LMFDB - Embedded newform 49.7.f.a.6.18

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			6.18
Character	$\chi$	$=$	49.6
Dual form			49.7.f.a.41.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.47311 - 5.60910i) q^{2} +(5.07295 - 10.5341i) q^{3} +(2.78804 + 12.2152i) q^{4} +(-43.9720 + 91.3088i) q^{5} +(-36.3949 - 75.5747i) q^{6} +(-131.478 + 316.801i) q^{7} +(494.672 + 238.222i) q^{8} +(369.292 + 463.077i) q^{9} +(315.469 + 655.077i) q^{10} +(-428.014 + 536.713i) q^{11} +(142.820 + 32.5977i) q^{12} +(-1450.93 - 1157.08i) q^{13} +(1188.85 + 2154.55i) q^{14} +(738.787 + 926.410i) q^{15} +(2826.46 - 1361.15i) q^{16} +(3686.32 + 841.378i) q^{17} +4249.33 q^{18} -1410.36i q^{19} +(-1237.95 - 282.555i) q^{20} +(2670.23 + 2992.11i) q^{21} +(1095.92 + 4801.55i) q^{22} +(-451.199 - 1976.83i) q^{23} +(5018.89 - 4002.43i) q^{24} +(3338.26 + 4186.05i) q^{25} +(-12980.4 + 2962.68i) q^{26} +(15061.2 - 3437.63i) q^{27} +(-4236.35 - 722.773i) q^{28} +(-2665.61 + 11678.8i) q^{29} +8501.00 q^{30} +905.569i q^{31} +(-2810.91 + 12315.4i) q^{32} +(3482.49 + 7231.46i) q^{33} +(21208.7 - 16913.3i) q^{34} +(-23145.4 - 25935.4i) q^{35} +(-4626.99 + 5802.06i) q^{36} +(4871.87 - 21345.1i) q^{37} +(-7910.83 - 6308.68i) q^{38} +(-19549.3 + 9414.45i) q^{39} +(-43503.5 + 34692.9i) q^{40} +(7872.51 - 16347.4i) q^{41} +(28727.2 - 1593.54i) q^{42} +(-69887.1 + 33655.8i) q^{43} +(-7749.39 - 3731.91i) q^{44} +(-58521.6 + 13357.2i) q^{45} +(-13106.5 - 6311.76i) q^{46} +(32136.0 + 25627.6i) q^{47} -36679.2i q^{48} +(-83076.3 - 83304.4i) q^{49} +38412.4 q^{50} +(27563.6 - 34563.7i) q^{51} +(10088.7 - 20949.5i) q^{52} +(-36039.9 - 157901. i) q^{53} +(48088.5 - 99856.7i) q^{54} +(-30186.0 - 62681.9i) q^{55} +(-140507. + 125392. i) q^{56} +(-14856.8 - 7154.67i) q^{57} +(53583.9 + 67192.1i) q^{58} +(-87879.1 - 182483. i) q^{59} +(-9256.53 + 11607.3i) q^{60} +(175790. + 40123.0i) q^{61} +(5079.42 + 4050.71i) q^{62} +(-195257. + 56107.6i) q^{63} +(181687. + 227828. i) q^{64} +(169452. - 81603.9i) q^{65} +(56139.5 + 12813.5i) q^{66} +141332. q^{67} +47375.0i q^{68} +(-23113.0 - 5275.39i) q^{69} +(-249006. + 13812.7i) q^{70} +(108225. + 474167. i) q^{71} +(72363.4 + 317045. i) q^{72} +(332186. - 264909. i) q^{73} +(-97934.1 - 122806. i) q^{74} +(61031.0 - 13929.9i) q^{75} +(17227.8 - 3932.14i) q^{76} +(-113757. - 206161. i) q^{77} +(-34639.6 + 151766. i) q^{78} +972618. q^{79} +317934. i q^{80} +(-55888.7 + 244865. i) q^{81} +(-56479.8 - 117282. i) q^{82} +(5829.41 - 4648.80i) q^{83} +(-29104.5 + 40959.5i) q^{84} +(-238920. + 299596. i) q^{85} +(-123833. + 542550. i) q^{86} +(109503. + 87325.7i) q^{87} +(-339584. + 163535. i) q^{88} +(-157142. + 125317. i) q^{89} +(-186852. + 388001. i) q^{90} +(557330. - 307527. i) q^{91} +(22889.5 - 11023.0i) q^{92} +(9539.34 + 4593.90i) q^{93} +(287495. - 65618.9i) q^{94} +(128778. + 62016.3i) q^{95} +(115472. + 92085.6i) q^{96} -1.41784e6i q^{97} +(-838871. + 93353.9i) q^{98} -406602. 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 $

$2$	4.47311	−	5.60910i	0.559138	−	0.701137i	−0.419260	−	0.907866i	$-0.637710\pi$
$2$	4.47311	−	5.60910i	0.559138	−	0.701137i	0.978398	+	0.206729i	$0.0662819\pi$
$3$	5.07295	−	10.5341i	0.187887	−	0.390151i	−0.785653	−	0.618667i	$-0.787673\pi$
$3$	5.07295	−	10.5341i	0.187887	−	0.390151i	0.973540	+	0.228516i	$0.0733873\pi$
$4$	2.78804	+	12.2152i	0.0435632	+	0.190863i
$5$	−43.9720	+	91.3088i	−0.351776	+	0.730471i	−0.999507	−	0.0313986i	$-0.990004\pi$
$5$	−43.9720	+	91.3088i	−0.351776	+	0.730471i	0.647731	+	0.761869i	$0.275718\pi$
$6$	−36.3949	−	75.5747i	−0.168495	−	0.349883i
$7$	−131.478	+	316.801i	−0.383317	+	0.923617i
$7$	−131.478	+	316.801i	−0.383317	+	0.923617i
$8$	494.672	+	238.222i	0.966157	+	0.465277i
$9$	369.292	+	463.077i	0.506573	+	0.635223i
$10$	315.469	+	655.077i	0.315469	+	0.655077i
$11$	−428.014	+	536.713i	−0.321574	+	0.403241i	−0.916174	−	0.400781i	$-0.868739\pi$
$11$	−428.014	+	536.713i	−0.321574	+	0.403241i	0.594600	+	0.804021i	$0.297310\pi$
$12$	142.820	+	32.5977i	0.0826503	+	0.0188644i
$13$	−1450.93	−	1157.08i	−0.660416	−	0.526664i	0.234943	−	0.972009i	$-0.424510\pi$
$13$	−1450.93	−	1157.08i	−0.660416	−	0.526664i	−0.895359	+	0.445345i	$0.853081\pi$
$14$	1188.85	+	2154.55i	0.433255	+	0.785187i
$15$	738.787	+	926.410i	0.218900	+	0.274492i
$16$	2826.46	−	1361.15i	0.690054	−	0.332313i
$17$	3686.32	+	841.378i	0.750319	+	0.171255i	0.580546	−	0.814228i	$-0.302839\pi$
$17$	3686.32	+	841.378i	0.750319	+	0.171255i	0.169773	+	0.985483i	$0.445696\pi$
$18$	4249.33			0.728623
$19$		−	1410.36i		−	0.205621i	−0.994701	−	0.102811i	$-0.967216\pi$
$19$		−	1410.36i		−	0.205621i	0.994701	−	0.102811i	$-0.0327836\pi$
$20$	−1237.95	−	282.555i	−0.154744	−	0.0353193i
$21$	2670.23	+	2992.11i	0.288330	+	0.323087i
$22$	1095.92	+	4801.55i	0.102923	+	0.450934i
$23$	−451.199	−	1976.83i	−0.0370838	−	0.162475i	0.952995	−	0.302984i	$-0.0979830\pi$
$23$	−451.199	−	1976.83i	−0.0370838	−	0.162475i	−0.990079	+	0.140510i	$0.955126\pi$
$24$	5018.89	−	4002.43i	0.363057	−	0.289528i
$25$	3338.26	+	4186.05i	0.213649	+	0.267907i
$26$	−12980.4	+	2962.68i	−0.738528	+	0.168564i
$27$	15061.2	−	3437.63i	0.765190	−	0.174650i
$28$	−4236.35	−	722.773i	−0.192983	−	0.0329252i
$29$	−2665.61	+	11678.8i	−0.109296	+	0.478855i	0.890423	+	0.455134i	$0.150409\pi$
$29$	−2665.61	+	11678.8i	−0.109296	+	0.478855i	−0.999719	+	0.0237213i	$0.992449\pi$
$30$	8501.00			0.314852
$31$			905.569i			0.0303974i	0.999884	+	0.0151987i	$0.00483808\pi$
$31$			905.569i			0.0303974i	−0.999884	+	0.0151987i	$0.995162\pi$
$32$	−2810.91	+	12315.4i	−0.0857821	+	0.375836i
$33$	3482.49	+	7231.46i	0.0969053	+	0.201226i
$34$	21208.7	−	16913.3i	0.539606	−	0.430321i
$35$	−23145.4	−	25935.4i	−0.539834	−	0.604908i
$36$	−4626.99	+	5802.06i	−0.0991724	+	0.124358i
$37$	4871.87	−	21345.1i	0.0961813	−	0.421398i	−0.903797	−	0.427961i	$-0.859232\pi$
$37$	4871.87	−	21345.1i	0.0961813	−	0.421398i	0.999978	+	0.00656327i	$0.00208917\pi$
$38$	−7910.83	−	6308.68i	−0.144169	−	0.114971i
$39$	−19549.3	+	9414.45i	−0.329562	+	0.158709i
$40$	−43503.5	+	34692.9i	−0.679742	+	0.542076i
$41$	7872.51	−	16347.4i	0.114225	−	0.237191i	−0.836017	−	0.548704i	$-0.815121\pi$
$41$	7872.51	−	16347.4i	0.114225	−	0.237191i	0.950242	+	0.311513i	$0.100836\pi$
$42$	28727.2	−	1593.54i	0.387745	−	0.0215087i
$43$	−69887.1	+	33655.8i	−0.879005	+	0.423307i	−0.818261	−	0.574847i	$-0.805062\pi$
$43$	−69887.1	+	33655.8i	−0.879005	+	0.423307i	−0.0607442	+	0.998153i	$0.519347\pi$
$44$	−7749.39	−	3731.91i	−0.0909724	−	0.0438100i
$45$	−58521.6	+	13357.2i	−0.642212	+	0.146581i
$46$	−13106.5	−	6311.76i	−0.134652	−	0.0648450i
$47$	32136.0	+	25627.6i	0.309527	+	0.246839i	0.765916	−	0.642941i	$-0.222286\pi$
$47$	32136.0	+	25627.6i	0.309527	+	0.246839i	−0.456389	+	0.889780i	$0.650857\pi$
$48$		−	36679.2i		−	0.331663i
$49$	−83076.3	−	83304.4i	−0.706137	−	0.708075i
$50$	38412.4			0.307299
$51$	27563.6	−	34563.7i	0.207791	−	0.260561i
$52$	10088.7	−	20949.5i	0.0717508	−	0.148992i
$53$	−36039.9	−	157901.i	−0.242078	−	1.06062i	−0.939121	−	0.343586i	$-0.888358\pi$
$53$	−36039.9	−	157901.i	−0.242078	−	1.06062i	0.697043	−	0.717029i	$-0.254499\pi$
$54$	48088.5	−	99856.7i	0.305393	−	0.634156i
$55$	−30186.0	−	62681.9i	−0.181433	−	0.376750i
$56$	−140507.	+	125392.i	−0.800081	+	0.714011i
$57$	−14856.8	−	7154.67i	−0.0802234	−	0.0386336i
$58$	53583.9	+	67192.1i	0.274632	+	0.344377i
$59$	−87879.1	−	182483.i	−0.427888	−	0.888518i	−0.997767	−	0.0667895i	$-0.978724\pi$
$59$	−87879.1	−	182483.i	−0.427888	−	0.888518i	0.569879	−	0.821728i	$-0.306990\pi$
$60$	−9256.53	+	11607.3i	−0.0428543	+	0.0537376i
$61$	175790.	+	40123.0i	0.774472	+	0.176768i	0.591451	−	0.806341i	$-0.298555\pi$
$61$	175790.	+	40123.0i	0.774472	+	0.176768i	0.183021	+	0.983109i	$0.441412\pi$
$62$	5079.42	+	4050.71i	0.0213127	+	0.0169963i
$63$	−195257.	+	56107.6i	−0.780881	+	0.224388i
$64$	181687.	+	227828.i	0.693081	+	0.869096i
$65$	169452.	−	81603.9i	0.617032	−	0.297147i
$66$	56139.5	+	12813.5i	0.195270	+	0.0445692i
$67$	141332.			0.469912			0.234956	−	0.972006i	$-0.424505\pi$
$67$	141332.			0.469912			0.234956	+	0.972006i	$0.424505\pi$
$68$			47375.0i			0.150668i
$69$	−23113.0	−	5275.39i	−0.0703573	−	0.0160586i
$70$	−249006.	+	13812.7i	−0.725965	+	0.0402702i
$71$	108225.	+	474167.i	0.302381	+	1.32482i	0.866522	+	0.499139i	$0.166350\pi$
$71$	108225.	+	474167.i	0.302381	+	1.32482i	−0.564141	+	0.825679i	$0.690792\pi$
$72$	72363.4	+	317045.i	0.193875	+	0.849422i
$73$	332186.	−	264909.i	0.853910	−	0.680971i	−0.0953565	−	0.995443i	$-0.530399\pi$
$73$	332186.	−	264909.i	0.853910	−	0.680971i	0.949267	+	0.314473i	$0.101828\pi$
$74$	−97934.1	−	122806.i	−0.241679	−	0.303056i
$75$	61031.0	−	13929.9i	0.144666	−	0.0330191i
$76$	17227.8	−	3932.14i	0.0392455	−	0.00895752i
$77$	−113757.	−	206161.i	−0.249175	−	0.451580i
$78$	−34639.6	+	151766.i	−0.0729942	+	0.319809i
$79$	972618.			1.97270			0.986350	−	0.164661i	$-0.0526531\pi$
$79$	972618.			1.97270			0.986350	+	0.164661i	$0.0526531\pi$
$80$			317934.i			0.620964i
$81$	−55888.7	+	244865.i	−0.105165	+	0.460756i
$82$	−56479.8	−	117282.i	−0.102436	−	0.212710i
$83$	5829.41	−	4648.80i	0.0101951	−	0.00813029i	−0.618379	−	0.785880i	$-0.712210\pi$
$83$	5829.41	−	4648.80i	0.0101951	−	0.00813029i	0.628574	+	0.777750i	$0.283639\pi$
$84$	−29104.5	+	40959.5i	−0.0491047	+	0.0691062i
$85$	−238920.	+	299596.i	−0.389041	+	0.487843i
$86$	−123833.	+	542550.i	−0.194689	+	0.852990i
$87$	109503.	+	87325.7i	0.166291	+	0.132612i
$88$	−339584.	+	163535.i	−0.498309	+	0.239973i
$89$	−157142.	+	125317.i	−0.222907	+	0.177762i	−0.728576	−	0.684965i	$-0.759817\pi$
$89$	−157142.	+	125317.i	−0.222907	+	0.177762i	0.505669	+	0.862728i	$0.331246\pi$
$90$	−186852.	+	388001.i	−0.256312	+	0.532238i
$91$	557330.	−	307527.i	0.739585	−	0.408093i
$92$	22889.5	−	11023.0i	0.0293949	−	0.0141558i
$93$	9539.34	+	4593.90i	0.0118596	+	0.00571127i
$94$	287495.	−	65618.9i	0.346136	−	0.0790034i
$95$	128778.	+	62016.3i	0.150200	+	0.0723327i
$96$	115472.	+	92085.6i	0.130515	+	0.104083i
$97$		−	1.41784e6i		−	1.55350i	−0.629810	−	0.776749i	$-0.716867\pi$
$97$		−	1.41784e6i		−	1.55350i	0.629810	−	0.776749i	$-0.283133\pi$
$98$	−838871.	+	93353.9i	−0.891286	+	0.0991868i
$99$	−406602.			−0.419048
$100$	−41826.3	+	52448.5i	−0.0418263	+	0.0524485i
$101$	667845.	−	1.38679e6i	0.648203	−	1.34601i	−0.274906	−	0.961471i	$-0.588647\pi$
$101$	667845.	−	1.38679e6i	0.648203	−	1.34601i	0.923110	−	0.384537i	$-0.125639\pi$
$102$	−70576.1	−	309214.i	−0.0665055	−	0.291380i
$103$	363891.	−	755627.i	0.333012	−	0.691506i	−0.665480	−	0.746416i	$-0.731773\pi$
$103$	363891.	−	755627.i	0.333012	−	0.691506i	0.998491	+	0.0549100i	$0.0174872\pi$
$104$	−442095.	−	918020.i	−0.393021	−	0.816117i
$105$	−390621.	+	112246.i	−0.337433	+	0.0969624i
$106$	−1.04689e6	−	504157.i	−0.878992	−	0.423300i
$107$	−507677.	−	636607.i	−0.414416	−	0.519661i	0.530185	−	0.847882i	$-0.322122\pi$
$107$	−507677.	−	636607.i	−0.414416	−	0.519661i	−0.944601	+	0.328221i	$0.893551\pi$
$108$	83982.7	+	174392.i	0.0666682	+	0.138438i
$109$	467646.	−	586410.i	0.361109	−	0.452816i	−0.567777	−	0.823182i	$-0.692196\pi$
$109$	467646.	−	586410.i	0.361109	−	0.452816i	0.928886	+	0.370366i	$0.120768\pi$
$110$	−486614.	−	111066.i	−0.365600	−	0.0834458i
$111$	−200136.	−	159603.i	−0.146338	−	0.116700i
$112$	59597.6	+	1.07439e6i	0.0424204	+	0.764727i
$113$	440738.	+	552668.i	0.305454	+	0.383027i	0.910739	−	0.412981i	$-0.135513\pi$
$113$	440738.	+	552668.i	0.305454	+	0.383027i	−0.605286	+	0.796008i	$0.706941\pi$
$114$	−106587.	+	51329.8i	−0.0719434	+	0.0346461i
$115$	200342.	+	45726.8i	0.131728	+	0.0300661i
$116$	−150091.			−0.0961568
$117$		−	1.09920e6i		−	0.686306i
$118$	−1.41666e6	−	323343.i	−0.862221	−	0.196796i
$119$	−751217.	+	1.05721e6i	−0.445784	+	0.627363i
$120$	144767.	+	634264.i	0.0837770	+	0.367051i
$121$	289345.	+	1.26770e6i	0.163328	+	0.715585i
$122$	1.01138e6	−	806551.i	0.556976	−	0.444173i
$123$	−132268.	−	165859.i	−0.0710789	−	0.0891302i
$124$	−11061.7	+	2524.77i	−0.00580173	+	0.00132421i
$125$	−2.07283e6	+	473110.i	−1.06129	+	0.242232i
$126$	−558691.	+	1.34619e6i	−0.279293	+	0.672968i
$127$	−675077.	+	2.95771e6i	−0.329566	+	1.44392i	0.490394	+	0.871501i	$0.336853\pi$
$127$	−675077.	+	2.95771e6i	−0.329566	+	1.44392i	−0.819960	+	0.572421i	$0.806004\pi$
$128$	1.28216e6			0.611382
$129$			906931.i			0.422479i
$130$	300254.	−	1.31550e6i	0.136665	−	0.598770i
$131$	−1.93641e6	−	4.02099e6i	−0.861356	−	1.78862i	−0.539998	−	0.841666i	$-0.681575\pi$
$131$	−1.93641e6	−	4.02099e6i	−0.861356	−	1.78862i	−0.321358	−	0.946958i	$-0.604139\pi$
$132$	−78624.5	+	62700.9i	−0.0341850	+	0.0272617i
$133$	446802.	+	185430.i	0.189915	+	0.0788181i
$134$	632193.	−	792745.i	0.262746	−	0.329473i
$135$	−348387.	+	1.52638e6i	−0.141599	+	0.620386i
$136$	1.62309e6	+	1.29437e6i	0.645245	+	0.514566i
$137$	3.83180e6	−	1.84530e6i	1.49019	−	0.717638i	0.501160	−	0.865355i	$-0.332907\pi$
$137$	3.83180e6	−	1.84530e6i	1.49019	−	0.717638i	0.989030	+	0.147717i	$0.0471924\pi$
$138$	−132977.	+	106046.i	−0.0505987	+	0.0403511i
$139$	−1.91235e6	+	3.97103e6i	−0.712070	+	1.47863i	0.158901	+	0.987294i	$0.449205\pi$
$139$	−1.91235e6	+	3.97103e6i	−0.712070	+	1.47863i	−0.870971	+	0.491334i	$0.836509\pi$
$140$	252277.	−	355035.i	0.0919375	−	0.129386i
$141$	432987.	−	208516.i	0.154461	−	0.0743843i
$142$	3.14375e6	+	1.51395e6i	1.09795	+	0.528746i
$143$	1.24204e6	−	283488.i	0.424745	−	0.0969452i
$144$	1.67411e6	+	806208.i	0.560656	+	0.269998i
$145$	−949165.	−	756934.i	−0.311342	−	0.248287i
$146$		−	3.04823e6i		−	0.979465i
$147$	−1.29898e6	+	452534.i	−0.408930	+	0.142462i
$148$	274318.			0.0846191
$149$	−2.11106e6	+	2.64719e6i	−0.638179	+	0.800251i	−0.990774	−	0.135525i	$-0.956728\pi$
$149$	−2.11106e6	+	2.64719e6i	−0.638179	+	0.800251i	0.352595	+	0.935776i	$0.385299\pi$
$150$	194864.	−	404639.i	0.0577374	−	0.119893i
$151$	−635617.	−	2.78482e6i	−0.184614	−	0.808847i	−0.979396	−	0.201951i	$-0.935272\pi$
$151$	−635617.	−	2.78482e6i	−0.184614	−	0.808847i	0.794781	−	0.606896i	$-0.207585\pi$
$152$	335978.	−	697665.i	0.0956708	−	0.198663i
$153$	971704.	+	2.01776e6i	0.271306	+	0.563373i
$154$	−1.66522e6	−	284107.i	−0.455943	−	0.0777893i
$155$	−82686.4	−	39819.7i	−0.0222044	−	0.0106931i
$156$	−169504.	−	212551.i	−0.0446484	−	0.0559873i
$157$	2.29463e6	+	4.76484e6i	0.592943	+	1.23126i	0.954305	+	0.298834i	$0.0965976\pi$
$157$	2.29463e6	+	4.76484e6i	0.592943	+	1.23126i	−0.361362	+	0.932426i	$0.617688\pi$
$158$	4.35062e6	−	5.45551e6i	1.10301	−	1.38313i
$159$	−1.84617e6	−	421377.i	−0.459284	−	0.104828i
$160$	−1.00090e6	−	798193.i	−0.244361	−	0.194871i
$161$	685584.	+	116969.i	0.164279	+	0.0280280i
$162$	1.12347e6	+	1.40879e6i	0.264252	+	0.331361i
$163$	2.68247e6	−	1.29181e6i	0.619401	−	0.298288i	−0.0977443	−	0.995212i	$-0.531163\pi$
$163$	2.68247e6	−	1.29181e6i	0.619401	−	0.298288i	0.717145	+	0.696924i	$0.245448\pi$
$164$	221636.	+	50587.1i	0.0502469	+	0.0114685i
$165$	−813428.			−0.181079
$166$		−	53492.3i		−	0.0116941i
$167$	−369549.	−	84347.1i	−0.0793455	−	0.0181101i	0.182664	−	0.983175i	$-0.441528\pi$
$167$	−369549.	−	84347.1i	−0.0793455	−	0.0181101i	−0.262009	+	0.965065i	$0.584385\pi$
$168$	608102.	+	2.11622e6i	0.128247	+	0.446306i
$169$	−307693.	−	1.34809e6i	−0.0637467	−	0.279292i
$170$	611750.	+	2.68025e6i	0.124517	+	0.545543i
$171$	653105.	−	520834.i	0.130615	−	0.104162i
$172$	−605962.	−	759852.i	−0.119086	−	0.149329i
$173$	4.34886e6	−	992599.i	0.839918	−	0.191706i	0.219141	−	0.975693i	$-0.429674\pi$
$173$	4.34886e6	−	992599.i	0.839918	−	0.191706i	0.620777	+	0.783987i	$0.286817\pi$
$174$	979636.	−	223596.i	0.185959	−	0.0424439i
$175$	−1.76505e6	+	507192.i	−0.329339	+	0.0946365i
$176$	−479218.	+	2.09959e6i	−0.0879013	+	0.385121i
$177$	−2.36810e6			−0.427051
$178$			1.44198e6i			0.255682i
$179$	70719.5	−	309842.i	0.0123305	−	0.0540234i	−0.968388	−	0.249447i	$-0.919751\pi$
$179$	70719.5	−	309842.i	0.0123305	−	0.0540234i	0.980719	+	0.195424i	$0.0626082\pi$
$180$	−326321.	−	677613.i	−0.0559536	−	0.116189i
$181$	−6.79835e6	+	5.42151e6i	−1.14648	+	0.914291i	−0.997221	−	0.0745068i	$-0.976262\pi$
$181$	−6.79835e6	+	5.42151e6i	−1.14648	+	0.914291i	−0.149264	+	0.988797i	$0.547690\pi$
$182$	768047.	−	4.50172e6i	0.127401	−	0.746730i
$183$	1.31443e6	−	1.64825e6i	0.214479	−	0.268949i
$184$	247728.	−	1.08537e6i	0.0397669	−	0.174230i
$185$	1.73477e6	+	1.38343e6i	0.273984	+	0.218495i
$186$	68438.1	−	32958.1i	0.0106355	−	0.00512180i
$187$	−2.02938e6	+	1.61837e6i	−0.310340	+	0.247488i
$188$	−223450.	+	463999.i	−0.0336285	+	0.0698302i
$189$	−891171.	+	5.22338e6i	−0.132001	+	0.773688i
$190$	923893.	−	444924.i	0.134698	−	0.0648671i
$191$	−5.34267e6	−	2.57289e6i	−0.766758	−	0.369251i	0.00926408	−	0.999957i	$-0.497051\pi$
$191$	−5.34267e6	−	2.57289e6i	−0.766758	−	0.369251i	−0.776022	+	0.630706i	$0.782765\pi$
$192$	3.32165e6	−	758145.i	0.469300	−	0.107115i
$193$	5.50542e6	+	2.65127e6i	0.765806	+	0.368793i	0.775654	−	0.631159i	$-0.217420\pi$
$193$	5.50542e6	+	2.65127e6i	0.765806	+	0.368793i	−0.00984781	+	0.999952i	$0.503135\pi$
$194$	−7.95278e6	−	6.34213e6i	−1.08922	−	0.868620i
$195$		−	2.19900e6i		−	0.296566i
$196$	785960.	−	1.24705e6i	0.104384	−	0.165621i
$197$	−4.72163e6			−0.617580			−0.308790	−	0.951130i	$-0.599924\pi$
$197$	−4.72163e6			−0.617580			−0.308790	+	0.951130i	$0.599924\pi$
$198$	−1.81877e6	+	2.28067e6i	−0.234306	+	0.293810i
$199$	−3.23876e6	+	6.72535e6i	−0.410979	+	0.853406i	0.588028	+	0.808841i	$0.299905\pi$
$199$	−3.23876e6	+	6.72535e6i	−0.410979	+	0.853406i	−0.999006	+	0.0445656i	$0.985810\pi$
$200$	654139.	+	2.86597e6i	0.0817674	+	0.358246i
$201$	716970.	−	1.48880e6i	0.0882903	−	0.183337i
$202$	−4.79132e6	−	9.94928e6i	−0.581301	−	1.20708i
$203$	−3.34938e6	−	2.37997e6i	−0.400384	−	0.284500i
$204$	499052.	+	240331.i	0.0587835	+	0.0283086i
$205$	1.14650e6	+	1.43766e6i	0.133079	+	0.166876i
$206$	−2.61066e6	−	5.42110e6i	−0.298641	−	0.620134i
$207$	748802.	−	938968.i	0.0844220	−	0.105862i
$208$	−5.67598e6	−	1.29550e6i	−0.630740	−	0.143962i
$209$	756957.	+	603653.i	0.0829149	+	0.0661224i
$210$	−1.11769e6	+	2.69312e6i	−0.120688	+	0.290802i
$211$	6.87508e6	+	8.62108e6i	0.731864	+	0.917728i	0.998944	−	0.0459461i	$-0.0146303\pi$
$211$	6.87508e6	+	8.62108e6i	0.731864	+	0.917728i	−0.267080	+	0.963674i	$0.586059\pi$
$212$	1.82832e6	−	880471.i	0.191886	−	0.0924075i
$213$	5.54394e6	+	1.26537e6i	0.573693	+	0.130942i
$214$	−5.84169e6			−0.596069
$215$		−	7.86122e6i		−	0.790997i
$216$	8.26929e6	+	1.88741e6i	0.820554	+	0.187286i
$217$	−286885.	−	119062.i	−0.0280756	−	0.0116518i
$218$	−1.19740e6	−	5.24615e6i	−0.115576	−	0.506374i
$219$	−1.10542e6	−	4.84314e6i	−0.105243	−	0.461100i
$220$	681513.	−	543488.i	0.0640038	−	0.0510413i
$221$	−4.37506e6	−	5.48616e6i	−0.405329	−	0.508266i
$222$	−1.79046e6	+	408660.i	−0.163646	+	0.0373511i
$223$	−5.75122e6	+	1.31268e6i	−0.518615	+	0.118370i	−0.473813	−	0.880625i	$-0.657123\pi$
$223$	−5.75122e6	+	1.31268e6i	−0.518615	+	0.118370i	−0.0448019	+	0.998996i	$0.514266\pi$
$224$	−3.53195e6	−	2.50969e6i	−0.314247	−	0.223294i
$225$	−705671.	+	3.09175e6i	−0.0619520	+	0.271429i
$226$	5.07144e6			0.439345
$227$		−	1.38496e7i		−	1.18402i	−0.805930	−	0.592011i	$-0.798334\pi$
$227$		−	1.38496e7i		−	1.18402i	0.805930	−	0.592011i	$-0.201666\pi$
$228$	45974.4	−	201427.i	0.00387892	−	0.0169947i
$229$	3.07719e6	+	6.38985e6i	0.256241	+	0.532089i	0.988914	−	0.148492i	$-0.0474418\pi$
$229$	3.07719e6	+	6.38985e6i	0.256241	+	0.532089i	−0.732673	+	0.680581i	$0.761727\pi$
$230$	1.15264e6	−	919198.i	0.0947348	−	0.0755485i
$231$	−2.74880e6	+	152480.i	−0.223001	+	0.0123702i
$232$	−4.10074e6	+	5.14217e6i	−0.328397	+	0.411796i
$233$	2.70128e6	−	1.18351e7i	0.213551	−	0.935630i	−0.748580	−	0.663044i	$-0.769264\pi$
$233$	2.70128e6	−	1.18351e7i	0.213551	−	0.935630i	0.962132	−	0.272585i	$-0.0878787\pi$
$234$	−6.16550e6	−	4.91682e6i	−0.481194	−	0.383740i
$235$	−3.75311e6	+	1.80740e6i	−0.289193	+	0.139268i
$236$	1.98406e6	−	1.58223e6i	0.150945	−	0.120374i
$237$	4.93404e6	−	1.02456e7i	0.370645	−	0.769651i
$238$	2.56969e6	+	8.94264e6i	0.190612	+	0.663338i
$239$	−1.28629e7	+	6.19442e6i	−0.942201	+	0.453740i	−0.840945	−	0.541120i	$-0.818000\pi$
$239$	−1.28629e7	+	6.19442e6i	−0.942201	+	0.453740i	−0.101256	+	0.994860i	$0.532286\pi$
$240$	3.34914e6	+	1.61286e6i	0.242270	+	0.116671i
$241$	1.19005e7	−	2.71620e6i	0.850184	−	0.194049i	0.224837	−	0.974396i	$-0.427815\pi$
$241$	1.19005e7	−	2.71620e6i	0.850184	−	0.194049i	0.625346	+	0.780347i	$0.284958\pi$
$242$	8.40494e6	+	4.04760e6i	0.593046	+	0.285596i
$243$	1.11009e7	+	8.85266e6i	0.773640	+	0.616957i
$244$			2.25918e6i			0.155518i
$245$	1.12595e7	−	3.92254e6i	0.765630	−	0.266728i
$246$	−1.52197e6			−0.102235
$247$	−1.63190e6	+	2.04634e6i	−0.108293	+	0.135796i
$248$	−215726.	+	447960.i	−0.0141432	+	0.0293687i
$249$	−19398.5	−	84990.5i	−0.00125652	−	0.00550519i
$250$	−6.61827e6	+	1.37430e7i	−0.423569	+	0.879550i
$251$	2.20918e6	+	4.58740e6i	0.139704	+	0.290099i	0.959068	−	0.283175i	$-0.0913876\pi$
$251$	2.20918e6	+	4.58740e6i	0.139704	+	0.290099i	−0.819364	+	0.573273i	$0.805673\pi$
$252$	−1.22975e6	−	2.22867e6i	−0.0768450	−	0.139266i
$253$	1.25411e6	+	603948.i	0.0774416	+	0.0372939i
$254$	1.35704e7	+	1.70167e7i	0.828115	+	1.03842i
$255$	1.94394e6	+	4.03664e6i	0.117237	+	0.243444i
$256$	−5.89272e6	+	7.38924e6i	−0.351234	+	0.440433i
$257$	2.91647e7	+	6.65665e6i	1.71814	+	0.392154i	0.964280	−	0.264885i	$-0.0853339\pi$
$257$	2.91647e7	+	6.65665e6i	1.71814	+	0.392154i	0.753857	+	0.657038i	$0.228191\pi$
$258$	5.08706e6	+	4.05680e6i	0.296216	+	0.236224i
$259$	6.12159e6	+	4.34981e6i	0.352342	+	0.250363i
$260$	1.46925e6	+	1.84238e6i	0.0835941	+	0.104824i
$261$	−6.39257e6	+	3.07850e6i	−0.359546	+	0.173148i
$262$	−3.12159e7	−	7.12482e6i	−1.73569	−	0.396159i
$263$	−2.40484e7			−1.32196			−0.660981	−	0.750403i	$-0.729859\pi$
$263$	−2.40484e7			−1.32196			−0.660981	+	0.750403i	$0.729859\pi$
$264$			4.40681e6i			0.239504i
$265$	1.60025e7	+	3.65247e6i	0.859906	+	0.196268i
$266$	3.03869e6	−	1.67671e6i	0.161451	−	0.0890866i
$267$	522923.	+	2.29108e6i	0.0274729	+	0.120367i
$268$	394040.	+	1.72640e6i	0.0204708	+	0.0896886i
$269$	−2.13138e6	+	1.69972e6i	−0.109497	+	0.0873212i	−0.676708	−	0.736252i	$-0.736594\pi$
$269$	−2.13138e6	+	1.69972e6i	−0.109497	+	0.0873212i	0.567211	+	0.823573i	$0.308023\pi$
$270$	7.00326e6	+	8.78181e6i	0.355802	+	0.446162i
$271$	−1.87875e6	+	428812.i	−0.0943976	+	0.0215456i	−0.269459	−	0.963012i	$-0.586845\pi$
$271$	−1.87875e6	+	428812.i	−0.0943976	+	0.0215456i	0.175061	+	0.984558i	$0.443988\pi$
$272$	1.15645e7	−	2.63952e6i	0.574671	−	0.131165i
$273$	−412209.	−	7.43102e6i	−0.0202595	−	0.365225i
$274$	6.78960e6	−	2.97472e7i	0.330060	−	1.44609i
$275$	−3.67553e6			−0.176735
$276$		−	297038.i		−	0.0141282i
$277$	−4.77974e6	+	2.09414e7i	−0.224887	+	0.985295i	0.728855	+	0.684669i	$0.240053\pi$
$277$	−4.77974e6	+	2.09414e7i	−0.224887	+	0.985295i	−0.953742	+	0.300627i	$0.902804\pi$
$278$	1.37198e7	+	2.84894e7i	0.638576	+	1.32602i
$279$	−419349.	+	334419.i	−0.0193091	+	0.0153985i
$280$	−5.27099e6	−	1.83433e7i	−0.240114	−	0.835608i
$281$	2.03429e7	−	2.55092e7i	0.916841	−	1.14968i	−0.0715018	−	0.997440i	$-0.522779\pi$
$281$	2.03429e7	−	2.55092e7i	0.916841	−	1.14968i	0.988343	−	0.152242i	$-0.0486494\pi$
$282$	767213.	−	3.36138e6i	0.0342112	−	0.149889i
$283$	−2.45840e6	−	1.96050e6i	−0.108466	−	0.0864985i	0.567755	−	0.823197i	$-0.307812\pi$
$283$	−2.45840e6	−	1.96050e6i	−0.108466	−	0.0864985i	−0.676221	+	0.736699i	$0.736383\pi$
$284$	−5.49031e6	+	2.64400e6i	−0.239686	+	0.115427i
$285$	1.30657e6	−	1.04195e6i	0.0564414	−	0.0450105i
$286$	3.96567e6	−	8.23481e6i	0.169519	−	0.352010i
$287$	4.14382e6	+	4.64334e6i	0.175289	+	0.196420i
$288$	−6.74102e6	+	3.24631e6i	−0.282194	+	0.135898i
$289$	−8.86618e6	−	4.26973e6i	−0.367318	−	0.176891i
$290$	−8.49143e6	+	1.93811e6i	−0.348166	+	0.0794667i
$291$	−1.49356e7	−	7.19261e6i	−0.606099	−	0.291882i
$292$	4.16207e6	+	3.31914e6i	0.167171	+	0.133314i
$293$			5.18936e6i			0.206306i	0.994666	+	0.103153i	$0.0328931\pi$
$293$			5.18936e6i			0.206306i	−0.994666	+	0.103153i	$0.967107\pi$
$294$	−3.27215e6	+	9.31032e6i	−0.128763	+	0.366372i
$295$	2.05265e7			0.799557
$296$	7.49484e6	−	9.39823e6i	0.288993	−	0.362386i
$297$	−4.60140e6	+	9.55491e6i	−0.175639	+	0.364718i
$298$	5.40534e6	+	2.36823e7i	0.204256	+	0.894902i
$299$	−1.63269e6	+	3.39033e6i	−0.0610789	+	0.126832i
$300$	340314.	+	706670.i	0.0126042	+	0.0261730i
$301$	−1.47361e6	−	2.65653e7i	−0.0540360	−	0.974125i
$302$	−1.84635e7	−	8.89156e6i	−0.670338	−	0.322818i
$303$	−1.12207e7	−	1.40703e7i	−0.403358	−	0.505795i
$304$	−1.91971e6	−	3.98632e6i	−0.0683306	−	0.141890i
$305$	−1.13934e7	+	1.42869e7i	−0.401565	+	0.503546i
$306$	1.56644e7	+	3.57529e6i	0.546700	+	0.124781i
$307$	−2.30291e7	−	1.83651e7i	−0.795907	−	0.634715i	0.138725	−	0.990331i	$-0.455700\pi$
$307$	−2.30291e7	−	1.83651e7i	−0.795907	−	0.634715i	−0.934632	+	0.355616i	$0.884271\pi$
$308$	2.20114e6	−	1.96435e6i	0.0753349	−	0.0672305i
$309$	−6.11384e6	−	7.66652e6i	−0.207223	−	0.259850i
$310$	−593218.	+	285679.i	−0.0199126	+	0.00958943i
$311$	−5.34760e7	−	1.22055e7i	−1.77778	−	0.405766i	−0.797489	−	0.603333i	$-0.793839\pi$
$311$	−5.34760e7	−	1.22055e7i	−1.77778	−	0.405766i	−0.980289	+	0.197566i	$0.936696\pi$
$312$	−1.19132e7			−0.392252
$313$		−	5.99062e6i		−	0.195361i	−0.995218	−	0.0976807i	$-0.968858\pi$
$313$		−	5.99062e6i		−	0.195361i	0.995218	−	0.0976807i	$-0.0311424\pi$
$314$	3.69906e7	+	8.44286e6i	1.19482	+	0.272710i
$315$	3.46271e6	−	2.02958e7i	0.110786	−	0.649345i
$316$	2.71170e6	+	1.18807e7i	0.0859371	+	0.376515i
$317$	−5.11183e6	−	2.23964e7i	−0.160472	−	0.703073i	−0.989580	−	0.143984i	$-0.954008\pi$
$317$	−5.11183e6	−	2.23964e7i	−0.160472	−	0.703073i	0.829108	−	0.559088i	$-0.188849\pi$
$318$	−1.06217e7	+	8.47050e6i	−0.330302	+	0.263407i
$319$	−5.12724e6	−	6.42936e6i	−0.157947	−	0.198060i
$320$	−2.87919e7	+	6.57156e6i	−0.878658	+	0.200548i
$321$	−9.28149e6	+	2.11844e6i	−0.280610	+	0.0640473i
$322$	3.72278e6	−	3.32229e6i	0.111506	−	0.0995108i
$323$	1.18664e6	−	5.19903e6i	0.0352138	−	0.154282i
$324$	−3.14689e6			−0.0925224
$325$		−	9.93633e6i		−	0.289451i
$326$	4.75308e6	−	2.08246e7i	0.137190	−	0.601069i
$327$	−3.80495e6	−	7.90105e6i	−0.108819	−	0.225965i
$328$	7.78863e6	−	6.21122e6i	0.220719	−	0.176017i
$329$	−1.23440e7	+	6.81125e6i	−0.346632	+	0.191267i
$330$	−3.63855e6	+	4.56260e6i	−0.101248	+	0.126961i
$331$	8.07994e6	−	3.54006e7i	0.222805	−	0.976171i	−0.732551	−	0.680712i	$-0.761670\pi$
$331$	8.07994e6	−	3.54006e7i	0.222805	−	0.976171i	0.955355	−	0.295459i	$-0.0954725\pi$
$332$	73038.7	+	58246.4i	0.00199590	+	0.00159168i
$333$	1.16836e7	−	5.62651e6i	0.316404	−	0.152372i
$334$	−2.12614e6	+	1.69554e6i	−0.0570628	+	0.0455061i
$335$	−6.21466e6	+	1.29049e7i	−0.165304	+	0.343257i
$336$	1.16200e7	+	4.82250e6i	0.306329	+	0.127132i
$337$	3.12883e7	−	1.50677e7i	0.817510	−	0.393692i	0.0220938	−	0.999756i	$-0.492967\pi$
$337$	3.12883e7	−	1.50677e7i	0.817510	−	0.393692i	0.795416	+	0.606064i	$0.207252\pi$
$338$	−8.93792e6	−	4.30427e6i	−0.231466	−	0.111468i
$339$	8.05770e6	−	1.83912e6i	0.206829	−	0.0472074i
$340$	−4.32575e6	−	2.08317e6i	−0.110059	−	0.0530016i
$341$	−486031.	−	387597.i	−0.0122575	−	0.00977500i
$342$		−	5.99307e6i		−	0.149820i
$343$	3.73135e7	−	1.53660e7i	0.924664	−	0.380783i
$344$	−4.25888e7			−1.04621
$345$	1.49802e6	−	1.87845e6i	0.0364804	−	0.0457449i
$346$	1.38853e7	−	2.88332e7i	0.335218	−	0.696088i
$347$	929726.	+	4.07340e6i	0.0222519	+	0.0974918i	0.984834	−	0.173497i	$-0.0555066\pi$
$347$	929726.	+	4.07340e6i	0.0222519	+	0.0974918i	−0.962583	+	0.270989i	$0.912649\pi$
$348$	−761403.	+	1.58107e6i	−0.0180666	+	0.0375157i
$349$	3.40977e7	+	7.08047e7i	0.802138	+	1.66566i	0.744786	+	0.667303i	$0.232552\pi$
$349$	3.40977e7	+	7.08047e7i	0.802138	+	1.66566i	0.0573524	+	0.998354i	$0.481734\pi$
$350$	−5.05036e6	+	1.21691e7i	−0.117793	+	0.283827i
$351$	−2.58305e7	−	1.24393e7i	−0.597325	−	0.287657i
$352$	−5.40672e6	−	6.77981e6i	−0.123967	−	0.155450i
$353$	3.32363e7	+	6.90159e7i	0.755594	+	1.56901i	0.820853	+	0.571140i	$0.193499\pi$
$353$	3.32363e7	+	6.90159e7i	0.755594	+	1.56901i	−0.0652584	+	0.997868i	$0.520787\pi$
$354$	−1.05927e7	+	1.32829e7i	−0.238780	+	0.299421i
$355$	−4.80545e7	−	1.09681e7i	−1.07411	−	0.245159i
$356$	−1.96889e6	−	1.57014e6i	−0.0436387	−	0.0348007i
$357$	7.32581e6	+	1.32765e7i	0.161009	+	0.291796i
$358$	−1.42160e6	−	1.78263e6i	−0.0309833	−	0.0388519i
$359$	−7.70741e7	+	3.71169e7i	−1.66581	+	0.802211i	−0.667467	+	0.744640i	$0.732621\pi$
$359$	−7.70741e7	+	3.71169e7i	−1.66581	+	0.802211i	−0.998341	+	0.0575712i	$0.981664\pi$
$360$	−3.21310e7	−	7.33368e6i	−0.688678	−	0.157186i
$361$	4.50568e7			0.957720
$362$			6.23836e7i			1.31506i
$363$	1.48219e7	+	3.38300e6i	0.309873	+	0.0707266i
$364$	5.31036e6	+	5.95050e6i	0.110108	+	0.123381i
$365$	9.58168e6	+	4.19801e7i	0.197044	+	0.863305i
$366$	−3.36558e6	−	1.47456e7i	−0.0686463	−	0.300759i
$367$	1.74745e7	−	1.39354e7i	0.353513	−	0.281917i	−0.430590	−	0.902548i	$-0.641695\pi$
$367$	1.74745e7	−	1.39354e7i	0.353513	−	0.281917i	0.784103	+	0.620630i	$0.213123\pi$
$368$	−3.96606e6	−	4.97329e6i	−0.0795823	−	0.0997930i
$369$	1.04774e7	−	2.39140e6i	0.208533	−	0.0475962i
$370$	1.55196e7	−	3.54225e6i	0.306390	−	0.0699316i
$371$	5.47616e7	+	9.34299e6i	1.07239	+	0.182963i
$372$	−29519.4	+	129333.i	−0.000573428	+	0.00251235i
$373$	1.04421e7			0.201215			0.100608	−	0.994926i	$-0.467921\pi$
$373$	1.04421e7			0.201215			0.100608	+	0.994926i	$0.467921\pi$
$374$			1.86221e7i			0.355971i
$375$	−5.53158e6	+	2.42354e7i	−0.104895	+	0.459575i
$376$	9.79174e6	+	2.03328e7i	0.184203	+	0.382501i
$377$	1.73809e7	−	1.38608e7i	0.324376	−	0.258682i
$378$	2.53121e7	+	2.83634e7i	0.468655	+	0.525149i
$379$	6.39612e7	−	8.02048e7i	1.17489	−	1.47327i	0.325477	−	0.945550i	$-0.394475\pi$
$379$	6.39612e7	−	8.02048e7i	1.17489	−	1.47327i	0.849417	−	0.527722i	$-0.176954\pi$
$380$	−398503.	+	1.74596e6i	−0.00726241	+	0.0318187i
$381$	2.77321e7	+	2.21156e7i	0.501427	+	0.399875i
$382$	−3.83299e7	+	1.84587e7i	−0.687619	+	0.331140i
$383$	3.77195e6	−	3.00803e6i	0.0671382	−	0.0535410i	−0.589346	−	0.807881i	$-0.700614\pi$
$383$	3.77195e6	−	3.00803e6i	0.0671382	−	0.0535410i	0.656484	+	0.754340i	$0.272043\pi$
$384$	6.50434e6	−	1.35064e7i	0.114871	−	0.238532i
$385$	2.38264e7	−	1.32168e6i	0.417520	−	0.0231604i
$386$	3.94976e7	−	1.90210e7i	0.686765	−	0.330729i
$387$	−4.13940e7	−	1.99343e7i	−0.714175	−	0.343928i
$388$	1.73192e7	−	3.95299e6i	0.296505	−	0.0676753i
$389$	4.11088e7	+	1.97970e7i	0.698371	+	0.336318i	0.749158	−	0.662392i	$-0.230458\pi$
$389$	4.11088e7	+	1.97970e7i	0.698371	+	0.336318i	−0.0507863	+	0.998710i	$0.516173\pi$
$390$	−1.23344e7	−	9.83635e6i	−0.207933	−	0.165821i
$391$		−	7.66685e6i		−	0.128259i
$392$	−2.12506e7	−	6.09989e7i	−0.352788	−	1.01266i
$393$	−5.21807e7			−0.859671
$394$	−2.11204e7	+	2.64841e7i	−0.345313	+	0.433008i
$395$	−4.27680e7	+	8.88086e7i	−0.693949	+	1.44100i
$396$	−1.13362e6	−	4.96673e6i	−0.0182551	−	0.0799807i
$397$	1.26224e7	−	2.62106e7i	0.201730	−	0.418896i	−0.775421	−	0.631445i	$-0.782462\pi$
$397$	1.26224e7	−	2.62106e7i	0.201730	−	0.418896i	0.977150	+	0.212549i	$0.0681765\pi$
$398$	2.32358e7	+	4.82497e7i	0.368561	+	0.765325i
$399$	4.21994e6	−	3.76597e6i	0.0664336	−	0.0592869i
$400$	1.51333e7	+	7.28783e6i	0.236458	+	0.113872i
$401$	−4.14467e7	−	5.19725e7i	−0.642772	−	0.806011i	0.348574	−	0.937281i	$-0.386666\pi$
$401$	−4.14467e7	−	5.19725e7i	−0.642772	−	0.806011i	−0.991347	+	0.131270i	$0.958094\pi$
$402$	−5.14376e6	−	1.06811e7i	−0.0791777	−	0.164414i
$403$	1.04782e6	−	1.31392e6i	0.0160092	−	0.0200749i
$404$	1.88020e7	+	4.29143e6i	0.285141	+	0.0650815i
$405$	−1.99008e7	−	1.58703e7i	−0.299574	−	0.238903i
$406$	−2.83316e7	+	8.14117e6i	−0.423344	+	0.121649i
$407$	9.37094e6	+	1.17508e7i	0.138995	+	0.174295i
$408$	2.18688e7	−	1.05315e7i	0.321991	−	0.155063i
$409$	−4.09724e7	−	9.35169e6i	−0.598855	−	0.136685i	−0.0876614	−	0.996150i	$-0.527939\pi$
$409$	−4.09724e7	−	9.35169e6i	−0.598855	−	0.136685i	−0.511194	+	0.859466i	$0.670796\pi$
$410$	1.31924e7			0.191413
$411$		−	4.97257e7i		−	0.716234i
$412$	1.02447e7	+	2.33829e6i	0.146490	+	0.0334353i
$413$	6.93648e7	−	3.84776e6i	0.984667	−	0.0546208i
$414$	−1.91729e6	−	8.40020e6i	−0.0270201	−	0.118383i
$415$	168145.	+	736693.i	0.00235256	+	0.0103072i
$416$	1.83283e7	−	1.46164e7i	0.254591	−	0.203030i
$417$	3.21299e7	+	4.02897e7i	0.443100	+	0.555630i
$418$	6.77190e6	−	1.54564e6i	0.0927218	−	0.0211631i
$419$	−6.53761e7	+	1.49217e7i	−0.888744	+	0.202850i	−0.642434	−	0.766341i	$-0.722075\pi$
$419$	−6.53761e7	+	1.49217e7i	−0.888744	+	0.202850i	−0.246310	+	0.969191i	$0.579218\pi$
$420$	−2.46018e6	−	4.45857e6i	−0.0332062	−	0.0601794i
$421$	1.61289e7	−	7.06653e7i	0.216151	−	0.947022i	−0.744140	−	0.668023i	$-0.767141\pi$
$421$	1.61289e7	−	7.06653e7i	0.216151	−	0.947022i	0.960292	−	0.278998i	$-0.0900023\pi$
$422$	7.91094e7			1.05267
$423$			2.43455e7i			0.321661i
$424$	1.97875e7	−	8.66948e7i	0.259594	−	1.13735i
$425$	8.78385e6	+	1.82399e7i	0.114424	+	0.237604i
$426$	3.18962e7	−	2.54364e7i	0.412582	−	0.329023i
$427$	−3.58235e7	+	5.04152e7i	−0.460134	+	0.647557i
$428$	6.36087e6	−	7.97628e6i	0.0811307	−	0.101735i
$429$	3.31453e6	−	1.45219e7i	0.0419807	−	0.183929i
$430$	−4.40944e7	−	3.51641e7i	−0.554597	−	0.442277i
$431$	5.11916e7	−	2.46526e7i	0.639392	−	0.307915i	−0.0859546	−	0.996299i	$-0.527394\pi$
$431$	5.11916e7	−	2.46526e7i	0.639392	−	0.307915i	0.725346	+	0.688384i	$0.241680\pi$
$432$	3.78909e7	−	3.02169e7i	0.469984	−	0.374800i
$433$	−6.59889e7	+	1.37027e8i	−0.812844	+	1.68789i	−0.0909813	+	0.995853i	$0.529000\pi$
$433$	−6.59889e7	+	1.37027e8i	−0.812844	+	1.68789i	−0.721863	+	0.692036i	$0.756714\pi$
$434$	−1.95110e6	+	1.07659e6i	−0.0238676	+	0.0131698i
$435$	−1.27887e7	+	6.15870e6i	−0.155367	+	0.0748206i
$436$	8.46694e6	+	4.07746e6i	0.102157	+	0.0491961i
$437$	−2.78804e6	+	636351.i	−0.0334083	+	0.00762523i
$438$	−3.21103e7	−	1.54635e7i	−0.382139	−	0.184029i
$439$	−8.36595e7	−	6.67163e7i	−0.988831	−	0.788566i	−0.0114242	−	0.999935i	$-0.503637\pi$
$439$	−8.36595e7	−	6.67163e7i	−0.988831	−	0.788566i	−0.977406	+	0.211369i	$0.932208\pi$
$440$		−	3.81979e7i		−	0.448417i
$441$	7.89696e6	−	6.92344e7i	0.0920755	−	0.807246i
$442$	−5.03425e7			−0.582999
$443$	−9.56358e7	+	1.19923e8i	−1.10004	+	1.37941i	−0.181825	+	0.983331i	$0.558200\pi$
$443$	−9.56358e7	+	1.19923e8i	−1.10004	+	1.37941i	−0.918217	+	0.396078i	$0.870371\pi$
$444$	1.39160e6	−	2.88968e6i	0.0158988	−	0.0330143i
$445$	−4.53267e6	−	1.98589e7i	−0.0514368	−	0.225359i
$446$	−1.83629e7	+	3.81309e7i	−0.206984	+	0.429806i
$447$	1.71764e7	+	3.56672e7i	0.192314	+	0.399343i
$448$	−9.60639e7	+	2.76042e7i	−1.06838	+	0.307002i
$449$	−2.64477e7	−	1.27365e7i	−0.292178	−	0.140706i	0.282053	−	0.959399i	$-0.408985\pi$
$449$	−2.64477e7	−	1.27365e7i	−0.292178	−	0.140706i	−0.574231	+	0.818693i	$0.694699\pi$
$450$	1.41854e7	+	1.77879e7i	0.155669	+	0.195203i
$451$	5.40434e6	+	1.12222e7i	0.0589132	+	0.122335i
$452$	−5.52217e6	+	6.92458e6i	−0.0597990	+	0.0749856i
$453$	−3.25600e7	−	7.43160e6i	−0.350259	−	0.0799444i
$454$	−7.76837e7	−	6.19507e7i	−0.830161	−	0.662031i
$455$	3.57300e6	+	6.44117e7i	0.0379314	+	0.683802i
$456$	−5.64486e6	−	7.07843e6i	−0.0595331	−	0.0746522i
$457$	7.65681e7	−	3.68733e7i	0.802231	−	0.386334i	0.0126035	−	0.999921i	$-0.495988\pi$
$457$	7.65681e7	−	3.68733e7i	0.802231	−	0.386334i	0.789628	+	0.613586i	$0.210274\pi$
$458$	4.96059e7	+	1.13222e7i	0.516342	+	0.117852i
$459$	5.84128e7			0.604046
$460$			2.57471e6i			0.0264518i
$461$	−1.61117e8	−	3.67738e7i	−1.64451	−	0.375349i	−0.702700	−	0.711486i	$-0.748022\pi$
$461$	−1.61117e8	−	3.67738e7i	−1.64451	−	0.375349i	−0.941813	+	0.336137i	$0.890880\pi$
$462$	−1.14404e7	+	1.61003e7i	−0.116015	+	0.163271i
$463$	3.26408e7	+	1.43009e8i	0.328865	+	1.44085i	0.821296	+	0.570502i	$0.193251\pi$
$463$	3.26408e7	+	1.43009e8i	0.328865	+	1.44085i	−0.492431	+	0.870352i	$0.663892\pi$
$464$	8.36238e6	+	3.66380e7i	0.0837097	+	0.366756i
$465$	−838928.	+	669023.i	−0.00834384	+	0.00665399i
$466$	−5.43011e7	−	6.80914e7i	−0.536600	−	0.672875i
$467$	1.66542e7	−	3.80122e6i	0.163521	−	0.0373226i	−0.139976	−	0.990155i	$-0.544703\pi$
$467$	1.66542e7	−	3.80122e6i	0.163521	−	0.0373226i	0.303498	+	0.952832i	$0.401846\pi$
$468$	1.34269e7	−	3.06461e6i	0.130990	−	0.0298977i
$469$	−1.85820e7	+	4.47741e7i	−0.180125	+	0.434018i
$470$	−6.65016e6	+	2.91363e7i	−0.0640529	+	0.280634i
$471$	6.18338e7			0.591784
$472$		−	1.11204e8i		−	1.05753i
$473$	1.18491e7	−	5.19145e7i	0.111970	−	0.490575i
$474$	−3.53983e7	−	7.35053e7i	−0.332390	−	0.690214i
$475$	5.90383e6	−	4.70814e6i	0.0550875	−	0.0439308i
$476$	−1.50084e7	−	6.22875e6i	−0.139160	−	0.0577537i
$477$	5.98112e7	−	7.50009e7i	0.551096	−	0.691053i
$478$	−2.27918e7	+	9.98573e7i	−0.208687	+	0.914316i
$479$	7.97048e7	+	6.35624e7i	0.725233	+	0.578354i	0.914990	−	0.403477i	$-0.132198\pi$
$479$	7.97048e7	+	6.35624e7i	0.725233	+	0.578354i	−0.189756	+	0.981831i	$0.560770\pi$
$480$	−1.34858e7	+	6.49440e6i	−0.121942	+	0.0587239i
$481$	−3.17667e7	+	2.53331e7i	−0.285455	+	0.227643i
$482$	3.79966e7	−	7.89007e7i	0.339315	−	0.704596i
$483$	4.71009e6	−	6.62862e6i	0.0418011	−	0.0588277i
$484$	−1.46786e7	+	7.06882e6i	−0.129463	+	0.0623463i
$485$	1.29461e8	+	6.23451e7i	1.13478	+	0.546484i
$486$	9.93109e7	−	2.26671e7i	0.865143	−	0.197463i
$487$	−1.41163e8	−	6.79805e7i	−1.22218	−	0.588569i	−0.292259	−	0.956339i	$-0.594407\pi$
$487$	−1.41163e8	−	6.79805e7i	−1.22218	−	0.588569i	−0.929917	+	0.367770i	$0.880121\pi$
$488$	7.74005e7	+	6.17248e7i	0.666015	+	0.531130i
$489$		−	3.48106e7i		−	0.297704i
$490$	2.83628e7	−	8.07013e7i	0.241080	−	0.685950i
$491$	−1.63730e8			−1.38320			−0.691598	−	0.722282i	$-0.743093\pi$
$491$	−1.63730e8			−1.38320			−0.691598	+	0.722282i	$0.743093\pi$
$492$	1.65724e6	−	2.07811e6i	0.0139152	−	0.0174491i
$493$	−1.96526e7	+	4.08090e7i	−0.164013	+	0.340577i
$494$	4.17844e6	+	1.83070e7i	0.0346604	+	0.151857i
$495$	1.78791e7	−	3.71264e7i	0.147411	−	0.306102i
$496$	1.23262e6	+	2.55956e6i	0.0101014	+	0.0209759i
$497$	−1.64446e8	−	2.80564e7i	−1.33953	−	0.228540i
$498$	−563492.	−	271363.i	−0.00456247	−	0.00219717i
$499$	7.93544e6	+	9.95072e6i	0.0638659	+	0.0800853i	0.812738	−	0.582629i	$-0.197976\pi$
$499$	7.93544e6	+	9.95072e6i	0.0638659	+	0.0800853i	−0.748872	+	0.662714i	$0.769404\pi$
$500$	−1.15583e7	−	2.40010e7i	−0.0924662	−	0.192008i
$501$	−2.76322e6	+	3.46497e6i	−0.0219737	+	0.0275541i
$502$	3.56131e7	+	8.12845e6i	0.281513	+	0.0642535i
$503$	−1.07674e8	−	8.58675e7i	−0.846075	−	0.674722i	0.101297	−	0.994856i	$-0.467701\pi$
$503$	−1.07674e8	−	8.58675e7i	−0.846075	−	0.674722i	−0.947372	+	0.320134i	$0.896272\pi$
$504$	−1.09954e8	−	1.87595e7i	−0.858856	−	0.146531i
$505$	9.72600e7	+	1.21960e8i	0.755197	+	0.946987i
$506$	8.99737e6	−	4.33291e6i	0.0694487	−	0.0334447i
$507$	−1.57618e7	−	3.59753e6i	−0.120943	−	0.0276046i
$508$	−3.80112e7			−0.289948
$509$		−	1.11391e8i		−	0.844692i	−0.906435	−	0.422346i	$-0.861207\pi$
$509$		−	1.11391e8i		−	0.844692i	0.906435	−	0.422346i	$-0.138793\pi$
$510$	3.13374e7	+	7.15255e6i	0.236239	+	0.0539201i
$511$	4.02484e7	+	1.40066e8i	0.301638	+	1.04971i
$512$	3.33479e7	+	1.46107e8i	0.248461	+	1.08858i
$513$	−4.84828e6	−	2.12417e7i	−0.0359117	−	0.157339i
$514$	1.67794e8	−	1.33812e8i	1.23563	−	0.985382i
$515$	5.29944e7	+	6.64529e7i	0.387979	+	0.486511i
$516$	−1.10784e7	+	2.52856e6i	−0.0806355	+	0.0184045i
$517$	−2.75093e7	+	6.27883e6i	−0.199071	+	0.0454367i
$518$	5.17810e7	−	1.48794e7i	0.372547	−	0.107053i
$519$	1.16054e7	−	5.08466e7i	0.0830154	−	0.363714i
$520$	1.03263e8			0.734405
$521$		−	2.05321e8i		−	1.45184i	−0.687777	−	0.725922i	$-0.741413\pi$
$521$		−	2.05321e8i		−	1.45184i	0.687777	−	0.725922i	$-0.258587\pi$
$522$	−1.13270e7	+	4.96270e7i	−0.0796352	+	0.348905i
$523$	−3.69782e6	−	7.67861e6i	−0.0258489	−	0.0536757i	0.887645	−	0.460529i	$-0.152340\pi$
$523$	−3.69782e6	−	7.67861e6i	−0.0258489	−	0.0536757i	−0.913493	+	0.406853i	$0.866626\pi$
$524$	4.37185e7	−	3.48643e7i	0.303858	−	0.242319i
$525$	−3.61120e6	+	2.11661e7i	−0.0249559	+	0.146273i
$526$	−1.07571e8	+	1.34890e8i	−0.739159	+	0.926876i
$527$	−761926.	+	3.33821e6i	−0.00520572	+	0.0228077i
$528$	1.96862e7	+	1.56992e7i	0.133740	+	0.106654i
$529$	1.29671e8	−	6.24465e7i	0.875946	−	0.421833i
$530$	9.20680e7	−	7.34218e7i	0.618417	−	0.493171i
$531$	5.20507e7	−	1.08084e8i	0.347650	−	0.721903i
$532$	−1.01937e6	+	5.97477e6i	−0.00677012	+	0.0396814i
$533$	−3.03378e7	+	1.46099e7i	−0.200356	+	0.0964865i
$534$	1.51900e7	+	7.31510e6i	0.0997546	+	0.0480393i
$535$	8.04515e7	−	1.83625e7i	0.525379	−	0.119914i
$536$	6.99131e7	+	3.36684e7i	0.454008	+	0.218639i
$537$	−2.90515e6	−	2.31678e6i	−0.0187605	−	0.0149610i
$538$			1.95581e7i			0.125597i
$539$	8.02684e7	−	8.93268e6i	0.512600	−	0.0570447i
$540$	−1.96164e7			−0.124577
$541$	−3.51102e7	+	4.40267e7i	−0.221738	+	0.278051i	−0.880241	−	0.474528i	$-0.842619\pi$
$541$	−3.51102e7	+	4.40267e7i	−0.221738	+	0.278051i	0.658502	+	0.752579i	$0.271190\pi$
$542$	−5.99859e6	+	1.24562e7i	−0.0376749	+	0.0782327i
$543$	2.26229e7	+	9.91174e7i	0.141302	+	0.619085i
$544$	−2.07238e7	+	4.30334e7i	−0.128728	+	0.267306i
$545$	3.29811e7	+	6.84859e7i	0.203739	+	0.423069i
$546$	−4.35252e7	−	3.09276e7i	−0.267401	−	0.190007i
$547$	2.51488e7	+	1.21110e7i	0.153658	+	0.0739980i	0.509133	−	0.860688i	$-0.329966\pi$
$547$	2.51488e7	+	1.21110e7i	0.153658	+	0.0739980i	−0.355474	+	0.934686i	$0.615681\pi$
$548$	3.32240e7	+	4.16615e7i	0.201888	+	0.253159i
$549$	4.63379e7	+	9.62217e7i	0.280040	+	0.581508i
$550$	−1.64410e7	+	2.06164e7i	−0.0988192	+	0.123915i
$551$	1.64713e7	+	3.75946e6i	0.0984628	+	0.0224735i
$552$	−1.01767e7	−	8.11561e6i	−0.0605045	−	0.0482507i
$553$	−1.27877e8	+	3.08126e8i	−0.756169	+	1.82202i
$554$	9.60821e7	+	1.20483e8i	0.565084	+	0.708593i
$555$	2.33736e7	−	1.12561e7i	0.136724	−	0.0658430i
$556$	−5.38387e7	−	1.22883e7i	−0.313235	−	0.0714939i
$557$	−1.09942e7			−0.0636206			−0.0318103	−	0.999494i	$-0.510127\pi$
$557$	−1.09942e7			−0.0636206			−0.0318103	+	0.999494i	$0.510127\pi$
$558$			3.84806e6i			0.0221482i
$559$	1.40344e8	+	3.20326e7i	0.803450	+	0.183382i
$560$	−1.00722e8	−	4.18011e7i	−0.573533	−	0.238026i
$561$	6.75316e6	+	2.95875e7i	0.0382489	+	0.167579i
$562$	−5.20876e7	−	2.28211e8i	−0.293444	−	1.28566i
$563$	−1.71768e8	+	1.36981e8i	−0.962539	+	0.767599i	−0.972632	−	0.232350i	$-0.925358\pi$
$563$	−1.71768e8	+	1.36981e8i	−0.962539	+	0.767599i	0.0100935	+	0.999949i	$0.496787\pi$
$564$	3.75425e6	+	4.70768e6i	0.0209260	+	0.0262404i
$565$	−6.98437e7	+	1.59414e7i	−0.387241	+	0.0883853i
$566$	−2.19933e7	+	5.01983e6i	−0.121295	+	0.0276847i
$567$	−7.02251e7	−	4.98998e7i	−0.385251	−	0.273747i
$568$	−5.94207e7	+	2.60339e8i	−0.324259	+	1.42067i
$569$	5.47177e7			0.297023			0.148512	−	0.988911i	$-0.452552\pi$
$569$	5.47177e7			0.297023			0.148512	+	0.988911i	$0.452552\pi$
$570$		−	1.19894e7i		−	0.0647403i
$571$	3.03109e7	−	1.32801e8i	0.162814	−	0.713334i	−0.825937	−	0.563762i	$-0.809353\pi$
$571$	3.03109e7	−	1.32801e8i	0.162814	−	0.713334i	0.988751	−	0.149572i	$-0.0477894\pi$
$572$	6.92573e6	+	1.43814e7i	0.0370065	+	0.0768447i
$573$	−5.42062e7	+	4.32280e7i	−0.288128	+	0.229774i
$574$	4.45807e7	−	2.47295e6i	0.235728	−	0.0130761i
$575$	6.76889e6	−	8.48792e6i	0.0356052	−	0.0446476i
$576$	−3.84066e7	+	1.68270e8i	−0.200973	+	0.880522i
$577$	8.92370e7	+	7.11641e7i	0.464534	+	0.370453i	0.827608	−	0.561307i	$-0.189701\pi$
$577$	8.92370e7	+	7.11641e7i	0.464534	+	0.370453i	−0.363074	+	0.931760i	$0.618273\pi$
$578$	−6.36086e7	+	3.06323e7i	−0.329407	+	0.158634i
$579$	5.58574e7	−	4.45448e7i	0.287770	−	0.229489i
$580$	6.59980e6	−	1.37046e7i	0.0338257	−	0.0702398i
$581$	706305.	+	2.45797e6i	0.00360134	+	0.0125328i
$582$	−1.07153e8	+	5.16019e7i	−0.543542	+	0.261756i
$583$	1.00173e8	+	4.82409e7i	0.505529	+	0.243450i
$584$	2.27430e8	−	5.19094e7i	1.14185	−	0.260620i
$585$	1.00366e8	+	4.83339e7i	0.501326	+	0.241426i
$586$	2.91076e7	+	2.32126e7i	0.144648	+	0.115353i
$587$		−	2.41046e8i		−	1.19175i	−0.803077	−	0.595875i	$-0.796805\pi$
$587$		−	2.41046e8i		−	1.19175i	0.803077	−	0.595875i	$-0.203195\pi$
$588$	−9.14941e6	−	1.46056e7i	−0.0450050	−	0.0718435i
$589$	1.27718e6			0.00625036
$590$	9.18173e7	−	1.15135e8i	0.447063	−	0.560599i
$591$	−2.39526e7	+	4.97381e7i	−0.116035	+	0.240950i
$592$	−1.52837e7	−	6.69624e7i	−0.0736655	−	0.322750i
$593$	−3.90322e7	+	8.10512e7i	−0.187180	+	0.388683i	−0.973349	−	0.229328i	$-0.926347\pi$
$593$	−3.90322e7	+	8.10512e7i	−0.187180	+	0.388683i	0.786169	+	0.618011i	$0.212061\pi$
$594$	3.30119e7	+	6.85498e7i	0.157511	+	0.327075i
$595$	−6.34997e7	−	1.15080e8i	−0.301454	−	0.546323i
$596$	−3.82217e7	−	1.84066e7i	−0.180539	−	0.0869431i
$597$	5.44154e7	+	6.82347e7i	0.255740	+	0.320688i
$598$	1.17134e7	+	2.43232e7i	0.0547749	+	0.113741i
$599$	1.15757e8	−	1.45155e8i	0.538602	−	0.675386i	−0.435840	−	0.900024i	$-0.643549\pi$
$599$	1.15757e8	−	1.45155e8i	0.538602	−	0.675386i	0.974442	+	0.224638i	$0.0721200\pi$
$600$	3.35088e7	+	7.64816e6i	0.155133	+	0.0354081i
$601$	−2.98490e8	−	2.38038e8i	−1.37501	−	1.09653i	−0.984394	−	0.175980i	$-0.943691\pi$
$601$	−2.98490e8	−	2.38038e8i	−1.37501	−	1.09653i	−0.390616	−	0.920554i	$-0.627738\pi$
$602$	−1.55599e8	−	1.10564e8i	−0.713209	−	0.506784i
$603$	5.21928e7	+	6.54477e7i	0.238045	+	0.298499i
$604$	3.22451e7	−	1.55284e7i	0.146336	−	0.0704719i
$605$	−1.28475e8	−	2.93237e7i	−0.580169	−	0.132420i
$606$	−1.29113e8			−0.580164
$607$		−	2.66720e8i		−	1.19258i	−0.802768	−	0.596292i	$-0.796640\pi$
$607$		−	2.66720e8i		−	1.19258i	0.802768	−	0.596292i	$-0.203360\pi$
$608$	1.73691e7	+	3.96438e6i	0.0772799	+	0.0176386i
$609$	−4.20620e7	+	2.32092e7i	−0.186225	+	0.102756i
$610$	2.91727e7	+	1.27814e8i	0.128525	+	0.563104i
$611$	−1.69740e7	−	7.43679e7i	−0.0744150	−	0.326033i
$612$	−2.19383e7	+	1.74952e7i	−0.0957080	+	0.0763246i
$613$	−1.19127e8	−	1.49380e8i	−0.517164	−	0.648503i	0.452840	−	0.891592i	$-0.350411\pi$
$613$	−1.19127e8	−	1.49380e8i	−0.517164	−	0.648503i	−0.970004	+	0.243089i	$0.921839\pi$
$614$	−2.06023e8	+	4.70235e7i	−0.890044	+	0.203147i
$615$	2.09605e7	−	4.78411e6i	0.0901109	−	0.0205672i
$616$	−7.16032e6	−	1.29081e8i	−0.0306331	−	0.552232i
$617$	6.20016e7	−	2.71647e8i	0.263966	−	1.15651i	−0.652941	−	0.757409i	$-0.726465\pi$
$617$	6.20016e7	−	2.71647e8i	0.263966	−	1.15651i	0.916907	−	0.399101i	$-0.130678\pi$
$618$	−7.03501e7			−0.298057
$619$		−	3.58695e8i		−	1.51235i	−0.654368	−	0.756177i	$-0.727065\pi$
$619$		−	3.58695e8i		−	1.51235i	0.654368	−	0.756177i	$-0.272935\pi$
$620$	255873.	−	1.12105e6i	0.00107362	−	0.00470382i
$621$	−1.35912e7	−	2.82224e7i	−0.0567523	−	0.117847i
$622$	−3.07666e8	+	2.45355e8i	−1.27852	+	1.01959i
$623$	−1.90398e7	−	6.62592e7i	−0.0787404	−	0.274020i
$624$	−4.24409e7	+	5.32192e7i	−0.174675	+	0.219035i
$625$	2.93316e7	−	1.28510e8i	0.120142	−	0.526377i
$626$	−3.36020e7	−	2.67967e7i	−0.136975	−	0.109234i
$627$	1.01989e7	−	4.91155e6i	0.0413764	−	0.0199258i
$628$	−5.18061e7	+	4.13140e7i	−0.209171	+	0.166808i
$629$	3.59185e7	−	7.45856e7i	0.144333	−	0.299711i
$630$	−9.83523e7	−	1.10208e8i	−0.393335	−	0.440750i
$631$	2.28388e8	−	1.09986e8i	0.909045	−	0.437773i	0.0798979	−	0.996803i	$-0.474541\pi$
$631$	2.28388e8	−	1.09986e8i	0.909045	−	0.437773i	0.829148	+	0.559030i	$0.188826\pi$
$632$	4.81127e8	+	2.31699e8i	1.90594	+	0.917851i
$633$	1.25692e8	−	2.86884e7i	0.495560	−	0.113108i
$634$	−1.48489e8	−	7.15087e7i	−0.582676	−	0.280602i
$635$	−2.40380e8	−	1.91697e8i	−0.938809	−	0.748676i
$636$		−	2.37262e7i		−	0.0922268i
$637$	2.41483e7	+	2.16995e8i	0.0934262	+	0.839522i
$638$	−5.89976e7			−0.227181
$639$	−1.79609e8	+	2.25223e8i	−0.688376	+	0.863197i
$640$	−5.63792e7	+	1.17073e8i	−0.215070	+	0.446597i
$641$	−4.62546e7	−	2.02654e8i	−0.175623	−	0.769453i	−0.983618	−	0.180264i	$-0.942305\pi$
$641$	−4.62546e7	−	2.02654e8i	−0.175623	−	0.769453i	0.807996	−	0.589189i	$-0.200552\pi$
$642$	−2.96346e7	+	6.15368e7i	−0.111994	+	0.232557i
$643$	7.73876e7	+	1.60697e8i	0.291097	+	0.604470i	0.994312	−	0.106508i	$-0.0339669\pi$
$643$	7.73876e7	+	1.60697e8i	0.291097	+	0.604470i	−0.703214	+	0.710978i	$0.748253\pi$
$644$	482638.	+	8.70067e6i	0.00180702	+	0.0325758i
$645$	−8.28108e7	−	3.98796e7i	−0.308608	−	0.148618i
$646$	−2.38539e7	−	2.99118e7i	−0.0884832	−	0.110954i
$647$	8.07059e7	+	1.67588e8i	0.297984	+	0.618770i	0.995175	−	0.0981155i	$-0.0312815\pi$
$647$	8.07059e7	+	1.67588e8i	0.297984	+	0.618770i	−0.697191	+	0.716885i	$0.745567\pi$
$648$	−8.59787e7	+	1.07814e8i	−0.315984	+	0.396232i
$649$	1.35555e8	+	3.09394e7i	0.495884	+	0.113182i
$650$	−5.57338e7	−	4.44462e7i	−0.202945	−	0.161843i
$651$	−2.70956e6	+	2.41807e6i	−0.00982100	+	0.00876449i
$652$	2.32586e7	+	2.91653e7i	0.0839151	+	0.105226i
$653$	−3.96677e8	+	1.91030e8i	−1.42462	+	0.686059i	−0.977988	−	0.208661i	$-0.933089\pi$
$653$	−3.96677e8	+	1.91030e8i	−1.42462	+	0.686059i	−0.446628	+	0.894720i	$0.647375\pi$
$654$	−6.13377e7	−	1.39999e7i	−0.219278	−	0.0500487i
$655$	4.52300e8			1.60954
$656$		−	5.69211e7i		−	0.201633i
$657$	2.45347e8	+	5.59988e7i	0.865136	+	0.197462i
$658$	−1.70111e7	+	9.97061e7i	−0.0597109	+	0.349981i
$659$	−5.93308e7	−	2.59945e8i	−0.207312	−	0.908292i	−0.966347	−	0.257242i	$-0.917186\pi$
$659$	−5.93308e7	−	2.59945e8i	−0.207312	−	0.908292i	0.759035	−	0.651049i	$-0.225671\pi$
$660$	−2.26787e6	−	9.93620e6i	−0.00788836	−	0.0345612i
$661$	−5.67991e7	+	4.52957e7i	−0.196669	+	0.156839i	−0.716873	−	0.697204i	$-0.754427\pi$
$661$	−5.67991e7	+	4.52957e7i	−0.196669	+	0.156839i	0.520204	+	0.854042i	$0.325856\pi$
$662$	−1.62423e8	−	2.03672e8i	−0.559851	−	0.702031i
$663$	−7.99861e7	+	1.82563e7i	−0.274457	+	0.0626429i
$664$	3.99109e6	−	910940.i	0.0136329	−	0.00311161i
$665$	−3.65782e7	+	3.26432e7i	−0.124382	+	0.111001i
$666$	2.07022e7	−	9.07022e7i	0.0700799	−	0.307040i
$667$	2.42897e7			0.0818550
$668$		−	4.74928e6i		−	0.0159330i
$669$	−1.53478e7	+	6.72429e7i	−0.0512586	+	0.224579i
$670$	4.45858e7	+	9.25834e7i	0.148242	+	0.307829i
$671$	−9.67754e7	+	7.71758e7i	−0.320330	+	0.255455i
$672$	−4.43547e7	+	2.44743e7i	−0.146161	+	0.0806497i
$673$	2.33107e8	−	2.92308e8i	0.764735	−	0.958947i	−0.235180	−	0.971952i	$-0.575568\pi$
$673$	2.33107e8	−	2.92308e8i	0.764735	−	0.958947i	0.999915	+	0.0130044i	$0.00413953\pi$
$674$	5.54400e7	−	2.42899e8i	0.181069	−	0.793315i
$675$	6.46684e7	+	5.15713e7i	0.210272	+	0.167686i
$676$	1.56094e7	−	7.51707e6i	0.0505295	−	0.0243337i
$677$	1.32665e8	−	1.05797e8i	0.427553	−	0.340962i	−0.385953	−	0.922518i	$-0.626127\pi$
$677$	1.32665e8	−	1.05797e8i	0.427553	−	0.340962i	0.813506	+	0.581556i	$0.197556\pi$
$678$	2.57271e7	−	5.34230e7i	0.0825472	−	0.171411i
$679$	4.49171e8	+	1.86414e8i	1.43484	+	0.595481i
$680$	−1.89557e8	+	9.12861e7i	−0.602857	+	0.290321i
$681$	−1.45893e8	−	7.02583e7i	−0.461947	−	0.222462i
$682$	−4.34813e6	+	992433.i	−0.0137072	+	0.00312859i
$683$	3.40370e8	+	1.63913e8i	1.06829	+	0.514461i	0.883555	−	0.468328i	$-0.155143\pi$
$683$	3.40370e8	+	1.63913e8i	1.06829	+	0.514461i	0.184734	+	0.982789i	$0.440858\pi$
$684$	8.18298e6	+	6.52571e6i	0.0255707	+	0.0203920i
$685$			4.31019e8i			1.34099i
$686$	8.07182e7	−	2.78029e8i	0.250034	−	0.861227i
$687$	8.29217e7			0.255740
$688$	−1.51722e8	+	1.90254e8i	−0.465891	+	0.584209i
$689$	−1.30413e8	+	2.70805e8i	−0.398716	+	0.827942i
$690$	−3.83564e6	−	1.68050e7i	−0.0116759	−	0.0511555i
$691$	−9.87176e7	+	2.04989e8i	−0.299199	+	0.621293i	−0.995320	−	0.0966309i	$-0.969193\pi$
$691$	−9.87176e7	+	2.04989e8i	−0.299199	+	0.621293i	0.696121	+	0.717924i	$0.254908\pi$
$692$	2.42496e7	+	5.03548e7i	0.0731790	+	0.151958i
$693$	5.34590e7	−	1.28812e8i	0.160628	−	0.387040i
$694$	2.70068e7	+	1.30058e7i	0.0807970	+	0.0389098i
$695$	−2.78501e8	−	3.49229e8i	−0.829606	−	1.04029i
$696$	3.33652e7	+	6.92835e7i	0.0989614	+	0.205496i
$697$	4.27750e7	−	5.36381e7i	0.126326	−	0.158407i
$698$	5.49673e8	+	1.25459e8i	1.61636	+	0.368924i
$699$	−1.10968e8	−	8.84943e7i	−0.324914	−	0.259110i
$700$	−1.11165e7	−	2.01464e7i	−0.0324096	−	0.0587358i
$701$	−1.36364e8	−	1.70995e8i	−0.395864	−	0.496398i	0.543457	−	0.839437i	$-0.317115\pi$
$701$	−1.36364e8	−	1.70995e8i	−0.395864	−	0.496398i	−0.939321	+	0.343039i	$0.888544\pi$
$702$	−1.85316e8	+	8.92433e7i	−0.535674	+	0.257967i
$703$	−3.01042e7	−	6.87108e6i	−0.0866484	−	0.0197769i
$704$	−2.00043e8			−0.573331
$705$			4.87044e7i			0.138996i
$706$	5.35787e8	+	1.22290e8i	1.52257	+	0.347517i
$707$	3.51531e8	+	3.93906e8i	0.994729	+	1.11464i
$708$	−6.60236e6	−	2.89268e7i	−0.0186037	−	0.0815081i
$709$	−5.49867e7	−	2.40913e8i	−0.154283	−	0.675960i	−0.991611	−	0.129258i	$-0.958740\pi$
$709$	−5.49867e7	−	2.40913e8i	−0.154283	−	0.675960i	0.837328	−	0.546702i	$-0.184117\pi$
$710$	−2.76474e8	+	2.20481e8i	−0.772467	+	0.616021i
$711$	3.59180e8	+	4.50398e8i	0.999317	+	1.25310i
$712$	−1.07587e8	+	2.45561e7i	−0.298072	+	0.0680329i
$713$	1.79016e6	−	408592.i	0.00493881	−	0.00112725i
$714$	1.07238e8	+	1.82962e7i	0.294616	+	0.0502650i
$715$	−2.87301e7	+	1.25875e8i	−0.0785994	+	0.344367i
$716$	3.98196e6			0.0108482
$717$			1.66922e8i			0.452853i
$718$	−1.36568e8	+	5.98344e8i	−0.368957	+	1.61651i
$719$	1.63892e8	+	3.40326e8i	0.440932	+	0.915605i	0.996457	+	0.0841048i	$0.0268031\pi$
$719$	1.63892e8	+	3.40326e8i	0.440932	+	0.915605i	−0.555525	+	0.831500i	$0.687483\pi$
$720$	−1.47228e8	+	1.17410e8i	−0.394451	+	0.314564i
$721$	1.91540e8	+	2.14629e8i	0.511038	+	0.572641i
$722$	2.01544e8	−	2.52728e8i	0.535498	−	0.671493i
$723$	3.17577e7	−	1.39140e8i	0.0840300	−	0.368159i
$724$	−8.51790e7	−	6.79280e7i	−0.224449	−	0.178992i
$725$	−5.77865e7	+	2.78285e7i	−0.151640	+	0.0730258i
$726$	8.52756e7	−	6.80050e7i	0.222851	−	0.177718i
$727$	1.78040e7	−	3.69703e7i	0.0463355	−	0.0962166i	−0.876516	−	0.481373i	$-0.840138\pi$
$727$	1.78040e7	−	3.69703e7i	0.0463355	−	0.0962166i	0.922851	+	0.385156i	$0.125853\pi$
$728$	3.48955e8	−	1.93570e7i	0.904431	−	0.0501700i
$729$	−1.53957e7	+	7.41420e6i	−0.0397391	+	0.0191373i
$730$	2.78330e8	+	1.34037e8i	0.715470	+	0.344552i
$731$	−2.85943e8	+	6.52647e7i	−0.732028	+	0.167081i
$732$	2.37984e7	+	1.14607e7i	0.0606757	+	0.0292199i
$733$	−3.83006e8	−	3.05437e8i	−0.972509	−	0.775550i	0.00197718	−	0.999998i	$-0.499371\pi$
$733$	−3.83006e8	−	3.05437e8i	−0.972509	−	0.775550i	−0.974486	+	0.224448i	$0.927942\pi$
$734$		−	1.60351e8i		−	0.405492i
$735$	1.57983e7	−	1.38507e8i	0.0397876	−	0.348826i
$736$	2.56137e7			0.0642450
$737$	−6.04922e7	+	7.58548e7i	−0.151111	+	0.189487i
$738$	3.34529e7	−	6.94656e7i	0.0832271	−	0.172823i
$739$	−4.60291e7	−	2.01667e8i	−0.114051	−	0.499690i	−0.999396	−	0.0347551i	$-0.988935\pi$
$739$	−4.60291e7	−	2.01667e8i	−0.114051	−	0.499690i	0.885345	−	0.464935i	$-0.153922\pi$
$740$	−1.20623e7	+	2.50476e7i	−0.0297670	+	0.0618118i
$741$	1.32777e7	+	2.75715e7i	0.0326339	+	0.0677651i
$742$	2.97360e8	−	2.65371e8i	0.727899	−	0.649594i
$743$	−2.40739e8	−	1.15934e8i	−0.586921	−	0.282646i	0.116762	−	0.993160i	$-0.462748\pi$
$743$	−2.40739e8	−	1.15934e8i	−0.586921	−	0.282646i	−0.703684	+	0.710513i	$0.748463\pi$
$744$	3.62448e6	+	4.54495e6i	0.00880090	+	0.0110360i
$745$	−1.48884e8	−	3.09161e8i	−0.360064	−	0.747681i
$746$	4.67086e7	−	5.85707e7i	0.112507	−	0.141079i
$747$	4.30550e6	+	982703.i	0.0103291	+	0.00235755i
$748$	−2.54268e7	−	2.02772e7i	−0.0607556	−	0.0484510i
$749$	2.68426e8	−	7.71329e7i	0.638820	−	0.183567i
$750$	1.11195e8	+	1.39435e8i	0.263575	+	0.330512i
$751$	−2.27981e8	+	1.09790e8i	−0.538243	+	0.259204i	−0.683197	−	0.730234i	$-0.739411\pi$
$751$	−2.27981e8	+	1.09790e8i	−0.538243	+	0.259204i	0.144954	+	0.989438i	$0.453697\pi$
$752$	1.25714e8	+	2.86935e7i	0.295618	+	0.0674729i
$753$	5.95311e7			0.139431
$754$		−	1.59492e8i		−	0.372071i
$755$	2.82228e8	+	6.44167e7i	0.655782	+	0.149678i
$756$	−6.62893e7	+	3.67716e6i	−0.153419	+	0.00851033i
$757$	−1.27324e8	−	5.57841e8i	−0.293509	−	1.28595i	−0.879605	−	0.475705i	$-0.842193\pi$
$757$	−1.27324e8	−	5.57841e8i	−0.293509	−	1.28595i	0.586096	−	0.810242i	$-0.300664\pi$
$758$	−1.63771e8	−	7.17529e8i	−0.376037	−	1.64752i
$759$	1.27241e7	−	1.01471e7i	0.0291005	−	0.0232069i
$760$	4.89293e7	+	6.13555e7i	0.111462	+	0.139770i
$761$	−1.24016e8	+	2.83058e7i	−0.281399	+	0.0642276i	−0.360891	−	0.932608i	$-0.617527\pi$
$761$	−1.24016e8	+	2.83058e7i	−0.281399	+	0.0642276i	0.0794918	+	0.996836i	$0.474670\pi$
$762$	2.48097e8	−	5.66265e7i	0.560734	−	0.127984i
$763$	1.24290e8	+	2.25250e8i	0.279810	+	0.507098i
$764$	1.65329e7	−	7.24352e7i	0.0370739	−	0.162431i
$765$	−2.26968e8			−0.506967
$766$		−	3.46125e7i		−	0.0770099i
$767$	−8.36408e7	+	3.66454e8i	−0.185367	+	0.812145i
$768$	4.79454e7	+	9.95596e7i	0.105843	+	0.219786i
$769$	−5.00716e8	+	3.99308e8i	−1.10106	+	0.878069i	−0.993237	−	0.116101i	$-0.962960\pi$
$769$	−5.00716e8	+	3.99308e8i	−1.10106	+	0.878069i	−0.107826	+	0.994170i	$0.534389\pi$
$770$	9.91647e7	−	1.39557e8i	0.217213	−	0.305688i
$771$	2.18073e8	−	2.73454e8i	0.475815	−	0.596653i
$772$	−1.70365e7	+	7.46418e7i	−0.0370278	+	0.162230i
$773$	2.46501e8	+	1.96578e8i	0.533678	+	0.425594i	0.852891	−	0.522089i	$-0.174847\pi$
$773$	2.46501e8	+	1.96578e8i	0.533678	+	0.425594i	−0.319213	+	0.947683i	$0.603419\pi$
$774$	−2.96973e8	+	1.43015e8i	−0.640463	+	0.308431i
$775$	−3.79076e6	+	3.02303e6i	−0.00814368	+	0.00649437i
$776$	3.37759e8	−	7.01364e8i	0.722806	−	1.50092i
$777$	7.68757e7	−	4.24190e7i	0.163880	−	0.0904268i
$778$	2.94927e8	−	1.42030e8i	0.626291	−	0.301606i
$779$	−2.30557e7	−	1.11031e7i	−0.0487715	−	0.0234871i
$780$	2.68612e7	−	6.13090e6i	0.0566033	−	0.0129193i
$781$	−3.00814e8	−	1.44864e8i	−0.631458	−	0.304094i
$782$	−4.30041e7	−	3.42947e7i	−0.0899270	−	0.0717144i
$783$			1.85060e8i			0.385503i
$784$	−3.48202e8	−	1.22377e8i	−0.722575	−	0.253952i
$785$	−5.35972e8			−1.10798
$786$	−2.33410e8	+	2.92687e8i	−0.480675	+	0.602748i
$787$	6.86531e7	−	1.42560e8i	0.140843	−	0.292464i	−0.818601	−	0.574363i	$-0.805250\pi$
$787$	6.86531e7	−	1.42560e8i	0.140843	−	0.292464i	0.959444	+	0.281899i	$0.0909643\pi$
$788$	−1.31641e7	−	5.76757e7i	−0.0269038	−	0.117873i
$789$	−1.21996e8	+	2.53328e8i	−0.248379	+	0.515765i
$790$	3.06831e8	+	6.37140e8i	0.622325	+	1.29227i
$791$	−2.33033e8	+	6.69627e7i	−0.470856	+	0.135302i
$792$	−2.01135e8	−	9.68614e7i	−0.404866	−	0.194973i
$793$	−2.08635e8	−	2.61620e8i	−0.418376	−	0.524627i
$794$	−9.05568e7	−	1.88043e8i	−0.180909	−	0.375661i
$795$	1.19655e8	−	1.50043e8i	0.238139	−	0.298617i
$796$	−9.11815e7	−	2.08116e7i	−0.180787	−	0.0412635i
$797$	−3.95432e8	−	3.15347e8i	−0.781082	−	0.622892i	0.149589	−	0.988748i	$-0.452205\pi$
$797$	−3.95432e8	−	3.15347e8i	−0.781082	−	0.622892i	−0.930672	+	0.365856i	$0.880776\pi$
$798$	−2.24746e6	−	4.05157e7i	−0.00442265	−	0.0797286i
$799$	9.69010e7	+	1.21510e8i	0.189971	+	0.238216i
$800$	−6.09364e7	+	2.93454e7i	−0.119016	+	0.0573152i
$801$	−1.16063e8	−	2.64906e7i	−0.225837	−	0.0515459i
$802$	−4.76915e8			−0.924523
$803$			2.91673e8i			0.563313i
$804$	2.01850e7	+	4.60709e6i	0.0388383	+	0.00886460i
$805$	−4.08268e7	+	5.74565e7i	−0.0782632	+	0.110142i
$806$	−2.68291e6	−	1.17546e7i	−0.00512391	−	0.0224493i
$807$	7.09259e6	+	3.10747e7i	0.0134954	+	0.0591270i
$808$	6.60728e8	−	5.26913e8i	1.25253	−	0.998861i
$809$	−4.23248e7	−	5.30737e7i	−0.0799374	−	0.100238i	0.740255	−	0.672327i	$-0.234705\pi$
$809$	−4.23248e7	−	5.30737e7i	−0.0799374	−	0.100238i	−0.820192	+	0.572088i	$0.806133\pi$
$810$	−1.78036e8	+	4.06356e7i	−0.335007	+	0.0764631i
$811$	1.65623e8	−	3.78024e7i	0.310498	−	0.0708691i	−0.0644327	−	0.997922i	$-0.520524\pi$
$811$	1.65623e8	−	3.78024e7i	0.310498	−	0.0708691i	0.374930	+	0.927053i	$0.377667\pi$
$812$	1.97336e7	−	4.75489e7i	0.0368585	−	0.0888121i
$813$	−5.01365e6	+	2.19662e7i	−0.00933002	+	0.0408775i
$814$	1.07829e8			0.199922
$815$			3.01737e8i			0.557385i
$816$	3.08611e7	−	1.35211e8i	0.0567990	−	0.248853i
$817$	4.74668e7	+	9.85658e7i	0.0870409	+	0.180742i
$818$	−2.35728e8	+	1.87987e8i	−0.430677	+	0.343454i
$819$	3.48226e8	+	1.44520e8i	0.633884	+	0.263072i
$820$	−1.43648e7	+	1.80129e7i	−0.0260531	+	0.0326696i
$821$	−1.91572e7	+	8.39331e7i	−0.0346180	+	0.151672i	−0.989283	−	0.146011i	$-0.953357\pi$
$821$	−1.91572e7	+	8.39331e7i	−0.0346180	+	0.151672i	0.954665	+	0.297682i	$0.0962137\pi$
$822$	−2.78916e8	−	2.22428e8i	−0.502178	−	0.400474i
$823$	−5.44008e8	+	2.61981e8i	−0.975901	+	0.469969i	−0.852694	−	0.522412i	$-0.825032\pi$
$823$	−5.44008e8	+	2.61981e8i	−0.975901	+	0.469969i	−0.123208	+	0.992381i	$0.539318\pi$
$824$	3.60014e8	−	2.87101e8i	0.643483	−	0.513161i
$825$	−1.86458e7	+	3.87184e7i	−0.0332062	+	0.0689533i
$826$	2.88694e8	−	4.06286e8i	0.512268	−	0.720927i
$827$	−4.37338e7	+	2.10611e7i	−0.0773216	+	0.0372361i	−0.472145	−	0.881521i	$-0.656520\pi$
$827$	−4.37338e7	+	2.10611e7i	−0.0773216	+	0.0372361i	0.394823	+	0.918757i	$0.370806\pi$
$828$	1.35574e7	+	6.52889e6i	0.0238828	+	0.0115013i
$829$	−7.24391e8	+	1.65338e8i	−1.27148	+	0.290207i	−0.804443	−	0.594030i	$-0.797536\pi$
$829$	−7.24391e8	+	1.65338e8i	−1.27148	+	0.290207i	−0.467038	+	0.884237i	$0.654679\pi$
$830$	4.88432e6	+	2.35216e6i	0.00854219	+	0.00411370i
$831$	1.96351e8	+	1.56585e8i	0.342161	+	0.272864i
$832$		−	5.40791e8i		−	0.938986i
$833$	−2.36155e8	−	3.76985e8i	−0.408566	−	0.652212i
$834$	3.69709e8			0.637327
$835$	2.39515e7	−	3.00342e7i	0.0411408	−	0.0515889i
$836$	−5.26333e6	+	1.09294e7i	−0.00900827	+	0.0187059i
$837$	3.11301e6	+	1.36390e7i	0.00530889	+	0.0232598i
$838$	−2.08737e8	+	4.33447e8i	−0.354705	+	0.736553i
$839$	1.10581e8	+	2.29623e8i	0.187238	+	0.388803i	0.973365	−	0.229262i	$-0.0736312\pi$
$839$	1.10581e8	+	2.29623e8i	0.187238	+	0.388803i	−0.786127	+	0.618065i	$0.787917\pi$
$840$	−2.19969e8	−	3.75293e7i	−0.371128	−	0.0633189i
$841$	4.06629e8	+	1.95822e8i	0.683612	+	0.329210i
$842$	−3.24222e8	−	4.06562e8i	−0.543133	−	0.681068i
$843$	−1.65518e8	−	3.43701e8i	−0.276288	−	0.573717i
$844$	−8.61403e7	+	1.08017e8i	−0.143278	+	0.179665i
$845$	1.36623e8	+	3.11832e7i	0.226440	+	0.0516833i
$846$	1.36556e8	+	1.08900e8i	0.225528	+	0.179853i
$847$	−4.39651e8	−	7.50098e7i	−0.723533	−	0.123443i
$848$	−3.16793e8	−	3.97246e8i	−0.519503	−	0.651436i
$849$	−3.31234e7	+	1.59514e7i	−0.0541268	+	0.0260661i
$850$	1.41600e8	+	3.23193e7i	0.230572	+	0.0526266i
$851$	−4.43938e7			−0.0720333
$852$			7.12483e7i			0.115201i
$853$	7.41278e8	+	1.69192e8i	1.19436	+	0.272604i	0.773069	−	0.634322i	$-0.218721\pi$
$853$	7.41278e8	+	1.69192e8i	1.19436	+	0.272604i	0.421289	+	0.906927i	$0.361578\pi$
$854$	1.22542e8	+	4.26450e8i	0.196748	+	0.684691i
$855$	1.88384e7	+	8.25363e7i	0.0301401	+	0.132053i
$856$	−9.94803e7	−	4.35852e8i	−0.158605	−	0.694892i
$857$	−8.81424e8	+	7.02912e8i	−1.40037	+	1.11676i	−0.422780	+	0.906232i	$0.638946\pi$
$857$	−8.81424e8	+	7.02912e8i	−1.40037	+	1.11676i	−0.977589	+	0.210525i	$0.932483\pi$
$858$	−6.66285e7	−	8.35495e7i	−0.105487	−	0.132276i
$859$	5.09766e7	−	1.16351e7i	0.0804251	−	0.0183565i	−0.182119	−	0.983276i	$-0.558296\pi$
$859$	5.09766e7	−	1.16351e7i	0.0804251	−	0.0183565i	0.262544	+	0.964920i	$0.415438\pi$
$860$	9.60265e7	−	2.19174e7i	0.150972	−	0.0344583i
$861$	6.99347e7	−	2.00959e7i	0.109568	−	0.0314847i
$862$	9.07068e7	−	3.97412e8i	0.141618	−	0.620468i
$863$	1.17901e9			1.83436			0.917182	−	0.398469i	$-0.130459\pi$
$863$	1.17901e9			1.83436			0.917182	+	0.398469i	$0.130459\pi$
$864$			1.95148e8i			0.302567i
$865$	−1.00595e8	+	4.40736e8i	−0.155428	+	0.680973i
$866$	4.73425e8	+	9.83076e8i	0.728949	+	1.51368i
$867$	−8.99553e7	+	7.17369e7i	−0.138029	+	0.110074i
$868$	654521.	−	3.83631e6i	0.00100084	−	0.00586617i
$869$	−4.16295e8	+	5.22017e8i	−0.634368	+	0.795473i
$870$	−2.26603e7	+	9.92814e7i	−0.0344119	+	0.150768i
$871$	−2.05064e8	−	1.63533e8i	−0.310337	−	0.247486i
$872$	3.71027e8	−	1.78677e8i	0.559572	−	0.269476i
$873$	6.56568e8	−	5.23595e8i	0.986817	−	0.786961i
$874$	−8.90183e6	+	1.84848e7i	−0.0133335	+	0.0276874i
$875$	1.22649e8	−	7.18877e8i	0.183080	−	1.07308i
$876$	5.60781e7	−	2.70058e7i	0.0834220	−	0.0401739i
$877$	5.86357e8	+	2.82375e8i	0.869288	+	0.418627i	0.814700	−	0.579882i	$-0.196901\pi$
$877$	5.86357e8	+	2.82375e8i	0.869288	+	0.418627i	0.0545875	+	0.998509i	$0.482616\pi$
$878$	−7.48436e8	+	1.70826e8i	−1.10579	+	0.252388i
$879$	5.46651e7	+	2.63253e7i	0.0804904	+	0.0387621i
$880$	−1.70639e8	−	1.36080e8i	−0.250398	−	0.199686i
$881$		−	4.66790e7i		−	0.0682643i	−0.999417	−	0.0341322i	$-0.989133\pi$
$881$		−	4.66790e7i		−	0.0682643i	0.999417	−	0.0341322i	$-0.0108667\pi$
$882$	−3.53018e8	−	3.53988e8i	−0.514507	−	0.515920i
$883$	6.99444e8			1.01595			0.507973	−	0.861373i	$-0.330395\pi$
$883$	6.99444e8			1.01595			0.507973	+	0.861373i	$0.330395\pi$
$884$	5.48167e7	−	6.87380e7i	0.0793517	−	0.0995039i
$885$	1.04130e8	−	2.16228e8i	0.150226	−	0.311948i
$886$	2.44873e8	+	1.07286e9i	0.352079	+	1.54256i
$887$	−2.91294e8	+	6.04877e8i	−0.417407	+	0.866755i	0.581188	+	0.813769i	$0.302588\pi$
$887$	−2.91294e8	+	6.04877e8i	−0.417407	+	0.866755i	−0.998595	+	0.0529859i	$0.983126\pi$
$888$	−6.09808e7	−	1.26628e8i	−0.0870872	−	0.180838i
$889$	−8.48246e8	−	6.02737e8i	−1.20730	−	0.857872i
$890$	−1.31666e8	−	6.34069e7i	−0.186768	−	0.0899428i
$891$	−1.07501e8	−	1.34802e8i	−0.151977	−	0.190574i
$892$	−3.20693e7	−	6.65925e7i	−0.0451850	−	0.0938277i
$893$	3.61441e7	−	4.53232e7i	0.0507555	−	0.0636453i
$894$	2.76893e8	+	6.31989e7i	0.387524	+	0.0884499i
$895$	2.51817e7	+	2.00817e7i	0.0351249	+	0.0280112i
$896$	−1.68575e8	+	4.06190e8i	−0.234353	+	0.564683i
$897$	2.74314e7	+	3.43979e7i	0.0380076	+	0.0476600i
$898$	−1.89744e8	+	9.13757e7i	−0.262022	+	0.126183i
$899$	−1.05760e7	−	2.41389e6i	−0.0145559	−	0.00332230i
$900$	−3.97338e7			−0.0545046
$901$		−	6.12397e8i		−	0.837257i
$902$	8.71207e7	+	1.98847e7i	0.118714	+	0.0270957i
$903$	−2.87316e8	−	1.19241e8i	−0.390209	−	0.161943i
$904$	8.63635e7	+	3.78383e8i	0.116903	+	0.512185i
$905$	−1.96094e8	−	8.59144e8i	−0.264557	−	1.15910i
$906$	−1.87329e8	+	1.49390e8i	−0.251895	+	0.200880i
$907$	1.73333e8	+	2.17353e8i	0.232306	+	0.291302i	0.884298	−	0.466924i	$-0.154638\pi$
$907$	1.73333e8	+	2.17353e8i	0.232306	+	0.291302i	−0.651992	+	0.758226i	$0.726066\pi$
$908$	1.69176e8	−	3.86133e7i	0.225986	−	0.0515797i
$909$	8.88822e8	−	2.02868e8i	1.18338	−	0.270098i
$910$	3.77274e8	+	2.68079e8i	0.500648	+	0.355745i
$911$	−1.24809e8	+	5.46823e8i	−0.165078	+	0.723256i	0.822839	+	0.568274i	$0.192389\pi$
$911$	−1.24809e8	+	5.46823e8i	−0.165078	+	0.723256i	−0.987917	+	0.154981i	$0.950468\pi$
$912$	−5.17308e7			−0.0681970
$913$			5.11847e6i			0.00672555i
$914$	1.35672e8	−	5.94416e8i	0.177685	−	0.778488i
$915$	9.27013e7	+	1.92496e8i	0.121010	+	0.251281i
$916$	−6.94741e7	+	5.54038e7i	−0.0903934	+	0.0720863i
$917$	1.52845e9	−	8.47849e7i	1.98218	−	0.109954i
$918$	2.61287e8	−	3.27643e8i	0.337745	−	0.423519i
$919$	−2.70133e7	+	1.18353e8i	−0.0348041	+	0.152487i	−0.989344	−	0.145596i	$-0.953490\pi$
$919$	−2.70133e7	+	1.18353e8i	−0.0348041	+	0.152487i	0.954540	+	0.298083i	$0.0963472\pi$
$920$	8.82106e7	+	7.03456e7i	0.113281	+	0.0903387i
$921$	−3.10285e8	+	1.49426e8i	−0.397175	+	0.191270i
$922$	−9.26959e8	+	7.39225e8i	−1.18268	+	0.943157i
$923$	3.91622e8	−	8.13211e8i	0.498037	−	1.03418i
$924$	−9.52634e6	−	3.31521e7i	−0.0120756	−	0.0420237i
$925$	1.05615e8	−	5.08615e7i	0.133445	−	0.0642635i
$926$	9.48156e8	+	4.56608e8i	1.19412	+	0.575057i
$927$	4.84296e8	−	1.10537e8i	0.607955	−	0.138762i
$928$	−1.36336e8	−	6.56560e7i	−0.170595	−	0.0821543i
$929$	5.42167e8	+	4.32364e8i	0.676217	+	0.539265i	0.900281	−	0.435309i	$-0.143361\pi$
$929$	5.42167e8	+	4.32364e8i	0.676217	+	0.539265i	−0.224064	+	0.974575i	$0.571932\pi$
$930$			7.69824e6i			0.00957067i
$931$	−1.17489e8	+	1.17167e8i	−0.145595	+	0.145197i
$932$	1.52100e8			0.187880
$933$	−3.99855e8	+	5.01403e8i	−0.492332	+	0.617364i
$934$	5.31747e7	−	1.10418e8i	0.0652626	−	0.135519i
$935$	−5.85360e7	−	2.56463e8i	−0.0716124	−	0.313755i
$936$	2.61852e8	−	5.43742e8i	0.319322	−	0.663079i
$937$	2.18484e8	+	4.53687e8i	0.265583	+	0.551490i	0.990527	−	0.137319i	$-0.0438485\pi$
$937$	2.18484e8	+	4.53687e8i	0.265583	+	0.551490i	−0.724944	+	0.688808i	$0.758134\pi$
$938$	1.68023e8	+	3.04507e8i	0.203592	+	0.368969i
$939$	−6.31057e7	−	3.03901e7i	−0.0762205	−	0.0367059i
$940$	−3.25417e7	−	4.08059e7i	−0.0391792	−	0.0491292i
$941$	−8.99117e7	−	1.86704e8i	−0.107906	−	0.224070i	0.840023	−	0.542551i	$-0.182542\pi$
$941$	−8.99117e7	−	1.86704e8i	−0.107906	−	0.224070i	−0.947929	+	0.318481i	$0.896827\pi$
$942$	2.76589e8	−	3.46832e8i	0.330889	−	0.414922i
$943$	−3.58682e7	−	8.18668e6i	−0.0427735	−	0.00976276i
$944$	−4.96774e8	−	3.96164e8i	−0.590531	−	0.470933i
$945$	−4.37754e8	−	3.11054e8i	−0.518722	−	0.368588i
$946$	−2.38191e8	−	2.98682e8i	−0.281353	−	0.352806i
$947$	9.21328e7	−	4.43688e7i	0.108484	−	0.0522430i	−0.378855	−	0.925456i	$-0.623682\pi$
$947$	9.21328e7	−	4.43688e7i	0.108484	−	0.0522430i	0.487339	+	0.873213i	$0.337968\pi$
$948$	1.38909e8	+	3.17051e7i	0.163044	+	0.0372138i
$949$	−7.88501e8			−0.922579
$950$		−	5.41752e7i		−	0.0631872i
$951$	−2.61857e8	−	5.97673e7i	−0.304455	−	0.0694899i
$952$	−6.23456e8	+	3.44014e8i	−0.722595	+	0.398718i
$953$	1.95514e8	+	8.56603e8i	0.225891	+	0.989694i	0.952952	+	0.303121i	$0.0980285\pi$
$953$	1.95514e8	+	8.56603e8i	0.225891	+	0.989694i	−0.727061	+	0.686573i	$0.759114\pi$
$954$	−1.53145e8	−	6.70974e8i	−0.176384	−	0.772788i
$955$	4.69856e8	−	3.74698e8i	0.539454	−	0.430200i
$956$	−1.11528e8	−	1.39852e8i	−0.127647	−	0.160065i
$957$	−9.37376e7	+	2.13950e7i	−0.106949	+	0.0244105i
$958$	7.13056e8	−	1.62750e8i	0.811011	−	0.185108i
$959$	8.07958e7	+	1.45653e9i	0.0916080	+	1.65145i
$960$	−7.68343e7	+	3.36633e8i	−0.0868444	+	0.380490i
$961$	8.86684e8			0.999076
$962$			2.91501e8i			0.327427i
$963$	1.07317e8	−	4.70188e8i	0.120169	−	0.526493i
$964$	6.63580e7	+	1.37794e8i	0.0740734	+	0.153815i
$965$	−4.84169e8	+	3.86112e8i	−0.538784	+	0.429666i
$966$	−1.61118e7	−	5.60699e7i	−0.0178737	−	0.0622011i
$967$	−3.46657e8	+	4.34695e8i	−0.383373	+	0.480734i	−0.935651	−	0.352925i	$-0.885187\pi$
$967$	−3.46657e8	+	4.34695e8i	−0.383373	+	0.480734i	0.552279	+	0.833659i	$0.313758\pi$
$968$	−1.58863e8	+	6.96025e8i	−0.175145	+	0.767360i
$969$	−4.87472e7	−	3.88746e7i	−0.0535770	−	0.0427262i
$970$	9.28792e8	−	4.47283e8i	1.01766	−	0.490080i
$971$	2.03707e8	−	1.62451e8i	0.222510	−	0.177446i	−0.505890	−	0.862598i	$-0.668836\pi$
$971$	2.03707e8	−	1.62451e8i	0.222510	−	0.177446i	0.728400	+	0.685152i	$0.240264\pi$
$972$	−7.71874e7	+	1.60281e8i	−0.0840519	+	0.174536i
$973$	−1.00659e9	−	1.12794e9i	−1.09274	−	1.22446i
$974$	−1.01275e9	+	4.87713e8i	−1.09603	+	0.527822i
$975$	−1.04670e8	−	5.04065e7i	−0.112930	−	0.0543841i
$976$	5.51479e8	−	1.25871e8i	0.593170	−	0.135387i
$977$	1.69432e8	+	8.15941e7i	0.181682	+	0.0874933i	0.522514	−	0.852631i	$-0.324994\pi$
$977$	1.69432e8	+	8.15941e7i	0.181682	+	0.0874933i	−0.340832	+	0.940124i	$0.610709\pi$
$978$	−1.95256e8	−	1.55712e8i	−0.208732	−	0.166458i
$979$		−	1.37978e8i		−	0.147049i
$980$	7.93065e7	+	1.26600e8i	0.0842618	+	0.134511i
$981$	4.44251e8			0.470567
$982$	−7.32382e8	+	9.18378e8i	−0.773398	+	0.969811i
$983$	4.89294e8	−	1.01603e9i	0.515121	−	1.06966i	−0.467493	−	0.883997i	$-0.654843\pi$
$983$	4.89294e8	−	1.01603e9i	0.515121	−	1.06966i	0.982614	−	0.185663i	$-0.0594432\pi$
$984$	−2.59182e7	−	1.13555e8i	−0.0272032	−	0.119185i
$985$	2.07620e8	−	4.31127e8i	0.217250	−	0.451124i
$986$	1.40993e8	+	2.92776e8i	0.147085	+	0.305425i
$987$	9.12980e6	+	1.64586e8i	0.00949532	+	0.171175i
$988$	−2.95462e7	−	1.42287e7i	−0.0306360	−	0.0147535i
$989$	9.80649e7	+	1.22969e8i	0.101374	+	0.127118i
$990$	−1.28270e8	−	2.66356e8i	−0.132197	−	0.274509i
$991$	−6.26882e8	+	7.86085e8i	−0.644117	+	0.807697i	−0.991511	−	0.130022i	$-0.958495\pi$
$991$	−6.26882e8	+	7.86085e8i	−0.644117	+	0.807697i	0.347394	+	0.937719i	$0.387067\pi$
$992$	−1.11524e7	−	2.54547e6i	−0.0114244	−	0.00260755i
$993$	−3.31923e8	−	2.64700e8i	−0.338992	−	0.270337i
$994$	−8.92954e8	+	7.96892e8i	−0.909222	+	0.811410i
$995$	−4.71669e8	−	5.91455e8i	−0.478816	−	0.600416i
$996$	984094.	−	473915.i	0.000995998	−	0.000479647i
$997$	1.78995e9	+	4.08545e8i	1.80616	+	0.412244i	0.986920	−	0.161211i	$-0.0515400\pi$
$997$	1.78995e9	+	4.08545e8i	1.80616	+	0.412244i	0.819237	+	0.573455i	$0.194397\pi$
$998$	9.13106e7			0.0918607
$999$		−	3.38231e8i		−	0.339247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.f.a.6.18	✓	162
49.41	odd	14	inner	49.7.f.a.41.18	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.f.a.6.18	✓	162	1.1	even	1	trivial
49.7.f.a.41.18	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+(4.47311 - 5.60910i) q^{2} +(5.07295 - 10.5341i) q^{3} +(2.78804 + 12.2152i) q^{4} +(-43.9720 + 91.3088i) q^{5} +(-36.3949 - 75.5747i) q^{6} +(-131.478 + 316.801i) q^{7} +(494.672 + 238.222i) q^{8} +(369.292 + 463.077i) q^{9} +(315.469 + 655.077i) q^{10} +(-428.014 + 536.713i) q^{11} +(142.820 + 32.5977i) q^{12} +(-1450.93 - 1157.08i) q^{13} +(1188.85 + 2154.55i) q^{14} +(738.787 + 926.410i) q^{15} +(2826.46 - 1361.15i) q^{16} +(3686.32 + 841.378i) q^{17} +4249.33 q^{18} -1410.36i q^{19} +(-1237.95 - 282.555i) q^{20} +(2670.23 + 2992.11i) q^{21} +(1095.92 + 4801.55i) q^{22} +(-451.199 - 1976.83i) q^{23} +(5018.89 - 4002.43i) q^{24} +(3338.26 + 4186.05i) q^{25} +(-12980.4 + 2962.68i) q^{26} +(15061.2 - 3437.63i) q^{27} +(-4236.35 - 722.773i) q^{28} +(-2665.61 + 11678.8i) q^{29} +8501.00 q^{30} +905.569i q^{31} +(-2810.91 + 12315.4i) q^{32} +(3482.49 + 7231.46i) q^{33} +(21208.7 - 16913.3i) q^{34} +(-23145.4 - 25935.4i) q^{35} +(-4626.99 + 5802.06i) q^{36} +(4871.87 - 21345.1i) q^{37} +(-7910.83 - 6308.68i) q^{38} +(-19549.3 + 9414.45i) q^{39} +(-43503.5 + 34692.9i) q^{40} +(7872.51 - 16347.4i) q^{41} +(28727.2 - 1593.54i) q^{42} +(-69887.1 + 33655.8i) q^{43} +(-7749.39 - 3731.91i) q^{44} +(-58521.6 + 13357.2i) q^{45} +(-13106.5 - 6311.76i) q^{46} +(32136.0 + 25627.6i) q^{47} -36679.2i q^{48} +(-83076.3 - 83304.4i) q^{49} +38412.4 q^{50} +(27563.6 - 34563.7i) q^{51} +(10088.7 - 20949.5i) q^{52} +(-36039.9 - 157901. i) q^{53} +(48088.5 - 99856.7i) q^{54} +(-30186.0 - 62681.9i) q^{55} +(-140507. + 125392. i) q^{56} +(-14856.8 - 7154.67i) q^{57} +(53583.9 + 67192.1i) q^{58} +(-87879.1 - 182483. i) q^{59} +(-9256.53 + 11607.3i) q^{60} +(175790. + 40123.0i) q^{61} +(5079.42 + 4050.71i) q^{62} +(-195257. + 56107.6i) q^{63} +(181687. + 227828. i) q^{64} +(169452. - 81603.9i) q^{65} +(56139.5 + 12813.5i) q^{66} +141332. q^{67} +47375.0i q^{68} +(-23113.0 - 5275.39i) q^{69} +(-249006. + 13812.7i) q^{70} +(108225. + 474167. i) q^{71} +(72363.4 + 317045. i) q^{72} +(332186. - 264909. i) q^{73} +(-97934.1 - 122806. i) q^{74} +(61031.0 - 13929.9i) q^{75} +(17227.8 - 3932.14i) q^{76} +(-113757. - 206161. i) q^{77} +(-34639.6 + 151766. i) q^{78} +972618. q^{79} +317934. i q^{80} +(-55888.7 + 244865. i) q^{81} +(-56479.8 - 117282. i) q^{82} +(5829.41 - 4648.80i) q^{83} +(-29104.5 + 40959.5i) q^{84} +(-238920. + 299596. i) q^{85} +(-123833. + 542550. i) q^{86} +(109503. + 87325.7i) q^{87} +(-339584. + 163535. i) q^{88} +(-157142. + 125317. i) q^{89} +(-186852. + 388001. i) q^{90} +(557330. - 307527. i) q^{91} +(22889.5 - 11023.0i) q^{92} +(9539.34 + 4593.90i) q^{93} +(287495. - 65618.9i) q^{94} +(128778. + 62016.3i) q^{95} +(115472. + 92085.6i) q^{96} -1.41784e6i q^{97} +(-838871. + 93353.9i) q^{98} -406602. 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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