LMFDB - Embedded newform 200.6.d.d.101.16

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			101.16
Root			$4.12326 - 3.87282i$ of defining polynomial
Character	$\chi$	$=$	200.101
Dual form			200.6.d.d.101.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.12326 + 3.87282i) q^{2} +18.2848i q^{3} +(2.00256 + 31.9373i) q^{4} +(-70.8136 + 75.3929i) q^{6} +2.25573 q^{7} +(-115.430 + 139.441i) q^{8} -91.3327 q^{9} +419.261i q^{11} +(-583.966 + 36.6163i) q^{12} +106.889i q^{13} +(9.30095 + 8.73602i) q^{14} +(-1015.98 + 127.912i) q^{16} -849.098 q^{17} +(-376.589 - 353.715i) q^{18} -335.414i q^{19} +41.2454i q^{21} +(-1623.72 + 1728.72i) q^{22} -3541.78 q^{23} +(-2549.65 - 2110.61i) q^{24} +(-413.961 + 440.731i) q^{26} +2773.20i q^{27} +(4.51722 + 72.0418i) q^{28} -5208.57i q^{29} +5637.83 q^{31} +(-4684.53 - 3407.29i) q^{32} -7666.09 q^{33} +(-3501.05 - 3288.40i) q^{34} +(-182.899 - 2916.92i) q^{36} +61.9860i q^{37} +(1299.00 - 1383.00i) q^{38} -1954.44 q^{39} +16286.1 q^{41} +(-159.736 + 170.066i) q^{42} +2417.19i q^{43} +(-13390.1 + 839.594i) q^{44} +(-14603.7 - 13716.7i) q^{46} +22781.9 q^{47} +(-2338.85 - 18576.9i) q^{48} -16801.9 q^{49} -15525.6i q^{51} +(-3413.74 + 214.051i) q^{52} -13667.5i q^{53} +(-10740.1 + 11434.6i) q^{54} +(-260.379 + 314.541i) q^{56} +6132.98 q^{57} +(20171.9 - 21476.3i) q^{58} -23407.1i q^{59} +33444.7i q^{61} +(23246.3 + 21834.3i) q^{62} -206.022 q^{63} +(-6119.73 - 32191.5i) q^{64} +(-31609.3 - 29689.4i) q^{66} +66162.9i q^{67} +(-1700.37 - 27117.9i) q^{68} -64760.7i q^{69} -51421.4 q^{71} +(10542.6 - 12735.5i) q^{72} -21271.6 q^{73} +(-240.060 + 255.584i) q^{74} +(10712.2 - 671.686i) q^{76} +945.738i q^{77} +(-8058.66 - 7569.18i) q^{78} +38418.7 q^{79} -72901.2 q^{81} +(67151.7 + 63073.0i) q^{82} +93166.7i q^{83} +(-1317.27 + 82.5963i) q^{84} +(-9361.33 + 9966.69i) q^{86} +95237.5 q^{87} +(-58462.3 - 48395.4i) q^{88} -60678.0 q^{89} +241.112i q^{91} +(-7092.62 - 113115. i) q^{92} +103086. i q^{93} +(93935.8 + 88230.2i) q^{94} +(62301.5 - 85655.5i) q^{96} -157428. q^{97} +(-69278.7 - 65070.8i) q^{98} -38292.2i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + q^{4} + 33 q^{6} + 196 q^{7} + 391 q^{8} - 1620 q^{9} + 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}+ \cdots - 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

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 $

$2$	4.12326	+	3.87282i	0.728896	+	0.684624i
$2$	4.12326	+	3.87282i	0.728896	+	0.684624i
$3$			18.2848i			1.17297i	0.809961	+	0.586484i	$0.199488\pi$
$3$			18.2848i			1.17297i	−0.809961	+	0.586484i	$0.800512\pi$
$4$	2.00256	+	31.9373i	0.0625799	+	0.998040i
$5$		0			0
$5$		0			0
$6$	−70.8136	+	75.3929i	−0.803042	+	0.854972i
$7$	2.25573			0.0173997			0.00869984	−	0.999962i	$-0.497231\pi$
$7$	2.25573			0.0173997			0.00869984	+	0.999962i	$0.497231\pi$
$8$	−115.430	+	139.441i	−0.637668	+	0.770311i
$9$	−91.3327			−0.375855
$10$		0			0
$11$			419.261i			1.04473i	0.852723	+	0.522363i	$0.174950\pi$
$11$			419.261i			1.04473i	−0.852723	+	0.522363i	$0.825050\pi$
$12$	−583.966	+	36.6163i	−1.17067	+	0.0734042i
$13$			106.889i			0.175418i	0.996146	+	0.0877090i	$0.0279546\pi$
$13$			106.889i			0.175418i	−0.996146	+	0.0877090i	$0.972045\pi$
$14$	9.30095	+	8.73602i	0.0126826	+	0.0119122i
$15$		0			0
$16$	−1015.98	+	127.912i	−0.992168	+	0.124914i
$17$	−849.098			−0.712584			−0.356292	−	0.934375i	$-0.615959\pi$
$17$	−849.098			−0.712584			−0.356292	+	0.934375i	$0.615959\pi$
$18$	−376.589	−	353.715i	−0.273959	−	0.257319i
$19$		−	335.414i		−	0.213156i	−0.994304	−	0.106578i	$-0.966011\pi$
$19$		−	335.414i		−	0.213156i	0.994304	−	0.106578i	$-0.0339894\pi$
$20$		0			0
$21$			41.2454i			0.0204093i
$22$	−1623.72	+	1728.72i	−0.715245	+	0.761497i
$23$	−3541.78			−1.39605			−0.698027	−	0.716071i	$-0.745938\pi$
$23$	−3541.78			−1.39605			−0.698027	+	0.716071i	$0.745938\pi$
$24$	−2549.65	−	2110.61i	−0.903551	−	0.747964i
$25$		0			0
$26$	−413.961	+	440.731i	−0.120095	+	0.127862i
$27$			2773.20i			0.732103i
$28$	4.51722	+	72.0418i	0.00108887	+	0.0173656i
$29$		−	5208.57i		−	1.15007i	−0.818129	−	0.575034i	$-0.804989\pi$
$29$		−	5208.57i		−	1.15007i	0.818129	−	0.575034i	$-0.195011\pi$
$30$		0			0
$31$	5637.83			1.05368			0.526839	−	0.849965i	$-0.323377\pi$
$31$	5637.83			1.05368			0.526839	+	0.849965i	$0.323377\pi$
$32$	−4684.53	−	3407.29i	−0.808707	−	0.588212i
$33$	−7666.09			−1.22543
$34$	−3501.05	−	3288.40i	−0.519400	−	0.487852i
$35$		0			0
$36$	−182.899	−	2916.92i	−0.0235209	−	0.375118i
$37$			61.9860i			0.00744370i	0.999993	+	0.00372185i	$0.00118470\pi$
$37$			61.9860i			0.00744370i	−0.999993	+	0.00372185i	$0.998815\pi$
$38$	1299.00	−	1383.00i	0.145932	−	0.155369i
$39$	−1954.44			−0.205760
$40$		0			0
$41$	16286.1			1.51306			0.756531	−	0.653958i	$-0.226893\pi$
$41$	16286.1			1.51306			0.756531	+	0.653958i	$0.226893\pi$
$42$	−159.736	+	170.066i	−0.0139727	+	0.0148762i
$43$			2417.19i			0.199361i	0.995020	+	0.0996803i	$0.0317820\pi$
$43$			2417.19i			0.199361i	−0.995020	+	0.0996803i	$0.968218\pi$
$44$	−13390.1	+	839.594i	−1.04268	+	0.0653789i
$45$		0			0
$46$	−14603.7	−	13716.7i	−1.01758	−	0.955772i
$47$	22781.9			1.50434			0.752170	−	0.658970i	$-0.229007\pi$
$47$	22781.9			1.50434			0.752170	+	0.658970i	$0.229007\pi$
$48$	−2338.85	−	18576.9i	−0.146521	−	1.16378i
$49$	−16801.9			−0.999697
$50$		0			0
$51$		−	15525.6i		−	0.835838i
$52$	−3413.74	+	214.051i	−0.175074	+	0.0109776i
$53$		−	13667.5i		−	0.668344i	−0.942512	−	0.334172i	$-0.891543\pi$
$53$		−	13667.5i		−	0.668344i	0.942512	−	0.334172i	$-0.108457\pi$
$54$	−10740.1	+	11434.6i	−0.501215	+	0.533627i
$55$		0			0
$56$	−260.379	+	314.541i	−0.0110952	+	0.0134032i
$57$	6132.98			0.250025
$58$	20171.9	−	21476.3i	0.787365	−	0.838281i
$59$		−	23407.1i		−	0.875423i	−0.899116	−	0.437711i	$-0.855789\pi$
$59$		−	23407.1i		−	0.875423i	0.899116	−	0.437711i	$-0.144211\pi$
$60$		0			0
$61$			33444.7i			1.15081i	0.817869	+	0.575405i	$0.195155\pi$
$61$			33444.7i			1.15081i	−0.817869	+	0.575405i	$0.804845\pi$
$62$	23246.3	+	21834.3i	0.768022	+	0.721373i
$63$	−206.022			−0.00653975
$64$	−6119.73	−	32191.5i	−0.186759	−	0.982406i
$65$		0			0
$66$	−31609.3	−	29689.4i	−0.893212	−	0.838960i
$67$			66162.9i			1.80064i	0.435226	+	0.900321i	$0.356668\pi$
$67$			66162.9i			1.80064i	−0.435226	+	0.900321i	$0.643332\pi$
$68$	−1700.37	−	27117.9i	−0.0445934	−	0.711187i
$69$		−	64760.7i		−	1.63753i
$70$		0			0
$71$	−51421.4			−1.21059			−0.605296	−	0.796001i	$-0.706945\pi$
$71$	−51421.4			−1.21059			−0.605296	+	0.796001i	$0.706945\pi$
$72$	10542.6	−	12735.5i	0.239670	−	0.289525i
$73$	−21271.6			−0.467189			−0.233595	−	0.972334i	$-0.575049\pi$
$73$	−21271.6			−0.467189			−0.233595	+	0.972334i	$0.575049\pi$
$74$	−240.060	+	255.584i	−0.00509614	+	0.00542569i
$75$		0			0
$76$	10712.2	−	671.686i	0.212738	−	0.0133393i
$77$			945.738i			0.0181779i
$78$	−8058.66	−	7569.18i	−0.149978	−	0.140868i
$79$	38418.7			0.692589			0.346294	−	0.938126i	$-0.387440\pi$
$79$	38418.7			0.692589			0.346294	+	0.938126i	$0.387440\pi$
$80$		0			0
$81$	−72901.2			−1.23459
$82$	67151.7	+	63073.0i	1.10286	+	1.03588i
$83$			93166.7i			1.48445i	0.670151	+	0.742225i	$0.266229\pi$
$83$			93166.7i			1.48445i	−0.670151	+	0.742225i	$0.733771\pi$
$84$	−1317.27	+	82.5963i	−0.0203693	+	0.00127721i
$85$		0			0
$86$	−9361.33	+	9966.69i	−0.136487	+	0.145313i
$87$	95237.5			1.34899
$88$	−58462.3	−	48395.4i	−0.804765	−	0.666189i
$89$	−60678.0			−0.812000			−0.406000	−	0.913873i	$-0.633077\pi$
$89$	−60678.0			−0.812000			−0.406000	+	0.913873i	$0.633077\pi$
$90$		0			0
$91$			241.112i			0.00305222i
$92$	−7092.62	−	113115.i	−0.0873649	−	1.39332i
$93$			103086.i			1.23593i
$94$	93935.8	+	88230.2i	1.09651	+	1.02991i
$95$		0			0
$96$	62301.5	−	85655.5i	0.689954	−	0.948587i
$97$	−157428.			−1.69884			−0.849418	−	0.527721i	$-0.823047\pi$
$97$	−157428.			−1.69884			−0.849418	+	0.527721i	$0.823047\pi$
$98$	−69278.7	−	65070.8i	−0.728676	−	0.684417i
$99$		−	38292.2i		−	0.392665i
$100$		0			0
$101$			124508.i			1.21449i	0.794516	+	0.607243i	$0.207725\pi$
$101$			124508.i			1.21449i	−0.794516	+	0.607243i	$0.792275\pi$
$102$	60127.7	−	64016.0i	0.572235	−	0.609239i
$103$	10346.4			0.0960938			0.0480469	−	0.998845i	$-0.484700\pi$
$103$	10346.4			0.0960938			0.0480469	+	0.998845i	$0.484700\pi$
$104$	−14904.7	−	12338.2i	−0.135126	−	0.111858i
$105$		0			0
$106$	52931.8	−	56354.7i	0.457564	−	0.487153i
$107$			70765.9i			0.597537i	0.954326	+	0.298769i	$0.0965758\pi$
$107$			70765.9i			0.597537i	−0.954326	+	0.298769i	$0.903424\pi$
$108$	−88568.5	+	5553.49i	−0.730668	+	0.0458149i
$109$		−	128453.i		−	1.03557i	−0.855511	−	0.517784i	$-0.826757\pi$
$109$		−	128453.i		−	1.03557i	0.855511	−	0.517784i	$-0.173243\pi$
$110$		0			0
$111$	−1133.40			−0.00873123
$112$	−2291.77	+	288.535i	−0.0172634	+	0.00217347i
$113$	115196.			0.848672			0.424336	−	0.905505i	$-0.360508\pi$
$113$	115196.			0.848672			0.424336	+	0.905505i	$0.360508\pi$
$114$	25287.9	+	23751.9i	0.182243	+	0.171173i
$115$		0			0
$116$	166348.	−	10430.5i	1.14781	−	0.0719712i
$117$		−	9762.45i		−	0.0659317i
$118$	90651.5	−	96513.6i	0.599335	−	0.638093i
$119$	−1915.33			−0.0123987
$120$		0			0
$121$	−14728.7			−0.0914537
$122$	−129525.	+	137901.i	−0.787872	+	0.838821i
$123$			297787.i			1.77477i
$124$	11290.1	+	180057.i	0.0659391	+	1.05161i
$125$		0			0
$126$	−849.481	−	797.884i	−0.00476680	−	0.00447727i
$127$	−146026.			−0.803378			−0.401689	−	0.915776i	$-0.631577\pi$
$127$	−146026.			−0.803378			−0.401689	+	0.915776i	$0.631577\pi$
$128$	99438.5	−	156434.i	0.536450	−	0.843932i
$129$	−44197.7			−0.233844
$130$		0			0
$131$			12998.0i			0.0661757i	0.999452	+	0.0330878i	$0.0105341\pi$
$131$			12998.0i			0.0661757i	−0.999452	+	0.0330878i	$0.989466\pi$
$132$	−15351.8	−	244834.i	−0.0766873	−	1.22303i
$133$		−	756.603i		−	0.00370885i
$134$	−256237.	+	272807.i	−1.23276	+	1.31248i
$135$		0			0
$136$	98011.6	−	118399.i	0.454392	−	0.548911i
$137$	−189204.			−0.861249			−0.430624	−	0.902531i	$-0.641707\pi$
$137$	−189204.			−0.861249			−0.430624	+	0.902531i	$0.641707\pi$
$138$	250806.	−	267025.i	1.12109	−	1.19359i
$139$		−	44334.4i		−	0.194627i	−0.995254	−	0.0973136i	$-0.968975\pi$
$139$		−	44334.4i		−	0.194627i	0.995254	−	0.0973136i	$-0.0310250\pi$
$140$		0			0
$141$			416562.i			1.76454i
$142$	−212024.	−	199146.i	−0.882396	−	0.828800i
$143$	−44814.3			−0.183264
$144$	92792.2	−	11682.6i	0.372911	−	0.0469497i
$145$		0			0
$146$	−87708.3	−	82381.0i	−0.340533	−	0.319849i
$147$		−	307219.i		−	1.17261i
$148$	−1979.66	+	124.130i	−0.00742911	+	0.000465826i
$149$			352240.i			1.29979i	0.760024	+	0.649895i	$0.225187\pi$
$149$			352240.i			1.29979i	−0.760024	+	0.649895i	$0.774813\pi$
$150$		0			0
$151$	446273.			1.59279			0.796395	−	0.604776i	$-0.206738\pi$
$151$	446273.			1.59279			0.796395	+	0.604776i	$0.206738\pi$
$152$	46770.6	+	38717.0i	0.164197	+	0.135923i
$153$	77550.5			0.267828
$154$	−3662.67	+	3899.52i	−0.0124450	+	0.0132498i
$155$		0			0
$156$	−3913.87	−	62419.4i	−0.0128764	−	0.205356i
$157$			383316.i			1.24110i	0.784165	+	0.620552i	$0.213091\pi$
$157$			383316.i			1.24110i	−0.784165	+	0.620552i	$0.786909\pi$
$158$	158410.	+	148789.i	0.504825	+	0.474163i
$159$	249907.			0.783946
$160$		0			0
$161$	−7989.29			−0.0242909
$162$	−300591.	−	282333.i	−0.899887	−	0.845229i
$163$			405200.i			1.19454i	0.802040	+	0.597270i	$0.203748\pi$
$163$			405200.i			1.19454i	−0.802040	+	0.597270i	$0.796252\pi$
$164$	32613.8	+	520133.i	0.0946872	+	1.51010i
$165$		0			0
$166$	−360818.	+	384150.i	−1.01629	+	1.08201i
$167$	193042.			0.535625			0.267812	−	0.963471i	$-0.413699\pi$
$167$	193042.			0.535625			0.267812	+	0.963471i	$0.413699\pi$
$168$	−5751.31	−	4760.97i	−0.0157215	−	0.0130143i
$169$	359868.			0.969229
$170$		0			0
$171$			30634.3i			0.0801157i
$172$	−77198.4	+	4840.55i	−0.198970	+	0.0124760i
$173$			599397.i			1.52265i	0.648372	+	0.761323i	$0.275450\pi$
$173$			599397.i			1.52265i	−0.648372	+	0.761323i	$0.724550\pi$
$174$	392689.	+	368838.i	0.983277	+	0.923554i
$175$		0			0
$176$	−53628.7	−	425960.i	−0.130501	−	1.03654i
$177$	427994.			1.02684
$178$	−250191.	−	234995.i	−0.591864	−	0.555915i
$179$		−	421278.i		−	0.982736i	−0.870952	−	0.491368i	$-0.836497\pi$
$179$		−	421278.i		−	0.982736i	0.870952	−	0.491368i	$-0.163503\pi$
$180$		0			0
$181$			183362.i			0.416018i	0.978127	+	0.208009i	$0.0666983\pi$
$181$			183362.i			0.416018i	−0.978127	+	0.208009i	$0.933302\pi$
$182$	−933.783	+	994.168i	−0.00208962	+	0.00222475i
$183$	−611529.			−1.34986
$184$	408829.	−	493871.i	0.890219	−	1.07540i
$185$		0			0
$186$	−399235.	+	425052.i	−0.846148	+	0.900866i
$187$		−	355994.i		−	0.744455i
$188$	45622.1	+	727593.i	0.0941414	+	1.50139i
$189$			6255.58i			0.0127384i
$190$		0			0
$191$	982533.			1.94878			0.974392	−	0.224856i	$-0.0721912\pi$
$191$	982533.			1.94878			0.974392	+	0.224856i	$0.0721912\pi$
$192$	588614.	−	111898.i	1.15233	−	0.219063i
$193$	164978.			0.318810			0.159405	−	0.987213i	$-0.449042\pi$
$193$	164978.			0.318810			0.159405	+	0.987213i	$0.449042\pi$
$194$	−649115.	−	609688.i	−1.23827	−	1.16306i
$195$		0			0
$196$	−33646.8	−	536607.i	−0.0625609	−	0.997738i
$197$			506605.i			0.930044i	0.885299	+	0.465022i	$0.153954\pi$
$197$			506605.i			0.930044i	−0.885299	+	0.465022i	$0.846046\pi$
$198$	148299.	−	157889.i	0.268828	−	0.286212i
$199$	475645.			0.851433			0.425716	−	0.904857i	$-0.360022\pi$
$199$	475645.			0.851433			0.425716	+	0.904857i	$0.360022\pi$
$200$		0			0
$201$	−1.20977e6			−2.11210
$202$	−482196.	+	513378.i	−0.831467	+	0.885235i
$203$		−	11749.1i		−	0.0200108i
$204$	495844.	−	31090.8i	0.834200	−	0.0523066i
$205$		0			0
$206$	42660.8	+	40069.7i	0.0700425	+	0.0657882i
$207$	323481.			0.524714
$208$	−13672.4	−	108597.i	−0.0219122	−	0.174044i
$209$	140626.			0.222690
$210$		0			0
$211$		−	260466.i		−	0.402759i	−0.979513	−	0.201379i	$-0.935458\pi$
$211$		−	260466.i		−	0.402759i	0.979513	−	0.201379i	$-0.0645424\pi$
$212$	436503.	−	27370.0i	0.667034	−	0.0418249i
$213$		−	940228.i		−	1.41999i
$214$	−274064.	+	291786.i	−0.409088	+	0.435543i
$215$		0			0
$216$	−386699.	−	320111.i	−0.563947	−	0.466838i
$217$	12717.4			0.0183337
$218$	497476.	−	529646.i	0.708975	−	0.754822i
$219$		−	388946.i		−	0.547998i
$220$		0			0
$221$		−	90759.2i		−	0.125000i
$222$	−4673.30	−	4389.45i	−0.00636416	−	0.00597761i
$223$	−624180.			−0.840519			−0.420260	−	0.907404i	$-0.638061\pi$
$223$	−624180.			−0.840519			−0.420260	+	0.907404i	$0.638061\pi$
$224$	−10567.0	−	7685.91i	−0.0140712	−	0.0102347i
$225$		0			0
$226$	474982.	+	446132.i	0.618594	+	0.581021i
$227$		−	656014.i		−	0.844984i	−0.906367	−	0.422492i	$-0.861155\pi$
$227$		−	656014.i		−	0.844984i	0.906367	−	0.422492i	$-0.138845\pi$
$228$	12281.6	+	195871.i	0.0156466	+	0.249535i
$229$			807777.i			1.01790i	0.860798	+	0.508948i	$0.169965\pi$
$229$			807777.i			1.01790i	−0.860798	+	0.508948i	$0.830035\pi$
$230$		0			0
$231$	−17292.6			−0.0213221
$232$	726290.	+	601227.i	0.885911	+	0.733362i
$233$	1.30452e6			1.57421			0.787103	−	0.616822i	$-0.211580\pi$
$233$	1.30452e6			1.57421			0.787103	+	0.616822i	$0.211580\pi$
$234$	37808.2	−	40253.1i	0.0451384	−	0.0480574i
$235$		0			0
$236$	747560.	−	46874.1i	0.873707	−	0.0547839i
$237$			702478.i			0.812385i
$238$	−7897.42	−	7417.74i	−0.00903739	−	0.00848847i
$239$	−1.21861e6			−1.37997			−0.689985	−	0.723824i	$-0.742383\pi$
$239$	−1.21861e6			−1.37997			−0.689985	+	0.723824i	$0.742383\pi$
$240$		0			0
$241$	−983578.			−1.09085			−0.545426	−	0.838159i	$-0.683632\pi$
$241$	−983578.			−1.09085			−0.545426	+	0.838159i	$0.683632\pi$
$242$	−60730.3	−	57041.6i	−0.0666603	−	0.0626114i
$243$		−	659093.i		−	0.716030i
$244$	−1.06813e6	+	66975.0i	−1.14855	+	0.0720175i
$245$		0			0
$246$	−1.15327e6	+	1.22785e6i	−1.21505	+	1.29363i
$247$	35852.1			0.0373914
$248$	−650776.	+	786147.i	−0.671897	+	0.811660i
$249$	−1.70353e6			−1.74121
$250$		0			0
$251$		−	1.60324e6i		−	1.60625i	−0.595809	−	0.803126i	$-0.703168\pi$
$251$		−	1.60324e6i		−	1.60625i	0.595809	−	0.803126i	$-0.296832\pi$
$252$	−412.570	−	6579.77i	−0.000409257	−	0.00652693i
$253$		−	1.48493e6i		−	1.45849i
$254$	−602102.	−	565531.i	−0.585579	−	0.550012i
$255$		0			0
$256$	1.01585e6	−	259913.i	0.968793	−	0.247872i
$257$	−1.07709e6			−1.01723			−0.508617	−	0.860993i	$-0.669843\pi$
$257$	−1.07709e6			−1.01723			−0.508617	+	0.860993i	$0.669843\pi$
$258$	−182239.	−	171170.i	−0.170448	−	0.160095i
$259$			139.823i			0.000129518i
$260$		0			0
$261$			475713.i			0.432259i
$262$	−50338.9	+	53594.2i	−0.0453055	+	0.0482352i
$263$	812889.			0.724673			0.362336	−	0.932047i	$-0.381979\pi$
$263$	812889.			0.724673			0.362336	+	0.932047i	$0.381979\pi$
$264$	884898.	−	1.06897e6i	0.781418	−	0.943964i
$265$		0			0
$266$	2930.19	−	3119.67i	0.00253917	−	0.00270337i
$267$		−	1.10948e6i		−	0.952451i
$268$	−2.11306e6	+	132495.i	−1.79711	+	0.112684i
$269$		−	113957.i		−	0.0960201i	−0.998847	−	0.0480101i	$-0.984712\pi$
$269$		−	113957.i		−	0.0960201i	0.998847	−	0.0480101i	$-0.0152880\pi$
$270$		0			0
$271$	372728.			0.308297			0.154148	−	0.988048i	$-0.450737\pi$
$271$	372728.			0.308297			0.154148	+	0.988048i	$0.450737\pi$
$272$	862667.	−	108610.i	0.707002	−	0.0890120i
$273$	−4408.68			−0.00358015
$274$	−780137.	−	732752.i	−0.627761	−	0.589632i
$275$		0			0
$276$	2.06828e6	−	129687.i	1.63432	−	0.102476i
$277$			914263.i			0.715932i	0.933735	+	0.357966i	$0.116530\pi$
$277$			914263.i			0.715932i	−0.933735	+	0.357966i	$0.883470\pi$
$278$	171699.	−	182802.i	0.133247	−	0.141863i
$279$	−514918.			−0.396030
$280$		0			0
$281$	−511184.			−0.386199			−0.193100	−	0.981179i	$-0.561854\pi$
$281$	−511184.			−0.386199			−0.193100	+	0.981179i	$0.561854\pi$
$282$	−1.61327e6	+	1.71759e6i	−1.20805	+	1.28617i
$283$		−	533078.i		−	0.395662i	−0.980236	−	0.197831i	$-0.936610\pi$
$283$		−	533078.i		−	0.395662i	0.980236	−	0.197831i	$-0.0633897\pi$
$284$	−102974.	−	1.64226e6i	−0.0757587	−	1.20822i
$285$		0			0
$286$	−184781.	−	173558.i	−0.133580	−	0.125467i
$287$	36736.9			0.0263268
$288$	427851.	+	311197.i	0.303956	+	0.221082i
$289$	−698889.			−0.492225
$290$		0			0
$291$		−	2.87853e6i		−	1.99268i
$292$	−42597.6	−	679357.i	−0.0292366	−	0.466273i
$293$		−	2.54648e6i		−	1.73289i	−0.499273	−	0.866445i	$-0.666400\pi$
$293$		−	2.54648e6i		−	1.73289i	0.499273	−	0.866445i	$-0.333600\pi$
$294$	1.18980e6	−	1.26674e6i	0.802799	−	0.854714i
$295$		0			0
$296$	−8643.40	−	7155.05i	−0.00573397	−	0.00474661i
$297$	−1.16269e6			−0.764847
$298$	−1.36416e6	+	1.45238e6i	−0.889868	+	0.947412i
$299$		−	378577.i		−	0.244893i
$300$		0			0
$301$			5452.51i			0.00346881i
$302$	1.84010e6	+	1.72834e6i	1.16098	+	1.09046i
$303$	−2.27659e6			−1.42455
$304$	42903.7	+	340774.i	0.0266263	+	0.211487i
$305$		0			0
$306$	319761.	+	300339.i	0.195219	+	0.183361i
$307$			740673.i			0.448518i	0.974530	+	0.224259i	$0.0719962\pi$
$307$			740673.i			0.448518i	−0.974530	+	0.224259i	$0.928004\pi$
$308$	−30204.3	+	1893.89i	−0.0181423	+	0.00113757i
$309$			189181.i			0.112715i
$310$		0			0
$311$	1.08876e6			0.638310			0.319155	−	0.947702i	$-0.396601\pi$
$311$	1.08876e6			0.638310			0.319155	+	0.947702i	$0.396601\pi$
$312$	225601.	−	272529.i	0.131206	−	0.158499i
$313$	−1.08277e6			−0.624705			−0.312353	−	0.949966i	$-0.601117\pi$
$313$	−1.08277e6			−0.624705			−0.312353	+	0.949966i	$0.601117\pi$
$314$	−1.48451e6	+	1.58051e6i	−0.849690	+	0.904636i
$315$		0			0
$316$	76935.7	+	1.22699e6i	0.0433421	+	0.691231i
$317$		−	2.93243e6i		−	1.63900i	−0.573078	−	0.819501i	$-0.694251\pi$
$317$		−	2.93243e6i		−	1.63900i	0.573078	−	0.819501i	$-0.305749\pi$
$318$	1.03043e6	+	967845.i	0.571415	+	0.536708i
$319$	2.18375e6			1.20151
$320$		0			0
$321$	−1.29394e6			−0.700892
$322$	−32941.9	−	30941.1i	−0.0177055	−	0.0166301i
$323$			284800.i			0.151892i
$324$	−145989.	−	2.32827e6i	−0.0772604	−	1.23217i
$325$		0			0
$326$	−1.56927e6	+	1.67075e6i	−0.817811	+	0.870696i
$327$	2.34874e6			1.21469
$328$	−1.87990e6	+	2.27095e6i	−0.964831	+	1.16553i
$329$	51389.8			0.0261750
$330$		0			0
$331$		−	357214.i		−	0.179209i	−0.995977	−	0.0896043i	$-0.971440\pi$
$331$		−	357214.i		−	0.179209i	0.995977	−	0.0896043i	$-0.0285602\pi$
$332$	−2.97549e6	+	186572.i	−1.48154	+	0.0928967i
$333$		−	5661.34i		−	0.00279775i
$334$	795963.	+	747617.i	0.390415	+	0.366702i
$335$		0			0
$336$	−5275.80	−	41904.5i	−0.00254941	−	0.0202494i
$337$	−1.45195e6			−0.696429			−0.348215	−	0.937415i	$-0.613212\pi$
$337$	−1.45195e6			−0.696429			−0.348215	+	0.937415i	$0.613212\pi$
$338$	1.48383e6	+	1.39370e6i	0.706467	+	0.663557i
$339$			2.10633e6i			0.995465i
$340$		0			0
$341$			2.36372e6i			1.10081i
$342$	−118641.	+	126313.i	−0.0548492	+	0.0583961i
$343$	−75812.5			−0.0347941
$344$	−337056.	−	279016.i	−0.153570	−	0.127126i
$345$		0			0
$346$	−2.32135e6	+	2.47147e6i	−1.04244	+	1.10985i
$347$			393735.i			0.175541i	0.996141	+	0.0877707i	$0.0279743\pi$
$347$			393735.i			0.175541i	−0.996141	+	0.0877707i	$0.972026\pi$
$348$	190719.	+	3.04163e6i	0.0844199	+	1.34635i
$349$			1.73875e6i			0.764140i	0.924133	+	0.382070i	$0.124789\pi$
$349$			1.73875e6i			0.764140i	−0.924133	+	0.382070i	$0.875211\pi$
$350$		0			0
$351$	−296424.			−0.128424
$352$	1.42854e6	−	1.96404e6i	0.614521	−	0.844877i
$353$	2.05124e6			0.876154			0.438077	−	0.898937i	$-0.355660\pi$
$353$	2.05124e6			0.876154			0.438077	+	0.898937i	$0.355660\pi$
$354$	1.76473e6	+	1.65754e6i	0.748462	+	0.703002i
$355$		0			0
$356$	−121511.	−	1.93789e6i	−0.0508149	−	0.810409i
$357$		−	35021.4i		−	0.0145433i
$358$	1.63153e6	−	1.73704e6i	0.672804	−	0.716312i
$359$	3.56728e6			1.46084			0.730418	−	0.683000i	$-0.239325\pi$
$359$	3.56728e6			1.46084			0.730418	+	0.683000i	$0.239325\pi$
$360$		0			0
$361$	2.36360e6			0.954564
$362$	−710126.	+	756048.i	−0.284816	+	0.303234i
$363$		−	269311.i		−	0.107272i
$364$	−7700.46	+	482.840i	−0.00304623	+	0.000191007i
$365$		0			0
$366$	−2.52149e6	−	2.36834e6i	−0.983910	−	0.924148i
$367$	3.72721e6			1.44450			0.722251	−	0.691631i	$-0.243107\pi$
$367$	3.72721e6			1.44450			0.722251	+	0.691631i	$0.243107\pi$
$368$	3.59838e6	−	453038.i	1.38512	−	0.174387i
$369$	−1.48745e6			−0.568691
$370$		0			0
$371$		−	30830.2i		−	0.0116290i
$372$	−3.29230e6	+	206436.i	−1.23351	+	0.0773444i
$373$		−	1.71134e6i		−	0.636891i	−0.947941	−	0.318446i	$-0.896839\pi$
$373$		−	1.71134e6i		−	0.636891i	0.947941	−	0.318446i	$-0.103161\pi$
$374$	1.37870e6	−	1.46786e6i	0.509672	−	0.542631i
$375$		0			0
$376$	−2.62972e6	+	3.17674e6i	−0.959269	+	1.15881i
$377$	556738.			0.201743
$378$	−24226.7	+	25793.4i	−0.00872098	+	0.00928494i
$379$			3.60174e6i			1.28799i	0.765028	+	0.643997i	$0.222725\pi$
$379$			3.60174e6i			1.28799i	−0.765028	+	0.643997i	$0.777275\pi$
$380$		0			0
$381$		−	2.67005e6i		−	0.942337i
$382$	4.05124e6	+	3.80517e6i	1.42046	+	1.33418i
$383$	3.80875e6			1.32674			0.663369	−	0.748293i	$-0.269126\pi$
$383$	3.80875e6			1.32674			0.663369	+	0.748293i	$0.269126\pi$
$384$	2.86037e6	+	1.81821e6i	0.989905	+	0.629239i
$385$		0			0
$386$	680246.	+	638929.i	0.232379	+	0.218265i
$387$		−	220768.i		−	0.0749306i
$388$	−315257.	−	5.02781e6i	−0.106313	−	1.69551i
$389$			431800.i			0.144680i	0.997380	+	0.0723401i	$0.0230467\pi$
$389$			431800.i			0.144680i	−0.997380	+	0.0723401i	$0.976953\pi$
$390$		0			0
$391$	3.00732e6			0.994805
$392$	1.93945e6	−	2.34288e6i	0.637475	−	0.770078i
$393$	−237665.			−0.0776220
$394$	−1.96199e6	+	2.08886e6i	−0.636731	+	0.677906i
$395$		0			0
$396$	1.22295e6	−	76682.3i	0.391896	−	0.0245730i
$397$		−	2.28465e6i		−	0.727518i	−0.931493	−	0.363759i	$-0.881493\pi$
$397$		−	2.28465e6i		−	0.727518i	0.931493	−	0.363759i	$-0.118507\pi$
$398$	1.96121e6	+	1.84209e6i	0.620606	+	0.582911i
$399$	13834.3			0.00435036
$400$		0			0
$401$	1.63473e6			0.507674			0.253837	−	0.967247i	$-0.418307\pi$
$401$	1.63473e6			0.507674			0.253837	+	0.967247i	$0.418307\pi$
$402$	−4.98821e6	−	4.68523e6i	−1.53950	−	1.44599i
$403$			602621.i			0.184834i
$404$	−3.97644e6	+	249334.i	−1.21211	+	0.0760024i
$405$		0			0
$406$	45502.2	−	48444.7i	0.0136999	−	0.0145858i
$407$	−25988.3			−0.00777663
$408$	2.16490e6	+	1.79212e6i	0.643855	+	0.532987i
$409$	5.21834e6			1.54250			0.771248	−	0.636534i	$-0.219633\pi$
$409$	5.21834e6			1.54250			0.771248	+	0.636534i	$0.219633\pi$
$410$		0			0
$411$		−	3.45955e6i		−	1.01022i
$412$	20719.2	+	330435.i	0.00601354	+	0.0959055i
$413$		−	52800.0i		−	0.0152321i
$414$	1.33379e6	+	1.25278e6i	0.382462	+	0.359231i
$415$		0			0
$416$	364201.	−	500724.i	0.103183	−	0.141862i
$417$	810644.			0.228292
$418$	579838.	+	544620.i	0.162318	+	0.152459i
$419$		−	666477.i		−	0.185460i	−0.995691	−	0.0927299i	$-0.970441\pi$
$419$		−	666477.i		−	0.185460i	0.995691	−	0.0927299i	$-0.0295593\pi$
$420$		0			0
$421$			6.82007e6i			1.87536i	0.347504	+	0.937678i	$0.387029\pi$
$421$			6.82007e6i			1.87536i	−0.347504	+	0.937678i	$0.612971\pi$
$422$	1.00874e6	−	1.07397e6i	0.275738	−	0.293569i
$423$	−2.08073e6			−0.565413
$424$	1.90581e6	+	1.57764e6i	0.514833	+	0.426181i
$425$		0			0
$426$	3.64133e6	−	3.87680e6i	0.972156	−	1.03502i
$427$			75442.2i			0.0200237i
$428$	−2.26007e6	+	141713.i	−0.596366	+	0.0373938i
$429$		−	819419.i		−	0.214963i
$430$		0			0
$431$	−1.38707e6			−0.359671			−0.179836	−	0.983697i	$-0.557557\pi$
$431$	−1.38707e6			−0.359671			−0.179836	+	0.983697i	$0.557557\pi$
$432$	−354727.	−	2.81752e6i	−0.0914502	−	0.726368i
$433$	−1.33169e6			−0.341336			−0.170668	−	0.985329i	$-0.554593\pi$
$433$	−1.33169e6			−0.341336			−0.170668	+	0.985329i	$0.554593\pi$
$434$	52437.2	+	49252.2i	0.0133633	+	0.0125517i
$435$		0			0
$436$	4.10245e6	−	257235.i	1.03354	−	0.0648058i
$437$			1.18797e6i			0.297577i
$438$	1.50632e6	−	1.60373e6i	0.375173	−	0.399434i
$439$	−2.78241e6			−0.689064			−0.344532	−	0.938775i	$-0.611962\pi$
$439$	−2.78241e6			−0.689064			−0.344532	+	0.938775i	$0.611962\pi$
$440$		0			0
$441$	1.53456e6			0.375741
$442$	351494.	−	374224.i	0.0855780	−	0.0911120i
$443$			4.63595e6i			1.12235i	0.827696	+	0.561177i	$0.189651\pi$
$443$			4.63595e6i			1.12235i	−0.827696	+	0.561177i	$0.810349\pi$
$444$	−2269.69	−	36197.7i	−0.000546399	−	0.00871411i
$445$		0			0
$446$	−2.57366e6	−	2.41734e6i	−0.612651	−	0.575440i
$447$	−6.44063e6			−1.52461
$448$	−13804.4	−	72615.1i	−0.00324955	−	0.0170935i
$449$	1.18197e6			0.276688			0.138344	−	0.990384i	$-0.455822\pi$
$449$	1.18197e6			0.276688			0.138344	+	0.990384i	$0.455822\pi$
$450$		0			0
$451$			6.82811e6i			1.58074i
$452$	230686.	+	3.67903e6i	0.0531098	+	0.847009i
$453$			8.16001e6i			1.86829i
$454$	2.54062e6	−	2.70492e6i	0.578496	−	0.615906i
$455$		0			0
$456$	−707931.	+	855190.i	−0.159433	+	0.192597i
$457$	−1.55240e6			−0.347708			−0.173854	−	0.984771i	$-0.555622\pi$
$457$	−1.55240e6			−0.347708			−0.173854	+	0.984771i	$0.555622\pi$
$458$	−3.12838e6	+	3.33068e6i	−0.696875	+	0.741940i
$459$		−	2.35472e6i		−	0.521684i
$460$		0			0
$461$		−	7.43437e6i		−	1.62926i	−0.579978	−	0.814632i	$-0.696939\pi$
$461$		−	7.43437e6i		−	1.62926i	0.579978	−	0.814632i	$-0.303061\pi$
$462$	−71301.9	−	66971.1i	−0.0155416	−	0.0145976i
$463$	−20179.5			−0.00437480			−0.00218740	−	0.999998i	$-0.500696\pi$
$463$	−20179.5			−0.00437480			−0.00218740	+	0.999998i	$0.500696\pi$
$464$	666241.	+	5.29180e6i	0.143660	+	1.14106i
$465$		0			0
$466$	5.37888e6	+	5.05218e6i	1.14743	+	1.07774i
$467$		−	3.58698e6i		−	0.761092i	−0.924762	−	0.380546i	$-0.875736\pi$
$467$		−	3.58698e6i		−	0.761092i	0.924762	−	0.380546i	$-0.124264\pi$
$468$	311786.	−	19549.8i	0.0658024	−	0.00412600i
$469$			149245.i			0.0313306i
$470$		0			0
$471$	−7.00885e6			−1.45578
$472$	3.26392e6	+	2.70189e6i	0.674348	+	0.558229i
$473$	−1.01343e6			−0.208277
$474$	−2.72057e6	+	2.89650e6i	−0.556178	+	0.592144i
$475$		0			0
$476$	−3835.56	−	61170.5i	−0.000775911	−	0.0123744i
$477$			1.24829e6i			0.251200i
$478$	−5.02464e6	−	4.71945e6i	−1.00585	−	0.944760i
$479$	183482.			0.0365388			0.0182694	−	0.999833i	$-0.494184\pi$
$479$	183482.			0.0365388			0.0182694	+	0.999833i	$0.494184\pi$
$480$		0			0
$481$	−6625.61			−0.00130576
$482$	−4.05555e6	−	3.80922e6i	−0.795119	−	0.746824i
$483$		−	146082.i		−	0.0284925i
$484$	−29495.1	−	470395.i	−0.00572316	−	0.0912744i
$485$		0			0
$486$	2.55255e6	−	2.71761e6i	0.490211	−	0.521912i
$487$	−6.68968e6			−1.27815			−0.639077	−	0.769143i	$-0.720683\pi$
$487$	−6.68968e6			−1.27815			−0.639077	+	0.769143i	$0.720683\pi$
$488$	−4.66358e6	−	3.86053e6i	−0.886481	−	0.733834i
$489$	−7.40899e6			−1.40116
$490$		0			0
$491$			9.90038e6i			1.85331i	0.375913	+	0.926655i	$0.377329\pi$
$491$			9.90038e6i			1.85331i	−0.375913	+	0.926655i	$0.622671\pi$
$492$	−9.51050e6	+	596335.i	−1.77129	+	0.111065i
$493$			4.42259e6i			0.819520i
$494$	147827.	+	138849.i	0.0272545	+	0.0255991i
$495$		0			0
$496$	−5.72792e6	+	721149.i	−1.04543	+	0.131620i
$497$	−115993.			−0.0210639
$498$	−7.02410e6	−	6.59747e6i	−1.26916	−	1.19208i
$499$		−	5.95907e6i		−	1.07134i	−0.844428	−	0.535670i	$-0.820059\pi$
$499$		−	5.95907e6i		−	1.07134i	0.844428	−	0.535670i	$-0.179941\pi$
$500$		0			0
$501$			3.52973e6i			0.628271i
$502$	6.20905e6	−	6.61057e6i	1.09968	−	1.17079i
$503$	3.69353e6			0.650910			0.325455	−	0.945557i	$-0.394482\pi$
$503$	3.69353e6			0.650910			0.325455	+	0.945557i	$0.394482\pi$
$504$	23781.1	−	28727.9i	0.00417019	−	0.00503765i
$505$		0			0
$506$	5.75087e6	−	6.12276e6i	0.998521	−	1.06309i
$507$			6.58010e6i			1.13687i
$508$	−292425.	−	4.66366e6i	−0.0502753	−	0.801803i
$509$		−	7.94222e6i		−	1.35877i	−0.733780	−	0.679387i	$-0.762246\pi$
$509$		−	7.94222e6i		−	1.35877i	0.733780	−	0.679387i	$-0.237754\pi$
$510$		0			0
$511$	−47982.9			−0.00812894
$512$	5.19522e6	+	2.86253e6i	0.875849	+	0.482586i
$513$	930172.			0.156052
$514$	−4.44114e6	−	4.17139e6i	−0.741458	−	0.696423i
$515$		0			0
$516$	−88508.4	−	1.41155e6i	−0.0146339	−	0.233385i
$517$			9.55157e6i			1.57162i
$518$	−541.510	+	576.528i	−8.86712e−5	+	9.44052e-5i
$519$	−1.09598e7			−1.78602
$520$		0			0
$521$	−1.06312e7			−1.71588			−0.857940	−	0.513749i	$-0.828256\pi$
$521$	−1.06312e7			−1.71588			−0.857940	+	0.513749i	$0.828256\pi$
$522$	−1.84235e6	+	1.96149e6i	−0.295935	+	0.315072i
$523$		−	3.13913e6i		−	0.501828i	−0.968009	−	0.250914i	$-0.919269\pi$
$523$		−	3.13913e6i		−	0.501828i	0.968009	−	0.250914i	$-0.0807312\pi$
$524$	−415121.	+	26029.2i	−0.0660460	+	0.00414127i
$525$		0			0
$526$	3.35175e6	+	3.14817e6i	0.528211	+	0.496128i
$527$	−4.78708e6			−0.750834
$528$	7.78859e6	−	980588.i	1.21583	−	0.153074i
$529$	6.10788e6			0.948967
$530$		0			0
$531$			2.13783e6i			0.329032i
$532$	24163.8	−	1515.14i	0.00370158	−	0.000232099i
$533$			1.74080e6i			0.265418i
$534$	4.29683e6	−	4.57469e6i	0.652071	−	0.694238i
$535$		0			0
$536$	−9.22584e6	−	7.63720e6i	−1.38706	−	1.14821i
$537$	7.70298e6			1.15272
$538$	441337.	−	469876.i	0.0657377	−	0.0699887i
$539$		−	7.04438e6i		−	1.04441i
$540$		0			0
$541$		−	1.20044e7i		−	1.76339i	−0.471821	−	0.881694i	$-0.656403\pi$
$541$		−	1.20044e7i		−	1.76339i	0.471821	−	0.881694i	$-0.343597\pi$
$542$	1.53686e6	+	1.44351e6i	0.224716	+	0.211067i
$543$	−3.35273e6			−0.487976
$544$	3.97763e6	+	2.89312e6i	0.576271	+	0.419150i
$545$		0			0
$546$	−18178.1	−	17074.0i	−0.00260956	−	0.00245106i
$547$			9.93035e6i			1.41905i	0.704682	+	0.709523i	$0.251090\pi$
$547$			9.93035e6i			1.41905i	−0.704682	+	0.709523i	$0.748910\pi$
$548$	−378891.	−	6.04266e6i	−0.0538969	−	0.859561i
$549$		−	3.05460e6i		−	0.432537i
$550$		0			0
$551$	−1.74703e6			−0.245144
$552$	9.03031e6	+	7.47534e6i	1.26141	+	1.04420i
$553$	86662.2			0.0120508
$554$	−3.54077e6	+	3.76974e6i	−0.490144	+	0.521840i
$555$		0			0
$556$	1.41592e6	−	88782.1i	0.194246	−	0.0121798i
$557$		−	8.72764e6i		−	1.19195i	−0.803002	−	0.595976i	$-0.796765\pi$
$557$		−	8.72764e6i		−	1.19195i	0.803002	−	0.595976i	$-0.203235\pi$
$558$	−2.12314e6	−	1.99419e6i	−0.288665	−	0.271132i
$559$	−258370.			−0.0349714
$560$		0			0
$561$	6.50926e6			0.873222
$562$	−2.10774e6	−	1.97972e6i	−0.281499	−	0.264401i
$563$		−	2.13884e6i		−	0.284386i	−0.989839	−	0.142193i	$-0.954585\pi$
$563$		−	2.13884e6i		−	0.284386i	0.989839	−	0.142193i	$-0.0454154\pi$
$564$	−1.33039e7	+	834189.i	−1.76108	+	0.110425i
$565$		0			0
$566$	2.06451e6	−	2.19802e6i	0.270880	−	0.288397i
$567$	−164445.			−0.0214814
$568$	5.93558e6	−	7.17026e6i	0.771956	−	0.932533i
$569$	2.98366e6			0.386339			0.193169	−	0.981165i	$-0.438123\pi$
$569$	2.98366e6			0.386339			0.193169	+	0.981165i	$0.438123\pi$
$570$		0			0
$571$			8.50264e6i			1.09135i	0.837997	+	0.545674i	$0.183726\pi$
$571$			8.50264e6i			1.09135i	−0.837997	+	0.545674i	$0.816274\pi$
$572$	−89743.2	−	1.43125e6i	−0.0114686	−	0.182905i
$573$			1.79654e7i			2.28586i
$574$	151476.	+	142275.i	0.0191895	+	0.0180239i
$575$		0			0
$576$	558931.	+	2.94013e6i	0.0701944	+	0.369242i
$577$	1.55926e7			1.94975			0.974874	−	0.222756i	$-0.0715054\pi$
$577$	1.55926e7			1.94975			0.974874	+	0.222756i	$0.0715054\pi$
$578$	−2.88170e6	−	2.70667e6i	−0.358781	−	0.336989i
$579$			3.01658e6i			0.373954i
$580$		0			0
$581$			210159.i			0.0258289i
$582$	1.11480e7	−	1.18689e7i	1.36424	−	1.45246i
$583$	5.73025e6			0.698236
$584$	2.45538e6	−	2.96614e6i	0.297912	−	0.359881i
$585$		0			0
$586$	9.86205e6	−	1.04998e7i	1.18638	−	1.26310i
$587$		−	1.01432e7i		−	1.21501i	−0.794314	−	0.607507i	$-0.792170\pi$
$587$		−	1.01432e7i		−	1.21501i	0.794314	−	0.607507i	$-0.207830\pi$
$588$	9.81174e6	−	615223.i	1.17031	−	0.0733820i
$589$		−	1.89101e6i		−	0.224598i
$590$		0			0
$591$	−9.26315e6			−1.09091
$592$	−7928.77	−	62976.5i	−0.000929826	−	0.00738540i
$593$	−1.44098e7			−1.68276			−0.841381	−	0.540442i	$-0.818257\pi$
$593$	−1.44098e7			−1.68276			−0.841381	+	0.540442i	$0.818257\pi$
$594$	−4.79409e6	−	4.50291e6i	−0.557494	−	0.523633i
$595$		0			0
$596$	−1.12496e7	+	705381.i	−1.29724	+	0.0813407i
$597$			8.69706e6i			0.998704i
$598$	1.46616e6	−	1.56097e6i	0.167660	−	0.178502i
$599$	−3.13415e6			−0.356905			−0.178452	−	0.983949i	$-0.557109\pi$
$599$	−3.13415e6			−0.356905			−0.178452	+	0.983949i	$0.557109\pi$
$600$		0			0
$601$	1.57244e7			1.77578			0.887889	−	0.460058i	$-0.152171\pi$
$601$	1.57244e7			1.77578			0.887889	+	0.460058i	$0.152171\pi$
$602$	−21116.6	+	22482.1i	−0.00237483	+	0.00252840i
$603$		−	6.04283e6i		−	0.676780i
$604$	893688.	+	1.42528e7i	0.0996766	+	1.58967i
$605$		0			0
$606$	−9.38699e6	−	8.81683e6i	−1.03835	−	0.975284i
$607$	1.03887e7			1.14443			0.572217	−	0.820102i	$-0.306083\pi$
$607$	1.03887e7			1.14443			0.572217	+	0.820102i	$0.306083\pi$
$608$	−1.14285e6	+	1.57126e6i	−0.125381	+	0.172381i
$609$	214830.			0.0234721
$610$		0			0
$611$			2.43513e6i			0.263888i
$612$	155299.	+	2.47675e6i	0.0167606	+	0.267303i
$613$		−	1.46355e7i		−	1.57310i	−0.617525	−	0.786551i	$-0.711865\pi$
$613$		−	1.46355e7i		−	1.57310i	0.617525	−	0.786551i	$-0.288135\pi$
$614$	−2.86849e6	+	3.05399e6i	−0.307067	+	0.326923i
$615$		0			0
$616$	−131875.	−	109167.i	−0.0140027	−	0.0115915i
$617$	6.06227e6			0.641095			0.320547	−	0.947233i	$-0.396133\pi$
$617$	6.06227e6			0.641095			0.320547	+	0.947233i	$0.396133\pi$
$618$	−732665.	+	780044.i	−0.0771674	+	0.0821576i
$619$		−	888836.i		−	0.0932384i	−0.998913	−	0.0466192i	$-0.985155\pi$
$619$		−	888836.i		−	0.0932384i	0.998913	−	0.0466192i	$-0.0148447\pi$
$620$		0			0
$621$		−	9.82207e6i		−	1.02205i
$622$	4.48925e6	+	4.21658e6i	0.465262	+	0.437003i
$623$	−136873.			−0.0141285
$624$	1.98567e6	−	249997.i	0.204148	−	0.0257024i
$625$		0			0
$626$	−4.46454e6	−	4.19337e6i	−0.455346	−	0.427688i
$627$			2.57132e6i			0.261208i
$628$	−1.22421e7	+	767613.i	−1.23867	+	0.0776682i
$629$		−	52632.2i		−	0.00530426i
$630$		0			0
$631$	5.86047e6			0.585948			0.292974	−	0.956120i	$-0.405355\pi$
$631$	5.86047e6			0.585948			0.292974	+	0.956120i	$0.405355\pi$
$632$	−4.43468e6	+	5.35716e6i	−0.441642	+	0.533509i
$633$	4.76256e6			0.472423
$634$	1.13568e7	−	1.20912e7i	1.12210	−	1.19466i
$635$		0			0
$636$	500453.	+	7.98136e6i	0.0490592	+	0.782409i
$637$		−	1.79594e6i		−	0.175365i
$638$	9.00418e6	+	8.45727e6i	0.875774	+	0.822581i
$639$	4.69645e6			0.455007
$640$		0			0
$641$	6.88679e6			0.662021			0.331011	−	0.943627i	$-0.392610\pi$
$641$	6.88679e6			0.662021			0.331011	+	0.943627i	$0.392610\pi$
$642$	−5.33525e6	−	5.01119e6i	−0.510878	−	0.479848i
$643$			7.66403e6i			0.731021i	0.930807	+	0.365510i	$0.119106\pi$
$643$			7.66403e6i			0.731021i	−0.930807	+	0.365510i	$0.880894\pi$
$644$	−15999.0	−	255156.i	−0.00152012	−	0.0242433i
$645$		0			0
$646$	−1.10298e6	+	1.17430e6i	−0.103989	+	0.110713i
$647$	−3.93185e6			−0.369263			−0.184631	−	0.982808i	$-0.559109\pi$
$647$	−3.93185e6			−0.369263			−0.184631	+	0.982808i	$0.559109\pi$
$648$	8.41500e6	−	1.01654e7i	0.787257	−	0.951017i
$649$	9.81369e6			0.914577
$650$		0			0
$651$			232535.i			0.0215048i
$652$	−1.29410e7	+	811436.i	−1.19220	+	0.0747542i
$653$			5.55582e6i			0.509876i	0.966957	+	0.254938i	$0.0820551\pi$
$653$			5.55582e6i			0.509876i	−0.966957	+	0.254938i	$0.917945\pi$
$654$	9.68446e6	+	9.09623e6i	0.885382	+	0.831605i
$655$		0			0
$656$	−1.65463e7	+	2.08319e6i	−1.50121	+	0.189003i
$657$	1.94279e6			0.175595
$658$	211893.	+	199023.i	0.0190789	+	0.0179200i
$659$		−	2.17299e6i		−	0.194914i	−0.995240	−	0.0974572i	$-0.968929\pi$
$659$		−	2.17299e6i		−	0.194914i	0.995240	−	0.0974572i	$-0.0310709\pi$
$660$		0			0
$661$			6.93458e6i			0.617329i	0.951171	+	0.308665i	$0.0998821\pi$
$661$			6.93458e6i			0.617329i	−0.951171	+	0.308665i	$0.900118\pi$
$662$	1.38343e6	−	1.47289e6i	0.122691	−	0.130625i
$663$	1.65951e6			0.146621
$664$	−1.29913e7	−	1.07542e7i	−1.14349	−	0.946586i
$665$		0			0
$666$	21925.4	−	23343.2i	0.00191541	−	0.00203927i
$667$			1.84476e7i			1.60556i
$668$	386578.	+	6.16524e6i	0.0335193	+	0.534575i
$669$		−	1.14130e7i		−	0.985902i
$670$		0			0
$671$	−1.40221e7			−1.20228
$672$	140535.	−	193215.i	0.0120050	−	0.0165051i
$673$	−7.72402e6			−0.657364			−0.328682	−	0.944441i	$-0.606604\pi$
$673$	−7.72402e6			−0.657364			−0.328682	+	0.944441i	$0.606604\pi$
$674$	−5.98677e6	−	5.62314e6i	−0.507625	−	0.476792i
$675$		0			0
$676$	720655.	+	1.14932e7i	0.0606542	+	0.967329i
$677$		−	1.38586e7i		−	1.16211i	−0.813865	−	0.581054i	$-0.802640\pi$
$677$		−	1.38586e7i		−	1.16211i	0.813865	−	0.581054i	$-0.197360\pi$
$678$	−8.15742e6	+	8.68493e6i	−0.681520	+	0.725591i
$679$	−355113.			−0.0295592
$680$		0			0
$681$	1.19951e7			0.991139
$682$	−9.15427e6	+	9.74625e6i	−0.753638	+	0.802373i
$683$		−	778871.i		−	0.0638872i	−0.999490	−	0.0319436i	$-0.989830\pi$
$683$		−	778871.i		−	0.0638872i	0.999490	−	0.0319436i	$-0.0101697\pi$
$684$	−978377.	+	61346.9i	−0.0799587	+	0.00501363i
$685$		0			0
$686$	−312595.	−	293608.i	−0.0253613	−	0.0238209i
$687$	−1.47700e7			−1.19396
$688$	−309188.	−	2.45581e6i	−0.0249030	−	0.197799i
$689$	1.46090e6			0.117239
$690$		0			0
$691$			6.98899e6i			0.556826i	0.960461	+	0.278413i	$0.0898084\pi$
$691$			6.98899e6i			0.556826i	−0.960461	+	0.278413i	$0.910192\pi$
$692$	−1.91431e7	+	1.20033e6i	−1.51966	+	0.0952871i
$693$		−	86376.8i		−	0.00683225i
$694$	−1.52486e6	+	1.62347e6i	−0.120180	+	0.127952i
$695$		0			0
$696$	−1.09933e7	+	1.32800e7i	−0.860210	+	1.03915i
$697$	−1.38285e7			−1.07818
$698$	−6.73386e6	+	7.16931e6i	−0.523149	+	0.556979i
$699$			2.38529e7i			1.84649i
$700$		0			0
$701$		−	4.14587e6i		−	0.318655i	−0.987226	−	0.159328i	$-0.949067\pi$
$701$		−	4.14587e6i		−	0.318655i	0.987226	−	0.159328i	$-0.0509326\pi$
$702$	−1.22223e6	−	1.14800e6i	−0.0936077	−	0.0879221i
$703$	20791.0			0.00158667
$704$	1.34966e7	−	2.56576e6i	1.02635	−	0.195112i
$705$		0			0
$706$	8.45781e6	+	7.94410e6i	0.638626	+	0.599836i
$707$			280855.i			0.0211317i
$708$	857081.	+	1.36690e7i	0.0642597	+	1.02483i
$709$			1.52511e7i			1.13943i	0.821843	+	0.569714i	$0.192946\pi$
$709$			1.52511e7i			1.13943i	−0.821843	+	0.569714i	$0.807054\pi$
$710$		0			0
$711$	−3.50889e6			−0.260313
$712$	7.00407e6	−	8.46102e6i	0.517787	−	0.625493i
$713$	−1.99680e7			−1.47099
$714$	135632.	−	144402.i	0.00995670	−	0.0106006i
$715$		0			0
$716$	1.34545e7	−	843634.i	0.980809	−	0.0614995i
$717$		−	2.22820e7i		−	1.61866i
$718$	1.47088e7	+	1.38154e7i	1.06480	+	1.00012i
$719$	−1.60151e6			−0.115534			−0.0577668	−	0.998330i	$-0.518398\pi$
$719$	−1.60151e6			−0.115534			−0.0577668	+	0.998330i	$0.518398\pi$
$720$		0			0
$721$	23338.6			0.00167200
$722$	9.74572e6	+	9.15378e6i	0.695779	+	0.653518i
$723$		−	1.79845e7i		−	1.27954i
$724$	−5.85607e6	+	367192.i	−0.415203	+	0.0260344i
$725$		0			0
$726$	1.04299e6	−	1.11044e6i	0.0734412	−	0.0781904i
$727$	6.15453e6			0.431876			0.215938	−	0.976407i	$-0.430719\pi$
$727$	6.15453e6			0.431876			0.215938	+	0.976407i	$0.430719\pi$
$728$	−33621.0	−	27831.6i	−0.00235116	−	0.00194630i
$729$	−5.66362e6			−0.394708
$730$		0			0
$731$		−	2.05243e6i		−	0.142061i
$732$	−1.22462e6	−	1.95306e7i	−0.0844742	−	1.34722i
$733$			7.15476e6i			0.491853i	0.969289	+	0.245926i	$0.0790921\pi$
$733$			7.15476e6i			0.491853i	−0.969289	+	0.245926i	$0.920908\pi$
$734$	1.53682e7	+	1.44348e7i	1.05289	+	0.988941i
$735$		0			0
$736$	1.65916e7	+	1.20679e7i	1.12900	+	0.821176i
$737$	−2.77395e7			−1.88118
$738$	−6.13314e6	−	5.76062e6i	−0.414517	−	0.389340i
$739$			2.74026e7i			1.84578i	0.385063	+	0.922890i	$0.374180\pi$
$739$			2.74026e7i			1.84578i	−0.385063	+	0.922890i	$0.625820\pi$
$740$		0			0
$741$			655547.i			0.0438589i
$742$	119400.	−	127121.i	0.00796147	−	0.00847631i
$743$	1.20016e7			0.797569			0.398785	−	0.917045i	$-0.369432\pi$
$743$	1.20016e7			0.797569			0.398785	+	0.917045i	$0.369432\pi$
$744$	−1.43745e7	−	1.18993e7i	−0.952052	−	0.788114i
$745$		0			0
$746$	6.62773e6	−	7.05632e6i	0.436031	−	0.464228i
$747$		−	8.50916e6i		−	0.557937i
$748$	1.13695e7	−	712898.i	0.742996	−	0.0465879i
$749$			159629.i			0.0103970i
$750$		0			0
$751$	3.38961e6			0.219305			0.109653	−	0.993970i	$-0.465026\pi$
$751$	3.38961e6			0.219305			0.109653	+	0.993970i	$0.465026\pi$
$752$	−2.31460e7	+	2.91409e6i	−1.49256	+	0.187914i
$753$	2.93148e7			1.88408
$754$	2.29558e6	+	2.15615e6i	0.147050	+	0.138118i
$755$		0			0
$756$	−199786.	+	12527.2i	−0.0127134	+	0.000797165i
$757$		−	3.47336e6i		−	0.220298i	−0.993915	−	0.110149i	$-0.964867\pi$
$757$		−	3.47336e6i		−	0.220298i	0.993915	−	0.110149i	$-0.0351328\pi$
$758$	−1.39489e7	+	1.48509e7i	−0.881792	+	0.938814i
$759$	2.71516e7			1.71077
$760$		0			0
$761$	−1.16257e6			−0.0727710			−0.0363855	−	0.999338i	$-0.511584\pi$
$761$	−1.16257e6			−0.0727710			−0.0363855	+	0.999338i	$0.511584\pi$
$762$	1.03406e7	−	1.10093e7i	0.645147	−	0.686866i
$763$		−	289755.i		−	0.0180186i
$764$	1.96758e6	+	3.13794e7i	0.121955	+	1.94496i
$765$		0			0
$766$	1.57045e7	+	1.47506e7i	0.967054	+	0.908317i
$767$	2.50196e6			0.153565
$768$	4.75244e6	+	1.85746e7i	0.290746	+	1.13636i
$769$	−1.71387e7			−1.04511			−0.522556	−	0.852605i	$-0.675021\pi$
$769$	−1.71387e7			−1.04511			−0.522556	+	0.852605i	$0.675021\pi$
$770$		0			0
$771$		−	1.96944e7i		−	1.19318i
$772$	330377.	+	5.26894e6i	0.0199511	+	0.318185i
$773$		−	3.17392e7i		−	1.91050i	−0.295800	−	0.955250i	$-0.595586\pi$
$773$		−	3.17392e7i		−	1.91050i	0.295800	−	0.955250i	$-0.404414\pi$
$774$	854995.	−	910285.i	0.0512993	−	0.0546166i
$775$		0			0
$776$	1.81719e7	−	2.19519e7i	1.08329	−	1.30863i
$777$	−2556.64			−0.000151921
$778$	−1.67228e6	+	1.78043e6i	−0.0990515	+	0.105457i
$779$		−	5.46258e6i		−	0.322518i
$780$		0			0
$781$		−	2.15590e7i		−	1.26474i
$782$	1.24000e7	+	1.16468e7i	0.725110	+	0.681068i
$783$	1.44444e7			0.841968
$784$	1.70704e7	−	2.14917e6i	0.991867	−	0.124877i
$785$		0			0
$786$	−979957.	−	920435.i	−0.0565784	−	0.0531419i
$787$		−	2.67032e6i		−	0.153683i	−0.997043	−	0.0768416i	$-0.975516\pi$
$787$		−	2.67032e6i		−	0.153683i	0.997043	−	0.0768416i	$-0.0244836\pi$
$788$	−1.61796e7	+	1.01450e6i	−0.928221	+	0.0582021i
$789$			1.48635e7i			0.850018i
$790$		0			0
$791$	259850.			0.0147666
$792$	5.33952e6	+	4.42008e6i	0.302475	+	0.250390i
$793$	−3.57487e6			−0.201873
$794$	8.84804e6	−	9.42021e6i	0.498076	−	0.530285i
$795$		0			0
$796$	952506.	+	1.51908e7i	0.0532826	+	0.849764i
$797$		−	3.37393e7i		−	1.88144i	−0.339188	−	0.940719i	$-0.610152\pi$
$797$		−	3.37393e7i		−	1.88144i	0.339188	−	0.940719i	$-0.389848\pi$
$798$	57042.5	+	53577.8i	0.00317096	+	0.00297836i
$799$	−1.93441e7			−1.07197
$800$		0			0
$801$	5.54189e6			0.305194
$802$	6.74042e6	+	6.33102e6i	0.370042	+	0.347566i
$803$		−	8.91835e6i		−	0.488085i
$804$	−2.42264e6	−	3.86369e7i	−0.132175	−	2.10796i
$805$		0			0
$806$	−2.33384e6	+	2.48477e6i	−0.126542	+	0.134725i
$807$	2.08369e6			0.112629
$808$	−1.73615e7	−	1.43719e7i	−0.935533	−	0.774439i
$809$	1.25443e6			0.0673870			0.0336935	−	0.999432i	$-0.489273\pi$
$809$	1.25443e6			0.0673870			0.0336935	+	0.999432i	$0.489273\pi$
$810$		0			0
$811$		−	1.12827e7i		−	0.602365i	−0.953567	−	0.301182i	$-0.902619\pi$
$811$		−	1.12827e7i		−	0.602365i	0.953567	−	0.301182i	$-0.0973813\pi$
$812$	375235.	−	23528.3i	0.0199716	−	0.00125228i
$813$			6.81525e6i			0.361622i
$814$	−107156.	−	100648.i	−0.00566836	−	0.00532407i
$815$		0			0
$816$	1.98591e6	+	1.57737e7i	0.104408	+	0.829291i
$817$	810760.			0.0424949
$818$	2.15166e7	+	2.02097e7i	1.12432	+	1.05603i
$819$		−	22021.4i		−	0.00114719i
$820$		0			0
$821$			1.21845e7i			0.630886i	0.948945	+	0.315443i	$0.102153\pi$
$821$			1.21845e7i			0.630886i	−0.948945	+	0.315443i	$0.897847\pi$
$822$	1.33982e7	−	1.42646e7i	0.691619	−	0.736344i
$823$	2.12650e7			1.09437			0.547187	−	0.837010i	$-0.315698\pi$
$823$	2.12650e7			1.09437			0.547187	+	0.837010i	$0.315698\pi$
$824$	−1.19429e6	+	1.44271e6i	−0.0612760	+	0.0740222i
$825$		0			0
$826$	204485.	−	217708.i	0.0104282	−	0.0111026i
$827$			6.06316e6i			0.308273i	0.988050	+	0.154136i	$0.0492596\pi$
$827$			6.06316e6i			0.308273i	−0.988050	+	0.154136i	$0.950740\pi$
$828$	647788.	+	1.03311e7i	0.0328365	+	0.523685i
$829$		−	727353.i		−	0.0367586i	−0.999831	−	0.0183793i	$-0.994149\pi$
$829$		−	727353.i		−	0.0367586i	0.999831	−	0.0183793i	$-0.00585064\pi$
$830$		0			0
$831$	−1.67171e7			−0.839765
$832$	3.44091e6	−	654131.i	0.172332	−	0.0327609i
$833$	1.42665e7			0.712368
$834$	3.34250e6	+	3.13948e6i	0.166401	+	0.156294i
$835$		0			0
$836$	281612.	+	4.49122e6i	0.0139359	+	0.222253i
$837$			1.56348e7i			0.771401i
$838$	2.58114e6	−	2.74806e6i	0.126970	−	0.135181i
$839$	−1.36723e7			−0.670560			−0.335280	−	0.942118i	$-0.608831\pi$
$839$	−1.36723e7			−0.670560			−0.335280	+	0.942118i	$0.608831\pi$
$840$		0			0
$841$	−6.61809e6			−0.322658
$842$	−2.64129e7	+	2.81209e7i	−1.28391	+	1.36694i
$843$		−	9.34688e6i		−	0.452999i
$844$	8.31858e6	−	521598.i	0.401969	−	0.0252046i
$845$		0			0
$846$	−8.57941e6	−	8.05831e6i	−0.412127	−	0.387095i
$847$	−33223.9			−0.00159126
$848$	1.74824e6	+	1.38859e7i	0.0834858	+	0.663109i
$849$	9.74720e6			0.464099
$850$		0			0
$851$		−	219541.i		−	0.0103918i
$852$	3.00283e7	−	1.88286e6i	1.41720	−	0.0888626i
$853$		−	3.66971e7i		−	1.72687i	−0.504462	−	0.863434i	$-0.668309\pi$
$853$		−	3.66971e7i		−	1.72687i	0.504462	−	0.863434i	$-0.331691\pi$
$854$	−292174.	+	311068.i	−0.0137087	+	0.0145952i
$855$		0			0
$856$	−9.86769e6	−	8.16853e6i	−0.460290	−	0.381030i
$857$	1.73498e7			0.806941			0.403470	−	0.914993i	$-0.367804\pi$
$857$	1.73498e7			0.806941			0.403470	+	0.914993i	$0.367804\pi$
$858$	3.17346e6	−	3.37868e6i	0.147169	−	0.156685i
$859$			1.90085e7i			0.878954i	0.898254	+	0.439477i	$0.144836\pi$
$859$			1.90085e7i			0.878954i	−0.898254	+	0.439477i	$0.855164\pi$
$860$		0			0
$861$			671726.i			0.0308805i
$862$	−5.71925e6	−	5.37187e6i	−0.262163	−	0.246239i
$863$	−3.46920e7			−1.58563			−0.792816	−	0.609460i	$-0.791386\pi$
$863$	−3.46920e7			−1.58563			−0.792816	+	0.609460i	$0.791386\pi$
$864$	9.44910e6	−	1.29911e7i	0.430632	−	0.592056i
$865$		0			0
$866$	−5.49089e6	−	5.15738e6i	−0.248799	−	0.233687i
$867$		−	1.27790e7i		−	0.577364i
$868$	25467.3	+	406159.i	0.00114732	+	0.0182977i
$869$			1.61075e7i			0.723566i
$870$		0			0
$871$	−7.07207e6			−0.315865
$872$	1.79117e7	+	1.48274e7i	0.797710	+	0.660349i
$873$	1.43783e7			0.638515
$874$	−4.60077e6	+	4.89829e6i	−0.203729	+	0.216903i
$875$		0			0
$876$	1.24219e7	−	778886.i	0.546924	−	0.0342937i
$877$			3.99003e7i			1.75177i	0.482520	+	0.875885i	$0.339721\pi$
$877$			3.99003e7i			1.75177i	−0.482520	+	0.875885i	$0.660279\pi$
$878$	−1.14726e7	−	1.07758e7i	−0.502256	−	0.471750i
$879$	4.65618e7			2.03262
$880$		0			0
$881$	−3.50875e7			−1.52304			−0.761522	−	0.648139i	$-0.775548\pi$
$881$	−3.50875e7			−1.52304			−0.761522	+	0.648139i	$0.775548\pi$
$882$	6.32741e6	+	5.94309e6i	0.273876	+	0.257241i
$883$			1.47881e7i			0.638279i	0.947708	+	0.319139i	$0.103394\pi$
$883$			1.47881e7i			0.638279i	−0.947708	+	0.319139i	$0.896606\pi$
$884$	2.89860e6	−	181750.i	0.124755	−	0.00782248i
$885$		0			0
$886$	−1.79542e7	+	1.91152e7i	−0.768390	+	0.818079i
$887$	1.17291e7			0.500560			0.250280	−	0.968173i	$-0.419477\pi$
$887$	1.17291e7			0.500560			0.250280	+	0.968173i	$0.419477\pi$
$888$	130828.	−	158043.i	0.00556762	−	0.00672576i
$889$	−329394.			−0.0139785
$890$		0			0
$891$		−	3.05646e7i		−	1.28981i
$892$	−1.24996e6	−	1.99346e7i	−0.0525996	−	0.838872i
$893$		−	7.64139e6i		−	0.320659i
$894$	−2.65564e7	−	2.49434e7i	−1.11128	−	1.04379i
$895$		0			0
$896$	224306.	−	352873.i	0.00933406	−	0.0146841i
$897$	6.92219e6			0.287252
$898$	4.87356e6	+	4.57755e6i	0.201677	+	0.189427i
$899$		−	2.93651e7i		−	1.21180i
$900$		0			0
$901$			1.16051e7i			0.476251i
$902$	−2.64440e7	+	2.81541e7i	−1.08221	+	1.15219i
$903$	−99697.9			−0.00406880
$904$	−1.32971e7	+	1.60630e7i	−0.541171	+	0.653742i
$905$		0			0
$906$	−3.16022e7	+	3.36458e7i	−1.27908	+	1.36179i
$907$		−	1.36136e7i		−	0.549483i	−0.961518	−	0.274742i	$-0.911408\pi$
$907$		−	1.36136e7i		−	0.549483i	0.961518	−	0.274742i	$-0.0885923\pi$
$908$	2.09513e7	−	1.31370e6i	0.843328	−	0.0528790i
$909$		−	1.13716e7i		−	0.456470i
$910$		0			0
$911$	1.26888e7			0.506551			0.253276	−	0.967394i	$-0.418492\pi$
$911$	1.26888e7			0.506551			0.253276	+	0.967394i	$0.418492\pi$
$912$	−6.23098e6	+	784484.i	−0.248067	+	0.0312318i
$913$	−3.90611e7			−1.55084
$914$	−6.40097e6	−	6.01218e6i	−0.253443	−	0.238049i
$915$		0			0
$916$	−2.57982e7	+	1.61762e6i	−1.01590	+	0.0636998i
$917$			29319.9i			0.00115144i
$918$	9.11941e6	−	9.70913e6i	0.357158	−	0.380254i
$919$	−4.25253e7			−1.66096			−0.830479	−	0.557050i	$-0.811933\pi$
$919$	−4.25253e7			−1.66096			−0.830479	+	0.557050i	$0.811933\pi$
$920$		0			0
$921$	−1.35430e7			−0.526098
$922$	2.87919e7	−	3.06538e7i	1.11543	−	1.18757i
$923$		−	5.49637e6i		−	0.212360i
$924$	−34629.4	−	552278.i	−0.00133434	−	0.0212803i
$925$		0			0
$926$	−83205.3	−	78151.5i	−0.00318877	−	0.00299509i
$927$	−944963.			−0.0361173
$928$	−1.77471e7	+	2.43997e7i	−0.676484	+	0.930068i
$929$	4.25450e6			0.161737			0.0808686	−	0.996725i	$-0.474231\pi$
$929$	4.25450e6			0.161737			0.0808686	+	0.996725i	$0.474231\pi$
$930$		0			0
$931$			5.63560e6i			0.213092i
$932$	2.61238e6	+	4.16629e7i	0.0985136	+	1.57112i
$933$			1.99078e7i			0.748718i
$934$	1.38917e7	−	1.47901e7i	0.521062	−	0.554757i
$935$		0			0
$936$	1.36129e6	+	1.12688e6i	0.0507879	+	0.0420425i
$937$	−1.07844e7			−0.401279			−0.200640	−	0.979665i	$-0.564302\pi$
$937$	−1.07844e7			−0.401279			−0.200640	+	0.979665i	$0.564302\pi$
$938$	−578000.	+	615377.i	−0.0214497	+	0.0228368i
$939$		−	1.97982e7i		−	0.732760i
$940$		0			0
$941$		−	112960.i		−	0.00415862i	−0.999998	−	0.00207931i	$-0.999338\pi$
$941$		−	112960.i		−	0.00415862i	0.999998	−	0.00207931i	$-0.000661865\pi$
$942$	−2.88993e7	−	2.71440e7i	−1.06111	−	0.996659i
$943$	−5.76817e7			−2.11232
$944$	2.99406e6	+	2.37811e7i	0.109353	+	0.868566i
$945$		0			0
$946$	−4.17864e6	−	3.92484e6i	−0.151813	−	0.142592i
$947$		−	1.62952e7i		−	0.590454i	−0.955427	−	0.295227i	$-0.904605\pi$
$947$		−	1.62952e7i		−	0.590454i	0.955427	−	0.295227i	$-0.0953953\pi$
$948$	−2.24352e7	+	1.40675e6i	−0.810792	+	0.0508389i
$949$		−	2.27370e6i		−	0.0819534i
$950$		0			0
$951$	5.36188e7			1.92250
$952$	221087.	−	267077.i	0.00790627	−	0.00955088i
$953$	1.07203e7			0.382363			0.191181	−	0.981555i	$-0.438768\pi$
$953$	1.07203e7			0.382363			0.191181	+	0.981555i	$0.438768\pi$
$954$	−4.83440e6	+	5.14703e6i	−0.171978	+	0.183099i
$955$		0			0
$956$	−2.44033e6	−	3.89190e7i	−0.0863583	−	1.37726i
$957$			3.99294e7i			1.40933i
$958$	756544.	+	710592.i	0.0266330	+	0.0250154i
$959$	−426792.			−0.0149855
$960$		0			0
$961$	3.15601e6			0.110238
$962$	−27319.1	−	25659.8i	−0.000951763	−	0.000893954i
$963$		−	6.46324e6i		−	0.224587i
$964$	−1.96967e6	−	3.14128e7i	−0.0682654	−	1.08871i
$965$		0			0
$966$	565750.	−	602335.i	0.0195066	−	0.0207680i
$967$	3.92793e7			1.35082			0.675411	−	0.737442i	$-0.263966\pi$
$967$	3.92793e7			1.35082			0.675411	+	0.737442i	$0.263966\pi$
$968$	1.70014e6	−	2.05379e6i	0.0583171	−	0.0704478i
$969$	−5.20750e6			−0.178164
$970$		0			0
$971$			2.76288e7i			0.940405i	0.882559	+	0.470202i	$0.155819\pi$
$971$			2.76288e7i			0.940405i	−0.882559	+	0.470202i	$0.844181\pi$
$972$	2.10496e7	−	1.31987e6i	0.714626	−	0.0448091i
$973$		−	100006.i		−	0.00338645i
$974$	−2.75833e7	−	2.59079e7i	−0.931642	−	0.875055i
$975$		0			0
$976$	−4.27800e6	−	3.39792e7i	−0.143753	−	1.14180i
$977$	2.56548e7			0.859868			0.429934	−	0.902860i	$-0.358537\pi$
$977$	2.56548e7			0.859868			0.429934	+	0.902860i	$0.358537\pi$
$978$	−3.05492e7	−	2.86937e7i	−1.02130	−	0.959266i
$979$		−	2.54399e7i		−	0.848318i
$980$		0			0
$981$			1.17320e7i			0.389223i
$982$	−3.83424e7	+	4.08218e7i	−1.26882	+	1.35087i
$983$	5.21860e6			0.172254			0.0861271	−	0.996284i	$-0.472551\pi$
$983$	5.21860e6			0.172254			0.0861271	+	0.996284i	$0.472551\pi$
$984$	−4.15238e7	−	3.43736e7i	−1.36713	−	1.13172i
$985$		0			0
$986$	−1.71279e7	+	1.82355e7i	−0.561063	+	0.597345i
$987$			939650.i			0.0307025i
$988$	71795.8	+	1.14502e6i	0.00233995	+	0.0373181i
$989$		−	8.56115e6i		−	0.278318i
$990$		0			0
$991$	4.76772e7			1.54215			0.771075	−	0.636744i	$-0.219719\pi$
$991$	4.76772e7			1.54215			0.771075	+	0.636744i	$0.219719\pi$
$992$	−2.64106e7	−	1.92097e7i	−0.852117	−	0.619786i
$993$	6.53158e6			0.210206
$994$	−478267.	−	449218.i	−0.0153534	−	0.0144209i
$995$		0			0
$996$	−3.41142e6	−	5.44061e7i	−0.108965	−	1.73780i
$997$			2.96368e7i			0.944263i	0.881528	+	0.472132i	$0.156515\pi$
$997$			2.96368e7i			0.944263i	−0.881528	+	0.472132i	$0.843485\pi$
$998$	2.30784e7	−	2.45708e7i	0.733465	−	0.780896i
$999$	−171900.			−0.00544955

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.6.d.d.101.16	yes	20
4.3	odd	2		800.6.d.b.401.5		20
5.2	odd	4		200.6.f.d.149.12		40
5.3	odd	4		200.6.f.d.149.29		40
5.4	even	2		200.6.d.c.101.5	✓	20
8.3	odd	2		800.6.d.b.401.16		20
8.5	even	2	inner	200.6.d.d.101.15	yes	20
20.3	even	4		800.6.f.d.49.32		40
20.7	even	4		800.6.f.d.49.9		40
20.19	odd	2		800.6.d.d.401.16		20
40.3	even	4		800.6.f.d.49.10		40
40.13	odd	4		200.6.f.d.149.11		40
40.19	odd	2		800.6.d.d.401.5		20
40.27	even	4		800.6.f.d.49.31		40
40.29	even	2		200.6.d.c.101.6	yes	20
40.37	odd	4		200.6.f.d.149.30		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.6.d.c.101.5	✓	20	5.4	even	2
200.6.d.c.101.6	yes	20	40.29	even	2
200.6.d.d.101.15	yes	20	8.5	even	2	inner
200.6.d.d.101.16	yes	20	1.1	even	1	trivial
200.6.f.d.149.11		40	40.13	odd	4
200.6.f.d.149.12		40	5.2	odd	4
200.6.f.d.149.29		40	5.3	odd	4
200.6.f.d.149.30		40	40.37	odd	4
800.6.d.b.401.5		20	4.3	odd	2
800.6.d.b.401.16		20	8.3	odd	2
800.6.d.d.401.5		20	40.19	odd	2
800.6.d.d.401.16		20	20.19	odd	2
800.6.f.d.49.9		40	20.7	even	4
800.6.f.d.49.10		40	40.3	even	4
800.6.f.d.49.31		40	40.27	even	4
800.6.f.d.49.32		40	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4.12326 + 3.87282i) q^{2} +18.2848i q^{3} +(2.00256 + 31.9373i) q^{4} +(-70.8136 + 75.3929i) q^{6} +2.25573 q^{7} +(-115.430 + 139.441i) q^{8} -91.3327 q^{9} +419.261i q^{11} +(-583.966 + 36.6163i) q^{12} +106.889i q^{13} +(9.30095 + 8.73602i) q^{14} +(-1015.98 + 127.912i) q^{16} -849.098 q^{17} +(-376.589 - 353.715i) q^{18} -335.414i q^{19} +41.2454i q^{21} +(-1623.72 + 1728.72i) q^{22} -3541.78 q^{23} +(-2549.65 - 2110.61i) q^{24} +(-413.961 + 440.731i) q^{26} +2773.20i q^{27} +(4.51722 + 72.0418i) q^{28} -5208.57i q^{29} +5637.83 q^{31} +(-4684.53 - 3407.29i) q^{32} -7666.09 q^{33} +(-3501.05 - 3288.40i) q^{34} +(-182.899 - 2916.92i) q^{36} +61.9860i q^{37} +(1299.00 - 1383.00i) q^{38} -1954.44 q^{39} +16286.1 q^{41} +(-159.736 + 170.066i) q^{42} +2417.19i q^{43} +(-13390.1 + 839.594i) q^{44} +(-14603.7 - 13716.7i) q^{46} +22781.9 q^{47} +(-2338.85 - 18576.9i) q^{48} -16801.9 q^{49} -15525.6i q^{51} +(-3413.74 + 214.051i) q^{52} -13667.5i q^{53} +(-10740.1 + 11434.6i) q^{54} +(-260.379 + 314.541i) q^{56} +6132.98 q^{57} +(20171.9 - 21476.3i) q^{58} -23407.1i q^{59} +33444.7i q^{61} +(23246.3 + 21834.3i) q^{62} -206.022 q^{63} +(-6119.73 - 32191.5i) q^{64} +(-31609.3 - 29689.4i) q^{66} +66162.9i q^{67} +(-1700.37 - 27117.9i) q^{68} -64760.7i q^{69} -51421.4 q^{71} +(10542.6 - 12735.5i) q^{72} -21271.6 q^{73} +(-240.060 + 255.584i) q^{74} +(10712.2 - 671.686i) q^{76} +945.738i q^{77} +(-8058.66 - 7569.18i) q^{78} +38418.7 q^{79} -72901.2 q^{81} +(67151.7 + 63073.0i) q^{82} +93166.7i q^{83} +(-1317.27 + 82.5963i) q^{84} +(-9361.33 + 9966.69i) q^{86} +95237.5 q^{87} +(-58462.3 - 48395.4i) q^{88} -60678.0 q^{89} +241.112i q^{91} +(-7092.62 - 113115. i) q^{92} +103086. i q^{93} +(93935.8 + 88230.2i) q^{94} +(62301.5 - 85655.5i) q^{96} -157428. q^{97} +(-69278.7 - 65070.8i) q^{98} -38292.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + q^{4} + 33 q^{6} + 196 q^{7} + 391 q^{8} - 1620 q^{9} + 241 q^{12} - 424 q^{14} - 55 q^{16} + 3368 q^{18} - 1197 q^{22} + 7184 q^{23} + 9459 q^{24} + 9172 q^{26} + 13492 q^{28} + 7160 q^{31}+ \cdots - 164655 q^{98}+O(q^{100}) \) 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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