LMFDB - Embedded newform 624.4.bv.h.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,4,Mod(49,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("624.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	624.bv (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$36.8171918436$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 $ x^10 + 70x^8 + 1645x^6 + 14700x^4 + 44100x^2 + 27648
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$-0.917374i$ of defining polynomial
Character	$\chi$	$=$	624.49
Dual form			624.4.bv.h.433.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +15.4704i q^{5} +(-17.8257 - 10.2917i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +15.4704i q^{5} +(-17.8257 - 10.2917i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(57.0209 - 32.9210i) q^{11} +(19.2429 - 42.7400i) q^{13} +(-40.1933 + 23.2056i) q^{15} +(22.1478 - 38.3611i) q^{17} +(-127.352 - 73.5266i) q^{19} -61.7500i q^{21} +(-26.5793 - 46.0367i) q^{23} -114.334 q^{25} -27.0000 q^{27} +(19.3128 + 33.4508i) q^{29} +88.3894i q^{31} +(171.063 + 98.7630i) q^{33} +(159.216 - 275.771i) q^{35} +(68.3803 - 39.4794i) q^{37} +(139.906 - 14.1155i) q^{39} +(307.410 - 177.483i) q^{41} +(203.923 - 353.205i) q^{43} +(-120.580 - 69.6169i) q^{45} +67.9674i q^{47} +(40.3369 + 69.8656i) q^{49} +132.887 q^{51} +226.572 q^{53} +(509.302 + 882.136i) q^{55} -441.160i q^{57} +(123.002 + 71.0154i) q^{59} +(-133.416 + 231.083i) q^{61} +(160.431 - 92.6250i) q^{63} +(661.206 + 297.696i) q^{65} +(-356.098 + 205.593i) q^{67} +(79.7379 - 138.110i) q^{69} +(79.2458 + 45.7526i) q^{71} +63.1328i q^{73} +(-171.500 - 297.047i) q^{75} -1355.25 q^{77} +287.115 q^{79} +(-40.5000 - 70.1481i) q^{81} -373.812i q^{83} +(593.463 + 342.636i) q^{85} +(-57.9385 + 100.352i) q^{87} +(103.406 - 59.7013i) q^{89} +(-782.885 + 563.829i) q^{91} +(-229.643 + 132.584i) q^{93} +(1137.49 - 1970.18i) q^{95} +(480.341 + 277.325i) q^{97} +592.578i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	$ 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) $ 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$			15.4704i			1.38372i	0.722034	+	0.691858i	$0.243208\pi$
$5$			15.4704i			1.38372i	−0.722034	+	0.691858i	$0.756792\pi$
$6$		0			0
$7$	−17.8257	−	10.2917i	−0.962497	−	0.555698i	−0.0655563	−	0.997849i	$-0.520882\pi$
$7$	−17.8257	−	10.2917i	−0.962497	−	0.555698i	−0.896941	+	0.442151i	$0.854216\pi$
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	57.0209	−	32.9210i	1.56295	−	0.902369i	0.565992	−	0.824411i	$-0.308493\pi$
$11$	57.0209	−	32.9210i	1.56295	−	0.902369i	0.996957	−	0.0779583i	$-0.0248401\pi$
$12$		0			0
$13$	19.2429	−	42.7400i	0.410540	−	0.911842i
$13$	19.2429	−	42.7400i	0.410540	−	0.911842i
$14$		0			0
$15$	−40.1933	+	23.2056i	−0.691858	+	0.399444i
$16$		0			0
$17$	22.1478	−	38.3611i	0.315979	−	0.547291i	−0.663666	−	0.748029i	$-0.731001\pi$
$17$	22.1478	−	38.3611i	0.315979	−	0.547291i	0.979645	+	0.200738i	$0.0643339\pi$
$18$		0			0
$19$	−127.352	−	73.5266i	−1.53771	−	0.887798i	−0.998972	−	0.0453247i	$-0.985568\pi$
$19$	−127.352	−	73.5266i	−1.53771	−	0.887798i	−0.538738	−	0.842473i	$-0.681099\pi$
$20$		0			0
$21$		−	61.7500i		−	0.641665i
$22$		0			0
$23$	−26.5793	−	46.0367i	−0.240964	−	0.417362i	0.720025	−	0.693948i	$-0.244130\pi$
$23$	−26.5793	−	46.0367i	−0.240964	−	0.417362i	−0.960989	+	0.276586i	$0.910797\pi$
$24$		0			0
$25$	−114.334			−0.914669
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	19.3128	+	33.4508i	0.123666	+	0.214195i	0.921211	−	0.389064i	$-0.127202\pi$
$29$	19.3128	+	33.4508i	0.123666	+	0.214195i	−0.797545	+	0.603260i	$0.793868\pi$
$30$		0			0
$31$			88.3894i			0.512104i	0.966663	+	0.256052i	$0.0824218\pi$
$31$			88.3894i			0.512104i	−0.966663	+	0.256052i	$0.917578\pi$
$32$		0			0
$33$	171.063	+	98.7630i	0.902369	+	0.520983i
$34$		0			0
$35$	159.216	−	275.771i	0.768928	−	1.33182i
$36$		0			0
$37$	68.3803	−	39.4794i	0.303828	−	0.175415i	−0.340333	−	0.940305i	$-0.610540\pi$
$37$	68.3803	−	39.4794i	0.303828	−	0.175415i	0.644161	+	0.764890i	$0.277206\pi$
$38$		0			0
$39$	139.906	−	14.1155i	0.574434	−	0.0579561i
$40$		0			0
$41$	307.410	−	177.483i	1.17096	−	0.676054i	0.217053	−	0.976160i	$-0.430355\pi$
$41$	307.410	−	177.483i	1.17096	−	0.676054i	0.953906	+	0.300106i	$0.0970221\pi$
$42$		0			0
$43$	203.923	−	353.205i	0.723208	−	1.25263i	−0.236499	−	0.971632i	$-0.576000\pi$
$43$	203.923	−	353.205i	0.723208	−	1.25263i	0.959707	−	0.281002i	$-0.0906666\pi$
$44$		0			0
$45$	−120.580	−	69.6169i	−0.399444	−	0.230619i
$46$		0			0
$47$			67.9674i			0.210938i	0.994423	+	0.105469i	$0.0336343\pi$
$47$			67.9674i			0.210938i	−0.994423	+	0.105469i	$0.966366\pi$
$48$		0			0
$49$	40.3369	+	69.8656i	0.117600	+	0.203690i
$50$		0			0
$51$	132.887			0.364861
$52$		0			0
$53$	226.572			0.587209			0.293604	−	0.955927i	$-0.405145\pi$
$53$	226.572			0.587209			0.293604	+	0.955927i	$0.405145\pi$
$54$		0			0
$55$	509.302	+	882.136i	1.24862	+	2.16268i
$56$		0			0
$57$		−	441.160i		−	1.02514i
$58$		0			0
$59$	123.002	+	71.0154i	0.271416	+	0.156702i	0.629531	−	0.776976i	$-0.283247\pi$
$59$	123.002	+	71.0154i	0.271416	+	0.156702i	−0.358115	+	0.933677i	$0.616580\pi$
$60$		0			0
$61$	−133.416	+	231.083i	−0.280035	+	0.485034i	−0.971393	−	0.237478i	$-0.923679\pi$
$61$	−133.416	+	231.083i	−0.280035	+	0.485034i	0.691358	+	0.722512i	$0.257013\pi$
$62$		0			0
$63$	160.431	−	92.6250i	0.320832	−	0.185233i
$64$		0			0
$65$	661.206	+	297.696i	1.26173	+	0.568071i
$66$		0			0
$67$	−356.098	+	205.593i	−0.649318	+	0.374884i	−0.788195	−	0.615426i	$-0.788984\pi$
$67$	−356.098	+	205.593i	−0.649318	+	0.374884i	0.138877	+	0.990310i	$0.455651\pi$
$68$		0			0
$69$	79.7379	−	138.110i	0.139121	−	0.240964i
$70$		0			0
$71$	79.2458	+	45.7526i	0.132461	+	0.0764765i	0.564766	−	0.825251i	$-0.308966\pi$
$71$	79.2458	+	45.7526i	0.132461	+	0.0764765i	−0.432305	+	0.901727i	$0.642300\pi$
$72$		0			0
$73$			63.1328i			0.101221i	0.998718	+	0.0506105i	$0.0161167\pi$
$73$			63.1328i			0.101221i	−0.998718	+	0.0506105i	$0.983883\pi$
$74$		0			0
$75$	−171.500	−	297.047i	−0.264042	−	0.457335i
$76$		0			0
$77$	−1355.25			−2.00578
$78$		0			0
$79$	287.115			0.408899			0.204449	−	0.978877i	$-0.434460\pi$
$79$	287.115			0.408899			0.204449	+	0.978877i	$0.434460\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	373.812i		−	0.494352i	−0.968971	−	0.247176i	$-0.920497\pi$
$83$		−	373.812i		−	0.494352i	0.968971	−	0.247176i	$-0.0795026\pi$
$84$		0			0
$85$	593.463	+	342.636i	0.757295	+	0.437224i
$86$		0			0
$87$	−57.9385	+	100.352i	−0.0713984	+	0.123666i
$88$		0			0
$89$	103.406	−	59.7013i	0.123157	−	0.0711047i	−0.437156	−	0.899386i	$-0.644014\pi$
$89$	103.406	−	59.7013i	0.123157	−	0.0711047i	0.560313	+	0.828281i	$0.310681\pi$
$90$		0			0
$91$	−782.885	+	563.829i	−0.901853	+	0.649509i
$92$		0			0
$93$	−229.643	+	132.584i	−0.256052	+	0.147832i
$94$		0			0
$95$	1137.49	−	1970.18i	1.22846	−	2.12775i
$96$		0			0
$97$	480.341	+	277.325i	0.502796	+	0.290290i	0.729868	−	0.683589i	$-0.239582\pi$
$97$	480.341	+	277.325i	0.502796	+	0.290290i	−0.227071	+	0.973878i	$0.572915\pi$
$98$		0			0
$99$			592.578i			0.601579i
$100$		0			0
$101$	−231.282	−	400.593i	−0.227856	−	0.394658i	0.729317	−	0.684176i	$-0.239838\pi$
$101$	−231.282	−	400.593i	−0.227856	−	0.394658i	−0.957172	+	0.289518i	$0.906505\pi$
$102$		0			0
$103$	1122.07			1.07341			0.536704	−	0.843771i	$-0.319669\pi$
$103$	1122.07			1.07341			0.536704	+	0.843771i	$0.319669\pi$
$104$		0			0
$105$	955.298			0.887881
$106$		0			0
$107$	301.378	+	522.002i	0.272293	+	0.471625i	0.969449	−	0.245295i	$-0.0788848\pi$
$107$	301.378	+	522.002i	0.272293	+	0.471625i	−0.697156	+	0.716920i	$0.745551\pi$
$108$		0			0
$109$		−	1421.89i		−	1.24947i	−0.780837	−	0.624735i	$-0.785207\pi$
$109$		−	1421.89i		−	1.24947i	0.780837	−	0.624735i	$-0.214793\pi$
$110$		0			0
$111$	205.141	+	118.438i	0.175415	+	0.101276i
$112$		0			0
$113$	198.359	−	343.569i	0.165134	−	0.286020i	−0.771569	−	0.636145i	$-0.780528\pi$
$113$	198.359	−	343.569i	0.165134	−	0.286020i	0.936703	+	0.350126i	$0.113861\pi$
$114$		0			0
$115$	712.207	−	411.193i	0.577510	−	0.333426i
$116$		0			0
$117$	246.532	+	342.314i	0.194803	+	0.270487i
$118$		0			0
$119$	−789.600	+	455.876i	−0.608257	+	0.351177i
$120$		0			0
$121$	1502.09	−	2601.69i	1.12854	−	1.95469i
$122$		0			0
$123$	922.229	+	532.449i	0.676054	+	0.390320i
$124$		0			0
$125$			165.013i			0.118074i
$126$		0			0
$127$	−218.934	−	379.205i	−0.152970	−	0.264952i	0.779348	−	0.626592i	$-0.215551\pi$
$127$	−218.934	−	379.205i	−0.152970	−	0.264952i	−0.932318	+	0.361639i	$0.882217\pi$
$128$		0			0
$129$	1223.54			0.835089
$130$		0			0
$131$	−1657.44			−1.10543			−0.552715	−	0.833370i	$-0.686408\pi$
$131$	−1657.44			−1.10543			−0.552715	+	0.833370i	$0.686408\pi$
$132$		0			0
$133$	1513.42	+	2621.33i	0.986695	+	1.70901i
$134$		0			0
$135$		−	417.701i		−	0.266296i
$136$		0			0
$137$	−1703.84	−	983.711i	−1.06254	−	0.613460i	−0.136410	−	0.990653i	$-0.543556\pi$
$137$	−1703.84	−	983.711i	−1.06254	−	0.613460i	−0.926135	+	0.377192i	$0.876890\pi$
$138$		0			0
$139$	1412.57	−	2446.64i	0.861960	−	1.49296i	−0.00807518	−	0.999967i	$-0.502570\pi$
$139$	1412.57	−	2446.64i	0.861960	−	1.49296i	0.870035	−	0.492990i	$-0.164096\pi$
$140$		0			0
$141$	−176.585	+	101.951i	−0.105469	+	0.0608925i
$142$		0			0
$143$	−309.797	−	3070.57i	−0.181165	−	1.79562i
$144$		0			0
$145$	−517.498	+	298.777i	−0.296385	+	0.171118i
$146$		0			0
$147$	−121.011	+	209.597i	−0.0678966	+	0.117600i
$148$		0			0
$149$	690.792	+	398.829i	0.379811	+	0.219284i	0.677736	−	0.735305i	$-0.262961\pi$
$149$	690.792	+	398.829i	0.379811	+	0.219284i	−0.297925	+	0.954589i	$0.596294\pi$
$150$		0			0
$151$			161.987i			0.0873003i	0.999047	+	0.0436501i	$0.0138987\pi$
$151$			161.987i			0.0873003i	−0.999047	+	0.0436501i	$0.986101\pi$
$152$		0			0
$153$	199.330	+	345.250i	0.105326	+	0.182430i
$154$		0			0
$155$	−1367.42			−0.708606
$156$		0			0
$157$	−342.000			−0.173851			−0.0869255	−	0.996215i	$-0.527704\pi$
$157$	−342.000			−0.173851			−0.0869255	+	0.996215i	$0.527704\pi$
$158$		0			0
$159$	339.858	+	588.652i	0.169513	+	0.293604i
$160$		0			0
$161$			1094.18i			0.535613i
$162$		0			0
$163$	−482.027	−	278.299i	−0.231628	−	0.133730i	0.379695	−	0.925112i	$-0.376029\pi$
$163$	−482.027	−	278.299i	−0.231628	−	0.133730i	−0.611323	+	0.791381i	$0.709362\pi$
$164$		0			0
$165$	−1527.90	+	2646.41i	−0.720892	+	1.24862i
$166$		0			0
$167$	−2716.22	+	1568.21i	−1.25861	+	0.726658i	−0.972804	−	0.231630i	$-0.925594\pi$
$167$	−2716.22	+	1568.21i	−1.25861	+	0.726658i	−0.285805	+	0.958288i	$0.592261\pi$
$168$		0			0
$169$	−1456.42	−	1644.89i	−0.662913	−	0.748696i
$170$		0			0
$171$	1146.17	−	661.739i	0.512570	−	0.295933i
$172$		0			0
$173$	1662.10	−	2878.84i	0.730444	−	1.26517i	−0.226249	−	0.974070i	$-0.572646\pi$
$173$	1662.10	−	2878.84i	0.730444	−	1.26517i	0.956693	−	0.291097i	$-0.0940204\pi$
$174$		0			0
$175$	2038.08	+	1176.68i	0.880366	+	0.508280i
$176$		0			0
$177$			426.092i			0.180944i
$178$		0			0
$179$	1656.62	+	2869.36i	0.691743	+	1.19813i	0.971266	+	0.237995i	$0.0764900\pi$
$179$	1656.62	+	2869.36i	0.691743	+	1.19813i	−0.279524	+	0.960139i	$0.590177\pi$
$180$		0			0
$181$	−76.0118			−0.0312150			−0.0156075	−	0.999878i	$-0.504968\pi$
$181$	−76.0118			−0.0312150			−0.0156075	+	0.999878i	$0.504968\pi$
$182$		0			0
$183$	−800.494			−0.323356
$184$		0			0
$185$	610.762	+	1057.87i	0.242725	+	0.420412i
$186$		0			0
$187$		−	2916.51i		−	1.14052i
$188$		0			0
$189$	481.294	+	277.875i	0.185233	+	0.106944i
$190$		0			0
$191$	−2036.70	+	3527.66i	−0.771572	+	1.33640i	0.165129	+	0.986272i	$0.447196\pi$
$191$	−2036.70	+	3527.66i	−0.771572	+	1.33640i	−0.936701	+	0.350130i	$0.886138\pi$
$192$		0			0
$193$	751.347	−	433.791i	0.280224	−	0.161787i	−0.353301	−	0.935510i	$-0.614941\pi$
$193$	751.347	−	433.791i	0.280224	−	0.161787i	0.633525	+	0.773723i	$0.281608\pi$
$194$		0			0
$195$	218.372	+	2164.41i	0.0801947	+	0.794853i
$196$		0			0
$197$	1634.79	−	943.846i	0.591238	−	0.341352i	−0.174349	−	0.984684i	$-0.555782\pi$
$197$	1634.79	−	943.846i	0.591238	−	0.341352i	0.765587	+	0.643332i	$0.222449\pi$
$198$		0			0
$199$	−1393.11	+	2412.94i	−0.496256	+	0.859540i	−0.999991	−	0.00431832i	$-0.998625\pi$
$199$	−1393.11	+	2412.94i	−0.496256	+	0.859540i	0.503735	+	0.863858i	$0.331959\pi$
$200$		0			0
$201$	−1068.29	−	616.780i	−0.374884	−	0.216439i
$202$		0			0
$203$		−	795.045i		−	0.274883i
$204$		0			0
$205$	2745.74	+	4755.75i	0.935466	+	1.62027i
$206$		0			0
$207$	478.428			0.160643
$208$		0			0
$209$	−9682.28			−3.20448
$210$		0			0
$211$	354.395	+	613.830i	0.115628	+	0.200274i	0.918031	−	0.396509i	$-0.129779\pi$
$211$	354.395	+	613.830i	0.115628	+	0.200274i	−0.802403	+	0.596783i	$0.796445\pi$
$212$		0			0
$213$			274.516i			0.0883075i
$214$		0			0
$215$	5464.22	+	3154.77i	1.73329	+	1.00071i
$216$		0			0
$217$	909.675	−	1575.60i	0.284575	−	0.492898i
$218$		0			0
$219$	−164.024	+	94.6992i	−0.0506105	+	0.0292200i
$220$		0			0
$221$	−1213.37	−	1684.78i	−0.369321	−	0.512808i
$222$		0			0
$223$	4673.62	−	2698.32i	1.40345	−	0.810281i	0.408703	−	0.912667i	$-0.365981\pi$
$223$	4673.62	−	2698.32i	1.40345	−	0.810281i	0.994745	+	0.102386i	$0.0326477\pi$
$224$		0			0
$225$	514.501	−	891.142i	0.152445	−	0.264042i
$226$		0			0
$227$	−2755.51	−	1590.90i	−0.805682	−	0.465160i	0.0397724	−	0.999209i	$-0.487337\pi$
$227$	−2755.51	−	1590.90i	−0.805682	−	0.465160i	−0.845454	+	0.534048i	$0.820670\pi$
$228$		0			0
$229$			2034.00i			0.586945i	0.955967	+	0.293473i	$0.0948110\pi$
$229$			2034.00i			0.586945i	−0.955967	+	0.293473i	$0.905189\pi$
$230$		0			0
$231$	−2032.87	−	3521.04i	−0.579018	−	1.00289i
$232$		0			0
$233$	2794.22			0.785645			0.392823	−	0.919614i	$-0.371499\pi$
$233$	2794.22			0.785645			0.392823	+	0.919614i	$0.371499\pi$
$234$		0			0
$235$	−1051.48			−0.291878
$236$		0			0
$237$	430.673	+	745.948i	0.118039	+	0.204449i
$238$		0			0
$239$		−	5493.81i		−	1.48688i	−0.668800	−	0.743442i	$-0.733192\pi$
$239$		−	5493.81i		−	1.48688i	0.668800	−	0.743442i	$-0.266808\pi$
$240$		0			0
$241$	−3517.16	−	2030.63i	−0.940084	−	0.542758i	−0.0500976	−	0.998744i	$-0.515953\pi$
$241$	−3517.16	−	2030.63i	−0.940084	−	0.542758i	−0.889987	+	0.455986i	$0.849287\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−1080.85	+	624.028i	−0.281849	+	0.162725i
$246$		0			0
$247$	−5593.15	+	4028.15i	−1.44082	+	1.03767i
$248$		0			0
$249$	971.193	−	560.719i	0.247176	−	0.142707i
$250$		0			0
$251$	1785.44	−	3092.47i	0.448988	−	0.777670i	−0.549332	−	0.835604i	$-0.685118\pi$
$251$	1785.44	−	3092.47i	0.448988	−	0.777670i	0.998320	+	0.0579336i	$0.0184512\pi$
$252$		0			0
$253$	−3031.15	−	1750.04i	−0.753228	−	0.434877i
$254$		0			0
$255$			2055.82i			0.504863i
$256$		0			0
$257$	−3759.13	−	6511.01i	−0.912405	−	1.58033i	−0.810656	−	0.585522i	$-0.800889\pi$
$257$	−3759.13	−	6511.01i	−0.912405	−	1.58033i	−0.101749	−	0.994810i	$-0.532444\pi$
$258$		0			0
$259$	−1625.23			−0.389912
$260$		0			0
$261$	−347.631			−0.0824437
$262$		0			0
$263$	−2330.09	−	4035.84i	−0.546310	−	0.946237i	−0.998523	−	0.0543273i	$-0.982699\pi$
$263$	−2330.09	−	4035.84i	−0.546310	−	0.946237i	0.452213	−	0.891910i	$-0.350635\pi$
$264$		0			0
$265$			3505.16i			0.812530i
$266$		0			0
$267$	310.217	+	179.104i	0.0711047	+	0.0410523i
$268$		0			0
$269$	−2673.72	+	4631.02i	−0.606021	+	1.04966i	0.385869	+	0.922554i	$0.373902\pi$
$269$	−2673.72	+	4631.02i	−0.606021	+	1.04966i	−0.991889	+	0.127105i	$0.959432\pi$
$270$		0			0
$271$	−2574.76	+	1486.54i	−0.577143	+	0.333214i	−0.759997	−	0.649926i	$-0.774800\pi$
$271$	−2574.76	+	1486.54i	−0.577143	+	0.333214i	0.182854	+	0.983140i	$0.441466\pi$
$272$		0			0
$273$	−2639.20	−	1188.25i	−0.585097	−	0.263429i
$274$		0			0
$275$	−6519.40	+	3763.98i	−1.42958	+	0.825369i
$276$		0			0
$277$	−382.076	+	661.776i	−0.0828764	+	0.143546i	−0.904484	−	0.426507i	$-0.859744\pi$
$277$	−382.076	+	661.776i	−0.0828764	+	0.143546i	0.821608	+	0.570053i	$0.193077\pi$
$278$		0			0
$279$	−688.928	−	397.752i	−0.147832	−	0.0853506i
$280$		0			0
$281$		−	7040.34i		−	1.49463i	−0.664469	−	0.747316i	$-0.731342\pi$
$281$		−	7040.34i		−	1.49463i	0.664469	−	0.747316i	$-0.268658\pi$
$282$		0			0
$283$	4517.58	+	7824.68i	0.948913	+	1.64357i	0.747720	+	0.664015i	$0.231149\pi$
$283$	4517.58	+	7824.68i	0.948913	+	1.64357i	0.201194	+	0.979551i	$0.435518\pi$
$284$		0			0
$285$	6824.92			1.41850
$286$		0			0
$287$	−7306.39			−1.50273
$288$		0			0
$289$	1475.45	+	2555.55i	0.300315	+	0.520161i
$290$		0			0
$291$			1663.95i			0.335197i
$292$		0			0
$293$	−1546.06	−	892.617i	−0.308265	−	0.177977i	0.337885	−	0.941188i	$-0.390289\pi$
$293$	−1546.06	−	892.617i	−0.308265	−	0.177977i	−0.646150	+	0.763211i	$0.723622\pi$
$294$		0			0
$295$	−1098.64	+	1902.89i	−0.216831	+	0.375562i
$296$		0			0
$297$	−1539.56	+	888.867i	−0.300790	+	0.173661i
$298$		0			0
$299$	−2479.07	+	250.120i	−0.479494	+	0.0483773i
$300$		0			0
$301$	−7270.13	+	4197.41i	−1.39217	+	0.803771i
$302$		0			0
$303$	693.847	−	1201.78i	0.131553	−	0.227856i
$304$		0			0
$305$	−3574.94	−	2063.99i	−0.671150	−	0.387488i
$306$		0			0
$307$		−	5323.13i		−	0.989600i	−0.869007	−	0.494800i	$-0.835241\pi$
$307$		−	5323.13i		−	0.989600i	0.869007	−	0.494800i	$-0.164759\pi$
$308$		0			0
$309$	1683.11	+	2915.23i	0.309866	+	0.536704i
$310$		0			0
$311$	6265.64			1.14242			0.571209	−	0.820805i	$-0.306475\pi$
$311$	6265.64			1.14242			0.571209	+	0.820805i	$0.306475\pi$
$312$		0			0
$313$	7193.77			1.29909			0.649547	−	0.760322i	$-0.274959\pi$
$313$	7193.77			1.29909			0.649547	+	0.760322i	$0.274959\pi$
$314$		0			0
$315$	1432.95	+	2481.94i	0.256309	+	0.443941i
$316$		0			0
$317$			9576.87i			1.69682i	0.529343	+	0.848408i	$0.322439\pi$
$317$			9576.87i			1.69682i	−0.529343	+	0.848408i	$0.677561\pi$
$318$		0			0
$319$	2202.47	+	1271.60i	0.386566	+	0.223184i
$320$		0			0
$321$	−904.134	+	1566.01i	−0.157208	+	0.272293i
$322$		0			0
$323$	−5641.13	+	3256.91i	−0.971767	+	0.561050i
$324$		0			0
$325$	−2200.11	+	4886.62i	−0.375509	+	0.834034i
$326$		0			0
$327$	3694.18	−	2132.83i	0.624735	−	0.360691i
$328$		0			0
$329$	699.498	−	1211.57i	0.117218	−	0.203027i
$330$		0			0
$331$	−4999.68	−	2886.56i	−0.830233	−	0.479335i	0.0236996	−	0.999719i	$-0.492455\pi$
$331$	−4999.68	−	2886.56i	−0.830233	−	0.479335i	−0.853932	+	0.520384i	$0.825789\pi$
$332$		0			0
$333$			710.629i			0.116944i
$334$		0			0
$335$	−3180.61	−	5508.98i	−0.518733	−	0.898471i
$336$		0			0
$337$	−1238.09			−0.200127			−0.100063	−	0.994981i	$-0.531905\pi$
$337$	−1238.09			−0.200127			−0.100063	+	0.994981i	$0.531905\pi$
$338$		0			0
$339$	1190.16			0.190680
$340$		0			0
$341$	2909.87	+	5040.04i	0.462106	+	0.800392i
$342$		0			0
$343$			5399.55i			0.849995i
$344$		0			0
$345$	2136.62	+	1233.58i	0.333426	+	0.192503i
$346$		0			0
$347$	2724.98	−	4719.81i	0.421570	−	0.730181i	−0.574523	−	0.818488i	$-0.694813\pi$
$347$	2724.98	−	4719.81i	0.421570	−	0.730181i	0.996093	+	0.0883076i	$0.0281459\pi$
$348$		0			0
$349$	−1189.95	+	687.016i	−0.182511	+	0.105373i	−0.588472	−	0.808518i	$-0.700270\pi$
$349$	−1189.95	+	687.016i	−0.182511	+	0.105373i	0.405961	+	0.913890i	$0.366937\pi$
$350$		0			0
$351$	−519.559	+	1153.98i	−0.0790085	+	0.175484i
$352$		0			0
$353$	5170.55	−	2985.22i	0.779606	−	0.450106i	−0.0566848	−	0.998392i	$-0.518053\pi$
$353$	5170.55	−	2985.22i	0.779606	−	0.450106i	0.836291	+	0.548287i	$0.184720\pi$
$354$		0			0
$355$	−707.811	+	1225.97i	−0.105822	+	0.183289i
$356$		0			0
$357$	−2368.80	−	1367.63i	−0.351177	−	0.202752i
$358$		0			0
$359$			7813.71i			1.14872i	0.818602	+	0.574362i	$0.194750\pi$
$359$			7813.71i			1.14872i	−0.818602	+	0.574362i	$0.805250\pi$
$360$		0			0
$361$	7382.82	+	12787.4i	1.07637	+	1.86433i
$362$		0			0
$363$	9012.52			1.30312
$364$		0			0
$365$	−976.690			−0.140061
$366$		0			0
$367$	844.195	+	1462.19i	0.120073	+	0.207972i	0.919796	−	0.392397i	$-0.128354\pi$
$367$	844.195	+	1462.19i	0.120073	+	0.207972i	−0.799724	+	0.600368i	$0.795021\pi$
$368$		0			0
$369$			3194.69i			0.450702i
$370$		0			0
$371$	−4038.80	−	2331.81i	−0.565187	−	0.326311i
$372$		0			0
$373$	−935.307	+	1620.00i	−0.129835	+	0.224880i	−0.923612	−	0.383328i	$-0.874778\pi$
$373$	−935.307	+	1620.00i	−0.129835	+	0.224880i	0.793778	+	0.608208i	$0.208111\pi$
$374$		0			0
$375$	−428.717	+	247.520i	−0.0590369	+	0.0340850i
$376$		0			0
$377$	1801.32	−	181.740i	0.246082	−	0.0248278i
$378$		0			0
$379$	−10103.9	+	5833.52i	−1.36941	+	0.790627i	−0.990852	−	0.134952i	$-0.956912\pi$
$379$	−10103.9	+	5833.52i	−1.36941	+	0.790627i	−0.378554	+	0.925579i	$0.623579\pi$
$380$		0			0
$381$	656.801	−	1137.61i	0.0883175	−	0.152970i
$382$		0			0
$383$	−5782.11	−	3338.30i	−0.771415	−	0.445376i	0.0619643	−	0.998078i	$-0.480263\pi$
$383$	−5782.11	−	3338.30i	−0.771415	−	0.445376i	−0.833379	+	0.552702i	$0.813597\pi$
$384$		0			0
$385$		−	20966.3i		−	2.77543i
$386$		0			0
$387$	1835.31	+	3178.84i	0.241069	+	0.417544i
$388$		0			0
$389$	−14285.3			−1.86194			−0.930969	−	0.365099i	$-0.881035\pi$
$389$	−14285.3			−1.86194			−0.930969	+	0.365099i	$0.881035\pi$
$390$		0			0
$391$	−2354.69			−0.304558
$392$		0			0
$393$	−2486.16	−	4306.16i	−0.319110	−	0.552715i
$394$		0			0
$395$			4441.79i			0.565800i
$396$		0			0
$397$	3091.09	+	1784.64i	0.390774	+	0.225614i	0.682496	−	0.730890i	$-0.260895\pi$
$397$	3091.09	+	1784.64i	0.390774	+	0.225614i	−0.291721	+	0.956503i	$0.594228\pi$
$398$		0			0
$399$	−4540.27	+	7863.98i	−0.569668	+	0.986695i
$400$		0			0
$401$	−432.448	+	249.674i	−0.0538540	+	0.0310926i	−0.526685	−	0.850060i	$-0.676565\pi$
$401$	−432.448	+	249.674i	−0.0538540	+	0.0310926i	0.472831	+	0.881153i	$0.343232\pi$
$402$		0			0
$403$	3777.77	+	1700.87i	0.466958	+	0.210239i
$404$		0			0
$405$	1085.22	−	626.552i	0.133148	−	0.0768731i
$406$		0			0
$407$	2599.40	−	4502.30i	0.316579	−	0.548331i
$408$		0			0
$409$	−9056.46	−	5228.75i	−1.09490	−	0.632140i	−0.160022	−	0.987114i	$-0.551156\pi$
$409$	−9056.46	−	5228.75i	−1.09490	−	0.632140i	−0.934876	+	0.354974i	$0.884490\pi$
$410$		0			0
$411$		−	5902.26i		−	0.708363i
$412$		0			0
$413$	−1461.73	−	2531.80i	−0.174158	−	0.301650i
$414$		0			0
$415$	5783.03			0.684043
$416$		0			0
$417$	8475.40			0.995305
$418$		0			0
$419$	−852.710	−	1476.94i	−0.0994215	−	0.172203i	0.812024	−	0.583624i	$-0.198366\pi$
$419$	−852.710	−	1476.94i	−0.0994215	−	0.172203i	−0.911445	+	0.411421i	$0.865033\pi$
$420$		0			0
$421$		−	8765.57i		−	1.01475i	−0.861727	−	0.507373i	$-0.830617\pi$
$421$		−	8765.57i		−	1.01475i	0.861727	−	0.507373i	$-0.169383\pi$
$422$		0			0
$423$	−529.754	−	305.853i	−0.0608925	−	0.0351563i
$424$		0			0
$425$	−2532.24	+	4385.97i	−0.289016	+	0.500590i
$426$		0			0
$427$	4756.45	−	2746.14i	0.539065	−	0.311229i
$428$		0			0
$429$	7512.88	−	5410.73i	0.845513	−	0.608934i
$430$		0			0
$431$	6997.81	−	4040.18i	0.782071	−	0.451529i	−0.0550930	−	0.998481i	$-0.517546\pi$
$431$	6997.81	−	4040.18i	0.782071	−	0.451529i	0.837164	+	0.546953i	$0.184212\pi$
$432$		0			0
$433$	−2062.24	+	3571.91i	−0.228880	+	0.396432i	−0.957476	−	0.288511i	$-0.906840\pi$
$433$	−2062.24	+	3571.91i	−0.228880	+	0.396432i	0.728596	+	0.684943i	$0.240173\pi$
$434$		0			0
$435$	−1552.49	−	896.332i	−0.171118	−	0.0987950i
$436$		0			0
$437$			7817.14i			0.855709i
$438$		0			0
$439$	3057.76	+	5296.19i	0.332435	+	0.575794i	0.982989	−	0.183666i	$-0.0587965\pi$
$439$	3057.76	+	5296.19i	0.332435	+	0.575794i	−0.650554	+	0.759460i	$0.725463\pi$
$440$		0			0
$441$	−726.064			−0.0784002
$442$		0			0
$443$	11058.8			1.18605			0.593025	−	0.805184i	$-0.297933\pi$
$443$	11058.8			1.18605			0.593025	+	0.805184i	$0.297933\pi$
$444$		0			0
$445$	923.603	+	1599.73i	0.0983887	+	0.170414i
$446$		0			0
$447$			2392.97i			0.253208i
$448$		0			0
$449$	209.588	+	121.006i	0.0220291	+	0.0127185i	0.510974	−	0.859596i	$-0.329285\pi$
$449$	209.588	+	121.006i	0.0220291	+	0.0127185i	−0.488945	+	0.872315i	$0.662618\pi$
$450$		0			0
$451$	11685.8	−	20240.5i	1.22010	−	2.11327i
$452$		0			0
$453$	−420.855	+	242.981i	−0.0436501	+	0.0252014i
$454$		0			0
$455$	−8722.67	−	12111.5i	−0.898736	−	1.24791i
$456$		0			0
$457$	9571.46	−	5526.08i	0.979724	−	0.565644i	0.0775372	−	0.996989i	$-0.475294\pi$
$457$	9571.46	−	5526.08i	0.979724	−	0.565644i	0.902187	+	0.431346i	$0.141961\pi$
$458$		0			0
$459$	−597.991	+	1035.75i	−0.0608101	+	0.105326i
$460$		0			0
$461$	237.086	+	136.882i	0.0239527	+	0.0138291i	0.511929	−	0.859028i	$-0.328931\pi$
$461$	237.086	+	136.882i	0.0239527	+	0.0138291i	−0.487976	+	0.872857i	$0.662265\pi$
$462$		0			0
$463$		−	11579.2i		−	1.16227i	−0.813808	−	0.581134i	$-0.802609\pi$
$463$		−	11579.2i		−	1.16227i	0.813808	−	0.581134i	$-0.197391\pi$
$464$		0			0
$465$	−2051.13	−	3552.66i	−0.204557	−	0.354303i
$466$		0			0
$467$	902.915			0.0894688			0.0447344	−	0.998999i	$-0.485756\pi$
$467$	902.915			0.0894688			0.0447344	+	0.998999i	$0.485756\pi$
$468$		0			0
$469$	8463.59			0.833289
$470$		0			0
$471$	−513.001	−	888.543i	−0.0501865	−	0.0869255i
$472$		0			0
$473$		−	26853.4i		−	2.61040i
$474$		0			0
$475$	14560.6	+	8406.56i	1.40650	+	0.812041i
$476$		0			0
$477$	−1019.57	+	1765.95i	−0.0978682	+	0.169513i
$478$		0			0
$479$	10451.9	−	6034.38i	0.996988	−	0.575611i	0.0896324	−	0.995975i	$-0.471431\pi$
$479$	10451.9	−	6034.38i	0.996988	−	0.575611i	0.907356	+	0.420364i	$0.138097\pi$
$480$		0			0
$481$	−371.514	−	3682.27i	−0.0352174	−	0.349059i
$482$		0			0
$483$	−2842.77	+	1641.27i	−0.267806	+	0.154618i
$484$		0			0
$485$	−4290.33	+	7431.07i	−0.401678	+	0.695727i
$486$		0			0
$487$	−9952.82	−	5746.26i	−0.926089	−	0.534678i	−0.0405163	−	0.999179i	$-0.512900\pi$
$487$	−9952.82	−	5746.26i	−0.926089	−	0.534678i	−0.885572	+	0.464501i	$0.846234\pi$
$488$		0			0
$489$		−	1669.79i		−	0.154418i
$490$		0			0
$491$	−7852.08	−	13600.2i	−0.721710	−	1.25004i	−0.960314	−	0.278921i	$-0.910023\pi$
$491$	−7852.08	−	13600.2i	−0.721710	−	1.25004i	0.238605	−	0.971117i	$-0.423310\pi$
$492$		0			0
$493$	1710.95			0.156303
$494$		0			0
$495$	−9167.43			−0.832415
$496$		0			0
$497$	−941.741	−	1631.14i	−0.0849957	−	0.147217i
$498$		0			0
$499$			9019.80i			0.809181i	0.914498	+	0.404591i	$0.132586\pi$
$499$			9019.80i			0.809181i	−0.914498	+	0.404591i	$0.867414\pi$
$500$		0			0
$501$	−8148.67	−	4704.64i	−0.726658	−	0.419536i
$502$		0			0
$503$	−3016.92	+	5225.46i	−0.267431	+	0.463204i	−0.968198	−	0.250186i	$-0.919508\pi$
$503$	−3016.92	+	5225.46i	−0.267431	+	0.463204i	0.700767	+	0.713391i	$0.252841\pi$
$504$		0			0
$505$	6197.33	−	3578.03i	0.546094	−	0.315288i
$506$		0			0
$507$	2088.91	−	6251.22i	0.182981	−	0.547587i
$508$		0			0
$509$	−19443.6	+	11225.8i	−1.69317	+	0.977551i	−0.741234	+	0.671246i	$0.765759\pi$
$509$	−19443.6	+	11225.8i	−1.69317	+	0.977551i	−0.951934	+	0.306304i	$0.900907\pi$
$510$		0			0
$511$	649.742	−	1125.39i	0.0562483	−	0.0974249i
$512$		0			0
$513$	3438.50	+	1985.22i	0.295933	+	0.170857i
$514$		0			0
$515$			17358.9i			1.48529i
$516$		0			0
$517$	2237.56	+	3875.56i	0.190344	+	0.329685i
$518$		0			0
$519$	9972.58			0.843445
$520$		0			0
$521$	15674.7			1.31808			0.659040	−	0.752108i	$-0.270963\pi$
$521$	15674.7			1.31808			0.659040	+	0.752108i	$0.270963\pi$
$522$		0			0
$523$	6755.39	+	11700.7i	0.564804	+	0.978270i	0.997068	+	0.0765223i	$0.0243816\pi$
$523$	6755.39	+	11700.7i	0.564804	+	0.978270i	−0.432264	+	0.901747i	$0.642285\pi$
$524$		0			0
$525$			7060.10i			0.586911i
$526$		0			0
$527$	3390.72	+	1957.63i	0.280270	+	0.161814i
$528$		0			0
$529$	4670.58	−	8089.68i	0.383873	−	0.664887i
$530$		0			0
$531$	−1107.02	+	639.138i	−0.0904719	+	0.0522340i
$532$		0			0
$533$	−1670.17	−	16554.0i	−0.135728	−	1.34528i
$534$		0			0
$535$	−8075.59	+	4662.44i	−0.652595	+	0.376776i
$536$		0			0
$537$	−4969.87	+	8608.07i	−0.399378	+	0.691743i
$538$		0			0
$539$	4600.09	+	2655.86i	0.367607	+	0.212238i
$540$		0			0
$541$			12103.6i			0.961875i	0.876755	+	0.480937i	$0.159704\pi$
$541$			12103.6i			0.961875i	−0.876755	+	0.480937i	$0.840296\pi$
$542$		0			0
$543$	−114.018	−	197.485i	−0.00901100	−	0.0156075i
$544$		0			0
$545$	21997.2			1.72891
$546$		0			0
$547$	15228.6			1.19036			0.595181	−	0.803592i	$-0.297080\pi$
$547$	15228.6			1.19036			0.595181	+	0.803592i	$0.297080\pi$
$548$		0			0
$549$	−1200.74	−	2079.74i	−0.0933449	−	0.161678i
$550$		0			0
$551$		−	5680.03i		−	0.439160i
$552$		0			0
$553$	−5118.03	−	2954.90i	−0.393564	−	0.227224i
$554$		0			0
$555$	−1832.29	+	3173.61i	−0.140137	+	0.242725i
$556$		0			0
$557$	20435.5	−	11798.5i	1.55454	−	0.897516i	0.556781	−	0.830660i	$-0.312036\pi$
$557$	20435.5	−	11798.5i	1.55454	−	0.897516i	0.997763	−	0.0668564i	$-0.0212969\pi$
$558$		0			0
$559$	−11171.9	−	15512.4i	−0.845298	−	1.17371i
$560$		0			0
$561$	7577.33	−	4374.77i	0.570258	−	0.329239i
$562$		0			0
$563$	−3970.81	+	6877.64i	−0.297246	+	0.514846i	−0.975505	−	0.219978i	$-0.929402\pi$
$563$	−3970.81	+	6877.64i	−0.297246	+	0.514846i	0.678259	+	0.734823i	$0.262735\pi$
$564$		0			0
$565$	5315.15	+	3068.70i	0.395770	+	0.228498i
$566$		0			0
$567$			1667.25i			0.123488i
$568$		0			0
$569$	1137.33	+	1969.91i	0.0837948	+	0.145137i	0.904877	−	0.425673i	$-0.139963\pi$
$569$	1137.33	+	1969.91i	0.0837948	+	0.145137i	−0.821082	+	0.570810i	$0.806629\pi$
$570$		0			0
$571$	−4499.84			−0.329794			−0.164897	−	0.986311i	$-0.552729\pi$
$571$	−4499.84			−0.329794			−0.164897	+	0.986311i	$0.552729\pi$
$572$		0			0
$573$	−12220.2			−0.890934
$574$		0			0
$575$	3038.91	+	5263.55i	0.220402	+	0.381748i
$576$		0			0
$577$			25253.3i			1.82202i	0.412381	+	0.911011i	$0.364697\pi$
$577$			25253.3i			1.82202i	−0.412381	+	0.911011i	$0.635303\pi$
$578$		0			0
$579$	2254.04	+	1301.37i	0.161787	+	0.0934079i
$580$		0			0
$581$	−3847.15	+	6663.47i	−0.274711	+	0.475813i
$582$		0			0
$583$	12919.3	−	7458.98i	0.917777	−	0.529879i
$584$		0			0
$585$	−5295.74	+	3813.96i	−0.374276	+	0.269552i
$586$		0			0
$587$	−9773.25	+	5642.59i	−0.687198	+	0.396754i	−0.802562	−	0.596569i	$-0.796530\pi$
$587$	−9773.25	+	5642.59i	−0.687198	+	0.396754i	0.115363	+	0.993323i	$0.463197\pi$
$588$		0			0
$589$	6498.97	−	11256.6i	0.454644	−	0.787467i
$590$		0			0
$591$	4904.37	+	2831.54i	0.341352	+	0.197079i
$592$		0			0
$593$			12824.5i			0.888090i	0.896005	+	0.444045i	$0.146457\pi$
$593$			12824.5i			0.888090i	−0.896005	+	0.444045i	$0.853543\pi$
$594$		0			0
$595$	−7052.59	−	12215.4i	−0.485929	−	0.841654i
$596$		0			0
$597$	−8358.65			−0.573027
$598$		0			0
$599$	26180.3			1.78581			0.892905	−	0.450245i	$-0.148664\pi$
$599$	26180.3			1.78581			0.892905	+	0.450245i	$0.148664\pi$
$600$		0			0
$601$	−8006.28	−	13867.3i	−0.543399	−	0.941195i	−0.998706	−	0.0508602i	$-0.983804\pi$
$601$	−8006.28	−	13867.3i	−0.543399	−	0.941195i	0.455307	−	0.890335i	$-0.349530\pi$
$602$		0			0
$603$		−	3700.68i		−	0.249923i
$604$		0			0
$605$	40249.2	+	23237.9i	2.70473	+	1.56158i
$606$		0			0
$607$	−4765.74	+	8254.50i	−0.318674	+	0.551960i	−0.980212	−	0.197952i	$-0.936571\pi$
$607$	−4765.74	+	8254.50i	−0.318674	+	0.551960i	0.661537	+	0.749912i	$0.269904\pi$
$608$		0			0
$609$	2065.59	−	1192.57i	0.137441	−	0.0793519i
$610$		0			0
$611$	2904.93	+	1307.89i	0.192342	+	0.0865984i
$612$		0			0
$613$	−8822.27	+	5093.54i	−0.581286	+	0.335605i	−0.761644	−	0.647996i	$-0.775608\pi$
$613$	−8822.27	+	5093.54i	−0.581286	+	0.335605i	0.180359	+	0.983601i	$0.442274\pi$
$614$		0			0
$615$	−8237.21	+	14267.3i	−0.540091	+	0.935466i
$616$		0			0
$617$	6939.13	+	4006.31i	0.452770	+	0.261407i	0.708999	−	0.705209i	$-0.249147\pi$
$617$	6939.13	+	4006.31i	0.452770	+	0.261407i	−0.256230	+	0.966616i	$0.582480\pi$
$618$		0			0
$619$		−	1886.59i		−	0.122501i	−0.998122	−	0.0612506i	$-0.980491\pi$
$619$		−	1886.59i		−	0.122501i	0.998122	−	0.0612506i	$-0.0195089\pi$
$620$		0			0
$621$	717.641	+	1242.99i	0.0463735	+	0.0803213i
$622$		0			0
$623$	−2457.70			−0.158051
$624$		0			0
$625$	−16844.5			−1.07805
$626$		0			0
$627$	−14523.4	−	25155.3i	−0.925055	−	1.60224i
$628$		0			0
$629$		−	3497.53i		−	0.221710i
$630$		0			0
$631$	12952.3	+	7478.04i	0.817154	+	0.471784i	0.849434	−	0.527695i	$-0.176943\pi$
$631$	12952.3	+	7478.04i	0.817154	+	0.471784i	−0.0322798	+	0.999479i	$0.510277\pi$
$632$		0			0
$633$	−1063.18	+	1841.49i	−0.0667579	+	0.115628i
$634$		0			0
$635$	5866.45	−	3387.00i	0.366619	−	0.211667i
$636$		0			0
$637$	3762.26	−	379.583i	0.234013	−	0.0236101i
$638$		0			0
$639$	−713.212	+	411.773i	−0.0441537	+	0.0254922i
$640$		0			0
$641$	11845.9	−	20517.6i	0.729927	−	1.26427i	−0.226986	−	0.973898i	$-0.572887\pi$
$641$	11845.9	−	20517.6i	0.729927	−	1.26427i	0.956913	−	0.290373i	$-0.0937794\pi$
$642$		0			0
$643$	−11822.4	−	6825.65i	−0.725083	−	0.418627i	0.0915374	−	0.995802i	$-0.470822\pi$
$643$	−11822.4	−	6825.65i	−0.725083	−	0.418627i	−0.816621	+	0.577175i	$0.804155\pi$
$644$		0			0
$645$			18928.6i			1.15553i
$646$		0			0
$647$	9066.14	+	15703.0i	0.550892	+	0.954172i	0.998211	+	0.0597977i	$0.0190456\pi$
$647$	9066.14	+	15703.0i	0.550892	+	0.954172i	−0.447319	+	0.894375i	$0.647621\pi$
$648$		0			0
$649$	9351.59			0.565612
$650$		0			0
$651$	5458.05			0.328599
$652$		0			0
$653$	−3181.74	−	5510.93i	−0.190675	−	0.330259i	0.754799	−	0.655956i	$-0.227734\pi$
$653$	−3181.74	−	5510.93i	−0.190675	−	0.330259i	−0.945474	+	0.325697i	$0.894401\pi$
$654$		0			0
$655$		−	25641.3i		−	1.52960i
$656$		0			0
$657$	−492.071	−	284.098i	−0.0292200	−	0.0168702i
$658$		0			0
$659$	−525.717	+	910.568i	−0.0310759	+	0.0538250i	−0.881145	−	0.472846i	$-0.843227\pi$
$659$	−525.717	+	910.568i	−0.0310759	+	0.0538250i	0.850069	+	0.526671i	$0.176560\pi$
$660$		0			0
$661$	7031.91	−	4059.87i	0.413781	−	0.238897i	−0.278632	−	0.960398i	$-0.589881\pi$
$661$	7031.91	−	4059.87i	0.413781	−	0.238897i	0.692413	+	0.721501i	$0.256548\pi$
$662$		0			0
$663$	2557.13	−	5679.59i	0.149790	−	0.332695i
$664$		0			0
$665$	−40553.0	+	23413.3i	−2.36478	+	1.36530i
$666$		0			0
$667$	1026.64	−	1778.20i	0.0595979	−	0.103227i
$668$		0			0
$669$	14020.9	+	8094.95i	0.810281	+	0.467816i
$670$		0			0
$671$			17568.7i			1.01078i
$672$		0			0
$673$	−95.1322	−	164.774i	−0.00544885	−	0.00943769i	0.863288	−	0.504711i	$-0.168401\pi$
$673$	−95.1322	−	164.774i	−0.00544885	−	0.00943769i	−0.868737	+	0.495274i	$0.835068\pi$
$674$		0			0
$675$	3087.01			0.176028
$676$		0			0
$677$	4861.93			0.276010			0.138005	−	0.990431i	$-0.455931\pi$
$677$	4861.93			0.276010			0.138005	+	0.990431i	$0.455931\pi$
$678$		0			0
$679$	−5708.27	−	9887.02i	−0.322627	−	0.558806i
$680$		0			0
$681$		−	9545.37i		−	0.537121i
$682$		0			0
$683$	−12591.7	−	7269.80i	−0.705426	−	0.407278i	0.103939	−	0.994584i	$-0.466855\pi$
$683$	−12591.7	−	7269.80i	−0.705426	−	0.407278i	−0.809365	+	0.587306i	$0.800189\pi$
$684$		0			0
$685$	15218.4	−	26359.1i	0.848855	−	1.47026i
$686$		0			0
$687$	−5284.49	+	3051.00i	−0.293473	+	0.169436i
$688$		0			0
$689$	4359.91	−	9683.70i	0.241073	−	0.535442i
$690$		0			0
$691$	−19144.8	+	11053.2i	−1.05398	+	0.608517i	−0.923762	−	0.382968i	$-0.874902\pi$
$691$	−19144.8	+	11053.2i	−1.05398	+	0.608517i	−0.130221	+	0.991485i	$0.541569\pi$
$692$		0			0
$693$	6098.62	−	10563.1i	0.334296	−	0.579018i
$694$		0			0
$695$	37850.5	+	21853.0i	2.06583	+	1.19271i
$696$		0			0
$697$		−	15723.4i		−	0.854474i
$698$		0			0
$699$	4191.33	+	7259.59i	0.226796	+	0.392823i
$700$		0			0
$701$	−229.971			−0.0123907			−0.00619535	−	0.999981i	$-0.501972\pi$
$701$	−229.971			−0.0123907			−0.00619535	+	0.999981i	$0.501972\pi$
$702$		0			0
$703$	−11611.1			−0.622934
$704$		0			0
$705$	−1577.23	−	2731.84i	−0.0842578	−	0.145939i
$706$		0			0
$707$			9521.12i			0.506476i
$708$		0			0
$709$	4158.85	+	2401.11i	0.220294	+	0.127187i	0.606087	−	0.795399i	$-0.292738\pi$
$709$	4158.85	+	2401.11i	0.220294	+	0.127187i	−0.385792	+	0.922586i	$0.626072\pi$
$710$		0			0
$711$	−1292.02	+	2237.84i	−0.0681498	+	0.118039i
$712$		0			0
$713$	4069.16	−	2349.33i	0.213732	−	0.123398i
$714$		0			0
$715$	47503.0	−	4792.69i	2.48463	−	0.250681i
$716$		0			0
$717$	14273.3	−	8240.72i	0.743442	−	0.429227i
$718$		0			0
$719$	5508.46	−	9540.94i	0.285718	−	0.494878i	−0.687065	−	0.726596i	$-0.741101\pi$
$719$	5508.46	−	9540.94i	0.285718	−	0.494878i	0.972783	+	0.231718i	$0.0744347\pi$
$720$		0			0
$721$	−20001.7	−	11548.0i	−1.03315	−	0.596491i
$722$		0			0
$723$		−	12183.8i		−	0.626723i
$724$		0			0
$725$	−2208.11	−	3824.55i	−0.113113	−	0.195918i
$726$		0			0
$727$	−13498.2			−0.688612			−0.344306	−	0.938857i	$-0.611886\pi$
$727$	−13498.2			−0.688612			−0.344306	+	0.938857i	$0.611886\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−9032.89	−	15645.4i	−0.457037	−	0.791610i
$732$		0			0
$733$			17014.7i			0.857368i	0.903455	+	0.428684i	$0.141023\pi$
$733$			17014.7i			0.857368i	−0.903455	+	0.428684i	$0.858977\pi$
$734$		0			0
$735$	−3242.55	−	1872.09i	−0.162725	−	0.0939495i
$736$		0			0
$737$	−13536.7	+	23446.2i	−0.676567	+	1.17185i
$738$		0			0
$739$	−11598.3	+	6696.31i	−0.577337	+	0.333326i	−0.760074	−	0.649836i	$-0.774838\pi$
$739$	−11598.3	+	6696.31i	−0.577337	+	0.333326i	0.182737	+	0.983162i	$0.441504\pi$
$740$		0			0
$741$	−18855.2	−	8489.20i	−0.934767	−	0.420862i
$742$		0			0
$743$	10216.1	−	5898.26i	0.504431	−	0.291233i	−0.226111	−	0.974102i	$-0.572601\pi$
$743$	10216.1	−	5898.26i	0.504431	−	0.291233i	0.730541	+	0.682868i	$0.239268\pi$
$744$		0			0
$745$	−6170.05	+	10686.8i	−0.303427	+	0.525551i
$746$		0			0
$747$	2913.58	+	1682.16i	0.142707	+	0.0823921i
$748$		0			0
$749$		−	12406.7i		−	0.605250i
$750$		0			0
$751$	6225.26	+	10782.5i	0.302480	+	0.523911i	0.976697	−	0.214622i	$-0.0688520\pi$
$751$	6225.26	+	10782.5i	0.302480	+	0.523911i	−0.674217	+	0.738534i	$0.735519\pi$
$752$		0			0
$753$	10712.6			0.518447
$754$		0			0
$755$	−2506.01			−0.120799
$756$		0			0
$757$	3514.92	+	6088.02i	0.168761	+	0.292302i	0.937984	−	0.346677i	$-0.112690\pi$
$757$	3514.92	+	6088.02i	0.168761	+	0.292302i	−0.769224	+	0.638980i	$0.779357\pi$
$758$		0			0
$759$		−	10500.2i		−	0.502152i
$760$		0			0
$761$	−15363.8	−	8870.29i	−0.731849	−	0.422533i	0.0872491	−	0.996187i	$-0.472192\pi$
$761$	−15363.8	−	8870.29i	−0.731849	−	0.422533i	−0.819098	+	0.573653i	$0.805526\pi$
$762$		0			0
$763$	−14633.6	+	25346.2i	−0.694328	+	1.20261i
$764$		0			0
$765$	−5341.16	+	3083.72i	−0.252432	+	0.145741i
$766$		0			0
$767$	5402.12	−	3890.58i	0.254314	−	0.183156i
$768$		0			0
$769$	−27692.4	+	15988.2i	−1.29859	+	0.749741i	−0.980160	−	0.198206i	$-0.936489\pi$
$769$	−27692.4	+	15988.2i	−1.29859	+	0.749741i	−0.318429	+	0.947947i	$0.603155\pi$
$770$		0			0
$771$	11277.4	−	19533.0i	0.526777	−	0.912405i
$772$		0			0
$773$	−1849.06	−	1067.56i	−0.0860364	−	0.0496732i	0.456365	−	0.889793i	$-0.349151\pi$
$773$	−1849.06	−	1067.56i	−0.0860364	−	0.0496732i	−0.542401	+	0.840120i	$0.682485\pi$
$774$		0			0
$775$		−	10105.9i		−	0.468405i
$776$		0			0
$777$	−2437.85	−	4222.48i	−0.112558	−	0.194956i
$778$		0			0
$779$	−52198.9			−2.40080
$780$		0			0
$781$	6024.89			0.276040
$782$		0			0
$783$	−521.446	−	903.172i	−0.0237995	−	0.0412219i
$784$		0			0
$785$		−	5290.89i		−	0.240560i
$786$		0			0
$787$	−10136.3	−	5852.18i	−0.459109	−	0.265067i	0.252560	−	0.967581i	$-0.418727\pi$
$787$	−10136.3	−	5852.18i	−0.459109	−	0.265067i	−0.711670	+	0.702514i	$0.752061\pi$
$788$		0			0
$789$	6990.28	−	12107.5i	0.315412	−	0.546310i
$790$		0			0
$791$	−7071.79	+	4082.90i	−0.317881	+	0.183529i
$792$		0			0
$793$	7309.17	+	10148.9i	0.327309	+	0.454474i
$794$		0			0
$795$	−9106.68	+	5257.75i	−0.406265	+	0.234557i
$796$		0			0
$797$	−74.8667	+	129.673i	−0.00332737	+	0.00576317i	−0.867684	−	0.497116i	$-0.834392\pi$
$797$	−74.8667	+	129.673i	−0.00332737	+	0.00576317i	0.864357	+	0.502879i	$0.167726\pi$
$798$		0			0
$799$	2607.31	+	1505.33i	0.115444	+	0.0666518i
$800$		0			0
$801$			1074.62i			0.0474032i
$802$		0			0
$803$	2078.40	+	3599.89i	0.0913387	+	0.158203i
$804$		0			0
$805$	−16927.4			−0.741135
$806$		0			0
$807$	−16042.3			−0.699772
$808$		0			0
$809$	−11760.4	−	20369.6i	−0.511093	−	0.885239i	−0.999917	−	0.0128565i	$-0.995908\pi$
$809$	−11760.4	−	20369.6i	−0.511093	−	0.885239i	0.488825	−	0.872382i	$-0.337426\pi$
$810$		0			0
$811$			29604.8i			1.28183i	0.767612	+	0.640915i	$0.221445\pi$
$811$			29604.8i			1.28183i	−0.767612	+	0.640915i	$0.778555\pi$
$812$		0			0
$813$	−7724.29	−	4459.62i	−0.333214	−	0.192381i
$814$		0			0
$815$	4305.39	−	7457.16i	0.185045	−	0.320507i
$816$		0			0
$817$	−51939.9	+	29987.5i	−2.22417	+	1.28413i
$818$		0			0
$819$	−871.632	−	8639.21i	−0.0371884	−	0.368594i
$820$		0			0
$821$	−37269.2	+	21517.4i	−1.58429	+	0.914691i	−0.590068	+	0.807353i	$0.700899\pi$
$821$	−37269.2	+	21517.4i	−1.58429	+	0.914691i	−0.994223	+	0.107338i	$0.965767\pi$
$822$		0			0
$823$	−2792.47	+	4836.71i	−0.118274	+	0.204857i	−0.919084	−	0.394062i	$-0.871069\pi$
$823$	−2792.47	+	4836.71i	−0.118274	+	0.204857i	0.800810	+	0.598919i	$0.204403\pi$
$824$		0			0
$825$	−19558.2	−	11291.9i	−0.825369	−	0.476527i
$826$		0			0
$827$			4788.13i			0.201330i	0.994920	+	0.100665i	$0.0320970\pi$
$827$			4788.13i			0.201330i	−0.994920	+	0.100665i	$0.967903\pi$
$828$		0			0
$829$	−16196.1	−	28052.5i	−0.678546	−	1.17528i	−0.975419	−	0.220359i	$-0.929277\pi$
$829$	−16196.1	−	28052.5i	−0.678546	−	1.17528i	0.296873	−	0.954917i	$-0.404056\pi$
$830$		0			0
$831$	−2292.46			−0.0956974
$832$		0			0
$833$	3573.50			0.148637
$834$		0			0
$835$	−24260.9	−	42021.1i	−1.00549	−	1.74156i
$836$		0			0
$837$		−	2386.51i		−	0.0985544i
$838$		0			0
$839$	11777.0	+	6799.43i	0.484607	+	0.279788i	0.722335	−	0.691544i	$-0.243069\pi$
$839$	11777.0	+	6799.43i	0.484607	+	0.279788i	−0.237727	+	0.971332i	$0.576402\pi$
$840$		0			0
$841$	11448.5	−	19829.4i	0.469414	−	0.813048i
$842$		0			0
$843$	18291.3	−	10560.5i	0.747316	−	0.431463i
$844$		0			0
$845$	25447.1	−	22531.4i	1.03598	−	0.917284i
$846$		0			0
$847$	−53551.4	+	30917.9i	−2.17243	+	1.25425i
$848$		0			0
$849$	−13552.8	+	23474.1i	−0.547855	+	0.948913i
$850$		0			0
$851$	−3635.00	−	2098.67i	−0.146423	−	0.0845375i
$852$		0			0
$853$			41037.0i			1.64722i	0.567155	+	0.823611i	$0.308044\pi$
$853$			41037.0i			1.64722i	−0.567155	+	0.823611i	$0.691956\pi$
$854$		0			0
$855$	10237.4	+	17731.7i	0.409487	+	0.709252i
$856$		0			0
$857$	39959.3			1.59275			0.796374	−	0.604804i	$-0.206749\pi$
$857$	39959.3			1.59275			0.796374	+	0.604804i	$0.206749\pi$
$858$		0			0
$859$	32570.5			1.29371			0.646853	−	0.762615i	$-0.276085\pi$
$859$	32570.5			1.29371			0.646853	+	0.762615i	$0.276085\pi$
$860$		0			0
$861$	−10959.6	−	18982.6i	−0.433800	−	0.751363i
$862$		0			0
$863$		−	16951.8i		−	0.668652i	−0.942457	−	0.334326i	$-0.891491\pi$
$863$		−	16951.8i		−	0.668652i	0.942457	−	0.334326i	$-0.108509\pi$
$864$		0			0
$865$	44536.8	+	25713.3i	1.75063	+	1.01073i
$866$		0			0
$867$	−4426.35	+	7666.65i	−0.173387	+	0.300315i
$868$		0			0
$869$	16371.6	−	9452.13i	0.639088	−	0.368978i
$870$		0			0
$871$	1934.70	+	19175.9i	0.0752639	+	0.745981i
$872$		0			0
$873$	−4323.07	+	2495.92i	−0.167599	+	0.0967632i
$874$		0			0
$875$	1698.26	−	2941.47i	0.0656134	−	0.113646i
$876$		0			0
$877$	−39784.5	−	22969.6i	−1.53184	−	0.884411i	−0.999277	−	0.0380232i	$-0.987894\pi$
$877$	−39784.5	−	22969.6i	−1.53184	−	0.884411i	−0.532568	−	0.846388i	$-0.678773\pi$
$878$		0			0
$879$		−	5355.70i		−	0.205510i
$880$		0			0
$881$	18980.3	+	32874.8i	0.725836	+	1.25718i	0.958629	+	0.284658i	$0.0918801\pi$
$881$	18980.3	+	32874.8i	0.725836	+	1.25718i	−0.232793	+	0.972526i	$0.574787\pi$
$882$		0			0
$883$	43172.9			1.64539			0.822697	−	0.568480i	$-0.192468\pi$
$883$	43172.9			1.64539			0.822697	+	0.568480i	$0.192468\pi$
$884$		0			0
$885$	−6591.82			−0.250375
$886$		0			0
$887$	14353.1	+	24860.4i	0.543327	+	0.941071i	0.998710	+	0.0507749i	$0.0161691\pi$
$887$	14353.1	+	24860.4i	0.543327	+	0.941071i	−0.455383	+	0.890296i	$0.650498\pi$
$888$		0			0
$889$			9012.78i			0.340021i
$890$		0			0
$891$	−4618.69	−	2666.60i	−0.173661	−	0.100263i
$892$		0			0
$893$	4997.41	−	8655.78i	0.187270	−	0.324361i
$894$		0			0
$895$	−44390.1	+	25628.7i	−1.65788	+	0.957175i
$896$		0			0
$897$	−4368.44	−	6065.64i	−0.162607	−	0.225781i
$898$		0			0
$899$	−2956.70	+	1707.05i	−0.109690	+	0.0633296i
$900$		0			0
$901$	5018.08	−	8691.57i	0.185545	−	0.321374i
$902$		0			0
$903$	−21810.4	−	12592.2i	−0.803771	−	0.464057i
$904$		0			0
$905$		−	1175.93i		−	0.0431927i
$906$		0			0
$907$	11178.0	+	19360.9i	0.409218	+	0.708786i	0.994802	−	0.101826i	$-0.0324684\pi$
$907$	11178.0	+	19360.9i	0.409218	+	0.708786i	−0.585585	+	0.810611i	$0.699135\pi$
$908$		0			0
$909$	4163.08			0.151904
$910$		0			0
$911$	−6953.80			−0.252897			−0.126449	−	0.991973i	$-0.540358\pi$
$911$	−6953.80			−0.252897			−0.126449	+	0.991973i	$0.540358\pi$
$912$		0			0
$913$	−12306.3	−	21315.1i	−0.446088	−	0.772647i
$914$		0			0
$915$		−	12384.0i		−	0.447433i
$916$		0			0
$917$	29545.0	+	17057.8i	1.06397	+	0.614285i
$918$		0			0
$919$	20312.6	−	35182.4i	0.729108	−	1.26285i	−0.228153	−	0.973625i	$-0.573269\pi$
$919$	20312.6	−	35182.4i	0.729108	−	1.26285i	0.957261	−	0.289227i	$-0.0933981\pi$
$920$		0			0
$921$	13829.9	−	7984.70i	0.494800	−	0.285673i
$922$		0			0
$923$	3480.39	−	2506.56i	0.124115	−	0.0893871i
$924$		0			0
$925$	−7818.17	+	4513.82i	−0.277902	+	0.160447i
$926$		0			0
$927$	−5049.32	+	8745.69i	−0.178901	+	0.309866i
$928$		0			0
$929$	37077.8	+	21406.9i	1.30946	+	0.756014i	0.982005	−	0.188854i	$-0.0604774\pi$
$929$	37077.8	+	21406.9i	1.30946	+	0.756014i	0.327450	+	0.944869i	$0.393811\pi$
$930$		0			0
$931$		−	11863.3i		−	0.417621i
$932$		0			0
$933$	9398.46	+	16278.6i	0.329788	+	0.571209i
$934$		0			0
$935$	45119.7			1.57815
$936$		0			0
$937$	43484.1			1.51608			0.758038	−	0.652210i	$-0.226158\pi$
$937$	43484.1			1.51608			0.758038	+	0.652210i	$0.226158\pi$
$938$		0			0
$939$	10790.7	+	18690.0i	0.375016	+	0.649547i
$940$		0			0
$941$			7108.58i			0.246263i	0.992390	+	0.123131i	$0.0392936\pi$
$941$			7108.58i			0.246263i	−0.992390	+	0.123131i	$0.960706\pi$
$942$		0			0
$943$	−16341.5	−	9434.75i	−0.564318	−	0.325809i
$944$		0			0
$945$	−4298.84	+	7445.81i	−0.147980	+	0.256309i
$946$		0			0
$947$	−1679.22	+	969.496i	−0.0576211	+	0.0332676i	−0.528534	−	0.848912i	$-0.677258\pi$
$947$	−1679.22	+	969.496i	−0.0576211	+	0.0332676i	0.470913	+	0.882180i	$0.343925\pi$
$948$		0			0
$949$	2698.30	+	1214.86i	0.0922976	+	0.0415553i
$950$		0			0
$951$	−24881.4	+	14365.3i	−0.848408	+	0.489829i
$952$		0			0
$953$	−23903.3	+	41401.8i	−0.812492	+	1.40728i	0.0986228	+	0.995125i	$0.468556\pi$
$953$	−23903.3	+	41401.8i	−0.812492	+	1.40728i	−0.911115	+	0.412153i	$0.864777\pi$
$954$		0			0
$955$	−54574.4	−	31508.5i	−1.84920	−	1.06764i
$956$		0			0
$957$			7629.58i			0.257711i
$958$		0			0
$959$	20248.1	+	35070.7i	0.681797	+	1.18091i
$960$		0			0
$961$	21978.3			0.737750
$962$		0			0
$963$	−5424.81			−0.181528
$964$		0			0
$965$	6710.92	+	11623.7i	0.223867	+	0.387750i
$966$		0			0
$967$		−	2832.71i		−	0.0942025i	−0.998890	−	0.0471013i	$-0.985002\pi$
$967$		−	2832.71i		−	0.0942025i	0.998890	−	0.0471013i	$-0.0149983\pi$
$968$		0			0
$969$	−16923.4	−	9770.72i	−0.561050	−	0.323922i
$970$		0			0
$971$	−20638.1	+	35746.3i	−0.682090	+	1.18142i	0.292251	+	0.956342i	$0.405596\pi$
$971$	−20638.1	+	35746.3i	−0.682090	+	1.18142i	−0.974342	+	0.225074i	$0.927738\pi$
$972$		0			0
$973$	−50360.0	+	29075.3i	−1.65927	+	0.957978i
$974$		0			0
$975$	−15996.0	+	1613.88i	−0.525417	+	0.0530106i
$976$		0			0
$977$	−3705.63	+	2139.45i	−0.121344	+	0.0700583i	−0.559444	−	0.828868i	$-0.688985\pi$
$977$	−3705.63	+	2139.45i	−0.121344	+	0.0700583i	0.438099	+	0.898927i	$0.355652\pi$
$978$		0			0
$979$	3930.85	−	6808.43i	0.128325	−	0.222266i
$980$		0			0
$981$	11082.5	+	6398.50i	0.360691	+	0.208245i
$982$		0			0
$983$		−	22652.9i		−	0.735011i	−0.930021	−	0.367505i	$-0.880212\pi$
$983$		−	22652.9i		−	0.735011i	0.930021	−	0.367505i	$-0.119788\pi$
$984$		0			0
$985$	14601.7	+	25290.9i	0.472333	+	0.818105i
$986$		0			0
$987$	4196.99			0.135351
$988$		0			0
$989$	−21680.5			−0.697068
$990$		0			0
$991$	11030.1	+	19104.7i	0.353565	+	0.612393i	0.986871	−	0.161508i	$-0.0516359\pi$
$991$	11030.1	+	19104.7i	0.353565	+	0.612393i	−0.633306	+	0.773901i	$0.718303\pi$
$992$		0			0
$993$		−	17319.4i		−	0.553488i
$994$		0			0
$995$	−37329.1	−	21552.0i	−1.18936	−	0.686677i
$996$		0			0
$997$	−17817.8	+	30861.3i	−0.565992	+	0.980327i	0.430964	+	0.902369i	$0.358173\pi$
$997$	−17817.8	+	30861.3i	−0.565992	+	0.980327i	−0.996957	+	0.0779583i	$0.975160\pi$
$998$		0			0
$999$	−1846.27	+	1065.94i	−0.0584718	+	0.0337587i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.4.bv.h.49.4		10
4.3	odd	2		39.4.j.c.10.3	yes	10
12.11	even	2		117.4.q.e.10.3		10
13.4	even	6	inner	624.4.bv.h.433.2		10
52.3	odd	6		507.4.b.i.337.5		10
52.11	even	12		507.4.a.r.1.6		10
52.15	even	12		507.4.a.r.1.5		10
52.23	odd	6		507.4.b.i.337.6		10
52.43	odd	6		39.4.j.c.4.3	✓	10
156.11	odd	12		1521.4.a.bk.1.5		10
156.95	even	6		117.4.q.e.82.3		10
156.119	odd	12		1521.4.a.bk.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.3	✓	10	52.43	odd	6
39.4.j.c.10.3	yes	10	4.3	odd	2
117.4.q.e.10.3		10	12.11	even	2
117.4.q.e.82.3		10	156.95	even	6
507.4.a.r.1.5		10	52.15	even	12
507.4.a.r.1.6		10	52.11	even	12
507.4.b.i.337.5		10	52.3	odd	6
507.4.b.i.337.6		10	52.23	odd	6
624.4.bv.h.49.4		10	1.1	even	1	trivial
624.4.bv.h.433.2		10	13.4	even	6	inner
1521.4.a.bk.1.5		10	156.11	odd	12
1521.4.a.bk.1.6		10	156.119	odd	12

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	624.bv (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +15.4704i q^{5} +(-17.8257 - 10.2917i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +15.4704i q^{5} +(-17.8257 - 10.2917i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(57.0209 - 32.9210i) q^{11} +(19.2429 - 42.7400i) q^{13} +(-40.1933 + 23.2056i) q^{15} +(22.1478 - 38.3611i) q^{17} +(-127.352 - 73.5266i) q^{19} -61.7500i q^{21} +(-26.5793 - 46.0367i) q^{23} -114.334 q^{25} -27.0000 q^{27} +(19.3128 + 33.4508i) q^{29} +88.3894i q^{31} +(171.063 + 98.7630i) q^{33} +(159.216 - 275.771i) q^{35} +(68.3803 - 39.4794i) q^{37} +(139.906 - 14.1155i) q^{39} +(307.410 - 177.483i) q^{41} +(203.923 - 353.205i) q^{43} +(-120.580 - 69.6169i) q^{45} +67.9674i q^{47} +(40.3369 + 69.8656i) q^{49} +132.887 q^{51} +226.572 q^{53} +(509.302 + 882.136i) q^{55} -441.160i q^{57} +(123.002 + 71.0154i) q^{59} +(-133.416 + 231.083i) q^{61} +(160.431 - 92.6250i) q^{63} +(661.206 + 297.696i) q^{65} +(-356.098 + 205.593i) q^{67} +(79.7379 - 138.110i) q^{69} +(79.2458 + 45.7526i) q^{71} +63.1328i q^{73} +(-171.500 - 297.047i) q^{75} -1355.25 q^{77} +287.115 q^{79} +(-40.5000 - 70.1481i) q^{81} -373.812i q^{83} +(593.463 + 342.636i) q^{85} +(-57.9385 + 100.352i) q^{87} +(103.406 - 59.7013i) q^{89} +(-782.885 + 563.829i) q^{91} +(-229.643 + 132.584i) q^{93} +(1137.49 - 1970.18i) q^{95} +(480.341 + 277.325i) q^{97} +592.578i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9}+O(q^{10}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9	\( 10 q + 15 q^{3} - 30 q^{7} - 45 q^{9} - 60 q^{11} + 25 q^{13} - 45 q^{15} + 105 q^{17} - 180 q^{19} + 60 q^{23} - 960 q^{25} - 270 q^{27} - 495 q^{29} - 180 q^{33} - 60 q^{35} - 405 q^{37} - 345 q^{39} + 1065 q^{41} + 370 q^{43} - 135 q^{45} + 775 q^{49} + 630 q^{51} + 330 q^{53} + 260 q^{55} - 780 q^{59} - 1375 q^{61} + 270 q^{63} + 1605 q^{65} - 1590 q^{67} - 180 q^{69} - 1620 q^{71} - 1440 q^{75} - 4320 q^{77} - 1100 q^{79} - 405 q^{81} + 525 q^{85} + 1485 q^{87} + 2040 q^{89} - 4770 q^{91} - 990 q^{93} + 1380 q^{95} - 3750 q^{97}+O(q^{100}) \) 10 * q + 15 * q^3 - 30 * q^7 - 45 * q^9 - 60 * q^11 + 25 * q^13 - 45 * q^15 + 105 * q^17 - 180 * q^19 + 60 * q^23 - 960 * q^25 - 270 * q^27 - 495 * q^29 - 180 * q^33 - 60 * q^35 - 405 * q^37 - 345 * q^39 + 1065 * q^41 + 370 * q^43 - 135 * q^45 + 775 * q^49 + 630 * q^51 + 330 * q^53 + 260 * q^55 - 780 * q^59 - 1375 * q^61 + 270 * q^63 + 1605 * q^65 - 1590 * q^67 - 180 * q^69 - 1620 * q^71 - 1440 * q^75 - 4320 * q^77 - 1100 * q^79 - 405 * q^81 + 525 * q^85 + 1485 * q^87 + 2040 * q^89 - 4770 * q^91 - 990 * q^93 + 1380 * q^95 - 3750 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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