LMFDB - Embedded newform 200.6.f.c.149.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,6,Mod(149,200)]

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, 1]))

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

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not 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} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 $ x^20 - 2x^19 - 17x^18 + 78x^17 + 253x^16 - 884x^15 + 2396x^14 + 19376x^13 - 109104x^12 - 96128x^11 + 3580672x^10 - 1538048x^9 - 27930624x^8 + 79364096x^7 + 157024256x^6 - 926941184x^5 + 4244635648x^4 + 20937965568x^3 - 73014444032x^2 - 137438953472*x + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{45}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.4
Root			$-3.80026 - 1.24819i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.6.f.c.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.04846 + 2.55207i) q^{2} +11.5927 q^{3} +(18.9739 - 25.7680i) q^{4} +(-58.5253 + 29.5854i) q^{6} +231.529i q^{7} +(-30.0270 + 178.512i) q^{8} -108.609 q^{9} +O(q^{10})$	\(q+(-5.04846 + 2.55207i) q^{2} +11.5927 q^{3} +(18.9739 - 25.7680i) q^{4} +(-58.5253 + 29.5854i) q^{6} +231.529i q^{7} +(-30.0270 + 178.512i) q^{8} -108.609 q^{9} +559.335i q^{11} +(219.959 - 298.721i) q^{12} +107.903 q^{13} +(-590.877 - 1168.86i) q^{14} +(-303.984 - 977.839i) q^{16} +441.735i q^{17} +(548.309 - 277.178i) q^{18} -1873.33i q^{19} +2684.04i q^{21} +(-1427.46 - 2823.78i) q^{22} -3835.50i q^{23} +(-348.095 + 2069.43i) q^{24} +(-544.743 + 275.376i) q^{26} -4076.10 q^{27} +(5966.04 + 4393.00i) q^{28} +3369.76i q^{29} -7955.88 q^{31} +(4030.16 + 4160.80i) q^{32} +6484.21i q^{33} +(-1127.34 - 2230.08i) q^{34} +(-2060.74 + 2798.64i) q^{36} +10687.6 q^{37} +(4780.87 + 9457.43i) q^{38} +1250.89 q^{39} -9963.87 q^{41} +(-6849.87 - 13550.3i) q^{42} +925.409 q^{43} +(14413.0 + 10612.8i) q^{44} +(9788.47 + 19363.4i) q^{46} -8063.78i q^{47} +(-3523.99 - 11335.8i) q^{48} -36798.5 q^{49} +5120.91i q^{51} +(2047.34 - 2780.45i) q^{52} -7952.45 q^{53} +(20578.0 - 10402.5i) q^{54} +(-41330.5 - 6952.12i) q^{56} -21717.0i q^{57} +(-8599.87 - 17012.1i) q^{58} +16801.2i q^{59} -11297.4i q^{61} +(40164.9 - 20304.0i) q^{62} -25146.1i q^{63} +(-30964.8 - 10720.3i) q^{64} +(-16548.2 - 32735.3i) q^{66} -33619.4 q^{67} +(11382.7 + 8381.43i) q^{68} -44463.9i q^{69} -8869.47 q^{71} +(3261.21 - 19388.0i) q^{72} +55505.3i q^{73} +(-53955.9 + 27275.5i) q^{74} +(-48272.0 - 35544.3i) q^{76} -129502. q^{77} +(-6315.05 + 3192.35i) q^{78} -69413.7 q^{79} -20861.0 q^{81} +(50302.2 - 25428.5i) q^{82} -10231.5 q^{83} +(69162.5 + 50926.7i) q^{84} +(-4671.89 + 2361.71i) q^{86} +39064.7i q^{87} +(-99847.8 - 16795.2i) q^{88} +92458.4 q^{89} +24982.6i q^{91} +(-98833.4 - 72774.4i) q^{92} -92230.2 q^{93} +(20579.3 + 40709.7i) q^{94} +(46720.5 + 48234.9i) q^{96} +88657.9i q^{97} +(185776. - 93912.3i) q^{98} -60748.9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9	$ 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9} + 1252 q^{12} - 2708 q^{14} + 3080 q^{16} + 2070 q^{18} + 8244 q^{22} - 1032 q^{24} - 8084 q^{26} + 11664 q^{27} + 22924 q^{28} + 7160 q^{31} + 14792 q^{32} - 21132 q^{34} + 18344 q^{36} - 3608 q^{37} - 16884 q^{38} + 44904 q^{39} + 11608 q^{41} - 49444 q^{42} - 51772 q^{43} - 72296 q^{44} - 28516 q^{46} - 85048 q^{48} - 18756 q^{49} - 111624 q^{52} + 928 q^{53} + 100584 q^{54} - 53624 q^{56} + 152344 q^{58} + 228648 q^{62} + 11264 q^{64} - 56688 q^{66} - 161604 q^{67} + 359040 q^{68} - 200312 q^{71} + 563448 q^{72} - 78876 q^{74} - 153872 q^{76} + 26008 q^{77} - 624640 q^{78} - 282080 q^{79} + 65172 q^{81} - 410576 q^{82} - 99092 q^{83} + 297128 q^{84} + 27452 q^{86} - 464496 q^{88} + 3160 q^{89} - 519244 q^{92} + 293472 q^{93} - 148820 q^{94} + 395168 q^{96} + 663674 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9 + 1252 * q^12 - 2708 * q^14 + 3080 * q^16 + 2070 * q^18 + 8244 * q^22 - 1032 * q^24 - 8084 * q^26 + 11664 * q^27 + 22924 * q^28 + 7160 * q^31 + 14792 * q^32 - 21132 * q^34 + 18344 * q^36 - 3608 * q^37 - 16884 * q^38 + 44904 * q^39 + 11608 * q^41 - 49444 * q^42 - 51772 * q^43 - 72296 * q^44 - 28516 * q^46 - 85048 * q^48 - 18756 * q^49 - 111624 * q^52 + 928 * q^53 + 100584 * q^54 - 53624 * q^56 + 152344 * q^58 + 228648 * q^62 + 11264 * q^64 - 56688 * q^66 - 161604 * q^67 + 359040 * q^68 - 200312 * q^71 + 563448 * q^72 - 78876 * q^74 - 153872 * q^76 + 26008 * q^77 - 624640 * q^78 - 282080 * q^79 + 65172 * q^81 - 410576 * q^82 - 99092 * q^83 + 297128 * q^84 + 27452 * q^86 - 464496 * q^88 + 3160 * q^89 - 519244 * q^92 + 293472 * q^93 - 148820 * q^94 + 395168 * q^96 + 663674 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.04846	+	2.55207i	−0.892450	+	0.451146i
$2$	−5.04846	+	2.55207i	−0.892450	+	0.451146i
$3$	11.5927			0.743673			0.371836	−	0.928298i	$-0.378728\pi$
$3$	11.5927			0.743673			0.371836	+	0.928298i	$0.378728\pi$
$4$	18.9739	−	25.7680i	0.592934	−	0.805251i
$5$		0			0
$5$		0			0
$6$	−58.5253	+	29.5854i	−0.663691	+	0.335505i
$7$			231.529i			1.78591i	0.450146	+	0.892955i	$0.351372\pi$
$7$			231.529i			1.78591i	−0.450146	+	0.892955i	$0.648628\pi$
$8$	−30.0270	+	178.512i	−0.165878	+	0.986146i
$9$	−108.609			−0.446951
$10$		0			0
$11$			559.335i			1.39377i	0.717184	+	0.696884i	$0.245431\pi$
$11$			559.335i			1.39377i	−0.717184	+	0.696884i	$0.754569\pi$
$12$	219.959	−	298.721i	0.440949	−	0.598843i
$13$	107.903			0.177082			0.0885411	−	0.996073i	$-0.471780\pi$
$13$	107.903			0.177082			0.0885411	+	0.996073i	$0.471780\pi$
$14$	−590.877	−	1168.86i	−0.805707	−	1.59384i
$15$		0			0
$16$	−303.984	−	977.839i	−0.296859	−	0.954921i
$17$			441.735i			0.370715i	0.982671	+	0.185357i	$0.0593443\pi$
$17$			441.735i			0.370715i	−0.982671	+	0.185357i	$0.940656\pi$
$18$	548.309	−	277.178i	0.398881	−	0.201640i
$19$		−	1873.33i		−	1.19050i	−0.803540	−	0.595251i	$-0.797053\pi$
$19$		−	1873.33i		−	1.19050i	0.803540	−	0.595251i	$-0.202947\pi$
$20$		0			0
$21$			2684.04i			1.32813i
$22$	−1427.46	−	2823.78i	−0.628794	−	1.24387i
$23$		−	3835.50i		−	1.51183i	−0.654670	−	0.755915i	$-0.727193\pi$
$23$		−	3835.50i		−	1.51183i	0.654670	−	0.755915i	$-0.272807\pi$
$24$	−348.095	+	2069.43i	−0.123359	+	0.733370i
$25$		0			0
$26$	−544.743	+	275.376i	−0.158037	+	0.0798900i
$27$	−4076.10			−1.07606
$28$	5966.04	+	4393.00i	1.43811	+	1.05893i
$29$			3369.76i			0.744054i	0.928222	+	0.372027i	$0.121337\pi$
$29$			3369.76i			0.744054i	−0.928222	+	0.372027i	$0.878663\pi$
$30$		0			0
$31$	−7955.88			−1.48691			−0.743454	−	0.668787i	$-0.766814\pi$
$31$	−7955.88			−1.48691			−0.743454	+	0.668787i	$0.766814\pi$
$32$	4030.16	+	4160.80i	0.695741	+	0.718293i
$33$			6484.21i			1.03651i
$34$	−1127.34	−	2230.08i	−0.167247	−	0.330844i
$35$		0			0
$36$	−2060.74	+	2798.64i	−0.265012	+	0.359908i
$37$	10687.6			1.28344			0.641720	−	0.766939i	$-0.278221\pi$
$37$	10687.6			1.28344			0.641720	+	0.766939i	$0.278221\pi$
$38$	4780.87	+	9457.43i	0.537091	+	1.06246i
$39$	1250.89			0.131691
$40$		0			0
$41$	−9963.87			−0.925696			−0.462848	−	0.886438i	$-0.653172\pi$
$41$	−9963.87			−0.925696			−0.462848	+	0.886438i	$0.653172\pi$
$42$	−6849.87	−	13550.3i	−0.599182	−	1.18529i
$43$	925.409			0.0763243			0.0381621	−	0.999272i	$-0.487850\pi$
$43$	925.409			0.0763243			0.0381621	+	0.999272i	$0.487850\pi$
$44$	14413.0	+	10612.8i	1.12233	+	0.826412i
$45$		0			0
$46$	9788.47	+	19363.4i	0.682056	+	1.34923i
$47$		−	8063.78i		−	0.532469i	−0.963908	−	0.266234i	$-0.914221\pi$
$47$		−	8063.78i		−	0.532469i	0.963908	−	0.266234i	$-0.0857795\pi$
$48$	−3523.99	−	11335.8i	−0.220766	−	0.710149i
$49$	−36798.5			−2.18947
$50$		0			0
$51$			5120.91i			0.275690i
$52$	2047.34	−	2780.45i	0.104998	−	0.142596i
$53$	−7952.45			−0.388876			−0.194438	−	0.980915i	$-0.562288\pi$
$53$	−7952.45			−0.388876			−0.194438	+	0.980915i	$0.562288\pi$
$54$	20578.0	−	10402.5i	0.960328	−	0.485460i
$55$		0			0
$56$	−41330.5	−	6952.12i	−1.76117	−	0.296242i
$57$		−	21717.0i		−	0.885344i
$58$	−8599.87	−	17012.1i	−0.335677	−	0.664031i
$59$			16801.2i			0.628361i	0.949363	+	0.314181i	$0.101730\pi$
$59$			16801.2i			0.628361i	−0.949363	+	0.314181i	$0.898270\pi$
$60$		0			0
$61$		−	11297.4i		−	0.388734i	−0.980929	−	0.194367i	$-0.937735\pi$
$61$		−	11297.4i		−	0.388734i	0.980929	−	0.194367i	$-0.0622653\pi$
$62$	40164.9	−	20304.0i	1.32699	−	0.670813i
$63$		−	25146.1i		−	0.798214i
$64$	−30964.8	−	10720.3i	−0.944969	−	0.327159i
$65$		0			0
$66$	−16548.2	−	32735.3i	−0.467617	−	0.925031i
$67$	−33619.4			−0.914963			−0.457481	−	0.889219i	$-0.651248\pi$
$67$	−33619.4			−0.914963			−0.457481	+	0.889219i	$0.651248\pi$
$68$	11382.7	+	8381.43i	0.298518	+	0.219809i
$69$		−	44463.9i		−	1.12431i
$70$		0			0
$71$	−8869.47			−0.208810			−0.104405	−	0.994535i	$-0.533294\pi$
$71$	−8869.47			−0.208810			−0.104405	+	0.994535i	$0.533294\pi$
$72$	3261.21	−	19388.0i	0.0741391	−	0.440759i
$73$			55505.3i			1.21907i	0.792761	+	0.609533i	$0.208643\pi$
$73$			55505.3i			1.21907i	−0.792761	+	0.609533i	$0.791357\pi$
$74$	−53955.9	+	27275.5i	−1.14541	+	0.579019i
$75$		0			0
$76$	−48272.0	−	35544.3i	−0.958653	−	0.705889i
$77$	−129502.			−2.48914
$78$	−6315.05	+	3192.35i	−0.117528	+	0.0594120i
$79$	−69413.7			−1.25135			−0.625673	−	0.780085i	$-0.715176\pi$
$79$	−69413.7			−1.25135			−0.625673	+	0.780085i	$0.715176\pi$
$80$		0			0
$81$	−20861.0			−0.353284
$82$	50302.2	−	25428.5i	0.826138	−	0.417625i
$83$	−10231.5			−0.163021			−0.0815106	−	0.996672i	$-0.525974\pi$
$83$	−10231.5			−0.163021			−0.0815106	+	0.996672i	$0.525974\pi$
$84$	69162.5	+	50926.7i	1.06948	+	0.787494i
$85$		0			0
$86$	−4671.89	+	2361.71i	−0.0681156	+	0.0344334i
$87$			39064.7i			0.553333i
$88$	−99847.8	−	16795.2i	−1.37446	−	0.231195i
$89$	92458.4			1.23729			0.618645	−	0.785671i	$-0.287682\pi$
$89$	92458.4			1.23729			0.618645	+	0.785671i	$0.287682\pi$
$90$		0			0
$91$			24982.6i			0.316253i
$92$	−98833.4	−	72774.4i	−1.21740	−	0.896415i
$93$	−92230.2			−1.10577
$94$	20579.3	+	40709.7i	0.240221	+	0.475201i
$95$		0			0
$96$	46720.5	+	48234.9i	0.517404	+	0.534174i
$97$			88657.9i			0.956727i	0.878162	+	0.478364i	$0.158770\pi$
$97$			88657.9i			0.956727i	−0.878162	+	0.478364i	$0.841230\pi$
$98$	185776.	−	93912.3i	1.95400	−	0.987773i
$99$		−	60748.9i		−	0.622946i
$100$		0			0
$101$		−	20080.2i		−	0.195869i	−0.995193	−	0.0979343i	$-0.968776\pi$
$101$		−	20080.2i		−	0.195869i	0.995193	−	0.0979343i	$-0.0312235\pi$
$102$	−13068.9	−	25852.7i	−0.124377	−	0.246040i
$103$			16926.9i			0.157212i	0.996906	+	0.0786059i	$0.0250469\pi$
$103$			16926.9i			0.157212i	−0.996906	+	0.0786059i	$0.974953\pi$
$104$	−3240.00	+	19261.9i	−0.0293739	+	0.174629i
$105$		0			0
$106$	40147.6	−	20295.2i	0.347052	−	0.175440i
$107$	69502.3			0.586867			0.293434	−	0.955979i	$-0.405202\pi$
$107$	69502.3			0.586867			0.293434	+	0.955979i	$0.405202\pi$
$108$	−77339.5	+	105033.i	−0.638031	+	0.866497i
$109$		−	229650.i		−	1.85140i	−0.378260	−	0.925699i	$-0.623477\pi$
$109$		−	229650.i		−	1.85140i	0.378260	−	0.925699i	$-0.376523\pi$
$110$		0			0
$111$	123898.			0.954459
$112$	226398.	−	70380.9i	1.70540	−	0.530163i
$113$			60045.6i			0.442369i	0.975232	+	0.221185i	$0.0709923\pi$
$113$			60045.6i			0.442369i	−0.975232	+	0.221185i	$0.929008\pi$
$114$	55423.2	+	109637.i	0.399420	+	0.790125i
$115$		0			0
$116$	86832.2	+	63937.5i	0.599151	+	0.441175i
$117$	−11719.2			−0.0791470
$118$	−42877.7	−	84820.0i	−0.283483	−	0.560781i
$119$	−102274.			−0.662063
$120$		0			0
$121$	−151805.			−0.942590
$122$	28831.7	+	57034.3i	0.175376	+	0.346926i
$123$	−115508.			−0.688415
$124$	−150954.	+	205007.i	−0.881638	+	1.19733i
$125$		0			0
$126$	64174.6	+	126949.i	0.360112	+	0.712366i
$127$			45815.4i			0.252059i	0.992026	+	0.126030i	$0.0402234\pi$
$127$			45815.4i			0.252059i	−0.992026	+	0.126030i	$0.959777\pi$
$128$	183683.	−	24903.0i	0.990934	−	0.134346i
$129$	10728.0			0.0567603
$130$		0			0
$131$			135284.i			0.688761i	0.938830	+	0.344381i	$0.111911\pi$
$131$			135284.i			0.688761i	−0.938830	+	0.344381i	$0.888089\pi$
$132$	167085.	+	123031.i	0.834649	+	0.614580i
$133$	433729.			2.12613
$134$	169726.	−	85799.2i	0.816559	−	0.412782i
$135$		0			0
$136$	−78854.9	−	13264.0i	−0.365579	−	0.0614932i
$137$			345313.i			1.57185i	0.618320	+	0.785927i	$0.287814\pi$
$137$			345313.i			1.57185i	−0.618320	+	0.785927i	$0.712186\pi$
$138$	113475.	+	224474.i	0.507227	+	1.00339i
$139$		−	116846.i		−	0.512951i	−0.966551	−	0.256475i	$-0.917439\pi$
$139$		−	116846.i		−	0.512951i	0.966551	−	0.256475i	$-0.0825612\pi$
$140$		0			0
$141$		−	93481.0i		−	0.395982i
$142$	44777.2	−	22635.5i	0.186353	−	0.0942040i
$143$			60353.9i			0.246811i
$144$	33015.4	+	106202.i	0.132681	+	0.426803i
$145$		0			0
$146$	−141653.	−	280216.i	−0.549977	−	1.08796i
$147$	−426594.			−1.62825
$148$	202785.	−	275398.i	0.760995	−	1.03349i
$149$			87842.0i			0.324143i	0.986779	+	0.162072i	$0.0518175\pi$
$149$			87842.0i			0.324143i	−0.986779	+	0.162072i	$0.948182\pi$
$150$		0			0
$151$	165109.			0.589288			0.294644	−	0.955607i	$-0.404799\pi$
$151$	165109.			0.589288			0.294644	+	0.955607i	$0.404799\pi$
$152$	334411.	+	56250.5i	1.17401	+	0.197478i
$153$		−	47976.5i		−	0.165691i
$154$	653786.	−	330498.i	2.22144	−	1.12297i
$155$		0			0
$156$	23734.2	−	32232.9i	0.0780841	−	0.106044i
$157$	−191163.			−0.618948			−0.309474	−	0.950908i	$-0.600153\pi$
$157$	−191163.			−0.618948			−0.309474	+	0.950908i	$0.600153\pi$
$158$	350432.	−	177149.i	1.11676	−	0.564541i
$159$	−92190.4			−0.289197
$160$		0			0
$161$	888029.			2.69999
$162$	105316.	−	53238.8i	0.315288	−	0.159383i
$163$	−478403.			−1.41034			−0.705172	−	0.709037i	$-0.749130\pi$
$163$	−478403.			−1.41034			−0.705172	+	0.709037i	$0.749130\pi$
$164$	−189053.	+	256749.i	−0.548877	+	0.745418i
$165$		0			0
$166$	51653.3	−	26111.5i	0.145488	−	0.0735464i
$167$			307544.i			0.853328i	0.904410	+	0.426664i	$0.140311\pi$
$167$			307544.i			0.853328i	−0.904410	+	0.426664i	$0.859689\pi$
$168$	−479133.	−	80593.9i	−1.30973	−	0.220307i
$169$	−359650.			−0.968642
$170$		0			0
$171$			203461.i			0.532096i
$172$	17558.6	−	23846.0i	0.0452552	−	0.0614602i
$173$	−55343.3			−0.140588			−0.0702942	−	0.997526i	$-0.522394\pi$
$173$	−55343.3			−0.140588			−0.0702942	+	0.997526i	$0.522394\pi$
$174$	−99695.8	−	197217.i	−0.249634	−	0.493822i
$175$		0			0
$176$	546940.	−	170029.i	1.33094	−	0.413753i
$177$			194771.i			0.467295i
$178$	−466773.	+	235960.i	−1.10422	+	0.558199i
$179$			703665.i			1.64147i	0.571308	+	0.820736i	$0.306436\pi$
$179$			703665.i			1.64147i	−0.571308	+	0.820736i	$0.693564\pi$
$180$		0			0
$181$		−	96255.4i		−	0.218388i	−0.994020	−	0.109194i	$-0.965173\pi$
$181$		−	96255.4i		−	0.218388i	0.994020	−	0.109194i	$-0.0348270\pi$
$182$	−63757.3	−	126124.i	−0.142676	−	0.282240i
$183$		−	130967.i		−	0.289091i
$184$	684682.	+	115169.i	1.49088	+	0.250778i
$185$		0			0
$186$	465620.	−	235378.i	0.986847	−	0.498865i
$187$	−247078.			−0.516690
$188$	−207788.	−	153001.i	−0.428771	−	0.315719i
$189$		−	943734.i		−	1.92174i
$190$		0			0
$191$	−504776.			−1.00119			−0.500594	−	0.865682i	$-0.666885\pi$
$191$	−504776.			−1.00119			−0.500594	+	0.865682i	$0.666885\pi$
$192$	−358965.	−	124278.i	−0.702748	−	0.243299i
$193$			233138.i			0.450527i	0.974298	+	0.225263i	$0.0723242\pi$
$193$			233138.i			0.450527i	−0.974298	+	0.225263i	$0.927676\pi$
$194$	−226261.	−	447586.i	−0.431624	−	0.853831i
$195$		0			0
$196$	−698210.	+	948225.i	−1.29821	+	1.76308i
$197$	322071.			0.591270			0.295635	−	0.955301i	$-0.404469\pi$
$197$	322071.			0.591270			0.295635	+	0.955301i	$0.404469\pi$
$198$	155035.	+	306688.i	0.281040	+	0.555948i
$199$	−457179.			−0.818377			−0.409189	−	0.912450i	$-0.634188\pi$
$199$	−457179.			−0.818377			−0.409189	+	0.912450i	$0.634188\pi$
$200$		0			0
$201$	−389740.			−0.680433
$202$	51246.1	+	101374.i	0.0883655	+	0.174803i
$203$	−780197.			−1.32881
$204$	131956.	+	97163.5i	0.222000	+	0.163466i
$205$		0			0
$206$	−43198.7	−	85455.0i	−0.0709256	−	0.140304i
$207$			416571.i			0.675714i
$208$	−32800.7	−	105512.i	−0.0525684	−	0.169100i
$209$	1.04782e6			1.65928
$210$		0			0
$211$		−	826083.i		−	1.27737i	−0.769468	−	0.638686i	$-0.779478\pi$
$211$		−	826083.i		−	1.27737i	0.769468	−	0.638686i	$-0.220522\pi$
$212$	−150889.	+	204919.i	−0.230578	+	0.313143i
$213$	−102821.			−0.155286
$214$	−350879.	+	177375.i	−0.523749	+	0.264763i
$215$		0			0
$216$	122393.	−	727631.i	0.178494	−	1.06115i
$217$		−	1.84201e6i		−	2.65548i
$218$	586082.	+	1.15938e6i	0.835252	+	1.65228i
$219$			643457.i			0.906586i
$220$		0			0
$221$			47664.5i			0.0656470i
$222$	−625495.	+	316197.i	−0.851807	+	0.430601i
$223$		−	1.03975e6i		−	1.40013i	−0.714079	−	0.700066i	$-0.753154\pi$
$223$		−	1.03975e6i		−	1.40013i	0.714079	−	0.700066i	$-0.246846\pi$
$224$	−963343.	+	933098.i	−1.28281	+	1.24253i
$225$		0			0
$226$	−153241.	−	303138.i	−0.199573	−	0.394792i
$227$	1.32339e6			1.70460			0.852302	−	0.523051i	$-0.175206\pi$
$227$	1.32339e6			1.70460			0.852302	+	0.523051i	$0.175206\pi$
$228$	−559603.	−	412055.i	−0.712924	−	0.524950i
$229$		−	1.12200e6i		−	1.41385i	−0.707288	−	0.706926i	$-0.750082\pi$
$229$		−	1.12200e6i		−	1.41385i	0.707288	−	0.706926i	$-0.249918\pi$
$230$		0			0
$231$	−1.50128e6			−1.85111
$232$	−601542.	−	101184.i	−0.733746	−	0.123422i
$233$		−	20887.8i		−	0.0252059i	−0.999921	−	0.0126030i	$-0.995988\pi$
$233$		−	20887.8i		−	0.0252059i	0.999921	−	0.0126030i	$-0.00401176\pi$
$234$	59164.1	−	29908.3i	0.0706348	−	0.0357069i
$235$		0			0
$236$	432933.	+	318783.i	0.505989	+	0.372577i
$237$	−804693.			−0.930592
$238$	516328.	−	261011.i	0.590858	−	0.298687i
$239$	−40580.0			−0.0459534			−0.0229767	−	0.999736i	$-0.507314\pi$
$239$	−40580.0			−0.0459534			−0.0229767	+	0.999736i	$0.507314\pi$
$240$		0			0
$241$	841414.			0.933184			0.466592	−	0.884473i	$-0.345482\pi$
$241$	841414.			0.933184			0.466592	+	0.884473i	$0.345482\pi$
$242$	766382.	−	387417.i	0.841215	−	0.425246i
$243$	748657.			0.813330
$244$	−291111.	−	214355.i	−0.313029	−	0.230494i
$245$		0			0
$246$	583139.	−	294785.i	0.614376	−	0.310576i
$247$		−	202138.i		−	0.210817i
$248$	238892.	−	1.42022e6i	0.246645	−	1.46631i
$249$	−118611.			−0.121234
$250$		0			0
$251$			1.24994e6i			1.25229i	0.779707	+	0.626144i	$0.215368\pi$
$251$			1.24994e6i			1.25229i	−0.779707	+	0.626144i	$0.784632\pi$
$252$	−647966.	−	477119.i	−0.642763	−	0.473288i
$253$	2.14533e6			2.10714
$254$	−116924.	−	231297.i	−0.113716	−	0.224950i
$255$		0			0
$256$	−863764.	+	594494.i	−0.823749	+	0.566954i
$257$			766259.i			0.723674i	0.932241	+	0.361837i	$0.117850\pi$
$257$			766259.i			0.723674i	−0.932241	+	0.361837i	$0.882150\pi$
$258$	−54159.9	+	27378.6i	−0.0506557	+	0.0256072i
$259$			2.47448e6i			2.29211i
$260$		0			0
$261$		−	365987.i		−	0.332556i
$262$	−345255.	−	682977.i	−0.310732	−	0.614685i
$263$			1.35524e6i			1.20817i	0.796921	+	0.604084i	$0.206461\pi$
$263$			1.35524e6i			1.20817i	−0.796921	+	0.604084i	$0.793539\pi$
$264$	−1.15751e6	−	194702.i	−1.02215	−	0.171933i
$265$		0			0
$266$	−2.18966e6	+	1.10691e6i	−1.89746	+	0.959196i
$267$	1.07184e6			0.920139
$268$	−637891.	+	866307.i	−0.542512	+	0.736775i
$269$			173063.i			0.145822i	0.997338	+	0.0729110i	$0.0232289\pi$
$269$			173063.i			0.145822i	−0.997338	+	0.0729110i	$0.976771\pi$
$270$		0			0
$271$	802529.			0.663800			0.331900	−	0.943315i	$-0.392310\pi$
$271$	802529.			0.663800			0.331900	+	0.943315i	$0.392310\pi$
$272$	431946.	−	134280.i	0.354003	−	0.110050i
$273$			289616.i			0.235188i
$274$	−881264.	−	1.74330e6i	−0.709136	−	1.40280i
$275$		0			0
$276$	−1.14575e6	−	843652.i	−0.905349	−	0.666639i
$277$	1.01003e6			0.790924			0.395462	−	0.918482i	$-0.370585\pi$
$277$	1.01003e6			0.790924			0.395462	+	0.918482i	$0.370585\pi$
$278$	298198.	+	589891.i	0.231416	+	0.457783i
$279$	864081.			0.664575
$280$		0			0
$281$	−2.24480e6			−1.69595			−0.847973	−	0.530039i	$-0.822177\pi$
$281$	−2.24480e6			−1.69595			−0.847973	+	0.530039i	$0.822177\pi$
$282$	238570.	+	471935.i	0.178646	+	0.353394i
$283$	−1.71474e6			−1.27272			−0.636361	−	0.771392i	$-0.719561\pi$
$283$	−1.71474e6			−1.27272			−0.636361	+	0.771392i	$0.719561\pi$
$284$	−168288.	+	228549.i	−0.123811	+	0.168145i
$285$		0			0
$286$	−154027.	−	304694.i	−0.111348	−	0.220267i
$287$		−	2.30692e6i		−	1.65321i
$288$	−437712.	−	451900.i	−0.310962	−	0.321042i
$289$	1.22473e6			0.862571
$290$		0			0
$291$			1.02779e6i			0.711492i
$292$	1.43026e6	+	1.05315e6i	0.981654	+	0.722825i
$293$	2.27442e6			1.54775			0.773876	−	0.633337i	$-0.218315\pi$
$293$	2.27442e6			1.54775			0.773876	+	0.633337i	$0.218315\pi$
$294$	2.15364e6	−	1.08870e6i	1.45313	−	0.734580i
$295$		0			0
$296$	−320917.	+	1.90786e6i	−0.212894	+	1.26566i
$297$		−	2.27991e6i		−	1.49978i
$298$	−224179.	−	443467.i	−0.146236	−	0.289281i
$299$		−	413862.i		−	0.267718i
$300$		0			0
$301$			214259.i			0.136308i
$302$	−833545.	+	421369.i	−0.525910	+	0.265855i
$303$		−	232784.i		−	0.145662i
$304$	−1.83182e6	+	569461.i	−1.13684	+	0.353411i
$305$		0			0
$306$	122439.	+	242207.i	0.0747511	+	0.147871i
$307$	−2.36152e6			−1.43003			−0.715015	−	0.699109i	$-0.753580\pi$
$307$	−2.36152e6			−1.43003			−0.715015	+	0.699109i	$0.753580\pi$
$308$	−2.45716e6	+	3.33702e6i	−1.47590	+	2.00439i
$309$			196229.i			0.116914i
$310$		0			0
$311$	797118.			0.467328			0.233664	−	0.972317i	$-0.424928\pi$
$311$	797118.			0.467328			0.233664	+	0.972317i	$0.424928\pi$
$312$	−37560.4	+	223298.i	−0.0218446	+	0.129867i
$313$			1.93581e6i			1.11687i	0.829549	+	0.558434i	$0.188598\pi$
$313$			1.93581e6i			1.11687i	−0.829549	+	0.558434i	$0.811402\pi$
$314$	965077.	−	487861.i	0.552380	−	0.279236i
$315$		0			0
$316$	−1.31705e6	+	1.78866e6i	−0.741966	+	1.00765i
$317$	2.34736e6			1.31200			0.655998	−	0.754763i	$-0.272248\pi$
$317$	2.34736e6			1.31200			0.655998	+	0.754763i	$0.272248\pi$
$318$	465420.	−	235276.i	0.258093	−	0.130470i
$319$	−1.88483e6			−1.03704
$320$		0			0
$321$	805720.			0.436437
$322$	−4.48318e6	+	2.26631e6i	−2.40961	+	1.21809i
$323$	827516.			0.441337
$324$	−395815.	+	537548.i	−0.209474	+	0.284482i
$325$		0			0
$326$	2.41520e6	−	1.22092e6i	1.25866	−	0.636271i
$327$		−	2.66226e6i		−	1.37683i
$328$	299186.	−	1.77867e6i	0.153552	−	0.912872i
$329$	1.86700e6			0.950941
$330$		0			0
$331$			291538.i			0.146260i	0.997322	+	0.0731300i	$0.0232988\pi$
$331$			291538.i			0.146260i	−0.997322	+	0.0731300i	$0.976701\pi$
$332$	−194131.	+	263646.i	−0.0966607	+	0.131273i
$333$	−1.16077e6			−0.573635
$334$	−784874.	−	1.55262e6i	−0.384976	−	0.761553i
$335$		0			0
$336$	2.62456e6	−	815905.i	1.26826	−	0.394268i
$337$			3.41829e6i			1.63958i	0.572661	+	0.819792i	$0.305911\pi$
$337$			3.41829e6i			1.63958i	−0.572661	+	0.819792i	$0.694089\pi$
$338$	1.81568e6	−	917852.i	0.864464	−	0.436999i
$339$			696091.i			0.328978i
$340$		0			0
$341$		−	4.45001e6i		−	2.07241i
$342$	−519246.	−	1.02716e6i	−0.240053	−	0.474869i
$343$		−	4.62860e6i		−	2.12429i
$344$	−27787.3	+	165196.i	−0.0126605	+	0.0752669i
$345$		0			0
$346$	279398.	−	141240.i	0.125468	−	0.0634260i
$347$	3.87943e6			1.72960			0.864798	−	0.502120i	$-0.167447\pi$
$347$	3.87943e6			1.72960			0.864798	+	0.502120i	$0.167447\pi$
$348$	1.00662e6	+	741209.i	0.445572	+	0.328090i
$349$			2.29111e6i			1.00689i	0.864027	+	0.503445i	$0.167934\pi$
$349$			2.29111e6i			1.00689i	−0.864027	+	0.503445i	$0.832066\pi$
$350$		0			0
$351$	−439823.			−0.190551
$352$	−2.32728e6	+	2.25421e6i	−1.00113	+	0.969702i
$353$		−	2.16132e6i		−	0.923171i	−0.887096	−	0.461586i	$-0.847281\pi$
$353$		−	2.16132e6i		−	0.923171i	0.887096	−	0.461586i	$-0.152719\pi$
$354$	−497069.	−	983293.i	−0.210818	−	0.417037i
$355$		0			0
$356$	1.75430e6	−	2.38247e6i	0.733631	−	0.996329i
$357$	−1.18564e6			−0.492358
$358$	−1.79580e6	−	3.55242e6i	−0.740544	−	1.46493i
$359$	−2.30863e6			−0.945408			−0.472704	−	0.881221i	$-0.656722\pi$
$359$	−2.30863e6			−0.945408			−0.472704	+	0.881221i	$0.656722\pi$
$360$		0			0
$361$	−1.03326e6			−0.417295
$362$	245651.	+	485942.i	0.0985250	+	0.194900i
$363$	−1.75983e6			−0.700979
$364$	643753.	+	474017.i	0.254663	+	0.187517i
$365$		0			0
$366$	334237.	+	661182.i	0.130422	+	0.257999i
$367$			1.68650e6i			0.653614i	0.945091	+	0.326807i	$0.105973\pi$
$367$			1.68650e6i			0.653614i	−0.945091	+	0.326807i	$0.894027\pi$
$368$	−3.75051e6	+	1.16593e6i	−1.44368	+	0.448800i
$369$	1.08217e6			0.413741
$370$		0			0
$371$		−	1.84122e6i		−	0.694498i
$372$	−1.74997e6	+	2.37659e6i	−0.655650	+	0.890425i
$373$	−171338.			−0.0637647			−0.0318824	−	0.999492i	$-0.510150\pi$
$373$	−171338.			−0.0637647			−0.0318824	+	0.999492i	$0.510150\pi$
$374$	1.24736e6	−	630561.i	0.461120	−	0.233103i
$375$		0			0
$376$	1.43948e6	+	242131.i	0.525092	+	0.0883246i
$377$			363607.i			0.131759i
$378$	2.40848e6	+	4.76440e6i	0.866987	+	1.71506i
$379$			1.11665e6i			0.399317i	0.979866	+	0.199658i	$0.0639832\pi$
$379$			1.11665e6i			0.399317i	−0.979866	+	0.199658i	$0.936017\pi$
$380$		0			0
$381$			531125.i			0.187449i
$382$	2.54834e6	−	1.28822e6i	0.893510	−	0.451682i
$383$		−	433589.i		−	0.151036i	−0.997144	−	0.0755182i	$-0.975939\pi$
$383$		−	433589.i		−	0.151036i	0.997144	−	0.0755182i	$-0.0240611\pi$
$384$	2.12939e6	−	288693.i	0.736931	−	0.0999098i
$385$		0			0
$386$	−594985.	−	1.17699e6i	−0.203254	−	0.402073i
$387$	−100508.			−0.0341132
$388$	2.28454e6	+	1.68218e6i	0.770406	+	0.567276i
$389$		−	3.20076e6i		−	1.07245i	−0.844074	−	0.536227i	$-0.819849\pi$
$389$		−	3.20076e6i		−	1.07245i	0.844074	−	0.536227i	$-0.180151\pi$
$390$		0			0
$391$	1.69428e6			0.560457
$392$	1.10495e6	−	6.56895e6i	0.363184	−	2.15914i
$393$			1.56831e6i			0.512213i
$394$	−1.62596e6	+	821948.i	−0.527679	+	0.266749i
$395$		0			0
$396$	−1.56538e6	−	1.15264e6i	−0.501628	−	0.369366i
$397$	1.44525e6			0.460220			0.230110	−	0.973165i	$-0.426091\pi$
$397$	1.44525e6			0.460220			0.230110	+	0.973165i	$0.426091\pi$
$398$	2.30805e6	−	1.16675e6i	0.730361	−	0.369208i
$399$	5.02810e6			1.58114
$400$		0			0
$401$	1.44642e6			0.449194			0.224597	−	0.974452i	$-0.427893\pi$
$401$	1.44642e6			0.449194			0.224597	+	0.974452i	$0.427893\pi$
$402$	1.96759e6	−	994645.i	0.607252	−	0.306975i
$403$	−858463.			−0.263305
$404$	−517428.	−	381000.i	−0.157723	−	0.116137i
$405$		0			0
$406$	3.93879e6	−	1.99112e6i	1.18590	−	0.599490i
$407$			5.97795e6i			1.78882i
$408$	−914141.	−	153766.i	−0.271871	−	0.0457308i
$409$	−2.45947e6			−0.726997			−0.363498	−	0.931595i	$-0.618418\pi$
$409$	−2.45947e6			−0.726997			−0.363498	+	0.931595i	$0.618418\pi$
$410$		0			0
$411$			4.00312e6i			1.16894i
$412$	436174.	+	321170.i	0.126595	+	0.0932162i
$413$	−3.88995e6			−1.12220
$414$	−1.06312e6	−	2.10304e6i	−0.304846	−	0.603041i
$415$		0			0
$416$	434866.	+	448962.i	0.123203	+	0.127197i
$417$		−	1.35456e6i		−	0.381467i
$418$	−5.28987e6	+	2.67411e6i	−1.48083	+	0.748580i
$419$			2.72546e6i			0.758410i	0.925313	+	0.379205i	$0.123802\pi$
$419$			2.72546e6i			0.758410i	−0.925313	+	0.379205i	$0.876198\pi$
$420$		0			0
$421$			6.51391e6i			1.79117i	0.444892	+	0.895584i	$0.353242\pi$
$421$			6.51391e6i			1.79117i	−0.444892	+	0.895584i	$0.646758\pi$
$422$	2.10822e6	+	4.17044e6i	0.576282	+	1.13999i
$423$			875800.i			0.237987i
$424$	238789.	−	1.41960e6i	0.0645058	−	0.383489i
$425$		0			0
$426$	519088.	−	262407.i	0.138585	−	0.0700569i
$427$	2.61567e6			0.694245
$428$	1.31873e6	−	1.79094e6i	0.347973	−	0.472575i
$429$			699665.i			0.183547i
$430$		0			0
$431$	3.85877e6			1.00059			0.500295	−	0.865855i	$-0.333225\pi$
$431$	3.85877e6			1.00059			0.500295	+	0.865855i	$0.333225\pi$
$432$	1.23907e6	+	3.98577e6i	0.319437	+	1.02755i
$433$		−	1.22019e6i		−	0.312757i	−0.987697	−	0.156379i	$-0.950018\pi$
$433$		−	1.22019e6i		−	0.312757i	0.987697	−	0.156379i	$-0.0499820\pi$
$434$	4.70095e6	+	9.29933e6i	1.19801	+	2.36989i
$435$		0			0
$436$	−5.91763e6	−	4.35735e6i	−1.49084	−	1.09776i
$437$	−7.18516e6			−1.79984
$438$	−1.64215e6	−	3.24846e6i	−0.409003	−	0.809083i
$439$	1.29701e6			0.321204			0.160602	−	0.987019i	$-0.448656\pi$
$439$	1.29701e6			0.321204			0.160602	+	0.987019i	$0.448656\pi$
$440$		0			0
$441$	3.99665e6			0.978588
$442$	−121643.	−	240632.i	−0.0296164	−	0.0585866i
$443$	2.57412e6			0.623188			0.311594	−	0.950215i	$-0.399137\pi$
$443$	2.57412e6			0.623188			0.311594	+	0.950215i	$0.399137\pi$
$444$	2.35083e6	−	3.19261e6i	0.565931	−	0.768579i
$445$		0			0
$446$	2.65353e6	+	5.24916e6i	0.631664	+	1.24955i
$447$			1.01833e6i			0.241056i
$448$	2.48207e6	−	7.16923e6i	0.584276	−	1.68763i
$449$	−52050.0			−0.0121844			−0.00609221	−	0.999981i	$-0.501939\pi$
$449$	−52050.0			−0.0121844			−0.00609221	+	0.999981i	$0.501939\pi$
$450$		0			0
$451$		−	5.57315e6i		−	1.29021i
$452$	1.54726e6	+	1.13930e6i	0.356218	+	0.262296i
$453$	1.91406e6			0.438238
$454$	−6.68108e6	+	3.37738e6i	−1.52127	+	0.769026i
$455$		0			0
$456$	3.87673e6	+	652096.i	0.873078	+	0.146859i
$457$		−	446306.i		−	0.0999637i	−0.998750	−	0.0499818i	$-0.984084\pi$
$457$		−	446306.i		−	0.0999637i	0.998750	−	0.0499818i	$-0.0159163\pi$
$458$	2.86342e6	+	5.66437e6i	0.637854	+	1.26179i
$459$		−	1.80056e6i		−	0.398910i
$460$		0			0
$461$		−	3.55954e6i		−	0.780085i	−0.920797	−	0.390043i	$-0.872460\pi$
$461$		−	3.55954e6i		−	0.780085i	0.920797	−	0.390043i	$-0.127540\pi$
$462$	7.57915e6	−	3.83137e6i	1.65202	−	0.835121i
$463$			2.31611e6i			0.502120i	0.967972	+	0.251060i	$0.0807791\pi$
$463$			2.31611e6i			0.502120i	−0.967972	+	0.251060i	$0.919221\pi$
$464$	3.29509e6	−	1.02435e6i	0.710513	−	0.220879i
$465$		0			0
$466$	53307.1	+	105451.i	0.0113716	+	0.0224950i
$467$	−7.14211e6			−1.51542			−0.757712	−	0.652589i	$-0.773683\pi$
$467$	−7.14211e6			−1.51542			−0.757712	+	0.652589i	$0.773683\pi$
$468$	−222359.	+	301982.i	−0.0469290	+	0.0637333i
$469$		−	7.78386e6i		−	1.63404i
$470$		0			0
$471$	−2.21609e6			−0.460295
$472$	−2.99920e6	−	504489.i	−0.619656	−	0.104231i
$473$			517614.i			0.106378i
$474$	4.06246e6	−	2.05363e6i	0.830507	−	0.419833i
$475$		0			0
$476$	−1.94054e6	+	2.63541e6i	−0.392560	+	0.533127i
$477$	863709.			0.173809
$478$	204867.	−	103563.i	0.0410111	−	0.0207317i
$479$	−2.43371e6			−0.484651			−0.242326	−	0.970195i	$-0.577910\pi$
$479$	−2.43371e6			−0.484651			−0.242326	+	0.970195i	$0.577910\pi$
$480$		0			0
$481$	1.15322e6			0.227274
$482$	−4.24785e6	+	2.14735e6i	−0.832820	+	0.421003i
$483$	1.02947e7			2.00791
$484$	−2.88033e6	+	3.91172e6i	−0.558894	+	0.759022i
$485$		0			0
$486$	−3.77956e6	+	1.91062e6i	−0.725857	+	0.366931i
$487$			967697.i			0.184892i	0.995718	+	0.0924458i	$0.0294685\pi$
$487$			967697.i			0.184892i	−0.995718	+	0.0924458i	$0.970532\pi$
$488$	2.01671e6	+	339227.i	0.383349	+	0.0644823i
$489$	−5.54599e6			−1.04883
$490$		0			0
$491$		−	1.94045e6i		−	0.363245i	−0.983368	−	0.181623i	$-0.941865\pi$
$491$		−	1.94045e6i		−	0.363245i	0.983368	−	0.181623i	$-0.0581349\pi$
$492$	−2.19164e6	+	2.97642e6i	−0.408184	+	0.554347i
$493$	−1.48854e6			−0.275832
$494$	515869.	+	1.02048e6i	0.0951092	+	0.188143i
$495$		0			0
$496$	2.41846e6	+	7.77957e6i	0.441402	+	1.41988i
$497$		−	2.05354e6i		−	0.372916i
$498$	598801.	−	302703.i	0.108196	−	0.0546944i
$499$		−	8.97327e6i		−	1.61324i	−0.591069	−	0.806621i	$-0.701294\pi$
$499$		−	8.97327e6i		−	1.61324i	0.591069	−	0.806621i	$-0.298706\pi$
$500$		0			0
$501$			3.56527e6i			0.634597i
$502$	−3.18993e6	−	6.31026e6i	−0.564965	−	1.11760i
$503$			1.02287e7i			1.80261i	0.433184	+	0.901306i	$0.357390\pi$
$503$			1.02287e7i			1.80261i	−0.433184	+	0.901306i	$0.642610\pi$
$504$	4.48887e6	+	755063.i	0.787156	+	0.132406i
$505$		0			0
$506$	−1.08306e7	+	5.47504e6i	−1.88052	+	0.950629i
$507$	−4.16932e6			−0.720352
$508$	1.18057e6	+	869296.i	0.202971	+	0.149454i
$509$			1.00938e7i			1.72687i	0.504459	+	0.863435i	$0.331692\pi$
$509$			1.00938e7i			1.72687i	−0.504459	+	0.863435i	$0.668308\pi$
$510$		0			0
$511$	−1.28511e7			−2.17714
$512$	2.84349e6	−	5.20567e6i	0.479376	−	0.877610i
$513$			7.63588e6i			1.28105i
$514$	−1.95555e6	−	3.86843e6i	−0.326483	−	0.645842i
$515$		0			0
$516$	203552.	−	276440.i	0.0336551	−	0.0457063i
$517$	4.51036e6			0.742138
$518$	−6.31505e6	−	1.24923e7i	−1.03408	−	2.04559i
$519$	−641579.			−0.104552
$520$		0			0
$521$	−4.23461e6			−0.683470			−0.341735	−	0.939796i	$-0.611015\pi$
$521$	−4.23461e6			−0.683470			−0.341735	+	0.939796i	$0.611015\pi$
$522$	934025.	+	1.84767e6i	0.150031	+	0.296789i
$523$	−5.78898e6			−0.925438			−0.462719	−	0.886505i	$-0.653126\pi$
$523$	−5.78898e6			−0.925438			−0.462719	+	0.886505i	$0.653126\pi$
$524$	3.48601e6	+	2.56687e6i	0.554626	+	0.408390i
$525$		0			0
$526$	−3.45867e6	−	6.84188e6i	−0.545060	−	1.07823i
$527$		−	3.51439e6i		−	0.551219i
$528$	6.34052e6	−	1.97109e6i	0.989783	−	0.307697i
$529$	−8.27474e6			−1.28563
$530$		0			0
$531$		−	1.82476e6i		−	0.280847i
$532$	8.22953e6	−	1.11764e7i	1.26065	−	1.71207i
$533$	−1.07513e6			−0.163924
$534$	−5.41116e6	+	2.73542e6i	−0.821178	+	0.415117i
$535$		0			0
$536$	1.00949e6	−	6.00146e6i	0.151772	−	0.902287i
$537$			8.15738e6i			1.22072i
$538$	−441669.	−	873701.i	−0.0657871	−	0.130139i
$539$		−	2.05827e7i		−	3.05162i
$540$		0			0
$541$			2.51591e6i			0.369574i	0.982779	+	0.184787i	$0.0591596\pi$
$541$			2.51591e6i			0.369574i	−0.982779	+	0.184787i	$0.940840\pi$
$542$	−4.05153e6	+	2.04811e6i	−0.592408	+	0.299471i
$543$		−	1.11586e6i		−	0.162409i
$544$	−1.83797e6	+	1.78027e6i	−0.266282	+	0.257921i
$545$		0			0
$546$	−739120.	−	1.46211e6i	−0.106104	−	0.209894i
$547$	−5.57811e6			−0.797111			−0.398556	−	0.917144i	$-0.630488\pi$
$547$	−5.57811e6			−0.797111			−0.398556	+	0.917144i	$0.630488\pi$
$548$	8.89805e6	+	6.55194e6i	1.26574	+	0.932005i
$549$			1.22700e6i			0.173745i
$550$		0			0
$551$	6.31268e6			0.885798
$552$	7.93731e6	+	1.33512e6i	1.10873	+	0.186497i
$553$		−	1.60713e7i		−	2.23479i
$554$	−5.09909e6	+	2.57766e6i	−0.705860	+	0.356822i
$555$		0			0
$556$	−3.01088e6	−	2.21702e6i	−0.413054	−	0.304146i
$557$	−954006.			−0.130291			−0.0651453	−	0.997876i	$-0.520751\pi$
$557$	−954006.			−0.130291			−0.0651453	+	0.997876i	$0.520751\pi$
$558$	−4.36228e6	+	2.20520e6i	−0.593100	+	0.299821i
$559$	99854.4			0.0135157
$560$		0			0
$561$	−2.86431e6			−0.384249
$562$	1.13328e7	−	5.72889e6i	1.51355	−	0.765120i
$563$	−9.17088e6			−1.21938			−0.609691	−	0.792639i	$-0.708707\pi$
$563$	−9.17088e6			−1.21938			−0.609691	+	0.792639i	$0.708707\pi$
$564$	−2.40882e6	−	1.77370e6i	−0.318865	−	0.234791i
$565$		0			0
$566$	8.65682e6	−	4.37615e6i	1.13584	−	0.574184i
$567$		−	4.82993e6i		−	0.630933i
$568$	266324.	−	1.58330e6i	0.0346369	−	0.205917i
$569$	8.51511e6			1.10258			0.551289	−	0.834314i	$-0.314136\pi$
$569$	8.51511e6			1.10258			0.551289	+	0.834314i	$0.314136\pi$
$570$		0			0
$571$			8.35546e6i			1.07246i	0.844073	+	0.536229i	$0.180152\pi$
$571$			8.35546e6i			1.07246i	−0.844073	+	0.536229i	$0.819848\pi$
$572$	1.55520e6	+	1.14515e6i	0.198745	+	0.146343i
$573$	−5.85172e6			−0.744556
$574$	5.88742e6	+	1.16464e7i	0.745840	+	1.47541i
$575$		0			0
$576$	3.36305e6	+	1.16433e6i	0.422355	+	0.146224i
$577$		−	2.48061e6i		−	0.310184i	−0.987900	−	0.155092i	$-0.950433\pi$
$577$		−	2.48061e6i		−	0.310184i	0.987900	−	0.155092i	$-0.0495674\pi$
$578$	−6.18298e6	+	3.12559e6i	−0.769801	+	0.389146i
$579$			2.70271e6i			0.335044i
$580$		0			0
$581$		−	2.36888e6i		−	0.291141i
$582$	−2.62298e6	−	5.18873e6i	−0.320987	−	0.634971i
$583$		−	4.44809e6i		−	0.542003i
$584$	−9.90834e6	−	1.66666e6i	−1.20218	−	0.202216i
$585$		0			0
$586$	−1.14823e7	+	5.80448e6i	−1.38129	+	0.698263i
$587$	−1.08423e7			−1.29875			−0.649374	−	0.760469i	$-0.724969\pi$
$587$	−1.08423e7			−1.29875			−0.649374	+	0.760469i	$0.724969\pi$
$588$	−8.09415e6	+	1.09925e7i	−0.965445	+	1.31115i
$589$			1.49040e7i			1.77017i
$590$		0			0
$591$	3.73368e6			0.439712
$592$	−3.24885e6	−	1.04507e7i	−0.381001	−	1.22558i
$593$		−	1.62349e6i		−	0.189589i	−0.995497	−	0.0947943i	$-0.969781\pi$
$593$		−	1.62349e6i		−	0.189589i	0.995497	−	0.0947943i	$-0.0302193\pi$
$594$	5.81848e6	+	1.15100e7i	0.676618	+	1.33847i
$595$		0			0
$596$	2.26352e6	+	1.66670e6i	0.261017	+	0.192195i
$597$	−5.29994e6			−0.608605
$598$	1.05620e6	+	2.08936e6i	0.120780	+	0.238925i
$599$	5.09707e6			0.580435			0.290217	−	0.956961i	$-0.406272\pi$
$599$	5.09707e6			0.580435			0.290217	+	0.956961i	$0.406272\pi$
$600$		0			0
$601$	−46987.4			−0.00530634			−0.00265317	−	0.999996i	$-0.500845\pi$
$601$	−46987.4			−0.00530634			−0.00265317	+	0.999996i	$0.500845\pi$
$602$	−546803.	−	1.08168e6i	−0.0614950	−	0.121648i
$603$	3.65138e6			0.408944
$604$	3.13276e6	−	4.25453e6i	0.349409	−	0.474525i
$605$		0			0
$606$	594081.	+	1.17520e6i	0.0657150	+	0.129996i
$607$			5.02427e6i			0.553479i	0.960945	+	0.276739i	$0.0892538\pi$
$607$			5.02427e6i			0.553479i	−0.960945	+	0.276739i	$0.910746\pi$
$608$	7.79454e6	−	7.54982e6i	0.855129	−	0.828281i
$609$	−9.04459e6			−0.988202
$610$		0			0
$611$		−	870105.i		−	0.0942907i
$612$	−1.23626e6	−	910300.i	−0.133423	−	0.0982440i
$613$	−9.19740e6			−0.988584			−0.494292	−	0.869296i	$-0.664573\pi$
$613$	−9.19740e6			−0.988584			−0.494292	+	0.869296i	$0.664573\pi$
$614$	1.19220e7	−	6.02675e6i	1.27623	−	0.645153i
$615$		0			0
$616$	3.88857e6	−	2.31176e7i	0.412893	−	2.45466i
$617$			8.76074e6i			0.926462i	0.886237	+	0.463231i	$0.153310\pi$
$617$			8.76074e6i			0.926462i	−0.886237	+	0.463231i	$0.846690\pi$
$618$	−500790.	−	990654.i	−0.0527454	−	0.104340i
$619$		−	750516.i		−	0.0787287i	−0.999225	−	0.0393643i	$-0.987467\pi$
$619$		−	750516.i		−	0.0787287i	0.999225	−	0.0393643i	$-0.0125333\pi$
$620$		0			0
$621$			1.56339e7i			1.62682i
$622$	−4.02422e6	+	2.03430e6i	−0.417067	+	0.210833i
$623$			2.14068e7i			2.20969i
$624$	−380249.	−	1.22317e6i	−0.0390937	−	0.125755i
$625$		0			0
$626$	−4.94032e6	−	9.77286e6i	−0.503871	−	0.996749i
$627$	1.21471e7			1.23396
$628$	−3.62710e6	+	4.92589e6i	−0.366995	+	0.498409i
$629$			4.72109e6i			0.475790i
$630$		0			0
$631$	−1.72922e6			−0.172893			−0.0864463	−	0.996257i	$-0.527551\pi$
$631$	−1.72922e6			−0.172893			−0.0864463	+	0.996257i	$0.527551\pi$
$632$	2.08429e6	−	1.23912e7i	0.207570	−	1.23401i
$633$		−	9.57653e6i		−	0.949946i
$634$	−1.18506e7	+	5.99064e6i	−1.17089	+	0.591902i
$635$		0			0
$636$	−1.74921e6	+	2.37557e6i	−0.171474	+	0.232876i
$637$	−3.97066e6			−0.387717
$638$	9.51548e6	−	4.81021e6i	0.925506	−	0.467857i
$639$	963305.			0.0933280
$640$		0			0
$641$	−1.99305e7			−1.91590			−0.957950	−	0.286936i	$-0.907363\pi$
$641$	−1.99305e7			−1.91590			−0.957950	+	0.286936i	$0.907363\pi$
$642$	−4.06764e6	+	2.05625e6i	−0.389498	+	0.196897i
$643$	1.82551e7			1.74123			0.870616	−	0.491963i	$-0.163721\pi$
$643$	1.82551e7			1.74123			0.870616	+	0.491963i	$0.163721\pi$
$644$	1.68493e7	−	2.28828e7i	1.60092	−	2.17417i
$645$		0			0
$646$	−4.17768e6	+	2.11188e6i	−0.393871	+	0.199107i
$647$			621345.i			0.0583542i	0.999574	+	0.0291771i	$0.00928867\pi$
$647$			621345.i			0.0583542i	−0.999574	+	0.0291771i	$0.990711\pi$
$648$	626395.	−	3.72394e6i	0.0586018	−	0.348389i
$649$	−9.39748e6			−0.875790
$650$		0			0
$651$		−	2.13539e7i		−	1.97481i
$652$	−9.07716e6	+	1.23275e7i	−0.836240	+	1.13568i
$653$	−1.14728e7			−1.05290			−0.526449	−	0.850207i	$-0.676477\pi$
$653$	−1.14728e7			−1.05290			−0.526449	+	0.850207i	$0.676477\pi$
$654$	6.79428e6	+	1.34403e7i	0.621154	+	1.22876i
$655$		0			0
$656$	3.02885e6	+	9.74307e6i	0.274801	+	0.883967i
$657$		−	6.02838e6i		−	0.544863i
$658$	−9.42545e6	+	4.76470e6i	−0.848667	+	0.429013i
$659$			1.17996e6i			0.105841i	0.998599	+	0.0529204i	$0.0168530\pi$
$659$			1.17996e6i			0.105841i	−0.998599	+	0.0529204i	$0.983147\pi$
$660$		0			0
$661$		−	1.87825e7i		−	1.67205i	−0.548688	−	0.836027i	$-0.684873\pi$
$661$		−	1.87825e7i		−	1.67205i	0.548688	−	0.836027i	$-0.315127\pi$
$662$	−744026.	−	1.47182e6i	−0.0659847	−	0.130530i
$663$			552561.i			0.0488198i
$664$	307221.	−	1.82644e6i	0.0270415	−	0.160763i
$665$		0			0
$666$	5.86010e6	−	2.96237e6i	0.511940	−	0.258793i
$667$	1.29247e7			1.12488
$668$	7.92481e6	+	5.83530e6i	0.687143	+	0.505967i
$669$		−	1.20536e7i		−	1.04124i
$670$		0			0
$671$	6.31902e6			0.541806
$672$	−1.11678e7	+	1.08171e7i	−0.953987	+	0.924036i
$673$		−	1.18969e7i		−	1.01250i	−0.862387	−	0.506250i	$-0.831031\pi$
$673$		−	1.18969e7i		−	1.01250i	0.862387	−	0.506250i	$-0.168969\pi$
$674$	−8.72371e6	−	1.72571e7i	−0.739693	−	1.46325i
$675$		0			0
$676$	−6.82396e6	+	9.26747e6i	−0.574341	+	0.780000i
$677$	−2.73577e6			−0.229407			−0.114704	−	0.993400i	$-0.536592\pi$
$677$	−2.73577e6			−0.229407			−0.114704	+	0.993400i	$0.536592\pi$
$678$	−1.77647e6	−	3.51419e6i	−0.148417	−	0.293596i
$679$	−2.05268e7			−1.70863
$680$		0			0
$681$	1.53417e7			1.26767
$682$	1.13567e7	+	2.24657e7i	0.934958	+	1.84952i
$683$	−5.35182e6			−0.438985			−0.219493	−	0.975614i	$-0.570440\pi$
$683$	−5.35182e6			−0.438985			−0.219493	+	0.975614i	$0.570440\pi$
$684$	5.24278e6	+	3.86044e6i	0.428471	+	0.315498i
$685$		0			0
$686$	1.18125e7	+	2.33673e7i	0.958367	+	1.89582i
$687$		−	1.30070e7i		−	1.05144i
$688$	−281309.	−	904902.i	−0.0226576	−	0.0728837i
$689$	−858092.			−0.0688630
$690$		0			0
$691$			6.84272e6i			0.545172i	0.962131	+	0.272586i	$0.0878790\pi$
$691$			6.84272e6i			0.545172i	−0.962131	+	0.272586i	$0.912121\pi$
$692$	−1.05008e6	+	1.42609e6i	−0.0833597	+	0.113209i
$693$	1.40651e7			1.11253
$694$	−1.95852e7	+	9.90058e6i	−1.54358	+	0.780301i
$695$		0			0
$696$	−6.97350e6	−	1.17300e6i	−0.545667	−	0.0917855i
$697$		−	4.40139e6i		−	0.343169i
$698$	−5.84707e6	−	1.15666e7i	−0.454255	−	0.898599i
$699$		−	242146.i		−	0.0187450i
$700$		0			0
$701$			1.33086e7i			1.02291i	0.859310	+	0.511455i	$0.170893\pi$
$701$			1.33086e7i			1.02291i	−0.859310	+	0.511455i	$0.829107\pi$
$702$	2.22043e6	−	1.12246e6i	0.170057	−	0.0859662i
$703$		−	2.00214e7i		−	1.52794i
$704$	5.99627e6	−	1.73197e7i	0.455984	−	1.31707i
$705$		0			0
$706$	5.51584e6	+	1.09113e7i	0.416485	+	0.823884i
$707$	4.64914e6			0.349804
$708$	5.01887e6	+	3.69556e6i	0.376290	+	0.277075i
$709$			5.66978e6i			0.423595i	0.977314	+	0.211797i	$0.0679317\pi$
$709$			5.66978e6i			0.423595i	−0.977314	+	0.211797i	$0.932068\pi$
$710$		0			0
$711$	7.53896e6			0.559291
$712$	−2.77625e6	+	1.65049e7i	−0.205239	+	1.22015i
$713$			3.05148e7i			2.24795i
$714$	5.98564e6	−	3.02583e6i	0.439405	−	0.222126i
$715$		0			0
$716$	1.81321e7	+	1.33513e7i	1.32180	+	0.973284i
$717$	−470432.			−0.0341743
$718$	1.16550e7	−	5.89180e6i	0.843729	−	0.426517i
$719$	2.39385e7			1.72693			0.863466	−	0.504408i	$-0.168289\pi$
$719$	2.39385e7			1.72693			0.863466	+	0.504408i	$0.168289\pi$
$720$		0			0
$721$	−3.91907e6			−0.280766
$722$	5.21639e6	−	2.63696e6i	0.372415	−	0.188261i
$723$	9.75427e6			0.693983
$724$	−2.48031e6	−	1.82634e6i	−0.175857	−	0.129490i
$725$		0			0
$726$	8.88444e6	−	4.49122e6i	0.625588	−	0.316244i
$727$			1.81741e7i			1.27531i	0.770321	+	0.637656i	$0.220096\pi$
$727$			1.81741e7i			1.27531i	−0.770321	+	0.637656i	$0.779904\pi$
$728$	−4.45968e6	−	750154.i	−0.311871	−	0.0524592i
$729$	1.37482e7			0.958135
$730$		0			0
$731$			408786.i			0.0282945i
$732$	−3.37477e6	−	2.48496e6i	−0.232791	−	0.171412i
$733$	−1.39671e7			−0.960169			−0.480085	−	0.877222i	$-0.659394\pi$
$733$	−1.39671e7			−0.960169			−0.480085	+	0.877222i	$0.659394\pi$
$734$	−4.30407e6	−	8.51423e6i	−0.294876	−	0.583318i
$735$		0			0
$736$	1.59587e7	−	1.54577e7i	1.08594	−	1.05184i
$737$		−	1.88045e7i		−	1.27525i
$738$	−5.46328e6	+	2.76177e6i	−0.369243	+	0.186658i
$739$		−	1.00299e7i		−	0.675597i	−0.941219	−	0.337798i	$-0.890318\pi$
$739$		−	1.00299e7i		−	0.675597i	0.941219	−	0.337798i	$-0.109682\pi$
$740$		0			0
$741$		−	2.34332e6i		−	0.156779i
$742$	4.69892e6	+	9.29532e6i	0.313320	+	0.619804i
$743$		−	8.29176e6i		−	0.551030i	−0.961297	−	0.275515i	$-0.911152\pi$
$743$		−	8.29176e6i		−	0.551030i	0.961297	−	0.275515i	$-0.0888483\pi$
$744$	2.76940e6	−	1.64642e7i	0.183423	−	1.09045i
$745$		0			0
$746$	864991.	−	437265.i	0.0569068	−	0.0287672i
$747$	1.11123e6			0.0728625
$748$	−4.68803e6	+	6.36672e6i	−0.306363	+	0.416066i
$749$			1.60918e7i			1.04809i
$750$		0			0
$751$	1.07708e7			0.696865			0.348432	−	0.937334i	$-0.386714\pi$
$751$	1.07708e7			0.696865			0.348432	+	0.937334i	$0.386714\pi$
$752$	−7.88508e6	+	2.45126e6i	−0.508466	+	0.158068i
$753$			1.44902e7i			0.931292i
$754$	−927951.	−	1.83566e6i	−0.0594425	−	0.117588i
$755$		0			0
$756$	−2.43182e7	−	1.79063e7i	−1.54749	−	1.13947i
$757$	2.72641e7			1.72923			0.864614	−	0.502437i	$-0.167563\pi$
$757$	2.72641e7			1.72923			0.864614	+	0.502437i	$0.167563\pi$
$758$	−2.84976e6	−	5.63734e6i	−0.180150	−	0.356370i
$759$	2.48702e7			1.56702
$760$		0			0
$761$	2.70646e7			1.69410			0.847052	−	0.531510i	$-0.178375\pi$
$761$	2.70646e7			1.69410			0.847052	+	0.531510i	$0.178375\pi$
$762$	−1.35547e6	−	2.68136e6i	−0.0845671	−	0.167289i
$763$	5.31705e7			3.30643
$764$	−9.57756e6	+	1.30071e7i	−0.593638	+	0.806207i
$765$		0			0
$766$	1.10655e6	+	2.18896e6i	0.0681395	+	0.134792i
$767$			1.81289e6i			0.111272i
$768$	−1.00134e7	+	6.89180e6i	−0.612600	+	0.421628i
$769$	1.10424e7			0.673361			0.336681	−	0.941619i	$-0.390696\pi$
$769$	1.10424e7			0.673361			0.336681	+	0.941619i	$0.390696\pi$
$770$		0			0
$771$			8.88302e6i			0.538176i
$772$	6.00752e6	+	4.42354e6i	0.362787	+	0.267132i
$773$	−1.78160e6			−0.107241			−0.0536207	−	0.998561i	$-0.517076\pi$
$773$	−1.78160e6			−0.107241			−0.0536207	+	0.998561i	$0.517076\pi$
$774$	507410.	−	256503.i	0.0304443	−	0.0153901i
$775$		0			0
$776$	−1.58265e7	−	2.66213e6i	−0.943473	−	0.158700i
$777$			2.86860e7i			1.70458i
$778$	8.16855e6	+	1.61589e7i	0.483834	+	0.957111i
$779$			1.86656e7i			1.10204i
$780$		0			0
$781$		−	4.96101e6i		−	0.291033i
$782$	−8.55349e6	+	4.32391e6i	−0.500180	+	0.252848i
$783$		−	1.37355e7i		−	0.800645i
$784$	1.11861e7	+	3.59830e7i	0.649965	+	2.09077i
$785$		0			0
$786$	−4.00244e6	−	7.91755e6i	−0.231083	−	0.457124i
$787$	−2.97053e6			−0.170961			−0.0854806	−	0.996340i	$-0.527243\pi$
$787$	−2.97053e6			−0.170961			−0.0854806	+	0.996340i	$0.527243\pi$
$788$	6.11094e6	−	8.29914e6i	0.350584	−	0.476121i
$789$			1.57109e7i			0.898481i
$790$		0			0
$791$	−1.39023e7			−0.790032
$792$	1.08444e7	+	1.82411e6i	0.614316	+	0.103333i
$793$		−	1.21902e6i		−	0.0688379i
$794$	−7.29627e6	+	3.68837e6i	−0.410723	+	0.207627i
$795$		0			0
$796$	−8.67446e6	+	1.17806e7i	−0.485244	+	0.658999i
$797$	9.06646e6			0.505583			0.252791	−	0.967521i	$-0.418651\pi$
$797$	9.06646e6			0.505583			0.252791	+	0.967521i	$0.418651\pi$
$798$	−2.53841e7	+	1.28321e7i	−1.41109	+	0.713327i
$799$	3.56206e6			0.197394
$800$		0			0
$801$	−1.00418e7			−0.553008
$802$	−7.30220e6	+	3.69137e6i	−0.400883	+	0.202652i
$803$	−3.10461e7			−1.69910
$804$	−7.39489e6	+	1.00428e7i	−0.403452	+	0.547919i
$805$		0			0
$806$	4.33391e6	−	2.19086e6i	0.234986	−	0.118789i
$807$			2.00627e6i			0.108444i
$808$	3.58455e6	+	602949.i	0.193155	+	0.0324902i
$809$	1.49840e7			0.804926			0.402463	−	0.915436i	$-0.368154\pi$
$809$	1.49840e7			0.804926			0.402463	+	0.915436i	$0.368154\pi$
$810$		0			0
$811$			1.54716e7i			0.826005i	0.910730	+	0.413003i	$0.135520\pi$
$811$			1.54716e7i			0.826005i	−0.910730	+	0.413003i	$0.864480\pi$
$812$	−1.48034e7	+	2.01041e7i	−0.787898	+	1.07003i
$813$	9.30348e6			0.493650
$814$	−1.52561e7	−	3.01794e7i	−0.807019	−	1.59643i
$815$		0			0
$816$	5.00743e6	−	1.55667e6i	0.263263	−	0.0818412i
$817$		−	1.73360e6i		−	0.0908642i
$818$	1.24165e7	−	6.27673e6i	0.648808	−	0.327982i
$819$		−	2.71334e6i		−	0.141349i
$820$		0			0
$821$			1.28381e7i			0.664726i	0.943152	+	0.332363i	$0.107846\pi$
$821$			1.28381e7i			0.664726i	−0.943152	+	0.332363i	$0.892154\pi$
$822$	−1.02162e7	−	2.02096e7i	−0.527365	−	1.04322i
$823$			1.52419e7i			0.784402i	0.919880	+	0.392201i	$0.128286\pi$
$823$			1.52419e7i			0.784402i	−0.919880	+	0.392201i	$0.871714\pi$
$824$	−3.02165e6	−	508266.i	−0.155034	−	0.0260779i
$825$		0			0
$826$	1.96382e7	−	9.92742e6i	1.00150	−	0.506275i
$827$	−3.93361e6			−0.199999			−0.0999994	−	0.994987i	$-0.531884\pi$
$827$	−3.93361e6			−0.199999			−0.0999994	+	0.994987i	$0.531884\pi$
$828$	1.07342e7	+	7.90396e6i	0.544119	+	0.400653i
$829$			4.75338e6i			0.240224i	0.992760	+	0.120112i	$0.0383253\pi$
$829$			4.75338e6i			0.240224i	−0.992760	+	0.120112i	$0.961675\pi$
$830$		0			0
$831$	1.17090e7			0.588188
$832$	−3.34119e6	−	1.15676e6i	−0.167337	−	0.0579340i
$833$		−	1.62552e7i		−	0.811670i
$834$	3.45693e6	+	6.83843e6i	0.172098	+	0.340441i
$835$		0			0
$836$	1.98812e7	−	2.70003e7i	0.983846	−	1.33614i
$837$	3.24290e7			1.60000
$838$	−6.95555e6	−	1.37594e7i	−0.342154	−	0.676843i
$839$	2.71998e6			0.133401			0.0667007	−	0.997773i	$-0.478753\pi$
$839$	2.71998e6			0.133401			0.0667007	+	0.997773i	$0.478753\pi$
$840$		0			0
$841$	9.15584e6			0.446383
$842$	−1.66240e7	−	3.28852e7i	−0.808079	−	1.59853i
$843$	−2.60233e7			−1.26123
$844$	−2.12865e7	−	1.56740e7i	−1.02861	−	0.757397i
$845$		0			0
$846$	−2.23510e6	−	4.42144e6i	−0.107367	−	0.212392i
$847$		−	3.51472e7i		−	1.68338i
$848$	2.41741e6	+	7.77622e6i	0.115441	+	0.371346i
$849$	−1.98785e7			−0.946488
$850$		0			0
$851$		−	4.09923e7i		−	1.94034i
$852$	−1.95092e6	+	2.64950e6i	−0.0920746	+	0.125045i
$853$	2.68253e7			1.26233			0.631164	−	0.775649i	$-0.282577\pi$
$853$	2.68253e7			1.26233			0.631164	+	0.775649i	$0.282577\pi$
$854$	−1.32051e7	+	6.67536e6i	−0.619579	+	0.313206i
$855$		0			0
$856$	−2.08695e6	+	1.24070e7i	−0.0973480	+	0.578737i
$857$		−	8.98268e6i		−	0.417786i	−0.977938	−	0.208893i	$-0.933014\pi$
$857$		−	8.98268e6i		−	0.417786i	0.977938	−	0.208893i	$-0.0669861\pi$
$858$	−1.78559e6	−	3.53223e6i	−0.0828065	−	0.163806i
$859$			2.14669e7i			0.992629i	0.868143	+	0.496315i	$0.165314\pi$
$859$			2.14669e7i			0.992629i	−0.868143	+	0.496315i	$0.834686\pi$
$860$		0			0
$861$		−	2.67435e7i		−	1.22945i
$862$	−1.94808e7	+	9.84785e6i	−0.892976	+	0.451412i
$863$		−	2.02164e7i		−	0.924013i	−0.886877	−	0.462006i	$-0.847130\pi$
$863$		−	2.02164e7i		−	0.924013i	0.886877	−	0.462006i	$-0.152870\pi$
$864$	−1.64274e7	−	1.69598e7i	−0.748658	−	0.772924i
$865$		0			0
$866$	3.11401e6	+	6.16007e6i	0.141099	+	0.279120i
$867$	1.41979e7			0.641470
$868$	−4.74651e7	−	3.49502e7i	−2.13833	−	1.57453i
$869$		−	3.88256e7i		−	1.74409i
$870$		0			0
$871$	−3.62764e6			−0.162024
$872$	4.09952e7	+	6.89571e6i	1.82575	+	0.307105i
$873$		−	9.62906e6i		−	0.427610i
$874$	3.62740e7	−	1.83370e7i	1.60626	−	0.811989i
$875$		0			0
$876$	1.65806e7	+	1.22089e7i	0.730030	+	0.537545i
$877$	−8.97881e6			−0.394203			−0.197101	−	0.980383i	$-0.563153\pi$
$877$	−8.97881e6			−0.394203			−0.197101	+	0.980383i	$0.563153\pi$
$878$	−6.54790e6	+	3.31006e6i	−0.286659	+	0.144910i
$879$	2.63667e7			1.15102
$880$		0			0
$881$	−2.96009e7			−1.28489			−0.642444	−	0.766333i	$-0.722080\pi$
$881$	−2.96009e7			−1.28489			−0.642444	+	0.766333i	$0.722080\pi$
$882$	−2.01769e7	+	1.01997e7i	−0.873340	+	0.441486i
$883$	−2.24867e7			−0.970565			−0.485282	−	0.874357i	$-0.661283\pi$
$883$	−2.24867e7			−0.970565			−0.485282	+	0.874357i	$0.661283\pi$
$884$	1.22822e6	+	904381.i	0.0528623	+	0.0389243i
$885$		0			0
$886$	−1.29953e7	+	6.56933e6i	−0.556164	+	0.281149i
$887$		−	1.24041e7i		−	0.529365i	−0.964336	−	0.264682i	$-0.914733\pi$
$887$		−	1.24041e7i		−	0.529365i	0.964336	−	0.264682i	$-0.0852671\pi$
$888$	−3.72029e6	+	2.21173e7i	−0.158323	+	0.941236i
$889$	−1.06076e7			−0.450155
$890$		0			0
$891$		−	1.16683e7i		−	0.492396i
$892$	−2.67924e7	−	1.97282e7i	−1.12746	−	0.830185i
$893$	−1.51061e7			−0.633905
$894$	−2.59884e6	−	5.14098e6i	−0.108752	−	0.215131i
$895$		0			0
$896$	5.76575e6	+	4.25279e7i	0.239931	+	1.76972i
$897$		−	4.79778e6i		−	0.199094i
$898$	262772.	−	132835.i	0.0108740	−	0.00549696i
$899$		−	2.68094e7i		−	1.10634i
$900$		0			0
$901$		−	3.51288e6i		−	0.144162i
$902$	1.42231e7	+	2.81358e7i	0.582072	+	1.15144i
$903$			2.48384e6i			0.101369i
$904$	−1.07188e7	−	1.80299e6i	−0.436241	−	0.0733791i
$905$		0			0
$906$	−9.66305e6	+	4.88481e6i	−0.391105	+	0.197709i
$907$	−1.05997e7			−0.427834			−0.213917	−	0.976852i	$-0.568622\pi$
$907$	−1.05997e7			−0.427834			−0.213917	+	0.976852i	$0.568622\pi$
$908$	2.51098e7	−	3.41012e7i	1.01072	−	1.37263i
$909$			2.18089e6i			0.0875437i
$910$		0			0
$911$	−4.24265e7			−1.69372			−0.846858	−	0.531818i	$-0.821509\pi$
$911$	−4.24265e7			−1.69372			−0.846858	+	0.531818i	$0.821509\pi$
$912$	−2.12357e7	+	6.60160e6i	−0.845434	+	0.262822i
$913$		−	5.72284e6i		−	0.227214i
$914$	1.13900e6	+	2.25316e6i	0.0450983	+	0.0892126i
$915$		0			0
$916$	−2.89117e7	−	2.12887e7i	−1.13851	−	0.838320i
$917$	−3.13222e7			−1.23007
$918$	4.59515e6	+	9.09004e6i	0.179967	+	0.356008i
$919$	−4.18031e7			−1.63275			−0.816376	−	0.577521i	$-0.804020\pi$
$919$	−4.18031e7			−1.63275			−0.816376	+	0.577521i	$0.804020\pi$
$920$		0			0
$921$	−2.73764e7			−1.06347
$922$	9.08421e6	+	1.79702e7i	0.351933	+	0.696187i
$923$	−957041.			−0.0369766
$924$	−2.84851e7	+	3.86851e7i	−1.09758	+	1.49061i
$925$		0			0
$926$	−5.91088e6	−	1.16928e7i	−0.226530	−	0.448117i
$927$		−	1.83842e6i		−	0.0702660i
$928$	−1.40209e7	+	1.35807e7i	−0.534449	+	0.517669i
$929$	1.67378e7			0.636295			0.318147	−	0.948041i	$-0.396939\pi$
$929$	1.67378e7			0.636295			0.318147	+	0.948041i	$0.396939\pi$
$930$		0			0
$931$			6.89357e7i			2.60657i
$932$	−538238.	−	396323.i	−0.0202971	−	0.0149454i
$933$	9.24076e6			0.347539
$934$	3.60567e7	−	1.82272e7i	1.35244	−	0.683678i
$935$		0			0
$936$	351894.	−	2.09202e6i	0.0131287	−	0.0780506i
$937$		−	4.81906e7i		−	1.79314i	−0.442904	−	0.896569i	$-0.646052\pi$
$937$		−	4.81906e7i		−	1.79314i	0.442904	−	0.896569i	$-0.353948\pi$
$938$	1.98650e7	+	3.92965e7i	0.737192	+	1.45830i
$939$			2.24413e7i			0.830584i
$940$		0			0
$941$		−	2.29054e7i		−	0.843263i	−0.906767	−	0.421632i	$-0.861458\pi$
$941$		−	2.29054e7i		−	0.843263i	0.906767	−	0.421632i	$-0.138542\pi$
$942$	1.11879e7	−	5.65563e6i	0.410790	−	0.207660i
$943$			3.82165e7i			1.39949i
$944$	1.64288e7	−	5.10728e6i	0.600035	−	0.186535i
$945$		0			0
$946$	−1.32099e6	−	2.61315e6i	−0.0479922	−	0.0949374i
$947$	1.56151e7			0.565810			0.282905	−	0.959148i	$-0.408702\pi$
$947$	1.56151e7			0.565810			0.282905	+	0.959148i	$0.408702\pi$
$948$	−1.52682e7	+	2.07354e7i	−0.551780	+	0.749361i
$949$			5.98918e6i			0.215875i
$950$		0			0
$951$	2.72123e7			0.975695
$952$	3.07100e6	−	1.82572e7i	0.109821	−	0.652891i
$953$			1.10672e7i			0.394733i	0.980330	+	0.197367i	$0.0632389\pi$
$953$			1.10672e7i			0.394733i	−0.980330	+	0.197367i	$0.936761\pi$
$954$	−4.36040e6	+	2.20424e6i	−0.155115	+	0.0784131i
$955$		0			0
$956$	−769961.	+	1.04567e6i	−0.0272473	+	0.0370040i
$957$	−2.18503e7			−0.771218
$958$	1.22865e7	−	6.21099e6i	0.432527	−	0.218649i
$959$	−7.99499e7			−2.80719
$960$		0			0
$961$	3.46669e7			1.21090
$962$	−5.82200e6	+	2.94310e6i	−0.202831	+	0.102534i
$963$	−7.54858e6			−0.262301
$964$	1.59649e7	−	2.16816e7i	0.553316	−	0.751448i
$965$		0			0
$966$	−5.19721e7	+	2.62727e7i	−1.79196	+	0.905861i
$967$			1.07940e7i			0.371206i	0.982625	+	0.185603i	$0.0594238\pi$
$967$			1.07940e7i			0.371206i	−0.982625	+	0.185603i	$0.940576\pi$
$968$	4.55826e6	−	2.70990e7i	0.156355	−	0.929532i
$969$	9.59315e6			0.328210
$970$		0			0
$971$		−	3.92390e7i		−	1.33558i	−0.744349	−	0.667790i	$-0.767240\pi$
$971$		−	3.92390e7i		−	1.33558i	0.744349	−	0.667790i	$-0.232760\pi$
$972$	1.42049e7	−	1.92914e7i	0.482251	−	0.654935i
$973$	2.70531e7			0.916084
$974$	−2.46963e6	−	4.88538e6i	−0.0834132	−	0.165006i
$975$		0			0
$976$	−1.10470e7	+	3.43422e6i	−0.371211	+	0.115399i
$977$			2.54755e7i			0.853860i	0.904285	+	0.426930i	$0.140405\pi$
$977$			2.54755e7i			0.853860i	−0.904285	+	0.426930i	$0.859595\pi$
$978$	2.79987e7	−	1.41537e7i	0.936032	−	0.473178i
$979$			5.17153e7i			1.72450i
$980$		0			0
$981$			2.49421e7i			0.827485i
$982$	4.95218e6	+	9.79631e6i	0.163877	+	0.324178i
$983$			1.56587e7i			0.516858i	0.966030	+	0.258429i	$0.0832048\pi$
$983$			1.56587e7i			0.516858i	−0.966030	+	0.258429i	$0.916795\pi$
$984$	3.46837e6	−	2.06196e7i	0.114193	−	0.678878i
$985$		0			0
$986$	7.51485e6	−	3.79887e6i	0.246166	−	0.124441i
$987$	2.16435e7			0.707189
$988$	−5.20869e6	−	3.83534e6i	−0.169760	−	0.125000i
$989$		−	3.54941e6i		−	0.115389i
$990$		0			0
$991$	−9.68181e6			−0.313164			−0.156582	−	0.987665i	$-0.550048\pi$
$991$	−9.68181e6			−0.313164			−0.156582	+	0.987665i	$0.550048\pi$
$992$	−3.20635e7	−	3.31028e7i	−1.03450	−	1.06803i
$993$			3.37972e6i			0.108770i
$994$	5.24077e6	+	1.03672e7i	0.168240	+	0.332809i
$995$		0			0
$996$	−2.25051e6	+	3.05637e6i	−0.0718839	+	0.0976241i
$997$	−3.15560e7			−1.00541			−0.502707	−	0.864457i	$-0.667662\pi$
$997$	−3.15560e7			−1.00541			−0.502707	+	0.864457i	$0.667662\pi$
$998$	2.29004e7	+	4.53012e7i	0.727809	+	1.43974i
$999$	−4.35637e7			−1.38106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.f.c.149.4		20
4.3	odd	2		800.6.f.b.49.5		20
5.2	odd	4		40.6.d.a.21.7	✓	20
5.3	odd	4		200.6.d.b.101.14		20
5.4	even	2		200.6.f.b.149.17		20
8.3	odd	2		800.6.f.c.49.15		20
8.5	even	2		200.6.f.b.149.18		20
15.2	even	4		360.6.k.b.181.14		20
20.3	even	4		800.6.d.c.401.6		20
20.7	even	4		160.6.d.a.81.15		20
20.19	odd	2		800.6.f.c.49.16		20
40.3	even	4		800.6.d.c.401.15		20
40.13	odd	4		200.6.d.b.101.13		20
40.19	odd	2		800.6.f.b.49.6		20
40.27	even	4		160.6.d.a.81.6		20
40.29	even	2	inner	200.6.f.c.149.3		20
40.37	odd	4		40.6.d.a.21.8	yes	20
120.77	even	4		360.6.k.b.181.13		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.d.a.21.7	✓	20	5.2	odd	4
40.6.d.a.21.8	yes	20	40.37	odd	4
160.6.d.a.81.6		20	40.27	even	4
160.6.d.a.81.15		20	20.7	even	4
200.6.d.b.101.13		20	40.13	odd	4
200.6.d.b.101.14		20	5.3	odd	4
200.6.f.b.149.17		20	5.4	even	2
200.6.f.b.149.18		20	8.5	even	2
200.6.f.c.149.3		20	40.29	even	2	inner
200.6.f.c.149.4		20	1.1	even	1	trivial
360.6.k.b.181.13		20	120.77	even	4
360.6.k.b.181.14		20	15.2	even	4
800.6.d.c.401.6		20	20.3	even	4
800.6.d.c.401.15		20	40.3	even	4
800.6.f.b.49.5		20	4.3	odd	2
800.6.f.b.49.6		20	40.19	odd	2
800.6.f.c.49.15		20	8.3	odd	2
800.6.f.c.49.16		20	20.19	odd	2

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.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.04846 + 2.55207i) q^{2} +11.5927 q^{3} +(18.9739 - 25.7680i) q^{4} +(-58.5253 + 29.5854i) q^{6} +231.529i q^{7} +(-30.0270 + 178.512i) q^{8} -108.609 q^{9} +O(q^{10})\)	\(q+(-5.04846 + 2.55207i) q^{2} +11.5927 q^{3} +(18.9739 - 25.7680i) q^{4} +(-58.5253 + 29.5854i) q^{6} +231.529i q^{7} +(-30.0270 + 178.512i) q^{8} -108.609 q^{9} +559.335i q^{11} +(219.959 - 298.721i) q^{12} +107.903 q^{13} +(-590.877 - 1168.86i) q^{14} +(-303.984 - 977.839i) q^{16} +441.735i q^{17} +(548.309 - 277.178i) q^{18} -1873.33i q^{19} +2684.04i q^{21} +(-1427.46 - 2823.78i) q^{22} -3835.50i q^{23} +(-348.095 + 2069.43i) q^{24} +(-544.743 + 275.376i) q^{26} -4076.10 q^{27} +(5966.04 + 4393.00i) q^{28} +3369.76i q^{29} -7955.88 q^{31} +(4030.16 + 4160.80i) q^{32} +6484.21i q^{33} +(-1127.34 - 2230.08i) q^{34} +(-2060.74 + 2798.64i) q^{36} +10687.6 q^{37} +(4780.87 + 9457.43i) q^{38} +1250.89 q^{39} -9963.87 q^{41} +(-6849.87 - 13550.3i) q^{42} +925.409 q^{43} +(14413.0 + 10612.8i) q^{44} +(9788.47 + 19363.4i) q^{46} -8063.78i q^{47} +(-3523.99 - 11335.8i) q^{48} -36798.5 q^{49} +5120.91i q^{51} +(2047.34 - 2780.45i) q^{52} -7952.45 q^{53} +(20578.0 - 10402.5i) q^{54} +(-41330.5 - 6952.12i) q^{56} -21717.0i q^{57} +(-8599.87 - 17012.1i) q^{58} +16801.2i q^{59} -11297.4i q^{61} +(40164.9 - 20304.0i) q^{62} -25146.1i q^{63} +(-30964.8 - 10720.3i) q^{64} +(-16548.2 - 32735.3i) q^{66} -33619.4 q^{67} +(11382.7 + 8381.43i) q^{68} -44463.9i q^{69} -8869.47 q^{71} +(3261.21 - 19388.0i) q^{72} +55505.3i q^{73} +(-53955.9 + 27275.5i) q^{74} +(-48272.0 - 35544.3i) q^{76} -129502. q^{77} +(-6315.05 + 3192.35i) q^{78} -69413.7 q^{79} -20861.0 q^{81} +(50302.2 - 25428.5i) q^{82} -10231.5 q^{83} +(69162.5 + 50926.7i) q^{84} +(-4671.89 + 2361.71i) q^{86} +39064.7i q^{87} +(-99847.8 - 16795.2i) q^{88} +92458.4 q^{89} +24982.6i q^{91} +(-98833.4 - 72774.4i) q^{92} -92230.2 q^{93} +(20579.3 + 40709.7i) q^{94} +(46720.5 + 48234.9i) q^{96} +88657.9i q^{97} +(185776. - 93912.3i) q^{98} -60748.9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9	\( 20 q + 2 q^{2} + 36 q^{3} + 32 q^{4} + 204 q^{6} + 248 q^{8} + 1620 q^{9} + 1252 q^{12} - 2708 q^{14} + 3080 q^{16} + 2070 q^{18} + 8244 q^{22} - 1032 q^{24} - 8084 q^{26} + 11664 q^{27} + 22924 q^{28} + 7160 q^{31} + 14792 q^{32} - 21132 q^{34} + 18344 q^{36} - 3608 q^{37} - 16884 q^{38} + 44904 q^{39} + 11608 q^{41} - 49444 q^{42} - 51772 q^{43} - 72296 q^{44} - 28516 q^{46} - 85048 q^{48} - 18756 q^{49} - 111624 q^{52} + 928 q^{53} + 100584 q^{54} - 53624 q^{56} + 152344 q^{58} + 228648 q^{62} + 11264 q^{64} - 56688 q^{66} - 161604 q^{67} + 359040 q^{68} - 200312 q^{71} + 563448 q^{72} - 78876 q^{74} - 153872 q^{76} + 26008 q^{77} - 624640 q^{78} - 282080 q^{79} + 65172 q^{81} - 410576 q^{82} - 99092 q^{83} + 297128 q^{84} + 27452 q^{86} - 464496 q^{88} + 3160 q^{89} - 519244 q^{92} + 293472 q^{93} - 148820 q^{94} + 395168 q^{96} + 663674 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 36 * q^3 + 32 * q^4 + 204 * q^6 + 248 * q^8 + 1620 * q^9 + 1252 * q^12 - 2708 * q^14 + 3080 * q^16 + 2070 * q^18 + 8244 * q^22 - 1032 * q^24 - 8084 * q^26 + 11664 * q^27 + 22924 * q^28 + 7160 * q^31 + 14792 * q^32 - 21132 * q^34 + 18344 * q^36 - 3608 * q^37 - 16884 * q^38 + 44904 * q^39 + 11608 * q^41 - 49444 * q^42 - 51772 * q^43 - 72296 * q^44 - 28516 * q^46 - 85048 * q^48 - 18756 * q^49 - 111624 * q^52 + 928 * q^53 + 100584 * q^54 - 53624 * q^56 + 152344 * q^58 + 228648 * q^62 + 11264 * q^64 - 56688 * q^66 - 161604 * q^67 + 359040 * q^68 - 200312 * q^71 + 563448 * q^72 - 78876 * q^74 - 153872 * q^76 + 26008 * q^77 - 624640 * q^78 - 282080 * q^79 + 65172 * q^81 - 410576 * q^82 - 99092 * q^83 + 297128 * q^84 + 27452 * q^86 - 464496 * q^88 + 3160 * q^89 - 519244 * q^92 + 293472 * q^93 - 148820 * q^94 + 395168 * q^96 + 663674 * q^98

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