LMFDB - Embedded newform 31.6.g.a.9.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,6,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, 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:	$4.97189841420$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$12$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			9.3
Character	$\chi$	$=$	31.9
Dual form			31.6.g.a.7.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.62800 + 8.08816i) q^{2} +(-19.6320 - 4.17290i) q^{3} +(-32.6234 - 23.7023i) q^{4} +(0.998763 + 1.72991i) q^{5} +(85.3440 - 147.820i) q^{6} +(87.1112 - 38.7844i) q^{7} +(57.2761 - 41.6135i) q^{8} +(146.010 + 65.0077i) q^{9} +(-16.6165 + 3.53195i) q^{10} +(18.2220 - 173.370i) q^{11} +(541.555 + 601.457i) q^{12} +(304.099 - 337.736i) q^{13} +(84.7660 + 806.495i) q^{14} +(-12.3889 - 38.1292i) q^{15} +(-212.698 - 654.618i) q^{16} +(-124.462 - 1184.18i) q^{17} +(-909.507 + 1010.11i) q^{18} +(-1310.86 - 1455.85i) q^{19} +(8.41974 - 80.1085i) q^{20} +(-1872.01 + 397.908i) q^{21} +(1354.36 + 603.000i) q^{22} +(-2481.31 + 1802.78i) q^{23} +(-1298.09 + 577.948i) q^{24} +(1560.50 - 2702.87i) q^{25} +(1932.49 + 3347.18i) q^{26} +(1350.51 + 981.201i) q^{27} +(-3761.15 - 799.456i) q^{28} +(-1341.67 + 4129.23i) q^{29} +340.954 q^{30} +(-4357.31 - 3105.32i) q^{31} +8119.13 q^{32} +(-1081.19 + 3327.56i) q^{33} +(9904.93 + 2105.36i) q^{34} +(154.097 + 111.958i) q^{35} +(-3222.50 - 5581.54i) q^{36} +(539.518 - 934.472i) q^{37} +(15220.1 - 6776.44i) q^{38} +(-7379.41 + 5361.46i) q^{39} +(129.193 + 57.5203i) q^{40} +(1215.05 - 258.267i) q^{41} +(1701.30 - 16186.8i) q^{42} +(-3936.77 - 4372.22i) q^{43} +(-4703.74 + 5224.03i) q^{44} +(33.3717 + 317.511i) q^{45} +(-8060.27 - 24807.0i) q^{46} +(-8401.37 - 25856.8i) q^{47} +(1444.03 + 13739.0i) q^{48} +(-5161.95 + 5732.92i) q^{49} +(17760.3 + 19724.8i) q^{50} +(-2498.03 + 23767.2i) q^{51} +(-17925.9 + 3810.27i) q^{52} +(35317.3 + 15724.3i) q^{53} +(-11485.3 + 8344.52i) q^{54} +(318.114 - 141.633i) q^{55} +(3375.43 - 5846.42i) q^{56} +(19659.6 + 34051.4i) q^{57} +(-29872.0 - 21703.3i) q^{58} +(-4162.58 - 884.783i) q^{59} +(-499.581 + 1537.55i) q^{60} -19176.8 q^{61} +(36567.4 - 27081.8i) q^{62} +15240.4 q^{63} +(-14530.8 + 44721.1i) q^{64} +(887.976 + 188.745i) q^{65} +(-24072.5 - 17489.7i) q^{66} +(-22096.4 - 38272.1i) q^{67} +(-24007.4 + 41582.1i) q^{68} +(56235.9 - 25037.8i) q^{69} +(-1310.50 + 952.135i) q^{70} +(-64398.8 - 28672.2i) q^{71} +(11068.1 - 2352.59i) q^{72} +(1379.12 - 13121.4i) q^{73} +(6140.31 + 6819.50i) q^{74} +(-41914.6 + 46550.9i) q^{75} +(8257.54 + 78565.3i) q^{76} +(-5136.73 - 15809.2i) q^{77} +(-23971.2 - 73775.8i) q^{78} +(1293.35 + 12305.4i) q^{79} +(919.993 - 1021.76i) q^{80} +(-48406.4 - 53760.8i) q^{81} +(-1104.25 + 10506.3i) q^{82} +(42954.9 - 9130.35i) q^{83} +(70502.6 + 31389.8i) q^{84} +(1924.21 - 1398.02i) q^{85} +(45709.1 - 20351.0i) q^{86} +(43570.5 - 75466.3i) q^{87} +(-6170.86 - 10688.3i) q^{88} +(37687.2 + 27381.3i) q^{89} +(-2655.78 - 564.503i) q^{90} +(13391.5 - 41214.9i) q^{91} +123679. q^{92} +(72584.4 + 79146.2i) q^{93} +231212. q^{94} +(1209.26 - 3721.72i) q^{95} +(-159395. - 33880.4i) q^{96} +(31971.2 + 23228.5i) q^{97} +(-32803.2 - 56816.8i) q^{98} +(13931.0 - 24129.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 6 q^{2} - 20 q^{3} - 346 q^{4} - 33 q^{5} + 283 q^{6} - 66 q^{7} - 271 q^{8} + 658 q^{9} + 896 q^{10} + 41 q^{11} - 1169 q^{12} + 149 q^{13} - 2 q^{14} + 4906 q^{15} - 2450 q^{16} - 3152 q^{17} - 3 q^{18}+ \cdots + 674326 q^{99}+O(q^{100}) $ 96 * q - 6 * q^2 - 20 * q^3 - 346 * q^4 - 33 * q^5 + 283 * q^6 - 66 * q^7 - 271 * q^8 + 658 * q^9 + 896 * q^10 + 41 * q^11 - 1169 * q^12 + 149 * q^13 - 2 * q^14 + 4906 * q^15 - 2450 * q^16 - 3152 * q^17 - 3 * q^18 - 5216 * q^19 + 7943 * q^20 - 14003 * q^21 - 8471 * q^22 + 13925 * q^23 + 25478 * q^24 - 18843 * q^25 + 12637 * q^26 + 3409 * q^27 - 10560 * q^28 + 6386 * q^29 - 25530 * q^30 - 39101 * q^31 + 31482 * q^32 + 17969 * q^33 - 18136 * q^34 + 5943 * q^35 - 9713 * q^36 + 40836 * q^37 + 18746 * q^38 + 55889 * q^39 + 15841 * q^40 - 46266 * q^41 + 8917 * q^42 - 137449 * q^43 + 28951 * q^44 + 69269 * q^45 - 97978 * q^46 + 5774 * q^47 - 112102 * q^48 - 146686 * q^49 + 58913 * q^50 + 149254 * q^51 + 263153 * q^52 + 62548 * q^53 + 144508 * q^54 + 13077 * q^55 - 103466 * q^56 + 68345 * q^57 - 52881 * q^58 - 149116 * q^59 + 65951 * q^60 - 204972 * q^61 - 62393 * q^62 - 80326 * q^63 - 205193 * q^64 - 296504 * q^65 - 268720 * q^66 - 105499 * q^67 + 497808 * q^68 + 448358 * q^69 + 351230 * q^70 + 93454 * q^71 + 192637 * q^72 + 74644 * q^73 - 83209 * q^74 - 323995 * q^75 - 446776 * q^76 - 249590 * q^77 - 588829 * q^78 + 396670 * q^79 - 236822 * q^80 + 616675 * q^81 + 449670 * q^82 + 518776 * q^83 + 578676 * q^84 + 463509 * q^85 - 95508 * q^86 - 360817 * q^87 + 238379 * q^88 + 239175 * q^89 - 1232679 * q^90 - 178840 * q^91 - 1350224 * q^92 - 65783 * q^93 + 580620 * q^94 - 276050 * q^95 - 1587604 * q^96 - 611799 * q^97 + 200092 * q^98 + 674326 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{15}\right)$

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 $

$2$	−2.62800	+	8.08816i	−0.464570	+	1.42980i	0.394953	+	0.918701i	$0.370761\pi$
$2$	−2.62800	+	8.08816i	−0.464570	+	1.42980i	−0.859523	+	0.511097i	$0.829239\pi$
$3$	−19.6320	−	4.17290i	−1.25939	−	0.267692i	−0.470597	−	0.882348i	$-0.655961\pi$
$3$	−19.6320	−	4.17290i	−1.25939	−	0.267692i	−0.788795	+	0.614656i	$0.789295\pi$
$4$	−32.6234	−	23.7023i	−1.01948	−	0.740697i
$5$	0.998763	+	1.72991i	0.0178664	+	0.0309455i	0.874820	−	0.484447i	$-0.160979\pi$
$5$	0.998763	+	1.72991i	0.0178664	+	0.0309455i	−0.856954	+	0.515393i	$0.827646\pi$
$6$	85.3440	−	147.820i	0.967821	−	1.67631i
$7$	87.1112	−	38.7844i	0.671938	−	0.299166i	−0.0422635	−	0.999106i	$-0.513457\pi$
$7$	87.1112	−	38.7844i	0.671938	−	0.299166i	0.714201	+	0.699941i	$0.246790\pi$
$8$	57.2761	−	41.6135i	0.316409	−	0.229884i
$9$	146.010	+	65.0077i	0.600863	+	0.267521i
$10$	−16.6165	+	3.53195i	−0.0525461	+	0.0111690i
$11$	18.2220	−	173.370i	0.0454060	−	0.432009i	−0.948078	−	0.318038i	$-0.896976\pi$
$11$	18.2220	−	173.370i	0.0454060	−	0.432009i	0.993484	−	0.113971i	$-0.0363572\pi$
$12$	541.555	+	601.457i	1.08565	+	1.20573i
$13$	304.099	−	337.736i	0.499065	−	0.554268i	−0.440004	−	0.897996i	$-0.645023\pi$
$13$	304.099	−	337.736i	0.499065	−	0.554268i	0.939069	+	0.343728i	$0.111690\pi$
$14$	84.7660	+	806.495i	0.115585	+	1.09972i
$15$	−12.3889	−	38.1292i	−0.0142169	−	0.0437552i
$16$	−212.698	−	654.618i	−0.207713	−	0.639275i
$17$	−124.462	−	1184.18i	−0.104452	−	0.993792i	−0.913718	−	0.406350i	$-0.866802\pi$
$17$	−124.462	−	1184.18i	−0.104452	−	0.993792i	0.809266	−	0.587442i	$-0.199865\pi$
$18$	−909.507	+	1010.11i	−0.661644	+	0.734831i
$19$	−1310.86	−	1455.85i	−0.833051	−	0.925196i	0.165082	−	0.986280i	$-0.447211\pi$
$19$	−1310.86	−	1455.85i	−0.833051	−	0.925196i	−0.998133	+	0.0610834i	$0.980544\pi$
$20$	8.41974	−	80.1085i	0.00470678	−	0.0447820i
$21$	−1872.01	+	397.908i	−0.926317	+	0.196895i
$22$	1354.36	+	603.000i	0.596592	+	0.265620i
$23$	−2481.31	+	1802.78i	−0.978052	+	0.710596i	−0.957272	−	0.289188i	$-0.906615\pi$
$23$	−2481.31	+	1802.78i	−0.978052	+	0.710596i	−0.0207795	+	0.999784i	$0.506615\pi$
$24$	−1298.09	+	577.948i	−0.460021	+	0.204814i
$25$	1560.50	−	2702.87i	0.499362	−	0.864920i
$26$	1932.49	+	3347.18i	0.560641	+	0.971058i
$27$	1350.51	+	981.201i	0.356523	+	0.259029i
$28$	−3761.15	−	799.456i	−0.906619	−	0.192708i
$29$	−1341.67	+	4129.23i	−0.296244	+	0.911746i	0.686556	+	0.727077i	$0.259122\pi$
$29$	−1341.67	+	4129.23i	−0.296244	+	0.911746i	−0.982801	+	0.184670i	$0.940878\pi$
$30$	340.954			0.0691659
$31$	−4357.31	−	3105.32i	−0.814356	−	0.580366i
$31$	−4357.31	−	3105.32i	−0.814356	−	0.580366i
$32$	8119.13			1.40163
$33$	−1081.19	+	3327.56i	−0.172829	+	0.531914i
$34$	9904.93	+	2105.36i	1.46945	+	0.312341i
$35$	154.097	+	111.958i	0.0212630	+	0.0154484i
$36$	−3222.50	−	5581.54i	−0.414417	−	0.717791i
$37$	539.518	−	934.472i	0.0647890	−	0.112218i	−0.831811	−	0.555058i	$-0.812696\pi$
$37$	539.518	−	934.472i	0.0647890	−	0.112218i	0.896600	+	0.442841i	$0.146029\pi$
$38$	15220.1	−	6776.44i	1.70985	−	0.761276i
$39$	−7379.41	+	5361.46i	−0.776891	+	0.564444i
$40$	129.193	+	57.5203i	0.0127670	+	0.00568422i
$41$	1215.05	−	258.267i	0.112885	−	0.0239944i	−0.151123	−	0.988515i	$-0.548289\pi$
$41$	1215.05	−	258.267i	0.112885	−	0.0239944i	0.264008	+	0.964521i	$0.414956\pi$
$42$	1701.30	−	16186.8i	0.148819	−	1.41592i
$43$	−3936.77	−	4372.22i	−0.324690	−	0.360605i	0.558596	−	0.829440i	$-0.311340\pi$
$43$	−3936.77	−	4372.22i	−0.324690	−	0.360605i	−0.883286	+	0.468835i	$0.844674\pi$
$44$	−4703.74	+	5224.03i	−0.366279	+	0.406794i
$45$	33.3717	+	317.511i	0.00245667	+	0.0233737i
$46$	−8060.27	−	24807.0i	−0.561636	−	1.72854i
$47$	−8401.37	−	25856.8i	−0.554760	−	1.70738i	−0.696575	−	0.717484i	$-0.745294\pi$
$47$	−8401.37	−	25856.8i	−0.554760	−	1.70738i	0.141815	−	0.989893i	$-0.454706\pi$
$48$	1444.03	+	13739.0i	0.0904633	+	0.860701i
$49$	−5161.95	+	5732.92i	−0.307131	+	0.341103i
$50$	17760.3	+	19724.8i	1.00467	+	1.11580i
$51$	−2498.03	+	23767.2i	−0.134484	+	1.27953i
$52$	−17925.9	+	3810.27i	−0.919332	+	0.195410i
$53$	35317.3	+	15724.3i	1.72702	+	0.768919i	0.996272	+	0.0862718i	$0.0274953\pi$
$53$	35317.3	+	15724.3i	1.72702	+	0.768919i	0.730748	+	0.682647i	$0.239171\pi$
$54$	−11485.3	+	8344.52i	−0.535989	+	0.389419i
$55$	318.114	−	141.633i	0.0141800	−	0.00631334i
$56$	3375.43	−	5846.42i	0.143833	−	0.249127i
$57$	19659.6	+	34051.4i	0.801469	+	1.38819i
$58$	−29872.0	−	21703.3i	−1.16599	−	0.847139i
$59$	−4162.58	−	884.783i	−0.155680	−	0.0330908i	0.129412	−	0.991591i	$-0.458691\pi$
$59$	−4162.58	−	884.783i	−0.155680	−	0.0330908i	−0.285092	+	0.958500i	$0.592024\pi$
$60$	−499.581	+	1537.55i	−0.0179155	+	0.0551381i
$61$	−19176.8			−0.659861			−0.329930	−	0.944005i	$-0.607025\pi$
$61$	−19176.8			−0.659861			−0.329930	+	0.944005i	$0.607025\pi$
$62$	36567.4	−	27081.8i	1.20813	−	0.894744i
$63$	15240.4			0.483776
$64$	−14530.8	+	44721.1i	−0.443444	+	1.36478i
$65$	887.976	+	188.745i	0.0260686	+	0.00554105i
$66$	−24072.5	−	17489.7i	−0.680239	−	0.494222i
$67$	−22096.4	−	38272.1i	−0.601360	−	1.04159i	−0.992615	−	0.121304i	$-0.961292\pi$
$67$	−22096.4	−	38272.1i	−0.601360	−	1.04159i	0.391255	−	0.920282i	$-0.372041\pi$
$68$	−24007.4	+	41582.1i	−0.629612	+	1.09052i
$69$	56235.9	−	25037.8i	1.42197	−	0.633102i
$70$	−1310.50	+	952.135i	−0.0319663	+	0.0232249i
$71$	−64398.8	−	28672.2i	−1.51611	−	0.675018i	−0.531072	−	0.847327i	$-0.678211\pi$
$71$	−64398.8	−	28672.2i	−1.51611	−	0.675018i	−0.985043	+	0.172309i	$0.944877\pi$
$72$	11068.1	−	2352.59i	0.251617	−	0.0534829i
$73$	1379.12	−	13121.4i	0.0302896	−	0.288186i	−0.968883	−	0.247519i	$-0.920385\pi$
$73$	1379.12	−	13121.4i	0.0302896	−	0.288186i	0.999173	−	0.0406676i	$-0.0129485\pi$
$74$	6140.31	+	6819.50i	0.130350	+	0.144768i
$75$	−41914.6	+	46550.9i	−0.860424	+	0.955597i
$76$	8257.54	+	78565.3i	0.163990	+	1.56026i
$77$	−5136.73	−	15809.2i	−0.0987324	−	0.303867i
$78$	−23971.2	−	73775.8i	−0.446122	−	1.37302i
$79$	1293.35	+	12305.4i	0.0233157	+	0.221835i	0.999975	+	0.00704093i	$0.00224122\pi$
$79$	1293.35	+	12305.4i	0.0233157	+	0.221835i	−0.976659	+	0.214794i	$0.931092\pi$
$80$	919.993	−	1021.76i	0.0160716	−	0.0178493i
$81$	−48406.4	−	53760.8i	−0.819767	−	0.910443i
$82$	−1104.25	+	10506.3i	−0.0181357	+	0.172550i
$83$	42954.9	−	9130.35i	0.684412	−	0.145476i	0.147433	−	0.989072i	$-0.452899\pi$
$83$	42954.9	−	9130.35i	0.684412	−	0.145476i	0.536979	+	0.843596i	$0.319566\pi$
$84$	70502.6	+	31389.8i	1.09020	+	0.485389i
$85$	1924.21	−	1398.02i	0.0288872	−	0.0209878i
$86$	45709.1	−	20351.0i	0.666433	−	0.296715i
$87$	43570.5	−	75466.3i	0.617155	−	1.06894i
$88$	−6170.86	−	10688.3i	−0.0849453	−	0.147130i
$89$	37687.2	+	27381.3i	0.504335	+	0.366420i	0.810670	−	0.585503i	$-0.199103\pi$
$89$	37687.2	+	27381.3i	0.504335	+	0.366420i	−0.306336	+	0.951924i	$0.599103\pi$
$90$	−2655.78	−	564.503i	−0.0345609	−	0.00734615i
$91$	13391.5	−	41214.9i	0.169522	−	0.521736i
$92$	123679.			1.52344
$93$	72584.4	+	79146.2i	0.870233	+	0.948905i
$94$	231212.			2.69893
$95$	1209.26	−	3721.72i	0.0137471	−	0.0423091i
$96$	−159395.	−	33880.4i	−1.76521	−	0.375206i
$97$	31971.2	+	23228.5i	0.345009	+	0.250663i	0.746772	−	0.665080i	$-0.231603\pi$
$97$	31971.2	+	23228.5i	0.345009	+	0.250663i	−0.401763	+	0.915743i	$0.631603\pi$
$98$	−32803.2	−	56816.8i	−0.345025	−	0.597601i
$99$	13931.0	−	24129.2i	0.142854	−	0.247431i
$100$	−114973.	+	51189.4i	−1.14973	+	0.511894i
$101$	−91390.6	+	66399.2i	−0.891453	+	0.647678i	−0.936256	−	0.351318i	$-0.885734\pi$
$101$	−91390.6	+	66399.2i	−0.891453	+	0.647678i	0.0448038	+	0.998996i	$0.485734\pi$
$102$	−185668.	−	82664.6i	−1.76700	−	0.786718i
$103$	89535.1	−	19031.3i	0.831573	−	0.176756i	0.227594	−	0.973756i	$-0.426914\pi$
$103$	89535.1	−	19031.3i	0.831573	−	0.176756i	0.603979	+	0.797000i	$0.293581\pi$
$104$	3363.22	−	31998.9i	0.0304910	−	0.290102i
$105$	−2558.04	−	2840.99i	−0.0226430	−	0.0251476i
$106$	−219994.	+	244328.i	−1.90172	+	2.11207i
$107$	22596.1	+	214987.i	0.190798	+	1.81532i	0.501879	+	0.864938i	$0.332642\pi$
$107$	22596.1	+	214987.i	0.190798	+	1.81532i	−0.311081	+	0.950383i	$0.600691\pi$
$108$	−20801.4	−	64020.3i	−0.171607	−	0.528151i
$109$	6433.00	+	19798.7i	0.0518618	+	0.159614i	0.973633	−	0.228120i	$-0.0732579\pi$
$109$	6433.00	+	19798.7i	0.0518618	+	0.159614i	−0.921771	+	0.387734i	$0.873258\pi$
$110$	309.550	+	2945.17i	0.00243921	+	0.0232075i
$111$	−14491.3	+	16094.2i	−0.111635	+	0.123983i
$112$	−43917.3	−	48775.2i	−0.330819	−	0.367412i
$113$	16513.2	−	157113.i	0.121656	−	1.15748i	−0.747956	−	0.663749i	$-0.768964\pi$
$113$	16513.2	−	157113.i	0.121656	−	1.15748i	0.869612	−	0.493735i	$-0.164369\pi$
$114$	−327078.	+	69522.7i	−2.35716	+	0.501031i
$115$	−5596.88	−	2491.89i	−0.0394641	−	0.0175705i
$116$	141642.	−	102909.i	0.977343	−	0.710082i
$117$	66356.9	−	29544.0i	0.448148	−	0.199528i
$118$	18095.5	−	31342.4i	0.119637	−	0.207218i
$119$	−56769.8	−	98328.2i	−0.367494	−	0.636518i
$120$	−2296.28	−	1668.35i	−0.0145570	−	0.0105763i
$121$	127806.	+	27166.1i	0.793577	+	0.168680i
$122$	50396.8	−	155105.i	0.306551	−	0.943468i
$123$	−24931.6			−0.148589
$124$	68547.1	+	204584.i	0.400345	+	1.19486i
$125$	12476.6			0.0714200
$126$	−40051.7	+	123267.i	−0.224747	+	0.691702i
$127$	−88880.5	−	18892.1i	−0.488987	−	0.103937i	−0.0431813	−	0.999067i	$-0.513749\pi$
$127$	−88880.5	−	18892.1i	−0.488987	−	0.103937i	−0.445805	+	0.895130i	$0.647083\pi$
$128$	−113332.	−	82340.6i	−0.611404	−	0.444211i
$129$	59041.7	+	102263.i	0.312381	+	0.541059i
$130$	−3860.20	+	6686.07i	−0.0200333	+	0.0346986i
$131$	72190.0	−	32141.1i	0.367535	−	0.163637i	−0.214655	−	0.976690i	$-0.568863\pi$
$131$	72190.0	−	32141.1i	0.367535	−	0.163637i	0.582190	+	0.813053i	$0.302196\pi$
$132$	114143.	−	82929.8i	0.570183	−	0.414263i
$133$	−170655.	−	75980.4i	−0.836545	−	0.372454i
$134$	367620.	−	78140.1i	1.76863	−	0.375934i
$135$	−348.551	+	3316.24i	−0.00164601	+	0.0156607i
$136$	−56406.6	−	62645.9i	−0.261507	−	0.290433i
$137$	−97065.2	+	107802.i	−0.441837	+	0.490710i	−0.922392	−	0.386255i	$-0.873769\pi$
$137$	−97065.2	+	107802.i	−0.441837	+	0.490710i	0.480555	+	0.876965i	$0.340435\pi$
$138$	54721.9	+	520644.i	0.244604	+	2.32725i
$139$	84393.2	+	259735.i	0.370485	+	1.14023i	0.946475	+	0.322778i	$0.104617\pi$
$139$	84393.2	+	259735.i	0.370485	+	1.14023i	−0.575990	+	0.817457i	$0.695383\pi$
$140$	−2373.51	−	7304.90i	−0.0102346	−	0.0314988i
$141$	57037.7	+	542677.i	0.241610	+	2.29876i
$142$	401146.	−	445518.i	1.66948	−	1.85415i
$143$	−53012.2	−	58876.0i	−0.216788	−	0.240768i
$144$	11499.2	−	109408.i	0.0462127	−	0.439684i
$145$	−8483.19	+	1803.16i	−0.0335073	+	0.00712219i
$146$	102504.	+	45637.6i	0.397977	+	0.177191i
$147$	125262.	−	91008.3i	0.478109	−	0.347366i
$148$	−39750.1	+	17697.9i	−0.149171	+	0.0664151i
$149$	38115.6	−	66018.2i	0.140649	−	0.243612i	−0.787092	−	0.616836i	$-0.788414\pi$
$149$	38115.6	−	66018.2i	0.140649	−	0.243612i	0.927741	+	0.373224i	$0.121748\pi$
$150$	−266360.	−	461348.i	−0.966585	−	1.67417i
$151$	−401263.	−	291534.i	−1.43214	−	1.04051i	−0.989613	−	0.143759i	$-0.954081\pi$
$151$	−401263.	−	291534.i	−1.43214	−	1.04051i	−0.442530	−	0.896754i	$-0.645919\pi$
$152$	−135664.	−	28836.3i	−0.476273	−	0.101235i
$153$	58808.1	−	180993.i	0.203099	−	0.625076i
$154$	141367.			0.480337
$155$	1020.00	−	10639.2i	0.00341013	−	0.0355697i
$156$	367821.			1.21011
$157$	107978.	−	332321.i	0.349611	−	1.07599i	−0.609458	−	0.792818i	$-0.708613\pi$
$157$	107978.	−	332321.i	0.349611	−	1.07599i	0.959069	−	0.283173i	$-0.0913871\pi$
$158$	−102927.	−	21877.9i	−0.328010	−	0.0697208i
$159$	−627732.	−	456074.i	−1.96916	−	1.43068i
$160$	8109.09	+	14045.4i	0.0250422	+	0.0433743i
$161$	−146230.	+	253278.i	−0.444604	+	0.770076i
$162$	562038.	−	250235.i	1.68259	−	0.749137i
$163$	−108500.	+	78830.2i	−0.319862	+	0.232393i	−0.736117	−	0.676855i	$-0.763342\pi$
$163$	−108500.	+	78830.2i	−0.319862	+	0.232393i	0.416255	+	0.909248i	$0.363342\pi$
$164$	−45760.7	−	20374.0i	−0.132857	−	0.0591515i
$165$	−6836.23	+	1453.09i	−0.0195482	+	0.00415510i
$166$	−39037.9	+	371421.i	−0.109955	+	1.04616i
$167$	231947.	+	257604.i	0.643573	+	0.714761i	0.973357	−	0.229296i	$-0.0736424\pi$
$167$	231947.	+	257604.i	0.643573	+	0.714761i	−0.329783	+	0.944057i	$0.606976\pi$
$168$	−90663.0	+	100691.i	−0.247832	+	0.275245i
$169$	17221.1	+	163848.i	0.0463815	+	0.441291i
$170$	6250.60	+	19237.4i	0.0165882	+	0.0510532i
$171$	−96756.1	−	297785.i	−0.253039	−	0.778775i
$172$	24799.1	+	235947.i	0.0639167	+	0.608127i
$173$	−52410.2	+	58207.5i	−0.133138	+	0.147864i	−0.806027	−	0.591879i	$-0.798386\pi$
$173$	−52410.2	+	58207.5i	−0.133138	+	0.147864i	0.672889	+	0.739743i	$0.265053\pi$
$174$	495880.	+	550731.i	1.24166	+	1.37901i
$175$	31108.1	−	295974.i	0.0767854	−	0.730564i
$176$	−117367.	+	24947.1i	−0.285604	+	0.0607070i
$177$	78027.5	+	34740.1i	0.187204	+	0.0833485i
$178$	−320507.	+	232862.i	−0.758206	+	0.550869i
$179$	−746077.	+	332175.i	−1.74041	+	0.774880i	−0.746410	+	0.665486i	$0.768224\pi$
$179$	−746077.	+	332175.i	−1.74041	+	0.774880i	−0.993998	+	0.109394i	$0.965109\pi$
$180$	6437.03	−	11149.3i	0.0148083	−	0.0256487i
$181$	−243671.	−	422050.i	−0.552850	−	0.957564i	−0.998067	−	0.0621418i	$-0.980207\pi$
$181$	−243671.	−	422050.i	−0.552850	−	0.957564i	0.445217	−	0.895423i	$-0.353126\pi$
$182$	298160.	+	216626.i	0.667223	+	0.484766i
$183$	376479.	+	80023.1i	0.831023	+	0.176639i
$184$	−67099.9	+	206512.i	−0.146109	+	0.449678i
$185$	2155.40			0.00463019
$186$	−830899.	+	379078.i	−1.76103	+	0.803426i
$187$	−207570.			−0.434070
$188$	−338783.	+	1.04267e6i	−0.699081	+	2.15155i
$189$	155700.	+	33095.0i	0.317054	+	0.0673919i
$190$	26923.9	+	19561.4i	0.0541071	+	0.0393111i
$191$	−212489.	−	368042.i	−0.421458	−	0.729986i	0.574625	−	0.818417i	$-0.305148\pi$
$191$	−212489.	−	368042.i	−0.421458	−	0.729986i	−0.996082	+	0.0884311i	$0.971815\pi$
$192$	471884.	−	817328.i	0.923810	−	1.60009i
$193$	813866.	−	362356.i	1.57275	−	0.700233i	0.579365	−	0.815068i	$-0.303301\pi$
$193$	813866.	−	362356.i	1.57275	−	0.700233i	0.993385	+	0.114835i	$0.0366341\pi$
$194$	−271896.	+	197544.i	−0.518679	+	0.376842i
$195$	−16645.1	−	7410.88i	−0.0313473	−	0.0139567i
$196$	304284.	−	64677.5i	0.565768	−	0.120258i
$197$	−2292.69	+	21813.5i	−0.00420902	+	0.0400461i	−0.996425	−	0.0844842i	$-0.973076\pi$
$197$	−2292.69	+	21813.5i	−0.00420902	+	0.0400461i	0.992216	+	0.124530i	$0.0397424\pi$
$198$	158550.	+	176088.i	0.287411	+	0.319202i
$199$	265982.	−	295403.i	0.476124	−	0.528789i	−0.456459	−	0.889744i	$-0.650883\pi$
$199$	265982.	−	295403.i	0.476124	−	0.528789i	0.932583	+	0.360955i	$0.117549\pi$
$200$	−23096.5	−	219748.i	−0.0408292	−	0.388463i
$201$	274090.	+	843563.i	0.478524	+	1.47274i
$202$	−296872.	−	913680.i	−0.511908	−	1.57549i
$203$	43275.4	+	411738.i	0.0737057	+	0.701263i
$204$	644831.	−	716157.i	1.08485	−	1.20485i
$205$	1660.33	+	1843.98i	0.00275936	+	0.00306458i
$206$	−81370.5	+	774189.i	−0.133598	+	1.27110i
$207$	−479490.	+	101919.i	−0.777775	+	0.165321i
$208$	−285770.	−	127233.i	−0.457992	−	0.203911i
$209$	−276288.	+	200735.i	−0.437519	+	0.317876i
$210$	29700.9	−	13223.7i	0.0464752	−	0.0206921i
$211$	538052.	−	931933.i	0.831990	−	1.44105i	−0.0644677	−	0.997920i	$-0.520535\pi$
$211$	538052.	−	931933.i	0.831990	−	1.44105i	0.896458	−	0.443129i	$-0.146132\pi$
$212$	−779469.	−	1.35008e6i	−1.19113	−	2.06310i
$213$	1.14463e6	+	831622.i	1.72869	+	1.25596i
$214$	−1.79824e6	−	382227.i	−2.68418	−	0.570541i
$215$	3631.65	−	11177.1i	0.00535806	−	0.0164904i
$216$	118183.			0.172354
$217$	−500008.	−	101513.i	−0.720822	−	0.146342i
$218$	−177041.			−0.252309
$219$	−81829.1	+	251844.i	−0.115292	+	0.354831i
$220$	−13735.0	−	2919.47i	−0.0191325	−	0.00406674i
$221$	−437790.	−	318073.i	−0.602955	−	0.438072i
$222$	−92089.2	−	159503.i	−0.125408	−	0.217214i
$223$	−319135.	+	552758.i	−0.429747	+	0.744343i	−0.996851	−	0.0793031i	$-0.974730\pi$
$223$	−319135.	+	552758.i	−0.429747	+	0.744343i	0.567104	+	0.823646i	$0.308064\pi$
$224$	707267.	−	314896.i	0.941811	−	0.419321i
$225$	403556.	−	293201.i	0.531432	−	0.386108i
$226$	1.22736e6	+	546454.i	1.59845	+	0.711676i
$227$	473546.	−	100655.i	0.609954	−	0.129650i	0.107430	−	0.994213i	$-0.465738\pi$
$227$	473546.	−	100655.i	0.609954	−	0.129650i	0.502525	+	0.864563i	$0.332405\pi$
$228$	165734.	−	1.57685e6i	0.211141	−	2.00888i
$229$	973217.	+	1.08087e6i	1.22637	+	1.36202i	0.910657	+	0.413164i	$0.135576\pi$
$229$	973217.	+	1.08087e6i	1.22637	+	1.36202i	0.315711	+	0.948855i	$0.397757\pi$
$230$	34863.5	−	38719.8i	0.0434561	−	0.0482629i
$231$	34873.7	+	331801.i	0.0430000	+	0.409118i
$232$	94986.2	+	292338.i	0.115862	+	0.356586i
$233$	−101914.	−	313658.i	−0.122982	−	0.378500i	0.870546	−	0.492087i	$-0.163766\pi$
$233$	−101914.	−	313658.i	−0.122982	−	0.378500i	−0.993528	+	0.113587i	$0.963766\pi$
$234$	64570.5	+	614347.i	0.0770894	+	0.733456i
$235$	36338.8	−	40358.4i	0.0429241	−	0.0476720i
$236$	114826.	+	127527.i	0.134203	+	0.149047i
$237$	25958.3	−	246977.i	0.0300197	−	0.285618i
$238$	944485.	−	200757.i	1.08082	−	0.229735i
$239$	−958050.	−	426551.i	−1.08491	−	0.483032i	−0.215186	−	0.976573i	$-0.569036\pi$
$239$	−958050.	−	426551.i	−1.08491	−	0.483032i	−0.869723	+	0.493541i	$0.835702\pi$
$240$	−22325.0	+	16220.0i	−0.0250186	+	0.0181771i
$241$	1.10247e6	−	490851.i	1.22271	−	0.544386i	0.309122	−	0.951022i	$-0.399965\pi$
$241$	1.10247e6	−	490851.i	1.22271	−	0.544386i	0.913590	+	0.406636i	$0.133298\pi$
$242$	−555599.	+	962326.i	−0.609851	+	1.05629i
$243$	523153.	+	906127.i	0.568346	+	0.984404i
$244$	625614.	+	454535.i	0.672716	+	0.488757i
$245$	−15073.0	−	3203.86i	−0.0160429	−	0.00341003i
$246$	65520.3	−	201651.i	0.0690300	−	0.212453i
$247$	−890326.			−0.928553
$248$	−378793.	+	3462.35i	−0.391086	+	0.00357472i
$249$	−881390.			−0.900886
$250$	−32788.4	+	100912.i	−0.0331796	+	0.102116i
$251$	722441.	+	153560.i	0.723800	+	0.153848i	0.555058	−	0.831812i	$-0.312696\pi$
$251$	722441.	+	153560.i	0.723800	+	0.153848i	0.168742	+	0.985660i	$0.446030\pi$
$252$	−497193.	−	361232.i	−0.493201	−	0.358331i
$253$	267334.	+	463036.i	0.262575	+	0.454793i
$254$	386381.	−	669231.i	0.375778	−	0.650866i
$255$	−43609.9	+	19416.4i	−0.0419986	+	0.0186990i
$256$	−253524.	+	184196.i	−0.241780	+	0.175663i
$257$	−607049.	−	270276.i	−0.573312	−	0.255255i	0.0995384	−	0.995034i	$-0.468263\pi$
$257$	−607049.	−	270276.i	−0.573312	−	0.255255i	−0.672850	+	0.739779i	$0.734930\pi$
$258$	−982283.	+	208791.i	−0.918729	+	0.195282i
$259$	10755.1	−	102328.i	0.00996242	−	0.0947861i
$260$	−24495.1	−	27204.6i	−0.0224722	−	0.0249579i
$261$	−464328.	+	515689.i	−0.421914	+	0.468583i
$262$	70246.5	+	668351.i	0.0632225	+	0.601522i
$263$	−113692.	−	349907.i	−0.101354	−	0.311935i	0.887504	−	0.460801i	$-0.152438\pi$
$263$	−113692.	−	349907.i	−0.101354	−	0.311935i	−0.988857	+	0.148866i	$0.952438\pi$
$264$	76545.2	+	235582.i	0.0675940	+	0.208033i
$265$	8072.05	+	76800.4i	0.00706105	+	0.0671814i
$266$	1.06302e6	−	1.18061e6i	0.921168	−	1.02306i
$267$	−625614.	−	694815.i	−0.537067	−	0.596473i
$268$	−186277.	+	1.77230e6i	−0.158424	+	1.50730i
$269$	2.01295e6	−	427866.i	1.69610	−	0.360518i	0.744446	−	0.667683i	$-0.232714\pi$
$269$	2.01295e6	−	427866.i	1.69610	−	0.360518i	0.951656	+	0.307165i	$0.0993803\pi$
$270$	−25906.3	−	11534.2i	−0.0216270	−	0.00962895i
$271$	631851.	−	459066.i	0.522626	−	0.379710i	−0.294966	−	0.955508i	$-0.595308\pi$
$271$	631851.	−	459066.i	0.522626	−	0.379710i	0.817592	+	0.575798i	$0.195308\pi$
$272$	−748712.	+	333348.i	−0.613610	+	0.273197i
$273$	−434888.	+	753249.i	−0.353160	+	0.611691i
$274$	−616831.	−	1.06838e6i	−0.496352	−	0.859707i
$275$	−440163.	−	319797.i	−0.350979	−	0.255001i
$276$	−2.42806e6	−	516100.i	−1.91861	−	0.407813i
$277$	−385162.	+	1.18541e6i	−0.301609	+	0.928256i	0.679312	+	0.733849i	$0.262278\pi$
$277$	−385162.	+	1.18541e6i	−0.301609	+	0.928256i	−0.980921	+	0.194407i	$0.937722\pi$
$278$	−2.32257e6			−1.80242
$279$	−434340.	−	736665.i	−0.334056	−	0.566578i
$280$	13485.0			0.0102791
$281$	345766.	−	1.06416e6i	0.261226	−	0.803972i	−0.731312	−	0.682043i	$-0.761092\pi$
$281$	345766.	−	1.06416e6i	0.261226	−	0.803972i	0.992539	−	0.121930i	$-0.0389082\pi$
$282$	−4.53916e6	−	964828.i	−3.39901	−	0.722482i
$283$	1.13949e6	+	827885.i	0.845752	+	0.614475i	0.923971	−	0.382461i	$-0.124924\pi$
$283$	1.13949e6	+	827885.i	0.845752	+	0.614475i	−0.0782195	+	0.996936i	$0.524924\pi$
$284$	1.42131e6	+	2.46179e6i	1.04567	+	1.81115i
$285$	−39270.5	+	68018.5i	−0.0286388	+	0.0496038i
$286$	615515.	−	274045.i	0.444963	−	0.198110i
$287$	95827.9	−	69623.0i	0.0686732	−	0.0498940i
$288$	1.18547e6	+	527806.i	0.842190	+	0.374967i
$289$	2038.09	−	433.209i	0.00143542	−	0.000305108i
$290$	7709.62	−	73352.1i	0.00538317	−	0.0512174i
$291$	−530728.	−	589433.i	−0.367400	−	0.408039i
$292$	−355999.	+	395377.i	−0.244338	+	0.271365i
$293$	−118185.	−	1.12445e6i	−0.0804253	−	0.765195i	−0.958196	−	0.286114i	$-0.907637\pi$
$293$	−118185.	−	1.12445e6i	−0.0804253	−	0.765195i	0.877770	−	0.479081i	$-0.159030\pi$
$294$	406900.	+	1.25231e6i	0.274549	+	0.844975i
$295$	−2626.83	−	8084.57i	−0.00175743	−	0.00540881i
$296$	−7985.20	−	75974.1i	−0.00529733	−	0.0504007i
$297$	194720.	−	216258.i	0.128091	−	0.142260i
$298$	433798.	+	481781.i	0.282974	+	0.314275i
$299$	−145701.	+	1.38625e6i	−0.0942508	+	0.896736i
$300$	2.47076e6	−	525177.i	1.58499	−	0.336901i
$301$	−512511.	−	228185.i	−0.326052	−	0.145168i
$302$	3.41250e6	−	2.47932e6i	2.15305	−	1.56429i
$303$	2.07126e6	−	922183.i	1.29607	−	0.577046i
$304$	−674211.	+	1.16777e6i	−0.418419	+	0.724724i
$305$	−19153.1	−	33174.2i	−0.0117893	−	0.0204197i
$306$	1.30935e6	+	951299.i	0.799379	+	0.580783i
$307$	2.82763e6	+	601030.i	1.71228	+	0.363957i	0.956696	−	0.291089i	$-0.0940177\pi$
$307$	2.82763e6	+	601030.i	1.71228	+	0.363957i	0.755588	+	0.655047i	$0.227351\pi$
$308$	−207137.	+	637503.i	−0.124418	+	0.382918i
$309$	−1.83717e6			−1.09459
$310$	83371.2	+	36209.8i	0.0492733	+	0.0214004i
$311$	1.07271e6			0.628897			0.314449	−	0.949274i	$-0.398180\pi$
$311$	1.07271e6			0.628897			0.314449	+	0.949274i	$0.398180\pi$
$312$	−199555.	+	614166.i	−0.116058	+	0.357190i
$313$	−2.21468e6	−	470745.i	−1.27776	−	0.271597i	−0.481446	−	0.876476i	$-0.659888\pi$
$313$	−2.21468e6	−	470745.i	−1.27776	−	0.271597i	−0.796318	+	0.604879i	$0.793222\pi$
$314$	2.40410e6	+	1.74668e6i	1.37603	+	0.999746i
$315$	15221.5	+	26364.4i	0.00864333	+	0.0149707i
$316$	249473.	−	432101.i	0.140542	−	0.243426i
$317$	−2.04420e6	+	910137.i	−1.14255	+	0.508696i	−0.888674	−	0.458540i	$-0.848373\pi$
$317$	−2.04420e6	+	910137.i	−1.14255	+	0.508696i	−0.253877	+	0.967236i	$0.581706\pi$
$318$	5.33848e6	−	3.87863e6i	2.96040	−	2.15085i
$319$	691438.	+	307848.i	0.380432	+	0.169379i
$320$	−91876.2	+	19528.9i	−0.0501566	+	0.0106611i
$321$	453516.	−	4.31492e6i	0.245658	−	2.33728i
$322$	−1.66426e6	−	1.84835e6i	−0.894504	−	0.993448i
$323$	−1.56084e6	+	1.73349e6i	−0.832439	+	0.924517i
$324$	304929.	+	2.90120e6i	0.161375	+	1.53538i
$325$	−438311.	−	1.34898e6i	−0.230183	−	0.708431i
$326$	−352452.	−	1.08474e6i	−0.183677	−	0.565301i
$327$	−43674.2	−	415533.i	−0.0225869	−	0.214900i
$328$	58846.0	−	65355.1i	0.0302018	−	0.0335425i
$329$	−1.73469e6	−	1.92657e6i	−0.883553	−	0.981285i
$330$	6212.84	−	59111.2i	0.00314055	−	0.0298803i
$331$	2.65690e6	−	564741.i	1.33292	−	0.283322i	0.514279	−	0.857623i	$-0.328060\pi$
$331$	2.65690e6	−	564741.i	1.33292	−	0.283322i	0.818644	+	0.574301i	$0.194726\pi$
$332$	−1.61775e6	−	720267.i	−0.805499	−	0.358631i
$333$	139523.	−	101369.i	0.0689500	−	0.0500951i
$334$	−2.69310e6	+	1.19904e6i	−1.32095	+	0.588124i
$335$	44138.1	−	76449.5i	0.0214883	−	0.0372188i
$336$	658650.	+	1.14082e6i	0.318278	+	0.551274i
$337$	−1.48601e6	−	1.07965e6i	−0.712766	−	0.517855i	0.171299	−	0.985219i	$-0.445204\pi$
$337$	−1.48601e6	−	1.07965e6i	−0.712766	−	0.517855i	−0.884065	+	0.467364i	$0.845204\pi$
$338$	−1.37049e6	−	291306.i	−0.652504	−	0.138694i
$339$	−979803.	+	3.01552e6i	−0.463062	+	1.42516i
$340$	−95910.8			−0.0449956
$341$	−617769.	+	698843.i	−0.287700	+	0.325457i
$342$	2.66281e6			1.23105
$343$	−722556.	+	2.22380e6i	−0.331617	+	1.02061i
$344$	−407426.	−	86601.1i	−0.185632	−	0.0394573i
$345$	99479.4	+	72276.0i	0.0449972	+	0.0326924i
$346$	−333057.	−	576872.i	−0.149565	−	0.259053i
$347$	−609857.	+	1.05630e6i	−0.271897	+	0.470939i	−0.969348	−	0.245693i	$-0.920984\pi$
$347$	−609857.	+	1.05630e6i	−0.271897	+	0.470939i	0.697451	+	0.716633i	$0.254318\pi$
$348$	−3.21014e6	+	1.42925e6i	−1.42094	+	0.632644i
$349$	−1.22458e6	+	889711.i	−0.538176	+	0.391008i	−0.823407	−	0.567451i	$-0.807930\pi$
$349$	−1.22458e6	+	889711.i	−0.538176	+	0.391008i	0.285231	+	0.958459i	$0.407930\pi$
$350$	2.31213e6	+	1.02943e6i	1.00889	+	0.449185i
$351$	742076.	−	157733.i	0.321500	−	0.0683369i
$352$	147946.	−	1.40762e6i	0.0636426	−	0.605519i
$353$	−668273.	−	742193.i	−0.285442	−	0.317015i	0.583323	−	0.812240i	$-0.301752\pi$
$353$	−668273.	−	742193.i	−0.285442	−	0.317015i	−0.868765	+	0.495225i	$0.835086\pi$
$354$	−486040.	+	539802.i	−0.206141	+	0.228943i
$355$	−14718.9	−	140041.i	−0.00619875	−	0.0589771i
$356$	−580484.	−	1.78655e6i	−0.242753	−	0.747118i
$357$	704189.	+	2.16727e6i	0.292428	+	0.900000i
$358$	−725992.	−	6.90735e6i	−0.299381	−	2.84842i
$359$	−1.24916e6	+	1.38733e6i	−0.511542	+	0.568124i	−0.942482	−	0.334256i	$-0.891515\pi$
$359$	−1.24916e6	+	1.38733e6i	−0.511542	+	0.568124i	0.430941	+	0.902380i	$0.358182\pi$
$360$	15124.1	+	16797.0i	0.00615055	+	0.00683088i
$361$	−142343.	+	1.35430e6i	−0.0574867	+	0.546949i
$362$	4.05398e6	−	861700.i	1.62596	−	0.345609i
$363$	−2.39573e6	−	1.06665e6i	−0.954270	−	0.424869i
$364$	−1.41377e6	+	1.02716e6i	−0.559274	+	0.406336i
$365$	24076.2	−	10719.4i	0.00945924	−	0.00421153i
$366$	−1.63663e6	+	2.83472e6i	−0.638627	+	1.10613i
$367$	1.35263e6	+	2.34282e6i	0.524219	+	0.907975i	0.999602	+	0.0281958i	$0.00897619\pi$
$367$	1.35263e6	+	2.34282e6i	0.524219	+	0.907975i	−0.475383	+	0.879779i	$0.657690\pi$
$368$	1.70790e6	+	1.24086e6i	0.657421	+	0.477644i
$369$	194199.	+	41278.2i	0.0742473	+	0.0157817i
$370$	−5664.40	+	17433.2i	−0.00215105	+	0.00662024i
$371$	3.68639e6			1.39048
$372$	−492003.	−	4.30244e6i	−0.184336	−	1.61197i
$373$	−3.75656e6			−1.39804			−0.699018	−	0.715104i	$-0.746379\pi$
$373$	−3.75656e6			−1.39804			−0.699018	+	0.715104i	$0.746379\pi$
$374$	545494.	−	1.67886e6i	0.201656	−	0.620633i
$375$	−244940.	−	52063.5i	−0.0899458	−	0.0191186i
$376$	−1.55719e6	−	1.13136e6i	−0.568030	−	0.412698i
$377$	986591.	+	1.70883e6i	0.357506	+	0.619219i
$378$	−676857.	+	1.17235e6i	−0.243650	+	0.422015i
$379$	−1.24598e6	+	554745.i	−0.445566	+	0.198379i	−0.617240	−	0.786775i	$-0.711749\pi$
$379$	−1.24598e6	+	554745.i	−0.445566	+	0.198379i	0.171674	+	0.985154i	$0.445082\pi$
$380$	−127663.	+	92752.9i	−0.0453531	+	0.0329510i
$381$	1.66606e6	+	741779.i	0.588003	+	0.261796i
$382$	3.53521e6	−	751432.i	1.23953	−	0.263470i
$383$	342299.	−	3.25675e6i	0.119236	−	1.13446i	−0.757282	−	0.653088i	$-0.773473\pi$
$383$	342299.	−	3.25675e6i	0.119236	−	1.13446i	0.876518	−	0.481369i	$-0.159860\pi$
$384$	1.88133e6	+	2.08943e6i	0.651085	+	0.723103i
$385$	22218.1	−	24675.7i	0.00763934	−	0.00848434i
$386$	791955.	+	7.53495e6i	0.270541	+	2.57402i
$387$	−290578.	−	894307.i	−0.0986247	−	0.303535i
$388$	−492443.	−	1.51558e6i	−0.166064	−	0.511094i
$389$	−110461.	−	1.05097e6i	−0.0370115	−	0.352141i	−0.997318	−	0.0731931i	$-0.976681\pi$
$389$	−110461.	−	1.05097e6i	−0.0370115	−	0.352141i	0.960306	−	0.278948i	$-0.0899856\pi$
$390$	103684.	−	115152.i	0.0345183	−	0.0383364i
$391$	2.44365e6	+	2.71394e6i	0.808344	+	0.897757i
$392$	−57089.1	+	543166.i	−0.0187645	+	0.178533i
$393$	−1.55135e6	+	329750.i	−0.506675	+	0.107697i
$394$	−170406.	−	75869.7i	−0.0553025	−	0.0246223i
$395$	−19995.5	+	14527.6i	−0.00644822	+	0.00468490i
$396$	−1.02639e6	+	456980.i	−0.328909	+	0.146440i
$397$	454886.	−	787886.i	0.144853	−	0.250892i	−0.784465	−	0.620173i	$-0.787062\pi$
$397$	454886.	−	787886.i	0.144853	−	0.250892i	0.929318	+	0.369280i	$0.120396\pi$
$398$	1.69027e6	+	2.92763e6i	0.534869	+	0.926421i
$399$	3.03323e6	+	2.20377e6i	0.953835	+	0.693002i
$400$	−2.10127e6	−	446638.i	−0.656645	−	0.139574i
$401$	−356234.	+	1.09638e6i	−0.110631	+	0.340486i	−0.991011	−	0.133783i	$-0.957287\pi$
$401$	−356234.	+	1.09638e6i	−0.110631	+	0.340486i	0.880380	+	0.474269i	$0.157287\pi$
$402$	−7.54319e6			−2.32804
$403$	−2.37383e6	+	527297.i	−0.728095	+	0.161731i
$404$	4.55529e6			1.38855
$405$	44654.6	−	137433.i	0.0135279	−	0.0416345i
$406$	−3.44393e6	−	732030.i	−1.03691	−	0.220401i
$407$	−152179.	−	110564.i	−0.0455374	−	0.0330848i
$408$	845958.	+	1.46524e6i	0.251593	+	0.435772i
$409$	−1.10443e6	+	1.91294e6i	−0.326461	+	0.565448i	−0.981807	−	0.189881i	$-0.939190\pi$
$409$	−1.10443e6	+	1.91294e6i	−0.326461	+	0.565448i	0.655346	+	0.755329i	$0.272523\pi$
$410$	−19277.8	+	8583.01i	−0.00566366	+	0.00252162i
$411$	2.35543e6	−	1.71132e6i	0.687805	−	0.499720i
$412$	−3.37203e6	−	1.50132e6i	−0.978696	−	0.435744i
$413$	−396923.	+	84368.6i	−0.114507	+	0.0243392i
$414$	435766.	−	4.14604e6i	0.124955	−	1.18886i
$415$	58696.4	+	65189.0i	0.0167298	+	0.0185804i
$416$	2.46902e6	−	2.74213e6i	0.699506	−	0.776881i
$417$	−572953.	−	5.45128e6i	−0.161354	−	1.53518i
$418$	−897492.	−	2.76220e6i	−0.251241	−	0.773240i
$419$	−2.04464e6	−	6.29277e6i	−0.568961	−	1.75108i	−0.655878	−	0.754867i	$-0.727701\pi$
$419$	−2.04464e6	−	6.29277e6i	−0.568961	−	1.75108i	0.0869163	−	0.996216i	$-0.472299\pi$
$420$	16114.0	+	153314.i	0.00445737	+	0.0424091i
$421$	2.56021e6	−	2.84340e6i	0.703995	−	0.781866i	−0.280012	−	0.959997i	$-0.590338\pi$
$421$	2.56021e6	−	2.84340e6i	0.703995	−	0.781866i	0.984007	+	0.178131i	$0.0570051\pi$
$422$	6.12363e6	+	6.80098e6i	1.67389	+	1.85905i
$423$	454207.	−	4.32149e6i	0.123425	−	1.17431i
$424$	2.67718e6	−	569051.i	0.723206	−	0.153722i
$425$	−3.39491e6	−	1.51151e6i	−0.911709	−	0.405919i
$426$	−9.73439e6	+	7.07244e6i	−2.59887	+	1.88819i
$427$	−1.67052e6	+	743762.i	−0.443385	+	0.197408i
$428$	4.35853e6	−	7.54920e6i	1.15009	−	1.99201i
$429$	795050.	+	1.37707e6i	0.208570	+	0.361253i
$430$	80857.9	+	58746.7i	0.0210888	+	0.0153219i
$431$	2.40247e6	+	510662.i	0.622968	+	0.132416i	0.508572	−	0.861019i	$-0.330174\pi$
$431$	2.40247e6	+	510662.i	0.622968	+	0.132416i	0.114396	+	0.993435i	$0.463507\pi$
$432$	355061.	−	1.09277e6i	0.0915364	−	0.281720i
$433$	4.60539e6			1.18045			0.590223	−	0.807240i	$-0.299040\pi$
$433$	4.60539e6			1.18045			0.590223	+	0.807240i	$0.299040\pi$
$434$	2.13507e6	−	3.77737e6i	0.544112	−	0.962644i
$435$	174066.			0.0441054
$436$	259409.	−	798380.i	0.0653536	−	0.201138i
$437$	5.87723e6	+	1.24924e6i	1.47221	+	0.312927i
$438$	−1.82191e6	−	1.32369e6i	−0.453776	−	0.329688i
$439$	−173966.	−	301318.i	−0.0430827	−	0.0746214i	0.843680	−	0.536846i	$-0.180385\pi$
$439$	−173966.	−	301318.i	−0.0430827	−	0.0746214i	−0.886763	+	0.462225i	$0.847051\pi$
$440$	12326.5	−	21350.1i	0.00303534	−	0.00525735i
$441$	−1.12638e6	+	501496.i	−0.275796	+	0.122792i
$442$	3.72314e6	−	2.70502e6i	0.906470	−	0.658589i
$443$	2.98868e6	+	1.33065e6i	0.723552	+	0.322146i	0.735260	−	0.677785i	$-0.237060\pi$
$443$	2.98868e6	+	1.33065e6i	0.723552	+	0.322146i	−0.0117078	+	0.999931i	$0.503727\pi$
$444$	854224.	−	181571.i	0.205643	−	0.0437108i
$445$	−9726.64	+	92542.8i	−0.00232843	+	0.0221535i
$446$	−3.63211e6	−	4.03387e6i	−0.864614	−	0.960251i
$447$	−1.02377e6	+	1.13701e6i	−0.242345	+	0.269152i
$448$	468689.	+	4.45928e6i	0.110329	+	1.04971i
$449$	−1.47060e6	−	4.52605e6i	−0.344254	−	1.05951i	−0.961982	−	0.273114i	$-0.911946\pi$
$449$	−1.47060e6	−	4.52605e6i	−0.344254	−	1.05951i	0.617727	−	0.786392i	$-0.288054\pi$
$450$	1.31091e6	+	4.03456e6i	0.305170	+	0.939215i
$451$	−22635.3	−	215360.i	−0.00524015	−	0.0498567i
$452$	−4.26265e6	+	4.73415e6i	−0.981371	+	1.08992i
$453$	6.66103e6	+	7.39783e6i	1.52509	+	1.69379i
$454$	−430364.	+	4.09464e6i	−0.0979932	+	0.932343i
$455$	84673.0	−	17997.8i	0.0191742	−	0.00407560i
$456$	2.54302e6	+	1.13223e6i	0.572714	+	0.254989i
$457$	4.06033e6	−	2.95000e6i	0.909433	−	0.660742i	−0.0314386	−	0.999506i	$-0.510009\pi$
$457$	4.06033e6	−	2.95000e6i	0.909433	−	0.660742i	0.940871	+	0.338764i	$0.110009\pi$
$458$	−1.12998e7	+	5.03101e6i	−2.51715	+	1.12071i
$459$	993831.	−	1.72137e6i	0.220182	−	0.381366i
$460$	123526.	+	213953.i	0.0272185	+	0.0471437i
$461$	−3.22308e6	−	2.34170e6i	−0.706348	−	0.513192i	0.175646	−	0.984453i	$-0.443799\pi$
$461$	−3.22308e6	−	2.34170e6i	−0.706348	−	0.513192i	−0.881993	+	0.471262i	$0.843799\pi$
$462$	−2.77531e6	−	589911.i	−0.604932	−	0.128582i
$463$	−2.22504e6	+	6.84798e6i	−0.482377	+	1.48460i	0.353368	+	0.935484i	$0.385036\pi$
$463$	−2.22504e6	+	6.84798e6i	−0.482377	+	1.48460i	−0.835745	+	0.549118i	$0.814964\pi$
$464$	2.98844e6			0.644390
$465$	−64421.1	+	204613.i	−0.0138164	+	0.0438834i
$466$	2.80474e6			0.598313
$467$	−1.19320e6	+	3.67230e6i	−0.253175	+	0.779194i	0.741008	+	0.671496i	$0.234348\pi$
$467$	−1.19320e6	+	3.67230e6i	−0.253175	+	0.779194i	−0.994184	+	0.107698i	$0.965652\pi$
$468$	−2.86505e6	−	608985.i	−0.604669	−	0.128526i
$469$	−3.40921e6	−	2.47693e6i	−0.715684	−	0.519975i
$470$	230926.	+	399976.i	0.0482202	+	0.0835198i
$471$	−3.50656e6	+	6.07354e6i	−0.728331	+	1.26151i
$472$	−275235.	+	122543.i	−0.0568655	+	0.0253182i
$473$	−829750.	+	602848.i	−0.170527	+	0.123895i
$474$	1.92937e6	+	859011.i	0.394430	+	0.175612i
$475$	−5.98059e6	+	1.27121e6i	−1.21621	+	0.258514i
$476$	−478579.	+	4.55338e6i	−0.0968136	+	0.921120i
$477$	4.13446e6	+	4.59179e6i	0.832000	+	0.924030i
$478$	5.96777e6	−	6.62788e6i	1.19465	−	1.32680i
$479$	−890216.	−	8.46984e6i	−0.177279	−	1.68669i	−0.615745	−	0.787946i	$-0.711145\pi$
$479$	−890216.	−	8.46984e6i	−0.177279	−	1.68669i	0.438466	−	0.898748i	$-0.355522\pi$
$480$	−100587.	−	309576.i	−0.0199269	−	0.0613288i
$481$	−151538.	−	466387.i	−0.0298648	−	0.0919145i
$482$	1.07279e6	+	1.02069e7i	0.210328	+	2.00114i
$483$	3.92770e6	−	4.36215e6i	0.766073	−	0.850811i
$484$	−3.52558e6	−	3.91556e6i	−0.684097	−	0.759767i
$485$	−8251.42	+	78507.0i	−0.00159285	+	0.0151549i
$486$	−8.70375e6	+	1.85004e6i	−1.67154	+	0.355296i
$487$	5.52485e6	+	2.45982e6i	1.05560	+	0.469982i	0.859783	−	0.510659i	$-0.170599\pi$
$487$	5.52485e6	+	2.45982e6i	1.05560	+	0.469982i	0.195814	+	0.980641i	$0.437265\pi$
$488$	−1.09837e6	+	798015.i	−0.208786	+	0.151692i
$489$	2.45903e6	−	1.09483e6i	0.465041	−	0.207050i
$490$	65525.2	−	113493.i	0.0123287	−	0.0213540i
$491$	−4.27420e6	−	7.40314e6i	−0.800113	−	1.38584i	−0.919541	−	0.392994i	$-0.871439\pi$
$491$	−4.27420e6	−	7.40314e6i	−0.800113	−	1.38584i	0.119428	−	0.992843i	$-0.461894\pi$
$492$	813354.	+	590936.i	0.151484	+	0.110060i
$493$	5.05674e6	+	1.07484e6i	0.937029	+	0.199172i
$494$	2.33978e6	−	7.20110e6i	0.431378	−	1.32764i
$495$	55655.0			0.0102092
$496$	−1.10601e6	+	3.51287e6i	−0.201861	+	0.641147i
$497$	−6.72189e6			−1.22068
$498$	2.31629e6	−	7.12882e6i	0.418524	−	1.28808i
$499$	2.55031e6	+	542085.i	0.458502	+	0.0974577i	0.431372	−	0.902174i	$-0.358030\pi$
$499$	2.55031e6	+	542085.i	0.458502	+	0.0974577i	0.0271304	+	0.999632i	$0.491363\pi$
$500$	−407028.	−	295723.i	−0.0728114	−	0.0529006i
$501$	−3.47863e6	−	6.02516e6i	−0.619175	−	1.07244i
$502$	−3.14059e6	+	5.43967e6i	−0.556228	+	0.963414i
$503$	−2.96093e6	+	1.31829e6i	−0.521805	+	0.232322i	−0.650699	−	0.759336i	$-0.725524\pi$
$503$	−2.96093e6	+	1.31829e6i	−0.521805	+	0.232322i	0.128894	+	0.991658i	$0.458857\pi$
$504$	872908.	−	634205.i	0.153071	−	0.111212i
$505$	−206142.	−	91780.3i	−0.0359698	−	0.0160148i
$506$	−4.44767e6	+	945381.i	−0.772246	+	0.164146i
$507$	345638.	−	3.28852e6i	0.0597175	−	0.568174i
$508$	2.45180e6	+	2.72300e6i	0.421527	+	0.468153i
$509$	−5.34326e6	+	5.93429e6i	−0.914139	+	1.01525i	0.0856823	+	0.996323i	$0.472693\pi$
$509$	−5.34326e6	+	5.93429e6i	−0.914139	+	1.01525i	−0.999821	+	0.0189311i	$0.993974\pi$
$510$	−42435.9	−	403751.i	−0.00722450	−	0.0687365i
$511$	−388770.	−	1.19651e6i	−0.0658628	−	0.202705i
$512$	−2.20879e6	−	6.79797e6i	−0.372375	−	1.14605i
$513$	−341836.	−	3.25236e6i	−0.0573489	−	0.545638i
$514$	3.78136e6	−	4.19962e6i	0.631306	−	0.701136i
$515$	122347.	+	135880.i	0.0203270	+	0.0225755i
$516$	497731.	−	4.73560e6i	0.0822945	−	0.782980i
$517$	−4.63588e6	+	985387.i	−0.762792	+	0.162136i
$518$	799380.	+	355907.i	0.130897	+	0.0582790i
$519$	1.27181e6	−	924025.i	0.207255	−	0.150579i
$520$	58714.1	−	26141.2i	0.00952213	−	0.00423953i
$521$	−2.82146e6	+	4.88692e6i	−0.455386	+	0.788752i	−0.998710	−	0.0507707i	$-0.983832\pi$
$521$	−2.82146e6	+	4.88692e6i	−0.455386	+	0.788752i	0.543324	+	0.839523i	$0.317166\pi$
$522$	−2.95072e6	−	5.11079e6i	−0.473971	−	0.820941i
$523$	4.02359e6	+	2.92331e6i	0.643219	+	0.467326i	0.860955	−	0.508682i	$-0.169867\pi$
$523$	4.02359e6	+	2.92331e6i	0.643219	+	0.467326i	−0.217735	+	0.976008i	$0.569867\pi$
$524$	−3.11690e6	−	662518.i	−0.495901	−	0.105407i
$525$	−1.84578e6	+	5.68074e6i	−0.292269	+	0.899511i
$526$	3.12889e6			0.493089
$527$	−3.13494e6	+	5.54633e6i	−0.491702	+	0.869920i
$528$	2.40825e6			0.375938
$529$	917960.	−	2.82519e6i	0.142621	−	0.438944i
$530$	−642387.	−	136544.i	−0.0993362	−	0.0211146i
$531$	−550259.	−	399787.i	−0.0846898	−	0.0615307i
$532$	3.76643e6	+	6.52365e6i	0.576967	+	0.999337i
$533$	282270.	−	488906.i	0.0430375	−	0.0745431i
$534$	7.26389e6	−	3.23409e6i	1.10234	−	0.490794i
$535$	−349340.	+	253810.i	−0.0527672	+	0.0383376i
$536$	−2.85823e6	−	1.27257e6i	−0.429720	−	0.191324i
$537$	1.60331e7	−	3.40794e6i	2.39929	−	0.509984i
$538$	−1.82939e6	+	1.74055e7i	−0.272490	+	2.59257i
$539$	899858.	+	999393.i	0.133414	+	0.148171i
$540$	89973.5	−	99925.6i	0.0132779	−	0.0147466i
$541$	1.08413e6	+	1.03148e7i	0.159254	+	1.51520i	0.723924	+	0.689880i	$0.242337\pi$
$541$	1.08413e6	+	1.03148e7i	0.159254	+	1.51520i	−0.564670	+	0.825317i	$0.690997\pi$
$542$	2.05250e6	+	6.31694e6i	0.300113	+	0.923652i
$543$	3.02257e6	+	9.30250e6i	0.439922	+	1.35394i
$544$	−1.01053e6	−	9.61452e6i	−0.146403	−	1.39293i
$545$	−27825.0	+	30902.7i	−0.00401276	+	0.00445662i
$546$	−4.94951e6	−	5.49699e6i	−0.710527	−	0.789120i
$547$	325274.	−	3.09478e6i	0.0464816	−	0.442243i	−0.946387	−	0.323034i	$-0.895297\pi$
$547$	325274.	−	3.09478e6i	0.0464816	−	0.442243i	0.992869	−	0.119210i	$-0.0380361\pi$
$548$	5.72175e6	−	1.21620e6i	0.813913	−	0.173002i
$549$	−2.80000e6	−	1.24664e6i	−0.396486	−	0.176527i
$550$	3.74332e6	−	2.71968e6i	0.527655	−	0.383364i
$551$	7.77029e6	−	3.45956e6i	1.09033	−	0.485447i
$552$	2.17906e6	−	3.77424e6i	0.304384	−	0.527208i
$553$	589924.	+	1.02178e6i	0.0820320	+	0.142084i
$554$	−8.57555e6	−	6.23050e6i	−1.18710	−	0.862480i
$555$	−42314.8	−	8994.28i	−0.00583122	−	0.00123946i
$556$	3.40313e6	−	1.04738e7i	0.466866	−	1.43687i
$557$	8.47139e6			1.15695			0.578477	−	0.815698i	$-0.303647\pi$
$557$	8.47139e6			1.15695			0.578477	+	0.815698i	$0.303647\pi$
$558$	7.09971e6	−	1.57705e6i	0.965285	−	0.214417i
$559$	−2.67383e6			−0.361913
$560$	40513.5	−	124688.i	0.00545921	−	0.0168017i
$561$	4.07500e6	+	866168.i	0.546664	+	0.116197i
$562$	7.69842e6	+	5.59323e6i	1.02816	+	0.747002i
$563$	−1.34839e6	−	2.33547e6i	−0.179285	−	0.310530i	0.762351	−	0.647164i	$-0.224045\pi$
$563$	−1.34839e6	−	2.33547e6i	−0.179285	−	0.310530i	−0.941636	+	0.336634i	$0.890712\pi$
$564$	1.10019e7	−	1.90559e7i	1.45637	−	2.52250i
$565$	288283.	−	128352.i	0.0379925	−	0.0169154i
$566$	−9.69064e6	+	7.04066e6i	−1.27149	+	0.923789i
$567$	−6.30182e6	−	2.80575e6i	−0.823206	−	0.366515i
$568$	−4.88166e6	+	1.03763e6i	−0.634888	+	0.134950i
$569$	147411.	−	1.40252e6i	0.0190875	−	0.181606i	−0.980824	−	0.194895i	$-0.937563\pi$
$569$	147411.	−	1.40252e6i	0.0190875	−	0.181606i	0.999912	+	0.0132890i	$0.00423015\pi$
$570$	−446942.	−	496379.i	−0.0576187	−	0.0639921i
$571$	905950.	−	1.00616e6i	0.116282	−	0.129145i	−0.682193	−	0.731172i	$-0.738974\pi$
$571$	905950.	−	1.00616e6i	0.116282	−	0.129145i	0.798475	+	0.602028i	$0.205640\pi$
$572$	333942.	+	3.17725e6i	0.0426758	+	0.406033i
$573$	2.63578e6	+	8.11210e6i	0.335369	+	1.03216i
$574$	311286.	+	958041.i	0.0394349	+	0.121368i
$575$	1.00058e6	+	9.51992e6i	0.126207	+	1.20078i
$576$	−5.02885e6	+	5.58510e6i	−0.631557	+	0.701415i
$577$	−8.41261e6	−	9.34315e6i	−1.05194	−	1.16830i	−0.985355	−	0.170518i	$-0.945456\pi$
$577$	−8.41261e6	−	9.34315e6i	−1.05194	−	1.16830i	−0.0665862	−	0.997781i	$-0.521211\pi$
$578$	−1852.24	+	17622.9i	−0.000230610	+	0.00219410i
$579$	−1.74899e7	+	3.71759e6i	−2.16815	+	0.460855i
$580$	319490.	+	142246.i	0.0394355	+	0.0175578i
$581$	3.38774e6	−	2.46134e6i	0.416361	−	0.302504i
$582$	6.16219e6	−	2.74358e6i	0.754097	−	0.335746i
$583$	3.36967e6	−	5.83644e6i	0.410597	−	0.711175i
$584$	−467037.	−	808933.i	−0.0566656	−	0.0981477i
$585$	117383.	+	85283.9i	0.0141813	+	0.0103033i
$586$	9.40535e6	+	1.99917e6i	1.13144	+	0.240495i
$587$	2.24573e6	−	6.91165e6i	0.269006	−	0.827916i	−0.721737	−	0.692167i	$-0.756656\pi$
$587$	2.24573e6	−	6.91165e6i	0.269006	−	0.827916i	0.990743	−	0.135749i	$-0.0433441\pi$
$588$	−6.24359e6			−0.744716
$589$	1.19092e6	+	1.04142e7i	0.141447	+	1.23691i
$590$	72292.6			0.00854996
$591$	136036.	−	418676.i	0.0160208	−	0.0493070i
$592$	−726476.	−	154417.i	−0.0851956	−	0.0181089i
$593$	−3.88693e6	−	2.82402e6i	−0.453910	−	0.329785i	0.337227	−	0.941423i	$-0.390511\pi$
$593$	−3.88693e6	−	2.82402e6i	−0.453910	−	0.329785i	−0.791138	+	0.611638i	$0.790511\pi$
$594$	1.23741e6	+	2.14326e6i	0.143895	+	0.249234i
$595$	113399.	−	196413.i	0.0131316	−	0.0227446i
$596$	−2.80824e6	+	1.25031e6i	−0.323832	+	0.144179i
$597$	−6.45445e6	+	4.68943e6i	−0.741179	+	0.538498i
$598$	−1.08293e7	−	4.82153e6i	−1.23837	−	0.551356i
$599$	−246760.	+	52450.5i	−0.0281001	+	0.00597287i	−0.221940	−	0.975060i	$-0.571239\pi$
$599$	−246760.	+	52450.5i	−0.0281001	+	0.00597287i	0.193840	+	0.981033i	$0.437906\pi$
$600$	−463559.	+	4.41047e6i	−0.0525686	+	0.500157i
$601$	−8.18491e6	−	9.09026e6i	−0.924331	−	1.02657i	−0.999567	−	0.0294082i	$-0.990638\pi$
$601$	−8.18491e6	−	9.09026e6i	−0.924331	−	1.02657i	0.0752361	−	0.997166i	$-0.476029\pi$
$602$	3.19247e6	−	3.54560e6i	0.359034	−	0.398748i
$603$	−738308.	−	7.02453e6i	−0.0826884	−	0.786727i
$604$	6.18052e6	+	1.90217e7i	0.689339	+	2.12157i
$605$	80653.4	+	248226.i	0.00895848	+	0.0275714i
$606$	2.01549e6	+	1.91762e7i	0.222946	+	2.12119i
$607$	−3.63085e6	+	4.03247e6i	−0.399979	+	0.444222i	−0.909166	−	0.416434i	$-0.863280\pi$
$607$	−3.63085e6	+	4.03247e6i	−0.399979	+	0.444222i	0.509187	+	0.860656i	$0.329946\pi$
$608$	−1.06430e7	−	1.18203e7i	−1.16763	−	1.29679i
$609$	868562.	−	8.26381e6i	0.0948981	−	0.902895i
$610$	318652.	−	67731.7i	0.0346731	−	0.00736999i
$611$	−1.12876e7	−	5.02557e6i	−1.22321	−	0.544606i
$612$	−6.20847e6	+	4.51072e6i	−0.670048	+	0.486818i
$613$	1.00594e7	−	4.47871e6i	1.08123	−	0.481396i	0.212745	−	0.977108i	$-0.431759\pi$
$613$	1.00594e7	−	4.47871e6i	1.08123	−	0.481396i	0.868487	+	0.495712i	$0.165093\pi$
$614$	−1.22922e7	+	2.12908e7i	−1.31586	+	2.27914i
$615$	−24900.7	−	43129.4i	−0.00265476	−	0.00459817i
$616$	−952089.	−	691733.i	−0.101094	−	0.0734492i
$617$	−1.61785e6	−	343885.i	−0.171090	−	0.0363664i	0.121570	−	0.992583i	$-0.461207\pi$
$617$	−1.61785e6	−	343885.i	−0.171090	−	0.0363664i	−0.292660	+	0.956217i	$0.594540\pi$
$618$	4.82808e6	−	1.48593e7i	0.508514	−	1.56505i
$619$	−1.00042e7			−1.04943			−0.524716	−	0.851277i	$-0.675828\pi$
$619$	−1.00042e7			−1.04943			−0.524716	+	0.851277i	$0.675828\pi$
$620$	−285450.	+	322911.i	−0.0298230	+	0.0337368i
$621$	−5.11992e6			−0.532763
$622$	−2.81907e6	+	8.67622e6i	−0.292167	+	0.899196i
$623$	4.34495e6	+	923547.i	0.448502	+	0.0953320i
$624$	5.07929e6	+	3.69032e6i	0.522206	+	0.379405i
$625$	−4.86412e6	−	8.42490e6i	−0.498086	−	0.862710i
$626$	9.62766e6	−	1.66756e7i	0.981939	−	1.70077i
$627$	6.26173e6	−	2.78790e6i	0.636101	−	0.283210i
$628$	−1.13994e7	+	8.28213e6i	−1.15341	+	0.837998i
$629$	−1.17373e6	−	522580.i	−0.118289	−	0.0526655i
$630$	−253242.	+	53828.2i	−0.0254205	+	0.00540330i
$631$	−341267.	+	3.24694e6i	−0.0341209	+	0.324639i	0.964126	+	0.265446i	$0.0855193\pi$
$631$	−341267.	+	3.24694e6i	−0.0341209	+	0.324639i	−0.998247	+	0.0591926i	$0.981147\pi$
$632$	586150.	+	650986.i	0.0583736	+	0.0648304i
$633$	−1.44519e7	+	1.60505e7i	−1.43356	+	1.59213i
$634$	−1.98917e6	−	1.89257e7i	−0.196539	−	1.86994i
$635$	−56088.9	−	172624.i	−0.00552004	−	0.0169889i
$636$	9.66876e6	+	2.97574e7i	0.947824	+	2.91710i
$637$	366473.	+	3.48676e6i	0.0357843	+	0.340465i
$638$	−4.30703e6	+	4.78344e6i	−0.418915	+	0.465252i
$639$	−7.53894e6	−	8.37284e6i	−0.730395	−	0.811186i
$640$	29249.7	−	278293.i	0.00282275	−	0.0268567i
$641$	7.39427e6	−	1.57170e6i	0.710804	−	0.151086i	0.161700	−	0.986840i	$-0.448302\pi$
$641$	7.39427e6	−	1.57170e6i	0.710804	−	0.151086i	0.549104	+	0.835754i	$0.314969\pi$
$642$	3.37079e7	+	1.50077e7i	3.22771	+	1.43707i
$643$	1.09681e7	−	7.96878e6i	1.04617	−	0.760089i	0.0746913	−	0.997207i	$-0.476203\pi$
$643$	1.09681e7	−	7.96878e6i	1.04617	−	0.760089i	0.971481	+	0.237118i	$0.0762029\pi$
$644$	1.07738e7	−	4.79681e6i	1.02366	−	0.455762i
$645$	−117937.	+	204273.i	−0.0111622	+	0.0193336i
$646$	−9.91885e6	−	1.71800e7i	−0.935148	−	1.61972i
$647$	1.86390e6	+	1.35420e6i	0.175050	+	0.127181i	0.671860	−	0.740678i	$-0.265496\pi$
$647$	1.86390e6	+	1.35420e6i	0.175050	+	0.127181i	−0.496811	+	0.867859i	$0.665496\pi$
$648$	−5.00970e6	−	1.06485e6i	−0.468678	−	0.0996206i
$649$	−229246.	+	705545.i	−0.0213643	+	0.0657526i
$650$	1.20627e7			1.11985
$651$	9.39255e6	+	4.07938e6i	0.868622	+	0.377261i
$652$	5.40811e6			0.498226
$653$	−3.25000e6	+	1.00025e7i	−0.298264	+	0.917962i	0.683842	+	0.729631i	$0.260308\pi$
$653$	−3.25000e6	+	1.00025e7i	−0.298264	+	0.917962i	−0.982106	+	0.188332i	$0.939692\pi$
$654$	3.47567e6	+	738777.i	0.317756	+	0.0675412i
$655$	127702.	+	92780.7i	0.0116304	+	0.00844996i
$656$	−427506.	−	740461.i	−0.0387866	−	0.0671804i
$657$	1.05436e6	−	1.82620e6i	0.0952959	−	0.165057i
$658$	2.01412e7	−	8.96744e6i	1.81351	−	0.807428i
$659$	−9.21217e6	+	6.69303e6i	−0.826320	+	0.600357i	−0.918516	−	0.395384i	$-0.870611\pi$
$659$	−9.21217e6	+	6.69303e6i	−0.826320	+	0.600357i	0.0921958	+	0.995741i	$0.470611\pi$
$660$	257463.	+	114630.i	0.0230067	+	0.0102432i
$661$	−5.47421e6	+	1.16358e6i	−0.487324	+	0.103584i	−0.445019	−	0.895521i	$-0.646803\pi$
$661$	−5.47421e6	+	1.16358e6i	−0.487324	+	0.103584i	−0.0423044	+	0.999105i	$0.513470\pi$
$662$	−2.41462e6	+	2.29736e7i	−0.214143	+	2.03743i
$663$	7.26739e6	+	8.07125e6i	0.642088	+	0.713111i
$664$	2.08034e6	−	2.31045e6i	0.183111	−	0.203366i
$665$	−39004.5	−	371103.i	−0.00342028	−	0.0325417i
$666$	453224.	+	1.39488e6i	0.0395938	+	0.121857i
$667$	−4.11499e6	−	1.26646e7i	−0.358141	−	1.10225i
$668$	−1.46112e6	−	1.39016e7i	−0.126690	−	1.20538i
$669$	8.57186e6	−	9.52002e6i	0.740474	−	0.822380i
$670$	502341.	+	557906.i	0.0432326	+	0.0480147i
$671$	−349439.	+	3.32469e6i	−0.0299616	+	0.285066i
$672$	−1.51991e7	+	3.23067e6i	−1.29836	+	0.275974i
$673$	−1.86831e6	−	831824.i	−0.159005	−	0.0707935i	0.325691	−	0.945476i	$-0.394403\pi$
$673$	−1.86831e6	−	831824.i	−0.159005	−	0.0707935i	−0.484696	+	0.874683i	$0.661070\pi$
$674$	1.26376e7	−	9.18177e6i	1.07156	−	0.778533i
$675$	4.75954e6	−	2.11908e6i	0.402073	−	0.179015i
$676$	3.32177e6	−	5.75347e6i	0.279578	−	0.484243i
$677$	9.94380e6	+	1.72232e7i	0.833837	+	1.44425i	0.894974	+	0.446118i	$0.147194\pi$
$677$	9.94380e6	+	1.72232e7i	0.833837	+	1.44425i	−0.0611377	+	0.998129i	$0.519473\pi$
$678$	−2.18151e7	−	1.58496e7i	−1.82257	−	1.32417i
$679$	3.68595e6	+	783474.i	0.306814	+	0.0652154i
$680$	52034.8	−	160147.i	0.00431540	−	0.0132814i
$681$	−9.71666e6			−0.802877
$682$	−4.02886e6	−	6.83318e6i	−0.331681	−	0.562551i
$683$	5.73572e6			0.470474			0.235237	−	0.971938i	$-0.424413\pi$
$683$	5.73572e6			0.470474			0.235237	+	0.971938i	$0.424413\pi$
$684$	−3.90167e6	+	1.20081e7i	−0.318867	+	0.981373i
$685$	−283432.	−	60245.4i	−0.0230793	−	0.00490566i
$686$	−1.60876e7	−	1.16883e7i	−1.30521	−	0.948290i
$687$	−1.45958e7	−	2.52807e7i	−1.17988	−	2.04360i
$688$	−2.02479e6	+	3.50704e6i	−0.163083	+	0.282468i
$689$	1.60506e7	−	7.14619e6i	1.28808	−	0.573491i
$690$	−846013.	+	614664.i	−0.0676479	+	0.0491491i
$691$	1.79673e6	+	799954.i	0.143148	+	0.0637338i	0.477061	−	0.878870i	$-0.341702\pi$
$691$	1.79673e6	+	799954.i	0.143148	+	0.0637338i	−0.333912	+	0.942604i	$0.608369\pi$
$692$	3.08945e6	−	656683.i	0.245254	−	0.0521304i
$693$	277709.	−	2.64223e6i	0.0219663	−	0.208996i
$694$	−6.94085e6	−	7.70859e6i	−0.547033	−	0.607542i
$695$	−365030.	+	405406.i	−0.0286659	+	0.0318367i
$696$	−644870.	−	6.13553e6i	−0.0504602	−	0.480097i
$697$	−457063.	−	1.40670e6i	−0.0356364	−	0.109678i
$698$	−3.97792e6	−	1.22428e7i	−0.309042	−	0.951134i
$699$	691900.	+	6.58299e6i	0.0535612	+	0.509601i
$700$	−8.03011e6	+	8.91835e6i	−0.619408	+	0.687922i
$701$	3.59975e6	+	3.99793e6i	0.276680	+	0.307284i	0.865429	−	0.501032i	$-0.167046\pi$
$701$	3.59975e6	+	3.99793e6i	0.276680	+	0.307284i	−0.588749	+	0.808316i	$0.700379\pi$
$702$	−674407.	+	6.41655e6i	−0.0516510	+	0.491427i
$703$	−2.06769e6	+	439500.i	−0.157796	+	0.0335406i
$704$	7.48853e6	+	3.33411e6i	0.569462	+	0.253541i
$705$	−881814.	+	640676.i	−0.0668197	+	0.0485473i
$706$	7.75920e6	−	3.45462e6i	0.585875	−	0.260848i
$707$	−5.38590e6	+	9.32864e6i	−0.405237	+	0.701892i
$708$	−1.72210e6	−	2.98277e6i	−0.129115	−	0.223634i
$709$	−1.49589e6	−	1.08683e6i	−0.111760	−	0.0811982i	0.530502	−	0.847684i	$-0.322004\pi$
$709$	−1.49589e6	−	1.08683e6i	−0.111760	−	0.0811982i	−0.642261	+	0.766486i	$0.722004\pi$
$710$	1.17135e6	+	248979.i	0.0872052	+	0.0185360i
$711$	−611106.	+	1.88079e6i	−0.0453359	+	0.139530i
$712$	3.29801e6			0.243810
$713$	1.64101e7	−	149996.i	1.20889	−	0.0110498i
$714$	−1.93798e7			−1.42267
$715$	48903.5	−	150509.i	0.00357746	−	0.0110103i
$716$	3.22129e7	+	6.84707e6i	2.34827	+	0.499139i
$717$	1.70284e7	+	1.23719e7i	1.23702	+	0.898748i
$718$	−7.93816e6	−	1.37493e7i	−0.574657	−	0.995335i
$719$	−421601.	+	730234.i	−0.0304144	+	0.0526793i	−0.880832	−	0.473429i	$-0.843016\pi$
$719$	−421601.	+	730234.i	−0.0304144	+	0.0526793i	0.850418	+	0.526108i	$0.176349\pi$
$720$	200750.	−	89379.6i	0.0144319	−	0.00642550i
$721$	7.06139e6	−	5.13040e6i	0.505886	−	0.367547i
$722$	−1.05797e7	−	4.71040e6i	−0.755320	−	0.336290i
$723$	−2.36919e7	+	5.03588e6i	−1.68560	+	0.358286i
$724$	−2.05419e6	+	1.95443e7i	−0.145644	+	1.38571i
$725$	9.06711e6	+	1.00700e7i	0.640654	+	0.711519i
$726$	1.49232e7	−	1.65739e7i	1.05080	−	1.16703i
$727$	−1.88025e6	−	1.78894e7i	−0.131941	−	1.25533i	−0.837403	−	0.546585i	$-0.815927\pi$
$727$	−1.88025e6	−	1.78894e7i	−0.131941	−	1.25533i	0.705463	−	0.708747i	$-0.250739\pi$
$728$	−948083.	−	2.91790e6i	−0.0663007	−	0.204052i
$729$	−1.05708e6	−	3.25334e6i	−0.0736694	−	0.226731i
$730$	23428.1	+	222903.i	0.00162716	+	0.0154814i
$731$	−4.68752e6	+	5.20602e6i	−0.324452	+	0.360340i
$732$	−1.03853e7	−	1.15340e7i	−0.716377	−	0.795617i
$733$	792672.	−	7.54177e6i	0.0544921	−	0.518458i	−0.932897	−	0.360144i	$-0.882728\pi$
$733$	792672.	−	7.54177e6i	0.0544921	−	0.518458i	0.987389	−	0.158314i	$-0.0506058\pi$
$734$	−2.25038e7	+	4.78333e6i	−1.54176	+	0.327711i
$735$	282543.	+	125796.i	0.0192915	+	0.00858913i
$736$	−2.01461e7	+	1.46370e7i	−1.37087	+	0.995996i
$737$	−7.03789e6	+	3.13347e6i	−0.477280	+	0.212499i
$738$	−844220.	+	1.46223e6i	−0.0570577	+	0.0988269i
$739$	1.08076e7	+	1.87193e7i	0.727979	+	1.26090i	0.957736	+	0.287649i	$0.0928736\pi$
$739$	1.08076e7	+	1.87193e7i	0.727979	+	1.26090i	−0.229757	+	0.973248i	$0.573793\pi$
$740$	−70316.6	−	51088.0i	−0.00472039	−	0.00342957i
$741$	1.74789e7	+	3.71525e6i	1.16941	+	0.248566i
$742$	−9.68783e6	+	2.98161e7i	−0.645977	+	1.98811i
$743$	9.52782e6			0.633172			0.316586	−	0.948564i	$-0.397463\pi$
$743$	9.52782e6			0.633172			0.316586	+	0.948564i	$0.397463\pi$
$744$	7.45090e6	+	1.51269e6i	0.493488	+	0.100189i
$745$	152274.			0.0100516
$746$	9.87225e6	−	3.03837e7i	0.649485	−	1.99891i
$747$	6.86538e6	+	1.45928e6i	0.450156	+	0.0956836i
$748$	6.77163e6	+	4.91988e6i	0.442527	+	0.321514i
$749$	1.03065e7	+	1.78514e7i	0.671286	+	1.16270i
$750$	1.06480e6	−	1.84429e6i	0.0691218	−	0.119722i
$751$	2.28657e7	−	1.01805e7i	1.47940	−	0.658671i	0.501010	−	0.865442i	$-0.332962\pi$
$751$	2.28657e7	−	1.01805e7i	1.47940	−	0.658671i	0.978389	+	0.206771i	$0.0662955\pi$
$752$	−1.51393e7	+	1.09994e7i	−0.976252	+	0.709289i
$753$	−1.35422e7	−	6.02936e6i	−0.870363	−	0.387511i
$754$	−1.64140e7	+	3.48891e6i	−1.05145	+	0.223492i
$755$	103561.	−	985321.i	0.00661197	−	0.0629087i
$756$	−4.29503e6	−	4.77011e6i	−0.273314	−	0.303546i
$757$	2.36711e6	−	2.62894e6i	0.150134	−	0.166741i	−0.663387	−	0.748277i	$-0.730881\pi$
$757$	2.36711e6	−	2.62894e6i	0.150134	−	0.166741i	0.813521	+	0.581536i	$0.197548\pi$
$758$	−1.21243e6	−	1.15355e7i	−0.0766452	−	0.729230i
$759$	−3.31609e6	−	1.02059e7i	−0.208940	−	0.643051i
$760$	−85612.0	−	263487.i	−0.00537651	−	0.0165472i
$761$	1.97821e6	+	1.88214e7i	0.123826	+	1.17812i	0.863212	+	0.504842i	$0.168449\pi$
$761$	1.97821e6	+	1.88214e7i	0.123826	+	1.17812i	−0.739386	+	0.673282i	$0.764884\pi$
$762$	−1.03781e7	+	1.15260e7i	−0.647483	+	0.719103i
$763$	1.32827e6	+	1.47519e6i	0.0825990	+	0.0917354i
$764$	−1.79132e6	+	1.70433e7i	−0.111030	+	1.05638i
$765$	371836.	−	79036.2i	0.0229720	−	0.00488284i
$766$	2.54416e7	+	1.13273e7i	1.56665	+	0.697518i
$767$	−1.56466e6	+	1.13679e6i	−0.0960355	+	0.0697739i
$768$	5.74582e6	−	2.55820e6i	0.351519	−	0.156506i
$769$	1.25172e7	−	2.16804e7i	0.763292	−	1.32206i	−0.177853	−	0.984057i	$-0.556915\pi$
$769$	1.25172e7	−	2.16804e7i	0.763292	−	1.32206i	0.941145	−	0.338004i	$-0.109752\pi$
$770$	141192.	+	244552.i	0.00858190	+	0.0148643i
$771$	1.07897e7	+	7.83920e6i	0.653694	+	0.474937i
$772$	−3.51398e7	−	7.46919e6i	−2.12205	−	0.451056i
$773$	5.96428e6	−	1.83562e7i	0.359012	−	1.10493i	−0.594634	−	0.803997i	$-0.702703\pi$
$773$	5.96428e6	−	1.83562e7i	0.359012	−	1.10493i	0.953646	−	0.300930i	$-0.0972971\pi$
$774$	7.99694e6			0.479813
$775$	−1.51929e7	+	6.93139e6i	−0.908628	+	0.414540i
$776$	2.79780e6			0.166787
$777$	−638148.	+	1.96402e6i	−0.0379201	+	0.116706i
$778$	8.79071e6	+	1.86852e6i	0.520685	+	0.110675i
$779$	−1.96876e6	−	1.43039e6i	−0.116238	−	0.0844520i
$780$	367365.	+	636296.i	0.0216203	+	0.0374475i
$781$	−6.14438e6	+	1.06424e7i	−0.360455	+	0.624326i
$782$	−2.83727e7	+	1.26323e7i	−1.65914	+	0.738698i
$783$	−5.86354e6	+	4.26011e6i	−0.341787	+	0.248323i
$784$	4.85081e6	+	2.15972e6i	0.281854	+	0.125489i
$785$	682729.	−	145118.i	0.0395434	−	0.00840521i
$786$	1.40989e6	−	1.34142e7i	0.0814007	−	0.774476i
$787$	1.71609e7	+	1.90591e7i	0.987649	+	1.09689i	0.995292	+	0.0969241i	$0.0309004\pi$
$787$	1.71609e7	+	1.90591e7i	0.987649	+	1.09689i	−0.00764322	+	0.999971i	$0.502433\pi$
$788$	591827.	−	657290.i	0.0339531	−	0.0377087i
$789$	771864.	+	7.34379e6i	0.0441416	+	0.419979i
$790$	−64953.2	−	199905.i	−0.00370282	−	0.0113961i
$791$	−4.65504e6	−	1.43267e7i	−0.264534	−	0.814152i
$792$	−206187.	−	1.96174e6i	−0.0116802	−	0.111129i
$793$	−5.83166e6	+	6.47672e6i	−0.329313	+	0.365740i
$794$	5.17711e6	+	5.74976e6i	0.291431	+	0.323667i
$795$	162011.	−	1.54143e6i	0.00909129	−	0.0864978i
$796$	−1.56790e7	+	3.33267e6i	−0.877072	+	0.186428i
$797$	−1.59032e7	−	7.08058e6i	−0.886829	−	0.394842i	−0.0878026	−	0.996138i	$-0.527984\pi$
$797$	−1.59032e7	−	7.08058e6i	−0.886829	−	0.394842i	−0.799026	+	0.601296i	$0.794651\pi$
$798$	−2.57958e7	+	1.87417e7i	−1.43398	+	1.04184i
$799$	−2.95734e7	+	1.31669e7i	−1.63883	+	0.729655i
$800$	1.26699e7	−	2.19450e7i	0.699922	−	1.21230i
$801$	3.72270e6	+	6.44790e6i	0.205011	+	0.355089i
$802$	−7.93149e6	−	5.76256e6i	−0.435430	−	0.316359i
$803$	−2.24973e6	−	478195.i	−0.123124	−	0.0261708i
$804$	1.10526e7	−	3.40165e7i	0.603011	−	1.85588i
$805$	−584198.			−0.0317739
$806$	1.97358e6	−	2.05857e7i	0.107008	−	1.11616i
$807$	−4.13036e7			−2.23256
$808$	−2.47139e6	+	7.60617e6i	−0.133172	+	0.409862i
$809$	1.66124e7	+	3.53108e6i	0.892406	+	0.189687i	0.631222	−	0.775602i	$-0.282554\pi$
$809$	1.66124e7	+	3.53108e6i	0.892406	+	0.189687i	0.261184	+	0.965289i	$0.415887\pi$
$810$	994227.	+	722348.i	0.0532443	+	0.0386842i
$811$	−5.61120e6	−	9.71888e6i	−0.299574	−	0.518877i	0.676465	−	0.736475i	$-0.263511\pi$
$811$	−5.61120e6	−	9.71888e6i	−0.299574	−	0.518877i	−0.976038	+	0.217598i	$0.930178\pi$
$812$	8.34735e6	−	1.44580e7i	0.444282	−	0.769518i
$813$	−1.43201e7	+	6.37573e6i	−0.759836	+	0.338301i
$814$	1.29419e6	−	940283.i	0.0684599	−	0.0497390i
$815$	−244735.	−	108963.i	−0.0129063	−	0.00574626i
$816$	1.60897e7	−	3.41998e6i	0.845908	−	0.179803i
$817$	−1.20478e6	+	1.14627e7i	−0.0631470	+	0.600804i
$818$	−1.25697e7	−	1.39601e7i	−0.656812	−	0.729464i
$819$	4.63458e6	−	5.14723e6i	0.241435	−	0.268141i
$820$	−10459.0	−	99510.5i	−0.000543193	−	0.00516814i
$821$	−5.40256e6	−	1.66274e7i	−0.279732	−	0.860926i	−0.987928	−	0.154911i	$-0.950491\pi$
$821$	−5.40256e6	−	1.66274e7i	−0.279732	−	0.860926i	0.708196	−	0.706015i	$-0.249509\pi$
$822$	7.65135e6	+	2.35484e7i	0.394965	+	1.21558i
$823$	−3.18258e6	−	3.02803e7i	−0.163787	−	1.55833i	−0.699934	−	0.714207i	$-0.746787\pi$
$823$	−3.18258e6	−	3.02803e7i	−0.163787	−	1.55833i	0.536147	−	0.844125i	$-0.319879\pi$
$824$	4.33626e6	−	4.81591e6i	0.222483	−	0.247093i
$825$	7.30678e6	+	8.11500e6i	0.373759	+	0.415101i
$826$	360728.	−	3.43210e6i	0.0183963	−	0.175029i
$827$	1.15134e7	−	2.44724e6i	0.585380	−	0.124426i	0.0943048	−	0.995543i	$-0.469937\pi$
$827$	1.15134e7	−	2.44724e6i	0.585380	−	0.124426i	0.491076	+	0.871117i	$0.336604\pi$
$828$	1.80583e7	+	8.04008e6i	0.915380	+	0.407554i
$829$	−2.75744e6	+	2.00340e6i	−0.139354	+	0.101247i	−0.655278	−	0.755388i	$-0.727449\pi$
$829$	−2.75744e6	+	2.00340e6i	−0.139354	+	0.101247i	0.515924	+	0.856634i	$0.327449\pi$
$830$	−681513.	+	303429.i	−0.0343383	+	0.0152884i
$831$	1.25081e7	−	2.16646e7i	0.628330	−	1.08830i
$832$	1.06852e7	+	1.85072e7i	0.535146	+	0.926900i
$833$	7.43128e6	+	5.39914e6i	0.371066	+	0.269595i
$834$	4.55966e7	+	9.69186e6i	2.26996	+	0.482494i
$835$	−213970.	+	658532.i	−0.0106203	+	0.0326859i
$836$	1.37714e7			0.681492
$837$	−2.83763e6	−	8.46915e6i	−0.140005	−	0.417856i
$838$	5.62703e7			2.76802
$839$	9.15334e6	−	2.81711e7i	0.448926	−	1.38165i	−0.429195	−	0.903212i	$-0.641203\pi$
$839$	9.15334e6	−	2.81711e7i	0.448926	−	1.38165i	0.878121	−	0.478439i	$-0.158797\pi$
$840$	−264738.	−	56271.7i	−0.0129455	−	0.00275164i
$841$	1.34341e6	+	976043.i	0.0654965	+	0.0475860i
$842$	1.62696e7	+	2.81798e7i	0.790856	+	1.36980i
$843$	−1.12287e7	+	1.94487e7i	−0.544203	+	0.942588i
$844$	−3.96421e7	+	1.76498e7i	−1.91558	+	0.852871i
$845$	−266242.	+	193436.i	−0.0128273	+	0.00931958i
$846$	3.37593e7	+	1.50306e7i	1.62169	+	0.722022i
$847$	1.21870e7	−	2.59043e6i	0.583698	−	0.124069i
$848$	2.78146e6	−	2.64638e7i	0.132826	−	1.26376i
$849$	−1.89157e7	−	2.10080e7i	−0.900643	−	1.00027i
$850$	2.11472e7	−	2.34864e7i	1.00394	−	1.11498i
$851$	345935.	+	3.29135e6i	0.0163746	+	0.155794i
$852$	−1.76304e7	−	5.42607e7i	−0.832075	−	2.56086i
$853$	6.78352e6	+	2.08775e7i	0.319215	+	0.982442i	0.973985	+	0.226614i	$0.0727654\pi$
$853$	6.78352e6	+	2.08775e7i	0.319215	+	0.982442i	−0.654770	+	0.755828i	$0.727235\pi$
$854$	−1.62554e6	−	1.54660e7i	−0.0762701	−	0.725661i
$855$	418504.	−	464795.i	0.0195787	−	0.0217444i
$856$	1.02406e7	+	1.13733e7i	0.477684	+	0.530522i
$857$	4.25040e6	−	4.04398e7i	0.197687	−	1.88086i	−0.224670	−	0.974435i	$-0.572131\pi$
$857$	4.25040e6	−	4.04398e7i	0.197687	−	1.88086i	0.422357	−	0.906429i	$-0.361203\pi$
$858$	−1.32273e7	+	2.81156e6i	−0.613415	+	0.130385i
$859$	−1.89708e7	−	8.44635e6i	−0.877209	−	0.390559i	−0.0818124	−	0.996648i	$-0.526071\pi$
$859$	−1.89708e7	−	8.44635e6i	−0.877209	−	0.390559i	−0.795397	+	0.606089i	$0.792738\pi$
$860$	−383399.	+	278556.i	−0.0176768	+	0.0128430i
$861$	−2.17182e6	+	966957.i	−0.0998427	+	0.0444528i
$862$	−1.04440e7	+	1.80896e7i	−0.478740	+	0.829202i
$863$	−158184.	−	273982.i	−0.00722994	−	0.0125226i	0.862388	−	0.506248i	$-0.168968\pi$
$863$	−158184.	−	273982.i	−0.00722994	−	0.0125226i	−0.869618	+	0.493726i	$0.835635\pi$
$864$	1.09649e7	+	7.96650e6i	0.499715	+	0.363064i
$865$	−153039.	−	32529.4i	−0.00695443	−	0.00147821i
$866$	−1.21030e7	+	3.72491e7i	−0.548400	+	1.68780i
$867$	−41819.5			−0.00188943
$868$	1.39059e7	+	1.51630e7i	0.626469	+	0.683104i
$869$	2.15696e6			0.0968932
$870$	−457447.	+	1.40788e6i	−0.0204900	+	0.0630618i
$871$	−1.96454e7	−	4.17576e6i	−0.877436	−	0.186505i
$872$	1.19235e6	+	866294.i	0.0531023	+	0.0385811i
$873$	3.15808e6	+	5.46995e6i	0.140245	+	0.242912i
$874$	−2.55495e7	+	4.42530e7i	−1.13137	+	1.95958i
$875$	1.08685e6	−	483896.i	0.0479898	−	0.0213664i
$876$	8.63883e6	−	6.27648e6i	0.380360	−	0.276348i
$877$	−1.19776e7	−	5.33276e6i	−0.525860	−	0.234128i	0.126597	−	0.991954i	$-0.459595\pi$
$877$	−1.19776e7	−	5.33276e6i	−0.525860	−	0.234128i	−0.652456	+	0.757827i	$0.726261\pi$
$878$	2.89429e6	−	615201.i	0.126709	−	0.0269327i
$879$	−2.37203e6	+	2.25684e7i	−0.103550	+	0.985210i
$880$	−160378.	−	178118.i	−0.00698133	−	0.00775355i
$881$	−602412.	+	669047.i	−0.0261489	+	0.0290413i	−0.756077	−	0.654482i	$-0.772887\pi$
$881$	−602412.	+	669047.i	−0.0261489	+	0.0290413i	0.729928	+	0.683524i	$0.239553\pi$
$882$	−1.09605e6	−	1.04283e7i	−0.0474418	−	0.451378i
$883$	4.06442e6	+	1.25090e7i	0.175427	+	0.539909i	0.999653	−	0.0263523i	$-0.00838917\pi$
$883$	4.06442e6	+	1.25090e7i	0.175427	+	0.539909i	−0.824226	+	0.566262i	$0.808389\pi$
$884$	6.74314e6	+	2.07533e7i	0.290223	+	0.893214i
$885$	17833.8	+	169678.i	0.000765396	+	0.00728226i
$886$	−1.86167e7	+	2.06760e7i	−0.796744	+	0.884874i
$887$	1.72073e7	+	1.91106e7i	0.734349	+	0.815578i	0.988442	−	0.151602i	$-0.0484433\pi$
$887$	1.72073e7	+	1.91106e7i	0.734349	+	0.815578i	−0.254092	+	0.967180i	$0.581777\pi$
$888$	−160268.	+	1.52484e6i	−0.00682045	+	0.0648923i
$889$	−8.47520e6	+	1.80146e6i	−0.359663	+	0.0764487i
$890$	−722940.	−	321873.i	−0.0305933	−	0.0136210i
$891$	−1.02026e7	+	7.41261e6i	−0.430542	+	0.312807i
$892$	2.35129e7	−	1.04686e7i	0.989452	−	0.440532i
$893$	−2.66307e7	+	4.61257e7i	−1.11752	+	1.93559i
$894$	−6.50588e6	−	1.12685e7i	−0.272246	−	0.471545i
$895$	−1.31979e6	−	958881.i	−0.0550739	−	0.0400135i
$896$	−1.30660e7	−	2.77727e6i	−0.543718	−	0.115571i
$897$	8.64511e6	−	2.66069e7i	0.358748	−	1.10411i
$898$	4.04722e7			1.67481
$899$	1.86686e7	−	1.38260e7i	0.770395	−	0.570555i
$900$	−2.01149e7			−0.827775
$901$	1.42247e7	−	4.37791e7i	0.583755	−	1.79661i
$902$	1.80135e6	+	382889.i	0.0737195	+	0.0156696i
$903$	9.10941e6	+	6.61837e6i	0.371767	+	0.270104i
$904$	−5.59220e6	−	9.68597e6i	−0.227594	−	0.394205i
$905$	486739.	−	843056.i	0.0197549	−	0.0342165i
$906$	−7.73400e7	+	3.44340e7i	−3.13028	+	1.39369i
$907$	2.38527e7	−	1.73300e7i	0.962763	−	0.699488i	0.00897189	−	0.999960i	$-0.497144\pi$
$907$	2.38527e7	−	1.73300e7i	0.962763	−	0.699488i	0.953791	+	0.300472i	$0.0971441\pi$
$908$	−1.78344e7	−	7.94040e6i	−0.717868	−	0.319616i
$909$	−1.76604e7	+	3.75383e6i	−0.708909	+	0.150683i
$910$	−76951.8	+	732147.i	−0.00308046	+	0.0293086i
$911$	1.16322e7	+	1.29188e7i	0.464370	+	0.515735i	0.929156	−	0.369688i	$-0.120535\pi$
$911$	1.16322e7	+	1.29188e7i	0.464370	+	0.515735i	−0.464786	+	0.885423i	$0.653869\pi$
$912$	1.81091e7	−	2.01122e7i	0.720957	−	0.800704i
$913$	−800209.	−	7.61348e6i	−0.0317707	−	0.302278i
$914$	1.31895e7	+	4.05932e7i	0.522232	+	1.60727i
$915$	237581.	+	731198.i	0.00938120	+	0.0288724i
$916$	−6.13063e6	−	5.83290e7i	−0.241416	−	2.29692i
$917$	5.04198e6	−	5.59969e6i	0.198006	−	0.219908i
$918$	1.13109e7	+	1.25620e7i	0.442986	+	0.491986i
$919$	−1.94458e6	+	1.85015e7i	−0.0759517	+	0.722632i	0.888590	+	0.458702i	$0.151685\pi$
$919$	−1.94458e6	+	1.85015e7i	−0.0759517	+	0.722632i	−0.964542	+	0.263930i	$0.914981\pi$
$920$	−424264.	+	90180.1i	−0.0165260	+	0.00351270i
$921$	−5.30038e7	−	2.35988e7i	−2.05901	−	0.916729i
$922$	2.74103e7	−	1.99148e7i	1.06191	−	0.771522i
$923$	−2.92673e7	+	1.30306e7i	−1.13078	+	0.503456i
$924$	6.72676e6	−	1.16511e7i	0.259194	−	0.448938i
$925$	−1.68384e6	−	2.91650e6i	−0.0647063	−	0.112075i
$926$	−4.95402e7	−	3.59930e7i	−1.89858	−	1.37940i
$927$	1.43102e7	+	3.04172e6i	0.546947	+	0.116257i
$928$	−1.08932e7	+	3.35258e7i	−0.415226	+	1.27793i
$929$	−2.45285e7			−0.932462			−0.466231	−	0.884663i	$-0.654388\pi$
$929$	−2.45285e7			−0.932462			−0.466231	+	0.884663i	$0.654388\pi$
$930$	−1.48564e6	−	1.05877e6i	−0.0563257	−	0.0401416i
$931$	1.51129e7			0.571443
$932$	−4.10964e6	+	1.26482e7i	−0.154976	+	0.476966i
$933$	−2.10593e7	−	4.47630e6i	−0.792028	−	0.168351i
$934$	−2.65664e7	−	1.93016e7i	−0.996473	−	0.723980i
$935$	−207313.	−	359076.i	−0.00775527	−	0.0134325i
$936$	2.57123e6	−	4.45351e6i	0.0959295	−	0.166155i
$937$	−2.73258e7	+	1.21662e7i	−1.01677	+	0.452696i	−0.846323	−	0.532671i	$-0.821188\pi$
$937$	−2.73258e7	+	1.21662e7i	−1.01677	+	0.452696i	−0.170449	+	0.985367i	$0.554522\pi$
$938$	2.89932e7	−	2.10648e7i	1.07594	−	0.781719i
$939$	4.15142e7	+	1.84833e7i	1.53650	+	0.684094i
$940$	−2.14208e6	+	455314.i	−0.0790709	+	0.0168070i
$941$	−2.75204e6	+	2.61839e7i	−0.101317	+	0.963964i	0.819265	+	0.573414i	$0.194382\pi$
$941$	−2.75204e6	+	2.61839e7i	−0.101317	+	0.963964i	−0.920582	+	0.390549i	$0.872285\pi$
$942$	−3.99085e7	−	4.43229e7i	−1.46534	−	1.62742i
$943$	−2.54932e6	+	2.83131e6i	−0.0933568	+	0.103683i
$944$	306178.	+	2.91309e6i	0.0111826	+	0.106396i
$945$	98255.7	+	302400.i	0.00357914	+	0.0110155i
$946$	−2.69535e6	−	8.29544e6i	−0.0979236	−	0.301378i
$947$	−872358.	−	8.29993e6i	−0.0316096	−	0.300746i	−0.998893	−	0.0470462i	$-0.985019\pi$
$947$	−872358.	−	8.29993e6i	−0.0316096	−	0.300746i	0.967283	−	0.253700i	$-0.0816475\pi$
$948$	−6.70077e6	+	7.44196e6i	−0.242161	+	0.268947i
$949$	−4.01219e6	−	4.45599e6i	−0.144616	−	0.160612i
$950$	5.43523e6	−	5.17127e7i	0.195393	−	1.85904i
$951$	4.39296e7	−	9.33753e6i	1.57509	−	0.334796i
$952$	−7.34333e6	−	3.26946e6i	−0.262604	−	0.116919i
$953$	9.58030e6	−	6.96049e6i	0.341701	−	0.248261i	−0.403678	−	0.914901i	$-0.632268\pi$
$953$	9.58030e6	−	6.96049e6i	0.341701	−	0.248261i	0.745379	+	0.666641i	$0.232268\pi$
$954$	−4.80045e7	+	2.13730e7i	−1.70770	+	0.760316i
$955$	424453.	−	735174.i	0.0150599	−	0.0260845i
$956$	2.11446e7	+	3.66235e7i	0.748264	+	1.29603i
$957$	−1.22897e7	−	8.92897e6i	−0.433771	−	0.315153i
$958$	7.08449e7	+	1.50585e7i	2.49399	+	0.530114i
$959$	−4.27444e6	+	1.31554e7i	−0.150083	+	0.461909i
$960$	1.88520e6			0.0660207
$961$	9.34313e6	+	2.70617e7i	0.326350	+	0.945249i
$962$	4.17046e6			0.145293
$963$	−1.06766e7	+	3.28592e7i	−0.370994	+	1.14180i
$964$	−4.76007e7	−	1.01178e7i	−1.64976	−	0.350667i
$965$	1.43970e6	+	1.04600e6i	0.0497685	+	0.0361589i
$966$	2.49598e7	+	4.32316e7i	0.860593	+	1.49059i
$967$	−1.70583e6	+	2.95458e6i	−0.0586636	+	0.101608i	−0.893866	−	0.448335i	$-0.852017\pi$
$967$	−1.70583e6	+	2.95458e6i	−0.0586636	+	0.101608i	0.835202	+	0.549943i	$0.185351\pi$
$968$	8.45073e6	−	3.76251e6i	0.289872	−	0.129059i
$969$	3.78761e7	−	2.75186e7i	1.29585	−	0.941492i
$970$	−613292.	−	273055.i	−0.0209285	−	0.00931797i
$971$	3.12000e6	−	663177.i	0.106196	−	0.0225726i	−0.154507	−	0.987992i	$-0.549379\pi$
$971$	3.12000e6	−	663177.i	0.106196	−	0.0225726i	0.260703	+	0.965419i	$0.416046\pi$
$972$	4.41027e6	−	4.19609e7i	0.149727	−	1.42455i
$973$	1.74253e7	+	1.93527e7i	0.590062	+	0.655330i
$974$	−3.44148e7	+	3.82215e7i	−1.16238	+	1.29095i
$975$	2.97573e6	+	2.83122e7i	0.100250	+	0.953810i
$976$	4.07888e6	+	1.25535e7i	0.137062	+	0.421833i
$977$	9.87088e6	+	3.03794e7i	0.330841	+	1.01822i	0.968735	+	0.248099i	$0.0798060\pi$
$977$	9.87088e6	+	3.03794e7i	0.330841	+	1.01822i	−0.637894	+	0.770125i	$0.720194\pi$
$978$	2.39283e6	+	2.27662e7i	0.0799953	+	0.761104i
$979$	5.43385e6	−	6.03490e6i	0.181197	−	0.201239i
$980$	415793.	+	461785.i	0.0138297	+	0.0153594i
$981$	−347790.	+	3.30900e6i	−0.0115384	+	0.109780i
$982$	7.11104e7	−	1.51150e7i	2.35318	−	0.500183i
$983$	−4.73058e6	−	2.10619e6i	−0.156146	−	0.0695206i	0.327176	−	0.944964i	$-0.393903\pi$
$983$	−4.73058e6	−	2.10619e6i	−0.156146	−	0.0695206i	−0.483321	+	0.875443i	$0.660570\pi$
$984$	−1.42798e6	+	1.03749e6i	−0.0470149	+	0.0341583i
$985$	−40025.3	+	17820.4i	−0.00131445	+	0.000585230i
$986$	−2.19826e7	+	3.80750e7i	−0.720091	+	1.24723i
$987$	2.60160e7	+	4.50611e7i	0.850057	+	1.47234i
$988$	2.90455e7	+	2.11028e7i	0.946643	+	0.687776i
$989$	1.76505e7	+	3.75173e6i	0.573808	+	0.121967i
$990$	−146262.	+	450147.i	−0.00474288	+	0.0145971i
$991$	−2.29296e7			−0.741672			−0.370836	−	0.928698i	$-0.620929\pi$
$991$	−2.29296e7			−0.741672			−0.370836	+	0.928698i	$0.620929\pi$
$992$	−3.53776e7	−	2.52125e7i	−1.14143	−	0.813461i
$993$	−5.45168e7			−1.75452
$994$	1.76652e7	−	5.43678e7i	0.567089	−	1.74532i
$995$	776674.	+	165087.i	0.0248703	+	0.00528634i
$996$	2.87539e7	+	2.08910e7i	0.918437	+	0.667283i
$997$	−1.91587e7	−	3.31838e7i	−0.610418	−	1.05727i	−0.991170	−	0.132598i	$-0.957668\pi$
$997$	−1.91587e7	−	3.31838e7i	−0.610418	−	1.05727i	0.380752	−	0.924677i	$-0.375665\pi$
$998$	−1.10867e7	+	1.92027e7i	−0.352351	+	0.610290i
$999$	1.64553e6	−	732636.i	0.0521665	−	0.0232260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.6.g.a.9.3	yes	96
31.7	even	15	inner	31.6.g.a.7.3	✓	96
31.10	even	15		961.6.a.j.1.8		48
31.21	odd	30		961.6.a.k.1.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.6.g.a.7.3	✓	96	31.7	even	15	inner
31.6.g.a.9.3	yes	96	1.1	even	1	trivial
961.6.a.j.1.8		48	31.10	even	15
961.6.a.k.1.8		48	31.21	odd	30

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.62800 + 8.08816i) q^{2} +(-19.6320 - 4.17290i) q^{3} +(-32.6234 - 23.7023i) q^{4} +(0.998763 + 1.72991i) q^{5} +(85.3440 - 147.820i) q^{6} +(87.1112 - 38.7844i) q^{7} +(57.2761 - 41.6135i) q^{8} +(146.010 + 65.0077i) q^{9} +(-16.6165 + 3.53195i) q^{10} +(18.2220 - 173.370i) q^{11} +(541.555 + 601.457i) q^{12} +(304.099 - 337.736i) q^{13} +(84.7660 + 806.495i) q^{14} +(-12.3889 - 38.1292i) q^{15} +(-212.698 - 654.618i) q^{16} +(-124.462 - 1184.18i) q^{17} +(-909.507 + 1010.11i) q^{18} +(-1310.86 - 1455.85i) q^{19} +(8.41974 - 80.1085i) q^{20} +(-1872.01 + 397.908i) q^{21} +(1354.36 + 603.000i) q^{22} +(-2481.31 + 1802.78i) q^{23} +(-1298.09 + 577.948i) q^{24} +(1560.50 - 2702.87i) q^{25} +(1932.49 + 3347.18i) q^{26} +(1350.51 + 981.201i) q^{27} +(-3761.15 - 799.456i) q^{28} +(-1341.67 + 4129.23i) q^{29} +340.954 q^{30} +(-4357.31 - 3105.32i) q^{31} +8119.13 q^{32} +(-1081.19 + 3327.56i) q^{33} +(9904.93 + 2105.36i) q^{34} +(154.097 + 111.958i) q^{35} +(-3222.50 - 5581.54i) q^{36} +(539.518 - 934.472i) q^{37} +(15220.1 - 6776.44i) q^{38} +(-7379.41 + 5361.46i) q^{39} +(129.193 + 57.5203i) q^{40} +(1215.05 - 258.267i) q^{41} +(1701.30 - 16186.8i) q^{42} +(-3936.77 - 4372.22i) q^{43} +(-4703.74 + 5224.03i) q^{44} +(33.3717 + 317.511i) q^{45} +(-8060.27 - 24807.0i) q^{46} +(-8401.37 - 25856.8i) q^{47} +(1444.03 + 13739.0i) q^{48} +(-5161.95 + 5732.92i) q^{49} +(17760.3 + 19724.8i) q^{50} +(-2498.03 + 23767.2i) q^{51} +(-17925.9 + 3810.27i) q^{52} +(35317.3 + 15724.3i) q^{53} +(-11485.3 + 8344.52i) q^{54} +(318.114 - 141.633i) q^{55} +(3375.43 - 5846.42i) q^{56} +(19659.6 + 34051.4i) q^{57} +(-29872.0 - 21703.3i) q^{58} +(-4162.58 - 884.783i) q^{59} +(-499.581 + 1537.55i) q^{60} -19176.8 q^{61} +(36567.4 - 27081.8i) q^{62} +15240.4 q^{63} +(-14530.8 + 44721.1i) q^{64} +(887.976 + 188.745i) q^{65} +(-24072.5 - 17489.7i) q^{66} +(-22096.4 - 38272.1i) q^{67} +(-24007.4 + 41582.1i) q^{68} +(56235.9 - 25037.8i) q^{69} +(-1310.50 + 952.135i) q^{70} +(-64398.8 - 28672.2i) q^{71} +(11068.1 - 2352.59i) q^{72} +(1379.12 - 13121.4i) q^{73} +(6140.31 + 6819.50i) q^{74} +(-41914.6 + 46550.9i) q^{75} +(8257.54 + 78565.3i) q^{76} +(-5136.73 - 15809.2i) q^{77} +(-23971.2 - 73775.8i) q^{78} +(1293.35 + 12305.4i) q^{79} +(919.993 - 1021.76i) q^{80} +(-48406.4 - 53760.8i) q^{81} +(-1104.25 + 10506.3i) q^{82} +(42954.9 - 9130.35i) q^{83} +(70502.6 + 31389.8i) q^{84} +(1924.21 - 1398.02i) q^{85} +(45709.1 - 20351.0i) q^{86} +(43570.5 - 75466.3i) q^{87} +(-6170.86 - 10688.3i) q^{88} +(37687.2 + 27381.3i) q^{89} +(-2655.78 - 564.503i) q^{90} +(13391.5 - 41214.9i) q^{91} +123679. q^{92} +(72584.4 + 79146.2i) q^{93} +231212. q^{94} +(1209.26 - 3721.72i) q^{95} +(-159395. - 33880.4i) q^{96} +(31971.2 + 23228.5i) q^{97} +(-32803.2 - 56816.8i) q^{98} +(13931.0 - 24129.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 6 q^{2} - 20 q^{3} - 346 q^{4} - 33 q^{5} + 283 q^{6} - 66 q^{7} - 271 q^{8} + 658 q^{9} + 896 q^{10} + 41 q^{11} - 1169 q^{12} + 149 q^{13} - 2 q^{14} + 4906 q^{15} - 2450 q^{16} - 3152 q^{17} - 3 q^{18}+ \cdots + 674326 q^{99}+O(q^{100}) \) 96 * q - 6 * q^2 - 20 * q^3 - 346 * q^4 - 33 * q^5 + 283 * q^6 - 66 * q^7 - 271 * q^8 + 658 * q^9 + 896 * q^10 + 41 * q^11 - 1169 * q^12 + 149 * q^13 - 2 * q^14 + 4906 * q^15 - 2450 * q^16 - 3152 * q^17 - 3 * q^18 - 5216 * q^19 + 7943 * q^20 - 14003 * q^21 - 8471 * q^22 + 13925 * q^23 + 25478 * q^24 - 18843 * q^25 + 12637 * q^26 + 3409 * q^27 - 10560 * q^28 + 6386 * q^29 - 25530 * q^30 - 39101 * q^31 + 31482 * q^32 + 17969 * q^33 - 18136 * q^34 + 5943 * q^35 - 9713 * q^36 + 40836 * q^37 + 18746 * q^38 + 55889 * q^39 + 15841 * q^40 - 46266 * q^41 + 8917 * q^42 - 137449 * q^43 + 28951 * q^44 + 69269 * q^45 - 97978 * q^46 + 5774 * q^47 - 112102 * q^48 - 146686 * q^49 + 58913 * q^50 + 149254 * q^51 + 263153 * q^52 + 62548 * q^53 + 144508 * q^54 + 13077 * q^55 - 103466 * q^56 + 68345 * q^57 - 52881 * q^58 - 149116 * q^59 + 65951 * q^60 - 204972 * q^61 - 62393 * q^62 - 80326 * q^63 - 205193 * q^64 - 296504 * q^65 - 268720 * q^66 - 105499 * q^67 + 497808 * q^68 + 448358 * q^69 + 351230 * q^70 + 93454 * q^71 + 192637 * q^72 + 74644 * q^73 - 83209 * q^74 - 323995 * q^75 - 446776 * q^76 - 249590 * q^77 - 588829 * q^78 + 396670 * q^79 - 236822 * q^80 + 616675 * q^81 + 449670 * q^82 + 518776 * q^83 + 578676 * q^84 + 463509 * q^85 - 95508 * q^86 - 360817 * q^87 + 238379 * q^88 + 239175 * q^89 - 1232679 * q^90 - 178840 * q^91 - 1350224 * q^92 - 65783 * q^93 + 580620 * q^94 - 276050 * q^95 - 1587604 * q^96 - 611799 * q^97 + 200092 * q^98 + 674326 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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