LMFDB - Embedded newform 252.4.e.a.71.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(71,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("252.71");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.e (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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.7
Character	$\chi$	$=$	252.71
Dual form			252.4.e.a.71.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.27330 - 1.68288i) q^{2} +(2.33582 + 7.65140i) q^{4} +4.43347i q^{5} -7.00000i q^{7} +(7.56635 - 21.3249i) q^{8} +O(q^{10})$	\(q+(-2.27330 - 1.68288i) q^{2} +(2.33582 + 7.65140i) q^{4} +4.43347i q^{5} -7.00000i q^{7} +(7.56635 - 21.3249i) q^{8} +(7.46100 - 10.0786i) q^{10} -56.3497 q^{11} +57.7685 q^{13} +(-11.7802 + 15.9131i) q^{14} +(-53.0878 + 35.7447i) q^{16} -109.513i q^{17} +124.047i q^{19} +(-33.9223 + 10.3558i) q^{20} +(128.100 + 94.8299i) q^{22} +156.583 q^{23} +105.344 q^{25} +(-131.325 - 97.2176i) q^{26} +(53.5598 - 16.3508i) q^{28} +210.142i q^{29} -120.682i q^{31} +(180.839 + 8.08203i) q^{32} +(-184.297 + 248.955i) q^{34} +31.0343 q^{35} +299.600 q^{37} +(208.757 - 281.997i) q^{38} +(94.5432 + 33.5452i) q^{40} -358.745i q^{41} -246.021i q^{43} +(-131.623 - 431.154i) q^{44} +(-355.960 - 263.510i) q^{46} +196.841 q^{47} -49.0000 q^{49} +(-239.480 - 177.282i) q^{50} +(134.937 + 442.010i) q^{52} +58.3356i q^{53} -249.825i q^{55} +(-149.274 - 52.9645i) q^{56} +(353.644 - 477.717i) q^{58} +225.410 q^{59} +481.655 q^{61} +(-203.094 + 274.347i) q^{62} +(-397.501 - 322.703i) q^{64} +256.115i q^{65} -486.195i q^{67} +(837.924 - 255.802i) q^{68} +(-70.5504 - 52.2270i) q^{70} +709.339 q^{71} +866.781 q^{73} +(-681.082 - 504.191i) q^{74} +(-949.136 + 289.753i) q^{76} +394.448i q^{77} +94.6682i q^{79} +(-158.473 - 235.363i) q^{80} +(-603.726 + 815.537i) q^{82} -208.611 q^{83} +485.521 q^{85} +(-414.024 + 559.281i) q^{86} +(-426.362 + 1201.65i) q^{88} +1134.03i q^{89} -404.380i q^{91} +(365.750 + 1198.08i) q^{92} +(-447.478 - 331.259i) q^{94} -549.960 q^{95} -1253.68 q^{97} +(111.392 + 82.4612i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 24 q^{4}+O(q^{10}) $ 36 * q - 24 * q^4	$ 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64} - 504 q^{70} - 2520 q^{76} + 1032 q^{82} - 3144 q^{85} + 2748 q^{88} + 5496 q^{94}+O(q^{100}) $ 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.27330	−	1.68288i	−0.803734	−	0.594988i
$2$	−2.27330	−	1.68288i	−0.803734	−	0.594988i
$3$		0			0
$3$		0			0
$4$	2.33582	+	7.65140i	0.291978	+	0.956425i
$5$			4.43347i			0.396542i	0.980147	+	0.198271i	$0.0635326\pi$
$5$			4.43347i			0.396542i	−0.980147	+	0.198271i	$0.936467\pi$
$6$		0			0
$7$		−	7.00000i		−	0.377964i
$7$		−	7.00000i		−	0.377964i
$8$	7.56635	−	21.3249i	0.334389	−	0.942435i
$9$		0			0
$10$	7.46100	−	10.0786i	0.235938	−	0.318714i
$11$	−56.3497			−1.54455			−0.772277	−	0.635287i	$-0.780882\pi$
$11$	−56.3497			−1.54455			−0.772277	+	0.635287i	$0.780882\pi$
$12$		0			0
$13$	57.7685			1.23247			0.616235	−	0.787562i	$-0.288657\pi$
$13$	57.7685			1.23247			0.616235	+	0.787562i	$0.288657\pi$
$14$	−11.7802	+	15.9131i	−0.224884	+	0.303783i
$15$		0			0
$16$	−53.0878	+	35.7447i	−0.829498	+	0.558510i
$17$		−	109.513i		−	1.56239i	−0.624285	−	0.781197i	$-0.714609\pi$
$17$		−	109.513i		−	1.56239i	0.624285	−	0.781197i	$-0.285391\pi$
$18$		0			0
$19$			124.047i			1.49781i	0.662677	+	0.748905i	$0.269420\pi$
$19$			124.047i			1.49781i	−0.662677	+	0.748905i	$0.730580\pi$
$20$	−33.9223	+	10.3558i	−0.379262	+	0.115782i
$21$		0			0
$22$	128.100	+	94.8299i	1.24141	+	0.918991i
$23$	156.583			1.41955			0.709777	−	0.704427i	$-0.248796\pi$
$23$	156.583			1.41955			0.709777	+	0.704427i	$0.248796\pi$
$24$		0			0
$25$	105.344			0.842755
$26$	−131.325	−	97.2176i	−0.990579	−	0.733305i
$27$		0			0
$28$	53.5598	−	16.3508i	0.361495	−	0.110357i
$29$			210.142i			1.34560i	0.739824	+	0.672801i	$0.234909\pi$
$29$			210.142i			1.34560i	−0.739824	+	0.672801i	$0.765091\pi$
$30$		0			0
$31$		−	120.682i		−	0.699198i	−0.936899	−	0.349599i	$-0.886318\pi$
$31$		−	120.682i		−	0.699198i	0.936899	−	0.349599i	$-0.113682\pi$
$32$	180.839	+	8.08203i	0.999003	+	0.0446473i
$33$		0			0
$34$	−184.297	+	248.955i	−0.929606	+	1.25575i
$35$	31.0343			0.149879
$36$		0			0
$37$	299.600			1.33119			0.665593	−	0.746314i	$-0.268178\pi$
$37$	299.600			1.33119			0.665593	+	0.746314i	$0.268178\pi$
$38$	208.757	−	281.997i	0.891180	−	1.20384i
$39$		0			0
$40$	94.5432	+	33.5452i	0.373715	+	0.132599i
$41$		−	358.745i		−	1.36650i	−0.730183	−	0.683251i	$-0.760565\pi$
$41$		−	358.745i		−	1.36650i	0.730183	−	0.683251i	$-0.239435\pi$
$42$		0			0
$43$		−	246.021i		−	0.872508i	−0.899824	−	0.436254i	$-0.856305\pi$
$43$		−	246.021i		−	0.872508i	0.899824	−	0.436254i	$-0.143695\pi$
$44$	−131.623	−	431.154i	−0.450976	−	1.47725i
$45$		0			0
$46$	−355.960	−	263.510i	−1.14094	−	0.844618i
$47$	196.841			0.610897			0.305448	−	0.952209i	$-0.401194\pi$
$47$	196.841			0.610897			0.305448	+	0.952209i	$0.401194\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	−239.480	−	177.282i	−0.677351	−	0.501429i
$51$		0			0
$52$	134.937	+	442.010i	0.359854	+	1.17877i
$53$			58.3356i			0.151189i	0.997139	+	0.0755944i	$0.0240854\pi$
$53$			58.3356i			0.151189i	−0.997139	+	0.0755944i	$0.975915\pi$
$54$		0			0
$55$		−	249.825i		−	0.612480i
$56$	−149.274	−	52.9645i	−0.356207	−	0.126387i
$57$		0			0
$58$	353.644	−	477.717i	0.800617	−	1.08151i
$59$	225.410			0.497388			0.248694	−	0.968582i	$-0.419999\pi$
$59$	225.410			0.497388			0.248694	+	0.968582i	$0.419999\pi$
$60$		0			0
$61$	481.655			1.01098			0.505489	−	0.862833i	$-0.331312\pi$
$61$	481.655			1.01098			0.505489	+	0.862833i	$0.331312\pi$
$62$	−203.094	+	274.347i	−0.416015	+	0.561970i
$63$		0			0
$64$	−397.501	−	322.703i	−0.776368	−	0.630279i
$65$			256.115i			0.488726i
$66$		0			0
$67$		−	486.195i		−	0.886540i	−0.896388	−	0.443270i	$-0.853818\pi$
$67$		−	486.195i		−	0.886540i	0.896388	−	0.443270i	$-0.146182\pi$
$68$	837.924	−	255.802i	1.49431	−	0.456185i
$69$		0			0
$70$	−70.5504	−	52.2270i	−0.120463	−	0.0891761i
$71$	709.339			1.18568			0.592839	−	0.805321i	$-0.298007\pi$
$71$	709.339			1.18568			0.592839	+	0.805321i	$0.298007\pi$
$72$		0			0
$73$	866.781			1.38971			0.694856	−	0.719149i	$-0.255468\pi$
$73$	866.781			1.38971			0.694856	+	0.719149i	$0.255468\pi$
$74$	−681.082	−	504.191i	−1.06992	−	0.792041i
$75$		0			0
$76$	−949.136	+	289.753i	−1.43254	+	0.437328i
$77$			394.448i			0.583786i
$78$		0			0
$79$			94.6682i			0.134823i	0.997725	+	0.0674115i	$0.0214740\pi$
$79$			94.6682i			0.134823i	−0.997725	+	0.0674115i	$0.978526\pi$
$80$	−158.473	−	235.363i	−0.221473	−	0.328930i
$81$		0			0
$82$	−603.726	+	815.537i	−0.813053	+	1.09831i
$83$	−208.611			−0.275880			−0.137940	−	0.990441i	$-0.544048\pi$
$83$	−208.611			−0.275880			−0.137940	+	0.990441i	$0.544048\pi$
$84$		0			0
$85$	485.521			0.619554
$86$	−414.024	+	559.281i	−0.519132	+	0.701265i
$87$		0			0
$88$	−426.362	+	1201.65i	−0.516481	+	1.45564i
$89$			1134.03i			1.35064i	0.737523	+	0.675322i	$0.235995\pi$
$89$			1134.03i			1.35064i	−0.737523	+	0.675322i	$0.764005\pi$
$90$		0			0
$91$		−	404.380i		−	0.465830i
$92$	365.750	+	1198.08i	0.414479	+	1.35770i
$93$		0			0
$94$	−447.478	−	331.259i	−0.490999	−	0.363476i
$95$	−549.960			−0.593945
$96$		0			0
$97$	−1253.68			−1.31229			−0.656144	−	0.754636i	$-0.727813\pi$
$97$	−1253.68			−1.31229			−0.656144	+	0.754636i	$0.727813\pi$
$98$	111.392	+	82.4612i	0.114819	+	0.0849983i
$99$		0			0
$100$	246.066	+	806.032i	0.246066	+	0.806032i
$101$			300.271i			0.295823i	0.989001	+	0.147912i	$0.0472551\pi$
$101$			300.271i			0.295823i	−0.989001	+	0.147912i	$0.952745\pi$
$102$		0			0
$103$		−	833.758i		−	0.797599i	−0.917038	−	0.398799i	$-0.869427\pi$
$103$		−	833.758i		−	0.797599i	0.917038	−	0.398799i	$-0.130573\pi$
$104$	437.097	−	1231.91i	0.412124	−	1.16152i
$105$		0			0
$106$	98.1718	−	132.614i	0.0899555	−	0.121516i
$107$	−150.440			−0.135922			−0.0679608	−	0.997688i	$-0.521649\pi$
$107$	−150.440			−0.135922			−0.0679608	+	0.997688i	$0.521649\pi$
$108$		0			0
$109$	−1033.05			−0.907779			−0.453889	−	0.891058i	$-0.649964\pi$
$109$	−1033.05			−0.907779			−0.453889	+	0.891058i	$0.649964\pi$
$110$	−420.426	+	567.928i	−0.364418	+	0.492271i
$111$		0			0
$112$	250.213	+	371.615i	0.211097	+	0.313521i
$113$			1022.25i			0.851018i	0.904954	+	0.425509i	$0.139905\pi$
$113$			1022.25i			0.851018i	−0.904954	+	0.425509i	$0.860095\pi$
$114$		0			0
$115$			694.205i			0.562912i
$116$	−1607.88	+	490.856i	−1.28697	+	0.392886i
$117$		0			0
$118$	−512.426	−	379.338i	−0.399768	−	0.295940i
$119$	−766.588			−0.590529
$120$		0			0
$121$	1844.29			1.38564
$122$	−1094.95	−	810.569i	−0.812558	−	0.601520i
$123$		0			0
$124$	923.387	−	281.892i	0.668731	−	0.204151i
$125$			1021.23i			0.730729i
$126$		0			0
$127$		−	12.8112i		−	0.00895125i	−0.999990	−	0.00447562i	$-0.998575\pi$
$127$		−	12.8112i		−	0.00895125i	0.999990	−	0.00447562i	$-0.00142464\pi$
$128$	360.569	+	1402.55i	0.248985	+	0.968507i
$129$		0			0
$130$	431.011	−	582.228i	0.290786	−	0.392806i
$131$	2012.16			1.34201			0.671005	−	0.741453i	$-0.265863\pi$
$131$	2012.16			1.34201			0.671005	+	0.741453i	$0.265863\pi$
$132$		0			0
$133$	868.331			0.566119
$134$	−818.208	+	1105.27i	−0.527481	+	0.712543i
$135$		0			0
$136$	−2335.34	−	828.611i	−1.47245	−	0.522447i
$137$		−	438.910i		−	0.273712i	−0.990591	−	0.136856i	$-0.956300\pi$
$137$		−	438.910i		−	0.273712i	0.990591	−	0.136856i	$-0.0436998\pi$
$138$		0			0
$139$			2441.97i			1.49011i	0.667003	+	0.745055i	$0.267577\pi$
$139$			2441.97i			1.49011i	−0.667003	+	0.745055i	$0.732423\pi$
$140$	72.4907	+	237.456i	0.0437613	+	0.143348i
$141$		0			0
$142$	−1612.54	−	1193.73i	−0.952970	−	0.705464i
$143$	−3255.24			−1.90362
$144$		0			0
$145$	−931.660			−0.533587
$146$	−1970.46	−	1458.69i	−1.11696	−	0.826863i
$147$		0			0
$148$	699.813	+	2292.36i	0.388677	+	1.27318i
$149$		−	209.794i		−	0.115349i	−0.998335	−	0.0576745i	$-0.981631\pi$
$149$		−	209.794i		−	0.115349i	0.998335	−	0.0576745i	$-0.0183685\pi$
$150$		0			0
$151$		−	1509.31i		−	0.813414i	−0.913559	−	0.406707i	$-0.866677\pi$
$151$		−	1509.31i		−	0.813414i	0.913559	−	0.406707i	$-0.133323\pi$
$152$	2645.29	+	938.586i	1.41159	+	0.500851i
$153$		0			0
$154$	663.809	−	896.701i	0.347346	−	0.469209i
$155$	535.041			0.277261
$156$		0			0
$157$	−2523.59			−1.28283			−0.641415	−	0.767194i	$-0.721652\pi$
$157$	−2523.59			−1.28283			−0.641415	+	0.767194i	$0.721652\pi$
$158$	159.315	−	215.210i	0.0802180	−	0.108362i
$159$		0			0
$160$	−35.8314	+	801.744i	−0.0177045	+	0.396146i
$161$		−	1096.08i		−	0.536541i
$162$		0			0
$163$		−	3085.08i		−	1.48247i	−0.671247	−	0.741234i	$-0.734241\pi$
$163$		−	3085.08i		−	1.48247i	0.671247	−	0.741234i	$-0.265759\pi$
$164$	2744.90	−	837.966i	1.30696	−	0.398989i
$165$		0			0
$166$	474.236	+	351.067i	0.221734	+	0.164145i
$167$	3264.18			1.51251			0.756256	−	0.654276i	$-0.227026\pi$
$167$	3264.18			1.51251			0.756256	+	0.654276i	$0.227026\pi$
$168$		0			0
$169$	1140.20			0.518982
$170$	−1103.74	−	817.074i	−0.497957	−	0.368628i
$171$		0			0
$172$	1882.40	−	574.662i	0.834489	−	0.254753i
$173$			14.4775i			0.00636247i	0.999995	+	0.00318123i	$0.00101262\pi$
$173$			14.4775i			0.00636247i	−0.999995	+	0.00318123i	$0.998987\pi$
$174$		0			0
$175$		−	737.410i		−	0.318531i
$176$	2991.49	−	2014.20i	1.28120	−	0.862649i
$177$		0			0
$178$	1908.44	−	2578.00i	0.803617	−	1.08556i
$179$	−173.527			−0.0724582			−0.0362291	−	0.999344i	$-0.511535\pi$
$179$	−173.527			−0.0724582			−0.0362291	+	0.999344i	$0.511535\pi$
$180$		0			0
$181$	−2824.72			−1.16000			−0.579999	−	0.814617i	$-0.696947\pi$
$181$	−2824.72			−1.16000			−0.579999	+	0.814617i	$0.696947\pi$
$182$	−680.523	+	919.278i	−0.277163	+	0.374404i
$183$		0			0
$184$	1184.76	−	3339.10i	0.474683	−	1.33784i
$185$			1328.27i			0.527871i
$186$		0			0
$187$			6171.00i			2.41320i
$188$	459.785	+	1506.11i	0.178368	+	0.584277i
$189$		0			0
$190$	1250.23	+	925.518i	0.477374	+	0.353390i
$191$	−3215.17			−1.21802			−0.609010	−	0.793163i	$-0.708433\pi$
$191$	−3215.17			−1.21802			−0.609010	+	0.793163i	$0.708433\pi$
$192$		0			0
$193$	−2254.38			−0.840797			−0.420399	−	0.907340i	$-0.638110\pi$
$193$	−2254.38			−0.840797			−0.420399	+	0.907340i	$0.638110\pi$
$194$	2849.99	+	2109.79i	1.05473	+	0.780795i
$195$		0			0
$196$	−114.455	−	374.919i	−0.0417112	−	0.136632i
$197$		−	3328.18i		−	1.20367i	−0.798621	−	0.601835i	$-0.794437\pi$
$197$		−	3328.18i		−	1.20367i	0.798621	−	0.601835i	$-0.205563\pi$
$198$		0			0
$199$			125.198i			0.0445981i	0.999751	+	0.0222990i	$0.00709859\pi$
$199$			125.198i			0.0445981i	−0.999751	+	0.0222990i	$0.992901\pi$
$200$	797.072	−	2246.45i	0.281808	−	0.794242i
$201$		0			0
$202$	505.321	−	682.608i	0.176011	−	0.237763i
$203$	1471.00			0.508590
$204$		0			0
$205$	1590.49			0.541875
$206$	−1403.12	+	1895.39i	−0.474562	+	0.641057i
$207$		0			0
$208$	−3066.81	+	2064.92i	−1.02233	+	0.688347i
$209$		−	6990.03i		−	2.31345i
$210$		0			0
$211$			712.104i			0.232338i	0.993229	+	0.116169i	$0.0370614\pi$
$211$			712.104i			0.232338i	−0.993229	+	0.116169i	$0.962939\pi$
$212$	−446.349	+	136.262i	−0.144601	+	0.0441438i
$213$		0			0
$214$	341.997	+	253.173i	0.109245	+	0.0808718i
$215$	1090.73			0.345986
$216$		0			0
$217$	−844.775			−0.264272
$218$	2348.43	+	1738.49i	0.729613	+	0.540118i
$219$		0			0
$220$	1911.51	−	583.547i	0.585791	−	0.178831i
$221$		−	6326.38i		−	1.92560i
$222$		0			0
$223$		−	2513.98i		−	0.754927i	−0.926024	−	0.377464i	$-0.876796\pi$
$223$		−	2513.98i		−	0.754927i	0.926024	−	0.377464i	$-0.123204\pi$
$224$	56.5742	−	1265.87i	0.0168751	−	0.377588i
$225$		0			0
$226$	1720.32	−	2323.88i	0.506346	−	0.683992i
$227$	−3000.49			−0.877310			−0.438655	−	0.898656i	$-0.644545\pi$
$227$	−3000.49			−0.877310			−0.438655	+	0.898656i	$0.644545\pi$
$228$		0			0
$229$	2429.81			0.701163			0.350582	−	0.936532i	$-0.385984\pi$
$229$	2429.81			0.701163			0.350582	+	0.936532i	$0.385984\pi$
$230$	1168.26	−	1578.14i	0.334926	−	0.452432i
$231$		0			0
$232$	4481.26	+	1590.01i	1.26814	+	0.449954i
$233$			995.374i			0.279868i	0.990161	+	0.139934i	$0.0446890\pi$
$233$			995.374i			0.279868i	−0.990161	+	0.139934i	$0.955311\pi$
$234$		0			0
$235$			872.687i			0.242246i
$236$	526.519	+	1724.70i	0.145226	+	0.475715i
$237$		0			0
$238$	1742.69	+	1290.08i	0.474629	+	0.351358i
$239$	3946.55			1.06812			0.534061	−	0.845446i	$-0.320665\pi$
$239$	3946.55			1.06812			0.534061	+	0.845446i	$0.320665\pi$
$240$		0			0
$241$	5183.31			1.38542			0.692710	−	0.721216i	$-0.256417\pi$
$241$	5183.31			1.38542			0.692710	+	0.721216i	$0.256417\pi$
$242$	−4192.64	−	3103.72i	−1.11369	−	0.824442i
$243$		0			0
$244$	1125.06	+	3685.34i	0.295183	+	0.966925i
$245$		−	217.240i		−	0.0566488i
$246$		0			0
$247$			7166.03i			1.84601i
$248$	−2573.53	−	913.123i	−0.658949	−	0.233804i
$249$		0			0
$250$	1718.60	−	2321.56i	0.434775	−	0.587312i
$251$	−2822.73			−0.709838			−0.354919	−	0.934897i	$-0.615491\pi$
$251$	−2822.73			−0.709838			−0.354919	+	0.934897i	$0.615491\pi$
$252$		0			0
$253$	−8823.39			−2.19258
$254$	−21.5597	+	29.1237i	−0.00532589	+	0.00719442i
$255$		0			0
$256$	1540.64	−	3795.21i	0.376133	−	0.926566i
$257$			1564.07i			0.379626i	0.981820	+	0.189813i	$0.0607882\pi$
$257$			1564.07i			0.379626i	−0.981820	+	0.189813i	$0.939212\pi$
$258$		0			0
$259$		−	2097.20i		−	0.503141i
$260$	−1959.64	+	598.240i	−0.467430	+	0.142697i
$261$		0			0
$262$	−4574.25	−	3386.23i	−1.07862	−	0.798480i
$263$	−5867.50			−1.37569			−0.687843	−	0.725859i	$-0.741442\pi$
$263$	−5867.50			−1.37569			−0.687843	+	0.725859i	$0.741442\pi$
$264$		0			0
$265$	−258.629			−0.0599527
$266$	−1973.98	−	1461.30i	−0.455010	−	0.336834i
$267$		0			0
$268$	3720.07	−	1135.67i	0.847909	−	0.258850i
$269$		−	124.008i		−	0.0281074i	−0.999901	−	0.0140537i	$-0.995526\pi$
$269$		−	124.008i		−	0.0281074i	0.999901	−	0.0140537i	$-0.00447357\pi$
$270$		0			0
$271$			4138.84i			0.927737i	0.885904	+	0.463869i	$0.153539\pi$
$271$			4138.84i			0.927737i	−0.885904	+	0.463869i	$0.846461\pi$
$272$	3914.49	+	5813.79i	0.872613	+	1.29600i
$273$		0			0
$274$	−738.633	+	997.775i	−0.162856	+	0.219992i
$275$	−5936.12			−1.30168
$276$		0			0
$277$	6188.40			1.34233			0.671164	−	0.741309i	$-0.265795\pi$
$277$	6188.40			1.34233			0.671164	+	0.741309i	$0.265795\pi$
$278$	4109.54	−	5551.34i	0.886597	−	1.19765i
$279$		0			0
$280$	234.817	−	661.803i	0.0501178	−	0.141251i
$281$		−	236.986i		−	0.0503110i	−0.999684	−	0.0251555i	$-0.991992\pi$
$281$		−	236.986i		−	0.0503110i	0.999684	−	0.0251555i	$-0.00800808\pi$
$282$		0			0
$283$			6523.13i			1.37018i	0.728460	+	0.685088i	$0.240236\pi$
$283$			6523.13i			1.37018i	−0.728460	+	0.685088i	$0.759764\pi$
$284$	1656.89	+	5427.44i	0.346192	+	1.13401i
$285$		0			0
$286$	7400.15	+	5478.18i	1.53000	+	1.13263i
$287$	−2511.22			−0.516489
$288$		0			0
$289$	−7080.00			−1.44107
$290$	2117.95	+	1567.87i	0.428862	+	0.317478i
$291$		0			0
$292$	2024.65	+	6632.09i	0.405766	+	1.32916i
$293$			3160.20i			0.630106i	0.949074	+	0.315053i	$0.102022\pi$
$293$			3160.20i			0.630106i	−0.949074	+	0.315053i	$0.897978\pi$
$294$		0			0
$295$			999.350i			0.197235i
$296$	2266.88	−	6388.93i	0.445134	−	1.25456i
$297$		0			0
$298$	−353.058	+	476.925i	−0.0686312	+	0.0927099i
$299$	9045.55			1.74956
$300$		0			0
$301$	−1722.15			−0.329777
$302$	−2539.98	+	3431.11i	−0.483972	+	0.653769i
$303$		0			0
$304$	−4434.03	−	6585.40i	−0.836543	−	1.24243i
$305$			2135.41i			0.400895i
$306$		0			0
$307$			1086.86i			0.202054i	0.994884	+	0.101027i	$0.0322128\pi$
$307$			1086.86i			0.202054i	−0.994884	+	0.101027i	$0.967787\pi$
$308$	−3018.08	+	921.362i	−0.558348	+	0.170453i
$309$		0			0
$310$	−1216.31	−	900.410i	−0.222844	−	0.164967i
$311$	−6295.60			−1.14788			−0.573940	−	0.818897i	$-0.694586\pi$
$311$	−6295.60			−1.14788			−0.573940	+	0.818897i	$0.694586\pi$
$312$		0			0
$313$	−9591.96			−1.73217			−0.866085	−	0.499896i	$-0.833372\pi$
$313$	−9591.96			−1.73217			−0.866085	+	0.499896i	$0.833372\pi$
$314$	5736.89	+	4246.90i	1.03106	+	0.763269i
$315$		0			0
$316$	−724.345	+	221.128i	−0.128948	+	0.0393653i
$317$		−	273.735i		−	0.0485000i	−0.999706	−	0.0242500i	$-0.992280\pi$
$317$		−	273.735i		−	0.0485000i	0.999706	−	0.0242500i	$-0.00771978\pi$
$318$		0			0
$319$		−	11841.5i		−	2.07835i
$320$	1430.70	−	1762.31i	0.249932	−	0.307862i
$321$		0			0
$322$	−1844.57	+	2491.72i	−0.319235	+	0.431236i
$323$	13584.7			2.34017
$324$		0			0
$325$	6085.59			1.03867
$326$	−5191.82	+	7013.33i	−0.882051	+	1.19151i
$327$		0			0
$328$	−7650.20	−	2714.39i	−1.28784	−	0.456943i
$329$		−	1377.88i		−	0.230897i
$330$		0			0
$331$		−	4864.23i		−	0.807741i	−0.914816	−	0.403871i	$-0.867665\pi$
$331$		−	4864.23i		−	0.807741i	0.914816	−	0.403871i	$-0.132335\pi$
$332$	−487.279	−	1596.17i	−0.0805509	−	0.263858i
$333$		0			0
$334$	−7420.47	−	5493.22i	−1.21566	−	0.899927i
$335$	2155.53			0.351550
$336$		0			0
$337$	1350.39			0.218281			0.109140	−	0.994026i	$-0.465190\pi$
$337$	1350.39			0.218281			0.109140	+	0.994026i	$0.465190\pi$
$338$	−2592.03	−	1918.83i	−0.417124	−	0.308788i
$339$		0			0
$340$	1134.09	+	3714.91i	0.180896	+	0.592557i
$341$			6800.40i			1.07995i
$342$		0			0
$343$			343.000i			0.0539949i
$344$	−5246.37	−	1861.48i	−0.822282	−	0.291757i
$345$		0			0
$346$	24.3640	−	32.9119i	0.00378559	−	0.00511373i
$347$	4052.56			0.626953			0.313477	−	0.949596i	$-0.398506\pi$
$347$	4052.56			0.626953			0.313477	+	0.949596i	$0.398506\pi$
$348$		0			0
$349$	4162.61			0.638451			0.319225	−	0.947679i	$-0.396577\pi$
$349$	4162.61			0.638451			0.319225	+	0.947679i	$0.396577\pi$
$350$	−1240.97	+	1676.36i	−0.189522	+	0.256015i
$351$		0			0
$352$	−10190.2	−	455.420i	−1.54301	−	0.0689602i
$353$		−	1598.24i		−	0.240979i	−0.992715	−	0.120489i	$-0.961554\pi$
$353$		−	1598.24i		−	0.240979i	0.992715	−	0.120489i	$-0.0384464\pi$
$354$		0			0
$355$			3144.84i			0.470171i
$356$	−8676.94	+	2648.90i	−1.29179	+	0.394358i
$357$		0			0
$358$	394.480	+	292.025i	0.0582372	+	0.0431118i
$359$	−8748.19			−1.28611			−0.643053	−	0.765822i	$-0.722332\pi$
$359$	−8748.19			−1.28611			−0.643053	+	0.765822i	$0.722332\pi$
$360$		0			0
$361$	−8528.73			−1.24344
$362$	6421.45	+	4753.67i	0.932331	+	0.690185i
$363$		0			0
$364$	3094.07	−	944.560i	0.445531	−	0.136012i
$365$			3842.85i			0.551079i
$366$		0			0
$367$			3013.68i			0.428646i	0.976763	+	0.214323i	$0.0687544\pi$
$367$			3013.68i			0.428646i	−0.976763	+	0.214323i	$0.931246\pi$
$368$	−8312.63	+	5596.99i	−1.17752	+	0.792835i
$369$		0			0
$370$	2235.32	−	3019.56i	0.314077	−	0.424268i
$371$	408.349			0.0571440
$372$		0			0
$373$	6514.46			0.904306			0.452153	−	0.891940i	$-0.350656\pi$
$373$	6514.46			0.904306			0.452153	+	0.891940i	$0.350656\pi$
$374$	10385.1	−	14028.6i	1.43583	−	1.93957i
$375$		0			0
$376$	1489.37	−	4197.60i	0.204277	−	0.575731i
$377$			12139.6i			1.65841i
$378$		0			0
$379$		−	10746.8i		−	1.45653i	−0.685295	−	0.728266i	$-0.740327\pi$
$379$		−	10746.8i		−	1.45653i	0.685295	−	0.728266i	$-0.259673\pi$
$380$	−1284.61	−	4207.97i	−0.173419	−	0.568063i
$381$		0			0
$382$	7309.06	+	5410.75i	0.978964	+	0.724707i
$383$	−132.519			−0.0176799			−0.00883996	−	0.999961i	$-0.502814\pi$
$383$	−132.519			−0.0176799			−0.00883996	+	0.999961i	$0.502814\pi$
$384$		0			0
$385$	−1748.77			−0.231496
$386$	5124.89	+	3793.85i	0.675778	+	0.500264i
$387$		0			0
$388$	−2928.38	−	9592.40i	−0.383159	−	1.25510i
$389$		−	1543.51i		−	0.201180i	−0.994928	−	0.100590i	$-0.967927\pi$
$389$		−	1543.51i		−	0.201180i	0.994928	−	0.100590i	$-0.0320730\pi$
$390$		0			0
$391$		−	17147.8i		−	2.21790i
$392$	−370.751	+	1044.92i	−0.0477698	+	0.134634i
$393$		0			0
$394$	−5600.93	+	7565.96i	−0.716169	+	0.967431i
$395$	−419.709			−0.0534629
$396$		0			0
$397$	4875.99			0.616421			0.308211	−	0.951318i	$-0.400270\pi$
$397$	4875.99			0.616421			0.308211	+	0.951318i	$0.400270\pi$
$398$	210.693	−	284.612i	0.0265353	−	0.0358450i
$399$		0			0
$400$	−5592.50	+	3765.50i	−0.699063	+	0.470687i
$401$			2293.38i			0.285600i	0.989752	+	0.142800i	$0.0456106\pi$
$401$			2293.38i			0.285600i	−0.989752	+	0.142800i	$0.954389\pi$
$402$		0			0
$403$		−	6971.63i		−	0.861741i
$404$	−2297.50	+	701.382i	−0.282933	+	0.0863738i
$405$		0			0
$406$	−3344.02	−	2475.51i	−0.408771	−	0.302605i
$407$	−16882.4			−2.05609
$408$		0			0
$409$	11822.0			1.42924			0.714620	−	0.699513i	$-0.246599\pi$
$409$	11822.0			1.42924			0.714620	+	0.699513i	$0.246599\pi$
$410$	−3615.66	−	2676.60i	−0.435524	−	0.322409i
$411$		0			0
$412$	6379.42	−	1947.51i	0.762843	−	0.232881i
$413$		−	1577.87i		−	0.187995i
$414$		0			0
$415$		−	924.871i		−	0.109398i
$416$	10446.8	+	466.887i	1.23124	+	0.0550265i
$417$		0			0
$418$	−11763.4	+	15890.5i	−1.37647	+	1.85940i
$419$	10580.2			1.23360			0.616799	−	0.787120i	$-0.288429\pi$
$419$	10580.2			1.23360			0.616799	+	0.787120i	$0.288429\pi$
$420$		0			0
$421$	−14140.8			−1.63701			−0.818506	−	0.574498i	$-0.805197\pi$
$421$	−14140.8			−1.63701			−0.818506	+	0.574498i	$0.805197\pi$
$422$	1198.39	−	1618.83i	0.138238	−	0.186738i
$423$		0			0
$424$	1244.00	+	441.387i	0.142486	+	0.0505558i
$425$		−	11536.5i		−	1.31671i
$426$		0			0
$427$		−	3371.59i		−	0.382114i
$428$	−351.402	−	1151.08i	−0.0396862	−	0.129999i
$429$		0			0
$430$	−2479.55	−	1835.56i	−0.278081	−	0.205858i
$431$	8892.74			0.993848			0.496924	−	0.867794i	$-0.334463\pi$
$431$	8892.74			0.993848			0.496924	+	0.867794i	$0.334463\pi$
$432$		0			0
$433$	8160.47			0.905698			0.452849	−	0.891587i	$-0.350408\pi$
$433$	8160.47			0.905698			0.452849	+	0.891587i	$0.350408\pi$
$434$	1920.43	+	1421.65i	0.212405	+	0.157239i
$435$		0			0
$436$	−2413.01	−	7904.25i	−0.265051	−	0.868222i
$437$			19423.7i			2.12622i
$438$		0			0
$439$			10235.6i			1.11280i	0.830916	+	0.556398i	$0.187817\pi$
$439$			10235.6i			1.11280i	−0.830916	+	0.556398i	$0.812183\pi$
$440$	−5327.49	−	1890.26i	−0.577223	−	0.204806i
$441$		0			0
$442$	−10646.5	+	14381.8i	−1.14571	+	1.54767i
$443$	8406.15			0.901553			0.450777	−	0.892637i	$-0.351147\pi$
$443$	8406.15			0.901553			0.450777	+	0.892637i	$0.351147\pi$
$444$		0			0
$445$	−5027.71			−0.535587
$446$	−4230.74	+	5715.05i	−0.449173	+	0.606761i
$447$		0			0
$448$	−2258.92	+	2782.50i	−0.238223	+	0.293440i
$449$		−	3880.89i		−	0.407908i	−0.978980	−	0.203954i	$-0.934621\pi$
$449$		−	3880.89i		−	0.407908i	0.978980	−	0.203954i	$-0.0653793\pi$
$450$		0			0
$451$			20215.2i			2.11064i
$452$	−7821.63	+	2387.79i	−0.813935	+	0.248479i
$453$		0			0
$454$	6821.02	+	5049.46i	0.705124	+	0.521989i
$455$	1792.81			0.184721
$456$		0			0
$457$	15637.1			1.60059			0.800297	−	0.599604i	$-0.204675\pi$
$457$	15637.1			1.60059			0.800297	+	0.599604i	$0.204675\pi$
$458$	−5523.70	−	4089.08i	−0.563549	−	0.417184i
$459$		0			0
$460$	−5311.64	+	1621.54i	−0.538383	+	0.164358i
$461$			4273.91i			0.431791i	0.976416	+	0.215896i	$0.0692671\pi$
$461$			4273.91i			0.431791i	−0.976416	+	0.215896i	$0.930733\pi$
$462$		0			0
$463$		−	7824.34i		−	0.785374i	−0.919672	−	0.392687i	$-0.871546\pi$
$463$		−	7824.34i		−	0.785374i	0.919672	−	0.392687i	$-0.128454\pi$
$464$	−7511.46	−	11156.0i	−0.751532	−	1.11617i
$465$		0			0
$466$	1675.10	−	2262.79i	0.166518	−	0.224939i
$467$	3379.38			0.334858			0.167429	−	0.985884i	$-0.446453\pi$
$467$	3379.38			0.334858			0.167429	+	0.985884i	$0.446453\pi$
$468$		0			0
$469$	−3403.37			−0.335081
$470$	1468.63	−	1983.88i	0.144134	−	0.194702i
$471$		0			0
$472$	1705.53	−	4806.84i	0.166321	−	0.468756i
$473$			13863.2i			1.34763i
$474$		0			0
$475$			13067.7i			1.26229i
$476$	−1790.61	−	5865.47i	−0.172422	−	0.564797i
$477$		0			0
$478$	−8971.70	−	6641.57i	−0.858486	−	0.635519i
$479$	−10265.0			−0.979168			−0.489584	−	0.871956i	$-0.662851\pi$
$479$	−10265.0			−0.979168			−0.489584	+	0.871956i	$0.662851\pi$
$480$		0			0
$481$	17307.4			1.64065
$482$	−11783.2	−	8722.89i	−1.11351	−	0.824308i
$483$		0			0
$484$	4307.94	+	14111.4i	0.404578	+	1.32526i
$485$		−	5558.15i		−	0.520377i
$486$		0			0
$487$		−	17652.0i		−	1.64249i	−0.570579	−	0.821243i	$-0.693281\pi$
$487$		−	17652.0i		−	1.64249i	0.570579	−	0.821243i	$-0.306719\pi$
$488$	3644.38	−	10271.2i	0.338060	−	0.952781i
$489$		0			0
$490$	−365.589	+	493.853i	−0.0337054	+	0.0455306i
$491$	10374.5			0.953558			0.476779	−	0.879023i	$-0.341804\pi$
$491$	10374.5			0.953558			0.476779	+	0.879023i	$0.341804\pi$
$492$		0			0
$493$	23013.2			2.10236
$494$	12059.6	−	16290.6i	1.09835	−	1.48370i
$495$		0			0
$496$	4313.74	+	6406.75i	0.390509	+	0.579983i
$497$		−	4965.38i		−	0.448144i
$498$		0			0
$499$			17817.2i			1.59841i	0.601059	+	0.799204i	$0.294745\pi$
$499$			17817.2i			1.59841i	−0.601059	+	0.799204i	$0.705255\pi$
$500$	−7813.80	+	2385.40i	−0.698888	+	0.213357i
$501$		0			0
$502$	6416.93	+	4750.32i	0.570521	+	0.422345i
$503$	11854.9			1.05087			0.525433	−	0.850835i	$-0.323903\pi$
$503$	11854.9			1.05087			0.525433	+	0.850835i	$0.323903\pi$
$504$		0			0
$505$	−1331.25			−0.117306
$506$	20058.2	+	14848.7i	1.76225	+	1.30456i
$507$		0			0
$508$	98.0234	−	29.9247i	0.00856120	−	0.00261357i
$509$			823.902i			0.0717462i	0.999356	+	0.0358731i	$0.0114212\pi$
$509$			823.902i			0.0717462i	−0.999356	+	0.0358731i	$0.988579\pi$
$510$		0			0
$511$		−	6067.47i		−	0.525262i
$512$	−9889.23	+	6034.96i	−0.853606	+	0.520919i
$513$		0			0
$514$	2632.14	−	3555.60i	0.225873	−	0.305118i
$515$	3696.44			0.316281
$516$		0			0
$517$	−11091.9			−0.943562
$518$	−3529.34	+	4767.57i	−0.299363	+	0.404392i
$519$		0			0
$520$	5461.62	+	1937.86i	0.460592	+	0.163424i
$521$			1237.47i			0.104058i	0.998646	+	0.0520291i	$0.0165689\pi$
$521$			1237.47i			0.104058i	−0.998646	+	0.0520291i	$0.983431\pi$
$522$		0			0
$523$		−	13252.2i		−	1.10799i	−0.832521	−	0.553993i	$-0.813103\pi$
$523$		−	13252.2i		−	1.10799i	0.832521	−	0.553993i	$-0.186897\pi$
$524$	4700.06	+	15395.8i	0.391838	+	1.28353i
$525$		0			0
$526$	13338.6	+	9874.30i	1.10569	+	0.818517i
$527$	−13216.2			−1.09242
$528$		0			0
$529$	12351.1			1.01513
$530$	587.943	+	435.242i	0.0481860	+	0.0356711i
$531$		0			0
$532$	2028.27	+	6643.95i	0.165294	+	0.541451i
$533$		−	20724.2i		−	1.68417i
$534$		0			0
$535$		−	666.973i		−	0.0538986i
$536$	−10368.0	−	3678.72i	−0.835507	−	0.296449i
$537$		0			0
$538$	−208.690	+	281.907i	−0.0167236	+	0.0225909i
$539$	2761.14			0.220650
$540$		0			0
$541$	−11301.5			−0.898131			−0.449066	−	0.893499i	$-0.648243\pi$
$541$	−11301.5			−0.898131			−0.449066	+	0.893499i	$0.648243\pi$
$542$	6965.18	−	9408.85i	0.551993	−	0.745654i
$543$		0			0
$544$	885.084	−	19804.1i	0.0697567	−	1.56084i
$545$		−	4579.98i		−	0.359972i
$546$		0			0
$547$			329.529i			0.0257580i	0.999917	+	0.0128790i	$0.00409963\pi$
$547$			329.529i			0.0257580i	−0.999917	+	0.0128790i	$0.995900\pi$
$548$	3358.27	−	1025.22i	0.261785	−	0.0799180i
$549$		0			0
$550$	13494.6	+	9989.79i	1.04620	+	0.774484i
$551$	−26067.6			−2.01546
$552$		0			0
$553$	662.678			0.0509583
$554$	−14068.1	−	10414.3i	−1.07888	−	0.798669i
$555$		0			0
$556$	−18684.5	+	5704.01i	−1.42518	+	0.435079i
$557$		−	18787.0i		−	1.42914i	−0.699565	−	0.714569i	$-0.746623\pi$
$557$		−	18787.0i		−	1.42914i	0.699565	−	0.714569i	$-0.253377\pi$
$558$		0			0
$559$		−	14212.3i		−	1.07534i
$560$	−1647.54	+	1109.31i	−0.124324	+	0.0837088i
$561$		0			0
$562$	−398.819	+	538.741i	−0.0299344	+	0.0404367i
$563$	−4799.22			−0.359259			−0.179630	−	0.983734i	$-0.557490\pi$
$563$	−4799.22			−0.359259			−0.179630	+	0.983734i	$0.557490\pi$
$564$		0			0
$565$	−4532.11			−0.337464
$566$	10977.7	−	14829.1i	0.815239	−	1.10126i
$567$		0			0
$568$	5367.11	−	15126.6i	0.396477	−	1.11742i
$569$		−	4484.19i		−	0.330381i	−0.986262	−	0.165191i	$-0.947176\pi$
$569$		−	4484.19i		−	0.330381i	0.986262	−	0.165191i	$-0.0528240\pi$
$570$		0			0
$571$			20389.8i			1.49437i	0.664616	+	0.747185i	$0.268595\pi$
$571$			20389.8i			1.49437i	−0.664616	+	0.747185i	$0.731405\pi$
$572$	−7603.67	−	24907.2i	−0.555814	−	1.82067i
$573$		0			0
$574$	5708.76	+	4226.08i	0.415120	+	0.307305i
$575$	16495.1			1.19634
$576$		0			0
$577$	−11090.8			−0.800203			−0.400102	−	0.916471i	$-0.631025\pi$
$577$	−11090.8			−0.800203			−0.400102	+	0.916471i	$0.631025\pi$
$578$	16095.0	+	11914.8i	1.15824	+	0.857422i
$579$		0			0
$580$	−2176.19	−	7128.50i	−0.155796	−	0.510336i
$581$			1460.28i			0.104273i
$582$		0			0
$583$		−	3287.19i		−	0.233519i
$584$	6558.37	−	18484.0i	0.464704	−	1.30971i
$585$		0			0
$586$	5318.25	−	7184.11i	0.374906	−	0.506438i
$587$	−760.483			−0.0534727			−0.0267364	−	0.999643i	$-0.508511\pi$
$587$	−760.483			−0.0534727			−0.0267364	+	0.999643i	$0.508511\pi$
$588$		0			0
$589$	14970.3			1.04727
$590$	1681.79	−	2271.83i	0.117353	−	0.158525i
$591$		0			0
$592$	−15905.1	+	10709.1i	−1.10422	+	0.743482i
$593$			26810.4i			1.85661i	0.371820	+	0.928305i	$0.378734\pi$
$593$			26810.4i			1.85661i	−0.371820	+	0.928305i	$0.621266\pi$
$594$		0			0
$595$		−	3398.65i		−	0.234170i
$596$	1605.22	−	490.042i	0.110323	−	0.0336794i
$597$		0			0
$598$	−20563.3	−	15222.6i	−1.40618	−	1.04097i
$599$	8951.39			0.610591			0.305295	−	0.952258i	$-0.401245\pi$
$599$	8951.39			0.610591			0.305295	+	0.952258i	$0.401245\pi$
$600$		0			0
$601$	−3952.86			−0.268287			−0.134144	−	0.990962i	$-0.542828\pi$
$601$	−3952.86			−0.268287			−0.134144	+	0.990962i	$0.542828\pi$
$602$	3914.96	+	2898.17i	0.265053	+	0.196213i
$603$		0			0
$604$	11548.3	−	3525.47i	0.777970	−	0.237499i
$605$			8176.62i			0.549466i
$606$		0			0
$607$		−	785.320i		−	0.0525126i	−0.999655	−	0.0262563i	$-0.991641\pi$
$607$		−	785.320i		−	0.0525126i	0.999655	−	0.0262563i	$-0.00835860\pi$
$608$	−1002.55	+	22432.6i	−0.0668732	+	1.49632i
$609$		0			0
$610$	3593.63	−	4854.43i	0.238528	−	0.322213i
$611$	11371.2			0.752912
$612$		0			0
$613$	1220.46			0.0804142			0.0402071	−	0.999191i	$-0.487198\pi$
$613$	1220.46			0.0804142			0.0402071	+	0.999191i	$0.487198\pi$
$614$	1829.06	−	2470.77i	0.120220	−	0.162398i
$615$		0			0
$616$	8411.56	+	2984.53i	0.550181	+	0.195212i
$617$		−	10661.3i		−	0.695634i	−0.937562	−	0.347817i	$-0.886923\pi$
$617$		−	10661.3i		−	0.695634i	0.937562	−	0.347817i	$-0.113077\pi$
$618$		0			0
$619$			4575.69i			0.297112i	0.988904	+	0.148556i	$0.0474626\pi$
$619$			4575.69i			0.297112i	−0.988904	+	0.148556i	$0.952537\pi$
$620$	1249.76	+	4093.81i	0.0809542	+	0.265180i
$621$		0			0
$622$	14311.8	+	10594.7i	0.922590	+	0.682975i
$623$	7938.23			0.510495
$624$		0			0
$625$	8640.47			0.552990
$626$	21805.4	+	16142.1i	1.39221	+	1.03062i
$627$		0			0
$628$	−5894.66	−	19309.0i	−0.374559	−	1.22693i
$629$		−	32809.9i		−	2.07984i
$630$		0			0
$631$		−	9365.83i		−	0.590884i	−0.955361	−	0.295442i	$-0.904533\pi$
$631$		−	9365.83i		−	0.590884i	0.955361	−	0.295442i	$-0.0954669\pi$
$632$	2018.79	+	716.293i	0.127062	+	0.0450833i
$633$		0			0
$634$	−460.664	+	622.284i	−0.0288569	+	0.0389811i
$635$	56.7980			0.00354954
$636$		0			0
$637$	−2830.66			−0.176067
$638$	−19927.8	+	26919.2i	−1.23660	+	1.67044i
$639$		0			0
$640$	−6218.16	+	1598.57i	−0.384054	+	0.0987330i
$641$		−	18934.0i		−	1.16669i	−0.812224	−	0.583346i	$-0.801743\pi$
$641$		−	18934.0i		−	1.16669i	0.812224	−	0.583346i	$-0.198257\pi$
$642$		0			0
$643$		−	17627.1i		−	1.08110i	−0.841313	−	0.540548i	$-0.818217\pi$
$643$		−	17627.1i		−	1.08110i	0.841313	−	0.540548i	$-0.181783\pi$
$644$	8386.53	−	2560.25i	0.513161	−	0.156658i
$645$		0			0
$646$	−30882.2	−	22861.5i	−1.88088	−	1.39237i
$647$	−12698.2			−0.771590			−0.385795	−	0.922584i	$-0.626073\pi$
$647$	−12698.2			−0.771590			−0.385795	+	0.922584i	$0.626073\pi$
$648$		0			0
$649$	−12701.8			−0.768242
$650$	−13834.4	−	10241.3i	−0.834815	−	0.617996i
$651$		0			0
$652$	23605.2	−	7206.21i	1.41787	−	0.432848i
$653$			29664.5i			1.77774i	0.458163	+	0.888868i	$0.348508\pi$
$653$			29664.5i			1.77774i	−0.458163	+	0.888868i	$0.651492\pi$
$654$		0			0
$655$			8920.86i			0.532163i
$656$	12823.2	+	19045.0i	0.763206	+	1.13351i
$657$		0			0
$658$	−2318.81	+	3132.35i	−0.137381	+	0.185580i
$659$	16933.7			1.00098			0.500489	−	0.865743i	$-0.333154\pi$
$659$	16933.7			1.00098			0.500489	+	0.865743i	$0.333154\pi$
$660$		0			0
$661$	−12431.5			−0.731515			−0.365757	−	0.930710i	$-0.619190\pi$
$661$	−12431.5			−0.731515			−0.365757	+	0.930710i	$0.619190\pi$
$662$	−8185.92	+	11057.9i	−0.480597	+	0.649210i
$663$		0			0
$664$	−1578.42	+	4448.60i	−0.0922511	+	0.259999i
$665$			3849.72i			0.224490i
$666$		0			0
$667$			32904.6i			1.91015i
$668$	7624.55	+	24975.5i	0.441621	+	1.44660i
$669$		0			0
$670$	−4900.18	−	3627.50i	−0.282553	−	0.209168i
$671$	−27141.2			−1.56151
$672$		0			0
$673$	−29850.7			−1.70975			−0.854874	−	0.518836i	$-0.826365\pi$
$673$	−29850.7			−1.70975			−0.854874	+	0.518836i	$0.826365\pi$
$674$	−3069.85	−	2272.55i	−0.175440	−	0.129874i
$675$		0			0
$676$	2663.32	+	8724.16i	0.151531	+	0.496368i
$677$		−	20058.2i		−	1.13870i	−0.822096	−	0.569349i	$-0.807195\pi$
$677$		−	20058.2i		−	1.13870i	0.822096	−	0.569349i	$-0.192805\pi$
$678$		0			0
$679$			8775.76i			0.495998i
$680$	3673.62	−	10353.7i	0.207172	−	0.583890i
$681$		0			0
$682$	11444.3	−	15459.4i	0.642557	−	0.867992i
$683$	−216.327			−0.0121194			−0.00605968	−	0.999982i	$-0.501929\pi$
$683$	−216.327			−0.0121194			−0.00605968	+	0.999982i	$0.501929\pi$
$684$		0			0
$685$	1945.89			0.108538
$686$	577.228	−	779.743i	0.0321263	−	0.0433976i
$687$		0			0
$688$	8793.94	+	13060.7i	0.487305	+	0.723743i
$689$			3369.96i			0.186336i
$690$		0			0
$691$		−	6625.25i		−	0.364741i	−0.983230	−	0.182371i	$-0.941623\pi$
$691$		−	6625.25i		−	0.364741i	0.983230	−	0.182371i	$-0.0583771\pi$
$692$	−110.773	+	33.8170i	−0.00608522	+	0.00185770i
$693$		0			0
$694$	−9212.70	−	6819.97i	−0.503904	−	0.373030i
$695$	−10826.4			−0.590891
$696$		0			0
$697$	−39287.1			−2.13502
$698$	−9462.87	−	7005.17i	−0.513145	−	0.379871i
$699$		0			0
$700$	5642.22	−	1722.46i	0.304651	−	0.0930042i
$701$			25374.8i			1.36718i	0.729866	+	0.683591i	$0.239583\pi$
$701$			25374.8i			1.36718i	−0.729866	+	0.683591i	$0.760417\pi$
$702$		0			0
$703$			37164.6i			1.99387i
$704$	22399.1	+	18184.2i	1.19914	+	0.973500i
$705$		0			0
$706$	−2689.64	+	3633.28i	−0.143380	+	0.193683i
$707$	2101.90			0.111811
$708$		0			0
$709$	−6731.40			−0.356563			−0.178281	−	0.983980i	$-0.557054\pi$
$709$	−6731.40			−0.356563			−0.178281	+	0.983980i	$0.557054\pi$
$710$	5292.38	−	7149.17i	0.279746	−	0.377892i
$711$		0			0
$712$	24183.1	+	8580.50i	1.27289	+	0.451640i
$713$		−	18896.7i		−	0.992549i
$714$		0			0
$715$		−	14432.0i		−	0.754863i
$716$	−405.329	−	1327.73i	−0.0211562	−	0.0693009i
$717$		0			0
$718$	19887.3	+	14722.2i	1.03369	+	0.765218i
$719$	−21594.3			−1.12007			−0.560035	−	0.828469i	$-0.689212\pi$
$719$	−21594.3			−1.12007			−0.560035	+	0.828469i	$0.689212\pi$
$720$		0			0
$721$	−5836.31			−0.301464
$722$	19388.4	+	14352.8i	0.999393	+	0.739830i
$723$		0			0
$724$	−6598.05	−	21613.1i	−0.338694	−	1.10945i
$725$			22137.3i			1.13401i
$726$		0			0
$727$			3985.18i			0.203304i	0.994820	+	0.101652i	$0.0324129\pi$
$727$			3985.18i			0.203304i	−0.994820	+	0.101652i	$0.967587\pi$
$728$	−8623.35	−	3059.68i	−0.439015	−	0.155768i
$729$		0			0
$730$	6467.06	−	8735.96i	0.327886	−	0.442921i
$731$	−26942.4			−1.36320
$732$		0			0
$733$	1869.26			0.0941921			0.0470960	−	0.998890i	$-0.485003\pi$
$733$	1869.26			0.0941921			0.0470960	+	0.998890i	$0.485003\pi$
$734$	5071.67	−	6851.02i	0.255039	−	0.344517i
$735$		0			0
$736$	28316.2	+	1265.51i	1.41814	+	0.0633793i
$737$			27397.0i			1.36931i
$738$		0			0
$739$		−	14523.0i		−	0.722919i	−0.932388	−	0.361460i	$-0.882279\pi$
$739$		−	14523.0i		−	0.722919i	0.932388	−	0.361460i	$-0.117721\pi$
$740$	−10163.1	+	3102.60i	−0.504869	+	0.154127i
$741$		0			0
$742$	−928.301	−	687.203i	−0.0459286	−	0.0340000i
$743$	−32744.1			−1.61678			−0.808388	−	0.588650i	$-0.799660\pi$
$743$	−32744.1			−1.61678			−0.808388	+	0.588650i	$0.799660\pi$
$744$		0			0
$745$	930.115			0.0457407
$746$	−14809.4	−	10963.1i	−0.726822	−	0.538051i
$747$		0			0
$748$	−47216.8	+	14414.4i	−2.30804	+	0.704602i
$749$			1053.08i			0.0513736i
$750$		0			0
$751$			520.293i			0.0252806i	0.999920	+	0.0126403i	$0.00402364\pi$
$751$			520.293i			0.0252806i	−0.999920	+	0.0126403i	$0.995976\pi$
$752$	−10449.8	+	7036.00i	−0.506737	+	0.341192i
$753$		0			0
$754$	20429.5	−	27597.0i	0.986736	−	1.33292i
$755$	6691.46			0.322553
$756$		0			0
$757$	18073.8			0.867771			0.433885	−	0.900968i	$-0.357142\pi$
$757$	18073.8			0.867771			0.433885	+	0.900968i	$0.357142\pi$
$758$	−18085.6	+	24430.7i	−0.866619	+	1.17066i
$759$		0			0
$760$	−4161.19	+	11727.8i	−0.198608	+	0.559754i
$761$		−	6065.42i		−	0.288924i	−0.989510	−	0.144462i	$-0.953855\pi$
$761$		−	6065.42i		−	0.288924i	0.989510	−	0.144462i	$-0.0461452\pi$
$762$		0			0
$763$			7231.32i			0.343108i
$764$	−7510.08	−	24600.6i	−0.355635	−	1.16494i
$765$		0			0
$766$	301.256	+	223.014i	0.0142100	+	0.0105193i
$767$	13021.6			0.613016
$768$		0			0
$769$	−35314.6			−1.65602			−0.828008	−	0.560716i	$-0.810526\pi$
$769$	−35314.6			−1.65602			−0.828008	+	0.560716i	$0.810526\pi$
$770$	3975.50	+	2942.98i	0.186061	+	0.137737i
$771$		0			0
$772$	−5265.84	−	17249.2i	−0.245494	−	0.804159i
$773$			19124.0i			0.889837i	0.895571	+	0.444918i	$0.146767\pi$
$773$			19124.0i			0.889837i	−0.895571	+	0.444918i	$0.853233\pi$
$774$		0			0
$775$		−	12713.2i		−	0.589252i
$776$	−9485.78	+	26734.6i	−0.438814	+	1.23675i
$777$		0			0
$778$	−2597.54	+	3508.86i	−0.119700	+	0.161695i
$779$	44501.4			2.04676
$780$		0			0
$781$	−39971.1			−1.83134
$782$	−28857.6	+	38982.1i	−1.31963	+	1.78260i
$783$		0			0
$784$	2601.30	−	1751.49i	0.118500	−	0.0797872i
$785$		−	11188.3i		−	0.508696i
$786$		0			0
$787$			36247.3i			1.64177i	0.571090	+	0.820887i	$0.306521\pi$
$787$			36247.3i			1.64177i	−0.571090	+	0.820887i	$0.693479\pi$
$788$	25465.2	−	7774.04i	1.15122	−	0.351445i
$789$		0			0
$790$	954.126	+	706.320i	0.0429700	+	0.0318098i
$791$	7155.74			0.321654
$792$		0			0
$793$	27824.5			1.24600
$794$	−11084.6	−	8205.72i	−0.495439	−	0.366763i
$795$		0			0
$796$	−957.937	+	292.440i	−0.0426547	+	0.0130217i
$797$		−	13707.8i		−	0.609229i	−0.952476	−	0.304615i	$-0.901472\pi$
$797$		−	13707.8i		−	0.609229i	0.952476	−	0.304615i	$-0.0985276\pi$
$798$		0			0
$799$		−	21556.5i		−	0.954461i
$800$	19050.3	+	851.396i	0.841914	+	0.0376267i
$801$		0			0
$802$	3859.48	−	5213.54i	0.169929	−	0.229547i
$803$	−48842.9			−2.14648
$804$		0			0
$805$	4859.43			0.212761
$806$	−11732.4	+	15848.6i	−0.512726	+	0.692611i
$807$		0			0
$808$	6403.25	+	2271.96i	0.278794	+	0.0989199i
$809$		−	37578.6i		−	1.63312i	−0.577262	−	0.816559i	$-0.695879\pi$
$809$		−	37578.6i		−	1.63312i	0.577262	−	0.816559i	$-0.304121\pi$
$810$		0			0
$811$			44053.0i			1.90741i	0.300740	+	0.953706i	$0.402766\pi$
$811$			44053.0i			1.90741i	−0.300740	+	0.953706i	$0.597234\pi$
$812$	3435.99	+	11255.2i	0.148497	+	0.486428i
$813$		0			0
$814$	38378.8	+	28411.0i	1.65255	+	1.22335i
$815$	13677.6			0.587860
$816$		0			0
$817$	30518.2			1.30685
$818$	−26875.0	−	19895.0i	−1.14873	−	0.850381i
$819$		0			0
$820$	3715.10	+	12169.5i	0.158216	+	0.518263i
$821$		−	20062.3i		−	0.852837i	−0.904526	−	0.426419i	$-0.859775\pi$
$821$		−	20062.3i		−	0.852837i	0.904526	−	0.426419i	$-0.140225\pi$
$822$		0			0
$823$		−	13409.5i		−	0.567952i	−0.958831	−	0.283976i	$-0.908346\pi$
$823$		−	13409.5i		−	0.567952i	0.958831	−	0.283976i	$-0.0916536\pi$
$824$	−17779.8	−	6308.51i	−0.751685	−	0.266708i
$825$		0			0
$826$	−2655.37	+	3586.98i	−0.111855	+	0.151098i
$827$	−28180.4			−1.18492			−0.592460	−	0.805600i	$-0.701843\pi$
$827$	−28180.4			−1.18492			−0.592460	+	0.805600i	$0.701843\pi$
$828$		0			0
$829$	24836.2			1.04053			0.520264	−	0.854006i	$-0.325834\pi$
$829$	24836.2			1.04053			0.520264	+	0.854006i	$0.325834\pi$
$830$	−1556.45	+	2102.51i	−0.0650904	+	0.0879268i
$831$		0			0
$832$	−22963.0	−	18642.1i	−0.956851	−	0.776801i
$833$			5366.11i			0.223199i
$834$		0			0
$835$			14471.6i			0.599774i
$836$	53483.5	−	16327.5i	2.21264	−	0.675476i
$837$		0			0
$838$	−24052.1	−	17805.3i	−0.991486	−	0.733977i
$839$	−30702.2			−1.26336			−0.631680	−	0.775230i	$-0.717634\pi$
$839$	−30702.2			−1.26336			−0.631680	+	0.775230i	$0.717634\pi$
$840$		0			0
$841$	−19770.8			−0.810643
$842$	32146.4	+	23797.3i	1.31572	+	0.974003i
$843$		0			0
$844$	−5448.59	+	1663.35i	−0.222213	+	0.0678375i
$845$			5055.06i			0.205798i
$846$		0			0
$847$		−	12910.0i		−	0.523724i
$848$	−2085.18	−	3096.91i	−0.0844405	−	0.125411i
$849$		0			0
$850$	−19414.6	+	26226.0i	−0.783430	+	1.05829i
$851$	46912.1			1.88969
$852$		0			0
$853$	−30659.5			−1.23067			−0.615336	−	0.788265i	$-0.710980\pi$
$853$	−30659.5			−1.23067			−0.615336	+	0.788265i	$0.710980\pi$
$854$	−5673.98	+	7664.65i	−0.227353	+	0.307118i
$855$		0			0
$856$	−1138.29	+	3208.12i	−0.0454507	+	0.128097i
$857$			3186.33i			0.127005i	0.997982	+	0.0635023i	$0.0202270\pi$
$857$			3186.33i			0.127005i	−0.997982	+	0.0635023i	$0.979773\pi$
$858$		0			0
$859$			19221.4i			0.763476i	0.924271	+	0.381738i	$0.124674\pi$
$859$			19221.4i			0.763476i	−0.924271	+	0.381738i	$0.875326\pi$
$860$	2547.75	+	8345.59i	0.101020	+	0.330910i
$861$		0			0
$862$	−20215.9	−	14965.4i	−0.798789	−	0.591328i
$863$	2988.88			0.117894			0.0589472	−	0.998261i	$-0.481226\pi$
$863$	2988.88			0.117894			0.0589472	+	0.998261i	$0.481226\pi$
$864$		0			0
$865$	−64.1858			−0.00252298
$866$	−18551.2	−	13733.1i	−0.727941	−	0.538880i
$867$		0			0
$868$	−1973.25	−	6463.71i	−0.0771617	−	0.252756i
$869$		−	5334.53i		−	0.208241i
$870$		0			0
$871$		−	28086.8i		−	1.09263i
$872$	−7816.39	+	22029.6i	−0.303551	+	0.855522i
$873$		0			0
$874$	32687.7	−	44155.9i	1.26508	−	1.70892i
$875$	7148.58			0.276190
$876$		0			0
$877$	−19493.5			−0.750568			−0.375284	−	0.926910i	$-0.622455\pi$
$877$	−19493.5			−0.750568			−0.375284	+	0.926910i	$0.622455\pi$
$878$	17225.2	−	23268.6i	0.662100	−	0.894392i
$879$		0			0
$880$	8929.91	+	13262.7i	0.342076	+	0.508051i
$881$			41443.9i			1.58488i	0.609949	+	0.792441i	$0.291190\pi$
$881$			41443.9i			1.58488i	−0.609949	+	0.792441i	$0.708810\pi$
$882$		0			0
$883$		−	528.509i		−	0.0201424i	−0.999949	−	0.0100712i	$-0.996794\pi$
$883$		−	528.509i		−	0.0201424i	0.999949	−	0.0100712i	$-0.00320581\pi$
$884$	48405.7	−	14777.3i	1.84170	−	0.562234i
$885$		0			0
$886$	−19109.7	−	14146.5i	−0.724609	−	0.536414i
$887$	4754.53			0.179979			0.0899896	−	0.995943i	$-0.471317\pi$
$887$	4754.53			0.179979			0.0899896	+	0.995943i	$0.471317\pi$
$888$		0			0
$889$	−89.6782			−0.00338325
$890$	11429.5	+	8461.03i	0.430470	+	0.318668i
$891$		0			0
$892$	19235.5	−	5872.23i	0.722032	−	0.220422i
$893$			24417.5i			0.915008i
$894$		0			0
$895$		−	769.328i		−	0.0287327i
$896$	9817.84	−	2523.98i	0.366061	−	0.0941075i
$897$		0			0
$898$	−6531.08	+	8822.45i	−0.242700	+	0.327850i
$899$	25360.4			0.940842
$900$		0			0
$901$	6388.48			0.236216
$902$	34019.8	−	45955.3i	1.25580	−	1.69639i
$903$		0			0
$904$	21799.3	+	7734.69i	0.802029	+	0.284571i
$905$		−	12523.3i		−	0.459988i
$906$		0			0
$907$			20866.6i			0.763908i	0.924181	+	0.381954i	$0.124749\pi$
$907$			20866.6i			0.763908i	−0.924181	+	0.381954i	$0.875251\pi$
$908$	−7008.61	−	22957.9i	−0.256155	−	0.839081i
$909$		0			0
$910$	−4075.59	−	3017.08i	−0.148467	−	0.109907i
$911$	18050.4			0.656463			0.328231	−	0.944597i	$-0.393547\pi$
$911$	18050.4			0.656463			0.328231	+	0.944597i	$0.393547\pi$
$912$		0			0
$913$	11755.2			0.426111
$914$	−35547.8	−	26315.3i	−1.28645	−	0.952334i
$915$		0			0
$916$	5675.61	+	18591.4i	0.204724	+	0.670610i
$917$		−	14085.1i		−	0.507232i
$918$		0			0
$919$		−	13610.2i		−	0.488530i	−0.969709	−	0.244265i	$-0.921453\pi$
$919$		−	13610.2i		−	0.488530i	0.969709	−	0.244265i	$-0.0785466\pi$
$920$	14803.8	+	5252.60i	0.530508	+	0.188232i
$921$		0			0
$922$	7192.48	−	9715.89i	0.256911	−	0.347045i
$923$	40977.5			1.46131
$924$		0			0
$925$	31561.1			1.12186
$926$	−13167.4	+	17787.1i	−0.467288	+	0.631232i
$927$		0			0
$928$	−1698.38	+	38001.9i	−0.0600775	+	1.34426i
$929$		−	42495.3i		−	1.50078i	−0.660996	−	0.750390i	$-0.729866\pi$
$929$		−	42495.3i		−	1.50078i	0.660996	−	0.750390i	$-0.270134\pi$
$930$		0			0
$931$		−	6078.32i		−	0.213973i
$932$	−7616.01	+	2325.02i	−0.267672	+	0.0817152i
$933$		0			0
$934$	−7682.35	−	5687.09i	−0.269137	−	0.199237i
$935$	−27359.0			−0.956935
$936$		0			0
$937$	22579.5			0.787234			0.393617	−	0.919274i	$-0.371224\pi$
$937$	22579.5			0.787234			0.393617	+	0.919274i	$0.371224\pi$
$938$	7736.89	+	5727.46i	0.269316	+	0.199369i
$939$		0			0
$940$	−6677.28	+	2038.44i	−0.231690	+	0.0707306i
$941$		−	35339.7i		−	1.22427i	−0.790753	−	0.612136i	$-0.790311\pi$
$941$		−	35339.7i		−	1.22427i	0.790753	−	0.612136i	$-0.209689\pi$
$942$		0			0
$943$		−	56173.3i		−	1.93982i
$944$	−11966.5	+	8057.21i	−0.412582	+	0.277796i
$945$		0			0
$946$	23330.1	−	31515.3i	0.801827	−	1.08314i
$947$	−40087.1			−1.37556			−0.687781	−	0.725918i	$-0.741415\pi$
$947$	−40087.1			−1.37556			−0.687781	+	0.725918i	$0.741415\pi$
$948$		0			0
$949$	50072.7			1.71278
$950$	21991.3	−	29706.8i	0.751046	−	1.01454i
$951$		0			0
$952$	−5800.27	+	16347.4i	−0.197466	+	0.556536i
$953$			26433.3i			0.898486i	0.893410	+	0.449243i	$0.148306\pi$
$953$			26433.3i			0.898486i	−0.893410	+	0.449243i	$0.851694\pi$
$954$		0			0
$955$		−	14254.4i		−	0.482996i
$956$	9218.44	+	30196.6i	0.311868	+	1.02158i
$957$		0			0
$958$	23335.5	+	17274.8i	0.786991	+	0.582593i
$959$	−3072.37			−0.103454
$960$		0			0
$961$	15226.8			0.511122
$962$	−39345.1	−	29126.4i	−1.31865	−	0.976166i
$963$		0			0
$964$	12107.3	+	39659.6i	0.404512	+	1.32505i
$965$		−	9994.73i		−	0.333411i
$966$		0			0
$967$		−	24348.4i		−	0.809713i	−0.914380	−	0.404857i	$-0.867321\pi$
$967$		−	24348.4i		−	0.809713i	0.914380	−	0.404857i	$-0.132679\pi$
$968$	13954.6	−	39329.3i	0.463344	−	1.30588i
$969$		0			0
$970$	−9353.71	+	12635.4i	−0.309618	+	0.418245i
$971$	28317.6			0.935895			0.467948	−	0.883756i	$-0.344994\pi$
$971$	28317.6			0.935895			0.467948	+	0.883756i	$0.344994\pi$
$972$		0			0
$973$	17093.8			0.563208
$974$	−29706.3	+	40128.5i	−0.977260	+	1.32012i
$975$		0			0
$976$	−25570.1	+	17216.6i	−0.838604	+	0.564642i
$977$			12737.5i			0.417102i	0.978011	+	0.208551i	$0.0668748\pi$
$977$			12737.5i			0.417102i	−0.978011	+	0.208551i	$0.933125\pi$
$978$		0			0
$979$		−	63902.5i		−	2.08614i
$980$	1662.19	−	507.435i	0.0541804	−	0.0165402i
$981$		0			0
$982$	−23584.5	−	17459.1i	−0.766407	−	0.567355i
$983$	28944.2			0.939143			0.469572	−	0.882894i	$-0.344408\pi$
$983$	28944.2			0.939143			0.469572	+	0.882894i	$0.344408\pi$
$984$		0			0
$985$	14755.4			0.477305
$986$	−52316.0	−	38728.5i	−1.68974	−	1.25088i
$987$		0			0
$988$	−54830.2	+	16738.6i	−1.76557	+	0.538994i
$989$		−	38522.6i		−	1.23857i
$990$		0			0
$991$			37965.7i			1.21697i	0.793564	+	0.608487i	$0.208223\pi$
$991$			37965.7i			1.21697i	−0.793564	+	0.608487i	$0.791777\pi$
$992$	975.356	−	21824.0i	0.0312173	−	0.698501i
$993$		0			0
$994$	−8356.14	+	11287.8i	−0.266640	+	0.360189i
$995$	−555.060			−0.0176850
$996$		0			0
$997$	−26374.0			−0.837787			−0.418894	−	0.908035i	$-0.637582\pi$
$997$	−26374.0			−0.837787			−0.418894	+	0.908035i	$0.637582\pi$
$998$	29984.2	−	40503.8i	0.951034	−	1.28470i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.e.a.71.7	✓	36
3.2	odd	2	inner	252.4.e.a.71.30	yes	36
4.3	odd	2	inner	252.4.e.a.71.29	yes	36
12.11	even	2	inner	252.4.e.a.71.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.e.a.71.7	✓	36	1.1	even	1	trivial
252.4.e.a.71.8	yes	36	12.11	even	2	inner
252.4.e.a.71.29	yes	36	4.3	odd	2	inner
252.4.e.a.71.30	yes	36	3.2	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.27330 - 1.68288i) q^{2} +(2.33582 + 7.65140i) q^{4} +4.43347i q^{5} -7.00000i q^{7} +(7.56635 - 21.3249i) q^{8} +O(q^{10})\)	\(q+(-2.27330 - 1.68288i) q^{2} +(2.33582 + 7.65140i) q^{4} +4.43347i q^{5} -7.00000i q^{7} +(7.56635 - 21.3249i) q^{8} +(7.46100 - 10.0786i) q^{10} -56.3497 q^{11} +57.7685 q^{13} +(-11.7802 + 15.9131i) q^{14} +(-53.0878 + 35.7447i) q^{16} -109.513i q^{17} +124.047i q^{19} +(-33.9223 + 10.3558i) q^{20} +(128.100 + 94.8299i) q^{22} +156.583 q^{23} +105.344 q^{25} +(-131.325 - 97.2176i) q^{26} +(53.5598 - 16.3508i) q^{28} +210.142i q^{29} -120.682i q^{31} +(180.839 + 8.08203i) q^{32} +(-184.297 + 248.955i) q^{34} +31.0343 q^{35} +299.600 q^{37} +(208.757 - 281.997i) q^{38} +(94.5432 + 33.5452i) q^{40} -358.745i q^{41} -246.021i q^{43} +(-131.623 - 431.154i) q^{44} +(-355.960 - 263.510i) q^{46} +196.841 q^{47} -49.0000 q^{49} +(-239.480 - 177.282i) q^{50} +(134.937 + 442.010i) q^{52} +58.3356i q^{53} -249.825i q^{55} +(-149.274 - 52.9645i) q^{56} +(353.644 - 477.717i) q^{58} +225.410 q^{59} +481.655 q^{61} +(-203.094 + 274.347i) q^{62} +(-397.501 - 322.703i) q^{64} +256.115i q^{65} -486.195i q^{67} +(837.924 - 255.802i) q^{68} +(-70.5504 - 52.2270i) q^{70} +709.339 q^{71} +866.781 q^{73} +(-681.082 - 504.191i) q^{74} +(-949.136 + 289.753i) q^{76} +394.448i q^{77} +94.6682i q^{79} +(-158.473 - 235.363i) q^{80} +(-603.726 + 815.537i) q^{82} -208.611 q^{83} +485.521 q^{85} +(-414.024 + 559.281i) q^{86} +(-426.362 + 1201.65i) q^{88} +1134.03i q^{89} -404.380i q^{91} +(365.750 + 1198.08i) q^{92} +(-447.478 - 331.259i) q^{94} -549.960 q^{95} -1253.68 q^{97} +(111.392 + 82.4612i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 24 q^{4}+O(q^{10}) \) 36 * q - 24 * q^4	\( 36 q - 24 q^{4} + 264 q^{10} - 468 q^{16} + 444 q^{22} - 900 q^{25} - 84 q^{28} - 432 q^{34} - 264 q^{37} + 1416 q^{40} + 180 q^{46} - 1764 q^{49} + 2736 q^{52} + 636 q^{58} - 3960 q^{61} + 1392 q^{64} - 504 q^{70} - 2520 q^{76} + 1032 q^{82} - 3144 q^{85} + 2748 q^{88} + 5496 q^{94}+O(q^{100}) \) 36 * q - 24 * q^4 + 264 * q^10 - 468 * q^16 + 444 * q^22 - 900 * q^25 - 84 * q^28 - 432 * q^34 - 264 * q^37 + 1416 * q^40 + 180 * q^46 - 1764 * q^49 + 2736 * q^52 + 636 * q^58 - 3960 * q^61 + 1392 * q^64 - 504 * q^70 - 2520 * q^76 + 1032 * q^82 - 3144 * q^85 + 2748 * q^88 + 5496 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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