LMFDB - Embedded newform 200.6.d.c.101.10

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

$q$-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	$0.0264546\pi$
$3$			2.58812i			0.166028i	−0.996548	+	0.0830139i	$0.973545\pi$
$4$	−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	$0.127660\pi$
$11$			313.336i			0.780780i	−0.920650	+	0.390390i	$0.872340\pi$
$12$	24.8585	−	79.0011i	0.0498336	−	0.158373i
$13$			627.354i			1.02957i	0.857320	+	0.514783i	$0.172128\pi$
$13$			627.354i			1.02957i	−0.857320	+	0.514783i	$0.827872\pi$
$14$	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	$0.0221732\pi$
$19$			219.049i			0.139205i	−0.997575	+	0.0696027i	$0.977827\pi$
$20$		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	$-0.762866\pi$
$29$		−	6140.83i		−	1.35591i	0.735102	−	0.677957i	$-0.237134\pi$
$30$		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	$-0.930816\pi$
$37$		−	3591.40i		−	0.431280i	0.976473	−	0.215640i	$-0.0691837\pi$
$38$	−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	$0.155945\pi$
$43$			11410.6i			0.941105i	−0.882372	+	0.470553i	$0.844055\pi$
$44$	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	$0.101189\pi$
$53$			12783.9i			0.625134i	−0.949896	+	0.312567i	$0.898811\pi$
$54$	−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	$-0.811014\pi$
$59$		−	29917.1i		−	1.11889i	0.828866	−	0.559447i	$-0.188986\pi$
$60$		0			0
$61$		−	17985.1i		−	0.618852i	−0.950923	−	0.309426i	$-0.899863\pi$
$61$		−	17985.1i		−	0.618852i	0.950923	−	0.309426i	$-0.100137\pi$
$62$	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	$-0.768364\pi$
$67$		−	48881.2i		−	1.33032i	0.746703	−	0.665158i	$-0.231636\pi$
$68$	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	$0.154093\pi$
$83$			58419.8i			0.930818i	−0.885096	+	0.465409i	$0.845907\pi$
$84$	−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	$-0.769107\pi$
$101$		−	136025.i		−	1.32683i	0.748253	−	0.663413i	$-0.230893\pi$
$102$	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	$0.0923717\pi$
$107$			67774.4i			0.572277i	−0.958188	+	0.286138i	$0.907628\pi$
$108$	11914.7	−	37865.3i	0.0982936	−	0.312379i
$109$		−	55567.6i		−	0.447977i	−0.974592	−	0.223988i	$-0.928092\pi$
$109$		−	55567.6i		−	0.447977i	0.974592	−	0.223988i	$-0.0719077\pi$
$110$		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	$0.356634\pi$
$131$			353658.i			1.80055i	−0.435322	+	0.900275i	$0.643366\pi$
$132$	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	$0.192885\pi$
$139$			259480.i			1.13911i	−0.821952	+	0.569557i	$0.807115\pi$
$140$		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	$0.124305\pi$
$149$			206318.i			0.761328i	−0.924713	+	0.380664i	$0.875695\pi$
$150$		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	$0.186508\pi$
$157$			341575.i			1.10595i	−0.833196	+	0.552977i	$0.813492\pi$
$158$	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	$0.236068\pi$
$163$			458266.i			1.35098i	−0.737370	+	0.675489i	$0.763932\pi$
$164$	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	$-0.620757\pi$
$173$		−	731330.i		−	1.85780i	0.370336	−	0.928898i	$-0.379243\pi$
$174$	−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	$0.121333\pi$
$179$			318951.i			0.744032i	−0.928226	+	0.372016i	$0.878667\pi$
$180$		0			0
$181$		−	586939.i		−	1.33167i	−0.746099	−	0.665835i	$-0.768076\pi$
$181$		−	586939.i		−	1.33167i	0.746099	−	0.665835i	$-0.231924\pi$
$182$	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	$0.134418\pi$
$197$			446496.i			0.819695i	−0.912154	+	0.409847i	$0.865582\pi$
$198$	−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	$0.336206\pi$
$211$			1.12592e6i			1.74101i	−0.492163	+	0.870503i	$0.663794\pi$
$212$	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	$-0.786050\pi$
$227$		−	966829.i		−	1.24533i	0.782488	−	0.622666i	$-0.213950\pi$
$228$	17305.1	+	5445.23i	0.0220463	+	0.00693711i
$229$		−	840679.i		−	1.05935i	−0.848199	−	0.529677i	$-0.822313\pi$
$229$		−	840679.i		−	1.05935i	0.848199	−	0.529677i	$-0.177687\pi$
$230$		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	$0.217950\pi$
$251$			1.26252e6i			1.26490i	−0.774602	+	0.632448i	$0.782050\pi$
$252$	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	$-0.612452\pi$
$269$		−	2.22703e6i		−	1.87649i	0.345976	−	0.938243i	$-0.387548\pi$
$270$		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	$0.104787\pi$
$277$			825684.i			0.646568i	−0.946302	+	0.323284i	$0.895213\pi$
$278$	−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	$0.208887\pi$
$283$			1.64409e6i			1.22028i	−0.792293	+	0.610141i	$0.791113\pi$
$284$	−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	$-0.791203\pi$
$293$		−	1.79254e6i		−	1.21983i	0.792465	−	0.609917i	$-0.208797\pi$
$294$	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	$-0.870633\pi$
$307$		−	1.30565e6i		−	0.790646i	0.918542	−	0.395323i	$-0.129367\pi$
$308$	−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	$0.111964\pi$
$317$			1.23286e6i			0.689075i	−0.938773	+	0.344538i	$0.888036\pi$
$318$	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	$0.314013\pi$
$331$			3.32521e6i			1.66820i	−0.551612	+	0.834101i	$0.685987\pi$
$332$	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	$-0.853370\pi$
$347$		−	1.99415e6i		−	0.889066i	0.895763	−	0.444533i	$-0.146630\pi$
$348$	−485132.	−	152652.i	−0.214740	−	0.0675701i
$349$			3.06586e6i			1.34737i	0.739017	+	0.673687i	$0.235290\pi$
$349$			3.06586e6i			1.34737i	−0.739017	+	0.673687i	$0.764710\pi$
$350$		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	$-0.892437\pi$
$373$		−	1.78163e6i		−	0.663047i	0.943447	−	0.331524i	$-0.107563\pi$
$374$	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	$0.278544\pi$
$379$			4.29296e6i			1.53518i	−0.640941	+	0.767590i	$0.721456\pi$
$380$		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	$-0.986583\pi$
$389$		−	251531.i		−	0.0842786i	0.999112	−	0.0421393i	$-0.0134173\pi$
$390$		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	$-0.971579\pi$
$397$		−	560036.i		−	0.178336i	0.996017	−	0.0891682i	$-0.0284209\pi$
$398$	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	$0.0720250\pi$
$419$			1.61245e6i			0.448695i	−0.974509	+	0.224347i	$0.927975\pi$
$420$		0			0
$421$			3.39591e6i			0.933795i	0.884312	+	0.466897i	$0.154628\pi$
$421$			3.39591e6i			0.933795i	−0.884312	+	0.466897i	$0.845372\pi$
$422$	−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	$-0.866659\pi$
$443$		−	3.36028e6i		−	0.813516i	0.913536	−	0.406758i	$-0.133341\pi$
$444$	−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	$-0.976049\pi$
$461$		−	686048.i		−	0.150349i	0.997170	−	0.0751747i	$-0.0239515\pi$
$462$	−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	$0.210819\pi$
$467$			5.79633e6i			1.22987i	−0.788576	+	0.614937i	$0.789181\pi$
$468$	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	$-0.787071\pi$
$491$		−	6.62569e6i		−	1.24030i	0.784483	−	0.620151i	$-0.212929\pi$
$492$	−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	$-0.843404\pi$
$499$		−	5.25473e6i		−	0.944710i	0.881408	−	0.472355i	$-0.156596\pi$
$500$		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	$0.148071\pi$
$509$			5.24405e6i			0.897164i	−0.893742	+	0.448582i	$0.851929\pi$
$510$		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	$0.157730\pi$
$523$			5.94878e6i			0.950985i	−0.879720	+	0.475493i	$0.842270\pi$
$524$	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	$0.402217\pi$
$541$			1.29778e7i			1.90637i	−0.302385	+	0.953186i	$0.597783\pi$
$542$	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	$-0.856224\pi$
$547$		−	6.10894e6i		−	0.872966i	0.899712	−	0.436483i	$-0.143776\pi$
$548$	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	$-0.756120\pi$
$557$		−	1.01541e7i		−	1.38676i	0.720570	−	0.693382i	$-0.243880\pi$
$558$	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	$0.00485721\pi$
$563$			229520.i			0.0305175i	−0.999884	+	0.0152588i	$0.995143\pi$
$564$	−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	$-0.751152\pi$
$571$		−	1.09781e7i		−	1.40909i	0.709660	−	0.704544i	$-0.248848\pi$
$572$	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	$0.267721\pi$
$587$			1.24448e7i			1.49071i	−0.666666	+	0.745357i	$0.732279\pi$
$588$	−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	$0.277872\pi$
$613$			1.42575e7i			1.53247i	−0.642561	+	0.766235i	$0.722128\pi$
$614$	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	$-0.884869\pi$
$619$		−	6.74663e6i		−	0.707718i	0.935299	−	0.353859i	$-0.115131\pi$
$620$		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	$-0.931226\pi$
$643$		−	4.49516e6i		−	0.428763i	0.976750	−	0.214382i	$-0.0687736\pi$
$644$	−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	$0.196356\pi$
$653$			1.26068e7i			1.15697i	−0.815693	+	0.578484i	$0.803644\pi$
$654$	−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	$0.109387\pi$
$659$			7.51240e6i			0.673853i	−0.941531	+	0.336927i	$0.890613\pi$
$660$		0			0
$661$			1.66707e7i			1.48405i	0.670371	+	0.742026i	$0.266135\pi$
$661$			1.66707e7i			1.48405i	−0.670371	+	0.742026i	$0.733865\pi$
$662$	−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	$-0.990904\pi$
$677$		−	681435.i		−	0.0571416i	0.999592	−	0.0285708i	$-0.00909561\pi$
$678$	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	$-0.852558\pi$
$683$		−	1.08945e7i		−	0.893629i	0.894627	−	0.446815i	$-0.147442\pi$
$684$	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	$0.175025\pi$
$691$			1.31179e7i			1.04513i	−0.852599	+	0.522565i	$0.824975\pi$
$692$	−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	$0.173504\pi$
$701$			1.34915e7i			1.03697i	−0.855087	+	0.518485i	$0.826496\pi$
$702$	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	$0.153100\pi$
$709$			1.23849e7i			0.925290i	−0.886544	+	0.462645i	$0.846900\pi$
$710$		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	$-0.677129\pi$
$733$		−	2.47037e7i		−	1.69825i	0.528190	−	0.849126i	$-0.322871\pi$
$734$	−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	$-0.908949\pi$
$739$		−	8.37792e6i		−	0.564319i	0.959367	−	0.282160i	$-0.0910508\pi$
$740$		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	$0.0974371\pi$
$757$			9.50255e6i			0.602699i	−0.953514	+	0.301350i	$0.902563\pi$
$758$	−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	$-0.966693\pi$
$773$		−	3.47037e6i		−	0.208894i	0.994530	−	0.104447i	$-0.0333073\pi$
$774$	−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	$0.0833260\pi$
$787$			8.99343e6i			0.517593i	−0.965932	+	0.258797i	$0.916674\pi$
$788$	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	$0.0590390\pi$
$797$			6.61412e6i			0.368830i	−0.982848	+	0.184415i	$0.940961\pi$
$798$	−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	$0.106892\pi$
$811$			1.23447e7i			0.659068i	−0.944144	+	0.329534i	$0.893108\pi$
$812$	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	$-0.828648\pi$
$821$		−	1.98036e7i		−	1.02538i	0.858573	−	0.512692i	$-0.171352\pi$
$822$	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	$-0.569624\pi$
$827$		−	3.83991e7i		−	1.95235i	0.216989	−	0.976174i	$-0.430376\pi$
$828$	7.26429e6	+	2.28579e6i	0.368228	+	0.115867i
$829$			1.17104e7i			0.591813i	0.955217	+	0.295907i	$0.0956217\pi$
$829$			1.17104e7i			0.591813i	−0.955217	+	0.295907i	$0.904378\pi$
$830$		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	$-0.990465\pi$
$853$		−	1.27294e6i		−	0.0599010i	0.999551	−	0.0299505i	$-0.00953496\pi$
$854$	−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	$0.0746840\pi$
$859$			1.00554e7i			0.464960i	−0.972601	+	0.232480i	$0.925316\pi$
$860$		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	$-0.899047\pi$
$877$		−	1.42067e7i		−	0.623727i	0.950127	−	0.311863i	$-0.100953\pi$
$878$	−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	$0.0659450\pi$
$883$			9.53131e6i			0.411387i	−0.978616	+	0.205694i	$0.934055\pi$
$884$	−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	$-0.899993\pi$
$907$		−	1.53129e7i		−	0.618073i	0.951050	−	0.309037i	$-0.100007\pi$
$908$	−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	$-0.835764\pi$
$941$		−	2.68027e7i		−	0.986743i	0.869819	−	0.493371i	$-0.164236\pi$
$942$	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	$-0.948334\pi$
$947$		−	8.91973e6i		−	0.323204i	0.986856	−	0.161602i	$-0.0516661\pi$
$948$	−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	$0.266984\pi$
$971$			4.37060e7i			1.48762i	−0.668390	+	0.743811i	$0.733016\pi$
$972$	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	$0.283533\pi$
$997$			4.88081e7i			1.55508i	−0.628832	+	0.777542i	$0.716467\pi$
$998$	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.101.10	yes	20
4.3	odd	2		800.6.d.d.401.9		20
5.2	odd	4		200.6.f.d.149.1		40
5.3	odd	4		200.6.f.d.149.40		40
5.4	even	2		200.6.d.d.101.11	yes	20
8.3	odd	2		800.6.d.d.401.12		20
8.5	even	2	inner	200.6.d.c.101.9	✓	20
20.3	even	4		800.6.f.d.49.24		40
20.7	even	4		800.6.f.d.49.17		40
20.19	odd	2		800.6.d.b.401.12		20
40.3	even	4		800.6.f.d.49.18		40
40.13	odd	4		200.6.f.d.149.2		40
40.19	odd	2		800.6.d.b.401.9		20
40.27	even	4		800.6.f.d.49.23		40
40.29	even	2		200.6.d.d.101.12	yes	20
40.37	odd	4		200.6.f.d.149.39		40

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