LMFDB - Embedded newform 200.6.f.d.149.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	200.f (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.0767639626$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.27
Character	$\chi$	$=$	200.149
Dual form			200.6.f.d.149.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.17296 - 5.22286i) q^{2} +8.95730 q^{3} +(-22.5565 - 22.6981i) q^{4} +(19.4639 - 46.7827i) q^{6} +179.198i q^{7} +(-167.563 + 68.4872i) q^{8} -162.767 q^{9} +O(q^{10})$	\(q+(2.17296 - 5.22286i) q^{2} +8.95730 q^{3} +(-22.5565 - 22.6981i) q^{4} +(19.4639 - 46.7827i) q^{6} +179.198i q^{7} +(-167.563 + 68.4872i) q^{8} -162.767 q^{9} -654.036i q^{11} +(-202.045 - 203.314i) q^{12} +160.722 q^{13} +(935.925 + 389.390i) q^{14} +(-6.40984 + 1023.98i) q^{16} +347.942i q^{17} +(-353.686 + 850.107i) q^{18} +2328.49i q^{19} +1605.13i q^{21} +(-3415.94 - 1421.19i) q^{22} +4128.97i q^{23} +(-1500.92 + 613.460i) q^{24} +(349.243 - 839.428i) q^{26} -3634.58 q^{27} +(4067.46 - 4042.08i) q^{28} +5004.15i q^{29} +2194.90 q^{31} +(5334.17 + 2258.55i) q^{32} -5858.40i q^{33} +(1817.25 + 756.064i) q^{34} +(3671.45 + 3694.50i) q^{36} +2400.35 q^{37} +(12161.4 + 5059.73i) q^{38} +1439.64 q^{39} -13875.1 q^{41} +(8383.37 + 3487.88i) q^{42} +9400.56 q^{43} +(-14845.4 + 14752.8i) q^{44} +(21565.0 + 8972.10i) q^{46} +5271.14i q^{47} +(-57.4149 + 9172.10i) q^{48} -15304.9 q^{49} +3116.62i q^{51} +(-3625.32 - 3648.09i) q^{52} -11915.0 q^{53} +(-7897.79 + 18982.9i) q^{54} +(-12272.8 - 30027.0i) q^{56} +20857.0i q^{57} +(26136.0 + 10873.8i) q^{58} +38457.4i q^{59} -37921.2i q^{61} +(4769.43 - 11463.6i) q^{62} -29167.5i q^{63} +(23387.0 - 22951.9i) q^{64} +(-30597.6 - 12730.1i) q^{66} +30414.5 q^{67} +(7897.63 - 7848.35i) q^{68} +36984.5i q^{69} -4849.25 q^{71} +(27273.8 - 11147.4i) q^{72} +39210.6i q^{73} +(5215.87 - 12536.7i) q^{74} +(52852.5 - 52522.6i) q^{76} +117202. q^{77} +(3128.27 - 7519.01i) q^{78} -68793.5 q^{79} +6996.32 q^{81} +(-30150.0 + 72467.5i) q^{82} -63154.8 q^{83} +(36433.4 - 36206.1i) q^{84} +(20427.0 - 49097.8i) q^{86} +44823.7i q^{87} +(44793.1 + 109593. i) q^{88} -29719.5 q^{89} +28801.0i q^{91} +(93720.0 - 93135.2i) q^{92} +19660.4 q^{93} +(27530.4 + 11454.0i) q^{94} +(47779.8 + 20230.5i) q^{96} -47746.8i q^{97} +(-33256.9 + 79935.3i) q^{98} +106455. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9}+O(q^{10}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9	$ 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49} - 177894 q^{54} - 73816 q^{56} - 230354 q^{64} + 262878 q^{66} - 15448 q^{71} - 4224 q^{74} + 111902 q^{76} + 15560 q^{79} + 193968 q^{81} + 195112 q^{84} - 131972 q^{86} + 6320 q^{89} + 117080 q^{94} + 115582 q^{96}+O(q^{100}) $ 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

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 $

$2$	2.17296	−	5.22286i	0.384129	−	0.923280i
$2$	2.17296	−	5.22286i	0.384129	−	0.923280i
$3$	8.95730			0.574611			0.287306	−	0.957839i	$-0.407240\pi$
$3$	8.95730			0.574611			0.287306	+	0.957839i	$0.407240\pi$
$4$	−22.5565	−	22.6981i	−0.704890	−	0.709316i
$5$		0			0
$5$		0			0
$6$	19.4639	−	46.7827i	0.220725	−	0.530527i
$7$			179.198i			1.38225i	0.722733	+	0.691127i	$0.242885\pi$
$7$			179.198i			1.38225i	−0.722733	+	0.691127i	$0.757115\pi$
$8$	−167.563	+	68.4872i	−0.925666	+	0.378342i
$9$	−162.767			−0.669822
$10$		0			0
$11$		−	654.036i		−	1.62975i	−0.579640	−	0.814873i	$-0.696807\pi$
$11$		−	654.036i		−	1.62975i	0.579640	−	0.814873i	$-0.303193\pi$
$12$	−202.045	−	203.314i	−0.405038	−	0.407581i
$13$	160.722			0.263765			0.131882	−	0.991265i	$-0.457898\pi$
$13$	160.722			0.263765			0.131882	+	0.991265i	$0.457898\pi$
$14$	935.925	+	389.390i	1.27621	+	0.530964i
$15$		0			0
$16$	−6.40984	+	1023.98i	−0.00625961	+	0.999980i
$17$			347.942i			0.292001i	0.989285	+	0.146001i	$0.0466401\pi$
$17$			347.942i			0.292001i	−0.989285	+	0.146001i	$0.953360\pi$
$18$	−353.686	+	850.107i	−0.257298	+	0.618433i
$19$			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
$22$	−3415.94	−	1421.19i	−1.50471	−	0.626032i
$23$			4128.97i			1.62751i	0.581211	+	0.813753i	$0.302579\pi$
$23$			4128.97i			1.62751i	−0.581211	+	0.813753i	$0.697421\pi$
$24$	−1500.92	+	613.460i	−0.531898	+	0.217399i
$25$		0			0
$26$	349.243	−	839.428i	0.101320	−	0.243529i
$27$	−3634.58			−0.959498
$28$	4067.46	−	4042.08i	0.980456	−	0.974337i
$29$			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	$0.434246\pi$
$32$	5334.17	+	2258.55i	0.920857	+	0.389901i
$33$		−	5858.40i		−	0.936470i
$34$	1817.25	+	756.064i	0.269599	+	0.112166i
$35$		0			0
$36$	3671.45	+	3694.50i	0.472151	+	0.475116i
$37$	2400.35			0.288251			0.144125	−	0.989559i	$-0.453963\pi$
$37$	2400.35			0.288251			0.144125	+	0.989559i	$0.453963\pi$
$38$	12161.4	+	5059.73i	1.36623	+	0.568418i
$39$	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	$0.722948\pi$
$42$	8383.37	+	3487.88i	0.733323	+	0.305098i
$43$	9400.56			0.775323			0.387661	−	0.921802i	$-0.373283\pi$
$43$	9400.56			0.775323			0.387661	+	0.921802i	$0.373283\pi$
$44$	−14845.4	+	14752.8i	−1.15601	+	1.14879i
$45$		0			0
$46$	21565.0	+	8972.10i	1.50264	+	0.625172i
$47$			5271.14i			0.348065i	0.984740	+	0.174032i	$0.0556797\pi$
$47$			5271.14i			0.348065i	−0.984740	+	0.174032i	$0.944320\pi$
$48$	−57.4149	+	9172.10i	−0.00359684	+	0.574600i
$49$	−15304.9			−0.910626
$50$		0			0
$51$			3116.62i			0.167787i
$52$	−3625.32	−	3648.09i	−0.185925	−	0.187093i
$53$	−11915.0			−0.582644			−0.291322	−	0.956625i	$-0.594095\pi$
$53$	−11915.0			−0.582644			−0.291322	+	0.956625i	$0.594095\pi$
$54$	−7897.79	+	18982.9i	−0.368571	+	0.885885i
$55$		0			0
$56$	−12272.8	−	30027.0i	−0.522965	−	1.27951i
$57$			20857.0i			0.850286i
$58$	26136.0	+	10873.8i	1.02016	+	0.424436i
$59$			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	$-0.773754\pi$
$61$		−	37921.2i		−	1.30484i	0.757857	−	0.652421i	$-0.226246\pi$
$62$	4769.43	−	11463.6i	0.157575	−	0.378742i
$63$		−	29167.5i		−	0.925864i
$64$	23387.0	−	22951.9i	0.713715	−	0.700436i
$65$		0			0
$66$	−30597.6	−	12730.1i	−0.864624	−	0.359725i
$67$	30414.5			0.827739			0.413870	−	0.910336i	$-0.364177\pi$
$67$	30414.5			0.827739			0.413870	+	0.910336i	$0.364177\pi$
$68$	7897.63	−	7848.35i	0.207121	−	0.205829i
$69$			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	$0.518180\pi$
$72$	27273.8	−	11147.4i	0.620031	−	0.253422i
$73$			39210.6i			0.861185i	0.902546	+	0.430593i	$0.141695\pi$
$73$			39210.6i			0.861185i	−0.902546	+	0.430593i	$0.858305\pi$
$74$	5215.87	−	12536.7i	0.110725	−	0.266136i
$75$		0			0
$76$	52852.5	−	52522.6i	1.04962	−	1.04307i
$77$	117202.			2.25272
$78$	3128.27	−	7519.01i	0.0582194	−	0.139934i
$79$	−68793.5			−1.24016			−0.620082	−	0.784537i	$-0.712901\pi$
$79$	−68793.5			−1.24016			−0.620082	+	0.784537i	$0.712901\pi$
$80$		0			0
$81$	6996.32			0.118483
$82$	−30150.0	+	72467.5i	−0.495167	+	1.19017i
$83$	−63154.8			−1.00626			−0.503131	−	0.864210i	$-0.667819\pi$
$83$	−63154.8			−1.00626			−0.503131	+	0.864210i	$0.667819\pi$
$84$	36433.4	−	36206.1i	0.563381	−	0.559865i
$85$		0			0
$86$	20427.0	−	49097.8i	0.297824	−	0.715839i
$87$			44823.7i			0.634907i
$88$	44793.1	+	109593.i	0.616601	+	1.50860i
$89$	−29719.5			−0.397709			−0.198855	−	0.980029i	$-0.563722\pi$
$89$	−29719.5			−0.397709			−0.198855	+	0.980029i	$0.563722\pi$
$90$		0			0
$91$			28801.0i			0.364590i
$92$	93720.0	−	93135.2i	1.15442	−	1.14721i
$93$	19660.4			0.235714
$94$	27530.4	+	11454.0i	0.321361	+	0.133702i
$95$		0			0
$96$	47779.8	+	20230.5i	0.529135	+	0.224041i
$97$		−	47746.8i		−	0.515247i	−0.966245	−	0.257623i	$-0.917061\pi$
$97$		−	47746.8i		−	0.515247i	0.966245	−	0.257623i	$-0.0829394\pi$
$98$	−33256.9	+	79935.3i	−0.349798	+	0.840763i
$99$			106455.i			1.09164i
$100$		0			0
$101$			178313.i			1.73932i	0.493649	+	0.869661i	$0.335663\pi$
$101$			178313.i			1.73932i	−0.493649	+	0.869661i	$0.664337\pi$
$102$	16277.7	+	6772.29i	0.154914	+	0.0644518i
$103$		−	202181.i		−	1.87779i	−0.344201	−	0.938896i	$-0.611850\pi$
$103$		−	202181.i		−	1.87779i	0.344201	−	0.938896i	$-0.388150\pi$
$104$	−26931.1	+	11007.4i	−0.244158	+	0.0997933i
$105$		0			0
$106$	−25890.8	+	62230.2i	−0.223810	+	0.537943i
$107$	−73035.1			−0.616698			−0.308349	−	0.951273i	$-0.599776\pi$
$107$	−73035.1			−0.616698			−0.308349	+	0.951273i	$0.599776\pi$
$108$	81983.3	+	82498.0i	0.676341	+	0.680588i
$109$		−	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
$112$	−183495.	−	1148.63i	−1.38223	−	0.00865238i
$113$		−	169893.i		−	1.25164i	−0.779969	−	0.625818i	$-0.784765\pi$
$113$		−	169893.i		−	1.25164i	0.779969	−	0.625818i	$-0.215235\pi$
$114$	108933.	+	45321.5i	0.785052	+	0.326619i
$115$		0			0
$116$	113585.	−	112876.i	0.783747	−	0.778856i
$117$	−26160.2			−0.176675
$118$	200858.	+	83566.5i	1.32796	+	0.552493i
$119$	−62350.5			−0.403620
$120$		0			0
$121$	−266712.			−1.65607
$122$	−198057.	−	82401.3i	−1.20473	−	0.501227i
$123$	−124283.			−0.740712
$124$	−49509.2	−	49820.1i	−0.289156	−	0.290971i
$125$		0			0
$126$	−152337.	−	63379.7i	−0.854831	−	0.355651i
$127$		−	113667.i		−	0.625351i	−0.949860	−	0.312676i	$-0.898775\pi$
$127$		−	113667.i		−	0.625351i	0.949860	−	0.312676i	$-0.101225\pi$
$128$	−69055.5	−	172021.i	−0.372540	−	0.928016i
$129$	84203.6			0.445509
$130$		0			0
$131$			214049.i			1.08977i	0.838510	+	0.544886i	$0.183427\pi$
$131$			214049.i			1.08977i	−0.838510	+	0.544886i	$0.816573\pi$
$132$	−132975.	+	132145.i	−0.664254	+	0.660109i
$133$	−417261.			−2.04540
$134$	66089.5	−	158851.i	0.317958	−	0.764235i
$135$		0			0
$136$	−23829.6	−	58302.3i	−0.110476	−	0.270295i
$137$			326516.i			1.48629i	0.669131	+	0.743144i	$0.266666\pi$
$137$			326516.i			1.48629i	−0.669131	+	0.743144i	$0.733334\pi$
$138$	193165.	+	80365.8i	0.863436	+	0.359231i
$139$		−	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
$142$	−10537.2	+	25327.0i	−0.0438536	+	0.105405i
$143$		−	105118.i		−	0.429870i
$144$	1043.31	−	166670.i	0.00419283	−	0.669809i
$145$		0			0
$146$	204791.	+	85203.1i	0.795115	+	0.330806i
$147$	−137091.			−0.523256
$148$	−54143.5	−	54483.5i	−0.203185	−	0.204461i
$149$			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	$0.312306\pi$
$152$	−159472.	−	390170.i	−0.559855	−	1.36976i
$153$		−	56633.4i		−	0.195589i
$154$	254675.	−	612129.i	0.865336	−	2.07989i
$155$		0			0
$156$	−32473.1	−	32677.0i	−0.106835	−	0.107506i
$157$	−226057.			−0.731930			−0.365965	−	0.930629i	$-0.619261\pi$
$157$	−226057.			−0.731930			−0.365965	+	0.930629i	$0.619261\pi$
$158$	−149485.	+	359298.i	−0.476383	+	1.14502i
$159$	−106726.			−0.334794
$160$		0			0
$161$	−739904.			−2.24963
$162$	15202.7	−	36540.8i	0.0455129	−	0.109393i
$163$	−281116.			−0.828737			−0.414368	−	0.910109i	$-0.635997\pi$
$163$	−281116.			−0.828737			−0.414368	+	0.910109i	$0.635997\pi$
$164$	312973.	+	314938.i	0.908650	+	0.914356i
$165$		0			0
$166$	−137233.	+	329848.i	−0.386534	+	0.929061i
$167$		−	249160.i		−	0.691332i	−0.938358	−	0.345666i	$-0.887653\pi$
$167$		−	249160.i		−	0.691332i	0.938358	−	0.345666i	$-0.112347\pi$
$168$	−109931.	−	268961.i	−0.300501	−	0.735218i
$169$	−345461.			−0.930428
$170$		0			0
$171$		−	379001.i		−	0.991175i
$172$	−212044.	−	213375.i	−0.546517	−	0.549949i
$173$	259080.			0.658142			0.329071	−	0.944305i	$-0.393265\pi$
$173$	259080.			0.658142			0.329071	+	0.944305i	$0.393265\pi$
$174$	234108.	+	97400.2i	0.586196	+	0.243886i
$175$		0			0
$176$	669720.	+	4192.27i	1.62971	+	0.0102016i
$177$			344475.i			0.826465i
$178$	−64579.2	+	155221.i	−0.152772	+	0.367197i
$179$		−	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	$0.254388\pi$
$181$			631854.i			1.43358i	−0.697292	+	0.716788i	$0.745612\pi$
$182$	150424.	+	62583.5i	0.336619	+	0.140050i
$183$		−	339672.i		−	0.749776i
$184$	−282782.	−	691865.i	−0.615754	−	1.50653i
$185$		0			0
$186$	42721.2	−	102683.i	0.0905443	−	0.217629i
$187$	227566.			0.475887
$188$	119645.	−	118898.i	0.246888	−	0.245347i
$189$		−	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	$0.495345\pi$
$192$	209485.	−	205587.i	0.410109	−	0.402479i
$193$			383951.i			0.741963i	0.928640	+	0.370982i	$0.120979\pi$
$193$			383951.i			0.741963i	−0.928640	+	0.370982i	$0.879021\pi$
$194$	−249375.	−	103752.i	−0.475717	−	0.197921i
$195$		0			0
$196$	345225.	+	347392.i	0.641891	+	0.645922i
$197$	676505.			1.24195			0.620977	−	0.783829i	$-0.286736\pi$
$197$	676505.			1.24195			0.620977	+	0.783829i	$0.286736\pi$
$198$	556001.	+	231323.i	1.00789	+	0.419330i
$199$	72641.1			0.130032			0.0650160	−	0.997884i	$-0.479290\pi$
$199$	72641.1			0.130032			0.0650160	+	0.997884i	$0.479290\pi$
$200$		0			0
$201$	272432.			0.475628
$202$	931305.	+	387468.i	1.60588	+	0.668124i
$203$	−896734.			−1.52730
$204$	70741.4	−	70300.0i	0.119014	−	0.118271i
$205$		0			0
$206$	−1.05596e6	−	439331.i	−1.73373	−	0.721314i
$207$		−	672060.i		−	1.09014i
$208$	−1030.20	+	164576.i	−0.00165107	+	0.263760i
$209$	1.52292e6			2.41163
$210$		0			0
$211$		−	945366.i		−	1.46182i	−0.682474	−	0.730910i	$-0.739096\pi$
$211$		−	945366.i		−	1.46182i	0.682474	−	0.730910i	$-0.260904\pi$
$212$	268760.	+	270447.i	0.410700	+	0.413279i
$213$	−43436.2			−0.0655999
$214$	−158702.	+	381452.i	−0.236891	+	0.569384i
$215$		0			0
$216$	609022.	−	248922.i	0.888175	−	0.363018i
$217$			393321.i			0.567020i
$218$	−669462.	−	278528.i	−0.954079	−	0.396943i
$219$			351221.i			0.494847i
$220$		0			0
$221$			55921.9i			0.0770196i
$222$	46720.1	−	112295.i	0.0636241	−	0.152925i
$223$		−	788483.i		−	1.06177i	−0.847444	−	0.530885i	$-0.821860\pi$
$223$		−	788483.i		−	1.06177i	0.847444	−	0.530885i	$-0.178140\pi$
$224$	−404727.	+	955873.i	−0.538942	+	1.27286i
$225$		0			0
$226$	−887324.	−	369170.i	−1.15561	−	0.480789i
$227$	109073.			0.140492			0.0702461	−	0.997530i	$-0.477622\pi$
$227$	109073.			0.140492			0.0702461	+	0.997530i	$0.477622\pi$
$228$	473415.	−	470461.i	0.603122	−	0.599359i
$229$			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
$232$	−342720.	−	838513.i	−0.418042	−	1.02280i
$233$			1.63628e6i			1.97455i	0.159019	+	0.987276i	$0.449167\pi$
$233$			1.63628e6i			1.97455i	−0.159019	+	0.987276i	$0.550833\pi$
$234$	−56845.1	+	136631.i	−0.0678661	+	0.163121i
$235$		0			0
$236$	872912.	−	867465.i	1.02021	−	1.01385i
$237$	−616204.			−0.712613
$238$	−135485.	+	325648.i	−0.155042	+	0.372654i
$239$	−1.57183e6			−1.77997			−0.889984	−	0.455992i	$-0.849285\pi$
$239$	−1.57183e6			−1.77997			−0.889984	+	0.455992i	$0.849285\pi$
$240$		0			0
$241$	−1.28582e6			−1.42606			−0.713032	−	0.701132i	$-0.752679\pi$
$241$	−1.28582e6			−1.42606			−0.713032	+	0.701132i	$0.752679\pi$
$242$	−579555.	+	1.39300e6i	−0.636145	+	1.52902i
$243$	945870.			1.02758
$244$	−860741.	+	855369.i	−0.925545	+	0.919770i
$245$		0			0
$246$	−270062.	+	649113.i	−0.284529	+	0.683884i
$247$			374240.i			0.390309i
$248$	−367785.	+	150322.i	−0.379721	+	0.155201i
$249$	−565697.			−0.578209
$250$		0			0
$251$			33849.3i			0.0339130i	0.999856	+	0.0169565i	$0.00539767\pi$
$251$			33849.3i			0.0339130i	−0.999856	+	0.0169565i	$0.994602\pi$
$252$	−662047.	+	657915.i	−0.656731	+	0.652633i
$253$	2.70050e6			2.65242
$254$	−593665.	−	246993.i	−0.577374	−	0.240215i
$255$		0			0
$256$	−1.04849e6	−	13127.1i	−0.999922	−	0.0125190i
$257$		−	135717.i		−	0.128175i	−0.997944	−	0.0640873i	$-0.979586\pi$
$257$		−	135717.i		−	0.128175i	0.997944	−	0.0640873i	$-0.0204136\pi$
$258$	182971.	−	439784.i	0.171133	−	0.411329i
$259$			430138.i			0.398436i
$260$		0			0
$261$		−	814510.i		−	0.740108i
$262$	1.11795e6	+	465121.i	1.00616	+	0.418613i
$263$		−	30802.7i		−	0.0274599i	−0.999906	−	0.0137300i	$-0.995629\pi$
$263$		−	30802.7i		−	0.0274599i	0.999906	−	0.0137300i	$-0.00437052\pi$
$264$	401225.	+	981653.i	0.354306	+	0.866859i
$265$		0			0
$266$	−906692.	+	2.17930e6i	−0.785698	+	1.88848i
$267$	−266206.			−0.228528
$268$	−686044.	−	690352.i	−0.583465	−	0.587129i
$269$			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	$0.0617380\pi$
$272$	−356286.	−	2230.25i	−0.291995	−	0.00182781i
$273$			257980.i			0.209498i
$274$	1.70535e6	+	709507.i	1.37226	+	0.570926i
$275$		0			0
$276$	839478.	−	834240.i	0.663341	−	0.659201i
$277$	363646.			0.284760			0.142380	−	0.989812i	$-0.454525\pi$
$277$	363646.			0.284760			0.142380	+	0.989812i	$0.454525\pi$
$278$	−385234.	−	160276.i	−0.298960	−	0.124382i
$279$	−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	$0.513668\pi$
$282$	246598.	+	102597.i	0.184658	+	0.0768265i
$283$	2.62353e6			1.94724			0.973621	−	0.228170i	$-0.0732743\pi$
$283$	2.62353e6			1.94724			0.973621	+	0.228170i	$0.0732743\pi$
$284$	109382.	+	110069.i	0.0804730	+	0.0809783i
$285$		0			0
$286$	−549016.	−	228417.i	−0.396890	−	0.165125i
$287$		−	2.48638e6i		−	1.78182i
$288$	−868226.	−	367616.i	−0.616810	−	0.261164i
$289$	1.29879e6			0.914735
$290$		0			0
$291$		−	427683.i		−	0.296067i
$292$	890008.	−	884454.i	0.610853	−	0.607041i
$293$	−92025.7			−0.0626239			−0.0313120	−	0.999510i	$-0.509969\pi$
$293$	−92025.7			−0.0626239			−0.0313120	+	0.999510i	$0.509969\pi$
$294$	−297892.	+	716005.i	−0.200998	+	0.483112i
$295$		0			0
$296$	−402211.	+	164393.i	−0.266824	+	0.109057i
$297$			2.37714e6i			1.56374i
$298$	1.93470e6	+	804927.i	1.26204	+	0.525068i
$299$			663617.i			0.429279i
$300$		0			0
$301$			1.68456e6i			1.07169i
$302$	677110.	−	1.62748e6i	0.427211	−	1.02683i
$303$			1.59721e6i			0.999434i
$304$	−2.38433e6	−	14925.3i	−1.47973	−	0.00926272i
$305$		0			0
$306$	−295788.	−	123062.i	−0.180583	−	0.0751312i
$307$	−622926.			−0.377216			−0.188608	−	0.982052i	$-0.560398\pi$
$307$	−622926.			−0.377216			−0.188608	+	0.982052i	$0.560398\pi$
$308$	−2.64366e6	−	2.66026e6i	−1.58792	−	1.59789i
$309$		−	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	$0.207513\pi$
$312$	−241230.	+	98596.6i	−0.140296	+	0.0573423i
$313$			2.66765e6i			1.53910i	0.638584	+	0.769552i	$0.279521\pi$
$313$			2.66765e6i			1.53910i	−0.638584	+	0.769552i	$0.720479\pi$
$314$	−491214.	+	1.18067e6i	−0.281155	+	0.675776i
$315$		0			0
$316$	1.55174e6	+	1.56148e6i	0.874180	+	0.879669i
$317$	1.44609e6			0.808253			0.404126	−	0.914703i	$-0.367576\pi$
$317$	1.44609e6			0.808253			0.404126	+	0.914703i	$0.367576\pi$
$318$	−231911.	+	557415.i	−0.128604	+	0.309108i
$319$	3.27290e6			1.80076
$320$		0			0
$321$	−654198.			−0.354361
$322$	−1.60778e6	+	3.86441e6i	−0.864146	+	2.07703i
$323$	−810181.			−0.432091
$324$	−157812.	−	158803.i	−0.0835178	−	0.0840422i
$325$		0			0
$326$	−610854.	+	1.46823e6i	−0.318342	+	0.765156i
$327$		−	1.14814e6i		−	0.593780i
$328$	2.32495e6	−	950264.i	1.19324	−	0.487708i
$329$	−944578.			−0.481114
$330$		0			0
$331$		−	1.67533e6i		−	0.840485i	−0.907412	−	0.420243i	$-0.861945\pi$
$331$		−	1.67533e6i		−	0.840485i	0.907412	−	0.420243i	$-0.138055\pi$
$332$	1.42455e6	+	1.43350e6i	0.709304	+	0.713758i
$333$	−390697.			−0.193077
$334$	−1.30133e6	−	541414.i	−0.638293	−	0.265561i
$335$		0			0
$336$	−1.64362e6	−	10288.6i	−0.794243	−	0.00497175i
$337$		−	2.19636e6i		−	1.05348i	−0.850025	−	0.526742i	$-0.823413\pi$
$337$		−	2.19636e6i		−	1.05348i	0.850025	−	0.526742i	$-0.176587\pi$
$338$	−750674.	+	1.80430e6i	−0.357404	+	0.859045i
$339$		−	1.52178e6i		−	0.719204i
$340$		0			0
$341$		−	1.43554e6i		−	0.668544i
$342$	−1.97947e6	−	823555.i	−0.915132	−	0.380739i
$343$			269174.i			0.123537i
$344$	−1.57519e6	+	643818.i	−0.717690	+	0.293337i
$345$		0			0
$346$	562971.	−	1.35314e6i	0.252811	−	0.607649i
$347$	−3.79947e6			−1.69395			−0.846973	−	0.531635i	$-0.821578\pi$
$347$	−3.79947e6			−1.69395			−0.846973	+	0.531635i	$0.821578\pi$
$348$	1.01741e6	−	1.01107e6i	0.450350	−	0.447539i
$349$		−	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
$352$	1.47717e6	−	3.48874e6i	0.635439	−	1.50076i
$353$		−	1.42770e6i		−	0.609820i	−0.952381	−	0.304910i	$-0.901374\pi$
$353$		−	1.42770e6i		−	0.609820i	0.952381	−	0.304910i	$-0.0986263\pi$
$354$	1.79914e6	+	748530.i	0.763058	+	0.317469i
$355$		0			0
$356$	670367.	+	674576.i	0.280342	+	0.282102i
$357$	−558492.			−0.231924
$358$	−1.11414e6	−	463534.i	−0.459442	−	0.191150i
$359$	987956.			0.404577			0.202289	−	0.979326i	$-0.435162\pi$
$359$	987956.			0.404577			0.202289	+	0.979326i	$0.435162\pi$
$360$		0			0
$361$	−2.94579e6			−1.18969
$362$	3.30008e6	+	1.37299e6i	1.32359	+	0.550677i
$363$	−2.38902e6			−0.951597
$364$	653730.	−	649650.i	0.258610	−	0.256996i
$365$		0			0
$366$	−1.77406e6	−	738093.i	−0.692253	−	0.288011i
$367$			2.25218e6i			0.872848i	0.899741	+	0.436424i	$0.143755\pi$
$367$			2.25218e6i			0.872848i	−0.899741	+	0.436424i	$0.856245\pi$
$368$	−4.22799e6	−	26466.1i	−1.62747	−	0.0101876i
$369$	2.25840e6			0.863445
$370$		0			0
$371$		−	2.13514e6i		−	0.805362i
$372$	−443469.	−	446254.i	−0.166152	−	0.167195i
$373$	2.21460e6			0.824184			0.412092	−	0.911142i	$-0.364798\pi$
$373$	2.21460e6			0.824184			0.412092	+	0.911142i	$0.364798\pi$
$374$	494493.	−	1.18855e6i	0.182802	−	0.439377i
$375$		0			0
$376$	−361006.	−	883251.i	−0.131687	−	0.322192i
$377$			804278.i			0.291442i
$378$	−3.40169e6	−	1.41527e6i	−1.22452	−	0.509459i
$379$		−	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
$382$	32044.8	−	77021.9i	0.0112357	−	0.0270057i
$383$		−	1.97304e6i		−	0.687287i	−0.939100	−	0.343643i	$-0.888339\pi$
$383$		−	1.97304e6i		−	0.687287i	0.939100	−	0.343643i	$-0.111661\pi$
$384$	−618551.	−	1.54084e6i	−0.214066	−	0.533248i
$385$		0			0
$386$	2.00532e6	+	834310.i	0.685040	+	0.285009i
$387$	−1.53010e6			−0.519328
$388$	−1.08376e6	+	1.07700e6i	−0.365473	+	0.363192i
$389$		−	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
$392$	2.56454e6	−	1.04819e6i	0.842936	−	0.344528i
$393$			1.91731e6i			0.626196i
$394$	1.47002e6	−	3.53329e6i	0.477070	−	1.14667i
$395$		0			0
$396$	2.41634e6	−	2.40126e6i	0.774318	−	0.769486i
$397$	3.46065e6			1.10200			0.551000	−	0.834506i	$-0.314247\pi$
$397$	3.46065e6			1.10200			0.551000	+	0.834506i	$0.314247\pi$
$398$	157846.	−	379394.i	0.0499490	−	0.120056i
$399$	−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	$0.423906\pi$
$402$	591984.	−	1.42287e6i	0.182703	−	0.439138i
$403$	352769.			0.108200
$404$	4.04738e6	−	4.02212e6i	1.23373	−	1.22603i
$405$		0			0
$406$	−1.94857e6	+	4.68351e6i	−0.586679	+	1.41012i
$407$		−	1.56992e6i		−	0.469776i
$408$	−213449.	−	522232.i	−0.0634809	−	0.155315i
$409$	644424.			0.190486			0.0952432	−	0.995454i	$-0.469637\pi$
$409$	644424.			0.190486			0.0952432	+	0.995454i	$0.469637\pi$
$410$		0			0
$411$			2.92470e6i			0.854038i
$412$	−4.58913e6	+	4.56049e6i	−1.33195	+	1.32364i
$413$	−6.89149e6			−1.98810
$414$	−3.51007e6	−	1.46036e6i	−1.00650	−	0.418754i
$415$		0			0
$416$	857319.	+	362998.i	0.242890	+	0.102842i
$417$		−	660684.i		−	0.186060i
$418$	3.30924e6	−	7.95399e6i	0.926377	−	2.22661i
$419$			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	$-0.928422\pi$
$421$		−	1.62181e6i		−	0.445960i	0.974823	−	0.222980i	$-0.0715784\pi$
$422$	−4.93751e6	−	2.05424e6i	−1.34967	−	0.561527i
$423$		−	857967.i		−	0.233141i
$424$	1.99651e6	−	816023.i	0.539334	−	0.220439i
$425$		0			0
$426$	−94385.2	+	226861.i	−0.0251988	+	0.0605670i
$427$	6.79540e6			1.80362
$428$	1.64742e6	+	1.65776e6i	0.434704	+	0.437434i
$429$		−	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	$0.546340\pi$
$432$	23297.1	−	3.72173e6i	0.00600609	−	0.959480i
$433$			936279.i			0.239986i	0.992775	+	0.119993i	$0.0382872\pi$
$433$			936279.i			0.239986i	−0.992775	+	0.119993i	$0.961713\pi$
$434$	2.05426e6	+	854672.i	0.523518	+	0.217809i
$435$		0			0
$436$	−2.90943e6	+	2.89127e6i	−0.732979	+	0.728405i
$437$	−9.61429e6			−2.40832
$438$	1.83438e6	+	763190.i	0.456882	+	0.190085i
$439$	−957065.			−0.237017			−0.118509	−	0.992953i	$-0.537811\pi$
$439$	−957065.			−0.237017			−0.118509	+	0.992953i	$0.537811\pi$
$440$		0			0
$441$	2.49113e6			0.609957
$442$	292072.	+	121516.i	0.0711106	+	0.0295854i
$443$	2.09764e6			0.507833			0.253917	−	0.967226i	$-0.418281\pi$
$443$	2.09764e6			0.507833			0.253917	+	0.967226i	$0.418281\pi$
$444$	−484980.	−	488025.i	−0.116752	−	0.117486i
$445$		0			0
$446$	−4.11813e6	−	1.71334e6i	−0.980310	−	0.407856i
$447$			3.31804e6i			0.785440i
$448$	4.11293e6	+	4.19090e6i	0.968181	+	0.986535i
$449$	297855.			0.0697251			0.0348626	−	0.999392i	$-0.488901\pi$
$449$	297855.			0.0697251			0.0348626	+	0.999392i	$0.488901\pi$
$450$		0			0
$451$			9.07479e6i			2.10085i
$452$	−3.85624e6	+	3.83218e6i	−0.887806	+	0.882266i
$453$	2.79116e6			0.639057
$454$	237011.	−	569672.i	0.0539671	−	0.129714i
$455$		0			0
$456$	−1.42844e6	−	3.49487e6i	−0.321699	−	0.787081i
$457$		−	1.68614e6i		−	0.377661i	−0.982010	−	0.188831i	$-0.939530\pi$
$457$		−	1.68614e6i		−	0.377661i	0.982010	−	0.188831i	$-0.0604697\pi$
$458$	653034.	+	271694.i	0.145470	+	0.0605223i
$459$		−	1.26462e6i		−	0.280175i
$460$		0			0
$461$			5.80196e6i			1.27152i	0.771887	+	0.635759i	$0.219313\pi$
$461$			5.80196e6i			1.27152i	−0.771887	+	0.635759i	$0.780687\pi$
$462$	2.28120e6	−	5.48302e6i	0.497232	−	1.19513i
$463$		−	3.84592e6i		−	0.833774i	−0.908958	−	0.416887i	$-0.863121\pi$
$463$		−	3.84592e6i		−	0.833774i	0.908958	−	0.416887i	$-0.136879\pi$
$464$	−5.12415e6	−	32075.9i	−1.10491	−	0.00691645i
$465$		0			0
$466$	8.54607e6	+	3.55558e6i	1.82306	+	0.758482i
$467$	−682895.			−0.144898			−0.0724488	−	0.997372i	$-0.523081\pi$
$467$	−682895.			−0.144898			−0.0724488	+	0.997372i	$0.523081\pi$
$468$	590082.	+	593787.i	0.124537	+	0.125319i
$469$			5.45021e6i			1.14415i
$470$		0			0
$471$	−2.02486e6			−0.420575
$472$	−2.63384e6	−	6.44406e6i	−0.544170	−	1.33139i
$473$		−	6.14830e6i		−	1.26358i
$474$	−1.33899e6	+	3.21834e6i	−0.273735	+	0.657941i
$475$		0			0
$476$	1.40641e6	+	1.41524e6i	0.284508	+	0.286294i
$477$	1.93936e6			0.390268
$478$	−3.41553e6	+	8.20947e6i	−0.683737	+	1.64341i
$479$	868534.			0.172961			0.0864805	−	0.996254i	$-0.472438\pi$
$479$	868534.			0.172961			0.0864805	+	0.996254i	$0.472438\pi$
$480$		0			0
$481$	385789.			0.0760304
$482$	−2.79404e6	+	6.71568e6i	−0.547792	+	1.31666i
$483$	−6.62754e6			−1.29266
$484$	6.01609e6	+	6.05386e6i	1.16735	+	1.17468i
$485$		0			0
$486$	2.05534e6	−	4.94014e6i	0.394723	−	0.948744i
$487$			1.42739e6i			0.272722i	0.990659	+	0.136361i	$0.0435407\pi$
$487$			1.42739e6i			0.272722i	−0.990659	+	0.136361i	$0.956459\pi$
$488$	2.59712e6	+	6.35421e6i	0.493676	+	1.20785i
$489$	−2.51804e6			−0.476201
$490$		0			0
$491$		−	2.37311e6i		−	0.444237i	−0.975020	−	0.222118i	$-0.928703\pi$
$491$		−	2.37311e6i		−	0.444237i	0.975020	−	0.222118i	$-0.0712972\pi$
$492$	2.80339e6	+	2.82099e6i	0.522120	+	0.525399i
$493$	−1.74115e6			−0.322641
$494$	1.95460e6	+	813209.i	0.360364	+	0.149929i
$495$		0			0
$496$	−14069.0	+	2.24753e6i	−0.00256778	+	0.410206i
$497$		−	868976.i		−	0.157804i
$498$	−1.22924e6	+	2.95455e6i	−0.222107	+	0.533849i
$499$		−	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
$502$	176790.	+	73553.2i	0.0313111	+	0.0130269i
$503$			3.36518e6i			0.593046i	0.955026	+	0.296523i	$0.0958272\pi$
$503$			3.36518e6i			0.593046i	−0.955026	+	0.296523i	$0.904173\pi$
$504$	1.99760e6	+	4.88740e6i	0.350293	+	0.857041i
$505$		0			0
$506$	5.86807e6	−	1.41043e7i	1.01887	−	2.44893i
$507$	−3.09440e6			−0.534634
$508$	−2.58002e6	+	2.56392e6i	−0.443572	+	0.440804i
$509$			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
$512$	−2.34690e6	+	5.44761e6i	−0.395657	+	0.918398i
$513$		−	8.46309e6i		−	1.41983i
$514$	−708831.	−	294908.i	−0.118341	−	0.0492355i
$515$		0			0
$516$	−1.89934e6	−	1.91126e6i	−0.314035	−	0.316007i
$517$	3.44752e6			0.567257
$518$	2.24655e6	+	934673.i	0.367868	+	0.153051i
$519$	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	$0.345433\pi$
$522$	−4.25407e6	−	1.76990e6i	−0.683327	−	0.284297i
$523$	−1.80930e6			−0.289238			−0.144619	−	0.989487i	$-0.546196\pi$
$523$	−1.80930e6			−0.289238			−0.144619	+	0.989487i	$0.546196\pi$
$524$	4.85852e6	−	4.82820e6i	0.772994	−	0.768170i
$525$		0			0
$526$	−160878.	−	66933.0i	−0.0253532	−	0.0105481i
$527$			763697.i			0.119783i
$528$	5.99888e6	+	37551.4i	0.936452	+	0.00586194i
$529$	−1.06121e7			−1.64878
$530$		0			0
$531$		−	6.25959e6i		−	0.963407i
$532$	9.41195e6	+	9.47105e6i	1.44178	+	1.45084i
$533$	−2.23003e6			−0.340010
$534$	−578456.	+	1.39036e6i	−0.0877843	+	0.210996i
$535$		0			0
$536$	−5.09636e6	+	2.08300e6i	−0.766210	+	0.313168i
$537$		−	1.91077e6i		−	0.285938i
$538$	6.53443e6	+	2.71864e6i	0.973312	+	0.404945i
$539$			1.00100e7i			1.48409i
$540$		0			0
$541$			1.13257e7i			1.66369i	0.555005	+	0.831847i	$0.312716\pi$
$541$			1.13257e7i			1.66369i	−0.555005	+	0.831847i	$0.687284\pi$
$542$	5.15566e6	−	1.23920e7i	0.753852	−	1.81194i
$543$			5.65971e6i			0.823748i
$544$	−785843.	+	1.85598e6i	−0.113851	+	0.268891i
$545$		0			0
$546$	1.34739e6	+	560580.i	0.193425	+	0.0804740i
$547$	8.98785e6			1.28436			0.642181	−	0.766553i	$-0.278030\pi$
$547$	8.98785e6			1.28436			0.642181	+	0.766553i	$0.278030\pi$
$548$	7.41130e6	−	7.36506e6i	1.05425	−	1.04767i
$549$			6.17231e6i			0.874011i
$550$		0			0
$551$	−1.16521e7			−1.63503
$552$	−2.53296e6	−	6.19725e6i	−0.353819	−	0.865667i
$553$		−	1.23276e7i		−	1.71422i
$554$	790188.	−	1.89927e6i	0.109385	−	0.262913i
$555$		0			0
$556$	−1.67420e6	+	1.66375e6i	−0.229678	+	0.228245i
$557$	2.29740e6			0.313761			0.156881	−	0.987618i	$-0.449856\pi$
$557$	2.29740e6			0.313761			0.156881	+	0.987618i	$0.449856\pi$
$558$	−776304.	+	1.86590e6i	−0.105547	+	0.253690i
$559$	1.51088e6			0.204503
$560$		0			0
$561$	2.03838e6			0.273450
$562$	−246920.	+	593489.i	−0.0329773	+	0.0792633i
$563$	9.84032e6			1.30839			0.654197	−	0.756325i	$-0.273007\pi$
$563$	9.84032e6			1.30839			0.654197	+	0.756325i	$0.273007\pi$
$564$	1.07170e6	−	1.06501e6i	0.141865	−	0.140979i
$565$		0			0
$566$	5.70083e6	−	1.37023e7i	0.747992	−	1.79785i
$567$			1.25373e6i			0.163774i
$568$	812557.	−	332112.i	0.105678	−	0.0431930i
$569$	−8.12763e6			−1.05241			−0.526203	−	0.850359i	$-0.676385\pi$
$569$	−8.12763e6			−1.05241			−0.526203	+	0.850359i	$0.676385\pi$
$570$		0			0
$571$			6.86636e6i			0.881325i	0.897673	+	0.440663i	$0.145256\pi$
$571$			6.86636e6i			0.881325i	−0.897673	+	0.440663i	$0.854744\pi$
$572$	−2.38598e6	+	2.37109e6i	−0.304914	+	0.303011i
$573$	132094.			0.0168072
$574$	−1.29860e7	−	5.40281e6i	−1.64511	−	0.684447i
$575$		0			0
$576$	−3.80663e6	+	3.73581e6i	−0.478062	+	0.469168i
$577$			1.29988e7i			1.62541i	0.582672	+	0.812707i	$0.302007\pi$
$577$			1.29988e7i			1.62541i	−0.582672	+	0.812707i	$0.697993\pi$
$578$	2.82223e6	−	6.78341e6i	0.351376	−	0.844556i
$579$			3.43916e6i			0.426340i
$580$		0			0
$581$		−	1.13172e7i		−	1.39091i
$582$	−2.23373e6	−	929338.i	−0.273352	−	0.113728i
$583$			7.79282e6i			0.949561i
$584$	−2.68543e6	−	6.57027e6i	−0.325822	−	0.797170i
$585$		0			0
$586$	−199968.	+	480637.i	−0.0240556	+	0.0578194i
$587$	1.35189e7			1.61936			0.809682	−	0.586869i	$-0.199639\pi$
$587$	1.35189e7			1.61936			0.809682	+	0.586869i	$0.199639\pi$
$588$	3.09228e6	+	3.11170e6i	0.368838	+	0.371154i
$589$			5.11081e6i			0.607018i
$590$		0			0
$591$	6.05966e6			0.713640
$592$	−15385.9	+	2.45791e6i	−0.00180434	+	0.288245i
$593$			5.10786e6i			0.596489i	0.954490	+	0.298244i	$0.0964010\pi$
$593$			5.10786e6i			0.596489i	−0.954490	+	0.298244i	$0.903599\pi$
$594$	1.24155e7	+	5.16544e6i	1.44377	+	0.600677i
$595$		0			0
$596$	8.40804e6	−	8.35557e6i	0.969569	−	0.963519i
$597$	650669.			0.0747178
$598$	3.46598e6	+	1.44201e6i	0.396344	+	0.164898i
$599$	−6.28928e6			−0.716199			−0.358100	−	0.933683i	$-0.616575\pi$
$599$	−6.28928e6			−0.716199			−0.358100	+	0.933683i	$0.616575\pi$
$600$		0			0
$601$	6.51315e6			0.735538			0.367769	−	0.929917i	$-0.380122\pi$
$601$	6.51315e6			0.735538			0.367769	+	0.929917i	$0.380122\pi$
$602$	8.79822e6	+	3.66048e6i	0.989472	+	0.411668i
$603$	−4.95047e6			−0.554438
$604$	−7.02877e6	−	7.07290e6i	−0.783947	−	0.788870i
$605$		0			0
$606$	8.34198e6	+	3.47066e6i	0.922757	+	0.383911i
$607$			1.53932e7i			1.69574i	0.530207	+	0.847868i	$0.322114\pi$
$607$			1.53932e7i			1.69574i	−0.530207	+	0.847868i	$0.677886\pi$
$608$	−5.25901e6	+	1.24206e7i	−0.576959	+	1.36265i
$609$	−8.03232e6			−0.877602
$610$		0			0
$611$			847188.i			0.0918073i
$612$	−1.28547e6	+	1.27745e6i	−0.138734	+	0.137869i
$613$	−1.45172e7			−1.56038			−0.780191	−	0.625542i	$-0.784878\pi$
$613$	−1.45172e7			−1.56038			−0.780191	+	0.625542i	$0.784878\pi$
$614$	−1.35359e6	+	3.25345e6i	−0.144900	+	0.348276i
$615$		0			0
$616$	−1.96387e7	+	8.02683e6i	−2.08527	+	0.852299i
$617$		−	1.70658e7i		−	1.80473i	−0.430968	−	0.902367i	$-0.641828\pi$
$617$		−	1.70658e7i		−	1.80473i	0.430968	−	0.902367i	$-0.358172\pi$
$618$	−9.45858e6	−	3.93523e6i	−0.996219	−	0.414475i
$619$		−	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
$622$	5.89258e6	−	1.41632e7i	0.610703	−	1.46786i
$623$		−	5.32567e6i		−	0.549736i
$624$	−9227.84	+	1.47416e6i	−0.000948721	+	0.151559i
$625$		0			0
$626$	1.39328e7	+	5.79670e6i	1.42102	+	0.591214i
$627$	1.36412e7			1.38575
$628$	5.09906e6	+	5.13108e6i	0.515930	+	0.519170i
$629$			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	$0.669921\pi$
$632$	1.15273e7	−	4.71147e6i	1.14798	−	0.469206i
$633$		−	8.46793e6i		−	0.839978i
$634$	3.14230e6	−	7.55272e6i	0.310473	−	0.746243i
$635$		0			0
$636$	2.40736e6	+	2.42248e6i	0.235993	+	0.237475i
$637$	−2.45983e6			−0.240191
$638$	7.11187e6	−	1.70939e7i	0.691723	−	1.66260i
$639$	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	$0.471006\pi$
$642$	−1.42155e6	+	3.41678e6i	−0.136120	+	0.327175i
$643$	4.41604e6			0.421216			0.210608	−	0.977571i	$-0.432456\pi$
$643$	4.41604e6			0.421216			0.210608	+	0.977571i	$0.432456\pi$
$644$	1.66896e7	+	1.67944e7i	1.58574	+	1.59570i
$645$		0			0
$646$	−1.76049e6	+	4.23146e6i	−0.165979	+	0.398941i
$647$			3.77794e6i			0.354809i	0.984138	+	0.177404i	$0.0567700\pi$
$647$			3.77794e6i			0.354809i	−0.984138	+	0.177404i	$0.943230\pi$
$648$	−1.17233e6	+	479159.i	−0.109676	+	0.0448272i
$649$	2.51525e7			2.34407
$650$		0			0
$651$			3.52310e6i			0.325816i
$652$	6.34099e6	+	6.38081e6i	0.584168	+	0.587836i
$653$	1.44071e7			1.32219			0.661096	−	0.750301i	$-0.270092\pi$
$653$	1.44071e7			1.32219			0.661096	+	0.750301i	$0.270092\pi$
$654$	−5.99657e6	−	2.49486e6i	−0.548225	−	0.228088i
$655$		0			0
$656$	88937.0	−	1.42078e7i	0.00806906	−	1.28904i
$657$		−	6.38218e6i		−	0.576841i
$658$	−2.05253e6	+	4.93339e6i	−0.184810	+	0.444203i
$659$		−	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	$-0.925487\pi$
$661$		−	5.21128e6i		−	0.463917i	0.972726	−	0.231959i	$-0.0745134\pi$
$662$	−8.75001e6	−	3.64042e6i	−0.776003	−	0.322855i
$663$			500910.i			0.0442563i
$664$	1.05824e7	−	4.32529e6i	0.931462	−	0.380711i
$665$		0			0
$666$	−848970.	+	2.04056e6i	−0.0741663	+	0.178264i
$667$	−2.06620e7			−1.79828
$668$	−5.65546e6	+	5.62017e6i	−0.490373	+	0.487313i
$669$		−	7.06268e6i		−	0.610104i
$670$		0			0
$671$	−2.48018e7			−2.12656
$672$	−3.62526e6	+	8.56204e6i	−0.309682	+	0.731399i
$673$			8.07486e6i			0.687222i	0.939112	+	0.343611i	$0.111650\pi$
$673$			8.07486e6i			0.687222i	−0.939112	+	0.343611i	$0.888350\pi$
$674$	−1.14713e7	−	4.77260e6i	−0.972660	−	0.404674i
$675$		0			0
$676$	7.79240e6	+	7.84133e6i	0.655850	+	0.659968i
$677$	−1.37198e7			−1.15047			−0.575236	−	0.817988i	$-0.695090\pi$
$677$	−1.37198e7			−1.15047			−0.575236	+	0.817988i	$0.695090\pi$
$678$	−7.94803e6	−	3.30676e6i	−0.664027	−	0.276267i
$679$	8.55613e6			0.712202
$680$		0			0
$681$	976999.			0.0807284
$682$	−7.49764e6	−	3.11938e6i	−0.617253	−	0.256807i
$683$	−502514.			−0.0412189			−0.0206094	−	0.999788i	$-0.506561\pi$
$683$	−502514.			−0.0412189			−0.0206094	+	0.999788i	$0.506561\pi$
$684$	−8.60262e6	+	8.54894e6i	−0.703057	+	0.698670i
$685$		0			0
$686$	1.40586e6	+	584905.i	0.114059	+	0.0474542i
$687$			1.11997e6i			0.0905343i
$688$	−60256.1	+	9.62598e6i	−0.00485322	+	0.775307i
$689$	−1.91500e6			−0.153681
$690$		0			0
$691$			9.54427e6i			0.760409i	0.924902	+	0.380205i	$0.124146\pi$
$691$			9.54427e6i			0.760409i	−0.924902	+	0.380205i	$0.875854\pi$
$692$	−5.84394e6	−	5.88064e6i	−0.463918	−	0.466831i
$693$	−1.90766e7			−1.50892
$694$	−8.25611e6	+	1.98441e7i	−0.650694	+	1.56399i
$695$		0			0
$696$	−3.06985e6	−	7.51082e6i	−0.240212	−	0.587711i
$697$		−	4.82771e6i		−	0.376409i
$698$	−1.17272e7	−	4.87909e6i	−0.911080	−	0.379053i
$699$			1.46567e7i			1.13460i
$700$		0			0
$701$			6.74508e6i			0.518432i	0.965819	+	0.259216i	$0.0834642\pi$
$701$			6.74508e6i			0.518432i	−0.965819	+	0.259216i	$0.916536\pi$
$702$	−1.26935e6	+	3.05096e6i	−0.0972161	+	0.233665i
$703$			5.58920e6i			0.426542i
$704$	−1.50114e7	−	1.52959e7i	−1.14153	−	1.16317i
$705$		0			0
$706$	−7.45670e6	−	3.10234e6i	−0.563034	−	0.234249i
$707$	−3.19534e7			−2.40419
$708$	7.81893e6	−	7.77014e6i	0.586225	−	0.582567i
$709$		−	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
$712$	4.97990e6	−	2.03540e6i	0.368146	−	0.150470i
$713$			9.06268e6i			0.667626i
$714$	−1.21358e6	+	2.91692e6i	−0.0890888	+	0.214131i
$715$		0			0
$716$	−4.84195e6	+	4.81173e6i	−0.352970	+	0.350767i
$717$	−1.40794e7			−1.02279
$718$	2.14679e6	−	5.15995e6i	0.155410	−	0.373538i
$719$	4.30858e6			0.310822			0.155411	−	0.987850i	$-0.450330\pi$
$719$	4.30858e6			0.310822			0.155411	+	0.987850i	$0.450330\pi$
$720$		0			0
$721$	3.62304e7			2.59559
$722$	−6.40108e6	+	1.53854e7i	−0.456993	+	1.09841i
$723$	−1.15175e7			−0.819432
$724$	1.43419e7	−	1.42524e7i	1.01686	−	1.01051i
$725$		0			0
$726$	−5.19125e6	+	1.24775e7i	−0.365536	+	0.878590i
$727$		−	9.51543e6i		−	0.667717i	−0.942623	−	0.333858i	$-0.891649\pi$
$727$		−	9.51543e6i		−	0.667717i	0.942623	−	0.333858i	$-0.108351\pi$
$728$	−1.97250e6	−	4.82600e6i	−0.137940	−	0.337489i
$729$	6.77234e6			0.471976
$730$		0			0
$731$			3.27085e6i			0.226395i
$732$	−7.70991e6	+	7.66180e6i	−0.531829	+	0.528510i
$733$	1.76887e7			1.21601			0.608004	−	0.793934i	$-0.291971\pi$
$733$	1.76887e7			1.21601			0.608004	+	0.793934i	$0.291971\pi$
$734$	1.17628e7	+	4.89391e6i	0.805883	+	0.335286i
$735$		0			0
$736$	−9.32548e6	+	2.20247e7i	−0.634566	+	1.49870i
$737$		−	1.98922e7i		−	1.34900i
$738$	4.90741e6	−	1.17953e7i	0.331674	−	0.797201i
$739$			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
$742$	−1.11515e7	−	4.63957e6i	−0.743574	−	0.309363i
$743$			1.92873e7i			1.28174i	0.767650	+	0.640869i	$0.221426\pi$
$743$			1.92873e7i			1.28174i	−0.767650	+	0.640869i	$0.778574\pi$
$744$	−3.29436e6	+	1.34648e6i	−0.218192	+	0.0891803i
$745$		0			0
$746$	4.81225e6	−	1.15666e7i	0.316593	−	0.760952i
$747$	1.02795e7			0.674016
$748$	−5.13310e6	−	5.16533e6i	−0.335448	−	0.337555i
$749$		−	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	$0.542235\pi$
$752$	−5.39754e6	−	33787.2i	−0.348058	−	0.00217875i
$753$			303199.i			0.0194868i
$754$	4.20063e6	+	1.74766e6i	0.269083	+	0.111951i
$755$		0			0
$756$	−1.47835e7	+	1.46912e7i	−0.940746	+	0.934875i
$757$	2.68495e7			1.70293			0.851465	−	0.524412i	$-0.175715\pi$
$757$	2.68495e7			1.70293			0.851465	+	0.524412i	$0.175715\pi$
$758$	−1.51235e7	−	6.29210e6i	−0.956047	−	0.397762i
$759$	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	$0.684140\pi$
$762$	−5.31764e6	−	2.21239e6i	−0.331766	−	0.138030i
$763$	2.29694e7			1.42837
$764$	−332642.	−	334731.i	−0.0206179	−	0.0207473i
$765$		0			0
$766$	−1.03049e7	−	4.28733e6i	−0.634558	−	0.264007i
$767$			6.18096e6i			0.379374i
$768$	−9.39168e6	−	117583.i	−0.574566	−	0.00719355i
$769$	−2.64035e7			−1.61007			−0.805037	−	0.593224i	$-0.797855\pi$
$769$	−2.64035e7			−1.61007			−0.805037	+	0.593224i	$0.797855\pi$
$770$		0			0
$771$		−	1.21566e6i		−	0.0736505i
$772$	8.71497e6	−	8.66058e6i	0.526287	−	0.523003i
$773$	3.92652e6			0.236352			0.118176	−	0.992993i	$-0.462295\pi$
$773$	3.92652e6			0.236352			0.118176	+	0.992993i	$0.462295\pi$
$774$	−3.32484e6	+	7.99148e6i	−0.199489	+	0.479485i
$775$		0			0
$776$	3.27005e6	+	8.00062e6i	0.194939	+	0.476946i
$777$			3.85288e6i			0.228946i
$778$	−1.02030e7	−	4.24495e6i	−0.604338	−	0.251434i
$779$		−	3.23080e7i		−	1.90751i
$780$		0			0
$781$			3.17158e6i			0.186058i
$782$	−3.12177e6	+	7.50338e6i	−0.182551	+	0.438773i
$783$		−	1.81880e7i		−	1.06018i
$784$	98102.0	−	1.56719e7i	0.00570017	−	0.910608i
$785$		0			0
$786$	1.00138e7	+	4.16623e6i	0.578154	+	0.240540i
$787$	3.36220e6			0.193503			0.0967513	−	0.995309i	$-0.469155\pi$
$787$	3.36220e6			0.193503			0.0967513	+	0.995309i	$0.469155\pi$
$788$	−1.52596e7	−	1.53554e7i	−0.875441	−	0.880938i
$789$		−	275909.i		−	0.0157788i
$790$		0			0
$791$	3.04444e7			1.73008
$792$	−7.29082e6	−	1.78380e7i	−0.413013	−	1.01049i
$793$		−	6.09477e6i		−	0.344171i
$794$	7.51985e6	−	1.80745e7i	0.423310	−	1.01745i
$795$		0			0
$796$	−1.63853e6	−	1.64882e6i	−0.0916582	−	0.0922338i
$797$	−3.41295e6			−0.190320			−0.0951600	−	0.995462i	$-0.530336\pi$
$797$	−3.41295e6			−0.190320			−0.0951600	+	0.995462i	$0.530336\pi$
$798$	−8.12152e6	+	1.95206e7i	−0.451471	+	1.08514i
$799$	−1.83405e6			−0.101635
$800$		0			0
$801$	4.83734e6			0.266395
$802$	3.31359e6	−	7.96443e6i	0.181913	−	0.437239i
$803$	2.56452e7			1.40351
$804$	−6.14510e6	−	6.18369e6i	−0.335266	−	0.337371i
$805$		0			0
$806$	766552.	−	1.84246e6i	0.0415627	−	0.0998989i
$807$			1.12067e7i			0.605749i
$808$	−1.22122e7	−	2.98788e7i	−0.658059	−	1.61003i
$809$	−472257.			−0.0253692			−0.0126846	−	0.999920i	$-0.504038\pi$
$809$	−472257.			−0.0253692			−0.0126846	+	0.999920i	$0.504038\pi$
$810$		0			0
$811$		−	1.92082e7i		−	1.02550i	−0.858539	−	0.512748i	$-0.828627\pi$
$811$		−	1.92082e7i		−	1.02550i	0.858539	−	0.512748i	$-0.171373\pi$
$812$	2.02272e7	+	2.03542e7i	1.07658	+	1.08334i
$813$	2.12525e7			1.12767
$814$	−8.19945e6	−	3.41137e6i	−0.433734	−	0.180454i
$815$		0			0
$816$	−3.19136e6	−	19977.1i	−0.167784	−	0.00105028i
$817$			2.18891e7i			1.14729i
$818$	1.40031e6	−	3.36574e6i	0.0731713	−	0.175872i
$819$		−	4.68785e6i		−	0.244210i
$820$		0			0
$821$		−	9.11118e6i		−	0.471755i	−0.971783	−	0.235878i	$-0.924204\pi$
$821$		−	9.11118e6i		−	0.471755i	0.971783	−	0.235878i	$-0.0757964\pi$
$822$	1.52753e7	+	6.35526e6i	0.788516	+	0.328061i
$823$			9.99422e6i			0.514339i	0.966366	+	0.257169i	$0.0827899\pi$
$823$			9.99422e6i			0.514339i	−0.966366	+	0.257169i	$0.917210\pi$
$824$	1.38468e7	+	3.38782e7i	0.710447	+	1.73821i
$825$		0			0
$826$	−1.49749e7	+	3.59933e7i	−0.763686	+	1.83557i
$827$	−2.26290e7			−1.15054			−0.575270	−	0.817964i	$-0.695103\pi$
$827$	−2.26290e7			−1.15054			−0.575270	+	0.817964i	$0.695103\pi$
$828$	−1.52545e7	+	1.51593e7i	−0.773254	+	0.768428i
$829$		−	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
$832$	3.75881e6	−	3.68887e6i	0.188253	−	0.184750i
$833$		−	5.32521e6i		−	0.265904i
$834$	−3.45066e6	−	1.43564e6i	−0.171786	−	0.0714711i
$835$		0			0
$836$	−3.43517e7	−	3.45674e7i	−1.69994	−	1.71061i
$837$	−7.97753e6			−0.393600
$838$	2.19050e7	+	9.11354e6i	1.07754	+	0.448309i
$839$	−7.31704e6			−0.358865			−0.179432	−	0.983770i	$-0.557426\pi$
$839$	−7.31704e6			−0.358865			−0.179432	+	0.983770i	$0.557426\pi$
$840$		0			0
$841$	−4.53041e6			−0.220876
$842$	−8.47050e6	−	3.52413e6i	−0.411745	−	0.171306i
$843$	−1.01785e6			−0.0493302
$844$	−2.14580e7	+	2.13241e7i	−1.03689	+	1.03042i
$845$		0			0
$846$	−4.48104e6	−	1.86433e6i	−0.215255	−	0.0895563i
$847$		−	4.77942e7i		−	2.28911i
$848$	76373.1	−	1.22007e7i	0.00364713	−	0.582632i
$849$	2.34998e7			1.11891
$850$		0			0
$851$			9.91099e6i			0.469130i
$852$	979768.	+	985921.i	0.0462407	+	0.0465311i
$853$	−1.97974e7			−0.931614			−0.465807	−	0.884886i	$-0.654236\pi$
$853$	−1.97974e7			−0.931614			−0.465807	+	0.884886i	$0.654236\pi$
$854$	1.47661e7	−	3.54914e7i	0.692823	−	1.66525i
$855$		0			0
$856$	1.22380e7	−	5.00197e6i	0.570856	−	0.233323i
$857$		−	1.46070e7i		−	0.679375i	−0.940538	−	0.339688i	$-0.889679\pi$
$857$		−	1.46070e7i		−	0.679375i	0.940538	−	0.339688i	$-0.110321\pi$
$858$	−4.91770e6	−	2.04600e6i	−0.228057	−	0.0948829i
$859$		−	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
$862$	−2.43134e6	+	5.84388e6i	−0.111449	+	0.267876i
$863$			2.79017e7i			1.27528i	0.770336	+	0.637638i	$0.220088\pi$
$863$			2.79017e7i			1.27528i	−0.770336	+	0.637638i	$0.779912\pi$
$864$	−1.93875e7	−	8.20885e6i	−0.883561	−	0.374109i
$865$		0			0
$866$	4.89005e6	+	2.03450e6i	0.221574	+	0.0921854i
$867$	1.16337e7			0.525617
$868$	8.92766e6	−	8.87195e6i	0.402196	−	0.399687i
$869$			4.49934e7i			2.02115i
$870$		0			0
$871$	4.88828e6			0.218329
$872$	8.77863e6	+	2.14781e7i	0.390963	+	0.956545i
$873$			7.77160e6i			0.345124i
$874$	−2.08915e7	+	5.02141e7i	−0.925104	+	2.22355i
$875$		0			0
$876$	7.97207e6	−	7.92232e6i	0.351003	−	0.348813i
$877$	2.39256e7			1.05042			0.525212	−	0.850971i	$-0.323986\pi$
$877$	2.39256e7			1.05042			0.525212	+	0.850971i	$0.323986\pi$
$878$	−2.07966e6	+	4.99861e6i	−0.0910452	+	0.218833i
$879$	−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	$0.690965\pi$
$882$	5.41312e6	−	1.30108e7i	0.234302	−	0.563161i
$883$	−1.84987e7			−0.798434			−0.399217	−	0.916857i	$-0.630718\pi$
$883$	−1.84987e7			−0.798434			−0.399217	+	0.916857i	$0.630718\pi$
$884$	1.26932e6	−	1.26140e6i	0.0546313	−	0.0542904i
$885$		0			0
$886$	4.55808e6	−	1.09557e7i	0.195073	−	0.468872i
$887$		−	1.75445e7i		−	0.748739i	−0.927280	−	0.374370i	$-0.877859\pi$
$887$		−	1.75445e7i		−	0.748739i	0.927280	−	0.374370i	$-0.122141\pi$
$888$	−3.60273e6	+	1.47252e6i	−0.153320	+	0.0626656i
$889$	2.03688e7			0.864394
$890$		0			0
$891$		−	4.57585e6i		−	0.193098i
$892$	−1.78971e7	+	1.77854e7i	−0.753130	+	0.748431i
$893$	−1.22738e7			−0.515052
$894$	1.73297e7	+	7.20997e6i	0.725181	+	0.301710i
$895$		0			0
$896$	3.08257e7	−	1.23746e7i	1.28275	−	0.514945i
$897$			5.94422e6i			0.246668i
$898$	647228.	−	1.55566e6i	0.0267834	−	0.0643758i
$899$			1.09836e7i			0.453259i
$900$		0			0
$901$		−	4.14572e6i		−	0.170133i
$902$	4.73963e7	+	1.97192e7i	1.93967	+	0.806997i
$903$			1.50891e7i			0.615807i
$904$	1.16355e7	+	2.84678e7i	0.473546	+	1.15860i
$905$		0			0
$906$	6.06508e6	−	1.45778e7i	0.245480	−	0.590028i
$907$	3.92259e7			1.58327			0.791635	−	0.610994i	$-0.209230\pi$
$907$	3.92259e7			1.58327			0.791635	+	0.610994i	$0.209230\pi$
$908$	−2.46030e6	−	2.47575e6i	−0.0990316	−	0.0996535i
$909$		−	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	$0.235318\pi$
$912$	−2.13572e7	−	133690.i	−0.850270	−	0.00532247i
$913$			4.13055e7i			1.63995i
$914$	−8.80646e6	−	3.66391e6i	−0.348687	−	0.145071i
$915$		0			0
$916$	2.83803e6	−	2.82032e6i	0.111758	−	0.111061i
$917$	−3.83572e7			−1.50634
$918$	−6.60494e6	−	2.74797e6i	−0.258679	−	0.107623i
$919$	1.51186e7			0.590504			0.295252	−	0.955419i	$-0.404596\pi$
$919$	1.51186e7			0.590504			0.295252	+	0.955419i	$0.404596\pi$
$920$		0			0
$921$	−5.57973e6			−0.216753
$922$	3.03028e7	+	1.26074e7i	1.17397	+	0.488427i
$923$	−779381.			−0.0301124
$924$	−2.36801e7	−	2.38288e7i	−0.912438	−	0.918167i
$925$		0			0
$926$	−2.00867e7	−	8.35704e6i	−0.769806	−	0.320276i
$927$			3.29084e7i			1.25779i
$928$	−1.13021e7	+	2.66930e7i	−0.430814	+	1.01748i
$929$	1.30954e6			0.0497827			0.0248913	−	0.999690i	$-0.492076\pi$
$929$	1.30954e6			0.0497827			0.0248913	+	0.999690i	$0.492076\pi$
$930$		0			0
$931$		−	3.56374e7i		−	1.34751i
$932$	3.71405e7	−	3.69088e7i	1.40058	−	1.39184i
$933$	2.42902e7			0.913539
$934$	−1.48390e6	+	3.56666e6i	−0.0556594	+	0.133781i
$935$		0			0
$936$	4.38349e6	−	1.79164e6i	0.163542	−	0.0668437i
$937$			2.90734e7i			1.08180i	0.841087	+	0.540900i	$0.181916\pi$
$937$			2.90734e7i			1.08180i	−0.841087	+	0.540900i	$0.818084\pi$
$938$	2.84657e7	+	1.18431e7i	1.05637	+	0.439499i
$939$			2.38950e7i			0.884387i
$940$		0			0
$941$			2.78133e7i			1.02395i	0.859000	+	0.511975i	$0.171086\pi$
$941$			2.78133e7i			1.02395i	−0.859000	+	0.511975i	$0.828914\pi$
$942$	−4.39995e6	+	1.05756e7i	−0.161555	+	0.388308i
$943$		−	5.72898e7i		−	2.09796i
$944$	−3.93796e7	−	246506.i	−1.43827	−	0.00900322i
$945$		0			0
$946$	−3.21117e7	−	1.33600e7i	−1.16664	−	0.485377i
$947$	−5.56136e6			−0.201514			−0.100757	−	0.994911i	$-0.532127\pi$
$947$	−5.56136e6			−0.201514			−0.100757	+	0.994911i	$0.532127\pi$
$948$	1.38994e7	+	1.39867e7i	0.502314	+	0.505468i
$949$			6.30201e6i			0.227150i
$950$		0			0
$951$	1.29531e7			0.464431
$952$	1.04477e7	−	4.27021e6i	0.373617	−	0.152706i
$953$			2.07308e7i			0.739408i	0.929150	+	0.369704i	$0.120541\pi$
$953$			2.07308e7i			0.739408i	−0.929150	+	0.369704i	$0.879459\pi$
$954$	4.21415e6	−	1.01290e7i	0.149913	−	0.360326i
$955$		0			0
$956$	3.54551e7	+	3.56777e7i	1.25468	+	1.26256i
$957$	2.93163e7			1.03474
$958$	1.88729e6	−	4.53623e6i	0.0664393	−	0.159691i
$959$	−5.85110e7			−2.05443
$960$		0			0
$961$	−2.38116e7			−0.831725
$962$	838305.	−	2.01492e6i	0.0292055	−	0.0701973i
$963$	1.18877e7			0.413078
$964$	2.90037e7	+	2.91858e7i	1.00522	+	1.01153i
$965$		0			0
$966$	−1.44014e7	+	3.46147e7i	−0.496548	+	1.19349i
$967$			1.25936e7i			0.433094i	0.976272	+	0.216547i	$0.0694795\pi$
$967$			1.25936e7i			0.433094i	−0.976272	+	0.216547i	$0.930520\pi$
$968$	4.46912e7	−	1.82664e7i	1.53297	−	0.626561i
$969$	−7.25703e6			−0.248285
$970$		0			0
$971$		−	2.22296e7i		−	0.756629i	−0.925677	−	0.378314i	$-0.876504\pi$
$971$		−	2.22296e7i		−	0.756629i	0.925677	−	0.378314i	$-0.123496\pi$
$972$	−2.13355e7	−	2.14695e7i	−0.724331	−	0.728880i
$973$	1.32175e7			0.447577
$974$	7.45506e6	+	3.10166e6i	0.251799	+	0.104760i
$975$		0			0
$976$	3.88306e7	+	243069.i	1.30482	+	0.00816780i
$977$		−	1.54083e6i		−	0.0516437i	−0.999667	−	0.0258218i	$-0.991780\pi$
$977$		−	1.54083e6i		−	0.0516437i	0.999667	−	0.0258218i	$-0.00822026\pi$
$978$	−5.47160e6	+	1.31514e7i	−0.182923	+	0.439667i
$979$			1.94376e7i			0.648165i
$980$		0			0
$981$			2.08633e7i			0.692167i
$982$	−1.23944e7	−	5.15668e6i	−0.410155	−	0.170644i
$983$		−	2.84625e7i		−	0.939482i	−0.882804	−	0.469741i	$-0.844347\pi$
$983$		−	2.84625e7i		−	0.939482i	0.882804	−	0.469741i	$-0.155653\pi$
$984$	2.08253e7	−	8.51180e6i	0.685652	−	0.280242i
$985$		0			0
$986$	−3.78346e6	+	9.09380e6i	−0.123936	+	0.297888i
$987$	−8.46087e6			−0.276453
$988$	8.49455e6	−	8.44154e6i	0.276852	−	0.275125i
$989$			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	$0.717081\pi$
$992$	1.17080e7	+	4.95728e6i	0.377748	+	0.159943i
$993$		−	1.50064e7i		−	0.482952i
$994$	−4.53854e6	−	1.88825e6i	−0.145697	−	0.0606169i
$995$		0			0
$996$	1.27601e7	+	1.28403e7i	0.407574	+	0.410133i
$997$	2.13564e6			0.0680441			0.0340221	−	0.999421i	$-0.489168\pi$
$997$	2.13564e6			0.0680441			0.0340221	+	0.999421i	$0.489168\pi$
$998$	−1.91474e7	−	7.96622e6i	−0.608531	−	0.253178i
$999$	−8.72426e6			−0.276576

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.17296 - 5.22286i) q^{2} +8.95730 q^{3} +(-22.5565 - 22.6981i) q^{4} +(19.4639 - 46.7827i) q^{6} +179.198i q^{7} +(-167.563 + 68.4872i) q^{8} -162.767 q^{9} +O(q^{10})\)	\(q+(2.17296 - 5.22286i) q^{2} +8.95730 q^{3} +(-22.5565 - 22.6981i) q^{4} +(19.4639 - 46.7827i) q^{6} +179.198i q^{7} +(-167.563 + 68.4872i) q^{8} -162.767 q^{9} -654.036i q^{11} +(-202.045 - 203.314i) q^{12} +160.722 q^{13} +(935.925 + 389.390i) q^{14} +(-6.40984 + 1023.98i) q^{16} +347.942i q^{17} +(-353.686 + 850.107i) q^{18} +2328.49i q^{19} +1605.13i q^{21} +(-3415.94 - 1421.19i) q^{22} +4128.97i q^{23} +(-1500.92 + 613.460i) q^{24} +(349.243 - 839.428i) q^{26} -3634.58 q^{27} +(4067.46 - 4042.08i) q^{28} +5004.15i q^{29} +2194.90 q^{31} +(5334.17 + 2258.55i) q^{32} -5858.40i q^{33} +(1817.25 + 756.064i) q^{34} +(3671.45 + 3694.50i) q^{36} +2400.35 q^{37} +(12161.4 + 5059.73i) q^{38} +1439.64 q^{39} -13875.1 q^{41} +(8383.37 + 3487.88i) q^{42} +9400.56 q^{43} +(-14845.4 + 14752.8i) q^{44} +(21565.0 + 8972.10i) q^{46} +5271.14i q^{47} +(-57.4149 + 9172.10i) q^{48} -15304.9 q^{49} +3116.62i q^{51} +(-3625.32 - 3648.09i) q^{52} -11915.0 q^{53} +(-7897.79 + 18982.9i) q^{54} +(-12272.8 - 30027.0i) q^{56} +20857.0i q^{57} +(26136.0 + 10873.8i) q^{58} +38457.4i q^{59} -37921.2i q^{61} +(4769.43 - 11463.6i) q^{62} -29167.5i q^{63} +(23387.0 - 22951.9i) q^{64} +(-30597.6 - 12730.1i) q^{66} +30414.5 q^{67} +(7897.63 - 7848.35i) q^{68} +36984.5i q^{69} -4849.25 q^{71} +(27273.8 - 11147.4i) q^{72} +39210.6i q^{73} +(5215.87 - 12536.7i) q^{74} +(52852.5 - 52522.6i) q^{76} +117202. q^{77} +(3128.27 - 7519.01i) q^{78} -68793.5 q^{79} +6996.32 q^{81} +(-30150.0 + 72467.5i) q^{82} -63154.8 q^{83} +(36433.4 - 36206.1i) q^{84} +(20427.0 - 49097.8i) q^{86} +44823.7i q^{87} +(44793.1 + 109593. i) q^{88} -29719.5 q^{89} +28801.0i q^{91} +(93720.0 - 93135.2i) q^{92} +19660.4 q^{93} +(27530.4 + 11454.0i) q^{94} +(47779.8 + 20230.5i) q^{96} -47746.8i q^{97} +(-33256.9 + 79935.3i) q^{98} +106455. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9}+O(q^{10}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9	\( 40 q - 2 q^{4} + 66 q^{6} + 3240 q^{9} + 848 q^{14} - 110 q^{16} - 18918 q^{24} + 18344 q^{26} + 14320 q^{31} + 19182 q^{34} + 29656 q^{36} - 44904 q^{39} - 11608 q^{41} + 23186 q^{44} - 75224 q^{46} - 125304 q^{49} - 177894 q^{54} - 73816 q^{56} - 230354 q^{64} + 262878 q^{66} - 15448 q^{71} - 4224 q^{74} + 111902 q^{76} + 15560 q^{79} + 193968 q^{81} + 195112 q^{84} - 131972 q^{86} + 6320 q^{89} + 117080 q^{94} + 115582 q^{96}+O(q^{100}) \) 40 * q - 2 * q^4 + 66 * q^6 + 3240 * q^9 + 848 * q^14 - 110 * q^16 - 18918 * q^24 + 18344 * q^26 + 14320 * q^31 + 19182 * q^34 + 29656 * q^36 - 44904 * q^39 - 11608 * q^41 + 23186 * q^44 - 75224 * q^46 - 125304 * q^49 - 177894 * q^54 - 73816 * q^56 - 230354 * q^64 + 262878 * q^66 - 15448 * q^71 - 4224 * q^74 + 111902 * q^76 + 15560 * q^79 + 193968 * q^81 + 195112 * q^84 - 131972 * q^86 + 6320 * q^89 + 117080 * q^94 + 115582 * q^96

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