LMFDB - Embedded newform 252.4.e.a.71.5

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			71.5
Character	$\chi$	$=$	252.71
Dual form			252.4.e.a.71.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36083 - 1.55771i) q^{2} +(3.14707 + 7.35499i) q^{4} -8.56325i q^{5} +7.00000i q^{7} +(4.02725 - 22.2661i) q^{8} +O(q^{10})$	\(q+(-2.36083 - 1.55771i) q^{2} +(3.14707 + 7.35499i) q^{4} -8.56325i q^{5} +7.00000i q^{7} +(4.02725 - 22.2661i) q^{8} +(-13.3391 + 20.2164i) q^{10} +21.7063 q^{11} -3.31405 q^{13} +(10.9040 - 16.5258i) q^{14} +(-44.1919 + 46.2934i) q^{16} -12.8227i q^{17} -7.76564i q^{19} +(62.9827 - 26.9492i) q^{20} +(-51.2450 - 33.8122i) q^{22} +74.9703 q^{23} +51.6707 q^{25} +(7.82392 + 5.16233i) q^{26} +(-51.4850 + 22.0295i) q^{28} -157.973i q^{29} -15.8295i q^{31} +(176.441 - 40.4527i) q^{32} +(-19.9740 + 30.2722i) q^{34} +59.9428 q^{35} -14.2978 q^{37} +(-12.0966 + 18.3334i) q^{38} +(-190.671 - 34.4863i) q^{40} -474.853i q^{41} -375.510i q^{43} +(68.3114 + 159.650i) q^{44} +(-176.992 - 116.782i) q^{46} -256.189 q^{47} -49.0000 q^{49} +(-121.986 - 80.4881i) q^{50} +(-10.4295 - 24.3748i) q^{52} -474.224i q^{53} -185.877i q^{55} +(155.863 + 28.1907i) q^{56} +(-246.076 + 372.948i) q^{58} -686.007 q^{59} +117.140 q^{61} +(-24.6577 + 37.3707i) q^{62} +(-479.563 - 179.343i) q^{64} +28.3790i q^{65} -421.362i q^{67} +(94.3106 - 40.3538i) q^{68} +(-141.515 - 93.3735i) q^{70} +5.74597 q^{71} +1017.59 q^{73} +(33.7547 + 22.2718i) q^{74} +(57.1162 - 24.4390i) q^{76} +151.944i q^{77} -683.881i q^{79} +(396.422 + 378.426i) q^{80} +(-739.683 + 1121.05i) q^{82} +130.643 q^{83} -109.804 q^{85} +(-584.936 + 886.516i) q^{86} +(87.4168 - 483.316i) q^{88} +205.662i q^{89} -23.1983i q^{91} +(235.937 + 551.406i) q^{92} +(604.819 + 399.068i) q^{94} -66.4991 q^{95} +1718.32 q^{97} +(115.681 + 76.3279i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.36083	−	1.55771i	−0.834681	−	0.550734i
$2$	−2.36083	−	1.55771i	−0.834681	−	0.550734i
$3$		0			0
$3$		0			0
$4$	3.14707	+	7.35499i	0.393384	+	0.919374i
$5$		−	8.56325i		−	0.765920i	−0.923765	−	0.382960i	$-0.874905\pi$
$5$		−	8.56325i		−	0.765920i	0.923765	−	0.382960i	$-0.125095\pi$
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$	4.02725	−	22.2661i	0.177981	−	0.984034i
$9$		0			0
$10$	−13.3391	+	20.2164i	−0.421818	+	0.639299i
$11$	21.7063			0.594973			0.297487	−	0.954726i	$-0.403852\pi$
$11$	21.7063			0.594973			0.297487	+	0.954726i	$0.403852\pi$
$12$		0			0
$13$	−3.31405			−0.0707040			−0.0353520	−	0.999375i	$-0.511255\pi$
$13$	−3.31405			−0.0707040			−0.0353520	+	0.999375i	$0.511255\pi$
$14$	10.9040	−	16.5258i	0.208158	−	0.315480i
$15$		0			0
$16$	−44.1919	+	46.2934i	−0.690498	+	0.723334i
$17$		−	12.8227i		−	0.182938i	−0.995808	−	0.0914692i	$-0.970844\pi$
$17$		−	12.8227i		−	0.182938i	0.995808	−	0.0914692i	$-0.0291563\pi$
$18$		0			0
$19$		−	7.76564i		−	0.0937663i	−0.998900	−	0.0468831i	$-0.985071\pi$
$19$		−	7.76564i		−	0.0937663i	0.998900	−	0.0468831i	$-0.0149288\pi$
$20$	62.9827	−	26.9492i	0.704168	−	0.301301i
$21$		0			0
$22$	−51.2450	−	33.8122i	−0.496613	−	0.327672i
$23$	74.9703			0.679669			0.339834	−	0.940485i	$-0.389629\pi$
$23$	74.9703			0.679669			0.339834	+	0.940485i	$0.389629\pi$
$24$		0			0
$25$	51.6707			0.413366
$26$	7.82392	+	5.16233i	0.0590152	+	0.0389391i
$27$		0			0
$28$	−51.4850	+	22.0295i	−0.347491	+	0.148685i
$29$		−	157.973i		−	1.01155i	−0.862667	−	0.505773i	$-0.831207\pi$
$29$		−	157.973i		−	1.01155i	0.862667	−	0.505773i	$-0.168793\pi$
$30$		0			0
$31$		−	15.8295i		−	0.0917114i	−0.998948	−	0.0458557i	$-0.985399\pi$
$31$		−	15.8295i		−	0.0917114i	0.998948	−	0.0458557i	$-0.0146014\pi$
$32$	176.441	−	40.4527i	0.974710	−	0.223472i
$33$		0			0
$34$	−19.9740	+	30.2722i	−0.100750	+	0.152695i
$35$	59.9428			0.289491
$36$		0			0
$37$	−14.2978			−0.0635281			−0.0317641	−	0.999495i	$-0.510113\pi$
$37$	−14.2978			−0.0635281			−0.0317641	+	0.999495i	$0.510113\pi$
$38$	−12.0966	+	18.3334i	−0.0516403	+	0.0782649i
$39$		0			0
$40$	−190.671	−	34.4863i	−0.753692	−	0.136319i
$41$		−	474.853i		−	1.80877i	−0.426719	−	0.904384i	$-0.640331\pi$
$41$		−	474.853i		−	1.80877i	0.426719	−	0.904384i	$-0.359669\pi$
$42$		0			0
$43$		−	375.510i		−	1.33174i	−0.746069	−	0.665869i	$-0.768061\pi$
$43$		−	375.510i		−	1.33174i	0.746069	−	0.665869i	$-0.231939\pi$
$44$	68.3114	+	159.650i	0.234053	+	0.547003i
$45$		0			0
$46$	−176.992	−	116.782i	−0.567306	−	0.374317i
$47$	−256.189			−0.795085			−0.397542	−	0.917584i	$-0.630137\pi$
$47$	−256.189			−0.795085			−0.397542	+	0.917584i	$0.630137\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$	−121.986	−	80.4881i	−0.345029	−	0.227655i
$51$		0			0
$52$	−10.4295	−	24.3748i	−0.0278138	−	0.0650034i
$53$		−	474.224i		−	1.22905i	−0.788897	−	0.614526i	$-0.789347\pi$
$53$		−	474.224i		−	1.22905i	0.788897	−	0.614526i	$-0.210653\pi$
$54$		0			0
$55$		−	185.877i		−	0.455702i
$56$	155.863	+	28.1907i	0.371930	+	0.0672705i
$57$		0			0
$58$	−246.076	+	372.948i	−0.557093	+	0.844318i
$59$	−686.007			−1.51374			−0.756869	−	0.653567i	$-0.773272\pi$
$59$	−686.007			−1.51374			−0.756869	+	0.653567i	$0.773272\pi$
$60$		0			0
$61$	117.140			0.245873			0.122936	−	0.992415i	$-0.460769\pi$
$61$	117.140			0.245873			0.122936	+	0.992415i	$0.460769\pi$
$62$	−24.6577	+	37.3707i	−0.0505086	+	0.0765498i
$63$		0			0
$64$	−479.563	−	179.343i	−0.936646	−	0.350279i
$65$			28.3790i			0.0541536i
$66$		0			0
$67$		−	421.362i		−	0.768322i	−0.923266	−	0.384161i	$-0.874491\pi$
$67$		−	421.362i		−	0.768322i	0.923266	−	0.384161i	$-0.125509\pi$
$68$	94.3106	−	40.3538i	0.168189	−	0.0719650i
$69$		0			0
$70$	−141.515	−	93.3735i	−0.241632	−	0.159432i
$71$	5.74597			0.00960453			0.00480226	−	0.999988i	$-0.498471\pi$
$71$	5.74597			0.00960453			0.00480226	+	0.999988i	$0.498471\pi$
$72$		0			0
$73$	1017.59			1.63151			0.815757	−	0.578395i	$-0.196321\pi$
$73$	1017.59			1.63151			0.815757	+	0.578395i	$0.196321\pi$
$74$	33.7547	+	22.2718i	0.0530257	+	0.0349871i
$75$		0			0
$76$	57.1162	−	24.4390i	0.0862063	−	0.0368861i
$77$			151.944i			0.224879i
$78$		0			0
$79$		−	683.881i		−	0.973957i	−0.873414	−	0.486979i	$-0.838099\pi$
$79$		−	683.881i		−	0.973957i	0.873414	−	0.486979i	$-0.161901\pi$
$80$	396.422	+	378.426i	0.554016	+	0.528867i
$81$		0			0
$82$	−739.683	+	1121.05i	−0.996151	+	1.50974i
$83$	130.643			0.172771			0.0863853	−	0.996262i	$-0.472468\pi$
$83$	130.643			0.172771			0.0863853	+	0.996262i	$0.472468\pi$
$84$		0			0
$85$	−109.804			−0.140116
$86$	−584.936	+	886.516i	−0.733433	+	1.11158i
$87$		0			0
$88$	87.4168	−	483.316i	0.105894	−	0.585474i
$89$			205.662i			0.244945i	0.992472	+	0.122473i	$0.0390824\pi$
$89$			205.662i			0.244945i	−0.992472	+	0.122473i	$0.960918\pi$
$90$		0			0
$91$		−	23.1983i		−	0.0267236i
$92$	235.937	+	551.406i	0.267371	+	0.624870i
$93$		0			0
$94$	604.819	+	399.068i	0.663642	+	0.437880i
$95$	−66.4991			−0.0718175
$96$		0			0
$97$	1718.32			1.79865			0.899325	−	0.437281i	$-0.144059\pi$
$97$	1718.32			1.79865			0.899325	+	0.437281i	$0.144059\pi$
$98$	115.681	+	76.3279i	0.119240	+	0.0786763i
$99$		0			0
$100$	162.611	+	380.038i	0.162611	+	0.380038i
$101$			749.578i			0.738473i	0.929335	+	0.369237i	$0.120381\pi$
$101$			749.578i			0.738473i	−0.929335	+	0.369237i	$0.879619\pi$
$102$		0			0
$103$			1309.32i			1.25254i	0.779608	+	0.626268i	$0.215418\pi$
$103$			1309.32i			1.25254i	−0.779608	+	0.626268i	$0.784582\pi$
$104$	−13.3465	+	73.7911i	−0.0125840	+	0.0695751i
$105$		0			0
$106$	−738.705	+	1119.57i	−0.676881	+	1.02587i
$107$	808.026			0.730045			0.365022	−	0.930999i	$-0.381061\pi$
$107$	808.026			0.730045			0.365022	+	0.930999i	$0.381061\pi$
$108$		0			0
$109$	1970.84			1.73185			0.865927	−	0.500171i	$-0.166730\pi$
$109$	1970.84			1.73185			0.865927	+	0.500171i	$0.166730\pi$
$110$	−289.542	+	438.824i	−0.250971	+	0.380366i
$111$		0			0
$112$	−324.054	−	309.343i	−0.273395	−	0.260984i
$113$		−	54.0014i		−	0.0449560i	−0.999747	−	0.0224780i	$-0.992844\pi$
$113$		−	54.0014i		−	0.0449560i	0.999747	−	0.0224780i	$-0.00715557\pi$
$114$		0			0
$115$		−	641.989i		−	0.520572i
$116$	1161.89	−	497.152i	0.929989	−	0.397926i
$117$		0			0
$118$	1619.55	+	1068.60i	1.26349	+	0.833667i
$119$	89.7586			0.0691442
$120$		0			0
$121$	−859.835			−0.646007
$122$	−276.548	−	182.470i	−0.205225	−	0.135411i
$123$		0			0
$124$	116.426	−	49.8164i	0.0843171	−	0.0360778i
$125$		−	1512.88i		−	1.08253i
$126$		0			0
$127$			2081.11i			1.45408i	0.686593	+	0.727042i	$0.259105\pi$
$127$			2081.11i			1.45408i	−0.686593	+	0.727042i	$0.740895\pi$
$128$	852.803	+	1170.42i	0.588890	+	0.808213i
$129$		0			0
$130$	44.2063	−	66.9982i	0.0298242	−	0.0452010i
$131$	−2793.54			−1.86315			−0.931574	−	0.363552i	$-0.881564\pi$
$131$	−2793.54			−1.86315			−0.931574	+	0.363552i	$0.881564\pi$
$132$		0			0
$133$	54.3594			0.0354403
$134$	−656.361	+	994.766i	−0.423141	+	0.641304i
$135$		0			0
$136$	−285.511	−	51.6400i	−0.180018	−	0.0325595i
$137$			1023.91i			0.638526i	0.947666	+	0.319263i	$0.103435\pi$
$137$			1023.91i			0.638526i	−0.947666	+	0.319263i	$0.896565\pi$
$138$		0			0
$139$		−	405.581i		−	0.247489i	−0.992314	−	0.123744i	$-0.960510\pi$
$139$		−	405.581i		−	0.247489i	0.992314	−	0.123744i	$-0.0394903\pi$
$140$	188.644	+	440.879i	0.113881	+	0.266150i
$141$		0			0
$142$	−13.5653	−	8.95057i	−0.00801671	−	0.00528954i
$143$	−71.9358			−0.0420670
$144$		0			0
$145$	−1352.76			−0.774764
$146$	−2402.37	−	1585.12i	−1.36179	−	0.898530i
$147$		0			0
$148$	−44.9961	−	105.160i	−0.0249909	−	0.0584061i
$149$			1155.02i			0.635055i	0.948249	+	0.317527i	$0.102853\pi$
$149$			1155.02i			0.635055i	−0.948249	+	0.317527i	$0.897147\pi$
$150$		0			0
$151$			257.997i			0.139043i	0.997580	+	0.0695215i	$0.0221473\pi$
$151$			257.997i			0.139043i	−0.997580	+	0.0695215i	$0.977853\pi$
$152$	−172.911	−	31.2741i	−0.0922692	−	0.0166886i
$153$		0			0
$154$	236.685	−	358.715i	0.123848	−	0.187702i
$155$	−135.552			−0.0702436
$156$		0			0
$157$	−1371.20			−0.697032			−0.348516	−	0.937303i	$-0.613314\pi$
$157$	−1371.20			−0.697032			−0.348516	+	0.937303i	$0.613314\pi$
$158$	−1065.29	+	1614.53i	−0.536391	+	0.812943i
$159$		0			0
$160$	−346.407	−	1510.91i	−0.171162	−	0.746551i
$161$			524.792i			0.256891i
$162$		0			0
$163$		−	2172.16i		−	1.04378i	−0.853012	−	0.521891i	$-0.825227\pi$
$163$		−	2172.16i		−	1.04378i	0.853012	−	0.521891i	$-0.174773\pi$
$164$	3492.54	−	1494.39i	1.66294	−	0.711540i
$165$		0			0
$166$	−308.427	−	203.504i	−0.144208	−	0.0951507i
$167$	−1007.38			−0.466789			−0.233394	−	0.972382i	$-0.574983\pi$
$167$	−1007.38			−0.466789			−0.233394	+	0.972382i	$0.574983\pi$
$168$		0			0
$169$	−2186.02			−0.995001
$170$	259.228	+	171.042i	0.116952	+	0.0771668i
$171$		0			0
$172$	2761.87	−	1181.76i	1.22437	−	0.523884i
$173$		−	612.490i		−	0.269172i	−0.990902	−	0.134586i	$-0.957030\pi$
$173$		−	612.490i		−	0.269172i	0.990902	−	0.134586i	$-0.0429704\pi$
$174$		0			0
$175$			361.695i			0.156238i
$176$	−959.244	+	1004.86i	−0.410828	+	0.430364i
$177$		0			0
$178$	320.362	−	485.534i	0.134900	−	0.204451i
$179$	3594.73			1.50102			0.750511	−	0.660858i	$-0.229807\pi$
$179$	3594.73			1.50102			0.750511	+	0.660858i	$0.229807\pi$
$180$		0			0
$181$	1483.03			0.609020			0.304510	−	0.952509i	$-0.401507\pi$
$181$	1483.03			0.609020			0.304510	+	0.952509i	$0.401507\pi$
$182$	−36.1363	+	54.7674i	−0.0147176	+	0.0223057i
$183$		0			0
$184$	301.924	−	1669.30i	0.120968	−	0.668817i
$185$			122.435i			0.0486575i
$186$		0			0
$187$		−	278.333i		−	0.108843i
$188$	−806.244	−	1884.27i	−0.312773	−	0.730980i
$189$		0			0
$190$	156.993	+	103.586i	0.0599447	+	0.0395523i
$191$	2378.27			0.900973			0.450487	−	0.892783i	$-0.351251\pi$
$191$	2378.27			0.900973			0.450487	+	0.892783i	$0.351251\pi$
$192$		0			0
$193$	389.891			0.145414			0.0727072	−	0.997353i	$-0.476836\pi$
$193$	389.891			0.145414			0.0727072	+	0.997353i	$0.476836\pi$
$194$	−4056.67	−	2676.65i	−1.50130	−	0.990578i
$195$		0			0
$196$	−154.206	−	360.395i	−0.0561977	−	0.131339i
$197$			660.622i			0.238921i	0.992839	+	0.119460i	$0.0381164\pi$
$197$			660.622i			0.238921i	−0.992839	+	0.119460i	$0.961884\pi$
$198$		0			0
$199$		−	3198.43i		−	1.13935i	−0.821870	−	0.569675i	$-0.807069\pi$
$199$		−	3198.43i		−	1.13935i	0.821870	−	0.569675i	$-0.192931\pi$
$200$	208.091	−	1150.51i	0.0735713	−	0.406766i
$201$		0			0
$202$	1167.63	−	1769.63i	0.406703	−	0.616390i
$203$	1105.81			0.382328
$204$		0			0
$205$	−4066.28			−1.38537
$206$	2039.54	−	3091.09i	0.689814	−	1.04547i
$207$		0			0
$208$	146.454	−	153.418i	0.0488210	−	0.0511426i
$209$		−	168.563i		−	0.0557884i
$210$		0			0
$211$			3398.47i			1.10882i	0.832245	+	0.554408i	$0.187055\pi$
$211$			3398.47i			1.10882i	−0.832245	+	0.554408i	$0.812945\pi$
$212$	3487.92	−	1492.42i	1.12996	−	0.483489i
$213$		0			0
$214$	−1907.61	−	1258.67i	−0.609354	−	0.402061i
$215$	−3215.59			−1.02001
$216$		0			0
$217$	110.806			0.0346637
$218$	−4652.82	−	3070.00i	−1.44554	−	0.953791i
$219$		0			0
$220$	1367.12	−	584.967i	0.418961	−	0.179266i
$221$			42.4949i			0.0129345i
$222$		0			0
$223$			3400.30i			1.02108i	0.859854	+	0.510541i	$0.170555\pi$
$223$			3400.30i			1.02108i	−0.859854	+	0.510541i	$0.829445\pi$
$224$	283.169	+	1235.09i	0.0844645	+	0.368406i
$225$		0			0
$226$	−84.1186	+	127.488i	−0.0247588	+	0.0375239i
$227$	5000.48			1.46209			0.731044	−	0.682331i	$-0.239034\pi$
$227$	5000.48			1.46209			0.731044	+	0.682331i	$0.239034\pi$
$228$		0			0
$229$	−4697.69			−1.35560			−0.677799	−	0.735247i	$-0.737066\pi$
$229$	−4697.69			−1.35560			−0.677799	+	0.735247i	$0.737066\pi$
$230$	−1000.03	+	1515.63i	−0.286697	+	0.434512i
$231$		0			0
$232$	−3517.45	−	636.196i	−0.995395	−	0.180036i
$233$			1158.63i			0.325771i	0.986645	+	0.162886i	$0.0520801\pi$
$233$			1158.63i			0.325771i	−0.986645	+	0.162886i	$0.947920\pi$
$234$		0			0
$235$			2193.81i			0.608972i
$236$	−2158.91	−	5045.58i	−0.595480	−	1.39169i
$237$		0			0
$238$	−211.905	−	139.818i	−0.0577133	−	0.0380801i
$239$	−1176.49			−0.318413			−0.159206	−	0.987245i	$-0.550894\pi$
$239$	−1176.49			−0.318413			−0.159206	+	0.987245i	$0.550894\pi$
$240$		0			0
$241$	−5943.22			−1.58853			−0.794266	−	0.607570i	$-0.792144\pi$
$241$	−5943.22			−1.58853			−0.794266	+	0.607570i	$0.792144\pi$
$242$	2029.93	+	1339.38i	0.539210	+	0.355778i
$243$		0			0
$244$	368.648	+	861.565i	0.0967224	+	0.226049i
$245$			419.599i			0.109417i
$246$		0			0
$247$			25.7357i			0.00662965i
$248$	−352.461	−	63.7492i	−0.0902472	−	0.0163229i
$249$		0			0
$250$	−2356.62	+	3571.65i	−0.596184	+	0.903563i
$251$	1088.50			0.273727			0.136864	−	0.990590i	$-0.456298\pi$
$251$	1088.50			0.273727			0.136864	+	0.990590i	$0.456298\pi$
$252$		0			0
$253$	1627.33			0.404385
$254$	3241.77	−	4913.15i	0.800813	−	1.21370i
$255$		0			0
$256$	−190.153	−	4091.58i	−0.0464242	−	0.998922i
$257$		−	2811.53i		−	0.682406i	−0.939990	−	0.341203i	$-0.889166\pi$
$257$		−	2811.53i		−	0.682406i	0.939990	−	0.341203i	$-0.110834\pi$
$258$		0			0
$259$		−	100.084i		−	0.0240114i
$260$	−208.728	+	89.3108i	−0.0497874	+	0.0213032i
$261$		0			0
$262$	6595.07	+	4351.52i	1.55513	+	1.02610i
$263$	3457.24			0.810580			0.405290	−	0.914188i	$-0.367170\pi$
$263$	3457.24			0.810580			0.405290	+	0.914188i	$0.367170\pi$
$264$		0			0
$265$	−4060.90			−0.941356
$266$	−128.334	−	84.6763i	−0.0295813	−	0.0195182i
$267$		0			0
$268$	3099.12	−	1326.06i	0.706376	−	0.302246i
$269$			990.668i			0.224543i	0.993678	+	0.112272i	$0.0358127\pi$
$269$			990.668i			0.224543i	−0.993678	+	0.112272i	$0.964187\pi$
$270$		0			0
$271$			6503.15i			1.45771i	0.684671	+	0.728853i	$0.259946\pi$
$271$			6503.15i			1.45771i	−0.684671	+	0.728853i	$0.740054\pi$
$272$	593.604	+	566.658i	0.132326	+	0.126319i
$273$		0			0
$274$	1594.95	−	2417.27i	0.351658	−	0.532966i
$275$	1121.58			0.245942
$276$		0			0
$277$	−1367.72			−0.296673			−0.148336	−	0.988937i	$-0.547392\pi$
$277$	−1367.72			−0.296673			−0.148336	+	0.988937i	$0.547392\pi$
$278$	−631.779	+	957.510i	−0.136301	+	0.206574i
$279$		0			0
$280$	241.404	−	1334.69i	0.0515238	−	0.284869i
$281$		−	2042.82i		−	0.433682i	−0.976207	−	0.216841i	$-0.930425\pi$
$281$		−	2042.82i		−	0.433682i	0.976207	−	0.216841i	$-0.0695753\pi$
$282$		0			0
$283$		−	8663.31i		−	1.81972i	−0.414917	−	0.909859i	$-0.636190\pi$
$283$		−	8663.31i		−	1.81972i	0.414917	−	0.909859i	$-0.363810\pi$
$284$	18.0830	+	42.2616i	0.00377827	+	0.00883016i
$285$		0			0
$286$	169.829	+	112.055i	0.0351125	+	0.0231677i
$287$	3323.97			0.683650
$288$		0			0
$289$	4748.58			0.966534
$290$	3193.64	+	2107.21i	0.646680	+	0.426689i
$291$		0			0
$292$	3202.44	+	7484.40i	0.641811	+	1.49997i
$293$			1375.01i			0.274161i	0.990560	+	0.137081i	$0.0437719\pi$
$293$			1375.01i			0.274161i	−0.990560	+	0.137081i	$0.956228\pi$
$294$		0			0
$295$			5874.45i			1.15940i
$296$	−57.5807	+	318.356i	−0.0113068	+	0.0625138i
$297$		0			0
$298$	1799.19	−	2726.82i	0.349746	−	0.530068i
$299$	−248.455			−0.0480553
$300$		0			0
$301$	2628.57			0.503350
$302$	401.885	−	609.088i	0.0765757	−	0.116057i
$303$		0			0
$304$	359.497	+	343.178i	0.0678243	+	0.0647454i
$305$		−	1003.10i		−	0.188319i
$306$		0			0
$307$			8491.74i			1.57866i	0.613968	+	0.789331i	$0.289572\pi$
$307$			8491.74i			1.57866i	−0.613968	+	0.789331i	$0.710428\pi$
$308$	−1117.55	+	478.179i	−0.206748	+	0.0884637i
$309$		0			0
$310$	320.015	+	211.150i	0.0586310	+	0.0386856i
$311$	−9308.50			−1.69722			−0.848612	−	0.529016i	$-0.822561\pi$
$311$	−9308.50			−1.69722			−0.848612	+	0.529016i	$0.822561\pi$
$312$		0			0
$313$	−2023.27			−0.365373			−0.182687	−	0.983171i	$-0.558479\pi$
$313$	−2023.27			−0.365373			−0.182687	+	0.983171i	$0.558479\pi$
$314$	3237.19	+	2135.94i	0.581799	+	0.383879i
$315$		0			0
$316$	5029.94	−	2152.22i	0.895431	−	0.383139i
$317$			8609.66i			1.52545i	0.646725	+	0.762724i	$0.276138\pi$
$317$			8609.66i			1.52545i	−0.646725	+	0.762724i	$0.723862\pi$
$318$		0			0
$319$		−	3429.01i		−	0.601843i
$320$	−1535.76	+	4106.61i	−0.268285	+	0.717396i
$321$		0			0
$322$	817.474	−	1238.95i	0.141478	−	0.214422i
$323$	−99.5761			−0.0171534
$324$		0			0
$325$	−171.239			−0.0292266
$326$	−3383.59	+	5128.10i	−0.574846	+	0.871225i
$327$		0			0
$328$	−10573.1	−	1912.35i	−1.77989	−	0.321926i
$329$		−	1793.32i		−	0.300514i
$330$		0			0
$331$		−	6708.22i		−	1.11395i	−0.830530	−	0.556974i	$-0.811962\pi$
$331$		−	6708.22i		−	1.11395i	0.830530	−	0.556974i	$-0.188038\pi$
$332$	411.144	+	960.881i	0.0679652	+	0.158841i
$333$		0			0
$334$	2378.27	+	1569.21i	0.389620	+	0.257076i
$335$	−3608.23			−0.588474
$336$		0			0
$337$	8360.58			1.35142			0.675712	−	0.737166i	$-0.263836\pi$
$337$	8360.58			1.35142			0.675712	+	0.737166i	$0.263836\pi$
$338$	5160.82	+	3405.18i	0.830508	+	0.547981i
$339$		0			0
$340$	−345.560	−	807.605i	−0.0551195	−	0.128819i
$341$		−	343.599i		−	0.0545658i
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$	−8361.16	−	1512.27i	−1.31048	−	0.237024i
$345$		0			0
$346$	−954.082	+	1445.99i	−0.148242	+	0.224673i
$347$	9630.65			1.48991			0.744957	−	0.667112i	$-0.232470\pi$
$347$	9630.65			1.48991			0.744957	+	0.667112i	$0.232470\pi$
$348$		0			0
$349$	−3239.64			−0.496888			−0.248444	−	0.968646i	$-0.579919\pi$
$349$	−3239.64			−0.496888			−0.248444	+	0.968646i	$0.579919\pi$
$350$	563.417	−	853.902i	0.0860454	−	0.130409i
$351$		0			0
$352$	3829.90	−	878.081i	0.579926	−	0.132960i
$353$			12900.6i			1.94513i	0.232630	+	0.972565i	$0.425267\pi$
$353$			12900.6i			1.94513i	−0.232630	+	0.972565i	$0.574733\pi$
$354$		0			0
$355$		−	49.2042i		−	0.00735630i
$356$	−1512.64	+	647.233i	−0.225196	+	0.0963575i
$357$		0			0
$358$	−8486.57	−	5599.56i	−1.25287	−	0.826664i
$359$	−11843.3			−1.74113			−0.870566	−	0.492051i	$-0.836247\pi$
$359$	−11843.3			−1.74113			−0.870566	+	0.492051i	$0.836247\pi$
$360$		0			0
$361$	6798.69			0.991208
$362$	−3501.18	−	2310.13i	−0.508337	−	0.335408i
$363$		0			0
$364$	170.624	−	73.0068i	0.0245690	−	0.0105126i
$365$		−	8713.92i		−	1.24961i
$366$		0			0
$367$		−	8206.96i		−	1.16730i	−0.812004	−	0.583651i	$-0.801624\pi$
$367$		−	8206.96i		−	1.16730i	0.812004	−	0.583651i	$-0.198376\pi$
$368$	−3313.08	+	3470.63i	−0.469310	+	0.491628i
$369$		0			0
$370$	190.719	−	289.050i	0.0267973	−	0.0406135i
$371$	3319.57			0.464538
$372$		0			0
$373$	6418.80			0.891026			0.445513	−	0.895275i	$-0.353021\pi$
$373$	6418.80			0.891026			0.445513	+	0.895275i	$0.353021\pi$
$374$	−433.562	+	657.098i	−0.0599438	+	0.0908495i
$375$		0			0
$376$	−1031.74	+	5704.34i	−0.141510	+	0.782390i
$377$			523.530i			0.0715203i
$378$		0			0
$379$		−	1827.59i		−	0.247697i	−0.992301	−	0.123848i	$-0.960476\pi$
$379$		−	1827.59i		−	0.247697i	0.992301	−	0.123848i	$-0.0395236\pi$
$380$	−209.277	−	489.100i	−0.0282518	−	0.0660272i
$381$		0			0
$382$	−5614.71	−	3704.66i	−0.752025	−	0.496197i
$383$	−13728.0			−1.83151			−0.915754	−	0.401740i	$-0.868406\pi$
$383$	−13728.0			−1.83151			−0.915754	+	0.401740i	$0.868406\pi$
$384$		0			0
$385$	1301.14			0.172239
$386$	−920.468	−	607.338i	−0.121375	−	0.0800846i
$387$		0			0
$388$	5407.68	+	12638.2i	0.707560	+	1.65363i
$389$			3109.11i			0.405240i	0.979257	+	0.202620i	$0.0649456\pi$
$389$			3109.11i			0.405240i	−0.979257	+	0.202620i	$0.935054\pi$
$390$		0			0
$391$		−	961.318i		−	0.124337i
$392$	−197.335	+	1091.04i	−0.0254258	+	0.140576i
$393$		0			0
$394$	1029.06	−	1559.62i	0.131582	−	0.199422i
$395$	−5856.24			−0.745974
$396$		0			0
$397$	7636.17			0.965362			0.482681	−	0.875796i	$-0.339663\pi$
$397$	7636.17			0.965362			0.482681	+	0.875796i	$0.339663\pi$
$398$	−4982.23	+	7550.96i	−0.627479	+	0.950994i
$399$		0			0
$400$	−2283.43	+	2392.01i	−0.285429	+	0.299002i
$401$		−	1066.34i		−	0.132795i	−0.997793	−	0.0663973i	$-0.978850\pi$
$401$		−	1066.34i		−	0.132795i	0.997793	−	0.0663973i	$-0.0211505\pi$
$402$		0			0
$403$			52.4596i			0.00648436i
$404$	−5513.14	+	2358.98i	−0.678934	+	0.290504i
$405$		0			0
$406$	−2610.63	−	1722.53i	−0.319122	−	0.210561i
$407$	−310.352			−0.0377975
$408$		0			0
$409$	−5811.87			−0.702637			−0.351318	−	0.936256i	$-0.614266\pi$
$409$	−5811.87			−0.702637			−0.351318	+	0.936256i	$0.614266\pi$
$410$	9599.82	+	6334.09i	1.15634	+	0.762972i
$411$		0			0
$412$	−9630.04	+	4120.52i	−1.15155	+	0.492727i
$413$		−	4802.05i		−	0.572139i
$414$		0			0
$415$		−	1118.73i		−	0.132329i
$416$	−584.735	+	134.062i	−0.0689159	+	0.0158004i
$417$		0			0
$418$	−262.573	+	397.950i	−0.0307246	+	0.0465655i
$419$	10409.1			1.21365			0.606823	−	0.794837i	$-0.292444\pi$
$419$	10409.1			1.21365			0.606823	+	0.794837i	$0.292444\pi$
$420$		0			0
$421$	6356.26			0.735832			0.367916	−	0.929859i	$-0.380071\pi$
$421$	6356.26			0.735832			0.367916	+	0.929859i	$0.380071\pi$
$422$	5293.83	−	8023.22i	0.610663	−	0.925508i
$423$		0			0
$424$	−10559.2	−	1909.82i	−1.20943	−	0.218748i
$425$		−	662.556i		−	0.0756205i
$426$		0			0
$427$			819.981i			0.0929312i
$428$	2542.91	+	5943.03i	0.287188	+	0.671185i
$429$		0			0
$430$	7591.46	+	5008.95i	0.851379	+	0.561752i
$431$	1336.06			0.149317			0.0746587	−	0.997209i	$-0.476213\pi$
$431$	1336.06			0.149317			0.0746587	+	0.997209i	$0.476213\pi$
$432$		0			0
$433$	6983.41			0.775061			0.387530	−	0.921857i	$-0.373328\pi$
$433$	6983.41			0.775061			0.387530	+	0.921857i	$0.373328\pi$
$434$	−261.595	−	172.604i	−0.0289331	−	0.0190905i
$435$		0			0
$436$	6202.37	+	14495.5i	0.681283	+	1.59222i
$437$		−	582.192i		−	0.0637300i
$438$		0			0
$439$		−	10153.6i		−	1.10388i	−0.833884	−	0.551940i	$-0.813888\pi$
$439$		−	10153.6i		−	1.10388i	0.833884	−	0.551940i	$-0.186112\pi$
$440$	−4138.76	−	748.572i	−0.448426	−	0.0811063i
$441$		0			0
$442$	66.1948	−	100.323i	0.00712345	−	0.0107962i
$443$	−1063.08			−0.114015			−0.0570073	−	0.998374i	$-0.518156\pi$
$443$	−1063.08			−0.114015			−0.0570073	+	0.998374i	$0.518156\pi$
$444$		0			0
$445$	1761.13			0.187609
$446$	5296.69	−	8027.55i	0.562345	−	0.852277i
$447$		0			0
$448$	1255.40	−	3356.94i	0.132393	−	0.354019i
$449$		−	11281.8i		−	1.18579i	−0.805278	−	0.592897i	$-0.797984\pi$
$449$		−	11281.8i		−	1.18579i	0.805278	−	0.592897i	$-0.202016\pi$
$450$		0			0
$451$		−	10307.3i		−	1.07617i
$452$	397.180	−	169.946i	0.0413314	−	0.0176849i
$453$		0			0
$454$	−11805.3	−	7789.31i	−1.22038	−	0.805221i
$455$	−198.653			−0.0204681
$456$		0			0
$457$	3258.29			0.333515			0.166758	−	0.985998i	$-0.446670\pi$
$457$	3258.29			0.333515			0.166758	+	0.985998i	$0.446670\pi$
$458$	11090.5	+	7317.65i	1.13149	+	0.746574i
$459$		0			0
$460$	4721.83	−	2020.39i	0.478601	−	0.204785i
$461$			6599.89i			0.666785i	0.942788	+	0.333392i	$0.108193\pi$
$461$			6599.89i			0.666785i	−0.942788	+	0.333392i	$0.891807\pi$
$462$		0			0
$463$			11380.8i			1.14236i	0.820826	+	0.571178i	$0.193513\pi$
$463$			11380.8i			1.14236i	−0.820826	+	0.571178i	$0.806487\pi$
$464$	7313.10	+	6981.12i	0.731686	+	0.698471i
$465$		0			0
$466$	1804.82	−	2735.34i	0.179413	−	0.271915i
$467$	−1789.46			−0.177316			−0.0886579	−	0.996062i	$-0.528258\pi$
$467$	−1789.46			−0.177316			−0.0886579	+	0.996062i	$0.528258\pi$
$468$		0			0
$469$	2949.54			0.290399
$470$	3417.32	−	5179.22i	0.335381	−	0.508297i
$471$		0			0
$472$	−2762.72	+	15274.7i	−0.269416	+	1.48957i
$473$		−	8150.94i		−	0.792348i
$474$		0			0
$475$		−	401.256i		−	0.0387598i
$476$	282.477	+	660.174i	0.0272002	+	0.0635694i
$477$		0			0
$478$	2777.49	+	1832.63i	0.265773	+	0.175361i
$479$	−6479.26			−0.618048			−0.309024	−	0.951054i	$-0.600002\pi$
$479$	−6479.26			−0.618048			−0.309024	+	0.951054i	$0.600002\pi$
$480$		0			0
$481$	47.3835			0.00449169
$482$	14030.9	+	9257.82i	1.32592	+	0.874859i
$483$		0			0
$484$	−2705.96	−	6324.08i	−0.254129	−	0.593922i
$485$		−	14714.4i		−	1.37762i
$486$		0			0
$487$			19022.5i			1.77000i	0.465588	+	0.885001i	$0.345843\pi$
$487$			19022.5i			1.77000i	−0.465588	+	0.885001i	$0.654157\pi$
$488$	471.752	−	2608.26i	0.0437607	−	0.241947i
$489$		0			0
$490$	653.615	−	990.604i	0.0602598	−	0.0913284i
$491$	13556.9			1.24606			0.623028	−	0.782200i	$-0.285902\pi$
$491$	13556.9			1.24606			0.623028	+	0.782200i	$0.285902\pi$
$492$		0			0
$493$	−2025.63			−0.185051
$494$	40.0888	−	60.7577i	0.00365117	−	0.00553364i
$495$		0			0
$496$	732.799	+	699.534i	0.0663380	+	0.0633266i
$497$			40.2218i			0.00363017i
$498$		0			0
$499$		−	12509.6i		−	1.12226i	−0.827729	−	0.561128i	$-0.810367\pi$
$499$		−	12509.6i		−	1.12226i	0.827729	−	0.561128i	$-0.189633\pi$
$500$	11127.2	−	4761.13i	0.995246	−	0.425848i
$501$		0			0
$502$	−2569.77	−	1695.57i	−0.228475	−	0.150751i
$503$	−7190.02			−0.637350			−0.318675	−	0.947864i	$-0.603238\pi$
$503$	−7190.02			−0.637350			−0.318675	+	0.947864i	$0.603238\pi$
$504$		0			0
$505$	6418.83			0.565612
$506$	−3841.85	−	2534.91i	−0.337532	−	0.222708i
$507$		0			0
$508$	−15306.5	+	6549.40i	−1.33685	+	0.572013i
$509$		−	15811.6i		−	1.37689i	−0.725289	−	0.688445i	$-0.758294\pi$
$509$		−	15811.6i		−	1.37689i	0.725289	−	0.688445i	$-0.241706\pi$
$510$		0			0
$511$			7123.16i			0.616654i
$512$	−5924.59	+	9955.75i	−0.511391	+	0.859348i
$513$		0			0
$514$	−4379.55	+	6637.55i	−0.375824	+	0.569591i
$515$	11212.0			0.959342
$516$		0			0
$517$	−5560.92			−0.473054
$518$	−155.903	+	236.283i	−0.0132239	+	0.0200418i
$519$		0			0
$520$	631.892	+	114.289i	0.0532890	+	0.00963831i
$521$			3862.04i			0.324758i	0.986728	+	0.162379i	$0.0519168\pi$
$521$			3862.04i			0.324758i	−0.986728	+	0.162379i	$0.948083\pi$
$522$		0			0
$523$		−	10949.7i		−	0.915481i	−0.889086	−	0.457741i	$-0.848659\pi$
$523$		−	10949.7i		−	0.915481i	0.889086	−	0.457741i	$-0.151341\pi$
$524$	−8791.45	−	20546.4i	−0.732932	−	1.71293i
$525$		0			0
$526$	−8161.97	−	5385.38i	−0.676576	−	0.446414i
$527$	−202.976			−0.0167775
$528$		0			0
$529$	−6546.46			−0.538050
$530$	9587.12	+	6325.71i	0.785731	+	0.518437i
$531$		0			0
$532$	171.073	+	399.813i	0.0139416	+	0.0325829i
$533$			1573.68i			0.127887i
$534$		0			0
$535$		−	6919.33i		−	0.559156i
$536$	−9382.11	−	1696.93i	−0.756055	−	0.136747i
$537$		0			0
$538$	1543.17	−	2338.80i	0.123664	−	0.187422i
$539$	−1063.61			−0.0849962
$540$		0			0
$541$	−18128.5			−1.44067			−0.720337	−	0.693624i	$-0.756013\pi$
$541$	−18128.5			−1.44067			−0.720337	+	0.693624i	$0.756013\pi$
$542$	10130.0	−	15352.9i	0.802808	−	1.21672i
$543$		0			0
$544$	−518.712	−	2262.45i	−0.0408816	−	0.178312i
$545$		−	16876.8i		−	1.32646i
$546$		0			0
$547$			7092.15i			0.554366i	0.960817	+	0.277183i	$0.0894009\pi$
$547$			7092.15i			0.554366i	−0.960817	+	0.277183i	$0.910599\pi$
$548$	−7530.82	+	3222.30i	−0.587045	+	0.251186i
$549$		0			0
$550$	−2647.87	−	1747.10i	−0.205283	−	0.135448i
$551$	−1226.76			−0.0948489
$552$		0			0
$553$	4787.17			0.368121
$554$	3228.96	+	2130.51i	0.247627	+	0.163388i
$555$		0			0
$556$	2983.05	−	1276.39i	0.227535	−	0.0973582i
$557$		−	12515.1i		−	0.952028i	−0.879438	−	0.476014i	$-0.842081\pi$
$557$		−	12515.1i		−	0.952028i	0.879438	−	0.476014i	$-0.157919\pi$
$558$		0			0
$559$			1244.46i			0.0941591i
$560$	−2648.98	+	2774.95i	−0.199893	+	0.209398i
$561$		0			0
$562$	−3182.13	+	4822.77i	−0.238844	+	0.361986i
$563$	−10891.8			−0.815337			−0.407668	−	0.913130i	$-0.633658\pi$
$563$	−10891.8			−0.815337			−0.407668	+	0.913130i	$0.633658\pi$
$564$		0			0
$565$	−462.427			−0.0344327
$566$	−13494.9	+	20452.6i	−1.00218	+	1.51888i
$567$		0			0
$568$	23.1405	−	127.941i	0.00170942	−	0.00945118i
$569$			1678.42i			0.123661i	0.998087	+	0.0618305i	$0.0196938\pi$
$569$			1678.42i			0.123661i	−0.998087	+	0.0618305i	$0.980306\pi$
$570$		0			0
$571$		−	1848.25i		−	0.135458i	−0.997704	−	0.0677292i	$-0.978425\pi$
$571$		−	1848.25i		−	0.135458i	0.997704	−	0.0677292i	$-0.0215754\pi$
$572$	−226.387	−	529.088i	−0.0165485	−	0.0386753i
$573$		0			0
$574$	−7847.34	−	5177.78i	−0.570630	−	0.376510i
$575$	3873.77			0.280952
$576$		0			0
$577$	−21166.6			−1.52717			−0.763586	−	0.645706i	$-0.776563\pi$
$577$	−21166.6			−1.52717			−0.763586	+	0.645706i	$0.776563\pi$
$578$	−11210.6	−	7396.92i	−0.806747	−	0.532303i
$579$		0			0
$580$	−4257.24	−	9949.55i	−0.304779	−	0.712298i
$581$			914.503i			0.0653012i
$582$		0			0
$583$		−	10293.7i		−	0.731253i
$584$	4098.11	−	22657.9i	0.290378	−	1.60546i
$585$		0			0
$586$	2141.88	−	3246.18i	0.150990	−	0.228837i
$587$	18612.1			1.30869			0.654347	−	0.756195i	$-0.272944\pi$
$587$	18612.1			1.30869			0.654347	+	0.756195i	$0.272944\pi$
$588$		0			0
$589$	−122.926			−0.00859944
$590$	9150.70	−	13868.6i	0.638522	−	0.967731i
$591$		0			0
$592$	631.846	−	661.893i	0.0438661	−	0.0459521i
$593$			23362.1i			1.61782i	0.587934	+	0.808909i	$0.299942\pi$
$593$			23362.1i			1.61782i	−0.587934	+	0.808909i	$0.700058\pi$
$594$		0			0
$595$		−	768.626i		−	0.0529589i
$596$	−8495.19	+	3634.94i	−0.583853	+	0.249820i
$597$		0			0
$598$	586.561	+	387.021i	0.0401108	+	0.0264657i
$599$	−18221.3			−1.24291			−0.621454	−	0.783451i	$-0.713458\pi$
$599$	−18221.3			−1.24291			−0.621454	+	0.783451i	$0.713458\pi$
$600$		0			0
$601$	9378.36			0.636524			0.318262	−	0.948003i	$-0.396901\pi$
$601$	9378.36			0.636524			0.318262	+	0.948003i	$0.396901\pi$
$602$	−6205.61	−	4094.55i	−0.420136	−	0.277212i
$603$		0			0
$604$	−1897.57	+	811.935i	−0.127833	+	0.0546973i
$605$			7362.98i			0.494790i
$606$		0			0
$607$			5533.30i			0.369999i	0.982739	+	0.185000i	$0.0592284\pi$
$607$			5533.30i			0.369999i	−0.982739	+	0.185000i	$0.940772\pi$
$608$	−314.141	−	1370.18i	−0.0209541	−	0.0913949i
$609$		0			0
$610$	−1562.54	+	2368.15i	−0.103714	+	0.157186i
$611$	849.022			0.0562156
$612$		0			0
$613$	26865.2			1.77011			0.885053	−	0.465491i	$-0.154122\pi$
$613$	26865.2			1.77011			0.885053	+	0.465491i	$0.154122\pi$
$614$	13227.7	−	20047.6i	0.869423	−	1.31768i
$615$		0			0
$616$	3383.21	+	611.917i	0.221288	+	0.0400241i
$617$		−	783.331i		−	0.0511114i	−0.999673	−	0.0255557i	$-0.991864\pi$
$617$		−	783.331i		−	0.0511114i	0.999673	−	0.0255557i	$-0.00813551\pi$
$618$		0			0
$619$		−	23547.8i		−	1.52902i	−0.644609	−	0.764512i	$-0.722980\pi$
$619$		−	23547.8i		−	1.52902i	0.644609	−	0.764512i	$-0.277020\pi$
$620$	−426.590	−	996.981i	−0.0276327	−	0.0645802i
$621$		0			0
$622$	21975.8	+	14500.0i	1.41664	+	0.934719i
$623$	−1439.63			−0.0925806
$624$		0			0
$625$	−6496.29			−0.415763
$626$	4776.60	+	3151.67i	0.304970	+	0.201223i
$627$		0			0
$628$	−4315.28	−	10085.2i	−0.274201	−	0.640833i
$629$			183.336i			0.0116217i
$630$		0			0
$631$			8638.36i			0.544989i	0.962157	+	0.272494i	$0.0878486\pi$
$631$			8638.36i			0.544989i	−0.962157	+	0.272494i	$0.912151\pi$
$632$	−15227.4	−	2754.16i	−0.958407	−	0.173346i
$633$		0			0
$634$	13411.4	−	20326.0i	0.840116	−	1.27326i
$635$	17821.1			1.11371
$636$		0			0
$637$	162.388			0.0101006
$638$	−5341.41	+	8095.33i	−0.331455	+	0.502346i
$639$		0			0
$640$	10022.6	−	7302.77i	0.619027	−	0.451043i
$641$			18554.5i			1.14331i	0.820496	+	0.571653i	$0.193698\pi$
$641$			18554.5i			1.14331i	−0.820496	+	0.571653i	$0.806302\pi$
$642$		0			0
$643$		−	1140.20i		−	0.0699305i	−0.999389	−	0.0349652i	$-0.988868\pi$
$643$		−	1140.20i		−	0.0699305i	0.999389	−	0.0349652i	$-0.0111320\pi$
$644$	−3859.84	+	1651.56i	−0.236179	+	0.101057i
$645$		0			0
$646$	235.083	+	155.111i	0.0143176	+	0.00944699i
$647$	−20077.3			−1.21997			−0.609983	−	0.792414i	$-0.708824\pi$
$647$	−20077.3			−1.21997			−0.609983	+	0.792414i	$0.708824\pi$
$648$		0			0
$649$	−14890.7			−0.900633
$650$	404.268	+	266.741i	0.0243949	+	0.0160961i
$651$		0			0
$652$	15976.2	−	6835.93i	0.959626	−	0.410607i
$653$			14747.7i			0.883802i	0.897064	+	0.441901i	$0.145696\pi$
$653$			14747.7i			0.883802i	−0.897064	+	0.441901i	$0.854304\pi$
$654$		0			0
$655$			23921.7i			1.42702i
$656$	21982.5	+	20984.6i	1.30834	+	1.24895i
$657$		0			0
$658$	−2793.48	+	4233.73i	−0.165503	+	0.250833i
$659$	22815.9			1.34868			0.674341	−	0.738420i	$-0.264428\pi$
$659$	22815.9			1.34868			0.674341	+	0.738420i	$0.264428\pi$
$660$		0			0
$661$	−18103.9			−1.06529			−0.532647	−	0.846338i	$-0.678802\pi$
$661$	−18103.9			−1.06529			−0.532647	+	0.846338i	$0.678802\pi$
$662$	−10449.5	+	15837.0i	−0.613489	+	0.929791i
$663$		0			0
$664$	526.133	−	2908.92i	0.0307499	−	0.170012i
$665$		−	465.494i		−	0.0271445i
$666$		0			0
$667$		−	11843.3i		−	0.687516i
$668$	−3170.31	−	7409.30i	−0.183627	−	0.429154i
$669$		0			0
$670$	8518.43	+	5620.58i	0.491188	+	0.324093i
$671$	2542.68			0.146288
$672$		0			0
$673$	6648.74			0.380817			0.190409	−	0.981705i	$-0.439019\pi$
$673$	6648.74			0.380817			0.190409	+	0.981705i	$0.439019\pi$
$674$	−19737.9	−	13023.4i	−1.12801	−	0.744275i
$675$		0			0
$676$	−6879.55	−	16078.1i	−0.391417	−	0.914778i
$677$			22847.9i			1.29707i	0.761185	+	0.648535i	$0.224618\pi$
$677$			22847.9i			1.29707i	−0.761185	+	0.648535i	$0.775382\pi$
$678$		0			0
$679$			12028.2i			0.679826i
$680$	−442.207	+	2444.90i	−0.0249380	+	0.137879i
$681$		0			0
$682$	−535.229	+	811.181i	−0.0300513	+	0.0455451i
$683$	−11858.9			−0.664375			−0.332188	−	0.943213i	$-0.607787\pi$
$683$	−11858.9			−0.664375			−0.332188	+	0.943213i	$0.607787\pi$
$684$		0			0
$685$	8767.96			0.489060
$686$	−534.295	+	809.766i	−0.0297368	+	0.0450685i
$687$		0			0
$688$	17383.6	+	16594.5i	0.963291	+	0.919563i
$689$			1571.60i			0.0868988i
$690$		0			0
$691$		−	9647.48i		−	0.531125i	−0.964094	−	0.265563i	$-0.914442\pi$
$691$		−	9647.48i		−	0.531125i	0.964094	−	0.265563i	$-0.0855577\pi$
$692$	4504.86	−	1927.55i	0.247470	−	0.105888i
$693$		0			0
$694$	−22736.4	−	15001.8i	−1.24360	−	0.820547i
$695$	−3473.10			−0.189557
$696$		0			0
$697$	−6088.87			−0.330893
$698$	7648.24	+	5046.42i	0.414743	+	0.273653i
$699$		0			0
$700$	−2660.27	+	1138.28i	−0.143641	+	0.0614614i
$701$			25293.6i			1.36281i	0.731908	+	0.681403i	$0.238630\pi$
$701$			25293.6i			1.36281i	−0.731908	+	0.681403i	$0.761370\pi$
$702$		0			0
$703$			111.031i			0.00595679i
$704$	−10409.5	−	3892.87i	−0.557279	−	0.208406i
$705$		0			0
$706$	20095.5	−	30456.2i	1.07125	−	1.62356i
$707$	−5247.05			−0.279117
$708$		0			0
$709$	−35294.4			−1.86955			−0.934773	−	0.355246i	$-0.884397\pi$
$709$	−35294.4			−1.86955			−0.934773	+	0.355246i	$0.884397\pi$
$710$	−76.6459	+	116.163i	−0.00405137	+	0.00614017i
$711$		0			0
$712$	4579.30	+	828.252i	0.241034	+	0.0435956i
$713$		−	1186.74i		−	0.0623334i
$714$		0			0
$715$			616.004i			0.0322199i
$716$	11312.9	+	26439.3i	0.590478	+	1.38000i
$717$		0			0
$718$	27960.1	+	18448.5i	1.45329	+	0.958901i
$719$	24223.6			1.25645			0.628225	−	0.778032i	$-0.283782\pi$
$719$	24223.6			1.25645			0.628225	+	0.778032i	$0.283782\pi$
$720$		0			0
$721$	−9165.24			−0.473414
$722$	−16050.6	−	10590.4i	−0.827342	−	0.545892i
$723$		0			0
$724$	4667.19	+	10907.7i	0.239579	+	0.559917i
$725$		−	8162.58i		−	0.418139i
$726$		0			0
$727$			37744.4i			1.92553i	0.270339	+	0.962765i	$0.412864\pi$
$727$			37744.4i			1.92553i	−0.270339	+	0.962765i	$0.587136\pi$
$728$	−516.538	−	93.4255i	−0.0262969	−	0.00475629i
$729$		0			0
$730$	−13573.8	+	20572.1i	−0.688202	+	1.04302i
$731$	−4815.04			−0.243626
$732$		0			0
$733$	7023.18			0.353898			0.176949	−	0.984220i	$-0.443377\pi$
$733$	7023.18			0.353898			0.176949	+	0.984220i	$0.443377\pi$
$734$	−12784.1	+	19375.3i	−0.642873	+	0.974325i
$735$		0			0
$736$	13227.9	−	3032.75i	0.662480	−	0.151887i
$737$		−	9146.23i		−	0.457131i
$738$		0			0
$739$			25657.1i			1.27715i	0.769560	+	0.638574i	$0.220476\pi$
$739$			25657.1i			1.27715i	−0.769560	+	0.638574i	$0.779524\pi$
$740$	−900.512	+	385.313i	−0.0447344	+	0.0191411i
$741$		0			0
$742$	−7836.96	−	5170.93i	−0.387741	−	0.255837i
$743$	−7453.40			−0.368020			−0.184010	−	0.982924i	$-0.558908\pi$
$743$	−7453.40			−0.368020			−0.184010	+	0.982924i	$0.558908\pi$
$744$		0			0
$745$	9890.75			0.486401
$746$	−15153.7	−	9998.63i	−0.743722	−	0.490718i
$747$		0			0
$748$	2047.14	−	875.933i	0.100068	−	0.0428172i
$749$			5656.18i			0.275931i
$750$		0			0
$751$			33308.5i			1.61843i	0.587510	+	0.809217i	$0.300108\pi$
$751$			33308.5i			1.61843i	−0.587510	+	0.809217i	$0.699892\pi$
$752$	11321.5	−	11859.8i	0.549005	−	0.575112i
$753$		0			0
$754$	815.508	−	1235.97i	0.0393887	−	0.0596966i
$755$	2209.29			0.106496
$756$		0			0
$757$	−8410.68			−0.403819			−0.201910	−	0.979404i	$-0.564715\pi$
$757$	−8410.68			−0.403819			−0.201910	+	0.979404i	$0.564715\pi$
$758$	−2846.86	+	4314.64i	−0.136415	+	0.206748i
$759$		0			0
$760$	−267.808	+	1480.68i	−0.0127821	+	0.0706708i
$761$			18340.4i			0.873638i	0.899549	+	0.436819i	$0.143895\pi$
$761$			18340.4i			0.873638i	−0.899549	+	0.436819i	$0.856105\pi$
$762$		0			0
$763$			13795.9i			0.654579i
$764$	7484.60	+	17492.2i	0.354428	+	0.828332i
$765$		0			0
$766$	32409.5	+	21384.2i	1.52872	+	1.00867i
$767$	2273.46			0.107027
$768$		0			0
$769$	9932.74			0.465779			0.232889	−	0.972503i	$-0.425182\pi$
$769$	9932.74			0.465779			0.232889	+	0.972503i	$0.425182\pi$
$770$	−3071.77	−	2026.80i	−0.143765	−	0.0948580i
$771$		0			0
$772$	1227.01	+	2867.65i	0.0572036	+	0.133690i
$773$		−	11064.1i		−	0.514808i	−0.966304	−	0.257404i	$-0.917133\pi$
$773$		−	11064.1i		−	0.514808i	0.966304	−	0.257404i	$-0.0828671\pi$
$774$		0			0
$775$		−	817.920i		−	0.0379104i
$776$	6920.10	−	38260.4i	0.320125	−	1.76993i
$777$		0			0
$778$	4843.10	−	7340.10i	0.223179	−	0.338246i
$779$	−3687.53			−0.169601
$780$		0			0
$781$	124.724			0.00571444
$782$	−1497.46	+	2269.51i	−0.0684769	+	0.103782i
$783$		0			0
$784$	2165.40	−	2268.38i	0.0986426	−	0.103333i
$785$			11742.0i			0.533871i
$786$		0			0
$787$			10817.8i			0.489976i	0.969526	+	0.244988i	$0.0787841\pi$
$787$			10817.8i			0.489976i	−0.969526	+	0.244988i	$0.921216\pi$
$788$	−4858.87	+	2079.02i	−0.219658	+	0.0939875i
$789$		0			0
$790$	13825.6	+	9122.34i	0.622650	+	0.410833i
$791$	378.010			0.0169918
$792$		0			0
$793$	−388.208			−0.0173842
$794$	−18027.7	−	11895.0i	−0.805769	−	0.531658i
$795$		0			0
$796$	23524.4	−	10065.7i	1.04749	−	0.448202i
$797$		−	11772.2i		−	0.523203i	−0.965176	−	0.261602i	$-0.915749\pi$
$797$		−	11772.2i		−	0.523203i	0.965176	−	0.261602i	$-0.0842507\pi$
$798$		0			0
$799$			3285.02i			0.145451i
$800$	9116.86	−	2090.22i	0.402912	−	0.0923757i
$801$		0			0
$802$	−1661.06	+	2517.46i	−0.0731346	+	0.110841i
$803$	22088.2			0.970707
$804$		0			0
$805$	4493.92			0.196758
$806$	81.7169	−	123.848i	0.00357116	−	0.00541237i
$807$		0			0
$808$	16690.2	+	3018.74i	0.726683	+	0.131434i
$809$		−	30715.2i		−	1.33485i	−0.744679	−	0.667423i	$-0.767397\pi$
$809$		−	30715.2i		−	1.33485i	0.744679	−	0.667423i	$-0.232603\pi$
$810$		0			0
$811$		−	23012.3i		−	0.996389i	−0.867065	−	0.498195i	$-0.833996\pi$
$811$		−	23012.3i		−	0.996389i	0.867065	−	0.498195i	$-0.166004\pi$
$812$	3480.06	+	8133.23i	0.150402	+	0.351503i
$813$		0			0
$814$	732.690	+	483.439i	0.0315489	+	0.0208164i
$815$	−18600.7			−0.799454
$816$		0			0
$817$	−2916.07			−0.124872
$818$	13720.9	+	9053.21i	0.586477	+	0.386966i
$819$		0			0
$820$	−12796.9	−	29907.5i	−0.544983	−	1.27368i
$821$			38552.9i			1.63886i	0.573179	+	0.819430i	$0.305710\pi$
$821$			38552.9i			1.63886i	−0.573179	+	0.819430i	$0.694290\pi$
$822$		0			0
$823$			2617.52i			0.110864i	0.998462	+	0.0554319i	$0.0176536\pi$
$823$			2617.52i			0.110864i	−0.998462	+	0.0554319i	$0.982346\pi$
$824$	29153.5	+	5272.96i	1.23254	+	0.222927i
$825$		0			0
$826$	−7480.21	+	11336.8i	−0.315096	+	0.477553i
$827$	21862.2			0.919253			0.459626	−	0.888112i	$-0.347983\pi$
$827$	21862.2			0.919253			0.459626	+	0.888112i	$0.347983\pi$
$828$		0			0
$829$	−8748.15			−0.366509			−0.183254	−	0.983066i	$-0.558663\pi$
$829$	−8748.15			−0.366509			−0.183254	+	0.983066i	$0.558663\pi$
$830$	−1742.66	+	2641.14i	−0.0728778	+	0.110452i
$831$		0			0
$832$	1589.29	+	594.350i	0.0662246	+	0.0247661i
$833$			628.310i			0.0261340i
$834$		0			0
$835$			8626.48i			0.357523i
$836$	1239.78	−	530.481i	0.0512904	−	0.0219463i
$837$		0			0
$838$	−24574.1	−	16214.4i	−1.01301	−	0.668396i
$839$	14994.8			0.617019			0.308509	−	0.951221i	$-0.400170\pi$
$839$	14994.8			0.617019			0.308509	+	0.951221i	$0.400170\pi$
$840$		0			0
$841$	−566.434			−0.0232250
$842$	−15006.1	−	9901.23i	−0.614185	−	0.405248i
$843$		0			0
$844$	−24995.7	+	10695.2i	−1.01942	+	0.436190i
$845$			18719.4i			0.762091i
$846$		0			0
$847$		−	6018.85i		−	0.244168i
$848$	21953.5	+	20956.9i	0.889015	+	0.848658i
$849$		0			0
$850$	−1032.07	+	1564.19i	−0.0416468	+	0.0631190i
$851$	−1071.91			−0.0431781
$852$		0			0
$853$	26358.3			1.05802			0.529009	−	0.848616i	$-0.322564\pi$
$853$	26358.3			1.05802			0.529009	+	0.848616i	$0.322564\pi$
$854$	1277.29	−	1935.84i	0.0511804	−	0.0775679i
$855$		0			0
$856$	3254.12	−	17991.6i	0.129934	−	0.718389i
$857$			34475.1i			1.37415i	0.726587	+	0.687075i	$0.241106\pi$
$857$			34475.1i			1.37415i	−0.726587	+	0.687075i	$0.758894\pi$
$858$		0			0
$859$		−	27352.8i		−	1.08646i	−0.839585	−	0.543228i	$-0.817202\pi$
$859$		−	27352.8i		−	1.08646i	0.839585	−	0.543228i	$-0.182798\pi$
$860$	−10119.7	−	23650.6i	−0.401253	−	0.937766i
$861$		0			0
$862$	−3154.22	−	2081.20i	−0.124632	−	0.0822342i
$863$	−29199.3			−1.15174			−0.575872	−	0.817540i	$-0.695337\pi$
$863$	−29199.3			−1.15174			−0.575872	+	0.817540i	$0.695337\pi$
$864$		0			0
$865$	−5244.90			−0.206164
$866$	−16486.7	−	10878.1i	−0.646928	−	0.426852i
$867$		0			0
$868$	348.715	+	814.979i	0.0136361	+	0.0318689i
$869$		−	14844.5i		−	0.579478i
$870$		0			0
$871$			1396.42i			0.0543234i
$872$	7937.05	−	43883.0i	0.308237	−	1.70420i
$873$		0			0
$874$	−906.887	+	1374.46i	−0.0350983	+	0.0531942i
$875$	10590.1			0.409156
$876$		0			0
$877$	−15879.6			−0.611422			−0.305711	−	0.952124i	$-0.598894\pi$
$877$	−15879.6			−0.611422			−0.305711	+	0.952124i	$0.598894\pi$
$878$	−15816.3	+	23970.9i	−0.607944	+	0.921387i
$879$		0			0
$880$	8604.86	+	8214.24i	0.329625	+	0.314662i
$881$			4985.53i			0.190655i	0.995446	+	0.0953274i	$0.0303898\pi$
$881$			4985.53i			0.190655i	−0.995446	+	0.0953274i	$0.969610\pi$
$882$		0			0
$883$		−	31674.1i		−	1.20715i	−0.797305	−	0.603577i	$-0.793742\pi$
$883$		−	31674.1i		−	1.20715i	0.797305	−	0.603577i	$-0.206258\pi$
$884$	−312.550	+	133.735i	−0.0118916	+	0.00508821i
$885$		0			0
$886$	2509.75	+	1655.97i	0.0951657	+	0.0627917i
$887$	−17415.3			−0.659245			−0.329622	−	0.944113i	$-0.606921\pi$
$887$	−17415.3			−0.659245			−0.329622	+	0.944113i	$0.606921\pi$
$888$		0			0
$889$	−14567.8			−0.549592
$890$	−4157.75	−	2743.34i	−0.156593	−	0.103322i
$891$		0			0
$892$	−25009.2	+	10701.0i	−0.938756	+	0.401677i
$893$			1989.47i			0.0745521i
$894$		0			0
$895$		−	30782.6i		−	1.14966i
$896$	−8192.93	+	5969.62i	−0.305476	+	0.222579i
$897$		0			0
$898$	−17573.8	+	26634.5i	−0.653057	+	0.989759i
$899$	−2500.62			−0.0927703
$900$		0			0
$901$	−6080.82			−0.224841
$902$	−16055.8	+	24333.8i	−0.592683	+	0.898257i
$903$		0			0
$904$	−1202.40	−	217.477i	−0.0442382	−	0.00800130i
$905$		−	12699.5i		−	0.466461i
$906$		0			0
$907$		−	11608.2i		−	0.424965i	−0.977165	−	0.212482i	$-0.931845\pi$
$907$		−	11608.2i		−	0.424965i	0.977165	−	0.212482i	$-0.0681548\pi$
$908$	15736.9	+	36778.5i	0.575161	+	1.34421i
$909$		0			0
$910$	468.987	+	309.444i	0.0170844	+	0.0112725i
$911$	29385.1			1.06868			0.534342	−	0.845268i	$-0.320559\pi$
$911$	29385.1			1.06868			0.534342	+	0.845268i	$0.320559\pi$
$912$		0			0
$913$	2835.79			0.102794
$914$	−7692.28	−	5075.48i	−0.278379	−	0.183678i
$915$		0			0
$916$	−14784.0	−	34551.5i	−0.533271	−	1.24630i
$917$		−	19554.7i		−	0.704204i
$918$		0			0
$919$			10820.3i			0.388386i	0.980963	+	0.194193i	$0.0622089\pi$
$919$			10820.3i			0.388386i	−0.980963	+	0.194193i	$0.937791\pi$
$920$	−14294.6	−	2585.45i	−0.512261	−	0.0926519i
$921$		0			0
$922$	10280.7	−	15581.3i	0.367221	−	0.556552i
$923$	−19.0424			−0.000679078
$924$		0			0
$925$	−738.777			−0.0262604
$926$	17728.0	−	26868.2i	0.629134	−	0.953502i
$927$		0			0
$928$	−6390.44	−	27873.0i	−0.226052	−	0.985964i
$929$		−	34921.6i		−	1.23330i	−0.787236	−	0.616652i	$-0.788489\pi$
$929$		−	34921.6i		−	1.23330i	0.787236	−	0.616652i	$-0.211511\pi$
$930$		0			0
$931$			380.516i			0.0133952i
$932$	−8521.75	+	3646.30i	−0.299506	+	0.128153i
$933$		0			0
$934$	4224.63	+	2787.47i	0.148002	+	0.0976539i
$935$	−2383.43			−0.0833654
$936$		0			0
$937$	646.905			0.0225544			0.0112772	−	0.999936i	$-0.496410\pi$
$937$	646.905			0.0225544			0.0112772	+	0.999936i	$0.496410\pi$
$938$	−6963.36	−	4594.53i	−0.242390	−	0.159932i
$939$		0			0
$940$	−16135.5	+	6904.07i	−0.559873	+	0.239560i
$941$		−	13682.3i		−	0.473997i	−0.971510	−	0.236998i	$-0.923836\pi$
$941$		−	13682.3i		−	0.473997i	0.971510	−	0.236998i	$-0.0761636\pi$
$942$		0			0
$943$		−	35599.8i		−	1.22936i
$944$	30315.9	−	31757.6i	1.04523	−	1.09494i
$945$		0			0
$946$	−12696.8	+	19243.0i	−0.436373	+	0.661358i
$947$	−16409.0			−0.563064			−0.281532	−	0.959552i	$-0.590843\pi$
$947$	−16409.0			−0.563064			−0.281532	+	0.959552i	$0.590843\pi$
$948$		0			0
$949$	−3372.36			−0.115354
$950$	−625.041	+	947.299i	−0.0213463	+	0.0323520i
$951$		0			0
$952$	361.480	−	1998.58i	0.0123063	−	0.0680402i
$953$		−	22674.7i		−	0.770729i	−0.922764	−	0.385364i	$-0.874076\pi$
$953$		−	22674.7i		−	0.770729i	0.922764	−	0.385364i	$-0.125924\pi$
$954$		0			0
$955$		−	20365.8i		−	0.690074i
$956$	−3702.49	−	8653.07i	−0.125259	−	0.292741i
$957$		0			0
$958$	15296.4	+	10092.8i	0.515872	+	0.340380i
$959$	−7167.34			−0.241340
$960$		0			0
$961$	29540.4			0.991589
$962$	−111.865	−	73.8099i	−0.00374913	−	0.00247373i
$963$		0			0
$964$	−18703.7	−	43712.3i	−0.624903	−	1.46046i
$965$		−	3338.73i		−	0.111376i
$966$		0			0
$967$			3826.69i			0.127258i	0.997974	+	0.0636288i	$0.0202674\pi$
$967$			3826.69i			0.127258i	−0.997974	+	0.0636288i	$0.979733\pi$
$968$	−3462.77	+	19145.2i	−0.114977	+	0.635693i
$969$		0			0
$970$	−22920.8	+	34738.3i	−0.758704	+	1.14987i
$971$	23281.9			0.769466			0.384733	−	0.923028i	$-0.374294\pi$
$971$	23281.9			0.769466			0.384733	+	0.923028i	$0.374294\pi$
$972$		0			0
$973$	2839.07			0.0935420
$974$	29631.6	−	44908.9i	0.974801	−	1.47739i
$975$		0			0
$976$	−5176.64	+	5422.81i	−0.169775	+	0.177848i
$977$		−	25463.1i		−	0.833815i	−0.908949	−	0.416908i	$-0.863114\pi$
$977$		−	25463.1i		−	0.833815i	0.908949	−	0.416908i	$-0.136886\pi$
$978$		0			0
$979$			4464.17i			0.145736i
$980$	−3086.15	+	1320.51i	−0.100595	+	0.0430430i
$981$		0			0
$982$	−32005.5	−	21117.7i	−1.04006	−	0.686245i
$983$	−20852.8			−0.676604			−0.338302	−	0.941038i	$-0.609852\pi$
$983$	−20852.8			−0.676604			−0.338302	+	0.941038i	$0.609852\pi$
$984$		0			0
$985$	5657.07			0.182994
$986$	4782.18	+	3155.35i	0.154458	+	0.101914i
$987$		0			0
$988$	−189.286	+	80.9920i	−0.00609513	+	0.00260800i
$989$		−	28152.1i		−	0.905141i
$990$		0			0
$991$		−	10884.3i		−	0.348890i	−0.984667	−	0.174445i	$-0.944187\pi$
$991$		−	10884.3i		−	0.348890i	0.984667	−	0.174445i	$-0.0558131\pi$
$992$	−640.345	−	2792.97i	−0.0204949	−	0.0893921i
$993$		0			0
$994$	62.6540	−	94.9570i	0.00199926	−	0.00303003i
$995$	−27389.0			−0.872652
$996$		0			0
$997$	25218.6			0.801085			0.400543	−	0.916278i	$-0.368822\pi$
$997$	25218.6			0.801085			0.400543	+	0.916278i	$0.368822\pi$
$998$	−19486.3	+	29533.1i	−0.618065	+	0.936726i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.e.a.71.5	✓	36
3.2	odd	2	inner	252.4.e.a.71.32	yes	36
4.3	odd	2	inner	252.4.e.a.71.31	yes	36
12.11	even	2	inner	252.4.e.a.71.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.e.a.71.5	✓	36	1.1	even	1	trivial
252.4.e.a.71.6	yes	36	12.11	even	2	inner
252.4.e.a.71.31	yes	36	4.3	odd	2	inner
252.4.e.a.71.32	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)

\(f(q)\)	\(=\)	\(q+(-2.36083 - 1.55771i) q^{2} +(3.14707 + 7.35499i) q^{4} -8.56325i q^{5} +7.00000i q^{7} +(4.02725 - 22.2661i) q^{8} +O(q^{10})\)	\(q+(-2.36083 - 1.55771i) q^{2} +(3.14707 + 7.35499i) q^{4} -8.56325i q^{5} +7.00000i q^{7} +(4.02725 - 22.2661i) q^{8} +(-13.3391 + 20.2164i) q^{10} +21.7063 q^{11} -3.31405 q^{13} +(10.9040 - 16.5258i) q^{14} +(-44.1919 + 46.2934i) q^{16} -12.8227i q^{17} -7.76564i q^{19} +(62.9827 - 26.9492i) q^{20} +(-51.2450 - 33.8122i) q^{22} +74.9703 q^{23} +51.6707 q^{25} +(7.82392 + 5.16233i) q^{26} +(-51.4850 + 22.0295i) q^{28} -157.973i q^{29} -15.8295i q^{31} +(176.441 - 40.4527i) q^{32} +(-19.9740 + 30.2722i) q^{34} +59.9428 q^{35} -14.2978 q^{37} +(-12.0966 + 18.3334i) q^{38} +(-190.671 - 34.4863i) q^{40} -474.853i q^{41} -375.510i q^{43} +(68.3114 + 159.650i) q^{44} +(-176.992 - 116.782i) q^{46} -256.189 q^{47} -49.0000 q^{49} +(-121.986 - 80.4881i) q^{50} +(-10.4295 - 24.3748i) q^{52} -474.224i q^{53} -185.877i q^{55} +(155.863 + 28.1907i) q^{56} +(-246.076 + 372.948i) q^{58} -686.007 q^{59} +117.140 q^{61} +(-24.6577 + 37.3707i) q^{62} +(-479.563 - 179.343i) q^{64} +28.3790i q^{65} -421.362i q^{67} +(94.3106 - 40.3538i) q^{68} +(-141.515 - 93.3735i) q^{70} +5.74597 q^{71} +1017.59 q^{73} +(33.7547 + 22.2718i) q^{74} +(57.1162 - 24.4390i) q^{76} +151.944i q^{77} -683.881i q^{79} +(396.422 + 378.426i) q^{80} +(-739.683 + 1121.05i) q^{82} +130.643 q^{83} -109.804 q^{85} +(-584.936 + 886.516i) q^{86} +(87.4168 - 483.316i) q^{88} +205.662i q^{89} -23.1983i q^{91} +(235.937 + 551.406i) q^{92} +(604.819 + 399.068i) q^{94} -66.4991 q^{95} +1718.32 q^{97} +(115.681 + 76.3279i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 24 q^{4}+O(q^{10}) \) 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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