LMFDB - Embedded newform 200.6.d.c.101.19

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			101.19
Root			$-5.37943 + 1.74979i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.c.101.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.37943 - 1.74979i) q^{2} +25.2673i q^{3} +(25.8765 - 18.8258i) q^{4} +(44.2124 + 135.923i) q^{6} -185.199 q^{7} +(106.259 - 146.550i) q^{8} -395.434 q^{9} +O(q^{10})$	\(q+(5.37943 - 1.74979i) q^{2} +25.2673i q^{3} +(25.8765 - 18.8258i) q^{4} +(44.2124 + 135.923i) q^{6} -185.199 q^{7} +(106.259 - 146.550i) q^{8} -395.434 q^{9} -574.919i q^{11} +(475.675 + 653.827i) q^{12} +65.8691i q^{13} +(-996.264 + 324.060i) q^{14} +(315.182 - 974.288i) q^{16} -1966.88 q^{17} +(-2127.21 + 691.927i) q^{18} +611.668i q^{19} -4679.47i q^{21} +(-1005.99 - 3092.74i) q^{22} -2976.41 q^{23} +(3702.92 + 2684.88i) q^{24} +(115.257 + 354.338i) q^{26} -3851.59i q^{27} +(-4792.29 + 3486.51i) q^{28} -4474.76i q^{29} +7724.41 q^{31} +(-9.30513 - 5792.61i) q^{32} +14526.6 q^{33} +(-10580.7 + 3441.64i) q^{34} +(-10232.4 + 7444.34i) q^{36} +7287.23i q^{37} +(1070.29 + 3290.42i) q^{38} -1664.33 q^{39} -6220.02 q^{41} +(-8188.09 - 25172.8i) q^{42} -14399.5i q^{43} +(-10823.3 - 14876.9i) q^{44} +(-16011.4 + 5208.11i) q^{46} -5910.00 q^{47} +(24617.6 + 7963.77i) q^{48} +17491.6 q^{49} -49697.7i q^{51} +(1240.04 + 1704.46i) q^{52} +20628.0i q^{53} +(-6739.48 - 20719.3i) q^{54} +(-19679.1 + 27140.9i) q^{56} -15455.2 q^{57} +(-7829.90 - 24071.6i) q^{58} -12426.8i q^{59} +19832.6i q^{61} +(41552.9 - 13516.1i) q^{62} +73233.9 q^{63} +(-10185.9 - 31144.6i) q^{64} +(78144.9 - 25418.6i) q^{66} -56232.3i q^{67} +(-50896.0 + 37028.1i) q^{68} -75205.8i q^{69} -55797.8 q^{71} +(-42018.5 + 57950.9i) q^{72} -3795.29 q^{73} +(12751.1 + 39201.1i) q^{74} +(11515.1 + 15827.8i) q^{76} +106474. i q^{77} +(-8953.14 + 2912.23i) q^{78} -74070.3 q^{79} +1228.55 q^{81} +(-33460.1 + 10883.7i) q^{82} +117441. i q^{83} +(-88094.5 - 121088. i) q^{84} +(-25196.1 - 77461.0i) q^{86} +113065. q^{87} +(-84254.5 - 61090.5i) q^{88} -28115.4 q^{89} -12198.9i q^{91} +(-77019.0 + 56033.3i) q^{92} +195175. i q^{93} +(-31792.4 + 10341.3i) q^{94} +(146363. - 235.115i) q^{96} -38940.1 q^{97} +(94094.9 - 30606.7i) q^{98} +227343. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) $ 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9	$ 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9} - 241 q^{12} - 424 q^{14} - 55 q^{16} - 3368 q^{18} + 1197 q^{22} - 7184 q^{23} + 9459 q^{24} + 9172 q^{26} - 13492 q^{28} + 7160 q^{31} + 7869 q^{32} - 2836 q^{33} - 9591 q^{34} + 14828 q^{36} + 21505 q^{38} + 22452 q^{39} - 5804 q^{41} - 14272 q^{42} - 11593 q^{44} - 37612 q^{46} + 44180 q^{47} + 66571 q^{48} + 62652 q^{49} + 6136 q^{52} + 88947 q^{54} - 36908 q^{56} + 43696 q^{57} - 84012 q^{58} + 87460 q^{62} - 1240 q^{63} + 115177 q^{64} + 131439 q^{66} - 143341 q^{68} - 7724 q^{71} - 25772 q^{72} - 105136 q^{73} + 2112 q^{74} + 55951 q^{76} - 10948 q^{78} - 7780 q^{79} + 96984 q^{81} + 117501 q^{82} - 97556 q^{84} - 65986 q^{86} - 106188 q^{87} - 122597 q^{88} - 3160 q^{89} + 88908 q^{92} - 58540 q^{94} + 57791 q^{96} - 73688 q^{97} + 164655 q^{98}+O(q^{100}) $ 20 * q - q^2 + q^4 + 33 * q^6 - 196 * q^7 - 391 * q^8 - 1620 * q^9 - 241 * q^12 - 424 * q^14 - 55 * q^16 - 3368 * q^18 + 1197 * q^22 - 7184 * q^23 + 9459 * q^24 + 9172 * q^26 - 13492 * q^28 + 7160 * q^31 + 7869 * q^32 - 2836 * q^33 - 9591 * q^34 + 14828 * q^36 + 21505 * q^38 + 22452 * q^39 - 5804 * q^41 - 14272 * q^42 - 11593 * q^44 - 37612 * q^46 + 44180 * q^47 + 66571 * q^48 + 62652 * q^49 + 6136 * q^52 + 88947 * q^54 - 36908 * q^56 + 43696 * q^57 - 84012 * q^58 + 87460 * q^62 - 1240 * q^63 + 115177 * q^64 + 131439 * q^66 - 143341 * q^68 - 7724 * q^71 - 25772 * q^72 - 105136 * q^73 + 2112 * q^74 + 55951 * q^76 - 10948 * q^78 - 7780 * q^79 + 96984 * q^81 + 117501 * q^82 - 97556 * q^84 - 65986 * q^86 - 106188 * q^87 - 122597 * q^88 - 3160 * q^89 + 88908 * q^92 - 58540 * q^94 + 57791 * q^96 - 73688 * q^97 + 164655 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	5.37943	−	1.74979i	0.950957	−	0.309323i
$2$	5.37943	−	1.74979i	0.950957	−	0.309323i
$3$			25.2673i			1.62089i	0.585811	+	0.810447i	$0.300776\pi$
$3$			25.2673i			1.62089i	−0.585811	+	0.810447i	$0.699224\pi$
$4$	25.8765	−	18.8258i	0.808639	−	0.588305i
$5$		0			0
$5$		0			0
$6$	44.2124	+	135.923i	0.501379	+	1.54140i
$7$	−185.199			−1.42854			−0.714271	−	0.699869i	$-0.753242\pi$
$7$	−185.199			−1.42854			−0.714271	+	0.699869i	$0.753242\pi$
$8$	106.259	−	146.550i	0.587005	−	0.809583i
$9$	−395.434			−1.62730
$10$		0			0
$11$		−	574.919i		−	1.43260i	−0.697792	−	0.716300i	$-0.745834\pi$
$11$		−	574.919i		−	1.43260i	0.697792	−	0.716300i	$-0.254166\pi$
$12$	475.675	+	653.827i	0.953580	+	1.31072i
$13$			65.8691i			0.108099i	0.998538	+	0.0540497i	$0.0172129\pi$
$13$			65.8691i			0.108099i	−0.998538	+	0.0540497i	$0.982787\pi$
$14$	−996.264	+	324.060i	−1.35848	+	0.441880i
$15$		0			0
$16$	315.182	−	974.288i	0.307795	−	0.951453i
$17$	−1966.88			−1.65065			−0.825327	−	0.564655i	$-0.809009\pi$
$17$	−1966.88			−1.65065			−0.825327	+	0.564655i	$0.809009\pi$
$18$	−2127.21	+	691.927i	−1.54749	+	0.503361i
$19$			611.668i			0.388715i	0.980931	+	0.194358i	$0.0622622\pi$
$19$			611.668i			0.388715i	−0.980931	+	0.194358i	$0.937738\pi$
$20$		0			0
$21$		−	4679.47i		−	2.31552i
$22$	−1005.99	−	3092.74i	−0.443136	−	1.36234i
$23$	−2976.41			−1.17320			−0.586602	−	0.809875i	$-0.699535\pi$
$23$	−2976.41			−1.17320			−0.586602	+	0.809875i	$0.699535\pi$
$24$	3702.92	+	2684.88i	1.31225	+	0.951474i
$25$		0			0
$26$	115.257	+	354.338i	0.0334376	+	0.102798i
$27$		−	3851.59i		−	1.01679i
$28$	−4792.29	+	3486.51i	−1.15518	+	0.840419i
$29$		−	4474.76i		−	0.988041i	−0.869450	−	0.494020i	$-0.835527\pi$
$29$		−	4474.76i		−	0.988041i	0.869450	−	0.494020i	$-0.164473\pi$
$30$		0			0
$31$	7724.41			1.44365			0.721824	−	0.692077i	$-0.243304\pi$
$31$	7724.41			1.44365			0.721824	+	0.692077i	$0.243304\pi$
$32$	−9.30513	−	5792.61i	−0.00160638	−	0.999999i
$33$	14526.6			2.32209
$34$	−10580.7	+	3441.64i	−1.56970	+	0.510585i
$35$		0			0
$36$	−10232.4	+	7444.34i	−1.31590	+	0.957349i
$37$			7287.23i			0.875101i	0.899194	+	0.437551i	$0.144154\pi$
$37$			7287.23i			0.875101i	−0.899194	+	0.437551i	$0.855846\pi$
$38$	1070.29	+	3290.42i	0.120238	+	0.369652i
$39$	−1664.33			−0.175218
$40$		0			0
$41$	−6220.02			−0.577873			−0.288936	−	0.957348i	$-0.593302\pi$
$41$	−6220.02			−0.577873			−0.288936	+	0.957348i	$0.593302\pi$
$42$	−8188.09	−	25172.8i	−0.716242	−	2.20196i
$43$		−	14399.5i		−	1.18762i	−0.804607	−	0.593808i	$-0.797624\pi$
$43$		−	14399.5i		−	1.18762i	0.804607	−	0.593808i	$-0.202376\pi$
$44$	−10823.3	−	14876.9i	−0.842806	−	1.15846i
$45$		0			0
$46$	−16011.4	+	5208.11i	−1.11567	+	0.362899i
$47$	−5910.00			−0.390250			−0.195125	−	0.980778i	$-0.562511\pi$
$47$	−5910.00			−0.390250			−0.195125	+	0.980778i	$0.562511\pi$
$48$	24617.6	+	7963.77i	1.54221	+	0.498903i
$49$	17491.6			1.04073
$50$		0			0
$51$		−	49697.7i		−	2.67554i
$52$	1240.04	+	1704.46i	0.0635954	+	0.0874134i
$53$			20628.0i			1.00871i	0.863495	+	0.504357i	$0.168271\pi$
$53$			20628.0i			1.00871i	−0.863495	+	0.504357i	$0.831729\pi$
$54$	−6739.48	−	20719.3i	−0.314515	−	0.966921i
$55$		0			0
$56$	−19679.1	+	27140.9i	−0.838562	+	1.15652i
$57$	−15455.2			−0.630067
$58$	−7829.90	−	24071.6i	−0.305623	−	0.939584i
$59$		−	12426.8i		−	0.464761i	−0.972625	−	0.232381i	$-0.925348\pi$
$59$		−	12426.8i		−	0.464761i	0.972625	−	0.232381i	$-0.0746515\pi$
$60$		0			0
$61$			19832.6i			0.682425i	0.939986	+	0.341212i	$0.110838\pi$
$61$			19832.6i			0.682425i	−0.939986	+	0.341212i	$0.889162\pi$
$62$	41552.9	−	13516.1i	1.37285	−	0.446553i
$63$	73233.9			2.32467
$64$	−10185.9	−	31144.6i	−0.310850	−	0.950459i
$65$		0			0
$66$	78144.9	−	25418.6i	2.20821	−	0.718276i
$67$		−	56232.3i		−	1.53038i	−0.643806	−	0.765189i	$-0.722646\pi$
$67$		−	56232.3i		−	1.53038i	0.643806	−	0.765189i	$-0.277354\pi$
$68$	−50896.0	+	37028.1i	−1.33478	+	0.971088i
$69$		−	75205.8i		−	1.90164i
$70$		0			0
$71$	−55797.8			−1.31363			−0.656813	−	0.754054i	$-0.728096\pi$
$71$	−55797.8			−1.31363			−0.656813	+	0.754054i	$0.728096\pi$
$72$	−42018.5	+	57950.9i	−0.955234	+	1.31743i
$73$	−3795.29			−0.0833562			−0.0416781	−	0.999131i	$-0.513270\pi$
$73$	−3795.29			−0.0833562			−0.0416781	+	0.999131i	$0.513270\pi$
$74$	12751.1	+	39201.1i	0.270689	+	0.832184i
$75$		0			0
$76$	11515.1	+	15827.8i	0.228683	+	0.314330i
$77$			106474.i			2.04653i
$78$	−8953.14	+	2912.23i	−0.166625	+	0.0541988i
$79$	−74070.3			−1.33529			−0.667647	−	0.744478i	$-0.732698\pi$
$79$	−74070.3			−1.33529			−0.667647	+	0.744478i	$0.732698\pi$
$80$		0			0
$81$	1228.55			0.0208055
$82$	−33460.1	+	10883.7i	−0.549532	+	0.178749i
$83$			117441.i			1.87122i	0.353032	+	0.935611i	$0.385151\pi$
$83$			117441.i			1.87122i	−0.353032	+	0.935611i	$0.614849\pi$
$84$	−88094.5	−	121088.i	−1.36223	−	1.87242i
$85$		0			0
$86$	−25196.1	−	77461.0i	−0.367356	−	1.12937i
$87$	113065.			1.60151
$88$	−84254.5	−	61090.5i	−1.15981	−	0.840944i
$89$	−28115.4			−0.376244			−0.188122	−	0.982146i	$-0.560240\pi$
$89$	−28115.4			−0.376244			−0.188122	+	0.982146i	$0.560240\pi$
$90$		0			0
$91$		−	12198.9i		−	0.154425i
$92$	−77019.0	+	56033.3i	−0.948699	+	0.690202i
$93$			195175.i			2.34000i
$94$	−31792.4	+	10341.3i	−0.371111	+	0.120713i
$95$		0			0
$96$	146363.	−	235.115i	1.62089	−	0.00260377i
$97$	−38940.1			−0.420211			−0.210105	−	0.977679i	$-0.567381\pi$
$97$	−38940.1			−0.420211			−0.210105	+	0.977679i	$0.567381\pi$
$98$	94094.9	−	30606.7i	0.989693	−	0.321922i
$99$			227343.i			2.33127i
$100$		0			0
$101$			137534.i			1.34155i	0.741662	+	0.670773i	$0.234038\pi$
$101$			137534.i			1.34155i	−0.741662	+	0.670773i	$0.765962\pi$
$102$	−86960.7	−	267345.i	−0.827604	−	2.54432i
$103$	−32564.0			−0.302443			−0.151222	−	0.988500i	$-0.548321\pi$
$103$	−32564.0			−0.302443			−0.151222	+	0.988500i	$0.548321\pi$
$104$	9653.12	+	6999.20i	0.0875154	+	0.0634549i
$105$		0			0
$106$	36094.8	+	110967.i	0.312018	+	0.959245i
$107$		−	154623.i		−	1.30561i	−0.757524	−	0.652807i	$-0.773591\pi$
$107$		−	154623.i		−	1.30561i	0.757524	−	0.652807i	$-0.226409\pi$
$108$	−72509.0	−	99665.4i	−0.598181	−	0.822214i
$109$			98459.1i			0.793761i	0.917870	+	0.396880i	$0.129907\pi$
$109$			98459.1i			0.793761i	−0.917870	+	0.396880i	$0.870093\pi$
$110$		0			0
$111$	−184128.			−1.41845
$112$	−58371.3	+	180437.i	−0.439698	+	1.35919i
$113$	132338.			0.974960			0.487480	−	0.873134i	$-0.337916\pi$
$113$	132338.			0.974960			0.487480	+	0.873134i	$0.337916\pi$
$114$	−83139.9	+	27043.3i	−0.599166	+	0.194894i
$115$		0			0
$116$	−84240.8	−	115791.i	−0.581269	−	0.798968i
$117$		−	26046.9i		−	0.175910i
$118$	−21744.4	−	66849.2i	−0.143761	−	0.441968i
$119$	364264.			2.35803
$120$		0			0
$121$	−169481.			−1.05234
$122$	34702.9	+	106688.i	0.211089	+	0.648957i
$123$		−	157163.i		−	0.936671i
$124$	199880.	−	145418.i	1.16739	−	0.849305i
$125$		0			0
$126$	393956.	−	128144.i	2.21066	−	0.719072i
$127$	324744.			1.78662			0.893309	−	0.449444i	$-0.148378\pi$
$127$	324744.			1.78662			0.893309	+	0.449444i	$0.148378\pi$
$128$	−109291.	−	149717.i	−0.589603	−	0.807693i
$129$	363835.			1.92500
$130$		0			0
$131$		−	177689.i		−	0.904651i	−0.891853	−	0.452326i	$-0.850594\pi$
$131$		−	177689.i		−	0.904651i	0.891853	−	0.452326i	$-0.149406\pi$
$132$	375898.	−	273475.i	1.87774	−	1.36610i
$133$		−	113280.i		−	0.555296i
$134$	−98394.8	−	302497.i	−0.473380	−	1.45532i
$135$		0			0
$136$	−209000.	+	288247.i	−0.968943	+	1.33634i
$137$	−19760.3			−0.0899480			−0.0449740	−	0.998988i	$-0.514320\pi$
$137$	−19760.3			−0.0899480			−0.0449740	+	0.998988i	$0.514320\pi$
$138$	−131595.	−	404564.i	−0.588221	−	1.80838i
$139$			55428.9i			0.243332i	0.992571	+	0.121666i	$0.0388237\pi$
$139$			55428.9i			0.243332i	−0.992571	+	0.121666i	$0.961176\pi$
$140$		0			0
$141$		−	149330.i		−	0.632555i
$142$	−300160.	+	97634.6i	−1.24920	+	0.406334i
$143$	37869.4			0.154863
$144$	−124633.	+	385266.i	−0.500874	+	1.54830i
$145$		0			0
$146$	−20416.5	+	6640.97i	−0.0792682	+	0.0257840i
$147$			441965.i			1.68692i
$148$	137188.	+	188568.i	0.514827	+	0.707641i
$149$			311409.i			1.14912i	0.818462	+	0.574560i	$0.194827\pi$
$149$			311409.i			1.14912i	−0.818462	+	0.574560i	$0.805173\pi$
$150$		0			0
$151$	−191117.			−0.682114			−0.341057	−	0.940043i	$-0.610785\pi$
$151$	−191117.			−0.682114			−0.341057	+	0.940043i	$0.610785\pi$
$152$	89640.0	+	64995.4i	0.314697	+	0.228178i
$153$	777772.			2.68611
$154$	186308.	+	572771.i	0.633038	+	1.94616i
$155$		0			0
$156$	−43067.0	+	31332.3i	−0.141688	+	0.103081i
$157$		−	30356.8i		−	0.0982895i	−0.998792	−	0.0491448i	$-0.984350\pi$
$157$		−	30356.8i		−	0.0982895i	0.998792	−	0.0491448i	$-0.0156496\pi$
$158$	−398456.	+	129608.i	−1.26981	+	0.413036i
$159$	−521214.			−1.63502
$160$		0			0
$161$	551229.			1.67597
$162$	6608.87	−	2149.70i	0.0197852	−	0.00643562i
$163$		−	79111.8i		−	0.233224i	−0.993178	−	0.116612i	$-0.962797\pi$
$163$		−	79111.8i		−	0.233224i	0.993178	−	0.116612i	$-0.0372033\pi$
$164$	−160952.	+	117097.i	−0.467290	+	0.339965i
$165$		0			0
$166$	205498.	+	631767.i	0.578811	+	1.77945i
$167$	−533772.			−1.48103			−0.740516	−	0.672038i	$-0.765419\pi$
$167$	−533772.			−1.48103			−0.740516	+	0.672038i	$0.765419\pi$
$168$	−685777.	−	497237.i	−1.87460	−	1.35922i
$169$	366954.			0.988315
$170$		0			0
$171$		−	241874.i		−	0.632556i
$172$	−271081.	−	372608.i	−0.698680	−	0.960352i
$173$			355303.i			0.902575i	0.892379	+	0.451288i	$0.149035\pi$
$173$			355303.i			0.902575i	−0.892379	+	0.451288i	$0.850965\pi$
$174$	608224.	−	197840.i	1.52297	−	0.495383i
$175$		0			0
$176$	−560137.	−	181204.i	−1.36305	−	0.440947i
$177$	313992.			0.753329
$178$	−151245.	+	49196.2i	−0.357792	+	0.116381i
$179$		−	610019.i		−	1.42302i	−0.702677	−	0.711509i	$-0.748012\pi$
$179$		−	610019.i		−	1.42302i	0.702677	−	0.711509i	$-0.251988\pi$
$180$		0			0
$181$		−	405423.i		−	0.919840i	−0.887960	−	0.459920i	$-0.847878\pi$
$181$		−	405423.i		−	0.919840i	0.887960	−	0.459920i	$-0.152122\pi$
$182$	−21345.5	−	65622.9i	−0.0477670	−	0.146851i
$183$	−501115.			−1.10614
$184$	−316272.	+	436194.i	−0.688677	+	0.949807i
$185$		0			0
$186$	341515.	+	1.04993e6i	0.723815	+	2.22524i
$187$			1.13080e6i			2.36473i
$188$	−152930.	+	111260.i	−0.315572	+	0.229586i
$189$			713309.i			1.45252i
$190$		0			0
$191$	−237405.			−0.470876			−0.235438	−	0.971889i	$-0.575653\pi$
$191$	−237405.			−0.470876			−0.235438	+	0.971889i	$0.575653\pi$
$192$	786939.	−	257370.i	1.54059	−	0.503855i
$193$	−363225.			−0.701911			−0.350956	−	0.936392i	$-0.614143\pi$
$193$	−363225.			−0.701911			−0.350956	+	0.936392i	$0.614143\pi$
$194$	−209475.	+	68137.0i	−0.399603	+	0.129981i
$195$		0			0
$196$	452621.	−	329293.i	0.841578	−	0.612269i
$197$		−	162663.i		−	0.298623i	−0.988790	−	0.149311i	$-0.952294\pi$
$197$		−	162663.i		−	0.298623i	0.988790	−	0.149311i	$-0.0477057\pi$
$198$	397802.	+	1.22297e6i	0.721115	+	2.21694i
$199$	306808.			0.549205			0.274602	−	0.961558i	$-0.411454\pi$
$199$	306808.			0.549205			0.274602	+	0.961558i	$0.411454\pi$
$200$		0			0
$201$	1.42083e6			2.48058
$202$	240655.	+	739852.i	0.414971	+	1.27575i
$203$			828721.i			1.41146i
$204$	−935597.	−	1.28600e6i	−1.57403	−	2.16354i
$205$		0			0
$206$	−175175.	+	56980.2i	−0.287611	+	0.0935525i
$207$	1.17698e6			1.90916
$208$	64175.4	+	20760.7i	0.102851	+	0.0332724i
$209$	351659.			0.556874
$210$		0			0
$211$			916430.i			1.41708i	0.705673	+	0.708538i	$0.250645\pi$
$211$			916430.i			1.41708i	−0.705673	+	0.708538i	$0.749355\pi$
$212$	388339.	+	533781.i	0.593432	+	0.815686i
$213$		−	1.40986e6i		−	2.12925i
$214$	−270558.	−	831784.i	−0.403856	−	1.24158i
$215$		0			0
$216$	−564451.	−	409267.i	−0.823174	−	0.596860i
$217$	−1.43055e6			−2.06231
$218$	172283.	+	529654.i	0.245528	+	0.754833i
$219$		−	95896.6i		−	0.135112i
$220$		0			0
$221$		−	129557.i		−	0.178435i
$222$	−990505.	+	322186.i	−1.34888	+	0.438758i
$223$	122070.			0.164379			0.0821897	−	0.996617i	$-0.473809\pi$
$223$	122070.			0.164379			0.0821897	+	0.996617i	$0.473809\pi$
$224$	1723.30	+	1.07278e6i	0.00229478	+	1.42854i
$225$		0			0
$226$	711900.	−	231563.i	0.927145	−	0.301577i
$227$			91677.1i			0.118085i	0.998255	+	0.0590427i	$0.0188048\pi$
$227$			91677.1i			0.118085i	−0.998255	+	0.0590427i	$0.981195\pi$
$228$	−399925.	+	290955.i	−0.509496	+	0.370671i
$229$		−	1.04406e6i		−	1.31564i	−0.753174	−	0.657821i	$-0.771478\pi$
$229$		−	1.04406e6i		−	1.31564i	0.753174	−	0.657821i	$-0.228522\pi$
$230$		0			0
$231$	−2.69031e6			−3.31721
$232$	−655777.	−	475485.i	−0.799901	−	0.579985i
$233$	706266.			0.852272			0.426136	−	0.904659i	$-0.359874\pi$
$233$	706266.			0.852272			0.426136	+	0.904659i	$0.359874\pi$
$234$	−45576.6	−	140117.i	−0.0544130	−	0.167283i
$235$		0			0
$236$	−233944.	−	321562.i	−0.273421	−	0.375824i
$237$		−	1.87155e6i		−	2.16437i
$238$	1.95953e6	−	637387.i	2.24239	−	0.729392i
$239$	244587.			0.276974			0.138487	−	0.990364i	$-0.455776\pi$
$239$	244587.			0.276974			0.138487	+	0.990364i	$0.455776\pi$
$240$		0			0
$241$	602450.			0.668156			0.334078	−	0.942545i	$-0.391575\pi$
$241$	602450.			0.668156			0.334078	+	0.942545i	$0.391575\pi$
$242$	−911711.	+	296557.i	−1.00073	+	0.325514i
$243$		−	904893.i		−	0.983064i
$244$	373363.	+	513197.i	0.401474	+	0.551835i
$245$		0			0
$246$	−275002.	−	845446.i	−0.289733	−	0.890734i
$247$	−40290.0			−0.0420199
$248$	820791.	−	1.13201e6i	0.847429	−	1.16875i
$249$	−2.96742e6			−3.03306
$250$		0			0
$251$		−	416637.i		−	0.417421i	−0.977977	−	0.208710i	$-0.933073\pi$
$251$		−	416637.i		−	0.417421i	0.977977	−	0.208710i	$-0.0669266\pi$
$252$	1.89503e6	−	1.37868e6i	1.87982	−	1.36761i
$253$			1.71120e6i			1.68073i
$254$	1.74694e6	−	568234.i	1.69900	−	0.552641i
$255$		0			0
$256$	−849897.	−	614155.i	−0.810525	−	0.585704i
$257$	−2065.15			−0.00195038			−0.000975191	−	1.00000i	$-0.500310\pi$
$257$	−2065.15			−0.00195038			−0.000975191		1.00000i	$0.500310\pi$
$258$	1.95723e6	−	636636.i	1.83059	−	0.595446i
$259$		−	1.34959e6i		−	1.25012i
$260$		0			0
$261$			1.76947e6i			1.60784i
$262$	−310918.	−	955863.i	−0.279829	−	0.860285i
$263$	−1.69358e6			−1.50979			−0.754897	−	0.655844i	$-0.772313\pi$
$263$	−1.69358e6			−1.50979			−0.754897	+	0.655844i	$0.772313\pi$
$264$	1.54359e6	−	2.12888e6i	1.36308	−	1.87993i
$265$		0			0
$266$	−198217.	−	609382.i	−0.171766	−	0.528063i
$267$		−	710400.i		−	0.609852i
$268$	−1.05861e6	−	1.45509e6i	−0.900329	−	1.23752i
$269$			404802.i			0.341085i	0.985350	+	0.170542i	$0.0545520\pi$
$269$			404802.i			0.341085i	−0.985350	+	0.170542i	$0.945448\pi$
$270$		0			0
$271$	826006.			0.683219			0.341609	−	0.939842i	$-0.389028\pi$
$271$	826006.			0.683219			0.341609	+	0.939842i	$0.389028\pi$
$272$	−619925.	+	1.91631e6i	−0.508062	+	1.57052i
$273$	308232.			0.250306
$274$	−106299.	+	34576.4i	−0.0855367	+	0.0278229i
$275$		0			0
$276$	−1.41581e6	−	1.94606e6i	−1.11875	−	1.53774i
$277$		−	1.86599e6i		−	1.46120i	−0.682804	−	0.730602i	$-0.739240\pi$
$277$		−	1.86599e6i		−	1.46120i	0.682804	−	0.730602i	$-0.260760\pi$
$278$	96989.1	+	298176.i	0.0752681	+	0.231398i
$279$	−3.05449e6			−2.34925
$280$		0			0
$281$	−687132.			−0.519128			−0.259564	−	0.965726i	$-0.583579\pi$
$281$	−687132.			−0.519128			−0.259564	+	0.965726i	$0.583579\pi$
$282$	−261296.	−	803307.i	−0.195663	−	0.601532i
$283$		−	341635.i		−	0.253569i	−0.991930	−	0.126784i	$-0.959534\pi$
$283$		−	341635.i		−	0.253569i	0.991930	−	0.126784i	$-0.0404657\pi$
$284$	−1.44385e6	+	1.05044e6i	−1.06225	+	0.772812i
$285$		0			0
$286$	203716.	−	66263.6i	0.147268	−	0.0479027i
$287$	1.15194e6			0.825516
$288$	3679.56	+	2.29060e6i	0.00261406	+	1.62730i
$289$	2.44877e6			1.72466
$290$		0			0
$291$		−	983908.i		−	0.681118i
$292$	−98208.7	+	71449.3i	−0.0674051	+	0.0490389i
$293$			1.13497e6i			0.772355i	0.922424	+	0.386178i	$0.126205\pi$
$293$			1.13497e6i			0.772355i	−0.922424	+	0.386178i	$0.873795\pi$
$294$	773347.	+	2.37752e6i	0.521802	+	1.60419i
$295$		0			0
$296$	1.06795e6	+	774336.i	0.708467	+	0.513689i
$297$	−2.21435e6			−1.45665
$298$	544901.	+	1.67520e6i	0.355449	+	1.09276i
$299$		−	196054.i		−	0.126823i
$300$		0			0
$301$			2.66677e6i			1.69656i
$302$	−1.02810e6	+	334415.i	−0.648661	+	0.210993i
$303$	−3.47510e6			−2.17451
$304$	595940.	+	192786.i	0.369844	+	0.119644i
$305$		0			0
$306$	4.18397e6	−	1.36094e6i	2.55438	−	0.830874i
$307$		−	3.14641e6i		−	1.90533i	−0.304030	−	0.952663i	$-0.598332\pi$
$307$		−	3.14641e6i		−	1.90533i	0.304030	−	0.952663i	$-0.401668\pi$
$308$	2.00446e6	+	2.75518e6i	1.20398	+	1.65490i
$309$		−	822802.i		−	0.490229i
$310$		0			0
$311$	−837157.			−0.490802			−0.245401	−	0.969422i	$-0.578920\pi$
$311$	−837157.			−0.490802			−0.245401	+	0.969422i	$0.578920\pi$
$312$	−176851.	+	243908.i	−0.102854	+	0.141853i
$313$	−529258.			−0.305356			−0.152678	−	0.988276i	$-0.548790\pi$
$313$	−529258.			−0.305356			−0.152678	+	0.988276i	$0.548790\pi$
$314$	−53118.1	−	163302.i	−0.0304032	−	0.0934691i
$315$		0			0
$316$	−1.91668e6	+	1.39443e6i	−1.07977	+	0.785560i
$317$			2.04482e6i			1.14290i	0.820638	+	0.571448i	$0.193618\pi$
$317$			2.04482e6i			1.14290i	−0.820638	+	0.571448i	$0.806382\pi$
$318$	−2.80383e6	+	912016.i	−1.55483	+	0.505749i
$319$	−2.57263e6			−1.41547
$320$		0			0
$321$	3.90690e6			2.11626
$322$	2.96529e6	−	964536.i	1.59378	−	0.518416i
$323$		−	1.20308e6i		−	0.641635i
$324$	31790.4	−	23128.3i	0.0168242	−	0.0122400i
$325$		0			0
$326$	−138429.	−	425576.i	−0.0721413	−	0.221786i
$327$	−2.48779e6			−1.28660
$328$	−660935.	+	911545.i	−0.339214	+	0.467836i
$329$	1.09453e6			0.557489
$330$		0			0
$331$			535804.i			0.268804i	0.990927	+	0.134402i	$0.0429114\pi$
$331$			535804.i			0.268804i	−0.990927	+	0.134402i	$0.957089\pi$
$332$	2.21092e6	+	3.03896e6i	1.10085	+	1.51314i
$333$		−	2.88162e6i		−	1.42405i
$334$	−2.87139e6	+	933990.i	−1.40840	+	0.458117i
$335$		0			0
$336$	−4.55915e6	−	1.47488e6i	−2.20311	−	0.712704i
$337$	−795512.			−0.381568			−0.190784	−	0.981632i	$-0.561103\pi$
$337$	−795512.			−0.381568			−0.190784	+	0.981632i	$0.561103\pi$
$338$	1.97400e6	−	642094.i	0.939845	−	0.305708i
$339$			3.34381e6i			1.58031i
$340$		0			0
$341$		−	4.44091e6i		−	2.06817i
$342$	−423230.	−	1.30114e6i	−0.195664	−	0.601534i
$343$	−126790.			−0.0581902
$344$	−2.11025e6	−	1.53008e6i	−0.961473	−	0.697136i
$345$		0			0
$346$	621706.	+	1.91132e6i	0.279187	+	0.858310i
$347$		−	1.16949e6i		−	0.521401i	−0.965420	−	0.260700i	$-0.916047\pi$
$347$		−	1.16949e6i		−	0.521401i	0.965420	−	0.260700i	$-0.0839534\pi$
$348$	2.92572e6	−	2.12853e6i	1.29504	−	0.942176i
$349$		−	1.63512e6i		−	0.718596i	−0.933223	−	0.359298i	$-0.883016\pi$
$349$		−	1.63512e6i		−	0.718596i	0.933223	−	0.359298i	$-0.116984\pi$
$350$		0			0
$351$	253700.			0.109914
$352$	−3.33028e6	+	5349.70i	−1.43260	+	0.00230130i
$353$	−2.34590e6			−1.00201			−0.501006	−	0.865444i	$-0.667037\pi$
$353$	−2.34590e6			−1.00201			−0.501006	+	0.865444i	$0.667037\pi$
$354$	1.68909e6	−	549420.i	0.716384	−	0.233022i
$355$		0			0
$356$	−727528.	+	529294.i	−0.304246	+	0.221346i
$357$			9.20396e6i			3.82212i
$358$	−1.06741e6	−	3.28155e6i	−0.440172	−	1.35323i
$359$	462114.			0.189240			0.0946200	−	0.995513i	$-0.469836\pi$
$359$	462114.			0.189240			0.0946200	+	0.995513i	$0.469836\pi$
$360$		0			0
$361$	2.10196e6			0.848900
$362$	−709407.	−	2.18094e6i	−0.284527	−	0.874728i
$363$		−	4.28232e6i		−	1.70574i
$364$	−229653.	−	315664.i	−0.0908487	−	0.124874i
$365$		0			0
$366$	−2.69571e6	+	876847.i	−1.05189	+	0.342154i
$367$	3.73676e6			1.44820			0.724102	−	0.689693i	$-0.242254\pi$
$367$	3.73676e6			1.44820			0.724102	+	0.689693i	$0.242254\pi$
$368$	−938111.	+	2.89988e6i	−0.361106	+	1.11625i
$369$	2.45961e6			0.940372
$370$		0			0
$371$		−	3.82029e6i		−	1.44099i
$372$	3.67431e6	+	5.05043e6i	1.37663	+	1.89222i
$373$		−	214685.i		−	0.0798970i	−0.999202	−	0.0399485i	$-0.987281\pi$
$373$		−	214685.i		−	0.0798970i	0.999202	−	0.0399485i	$-0.0127194\pi$
$374$	1.97866e6	+	6.08305e6i	0.731464	+	2.24876i
$375$		0			0
$376$	−627993.	+	866112.i	−0.229079	+	0.315940i
$377$	294748.			0.106807
$378$	1.24814e6	+	3.83719e6i	0.449298	+	1.38129i
$379$		−	2.28648e6i		−	0.817652i	−0.912612	−	0.408826i	$-0.865938\pi$
$379$		−	2.28648e6i		−	0.817652i	0.912612	−	0.408826i	$-0.134062\pi$
$380$		0			0
$381$			8.20538e6i			2.89592i
$382$	−1.27710e6	+	415410.i	−0.447783	+	0.145653i
$383$	1.69175e6			0.589302			0.294651	−	0.955605i	$-0.404797\pi$
$383$	1.69175e6			0.589302			0.294651	+	0.955605i	$0.404797\pi$
$384$	3.78294e6	−	2.76149e6i	1.30919	−	0.955685i
$385$		0			0
$386$	−1.95394e6	+	635568.i	−0.667487	+	0.217117i
$387$			5.69404e6i			1.93261i
$388$	−1.00763e6	+	733076.i	−0.339799	+	0.247212i
$389$		−	2.43317e6i		−	0.815266i	−0.913146	−	0.407633i	$-0.866354\pi$
$389$		−	2.43317e6i		−	0.815266i	0.913146	−	0.407633i	$-0.133646\pi$
$390$		0			0
$391$	5.85426e6			1.93656
$392$	1.85865e6	−	2.56340e6i	0.610916	−	0.842561i
$393$	4.48970e6			1.46634
$394$	−284626.	−	875033.i	−0.0923708	−	0.283978i
$395$		0			0
$396$	4.27990e6	+	5.88282e6i	1.37150	+	1.88516i
$397$		−	3.05521e6i		−	0.972893i	−0.873710	−	0.486446i	$-0.838293\pi$
$397$		−	3.05521e6i		−	0.972893i	0.873710	−	0.486446i	$-0.161707\pi$
$398$	1.65045e6	−	536851.i	0.522270	−	0.169881i
$399$	2.86228e6			0.900077
$400$		0			0
$401$	−131858.			−0.0409493			−0.0204746	−	0.999790i	$-0.506518\pi$
$401$	−131858.			−0.0409493			−0.0204746	+	0.999790i	$0.506518\pi$
$402$	7.64327e6	−	2.48617e6i	2.35893	−	0.767300i
$403$			508800.i			0.156057i
$404$	2.58918e6	+	3.55888e6i	0.789238	+	1.08483i
$405$		0			0
$406$	1.45009e6	+	4.45804e6i	0.436596	+	1.34224i
$407$	4.18957e6			1.25367
$408$	−7.28321e6	−	5.28085e6i	−2.16607	−	1.57055i
$409$	−2.64156e6			−0.780821			−0.390411	−	0.920641i	$-0.627667\pi$
$409$	−2.64156e6			−0.780821			−0.390411	+	0.920641i	$0.627667\pi$
$410$		0			0
$411$		−	499288.i		−	0.145796i
$412$	−842640.	+	613041.i	−0.244568	+	0.177929i
$413$			2.30143e6i			0.663931i
$414$	6.33145e6	−	2.05946e6i	1.81553	−	0.590545i
$415$		0			0
$416$	381554.	−	612.920i	0.108099	−	0.000173648i
$417$	−1.40054e6			−0.394416
$418$	1.89173e6	−	615331.i	0.529563	−	0.172254i
$419$			1.36333e6i			0.379372i	0.981845	+	0.189686i	$0.0607470\pi$
$419$			1.36333e6i			0.379372i	−0.981845	+	0.189686i	$0.939253\pi$
$420$		0			0
$421$		−	3.78864e6i		−	1.04178i	−0.853623	−	0.520892i	$-0.825599\pi$
$421$		−	3.78864e6i		−	1.04178i	0.853623	−	0.520892i	$-0.174401\pi$
$422$	1.60356e6	+	4.92987e6i	0.438334	+	1.34758i
$423$	2.33702e6			0.635054
$424$	3.02304e6	+	2.19192e6i	0.816638	+	0.592121i
$425$		0			0
$426$	−2.46696e6	−	7.58423e6i	−0.658625	−	2.02482i
$427$		−	3.67297e6i		−	0.974873i
$428$	−2.91090e6	−	4.00110e6i	−0.768100	−	1.05577i
$429$			956855.i			0.251017i
$430$		0			0
$431$	−6.99954e6			−1.81500			−0.907499	−	0.420054i	$-0.862011\pi$
$431$	−6.99954e6			−1.81500			−0.907499	+	0.420054i	$0.862011\pi$
$432$	−3.75255e6	−	1.21395e6i	−0.967425	−	0.312962i
$433$	−1.07862e6			−0.276470			−0.138235	−	0.990399i	$-0.544143\pi$
$433$	−1.07862e6			−0.276470			−0.138235	+	0.990399i	$0.544143\pi$
$434$	−7.69555e6	+	2.50317e6i	−1.96117	+	0.637920i
$435$		0			0
$436$	1.85357e6	+	2.54777e6i	0.466974	+	0.641866i
$437$		−	1.82058e6i		−	0.456043i
$438$	−167799.	−	515869.i	−0.0417931	−	0.128485i
$439$	6.18225e6			1.53104			0.765518	−	0.643415i	$-0.222483\pi$
$439$	6.18225e6			1.53104			0.765518	+	0.643415i	$0.222483\pi$
$440$		0			0
$441$	−6.91678e6			−1.69359
$442$	−226697.	−	696941.i	−0.0551939	−	0.169684i
$443$		−	1.96693e6i		−	0.476189i	−0.971242	−	0.238094i	$-0.923477\pi$
$443$		−	1.96693e6i		−	0.476189i	0.971242	−	0.238094i	$-0.0765228\pi$
$444$	−4.76459e6	+	3.46636e6i	−1.14701	+	0.834480i
$445$		0			0
$446$	656667.	−	213597.i	0.156318	−	0.0508462i
$447$	−7.86845e6			−1.86260
$448$	1.88642e6	+	5.76795e6i	0.444062	+	1.35777i
$449$	−3.64999e6			−0.854430			−0.427215	−	0.904150i	$-0.640505\pi$
$449$	−3.64999e6			−0.854430			−0.427215	+	0.904150i	$0.640505\pi$
$450$		0			0
$451$			3.57601e6i			0.827860i
$452$	3.42443e6	−	2.49135e6i	0.788391	−	0.573574i
$453$		−	4.82900e6i		−	1.10564i
$454$	160416.	+	493170.i	0.0365265	+	0.112294i
$455$		0			0
$456$	−1.64225e6	+	2.26496e6i	−0.369852	+	0.510091i
$457$	−512099.			−0.114700			−0.0573500	−	0.998354i	$-0.518265\pi$
$457$	−512099.			−0.114700			−0.0573500	+	0.998354i	$0.518265\pi$
$458$	−1.82689e6	−	5.61646e6i	−0.406958	−	1.25112i
$459$			7.57562e6i			1.67836i
$460$		0			0
$461$			1.17026e6i			0.256466i	0.991744	+	0.128233i	$0.0409306\pi$
$461$			1.17026e6i			0.256466i	−0.991744	+	0.128233i	$0.959069\pi$
$462$	−1.44723e7	+	4.70749e6i	−3.15453	+	1.02609i
$463$	2.99324e6			0.648918			0.324459	−	0.945900i	$-0.394818\pi$
$463$	2.99324e6			0.648918			0.324459	+	0.945900i	$0.394818\pi$
$464$	−4.35970e6	−	1.41036e6i	−0.940074	−	0.304114i
$465$		0			0
$466$	3.79930e6	−	1.23582e6i	0.810474	−	0.263627i
$467$		−	814584.i		−	0.172840i	−0.996259	−	0.0864198i	$-0.972457\pi$
$467$		−	814584.i		−	0.172840i	0.996259	−	0.0864198i	$-0.0275426\pi$
$468$	−490352.	−	674000.i	−0.103489	−	0.142248i
$469$			1.04141e7i			2.18621i
$470$		0			0
$471$	767033.			0.159317
$472$	−1.82115e6	−	1.32047e6i	−0.376263	−	0.272817i
$473$	−8.27854e6			−1.70138
$474$	−3.27483e6	−	1.00679e7i	−0.669488	−	2.05822i
$475$		0			0
$476$	9.42587e6	−	6.85755e6i	1.90680	−	1.38724i
$477$		−	8.15703e6i		−	1.64148i
$478$	1.31574e6	−	427977.i	0.263390	−	0.0856742i
$479$	3.00391e6			0.598202			0.299101	−	0.954222i	$-0.403313\pi$
$479$	3.00391e6			0.598202			0.299101	+	0.954222i	$0.403313\pi$
$480$		0			0
$481$	−480003.			−0.0945979
$482$	3.24083e6	−	1.05416e6i	0.635388	−	0.206676i
$483$			1.39280e7i			2.71658i
$484$	−4.38557e6	+	3.19061e6i	−0.850966	+	0.619099i
$485$		0			0
$486$	−1.58338e6	−	4.86781e6i	−0.304084	−	0.934852i
$487$	7.07824e6			1.35239			0.676196	−	0.736722i	$-0.263627\pi$
$487$	7.07824e6			1.35239			0.676196	+	0.736722i	$0.263627\pi$
$488$	2.90647e6	+	2.10740e6i	0.552479	+	0.400587i
$489$	1.99894e6			0.378031
$490$		0			0
$491$			1.91785e6i			0.359014i	0.983757	+	0.179507i	$0.0574502\pi$
$491$			1.91785e6i			0.359014i	−0.983757	+	0.179507i	$0.942550\pi$
$492$	−2.95871e6	−	4.06682e6i	−0.551048	−	0.757429i
$493$			8.80133e6i			1.63091i
$494$	−216737.	+	70499.1i	−0.0399591	+	0.0129977i
$495$		0			0
$496$	2.43459e6	−	7.52580e6i	0.444347	−	1.37356i
$497$	1.03337e7			1.87657
$498$	−1.59630e7	+	5.19236e6i	−2.88431	+	0.938192i
$499$		−	2.99398e6i		−	0.538267i	−0.963103	−	0.269133i	$-0.913263\pi$
$499$		−	2.99398e6i		−	0.538267i	0.963103	−	0.269133i	$-0.0867372\pi$
$500$		0			0
$501$		−	1.34870e7i		−	2.40060i
$502$	−729029.	−	2.24127e6i	−0.129118	−	0.396949i
$503$	−3.15402e6			−0.555832			−0.277916	−	0.960605i	$-0.589644\pi$
$503$	−3.15402e6			−0.555832			−0.277916	+	0.960605i	$0.589644\pi$
$504$	7.78178e6	−	1.07324e7i	1.36459	−	1.88201i
$505$		0			0
$506$	2.99424e6	+	9.20526e6i	0.519889	+	1.59831i
$507$			9.27193e6i			1.60195i
$508$	8.40322e6	−	6.11355e6i	1.44473	−	1.05108i
$509$			4.01915e6i			0.687606i	0.939042	+	0.343803i	$0.111715\pi$
$509$			4.01915e6i			0.687606i	−0.939042	+	0.343803i	$0.888285\pi$
$510$		0			0
$511$	702884.			0.119078
$512$	−5.64660e6	−	1.81666e6i	−0.951946	−	0.306266i
$513$	2.35589e6			0.395241
$514$	−11109.3	+	3613.59i	−0.00185473	+	0.000603297i
$515$		0			0
$516$	9.41477e6	−	6.84948e6i	1.55663	−	1.13249i
$517$			3.39777e6i			0.559073i
$518$	−2.36150e6	−	7.26001e6i	−0.386690	−	1.18881i
$519$	−8.97752e6			−1.46298
$520$		0			0
$521$	−2.01168e6			−0.324687			−0.162344	−	0.986734i	$-0.551905\pi$
$521$	−2.01168e6			−0.324687			−0.162344	+	0.986734i	$0.551905\pi$
$522$	3.09621e6	+	9.51875e6i	0.497341	+	1.52899i
$523$			1.04130e7i			1.66464i	0.554295	+	0.832320i	$0.312988\pi$
$523$			1.04130e7i			1.66464i	−0.554295	+	0.832320i	$0.687012\pi$
$524$	−3.34512e6	−	4.59795e6i	−0.532211	−	0.731536i
$525$		0			0
$526$	−9.11052e6	+	2.96342e6i	−1.43575	+	0.467013i
$527$	−1.51930e7			−2.38296
$528$	4.57853e6	−	1.41531e7i	0.714728	−	2.20936i
$529$	2.42270e6			0.376409
$530$		0			0
$531$			4.91399e6i			0.756306i
$532$	−2.13259e6	−	2.93129e6i	−0.326684	−	0.449034i
$533$		−	409707.i		−	0.0624676i
$534$	−1.24305e6	−	3.82154e6i	−0.188641	−	0.579943i
$535$		0			0
$536$	−8.24085e6	−	5.97520e6i	−1.23897	−	0.898339i
$537$	1.54135e7			2.30656
$538$	708320.	+	2.17760e6i	0.105505	+	0.324357i
$539$		−	1.00563e7i		−	1.49096i
$540$		0			0
$541$			4.03497e6i			0.592717i	0.955077	+	0.296358i	$0.0957723\pi$
$541$			4.03497e6i			0.592717i	−0.955077	+	0.296358i	$0.904228\pi$
$542$	4.44344e6	−	1.44534e6i	0.649712	−	0.211335i
$543$	1.02439e7			1.49096
$544$	18302.1	+	1.13934e7i	0.00265157	+	1.65065i
$545$		0			0
$546$	1.65811e6	−	539342.i	0.238030	−	0.0774253i
$547$		−	3.72273e6i		−	0.531978i	−0.963976	−	0.265989i	$-0.914302\pi$
$547$		−	3.72273e6i		−	0.531978i	0.963976	−	0.265989i	$-0.0856985\pi$
$548$	−511326.	+	372002.i	−0.0727354	+	0.0529168i
$549$		−	7.84248e6i		−	1.11051i
$550$		0			0
$551$	2.73707e6			0.384066
$552$	−1.10214e7	−	7.99132e6i	−1.53954	−	1.11627i
$553$	1.37177e7			1.90752
$554$	−3.26510e6	−	1.00380e7i	−0.451983	−	1.38954i
$555$		0			0
$556$	1.04349e6	+	1.43430e6i	0.143153	+	0.196768i
$557$		−	1.07331e7i		−	1.46584i	−0.680316	−	0.732919i	$-0.738157\pi$
$557$		−	1.07331e7i		−	1.46584i	0.680316	−	0.732919i	$-0.261843\pi$
$558$	−1.64314e7	+	5.34473e6i	−2.23403	+	0.726675i
$559$	948480.			0.128380
$560$		0			0
$561$	−2.85722e7			−3.83298
$562$	−3.69637e6	+	1.20234e6i	−0.493668	+	0.160578i
$563$		−	1.10773e7i		−	1.47287i	−0.676511	−	0.736433i	$-0.736509\pi$
$563$		−	1.10773e7i		−	1.47287i	0.676511	−	0.736433i	$-0.263491\pi$
$564$	−2.81124e6	−	3.86412e6i	−0.372135	−	0.511508i
$565$		0			0
$566$	−597790.	−	1.83780e6i	−0.0784346	−	0.241133i
$567$	−227525.			−0.0297216
$568$	−5.92904e6	+	8.17718e6i	−0.771105	+	1.06349i
$569$	6.94176e6			0.898854			0.449427	−	0.893317i	$-0.351628\pi$
$569$	6.94176e6			0.898854			0.449427	+	0.893317i	$0.351628\pi$
$570$		0			0
$571$			1.13064e7i			1.45122i	0.688107	+	0.725609i	$0.258442\pi$
$571$			1.13064e7i			1.45122i	−0.688107	+	0.725609i	$0.741558\pi$
$572$	979925.	−	712920.i	0.125228	−	0.0911068i
$573$		−	5.99858e6i		−	0.763241i
$574$	6.19678e6	−	2.01566e6i	0.785030	−	0.255351i
$575$		0			0
$576$	4.02786e6	+	1.23156e7i	0.505846	+	1.54668i
$577$	−1.47805e6			−0.184820			−0.0924101	−	0.995721i	$-0.529457\pi$
$577$	−1.47805e6			−0.184820			−0.0924101	+	0.995721i	$0.529457\pi$
$578$	1.31730e7	−	4.28484e6i	1.64008	−	0.533476i
$579$		−	9.17769e6i		−	1.13772i
$580$		0			0
$581$		−	2.17500e7i		−	2.67312i
$582$	−1.72164e6	−	5.29286e6i	−0.210685	−	0.647714i
$583$	1.18595e7			1.44509
$584$	−403285.	+	556201.i	−0.0489305	+	0.0674838i
$585$		0			0
$586$	1.98597e6	+	6.10551e6i	0.238907	+	0.734477i
$587$		−	967824.i		−	0.115931i	−0.998319	−	0.0579657i	$-0.981539\pi$
$587$		−	967824.i		−	0.115931i	0.998319	−	0.0579657i	$-0.0184614\pi$
$588$	8.32033e6	+	1.14365e7i	0.992424	+	1.36411i
$589$			4.72477e6i			0.561168i
$590$		0			0
$591$	4.11005e6			0.484036
$592$	7.09986e6	+	2.29680e6i	0.832618	+	0.269351i
$593$	1.26252e7			1.47435			0.737177	−	0.675699i	$-0.236158\pi$
$593$	1.26252e7			1.47435			0.737177	+	0.675699i	$0.236158\pi$
$594$	−1.19119e7	+	3.87465e6i	−1.38521	+	0.450575i
$595$		0			0
$596$	5.86251e6	+	8.05816e6i	0.676033	+	0.929224i
$597$			7.75220e6i			0.890204i
$598$	−343053.	−	1.05466e6i	−0.0392291	−	0.120603i
$599$	4.49357e6			0.511710			0.255855	−	0.966715i	$-0.417643\pi$
$599$	4.49357e6			0.511710			0.255855	+	0.966715i	$0.417643\pi$
$600$		0			0
$601$	6.32166e6			0.713913			0.356956	−	0.934121i	$-0.383814\pi$
$601$	6.32166e6			0.713913			0.356956	+	0.934121i	$0.383814\pi$
$602$	4.66629e6	+	1.43457e7i	0.524784	+	1.61335i
$603$			2.22361e7i			2.49038i
$604$	−4.94543e6	+	3.59792e6i	−0.551584	+	0.401291i
$605$		0			0
$606$	−1.86940e7	+	6.08070e6i	−2.06786	+	0.672624i
$607$	−1.12652e7			−1.24099			−0.620493	−	0.784212i	$-0.713067\pi$
$607$	−1.12652e7			−1.24099			−0.620493	+	0.784212i	$0.713067\pi$
$608$	3.54315e6	−	5691.65i	0.388715	−	0.000624423i
$609$	−2.09395e7			−2.28783
$610$		0			0
$611$		−	389286.i		−	0.0421858i
$612$	2.01260e7	−	1.46422e7i	2.17209	−	1.58025i
$613$			2.50596e6i			0.269354i	0.990890	+	0.134677i	$0.0429996\pi$
$613$			2.50596e6i			0.269354i	−0.990890	+	0.134677i	$0.957000\pi$
$614$	−5.50556e6	−	1.69259e7i	−0.589360	−	1.81188i
$615$		0			0
$616$	1.56038e7	+	1.13139e7i	1.65684	+	1.20132i
$617$	−8.68891e6			−0.918867			−0.459433	−	0.888212i	$-0.651947\pi$
$617$	−8.68891e6			−0.918867			−0.459433	+	0.888212i	$0.651947\pi$
$618$	−1.43973e6	−	4.42620e6i	−0.151639	−	0.466187i
$619$			3.52743e6i			0.370026i	0.982736	+	0.185013i	$0.0592327\pi$
$619$			3.52743e6i			0.370026i	−0.982736	+	0.185013i	$0.940767\pi$
$620$		0			0
$621$			1.14639e7i			1.19290i
$622$	−4.50343e6	+	1.46485e6i	−0.466732	+	0.151816i
$623$	5.20695e6			0.537481
$624$	−524566.	+	1.62154e6i	−0.0539310	+	0.166711i
$625$		0			0
$626$	−2.84711e6	+	926092.i	−0.290381	+	0.0944536i
$627$			8.88547e6i			0.902634i
$628$	−571490.	−	785527.i	−0.0578242	−	0.0794807i
$629$		−	1.43331e7i		−	1.44449i
$630$		0			0
$631$	1.36732e7			1.36709			0.683544	−	0.729909i	$-0.260438\pi$
$631$	1.36732e7			1.36709			0.683544	+	0.729909i	$0.260438\pi$
$632$	−7.87066e6	+	1.08550e7i	−0.783824	+	1.08103i
$633$	−2.31557e7			−2.29693
$634$	3.57801e6	+	1.10000e7i	0.353524	+	1.08685i
$635$		0			0
$636$	−1.34872e7	+	9.81225e6i	−1.32214	+	0.961891i
$637$			1.15216e6i			0.112503i
$638$	−1.38392e7	+	4.50156e6i	−1.34605	+	0.437836i
$639$	2.20644e7			2.13766
$640$		0			0
$641$	3.09731e6			0.297742			0.148871	−	0.988857i	$-0.452436\pi$
$641$	3.09731e6			0.297742			0.148871	+	0.988857i	$0.452436\pi$
$642$	2.10169e7	−	6.83627e6i	2.01248	−	0.654608i
$643$		−	1.56372e7i		−	1.49152i	−0.666212	−	0.745762i	$-0.732086\pi$
$643$		−	1.56372e7i		−	1.49152i	0.666212	−	0.745762i	$-0.267914\pi$
$644$	1.42638e7	−	1.03773e7i	1.35526	−	0.985983i
$645$		0			0
$646$	−2.10514e6	−	6.47187e6i	−0.198472	−	0.610167i
$647$	−2.67797e6			−0.251504			−0.125752	−	0.992062i	$-0.540134\pi$
$647$	−2.67797e6			−0.251504			−0.125752	+	0.992062i	$0.540134\pi$
$648$	130544.	−	180044.i	0.0122130	−	0.0168438i
$649$	−7.14442e6			−0.665817
$650$		0			0
$651$		−	3.61461e7i		−	3.34279i
$652$	−1.48934e6	−	2.04713e6i	−0.137207	−	0.188594i
$653$			1.36294e7i			1.25082i	0.780297	+	0.625409i	$0.215068\pi$
$653$			1.36294e7i			1.25082i	−0.780297	+	0.625409i	$0.784932\pi$
$654$	−1.33829e7	+	4.35312e6i	−1.22350	+	0.397975i
$655$		0			0
$656$	−1.96044e6	+	6.06009e6i	−0.177866	+	0.549819i
$657$	1.50079e6			0.135646
$658$	5.88792e6	−	1.91519e6i	0.530148	−	0.172444i
$659$			9.26345e6i			0.830920i	0.909611	+	0.415460i	$0.136379\pi$
$659$			9.26345e6i			0.830920i	−0.909611	+	0.415460i	$0.863621\pi$
$660$		0			0
$661$		−	5.35606e6i		−	0.476806i	−0.971166	−	0.238403i	$-0.923376\pi$
$661$		−	5.35606e6i		−	0.476806i	0.971166	−	0.238403i	$-0.0766239\pi$
$662$	937546.	+	2.88232e6i	0.0831472	+	0.255621i
$663$	3.27354e6			0.289224
$664$	1.72110e7	+	1.24792e7i	1.51491	+	1.09842i
$665$		0			0
$666$	−5.04224e6	−	1.55015e7i	−0.440492	−	1.35421i
$667$			1.33187e7i			1.15917i
$668$	−1.38121e7	+	1.00487e7i	−1.19762	+	0.871299i
$669$			3.08438e6i			0.266442i
$670$		0			0
$671$	1.14021e7			0.977642
$672$	−2.71063e7	+	43543.0i	−2.31551	+	0.00371959i
$673$	−1.80861e7			−1.53924			−0.769621	−	0.638501i	$-0.779555\pi$
$673$	−1.80861e7			−1.53924			−0.769621	+	0.638501i	$0.779555\pi$
$674$	−4.27940e6	+	1.39198e6i	−0.362855	+	0.118028i
$675$		0			0
$676$	9.49547e6	−	6.90819e6i	0.799190	−	0.581430i
$677$			1.52433e7i			1.27822i	0.769114	+	0.639111i	$0.220698\pi$
$677$			1.52433e7i			1.27822i	−0.769114	+	0.639111i	$0.779302\pi$
$678$	5.85097e6	+	1.79878e7i	0.488825	+	1.50281i
$679$	7.21166e6			0.600289
$680$		0			0
$681$	−2.31643e6			−0.191404
$682$	−7.77068e6	−	2.38896e7i	−0.639732	−	1.96674i
$683$		−	2.13600e7i		−	1.75206i	−0.482256	−	0.876031i	$-0.660182\pi$
$683$		−	2.13600e7i		−	1.75206i	0.482256	−	0.876031i	$-0.339818\pi$
$684$	−4.55347e6	−	6.25885e6i	−0.372136	−	0.511510i
$685$		0			0
$686$	−682057.	+	221856.i	−0.0553364	+	0.0179995i
$687$	2.63806e7			2.13252
$688$	−1.40292e7	−	4.53845e6i	−1.12996	−	0.365541i
$689$	−1.35875e6			−0.109041
$690$		0			0
$691$			5.43768e6i			0.433230i	0.976257	+	0.216615i	$0.0695016\pi$
$691$			5.43768e6i			0.433230i	−0.976257	+	0.216615i	$0.930498\pi$
$692$	6.68884e6	+	9.19397e6i	0.530989	+	0.729858i
$693$		−	4.21036e7i		−	3.33032i
$694$	−2.04636e6	−	6.29117e6i	−0.161281	−	0.495830i
$695$		0			0
$696$	1.20142e7	−	1.65697e7i	0.940095	−	1.29656i
$697$	1.22340e7			0.953868
$698$	−2.86111e6	−	8.79599e6i	−0.222278	−	0.683354i
$699$			1.78454e7i			1.38144i
$700$		0			0
$701$			8.82961e6i			0.678651i	0.940669	+	0.339326i	$0.110199\pi$
$701$			8.82961e6i			0.678651i	−0.940669	+	0.339326i	$0.889801\pi$
$702$	1.36476e6	−	443923.i	0.104524	−	0.0339989i
$703$	−4.45737e6			−0.340165
$704$	−1.79057e7	+	5.85608e6i	−1.36163	+	0.445323i
$705$		0			0
$706$	−1.26196e7	+	4.10484e6i	−0.952871	+	0.309945i
$707$		−	2.54711e7i		−	1.91646i
$708$	8.12499e6	−	5.91113e6i	0.609171	−	0.443187i
$709$		−	1.19737e7i		−	0.894566i	−0.894393	−	0.447283i	$-0.852392\pi$
$709$		−	1.19737e7i		−	0.894566i	0.894393	−	0.447283i	$-0.147608\pi$
$710$		0			0
$711$	2.92899e7			2.17292
$712$	−2.98753e6	+	4.12032e6i	−0.220857	+	0.304601i
$713$	−2.29911e7			−1.69369
$714$	1.61050e7	+	4.95120e7i	1.18227	+	3.63467i
$715$		0			0
$716$	−1.14841e7	−	1.57851e7i	−0.837169	−	1.15071i
$717$			6.18004e6i			0.448945i
$718$	2.48591e6	−	808603.i	0.179959	−	0.0585362i
$719$	−6.87706e6			−0.496113			−0.248056	−	0.968746i	$-0.579792\pi$
$719$	−6.87706e6			−0.496113			−0.248056	+	0.968746i	$0.579792\pi$
$720$		0			0
$721$	6.03081e6			0.432053
$722$	1.13073e7	−	3.67800e6i	0.807268	−	0.262584i
$723$			1.52222e7i			1.08301i
$724$	−7.63240e6	−	1.04909e7i	−0.541146	−	0.743819i
$725$		0			0
$726$	−7.49317e6	−	2.30364e7i	−0.527623	−	1.62208i
$727$	−2.24438e7			−1.57493			−0.787464	−	0.616360i	$-0.788606\pi$
$727$	−2.24438e7			−1.57493			−0.787464	+	0.616360i	$0.788606\pi$
$728$	−1.78775e6	−	1.29624e6i	−0.125019	−	0.0906480i
$729$	2.31627e7			1.61425
$730$		0			0
$731$			2.83221e7i			1.96034i
$732$	−1.29671e7	+	9.43387e6i	−0.894467	+	0.650747i
$733$			2.81360e7i			1.93420i	0.254393	+	0.967101i	$0.418124\pi$
$733$			2.81360e7i			1.93420i	−0.254393	+	0.967101i	$0.581876\pi$
$734$	2.01016e7	−	6.53855e6i	1.37718	−	0.447962i
$735$		0			0
$736$	27695.9	+	1.72412e7i	0.00188461	+	1.17320i
$737$	−3.23290e7			−2.19242
$738$	1.32313e7	−	4.30380e6i	0.894254	−	0.290878i
$739$			1.34928e7i			0.908845i	0.890786	+	0.454422i	$0.150154\pi$
$739$			1.34928e7i			0.908845i	−0.890786	+	0.454422i	$0.849846\pi$
$740$		0			0
$741$		−	1.01802e6i		−	0.0681098i
$742$	−6.68471e6	−	2.05510e7i	−0.445731	−	1.37032i
$743$	−3.12986e6			−0.207995			−0.103997	−	0.994578i	$-0.533163\pi$
$743$	−3.12986e6			−0.207995			−0.103997	+	0.994578i	$0.533163\pi$
$744$	2.86029e7	+	2.07391e7i	1.89443	+	1.37359i
$745$		0			0
$746$	−375655.	−	1.15488e6i	−0.0247139	−	0.0759786i
$747$		−	4.64403e7i		−	3.04504i
$748$	2.12881e7	+	2.92611e7i	1.39118	+	1.91221i
$749$			2.86360e7i			1.86513i
$750$		0			0
$751$	−2.80509e7			−1.81487			−0.907437	−	0.420188i	$-0.861964\pi$
$751$	−2.80509e7			−1.81487			−0.907437	+	0.420188i	$0.861964\pi$
$752$	−1.86272e6	+	5.75804e6i	−0.120117	+	0.371305i
$753$	1.05273e7			0.676595
$754$	1.58558e6	−	515748.i	0.101568	−	0.0330377i
$755$		0			0
$756$	1.34286e7	+	1.84579e7i	0.854527	+	1.17457i
$757$			2.74473e7i			1.74084i	0.492308	+	0.870421i	$0.336153\pi$
$757$			2.74473e7i			1.74084i	−0.492308	+	0.870421i	$0.663847\pi$
$758$	−4.00086e6	−	1.22999e7i	−0.252918	−	0.777552i
$759$	−4.32373e7			−2.72429
$760$		0			0
$761$	−2.29174e7			−1.43451			−0.717255	−	0.696810i	$-0.754602\pi$
$761$	−2.29174e7			−1.43451			−0.717255	+	0.696810i	$0.754602\pi$
$762$	1.43577e7	+	4.41403e7i	0.895773	+	2.75389i
$763$		−	1.82345e7i		−	1.13392i
$764$	−6.14320e6	+	4.46933e6i	−0.380769	+	0.277019i
$765$		0			0
$766$	9.10062e6	−	2.96020e6i	0.560401	−	0.182284i
$767$	818543.			0.0502404
$768$	1.55180e7	−	2.14746e7i	0.949365	−	1.31378i
$769$	−1.75616e7			−1.07090			−0.535448	−	0.844568i	$-0.679857\pi$
$769$	−1.75616e7			−1.07090			−0.535448	+	0.844568i	$0.679857\pi$
$770$		0			0
$771$		−	52180.8i		−	0.00316136i
$772$	−9.39897e6	+	6.83798e6i	−0.567593	+	0.412938i
$773$		−	3.23291e7i		−	1.94601i	−0.230785	−	0.973005i	$-0.574129\pi$
$773$		−	3.23291e7i		−	1.94601i	0.230785	−	0.973005i	$-0.425871\pi$
$774$	9.96340e6	+	3.06307e7i	0.597799	+	1.83783i
$775$		0			0
$776$	−4.13774e6	+	5.70667e6i	−0.246666	+	0.340196i
$777$	3.41004e7			2.02631
$778$	−4.25755e6	−	1.30891e7i	−0.252180	−	0.775283i
$779$		−	3.80459e6i		−	0.224628i
$780$		0			0
$781$			3.20792e7i			1.88190i
$782$	3.14926e7	−	1.02437e7i	1.84158	−	0.599020i
$783$	−1.72349e7			−1.00463
$784$	5.51304e6	−	1.70419e7i	0.320332	−	0.990209i
$785$		0			0
$786$	2.41520e7	−	7.85605e6i	1.39443	−	0.453573i
$787$		−	1.69534e7i		−	0.975707i	−0.872926	−	0.487853i	$-0.837780\pi$
$787$		−	1.69534e7i		−	0.975707i	0.872926	−	0.487853i	$-0.162220\pi$
$788$	−3.06225e6	−	4.20914e6i	−0.175681	−	0.241478i
$789$		−	4.27922e7i		−	2.44722i
$790$		0			0
$791$	−2.45088e7			−1.39277
$792$	3.33171e7	+	2.41573e7i	1.88736	+	1.36847i
$793$	−1.30635e6			−0.0737697
$794$	−5.34598e6	−	1.64353e7i	−0.300938	−	0.925179i
$795$		0			0
$796$	7.93911e6	−	5.77590e6i	0.444109	−	0.323100i
$797$		−	1.44730e7i		−	0.807073i	−0.914963	−	0.403537i	$-0.867781\pi$
$797$		−	1.44730e7i		−	0.807073i	0.914963	−	0.403537i	$-0.132219\pi$
$798$	1.53974e7	−	5.00839e6i	0.855935	−	0.278414i
$799$	1.16243e7			0.644168
$800$		0			0
$801$	1.11178e7			0.612262
$802$	−709322.	+	230725.i	−0.0389410	+	0.0126665i
$803$			2.18199e6i			0.119416i
$804$	3.67662e7	−	2.67483e7i	2.00589	−	1.45934i
$805$		0			0
$806$	890294.	+	2.73705e6i	0.0482721	+	0.148404i
$807$	−1.02282e7			−0.552863
$808$	2.01556e7	+	1.46142e7i	1.08609	+	0.787495i
$809$	2.41458e7			1.29709			0.648544	−	0.761177i	$-0.275378\pi$
$809$	2.41458e7			1.29709			0.648544	+	0.761177i	$0.275378\pi$
$810$		0			0
$811$			1.55615e7i			0.830803i	0.909638	+	0.415402i	$0.136359\pi$
$811$			1.55615e7i			0.830803i	−0.909638	+	0.415402i	$0.863641\pi$
$812$	1.56013e7	+	2.14443e7i	0.830368	+	1.14136i
$813$			2.08709e7i			1.10743i
$814$	2.25375e7	−	7.33088e6i	1.19219	−	0.387789i
$815$		0			0
$816$	−4.84199e7	−	1.56638e7i	−2.54565	−	0.823516i
$817$	8.80770e6			0.461644
$818$	−1.42101e7	+	4.62217e6i	−0.742527	+	0.241526i
$819$			4.82385e6i			0.251295i
$820$		0			0
$821$			1.97285e7i			1.02150i	0.859730	+	0.510749i	$0.170632\pi$
$821$			1.97285e7i			1.02150i	−0.859730	+	0.510749i	$0.829368\pi$
$822$	−873650.	−	2.68588e6i	−0.0450980	−	0.138646i
$823$	−2.08659e7			−1.07384			−0.536919	−	0.843634i	$-0.680412\pi$
$823$	−2.08659e7			−1.07384			−0.536919	+	0.843634i	$0.680412\pi$
$824$	−3.46022e6	+	4.77225e6i	−0.177536	+	0.244853i
$825$		0			0
$826$	4.02703e6	+	1.23804e7i	0.205369	+	0.631370i
$827$			4.63684e6i			0.235753i	0.993028	+	0.117877i	$0.0376088\pi$
$827$			4.63684e6i			0.235753i	−0.993028	+	0.117877i	$0.962391\pi$
$828$	3.04559e7	−	2.21575e7i	1.54382	−	1.12317i
$829$			3.84848e6i			0.194493i	0.995260	+	0.0972464i	$0.0310035\pi$
$829$			3.84848e6i			0.194493i	−0.995260	+	0.0972464i	$0.968997\pi$
$830$		0			0
$831$	4.71485e7			2.36846
$832$	2.05147e6	−	670937.i	0.102744	−	0.0336027i
$833$	−3.44040e7			−1.71789
$834$	−7.53408e6	+	2.45065e6i	−0.375073	+	0.122002i
$835$		0			0
$836$	9.09970e6	−	6.62026e6i	0.450310	−	0.327612i
$837$		−	2.97512e7i		−	1.46788i
$838$	2.38554e6	+	7.33393e6i	0.117348	+	0.360767i
$839$	369751.			0.0181344			0.00906722	−	0.999959i	$-0.497114\pi$
$839$	369751.			0.0181344			0.00906722	+	0.999959i	$0.497114\pi$
$840$		0			0
$841$	487665.			0.0237756
$842$	−6.62933e6	−	2.03807e7i	−0.322247	−	0.990692i
$843$		−	1.73619e7i		−	0.841451i
$844$	1.72525e7	+	2.37140e7i	0.833673	+	1.14590i
$845$		0			0
$846$	1.25718e7	−	4.08929e6i	0.603909	−	0.196437i
$847$	3.13877e7			1.50332
$848$	2.00977e7	+	6.50158e6i	0.959745	+	0.310477i
$849$	8.63217e6			0.411009
$850$		0			0
$851$		−	2.16898e7i		−	1.02667i
$852$	−2.65416e7	−	3.64821e7i	−1.25265	−	1.72179i
$853$			2.12932e7i			1.00200i	0.865447	+	0.501000i	$0.167034\pi$
$853$			2.12932e7i			1.00200i	−0.865447	+	0.501000i	$0.832966\pi$
$854$	−6.42694e6	−	1.97585e7i	−0.301550	−	0.927062i
$855$		0			0
$856$	−2.26600e7	−	1.64301e7i	−1.05700	−	0.766403i
$857$	−3.65134e7			−1.69824			−0.849121	−	0.528198i	$-0.822868\pi$
$857$	−3.65134e7			−1.69824			−0.849121	+	0.528198i	$0.822868\pi$
$858$	1.67430e6	+	5.14733e6i	0.0776452	+	0.238706i
$859$		−	2.21742e7i		−	1.02533i	−0.858588	−	0.512666i	$-0.828658\pi$
$859$		−	2.21742e7i		−	1.02533i	0.858588	−	0.512666i	$-0.171342\pi$
$860$		0			0
$861$			2.91064e7i			1.33807i
$862$	−3.76535e7	+	1.22477e7i	−1.72599	+	0.561420i
$863$	1.76878e7			0.808439			0.404220	−	0.914662i	$-0.367543\pi$
$863$	1.76878e7			0.808439			0.404220	+	0.914662i	$0.367543\pi$
$864$	−2.23107e7	+	35839.5i	−1.01679	+	0.00163334i
$865$		0			0
$866$	−5.80235e6	+	1.88736e6i	−0.262911	+	0.0855185i
$867$			6.18737e7i			2.79549i
$868$	−3.70176e7	+	2.69312e7i	−1.66767	+	1.21327i
$869$			4.25845e7i			1.91294i
$870$		0			0
$871$	3.70397e6			0.165433
$872$	1.44292e7	+	1.04622e7i	0.642615	+	0.465942i
$873$	1.53982e7			0.683809
$874$	−3.18563e6	−	9.79366e6i	−0.141064	−	0.433677i
$875$		0			0
$876$	−1.80533e6	−	2.48146e6i	−0.0794869	−	0.109257i
$877$			8.63639e6i			0.379169i	0.981864	+	0.189585i	$0.0607142\pi$
$877$			8.63639e6i			0.379169i	−0.981864	+	0.189585i	$0.939286\pi$
$878$	3.32569e7	−	1.08177e7i	1.45595	−	0.473584i
$879$	−2.86777e7			−1.25191
$880$		0			0
$881$	−1.47043e7			−0.638269			−0.319135	−	0.947709i	$-0.603392\pi$
$881$	−1.47043e7			−0.638269			−0.319135	+	0.947709i	$0.603392\pi$
$882$	−3.72083e7	+	1.21029e7i	−1.61053	+	0.523864i
$883$		−	1.00513e7i		−	0.433832i	−0.976190	−	0.216916i	$-0.930400\pi$
$883$		−	1.00513e7i		−	0.433832i	0.976190	−	0.216916i	$-0.0695997\pi$
$884$	−2.43900e6	−	3.35247e6i	−0.104974	−	0.144289i
$885$		0			0
$886$	−3.44172e6	−	1.05809e7i	−0.147296	−	0.452835i
$887$	−7.52032e6			−0.320943			−0.160471	−	0.987041i	$-0.551301\pi$
$887$	−7.52032e6			−0.320943			−0.160471	+	0.987041i	$0.551301\pi$
$888$	−1.95654e7	+	2.69840e7i	−0.832636	+	1.14835i
$889$	−6.01422e7			−2.55226
$890$		0			0
$891$		−	706315.i		−	0.0298060i
$892$	3.15874e6	−	2.29806e6i	0.132924	−	0.0967052i
$893$		−	3.61496e6i		−	0.151696i
$894$	−4.23278e7	+	1.37682e7i	−1.77126	+	0.576145i
$895$		0			0
$896$	2.02406e7	+	2.77274e7i	0.842273	+	1.15382i
$897$	4.95374e6			0.205566
$898$	−1.96349e7	+	6.38673e6i	−0.812526	+	0.264294i
$899$		−	3.45649e7i		−	1.42638i
$900$		0			0
$901$		−	4.05729e7i		−	1.66504i
$902$	6.25727e6	+	1.92369e7i	0.256076	+	0.787260i
$903$	−6.73819e7			−2.74994
$904$	1.40621e7	−	1.93941e7i	0.572307	−	0.789311i
$905$		0			0
$906$	−8.44975e6	−	2.59773e7i	−0.341998	−	1.05141i
$907$			1.20026e7i			0.484457i	0.970219	+	0.242229i	$0.0778784\pi$
$907$			1.20026e7i			0.484457i	−0.970219	+	0.242229i	$0.922122\pi$
$908$	1.72589e6	+	2.37228e6i	0.0694702	+	0.0954885i
$909$		−	5.43855e7i		−	2.18310i
$910$		0			0
$911$	−1.14643e7			−0.457671			−0.228836	−	0.973465i	$-0.573492\pi$
$911$	−1.14643e7			−0.457671			−0.228836	+	0.973465i	$0.573492\pi$
$912$	−4.87118e6	+	1.50578e7i	−0.193931	+	0.599479i
$913$	6.75192e7			2.68071
$914$	−2.75480e6	+	896067.i	−0.109075	+	0.0354793i
$915$		0			0
$916$	−1.96553e7	−	2.70166e7i	−0.773999	−	1.06388i
$917$			3.29077e7i			1.29233i
$918$	1.32558e7	+	4.07525e7i	0.519156	+	1.59605i
$919$	1.71829e7			0.671133			0.335567	−	0.942016i	$-0.391072\pi$
$919$	1.71829e7			0.671133			0.335567	+	0.942016i	$0.391072\pi$
$920$		0			0
$921$	7.95011e7			3.08833
$922$	2.04771e6	+	6.29533e6i	0.0793308	+	0.243889i
$923$		−	3.67535e6i		−	0.142002i
$924$	−6.96158e7	+	5.06472e7i	−2.68243	+	1.95153i
$925$		0			0
$926$	1.61019e7	−	5.23755e6i	0.617093	−	0.200725i
$927$	1.28769e7			0.492166
$928$	−2.59206e7	+	41638.2i	−0.988039	+	0.00158717i
$929$	−1.26147e7			−0.479554			−0.239777	−	0.970828i	$-0.577074\pi$
$929$	−1.26147e7			−0.479554			−0.239777	+	0.970828i	$0.577074\pi$
$930$		0			0
$931$			1.06991e7i			0.404549i
$932$	1.82756e7	−	1.32960e7i	0.689181	−	0.501396i
$933$		−	2.11527e7i		−	0.795538i
$934$	−1.42535e6	−	4.38199e6i	−0.0534632	−	0.164363i
$935$		0			0
$936$	−3.81717e6	−	2.76772e6i	−0.142414	−	0.103260i
$937$	−1.36188e7			−0.506747			−0.253374	−	0.967368i	$-0.581540\pi$
$937$	−1.36188e7			−0.506747			−0.253374	+	0.967368i	$0.581540\pi$
$938$	1.82226e7	+	5.60222e7i	0.676244	+	2.07899i
$939$		−	1.33729e7i		−	0.494950i
$940$		0			0
$941$		−	4.59567e7i		−	1.69190i	−0.533261	−	0.845951i	$-0.679034\pi$
$941$		−	4.59567e7i		−	1.69190i	0.533261	−	0.845951i	$-0.320966\pi$
$942$	4.12620e6	−	1.34215e6i	0.151504	−	0.0492803i
$943$	1.85134e7			0.677963
$944$	−1.21073e7	−	3.91670e6i	−0.442198	−	0.143051i
$945$		0			0
$946$	−4.45338e7	+	1.44857e7i	−1.61794	+	0.526275i
$947$		−	5.53327e6i		−	0.200497i	−0.994962	−	0.100248i	$-0.968036\pi$
$947$		−	5.53327e6i		−	0.200497i	0.994962	−	0.100248i	$-0.0319637\pi$
$948$	−3.52334e7	−	4.84292e7i	−1.27331	−	1.75019i
$949$		−	249992.i		−	0.00901076i
$950$		0			0
$951$	−5.16670e7			−1.85252
$952$	3.87065e7	−	5.33830e7i	1.38418	−	1.90902i
$953$	2.16609e6			0.0772581			0.0386290	−	0.999254i	$-0.487701\pi$
$953$	2.16609e6			0.0772581			0.0386290	+	0.999254i	$0.487701\pi$
$954$	−1.42731e7	−	4.38801e7i	−0.507747	−	1.56098i
$955$		0			0
$956$	6.32904e6	−	4.60454e6i	0.223972	−	0.162945i
$957$		−	6.50032e7i		−	2.29432i
$958$	1.61593e7	−	5.25621e6i	0.568864	−	0.185037i
$959$	3.65958e6			0.128495
$960$		0			0
$961$	3.10374e7			1.08412
$962$	−2.58214e6	+	839906.i	−0.0899586	+	0.0292613i
$963$			6.11432e7i			2.12463i
$964$	1.55893e7	−	1.13416e7i	0.540297	−	0.393080i
$965$		0			0
$966$	2.43712e7	+	7.49248e7i	0.840298	+	2.58335i
$967$	−2.88706e7			−0.992865			−0.496433	−	0.868075i	$-0.665357\pi$
$967$	−2.88706e7			−0.992865			−0.496433	+	0.868075i	$0.665357\pi$
$968$	−1.80089e7	+	2.48375e7i	−0.617731	+	0.851960i
$969$	3.03985e7			1.04002
$970$		0			0
$971$		−	1.96724e7i		−	0.669592i	−0.942291	−	0.334796i	$-0.891333\pi$
$971$		−	1.96724e7i		−	0.669592i	0.942291	−	0.334796i	$-0.108667\pi$
$972$	−1.70353e7	−	2.34154e7i	−0.578341	−	0.794944i
$973$		−	1.02654e7i		−	0.347610i
$974$	3.80768e7	−	1.23854e7i	1.28607	−	0.418325i
$975$		0			0
$976$	1.93226e7	+	6.25087e6i	0.649295	+	0.210047i
$977$	−3.27929e7			−1.09912			−0.549558	−	0.835455i	$-0.685204\pi$
$977$	−3.27929e7			−1.09912			−0.549558	+	0.835455i	$0.685204\pi$
$978$	1.07531e7	−	3.49773e6i	0.359491	−	0.116933i
$979$			1.61641e7i			0.539008i
$980$		0			0
$981$		−	3.89341e7i		−	1.29169i
$982$	3.35584e6	+	1.03169e7i	0.111051	+	0.341407i
$983$	−1.63310e7			−0.539048			−0.269524	−	0.962994i	$-0.586866\pi$
$983$	−1.63310e7			−0.539048			−0.269524	+	0.962994i	$0.586866\pi$
$984$	−2.30322e7	−	1.67000e7i	−0.758313	−	0.549831i
$985$		0			0
$986$	1.54005e7	+	4.73461e7i	0.504478	+	1.55093i
$987$			2.76557e7i			0.903631i
$988$	−1.04256e6	+	758489.i	−0.0339789	+	0.0247205i
$989$			4.28588e7i			1.39332i
$990$		0			0
$991$	−8.71507e6			−0.281895			−0.140947	−	0.990017i	$-0.545015\pi$
$991$	−8.71507e6			−0.281895			−0.140947	+	0.990017i	$0.545015\pi$
$992$	−71876.6	−	4.47445e7i	−0.00231904	−	1.44365i
$993$	−1.35383e7			−0.435703
$994$	5.55894e7	−	1.80818e7i	1.78454	−	0.580465i
$995$		0			0
$996$	−7.67862e7	+	5.58639e7i	−2.45265	+	1.78436i
$997$		−	5.34960e7i		−	1.70445i	−0.523177	−	0.852224i	$-0.675254\pi$
$997$		−	5.34960e7i		−	1.70445i	0.523177	−	0.852224i	$-0.324746\pi$
$998$	−5.23884e6	−	1.61059e7i	−0.166498	−	0.511869i
$999$	2.80674e7			0.889792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.d.c.101.19	✓	20
4.3	odd	2		800.6.d.d.401.2		20
5.2	odd	4		200.6.f.d.149.24		40
5.3	odd	4		200.6.f.d.149.17		40
5.4	even	2		200.6.d.d.101.2	yes	20
8.3	odd	2		800.6.d.d.401.19		20
8.5	even	2	inner	200.6.d.c.101.20	yes	20
20.3	even	4		800.6.f.d.49.38		40
20.7	even	4		800.6.f.d.49.3		40
20.19	odd	2		800.6.d.b.401.19		20
40.3	even	4		800.6.f.d.49.4		40
40.13	odd	4		200.6.f.d.149.23		40
40.19	odd	2		800.6.d.b.401.2		20
40.27	even	4		800.6.f.d.49.37		40
40.29	even	2		200.6.d.d.101.1	yes	20
40.37	odd	4		200.6.f.d.149.18		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.19	✓	20	1.1	even	1	trivial
200.6.d.c.101.20	yes	20	8.5	even	2	inner
200.6.d.d.101.1	yes	20	40.29	even	2
200.6.d.d.101.2	yes	20	5.4	even	2
200.6.f.d.149.17		40	5.3	odd	4
200.6.f.d.149.18		40	40.37	odd	4
200.6.f.d.149.23		40	40.13	odd	4
200.6.f.d.149.24		40	5.2	odd	4
800.6.d.b.401.2		20	40.19	odd	2
800.6.d.b.401.19		20	20.19	odd	2
800.6.d.d.401.2		20	4.3	odd	2
800.6.d.d.401.19		20	8.3	odd	2
800.6.f.d.49.3		40	20.7	even	4
800.6.f.d.49.4		40	40.3	even	4
800.6.f.d.49.37		40	40.27	even	4
800.6.f.d.49.38		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)

\(f(q)\)	\(=\)	\(q+(5.37943 - 1.74979i) q^{2} +25.2673i q^{3} +(25.8765 - 18.8258i) q^{4} +(44.2124 + 135.923i) q^{6} -185.199 q^{7} +(106.259 - 146.550i) q^{8} -395.434 q^{9} +O(q^{10})\)	\(q+(5.37943 - 1.74979i) q^{2} +25.2673i q^{3} +(25.8765 - 18.8258i) q^{4} +(44.2124 + 135.923i) q^{6} -185.199 q^{7} +(106.259 - 146.550i) q^{8} -395.434 q^{9} -574.919i q^{11} +(475.675 + 653.827i) q^{12} +65.8691i q^{13} +(-996.264 + 324.060i) q^{14} +(315.182 - 974.288i) q^{16} -1966.88 q^{17} +(-2127.21 + 691.927i) q^{18} +611.668i q^{19} -4679.47i q^{21} +(-1005.99 - 3092.74i) q^{22} -2976.41 q^{23} +(3702.92 + 2684.88i) q^{24} +(115.257 + 354.338i) q^{26} -3851.59i q^{27} +(-4792.29 + 3486.51i) q^{28} -4474.76i q^{29} +7724.41 q^{31} +(-9.30513 - 5792.61i) q^{32} +14526.6 q^{33} +(-10580.7 + 3441.64i) q^{34} +(-10232.4 + 7444.34i) q^{36} +7287.23i q^{37} +(1070.29 + 3290.42i) q^{38} -1664.33 q^{39} -6220.02 q^{41} +(-8188.09 - 25172.8i) q^{42} -14399.5i q^{43} +(-10823.3 - 14876.9i) q^{44} +(-16011.4 + 5208.11i) q^{46} -5910.00 q^{47} +(24617.6 + 7963.77i) q^{48} +17491.6 q^{49} -49697.7i q^{51} +(1240.04 + 1704.46i) q^{52} +20628.0i q^{53} +(-6739.48 - 20719.3i) q^{54} +(-19679.1 + 27140.9i) q^{56} -15455.2 q^{57} +(-7829.90 - 24071.6i) q^{58} -12426.8i q^{59} +19832.6i q^{61} +(41552.9 - 13516.1i) q^{62} +73233.9 q^{63} +(-10185.9 - 31144.6i) q^{64} +(78144.9 - 25418.6i) q^{66} -56232.3i q^{67} +(-50896.0 + 37028.1i) q^{68} -75205.8i q^{69} -55797.8 q^{71} +(-42018.5 + 57950.9i) q^{72} -3795.29 q^{73} +(12751.1 + 39201.1i) q^{74} +(11515.1 + 15827.8i) q^{76} +106474. i q^{77} +(-8953.14 + 2912.23i) q^{78} -74070.3 q^{79} +1228.55 q^{81} +(-33460.1 + 10883.7i) q^{82} +117441. i q^{83} +(-88094.5 - 121088. i) q^{84} +(-25196.1 - 77461.0i) q^{86} +113065. q^{87} +(-84254.5 - 61090.5i) q^{88} -28115.4 q^{89} -12198.9i q^{91} +(-77019.0 + 56033.3i) q^{92} +195175. i q^{93} +(-31792.4 + 10341.3i) q^{94} +(146363. - 235.115i) q^{96} -38940.1 q^{97} +(94094.9 - 30606.7i) q^{98} +227343. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) \) 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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