LMFDB - Embedded newform 200.6.d.c.101.4

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			101.4
Root			$5.22286 - 2.17296i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.c.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.22286 + 2.17296i) q^{2} -8.95730i q^{3} +(22.5565 - 22.6981i) q^{4} +(19.4639 + 46.7827i) q^{6} +179.198 q^{7} +(-68.4872 + 167.563i) q^{8} +162.767 q^{9} +O(q^{10})$	\(q+(-5.22286 + 2.17296i) q^{2} -8.95730i q^{3} +(22.5565 - 22.6981i) q^{4} +(19.4639 + 46.7827i) q^{6} +179.198 q^{7} +(-68.4872 + 167.563i) q^{8} +162.767 q^{9} +654.036i q^{11} +(-203.314 - 202.045i) q^{12} -160.722i q^{13} +(-935.925 + 389.390i) q^{14} +(-6.40984 - 1023.98i) q^{16} +347.942 q^{17} +(-850.107 + 353.686i) q^{18} +2328.49i q^{19} -1605.13i q^{21} +(-1421.19 - 3415.94i) q^{22} -4128.97 q^{23} +(1500.92 + 613.460i) q^{24} +(349.243 + 839.428i) q^{26} -3634.58i q^{27} +(4042.08 - 4067.46i) q^{28} +5004.15i q^{29} +2194.90 q^{31} +(2258.55 + 5334.17i) q^{32} +5858.40 q^{33} +(-1817.25 + 756.064i) q^{34} +(3671.45 - 3694.50i) q^{36} +2400.35i q^{37} +(-5059.73 - 12161.4i) q^{38} -1439.64 q^{39} -13875.1 q^{41} +(3487.88 + 8383.37i) q^{42} -9400.56i q^{43} +(14845.4 + 14752.8i) q^{44} +(21565.0 - 8972.10i) q^{46} +5271.14 q^{47} +(-9172.10 + 57.4149i) q^{48} +15304.9 q^{49} -3116.62i q^{51} +(-3648.09 - 3625.32i) q^{52} +11915.0i q^{53} +(7897.79 + 18982.9i) q^{54} +(-12272.8 + 30027.0i) q^{56} +20857.0 q^{57} +(-10873.8 - 26136.0i) q^{58} +38457.4i q^{59} +37921.2i q^{61} +(-11463.6 + 4769.43i) q^{62} +29167.5 q^{63} +(-23387.0 - 22951.9i) q^{64} +(-30597.6 + 12730.1i) q^{66} +30414.5i q^{67} +(7848.35 - 7897.63i) q^{68} +36984.5i q^{69} -4849.25 q^{71} +(-11147.4 + 27273.8i) q^{72} -39210.6 q^{73} +(-5215.87 - 12536.7i) q^{74} +(52852.5 + 52522.6i) q^{76} +117202. i q^{77} +(7519.01 - 3128.27i) q^{78} +68793.5 q^{79} +6996.32 q^{81} +(72467.5 - 30150.0i) q^{82} +63154.8i q^{83} +(-36433.4 - 36206.1i) q^{84} +(20427.0 + 49097.8i) q^{86} +44823.7 q^{87} +(-109593. - 44793.1i) q^{88} +29719.5 q^{89} -28801.0i q^{91} +(-93135.2 + 93720.0i) q^{92} -19660.4i q^{93} +(-27530.4 + 11454.0i) q^{94} +(47779.8 - 20230.5i) q^{96} -47746.8 q^{97} +(-79935.3 + 33256.9i) q^{98} +106455. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.22286	+	2.17296i	−0.923280	+	0.384129i
$2$	−5.22286	+	2.17296i	−0.923280	+	0.384129i
$3$		−	8.95730i		−	0.574611i	−0.957839	−	0.287306i	$-0.907240\pi$
$3$		−	8.95730i		−	0.574611i	0.957839	−	0.287306i	$-0.0927595\pi$
$4$	22.5565	−	22.6981i	0.704890	−	0.709316i
$5$		0			0
$5$		0			0
$6$	19.4639	+	46.7827i	0.220725	+	0.530527i
$7$	179.198			1.38225			0.691127	−	0.722733i	$-0.257115\pi$
$7$	179.198			1.38225			0.691127	+	0.722733i	$0.257115\pi$
$8$	−68.4872	+	167.563i	−0.378342	+	0.925666i
$9$	162.767			0.669822
$10$		0			0
$11$			654.036i			1.62975i	0.579640	+	0.814873i	$0.303193\pi$
$11$			654.036i			1.62975i	−0.579640	+	0.814873i	$0.696807\pi$
$12$	−203.314	−	202.045i	−0.407581	−	0.405038i
$13$		−	160.722i		−	0.263765i	−0.991265	−	0.131882i	$-0.957898\pi$
$13$		−	160.722i		−	0.263765i	0.991265	−	0.131882i	$-0.0421021\pi$
$14$	−935.925	+	389.390i	−1.27621	+	0.530964i
$15$		0			0
$16$	−6.40984	−	1023.98i	−0.00625961	−	0.999980i
$17$	347.942			0.292001			0.146001	−	0.989285i	$-0.453360\pi$
$17$	347.942			0.292001			0.146001	+	0.989285i	$0.453360\pi$
$18$	−850.107	+	353.686i	−0.618433	+	0.257298i
$19$			2328.49i			1.47976i	0.672739	+	0.739880i	$0.265118\pi$
$19$			2328.49i			1.47976i	−0.672739	+	0.739880i	$0.734882\pi$
$20$		0			0
$21$		−	1605.13i		−	0.794259i
$22$	−1421.19	−	3415.94i	−0.626032	−	1.50471i
$23$	−4128.97			−1.62751			−0.813753	−	0.581211i	$-0.802579\pi$
$23$	−4128.97			−1.62751			−0.813753	+	0.581211i	$0.802579\pi$
$24$	1500.92	+	613.460i	0.531898	+	0.217399i
$25$		0			0
$26$	349.243	+	839.428i	0.101320	+	0.243529i
$27$		−	3634.58i		−	0.959498i
$28$	4042.08	−	4067.46i	0.974337	−	0.980456i
$29$			5004.15i			1.10493i	0.833535	+	0.552466i	$0.186313\pi$
$29$			5004.15i			1.10493i	−0.833535	+	0.552466i	$0.813687\pi$
$30$		0			0
$31$	2194.90			0.410214			0.205107	−	0.978740i	$-0.434246\pi$
$31$	2194.90			0.410214			0.205107	+	0.978740i	$0.434246\pi$
$32$	2258.55	+	5334.17i	0.389901	+	0.920857i
$33$	5858.40			0.936470
$34$	−1817.25	+	756.064i	−0.269599	+	0.112166i
$35$		0			0
$36$	3671.45	−	3694.50i	0.472151	−	0.475116i
$37$			2400.35i			0.288251i	0.989559	+	0.144125i	$0.0460369\pi$
$37$			2400.35i			0.288251i	−0.989559	+	0.144125i	$0.953963\pi$
$38$	−5059.73	−	12161.4i	−0.568418	−	1.36623i
$39$	−1439.64			−0.151562
$40$		0			0
$41$	−13875.1			−1.28907			−0.644533	−	0.764576i	$-0.722948\pi$
$41$	−13875.1			−1.28907			−0.644533	+	0.764576i	$0.722948\pi$
$42$	3487.88	+	8383.37i	0.305098	+	0.733323i
$43$		−	9400.56i		−	0.775323i	−0.921802	−	0.387661i	$-0.873283\pi$
$43$		−	9400.56i		−	0.775323i	0.921802	−	0.387661i	$-0.126717\pi$
$44$	14845.4	+	14752.8i	1.15601	+	1.14879i
$45$		0			0
$46$	21565.0	−	8972.10i	1.50264	−	0.625172i
$47$	5271.14			0.348065			0.174032	−	0.984740i	$-0.444320\pi$
$47$	5271.14			0.348065			0.174032	+	0.984740i	$0.444320\pi$
$48$	−9172.10	+	57.4149i	−0.574600	+	0.00359684i
$49$	15304.9			0.910626
$50$		0			0
$51$		−	3116.62i		−	0.167787i
$52$	−3648.09	−	3625.32i	−0.187093	−	0.185925i
$53$			11915.0i			0.582644i	0.956625	+	0.291322i	$0.0940951\pi$
$53$			11915.0i			0.582644i	−0.956625	+	0.291322i	$0.905905\pi$
$54$	7897.79	+	18982.9i	0.368571	+	0.885885i
$55$		0			0
$56$	−12272.8	+	30027.0i	−0.522965	+	1.27951i
$57$	20857.0			0.850286
$58$	−10873.8	−	26136.0i	−0.424436	−	1.02016i
$59$			38457.4i			1.43830i	0.694853	+	0.719151i	$0.255469\pi$
$59$			38457.4i			1.43830i	−0.694853	+	0.719151i	$0.744531\pi$
$60$		0			0
$61$			37921.2i			1.30484i	0.757857	+	0.652421i	$0.226246\pi$
$61$			37921.2i			1.30484i	−0.757857	+	0.652421i	$0.773754\pi$
$62$	−11463.6	+	4769.43i	−0.378742	+	0.157575i
$63$	29167.5			0.925864
$64$	−23387.0	−	22951.9i	−0.713715	−	0.700436i
$65$		0			0
$66$	−30597.6	+	12730.1i	−0.864624	+	0.359725i
$67$			30414.5i			0.827739i	0.910336	+	0.413870i	$0.135823\pi$
$67$			30414.5i			0.827739i	−0.910336	+	0.413870i	$0.864177\pi$
$68$	7848.35	−	7897.63i	0.205829	−	0.207121i
$69$			36984.5i			0.935183i
$70$		0			0
$71$	−4849.25			−0.114164			−0.0570820	−	0.998369i	$-0.518180\pi$
$71$	−4849.25			−0.114164			−0.0570820	+	0.998369i	$0.518180\pi$
$72$	−11147.4	+	27273.8i	−0.253422	+	0.620031i
$73$	−39210.6			−0.861185			−0.430593	−	0.902546i	$-0.641695\pi$
$73$	−39210.6			−0.861185			−0.430593	+	0.902546i	$0.641695\pi$
$74$	−5215.87	−	12536.7i	−0.110725	−	0.266136i
$75$		0			0
$76$	52852.5	+	52522.6i	1.04962	+	1.04307i
$77$			117202.i			2.25272i
$78$	7519.01	−	3128.27i	0.139934	−	0.0582194i
$79$	68793.5			1.24016			0.620082	−	0.784537i	$-0.287099\pi$
$79$	68793.5			1.24016			0.620082	+	0.784537i	$0.287099\pi$
$80$		0			0
$81$	6996.32			0.118483
$82$	72467.5	−	30150.0i	1.19017	−	0.495167i
$83$			63154.8i			1.00626i	0.864210	+	0.503131i	$0.167819\pi$
$83$			63154.8i			1.00626i	−0.864210	+	0.503131i	$0.832181\pi$
$84$	−36433.4	−	36206.1i	−0.563381	−	0.559865i
$85$		0			0
$86$	20427.0	+	49097.8i	0.297824	+	0.715839i
$87$	44823.7			0.634907
$88$	−109593.	−	44793.1i	−1.50860	−	0.616601i
$89$	29719.5			0.397709			0.198855	−	0.980029i	$-0.436278\pi$
$89$	29719.5			0.397709			0.198855	+	0.980029i	$0.436278\pi$
$90$		0			0
$91$		−	28801.0i		−	0.364590i
$92$	−93135.2	+	93720.0i	−1.14721	+	1.15442i
$93$		−	19660.4i		−	0.235714i
$94$	−27530.4	+	11454.0i	−0.321361	+	0.133702i
$95$		0			0
$96$	47779.8	−	20230.5i	0.529135	−	0.224041i
$97$	−47746.8			−0.515247			−0.257623	−	0.966245i	$-0.582939\pi$
$97$	−47746.8			−0.515247			−0.257623	+	0.966245i	$0.582939\pi$
$98$	−79935.3	+	33256.9i	−0.840763	+	0.349798i
$99$			106455.i			1.09164i
$100$		0			0
$101$		−	178313.i		−	1.73932i	−0.493649	−	0.869661i	$-0.664337\pi$
$101$		−	178313.i		−	1.73932i	0.493649	−	0.869661i	$-0.335663\pi$
$102$	6772.29	+	16277.7i	0.0644518	+	0.154914i
$103$	202181.			1.87779			0.938896	−	0.344201i	$-0.111850\pi$
$103$	202181.			1.87779			0.938896	+	0.344201i	$0.111850\pi$
$104$	26931.1	+	11007.4i	0.244158	+	0.0997933i
$105$		0			0
$106$	−25890.8	−	62230.2i	−0.223810	−	0.537943i
$107$		−	73035.1i		−	0.616698i	−0.951273	−	0.308349i	$-0.900224\pi$
$107$		−	73035.1i		−	0.616698i	0.951273	−	0.308349i	$-0.0997764\pi$
$108$	−82498.0	−	81983.3i	−0.680588	−	0.676341i
$109$		−	128179.i		−	1.03336i	−0.856179	−	0.516680i	$-0.827168\pi$
$109$		−	128179.i		−	1.03336i	0.856179	−	0.516680i	$-0.172832\pi$
$110$		0			0
$111$	21500.7			0.165632
$112$	−1148.63	−	183495.i	−0.00865238	−	1.38223i
$113$	169893.			1.25164			0.625818	−	0.779969i	$-0.284765\pi$
$113$	169893.			1.25164			0.625818	+	0.779969i	$0.284765\pi$
$114$	−108933.	+	45321.5i	−0.785052	+	0.326619i
$115$		0			0
$116$	113585.	+	112876.i	0.783747	+	0.778856i
$117$		−	26160.2i		−	0.176675i
$118$	−83566.5	−	200858.i	−0.552493	−	1.32796i
$119$	62350.5			0.403620
$120$		0			0
$121$	−266712.			−1.65607
$122$	−82401.3	−	198057.i	−0.501227	−	1.20473i
$123$			124283.i			0.740712i
$124$	49509.2	−	49820.1i	0.289156	−	0.290971i
$125$		0			0
$126$	−152337.	+	63379.7i	−0.854831	+	0.355651i
$127$	−113667.			−0.625351			−0.312676	−	0.949860i	$-0.601225\pi$
$127$	−113667.			−0.625351			−0.312676	+	0.949860i	$0.601225\pi$
$128$	172021.	+	69055.5i	0.928016	+	0.372540i
$129$	−84203.6			−0.445509
$130$		0			0
$131$		−	214049.i		−	1.08977i	−0.838510	−	0.544886i	$-0.816573\pi$
$131$		−	214049.i		−	1.08977i	0.838510	−	0.544886i	$-0.183427\pi$
$132$	132145.	−	132975.i	0.660109	−	0.664254i
$133$			417261.i			2.04540i
$134$	−66089.5	−	158851.i	−0.317958	−	0.764235i
$135$		0			0
$136$	−23829.6	+	58302.3i	−0.110476	+	0.270295i
$137$	326516.			1.48629			0.743144	−	0.669131i	$-0.233334\pi$
$137$	326516.			1.48629			0.743144	+	0.669131i	$0.233334\pi$
$138$	−80365.8	−	193165.i	−0.359231	−	0.863436i
$139$		−	73759.3i		−	0.323802i	−0.986807	−	0.161901i	$-0.948237\pi$
$139$		−	73759.3i		−	0.323802i	0.986807	−	0.161901i	$-0.0517625\pi$
$140$		0			0
$141$		−	47215.2i		−	0.200002i
$142$	25327.0	−	10537.2i	0.105405	−	0.0438536i
$143$	105118.			0.429870
$144$	−1043.31	−	166670.i	−0.00419283	−	0.669809i
$145$		0			0
$146$	204791.	−	85203.1i	0.795115	−	0.330806i
$147$		−	137091.i		−	0.523256i
$148$	54483.5	+	54143.5i	0.204461	+	0.203185i
$149$			370429.i			1.36691i	0.729994	+	0.683453i	$0.239523\pi$
$149$			370429.i			1.36691i	−0.729994	+	0.683453i	$0.760477\pi$
$150$		0			0
$151$	311607.			1.11216			0.556078	−	0.831130i	$-0.312306\pi$
$151$	311607.			1.11216			0.556078	+	0.831130i	$0.312306\pi$
$152$	−390170.	−	159472.i	−1.36976	−	0.559855i
$153$	56633.4			0.195589
$154$	−254675.	−	612129.i	−0.865336	−	2.07989i
$155$		0			0
$156$	−32473.1	+	32677.0i	−0.106835	+	0.107506i
$157$		−	226057.i		−	0.731930i	−0.930629	−	0.365965i	$-0.880739\pi$
$157$		−	226057.i		−	0.731930i	0.930629	−	0.365965i	$-0.119261\pi$
$158$	−359298.	+	149485.i	−1.14502	+	0.476383i
$159$	106726.			0.334794
$160$		0			0
$161$	−739904.			−2.24963
$162$	−36540.8	+	15202.7i	−0.109393	+	0.0455129i
$163$			281116.i			0.828737i	0.910109	+	0.414368i	$0.135997\pi$
$163$			281116.i			0.828737i	−0.910109	+	0.414368i	$0.864003\pi$
$164$	−312973.	+	314938.i	−0.908650	+	0.914356i
$165$		0			0
$166$	−137233.	−	329848.i	−0.386534	−	0.929061i
$167$	−249160.			−0.691332			−0.345666	−	0.938358i	$-0.612347\pi$
$167$	−249160.			−0.691332			−0.345666	+	0.938358i	$0.612347\pi$
$168$	268961.	+	109931.i	0.735218	+	0.300501i
$169$	345461.			0.930428
$170$		0			0
$171$			379001.i			0.991175i
$172$	−213375.	−	212044.i	−0.549949	−	0.546517i
$173$		−	259080.i		−	0.658142i	−0.944305	−	0.329071i	$-0.893265\pi$
$173$		−	259080.i		−	0.658142i	0.944305	−	0.329071i	$-0.106735\pi$
$174$	−234108.	+	97400.2i	−0.586196	+	0.243886i
$175$		0			0
$176$	669720.	−	4192.27i	1.62971	−	0.0102016i
$177$	344475.			0.826465
$178$	−155221.	+	64579.2i	−0.367197	+	0.152772i
$179$		−	213319.i		−	0.497620i	−0.968552	−	0.248810i	$-0.919961\pi$
$179$		−	213319.i		−	0.497620i	0.968552	−	0.248810i	$-0.0800394\pi$
$180$		0			0
$181$		−	631854.i		−	1.43358i	−0.697292	−	0.716788i	$-0.745612\pi$
$181$		−	631854.i		−	1.43358i	0.697292	−	0.716788i	$-0.254388\pi$
$182$	62583.5	+	150424.i	0.140050	+	0.336619i
$183$	339672.			0.749776
$184$	282782.	−	691865.i	0.615754	−	1.50653i
$185$		0			0
$186$	42721.2	+	102683.i	0.0905443	+	0.217629i
$187$			227566.i			0.475887i
$188$	118898.	−	119645.i	0.245347	−	0.246888i
$189$		−	651308.i		−	1.32627i
$190$		0			0
$191$	14747.1			0.0292498			0.0146249	−	0.999893i	$-0.495345\pi$
$191$	14747.1			0.0292498			0.0146249	+	0.999893i	$0.495345\pi$
$192$	−205587.	+	209485.i	−0.402479	+	0.410109i
$193$	−383951.			−0.741963			−0.370982	−	0.928640i	$-0.620979\pi$
$193$	−383951.			−0.741963			−0.370982	+	0.928640i	$0.620979\pi$
$194$	249375.	−	103752.i	0.475717	−	0.197921i
$195$		0			0
$196$	345225.	−	347392.i	0.641891	−	0.645922i
$197$			676505.i			1.24195i	0.783829	+	0.620977i	$0.213264\pi$
$197$			676505.i			1.24195i	−0.783829	+	0.620977i	$0.786736\pi$
$198$	−231323.	−	556001.i	−0.419330	−	1.00789i
$199$	−72641.1			−0.130032			−0.0650160	−	0.997884i	$-0.520710\pi$
$199$	−72641.1			−0.130032			−0.0650160	+	0.997884i	$0.520710\pi$
$200$		0			0
$201$	272432.			0.475628
$202$	387468.	+	931305.i	0.668124	+	1.60588i
$203$			896734.i			1.52730i
$204$	−70741.4	−	70300.0i	−0.119014	−	0.118271i
$205$		0			0
$206$	−1.05596e6	+	439331.i	−1.73373	+	0.721314i
$207$	−672060.			−1.09014
$208$	−164576.	+	1030.20i	−0.263760	+	0.00165107i
$209$	−1.52292e6			−2.41163
$210$		0			0
$211$			945366.i			1.46182i	0.682474	+	0.730910i	$0.260904\pi$
$211$			945366.i			1.46182i	−0.682474	+	0.730910i	$0.739096\pi$
$212$	270447.	+	268760.i	0.413279	+	0.410700i
$213$			43436.2i			0.0655999i
$214$	158702.	+	381452.i	0.236891	+	0.569384i
$215$		0			0
$216$	609022.	+	248922.i	0.888175	+	0.363018i
$217$	393321.			0.567020
$218$	278528.	+	669462.i	0.396943	+	0.954079i
$219$			351221.i			0.494847i
$220$		0			0
$221$		−	55921.9i		−	0.0770196i
$222$	−112295.	+	46720.1i	−0.152925	+	0.0636241i
$223$	788483.			1.06177			0.530885	−	0.847444i	$-0.321860\pi$
$223$	788483.			1.06177			0.530885	+	0.847444i	$0.321860\pi$
$224$	404727.	+	955873.i	0.538942	+	1.27286i
$225$		0			0
$226$	−887324.	+	369170.i	−1.15561	+	0.480789i
$227$			109073.i			0.140492i	0.997530	+	0.0702461i	$0.0223785\pi$
$227$			109073.i			0.140492i	−0.997530	+	0.0702461i	$0.977622\pi$
$228$	470461.	−	473415.i	0.599359	−	0.603122i
$229$			125034.i			0.157557i	0.996892	+	0.0787787i	$0.0251021\pi$
$229$			125034.i			0.157557i	−0.996892	+	0.0787787i	$0.974898\pi$
$230$		0			0
$231$	1.04981e6			1.29444
$232$	−838513.	−	342720.i	−1.02280	−	0.418042i
$233$	−1.63628e6			−1.97455			−0.987276	−	0.159019i	$-0.949167\pi$
$233$	−1.63628e6			−1.97455			−0.987276	+	0.159019i	$0.949167\pi$
$234$	56845.1	+	136631.i	0.0678661	+	0.163121i
$235$		0			0
$236$	872912.	+	867465.i	1.02021	+	1.01385i
$237$		−	616204.i		−	0.712613i
$238$	−325648.	+	135485.i	−0.372654	+	0.155042i
$239$	1.57183e6			1.77997			0.889984	−	0.455992i	$-0.150715\pi$
$239$	1.57183e6			1.77997			0.889984	+	0.455992i	$0.150715\pi$
$240$		0			0
$241$	−1.28582e6			−1.42606			−0.713032	−	0.701132i	$-0.752679\pi$
$241$	−1.28582e6			−1.42606			−0.713032	+	0.701132i	$0.752679\pi$
$242$	1.39300e6	−	579555.i	1.52902	−	0.636145i
$243$		−	945870.i		−	1.02758i
$244$	860741.	+	855369.i	0.925545	+	0.919770i
$245$		0			0
$246$	−270062.	−	649113.i	−0.284529	−	0.683884i
$247$	374240.			0.390309
$248$	−150322.	+	367785.i	−0.155201	+	0.379721i
$249$	565697.			0.578209
$250$		0			0
$251$		−	33849.3i		−	0.0339130i	−0.999856	−	0.0169565i	$-0.994602\pi$
$251$		−	33849.3i		−	0.0339130i	0.999856	−	0.0169565i	$-0.00539767\pi$
$252$	657915.	−	662047.i	0.652633	−	0.656731i
$253$		−	2.70050e6i		−	2.65242i
$254$	593665.	−	246993.i	0.577374	−	0.240215i
$255$		0			0
$256$	−1.04849e6	+	13127.1i	−0.999922	+	0.0125190i
$257$	−135717.			−0.128175			−0.0640873	−	0.997944i	$-0.520414\pi$
$257$	−135717.			−0.128175			−0.0640873	+	0.997944i	$0.520414\pi$
$258$	439784.	−	182971.i	0.411329	−	0.171133i
$259$			430138.i			0.398436i
$260$		0			0
$261$			814510.i			0.740108i
$262$	465121.	+	1.11795e6i	0.418613	+	1.00616i
$263$	30802.7			0.0274599			0.0137300	−	0.999906i	$-0.495629\pi$
$263$	30802.7			0.0274599			0.0137300	+	0.999906i	$0.495629\pi$
$264$	−401225.	+	981653.i	−0.354306	+	0.866859i
$265$		0			0
$266$	−906692.	−	2.17930e6i	−0.785698	−	1.88848i
$267$		−	266206.i		−	0.228528i
$268$	690352.	+	686044.i	0.587129	+	0.583465i
$269$			1.25112e6i			1.05419i	0.849807	+	0.527095i	$0.176719\pi$
$269$			1.25112e6i			1.05419i	−0.849807	+	0.527095i	$0.823281\pi$
$270$		0			0
$271$	2.37264e6			1.96250			0.981250	−	0.192742i	$-0.0617380\pi$
$271$	2.37264e6			1.96250			0.981250	+	0.192742i	$0.0617380\pi$
$272$	−2230.25	−	356286.i	−0.00182781	−	0.291995i
$273$	−257980.			−0.209498
$274$	−1.70535e6	+	709507.i	−1.37226	+	0.570926i
$275$		0			0
$276$	839478.	+	834240.i	0.663341	+	0.659201i
$277$			363646.i			0.284760i	0.989812	+	0.142380i	$0.0454755\pi$
$277$			363646.i			0.284760i	−0.989812	+	0.142380i	$0.954525\pi$
$278$	160276.	+	385234.i	0.124382	+	0.298960i
$279$	357257.			0.274770
$280$		0			0
$281$	−113633.			−0.0858497			−0.0429248	−	0.999078i	$-0.513668\pi$
$281$	−113633.			−0.0858497			−0.0429248	+	0.999078i	$0.513668\pi$
$282$	102597.	+	246598.i	0.0768265	+	0.184658i
$283$		−	2.62353e6i		−	1.94724i	−0.228170	−	0.973621i	$-0.573274\pi$
$283$		−	2.62353e6i		−	1.94724i	0.228170	−	0.973621i	$-0.426726\pi$
$284$	−109382.	+	110069.i	−0.0804730	+	0.0809783i
$285$		0			0
$286$	−549016.	+	228417.i	−0.396890	+	0.165125i
$287$	−2.48638e6			−1.78182
$288$	367616.	+	868226.i	0.261164	+	0.616810i
$289$	−1.29879e6			−0.914735
$290$		0			0
$291$			427683.i			0.296067i
$292$	−884454.	+	890008.i	−0.607041	+	0.610853i
$293$			92025.7i			0.0626239i	0.999510	+	0.0313120i	$0.00996853\pi$
$293$			92025.7i			0.0626239i	−0.999510	+	0.0313120i	$0.990031\pi$
$294$	297892.	+	716005.i	0.200998	+	0.483112i
$295$		0			0
$296$	−402211.	−	164393.i	−0.266824	−	0.109057i
$297$	2.37714e6			1.56374
$298$	−804927.	−	1.93470e6i	−0.525068	−	1.26204i
$299$			663617.i			0.429279i
$300$		0			0
$301$		−	1.68456e6i		−	1.07169i
$302$	−1.62748e6	+	677110.i	−1.02683	+	0.427211i
$303$	−1.59721e6			−0.999434
$304$	2.38433e6	−	14925.3i	1.47973	−	0.00926272i
$305$		0			0
$306$	−295788.	+	123062.i	−0.180583	+	0.0751312i
$307$		−	622926.i		−	0.377216i	−0.982052	−	0.188608i	$-0.939602\pi$
$307$		−	622926.i		−	0.377216i	0.982052	−	0.188608i	$-0.0603976\pi$
$308$	2.66026e6	+	2.64366e6i	1.59789	+	1.58792i
$309$		−	1.81100e6i		−	1.07900i
$310$		0			0
$311$	2.71178e6			1.58984			0.794919	−	0.606716i	$-0.207513\pi$
$311$	2.71178e6			1.58984			0.794919	+	0.606716i	$0.207513\pi$
$312$	98596.6	−	241230.i	0.0573423	−	0.140296i
$313$	−2.66765e6			−1.53910			−0.769552	−	0.638584i	$-0.779521\pi$
$313$	−2.66765e6			−1.53910			−0.769552	+	0.638584i	$0.779521\pi$
$314$	491214.	+	1.18067e6i	0.281155	+	0.675776i
$315$		0			0
$316$	1.55174e6	−	1.56148e6i	0.874180	−	0.879669i
$317$			1.44609e6i			0.808253i	0.914703	+	0.404126i	$0.132424\pi$
$317$			1.44609e6i			0.808253i	−0.914703	+	0.404126i	$0.867576\pi$
$318$	−557415.	+	231911.i	−0.309108	+	0.128604i
$319$	−3.27290e6			−1.80076
$320$		0			0
$321$	−654198.			−0.354361
$322$	3.86441e6	−	1.60778e6i	2.07703	−	0.864146i
$323$			810181.i			0.432091i
$324$	157812.	−	158803.i	0.0835178	−	0.0840422i
$325$		0			0
$326$	−610854.	−	1.46823e6i	−0.318342	−	0.765156i
$327$	−1.14814e6			−0.593780
$328$	950264.	−	2.32495e6i	0.487708	−	1.19324i
$329$	944578.			0.481114
$330$		0			0
$331$			1.67533e6i			0.840485i	0.907412	+	0.420243i	$0.138055\pi$
$331$			1.67533e6i			0.840485i	−0.907412	+	0.420243i	$0.861945\pi$
$332$	1.43350e6	+	1.42455e6i	0.713758	+	0.709304i
$333$			390697.i			0.193077i
$334$	1.30133e6	−	541414.i	0.638293	−	0.265561i
$335$		0			0
$336$	−1.64362e6	+	10288.6i	−0.794243	+	0.00497175i
$337$	−2.19636e6			−1.05348			−0.526742	−	0.850025i	$-0.676587\pi$
$337$	−2.19636e6			−1.05348			−0.526742	+	0.850025i	$0.676587\pi$
$338$	−1.80430e6	+	750674.i	−0.859045	+	0.357404i
$339$		−	1.52178e6i		−	0.719204i
$340$		0			0
$341$			1.43554e6i			0.668544i
$342$	−823555.	−	1.97947e6i	−0.380739	−	0.915132i
$343$	−269174.			−0.123537
$344$	1.57519e6	+	643818.i	0.717690	+	0.293337i
$345$		0			0
$346$	562971.	+	1.35314e6i	0.252811	+	0.607649i
$347$		−	3.79947e6i		−	1.69395i	−0.531635	−	0.846973i	$-0.678422\pi$
$347$		−	3.79947e6i		−	1.69395i	0.531635	−	0.846973i	$-0.321578\pi$
$348$	1.01107e6	−	1.01741e6i	0.447539	−	0.450350i
$349$		−	2.24537e6i		−	0.986787i	−0.869806	−	0.493394i	$-0.835756\pi$
$349$		−	2.24537e6i		−	0.986787i	0.869806	−	0.493394i	$-0.164244\pi$
$350$		0			0
$351$	−584156.			−0.253082
$352$	−3.48874e6	+	1.47717e6i	−1.50076	+	0.635439i
$353$	1.42770e6			0.609820			0.304910	−	0.952381i	$-0.401374\pi$
$353$	1.42770e6			0.609820			0.304910	+	0.952381i	$0.401374\pi$
$354$	−1.79914e6	+	748530.i	−0.763058	+	0.317469i
$355$		0			0
$356$	670367.	−	674576.i	0.280342	−	0.282102i
$357$		−	558492.i		−	0.231924i
$358$	463534.	+	1.11414e6i	0.191150	+	0.459442i
$359$	−987956.			−0.404577			−0.202289	−	0.979326i	$-0.564838\pi$
$359$	−987956.			−0.404577			−0.202289	+	0.979326i	$0.564838\pi$
$360$		0			0
$361$	−2.94579e6			−1.18969
$362$	1.37299e6	+	3.30008e6i	0.550677	+	1.32359i
$363$			2.38902e6i			0.951597i
$364$	−653730.	−	649650.i	−0.258610	−	0.256996i
$365$		0			0
$366$	−1.77406e6	+	738093.i	−0.692253	+	0.288011i
$367$	2.25218e6			0.872848			0.436424	−	0.899741i	$-0.356245\pi$
$367$	2.25218e6			0.872848			0.436424	+	0.899741i	$0.356245\pi$
$368$	26466.1	+	4.22799e6i	0.0101876	+	1.62747i
$369$	−2.25840e6			−0.863445
$370$		0			0
$371$			2.13514e6i			0.805362i
$372$	−446254.	−	443469.i	−0.167195	−	0.166152i
$373$		−	2.21460e6i		−	0.824184i	−0.911142	−	0.412092i	$-0.864798\pi$
$373$		−	2.21460e6i		−	0.824184i	0.911142	−	0.412092i	$-0.135202\pi$
$374$	−494493.	−	1.18855e6i	−0.182802	−	0.439377i
$375$		0			0
$376$	−361006.	+	883251.i	−0.131687	+	0.322192i
$377$	804278.			0.291442
$378$	1.41527e6	+	3.40169e6i	0.509459	+	1.22452i
$379$		−	2.89564e6i		−	1.03549i	−0.855535	−	0.517745i	$-0.826772\pi$
$379$		−	2.89564e6i		−	1.03549i	0.855535	−	0.517745i	$-0.173228\pi$
$380$		0			0
$381$			1.01815e6i			0.359334i
$382$	−77021.9	+	32044.8i	−0.0270057	+	0.0112357i
$383$	1.97304e6			0.687287			0.343643	−	0.939100i	$-0.388339\pi$
$383$	1.97304e6			0.687287			0.343643	+	0.939100i	$0.388339\pi$
$384$	618551.	−	1.54084e6i	0.214066	−	0.533248i
$385$		0			0
$386$	2.00532e6	−	834310.i	0.685040	−	0.285009i
$387$		−	1.53010e6i		−	0.519328i
$388$	−1.07700e6	+	1.08376e6i	−0.363192	+	0.365473i
$389$		−	1.95353e6i		−	0.654555i	−0.944928	−	0.327278i	$-0.893869\pi$
$389$		−	1.95353e6i		−	0.654555i	0.944928	−	0.327278i	$-0.106131\pi$
$390$		0			0
$391$	−1.43664e6			−0.475233
$392$	−1.04819e6	+	2.56454e6i	−0.344528	+	0.842936i
$393$	−1.91731e6			−0.626196
$394$	−1.47002e6	−	3.53329e6i	−0.477070	−	1.14667i
$395$		0			0
$396$	2.41634e6	+	2.40126e6i	0.774318	+	0.769486i
$397$			3.46065e6i			1.10200i	0.834506	+	0.551000i	$0.185753\pi$
$397$			3.46065e6i			1.10200i	−0.834506	+	0.551000i	$0.814247\pi$
$398$	379394.	−	157846.i	0.120056	−	0.0499490i
$399$	3.73754e6			1.17531
$400$		0			0
$401$	1.52492e6			0.473572			0.236786	−	0.971562i	$-0.423906\pi$
$401$	1.52492e6			0.473572			0.236786	+	0.971562i	$0.423906\pi$
$402$	−1.42287e6	+	591984.i	−0.439138	+	0.182703i
$403$		−	352769.i		−	0.108200i
$404$	−4.04738e6	−	4.02212e6i	−1.23373	−	1.22603i
$405$		0			0
$406$	−1.94857e6	−	4.68351e6i	−0.586679	−	1.41012i
$407$	−1.56992e6			−0.469776
$408$	522232.	+	213449.i	0.155315	+	0.0634809i
$409$	−644424.			−0.190486			−0.0952432	−	0.995454i	$-0.530363\pi$
$409$	−644424.			−0.190486			−0.0952432	+	0.995454i	$0.530363\pi$
$410$		0			0
$411$		−	2.92470e6i		−	0.854038i
$412$	4.56049e6	−	4.58913e6i	1.32364	−	1.33195i
$413$			6.89149e6i			1.98810i
$414$	3.51007e6	−	1.46036e6i	1.00650	−	0.418754i
$415$		0			0
$416$	857319.	−	362998.i	0.242890	−	0.102842i
$417$	−660684.			−0.186060
$418$	7.95399e6	−	3.30924e6i	2.22661	−	0.926377i
$419$			4.19407e6i			1.16708i	0.812085	+	0.583540i	$0.198333\pi$
$419$			4.19407e6i			1.16708i	−0.812085	+	0.583540i	$0.801667\pi$
$420$		0			0
$421$			1.62181e6i			0.445960i	0.974823	+	0.222980i	$0.0715784\pi$
$421$			1.62181e6i			0.445960i	−0.974823	+	0.222980i	$0.928422\pi$
$422$	−2.05424e6	−	4.93751e6i	−0.561527	−	1.34967i
$423$	857967.			0.233141
$424$	−1.99651e6	−	816023.i	−0.539334	−	0.220439i
$425$		0			0
$426$	−94385.2	−	226861.i	−0.0251988	−	0.0605670i
$427$			6.79540e6i			1.80362i
$428$	−1.65776e6	−	1.64742e6i	−0.437434	−	0.434704i
$429$		−	941573.i		−	0.247008i
$430$		0			0
$431$	−1.11890e6			−0.290135			−0.145067	−	0.989422i	$-0.546340\pi$
$431$	−1.11890e6			−0.290135			−0.145067	+	0.989422i	$0.546340\pi$
$432$	−3.72173e6	+	23297.1i	−0.959480	+	0.00600609i
$433$	−936279.			−0.239986			−0.119993	−	0.992775i	$-0.538287\pi$
$433$	−936279.			−0.239986			−0.119993	+	0.992775i	$0.538287\pi$
$434$	−2.05426e6	+	854672.i	−0.523518	+	0.217809i
$435$		0			0
$436$	−2.90943e6	−	2.89127e6i	−0.732979	−	0.728405i
$437$		−	9.61429e6i		−	2.40832i
$438$	−763190.	−	1.83438e6i	−0.190085	−	0.456882i
$439$	957065.			0.237017			0.118509	−	0.992953i	$-0.462189\pi$
$439$	957065.			0.237017			0.118509	+	0.992953i	$0.462189\pi$
$440$		0			0
$441$	2.49113e6			0.609957
$442$	121516.	+	292072.i	0.0295854	+	0.0711106i
$443$		−	2.09764e6i		−	0.507833i	−0.967226	−	0.253917i	$-0.918281\pi$
$443$		−	2.09764e6i		−	0.507833i	0.967226	−	0.253917i	$-0.0817189\pi$
$444$	484980.	−	488025.i	0.116752	−	0.117486i
$445$		0			0
$446$	−4.11813e6	+	1.71334e6i	−0.980310	+	0.407856i
$447$	3.31804e6			0.785440
$448$	−4.19090e6	−	4.11293e6i	−0.986535	−	0.968181i
$449$	−297855.			−0.0697251			−0.0348626	−	0.999392i	$-0.511099\pi$
$449$	−297855.			−0.0697251			−0.0348626	+	0.999392i	$0.511099\pi$
$450$		0			0
$451$		−	9.07479e6i		−	2.10085i
$452$	3.83218e6	−	3.85624e6i	0.882266	−	0.887806i
$453$		−	2.79116e6i		−	0.639057i
$454$	−237011.	−	569672.i	−0.0539671	−	0.129714i
$455$		0			0
$456$	−1.42844e6	+	3.49487e6i	−0.321699	+	0.787081i
$457$	−1.68614e6			−0.377661			−0.188831	−	0.982010i	$-0.560470\pi$
$457$	−1.68614e6			−0.377661			−0.188831	+	0.982010i	$0.560470\pi$
$458$	−271694.	−	653034.i	−0.0605223	−	0.145470i
$459$		−	1.26462e6i		−	0.280175i
$460$		0			0
$461$		−	5.80196e6i		−	1.27152i	−0.771887	−	0.635759i	$-0.780687\pi$
$461$		−	5.80196e6i		−	1.27152i	0.771887	−	0.635759i	$-0.219313\pi$
$462$	−5.48302e6	+	2.28120e6i	−1.19513	+	0.497232i
$463$	3.84592e6			0.833774			0.416887	−	0.908958i	$-0.363121\pi$
$463$	3.84592e6			0.833774			0.416887	+	0.908958i	$0.363121\pi$
$464$	5.12415e6	−	32075.9i	1.10491	−	0.00691645i
$465$		0			0
$466$	8.54607e6	−	3.55558e6i	1.82306	−	0.758482i
$467$		−	682895.i		−	0.144898i	−0.997372	−	0.0724488i	$-0.976919\pi$
$467$		−	682895.i		−	0.144898i	0.997372	−	0.0724488i	$-0.0230814\pi$
$468$	−593787.	−	590082.i	−0.125319	−	0.124537i
$469$			5.45021e6i			1.14415i
$470$		0			0
$471$	−2.02486e6			−0.420575
$472$	−6.44406e6	−	2.63384e6i	−1.33139	−	0.544170i
$473$	6.14830e6			1.26358
$474$	1.33899e6	+	3.21834e6i	0.273735	+	0.657941i
$475$		0			0
$476$	1.40641e6	−	1.41524e6i	0.284508	−	0.286294i
$477$			1.93936e6i			0.390268i
$478$	−8.20947e6	+	3.41553e6i	−1.64341	+	0.683737i
$479$	−868534.			−0.172961			−0.0864805	−	0.996254i	$-0.527562\pi$
$479$	−868534.			−0.172961			−0.0864805	+	0.996254i	$0.527562\pi$
$480$		0			0
$481$	385789.			0.0760304
$482$	6.71568e6	−	2.79404e6i	1.31666	−	0.547792i
$483$			6.62754e6i			1.29266i
$484$	−6.01609e6	+	6.05386e6i	−1.16735	+	1.17468i
$485$		0			0
$486$	2.05534e6	+	4.94014e6i	0.394723	+	0.948744i
$487$	1.42739e6			0.272722			0.136361	−	0.990659i	$-0.456459\pi$
$487$	1.42739e6			0.272722			0.136361	+	0.990659i	$0.456459\pi$
$488$	−6.35421e6	−	2.59712e6i	−1.20785	−	0.493676i
$489$	2.51804e6			0.476201
$490$		0			0
$491$			2.37311e6i			0.444237i	0.975020	+	0.222118i	$0.0712972\pi$
$491$			2.37311e6i			0.444237i	−0.975020	+	0.222118i	$0.928703\pi$
$492$	2.82099e6	+	2.80339e6i	0.525399	+	0.522120i
$493$			1.74115e6i			0.322641i
$494$	−1.95460e6	+	813209.i	−0.360364	+	0.149929i
$495$		0			0
$496$	−14069.0	−	2.24753e6i	−0.00256778	−	0.410206i
$497$	−868976.			−0.157804
$498$	−2.95455e6	+	1.22924e6i	−0.533849	+	0.222107i
$499$		−	3.66607e6i		−	0.659097i	−0.944139	−	0.329548i	$-0.893103\pi$
$499$		−	3.66607e6i		−	0.659097i	0.944139	−	0.329548i	$-0.106897\pi$
$500$		0			0
$501$			2.23180e6i			0.397247i
$502$	73553.2	+	176790.i	0.0130269	+	0.0313111i
$503$	−3.36518e6			−0.593046			−0.296523	−	0.955026i	$-0.595827\pi$
$503$	−3.36518e6			−0.593046			−0.296523	+	0.955026i	$0.595827\pi$
$504$	−1.99760e6	+	4.88740e6i	−0.350293	+	0.857041i
$505$		0			0
$506$	5.86807e6	+	1.41043e7i	1.01887	+	2.44893i
$507$		−	3.09440e6i		−	0.534634i
$508$	−2.56392e6	+	2.58002e6i	−0.440804	+	0.443572i
$509$			5.94861e6i			1.01770i	0.860854	+	0.508851i	$0.169930\pi$
$509$			5.94861e6i			1.01770i	−0.860854	+	0.508851i	$0.830070\pi$
$510$		0			0
$511$	−7.02646e6			−1.19038
$512$	5.44761e6	−	2.34690e6i	0.918398	−	0.395657i
$513$	8.46309e6			1.41983
$514$	708831.	−	294908.i	0.118341	−	0.0492355i
$515$		0			0
$516$	−1.89934e6	+	1.91126e6i	−0.314035	+	0.316007i
$517$			3.44752e6i			0.567257i
$518$	−934673.	−	2.24655e6i	−0.153051	−	0.367868i
$519$	−2.32066e6			−0.378176
$520$		0			0
$521$	5.78347e6			0.933456			0.466728	−	0.884401i	$-0.345433\pi$
$521$	5.78347e6			0.933456			0.466728	+	0.884401i	$0.345433\pi$
$522$	−1.76990e6	−	4.25407e6i	−0.284297	−	0.683327i
$523$			1.80930e6i			0.289238i	0.989487	+	0.144619i	$0.0461956\pi$
$523$			1.80930e6i			0.289238i	−0.989487	+	0.144619i	$0.953804\pi$
$524$	−4.85852e6	−	4.82820e6i	−0.772994	−	0.768170i
$525$		0			0
$526$	−160878.	+	66933.0i	−0.0253532	+	0.0105481i
$527$	763697.			0.119783
$528$	−37551.4	−	5.99888e6i	−0.00586194	−	0.936452i
$529$	1.06121e7			1.64878
$530$		0			0
$531$			6.25959e6i			0.963407i
$532$	9.47105e6	+	9.41195e6i	1.45084	+	1.44178i
$533$			2.23003e6i			0.340010i
$534$	578456.	+	1.39036e6i	0.0877843	+	0.210996i
$535$		0			0
$536$	−5.09636e6	−	2.08300e6i	−0.766210	−	0.313168i
$537$	−1.91077e6			−0.285938
$538$	−2.71864e6	−	6.53443e6i	−0.404945	−	0.973312i
$539$			1.00100e7i			1.48409i
$540$		0			0
$541$		−	1.13257e7i		−	1.66369i	−0.555005	−	0.831847i	$-0.687284\pi$
$541$		−	1.13257e7i		−	1.66369i	0.555005	−	0.831847i	$-0.312716\pi$
$542$	−1.23920e7	+	5.15566e6i	−1.81194	+	0.753852i
$543$	−5.65971e6			−0.823748
$544$	785843.	+	1.85598e6i	0.113851	+	0.268891i
$545$		0			0
$546$	1.34739e6	−	560580.i	0.193425	−	0.0804740i
$547$			8.98785e6i			1.28436i	0.766553	+	0.642181i	$0.221970\pi$
$547$			8.98785e6i			1.28436i	−0.766553	+	0.642181i	$0.778030\pi$
$548$	7.36506e6	−	7.41130e6i	1.04767	−	1.05425i
$549$			6.17231e6i			0.874011i
$550$		0			0
$551$	−1.16521e7			−1.63503
$552$	−6.19725e6	−	2.53296e6i	−0.865667	−	0.353819i
$553$	1.23276e7			1.71422
$554$	−790188.	−	1.89927e6i	−0.109385	−	0.262913i
$555$		0			0
$556$	−1.67420e6	−	1.66375e6i	−0.229678	−	0.228245i
$557$			2.29740e6i			0.313761i	0.987618	+	0.156881i	$0.0501438\pi$
$557$			2.29740e6i			0.313761i	−0.987618	+	0.156881i	$0.949856\pi$
$558$	−1.86590e6	+	776304.i	−0.253690	+	0.105547i
$559$	−1.51088e6			−0.204503
$560$		0			0
$561$	2.03838e6			0.273450
$562$	593489.	−	246920.i	0.0792633	−	0.0329773i
$563$		−	9.84032e6i		−	1.30839i	−0.756325	−	0.654197i	$-0.773007\pi$
$563$		−	9.84032e6i		−	1.30839i	0.756325	−	0.654197i	$-0.226993\pi$
$564$	−1.07170e6	−	1.06501e6i	−0.141865	−	0.140979i
$565$		0			0
$566$	5.70083e6	+	1.37023e7i	0.747992	+	1.79785i
$567$	1.25373e6			0.163774
$568$	332112.	−	812557.i	0.0431930	−	0.105678i
$569$	8.12763e6			1.05241			0.526203	−	0.850359i	$-0.323615\pi$
$569$	8.12763e6			1.05241			0.526203	+	0.850359i	$0.323615\pi$
$570$		0			0
$571$		−	6.86636e6i		−	0.881325i	−0.897673	−	0.440663i	$-0.854744\pi$
$571$		−	6.86636e6i		−	0.881325i	0.897673	−	0.440663i	$-0.145256\pi$
$572$	2.37109e6	−	2.38598e6i	0.303011	−	0.304914i
$573$		−	132094.i		−	0.0168072i
$574$	1.29860e7	−	5.40281e6i	1.64511	−	0.684447i
$575$		0			0
$576$	−3.80663e6	−	3.73581e6i	−0.478062	−	0.469168i
$577$	1.29988e7			1.62541			0.812707	−	0.582672i	$-0.197993\pi$
$577$	1.29988e7			1.62541			0.812707	+	0.582672i	$0.197993\pi$
$578$	6.78341e6	−	2.82223e6i	0.844556	−	0.351376i
$579$			3.43916e6i			0.426340i
$580$		0			0
$581$			1.13172e7i			1.39091i
$582$	−929338.	−	2.23373e6i	−0.113728	−	0.273352i
$583$	−7.79282e6			−0.949561
$584$	2.68543e6	−	6.57027e6i	0.325822	−	0.797170i
$585$		0			0
$586$	−199968.	−	480637.i	−0.0240556	−	0.0578194i
$587$			1.35189e7i			1.61936i	0.586869	+	0.809682i	$0.300361\pi$
$587$			1.35189e7i			1.61936i	−0.586869	+	0.809682i	$0.699639\pi$
$588$	−3.11170e6	−	3.09228e6i	−0.371154	−	0.368838i
$589$			5.11081e6i			0.607018i
$590$		0			0
$591$	6.05966e6			0.713640
$592$	2.45791e6	−	15385.9i	0.288245	−	0.00180434i
$593$	−5.10786e6			−0.596489			−0.298244	−	0.954490i	$-0.596401\pi$
$593$	−5.10786e6			−0.596489			−0.298244	+	0.954490i	$0.596401\pi$
$594$	−1.24155e7	+	5.16544e6i	−1.44377	+	0.600677i
$595$		0			0
$596$	8.40804e6	+	8.35557e6i	0.969569	+	0.963519i
$597$			650669.i			0.0747178i
$598$	−1.44201e6	−	3.46598e6i	−0.164898	−	0.396344i
$599$	6.28928e6			0.716199			0.358100	−	0.933683i	$-0.383425\pi$
$599$	6.28928e6			0.716199			0.358100	+	0.933683i	$0.383425\pi$
$600$		0			0
$601$	6.51315e6			0.735538			0.367769	−	0.929917i	$-0.380122\pi$
$601$	6.51315e6			0.735538			0.367769	+	0.929917i	$0.380122\pi$
$602$	3.66048e6	+	8.79822e6i	0.411668	+	0.989472i
$603$			4.95047e6i			0.554438i
$604$	7.02877e6	−	7.07290e6i	0.783947	−	0.788870i
$605$		0			0
$606$	8.34198e6	−	3.47066e6i	0.922757	−	0.383911i
$607$	1.53932e7			1.69574			0.847868	−	0.530207i	$-0.177886\pi$
$607$	1.53932e7			1.69574			0.847868	+	0.530207i	$0.177886\pi$
$608$	−1.24206e7	+	5.25901e6i	−1.36265	+	0.576959i
$609$	8.03232e6			0.877602
$610$		0			0
$611$		−	847188.i		−	0.0918073i
$612$	1.27745e6	−	1.28547e6i	0.137869	−	0.138734i
$613$			1.45172e7i			1.56038i	0.625542	+	0.780191i	$0.284878\pi$
$613$			1.45172e7i			1.56038i	−0.625542	+	0.780191i	$0.715122\pi$
$614$	1.35359e6	+	3.25345e6i	0.144900	+	0.348276i
$615$		0			0
$616$	−1.96387e7	−	8.02683e6i	−2.08527	−	0.852299i
$617$	−1.70658e7			−1.80473			−0.902367	−	0.430968i	$-0.858172\pi$
$617$	−1.70658e7			−1.80473			−0.902367	+	0.430968i	$0.858172\pi$
$618$	3.93523e6	+	9.45858e6i	0.414475	+	0.996219i
$619$		−	8.54741e6i		−	0.896619i	−0.893879	−	0.448309i	$-0.852026\pi$
$619$		−	8.54741e6i		−	0.896619i	0.893879	−	0.448309i	$-0.147974\pi$
$620$		0			0
$621$			1.50071e7i			1.56159i
$622$	−1.41632e7	+	5.89258e6i	−1.46786	+	0.610703i
$623$	5.32567e6			0.549736
$624$	9227.84	+	1.47416e6i	0.000948721	+	0.151559i
$625$		0			0
$626$	1.39328e7	−	5.79670e6i	1.42102	−	0.591214i
$627$			1.36412e7i			1.38575i
$628$	−5.13108e6	−	5.09906e6i	−0.519170	−	0.515930i
$629$			835183.i			0.0841695i
$630$		0			0
$631$	−1.01783e7			−1.01766			−0.508828	−	0.860868i	$-0.669921\pi$
$631$	−1.01783e7			−1.01766			−0.508828	+	0.860868i	$0.669921\pi$
$632$	−4.71147e6	+	1.15273e7i	−0.469206	+	1.14798i
$633$	8.46793e6			0.839978
$634$	−3.14230e6	−	7.55272e6i	−0.310473	−	0.746243i
$635$		0			0
$636$	2.40736e6	−	2.42248e6i	0.235993	−	0.237475i
$637$		−	2.45983e6i		−	0.240191i
$638$	1.70939e7	−	7.11187e6i	1.66260	−	0.691723i
$639$	−789297.			−0.0764695
$640$		0			0
$641$	1.89248e6			0.181922			0.0909612	−	0.995854i	$-0.471006\pi$
$641$	1.89248e6			0.181922			0.0909612	+	0.995854i	$0.471006\pi$
$642$	3.41678e6	−	1.42155e6i	0.327175	−	0.136120i
$643$		−	4.41604e6i		−	0.421216i	−0.977571	−	0.210608i	$-0.932456\pi$
$643$		−	4.41604e6i		−	0.421216i	0.977571	−	0.210608i	$-0.0675444\pi$
$644$	−1.66896e7	+	1.67944e7i	−1.58574	+	1.59570i
$645$		0			0
$646$	−1.76049e6	−	4.23146e6i	−0.165979	−	0.398941i
$647$	3.77794e6			0.354809			0.177404	−	0.984138i	$-0.443230\pi$
$647$	3.77794e6			0.354809			0.177404	+	0.984138i	$0.443230\pi$
$648$	−479159.	+	1.17233e6i	−0.0448272	+	0.109676i
$649$	−2.51525e7			−2.34407
$650$		0			0
$651$		−	3.52310e6i		−	0.325816i
$652$	6.38081e6	+	6.34099e6i	0.587836	+	0.584168i
$653$		−	1.44071e7i		−	1.32219i	−0.750301	−	0.661096i	$-0.770092\pi$
$653$		−	1.44071e7i		−	1.32219i	0.750301	−	0.661096i	$-0.229908\pi$
$654$	5.99657e6	−	2.49486e6i	0.548225	−	0.228088i
$655$		0			0
$656$	88937.0	+	1.42078e7i	0.00806906	+	1.28904i
$657$	−6.38218e6			−0.576841
$658$	−4.93339e6	+	2.05253e6i	−0.444203	+	0.184810i
$659$		−	1.01081e7i		−	0.906686i	−0.891336	−	0.453343i	$-0.850231\pi$
$659$		−	1.01081e7i		−	0.906686i	0.891336	−	0.453343i	$-0.149769\pi$
$660$		0			0
$661$			5.21128e6i			0.463917i	0.972726	+	0.231959i	$0.0745134\pi$
$661$			5.21128e6i			0.463917i	−0.972726	+	0.231959i	$0.925487\pi$
$662$	−3.64042e6	−	8.75001e6i	−0.322855	−	0.776003i
$663$	−500910.			−0.0442563
$664$	−1.05824e7	−	4.32529e6i	−0.931462	−	0.380711i
$665$		0			0
$666$	−848970.	−	2.04056e6i	−0.0741663	−	0.178264i
$667$		−	2.06620e7i		−	1.79828i
$668$	−5.62017e6	+	5.65546e6i	−0.487313	+	0.490373i
$669$		−	7.06268e6i		−	0.610104i
$670$		0			0
$671$	−2.48018e7			−2.12656
$672$	8.56204e6	−	3.62526e6i	0.731399	−	0.309682i
$673$	−8.07486e6			−0.687222			−0.343611	−	0.939112i	$-0.611650\pi$
$673$	−8.07486e6			−0.687222			−0.343611	+	0.939112i	$0.611650\pi$
$674$	1.14713e7	−	4.77260e6i	0.972660	−	0.404674i
$675$		0			0
$676$	7.79240e6	−	7.84133e6i	0.655850	−	0.659968i
$677$		−	1.37198e7i		−	1.15047i	−0.817988	−	0.575236i	$-0.804910\pi$
$677$		−	1.37198e7i		−	1.15047i	0.817988	−	0.575236i	$-0.195090\pi$
$678$	3.30676e6	+	7.94803e6i	0.276267	+	0.664027i
$679$	−8.55613e6			−0.712202
$680$		0			0
$681$	976999.			0.0807284
$682$	−3.11938e6	−	7.49764e6i	−0.256807	−	0.617253i
$683$			502514.i			0.0412189i	0.999788	+	0.0206094i	$0.00656065\pi$
$683$			502514.i			0.0412189i	−0.999788	+	0.0206094i	$0.993439\pi$
$684$	8.60262e6	+	8.54894e6i	0.703057	+	0.698670i
$685$		0			0
$686$	1.40586e6	−	584905.i	0.114059	−	0.0474542i
$687$	1.11997e6			0.0905343
$688$	−9.62598e6	+	60256.1i	−0.775307	+	0.00485322i
$689$	1.91500e6			0.153681
$690$		0			0
$691$		−	9.54427e6i		−	0.760409i	−0.924902	−	0.380205i	$-0.875854\pi$
$691$		−	9.54427e6i		−	0.760409i	0.924902	−	0.380205i	$-0.124146\pi$
$692$	−5.88064e6	−	5.84394e6i	−0.466831	−	0.463918i
$693$			1.90766e7i			1.50892i
$694$	8.25611e6	+	1.98441e7i	0.650694	+	1.56399i
$695$		0			0
$696$	−3.06985e6	+	7.51082e6i	−0.240212	+	0.587711i
$697$	−4.82771e6			−0.376409
$698$	4.87909e6	+	1.17272e7i	0.379053	+	0.911080i
$699$			1.46567e7i			1.13460i
$700$		0			0
$701$		−	6.74508e6i		−	0.518432i	−0.965819	−	0.259216i	$-0.916536\pi$
$701$		−	6.74508e6i		−	0.518432i	0.965819	−	0.259216i	$-0.0834642\pi$
$702$	3.05096e6	−	1.26935e6i	0.233665	−	0.0972161i
$703$	−5.58920e6			−0.426542
$704$	1.50114e7	−	1.52959e7i	1.14153	−	1.16317i
$705$		0			0
$706$	−7.45670e6	+	3.10234e6i	−0.563034	+	0.234249i
$707$		−	3.19534e7i		−	2.40419i
$708$	7.77014e6	−	7.81893e6i	0.582567	−	0.586225i
$709$		−	1.30715e7i		−	0.976587i	−0.872679	−	0.488294i	$-0.837619\pi$
$709$		−	1.30715e7i		−	0.976587i	0.872679	−	0.488294i	$-0.162381\pi$
$710$		0			0
$711$	1.11973e7			0.830690
$712$	−2.03540e6	+	4.97990e6i	−0.150470	+	0.368146i
$713$	−9.06268e6			−0.667626
$714$	1.21358e6	+	2.91692e6i	0.0890888	+	0.214131i
$715$		0			0
$716$	−4.84195e6	−	4.81173e6i	−0.352970	−	0.350767i
$717$		−	1.40794e7i		−	1.02279i
$718$	5.15995e6	−	2.14679e6i	0.373538	−	0.155410i
$719$	−4.30858e6			−0.310822			−0.155411	−	0.987850i	$-0.549670\pi$
$719$	−4.30858e6			−0.310822			−0.155411	+	0.987850i	$0.549670\pi$
$720$		0			0
$721$	3.62304e7			2.59559
$722$	1.53854e7	−	6.40108e6i	1.09841	−	0.456993i
$723$			1.15175e7i			0.819432i
$724$	−1.43419e7	−	1.42524e7i	−1.01686	−	1.01051i
$725$		0			0
$726$	−5.19125e6	−	1.24775e7i	−0.365536	−	0.878590i
$727$	−9.51543e6			−0.667717			−0.333858	−	0.942623i	$-0.608351\pi$
$727$	−9.51543e6			−0.667717			−0.333858	+	0.942623i	$0.608351\pi$
$728$	4.82600e6	+	1.97250e6i	0.337489	+	0.137940i
$729$	−6.77234e6			−0.471976
$730$		0			0
$731$		−	3.27085e6i		−	0.226395i
$732$	7.66180e6	−	7.70991e6i	0.528510	−	0.531829i
$733$		−	1.76887e7i		−	1.21601i	−0.793934	−	0.608004i	$-0.791971\pi$
$733$		−	1.76887e7i		−	1.21601i	0.793934	−	0.608004i	$-0.208029\pi$
$734$	−1.17628e7	+	4.89391e6i	−0.805883	+	0.335286i
$735$		0			0
$736$	−9.32548e6	−	2.20247e7i	−0.634566	−	1.49870i
$737$	−1.98922e7			−1.34900
$738$	1.17953e7	−	4.90741e6i	0.797201	−	0.331674i
$739$			2.27908e6i			0.153514i	0.997050	+	0.0767572i	$0.0244566\pi$
$739$			2.27908e6i			0.153514i	−0.997050	+	0.0767572i	$0.975543\pi$
$740$		0			0
$741$		−	3.35218e6i		−	0.224276i
$742$	−4.63957e6	−	1.11515e7i	−0.309363	−	0.743574i
$743$	−1.92873e7			−1.28174			−0.640869	−	0.767650i	$-0.721426\pi$
$743$	−1.92873e7			−1.28174			−0.640869	+	0.767650i	$0.721426\pi$
$744$	3.29436e6	+	1.34648e6i	0.218192	+	0.0891803i
$745$		0			0
$746$	4.81225e6	+	1.15666e7i	0.316593	+	0.760952i
$747$			1.02795e7i			0.674016i
$748$	5.16533e6	+	5.13310e6i	0.337555	+	0.335448i
$749$		−	1.30877e7i		−	0.852433i
$750$		0			0
$751$	−4.08961e6			−0.264595			−0.132298	−	0.991210i	$-0.542235\pi$
$751$	−4.08961e6			−0.264595			−0.132298	+	0.991210i	$0.542235\pi$
$752$	−33787.2	−	5.39754e6i	−0.00217875	−	0.348058i
$753$	−303199.			−0.0194868
$754$	−4.20063e6	+	1.74766e6i	−0.269083	+	0.111951i
$755$		0			0
$756$	−1.47835e7	−	1.46912e7i	−0.940746	−	0.934875i
$757$			2.68495e7i			1.70293i	0.524412	+	0.851465i	$0.324285\pi$
$757$			2.68495e7i			1.70293i	−0.524412	+	0.851465i	$0.675715\pi$
$758$	6.29210e6	+	1.51235e7i	0.397762	+	0.956047i
$759$	−2.41892e7			−1.52411
$760$		0			0
$761$	−1.74699e7			−1.09353			−0.546764	−	0.837287i	$-0.684140\pi$
$761$	−1.74699e7			−1.09353			−0.546764	+	0.837287i	$0.684140\pi$
$762$	−2.21239e6	−	5.31764e6i	−0.138030	−	0.331766i
$763$		−	2.29694e7i		−	1.42837i
$764$	332642.	−	334731.i	0.0206179	−	0.0207473i
$765$		0			0
$766$	−1.03049e7	+	4.28733e6i	−0.634558	+	0.264007i
$767$	6.18096e6			0.379374
$768$	117583.	+	9.39168e6i	0.00719355	+	0.574566i
$769$	2.64035e7			1.61007			0.805037	−	0.593224i	$-0.202145\pi$
$769$	2.64035e7			1.61007			0.805037	+	0.593224i	$0.202145\pi$
$770$		0			0
$771$			1.21566e6i			0.0736505i
$772$	−8.66058e6	+	8.71497e6i	−0.523003	+	0.526287i
$773$		−	3.92652e6i		−	0.236352i	−0.992993	−	0.118176i	$-0.962295\pi$
$773$		−	3.92652e6i		−	0.236352i	0.992993	−	0.118176i	$-0.0377047\pi$
$774$	3.32484e6	+	7.99148e6i	0.199489	+	0.479485i
$775$		0			0
$776$	3.27005e6	−	8.00062e6i	0.194939	−	0.476946i
$777$	3.85288e6			0.228946
$778$	4.24495e6	+	1.02030e7i	0.251434	+	0.604338i
$779$		−	3.23080e7i		−	1.90751i
$780$		0			0
$781$		−	3.17158e6i		−	0.186058i
$782$	7.50338e6	−	3.12177e6i	0.438773	−	0.182551i
$783$	1.81880e7			1.06018
$784$	−98102.0	−	1.56719e7i	−0.00570017	−	0.910608i
$785$		0			0
$786$	1.00138e7	−	4.16623e6i	0.578154	−	0.240540i
$787$			3.36220e6i			0.193503i	0.995309	+	0.0967513i	$0.0308451\pi$
$787$			3.36220e6i			0.193503i	−0.995309	+	0.0967513i	$0.969155\pi$
$788$	1.53554e7	+	1.52596e7i	0.880938	+	0.875441i
$789$		−	275909.i		−	0.0157788i
$790$		0			0
$791$	3.04444e7			1.73008
$792$	−1.78380e7	−	7.29082e6i	−1.01049	−	0.413013i
$793$	6.09477e6			0.344171
$794$	−7.51985e6	−	1.80745e7i	−0.423310	−	1.01745i
$795$		0			0
$796$	−1.63853e6	+	1.64882e6i	−0.0916582	+	0.0922338i
$797$		−	3.41295e6i		−	0.190320i	−0.995462	−	0.0951600i	$-0.969664\pi$
$797$		−	3.41295e6i		−	0.190320i	0.995462	−	0.0951600i	$-0.0303363\pi$
$798$	−1.95206e7	+	8.12152e6i	−1.08514	+	0.451471i
$799$	1.83405e6			0.101635
$800$		0			0
$801$	4.83734e6			0.266395
$802$	−7.96443e6	+	3.31359e6i	−0.437239	+	0.181913i
$803$		−	2.56452e7i		−	1.40351i
$804$	6.14510e6	−	6.18369e6i	0.335266	−	0.337371i
$805$		0			0
$806$	766552.	+	1.84246e6i	0.0415627	+	0.0998989i
$807$	1.12067e7			0.605749
$808$	2.98788e7	+	1.22122e7i	1.61003	+	0.658059i
$809$	472257.			0.0253692			0.0126846	−	0.999920i	$-0.495962\pi$
$809$	472257.			0.0253692			0.0126846	+	0.999920i	$0.495962\pi$
$810$		0			0
$811$			1.92082e7i			1.02550i	0.858539	+	0.512748i	$0.171373\pi$
$811$			1.92082e7i			1.02550i	−0.858539	+	0.512748i	$0.828627\pi$
$812$	2.03542e7	+	2.02272e7i	1.08334	+	1.07658i
$813$		−	2.12525e7i		−	1.12767i
$814$	8.19945e6	−	3.41137e6i	0.433734	−	0.180454i
$815$		0			0
$816$	−3.19136e6	+	19977.1i	−0.167784	+	0.00105028i
$817$	2.18891e7			1.14729
$818$	3.36574e6	−	1.40031e6i	0.175872	−	0.0731713i
$819$		−	4.68785e6i		−	0.244210i
$820$		0			0
$821$			9.11118e6i			0.471755i	0.971783	+	0.235878i	$0.0757964\pi$
$821$			9.11118e6i			0.471755i	−0.971783	+	0.235878i	$0.924204\pi$
$822$	6.35526e6	+	1.52753e7i	0.328061	+	0.788516i
$823$	−9.99422e6			−0.514339			−0.257169	−	0.966366i	$-0.582790\pi$
$823$	−9.99422e6			−0.514339			−0.257169	+	0.966366i	$0.582790\pi$
$824$	−1.38468e7	+	3.38782e7i	−0.710447	+	1.73821i
$825$		0			0
$826$	−1.49749e7	−	3.59933e7i	−0.763686	−	1.83557i
$827$		−	2.26290e7i		−	1.15054i	−0.817964	−	0.575270i	$-0.804897\pi$
$827$		−	2.26290e7i		−	1.15054i	0.817964	−	0.575270i	$-0.195103\pi$
$828$	−1.51593e7	+	1.52545e7i	−0.768428	+	0.773254i
$829$		−	2.43090e7i		−	1.22852i	−0.789106	−	0.614258i	$-0.789456\pi$
$829$		−	2.43090e7i		−	1.22852i	0.789106	−	0.614258i	$-0.210544\pi$
$830$		0			0
$831$	3.25728e6			0.163626
$832$	−3.68887e6	+	3.75881e6i	−0.184750	+	0.188253i
$833$	5.32521e6			0.265904
$834$	3.45066e6	−	1.43564e6i	0.171786	−	0.0714711i
$835$		0			0
$836$	−3.43517e7	+	3.45674e7i	−1.69994	+	1.71061i
$837$		−	7.97753e6i		−	0.393600i
$838$	−9.11354e6	−	2.19050e7i	−0.448309	−	1.07754i
$839$	7.31704e6			0.358865			0.179432	−	0.983770i	$-0.442574\pi$
$839$	7.31704e6			0.358865			0.179432	+	0.983770i	$0.442574\pi$
$840$		0			0
$841$	−4.53041e6			−0.220876
$842$	−3.52413e6	−	8.47050e6i	−0.171306	−	0.411745i
$843$			1.01785e6i			0.0493302i
$844$	2.14580e7	+	2.13241e7i	1.03689	+	1.03042i
$845$		0			0
$846$	−4.48104e6	+	1.86433e6i	−0.215255	+	0.0895563i
$847$	−4.77942e7			−2.28911
$848$	1.22007e7	−	76373.1i	0.582632	−	0.00364713i
$849$	−2.34998e7			−1.11891
$850$		0			0
$851$		−	9.91099e6i		−	0.469130i
$852$	985921.	+	979768.i	0.0465311	+	0.0462407i
$853$			1.97974e7i			0.931614i	0.884886	+	0.465807i	$0.154236\pi$
$853$			1.97974e7i			0.931614i	−0.884886	+	0.465807i	$0.845764\pi$
$854$	−1.47661e7	−	3.54914e7i	−0.692823	−	1.66525i
$855$		0			0
$856$	1.22380e7	+	5.00197e6i	0.570856	+	0.233323i
$857$	−1.46070e7			−0.679375			−0.339688	−	0.940538i	$-0.610321\pi$
$857$	−1.46070e7			−0.679375			−0.339688	+	0.940538i	$0.610321\pi$
$858$	2.04600e6	+	4.91770e6i	0.0948829	+	0.228057i
$859$		−	8.07668e6i		−	0.373465i	−0.982411	−	0.186733i	$-0.940210\pi$
$859$		−	8.07668e6i		−	0.373465i	0.982411	−	0.186733i	$-0.0597898\pi$
$860$		0			0
$861$			2.22713e7i			1.02385i
$862$	5.84388e6	−	2.43134e6i	0.267876	−	0.111449i
$863$	−2.79017e7			−1.27528			−0.637638	−	0.770336i	$-0.720088\pi$
$863$	−2.79017e7			−1.27528			−0.637638	+	0.770336i	$0.720088\pi$
$864$	1.93875e7	−	8.20885e6i	0.883561	−	0.374109i
$865$		0			0
$866$	4.89005e6	−	2.03450e6i	0.221574	−	0.0921854i
$867$			1.16337e7i			0.525617i
$868$	8.87195e6	−	8.92766e6i	0.399687	−	0.402196i
$869$			4.49934e7i			2.02115i
$870$		0			0
$871$	4.88828e6			0.218329
$872$	2.14781e7	+	8.77863e6i	0.956545	+	0.390963i
$873$	−7.77160e6			−0.345124
$874$	2.08915e7	+	5.02141e7i	0.925104	+	2.22355i
$875$		0			0
$876$	7.97207e6	+	7.92232e6i	0.351003	+	0.348813i
$877$			2.39256e7i			1.05042i	0.850971	+	0.525212i	$0.176014\pi$
$877$			2.39256e7i			1.05042i	−0.850971	+	0.525212i	$0.823986\pi$
$878$	−4.99861e6	+	2.07966e6i	−0.218833	+	0.0910452i
$879$	824302.			0.0359844
$880$		0			0
$881$	−2.60137e7			−1.12918			−0.564589	−	0.825373i	$-0.690965\pi$
$881$	−2.60137e7			−1.12918			−0.564589	+	0.825373i	$0.690965\pi$
$882$	−1.30108e7	+	5.41312e6i	−0.563161	+	0.234302i
$883$			1.84987e7i			0.798434i	0.916857	+	0.399217i	$0.130718\pi$
$883$			1.84987e7i			0.798434i	−0.916857	+	0.399217i	$0.869282\pi$
$884$	−1.26932e6	−	1.26140e6i	−0.0546313	−	0.0542904i
$885$		0			0
$886$	4.55808e6	+	1.09557e7i	0.195073	+	0.468872i
$887$	−1.75445e7			−0.748739			−0.374370	−	0.927280i	$-0.622141\pi$
$887$	−1.75445e7			−0.748739			−0.374370	+	0.927280i	$0.622141\pi$
$888$	−1.47252e6	+	3.60273e6i	−0.0626656	+	0.153320i
$889$	−2.03688e7			−0.864394
$890$		0			0
$891$			4.57585e6i			0.193098i
$892$	1.77854e7	−	1.78971e7i	0.748431	−	0.753130i
$893$			1.22738e7i			0.515052i
$894$	−1.73297e7	+	7.20997e6i	−0.725181	+	0.301710i
$895$		0			0
$896$	3.08257e7	+	1.23746e7i	1.28275	+	0.514945i
$897$	5.94422e6			0.246668
$898$	1.55566e6	−	647228.i	0.0643758	−	0.0267834i
$899$			1.09836e7i			0.453259i
$900$		0			0
$901$			4.14572e6i			0.170133i
$902$	1.97192e7	+	4.73963e7i	0.806997	+	1.93967i
$903$	−1.50891e7			−0.615807
$904$	−1.16355e7	+	2.84678e7i	−0.473546	+	1.15860i
$905$		0			0
$906$	6.06508e6	+	1.45778e7i	0.245480	+	0.590028i
$907$			3.92259e7i			1.58327i	0.610994	+	0.791635i	$0.290770\pi$
$907$			3.92259e7i			1.58327i	−0.610994	+	0.791635i	$0.709230\pi$
$908$	2.47575e6	+	2.46030e6i	0.0996535	+	0.0990316i
$909$		−	2.90235e7i		−	1.16504i
$910$		0			0
$911$	3.70208e7			1.47791			0.738957	−	0.673752i	$-0.235318\pi$
$911$	3.70208e7			1.47791			0.738957	+	0.673752i	$0.235318\pi$
$912$	−133690.	−	2.13572e7i	−0.00532247	−	0.850270i
$913$	−4.13055e7			−1.63995
$914$	8.80646e6	−	3.66391e6i	0.348687	−	0.145071i
$915$		0			0
$916$	2.83803e6	+	2.82032e6i	0.111758	+	0.111061i
$917$		−	3.83572e7i		−	1.50634i
$918$	2.74797e6	+	6.60494e6i	0.107623	+	0.258679i
$919$	−1.51186e7			−0.590504			−0.295252	−	0.955419i	$-0.595404\pi$
$919$	−1.51186e7			−0.590504			−0.295252	+	0.955419i	$0.595404\pi$
$920$		0			0
$921$	−5.57973e6			−0.216753
$922$	1.26074e7	+	3.03028e7i	0.488427	+	1.17397i
$923$			779381.i			0.0301124i
$924$	2.36801e7	−	2.38288e7i	0.912438	−	0.918167i
$925$		0			0
$926$	−2.00867e7	+	8.35704e6i	−0.769806	+	0.320276i
$927$	3.29084e7			1.25779
$928$	−2.66930e7	+	1.13021e7i	−1.01748	+	0.430814i
$929$	−1.30954e6			−0.0497827			−0.0248913	−	0.999690i	$-0.507924\pi$
$929$	−1.30954e6			−0.0497827			−0.0248913	+	0.999690i	$0.507924\pi$
$930$		0			0
$931$			3.56374e7i			1.34751i
$932$	−3.69088e7	+	3.71405e7i	−1.39184	+	1.40058i
$933$		−	2.42902e7i		−	0.913539i
$934$	1.48390e6	+	3.56666e6i	0.0556594	+	0.133781i
$935$		0			0
$936$	4.38349e6	+	1.79164e6i	0.163542	+	0.0668437i
$937$	2.90734e7			1.08180			0.540900	−	0.841087i	$-0.318084\pi$
$937$	2.90734e7			1.08180			0.540900	+	0.841087i	$0.318084\pi$
$938$	−1.18431e7	−	2.84657e7i	−0.439499	−	1.05637i
$939$			2.38950e7i			0.884387i
$940$		0			0
$941$		−	2.78133e7i		−	1.02395i	−0.859000	−	0.511975i	$-0.828914\pi$
$941$		−	2.78133e7i		−	1.02395i	0.859000	−	0.511975i	$-0.171086\pi$
$942$	1.05756e7	−	4.39995e6i	0.388308	−	0.161555i
$943$	5.72898e7			2.09796
$944$	3.93796e7	−	246506.i	1.43827	−	0.00900322i
$945$		0			0
$946$	−3.21117e7	+	1.33600e7i	−1.16664	+	0.485377i
$947$		−	5.56136e6i		−	0.201514i	−0.994911	−	0.100757i	$-0.967873\pi$
$947$		−	5.56136e6i		−	0.201514i	0.994911	−	0.100757i	$-0.0321265\pi$
$948$	−1.39867e7	−	1.38994e7i	−0.505468	−	0.502314i
$949$			6.30201e6i			0.227150i
$950$		0			0
$951$	1.29531e7			0.464431
$952$	−4.27021e6	+	1.04477e7i	−0.152706	+	0.373617i
$953$	−2.07308e7			−0.739408			−0.369704	−	0.929150i	$-0.620541\pi$
$953$	−2.07308e7			−0.739408			−0.369704	+	0.929150i	$0.620541\pi$
$954$	−4.21415e6	−	1.01290e7i	−0.149913	−	0.360326i
$955$		0			0
$956$	3.54551e7	−	3.56777e7i	1.25468	−	1.26256i
$957$			2.93163e7i			1.03474i
$958$	4.53623e6	−	1.88729e6i	0.159691	−	0.0664393i
$959$	5.85110e7			2.05443
$960$		0			0
$961$	−2.38116e7			−0.831725
$962$	−2.01492e6	+	838305.i	−0.0701973	+	0.0292055i
$963$		−	1.18877e7i		−	0.413078i
$964$	−2.90037e7	+	2.91858e7i	−1.00522	+	1.01153i
$965$		0			0
$966$	−1.44014e7	−	3.46147e7i	−0.496548	−	1.19349i
$967$	1.25936e7			0.433094			0.216547	−	0.976272i	$-0.430520\pi$
$967$	1.25936e7			0.433094			0.216547	+	0.976272i	$0.430520\pi$
$968$	1.82664e7	−	4.46912e7i	0.626561	−	1.53297i
$969$	7.25703e6			0.248285
$970$		0			0
$971$			2.22296e7i			0.756629i	0.925677	+	0.378314i	$0.123496\pi$
$971$			2.22296e7i			0.756629i	−0.925677	+	0.378314i	$0.876504\pi$
$972$	−2.14695e7	−	2.13355e7i	−0.728880	−	0.724331i
$973$		−	1.32175e7i		−	0.447577i
$974$	−7.45506e6	+	3.10166e6i	−0.251799	+	0.104760i
$975$		0			0
$976$	3.88306e7	−	243069.i	1.30482	−	0.00816780i
$977$	−1.54083e6			−0.0516437			−0.0258218	−	0.999667i	$-0.508220\pi$
$977$	−1.54083e6			−0.0516437			−0.0258218	+	0.999667i	$0.508220\pi$
$978$	−1.31514e7	+	5.47160e6i	−0.439667	+	0.182923i
$979$			1.94376e7i			0.648165i
$980$		0			0
$981$		−	2.08633e7i		−	0.692167i
$982$	−5.15668e6	−	1.23944e7i	−0.170644	−	0.410155i
$983$	2.84625e7			0.939482			0.469741	−	0.882804i	$-0.344347\pi$
$983$	2.84625e7			0.939482			0.469741	+	0.882804i	$0.344347\pi$
$984$	−2.08253e7	−	8.51180e6i	−0.685652	−	0.280242i
$985$		0			0
$986$	−3.78346e6	−	9.09380e6i	−0.123936	−	0.297888i
$987$		−	8.46087e6i		−	0.276453i
$988$	8.44154e6	−	8.49455e6i	0.275125	−	0.276852i
$989$			3.88147e7i			1.26184i
$990$		0			0
$991$	−3.89747e7			−1.26066			−0.630331	−	0.776327i	$-0.717081\pi$
$991$	−3.89747e7			−1.26066			−0.630331	+	0.776327i	$0.717081\pi$
$992$	4.95728e6	+	1.17080e7i	0.159943	+	0.377748i
$993$	1.50064e7			0.482952
$994$	4.53854e6	−	1.88825e6i	0.145697	−	0.0606169i
$995$		0			0
$996$	1.27601e7	−	1.28403e7i	0.407574	−	0.410133i
$997$			2.13564e6i			0.0680441i	0.999421	+	0.0340221i	$0.0108317\pi$
$997$			2.13564e6i			0.0680441i	−0.999421	+	0.0340221i	$0.989168\pi$
$998$	7.96622e6	+	1.91474e7i	0.253178	+	0.608531i
$999$	8.72426e6			0.276576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.d.c.101.4	yes	20
4.3	odd	2		800.6.d.d.401.13		20
5.2	odd	4		200.6.f.d.149.13		40
5.3	odd	4		200.6.f.d.149.28		40
5.4	even	2		200.6.d.d.101.17	yes	20
8.3	odd	2		800.6.d.d.401.8		20
8.5	even	2	inner	200.6.d.c.101.3	✓	20
20.3	even	4		800.6.f.d.49.16		40
20.7	even	4		800.6.f.d.49.25		40
20.19	odd	2		800.6.d.b.401.8		20
40.3	even	4		800.6.f.d.49.26		40
40.13	odd	4		200.6.f.d.149.14		40
40.19	odd	2		800.6.d.b.401.13		20
40.27	even	4		800.6.f.d.49.15		40
40.29	even	2		200.6.d.d.101.18	yes	20
40.37	odd	4		200.6.f.d.149.27		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.3	✓	20	8.5	even	2	inner
200.6.d.c.101.4	yes	20	1.1	even	1	trivial
200.6.d.d.101.17	yes	20	5.4	even	2
200.6.d.d.101.18	yes	20	40.29	even	2
200.6.f.d.149.13		40	5.2	odd	4
200.6.f.d.149.14		40	40.13	odd	4
200.6.f.d.149.27		40	40.37	odd	4
200.6.f.d.149.28		40	5.3	odd	4
800.6.d.b.401.8		20	20.19	odd	2
800.6.d.b.401.13		20	40.19	odd	2
800.6.d.d.401.8		20	8.3	odd	2
800.6.d.d.401.13		20	4.3	odd	2
800.6.f.d.49.15		40	40.27	even	4
800.6.f.d.49.16		40	20.3	even	4
800.6.f.d.49.25		40	20.7	even	4
800.6.f.d.49.26		40	40.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.22286 + 2.17296i) q^{2} -8.95730i q^{3} +(22.5565 - 22.6981i) q^{4} +(19.4639 + 46.7827i) q^{6} +179.198 q^{7} +(-68.4872 + 167.563i) q^{8} +162.767 q^{9} +O(q^{10})\)	\(q+(-5.22286 + 2.17296i) q^{2} -8.95730i q^{3} +(22.5565 - 22.6981i) q^{4} +(19.4639 + 46.7827i) q^{6} +179.198 q^{7} +(-68.4872 + 167.563i) q^{8} +162.767 q^{9} +654.036i q^{11} +(-203.314 - 202.045i) q^{12} -160.722i q^{13} +(-935.925 + 389.390i) q^{14} +(-6.40984 - 1023.98i) q^{16} +347.942 q^{17} +(-850.107 + 353.686i) q^{18} +2328.49i q^{19} -1605.13i q^{21} +(-1421.19 - 3415.94i) q^{22} -4128.97 q^{23} +(1500.92 + 613.460i) q^{24} +(349.243 + 839.428i) q^{26} -3634.58i q^{27} +(4042.08 - 4067.46i) q^{28} +5004.15i q^{29} +2194.90 q^{31} +(2258.55 + 5334.17i) q^{32} +5858.40 q^{33} +(-1817.25 + 756.064i) q^{34} +(3671.45 - 3694.50i) q^{36} +2400.35i q^{37} +(-5059.73 - 12161.4i) q^{38} -1439.64 q^{39} -13875.1 q^{41} +(3487.88 + 8383.37i) q^{42} -9400.56i q^{43} +(14845.4 + 14752.8i) q^{44} +(21565.0 - 8972.10i) q^{46} +5271.14 q^{47} +(-9172.10 + 57.4149i) q^{48} +15304.9 q^{49} -3116.62i q^{51} +(-3648.09 - 3625.32i) q^{52} +11915.0i q^{53} +(7897.79 + 18982.9i) q^{54} +(-12272.8 + 30027.0i) q^{56} +20857.0 q^{57} +(-10873.8 - 26136.0i) q^{58} +38457.4i q^{59} +37921.2i q^{61} +(-11463.6 + 4769.43i) q^{62} +29167.5 q^{63} +(-23387.0 - 22951.9i) q^{64} +(-30597.6 + 12730.1i) q^{66} +30414.5i q^{67} +(7848.35 - 7897.63i) q^{68} +36984.5i q^{69} -4849.25 q^{71} +(-11147.4 + 27273.8i) q^{72} -39210.6 q^{73} +(-5215.87 - 12536.7i) q^{74} +(52852.5 + 52522.6i) q^{76} +117202. i q^{77} +(7519.01 - 3128.27i) q^{78} +68793.5 q^{79} +6996.32 q^{81} +(72467.5 - 30150.0i) q^{82} +63154.8i q^{83} +(-36433.4 - 36206.1i) q^{84} +(20427.0 + 49097.8i) q^{86} +44823.7 q^{87} +(-109593. - 44793.1i) q^{88} +29719.5 q^{89} -28801.0i q^{91} +(-93135.2 + 93720.0i) q^{92} -19660.4i q^{93} +(-27530.4 + 11454.0i) q^{94} +(47779.8 - 20230.5i) q^{96} -47746.8 q^{97} +(-79935.3 + 33256.9i) q^{98} +106455. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} + q^{4} + 33 q^{6} - 196 q^{7} - 391 q^{8} - 1620 q^{9}+O(q^{10}) \) 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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