LMFDB - Embedded newform 200.6.d.d.101.3

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			101.3
Root			$-5.25771 + 2.08722i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.d.101.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.25771 - 2.08722i) q^{2} -10.4354i q^{3} +(23.2871 + 21.9480i) q^{4} +(-21.7810 + 54.8666i) q^{6} -66.0164 q^{7} +(-76.6266 - 164.001i) q^{8} +134.101 q^{9} +141.942i q^{11} +(229.037 - 243.011i) q^{12} -246.793i q^{13} +(347.095 + 137.790i) q^{14} +(60.5748 + 1022.21i) q^{16} -297.407 q^{17} +(-705.067 - 279.898i) q^{18} -174.593i q^{19} +688.910i q^{21} +(296.263 - 746.288i) q^{22} -1576.89 q^{23} +(-1711.43 + 799.633i) q^{24} +(-515.110 + 1297.57i) q^{26} -3935.22i q^{27} +(-1537.33 - 1448.92i) q^{28} -922.162i q^{29} -6194.91 q^{31} +(1815.08 - 5500.90i) q^{32} +1481.22 q^{33} +(1563.68 + 620.752i) q^{34} +(3122.83 + 2943.25i) q^{36} -13956.6i q^{37} +(-364.413 + 917.960i) q^{38} -2575.40 q^{39} -3008.44 q^{41} +(1437.90 - 3622.09i) q^{42} +16270.0i q^{43} +(-3115.33 + 3305.40i) q^{44} +(8290.83 + 3291.31i) q^{46} +1004.93 q^{47} +(10667.2 - 632.125i) q^{48} -12448.8 q^{49} +3103.57i q^{51} +(5416.60 - 5747.09i) q^{52} +22990.4i q^{53} +(-8213.66 + 20690.3i) q^{54} +(5058.61 + 10826.8i) q^{56} -1821.96 q^{57} +(-1924.75 + 4848.46i) q^{58} +31893.8i q^{59} +21370.1i q^{61} +(32571.1 + 12930.1i) q^{62} -8852.89 q^{63} +(-21024.7 + 25133.7i) q^{64} +(-7787.85 - 3091.63i) q^{66} +38648.6i q^{67} +(-6925.73 - 6527.47i) q^{68} +16455.5i q^{69} -30998.5 q^{71} +(-10275.7 - 21992.8i) q^{72} -79573.5 q^{73} +(-29130.4 + 73379.8i) q^{74} +(3831.96 - 4065.76i) q^{76} -9370.46i q^{77} +(13540.7 + 5375.41i) q^{78} +23301.9 q^{79} -8479.17 q^{81} +(15817.5 + 6279.25i) q^{82} +66705.7i q^{83} +(-15120.2 + 16042.7i) q^{84} +(33959.0 - 85543.0i) q^{86} -9623.18 q^{87} +(23278.6 - 10876.5i) q^{88} +66188.9 q^{89} +16292.4i q^{91} +(-36721.1 - 34609.5i) q^{92} +64646.7i q^{93} +(-5283.64 - 2097.51i) q^{94} +(-57404.4 - 18941.2i) q^{96} -12550.8 q^{97} +(65452.4 + 25983.4i) q^{98} +19034.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + q^{4} + 33 q^{6} + 196 q^{7} + 391 q^{8} - 1620 q^{9} + 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}+ \cdots - 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

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	$-0.581947\pi$
$7$	−66.0164			−0.509221			−0.254611	+	0.967044i	$0.581947\pi$
$8$	−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	$0.0565898\pi$
$11$			141.942i			0.353694i	−0.984238	+	0.176847i	$0.943410\pi$
$12$	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	$-0.539827\pi$
$17$	−297.407			−0.249591			−0.124795	+	0.992182i	$0.539827\pi$
$18$	−705.067	−	279.898i	−0.512919	−	0.203619i
$19$		−	174.593i		−	0.110954i	−0.998460	−	0.0554770i	$-0.982332\pi$
$19$		−	174.593i		−	0.110954i	0.998460	−	0.0554770i	$-0.0176680\pi$
$20$		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	$-0.600590\pi$
$23$	−1576.89			−0.621558			−0.310779	+	0.950482i	$0.600590\pi$
$24$	−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	$-0.967537\pi$
$29$		−	922.162i		−	0.203616i	0.994804	−	0.101808i	$-0.0324628\pi$
$30$		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	$-0.489437\pi$
$47$	1004.93			0.0663578			0.0331789	+	0.999449i	$0.489437\pi$
$48$	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	$0.203408\pi$
$59$			31893.8i			1.19282i	−0.802678	+	0.596412i	$0.796592\pi$
$60$		0			0
$61$			21370.1i			0.735328i	0.929959	+	0.367664i	$0.119842\pi$
$61$			21370.1i			0.735328i	−0.929959	+	0.367664i	$0.880158\pi$
$62$	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	$-0.838377\pi$
$73$	−79573.5			−1.74768			−0.873838	+	0.486217i	$0.838377\pi$
$74$	−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	$-0.521572\pi$
$97$	−12550.8			−0.135439			−0.0677194	+	0.997704i	$0.521572\pi$
$98$	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	$0.152693\pi$
$101$			94627.3i			0.923024i	−0.887134	+	0.461512i	$0.847307\pi$
$102$	6477.83	−	16317.7i	0.0616494	−	0.155295i
$103$	−74704.4			−0.693830			−0.346915	−	0.937897i	$-0.612771\pi$
$103$	−74704.4			−0.693830			−0.346915	+	0.937897i	$0.612771\pi$
$104$	−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	$-0.766509\pi$
$109$		−	166091.i		−	1.33900i	0.742814	−	0.669498i	$-0.233491\pi$
$110$		0			0
$111$	−145643.			−1.12198
$112$	−3998.93	−	67482.4i	−0.0301230	−	0.508329i
$113$	−174815.			−1.28790			−0.643951	−	0.765067i	$-0.722706\pi$
$113$	−174815.			−1.28790			−0.643951	+	0.765067i	$0.722706\pi$
$114$	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	$-0.584063\pi$
$127$	−94893.2			−0.522067			−0.261033	+	0.965330i	$0.584063\pi$
$128$	163001.	−	88262.5i	0.879360	−	0.476158i
$129$	169785.			0.898307
$130$		0			0
$131$			263177.i			1.33989i	0.742409	+	0.669947i	$0.233683\pi$
$131$			263177.i			1.33989i	−0.742409	+	0.669947i	$0.766317\pi$
$132$	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	$-0.491276\pi$
$137$	12040.5			0.0548080			0.0274040	+	0.999624i	$0.491276\pi$
$138$	34346.3	−	86518.5i	0.153526	−	0.386733i
$139$		−	357698.i		−	1.57029i	−0.619312	−	0.785145i	$-0.712588\pi$
$139$		−	357698.i		−	1.57029i	0.619312	−	0.785145i	$-0.287412\pi$
$140$		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	$-0.767604\pi$
$149$		−	361479.i		−	1.33388i	0.745111	−	0.666940i	$-0.232396\pi$
$150$		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	$-0.944282\pi$
$167$	−709796.			−1.96944			−0.984719	+	0.174152i	$0.944282\pi$
$168$	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	$-0.899618\pi$
$179$		−	265918.i		−	0.620318i	0.950685	−	0.310159i	$-0.100382\pi$
$180$		0			0
$181$		−	836091.i		−	1.89696i	−0.316843	−	0.948478i	$-0.602623\pi$
$181$		−	836091.i		−	1.89696i	0.316843	−	0.948478i	$-0.397377\pi$
$182$	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	$-0.734312\pi$
$193$	−694883.			−1.34282			−0.671411	+	0.741085i	$0.734312\pi$
$194$	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	$0.0380903\pi$
$211$			154406.i			0.238758i	−0.992849	+	0.119379i	$0.961910\pi$
$212$	−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	$-0.314438\pi$
$223$	817613.			1.10100			0.550498	+	0.834836i	$0.314438\pi$
$224$	−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	$0.130777\pi$
$229$			633888.i			0.798774i	−0.916783	+	0.399387i	$0.869223\pi$
$230$		0			0
$231$	−97785.0			−0.120571
$232$	−151236.	+	70662.1i	−0.184474	+	0.0861920i
$233$	−245572.			−0.296339			−0.148169	−	0.988962i	$-0.547338\pi$
$233$	−245572.			−0.296339			−0.148169	+	0.988962i	$0.547338\pi$
$234$	−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	$0.259308\pi$
$251$			1.45223e6i			1.45496i	−0.686130	+	0.727479i	$0.740692\pi$
$252$	−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	$-0.209458\pi$
$257$	1.67551e6			1.58240			0.791198	+	0.611560i	$0.209458\pi$
$258$	−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	$-0.356512\pi$
$263$	977406.			0.871336			0.435668	+	0.900107i	$0.356512\pi$
$264$	−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	$-0.997890\pi$
$269$		−	15731.4i		−	0.0132552i	0.999978	−	0.00662760i	$-0.00210964\pi$
$270$		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	$-0.530761\pi$
$313$	−334474.			−0.192975			−0.0964877	+	0.995334i	$0.530761\pi$
$314$	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	$-0.803937\pi$
$331$		−	2.30318e6i		−	1.15547i	0.816225	−	0.577734i	$-0.196063\pi$
$332$	−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	$-0.446405\pi$
$337$	698751.			0.335156			0.167578	+	0.985859i	$0.446405\pi$
$338$	−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	$-0.991505\pi$
$349$		−	121442.i		−	0.0533711i	0.999644	−	0.0266855i	$-0.00849528\pi$
$350$		0			0
$351$	−971186.			−0.420760
$352$	780806.	+	257635.i	0.335882	+	0.110828i
$353$	56609.0			0.0241796			0.0120898	−	0.999927i	$-0.496152\pi$
$353$	56609.0			0.0241796			0.0120898	+	0.999927i	$0.496152\pi$
$354$	−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	$-0.481233\pi$
$367$	304081.			0.117849			0.0589243	+	0.998262i	$0.481233\pi$
$368$	−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	$-0.956573\pi$
$379$		−	760659.i		−	0.272014i	0.990708	−	0.136007i	$-0.0434270\pi$
$380$		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	$-0.397917\pi$
$383$	1.80993e6			0.630470			0.315235	+	0.949014i	$0.397917\pi$
$384$	−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	$-0.755591\pi$
$389$		−	4.14597e6i		−	1.38916i	0.719416	−	0.694579i	$-0.244409\pi$
$390$		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	$-0.798861\pi$
$419$		−	4.24535e6i		−	1.18135i	0.806909	−	0.590675i	$-0.201139\pi$
$420$		0			0
$421$		−	5.17330e6i		−	1.42253i	−0.702922	−	0.711267i	$-0.748122\pi$
$421$		−	5.17330e6i		−	1.42253i	0.702922	−	0.711267i	$-0.251878\pi$
$422$	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	$-0.590345\pi$
$433$	−2.18503e6			−0.560063			−0.280031	+	0.959991i	$0.590345\pi$
$434$	−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	$-0.538076\pi$
$457$	−1.06559e6			−0.238671			−0.119335	+	0.992854i	$0.538076\pi$
$458$	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	$0.274477\pi$
$461$			6.92975e6i			1.51868i	−0.650696	+	0.759339i	$0.725523\pi$
$462$	514125.	+	204098.i	0.112063	+	0.0444871i
$463$	−7.21004e6			−1.56310			−0.781548	−	0.623845i	$-0.785569\pi$
$463$	−7.21004e6			−1.56310			−0.781548	+	0.623845i	$0.785569\pi$
$464$	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	$-0.355807\pi$
$487$	4.58130e6			0.875320			0.437660	+	0.899141i	$0.355807\pi$
$488$	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	$0.280359\pi$
$491$			8.23983e6i			1.54246i	−0.636555	+	0.771231i	$0.719641\pi$
$492$	−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	$-0.867580\pi$
$499$		−	4.49557e6i		−	0.808228i	0.914709	−	0.404114i	$-0.132420\pi$
$500$		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	$-0.686951\pi$
$503$	−6.28876e6			−1.10827			−0.554134	+	0.832427i	$0.686951\pi$
$504$	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	$0.249771\pi$
$509$			8.26032e6i			1.41320i	−0.707615	+	0.706598i	$0.750229\pi$
$510$		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	$0.0436285\pi$
$541$			1.86030e6i			0.273268i	−0.990622	+	0.136634i	$0.956372\pi$
$542$	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	$-0.774409\pi$
$571$		−	1.01416e7i		−	1.30172i	0.759198	−	0.650860i	$-0.225591\pi$
$572$	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	$-0.576533\pi$
$577$	−3.80870e6			−0.476253			−0.238126	+	0.971234i	$0.576533\pi$
$578$	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	$-0.231868\pi$
$593$	1.27800e7			1.49243			0.746216	+	0.665704i	$0.231868\pi$
$594$	−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	$-0.531790\pi$
$607$	−1.81019e6			−0.199413			−0.0997065	+	0.995017i	$0.531790\pi$
$608$	−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	$-0.613499\pi$
$617$	−6.60152e6			−0.698122			−0.349061	+	0.937100i	$0.613499\pi$
$618$	1.62714e6	−	4.09877e6i	0.171377	−	0.431701i
$619$		−	8.83255e6i		−	0.926530i	−0.886220	−	0.463265i	$-0.846678\pi$
$619$		−	8.83255e6i		−	0.926530i	0.886220	−	0.463265i	$-0.153322\pi$
$620$		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	$-0.268890\pi$
$647$	1.41387e7			1.32785			0.663924	+	0.747800i	$0.268890\pi$
$648$	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	$0.0746043\pi$
$659$			5.17814e6i			0.464473i	−0.972659	+	0.232236i	$0.925396\pi$
$660$		0			0
$661$		−	1.15802e7i		−	1.03089i	−0.856923	−	0.515444i	$-0.827627\pi$
$661$		−	1.15802e7i		−	1.03089i	0.856923	−	0.515444i	$-0.172373\pi$
$662$	−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	$-0.546791\pi$
$673$	−3.44202e6			−0.292938			−0.146469	+	0.989215i	$0.546791\pi$
$674$	−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	$-0.905087\pi$
$691$		−	7.37470e6i		−	0.587556i	0.955874	−	0.293778i	$-0.0949127\pi$
$692$	−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	$0.313155\pi$
$701$			2.16654e7i			1.66522i	−0.553857	+	0.832612i	$0.686845\pi$
$702$	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	$-0.934573\pi$
$709$		−	5.46373e6i		−	0.408201i	0.978950	−	0.204100i	$-0.0654269\pi$
$710$		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	$-0.539836\pi$
$727$	−3.55756e6			−0.249641			−0.124821	+	0.992179i	$0.539836\pi$
$728$	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	$-0.871599\pi$
$739$		−	1.16551e7i		−	0.785063i	0.919739	−	0.392531i	$-0.128401\pi$
$740$		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	$-0.202792\pi$
$743$	2.41917e7			1.60766			0.803829	+	0.594860i	$0.202792\pi$
$744$	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	$-0.973211\pi$
$811$		−	3.14901e6i		−	0.168121i	0.996461	−	0.0840604i	$-0.0267889\pi$
$812$	−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	$-0.827864\pi$
$821$		−	1.98853e7i		−	1.02961i	0.857306	−	0.514807i	$-0.172136\pi$
$822$	−262255.	+	660623.i	−0.0135377	+	0.0341015i
$823$	1.53764e7			0.791328			0.395664	−	0.918395i	$-0.370515\pi$
$823$	1.53764e7			0.791328			0.395664	+	0.918395i	$0.370515\pi$
$824$	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	$0.268592\pi$
$829$			2.95693e7i			1.49436i	−0.664623	+	0.747179i	$0.731408\pi$
$830$		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	$-0.380788\pi$
$857$	1.57309e7			0.731646			0.365823	+	0.930684i	$0.380788\pi$
$858$	−762994.	+	1.92199e6i	−0.0353837	+	0.0891317i
$859$			3.33475e7i			1.54199i	0.636844	+	0.770993i	$0.280240\pi$
$859$			3.33475e7i			1.54199i	−0.636844	+	0.770993i	$0.719760\pi$
$860$		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	$-0.488209\pi$
$863$	1.62060e6			0.0740709			0.0370355	+	0.999314i	$0.488209\pi$
$864$	−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	$-0.399121\pi$
$887$	1.46048e7			0.623285			0.311643	+	0.950199i	$0.399121\pi$
$888$	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	$-0.499632\pi$
$937$	62078.6			0.00230990			0.00115495	+	0.999999i	$0.499632\pi$
$938$	−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	$-0.973873\pi$
$941$		−	4.45412e6i		−	0.163979i	0.996633	−	0.0819894i	$-0.0261274\pi$
$942$	−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	$-0.635817\pi$
$953$	−2.32064e7			−0.827706			−0.413853	+	0.910344i	$0.635817\pi$
$954$	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	$-0.869147\pi$
$967$	−5.33110e7			−1.83337			−0.916686	+	0.399607i	$0.869147\pi$
$968$	−1.07970e7	−	2.31083e7i	−0.370351	−	0.792648i
$969$	541863.			0.0185387
$970$		0			0
$971$			2.49744e7i			0.850056i	0.905180	+	0.425028i	$0.139736\pi$
$971$			2.49744e7i			0.850056i	−0.905180	+	0.425028i	$0.860264\pi$
$972$	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	$-0.267723\pi$
$977$	3.97806e7			1.33332			0.666661	+	0.745361i	$0.267723\pi$
$978$	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	$-0.284103\pi$
$983$	3.80176e7			1.25488			0.627439	+	0.778666i	$0.284103\pi$
$984$	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.d.101.3	yes	20
4.3	odd	2		800.6.d.b.401.14		20
5.2	odd	4		200.6.f.d.149.25		40
5.3	odd	4		200.6.f.d.149.16		40
5.4	even	2		200.6.d.c.101.18	yes	20
8.3	odd	2		800.6.d.b.401.7		20
8.5	even	2	inner	200.6.d.d.101.4	yes	20
20.3	even	4		800.6.f.d.49.14		40
20.7	even	4		800.6.f.d.49.27		40
20.19	odd	2		800.6.d.d.401.7		20
40.3	even	4		800.6.f.d.49.28		40
40.13	odd	4		200.6.f.d.149.26		40
40.19	odd	2		800.6.d.d.401.14		20
40.27	even	4		800.6.f.d.49.13		40
40.29	even	2		200.6.d.c.101.17	✓	20
40.37	odd	4		200.6.f.d.149.15		40

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

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