LMFDB - Embedded newform 200.6.d.c.101.9

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			101.9
Root			$0.858917 + 5.59127i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.c.101.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.858917 - 5.59127i) q^{2} -2.58812i q^{3} +(-30.5245 + 9.60487i) q^{4} +(-14.4709 + 2.22298i) q^{6} -27.4015 q^{7} +(79.9214 + 162.421i) q^{8} +236.302 q^{9} +O(q^{10})$	\(q+(-0.858917 - 5.59127i) q^{2} -2.58812i q^{3} +(-30.5245 + 9.60487i) q^{4} +(-14.4709 + 2.22298i) q^{6} -27.4015 q^{7} +(79.9214 + 162.421i) q^{8} +236.302 q^{9} -313.336i q^{11} +(24.8585 + 79.0011i) q^{12} -627.354i q^{13} +(23.5356 + 153.209i) q^{14} +(839.493 - 586.368i) q^{16} -1598.17 q^{17} +(-202.964 - 1321.23i) q^{18} -219.049i q^{19} +70.9184i q^{21} +(-1751.95 + 269.130i) q^{22} -1007.11 q^{23} +(420.365 - 206.846i) q^{24} +(-3507.70 + 538.845i) q^{26} -1240.49i q^{27} +(836.419 - 263.188i) q^{28} +6140.83i q^{29} -2244.61 q^{31} +(-3999.60 - 4190.19i) q^{32} -810.951 q^{33} +(1372.70 + 8935.80i) q^{34} +(-7212.99 + 2269.65i) q^{36} +3591.40i q^{37} +(-1224.76 + 188.145i) q^{38} -1623.67 q^{39} -608.697 q^{41} +(396.524 - 60.9130i) q^{42} -11410.6i q^{43} +(3009.55 + 9564.44i) q^{44} +(865.025 + 5631.03i) q^{46} -16909.4 q^{47} +(-1517.59 - 2172.71i) q^{48} -16056.2 q^{49} +4136.26i q^{51} +(6025.66 + 19149.7i) q^{52} -12783.9i q^{53} +(-6935.91 + 1065.48i) q^{54} +(-2189.97 - 4450.58i) q^{56} -566.923 q^{57} +(34335.0 - 5274.47i) q^{58} +29917.1i q^{59} +17985.1i q^{61} +(1927.93 + 12550.2i) q^{62} -6475.03 q^{63} +(-19993.1 + 25961.8i) q^{64} +(696.540 + 4534.24i) q^{66} +48881.2i q^{67} +(48783.4 - 15350.2i) q^{68} +2606.52i q^{69} +37296.0 q^{71} +(18885.6 + 38380.3i) q^{72} -26092.7 q^{73} +(20080.5 - 3084.71i) q^{74} +(2103.93 + 6686.35i) q^{76} +8585.89i q^{77} +(1394.60 + 9078.35i) q^{78} -77636.5 q^{79} +54210.8 q^{81} +(522.820 + 3403.38i) q^{82} -58419.8i q^{83} +(-681.162 - 2164.75i) q^{84} +(-63799.8 + 9800.78i) q^{86} +15893.2 q^{87} +(50892.4 - 25042.3i) q^{88} -81513.8 q^{89} +17190.5i q^{91} +(30741.6 - 9673.17i) q^{92} +5809.30i q^{93} +(14523.7 + 94544.7i) q^{94} +(-10844.7 + 10351.4i) q^{96} -28396.6 q^{97} +(13790.9 + 89774.2i) q^{98} -74041.9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.858917	−	5.59127i	−0.151837	−	0.988406i
$2$	−0.858917	−	5.59127i	−0.151837	−	0.988406i
$3$		−	2.58812i		−	0.166028i	−0.996548	−	0.0830139i	$-0.973545\pi$
$3$		−	2.58812i		−	0.166028i	0.996548	−	0.0830139i	$-0.0264546\pi$
$4$	−30.5245	+	9.60487i	−0.953891	+	0.300152i
$5$		0			0
$5$		0			0
$6$	−14.4709	+	2.22298i	−0.164103	+	0.0252091i
$7$	−27.4015			−0.211363			−0.105682	−	0.994400i	$-0.533702\pi$
$7$	−27.4015			−0.211363			−0.105682	+	0.994400i	$0.533702\pi$
$8$	79.9214	+	162.421i	0.441508	+	0.897257i
$9$	236.302			0.972435
$10$		0			0
$11$		−	313.336i		−	0.780780i	−0.920650	−	0.390390i	$-0.872340\pi$
$11$		−	313.336i		−	0.780780i	0.920650	−	0.390390i	$-0.127660\pi$
$12$	24.8585	+	79.0011i	0.0498336	+	0.158373i
$13$		−	627.354i		−	1.02957i	−0.857320	−	0.514783i	$-0.827872\pi$
$13$		−	627.354i		−	1.02957i	0.857320	−	0.514783i	$-0.172128\pi$
$14$	23.5356	+	153.209i	0.0320927	+	0.208913i
$15$		0			0
$16$	839.493	−	586.368i	0.819817	−	0.572625i
$17$	−1598.17			−1.34122			−0.670611	−	0.741809i	$-0.733968\pi$
$17$	−1598.17			−1.34122			−0.670611	+	0.741809i	$0.733968\pi$
$18$	−202.964	−	1321.23i	−0.147651	−	0.961160i
$19$		−	219.049i		−	0.139205i	−0.997575	−	0.0696027i	$-0.977827\pi$
$19$		−	219.049i		−	0.139205i	0.997575	−	0.0696027i	$-0.0221732\pi$
$20$		0			0
$21$			70.9184i			0.0350922i
$22$	−1751.95	+	269.130i	−0.771728	+	0.118551i
$23$	−1007.11			−0.396970			−0.198485	−	0.980104i	$-0.563602\pi$
$23$	−1007.11			−0.396970			−0.198485	+	0.980104i	$0.563602\pi$
$24$	420.365	−	206.846i	0.148970	−	0.0733026i
$25$		0			0
$26$	−3507.70	+	538.845i	−1.01763	+	0.156326i
$27$		−	1240.49i		−	0.327479i
$28$	836.419	−	263.188i	0.201618	−	0.0634412i
$29$			6140.83i			1.35591i	0.735102	+	0.677957i	$0.237134\pi$
$29$			6140.83i			1.35591i	−0.735102	+	0.677957i	$0.762866\pi$
$30$		0			0
$31$	−2244.61			−0.419504			−0.209752	−	0.977755i	$-0.567266\pi$
$31$	−2244.61			−0.419504			−0.209752	+	0.977755i	$0.567266\pi$
$32$	−3999.60	−	4190.19i	−0.690464	−	0.723367i
$33$	−810.951			−0.129631
$34$	1372.70	+	8935.80i	0.203647	+	1.32567i
$35$		0			0
$36$	−7212.99	+	2269.65i	−0.927597	+	0.291878i
$37$			3591.40i			0.431280i	0.976473	+	0.215640i	$0.0691837\pi$
$37$			3591.40i			0.431280i	−0.976473	+	0.215640i	$0.930816\pi$
$38$	−1224.76	+	188.145i	−0.137591	+	0.0211365i
$39$	−1623.67			−0.170937
$40$		0			0
$41$	−608.697			−0.0565511			−0.0282756	−	0.999600i	$-0.509002\pi$
$41$	−608.697			−0.0565511			−0.0282756	+	0.999600i	$0.509002\pi$
$42$	396.524	−	60.9130i	0.0346853	−	0.00532828i
$43$		−	11410.6i		−	0.941105i	−0.882372	−	0.470553i	$-0.844055\pi$
$43$		−	11410.6i		−	0.941105i	0.882372	−	0.470553i	$-0.155945\pi$
$44$	3009.55	+	9564.44i	0.234353	+	0.744780i
$45$		0			0
$46$	865.025	+	5631.03i	0.0602746	+	0.392367i
$47$	−16909.4			−1.11656			−0.558280	−	0.829652i	$-0.688539\pi$
$47$	−16909.4			−1.11656			−0.558280	+	0.829652i	$0.688539\pi$
$48$	−1517.59	−	2172.71i	−0.0950717	−	0.136113i
$49$	−16056.2			−0.955326
$50$		0			0
$51$			4136.26i			0.222680i
$52$	6025.66	+	19149.7i	0.309027	+	0.982095i
$53$		−	12783.9i		−	0.625134i	−0.949896	−	0.312567i	$-0.898811\pi$
$53$		−	12783.9i		−	0.625134i	0.949896	−	0.312567i	$-0.101189\pi$
$54$	−6935.91	+	1065.48i	−0.323682	+	0.0497233i
$55$		0			0
$56$	−2189.97	−	4450.58i	−0.0933185	−	0.189647i
$57$	−566.923			−0.0231120
$58$	34335.0	−	5274.47i	1.34019	−	0.205877i
$59$			29917.1i			1.11889i	0.828866	+	0.559447i	$0.188986\pi$
$59$			29917.1i			1.11889i	−0.828866	+	0.559447i	$0.811014\pi$
$60$		0			0
$61$			17985.1i			0.618852i	0.950923	+	0.309426i	$0.100137\pi$
$61$			17985.1i			0.618852i	−0.950923	+	0.309426i	$0.899863\pi$
$62$	1927.93	+	12550.2i	0.0636960	+	0.414640i
$63$	−6475.03			−0.205537
$64$	−19993.1	+	25961.8i	−0.610142	+	0.792292i
$65$		0			0
$66$	696.540	+	4534.24i	0.0196828	+	0.128128i
$67$			48881.2i			1.33032i	0.746703	+	0.665158i	$0.231636\pi$
$67$			48881.2i			1.33032i	−0.746703	+	0.665158i	$0.768364\pi$
$68$	48783.4	−	15350.2i	1.27938	−	0.402571i
$69$			2606.52i			0.0659081i
$70$		0			0
$71$	37296.0			0.878044			0.439022	−	0.898476i	$-0.355325\pi$
$71$	37296.0			0.878044			0.439022	+	0.898476i	$0.355325\pi$
$72$	18885.6	+	38380.3i	0.429337	+	0.872524i
$73$	−26092.7			−0.573075			−0.286538	−	0.958069i	$-0.592504\pi$
$73$	−26092.7			−0.573075			−0.286538	+	0.958069i	$0.592504\pi$
$74$	20080.5	−	3084.71i	0.426279	−	0.0654840i
$75$		0			0
$76$	2103.93	+	6686.35i	0.0417828	+	0.132787i
$77$			8585.89i			0.165028i
$78$	1394.60	+	9078.35i	0.0259544	+	0.168955i
$79$	−77636.5			−1.39958			−0.699791	−	0.714348i	$-0.746723\pi$
$79$	−77636.5			−1.39958			−0.699791	+	0.714348i	$0.746723\pi$
$80$		0			0
$81$	54210.8			0.918064
$82$	522.820	+	3403.38i	0.00858653	+	0.0558954i
$83$		−	58419.8i		−	0.930818i	−0.885096	−	0.465409i	$-0.845907\pi$
$83$		−	58419.8i		−	0.930818i	0.885096	−	0.465409i	$-0.154093\pi$
$84$	−681.162	−	2164.75i	−0.0105330	−	0.0334741i
$85$		0			0
$86$	−63799.8	+	9800.78i	−0.930194	+	0.142894i
$87$	15893.2			0.225120
$88$	50892.4	−	25042.3i	0.700561	−	0.344720i
$89$	−81513.8			−1.09083			−0.545414	−	0.838167i	$-0.683627\pi$
$89$	−81513.8			−1.09083			−0.545414	+	0.838167i	$0.683627\pi$
$90$		0			0
$91$			17190.5i			0.217613i
$92$	30741.6	−	9673.17i	0.378666	−	0.119151i
$93$			5809.30i			0.0696493i
$94$	14523.7	+	94544.7i	0.169535	+	1.10361i
$95$		0			0
$96$	−10844.7	+	10351.4i	−0.120099	+	0.114636i
$97$	−28396.6			−0.306434			−0.153217	−	0.988193i	$-0.548963\pi$
$97$	−28396.6			−0.306434			−0.153217	+	0.988193i	$0.548963\pi$
$98$	13790.9	+	89774.2i	0.145053	+	0.944249i
$99$		−	74041.9i		−	0.759258i
$100$		0			0
$101$			136025.i			1.32683i	0.748253	+	0.663413i	$0.230893\pi$
$101$			136025.i			1.32683i	−0.748253	+	0.663413i	$0.769107\pi$
$102$	23126.9	−	3552.70i	0.220099	−	0.0338110i
$103$	−166600.			−1.54733			−0.773665	−	0.633595i	$-0.781579\pi$
$103$	−166600.			−1.54733			−0.773665	+	0.633595i	$0.781579\pi$
$104$	101895.	−	50139.0i	0.923786	−	0.454562i
$105$		0			0
$106$	−71478.1	+	10980.3i	−0.617886	+	0.0949182i
$107$		−	67774.4i		−	0.572277i	−0.958188	−	0.286138i	$-0.907628\pi$
$107$		−	67774.4i		−	0.572277i	0.958188	−	0.286138i	$-0.0923717\pi$
$108$	11914.7	+	37865.3i	0.0982936	+	0.312379i
$109$			55567.6i			0.447977i	0.974592	+	0.223988i	$0.0719077\pi$
$109$			55567.6i			0.447977i	−0.974592	+	0.223988i	$0.928092\pi$
$110$		0			0
$111$	9294.96			0.0716044
$112$	−23003.4	+	16067.4i	−0.173279	+	0.121032i
$113$	−170497.			−1.25609			−0.628045	−	0.778177i	$-0.716145\pi$
$113$	−170497.			−1.25609			−0.628045	+	0.778177i	$0.716145\pi$
$114$	486.940	+	3169.82i	0.00350924	+	0.0228440i
$115$		0			0
$116$	−58981.9	−	187446.i	−0.406981	−	1.29339i
$117$		−	148245.i		−	1.00119i
$118$	167274.	−	25696.3i	1.10592	−	0.169889i
$119$	43792.3			0.283485
$120$		0			0
$121$	62871.4			0.390382
$122$	100559.	−	15447.7i	0.611677	−	0.0939644i
$123$			1575.38i			0.00938906i
$124$	68515.5	−	21559.1i	0.400161	−	0.125915i
$125$		0			0
$126$	5561.51	+	36203.6i	0.0312080	+	0.203154i
$127$	−313764.			−1.72621			−0.863106	−	0.505022i	$-0.831484\pi$
$127$	−313764.			−1.72621			−0.863106	+	0.505022i	$0.831484\pi$
$128$	162332.	+	89487.9i	0.875748	+	0.482769i
$129$	−29532.0			−0.156250
$130$		0			0
$131$		−	353658.i		−	1.80055i	−0.435322	−	0.900275i	$-0.643366\pi$
$131$		−	353658.i		−	1.80055i	0.435322	−	0.900275i	$-0.356634\pi$
$132$	24753.9	−	7789.08i	0.123654	−	0.0389091i
$133$			6002.26i			0.0294229i
$134$	273308.	−	41984.9i	1.31489	−	0.201991i
$135$		0			0
$136$	−127728.	−	259576.i	−0.592160	−	1.20342i
$137$	−72750.1			−0.331156			−0.165578	−	0.986197i	$-0.552949\pi$
$137$	−72750.1			−0.331156			−0.165578	+	0.986197i	$0.552949\pi$
$138$	14573.8	−	2238.79i	0.0651439	−	0.0100073i
$139$		−	259480.i		−	1.13911i	−0.821952	−	0.569557i	$-0.807115\pi$
$139$		−	259480.i		−	1.13911i	0.821952	−	0.569557i	$-0.192885\pi$
$140$		0			0
$141$			43763.4i			0.185380i
$142$	−32034.2	−	208532.i	−0.133319	−	0.867864i
$143$	−196573.			−0.803865
$144$	198374.	−	138560.i	0.797219	−	0.556841i
$145$		0			0
$146$	22411.5	+	145891.i	0.0870137	+	0.566431i
$147$			41555.2i			0.158611i
$148$	−34494.9	−	109626.i	−0.129450	−	0.411394i
$149$		−	206318.i		−	0.761328i	−0.924713	−	0.380664i	$-0.875695\pi$
$149$		−	206318.i		−	0.761328i	0.924713	−	0.380664i	$-0.124305\pi$
$150$		0			0
$151$	435318.			1.55369			0.776845	−	0.629692i	$-0.216819\pi$
$151$	435318.			1.55369			0.776845	+	0.629692i	$0.216819\pi$
$152$	35578.1	−	17506.7i	0.124903	−	0.0614603i
$153$	−377650.			−1.30425
$154$	48006.0	−	7374.57i	0.163115	−	0.0250573i
$155$		0			0
$156$	49561.7	−	15595.1i	0.163055	−	0.0513070i
$157$		−	341575.i		−	1.10595i	−0.833196	−	0.552977i	$-0.813492\pi$
$157$		−	341575.i		−	1.10595i	0.833196	−	0.552977i	$-0.186508\pi$
$158$	66683.3	+	434086.i	0.212508	+	1.38335i
$159$	−33086.2			−0.103790
$160$		0			0
$161$	27596.4			0.0839049
$162$	−46562.6	−	303107.i	−0.139396	−	0.907420i
$163$		−	458266.i		−	1.35098i	−0.737370	−	0.675489i	$-0.763932\pi$
$163$		−	458266.i		−	1.35098i	0.737370	−	0.675489i	$-0.236068\pi$
$164$	18580.2	−	5846.45i	0.0539436	−	0.0169739i
$165$		0			0
$166$	−326641.	+	50177.7i	−0.920025	+	0.141332i
$167$	443800.			1.23139			0.615696	−	0.787984i	$-0.288875\pi$
$167$	443800.			1.23139			0.615696	+	0.787984i	$0.288875\pi$
$168$	−11518.6	+	5667.90i	−0.0314867	+	0.0154935i
$169$	−22280.4			−0.0600075
$170$		0			0
$171$		−	51761.5i		−	0.135368i
$172$	109598.	+	348304.i	0.282475	+	0.897712i
$173$			731330.i			1.85780i	0.370336	+	0.928898i	$0.379243\pi$
$173$			731330.i			1.85780i	−0.370336	+	0.928898i	$0.620757\pi$
$174$	−13650.9	−	88863.1i	−0.0341814	−	0.222509i
$175$		0			0
$176$	−183730.	−	263044.i	−0.447094	−	0.640097i
$177$	77428.9			0.185768
$178$	70013.6	+	455765.i	0.165627	+	1.07818i
$179$		−	318951.i		−	0.744032i	−0.928226	−	0.372016i	$-0.878667\pi$
$179$		−	318951.i		−	0.744032i	0.928226	−	0.372016i	$-0.121333\pi$
$180$		0			0
$181$			586939.i			1.33167i	0.746099	+	0.665835i	$0.231924\pi$
$181$			586939.i			1.33167i	−0.746099	+	0.665835i	$0.768076\pi$
$182$	96116.5	−	14765.2i	0.215090	−	0.0330416i
$183$	46547.4			0.102747
$184$	−80489.8	−	163576.i	−0.175265	−	0.356184i
$185$		0			0
$186$	32481.4	−	4989.71i	0.0688417	−	0.0105753i
$187$			500765.i			1.04720i
$188$	516150.	−	162412.i	1.06508	−	0.335138i
$189$			33991.3i			0.0692171i
$190$		0			0
$191$	−97320.1			−0.193027			−0.0965137	−	0.995332i	$-0.530769\pi$
$191$	−97320.1			−0.193027			−0.0965137	+	0.995332i	$0.530769\pi$
$192$	67192.3	+	51744.6i	0.131543	+	0.101301i
$193$	−52528.5			−0.101508			−0.0507541	−	0.998711i	$-0.516162\pi$
$193$	−52528.5			−0.101508			−0.0507541	+	0.998711i	$0.516162\pi$
$194$	24390.4	+	158773.i	0.0465280	+	0.302882i
$195$		0			0
$196$	490107.	−	154217.i	0.911277	−	0.286743i
$197$		−	446496.i		−	0.819695i	−0.912154	−	0.409847i	$-0.865582\pi$
$197$		−	446496.i		−	0.819695i	0.912154	−	0.409847i	$-0.134418\pi$
$198$	−413988.	+	63595.8i	−0.750455	+	0.115283i
$199$	−518787.			−0.928659			−0.464329	−	0.885663i	$-0.653705\pi$
$199$	−518787.			−0.928659			−0.464329	+	0.885663i	$0.653705\pi$
$200$		0			0
$201$	126510.			0.220870
$202$	760550.	−	116834.i	1.31144	−	0.201461i
$203$		−	168268.i		−	0.286591i
$204$	−39728.2	−	126257.i	−0.0668380	−	0.212413i
$205$		0			0
$206$	143096.	+	931507.i	0.234941	+	1.52939i
$207$	−237982.			−0.386028
$208$	−367861.	−	526659.i	−0.589556	−	0.844057i
$209$	−68635.8			−0.108689
$210$		0			0
$211$		−	1.12592e6i		−	1.74101i	−0.492163	−	0.870503i	$-0.663794\pi$
$211$		−	1.12592e6i		−	1.74101i	0.492163	−	0.870503i	$-0.336206\pi$
$212$	122788.	+	390222.i	0.187635	+	0.596310i
$213$		−	96526.5i		−	0.145780i
$214$	−378945.	+	58212.6i	−0.565641	+	0.0868925i
$215$		0			0
$216$	201481.	−	99141.7i	0.293833	−	0.144585i
$217$	61505.6			0.0886677
$218$	310693.	−	47728.0i	0.442783	−	0.0680192i
$219$			67530.9i			0.0951464i
$220$		0			0
$221$			1.00262e6i			1.38088i
$222$	−7983.60	−	51970.6i	−0.0108722	−	0.0707742i
$223$	138775.			0.186874			0.0934368	−	0.995625i	$-0.470215\pi$
$223$	138775.			0.186874			0.0934368	+	0.995625i	$0.470215\pi$
$224$	109595.	+	114818.i	0.145939	+	0.152893i
$225$		0			0
$226$	146443.	+	953294.i	0.190720	+	1.24153i
$227$			966829.i			1.24533i	0.782488	+	0.622666i	$0.213950\pi$
$227$			966829.i			1.24533i	−0.782488	+	0.622666i	$0.786050\pi$
$228$	17305.1	−	5445.23i	0.0220463	−	0.00693711i
$229$			840679.i			1.05935i	0.848199	+	0.529677i	$0.177687\pi$
$229$			840679.i			1.05935i	−0.848199	+	0.529677i	$0.822313\pi$
$230$		0			0
$231$	22221.3			0.0273993
$232$	−997400.	+	490784.i	−1.21660	+	0.598646i
$233$	977446.			1.17951			0.589757	−	0.807581i	$-0.299224\pi$
$233$	977446.			1.17951			0.589757	+	0.807581i	$0.299224\pi$
$234$	−828876.	+	127330.i	−0.989578	+	0.152017i
$235$		0			0
$236$	−287349.	−	913204.i	−0.335838	−	1.06730i
$237$			200932.i			0.232370i
$238$	−37614.0	−	244855.i	−0.0430434	−	0.280199i
$239$	1.17543e6			1.33108			0.665538	−	0.746364i	$-0.268202\pi$
$239$	1.17543e6			1.33108			0.665538	+	0.746364i	$0.268202\pi$
$240$		0			0
$241$	−615094.			−0.682180			−0.341090	−	0.940031i	$-0.610796\pi$
$241$	−615094.			−0.682180			−0.341090	+	0.940031i	$0.610796\pi$
$242$	−54001.4	−	351531.i	−0.0592743	−	0.385856i
$243$		−	441743.i		−	0.479903i
$244$	−172744.	−	548985.i	−0.185750	−	0.590318i
$245$		0			0
$246$	8808.36	−	1353.12i	0.00928020	−	0.00142560i
$247$	−137421.			−0.143321
$248$	−179392.	−	364571.i	−0.185214	−	0.376403i
$249$	−151197.			−0.154542
$250$		0			0
$251$		−	1.26252e6i		−	1.26490i	−0.774602	−	0.632448i	$-0.782050\pi$
$251$		−	1.26252e6i		−	1.26490i	0.774602	−	0.632448i	$-0.217950\pi$
$252$	197647.	−	62191.8i	0.196060	−	0.0616924i
$253$			315564.i			0.309946i
$254$	269498.	+	1.75434e6i	0.262102	+	1.70620i
$255$		0			0
$256$	360921.	−	984504.i	0.344201	−	0.938896i
$257$	346343.			0.327095			0.163547	−	0.986535i	$-0.447706\pi$
$257$	346343.			0.327095			0.163547	+	0.986535i	$0.447706\pi$
$258$	25365.6	+	165122.i	0.0237244	+	0.154438i
$259$		−	98409.8i		−	0.0911567i
$260$		0			0
$261$			1.45109e6i			1.31854i
$262$	−1.97740e6	+	303763.i	−1.77967	+	0.273389i
$263$	1.93221e6			1.72252			0.861262	−	0.508162i	$-0.169675\pi$
$263$	1.93221e6			1.72252			0.861262	+	0.508162i	$0.169675\pi$
$264$	−64812.4	−	131715.i	−0.0572332	−	0.116313i
$265$		0			0
$266$	33560.3	−	5155.45i	0.0290818	−	0.00446748i
$267$			210967.i			0.181108i
$268$	−469498.	−	1.49208e6i	−0.399297	−	1.26898i
$269$			2.22703e6i			1.87649i	0.345976	+	0.938243i	$0.387548\pi$
$269$			2.22703e6i			1.87649i	−0.345976	+	0.938243i	$0.612452\pi$
$270$		0			0
$271$	−512488.			−0.423897			−0.211948	−	0.977281i	$-0.567981\pi$
$271$	−512488.			−0.423897			−0.211948	+	0.977281i	$0.567981\pi$
$272$	−1.34165e6	+	937117.i	−1.09956	+	0.768018i
$273$	44491.0			0.0361298
$274$	62486.3	+	406765.i	0.0502816	+	0.327316i
$275$		0			0
$276$	−25035.3	−	79562.9i	−0.0197825	−	0.0628692i
$277$		−	825684.i		−	0.646568i	−0.946302	−	0.323284i	$-0.895213\pi$
$277$		−	825684.i		−	0.646568i	0.946302	−	0.323284i	$-0.104787\pi$
$278$	−1.45082e6	+	222872.i	−1.12591	+	0.172959i
$279$	−530404.			−0.407940
$280$		0			0
$281$	−2.18865e6			−1.65352			−0.826762	−	0.562552i	$-0.809820\pi$
$281$	−2.18865e6			−1.65352			−0.826762	+	0.562552i	$0.809820\pi$
$282$	244693.	−	37589.1i	0.183231	−	0.0281475i
$283$		−	1.64409e6i		−	1.22028i	−0.792293	−	0.610141i	$-0.791113\pi$
$283$		−	1.64409e6i		−	1.22028i	0.792293	−	0.610141i	$-0.208887\pi$
$284$	−1.13844e6	+	358223.i	−0.837559	+	0.263547i
$285$		0			0
$286$	168840.	+	1.09909e6i	0.122056	+	0.794545i
$287$	16679.2			0.0119528
$288$	−945111.	−	990148.i	−0.671431	−	0.703427i
$289$	1.13429e6			0.798879
$290$		0			0
$291$			73493.9i			0.0508767i
$292$	796467.	−	250617.i	0.546651	−	0.172010i
$293$			1.79254e6i			1.21983i	0.792465	+	0.609917i	$0.208797\pi$
$293$			1.79254e6i			1.21983i	−0.792465	+	0.609917i	$0.791203\pi$
$294$	232346.	−	35692.5i	0.156772	−	0.0240829i
$295$		0			0
$296$	−583318.	+	287030.i	−0.386969	+	0.190413i
$297$	−388690.			−0.255689
$298$	−1.15358e6	+	177210.i	−0.752501	+	0.115597i
$299$			631815.i			0.408707i
$300$		0			0
$301$			312669.i			0.198915i
$302$	−373902.	−	2.43398e6i	−0.235907	−	1.53568i
$303$	352048.			0.220290
$304$	−128443.	−	183890.i	−0.0797126	−	0.114123i
$305$		0			0
$306$	324370.	+	2.11154e6i	0.198033	+	1.28913i
$307$			1.30565e6i			0.790646i	0.918542	+	0.395323i	$0.129367\pi$
$307$			1.30565e6i			0.790646i	−0.918542	+	0.395323i	$0.870633\pi$
$308$	−82466.4	−	262080.i	−0.0495336	−	0.157419i
$309$			431182.i			0.256900i
$310$		0			0
$311$	−996126.			−0.584001			−0.292000	−	0.956418i	$-0.594321\pi$
$311$	−996126.			−0.584001			−0.292000	+	0.956418i	$0.594321\pi$
$312$	−129766.	−	263718.i	−0.0754699	−	0.153374i
$313$	887076.			0.511800			0.255900	−	0.966703i	$-0.417628\pi$
$313$	887076.			0.511800			0.255900	+	0.966703i	$0.417628\pi$
$314$	−1.90984e6	+	293385.i	−1.09313	+	0.167924i
$315$		0			0
$316$	2.36982e6	−	745688.i	1.33505	−	0.420087i
$317$		−	1.23286e6i		−	0.689075i	−0.938773	−	0.344538i	$-0.888036\pi$
$317$		−	1.23286e6i		−	0.689075i	0.938773	−	0.344538i	$-0.111964\pi$
$318$	28418.3	+	184994.i	0.0157591	+	0.102586i
$319$	1.92414e6			1.05867
$320$		0			0
$321$	−175408.			−0.0950139
$322$	−23703.0	−	154299.i	−0.0127398	−	0.0829321i
$323$			350077.i			0.186706i
$324$	−1.65476e6	+	520687.i	−0.875733	+	0.275559i
$325$		0			0
$326$	−2.56229e6	+	393612.i	−1.33531	+	0.205128i
$327$	143815.			0.0743766
$328$	−48647.9	−	98865.1i	−0.0249678	−	0.0507409i
$329$	463342.			0.236000
$330$		0			0
$331$		−	3.32521e6i		−	1.66820i	−0.551612	−	0.834101i	$-0.685987\pi$
$331$		−	3.32521e6i		−	1.66820i	0.551612	−	0.834101i	$-0.314013\pi$
$332$	561114.	+	1.78324e6i	0.279387	+	0.887899i
$333$			848653.i			0.419391i
$334$	−381188.	−	2.48140e6i	−0.186970	−	1.21711i
$335$		0			0
$336$	41584.3	+	59535.5i	0.0200947	+	0.0287692i
$337$	902443.			0.432858			0.216429	−	0.976298i	$-0.430559\pi$
$337$	902443.			0.432858			0.216429	+	0.976298i	$0.430559\pi$
$338$	19137.0	+	124575.i	0.00911133	+	0.0593117i
$339$			441267.i			0.208546i
$340$		0			0
$341$			703316.i			0.327540i
$342$	−289412.	+	44458.9i	−0.133799	+	0.0205538i
$343$	900501.			0.413284
$344$	1.85332e6	−	911953.i	0.844414	−	0.415505i
$345$		0			0
$346$	4.08906e6	−	628152.i	1.83626	−	0.282081i
$347$			1.99415e6i			0.889066i	0.895763	+	0.444533i	$0.146630\pi$
$347$			1.99415e6i			0.889066i	−0.895763	+	0.444533i	$0.853370\pi$
$348$	−485132.	+	152652.i	−0.214740	+	0.0675701i
$349$		−	3.06586e6i		−	1.34737i	−0.739017	−	0.673687i	$-0.764710\pi$
$349$		−	3.06586e6i		−	1.34737i	0.739017	−	0.673687i	$-0.235290\pi$
$350$		0			0
$351$	−778226.			−0.337162
$352$	−1.31294e6	+	1.25322e6i	−0.564790	+	0.539101i
$353$	2.66290e6			1.13741			0.568705	−	0.822541i	$-0.307444\pi$
$353$	2.66290e6			1.13741			0.568705	+	0.822541i	$0.307444\pi$
$354$	−66505.0	−	432926.i	−0.0282063	−	0.183614i
$355$		0			0
$356$	2.48817e6	−	782929.i	1.04053	−	0.327414i
$357$		−	113340.i		−	0.0470665i
$358$	−1.78334e6	+	273953.i	−0.735405	+	0.112971i
$359$	39323.6			0.0161034			0.00805169	−	0.999968i	$-0.497437\pi$
$359$	39323.6			0.0161034			0.00805169	+	0.999968i	$0.497437\pi$
$360$		0			0
$361$	2.42812e6			0.980622
$362$	3.28173e6	−	504132.i	1.31623	−	0.202196i
$363$		−	162719.i		−	0.0648143i
$364$	−165112.	−	524731.i	−0.0653169	−	0.207579i
$365$		0			0
$366$	−39980.4	−	260259.i	−0.0156007	−	0.101555i
$367$	851976.			0.330189			0.165094	−	0.986278i	$-0.447207\pi$
$367$	851976.			0.330189			0.165094	+	0.986278i	$0.447207\pi$
$368$	−845463.	+	590538.i	−0.325443	+	0.227315i
$369$	−143836.			−0.0549923
$370$		0			0
$371$			350298.i			0.132130i
$372$	−55797.6	−	177326.i	−0.0209054	−	0.0664379i
$373$			1.78163e6i			0.663047i	0.943447	+	0.331524i	$0.107563\pi$
$373$			1.78163e6i			0.663047i	−0.943447	+	0.331524i	$0.892437\pi$
$374$	2.79991e6	−	430116.i	1.03506	−	0.159003i
$375$		0			0
$376$	−1.35142e6	−	2.74643e6i	−0.492970	−	1.00184i
$377$	3.85248e6			1.39600
$378$	190054.	−	29195.7i	0.0684146	−	0.0105097i
$379$		−	4.29296e6i		−	1.53518i	−0.640941	−	0.767590i	$-0.721456\pi$
$379$		−	4.29296e6i		−	1.53518i	0.640941	−	0.767590i	$-0.278544\pi$
$380$		0			0
$381$			812059.i			0.286599i
$382$	83589.9	+	544143.i	0.0293086	+	0.190789i
$383$	1.06598e6			0.371322			0.185661	−	0.982614i	$-0.440557\pi$
$383$	1.06598e6			0.371322			0.185661	+	0.982614i	$0.440557\pi$
$384$	231605.	−	420134.i	0.0801531	−	0.145399i
$385$		0			0
$386$	45117.6	+	293701.i	0.0154127	+	0.100331i
$387$		−	2.69635e6i		−	0.915164i
$388$	866794.	−	272746.i	0.292305	−	0.0919770i
$389$			251531.i			0.0842786i	0.999112	+	0.0421393i	$0.0134173\pi$
$389$			251531.i			0.0842786i	−0.999112	+	0.0421393i	$0.986583\pi$
$390$		0			0
$391$	1.60954e6			0.532425
$392$	−1.28323e6	−	2.60786e6i	−0.421784	−	0.857173i
$393$	−915308.			−0.298941
$394$	−2.49648e6	+	383503.i	−0.810191	+	0.124460i
$395$		0			0
$396$	711162.	+	2.26009e6i	0.227893	+	0.724249i
$397$			560036.i			0.178336i	0.996017	+	0.0891682i	$0.0284209\pi$
$397$			560036.i			0.178336i	−0.996017	+	0.0891682i	$0.971579\pi$
$398$	445595.	+	2.90067e6i	0.141004	+	0.917891i
$399$	15534.6			0.00488503
$400$		0			0
$401$	319882.			0.0993410			0.0496705	−	0.998766i	$-0.484183\pi$
$401$	319882.			0.0993410			0.0496705	+	0.998766i	$0.484183\pi$
$402$	−108662.	−	707353.i	−0.0335361	−	0.218309i
$403$			1.40816e6i			0.431907i
$404$	−1.30650e6	−	4.15209e6i	−0.398250	−	1.26565i
$405$		0			0
$406$	−940832.	+	144528.i	−0.283268	+	0.0435149i
$407$	1.12531e6			0.336735
$408$	−671815.	+	330575.i	−0.199802	+	0.0983151i
$409$	−221487.			−0.0654695			−0.0327348	−	0.999464i	$-0.510422\pi$
$409$	−221487.			−0.0654695			−0.0327348	+	0.999464i	$0.510422\pi$
$410$		0			0
$411$			188286.i			0.0549811i
$412$	5.08540e6	−	1.60018e6i	1.47598	−	0.464435i
$413$		−	819773.i		−	0.236493i
$414$	204407.	+	1.33062e6i	0.0586131	+	0.381552i
$415$		0			0
$416$	−2.62873e6	+	2.50916e6i	−0.744754	+	0.710879i
$417$	−671565.			−0.189125
$418$	58952.5	+	383761.i	0.0165029	+	0.107429i
$419$		−	1.61245e6i		−	0.448695i	−0.974509	−	0.224347i	$-0.927975\pi$
$419$		−	1.61245e6i		−	0.448695i	0.974509	−	0.224347i	$-0.0720250\pi$
$420$		0			0
$421$		−	3.39591e6i		−	0.933795i	−0.884312	−	0.466897i	$-0.845372\pi$
$421$		−	3.39591e6i		−	0.933795i	0.884312	−	0.466897i	$-0.154628\pi$
$422$	−6.29530e6	+	967069.i	−1.72082	+	0.264348i
$423$	−3.99571e6			−1.08578
$424$	2.07637e6	−	1.02171e6i	0.560906	−	0.276002i
$425$		0			0
$426$	−539705.	+	82908.2i	−0.144090	+	0.0221347i
$427$		−	492818.i		−	0.130803i
$428$	650964.	+	2.06878e6i	0.171770	+	0.545890i
$429$			508754.i			0.133464i
$430$		0			0
$431$	2.08841e6			0.541530			0.270765	−	0.962645i	$-0.412723\pi$
$431$	2.08841e6			0.541530			0.270765	+	0.962645i	$0.412723\pi$
$432$	−727383.	−	1.04138e6i	−0.187523	−	0.268473i
$433$	−4.35432e6			−1.11609			−0.558047	−	0.829810i	$-0.688449\pi$
$433$	−4.35432e6			−1.11609			−0.558047	+	0.829810i	$0.688449\pi$
$434$	−52828.2	−	343894.i	−0.0134630	−	0.0876396i
$435$		0			0
$436$	−533719.	−	1.69617e6i	−0.134461	−	0.427321i
$437$			220606.i			0.0552604i
$438$	377583.	−	58003.5i	0.0940433	−	0.0144467i
$439$	3.21572e6			0.796375			0.398187	−	0.917304i	$-0.369639\pi$
$439$	3.21572e6			0.796375			0.398187	+	0.917304i	$0.369639\pi$
$440$		0			0
$441$	−3.79410e6			−0.928992
$442$	5.60591e6	−	861167.i	1.36487	−	0.209668i
$443$			3.36028e6i			0.813516i	0.913536	+	0.406758i	$0.133341\pi$
$443$			3.36028e6i			0.813516i	−0.913536	+	0.406758i	$0.866659\pi$
$444$	−283724.	+	89276.9i	−0.0683029	+	0.0214922i
$445$		0			0
$446$	−119196.	−	775926.i	−0.0283743	−	0.184707i
$447$	−533976.			−0.126402
$448$	547842.	−	711394.i	0.128962	−	0.167462i
$449$	963097.			0.225452			0.112726	−	0.993626i	$-0.464042\pi$
$449$	963097.			0.225452			0.112726	+	0.993626i	$0.464042\pi$
$450$		0			0
$451$			190727.i			0.0441540i
$452$	5.20434e6	−	1.63760e6i	1.19817	−	0.377018i
$453$		−	1.12665e6i		−	0.257956i
$454$	5.40580e6	−	830426.i	1.23089	−	0.189087i
$455$		0			0
$456$	−45309.3	−	92080.2i	−0.0102041	−	0.0207374i
$457$	−6.88516e6			−1.54214			−0.771069	−	0.636752i	$-0.780278\pi$
$457$	−6.88516e6			−1.54214			−0.771069	+	0.636752i	$0.780278\pi$
$458$	4.70046e6	−	722073.i	1.04707	−	0.160849i
$459$			1.98251e6i			0.439222i
$460$		0			0
$461$			686048.i			0.150349i	0.997170	+	0.0751747i	$0.0239515\pi$
$461$			686048.i			0.150349i	−0.997170	+	0.0751747i	$0.976049\pi$
$462$	−19086.3	−	124245.i	−0.00416022	−	0.0270816i
$463$	104740.			0.0227070			0.0113535	−	0.999936i	$-0.496386\pi$
$463$	104740.			0.0227070			0.0113535	+	0.999936i	$0.496386\pi$
$464$	3.60079e6	+	5.15518e6i	0.776430	+	1.11160i
$465$		0			0
$466$	−839546.	−	5.46516e6i	−0.179093	−	1.16584i
$467$		−	5.79633e6i		−	1.22987i	−0.788576	−	0.614937i	$-0.789181\pi$
$467$		−	5.79633e6i		−	1.22987i	0.788576	−	0.614937i	$-0.210819\pi$
$468$	1.42387e6	+	4.52510e6i	0.300508	+	0.955023i
$469$		−	1.33942e6i		−	0.281180i
$470$		0			0
$471$	−884037.			−0.183619
$472$	−4.85916e6	+	2.39101e6i	−1.00394	+	0.494000i
$473$	−3.57536e6			−0.734797
$474$	1.12347e6	−	172584.i	0.229675	−	0.0352822i
$475$		0			0
$476$	−1.33674e6	+	420620.i	−0.270414	+	0.0850888i
$477$		−	3.02085e6i		−	0.607902i
$478$	−1.00960e6	−	6.57215e6i	−0.202106	−	1.31564i
$479$	−9.29136e6			−1.85029			−0.925146	−	0.379611i	$-0.876058\pi$
$479$	−9.29136e6			−1.85029			−0.925146	+	0.379611i	$0.876058\pi$
$480$		0			0
$481$	2.25308e6			0.444031
$482$	528315.	+	3.43916e6i	0.103580	+	0.674271i
$483$		−	71422.7i		−	0.0139306i
$484$	−1.91912e6	+	603872.i	−0.372382	+	0.117174i
$485$		0			0
$486$	−2.46990e6	+	379420.i	−0.474339	+	0.0728669i
$487$	−6.53708e6			−1.24900			−0.624498	−	0.781026i	$-0.714696\pi$
$487$	−6.53708e6			−1.24900			−0.624498	+	0.781026i	$0.714696\pi$
$488$	−2.92115e6	+	1.43739e6i	−0.555270	+	0.273228i
$489$	−1.18605e6			−0.224300
$490$		0			0
$491$			6.62569e6i			1.24030i	0.784483	+	0.620151i	$0.212929\pi$
$491$			6.62569e6i			1.24030i	−0.784483	+	0.620151i	$0.787071\pi$
$492$	−15131.3	−	48087.7i	−0.00281815	−	0.00895614i
$493$		−	9.81410e6i		−	1.81858i
$494$	118033.	+	768358.i	0.0217614	+	0.141660i
$495$		0			0
$496$	−1.88433e6	+	1.31616e6i	−0.343916	+	0.240218i
$497$	−1.02197e6			−0.185586
$498$	129866.	+	845384.i	0.0234651	+	0.152750i
$499$			5.25473e6i			0.944710i	0.881408	+	0.472355i	$0.156596\pi$
$499$			5.25473e6i			0.944710i	−0.881408	+	0.472355i	$0.843404\pi$
$500$		0			0
$501$		−	1.14861e6i		−	0.204445i
$502$	−7.05911e6	+	1.08440e6i	−1.25023	+	0.192058i
$503$	−8.78835e6			−1.54877			−0.774386	−	0.632713i	$-0.781941\pi$
$503$	−8.78835e6			−1.54877			−0.774386	+	0.632713i	$0.781941\pi$
$504$	−517493.	−	1.05168e6i	−0.0907462	−	0.184420i
$505$		0			0
$506$	1.76440e6	−	271044.i	0.306353	−	0.0470612i
$507$			57664.2i			0.00996292i
$508$	9.57751e6	−	3.01367e6i	1.64662	−	0.518126i
$509$		−	5.24405e6i		−	0.897164i	−0.893742	−	0.448582i	$-0.851929\pi$
$509$		−	5.24405e6i		−	0.897164i	0.893742	−	0.448582i	$-0.148071\pi$
$510$		0			0
$511$	714979.			0.121127
$512$	−5.81462e6	−	1.17240e6i	−0.980272	−	0.197651i
$513$	−271727.			−0.0455869
$514$	−297480.	−	1.93650e6i	−0.0496650	−	0.323302i
$515$		0			0
$516$	901452.	−	283651.i	0.149045	−	0.0468987i
$517$			5.29831e6i			0.871788i
$518$	−550235.	+	84525.8i	−0.0900998	+	0.0138409i
$519$	1.89277e6			0.308446
$520$		0			0
$521$	1.02485e7			1.65412			0.827059	−	0.562115i	$-0.190012\pi$
$521$	1.02485e7			1.65412			0.827059	+	0.562115i	$0.190012\pi$
$522$	8.11342e6	−	1.24636e6i	1.30325	−	0.200202i
$523$		−	5.94878e6i		−	0.950985i	−0.879720	−	0.475493i	$-0.842270\pi$
$523$		−	5.94878e6i		−	0.950985i	0.879720	−	0.475493i	$-0.157730\pi$
$524$	3.39684e6	+	1.07952e7i	0.540439	+	1.71753i
$525$		0			0
$526$	−1.65961e6	−	1.08035e7i	−0.261542	−	1.70255i
$527$	3.58726e6			0.562648
$528$	−680788.	+	475516.i	−0.106274	+	0.0742301i
$529$	−5.42207e6			−0.842415
$530$		0			0
$531$			7.06945e6i			1.08805i
$532$	−57651.0	−	183216.i	−0.00883136	−	0.0280663i
$533$			381868.i			0.0582231i
$534$	1.17957e6	−	181203.i	0.179008	−	0.0274988i
$535$		0			0
$536$	−7.93933e6	+	3.90666e6i	−1.19364	+	0.587345i
$537$	−825483.			−0.123530
$538$	1.24519e7	−	1.91283e6i	1.85473	−	0.284919i
$539$			5.03097e6i			0.745899i
$540$		0			0
$541$		−	1.29778e7i		−	1.90637i	−0.302385	−	0.953186i	$-0.597783\pi$
$541$		−	1.29778e7i		−	1.90637i	0.302385	−	0.953186i	$-0.402217\pi$
$542$	440184.	+	2.86545e6i	0.0643630	+	0.418982i
$543$	1.51907e6			0.221094
$544$	6.39204e6	+	6.69664e6i	0.926066	+	0.970196i
$545$		0			0
$546$	−38214.0	−	248761.i	−0.00548582	−	0.0357109i
$547$			6.10894e6i			0.872966i	0.899712	+	0.436483i	$0.143776\pi$
$547$			6.10894e6i			0.872966i	−0.899712	+	0.436483i	$0.856224\pi$
$548$	2.22066e6	−	698756.i	0.315887	−	0.0993971i
$549$			4.24990e6i			0.601794i
$550$		0			0
$551$	1.34514e6			0.188751
$552$	−423354.	+	208317.i	−0.0591365	+	0.0290989i
$553$	2.12736e6			0.295820
$554$	−4.61662e6	+	709194.i	−0.639072	+	0.0981727i
$555$		0			0
$556$	2.49227e6	+	7.92050e6i	0.341907	+	1.08659i
$557$			1.01541e7i			1.38676i	0.720570	+	0.693382i	$0.243880\pi$
$557$			1.01541e7i			1.38676i	−0.720570	+	0.693382i	$0.756120\pi$
$558$	455573.	+	2.96563e6i	0.0619402	+	0.403210i
$559$	−7.15850e6			−0.968931
$560$		0			0
$561$	1.29604e6			0.173864
$562$	1.87987e6	+	1.22373e7i	0.251065	+	1.63435i
$563$		−	229520.i		−	0.0305175i	−0.999884	−	0.0152588i	$-0.995143\pi$
$563$		−	229520.i		−	0.0305175i	0.999884	−	0.0152588i	$-0.00485721\pi$
$564$	−420342.	−	1.33586e6i	−0.0556423	−	0.176833i
$565$		0			0
$566$	−9.19256e6	+	1.41214e6i	−1.20613	+	0.185283i
$567$	−1.48546e6			−0.194045
$568$	2.98075e6	+	6.05765e6i	0.387663	+	0.787832i
$569$	−5.11894e6			−0.662826			−0.331413	−	0.943486i	$-0.607525\pi$
$569$	−5.11894e6			−0.662826			−0.331413	+	0.943486i	$0.607525\pi$
$570$		0			0
$571$			1.09781e7i			1.40909i	0.709660	+	0.704544i	$0.248848\pi$
$571$			1.09781e7i			1.40909i	−0.709660	+	0.704544i	$0.751152\pi$
$572$	6.00029e6	−	1.88806e6i	0.766800	−	0.241282i
$573$			251876.i			0.0320479i
$574$	−14326.1	−	93257.9i	−0.00181488	−	0.0118142i
$575$		0			0
$576$	−4.72441e6	+	6.13482e6i	−0.593323	+	0.770452i
$577$	−3.09452e6			−0.386949			−0.193474	−	0.981105i	$-0.561976\pi$
$577$	−3.09452e6			−0.386949			−0.193474	+	0.981105i	$0.561976\pi$
$578$	−974264.	−	6.34214e6i	−0.121299	−	0.789616i
$579$			135950.i			0.0168532i
$580$		0			0
$581$			1.60079e6i			0.196741i
$582$	410924.	−	63125.1i	0.0502868	−	0.00772494i
$583$	−4.00565e6			−0.488093
$584$	−2.08536e6	−	4.23800e6i	−0.253017	−	0.514196i
$585$		0			0
$586$	1.00226e7	−	1.53965e6i	1.20569	−	0.185215i
$587$		−	1.24448e7i		−	1.49071i	−0.666666	−	0.745357i	$-0.732279\pi$
$587$		−	1.24448e7i		−	1.49071i	0.666666	−	0.745357i	$-0.267721\pi$
$588$	−399133.	−	1.26845e6i	−0.0476073	−	0.151297i
$589$			491677.i			0.0583972i
$590$		0			0
$591$	−1.15558e6			−0.136092
$592$	2.10588e6	+	3.01495e6i	0.246962	+	0.353571i
$593$	−7.81508e6			−0.912634			−0.456317	−	0.889817i	$-0.650832\pi$
$593$	−7.81508e6			−0.912634			−0.456317	+	0.889817i	$0.650832\pi$
$594$	333853.	+	2.17327e6i	0.0388230	+	0.252725i
$595$		0			0
$596$	1.98166e6	+	6.29777e6i	0.228514	+	0.726225i
$597$			1.34268e6i			0.154183i
$598$	3.53265e6	−	542677.i	0.403968	−	0.0620567i
$599$	−8.68576e6			−0.989101			−0.494550	−	0.869149i	$-0.664667\pi$
$599$	−8.68576e6			−0.989101			−0.494550	+	0.869149i	$0.664667\pi$
$600$		0			0
$601$	−3.99770e6			−0.451465			−0.225733	−	0.974189i	$-0.572478\pi$
$601$	−3.99770e6			−0.451465			−0.225733	+	0.974189i	$0.572478\pi$
$602$	1.74821e6	−	268556.i	0.196609	−	0.0302026i
$603$			1.15507e7i			1.29365i
$604$	−1.32879e7	+	4.18117e6i	−1.48205	+	0.466343i
$605$		0			0
$606$	−302380.	−	1.96839e6i	−0.0334481	−	0.217736i
$607$	2.96166e6			0.326259			0.163130	−	0.986605i	$-0.447841\pi$
$607$	2.96166e6			0.326259			0.163130	+	0.986605i	$0.447841\pi$
$608$	−917854.	+	876105.i	−0.100697	+	0.0961164i
$609$	−435498.			−0.0475820
$610$		0			0
$611$			1.06082e7i			1.14957i
$612$	1.15276e7	−	3.62728e6i	1.24411	−	0.391474i
$613$		−	1.42575e7i		−	1.53247i	−0.642561	−	0.766235i	$-0.722128\pi$
$613$		−	1.42575e7i		−	1.53247i	0.642561	−	0.766235i	$-0.277872\pi$
$614$	7.30026e6	−	1.12145e6i	0.781479	−	0.120049i
$615$		0			0
$616$	−1.39453e6	+	686197.i	−0.148073	+	0.0728613i
$617$	4.11383e6			0.435044			0.217522	−	0.976055i	$-0.430203\pi$
$617$	4.11383e6			0.435044			0.217522	+	0.976055i	$0.430203\pi$
$618$	2.41085e6	−	370349.i	0.253921	−	0.0390068i
$619$			6.74663e6i			0.707718i	0.935299	+	0.353859i	$0.115131\pi$
$619$			6.74663e6i			0.707718i	−0.935299	+	0.353859i	$0.884869\pi$
$620$		0			0
$621$			1.24931e6i			0.129999i
$622$	855590.	+	5.56961e6i	0.0886726	+	0.577229i
$623$	2.23360e6			0.230561
$624$	−1.36306e6	+	952067.i	−0.140137	+	0.0978827i
$625$		0			0
$626$	−761925.	−	4.95988e6i	−0.0777099	−	0.505866i
$627$			177638.i			0.0180454i
$628$	3.28079e6	+	1.04264e7i	0.331955	+	1.05496i
$629$		−	5.73967e6i		−	0.578442i
$630$		0			0
$631$	5.01676e6			0.501591			0.250795	−	0.968040i	$-0.419308\pi$
$631$	5.01676e6			0.501591			0.250795	+	0.968040i	$0.419308\pi$
$632$	−6.20482e6	−	1.26098e7i	−0.617926	−	1.25579i
$633$	−2.91401e6			−0.289055
$634$	−6.89327e6	+	1.05893e6i	−0.681086	+	0.104627i
$635$		0			0
$636$	1.00994e6	−	317789.i	0.0990041	−	0.0311527i
$637$			1.00729e7i			0.983571i
$638$	−1.65268e6	−	1.07584e7i	−0.160745	−	1.04640i
$639$	8.81311e6			0.853841
$640$		0			0
$641$	−1.79114e6			−0.172180			−0.0860902	−	0.996287i	$-0.527437\pi$
$641$	−1.79114e6			−0.172180			−0.0860902	+	0.996287i	$0.527437\pi$
$642$	150661.	+	980753.i	0.0144266	+	0.0939122i
$643$			4.49516e6i			0.428763i	0.976750	+	0.214382i	$0.0687736\pi$
$643$			4.49516e6i			0.428763i	−0.976750	+	0.214382i	$0.931226\pi$
$644$	−842366.	+	265060.i	−0.0800362	+	0.0251842i
$645$		0			0
$646$	1.95737e6	−	300687.i	0.184541	−	0.0283487i
$647$	2.47054e6			0.232023			0.116012	−	0.993248i	$-0.462989\pi$
$647$	2.47054e6			0.232023			0.116012	+	0.993248i	$0.462989\pi$
$648$	4.33260e6	+	8.80496e6i	0.405332	+	0.823740i
$649$	9.37410e6			0.873610
$650$		0			0
$651$		−	159184.i		−	0.0147213i
$652$	4.40158e6	+	1.39883e7i	0.405499	+	1.28869i
$653$		−	1.26068e7i		−	1.15697i	−0.815693	−	0.578484i	$-0.803644\pi$
$653$		−	1.26068e7i		−	1.15697i	0.815693	−	0.578484i	$-0.196356\pi$
$654$	−123526.	−	804111.i	−0.0112931	−	0.0735142i
$655$		0			0
$656$	−510996.	+	356920.i	−0.0463616	+	0.0323826i
$657$	−6.16574e6			−0.557278
$658$	−397972.	−	2.59067e6i	−0.0358334	−	0.233264i
$659$		−	7.51240e6i		−	0.673853i	−0.941531	−	0.336927i	$-0.890613\pi$
$659$		−	7.51240e6i		−	0.673853i	0.941531	−	0.336927i	$-0.109387\pi$
$660$		0			0
$661$		−	1.66707e7i		−	1.48405i	−0.670371	−	0.742026i	$-0.733865\pi$
$661$		−	1.66707e7i		−	1.48405i	0.670371	−	0.742026i	$-0.266135\pi$
$662$	−1.85921e7	+	2.85608e6i	−1.64886	+	0.253294i
$663$	2.59490e6			0.229264
$664$	9.48860e6	−	4.66899e6i	0.835183	−	0.410963i
$665$		0			0
$666$	4.74504e6	−	728923.i	0.414529	−	0.0636789i
$667$		−	6.18450e6i		−	0.538257i
$668$	−1.35468e7	+	4.26264e6i	−1.17461	+	0.369605i
$669$		−	359165.i		−	0.0310262i
$670$		0			0
$671$	5.63537e6			0.483188
$672$	297161.	−	283645.i	0.0253845	−	0.0242299i
$673$	1.75455e7			1.49323			0.746617	−	0.665254i	$-0.231677\pi$
$673$	1.75455e7			1.49323			0.746617	+	0.665254i	$0.231677\pi$
$674$	−775124.	−	5.04580e6i	−0.0657236	−	0.427839i
$675$		0			0
$676$	680097.	−	214000.i	0.0572406	−	0.0180114i
$677$			681435.i			0.0571416i	0.999592	+	0.0285708i	$0.00909561\pi$
$677$			681435.i			0.0571416i	−0.999592	+	0.0285708i	$0.990904\pi$
$678$	2.46724e6	−	379011.i	0.206128	−	0.0316649i
$679$	778111.			0.0647690
$680$		0			0
$681$	2.50227e6			0.206760
$682$	3.93243e6	−	604090.i	0.323743	−	0.0497326i
$683$			1.08945e7i			0.893629i	0.894627	+	0.446815i	$0.147442\pi$
$683$			1.08945e7i			0.893629i	−0.894627	+	0.446815i	$0.852558\pi$
$684$	497163.	+	1.58000e6i	0.0406311	+	0.129127i
$685$		0			0
$686$	−773456.	−	5.03494e6i	−0.0627516	−	0.408492i
$687$	2.17578e6			0.175882
$688$	−6.69083e6	−	9.57914e6i	−0.538901	−	0.771535i
$689$	−8.02003e6			−0.643617
$690$		0			0
$691$		−	1.31179e7i		−	1.04513i	−0.852599	−	0.522565i	$-0.824975\pi$
$691$		−	1.31179e7i		−	1.04513i	0.852599	−	0.522565i	$-0.175025\pi$
$692$	−7.02433e6	−	2.23235e7i	−0.557622	−	1.77214i
$693$			2.02886e6i			0.160479i
$694$	1.11498e7	−	1.71281e6i	0.878757	−	0.134993i
$695$		0			0
$696$	1.27021e6	+	2.58139e6i	0.0993920	+	0.201990i
$697$	972801.			0.0758477
$698$	−1.71420e7	+	2.63332e6i	−1.33175	+	0.204581i
$699$		−	2.52975e6i		−	0.195832i
$700$		0			0
$701$		−	1.34915e7i		−	1.03697i	−0.855087	−	0.518485i	$-0.826496\pi$
$701$		−	1.34915e7i		−	1.03697i	0.855087	−	0.518485i	$-0.173504\pi$
$702$	668432.	+	4.35127e6i	0.0511934	+	0.333252i
$703$	786690.			0.0600365
$704$	8.13478e6	+	6.26457e6i	0.618606	+	0.476387i
$705$		0			0
$706$	−2.28721e6	−	1.48890e7i	−0.172700	−	1.12422i
$707$		−	3.72728e6i		−	0.280443i
$708$	−2.36348e6	+	743694.i	−0.177202	+	0.0557585i
$709$		−	1.23849e7i		−	0.925290i	−0.886544	−	0.462645i	$-0.846900\pi$
$709$		−	1.23849e7i		−	0.925290i	0.886544	−	0.462645i	$-0.153100\pi$
$710$		0			0
$711$	−1.83456e7			−1.36100
$712$	−6.51470e6	−	1.32395e7i	−0.481609	−	0.978753i
$713$	2.26057e6			0.166530
$714$	−633713.	+	97349.4i	−0.0465208	+	0.00714641i
$715$		0			0
$716$	3.06348e6	+	9.73583e6i	0.223323	+	0.709726i
$717$		−	3.04216e6i		−	0.220996i
$718$	−33775.7	−	219869.i	−0.00244508	−	0.0159167i
$719$	1.59608e7			1.15142			0.575710	−	0.817654i	$-0.304726\pi$
$719$	1.59608e7			1.15142			0.575710	+	0.817654i	$0.304726\pi$
$720$		0			0
$721$	4.56511e6			0.327049
$722$	−2.08555e6	−	1.35762e7i	−0.148894	−	0.969252i
$723$			1.59194e6i			0.113261i
$724$	−5.63747e6	−	1.79160e7i	−0.399704	−	1.27027i
$725$		0			0
$726$	−909804.	+	139762.i	−0.0640628	+	0.00984118i
$727$	−1.58056e7			−1.10911			−0.554554	−	0.832148i	$-0.687111\pi$
$727$	−1.58056e7			−1.10911			−0.554554	+	0.832148i	$0.687111\pi$
$728$	−2.79209e6	+	1.37389e6i	−0.195255	+	0.0960777i
$729$	1.20299e7			0.838387
$730$		0			0
$731$			1.82361e7i			1.26223i
$732$	−1.42084e6	+	447082.i	−0.0980092	+	0.0308397i
$733$			2.47037e7i			1.69825i	0.528190	+	0.849126i	$0.322871\pi$
$733$			2.47037e7i			1.69825i	−0.528190	+	0.849126i	$0.677129\pi$
$734$	−731777.	−	4.76363e6i	−0.0501347	−	0.326361i
$735$		0			0
$736$	4.02804e6	+	4.21998e6i	0.274094	+	0.287155i
$737$	1.53162e7			1.03868
$738$	123543.	+	804225.i	0.00834984	+	0.0543547i
$739$			8.37792e6i			0.564319i	0.959367	+	0.282160i	$0.0910508\pi$
$739$			8.37792e6i			0.564319i	−0.959367	+	0.282160i	$0.908949\pi$
$740$		0			0
$741$			355662.i			0.0237953i
$742$	1.95861e6	−	300877.i	0.130599	−	0.0200622i
$743$	−1.37134e6			−0.0911323			−0.0455662	−	0.998961i	$-0.514509\pi$
$743$	−1.37134e6			−0.0911323			−0.0455662	+	0.998961i	$0.514509\pi$
$744$	−943553.	+	464288.i	−0.0624933	+	0.0307507i
$745$		0			0
$746$	9.96155e6	−	1.53027e6i	0.655360	−	0.100675i
$747$		−	1.38047e7i		−	0.905160i
$748$	−4.80978e6	−	1.52856e7i	−0.314319	−	0.998915i
$749$			1.85712e6i			0.120958i
$750$		0			0
$751$	−2.32593e7			−1.50486			−0.752431	−	0.658671i	$-0.771119\pi$
$751$	−2.32593e7			−1.50486			−0.752431	+	0.658671i	$0.771119\pi$
$752$	−1.41953e7	+	9.91511e6i	−0.915376	+	0.639371i
$753$	−3.26756e6			−0.210008
$754$	−3.30896e6	−	2.15402e7i	−0.211964	−	1.37982i
$755$		0			0
$756$	−326482.	−	1.03757e6i	−0.0207757	−	0.0660256i
$757$		−	9.50255e6i		−	0.602699i	−0.953514	−	0.301350i	$-0.902563\pi$
$757$		−	9.50255e6i		−	0.602699i	0.953514	−	0.301350i	$-0.0974371\pi$
$758$	−2.40031e7	+	3.68730e6i	−1.51738	+	0.233096i
$759$	816718.			0.0514597
$760$		0			0
$761$	−1.85691e6			−0.116233			−0.0581164	−	0.998310i	$-0.518509\pi$
$761$	−1.85691e6			−0.116233			−0.0581164	+	0.998310i	$0.518509\pi$
$762$	4.54044e6	−	697492.i	0.283276	−	0.0435163i
$763$		−	1.52264e6i		−	0.0946858i
$764$	2.97065e6	−	934747.i	0.184127	−	0.0579376i
$765$		0			0
$766$	−915585.	−	5.96016e6i	−0.0563802	−	0.367017i
$767$	1.87686e7			1.15198
$768$	−2.54801e6	−	934106.i	−0.155883	−	0.0571469i
$769$	3.11565e7			1.89991			0.949955	−	0.312386i	$-0.101128\pi$
$769$	3.11565e7			1.89991			0.949955	+	0.312386i	$0.101128\pi$
$770$		0			0
$771$		−	896377.i		−	0.0543069i
$772$	1.60341e6	−	504529.i	0.0968278	−	0.0304679i
$773$			3.47037e6i			0.208894i	0.994530	+	0.104447i	$0.0333073\pi$
$773$			3.47037e6i			0.208894i	−0.994530	+	0.104447i	$0.966693\pi$
$774$	−1.50760e7	+	2.31594e6i	−0.904553	+	0.138955i
$775$		0			0
$776$	−2.26950e6	−	4.61221e6i	−0.135293	−	0.274951i
$777$	−254696.			−0.0151346
$778$	1.40638e6	−	216044.i	0.0833015	−	0.0127966i
$779$			133334.i			0.00787223i
$780$		0			0
$781$		−	1.16862e7i		−	0.685560i
$782$	−1.38246e6	−	8.99934e6i	−0.0808416	−	0.526252i
$783$	7.61764e6			0.444034
$784$	−1.34790e7	+	9.41482e6i	−0.783192	+	0.547043i
$785$		0			0
$786$	786174.	+	5.11773e6i	0.0453902	+	0.295475i
$787$		−	8.99343e6i		−	0.517593i	−0.965932	−	0.258797i	$-0.916674\pi$
$787$		−	8.99343e6i		−	0.517593i	0.965932	−	0.258797i	$-0.0833260\pi$
$788$	4.28854e6	+	1.36291e7i	0.246033	+	0.781900i
$789$		−	5.00079e6i		−	0.285987i
$790$		0			0
$791$	4.67188e6			0.265491
$792$	1.20259e7	−	5.91753e6i	0.681250	−	0.335218i
$793$	1.12830e7			0.637150
$794$	3.13131e6	−	481025.i	0.176269	−	0.0270780i
$795$		0			0
$796$	1.58357e7	−	4.98288e6i	0.885839	−	0.278739i
$797$		−	6.61412e6i		−	0.368830i	−0.982848	−	0.184415i	$-0.940961\pi$
$797$		−	6.61412e6i		−	0.368830i	0.982848	−	0.184415i	$-0.0590390\pi$
$798$	−13342.9	−	86857.9i	−0.000741726	−	0.00482839i
$799$	2.70240e7			1.49756
$800$		0			0
$801$	−1.92618e7			−1.06076
$802$	−274752.	−	1.78854e6i	−0.0150836	−	0.0981892i
$803$			8.17578e6i			0.447446i
$804$	−3.86167e6	+	1.21512e6i	−0.210686	+	0.0662945i
$805$		0			0
$806$	7.87341e6	−	1.20950e6i	0.426899	−	0.0655793i
$807$	5.76382e6			0.311549
$808$	−2.20933e7	+	1.08713e7i	−1.19051	+	0.585804i
$809$	−1.45192e7			−0.779957			−0.389978	−	0.920824i	$-0.627518\pi$
$809$	−1.45192e7			−0.779957			−0.389978	+	0.920824i	$0.627518\pi$
$810$		0			0
$811$		−	1.23447e7i		−	0.659068i	−0.944144	−	0.329534i	$-0.893108\pi$
$811$		−	1.23447e7i		−	0.659068i	0.944144	−	0.329534i	$-0.106892\pi$
$812$	1.61619e6	+	5.13631e6i	0.0860208	+	0.273376i
$813$			1.32638e6i			0.0703787i
$814$	−966552.	−	6.29193e6i	−0.0511286	−	0.332830i
$815$		0			0
$816$	2.42537e6	+	3.47236e6i	0.127512	+	0.182557i
$817$	−2.49948e6			−0.131007
$818$	190239.	+	1.23839e6i	0.00994066	+	0.0647104i
$819$			4.06214e6i			0.211614i
$820$		0			0
$821$			1.98036e7i			1.02538i	0.858573	+	0.512692i	$0.171352\pi$
$821$			1.98036e7i			1.02538i	−0.858573	+	0.512692i	$0.828648\pi$
$822$	1.05276e6	−	161722.i	0.0543436	−	0.00834814i
$823$	1.28299e7			0.660275			0.330137	−	0.943933i	$-0.392905\pi$
$823$	1.28299e7			0.660275			0.330137	+	0.943933i	$0.392905\pi$
$824$	−1.33149e7	−	2.70594e7i	−0.683158	−	1.38835i
$825$		0			0
$826$	−4.58357e6	+	704117.i	−0.233751	+	0.0359083i
$827$			3.83991e7i			1.95235i	0.216989	+	0.976174i	$0.430376\pi$
$827$			3.83991e7i			1.95235i	−0.216989	+	0.976174i	$0.569624\pi$
$828$	7.26429e6	−	2.28579e6i	0.368228	−	0.115867i
$829$		−	1.17104e7i		−	0.591813i	−0.955217	−	0.295907i	$-0.904378\pi$
$829$		−	1.17104e7i		−	0.591813i	0.955217	−	0.295907i	$-0.0956217\pi$
$830$		0			0
$831$	−2.13697e6			−0.107348
$832$	1.62873e7	+	1.25428e7i	0.815718	+	0.628182i
$833$	2.56605e7			1.28130
$834$	576819.	+	3.75490e6i	0.0287160	+	0.186932i
$835$		0			0
$836$	2.09508e6	−	659238.i	0.103677	−	0.0326232i
$837$			2.78441e6i			0.137379i
$838$	−9.01563e6	+	1.38496e6i	−0.443492	+	0.0681282i
$839$	−2.39114e7			−1.17273			−0.586367	−	0.810046i	$-0.699442\pi$
$839$	−2.39114e7			−1.17273			−0.586367	+	0.810046i	$0.699442\pi$
$840$		0			0
$841$	−1.71987e7			−0.838503
$842$	−1.89875e7	+	2.91681e6i	−0.922968	+	0.141784i
$843$			5.66448e6i			0.274531i
$844$	1.08143e7	+	3.43681e7i	0.522567	+	1.66073i
$845$		0			0
$846$	3.43198e6	+	2.23411e7i	0.164861	+	1.07319i
$847$	−1.72277e6			−0.0825125
$848$	−7.49607e6	−	1.07320e7i	−0.357968	−	0.512496i
$849$	−4.25511e6			−0.202601
$850$		0			0
$851$		−	3.61694e6i		−	0.171205i
$852$	927124.	+	2.94642e6i	0.0437561	+	0.139058i
$853$			1.27294e6i			0.0599010i	0.999551	+	0.0299505i	$0.00953496\pi$
$853$			1.27294e6i			0.0599010i	−0.999551	+	0.0299505i	$0.990465\pi$
$854$	−2.75548e6	+	423290.i	−0.129286	+	0.0198606i
$855$		0			0
$856$	1.10080e7	−	5.41662e6i	0.513479	−	0.252665i
$857$	1.88053e7			0.874636			0.437318	−	0.899307i	$-0.355928\pi$
$857$	1.88053e7			0.874636			0.437318	+	0.899307i	$0.355928\pi$
$858$	2.84458e6	−	436977.i	0.131917	−	0.0202647i
$859$		−	1.00554e7i		−	0.464960i	−0.972601	−	0.232480i	$-0.925316\pi$
$859$		−	1.00554e7i		−	0.464960i	0.972601	−	0.232480i	$-0.0746840\pi$
$860$		0			0
$861$		−	43167.8i		−	0.00198450i
$862$	−1.79377e6	−	1.16769e7i	−0.0822241	−	0.535252i
$863$	2.96146e7			1.35357			0.676783	−	0.736183i	$-0.263374\pi$
$863$	2.96146e7			1.35357			0.676783	+	0.736183i	$0.263374\pi$
$864$	−5.19788e6	+	4.96146e6i	−0.236887	+	0.226113i
$865$		0			0
$866$	3.74000e6	+	2.43462e7i	0.169464	+	1.10315i
$867$		−	2.93569e6i		−	0.132636i
$868$	−1.87743e6	+	590753.i	−0.0845793	+	0.0266138i
$869$			2.43263e7i			1.09277i
$870$		0			0
$871$	3.06658e7			1.36965
$872$	−9.02534e6	+	4.44104e6i	−0.401950	+	0.197785i
$873$	−6.71017e6			−0.297988
$874$	1.23347e6	−	189482.i	0.0546197	−	0.00839055i
$875$		0			0
$876$	−648626.	−	2.06135e6i	−0.0285584	−	0.0907594i
$877$			1.42067e7i			0.623727i	0.950127	+	0.311863i	$0.100953\pi$
$877$			1.42067e7i			0.623727i	−0.950127	+	0.311863i	$0.899047\pi$
$878$	−2.76204e6	−	1.79800e7i	−0.120919	−	0.787141i
$879$	4.63932e6			0.202526
$880$		0			0
$881$	1.88875e7			0.819851			0.409925	−	0.912119i	$-0.365555\pi$
$881$	1.88875e7			0.819851			0.409925	+	0.912119i	$0.365555\pi$
$882$	3.25881e6	+	2.12138e7i	0.141055	+	0.918221i
$883$		−	9.53131e6i		−	0.411387i	−0.978616	−	0.205694i	$-0.934055\pi$
$883$		−	9.53131e6i		−	0.411387i	0.978616	−	0.205694i	$-0.0659450\pi$
$884$	−9.63003e6	−	3.06045e7i	−0.414474	−	1.31721i
$885$		0			0
$886$	1.87882e7	−	2.88620e6i	0.804084	−	0.123522i
$887$	3.28115e7			1.40029			0.700143	−	0.714002i	$-0.253119\pi$
$887$	3.28115e7			1.40029			0.700143	+	0.714002i	$0.253119\pi$
$888$	742866.	+	1.50970e6i	0.0316139	+	0.0642476i
$889$	8.59762e6			0.364858
$890$		0			0
$891$		−	1.69862e7i		−	0.716806i
$892$	−4.23603e6	+	1.33291e6i	−0.178257	+	0.0560905i
$893$			3.70397e6i			0.155431i
$894$	458641.	+	2.98560e6i	0.0191924	+	0.124936i
$895$		0			0
$896$	−4.44814e6	−	2.45210e6i	−0.185101	−	0.102040i
$897$	1.63521e6			0.0678568
$898$	−827221.	−	5.38493e6i	−0.0342319	−	0.222838i
$899$		−	1.37837e7i		−	0.568811i
$900$		0			0
$901$			2.04308e7i			0.838444i
$902$	1.06640e6	−	163818.i	0.0436421	−	0.00670419i
$903$	809223.			0.0330255
$904$	−1.36264e7	−	2.76923e7i	−0.554573	−	1.12704i
$905$		0			0
$906$	−6.29942e6	+	967703.i	−0.254965	+	0.0391671i
$907$			1.53129e7i			0.618073i	0.951050	+	0.309037i	$0.100007\pi$
$907$			1.53129e7i			0.618073i	−0.951050	+	0.309037i	$0.899993\pi$
$908$	−9.28627e6	−	2.95120e7i	−0.373789	−	1.18791i
$909$			3.21429e7i			1.29025i
$910$		0			0
$911$	−5.70920e6			−0.227918			−0.113959	−	0.993485i	$-0.536353\pi$
$911$	−5.70920e6			−0.227918			−0.113959	+	0.993485i	$0.536353\pi$
$912$	−475928.	+	332426.i	−0.0189476	+	0.0132345i
$913$	−1.83050e7			−0.726764
$914$	5.91378e6	+	3.84967e7i	0.234153	+	1.52426i
$915$		0			0
$916$	−8.07461e6	−	2.56613e7i	−0.317968	−	1.01051i
$917$			9.69077e6i			0.380570i
$918$	1.10848e7	−	1.70282e6i	0.434130	−	0.0666900i
$919$	−9.51702e6			−0.371717			−0.185858	−	0.982577i	$-0.559507\pi$
$919$	−9.51702e6			−0.371717			−0.185858	+	0.982577i	$0.559507\pi$
$920$		0			0
$921$	3.37919e6			0.131269
$922$	3.83588e6	−	589258.i	0.148606	−	0.0228285i
$923$		−	2.33978e7i		−	0.904005i
$924$	−678295.	+	213433.i	−0.0261360	+	0.00822396i
$925$		0			0
$926$	−89962.9	−	585629.i	−0.00344775	−	0.0224437i
$927$	−3.93680e7			−1.50468
$928$	2.57312e7	−	2.45608e7i	0.980823	−	0.936210i
$929$	−2.79927e7			−1.06416			−0.532078	−	0.846695i	$-0.678589\pi$
$929$	−2.79927e7			−1.06416			−0.532078	+	0.846695i	$0.678589\pi$
$930$		0			0
$931$			3.51708e6i			0.132987i
$932$	−2.98361e7	+	9.38825e6i	−1.12513	+	0.354034i
$933$			2.57809e6i			0.0969604i
$934$	−3.24088e7	+	4.97857e6i	−1.21562	+	0.186740i
$935$		0			0
$936$	2.40781e7	−	1.18479e7i	0.898322	−	0.442031i
$937$	−6.87551e6			−0.255832			−0.127916	−	0.991785i	$-0.540829\pi$
$937$	−6.87551e6			−0.255832			−0.127916	+	0.991785i	$0.540829\pi$
$938$	−7.48905e6	+	1.15045e6i	−0.277920	+	0.0426934i
$939$		−	2.29586e6i		−	0.0849730i
$940$		0			0
$941$			2.68027e7i			0.986743i	0.869819	+	0.493371i	$0.164236\pi$
$941$			2.68027e7i			0.986743i	−0.869819	+	0.493371i	$0.835764\pi$
$942$	759315.	+	4.94289e6i	0.0278801	+	0.181490i
$943$	613025.			0.0224491
$944$	1.75424e7	+	2.51152e7i	0.640707	+	0.917289i
$945$		0			0
$946$	3.07094e6	+	1.99908e7i	0.111569	+	0.726277i
$947$			8.91973e6i			0.323204i	0.986856	+	0.161602i	$0.0516661\pi$
$947$			8.91973e6i			0.323204i	−0.986856	+	0.161602i	$0.948334\pi$
$948$	−1.92993e6	−	6.13337e6i	−0.0697462	−	0.221655i
$949$			1.63694e7i			0.590019i
$950$		0			0
$951$	−3.19080e6			−0.114406
$952$	3.49995e6	+	7.11279e6i	0.125161	+	0.254359i
$953$	3.25154e7			1.15973			0.579865	−	0.814713i	$-0.303105\pi$
$953$	3.25154e7			1.15973			0.579865	+	0.814713i	$0.303105\pi$
$954$	−1.68904e7	+	2.59466e6i	−0.600854	+	0.0923018i
$955$		0			0
$956$	−3.58795e7	+	1.12899e7i	−1.26970	+	0.399525i
$957$		−	4.97991e6i		−	0.175769i
$958$	7.98051e6	+	5.19505e7i	0.280942	+	1.82884i
$959$	1.99347e6			0.0699942
$960$		0			0
$961$	−2.35909e7			−0.824017
$962$	−1.93521e6	−	1.25976e7i	−0.0674202	−	0.438883i
$963$		−	1.60152e7i		−	0.556502i
$964$	1.87755e7	−	5.90790e6i	0.650726	−	0.204758i
$965$		0			0
$966$	−399343.	+	61346.2i	−0.0137690	+	0.00211517i
$967$	−1.43390e7			−0.493121			−0.246561	−	0.969127i	$-0.579300\pi$
$967$	−1.43390e7			−0.493121			−0.246561	+	0.969127i	$0.579300\pi$
$968$	5.02478e6	+	1.02116e7i	0.172357	+	0.350273i
$969$	906041.			0.0309983
$970$		0			0
$971$		−	4.37060e7i		−	1.48762i	−0.668390	−	0.743811i	$-0.733016\pi$
$971$		−	4.37060e7i		−	1.48762i	0.668390	−	0.743811i	$-0.266984\pi$
$972$	4.24288e6	+	1.34840e7i	0.144044	+	0.457776i
$973$			7.11015e6i			0.240767i
$974$	5.61481e6	+	3.65505e7i	0.189643	+	1.23451i
$975$		0			0
$976$	1.05459e7	+	1.50983e7i	0.354370	+	0.507346i
$977$	−7.03004e6			−0.235625			−0.117813	−	0.993036i	$-0.537588\pi$
$977$	−7.03004e6			−0.235625			−0.117813	+	0.993036i	$0.537588\pi$
$978$	1.01872e6	+	6.63150e6i	0.0340569	+	0.221699i
$979$			2.55412e7i			0.851696i
$980$		0			0
$981$			1.31307e7i			0.435628i
$982$	3.70460e7	−	5.69092e6i	1.22592	−	0.188323i
$983$	−3.83715e7			−1.26656			−0.633279	−	0.773924i	$-0.718291\pi$
$983$	−3.83715e7			−1.26656			−0.633279	+	0.773924i	$0.718291\pi$
$984$	−255875.	+	125907.i	−0.00842441	+	0.00414534i
$985$		0			0
$986$	−5.48732e7	+	8.42950e6i	−1.79750	+	0.276127i
$987$		−	1.19918e6i		−	0.0391826i
$988$	4.19471e6	−	1.31991e6i	0.136713	−	0.0430182i
$989$			1.14918e7i			0.373591i
$990$		0			0
$991$	−5.24440e7			−1.69634			−0.848168	−	0.529727i	$-0.822294\pi$
$991$	−5.24440e7			−1.69634			−0.848168	+	0.529727i	$0.822294\pi$
$992$	8.97751e6	+	9.40532e6i	0.289652	+	0.303455i
$993$	−8.60602e6			−0.276968
$994$	877785.	+	5.71409e6i	0.0281788	+	0.183435i
$995$		0			0
$996$	4.61522e6	−	1.45223e6i	0.147416	−	0.0463860i
$997$		−	4.88081e7i		−	1.55508i	−0.628832	−	0.777542i	$-0.716467\pi$
$997$		−	4.88081e7i		−	1.55508i	0.628832	−	0.777542i	$-0.283533\pi$
$998$	2.93806e7	−	4.51337e6i	0.933757	−	0.143442i
$999$	4.45509e6			0.141235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.d.c.101.9	✓	20
4.3	odd	2		800.6.d.d.401.12		20
5.2	odd	4		200.6.f.d.149.39		40
5.3	odd	4		200.6.f.d.149.2		40
5.4	even	2		200.6.d.d.101.12	yes	20
8.3	odd	2		800.6.d.d.401.9		20
8.5	even	2	inner	200.6.d.c.101.10	yes	20
20.3	even	4		800.6.f.d.49.18		40
20.7	even	4		800.6.f.d.49.23		40
20.19	odd	2		800.6.d.b.401.9		20
40.3	even	4		800.6.f.d.49.24		40
40.13	odd	4		200.6.f.d.149.40		40
40.19	odd	2		800.6.d.b.401.12		20
40.27	even	4		800.6.f.d.49.17		40
40.29	even	2		200.6.d.d.101.11	yes	20
40.37	odd	4		200.6.f.d.149.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.9	✓	20	1.1	even	1	trivial
200.6.d.c.101.10	yes	20	8.5	even	2	inner
200.6.d.d.101.11	yes	20	40.29	even	2
200.6.d.d.101.12	yes	20	5.4	even	2
200.6.f.d.149.1		40	40.37	odd	4
200.6.f.d.149.2		40	5.3	odd	4
200.6.f.d.149.39		40	5.2	odd	4
200.6.f.d.149.40		40	40.13	odd	4
800.6.d.b.401.9		20	20.19	odd	2
800.6.d.b.401.12		20	40.19	odd	2
800.6.d.d.401.9		20	8.3	odd	2
800.6.d.d.401.12		20	4.3	odd	2
800.6.f.d.49.17		40	40.27	even	4
800.6.f.d.49.18		40	20.3	even	4
800.6.f.d.49.23		40	20.7	even	4
800.6.f.d.49.24		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)

\(f(q)\)	\(=\)	\(q+(-0.858917 - 5.59127i) q^{2} -2.58812i q^{3} +(-30.5245 + 9.60487i) q^{4} +(-14.4709 + 2.22298i) q^{6} -27.4015 q^{7} +(79.9214 + 162.421i) q^{8} +236.302 q^{9} +O(q^{10})\)	\(q+(-0.858917 - 5.59127i) q^{2} -2.58812i q^{3} +(-30.5245 + 9.60487i) q^{4} +(-14.4709 + 2.22298i) q^{6} -27.4015 q^{7} +(79.9214 + 162.421i) q^{8} +236.302 q^{9} -313.336i q^{11} +(24.8585 + 79.0011i) q^{12} -627.354i q^{13} +(23.5356 + 153.209i) q^{14} +(839.493 - 586.368i) q^{16} -1598.17 q^{17} +(-202.964 - 1321.23i) q^{18} -219.049i q^{19} +70.9184i q^{21} +(-1751.95 + 269.130i) q^{22} -1007.11 q^{23} +(420.365 - 206.846i) q^{24} +(-3507.70 + 538.845i) q^{26} -1240.49i q^{27} +(836.419 - 263.188i) q^{28} +6140.83i q^{29} -2244.61 q^{31} +(-3999.60 - 4190.19i) q^{32} -810.951 q^{33} +(1372.70 + 8935.80i) q^{34} +(-7212.99 + 2269.65i) q^{36} +3591.40i q^{37} +(-1224.76 + 188.145i) q^{38} -1623.67 q^{39} -608.697 q^{41} +(396.524 - 60.9130i) q^{42} -11410.6i q^{43} +(3009.55 + 9564.44i) q^{44} +(865.025 + 5631.03i) q^{46} -16909.4 q^{47} +(-1517.59 - 2172.71i) q^{48} -16056.2 q^{49} +4136.26i q^{51} +(6025.66 + 19149.7i) q^{52} -12783.9i q^{53} +(-6935.91 + 1065.48i) q^{54} +(-2189.97 - 4450.58i) q^{56} -566.923 q^{57} +(34335.0 - 5274.47i) q^{58} +29917.1i q^{59} +17985.1i q^{61} +(1927.93 + 12550.2i) q^{62} -6475.03 q^{63} +(-19993.1 + 25961.8i) q^{64} +(696.540 + 4534.24i) q^{66} +48881.2i q^{67} +(48783.4 - 15350.2i) q^{68} +2606.52i q^{69} +37296.0 q^{71} +(18885.6 + 38380.3i) q^{72} -26092.7 q^{73} +(20080.5 - 3084.71i) q^{74} +(2103.93 + 6686.35i) q^{76} +8585.89i q^{77} +(1394.60 + 9078.35i) q^{78} -77636.5 q^{79} +54210.8 q^{81} +(522.820 + 3403.38i) q^{82} -58419.8i q^{83} +(-681.162 - 2164.75i) q^{84} +(-63799.8 + 9800.78i) q^{86} +15893.2 q^{87} +(50892.4 - 25042.3i) q^{88} -81513.8 q^{89} +17190.5i q^{91} +(30741.6 - 9673.17i) q^{92} +5809.30i q^{93} +(14523.7 + 94544.7i) q^{94} +(-10844.7 + 10351.4i) q^{96} -28396.6 q^{97} +(13790.9 + 89774.2i) q^{98} -74041.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) \) 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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