LMFDB - Embedded newform 201.4.d.b.200.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(200,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("201.200");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			200.11
Character	$\chi$	$=$	201.200
Dual form			201.4.d.b.200.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.59475 q^{2} +(-2.38300 - 4.61750i) q^{3} +4.92223 q^{4} -8.49412 q^{5} +(8.56630 + 16.5988i) q^{6} -6.53043i q^{7} +11.0638 q^{8} +(-15.6426 + 22.0070i) q^{9} +O(q^{10})$	\(q-3.59475 q^{2} +(-2.38300 - 4.61750i) q^{3} +4.92223 q^{4} -8.49412 q^{5} +(8.56630 + 16.5988i) q^{6} -6.53043i q^{7} +11.0638 q^{8} +(-15.6426 + 22.0070i) q^{9} +30.5342 q^{10} -67.1912 q^{11} +(-11.7297 - 22.7284i) q^{12} +7.81000i q^{13} +23.4753i q^{14} +(20.2415 + 39.2216i) q^{15} -79.1495 q^{16} +108.570i q^{17} +(56.2312 - 79.1098i) q^{18} +16.7483 q^{19} -41.8100 q^{20} +(-30.1543 + 15.5620i) q^{21} +241.535 q^{22} -147.274i q^{23} +(-26.3651 - 51.0871i) q^{24} -52.8499 q^{25} -28.0750i q^{26} +(138.894 + 19.7868i) q^{27} -32.1443i q^{28} -126.302i q^{29} +(-72.7632 - 140.992i) q^{30} +66.6875i q^{31} +196.012 q^{32} +(160.117 + 310.255i) q^{33} -390.280i q^{34} +55.4703i q^{35} +(-76.9965 + 108.324i) q^{36} +346.440 q^{37} -60.2061 q^{38} +(36.0627 - 18.6112i) q^{39} -93.9773 q^{40} +274.969 q^{41} +(108.397 - 55.9416i) q^{42} -17.6268i q^{43} -330.731 q^{44} +(132.870 - 186.930i) q^{45} +529.414i q^{46} -519.523i q^{47} +(188.613 + 365.473i) q^{48} +300.353 q^{49} +189.982 q^{50} +(501.320 - 258.722i) q^{51} +38.4426i q^{52} -208.538 q^{53} +(-499.288 - 71.1288i) q^{54} +570.730 q^{55} -72.2514i q^{56} +(-39.9114 - 77.3355i) q^{57} +454.025i q^{58} +392.806i q^{59} +(99.6334 + 193.058i) q^{60} +623.723i q^{61} -239.725i q^{62} +(143.715 + 102.153i) q^{63} -71.4192 q^{64} -66.3391i q^{65} +(-575.580 - 1115.29i) q^{66} +(-324.851 + 441.854i) q^{67} +534.405i q^{68} +(-680.038 + 350.955i) q^{69} -199.402i q^{70} -619.089i q^{71} +(-173.067 + 243.482i) q^{72} -417.990 q^{73} -1245.36 q^{74} +(125.942 + 244.035i) q^{75} +82.4392 q^{76} +438.787i q^{77} +(-129.636 + 66.9028i) q^{78} -1118.27i q^{79} +672.305 q^{80} +(-239.619 - 688.494i) q^{81} -988.445 q^{82} +294.349i q^{83} +(-148.426 + 76.5999i) q^{84} -922.203i q^{85} +63.3641i q^{86} +(-583.200 + 300.978i) q^{87} -743.390 q^{88} -381.409i q^{89} +(-477.635 + 671.968i) q^{90} +51.0026 q^{91} -724.918i q^{92} +(307.930 - 158.917i) q^{93} +1867.56i q^{94} -142.262 q^{95} +(-467.098 - 905.086i) q^{96} +1403.86i q^{97} -1079.70 q^{98} +(1051.04 - 1478.68i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9}+O(q^{10}) $ 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9	$ 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9} - 36 q^{10} + 20 q^{15} + 556 q^{16} + 128 q^{19} + 96 q^{22} - 904 q^{24} + 2080 q^{25} - 236 q^{33} - 1574 q^{36} + 1004 q^{37} - 176 q^{39} - 648 q^{40} - 1220 q^{49} + 2188 q^{54} - 1344 q^{55} + 550 q^{60} + 4336 q^{64} - 3512 q^{67} + 3968 q^{73} - 3316 q^{76} - 1170 q^{81} + 4020 q^{82} - 9270 q^{84} + 2436 q^{88} + 746 q^{90} - 3408 q^{91} - 1412 q^{93} - 7032 q^{96}+O(q^{100}) $ 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9 - 36 * q^10 + 20 * q^15 + 556 * q^16 + 128 * q^19 + 96 * q^22 - 904 * q^24 + 2080 * q^25 - 236 * q^33 - 1574 * q^36 + 1004 * q^37 - 176 * q^39 - 648 * q^40 - 1220 * q^49 + 2188 * q^54 - 1344 * q^55 + 550 * q^60 + 4336 * q^64 - 3512 * q^67 + 3968 * q^73 - 3316 * q^76 - 1170 * q^81 + 4020 * q^82 - 9270 * q^84 + 2436 * q^88 + 746 * q^90 - 3408 * q^91 - 1412 * q^93 - 7032 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−3.59475			−1.27094			−0.635468	−	0.772127i	$-0.719193\pi$
$2$	−3.59475			−1.27094			−0.635468	+	0.772127i	$0.719193\pi$
$3$	−2.38300	−	4.61750i	−0.458609	−	0.888638i
$3$	−2.38300	−	4.61750i	−0.458609	−	0.888638i
$4$	4.92223			0.615279
$5$	−8.49412			−0.759737			−0.379869	−	0.925040i	$-0.624031\pi$
$5$	−8.49412			−0.759737			−0.379869	+	0.925040i	$0.624031\pi$
$6$	8.56630	+	16.5988i	0.582863	+	1.12940i
$7$		−	6.53043i		−	0.352610i	−0.984336	−	0.176305i	$-0.943585\pi$
$7$		−	6.53043i		−	0.352610i	0.984336	−	0.176305i	$-0.0564145\pi$
$8$	11.0638			0.488956
$9$	−15.6426	+	22.0070i	−0.579355	+	0.815075i
$10$	30.5342			0.965578
$11$	−67.1912			−1.84172			−0.920859	−	0.389896i	$-0.872511\pi$
$11$	−67.1912			−1.84172			−0.920859	+	0.389896i	$0.872511\pi$
$12$	−11.7297	−	22.7284i	−0.282173	−	0.546760i
$13$			7.81000i			0.166623i	0.996524	+	0.0833117i	$0.0265497\pi$
$13$			7.81000i			0.166623i	−0.996524	+	0.0833117i	$0.973450\pi$
$14$			23.4753i			0.448145i
$15$	20.2415	+	39.2216i	0.348422	+	0.675131i
$16$	−79.1495			−1.23671
$17$			108.570i			1.54894i	0.632611	+	0.774470i	$0.281983\pi$
$17$			108.570i			1.54894i	−0.632611	+	0.774470i	$0.718017\pi$
$18$	56.2312	−	79.1098i	0.736324	−	1.03591i
$19$	16.7483			0.202228			0.101114	−	0.994875i	$-0.467759\pi$
$19$	16.7483			0.202228			0.101114	+	0.994875i	$0.467759\pi$
$20$	−41.8100			−0.467450
$21$	−30.1543	+	15.5620i	−0.313343	+	0.161710i
$22$	241.535			2.34071
$23$		−	147.274i		−	1.33516i	−0.744536	−	0.667582i	$-0.767329\pi$
$23$		−	147.274i		−	1.33516i	0.744536	−	0.667582i	$-0.232671\pi$
$24$	−26.3651	−	51.0871i	−0.224240	−	0.434505i
$25$	−52.8499			−0.422799
$26$		−	28.0750i		−	0.211768i
$27$	138.894	+	19.7868i	0.990004	+	0.141036i
$28$		−	32.1443i		−	0.216954i
$29$		−	126.302i		−	0.808749i	−0.914594	−	0.404374i	$-0.867489\pi$
$29$		−	126.302i		−	0.808749i	0.914594	−	0.404374i	$-0.132511\pi$
$30$	−72.7632	−	140.992i	−0.442823	−	0.858049i
$31$			66.6875i			0.386369i	0.981162	+	0.193184i	$0.0618816\pi$
$31$			66.6875i			0.386369i	−0.981162	+	0.193184i	$0.938118\pi$
$32$	196.012			1.08282
$33$	160.117	+	310.255i	0.844629	+	1.63662i
$34$		−	390.280i		−	1.96860i
$35$			55.4703i			0.267891i
$36$	−76.9965	+	108.324i	−0.356465	+	0.501499i
$37$	346.440			1.53931			0.769653	−	0.638462i	$-0.220429\pi$
$37$	346.440			1.53931			0.769653	+	0.638462i	$0.220429\pi$
$38$	−60.2061			−0.257019
$39$	36.0627	−	18.6112i	0.148068	−	0.0764150i
$40$	−93.9773			−0.371478
$41$	274.969			1.04739			0.523694	−	0.851906i	$-0.324553\pi$
$41$	274.969			1.04739			0.523694	+	0.851906i	$0.324553\pi$
$42$	108.397	−	55.9416i	0.398239	−	0.205523i
$43$		−	17.6268i		−	0.0625132i	−0.999511	−	0.0312566i	$-0.990049\pi$
$43$		−	17.6268i		−	0.0625132i	0.999511	−	0.0312566i	$-0.00995091\pi$
$44$	−330.731			−1.13317
$45$	132.870	−	186.930i	0.440158	−	0.619243i
$46$			529.414i			1.69691i
$47$		−	519.523i		−	1.61234i	−0.591681	−	0.806172i	$-0.701535\pi$
$47$		−	519.523i		−	1.61234i	0.591681	−	0.806172i	$-0.298465\pi$
$48$	188.613	+	365.473i	0.567167	+	1.09899i
$49$	300.353			0.875666
$50$	189.982			0.537351
$51$	501.320	−	258.722i	1.37645	−	0.710358i
$52$			38.4426i			0.102520i
$53$	−208.538			−0.540471			−0.270235	−	0.962794i	$-0.587102\pi$
$53$	−208.538			−0.540471			−0.270235	+	0.962794i	$0.587102\pi$
$54$	−499.288	−	71.1288i	−1.25823	−	0.179248i
$55$	570.730			1.39922
$56$		−	72.2514i		−	0.172411i
$57$	−39.9114	−	77.3355i	−0.0927436	−	0.179708i
$58$			454.025i			1.02787i
$59$			392.806i			0.866762i	0.901211	+	0.433381i	$0.142679\pi$
$59$			392.806i			0.866762i	−0.901211	+	0.433381i	$0.857321\pi$
$60$	99.6334	+	193.058i	0.214377	+	0.415394i
$61$			623.723i			1.30917i	0.755987	+	0.654586i	$0.227157\pi$
$61$			623.723i			1.30917i	−0.755987	+	0.654586i	$0.772843\pi$
$62$		−	239.725i		−	0.491050i
$63$	143.715	+	102.153i	0.287404	+	0.204287i
$64$	−71.4192			−0.139491
$65$		−	66.3391i		−	0.126590i
$66$	−575.580	−	1115.29i	−1.07347	−	2.08004i
$67$	−324.851	+	441.854i	−0.592342	+	0.805687i
$67$	−324.851	+	441.854i	−0.592342	+	0.805687i
$68$			534.405i			0.953030i
$69$	−680.038	+	350.955i	−1.18648	+	0.612319i
$70$		−	199.402i		−	0.340472i
$71$		−	619.089i		−	1.03482i	−0.855737	−	0.517411i	$-0.826896\pi$
$71$		−	619.089i		−	1.03482i	0.855737	−	0.517411i	$-0.173104\pi$
$72$	−173.067	+	243.482i	−0.283279	+	0.398536i
$73$	−417.990			−0.670165			−0.335083	−	0.942189i	$-0.608764\pi$
$73$	−417.990			−0.670165			−0.335083	+	0.942189i	$0.608764\pi$
$74$	−1245.36			−1.95636
$75$	125.942	+	244.035i	0.193900	+	0.375716i
$76$	82.4392			0.124427
$77$			438.787i			0.649408i
$78$	−129.636	+	66.9028i	−0.188185	+	0.0971186i
$79$		−	1118.27i		−	1.59259i	−0.604907	−	0.796296i	$-0.706790\pi$
$79$		−	1118.27i		−	1.59259i	0.604907	−	0.796296i	$-0.293210\pi$
$80$	672.305			0.939575
$81$	−239.619	−	688.494i	−0.328695	−	0.944436i
$82$	−988.445			−1.33116
$83$			294.349i			0.389265i	0.980876	+	0.194632i	$0.0623514\pi$
$83$			294.349i			0.389265i	−0.980876	+	0.194632i	$0.937649\pi$
$84$	−148.426	+	76.5999i	−0.192793	+	0.0994969i
$85$		−	922.203i		−	1.17679i
$86$			63.3641i			0.0794503i
$87$	−583.200	+	300.978i	−0.718685	+	0.370900i
$88$	−743.390			−0.900519
$89$		−	381.409i		−	0.454262i	−0.973864	−	0.227131i	$-0.927065\pi$
$89$		−	381.409i		−	0.454262i	0.973864	−	0.227131i	$-0.0729345\pi$
$90$	−477.635	+	671.968i	−0.559412	+	0.787018i
$91$	51.0026			0.0587531
$92$		−	724.918i		−	0.821499i
$93$	307.930	−	158.917i	0.343342	−	0.177192i
$94$			1867.56i			2.04919i
$95$	−142.262			−0.153640
$96$	−467.098	−	905.086i	−0.496593	−	0.962239i
$97$			1403.86i			1.46949i	0.678344	+	0.734744i	$0.262698\pi$
$97$			1403.86i			1.46949i	−0.678344	+	0.734744i	$0.737302\pi$
$98$	−1079.70			−1.11292
$99$	1051.04	−	1478.68i	1.06701	−	1.50114i
$100$	−260.140			−0.260140
$101$	1022.45			1.00730			0.503651	−	0.863907i	$-0.331990\pi$
$101$	1022.45			1.00730			0.503651	+	0.863907i	$0.331990\pi$
$102$	−1802.12	+	930.039i	−1.74938	+	0.902820i
$103$	−65.2924			−0.0624607			−0.0312303	−	0.999512i	$-0.509943\pi$
$103$	−65.2924			−0.0624607			−0.0312303	+	0.999512i	$0.509943\pi$
$104$			86.4083i			0.0814715i
$105$	256.134	−	132.186i	0.238058	−	0.122857i
$106$	749.644			0.686904
$107$			1642.91i			1.48436i	0.670202	+	0.742179i	$0.266208\pi$
$107$			1642.91i			1.48436i	−0.670202	+	0.742179i	$0.733792\pi$
$108$	683.667	+	97.3955i	0.609129	+	0.0867767i
$109$			93.2444i			0.0819375i	0.999160	+	0.0409688i	$0.0130444\pi$
$109$			93.2444i			0.0819375i	−0.999160	+	0.0409688i	$0.986956\pi$
$110$	−2051.63			−1.77832
$111$	−825.567	−	1599.68i	−0.705940	−	1.36789i
$112$			516.880i			0.436077i
$113$	657.893			0.547694			0.273847	−	0.961773i	$-0.411704\pi$
$113$	657.893			0.547694			0.273847	+	0.961773i	$0.411704\pi$
$114$	143.471	+	278.002i	0.117871	+	0.228397i
$115$			1250.96i			1.01437i
$116$		−	621.688i		−	0.497606i
$117$	−171.875	−	122.169i	−0.135811	−	0.0965341i
$118$		−	1412.04i		−	1.10160i
$119$	709.006			0.546172
$120$	223.948	+	433.940i	0.170363	+	0.330109i
$121$	3183.65			2.39193
$122$		−	2242.13i		−	1.66388i
$123$	−655.252	−	1269.67i	−0.480342	−	0.930750i
$124$			328.252i			0.237725i
$125$	1510.68			1.08095
$126$	−516.621	−	367.214i	−0.365272	−	0.259635i
$127$	254.994			0.178166			0.0890829	−	0.996024i	$-0.471606\pi$
$127$	254.994			0.178166			0.0890829	+	0.996024i	$0.471606\pi$
$128$	−1311.36			−0.905541
$129$	−81.3919	+	42.0048i	−0.0555516	+	0.0286691i
$130$			238.472i			0.160888i
$131$			1759.48i			1.17348i	0.809775	+	0.586741i	$0.199589\pi$
$131$			1759.48i			1.17348i	−0.809775	+	0.586741i	$0.800411\pi$
$132$	788.132	+	1527.15i	0.519682	+	1.00698i
$133$		−	109.374i		−	0.0713077i
$134$	1167.76	−	1588.35i	0.752829	−	1.02398i
$135$	−1179.78	−	168.072i	−0.752143	−	0.107151i
$136$			1201.19i			0.757363i
$137$	1512.95			0.943504			0.471752	−	0.881731i	$-0.343622\pi$
$137$	1512.95			0.943504			0.471752	+	0.881731i	$0.343622\pi$
$138$	2444.57	−	1261.59i	1.50794	−	0.778218i
$139$		−	1192.52i		−	0.727683i	−0.931461	−	0.363842i	$-0.881465\pi$
$139$		−	1192.52i		−	0.727683i	0.931461	−	0.363842i	$-0.118535\pi$
$140$			273.037i			0.164828i
$141$	−2398.90	+	1238.02i	−1.43279	+	0.739436i
$142$			2225.47i			1.31519i
$143$		−	524.763i		−	0.306873i
$144$	1238.10	−	1741.84i	0.716495	−	1.00801i
$145$			1072.83i			0.614436i
$146$	1502.57			0.851737
$147$	−715.743	−	1386.88i	−0.401588	−	0.778150i
$148$	1705.26			0.947103
$149$			3176.49i			1.74650i	0.487275	+	0.873249i	$0.337991\pi$
$149$			3176.49i			1.74650i	−0.487275	+	0.873249i	$0.662009\pi$
$150$	−452.728	−	877.243i	−0.246434	−	0.477511i
$151$	−53.8807			−0.0290381			−0.0145190	−	0.999895i	$-0.504622\pi$
$151$	−53.8807			−0.0290381			−0.0145190	+	0.999895i	$0.504622\pi$
$152$	185.300			0.0988806
$153$	−2389.29	−	1698.31i	−1.26250	−	0.897387i
$154$		−	1577.33i		−	0.825357i
$155$		−	566.452i		−	0.293539i
$156$	177.509	−	91.6089i	0.0911031	−	0.0470165i
$157$	−2949.43			−1.49930			−0.749651	−	0.661833i	$-0.769779\pi$
$157$	−2949.43			−1.49930			−0.749651	+	0.661833i	$0.769779\pi$
$158$			4019.89i			2.02408i
$159$	496.948	+	962.926i	0.247865	+	0.480283i
$160$	−1664.95			−0.822662
$161$	−961.764			−0.470792
$162$	861.369	+	2474.96i	0.417750	+	1.20032i
$163$	2848.85			1.36895			0.684476	−	0.729035i	$-0.260031\pi$
$163$	2848.85			1.36895			0.684476	+	0.729035i	$0.260031\pi$
$164$	1353.46			0.644436
$165$	−1360.05	−	2635.34i	−0.641696	−	1.24340i
$166$		−	1058.11i		−	0.494731i
$167$			1041.83i			0.482749i	0.970432	+	0.241374i	$0.0775982\pi$
$167$			1041.83i			0.482749i	−0.970432	+	0.241374i	$0.922402\pi$
$168$	−333.621	+	172.175i	−0.153211	+	0.0790691i
$169$	2136.00			0.972237
$170$			3315.09i			1.49562i
$171$	−261.988	+	368.581i	−0.117162	+	0.164831i
$172$		−	86.7634i		−	0.0384631i
$173$			1163.21i			0.511200i	0.966783	+	0.255600i	$0.0822730\pi$
$173$			1163.21i			0.511200i	−0.966783	+	0.255600i	$0.917727\pi$
$174$	2096.46	−	1081.94i	0.913403	−	0.471390i
$175$			345.133i			0.149083i
$176$	5318.15			2.27767
$177$	1813.78	−	936.057i	0.770237	−	0.397505i
$178$			1371.07i			0.577338i
$179$	1443.20			0.602626			0.301313	−	0.953525i	$-0.402575\pi$
$179$	1443.20			0.602626			0.301313	+	0.953525i	$0.402575\pi$
$180$	654.017	−	920.115i	0.270820	−	0.381007i
$181$	2219.77			0.911569			0.455785	−	0.890090i	$-0.349359\pi$
$181$	2219.77			0.911569			0.455785	+	0.890090i	$0.349359\pi$
$182$	−183.342			−0.0746714
$183$	2880.04	−	1486.33i	1.16338	−	0.600399i
$184$		−	1629.41i		−	0.652836i
$185$	−2942.70			−1.16947
$186$	−1106.93	+	571.266i	−0.436366	+	0.225200i
$187$		−	7294.91i		−	2.85271i
$188$		−	2557.21i		−	0.992042i
$189$	129.217	−	907.036i	0.0497308	−	0.349086i
$190$	511.398			0.195267
$191$	2415.82			0.915196			0.457598	−	0.889159i	$-0.348710\pi$
$191$	2415.82			0.915196			0.457598	+	0.889159i	$0.348710\pi$
$192$	170.192	+	329.778i	0.0639716	+	0.123957i
$193$	131.655			0.0491022			0.0245511	−	0.999699i	$-0.492184\pi$
$193$	131.655			0.0491022			0.0245511	+	0.999699i	$0.492184\pi$
$194$		−	5046.53i		−	1.86763i
$195$	−306.321	+	158.086i	−0.112493	+	0.0580553i
$196$	1478.41			0.538779
$197$	−4907.85			−1.77497			−0.887486	−	0.460834i	$-0.847550\pi$
$197$	−4907.85			−1.77497			−0.887486	+	0.460834i	$0.847550\pi$
$198$	−3778.24	+	5315.48i	−1.35610	+	1.90785i
$199$	−506.561			−0.180448			−0.0902240	−	0.995922i	$-0.528758\pi$
$199$	−506.561			−0.180448			−0.0902240	+	0.995922i	$0.528758\pi$
$200$	−584.721			−0.206730
$201$	2814.38	+	447.061i	0.987617	+	0.156882i
$202$	−3675.45			−1.28022
$203$	−824.807			−0.285173
$204$	2467.61	−	1273.49i	0.846899	−	0.437068i
$205$	−2335.62			−0.795740
$206$	234.710			0.0793836
$207$	3241.07	+	2303.75i	1.08826	+	0.773535i
$208$		−	618.157i		−	0.206065i
$209$	−1125.34			−0.372447
$210$	−920.737	+	475.175i	−0.302557	+	0.156144i
$211$	−3306.92			−1.07895			−0.539473	−	0.842003i	$-0.681377\pi$
$211$	−3306.92			−1.07895			−0.539473	+	0.842003i	$0.681377\pi$
$212$	−1026.47			−0.332540
$213$	−2858.64	+	1475.29i	−0.919583	+	0.474579i
$214$		−	5905.86i		−	1.88652i
$215$			149.725i			0.0474936i
$216$	1536.69	+	218.918i	0.484068	+	0.0689605i
$217$	435.498			0.136238
$218$		−	335.190i		−	0.104137i
$219$	996.072	+	1930.07i	0.307344	+	0.595534i
$220$	2809.26			0.860912
$221$	−847.928			−0.258090
$222$	2967.71	+	5750.47i	0.897205	+	1.73850i
$223$	1812.70			0.544338			0.272169	−	0.962249i	$-0.412259\pi$
$223$	1812.70			0.544338			0.272169	+	0.962249i	$0.412259\pi$
$224$		−	1280.04i		−	0.381815i
$225$	826.710	−	1163.07i	0.244951	−	0.344613i
$226$	−2364.96			−0.696084
$227$			4199.76i			1.22796i	0.789320	+	0.613982i	$0.210433\pi$
$227$			4199.76i			1.22796i	−0.789320	+	0.613982i	$0.789567\pi$
$228$	−196.453	−	380.663i	−0.0570632	−	0.110570i
$229$		−	4511.73i		−	1.30194i	−0.759105	−	0.650968i	$-0.774363\pi$
$229$		−	4511.73i		−	1.30194i	0.759105	−	0.650968i	$-0.225637\pi$
$230$		−	4496.90i		−	1.28920i
$231$	2026.10	−	1045.63i	0.577089	−	0.297825i
$232$		−	1397.38i		−	0.395442i
$233$	1313.11			0.369206			0.184603	−	0.982813i	$-0.440900\pi$
$233$	1313.11			0.369206			0.184603	+	0.982813i	$0.440900\pi$
$234$	617.847	+	439.166i	0.172607	+	0.122689i
$235$			4412.89i			1.22496i
$236$			1933.48i			0.533300i
$237$	−5163.59	+	2664.83i	−1.41524	+	0.730377i
$238$	−2548.70			−0.694150
$239$	204.701			0.0554017			0.0277008	−	0.999616i	$-0.491181\pi$
$239$	204.701			0.0554017			0.0277008	+	0.999616i	$0.491181\pi$
$240$	−1602.11	−	3104.37i	−0.430898	−	0.834942i
$241$	−3140.81			−0.839492			−0.419746	−	0.907642i	$-0.637881\pi$
$241$	−3140.81			−0.839492			−0.419746	+	0.907642i	$0.637881\pi$
$242$	−11444.4			−3.03998
$243$	−2608.11	+	2747.12i	−0.688520	+	0.725218i
$244$			3070.11i			0.805507i
$245$	−2551.24			−0.665276
$246$	2355.47	+	4564.14i	0.610484	+	1.18292i
$247$			130.805i			0.0336959i
$248$			737.818i			0.188917i
$249$	1359.16	−	701.434i	0.345916	−	0.178520i
$250$	−5430.51			−1.37382
$251$	3063.85			0.770471			0.385235	−	0.922818i	$-0.374120\pi$
$251$	3063.85			0.770471			0.385235	+	0.922818i	$0.374120\pi$
$252$	707.400	+	502.820i	0.176833	+	0.125693i
$253$			9895.52i			2.45900i
$254$	−916.640			−0.226437
$255$	−4258.27	+	2197.61i	−1.04574	+	0.539685i
$256$	5285.38			1.29038
$257$			2060.63i			0.500150i	0.968227	+	0.250075i	$0.0804552\pi$
$257$			2060.63i			0.500150i	−0.968227	+	0.250075i	$0.919545\pi$
$258$	292.584	−	150.997i	0.0706026	−	0.0364366i
$259$		−	2262.40i		−	0.542775i
$260$		−	326.536i		−	0.0778881i
$261$	2779.53	+	1975.69i	0.659191	+	0.468553i
$262$		−	6324.88i		−	1.49142i
$263$		−	8017.53i		−	1.87978i	−0.341479	−	0.939890i	$-0.610928\pi$
$263$		−	8017.53i		−	1.87978i	0.341479	−	0.939890i	$-0.389072\pi$
$264$	1771.50	+	3432.60i	0.412986	+	0.800235i
$265$	1771.35			0.410616
$266$			393.172i			0.0906275i
$267$	−1761.16	+	908.900i	−0.403674	+	0.208329i
$268$	−1598.99	+	2174.91i	−0.364455	+	0.495722i
$269$			1744.16i			0.395328i	0.980270	+	0.197664i	$0.0633355\pi$
$269$			1744.16i			0.395328i	−0.980270	+	0.197664i	$0.936665\pi$
$270$	4241.02	+	604.176i	0.955926	+	0.136181i
$271$			3723.65i			0.834671i	0.908752	+	0.417335i	$0.137036\pi$
$271$			3723.65i			0.834671i	−0.908752	+	0.417335i	$0.862964\pi$
$272$		−	8593.22i		−	1.91559i
$273$	−121.539	−	235.505i	−0.0269447	−	0.0522102i
$274$	−5438.68			−1.19913
$275$	3551.05			0.778677
$276$	−3347.31	+	1727.48i	−0.730015	+	0.376747i
$277$	490.969			0.106496			0.0532482	−	0.998581i	$-0.483043\pi$
$277$	490.969			0.106496			0.0532482	+	0.998581i	$0.483043\pi$
$278$			4286.80i			0.924839i
$279$	−1467.59	−	1043.17i	−0.314920	−	0.223845i
$280$			613.712i			0.130987i
$281$	−5369.39			−1.13990			−0.569948	−	0.821680i	$-0.693037\pi$
$281$	−5369.39			−1.13990			−0.569948	+	0.821680i	$0.693037\pi$
$282$	8623.43	−	4450.39i	1.82099	−	0.939776i
$283$	2514.78			0.528226			0.264113	−	0.964492i	$-0.414921\pi$
$283$	2514.78			0.528226			0.264113	+	0.964492i	$0.414921\pi$
$284$		−	3047.30i		−	0.636705i
$285$	339.012	+	656.897i	0.0704608	+	0.136531i
$286$			1886.39i			0.390016i
$287$		−	1795.67i		−	0.369320i
$288$	−3066.14	+	4313.65i	−0.627340	+	0.882583i
$289$	−6874.35			−1.39922
$290$		−	3856.54i		−	0.780910i
$291$	6482.32	−	3345.40i	1.30584	−	0.673921i
$292$	−2057.45			−0.412339
$293$		−	2375.67i		−	0.473680i	−0.971549	−	0.236840i	$-0.923888\pi$
$293$		−	2375.67i		−	0.473680i	0.971549	−	0.236840i	$-0.0761116\pi$
$294$	2572.92	+	4985.49i	0.510393	+	0.988979i
$295$		−	3336.54i		−	0.658511i
$296$	3832.94			0.752653
$297$	−9332.43	−	1329.50i	−1.82331	−	0.259749i
$298$		−	11418.7i		−	2.21969i
$299$	1150.21			0.222470
$300$	619.914	+	1201.19i	0.119302	+	0.231170i
$301$	−115.111			−0.0220428
$302$	193.688			0.0369055
$303$	−2436.50	−	4721.16i	−0.461958	−	0.895127i
$304$	−1325.62			−0.250098
$305$		−	5297.98i		−	0.994627i
$306$	8588.91	+	6105.00i	1.60456	+	1.14052i
$307$	2262.50			0.420612			0.210306	−	0.977636i	$-0.432554\pi$
$307$	2262.50			0.420612			0.210306	+	0.977636i	$0.432554\pi$
$308$			2159.81i			0.399567i
$309$	155.592	+	301.488i	0.0286450	+	0.0555049i
$310$			2036.25i			0.373069i
$311$	10018.5			1.82669			0.913343	−	0.407191i	$-0.133492\pi$
$311$	10018.5			1.82669			0.913343	+	0.407191i	$0.133492\pi$
$312$	398.990	−	205.911i	0.0723986	−	0.0373636i
$313$			2973.43i			0.536959i	0.963285	+	0.268479i	$0.0865211\pi$
$313$			2973.43i			0.536959i	−0.963285	+	0.268479i	$0.913479\pi$
$314$	10602.5			1.90552
$315$	−1220.74	−	867.699i	−0.218351	−	0.155204i
$316$		−	5504.37i		−	0.979888i
$317$			141.178i			0.0250138i	0.999922	+	0.0125069i	$0.00398117\pi$
$317$			141.178i			0.0250138i	−0.999922	+	0.0125069i	$0.996019\pi$
$318$	−1786.40	−	3461.48i	−0.315021	−	0.610409i
$319$			8486.39i			1.48949i
$320$	606.643			0.105976
$321$	7586.14	−	3915.06i	1.31906	−	0.680740i
$322$	3457.30			0.598347
$323$			1818.36i			0.313239i
$324$	−1179.46	−	3388.93i	−0.202239	−	0.581092i
$325$		−	412.758i		−	0.0704483i
$326$	−10240.9			−1.73985
$327$	430.556	−	222.202i	0.0728128	−	0.0375773i
$328$	3042.20			0.512127
$329$	−3392.71			−0.568529
$330$	4889.04	+	9473.41i	0.815555	+	1.58028i
$331$			5413.73i			0.898989i	0.893283	+	0.449495i	$0.148396\pi$
$331$			5413.73i			0.898989i	−0.893283	+	0.449495i	$0.851604\pi$
$332$			1448.85i			0.239507i
$333$	−5419.21	+	7624.11i	−0.891805	+	1.25465i
$334$		−	3745.11i		−	0.613543i
$335$	2759.32	−	3753.16i	0.450024	−	0.612110i
$336$	2386.69	−	1231.73i	0.387514	−	0.199989i
$337$			10470.6i			1.69249i	0.532796	+	0.846244i	$0.321141\pi$
$337$			10470.6i			1.69249i	−0.532796	+	0.846244i	$0.678859\pi$
$338$	−7678.40			−1.23565
$339$	−1567.76	−	3037.82i	−0.251177	−	0.486701i
$340$		−	4539.30i		−	0.724053i
$341$		−	4480.81i		−	0.711583i
$342$	941.780	−	1324.96i	0.148905	−	0.209490i
$343$		−	4201.37i		−	0.661379i
$344$		−	195.020i		−	0.0305662i
$345$	5776.33	−	2981.05i	0.901411	−	0.465201i
$346$		−	4181.47i		−	0.649702i
$347$	−4222.47			−0.653240			−0.326620	−	0.945156i	$-0.605910\pi$
$347$	−4222.47			−0.653240			−0.326620	+	0.945156i	$0.605910\pi$
$348$	−2870.65	+	1481.49i	−0.442192	+	0.228207i
$349$	−6404.44			−0.982298			−0.491149	−	0.871076i	$-0.663423\pi$
$349$	−6404.44			−0.982298			−0.491149	+	0.871076i	$0.663423\pi$
$350$		−	1240.67i		−	0.189475i
$351$	−154.535	+	1084.76i	−0.0234999	+	0.164958i
$352$	−13170.3			−1.99426
$353$	1264.04			0.190590			0.0952949	−	0.995449i	$-0.469621\pi$
$353$	1264.04			0.190590			0.0952949	+	0.995449i	$0.469621\pi$
$354$	−6520.08	+	3364.89i	−0.978923	+	0.505203i
$355$			5258.62i			0.786193i
$356$		−	1877.39i		−	0.279498i
$357$	−1689.56	−	3273.83i	−0.250479	−	0.485349i
$358$	−5187.96			−0.765899
$359$			3013.14i			0.442973i	0.975163	+	0.221486i	$0.0710908\pi$
$359$			3013.14i			0.442973i	−0.975163	+	0.221486i	$0.928909\pi$
$360$	1470.05	−	2068.16i	0.215218	−	0.302782i
$361$	−6578.49			−0.959104
$362$	−7979.51			−1.15855
$363$	−7586.65	−	14700.5i	−1.09696	−	2.12556i
$364$	251.047			0.0361495
$365$	3550.46			0.509149
$366$	−10353.0	+	5343.00i	−1.47858	+	0.763068i
$367$			622.167i			0.0884928i	0.999021	+	0.0442464i	$0.0140887\pi$
$367$			622.167i			0.0884928i	−0.999021	+	0.0442464i	$0.985911\pi$
$368$			11656.7i			1.65121i
$369$	−4301.23	+	6051.25i	−0.606810	+	0.853700i
$370$	10578.3			1.48632
$371$			1361.85i			0.190576i
$372$	1515.70	−	782.224i	0.211251	−	0.109023i
$373$			529.806i			0.0735451i	0.999324	+	0.0367725i	$0.0117077\pi$
$373$			529.806i			0.0735451i	−0.999324	+	0.0367725i	$0.988292\pi$
$374$			26223.4i			3.62561i
$375$	−3599.95	−	6975.56i	−0.495735	−	0.960577i
$376$		−	5747.90i		−	0.788365i
$377$	986.419			0.134756
$378$	−464.502	+	3260.57i	−0.0632047	+	0.443665i
$379$		−	13937.8i		−	1.88901i	−0.328496	−	0.944505i	$-0.606542\pi$
$379$		−	13937.8i		−	1.88901i	0.328496	−	0.944505i	$-0.393458\pi$
$380$	−700.249			−0.0945316
$381$	−607.652	−	1177.44i	−0.0817085	−	0.158325i
$382$	−8684.26			−1.16316
$383$	2027.42			0.270487			0.135243	−	0.990812i	$-0.456818\pi$
$383$	2027.42			0.270487			0.135243	+	0.990812i	$0.456818\pi$
$384$	3124.98	+	6055.22i	0.415289	+	0.804698i
$385$		−	3727.11i		−	0.493380i
$386$	−473.266			−0.0624057
$387$	387.914	+	275.730i	0.0509530	+	0.0362174i
$388$			6910.12i			0.904145i
$389$		−	10012.9i		−	1.30508i	−0.757756	−	0.652538i	$-0.773704\pi$
$389$		−	10012.9i		−	1.30508i	0.757756	−	0.652538i	$-0.226296\pi$
$390$	1101.15	−	568.280i	0.142971	−	0.0737846i
$391$	15989.5			2.06809
$392$	3323.05			0.428162
$393$	8124.38	−	4192.84i	1.04280	−	0.538170i
$394$	17642.5			2.25588
$395$			9498.69i			1.20995i
$396$	5173.48	−	7278.40i	0.656508	−	0.923619i
$397$	8102.32			1.02429			0.512146	−	0.858899i	$-0.328851\pi$
$397$	8102.32			1.02429			0.512146	+	0.858899i	$0.328851\pi$
$398$	1820.96			0.229338
$399$	−505.034	+	260.638i	−0.0633667	+	0.0327023i
$400$	4183.05			0.522881
$401$	5276.29			0.657071			0.328535	−	0.944492i	$-0.393445\pi$
$401$	5276.29			0.657071			0.328535	+	0.944492i	$0.393445\pi$
$402$	−10117.0	−	1607.07i	−1.25520	−	0.199387i
$403$	−520.830			−0.0643781
$404$	5032.73			0.619772
$405$	2035.35	+	5848.15i	0.249722	+	0.717523i
$406$	2964.98			0.362437
$407$	−23277.7			−2.83497
$408$	5546.51	−	2862.45i	0.673022	−	0.347334i
$409$			637.861i			0.0771154i	0.999256	+	0.0385577i	$0.0122763\pi$
$409$			637.861i			0.0771154i	−0.999256	+	0.0385577i	$0.987724\pi$
$410$	8395.97			1.01133
$411$	−3605.36	−	6986.05i	−0.432700	−	0.838434i
$412$	−321.384			−0.0384308
$413$	2565.19			0.305629
$414$	−11650.8	−	8281.41i	−1.38311	−	0.983113i
$415$		−	2500.23i		−	0.295739i
$416$			1530.85i			0.180424i
$417$	−5506.45	+	2841.77i	−0.646647	+	0.333722i
$418$	4045.32			0.473357
$419$			9107.37i			1.06187i	0.847412	+	0.530936i	$0.178159\pi$
$419$			9107.37i			1.06187i	−0.847412	+	0.530936i	$0.821841\pi$
$420$	1260.75	−	650.649i	0.146472	−	0.0755915i
$421$	−4346.28			−0.503147			−0.251573	−	0.967838i	$-0.580948\pi$
$421$	−4346.28			−0.503147			−0.251573	+	0.967838i	$0.580948\pi$
$422$	11887.5			1.37127
$423$	11433.2	+	8126.68i	1.31418	+	0.934120i
$424$	−2307.23			−0.264266
$425$		−	5737.89i		−	0.654891i
$426$	10276.1	−	5303.31i	1.16873	−	0.603160i
$427$	4073.18			0.461628
$428$			8086.79i			0.913294i
$429$	−2423.09	+	1250.51i	−0.272699	+	0.140735i
$430$		−	538.222i		−	0.0603614i
$431$			12076.5i			1.34967i	0.737970	+	0.674834i	$0.235785\pi$
$431$			12076.5i			1.34967i	−0.737970	+	0.674834i	$0.764215\pi$
$432$	−10993.4	−	1566.12i	−1.22435	−	0.174421i
$433$		−	1568.00i		−	0.174026i	−0.996207	−	0.0870129i	$-0.972268\pi$
$433$		−	1568.00i		−	0.174026i	0.996207	−	0.0870129i	$-0.0277321\pi$
$434$	−1565.51			−0.173149
$435$	4953.77	−	2556.55i	0.546012	−	0.281786i
$436$			458.971i			0.0504145i
$437$		−	2466.60i		−	0.270008i
$438$	−3580.63	−	6938.12i	−0.390614	−	0.756886i
$439$	6485.58			0.705103			0.352551	−	0.935792i	$-0.385314\pi$
$439$	6485.58			0.705103			0.352551	+	0.935792i	$0.385314\pi$
$440$	6314.44			0.684158
$441$	−4698.31	+	6609.89i	−0.507322	+	0.713734i
$442$	3048.09			0.328015
$443$	4762.90			0.510817			0.255409	−	0.966833i	$-0.417790\pi$
$443$	4762.90			0.510817			0.255409	+	0.966833i	$0.417790\pi$
$444$	−4063.63	−	7874.02i	−0.434350	−	0.841632i
$445$			3239.74i			0.345120i
$446$	−6516.21			−0.691820
$447$	14667.4	−	7569.58i	1.55200	−	0.800960i
$448$			466.398i			0.0491858i
$449$		−	9428.99i		−	0.991050i	−0.868594	−	0.495525i	$-0.834976\pi$
$449$		−	9428.99i		−	0.991050i	0.868594	−	0.495525i	$-0.165024\pi$
$450$	−2971.82	+	4180.95i	−0.311317	+	0.437982i
$451$	−18475.5			−1.92899
$452$	3238.30			0.336984
$453$	128.398	+	248.794i	0.0133171	+	0.0258043i
$454$		−	15097.1i		−	1.56066i
$455$	−433.223			−0.0446369
$456$	−441.571	−	855.625i	−0.0453475	−	0.0878691i
$457$	−495.331			−0.0507016			−0.0253508	−	0.999679i	$-0.508070\pi$
$457$	−495.331			−0.0507016			−0.0253508	+	0.999679i	$0.508070\pi$
$458$			16218.5i			1.65468i
$459$	−2148.25	+	15079.6i	−0.218457	+	1.53346i
$460$			6157.54i			0.624123i
$461$		−	18448.3i		−	1.86382i	−0.362689	−	0.931910i	$-0.618141\pi$
$461$		−	18448.3i		−	1.86382i	0.362689	−	0.931910i	$-0.381859\pi$
$462$	−7283.32	+	3758.78i	−0.733443	+	0.378516i
$463$		−	80.3662i		−	0.00806681i	−0.999992	−	0.00403341i	$-0.998716\pi$
$463$		−	80.3662i		−	0.00806681i	0.999992	−	0.00403341i	$-0.00128388\pi$
$464$			9996.75i			1.00019i
$465$	−2615.59	+	1349.86i	−0.260850	+	0.134620i
$466$	−4720.32			−0.469237
$467$			6372.82i			0.631475i	0.948847	+	0.315738i	$0.102252\pi$
$467$			6372.82i			0.631475i	−0.948847	+	0.315738i	$0.897748\pi$
$468$	−846.008	−	601.342i	−0.0835614	−	0.0593954i
$469$	2885.49	+	2121.42i	0.284093	+	0.208866i
$470$		−	15863.2i		−	1.55684i
$471$	7028.51	+	13619.0i	0.687594	+	1.33234i
$472$			4345.93i			0.423808i
$473$			1184.37i			0.115132i
$474$	18561.8	−	9579.40i	1.79868	−	0.928263i
$475$	−885.149			−0.0855019
$476$	3489.89			0.336048
$477$	3262.08	−	4589.31i	0.313125	−	0.440524i
$478$	−735.849			−0.0704120
$479$			7011.02i			0.668772i	0.942436	+	0.334386i	$0.108529\pi$
$479$			7011.02i			0.668772i	−0.942436	+	0.334386i	$0.891471\pi$
$480$	3967.58	+	7687.91i	0.377280	+	0.731049i
$481$			2705.69i			0.256484i
$482$	11290.4			1.06694
$483$	2291.89	+	4440.94i	0.215910	+	0.418364i
$484$	15670.7			1.47170
$485$		−	11924.6i		−	1.11642i
$486$	9375.50	−	9875.22i	0.875064	−	0.921706i
$487$		−	4375.15i		−	0.407098i	−0.979065	−	0.203549i	$-0.934752\pi$
$487$		−	4375.15i		−	0.407098i	0.979065	−	0.203549i	$-0.0652477\pi$
$488$			6900.75i			0.640128i
$489$	−6788.82	−	13154.6i	−0.627814	−	1.21650i
$490$	9171.07			0.845524
$491$		−	8124.36i		−	0.746735i	−0.927683	−	0.373368i	$-0.878203\pi$
$491$		−	8124.36i		−	0.746735i	0.927683	−	0.373368i	$-0.121797\pi$
$492$	−3225.30	−	6249.61i	−0.295544	−	0.572671i
$493$	13712.6			1.25270
$494$		−	470.210i		−	0.0428254i
$495$	−8927.69	+	12560.1i	−0.810647	+	1.14047i
$496$		−	5278.28i		−	0.477827i
$497$	−4042.92			−0.364889
$498$	−4885.82	+	2521.48i	−0.439637	+	0.226888i
$499$			2280.68i			0.204604i	0.994753	+	0.102302i	$0.0326208\pi$
$499$			2280.68i			0.204604i	−0.994753	+	0.102302i	$0.967379\pi$
$500$	7435.91			0.665088
$501$	4810.64	−	2482.68i	0.428989	−	0.221393i
$502$	−11013.8			−0.979219
$503$	13498.2			1.19653			0.598266	−	0.801298i	$-0.295857\pi$
$503$	13498.2			1.19653			0.598266	+	0.801298i	$0.295857\pi$
$504$	1590.04	+	1130.20i	0.140528	+	0.0998871i
$505$	−8684.81			−0.765285
$506$		−	35571.9i		−	3.12523i
$507$	−5090.10	−	9863.00i	−0.445877	−	0.863967i
$508$	1255.14			0.109622
$509$		−	2709.13i		−	0.235914i	−0.993019	−	0.117957i	$-0.962366\pi$
$509$		−	2709.13i		−	0.235914i	0.993019	−	0.117957i	$-0.0376345\pi$
$510$	15307.4	−	7899.87i	1.32907	−	0.685906i
$511$			2729.66i			0.236307i
$512$	−8508.71			−0.734444
$513$	2326.24	+	331.397i	0.200207	+	0.0285215i
$514$		−	7407.45i		−	0.635658i
$515$	554.601			0.0474537
$516$	−400.630	+	206.757i	−0.0341798	+	0.0176395i
$517$			34907.3i			2.96948i
$518$			8132.76i			0.689832i
$519$	5371.14	−	2771.94i	0.454272	−	0.234441i
$520$		−	733.962i		−	0.0618969i
$521$	11652.6			0.979867			0.489934	−	0.871760i	$-0.337021\pi$
$521$	11652.6			0.979867			0.489934	+	0.871760i	$0.337021\pi$
$522$	−9991.73	−	7102.12i	−0.837790	−	0.595501i
$523$	12687.7			1.06079			0.530396	−	0.847750i	$-0.322043\pi$
$523$	12687.7			1.06079			0.530396	+	0.847750i	$0.322043\pi$
$524$			8660.55i			0.722019i
$525$	1593.65	−	822.452i	0.132481	−	0.0683710i
$526$			28821.0i			2.38908i
$527$	−7240.24			−0.598462
$528$	−12673.2	−	24556.5i	−1.04456	−	2.02403i
$529$	−9522.68			−0.782664
$530$	−6367.56			−0.521867
$531$	−8644.48	−	6144.50i	−0.706476	−	0.502163i
$532$		−	538.364i		−	0.0438741i
$533$			2147.51i			0.174519i
$534$	6330.92	−	3267.27i	0.513045	−	0.264772i
$535$		−	13955.1i		−	1.12772i
$536$	−3594.09	+	4888.58i	−0.289629	+	0.393945i
$537$	−3439.16	−	6663.99i	−0.276370	−	0.535517i
$538$		−	6269.81i		−	0.502436i
$539$	−20181.1			−1.61273
$540$	−5807.15	−	827.289i	−0.462778	−	0.0659275i
$541$			19405.0i			1.54212i	0.636763	+	0.771060i	$0.280273\pi$
$541$			19405.0i			1.54212i	−0.636763	+	0.771060i	$0.719727\pi$
$542$		−	13385.6i		−	1.06081i
$543$	−5289.71	−	10249.8i	−0.418054	−	0.810055i
$544$			21281.0i			1.67723i
$545$		−	792.029i		−	0.0622510i
$546$	436.904	+	846.580i	0.0342450	+	0.0663559i
$547$			12228.4i			0.955849i	0.878401	+	0.477925i	$0.158611\pi$
$547$			12228.4i			0.955849i	−0.878401	+	0.477925i	$0.841389\pi$
$548$	7447.09			0.580518
$549$	−13726.3	−	9756.65i	−1.06707	−	0.758476i
$550$	−12765.1			−0.989649
$551$		−	2115.35i		−	0.163552i
$552$	−7523.81	+	3882.90i	−0.580135	+	0.299397i
$553$	−7302.76			−0.561564
$554$	−1764.91			−0.135350
$555$	7012.46	+	13587.9i	0.536329	+	1.03923i
$556$		−	5869.85i		−	0.447728i
$557$			8573.54i			0.652195i	0.945336	+	0.326097i	$0.105734\pi$
$557$			8573.54i			0.652195i	−0.945336	+	0.326097i	$0.894266\pi$
$558$	5275.64	+	3749.92i	0.400243	+	0.284493i
$559$	137.666			0.0104162
$560$		−	4390.44i		−	0.331304i
$561$	−33684.3	+	17383.8i	−2.53503	+	1.30828i
$562$	19301.6			1.44874
$563$	1335.68			0.0999859			0.0499930	−	0.998750i	$-0.484080\pi$
$563$	1335.68			0.0999859			0.0499930	+	0.998750i	$0.484080\pi$
$564$	−11807.9	+	6093.84i	−0.881566	+	0.454959i
$565$	−5588.22			−0.416103
$566$	−9040.00			−0.671342
$567$	−4496.16	+	1564.81i	−0.333018	+	0.115901i
$568$		−	6849.48i		−	0.505982i
$569$		−	15626.3i		−	1.15130i	−0.817697	−	0.575649i	$-0.804749\pi$
$569$		−	15626.3i		−	1.15130i	0.817697	−	0.575649i	$-0.195251\pi$
$570$	−1218.66	−	2361.38i	−0.0895512	−	0.173522i
$571$	16581.9			1.21529			0.607645	−	0.794209i	$-0.292114\pi$
$571$	16581.9			1.21529			0.607645	+	0.794209i	$0.292114\pi$
$572$		−	2583.00i		−	0.188813i
$573$	−5756.90	−	11155.0i	−0.419717	−	0.813278i
$574$			6454.97i			0.469382i
$575$			7783.43i			0.564507i
$576$	1117.18	−	1571.72i	0.0808146	−	0.113695i
$577$		−	19044.2i		−	1.37404i	−0.726638	−	0.687020i	$-0.758918\pi$
$577$		−	19044.2i		−	1.37404i	0.726638	−	0.687020i	$-0.241082\pi$
$578$	24711.6			1.77831
$579$	−313.734	−	607.916i	−0.0225187	−	0.0436340i
$580$			5280.69i			0.378050i
$581$	1922.22			0.137259
$582$	−23302.3	+	12025.9i	−1.65964	+	0.856510i
$583$	14011.9			0.995395
$584$	−4624.56			−0.327681
$585$	1459.93	+	1037.71i	0.103180	+	0.0733406i
$586$			8539.94i			0.602016i
$587$	−20048.0			−1.40966			−0.704828	−	0.709378i	$-0.748976\pi$
$587$	−20048.0			−1.40966			−0.704828	+	0.709378i	$0.748976\pi$
$588$	−3523.05	−	6826.56i	−0.247089	−	0.478780i
$589$			1116.91i			0.0781346i
$590$			11994.0i			0.836925i
$591$	11695.4	+	22662.0i	0.814019	+	1.57731i
$592$	−27420.5			−1.90368
$593$	−18479.9			−1.27973			−0.639863	−	0.768489i	$-0.721009\pi$
$593$	−18479.9			−1.27973			−0.639863	+	0.768489i	$0.721009\pi$
$594$	33547.8	+	4779.23i	2.31731	+	0.330125i
$595$	−6022.38			−0.414947
$596$			15635.4i			1.07458i
$597$	1207.14	+	2339.04i	0.0827551	+	0.160353i
$598$	−4134.72			−0.282745
$599$	10836.9			0.739207			0.369604	−	0.929189i	$-0.379493\pi$
$599$	10836.9			0.739207			0.369604	+	0.929189i	$0.379493\pi$
$600$	1393.39	+	2699.95i	0.0948084	+	0.183708i
$601$	13822.9			0.938185			0.469093	−	0.883149i	$-0.344581\pi$
$601$	13822.9			0.938185			0.469093	+	0.883149i	$0.344581\pi$
$602$	413.795			0.0280150
$603$	−4642.37	−	14060.7i	−0.313519	−	0.949582i
$604$	−265.213			−0.0178665
$605$	−27042.3			−1.81723
$606$	8758.61	+	16971.4i	0.587119	+	1.13765i
$607$	3413.21			0.228234			0.114117	−	0.993467i	$-0.463596\pi$
$607$	3413.21			0.228234			0.114117	+	0.993467i	$0.463596\pi$
$608$	3282.88			0.218978
$609$	1965.52	+	3808.55i	0.130783	+	0.253416i
$610$			19044.9i			1.26411i
$611$	4057.47			0.268654
$612$	−11760.7	−	8359.47i	−0.776791	−	0.552143i
$613$	1121.43			0.0738893			0.0369446	−	0.999317i	$-0.488237\pi$
$613$	1121.43			0.0738893			0.0369446	+	0.999317i	$0.488237\pi$
$614$	−8133.14			−0.534571
$615$	5565.79	+	10784.7i	0.364934	+	0.707125i
$616$			4854.66i			0.317532i
$617$			18220.8i			1.18888i	0.804139	+	0.594441i	$0.202627\pi$
$617$			18220.8i			1.18888i	−0.804139	+	0.594441i	$0.797373\pi$
$618$	−559.314	−	1083.77i	−0.0364060	−	0.0705433i
$619$	−19851.1			−1.28899			−0.644493	−	0.764610i	$-0.722931\pi$
$619$	−19851.1			−1.28899			−0.644493	+	0.764610i	$0.722931\pi$
$620$		−	2788.21i		−	0.180608i
$621$	2914.09	−	20455.5i	0.188307	−	1.32182i
$622$	−36014.2			−2.32160
$623$	−2490.77			−0.160177
$624$	−2854.34	+	1473.07i	−0.183117	+	0.0945032i
$625$	−6225.64			−0.398441
$626$		−	10688.7i		−	0.682440i
$627$	2681.69	+	5196.26i	0.170808	+	0.330971i
$628$	−14517.8			−0.922490
$629$			37612.8i			2.38429i
$630$	4388.24	+	3119.16i	0.277511	+	0.197254i
$631$		−	18580.8i		−	1.17225i	−0.810220	−	0.586125i	$-0.800653\pi$
$631$		−	18580.8i		−	1.17225i	0.810220	−	0.586125i	$-0.199347\pi$
$632$		−	12372.3i		−	0.778707i
$633$	7880.40	+	15269.7i	0.494815	+	0.958793i
$634$		−	507.501i		−	0.0317909i
$635$	−2165.95			−0.135359
$636$	2446.09	+	4739.75i	0.152506	+	0.295508i
$637$			2345.76i			0.145906i
$638$		−	30506.4i		−	1.89304i
$639$	13624.3	+	9684.16i	0.843458	+	0.599530i
$640$	11138.9			0.687973
$641$	−26714.4			−1.64611			−0.823055	−	0.567961i	$-0.807732\pi$
$641$	−26714.4			−1.64611			−0.823055	+	0.567961i	$0.807732\pi$
$642$	−27270.3	+	14073.7i	−1.67644	+	0.865177i
$643$	28383.1			1.74078			0.870389	−	0.492365i	$-0.163868\pi$
$643$	28383.1			1.74078			0.870389	+	0.492365i	$0.163868\pi$
$644$	−4734.02			−0.289669
$645$	691.353	−	356.794i	0.0422046	−	0.0217810i
$646$		−	6536.55i		−	0.398107i
$647$	−4559.77			−0.277068			−0.138534	−	0.990358i	$-0.544239\pi$
$647$	−4559.77			−0.277068			−0.138534	+	0.990358i	$0.544239\pi$
$648$	−2651.09	−	7617.36i	−0.160717	−	0.461788i
$649$		−	26393.1i		−	1.59633i
$650$			1483.76i			0.0895353i
$651$	−1037.79	−	2010.91i	−0.0624798	−	0.121066i
$652$	14022.7			0.842288
$653$	−15509.5			−0.929457			−0.464729	−	0.885453i	$-0.653848\pi$
$653$	−15509.5			−0.929457			−0.464729	+	0.885453i	$0.653848\pi$
$654$	−1547.74	+	798.760i	−0.0925405	+	0.0477584i
$655$		−	14945.2i		−	0.891538i
$656$	−21763.7			−1.29532
$657$	6538.45	−	9198.72i	0.388264	−	0.546235i
$658$	12195.9			0.722564
$659$			5744.08i			0.339541i	0.985484	+	0.169771i	$0.0543027\pi$
$659$			5744.08i			0.339541i	−0.985484	+	0.169771i	$0.945697\pi$
$660$	−6694.49	−	12971.8i	−0.394822	−	0.765039i
$661$		−	14302.4i		−	0.841602i	−0.907153	−	0.420801i	$-0.861749\pi$
$661$		−	14302.4i		−	0.841602i	0.907153	−	0.420801i	$-0.138251\pi$
$662$		−	19461.0i		−	1.14256i
$663$	2020.61	+	3915.31i	0.118362	+	0.229348i
$664$			3256.62i			0.190333i
$665$			929.035i			0.0541751i
$666$	19480.7	−	27406.8i	1.13343	−	1.59458i
$667$	−18601.0			−1.07981
$668$			5128.12i			0.297025i
$669$	−4319.67	−	8370.15i	−0.249639	−	0.483720i
$670$	−9919.09	+	13491.7i	−0.571952	+	0.777953i
$671$		−	41908.7i		−	2.41113i
$672$	−5910.60	+	3050.35i	−0.339295	+	0.175104i
$673$			13396.6i			0.767313i	0.923476	+	0.383657i	$0.125335\pi$
$673$			13396.6i			0.767313i	−0.923476	+	0.383657i	$0.874665\pi$
$674$		−	37639.1i		−	2.15104i
$675$	−7340.53	−	1045.73i	−0.418573	−	0.0596301i
$676$	10513.9			0.598197
$677$	13040.6			0.740314			0.370157	−	0.928969i	$-0.379304\pi$
$677$	13040.6			0.740314			0.370157	+	0.928969i	$0.379304\pi$
$678$	5635.71	+	10920.2i	0.319230	+	0.618567i
$679$	9167.81			0.518156
$680$		−	10203.1i		−	0.575397i
$681$	19392.4	−	10008.0i	1.09121	−	0.563155i
$682$			16107.4i			0.904376i
$683$	20330.6			1.13899			0.569495	−	0.821995i	$-0.307139\pi$
$683$	20330.6			1.13899			0.569495	+	0.821995i	$0.307139\pi$
$684$	−1289.56	+	1814.24i	−0.0720873	+	0.101417i
$685$	−12851.2			−0.716815
$686$			15102.9i			0.840570i
$687$	−20832.9	+	10751.5i	−1.15695	+	0.597080i
$688$			1395.16i			0.0773108i
$689$		−	1628.68i		−	0.0900551i
$690$	−20764.5	+	10716.1i	−1.14564	+	0.591241i
$691$	985.349			0.0542467			0.0271233	−	0.999632i	$-0.491365\pi$
$691$	985.349			0.0542467			0.0271233	+	0.999632i	$0.491365\pi$
$692$			5725.61i			0.314530i
$693$	−9656.40	−	6863.77i	−0.529317	−	0.376238i
$694$	15178.7			0.830226
$695$			10129.4i			0.552848i
$696$	−6452.41	+	3329.97i	−0.351405	+	0.181353i
$697$			29853.3i			1.62234i
$698$	23022.4			1.24844
$699$	−3129.15	−	6063.30i	−0.169321	−	0.328090i
$700$			1698.82i			0.0917279i
$701$	23693.8			1.27661			0.638304	−	0.769784i	$-0.279636\pi$
$701$	23693.8			1.27661			0.638304	+	0.769784i	$0.279636\pi$
$702$	555.516	−	3899.44i	0.0298669	−	0.209651i
$703$	5802.29			0.311291
$704$	4798.74			0.256902
$705$	20376.5	−	10515.9i	1.08854	−	0.561777i
$706$	−4543.92			−0.242227
$707$		−	6677.03i		−	0.355185i
$708$	8927.84	−	4607.49i	0.473911	−	0.244576i
$709$	14347.4			0.759985			0.379993	−	0.924990i	$-0.375927\pi$
$709$	14347.4			0.759985			0.379993	+	0.924990i	$0.375927\pi$
$710$		−	18903.4i		−	0.999201i
$711$	24609.7	+	17492.6i	1.29808	+	0.922677i
$712$		−	4219.84i		−	0.222114i
$713$	9821.35			0.515866
$714$	6073.56	+	11768.6i	0.318343	+	0.616848i
$715$			4457.40i			0.233143i
$716$	7103.78			0.370783
$717$	−487.803	−	945.206i	−0.0254077	−	0.0492320i
$718$		−	10831.5i		−	0.562990i
$719$			13500.0i			0.700229i	0.936707	+	0.350114i	$0.113857\pi$
$719$			13500.0i			0.700229i	−0.936707	+	0.350114i	$0.886143\pi$
$720$	−10516.6	+	14795.4i	−0.544348	+	0.765824i
$721$			426.387i			0.0220243i
$722$	23648.0			1.21896
$723$	7484.57	+	14502.7i	0.384999	+	0.746004i
$724$	10926.2			0.560869
$725$			6675.06i			0.341938i
$726$	27272.1	+	52844.7i	1.39416	+	2.70145i
$727$			590.641i			0.0301316i	0.999887	+	0.0150658i	$0.00479578\pi$
$727$			590.641i			0.0301316i	−0.999887	+	0.0150658i	$0.995204\pi$
$728$	564.283			0.0287277
$729$	18900.0	+	5496.54i	0.960218	+	0.279253i
$730$	−12763.0			−0.647096
$731$	1913.74			0.0968292
$732$	14176.2	−	7316.08i	0.715804	−	0.369413i
$733$		−	25587.0i		−	1.28933i	−0.764466	−	0.644664i	$-0.776997\pi$
$733$		−	25587.0i		−	1.28933i	0.764466	−	0.644664i	$-0.223003\pi$
$734$		−	2236.54i		−	0.112469i
$735$	6079.61	+	11780.3i	0.305102	+	0.591190i
$736$		−	28867.5i		−	1.44575i
$737$	21827.1	−	29688.7i	1.09093	−	1.48385i
$738$	15461.8	−	21752.7i	0.771217	−	1.08500i
$739$		−	7612.71i		−	0.378942i	−0.981886	−	0.189471i	$-0.939323\pi$
$739$		−	7612.71i		−	0.378942i	0.981886	−	0.189471i	$-0.0606773\pi$
$740$	−14484.7			−0.719549
$741$	603.990	−	311.708i	0.0299435	−	0.0154533i
$742$		−	4895.50i		−	0.242209i
$743$		−	24130.8i		−	1.19149i	−0.803175	−	0.595744i	$-0.796857\pi$
$743$		−	24130.8i		−	1.19149i	0.803175	−	0.595744i	$-0.203143\pi$
$744$	3406.87	−	1758.22i	0.167879	−	0.0866392i
$745$		−	26981.5i		−	1.32688i
$746$		−	1904.52i		−	0.0934711i
$747$	−6477.74	−	4604.38i	−0.317280	−	0.225523i
$748$		−	35907.3i		−	1.75521i
$749$	10728.9			0.523400
$750$	12940.9	+	25075.4i	0.630048	+	1.22083i
$751$	−12191.0			−0.592351			−0.296175	−	0.955134i	$-0.595711\pi$
$751$	−12191.0			−0.592351			−0.296175	+	0.955134i	$0.595711\pi$
$752$			41120.0i			1.99400i
$753$	−7301.15	−	14147.3i	−0.353345	−	0.684670i
$754$	−3545.93			−0.171267
$755$	457.669			0.0220613
$756$	636.034	−	4464.64i	0.0305983	−	0.214785i
$757$			33303.9i			1.59901i	0.600659	+	0.799505i	$0.294905\pi$
$757$			33303.9i			1.59901i	−0.600659	+	0.799505i	$0.705095\pi$
$758$			50102.8i			2.40081i
$759$	45692.6	−	23581.1i	2.18516	−	1.12772i
$760$	−1573.96			−0.0751233
$761$		−	30234.7i		−	1.44022i	−0.693861	−	0.720109i	$-0.744092\pi$
$761$		−	30234.7i		−	1.44022i	0.693861	−	0.720109i	$-0.255908\pi$
$762$	2184.36	+	4232.59i	0.103846	+	0.201221i
$763$	608.926			0.0288920
$764$	11891.2			0.563101
$765$	20294.9	+	14425.6i	0.959170	+	0.681778i
$766$	−7288.07			−0.343771
$767$	−3067.81			−0.144423
$768$	−12595.1	−	24405.2i	−0.591778	−	1.14668i
$769$		−	9455.03i		−	0.443377i	−0.975117	−	0.221689i	$-0.928843\pi$
$769$		−	9455.03i		−	0.443377i	0.975117	−	0.221689i	$-0.0711569\pi$
$770$			13398.0i			0.627054i
$771$	9514.95	−	4910.48i	0.444452	−	0.229373i
$772$	648.035			0.0302115
$773$			27200.8i			1.26565i	0.774296	+	0.632824i	$0.218104\pi$
$773$			27200.8i			1.26565i	−0.774296	+	0.632824i	$0.781896\pi$
$774$	−1394.46	−	991.179i	−0.0647580	−	0.0460300i
$775$		−	3524.43i		−	0.163357i
$776$			15532.0i			0.718515i
$777$	−10446.6	+	5391.31i	−0.482330	+	0.248922i
$778$			35993.9i			1.65867i
$779$	4605.27			0.211811
$780$	−1507.78	+	778.137i	−0.0692144	+	0.0357202i
$781$			41597.3i			1.90585i
$782$	−57478.2			−2.62841
$783$	2499.12	−	17542.6i	0.114063	−	0.800665i
$784$	−23772.8			−1.08295
$785$	25052.9			1.13908
$786$	−29205.1	+	15072.2i	−1.32533	+	0.683979i
$787$		−	8456.24i		−	0.383014i	−0.981491	−	0.191507i	$-0.938662\pi$
$787$		−	8456.24i		−	0.383014i	0.981491	−	0.191507i	$-0.0613375\pi$
$788$	−24157.6			−1.09210
$789$	−37020.9	+	19105.8i	−1.67044	+	0.862084i
$790$		−	34145.4i		−	1.53777i
$791$		−	4296.33i		−	0.193122i
$792$	11628.5	−	16359.8i	0.521720	−	0.733990i
$793$	−4871.28			−0.218139
$794$	−29125.8			−1.30181
$795$	−4221.13	−	8179.21i	−0.188312	−	0.364889i
$796$	−2493.41			−0.111026
$797$			12793.6i			0.568596i	0.958736	+	0.284298i	$0.0917605\pi$
$797$			12793.6i			0.568596i	−0.958736	+	0.284298i	$0.908239\pi$
$798$	1815.47	−	936.930i	0.0805350	−	0.0415626i
$799$	56404.4			2.49743
$800$	−10359.2			−0.457818
$801$	8393.69	+	5966.23i	0.370258	+	0.263179i
$802$	−18966.9			−0.835095
$803$	28085.3			1.23426
$804$	13853.0	+	2200.54i	0.607660	+	0.0965262i
$805$	8169.33			0.357679
$806$	1872.25			0.0818204
$807$	8053.65	−	4156.33i	0.351303	−	0.181301i
$808$	11312.2			0.492526
$809$	35180.0			1.52888			0.764440	−	0.644695i	$-0.223016\pi$
$809$	35180.0			1.52888			0.764440	+	0.644695i	$0.223016\pi$
$810$	−7316.57	−	21022.6i	−0.317380	−	0.911926i
$811$		−	44682.9i		−	1.93468i	−0.253475	−	0.967342i	$-0.581574\pi$
$811$		−	44682.9i		−	1.93468i	0.253475	−	0.967342i	$-0.418426\pi$
$812$	−4059.89			−0.175461
$813$	17194.0	−	8873.48i	0.741720	−	0.382788i
$814$	83677.5			3.60306
$815$	−24198.5			−1.04004
$816$	−39679.2	+	20477.7i	−1.70227	+	0.878507i
$817$		−	295.220i		−	0.0126419i
$818$		−	2292.95i		−	0.0980087i
$819$	−797.814	+	1122.42i	−0.0340389	+	0.0478882i
$820$	−11496.5			−0.489602
$821$			6879.53i			0.292445i	0.989252	+	0.146222i	$0.0467115\pi$
$821$			6879.53i			0.292445i	−0.989252	+	0.146222i	$0.953289\pi$
$822$	12960.4	+	25113.1i	0.549934	+	1.06560i
$823$	−33114.7			−1.40256			−0.701280	−	0.712886i	$-0.747388\pi$
$823$	−33114.7			−1.40256			−0.701280	+	0.712886i	$0.747388\pi$
$824$	−722.382			−0.0305405
$825$	−8462.16	−	16397.0i	−0.357109	−	0.691962i
$826$	−9221.22			−0.388435
$827$			21054.5i			0.885294i	0.896696	+	0.442647i	$0.145961\pi$
$827$			21054.5i			0.885294i	−0.896696	+	0.442647i	$0.854039\pi$
$828$	15953.3	+	11339.6i	0.669583	+	0.475940i
$829$	35997.7			1.50814			0.754072	−	0.656792i	$-0.228087\pi$
$829$	35997.7			1.50814			0.754072	+	0.656792i	$0.228087\pi$
$830$			8987.72i			0.375865i
$831$	−1169.98	−	2267.05i	−0.0488402	−	0.0946367i
$832$		−	557.783i		−	0.0232424i
$833$			32609.2i			1.35635i
$834$	19794.3	−	10215.5i	0.821847	−	0.424140i
$835$		−	8849.41i		−	0.366762i
$836$	−5539.19			−0.229159
$837$	−1319.54	+	9262.48i	−0.0544920	+	0.382507i
$838$		−	32738.7i		−	1.34957i
$839$			6328.64i			0.260416i	0.991487	+	0.130208i	$0.0415645\pi$
$839$			6328.64i			0.260416i	−0.991487	+	0.130208i	$0.958436\pi$
$840$	2833.82	−	1462.48i	0.116400	−	0.0600718i
$841$	8436.78			0.345926
$842$	15623.8			0.639467
$843$	12795.3	+	24793.2i	0.522767	+	1.01296i
$844$	−16277.4			−0.663853
$845$	−18143.5			−0.738644
$846$	−41099.3	−	29213.4i	−1.67024	−	1.18721i
$847$		−	20790.6i		−	0.843417i
$848$	16505.7			0.668406
$849$	−5992.72	−	11612.0i	−0.242249	−	0.469402i
$850$			20626.3i			0.832325i
$851$		−	51021.6i		−	2.05523i
$852$	−14070.9	+	7261.73i	−0.565800	+	0.291999i
$853$	−16213.6			−0.650812			−0.325406	−	0.945574i	$-0.605501\pi$
$853$	−16213.6			−0.650812			−0.325406	+	0.945574i	$0.605501\pi$
$854$	−14642.1			−0.586699
$855$	2225.35	−	3130.77i	0.0890123	−	0.125228i
$856$			18176.9i			0.725785i
$857$	30654.5			1.22186			0.610932	−	0.791683i	$-0.290795\pi$
$857$	30654.5			1.22186			0.610932	+	0.791683i	$0.290795\pi$
$858$	8710.41	−	4495.28i	0.346583	−	0.178865i
$859$	−30503.0			−1.21158			−0.605791	−	0.795624i	$-0.707143\pi$
$859$	−30503.0			−1.21158			−0.605791	+	0.795624i	$0.707143\pi$
$860$			736.979i			0.0292218i
$861$	−8291.48	+	4279.08i	−0.328192	+	0.169373i
$862$		−	43412.2i		−	1.71534i
$863$		−	26655.1i		−	1.05139i	−0.850672	−	0.525696i	$-0.823805\pi$
$863$		−	26655.1i		−	1.05139i	0.850672	−	0.525696i	$-0.176195\pi$
$864$	27224.9	+	3878.46i	1.07200	+	0.152718i
$865$		−	9880.48i		−	0.388377i
$866$			5636.56i			0.221176i
$867$	16381.6	+	31742.3i	0.641693	+	1.24340i
$868$	2143.62			0.0838241
$869$			75137.6i			2.93311i
$870$	−17807.6	+	9190.14i	−0.693946	+	0.358132i
$871$	−3450.88	−	2537.09i	−0.134246	−	0.0986980i
$872$			1031.64i			0.0400638i
$873$	−30894.8	−	21960.0i	−1.19774	−	0.851356i
$874$			8866.80i			0.343163i
$875$		−	9865.38i		−	0.381155i
$876$	4902.90	+	9500.25i	0.189102	+	0.366420i
$877$	−14109.5			−0.543265			−0.271633	−	0.962401i	$-0.587564\pi$
$877$	−14109.5			−0.543265			−0.271633	+	0.962401i	$0.587564\pi$
$878$	−23314.1			−0.896140
$879$	−10969.7	+	5661.23i	−0.420930	+	0.217234i
$880$	−45173.0			−1.73043
$881$		−	23425.8i		−	0.895841i	−0.894073	−	0.447921i	$-0.852165\pi$
$881$		−	23425.8i		−	0.895841i	0.894073	−	0.447921i	$-0.147835\pi$
$882$	16889.2	−	23760.9i	0.644774	−	0.907110i
$883$			33441.8i			1.27452i	0.770647	+	0.637262i	$0.219933\pi$
$883$			33441.8i			1.27452i	−0.770647	+	0.637262i	$0.780067\pi$
$884$	−4173.70			−0.158797
$885$	−15406.5	+	7950.98i	−0.585178	+	0.301999i
$886$	−17121.4			−0.649216
$887$		−	1674.78i		−	0.0633975i	−0.999497	−	0.0316987i	$-0.989908\pi$
$887$		−	1674.78i		−	0.0633975i	0.999497	−	0.0316987i	$-0.0100917\pi$
$888$	−9133.91	−	17698.6i	−0.345173	−	0.668836i
$889$		−	1665.22i		−	0.0628231i
$890$		−	11646.0i		−	0.438625i
$891$	16100.2	+	46260.7i	0.605363	+	1.73939i
$892$	8922.54			0.334920
$893$		−	8701.15i		−	0.326061i
$894$	−52725.8	+	27210.8i	−1.97250	+	1.01797i
$895$	−12258.7			−0.457837
$896$			8563.77i			0.319303i
$897$	−2740.96	−	5311.10i	−0.102027	−	0.197695i
$898$			33894.9i			1.25956i
$899$	8422.78			0.312475
$900$	4069.26	−	5724.90i	0.150713	−	0.212033i
$901$		−	22640.9i		−	0.837157i
$902$	66414.8			2.45163
$903$	274.310	+	531.524i	0.0101090	+	0.0195881i
$904$	7278.80			0.267798
$905$	−18855.0			−0.692553
$906$	−461.558	−	894.352i	−0.0169252	−	0.0327957i
$907$	−54445.5			−1.99320			−0.996600	−	0.0823969i	$-0.973742\pi$
$907$	−54445.5			−1.99320			−0.996600	+	0.0823969i	$0.973742\pi$
$908$			20672.2i			0.755540i
$909$	−15993.8	+	22501.1i	−0.583586	+	0.821027i
$910$	1557.33			0.0567306
$911$			23538.7i			0.856062i	0.903764	+	0.428031i	$0.140793\pi$
$911$			23538.7i			0.856062i	−0.903764	+	0.428031i	$0.859207\pi$
$912$	3158.96	+	6121.06i	0.114697	+	0.222246i
$913$		−	19777.6i		−	0.716916i
$914$	1780.59			0.0644385
$915$	−24463.4	+	12625.1i	−0.883864	+	0.456145i
$916$		−	22207.8i		−	0.801054i
$917$	11490.1			0.413782
$918$	7722.42	−	54207.5i	0.277645	−	1.94893i
$919$		−	19237.0i		−	0.690502i	−0.938510	−	0.345251i	$-0.887794\pi$
$919$		−	19237.0i		−	0.690502i	0.938510	−	0.345251i	$-0.112206\pi$
$920$			13840.4i			0.495984i
$921$	−5391.55	−	10447.1i	−0.192897	−	0.373772i
$922$			66316.9i			2.36880i
$923$	4835.09			0.172426
$924$	9972.93	−	5146.84i	0.355071	−	0.183245i
$925$	−18309.3			−0.650818
$926$			288.896i			0.0102524i
$927$	1021.34	−	1436.89i	0.0361869	−	0.0509102i
$928$		−	24756.8i		−	0.875733i
$929$	−37709.8			−1.33178			−0.665888	−	0.746052i	$-0.731947\pi$
$929$	−37709.8			−1.33178			−0.665888	+	0.746052i	$0.731947\pi$
$930$	9402.40	−	4852.40i	0.331523	−	0.171093i
$931$	5030.42			0.177084
$932$	6463.45			0.227165
$933$	−23874.2	−	46260.6i	−0.837735	−	1.62326i
$934$		−	22908.7i		−	0.802565i
$935$			61963.9i			2.16731i
$936$	−1901.59	−	1351.65i	−0.0664054	−	0.0472009i
$937$			53973.5i			1.88179i	0.338697	+	0.940895i	$0.390014\pi$
$937$			53973.5i			1.88179i	−0.338697	+	0.940895i	$0.609986\pi$
$938$	−10372.6	−	7625.97i	−0.361064	−	0.265455i
$939$	13729.8	−	7085.69i	0.477162	−	0.246254i
$940$			21721.3i			0.753691i
$941$	−1400.72			−0.0485252			−0.0242626	−	0.999706i	$-0.507724\pi$
$941$	−1400.72			−0.0485252			−0.0242626	+	0.999706i	$0.507724\pi$
$942$	−25265.7	−	48957.0i	−0.873888	−	1.69332i
$943$		−	40495.8i		−	1.39844i
$944$		−	31090.4i		−	1.07193i
$945$	−1097.58	+	7704.47i	−0.0377824	+	0.265213i
$946$		−	4257.51i		−	0.146325i
$947$		−	49591.2i		−	1.70169i	−0.525420	−	0.850843i	$-0.676092\pi$
$947$		−	49591.2i		−	1.70169i	0.525420	−	0.850843i	$-0.323908\pi$
$948$	−25416.4	+	13116.9i	−0.870766	+	0.449386i
$949$		−	3264.50i		−	0.111665i
$950$	3181.89			0.108667
$951$	651.891	−	336.429i	0.0222282	−	0.0114715i
$952$	7844.30			0.267054
$953$			12328.5i			0.419054i	0.977803	+	0.209527i	$0.0671923\pi$
$953$			12328.5i			0.419054i	−0.977803	+	0.209527i	$0.932808\pi$
$954$	−11726.4	+	16497.4i	−0.397962	+	0.559878i
$955$	−20520.2			−0.695308
$956$	1007.59			0.0340875
$957$	39185.9	−	20223.1i	1.32361	−	0.683092i
$958$		−	25202.9i		−	0.849967i
$959$		−	9880.21i		−	0.332689i
$960$	−1445.63	−	2801.17i	−0.0486016	−	0.0941744i
$961$	25343.8			0.850719
$962$		−	9726.29i		−	0.325975i
$963$	−36155.6	−	25699.4i	−1.20986	−	0.859971i
$964$	−15459.8			−0.516522
$965$	−1118.29			−0.0373047
$966$	−8238.76	−	15964.1i	−0.274407	−	0.531714i
$967$	3156.58			0.104973			0.0524864	−	0.998622i	$-0.483285\pi$
$967$	3156.58			0.104973			0.0524864	+	0.998622i	$0.483285\pi$
$968$	35223.3			1.16955
$969$	8396.28	−	4333.16i	0.278356	−	0.143654i
$970$			42865.8i			1.41890i
$971$			19215.6i			0.635076i	0.948246	+	0.317538i	$0.102856\pi$
$971$			19215.6i			0.635076i	−0.948246	+	0.317538i	$0.897144\pi$
$972$	−12837.7	+	13522.0i	−0.423632	+	0.446211i
$973$	−7787.65			−0.256589
$974$			15727.6i			0.517396i
$975$	−1905.91	+	983.603i	−0.0626030	+	0.0323082i
$976$		−	49367.4i		−	1.61907i
$977$		−	19558.3i		−	0.640455i	−0.947341	−	0.320227i	$-0.896241\pi$
$977$		−	19558.3i		−	0.640455i	0.947341	−	0.320227i	$-0.103759\pi$
$978$	24404.1	+	47287.4i	0.797911	+	1.54610i
$979$			25627.3i			0.836622i
$980$	−12557.8			−0.409330
$981$	−2052.03	−	1458.58i	−0.0667853	−	0.0474710i
$982$			29205.0i			0.949053i
$983$	36708.3			1.19106			0.595530	−	0.803333i	$-0.296942\pi$
$983$	36708.3			1.19106			0.595530	+	0.803333i	$0.296942\pi$
$984$	−7249.58	−	14047.4i	−0.234866	−	0.455095i
$985$	41687.8			1.34851
$986$	−49293.2			−1.59211
$987$	8084.83	+	15665.8i	0.260733	+	0.505216i
$988$			643.850i			0.0207324i
$989$	−2595.98			−0.0834654
$990$	32092.8	−	45150.3i	1.03028	−	1.44947i
$991$			8456.73i			0.271077i	0.990772	+	0.135538i	$0.0432764\pi$
$991$			8456.73i			0.271077i	−0.990772	+	0.135538i	$0.956724\pi$
$992$			13071.6i			0.418370i
$993$	24997.9	−	12900.9i	0.798876	−	0.412285i
$994$	14533.3			0.463750
$995$	4302.79			0.137093
$996$	6690.08	−	3452.62i	0.212835	−	0.109840i
$997$	30930.3			0.982520			0.491260	−	0.871013i	$-0.336537\pi$
$997$	30930.3			0.982520			0.491260	+	0.871013i	$0.336537\pi$
$998$		−	8198.49i		−	0.260039i
$999$	48118.3	+	6854.95i	1.52392	+	0.217098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.d.b.200.11	✓	64
3.2	odd	2	inner	201.4.d.b.200.53	yes	64
67.66	odd	2	inner	201.4.d.b.200.54	yes	64
201.200	even	2	inner	201.4.d.b.200.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.d.b.200.11	✓	64	1.1	even	1	trivial
201.4.d.b.200.12	yes	64	201.200	even	2	inner
201.4.d.b.200.53	yes	64	3.2	odd	2	inner
201.4.d.b.200.54	yes	64	67.66	odd	2	inner

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.59475 q^{2} +(-2.38300 - 4.61750i) q^{3} +4.92223 q^{4} -8.49412 q^{5} +(8.56630 + 16.5988i) q^{6} -6.53043i q^{7} +11.0638 q^{8} +(-15.6426 + 22.0070i) q^{9} +O(q^{10})\)	\(q-3.59475 q^{2} +(-2.38300 - 4.61750i) q^{3} +4.92223 q^{4} -8.49412 q^{5} +(8.56630 + 16.5988i) q^{6} -6.53043i q^{7} +11.0638 q^{8} +(-15.6426 + 22.0070i) q^{9} +30.5342 q^{10} -67.1912 q^{11} +(-11.7297 - 22.7284i) q^{12} +7.81000i q^{13} +23.4753i q^{14} +(20.2415 + 39.2216i) q^{15} -79.1495 q^{16} +108.570i q^{17} +(56.2312 - 79.1098i) q^{18} +16.7483 q^{19} -41.8100 q^{20} +(-30.1543 + 15.5620i) q^{21} +241.535 q^{22} -147.274i q^{23} +(-26.3651 - 51.0871i) q^{24} -52.8499 q^{25} -28.0750i q^{26} +(138.894 + 19.7868i) q^{27} -32.1443i q^{28} -126.302i q^{29} +(-72.7632 - 140.992i) q^{30} +66.6875i q^{31} +196.012 q^{32} +(160.117 + 310.255i) q^{33} -390.280i q^{34} +55.4703i q^{35} +(-76.9965 + 108.324i) q^{36} +346.440 q^{37} -60.2061 q^{38} +(36.0627 - 18.6112i) q^{39} -93.9773 q^{40} +274.969 q^{41} +(108.397 - 55.9416i) q^{42} -17.6268i q^{43} -330.731 q^{44} +(132.870 - 186.930i) q^{45} +529.414i q^{46} -519.523i q^{47} +(188.613 + 365.473i) q^{48} +300.353 q^{49} +189.982 q^{50} +(501.320 - 258.722i) q^{51} +38.4426i q^{52} -208.538 q^{53} +(-499.288 - 71.1288i) q^{54} +570.730 q^{55} -72.2514i q^{56} +(-39.9114 - 77.3355i) q^{57} +454.025i q^{58} +392.806i q^{59} +(99.6334 + 193.058i) q^{60} +623.723i q^{61} -239.725i q^{62} +(143.715 + 102.153i) q^{63} -71.4192 q^{64} -66.3391i q^{65} +(-575.580 - 1115.29i) q^{66} +(-324.851 + 441.854i) q^{67} +534.405i q^{68} +(-680.038 + 350.955i) q^{69} -199.402i q^{70} -619.089i q^{71} +(-173.067 + 243.482i) q^{72} -417.990 q^{73} -1245.36 q^{74} +(125.942 + 244.035i) q^{75} +82.4392 q^{76} +438.787i q^{77} +(-129.636 + 66.9028i) q^{78} -1118.27i q^{79} +672.305 q^{80} +(-239.619 - 688.494i) q^{81} -988.445 q^{82} +294.349i q^{83} +(-148.426 + 76.5999i) q^{84} -922.203i q^{85} +63.3641i q^{86} +(-583.200 + 300.978i) q^{87} -743.390 q^{88} -381.409i q^{89} +(-477.635 + 671.968i) q^{90} +51.0026 q^{91} -724.918i q^{92} +(307.930 - 158.917i) q^{93} +1867.56i q^{94} -142.262 q^{95} +(-467.098 - 905.086i) q^{96} +1403.86i q^{97} -1079.70 q^{98} +(1051.04 - 1478.68i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9}+O(q^{10}) \) 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9	\( 64 q + 268 q^{4} - 46 q^{6} + 22 q^{9} - 36 q^{10} + 20 q^{15} + 556 q^{16} + 128 q^{19} + 96 q^{22} - 904 q^{24} + 2080 q^{25} - 236 q^{33} - 1574 q^{36} + 1004 q^{37} - 176 q^{39} - 648 q^{40} - 1220 q^{49} + 2188 q^{54} - 1344 q^{55} + 550 q^{60} + 4336 q^{64} - 3512 q^{67} + 3968 q^{73} - 3316 q^{76} - 1170 q^{81} + 4020 q^{82} - 9270 q^{84} + 2436 q^{88} + 746 q^{90} - 3408 q^{91} - 1412 q^{93} - 7032 q^{96}+O(q^{100}) \) 64 * q + 268 * q^4 - 46 * q^6 + 22 * q^9 - 36 * q^10 + 20 * q^15 + 556 * q^16 + 128 * q^19 + 96 * q^22 - 904 * q^24 + 2080 * q^25 - 236 * q^33 - 1574 * q^36 + 1004 * q^37 - 176 * q^39 - 648 * q^40 - 1220 * q^49 + 2188 * q^54 - 1344 * q^55 + 550 * q^60 + 4336 * q^64 - 3512 * q^67 + 3968 * q^73 - 3316 * q^76 - 1170 * q^81 + 4020 * q^82 - 9270 * q^84 + 2436 * q^88 + 746 * q^90 - 3408 * q^91 - 1412 * q^93 - 7032 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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