.979			−0.428089
$933$	−185.445	−	36.4021i	−0.198762	−	0.0390162i
$934$	−1283.94			−1.37467
$935$		0			0
$936$	172.294	−	421.952i	0.184075	−	0.450803i
$937$		−	373.890i		−	0.399029i	−0.979895	−	0.199514i	$-0.936064\pi$
$937$		−	373.890i		−	0.399029i	0.979895	−	0.199514i	$-0.0639364\pi$
$938$	108.843			0.116037
$939$	−1274.33	−	250.146i	−1.35711	−	0.266396i
$940$		0			0
$941$			1213.46i			1.28954i	0.764376	+	0.644771i	$0.223047\pi$
$941$			1213.46i			1.28954i	−0.764376	+	0.644771i	$0.776953\pi$
$942$	−9.39477	−	1.84416i	−0.00997322	−	0.00195770i
$943$			1957.55i			2.07587i
$944$		−	364.612i		−	0.386242i
$945$		0			0
$946$	−204.067			−0.215715
$947$	889.938			0.939745			0.469872	−	0.882734i	$-0.344300\pi$
$947$	889.938			0.939745			0.469872	+	0.882734i	$0.344300\pi$
$948$	−136.368	+	694.704i	−0.143848	+	0.732810i
$949$	842.006			0.887256
$950$		0			0
$951$	−192.812	+	982.249i	−0.202746	+	1.03286i
$952$		−	102.847i		−	0.108032i
$953$	−905.485			−0.950142			−0.475071	−	0.879948i	$-0.657578\pi$
$953$	−905.485			−0.950142			−0.475071	+	0.879948i	$0.657578\pi$
$954$	1035.49	+	422.817i	1.08542	+	0.443204i
$955$		0			0
$956$		−	33.6669i		−	0.0352165i
$957$	−295.539	+	1505.58i	−0.308819	+	1.57323i
$958$			111.882i			0.116787i
$959$			548.713i			0.572172i
$960$		0			0
$961$	−960.993			−0.999993
$962$	1605.95			1.66939
$963$	−172.620	−	70.4853i	−0.179252	−	0.0731934i
$964$	−59.3888			−0.0616066
$965$		0			0
$966$	459.443	+	90.1870i	0.475614	+	0.0933613i
$967$		−	223.925i		−	0.231567i	−0.993274	−	0.115783i	$-0.963062\pi$
$967$		−	223.925i		−	0.231567i	0.993274	−	0.115783i	$-0.0369378\pi$
$968$	−233.514			−0.241234
$969$	−264.378	+	1346.83i	−0.272836	+	1.38992i
$970$		0			0
$971$			669.938i			0.689946i	0.938613	+	0.344973i	$0.112112\pi$
$971$			669.938i			0.689946i	−0.938613	+	0.344973i	$0.887888\pi$
$972$	400.663	−	275.073i	0.412205	−	0.282997i
$973$			110.063i			0.113118i
$974$			23.4328i			0.0240583i
$975$		0			0
$976$	154.059			0.157847
$977$	−270.879			−0.277256			−0.138628	−	0.990345i	$-0.544269\pi$
$977$	−270.879			−0.277256			−0.138628	+	0.990345i	$0.544269\pi$
$978$	−155.272	−	30.4792i	−0.158765	−	0.0311649i
$979$	−1467.77			−1.49925
$980$		0			0
$981$	1342.16	+	548.041i	1.36816	+	0.558655i
$982$		−	568.222i		−	0.578638i
$983$	−1340.81			−1.36400			−0.681998	−	0.731354i	$-0.738889\pi$
$983$	−1340.81			−1.36400			−0.681998	+	0.731354i	$0.738889\pi$
$984$	390.762	+	76.7050i	0.397116	+	0.0779523i
$985$		0			0
$986$		−	696.718i		−	0.706611i
$987$	344.026	+	67.5310i	0.348557	+	0.0684205i
$988$			1192.06i			1.20654i
$989$			421.860i			0.426552i
$990$		0			0
$991$	−9.34461			−0.00942948			−0.00471474	−	0.999989i	$-0.501501\pi$
$991$	−9.34461			−0.00942948			−0.00471474	+	0.999989i	$0.501501\pi$
$992$	−0.459300			−0.000463004
$993$	112.953	−	575.423i	0.113750	−	0.579480i
$994$	−102.163			−0.102779
$995$		0			0
$996$	105.151	−	535.677i	0.105574	−	0.537828i
$997$			112.893i			0.113233i	0.998396	+	0.0566165i	$0.0180312\pi$
$997$			112.893i			0.113233i	−0.998396	+	0.0566165i	$0.981969\pi$
$998$	−531.816			−0.532882
$999$	1431.00	+	940.609i	1.43244	+	0.941550i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.3.c.b.449.27		32
3.2	odd	2	inner	1050.3.c.b.449.5		32
5.2	odd	4		1050.3.e.b.701.10	yes	16
5.3	odd	4		1050.3.e.c.701.7	yes	16
5.4	even	2	inner	1050.3.c.b.449.6		32
15.2	even	4		1050.3.e.b.701.2	✓	16
15.8	even	4		1050.3.e.c.701.15	yes	16
15.14	odd	2	inner	1050.3.c.b.449.28		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.3.c.b.449.5		32	3.2	odd	2	inner
1050.3.c.b.449.6		32	5.4	even	2	inner
1050.3.c.b.449.27		32	1.1	even	1	trivial
1050.3.c.b.449.28		32	15.14	odd	2	inner
1050.3.e.b.701.2	✓	16	15.2	even	4
1050.3.e.b.701.10	yes	16	5.2	odd	4
1050.3.e.c.701.7	yes	16	5.3	odd	4
1050.3.e.c.701.15	yes	16	15.8	even	4

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(0.577861 - 2.94382i) q^{3} +2.00000 q^{4} +(0.817218 - 4.16319i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-8.33215 - 3.40224i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(0.577861 - 2.94382i) q^{3} +2.00000 q^{4} +(0.817218 - 4.16319i) q^{6} +2.64575i q^{7} +2.82843 q^{8} +(-8.33215 - 3.40224i) q^{9} +14.2674i q^{11} +(1.15572 - 5.88764i) q^{12} +17.9044i q^{13} +3.74166i q^{14} +4.00000 q^{16} -13.7434 q^{17} +(-11.7834 - 4.81149i) q^{18} +33.2895 q^{19} +(7.78862 + 1.52888i) q^{21} +20.1772i q^{22} +41.7116 q^{23} +(1.63444 - 8.32638i) q^{24} +25.3207i q^{26} +(-14.8304 + 22.5623i) q^{27} +5.29150i q^{28} +35.8465i q^{29} -0.0811935 q^{31} +5.65685 q^{32} +(42.0008 + 8.24459i) q^{33} -19.4362 q^{34} +(-16.6643 - 6.80447i) q^{36} -63.4244i q^{37} +47.0785 q^{38} +(52.7074 + 10.3463i) q^{39} +46.9306i q^{41} +(11.0148 + 2.16216i) q^{42} +10.1137i q^{43} +28.5349i q^{44} +58.9891 q^{46} +44.1704 q^{47} +(2.31144 - 11.7753i) q^{48} -7.00000 q^{49} +(-7.94180 + 40.4582i) q^{51} +35.8089i q^{52} -87.8765 q^{53} +(-20.9733 + 31.9080i) q^{54} +7.48331i q^{56} +(19.2367 - 97.9983i) q^{57} +50.6946i q^{58} -91.1530i q^{59} +38.5147 q^{61} -0.114825 q^{62} +(9.00147 - 22.0448i) q^{63} +8.00000 q^{64} +(59.3980 + 11.6596i) q^{66} -29.0894i q^{67} -27.4869 q^{68} +(24.1035 - 122.791i) q^{69} +27.3041i q^{71} +(-23.5669 - 9.62298i) q^{72} -47.0278i q^{73} -89.6956i q^{74} +66.5790 q^{76} -37.7481 q^{77} +(74.5396 + 14.6318i) q^{78} -117.994 q^{79} +(57.8496 + 56.6959i) q^{81} +66.3698i q^{82} +90.9832 q^{83} +(15.5772 + 3.05775i) q^{84} +14.3030i q^{86} +(105.526 + 20.7143i) q^{87} +40.3544i q^{88} +102.875i q^{89} -47.3707 q^{91} +83.4232 q^{92} +(-0.0469185 + 0.239019i) q^{93} +62.4663 q^{94} +(3.26887 - 16.6528i) q^{96} +25.1998i q^{97} -9.89949 q^{98} +(48.5412 - 118.878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9}+O(q^{10}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9	\( 32 q + 64 q^{4} - 16 q^{6} - 16 q^{9} + 128 q^{16} + 48 q^{19} + 56 q^{21} - 32 q^{24} + 48 q^{31} + 256 q^{34} - 32 q^{36} + 192 q^{39} + 160 q^{46} - 224 q^{49} + 288 q^{51} - 80 q^{54} - 112 q^{61} + 256 q^{64} - 192 q^{66} + 344 q^{69} + 96 q^{76} - 256 q^{79} + 160 q^{81} + 112 q^{84} - 448 q^{91} + 416 q^{94} - 64 q^{96} - 304 q^{99}+O(q^{100}) \) 32 * q + 64 * q^4 - 16 * q^6 - 16 * q^9 + 128 * q^16 + 48 * q^19 + 56 * q^21 - 32 * q^24 + 48 * q^31 + 256 * q^34 - 32 * q^36 + 192 * q^39 + 160 * q^46 - 224 * q^49 + 288 * q^51 - 80 * q^54 - 112 * q^61 + 256 * q^64 - 192 * q^66 + 344 * q^69 + 96 * q^76 - 256 * q^79 + 160 * q^81 + 112 * q^84 - 448 * q^91 + 416 * q^94 - 64 * q^96 - 304 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more