LMFDB - Embedded newform 252.4.e.a.71.6

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

$q$-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	$0.125095\pi$
$5$			8.56325i			0.765920i	−0.923765	+	0.382960i	$0.874905\pi$
$6$		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	$0.0291563\pi$
$17$			12.8227i			0.182938i	−0.995808	+	0.0914692i	$0.970844\pi$
$18$		0			0
$19$			7.76564i			0.0937663i	0.998900	+	0.0468831i	$0.0149288\pi$
$19$			7.76564i			0.0937663i	−0.998900	+	0.0468831i	$0.985071\pi$
$20$	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	$0.168793\pi$
$29$			157.973i			1.01155i	−0.862667	+	0.505773i	$0.831207\pi$
$30$		0			0
$31$			15.8295i			0.0917114i	0.998948	+	0.0458557i	$0.0146014\pi$
$31$			15.8295i			0.0917114i	−0.998948	+	0.0458557i	$0.985399\pi$
$32$	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	$0.359669\pi$
$41$			474.853i			1.80877i	−0.426719	+	0.904384i	$0.640331\pi$
$42$		0			0
$43$			375.510i			1.33174i	0.746069	+	0.665869i	$0.231939\pi$
$43$			375.510i			1.33174i	−0.746069	+	0.665869i	$0.768061\pi$
$44$	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	$0.210653\pi$
$53$			474.224i			1.22905i	−0.788897	+	0.614526i	$0.789347\pi$
$54$		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	$0.125509\pi$
$67$			421.362i			0.768322i	−0.923266	+	0.384161i	$0.874491\pi$
$68$	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	$0.161901\pi$
$79$			683.881i			0.973957i	−0.873414	+	0.486979i	$0.838099\pi$
$80$	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	$-0.960918\pi$
$89$		−	205.662i		−	0.244945i	0.992472	−	0.122473i	$-0.0390824\pi$
$90$		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	$-0.879619\pi$
$101$		−	749.578i		−	0.738473i	0.929335	−	0.369237i	$-0.120381\pi$
$102$		0			0
$103$		−	1309.32i		−	1.25254i	−0.779608	−	0.626268i	$-0.784582\pi$
$103$		−	1309.32i		−	1.25254i	0.779608	−	0.626268i	$-0.215418\pi$
$104$	−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	$0.00715557\pi$
$113$			54.0014i			0.0449560i	−0.999747	+	0.0224780i	$0.992844\pi$
$114$		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	$-0.740895\pi$
$127$		−	2081.11i		−	1.45408i	0.686593	−	0.727042i	$-0.259105\pi$
$128$	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	$-0.896565\pi$
$137$		−	1023.91i		−	0.638526i	0.947666	−	0.319263i	$-0.103435\pi$
$138$		0			0
$139$			405.581i			0.247489i	0.992314	+	0.123744i	$0.0394903\pi$
$139$			405.581i			0.247489i	−0.992314	+	0.123744i	$0.960510\pi$
$140$	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	$-0.897147\pi$
$149$		−	1155.02i		−	0.635055i	0.948249	−	0.317527i	$-0.102853\pi$
$150$		0			0
$151$		−	257.997i		−	0.139043i	−0.997580	−	0.0695215i	$-0.977853\pi$
$151$		−	257.997i		−	0.139043i	0.997580	−	0.0695215i	$-0.0221473\pi$
$152$	−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	$0.174773\pi$
$163$			2172.16i			1.04378i	−0.853012	+	0.521891i	$0.825227\pi$
$164$	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	$0.0429704\pi$
$173$			612.490i			0.269172i	−0.990902	+	0.134586i	$0.957030\pi$
$174$		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	$-0.961884\pi$
$197$		−	660.622i		−	0.238921i	0.992839	−	0.119460i	$-0.0381164\pi$
$198$		0			0
$199$			3198.43i			1.13935i	0.821870	+	0.569675i	$0.192931\pi$
$199$			3198.43i			1.13935i	−0.821870	+	0.569675i	$0.807069\pi$
$200$	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	$-0.812945\pi$
$211$		−	3398.47i		−	1.10882i	0.832245	−	0.554408i	$-0.187055\pi$
$212$	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	$-0.829445\pi$
$223$		−	3400.30i		−	1.02108i	0.859854	−	0.510541i	$-0.170555\pi$
$224$	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	$-0.947920\pi$
$233$		−	1158.63i		−	0.325771i	0.986645	−	0.162886i	$-0.0520801\pi$
$234$		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	$0.110834\pi$
$257$			2811.53i			0.682406i	−0.939990	+	0.341203i	$0.889166\pi$
$258$		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	$-0.964187\pi$
$269$		−	990.668i		−	0.224543i	0.993678	−	0.112272i	$-0.0358127\pi$
$270$		0			0
$271$		−	6503.15i		−	1.45771i	−0.684671	−	0.728853i	$-0.740054\pi$
$271$		−	6503.15i		−	1.45771i	0.684671	−	0.728853i	$-0.259946\pi$
$272$	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	$0.0695753\pi$
$281$			2042.82i			0.433682i	−0.976207	+	0.216841i	$0.930425\pi$
$282$		0			0
$283$			8663.31i			1.81972i	0.414917	+	0.909859i	$0.363810\pi$
$283$			8663.31i			1.81972i	−0.414917	+	0.909859i	$0.636190\pi$
$284$	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	$-0.956228\pi$
$293$		−	1375.01i		−	0.274161i	0.990560	−	0.137081i	$-0.0437719\pi$
$294$		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	$-0.710428\pi$
$307$		−	8491.74i		−	1.57866i	0.613968	−	0.789331i	$-0.289572\pi$
$308$	−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	$-0.723862\pi$
$317$		−	8609.66i		−	1.52545i	0.646725	−	0.762724i	$-0.276138\pi$
$318$		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	$0.188038\pi$
$331$			6708.22i			1.11395i	−0.830530	+	0.556974i	$0.811962\pi$
$332$	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	$-0.574733\pi$
$353$		−	12900.6i		−	1.94513i	0.232630	−	0.972565i	$-0.425267\pi$
$354$		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	$0.198376\pi$
$367$			8206.96i			1.16730i	−0.812004	+	0.583651i	$0.801624\pi$
$368$	−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	$0.0395236\pi$
$379$			1827.59i			0.247697i	−0.992301	+	0.123848i	$0.960476\pi$
$380$	−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	$-0.935054\pi$
$389$		−	3109.11i		−	0.405240i	0.979257	−	0.202620i	$-0.0649456\pi$
$390$		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	$0.0211505\pi$
$401$			1066.34i			0.132795i	−0.997793	+	0.0663973i	$0.978850\pi$
$402$		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	$0.186112\pi$
$439$			10153.6i			1.10388i	−0.833884	+	0.551940i	$0.813888\pi$
$440$	−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	$0.202016\pi$
$449$			11281.8i			1.18579i	−0.805278	+	0.592897i	$0.797984\pi$
$450$		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	$-0.891807\pi$
$461$		−	6599.89i		−	0.666785i	0.942788	−	0.333392i	$-0.108193\pi$
$462$		0			0
$463$		−	11380.8i		−	1.14236i	−0.820826	−	0.571178i	$-0.806487\pi$
$463$		−	11380.8i		−	1.14236i	0.820826	−	0.571178i	$-0.193513\pi$
$464$	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	$-0.654157\pi$
$487$		−	19022.5i		−	1.77000i	0.465588	−	0.885001i	$-0.345843\pi$
$488$	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	$0.189633\pi$
$499$			12509.6i			1.12226i	−0.827729	+	0.561128i	$0.810367\pi$
$500$	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	$0.241706\pi$
$509$			15811.6i			1.37689i	−0.725289	+	0.688445i	$0.758294\pi$
$510$		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	$-0.948083\pi$
$521$		−	3862.04i		−	0.324758i	0.986728	−	0.162379i	$-0.0519168\pi$
$522$		0			0
$523$			10949.7i			0.915481i	0.889086	+	0.457741i	$0.151341\pi$
$523$			10949.7i			0.915481i	−0.889086	+	0.457741i	$0.848659\pi$
$524$	−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	$-0.910599\pi$
$547$		−	7092.15i		−	0.554366i	0.960817	−	0.277183i	$-0.0894009\pi$
$548$	−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	$0.157919\pi$
$557$			12515.1i			0.952028i	−0.879438	+	0.476014i	$0.842081\pi$
$558$		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	$-0.980306\pi$
$569$		−	1678.42i		−	0.123661i	0.998087	−	0.0618305i	$-0.0196938\pi$
$570$		0			0
$571$			1848.25i			0.135458i	0.997704	+	0.0677292i	$0.0215754\pi$
$571$			1848.25i			0.135458i	−0.997704	+	0.0677292i	$0.978425\pi$
$572$	−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	$-0.700058\pi$
$593$		−	23362.1i		−	1.61782i	0.587934	−	0.808909i	$-0.299942\pi$
$594$		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	$-0.940772\pi$
$607$		−	5533.30i		−	0.369999i	0.982739	−	0.185000i	$-0.0592284\pi$
$608$	−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	$0.00813551\pi$
$617$			783.331i			0.0511114i	−0.999673	+	0.0255557i	$0.991864\pi$
$618$		0			0
$619$			23547.8i			1.52902i	0.644609	+	0.764512i	$0.277020\pi$
$619$			23547.8i			1.52902i	−0.644609	+	0.764512i	$0.722980\pi$
$620$	−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	$-0.912151\pi$
$631$		−	8638.36i		−	0.544989i	0.962157	−	0.272494i	$-0.0878486\pi$
$632$	−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	$-0.806302\pi$
$641$		−	18554.5i		−	1.14331i	0.820496	−	0.571653i	$-0.193698\pi$
$642$		0			0
$643$			1140.20i			0.0699305i	0.999389	+	0.0349652i	$0.0111320\pi$
$643$			1140.20i			0.0699305i	−0.999389	+	0.0349652i	$0.988868\pi$
$644$	−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	$-0.854304\pi$
$653$		−	14747.7i		−	0.883802i	0.897064	−	0.441901i	$-0.145696\pi$
$654$		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	$-0.775382\pi$
$677$		−	22847.9i		−	1.29707i	0.761185	−	0.648535i	$-0.224618\pi$
$678$		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	$0.0855577\pi$
$691$			9647.48i			0.531125i	−0.964094	+	0.265563i	$0.914442\pi$
$692$	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	$-0.761370\pi$
$701$		−	25293.6i		−	1.36281i	0.731908	−	0.681403i	$-0.238630\pi$
$702$		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	$-0.587136\pi$
$727$		−	37744.4i		−	1.92553i	0.270339	−	0.962765i	$-0.412864\pi$
$728$	−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	$-0.779524\pi$
$739$		−	25657.1i		−	1.27715i	0.769560	−	0.638574i	$-0.220476\pi$
$740$	−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	$-0.699892\pi$
$751$		−	33308.5i		−	1.61843i	0.587510	−	0.809217i	$-0.300108\pi$
$752$	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	$-0.856105\pi$
$761$		−	18340.4i		−	0.873638i	0.899549	−	0.436819i	$-0.143895\pi$
$762$		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	$0.0828671\pi$
$773$			11064.1i			0.514808i	−0.966304	+	0.257404i	$0.917133\pi$
$774$		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	$-0.921216\pi$
$787$		−	10817.8i		−	0.489976i	0.969526	−	0.244988i	$-0.0787841\pi$
$788$	−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	$0.0842507\pi$
$797$			11772.2i			0.523203i	−0.965176	+	0.261602i	$0.915749\pi$
$798$		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	$0.232603\pi$
$809$			30715.2i			1.33485i	−0.744679	+	0.667423i	$0.767397\pi$
$810$		0			0
$811$			23012.3i			0.996389i	0.867065	+	0.498195i	$0.166004\pi$
$811$			23012.3i			0.996389i	−0.867065	+	0.498195i	$0.833996\pi$
$812$	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	$-0.694290\pi$
$821$		−	38552.9i		−	1.63886i	0.573179	−	0.819430i	$-0.305710\pi$
$822$		0			0
$823$		−	2617.52i		−	0.110864i	−0.998462	−	0.0554319i	$-0.982346\pi$
$823$		−	2617.52i		−	0.110864i	0.998462	−	0.0554319i	$-0.0176536\pi$
$824$	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	$-0.758894\pi$
$857$		−	34475.1i		−	1.37415i	0.726587	−	0.687075i	$-0.241106\pi$
$858$		0			0
$859$			27352.8i			1.08646i	0.839585	+	0.543228i	$0.182798\pi$
$859$			27352.8i			1.08646i	−0.839585	+	0.543228i	$0.817202\pi$
$860$	−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	$-0.969610\pi$
$881$		−	4985.53i		−	0.190655i	0.995446	−	0.0953274i	$-0.0303898\pi$
$882$		0			0
$883$			31674.1i			1.20715i	0.797305	+	0.603577i	$0.206258\pi$
$883$			31674.1i			1.20715i	−0.797305	+	0.603577i	$0.793742\pi$
$884$	−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	$0.0681548\pi$
$907$			11608.2i			0.424965i	−0.977165	+	0.212482i	$0.931845\pi$
$908$	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	$-0.937791\pi$
$919$		−	10820.3i		−	0.388386i	0.980963	−	0.194193i	$-0.0622089\pi$
$920$	−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	$0.211511\pi$
$929$			34921.6i			1.23330i	−0.787236	+	0.616652i	$0.788489\pi$
$930$		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	$0.0761636\pi$
$941$			13682.3i			0.473997i	−0.971510	+	0.236998i	$0.923836\pi$
$942$		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	$0.125924\pi$
$953$			22674.7i			0.770729i	−0.922764	+	0.385364i	$0.874076\pi$
$954$		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	$-0.979733\pi$
$967$		−	3826.69i		−	0.127258i	0.997974	−	0.0636288i	$-0.0202674\pi$
$968$	−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	$0.136886\pi$
$977$			25463.1i			0.833815i	−0.908949	+	0.416908i	$0.863114\pi$
$978$		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	$0.0558131\pi$
$991$			10884.3i			0.348890i	−0.984667	+	0.174445i	$0.944187\pi$
$992$	−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.71.6	yes	36
3.2	odd	2	inner	252.4.e.a.71.31	yes	36
4.3	odd	2	inner	252.4.e.a.71.32	yes	36
12.11	even	2	inner	252.4.e.a.71.5	✓	36

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