LMFDB - Embedded newform 21.9.f.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,9,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	21.f (of order $6$, degree $2$, 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:	$8.55495081128$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 1331 x^{10} + 1482 x^{9} + 1359381 x^{8} + 1222227 x^{7} + 474169529 x^{6} + \cdots + 556282980265104 $ x^12 - 3x^11 + 1331x^10 + 1482x^9 + 1359381x^8 + 1222227x^7 + 474169529x^6 + 1911324162x^5 + 121870629463x^4 + 259296590901x^3 + 9508380016437x^2 - 12075311354004*x + 556282980265104
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{5}\cdot 7^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.2
Root			$9.75345 + 16.8935i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.9.f.b.10.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.25345 + 16.0274i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-43.2526 - 74.9157i) q^{4} +(-255.810 - 147.692i) q^{5} +865.482i q^{6} +(-2399.31 - 89.9896i) q^{7} -3136.82 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})$	\(q+(-9.25345 + 16.0274i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-43.2526 - 74.9157i) q^{4} +(-255.810 - 147.692i) q^{5} +865.482i q^{6} +(-2399.31 - 89.9896i) q^{7} -3136.82 q^{8} +(1093.50 - 1894.00i) q^{9} +(4734.26 - 2733.32i) q^{10} +(115.139 + 199.427i) q^{11} +(-3503.46 - 2022.73i) q^{12} -55356.7i q^{13} +(23644.2 - 37622.1i) q^{14} -13813.8 q^{15} +(40099.1 - 69453.7i) q^{16} +(-43402.5 + 25058.4i) q^{17} +(20237.3 + 35052.0i) q^{18} +(-20351.5 - 11750.0i) q^{19} +25552.3i q^{20} +(-99276.4 + 52457.8i) q^{21} -4261.75 q^{22} +(-206932. + 358416. i) q^{23} +(-127041. + 73347.3i) q^{24} +(-151687. - 262729. i) q^{25} +(887226. + 512240. i) q^{26} -102276. i q^{27} +(97034.9 + 183639. i) q^{28} -248134. q^{29} +(127825. - 221399. i) q^{30} +(252532. - 145800. i) q^{31} +(340597. + 589931. i) q^{32} +(9326.30 + 5384.54i) q^{33} -927508. i q^{34} +(600478. + 377380. i) q^{35} -189187. q^{36} +(-1.28547e6 + 2.22650e6i) q^{37} +(376644. - 217455. i) q^{38} +(-1.29439e6 - 2.24194e6i) q^{39} +(802432. + 463284. i) q^{40} -546171. i q^{41} +(77884.4 - 2.07656e6i) q^{42} -4.35029e6 q^{43} +(9960.17 - 17251.5i) q^{44} +(-559457. + 323003. i) q^{45} +(-3.82967e6 - 6.63318e6i) q^{46} +(4.22752e6 + 2.44076e6i) q^{47} -3.75050e6i q^{48} +(5.74860e6 + 431827. i) q^{49} +5.61449e6 q^{50} +(-1.17187e6 + 2.02973e6i) q^{51} +(-4.14709e6 + 2.39432e6i) q^{52} +(-981917. - 1.70073e6i) q^{53} +(1.63922e6 + 946404. i) q^{54} -68020.8i q^{55} +(7.52622e6 + 282281. i) q^{56} -1.09898e6 q^{57} +(2.29609e6 - 3.97695e6i) q^{58} +(-1.79089e7 + 1.03397e7i) q^{59} +(597481. + 1.03487e6i) q^{60} +(1.11373e7 + 6.43009e6i) q^{61} +5.39659e6i q^{62} +(-2.79409e6 + 4.44589e6i) q^{63} +7.92396e6 q^{64} +(-8.17575e6 + 1.41608e7i) q^{65} +(-172601. + 99651.2i) q^{66} +(-4.83469e6 - 8.37393e6i) q^{67} +(3.75454e6 + 2.16769e6i) q^{68} +1.93545e7i q^{69} +(-1.16049e7 + 6.13207e6i) q^{70} +1.20982e7 q^{71} +(-3.43011e6 + 5.94113e6i) q^{72} +(875858. - 505677. i) q^{73} +(-2.37900e7 - 4.12056e7i) q^{74} +(-1.22866e7 - 7.09368e6i) q^{75} +2.03287e6i q^{76} +(-258309. - 488850. i) q^{77} +4.79102e7 q^{78} +(2.12518e7 - 3.68092e7i) q^{79} +(-2.05155e7 + 1.18446e7i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(8.75372e6 + 5.05397e6i) q^{82} -7.57347e7i q^{83} +(8.22388e6 + 5.16843e6i) q^{84} +1.48037e7 q^{85} +(4.02552e7 - 6.97240e7i) q^{86} +(-1.00494e7 + 5.80204e6i) q^{87} +(-361172. - 625568. i) q^{88} +(-8.68583e7 - 5.01477e7i) q^{89} -1.19556e7i q^{90} +(-4.98153e6 + 1.32818e8i) q^{91} +3.58014e7 q^{92} +(6.81837e6 - 1.18098e7i) q^{93} +(-7.82382e7 + 4.51709e7i) q^{94} +(3.47075e6 + 6.01152e6i) q^{95} +(2.75883e7 + 1.59281e7i) q^{96} -4.22699e7i q^{97} +(-6.01155e7 + 8.81396e7i) q^{98} +503620. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−9.25345	+	16.0274i	−0.578341	+	1.00172i	0.417329	+	0.908755i	$0.362966\pi$
$2$	−9.25345	+	16.0274i	−0.578341	+	1.00172i	−0.995670	+	0.0929599i	$0.970367\pi$
$3$	40.5000	−	23.3827i	0.500000	−	0.288675i
$3$	40.5000	−	23.3827i	0.500000	−	0.288675i
$4$	−43.2526	−	74.9157i	−0.168956	−	0.292640i
$5$	−255.810	−	147.692i	−0.409297	−	0.236308i	0.281191	−	0.959652i	$-0.409271\pi$
$5$	−255.810	−	147.692i	−0.409297	−	0.236308i	−0.690487	+	0.723344i	$0.742604\pi$
$6$			865.482i			0.667810i
$7$	−2399.31	−	89.9896i	−0.999297	−	0.0374801i
$7$	−2399.31	−	89.9896i	−0.999297	−	0.0374801i
$8$	−3136.82			−0.765826
$9$	1093.50	−	1894.00i	0.166667	−	0.288675i
$10$	4734.26	−	2733.32i	0.473426	−	0.273332i
$11$	115.139	+	199.427i	0.00786418	+	0.0136212i	0.869931	−	0.493174i	$-0.164163\pi$
$11$	115.139	+	199.427i	0.00786418	+	0.0136212i	−0.862067	+	0.506795i	$0.830830\pi$
$12$	−3503.46	−	2022.73i	−0.168956	−	0.0975465i
$13$		−	55356.7i		−	1.93819i	−0.246687	−	0.969095i	$-0.579342\pi$
$13$		−	55356.7i		−	1.93819i	0.246687	−	0.969095i	$-0.420658\pi$
$14$	23644.2	−	37622.1i	0.615479	−	0.979335i
$15$	−13813.8			−0.272864
$16$	40099.1	−	69453.7i	0.611864	−	1.05978i
$17$	−43402.5	+	25058.4i	−0.519660	+	0.300026i	−0.736795	−	0.676116i	$-0.763662\pi$
$17$	−43402.5	+	25058.4i	−0.519660	+	0.300026i	0.217136	+	0.976141i	$0.430329\pi$
$18$	20237.3	+	35052.0i	0.192780	+	0.333905i
$19$	−20351.5	−	11750.0i	−0.156165	−	0.0901617i	0.419881	−	0.907579i	$-0.362072\pi$
$19$	−20351.5	−	11750.0i	−0.156165	−	0.0901617i	−0.576046	+	0.817417i	$0.695405\pi$
$20$			25552.3i			0.159702i
$21$	−99276.4	+	52457.8i	−0.510468	+	0.269732i
$22$	−4261.75			−0.0181927
$23$	−206932.	+	358416.i	−0.739462	+	1.28079i	0.213276	+	0.976992i	$0.431587\pi$
$23$	−206932.	+	358416.i	−0.739462	+	1.28079i	−0.952738	+	0.303794i	$0.901747\pi$
$24$	−127041.	+	73347.3i	−0.382913	+	0.221075i
$25$	−151687.	−	262729.i	−0.388318	−	0.672586i
$26$	887226.	+	512240.i	1.94151	+	1.12093i
$27$		−	102276.i		−	0.192450i
$28$	97034.9	+	183639.i	0.157869	+	0.298766i
$29$	−248134.			−0.350828			−0.175414	−	0.984495i	$-0.556126\pi$
$29$	−248134.			−0.350828			−0.175414	+	0.984495i	$0.556126\pi$
$30$	127825.	−	221399.i	0.157809	−	0.273332i
$31$	252532.	−	145800.i	0.273445	−	0.157874i	−0.357007	−	0.934102i	$-0.616203\pi$
$31$	252532.	−	145800.i	0.273445	−	0.157874i	0.630452	+	0.776228i	$0.282869\pi$
$32$	340597.	+	589931.i	0.324818	+	0.562602i
$33$	9326.30	+	5384.54i	0.00786418	+	0.00454039i
$34$		−	927508.i		−	0.694068i
$35$	600478.	+	377380.i	0.400152	+	0.251482i
$36$	−189187.			−0.112637
$37$	−1.28547e6	+	2.22650e6i	−0.685890	+	1.18800i	0.287266	+	0.957851i	$0.407254\pi$
$37$	−1.28547e6	+	2.22650e6i	−0.685890	+	1.18800i	−0.973156	+	0.230146i	$0.926080\pi$
$38$	376644.	−	217455.i	0.180633	−	0.104288i
$39$	−1.29439e6	−	2.24194e6i	−0.559507	−	0.969095i
$40$	802432.	+	463284.i	0.313450	+	0.180970i
$41$		−	546171.i		−	0.193283i	−0.995319	−	0.0966414i	$-0.969190\pi$
$41$		−	546171.i		−	0.193283i	0.995319	−	0.0966414i	$-0.0308100\pi$
$42$	77884.4	−	2.07656e6i	0.0250296	−	0.667341i
$43$	−4.35029e6			−1.27246			−0.636230	−	0.771499i	$-0.719507\pi$
$43$	−4.35029e6			−1.27246			−0.636230	+	0.771499i	$0.719507\pi$
$44$	9960.17	−	17251.5i	0.00265739	−	0.00460274i
$45$	−559457.	+	323003.i	−0.136432	+	0.0787692i
$46$	−3.82967e6	−	6.63318e6i	−0.855322	−	1.48146i
$47$	4.22752e6	+	2.44076e6i	0.866351	+	0.500188i	0.866134	−	0.499812i	$-0.166598\pi$
$47$	4.22752e6	+	2.44076e6i	0.866351	+	0.500188i	0.000217270		1.00000i	$0.499931\pi$
$48$		−	3.75050e6i		−	0.706519i
$49$	5.74860e6	+	431827.i	0.997190	+	0.0749075i
$50$	5.61449e6			0.898319
$51$	−1.17187e6	+	2.02973e6i	−0.173220	+	0.300026i
$52$	−4.14709e6	+	2.39432e6i	−0.567191	+	0.327468i
$53$	−981917.	−	1.70073e6i	−0.124443	−	0.215542i	0.797072	−	0.603884i	$-0.206381\pi$
$53$	−981917.	−	1.70073e6i	−0.124443	−	0.215542i	−0.921515	+	0.388342i	$0.873048\pi$
$54$	1.63922e6	+	946404.i	0.192780	+	0.111302i
$55$		−	68020.8i		−	0.00743346i
$56$	7.52622e6	+	282281.i	0.765288	+	0.0287032i
$57$	−1.09898e6			−0.104110
$58$	2.29609e6	−	3.97695e6i	0.202898	−	0.351430i
$59$	−1.79089e7	+	1.03397e7i	−1.47795	+	0.853297i	−0.999689	−	0.0249186i	$-0.992067\pi$
$59$	−1.79089e7	+	1.03397e7i	−1.47795	+	0.853297i	−0.478265	+	0.878216i	$0.658734\pi$
$60$	597481.	+	1.03487e6i	0.0461020	+	0.0798509i
$61$	1.11373e7	+	6.43009e6i	0.804375	+	0.464406i	0.844999	−	0.534768i	$-0.179601\pi$
$61$	1.11373e7	+	6.43009e6i	0.804375	+	0.464406i	−0.0406235	+	0.999175i	$0.512934\pi$
$62$			5.39659e6i			0.365219i
$63$	−2.79409e6	+	4.44589e6i	−0.177369	+	0.282226i
$64$	7.92396e6			0.472305
$65$	−8.17575e6	+	1.41608e7i	−0.458009	+	0.793295i
$66$	−172601.	+	99651.2i	−0.00909635	+	0.00525178i
$67$	−4.83469e6	−	8.37393e6i	−0.239922	−	0.415556i	0.720770	−	0.693174i	$-0.243788\pi$
$67$	−4.83469e6	−	8.37393e6i	−0.239922	−	0.415556i	−0.960692	+	0.277618i	$0.910455\pi$
$68$	3.75454e6	+	2.16769e6i	0.175599	+	0.101382i
$69$			1.93545e7i			0.853857i
$70$	−1.16049e7	+	6.13207e6i	−0.483338	+	0.255396i
$71$	1.20982e7			0.476090			0.238045	−	0.971254i	$-0.423493\pi$
$71$	1.20982e7			0.476090			0.238045	+	0.971254i	$0.423493\pi$
$72$	−3.43011e6	+	5.94113e6i	−0.127638	+	0.221075i
$73$	875858.	−	505677.i	0.0308420	−	0.0178066i	−0.484500	−	0.874791i	$-0.660998\pi$
$73$	875858.	−	505677.i	0.0308420	−	0.0178066i	0.515342	+	0.856985i	$0.327665\pi$
$74$	−2.37900e7	−	4.12056e7i	−0.793356	−	1.37413i
$75$	−1.22866e7	−	7.09368e6i	−0.388318	−	0.224195i
$76$			2.03287e6i			0.0609333i
$77$	−258309.	−	488850.i	−0.00734813	−	0.0139063i
$78$	4.79102e7			1.29434
$79$	2.12518e7	−	3.68092e7i	0.545617	−	0.945036i	−0.452951	−	0.891536i	$-0.649629\pi$
$79$	2.12518e7	−	3.68092e7i	0.545617	−	0.945036i	0.998568	−	0.0535009i	$-0.0170380\pi$
$80$	−2.05155e7	+	1.18446e7i	−0.500867	+	0.289176i
$81$	−2.39148e6	−	4.14217e6i	−0.0555556	−	0.0962250i
$82$	8.75372e6	+	5.05397e6i	0.193614	+	0.111783i
$83$		−	7.57347e7i		−	1.59582i	−0.602780	−	0.797908i	$-0.705940\pi$
$83$		−	7.57347e7i		−	1.59582i	0.602780	−	0.797908i	$-0.294060\pi$
$84$	8.22388e6	+	5.16843e6i	0.165181	+	0.103810i
$85$	1.48037e7			0.283593
$86$	4.02552e7	−	6.97240e7i	0.735915	−	1.27464i
$87$	−1.00494e7	+	5.80204e6i	−0.175414	+	0.101275i
$88$	−361172.	−	625568.i	−0.00602259	−	0.0104314i
$89$	−8.68583e7	−	5.01477e7i	−1.38437	−	0.799265i	−0.391694	−	0.920096i	$-0.628111\pi$
$89$	−8.68583e7	−	5.01477e7i	−1.38437	−	0.799265i	−0.992673	+	0.120831i	$0.961444\pi$
$90$		−	1.19556e7i		−	0.182222i
$91$	−4.98153e6	+	1.32818e8i	−0.0726435	+	1.93683i
$92$	3.58014e7			0.499745
$93$	6.81837e6	−	1.18098e7i	0.0911483	−	0.157874i
$94$	−7.82382e7	+	4.51709e7i	−1.00209	+	0.578558i
$95$	3.47075e6	+	6.01152e6i	0.0426118	+	0.0738057i
$96$	2.75883e7	+	1.59281e7i	0.324818	+	0.187534i
$97$		−	4.22699e7i		−	0.477468i	−0.971085	−	0.238734i	$-0.923268\pi$
$97$		−	4.22699e7i		−	0.477468i	0.971085	−	0.238734i	$-0.0767324\pi$
$98$	−6.01155e7	+	8.81396e7i	−0.651752	+	0.955579i
$99$	503620.			0.00524279
$100$	−1.31217e7	+	2.27274e7i	−0.131217	+	0.227274i
$101$	−6.15931e7	+	3.55608e7i	−0.591898	+	0.341732i	−0.765848	−	0.643022i	$-0.777680\pi$
$101$	−6.15931e7	+	3.55608e7i	−0.591898	+	0.341732i	0.173950	+	0.984755i	$0.444347\pi$
$102$	−2.16876e7	−	3.75641e7i	−0.200360	−	0.347034i
$103$	7.75832e7	+	4.47927e7i	0.689316	+	0.397977i	0.803356	−	0.595499i	$-0.203046\pi$
$103$	7.75832e7	+	4.47927e7i	0.689316	+	0.397977i	−0.114040	+	0.993476i	$0.536379\pi$
$104$			1.73644e8i			1.48432i
$105$	3.31435e7	+	1.24310e6i	0.272673	+	0.0102270i
$106$	3.63445e7			0.287882
$107$	1.00028e8	−	1.73254e8i	0.763109	−	1.32174i	−0.178131	−	0.984007i	$-0.557005\pi$
$107$	1.00028e8	−	1.73254e8i	0.763109	−	1.32174i	0.941241	−	0.337737i	$-0.109661\pi$
$108$	−7.66207e6	+	4.42370e6i	−0.0563185	+	0.0325155i
$109$	1.22305e7	+	2.11839e7i	0.0866441	+	0.150072i	0.906091	−	0.423084i	$-0.139052\pi$
$109$	1.22305e7	+	2.11839e7i	0.0866441	+	0.150072i	−0.819447	+	0.573156i	$0.805719\pi$
$110$	1.09020e6	+	629427.i	0.00744621	+	0.00429907i
$111$			1.20231e8i			0.791998i
$112$	−1.02460e8	+	1.63033e8i	−0.651154	+	1.03610i
$113$	1.72425e8			1.05751			0.528757	−	0.848773i	$-0.322658\pi$
$113$	1.72425e8			1.05751			0.528757	+	0.848773i	$0.322658\pi$
$114$	1.01694e7	−	1.76139e7i	0.0602109	−	0.104288i
$115$	1.05871e8	−	6.11244e7i	0.605319	−	0.349481i
$116$	1.07324e7	+	1.85891e7i	0.0592743	+	0.102666i
$117$	−1.04845e8	−	6.05325e7i	−0.559507	−	0.323032i
$118$		−	3.82712e8i		−	1.97399i
$119$	1.06391e8	−	5.62173e7i	0.530539	−	0.280338i
$120$	4.33313e7			0.208967
$121$	1.07153e8	−	1.85594e8i	0.499876	−	0.865811i
$122$	−2.06116e8	+	1.19001e8i	−0.930406	+	0.537170i
$123$	−1.27709e7	−	2.21199e7i	−0.0557959	−	0.0966414i
$124$	−2.18454e7	−	1.26124e7i	−0.0924001	−	0.0533472i
$125$			2.04996e8i			0.839664i
$126$	−4.54013e7	−	8.59219e7i	−0.180130	−	0.340896i
$127$	−3.32395e8			−1.27773			−0.638865	−	0.769319i	$-0.720596\pi$
$127$	−3.32395e8			−1.27773			−0.638865	+	0.769319i	$0.720596\pi$
$128$	−1.60517e8	+	2.78023e8i	−0.597971	+	1.03572i
$129$	−1.76187e8	+	1.01721e8i	−0.636230	+	0.367328i
$130$	−1.51308e8	−	2.62073e8i	−0.529770	−	0.917589i
$131$	4.41091e8	+	2.54664e8i	1.49776	+	0.864734i	0.999997	−	0.00257625i	$-0.000820048\pi$
$131$	4.41091e8	+	2.54664e8i	1.49776	+	0.864734i	0.497767	+	0.867311i	$0.334153\pi$
$132$		−	931582.i		−	0.00306850i
$133$	4.77723e7	+	3.00233e7i	0.152676	+	0.0959514i
$134$	1.78950e8			0.555026
$135$	−1.51053e7	+	2.61632e7i	−0.0454774	+	0.0787692i
$136$	1.36146e8	−	7.86039e7i	0.397969	−	0.229767i
$137$	−2.87068e8	−	4.97217e8i	−0.814897	−	1.41144i	−0.909402	−	0.415919i	$-0.863460\pi$
$137$	−2.87068e8	−	4.97217e8i	−0.814897	−	1.41144i	0.0945043	−	0.995524i	$-0.469873\pi$
$138$	−3.10203e8	−	1.79096e8i	−0.855322	−	0.493820i
$139$		−	2.72891e8i		−	0.731021i	−0.930807	−	0.365510i	$-0.880894\pi$
$139$		−	2.72891e8i		−	0.731021i	0.930807	−	0.365510i	$-0.119106\pi$
$140$	2.29944e6	−	6.13080e7i	0.00598564	−	0.159590i
$141$	2.28286e8			0.577568
$142$	−1.11951e8	+	1.93904e8i	−0.275342	+	0.476907i
$143$	1.10396e7	−	6.37374e6i	0.0264004	−	0.0152423i
$144$	−8.76967e7	−	1.51895e8i	−0.203955	−	0.353260i
$145$	6.34752e7	+	3.66474e7i	0.143593	+	0.0829032i
$146$			1.87170e7i			0.0411932i
$147$	2.42916e8	−	1.16929e8i	0.520219	−	0.250410i
$148$	2.22400e8			0.463540
$149$	3.68050e6	−	6.37481e6i	0.00746727	−	0.0129337i	−0.862268	−	0.506453i	$-0.830956\pi$
$149$	3.68050e6	−	6.37481e6i	0.00746727	−	0.0129337i	0.869735	+	0.493519i	$0.164290\pi$
$150$	2.27387e8	−	1.31282e8i	0.449160	−	0.259322i
$151$	2.30287e8	+	3.98870e8i	0.442958	+	0.767226i	0.997907	−	0.0646584i	$-0.0205958\pi$
$151$	2.30287e8	+	3.98870e8i	0.442958	+	0.767226i	−0.554950	+	0.831884i	$0.687262\pi$
$152$	6.38391e7	+	3.68575e7i	0.119595	+	0.0690481i
$153$			1.09606e8i			0.200017i
$154$	1.02253e7	+	383513.i	0.0181799	+	0.000681864i
$155$	−8.61338e7			−0.149227
$156$	−1.11971e8	+	1.93940e8i	−0.189064	+	0.327468i
$157$	−4.72161e8	+	2.72602e8i	−0.777126	+	0.448674i	−0.835411	−	0.549626i	$-0.814770\pi$
$157$	−4.72161e8	+	2.72602e8i	−0.777126	+	0.448674i	0.0582846	+	0.998300i	$0.481437\pi$
$158$	3.93305e8	+	6.81225e8i	0.631105	+	1.09311i
$159$	−7.95353e7	−	4.59197e7i	−0.124443	−	0.0718473i
$160$		−	2.01214e8i		−	0.307028i
$161$	5.28748e8	−	8.41332e8i	0.786947	−	1.25217i
$162$	8.85179e7			0.128520
$163$	−5.24689e8	+	9.08787e8i	−0.743278	+	1.28740i	0.207717	+	0.978189i	$0.433397\pi$
$163$	−5.24689e8	+	9.08787e8i	−0.743278	+	1.28740i	−0.950995	+	0.309206i	$0.899937\pi$
$164$	−4.09168e7	+	2.36233e7i	−0.0565622	+	0.0326562i
$165$	−1.59051e6	−	2.75484e6i	−0.00214586	−	0.00371673i
$166$	1.21383e9	+	7.00807e8i	1.59855	+	0.922925i
$167$			7.68691e8i			0.988294i	0.869378	+	0.494147i	$0.164519\pi$
$167$			7.68691e8i			0.988294i	−0.869378	+	0.494147i	$0.835481\pi$
$168$	3.11412e8	−	1.64551e8i	0.390930	−	0.206568i
$169$	−2.24863e9			−2.75658
$170$	−1.36986e8	+	2.37266e8i	−0.164013	+	0.284080i
$171$	−4.45088e7	+	2.56972e7i	−0.0520549	+	0.0300539i
$172$	1.88161e8	+	3.25905e8i	0.214989	+	0.372372i
$173$	−9.76950e8	−	5.64042e8i	−1.09066	−	0.629691i	−0.156905	−	0.987614i	$-0.550152\pi$
$173$	−9.76950e8	−	5.64042e8i	−1.09066	−	0.629691i	−0.933751	+	0.357923i	$0.883485\pi$
$174$		−	2.14755e8i		−	0.234286i
$175$	3.40301e8	+	6.44019e8i	0.362836	+	0.686667i
$176$	1.84680e7			0.0192472
$177$	−4.83540e8	+	8.37516e8i	−0.492651	+	0.853297i
$178$	1.60748e9	−	9.28078e8i	1.60127	−	0.924494i
$179$	−2.35515e8	−	4.07924e8i	−0.229407	−	0.397344i	0.728226	−	0.685337i	$-0.240345\pi$
$179$	−2.35515e8	−	4.07924e8i	−0.229407	−	0.397344i	−0.957632	+	0.287993i	$0.907012\pi$
$180$	4.83960e7	+	2.79414e7i	0.0461020	+	0.0266170i
$181$			4.04883e7i			0.0377238i	0.999822	+	0.0188619i	$0.00600429\pi$
$181$			4.04883e7i			0.0377238i	−0.999822	+	0.0188619i	$0.993996\pi$
$182$	−2.08264e9	−	1.30887e9i	−1.89814	−	1.19291i
$183$	6.01412e8			0.536250
$184$	6.49108e8	−	1.12429e9i	0.566299	−	0.980859i
$185$	6.57673e8	−	3.79707e8i	0.561465	−	0.324162i
$186$	1.26187e8	+	2.18562e8i	0.105430	+	0.182609i
$187$	−9.99468e6	−	5.77043e6i	−0.00817340	−	0.00471891i
$188$		−	4.22277e8i		−	0.338038i
$189$	−9.20377e6	+	2.45392e8i	−0.00721304	+	0.192315i
$190$	−1.28466e8			−0.0985764
$191$	1.03944e9	−	1.80036e9i	0.781028	−	1.35278i	−0.150316	−	0.988638i	$-0.548029\pi$
$191$	1.03944e9	−	1.80036e9i	0.781028	−	1.35278i	0.931344	−	0.364141i	$-0.118638\pi$
$192$	3.20921e8	−	1.85284e8i	0.236153	−	0.136343i
$193$	2.45196e6	+	4.24692e6i	0.00176720	+	0.00306087i	0.866908	−	0.498469i	$-0.166104\pi$
$193$	2.45196e6	+	4.24692e6i	0.00176720	+	0.00306087i	−0.865140	+	0.501530i	$0.832771\pi$
$194$	6.77479e8	+	3.91143e8i	0.478287	+	0.276139i
$195$			7.64684e8i			0.528863i
$196$	−2.16292e8	−	4.49339e8i	−0.146560	−	0.304473i
$197$	−2.45189e9			−1.62793			−0.813965	−	0.580914i	$-0.802695\pi$
$197$	−2.45189e9			−1.62793			−0.813965	+	0.580914i	$0.802695\pi$
$198$	−4.66022e6	+	8.07174e6i	−0.00303212	+	0.00525178i
$199$	2.01378e9	−	1.16266e9i	1.28410	−	0.741378i	0.306508	−	0.951868i	$-0.400839\pi$
$199$	2.01378e9	−	1.16266e9i	1.28410	−	0.741378i	0.977596	+	0.210490i	$0.0675061\pi$
$200$	4.75814e8	+	8.24133e8i	0.297384	+	0.515083i
$201$	−3.91610e8	−	2.26096e8i	−0.239922	−	0.138519i
$202$		−	1.31624e9i		−	0.790551i
$203$	5.95351e8	+	2.23295e7i	0.350581	+	0.0131490i
$204$	2.02745e8			0.117066
$205$	−8.06652e7	+	1.39716e8i	−0.0456742	+	0.0791100i
$206$	−1.43582e9	+	8.28973e8i	−0.797319	+	0.460332i
$207$	4.52560e8	+	7.83857e8i	0.246487	+	0.426929i
$208$	−3.84472e9	−	2.21975e9i	−2.05405	−	1.18591i
$209$		−	5.41154e6i		−	0.00283619i
$210$	−3.26616e8	+	5.19703e8i	−0.167942	+	0.267226i
$211$	1.23954e9			0.625363			0.312682	−	0.949858i	$-0.398773\pi$
$211$	1.23954e9			0.625363			0.312682	+	0.949858i	$0.398773\pi$
$212$	−8.49410e7	+	1.47122e8i	−0.0420507	+	0.0728340i
$213$	4.89979e8	−	2.82890e8i	0.238045	−	0.137435i
$214$	1.85121e9	+	3.20639e9i	0.882674	+	1.52884i
$215$	1.11285e9	+	6.42504e8i	0.520814	+	0.300692i
$216$			3.20821e8i			0.147383i
$217$	−6.19024e8	+	3.27093e8i	−0.279170	+	0.147514i
$218$	−4.52698e8			−0.200439
$219$	2.36482e7	−	4.09598e7i	0.0102807	−	0.0178066i
$220$	−5.09583e6	+	2.94208e6i	−0.00217533	+	0.00125592i
$221$	1.38715e9	+	2.40262e9i	0.581507	+	1.00720i
$222$	−1.92699e9	−	1.11255e9i	−0.793356	−	0.458045i
$223$			2.69335e9i			1.08911i	0.838724	+	0.544557i	$0.183302\pi$
$223$			2.69335e9i			1.08911i	−0.838724	+	0.544557i	$0.816698\pi$
$224$	−7.64110e8	−	1.44608e9i	−0.303504	−	0.574381i
$225$	−6.63477e8			−0.258878
$226$	−1.59553e9	+	2.76353e9i	−0.611604	+	1.05933i
$227$	−3.62075e8	+	2.09044e8i	−0.136363	+	0.0787291i	−0.566629	−	0.823973i	$-0.691753\pi$
$227$	−3.62075e8	+	2.09044e8i	−0.136363	+	0.0787291i	0.430267	+	0.902702i	$0.358420\pi$
$228$	4.75339e7	+	8.23311e7i	0.0175899	+	0.0304666i
$229$	−4.89998e8	−	2.82900e8i	−0.178177	−	0.102871i	0.408259	−	0.912866i	$-0.366136\pi$
$229$	−4.89998e8	−	2.82900e8i	−0.178177	−	0.102871i	−0.586436	+	0.809996i	$0.699469\pi$
$230$			2.26245e9i			0.808476i
$231$	−2.18922e7	−	1.37585e7i	−0.00768848	−	0.00483195i
$232$	7.78352e8			0.268673
$233$	1.29941e9	−	2.25065e9i	0.440883	−	0.763631i	−0.556872	−	0.830598i	$-0.687999\pi$
$233$	1.29941e9	−	2.25065e9i	0.440883	−	0.763631i	0.997755	+	0.0669667i	$0.0213321\pi$
$234$	1.94036e9	−	1.12027e9i	0.647172	−	0.373645i
$235$	−7.20962e8	−	1.24874e9i	−0.236396	−	0.409451i
$236$	1.54921e9	+	8.94439e8i	0.499417	+	0.288339i
$237$		−	1.98770e9i		−	0.630024i
$238$	−8.34661e7	+	2.22538e9i	−0.0260137	+	0.693580i
$239$	2.17205e9			0.665700			0.332850	−	0.942980i	$-0.391990\pi$
$239$	2.17205e9			0.665700			0.332850	+	0.942980i	$0.391990\pi$
$240$	−5.53919e8	+	9.59416e8i	−0.166956	+	0.289176i
$241$	2.49009e9	−	1.43765e9i	0.738154	−	0.426173i	−0.0832439	−	0.996529i	$-0.526528\pi$
$241$	2.49009e9	−	1.43765e9i	0.738154	−	0.426173i	0.821398	+	0.570356i	$0.193195\pi$
$242$	1.98307e9	+	3.43477e9i	0.578197	+	1.00147i
$243$	−1.93710e8	−	1.11839e8i	−0.0555556	−	0.0320750i
$244$		−	1.11247e9i		−	0.313856i
$245$	−1.40678e9	−	9.59490e8i	−0.390445	−	0.266303i
$246$	4.72701e8			0.129076
$247$	−6.50438e8	+	1.12659e9i	−0.174750	+	0.302677i
$248$	−7.92149e8	+	4.57347e8i	−0.209411	+	0.120904i
$249$	−1.77088e9	−	3.06726e9i	−0.460672	−	0.797908i
$250$	−3.28556e9	−	1.89692e9i	−0.841105	−	0.485612i
$251$			1.14135e9i			0.287557i	0.989610	+	0.143778i	$0.0459252\pi$
$251$			1.14135e9i			0.287557i	−0.989610	+	0.143778i	$0.954075\pi$
$252$	4.53919e8	+	1.70249e7i	0.112558	+	0.00422164i
$253$	−9.53041e7			−0.0232611
$254$	3.07580e9	−	5.32744e9i	0.738963	−	1.27992i
$255$	5.99552e8	−	3.46151e8i	0.141797	−	0.0818663i
$256$	−1.95640e9	−	3.38858e9i	−0.455510	−	0.788966i
$257$	2.88404e9	+	1.66510e9i	0.661101	+	0.381687i	0.792697	−	0.609616i	$-0.208677\pi$
$257$	2.88404e9	+	1.66510e9i	0.661101	+	0.381687i	−0.131595	+	0.991304i	$0.542010\pi$
$258$		−	3.76510e9i		−	0.849762i
$259$	3.28460e9	−	5.22639e9i	0.729935	−	1.16146i
$260$	1.41449e9			0.309533
$261$	−2.71334e8	+	4.69965e8i	−0.0584713	+	0.101275i
$262$	−8.16323e9	+	4.71304e9i	−1.73244	+	1.00022i
$263$	−2.04981e9	−	3.55038e9i	−0.428441	−	0.742081i	0.568294	−	0.822825i	$-0.307604\pi$
$263$	−2.04981e9	−	3.55038e9i	−0.428441	−	0.742081i	−0.996735	+	0.0807445i	$0.974270\pi$
$264$	−2.92549e7	−	1.68903e7i	−0.00602259	−	0.00347715i
$265$			5.80086e8i			0.117627i
$266$	−9.23254e8	+	4.87849e8i	−0.184414	+	0.0974449i
$267$	−4.69035e9			−0.922911
$268$	−4.18226e8	+	7.24389e8i	−0.0810722	+	0.140421i
$269$	−5.00053e9	+	2.88706e9i	−0.955008	+	0.551374i	−0.894633	−	0.446802i	$-0.852563\pi$
$269$	−5.00053e9	+	2.88706e9i	−0.955008	+	0.551374i	−0.0603748	+	0.998176i	$0.519230\pi$
$270$	−2.79553e8	−	4.84200e8i	−0.0526028	−	0.0911108i
$271$	8.34317e8	+	4.81693e8i	0.154687	+	0.0893087i	0.575346	−	0.817910i	$-0.304868\pi$
$271$	8.34317e8	+	4.81693e8i	0.154687	+	0.0893087i	−0.420658	+	0.907219i	$0.638201\pi$
$272$			4.01928e9i			0.734299i
$273$	2.90389e9	+	5.49561e9i	0.522793	+	0.989385i
$274$	1.06255e10			1.88515
$275$	3.49302e7	−	6.05009e7i	0.00610760	−	0.0105787i
$276$	1.44996e9	−	8.37132e8i	0.249873	−	0.144264i
$277$	−4.74181e9	−	8.21306e9i	−0.805425	−	1.39504i	−0.916004	−	0.401170i	$-0.868604\pi$
$277$	−4.74181e9	−	8.21306e9i	−0.805425	−	1.39504i	0.110578	−	0.993867i	$-0.464730\pi$
$278$	4.37374e9	+	2.52518e9i	0.732275	+	0.422779i
$279$		−	6.37727e8i		−	0.105249i
$280$	−1.88359e9	−	1.18377e9i	−0.306447	−	0.192591i
$281$	−8.67661e9			−1.39163			−0.695816	−	0.718220i	$-0.744957\pi$
$281$	−8.67661e9			−1.39163			−0.695816	+	0.718220i	$0.744957\pi$
$282$	−2.11243e9	+	3.65884e9i	−0.334031	+	0.578558i
$283$	3.09682e9	−	1.78795e9i	0.482804	−	0.278747i	−0.238780	−	0.971074i	$-0.576748\pi$
$283$	3.09682e9	−	1.78795e9i	0.482804	−	0.278747i	0.721584	+	0.692327i	$0.243414\pi$
$284$	−5.23281e8	−	9.06349e8i	−0.0804381	−	0.139323i
$285$	2.81131e8	+	1.62311e8i	0.0426118	+	0.0246019i
$286$			2.35916e8i			0.0352609i
$287$	−4.91497e7	+	1.31044e9i	−0.00724425	+	0.193147i
$288$	1.48977e9			0.216545
$289$	−2.23203e9	+	3.86599e9i	−0.319969	+	0.554203i
$290$	−1.17473e9	+	6.78230e8i	−0.166091	+	0.0958926i
$291$	−9.88384e8	−	1.71193e9i	−0.137833	−	0.238734i
$292$	−7.57663e7	−	4.37437e7i	−0.0104218	−	0.00601706i
$293$		−	6.92201e9i		−	0.939207i	−0.882877	−	0.469604i	$-0.844397\pi$
$293$		−	6.92201e9i		−	0.939207i	0.882877	−	0.469604i	$-0.155603\pi$
$294$	−3.73738e8	+	4.97531e9i	−0.0500240	+	0.665934i
$295$	6.10838e9			0.806562
$296$	4.03229e9	−	6.98413e9i	0.525272	−	0.909799i
$297$	2.03966e7	−	1.17760e7i	0.00262139	−	0.00151346i
$298$	6.81147e7	+	1.17978e8i	0.00863725	+	0.0149602i
$299$	1.98407e10	+	1.14551e10i	2.48241	+	1.43322i
$300$			1.22728e9i			0.151516i
$301$	1.04377e10	+	3.91481e8i	1.27157	+	0.0476919i
$302$	−8.52381e9			−1.02472
$303$	−1.66301e9	+	2.88043e9i	−0.197299	+	0.341732i
$304$	−1.63216e9	+	9.42325e8i	−0.191103	+	0.110333i
$305$	−1.89935e9	−	3.28977e9i	−0.219485	−	0.380160i
$306$	−1.75670e9	−	1.01423e9i	−0.200360	−	0.115678i
$307$			3.50393e9i			0.394459i	0.980357	+	0.197230i	$0.0631945\pi$
$307$			3.50393e9i			0.394459i	−0.980357	+	0.197230i	$0.936806\pi$
$308$	−2.54500e7	+	4.04955e7i	−0.00282804	+	0.00449991i
$309$	4.18949e9			0.459544
$310$	7.97035e8	−	1.38050e9i	0.0863039	−	0.149483i
$311$	−1.12671e10	+	6.50504e9i	−1.20440	+	0.695358i	−0.961529	−	0.274702i	$-0.911421\pi$
$311$	−1.12671e10	+	6.50504e9i	−1.20440	+	0.695358i	−0.242866	+	0.970060i	$0.578088\pi$
$312$	4.06026e9	+	7.03258e9i	0.428485	+	0.742158i
$313$	−1.01089e9	−	5.83638e8i	−0.105324	−	0.0608088i	0.446413	−	0.894827i	$-0.352701\pi$
$313$	−1.01089e9	−	5.83638e8i	−0.105324	−	0.0608088i	−0.551737	+	0.834018i	$0.686035\pi$
$314$		−	1.00900e10i		−	1.03795i
$315$	1.37138e9	−	7.24640e8i	0.139289	−	0.0736003i
$316$	−3.67679e9			−0.368740
$317$	−7.39679e9	+	1.28116e10i	−0.732498	+	1.26872i	0.223314	+	0.974747i	$0.428312\pi$
$317$	−7.39679e9	+	1.28116e10i	−0.732498	+	1.26872i	−0.955812	+	0.293977i	$0.905021\pi$
$318$	1.47195e9	−	8.49831e8i	0.143941	−	0.0831044i
$319$	−2.85700e7	−	4.94847e7i	−0.00275897	−	0.00477868i
$320$	−2.02703e9	−	1.17031e9i	−0.193313	−	0.111609i
$321$		−	9.35570e9i		−	0.881162i
$322$	8.59165e9	+	1.62597e10i	0.799196	+	1.51248i
$323$	1.17774e9			0.108203
$324$	−2.06876e8	+	3.58320e8i	−0.0187728	+	0.0325155i
$325$	−1.45438e10	+	8.39686e9i	−1.30360	+	0.752633i
$326$	−9.71036e9	−	1.68188e10i	−0.859736	−	1.48911i
$327$	9.90672e8	+	5.71965e8i	0.0866441	+	0.0500240i
$328$			1.71324e9i			0.148021i
$329$	−9.92350e9	−	6.23658e9i	−0.846995	−	0.532308i
$330$	5.88708e7			0.00496414
$331$	−4.62328e9	+	8.00775e9i	−0.385157	+	0.667112i	−0.991791	−	0.127870i	$-0.959186\pi$
$331$	−4.62328e9	+	8.00775e9i	−0.385157	+	0.667112i	0.606634	+	0.794981i	$0.292519\pi$
$332$	−5.67372e9	+	3.27573e9i	−0.466999	+	0.269622i
$333$	2.81132e9	+	4.86935e9i	0.228630	+	0.395999i
$334$	−1.23202e10	−	7.11304e9i	−0.989989	−	0.571570i
$335$			2.85618e9i			0.226781i
$336$	−3.37506e8	+	8.99862e9i	−0.0264804	+	0.706023i
$337$	1.78629e10			1.38494			0.692471	−	0.721446i	$-0.256522\pi$
$337$	1.78629e10			1.38494			0.692471	+	0.721446i	$0.256522\pi$
$338$	2.08076e10	−	3.60398e10i	1.59424	−	2.76131i
$339$	6.98321e9	−	4.03176e9i	0.528757	−	0.305278i
$340$	−6.40301e8	−	1.10903e9i	−0.0479146	−	0.0829906i
$341$	5.81529e7	+	3.35746e7i	0.00430084	+	0.00248309i
$342$		−	9.51149e8i		−	0.0695255i
$343$	−1.37538e10	−	1.55340e9i	−0.993682	−	0.112230i
$344$	1.36461e10			0.974483
$345$	2.85851e9	−	4.95108e9i	0.201773	−	0.349481i
$346$	1.80803e10	−	1.04387e10i	1.26154	−	0.728351i
$347$	−1.71139e9	−	2.96422e9i	−0.118041	−	0.204452i	0.800950	−	0.598731i	$-0.204328\pi$
$347$	−1.71139e9	−	2.96422e9i	−0.118041	−	0.204452i	−0.918991	+	0.394278i	$0.870995\pi$
$348$	8.69328e8	+	5.01907e8i	0.0592743	+	0.0342220i
$349$			1.32787e9i			0.0895061i	0.998998	+	0.0447531i	$0.0142501\pi$
$349$			1.32787e9i			0.0895061i	−0.998998	+	0.0447531i	$0.985750\pi$
$350$	−1.34709e10	−	5.05246e8i	−0.897688	−	0.0336691i
$351$	−5.66165e9			−0.373005
$352$	−7.84322e7	+	1.35849e8i	−0.00510886	+	0.00884880i
$353$	−1.55291e8	+	8.96574e7i	−0.0100011	+	0.00577414i	−0.504992	−	0.863124i	$-0.668505\pi$
$353$	−1.55291e8	+	8.96574e7i	−0.0100011	+	0.00577414i	0.494991	+	0.868898i	$0.335171\pi$
$354$	−8.94883e9	−	1.54998e10i	−0.569840	−	0.986993i
$355$	−3.09486e9	−	1.78682e9i	−0.194862	−	0.112504i
$356$			8.67607e9i			0.540161i
$357$	2.99433e9	−	4.76451e9i	0.184343	−	0.293322i
$358$	8.71730e9			0.530701
$359$	5.83839e9	−	1.01124e10i	0.351492	−	0.608802i	−0.635019	−	0.772496i	$-0.719008\pi$
$359$	5.83839e9	−	1.01124e10i	0.351492	−	0.608802i	0.986511	+	0.163695i	$0.0523411\pi$
$360$	1.75492e9	−	1.01320e9i	0.104483	−	0.0603235i
$361$	−8.21566e9	−	1.42299e10i	−0.483742	−	0.837865i
$362$	−6.48925e8	−	3.74657e8i	−0.0377885	−	0.0218172i
$363$		−	1.00221e10i		−	0.577207i
$364$	1.01656e10	−	5.37153e9i	0.579066	−	0.305980i
$365$	−2.98738e8			−0.0168314
$366$	−5.56513e9	+	9.63909e9i	−0.310135	+	0.537170i
$367$	−4.41847e8	+	2.55101e8i	−0.0243561	+	0.0140620i	−0.512129	−	0.858909i	$-0.671143\pi$
$367$	−4.41847e8	+	2.55101e8i	−0.0243561	+	0.0140620i	0.487773	+	0.872971i	$0.337810\pi$
$368$	1.65956e10	+	2.87444e10i	0.904900	+	1.56733i
$369$	−1.03445e9	−	5.97238e8i	−0.0557959	−	0.0322138i
$370$			1.40544e10i			0.749904i
$371$	2.20288e9	+	4.16895e9i	0.116277	+	0.220055i
$372$	−1.17965e9			−0.0616001
$373$	−4.38767e9	+	7.59967e9i	−0.226672	+	0.392608i	−0.956820	−	0.290681i	$-0.906118\pi$
$373$	−4.38767e9	+	7.59967e9i	−0.226672	+	0.392608i	0.730147	+	0.683290i	$0.239451\pi$
$374$	1.84971e8	−	1.06793e8i	0.00945401	−	0.00545828i
$375$	4.79336e9	+	8.30235e9i	0.242390	+	0.419832i
$376$	−1.32610e10	−	7.65623e9i	−0.663474	−	0.383057i
$377$			1.37359e10i			0.679971i
$378$	−3.84784e9	−	2.41823e9i	−0.188473	−	0.118449i
$379$	−2.31042e10			−1.11978			−0.559892	−	0.828566i	$-0.689157\pi$
$379$	−2.31042e10			−1.11978			−0.559892	+	0.828566i	$0.689157\pi$
$380$	3.00238e8	−	5.20028e8i	0.0143990	−	0.0249398i
$381$	−1.34620e10	+	7.77228e9i	−0.638865	+	0.368849i
$382$	1.92368e10	+	3.33192e10i	0.903400	+	1.56473i
$383$	−8.33836e8	−	4.81415e8i	−0.0387512	−	0.0223730i	0.480499	−	0.876995i	$-0.340455\pi$
$383$	−8.33836e8	−	4.81415e8i	−0.0387512	−	0.0223730i	−0.519250	+	0.854622i	$0.673789\pi$
$384$			1.50132e10i			0.690478i
$385$	−6.12117e6	+	1.63203e8i	−0.000278607	+	0.00742824i
$386$	−9.07564e7			−0.00408816
$387$	−4.75704e9	+	8.23943e9i	−0.212077	+	0.367328i
$388$	−3.16668e9	+	1.82829e9i	−0.139726	+	0.0806709i
$389$	2.07777e10	+	3.59881e10i	0.907401	+	1.57167i	0.817661	+	0.575700i	$0.195270\pi$
$389$	2.07777e10	+	3.59881e10i	0.907401	+	1.57167i	0.0897401	+	0.995965i	$0.471396\pi$
$390$	−1.22559e10	−	7.07596e9i	−0.529770	−	0.305863i
$391$		−	2.07416e10i		−	0.887430i
$392$	−1.80323e10	−	1.35456e9i	−0.763674	−	0.0573661i
$393$	2.38189e10			0.998509
$394$	2.26884e10	−	3.92975e10i	0.941498	−	1.63072i
$395$	−1.08729e10	+	6.27746e9i	−0.446638	+	0.257867i
$396$	−2.17829e7	−	3.77291e7i	−0.000885798	−	0.00153425i
$397$	−6.19632e9	−	3.57744e9i	−0.249443	−	0.144016i	0.370066	−	0.929005i	$-0.379335\pi$
$397$	−6.19632e9	−	3.57744e9i	−0.249443	−	0.144016i	−0.619509	+	0.784989i	$0.712668\pi$
$398$			4.30344e10i			1.71508i
$399$	2.63680e9	+	9.88970e7i	0.104037	+	0.00390204i
$400$	−2.43300e10			−0.950389
$401$	−1.05411e10	+	1.82578e10i	−0.407671	+	0.706107i	−0.994628	−	0.103511i	$-0.966992\pi$
$401$	−1.05411e10	+	1.82578e10i	−0.407671	+	0.706107i	0.586957	+	0.809618i	$0.300326\pi$
$402$	7.24748e9	−	4.18434e9i	0.277513	−	0.160222i
$403$	−8.07098e9	−	1.39793e10i	−0.305989	−	0.529989i
$404$	5.32813e9	+	3.07620e9i	0.200009	+	0.115475i
$405$			1.41281e9i			0.0525128i
$406$	−5.86693e9	+	9.33533e9i	−0.215927	+	0.343578i
$407$	−5.92033e8			−0.0215759
$408$	3.67594e9	−	6.36691e9i	0.132656	−	0.229767i
$409$	4.71459e10	−	2.72197e10i	1.68481	−	0.972725i	0.726424	−	0.687247i	$-0.241181\pi$
$409$	4.71459e10	−	2.72197e10i	1.68481	−	0.972725i	0.958385	−	0.285478i	$-0.0921522\pi$
$410$	−1.49286e9	−	2.58571e9i	−0.0528305	−	0.0915050i
$411$	−2.32525e10	−	1.34249e10i	−0.814897	−	0.470481i
$412$		−	7.74960e9i		−	0.268962i
$413$	4.38995e10	−	2.31966e10i	1.50890	−	0.797304i
$414$	−1.67510e10			−0.570215
$415$	−1.11854e10	+	1.93737e10i	−0.377103	+	0.653162i
$416$	3.26566e10	−	1.88543e10i	1.09043	−	0.629560i
$417$	−6.38092e9	−	1.10521e10i	−0.211028	−	0.365510i
$418$	8.67331e7	+	5.00754e7i	0.00284106	+	0.00164028i
$419$		−	3.30238e10i		−	1.07145i	−0.844394	−	0.535723i	$-0.820039\pi$
$419$		−	3.30238e10i		−	1.07145i	0.844394	−	0.535723i	$-0.179961\pi$
$420$	−1.34042e9	−	2.53674e9i	−0.0430767	−	0.0815227i
$421$	2.09592e10			0.667185			0.333592	−	0.942717i	$-0.391739\pi$
$421$	2.09592e10			0.667185			0.333592	+	0.942717i	$0.391739\pi$
$422$	−1.14701e10	+	1.98667e10i	−0.361673	+	0.626436i
$423$	9.24558e9	−	5.33794e9i	0.288784	−	0.166729i
$424$	3.08010e9	+	5.33489e9i	0.0953018	+	0.165068i
$425$	1.31671e10	+	7.60206e9i	0.403586	+	0.233010i
$426$			1.04708e10i			0.317938i
$427$	−2.61431e10	−	1.64300e10i	−0.786404	−	0.494228i
$428$	−1.73059e10			−0.515726
$429$	2.98070e8	−	5.16273e8i	0.00880014	−	0.0152423i
$430$	−2.05954e10	+	1.18907e10i	−0.602415	+	0.347805i
$431$	−8.89913e9	−	1.54138e10i	−0.257893	−	0.446683i	0.707785	−	0.706428i	$-0.249695\pi$
$431$	−8.89913e9	−	1.54138e10i	−0.257893	−	0.446683i	−0.965677	+	0.259745i	$0.916361\pi$
$432$	−7.10343e9	−	4.10117e9i	−0.203955	−	0.117753i
$433$		−	3.61300e10i		−	1.02782i	−0.857845	−	0.513909i	$-0.828197\pi$
$433$		−	3.61300e10i		−	1.02782i	0.857845	−	0.513909i	$-0.171803\pi$
$434$	4.85638e8	−	1.29481e10i	0.0136884	−	0.364962i
$435$	3.42766e9			0.0957284
$436$	1.05800e9	−	1.83252e9i	0.0292780	−	0.0507110i
$437$	8.42276e9	−	4.86288e9i	0.230956	−	0.133342i
$438$	4.37654e8	+	7.58039e8i	0.0118914	+	0.0205966i
$439$	5.92320e10	+	3.41976e10i	1.59477	+	0.920742i	0.992472	+	0.122471i	$0.0390820\pi$
$439$	5.92320e10	+	3.41976e10i	1.59477	+	0.920742i	0.602299	+	0.798270i	$0.294251\pi$
$440$			2.13369e8i			0.00569274i
$441$	7.10398e9	−	1.04156e10i	0.187822	−	0.275380i
$442$	−5.13437e10			−1.34524
$443$	−3.55113e9	+	6.15073e9i	−0.0922043	+	0.159703i	−0.908438	−	0.418019i	$-0.862725\pi$
$443$	−3.55113e9	+	6.15073e9i	−0.0922043	+	0.159703i	0.816234	+	0.577721i	$0.196058\pi$
$444$	9.00718e9	−	5.20030e9i	0.231770	−	0.133812i
$445$	1.48128e10	+	2.56566e10i	0.377744	+	0.654273i
$446$	−4.31675e10	−	2.49228e10i	−1.09098	−	0.629879i
$447$		−	3.44240e8i		−	0.00862246i
$448$	−1.90121e10	−	7.13075e8i	−0.471973	−	0.0177020i
$449$	−3.13206e10			−0.770627			−0.385313	−	0.922786i	$-0.625907\pi$
$449$	−3.13206e10			−0.770627			−0.385313	+	0.922786i	$0.625907\pi$
$450$	6.13945e9	−	1.06338e10i	0.149720	−	0.259322i
$451$	1.08921e8	−	6.28859e7i	0.00263274	−	0.00152001i
$452$	−7.45783e9	−	1.29173e10i	−0.178673	−	0.309471i
$453$	1.86533e10	+	1.07695e10i	0.442958	+	0.255742i
$454$		−	7.73753e9i		−	0.182129i
$455$	2.08905e10	−	3.32405e10i	0.487420	−	0.775571i
$456$	3.44731e9			0.0797299
$457$	−2.95777e10	+	5.12301e10i	−0.678110	+	1.17452i	0.297440	+	0.954741i	$0.403867\pi$
$457$	−2.95777e10	+	5.12301e10i	−0.678110	+	1.17452i	−0.975550	+	0.219780i	$0.929466\pi$
$458$	9.06834e9	−	5.23561e9i	0.206094	−	0.118989i
$459$	2.56287e9	+	4.43903e9i	0.0577400	+	0.100009i
$460$	−9.15836e9	−	5.28758e9i	−0.204544	−	0.118093i
$461$		−	3.95980e10i		−	0.876739i	−0.898795	−	0.438369i	$-0.855556\pi$
$461$		−	3.95980e10i		−	0.876739i	0.898795	−	0.438369i	$-0.144444\pi$
$462$	4.23091e8	−	2.23562e8i	0.00928680	−	0.00490716i
$463$	−7.73153e10			−1.68245			−0.841223	−	0.540688i	$-0.818164\pi$
$463$	−7.73153e10			−1.68245			−0.841223	+	0.540688i	$0.818164\pi$
$464$	−9.94994e9	+	1.72338e10i	−0.214659	+	0.371800i
$465$	−3.48842e9	+	2.01404e9i	−0.0746134	+	0.0430781i
$466$	2.40481e10	+	4.16525e10i	0.509961	+	0.883278i
$467$	9.55445e9	+	5.51626e9i	0.200881	+	0.115978i	0.597066	−	0.802192i	$-0.296333\pi$
$467$	9.55445e9	+	5.51626e9i	0.200881	+	0.115978i	−0.396186	+	0.918170i	$0.629666\pi$
$468$			1.04728e10i			0.218312i
$469$	1.08464e10	+	2.05267e10i	0.224178	+	0.424257i
$470$	2.66855e10			0.546871
$471$	−1.27483e10	+	2.20808e10i	−0.259042	+	0.448674i
$472$	5.61770e10	−	3.24338e10i	1.13186	−	0.653477i
$473$	−5.00890e8	−	8.67567e8i	−0.0100069	−	0.0173324i
$474$	3.18577e10	+	1.83931e10i	0.631105	+	0.364369i
$475$			7.12924e9i			0.140045i
$476$	−8.81325e9	−	5.53883e9i	−0.171676	−	0.107892i
$477$	−4.29490e9			−0.0829621
$478$	−2.00990e10	+	3.48124e10i	−0.385001	+	0.666842i
$479$	−2.59730e10	+	1.49955e10i	−0.493379	+	0.284853i	−0.725975	−	0.687721i	$-0.758611\pi$
$479$	−2.59730e10	+	1.49955e10i	−0.493379	+	0.284853i	0.232596	+	0.972573i	$0.425278\pi$
$480$	−4.70492e9	−	8.14916e9i	−0.0886313	−	0.153514i
$481$	1.23251e11	+	7.11593e10i	2.30256	+	1.32939i
$482$			5.32130e10i			0.985893i
$483$	1.74170e9	−	4.64375e10i	0.0320026	−	0.853257i
$484$	−1.85386e10			−0.337828
$485$	−6.24294e9	+	1.08131e10i	−0.112829	+	0.195426i
$486$	3.58498e9	−	2.06979e9i	0.0642601	−	0.0371006i
$487$	−1.12931e10	−	1.95603e10i	−0.200770	−	0.347743i	0.748007	−	0.663691i	$-0.231011\pi$
$487$	−1.12931e10	−	1.95603e10i	−0.200770	−	0.347743i	−0.948777	+	0.315948i	$0.897678\pi$
$488$	−3.49356e10	−	2.01701e10i	−0.616011	−	0.355654i
$489$			4.90745e10i			0.858263i
$490$	2.83957e10	−	1.36684e10i	0.492570	−	0.237101i
$491$	2.92203e10			0.502757			0.251379	−	0.967889i	$-0.419116\pi$
$491$	2.92203e10			0.502757			0.251379	+	0.967889i	$0.419116\pi$
$492$	−1.10475e9	+	1.91349e9i	−0.0188541	+	0.0326562i
$493$	1.07696e10	−	6.21785e9i	0.182311	−	0.105257i
$494$	−1.20376e10	−	2.08497e10i	−0.202131	−	0.350100i
$495$	−1.28831e8	−	7.43808e7i	−0.00214586	−	0.00123891i
$496$		−	2.33857e10i		−	0.386388i
$497$	−2.90275e10	−	1.08872e9i	−0.475756	−	0.0178439i
$498$	6.55470e10			1.06570
$499$	2.77930e10	−	4.81389e10i	0.448264	−	0.776416i	−0.550009	−	0.835158i	$-0.685376\pi$
$499$	2.77930e10	−	4.81389e10i	0.448264	−	0.776416i	0.998273	+	0.0587428i	$0.0187092\pi$
$500$	1.53574e10	−	8.86662e9i	0.245719	−	0.141866i
$501$	1.79741e10	+	3.11320e10i	0.285296	+	0.494147i
$502$	−1.82929e10	−	1.05614e10i	−0.288050	−	0.166306i
$503$		−	9.46993e9i		−	0.147936i	−0.997261	−	0.0739682i	$-0.976434\pi$
$503$		−	9.46993e9i		−	0.147936i	0.997261	−	0.0739682i	$-0.0235663\pi$
$504$	8.76456e9	−	1.39460e10i	0.135834	−	0.216136i
$505$	2.10082e10			0.323016
$506$	8.81892e8	−	1.52748e9i	0.0134528	−	0.0233010i
$507$	−9.10695e10	+	5.25790e10i	−1.37829	+	0.795757i
$508$	1.43769e10	+	2.49016e10i	0.215880	+	0.373914i
$509$	−8.02061e10	−	4.63070e10i	−1.19491	−	0.689884i	−0.235497	−	0.971875i	$-0.575672\pi$
$509$	−8.02061e10	−	4.63070e10i	−1.19491	−	0.689884i	−0.959417	+	0.281992i	$0.909005\pi$
$510$			1.28124e10i			0.189386i
$511$	−2.14696e9	+	1.13446e9i	−0.0314877	+	0.0166382i
$512$	−9.77081e9			−0.142184
$513$	−1.20174e9	+	2.08147e9i	−0.0173516	+	0.0300539i
$514$	−5.33745e10	+	3.08158e10i	−0.764684	+	0.441490i
$515$	−1.32311e10	−	2.29169e10i	−0.188090	−	0.325781i
$516$	1.52411e10	+	8.79944e9i	0.214989	+	0.124124i
$517$			1.12411e9i			0.0157343i
$518$	5.33717e10	+	1.01006e11i	0.741296	+	1.40290i
$519$	−5.27553e10			−0.727104
$520$	2.56459e10	−	4.44199e10i	0.350755	−	0.607526i
$521$	1.33291e10	−	7.69555e9i	0.180905	−	0.104445i	−0.406813	−	0.913511i	$-0.633360\pi$
$521$	1.33291e10	−	7.69555e9i	0.180905	−	0.104445i	0.587718	+	0.809066i	$0.300027\pi$
$522$	−5.02156e9	−	8.69759e9i	−0.0676326	−	0.117143i
$523$	−6.34041e10	−	3.66064e10i	−0.847443	−	0.489271i	0.0123445	−	0.999924i	$-0.496071\pi$
$523$	−6.34041e10	−	3.66064e10i	−0.847443	−	0.489271i	−0.859787	+	0.510653i	$0.829404\pi$
$524$		−	4.40596e10i		−	0.584407i
$525$	2.88411e10	+	1.81256e10i	0.379642	+	0.238592i
$526$	7.58712e10			0.991138
$527$	−7.30702e9	+	1.26561e10i	−0.0947322	+	0.164081i
$528$	7.47952e8	−	4.31830e8i	0.00962361	−	0.00555620i
$529$	−4.64861e10	−	8.05163e10i	−0.593609	−	1.02816i
$530$	−9.29729e9	−	5.36779e9i	−0.117829	−	0.0680287i
$531$			4.52259e10i			0.568865i
$532$	1.82937e8	−	4.87748e9i	0.00228378	−	0.0608904i
$533$	−3.02342e10			−0.374619
$534$	4.34019e10	−	7.51743e10i	0.533757	−	0.924494i
$535$	−5.11764e10	+	2.95467e10i	−0.624676	+	0.360657i
$536$	1.51656e10	+	2.62675e10i	0.183738	+	0.318244i
$537$	−1.90767e10	−	1.10139e10i	−0.229407	−	0.132448i
$538$		−	1.06861e11i		−	1.27553i
$539$	5.75773e8	+	1.19615e9i	0.00682176	+	0.0141720i
$540$	2.61338e9			0.0307346
$541$	3.39614e10	−	5.88228e10i	0.396457	−	0.686684i	−0.596829	−	0.802368i	$-0.703573\pi$
$541$	3.39614e10	−	5.88228e10i	0.396457	−	0.686684i	0.993286	+	0.115685i	$0.0369063\pi$
$542$	−1.54406e10	+	8.91465e9i	−0.178924	+	0.103302i
$543$	9.46726e8	+	1.63978e9i	0.0108899	+	0.0188619i
$544$	−2.95655e10	−	1.70696e10i	−0.337590	−	0.194908i
$545$		−	7.22541e9i		−	0.0818986i
$546$	−1.14952e11	−	4.31142e9i	−1.29343	−	0.0485121i
$547$	2.13960e10			0.238992			0.119496	−	0.992835i	$-0.461872\pi$
$547$	2.13960e10			0.238992			0.119496	+	0.992835i	$0.461872\pi$
$548$	−2.48329e10	+	4.30119e10i	−0.275363	+	0.476942i
$549$	2.43572e10	−	1.40626e10i	0.268125	−	0.154802i
$550$	6.46450e8	+	1.11968e9i	0.00706455	+	0.0122362i
$551$	5.04990e9	+	2.91556e9i	0.0547869	+	0.0316312i
$552$		−	6.07116e10i		−	0.653906i
$553$	−5.43022e10	+	8.64045e10i	−0.580654	+	0.923923i
$554$	1.75512e11			1.86324
$555$	1.77572e10	−	3.07563e10i	0.187155	−	0.324162i
$556$	−2.04438e10	+	1.18032e10i	−0.213926	+	0.123510i
$557$	−3.46654e10	−	6.00422e10i	−0.360143	−	0.623786i	0.627841	−	0.778342i	$-0.283939\pi$
$557$	−3.46654e10	−	6.00422e10i	−0.360143	−	0.623786i	−0.987984	+	0.154556i	$0.950605\pi$
$558$	1.02211e10	+	5.90118e9i	0.105430	+	0.0608698i
$559$			2.40817e11i			2.46627i
$560$	5.02891e10	−	2.65728e10i	0.511354	−	0.270200i
$561$	−5.39713e8			−0.00544893
$562$	8.02885e10	−	1.39064e11i	0.804838	−	1.39402i
$563$	1.30197e11	−	7.51693e10i	1.29589	−	0.748182i	0.316197	−	0.948693i	$-0.397594\pi$
$563$	1.30197e11	−	7.51693e10i	1.29589	−	0.748182i	0.979691	+	0.200512i	$0.0642605\pi$
$564$	−9.87397e9	−	1.71022e10i	−0.0975832	−	0.169019i
$565$	−4.41081e10	−	2.54658e10i	−0.432837	−	0.249899i
$566$			6.61789e10i			0.644842i
$567$	5.36517e9	+	1.01536e10i	0.0519100	+	0.0982397i
$568$	−3.79501e10			−0.364602
$569$	−5.42571e10	+	9.39761e10i	−0.517616	+	0.896537i	0.482175	+	0.876075i	$0.339847\pi$
$569$	−5.42571e10	+	9.39761e10i	−0.517616	+	0.896537i	−0.999791	+	0.0204620i	$0.993486\pi$
$570$	−5.20286e9	+	3.00387e9i	−0.0492882	+	0.0284566i
$571$	−4.21913e10	−	7.30776e10i	−0.396898	−	0.687448i	0.596443	−	0.802655i	$-0.296580\pi$
$571$	−4.21913e10	−	7.30776e10i	−0.396898	−	0.687448i	−0.993341	+	0.115208i	$0.963247\pi$
$572$	−9.54987e8	−	5.51362e8i	−0.00892099	−	0.00515054i
$573$		−	9.72197e10i		−	0.901853i
$574$	−2.05481e10	−	1.29138e10i	−0.189289	−	0.118961i
$575$	1.25555e11			1.14858
$576$	8.66485e9	−	1.50080e10i	0.0787175	−	0.136343i
$577$	5.87565e10	−	3.39231e10i	0.530093	−	0.306050i	−0.210961	−	0.977494i	$-0.567659\pi$
$577$	5.87565e10	−	3.39231e10i	0.530093	−	0.306050i	0.741054	+	0.671445i	$0.234326\pi$
$578$	−4.13079e10	−	7.15474e10i	−0.370102	−	0.641036i
$579$	1.98609e8	+	1.14667e8i	0.00176720	+	0.00102029i
$580$		−	6.34039e9i		−	0.0560279i
$581$	−6.81534e9	+	1.81711e11i	−0.0598113	+	1.59469i
$582$	3.65839e10			0.318858
$583$	2.26115e8	−	3.91642e8i	0.00195729	−	0.00339012i
$584$	−2.74741e9	+	1.58622e9i	−0.0236196	+	0.0136368i
$585$	1.78804e10	+	3.09697e10i	0.152670	+	0.264432i
$586$	1.10942e11	+	6.40524e10i	0.940818	+	0.543182i
$587$		−	6.54347e10i		−	0.551132i	−0.961282	−	0.275566i	$-0.911135\pi$
$587$		−	6.54347e10i		−	0.551132i	0.961282	−	0.275566i	$-0.0888653\pi$
$588$	−1.92666e10	−	1.31407e10i	−0.161174	−	0.109929i
$589$	−6.85255e9			−0.0569366
$590$	−5.65236e10	+	9.79017e10i	−0.466468	+	0.807946i
$591$	−9.93015e10	+	5.73317e10i	−0.813965	+	0.469943i
$592$	1.03092e11	+	1.78561e11i	0.839343	+	1.45378i
$593$	−4.76797e10	−	2.75279e10i	−0.385580	−	0.222615i	0.294663	−	0.955601i	$-0.404793\pi$
$593$	−4.76797e10	−	2.75279e10i	−0.385580	−	0.222615i	−0.680243	+	0.732986i	$0.738126\pi$
$594$			4.35874e8i			0.00350119i
$595$	−3.55188e10	−	1.33218e9i	−0.283394	−	0.0106291i
$596$	−6.36765e8			−0.00504655
$597$	5.43721e10	−	9.41753e10i	0.428035	−	0.741378i
$598$	−3.67191e11	+	2.11998e11i	−2.87135	+	1.65778i
$599$	8.82655e10	+	1.52880e11i	0.685620	+	1.18753i	0.973242	+	0.229785i	$0.0738021\pi$
$599$	8.82655e10	+	1.52880e11i	0.685620	+	1.18753i	−0.287622	+	0.957744i	$0.592865\pi$
$600$	3.85409e10	+	2.22516e10i	0.297384	+	0.171694i
$601$			1.50374e11i			1.15259i	0.817242	+	0.576295i	$0.195502\pi$
$601$			1.50374e11i			1.15259i	−0.817242	+	0.576295i	$0.804498\pi$
$602$	−1.02859e11	+	1.63667e11i	−0.783172	+	1.24616i
$603$	−2.11469e10			−0.159948
$604$	1.99211e10	−	3.45043e10i	0.149680	−	0.259254i
$605$	−5.48217e10	+	3.16513e10i	−0.409195	+	0.236249i
$606$	−3.07772e10	−	5.33078e10i	−0.228212	−	0.395276i
$607$	1.17275e10	+	6.77088e9i	0.0863875	+	0.0498758i	0.542571	−	0.840010i	$-0.317451\pi$
$607$	1.17275e10	+	6.77088e9i	0.0863875	+	0.0498758i	−0.456184	+	0.889885i	$0.650784\pi$
$608$		−	1.60080e10i		−	0.117145i
$609$	2.46338e10	−	1.30166e10i	0.179086	−	0.0946296i
$610$	7.03021e10			0.507749
$611$	1.35112e11	−	2.34021e11i	0.969460	−	1.67915i
$612$	8.21119e9	−	4.74073e9i	0.0585329	−	0.0337940i
$613$	−2.88838e10	−	5.00282e10i	−0.204556	−	0.354302i	0.745435	−	0.666578i	$-0.232242\pi$
$613$	−2.88838e10	−	5.00282e10i	−0.204556	−	0.354302i	−0.949991	+	0.312277i	$0.898908\pi$
$614$	−5.61591e10	−	3.24235e10i	−0.395136	−	0.228132i
$615$			7.54468e9i			0.0527400i
$616$	8.10270e8	+	1.53344e9i	0.00562739	+	0.0106498i
$617$	−1.99209e10			−0.137457			−0.0687287	−	0.997635i	$-0.521894\pi$
$617$	−1.99209e10			−0.137457			−0.0687287	+	0.997635i	$0.521894\pi$
$618$	−3.87672e10	+	6.71468e10i	−0.265773	+	0.460332i
$619$	−1.98047e10	+	1.14342e10i	−0.134898	+	0.0778833i	−0.565930	−	0.824453i	$-0.691483\pi$
$619$	−1.98047e10	+	1.14342e10i	−0.134898	+	0.0778833i	0.431032	+	0.902336i	$0.358149\pi$
$620$	3.72551e9	+	6.45278e9i	0.0252127	+	0.0436697i
$621$	3.66574e10	+	2.11641e10i	0.246487	+	0.142310i
$622$		−	2.40776e11i		−	1.60861i
$623$	2.03887e11	+	1.28136e11i	1.35344	+	0.850589i
$624$	−2.07615e11			−1.36937
$625$	−2.89762e10	+	5.01883e10i	−0.189899	+	0.328914i
$626$	1.87085e10	−	1.08013e10i	0.121826	−	0.0703364i
$627$	−1.26536e8	−	2.19167e8i	−0.000818738	−	0.00141810i
$628$	4.08444e10	+	2.35815e10i	0.262600	+	0.151612i
$629$		−	1.28847e11i		−	0.823139i
$630$	−1.07588e9	+	2.86851e10i	−0.00682968	+	0.182094i
$631$	1.55952e11			0.983727			0.491864	−	0.870672i	$-0.336316\pi$
$631$	1.55952e11			0.983727			0.491864	+	0.870672i	$0.336316\pi$
$632$	−6.66632e10	+	1.15464e11i	−0.417848	+	0.723733i
$633$	5.02016e10	−	2.89839e10i	0.312682	−	0.180527i
$634$	−1.36892e11	−	2.37103e11i	−0.847267	−	1.46751i
$635$	8.50300e10	+	4.90921e10i	0.522971	+	0.301937i
$636$			7.94459e9i			0.0485560i
$637$	2.39045e10	−	3.18224e11i	0.145185	−	1.93275i
$638$	1.05748e9			0.00638251
$639$	1.32294e10	−	2.29141e10i	0.0793483	−	0.137435i
$640$	8.21237e10	−	4.74141e10i	0.489495	−	0.282610i
$641$	−8.57573e10	−	1.48536e11i	−0.507971	−	0.879831i	−0.999957	−	0.00922864i	$-0.997062\pi$
$641$	−8.57573e10	−	1.48536e11i	−0.507971	−	0.879831i	0.491986	−	0.870603i	$-0.336271\pi$
$642$	1.49948e11	+	8.65725e10i	0.882674	+	0.509612i
$643$			3.70458e10i			0.216718i	0.994112	+	0.108359i	$0.0345596\pi$
$643$			3.70458e10i			0.216718i	−0.994112	+	0.108359i	$0.965440\pi$
$644$	−8.58987e10	−	3.22175e9i	−0.499394	−	0.0187305i
$645$	6.00938e10			0.347209
$646$	−1.08982e10	+	1.88762e10i	−0.0625783	+	0.108389i
$647$	1.05259e11	−	6.07715e10i	0.600680	−	0.346803i	−0.168629	−	0.985680i	$-0.553934\pi$
$647$	1.05259e11	−	6.07715e10i	0.600680	−	0.346803i	0.769309	+	0.638877i	$0.220601\pi$
$648$	7.50166e9	+	1.29933e10i	0.0425459	+	0.0736916i
$649$	−4.12404e9	−	2.38102e9i	−0.0232458	−	0.0134210i
$650$		−	3.10800e11i		−	1.74111i
$651$	−1.74222e10	+	2.77217e10i	−0.0970014	+	0.154346i
$652$	9.07766e10			0.502324
$653$	3.96756e9	−	6.87202e9i	0.0218208	−	0.0377948i	−0.854909	−	0.518778i	$-0.826387\pi$
$653$	3.96756e9	−	6.87202e9i	0.0218208	−	0.0377948i	0.876730	+	0.480984i	$0.159720\pi$
$654$	−1.83343e10	+	1.05853e10i	−0.100220	+	0.0578618i
$655$	−7.52238e10	−	1.30291e11i	−0.408686	−	0.707866i
$656$	−3.79336e10	−	2.19010e10i	−0.204837	−	0.118263i
$657$		−	2.21183e9i		−	0.0118711i
$658$	1.91783e11	−	1.01338e11i	1.02307	−	0.540593i
$659$	−3.29114e11			−1.74504			−0.872519	−	0.488581i	$-0.837515\pi$
$659$	−3.29114e11			−1.74504			−0.872519	+	0.488581i	$0.837515\pi$
$660$	−1.37587e8	+	2.38308e8i	−0.000725108	+	0.00125592i
$661$	5.49335e10	−	3.17159e10i	0.287761	−	0.166139i	−0.349171	−	0.937059i	$-0.613537\pi$
$661$	5.49335e10	−	3.17159e10i	0.287761	−	0.166139i	0.636932	+	0.770920i	$0.280203\pi$
$662$	−8.55625e10	−	1.48199e11i	−0.445504	−	0.771635i
$663$	1.12359e11	+	6.48707e10i	0.581507	+	0.335733i
$664$			2.37566e11i			1.22212i
$665$	−7.78645e9	−	1.47359e10i	−0.0398156	−	0.0753510i
$666$	−1.04058e11			−0.528904
$667$	5.13468e10	−	8.89353e10i	0.259424	−	0.449335i
$668$	5.75871e10	−	3.32479e10i	0.289214	−	0.166978i
$669$	6.29777e10	+	1.09081e11i	0.314400	+	0.544557i
$670$	−4.57773e10	−	2.64296e10i	−0.227170	−	0.131157i
$671$			2.96143e9i			0.0146087i
$672$	−6.47597e10	−	4.06992e10i	−0.317561	−	0.199576i
$673$	1.76882e10			0.0862229			0.0431114	−	0.999070i	$-0.486273\pi$
$673$	1.76882e10			0.0862229			0.0431114	+	0.999070i	$0.486273\pi$
$674$	−1.65293e11	+	2.86296e11i	−0.800968	+	1.38732i
$675$	−2.68708e10	+	1.55139e10i	−0.129439	+	0.0747317i
$676$	9.72591e10	+	1.68458e11i	0.465740	+	0.806685i
$677$	−1.55435e11	−	8.97403e10i	−0.739935	−	0.427202i	0.0821106	−	0.996623i	$-0.473834\pi$
$677$	−1.55435e11	−	8.97403e10i	−0.739935	−	0.427202i	−0.822046	+	0.569421i	$0.807167\pi$
$678$			1.49231e11i			0.706219i
$679$	−3.80386e9	+	1.01419e11i	−0.0178955	+	0.477133i
$680$	−4.64367e10			−0.217183
$681$	−9.77604e9	+	1.69326e10i	−0.0454542	+	0.0787291i
$682$	−1.07623e9	+	6.21361e8i	−0.00497470	+	0.00287215i
$683$	2.68986e10	+	4.65897e10i	0.123608	+	0.214095i	0.921188	−	0.389118i	$-0.127220\pi$
$683$	2.68986e10	+	4.65897e10i	0.123608	+	0.214095i	−0.797580	+	0.603213i	$0.793887\pi$
$684$	3.85024e9	+	2.22294e9i	0.0175899	+	0.0101555i
$685$			1.69591e11i			0.770265i
$686$	1.52168e11	−	2.06065e11i	0.687109	−	0.930480i
$687$	−2.64599e10			−0.118785
$688$	−1.74443e11	+	3.02143e11i	−0.778572	+	1.34853i
$689$	−9.41467e10	+	5.43556e10i	−0.417761	+	0.241195i
$690$	5.29021e10	+	9.16291e10i	0.233387	+	0.404238i
$691$	−1.44060e11	−	8.31732e10i	−0.631876	−	0.364814i	0.149602	−	0.988746i	$-0.452201\pi$
$691$	−1.44060e11	−	8.31732e10i	−0.631876	−	0.364814i	−0.781478	+	0.623932i	$0.785534\pi$
$692$			9.75853e10i			0.425559i
$693$	−1.20834e9	−	4.53206e7i	−0.00523910	−	0.000196500i
$694$	6.33451e10			0.273071
$695$	−4.03038e10	+	6.98083e10i	−0.172746	+	0.299204i
$696$	3.15232e10	−	1.82000e10i	0.134336	−	0.0775592i
$697$	1.36862e10	+	2.37052e10i	0.0579898	+	0.100441i
$698$	−2.12823e10	−	1.22873e10i	−0.0896597	−	0.0517650i
$699$		−	1.21535e11i		−	0.509088i
$700$	3.35283e10	−	5.33494e10i	0.139643	−	0.222196i
$701$	−2.19065e11			−0.907194			−0.453597	−	0.891207i	$-0.649859\pi$
$701$	−2.19065e11			−0.907194			−0.453597	+	0.891207i	$0.649859\pi$
$702$	5.23898e10	−	9.07418e10i	0.215724	−	0.373645i
$703$	5.23225e10	−	3.02084e10i	0.214224	−	0.123682i
$704$	9.12361e8	+	1.58026e9i	0.00371429	+	0.00643334i
$705$	−5.83979e10	−	3.37161e10i	−0.236396	−	0.136484i
$706$		−	3.31856e9i		−	0.0133577i
$707$	1.50981e11	−	7.97788e10i	0.604290	−	0.319308i
$708$	8.36576e10			0.332945
$709$	−1.05193e11	+	1.82199e11i	−0.416295	+	0.721044i	−0.995563	−	0.0940928i	$-0.970005\pi$
$709$	−1.05193e11	+	1.82199e11i	−0.416295	+	0.721044i	0.579268	+	0.815137i	$0.303338\pi$
$710$	5.72762e10	−	3.30684e10i	0.225393	−	0.130131i
$711$	−4.64777e10	−	8.05018e10i	−0.181872	−	0.315012i
$712$	2.72459e11	+	1.57304e11i	1.06018	+	0.612097i
$713$			1.20682e11i			0.466966i
$714$	4.86550e10	+	9.20796e10i	0.187212	+	0.354300i
$715$	−3.76541e9			−0.0144075
$716$	−2.03733e10	+	3.52876e10i	−0.0775191	+	0.134267i
$717$	8.79681e10	−	5.07884e10i	0.332850	−	0.192171i
$718$	1.08050e11	+	1.87149e11i	0.406564	+	0.704190i
$719$	2.56192e11	+	1.47913e11i	0.958629	+	0.553465i	0.895751	−	0.444556i	$-0.146639\pi$
$719$	2.56192e11	+	1.47913e11i	0.958629	+	0.553465i	0.0628784	+	0.998021i	$0.479972\pi$
$720$			5.18085e10i			0.192784i
$721$	−1.82115e11	−	1.14453e11i	−0.673916	−	0.423533i
$722$	3.04093e11			1.11907
$723$	6.72324e10	−	1.16450e11i	0.246051	−	0.426173i
$724$	3.03321e9	−	1.75123e9i	0.0110395	−	0.00637365i
$725$	3.76386e10	+	6.51919e10i	0.136233	+	0.235962i
$726$	1.60629e11	+	9.27389e10i	0.578197	+	0.333822i
$727$			9.87942e10i			0.353666i	0.984241	+	0.176833i	$0.0565853\pi$
$727$			9.87942e10i			0.353666i	−0.984241	+	0.176833i	$0.943415\pi$
$728$	1.56262e10	−	4.16626e11i	0.0556323	−	1.48327i
$729$	−1.04604e10			−0.0370370
$730$	2.76436e9	−	4.78801e9i	0.00973426	−	0.0168602i
$731$	1.88813e11	−	1.09011e11i	0.661246	−	0.381771i
$732$	−2.60126e10	−	4.50552e10i	−0.0906024	−	0.156928i
$733$	−1.58013e11	−	9.12291e10i	−0.547366	−	0.316022i	0.200693	−	0.979654i	$-0.435681\pi$
$733$	−1.58013e11	−	9.12291e10i	−0.547366	−	0.316022i	−0.748059	+	0.663632i	$0.769014\pi$
$734$		−	9.44225e9i		−	0.0325305i
$735$	−7.94098e10	−	5.96515e9i	−0.272098	−	0.0204396i
$736$	−2.81921e11			−0.960763
$737$	1.11333e9	−	1.92834e9i	0.00377358	−	0.00653602i
$738$	1.91444e10	−	1.10530e10i	0.0645381	−	0.0372611i
$739$	1.17506e11	+	2.03527e11i	0.393988	+	0.682407i	0.992971	−	0.118354i	$-0.0377619\pi$
$739$	1.17506e11	+	2.03527e11i	0.393988	+	0.682407i	−0.598984	+	0.800761i	$0.704429\pi$
$740$	−5.68921e10	−	3.28467e10i	−0.189725	−	0.109538i
$741$			6.08360e10i			0.201784i
$742$	−8.72018e10	−	3.27063e9i	−0.287680	−	0.0107898i
$743$	−2.11541e11			−0.694127			−0.347064	−	0.937842i	$-0.612821\pi$
$743$	−2.11541e11			−0.694127			−0.347064	+	0.937842i	$0.612821\pi$
$744$	−2.13880e10	+	3.70451e10i	−0.0698037	+	0.120904i
$745$	−1.88302e9	+	1.08716e9i	−0.00611266	+	0.00352914i
$746$	−8.12022e10	−	1.40646e11i	−0.262188	−	0.454122i
$747$	−1.43441e11	−	8.28159e10i	−0.460672	−	0.265969i
$748$			9.98345e8i			0.00318915i
$749$	−2.55590e11	+	4.06688e11i	−0.812112	+	1.29221i
$750$	−1.77420e11			−0.560736
$751$	3.84859e10	−	6.66596e10i	0.120988	−	0.209557i	−0.799170	−	0.601106i	$-0.794727\pi$
$751$	3.84859e10	−	6.66596e10i	0.120988	−	0.209557i	0.920158	+	0.391548i	$0.128060\pi$
$752$	3.39039e11	−	1.95744e11i	1.06018	−	0.612094i
$753$	2.66878e10	+	4.62246e10i	0.0830105	+	0.143778i
$754$	−2.20151e11	−	1.27104e11i	−0.681137	−	0.393255i
$755$		−	1.36047e11i		−	0.418697i
$756$	1.87818e10	−	9.92433e9i	0.0574976	−	0.0303818i
$757$	4.61229e11			1.40454			0.702269	−	0.711912i	$-0.252170\pi$
$757$	4.61229e11			1.40454			0.702269	+	0.711912i	$0.252170\pi$
$758$	2.13794e11	−	3.70301e11i	0.647616	−	1.12170i
$759$	−3.85982e9	+	2.22847e9i	−0.0116305	+	0.00671489i
$760$	−1.08871e10	−	1.88571e10i	−0.0326332	−	0.0565223i
$761$	−4.22076e11	−	2.43686e11i	−1.25850	−	0.726594i	−0.285715	−	0.958315i	$-0.592231\pi$
$761$	−4.22076e11	−	2.43686e11i	−1.25850	−	0.726594i	−0.972782	+	0.231721i	$0.925564\pi$
$762$		−	2.87682e11i		−	0.853281i
$763$	−2.74385e10	−	5.19274e10i	−0.0809585	−	0.153214i
$764$	−1.79834e11			−0.527836
$765$	1.61879e10	−	2.80383e10i	0.0472655	−	0.0818663i
$766$	1.54317e10	−	8.90950e9i	0.0448228	−	0.0258785i
$767$	5.72372e11	+	9.91377e11i	1.65385	+	2.86456i
$768$	−1.58468e11	−	9.14917e10i	−0.455510	−	0.262989i
$769$		−	6.16424e10i		−	0.176268i	−0.996109	−	0.0881341i	$-0.971910\pi$
$769$		−	6.16424e10i		−	0.176268i	0.996109	−	0.0881341i	$-0.0280904\pi$
$770$	−2.55909e9	−	1.60830e9i	−0.00727985	−	0.00457514i
$771$	1.55738e11			0.440734
$772$	2.12108e8	−	3.67381e8i	0.000597155	−	0.00103430i
$773$	−4.47268e11	+	2.58230e11i	−1.25271	+	0.723252i	−0.971647	−	0.236438i	$-0.924020\pi$
$773$	−4.47268e11	+	2.58230e11i	−1.25271	+	0.723252i	−0.281062	+	0.959690i	$0.590687\pi$
$774$	−8.80380e10	−	1.52486e11i	−0.245305	−	0.424881i
$775$	−7.66115e10	−	4.42317e10i	−0.212367	−	0.122610i
$776$			1.32593e11i			0.365657i
$777$	1.08195e10	−	2.88471e11i	0.0296841	−	0.791441i
$778$	−7.69062e11			−2.09915
$779$	−6.41749e9	+	1.11154e10i	−0.0174267	+	0.0301839i
$780$	5.72868e10	−	3.30746e10i	0.154766	−	0.0893544i
$781$	1.39299e9	+	2.41272e9i	0.00374406	+	0.00648490i
$782$	3.32434e11	+	1.91931e11i	0.888952	+	0.513237i
$783$			2.53781e10i			0.0675168i
$784$	2.60506e11	−	3.81946e11i	0.689530	−	1.01097i
$785$	1.61045e11			0.424100
$786$	−2.20407e11	+	3.81757e11i	−0.577478	+	1.00022i
$787$	3.35391e11	−	1.93638e11i	0.874284	−	0.504768i	0.00551481	−	0.999985i	$-0.498245\pi$
$787$	3.35391e11	−	1.93638e11i	0.874284	−	0.504768i	0.868770	+	0.495216i	$0.164911\pi$
$788$	1.06051e11	+	1.83685e11i	0.275048	+	0.476397i
$789$	−1.66035e11	−	9.58601e10i	−0.428441	−	0.247360i
$790$		−	2.32353e11i		−	0.596539i
$791$	−4.13702e11	−	1.55165e10i	−1.05677	−	0.0396357i
$792$	−1.57977e9			−0.00401506
$793$	3.55949e11	−	6.16521e11i	0.900108	−	1.55903i
$794$	1.14675e11	−	6.62074e10i	0.288526	−	0.166581i
$795$	1.35640e10	+	2.34935e10i	0.0339561	+	0.0588137i
$796$	−1.74203e11	−	1.00576e11i	−0.433913	−	0.250520i
$797$		−	2.31294e11i		−	0.573232i	−0.958045	−	0.286616i	$-0.907470\pi$
$797$		−	2.31294e11i		−	0.573232i	0.958045	−	0.286616i	$-0.0925304\pi$
$798$	−2.59846e10	+	4.13461e10i	−0.0640773	+	0.101958i
$799$	−2.44646e11			−0.600277
$800$	1.03328e11	−	1.78969e11i	0.252265	−	0.436936i
$801$	−1.89959e11	+	1.09673e11i	−0.461456	+	0.266422i
$802$	−1.95084e11	−	3.37895e11i	−0.471545	−	0.816740i
$803$	2.01692e8	+	1.16447e8i	0.000485094	+	0.000280069i
$804$			3.91170e10i			0.0936141i
$805$	−2.59517e11	+	1.37129e11i	−0.617992	+	0.326548i
$806$	2.98737e11			0.707863
$807$	−1.35014e11	+	2.33852e11i	−0.318336	+	0.551374i
$808$	1.93207e11	−	1.11548e11i	0.453291	−	0.261708i
$809$	1.51253e11	+	2.61978e11i	0.353110	+	0.611605i	0.986793	−	0.161988i	$-0.0517907\pi$
$809$	1.51253e11	+	2.61978e11i	0.353110	+	0.611605i	−0.633682	+	0.773593i	$0.718457\pi$
$810$	−2.26438e10	−	1.30734e10i	−0.0526028	−	0.0303703i
$811$		−	9.17544e10i		−	0.212101i	−0.994361	−	0.106051i	$-0.966179\pi$
$811$		−	9.17544e10i		−	0.212101i	0.994361	−	0.106051i	$-0.0338206\pi$
$812$	−2.40777e10	−	4.55670e10i	−0.0553847	−	0.104816i
$813$	4.50531e10			0.103125
$814$	5.47835e9	−	9.48878e9i	0.0124782	−	0.0216129i
$815$	2.68442e11	−	1.54985e11i	0.608442	−	0.351284i
$816$	9.39816e10	+	1.62781e11i	0.211974	+	0.367149i
$817$	8.85350e10	+	5.11157e10i	0.198713	+	0.114727i
$818$			1.00750e12i			2.25026i
$819$	2.46110e11	+	1.54671e11i	0.547007	+	0.343775i
$820$	1.39559e10			0.0308676
$821$	−1.04976e10	+	1.81823e10i	−0.0231056	+	0.0400200i	−0.877347	−	0.479857i	$-0.840689\pi$
$821$	−1.04976e10	+	1.81823e10i	−0.0231056	+	0.0400200i	0.854241	+	0.519877i	$0.174022\pi$
$822$	4.30332e11	−	2.48452e11i	0.942576	−	0.544197i
$823$	3.16378e11	+	5.47983e11i	0.689615	+	1.19445i	0.971962	+	0.235136i	$0.0755537\pi$
$823$	3.16378e11	+	5.47983e11i	0.689615	+	1.19445i	−0.282347	+	0.959312i	$0.591113\pi$
$824$	−2.43365e11	−	1.40507e11i	−0.527896	−	0.304781i
$825$		−	3.26705e9i		−	0.00705245i
$826$	−3.44401e10	+	9.18246e11i	−0.0739851	+	1.97260i
$827$	4.14570e11			0.886290			0.443145	−	0.896450i	$-0.353863\pi$
$827$	4.14570e11			0.886290			0.443145	+	0.896450i	$0.353863\pi$
$828$	3.91488e10	−	6.78077e10i	0.0832908	−	0.144264i
$829$	4.82641e11	−	2.78653e11i	1.02189	−	0.589991i	0.107242	−	0.994233i	$-0.465798\pi$
$829$	4.82641e11	−	2.78653e11i	1.02189	−	0.589991i	0.914652	+	0.404242i	$0.132465\pi$
$830$	−2.07008e11	−	3.58548e11i	−0.436188	−	0.755500i
$831$	−3.84087e11	−	2.21753e11i	−0.805425	−	0.465013i
$832$		−	4.38644e11i		−	0.915417i
$833$	−2.60325e11	+	1.25309e11i	−0.540674	+	0.260256i
$834$	2.36182e11			0.488183
$835$	1.13530e11	−	1.96639e11i	0.233541	−	0.404505i
$836$	−4.05409e8	+	2.34063e8i	−0.000829982	+	0.000479190i
$837$	−1.49118e10	−	2.58279e10i	−0.0303828	−	0.0526245i
$838$	5.29286e11	+	3.05584e11i	1.07328	+	0.619661i
$839$			6.78936e11i			1.37019i	0.728453	+	0.685095i	$0.240239\pi$
$839$			6.78936e11i			1.37019i	−0.728453	+	0.685095i	$0.759761\pi$
$840$	−1.03965e11	−	3.89937e9i	−0.208820	−	0.00783208i
$841$	−4.38676e11			−0.876920
$842$	−1.93945e11	+	3.35922e11i	−0.385860	+	0.668329i
$843$	−3.51403e11	+	2.02882e11i	−0.695816	+	0.401730i
$844$	−5.36136e10	−	9.28614e10i	−0.105659	−	0.183006i
$845$	5.75223e11	+	3.32105e11i	1.12826	+	0.651401i
$846$			1.97577e11i			0.385705i
$847$	−2.73795e11	+	4.35656e11i	−0.531976	+	0.846467i
$848$	−1.57496e11			−0.304569
$849$	8.36142e10	−	1.44824e11i	0.160935	−	0.278747i
$850$	−2.43683e11	+	1.40690e11i	−0.466820	+	0.269519i
$851$	−5.32009e11	−	9.21466e11i	−1.01438	−	1.75696i
$852$	−4.23858e10	−	2.44714e10i	−0.0804381	−	0.0464409i
$853$		−	4.10794e11i		−	0.775941i	−0.921672	−	0.387970i	$-0.873176\pi$
$853$		−	4.10794e11i		−	0.775941i	0.921672	−	0.387970i	$-0.126824\pi$
$854$	5.05246e11	−	2.66973e11i	0.949885	−	0.501921i
$855$	1.51811e10			0.0284078
$856$	−3.13770e11	+	5.43466e11i	−0.584409	+	1.01223i
$857$	−6.93001e11	+	4.00105e11i	−1.28473	+	0.741737i	−0.977709	−	0.209966i	$-0.932665\pi$
$857$	−6.93001e11	+	4.00105e11i	−1.28473	+	0.741737i	−0.307018	+	0.951704i	$0.599331\pi$
$858$	5.51636e9	+	9.55461e9i	0.0101790	+	0.0176305i
$859$	−3.26854e11	−	1.88709e11i	−0.600317	−	0.346593i	0.168849	−	0.985642i	$-0.445995\pi$
$859$	−3.26854e11	−	1.88709e11i	−0.600317	−	0.346593i	−0.769166	+	0.639049i	$0.779328\pi$
$860$		−	1.11160e11i		−	0.203214i
$861$	2.86509e10	+	5.42219e10i	0.0521346	+	0.0986647i
$862$	3.29391e11			0.596599
$863$	3.81724e11	−	6.61165e11i	0.688186	−	1.19197i	−0.284238	−	0.958754i	$-0.591740\pi$
$863$	3.81724e11	−	6.61165e11i	0.688186	−	1.19197i	0.972424	−	0.233220i	$-0.0749262\pi$
$864$	6.03357e10	−	3.48348e10i	0.108273	−	0.0625113i
$865$	1.66609e11	+	2.88576e11i	0.297601	+	0.515461i
$866$	5.79072e11	+	3.34327e11i	1.02958	+	0.594429i
$867$			2.08763e11i			0.369469i
$868$	5.12789e10	+	3.22270e10i	0.0903357	+	0.0567729i
$869$	9.78770e9			0.0171633
$870$	−3.17177e10	+	5.49366e10i	−0.0553636	+	0.0958926i
$871$	−4.63553e11	+	2.67632e11i	−0.805428	+	0.465014i
$872$	−3.83650e10	−	6.64501e10i	−0.0663543	−	0.114929i
$873$	−8.00591e10	−	4.62222e10i	−0.137833	−	0.0795780i
$874$			1.79994e11i			0.308469i
$875$	1.84475e10	−	4.91850e11i	0.0314707	−	0.839074i
$876$	−4.09138e9			−0.00694790
$877$	−4.35241e11	+	7.53859e11i	−0.735752	+	1.27436i	0.218641	+	0.975805i	$0.429838\pi$
$877$	−4.35241e11	+	7.53859e11i	−0.735752	+	1.27436i	−0.954393	+	0.298554i	$0.903496\pi$
$878$	−1.09620e12	+	6.32892e11i	−1.84464	+	1.06500i
$879$	−1.61855e11	−	2.80341e11i	−0.271126	−	0.469604i
$880$	−4.72430e9	−	2.72757e9i	−0.00787783	−	0.00454826i
$881$		−	8.20546e11i		−	1.36207i	−0.732251	−	0.681035i	$-0.761530\pi$
$881$		−	8.20546e11i		−	1.36207i	0.732251	−	0.681035i	$-0.238470\pi$
$882$	1.01200e11	+	2.10239e11i	0.167227	+	0.347408i
$883$	2.47321e11			0.406835			0.203417	−	0.979092i	$-0.434795\pi$
$883$	2.47321e11			0.406835			0.203417	+	0.979092i	$0.434795\pi$
$884$	1.19996e11	−	2.07839e11i	0.196498	−	0.340344i
$885$	2.47389e11	−	1.42830e11i	0.403281	−	0.232834i
$886$	−6.57203e10	−	1.13831e11i	−0.106651	−	0.184725i
$887$	−2.78910e11	−	1.61029e11i	−0.450577	−	0.260141i	0.257497	−	0.966279i	$-0.417102\pi$
$887$	−2.78910e11	−	1.61029e11i	−0.450577	−	0.260141i	−0.708074	+	0.706138i	$0.750436\pi$
$888$		−	3.77143e11i		−	0.606532i
$889$	7.97519e11	+	2.99121e10i	1.27683	+	0.0478894i
$890$	−5.48279e11			−0.873860
$891$	5.50709e8	−	9.53855e8i	0.000873798	−	0.00151346i
$892$	2.01774e11	−	1.16494e11i	0.318718	−	0.184012i
$893$	−5.73576e10	−	9.93463e10i	−0.0901956	−	0.156223i
$894$	5.51729e9	+	3.18541e9i	0.00863725	+	0.00498672i
$895$			1.39135e11i			0.216842i
$896$	4.10149e11	−	6.52620e11i	0.636370	−	1.01258i
$897$	1.07140e12			1.65494
$898$	2.89823e11	−	5.01988e11i	0.445685	−	0.771949i
$899$	−6.26618e10	+	3.61778e10i	−0.0959321	+	0.0553864i
$900$	2.86971e10	+	4.97049e10i	0.0437389	+	0.0757581i
$901$	8.52353e10	+	4.92106e10i	0.129336	+	0.0746723i
$902$			2.32764e9i			0.00351634i
$903$	4.31881e11	−	2.28207e11i	0.649550	−	0.343224i
$904$	−5.40867e11			−0.809872
$905$	5.97981e9	−	1.03573e10i	0.00891442	−	0.0154402i
$906$	−3.45214e11	+	1.99310e11i	−0.512361	+	0.295812i
$907$	−5.21088e11	−	9.02551e11i	−0.769985	−	1.33365i	−0.937571	−	0.347795i	$-0.886931\pi$
$907$	−5.21088e11	−	9.02551e11i	−0.769985	−	1.33365i	0.167586	−	0.985857i	$-0.446403\pi$
$908$	3.13214e10	+	1.80834e10i	0.0460785	+	0.0266034i
$909$			1.55543e11i			0.227822i
$910$	3.39451e11	+	6.42410e11i	0.495007	+	0.936800i
$911$	5.04016e11			0.731763			0.365882	−	0.930661i	$-0.380767\pi$
$911$	5.04016e11			0.731763			0.365882	+	0.930661i	$0.380767\pi$
$912$	−4.40682e10	+	7.63283e10i	−0.0637009	+	0.110333i
$913$	1.51036e10	−	8.72006e9i	0.0217369	−	0.0125498i
$914$	−5.47392e11	−	9.48110e11i	−0.784356	−	1.35855i
$915$	−1.53847e11	−	8.88238e10i	−0.219485	−	0.126720i
$916$			4.89447e10i			0.0695223i
$917$	−1.03540e12	−	6.50713e11i	−1.46430	−	0.920263i
$918$	−9.48617e10			−0.133573
$919$	−2.30719e11	+	3.99617e11i	−0.323460	+	0.560250i	−0.981200	−	0.192996i	$-0.938180\pi$
$919$	−2.30719e11	+	3.99617e11i	−0.323460	+	0.560250i	0.657739	+	0.753246i	$0.271513\pi$
$920$	−3.32097e11	+	1.91736e11i	−0.463569	+	0.267641i
$921$	8.19314e10	+	1.41909e11i	0.113871	+	0.197230i
$922$	6.34655e11	+	3.66419e11i	0.878242	+	0.507053i
$923$		−	6.69719e11i		−	0.922753i
$924$	−8.38327e7	+	2.23516e9i	−0.000115007	+	0.00306634i
$925$	7.79953e11			1.06537
$926$	7.15433e11	−	1.23917e12i	0.973027	−	1.68533i
$927$	1.69674e11	−	9.79616e10i	0.229772	−	0.132659i
$928$	−8.45135e10	−	1.46382e11i	−0.113955	−	0.197376i
$929$	6.44296e11	+	3.71984e11i	0.865013	+	0.499415i	0.865688	−	0.500584i	$-0.166882\pi$
$929$	6.44296e11	+	3.71984e11i	0.865013	+	0.499415i	−0.000674954		1.00000i	$0.500215\pi$
$930$		−	7.45473e10i		−	0.0996552i
$931$	−1.11919e11	−	7.63342e10i	−0.148972	−	0.101606i
$932$	−2.24812e11			−0.297958
$933$	−3.04211e11	+	5.26908e11i	−0.401465	+	0.695358i
$934$	−1.76823e11	+	1.02089e11i	−0.232355	+	0.134150i
$935$	1.70450e9	+	2.95227e9i	0.00223023	+	0.00386287i
$936$	3.28881e11	+	1.89880e11i	0.428485	+	0.247386i
$937$		−	1.36134e12i		−	1.76608i	−0.469300	−	0.883039i	$-0.655494\pi$
$937$		−	1.36134e12i		−	1.76608i	0.469300	−	0.883039i	$-0.344506\pi$
$938$	−4.29358e11	−	1.61037e10i	−0.554636	−	0.0208024i
$939$	−5.45881e10			−0.0702160
$940$	−6.23670e10	+	1.08023e11i	−0.0798810	+	0.138358i
$941$	9.56680e11	−	5.52339e11i	1.22014	−	0.704446i	0.255189	−	0.966891i	$-0.417862\pi$
$941$	9.56680e11	−	5.52339e11i	1.22014	−	0.704446i	0.964947	+	0.262446i	$0.0845291\pi$
$942$	−2.35932e11	−	4.08647e11i	−0.299629	−	0.518973i
$943$	1.95757e11	+	1.13020e11i	0.247554	+	0.142925i
$944$			1.65845e12i			2.08841i
$945$	3.85969e10	−	6.14144e10i	0.0483977	−	0.0770093i
$946$	1.85398e10			0.0231495
$947$	−1.94906e11	+	3.37588e11i	−0.242341	+	0.419746i	−0.961381	−	0.275222i	$-0.911248\pi$
$947$	−1.94906e11	+	3.37588e11i	−0.242341	+	0.419746i	0.719040	+	0.694969i	$0.244582\pi$
$948$	−1.48910e11	+	8.59732e10i	−0.184370	+	0.106446i
$949$	−2.79926e10	−	4.84846e10i	−0.0345126	−	0.0597776i
$950$	−1.14264e11	−	6.59701e10i	−0.140286	−	0.0809939i
$951$			6.91828e11i			0.845816i
$952$	−3.33730e11	+	1.76344e11i	−0.406301	+	0.214690i
$953$	2.03416e10			0.0246611			0.0123306	−	0.999924i	$-0.496075\pi$
$953$	2.03416e10			0.0246611			0.0123306	+	0.999924i	$0.496075\pi$
$954$	3.97427e10	−	6.88363e10i	0.0479804	−	0.0831044i
$955$	−5.31800e11	+	3.07035e11i	−0.639344	+	0.369125i
$956$	−9.39470e10	−	1.62721e11i	−0.112474	−	0.194810i
$957$	−2.31417e9	−	1.33609e9i	−0.00275897	−	0.00159289i
$958$		−	5.55042e11i		−	0.658967i
$959$	6.44022e11	+	1.21881e12i	0.761424	+	1.44099i
$960$	−1.09460e11			−0.128875
$961$	−3.83931e11	+	6.64987e11i	−0.450152	+	0.779686i
$962$	−2.28100e12	+	1.31694e12i	−2.66333	+	1.53768i
$963$	−2.18761e11	−	3.78906e11i	−0.254370	−	0.440581i
$964$	−2.15406e11	−	1.24365e11i	−0.249430	−	0.144009i
$965$		−	1.44854e9i		−	0.00167041i
$966$	7.28157e11	+	4.57622e11i	0.836213	+	0.525531i
$967$	5.30714e11			0.606952			0.303476	−	0.952839i	$-0.401853\pi$
$967$	5.30714e11			0.606952			0.303476	+	0.952839i	$0.401853\pi$
$968$	−3.36120e11	+	5.82176e11i	−0.382818	+	0.663060i
$969$	4.76986e10	−	2.75388e10i	0.0541016	−	0.0312356i
$970$	−1.15537e11	−	2.00117e11i	−0.130508	−	0.226046i
$971$	5.14783e11	+	2.97210e11i	0.579092	+	0.334339i	0.760772	−	0.649019i	$-0.224820\pi$
$971$	5.14783e11	+	2.97210e11i	0.579092	+	0.334339i	−0.181680	+	0.983358i	$0.558154\pi$
$972$			1.93493e10i			0.0216770i
$973$	−2.45573e10	+	6.54751e11i	−0.0273987	+	0.730507i
$974$	4.18001e11			0.464453
$975$	−3.92682e11	+	6.80146e11i	−0.434533	+	0.752633i
$976$	8.93187e11	−	5.15682e11i	0.984336	−	0.568307i
$977$	5.92498e11	+	1.02624e12i	0.650292	+	1.12634i	0.983052	+	0.183327i	$0.0586867\pi$
$977$	5.92498e11	+	1.02624e12i	0.650292	+	1.12634i	−0.332760	+	0.943011i	$0.607980\pi$
$978$	−7.86539e11	−	4.54109e11i	−0.859736	−	0.496369i
$979$		−	2.30959e10i		−	0.0251423i
$980$	−1.10342e10	+	1.46890e11i	−0.0119629	+	0.159253i
$981$	5.34963e10			0.0577627
$982$	−2.70388e11	+	4.68327e11i	−0.290765	+	0.503620i
$983$	1.20848e11	−	6.97714e10i	0.129427	−	0.0747246i	−0.433889	−	0.900966i	$-0.642859\pi$
$983$	1.20848e11	−	6.97714e10i	0.129427	−	0.0747246i	0.563315	+	0.826242i	$0.309526\pi$
$984$	4.00602e10	+	6.93863e10i	0.0427300	+	0.0740105i
$985$	6.27218e11	+	3.62125e11i	0.666306	+	0.384692i
$986$			2.30146e11i			0.243498i
$987$	−5.47729e11	−	2.05434e10i	−0.577162	−	0.0216473i
$988$	1.12533e11			0.118100
$989$	9.00213e11	−	1.55921e12i	0.940936	−	1.62975i
$990$	2.38427e9	−	1.37656e9i	0.00248207	−	0.00143302i
$991$	−3.42136e11	−	5.92597e11i	−0.354735	−	0.614420i	0.632337	−	0.774693i	$-0.282096\pi$
$991$	−3.42136e11	−	5.92597e11i	−0.354735	−	0.614420i	−0.987073	+	0.160274i	$0.948762\pi$
$992$	1.72023e11	+	9.93176e10i	0.177640	+	0.102560i
$993$			4.32418e11i			0.444741i
$994$	2.86054e11	−	4.55162e11i	0.293023	−	0.466252i
$995$	−6.86862e11			−0.700772
$996$	−1.53191e11	+	2.65334e11i	−0.155666	+	0.269622i
$997$	−1.04064e12	+	6.00816e11i	−1.05323	+	0.608080i	−0.923551	−	0.383476i	$-0.874727\pi$
$997$	−1.04064e12	+	6.00816e11i	−1.05323	+	0.608080i	−0.129675	+	0.991557i	$0.541394\pi$
$998$	5.14363e11	+	8.90902e11i	0.518498	+	0.898065i
$999$	2.27717e11	+	1.31472e11i	0.228630	+	0.132000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.9.f.b.19.2	yes	12
3.2	odd	2		63.9.m.d.19.5		12
7.2	even	3		147.9.d.b.97.10		12
7.3	odd	6	inner	21.9.f.b.10.2	✓	12
7.5	odd	6		147.9.d.b.97.9		12
21.17	even	6		63.9.m.d.10.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.9.f.b.10.2	✓	12	7.3	odd	6	inner
21.9.f.b.19.2	yes	12	1.1	even	1	trivial
63.9.m.d.10.5		12	21.17	even	6
63.9.m.d.19.5		12	3.2	odd	2
147.9.d.b.97.9		12	7.5	odd	6
147.9.d.b.97.10		12	7.2	even	3

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-9.25345 + 16.0274i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-43.2526 - 74.9157i) q^{4} +(-255.810 - 147.692i) q^{5} +865.482i q^{6} +(-2399.31 - 89.9896i) q^{7} -3136.82 q^{8} +(1093.50 - 1894.00i) q^{9} +O(q^{10})\)	\(q+(-9.25345 + 16.0274i) q^{2} +(40.5000 - 23.3827i) q^{3} +(-43.2526 - 74.9157i) q^{4} +(-255.810 - 147.692i) q^{5} +865.482i q^{6} +(-2399.31 - 89.9896i) q^{7} -3136.82 q^{8} +(1093.50 - 1894.00i) q^{9} +(4734.26 - 2733.32i) q^{10} +(115.139 + 199.427i) q^{11} +(-3503.46 - 2022.73i) q^{12} -55356.7i q^{13} +(23644.2 - 37622.1i) q^{14} -13813.8 q^{15} +(40099.1 - 69453.7i) q^{16} +(-43402.5 + 25058.4i) q^{17} +(20237.3 + 35052.0i) q^{18} +(-20351.5 - 11750.0i) q^{19} +25552.3i q^{20} +(-99276.4 + 52457.8i) q^{21} -4261.75 q^{22} +(-206932. + 358416. i) q^{23} +(-127041. + 73347.3i) q^{24} +(-151687. - 262729. i) q^{25} +(887226. + 512240. i) q^{26} -102276. i q^{27} +(97034.9 + 183639. i) q^{28} -248134. q^{29} +(127825. - 221399. i) q^{30} +(252532. - 145800. i) q^{31} +(340597. + 589931. i) q^{32} +(9326.30 + 5384.54i) q^{33} -927508. i q^{34} +(600478. + 377380. i) q^{35} -189187. q^{36} +(-1.28547e6 + 2.22650e6i) q^{37} +(376644. - 217455. i) q^{38} +(-1.29439e6 - 2.24194e6i) q^{39} +(802432. + 463284. i) q^{40} -546171. i q^{41} +(77884.4 - 2.07656e6i) q^{42} -4.35029e6 q^{43} +(9960.17 - 17251.5i) q^{44} +(-559457. + 323003. i) q^{45} +(-3.82967e6 - 6.63318e6i) q^{46} +(4.22752e6 + 2.44076e6i) q^{47} -3.75050e6i q^{48} +(5.74860e6 + 431827. i) q^{49} +5.61449e6 q^{50} +(-1.17187e6 + 2.02973e6i) q^{51} +(-4.14709e6 + 2.39432e6i) q^{52} +(-981917. - 1.70073e6i) q^{53} +(1.63922e6 + 946404. i) q^{54} -68020.8i q^{55} +(7.52622e6 + 282281. i) q^{56} -1.09898e6 q^{57} +(2.29609e6 - 3.97695e6i) q^{58} +(-1.79089e7 + 1.03397e7i) q^{59} +(597481. + 1.03487e6i) q^{60} +(1.11373e7 + 6.43009e6i) q^{61} +5.39659e6i q^{62} +(-2.79409e6 + 4.44589e6i) q^{63} +7.92396e6 q^{64} +(-8.17575e6 + 1.41608e7i) q^{65} +(-172601. + 99651.2i) q^{66} +(-4.83469e6 - 8.37393e6i) q^{67} +(3.75454e6 + 2.16769e6i) q^{68} +1.93545e7i q^{69} +(-1.16049e7 + 6.13207e6i) q^{70} +1.20982e7 q^{71} +(-3.43011e6 + 5.94113e6i) q^{72} +(875858. - 505677. i) q^{73} +(-2.37900e7 - 4.12056e7i) q^{74} +(-1.22866e7 - 7.09368e6i) q^{75} +2.03287e6i q^{76} +(-258309. - 488850. i) q^{77} +4.79102e7 q^{78} +(2.12518e7 - 3.68092e7i) q^{79} +(-2.05155e7 + 1.18446e7i) q^{80} +(-2.39148e6 - 4.14217e6i) q^{81} +(8.75372e6 + 5.05397e6i) q^{82} -7.57347e7i q^{83} +(8.22388e6 + 5.16843e6i) q^{84} +1.48037e7 q^{85} +(4.02552e7 - 6.97240e7i) q^{86} +(-1.00494e7 + 5.80204e6i) q^{87} +(-361172. - 625568. i) q^{88} +(-8.68583e7 - 5.01477e7i) q^{89} -1.19556e7i q^{90} +(-4.98153e6 + 1.32818e8i) q^{91} +3.58014e7 q^{92} +(6.81837e6 - 1.18098e7i) q^{93} +(-7.82382e7 + 4.51709e7i) q^{94} +(3.47075e6 + 6.01152e6i) q^{95} +(2.75883e7 + 1.59281e7i) q^{96} -4.22699e7i q^{97} +(-6.01155e7 + 8.81396e7i) q^{98} +503620. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9	\( 12 q + 3 q^{2} + 486 q^{3} - 1117 q^{4} + 1389 q^{5} - 1226 q^{7} + 3558 q^{8} + 13122 q^{9} - 19731 q^{10} + 18081 q^{11} - 90477 q^{12} - 175188 q^{14} + 75006 q^{15} - 298849 q^{16} + 63306 q^{17} - 6561 q^{18} + 476265 q^{19} - 154953 q^{21} + 419258 q^{22} - 66384 q^{23} + 144099 q^{24} + 792375 q^{25} + 1890762 q^{26} - 4229651 q^{28} + 671106 q^{29} - 532737 q^{30} + 717240 q^{31} + 895149 q^{32} + 1464561 q^{33} + 3454614 q^{35} - 4885758 q^{36} + 2289443 q^{37} - 6275988 q^{38} - 930933 q^{39} + 8773863 q^{40} - 4123629 q^{42} - 10119958 q^{43} + 14123901 q^{44} + 3037743 q^{45} - 19926544 q^{46} - 4198782 q^{47} + 8565642 q^{49} - 1162248 q^{50} + 1709262 q^{51} - 26384844 q^{52} - 209511 q^{53} - 531441 q^{54} + 70081743 q^{56} + 25718310 q^{57} + 1938935 q^{58} - 97052259 q^{59} - 51464727 q^{60} - 24195864 q^{61} - 9869931 q^{63} + 272849458 q^{64} + 30440562 q^{65} + 16979949 q^{66} - 57546057 q^{67} - 32476050 q^{68} - 108189027 q^{70} + 224566620 q^{71} + 3890673 q^{72} - 193344135 q^{73} - 71015400 q^{74} + 64182375 q^{75} + 92041617 q^{77} + 102101148 q^{78} - 29314488 q^{79} - 735358533 q^{80} - 28697814 q^{81} + 321118926 q^{82} - 120939804 q^{84} + 248647620 q^{85} + 127268268 q^{86} + 27179793 q^{87} - 487070897 q^{88} + 119863098 q^{89} + 100090965 q^{91} + 364039200 q^{92} + 19365480 q^{93} - 191086092 q^{94} - 95584488 q^{95} + 72507069 q^{96} + 24200217 q^{98} + 79086294 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 486 * q^3 - 1117 * q^4 + 1389 * q^5 - 1226 * q^7 + 3558 * q^8 + 13122 * q^9 - 19731 * q^10 + 18081 * q^11 - 90477 * q^12 - 175188 * q^14 + 75006 * q^15 - 298849 * q^16 + 63306 * q^17 - 6561 * q^18 + 476265 * q^19 - 154953 * q^21 + 419258 * q^22 - 66384 * q^23 + 144099 * q^24 + 792375 * q^25 + 1890762 * q^26 - 4229651 * q^28 + 671106 * q^29 - 532737 * q^30 + 717240 * q^31 + 895149 * q^32 + 1464561 * q^33 + 3454614 * q^35 - 4885758 * q^36 + 2289443 * q^37 - 6275988 * q^38 - 930933 * q^39 + 8773863 * q^40 - 4123629 * q^42 - 10119958 * q^43 + 14123901 * q^44 + 3037743 * q^45 - 19926544 * q^46 - 4198782 * q^47 + 8565642 * q^49 - 1162248 * q^50 + 1709262 * q^51 - 26384844 * q^52 - 209511 * q^53 - 531441 * q^54 + 70081743 * q^56 + 25718310 * q^57 + 1938935 * q^58 - 97052259 * q^59 - 51464727 * q^60 - 24195864 * q^61 - 9869931 * q^63 + 272849458 * q^64 + 30440562 * q^65 + 16979949 * q^66 - 57546057 * q^67 - 32476050 * q^68 - 108189027 * q^70 + 224566620 * q^71 + 3890673 * q^72 - 193344135 * q^73 - 71015400 * q^74 + 64182375 * q^75 + 92041617 * q^77 + 102101148 * q^78 - 29314488 * q^79 - 735358533 * q^80 - 28697814 * q^81 + 321118926 * q^82 - 120939804 * q^84 + 248647620 * q^85 + 127268268 * q^86 + 27179793 * q^87 - 487070897 * q^88 + 119863098 * q^89 + 100090965 * q^91 + 364039200 * q^92 + 19365480 * q^93 - 191086092 * q^94 - 95584488 * q^95 + 72507069 * q^96 + 24200217 * q^98 + 79086294 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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