LMFDB - Embedded newform 49.7.h.a.3.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(3,49)] 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("49.3"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.h (of order $42$, degree $12$, 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:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	49.3
Dual form			49.7.h.a.33.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.21887 + 10.7495i) q^{2} +(22.3732 + 1.67664i) q^{3} +(-50.8375 - 47.1703i) q^{4} +(-46.9023 + 68.7930i) q^{5} +(-112.413 + 233.427i) q^{6} +(65.6154 - 336.665i) q^{7} +(55.6673 - 26.8080i) q^{8} +(-223.109 - 33.6282i) q^{9} +(-541.616 - 794.405i) q^{10} +(-1437.72 + 216.702i) q^{11} +(-1058.31 - 1140.59i) q^{12} +(-2691.13 + 2146.11i) q^{13} +(3342.16 + 2125.68i) q^{14} +(-1164.70 + 1460.48i) q^{15} +(-278.365 - 3714.53i) q^{16} +(1400.51 - 4540.35i) q^{17} +(1302.75 - 2256.43i) q^{18} +(-1179.71 + 681.106i) q^{19} +(5629.38 - 1284.87i) q^{20} +(2032.49 - 7422.27i) q^{21} +(3736.13 - 16369.0i) q^{22} +(13479.9 - 4157.99i) q^{23} +(1290.40 - 506.446i) q^{24} +(3175.80 + 8091.80i) q^{25} +(-11716.0 - 37982.5i) q^{26} +(-20881.0 - 4765.95i) q^{27} +(-19216.3 + 14020.1i) q^{28} +(4121.71 + 18058.4i) q^{29} +(-10785.8 - 18681.5i) q^{30} +(-21077.7 - 12169.2i) q^{31} +(44882.3 + 13844.4i) q^{32} +(-32529.8 + 2437.77i) q^{33} +(42897.9 + 34209.9i) q^{34} +(20082.7 + 20304.3i) q^{35} +(9756.04 + 12233.7i) q^{36} +(-26576.2 + 24659.1i) q^{37} +(-2344.51 - 15554.8i) q^{38} +(-63807.5 + 43503.2i) q^{39} +(-766.724 + 5086.88i) q^{40} +(44372.6 + 92140.7i) q^{41} +(71210.8 + 53161.8i) q^{42} +(-105445. - 50779.5i) q^{43} +(83312.2 + 56801.3i) q^{44} +(12777.7 - 13771.1i) q^{45} +(-12173.5 + 162444. i) q^{46} +(-113948. - 44721.4i) q^{47} -83572.5i q^{48} +(-109038. - 44180.9i) q^{49} -100381. q^{50} +(38946.5 - 99234.0i) q^{51} +(238043. + 17838.9i) q^{52} +(121034. + 112303. i) q^{53} +(139326. - 204353. i) q^{54} +(52525.0 - 109069. i) q^{55} +(-5372.68 - 20500.3i) q^{56} +(-27535.9 + 13260.6i) q^{57} +(-211507. - 31879.6i) q^{58} +(130438. + 191317. i) q^{59} +(128102. - 19308.2i) q^{60} +(50970.6 + 54933.2i) q^{61} +(219737. - 175235. i) q^{62} +(-25960.8 + 72906.5i) q^{63} +(-189535. + 237669. i) q^{64} +(-21416.9 - 285789. i) q^{65} +(111034. - 359964. i) q^{66} +(-247053. + 427909. i) q^{67} +(-285368. + 164757. i) q^{68} +(308560. - 70426.7i) q^{69} +(-302987. + 130218. i) q^{70} +(7737.36 - 33899.6i) q^{71} +(-13321.4 + 4109.10i) q^{72} +(221585. - 86965.5i) q^{73} +(-152952. - 389715. i) q^{74} +(57485.7 + 186364. i) q^{75} +(92101.5 + 21021.6i) q^{76} +(-21380.7 + 498251. i) q^{77} +(-198442. - 869433. i) q^{78} +(-317552. - 550016. i) q^{79} +(268589. + 155070. i) q^{80} +(-302008. - 93157.1i) q^{81} +(-1.17767e6 + 88254.1i) q^{82} +(-555604. - 443079. i) q^{83} +(-453438. + 281456. i) q^{84} +(246657. + 309298. i) q^{85} +(990711. - 919245. i) q^{86} +(61938.4 + 410934. i) q^{87} +(-74224.9 + 50605.7i) q^{88} +(-8277.34 + 54916.6i) q^{89} +(94124.8 + 195452. i) q^{90} +(545941. + 1.04683e6i) q^{91} +(-881418. - 424468. i) q^{92} +(-451173. - 307604. i) q^{93} +(961465. - 1.03621e6i) q^{94} +(8475.77 - 113101. i) q^{95} +(980948. + 384994. i) q^{96} +905298. i q^{97} +(934940. - 985713. i) q^{98} +328056. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 13 q^{2} - 11 q^{3} + 819 q^{4} - 179 q^{5} + 770 q^{6} + 392 q^{7} + 828 q^{8} - 1160 q^{9} - 2594 q^{10} - 5305 q^{11} + 7497 q^{12} - 14 q^{13} - 11403 q^{14} - 6196 q^{15} + 27903 q^{16} - 5107 q^{17}+ \cdots - 4449616 q^{99}+O(q^{100}) $ 324 * q - 13 * q^2 - 11 * q^3 + 819 * q^4 - 179 * q^5 + 770 * q^6 + 392 * q^7 + 828 * q^8 - 1160 * q^9 - 2594 * q^10 - 5305 * q^11 + 7497 * q^12 - 14 * q^13 - 11403 * q^14 - 6196 * q^15 + 27903 * q^16 - 5107 * q^17 - 11538 * q^18 - 30006 * q^19 - 50190 * q^20 + 8953 * q^21 + 33042 * q^22 + 54531 * q^23 + 90184 * q^24 - 92804 * q^25 - 93366 * q^26 - 11774 * q^27 - 19180 * q^28 - 80398 * q^29 + 15851 * q^30 + 39378 * q^31 - 197841 * q^32 + 36697 * q^33 - 54698 * q^34 - 819 * q^35 + 706300 * q^36 + 15331 * q^37 - 304462 * q^38 - 179298 * q^39 - 515414 * q^40 - 116046 * q^41 + 1203482 * q^42 - 225018 * q^43 + 1373764 * q^44 + 465772 * q^45 + 1100364 * q^46 + 270021 * q^47 - 767900 * q^49 - 1164040 * q^50 - 1215743 * q^51 - 3954790 * q^52 + 141807 * q^53 - 1093487 * q^54 + 991354 * q^55 - 596680 * q^56 - 388207 * q^57 + 381012 * q^58 + 2015849 * q^59 + 5807298 * q^60 + 258821 * q^61 - 525742 * q^62 - 1265432 * q^63 + 872972 * q^64 - 70154 * q^65 + 497766 * q^66 - 324190 * q^67 - 799617 * q^68 - 2216774 * q^69 + 56140 * q^70 - 1031026 * q^71 + 4633092 * q^72 + 1268305 * q^73 - 1444192 * q^74 - 1699244 * q^75 - 5464011 * q^76 - 2274741 * q^77 - 1285956 * q^78 - 515710 * q^79 + 8314050 * q^80 - 1069027 * q^81 + 357910 * q^82 - 3183054 * q^83 - 10099096 * q^84 - 1596848 * q^85 - 5387681 * q^86 - 4197040 * q^87 - 1024645 * q^88 + 983769 * q^89 + 18547774 * q^90 + 13421086 * q^91 + 5294506 * q^92 + 15477850 * q^93 + 8903632 * q^94 + 5236430 * q^95 + 7804258 * q^96 - 10234553 * q^98 - 4449616 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{42}\right)$

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 $

$2$	−4.21887	+	10.7495i	−0.527358	+	1.34369i	0.380644	+	0.924722i	$0.375702\pi$
$2$	−4.21887	+	10.7495i	−0.527358	+	1.34369i	−0.908002	+	0.418965i	$0.862393\pi$
$3$	22.3732	+	1.67664i	0.828637	+	0.0620978i	0.482293	−	0.876010i	$-0.339804\pi$
$3$	22.3732	+	1.67664i	0.828637	+	0.0620978i	0.346344	+	0.938108i	$0.387423\pi$
$4$	−50.8375	−	47.1703i	−0.794336	−	0.737036i
$5$	−46.9023	+	68.7930i	−0.375218	+	0.550344i	−0.966680	−	0.255989i	$-0.917599\pi$
$5$	−46.9023	+	68.7930i	−0.375218	+	0.550344i	0.591461	+	0.806333i	$0.298551\pi$
$6$	−112.413	+	233.427i	−0.520429	+	1.08068i
$7$	65.6154	−	336.665i	0.191299	−	0.981532i
$7$	65.6154	−	336.665i	0.191299	−	0.981532i
$8$	55.6673	−	26.8080i	0.108725	−	0.0523593i
$9$	−223.109	−	33.6282i	−0.306048	−	0.0461293i
$10$	−541.616	−	794.405i	−0.541616	−	0.794405i
$11$	−1437.72	+	216.702i	−1.08018	+	0.162811i	−0.664938	−	0.746898i	$-0.731542\pi$
$11$	−1437.72	+	216.702i	−1.08018	+	0.162811i	−0.415245	+	0.909710i	$0.636304\pi$
$12$	−1058.31	−	1140.59i	−0.612448	−	0.660062i
$13$	−2691.13	+	2146.11i	−1.22491	+	0.976836i	−0.224916	+	0.974378i	$0.572211\pi$
$13$	−2691.13	+	2146.11i	−1.22491	+	0.976836i	−0.999997	+	0.00245756i	$0.999218\pi$
$14$	3342.16	+	2125.68i	1.21799	+	0.774664i
$15$	−1164.70	+	1460.48i	−0.345095	+	0.432735i
$16$	−278.365	−	3714.53i	−0.0679603	−	0.906867i
$17$	1400.51	−	4540.35i	0.285063	−	0.924150i	−0.693893	−	0.720078i	$-0.744106\pi$
$17$	1400.51	−	4540.35i	0.285063	−	0.924150i	0.978956	−	0.204072i	$-0.0654178\pi$
$18$	1302.75	−	2256.43i	0.223380	−	0.386906i
$19$	−1179.71	+	681.106i	−0.171995	+	0.0993011i	−0.583526	−	0.812094i	$-0.698327\pi$
$19$	−1179.71	+	681.106i	−0.171995	+	0.0993011i	0.411531	+	0.911396i	$0.364994\pi$
$20$	5629.38	−	1284.87i	0.703673	−	0.160609i
$21$	2032.49	−	7422.27i	0.219468	−	0.801454i
$22$	3736.13	−	16369.0i	0.350876	−	1.53729i
$23$	13479.9	−	4157.99i	1.10791	−	0.341744i	0.313779	−	0.949496i	$-0.398405\pi$
$23$	13479.9	−	4157.99i	1.10791	−	0.341744i	0.794126	+	0.607753i	$0.207929\pi$
$24$	1290.40	−	506.446i	0.0933452	−	0.0366353i
$25$	3175.80	+	8091.80i	0.203251	+	0.517875i
$26$	−11716.0	−	37982.5i	−0.666593	−	2.16104i
$27$	−20881.0	−	4765.95i	−1.06086	−	0.242135i
$28$	−19216.3	+	14020.1i	−0.875380	+	0.638672i
$29$	4121.71	+	18058.4i	0.168999	+	0.740431i	0.986400	+	0.164363i	$0.0525567\pi$
$29$	4121.71	+	18058.4i	0.168999	+	0.740431i	−0.817401	+	0.576069i	$0.804586\pi$
$30$	−10785.8	−	18681.5i	−0.399472	−	0.691906i
$31$	−21077.7	−	12169.2i	−0.707520	−	0.408487i	0.102622	−	0.994720i	$-0.467277\pi$
$31$	−21077.7	−	12169.2i	−0.707520	−	0.408487i	−0.810142	+	0.586234i	$0.800610\pi$
$32$	44882.3	+	13844.4i	1.36970	+	0.422496i
$33$	−32529.8	+	2437.77i	−0.905190	+	0.0678346i
$34$	42897.9	+	34209.9i	1.09144	+	0.870393i
$35$	20082.7	+	20304.3i	0.468402	+	0.473569i
$36$	9756.04	+	12233.7i	0.209106	+	0.262210i
$37$	−26576.2	+	24659.1i	−0.524673	+	0.486825i	−0.897463	−	0.441091i	$-0.854592\pi$
$37$	−26576.2	+	24659.1i	−0.524673	+	0.486825i	0.372790	+	0.927916i	$0.378401\pi$
$38$	−2344.51	−	15554.8i	−0.0427268	−	0.283474i
$39$	−63807.5	+	43503.2i	−1.07567	+	0.733378i
$40$	−766.724	+	5086.88i	−0.0119801	+	0.0794825i
$41$	44372.6	+	92140.7i	0.643819	+	1.33690i	0.925993	+	0.377540i	$0.123230\pi$
$41$	44372.6	+	92140.7i	0.643819	+	1.33690i	−0.282174	+	0.959363i	$0.591056\pi$
$42$	71210.8	+	53161.8i	0.961166	+	0.717550i
$43$	−105445.	−	50779.5i	−1.32623	−	0.638679i	−0.369386	−	0.929276i	$-0.620432\pi$
$43$	−105445.	−	50779.5i	−1.32623	−	0.638679i	−0.956846	+	0.290597i	$0.906146\pi$
$44$	83312.2	+	56801.3i	0.978026	+	0.666807i
$45$	12777.7	−	13771.1i	0.140222	−	0.151123i
$46$	−12173.5	+	162444.i	−0.125067	+	1.66890i
$47$	−113948.	−	44721.4i	−1.09752	−	0.430747i	−0.253655	−	0.967295i	$-0.581633\pi$
$47$	−113948.	−	44721.4i	−1.09752	−	0.430747i	−0.843870	+	0.536548i	$0.819728\pi$
$48$		−	83572.5i		−	0.755683i
$49$	−109038.	−	44180.9i	−0.926810	−	0.375531i
$50$	−100381.			−0.803048
$51$	38946.5	−	99234.0i	0.293601	−	0.748083i
$52$	238043.	+	17838.9i	1.69296	+	0.126869i
$53$	121034.	+	112303.i	0.812979	+	0.754334i	0.972511	−	0.232859i	$-0.0748080\pi$
$53$	121034.	+	112303.i	0.812979	+	0.754334i	−0.159532	+	0.987193i	$0.550998\pi$
$54$	139326.	−	204353.i	0.884810	−	1.29778i
$55$	52525.0	−	109069.i	0.315702	−	0.655562i
$56$	−5372.68	−	20500.3i	−0.0305934	−	0.116734i
$57$	−27535.9	+	13260.6i	−0.148687	+	0.0716041i
$58$	−211507.	−	31879.6i	−1.08403	−	0.163391i
$59$	130438.	+	191317.i	0.635108	+	0.931533i	1.00000		0.000482931i	$0.000153722\pi$
$59$	130438.	+	191317.i	0.635108	+	0.931533i	−0.364891	+	0.931050i	$0.618894\pi$
$60$	128102.	−	19308.2i	0.593063	−	0.0893899i
$61$	50970.6	+	54933.2i	0.224559	+	0.242017i	0.835275	−	0.549833i	$-0.185309\pi$
$61$	50970.6	+	54933.2i	0.224559	+	0.242017i	−0.610716	+	0.791850i	$0.709118\pi$
$62$	219737.	−	175235.i	0.921995	−	0.735266i
$63$	−25960.8	+	72906.5i	−0.103824	+	0.291571i
$64$	−189535.	+	237669.i	−0.723017	+	0.906635i
$65$	−21416.9	−	285789.i	−0.0779860	−	1.04065i
$66$	111034.	−	359964.i	0.386211	−	1.25206i
$67$	−247053.	+	427909.i	−0.821422	+	1.42274i	0.0832020	+	0.996533i	$0.473485\pi$
$67$	−247053.	+	427909.i	−0.821422	+	1.42274i	−0.904624	+	0.426211i	$0.859848\pi$
$68$	−285368.	+	164757.i	−0.907567	+	0.523984i
$69$	308560.	−	70426.7i	0.939273	−	0.214383i
$70$	−302987.	+	130218.i	−0.883344	+	0.379645i
$71$	7737.36	−	33899.6i	0.0216181	−	0.0947152i	−0.962968	−	0.269616i	$-0.913103\pi$
$71$	7737.36	−	33899.6i	0.0216181	−	0.0947152i	0.984586	+	0.174901i	$0.0559604\pi$
$72$	−13321.4	+	4109.10i	−0.0356904	+	0.0110090i
$73$	221585.	−	86965.5i	0.569601	−	0.223552i	−0.0630215	−	0.998012i	$-0.520074\pi$
$73$	221585.	−	86965.5i	0.569601	−	0.223552i	0.632623	+	0.774460i	$0.281978\pi$
$74$	−152952.	−	389715.i	−0.377450	−	0.961727i
$75$	57485.7	+	186364.i	0.136262	+	0.441752i
$76$	92101.5	+	21021.6i	0.209810	+	0.0478877i
$77$	−21380.7	+	498251.i	−0.0468328	+	1.09138i
$78$	−198442.	−	869433.i	−0.418168	−	1.83211i
$79$	−317552.	−	550016.i	−0.644070	−	1.11556i	−0.984515	−	0.175298i	$-0.943911\pi$
$79$	−317552.	−	550016.i	−0.644070	−	1.11556i	0.340445	−	0.940264i	$-0.389422\pi$
$80$	268589.	+	155070.i	0.524589	+	0.302871i
$81$	−302008.	−	93157.1i	−0.568281	−	0.175292i
$82$	−1.17767e6	+	88254.1i	−2.13590	+	0.160064i
$83$	−555604.	−	443079.i	−0.971697	−	0.774902i	0.00264012	−	0.999997i	$-0.499160\pi$
$83$	−555604.	−	443079.i	−0.971697	−	0.774902i	−0.974337	+	0.225094i	$0.927731\pi$
$84$	−453438.	+	281456.i	−0.765032	+	0.474868i
$85$	246657.	+	309298.i	0.401640	+	0.503641i
$86$	990711.	−	919245.i	1.55758	−	1.44523i
$87$	61938.4	+	410934.i	0.0940594	+	0.624043i
$88$	−74224.9	+	50605.7i	−0.108918	+	0.0742594i
$89$	−8277.34	+	54916.6i	−0.0117414	+	0.0778993i	−0.993934	−	0.109977i	$-0.964922\pi$
$89$	−8277.34	+	54916.6i	−0.0117414	+	0.0778993i	0.982193	+	0.187876i	$0.0601604\pi$
$90$	94124.8	+	195452.i	0.129115	+	0.268110i
$91$	545941.	+	1.04683e6i	0.724471	+	1.38916i
$92$	−881418.	−	424468.i	−1.13193	−	0.545107i
$93$	−451173.	−	307604.i	−0.560911	−	0.382423i
$94$	961465.	−	1.03621e6i	1.15758	−	1.24757i
$95$	8475.77	−	113101.i	0.00988572	−	0.131916i
$96$	980948.	+	384994.i	1.10875	+	0.435151i
$97$			905298.i			0.991919i	0.868346	+	0.495960i	$0.165184\pi$
$97$			905298.i			0.991919i	−0.868346	+	0.495960i	$0.834816\pi$
$98$	934940.	−	985713.i	0.993357	−	1.04730i
$99$	328056.			0.338098
$100$	220243.	−	561170.i	0.220243	−	0.561170i
$101$	599079.	+	44894.8i	0.581460	+	0.0435744i	0.362214	−	0.932095i	$-0.382021\pi$
$101$	599079.	+	44894.8i	0.581460	+	0.0435744i	0.219246	+	0.975670i	$0.429640\pi$
$102$	902405.	+	837310.i	0.850357	+	0.789016i
$103$	168560.	−	247232.i	0.154256	−	0.226252i	−0.741330	−	0.671141i	$-0.765805\pi$
$103$	168560.	−	247232.i	0.154256	−	0.226252i	0.895586	+	0.444889i	$0.146757\pi$
$104$	−92275.4	+	191612.i	−0.0820325	+	0.170342i
$105$	415272.	+	487943.i	0.358727	+	0.421503i
$106$	−1.71783e6	+	827262.i	−1.44232	+	0.694585i
$107$	−115558.	−	17417.5i	−0.0943294	−	0.0142179i	0.101708	−	0.994814i	$-0.467569\pi$
$107$	−115558.	−	17417.5i	−0.0943294	−	0.0142179i	−0.196037	+	0.980596i	$0.562807\pi$
$108$	836726.	+	1.22725e6i	0.664220	+	0.974232i
$109$	293350.	−	44215.3i	0.226520	−	0.0341424i	−0.0348015	−	0.999394i	$-0.511080\pi$
$109$	293350.	−	44215.3i	0.226520	−	0.0341424i	0.261321	+	0.965252i	$0.415842\pi$
$110$	950843.	+	1.02477e6i	0.714382	+	0.769921i
$111$	−635940.	+	507145.i	−0.464994	+	0.370820i
$112$	−1.26882e6	−	150014.i	−0.903119	−	0.106777i
$113$	536637.	−	672922.i	0.371916	−	0.466368i	−0.560289	−	0.828297i	$-0.689310\pi$
$113$	536637.	−	672922.i	0.371916	−	0.466368i	0.932206	+	0.361928i	$0.117882\pi$
$114$	−26374.3	−	351941.i	−0.0178019	−	0.237550i
$115$	−346197.	+	1.12234e6i	−0.227630	+	0.737958i
$116$	642282.	−	1.11247e6i	0.411483	−	0.712709i
$117$	672586.	−	388317.i	0.419943	−	0.242454i
$118$	−2.60686e6	+	595000.i	−1.58662	+	0.362135i
$119$	−1.43668e6	−	769421.i	−0.852551	−	0.456587i
$120$	−25682.9	+	112524.i	−0.0148628	+	0.0651182i
$121$	327234.	−	100938.i	0.184715	−	0.0569770i
$122$	−805542.	+	316152.i	−0.443618	+	0.174107i
$123$	838271.	+	2.13588e6i	0.450473	+	1.14779i
$124$	497513.	+	1.61290e6i	0.260939	+	0.845944i
$125$	−1.97394e6	−	450539.i	−1.01066	−	0.230676i
$126$	−674183.	−	586649.i	−0.337028	−	0.293269i
$127$	478138.	+	2.09486e6i	0.233422	+	1.02269i	0.946778	+	0.321887i	$0.104317\pi$
$127$	478138.	+	2.09486e6i	0.233422	+	1.02269i	−0.713356	+	0.700802i	$0.752826\pi$
$128$	−252191.	−	436808.i	−0.120254	−	0.208286i
$129$	−2.27400e6	−	1.31289e6i	−1.05930	−	0.611589i
$130$	3.16244e6	+	975483.i	1.43944	+	0.444007i
$131$	915225.	−	68586.6i	0.407112	−	0.0305088i	0.130399	−	0.991462i	$-0.458374\pi$
$131$	915225.	−	68586.6i	0.407112	−	0.0305088i	0.276713	+	0.960953i	$0.410755\pi$
$132$	1.76872e6	+	1.41051e6i	0.769021	+	0.613274i
$133$	151898.	+	441859.i	0.0645649	+	0.187814i
$134$	−3.55752e6	−	4.46099e6i	−1.47854	−	1.85403i
$135$	1.30723e6	−	1.21293e6i	0.531314	−	0.492987i
$136$	−43754.8	−	290294.i	−0.0173944	−	0.115404i
$137$	1.63207e6	−	1.11273e6i	0.634713	−	0.432740i	−0.202753	−	0.979230i	$-0.564989\pi$
$137$	1.63207e6	−	1.11273e6i	0.634713	−	0.432740i	0.837466	+	0.546490i	$0.184036\pi$
$138$	−544720.	+	3.61398e6i	−0.207270	+	1.37515i
$139$	643027.	+	1.33526e6i	0.239433	+	0.497189i	0.985711	−	0.168447i	$-0.0538750\pi$
$139$	643027.	+	1.33526e6i	0.239433	+	0.497189i	−0.746277	+	0.665635i	$0.768161\pi$
$140$	−63197.2	−	1.97953e6i	−0.0230310	−	0.721402i
$141$	−2.47441e6	−	1.19161e6i	−0.882701	−	0.425086i
$142$	331761.	+	226191.i	0.115867	+	0.0789968i
$143$	3.40404e6	−	3.66868e6i	1.16409	−	1.25459i
$144$	−62807.2	+	838104.i	−0.0210340	+	0.280679i
$145$	−1.43561e6	−	563435.i	−0.470904	−	0.184816i
$146$			2.74882e6i			0.883258i
$147$	−2.36546e6	−	1.17129e6i	−0.744669	−	0.368732i
$148$	2.51425e6			0.775574
$149$	−1.53781e6	+	3.91827e6i	−0.464883	+	1.18450i	0.485726	+	0.874111i	$0.338555\pi$
$149$	−1.53781e6	+	3.91827e6i	−0.464883	+	1.18450i	−0.950609	+	0.310391i	$0.899540\pi$
$150$	−2.24584e6	−	168303.i	−0.665435	−	0.0498675i
$151$	−3.90353e6	−	3.62195e6i	−1.13378	−	1.05199i	−0.998123	−	0.0612333i	$-0.980497\pi$
$151$	−3.90353e6	−	3.62195e6i	−1.13378	−	1.05199i	−0.135652	−	0.990757i	$-0.543313\pi$
$152$	−47412.2	+	69541.0i	−0.0135008	+	0.0198020i
$153$	−465151.	+	965895.i	−0.129873	+	0.269684i
$154$	−5.26574e6	−	2.33189e6i	−1.44177	−	0.638477i
$155$	1.82575e6	−	879236.i	0.490283	−	0.236108i
$156$	5.29588e6	+	798225.i	1.39497	+	0.210258i
$157$	−1.14056e6	−	1.67290e6i	−0.294727	−	0.432286i	0.650103	−	0.759846i	$-0.274726\pi$
$157$	−1.14056e6	−	1.67290e6i	−0.294727	−	0.432286i	−0.944830	+	0.327561i	$0.893773\pi$
$158$	7.25210e6	−	1.09308e6i	1.83862	−	0.277128i
$159$	2.51962e6	+	2.71551e6i	0.626822	+	0.675553i
$160$	−3.05748e6	+	2.43826e6i	−0.746455	+	0.595278i
$161$	−515365.	−	4.81104e6i	−0.123492	−	1.15282i
$162$	2.27552e6	−	2.85342e6i	0.535225	−	0.671151i
$163$	−318779.	−	4.25381e6i	−0.0736083	−	0.982234i	−0.904686	−	0.426078i	$-0.859895\pi$
$163$	−318779.	−	4.25381e6i	−0.0736083	−	0.982234i	0.831078	−	0.556156i	$-0.187724\pi$
$164$	2.09051e6	−	6.77728e6i	0.473938	−	1.53647i
$165$	1.35802e6	−	2.35216e6i	0.302311	−	0.523619i
$166$	7.10689e6	−	4.10317e6i	1.55366	−	0.897005i
$167$	−2.69034e6	+	614052.i	−0.577640	+	0.131843i	−0.501352	−	0.865243i	$-0.667164\pi$
$167$	−2.69034e6	+	614052.i	−0.577640	+	0.131843i	−0.0762879	+	0.997086i	$0.524307\pi$
$168$	−85832.6	−	467665.i	−0.0181019	−	0.0986295i
$169$	1.56236e6	−	6.84514e6i	0.323683	−	1.41815i
$170$	−4.36541e6	+	1.34655e6i	−0.888544	+	0.274079i
$171$	286108.	−	112289.i	0.0572192	−	0.0224569i
$172$	2.96526e6	+	7.55536e6i	0.582744	+	1.48481i
$173$	1.85385e6	+	6.01002e6i	0.358043	+	1.16075i	0.938157	+	0.346211i	$0.112532\pi$
$173$	1.85385e6	+	6.01002e6i	0.358043	+	1.16075i	−0.580113	+	0.814536i	$0.696992\pi$
$174$	−4.67865e6	−	1.06787e6i	−0.888122	−	0.202708i
$175$	2.93261e6	−	538235.i	0.547193	−	0.100429i
$176$	1.20516e6	+	5.28014e6i	0.221058	+	0.968517i
$177$	2.59754e6	+	4.49908e6i	0.468428	+	0.811342i
$178$	−555404.	−	320663.i	−0.0984803	−	0.0568576i
$179$	−8.84363e6	−	2.72790e6i	−1.54195	−	0.475630i	−0.596837	−	0.802362i	$-0.703576\pi$
$179$	−8.84363e6	−	2.72790e6i	−1.54195	−	0.475630i	−0.945117	+	0.326733i	$0.894052\pi$
$180$	−1.29917e6	+	97359.6i	−0.222766	+	0.0166940i
$181$	1.40110e6	+	1.11734e6i	0.236284	+	0.188430i	0.734472	−	0.678639i	$-0.237430\pi$
$181$	1.40110e6	+	1.11734e6i	0.236284	+	0.188430i	−0.498188	+	0.867069i	$0.666001\pi$
$182$	−1.35561e7	+	1.45215e6i	−2.24865	+	0.240878i
$183$	1.04827e6	+	1.31449e6i	0.171049	+	0.214489i
$184$	638922.	−	592833.i	0.102564	−	0.0951653i
$185$	−449891.	−	2.98483e6i	−0.0710546	−	0.471416i
$186$	5.21003e6	−	3.55214e6i	0.809658	−	0.552015i
$187$	−1.02965e6	+	6.83126e6i	−0.157458	+	1.04466i
$188$	3.68332e6	+	7.64850e6i	0.554328	+	1.15107i
$189$	−2.97465e6	+	6.71719e6i	−0.440605	+	0.994952i
$190$	1.18002e6	+	568270.i	0.172040	+	0.0828502i
$191$	−4.87337e6	−	3.32261e6i	−0.699406	−	0.476847i	0.160673	−	0.987008i	$-0.448634\pi$
$191$	−4.87337e6	−	3.32261e6i	−0.699406	−	0.476847i	−0.860079	+	0.510161i	$0.829586\pi$
$192$	−4.63898e6	+	4.99963e6i	−0.655419	+	0.706373i
$193$	196866.	−	2.62699e6i	0.0273841	−	0.365415i	−0.966631	−	0.256173i	$-0.917538\pi$
$193$	196866.	−	2.62699e6i	0.0273841	−	0.365415i	0.994015	−	0.109243i	$-0.0348425\pi$
$194$	−9.73149e6	−	3.81933e6i	−1.33283	−	0.523097i
$195$		−	6.42992e6i		−	0.867164i
$196$	3.45921e6	+	7.38941e6i	0.459418	+	0.981390i
$197$	8.80718e6			1.15196			0.575981	−	0.817463i	$-0.304620\pi$
$197$	8.80718e6			1.15196			0.575981	+	0.817463i	$0.304620\pi$
$198$	−1.38402e6	+	3.52644e6i	−0.178299	+	0.454298i
$199$	1.16586e7	+	873691.i	1.47940	+	0.110866i	0.789820	−	0.613339i	$-0.210174\pi$
$199$	1.16586e7	+	873691.i	1.47940	+	0.110866i	0.689585	+	0.724205i	$0.257793\pi$
$200$	393713.	+	365312.i	0.0492141	+	0.0456640i
$201$	−6.24482e6	+	9.15947e6i	−0.769010	+	1.12793i
$202$	−3.01003e6	+	6.25039e6i	−0.365188	+	0.758321i
$203$	6.35008e6	−	202729.i	0.759086	−	0.0242341i
$204$	−6.66084e6	+	3.20769e6i	−0.784582	+	0.377835i
$205$	−8.41982e6	−	1.26908e6i	−0.977330	−	0.147309i
$206$	1.94648e6	+	2.85497e6i	0.222664	+	0.326587i
$207$	−3.14731e6	+	474380.i	−0.354836	+	0.0534830i
$208$	8.72089e6	+	9.39889e6i	0.969105	+	1.04445i
$209$	1.54850e6	−	1.23489e6i	0.169618	−	0.135266i
$210$	−6.99712e6	+	2.40540e6i	−0.755546	+	0.259734i
$211$	9.79466e6	−	1.22821e7i	1.04266	−	1.30745i	0.0924903	−	0.995714i	$-0.470517\pi$
$211$	9.79466e6	−	1.22821e7i	1.04266	−	1.30745i	0.950168	−	0.311738i	$-0.100911\pi$
$212$	−855691.	−	1.14184e7i	−0.0898069	−	1.19839i
$213$	229947.	−	745470.i	0.0237952	−	0.0771421i
$214$	674751.	−	1.16870e6i	0.0688497	−	0.119251i
$215$	8.43887e6	−	4.87219e6i	0.849120	−	0.490240i
$216$	−1.29015e6	+	294469.i	−0.128021	+	0.0292199i
$217$	−5.47998e6	+	6.29765e6i	−0.536290	+	0.616311i
$218$	−762310.	+	3.33990e6i	−0.0735804	+	0.322377i
$219$	5.10336e6	−	1.57418e6i	0.485875	−	0.149872i
$220$	−7.81507e6	+	3.06719e6i	−0.733947	+	0.288053i
$221$	5.97511e6	+	1.52243e7i	0.553566	+	1.41046i
$222$	−2.76861e6	−	8.97561e6i	−0.253048	−	0.820361i
$223$	1.96093e7	+	4.47569e6i	1.76826	+	0.403595i	0.977905	−	0.209049i	$-0.0670367\pi$
$223$	1.96093e7	+	4.47569e6i	1.76826	+	0.403595i	0.790359	+	0.612643i	$0.209894\pi$
$224$	7.60588e6	−	1.42019e7i	0.676715	−	1.26358i
$225$	−436435.	−	1.91215e6i	−0.0383153	−	0.167870i
$226$	4.96957e6	+	8.60754e6i	0.430520	+	0.745682i
$227$	7.45701e6	+	4.30530e6i	0.637510	+	0.368066i	0.783655	−	0.621197i	$-0.213353\pi$
$227$	7.45701e6	+	4.30530e6i	0.637510	+	0.368066i	−0.146145	+	0.989263i	$0.546687\pi$
$228$	2.02536e6	+	624741.i	0.170883	+	0.0527103i
$229$	−1.56813e7	+	1.17515e6i	−1.30580	+	0.0978561i	−0.709385	−	0.704821i	$-0.751027\pi$
$229$	−1.56813e7	+	1.17515e6i	−1.30580	+	0.0978561i	−0.596414	+	0.802677i	$0.703408\pi$
$230$	−1.06041e7	−	8.45645e6i	−0.871542	−	0.695031i
$231$	−1.31374e6	+	1.11116e7i	−0.106580	+	0.901449i
$232$	713553.	+	894767.i	0.0571429	+	0.0716549i
$233$	−1.90944e6	+	1.77170e6i	−0.150951	+	0.140062i	−0.752034	−	0.659125i	$-0.770927\pi$
$233$	−1.90944e6	+	1.77170e6i	−0.150951	+	0.140062i	0.601082	+	0.799187i	$0.294736\pi$
$234$	1.33667e6	+	8.86821e6i	0.104322	+	0.692131i
$235$	8.42096e6	−	5.74131e6i	0.648870	−	0.442392i
$236$	2.39336e6	−	1.58789e7i	0.182084	−	1.20805i
$237$	−6.18247e6	−	1.28380e7i	−0.464427	−	0.964392i
$238$	1.43321e7	−	1.21975e7i	1.06311	−	0.904777i
$239$	−1.45273e7	−	6.99599e6i	−1.06412	−	0.512455i	−0.181915	−	0.983314i	$-0.558230\pi$
$239$	−1.45273e7	−	6.99599e6i	−1.06412	−	0.512455i	−0.882208	+	0.470859i	$0.843944\pi$
$240$	5.74921e6	+	3.91974e6i	0.415886	+	0.283546i
$241$	9.49529e6	−	1.02335e7i	0.678355	−	0.731093i	−0.296228	−	0.955117i	$-0.595729\pi$
$241$	9.49529e6	−	1.02335e7i	0.678355	−	0.731093i	0.974584	+	0.224024i	$0.0719194\pi$
$242$	−295520.	+	3.94344e6i	−0.0208517	+	0.278246i
$243$	7.93370e6	+	3.11375e6i	0.552913	+	0.217003i
$244$		−	5.19697e6i		−	0.357751i
$245$	8.15348e6	−	5.42889e6i	0.554428	−	0.369158i
$246$	−2.64962e7			−1.77983
$247$	1.71303e6	−	4.36473e6i	0.113678	−	0.289646i
$248$	−1.49957e6	−	112377.i	−0.0983134	−	0.00736757i
$249$	−1.16877e7	−	1.08446e7i	−0.757064	−	0.702453i
$250$	1.31708e7	−	1.93181e7i	0.842934	−	1.23636i
$251$	4.90050e6	−	1.01760e7i	0.309898	−	0.643510i	−0.686608	−	0.727028i	$-0.740901\pi$
$251$	4.90050e6	−	1.01760e7i	0.309898	−	0.643510i	0.996506	+	0.0835176i	$0.0266155\pi$
$252$	4.75881e6	−	2.48180e6i	0.297369	−	0.155084i
$253$	−1.84793e7	+	8.89916e6i	−1.14110	+	0.549525i
$254$	−2.45359e7	−	3.69819e6i	−1.49727	−	0.225677i
$255$	4.99993e6	+	7.33355e6i	0.301539	+	0.442276i
$256$	−1.34786e7	+	2.03158e6i	−0.803388	+	0.121091i
$257$	−3.14072e6	−	3.38489e6i	−0.185025	−	0.199409i	0.633727	−	0.773557i	$-0.281524\pi$
$257$	−3.14072e6	−	3.38489e6i	−0.185025	−	0.199409i	−0.818752	+	0.574147i	$0.805334\pi$
$258$	2.37066e7	−	1.89054e7i	1.38042	−	1.10085i
$259$	6.55807e6	+	1.05653e7i	0.377465	+	0.608112i
$260$	−1.23920e7	+	1.55390e7i	−0.705050	+	0.884105i
$261$	−312318.	−	4.16759e6i	−0.0175661	−	0.234403i
$262$	−3.12394e6	+	1.01276e7i	−0.173700	+	0.563120i
$263$	−6.57651e6	+	1.13908e7i	−0.361517	+	0.626165i	−0.988211	−	0.153100i	$-0.951074\pi$
$263$	−6.57651e6	+	1.13908e7i	−0.361517	+	0.626165i	0.626694	+	0.779265i	$0.284408\pi$
$264$	−1.74550e6	+	1.00776e6i	−0.0948652	+	0.0547705i
$265$	−1.34024e7	+	3.05902e6i	−0.720188	+	0.164378i
$266$	−5.39059e6	−	231319.i	−0.286412	−	0.0122904i
$267$	−277266.	+	1.21478e6i	−0.0145667	+	0.0638211i
$268$	3.27442e7	−	1.01002e7i	1.70110	−	0.524719i
$269$	−2.47428e7	+	9.71083e6i	−1.27114	+	0.498884i	−0.902500	−	0.430690i	$-0.858270\pi$
$269$	−2.47428e7	+	9.71083e6i	−1.27114	+	0.498884i	−0.368636	+	0.929574i	$0.620175\pi$
$270$	7.52339e6	+	1.91693e7i	0.382228	+	0.973900i
$271$	−8.88251e6	−	2.87964e7i	−0.446301	−	1.44687i	−0.847458	−	0.530863i	$-0.821868\pi$
$271$	−8.88251e6	−	2.87964e7i	−0.446301	−	1.44687i	0.401157	−	0.916009i	$-0.368608\pi$
$272$	−1.72551e7	−	3.93836e6i	−0.857454	−	0.195708i
$273$	1.04593e7	+	2.43363e7i	0.514060	+	1.19610i
$274$	5.07577e6	+	2.22384e7i	0.246746	+	1.08106i
$275$	−6.31943e6	−	1.09456e7i	−0.303864	−	0.526308i
$276$	−1.90084e7	−	1.09745e7i	−0.904106	−	0.521986i
$277$	−3.53891e7	−	1.09161e7i	−1.66506	−	0.513604i	−0.687848	−	0.725855i	$-0.741445\pi$
$277$	−3.53891e7	−	1.09161e7i	−1.66506	−	0.513604i	−0.977215	+	0.212251i	$0.931921\pi$
$278$	−1.70662e7	+	1.27894e6i	−0.794333	+	0.0595270i
$279$	4.29340e6	+	3.42387e6i	0.197692	+	0.157654i
$280$	1.66227e6	+	591907.i	0.0757228	+	0.0269637i
$281$	2.29689e7	+	2.88021e7i	1.03519	+	1.29809i	0.953487	+	0.301435i	$0.0974656\pi$
$281$	2.29689e7	+	2.88021e7i	1.03519	+	1.29809i	0.0817065	+	0.996656i	$0.473963\pi$
$282$	2.32484e7	−	2.15714e7i	1.03668	−	0.961901i
$283$	2.06708e6	+	1.37142e7i	0.0912009	+	0.605078i	0.987012	+	0.160644i	$0.0513571\pi$
$283$	2.06708e6	+	1.37142e7i	0.0912009	+	0.605078i	−0.895812	+	0.444434i	$0.853405\pi$
$284$	−1.99240e6	+	1.35840e6i	−0.0869806	+	0.0593023i
$285$	379260.	−	2.51623e6i	0.0163833	−	0.108696i
$286$	2.50753e7	+	5.20694e7i	1.07188	+	2.22579i
$287$	3.39321e7	−	8.89288e6i	1.43538	−	0.376181i
$288$	−9.54807e6	−	4.59811e6i	−0.399704	−	0.192487i
$289$	1.29006e6	+	879545.i	0.0534459	+	0.0364388i
$290$	1.21133e7	−	1.30550e7i	0.496670	−	0.535283i
$291$	−1.51786e6	+	2.02544e7i	−0.0615959	+	0.821941i
$292$	−1.53670e7	−	6.03110e6i	−0.617221	−	0.242241i
$293$		−	3.07642e7i		−	1.22305i	−0.791227	−	0.611523i	$-0.790557\pi$
$293$		−	3.07642e7i		−	1.22305i	0.791227	−	0.611523i	$-0.209443\pi$
$294$	2.25703e7	−	2.04860e7i	0.888168	−	0.806148i
$295$	−1.92791e7			−0.750968
$296$	−818367.	+	2.08516e6i	−0.0315553	+	0.0804017i
$297$	3.10539e7	+	2.32717e6i	1.18535	+	0.0888297i
$298$	−3.56317e7	−	3.30613e7i	−1.34644	−	1.24931i
$299$	−2.73527e7	+	4.01190e7i	−1.02326	+	1.50085i
$300$	5.86842e6	−	1.21859e7i	0.217349	−	0.451330i
$301$	−2.40145e7	+	3.21677e7i	−0.880590	+	1.17956i
$302$	5.54026e7	−	2.66805e7i	2.01145	−	0.968664i
$303$	1.33280e7	+	2.00888e6i	0.479114	+	0.0722147i
$304$	2.85838e6	+	4.19247e6i	0.101742	+	0.149228i
$305$	−6.16966e6	+	929927.i	−0.217451	+	0.0327755i
$306$	−8.42048e6	−	9.07512e6i	−0.293882	−	0.316729i
$307$	2.46383e7	−	1.96484e7i	0.851520	−	0.679065i	−0.0971713	−	0.995268i	$-0.530979\pi$
$307$	2.46383e7	−	1.96484e7i	0.851520	−	0.679065i	0.948692	+	0.316203i	$0.102408\pi$
$308$	2.45896e7	−	2.43213e7i	0.841587	−	0.832405i
$309$	4.18574e6	−	5.24875e6i	0.141872	−	0.177902i
$310$	1.74874e6	+	2.33353e7i	0.0587002	+	0.783300i
$311$	1.11172e7	−	3.60411e7i	0.369585	−	1.19817i	−0.559666	−	0.828718i	$-0.689071\pi$
$311$	1.11172e7	−	3.60411e7i	0.369585	−	1.19817i	0.929251	−	0.369448i	$-0.120453\pi$
$312$	−2.38576e6	+	4.13226e6i	−0.0785531	+	0.136058i
$313$	8.06671e6	−	4.65732e6i	0.263065	−	0.151881i	−0.362667	−	0.931919i	$-0.618134\pi$
$313$	8.06671e6	−	4.65732e6i	0.263065	−	0.151881i	0.625732	+	0.780038i	$0.284800\pi$
$314$	2.27947e7	−	5.20274e6i	0.736284	−	0.168052i
$315$	−3.79784e6	−	5.20541e6i	−0.121508	−	0.166542i
$316$	−9.80088e6	+	4.29405e7i	−0.310602	+	1.36083i
$317$	−3.88121e7	+	1.19719e7i	−1.21840	+	0.375826i	−0.836288	−	0.548291i	$-0.815279\pi$
$317$	−3.88121e7	+	1.19719e7i	−1.21840	+	0.375826i	−0.382110	+	0.924117i	$0.624802\pi$
$318$	−3.98203e7	+	1.56283e7i	−1.23829	+	0.485994i
$319$	−9.83916e6	−	2.50698e7i	−0.303100	−	0.772286i
$320$	−7.46035e6	−	2.41859e7i	−0.227672	−	0.738094i
$321$	−2.55619e6	−	583433.i	−0.0772819	−	0.0176391i
$322$	5.38905e7	+	1.47572e7i	1.61415	+	0.442015i
$323$	1.44026e6	+	6.31020e6i	0.0427399	+	0.187256i
$324$	1.09591e7	+	1.89817e7i	0.322210	+	0.558084i
$325$	−2.59124e7	−	1.49605e7i	−0.754844	−	0.435809i
$326$	4.70712e7	+	1.45195e7i	1.35863	+	0.419083i
$327$	6.63730e6	−	497397.i	0.189823	−	0.0142253i
$328$	4.94021e6	+	3.93969e6i	0.139999	+	0.111645i
$329$	−2.25329e7	+	3.54280e7i	−0.632746	+	0.994854i
$330$	1.95552e7	+	2.45215e7i	0.544153	+	0.682347i
$331$	−4.97582e7	+	4.61688e7i	−1.37208	+	1.27311i	−0.446387	+	0.894840i	$0.647289\pi$
$331$	−4.97582e7	+	4.61688e7i	−1.37208	+	1.27311i	−0.925697	+	0.378267i	$0.876520\pi$
$332$	7.34532e6	+	4.87330e7i	0.200723	+	1.33171i
$333$	6.75864e6	−	4.60796e6i	0.183032	−	0.124789i
$334$	4.74943e6	−	3.15104e7i	0.127468	−	0.845696i
$335$	−1.78498e7	−	3.70654e7i	−0.474787	−	0.985904i
$336$	−2.81360e7	−	5.48364e6i	−0.741727	−	0.144561i
$337$	−2.12994e7	−	1.02573e7i	−0.556517	−	0.268004i	0.134414	−	0.990925i	$-0.457085\pi$
$337$	−2.12994e7	−	1.02573e7i	−0.556517	−	0.268004i	−0.690931	+	0.722921i	$0.742799\pi$
$338$	6.69904e7	+	4.56733e7i	1.73485	+	1.18280i
$339$	1.31345e7	−	1.41557e7i	0.337144	−	0.363355i
$340$	2.05026e6	−	2.73589e7i	0.0521642	−	0.696083i
$341$	3.29410e7	+	1.29284e7i	0.830757	+	0.326048i
$342$			3.54925e6i			0.0887275i
$343$	−2.20288e7	+	3.38105e7i	−0.545893	+	0.837855i
$344$	−7.23112e6			−0.177636
$345$	−9.62729e6	+	2.45299e7i	−0.234448	+	0.597364i
$346$	−7.24258e7	−	5.42756e6i	−1.74850	−	0.131032i
$347$	3.58552e7	+	3.32687e7i	0.858150	+	0.796247i	0.980557	−	0.196233i	$-0.0628709\pi$
$347$	3.58552e7	+	3.32687e7i	0.858150	+	0.796247i	−0.122407	+	0.992480i	$0.539061\pi$
$348$	1.62351e7	−	2.38125e7i	0.385228	−	0.565025i
$349$	−9.86323e6	+	2.04812e7i	−0.232029	+	0.481814i	−0.984179	−	0.177179i	$-0.943303\pi$
$349$	−9.86323e6	+	2.04812e7i	−0.232029	+	0.481814i	0.752149	+	0.658993i	$0.229017\pi$
$350$	−6.58654e6	+	3.37948e7i	−0.153622	+	0.788217i
$351$	6.64218e7	−	3.19871e7i	1.53599	−	0.739695i
$352$	−6.75284e7	−	1.01783e7i	−1.54831	−	0.233371i
$353$	4.76145e7	+	6.98376e7i	1.08247	+	1.58769i	0.770324	+	0.637652i	$0.220094\pi$
$353$	4.76145e7	+	6.98376e7i	1.08247	+	1.58769i	0.312143	+	0.950035i	$0.398953\pi$
$354$	−5.93215e7	+	8.94128e6i	−1.33722	+	0.201553i
$355$	1.96916e6	+	2.12225e6i	0.0440144	+	0.0474363i
$356$	3.01123e6	−	2.40138e6i	0.0667412	−	0.0532243i
$357$	−3.08532e7	−	1.96232e7i	−0.678102	−	0.431286i
$358$	6.66336e7	−	8.35559e7i	1.45226	−	1.82108i
$359$	1.40990e6	+	1.88138e7i	0.0304723	+	0.406625i	0.991494	+	0.130152i	$0.0415465\pi$
$359$	1.40990e6	+	1.88138e7i	0.0304723	+	0.406625i	−0.961022	+	0.276473i	$0.910834\pi$
$360$	342126.	−	1.10914e6i	0.00733294	−	0.0237728i
$361$	−2.25951e7	+	3.91359e7i	−0.480279	+	0.831867i
$362$	−1.79219e7	+	1.03472e7i	−0.377798	+	0.218122i
$363$	7.49050e6	−	1.70966e6i	0.156600	−	0.0357429i
$364$	2.16250e7	−	7.89704e7i	0.448386	−	1.63742i
$365$	−4.41020e6	+	1.93224e7i	−0.0906943	+	0.397358i
$366$	−1.85526e7	+	5.72273e6i	−0.378410	+	0.116724i
$367$	−3.83727e7	+	1.50602e7i	−0.776290	+	0.304672i	−0.720211	−	0.693755i	$-0.755955\pi$
$367$	−3.83727e7	+	1.50602e7i	−0.776290	+	0.304672i	−0.0560792	+	0.998426i	$0.517860\pi$
$368$	−1.91973e7	−	4.89139e7i	−0.385209	−	0.981497i
$369$	−6.80139e6	−	2.20496e7i	−0.135369	−	0.438855i
$370$	3.39835e7	+	7.75650e6i	0.670907	+	0.153130i
$371$	4.57502e7	−	3.33791e7i	0.895925	−	0.653662i
$372$	8.42670e6	+	3.69198e7i	0.163693	+	0.717184i
$373$	−3.72290e7	−	6.44825e7i	−0.717389	−	1.24255i	−0.962031	−	0.272941i	$-0.912004\pi$
$373$	−3.72290e7	−	6.44825e7i	−0.717389	−	1.24255i	0.244642	−	0.969614i	$-0.421330\pi$
$374$	−6.90887e7	−	3.98884e7i	−1.32066	−	0.762485i
$375$	−4.34079e7	−	1.33896e7i	−0.823143	−	0.253906i
$376$	−7.54209e6	+	565201.i	−0.141882	+	0.0106326i
$377$	−4.98473e7	−	3.97519e7i	−0.930288	−	0.741880i
$378$	−5.96568e7	−	6.03149e7i	−1.10455	−	1.11673i
$379$	3.46716e6	+	4.34769e6i	0.0636879	+	0.0798621i	0.812655	−	0.582745i	$-0.198021\pi$
$379$	3.46716e6	+	4.34769e6i	0.0636879	+	0.0798621i	−0.748967	+	0.662607i	$0.769450\pi$
$380$	−5.76591e6	+	5.34998e6i	−0.105079	+	0.0974993i
$381$	7.18515e6	+	4.76703e7i	0.129915	+	0.861932i
$382$	5.62765e7	−	3.83687e7i	1.00957	−	0.688314i
$383$	−6.40400e6	+	4.24877e7i	−0.113987	+	0.756253i	0.856684	+	0.515841i	$0.172521\pi$
$383$	−6.40400e6	+	4.24877e7i	−0.113987	+	0.756253i	−0.970671	+	0.240412i	$0.922718\pi$
$384$	−4.90996e6	−	1.01956e7i	−0.0867130	−	0.180061i
$385$	−3.32734e7	−	2.48400e7i	−0.583062	−	0.435280i
$386$	2.74083e7	+	1.31991e7i	0.476563	+	0.229500i
$387$	2.18180e7	+	1.48753e7i	0.376428	+	0.256644i
$388$	4.27032e7	−	4.60231e7i	0.731080	−	0.787917i
$389$	3.92138e6	−	5.23271e7i	0.0666177	−	0.888951i	−0.859359	−	0.511372i	$-0.829137\pi$
$389$	3.92138e6	−	5.23271e7i	0.0666177	−	0.888951i	0.925977	−	0.377579i	$-0.123243\pi$
$390$	6.91184e7	+	2.71270e7i	1.16520	+	0.457306i
$391$		−	6.70267e7i		−	1.12129i
$392$	−7.25427e6	+	463663.i	−0.120430	+	0.00769741i
$393$	2.05915e7			0.339243
$394$	−3.71563e7	+	9.46727e7i	−0.607496	+	1.54788i
$395$	5.27312e7	+	3.95166e6i	0.855611	+	0.0641192i
$396$	−1.66776e7	−	1.54745e7i	−0.268563	−	0.249190i
$397$	2.00728e7	−	2.94414e7i	0.320801	−	0.470529i	−0.631635	−	0.775266i	$-0.717616\pi$
$397$	2.00728e7	−	2.94414e7i	0.320801	−	0.470529i	0.952437	+	0.304736i	$0.0985684\pi$
$398$	−5.85778e7	+	1.21638e8i	−0.929145	+	1.92939i
$399$	2.65760e6	+	1.01405e7i	0.0418380	+	0.159639i
$400$	2.91732e7	−	1.40491e7i	0.455831	−	0.219516i
$401$	−5.66915e7	−	8.54486e6i	−0.879194	−	0.132517i	−0.306092	−	0.952002i	$-0.599022\pi$
$401$	−5.66915e7	−	8.54486e6i	−0.879194	−	0.132517i	−0.573101	+	0.819485i	$0.694260\pi$
$402$	−7.21136e7	−	1.05771e8i	−1.11004	−	1.62813i
$403$	8.28395e7	−	1.24860e7i	1.26568	−	0.190770i
$404$	−2.83380e7	−	3.05411e7i	−0.429759	−	0.463170i
$405$	2.05734e7	−	1.64068e7i	0.309700	−	0.246978i
$406$	−2.46109e7	+	6.91154e7i	−0.367747	+	1.03275i
$407$	3.28656e7	−	4.12122e7i	0.487482	−	0.611283i
$408$	−492216.	−	6.56817e6i	−0.00724728	−	0.0967083i
$409$	2.06397e7	−	6.69124e7i	0.301672	−	0.977995i	−0.670140	−	0.742235i	$-0.733766\pi$
$409$	2.06397e7	−	6.69124e7i	0.301672	−	0.977995i	0.971811	−	0.235760i	$-0.0757580\pi$
$410$	4.91641e7	−	8.51547e7i	0.713340	−	1.23554i
$411$	3.83803e7	−	2.21589e7i	0.552819	−	0.319170i
$412$	−2.02311e7	+	4.61763e6i	−0.289287	+	0.0660278i
$413$	7.29687e7	−	3.13606e7i	1.03582	−	0.445178i
$414$	8.17872e6	−	3.58333e7i	0.115261	−	0.504994i
$415$	5.65398e7	−	1.74402e7i	0.791062	−	0.244010i
$416$	−1.50496e8	+	5.90652e7i	−2.09047	+	0.820450i
$417$	1.21478e7	+	3.09521e7i	0.167529	+	0.426857i
$418$	6.74151e6	+	2.18554e7i	0.0923056	+	0.299247i
$419$	6.67696e7	+	1.52397e7i	0.907689	+	0.207174i	0.650784	−	0.759263i	$-0.274440\pi$
$419$	6.67696e7	+	1.52397e7i	0.907689	+	0.207174i	0.256904	+	0.966437i	$0.417297\pi$
$420$	1.90503e6	−	4.43943e7i	0.0257131	−	0.599210i
$421$	1.49698e7	+	6.55870e7i	0.200618	+	0.878964i	0.970562	+	0.240853i	$0.0774270\pi$
$421$	1.49698e7	+	6.55870e7i	0.200618	+	0.878964i	−0.769944	+	0.638112i	$0.779716\pi$
$422$	9.07042e7	+	1.57104e8i	1.20695	+	2.09050i
$423$	2.39190e7	+	1.38096e7i	0.316025	+	0.182457i
$424$	9.74825e6	+	3.00694e6i	0.127888	+	0.0394481i
$425$	4.11873e7	−	3.08656e6i	0.536534	−	0.0402076i
$426$	7.04331e6	+	5.61685e6i	0.0911062	+	0.0726548i
$427$	2.18386e7	−	1.35556e7i	0.280505	−	0.174114i
$428$	5.05307e6	+	6.33635e6i	0.0644501	+	0.0808179i
$429$	8.23104e7	−	7.63728e7i	1.04252	−	0.967313i
$430$	1.67711e7	+	1.11269e8i	0.210938	+	1.39948i
$431$	−2.09979e7	+	1.43161e7i	−0.262267	+	0.178811i	−0.687313	−	0.726361i	$-0.741210\pi$
$431$	−2.09979e7	+	1.43161e7i	−0.262267	+	0.178811i	0.425047	+	0.905171i	$0.360258\pi$
$432$	−1.18907e7	+	7.88897e7i	−0.147488	+	0.978518i
$433$	1.11722e7	+	2.31993e7i	0.137618	+	0.285766i	0.958376	−	0.285510i	$-0.0921629\pi$
$433$	1.11722e7	+	2.31993e7i	0.137618	+	0.285766i	−0.820758	+	0.571276i	$0.806449\pi$
$434$	−4.45773e7	−	8.54760e7i	−0.545311	−	1.04562i
$435$	−3.11745e7	−	1.50128e7i	−0.378731	−	0.182387i
$436$	−1.69988e7	−	1.15896e7i	−0.205097	−	0.139833i
$437$	−1.30703e7	+	1.40865e7i	−0.156618	+	0.168794i
$438$	−4.60878e6	+	6.14998e7i	−0.0548483	+	0.731900i
$439$	−1.85679e6	−	728735.i	−0.0219466	−	0.00861342i	0.354342	−	0.935116i	$-0.384705\pi$
$439$	−1.85679e6	−	728735.i	−0.0219466	−	0.00861342i	−0.376289	+	0.926502i	$0.622800\pi$
$440$		−	7.47968e6i		−	0.0878061i
$441$	2.28417e7	+	1.35239e7i	0.266325	+	0.157684i
$442$	−1.88862e8			−2.18715
$443$	1.18527e7	−	3.02002e7i	0.136334	−	0.347375i	−0.846359	−	0.532612i	$-0.821210\pi$
$443$	1.18527e7	−	3.02002e7i	0.136334	−	0.347375i	0.982694	+	0.185238i	$0.0593056\pi$
$444$	5.62518e7	+	4.21549e6i	0.642669	+	0.0481614i
$445$	−3.38965e6	−	3.14514e6i	−0.0384658	−	0.0356911i
$446$	−1.30840e8	+	1.91908e8i	−1.47481	+	2.16316i
$447$	−4.09752e7	+	8.50860e7i	−0.458774	+	0.952654i
$448$	6.75785e7	+	7.94045e7i	0.751579	+	0.883102i
$449$	−3.76545e7	+	1.81335e7i	−0.415985	+	0.200328i	−0.630156	−	0.776468i	$-0.717009\pi$
$449$	−3.76545e7	+	1.81335e7i	−0.415985	+	0.200328i	0.214171	+	0.976796i	$0.431295\pi$
$450$	2.23959e7	+	3.37564e6i	0.245771	+	0.0370440i
$451$	−8.37627e7	−	1.22857e8i	−0.913105	−	1.33928i
$452$	−5.90232e7	+	8.89632e6i	−0.639157	+	0.0963374i
$453$	−8.12618e7	−	8.75794e7i	−0.874162	−	0.942123i
$454$	−7.77400e7	+	6.19955e7i	−0.830762	+	0.662511i
$455$	−9.76205e7	−	1.15418e7i	−1.03635	−	0.122529i
$456$	−1.17736e6	+	1.47636e6i	−0.0124169	+	0.0155703i
$457$	4.46256e6	+	5.95487e7i	0.0467558	+	0.623912i	0.970531	+	0.240977i	$0.0774678\pi$
$457$	4.46256e6	+	5.95487e7i	0.0467558	+	0.623912i	−0.923775	+	0.382935i	$0.874913\pi$
$458$	5.35251e7	−	1.73524e8i	0.557136	−	1.80619i
$459$	−5.08832e7	+	8.81323e7i	−0.526182	+	0.911374i
$460$	7.05410e7	−	4.07269e7i	0.724716	−	0.418415i
$461$	−1.33636e8	+	3.05016e7i	−1.36402	+	0.311329i	−0.841021	−	0.541003i	$-0.818045\pi$
$461$	−1.33636e8	+	3.05016e7i	−1.36402	+	0.311329i	−0.523001	+	0.852332i	$0.675188\pi$
$462$	−1.13902e8	−	6.10005e7i	−1.15506	−	0.618596i
$463$	−6.09988e6	+	2.67253e7i	−0.0614580	+	0.269265i	−0.996316	−	0.0857564i	$-0.972669\pi$
$463$	−6.09988e6	+	2.67253e7i	−0.0614580	+	0.269265i	0.934858	+	0.355022i	$0.115526\pi$
$464$	6.59310e7	−	2.03370e7i	0.659987	−	0.203579i
$465$	4.23221e7	−	1.66102e7i	0.420928	−	0.165202i
$466$	−1.09892e7	−	2.80000e7i	−0.108595	−	0.276695i
$467$	2.19900e7	+	7.12900e7i	0.215911	+	0.699967i	0.997130	+	0.0757098i	$0.0241223\pi$
$467$	2.19900e7	+	7.12900e7i	0.215911	+	0.699967i	−0.781219	+	0.624258i	$0.785402\pi$
$468$	−5.25096e7	−	1.19850e7i	−0.512273	−	0.116923i
$469$	1.27852e8	+	1.11252e8i	1.23933	+	1.07842i
$470$	2.61893e7	+	1.14743e8i	0.252250	+	1.10518i
$471$	−2.27132e7	−	3.93404e7i	−0.217378	−	0.376510i
$472$	1.23900e7	+	7.15335e6i	0.117827	+	0.0680273i
$473$	1.62604e8	+	5.01568e7i	1.53656	+	0.473965i
$474$	1.64085e8	−	1.22965e7i	1.54076	−	0.115464i
$475$	−9.25789e6	−	7.38292e6i	−0.0863836	−	0.0688886i
$476$	3.67436e7	+	1.06884e8i	0.340691	+	0.991044i
$477$	−2.32272e7	−	2.91259e7i	−0.214013	−	0.268364i
$478$	1.36492e8	−	1.26646e8i	1.24975	−	1.15960i
$479$	1.89796e7	+	1.25921e8i	0.172695	+	1.14576i	0.892323	+	0.451397i	$0.149074\pi$
$479$	1.89796e7	+	1.25921e8i	0.172695	+	1.14576i	−0.719628	+	0.694359i	$0.755688\pi$
$480$	−7.24936e7	+	4.94253e7i	−0.655505	+	0.446916i
$481$	1.85990e7	−	1.23397e8i	0.167130	−	1.10884i
$482$	6.99455e7	+	1.45243e8i	0.624624	+	1.29705i
$483$	−3.46398e6	−	1.08502e8i	−0.0307422	−	0.962937i
$484$	−2.13970e7	−	1.03043e7i	−0.188720	−	0.0908827i
$485$	−6.22782e7	−	4.24605e7i	−0.545897	−	0.372186i
$486$	−6.69425e7	+	7.21468e7i	−0.583167	+	0.628504i
$487$	2.52601e6	−	3.37072e7i	0.0218700	−	0.291834i	−0.975535	−	0.219843i	$-0.929446\pi$
$487$	2.52601e6	−	3.37072e7i	0.0218700	−	0.291834i	0.997405	−	0.0719915i	$-0.0229354\pi$
$488$	4.31004e6	+	1.69157e6i	0.0370870	+	0.0145556i
$489$		−	9.57057e7i		−	0.818486i
$490$	2.39594e7	+	1.10550e8i	0.203651	+	0.939656i
$491$	−1.78941e8			−1.51170			−0.755850	−	0.654745i	$-0.772776\pi$
$491$	−1.78941e8			−1.51170			−0.755850	+	0.654745i	$0.772776\pi$
$492$	5.81345e7	−	1.48124e8i	0.488134	−	1.24374i
$493$	8.77639e7	+	6.57699e6i	0.732445	+	0.0548892i
$494$	3.96916e7	+	3.68285e7i	0.329244	+	0.305494i
$495$	−1.53866e7	+	2.25680e7i	−0.126861	+	0.186070i
$496$	−3.93356e7	+	8.16813e7i	−0.322360	+	0.669387i
$497$	−1.09051e7	−	4.82924e6i	−0.0888304	−	0.0393377i
$498$	1.65883e8	−	7.98853e7i	1.34312	−	0.646813i
$499$	−1.17203e8	−	1.76656e7i	−0.943275	−	0.142176i	−0.340641	−	0.940193i	$-0.610644\pi$
$499$	−1.17203e8	−	1.76656e7i	−0.943275	−	0.142176i	−0.602634	+	0.798018i	$0.705882\pi$
$500$	7.90981e7	+	1.16016e8i	0.632785	+	0.928125i
$501$	−6.12210e7	+	9.22758e6i	−0.486841	+	0.0733795i
$502$	8.87122e7	+	9.56090e7i	0.701249	+	0.755766i
$503$	1.25244e8	−	9.98786e7i	0.984129	−	0.784817i	0.00754925	−	0.999972i	$-0.497597\pi$
$503$	1.25244e8	−	9.98786e7i	0.984129	−	0.784817i	0.976580	+	0.215155i	$0.0690255\pi$
$504$	509305.	+	4.75447e6i	0.00397820	+	0.0371373i
$505$	−3.11866e7	+	3.91068e7i	−0.242155	+	0.303653i
$506$	−1.76998e7	−	2.36188e8i	−0.136621	−	1.82308i
$507$	4.64318e7	−	1.50528e8i	0.356280	−	1.15503i
$508$	7.45078e7	−	1.29051e8i	0.568343	−	0.984399i
$509$	−1.91816e8	+	1.10745e8i	−1.45456	+	0.839789i	−0.998735	−	0.0502816i	$-0.983988\pi$
$509$	−1.91816e8	+	1.10745e8i	−1.45456	+	0.839789i	−0.455822	+	0.890071i	$0.650655\pi$
$510$	−9.99260e7	+	2.28075e7i	−0.753300	+	0.171936i
$511$	−1.47389e7	−	8.03061e7i	−0.110460	−	0.601847i
$512$	4.22092e7	−	1.84930e8i	0.314483	−	1.37784i
$513$	2.78796e7	−	8.59973e6i	0.206507	−	0.0636990i
$514$	4.96362e7	−	1.94808e7i	0.365518	−	0.143455i
$515$	9.10198e6	+	2.31915e7i	0.0666368	+	0.169788i
$516$	5.36747e7	+	1.74009e8i	0.390680	+	1.26655i
$517$	1.73517e8	+	3.96042e7i	1.25566	+	0.286596i
$518$	−1.41240e8	+	2.59223e7i	−1.01617	+	0.186502i
$519$	3.13998e7	+	1.37572e8i	0.224608	+	0.984072i
$520$	−8.85364e6	−	1.53349e7i	−0.0629668	−	0.109062i
$521$	1.16258e8	+	6.71217e7i	0.822073	+	0.474624i	0.851131	−	0.524954i	$-0.175917\pi$
$521$	1.16258e8	+	6.71217e7i	0.822073	+	0.474624i	−0.0290579	+	0.999578i	$0.509251\pi$
$522$	4.61171e7	+	1.42252e7i	0.324228	+	0.100011i
$523$	−2.09009e7	+	1.56630e6i	−0.146103	+	0.0109489i	−0.147581	−	0.989050i	$-0.547149\pi$
$523$	−2.09009e7	+	1.56630e6i	−0.146103	+	0.0109489i	0.00147785	+	0.999999i	$0.499530\pi$
$524$	−4.97630e7	−	3.96847e7i	−0.345870	−	0.275822i
$525$	6.65143e7	−	7.12510e6i	0.459660	−	0.0492394i
$526$	−9.47005e7	−	1.18751e8i	−0.650721	−	0.815978i
$527$	−8.47722e7	+	7.86571e7i	−0.579191	+	0.537410i
$528$	1.81103e7	+	1.20154e8i	0.123034	+	0.816276i
$529$	4.21054e7	−	2.87070e7i	0.284427	−	0.193919i
$530$	2.36602e7	−	1.56975e8i	0.158924	−	1.05439i
$531$	−2.26682e7	−	4.70710e7i	−0.151403	−	0.314391i
$532$	1.31205e7	−	2.96281e7i	0.0871397	−	0.196774i
$533$	−3.17157e8	−	1.52735e8i	−2.09456	−	1.00869i
$534$	−1.18885e7	−	8.10547e6i	−0.0780737	−	0.0532297i
$535$	6.61812e6	−	7.13263e6i	0.0432188	−	0.0465788i
$536$	−2.28143e6	+	3.04435e7i	−0.0148154	+	0.197697i
$537$	−1.93287e8	−	7.58594e7i	−1.24818	−	0.489876i
$538$		−	3.06941e8i		−	1.97110i
$539$	1.66341e8	+	3.98911e7i	1.06226	+	0.254747i
$540$	−1.23671e8			−0.785391
$541$	8.46404e7	−	2.15660e8i	0.534547	−	1.36200i	−0.367362	−	0.930078i	$-0.619739\pi$
$541$	8.46404e7	−	2.15660e8i	0.534547	−	1.36200i	0.901909	−	0.431926i	$-0.142166\pi$
$542$	3.47021e8	+	2.60056e7i	2.17950	+	0.163331i
$543$	2.94738e7	+	2.73477e7i	0.184093	+	0.170813i
$544$	1.25716e8	−	1.84392e8i	0.780900	−	1.14537i
$545$	−1.07171e7	+	2.22542e7i	−0.0662043	+	0.137475i
$546$	−3.05729e8	+	9.76052e6i	−1.87827	+	0.0599646i
$547$	−2.48681e8	+	1.19759e8i	−1.51943	+	0.731719i	−0.992957	−	0.118473i	$-0.962200\pi$
$547$	−2.48681e8	+	1.19759e8i	−1.51943	+	0.731719i	−0.526473	+	0.850192i	$0.676486\pi$
$548$	−1.35458e8	−	2.04170e7i	−0.823120	−	0.124065i
$549$	−9.52468e6	−	1.39701e7i	−0.0575616	−	0.0844274i
$550$	1.44320e8	−	2.17528e7i	0.867439	−	0.130745i
$551$	−1.71621e7	−	1.84963e7i	−0.102592	−	0.110568i
$552$	1.52887e7	−	1.21923e7i	0.0908977	−	0.0724885i
$553$	−2.06008e8	+	7.08192e7i	−1.21817	+	0.418770i
$554$	2.66645e8	−	3.34362e8i	1.56821	−	1.96647i
$555$	−5.06101e6	−	6.75345e7i	−0.0296046	−	0.395045i
$556$	3.02947e7	−	9.82130e7i	0.176255	−	0.571406i
$557$	−1.06358e8	+	1.84217e8i	−0.615467	+	1.06602i	0.374836	+	0.927091i	$0.377699\pi$
$557$	−1.06358e8	+	1.84217e8i	−0.615467	+	1.06602i	−0.990302	+	0.138928i	$0.955634\pi$
$558$	−5.49181e7	+	3.17070e7i	−0.316092	+	0.182496i
$559$	3.92744e8	−	8.96413e7i	2.24840	−	0.513183i
$560$	6.98304e7	−	8.02498e7i	0.397631	−	0.456962i
$561$	−3.44901e7	+	1.51111e8i	−0.195346	+	0.855868i
$562$	−4.06511e8	+	1.25392e8i	−2.29015	+	0.706417i
$563$	5.94394e7	−	2.33283e7i	0.333081	−	0.130725i	−0.192906	−	0.981217i	$-0.561791\pi$
$563$	5.94394e7	−	2.33283e7i	0.333081	−	0.130725i	0.525987	+	0.850493i	$0.323696\pi$
$564$	6.95840e7	+	1.77297e8i	0.387857	+	0.988244i
$565$	2.11228e7	+	6.84785e7i	0.117113	+	0.379672i
$566$	−1.56142e8	−	3.56383e7i	−0.861131	−	0.196548i
$567$	−5.11792e7	+	9.55631e7i	−0.280766	+	0.524253i
$568$	−478061.	−	2.09452e6i	−0.00260879	−	0.0114298i
$569$	3.31023e7	+	5.73348e7i	0.179689	+	0.311230i	0.941774	−	0.336247i	$-0.109158\pi$
$569$	3.31023e7	+	5.73348e7i	0.179689	+	0.311230i	−0.762085	+	0.647477i	$0.775824\pi$
$570$	2.54481e7	+	1.46925e7i	0.137414	+	0.0793361i
$571$	9.46117e7	+	2.91839e7i	0.508202	+	0.156760i	0.538244	−	0.842789i	$-0.319088\pi$
$571$	9.46117e7	+	2.91839e7i	0.508202	+	0.156760i	−0.0300417	+	0.999549i	$0.509564\pi$
$572$	−3.46106e8	+	2.59371e7i	−1.84936	+	0.138590i
$573$	−1.03462e8	−	8.25083e7i	−0.549943	−	0.438565i
$574$	−4.75611e7	+	4.02271e8i	−0.251487	+	2.12708i
$575$	7.64550e7	+	9.58716e7i	0.402163	+	0.504297i
$576$	5.02792e7	−	4.66523e7i	0.263100	−	0.244121i
$577$	1.71160e7	+	1.13557e8i	0.0890994	+	0.591136i	0.988174	+	0.153339i	$0.0490028\pi$
$577$	1.71160e7	+	1.13557e8i	0.0890994	+	0.591136i	−0.899074	+	0.437796i	$0.855759\pi$
$578$	−1.48972e7	+	1.01568e7i	−0.0771475	+	0.0525983i
$579$	8.80903e6	−	5.84441e7i	0.0453829	−	0.301096i
$580$	4.64054e7	+	9.63617e7i	0.237840	+	0.493879i
$581$	−1.85626e8	+	1.57980e8i	−0.946476	+	0.805514i
$582$	−2.11321e8	−	1.01767e8i	−1.07195	−	0.516223i
$583$	−1.98349e8	−	1.35232e8i	−1.00098	−	0.682457i
$584$	1.00036e7	−	1.07814e7i	0.0502250	−	0.0541297i
$585$	−4.83227e6	+	6.44822e7i	−0.0241370	+	0.322086i
$586$	3.30700e8	+	1.29790e8i	1.64339	+	0.644983i
$587$			1.46918e8i			0.726374i	0.931716	+	0.363187i	$0.118311\pi$
$587$			1.46918e8i			0.726374i	−0.931716	+	0.363187i	$0.881689\pi$
$588$	6.50041e7	+	1.71125e8i	0.319749	+	0.841745i
$589$	3.31542e7			0.162253
$590$	8.13361e7	−	2.07241e8i	0.396029	−	1.00907i
$591$	1.97045e8	+	1.47665e7i	0.954558	+	0.0715342i
$592$	9.89949e7	+	9.18539e7i	0.477142	+	0.442723i
$593$	7.65509e7	−	1.12280e8i	0.367102	−	0.538439i	−0.597597	−	0.801797i	$-0.703878\pi$
$593$	7.65509e7	−	1.12280e8i	0.367102	−	0.538439i	0.964698	+	0.263358i	$0.0848300\pi$
$594$	−1.56028e8	+	3.23996e8i	−0.744464	+	1.54589i
$595$	1.20315e8	−	6.27462e7i	0.571173	−	0.297877i
$596$	2.63005e8	−	1.26656e8i	1.24229	−	0.598257i
$597$	2.59375e8	+	3.90945e7i	1.21900	+	0.183735i
$598$	−3.15862e8	−	4.63284e8i	−1.47704	−	2.16643i
$599$	−2.45806e8	+	3.70492e7i	−1.14370	+	0.172385i	−0.693441	−	0.720514i	$-0.743906\pi$
$599$	−2.45806e8	+	3.70492e7i	−1.14370	+	0.172385i	−0.450258	+	0.892899i	$0.648668\pi$
$600$	8.19612e6	+	8.83332e6i	0.0379450	+	0.0408950i
$601$	9.19722e7	−	7.33454e7i	0.423675	−	0.337870i	−0.388329	−	0.921521i	$-0.626948\pi$
$601$	9.19722e7	−	7.33454e7i	0.423675	−	0.337870i	0.812005	+	0.583651i	$0.198376\pi$
$602$	−2.44472e8	−	3.93855e8i	−1.12057	−	1.80529i
$603$	6.95096e7	−	8.71622e7i	0.317024	−	0.397536i
$604$	2.75974e7	+	3.68262e8i	0.125244	+	1.67127i
$605$	−8.40417e6	+	2.72456e7i	−0.0379515	+	0.123036i
$606$	−7.78237e7	+	1.34795e8i	−0.349698	+	0.605696i
$607$	−1.31885e8	+	7.61440e7i	−0.589699	+	0.340463i	−0.764979	−	0.644056i	$-0.777250\pi$
$607$	−1.31885e8	+	7.61440e7i	−0.589699	+	0.340463i	0.175279	+	0.984519i	$0.443917\pi$
$608$	−6.23776e7	+	1.42373e7i	−0.277535	+	0.0633456i
$609$	1.42411e8	+	6.11110e6i	0.630512	+	0.0270563i
$610$	1.60327e7	−	7.02440e7i	0.0706347	−	0.309471i
$611$	4.02627e8	−	1.24194e8i	1.76514	−	0.544474i
$612$	6.92087e7	−	2.71624e7i	0.301930	−	0.118499i
$613$	−1.63784e7	−	4.17314e7i	−0.0711032	−	0.181168i	0.890904	−	0.454191i	$-0.150072\pi$
$613$	−1.63784e7	−	4.17314e7i	−0.0711032	−	0.181168i	−0.962007	+	0.273023i	$0.911976\pi$
$614$	1.07264e8	+	3.47743e8i	0.463394	+	1.50229i
$615$	−1.86250e8	−	4.25105e7i	−0.800704	−	0.182755i
$616$	1.21669e7	+	2.83095e7i	0.0520520	+	0.121113i
$617$	3.84303e7	+	1.68374e8i	0.163613	+	0.716837i	0.988460	+	0.151481i	$0.0484042\pi$
$617$	3.84303e7	+	1.68374e8i	0.163613	+	0.716837i	−0.824847	+	0.565356i	$0.808739\pi$
$618$	3.87623e7	+	6.71383e7i	0.164227	+	0.284449i
$619$	−8.83748e7	−	5.10232e7i	−0.372612	−	0.215127i	0.301987	−	0.953312i	$-0.402350\pi$
$619$	−8.83748e7	−	5.10232e7i	−0.372612	−	0.215127i	−0.674599	+	0.738185i	$0.735683\pi$
$620$	−1.34291e8	−	4.14231e7i	−0.563469	−	0.173807i
$621$	−3.01290e8	+	2.25786e7i	−1.25809	+	0.0942805i
$622$	3.40522e8	+	2.71557e8i	1.41506	+	1.12847i
$623$	1.79454e7	+	6.39007e6i	0.0742145	+	0.0264266i
$624$	1.79356e8	+	2.24905e8i	0.738178	+	0.925647i
$625$	2.40107e7	−	2.22787e7i	0.0983477	−	0.0912534i
$626$	1.60314e7	+	1.06362e8i	0.0653506	+	0.433573i
$627$	3.67154e7	−	2.50321e7i	0.148952	−	0.101554i
$628$	−2.09278e7	+	1.38847e8i	−0.0844976	+	0.560605i
$629$	7.47408e7	+	1.55201e8i	0.300335	+	0.623652i
$630$	7.19781e7	−	1.88639e7i	0.287858	−	0.0754414i
$631$	−2.82139e8	−	1.35871e8i	−1.12299	−	0.540802i	−0.222173	−	0.975007i	$-0.571315\pi$
$631$	−2.82139e8	−	1.35871e8i	−1.12299	−	0.540802i	−0.900814	+	0.434205i	$0.857029\pi$
$632$	−3.24221e7	−	2.21050e7i	−0.128437	−	0.0875667i
$633$	2.39731e8	−	2.58368e8i	0.945175	−	1.01866i
$634$	3.50506e7	−	4.67718e8i	0.137540	−	1.83534i
$635$	−1.66537e8	−	6.53611e7i	−0.650415	−	0.255269i
$636$		−	2.56901e8i		−	0.998607i
$637$	3.88253e8	−	1.15111e8i	1.50209	−	0.445348i
$638$	3.10998e8			1.19755
$639$	−2.86626e6	+	7.30310e6i	−0.0109853	+	0.0279901i
$640$	4.18777e7	+	3.13830e6i	0.159751	+	0.0119717i
$641$	3.51094e8	+	3.25768e8i	1.33306	+	1.23690i	0.949647	+	0.313321i	$0.101442\pi$
$641$	3.51094e8	+	3.25768e8i	1.33306	+	1.23690i	0.383412	+	0.923577i	$0.374749\pi$
$642$	1.70558e7	−	2.50163e7i	0.0644567	−	0.0945406i
$643$	−2.07803e8	+	4.31507e8i	−0.781661	+	1.62314i	0.000452007		1.00000i	$0.499856\pi$
$643$	−2.07803e8	+	4.31507e8i	−0.781661	+	1.62314i	−0.782113	+	0.623136i	$0.785858\pi$
$644$	−2.00738e8	+	2.68891e8i	−0.751576	+	1.00674i
$645$	1.96973e8	−	9.48574e7i	0.734055	−	0.353502i
$646$	−7.39077e7	−	1.11398e7i	−0.274152	−	0.0413218i
$647$	−6.33284e7	−	9.28857e7i	−0.233822	−	0.342954i	0.691338	−	0.722532i	$-0.257022\pi$
$647$	−6.33284e7	−	9.28857e7i	−0.233822	−	0.342954i	−0.925160	+	0.379578i	$0.876069\pi$
$648$	−1.93093e7	+	2.91041e6i	−0.0709647	+	0.0106962i
$649$	−2.28993e8	−	2.46795e8i	−0.837698	−	0.902823i
$650$	2.70139e8	−	2.15429e8i	0.983664	−	0.784446i
$651$	−1.33164e8	+	1.31711e8i	−0.482662	+	0.477395i
$652$	−1.84447e8	+	2.31290e8i	−0.665472	+	0.834476i
$653$	−1.31093e7	−	1.74931e8i	−0.0470802	−	0.628242i	−0.969977	−	0.243195i	$-0.921804\pi$
$653$	−1.31093e7	−	1.74931e8i	−0.0470802	−	0.628242i	0.922897	−	0.385046i	$-0.125815\pi$
$654$	−2.26551e7	+	7.34461e7i	−0.0809903	+	0.262564i
$655$	−3.82079e7	+	6.61779e7i	−0.135966	+	0.235499i
$656$	3.29907e8	−	1.90472e8i	1.16864	−	0.674714i
$657$	−5.23619e7	+	1.19513e7i	−0.184637	+	0.0421423i
$658$	−2.85770e8	−	3.91684e8i	−1.00309	−	1.37486i
$659$	−1.17190e7	+	5.13445e7i	−0.0409483	+	0.179406i	−0.991266	−	0.131874i	$-0.957901\pi$
$659$	−1.17190e7	+	5.13445e7i	−0.0409483	+	0.179406i	0.950318	+	0.311280i	$0.100758\pi$
$660$	−1.79991e8	+	5.55197e7i	−0.626063	+	0.193115i
$661$	−4.05463e8	+	1.59133e8i	−1.40394	+	0.551004i	−0.941911	−	0.335863i	$-0.890972\pi$
$661$	−4.05463e8	+	1.59133e8i	−1.40394	+	0.551004i	−0.462024	+	0.886867i	$0.652877\pi$
$662$	−2.86369e8	−	7.29655e8i	−0.987078	−	2.51503i
$663$	1.08157e8	+	3.50635e8i	0.371119	+	1.20314i
$664$	−4.28070e7	−	9.77042e6i	−0.146221	−	0.0333741i
$665$	−3.75212e7	−	1.02747e7i	−0.127588	−	0.0349384i
$666$	2.10195e7	+	9.20923e7i	0.0711539	+	0.311746i
$667$	1.30647e8	+	2.26287e8i	0.440272	+	0.762574i
$668$	1.65735e8	+	9.56872e7i	0.556013	+	0.321014i
$669$	4.31218e8	+	1.33013e8i	1.44019	+	0.444239i
$670$	4.73741e8	−	3.55020e7i	1.57513	−	0.118040i
$671$	−8.51857e7	−	6.79334e7i	−0.281968	−	0.224862i
$672$	1.93979e8	−	3.04990e8i	0.639216	−	1.00503i
$673$	1.34024e8	+	1.68061e8i	0.439682	+	0.551343i	0.951459	−	0.307775i	$-0.0995843\pi$
$673$	1.34024e8	+	1.68061e8i	0.439682	+	0.551343i	−0.511778	+	0.859118i	$0.671013\pi$
$674$	2.00120e8	−	1.85684e8i	0.653597	−	0.606450i
$675$	−2.77487e7	−	1.84101e8i	−0.0902259	−	0.598610i
$676$	−4.02314e8	+	2.74293e8i	−1.30234	+	0.887921i
$677$	3.48740e7	−	2.31374e8i	0.112392	−	0.745673i	−0.859653	−	0.510878i	$-0.829320\pi$
$677$	3.48740e7	−	2.31374e8i	0.112392	−	0.745673i	0.972045	−	0.234794i	$-0.0754417\pi$
$678$	9.67534e7	+	2.00910e8i	0.310440	+	0.644634i
$679$	3.04782e8	+	5.94015e7i	0.973600	+	0.189753i
$680$	2.20224e7	+	1.06054e7i	0.0700387	+	0.0337289i
$681$	1.59619e8	+	1.08826e8i	0.505408	+	0.344581i
$682$	−2.77948e8	+	2.99556e8i	−0.876214	+	0.944334i
$683$	−1.72585e7	+	2.30299e8i	−0.0541679	+	0.722821i	0.902323	+	0.431060i	$0.141860\pi$
$683$	−1.72585e7	+	2.30299e8i	−0.0541679	+	0.722821i	−0.956491	+	0.291761i	$0.905759\pi$
$684$	−1.98417e7	−	7.78731e6i	−0.0620028	−	0.0243343i
$685$			1.64465e8i			0.511683i
$686$	−2.70509e8	−	3.79440e8i	−0.837933	−	1.17536i
$687$	−3.52812e8			−1.08811
$688$	−1.59270e8	+	4.05812e8i	−0.489066	+	1.24612i
$689$	−5.66733e8	−	4.24707e7i	−1.73269	−	0.129847i
$690$	−2.23068e8	−	2.06977e8i	−0.679032	−	0.630050i
$691$	2.19166e7	−	3.21457e7i	0.0664260	−	0.0974291i	−0.791588	−	0.611055i	$-0.790746\pi$
$691$	2.19166e7	−	3.21457e7i	0.0664260	−	0.0974291i	0.858014	+	0.513626i	$0.171698\pi$
$692$	1.89250e8	−	3.92981e8i	0.571106	−	1.18591i
$693$	2.15255e7	−	1.10445e8i	0.0646776	−	0.331854i
$694$	−5.08890e8	+	2.45069e8i	−1.52246	+	0.733178i
$695$	−1.22016e8	−	1.83909e7i	−0.363465	−	0.0547835i
$696$	1.44643e7	+	2.12152e7i	0.0429011	+	0.0629244i
$697$	4.80496e8	−	7.24231e7i	1.41903	−	0.213884i
$698$	−1.78551e8	−	1.92432e8i	−0.525044	−	0.565863i
$699$	−4.56907e7	+	3.64371e7i	−0.133782	+	0.106687i
$700$	−1.74475e8	−	1.10970e8i	−0.508674	−	0.323527i
$701$	2.71214e8	−	3.40092e8i	0.787334	−	0.987285i	−0.212615	−	0.977136i	$-0.568198\pi$
$701$	2.71214e8	−	3.40092e8i	0.787334	−	0.987285i	0.999948	−	0.0101491i	$-0.00323061\pi$
$702$	6.36200e7	+	8.48950e8i	0.183900	+	2.45398i
$703$	1.45568e7	−	4.71919e7i	0.0418986	−	0.135832i
$704$	2.20995e8	−	3.82775e8i	0.633380	−	1.09705i
$705$	1.98030e8	−	1.14333e8i	0.565150	−	0.326289i
$706$	−9.51598e8	+	2.17196e8i	−2.70420	+	0.617217i
$707$	5.44233e7	−	1.98743e8i	0.154002	−	0.562386i
$708$	8.01703e7	−	3.51249e8i	0.225899	−	0.989726i
$709$	−6.16992e8	+	1.90317e8i	−1.73118	+	0.533997i	−0.990457	−	0.137820i	$-0.955991\pi$
$709$	−6.16992e8	+	1.90317e8i	−1.73118	+	0.533997i	−0.740718	+	0.671816i	$0.765514\pi$
$710$	−3.11207e7	+	1.22140e7i	−0.0869509	+	0.0341257i
$711$	5.23525e7	+	1.33392e8i	0.145656	+	0.371126i
$712$	1.01142e6	+	3.27896e6i	0.00280216	+	0.00908439i
$713$	−3.34725e8	−	7.63988e7i	−0.923463	−	0.210774i
$714$	3.41105e8	−	2.48868e8i	0.937116	−	0.683715i
$715$	9.27226e7	+	4.06244e8i	0.253669	+	1.11140i
$716$	3.20912e8	+	5.55836e8i	0.874273	+	1.51429i
$717$	−3.13293e8	−	1.80880e8i	−0.849950	−	0.490719i
$718$	−2.08187e8	−	6.42173e7i	−0.562446	−	0.173492i
$719$	−2.98659e8	+	2.23814e7i	−0.803507	+	0.0602145i	−0.470150	−	0.882586i	$-0.655800\pi$
$719$	−2.98659e8	+	2.23814e7i	−0.803507	+	0.0602145i	−0.333356	+	0.942801i	$0.608181\pi$
$720$	−5.47099e7	−	4.36297e7i	−0.146578	−	0.116892i
$721$	−7.21742e7	−	7.29704e7i	−0.192565	−	0.194689i
$722$	−3.25365e8	−	4.07995e8i	−0.864490	−	1.08404i
$723$	2.29598e8	−	2.13036e8i	0.607510	−	0.563687i
$724$	−1.85232e7	−	1.22893e8i	−0.0488091	−	0.323827i
$725$	−1.33035e8	+	9.07018e7i	−0.349102	+	0.238014i
$726$	−1.32235e7	+	8.77320e7i	−0.0345570	+	0.229270i
$727$	−87621.9	−	181949.i	−0.000228039	−	0.000473528i	0.900855	−	0.434120i	$-0.142941\pi$
$727$	−87621.9	−	181949.i	−0.000228039	−	0.000473528i	−0.901083	+	0.433647i	$0.857227\pi$
$728$	5.84544e7	+	4.36386e7i	0.151504	+	0.113104i
$729$	3.79865e8	+	1.82933e8i	0.980497	+	0.472183i
$730$	−1.89100e8	−	1.28926e8i	−0.486096	−	0.331414i
$731$	−3.78233e8	+	4.07638e8i	−0.968295	+	1.04357i
$732$	8.71344e6	−	1.16273e8i	0.0222155	−	0.296445i
$733$	5.04998e8	+	1.98197e8i	1.28226	+	0.503252i	0.906007	−	0.423263i	$-0.139115\pi$
$733$	5.04998e8	+	1.98197e8i	1.28226	+	0.503252i	0.376258	+	0.926515i	$0.377211\pi$
$734$		−	4.76024e8i		−	1.20376i
$735$	1.91522e8	−	1.07791e8i	0.482343	−	0.271469i
$736$	6.62573e8			1.66188
$737$	2.62466e8	−	6.68751e8i	0.655647	−	1.67056i
$738$	2.65716e8	+	1.99127e7i	0.661072	+	0.0495405i
$739$	−2.90523e8	−	2.69565e8i	−0.719857	−	0.667930i	0.232610	−	0.972570i	$-0.425273\pi$
$739$	−2.90523e8	−	2.69565e8i	−0.719857	−	0.667930i	−0.952468	+	0.304640i	$0.901464\pi$
$740$	−1.17924e8	+	1.72963e8i	−0.291010	+	0.426833i
$741$	4.56441e7	−	9.47809e7i	0.112184	−	0.232952i
$742$	1.65795e8	+	6.32614e8i	0.405843	+	1.54856i
$743$	6.46061e6	−	3.11126e6i	0.0157510	−	0.00758526i	−0.425992	−	0.904727i	$-0.640075\pi$
$743$	6.46061e6	−	3.11126e6i	0.0157510	−	0.00758526i	0.441743	+	0.897142i	$0.354360\pi$
$744$	−3.33618e7	−	5.02849e6i	−0.0810086	−	0.0122101i
$745$	−1.97423e8	−	2.89567e8i	−0.477452	−	0.700293i
$746$	8.50219e8	−	1.28150e8i	2.04793	−	0.308675i
$747$	1.09060e8	+	1.17539e8i	0.261640	+	0.281981i
$748$	3.74577e8	−	2.98716e8i	0.895028	−	0.713761i
$749$	−1.34462e7	+	3.77614e7i	−0.0320004	+	0.0898674i
$750$	3.27064e8	−	4.10125e8i	0.775262	−	0.972147i
$751$	3.26001e6	+	4.35018e7i	0.00769660	+	0.102704i	0.999729	−	0.0232789i	$-0.00741059\pi$
$751$	3.26001e6	+	4.35018e7i	0.00769660	+	0.102704i	−0.992032	+	0.125983i	$0.959792\pi$
$752$	−1.34400e8	+	4.35713e8i	−0.316042	+	1.02458i
$753$	1.26701e8	−	2.19453e8i	0.296754	−	0.513992i
$754$	6.37612e8	−	3.68125e8i	1.48745	−	0.858780i
$755$	4.32250e8	−	9.86581e7i	1.00437	−	0.229241i
$756$	4.68076e8	−	2.01170e8i	1.08330	−	0.465584i
$757$	−1.64623e7	+	7.21260e7i	−0.0379492	+	0.166266i	−0.990352	−	0.138577i	$-0.955747\pi$
$757$	−1.64623e7	+	7.21260e7i	−0.0379492	+	0.166266i	0.952402	+	0.304844i	$0.0986042\pi$
$758$	−6.13629e7	+	1.89280e7i	−0.140896	+	0.0434606i
$759$	−4.28362e8	+	1.68120e8i	−0.979683	+	0.384497i
$760$	−2.56019e6	−	6.52327e6i	−0.00583219	−	0.0148602i
$761$	−1.09842e8	−	3.56099e8i	−0.249238	−	0.808009i	−0.990586	−	0.136889i	$-0.956290\pi$
$761$	−1.09842e8	−	3.56099e8i	−0.249238	−	0.808009i	0.741349	−	0.671120i	$-0.234187\pi$
$762$	−5.42745e8	−	1.23878e8i	−1.22668	−	0.279982i
$763$	4.36247e6	−	1.01662e8i	0.00982108	−	0.228868i
$764$	9.10216e7	+	3.98792e8i	0.204110	+	0.894264i
$765$	−4.46302e7	−	7.73018e7i	−0.0996884	−	0.172665i
$766$	−4.29704e8	−	2.48090e8i	−0.956056	−	0.551979i
$767$	−7.61614e8	−	2.34927e8i	−1.68791	−	0.520650i
$768$	−3.04966e8	+	2.28540e7i	−0.673237	+	0.0504521i
$769$	1.48495e8	+	1.18421e8i	0.326538	+	0.260405i	0.773012	−	0.634391i	$-0.218749\pi$
$769$	1.48495e8	+	1.18421e8i	0.326538	+	0.260405i	−0.446474	+	0.894796i	$0.647321\pi$
$770$	4.07393e8	−	2.52876e8i	0.892362	−	0.553904i
$771$	−6.45927e7	−	8.09967e7i	−0.140935	−	0.176728i
$772$	−1.33924e8	+	1.24263e8i	−0.291076	+	0.270079i
$773$	5.61454e7	+	3.72500e8i	0.121556	+	0.806470i	0.963656	+	0.267148i	$0.0860813\pi$
$773$	5.61454e7	+	3.72500e8i	0.121556	+	0.806470i	−0.842100	+	0.539322i	$0.818681\pi$
$774$	−2.51949e8	+	1.71776e8i	−0.543362	+	0.370458i
$775$	3.15324e7	−	2.09204e8i	0.0677410	−	0.449432i
$776$	2.42692e7	+	5.03955e7i	0.0519362	+	0.107847i
$777$	1.29011e8	+	2.47376e8i	0.275019	+	0.527344i
$778$	5.45946e8	+	2.62914e8i	1.15934	+	0.558309i
$779$	−1.15104e8	−	7.84769e7i	−0.243489	−	0.166008i
$780$	−3.03301e8	+	3.26881e8i	−0.639131	+	0.688820i
$781$	−3.77808e6	+	5.04150e7i	−0.00793082	+	0.105829i
$782$	7.20503e8	+	2.82777e8i	1.50666	+	0.591321i
$783$		−	3.96721e8i		−	0.826418i
$784$	−1.33759e8	+	4.17324e8i	−0.277570	+	0.866014i
$785$	1.68579e8			0.348493
$786$	−8.68728e7	+	2.21348e8i	−0.178902	+	0.455836i
$787$	9.07984e8	+	6.80440e7i	1.86275	+	0.139594i	0.958075	−	0.286516i	$-0.0924973\pi$
$787$	9.07984e8	+	6.80440e7i	1.86275	+	0.139594i	0.904671	+	0.426110i	$0.140116\pi$
$788$	−4.47735e8	−	4.15437e8i	−0.915044	−	0.849037i
$789$	−1.66236e8	+	2.43823e8i	−0.338449	+	0.496414i
$790$	−2.64944e8	+	5.50162e8i	−0.537369	+	1.11586i
$791$	−1.91338e8	−	2.24821e8i	−0.386608	−	0.454263i
$792$	1.82620e7	−	8.79452e6i	0.0367598	−	0.0177026i
$793$	−2.55061e8	−	3.84443e7i	−0.511476	−	0.0770925i
$794$	2.31795e8	+	3.39982e8i	0.463067	+	0.679194i
$795$	−3.04984e8	+	4.59690e7i	−0.606982	+	0.0914878i
$796$	−5.51481e8	−	5.94356e8i	−1.09343	−	1.17844i
$797$	−1.69943e8	+	1.35525e8i	−0.335682	+	0.267697i	−0.776794	−	0.629755i	$-0.783155\pi$
$797$	−1.69943e8	+	1.35525e8i	−0.335682	+	0.267697i	0.441112	+	0.897452i	$0.354584\pi$
$798$	−1.20217e8	−	1.42134e7i	−0.236569	−	0.0279699i
$799$	−3.62637e8	+	4.54732e8i	−0.710938	+	0.891488i
$800$	3.05113e7	+	4.07145e8i	0.0595924	+	0.795206i
$801$	3.69349e6	−	1.19740e7i	0.00718687	−	0.0232993i
$802$	3.31027e8	−	5.73355e8i	0.641711	−	1.11148i
$803$	−2.99732e8	+	1.73050e8i	−0.578877	+	0.334215i
$804$	7.49526e8	−	1.71074e8i	1.44218	−	0.329167i
$805$	3.55138e8	+	1.90195e8i	0.680784	+	0.364596i
$806$	−2.15270e8	+	9.43160e8i	−0.411129	+	1.80128i
$807$	−5.69857e8	+	1.75778e8i	−1.08429	+	0.334459i
$808$	3.45527e7	−	1.35609e7i	0.0655009	−	0.0257072i
$809$	−2.28917e8	−	5.83270e8i	−0.432346	−	1.10160i	−0.966603	−	0.256278i	$-0.917504\pi$
$809$	−2.28917e8	−	5.83270e8i	−0.432346	−	1.10160i	0.534257	−	0.845322i	$-0.320592\pi$
$810$	8.95679e7	+	2.90372e8i	0.168538	+	0.546386i
$811$	1.73001e8	+	3.94864e7i	0.324330	+	0.0740261i	0.381586	−	0.924333i	$-0.375378\pi$
$811$	1.73001e8	+	3.94864e7i	0.324330	+	0.0740261i	−0.0572563	+	0.998360i	$0.518235\pi$
$812$	−3.32385e8	−	2.89229e8i	−0.620831	−	0.540224i
$813$	−1.50449e8	−	6.59160e8i	−0.279974	−	1.22665i
$814$	3.04354e8	+	5.27157e8i	0.564295	+	0.977388i
$815$	3.07584e8	+	1.77584e8i	0.568186	+	0.328042i
$816$	−3.79449e8	−	1.17044e8i	−0.698365	−	0.215417i
$817$	1.58980e8	−	1.19139e7i	0.291526	−	0.0218469i
$818$	6.32198e8	+	5.04161e8i	1.15503	+	0.921106i
$819$	−8.66011e7	−	2.51916e8i	−0.157642	−	0.458568i
$820$	3.68180e8	+	4.61683e8i	0.667756	+	0.837340i
$821$	3.47291e8	−	3.22239e8i	0.627573	−	0.582303i	−0.300921	−	0.953649i	$-0.597294\pi$
$821$	3.47291e8	−	3.22239e8i	0.627573	−	0.582303i	0.928495	+	0.371346i	$0.121104\pi$
$822$	7.62754e7	+	5.06054e8i	0.137331	+	0.911132i
$823$	−2.10588e7	+	1.43576e7i	−0.0377776	+	0.0257563i	−0.582062	−	0.813145i	$-0.697754\pi$
$823$	−2.10588e7	+	1.43576e7i	−0.0377776	+	0.0257563i	0.544284	+	0.838901i	$0.316801\pi$
$824$	2.75549e6	−	1.82815e7i	0.00492512	−	0.0326760i
$825$	−1.23034e8	−	2.55483e8i	−0.219111	−	0.454988i
$826$	2.92654e7	+	9.16682e8i	0.0519296	+	1.62659i
$827$	2.36182e8	+	1.13739e8i	0.417572	+	0.201092i	0.630859	−	0.775898i	$-0.282703\pi$
$827$	2.36182e8	+	1.13739e8i	0.417572	+	0.201092i	−0.213287	+	0.976990i	$0.568417\pi$
$828$	1.82378e8	+	1.24343e8i	0.321278	+	0.219044i
$829$	4.70689e8	−	5.07282e8i	0.826172	−	0.890401i	−0.169290	−	0.985566i	$-0.554147\pi$
$829$	4.70689e8	−	5.07282e8i	0.826172	−	0.890401i	0.995462	+	0.0951650i	$0.0303379\pi$
$830$	−5.10603e7	+	6.81353e8i	−0.0892996	+	1.19162i
$831$	−7.73466e8	−	3.03563e8i	−1.34784	−	0.528988i
$832$		−	1.04636e9i		−	1.81682i
$833$	−3.53306e8	+	4.33196e8i	−0.611246	+	0.749461i
$834$	−3.83970e8			−0.661910
$835$	8.39405e7	−	2.13877e8i	0.144182	−	0.367371i
$836$	−1.36972e8	−	1.02646e7i	−0.234430	−	0.0175681i
$837$	3.82126e8	+	3.54561e8i	0.651674	+	0.604665i
$838$	−4.45512e8	+	6.53445e8i	−0.757054	+	1.11039i
$839$	−6.86175e7	+	1.42486e8i	−0.116185	+	0.241260i	−0.950949	−	0.309347i	$-0.899889\pi$
$839$	−6.86175e7	+	1.42486e8i	−0.116185	+	0.241260i	0.834764	+	0.550607i	$0.185604\pi$
$840$	3.61978e7	+	1.60299e7i	0.0610724	+	0.0270453i
$841$	2.26801e8	−	1.09221e8i	0.381291	−	0.183620i
$842$	−7.68182e8	−	1.15785e8i	−1.28685	−	0.193961i
$843$	4.65597e8	+	6.82906e8i	0.777191	+	1.13993i
$844$	−1.07729e9	+	1.62375e8i	−1.79186	+	0.270079i
$845$	3.97620e8	+	4.28532e8i	0.659019	+	0.710253i
$846$	−2.49357e8	+	1.98856e8i	−0.411824	+	0.328418i
$847$	−1.25109e7	−	1.16791e8i	−0.0205891	−	0.192203i
$848$	3.83461e8	−	4.80845e8i	0.628830	−	0.788528i
$849$	2.32535e7	+	3.10297e8i	0.0379984	+	0.507054i
$850$	−1.40585e8	+	4.55765e8i	−0.228919	+	0.742137i
$851$	−2.55712e8	+	4.42906e8i	−0.414918	+	0.718660i
$852$	−4.68540e7	+	2.70512e7i	−0.0757578	+	0.0437388i
$853$	9.12066e8	−	2.08173e8i	1.46953	−	0.335411i	0.588512	−	0.808489i	$-0.299714\pi$
$853$	9.12066e8	−	2.08173e8i	1.46953	−	0.335411i	0.881021	+	0.473077i	$0.156857\pi$
$854$	5.35815e7	+	2.91943e8i	0.0860283	+	0.468731i
$855$	−5.69442e6	+	2.49489e7i	−0.00911068	+	0.0399165i
$856$	−6.89971e6	+	2.12828e6i	−0.0110004	+	0.00339318i
$857$	1.16235e8	−	4.56190e7i	0.184670	−	0.0724776i	−0.271204	−	0.962522i	$-0.587422\pi$
$857$	1.16235e8	−	4.56190e7i	0.184670	−	0.0724776i	0.455874	+	0.890044i	$0.349327\pi$
$858$	4.73713e8	+	1.20700e9i	0.749987	+	1.91094i
$859$	−3.45998e8	−	1.12170e9i	−0.545877	−	1.76969i	−0.633729	−	0.773555i	$-0.718476\pi$
$859$	−3.45998e8	−	1.12170e9i	−0.545877	−	1.76969i	0.0878521	−	0.996134i	$-0.472000\pi$
$860$	−6.58834e8	−	1.50374e8i	−1.03581	−	0.236417i
$861$	7.74080e8	−	1.42070e8i	1.21276	−	0.222584i
$862$	−6.53037e7	−	2.86114e8i	−0.101957	−	0.446702i
$863$	1.52667e8	+	2.64427e8i	0.237527	+	0.411408i	0.960004	−	0.279986i	$-0.0903300\pi$
$863$	1.52667e8	+	2.64427e8i	0.237527	+	0.411408i	−0.722477	+	0.691395i	$0.756997\pi$
$864$	−8.71205e8	−	5.02991e8i	−1.35076	−	0.779864i
$865$	−5.00397e8	−	1.54352e8i	−0.773155	−	0.238487i
$866$	−2.96515e8	+	2.22207e7i	−0.456554	+	0.0342140i
$867$	2.73880e7	+	2.18412e7i	0.0420245	+	0.0335134i
$868$	5.75651e8	−	6.16645e7i	0.880238	−	0.0942922i
$869$	5.75741e8	+	7.21957e8i	0.877340	+	1.10015i
$870$	2.92901e8	−	2.71773e8i	0.444799	−	0.412713i
$871$	−2.53485e8	−	1.68176e9i	−0.383617	−	2.54513i
$872$	1.51447e7	−	1.03255e7i	0.0228407	−	0.0155726i
$873$	3.04436e7	−	2.01980e8i	0.0457565	−	0.303575i
$874$	−9.62804e7	−	1.99928e8i	−0.144213	−	0.299461i
$875$	−2.81202e8	+	6.34995e8i	−0.419753	+	0.947864i
$876$	−3.33697e8	−	1.60700e8i	−0.496409	−	0.239058i
$877$	1.47464e8	+	1.00539e8i	0.218618	+	0.149052i	0.667678	−	0.744450i	$-0.267288\pi$
$877$	1.47464e8	+	1.00539e8i	0.218618	+	0.149052i	−0.449059	+	0.893502i	$0.648241\pi$
$878$	1.56671e7	−	1.68851e7i	0.0231475	−	0.0249471i
$879$	5.15805e7	−	6.88293e8i	0.0759484	−	1.01346i
$880$	−4.19761e8	−	1.64744e8i	−0.615963	−	0.241748i
$881$		−	3.20702e8i		−	0.469001i	−0.972116	−	0.234501i	$-0.924654\pi$
$881$		−	3.20702e8i		−	0.469001i	0.972116	−	0.234501i	$-0.0753455\pi$
$882$	−2.41741e8	+	1.88481e8i	−0.352326	+	0.274702i
$883$	−4.29379e8			−0.623676			−0.311838	−	0.950135i	$-0.600945\pi$
$883$	−4.29379e8			−0.623676			−0.311838	+	0.950135i	$0.600945\pi$
$884$	4.14377e8	−	1.05582e9i	0.599845	−	1.52838i
$885$	−4.31336e8	−	3.23242e7i	−0.622280	−	0.0466334i
$886$	2.74632e8	+	2.54821e8i	0.394866	+	0.366382i
$887$	−2.17328e8	+	3.18762e8i	−0.311419	+	0.456768i	−0.949757	−	0.312988i	$-0.898670\pi$
$887$	−2.17328e8	+	3.18762e8i	−0.311419	+	0.456768i	0.638338	+	0.769756i	$0.279622\pi$
$888$	−2.18055e7	+	4.52797e7i	−0.0311407	+	0.0646643i
$889$	7.36639e8	−	2.35175e7i	1.04845	−	0.0334723i
$890$	4.81091e7	−	2.31681e7i	0.0682429	−	0.0328640i
$891$	4.54391e8	+	6.84885e7i	0.642387	+	0.0968243i
$892$	−7.85768e8	−	1.15251e9i	−1.10713	−	1.62386i
$893$	1.64886e8	−	2.48526e7i	0.231542	−	0.0348993i
$894$	−7.41762e8	−	7.99429e8i	−1.03813	−	1.11884i
$895$	6.02447e8	−	4.80435e8i	0.840330	−	0.670141i
$896$	−1.63606e8	+	5.62428e7i	−0.227444	+	0.0781885i
$897$	−6.79232e8	+	8.51730e8i	−0.941111	+	1.18012i
$898$	−3.60662e7	−	4.81270e8i	−0.0498048	−	0.664599i
$899$	1.32880e8	−	4.30788e8i	0.182887	−	0.592904i
$900$	−6.80093e7	+	1.17796e8i	−0.0932913	+	0.161585i
$901$	6.79404e8	−	3.92254e8i	0.928868	−	0.536282i
$902$	1.67404e9	−	3.82088e8i	2.28111	−	0.520648i
$903$	−5.91215e8	+	6.79430e8i	−0.802938	+	0.922744i
$904$	1.18335e7	−	5.18459e7i	0.0160180	−	0.0701793i
$905$	−1.42580e8	+	4.39802e7i	−0.192360	+	0.0593351i
$906$	1.28427e9	−	5.04038e8i	1.72691	−	0.677764i
$907$	3.82196e8	+	9.73819e8i	0.512229	+	1.30514i	0.919952	+	0.392032i	$0.128228\pi$
$907$	3.82196e8	+	9.73819e8i	0.512229	+	1.30514i	−0.407723	+	0.913106i	$0.633677\pi$
$908$	−1.76013e8	−	5.70620e8i	−0.235119	−	0.762236i
$909$	−1.32150e8	−	3.01624e7i	−0.175944	−	0.0401582i
$910$	5.35916e8	−	1.00068e9i	0.711169	−	1.32791i
$911$	−2.44991e8	−	1.07337e9i	−0.324037	−	1.41970i	−0.830299	−	0.557319i	$-0.811830\pi$
$911$	−2.44991e8	−	1.07337e9i	−0.324037	−	1.41970i	0.506262	−	0.862380i	$-0.331027\pi$
$912$	5.69218e7	+	9.85914e7i	0.0750402	+	0.129973i
$913$	8.94821e8	+	5.16625e8i	1.17577	+	0.678833i
$914$	−6.58945e8	−	2.03258e8i	−0.863000	−	0.266200i
$915$	−1.39594e8	+	1.04611e7i	−0.182223	+	0.0136558i
$916$	8.52632e8	+	6.79951e8i	1.10937	+	0.884690i
$917$	3.69621e7	−	3.12625e8i	0.0479345	−	0.405430i
$918$	−7.32708e8	−	9.18787e8i	−0.947115	−	1.18765i
$919$	−3.11802e8	+	2.89310e8i	−0.401729	+	0.372750i	−0.855005	−	0.518621i	$-0.826446\pi$
$919$	−3.11802e8	+	2.89310e8i	−0.401729	+	0.372750i	0.453276	+	0.891370i	$0.350255\pi$
$920$	1.08159e7	+	7.17586e7i	0.0138899	+	0.0921532i
$921$	5.84180e8	−	3.98287e8i	0.747770	−	0.509821i
$922$	2.35916e8	−	1.56520e9i	0.300999	−	1.99700i
$923$	5.19299e7	+	1.07834e8i	0.0660408	+	0.137135i
$924$	5.90926e8	−	5.02917e8i	0.749061	−	0.637501i
$925$	−2.83938e8	−	1.36737e8i	−0.358755	−	0.172767i
$926$	−2.61549e8	−	1.78321e8i	−0.329398	−	0.224579i
$927$	−4.59211e7	+	4.94912e7i	−0.0576465	+	0.0621282i
$928$	−6.50149e7	+	8.67564e8i	−0.0813522	+	1.08557i
$929$	−3.55385e8	−	1.39478e8i	−0.443253	−	0.173964i	0.133209	−	0.991088i	$-0.457472\pi$
$929$	−3.55385e8	−	1.39478e8i	−0.443253	−	0.173964i	−0.576462	+	0.817124i	$0.695567\pi$
$930$			5.25017e8i			0.652717i
$931$	1.58725e8	−	2.21460e7i	0.196697	−	0.0274439i
$932$	1.80642e8			0.223137
$933$	3.09156e8	−	7.87716e8i	0.380656	−	0.969895i
$934$	−8.59104e8	−	6.43810e7i	−1.05440	−	0.0790163i
$935$	−4.21650e8	−	3.91234e8i	−0.515843	−	0.478633i
$936$	2.70310e7	−	3.96472e7i	0.0329636	−	0.0483488i
$937$	1.29658e8	−	2.69238e8i	0.157609	−	0.327278i	−0.807179	−	0.590306i	$-0.799007\pi$
$937$	1.29658e8	−	2.69238e8i	0.157609	−	0.327278i	0.964788	+	0.263028i	$0.0847212\pi$
$938$	−1.73529e9	+	9.04984e8i	−2.10263	+	1.09656i
$939$	1.88287e8	−	9.06741e7i	0.227417	−	0.109518i
$940$	−6.98920e8	−	1.05345e8i	−0.841480	−	0.126833i
$941$	6.88345e8	+	1.00962e9i	0.826108	+	1.21168i	0.974863	+	0.222804i	$0.0715211\pi$
$941$	6.88345e8	+	1.00962e9i	0.826108	+	1.21168i	−0.148755	+	0.988874i	$0.547527\pi$
$942$	5.18714e8	−	7.81835e7i	0.620547	−	0.0935325i
$943$	9.81259e8	+	1.05755e9i	1.17017	+	1.26114i
$944$	6.74344e8	−	5.37771e8i	0.801614	−	0.639266i
$945$	−3.22578e8	−	5.19687e8i	−0.382243	−	0.615809i
$946$	−1.22517e9	+	1.53631e9i	−1.44718	+	1.81470i
$947$	1.18753e8	+	1.58465e9i	0.139829	+	1.86588i	0.422101	+	0.906549i	$0.361293\pi$
$947$	1.18753e8	+	1.58465e9i	0.139829	+	1.86588i	−0.282273	+	0.959334i	$0.591088\pi$
$948$	−2.91273e8	+	9.44283e8i	−0.341881	+	1.10835i
$949$	−4.09676e8	+	7.09580e8i	−0.479338	+	0.830238i
$950$	1.18421e8	−	6.83701e7i	0.138120	−	0.0797435i
$951$	−8.88423e8	+	2.02777e8i	−1.03295	+	0.235763i
$952$	−1.00603e8	−	4.31703e6i	−0.116600	−	0.00500351i
$953$	−8.35408e7	+	3.66016e8i	−0.0965206	+	0.422884i	−0.999983	−	0.00578244i	$-0.998159\pi$
$953$	−8.35408e7	+	3.66016e8i	−0.0965206	+	0.422884i	0.903463	+	0.428667i	$0.141017\pi$
$954$	4.11081e8	−	1.26802e8i	0.473459	−	0.146043i
$955$	4.57145e8	−	1.79416e8i	0.524860	−	0.205992i
$956$	4.08530e8	+	1.04092e9i	0.467574	+	1.19136i
$957$	−1.78101e8	−	5.77388e8i	−0.203203	−	0.658767i
$958$	−1.43366e9	−	3.27224e8i	−1.63061	−	0.372176i
$959$	−2.67528e8	−	6.22474e8i	−0.303328	−	0.705773i
$960$	−1.26361e8	−	5.53624e8i	−0.142823	−	0.625750i
$961$	−1.47571e8	−	2.55601e8i	−0.166277	−	0.288000i
$962$	1.24798e9	+	7.20524e8i	1.40179	+	0.809325i
$963$	2.51962e7	+	7.77199e6i	0.0282134	+	0.00870269i
$964$	−9.65434e8	+	7.23493e7i	−1.07768	+	0.0807613i
$965$	1.71485e8	+	1.36755e8i	0.190829	+	0.152181i
$966$	1.18096e9	+	4.20521e8i	1.31010	+	0.466505i
$967$	−1.94566e8	−	2.43978e8i	−0.215173	−	0.269818i	0.662517	−	0.749047i	$-0.269488\pi$
$967$	−1.94566e8	−	2.43978e8i	−0.215173	−	0.269818i	−0.877690	+	0.479228i	$0.840917\pi$
$968$	1.55103e7	−	1.43914e7i	0.0170999	−	0.0158664i
$969$	2.16433e7	+	1.43594e8i	0.0237877	+	0.157821i
$970$	7.19173e8	−	4.90324e8i	0.787985	−	0.537239i
$971$	−2.56796e7	+	1.70373e8i	−0.0280499	+	0.186099i	−0.998468	−	0.0553315i	$-0.982378\pi$
$971$	−2.56796e7	+	1.70373e8i	−0.0280499	+	0.186099i	0.970418	+	0.241430i	$0.0776165\pi$
$972$	−2.56453e8	−	5.32530e8i	−0.279260	−	0.579890i
$973$	4.91728e8	−	1.28871e8i	0.533810	−	0.139900i
$974$	3.51679e8	+	1.69360e8i	0.380601	+	0.183288i
$975$	−5.54659e8	−	3.78160e8i	−0.598429	−	0.408002i
$976$	1.89862e8	−	2.04623e8i	0.204216	−	0.220092i
$977$	−1.25852e8	+	1.67938e9i	−0.134951	+	1.80079i	0.361128	+	0.932516i	$0.382392\pi$
$977$	−1.25852e8	+	1.67938e9i	−0.134951	+	1.80079i	−0.496078	+	0.868278i	$0.665227\pi$
$978$	1.02879e9	+	4.03770e8i	1.09979	+	0.431636i
$979$		−	8.07485e7i		−	0.0860571i
$980$	−6.70585e8	−	1.08611e8i	−0.712485	−	0.115397i
$981$	−6.69358e7			−0.0709008
$982$	7.54928e8	−	1.92353e9i	0.797207	−	2.03125i
$983$	6.54024e8	+	4.90123e7i	0.688546	+	0.0515994i	0.414408	−	0.910091i	$-0.363989\pi$
$983$	6.54024e8	+	4.90123e7i	0.688546	+	0.0515994i	0.274138	+	0.961690i	$0.411608\pi$
$984$	1.03923e8	+	9.64264e7i	0.109075	+	0.101207i
$985$	−4.13077e8	+	6.05872e8i	−0.432237	+	0.633975i
$986$	−4.40963e8	+	9.15670e8i	−0.460015	+	0.955230i
$987$	−5.63534e8	+	7.54859e8i	−0.586095	+	0.785081i
$988$	−2.92972e8	+	1.41088e8i	−0.303777	+	0.146291i
$989$	−1.63252e9	−	2.46063e8i	−1.68760	−	0.254365i
$990$	−1.77680e8	−	2.60609e8i	−0.183119	−	0.268587i
$991$	2.37770e8	−	3.58380e7i	0.244307	−	0.0368233i	−0.0257473	−	0.999668i	$-0.508197\pi$
$991$	2.37770e8	−	3.58380e7i	0.244307	−	0.0368233i	0.270054	+	0.962845i	$0.412958\pi$
$992$	−7.77542e8	−	8.37991e8i	−0.796505	−	0.858428i
$993$	−1.19066e9	+	9.49518e8i	−1.21602	+	0.969740i
$994$	9.79192e7	−	9.68508e7i	0.0997031	−	0.0986152i
$995$	−6.06919e8	+	7.61052e8i	−0.616114	+	0.772583i
$996$	8.26306e7	+	1.10263e9i	0.0836302	+	1.11597i
$997$	−4.31293e8	+	1.39822e9i	−0.435198	+	1.41088i	0.426976	+	0.904263i	$0.359579\pi$
$997$	−4.31293e8	+	1.39822e9i	−0.435198	+	1.41088i	−0.862173	+	0.506613i	$0.830897\pi$
$998$	6.84361e8	−	1.18535e9i	0.688484	−	1.19249i
$999$	6.72463e8	−	3.88247e8i	0.674484	−	0.389414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.h.a.3.5	✓	324
49.33	odd	42	inner	49.7.h.a.33.5	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.h.a.3.5	✓	324	1.1	even	1	trivial
49.7.h.a.33.5	yes	324	49.33	odd	42	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.h (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.21887 + 10.7495i) q^{2} +(22.3732 + 1.67664i) q^{3} +(-50.8375 - 47.1703i) q^{4} +(-46.9023 + 68.7930i) q^{5} +(-112.413 + 233.427i) q^{6} +(65.6154 - 336.665i) q^{7} +(55.6673 - 26.8080i) q^{8} +(-223.109 - 33.6282i) q^{9} +(-541.616 - 794.405i) q^{10} +(-1437.72 + 216.702i) q^{11} +(-1058.31 - 1140.59i) q^{12} +(-2691.13 + 2146.11i) q^{13} +(3342.16 + 2125.68i) q^{14} +(-1164.70 + 1460.48i) q^{15} +(-278.365 - 3714.53i) q^{16} +(1400.51 - 4540.35i) q^{17} +(1302.75 - 2256.43i) q^{18} +(-1179.71 + 681.106i) q^{19} +(5629.38 - 1284.87i) q^{20} +(2032.49 - 7422.27i) q^{21} +(3736.13 - 16369.0i) q^{22} +(13479.9 - 4157.99i) q^{23} +(1290.40 - 506.446i) q^{24} +(3175.80 + 8091.80i) q^{25} +(-11716.0 - 37982.5i) q^{26} +(-20881.0 - 4765.95i) q^{27} +(-19216.3 + 14020.1i) q^{28} +(4121.71 + 18058.4i) q^{29} +(-10785.8 - 18681.5i) q^{30} +(-21077.7 - 12169.2i) q^{31} +(44882.3 + 13844.4i) q^{32} +(-32529.8 + 2437.77i) q^{33} +(42897.9 + 34209.9i) q^{34} +(20082.7 + 20304.3i) q^{35} +(9756.04 + 12233.7i) q^{36} +(-26576.2 + 24659.1i) q^{37} +(-2344.51 - 15554.8i) q^{38} +(-63807.5 + 43503.2i) q^{39} +(-766.724 + 5086.88i) q^{40} +(44372.6 + 92140.7i) q^{41} +(71210.8 + 53161.8i) q^{42} +(-105445. - 50779.5i) q^{43} +(83312.2 + 56801.3i) q^{44} +(12777.7 - 13771.1i) q^{45} +(-12173.5 + 162444. i) q^{46} +(-113948. - 44721.4i) q^{47} -83572.5i q^{48} +(-109038. - 44180.9i) q^{49} -100381. q^{50} +(38946.5 - 99234.0i) q^{51} +(238043. + 17838.9i) q^{52} +(121034. + 112303. i) q^{53} +(139326. - 204353. i) q^{54} +(52525.0 - 109069. i) q^{55} +(-5372.68 - 20500.3i) q^{56} +(-27535.9 + 13260.6i) q^{57} +(-211507. - 31879.6i) q^{58} +(130438. + 191317. i) q^{59} +(128102. - 19308.2i) q^{60} +(50970.6 + 54933.2i) q^{61} +(219737. - 175235. i) q^{62} +(-25960.8 + 72906.5i) q^{63} +(-189535. + 237669. i) q^{64} +(-21416.9 - 285789. i) q^{65} +(111034. - 359964. i) q^{66} +(-247053. + 427909. i) q^{67} +(-285368. + 164757. i) q^{68} +(308560. - 70426.7i) q^{69} +(-302987. + 130218. i) q^{70} +(7737.36 - 33899.6i) q^{71} +(-13321.4 + 4109.10i) q^{72} +(221585. - 86965.5i) q^{73} +(-152952. - 389715. i) q^{74} +(57485.7 + 186364. i) q^{75} +(92101.5 + 21021.6i) q^{76} +(-21380.7 + 498251. i) q^{77} +(-198442. - 869433. i) q^{78} +(-317552. - 550016. i) q^{79} +(268589. + 155070. i) q^{80} +(-302008. - 93157.1i) q^{81} +(-1.17767e6 + 88254.1i) q^{82} +(-555604. - 443079. i) q^{83} +(-453438. + 281456. i) q^{84} +(246657. + 309298. i) q^{85} +(990711. - 919245. i) q^{86} +(61938.4 + 410934. i) q^{87} +(-74224.9 + 50605.7i) q^{88} +(-8277.34 + 54916.6i) q^{89} +(94124.8 + 195452. i) q^{90} +(545941. + 1.04683e6i) q^{91} +(-881418. - 424468. i) q^{92} +(-451173. - 307604. i) q^{93} +(961465. - 1.03621e6i) q^{94} +(8475.77 - 113101. i) q^{95} +(980948. + 384994. i) q^{96} +905298. i q^{97} +(934940. - 985713. i) q^{98} +328056. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 13 q^{2} - 11 q^{3} + 819 q^{4} - 179 q^{5} + 770 q^{6} + 392 q^{7} + 828 q^{8} - 1160 q^{9} - 2594 q^{10} - 5305 q^{11} + 7497 q^{12} - 14 q^{13} - 11403 q^{14} - 6196 q^{15} + 27903 q^{16} - 5107 q^{17}+ \cdots - 4449616 q^{99}+O(q^{100}) \) 324 * q - 13 * q^2 - 11 * q^3 + 819 * q^4 - 179 * q^5 + 770 * q^6 + 392 * q^7 + 828 * q^8 - 1160 * q^9 - 2594 * q^10 - 5305 * q^11 + 7497 * q^12 - 14 * q^13 - 11403 * q^14 - 6196 * q^15 + 27903 * q^16 - 5107 * q^17 - 11538 * q^18 - 30006 * q^19 - 50190 * q^20 + 8953 * q^21 + 33042 * q^22 + 54531 * q^23 + 90184 * q^24 - 92804 * q^25 - 93366 * q^26 - 11774 * q^27 - 19180 * q^28 - 80398 * q^29 + 15851 * q^30 + 39378 * q^31 - 197841 * q^32 + 36697 * q^33 - 54698 * q^34 - 819 * q^35 + 706300 * q^36 + 15331 * q^37 - 304462 * q^38 - 179298 * q^39 - 515414 * q^40 - 116046 * q^41 + 1203482 * q^42 - 225018 * q^43 + 1373764 * q^44 + 465772 * q^45 + 1100364 * q^46 + 270021 * q^47 - 767900 * q^49 - 1164040 * q^50 - 1215743 * q^51 - 3954790 * q^52 + 141807 * q^53 - 1093487 * q^54 + 991354 * q^55 - 596680 * q^56 - 388207 * q^57 + 381012 * q^58 + 2015849 * q^59 + 5807298 * q^60 + 258821 * q^61 - 525742 * q^62 - 1265432 * q^63 + 872972 * q^64 - 70154 * q^65 + 497766 * q^66 - 324190 * q^67 - 799617 * q^68 - 2216774 * q^69 + 56140 * q^70 - 1031026 * q^71 + 4633092 * q^72 + 1268305 * q^73 - 1444192 * q^74 - 1699244 * q^75 - 5464011 * q^76 - 2274741 * q^77 - 1285956 * q^78 - 515710 * q^79 + 8314050 * q^80 - 1069027 * q^81 + 357910 * q^82 - 3183054 * q^83 - 10099096 * q^84 - 1596848 * q^85 - 5387681 * q^86 - 4197040 * q^87 - 1024645 * q^88 + 983769 * q^89 + 18547774 * q^90 + 13421086 * q^91 + 5294506 * q^92 + 15477850 * q^93 + 8903632 * q^94 + 5236430 * q^95 + 7804258 * q^96 - 10234553 * q^98 - 4449616 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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