LMFDB - Embedded newform 200.4.f.c.149.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,4,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, 4, names="a")

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

chi := DirichletCharacter("200.149");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
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:	$11.8003820011$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{11} + 7x^{10} - 12x^{9} + 21x^{8} - 68x^{6} + 336x^{4} - 768x^{3} + 1792x^{2} - 4096x + 4096 $ x^12 - 4x^11 + 7x^10 - 12x^9 + 21x^8 - 68x^6 + 336x^4 - 768x^3 + 1792x^2 - 4096*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	no (minimal twist has level 40)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.10
Root			$1.98839 + 0.215211i$ of defining polynomial
Character	$\chi$	$=$	200.149
Dual form			200.4.f.c.149.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.77318 + 2.20360i) q^{2} +9.57890 q^{3} +(-1.71169 + 7.81474i) q^{4} +(16.9851 + 21.1081i) q^{6} +21.5703i q^{7} +(-20.2557 + 10.0850i) q^{8} +64.7554 q^{9} -37.2871i q^{11} +(-16.3961 + 74.8566i) q^{12} -24.1097 q^{13} +(-47.5322 + 38.2479i) q^{14} +(-58.1402 - 26.7528i) q^{16} -14.4940i q^{17} +(114.823 + 142.695i) q^{18} -26.6887i q^{19} +206.620i q^{21} +(82.1658 - 66.1166i) q^{22} +8.36366i q^{23} +(-194.027 + 96.6035i) q^{24} +(-42.7508 - 53.1282i) q^{26} +361.655 q^{27} +(-168.566 - 36.9216i) q^{28} -104.553i q^{29} +204.288 q^{31} +(-44.1404 - 175.555i) q^{32} -357.170i q^{33} +(31.9389 - 25.7004i) q^{34} +(-110.841 + 506.046i) q^{36} +130.923 q^{37} +(58.8111 - 47.3237i) q^{38} -230.945 q^{39} -437.963 q^{41} +(-455.307 + 366.373i) q^{42} +308.764 q^{43} +(291.389 + 63.8240i) q^{44} +(-18.4301 + 14.8302i) q^{46} +97.1081i q^{47} +(-556.920 - 256.263i) q^{48} -122.277 q^{49} -138.836i q^{51} +(41.2684 - 188.411i) q^{52} -154.502 q^{53} +(641.279 + 796.943i) q^{54} +(-217.537 - 436.920i) q^{56} -255.648i q^{57} +(230.392 - 185.390i) q^{58} -544.088i q^{59} +374.601i q^{61} +(362.238 + 450.168i) q^{62} +1396.79i q^{63} +(308.584 - 408.558i) q^{64} +(787.058 - 633.325i) q^{66} -19.3982 q^{67} +(113.267 + 24.8092i) q^{68} +80.1147i q^{69} -955.725 q^{71} +(-1311.66 + 653.060i) q^{72} -127.417i q^{73} +(232.150 + 288.502i) q^{74} +(208.565 + 45.6828i) q^{76} +804.293 q^{77} +(-409.506 - 508.910i) q^{78} -973.871 q^{79} +1715.87 q^{81} +(-776.586 - 965.094i) q^{82} -55.0210 q^{83} +(-1614.68 - 353.669i) q^{84} +(547.493 + 680.392i) q^{86} -1001.50i q^{87} +(376.041 + 755.275i) q^{88} +919.812 q^{89} -520.054i q^{91} +(-65.3598 - 14.3160i) q^{92} +1956.85 q^{93} +(-213.987 + 172.190i) q^{94} +(-422.816 - 1681.63i) q^{96} +297.986i q^{97} +(-216.818 - 269.449i) q^{98} -2414.54i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 12 q^{3} - 16 q^{4} - 36 q^{6} - 24 q^{8} + 108 q^{9} - 164 q^{12} - 68 q^{14} - 56 q^{16} + 450 q^{18} + 492 q^{22} - 360 q^{24} - 308 q^{26} + 432 q^{27} + 628 q^{28} - 264 q^{31} + 856 q^{32}+ \cdots + 638 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 + 12 * q^3 - 16 * q^4 - 36 * q^6 - 24 * q^8 + 108 * q^9 - 164 * q^12 - 68 * q^14 - 56 * q^16 + 450 * q^18 + 492 * q^22 - 360 * q^24 - 308 * q^26 + 432 * q^27 + 628 * q^28 - 264 * q^31 + 856 * q^32 + 180 * q^34 + 440 * q^36 + 136 * q^37 - 1388 * q^38 - 600 * q^39 + 40 * q^41 - 2332 * q^42 - 1204 * q^43 + 472 * q^44 - 1268 * q^46 - 2536 * q^48 - 1308 * q^49 - 1272 * q^52 + 1056 * q^53 + 1512 * q^54 - 728 * q^56 + 1528 * q^58 + 2104 * q^62 + 2048 * q^64 + 2928 * q^66 - 2412 * q^67 + 960 * q^68 - 1592 * q^71 + 744 * q^72 + 420 * q^74 + 2256 * q^76 + 824 * q^77 - 160 * q^78 - 2016 * q^79 + 2508 * q^81 + 352 * q^82 + 3556 * q^83 - 1048 * q^84 - 244 * q^86 + 1008 * q^88 + 424 * q^89 + 1068 * q^92 + 2784 * q^93 - 292 * q^94 - 5920 * q^96 + 638 * 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 $

$2$	1.77318	+	2.20360i	0.626913	+	0.779090i
$2$	1.77318	+	2.20360i	0.626913	+	0.779090i
$3$	9.57890			1.84346			0.921730	−	0.387831i	$-0.126776\pi$
$3$	9.57890			1.84346			0.921730	+	0.387831i	$0.126776\pi$
$4$	−1.71169	+	7.81474i	−0.213961	+	0.976842i
$5$		0			0
$5$		0			0
$6$	16.9851	+	21.1081i	1.15569	+	1.43622i
$7$			21.5703i			1.16469i	0.812943	+	0.582343i	$0.197864\pi$
$7$			21.5703i			1.16469i	−0.812943	+	0.582343i	$0.802136\pi$
$8$	−20.2557	+	10.0850i	−0.895183	+	0.445699i
$9$	64.7554			2.39835
$10$		0			0
$11$		−	37.2871i		−	1.02204i	−0.859568	−	0.511022i	$-0.829267\pi$
$11$		−	37.2871i		−	1.02204i	0.859568	−	0.511022i	$-0.170733\pi$
$12$	−16.3961	+	74.8566i	−0.394429	+	1.80077i
$13$	−24.1097			−0.514372			−0.257186	−	0.966362i	$-0.582795\pi$
$13$	−24.1097			−0.514372			−0.257186	+	0.966362i	$0.582795\pi$
$14$	−47.5322	+	38.2479i	−0.907394	+	0.730156i
$15$		0			0
$16$	−58.1402	−	26.7528i	−0.908441	−	0.418013i
$17$		−	14.4940i		−	0.206783i	−0.994641	−	0.103391i	$-0.967031\pi$
$17$		−	14.4940i		−	0.206783i	0.994641	−	0.103391i	$-0.0329694\pi$
$18$	114.823	+	142.695i	1.50355	+	1.86853i
$19$		−	26.6887i		−	0.322253i	−0.986934	−	0.161126i	$-0.948487\pi$
$19$		−	26.6887i		−	0.322253i	0.986934	−	0.161126i	$-0.0515127\pi$
$20$		0			0
$21$			206.620i			2.14705i
$22$	82.1658	−	66.1166i	0.796264	−	0.640732i
$23$			8.36366i			0.0758236i	0.999281	+	0.0379118i	$0.0120706\pi$
$23$			8.36366i			0.0758236i	−0.999281	+	0.0379118i	$0.987929\pi$
$24$	−194.027	+	96.6035i	−1.65023	+	0.821630i
$25$		0			0
$26$	−42.7508	−	53.1282i	−0.322466	−	0.400742i
$27$	361.655			2.57780
$28$	−168.566	−	36.9216i	−1.13771	−	0.249198i
$29$		−	104.553i		−	0.669481i	−0.942310	−	0.334741i	$-0.891351\pi$
$29$		−	104.553i		−	0.669481i	0.942310	−	0.334741i	$-0.108649\pi$
$30$		0			0
$31$	204.288			1.18359			0.591793	−	0.806090i	$-0.298420\pi$
$31$	204.288			1.18359			0.591793	+	0.806090i	$0.298420\pi$
$32$	−44.1404	−	175.555i	−0.243843	−	0.969815i
$33$		−	357.170i		−	1.88410i
$34$	31.9389	−	25.7004i	0.161102	−	0.129635i
$35$		0			0
$36$	−110.841	+	506.046i	−0.513154	+	2.34281i
$37$	130.923			0.581720			0.290860	−	0.956766i	$-0.406059\pi$
$37$	130.923			0.581720			0.290860	+	0.956766i	$0.406059\pi$
$38$	58.8111	−	47.3237i	0.251064	−	0.202024i
$39$	−230.945			−0.948225
$40$		0			0
$41$	−437.963			−1.66825			−0.834126	−	0.551574i	$-0.814027\pi$
$41$	−437.963			−1.66825			−0.834126	+	0.551574i	$0.814027\pi$
$42$	−455.307	+	366.373i	−1.67275	+	1.34601i
$43$	308.764			1.09503			0.547513	−	0.836797i	$-0.315575\pi$
$43$	308.764			1.09503			0.547513	+	0.836797i	$0.315575\pi$
$44$	291.389	+	63.8240i	0.998376	+	0.218678i
$45$		0			0
$46$	−18.4301	+	14.8302i	−0.0590734	+	0.0475348i
$47$			97.1081i			0.301376i	0.988581	+	0.150688i	$0.0481489\pi$
$47$			97.1081i			0.301376i	−0.988581	+	0.150688i	$0.951851\pi$
$48$	−556.920	−	256.263i	−1.67468	−	0.770591i
$49$	−122.277			−0.356492
$50$		0			0
$51$		−	138.836i		−	0.381196i
$52$	41.2684	−	188.411i	0.110056	−	0.502461i
$53$	−154.502			−0.400425			−0.200212	−	0.979753i	$-0.564163\pi$
$53$	−154.502			−0.400425			−0.200212	+	0.979753i	$0.564163\pi$
$54$	641.279	+	796.943i	1.61606	+	2.00834i
$55$		0			0
$56$	−217.537	−	436.920i	−0.519100	−	1.04261i
$57$		−	255.648i		−	0.594060i
$58$	230.392	−	185.390i	0.521586	−	0.419706i
$59$		−	544.088i		−	1.20058i	−0.799782	−	0.600290i	$-0.795052\pi$
$59$		−	544.088i		−	1.20058i	0.799782	−	0.600290i	$-0.204948\pi$
$60$		0			0
$61$			374.601i			0.786275i	0.919480	+	0.393137i	$0.128610\pi$
$61$			374.601i			0.786275i	−0.919480	+	0.393137i	$0.871390\pi$
$62$	362.238	+	450.168i	0.742005	+	0.922120i
$63$			1396.79i			2.79332i
$64$	308.584	−	408.558i	0.602704	−	0.797965i
$65$		0			0
$66$	787.058	−	633.325i	1.46788	−	1.18116i
$67$	−19.3982			−0.0353711			−0.0176855	−	0.999844i	$-0.505630\pi$
$67$	−19.3982			−0.0353711			−0.0176855	+	0.999844i	$0.505630\pi$
$68$	113.267	+	24.8092i	0.201994	+	0.0442435i
$69$			80.1147i			0.139778i
$70$		0			0
$71$	−955.725			−1.59752			−0.798759	−	0.601651i	$-0.794510\pi$
$71$	−955.725			−1.59752			−0.798759	+	0.601651i	$0.794510\pi$
$72$	−1311.66	+	653.060i	−2.14696	+	1.06894i
$73$		−	127.417i		−	0.204287i	−0.994770	−	0.102144i	$-0.967430\pi$
$73$		−	127.417i		−	0.204287i	0.994770	−	0.102144i	$-0.0325702\pi$
$74$	232.150	+	288.502i	0.364687	+	0.453212i
$75$		0			0
$76$	208.565	+	45.6828i	0.314790	+	0.0689496i
$77$	804.293			1.19036
$78$	−409.506	−	508.910i	−0.594454	−	0.738753i
$79$	−973.871			−1.38695			−0.693475	−	0.720481i	$-0.743921\pi$
$79$	−973.871			−1.38695			−0.693475	+	0.720481i	$0.743921\pi$
$80$		0			0
$81$	1715.87			2.35373
$82$	−776.586	−	965.094i	−1.04585	−	1.29972i
$83$	−55.0210			−0.0727631			−0.0363816	−	0.999338i	$-0.511583\pi$
$83$	−55.0210			−0.0727631			−0.0363816	+	0.999338i	$0.511583\pi$
$84$	−1614.68	−	353.669i	−2.09733	−	0.459386i
$85$		0			0
$86$	547.493	+	680.392i	0.686485	+	0.853123i
$87$		−	1001.50i		−	1.23416i
$88$	376.041	+	755.275i	0.455525	+	0.914916i
$89$	919.812			1.09550			0.547752	−	0.836641i	$-0.315484\pi$
$89$	919.812			1.09550			0.547752	+	0.836641i	$0.315484\pi$
$90$		0			0
$91$		−	520.054i		−	0.599082i
$92$	−65.3598	−	14.3160i	−0.0740677	−	0.0162233i
$93$	1956.85			2.18189
$94$	−213.987	+	172.190i	−0.234799	+	0.188936i
$95$		0			0
$96$	−422.816	−	1681.63i	−0.449516	−	1.78782i
$97$			297.986i			0.311916i	0.987764	+	0.155958i	$0.0498465\pi$
$97$			297.986i			0.311916i	−0.987764	+	0.155958i	$0.950154\pi$
$98$	−216.818	−	269.449i	−0.223489	−	0.277739i
$99$		−	2414.54i		−	2.45122i
$100$		0			0
$101$		−	1793.53i		−	1.76696i	−0.468469	−	0.883480i	$-0.655194\pi$
$101$		−	1793.53i		−	1.76696i	0.468469	−	0.883480i	$-0.344806\pi$
$102$	305.939	−	246.181i	0.296986	−	0.238976i
$103$		−	2084.11i		−	1.99372i	−0.0791611	−	0.996862i	$-0.525224\pi$
$103$		−	2084.11i		−	1.99372i	0.0791611	−	0.996862i	$-0.474776\pi$
$104$	488.359	−	243.147i	0.460457	−	0.229255i
$105$		0			0
$106$	−273.960	−	340.461i	−0.251031	−	0.311967i
$107$	67.2542			0.0607637			0.0303818	−	0.999538i	$-0.490328\pi$
$107$	67.2542			0.0607637			0.0303818	+	0.999538i	$0.490328\pi$
$108$	−619.042	+	2826.24i	−0.551550	+	2.51810i
$109$			1459.15i			1.28222i	0.767451	+	0.641108i	$0.221525\pi$
$109$			1459.15i			1.28222i	−0.767451	+	0.641108i	$0.778475\pi$
$110$		0			0
$111$	1254.10			1.07238
$112$	577.066	−	1254.10i	0.486854	−	1.05805i
$113$		−	458.263i		−	0.381502i	−0.981638	−	0.190751i	$-0.938908\pi$
$113$		−	458.263i		−	0.381502i	0.981638	−	0.190751i	$-0.0610923\pi$
$114$	563.346	−	453.309i	0.462826	−	0.372424i
$115$		0			0
$116$	817.052	+	178.962i	0.653978	+	0.143243i
$117$	−1561.24			−1.23364
$118$	1198.95	−	964.764i	0.935360	−	0.752659i
$119$	312.639			0.240837
$120$		0			0
$121$	−59.3283			−0.0445743
$122$	−825.471	+	664.234i	−0.612579	+	0.492926i
$123$	−4195.21			−3.07536
$124$	−349.678	+	1596.46i	−0.253242	+	1.15618i
$125$		0			0
$126$	−3077.97	+	2476.76i	−2.17625	+	1.75117i
$127$			208.685i			0.145809i	0.997339	+	0.0729047i	$0.0232269\pi$
$127$			208.685i			0.145809i	−0.997339	+	0.0729047i	$0.976773\pi$
$128$	1447.47	−	44.4492i	0.999529	−	0.0306937i
$129$	2957.62			2.01864
$130$		0			0
$131$			1784.69i			1.19030i	0.803616	+	0.595148i	$0.202906\pi$
$131$			1784.69i			1.19030i	−0.803616	+	0.595148i	$0.797094\pi$
$132$	2791.19	+	611.364i	1.84047	+	0.403124i
$133$	575.682			0.375323
$134$	−34.3963	−	42.7457i	−0.0221746	−	0.0275572i
$135$		0			0
$136$	146.172	+	293.585i	0.0921629	+	0.185108i
$137$			2380.60i			1.48459i	0.670075	+	0.742293i	$0.266262\pi$
$137$			2380.60i			1.48459i	−0.670075	+	0.742293i	$0.733738\pi$
$138$	−176.541	+	142.057i	−0.108899	+	0.0876285i
$139$			2858.52i			1.74429i	0.489245	+	0.872146i	$0.337272\pi$
$139$			2858.52i			1.74429i	−0.489245	+	0.872146i	$0.662728\pi$
$140$		0			0
$141$			930.189i			0.555575i
$142$	−1694.67	−	2106.04i	−1.00150	−	1.24461i
$143$			898.983i			0.525711i
$144$	−3764.89	−	1732.39i	−2.17876	−	1.00254i
$145$		0			0
$146$	280.775	−	225.932i	0.159158	−	0.128070i
$147$	−1171.28			−0.657179
$148$	−224.100	+	1023.13i	−0.124466	+	0.568248i
$149$		−	897.894i		−	0.493680i	−0.969056	−	0.246840i	$-0.920608\pi$
$149$		−	897.894i		−	0.493680i	0.969056	−	0.246840i	$-0.0793922\pi$
$150$		0			0
$151$	−3431.32			−1.84925			−0.924625	−	0.380878i	$-0.875622\pi$
$151$	−3431.32			−1.84925			−0.924625	+	0.380878i	$0.875622\pi$
$152$	269.156	+	540.597i	0.143628	+	0.288475i
$153$		−	938.563i		−	0.495937i
$154$	1426.15	+	1772.34i	0.746251	+	0.927397i
$155$		0			0
$156$	395.306	−	1804.77i	0.202884	−	0.926266i
$157$	−571.369			−0.290447			−0.145224	−	0.989399i	$-0.546390\pi$
$157$	−571.369			−0.290447			−0.145224	+	0.989399i	$0.546390\pi$
$158$	−1726.85	−	2146.02i	−0.869496	−	1.08056i
$159$	−1479.96			−0.738167
$160$		0			0
$161$	−180.406			−0.0883106
$162$	3042.53	+	3781.08i	1.47558	+	1.83376i
$163$	−236.962			−0.113867			−0.0569333	−	0.998378i	$-0.518132\pi$
$163$	−236.962			−0.113867			−0.0569333	+	0.998378i	$0.518132\pi$
$164$	749.657	−	3422.57i	0.356941	−	1.62962i
$165$		0			0
$166$	−97.5619	−	121.244i	−0.0456161	−	0.0566890i
$167$			1448.46i			0.671169i	0.942010	+	0.335585i	$0.108934\pi$
$167$			1448.46i			0.671169i	−0.942010	+	0.335585i	$0.891066\pi$
$168$	−2083.76	−	4185.22i	−0.956940	−	1.92200i
$169$	−1615.72			−0.735421
$170$		0			0
$171$		−	1728.24i		−	0.772874i
$172$	−528.509	+	2412.91i	−0.234293	+	1.06967i
$173$	2529.74			1.11175			0.555875	−	0.831266i	$-0.312383\pi$
$173$	2529.74			1.11175			0.555875	+	0.831266i	$0.312383\pi$
$174$	2206.91	−	1775.84i	0.961523	−	0.773712i
$175$		0			0
$176$	−997.536	+	2167.88i	−0.427228	+	0.928467i
$177$		−	5211.77i		−	2.21322i
$178$	1630.99	+	2026.90i	0.686785	+	0.853496i
$179$			141.524i			0.0590949i	0.999563	+	0.0295475i	$0.00940662\pi$
$179$			141.524i			0.0590949i	−0.999563	+	0.0295475i	$0.990593\pi$
$180$		0			0
$181$			3457.79i			1.41997i	0.704215	+	0.709987i	$0.251299\pi$
$181$			3457.79i			1.41997i	−0.704215	+	0.709987i	$0.748701\pi$
$182$	1145.99	−	922.147i	0.466739	−	0.375572i
$183$			3588.27i			1.44947i
$184$	−84.3477	−	169.411i	−0.0337945	−	0.0678760i
$185$		0			0
$186$	3469.85	+	4312.12i	1.36786	+	1.69989i
$187$	−540.438			−0.211341
$188$	−758.874	−	166.219i	−0.294397	−	0.0644828i
$189$			7801.01i			3.00233i
$190$		0			0
$191$	−1416.99			−0.536804			−0.268402	−	0.963307i	$-0.586496\pi$
$191$	−1416.99			−0.536804			−0.268402	+	0.963307i	$0.586496\pi$
$192$	2955.90	−	3913.54i	1.11106	−	1.47102i
$193$			2681.12i			0.999955i	0.866038	+	0.499978i	$0.166658\pi$
$193$			2681.12i			0.999955i	−0.866038	+	0.499978i	$0.833342\pi$
$194$	−656.641	+	528.381i	−0.243011	+	0.195544i
$195$		0			0
$196$	209.300	−	955.560i	0.0762755	−	0.348236i
$197$	2697.74			0.975664			0.487832	−	0.872938i	$-0.337788\pi$
$197$	2697.74			0.975664			0.487832	+	0.872938i	$0.337788\pi$
$198$	5320.68	−	4281.41i	1.90972	−	1.53670i
$199$	−3543.25			−1.26218			−0.631091	−	0.775709i	$-0.717393\pi$
$199$	−3543.25			−1.26218			−0.631091	+	0.775709i	$0.717393\pi$
$200$		0			0
$201$	−185.813			−0.0652052
$202$	3952.22	−	3180.25i	1.37662	−	1.10773i
$203$	2255.23			0.779735
$204$	1084.97	+	237.645i	0.372368	+	0.0815611i
$205$		0			0
$206$	4592.54	−	3695.50i	1.55329	−	1.24989i
$207$			541.592i			0.181851i
$208$	1401.75	+	645.004i	0.467277	+	0.215014i
$209$	−995.143			−0.329356
$210$		0			0
$211$		−	152.205i		−	0.0496598i	−0.999692	−	0.0248299i	$-0.992096\pi$
$211$		−	152.205i		−	0.0496598i	0.999692	−	0.0248299i	$-0.00790441\pi$
$212$	264.460	−	1207.39i	0.0856754	−	0.391152i
$213$	−9154.80			−2.94496
$214$	119.254	+	148.201i	0.0380935	+	0.0473403i
$215$		0			0
$216$	−7325.57	+	3647.30i	−2.30760	+	1.14892i
$217$			4406.54i			1.37851i
$218$	−3215.39	+	2587.34i	−0.998961	+	0.803837i
$219$		−	1220.51i		−	0.376596i
$220$		0			0
$221$			349.446i			0.106363i
$222$	2223.74	+	2763.53i	0.672287	+	0.835478i
$223$			2065.40i			0.620222i	0.950700	+	0.310111i	$0.100366\pi$
$223$			2065.40i			0.620222i	−0.950700	+	0.310111i	$0.899634\pi$
$224$	3786.77	−	952.120i	1.12953	−	0.284001i
$225$		0			0
$226$	1009.83	−	812.580i	0.297224	−	0.239168i
$227$	−2940.45			−0.859757			−0.429878	−	0.902887i	$-0.641444\pi$
$227$	−2940.45			−0.859757			−0.429878	+	0.902887i	$0.641444\pi$
$228$	1997.82	+	437.591i	0.580303	+	0.127106i
$229$		−	4949.77i		−	1.42834i	−0.699971	−	0.714171i	$-0.746804\pi$
$229$		−	4949.77i		−	1.42834i	0.699971	−	0.714171i	$-0.253196\pi$
$230$		0			0
$231$	7704.25			2.19438
$232$	1054.42	+	2117.79i	0.298387	+	0.599308i
$233$		−	5193.31i		−	1.46019i	−0.683344	−	0.730096i	$-0.739475\pi$
$233$		−	5193.31i		−	1.46019i	0.683344	−	0.730096i	$-0.260525\pi$
$234$	−2768.35	−	3440.34i	−0.773387	−	0.961119i
$235$		0			0
$236$	4251.90	+	931.311i	1.17278	+	0.256878i
$237$	−9328.62			−2.55679
$238$	554.364	+	688.930i	0.150983	+	0.187633i
$239$	2066.30			0.559238			0.279619	−	0.960111i	$-0.409792\pi$
$239$	2066.30			0.559238			0.279619	+	0.960111i	$0.409792\pi$
$240$		0			0
$241$	−2309.08			−0.617181			−0.308591	−	0.951195i	$-0.599857\pi$
$241$	−2309.08			−0.617181			−0.308591	+	0.951195i	$0.599857\pi$
$242$	−105.200	−	130.736i	−0.0279442	−	0.0347273i
$243$	6671.42			1.76120
$244$	−2927.41	−	641.202i	−0.768066	−	0.168232i
$245$		0			0
$246$	−7438.84	−	9244.55i	−1.92798	−	2.39598i
$247$			643.457i			0.165758i
$248$	−4137.99	+	2060.25i	−1.05953	+	0.527524i
$249$	−527.041			−0.134136
$250$		0			0
$251$		−	3802.60i		−	0.956246i	−0.878293	−	0.478123i	$-0.841317\pi$
$251$		−	3802.60i		−	0.956246i	0.878293	−	0.478123i	$-0.158683\pi$
$252$	−10915.6	−	2390.88i	−2.72863	−	0.597663i
$253$	311.857			0.0774951
$254$	−459.858	+	370.035i	−0.113599	+	0.0914097i
$255$		0			0
$256$	2664.57	+	3110.83i	0.650530	+	0.759480i
$257$			6168.56i			1.49721i	0.663013	+	0.748607i	$0.269277\pi$
$257$			6168.56i			1.49721i	−0.663013	+	0.748607i	$0.730723\pi$
$258$	5244.39	+	6517.41i	1.26551	+	1.57270i
$259$			2824.05i			0.677521i
$260$		0			0
$261$		−	6770.36i		−	1.60565i
$262$	−3932.73	+	3164.56i	−0.927347	+	0.746211i
$263$			1636.11i			0.383599i	0.981434	+	0.191800i	$0.0614324\pi$
$263$			1636.11i			0.383599i	−0.981434	+	0.191800i	$0.938568\pi$
$264$	3602.07	+	7234.71i	0.839742	+	1.68661i
$265$		0			0
$266$	1020.79	+	1268.57i	0.235295	+	0.292410i
$267$	8810.79			2.01952
$268$	33.2036	−	151.591i	0.00756804	−	0.0345520i
$269$			2262.24i			0.512756i	0.966577	+	0.256378i	$0.0825292\pi$
$269$			2262.24i			0.512756i	−0.966577	+	0.256378i	$0.917471\pi$
$270$		0			0
$271$	41.6380			0.00933332			0.00466666	−	0.999989i	$-0.498515\pi$
$271$	41.6380			0.00933332			0.00466666	+	0.999989i	$0.498515\pi$
$272$	−387.755	+	842.683i	−0.0864378	+	0.187850i
$273$		−	4981.55i		−	1.10438i
$274$	−5245.88	+	4221.22i	−1.15663	+	0.930706i
$275$		0			0
$276$	−626.075	−	137.132i	−0.136541	−	0.0299071i
$277$	2139.00			0.463971			0.231986	−	0.972719i	$-0.425478\pi$
$277$	2139.00			0.463971			0.231986	+	0.972719i	$0.425478\pi$
$278$	−6299.03	+	5068.66i	−1.35896	+	1.09352i
$279$	13228.7			2.83865
$280$		0			0
$281$	−1493.53			−0.317069			−0.158534	−	0.987353i	$-0.550677\pi$
$281$	−1493.53			−0.317069			−0.158534	+	0.987353i	$0.550677\pi$
$282$	−2049.76	+	1649.39i	−0.432843	+	0.348297i
$283$	−1090.20			−0.228995			−0.114498	−	0.993424i	$-0.536526\pi$
$283$	−1090.20			−0.228995			−0.114498	+	0.993424i	$0.536526\pi$
$284$	1635.91	−	7468.74i	0.341807	−	1.56052i
$285$		0			0
$286$	−1981.00	+	1594.05i	−0.409576	+	0.329575i
$287$		−	9446.98i		−	1.94299i
$288$	−2858.33	−	11368.1i	−0.584822	−	2.32595i
$289$	4702.92			0.957241
$290$		0			0
$291$			2854.38i			0.575005i
$292$	995.727	+	218.098i	0.199557	+	0.0437096i
$293$	−4067.51			−0.811011			−0.405506	−	0.914093i	$-0.632905\pi$
$293$	−4067.51			−0.811011			−0.405506	+	0.914093i	$0.632905\pi$
$294$	−2076.88	−	2581.02i	−0.411994	−	0.512001i
$295$		0			0
$296$	−2651.94	+	1320.36i	−0.520746	+	0.259272i
$297$		−	13485.1i		−	2.63463i
$298$	1978.60	−	1592.12i	0.384621	−	0.309494i
$299$		−	201.646i		−	0.0390016i
$300$		0			0
$301$			6660.13i			1.27536i
$302$	−6084.33	−	7561.25i	−1.15932	−	1.44073i
$303$		−	17180.1i		−	3.25732i
$304$	−713.998	+	1551.69i	−0.134706	+	0.292748i
$305$		0			0
$306$	2068.22	−	1664.24i	0.386379	−	0.310909i
$307$	−6736.05			−1.25227			−0.626135	−	0.779715i	$-0.715364\pi$
$307$	−6736.05			−1.25227			−0.626135	+	0.779715i	$0.715364\pi$
$308$	−1376.70	+	6285.34i	−0.254691	+	1.16279i
$309$		−	19963.5i		−	3.67535i
$310$		0			0
$311$	3274.35			0.597014			0.298507	−	0.954407i	$-0.403511\pi$
$311$	3274.35			0.597014			0.298507	+	0.954407i	$0.403511\pi$
$312$	4677.95	−	2329.09i	0.848835	−	0.422624i
$313$			9357.60i			1.68985i	0.534885	+	0.844925i	$0.320355\pi$
$313$			9357.60i			1.68985i	−0.534885	+	0.844925i	$0.679645\pi$
$314$	−1013.14	−	1259.07i	−0.182085	−	0.226284i
$315$		0			0
$316$	1666.97	−	7610.55i	0.296754	−	1.35483i
$317$	9064.68			1.60607			0.803033	−	0.595934i	$-0.203218\pi$
$317$	9064.68			1.60607			0.803033	+	0.595934i	$0.203218\pi$
$318$	−2624.23	−	3261.24i	−0.462766	−	0.575098i
$319$	−3898.47			−0.684239
$320$		0			0
$321$	644.222			0.112015
$322$	−319.892	−	397.543i	−0.0553630	−	0.0688019i
$323$	−386.825			−0.0666362
$324$	−2937.03	+	13409.0i	−0.503606	+	2.29922i
$325$		0			0
$326$	−420.175	−	522.168i	−0.0713844	−	0.0887123i
$327$			13977.1i			2.36371i
$328$	8871.23	−	4416.87i	1.49339	−	0.743539i
$329$	−2094.65			−0.351008
$330$		0			0
$331$			280.089i			0.0465108i	0.999730	+	0.0232554i	$0.00740310\pi$
$331$			280.089i			0.0465108i	−0.999730	+	0.0232554i	$0.992597\pi$
$332$	94.1789	−	429.975i	0.0155685	−	0.0710781i
$333$	8477.98			1.39517
$334$	−3191.83	+	2568.38i	−0.522901	+	0.420764i
$335$		0			0
$336$	5527.66	−	12012.9i	0.897496	−	1.95047i
$337$		−	5748.75i		−	0.929242i	−0.885510	−	0.464621i	$-0.846191\pi$
$337$		−	5748.75i		−	0.929242i	0.885510	−	0.464621i	$-0.153809\pi$
$338$	−2864.96	−	3560.40i	−0.461045	−	0.572959i
$339$		−	4389.65i		−	0.703284i
$340$		0			0
$341$		−	7617.30i		−	1.20968i
$342$	3808.34	−	3064.47i	0.602138	−	0.484525i
$343$			4761.06i			0.749484i
$344$	−6254.23	+	3113.90i	−0.980248	+	0.488052i
$345$		0			0
$346$	4485.68	+	5574.53i	0.696969	+	0.866152i
$347$	−2911.52			−0.450428			−0.225214	−	0.974309i	$-0.572308\pi$
$347$	−2911.52			−0.450428			−0.225214	+	0.974309i	$0.572308\pi$
$348$	7826.46	+	1714.26i	1.20558	+	0.264063i
$349$			5665.17i			0.868910i	0.900693	+	0.434455i	$0.143059\pi$
$349$			5665.17i			0.868910i	−0.900693	+	0.434455i	$0.856941\pi$
$350$		0			0
$351$	−8719.42			−1.32595
$352$	−6545.95	+	1645.87i	−0.991193	+	0.249219i
$353$			9428.18i			1.42156i	0.703414	+	0.710781i	$0.251658\pi$
$353$			9428.18i			1.42156i	−0.703414	+	0.710781i	$0.748342\pi$
$354$	11484.6	−	9241.38i	1.72430	−	1.38750i
$355$		0			0
$356$	−1574.43	+	7188.09i	−0.234396	+	1.07013i
$357$	2994.74			0.443973
$358$	−311.862	+	250.947i	−0.0460403	+	0.0370474i
$359$	−4573.16			−0.672318			−0.336159	−	0.941805i	$-0.609128\pi$
$359$	−4573.16			−0.672318			−0.336159	+	0.941805i	$0.609128\pi$
$360$		0			0
$361$	6146.71			0.896153
$362$	−7619.57	+	6131.26i	−1.10629	+	0.890199i
$363$	−568.300			−0.0821709
$364$	4064.08	+	890.172i	0.585208	+	0.128180i
$365$		0			0
$366$	−7907.10	+	6362.63i	−1.12926	+	0.908689i
$367$		−	2717.97i		−	0.386585i	−0.981141	−	0.193293i	$-0.938083\pi$
$367$		−	2717.97i		−	0.386585i	0.981141	−	0.193293i	$-0.0619166\pi$
$368$	223.751	−	486.265i	0.0316952	−	0.0688813i
$369$	−28360.5			−4.00105
$370$		0			0
$371$		−	3332.65i		−	0.466369i
$372$	−3349.53	+	15292.3i	−0.466841	+	2.13137i
$373$	5627.51			0.781183			0.390592	−	0.920564i	$-0.372270\pi$
$373$	5627.51			0.781183			0.390592	+	0.920564i	$0.372270\pi$
$374$	−958.292	−	1190.91i	−0.132492	−	0.164654i
$375$		0			0
$376$	−979.338	−	1966.99i	−0.134323	−	0.269786i
$377$			2520.74i			0.344363i
$378$	−17190.3	+	13832.6i	−2.33908	+	1.88220i
$379$			8066.74i			1.09330i	0.837361	+	0.546650i	$0.184097\pi$
$379$			8066.74i			1.09330i	−0.837361	+	0.546650i	$0.815903\pi$
$380$		0			0
$381$			1998.97i			0.268794i
$382$	−2512.57	−	3122.47i	−0.336529	−	0.418219i
$383$		−	10607.8i		−	1.41523i	−0.706600	−	0.707613i	$-0.749772\pi$
$383$		−	10607.8i		−	1.41523i	0.706600	−	0.707613i	$-0.250228\pi$
$384$	13865.2	−	425.775i	1.84259	−	0.0565826i
$385$		0			0
$386$	−5908.11	+	4754.10i	−0.779055	+	0.626884i
$387$	19994.1			2.62625
$388$	−2328.68	−	510.059i	−0.304693	−	0.0667380i
$389$		−	8992.58i		−	1.17209i	−0.810280	−	0.586044i	$-0.800685\pi$
$389$		−	8992.58i		−	1.17209i	0.810280	−	0.586044i	$-0.199315\pi$
$390$		0			0
$391$	121.223			0.0156790
$392$	2476.80	−	1233.16i	0.319125	−	0.158888i
$393$			17095.3i			2.19426i
$394$	4783.56	+	5944.73i	0.611656	+	0.760130i
$395$		0			0
$396$	18869.0	+	4132.95i	2.39445	+	0.524466i
$397$	8977.17			1.13489			0.567445	−	0.823411i	$-0.307932\pi$
$397$	8977.17			1.13489			0.567445	+	0.823411i	$0.307932\pi$
$398$	−6282.81	−	7807.90i	−0.791278	−	0.983353i
$399$	5514.40			0.691893
$400$		0			0
$401$	−3165.72			−0.394236			−0.197118	−	0.980380i	$-0.563158\pi$
$401$	−3165.72			−0.394236			−0.197118	+	0.980380i	$0.563158\pi$
$402$	−329.479	−	409.457i	−0.0408779	−	0.0508007i
$403$	−4925.33			−0.608804
$404$	14016.0	+	3069.97i	1.72604	+	0.378061i
$405$		0			0
$406$	3998.92	+	4969.62i	0.488826	+	0.607483i
$407$		−	4881.75i		−	0.594543i
$408$	1400.17	+	2812.22i	0.169899	+	0.341240i
$409$	5417.61			0.654972			0.327486	−	0.944856i	$-0.393798\pi$
$409$	5417.61			0.654972			0.327486	+	0.944856i	$0.393798\pi$
$410$		0			0
$411$			22803.5i			2.73678i
$412$	16286.8	+	3567.35i	1.94755	+	0.426580i
$413$	11736.1			1.39830
$414$	−1193.45	+	960.338i	−0.141679	+	0.114005i
$415$		0			0
$416$	1064.21	+	4232.59i	0.125426	+	0.498846i
$417$			27381.5i			3.21554i
$418$	−1764.56	−	2192.90i	−0.206478	−	0.256598i
$419$			6198.14i			0.722670i	0.932436	+	0.361335i	$0.117679\pi$
$419$			6198.14i			0.722670i	−0.932436	+	0.361335i	$0.882321\pi$
$420$		0			0
$421$		−	4344.57i		−	0.502949i	−0.967864	−	0.251474i	$-0.919085\pi$
$421$		−	4344.57i		−	0.502949i	0.967864	−	0.251474i	$-0.0809154\pi$
$422$	335.398	−	269.886i	0.0386894	−	0.0311323i
$423$			6288.27i			0.722804i
$424$	3129.54	−	1558.16i	0.358453	−	0.178469i
$425$		0			0
$426$	−16233.1	−	20173.5i	−1.84623	−	2.29439i
$427$	−8080.25			−0.915763
$428$	−115.118	+	525.574i	−0.0130011	+	0.0593565i
$429$			8611.27i			0.969128i
$430$		0			0
$431$	4750.74			0.530940			0.265470	−	0.964119i	$-0.414473\pi$
$431$	4750.74			0.530940			0.265470	+	0.964119i	$0.414473\pi$
$432$	−21026.7	−	9675.31i	−2.34178	−	1.07755i
$433$		−	4210.26i		−	0.467280i	−0.972323	−	0.233640i	$-0.924936\pi$
$433$		−	4210.26i		−	0.467280i	0.972323	−	0.233640i	$-0.0750638\pi$
$434$	−9710.25	+	7813.58i	−1.07398	+	0.864202i
$435$		0			0
$436$	−11402.9	−	2497.62i	−1.25252	−	0.274345i
$437$	223.215			0.0244344
$438$	2689.52	−	2164.18i	0.293402	−	0.236093i
$439$	5776.50			0.628012			0.314006	−	0.949421i	$-0.398329\pi$
$439$	5776.50			0.628012			0.314006	+	0.949421i	$0.398329\pi$
$440$		0			0
$441$	−7918.08			−0.854992
$442$	−770.038	+	619.629i	−0.0828665	+	0.0666804i
$443$	11981.6			1.28502			0.642510	−	0.766278i	$-0.277893\pi$
$443$	11981.6			1.28502			0.642510	+	0.766278i	$0.277893\pi$
$444$	−2146.63	+	9800.46i	−0.229447	+	1.04754i
$445$		0			0
$446$	−4551.32	+	3662.32i	−0.483209	+	0.388825i
$447$		−	8600.84i		−	0.910080i
$448$	8812.71	+	6656.25i	0.929378	+	0.701961i
$449$	5567.58			0.585190			0.292595	−	0.956236i	$-0.405481\pi$
$449$	5567.58			0.585190			0.292595	+	0.956236i	$0.405481\pi$
$450$		0			0
$451$			16330.4i			1.70503i
$452$	3581.20	+	784.404i	0.372667	+	0.0816267i
$453$	−32868.3			−3.40902
$454$	−5213.94	−	6479.58i	−0.538992	−	0.669828i
$455$		0			0
$456$	2578.22	+	5178.33i	0.264772	+	0.531792i
$457$		−	7283.56i		−	0.745538i	−0.927924	−	0.372769i	$-0.878408\pi$
$457$		−	7283.56i		−	0.745538i	0.927924	−	0.372769i	$-0.121592\pi$
$458$	10907.3	−	8776.82i	1.11281	−	0.895445i
$459$		−	5241.82i		−	0.533044i
$460$		0			0
$461$		−	11901.1i		−	1.20236i	−0.799113	−	0.601181i	$-0.794697\pi$
$461$		−	11901.1i		−	1.20236i	0.799113	−	0.601181i	$-0.205303\pi$
$462$	13661.0	+	16977.1i	1.37569	+	1.70962i
$463$		−	4915.73i		−	0.493419i	−0.969089	−	0.246710i	$-0.920651\pi$
$463$		−	4915.73i		−	0.493419i	0.969089	−	0.246710i	$-0.0793494\pi$
$464$	−2797.08	+	6078.72i	−0.279852	+	0.608184i
$465$		0			0
$466$	11444.0	−	9208.65i	1.13762	−	0.915413i
$467$	3110.15			0.308181			0.154091	−	0.988057i	$-0.450755\pi$
$467$	3110.15			0.308181			0.154091	+	0.988057i	$0.450755\pi$
$468$	2672.35	−	12200.7i	0.263952	−	1.20508i
$469$		−	418.424i		−	0.0411962i
$470$		0			0
$471$	−5473.09			−0.535428
$472$	5487.14	+	11020.9i	0.535098	+	1.07474i
$473$		−	11512.9i		−	1.11916i
$474$	−16541.3	−	20556.5i	−1.60288	−	1.99197i
$475$		0			0
$476$	−535.141	+	2443.19i	−0.0515297	+	0.235259i
$477$	−10004.8			−0.960358
$478$	3663.92	+	4553.30i	0.350594	+	0.435697i
$479$	−6590.43			−0.628652			−0.314326	−	0.949315i	$-0.601779\pi$
$479$	−6590.43			−0.628652			−0.314326	+	0.949315i	$0.601779\pi$
$480$		0			0
$481$	−3156.52			−0.299221
$482$	−4094.40	−	5088.28i	−0.386919	−	0.480840i
$483$	−1728.10			−0.162797
$484$	101.552	−	463.635i	0.00953717	−	0.0435420i
$485$		0			0
$486$	11829.6	+	14701.1i	1.10412	+	1.37213i
$487$			3139.99i			0.292169i	0.989272	+	0.146085i	$0.0466672\pi$
$487$			3139.99i			0.292169i	−0.989272	+	0.146085i	$0.953333\pi$
$488$	−3777.86	−	7587.80i	−0.350442	−	0.703860i
$489$	−2269.83			−0.209909
$490$		0			0
$491$		−	12057.6i		−	1.10825i	−0.832433	−	0.554126i	$-0.813053\pi$
$491$		−	12057.6i		−	1.10825i	0.832433	−	0.554126i	$-0.186947\pi$
$492$	7180.90	−	32784.4i	0.658008	−	3.00414i
$493$	−1515.38			−0.138437
$494$	−1417.92	+	1140.96i	−0.129140	+	0.103916i
$495$		0			0
$496$	−11877.3	−	5465.28i	−1.07522	−	0.494754i
$497$		−	20615.3i		−	1.86061i
$498$	−934.536	−	1161.39i	−0.0840915	−	0.104504i
$499$		−	8458.64i		−	0.758839i	−0.925225	−	0.379420i	$-0.876124\pi$
$499$		−	8458.64i		−	0.758839i	0.925225	−	0.379420i	$-0.123876\pi$
$500$		0			0
$501$			13874.7i			1.23727i
$502$	8379.40	−	6742.67i	0.745001	−	0.599483i
$503$		−	16896.2i		−	1.49774i	−0.662718	−	0.748869i	$-0.730597\pi$
$503$		−	16896.2i		−	1.49774i	0.662718	−	0.748869i	$-0.269403\pi$
$504$	−14086.7	−	28293.0i	−1.24498	−	2.50053i
$505$		0			0
$506$	552.977	+	687.207i	0.0485826	+	0.0603756i
$507$	−15476.8			−1.35572
$508$	−1630.82	−	357.204i	−0.142433	−	0.0311976i
$509$		−	6849.13i		−	0.596429i	−0.954499	−	0.298214i	$-0.903609\pi$
$509$		−	6849.13i		−	0.596429i	0.954499	−	0.298214i	$-0.0963910\pi$
$510$		0			0
$511$	2748.41			0.237931
$512$	−2130.27	+	11387.7i	−0.183878	+	0.982949i
$513$		−	9652.10i		−	0.830703i
$514$	−13593.0	+	10937.9i	−1.16646	+	0.938623i
$515$		0			0
$516$	−5062.54	+	23113.0i	−0.431910	+	1.97189i
$517$	3620.88			0.308019
$518$	−6223.07	+	5007.54i	−0.527849	+	0.424746i
$519$	24232.1			2.04947
$520$		0			0
$521$	11044.1			0.928696			0.464348	−	0.885653i	$-0.346289\pi$
$521$	11044.1			0.928696			0.464348	+	0.885653i	$0.346289\pi$
$522$	14919.1	−	12005.0i	1.25094	−	1.00660i
$523$	3115.75			0.260502			0.130251	−	0.991481i	$-0.458422\pi$
$523$	3115.75			0.260502			0.130251	+	0.991481i	$0.458422\pi$
$524$	−13946.8	−	3054.83i	−1.16273	−	0.254677i
$525$		0			0
$526$	−3605.32	+	2901.10i	−0.298858	+	0.240483i
$527$		−	2960.94i		−	0.244745i
$528$	−9555.30	+	20765.9i	−0.787578	+	1.71159i
$529$	12097.0			0.994251
$530$		0			0
$531$		−	35232.6i		−	2.87941i
$532$	−985.390	+	4498.80i	−0.0803046	+	0.366631i
$533$	10559.2			0.858103
$534$	15623.1	+	19415.4i	1.26606	+	1.57339i
$535$		0			0
$536$	392.923	−	195.631i	0.0316636	−	0.0157649i
$537$			1355.64i			0.108939i
$538$	−4985.07	+	4011.36i	−0.399483	+	0.321453i
$539$			4559.35i			0.364350i
$540$		0			0
$541$			14840.6i			1.17938i	0.807629	+	0.589691i	$0.200751\pi$
$541$			14840.6i			1.17938i	−0.807629	+	0.589691i	$0.799249\pi$
$542$	73.8316	+	91.7535i	0.00585118	+	0.00727150i
$543$			33121.8i			2.61767i
$544$	−2544.49	+	639.769i	−0.200541	+	0.0504226i
$545$		0			0
$546$	10977.3	−	8833.16i	0.860414	−	0.692352i
$547$	−12622.8			−0.986679			−0.493340	−	0.869837i	$-0.664224\pi$
$547$	−12622.8			−0.986679			−0.493340	+	0.869837i	$0.664224\pi$
$548$	−18603.8	−	4074.85i	−1.45021	−	0.317644i
$549$			24257.5i			1.88576i
$550$		0			0
$551$	−2790.37			−0.215742
$552$	−807.958	−	1622.78i	−0.0622989	−	0.125127i
$553$		−	21006.7i		−	1.61536i
$554$	3792.83	+	4713.50i	0.290870	+	0.361475i
$555$		0			0
$556$	−22338.6	−	4892.91i	−1.70390	−	0.373211i
$557$	−13382.1			−1.01798			−0.508992	−	0.860771i	$-0.669982\pi$
$557$	−13382.1			−1.01798			−0.508992	+	0.860771i	$0.669982\pi$
$558$	23456.9	+	29150.8i	1.77959	+	2.21156i
$559$	−7444.23			−0.563251
$560$		0			0
$561$	−5176.80			−0.389599
$562$	−2648.28	−	3291.13i	−0.198774	−	0.247025i
$563$	−153.895			−0.0115203			−0.00576014	−	0.999983i	$-0.501834\pi$
$563$	−153.895			−0.0115203			−0.00576014	+	0.999983i	$0.501834\pi$
$564$	−7269.18	−	1592.20i	−0.542709	−	0.118872i
$565$		0			0
$566$	−1933.12	−	2402.37i	−0.143560	−	0.178408i
$567$			37011.7i			2.74135i
$568$	19358.9	−	9638.52i	1.43007	−	0.712013i
$569$	5395.71			0.397539			0.198770	−	0.980046i	$-0.436305\pi$
$569$	5395.71			0.397539			0.198770	+	0.980046i	$0.436305\pi$
$570$		0			0
$571$		−	22390.5i		−	1.64100i	−0.571646	−	0.820500i	$-0.693695\pi$
$571$		−	22390.5i		−	1.64100i	0.571646	−	0.820500i	$-0.306305\pi$
$572$	−7025.31	−	1538.78i	−0.513537	−	0.112482i
$573$	−13573.2			−0.989578
$574$	20817.4	−	16751.2i	1.51376	−	1.21808i
$575$		0			0
$576$	19982.5	−	26456.3i	1.44549	−	1.91380i
$577$		−	1935.38i		−	0.139638i	−0.997560	−	0.0698188i	$-0.977758\pi$
$577$		−	1935.38i		−	0.139638i	0.997560	−	0.0698188i	$-0.0222421\pi$
$578$	8339.12	+	10363.4i	0.600106	+	0.745777i
$579$			25682.2i			1.84338i
$580$		0			0
$581$		−	1186.82i		−	0.0847461i
$582$	−6289.90	+	5061.31i	−0.447981	+	0.360478i
$583$			5760.94i			0.409252i
$584$	1285.00	+	2580.91i	0.0910508	+	0.182875i
$585$		0			0
$586$	−7212.41	−	8963.15i	−0.508433	−	0.631851i
$587$	7905.44			0.555865			0.277932	−	0.960601i	$-0.410351\pi$
$587$	7905.44			0.555865			0.277932	+	0.960601i	$0.410351\pi$
$588$	2004.86	−	9153.22i	0.140611	−	0.641960i
$589$		−	5452.17i		−	0.381414i
$590$		0			0
$591$	25841.4			1.79860
$592$	−7611.90	−	3502.57i	−0.528458	−	0.243166i
$593$			11141.6i			0.771552i	0.922592	+	0.385776i	$0.126066\pi$
$593$			11141.6i			0.771552i	−0.922592	+	0.385776i	$0.873934\pi$
$594$	29715.7	−	23911.4i	2.05261	−	1.65168i
$595$		0			0
$596$	7016.81	+	1536.92i	0.482248	+	0.105629i
$597$	−33940.4			−2.32678
$598$	444.346	−	357.553i	0.0303857	−	0.0244506i
$599$	−278.847			−0.0190207			−0.00951033	−	0.999955i	$-0.503027\pi$
$599$	−278.847			−0.0190207			−0.00951033	+	0.999955i	$0.503027\pi$
$600$		0			0
$601$	18890.7			1.28214			0.641071	−	0.767482i	$-0.278490\pi$
$601$	18890.7			1.28214			0.641071	+	0.767482i	$0.278490\pi$
$602$	−14676.2	+	11809.6i	−0.993620	+	0.799539i
$603$	−1256.14			−0.0848321
$604$	5873.36	−	26814.9i	0.395668	−	1.80643i
$605$		0			0
$606$	37857.9	−	30463.3i	2.53774	−	2.04206i
$607$			5398.05i			0.360956i	0.983579	+	0.180478i	$0.0577644\pi$
$607$			5398.05i			0.360956i	−0.983579	+	0.180478i	$0.942236\pi$
$608$	−4685.34	+	1178.05i	−0.312525	+	0.0785792i
$609$	21602.6			1.43741
$610$		0			0
$611$		−	2341.25i		−	0.155019i
$612$	7334.62	+	1606.53i	0.484452	+	0.106111i
$613$	−14412.8			−0.949635			−0.474817	−	0.880084i	$-0.657486\pi$
$613$	−14412.8			−0.949635			−0.474817	+	0.880084i	$0.657486\pi$
$614$	−11944.2	−	14843.5i	−0.785063	−	0.975630i
$615$		0			0
$616$	−16291.5	+	8111.32i	−1.06559	+	0.530543i
$617$			13226.3i			0.863001i	0.902113	+	0.431500i	$0.142016\pi$
$617$			13226.3i			0.863001i	−0.902113	+	0.431500i	$0.857984\pi$
$618$	43991.5	−	35398.8i	2.86343	−	2.30412i
$619$		−	14179.4i		−	0.920705i	−0.887736	−	0.460352i	$-0.847723\pi$
$619$		−	14179.4i		−	0.920705i	0.887736	−	0.460352i	$-0.152277\pi$
$620$		0			0
$621$			3024.76i			0.195458i
$622$	5806.00	+	7215.35i	0.374275	+	0.465127i
$623$			19840.6i			1.27592i
$624$	13427.2	+	6178.43i	0.861407	+	0.396371i
$625$		0			0
$626$	−20620.4	+	16592.7i	−1.31654	+	1.05939i
$627$	−9532.38			−0.607156
$628$	978.007	−	4465.10i	0.0621444	−	0.283721i
$629$		−	1897.60i		−	0.120290i
$630$		0			0
$631$	1533.79			0.0967657			0.0483828	−	0.998829i	$-0.484593\pi$
$631$	1533.79			0.0967657			0.0483828	+	0.998829i	$0.484593\pi$
$632$	19726.4	−	9821.52i	1.24157	−	0.618163i
$633$		−	1457.96i		−	0.0915459i
$634$	16073.3	+	19974.9i	1.00686	+	1.25127i
$635$		0			0
$636$	2533.24	−	11565.5i	0.157939	−	0.721073i
$637$	2948.06			0.183370
$638$	−6912.67	−	8590.66i	−0.428958	−	0.533084i
$639$	−61888.4			−3.83140
$640$		0			0
$641$	−26682.6			−1.64415			−0.822074	−	0.569381i	$-0.807183\pi$
$641$	−26682.6			−1.64415			−0.822074	+	0.569381i	$0.807183\pi$
$642$	1142.32	+	1419.61i	0.0702239	+	0.0872701i
$643$	−16498.3			−1.01186			−0.505931	−	0.862574i	$-0.668851\pi$
$643$	−16498.3			−1.01186			−0.505931	+	0.862574i	$0.668851\pi$
$644$	308.800	−	1409.83i	0.0188951	−	0.0862655i
$645$		0			0
$646$	−685.909	−	852.406i	−0.0417751	−	0.0519156i
$647$		−	20127.5i		−	1.22302i	−0.791236	−	0.611510i	$-0.790562\pi$
$647$		−	20127.5i		−	1.22302i	0.791236	−	0.611510i	$-0.209438\pi$
$648$	−34756.0	+	17304.6i	−2.10701	+	1.04905i
$649$	−20287.5			−1.22705
$650$		0			0
$651$			42209.9i			2.54122i
$652$	405.605	−	1851.79i	0.0243631	−	0.111230i
$653$	21447.4			1.28530			0.642650	−	0.766160i	$-0.277835\pi$
$653$	21447.4			1.28530			0.642650	+	0.766160i	$0.277835\pi$
$654$	−30799.9	+	24783.8i	−1.84155	+	1.48184i
$655$		0			0
$656$	25463.3	+	11716.7i	1.51551	+	0.697351i
$657$		−	8250.91i		−	0.489953i
$658$	−3714.18	−	4615.76i	−0.220051	−	0.273467i
$659$			19402.5i			1.14691i	0.819237	+	0.573455i	$0.194397\pi$
$659$			19402.5i			1.14691i	−0.819237	+	0.573455i	$0.805603\pi$
$660$		0			0
$661$		−	9326.38i		−	0.548796i	−0.961616	−	0.274398i	$-0.911521\pi$
$661$		−	9326.38i		−	0.548796i	0.961616	−	0.274398i	$-0.0884786\pi$
$662$	−617.204	+	496.647i	−0.0362361	+	0.0291582i
$663$			3347.31i			0.196076i
$664$	1114.49	−	554.888i	0.0651363	−	0.0324305i
$665$		0			0
$666$	15033.0	+	18682.1i	0.874648	+	1.08696i
$667$	874.443			0.0507625
$668$	−11319.3	−	2479.32i	−0.655626	−	0.143604i
$669$			19784.3i			1.14336i
$670$		0			0
$671$	13967.8			0.803608
$672$	36273.1	−	9120.27i	2.08224	−	0.523545i
$673$			15027.4i			0.860718i	0.902658	+	0.430359i	$0.141613\pi$
$673$			15027.4i			0.860718i	−0.902658	+	0.430359i	$0.858387\pi$
$674$	12667.9	−	10193.6i	0.723963	−	0.582553i
$675$		0			0
$676$	2765.61	−	12626.4i	0.157352	−	0.718390i
$677$	−9717.31			−0.551649			−0.275825	−	0.961208i	$-0.588951\pi$
$677$	−9717.31			−0.551649			−0.275825	+	0.961208i	$0.588951\pi$
$678$	9673.03	−	7783.63i	0.547921	−	0.440898i
$679$	−6427.63			−0.363284
$680$		0			0
$681$	−28166.3			−1.58493
$682$	16785.5	−	13506.8i	0.942447	−	0.758362i
$683$	11473.9			0.642804			0.321402	−	0.946943i	$-0.395846\pi$
$683$	11473.9			0.642804			0.321402	+	0.946943i	$0.395846\pi$
$684$	13505.7	+	2958.21i	0.754976	+	0.165365i
$685$		0			0
$686$	−10491.5	+	8442.20i	−0.583916	+	0.469861i
$687$		−	47413.4i		−	2.63309i
$688$	−17951.6	−	8260.32i	−0.994766	−	0.457735i
$689$	3725.01			0.205967
$690$		0			0
$691$		−	28412.6i		−	1.56421i	−0.623149	−	0.782103i	$-0.714147\pi$
$691$		−	28412.6i		−	1.56421i	0.623149	−	0.782103i	$-0.285853\pi$
$692$	−4330.13	+	19769.3i	−0.237871	+	1.08600i
$693$	52082.3			2.85490
$694$	−5162.64	−	6415.82i	−0.282379	−	0.350924i
$695$		0			0
$696$	10100.2	+	20286.1i	0.550066	+	1.10480i
$697$			6347.82i			0.344965i
$698$	−12483.8	+	10045.3i	−0.676959	+	0.544731i
$699$		−	49746.2i		−	2.69181i
$700$		0			0
$701$		−	12291.3i		−	0.662250i	−0.943587	−	0.331125i	$-0.892572\pi$
$701$		−	12291.3i		−	0.662250i	0.943587	−	0.331125i	$-0.107428\pi$
$702$	−15461.1	−	19214.1i	−0.831254	−	1.03303i
$703$		−	3494.17i		−	0.187461i
$704$	−15233.9	−	11506.2i	−0.815555	−	0.615990i
$705$		0			0
$706$	−20775.9	+	16717.8i	−1.10752	+	0.891195i
$707$	38686.9			2.05795
$708$	40728.6	+	8920.94i	2.16197	+	0.473544i
$709$			12774.2i			0.676650i	0.941029	+	0.338325i	$0.109860\pi$
$709$			12774.2i			0.676650i	−0.941029	+	0.338325i	$0.890140\pi$
$710$		0			0
$711$	−63063.4			−3.32639
$712$	−18631.4	+	9276.33i	−0.980676	+	0.488266i
$713$			1708.59i			0.0897438i
$714$	5310.20	+	6599.20i	0.278332	+	0.345895i
$715$		0			0
$716$	−1105.97	−	242.245i	−0.0577264	−	0.0126440i
$717$	19792.9			1.03093
$718$	−8109.02	−	10077.4i	−0.421485	−	0.523796i
$719$	15748.6			0.816861			0.408430	−	0.912790i	$-0.366076\pi$
$719$	15748.6			0.816861			0.408430	+	0.912790i	$0.366076\pi$
$720$		0			0
$721$	44954.8			2.32206
$722$	10899.2	+	13544.9i	0.561810	+	0.698184i
$723$	−22118.4			−1.13775
$724$	−27021.7	−	5918.66i	−1.38709	−	0.303820i
$725$		0			0
$726$	−1007.70	−	1252.31i	−0.0515140	−	0.0640185i
$727$			9536.44i			0.486502i	0.969963	+	0.243251i	$0.0782138\pi$
$727$			9536.44i			0.486502i	−0.969963	+	0.243251i	$0.921786\pi$
$728$	5244.76	+	10534.0i	0.267010	+	0.536288i
$729$	17576.5			0.892980
$730$		0			0
$731$		−	4475.22i		−	0.226432i
$732$	−28041.4	−	6142.01i	−1.41590	−	0.310130i
$733$	−34913.5			−1.75929			−0.879645	−	0.475631i	$-0.842220\pi$
$733$	−34913.5			−1.75929			−0.879645	+	0.475631i	$0.842220\pi$
$734$	5989.31	−	4819.43i	0.301184	−	0.242355i
$735$		0			0
$736$	1468.28	−	369.175i	0.0735348	−	0.0184891i
$737$			723.301i			0.0361508i
$738$	−50288.1	−	62495.1i	−2.50831	−	3.11718i
$739$		−	19324.3i		−	0.961918i	−0.876743	−	0.480959i	$-0.840289\pi$
$739$		−	19324.3i		−	0.961918i	0.876743	−	0.480959i	$-0.159711\pi$
$740$		0			0
$741$			6163.61i			0.305568i
$742$	7343.83	−	5909.38i	0.363343	−	0.292372i
$743$			7053.57i			0.348278i	0.984721	+	0.174139i	$0.0557142\pi$
$743$			7053.57i			0.348278i	−0.984721	+	0.174139i	$0.944286\pi$
$744$	−39637.4	+	19734.9i	−1.95319	+	0.972469i
$745$		0			0
$746$	9978.56	+	12400.8i	0.489733	+	0.608612i
$747$	−3562.91			−0.174511
$748$	925.063	−	4223.38i	0.0452188	−	0.206447i
$749$			1450.69i			0.0707705i
$750$		0			0
$751$	−36810.6			−1.78860			−0.894299	−	0.447471i	$-0.852325\pi$
$751$	−36810.6			−1.78860			−0.894299	+	0.447471i	$0.852325\pi$
$752$	2597.92	−	5645.89i	0.125979	−	0.273782i
$753$		−	36424.7i		−	1.76280i
$754$	−5554.70	+	4469.72i	−0.268289	+	0.215885i
$755$		0			0
$756$	−60962.8	−	13352.9i	−2.93280	−	0.642382i
$757$	28515.3			1.36910			0.684549	−	0.728967i	$-0.259999\pi$
$757$	28515.3			1.36910			0.684549	+	0.728967i	$0.259999\pi$
$758$	−17775.9	+	14303.8i	−0.851779	+	0.685403i
$759$	2987.24			0.142859
$760$		0			0
$761$	1517.92			0.0723057			0.0361528	−	0.999346i	$-0.488490\pi$
$761$	1517.92			0.0723057			0.0361528	+	0.999346i	$0.488490\pi$
$762$	−4404.93	+	3544.53i	−0.209415	+	0.168510i
$763$	−31474.3			−1.49338
$764$	2425.44	−	11073.4i	0.114855	−	0.524373i
$765$		0			0
$766$	23375.3	−	18809.4i	1.10259	−	0.887223i
$767$			13117.8i			0.617545i
$768$	25523.7	+	29798.4i	1.19923	+	1.40007i
$769$	10413.9			0.488341			0.244171	−	0.969732i	$-0.421484\pi$
$769$	10413.9			0.488341			0.244171	+	0.969732i	$0.421484\pi$
$770$		0			0
$771$			59088.0i			2.76006i
$772$	−20952.3	−	4589.25i	−0.976798	−	0.213952i
$773$	32909.8			1.53129			0.765643	−	0.643266i	$-0.222421\pi$
$773$	32909.8			1.53129			0.765643	+	0.643266i	$0.222421\pi$
$774$	35453.2	+	44059.1i	1.64643	+	2.04609i
$775$		0			0
$776$	−3005.19	−	6035.90i	−0.139021	−	0.279222i
$777$			27051.3i			1.24898i
$778$	19816.0	−	15945.4i	0.913161	−	0.734796i
$779$			11688.6i			0.537599i
$780$		0			0
$781$			35636.2i			1.63273i
$782$	214.949	+	267.126i	0.00982936	+	0.0122153i
$783$		−	37812.1i		−	1.72579i
$784$	7109.20	+	3271.25i	0.323852	+	0.149018i
$785$		0			0
$786$	−37671.2	+	30313.0i	−1.70953	+	1.37561i
$787$	−35511.6			−1.60845			−0.804226	−	0.594324i	$-0.797420\pi$
$787$	−35511.6			−1.60845			−0.804226	+	0.594324i	$0.797420\pi$
$788$	−4617.69	+	21082.1i	−0.208754	+	0.953070i
$789$			15672.1i			0.707150i
$790$		0			0
$791$	9884.85			0.444330
$792$	24350.7	+	48908.2i	1.09251	+	2.19429i
$793$		−	9031.54i		−	0.404438i
$794$	15918.1	+	19782.1i	0.711477	+	0.884181i
$795$		0			0
$796$	6064.95	−	27689.6i	0.270058	−	1.23295i
$797$	22692.3			1.00853			0.504267	−	0.863548i	$-0.331763\pi$
$797$	22692.3			1.00853			0.504267	+	0.863548i	$0.331763\pi$
$798$	9778.01	+	12151.5i	0.433757	+	0.539047i
$799$	1407.48			0.0623193
$800$		0			0
$801$	59562.8			2.62740
$802$	−5613.39	−	6975.98i	−0.247152	−	0.307145i
$803$	−4751.00			−0.208791
$804$	318.055	−	1452.08i	0.0139514	−	0.0636952i
$805$		0			0
$806$	−8733.47	−	10853.4i	−0.381667	−	0.474313i
$807$			21669.8i			0.945246i
$808$	18087.8	+	36329.2i	0.787533	+	1.58175i
$809$	22716.0			0.987209			0.493604	−	0.869687i	$-0.335679\pi$
$809$	22716.0			0.987209			0.493604	+	0.869687i	$0.335679\pi$
$810$		0			0
$811$			17237.0i			0.746327i	0.927766	+	0.373164i	$0.121727\pi$
$811$			17237.0i			0.746327i	−0.927766	+	0.373164i	$0.878273\pi$
$812$	−3860.26	+	17624.0i	−0.166833	+	0.761678i
$813$	398.847			0.0172056
$814$	10757.4	−	8656.20i	0.463203	−	0.372727i
$815$		0			0
$816$	−3714.26	+	8071.98i	−0.159345	+	0.346294i
$817$		−	8240.51i		−	0.352875i
$818$	9606.38	+	11938.2i	0.410610	+	0.510282i
$819$		−	33676.3i		−	1.43681i
$820$		0			0
$821$			15695.7i			0.667217i	0.942712	+	0.333609i	$0.108266\pi$
$821$			15695.7i			0.667217i	−0.942712	+	0.333609i	$0.891734\pi$
$822$	−50249.8	+	40434.7i	−2.13219	+	1.71572i
$823$		−	16856.0i		−	0.713927i	−0.934118	−	0.356963i	$-0.883812\pi$
$823$		−	16856.0i		−	0.713927i	0.934118	−	0.356963i	$-0.116188\pi$
$824$	21018.3	+	42215.1i	0.888602	+	1.78475i
$825$		0			0
$826$	20810.2	+	25861.7i	0.876611	+	1.08940i
$827$	−3712.67			−0.156109			−0.0780544	−	0.996949i	$-0.524871\pi$
$827$	−3712.67			−0.156109			−0.0780544	+	0.996949i	$0.524871\pi$
$828$	−4232.40	−	927.038i	−0.177640	−	0.0389092i
$829$		−	22469.6i		−	0.941376i	−0.882300	−	0.470688i	$-0.844006\pi$
$829$		−	22469.6i		−	0.941376i	0.882300	−	0.470688i	$-0.155994\pi$
$830$		0			0
$831$	20489.3			0.855313
$832$	−7439.89	+	9850.23i	−0.310014	+	0.410451i
$833$			1772.27i			0.0737163i
$834$	−60337.8	+	48552.2i	−2.50519	+	2.01586i
$835$		0			0
$836$	1703.38	−	7776.78i	0.0704696	−	0.321729i
$837$	73881.8			3.05105
$838$	−13658.2	+	10990.4i	−0.563025	+	0.453051i
$839$	31935.2			1.31409			0.657046	−	0.753850i	$-0.271806\pi$
$839$	31935.2			1.31409			0.657046	+	0.753850i	$0.271806\pi$
$840$		0			0
$841$	13457.7			0.551795
$842$	9573.69	−	7703.69i	0.391842	−	0.315305i
$843$	−14306.3			−0.584504
$844$	1189.44	+	260.528i	0.0485098	+	0.0106253i
$845$		0			0
$846$	−13856.8	+	11150.2i	−0.563129	+	0.453135i
$847$		−	1279.73i		−	0.0519150i
$848$	8982.79	+	4133.37i	0.363762	+	0.167383i
$849$	−10442.9			−0.422144
$850$		0			0
$851$			1095.00i			0.0441081i
$852$	15670.2	−	71542.4i	0.630108	−	2.87676i
$853$	14782.2			0.593355			0.296678	−	0.954978i	$-0.404121\pi$
$853$	14782.2			0.593355			0.296678	+	0.954978i	$0.404121\pi$
$854$	−14327.7	−	17805.6i	−0.574103	−	0.713461i
$855$		0			0
$856$	−1362.28	+	678.261i	−0.0543946	+	0.0270823i
$857$		−	7222.91i		−	0.287900i	−0.989585	−	0.143950i	$-0.954020\pi$
$857$		−	7222.91i		−	0.287900i	0.989585	−	0.143950i	$-0.0459804\pi$
$858$	−18975.8	+	15269.3i	−0.755038	+	0.607559i
$859$		−	4646.96i		−	0.184578i	−0.995732	−	0.0922889i	$-0.970582\pi$
$859$		−	4646.96i		−	0.184578i	0.995732	−	0.0922889i	$-0.0294183\pi$
$860$		0			0
$861$		−	90491.7i		−	3.58182i
$862$	8423.90	+	10468.7i	0.332853	+	0.413650i
$863$		−	8122.19i		−	0.320374i	−0.987087	−	0.160187i	$-0.948790\pi$
$863$		−	8122.19i		−	0.320374i	0.987087	−	0.160187i	$-0.0512097\pi$
$864$	−15963.6	−	63490.5i	−0.628580	−	2.49999i
$865$		0			0
$866$	9277.73	−	7465.54i	0.364053	−	0.292944i
$867$	45048.9			1.76464
$868$	−34436.0	−	7542.64i	−1.34658	−	0.294947i
$869$			36312.8i			1.41752i
$870$		0			0
$871$	467.685			0.0181939
$872$	−14715.6	−	29556.1i	−0.571483	−	1.14782i
$873$			19296.2i			0.748083i
$874$	395.799	+	491.876i	0.0153182	+	0.0190366i
$875$		0			0
$876$	9537.98	+	2089.14i	0.367875	+	0.0805770i
$877$	−31986.1			−1.23158			−0.615790	−	0.787910i	$-0.711163\pi$
$877$	−31986.1			−1.23158			−0.615790	+	0.787910i	$0.711163\pi$
$878$	10242.8	+	12729.1i	0.393709	+	0.489278i
$879$	−38962.3			−1.49507
$880$		0			0
$881$	−29450.6			−1.12624			−0.563118	−	0.826376i	$-0.690398\pi$
$881$	−29450.6			−1.12624			−0.563118	+	0.826376i	$0.690398\pi$
$882$	−14040.1	−	17448.3i	−0.536005	−	0.666115i
$883$	46156.5			1.75911			0.879553	−	0.475801i	$-0.157842\pi$
$883$	46156.5			1.75911			0.879553	+	0.475801i	$0.157842\pi$
$884$	−2730.83	−	598.143i	−0.103900	−	0.0227576i
$885$		0			0
$886$	21245.5	+	26402.7i	0.805595	+	1.00115i
$887$			41051.2i			1.55396i	0.629523	+	0.776982i	$0.283250\pi$
$887$			41051.2i			1.55396i	−0.629523	+	0.776982i	$0.716750\pi$
$888$	−25402.6	+	12647.6i	−0.959974	+	0.477958i
$889$	−4501.39			−0.169822
$890$		0			0
$891$		−	63979.7i		−	2.40561i
$892$	−16140.6	−	3535.33i	−0.605859	−	0.132704i
$893$	2591.69			0.0971192
$894$	18952.8	−	15250.8i	0.709034	−	0.570541i
$895$		0			0
$896$	958.782	+	31222.4i	0.0357485	+	1.16414i
$897$		−	1931.54i		−	0.0718979i
$898$	9872.31	+	12268.7i	0.366863	+	0.455916i
$899$		−	21358.8i		−	0.792389i
$900$		0			0
$901$			2239.35i			0.0828008i
$902$	−35985.6	+	28956.6i	−1.32837	+	1.06890i
$903$			63796.7i			2.35108i
$904$	4621.59	+	9282.42i	0.170035	+	0.341514i
$905$		0			0
$906$	−58281.3	−	72428.5i	−2.13716	−	2.65593i
$907$	27915.8			1.02197			0.510987	−	0.859588i	$-0.329280\pi$
$907$	27915.8			1.02197			0.510987	+	0.859588i	$0.329280\pi$
$908$	5033.15	−	22978.9i	0.183955	−	0.839847i
$909$		−	116141.i		−	4.23778i
$910$		0			0
$911$	−6557.22			−0.238475			−0.119237	−	0.992866i	$-0.538045\pi$
$911$	−6557.22			−0.238475			−0.119237	+	0.992866i	$0.538045\pi$
$912$	−6839.31	+	14863.4i	−0.248325	+	0.539669i
$913$			2051.57i			0.0743671i
$914$	16050.0	−	12915.0i	0.580841	−	0.467387i
$915$		0			0
$916$	38681.2	+	8472.48i	1.39526	+	0.305610i
$917$	−38496.2			−1.38632
$918$	11550.9	−	9294.67i	0.415289	−	0.334172i
$919$	11493.0			0.412534			0.206267	−	0.978496i	$-0.433869\pi$
$919$	11493.0			0.412534			0.206267	+	0.978496i	$0.433869\pi$
$920$		0			0
$921$	−64524.0			−2.30851
$922$	26225.2	−	21102.7i	0.936748	−	0.753776i
$923$	23042.3			0.821719
$924$	−13187.3	+	60206.7i	−0.469513	+	2.14356i
$925$		0			0
$926$	10832.3	−	8716.45i	0.384418	−	0.309331i
$927$		−	134957.i		−	4.78164i
$928$	−18354.8	+	4615.00i	−0.649273	+	0.163249i
$929$	−56597.2			−1.99881			−0.999405	−	0.0345020i	$-0.989015\pi$
$929$	−56597.2			−1.99881			−0.999405	+	0.0345020i	$0.989015\pi$
$930$		0			0
$931$			3263.40i			0.114880i
$932$	40584.3	+	8889.34i	1.42638	+	0.312425i
$933$	31364.7			1.10057
$934$	5514.84	+	6853.52i	0.193203	+	0.240101i
$935$		0			0
$936$	31623.9	−	15745.1i	1.10434	−	0.549834i
$937$		−	37901.5i		−	1.32144i	−0.750633	−	0.660720i	$-0.770251\pi$
$937$		−	37901.5i		−	1.32144i	0.750633	−	0.660720i	$-0.229749\pi$
$938$	922.037	−	741.939i	0.0320955	−	0.0258264i
$939$			89635.5i			3.11517i
$940$		0			0
$941$		−	4449.85i		−	0.154156i	−0.997025	−	0.0770781i	$-0.975441\pi$
$941$		−	4449.85i		−	0.154156i	0.997025	−	0.0770781i	$-0.0245591\pi$
$942$	−9704.75	−	12060.5i	−0.335666	−	0.417146i
$943$		−	3662.97i		−	0.126493i
$944$	−14555.9	+	31633.4i	−0.501858	+	1.09066i
$945$		0			0
$946$	25369.9	−	20414.4i	0.871929	−	0.701618i
$947$	−225.160			−0.00772620			−0.00386310	−	0.999993i	$-0.501230\pi$
$947$	−225.160			−0.00772620			−0.00386310	+	0.999993i	$0.501230\pi$
$948$	15967.7	−	72900.7i	0.547054	−	2.49758i
$949$			3071.98i			0.105080i
$950$		0			0
$951$	86829.7			2.96072
$952$	−6332.71	+	3152.97i	−0.215593	+	0.107341i
$953$		−	4845.81i		−	0.164713i	−0.996603	−	0.0823563i	$-0.973755\pi$
$953$		−	4845.81i		−	0.164713i	0.996603	−	0.0823563i	$-0.0262445\pi$
$954$	−17740.4	−	22046.7i	−0.602060	−	0.748205i
$955$		0			0
$956$	−3536.87	+	16147.6i	−0.119655	+	0.546288i
$957$	−37343.1			−1.26137
$958$	−11686.0	−	14522.7i	−0.394110	−	0.489777i
$959$	−51350.2			−1.72908
$960$		0			0
$961$	11942.5			0.400876
$962$	−5597.07	−	6955.71i	−0.187585	−	0.233120i
$963$	4355.07			0.145732
$964$	3952.43	−	18044.8i	0.132053	−	0.602889i
$965$		0			0
$966$	−3064.22	−	3808.03i	−0.102060	−	0.126834i
$967$			40394.8i			1.34334i	0.740851	+	0.671670i	$0.234423\pi$
$967$			40394.8i			1.34334i	−0.740851	+	0.671670i	$0.765577\pi$
$968$	1201.74	−	598.328i	0.0399021	−	0.0198667i
$969$	−3705.36			−0.122841
$970$		0			0
$971$			29066.2i			0.960637i	0.877094	+	0.480318i	$0.159479\pi$
$971$			29066.2i			0.960637i	−0.877094	+	0.480318i	$0.840521\pi$
$972$	−11419.4	+	52135.4i	−0.376829	+	1.72042i
$973$	−61659.1			−2.03155
$974$	−6919.28	+	5567.75i	−0.227626	+	0.183165i
$975$		0			0
$976$	10021.6	−	21779.4i	0.328673	−	0.714284i
$977$			42580.5i			1.39434i	0.716906	+	0.697170i	$0.245558\pi$
$977$			42580.5i			1.39434i	−0.716906	+	0.697170i	$0.754442\pi$
$978$	−4024.81	−	5001.80i	−0.131594	−	0.163538i
$979$		−	34297.1i		−	1.11965i
$980$		0			0
$981$			94488.0i			3.07520i
$982$	26570.1	−	21380.2i	0.863427	−	0.694777i
$983$			40586.0i			1.31688i	0.752633	+	0.658440i	$0.228783\pi$
$983$			40586.0i			1.31688i	−0.752633	+	0.658440i	$0.771217\pi$
$984$	84976.7	−	42308.8i	2.75301	−	1.37068i
$985$		0			0
$986$	−2687.04	−	3339.30i	−0.0867879	−	0.107855i
$987$	−20064.4			−0.647070
$988$	−5028.45	−	1101.40i	−0.161919	−	0.0354658i
$989$			2582.40i			0.0830288i
$990$		0			0
$991$	−50370.4			−1.61460			−0.807299	−	0.590142i	$-0.799072\pi$
$991$	−50370.4			−1.61460			−0.807299	+	0.590142i	$0.799072\pi$
$992$	−9017.34	−	35863.8i	−0.288610	−	1.14786i
$993$			2682.95i			0.0857409i
$994$	45427.8	−	36554.5i	1.44958	−	1.16644i
$995$		0			0
$996$	902.131	−	4118.69i	0.0286999	−	0.131030i
$997$	−22467.5			−0.713694			−0.356847	−	0.934163i	$-0.616148\pi$
$997$	−22467.5			−0.713694			−0.356847	+	0.934163i	$0.616148\pi$
$998$	18639.5	−	14998.7i	0.591204	−	0.475726i
$999$	47349.1			1.49956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.4.f.c.149.10		12
4.3	odd	2		800.4.f.b.49.1		12
5.2	odd	4		200.4.d.b.101.4		12
5.3	odd	4		40.4.d.a.21.9	✓	12
5.4	even	2		200.4.f.b.149.3		12
8.3	odd	2		800.4.f.c.49.11		12
8.5	even	2		200.4.f.b.149.4		12
15.8	even	4		360.4.k.c.181.4		12
20.3	even	4		160.4.d.a.81.1		12
20.7	even	4		800.4.d.d.401.12		12
20.19	odd	2		800.4.f.c.49.12		12
40.3	even	4		160.4.d.a.81.12		12
40.13	odd	4		40.4.d.a.21.10	yes	12
40.19	odd	2		800.4.f.b.49.2		12
40.27	even	4		800.4.d.d.401.1		12
40.29	even	2	inner	200.4.f.c.149.9		12
40.37	odd	4		200.4.d.b.101.3		12
60.23	odd	4		1440.4.k.c.721.2		12
80.3	even	4		1280.4.a.bd.1.6		6
80.13	odd	4		1280.4.a.bb.1.1		6
80.43	even	4		1280.4.a.ba.1.1		6
80.53	odd	4		1280.4.a.bc.1.6		6
120.53	even	4		360.4.k.c.181.3		12
120.83	odd	4		1440.4.k.c.721.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.4.d.a.21.9	✓	12	5.3	odd	4
40.4.d.a.21.10	yes	12	40.13	odd	4
160.4.d.a.81.1		12	20.3	even	4
160.4.d.a.81.12		12	40.3	even	4
200.4.d.b.101.3		12	40.37	odd	4
200.4.d.b.101.4		12	5.2	odd	4
200.4.f.b.149.3		12	5.4	even	2
200.4.f.b.149.4		12	8.5	even	2
200.4.f.c.149.9		12	40.29	even	2	inner
200.4.f.c.149.10		12	1.1	even	1	trivial
360.4.k.c.181.3		12	120.53	even	4
360.4.k.c.181.4		12	15.8	even	4
800.4.d.d.401.1		12	40.27	even	4
800.4.d.d.401.12		12	20.7	even	4
800.4.f.b.49.1		12	4.3	odd	2
800.4.f.b.49.2		12	40.19	odd	2
800.4.f.c.49.11		12	8.3	odd	2
800.4.f.c.49.12		12	20.19	odd	2
1280.4.a.ba.1.1		6	80.43	even	4
1280.4.a.bb.1.1		6	80.13	odd	4
1280.4.a.bc.1.6		6	80.53	odd	4
1280.4.a.bd.1.6		6	80.3	even	4
1440.4.k.c.721.2		12	60.23	odd	4
1440.4.k.c.721.8		12	120.83	odd	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	200.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.77318 + 2.20360i) q^{2} +9.57890 q^{3} +(-1.71169 + 7.81474i) q^{4} +(16.9851 + 21.1081i) q^{6} +21.5703i q^{7} +(-20.2557 + 10.0850i) q^{8} +64.7554 q^{9} -37.2871i q^{11} +(-16.3961 + 74.8566i) q^{12} -24.1097 q^{13} +(-47.5322 + 38.2479i) q^{14} +(-58.1402 - 26.7528i) q^{16} -14.4940i q^{17} +(114.823 + 142.695i) q^{18} -26.6887i q^{19} +206.620i q^{21} +(82.1658 - 66.1166i) q^{22} +8.36366i q^{23} +(-194.027 + 96.6035i) q^{24} +(-42.7508 - 53.1282i) q^{26} +361.655 q^{27} +(-168.566 - 36.9216i) q^{28} -104.553i q^{29} +204.288 q^{31} +(-44.1404 - 175.555i) q^{32} -357.170i q^{33} +(31.9389 - 25.7004i) q^{34} +(-110.841 + 506.046i) q^{36} +130.923 q^{37} +(58.8111 - 47.3237i) q^{38} -230.945 q^{39} -437.963 q^{41} +(-455.307 + 366.373i) q^{42} +308.764 q^{43} +(291.389 + 63.8240i) q^{44} +(-18.4301 + 14.8302i) q^{46} +97.1081i q^{47} +(-556.920 - 256.263i) q^{48} -122.277 q^{49} -138.836i q^{51} +(41.2684 - 188.411i) q^{52} -154.502 q^{53} +(641.279 + 796.943i) q^{54} +(-217.537 - 436.920i) q^{56} -255.648i q^{57} +(230.392 - 185.390i) q^{58} -544.088i q^{59} +374.601i q^{61} +(362.238 + 450.168i) q^{62} +1396.79i q^{63} +(308.584 - 408.558i) q^{64} +(787.058 - 633.325i) q^{66} -19.3982 q^{67} +(113.267 + 24.8092i) q^{68} +80.1147i q^{69} -955.725 q^{71} +(-1311.66 + 653.060i) q^{72} -127.417i q^{73} +(232.150 + 288.502i) q^{74} +(208.565 + 45.6828i) q^{76} +804.293 q^{77} +(-409.506 - 508.910i) q^{78} -973.871 q^{79} +1715.87 q^{81} +(-776.586 - 965.094i) q^{82} -55.0210 q^{83} +(-1614.68 - 353.669i) q^{84} +(547.493 + 680.392i) q^{86} -1001.50i q^{87} +(376.041 + 755.275i) q^{88} +919.812 q^{89} -520.054i q^{91} +(-65.3598 - 14.3160i) q^{92} +1956.85 q^{93} +(-213.987 + 172.190i) q^{94} +(-422.816 - 1681.63i) q^{96} +297.986i q^{97} +(-216.818 - 269.449i) q^{98} -2414.54i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 12 q^{3} - 16 q^{4} - 36 q^{6} - 24 q^{8} + 108 q^{9} - 164 q^{12} - 68 q^{14} - 56 q^{16} + 450 q^{18} + 492 q^{22} - 360 q^{24} - 308 q^{26} + 432 q^{27} + 628 q^{28} - 264 q^{31} + 856 q^{32}+ \cdots + 638 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 + 12 * q^3 - 16 * q^4 - 36 * q^6 - 24 * q^8 + 108 * q^9 - 164 * q^12 - 68 * q^14 - 56 * q^16 + 450 * q^18 + 492 * q^22 - 360 * q^24 - 308 * q^26 + 432 * q^27 + 628 * q^28 - 264 * q^31 + 856 * q^32 + 180 * q^34 + 440 * q^36 + 136 * q^37 - 1388 * q^38 - 600 * q^39 + 40 * q^41 - 2332 * q^42 - 1204 * q^43 + 472 * q^44 - 1268 * q^46 - 2536 * q^48 - 1308 * q^49 - 1272 * q^52 + 1056 * q^53 + 1512 * q^54 - 728 * q^56 + 1528 * q^58 + 2104 * q^62 + 2048 * q^64 + 2928 * q^66 - 2412 * q^67 + 960 * q^68 - 1592 * q^71 + 744 * q^72 + 420 * q^74 + 2256 * q^76 + 824 * q^77 - 160 * q^78 - 2016 * q^79 + 2508 * q^81 + 352 * q^82 + 3556 * q^83 - 1048 * q^84 - 244 * q^86 + 1008 * q^88 + 424 * q^89 + 1068 * q^92 + 2784 * q^93 - 292 * q^94 - 5920 * q^96 + 638 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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