LMFDB - Embedded newform 49.7.f.a.6.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(6,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.6"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([9])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.f (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.2726500974$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			6.11
Character	$\chi$	$=$	49.6
Dual form			49.7.f.a.41.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.75625 + 3.45623i) q^{2} +(14.4977 - 30.1049i) q^{3} +(9.89275 + 43.3430i) q^{4} +(0.876306 - 1.81967i) q^{5} +(64.0898 + 133.084i) q^{6} +(-48.8736 + 339.500i) q^{7} +(-431.975 - 208.028i) q^{8} +(-241.594 - 302.950i) q^{9} +(3.87387 + 8.04417i) q^{10} +(333.642 - 418.374i) q^{11} +(1448.26 + 330.555i) q^{12} +(3124.66 + 2491.83i) q^{13} +(-1038.68 - 1104.66i) q^{14} +(-42.0764 - 52.7622i) q^{15} +(-653.892 + 314.898i) q^{16} +(-221.119 - 50.4689i) q^{17} +1712.96 q^{18} +6374.22i q^{19} +(87.5389 + 19.9802i) q^{20} +(9512.05 + 6393.32i) q^{21} +(526.395 + 2306.29i) q^{22} +(1145.33 + 5018.02i) q^{23} +(-12525.3 + 9988.61i) q^{24} +(9739.48 + 12212.9i) q^{25} +(-17224.7 + 3931.41i) q^{26} +(11125.2 - 2539.25i) q^{27} +(-15198.4 + 1240.26i) q^{28} +(-4125.63 + 18075.6i) q^{29} +298.331 q^{30} +11104.9i q^{31} +(7542.03 - 33043.8i) q^{32} +(-7758.04 - 16109.7i) q^{33} +(783.890 - 625.131i) q^{34} +(574.950 + 386.440i) q^{35} +(10740.7 - 13468.4i) q^{36} +(15755.9 - 69031.3i) q^{37} +(-22030.7 - 17568.9i) q^{38} +(120317. - 57941.5i) q^{39} +(-757.085 + 603.755i) q^{40} +(4657.83 - 9672.08i) q^{41} +(-48314.3 + 15254.2i) q^{42} +(-547.799 + 263.806i) q^{43} +(21434.2 + 10322.2i) q^{44} +(-762.978 + 174.145i) q^{45} +(-20500.2 - 9872.38i) q^{46} +(-138769. - 110664. i) q^{47} +24250.6i q^{48} +(-112872. - 33185.2i) q^{49} -69055.1 q^{50} +(-4725.08 + 5925.06i) q^{51} +(-77091.9 + 160083. i) q^{52} +(-2793.08 - 12237.3i) q^{53} +(-21887.5 + 45449.9i) q^{54} +(-468.930 - 973.742i) q^{55} +(91737.8 - 136489. i) q^{56} +(191895. + 92411.8i) q^{57} +(-51102.0 - 64079.8i) q^{58} +(99204.5 + 206000. i) q^{59} +(1870.62 - 2345.68i) q^{60} +(-274331. - 62614.4i) q^{61} +(-38380.9 - 30607.8i) q^{62} +(114659. - 67215.0i) q^{63} +(64458.6 + 80828.5i) q^{64} +(7272.46 - 3502.23i) q^{65} +(77061.9 + 17588.9i) q^{66} +241813. q^{67} -10083.2i q^{68} +(167671. + 38269.9i) q^{69} +(-2920.33 + 922.031i) q^{70} +(-66734.4 - 292382. i) q^{71} +(41340.6 + 181125. i) q^{72} +(70078.0 - 55885.4i) q^{73} +(195160. + 244723. i) q^{74} +(508869. - 116146. i) q^{75} +(-276278. + 63058.6i) q^{76} +(125732. + 133719. i) q^{77} +(-131364. + 575542. i) q^{78} -507556. q^{79} +1465.81i q^{80} +(147703. - 647131. i) q^{81} +(20590.8 + 42757.2i) q^{82} +(-663344. + 528999. i) q^{83} +(-183005. + 475528. i) q^{84} +(-285.604 + 358.136i) q^{85} +(598.096 - 2620.43i) q^{86} +(484350. + 386256. i) q^{87} +(-231159. + 111320. i) q^{88} +(1.05133e6 - 838410. i) q^{89} +(1501.07 - 3117.01i) q^{90} +(-998690. + 939037. i) q^{91} +(-206165. + 99283.9i) q^{92} +(334310. + 160995. i) q^{93} +(764963. - 174598. i) q^{94} +(11599.0 + 5585.77i) q^{95} +(-885436. - 706112. i) q^{96} +283851. i q^{97} +(425798. - 298643. i) q^{98} -207352. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 5 q^{2} - 7 q^{3} - 837 q^{4} - 7 q^{5} - 791 q^{6} + 70 q^{7} - 843 q^{8} + 2990 q^{9} - 7 q^{10} + 1171 q^{11} - 13482 q^{12} - 7 q^{13} + 22533 q^{14} + 6181 q^{15} - 17901 q^{16} - 3143 q^{17}+ \cdots + 4449580 q^{99}+O(q^{100}) $ 162 * q - 5 * q^2 - 7 * q^3 - 837 * q^4 - 7 * q^5 - 791 * q^6 + 70 * q^7 - 843 * q^8 + 2990 * q^9 - 7 * q^10 + 1171 * q^11 - 13482 * q^12 - 7 * q^13 + 22533 * q^14 + 6181 * q^15 - 17901 * q^16 - 3143 * q^17 - 22692 * q^18 + 50169 * q^20 + 28553 * q^21 - 33057 * q^22 - 49677 * q^23 - 119077 * q^24 + 30038 * q^25 + 59577 * q^26 + 11753 * q^27 + 42994 * q^28 + 80383 * q^29 + 27328 * q^30 + 253875 * q^32 - 7 * q^33 + 54677 * q^34 - 74067 * q^35 - 193099 * q^36 + 118463 * q^37 - 121079 * q^38 - 304143 * q^39 - 702079 * q^40 - 58023 * q^41 - 1137479 * q^42 + 93963 * q^43 + 352505 * q^44 + 1333577 * q^45 + 782877 * q^46 + 408261 * q^47 - 149338 * q^49 + 1164004 * q^50 - 911743 * q^51 + 721273 * q^52 - 992325 * q^53 - 576646 * q^54 - 1502935 * q^55 + 1368514 * q^56 + 116032 * q^57 + 2610717 * q^58 + 24493 * q^59 - 1027131 * q^60 + 563101 * q^61 - 262199 * q^62 - 966154 * q^63 - 2839067 * q^64 - 140287 * q^65 - 1523319 * q^66 - 1313660 * q^67 + 2216753 * q^69 + 1806959 * q^70 + 1031011 * q^71 - 3123354 * q^72 - 846727 * q^73 + 1270357 * q^74 + 873173 * q^75 + 5463990 * q^76 + 1565235 * q^77 + 1006005 * q^78 + 82420 * q^79 + 2259538 * q^81 - 7672672 * q^82 - 3860031 * q^83 - 9104942 * q^84 + 1596833 * q^85 + 224039 * q^86 + 2590525 * q^87 + 4179421 * q^88 + 5417433 * q^89 + 6759578 * q^90 - 6163507 * q^91 - 7060306 * q^92 + 1903160 * q^93 + 4029998 * q^94 + 2115400 * q^95 + 957950 * q^96 - 1546783 * q^98 + 4449580 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

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 $

$2$	−2.75625	+	3.45623i	−0.344531	+	0.432028i	−0.923663	−	0.383206i	$-0.874820\pi$
$2$	−2.75625	+	3.45623i	−0.344531	+	0.432028i	0.579132	+	0.815234i	$0.303392\pi$
$3$	14.4977	−	30.1049i	0.536953	−	1.11499i	−0.439296	−	0.898343i	$-0.644772\pi$
$3$	14.4977	−	30.1049i	0.536953	−	1.11499i	0.976249	−	0.216652i	$-0.0695138\pi$
$4$	9.89275	+	43.3430i	0.154574	+	0.677234i
$5$	0.876306	−	1.81967i	0.00701045	−	0.0145573i	−0.897434	−	0.441148i	$-0.854571\pi$
$5$	0.876306	−	1.81967i	0.00701045	−	0.0145573i	0.904445	+	0.426591i	$0.140286\pi$
$6$	64.0898	+	133.084i	0.296712	+	0.616129i
$7$	−48.8736	+	339.500i	−0.142489	+	0.989796i
$7$	−48.8736	+	339.500i	−0.142489	+	0.989796i
$8$	−431.975	−	208.028i	−0.843701	−	0.406305i
$9$	−241.594	−	302.950i	−0.331405	−	0.415569i
$10$	3.87387	+	8.04417i	0.00387387	+	0.00804417i
$11$	333.642	−	418.374i	0.250670	−	0.314331i	−0.640537	−	0.767928i	$-0.721288\pi$
$11$	333.642	−	418.374i	0.250670	−	0.314331i	0.891207	+	0.453597i	$0.149859\pi$
$12$	1448.26	+	330.555i	0.838111	+	0.191293i
$13$	3124.66	+	2491.83i	1.42224	+	1.13420i	0.970231	+	0.242183i	$0.0778633\pi$
$13$	3124.66	+	2491.83i	1.42224	+	1.13420i	0.452007	+	0.892014i	$0.350708\pi$
$14$	−1038.68	−	1104.66i	−0.378528	−	0.402575i
$15$	−42.0764	−	52.7622i	−0.0124671	−	0.0156332i
$16$	−653.892	+	314.898i	−0.159642	+	0.0768794i
$17$	−221.119	−	50.4689i	−0.0450068	−	0.0102725i	0.199958	−	0.979804i	$-0.435919\pi$
$17$	−221.119	−	50.4689i	−0.0450068	−	0.0102725i	−0.244965	+	0.969532i	$0.578776\pi$
$18$	1712.96			0.293717
$19$			6374.22i			0.929322i	0.885489	+	0.464661i	$0.153824\pi$
$19$			6374.22i			0.929322i	−0.885489	+	0.464661i	$0.846176\pi$
$20$	87.5389	+	19.9802i	0.0109424	+	0.00249752i
$21$	9512.05	+	6393.32i	1.02711	+	0.690349i
$22$	526.395	+	2306.29i	0.0494360	+	0.216593i
$23$	1145.33	+	5018.02i	0.0941341	+	0.412428i	0.999936	−	0.0112720i	$-0.00358808\pi$
$23$	1145.33	+	5018.02i	0.0941341	+	0.412428i	−0.905802	+	0.423700i	$0.860731\pi$
$24$	−12525.3	+	9988.61i	−0.906056	+	0.722556i
$25$	9739.48	+	12212.9i	0.623327	+	0.781627i
$26$	−17224.7	+	3931.41i	−0.980010	+	0.223681i
$27$	11125.2	−	2539.25i	0.565217	−	0.129007i
$28$	−15198.4	+	1240.26i	−0.692349	+	0.0564988i
$29$	−4125.63	+	18075.6i	−0.169159	+	0.741136i	0.817176	+	0.576388i	$0.195538\pi$
$29$	−4125.63	+	18075.6i	−0.169159	+	0.741136i	−0.986336	+	0.164748i	$0.947319\pi$
$30$	298.331			0.0110493
$31$			11104.9i			0.372759i	0.982478	+	0.186380i	$0.0596754\pi$
$31$			11104.9i			0.372759i	−0.982478	+	0.186380i	$0.940325\pi$
$32$	7542.03	−	33043.8i	0.230164	−	1.00842i
$33$	−7758.04	−	16109.7i	−0.215879	−	0.448277i
$34$	783.890	−	625.131i	0.0199443	−	0.0159050i
$35$	574.950	+	386.440i	0.0134099	+	0.00901318i
$36$	10740.7	−	13468.4i	0.230211	−	0.288675i
$37$	15755.9	−	69031.3i	0.311056	−	1.36283i	−0.541723	−	0.840557i	$-0.682228\pi$
$37$	15755.9	−	69031.3i	0.311056	−	1.36283i	0.852780	−	0.522271i	$-0.174915\pi$
$38$	−22030.7	−	17568.9i	−0.401493	−	0.320180i
$39$	120317.	−	57941.5i	2.02830	−	0.976777i
$40$	−757.085	+	603.755i	−0.0118295	+	0.00943367i
$41$	4657.83	−	9672.08i	0.0675822	−	0.140336i	−0.864441	−	0.502734i	$-0.832328\pi$
$41$	4657.83	−	9672.08i	0.0675822	−	0.140336i	0.932023	+	0.362398i	$0.118042\pi$
$42$	−48314.3	+	15254.2i	−0.652121	+	0.205893i
$43$	−547.799	+	263.806i	−0.00688995	+	0.00331802i	−0.437326	−	0.899303i	$-0.644074\pi$
$43$	−547.799	+	263.806i	−0.00688995	+	0.00331802i	0.430436	+	0.902621i	$0.358360\pi$
$44$	21434.2	+	10322.2i	0.251623	+	0.121175i
$45$	−762.978	+	174.145i	−0.00837288	+	0.00191105i
$46$	−20500.2	−	9872.38i	−0.210613	−	0.101426i
$47$	−138769.	−	110664.i	−1.33659	−	1.06590i	−0.991879	−	0.127187i	$-0.959405\pi$
$47$	−138769.	−	110664.i	−1.33659	−	1.06590i	−0.344712	−	0.938708i	$-0.612023\pi$
$48$			24250.6i			0.219280i
$49$	−112872.	−	33185.2i	−0.959394	−	0.282070i
$50$	−69055.1			−0.552440
$51$	−4725.08	+	5925.06i	−0.0356204	+	0.0446665i
$52$	−77091.9	+	160083.i	−0.548275	+	1.13851i
$53$	−2793.08	−	12237.3i	−0.0187610	−	0.0821973i	0.964681	−	0.263422i	$-0.0848511\pi$
$53$	−2793.08	−	12237.3i	−0.0187610	−	0.0821973i	−0.983442	+	0.181224i	$0.941994\pi$
$54$	−21887.5	+	45449.9i	−0.139000	+	0.288637i
$55$	−468.930	−	973.742i	−0.00281851	−	0.00585270i
$56$	91737.8	−	136489.i	0.522377	−	0.777199i
$57$	191895.	+	92411.8i	1.03619	+	0.499003i
$58$	−51102.0	−	64079.8i	−0.261911	−	0.328426i
$59$	99204.5	+	206000.i	0.483032	+	1.00303i	0.990001	+	0.141061i	$0.0450515\pi$
$59$	99204.5	+	206000.i	0.483032	+	1.00303i	−0.506969	+	0.861964i	$0.669234\pi$
$60$	1870.62	−	2345.68i	0.00866026	−	0.0108596i
$61$	−274331.	−	62614.4i	−1.20861	−	0.275857i	−0.429687	−	0.902978i	$-0.641376\pi$
$61$	−274331.	−	62614.4i	−1.20861	−	0.275857i	−0.778922	+	0.627121i	$0.784233\pi$
$62$	−38380.9	−	30607.8i	−0.161042	−	0.128427i
$63$	114659.	−	67215.0i	0.458550	−	0.268810i
$64$	64458.6	+	80828.5i	0.245890	+	0.308336i
$65$	7272.46	−	3502.23i	0.0264814	−	0.0127528i
$66$	77061.9	+	17588.9i	0.268045	+	0.0611796i
$67$	241813.			0.803999			0.401999	−	0.915640i	$-0.368315\pi$
$67$	241813.			0.803999			0.401999	+	0.915640i	$0.368315\pi$
$68$		−	10083.2i		−	0.0320680i
$69$	167671.	+	38269.9i	0.510401	+	0.116496i
$70$	−2920.33	+	922.031i	−0.00851407	+	0.00268814i
$71$	−66734.4	−	292382.i	−0.186455	−	0.816914i	−0.978466	−	0.206407i	$-0.933823\pi$
$71$	−66734.4	−	292382.i	−0.186455	−	0.816914i	0.792011	−	0.610507i	$-0.209034\pi$
$72$	41340.6	+	181125.i	0.110759	+	0.485267i
$73$	70078.0	−	55885.4i	0.180141	−	0.143658i	−0.529268	−	0.848455i	$-0.677533\pi$
$73$	70078.0	−	55885.4i	0.180141	−	0.143658i	0.709409	+	0.704797i	$0.248962\pi$
$74$	195160.	+	244723.i	0.481611	+	0.603921i
$75$	508869.	−	116146.i	1.20621	−	0.275309i
$76$	−276278.	+	63058.6i	−0.629368	+	0.143649i
$77$	125732.	+	133719.i	0.275406	+	0.292901i
$78$	−131364.	+	575542.i	−0.276816	+	1.21281i
$79$	−507556.			−1.02944			−0.514722	−	0.857357i	$-0.672105\pi$
$79$	−507556.			−1.02944			−0.514722	+	0.857357i	$0.672105\pi$
$80$			1465.81i			0.00286292i
$81$	147703.	−	647131.i	0.277930	−	1.21769i
$82$	20590.8	+	42757.2i	0.0373449	+	0.0775474i
$83$	−663344.	+	528999.i	−1.16012	+	0.925169i	−0.998100	−	0.0616179i	$-0.980374\pi$
$83$	−663344.	+	528999.i	−1.16012	+	0.925169i	−0.162025	+	0.986787i	$0.551803\pi$
$84$	−183005.	+	475528.i	−0.308763	+	0.802302i
$85$	−285.604	+	358.136i	−0.000465059	+	0.000583165i
$86$	598.096	−	2620.43i	0.000940320	−	0.00411981i
$87$	484350.	+	386256.i	0.735532	+	0.586567i
$88$	−231159.	+	111320.i	−0.339205	+	0.163353i
$89$	1.05133e6	−	838410.i	1.49132	−	1.18929i	0.558204	−	0.829704i	$-0.311491\pi$
$89$	1.05133e6	−	838410.i	1.49132	−	1.18929i	0.933113	−	0.359582i	$-0.117081\pi$
$90$	1501.07	−	3117.01i	0.00205909	−	0.00427574i
$91$	−998690.	+	939037.i	−1.32528	+	1.24612i
$92$	−206165.	+	99283.9i	−0.264760	+	0.127502i
$93$	334310.	+	160995.i	0.415624	+	0.200154i
$94$	764963.	−	174598.i	0.920994	−	0.210211i
$95$	11599.0	+	5585.77i	0.0135285	+	0.00651497i
$96$	−885436.	−	706112.i	−1.00079	−	0.798105i
$97$			283851.i			0.311010i	0.987835	+	0.155505i	$0.0497005\pi$
$97$			283851.i			0.311010i	−0.987835	+	0.155505i	$0.950299\pi$
$98$	425798.	−	298643.i	0.452403	−	0.317303i
$99$	−207352.			−0.213699
$100$	−432994.	+	542958.i	−0.432994	+	0.542958i
$101$	575225.	−	1.19447e6i	0.558308	−	1.15934i	−0.410576	−	0.911826i	$-0.634673\pi$
$101$	575225.	−	1.19447e6i	0.558308	−	1.15934i	0.968885	−	0.247513i	$-0.0796132\pi$
$102$	−7454.86	−	32661.9i	−0.00702488	−	0.0307780i
$103$	172288.	−	357759.i	0.157668	−	0.327400i	−0.807139	−	0.590362i	$-0.798985\pi$
$103$	172288.	−	357759.i	0.157668	−	0.327400i	0.964806	+	0.262962i	$0.0846993\pi$
$104$	−831403.	−	1.72643e6i	−0.739114	−	1.53479i
$105$	19969.2	−	11706.3i	0.0172501	−	0.0101123i
$106$	49993.2	+	24075.5i	0.0419753	+	0.0202142i
$107$	1.29091e6	+	1.61875e6i	1.05377	+	1.32139i	0.944911	+	0.327328i	$0.106148\pi$
$107$	1.29091e6	+	1.61875e6i	1.05377	+	1.32139i	0.108859	+	0.994057i	$0.465280\pi$
$108$	220117.	+	457077.i	0.174736	+	0.362843i
$109$	664310.	−	833019.i	0.512970	−	0.643243i	−0.456130	−	0.889913i	$-0.650765\pi$
$109$	664310.	−	833019.i	0.512970	−	0.643243i	0.969100	+	0.246670i	$0.0793363\pi$
$110$	4657.96	+	1063.15i	0.00349959	+	0.000798759i
$111$	−1.84975e6	−	1.47513e6i	−1.35252	−	1.07860i
$112$	−74949.8	−	237387.i	−0.0533478	−	0.168967i
$113$	−457202.	−	573313.i	−0.316864	−	0.397335i	0.597737	−	0.801692i	$-0.296067\pi$
$113$	−457202.	−	573313.i	−0.316864	−	0.397335i	−0.914601	+	0.404357i	$0.867495\pi$
$114$	−848306.	+	408523.i	−0.572582	+	0.275741i
$115$	10134.8	+	2313.20i	0.00666379	+	0.00152097i
$116$	−824262.			−0.528070
$117$		−	1.54863e6i		−	0.966916i
$118$	−985416.	−	224915.i	−0.599755	−	0.136890i
$119$	27941.1	−	72603.2i	0.0165807	−	0.0430839i
$120$	7199.94	+	31545.0i	0.00416663	+	0.0182552i
$121$	330490.	+	1.44797e6i	0.186553	+	0.817341i
$122$	972535.	−	775570.i	0.535581	−	0.427112i
$123$	−223649.	−	280447.i	−0.120185	−	0.150708i
$124$	−481318.	+	109858.i	−0.252445	+	0.0576189i
$125$	61524.5	−	14042.6i	0.0315006	−	0.00718980i
$126$	−83718.4	+	581549.i	−0.0418513	+	0.290720i
$127$	61866.3	−	271054.i	0.0302025	−	0.132326i	−0.957579	−	0.288171i	$-0.906953\pi$
$127$	61866.3	−	271054.i	0.0302025	−	0.132326i	0.987782	+	0.155845i	$0.0498100\pi$
$128$	1.71216e6			0.816423
$129$			20316.0i			0.00946388i
$130$	−7940.20	+	34788.3i	−0.00361411	+	0.0158344i
$131$	778567.	+	1.61671e6i	0.346324	+	0.719148i	0.999268	−	0.0382576i	$-0.0121807\pi$
$131$	778567.	+	1.61671e6i	0.346324	+	0.719148i	−0.652944	+	0.757406i	$0.726466\pi$
$132$	621495.	−	495626.i	0.270219	−	0.215493i
$133$	−2.16405e6	−	311531.i	−0.919840	−	0.132418i
$134$	−666497.	+	835760.i	−0.277002	+	0.347350i
$135$	5128.46	−	22469.3i	0.00208442	−	0.00913246i
$136$	85018.8	+	67800.2i	0.0337986	+	0.0269535i
$137$	3.21492e6	−	1.54822e6i	1.25028	−	0.602104i	0.312695	−	0.949854i	$-0.398768\pi$
$137$	3.21492e6	−	1.54822e6i	1.25028	−	0.602104i	0.937587	+	0.347750i	$0.113054\pi$
$138$	−594413.	+	474029.i	−0.226178	+	0.180371i
$139$	1.04141e6	−	2.16251e6i	0.387772	−	0.805217i	−0.612123	−	0.790762i	$-0.709684\pi$
$139$	1.04141e6	−	2.16251e6i	0.387772	−	0.805217i	0.999896	−	0.0144547i	$-0.00460124\pi$
$140$	−11061.6	+	28743.0i	−0.00403120	+	0.0104748i
$141$	−5.34337e6	+	2.57323e6i	−1.90616	+	0.917956i
$142$	1.19448e6	+	575229.i	0.417169	+	0.200898i
$143$	2.08504e6	−	475896.i	0.713026	−	0.162743i
$144$	253375.	+	122019.i	0.0848547	+	0.0408639i
$145$	29276.2	+	23347.0i	0.00960309	+	0.00765821i
$146$			396239.i			0.127321i
$147$	−2.63542e6	+	2.91688e6i	−0.829656	+	0.918261i
$148$	3.14789e6			0.971034
$149$	1.13137e6	−	1.41869e6i	0.342016	−	0.428874i	−0.580841	−	0.814017i	$-0.697276\pi$
$149$	1.13137e6	−	1.41869e6i	0.342016	−	0.428874i	0.922857	+	0.385143i	$0.125848\pi$
$150$	−1.00114e6	+	2.07889e6i	−0.296635	+	0.615968i
$151$	566547.	+	2.48221e6i	0.164553	+	0.720953i	0.988114	+	0.153725i	$0.0491270\pi$
$151$	566547.	+	2.48221e6i	0.164553	+	0.720953i	−0.823561	+	0.567228i	$0.808016\pi$
$152$	1.32602e6	−	2.75350e6i	0.377588	−	0.784070i
$153$	38131.5	+	79180.8i	0.0106466	+	0.0221078i
$154$	−808711.	+	65994.5i	−0.221427	+	0.0180695i
$155$	20207.2	+	9731.26i	0.00542638	+	0.00261321i
$156$	3.70162e6	+	4.64168e6i	0.975029	+	1.22265i
$157$	476819.	+	990125.i	0.123212	+	0.255853i	0.953447	−	0.301561i	$-0.0975077\pi$
$157$	476819.	+	990125.i	0.123212	+	0.255853i	−0.830234	+	0.557414i	$0.811793\pi$
$158$	1.39895e6	−	1.75423e6i	0.354676	−	0.444749i
$159$	−408895.	−	93327.7i	−0.101723	−	0.0232177i
$160$	−53519.6	−	42680.5i	−0.0130663	−	0.0104200i
$161$	−1.75959e6	+	143591.i	−0.421633	+	0.0344072i
$162$	1.82952e6	+	2.29415e6i	0.430321	+	0.539606i
$163$	−2.49377e6	+	1.20094e6i	−0.575830	+	0.277305i	−0.699048	−	0.715074i	$-0.746393\pi$
$163$	−2.49377e6	+	1.20094e6i	−0.575830	+	0.277305i	0.123218	+	0.992380i	$0.460678\pi$
$164$	465295.	+	106201.i	0.105487	+	0.0240766i
$165$	−36112.8			−0.00803913
$166$		−	3.75072e6i		−	0.819956i
$167$	604898.	+	138064.i	0.129877	+	0.0296436i	0.286965	−	0.957941i	$-0.407354\pi$
$167$	604898.	+	138064.i	0.129877	+	0.0296436i	−0.157088	+	0.987585i	$0.550211\pi$
$168$	−2.77898e6	−	4.74053e6i	−0.586080	−	0.999767i
$169$	2.48019e6	+	1.08664e7i	0.513837	+	2.25127i
$170$	−450.604	−	1974.23i	−9.17167e−5	−	0.000401837i
$171$	1.93107e6	−	1.53998e6i	0.386197	−	0.307982i
$172$	−16853.4	−	21133.5i	−0.00331209	−	0.00415322i
$173$	−5.28337e6	+	1.20589e6i	−1.02040	+	0.232901i	−0.699820	−	0.714319i	$-0.746737\pi$
$173$	−5.28337e6	+	1.20589e6i	−1.02040	+	0.232901i	−0.320585	+	0.947220i	$0.603879\pi$
$174$	−2.66998e6	+	609405.i	−0.506827	+	0.115680i
$175$	−4.62230e6	+	2.70967e6i	−0.862469	+	0.505594i
$176$	−86421.0	+	378635.i	−0.0158519	+	0.0694517i
$177$	7.63985e6			1.37773
$178$			5.94451e6i			1.05404i
$179$	2.32293e6	−	1.01774e7i	0.405021	−	1.77451i	−0.201543	−	0.979480i	$-0.564596\pi$
$179$	2.32293e6	−	1.01774e7i	0.405021	−	1.77451i	0.606565	−	0.795034i	$-0.292547\pi$
$180$	−15095.9	−	31347.0i	−0.00258846	−	0.00537500i
$181$	−1.69054e6	+	1.34816e6i	−0.285095	+	0.227355i	−0.755586	−	0.655049i	$-0.772648\pi$
$181$	−1.69054e6	+	1.34816e6i	−0.285095	+	0.227355i	0.470492	+	0.882404i	$0.344077\pi$
$182$	−492885.	−	6.03992e6i	−0.0817582	−	1.00188i
$183$	−5.86218e6	+	7.35094e6i	−0.956546	+	1.19947i
$184$	549135.	−	2.40592e6i	0.0881507	−	0.386213i
$185$	−111807.	−	89163.1i	−0.0176585	−	0.0140822i
$186$	−1.47788e6	+	711709.i	−0.229668	+	0.110602i
$187$	−94889.4	+	75671.8i	−0.0145109	+	0.0115720i
$188$	3.42372e6	−	7.10943e6i	0.515258	−	1.06994i
$189$	318347.	+	3.90110e6i	0.0471537	+	0.577832i
$190$	−51275.3	+	24692.9i	−0.00747562	+	0.00360007i
$191$	−1.03149e7	−	4.96738e6i	−1.48035	−	0.712898i	−0.492789	−	0.870149i	$-0.664023\pi$
$191$	−1.03149e7	−	4.96738e6i	−1.48035	−	0.712898i	−0.987559	+	0.157251i	$0.949737\pi$
$192$	3.36783e6	−	768686.i	0.475825	−	0.108604i
$193$	8.96016e6	+	4.31499e6i	1.24636	+	0.600216i	0.936534	−	0.350577i	$-0.114015\pi$
$193$	8.96016e6	+	4.31499e6i	1.24636	+	0.600216i	0.309827	+	0.950793i	$0.399729\pi$
$194$	−981052.	−	782363.i	−0.134365	−	0.107153i
$195$		−	269711.i		−	0.0363743i
$196$	321734.	−	5.22049e6i	0.0427296	−	0.693335i
$197$	375911.			0.0491684			0.0245842	−	0.999698i	$-0.492174\pi$
$197$	375911.			0.0491684			0.0245842	+	0.999698i	$0.492174\pi$
$198$	571514.	−	716656.i	0.0736261	−	0.0923242i
$199$	5.91410e6	−	1.22808e7i	0.750463	−	1.55835i	−0.0771280	−	0.997021i	$-0.524575\pi$
$199$	5.91410e6	−	1.22808e7i	0.750463	−	1.55835i	0.827591	−	0.561331i	$-0.189711\pi$
$200$	−1.66658e6	−	7.30177e6i	−0.208323	−	0.912721i
$201$	3.50574e6	−	7.27975e6i	0.431710	−	0.896454i
$202$	2.54289e6	+	5.28036e6i	0.308513	+	0.640633i
$203$	−5.93502e6	−	2.28407e6i	−0.709470	−	0.273037i
$204$	−303554.	−	146184.i	−0.0357557	−	0.0172190i
$205$	−13518.3	−	16951.4i	−0.00156914	−	0.00196763i
$206$	761629.	+	1.58154e6i	0.0871248	+	0.180916i
$207$	1.24350e6	−	1.55930e6i	0.140196	−	0.175800i
$208$	−2.82786e6	−	645441.i	−0.314245	−	0.0717243i
$209$	2.66681e6	+	2.12671e6i	0.292114	+	0.232954i
$210$	−14580.5	+	101283.i	−0.00157440	+	0.0109366i
$211$	−7.43437e6	−	9.32240e6i	−0.791401	−	0.992386i	−0.999897	−	0.0143626i	$-0.995428\pi$
$211$	−7.43437e6	−	9.32240e6i	−0.791401	−	0.992386i	0.208495	−	0.978023i	$-0.433143\pi$
$212$	502769.	−	242121.i	0.0527668	−	0.0254112i
$213$	−9.76963e6	−	2.22985e6i	−1.01097	−	0.230748i
$214$	−9.15285e6			−0.933932
$215$			1227.99i			0.000123560i
$216$	−5.33403e6	−	1.21746e6i	−0.529290	−	0.120807i
$217$	−3.77010e6	−	542735.i	−0.368956	−	0.0531140i
$218$	1.04810e6	+	4.59201e6i	0.101165	+	0.443235i
$219$	−666448.	−	2.91990e6i	−0.0634504	−	0.277994i
$220$	37565.9	−	29957.8i	0.00352797	−	0.00281347i
$221$	−565160.	−	708688.i	−0.0523594	−	0.0656566i
$222$	1.01967e7	−	2.32734e6i	0.931972	−	0.212717i
$223$	−352947.	+	80557.9i	−0.0318270	+	0.00726429i	−0.238405	−	0.971166i	$-0.576624\pi$
$223$	−352947.	+	80557.9i	−0.0318270	+	0.00726429i	0.206578	+	0.978430i	$0.433767\pi$
$224$	1.08498e7	+	4.17549e6i	0.965331	+	0.371504i
$225$	1.34690e6	−	5.90115e6i	0.118246	−	0.518071i
$226$	3.24166e6			0.280829
$227$			1.76009e7i			1.50473i	0.658749	+	0.752363i	$0.271086\pi$
$227$			1.76009e7i			1.50473i	−0.658749	+	0.752363i	$0.728914\pi$
$228$	−2.10703e6	+	9.23151e6i	−0.177773	+	0.778875i
$229$	5.15256e6	+	1.06994e7i	0.429059	+	0.890950i	0.997662	+	0.0683378i	$0.0217696\pi$
$229$	5.15256e6	+	1.06994e7i	0.429059	+	0.890950i	−0.568604	+	0.822612i	$0.692516\pi$
$230$	−35928.9	+	28652.3i	−0.00295298	+	0.00235492i
$231$	5.84842e6	−	1.84651e6i	0.474463	−	0.149802i
$232$	5.54240e6	−	6.94995e6i	0.443847	−	0.556567i
$233$	−443162.	+	1.94162e6i	−0.0350344	+	0.153496i	−0.989420	−	0.145083i	$-0.953655\pi$
$233$	−443162.	+	1.94162e6i	−0.0350344	+	0.153496i	0.954385	+	0.298578i	$0.0965124\pi$
$234$	5.35240e6	+	4.26840e6i	0.417735	+	0.333133i
$235$	−322977.	+	155537.i	−0.0248867	+	0.0119848i
$236$	−7.94726e6	+	6.33773e6i	−0.604619	+	0.482167i
$237$	−7.35842e6	+	1.52799e7i	−0.552764	+	1.14783i
$238$	173921.	+	296683.i	0.0129009	+	0.0220071i
$239$	1.29777e7	−	6.24974e6i	0.950615	−	0.457792i	0.106713	−	0.994290i	$-0.465967\pi$
$239$	1.29777e7	−	6.24974e6i	0.950615	−	0.457792i	0.843902	+	0.536498i	$0.180253\pi$
$240$	44128.1	+	21251.0i	0.00319214	+	0.00153725i
$241$	−1.03099e7	+	2.35317e6i	−0.736553	+	0.168113i	−0.574311	−	0.818637i	$-0.694730\pi$
$241$	−1.03099e7	+	2.35317e6i	−0.736553	+	0.168113i	−0.162243	+	0.986751i	$0.551873\pi$
$242$	−5.91542e6	−	2.84872e6i	−0.417388	−	0.201003i
$243$	−1.08365e7	−	8.64182e6i	−0.755215	−	0.602264i
$244$		−	1.25098e7i		−	0.861152i
$245$	−159296.	+	176309.i	−0.0108320	+	0.0119888i
$246$	1.58572e6			0.106517
$247$	−1.58835e7	+	1.99172e7i	−1.05403	+	1.32172i
$248$	2.31013e6	−	4.79702e6i	0.151454	−	0.314497i
$249$	6.30846e6	+	2.76392e7i	0.408626	+	1.79031i
$250$	−121043.	+	251347.i	−0.00774672	+	0.0160862i
$251$	−4.90853e6	−	1.01927e7i	−0.310406	−	0.644565i	0.686152	−	0.727458i	$-0.259298\pi$
$251$	−4.90853e6	−	1.01927e7i	−0.310406	−	0.644565i	−0.996558	+	0.0828928i	$0.973584\pi$
$252$	4.04759e6	+	4.30472e6i	0.252927	+	0.268994i
$253$	2.48154e6	+	1.19505e6i	0.153236	+	0.0737943i
$254$	766305.	+	960916.i	0.0467628	+	0.0586387i
$255$	6641.03	+	13790.2i	0.000400512	+	0.000831671i
$256$	−8.84449e6	+	1.10906e7i	−0.527173	+	0.661054i
$257$	1.83789e6	+	419486.i	0.108273	+	0.0247126i	0.276314	−	0.961067i	$-0.410887\pi$
$257$	1.83789e6	+	419486.i	0.108273	+	0.0247126i	−0.168041	+	0.985780i	$0.553744\pi$
$258$	−70216.7	−	55995.9i	−0.00408866	−	0.00326060i
$259$	2.26661e7	+	8.72296e6i	1.30460	+	0.502070i
$260$	223742.	+	280563.i	0.0127300	+	0.0159629i
$261$	6.47271e6	−	3.11709e6i	0.364053	−	0.175319i
$262$	−7.73364e6	−	1.76515e6i	−0.430012	−	0.0981473i
$263$	−4.39759e6			−0.241740			−0.120870	−	0.992668i	$-0.538568\pi$
$263$	−4.39759e6			−0.241740			−0.120870	+	0.992668i	$0.538568\pi$
$264$			8.57289e6i			0.465925i
$265$	−24715.4	−	5641.13i	−0.00132810	−	0.000303130i
$266$	7.04138e6	−	6.62078e6i	0.374121	−	0.351775i
$267$	−9.99827e6	−	4.38053e7i	−0.525280	−	2.30140i
$268$	2.39220e6	+	1.04809e7i	0.124277	+	0.544495i
$269$	1.88668e7	−	1.50457e7i	0.969261	−	0.772959i	−0.00462728	−	0.999989i	$-0.501473\pi$
$269$	1.88668e7	−	1.50457e7i	0.969261	−	0.772959i	0.973888	+	0.227030i	$0.0729015\pi$
$270$	63523.5	+	79656.0i	0.00322733	+	0.00404694i
$271$	1.80605e7	−	4.12219e6i	0.907448	−	0.207119i	0.256770	−	0.966473i	$-0.417342\pi$
$271$	1.80605e7	−	4.12219e6i	0.907448	−	0.207119i	0.650678	+	0.759354i	$0.274485\pi$
$272$	160480.	−	36628.6i	0.00797471	−	0.00182018i
$273$	1.37908e7	+	4.36793e7i	0.677801	+	2.14678i
$274$	−3.51010e6	+	1.53788e7i	−0.170635	+	0.747601i
$275$	8.35908e6			0.401939
$276$			7.64597e6i			0.363668i
$277$	6.18916e6	−	2.71165e7i	0.291200	−	1.27583i	−0.591656	−	0.806190i	$-0.701526\pi$
$277$	6.18916e6	−	2.71165e7i	0.291200	−	1.27583i	0.882857	−	0.469642i	$-0.155617\pi$
$278$	4.60373e6	+	9.55974e6i	0.214277	+	0.444951i
$279$	3.36421e6	−	2.68287e6i	0.154907	−	0.123534i
$280$	−167973.	−	286538.i	−0.00765185	−	0.0130529i
$281$	1.56548e7	−	1.96306e7i	0.705553	−	0.884736i	−0.291872	−	0.956458i	$-0.594278\pi$
$281$	1.56548e7	−	1.96306e7i	0.705553	−	0.884736i	0.997425	+	0.0717219i	$0.0228494\pi$
$282$	5.83399e6	−	2.55604e7i	0.260147	−	1.13978i
$283$	−2.32866e7	−	1.85704e7i	−1.02742	−	0.819337i	−0.0436956	−	0.999045i	$-0.513913\pi$
$283$	−2.32866e7	−	1.85704e7i	−1.02742	−	0.819337i	−0.983720	+	0.179708i	$0.942485\pi$
$284$	1.20125e7	−	5.78493e6i	0.524420	−	0.252548i
$285$	336318.	−	268204.i	0.0145283	−	0.0115859i
$286$	−4.10207e6	+	8.51804e6i	−0.175350	+	0.364117i
$287$	3.05603e6	+	2.05404e6i	0.129274	+	0.0868888i
$288$	−1.18327e7	+	5.69833e6i	−0.495344	+	0.238545i
$289$	−2.17009e7	−	1.04506e7i	−0.899049	−	0.432959i
$290$	−161385.	+	36835.1i	−0.00661712	+	0.00151032i
$291$	8.54528e6	+	4.11519e6i	0.346775	+	0.166998i
$292$	3.11550e6	+	2.48453e6i	0.125135	+	0.0997920i
$293$			2.60252e7i			1.03464i	0.855791	+	0.517322i	$0.173071\pi$
$293$			2.60252e7i			1.03464i	−0.855791	+	0.517322i	$0.826929\pi$
$294$	−2.81751e6	−	1.71482e7i	−0.110873	−	0.674804i
$295$	461786.			0.0179877
$296$	−2.11666e7	+	2.65421e7i	−0.816162	+	1.02344i
$297$	2.64947e6	−	5.50168e6i	0.101132	−	0.210003i
$298$	1.78499e6	+	7.82055e6i	0.0674507	+	0.295521i
$299$	−8.92528e6	+	1.85335e7i	−0.333894	+	0.693338i
$300$	1.00682e7	+	2.09069e7i	0.372897	+	0.774329i
$301$	−62789.3	−	198871.i	−0.00230243	−	0.00729243i
$302$	−1.01406e7	−	4.88346e6i	−0.368165	−	0.177299i
$303$	−2.76198e7	−	3.46342e7i	−0.992872	−	1.24502i
$304$	−2.00723e6	−	4.16805e6i	−0.0714457	−	0.148359i
$305$	−354336.	+	444323.i	−0.0124886	+	0.0156603i
$306$	−378766.	−	86451.0i	−0.0132193	−	0.00301721i
$307$	−1.44082e6	−	1.14901e6i	−0.0497960	−	0.0397109i	0.598276	−	0.801290i	$-0.295853\pi$
$307$	−1.44082e6	−	1.14901e6i	−0.0497960	−	0.0397109i	−0.648072	+	0.761579i	$0.724424\pi$
$308$	−4.55195e6	+	6.77244e6i	−0.155792	+	0.231789i
$309$	−8.27251e6	−	1.03734e7i	−0.280390	−	0.351597i
$310$	−89329.4	+	43018.8i	−0.00299854	+	0.00144402i
$311$	−4.00113e7	−	9.13231e6i	−1.33015	−	0.303598i	−0.502372	−	0.864652i	$-0.667539\pi$
$311$	−4.00113e7	−	9.13231e6i	−1.33015	−	0.303598i	−0.827780	+	0.561053i	$0.810396\pi$
$312$	−6.40273e7			−2.10815
$313$			2.78942e7i			0.909663i	0.890577	+	0.454832i	$0.150301\pi$
$313$			2.78942e7i			0.909663i	−0.890577	+	0.454832i	$0.849699\pi$
$314$	−4.73633e6	−	1.08104e6i	−0.152986	−	0.0349181i
$315$	−21832.7	−	267542.i	−0.000698515	−	0.00855975i
$316$	−5.02113e6	−	2.19990e7i	−0.159126	−	0.697175i
$317$	3.00992e6	+	1.31873e7i	0.0944881	+	0.413980i	0.999945	−	0.0104581i	$-0.00332896\pi$
$317$	3.00992e6	+	1.31873e7i	0.0944881	+	0.413980i	−0.905457	+	0.424438i	$0.860472\pi$
$318$	1.44958e6	−	1.15600e6i	0.0450775	−	0.0359481i
$319$	6.18586e6	+	7.75683e6i	0.190559	+	0.238953i
$320$	203567.	−	46462.7i	0.00621236	−	0.00141793i
$321$	6.74477e7	−	1.53945e7i	2.03916	−	0.465426i
$322$	4.35359e6	−	6.47732e6i	0.130401	−	0.194012i
$323$	321700.	−	1.40946e6i	0.00954648	−	0.0418259i
$324$	2.95098e7			0.867622
$325$			6.24304e7i			1.81864i
$326$	2.72275e6	−	1.19291e7i	0.0785876	−	0.344315i
$327$	−1.54469e7	−	3.20759e7i	−0.441772	−	0.917350i
$328$	−4.02413e6	+	3.20914e6i	−0.114038	+	0.0909425i
$329$	4.43528e7	−	4.17035e7i	1.24547	−	1.17107i
$330$	99535.8	−	124814.i	0.00276973	−	0.00347313i
$331$	1.56088e7	−	6.83864e7i	0.430412	−	1.88576i	−0.0327129	−	0.999465i	$-0.510415\pi$
$331$	1.56088e7	−	6.83864e7i	0.430412	−	1.88576i	0.463125	−	0.886293i	$-0.346728\pi$
$332$	−2.94907e7	−	2.35180e7i	−0.805881	−	0.642669i
$333$	−2.47196e7	+	1.19043e7i	−0.669434	+	0.322383i
$334$	−2.14443e6	+	1.71013e6i	−0.0575536	+	0.0458974i
$335$	211902.	−	440020.i	0.00563639	−	0.0117041i
$336$	−8.23310e6	−	1.18522e6i	−0.217043	−	0.0312450i
$337$	5.38010e7	−	2.59092e7i	1.40573	−	0.676962i	0.431412	−	0.902155i	$-0.358015\pi$
$337$	5.38010e7	−	2.59092e7i	1.40573	−	0.676962i	0.974314	+	0.225193i	$0.0723012\pi$
$338$	−4.43929e7	−	2.13785e7i	−1.14964	−	0.553639i
$339$	−2.38879e7	+	5.45226e6i	−0.613167	+	0.139951i
$340$	−18348.1	−	8835.98i	−0.000466825	−	0.000224811i
$341$	4.64599e6	+	3.70505e6i	0.117170	+	0.0934397i
$342$			1.09188e7i			0.272957i
$343$	1.67828e7	−	3.66981e7i	0.415894	−	0.909413i
$344$	291515.			0.00716119
$345$	216570.	−	271570.i	0.00527401	−	0.00661340i
$346$	1.03944e7	−	2.15842e7i	0.250941	−	0.521085i
$347$	9.60133e6	+	4.20662e7i	0.229796	+	1.00680i	0.949806	+	0.312839i	$0.101280\pi$
$347$	9.60133e6	+	4.20662e7i	0.229796	+	1.00680i	−0.720010	+	0.693964i	$0.755863\pi$
$348$	−1.19499e7	+	2.48143e7i	−0.283549	+	0.588795i
$349$	−9.75404e6	−	2.02545e7i	−0.229461	−	0.476480i	0.754169	−	0.656680i	$-0.228040\pi$
$349$	−9.75404e6	−	2.02545e7i	−0.229461	−	0.476480i	−0.983630	+	0.180200i	$0.942325\pi$
$350$	3.37497e6	−	2.34442e7i	0.0787165	−	0.546804i
$351$	4.10897e7	+	1.97878e7i	0.950192	+	0.457588i
$352$	−1.13083e7	−	1.41802e7i	−0.259281	−	0.325128i
$353$	8.72439e6	+	1.81164e7i	0.198340	+	0.411858i	0.976289	−	0.216469i	$-0.0694542\pi$
$353$	8.72439e6	+	1.81164e7i	0.198340	+	0.411858i	−0.777949	+	0.628327i	$0.783740\pi$
$354$	−2.10573e7	+	2.64051e7i	−0.474672	+	0.595220i
$355$	−590519.	−	134782.i	−0.0131992	−	0.00301264i
$356$	4.67397e7	+	3.72737e7i	1.03594	+	0.826138i
$357$	−1.78063e6	−	1.89374e6i	−0.0391353	−	0.0416214i
$358$	2.87729e7	+	3.60801e7i	0.627098	+	0.786355i
$359$	1.10073e7	−	5.30085e6i	0.237902	−	0.114568i	−0.311135	−	0.950366i	$-0.600709\pi$
$359$	1.10073e7	−	5.30085e6i	0.237902	−	0.114568i	0.549037	+	0.835798i	$0.314995\pi$
$360$	365815.	+	83494.8i	0.00784068	+	0.00178958i
$361$	6.41520e6			0.136360
$362$		−	9.55873e6i		−	0.201500i
$363$	4.83823e7	+	1.10429e7i	1.01150	+	0.230869i
$364$	−5.05804e7	−	3.39965e7i	−1.04877	−	0.704905i
$365$	−40283.0	−	176492.i	−0.000828407	−	0.00362949i
$366$	−9.24889e6	−	4.05220e7i	−0.188645	−	0.826510i
$367$	−1.60562e7	+	1.28044e7i	−0.324820	+	0.259036i	−0.772299	−	0.635259i	$-0.780893\pi$
$367$	−1.60562e7	+	1.28044e7i	−0.324820	+	0.259036i	0.447479	+	0.894295i	$0.352322\pi$
$368$	−2.32909e6	−	2.92058e6i	−0.0467350	−	0.0586038i
$369$	−4.05546e6	+	925632.i	−0.0807162	+	0.0184230i
$370$	616336.	−	140675.i	0.0121678	−	0.00277722i
$371$	4.29107e6	−	350171.i	0.0840318	−	0.00685738i
$372$	−3.67077e6	+	1.60827e7i	−0.0713064	+	0.312414i
$373$	1.29080e7			0.248733			0.124366	−	0.992236i	$-0.460310\pi$
$373$	1.29080e7			0.248733			0.124366	+	0.992236i	$0.460310\pi$
$374$		−	536529.i		−	0.0102560i
$375$	469217.	−	2.05577e6i	0.00889774	−	0.0389836i
$376$	3.69234e7	+	7.66721e7i	0.694605	+	1.44236i
$377$	−5.79324e7	+	4.61996e7i	−1.08118	+	0.862211i
$378$	−1.43605e7	−	9.65211e6i	−0.265885	−	0.178709i
$379$	−5.20564e7	+	6.52767e7i	−0.956217	+	1.19906i	0.0237135	+	0.999719i	$0.492451\pi$
$379$	−5.20564e7	+	6.52767e7i	−0.956217	+	1.19906i	−0.979931	+	0.199339i	$0.936120\pi$
$380$	−127358.	+	557992.i	−0.00232100	+	0.0101690i
$381$	−7.26313e6	−	5.79215e6i	−0.131325	−	0.104728i
$382$	4.55987e7	−	2.19592e7i	0.818017	−	0.393936i
$383$	−6.50199e7	+	5.18516e7i	−1.15731	+	0.922924i	−0.997931	−	0.0642931i	$-0.979521\pi$
$383$	−6.50199e7	+	5.18516e7i	−1.15731	+	0.922924i	−0.159379	+	0.987217i	$0.550949\pi$
$384$	2.48225e7	−	5.15444e7i	0.438381	−	0.910307i
$385$	353504.	−	111611.i	0.00619458	−	0.00195581i
$386$	−3.96100e7	+	1.90752e7i	−0.688720	+	0.331670i
$387$	212265.	+	102221.i	0.00366223	+	0.00176364i
$388$	−1.23029e7	+	2.80806e6i	−0.210627	+	0.0480742i
$389$	2.67571e6	+	1.28856e6i	0.0454559	+	0.0218904i	0.456474	−	0.889737i	$-0.349112\pi$
$389$	2.67571e6	+	1.28856e6i	0.0454559	+	0.0218904i	−0.411018	+	0.911627i	$0.634827\pi$
$390$	932182.	+	743390.i	0.0157147	+	0.0125321i
$391$		−	1.16738e6i		−	0.0195291i
$392$	4.18543e7	+	3.78157e7i	0.694836	+	0.627789i
$393$	5.99583e7			0.987806
$394$	−1.03610e6	+	1.29923e6i	−0.0169400	+	0.0212421i
$395$	−444775.	+	923584.i	−0.00721687	+	0.0149860i
$396$	−2.05128e6	−	8.98727e6i	−0.0330324	−	0.144724i
$397$	−7.18805e6	+	1.49261e7i	−0.114879	+	0.238548i	−0.950478	−	0.310791i	$-0.899406\pi$
$397$	−7.18805e6	+	1.49261e7i	−0.114879	+	0.238548i	0.835600	+	0.549339i	$0.185120\pi$
$398$	2.61443e7	+	5.42892e7i	0.414694	+	0.861122i
$399$	−4.07524e7	+	6.06319e7i	−0.641556	+	0.954514i
$400$	−1.02144e7	−	4.91900e6i	−0.159600	−	0.0768593i
$401$	6.59797e7	+	8.27359e7i	1.02324	+	1.28310i	0.958468	+	0.285201i	$0.0920604\pi$
$401$	6.59797e7	+	8.27359e7i	1.02324	+	1.28310i	0.0647713	+	0.997900i	$0.479368\pi$
$402$	1.54978e7	+	3.21814e7i	0.238556	+	0.495367i
$403$	−2.76714e7	+	3.46989e7i	−0.422782	+	0.530152i
$404$	5.74623e7	+	1.31154e7i	0.871443	+	0.198901i
$405$	−1.04813e6	−	835856.i	−0.0157779	−	0.0125825i
$406$	2.42527e7	−	1.42173e7i	0.362394	−	0.212441i
$407$	−2.36241e7	−	2.96236e7i	−0.350406	−	0.439395i
$408$	3.27370e6	−	1.57653e6i	0.0482012	−	0.0232125i
$409$	−4.73554e7	−	1.08086e7i	−0.692150	−	0.157979i	−0.138045	−	0.990426i	$-0.544082\pi$
$409$	−4.73554e7	−	1.08086e7i	−0.692150	−	0.157979i	−0.554104	+	0.832447i	$0.686939\pi$
$410$	95847.7			0.00139069
$411$		−	1.19230e8i		−	1.71736i
$412$	1.72107e7	+	3.92824e6i	0.246098	+	0.0561702i
$413$	−7.47856e7	+	2.36120e7i	−1.06162	+	0.335183i
$414$	1.96190e6	+	8.59564e6i	0.0276488	+	0.121137i
$415$	381311.	+	1.67063e6i	0.00533501	+	0.0233742i
$416$	1.05906e8	−	8.44570e7i	1.47109	−	1.17316i
$417$	−5.00039e7	−	6.27029e7i	−0.689597	−	0.864728i
$418$	−1.47008e7	+	3.35536e6i	−0.201285	+	0.0459420i
$419$	−5.49876e7	+	1.25505e7i	−0.747519	+	0.170616i	−0.579279	−	0.815130i	$-0.696666\pi$
$419$	−5.49876e7	+	1.25505e7i	−0.747519	+	0.170616i	−0.168241	+	0.985746i	$0.553809\pi$
$420$	704935.	+	749717.i	0.00951483	+	0.0101193i
$421$	1.78279e7	−	7.81090e7i	0.238920	−	1.04678i	−0.703065	−	0.711126i	$-0.748186\pi$
$421$	1.78279e7	−	7.81090e7i	0.238920	−	1.04678i	0.941986	−	0.335653i	$-0.108957\pi$
$422$	5.27113e7			0.701401
$423$			6.87759e7i			0.908689i
$424$	−1.33916e6	+	5.86724e6i	−0.0175685	+	0.0769727i
$425$	−1.53721e6	−	3.19205e6i	−0.0200247	−	0.0415817i
$426$	3.46344e7	−	2.76200e7i	0.448001	−	0.357269i
$427$	3.46652e7	−	9.00754e7i	0.445256	−	1.15697i
$428$	−5.73909e7	+	7.19659e7i	−0.732001	+	0.917900i
$429$	1.59015e7	−	6.96691e7i	0.201403	−	0.882406i
$430$	−4244.20	−	3384.64i	−5.33815e−5	−	4.25703e-5i
$431$	−1.00755e7	+	4.85210e6i	−0.125844	+	0.0606035i	−0.495747	−	0.868467i	$-0.665106\pi$
$431$	−1.00755e7	+	4.85210e6i	−0.125844	+	0.0606035i	0.369902	+	0.929071i	$0.379391\pi$
$432$	−6.47506e6	+	5.16369e6i	−0.0803142	+	0.0640484i
$433$	4.98654e7	−	1.03547e8i	0.614237	−	1.27548i	−0.329305	−	0.944223i	$-0.606815\pi$
$433$	4.98654e7	−	1.03547e8i	0.614237	−	1.27548i	0.943542	−	0.331252i	$-0.107471\pi$
$434$	1.22672e7	−	1.15344e7i	0.150063	−	0.141100i
$435$	1.12730e6	−	542878.i	0.0136953	−	0.00659530i
$436$	4.26774e7	+	2.05523e7i	0.514918	+	0.247971i
$437$	−3.19859e7	+	7.30058e6i	−0.383279	+	0.0874809i
$438$	1.19287e7	+	5.74458e6i	0.141962	+	0.0683653i
$439$	−4.96887e6	−	3.96254e6i	−0.0587306	−	0.0468361i	0.593685	−	0.804698i	$-0.297673\pi$
$439$	−4.96887e6	−	3.96254e6i	−0.0587306	−	0.0468361i	−0.652415	+	0.757862i	$0.726244\pi$
$440$			518183.i			0.00608310i
$441$	1.72157e7	+	4.22118e7i	0.200729	+	0.492173i
$442$	4.00711e6			0.0464049
$443$	−7.47793e7	+	9.37703e7i	−0.860142	+	1.07858i	0.135989	+	0.990710i	$0.456579\pi$
$443$	−7.47793e7	+	9.37703e7i	−0.860142	+	1.07858i	−0.996132	+	0.0878740i	$0.971993\pi$
$444$	4.56373e7	−	9.47668e7i	0.521400	−	1.08270i
$445$	−604339.	−	2.64778e6i	−0.00685804	−	0.0300471i
$446$	694383.	−	1.44190e6i	0.00782699	−	0.0162529i
$447$	−2.63073e7	−	5.46276e7i	−0.294546	−	0.611631i
$448$	−3.05916e7	+	1.79333e7i	−0.340227	+	0.199447i
$449$	2.95918e7	+	1.42507e7i	0.326913	+	0.157433i	0.590140	−	0.807301i	$-0.299072\pi$
$449$	2.95918e7	+	1.42507e7i	0.326913	+	0.157433i	−0.263227	+	0.964734i	$0.584787\pi$
$450$	1.66833e7	+	2.09202e7i	0.183082	+	0.229577i
$451$	−2.49250e6	−	5.17573e6i	−0.0271710	−	0.0564212i
$452$	2.03261e7	−	2.54881e7i	0.220110	−	0.276009i
$453$	8.29401e7	+	1.89305e7i	0.892216	+	0.203642i
$454$	−6.08327e7	−	4.85124e7i	−0.650084	−	0.518424i
$455$	833577.	+	2.64017e6i	0.00884935	+	0.0280283i
$456$	−6.36696e7	−	7.98392e7i	−0.671487	−	0.842018i
$457$	−1.21610e8	+	5.85643e7i	−1.27415	+	0.613599i	−0.943880	−	0.330288i	$-0.892854\pi$
$457$	−1.21610e8	+	5.85643e7i	−1.27415	+	0.613599i	−0.330270	+	0.943886i	$0.607140\pi$
$458$	−5.11813e7	−	1.16818e7i	−0.532739	−	0.121594i
$459$	−2.58813e6			−0.0267639
$460$			462155.i			0.00474804i
$461$	−1.26913e8	−	2.89672e7i	−1.29540	−	0.295667i	−0.481386	−	0.876509i	$-0.659867\pi$
$461$	−1.26913e8	−	2.89672e7i	−1.29540	−	0.295667i	−0.814017	+	0.580841i	$0.802724\pi$
$462$	−9.73773e6	+	2.53029e7i	−0.0987488	+	0.256593i
$463$	−1.84248e7	−	8.07243e7i	−0.185635	−	0.813320i	−0.978883	−	0.204421i	$-0.934469\pi$
$463$	−1.84248e7	−	8.07243e7i	−0.185635	−	0.813320i	0.793248	−	0.608899i	$-0.208388\pi$
$464$	−2.99424e6	−	1.31186e7i	−0.0299732	−	0.131321i
$465$	585917.	−	467253.i	0.00582743	−	0.00464722i
$466$	−5.48921e6	−	6.88325e6i	−0.0542440	−	0.0680198i
$467$	−1.57100e8	+	3.58570e7i	−1.54250	+	0.352066i	−0.907368	−	0.420337i	$-0.861912\pi$
$467$	−1.57100e8	+	3.58570e7i	−1.54250	+	0.352066i	−0.635133	+	0.772403i	$0.719055\pi$
$468$	6.71220e7	−	1.53202e7i	0.654828	−	0.149460i
$469$	−1.18183e7	+	8.20956e7i	−0.114561	+	0.795795i
$470$	352632.	−	1.54498e6i	0.00339647	−	0.0148809i
$471$	3.67204e7			0.351434
$472$		−	1.09624e8i		−	1.04251i
$473$	−72399.2	+	317202.i	−0.000684149	+	0.00299745i
$474$	−3.25292e7	−	6.75476e7i	−0.305449	−	0.634271i
$475$	−7.78479e7	+	6.20816e7i	−0.726384	+	0.579272i
$476$	3.42325e6	+	492803.i	0.0317408	+	0.00456933i
$477$	−3.03249e6	+	3.80262e6i	−0.0279411	+	0.0350371i
$478$	−1.41693e7	+	6.20797e7i	−0.129737	+	0.568416i
$479$	−5.30246e7	−	4.22857e7i	−0.482471	−	0.384758i	0.351833	−	0.936063i	$-0.385559\pi$
$479$	−5.30246e7	−	4.22857e7i	−0.482471	−	0.384758i	−0.834304	+	0.551305i	$0.814130\pi$
$480$	−2.06080e6	+	992430.i	−0.0186343	+	0.00897380i
$481$	2.21246e8	−	1.76438e8i	1.98811	−	1.58547i
$482$	2.02836e7	−	4.21193e7i	0.181136	−	0.376132i
$483$	−2.11873e7	+	5.50541e7i	−0.188033	+	0.488594i
$484$	−5.94898e7	+	2.86488e7i	−0.524695	+	0.252680i
$485$	516514.	+	248740.i	0.00452748	+	0.00218032i
$486$	5.97362e7	−	1.36344e7i	0.520390	−	0.118776i
$487$	1.54957e8	+	7.46234e7i	1.34161	+	0.646083i	0.960456	−	0.278430i	$-0.0898142\pi$
$487$	1.54957e8	+	7.46234e7i	1.34161	+	0.646083i	0.381149	+	0.924514i	$0.375528\pi$
$488$	1.05479e8	+	8.41165e7i	0.907623	+	0.723805i
$489$			9.24856e7i			0.790947i
$490$	−170303.	−	1.03651e6i	−0.00144755	−	0.00881023i
$491$	6.66396e7			0.562973			0.281487	−	0.959565i	$-0.409172\pi$
$491$	6.66396e7			0.562973			0.281487	+	0.959565i	$0.409172\pi$
$492$	9.94289e6	−	1.24680e7i	0.0834867	−	0.104689i
$493$	1.82451e6	−	3.78863e6i	0.0152267	−	0.0316185i
$494$	−2.50597e7	−	1.09794e8i	−0.207872	−	0.910745i
$495$	−181704.	+	377313.i	−0.00149813	+	0.00311090i
$496$	−3.49690e6	−	7.26139e6i	−0.0286575	−	0.0595079i
$497$	1.02525e8	−	8.36654e6i	0.835146	−	0.0681517i
$498$	−1.12915e8	−	5.43770e7i	−0.914247	−	0.440278i
$499$	−3.50617e6	−	4.39660e6i	−0.0282184	−	0.0353847i	0.767522	−	0.641022i	$-0.221489\pi$
$499$	−3.50617e6	−	4.39660e6i	−0.0282184	−	0.0353847i	−0.795740	+	0.605638i	$0.792918\pi$
$500$	1.21729e6	+	2.52774e6i	0.00973835	+	0.0202219i
$501$	1.29261e7	−	1.62088e7i	0.102790	−	0.128895i
$502$	4.87573e7	+	1.11285e7i	0.385415	+	0.0879684i
$503$	−1.65954e8	−	1.32344e8i	−1.30402	−	1.03992i	−0.996075	−	0.0885120i	$-0.971789\pi$
$503$	−1.65954e8	−	1.32344e8i	−1.30402	−	1.03992i	−0.307940	−	0.951406i	$-0.599640\pi$
$504$	−6.35125e7	+	5.18291e6i	−0.496098	+	0.0404839i
$505$	−1.66946e6	−	2.09344e6i	−0.0129629	−	0.0162550i
$506$	−1.09701e7	+	5.28291e6i	−0.0846756	+	0.0407776i
$507$	3.63090e8	+	8.28729e7i	2.78606	+	0.635900i
$508$	1.23603e7			0.0942841
$509$		−	3.62056e7i		−	0.274551i	−0.990533	−	0.137275i	$-0.956165\pi$
$509$		−	3.62056e7i		−	0.274551i	0.990533	−	0.137275i	$-0.0438345\pi$
$510$	−65966.5	−	15056.4i	−0.000497294	−	0.000113504i
$511$	1.55481e7	+	2.65228e7i	0.116524	+	0.198773i
$512$	1.04293e7	+	4.56940e7i	0.0777047	+	0.340446i
$513$	1.61857e7	+	7.09142e7i	0.119889	+	0.525269i
$514$	−6.51552e6	+	5.19595e6i	−0.0479799	+	0.0382627i
$515$	−500026.	−	627013.i	−0.00366076	−	0.00459045i
$516$	−880556.	+	200981.i	−0.00640926	+	0.00146287i
$517$	−9.25983e7	+	2.11350e7i	−0.670087	+	0.152943i
$518$	−9.26218e7	+	5.42965e7i	−0.666383	+	0.390645i
$519$	−4.02936e7	+	1.76538e8i	−0.288227	+	1.26280i
$520$	−3.87009e6			−0.0275239
$521$			2.47028e8i			1.74676i	0.487043	+	0.873378i	$0.338075\pi$
$521$			2.47028e8i			1.74676i	−0.487043	+	0.873378i	$0.661925\pi$
$522$	−7.06702e6	+	3.09626e7i	−0.0496849	+	0.217684i
$523$	−5.86780e7	−	1.21846e8i	−0.410176	−	0.851740i	−0.999053	−	0.0435166i	$-0.986144\pi$
$523$	−5.86780e7	−	1.21846e8i	−0.410176	−	0.851740i	0.588877	−	0.808223i	$-0.299570\pi$
$524$	−6.23709e7	+	4.97391e7i	−0.433499	+	0.345704i
$525$	1.45613e7	+	1.78438e8i	0.100629	+	1.23313i
$526$	1.21209e7	−	1.51991e7i	0.0832868	−	0.104438i
$527$	560450.	−	2.45549e6i	0.00382917	−	0.0167767i
$528$	1.01458e7	+	8.09104e6i	0.0689265	+	0.0549671i
$529$	1.09507e8	−	5.27358e7i	0.739733	−	0.356237i
$530$	87618.8	−	69873.6i	0.000588531	−	0.000469338i
$531$	3.84405e7	−	7.98225e7i	0.256747	−	0.533141i
$532$	−7.90570e6	−	9.68782e7i	−0.0525056	−	0.643415i
$533$	3.86553e7	−	1.86154e7i	0.255286	−	0.122939i
$534$	1.78959e8	+	8.61819e7i	1.17525	+	0.565969i
$535$	4.07683e6	−	930510.i	0.0266233	−	0.00607659i
$536$	−1.04457e8	−	5.03039e7i	−0.678335	−	0.326669i
$537$	−2.72713e8	−	2.17481e8i	−1.76110	−	1.40443i
$538$			1.06678e8i			0.685056i
$539$	−5.15426e7	+	3.61506e7i	−0.329155	+	0.230860i
$540$	1.02462e6			0.00650701
$541$	−7.33677e7	+	9.20002e7i	−0.463354	+	0.581028i	−0.957530	−	0.288334i	$-0.906899\pi$
$541$	−7.33677e7	+	9.20002e7i	−0.463354	+	0.581028i	0.494176	+	0.869362i	$0.335470\pi$
$542$	−3.55320e7	+	7.37829e7i	−0.223163	+	0.463402i
$543$	1.60772e7	+	7.04386e7i	0.100418	+	0.439958i
$544$	−3.33537e6	+	6.92596e6i	−0.0207180	+	0.0430213i
$545$	−933679.	−	1.93880e6i	−0.00576777	−	0.0119769i
$546$	−1.88977e8	−	7.27269e7i	−1.16099	−	0.446804i
$547$	2.02762e8	+	9.76452e7i	1.23887	+	0.596608i	0.934506	−	0.355948i	$-0.115842\pi$
$547$	2.02762e8	+	9.76452e7i	1.23887	+	0.596608i	0.304364	+	0.952556i	$0.401556\pi$
$548$	9.89089e7	+	1.24028e8i	0.601027	+	0.753664i
$549$	4.73079e7	+	9.82359e7i	0.285902	+	0.593681i
$550$	−2.30397e7	+	2.88909e7i	−0.138480	+	0.173649i
$551$	−1.15218e8	−	2.62977e7i	−0.688754	−	0.157204i
$552$	−6.44686e7	−	5.14120e7i	−0.383293	−	0.305666i
$553$	2.48061e7	−	1.72315e8i	0.146684	−	1.01894i
$554$	7.66618e7	+	9.61308e7i	0.450868	+	0.565371i
$555$	−4.30519e6	+	2.07327e6i	−0.0251834	+	0.0121277i
$556$	1.04032e8	+	2.37446e7i	0.605260	+	0.138147i
$557$	2.57280e8			1.48881			0.744406	−	0.667727i	$-0.232733\pi$
$557$	2.57280e8			1.48881			0.744406	+	0.667727i	$0.232733\pi$
$558$			1.90221e7i			0.109486i
$559$	−2.36904e6	−	540719.i	−0.0135624	−	0.00309554i
$560$	−497644.	−	71639.7i	−0.00283371	−	0.000407934i
$561$	902407.	+	3.95370e6i	0.00511109	+	0.0223932i
$562$	2.46990e7	+	1.08213e8i	0.139146	+	0.609638i
$563$	4.22525e7	−	3.36952e7i	0.236770	−	0.188818i	−0.497916	−	0.867225i	$-0.665901\pi$
$563$	4.22525e7	−	3.36952e7i	0.236770	−	0.188818i	0.734686	+	0.678408i	$0.237330\pi$
$564$	−1.64392e8	−	2.06141e8i	−0.916313	−	1.14902i
$565$	−1.44389e6	+	329558.i	−0.00800550	+	0.00182720i
$566$	1.28367e8	−	2.92989e7i	0.707953	−	0.161586i
$567$	2.12482e8	+	8.17729e7i	1.16566	+	0.448601i
$568$	−3.19962e7	+	1.40185e8i	−0.174604	+	0.764989i
$569$	5.02229e7			0.272625			0.136312	−	0.990666i	$-0.456475\pi$
$569$	5.02229e7			0.272625			0.136312	+	0.990666i	$0.456475\pi$
$570$			1.90163e6i			0.0102684i
$571$	1.93884e6	−	8.49463e6i	0.0104144	−	0.0456285i	−0.969454	−	0.245274i	$-0.921122\pi$
$571$	1.93884e6	−	8.49463e6i	0.0104144	−	0.0456285i	0.979868	+	0.199646i	$0.0639791\pi$
$572$	4.12535e7	+	8.56637e7i	0.220431	+	0.457729i
$573$	−2.99085e8	+	2.38512e8i	−1.58975	+	1.26779i
$574$	−1.55224e7	+	4.90087e6i	−0.0820774	+	0.0259142i
$575$	−5.01297e7	+	6.28607e7i	−0.263689	+	0.330656i
$576$	8.91414e6	−	3.90554e7i	0.0466458	−	0.204368i
$577$	1.38744e8	+	1.10645e8i	0.722250	+	0.575975i	0.914119	−	0.405446i	$-0.132884\pi$
$577$	1.38744e8	+	1.10645e8i	0.722250	+	0.575975i	−0.191870	+	0.981420i	$0.561455\pi$
$578$	9.59325e7	−	4.61986e7i	0.496801	−	0.239247i
$579$	2.59804e8	−	2.07187e8i	1.33848	−	1.06740i
$580$	−722306.	+	1.49988e6i	−0.00370201	+	0.00768730i
$581$	−1.47175e8	−	2.51060e8i	−0.750424	−	1.28011i
$582$	−3.77759e7	+	1.81919e7i	−0.191622	+	0.0922805i
$583$	−6.05165e6	−	2.91432e6i	−0.0305400	−	0.0147073i
$584$	−4.18977e7	+	9.56288e6i	−0.210354	+	0.0480120i
$585$	−2.81799e6	−	1.35707e6i	−0.0140757	−	0.00677852i
$586$	−8.99489e7	−	7.17319e7i	−0.446995	−	0.356467i
$587$		−	2.24272e8i		−	1.10882i	−0.832244	−	0.554409i	$-0.812944\pi$
$587$		−	2.24272e8i		−	1.10882i	0.832244	−	0.554409i	$-0.187056\pi$
$588$	−1.52498e8	−	8.53710e7i	−0.750121	−	0.419932i
$589$	−7.07849e7			−0.346413
$590$	−1.27280e6	+	1.59604e6i	−0.00619731	+	0.00777117i
$591$	5.44985e6	−	1.13167e7i	0.0264011	−	0.0548225i
$592$	1.14351e7	+	5.01006e7i	0.0551158	+	0.241478i
$593$	3.16788e7	−	6.57817e7i	0.151916	−	0.315458i	−0.811097	−	0.584912i	$-0.801129\pi$
$593$	3.16788e7	−	6.57817e7i	0.151916	−	0.315458i	0.963013	+	0.269454i	$0.0868433\pi$
$594$	1.17125e7	+	2.43212e7i	0.0558841	+	0.116045i
$595$	−107629.	−	114466.i	−0.000510949	−	0.000543408i
$596$	7.26828e7	+	3.50022e7i	0.343315	+	0.165332i
$597$	−2.83969e8	−	3.56086e8i	−1.33459	−	1.67352i
$598$	−3.94558e7	−	8.19308e7i	−0.184505	−	0.383128i
$599$	1.79174e8	−	2.24677e8i	0.833669	−	1.04539i	−0.164588	−	0.986362i	$-0.552629\pi$
$599$	1.79174e8	−	2.24677e8i	0.833669	−	1.04539i	0.998256	−	0.0590252i	$-0.0187992\pi$
$600$	−2.43980e8	−	5.56869e7i	−1.12954	−	0.257810i
$601$	1.20219e8	+	9.58713e7i	0.553795	+	0.441637i	0.859974	−	0.510337i	$-0.170479\pi$
$601$	1.20219e8	+	9.58713e7i	0.553795	+	0.441637i	−0.306180	+	0.951974i	$0.599051\pi$
$602$	860406.	+	331124.i	0.00394379	+	0.00151775i
$603$	−5.84206e7	−	7.32572e7i	−0.266449	−	0.334117i
$604$	−1.01981e8	+	4.91117e7i	−0.462818	+	0.222881i
$605$	2.92443e6	+	667483.i	0.0132061	+	0.00301421i
$606$	1.95831e8			0.879959
$607$			4.11952e7i			0.184196i	0.995750	+	0.0920981i	$0.0293573\pi$
$607$			4.11952e7i			0.184196i	−0.995750	+	0.0920981i	$0.970643\pi$
$608$	2.10628e8	+	4.80746e7i	0.937144	+	0.213897i
$609$	−1.54806e8	+	1.45559e8i	−0.685387	+	0.644448i
$610$	−559043.	−	2.44933e6i	−0.00246295	−	0.0107909i
$611$	−1.57848e8	−	6.91577e8i	−0.692015	−	3.03191i
$612$	−3.05471e6	+	2.43605e6i	−0.0133265	+	0.0106275i
$613$	1.28180e8	+	1.60732e8i	0.556466	+	0.697786i	0.977900	−	0.209073i	$-0.0670446\pi$
$613$	1.28180e8	+	1.60732e8i	0.556466	+	0.697786i	−0.421434	+	0.906859i	$0.638473\pi$
$614$	7.94250e6	−	1.81282e6i	0.0343125	−	0.00783160i
$615$	−706305.	+	161209.i	−0.00303645	+	0.000693051i
$616$	−2.64957e7	−	8.39191e7i	−0.113353	−	0.359020i
$617$	−1.87404e7	+	8.21069e7i	−0.0797852	+	0.349562i	−0.999026	−	0.0441349i	$-0.985947\pi$
$617$	−1.87404e7	+	8.21069e7i	−0.0797852	+	0.349562i	0.919240	+	0.393697i	$0.128804\pi$
$618$	5.86539e7			0.248503
$619$		−	1.15616e8i		−	0.487468i	−0.969842	−	0.243734i	$-0.921628\pi$
$619$		−	1.15616e8i		−	0.487468i	0.969842	−	0.243734i	$-0.0783724\pi$
$620$	−221877.	+	972108.i	−0.000930974	+	0.00407887i
$621$	2.54840e7	+	5.29180e7i	0.106412	+	0.220968i
$622$	1.41844e8	−	1.13117e8i	0.589442	−	0.470064i
$623$	2.33258e8	+	3.97904e8i	0.964655	+	1.64556i
$624$	−6.04285e7	+	7.57750e7i	−0.248707	+	0.311869i
$625$	−5.42839e7	+	2.37833e8i	−0.222347	+	0.974164i
$626$	−9.64086e7	−	7.68833e7i	−0.393000	−	0.313407i
$627$	1.02687e8	−	4.94514e7i	0.416594	−	0.200621i
$628$	−3.81979e7	+	3.04618e7i	−0.154227	+	0.122992i
$629$	−6.96787e6	+	1.44689e7i	−0.0279993	+	0.0581412i
$630$	984863.	+	661954.i	0.00393871	+	0.00264732i
$631$	−9.40928e7	+	4.53127e7i	−0.374514	+	0.180357i	−0.611666	−	0.791116i	$-0.709500\pi$
$631$	−9.40928e7	+	4.53127e7i	−0.374514	+	0.180357i	0.237152	+	0.971473i	$0.423786\pi$
$632$	2.19252e8	+	1.05586e8i	0.868544	+	0.418269i
$633$	−3.88431e8	+	8.86569e7i	−1.53145	+	0.349544i
$634$	−5.38744e7	−	2.59446e7i	−0.211405	−	0.101807i
$635$	−439015.	−	350103.i	−0.00171458	−	0.00136733i
$636$		−	1.86460e7i		−	0.0724793i
$637$	−2.69993e8	−	3.84950e8i	−1.04456	−	1.48931i
$638$	−4.38591e7			−0.168888
$639$	−7.24545e7	+	9.08551e7i	−0.277692	+	0.348214i
$640$	1.50038e6	−	3.11557e6i	0.00572349	−	0.0118850i
$641$	−1.15520e8	−	5.06126e8i	−0.438614	−	1.92169i	−0.384404	−	0.923165i	$-0.625593\pi$
$641$	−1.15520e8	−	5.06126e8i	−0.438614	−	1.92169i	−0.0542103	−	0.998530i	$-0.517264\pi$
$642$	−1.32696e8	+	2.75545e8i	−0.501478	+	1.04133i
$643$	8.96214e7	+	1.86101e8i	0.337116	+	0.700028i	0.998760	−	0.0497902i	$-0.0158553\pi$
$643$	8.96214e7	+	1.86101e8i	0.337116	+	0.700028i	−0.661644	+	0.749818i	$0.730141\pi$
$644$	−2.36309e7	−	7.48455e7i	−0.0884753	−	0.280226i
$645$	36968.4	+	17803.0i	0.000137769	+	6.63460e-5i
$646$	3.98472e6	+	4.99668e6i	0.0147809	+	0.0185346i
$647$	−1.03623e8	−	2.15175e8i	−0.382597	−	0.794472i	−0.999970	−	0.00780057i	$-0.997517\pi$
$647$	−1.03623e8	−	2.15175e8i	−0.382597	−	0.794472i	0.617372	−	0.786671i	$-0.288197\pi$
$648$	−1.98426e8	+	2.48818e8i	−0.729244	+	0.914443i
$649$	1.19284e8	+	2.72258e7i	0.436363	+	0.0995971i
$650$	−2.15773e8	−	1.72073e8i	−0.785702	−	0.626576i
$651$	−7.09969e7	+	1.05630e8i	−0.257334	+	0.382864i
$652$	−7.67225e7	−	9.62070e7i	−0.276809	−	0.347107i
$653$	2.85283e8	−	1.37385e8i	1.02456	−	0.493401i	0.155356	−	0.987859i	$-0.450347\pi$
$653$	2.85283e8	−	1.37385e8i	1.02456	−	0.493401i	0.869202	+	0.494457i	$0.164633\pi$
$654$	1.53437e8	+	3.50210e7i	0.548525	+	0.125197i
$655$	3.62414e6			0.0128968
$656$			7.79124e6i			0.0275991i
$657$	−3.38609e7	−	7.72853e6i	−0.119400	−	0.0272522i
$658$	2.18895e7	+	2.68238e8i	0.0768347	+	0.941549i
$659$	−1.52485e7	−	6.68082e7i	−0.0532809	−	0.233439i	0.941275	−	0.337640i	$-0.109629\pi$
$659$	−1.52485e7	−	6.68082e7i	−0.0532809	−	0.233439i	−0.994556	+	0.104201i	$0.966771\pi$
$660$	−357255.	−	1.56524e6i	−0.00124264	−	0.00544437i
$661$	−3.12664e8	+	2.49341e8i	−1.08261	+	0.863357i	−0.991189	−	0.132455i	$-0.957714\pi$
$661$	−3.12664e8	+	2.49341e8i	−1.08261	+	0.863357i	−0.0914259	+	0.995812i	$0.529142\pi$
$662$	1.93337e8	+	2.42437e8i	0.666410	+	0.835652i
$663$	−2.95285e7	+	6.73969e6i	−0.101321	+	0.0231259i
$664$	3.96595e8	−	9.05202e7i	1.35470	−	0.309201i
$665$	−2.46325e6	+	3.66485e6i	−0.00837614	+	0.0124621i
$666$	2.69892e7	−	1.18248e8i	0.0913625	−	0.400285i
$667$	−9.54287e7			−0.321589
$668$			2.75839e7i			0.0925393i
$669$	−2.69175e6	+	1.17933e7i	−0.00898993	+	0.0393875i
$670$	936752.	+	1.94518e6i	0.00311458	+	0.00646750i
$671$	−1.17725e8	+	9.38824e7i	−0.389673	+	0.310754i
$672$	2.83000e8	−	2.66096e8i	0.932563	−	0.876859i
$673$	1.27158e8	−	1.59451e8i	0.417155	−	0.523096i	−0.528208	−	0.849115i	$-0.677136\pi$
$673$	1.27158e8	−	1.59451e8i	0.417155	−	0.523096i	0.945363	+	0.326019i	$0.105707\pi$
$674$	−5.87409e7	+	2.57361e8i	−0.191850	+	0.840548i
$675$	1.39365e8	+	1.11140e8i	0.453150	+	0.361375i
$676$	−4.46448e8	+	2.14998e8i	−1.44521	+	0.695976i
$677$	1.78141e8	−	1.42063e8i	0.574115	−	0.457842i	−0.292886	−	0.956147i	$-0.594616\pi$
$677$	1.78141e8	−	1.42063e8i	0.574115	−	0.457842i	0.867001	+	0.498306i	$0.166044\pi$
$678$	4.69968e7	−	9.75898e7i	0.150792	−	0.313123i
$679$	−9.63673e7	−	1.38728e7i	−0.307837	−	0.0443154i
$680$	197876.	−	95292.3i	0.000629314	−	0.000303062i
$681$	5.29873e8	+	2.55173e8i	1.67776	+	0.807967i
$682$	−2.56110e7	+	5.84554e6i	−0.0807371	+	0.0184277i
$683$	−1.52186e8	−	7.32890e7i	−0.477653	−	0.230026i	0.179536	−	0.983751i	$-0.442540\pi$
$683$	−1.52186e8	−	7.32890e7i	−0.477653	−	0.230026i	−0.657189	+	0.753726i	$0.728255\pi$
$684$	8.58507e7	+	6.84636e7i	0.268272	+	0.213940i
$685$		−	7.20680e6i		−	0.0224218i
$686$	8.05792e7	+	1.59154e8i	0.249604	+	0.492999i
$687$	3.96805e8			1.22379
$688$	275130.	−	345002.i	0.000844835	−	0.00105939i
$689$	2.17658e7	−	4.51972e7i	0.0665453	−	0.138183i
$690$	341687.	+	1.49703e6i	0.00104011	+	0.00455704i
$691$	−3.04392e7	+	6.32076e7i	−0.0922569	+	0.191573i	−0.941991	−	0.335638i	$-0.891048\pi$
$691$	−3.04392e7	+	6.32076e7i	−0.0922569	+	0.191573i	0.849734	+	0.527211i	$0.176762\pi$
$692$	−1.04534e8	−	2.17067e8i	−0.315457	−	0.655052i
$693$	1.01341e7	−	7.03962e7i	0.0304498	−	0.211519i
$694$	−1.71854e8	−	8.27604e7i	−0.514139	−	0.247596i
$695$	−3.02245e6	−	3.79003e6i	−0.00900337	−	0.0112899i
$696$	−1.28875e8	−	2.67612e8i	−0.382244	−	0.793738i
$697$	−1.51807e6	+	1.90360e6i	−0.00448326	+	0.00562183i
$698$	9.68885e7	+	2.21142e7i	0.284909	+	0.0650286i
$699$	5.20273e7	+	4.14904e7i	0.152335	+	0.121483i
$700$	−1.63172e8	−	1.73538e8i	−0.475721	−	0.505941i
$701$	−1.42983e8	−	1.79294e8i	−0.415077	−	0.520491i	0.529708	−	0.848180i	$-0.322301\pi$
$701$	−1.42983e8	−	1.79294e8i	−0.415077	−	0.520491i	−0.944786	+	0.327689i	$0.893730\pi$
$702$	−1.81644e8	+	8.74753e7i	−0.525062	+	0.252856i
$703$	4.40021e8	+	1.00432e8i	1.26651	+	0.289072i
$704$	5.53227e7			0.158557
$705$			1.19781e7i			0.0341838i
$706$	−8.66609e7	−	1.97798e7i	−0.246269	−	0.0562092i
$707$	3.77409e8	+	2.53667e8i	1.06796	+	0.717804i
$708$	7.55792e7	+	3.31134e8i	0.212962	+	0.933048i
$709$	−6.34740e7	−	2.78098e8i	−0.178097	−	0.780296i	−0.982508	−	0.186222i	$-0.940376\pi$
$709$	−6.34740e7	−	2.78098e8i	−0.178097	−	0.780296i	0.804410	−	0.594074i	$-0.202481\pi$
$710$	2.09345e6	−	1.66947e6i	0.00584909	−	0.00466449i
$711$	1.22623e8	+	1.53764e8i	0.341163	+	0.427805i
$712$	−6.28562e8	+	1.43465e8i	−1.74144	+	0.397472i
$713$	−5.57244e7	+	1.27187e7i	−0.153736	+	0.0350893i
$714$	1.14531e7	−	934622.i	0.0314649	−	0.00256768i
$715$	961157.	−	4.21110e6i	0.00262952	−	0.0115207i
$716$	4.64101e8			1.26437
$717$		−	4.81300e8i		−	1.30574i
$718$	−1.20180e7	+	5.26542e7i	−0.0324682	+	0.142253i
$719$	1.73790e8	+	3.60878e8i	0.467560	+	0.970899i	0.992782	+	0.119934i	$0.0382682\pi$
$719$	1.73790e8	+	3.60878e8i	0.467560	+	0.970899i	−0.525222	+	0.850966i	$0.676018\pi$
$720$	444068.	−	354132.i	0.00118974	−	0.000948786i
$721$	1.13039e8	+	7.59767e7i	0.301594	+	0.202710i
$722$	−1.76819e7	+	2.21724e7i	−0.0469804	+	0.0589115i
$723$	−7.86286e7	+	3.44494e8i	−0.208049	+	0.911522i
$724$	−7.51572e7	−	5.99359e7i	−0.198041	−	0.157932i
$725$	−2.60937e8	+	1.25661e8i	−0.684734	+	0.329750i
$726$	−1.71520e8	+	1.36783e8i	−0.448235	+	0.357456i
$727$	1.45162e8	−	3.01432e8i	0.377789	−	0.784487i	−0.622210	−	0.782851i	$-0.713765\pi$
$727$	1.45162e8	−	3.01432e8i	0.377789	−	0.784487i	0.999999	−	0.00163648i	$-0.000520907\pi$
$728$	6.26755e8	−	1.97885e8i	1.62444	−	0.512883i
$729$	1.87045e7	−	9.00761e6i	0.0482796	−	0.0232502i
$730$	721024.	+	347227.i	0.00185345	+	0.000892576i
$731$	134443.	−	30685.6i	0.000344179	−	7.85567e-5i
$732$	−3.76605e8	−	1.81363e8i	−0.960180	−	0.462398i
$733$	4.60170e8	+	3.66973e8i	1.16844	+	0.931799i	0.998559	−	0.0536657i	$-0.0170905\pi$
$733$	4.60170e8	+	3.66973e8i	1.16844	+	0.931799i	0.169880	+	0.985465i	$0.445662\pi$
$734$		−	9.07857e7i		−	0.229577i
$735$	2.99831e6	+	7.35167e6i	0.00755119	+	0.0185150i
$736$	1.74452e8			0.437566
$737$	8.06791e7	−	1.01168e8i	0.201539	−	0.252721i
$738$	7.97866e6	−	1.65679e7i	0.0198500	−	0.0412190i
$739$	8.23407e7	+	3.60758e8i	0.204024	+	0.893888i	0.968456	+	0.249184i	$0.0801623\pi$
$739$	8.23407e7	+	3.60758e8i	0.204024	+	0.893888i	−0.764432	+	0.644704i	$0.776981\pi$
$740$	2.75852e6	−	5.72812e6i	0.00680739	−	0.0141357i
$741$	3.69332e8	+	7.66925e8i	0.907741	+	1.88494i
$742$	−1.06170e7	+	1.57961e7i	−0.0259890	+	0.0386667i
$743$	−2.57046e8	−	1.23787e8i	−0.626677	−	0.301792i	0.0934605	−	0.995623i	$-0.470207\pi$
$743$	−2.57046e8	−	1.23787e8i	−0.626677	−	0.301792i	−0.720138	+	0.693831i	$0.755921\pi$
$744$	−1.10922e8	−	1.39092e8i	−0.269339	−	0.337741i
$745$	−1.59013e6	−	3.30193e6i	−0.00384559	−	0.00798545i
$746$	−3.55777e7	+	4.46130e7i	−0.0856962	+	0.107460i
$747$	3.20520e8	+	7.31567e7i	0.768942	+	0.175506i
$748$	−4.21856e6	−	3.36419e6i	−0.0100800	−	0.00803850i
$749$	−6.12659e8	+	3.59151e8i	−1.45805	+	0.854735i
$750$	5.81194e6	+	7.28794e6i	0.0137764	+	0.0172751i
$751$	−6.00333e8	+	2.89105e8i	−1.41734	+	0.682553i	−0.976596	−	0.215083i	$-0.930998\pi$
$751$	−6.00333e8	+	2.89105e8i	−1.41734	+	0.682553i	−0.440739	+	0.897635i	$0.645284\pi$
$752$	1.25588e8	+	2.86646e7i	0.295321	+	0.0674051i
$753$	−3.78012e8			−0.885360
$754$		−	3.27565e8i		−	0.764158i
$755$	5.01326e6	+	1.14424e6i	0.0116488	+	0.00265875i
$756$	−1.65936e8	+	5.23907e7i	−0.384038	+	0.121252i
$757$	−8.27958e7	−	3.62752e8i	−0.190862	−	0.836223i	−0.976151	−	0.217093i	$-0.930343\pi$
$757$	−8.27958e7	−	3.62752e8i	−0.190862	−	0.836223i	0.785288	−	0.619130i	$-0.212515\pi$
$758$	−8.21305e7	−	3.59837e8i	−0.188581	−	0.826225i
$759$	7.19534e7	−	5.73809e7i	0.164561	−	0.131233i
$760$	−3.84847e6	−	4.82583e6i	−0.00876692	−	0.0109934i
$761$	3.53112e8	−	8.05955e7i	0.801232	−	0.182876i	0.197750	−	0.980252i	$-0.436637\pi$
$761$	3.53112e8	−	8.05955e7i	0.801232	−	0.182876i	0.603482	+	0.797376i	$0.293779\pi$
$762$	4.00379e7	−	9.13840e6i	0.0904913	−	0.0206540i
$763$	2.50343e8	+	2.66246e8i	0.563588	+	0.599390i
$764$	1.13259e8	−	4.96218e8i	0.253975	−	1.11274i
$765$	177498.			0.000396468
$766$		−	3.67639e8i		−	0.817967i
$767$	−2.03338e8	+	8.90881e8i	−0.450642	+	1.97439i
$768$	2.05657e8	+	4.27052e8i	0.454005	+	0.942750i
$769$	−5.38967e8	+	4.29812e8i	−1.18518	+	0.945148i	−0.999299	−	0.0374251i	$-0.988084\pi$
$769$	−5.38967e8	+	4.29812e8i	−1.18518	+	0.945148i	−0.185878	+	0.982573i	$0.559513\pi$
$770$	−588590.	+	1.52942e6i	−0.00128926	+	0.00335007i
$771$	3.92738e7	−	4.92478e7i	0.0856920	−	0.107454i
$772$	−9.83837e7	+	4.31047e8i	−0.213831	+	0.936856i
$773$	−5.27746e8	−	4.20863e8i	−1.14258	−	0.911176i	−0.145638	−	0.989338i	$-0.546524\pi$
$773$	−5.27746e8	−	4.20863e8i	−1.14258	−	0.911176i	−0.996941	+	0.0781617i	$0.975095\pi$
$774$	−938355.	+	451888.i	−0.00202369	+	0.000974559i
$775$	−1.35623e8	+	1.08156e8i	−0.291359	+	0.232351i
$776$	5.90489e7	−	1.22616e8i	0.126365	−	0.262400i
$777$	5.91210e8	−	5.55896e8i	1.26031	−	1.18503i
$778$	−1.18285e7	+	5.69629e6i	−0.0251183	+	0.0120963i
$779$	6.16520e7	+	2.96900e7i	0.130417	+	0.0628056i
$780$	1.16901e7	−	2.66818e6i	0.0246339	−	0.00562253i
$781$	−1.44591e8	−	6.96312e7i	−0.303520	−	0.146167i
$782$	4.03473e6	+	3.21759e6i	0.00843712	+	0.00672838i
$783$			2.11570e8i			0.440725i
$784$	8.42559e7	−	1.38435e7i	0.174845	−	0.0287275i
$785$	2.21954e6			0.00458832
$786$	−1.65260e8	+	2.07229e8i	−0.340330	+	0.426760i
$787$	−2.12062e8	+	4.40352e8i	−0.435050	+	0.903391i	0.562036	+	0.827113i	$0.310018\pi$
$787$	−2.12062e8	+	4.40352e8i	−0.435050	+	0.903391i	−0.997087	+	0.0762785i	$0.975696\pi$
$788$	3.71879e6	+	1.62931e7i	0.00760016	+	0.0332985i
$789$	−6.37552e7	+	1.32389e8i	−0.129803	+	0.269538i
$790$	−1.96621e6	−	4.08287e6i	−0.00398793	−	0.00828103i
$791$	2.16985e8	−	1.27200e8i	0.438430	−	0.257015i
$792$	8.95710e7	+	4.31351e7i	0.180299	+	0.0868272i
$793$	−7.01167e8	−	8.79236e8i	−1.40605	−	1.76314i
$794$	−3.17761e7	−	6.59837e7i	−0.0634802	−	0.131818i
$795$	−528143.	+	662270.i	−0.00105111	+	0.00131806i
$796$	5.90791e8	+	1.34844e8i	1.17137	+	0.267358i
$797$	−4.63856e8	−	3.69913e8i	−0.916238	−	0.730675i	0.0471214	−	0.998889i	$-0.484995\pi$
$797$	−4.63856e8	−	3.69913e8i	−0.916238	−	0.730675i	−0.963359	+	0.268214i	$0.913567\pi$
$798$	−9.72337e7	−	3.07966e8i	−0.191341	−	0.606030i
$799$	2.50993e7	+	3.14735e7i	0.0492063	+	0.0617028i
$800$	4.77017e8	−	2.29719e8i	0.931674	−	0.448670i
$801$	−5.07992e8	−	1.15946e8i	−0.988460	−	0.225610i
$802$	−4.67810e8			−0.906873
$803$		−	4.79646e7i		−	0.0926347i
$804$	3.50207e8	+	7.99325e7i	0.673840	+	0.153800i
$805$	−1.28066e6	+	3.32771e6i	−0.00245496	+	0.00637907i
$806$	−4.36578e7	−	1.91277e8i	−0.0833791	−	0.365308i
$807$	−1.79425e8	−	7.86110e8i	−0.341398	−	1.49576i
$808$	−4.96966e8	+	3.96317e8i	−0.942091	+	0.751292i
$809$	−3.65813e8	−	4.58715e8i	−0.690898	−	0.866359i	0.305409	−	0.952221i	$-0.401207\pi$
$809$	−3.65813e8	−	4.58715e8i	−0.690898	−	0.866359i	−0.996307	+	0.0858626i	$0.972635\pi$
$810$	5.77781e6	−	1.31875e6i	0.0108720	−	0.00248146i
$811$	6.91119e8	−	1.57743e8i	1.29566	−	0.295726i	0.481540	−	0.876424i	$-0.340078\pi$
$811$	6.91119e8	−	1.57743e8i	1.29566	−	0.295726i	0.814119	+	0.580699i	$0.197221\pi$
$812$	4.02847e7	−	2.79837e8i	0.0752440	−	0.522682i
$813$	1.37738e8	−	6.03471e8i	0.256320	−	1.12301i
$814$	1.67500e8			0.310557
$815$			5.59023e6i			0.0103266i
$816$	1.22390e6	−	5.36227e6i	0.00225256	−	0.00986912i
$817$	−1.68156e6	−	3.49179e6i	−0.00308351	−	0.00640298i
$818$	1.67880e8	−	1.33880e8i	0.306718	−	0.244600i
$819$	5.25759e8	+	7.56870e7i	0.957050	+	0.137775i
$820$	600991.	−	753619.i	0.00109000	−	0.00136682i
$821$	1.24847e8	−	5.46990e8i	0.225605	−	0.988439i	−0.727573	−	0.686030i	$-0.759352\pi$
$821$	1.24847e8	−	5.46990e8i	0.225605	−	0.988439i	0.953178	−	0.302409i	$-0.0977910\pi$
$822$	4.12087e8	+	3.28628e8i	0.741948	+	0.591684i
$823$	−2.25561e8	+	1.08624e8i	−0.404636	+	0.194862i	−0.625121	−	0.780528i	$-0.714950\pi$
$823$	−2.25561e8	+	1.08624e8i	−0.404636	+	0.194862i	0.220485	+	0.975390i	$0.429236\pi$
$824$	−1.48848e8	+	1.18702e8i	−0.266049	+	0.212167i
$825$	1.21188e8	−	2.51649e8i	0.215823	−	0.448160i
$826$	1.24519e8	−	3.23556e8i	0.220952	−	0.574130i
$827$	1.42913e8	−	6.88234e7i	0.252672	−	0.121680i	−0.303261	−	0.952907i	$-0.598075\pi$
$827$	1.42913e8	−	6.88234e7i	0.252672	−	0.121680i	0.555933	+	0.831227i	$0.312361\pi$
$828$	7.98864e7	+	3.84712e7i	0.140728	+	0.0677712i
$829$	4.14278e8	−	9.45562e7i	0.727157	−	0.165969i	0.157110	−	0.987581i	$-0.449782\pi$
$829$	4.14278e8	−	9.45562e7i	0.727157	−	0.165969i	0.570047	+	0.821612i	$0.306925\pi$
$830$	−6.82507e6	−	3.28678e6i	−0.0119364	−	0.00574826i
$831$	−7.26609e8	−	5.79451e8i	−1.26619	−	1.00975i
$832$			4.13181e8i			0.717415i
$833$	2.32832e7	+	1.30344e7i	0.0402817	+	0.0225505i
$834$	3.54538e8			0.611174
$835$	781307.	−	979728.i	0.00134203	−	0.00168285i
$836$	−6.57958e7	+	1.36626e8i	−0.112611	+	0.233838i
$837$	2.81980e7	+	1.23543e8i	0.0480886	+	0.210690i
$838$	1.08182e8	−	2.24642e8i	0.183832	−	0.381732i
$839$	1.94532e8	+	4.03950e8i	0.329386	+	0.683977i	0.998233	−	0.0594232i	$-0.0189261\pi$
$839$	1.94532e8	+	4.03950e8i	0.329386	+	0.683977i	−0.668847	+	0.743400i	$0.733212\pi$
$840$	−1.10614e7	+	902663.i	−0.0186626	+	0.00152296i
$841$	2.26212e8	+	1.08938e8i	0.380301	+	0.183143i
$842$	2.20824e8	+	2.76905e8i	0.369922	+	0.463868i
$843$	−3.64015e8	−	7.55885e8i	−0.607627	−	1.26175i
$844$	3.30514e8	−	4.14452e8i	0.549747	−	0.689361i
$845$	2.19467e7	+	5.00920e6i	0.0363747	+	0.00830229i
$846$	−2.37705e8	−	1.89563e8i	−0.392579	−	0.313071i
$847$	−5.07738e8	+	4.14338e7i	−0.835583	+	0.0681874i
$848$	5.67987e6	+	7.12233e6i	0.00931432	+	0.0116798i
$849$	−8.96662e8	+	4.31810e8i	−1.46523	+	0.705618i
$850$	1.52694e7	+	3.48513e6i	0.0248636	+	0.00567496i
$851$	3.64446e8			0.591350
$852$		−	4.45504e8i		−	0.720332i
$853$	7.84447e8	+	1.79045e8i	1.26391	+	0.288479i	0.801397	−	0.598133i	$-0.204090\pi$
$853$	7.84447e8	+	1.79045e8i	1.26391	+	0.288479i	0.462514	+	0.886612i	$0.346948\pi$
$854$	2.15775e8	+	3.68081e8i	0.346440	+	0.590975i
$855$	−1.11004e6	−	4.86339e6i	−0.00177599	−	0.00778110i
$856$	−2.20896e8	−	9.67807e8i	−0.352181	−	1.54301i
$857$	−7.59931e8	+	6.06025e8i	−1.20735	+	0.962826i	−0.999881	−	0.0154160i	$-0.995093\pi$
$857$	−7.59931e8	+	6.06025e8i	−1.20735	+	0.962826i	−0.207465	+	0.978242i	$0.566521\pi$
$858$	1.96964e8	+	2.46985e8i	0.311834	+	0.391028i
$859$	−4.27938e8	+	9.76740e7i	−0.675152	+	0.154099i	−0.546332	−	0.837569i	$-0.683976\pi$
$859$	−4.27938e8	+	9.76740e7i	−0.675152	+	0.154099i	−0.128820	+	0.991668i	$0.541119\pi$
$860$	−53224.6	+	12148.2i	−8.36791e−5	+	1.90992e-5i
$861$	1.06142e8	−	6.22223e7i	0.166295	−	0.0974848i
$862$	1.10006e7	−	4.81967e7i	0.0171749	−	0.0752481i
$863$	−7.06212e8			−1.09876			−0.549380	−	0.835573i	$-0.685136\pi$
$863$	−7.06212e8			−1.09876			−0.549380	+	0.835573i	$0.685136\pi$
$864$		−	3.86769e8i		−	0.599667i
$865$	−2.43552e6	+	1.06707e7i	−0.00376308	+	0.0164871i
$866$	2.20439e8	+	4.57746e8i	0.339418	+	0.704808i
$867$	−6.29227e8	+	5.01791e8i	−0.965494	+	0.769956i
$868$	−1.37729e7	−	1.68777e8i	−0.0210604	−	0.258079i
$869$	−1.69342e8	+	2.12348e8i	−0.258051	+	0.323586i
$870$	−1.23080e6	+	5.39250e6i	−0.00186909	+	0.00818903i
$871$	7.55583e8	+	6.02557e8i	1.14348	+	0.911893i
$872$	−4.60257e8	+	2.21648e8i	−0.694146	+	0.334283i
$873$	8.59924e7	−	6.85767e7i	0.129246	−	0.103070i
$874$	6.29287e7	−	1.30673e8i	0.0942572	−	0.195727i
$875$	1.76053e6	+	2.15739e7i	0.00262796	+	0.0322036i
$876$	1.19964e8	−	5.77717e7i	0.178459	−	0.0859415i
$877$	1.08546e9	+	5.22730e8i	1.60922	+	0.774958i	0.999839	−	0.0179210i	$-0.00570474\pi$
$877$	1.08546e9	+	5.22730e8i	1.60922	+	0.774958i	0.609378	+	0.792879i	$0.291419\pi$
$878$	2.73909e7	−	6.25179e6i	0.0404690	−	0.00923678i
$879$	7.83485e8	+	3.77306e8i	1.15362	+	0.555556i
$880$	613259.	+	489058.i	0.000899903	+	0.000717649i
$881$			2.32321e8i			0.339751i	0.985465	+	0.169876i	$0.0543366\pi$
$881$			2.32321e8i			0.339751i	−0.985465	+	0.169876i	$0.945663\pi$
$882$	−1.93344e8	−	5.68448e7i	−0.281790	−	0.0828486i
$883$	−1.19882e9			−1.74130			−0.870650	−	0.491904i	$-0.836301\pi$
$883$	−1.19882e9			−1.74130			−0.870650	+	0.491904i	$0.836301\pi$
$884$	2.51257e7	−	3.15066e7i	0.0363715	−	0.0456084i
$885$	6.69485e6	−	1.39020e7i	0.00965853	−	0.0200561i
$886$	−1.17981e8	−	5.16908e8i	−0.169633	−	0.743211i
$887$	−5.71948e8	+	1.18766e9i	−0.819569	+	1.70185i	−0.113695	+	0.993516i	$0.536269\pi$
$887$	−5.71948e8	+	1.18766e9i	−0.819569	+	1.70185i	−0.705874	+	0.708337i	$0.749446\pi$
$888$	4.92178e8	+	1.02202e9i	0.702884	+	1.45955i
$889$	8.89993e7	+	3.42510e7i	0.126672	+	0.0487493i
$890$	1.08170e7	+	5.20921e6i	0.0153440	+	0.00738927i
$891$	−2.21463e8	−	2.77705e8i	−0.313089	−	0.392601i
$892$	−6.98323e6	−	1.45008e7i	−0.00983925	−	0.0204314i
$893$	7.05400e8	−	8.84543e8i	0.990560	−	1.24212i
$894$	2.61315e8	+	5.96434e7i	0.365722	+	0.0834737i
$895$	−1.64840e7	−	1.31455e7i	−0.0229928	−	0.0183362i
$896$	−8.36796e7	+	5.81280e8i	−0.116331	+	0.808093i
$897$	4.28553e8	+	5.37389e8i	0.593783	+	0.744580i
$898$	−1.30816e8	+	6.29976e7i	−0.180647	+	0.0869952i
$899$	−2.00727e8	−	4.58146e7i	−0.276265	−	0.0630557i
$900$	2.69098e8			0.369133
$901$			2.84686e6i			0.00389216i
$902$	2.47584e7	+	5.65095e6i	0.0337368	+	0.00770020i
$903$	−6.89729e6	−	992917.i	−0.00936731	−	0.00134850i
$904$	7.82346e7	+	3.42768e8i	0.105899	+	0.463975i
$905$	971773.	+	4.25762e6i	0.00131105	+	0.00574408i
$906$	−2.94032e8	+	2.34482e8i	−0.395375	+	0.315301i
$907$	4.68457e8	+	5.87426e8i	0.627838	+	0.787284i	0.989424	−	0.145055i	$-0.0463359\pi$
$907$	4.68457e8	+	5.87426e8i	0.627838	+	0.787284i	−0.361586	+	0.932339i	$0.617765\pi$
$908$	−7.62875e8	+	1.74121e8i	−1.01905	+	0.232592i
$909$	−5.00835e8	+	1.14312e8i	−0.666811	+	0.152195i
$910$	−1.14226e7	−	4.39593e6i	−0.0151579	−	0.00583346i
$911$	−2.24298e8	+	9.82713e8i	−0.296667	+	1.29979i	0.578388	+	0.815762i	$0.303682\pi$
$911$	−2.24298e8	+	9.82713e8i	−0.296667	+	1.29979i	−0.875055	+	0.484023i	$0.839175\pi$
$912$	−1.54579e8			−0.203782
$913$			4.54023e8i			0.596575i
$914$	1.32776e8	−	5.81729e8i	0.173892	−	0.761873i
$915$	8.23921e6	+	1.71089e7i	0.0107553	+	0.0223336i
$916$	−4.12771e8	+	3.29174e8i	−0.537060	+	0.428291i
$917$	−5.86925e8	+	1.85309e8i	−0.761158	+	0.240319i
$918$	7.13354e6	−	8.94517e6i	0.00922098	−	0.0115627i
$919$	1.25666e8	−	5.50578e8i	0.161909	−	0.709370i	−0.827166	−	0.561957i	$-0.810048\pi$
$919$	1.25666e8	−	5.50578e8i	0.161909	−	0.709370i	0.989075	−	0.147412i	$-0.0470944\pi$
$920$	−3.89676e6	−	3.10757e6i	−0.00500427	−	0.00399077i
$921$	−5.54795e7	+	2.67175e7i	−0.0710156	+	0.0341993i
$922$	4.49922e8	−	3.58801e8i	0.574043	−	0.457784i
$923$	5.20045e8	−	1.07989e9i	0.661357	−	1.37332i
$924$	1.37890e8	+	2.35221e8i	0.174791	+	0.298167i
$925$	9.96529e8	−	4.79903e8i	1.25911	−	0.606357i
$926$	3.29785e8	+	1.58816e8i	0.415334	+	0.200014i
$927$	−1.50007e8	+	3.42381e7i	−0.188309	+	0.0429804i
$928$	5.66169e8	+	2.72653e8i	0.708439	+	0.341166i
$929$	−1.19360e9	−	9.51863e8i	−1.48871	−	1.18721i	−0.935074	−	0.354452i	$-0.884667\pi$
$929$	−1.19360e9	−	9.51863e8i	−1.48871	−	1.18721i	−0.553639	−	0.832757i	$-0.686761\pi$
$930$			3.31292e6i			0.00411872i
$931$	2.11530e8	−	7.19469e8i	0.262134	−	0.891586i
$932$	−8.85396e7			−0.109368
$933$	−8.55000e8	+	1.07214e9i	−1.05274	+	1.32009i
$934$	3.09076e8	−	6.41804e8i	0.379337	−	0.787701i
$935$	54545.4	+	238979.i	6.67303e−5	+	0.000292365i
$936$	−3.22158e8	+	6.68968e8i	−0.392863	+	0.815788i
$937$	8.23564e6	+	1.71015e7i	0.0100110	+	0.0207881i	0.905914	−	0.423461i	$-0.139185\pi$
$937$	8.23564e6	+	1.71015e7i	0.0100110	+	0.0207881i	−0.895903	+	0.444249i	$0.853471\pi$
$938$	−2.51167e8	−	2.67122e8i	−0.304336	−	0.323669i
$939$	8.39751e8	+	4.04403e8i	1.01427	+	0.488447i
$940$	−9.93658e6	−	1.24601e7i	−0.0119634	−	0.0150016i
$941$	5.86261e8	+	1.21738e9i	0.703594	+	1.46103i	0.879144	+	0.476557i	$0.158115\pi$
$941$	5.86261e8	+	1.21738e9i	0.703594	+	1.46103i	−0.175550	+	0.984470i	$0.556170\pi$
$942$	−1.01210e8	+	1.26914e8i	−0.121080	+	0.151830i
$943$	5.38694e7	+	1.22953e7i	0.0642402	+	0.0146624i
$944$	−1.29738e8	−	1.03463e8i	−0.154224	−	0.122990i
$945$	7.37767e6	+	2.83927e6i	0.00874227	+	0.00336443i
$946$	−896771.	−	1.12451e6i	−0.00105927	−	0.00132829i
$947$	1.00214e9	−	4.82606e8i	1.17999	−	0.568254i	0.262083	−	0.965045i	$-0.415591\pi$
$947$	1.00214e9	−	4.82606e8i	1.17999	−	0.568254i	0.917909	+	0.396791i	$0.129876\pi$
$948$	−7.35072e8	−	1.67775e8i	−0.862789	−	0.196926i
$949$	3.58227e8			0.419140
$950$		−	4.40172e8i		−	0.513395i
$951$	4.40640e8	+	1.00573e8i	0.512321	+	0.116934i
$952$	−2.71734e7	+	2.55502e7i	−0.0314943	+	0.0296131i
$953$	−2.45002e8	−	1.07342e9i	−0.283068	−	1.24020i	−0.893837	−	0.448392i	$-0.851997\pi$
$953$	−2.45002e8	−	1.07342e9i	−0.283068	−	1.24020i	0.610769	−	0.791809i	$-0.290860\pi$
$954$	−4.78442e6	−	2.09619e7i	−0.00551042	−	0.0241427i
$955$	−1.80780e7	+	1.44167e7i	−0.0207558	+	0.0165522i
$956$	3.99268e8	+	5.00666e8i	0.456973	+	0.573026i
$957$	3.23199e8	−	7.37681e7i	0.368752	−	0.0841653i
$958$	2.92298e8	−	6.67151e7i	0.332452	−	0.0758801i
$959$	3.68497e8	+	1.16713e9i	0.417809	+	1.32332i
$960$	1.55250e6	−	6.80195e6i	0.00175476	−	0.00768811i
$961$	7.64186e8			0.861051
$962$			1.25098e9i			1.40516i
$963$	1.78524e8	−	7.82163e8i	0.199902	−	0.875827i
$964$	−2.03987e8	−	4.23583e8i	−0.227704	−	0.472833i
$965$	1.57037e7	−	1.25233e7i	0.0174751	−	0.0139359i
$966$	−1.31882e8	−	2.24971e8i	−0.146303	−	0.249571i
$967$	7.54806e8	−	9.46497e8i	0.834749	−	1.04674i	−0.163438	−	0.986554i	$-0.552258\pi$
$967$	7.54806e8	−	9.46497e8i	0.834749	−	1.04674i	0.998187	−	0.0601891i	$-0.0191704\pi$
$968$	1.58455e8	−	6.94238e8i	0.174695	−	0.765389i
$969$	−3.77676e7	−	3.01187e7i	−0.0415096	−	0.0331028i
$970$	−2.28334e6	+	1.09960e6i	−0.00250182	+	0.00120481i
$971$	−8.79212e7	+	7.01149e7i	−0.0960365	+	0.0765865i	−0.670331	−	0.742062i	$-0.733848\pi$
$971$	−8.79212e7	+	7.01149e7i	−0.0960365	+	0.0765865i	0.574295	+	0.818649i	$0.305276\pi$
$972$	2.67359e8	−	5.55178e8i	0.291137	−	0.604551i
$973$	6.83274e8	+	4.59248e8i	0.741748	+	0.498550i
$974$	−6.85016e8	+	3.29886e8i	−0.741351	+	0.357016i
$975$	1.87946e9	+	9.05099e8i	2.02777	+	0.976522i
$976$	1.99100e8	−	4.54434e7i	0.214152	−	0.0488788i
$977$	−1.43821e9	−	6.92605e8i	−1.54219	−	0.742680i	−0.546681	−	0.837341i	$-0.684109\pi$
$977$	−1.43821e9	−	6.92605e8i	−1.54219	−	0.742680i	−0.995510	+	0.0946612i	$0.969823\pi$
$978$	−3.19651e8	−	2.54913e8i	−0.341712	−	0.272506i
$979$		−	7.19579e8i		−	0.766886i
$980$	−9.21762e6	−	5.16020e6i	−0.00979356	−	0.00548262i
$981$	−4.12856e8			−0.437313
$982$	−1.83675e8	+	2.30321e8i	−0.193962	+	0.243220i
$983$	−4.30663e8	+	8.94281e8i	−0.453395	+	0.941485i	0.541512	+	0.840693i	$0.317852\pi$
$983$	−4.30663e8	+	8.94281e8i	−0.453395	+	0.941485i	−0.994908	+	0.100792i	$0.967862\pi$
$984$	3.82699e7	+	1.67671e8i	0.0401672	+	0.175984i
$985$	329413.	−	684033.i	0.000344693	−	0.000715761i
$986$	8.06556e6	+	1.67483e7i	0.00841402	+	0.0174719i
$987$	−6.12463e8	−	1.93984e9i	−0.636984	−	2.01750i
$988$	−1.02040e9	−	4.91401e8i	−1.05804	−	0.509524i
$989$	−1.95119e6	−	2.44672e6i	−0.00201703	−	0.00252927i
$990$	−803256.	−	1.66798e6i	−0.000827843	−	0.00171903i
$991$	−7.37300e8	+	9.24545e8i	−0.757571	+	0.949964i	−0.999795	−	0.0202563i	$-0.993552\pi$
$991$	−7.37300e8	+	9.24545e8i	−0.757571	+	0.949964i	0.242224	+	0.970220i	$0.422123\pi$
$992$	3.66947e8	+	8.37532e7i	0.375896	+	0.0857959i
$993$	−1.83247e9	−	1.46135e9i	−1.87150	−	1.49247i
$994$	−2.53669e8	+	3.77411e8i	−0.258290	+	0.384287i
$995$	−1.71643e7	−	2.15234e7i	−0.0174244	−	0.0218495i
$996$	−1.13556e9	+	5.46855e8i	−1.14929	+	0.553470i
$997$	1.28288e8	+	2.92808e7i	0.129449	+	0.0295459i	0.286755	−	0.958004i	$-0.407424\pi$
$997$	1.28288e8	+	2.92808e7i	0.129449	+	0.0295459i	−0.157305	+	0.987550i	$0.550281\pi$
$998$	2.48595e7			0.0250093
$999$		−	8.07993e8i		−	0.810422i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.f.a.6.11	✓	162
49.41	odd	14	inner	49.7.f.a.41.11	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.f.a.6.11	✓	162	1.1	even	1	trivial
49.7.f.a.41.11	yes	162	49.41	odd	14	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.f (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.75625 + 3.45623i) q^{2} +(14.4977 - 30.1049i) q^{3} +(9.89275 + 43.3430i) q^{4} +(0.876306 - 1.81967i) q^{5} +(64.0898 + 133.084i) q^{6} +(-48.8736 + 339.500i) q^{7} +(-431.975 - 208.028i) q^{8} +(-241.594 - 302.950i) q^{9} +(3.87387 + 8.04417i) q^{10} +(333.642 - 418.374i) q^{11} +(1448.26 + 330.555i) q^{12} +(3124.66 + 2491.83i) q^{13} +(-1038.68 - 1104.66i) q^{14} +(-42.0764 - 52.7622i) q^{15} +(-653.892 + 314.898i) q^{16} +(-221.119 - 50.4689i) q^{17} +1712.96 q^{18} +6374.22i q^{19} +(87.5389 + 19.9802i) q^{20} +(9512.05 + 6393.32i) q^{21} +(526.395 + 2306.29i) q^{22} +(1145.33 + 5018.02i) q^{23} +(-12525.3 + 9988.61i) q^{24} +(9739.48 + 12212.9i) q^{25} +(-17224.7 + 3931.41i) q^{26} +(11125.2 - 2539.25i) q^{27} +(-15198.4 + 1240.26i) q^{28} +(-4125.63 + 18075.6i) q^{29} +298.331 q^{30} +11104.9i q^{31} +(7542.03 - 33043.8i) q^{32} +(-7758.04 - 16109.7i) q^{33} +(783.890 - 625.131i) q^{34} +(574.950 + 386.440i) q^{35} +(10740.7 - 13468.4i) q^{36} +(15755.9 - 69031.3i) q^{37} +(-22030.7 - 17568.9i) q^{38} +(120317. - 57941.5i) q^{39} +(-757.085 + 603.755i) q^{40} +(4657.83 - 9672.08i) q^{41} +(-48314.3 + 15254.2i) q^{42} +(-547.799 + 263.806i) q^{43} +(21434.2 + 10322.2i) q^{44} +(-762.978 + 174.145i) q^{45} +(-20500.2 - 9872.38i) q^{46} +(-138769. - 110664. i) q^{47} +24250.6i q^{48} +(-112872. - 33185.2i) q^{49} -69055.1 q^{50} +(-4725.08 + 5925.06i) q^{51} +(-77091.9 + 160083. i) q^{52} +(-2793.08 - 12237.3i) q^{53} +(-21887.5 + 45449.9i) q^{54} +(-468.930 - 973.742i) q^{55} +(91737.8 - 136489. i) q^{56} +(191895. + 92411.8i) q^{57} +(-51102.0 - 64079.8i) q^{58} +(99204.5 + 206000. i) q^{59} +(1870.62 - 2345.68i) q^{60} +(-274331. - 62614.4i) q^{61} +(-38380.9 - 30607.8i) q^{62} +(114659. - 67215.0i) q^{63} +(64458.6 + 80828.5i) q^{64} +(7272.46 - 3502.23i) q^{65} +(77061.9 + 17588.9i) q^{66} +241813. q^{67} -10083.2i q^{68} +(167671. + 38269.9i) q^{69} +(-2920.33 + 922.031i) q^{70} +(-66734.4 - 292382. i) q^{71} +(41340.6 + 181125. i) q^{72} +(70078.0 - 55885.4i) q^{73} +(195160. + 244723. i) q^{74} +(508869. - 116146. i) q^{75} +(-276278. + 63058.6i) q^{76} +(125732. + 133719. i) q^{77} +(-131364. + 575542. i) q^{78} -507556. q^{79} +1465.81i q^{80} +(147703. - 647131. i) q^{81} +(20590.8 + 42757.2i) q^{82} +(-663344. + 528999. i) q^{83} +(-183005. + 475528. i) q^{84} +(-285.604 + 358.136i) q^{85} +(598.096 - 2620.43i) q^{86} +(484350. + 386256. i) q^{87} +(-231159. + 111320. i) q^{88} +(1.05133e6 - 838410. i) q^{89} +(1501.07 - 3117.01i) q^{90} +(-998690. + 939037. i) q^{91} +(-206165. + 99283.9i) q^{92} +(334310. + 160995. i) q^{93} +(764963. - 174598. i) q^{94} +(11599.0 + 5585.77i) q^{95} +(-885436. - 706112. i) q^{96} +283851. i q^{97} +(425798. - 298643. i) q^{98} -207352. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 5 q^{2} - 7 q^{3} - 837 q^{4} - 7 q^{5} - 791 q^{6} + 70 q^{7} - 843 q^{8} + 2990 q^{9} - 7 q^{10} + 1171 q^{11} - 13482 q^{12} - 7 q^{13} + 22533 q^{14} + 6181 q^{15} - 17901 q^{16} - 3143 q^{17}+ \cdots + 4449580 q^{99}+O(q^{100}) \) 162 * q - 5 * q^2 - 7 * q^3 - 837 * q^4 - 7 * q^5 - 791 * q^6 + 70 * q^7 - 843 * q^8 + 2990 * q^9 - 7 * q^10 + 1171 * q^11 - 13482 * q^12 - 7 * q^13 + 22533 * q^14 + 6181 * q^15 - 17901 * q^16 - 3143 * q^17 - 22692 * q^18 + 50169 * q^20 + 28553 * q^21 - 33057 * q^22 - 49677 * q^23 - 119077 * q^24 + 30038 * q^25 + 59577 * q^26 + 11753 * q^27 + 42994 * q^28 + 80383 * q^29 + 27328 * q^30 + 253875 * q^32 - 7 * q^33 + 54677 * q^34 - 74067 * q^35 - 193099 * q^36 + 118463 * q^37 - 121079 * q^38 - 304143 * q^39 - 702079 * q^40 - 58023 * q^41 - 1137479 * q^42 + 93963 * q^43 + 352505 * q^44 + 1333577 * q^45 + 782877 * q^46 + 408261 * q^47 - 149338 * q^49 + 1164004 * q^50 - 911743 * q^51 + 721273 * q^52 - 992325 * q^53 - 576646 * q^54 - 1502935 * q^55 + 1368514 * q^56 + 116032 * q^57 + 2610717 * q^58 + 24493 * q^59 - 1027131 * q^60 + 563101 * q^61 - 262199 * q^62 - 966154 * q^63 - 2839067 * q^64 - 140287 * q^65 - 1523319 * q^66 - 1313660 * q^67 + 2216753 * q^69 + 1806959 * q^70 + 1031011 * q^71 - 3123354 * q^72 - 846727 * q^73 + 1270357 * q^74 + 873173 * q^75 + 5463990 * q^76 + 1565235 * q^77 + 1006005 * q^78 + 82420 * q^79 + 2259538 * q^81 - 7672672 * q^82 - 3860031 * q^83 - 9104942 * q^84 + 1596833 * q^85 + 224039 * q^86 + 2590525 * q^87 + 4179421 * q^88 + 5417433 * q^89 + 6759578 * q^90 - 6163507 * q^91 - 7060306 * q^92 + 1903160 * q^93 + 4029998 * q^94 + 2115400 * q^95 + 957950 * q^96 - 1546783 * q^98 + 4449580 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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