LMFDB - Embedded newform 33.6.e.b.16.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,6,Mod(4,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("33.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.e (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 78 x^{18} + 79 x^{17} + 10573 x^{16} - 33409 x^{15} + 1262953 x^{14} + \cdots + 25599187870096 $ x^20 - x^19 + 78x^18 + 79x^17 + 10573x^16 - 33409x^15 + 1262953x^14 - 1581925x^13 + 89291182x^12 - 100741271x^11 + 2277268901x^10 - 1144062486x^9 + 70677624924x^8 + 93641098134x^7 + 1732079176577x^6 + 1113900934906x^5 + 27749747552381x^4 + 4154923377746x^3 + 57625758470132x^2 + 60036938210920x + 25599187870096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.3
Root			$0.527694 - 1.62407i$ of defining polynomial
Character	$\chi$	$=$	33.16
Dual form			33.6.e.b.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.218677 + 0.673018i) q^{2} +(7.28115 + 5.29007i) q^{3} +(25.4834 - 18.5148i) q^{4} +(-21.0138 + 64.6739i) q^{5} +(-1.96809 + 6.05716i) q^{6} +(98.3565 - 71.4602i) q^{7} +(36.3535 + 26.4124i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})$	\(q+(0.218677 + 0.673018i) q^{2} +(7.28115 + 5.29007i) q^{3} +(25.4834 - 18.5148i) q^{4} +(-21.0138 + 64.6739i) q^{5} +(-1.96809 + 6.05716i) q^{6} +(98.3565 - 71.4602i) q^{7} +(36.3535 + 26.4124i) q^{8} +(25.0304 + 77.0356i) q^{9} -48.1219 q^{10} +(251.233 + 312.943i) q^{11} +283.493 q^{12} +(235.729 + 725.500i) q^{13} +(69.6023 + 50.5690i) q^{14} +(-495.134 + 359.736i) q^{15} +(301.655 - 928.399i) q^{16} +(468.035 - 1440.46i) q^{17} +(-46.3727 + 33.6918i) q^{18} +(-2013.29 - 1462.74i) q^{19} +(661.919 + 2037.18i) q^{20} +1094.18 q^{21} +(-155.677 + 237.517i) q^{22} -3942.75 q^{23} +(124.972 + 384.625i) q^{24} +(-1212.95 - 881.262i) q^{25} +(-436.726 + 317.300i) q^{26} +(-225.273 + 693.320i) q^{27} +(1183.39 - 3642.10i) q^{28} +(178.184 - 129.459i) q^{29} +(-350.383 - 254.568i) q^{30} +(-2884.27 - 8876.86i) q^{31} +2128.73 q^{32} +(173.774 + 3607.62i) q^{33} +1071.81 q^{34} +(2554.76 + 7862.75i) q^{35} +(2064.16 + 1499.70i) q^{36} +(-1615.79 + 1173.94i) q^{37} +(544.191 - 1674.85i) q^{38} +(-2121.56 + 6529.50i) q^{39} +(-2472.12 + 1796.10i) q^{40} +(5162.61 + 3750.86i) q^{41} +(239.271 + 736.401i) q^{42} +8057.77 q^{43} +(12196.3 + 3323.33i) q^{44} -5508.17 q^{45} +(-862.188 - 2653.54i) q^{46} +(-8202.70 - 5959.61i) q^{47} +(7107.69 - 5164.04i) q^{48} +(-626.201 + 1927.25i) q^{49} +(327.860 - 1009.05i) q^{50} +(11028.0 - 8012.29i) q^{51} +(19439.7 + 14123.7i) q^{52} +(-1928.76 - 5936.11i) q^{53} -515.879 q^{54} +(-25518.6 + 9672.06i) q^{55} +5463.04 q^{56} +(-6921.07 - 21300.9i) q^{57} +(126.093 + 91.6117i) q^{58} +(-19392.6 + 14089.6i) q^{59} +(-5957.27 + 18334.6i) q^{60} +(-1962.60 + 6040.27i) q^{61} +(5343.56 - 3882.32i) q^{62} +(7966.88 + 5788.28i) q^{63} +(-9187.46 - 28276.1i) q^{64} -51874.5 q^{65} +(-2389.99 + 905.856i) q^{66} +40747.3 q^{67} +(-14742.7 - 45373.5i) q^{68} +(-28707.8 - 20857.4i) q^{69} +(-4733.10 + 3438.80i) q^{70} +(9412.20 - 28967.8i) q^{71} +(-1124.75 + 3461.62i) q^{72} +(5433.41 - 3947.60i) q^{73} +(-1143.42 - 830.742i) q^{74} +(-4169.76 - 12833.2i) q^{75} -78387.8 q^{76} +(47073.3 + 12826.8i) q^{77} -4858.40 q^{78} +(28395.2 + 87391.3i) q^{79} +(53704.3 + 39018.4i) q^{80} +(-5307.96 + 3856.46i) q^{81} +(-1395.45 + 4294.75i) q^{82} +(18730.2 - 57645.7i) q^{83} +(27883.4 - 20258.5i) q^{84} +(83325.1 + 60539.2i) q^{85} +(1762.05 + 5423.02i) q^{86} +1982.23 q^{87} +(867.623 + 18012.2i) q^{88} -98913.7 q^{89} +(-1204.51 - 3707.10i) q^{90} +(75029.9 + 54512.4i) q^{91} +(-100475. + 72999.2i) q^{92} +(25958.4 - 79891.7i) q^{93} +(2217.18 - 6823.79i) q^{94} +(136908. - 99469.5i) q^{95} +(15499.6 + 11261.1i) q^{96} +(-26727.7 - 82259.4i) q^{97} -1434.01 q^{98} +(-17819.3 + 27186.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) $ 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9 - 424 * q^10 + 2289 * q^11 - 2682 * q^12 - 847 * q^13 + 2022 * q^14 - 396 * q^15 - 7148 * q^16 + 2482 * q^17 + 81 * q^18 + 2958 * q^19 + 8037 * q^20 - 1404 * q^21 + 7441 * q^22 + 8140 * q^23 - 4626 * q^24 - 13120 * q^25 - 13508 * q^26 + 3645 * q^27 + 27819 * q^28 - 20210 * q^29 + 11106 * q^30 + 5540 * q^31 - 4626 * q^32 + 639 * q^33 + 16540 * q^34 - 34101 * q^35 + 648 * q^36 - 25173 * q^37 - 55878 * q^38 + 7623 * q^39 + 22689 * q^40 + 54349 * q^41 + 32292 * q^42 - 21688 * q^43 + 24587 * q^44 - 5346 * q^45 + 44155 * q^46 - 48387 * q^47 - 43083 * q^48 - 78880 * q^49 + 19956 * q^50 + 7317 * q^51 + 109051 * q^52 - 74382 * q^53 + 10206 * q^54 - 47630 * q^55 + 168894 * q^56 + 52983 * q^57 + 1501 * q^58 - 108412 * q^59 - 72333 * q^60 + 16737 * q^61 + 132685 * q^62 - 11259 * q^63 - 157030 * q^64 - 134194 * q^65 - 127539 * q^66 + 20178 * q^67 + 387013 * q^68 + 19305 * q^69 - 411988 * q^70 + 143157 * q^71 + 41634 * q^72 + 164980 * q^73 + 286114 * q^74 - 96255 * q^75 + 46868 * q^76 - 367461 * q^77 - 152658 * q^78 + 369613 * q^79 - 107448 * q^80 - 32805 * q^81 - 184129 * q^82 + 267741 * q^83 + 279819 * q^84 + 379937 * q^85 - 290531 * q^86 + 214920 * q^87 - 740846 * q^88 + 205492 * q^89 + 117126 * q^90 + 394559 * q^91 - 483181 * q^92 - 49860 * q^93 + 561327 * q^94 + 267881 * q^95 + 228564 * q^96 - 300567 * q^97 - 2296174 * q^98 - 115506 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.218677	+	0.673018i	0.0386569	+	0.118974i	0.968523	−	0.248925i	$-0.0800773\pi$
$2$	0.218677	+	0.673018i	0.0386569	+	0.118974i	−0.929866	+	0.367899i	$0.880077\pi$
$3$	7.28115	+	5.29007i	0.467086	+	0.339358i
$3$	7.28115	+	5.29007i	0.467086	+	0.339358i
$4$	25.4834	−	18.5148i	0.796357	−	0.578587i
$5$	−21.0138	+	64.6739i	−0.375907	+	1.15692i	0.566958	+	0.823747i	$0.308120\pi$
$5$	−21.0138	+	64.6739i	−0.375907	+	1.15692i	−0.942865	+	0.333175i	$0.891880\pi$
$6$	−1.96809	+	6.05716i	−0.0223186	+	0.0686896i
$7$	98.3565	−	71.4602i	0.758679	−	0.551213i	−0.139826	−	0.990176i	$-0.544654\pi$
$7$	98.3565	−	71.4602i	0.758679	−	0.551213i	0.898505	+	0.438963i	$0.144654\pi$
$8$	36.3535	+	26.4124i	0.200827	+	0.145909i
$9$	25.0304	+	77.0356i	0.103006	+	0.317019i
$10$	−48.1219			−0.152175
$11$	251.233	+	312.943i	0.626029	+	0.779800i
$11$	251.233	+	312.943i	0.626029	+	0.779800i
$12$	283.493			0.568315
$13$	235.729	+	725.500i	0.386861	+	1.19064i	0.935121	+	0.354328i	$0.115290\pi$
$13$	235.729	+	725.500i	0.386861	+	1.19064i	−0.548260	+	0.836308i	$0.684710\pi$
$14$	69.6023	+	50.5690i	0.0949081	+	0.0689548i
$15$	−495.134	+	359.736i	−0.568191	+	0.412815i
$16$	301.655	−	928.399i	0.294585	−	0.906640i
$17$	468.035	−	1440.46i	0.392786	−	1.20887i	−0.537887	−	0.843017i	$-0.680777\pi$
$17$	468.035	−	1440.46i	0.392786	−	1.20887i	0.930673	−	0.365853i	$-0.119223\pi$
$18$	−46.3727	+	33.6918i	−0.0337351	+	0.0245100i
$19$	−2013.29	−	1462.74i	−1.27945	−	0.929573i	−0.279911	−	0.960026i	$-0.590305\pi$
$19$	−2013.29	−	1462.74i	−1.27945	−	0.929573i	−0.999536	+	0.0304534i	$0.990305\pi$
$20$	661.919	+	2037.18i	0.370024	+	1.13882i
$21$	1094.18			0.541427
$22$	−155.677	+	237.517i	−0.0685755	+	0.104626i
$23$	−3942.75			−1.55410			−0.777052	−	0.629437i	$-0.783286\pi$
$23$	−3942.75			−1.55410			−0.777052	+	0.629437i	$0.783286\pi$
$24$	124.972	+	384.625i	0.0442879	+	0.136304i
$25$	−1212.95	−	881.262i	−0.388145	−	0.282004i
$26$	−436.726	+	317.300i	−0.126700	+	0.0920527i
$27$	−225.273	+	693.320i	−0.0594703	+	0.183031i
$28$	1183.39	−	3642.10i	0.285255	−	0.877924i
$29$	178.184	−	129.459i	0.0393437	−	0.0285848i	−0.567940	−	0.823070i	$-0.692259\pi$
$29$	178.184	−	129.459i	0.0393437	−	0.0285848i	0.607283	+	0.794485i	$0.292259\pi$
$30$	−350.383	−	254.568i	−0.0710788	−	0.0516417i
$31$	−2884.27	−	8876.86i	−0.539052	−	1.65903i	−0.734726	−	0.678364i	$-0.762689\pi$
$31$	−2884.27	−	8876.86i	−0.539052	−	1.65903i	0.195674	−	0.980669i	$-0.437311\pi$
$32$	2128.73			0.367490
$33$	173.774	+	3607.62i	0.0277779	+	0.576682i
$34$	1071.81			0.159008
$35$	2554.76	+	7862.75i	0.352517	+	1.08494i
$36$	2064.16	+	1499.70i	0.265452	+	0.192862i
$37$	−1615.79	+	1173.94i	−0.194035	+	0.140975i	−0.680561	−	0.732691i	$-0.738264\pi$
$37$	−1615.79	+	1173.94i	−0.194035	+	0.140975i	0.486526	+	0.873666i	$0.338264\pi$
$38$	544.191	−	1674.85i	0.0611353	−	0.188155i
$39$	−2121.56	+	6529.50i	−0.223354	+	0.687414i
$40$	−2472.12	+	1796.10i	−0.244297	+	0.177492i
$41$	5162.61	+	3750.86i	0.479634	+	0.348474i	0.801184	−	0.598418i	$-0.204204\pi$
$41$	5162.61	+	3750.86i	0.479634	+	0.348474i	−0.321550	+	0.946893i	$0.604204\pi$
$42$	239.271	+	736.401i	0.0209299	+	0.0644156i
$43$	8057.77			0.664575			0.332287	−	0.943178i	$-0.392180\pi$
$43$	8057.77			0.664575			0.332287	+	0.943178i	$0.392180\pi$
$44$	12196.3	+	3323.33i	0.949724	+	0.258787i
$45$	−5508.17			−0.405486
$46$	−862.188	−	2653.54i	−0.0600769	−	0.184898i
$47$	−8202.70	−	5959.61i	−0.541642	−	0.393526i	0.283053	−	0.959104i	$-0.408653\pi$
$47$	−8202.70	−	5959.61i	−0.541642	−	0.393526i	−0.824694	+	0.565579i	$0.808653\pi$
$48$	7107.69	−	5164.04i	0.445272	−	0.323509i
$49$	−626.201	+	1927.25i	−0.0372583	+	0.114669i
$50$	327.860	−	1009.05i	0.0185466	−	0.0570805i
$51$	11028.0	−	8012.29i	0.593705	−	0.431352i
$52$	19439.7	+	14123.7i	0.996966	+	0.724338i
$53$	−1928.76	−	5936.11i	−0.0943166	−	0.290277i	0.892758	−	0.450536i	$-0.148767\pi$
$53$	−1928.76	−	5936.11i	−0.0943166	−	0.290277i	−0.987075	+	0.160259i	$0.948767\pi$
$54$	−515.879			−0.0240748
$55$	−25518.6	+	9672.06i	−1.13750	+	0.431134i
$56$	5463.04			0.232790
$57$	−6921.07	−	21300.9i	−0.282154	−	0.868381i
$58$	126.093	+	91.6117i	0.00492175	+	0.00357586i
$59$	−19392.6	+	14089.6i	−0.725282	+	0.526948i	−0.888067	−	0.459713i	$-0.847952\pi$
$59$	−19392.6	+	14089.6i	−0.725282	+	0.526948i	0.162785	+	0.986662i	$0.447952\pi$
$60$	−5957.27	+	18334.6i	−0.213633	+	0.657496i
$61$	−1962.60	+	6040.27i	−0.0675317	+	0.207841i	−0.979128	−	0.203246i	$-0.934851\pi$
$61$	−1962.60	+	6040.27i	−0.0675317	+	0.207841i	0.911596	+	0.411087i	$0.134851\pi$
$62$	5343.56	−	3882.32i	0.176543	−	0.128266i
$63$	7966.88	+	5788.28i	0.252893	+	0.183738i
$64$	−9187.46	−	28276.1i	−0.280379	−	0.862918i
$65$	−51874.5			−1.52290
$66$	−2389.99	+	905.856i	−0.0675362	+	0.0255976i
$67$	40747.3			1.10895			0.554475	−	0.832201i	$-0.312919\pi$
$67$	40747.3			1.10895			0.554475	+	0.832201i	$0.312919\pi$
$68$	−14742.7	−	45373.5i	−0.386639	−	1.18995i
$69$	−28707.8	−	20857.4i	−0.725900	−	0.527397i
$70$	−4733.10	+	3438.80i	−0.115452	+	0.0838807i
$71$	9412.20	−	28967.8i	0.221588	−	0.681976i	−0.777033	−	0.629460i	$-0.783276\pi$
$71$	9412.20	−	28967.8i	0.221588	−	0.681976i	0.998620	−	0.0525160i	$-0.0167240\pi$
$72$	−1124.75	+	3461.62i	−0.0255696	+	0.0786953i
$73$	5433.41	−	3947.60i	0.119334	−	0.0867014i	−0.526517	−	0.850164i	$-0.676502\pi$
$73$	5433.41	−	3947.60i	0.119334	−	0.0867014i	0.645852	+	0.763463i	$0.276502\pi$
$74$	−1143.42	−	830.742i	−0.0242731	−	0.0176355i
$75$	−4169.76	−	12833.2i	−0.0855969	−	0.263440i
$76$	−78387.8			−1.55673
$77$	47073.3	+	12826.8i	0.904791	+	0.246543i
$78$	−4858.40			−0.0904185
$79$	28395.2	+	87391.3i	0.511890	+	1.57544i	0.788870	+	0.614560i	$0.210666\pi$
$79$	28395.2	+	87391.3i	0.511890	+	1.57544i	−0.276980	+	0.960876i	$0.589334\pi$
$80$	53704.3	+	39018.4i	0.938175	+	0.681624i
$81$	−5307.96	+	3856.46i	−0.0898908	+	0.0653095i
$82$	−1395.45	+	4294.75i	−0.0229182	+	0.0705348i
$83$	18730.2	−	57645.7i	0.298434	−	0.918485i	−0.683612	−	0.729845i	$-0.739592\pi$
$83$	18730.2	−	57645.7i	0.298434	−	0.918485i	0.982046	−	0.188640i	$-0.0604079\pi$
$84$	27883.4	−	20258.5i	0.431169	−	0.313263i
$85$	83325.1	+	60539.2i	1.25092	+	0.908845i
$86$	1762.05	+	5423.02i	0.0256904	+	0.0790670i
$87$	1982.23			0.0280774
$88$	867.623	+	18012.2i	0.0119433	+	0.247948i
$89$	−98913.7			−1.32367			−0.661837	−	0.749647i	$-0.730223\pi$
$89$	−98913.7			−1.32367			−0.661837	+	0.749647i	$0.730223\pi$
$90$	−1204.51	−	3707.10i	−0.0156749	−	0.0482423i
$91$	75029.9	+	54512.4i	0.949797	+	0.690068i
$92$	−100475.	+	72999.2i	−1.23762	+	0.899184i
$93$	25958.4	−	79891.7i	0.311222	−	0.957843i
$94$	2217.18	−	6823.79i	0.0258811	−	0.0796537i
$95$	136908.	−	99469.5i	1.55640	−	1.13079i
$96$	15499.6	+	11261.1i	0.171649	+	0.124710i
$97$	−26727.7	−	82259.4i	−0.288425	−	0.887679i	−0.985351	−	0.170537i	$-0.945450\pi$
$97$	−26727.7	−	82259.4i	−0.288425	−	0.887679i	0.696927	−	0.717142i	$-0.254550\pi$
$98$	−1434.01			−0.0150829
$99$	−17819.3	+	27186.9i	−0.182727	+	0.278787i
$100$	−47226.6			−0.472266
$101$	33706.2	+	103737.i	0.328781	+	1.01188i	0.969705	+	0.244280i	$0.0785515\pi$
$101$	33706.2	+	103737.i	0.328781	+	1.01188i	−0.640924	+	0.767605i	$0.721448\pi$
$102$	7803.98	+	5669.92i	0.0742704	+	0.0539606i
$103$	−60341.7	+	43840.8i	−0.560434	+	0.407179i	−0.831618	−	0.555349i	$-0.812585\pi$
$103$	−60341.7	+	43840.8i	−0.560434	+	0.407179i	0.271184	+	0.962528i	$0.412585\pi$
$104$	−10592.6	+	32600.6i	−0.0960326	+	0.295558i
$105$	−22992.9	+	70764.8i	−0.203526	+	0.626389i
$106$	3573.33	−	2596.18i	0.0308893	−	0.0224424i
$107$	16485.2	+	11977.2i	0.139198	+	0.101133i	0.655205	−	0.755451i	$-0.272582\pi$
$107$	16485.2	+	11977.2i	0.139198	+	0.101133i	−0.516007	+	0.856584i	$0.672582\pi$
$108$	7095.94	+	21839.1i	0.0585397	+	0.180167i
$109$	40161.6			0.323776			0.161888	−	0.986809i	$-0.448242\pi$
$109$	40161.6			0.323776			0.161888	+	0.986809i	$0.448242\pi$
$110$	−12089.8	−	15059.4i	−0.0952658	−	0.118666i
$111$	−17975.0			−0.138472
$112$	−36673.8	−	112870.i	−0.276256	−	0.850228i
$113$	71373.8	+	51856.1i	0.525827	+	0.382036i	0.818794	−	0.574087i	$-0.194643\pi$
$113$	71373.8	+	51856.1i	0.525827	+	0.382036i	−0.292968	+	0.956122i	$0.594643\pi$
$114$	12822.4	−	9316.01i	0.0924074	−	0.0671379i
$115$	82852.3	−	254993.i	0.584198	−	1.79798i
$116$	2143.85	−	6598.09i	0.0147928	−	0.0455274i
$117$	−49988.9	+	36319.1i	−0.337605	+	0.245284i
$118$	−13723.3	−	9970.53i	−0.0907303	−	0.0659194i
$119$	−56901.5	−	175125.i	−0.368346	−	1.13365i
$120$	−27501.3			−0.174341
$121$	−34815.4	+	157243.i	−0.216176	+	0.976354i
$122$	−4494.38			−0.0273382
$123$	17747.5	+	54621.1i	0.105773	+	0.325535i
$124$	−237854.	−	172811.i	−1.38917	−	1.00929i
$125$	−89438.1	+	64980.6i	−0.511974	+	0.371971i
$126$	−2153.44	+	6627.61i	−0.0120839	+	0.0371904i
$127$	17862.4	−	54974.8i	0.0982722	−	0.302451i	−0.889820	−	0.456311i	$-0.849171\pi$
$127$	17862.4	−	54974.8i	0.0982722	−	0.302451i	0.988093	+	0.153860i	$0.0491705\pi$
$128$	72130.9	−	52406.1i	0.389131	−	0.282720i
$129$	58669.9	+	42626.2i	0.310414	+	0.225529i
$130$	−11343.7	−	34912.4i	−0.0588705	−	0.181185i
$131$	−197773.			−1.00691			−0.503454	−	0.864022i	$-0.667938\pi$
$131$	−197773.			−1.00691			−0.503454	+	0.864022i	$0.667938\pi$
$132$	71222.7	+	88717.1i	0.355782	+	0.443172i
$133$	−302548.			−1.48308
$134$	8910.48	+	27423.6i	0.0428686	+	0.131936i
$135$	−40105.9	−	29138.6i	−0.189397	−	0.137605i
$136$	55060.7	−	40004.0i	0.255267	−	0.185462i
$137$	−15397.3	+	47388.2i	−0.0700881	+	0.215709i	−0.979965	−	0.199169i	$-0.936176\pi$
$137$	−15397.3	+	47388.2i	−0.0700881	+	0.215709i	0.909877	+	0.414878i	$0.136176\pi$
$138$	7759.69	−	23881.9i	0.0346854	−	0.106751i
$139$	289991.	−	210691.i	1.27305	−	0.924928i	0.273735	−	0.961805i	$-0.411741\pi$
$139$	289991.	−	210691.i	1.27305	−	0.924928i	0.999320	+	0.0368767i	$0.0117409\pi$
$140$	210681.	+	153069.i	0.908460	+	0.660035i
$141$	−28198.4	−	86785.7i	−0.119447	−	0.367621i
$142$	21554.1			0.0897032
$143$	−167817.	+	256039.i	−0.686272	+	1.04705i
$144$	79070.3			0.317766
$145$	4628.25	+	14244.3i	0.0182809	+	0.0562628i
$146$	3844.96	+	2793.53i	0.0149283	+	0.0108460i
$147$	−14754.7	+	10719.9i	−0.0563168	+	0.0409166i
$148$	−19440.6	+	59832.0i	−0.0729551	+	0.224533i
$149$	19426.9	−	59789.8i	0.0716865	−	0.220628i	−0.908794	−	0.417245i	$-0.862996\pi$
$149$	19426.9	−	59789.8i	0.0716865	−	0.220628i	0.980480	+	0.196617i	$0.0629955\pi$
$150$	7725.15	−	5612.65i	0.0280336	−	0.0203676i
$151$	232613.	+	169003.i	0.830215	+	0.603187i	0.919620	−	0.392809i	$-0.128496\pi$
$151$	232613.	+	169003.i	0.830215	+	0.603187i	−0.0894048	+	0.995995i	$0.528496\pi$
$152$	−34555.7	−	106351.i	−0.121314	−	0.373366i
$153$	122682.			0.423694
$154$	1661.15	+	34486.1i	0.00564425	+	0.117177i
$155$	634710.			2.12200
$156$	66827.6	+	205674.i	0.219859	+	0.676657i
$157$	14194.2	+	10312.7i	0.0459581	+	0.0333905i	0.610527	−	0.791995i	$-0.290958\pi$
$157$	14194.2	+	10312.7i	0.0459581	+	0.0333905i	−0.564569	+	0.825386i	$0.690958\pi$
$158$	−52606.6	+	38220.9i	−0.167648	+	0.121803i
$159$	17358.8	−	53425.0i	0.0544537	−	0.167591i
$160$	−44732.7	+	137673.i	−0.138142	+	0.425157i
$161$	−387795.	+	281750.i	−1.17907	+	0.856641i
$162$	−3756.19	−	2729.03i	−0.0112450	−	0.00816999i
$163$	39602.8	+	121885.i	0.116750	+	0.359320i	0.992308	−	0.123793i	$-0.0395060\pi$
$163$	39602.8	+	121885.i	0.116750	+	0.359320i	−0.875558	+	0.483113i	$0.839506\pi$
$164$	201007.			0.583582
$165$	−236971.	−	64571.3i	−0.677617	−	0.184642i
$166$	42892.5			0.120812
$167$	−218504.	−	672486.i	−0.606273	−	1.86592i	−0.487792	−	0.872960i	$-0.662197\pi$
$167$	−218504.	−	672486.i	−0.606273	−	1.86592i	−0.118481	−	0.992956i	$-0.537803\pi$
$168$	39777.2	+	28899.8i	0.108733	+	0.0789991i
$169$	−170399.	+	123802.i	−0.458935	+	0.333436i
$170$	−22522.7	+	69317.8i	−0.0597721	+	0.183960i
$171$	62289.7	−	191708.i	0.162902	−	0.501360i
$172$	205340.	−	149188.i	0.529239	−	0.384514i
$173$	270924.	+	196837.i	0.688227	+	0.500026i	0.876077	−	0.482172i	$-0.160152\pi$
$173$	270924.	+	196837.i	0.688227	+	0.500026i	−0.187850	+	0.982198i	$0.560152\pi$
$174$	433.468	+	1334.08i	0.00108539	+	0.00334047i
$175$	−182277.			−0.449922
$176$	366321.	−	138843.i	0.891417	−	0.337865i
$177$	−215736.			−0.517593
$178$	−21630.1	−	66570.7i	−0.0511692	−	0.157483i
$179$	−110419.	−	80224.4i	−0.257581	−	0.187143i	0.451499	−	0.892272i	$-0.350889\pi$
$179$	−110419.	−	80224.4i	−0.257581	−	0.187143i	−0.709080	+	0.705128i	$0.750889\pi$
$180$	−140367.	+	101983.i	−0.322912	+	0.234609i
$181$	−174146.	+	535966.i	−0.395109	+	1.21602i	0.533768	+	0.845631i	$0.320776\pi$
$181$	−174146.	+	535966.i	−0.395109	+	1.21602i	−0.928877	+	0.370389i	$0.879224\pi$
$182$	−20280.5	+	62417.0i	−0.0453838	+	0.139677i
$183$	−46243.4	+	33597.8i	−0.102076	+	0.0741623i
$184$	−143333.	−	104137.i	−0.312105	−	0.226758i
$185$	−41969.4	−	129168.i	−0.0901578	−	0.277477i
$186$	59445.0			0.125989
$187$	568368.	−	215423.i	1.18857	−	0.450493i
$188$	−319374.			−0.659029
$189$	27387.7	+	84290.7i	0.0557700	+	0.171643i
$190$	96883.3	+	70389.9i	0.194700	+	0.141458i
$191$	−41167.4	+	29909.8i	−0.0816525	+	0.0593240i	−0.627863	−	0.778324i	$-0.716070\pi$
$191$	−41167.4	+	29909.8i	−0.0816525	+	0.0593240i	0.546210	+	0.837648i	$0.316070\pi$
$192$	82687.2	−	254485.i	0.161877	−	0.498206i
$193$	71313.5	−	219480.i	0.137809	−	0.424133i	−0.858207	−	0.513303i	$-0.828422\pi$
$193$	71313.5	−	219480.i	0.137809	−	0.424133i	0.996016	+	0.0891703i	$0.0284215\pi$
$194$	49517.3	−	35976.4i	0.0944610	−	0.0686299i
$195$	−377706.	−	274419.i	−0.711324	−	0.516807i
$196$	19724.8	+	60706.8i	0.0366753	+	0.112875i
$197$	−977689.			−1.79488			−0.897440	−	0.441137i	$-0.854575\pi$
$197$	−977689.			−1.79488			−0.897440	+	0.441137i	$0.854575\pi$
$198$	−22193.9	−	6047.55i	−0.0402320	−	0.0109627i
$199$	−474924.			−0.850142			−0.425071	−	0.905160i	$-0.639751\pi$
$199$	−474924.			−0.850142			−0.425071	+	0.905160i	$0.639751\pi$
$200$	−20818.9	−	64073.9i	−0.0368029	−	0.113268i
$201$	296687.	+	215556.i	0.517975	+	0.376331i
$202$	−62446.2	+	45369.8i	−0.107678	+	0.0782327i
$203$	8274.47	−	25466.2i	0.0140929	−	0.0433734i
$204$	132685.	−	408361.i	0.223226	−	0.687019i
$205$	−351069.	+	255066.i	−0.583455	+	0.423905i
$206$	−42700.9	−	31024.0i	−0.0701083	−	0.0509366i
$207$	−98688.6	−	303732.i	−0.160081	−	0.492680i
$208$	744662.			1.19344
$209$	−48049.7	−	997533.i	−0.0760896	−	1.57965i
$210$	−52653.9			−0.0823916
$211$	259039.	+	797240.i	0.400552	+	1.23277i	0.924552	+	0.381055i	$0.124439\pi$
$211$	259039.	+	797240.i	0.400552	+	1.23277i	−0.524000	+	0.851718i	$0.675561\pi$
$212$	−159057.	−	115562.i	−0.243060	−	0.176593i
$213$	221773.	−	161128.i	0.334935	−	0.243344i
$214$	−4455.93	+	13713.9i	−0.00665126	+	0.0204705i
$215$	−169325.	+	521128.i	−0.249818	+	0.768861i
$216$	−26501.7	+	19254.6i	−0.0386491	+	0.0280802i
$217$	−918029.	−	666987.i	−1.32345	−	0.961541i
$218$	8782.40	+	27029.4i	0.0125162	+	0.0385209i
$219$	60444.5			0.0851622
$220$	−471224.	+	718948.i	−0.656404	+	1.00148i
$221$	1.15538e6			1.59128
$222$	−3930.72	−	12097.5i	−0.00535291	−	0.0164746i
$223$	643901.	+	467822.i	0.867076	+	0.629968i	0.929801	−	0.368063i	$-0.119979\pi$
$223$	643901.	+	467822.i	0.867076	+	0.629968i	−0.0627247	+	0.998031i	$0.519979\pi$
$224$	209374.	−	152119.i	0.278807	−	0.202565i
$225$	37527.9	−	115499.i	0.0494194	−	0.152097i
$226$	−19292.3	+	59375.6i	−0.0251254	+	0.0773280i
$227$	−57037.1	+	41439.9i	−0.0734671	+	0.0533770i	−0.623913	−	0.781494i	$-0.714458\pi$
$227$	−57037.1	+	41439.9i	−0.0734671	+	0.0533770i	0.550445	+	0.834871i	$0.314458\pi$
$228$	−570754.	−	414677.i	−0.727129	−	0.528290i
$229$	306524.	+	943385.i	0.386257	+	1.18878i	0.935564	+	0.353156i	$0.114891\pi$
$229$	306524.	+	943385.i	0.386257	+	1.18878i	−0.549308	+	0.835620i	$0.685109\pi$
$230$	189733.			0.236495
$231$	274893.	+	342415.i	0.338949	+	0.422205i
$232$	9896.93			0.0120720
$233$	−185502.	−	570917.i	−0.223851	−	0.688943i	−0.998406	−	0.0564364i	$-0.982026\pi$
$233$	−185502.	−	570917.i	−0.223851	−	0.688943i	0.774555	−	0.632506i	$-0.217974\pi$
$234$	−35374.8	−	25701.3i	−0.0422332	−	0.0306842i
$235$	557801.	−	405266.i	0.658885	−	0.478708i
$236$	−233325.	+	718101.i	−0.272698	+	0.839278i
$237$	−255557.	+	786522.i	−0.295540	+	0.909578i
$238$	105419.	−	76591.4i	0.120636	−	0.0876471i
$239$	844505.	+	613569.i	0.956329	+	0.694814i	0.952295	−	0.305178i	$-0.0987159\pi$
$239$	844505.	+	613569.i	0.956329	+	0.694814i	0.00403405	+	0.999992i	$0.498716\pi$
$240$	184619.	+	568198.i	0.206894	+	0.636754i
$241$	380836.			0.422372			0.211186	−	0.977446i	$-0.432267\pi$
$241$	380836.			0.422372			0.211186	+	0.977446i	$0.432267\pi$
$242$	−113441.	+	10954.0i	−0.124517	+	0.0120235i
$243$	−59049.0			−0.0641500
$244$	61820.5	+	190264.i	0.0664749	+	0.204589i
$245$	−111484.	−	80997.7i	−0.118658	−	0.0862099i
$246$	−32880.0	+	23888.7i	−0.0346413	+	0.0251684i
$247$	586627.	−	1.80545e6i	0.611814	−	1.88297i
$248$	129606.	−	398885.i	0.133812	−	0.411831i
$249$	441328.	−	320643.i	0.451090	−	0.327736i
$250$	−63291.1	−	45983.7i	−0.0640461	−	0.0465322i
$251$	450386.	+	1.38615e6i	0.451233	+	1.38875i	0.875501	+	0.483216i	$0.160531\pi$
$251$	450386.	+	1.38615e6i	0.451233	+	1.38875i	−0.424268	+	0.905537i	$0.639469\pi$
$252$	310192.			0.307701
$253$	−990548.	−	1.23386e6i	−0.972913	−	1.21189i
$254$	40905.1			0.0397826
$255$	286446.	+	881591.i	0.275863	+	0.849018i
$256$	−718655.	−	522134.i	−0.685363	−	0.497945i
$257$	1.16079e6	−	843366.i	1.09628	−	0.796495i	0.115833	−	0.993269i	$-0.463046\pi$
$257$	1.16079e6	−	843366.i	1.09628	−	0.796495i	0.980449	+	0.196773i	$0.0630463\pi$
$258$	−15858.4	+	48807.2i	−0.0148324	+	0.0456494i
$259$	−75033.5	+	230929.i	−0.0695034	+	0.213909i
$260$	−1.32194e6	+	960445.i	−1.21277	+	0.881128i
$261$	14432.9	+	10486.1i	0.0131146	+	0.00952828i
$262$	−43248.4	−	133105.i	−0.0389240	−	0.119796i
$263$	−184421.			−0.164408			−0.0822038	−	0.996616i	$-0.526196\pi$
$263$	−184421.			−0.164408			−0.0822038	+	0.996616i	$0.526196\pi$
$264$	−88968.5	+	135739.i	−0.0785645	+	0.119866i
$265$	424442.			0.371282
$266$	−66160.2	−	203620.i	−0.0573314	−	0.176448i
$267$	−720206.	−	523260.i	−0.618270	−	0.449200i
$268$	1.03838e6	−	754427.i	0.883119	−	0.641624i
$269$	−605230.	+	1.86271e6i	−0.509964	+	1.56951i	0.282297	+	0.959327i	$0.408904\pi$
$269$	−605230.	+	1.86271e6i	−0.509964	+	1.56951i	−0.792261	+	0.610182i	$0.791096\pi$
$270$	10840.6	−	33363.9i	0.00904989	−	0.0278527i
$271$	−734758.	+	533833.i	−0.607745	+	0.441552i	−0.848619	−	0.529004i	$-0.822566\pi$
$271$	−734758.	+	533833.i	−0.607745	+	0.441552i	0.240875	+	0.970556i	$0.422566\pi$
$272$	−1.19614e6	−	869046.i	−0.980301	−	0.712230i
$273$	257930.	+	793826.i	0.209457	+	0.644642i
$274$	−35260.1			−0.0283731
$275$	−28948.7	−	600987.i	−0.0230833	−	0.479218i
$276$	−1.11774e6			−0.883220
$277$	141817.	+	436469.i	0.111053	+	0.341785i	0.991103	−	0.133095i	$-0.0424914\pi$
$277$	141817.	+	436469.i	0.111053	+	0.341785i	−0.880051	+	0.474880i	$0.842491\pi$
$278$	205213.	+	149096.i	0.159255	+	0.115705i
$279$	611640.	−	444382.i	0.470419	−	0.341780i
$280$	−114799.	+	353316.i	−0.0875073	+	0.269320i
$281$	−429990.	+	1.32337e6i	−0.324857	+	0.999808i	0.646648	+	0.762789i	$0.276170\pi$
$281$	−429990.	+	1.32337e6i	−0.324857	+	0.999808i	−0.971505	+	0.237019i	$0.923830\pi$
$282$	52242.0	−	37956.0i	0.0391198	−	0.0284222i
$283$	−1.94247e6	−	1.41129e6i	−1.44174	−	1.04749i	−0.987674	−	0.156522i	$-0.949972\pi$
$283$	−1.94247e6	−	1.41129e6i	−1.44174	−	1.04749i	−0.454070	−	0.890966i	$-0.650028\pi$
$284$	−296477.	−	912463.i	−0.218120	−	0.671304i
$285$	1.52305e6			1.11071
$286$	−209016.	−	56954.1i	−0.151100	−	0.0411728i
$287$	775814.			0.555972
$288$	53282.8	+	163988.i	0.0378535	+	0.116501i
$289$	−707188.	−	513802.i	−0.498070	−	0.361869i
$290$	−8574.57	+	6229.79i	−0.00598711	+	0.00434989i
$291$	240549.	−	740335.i	0.166522	−	0.512502i
$292$	65372.8	−	201197.i	0.0448683	−	0.138090i
$293$	974659.	−	708131.i	0.663259	−	0.481886i	−0.204503	−	0.978866i	$-0.565558\pi$
$293$	974659.	−	708131.i	0.663259	−	0.481886i	0.867762	+	0.496980i	$0.165558\pi$
$294$	−10441.2	−	7585.99i	−0.00704503	−	0.00511852i
$295$	−503714.	−	1.55027e6i	−0.337000	−	1.03718i
$296$	−89746.2			−0.0595370
$297$	−273566.	+	103687.i	−0.179958	+	0.0682076i
$298$	44487.8			0.0290202
$299$	−929422.	−	2.86047e6i	−0.601222	−	1.85037i
$300$	−343864.	−	249832.i	−0.220589	−	0.160267i
$301$	792535.	−	575810.i	0.504199	−	0.366322i
$302$	−62875.0	+	193509.i	−0.0396699	+	0.122091i
$303$	−303356.	+	933634.i	−0.189822	+	0.584212i
$304$	−1.96533e6	+	1.42789e6i	−1.21969	+	0.886159i
$305$	−349406.	−	253858.i	−0.215070	−	0.156258i
$306$	26827.7	+	82567.1i	0.0163787	+	0.0504085i
$307$	579150.			0.350708			0.175354	−	0.984505i	$-0.443893\pi$
$307$	579150.			0.350708			0.175354	+	0.984505i	$0.443893\pi$
$308$	1.43708e6	−	544681.i	0.863183	−	0.327164i
$309$	−671277.			−0.399950
$310$	138796.	+	427171.i	0.0820302	+	0.252463i
$311$	1.86517e6	+	1.35513e6i	1.09350	+	0.794473i	0.979987	−	0.199063i	$-0.0637900\pi$
$311$	1.86517e6	+	1.35513e6i	1.09350	+	0.794473i	0.113512	+	0.993537i	$0.463790\pi$
$312$	−249586.	+	181335.i	−0.145155	+	0.105462i
$313$	−105062.	+	323347.i	−0.0606155	+	0.186555i	−0.976779	−	0.214249i	$-0.931269\pi$
$313$	−105062.	+	323347.i	−0.0606155	+	0.186555i	0.916163	+	0.400805i	$0.131269\pi$
$314$	−3836.69	+	11808.1i	−0.00219600	+	0.00675859i
$315$	−541765.	+	393615.i	−0.307634	+	0.223509i
$316$	2.34164e6	+	1.70130e6i	1.31917	+	0.958436i
$317$	715327.	+	2.20155e6i	0.399813	+	1.23050i	0.925150	+	0.379602i	$0.123939\pi$
$317$	715327.	+	2.20155e6i	0.399813	+	1.23050i	−0.525337	+	0.850894i	$0.676061\pi$
$318$	39751.9			0.0220440
$319$	85278.8	+	23237.3i	0.0469207	+	0.0127853i
$320$	2.02179e6			1.10373
$321$	56671.0	+	174415.i	0.0306971	+	0.0944761i
$322$	−274424.	−	199381.i	−0.147497	−	0.107163i
$323$	−3.04931e6	+	2.21546e6i	−1.62628	+	1.18156i
$324$	−63863.4	+	196551.i	−0.0337979	+	0.104019i
$325$	353427.	−	1.08774e6i	0.185606	−	0.571236i
$326$	−73370.5	+	53306.8i	−0.0382365	+	0.0277804i
$327$	292423.	+	212457.i	0.151231	+	0.109876i
$328$	88610.0	+	272714.i	0.0454777	+	0.139966i
$329$	−1.23266e6			−0.627849
$330$	−8362.34	−	173606.i	−0.00422710	−	0.0877564i
$331$	−940125.			−0.471645			−0.235823	−	0.971796i	$-0.575778\pi$
$331$	−940125.			−0.471645			−0.235823	+	0.971796i	$0.575778\pi$
$332$	−589988.	−	1.81580e6i	−0.293764	−	0.904111i
$333$	−130879.	−	95089.2i	−0.0646784	−	0.0469916i
$334$	404813.	−	294114.i	0.198559	−	0.144261i
$335$	−856256.	+	2.63529e6i	−0.416861	+	1.28297i
$336$	330065.	−	1.01583e6i	0.159496	−	0.490879i
$337$	−347259.	+	252299.i	−0.166563	+	0.121015i	−0.667944	−	0.744211i	$-0.732826\pi$
$337$	−347259.	+	252299.i	−0.166563	+	0.121015i	0.501381	+	0.865227i	$0.332826\pi$
$338$	−120584.	−	87609.2i	−0.0574112	−	0.0417117i
$339$	245361.	+	755144.i	0.115960	+	0.356887i
$340$	3.24428e6			1.52202
$341$	2.05333e6	−	3.13277e6i	0.956252	−	1.45896i
$342$	142644.			0.0659460
$343$	707550.	+	2.17762e6i	0.324730	+	0.999415i
$344$	292928.	+	212825.i	0.133464	+	0.0969675i
$345$	1.95219e6	−	1.41835e6i	0.883028	−	0.641557i
$346$	−73230.4	+	225380.i	−0.0328853	+	0.101210i
$347$	914247.	−	2.81376e6i	0.407605	−	1.25448i	−0.511095	−	0.859524i	$-0.670760\pi$
$347$	914247.	−	2.81376e6i	0.407605	−	1.25448i	0.918700	−	0.394955i	$-0.129240\pi$
$348$	50514.0	−	36700.6i	0.0223596	−	0.0162452i
$349$	−2.03686e6	−	1.47987e6i	−0.895154	−	0.650368i	0.0420624	−	0.999115i	$-0.486607\pi$
$349$	−2.03686e6	−	1.47987e6i	−0.895154	−	0.650368i	−0.937217	+	0.348747i	$0.886607\pi$
$350$	−39859.7	−	122676.i	−0.0173926	−	0.0535289i
$351$	−556107.			−0.240930
$352$	534805.	+	666170.i	0.230059	+	0.286568i
$353$	1.01799e6			0.434818			0.217409	−	0.976081i	$-0.430239\pi$
$353$	1.01799e6			0.434818			0.217409	+	0.976081i	$0.430239\pi$
$354$	−47176.4	−	145194.i	−0.0200086	−	0.0615801i
$355$	1.67567e6	+	1.21745e6i	0.705697	+	0.512719i
$356$	−2.52066e6	+	1.83137e6i	−1.05412	+	0.765861i
$357$	512113.	−	1.57612e6i	0.212665	−	0.654515i
$358$	29846.3	−	91857.5i	0.0123079	−	0.0378797i
$359$	−566108.	+	411302.i	−0.231827	+	0.168432i	−0.697634	−	0.716454i	$-0.745764\pi$
$359$	−566108.	+	411302.i	−0.231827	+	0.168432i	0.465808	+	0.884886i	$0.345764\pi$
$360$	−200241.	−	145484.i	−0.0814325	−	0.0591642i
$361$	1.14857e6	+	3.53493e6i	0.463862	+	1.42762i
$362$	−398796.			−0.159948
$363$	−1.08532e6	+	960733.i	−0.432307	+	0.382680i
$364$	2.92130e6			1.15564
$365$	141130.	+	434354.i	0.0554482	+	0.170652i
$366$	−32724.3	−	23775.6i	−0.0127693	−	0.00927745i
$367$	−1.48792e6	+	1.08104e6i	−0.576654	+	0.418963i	−0.837516	−	0.546413i	$-0.815993\pi$
$367$	−1.48792e6	+	1.08104e6i	−0.576654	+	0.418963i	0.260863	+	0.965376i	$0.415993\pi$
$368$	−1.18935e6	+	3.66045e6i	−0.457816	+	1.40901i
$369$	−159727.	+	491590.i	−0.0610679	+	0.187948i
$370$	77754.9	−	56492.3i	0.0295273	−	0.0214528i
$371$	−613902.	−	446026.i	−0.231560	−	0.168238i
$372$	−817669.	−	2.51653e6i	−0.306352	−	0.942854i
$373$	−1.34999e6			−0.502409			−0.251204	−	0.967934i	$-0.580827\pi$
$373$	−1.34999e6			−0.502409			−0.251204	+	0.967934i	$0.580827\pi$
$374$	269272.	+	335414.i	0.0995435	+	0.123994i
$375$	−994964.			−0.365367
$376$	−140789.	−	433305.i	−0.0513571	−	0.158061i
$377$	135925.	+	98755.6i	0.0492547	+	0.0357856i
$378$	−50740.1	+	36864.8i	−0.0182651	+	0.0132704i
$379$	830310.	−	2.55543e6i	0.296922	−	0.913832i	−0.685647	−	0.727934i	$-0.740481\pi$
$379$	830310.	−	2.55543e6i	0.296922	−	0.913832i	0.982569	−	0.185898i	$-0.0595193\pi$
$380$	1.64723e6	−	5.06964e6i	0.585187	−	1.80102i
$381$	420879.	−	305787.i	0.148541	−	0.107921i
$382$	−29132.2	−	21165.8i	−0.0102144	−	0.00742123i
$383$	−1.26926e6	−	3.90639e6i	−0.442134	−	1.36075i	−0.885596	−	0.464456i	$-0.846250\pi$
$383$	−1.26926e6	−	3.90639e6i	−0.442134	−	1.36075i	0.443462	−	0.896293i	$-0.353750\pi$
$384$	802428.			0.277701
$385$	−1.81875e6	+	2.77487e6i	−0.625348	+	0.954095i
$386$	163309.			0.0557880
$387$	201689.	+	620735.i	0.0684550	+	0.210683i
$388$	−2.20413e6	−	1.60139e6i	−0.743289	−	0.540031i
$389$	3.15344e6	−	2.29111e6i	1.05660	−	0.767664i	0.0831428	−	0.996538i	$-0.473504\pi$
$389$	3.15344e6	−	2.29111e6i	1.05660	−	0.767664i	0.973456	+	0.228874i	$0.0735042\pi$
$390$	102094.	−	314212.i	0.0339889	−	0.104607i
$391$	−1.84534e6	+	5.67939e6i	−0.610430	+	1.87871i
$392$	−73667.7	+	53522.7i	−0.0242138	+	0.0175923i
$393$	−1.44002e6	−	1.04623e6i	−0.470313	−	0.341702i
$394$	−213798.	−	658002.i	−0.0693846	−	0.213544i
$395$	−6.24863e6			−2.01508
$396$	49263.7	+	1.02274e6i	0.0157866	+	0.327737i
$397$	−5.10196e6			−1.62465			−0.812327	−	0.583203i	$-0.801799\pi$
$397$	−5.10196e6			−1.62465			−0.812327	+	0.583203i	$0.801799\pi$
$398$	−103855.	−	319632.i	−0.0328639	−	0.101145i
$399$	−2.20290e6	−	1.60050e6i	−0.692727	−	0.503296i
$400$	−1.18406e6	+	860267.i	−0.370018	+	0.268834i
$401$	1.40628e6	−	4.32809e6i	0.436729	−	1.34411i	−0.454576	−	0.890708i	$-0.650209\pi$
$401$	1.40628e6	−	4.32809e6i	0.436729	−	1.34411i	0.891305	−	0.453404i	$-0.149791\pi$
$402$	−80194.3	+	246813.i	−0.0247502	+	0.0761733i
$403$	5.76025e6	−	4.18507e6i	1.76677	−	1.28363i
$404$	2.77962e6	+	2.01951e6i	0.847290	+	0.615592i
$405$	−137872.	−	424325.i	−0.0417674	−	0.128547i
$406$	18948.6			0.00570509
$407$	−773315.	−	210718.i	−0.231404	−	0.0630544i
$408$	612529.			0.182170
$409$	−940604.	−	2.89488e6i	−0.278034	−	0.855702i	−0.988401	−	0.151870i	$-0.951471\pi$
$409$	−940604.	−	2.89488e6i	−0.278034	−	0.855702i	0.710366	−	0.703832i	$-0.248529\pi$
$410$	−248435.	−	180498.i	−0.0729882	−	0.0530290i
$411$	−362797.	+	263587.i	−0.105940	+	0.0769698i
$412$	−726009.	+	2.23442e6i	−0.210717	+	0.648519i
$413$	−900549.	+	2.77160e6i	−0.259796	+	0.799569i
$414$	182836.	−	132838.i	0.0524278	−	0.0380910i
$415$	3.33458e6	+	2.42271e6i	0.950432	+	0.690529i
$416$	501803.	+	1.54439e6i	0.142167	+	0.437546i
$417$	3.22603e6			0.908508
$418$	660850.	−	250475.i	0.184996	−	0.0701172i
$419$	−2.68510e6			−0.747180			−0.373590	−	0.927594i	$-0.621873\pi$
$419$	−2.68510e6			−0.747180			−0.373590	+	0.927594i	$0.621873\pi$
$420$	724258.	+	2.22904e6i	0.200341	+	0.616586i
$421$	−1.49400e6	−	1.08546e6i	−0.410815	−	0.298474i	0.363117	−	0.931744i	$-0.381713\pi$
$421$	−1.49400e6	−	1.08546e6i	−0.410815	−	0.298474i	−0.773932	+	0.633269i	$0.781713\pi$
$422$	−479911.	+	348676.i	−0.131184	+	0.0953105i
$423$	253785.	−	781071.i	0.0689629	−	0.212246i
$424$	86669.5	−	266741.i	0.0234127	−	0.0720569i
$425$	−1.83713e6	+	1.33475e6i	−0.493364	+	0.358450i
$426$	156938.	+	114022.i	0.0418991	+	0.0304415i
$427$	238604.	+	734348.i	0.0633298	+	0.194909i
$428$	641853.			0.169366
$429$	−2.57637e6	+	976495.i	−0.675872	+	0.256169i
$430$	−387755.			−0.101132
$431$	174390.	+	536716.i	0.0452197	+	0.139172i	0.971117	−	0.238603i	$-0.0766894\pi$
$431$	174390.	+	536716.i	0.0452197	+	0.139172i	−0.925898	+	0.377775i	$0.876689\pi$
$432$	575723.	+	418287.i	0.148424	+	0.107836i
$433$	2.23541e6	−	1.62412e6i	0.572976	−	0.416292i	−0.263209	−	0.964739i	$-0.584781\pi$
$433$	2.23541e6	−	1.62412e6i	0.572976	−	0.416292i	0.836185	+	0.548447i	$0.184781\pi$
$434$	248142.	−	763704.i	0.0632378	−	0.194626i
$435$	−41654.3	+	128199.i	−0.0105545	+	0.0324833i
$436$	1.02345e6	−	743583.i	0.257841	−	0.187332i
$437$	7.93790e6	+	5.76722e6i	1.98839	+	1.44465i
$438$	13217.8	+	40680.2i	0.00329211	+	0.0101321i
$439$	2.29521e6			0.568408			0.284204	−	0.958764i	$-0.408271\pi$
$439$	2.29521e6			0.568408			0.284204	+	0.958764i	$0.408271\pi$
$440$	−1.18315e6	−	322393.i	−0.291346	−	0.0793878i
$441$	−164141.			−0.0401902
$442$	252656.	+	777594.i	0.0615139	+	0.189320i
$443$	4.97387e6	+	3.61373e6i	1.20416	+	0.874875i	0.994688	−	0.102939i	$-0.0328247\pi$
$443$	4.97387e6	+	3.61373e6i	1.20416	+	0.874875i	0.209474	+	0.977814i	$0.432825\pi$
$444$	−458065.	+	332804.i	−0.110273	+	0.0801182i
$445$	2.07855e6	−	6.39713e6i	0.497578	−	1.53139i
$446$	−174046.	+	535659.i	−0.0414312	+	0.127512i
$447$	457742.	−	332569.i	0.108356	−	0.0787251i
$448$	−2.92426e6	−	2.12460e6i	−0.688369	−	0.500130i
$449$	−811666.	−	2.49805e6i	−0.190003	−	0.584770i	0.809995	−	0.586436i	$-0.199470\pi$
$449$	−811666.	−	2.49805e6i	−0.190003	−	0.584770i	−0.999999	+	0.00166614i	$0.999470\pi$
$450$	85939.3			0.0200060
$451$	123212.	+	2.55794e6i	0.0285242	+	0.592174i
$452$	2.77895e6			0.639786
$453$	799651.	+	2.46107e6i	0.183086	+	0.563480i
$454$	−40362.5	−	29325.1i	−0.00919048	−	0.00667727i
$455$	−5.10219e6	+	3.70696e6i	−1.15539	+	0.839440i
$456$	311001.	−	957163.i	0.0700406	−	0.215563i
$457$	−211450.	+	650775.i	−0.0473605	+	0.145761i	−0.971940	−	0.235228i	$-0.924416\pi$
$457$	−211450.	+	650775.i	−0.0473605	+	0.145761i	0.924580	+	0.380989i	$0.124416\pi$
$458$	−567885.	+	412592.i	−0.126502	+	0.0919089i
$459$	893266.	+	648996.i	0.197902	+	0.143784i
$460$	−2.60978e6	−	8.03209e6i	−0.575056	−	1.76984i
$461$	−2.07232e6			−0.454156			−0.227078	−	0.973877i	$-0.572917\pi$
$461$	−2.07232e6			−0.454156			−0.227078	+	0.973877i	$0.572917\pi$
$462$	−170339.	+	259886.i	−0.0371286	+	0.0566472i
$463$	−2.80415e6			−0.607923			−0.303961	−	0.952684i	$-0.598309\pi$
$463$	−2.80415e6			−0.607923			−0.303961	+	0.952684i	$0.598309\pi$
$464$	−66439.0	−	204478.i	−0.0143261	−	0.0440912i
$465$	4.62142e6	+	3.35766e6i	0.991159	+	0.720119i
$466$	343672.	−	249692.i	0.0733128	−	0.0532648i
$467$	755641.	−	2.32562e6i	0.160333	−	0.493455i	−0.838329	−	0.545165i	$-0.816467\pi$
$467$	755641.	−	2.32562e6i	0.160333	−	0.493455i	0.998662	+	0.0517099i	$0.0164671\pi$
$468$	−601448.	+	1.85107e6i	−0.126936	+	0.390668i
$469$	4.00776e6	−	2.91181e6i	0.841337	−	0.611267i
$470$	394730.	+	286788.i	0.0824243	+	0.0598847i
$471$	48795.4	+	150177.i	0.0101351	+	0.0311925i
$472$	−1.07713e6			−0.222543
$473$	2.02437e6	+	2.52162e6i	0.416043	+	0.518236i
$474$	−585227.			−0.119641
$475$	1.15297e6	+	3.54847e6i	0.234468	+	0.721618i
$476$	−4.69244e6	−	3.40926e6i	−0.949252	−	0.689672i
$477$	409014.	−	297166.i	0.0823080	−	0.0598003i
$478$	−228269.	+	702540.i	−0.0456959	+	0.140638i
$479$	−1.79426e6	+	5.52215e6i	−0.357311	+	1.09969i	0.597347	+	0.801983i	$0.296221\pi$
$479$	−1.79426e6	+	5.52215e6i	−0.357311	+	1.09969i	−0.954658	+	0.297706i	$0.903779\pi$
$480$	−1.05401e6	+	765780.i	−0.208804	+	0.151705i
$481$	−1.23258e6	−	895524.i	−0.242914	−	0.176488i
$482$	83279.9	+	256309.i	0.0163276	+	0.0502512i
$483$	−4.31407e6			−0.841433
$484$	2.02410e6	+	4.65168e6i	0.392752	+	0.902603i
$485$	5.88169e6			1.13540
$486$	−12912.6	−	39741.0i	−0.00247984	−	0.00763218i
$487$	1.95737e6	+	1.42212e6i	0.373983	+	0.271714i	0.758860	−	0.651253i	$-0.225756\pi$
$487$	1.95737e6	+	1.42212e6i	0.373983	+	0.271714i	−0.384878	+	0.922967i	$0.625756\pi$
$488$	−230885.	+	167748.i	−0.0438881	+	0.0318866i
$489$	−356425.	+	1.09696e6i	−0.0674057	+	0.207453i
$490$	30134.0	−	92742.8i	0.00566978	−	0.0174498i
$491$	8.16801e6	−	5.93440e6i	1.52902	−	1.11090i	0.572235	−	0.820089i	$-0.306076\pi$
$491$	8.16801e6	−	5.93440e6i	1.52902	−	1.11090i	0.956782	−	0.290807i	$-0.0939237\pi$
$492$	1.46356e6	+	1.06334e6i	0.272583	+	0.198043i
$493$	−103084.	−	317259.i	−0.0191017	−	0.0587891i
$494$	1.34338e6			0.247675
$495$	−1.38383e6	−	1.72374e6i	−0.253846	−	0.316198i
$496$	−9.11132e6			−1.66294
$497$	−1.14429e6	−	3.52177e6i	−0.207800	−	0.639543i
$498$	312307.	+	226904.i	0.0564297	+	0.0409986i
$499$	−455391.	+	330861.i	−0.0818715	+	0.0594831i	−0.627968	−	0.778239i	$-0.716113\pi$
$499$	−455391.	+	330861.i	−0.0818715	+	0.0594831i	0.546097	+	0.837722i	$0.316113\pi$
$500$	−1.07609e6	+	3.31185e6i	−0.192496	+	0.592443i
$501$	1.96654e6	−	6.05238e6i	0.350032	−	1.07729i
$502$	−834412.	+	606236.i	−0.147782	+	0.107370i
$503$	−86772.0	−	63043.6i	−0.0152918	−	0.0111102i	0.580113	−	0.814536i	$-0.303008\pi$
$503$	−86772.0	−	63043.6i	−0.0152918	−	0.0111102i	−0.595405	+	0.803426i	$0.703008\pi$
$504$	136742.	+	420848.i	0.0239787	+	0.0737988i
$505$	−7.41738e6			−1.29426
$506$	613797.	−	936471.i	0.106573	−	0.162599i
$507$	−1.89563e6			−0.327517
$508$	−562652.	−	1.73166e6i	−0.0967343	−	0.297718i
$509$	−1.78306e6	−	1.29547e6i	−0.305051	−	0.221633i	0.424719	−	0.905325i	$-0.360373\pi$
$509$	−1.78306e6	−	1.29547e6i	−0.305051	−	0.221633i	−0.729770	+	0.683693i	$0.760373\pi$
$510$	−530687.	+	385567.i	−0.0903469	+	0.0656409i
$511$	252315.	−	776545.i	0.0427455	−	0.131557i
$512$	1.07590e6	−	3.31128e6i	0.181383	−	0.558241i
$513$	1.46769e6	−	1.06634e6i	0.246230	−	0.178896i
$514$	821439.	+	596810.i	0.137141	+	0.0996388i
$515$	−1.56734e6	−	4.82379e6i	−0.260403	−	0.801439i
$516$	2.28432e6			0.377688
$517$	−195768.	−	4.06422e6i	−0.0322118	−	0.668731i
$518$	−171828.			−0.0281364
$519$	931352.	+	2.86641e6i	0.151773	+	0.467110i
$520$	−1.88582e6	−	1.37013e6i	−0.305838	−	0.222204i
$521$	−1.89567e6	+	1.37728e6i	−0.305962	+	0.222295i	−0.730162	−	0.683274i	$-0.760555\pi$
$521$	−1.89567e6	+	1.37728e6i	−0.305962	+	0.222295i	0.424200	+	0.905569i	$0.360555\pi$
$522$	−3901.21	+	12006.7i	−0.000626647	+	0.00192862i
$523$	3.51985e6	−	1.08330e7i	0.562690	−	1.73178i	−0.112026	−	0.993705i	$-0.535734\pi$
$523$	3.51985e6	−	1.08330e7i	0.562690	−	1.73178i	0.674716	−	0.738077i	$-0.264266\pi$
$524$	−5.03994e6	+	3.66173e6i	−0.801857	+	0.582584i
$525$	−1.32719e6	−	964258.i	−0.210152	−	0.152685i
$526$	−40328.7	−	124119.i	−0.00635550	−	0.0195602i
$527$	−1.41367e7			−2.21729
$528$	3.40173e6	+	926926.i	0.531025	+	0.144697i
$529$	9.10895e6			1.41524
$530$	92815.5	+	285657.i	0.0143526	+	0.0441728i
$531$	−1.57080e6	−	1.14126e6i	−0.241761	−	0.175649i
$532$	−7.70995e6	+	5.60161e6i	−1.18106	+	0.858092i
$533$	−1.50427e6	+	4.62966e6i	−0.229354	+	0.705881i
$534$	194671.	−	599136.i	0.0295426	−	0.0909227i
$535$	−1.12103e6	+	814474.i	−0.169329	+	0.123025i
$536$	1.48131e6	+	1.07623e6i	0.222707	+	0.161806i
$537$	−379588.	−	1.16825e6i	−0.0568038	−	0.174824i
$538$	−1.38598e6			−0.206444
$539$	−760440.	+	288222.i	−0.112744	+	0.0427322i
$540$	−1.56153e6			−0.230444
$541$	−295101.	−	908226.i	−0.0433488	−	0.133414i	0.927040	−	0.374963i	$-0.122345\pi$
$541$	−295101.	−	908226.i	−0.0433488	−	0.133414i	−0.970389	+	0.241549i	$0.922345\pi$
$542$	−519953.	−	377768.i	−0.0760267	−	0.0552366i
$543$	−4.10328e6	+	2.98121e6i	−0.597216	+	0.433903i
$544$	996318.	−	3.06635e6i	0.144345	−	0.444247i
$545$	−843948.	+	2.59740e6i	−0.121709	+	0.374583i
$546$	−477856.	+	347183.i	−0.0685986	+	0.0498398i
$547$	7.03984e6	+	5.11474e6i	1.00599	+	0.730895i	0.963364	−	0.268196i	$-0.0864274\pi$
$547$	7.03984e6	+	5.11474e6i	1.00599	+	0.730895i	0.0426268	+	0.999091i	$0.486427\pi$
$548$	485004.	+	1.49269e6i	0.0689913	+	0.212333i
$549$	−514440.			−0.0728457
$550$	398144.	−	150905.i	0.0561221	−	0.0212714i
$551$	−548101.			−0.0769098
$552$	−492734.	−	1.51648e6i	−0.0688280	−	0.211831i
$553$	9.03785e6	+	6.56639e6i	1.25676	+	0.913090i
$554$	−262739.	+	190891.i	−0.0363706	+	0.0264248i
$555$	377724.	−	1.16252e6i	0.0520526	−	0.160201i
$556$	3.48906e6	−	1.07382e7i	0.478654	−	1.47315i
$557$	6.85295e6	−	4.97896e6i	0.935922	−	0.679987i	−0.0115134	−	0.999934i	$-0.503665\pi$
$557$	6.85295e6	−	4.97896e6i	0.935922	−	0.679987i	0.947436	+	0.319946i	$0.103665\pi$
$558$	432828.	+	314468.i	0.0588478	+	0.0427554i
$559$	1.89945e6	+	5.84591e6i	0.257098	+	0.791267i
$560$	8.07043e6			1.08749
$561$	5.27798e6	+	1.43818e6i	0.708044	+	0.192932i
$562$	−984682.			−0.131509
$563$	−1.73222e6	−	5.33123e6i	−0.230321	−	0.708854i	−0.997708	−	0.0676698i	$-0.978444\pi$
$563$	−1.73222e6	−	5.33123e6i	−0.230321	−	0.708854i	0.767387	−	0.641184i	$-0.221556\pi$
$564$	−2.32541e6	−	1.68951e6i	−0.307823	−	0.223647i
$565$	−4.85357e6	+	3.52633e6i	−0.639647	+	0.464731i
$566$	525048.	−	1.61593e6i	0.0688903	−	0.212023i
$567$	−246489.	+	758616.i	−0.0321989	+	0.0990979i
$568$	1.10727e6	−	804482.i	0.144007	−	0.104627i
$569$	−731242.	−	531278.i	−0.0946848	−	0.0687925i	0.539436	−	0.842027i	$-0.318638\pi$
$569$	−731242.	−	531278.i	−0.0946848	−	0.0687925i	−0.634120	+	0.773234i	$0.718638\pi$
$570$	333055.	+	1.02504e6i	0.0429368	+	0.132146i
$571$	969049.			0.124381			0.0621907	−	0.998064i	$-0.480191\pi$
$571$	969049.			0.124381			0.0621907	+	0.998064i	$0.480191\pi$
$572$	463952.	+	9.63184e6i	0.0592902	+	1.23089i
$573$	−457971.			−0.0582708
$574$	169652.	+	522136.i	0.0214922	+	0.0661461i
$575$	4.78237e6	+	3.47460e6i	0.603217	+	0.438263i
$576$	1.94830e6	−	1.41552e6i	0.244681	−	0.177771i
$577$	−3.09709e6	+	9.53185e6i	−0.387270	+	1.19189i	0.547550	+	0.836773i	$0.315560\pi$
$577$	−3.09709e6	+	9.53185e6i	−0.387270	+	1.19189i	−0.934820	+	0.355121i	$0.884440\pi$
$578$	191152.	−	588306.i	0.0237991	−	0.0732460i
$579$	1.68031e6	−	1.22082e6i	0.208302	−	0.151340i
$580$	381674.	+	277302.i	0.0471110	+	0.0342281i
$581$	−2.27714e6	−	7.00830e6i	−0.279865	−	0.861336i
$582$	550861.			0.0674116
$583$	1.37310e6	−	2.09493e6i	0.167313	−	0.255270i
$584$	301789.			0.0366160
$585$	−1.29844e6	−	3.99618e6i	−0.156867	−	0.482787i
$586$	689720.	+	501111.i	0.0829714	+	0.0602823i
$587$	6.16732e6	−	4.48082e6i	0.738756	−	0.536738i	−0.153565	−	0.988138i	$-0.549076\pi$
$587$	6.16732e6	−	4.48082e6i	0.738756	−	0.536738i	0.892321	+	0.451401i	$0.149076\pi$
$588$	−177524.	+	546361.i	−0.0211745	+	0.0651683i
$589$	−7.17768e6	+	2.20906e7i	−0.852503	+	2.62373i
$590$	933211.	−	678017.i	0.110370	−	0.0801883i
$591$	−7.11871e6	−	5.17204e6i	−0.838363	−	0.609107i
$592$	602474.	+	1.85422e6i	0.0706535	+	0.217449i
$593$	1.39431e7			1.62825			0.814126	−	0.580688i	$-0.197216\pi$
$593$	1.39431e7			1.62825			0.814126	+	0.580688i	$0.197216\pi$
$594$	−129606.	−	161441.i	−0.0150715	−	0.0187736i
$595$	1.25217e7			1.45001
$596$	−611932.	−	1.88333e6i	−0.0705647	−	0.217176i
$597$	−3.45799e6	−	2.51238e6i	−0.397090	−	0.288502i
$598$	1.72190e6	−	1.25103e6i	0.196904	−	0.143059i
$599$	−1.32183e6	+	4.06816e6i	−0.150524	+	0.463267i	−0.997680	−	0.0680784i	$-0.978313\pi$
$599$	−1.32183e6	+	4.06816e6i	−0.150524	+	0.463267i	0.847156	+	0.531345i	$0.178313\pi$
$600$	187370.	−	576665.i	0.0212482	−	0.0653952i
$601$	−1.39721e7	+	1.01513e7i	−1.57789	+	1.14640i	−0.658817	+	0.752303i	$0.728943\pi$
$601$	−1.39721e7	+	1.01513e7i	−1.57789	+	1.14640i	−0.919069	+	0.394097i	$0.871057\pi$
$602$	560839.	+	407474.i	0.0630735	+	0.0458256i
$603$	1.01992e6	+	3.13899e6i	0.114228	+	0.351558i
$604$	9.05681e6			1.01014
$605$	−9.43790e6	−	5.55592e6i	−1.04830	−	0.617117i
$606$	−694689.			−0.0768438
$607$	3.89698e6	+	1.19937e7i	0.429296	+	1.32124i	0.898820	+	0.438317i	$0.144425\pi$
$607$	3.89698e6	+	1.19937e7i	0.429296	+	1.32124i	−0.469525	+	0.882919i	$0.655575\pi$
$608$	−4.28574e6	−	3.11378e6i	−0.470183	−	0.341608i
$609$	194966.	−	141651.i	0.0213017	−	0.0154766i
$610$	94444.2	−	290669.i	0.0102766	−	0.0316282i
$611$	2.39008e6	−	7.35591e6i	0.259006	−	0.797138i
$612$	3.12635e6	−	2.27143e6i	0.337411	−	0.245144i
$613$	−231434.	−	168147.i	−0.0248757	−	0.0180733i	0.575278	−	0.817958i	$-0.304894\pi$
$613$	−231434.	−	168147.i	−0.0248757	−	0.0180733i	−0.600154	+	0.799885i	$0.704894\pi$
$614$	126647.	+	389779.i	0.0135573	+	0.0417251i
$615$	−3.90550e6			−0.416379
$616$	1.37249e6	+	1.70962e6i	0.145733	+	0.181530i
$617$	−1.37967e7			−1.45903			−0.729514	−	0.683966i	$-0.760254\pi$
$617$	−1.37967e7			−1.45903			−0.729514	+	0.683966i	$0.760254\pi$
$618$	−146793.	−	451782.i	−0.0154608	−	0.0475836i
$619$	−9.71230e6	−	7.05640e6i	−1.01882	−	0.740213i	−0.0527758	−	0.998606i	$-0.516807\pi$
$619$	−9.71230e6	−	7.05640e6i	−1.01882	−	0.740213i	−0.966040	+	0.258394i	$0.916807\pi$
$620$	1.61746e7	−	1.17515e7i	1.68987	−	1.22776i
$621$	888197.	−	2.73359e6i	0.0924231	−	0.284449i
$622$	−504155.	+	1.55163e6i	−0.0522502	+	0.160810i
$623$	−9.72881e6	+	7.06839e6i	−1.00424	+	0.729626i
$624$	5.42200e6	+	3.93931e6i	0.557440	+	0.405004i
$625$	−3.77095e6	−	1.16058e7i	−0.386145	−	1.18843i
$626$	−240593.			−0.0245384
$627$	4.92716e6	−	7.51737e6i	0.500527	−	0.763655i
$628$	552655.			0.0559184
$629$	934771.	+	2.87693e6i	0.0942061	+	0.289936i
$630$	−383381.	−	278543.i	−0.0384840	−	0.0279602i
$631$	8.56938e6	−	6.22602e6i	0.856793	−	0.622497i	−0.0702174	−	0.997532i	$-0.522369\pi$
$631$	8.56938e6	−	6.22602e6i	0.856793	−	0.622497i	0.927011	+	0.375035i	$0.122369\pi$
$632$	−1.27595e6	+	3.92696e6i	−0.127069	+	0.391079i
$633$	−2.33135e6	+	7.17516e6i	−0.231259	+	0.711742i
$634$	−1.32526e6	+	962855.i	−0.130941	+	0.0951345i
$635$	3.18008e6	+	2.31046e6i	0.312970	+	0.227386i
$636$	−546790.	−	1.68285e6i	−0.0536016	−	0.164969i
$637$	−1.54583e6			−0.150943
$638$	3009.36	+	62475.6i	0.000292700	+	0.00607658i
$639$	2.46714e6			0.239024
$640$	1.87356e6	+	5.76624e6i	0.180808	+	0.556471i
$641$	−9.47662e6	−	6.88517e6i	−0.910979	−	0.661865i	0.0302830	−	0.999541i	$-0.490359\pi$
$641$	−9.47662e6	−	6.88517e6i	−0.910979	−	0.661865i	−0.941262	+	0.337676i	$0.890359\pi$
$642$	−104992.	+	76281.1i	−0.0100535	+	0.00730432i
$643$	3.20838e6	−	9.87438e6i	0.306026	−	0.941851i	−0.673266	−	0.739400i	$-0.735109\pi$
$643$	3.20838e6	−	9.87438e6i	0.306026	−	0.941851i	0.979292	−	0.202451i	$-0.0648907\pi$
$644$	−4.66581e6	+	1.43599e7i	−0.443315	+	1.36438i
$645$	−3.98968e6	+	2.89867e6i	−0.377606	+	0.274347i
$646$	−2.15785e6	−	1.56777e6i	−0.203442	−	0.147809i
$647$	2.57348e6	+	7.92035e6i	0.241691	+	0.743847i	0.996163	+	0.0875157i	$0.0278928\pi$
$647$	2.57348e6	+	7.92035e6i	0.241691	+	0.743847i	−0.754472	+	0.656332i	$0.772107\pi$
$648$	−294821.			−0.0275817
$649$	−9.28130e6	−	2.52903e6i	−0.864962	−	0.235690i
$650$	809352.			0.0751371
$651$	−3.15590e6	−	9.71287e6i	−0.291858	−	0.898245i
$652$	3.26589e6	+	2.37281e6i	0.300872	+	0.218597i
$653$	−1.29140e7	+	9.38255e6i	−1.18516	+	0.861069i	−0.992744	−	0.120245i	$-0.961632\pi$
$653$	−1.29140e7	+	9.38255e6i	−1.18516	+	0.861069i	−0.192415	+	0.981314i	$0.561632\pi$
$654$	−79041.6	+	243265.i	−0.00722622	+	0.0222400i
$655$	4.15597e6	−	1.27908e7i	0.378503	−	1.16491i
$656$	5.03962e6	−	3.66150e6i	0.457234	−	0.332200i
$657$	440106.	+	319756.i	0.0397781	+	0.0289005i
$658$	−269555.	−	829605.i	−0.0242707	−	0.0746976i
$659$	6.25755e6			0.561294			0.280647	−	0.959811i	$-0.409451\pi$
$659$	6.25755e6			0.561294			0.280647	+	0.959811i	$0.409451\pi$
$660$	−7.23434e6	+	2.74196e6i	−0.646456	+	0.245020i
$661$	−3.66252e6			−0.326044			−0.163022	−	0.986622i	$-0.552124\pi$
$661$	−3.66252e6			−0.326044			−0.163022	+	0.986622i	$0.552124\pi$
$662$	−205583.	−	632721.i	−0.0182324	−	0.0561134i
$663$	8.41253e6	+	6.11206e6i	0.743264	+	0.540013i
$664$	2.20347e6	−	1.60091e6i	0.193949	−	0.140912i
$665$	6.35769e6	−	1.95670e7i	0.557500	−	1.71581i
$666$	35376.5	−	108878.i	0.00309050	−	0.00951159i
$667$	−702537.	+	510423.i	−0.0611441	+	0.0444238i
$668$	−1.80192e7	−	1.30917e7i	−1.56240	−	1.13515i
$669$	2.21354e6	+	6.81256e6i	0.191215	+	0.588498i
$670$	−1.96084e6			−0.168754
$671$	−2.38333e6	+	903330.i	−0.204351	+	0.0774533i
$672$	2.32921e6			0.198969
$673$	−4.79124e6	−	1.47459e7i	−0.407765	−	1.25497i	−0.918564	−	0.395272i	$-0.870650\pi$
$673$	−4.79124e6	−	1.47459e7i	−0.407765	−	1.25497i	0.510799	−	0.859700i	$-0.329350\pi$
$674$	−245739.	−	178540.i	−0.0208365	−	0.0151386i
$675$	884243.	−	642440.i	0.0746985	−	0.0542717i
$676$	−2.05018e6	+	6.30982e6i	−0.172554	+	0.531068i
$677$	−2.07450e6	+	6.38465e6i	−0.173957	+	0.535384i	−0.999584	−	0.0288316i	$-0.990821\pi$
$677$	−2.07450e6	+	6.38465e6i	−0.173957	+	0.535384i	0.825627	+	0.564216i	$0.190821\pi$
$678$	−454571.	+	330265.i	−0.0379776	+	0.0275923i
$679$	−8.50712e6	−	6.18078e6i	−0.708122	−	0.514481i
$680$	1.43018e6	+	4.40163e6i	0.118609	+	0.365040i
$681$	−634516.			−0.0524294
$682$	2.55742e6	+	696863.i	0.210543	+	0.0573702i
$683$	−3.34347e6			−0.274249			−0.137125	−	0.990554i	$-0.543786\pi$
$683$	−3.34347e6			−0.274249			−0.137125	+	0.990554i	$0.543786\pi$
$684$	−1.96208e6	−	6.03865e6i	−0.160352	−	0.493514i
$685$	−2.74122e6	−	1.99161e6i	−0.223212	−	0.162173i
$686$	−1.31085e6	+	952388.i	−0.106351	+	0.0772687i
$687$	−2.75872e6	+	8.49046e6i	−0.223005	+	0.686340i
$688$	2.43067e6	−	7.48083e6i	0.195774	−	0.602530i
$689$	3.85198e6	−	2.79863e6i	0.309126	−	0.224594i
$690$	1.38147e6	+	1.00370e6i	0.110464	+	0.0802566i
$691$	1.39533e6	+	4.29438e6i	0.111168	+	0.342141i	0.991129	−	0.132906i	$-0.0424309\pi$
$691$	1.39533e6	+	4.29438e6i	0.111168	+	0.342141i	−0.879960	+	0.475047i	$0.842431\pi$
$692$	1.05485e7			0.837382
$693$	190140.	+	3.94738e6i	0.0150397	+	0.312231i
$694$	2.09364e6			0.165007
$695$	7.53237e6	+	2.31822e7i	0.591520	+	1.82051i
$696$	72061.1	+	52355.4i	0.00563868	+	0.00409674i
$697$	7.81925e6	−	5.68102e6i	0.609654	−	0.442939i
$698$	550562.	−	1.69446e6i	0.0427728	−	0.131641i
$699$	1.66952e6	−	5.13825e6i	0.129240	−	0.397761i
$700$	−4.64504e6	+	3.37482e6i	−0.358298	+	0.260319i
$701$	−1.57876e7	−	1.14704e7i	−1.21345	−	0.881624i	−0.217911	−	0.975969i	$-0.569924\pi$
$701$	−1.57876e7	−	1.14704e7i	−1.21345	−	0.881624i	−0.995540	+	0.0943450i	$0.969924\pi$
$702$	−121608.	−	374270.i	−0.00931361	−	0.0286644i
$703$	4.97023e6			0.379304
$704$	6.54061e6	−	9.97903e6i	0.497378	−	0.758851i
$705$	6.20532e6			0.470210
$706$	222611.	+	685126.i	0.0168087	+	0.0517320i
$707$	1.07283e7	+	7.79457e6i	0.807203	+	0.586467i
$708$	−5.49768e6	+	3.99430e6i	−0.412189	+	0.299473i
$709$	−4.19073e6	+	1.28977e7i	−0.313094	+	0.963603i	0.663438	+	0.748231i	$0.269097\pi$
$709$	−4.19073e6	+	1.28977e7i	−0.313094	+	0.963603i	−0.976532	+	0.215372i	$0.930903\pi$
$710$	−452933.	+	1.39398e6i	−0.0337200	+	0.103780i
$711$	−6.02150e6	+	4.37488e6i	−0.446715	+	0.324558i
$712$	−3.59586e6	−	2.61254e6i	−0.265829	−	0.193136i
$713$	1.13719e7	+	3.49992e7i	0.837743	+	2.57831i
$714$	1.17275e6			0.0860911
$715$	−1.30326e7	−	1.62337e7i	−0.953377	−	1.18755i
$716$	−4.29920e6			−0.313405
$717$	2.90315e6	+	8.93498e6i	0.210898	+	0.649076i
$718$	−400608.	−	291059.i	−0.0290007	−	0.0210703i
$719$	1.71175e7	−	1.24366e7i	1.23486	−	0.897181i	0.237619	−	0.971358i	$-0.423633\pi$
$719$	1.71175e7	−	1.24366e7i	1.23486	−	0.897181i	0.997245	+	0.0741772i	$0.0236331\pi$
$720$	−1.66157e6	+	5.11378e6i	−0.119450	+	0.367630i
$721$	−2.80213e6	+	8.62405e6i	−0.200747	+	0.617836i
$722$	−2.12791e6	+	1.54601e6i	−0.151918	+	0.110375i
$723$	2.77292e6	+	2.01465e6i	0.197284	+	0.143335i
$724$	5.48546e6	+	1.68825e7i	0.388926	+	1.19699i
$725$	−330216.			−0.0233321
$726$	−883925.	−	520351.i	−0.0622406	−	0.0366399i
$727$	4.56968e6			0.320664			0.160332	−	0.987063i	$-0.448744\pi$
$727$	4.56968e6			0.320664			0.160332	+	0.987063i	$0.448744\pi$
$728$	1.28780e6	+	3.96343e6i	0.0900573	+	0.277168i
$729$	−429945.	−	312373.i	−0.0299636	−	0.0217698i
$730$	−261466.	+	189966.i	−0.0181597	+	0.0131938i
$731$	3.77132e6	−	1.16069e7i	0.261036	−	0.803385i
$732$	−556384.	+	1.71237e6i	−0.0383793	+	0.118119i
$733$	1.09393e7	−	7.94789e6i	0.752023	−	0.546376i	−0.144431	−	0.989515i	$-0.546135\pi$
$733$	1.09393e7	−	7.94789e6i	0.752023	−	0.546376i	0.896453	+	0.443139i	$0.146135\pi$
$734$	−1.05293e6	−	765000.i	−0.0721373	−	0.0524108i
$735$	−383247.	−	1.17951e6i	−0.0261674	−	0.0805349i
$736$	−8.39304e6			−0.571117
$737$	1.02370e7	+	1.27516e7i	0.694234	+	0.864759i
$738$	−365778.			−0.0247216
$739$	−6.51749e6	−	2.00588e7i	−0.439005	−	1.35112i	−0.888926	−	0.458050i	$-0.848548\pi$
$739$	−6.51749e6	−	2.00588e7i	−0.439005	−	1.35112i	0.449921	−	0.893068i	$-0.351452\pi$
$740$	−3.46105e6	−	2.51460e6i	−0.232342	−	0.168807i
$741$	1.38223e7	−	1.00425e7i	0.924771	−	0.671886i
$742$	165937.	−	510702.i	0.0110646	−	0.0340532i
$743$	6.16504e6	−	1.89740e7i	0.409698	−	1.26092i	−0.507210	−	0.861822i	$-0.669323\pi$
$743$	6.16504e6	−	1.89740e7i	0.409698	−	1.26092i	0.916908	−	0.399098i	$-0.130677\pi$
$744$	3.05381e6	−	2.21872e6i	0.202260	−	0.146950i
$745$	3.45861e6	+	2.51282e6i	0.228302	+	0.165871i
$746$	−295210.	−	908564.i	−0.0194216	−	0.0597735i
$747$	4.90960e6			0.321917
$748$	1.04954e7	−	1.60129e7i	0.685878	−	1.04645i
$749$	2.47732e6			0.161353
$750$	−217576.	−	669629.i	−0.0141240	−	0.0434691i
$751$	1.23528e7	+	8.97484e6i	0.799219	+	0.580666i	0.910685	−	0.413102i	$-0.135555\pi$
$751$	1.23528e7	+	8.97484e6i	0.799219	+	0.580666i	−0.111466	+	0.993768i	$0.535555\pi$
$752$	−8.00729e6	+	5.81763e6i	−0.516346	+	0.375147i
$753$	−4.05348e6	+	1.24753e7i	−0.260520	+	0.801797i
$754$	−36740.5	+	113076.i	−0.00235352	+	0.00724338i
$755$	−1.58182e7	+	1.14926e7i	−1.00992	+	0.733752i
$756$	2.25856e6	+	1.64094e6i	0.143723	+	0.104421i
$757$	1.78502e6	+	5.49373e6i	0.113215	+	0.348440i	0.991571	−	0.129568i	$-0.0413591\pi$
$757$	1.78502e6	+	5.49373e6i	0.113215	+	0.348440i	−0.878356	+	0.478008i	$0.841359\pi$
$758$	1.90142e6			0.120200
$759$	−685148.	−	1.42240e7i	−0.0431698	−	0.896223i
$760$	7.60431e6			0.477558
$761$	8.09522e6	+	2.49145e7i	0.506719	+	1.55952i	0.797862	+	0.602840i	$0.205964\pi$
$761$	8.09522e6	+	2.49145e7i	0.506719	+	1.55952i	−0.291143	+	0.956679i	$0.594036\pi$
$762$	297836.	+	216391.i	0.0185819	+	0.0135005i
$763$	3.95015e6	−	2.86995e6i	0.245642	−	0.178469i
$764$	−495311.	+	1.52441e6i	−0.0307004	+	0.0944861i
$765$	−2.57802e6	+	7.93432e6i	−0.159269	+	0.490181i
$766$	2.35151e6	−	1.70847e6i	0.144802	−	0.105205i
$767$	−1.47934e7	−	1.07480e7i	−0.907987	−	0.659691i
$768$	−2.47052e6	−	7.60347e6i	−0.151142	−	0.465167i
$769$	−1.85042e7			−1.12838			−0.564188	−	0.825646i	$-0.690811\pi$
$769$	−1.85042e7			−1.12838			−0.564188	+	0.825646i	$0.690811\pi$
$770$	−2.26526e6	−	617252.i	−0.137686	−	0.0375177i
$771$	1.29134e7			0.782355
$772$	−2.24632e6	−	6.91346e6i	−0.135653	−	0.417496i
$773$	6.40935e6	+	4.65667e6i	0.385803	+	0.280302i	0.763733	−	0.645532i	$-0.223364\pi$
$773$	6.40935e6	+	4.65667e6i	0.385803	+	0.280302i	−0.377931	+	0.925834i	$0.623364\pi$
$774$	−373661.	+	271481.i	−0.0224195	+	0.0162887i
$775$	−4.32436e6	+	1.33090e7i	−0.258623	+	0.795960i
$776$	1.20102e6	−	3.69636e6i	0.0715972	−	0.220353i
$777$	−1.76796e6	+	1.28450e6i	−0.105056	+	0.0763276i
$778$	2.23154e6	+	1.62131e6i	0.132177	+	0.0960321i
$779$	−4.90730e6	−	1.51031e7i	−0.289734	−	0.891709i
$780$	−1.47061e7			−0.865485
$781$	1.14299e7	−	4.33217e6i	0.670525	−	0.254143i
$782$	−4.22586e6			−0.247115
$783$	49616.0	+	152702.i	0.00289213	+	0.00890105i
$784$	1.60036e6	+	1.16273e6i	0.0929880	+	0.0675598i
$785$	−965238.	+	701286.i	−0.0559062	+	0.0406182i
$786$	389236.	−	1.19794e6i	0.0224728	−	0.0691641i
$787$	−4.10630e6	+	1.26379e7i	−0.236327	+	0.727340i	0.760616	+	0.649202i	$0.224897\pi$
$787$	−4.10630e6	+	1.26379e7i	−0.236327	+	0.727340i	−0.996943	+	0.0781372i	$0.975103\pi$
$788$	−2.49149e7	+	1.81017e7i	−1.42936	+	1.03849i
$789$	−1.34280e6	−	975602.i	−0.0767925	−	0.0557930i
$790$	−1.36643e6	−	4.20544e6i	−0.0778968	−	0.239742i
$791$	1.07257e7			0.609517
$792$	−1.36586e6	+	517690.i	−0.0773739	+	0.0293263i
$793$	−4.84486e6			−0.273589
$794$	−1.11568e6	−	3.43371e6i	−0.0628041	−	0.193291i
$795$	3.09043e6	+	2.24533e6i	0.173421	+	0.125997i
$796$	−1.21027e7	+	8.79311e6i	−0.677016	+	0.491881i
$797$	5.59884e6	−	1.72315e7i	0.312214	−	0.960896i	−0.664672	−	0.747135i	$-0.731429\pi$
$797$	5.59884e6	−	1.72315e7i	0.312214	−	0.960896i	0.976886	−	0.213761i	$-0.0685713\pi$
$798$	595442.	−	1.83258e6i	0.0331003	−	0.101872i
$799$	−1.24237e7	+	9.02638e6i	−0.688471	+	0.500203i
$800$	−2.58205e6	−	1.87597e6i	−0.142639	−	0.103633i
$801$	−2.47585e6	−	7.61987e6i	−0.136346	−	0.419630i
$802$	3.22040e6			0.176797
$803$	2.60042e6	+	708580.i	0.142316	+	0.0387793i
$804$	1.15516e7			0.630233
$805$	−1.00728e7	−	3.10009e7i	−0.547848	−	1.68610i
$806$	4.07626e6	+	2.96158e6i	0.221016	+	0.160578i
$807$	−1.42606e7	+	1.03609e7i	−0.770823	+	0.560035i
$808$	−1.51460e6	+	4.66147e6i	−0.0816151	+	0.251185i
$809$	3.08932e6	−	9.50796e6i	0.165956	−	0.510759i	−0.833150	−	0.553047i	$-0.813465\pi$
$809$	3.08932e6	−	9.50796e6i	0.165956	−	0.510759i	0.999105	+	0.0422883i	$0.0134648\pi$
$810$	255429.	−	185580.i	0.0136791	−	0.00993846i
$811$	−1.76838e7	−	1.28480e7i	−0.944113	−	0.685938i	0.00529445	−	0.999986i	$-0.498315\pi$
$811$	−1.76838e7	−	1.28480e7i	−0.944113	−	0.685938i	−0.949407	+	0.314048i	$0.898315\pi$
$812$	−260639.	−	802165.i	−0.0138723	−	0.0426947i
$813$	−8.17390e6			−0.433713
$814$	−27289.1	−	566534.i	−0.00144354	−	0.0299685i
$815$	−8.71498e6			−0.459592
$816$	−4.11196e6	−	1.26553e7i	−0.216184	−	0.665346i
$817$	−1.62226e7	−	1.17864e7i	−0.850288	−	0.617771i
$818$	1.74262e6	−	1.26609e6i	0.0910582	−	0.0661576i
$819$	−2.32137e6	+	7.14444e6i	−0.120930	+	0.372184i
$820$	−4.22393e6	+	1.29999e7i	−0.219372	+	0.675159i
$821$	1.79860e7	−	1.30676e7i	0.931271	−	0.676608i	−0.0150326	−	0.999887i	$-0.504785\pi$
$821$	1.79860e7	−	1.30676e7i	0.931271	−	0.676608i	0.946304	+	0.323279i	$0.104785\pi$
$822$	−256734.	−	186528.i	−0.0132527	−	0.00962865i
$823$	3.69500e6	+	1.13720e7i	0.190158	+	0.585246i	0.999999	−	0.00140327i	$-0.000446674\pi$
$823$	3.69500e6	+	1.13720e7i	0.190158	+	0.585246i	−0.809841	+	0.586649i	$0.800447\pi$
$824$	−3.35157e6			−0.171961
$825$	2.96848e6	−	4.52902e6i	0.151845	−	0.231670i
$826$	−2.06227e6			−0.105171
$827$	−180591.	−	555802.i	−0.00918190	−	0.0282590i	0.946361	−	0.323112i	$-0.104729\pi$
$827$	−180591.	−	555802.i	−0.00918190	−	0.0282590i	−0.955543	+	0.294853i	$0.904729\pi$
$828$	−8.13846e6	−	5.91293e6i	−0.412540	−	0.299728i
$829$	9.21273e6	−	6.69344e6i	0.465589	−	0.338270i	−0.330131	−	0.943935i	$-0.607093\pi$
$829$	9.21273e6	−	6.69344e6i	0.465589	−	0.338270i	0.795720	+	0.605665i	$0.207093\pi$
$830$	−901335.	+	2.77402e6i	−0.0454141	+	0.139770i
$831$	−1.27636e6	+	3.92822e6i	−0.0641164	+	0.197330i
$832$	1.83486e7	−	1.33310e7i	0.918954	−	0.667659i
$833$	2.48304e6	+	1.80404e6i	0.123986	+	0.0900810i
$834$	705459.	+	2.17118e6i	0.0351201	+	0.108089i
$835$	4.80839e7			2.38662
$836$	−1.96936e7	−	2.45309e7i	−0.974560	−	1.21394i
$837$	6.80425e6			0.335712
$838$	−587169.	−	1.80712e6i	−0.0288837	−	0.0888949i
$839$	−1.12966e7	−	8.20749e6i	−0.554044	−	0.402537i	0.275230	−	0.961378i	$-0.411246\pi$
$839$	−1.12966e7	−	8.20749e6i	−0.554044	−	0.402537i	−0.829274	+	0.558842i	$0.811246\pi$
$840$	−2.70494e6	+	1.96525e6i	−0.132269	+	0.0960992i
$841$	−6.32330e6	+	1.94611e7i	−0.308286	+	0.948807i
$842$	403828.	−	1.24285e6i	0.0196298	−	0.0604143i
$843$	−1.01316e7	+	7.36101e6i	−0.491029	+	0.356753i
$844$	2.13619e7	+	1.55204e7i	1.03225	+	0.749973i
$845$	−4.42604e6	−	1.36220e7i	−0.213243	−	0.656293i
$846$	581172.			0.0279176
$847$	7.81228e6	+	1.79538e7i	0.374170	+	0.859899i
$848$	−6.09290e6			−0.290961
$849$	−6.67762e6	−	2.05516e7i	−0.317945	−	0.978535i
$850$	−1.30005e6	−	944541.i	−0.0617181	−	0.0448408i
$851$	6.37066e6	−	4.62856e6i	0.301551	−	0.219090i
$852$	2.66829e6	−	8.21216e6i	0.125932	−	0.387578i
$853$	721225.	−	2.21970e6i	0.0339390	−	0.104453i	−0.932652	−	0.360777i	$-0.882511\pi$
$853$	721225.	−	2.21970e6i	0.0339390	−	0.104453i	0.966591	+	0.256324i	$0.0825114\pi$
$854$	−442052.	+	321170.i	−0.0207410	+	0.0150692i
$855$	1.10896e7	+	8.05703e6i	0.518798	+	0.376929i
$856$	282948.	+	870825.i	0.0131984	+	0.0406206i
$857$	1.72420e7			0.801929			0.400964	−	0.916094i	$-0.368675\pi$
$857$	1.72420e7			0.801929			0.400964	+	0.916094i	$0.368675\pi$
$858$	−1.22059e6	−	1.52040e6i	−0.0566046	−	0.0705083i
$859$	−7.29067e6			−0.337120			−0.168560	−	0.985691i	$-0.553912\pi$
$859$	−7.29067e6			−0.337120			−0.168560	+	0.985691i	$0.553912\pi$
$860$	5.33359e6	+	1.64151e7i	0.245909	+	0.756829i
$861$	5.64882e6	+	4.10411e6i	0.259687	+	0.188673i
$862$	−323085.	+	234735.i	−0.0148098	+	0.0107599i
$863$	435484.	−	1.34028e6i	0.0199042	−	0.0612589i	−0.940611	−	0.339486i	$-0.889747\pi$
$863$	435484.	−	1.34028e6i	0.0199042	−	0.0612589i	0.960515	+	0.278227i	$0.0897468\pi$
$864$	−479545.	+	1.47589e6i	−0.0218547	+	0.0672619i
$865$	−1.84234e7	+	1.33854e7i	−0.837200	+	0.608261i
$866$	1.58189e6	+	1.14931e6i	0.0716773	+	0.0520766i
$867$	−2.43109e6	−	7.48214e6i	−0.109838	−	0.338048i
$868$	−3.57436e7			−1.61027
$869$	−2.02147e7	+	3.08416e7i	−0.908067	+	1.38544i
$870$	−95388.8			−0.00427267
$871$	9.60533e6	+	2.95622e7i	0.429009	+	1.32035i
$872$	1.46001e6	+	1.06076e6i	0.0650228	+	0.0472418i
$873$	5.66790e6	−	4.11797e6i	0.251702	−	0.182872i
$874$	−2.14561e6	+	6.60351e6i	−0.0950106	+	0.292413i
$875$	−4.15330e6	+	1.27825e7i	−0.183389	+	0.564413i
$876$	1.54033e6	−	1.11912e6i	0.0678195	−	0.0492737i
$877$	3.13527e7	+	2.27791e7i	1.37650	+	1.00008i	0.997198	+	0.0748115i	$0.0238355\pi$
$877$	3.13527e7	+	2.27791e7i	1.37650	+	1.00008i	0.379301	+	0.925273i	$0.376164\pi$
$878$	501908.	+	1.54471e6i	0.0219729	+	0.0676257i
$879$	1.08427e7			0.473331
$880$	1.28172e6	+	2.66091e7i	0.0557939	+	1.15830i
$881$	−1.25778e7			−0.545966			−0.272983	−	0.962019i	$-0.588010\pi$
$881$	−1.25778e7			−0.545966			−0.272983	+	0.962019i	$0.588010\pi$
$882$	−35893.7	−	110470.i	−0.00155363	−	0.00478158i
$883$	−1.56261e7	−	1.13530e7i	−0.674448	−	0.490015i	0.197063	−	0.980391i	$-0.436860\pi$
$883$	−1.56261e7	−	1.13530e7i	−0.674448	−	0.490015i	−0.871511	+	0.490376i	$0.836860\pi$
$884$	2.94431e7	−	2.13917e7i	1.26722	−	0.920693i
$885$	4.53343e6	−	1.39525e7i	0.194567	−	0.598815i
$886$	−1.34443e6	+	4.13774e6i	−0.0575380	+	0.177084i
$887$	1.81433e7	−	1.31819e7i	0.774298	−	0.562561i	−0.128964	−	0.991649i	$-0.541165\pi$
$887$	1.81433e7	−	1.31819e7i	0.774298	−	0.562561i	0.903262	+	0.429089i	$0.141165\pi$
$888$	−653456.	−	474763.i	−0.0278089	−	0.0202043i
$889$	−2.17163e6	−	6.68358e6i	−0.0921576	−	0.283632i
$890$	4.75991e6			0.201430
$891$	−2.54038e6	−	692220.i	−0.107203	−	0.0292112i
$892$	2.50704e7			1.05499
$893$	7.79705e6	+	2.39969e7i	0.327191	+	1.00699i
$894$	323923.	+	235343.i	0.0135549	+	0.00984823i
$895$	7.50876e6	−	5.45543e6i	0.313336	−	0.227652i
$896$	3.34959e6	−	1.03090e7i	0.139387	−	0.428988i
$897$	8.36480e6	−	2.57442e7i	0.347116	−	1.06831i
$898$	1.50374e6	−	1.09253e6i	0.0622274	−	0.0452109i
$899$	−1.66312e6	−	1.20832e6i	−0.0686315	−	0.0498637i
$900$	−1.18210e6	−	3.63813e6i	−0.0486460	−	0.149717i
$901$	−9.45347e6			−0.387953
$902$	−1.69460e6	+	642286.i	−0.0693505	+	0.0262852i
$903$	8.81664e6			0.359819
$904$	1.22505e6	+	3.77030e6i	0.0498576	+	0.153446i
$905$	−3.10035e7	−	2.25254e7i	−1.25832	−	0.914220i
$906$	−1.48148e6	+	1.07636e6i	−0.0599619	+	0.0435649i
$907$	−1.37142e6	+	4.22079e6i	−0.0553544	+	0.170363i	−0.974911	−	0.222593i	$-0.928548\pi$
$907$	−1.37142e6	+	4.22079e6i	−0.0553544	+	0.170363i	0.919557	+	0.392957i	$0.128548\pi$
$908$	−686250.	+	2.11206e6i	−0.0276228	+	0.0850142i
$909$	−7.14777e6	+	5.19316e6i	−0.286920	+	0.208460i
$910$	−3.61058e6	−	2.62324e6i	−0.144535	−	0.105011i
$911$	−2.41963e6	−	7.44684e6i	−0.0965945	−	0.297287i	0.891071	−	0.453863i	$-0.149954\pi$
$911$	−2.41963e6	−	7.44684e6i	−0.0965945	−	0.297287i	−0.987666	+	0.156576i	$0.949954\pi$
$912$	−2.18635e7			−0.870427
$913$	2.27455e7	−	8.62099e6i	0.903063	−	0.342279i
$914$	−484222.			−0.0191725
$915$	−1.20115e6	−	3.69676e6i	−0.0474291	−	0.145972i
$916$	2.52778e7	+	1.83654e7i	0.995408	+	0.723207i
$917$	−1.94523e7	+	1.41329e7i	−0.763920	+	0.555020i
$918$	−241449.	+	743104.i	−0.00945625	+	0.0291033i
$919$	485178.	−	1.49322e6i	0.0189501	−	0.0583225i	−0.941134	−	0.338033i	$-0.890238\pi$
$919$	485178.	−	1.49322e6i	0.0189501	−	0.0583225i	0.960084	+	0.279710i	$0.0902385\pi$
$920$	9.74694e6	−	7.08157e6i	0.379663	−	0.275842i
$921$	4.21688e6	+	3.06375e6i	0.163811	+	0.119016i
$922$	−453169.	−	1.39471e6i	−0.0175563	−	0.0540327i
$923$	2.32349e7			0.897709
$924$	1.33450e7	+	3.63632e6i	0.514206	+	0.140114i
$925$	2.99443e6			0.115069
$926$	−613201.	−	1.88724e6i	−0.0235004	−	0.0723269i
$927$	−4.88767e6	−	3.55110e6i	−0.186811	−	0.135726i
$928$	379306.	−	275582.i	0.0144584	−	0.0105046i
$929$	−2.28281e6	+	7.02578e6i	−0.0867823	+	0.267088i	−0.985025	−	0.172411i	$-0.944844\pi$
$929$	−2.28281e6	+	7.02578e6i	−0.0867823	+	0.267088i	0.898243	+	0.439500i	$0.144844\pi$
$930$	−1.24917e6	+	3.84454e6i	−0.0473602	+	0.145760i
$931$	4.07979e6	−	2.96414e6i	0.154264	−	0.112079i
$932$	−1.52976e7	−	1.11144e7i	−0.576879	−	0.419127i
$933$	6.41189e6	+	1.97338e7i	0.241147	+	0.742175i
$934$	1.73043e6			0.0649062
$935$	1.98866e6	+	4.12854e7i	0.0743929	+	1.54443i
$936$	−2.77654e6			−0.103589
$937$	−6.80260e6	−	2.09363e7i	−0.253120	−	0.779022i	−0.994194	−	0.107600i	$-0.965684\pi$
$937$	−6.80260e6	−	2.09363e7i	−0.253120	−	0.779022i	0.741075	−	0.671423i	$-0.234316\pi$
$938$	2.83610e6	+	2.06055e6i	0.105248	+	0.0764674i
$939$	−2.47550e6	+	1.79855e6i	−0.0916217	+	0.0665671i
$940$	6.71126e6	−	2.06551e7i	0.247733	−	0.762445i
$941$	−118351.	+	364247.i	−0.00435711	+	0.0134098i	−0.953211	−	0.302304i	$-0.902244\pi$
$941$	−118351.	+	364247.i	−0.00435711	+	0.0134098i	0.948854	+	0.315714i	$0.102244\pi$
$942$	−90401.2	+	65680.3i	−0.00331930	+	0.00241162i
$943$	−2.03549e7	−	1.47887e7i	−0.745401	−	0.541565i
$944$	7.23086e6	+	2.22543e7i	0.264095	+	0.812801i
$945$	−6.02693e6			−0.219541
$946$	−1.25441e6	+	1.91386e6i	−0.0455735	+	0.0695316i
$947$	−2.59536e7			−0.940422			−0.470211	−	0.882554i	$-0.655822\pi$
$947$	−2.59536e7			−0.940422			−0.470211	+	0.882554i	$0.655822\pi$
$948$	8.04983e6	+	2.47748e7i	0.290915	+	0.895344i
$949$	4.14480e6	+	3.01137e6i	0.149396	+	0.108542i
$950$	−2.13606e6	+	1.55194e6i	−0.0767899	+	0.0557911i
$951$	−6.43794e6	+	1.98139e7i	−0.230832	+	0.710427i
$952$	2.55689e6	−	7.86930e6i	0.0914366	−	0.281413i
$953$	3.51812e7	−	2.55607e7i	1.25481	−	0.911675i	0.256322	−	0.966591i	$-0.417489\pi$
$953$	3.51812e7	−	2.55607e7i	1.25481	−	0.911675i	0.998491	+	0.0549167i	$0.0174893\pi$
$954$	289440.	+	210290.i	0.0102964	+	0.00748081i
$955$	−1.06930e6	−	3.29097e6i	−0.0379395	−	0.116766i
$956$	3.28810e7			1.16359
$957$	498001.	+	620325.i	0.0175772	+	0.0218947i
$958$	−4.10887e6			−0.144647
$959$	1.87194e6	+	5.76123e6i	0.0657272	+	0.202287i
$960$	1.47210e7	+	1.06954e7i	0.515535	+	0.374558i
$961$	−4.73181e7	+	3.43786e7i	−1.65280	+	1.20083i
$962$	333166.	−	1.02538e6i	0.0116071	−	0.0357229i
$963$	−510039.	+	1.56974e6i	−0.0177230	+	0.0545458i
$964$	9.70500e6	−	7.05109e6i	0.336359	−	0.244379i
$965$	1.26961e7	+	9.22424e6i	0.438885	+	0.318869i
$966$	−943387.	−	2.90345e6i	−0.0325272	−	0.100109i
$967$	−5.37149e7			−1.84726			−0.923631	−	0.383282i	$-0.874794\pi$
$967$	−5.37149e7			−1.84726			−0.923631	+	0.383282i	$0.874794\pi$
$968$	−5.41882e6	+	4.79677e6i	−0.185873	+	0.164536i
$969$	−3.39224e7			−1.16059
$970$	1.28619e6	+	3.95848e6i	0.0438910	+	0.135082i
$971$	−7.76606e6	−	5.64237e6i	−0.264334	−	0.192050i	0.447722	−	0.894173i	$-0.352236\pi$
$971$	−7.76606e6	−	5.64237e6i	−0.264334	−	0.192050i	−0.712055	+	0.702123i	$0.752236\pi$
$972$	−1.50477e6	+	1.09328e6i	−0.0510863	+	0.0371164i
$973$	1.34665e7	−	4.14456e7i	0.456008	−	1.40345i
$974$	−529077.	+	1.62833e6i	−0.0178699	+	0.0549978i
$975$	8.32756e6	−	6.05032e6i	0.280547	−	0.203830i
$976$	5.01575e6	+	3.64416e6i	0.168543	+	0.122454i
$977$	−1.67523e7	−	5.15583e7i	−0.561485	−	1.72807i	−0.678170	−	0.734905i	$-0.737227\pi$
$977$	−1.67523e7	−	5.15583e7i	−0.561485	−	1.72807i	0.116685	−	0.993169i	$-0.462773\pi$
$978$	−816219.			−0.0272872
$979$	−2.48503e7	−	3.09543e7i	−0.828658	−	1.03220i
$980$	−4.34064e6			−0.144374
$981$	1.00526e6	+	3.09387e6i	0.0333507	+	0.102643i
$982$	5.78011e6	+	4.19950e6i	0.191275	+	0.138969i
$983$	−2.11654e7	+	1.53776e7i	−0.698623	+	0.507579i	−0.879483	−	0.475930i	$-0.842112\pi$
$983$	−2.11654e7	+	1.53776e7i	−0.698623	+	0.507579i	0.180861	+	0.983509i	$0.442112\pi$
$984$	−797490.	+	2.45442e6i	−0.0262565	+	0.0808093i
$985$	2.05450e7	−	6.32310e7i	0.674707	−	2.07654i
$986$	190979.	−	138754.i	0.00625595	−	0.00454521i
$987$	−8.97522e6	−	6.52088e6i	−0.293260	−	0.213066i
$988$	−1.84783e7	−	5.68704e7i	−0.602240	−	1.85350i
$989$	−3.17698e7			−1.03282
$990$	857498.	−	1.30829e6i	0.0278064	−	0.0424243i
$991$	−9.37957e6			−0.303388			−0.151694	−	0.988427i	$-0.548473\pi$
$991$	−9.37957e6			−0.303388			−0.151694	+	0.988427i	$0.548473\pi$
$992$	−6.13981e6	−	1.88964e7i	−0.198096	−	0.609677i
$993$	−6.84519e6	−	4.97332e6i	−0.220299	−	0.160057i
$994$	2.11998e6	−	1.54026e6i	0.0680560	−	0.0494456i
$995$	9.97997e6	−	3.07152e7i	0.319574	−	0.983548i
$996$	5.30989e6	−	1.63422e7i	0.169605	−	0.521989i
$997$	1.29115e7	−	9.38078e6i	0.411377	−	0.298883i	−0.362782	−	0.931874i	$-0.618173\pi$
$997$	1.29115e7	−	9.38078e6i	0.411377	−	0.298883i	0.774159	+	0.632991i	$0.218173\pi$
$998$	−322258.	−	234134.i	−0.0102418	−	0.00744113i
$999$	−449922.	−	1.38472e6i	−0.0142634	−	0.0438983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.6.e.b.16.3	✓	20
3.2	odd	2		99.6.f.b.82.3		20
11.3	even	5		363.6.a.r.1.6		10
11.8	odd	10		363.6.a.t.1.5		10
11.9	even	5	inner	33.6.e.b.31.3	yes	20
33.8	even	10		1089.6.a.bi.1.6		10
33.14	odd	10		1089.6.a.bk.1.5		10
33.20	odd	10		99.6.f.b.64.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.6.e.b.16.3	✓	20	1.1	even	1	trivial
33.6.e.b.31.3	yes	20	11.9	even	5	inner
99.6.f.b.64.3		20	33.20	odd	10
99.6.f.b.82.3		20	3.2	odd	2
363.6.a.r.1.6		10	11.3	even	5
363.6.a.t.1.5		10	11.8	odd	10
1089.6.a.bi.1.6		10	33.8	even	10
1089.6.a.bk.1.5		10	33.14	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.218677 + 0.673018i) q^{2} +(7.28115 + 5.29007i) q^{3} +(25.4834 - 18.5148i) q^{4} +(-21.0138 + 64.6739i) q^{5} +(-1.96809 + 6.05716i) q^{6} +(98.3565 - 71.4602i) q^{7} +(36.3535 + 26.4124i) q^{8} +(25.0304 + 77.0356i) q^{9} +O(q^{10})\)	\(q+(0.218677 + 0.673018i) q^{2} +(7.28115 + 5.29007i) q^{3} +(25.4834 - 18.5148i) q^{4} +(-21.0138 + 64.6739i) q^{5} +(-1.96809 + 6.05716i) q^{6} +(98.3565 - 71.4602i) q^{7} +(36.3535 + 26.4124i) q^{8} +(25.0304 + 77.0356i) q^{9} -48.1219 q^{10} +(251.233 + 312.943i) q^{11} +283.493 q^{12} +(235.729 + 725.500i) q^{13} +(69.6023 + 50.5690i) q^{14} +(-495.134 + 359.736i) q^{15} +(301.655 - 928.399i) q^{16} +(468.035 - 1440.46i) q^{17} +(-46.3727 + 33.6918i) q^{18} +(-2013.29 - 1462.74i) q^{19} +(661.919 + 2037.18i) q^{20} +1094.18 q^{21} +(-155.677 + 237.517i) q^{22} -3942.75 q^{23} +(124.972 + 384.625i) q^{24} +(-1212.95 - 881.262i) q^{25} +(-436.726 + 317.300i) q^{26} +(-225.273 + 693.320i) q^{27} +(1183.39 - 3642.10i) q^{28} +(178.184 - 129.459i) q^{29} +(-350.383 - 254.568i) q^{30} +(-2884.27 - 8876.86i) q^{31} +2128.73 q^{32} +(173.774 + 3607.62i) q^{33} +1071.81 q^{34} +(2554.76 + 7862.75i) q^{35} +(2064.16 + 1499.70i) q^{36} +(-1615.79 + 1173.94i) q^{37} +(544.191 - 1674.85i) q^{38} +(-2121.56 + 6529.50i) q^{39} +(-2472.12 + 1796.10i) q^{40} +(5162.61 + 3750.86i) q^{41} +(239.271 + 736.401i) q^{42} +8057.77 q^{43} +(12196.3 + 3323.33i) q^{44} -5508.17 q^{45} +(-862.188 - 2653.54i) q^{46} +(-8202.70 - 5959.61i) q^{47} +(7107.69 - 5164.04i) q^{48} +(-626.201 + 1927.25i) q^{49} +(327.860 - 1009.05i) q^{50} +(11028.0 - 8012.29i) q^{51} +(19439.7 + 14123.7i) q^{52} +(-1928.76 - 5936.11i) q^{53} -515.879 q^{54} +(-25518.6 + 9672.06i) q^{55} +5463.04 q^{56} +(-6921.07 - 21300.9i) q^{57} +(126.093 + 91.6117i) q^{58} +(-19392.6 + 14089.6i) q^{59} +(-5957.27 + 18334.6i) q^{60} +(-1962.60 + 6040.27i) q^{61} +(5343.56 - 3882.32i) q^{62} +(7966.88 + 5788.28i) q^{63} +(-9187.46 - 28276.1i) q^{64} -51874.5 q^{65} +(-2389.99 + 905.856i) q^{66} +40747.3 q^{67} +(-14742.7 - 45373.5i) q^{68} +(-28707.8 - 20857.4i) q^{69} +(-4733.10 + 3438.80i) q^{70} +(9412.20 - 28967.8i) q^{71} +(-1124.75 + 3461.62i) q^{72} +(5433.41 - 3947.60i) q^{73} +(-1143.42 - 830.742i) q^{74} +(-4169.76 - 12833.2i) q^{75} -78387.8 q^{76} +(47073.3 + 12826.8i) q^{77} -4858.40 q^{78} +(28395.2 + 87391.3i) q^{79} +(53704.3 + 39018.4i) q^{80} +(-5307.96 + 3856.46i) q^{81} +(-1395.45 + 4294.75i) q^{82} +(18730.2 - 57645.7i) q^{83} +(27883.4 - 20258.5i) q^{84} +(83325.1 + 60539.2i) q^{85} +(1762.05 + 5423.02i) q^{86} +1982.23 q^{87} +(867.623 + 18012.2i) q^{88} -98913.7 q^{89} +(-1204.51 - 3707.10i) q^{90} +(75029.9 + 54512.4i) q^{91} +(-100475. + 72999.2i) q^{92} +(25958.4 - 79891.7i) q^{93} +(2217.18 - 6823.79i) q^{94} +(136908. - 99469.5i) q^{95} +(15499.6 + 11261.1i) q^{96} +(-26727.7 - 82259.4i) q^{97} -1434.01 q^{98} +(-17819.3 + 27186.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9}+O(q^{10}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9	\( 20 q + 6 q^{2} + 45 q^{3} + 8 q^{4} - 11 q^{5} - 54 q^{6} - 139 q^{7} - 76 q^{8} - 405 q^{9} - 424 q^{10} + 2289 q^{11} - 2682 q^{12} - 847 q^{13} + 2022 q^{14} - 396 q^{15} - 7148 q^{16} + 2482 q^{17} + 81 q^{18} + 2958 q^{19} + 8037 q^{20} - 1404 q^{21} + 7441 q^{22} + 8140 q^{23} - 4626 q^{24} - 13120 q^{25} - 13508 q^{26} + 3645 q^{27} + 27819 q^{28} - 20210 q^{29} + 11106 q^{30} + 5540 q^{31} - 4626 q^{32} + 639 q^{33} + 16540 q^{34} - 34101 q^{35} + 648 q^{36} - 25173 q^{37} - 55878 q^{38} + 7623 q^{39} + 22689 q^{40} + 54349 q^{41} + 32292 q^{42} - 21688 q^{43} + 24587 q^{44} - 5346 q^{45} + 44155 q^{46} - 48387 q^{47} - 43083 q^{48} - 78880 q^{49} + 19956 q^{50} + 7317 q^{51} + 109051 q^{52} - 74382 q^{53} + 10206 q^{54} - 47630 q^{55} + 168894 q^{56} + 52983 q^{57} + 1501 q^{58} - 108412 q^{59} - 72333 q^{60} + 16737 q^{61} + 132685 q^{62} - 11259 q^{63} - 157030 q^{64} - 134194 q^{65} - 127539 q^{66} + 20178 q^{67} + 387013 q^{68} + 19305 q^{69} - 411988 q^{70} + 143157 q^{71} + 41634 q^{72} + 164980 q^{73} + 286114 q^{74} - 96255 q^{75} + 46868 q^{76} - 367461 q^{77} - 152658 q^{78} + 369613 q^{79} - 107448 q^{80} - 32805 q^{81} - 184129 q^{82} + 267741 q^{83} + 279819 q^{84} + 379937 q^{85} - 290531 q^{86} + 214920 q^{87} - 740846 q^{88} + 205492 q^{89} + 117126 q^{90} + 394559 q^{91} - 483181 q^{92} - 49860 q^{93} + 561327 q^{94} + 267881 q^{95} + 228564 q^{96} - 300567 q^{97} - 2296174 q^{98} - 115506 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 + 45 * q^3 + 8 * q^4 - 11 * q^5 - 54 * q^6 - 139 * q^7 - 76 * q^8 - 405 * q^9 - 424 * q^10 + 2289 * q^11 - 2682 * q^12 - 847 * q^13 + 2022 * q^14 - 396 * q^15 - 7148 * q^16 + 2482 * q^17 + 81 * q^18 + 2958 * q^19 + 8037 * q^20 - 1404 * q^21 + 7441 * q^22 + 8140 * q^23 - 4626 * q^24 - 13120 * q^25 - 13508 * q^26 + 3645 * q^27 + 27819 * q^28 - 20210 * q^29 + 11106 * q^30 + 5540 * q^31 - 4626 * q^32 + 639 * q^33 + 16540 * q^34 - 34101 * q^35 + 648 * q^36 - 25173 * q^37 - 55878 * q^38 + 7623 * q^39 + 22689 * q^40 + 54349 * q^41 + 32292 * q^42 - 21688 * q^43 + 24587 * q^44 - 5346 * q^45 + 44155 * q^46 - 48387 * q^47 - 43083 * q^48 - 78880 * q^49 + 19956 * q^50 + 7317 * q^51 + 109051 * q^52 - 74382 * q^53 + 10206 * q^54 - 47630 * q^55 + 168894 * q^56 + 52983 * q^57 + 1501 * q^58 - 108412 * q^59 - 72333 * q^60 + 16737 * q^61 + 132685 * q^62 - 11259 * q^63 - 157030 * q^64 - 134194 * q^65 - 127539 * q^66 + 20178 * q^67 + 387013 * q^68 + 19305 * q^69 - 411988 * q^70 + 143157 * q^71 + 41634 * q^72 + 164980 * q^73 + 286114 * q^74 - 96255 * q^75 + 46868 * q^76 - 367461 * q^77 - 152658 * q^78 + 369613 * q^79 - 107448 * q^80 - 32805 * q^81 - 184129 * q^82 + 267741 * q^83 + 279819 * q^84 + 379937 * q^85 - 290531 * q^86 + 214920 * q^87 - 740846 * q^88 + 205492 * q^89 + 117126 * q^90 + 394559 * q^91 - 483181 * q^92 - 49860 * q^93 + 561327 * q^94 + 267881 * q^95 + 228564 * q^96 - 300567 * q^97 - 2296174 * q^98 - 115506 * q^99

Introduction

L-functions

Modular forms

Varieties

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