LMFDB - Embedded newform 200.6.d.c.101.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(101,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("200.101");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.d (of order $2$, degree $1$, 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:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$20$
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} - 130 x^{17} + 144 x^{16} + 1560 x^{15} - 12320 x^{14} - 56128 x^{13} + \cdots + 11\!\cdots\!24 $ x^20 - x^19 - 130x^17 + 144x^16 + 1560x^15 - 12320x^14 - 56128x^13 + 672256x^12 - 4183040x^11 + 25763840x^10 - 133857280x^9 + 688390144x^8 - 1839202304x^7 - 12918456320x^6 + 52344913920x^5 + 154618822656x^4 - 4466765987840x^3 - 35184372088832x + 1125899906842624
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{49}\cdot 5^{4}\cdot 31 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.17
Root			$-5.25771 + 2.08722i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.c.101.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.25771 - 2.08722i) q^{2} -10.4354i q^{3} +(23.2871 - 21.9480i) q^{4} +(-21.7810 - 54.8666i) q^{6} +66.0164 q^{7} +(76.6266 - 164.001i) q^{8} +134.101 q^{9} +O(q^{10})$	\(q+(5.25771 - 2.08722i) q^{2} -10.4354i q^{3} +(23.2871 - 21.9480i) q^{4} +(-21.7810 - 54.8666i) q^{6} +66.0164 q^{7} +(76.6266 - 164.001i) q^{8} +134.101 q^{9} -141.942i q^{11} +(-229.037 - 243.011i) q^{12} -246.793i q^{13} +(347.095 - 137.790i) q^{14} +(60.5748 - 1022.21i) q^{16} +297.407 q^{17} +(705.067 - 279.898i) q^{18} +174.593i q^{19} -688.910i q^{21} +(-296.263 - 746.288i) q^{22} +1576.89 q^{23} +(-1711.43 - 799.633i) q^{24} +(-515.110 - 1297.57i) q^{26} -3935.22i q^{27} +(1537.33 - 1448.92i) q^{28} +922.162i q^{29} -6194.91 q^{31} +(-1815.08 - 5500.90i) q^{32} -1481.22 q^{33} +(1563.68 - 620.752i) q^{34} +(3122.83 - 2943.25i) q^{36} -13956.6i q^{37} +(364.413 + 917.960i) q^{38} -2575.40 q^{39} -3008.44 q^{41} +(-1437.90 - 3622.09i) q^{42} +16270.0i q^{43} +(-3115.33 - 3305.40i) q^{44} +(8290.83 - 3291.31i) q^{46} -1004.93 q^{47} +(-10667.2 - 632.125i) q^{48} -12448.8 q^{49} -3103.57i q^{51} +(-5416.60 - 5747.09i) q^{52} +22990.4i q^{53} +(-8213.66 - 20690.3i) q^{54} +(5058.61 - 10826.8i) q^{56} +1821.96 q^{57} +(1924.75 + 4848.46i) q^{58} -31893.8i q^{59} -21370.1i q^{61} +(-32571.1 + 12930.1i) q^{62} +8852.89 q^{63} +(-21024.7 - 25133.7i) q^{64} +(-7787.85 + 3091.63i) q^{66} +38648.6i q^{67} +(6925.73 - 6527.47i) q^{68} -16455.5i q^{69} -30998.5 q^{71} +(10275.7 - 21992.8i) q^{72} +79573.5 q^{73} +(-29130.4 - 73379.8i) q^{74} +(3831.96 + 4065.76i) q^{76} -9370.46i q^{77} +(-13540.7 + 5375.41i) q^{78} +23301.9 q^{79} -8479.17 q^{81} +(-15817.5 + 6279.25i) q^{82} +66705.7i q^{83} +(-15120.2 - 16042.7i) q^{84} +(33959.0 + 85543.0i) q^{86} +9623.18 q^{87} +(-23278.6 - 10876.5i) q^{88} +66188.9 q^{89} -16292.4i q^{91} +(36721.1 - 34609.5i) q^{92} +64646.7i q^{93} +(-5283.64 + 2097.51i) q^{94} +(-57404.4 + 18941.2i) q^{96} +12550.8 q^{97} +(-65452.4 + 25983.4i) q^{98} -19034.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) $ 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9	$ 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9} - 241 q^{12} - 424 q^{14} - 55 q^{16} - 3368 q^{18} + 1197 q^{22} - 7184 q^{23} + 9459 q^{24} + 9172 q^{26} - 13492 q^{28} + 7160 q^{31} + 7869 q^{32} - 2836 q^{33} - 9591 q^{34} + 14828 q^{36} + 21505 q^{38} + 22452 q^{39} - 5804 q^{41} - 14272 q^{42} - 11593 q^{44} - 37612 q^{46} + 44180 q^{47} + 66571 q^{48} + 62652 q^{49} + 6136 q^{52} + 88947 q^{54} - 36908 q^{56} + 43696 q^{57} - 84012 q^{58} + 87460 q^{62} - 1240 q^{63} + 115177 q^{64} + 131439 q^{66} - 143341 q^{68} - 7724 q^{71} - 25772 q^{72} - 105136 q^{73} + 2112 q^{74} + 55951 q^{76} - 10948 q^{78} - 7780 q^{79} + 96984 q^{81} + 117501 q^{82} - 97556 q^{84} - 65986 q^{86} - 106188 q^{87} - 122597 q^{88} - 3160 q^{89} + 88908 q^{92} - 58540 q^{94} + 57791 q^{96} - 73688 q^{97} + 164655 q^{98}+O(q^{100}) $ 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9 - 241 * q^12 - 424 * q^14 - 55 * q^16 - 3368 * q^18 + 1197 * q^22 - 7184 * q^23 + 9459 * q^24 + 9172 * q^26 - 13492 * q^28 + 7160 * q^31 + 7869 * q^32 - 2836 * q^33 - 9591 * q^34 + 14828 * q^36 + 21505 * q^38 + 22452 * q^39 - 5804 * q^41 - 14272 * q^42 - 11593 * q^44 - 37612 * q^46 + 44180 * q^47 + 66571 * q^48 + 62652 * q^49 + 6136 * q^52 + 88947 * q^54 - 36908 * q^56 + 43696 * q^57 - 84012 * q^58 + 87460 * q^62 - 1240 * q^63 + 115177 * q^64 + 131439 * q^66 - 143341 * q^68 - 7724 * q^71 - 25772 * q^72 - 105136 * q^73 + 2112 * q^74 + 55951 * q^76 - 10948 * q^78 - 7780 * q^79 + 96984 * q^81 + 117501 * q^82 - 97556 * q^84 - 65986 * q^86 - 106188 * q^87 - 122597 * q^88 - 3160 * q^89 + 88908 * q^92 - 58540 * q^94 + 57791 * q^96 - 73688 * q^97 + 164655 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	5.25771	−	2.08722i	0.929441	−	0.368971i
$2$	5.25771	−	2.08722i	0.929441	−	0.368971i
$3$		−	10.4354i		−	0.669434i	−0.942319	−	0.334717i	$-0.891359\pi$
$3$		−	10.4354i		−	0.669434i	0.942319	−	0.334717i	$-0.108641\pi$
$4$	23.2871	−	21.9480i	0.727721	−	0.685874i
$5$		0			0
$5$		0			0
$6$	−21.7810	−	54.8666i	−0.247002	−	0.622200i
$7$	66.0164			0.509221			0.254611	−	0.967044i	$-0.418053\pi$
$7$	66.0164			0.509221			0.254611	+	0.967044i	$0.418053\pi$
$8$	76.6266	−	164.001i	0.423306	−	0.905987i
$9$	134.101			0.551858
$10$		0			0
$11$		−	141.942i		−	0.353694i	−0.984238	−	0.176847i	$-0.943410\pi$
$11$		−	141.942i		−	0.353694i	0.984238	−	0.176847i	$-0.0565898\pi$
$12$	−229.037	−	243.011i	−0.459147	−	0.487161i
$13$		−	246.793i		−	0.405018i	−0.979280	−	0.202509i	$-0.935090\pi$
$13$		−	246.793i		−	0.405018i	0.979280	−	0.202509i	$-0.0649096\pi$
$14$	347.095	−	137.790i	0.473291	−	0.187888i
$15$		0			0
$16$	60.5748	−	1022.21i	0.0591551	−	0.998249i
$17$	297.407			0.249591			0.124795	−	0.992182i	$-0.460173\pi$
$17$	297.407			0.249591			0.124795	+	0.992182i	$0.460173\pi$
$18$	705.067	−	279.898i	0.512919	−	0.203619i
$19$			174.593i			0.110954i	0.998460	+	0.0554770i	$0.0176680\pi$
$19$			174.593i			0.110954i	−0.998460	+	0.0554770i	$0.982332\pi$
$20$		0			0
$21$		−	688.910i		−	0.340890i
$22$	−296.263	−	746.288i	−0.130503	−	0.328738i
$23$	1576.89			0.621558			0.310779	−	0.950482i	$-0.399410\pi$
$23$	1576.89			0.621558			0.310779	+	0.950482i	$0.399410\pi$
$24$	−1711.43	−	799.633i	−0.606499	−	0.283376i
$25$		0			0
$26$	−515.110	−	1297.57i	−0.149440	−	0.376441i
$27$		−	3935.22i		−	1.03887i
$28$	1537.33	−	1448.92i	0.370571	−	0.349261i
$29$			922.162i			0.203616i	0.994804	+	0.101808i	$0.0324628\pi$
$29$			922.162i			0.203616i	−0.994804	+	0.101808i	$0.967537\pi$
$30$		0			0
$31$	−6194.91			−1.15779			−0.578897	−	0.815401i	$-0.696516\pi$
$31$	−6194.91			−1.15779			−0.578897	+	0.815401i	$0.696516\pi$
$32$	−1815.08	−	5500.90i	−0.313344	−	0.949640i
$33$	−1481.22			−0.236775
$34$	1563.68	−	620.752i	0.231980	−	0.0920918i
$35$		0			0
$36$	3122.83	−	2943.25i	0.401598	−	0.378505i
$37$		−	13956.6i		−	1.67601i	−0.545666	−	0.838003i	$-0.683723\pi$
$37$		−	13956.6i		−	1.67601i	0.545666	−	0.838003i	$-0.316277\pi$
$38$	364.413	+	917.960i	0.0409388	+	0.103125i
$39$	−2575.40			−0.271133
$40$		0			0
$41$	−3008.44			−0.279500			−0.139750	−	0.990187i	$-0.544630\pi$
$41$	−3008.44			−0.279500			−0.139750	+	0.990187i	$0.544630\pi$
$42$	−1437.90	−	3622.09i	−0.125779	−	0.316837i
$43$			16270.0i			1.34189i	0.741508	+	0.670944i	$0.234111\pi$
$43$			16270.0i			1.34189i	−0.741508	+	0.670944i	$0.765889\pi$
$44$	−3115.33	−	3305.40i	−0.242589	−	0.257391i
$45$		0			0
$46$	8290.83	−	3291.31i	0.577701	−	0.229337i
$47$	−1004.93			−0.0663578			−0.0331789	−	0.999449i	$-0.510563\pi$
$47$	−1004.93			−0.0663578			−0.0331789	+	0.999449i	$0.510563\pi$
$48$	−10667.2	−	632.125i	−0.668262	−	0.0396004i
$49$	−12448.8			−0.740694
$50$		0			0
$51$		−	3103.57i		−	0.167085i
$52$	−5416.60	−	5747.09i	−0.277791	−	0.294740i
$53$			22990.4i			1.12424i	0.827057	+	0.562118i	$0.190013\pi$
$53$			22990.4i			1.12424i	−0.827057	+	0.562118i	$0.809987\pi$
$54$	−8213.66	−	20690.3i	−0.383312	−	0.965565i
$55$		0			0
$56$	5058.61	−	10826.8i	0.215556	−	0.461348i
$57$	1821.96			0.0742764
$58$	1924.75	+	4848.46i	0.0751285	+	0.189249i
$59$		−	31893.8i		−	1.19282i	−0.802678	−	0.596412i	$-0.796592\pi$
$59$		−	31893.8i		−	1.19282i	0.802678	−	0.596412i	$-0.203408\pi$
$60$		0			0
$61$		−	21370.1i		−	0.735328i	−0.929959	−	0.367664i	$-0.880158\pi$
$61$		−	21370.1i		−	0.735328i	0.929959	−	0.367664i	$-0.119842\pi$
$62$	−32571.1	+	12930.1i	−1.07610	+	0.427192i
$63$	8852.89			0.281018
$64$	−21024.7	−	25133.7i	−0.641624	−	0.767019i
$65$		0			0
$66$	−7787.85	+	3091.63i	−0.220068	+	0.0873631i
$67$			38648.6i			1.05183i	0.850536	+	0.525916i	$0.176277\pi$
$67$			38648.6i			1.05183i	−0.850536	+	0.525916i	$0.823723\pi$
$68$	6925.73	−	6527.47i	0.181632	−	0.171188i
$69$		−	16455.5i		−	0.416092i
$70$		0			0
$71$	−30998.5			−0.729784			−0.364892	−	0.931050i	$-0.618894\pi$
$71$	−30998.5			−0.729784			−0.364892	+	0.931050i	$0.618894\pi$
$72$	10275.7	−	21992.8i	0.233605	−	0.499976i
$73$	79573.5			1.74768			0.873838	−	0.486217i	$-0.161623\pi$
$73$	79573.5			1.74768			0.873838	+	0.486217i	$0.161623\pi$
$74$	−29130.4	−	73379.8i	−0.618398	−	1.55775i
$75$		0			0
$76$	3831.96	+	4065.76i	0.0761004	+	0.0807436i
$77$		−	9370.46i		−	0.180109i
$78$	−13540.7	+	5375.41i	−0.252002	+	0.100040i
$79$	23301.9			0.420072			0.210036	−	0.977694i	$-0.432642\pi$
$79$	23301.9			0.420072			0.210036	+	0.977694i	$0.432642\pi$
$80$		0			0
$81$	−8479.17			−0.143596
$82$	−15817.5	+	6279.25i	−0.259778	+	0.103127i
$83$			66705.7i			1.06284i	0.847109	+	0.531420i	$0.178341\pi$
$83$			66705.7i			1.06284i	−0.847109	+	0.531420i	$0.821659\pi$
$84$	−15120.2	−	16042.7i	−0.233808	−	0.248073i
$85$		0			0
$86$	33959.0	+	85543.0i	0.495118	+	1.24721i
$87$	9623.18			0.136308
$88$	−23278.6	−	10876.5i	−0.320442	−	0.149721i
$89$	66188.9			0.885748			0.442874	−	0.896584i	$-0.353959\pi$
$89$	66188.9			0.885748			0.442874	+	0.896584i	$0.353959\pi$
$90$		0			0
$91$		−	16292.4i		−	0.206244i
$92$	36721.1	−	34609.5i	0.452320	−	0.426310i
$93$			64646.7i			0.775066i
$94$	−5283.64	+	2097.51i	−0.0616756	+	0.0244841i
$95$		0			0
$96$	−57404.4	+	18941.2i	−0.635721	+	0.209763i
$97$	12550.8			0.135439			0.0677194	−	0.997704i	$-0.478428\pi$
$97$	12550.8			0.135439			0.0677194	+	0.997704i	$0.478428\pi$
$98$	−65452.4	+	25983.4i	−0.688431	+	0.273295i
$99$		−	19034.6i		−	0.195189i
$100$		0			0
$101$		−	94627.3i		−	0.923024i	−0.887134	−	0.461512i	$-0.847307\pi$
$101$		−	94627.3i		−	0.923024i	0.887134	−	0.461512i	$-0.152693\pi$
$102$	−6477.83	−	16317.7i	−0.0616494	−	0.155295i
$103$	74704.4			0.693830			0.346915	−	0.937897i	$-0.387229\pi$
$103$	74704.4			0.693830			0.346915	+	0.937897i	$0.387229\pi$
$104$	−40474.3	−	18910.9i	−0.366941	−	0.171447i
$105$		0			0
$106$	47986.0	+	120877.i	0.414810	+	1.04491i
$107$			95390.0i			0.805459i	0.915319	+	0.402729i	$0.131938\pi$
$107$			95390.0i			0.805459i	−0.915319	+	0.402729i	$0.868062\pi$
$108$	−86370.1	−	91639.8i	−0.712531	−	0.756005i
$109$			166091.i			1.33900i	0.742814	+	0.669498i	$0.233491\pi$
$109$			166091.i			1.33900i	−0.742814	+	0.669498i	$0.766509\pi$
$110$		0			0
$111$	−145643.			−1.12198
$112$	3998.93	−	67482.4i	0.0301230	−	0.508329i
$113$	174815.			1.28790			0.643951	−	0.765067i	$-0.277294\pi$
$113$	174815.			1.28790			0.643951	+	0.765067i	$0.277294\pi$
$114$	9579.33	−	3802.82i	0.0690356	−	0.0274059i
$115$		0			0
$116$	20239.6	+	21474.5i	0.139655	+	0.148176i
$117$		−	33095.3i		−	0.223512i
$118$	−66569.3	−	167688.i	−0.440118	−	1.10866i
$119$	19633.7			0.127097
$120$		0			0
$121$	140904.			0.874901
$122$	−44603.9	−	112358.i	−0.271315	−	0.683444i
$123$			31394.4i			0.187107i
$124$	−144261.	+	135966.i	−0.842550	+	0.794100i
$125$		0			0
$126$	46545.9	−	18477.9i	0.261189	−	0.103687i
$127$	94893.2			0.522067			0.261033	−	0.965330i	$-0.415937\pi$
$127$	94893.2			0.522067			0.261033	+	0.965330i	$0.415937\pi$
$128$	−163001.	−	88262.5i	−0.879360	−	0.476158i
$129$	169785.			0.898307
$130$		0			0
$131$		−	263177.i		−	1.33989i	−0.742409	−	0.669947i	$-0.766317\pi$
$131$		−	263177.i		−	1.33989i	0.742409	−	0.669947i	$-0.233683\pi$
$132$	−34493.4	+	32509.8i	−0.172306	+	0.162398i
$133$			11526.0i			0.0565001i
$134$	80667.9	+	203203.i	0.388096	+	0.977616i
$135$		0			0
$136$	22789.3	−	48775.1i	0.105653	−	0.226126i
$137$	−12040.5			−0.0548080			−0.0274040	−	0.999624i	$-0.508724\pi$
$137$	−12040.5			−0.0548080			−0.0274040	+	0.999624i	$0.508724\pi$
$138$	−34346.3	−	86518.5i	−0.153526	−	0.386733i
$139$			357698.i			1.57029i	0.619312	+	0.785145i	$0.287412\pi$
$139$			357698.i			1.57029i	−0.619312	+	0.785145i	$0.712588\pi$
$140$		0			0
$141$			10486.9i			0.0444222i
$142$	−162981.	+	64700.5i	−0.678291	+	0.269269i
$143$	−35030.2			−0.143253
$144$	8123.16	−	137079.i	0.0326452	−	0.550891i
$145$		0			0
$146$	418374.	−	166087.i	1.62436	−	0.644842i
$147$			129909.i			0.495846i
$148$	−306319.	−	325008.i	−1.14953	−	1.21966i
$149$			361479.i			1.33388i	0.745111	+	0.666940i	$0.232396\pi$
$149$			361479.i			1.33388i	−0.745111	+	0.666940i	$0.767604\pi$
$150$		0			0
$151$	−337938.			−1.20613			−0.603067	−	0.797691i	$-0.706055\pi$
$151$	−337938.			−1.20613			−0.603067	+	0.797691i	$0.706055\pi$
$152$	28633.5	+	13378.5i	0.100523	+	0.0469675i
$153$	39882.7			0.137739
$154$	−19558.2	−	49267.2i	−0.0664548	−	0.167400i
$155$		0			0
$156$	−59973.4	+	56524.7i	−0.197309	+	0.185963i
$157$			155005.i			0.501876i	0.968003	+	0.250938i	$0.0807391\pi$
$157$			155005.i			0.501876i	−0.968003	+	0.250938i	$0.919261\pi$
$158$	122515.	−	48636.1i	0.390432	−	0.154994i
$159$	239915.			0.752602
$160$		0			0
$161$	104100.			0.316510
$162$	−44581.0	+	17697.9i	−0.133464	+	0.0529826i
$163$		−	126397.i		−	0.372621i	−0.982491	−	0.186311i	$-0.940347\pi$
$163$		−	126397.i		−	0.372621i	0.982491	−	0.186311i	$-0.0596531\pi$
$164$	−70057.7	+	66029.0i	−0.203398	+	0.191701i
$165$		0			0
$166$	139229.	+	350719.i	0.392157	+	0.987846i
$167$	709796.			1.96944			0.984719	−	0.174152i	$-0.0557183\pi$
$167$	709796.			1.96944			0.984719	+	0.174152i	$0.0557183\pi$
$168$	−112982.	−	52788.8i	−0.308842	−	0.144301i
$169$	310386.			0.835960
$170$		0			0
$171$			23413.2i			0.0612308i
$172$	357093.	+	378881.i	0.920366	+	0.976520i
$173$			395365.i			1.00435i	0.864767	+	0.502173i	$0.167466\pi$
$173$			395365.i			1.00435i	−0.864767	+	0.502173i	$0.832534\pi$
$174$	50595.9	−	20085.6i	0.126690	−	0.0502936i
$175$		0			0
$176$	−145094.	−	8598.08i	−0.353075	−	0.0209228i
$177$	−332826.			−0.798517
$178$	348002.	−	138150.i	0.823250	−	0.326815i
$179$			265918.i			0.620318i	0.950685	+	0.310159i	$0.100382\pi$
$179$			265918.i			0.620318i	−0.950685	+	0.310159i	$0.899618\pi$
$180$		0			0
$181$			836091.i			1.89696i	0.316843	+	0.948478i	$0.397377\pi$
$181$			836091.i			1.89696i	−0.316843	+	0.948478i	$0.602623\pi$
$182$	−34005.7	−	85660.6i	−0.0760980	−	0.191692i
$183$	−223006.			−0.492254
$184$	120832.	−	258612.i	0.263109	−	0.563123i
$185$		0			0
$186$	134932.	+	339894.i	0.285977	+	0.720378i
$187$		−	42214.4i		−	0.0882788i
$188$	−23401.9	+	22056.2i	−0.0482899	+	0.0455130i
$189$		−	259789.i		−	0.529013i
$190$		0			0
$191$	−770184.			−1.52761			−0.763803	−	0.645450i	$-0.776670\pi$
$191$	−770184.			−1.52761			−0.763803	+	0.645450i	$0.776670\pi$
$192$	−262281.	+	219403.i	−0.513469	+	0.429525i
$193$	694883.			1.34282			0.671411	−	0.741085i	$-0.265688\pi$
$193$	694883.			1.34282			0.671411	+	0.741085i	$0.265688\pi$
$194$	65988.7	−	26196.3i	0.125882	−	0.0499730i
$195$		0			0
$196$	−289897.	+	273227.i	−0.539018	+	0.508022i
$197$			304179.i			0.558424i	0.960229	+	0.279212i	$0.0900733\pi$
$197$			304179.i			0.558424i	−0.960229	+	0.279212i	$0.909927\pi$
$198$	−39729.2	−	100078.i	−0.0720190	−	0.181416i
$199$	−575412.			−1.03002			−0.515011	−	0.857184i	$-0.672212\pi$
$199$	−575412.			−1.03002			−0.515011	+	0.857184i	$0.672212\pi$
$200$		0			0
$201$	403315.			0.704133
$202$	−197508.	−	497523.i	−0.340569	−	0.857896i
$203$			60877.8i			0.103686i
$204$	−68117.1	−	72273.1i	−0.114599	−	0.121591i
$205$		0			0
$206$	392774.	−	155924.i	0.644874	−	0.256003i
$207$	211463.			0.343011
$208$	−252274.	−	14949.4i	−0.404309	−	0.0239589i
$209$	24782.0			0.0392438
$210$		0			0
$211$		−	154406.i		−	0.238758i	−0.992849	−	0.119379i	$-0.961910\pi$
$211$		−	154406.i		−	0.238758i	0.992849	−	0.119379i	$-0.0380903\pi$
$212$	504593.	+	535379.i	0.771083	+	0.818129i
$213$			323483.i			0.488543i
$214$	199099.	+	501533.i	0.297191	+	0.748626i
$215$		0			0
$216$	−645381.	−	301543.i	−0.941200	−	0.439759i
$217$	−408966.			−0.589573
$218$	346667.	+	873258.i	0.494051	+	1.24452i
$219$		−	830385.i		−	1.16995i
$220$		0			0
$221$		−	73398.0i		−	0.101089i
$222$	−765751.	+	303989.i	−1.04281	+	0.413977i
$223$	−817613.			−1.10100			−0.550498	−	0.834836i	$-0.685562\pi$
$223$	−817613.			−1.10100			−0.550498	+	0.834836i	$0.685562\pi$
$224$	−119825.	−	363149.i	−0.159561	−	0.483577i
$225$		0			0
$226$	919128.	−	364877.i	1.19703	−	0.475199i
$227$		−	45598.7i		−	0.0587338i	−0.999569	−	0.0293669i	$-0.990651\pi$
$227$		−	45598.7i		−	0.0587338i	0.999569	−	0.0293669i	$-0.00934912\pi$
$228$	42428.0	−	39988.2i	0.0540525	−	0.0509442i
$229$		−	633888.i		−	0.798774i	−0.916783	−	0.399387i	$-0.869223\pi$
$229$		−	633888.i		−	0.798774i	0.916783	−	0.399387i	$-0.130777\pi$
$230$		0			0
$231$	−97785.0			−0.120571
$232$	151236.	+	70662.1i	0.184474	+	0.0861920i
$233$	245572.			0.296339			0.148169	−	0.988962i	$-0.452662\pi$
$233$	245572.			0.296339			0.148169	+	0.988962i	$0.452662\pi$
$234$	−69077.0	−	174006.i	−0.0824696	−	0.207742i
$235$		0			0
$236$	−700004.	−	742713.i	−0.818126	−	0.868043i
$237$		−	243166.i		−	0.281211i
$238$	103228.	−	40979.8i	0.118129	−	0.0468951i
$239$	−1.13159e6			−1.28142			−0.640711	−	0.767782i	$-0.721361\pi$
$239$	−1.13159e6			−1.28142			−0.640711	+	0.767782i	$0.721361\pi$
$240$		0			0
$241$	1.56424e6			1.73484			0.867421	−	0.497575i	$-0.165776\pi$
$241$	1.56424e6			1.73484			0.867421	+	0.497575i	$0.165776\pi$
$242$	740831.	−	294096.i	0.813168	−	0.322813i
$243$		−	867775.i		−	0.942739i
$244$	−469029.	−	497646.i	−0.504342	−	0.535114i
$245$		0			0
$246$	65526.8	+	165063.i	0.0690369	+	0.173905i
$247$	43088.4			0.0449384
$248$	−474695.	+	1.01597e6i	−0.490101	+	1.04895i
$249$	696104.			0.711501
$250$		0			0
$251$		−	1.45223e6i		−	1.45496i	−0.686130	−	0.727479i	$-0.740692\pi$
$251$		−	1.45223e6i		−	1.45496i	0.686130	−	0.727479i	$-0.259308\pi$
$252$	206158.	−	194303.i	0.204502	−	0.192743i
$253$		−	223826.i		−	0.219841i
$254$	498921.	−	198063.i	0.485230	−	0.192627i
$255$		0			0
$256$	−1.04124e6	−	123840.i	−0.993001	−	0.118103i
$257$	−1.67551e6			−1.58240			−0.791198	−	0.611560i	$-0.790542\pi$
$257$	−1.67551e6			−1.58240			−0.791198	+	0.611560i	$0.790542\pi$
$258$	892680.	−	354377.i	0.834923	−	0.331449i
$259$		−	921364.i		−	0.853458i
$260$		0			0
$261$			123663.i			0.112367i
$262$	−549308.	−	1.38371e6i	−0.494382	−	1.24535i
$263$	−977406.			−0.871336			−0.435668	−	0.900107i	$-0.643488\pi$
$263$	−977406.			−0.871336			−0.435668	+	0.900107i	$0.643488\pi$
$264$	−113501.	+	242922.i	−0.100228	+	0.214515i
$265$		0			0
$266$	24057.2	+	60600.4i	0.0208469	+	0.0525135i
$267$		−	690711.i		−	0.592950i
$268$	848257.	+	900012.i	0.721424	+	0.765440i
$269$			15731.4i			0.0132552i	0.999978	+	0.00662760i	$0.00210964\pi$
$269$			15731.4i			0.0132552i	−0.999978	+	0.00662760i	$0.997890\pi$
$270$		0			0
$271$	−861364.			−0.712465			−0.356233	−	0.934397i	$-0.615939\pi$
$271$	−861364.			−0.712465			−0.356233	+	0.934397i	$0.615939\pi$
$272$	18015.4	−	304011.i	0.0147646	−	0.249154i
$273$	−170018.			−0.138067
$274$	−63305.6	+	25131.2i	−0.0509408	+	0.0202226i
$275$		0			0
$276$	−361165.	−	383201.i	−0.285387	−	0.302799i
$277$		−	2.16950e6i		−	1.69887i	−0.527693	−	0.849435i	$-0.676943\pi$
$277$		−	2.16950e6i		−	1.69887i	0.527693	−	0.849435i	$-0.323057\pi$
$278$	746593.	+	1.88067e6i	0.579391	+	1.45949i
$279$	−830746.			−0.638937
$280$		0			0
$281$	1.81796e6			1.37347			0.686736	−	0.726907i	$-0.259043\pi$
$281$	1.81796e6			1.37347			0.686736	+	0.726907i	$0.259043\pi$
$282$	21888.4	+	55137.2i	0.0163905	+	0.0412878i
$283$		−	998020.i		−	0.740753i	−0.928882	−	0.370376i	$-0.879229\pi$
$283$		−	998020.i		−	0.740753i	0.928882	−	0.370376i	$-0.120771\pi$
$284$	−721864.	+	680353.i	−0.531079	+	0.500540i
$285$		0			0
$286$	−184179.	+	73115.6i	−0.133145	+	0.0528560i
$287$	−198606.			−0.142327
$288$	−243405.	−	737679.i	−0.172921	−	0.524066i
$289$	−1.33141e6			−0.937704
$290$		0			0
$291$		−	130974.i		−	0.0906674i
$292$	1.85303e6	−	1.74647e6i	1.27182	−	1.19869i
$293$		−	399603.i		−	0.271932i	−0.990714	−	0.135966i	$-0.956586\pi$
$293$		−	399603.i		−	0.271932i	0.990714	−	0.135966i	$-0.0434138\pi$
$294$	271149.	+	683025.i	0.182953	+	0.460859i
$295$		0			0
$296$	−2.28890e6	−	1.06945e6i	−1.51844	−	0.709463i
$297$	−558571.			−0.367441
$298$	754484.	+	1.90055e6i	0.492163	+	1.23976i
$299$		−	389165.i		−	0.251742i
$300$		0			0
$301$			1.07409e6i			0.683318i
$302$	−1.77678e6	+	705350.i	−1.12103	+	0.445028i
$303$	−987479.			−0.617904
$304$	178470.	+	10575.9i	0.110760	+	0.00656349i
$305$		0			0
$306$	209692.	−	83243.7i	0.128020	−	0.0508216i
$307$		−	368112.i		−	0.222912i	−0.993769	−	0.111456i	$-0.964449\pi$
$307$		−	368112.i		−	0.222912i	0.993769	−	0.111456i	$-0.0355515\pi$
$308$	−205662.	−	218211.i	−0.123532	−	0.131069i
$309$		−	779573.i		−	0.464473i
$310$		0			0
$311$	−1.13519e6			−0.665530			−0.332765	−	0.943010i	$-0.607982\pi$
$311$	−1.13519e6			−0.665530			−0.332765	+	0.943010i	$0.607982\pi$
$312$	−197344.	+	422368.i	−0.114772	+	0.245643i
$313$	334474.			0.192975			0.0964877	−	0.995334i	$-0.469239\pi$
$313$	334474.			0.192975			0.0964877	+	0.995334i	$0.469239\pi$
$314$	323529.	+	814972.i	0.185178	+	0.466464i
$315$		0			0
$316$	542633.	−	511429.i	0.305695	−	0.288116i
$317$		−	837898.i		−	0.468321i	−0.972198	−	0.234160i	$-0.924766\pi$
$317$		−	837898.i		−	0.468321i	0.972198	−	0.234160i	$-0.0752341\pi$
$318$	1.26141e6	−	500755.i	0.699499	−	0.277688i
$319$	130893.			0.0720179
$320$		0			0
$321$	995437.			0.539202
$322$	547330.	−	217280.i	0.294178	−	0.116783i
$323$			51925.2i			0.0276931i
$324$	−197455.	+	186100.i	−0.104497	+	0.0984884i
$325$		0			0
$326$	−263818.	−	664559.i	−0.137486	−	0.346330i
$327$	1.73323e6			0.896370
$328$	−230526.	+	493387.i	−0.118314	+	0.253223i
$329$	−66341.9			−0.0337908
$330$		0			0
$331$			2.30318e6i			1.15547i	0.816225	+	0.577734i	$0.196063\pi$
$331$			2.30318e6i			1.15547i	−0.816225	+	0.577734i	$0.803937\pi$
$332$	1.46405e6	+	1.55338e6i	0.728973	+	0.773450i
$333$		−	1.87160e6i		−	0.924917i
$334$	3.73190e6	−	1.48150e6i	1.83048	−	0.726665i
$335$		0			0
$336$	−704209.	−	41730.6i	−0.340293	−	0.0201654i
$337$	−698751.			−0.335156			−0.167578	−	0.985859i	$-0.553595\pi$
$337$	−698751.			−0.335156			−0.167578	+	0.985859i	$0.553595\pi$
$338$	1.63192e6	−	647843.i	0.776976	−	0.308445i
$339$		−	1.82427e6i		−	0.862166i
$340$		0			0
$341$			879315.i			0.409505i
$342$	48868.3	+	123100.i	0.0225924	+	0.0569104i
$343$	−1.93136e6			−0.886398
$344$	2.66830e6	+	1.24671e6i	1.21573	+	0.568030i
$345$		0			0
$346$	825212.	+	2.07872e6i	0.370574	+	0.933480i
$347$			3.30033e6i			1.47141i	0.677301	+	0.735706i	$0.263149\pi$
$347$			3.30033e6i			1.47141i	−0.677301	+	0.735706i	$0.736851\pi$
$348$	224096.	−	211209.i	0.0991940	−	0.0934898i
$349$			121442.i			0.0533711i	0.999644	+	0.0266855i	$0.00849528\pi$
$349$			121442.i			0.0533711i	−0.999644	+	0.0266855i	$0.991505\pi$
$350$		0			0
$351$	−971186.			−0.420760
$352$	−780806.	+	257635.i	−0.335882	+	0.110828i
$353$	−56609.0			−0.0241796			−0.0120898	−	0.999927i	$-0.503848\pi$
$353$	−56609.0			−0.0241796			−0.0120898	+	0.999927i	$0.503848\pi$
$354$	−1.74990e6	+	694680.i	−0.742175	+	0.294630i
$355$		0			0
$356$	1.54135e6	−	1.45271e6i	0.644577	−	0.607511i
$357$		−	204887.i		−	0.0850831i
$358$	555027.	+	1.39812e6i	0.228879	+	0.576549i
$359$	−446755.			−0.182950			−0.0914751	−	0.995807i	$-0.529158\pi$
$359$	−446755.			−0.182950			−0.0914751	+	0.995807i	$0.529158\pi$
$360$		0			0
$361$	2.44562e6			0.987689
$362$	1.74510e6	+	4.39593e6i	0.699922	+	1.76311i
$363$		−	1.47039e6i		−	0.585688i
$364$	−357584.	−	379402.i	−0.141457	−	0.150088i
$365$		0			0
$366$	−1.17250e6	+	465462.i	−0.457521	+	0.181627i
$367$	−304081.			−0.117849			−0.0589243	−	0.998262i	$-0.518767\pi$
$367$	−304081.			−0.117849			−0.0589243	+	0.998262i	$0.518767\pi$
$368$	95519.7	−	1.61191e6i	0.0367683	−	0.620469i
$369$	−403436.			−0.154244
$370$		0			0
$371$			1.51774e6i			0.572484i
$372$	1.41886e6	+	1.50543e6i	0.531598	+	0.564032i
$373$			932701.i			0.347112i	0.984824	+	0.173556i	$0.0555258\pi$
$373$			932701.i			0.347112i	−0.984824	+	0.173556i	$0.944474\pi$
$374$	−88110.5	−	221951.i	−0.0325723	−	0.0820499i
$375$		0			0
$376$	−77004.5	+	164810.i	−0.0280896	+	0.0601193i
$377$	227583.			0.0824683
$378$	−542236.	−	1.36590e6i	−0.195190	−	0.491686i
$379$			760659.i			0.272014i	0.990708	+	0.136007i	$0.0434270\pi$
$379$			760659.i			0.272014i	−0.990708	+	0.136007i	$0.956573\pi$
$380$		0			0
$381$		−	990254.i		−	0.349489i
$382$	−4.04941e6	+	1.60754e6i	−1.41982	+	0.563642i
$383$	−1.80993e6			−0.630470			−0.315235	−	0.949014i	$-0.602083\pi$
$383$	−1.80993e6			−0.630470			−0.315235	+	0.949014i	$0.602083\pi$
$384$	−921059.	+	1.70099e6i	−0.318757	+	0.588673i
$385$		0			0
$386$	3.65350e6	−	1.45037e6i	1.24807	−	0.495463i
$387$			2.18183e6i			0.740532i
$388$	292272.	−	275465.i	0.0985617	−	0.0928939i
$389$			4.14597e6i			1.38916i	0.719416	+	0.694579i	$0.244409\pi$
$389$			4.14597e6i			1.38916i	−0.719416	+	0.694579i	$0.755591\pi$
$390$		0			0
$391$	468977.			0.155135
$392$	−953912.	+	2.04162e6i	−0.313540	+	0.671059i
$393$	−2.74637e6			−0.896971
$394$	634888.	+	1.59929e6i	0.206042	+	0.519022i
$395$		0			0
$396$	−417770.	−	443259.i	−0.133875	−	0.142043i
$397$			1.67426e6i			0.533145i	0.963815	+	0.266573i	$0.0858912\pi$
$397$			1.67426e6i			0.533145i	−0.963815	+	0.266573i	$0.914109\pi$
$398$	−3.02535e6	+	1.20101e6i	−0.957344	+	0.380048i
$399$	120279.			0.0378231
$400$		0			0
$401$	−2.20886e6			−0.685975			−0.342987	−	0.939340i	$-0.611439\pi$
$401$	−2.20886e6			−0.685975			−0.342987	+	0.939340i	$0.611439\pi$
$402$	2.12051e6	−	841806.i	0.654450	−	0.259805i
$403$			1.52886e6i			0.468927i
$404$	−2.07688e6	−	2.20359e6i	−0.633078	−	0.671704i
$405$		0			0
$406$	127065.	+	320078.i	0.0382570	+	0.0963697i
$407$	−1.98102e6			−0.592793
$408$	−508990.	−	237816.i	−0.151377	−	0.0707280i
$409$	1.59010e6			0.470019			0.235010	−	0.971993i	$-0.424488\pi$
$409$	1.59010e6			0.470019			0.235010	+	0.971993i	$0.424488\pi$
$410$		0			0
$411$			125648.i			0.0366904i
$412$	1.73965e6	−	1.63961e6i	0.504914	−	0.475879i
$413$		−	2.10551e6i		−	0.607411i
$414$	1.11181e6	−	441369.i	0.318809	−	0.126561i
$415$		0			0
$416$	−1.35758e6	+	447949.i	−0.384622	+	0.126910i
$417$	3.73274e6			1.05121
$418$	130297.	−	51725.4i	0.0364748	−	0.0144798i
$419$			4.24535e6i			1.18135i	0.806909	+	0.590675i	$0.201139\pi$
$419$			4.24535e6i			1.18135i	−0.806909	+	0.590675i	$0.798861\pi$
$420$		0			0
$421$			5.17330e6i			1.42253i	0.702922	+	0.711267i	$0.251878\pi$
$421$			5.17330e6i			1.42253i	−0.702922	+	0.711267i	$0.748122\pi$
$422$	−322278.	−	811822.i	−0.0880947	−	0.221911i
$423$	−134763.			−0.0366200
$424$	3.77046e6	+	1.76168e6i	1.01854	+	0.475896i
$425$		0			0
$426$	675179.	+	1.70078e6i	0.180258	+	0.454072i
$427$		−	1.41077e6i		−	0.374445i
$428$	2.09362e6	+	2.22135e6i	0.552443	+	0.586149i
$429$			365556.i			0.0958982i
$430$		0			0
$431$	1.02248e6			0.265132			0.132566	−	0.991174i	$-0.457678\pi$
$431$	1.02248e6			0.265132			0.132566	+	0.991174i	$0.457678\pi$
$432$	−4.02261e6	−	238375.i	−1.03705	−	0.0614542i
$433$	2.18503e6			0.560063			0.280031	−	0.959991i	$-0.409655\pi$
$433$	2.18503e6			0.560063			0.280031	+	0.959991i	$0.409655\pi$
$434$	−2.15022e6	+	853599.i	−0.547973	+	0.217535i
$435$		0			0
$436$	3.64535e6	+	3.86777e6i	0.918382	+	0.974416i
$437$			275314.i			0.0689643i
$438$	−1.73319e6	−	4.36592e6i	−0.431679	−	1.08740i
$439$	1.22033e6			0.302216			0.151108	−	0.988517i	$-0.451716\pi$
$439$	1.22033e6			0.302216			0.151108	+	0.988517i	$0.451716\pi$
$440$		0			0
$441$	−1.66941e6			−0.408758
$442$	−153197.	−	385905.i	−0.0372989	−	0.0939561i
$443$		−	509711.i		−	0.123400i	−0.998095	−	0.0617000i	$-0.980348\pi$
$443$		−	509711.i		−	0.123400i	0.998095	−	0.0617000i	$-0.0196522\pi$
$444$	−3.39161e6	+	3.19658e6i	−0.816485	+	0.769533i
$445$		0			0
$446$	−4.29878e6	+	1.70654e6i	−1.02331	+	0.406236i
$447$	3.77219e6			0.892945
$448$	−1.38798e6	−	1.65923e6i	−0.326729	−	0.390582i
$449$	3.54089e6			0.828890			0.414445	−	0.910074i	$-0.363976\pi$
$449$	3.54089e6			0.828890			0.414445	+	0.910074i	$0.363976\pi$
$450$		0			0
$451$			427022.i			0.0988573i
$452$	4.07093e6	−	3.83683e6i	0.937233	−	0.883338i
$453$			3.52654e6i			0.807427i
$454$	−95174.4	−	239745.i	−0.0216711	−	0.0545896i
$455$		0			0
$456$	139610.	−	298803.i	0.0314417	−	0.0672935i
$457$	1.06559e6			0.238671			0.119335	−	0.992854i	$-0.461924\pi$
$457$	1.06559e6			0.238671			0.119335	+	0.992854i	$0.461924\pi$
$458$	−1.32306e6	−	3.33280e6i	−0.294724	−	0.742413i
$459$		−	1.17036e6i		−	0.259292i
$460$		0			0
$461$		−	6.92975e6i		−	1.51868i	−0.650696	−	0.759339i	$-0.725523\pi$
$461$		−	6.92975e6i		−	1.51868i	0.650696	−	0.759339i	$-0.274477\pi$
$462$	−514125.	+	204098.i	−0.112063	+	0.0444871i
$463$	7.21004e6			1.56310			0.781548	−	0.623845i	$-0.214431\pi$
$463$	7.21004e6			1.56310			0.781548	+	0.623845i	$0.214431\pi$
$464$	942641.	+	55859.8i	0.203260	+	0.0120449i
$465$		0			0
$466$	1.29114e6	−	512561.i	0.275429	−	0.109340i
$467$		−	3.00541e6i		−	0.637693i	−0.947806	−	0.318846i	$-0.896705\pi$
$467$		−	3.00541e6i		−	0.637693i	0.947806	−	0.318846i	$-0.103295\pi$
$468$	−726374.	−	770692.i	−0.153301	−	0.162655i
$469$			2.55144e6i			0.535615i
$470$		0			0
$471$	1.61755e6			0.335973
$472$	−5.23062e6	−	2.44391e6i	−1.08068	−	0.504930i
$473$	2.30939e6			0.474618
$474$	−507540.	−	1.27850e6i	−0.103759	−	0.261369i
$475$		0			0
$476$	457212.	−	430920.i	0.0924911	−	0.0871724i
$477$			3.08305e6i			0.620418i
$478$	−5.94955e6	+	2.36186e6i	−1.19101	+	0.472808i
$479$	2.47740e6			0.493353			0.246676	−	0.969098i	$-0.420662\pi$
$479$	2.47740e6			0.493353			0.246676	+	0.969098i	$0.420662\pi$
$480$		0			0
$481$	−3.44439e6			−0.678813
$482$	8.22431e6	−	3.26490e6i	1.61243	−	0.640107i
$483$		−	1.08633e6i		−	0.211883i
$484$	3.28123e6	−	3.09255e6i	0.636683	−	0.600071i
$485$		0			0
$486$	−1.81123e6	−	4.56251e6i	−0.347843	−	0.876220i
$487$	−4.58130e6			−0.875320			−0.437660	−	0.899141i	$-0.644193\pi$
$487$	−4.58130e6			−0.875320			−0.437660	+	0.899141i	$0.644193\pi$
$488$	−3.50471e6	−	1.63751e6i	−0.666198	−	0.311269i
$489$	−1.31901e6			−0.249446
$490$		0			0
$491$		−	8.23983e6i		−	1.54246i	−0.636555	−	0.771231i	$-0.719641\pi$
$491$		−	8.23983e6i		−	1.54246i	0.636555	−	0.771231i	$-0.280359\pi$
$492$	689042.	+	731083.i	0.128331	+	0.136161i
$493$			274257.i			0.0508207i
$494$	226546.	−	89934.7i	0.0417676	−	0.0165810i
$495$		0			0
$496$	−375255.	+	6.33248e6i	−0.0684893	+	1.15577i
$497$	−2.04641e6			−0.371622
$498$	3.65991e6	−	1.45292e6i	0.661298	−	0.262523i
$499$			4.49557e6i			0.808228i	0.914709	+	0.404114i	$0.132420\pi$
$499$			4.49557e6i			0.808228i	−0.914709	+	0.404114i	$0.867580\pi$
$500$		0			0
$501$		−	7.40704e6i		−	1.31841i
$502$	−3.03111e6	−	7.63539e6i	−0.536837	−	1.35230i
$503$	6.28876e6			1.10827			0.554134	−	0.832427i	$-0.313049\pi$
$503$	6.28876e6			1.10827			0.554134	+	0.832427i	$0.313049\pi$
$504$	678366.	−	1.45188e6i	0.118956	−	0.254598i
$505$		0			0
$506$	−467173.	−	1.17681e6i	−0.0811151	−	0.204329i
$507$		−	3.23902e6i		−	0.559620i
$508$	2.20979e6	−	2.08271e6i	0.379919	−	0.358072i
$509$		−	8.26032e6i		−	1.41320i	−0.707615	−	0.706598i	$-0.750229\pi$
$509$		−	8.26032e6i		−	1.41320i	0.707615	−	0.706598i	$-0.249771\pi$
$510$		0			0
$511$	5.25315e6			0.889954
$512$	−5.73301e6	+	1.52217e6i	−0.966513	+	0.256619i
$513$	687063.			0.115266
$514$	−8.80937e6	+	3.49716e6i	−1.47074	+	0.583859i
$515$		0			0
$516$	3.95379e6	−	3.72643e6i	0.653716	−	0.616125i
$517$			142642.i			0.0234704i
$518$	−1.92309e6	−	4.84427e6i	−0.314901	−	0.793238i
$519$	4.12581e6			0.672344
$520$		0			0
$521$	−1.09563e7			−1.76835			−0.884176	−	0.467154i	$-0.845279\pi$
$521$	−1.09563e7			−1.76835			−0.884176	+	0.467154i	$0.845279\pi$
$522$	258112.	+	650186.i	0.0414602	+	0.104439i
$523$			9.74999e6i			1.55865i	0.626617	+	0.779327i	$0.284439\pi$
$523$			9.74999e6i			1.55865i	−0.626617	+	0.779327i	$0.715561\pi$
$524$	−5.77620e6	−	6.12863e6i	−0.918997	−	0.975068i
$525$		0			0
$526$	−5.13892e6	+	2.04006e6i	−0.809855	+	0.321498i
$527$	−1.84241e6			−0.288975
$528$	−89724.8	+	1.51412e6i	−0.0140064	+	0.236360i
$529$	−3.94977e6			−0.613666
$530$		0			0
$531$		−	4.27701e6i		−	0.658269i
$532$	252972.	+	268407.i	0.0387520	+	0.0411163i
$533$			742461.i			0.113202i
$534$	−1.44166e6	−	3.63156e6i	−0.218781	−	0.551112i
$535$		0			0
$536$	6.33841e6	+	2.96151e6i	0.952946	+	0.445247i
$537$	2.77497e6			0.415262
$538$	32834.8	+	82711.0i	0.00489078	+	0.0123199i
$539$			1.76701e6i			0.261979i
$540$		0			0
$541$		−	1.86030e6i		−	0.273268i	−0.990622	−	0.136634i	$-0.956372\pi$
$541$		−	1.86030e6i		−	0.273268i	0.990622	−	0.136634i	$-0.0436285\pi$
$542$	−4.52880e6	+	1.79785e6i	−0.662194	+	0.262879i
$543$	8.72499e6			1.26989
$544$	−539817.	−	1.63601e6i	−0.0782077	−	0.237021i
$545$		0			0
$546$	−893907.	+	354865.i	−0.128325	+	0.0509426i
$547$		−	725841.i		−	0.103723i	−0.998654	−	0.0518613i	$-0.983485\pi$
$547$		−	725841.i		−	0.103723i	0.998654	−	0.0518613i	$-0.0165154\pi$
$548$	−280389.	+	264265.i	−0.0398849	+	0.0375914i
$549$		−	2.86576e6i		−	0.405796i
$550$		0			0
$551$	−161003.			−0.0225920
$552$	−2.69873e6	−	1.26093e6i	−0.376974	−	0.176134i
$553$	1.53831e6			0.213910
$554$	−4.52821e6	−	1.14066e7i	−0.626834	−	1.57900i
$555$		0			0
$556$	7.85074e6	+	8.32974e6i	1.07702	+	1.14273i
$557$			4.72234e6i			0.644939i	0.946580	+	0.322470i	$0.104513\pi$
$557$			4.72234e6i			0.644939i	−0.946580	+	0.322470i	$0.895487\pi$
$558$	−4.36783e6	+	1.73395e6i	−0.593854	+	0.235749i
$559$	4.01533e6			0.543490
$560$		0			0
$561$	−440526.			−0.0590969
$562$	9.55833e6	−	3.79448e6i	1.27656	−	0.506771i
$563$			4.74239e6i			0.630560i	0.948999	+	0.315280i	$0.102098\pi$
$563$			4.74239e6i			0.630560i	−0.948999	+	0.315280i	$0.897902\pi$
$564$	230166.	+	244209.i	0.0304680	+	0.0323269i
$565$		0			0
$566$	−2.08308e6	−	5.24730e6i	−0.273316	−	0.688486i
$567$	−559764.			−0.0731219
$568$	−2.37531e6	+	5.08379e6i	−0.308922	+	0.661175i
$569$	−2.99470e6			−0.387768			−0.193884	−	0.981024i	$-0.562109\pi$
$569$	−2.99470e6			−0.387768			−0.193884	+	0.981024i	$0.562109\pi$
$570$		0			0
$571$			1.01416e7i			1.30172i	0.759198	+	0.650860i	$0.225591\pi$
$571$			1.01416e7i			1.30172i	−0.759198	+	0.650860i	$0.774409\pi$
$572$	−815750.	+	768841.i	−0.104248	+	0.0982531i
$573$			8.03722e6i			1.02263i
$574$	−1.04421e6	+	414533.i	−0.132285	+	0.0525146i
$575$		0			0
$576$	−2.81945e6	−	3.37046e6i	−0.354085	−	0.423285i
$577$	3.80870e6			0.476253			0.238126	−	0.971234i	$-0.423467\pi$
$577$	3.80870e6			0.476253			0.238126	+	0.971234i	$0.423467\pi$
$578$	−7.00015e6	+	2.77893e6i	−0.871541	+	0.345986i
$579$		−	7.25142e6i		−	0.898931i
$580$		0			0
$581$			4.40367e6i			0.541220i
$582$	−273370.	−	688621.i	−0.0334536	−	0.0842700i
$583$	3.26330e6			0.397635
$584$	6.09744e6	−	1.30501e7i	0.739802	−	1.58337i
$585$		0			0
$586$	−834058.	−	2.10100e6i	−0.100335	−	0.252745i
$587$		−	3.40054e6i		−	0.407335i	−0.979040	−	0.203668i	$-0.934714\pi$
$587$		−	3.40054e6i		−	0.407335i	0.979040	−	0.203668i	$-0.0652862\pi$
$588$	2.85124e6	+	3.02520e6i	0.340088	+	0.360837i
$589$		−	1.08159e6i		−	0.128462i
$590$		0			0
$591$	3.17425e6			0.373828
$592$	−1.42665e7	−	845418.i	−1.67307	−	0.0991442i
$593$	−1.27800e7			−1.49243			−0.746216	−	0.665704i	$-0.768132\pi$
$593$	−1.27800e7			−1.49243			−0.746216	+	0.665704i	$0.768132\pi$
$594$	−2.93681e6	+	1.16586e6i	−0.341515	+	0.135575i
$595$		0			0
$596$	7.93372e6	+	8.41778e6i	0.914873	+	0.970693i
$597$			6.00468e6i			0.689532i
$598$	−812272.	−	2.04612e6i	−0.0928856	−	0.233980i
$599$	−614365.			−0.0699616			−0.0349808	−	0.999388i	$-0.511137\pi$
$599$	−614365.			−0.0699616			−0.0349808	+	0.999388i	$0.511137\pi$
$600$		0			0
$601$	−1.12864e7			−1.27459			−0.637294	−	0.770621i	$-0.719946\pi$
$601$	−1.12864e7			−1.27459			−0.637294	+	0.770621i	$0.719946\pi$
$602$	2.24185e6	+	5.64724e6i	0.252125	+	0.635104i
$603$			5.18283e6i			0.580462i
$604$	−7.86959e6	+	7.41706e6i	−0.877728	+	0.827255i
$605$		0			0
$606$	−5.19188e6	+	2.06108e6i	−0.574305	+	0.227989i
$607$	1.81019e6			0.199413			0.0997065	−	0.995017i	$-0.468210\pi$
$607$	1.81019e6			0.199413			0.0997065	+	0.995017i	$0.468210\pi$
$608$	960419.	−	316901.i	0.105366	−	0.0347668i
$609$	635287.			0.0694108
$610$		0			0
$611$			248010.i			0.0268761i
$612$	928750.	−	875343.i	0.100235	−	0.0944713i
$613$			1.08728e7i			1.16867i	0.811513	+	0.584335i	$0.198645\pi$
$613$			1.08728e7i			1.16867i	−0.811513	+	0.584335i	$0.801355\pi$
$614$	−768329.	−	1.93543e6i	−0.0822482	−	0.207184i
$615$		0			0
$616$	−1.53677e6	−	718026.i	−0.163176	−	0.0762410i
$617$	6.60152e6			0.698122			0.349061	−	0.937100i	$-0.386501\pi$
$617$	6.60152e6			0.698122			0.349061	+	0.937100i	$0.386501\pi$
$618$	−1.62714e6	−	4.09877e6i	−0.171377	−	0.431701i
$619$			8.83255e6i			0.926530i	0.886220	+	0.463265i	$0.153322\pi$
$619$			8.83255e6i			0.926530i	−0.886220	+	0.463265i	$0.846678\pi$
$620$		0			0
$621$		−	6.20541e6i		−	0.645716i
$622$	−5.96850e6	+	2.36938e6i	−0.618570	+	0.245561i
$623$	4.36955e6			0.451042
$624$	−156004.	+	2.63259e6i	−0.0160389	+	0.270658i
$625$		0			0
$626$	1.75857e6	−	698120.i	0.179359	−	0.0712023i
$627$		−	258611.i		−	0.0262711i
$628$	3.40204e6	+	3.60961e6i	0.344224	+	0.365226i
$629$		−	4.15079e6i		−	0.418316i
$630$		0			0
$631$	1.48464e7			1.48439			0.742194	−	0.670185i	$-0.233785\pi$
$631$	1.48464e7			1.48439			0.742194	+	0.670185i	$0.233785\pi$
$632$	1.78555e6	−	3.82154e6i	0.177819	−	0.380580i
$633$	−1.61129e6			−0.159833
$634$	−1.74887e6	−	4.40543e6i	−0.172797	−	0.435276i
$635$		0			0
$636$	5.58692e6	−	5.26565e6i	0.547684	−	0.516190i
$637$			3.07229e6i			0.299995i
$638$	688198.	−	273202.i	0.0669363	−	0.0265725i
$639$	−4.15694e6			−0.402737
$640$		0			0
$641$	−1.42105e7			−1.36604			−0.683022	−	0.730398i	$-0.739335\pi$
$641$	−1.42105e7			−1.36604			−0.683022	+	0.730398i	$0.739335\pi$
$642$	5.23372e6	−	2.07769e6i	0.501156	−	0.198950i
$643$			7.89022e6i			0.752595i	0.926499	+	0.376298i	$0.122803\pi$
$643$			7.89022e6i			0.752595i	−0.926499	+	0.376298i	$0.877197\pi$
$644$	2.42419e6	−	2.28479e6i	0.230331	−	0.217086i
$645$		0			0
$646$	108379.	+	273008.i	0.0102180	+	0.0257391i
$647$	−1.41387e7			−1.32785			−0.663924	−	0.747800i	$-0.731110\pi$
$647$	−1.41387e7			−1.32785			−0.663924	+	0.747800i	$0.731110\pi$
$648$	−649730.	+	1.39059e6i	−0.0607848	+	0.130096i
$649$	−4.52706e6			−0.421895
$650$		0			0
$651$			4.26774e6i			0.394680i
$652$	−2.77416e6	−	2.94342e6i	−0.255571	−	0.271164i
$653$		−	2.09667e7i		−	1.92419i	−0.272720	−	0.962094i	$-0.587923\pi$
$653$		−	2.09667e7i		−	1.92419i	0.272720	−	0.962094i	$-0.412077\pi$
$654$	9.11284e6	−	3.61763e6i	0.833123	−	0.330735i
$655$		0			0
$656$	−182235.	+	3.07524e6i	−0.0165338	+	0.279010i
$657$	1.06709e7			0.964469
$658$	−348807.	+	138470.i	−0.0314065	+	0.0124678i
$659$		−	5.17814e6i		−	0.464473i	−0.972659	−	0.232236i	$-0.925396\pi$
$659$		−	5.17814e6i		−	0.464473i	0.972659	−	0.232236i	$-0.0746043\pi$
$660$		0			0
$661$			1.15802e7i			1.03089i	0.856923	+	0.515444i	$0.172373\pi$
$661$			1.15802e7i			1.03089i	−0.856923	+	0.515444i	$0.827627\pi$
$662$	4.80723e6	+	1.21095e7i	0.426334	+	1.07394i
$663$	−765941.			−0.0676724
$664$	1.09398e7	+	5.11143e6i	0.962918	+	0.449906i
$665$		0			0
$666$	−3.90643e6	−	9.84034e6i	−0.341267	−	0.859655i
$667$			1.45415e6i			0.126559i
$668$	1.65291e7	−	1.55786e7i	1.43320	−	1.35079i
$669$			8.53216e6i			0.737045i
$670$		0			0
$671$	−3.03330e6			−0.260081
$672$	−3.78963e6	+	1.25043e6i	−0.323723	+	0.106816i
$673$	3.44202e6			0.292938			0.146469	−	0.989215i	$-0.453209\pi$
$673$	3.44202e6			0.292938			0.146469	+	0.989215i	$0.453209\pi$
$674$	−3.67383e6	+	1.45844e6i	−0.311508	+	0.123663i
$675$		0			0
$676$	7.22798e6	−	6.81234e6i	0.608346	−	0.573363i
$677$		−	1.81661e7i		−	1.52332i	−0.647980	−	0.761658i	$-0.724386\pi$
$677$		−	1.81661e7i		−	1.52332i	0.647980	−	0.761658i	$-0.275614\pi$
$678$	−3.80765e6	−	9.59151e6i	−0.318114	−	0.801332i
$679$	828560.			0.0689683
$680$		0			0
$681$	−475843.			−0.0393184
$682$	1.83532e6	+	4.62319e6i	0.151095	+	0.380610i
$683$		−	1.58711e7i		−	1.30184i	−0.759148	−	0.650918i	$-0.774384\pi$
$683$		−	1.58711e7i		−	1.30184i	0.759148	−	0.650918i	$-0.225616\pi$
$684$	513871.	+	545224.i	0.0419966	+	0.0445589i
$685$		0			0
$686$	−1.01546e7	+	4.03117e6i	−0.823855	+	0.327055i
$687$	−6.61490e6			−0.534726
$688$	1.66313e7	+	985552.i	1.33954	+	0.0793795i
$689$	5.67388e6			0.455336
$690$		0			0
$691$			7.37470e6i			0.587556i	0.955874	+	0.293778i	$0.0949127\pi$
$691$			7.37470e6i			0.587556i	−0.955874	+	0.293778i	$0.905087\pi$
$692$	8.67746e6	+	9.20690e6i	0.688854	+	0.730883i
$693$		−	1.25659e6i		−	0.0993943i
$694$	6.88851e6	+	1.73522e7i	0.542908	+	1.36759i
$695$		0			0
$696$	737391.	−	1.57821e6i	0.0576999	−	0.123493i
$697$	−894730.			−0.0697605
$698$	253476.	+	638508.i	0.0196924	+	0.0496052i
$699$		−	2.56265e6i		−	0.198379i
$700$		0			0
$701$		−	2.16654e7i		−	1.66522i	−0.553857	−	0.832612i	$-0.686845\pi$
$701$		−	2.16654e7i		−	1.66522i	0.553857	−	0.832612i	$-0.313155\pi$
$702$	−5.10622e6	+	2.02707e6i	−0.391072	+	0.155248i
$703$	2.43673e6			0.185960
$704$	−3.56751e6	+	2.98428e6i	−0.271290	+	0.226939i
$705$		0			0
$706$	−297634.	+	118155.i	−0.0224735	+	0.00892157i
$707$		−	6.24695e6i		−	0.470023i
$708$	−7.75055e6	+	7.30486e6i	−0.581098	+	0.547682i
$709$			5.46373e6i			0.408201i	0.978950	+	0.204100i	$0.0654269\pi$
$709$			5.46373e6i			0.408201i	−0.978950	+	0.204100i	$0.934573\pi$
$710$		0			0
$711$	3.12482e6			0.231820
$712$	5.07183e6	−	1.08551e7i	0.374942	−	0.802476i
$713$	−9.76869e6			−0.719635
$714$	−427643.	−	1.07723e6i	−0.0313932	−	0.0790797i
$715$		0			0
$716$	5.83635e6	+	6.19244e6i	0.425460	+	0.451418i
$717$			1.18086e7i			0.857829i
$718$	−2.34891e6	+	932473.i	−0.170041	+	0.0675034i
$719$	1.42857e7			1.03058			0.515288	−	0.857017i	$-0.327685\pi$
$719$	1.42857e7			1.03058			0.515288	+	0.857017i	$0.327685\pi$
$720$		0			0
$721$	4.93171e6			0.353313
$722$	1.28583e7	−	5.10453e6i	0.917999	−	0.364429i
$723$		−	1.63235e7i		−	1.16136i
$724$	1.83505e7	+	1.94701e7i	1.30107	+	1.38045i
$725$		0			0
$726$	−3.06903e6	−	7.73090e6i	−0.216102	−	0.544363i
$727$	3.55756e6			0.249641			0.124821	−	0.992179i	$-0.460164\pi$
$727$	3.55756e6			0.249641			0.124821	+	0.992179i	$0.460164\pi$
$728$	−2.67197e6	−	1.24843e6i	−0.186854	−	0.0873043i
$729$	−1.11161e7			−0.774697
$730$		0			0
$731$			4.83881e6i			0.334923i
$732$	−5.19316e6	+	4.89453e6i	−0.358223	+	0.337624i
$733$		−	1.61816e7i		−	1.11240i	−0.831048	−	0.556201i	$-0.812258\pi$
$733$		−	1.61816e7i		−	1.11240i	0.831048	−	0.556201i	$-0.187742\pi$
$734$	−1.59877e6	+	634683.i	−0.109533	+	0.0434827i
$735$		0			0
$736$	−2.86218e6	−	8.67431e6i	−0.194761	−	0.590256i
$737$	5.48584e6			0.372027
$738$	−2.12115e6	+	842057.i	−0.143361	+	0.0569116i
$739$			1.16551e7i			0.785063i	0.919739	+	0.392531i	$0.128401\pi$
$739$			1.16551e7i			0.785063i	−0.919739	+	0.392531i	$0.871599\pi$
$740$		0			0
$741$		−	449647.i		−	0.0300833i
$742$	3.16786e6	+	7.97986e6i	0.211230	+	0.532090i
$743$	−2.41917e7			−1.60766			−0.803829	−	0.594860i	$-0.797208\pi$
$743$	−2.41917e7			−1.60766			−0.803829	+	0.594860i	$0.797208\pi$
$744$	1.06021e7	+	4.95365e6i	0.702200	+	0.328090i
$745$		0			0
$746$	1.94675e6	+	4.90387e6i	0.128074	+	0.322620i
$747$			8.94532e6i			0.586536i
$748$	−926519.	−	983049.i	−0.0605481	−	0.0642423i
$749$			6.29730e6i			0.410157i
$750$		0			0
$751$	2.13480e7			1.38120			0.690601	−	0.723236i	$-0.257346\pi$
$751$	2.13480e7			1.38120			0.690601	+	0.723236i	$0.257346\pi$
$752$	−60873.5	+	1.02725e6i	−0.00392540	+	0.0662416i
$753$	−1.51546e7			−0.973998
$754$	1.19657e6	−	475015.i	0.0766494	−	0.0304284i
$755$		0			0
$756$	−5.70184e6	−	6.04972e6i	−0.362836	−	0.384974i
$757$		−	1.68129e7i		−	1.06636i	−0.846002	−	0.533179i	$-0.820997\pi$
$757$		−	1.68129e7i		−	1.06636i	0.846002	−	0.533179i	$-0.179003\pi$
$758$	1.58766e6	+	3.99933e6i	0.100365	+	0.252821i
$759$	−2.33572e6			−0.147169
$760$		0			0
$761$	1.07818e7			0.674888			0.337444	−	0.941346i	$-0.390438\pi$
$761$	1.07818e7			0.674888			0.337444	+	0.941346i	$0.390438\pi$
$762$	−2.06687e6	−	5.20647e6i	−0.128951	−	0.324830i
$763$			1.09647e7i			0.681845i
$764$	−1.79353e7	+	1.69040e7i	−1.11167	+	1.04774i
$765$		0			0
$766$	−9.51608e6	+	3.77771e6i	−0.585985	+	0.232625i
$767$	−7.87117e6			−0.483116
$768$	−1.29233e6	+	1.08658e7i	−0.0790622	+	0.664749i
$769$	−3.03763e6			−0.185233			−0.0926166	−	0.995702i	$-0.529523\pi$
$769$	−3.03763e6			−0.185233			−0.0926166	+	0.995702i	$0.529523\pi$
$770$		0			0
$771$			1.74847e7i			1.05931i
$772$	1.61818e7	−	1.52513e7i	0.977200	−	0.921006i
$773$		−	2.73040e7i		−	1.64353i	−0.569828	−	0.821764i	$-0.692990\pi$
$773$		−	2.73040e7i		−	1.64353i	0.569828	−	0.821764i	$-0.307010\pi$
$774$	4.55395e6	+	1.14714e7i	0.273235	+	0.688280i
$775$		0			0
$776$	961727.	−	2.05835e6i	0.0573321	−	0.122706i
$777$	−9.61485e6			−0.571334
$778$	8.65353e6	+	2.17983e7i	0.512559	+	1.29114i
$779$		−	525252.i		−	0.0310116i
$780$		0			0
$781$			4.39997e6i			0.258120i
$782$	2.46575e6	−	978857.i	0.144189	−	0.0572404i
$783$	3.62891e6			0.211530
$784$	−754086.	+	1.27253e7i	−0.0438158	+	0.739397i
$785$		0			0
$786$	−1.44396e7	+	5.73227e6i	−0.833681	+	0.330956i
$787$			1.58229e7i			0.910644i	0.890327	+	0.455322i	$0.150476\pi$
$787$			1.58229e7i			0.910644i	−0.890327	+	0.455322i	$0.849524\pi$
$788$	6.67611e6	+	7.08345e6i	0.383008	+	0.406377i
$789$			1.01997e7i			0.583302i
$790$		0			0
$791$	1.15407e7			0.655827
$792$	−3.12169e6	−	1.45855e6i	−0.176838	−	0.0826246i
$793$	−5.27398e6			−0.297821
$794$	3.49453e6	+	8.80276e6i	0.196715	+	0.495527i
$795$		0			0
$796$	−1.33997e7	+	1.26291e7i	−0.749568	+	0.706464i
$797$		−	5.53728e6i		−	0.308781i	−0.988010	−	0.154390i	$-0.950659\pi$
$797$		−	5.53728e6i		−	0.308781i	0.988010	−	0.154390i	$-0.0493414\pi$
$798$	632392.	−	251048.i	0.0351544	−	0.0139556i
$799$	−298874.			−0.0165623
$800$		0			0
$801$	8.87602e6			0.488807
$802$	−1.16136e7	+	4.61037e6i	−0.637573	+	0.253105i
$803$		−	1.12948e7i		−	0.618143i
$804$	9.39203e6	−	8.85194e6i	0.512412	−	0.482946i
$805$		0			0
$806$	3.19106e6	+	8.03831e6i	0.173021	+	0.435840i
$807$	164164.			0.00887348
$808$	−1.55190e7	−	7.25097e6i	−0.836248	−	0.390722i
$809$	−4.59562e6			−0.246873			−0.123436	−	0.992352i	$-0.539391\pi$
$809$	−4.59562e6			−0.246873			−0.123436	+	0.992352i	$0.539391\pi$
$810$		0			0
$811$			3.14901e6i			0.168121i	0.996461	+	0.0840604i	$0.0267889\pi$
$811$			3.14901e6i			0.168121i	−0.996461	+	0.0840604i	$0.973211\pi$
$812$	1.33614e6	+	1.41767e6i	0.0711153	+	0.0754542i
$813$			8.98872e6i			0.476949i
$814$	−1.04156e7	+	4.13482e6i	−0.550966	+	0.218724i
$815$		0			0
$816$	−3.17249e6	−	187998.i	−0.166792	−	0.00988391i
$817$	−2.84063e6			−0.148888
$818$	8.36027e6	−	3.31888e6i	0.436855	−	0.173423i
$819$		−	2.18483e6i		−	0.113817i
$820$		0			0
$821$			1.98853e7i			1.02961i	0.857306	+	0.514807i	$0.172136\pi$
$821$			1.98853e7i			1.02961i	−0.857306	+	0.514807i	$0.827864\pi$
$822$	262255.	+	660623.i	0.0135377	+	0.0341015i
$823$	−1.53764e7			−0.791328			−0.395664	−	0.918395i	$-0.629485\pi$
$823$	−1.53764e7			−0.791328			−0.395664	+	0.918395i	$0.629485\pi$
$824$	5.72434e6	−	1.22516e7i	0.293702	−	0.628600i
$825$		0			0
$826$	−4.39466e6	−	1.10702e7i	−0.224117	−	0.564553i
$827$		−	8.95740e6i		−	0.455426i	−0.973728	−	0.227713i	$-0.926875\pi$
$827$		−	8.95740e6i		−	0.455426i	0.973728	−	0.227713i	$-0.0731248\pi$
$828$	4.92435e6	−	4.64118e6i	0.249616	−	0.235262i
$829$		−	2.95693e7i		−	1.49436i	−0.664623	−	0.747179i	$-0.731408\pi$
$829$		−	2.95693e7i		−	1.49436i	0.664623	−	0.747179i	$-0.268592\pi$
$830$		0			0
$831$	−2.26397e7			−1.13728
$832$	−6.20282e6	+	5.18876e6i	−0.310657	+	0.259869i
$833$	−3.70237e6			−0.184870
$834$	1.96257e7	−	7.79104e6i	0.977034	−	0.387865i
$835$		0			0
$836$	577100.	−	543914.i	0.0285585	−	0.0269163i
$837$			2.43784e7i			1.20279i
$838$	8.86097e6	+	2.23208e7i	0.435884	+	1.09800i
$839$	−1.26360e7			−0.619732			−0.309866	−	0.950780i	$-0.600284\pi$
$839$	−1.26360e7			−0.619732			−0.309866	+	0.950780i	$0.600284\pi$
$840$		0			0
$841$	1.96608e7			0.958540
$842$	1.07978e7	+	2.71997e7i	0.524874	+	1.32216i
$843$		−	1.89713e7i		−	0.919449i
$844$	−3.38889e6	−	3.59566e6i	−0.163758	−	0.173749i
$845$		0			0
$846$	−708544.	+	281279.i	−0.0340362	+	0.0135117i
$847$	9.30194e6			0.445518
$848$	2.35010e7	+	1.39264e6i	1.12227	+	0.0665042i
$849$	−1.04148e7			−0.495885
$850$		0			0
$851$		−	2.20080e7i		−	1.04173i
$852$	7.09979e6	+	7.53297e6i	0.335078	+	0.355523i
$853$			6.41059e6i			0.301665i	0.988559	+	0.150833i	$0.0481954\pi$
$853$			6.41059e6i			0.301665i	−0.988559	+	0.150833i	$0.951805\pi$
$854$	−2.94459e6	−	7.41744e6i	−0.138159	−	0.348024i
$855$		0			0
$856$	1.56441e7	+	7.30941e6i	0.729735	+	0.340956i
$857$	−1.57309e7			−0.731646			−0.365823	−	0.930684i	$-0.619212\pi$
$857$	−1.57309e7			−0.731646			−0.365823	+	0.930684i	$0.619212\pi$
$858$	762994.	+	1.92199e6i	0.0353837	+	0.0891317i
$859$		−	3.33475e7i		−	1.54199i	−0.636844	−	0.770993i	$-0.719760\pi$
$859$		−	3.33475e7i		−	1.54199i	0.636844	−	0.770993i	$-0.280240\pi$
$860$		0			0
$861$			2.07254e6i			0.0952787i
$862$	5.37591e6	−	2.13414e6i	0.246425	−	0.0978261i
$863$	−1.62060e6			−0.0740709			−0.0370355	−	0.999314i	$-0.511791\pi$
$863$	−1.62060e6			−0.0740709			−0.0370355	+	0.999314i	$0.511791\pi$
$864$	−2.16473e7	+	7.14275e6i	−0.986549	+	0.325522i
$865$		0			0
$866$	1.14882e7	−	4.56062e6i	0.520545	−	0.206647i
$867$			1.38938e7i			0.627732i
$868$	−9.52361e6	+	8.97596e6i	−0.429044	+	0.404372i
$869$		−	3.30751e6i		−	0.148577i
$870$		0			0
$871$	9.53820e6			0.426011
$872$	2.72391e7	+	1.27270e7i	1.21311	+	0.566805i
$873$	1.68308e6			0.0747430
$874$	574639.	+	1.44752e6i	0.0254458	+	0.0640983i
$875$		0			0
$876$	−1.82252e7	−	1.93372e7i	−0.802441	−	0.851400i
$877$		−	5.93461e6i		−	0.260551i	−0.991478	−	0.130276i	$-0.958414\pi$
$877$		−	5.93461e6i		−	0.260551i	0.991478	−	0.130276i	$-0.0415863\pi$
$878$	6.41617e6	−	2.54710e6i	0.280892	−	0.111509i
$879$	−4.17004e6			−0.182041
$880$		0			0
$881$	7.17940e6			0.311637			0.155818	−	0.987786i	$-0.450199\pi$
$881$	7.17940e6			0.311637			0.155818	+	0.987786i	$0.450199\pi$
$882$	−8.77726e6	+	3.48441e6i	−0.379916	+	0.150820i
$883$			5.72329e6i			0.247027i	0.992343	+	0.123513i	$0.0394162\pi$
$883$			5.72329e6i			0.247027i	−0.992343	+	0.123513i	$0.960584\pi$
$884$	−1.61093e6	−	1.70922e6i	−0.0693342	−	0.0735645i
$885$		0			0
$886$	−1.06388e6	−	2.67992e6i	−0.0455310	−	0.114693i
$887$	−1.46048e7			−0.623285			−0.311643	−	0.950199i	$-0.600879\pi$
$887$	−1.46048e7			−0.623285			−0.311643	+	0.950199i	$0.600879\pi$
$888$	−1.11602e7	+	2.38857e7i	−0.474939	+	1.01650i
$889$	6.26451e6			0.265847
$890$		0			0
$891$			1.20355e6i			0.0507889i
$892$	−1.90398e7	+	1.79449e7i	−0.801218	+	0.755144i
$893$		−	175454.i		−	0.00736266i
$894$	1.98331e7	−	7.87338e6i	0.829940	−	0.329471i
$895$		0			0
$896$	−1.07608e7	−	5.82677e6i	−0.447788	−	0.242470i
$897$	−4.06111e6			−0.168525
$898$	1.86170e7	−	7.39060e6i	0.770404	−	0.305836i
$899$		−	5.71272e6i		−	0.235745i
$900$		0			0
$901$			6.83751e6i			0.280599i
$902$	891287.	+	2.24516e6i	0.0364755	+	0.0918821i
$903$	1.12086e7			0.457437
$904$	1.33955e7	−	2.86699e7i	0.545177	−	1.16682i
$905$		0			0
$906$	7.36065e6	+	1.85415e7i	0.297917	+	0.750456i
$907$		−	5.43818e6i		−	0.219501i	−0.993959	−	0.109750i	$-0.964995\pi$
$907$		−	5.43818e6i		−	0.219501i	0.993959	−	0.109750i	$-0.0350051\pi$
$908$	−1.00080e6	−	1.06186e6i	−0.0402840	−	0.0427418i
$909$		−	1.26897e7i		−	0.509378i
$910$		0			0
$911$	−3.71033e7			−1.48121			−0.740605	−	0.671941i	$-0.765461\pi$
$911$	−3.71033e7			−1.48121			−0.740605	+	0.671941i	$0.765461\pi$
$912$	110365.	−	1.86242e6i	0.00439383	−	0.0741464i
$913$	9.46831e6			0.375920
$914$	5.60256e6	−	2.22411e6i	0.221830	−	0.0880626i
$915$		0			0
$916$	−1.39125e7	−	1.47614e7i	−0.547858	−	0.581284i
$917$		−	1.73740e7i		−	0.682302i
$918$	−2.44280e6	−	6.15343e6i	−0.0956711	−	0.240996i
$919$	−2.24895e7			−0.878398			−0.439199	−	0.898390i	$-0.644738\pi$
$919$	−2.24895e7			−0.878398			−0.439199	+	0.898390i	$0.644738\pi$
$920$		0			0
$921$	−3.84142e6			−0.149225
$922$	−1.44639e7	−	3.64346e7i	−0.560348	−	1.41152i
$923$			7.65021e6i			0.295576i
$924$	−2.27713e6	+	2.14618e6i	−0.0877419	+	0.0826963i
$925$		0			0
$926$	3.79083e7	−	1.50489e7i	1.45280	−	0.576737i
$927$	1.00180e7			0.382895
$928$	5.07272e6	−	1.67380e6i	0.193362	−	0.0638019i
$929$	2.80271e7			1.06547			0.532733	−	0.846283i	$-0.321165\pi$
$929$	2.80271e7			1.06547			0.532733	+	0.846283i	$0.321165\pi$
$930$		0			0
$931$		−	2.17348e6i		−	0.0821830i
$932$	5.71864e6	−	5.38979e6i	0.215652	−	0.203251i
$933$			1.18462e7i			0.445528i
$934$	−6.27294e6	−	1.58016e7i	−0.235290	−	0.592698i
$935$		0			0
$936$	−5.42767e6	−	2.53598e6i	−0.202499	−	0.0946142i
$937$	−62078.6			−0.00230990			−0.00115495	−	0.999999i	$-0.500368\pi$
$937$	−62078.6			−0.00230990			−0.00115495	+	0.999999i	$0.500368\pi$
$938$	5.32540e6	+	1.34147e7i	0.197626	+	0.497823i
$939$		−	3.49039e6i		−	0.129184i
$940$		0			0
$941$			4.45412e6i			0.163979i	0.996633	+	0.0819894i	$0.0261274\pi$
$941$			4.45412e6i			0.163979i	−0.996633	+	0.0819894i	$0.973873\pi$
$942$	8.50460e6	−	3.37617e6i	0.312267	−	0.123964i
$943$	−4.74397e6			−0.173725
$944$	−3.26021e7	−	1.93196e6i	−1.19074	−	0.0705616i
$945$		0			0
$946$	1.21421e7	−	4.82019e6i	0.441130	−	0.175120i
$947$		−	4.59793e7i		−	1.66605i	−0.553237	−	0.833024i	$-0.686608\pi$
$947$		−	4.59793e7i		−	1.66605i	0.553237	−	0.833024i	$-0.313392\pi$
$948$	−5.33699e6	−	5.66262e6i	−0.192875	−	0.204643i
$949$		−	1.96382e7i		−	0.707841i
$950$		0			0
$951$	−8.74385e6			−0.313510
$952$	1.50446e6	−	3.21995e6i	0.0538009	−	0.115148i
$953$	2.32064e7			0.827706			0.413853	−	0.910344i	$-0.364183\pi$
$953$	2.32064e7			0.827706			0.413853	+	0.910344i	$0.364183\pi$
$954$	6.43498e6	+	1.62098e7i	0.228916	+	0.576642i
$955$		0			0
$956$	−2.63513e7	+	2.48360e7i	−0.932518	+	0.878894i
$957$		−	1.36593e6i		−	0.0482112i
$958$	1.30255e7	−	5.17087e6i	0.458542	−	0.182033i
$959$	−794872.			−0.0279094
$960$		0			0
$961$	9.74779e6			0.340485
$962$	−1.81096e7	+	7.18919e6i	−0.630917	+	0.250462i
$963$			1.27919e7i			0.444499i
$964$	3.64265e7	−	3.43318e7i	1.26248	−	1.18988i
$965$		0			0
$966$	−2.26741e6	−	5.71164e6i	−0.0781786	−	0.196933i
$967$	5.33110e7			1.83337			0.916686	−	0.399607i	$-0.130853\pi$
$967$	5.33110e7			1.83337			0.916686	+	0.399607i	$0.130853\pi$
$968$	1.07970e7	−	2.31083e7i	0.370351	−	0.792648i
$969$	541863.			0.0185387
$970$		0			0
$971$		−	2.49744e7i		−	0.850056i	−0.905180	−	0.425028i	$-0.860264\pi$
$971$		−	2.49744e7i		−	0.850056i	0.905180	−	0.425028i	$-0.139736\pi$
$972$	−1.90459e7	−	2.02079e7i	−0.646600	−	0.686051i
$973$			2.36139e7i			0.799625i
$974$	−2.40872e7	+	9.56217e6i	−0.813558	+	0.322968i
$975$		0			0
$976$	−2.18446e7	−	1.29449e6i	−0.734041	−	0.0434984i
$977$	−3.97806e7			−1.33332			−0.666661	−	0.745361i	$-0.732277\pi$
$977$	−3.97806e7			−1.33332			−0.666661	+	0.745361i	$0.732277\pi$
$978$	−6.93497e6	+	2.75306e6i	−0.231845	+	0.0920382i
$979$		−	9.39495e6i		−	0.313284i
$980$		0			0
$981$			2.22730e7i			0.738936i
$982$	−1.71983e7	−	4.33227e7i	−0.569124	−	1.43363i
$983$	−3.80176e7			−1.25488			−0.627439	−	0.778666i	$-0.715897\pi$
$983$	−3.80176e7			−1.25488			−0.627439	+	0.778666i	$0.715897\pi$
$984$	5.14871e6	+	2.40564e6i	0.169516	+	0.0792034i
$985$		0			0
$986$	572434.	+	1.44197e6i	0.0187514	+	0.0472349i
$987$			692308.i			0.0226207i
$988$	1.00340e6	−	945702.i	0.0327026	−	0.0308221i
$989$			2.56560e7i			0.834061i
$990$		0			0
$991$	−4.34863e7			−1.40659			−0.703296	−	0.710897i	$-0.748289\pi$
$991$	−4.34863e7			−1.40659			−0.703296	+	0.710897i	$0.748289\pi$
$992$	1.12443e7	+	3.40776e7i	0.362787	+	1.09949i
$993$	2.40347e7			0.773510
$994$	−1.07594e7	+	4.27129e6i	−0.345400	+	0.137118i
$995$		0			0
$996$	1.62102e7	−	1.52780e7i	0.517774	−	0.488000i
$997$		−	9.27058e6i		−	0.295372i	−0.989034	−	0.147686i	$-0.952818\pi$
$997$		−	9.27058e6i		−	0.295372i	0.989034	−	0.147686i	$-0.0471825\pi$
$998$	9.38323e6	+	2.36364e7i	0.298213	+	0.751200i
$999$	−5.49223e7			−1.74115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.d.c.101.17	✓	20
4.3	odd	2		800.6.d.d.401.14		20
5.2	odd	4		200.6.f.d.149.26		40
5.3	odd	4		200.6.f.d.149.15		40
5.4	even	2		200.6.d.d.101.4	yes	20
8.3	odd	2		800.6.d.d.401.7		20
8.5	even	2	inner	200.6.d.c.101.18	yes	20
20.3	even	4		800.6.f.d.49.13		40
20.7	even	4		800.6.f.d.49.28		40
20.19	odd	2		800.6.d.b.401.7		20
40.3	even	4		800.6.f.d.49.27		40
40.13	odd	4		200.6.f.d.149.25		40
40.19	odd	2		800.6.d.b.401.14		20
40.27	even	4		800.6.f.d.49.14		40
40.29	even	2		200.6.d.d.101.3	yes	20
40.37	odd	4		200.6.f.d.149.16		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.17	✓	20	1.1	even	1	trivial
200.6.d.c.101.18	yes	20	8.5	even	2	inner
200.6.d.d.101.3	yes	20	40.29	even	2
200.6.d.d.101.4	yes	20	5.4	even	2
200.6.f.d.149.15		40	5.3	odd	4
200.6.f.d.149.16		40	40.37	odd	4
200.6.f.d.149.25		40	40.13	odd	4
200.6.f.d.149.26		40	5.2	odd	4
800.6.d.b.401.7		20	20.19	odd	2
800.6.d.b.401.14		20	40.19	odd	2
800.6.d.d.401.7		20	8.3	odd	2
800.6.d.d.401.14		20	4.3	odd	2
800.6.f.d.49.13		40	20.3	even	4
800.6.f.d.49.14		40	40.27	even	4
800.6.f.d.49.27		40	40.3	even	4
800.6.f.d.49.28		40	20.7	even	4

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(5.25771 - 2.08722i) q^{2} -10.4354i q^{3} +(23.2871 - 21.9480i) q^{4} +(-21.7810 - 54.8666i) q^{6} +66.0164 q^{7} +(76.6266 - 164.001i) q^{8} +134.101 q^{9} +O(q^{10})\)	\(q+(5.25771 - 2.08722i) q^{2} -10.4354i q^{3} +(23.2871 - 21.9480i) q^{4} +(-21.7810 - 54.8666i) q^{6} +66.0164 q^{7} +(76.6266 - 164.001i) q^{8} +134.101 q^{9} -141.942i q^{11} +(-229.037 - 243.011i) q^{12} -246.793i q^{13} +(347.095 - 137.790i) q^{14} +(60.5748 - 1022.21i) q^{16} +297.407 q^{17} +(705.067 - 279.898i) q^{18} +174.593i q^{19} -688.910i q^{21} +(-296.263 - 746.288i) q^{22} +1576.89 q^{23} +(-1711.43 - 799.633i) q^{24} +(-515.110 - 1297.57i) q^{26} -3935.22i q^{27} +(1537.33 - 1448.92i) q^{28} +922.162i q^{29} -6194.91 q^{31} +(-1815.08 - 5500.90i) q^{32} -1481.22 q^{33} +(1563.68 - 620.752i) q^{34} +(3122.83 - 2943.25i) q^{36} -13956.6i q^{37} +(364.413 + 917.960i) q^{38} -2575.40 q^{39} -3008.44 q^{41} +(-1437.90 - 3622.09i) q^{42} +16270.0i q^{43} +(-3115.33 - 3305.40i) q^{44} +(8290.83 - 3291.31i) q^{46} -1004.93 q^{47} +(-10667.2 - 632.125i) q^{48} -12448.8 q^{49} -3103.57i q^{51} +(-5416.60 - 5747.09i) q^{52} +22990.4i q^{53} +(-8213.66 - 20690.3i) q^{54} +(5058.61 - 10826.8i) q^{56} +1821.96 q^{57} +(1924.75 + 4848.46i) q^{58} -31893.8i q^{59} -21370.1i q^{61} +(-32571.1 + 12930.1i) q^{62} +8852.89 q^{63} +(-21024.7 - 25133.7i) q^{64} +(-7787.85 + 3091.63i) q^{66} +38648.6i q^{67} +(6925.73 - 6527.47i) q^{68} -16455.5i q^{69} -30998.5 q^{71} +(10275.7 - 21992.8i) q^{72} +79573.5 q^{73} +(-29130.4 - 73379.8i) q^{74} +(3831.96 + 4065.76i) q^{76} -9370.46i q^{77} +(-13540.7 + 5375.41i) q^{78} +23301.9 q^{79} -8479.17 q^{81} +(-15817.5 + 6279.25i) q^{82} +66705.7i q^{83} +(-15120.2 - 16042.7i) q^{84} +(33959.0 + 85543.0i) q^{86} +9623.18 q^{87} +(-23278.6 - 10876.5i) q^{88} +66188.9 q^{89} -16292.4i q^{91} +(36721.1 - 34609.5i) q^{92} +64646.7i q^{93} +(-5283.64 + 2097.51i) q^{94} +(-57404.4 + 18941.2i) q^{96} +12550.8 q^{97} +(-65452.4 + 25983.4i) q^{98} -19034.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) \) 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9	\( 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9} - 241 q^{12} - 424 q^{14} - 55 q^{16} - 3368 q^{18} + 1197 q^{22} - 7184 q^{23} + 9459 q^{24} + 9172 q^{26} - 13492 q^{28} + 7160 q^{31} + 7869 q^{32} - 2836 q^{33} - 9591 q^{34} + 14828 q^{36} + 21505 q^{38} + 22452 q^{39} - 5804 q^{41} - 14272 q^{42} - 11593 q^{44} - 37612 q^{46} + 44180 q^{47} + 66571 q^{48} + 62652 q^{49} + 6136 q^{52} + 88947 q^{54} - 36908 q^{56} + 43696 q^{57} - 84012 q^{58} + 87460 q^{62} - 1240 q^{63} + 115177 q^{64} + 131439 q^{66} - 143341 q^{68} - 7724 q^{71} - 25772 q^{72} - 105136 q^{73} + 2112 q^{74} + 55951 q^{76} - 10948 q^{78} - 7780 q^{79} + 96984 q^{81} + 117501 q^{82} - 97556 q^{84} - 65986 q^{86} - 106188 q^{87} - 122597 q^{88} - 3160 q^{89} + 88908 q^{92} - 58540 q^{94} + 57791 q^{96} - 73688 q^{97} + 164655 q^{98}+O(q^{100}) \) 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9 - 241 * q^12 - 424 * q^14 - 55 * q^16 - 3368 * q^18 + 1197 * q^22 - 7184 * q^23 + 9459 * q^24 + 9172 * q^26 - 13492 * q^28 + 7160 * q^31 + 7869 * q^32 - 2836 * q^33 - 9591 * q^34 + 14828 * q^36 + 21505 * q^38 + 22452 * q^39 - 5804 * q^41 - 14272 * q^42 - 11593 * q^44 - 37612 * q^46 + 44180 * q^47 + 66571 * q^48 + 62652 * q^49 + 6136 * q^52 + 88947 * q^54 - 36908 * q^56 + 43696 * q^57 - 84012 * q^58 + 87460 * q^62 - 1240 * q^63 + 115177 * q^64 + 131439 * q^66 - 143341 * q^68 - 7724 * q^71 - 25772 * q^72 - 105136 * q^73 + 2112 * q^74 + 55951 * q^76 - 10948 * q^78 - 7780 * q^79 + 96984 * q^81 + 117501 * q^82 - 97556 * q^84 - 65986 * q^86 - 106188 * q^87 - 122597 * q^88 - 3160 * q^89 + 88908 * q^92 - 58540 * q^94 + 57791 * q^96 - 73688 * q^97 + 164655 * q^98

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