LMFDB - Embedded newform 117.4.q.e.10.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(10,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("117.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, degree $2$, 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:	$6.90322347067$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.3
Root			$-0.917374i$ of defining polynomial
Character	$\chi$	$=$	117.10
Dual form			117.4.q.e.82.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.794469 - 0.458687i) q^{2} +(-3.57921 + 6.19938i) q^{4} -15.4704i q^{5} +(17.8257 + 10.2917i) q^{7} +13.9059i q^{8} +O(q^{10})$	\(q+(0.794469 - 0.458687i) q^{2} +(-3.57921 + 6.19938i) q^{4} -15.4704i q^{5} +(17.8257 + 10.2917i) q^{7} +13.9059i q^{8} +(-7.09608 - 12.2908i) q^{10} +(57.0209 - 32.9210i) q^{11} +(19.2429 - 42.7400i) q^{13} +18.8826 q^{14} +(-22.2552 - 38.5472i) q^{16} +(-22.1478 + 38.3611i) q^{17} +(127.352 + 73.5266i) q^{19} +(95.9069 + 55.3719i) q^{20} +(30.2009 - 52.3094i) q^{22} +(-26.5793 - 46.0367i) q^{23} -114.334 q^{25} +(-4.31639 - 42.7821i) q^{26} +(-127.604 + 73.6721i) q^{28} +(-19.3128 - 33.4508i) q^{29} -88.3894i q^{31} +(-131.705 - 76.0401i) q^{32} +40.6357i q^{34} +(159.216 - 275.771i) q^{35} +(68.3803 - 39.4794i) q^{37} +134.903 q^{38} +215.131 q^{40} +(-307.410 + 177.483i) q^{41} +(-203.923 + 353.205i) q^{43} +471.325i q^{44} +(-42.2329 - 24.3832i) q^{46} +67.9674i q^{47} +(40.3369 + 69.8656i) q^{49} +(-90.8345 + 52.4433i) q^{50} +(196.087 + 272.270i) q^{52} -226.572 q^{53} +(-509.302 - 882.136i) q^{55} +(-143.115 + 247.883i) q^{56} +(-30.6869 - 17.7171i) q^{58} +(123.002 + 71.0154i) q^{59} +(-133.416 + 231.083i) q^{61} +(-40.5431 - 70.2227i) q^{62} +216.569 q^{64} +(-661.206 - 297.696i) q^{65} +(356.098 - 205.593i) q^{67} +(-158.543 - 274.605i) q^{68} -292.122i q^{70} +(79.2458 + 45.7526i) q^{71} +63.1328i q^{73} +(36.2173 - 62.7303i) q^{74} +(-911.638 + 526.335i) q^{76} +1355.25 q^{77} -287.115 q^{79} +(-596.341 + 344.298i) q^{80} +(-162.818 + 282.010i) q^{82} -373.812i q^{83} +(593.463 + 342.636i) q^{85} +374.147i q^{86} +(457.798 + 792.929i) q^{88} +(-103.406 + 59.7013i) q^{89} +(782.885 - 563.829i) q^{91} +380.532 q^{92} +(31.1758 + 53.9980i) q^{94} +(1137.49 - 1970.18i) q^{95} +(480.341 + 277.325i) q^{97} +(64.0928 + 37.0040i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) $ 10 * q + 30 * q^4 + 30 * q^7	$ 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29} - 1440 q^{32} - 60 q^{35} - 405 q^{37} + 1380 q^{38} + 2000 q^{40} - 1065 q^{41} - 370 q^{43} - 390 q^{46} + 775 q^{49} + 4320 q^{50} + 2940 q^{52} - 330 q^{53} - 260 q^{55} + 2670 q^{56} + 2040 q^{58} - 780 q^{59} - 1375 q^{61} + 780 q^{62} - 3140 q^{64} - 1605 q^{65} + 1590 q^{67} + 600 q^{68} - 1620 q^{71} - 2190 q^{74} - 5190 q^{76} + 4320 q^{77} + 1100 q^{79} - 8430 q^{80} - 2390 q^{82} + 525 q^{85} + 3170 q^{88} - 2040 q^{89} + 4770 q^{91} + 1740 q^{92} - 3230 q^{94} + 1380 q^{95} - 3750 q^{97} - 180 q^{98}+O(q^{100}) $ 10 * q + 30 * q^4 + 30 * q^7 + 40 * q^10 - 60 * q^11 + 25 * q^13 + 60 * q^14 - 250 * q^16 - 105 * q^17 + 180 * q^19 - 510 * q^20 - 290 * q^22 + 60 * q^23 - 960 * q^25 + 30 * q^26 + 150 * q^28 + 495 * q^29 - 1440 * q^32 - 60 * q^35 - 405 * q^37 + 1380 * q^38 + 2000 * q^40 - 1065 * q^41 - 370 * q^43 - 390 * q^46 + 775 * q^49 + 4320 * q^50 + 2940 * q^52 - 330 * q^53 - 260 * q^55 + 2670 * q^56 + 2040 * q^58 - 780 * q^59 - 1375 * q^61 + 780 * q^62 - 3140 * q^64 - 1605 * q^65 + 1590 * q^67 + 600 * q^68 - 1620 * q^71 - 2190 * q^74 - 5190 * q^76 + 4320 * q^77 + 1100 * q^79 - 8430 * q^80 - 2390 * q^82 + 525 * q^85 + 3170 * q^88 - 2040 * q^89 + 4770 * q^91 + 1740 * q^92 - 3230 * q^94 + 1380 * q^95 - 3750 * q^97 - 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.794469	−	0.458687i	0.280887	−	0.162170i	−0.352938	−	0.935647i	$-0.614817\pi$
$2$	0.794469	−	0.458687i	0.280887	−	0.162170i	0.633825	+	0.773476i	$0.281484\pi$
$3$		0			0
$3$		0			0
$4$	−3.57921	+	6.19938i	−0.447402	+	0.774922i
$5$		−	15.4704i		−	1.38372i	−0.722034	−	0.691858i	$-0.756792\pi$
$5$		−	15.4704i		−	1.38372i	0.722034	−	0.691858i	$-0.243208\pi$
$6$		0			0
$7$	17.8257	+	10.2917i	0.962497	+	0.555698i	0.896941	−	0.442151i	$-0.145784\pi$
$7$	17.8257	+	10.2917i	0.962497	+	0.555698i	0.0655563	+	0.997849i	$0.479118\pi$
$8$			13.9059i			0.614562i
$9$		0			0
$10$	−7.09608	−	12.2908i	−0.224398	−	0.388668i
$11$	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
$14$	18.8826			0.360471
$15$		0			0
$16$	−22.2552	−	38.5472i	−0.347738	−	0.602300i
$17$	−22.1478	+	38.3611i	−0.315979	+	0.547291i	−0.979645	−	0.200738i	$-0.935666\pi$
$17$	−22.1478	+	38.3611i	−0.315979	+	0.547291i	0.663666	+	0.748029i	$0.268999\pi$
$18$		0			0
$19$	127.352	+	73.5266i	1.53771	+	0.887798i	0.998972	+	0.0453247i	$0.0144322\pi$
$19$	127.352	+	73.5266i	1.53771	+	0.887798i	0.538738	+	0.842473i	$0.318901\pi$
$20$	95.9069	+	55.3719i	1.07227	+	0.619077i
$21$		0			0
$22$	30.2009	−	52.3094i	0.292675	−	0.506928i
$23$	−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
$26$	−4.31639	−	42.7821i	−0.0325582	−	0.322702i
$27$		0			0
$28$	−127.604	+	73.6721i	−0.861245	+	0.497240i
$29$	−19.3128	−	33.4508i	−0.123666	−	0.214195i	0.797545	−	0.603260i	$-0.206132\pi$
$29$	−19.3128	−	33.4508i	−0.123666	−	0.214195i	−0.921211	+	0.389064i	$0.872798\pi$
$30$		0			0
$31$		−	88.3894i		−	0.512104i	−0.966663	−	0.256052i	$-0.917578\pi$
$31$		−	88.3894i		−	0.512104i	0.966663	−	0.256052i	$-0.0824218\pi$
$32$	−131.705	−	76.0401i	−0.727576	−	0.420066i
$33$		0			0
$34$			40.6357i			0.204969i
$35$	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	$0.277206\pi$
$38$	134.903			0.575898
$39$		0			0
$40$	215.131			0.850379
$41$	−307.410	+	177.483i	−1.17096	+	0.676054i	−0.953906	−	0.300106i	$-0.902978\pi$
$41$	−307.410	+	177.483i	−1.17096	+	0.676054i	−0.217053	+	0.976160i	$0.569645\pi$
$42$		0			0
$43$	−203.923	+	353.205i	−0.723208	+	1.25263i	0.236499	+	0.971632i	$0.424000\pi$
$43$	−203.923	+	353.205i	−0.723208	+	1.25263i	−0.959707	+	0.281002i	$0.909333\pi$
$44$			471.325i			1.61489i
$45$		0			0
$46$	−42.2329	−	24.3832i	−0.135367	−	0.0781544i
$47$			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
$50$	−90.8345	+	52.4433i	−0.256919	+	0.148332i
$51$		0			0
$52$	196.087	+	272.270i	0.522931	+	0.726097i
$53$	−226.572			−0.587209			−0.293604	−	0.955927i	$-0.594855\pi$
$53$	−226.572			−0.587209			−0.293604	+	0.955927i	$0.594855\pi$
$54$		0			0
$55$	−509.302	−	882.136i	−1.24862	−	2.16268i
$56$	−143.115	+	247.883i	−0.341511	+	0.591514i
$57$		0			0
$58$	−30.6869	−	17.7171i	−0.0694722	−	0.0401098i
$59$	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	$0.257013\pi$
$62$	−40.5431	−	70.2227i	−0.0830480	−	0.143843i
$63$		0			0
$64$	216.569			0.422987
$65$	−661.206	−	297.696i	−1.26173	−	0.568071i
$66$		0			0
$67$	356.098	−	205.593i	0.649318	−	0.374884i	−0.138877	−	0.990310i	$-0.544349\pi$
$67$	356.098	−	205.593i	0.649318	−	0.374884i	0.788195	+	0.615426i	$0.211016\pi$
$68$	−158.543	−	274.605i	−0.282739	−	0.489718i
$69$		0			0
$70$		−	292.122i		−	0.498789i
$71$	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	$0.983883\pi$
$74$	36.2173	−	62.7303i	0.0568943	−	0.0985439i
$75$		0			0
$76$	−911.638	+	526.335i	−1.37595	+	0.794404i
$77$	1355.25			2.00578
$78$		0			0
$79$	−287.115			−0.408899			−0.204449	−	0.978877i	$-0.565540\pi$
$79$	−287.115			−0.408899			−0.204449	+	0.978877i	$0.565540\pi$
$80$	−596.341	+	344.298i	−0.833412	+	0.481170i
$81$		0			0
$82$	−162.818	+	282.010i	−0.219272	+	0.379790i
$83$		−	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
$86$			374.147i			0.469132i
$87$		0			0
$88$	457.798	+	792.929i	0.554561	+	0.960528i
$89$	−103.406	+	59.7013i	−0.123157	+	0.0711047i	−0.560313	−	0.828281i	$-0.689319\pi$
$89$	−103.406	+	59.7013i	−0.123157	+	0.0711047i	0.437156	+	0.899386i	$0.355986\pi$
$90$		0			0
$91$	782.885	−	563.829i	0.901853	−	0.649509i
$92$	380.532			0.431231
$93$		0			0
$94$	31.1758	+	53.9980i	0.0342078	+	0.0592497i
$95$	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	$0.572915\pi$
$98$	64.0928	+	37.0040i	0.0660648	+	0.0381426i
$99$		0			0
$100$	409.224	−	708.797i	0.409224	−	0.708797i
$101$	231.282	+	400.593i	0.227856	+	0.394658i	0.957172	−	0.289518i	$-0.0934952\pi$
$101$	231.282	+	400.593i	0.227856	+	0.394658i	−0.729317	+	0.684176i	$0.760162\pi$
$102$		0			0
$103$	−1122.07			−1.07341			−0.536704	−	0.843771i	$-0.680331\pi$
$103$	−1122.07			−1.07341			−0.536704	+	0.843771i	$0.680331\pi$
$104$	594.340	+	267.591i	0.560383	+	0.252302i
$105$		0			0
$106$	−180.005	+	103.926i	−0.164939	+	0.0952279i
$107$	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	$-0.214793\pi$
$110$	−809.249	−	467.220i	−0.701444	−	0.404979i
$111$		0			0
$112$		−	916.174i		−	0.772949i
$113$	−198.359	+	343.569i	−0.165134	+	0.286020i	−0.936703	−	0.350126i	$-0.886139\pi$
$113$	−198.359	+	343.569i	−0.165134	+	0.286020i	0.771569	+	0.636145i	$0.219472\pi$
$114$		0			0
$115$	−712.207	+	411.193i	−0.577510	+	0.333426i
$116$	276.499			0.221313
$117$		0			0
$118$	130.295			0.101650
$119$	−789.600	+	455.876i	−0.608257	+	0.351177i
$120$		0			0
$121$	1502.09	−	2601.69i	1.12854	−	1.95469i
$122$			244.784i			0.181653i
$123$		0			0
$124$	547.960	+	316.365i	0.396841	+	0.229116i
$125$		−	165.013i		−	0.118074i
$126$		0			0
$127$	218.934	+	379.205i	0.152970	+	0.264952i	0.932318	−	0.361639i	$-0.117783\pi$
$127$	218.934	+	379.205i	0.152970	+	0.264952i	−0.779348	+	0.626592i	$0.784449\pi$
$128$	1225.70	−	707.659i	0.846388	−	0.488662i
$129$		0			0
$130$	−661.857	+	66.7764i	−0.446528	+	0.0450514i
$131$	−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
$134$	188.606	−	326.675i	0.121590	−	0.210600i
$135$		0			0
$136$	−533.448	−	307.986i	−0.336344	−	0.194188i
$137$	1703.84	+	983.711i	1.06254	+	0.613460i	0.926135	−	0.377192i	$-0.123110\pi$
$137$	1703.84	+	983.711i	1.06254	+	0.613460i	0.136410	+	0.990653i	$0.456444\pi$
$138$		0			0
$139$	−1412.57	+	2446.64i	−0.861960	+	1.49296i	0.00807518	+	0.999967i	$0.497430\pi$
$139$	−1412.57	+	2446.64i	−0.861960	+	1.49296i	−0.870035	+	0.492990i	$0.835904\pi$
$140$	1139.74	+	1974.08i	0.688039	+	1.19172i
$141$		0			0
$142$	83.9445			0.0496089
$143$	−309.797	−	3070.57i	−0.181165	−	1.79562i
$144$		0			0
$145$	−517.498	+	298.777i	−0.296385	+	0.171118i
$146$	28.9582	+	50.1571i	0.0164150	+	0.0284317i
$147$		0			0
$148$			565.220i			0.313924i
$149$	−690.792	−	398.829i	−0.379811	−	0.219284i	0.297925	−	0.954589i	$-0.403706\pi$
$149$	−690.792	−	398.829i	−0.379811	−	0.219284i	−0.677736	+	0.735305i	$0.737039\pi$
$150$		0			0
$151$		−	161.987i		−	0.0873003i	−0.999047	−	0.0436501i	$-0.986101\pi$
$151$		−	161.987i		−	0.0873003i	0.999047	−	0.0436501i	$-0.0138987\pi$
$152$	−1022.46	+	1770.95i	−0.545606	+	0.945018i
$153$		0			0
$154$	1076.70	−	621.635i	0.563397	−	0.325278i
$155$	−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	$0.527704\pi$
$158$	−228.104	+	131.696i	−0.114854	+	0.0663112i
$159$		0			0
$160$	−1176.37	+	2037.54i	−0.581252	+	1.00676i
$161$		−	1094.18i		−	0.535613i
$162$		0			0
$163$	482.027	+	278.299i	0.231628	+	0.133730i	0.611323	−	0.791381i	$-0.290638\pi$
$163$	482.027	+	278.299i	0.231628	+	0.133730i	−0.379695	+	0.925112i	$0.623971\pi$
$164$		−	2541.00i		−	1.20987i
$165$		0			0
$166$	−171.463	−	296.982i	−0.0801693	−	0.138857i
$167$	−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
$170$	628.650			0.283619
$171$		0			0
$172$	−1459.77	−	2528.39i	−0.647129	−	1.12086i
$173$	−1662.10	+	2878.84i	−0.730444	+	1.26517i	0.226249	+	0.974070i	$0.427354\pi$
$173$	−1662.10	+	2878.84i	−0.730444	+	1.26517i	−0.956693	+	0.291097i	$0.905980\pi$
$174$		0			0
$175$	−2038.08	−	1176.68i	−0.880366	−	0.508280i
$176$	−2538.02	−	1465.33i	−1.08699	−	0.627576i
$177$		0			0
$178$	−54.7684	+	94.8616i	−0.0230622	+	0.0399448i
$179$	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	$0.504968\pi$
$182$	363.357	−	807.044i	0.147988	−	0.328693i
$183$		0			0
$184$	640.184	−	369.610i	0.256494	−	0.148087i
$185$	−610.762	−	1057.87i	−0.242725	−	0.420412i
$186$		0			0
$187$			2916.51i			1.14052i
$188$	−421.356	−	243.270i	−0.163460	−	0.0943738i
$189$		0			0
$190$		−	2087.00i		−	0.796879i
$191$	−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	$0.281608\pi$
$194$	508.821			0.188305
$195$		0			0
$196$	−577.497			−0.210458
$197$	−1634.79	+	943.846i	−0.591238	+	0.341352i	−0.765587	−	0.643332i	$-0.777551\pi$
$197$	−1634.79	+	943.846i	−0.591238	+	0.341352i	0.174349	+	0.984684i	$0.444218\pi$
$198$		0			0
$199$	1393.11	−	2412.94i	0.496256	−	0.859540i	−0.503735	−	0.863858i	$-0.668041\pi$
$199$	1393.11	−	2412.94i	0.496256	−	0.859540i	0.999991	+	0.00431832i	$0.00137457\pi$
$200$		−	1589.92i		−	0.562120i
$201$		0			0
$202$	367.493	+	212.172i	0.128004	+	0.0739029i
$203$		−	795.045i		−	0.274883i
$204$		0			0
$205$	2745.74	+	4755.75i	0.935466	+	1.62027i
$206$	−891.451	+	514.680i	−0.301507	+	0.174075i
$207$		0			0
$208$	−2075.76	+	209.429i	−0.691963	+	0.0698139i
$209$	9682.28			3.20448
$210$		0			0
$211$	−354.395	−	613.830i	−0.115628	−	0.200274i	0.802403	−	0.596783i	$-0.203555\pi$
$211$	−354.395	−	613.830i	−0.115628	−	0.200274i	−0.918031	+	0.396509i	$0.870221\pi$
$212$	810.950	−	1404.61i	0.262718	−	0.455041i
$213$		0			0
$214$	478.871	+	276.476i	0.152967	+	0.0883156i
$215$	5464.22	+	3154.77i	1.73329	+	1.00071i
$216$		0			0
$217$	909.675	−	1575.60i	0.284575	−	0.492898i
$218$	−652.202	−	1129.65i	−0.202627	−	0.350960i
$219$		0			0
$220$	7291.59			2.23454
$221$	1213.37	+	1684.78i	0.369321	+	0.512808i
$222$		0			0
$223$	−4673.62	+	2698.32i	−1.40345	+	0.810281i	−0.994745	−	0.102386i	$-0.967352\pi$
$223$	−4673.62	+	2698.32i	−1.40345	+	0.810281i	−0.408703	+	0.912667i	$0.634019\pi$
$224$	−1565.16	−	2710.94i	−0.466860	−	0.808625i
$225$		0			0
$226$			363.940i			0.107119i
$227$	−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	$0.905189\pi$
$230$	−377.218	+	653.360i	−0.108143	+	0.187310i
$231$		0			0
$232$	465.165	−	268.563i	0.131636	−	0.0760001i
$233$	−2794.22			−0.785645			−0.392823	−	0.919614i	$-0.628501\pi$
$233$	−2794.22			−0.785645			−0.392823	+	0.919614i	$0.628501\pi$
$234$		0			0
$235$	1051.48			0.291878
$236$	−880.502	+	508.358i	−0.242864	+	0.140217i
$237$		0			0
$238$	−418.209	+	724.359i	−0.113901	+	0.197282i
$239$		−	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	$0.849287\pi$
$242$		−	2755.95i		−	0.732062i
$243$		0			0
$244$	−955.046	−	1654.19i	−0.250576	−	0.434010i
$245$	1080.85	−	624.028i	0.281849	−	0.162725i
$246$		0			0
$247$	5593.15	−	4028.15i	1.44082	−	1.03767i
$248$	1229.14			0.314719
$249$		0			0
$250$	−75.6894	−	131.098i	−0.0191481	−	0.0331654i
$251$	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
$254$	347.872	+	200.844i	0.0859348	+	0.0496145i
$255$		0			0
$256$	−217.089	+	376.010i	−0.0530003	+	0.0917993i
$257$	3759.13	+	6511.01i	0.912405	+	1.58033i	0.810656	+	0.585522i	$0.199111\pi$
$257$	3759.13	+	6511.01i	0.912405	+	1.58033i	0.101749	+	0.994810i	$0.467556\pi$
$258$		0			0
$259$	1625.23			0.389912
$260$	4212.13	−	3033.55i	1.00471	−	0.723587i
$261$		0			0
$262$	−1316.79	+	760.246i	−0.310501	+	0.179268i
$263$	−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
$266$	2404.73	+	1388.37i	0.554300	+	0.320025i
$267$		0			0
$268$			2943.45i			0.670895i
$269$	2673.72	−	4631.02i	0.606021	−	1.04966i	−0.385869	−	0.922554i	$-0.626098\pi$
$269$	2673.72	−	4631.02i	0.606021	−	1.04966i	0.991889	−	0.127105i	$-0.0405684\pi$
$270$		0			0
$271$	2574.76	−	1486.54i	0.577143	−	0.333214i	−0.182854	−	0.983140i	$-0.558534\pi$
$271$	2574.76	−	1486.54i	0.577143	−	0.333214i	0.759997	+	0.649926i	$0.225200\pi$
$272$	1971.62			0.439511
$273$		0			0
$274$	1804.86			0.397940
$275$	−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	$0.193077\pi$
$278$			2591.70i			0.559137i
$279$		0			0
$280$	3834.85	+	2214.05i	0.818487	+	0.472554i
$281$			7040.34i			1.49463i	0.664469	+	0.747316i	$0.268658\pi$
$281$			7040.34i			1.49463i	−0.664469	+	0.747316i	$0.731342\pi$
$282$		0			0
$283$	−4517.58	−	7824.68i	−0.948913	−	1.64357i	−0.747720	−	0.664015i	$-0.768851\pi$
$283$	−4517.58	−	7824.68i	−0.948913	−	1.64357i	−0.201194	−	0.979551i	$-0.564482\pi$
$284$	−567.275	+	327.517i	−0.118527	+	0.0684314i
$285$		0			0
$286$	−1654.55	−	2297.37i	−0.342083	−	0.474988i
$287$	−7306.39			−1.50273
$288$		0			0
$289$	1475.45	+	2555.55i	0.300315	+	0.520161i
$290$	−274.091	+	474.739i	−0.0555005	+	0.0961297i
$291$		0			0
$292$	−391.384	−	225.966i	−0.0784384	−	0.0452865i
$293$	1546.06	+	892.617i	0.308265	+	0.177977i	0.646150	−	0.763211i	$-0.276378\pi$
$293$	1546.06	+	892.617i	0.308265	+	0.177977i	−0.337885	+	0.941188i	$0.609711\pi$
$294$		0			0
$295$	1098.64	−	1902.89i	0.216831	−	0.375562i
$296$	548.998	+	950.892i	0.107804	+	0.186721i
$297$		0			0
$298$	−731.751			−0.142246
$299$	−2479.07	+	250.120i	−0.479494	+	0.0483773i
$300$		0			0
$301$	−7270.13	+	4197.41i	−1.39217	+	0.803771i
$302$	−74.3015	−	128.694i	−0.0141575	−	0.0245215i
$303$		0			0
$304$		−	6545.40i		−	1.23488i
$305$	3574.94	+	2063.99i	0.671150	+	0.387488i
$306$		0			0
$307$			5323.13i			0.989600i	0.869007	+	0.494800i	$0.164759\pi$
$307$			5323.13i			0.989600i	−0.869007	+	0.494800i	$0.835241\pi$
$308$	−4850.72	+	8401.70i	−0.897388	+	1.55432i
$309$		0			0
$310$	−1086.37	+	627.218i	−0.199038	+	0.114915i
$311$	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	$0.274959\pi$
$314$	−271.709	+	156.871i	−0.0488325	+	0.0281935i
$315$		0			0
$316$	1027.65	−	1779.94i	0.182942	−	0.316865i
$317$		−	9576.87i		−	1.69682i	−0.529343	−	0.848408i	$-0.677561\pi$
$317$		−	9576.87i		−	1.69682i	0.529343	−	0.848408i	$-0.322439\pi$
$318$		0			0
$319$	−2202.47	−	1271.60i	−0.386566	−	0.223184i
$320$		−	3350.41i		−	0.585293i
$321$		0			0
$322$	−501.887	−	869.294i	−0.0868604	−	0.150447i
$323$	−5641.13	+	3256.91i	−0.971767	+	0.561050i
$324$		0			0
$325$	−2200.11	+	4886.62i	−0.375509	+	0.834034i
$326$	510.608			0.0867483
$327$		0			0
$328$	−2468.07	−	4274.82i	−0.415477	−	0.719627i
$329$	−699.498	+	1211.57i	−0.117218	+	0.203027i
$330$		0			0
$331$	4999.68	+	2886.56i	0.830233	+	0.479335i	0.853932	−	0.520384i	$-0.174211\pi$
$331$	4999.68	+	2886.56i	0.830233	+	0.479335i	−0.0236996	+	0.999719i	$0.507545\pi$
$332$	2317.40	+	1337.95i	0.383085	+	0.221174i
$333$		0			0
$334$	−1438.64	+	2491.79i	−0.235685	+	0.408218i
$335$	−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	$0.531905\pi$
$338$	−1911.57	−	638.770i	−0.307620	−	0.102794i
$339$		0			0
$340$	−4248.26	+	2452.73i	−0.677630	+	0.391230i
$341$	−2909.87	−	5040.04i	−0.462106	−	0.800392i
$342$		0			0
$343$		−	5399.55i		−	0.849995i
$344$	−4911.65	−	2835.74i	−0.769820	−	0.444456i
$345$		0			0
$346$			3049.53i			0.473826i
$347$	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	$0.366937\pi$
$350$	−2158.92			−0.329711
$351$		0			0
$352$	−10013.3			−1.51622
$353$	−5170.55	+	2985.22i	−0.779606	+	0.450106i	−0.836291	−	0.548287i	$-0.815280\pi$
$353$	−5170.55	+	2985.22i	−0.779606	+	0.450106i	0.0566848	+	0.998392i	$0.481947\pi$
$354$		0			0
$355$	707.811	−	1225.97i	0.105822	−	0.183289i
$356$		−	854.734i		−	0.127249i
$357$		0			0
$358$	2632.27	+	1519.74i	0.388603	+	0.224360i
$359$			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
$362$	−60.3891	+	34.8656i	−0.00876790	+	0.00506215i
$363$		0			0
$364$	693.279	+	6871.46i	0.0998288	+	0.989457i
$365$	976.690			0.140061
$366$		0			0
$367$	−844.195	−	1462.19i	−0.120073	−	0.207972i	0.799724	−	0.600368i	$-0.204979\pi$
$367$	−844.195	−	1462.19i	−0.120073	−	0.207972i	−0.919796	+	0.392397i	$0.871646\pi$
$368$	−1183.06	+	2049.12i	−0.167585	+	0.290265i
$369$		0			0
$370$	−970.463	−	560.297i	−0.136357	−	0.0787256i
$371$	−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	$0.208111\pi$
$374$	1337.77	+	2317.08i	0.184958	+	0.320357i
$375$		0			0
$376$	−945.151			−0.129634
$377$	−1801.32	+	181.740i	−0.246082	+	0.0248278i
$378$		0			0
$379$	10103.9	−	5833.52i	1.36941	−	0.790627i	0.378554	−	0.925579i	$-0.376421\pi$
$379$	10103.9	−	5833.52i	1.36941	−	0.790627i	0.990852	+	0.134952i	$0.0430882\pi$
$380$	8142.61	+	14103.4i	1.09923	+	1.90392i
$381$		0			0
$382$			3736.82i			0.500504i
$383$	−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
$386$	397.948	−	689.266i	0.0524742	−	0.0908879i
$387$		0			0
$388$	−3438.48	+	1985.21i	−0.449904	+	0.259752i
$389$	14285.3			1.86194			0.930969	−	0.365099i	$-0.118965\pi$
$389$	14285.3			1.86194			0.930969	+	0.365099i	$0.118965\pi$
$390$		0			0
$391$	2354.69			0.304558
$392$	−971.547	+	560.923i	−0.125180	+	0.0722726i
$393$		0			0
$394$	−865.860	+	1499.71i	−0.110714	+	0.191763i
$395$			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	$0.594228\pi$
$398$		−	2556.00i		−	0.321912i
$399$		0			0
$400$	2544.52	+	4407.24i	0.318065	+	0.550905i
$401$	432.448	−	249.674i	0.0538540	−	0.0310926i	−0.472831	−	0.881153i	$-0.656768\pi$
$401$	432.448	−	249.674i	0.0538540	−	0.0310926i	0.526685	+	0.850060i	$0.323435\pi$
$402$		0			0
$403$	−3777.77	−	1700.87i	−0.466958	−	0.210239i
$404$	−3311.23			−0.407772
$405$		0			0
$406$	−364.677	−	631.639i	−0.0445778	−	0.0772111i
$407$	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	$0.884490\pi$
$410$	4362.80	+	2518.87i	0.525521	+	0.303410i
$411$		0			0
$412$	4016.13	−	6956.15i	0.480245	−	0.831808i
$413$	1461.73	+	2531.80i	0.174158	+	0.301650i
$414$		0			0
$415$	−5783.03			−0.684043
$416$	−5784.35	+	4165.86i	−0.681734	+	0.490981i
$417$		0			0
$418$	7692.27	−	4441.13i	0.900099	−	0.519672i
$419$	−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	$-0.169383\pi$
$422$	−563.111	−	325.112i	−0.0649569	−	0.0375029i
$423$		0			0
$424$		−	3150.70i		−	0.360876i
$425$	2532.24	−	4385.97i	0.289016	−	0.500590i
$426$		0			0
$427$	−4756.45	+	2746.14i	−0.539065	+	0.311229i
$428$	−4314.79			−0.487297
$429$		0			0
$430$	5788.21			0.649145
$431$	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	$0.240173\pi$
$434$		−	1669.02i		−	0.184598i
$435$		0			0
$436$	8814.83	+	5089.24i	0.968242	+	0.559015i
$437$		−	7817.14i		−	0.855709i
$438$		0			0
$439$	−3057.76	−	5296.19i	−0.332435	−	0.575794i	0.650554	−	0.759460i	$-0.274537\pi$
$439$	−3057.76	−	5296.19i	−0.332435	−	0.575794i	−0.982989	+	0.183666i	$0.941203\pi$
$440$	12266.9	−	7082.32i	1.32910	−	0.767355i
$441$		0			0
$442$	1736.77	+	781.948i	0.186900	+	0.0841482i
$443$	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
$446$	−2475.37	+	4287.46i	−0.262807	+	0.455195i
$447$		0			0
$448$	3860.50	+	2228.86i	0.407123	+	0.235053i
$449$	−209.588	−	121.006i	−0.0220291	−	0.0127185i	0.488945	−	0.872315i	$-0.337382\pi$
$449$	−209.588	−	121.006i	−0.0220291	−	0.0127185i	−0.510974	+	0.859596i	$0.670715\pi$
$450$		0			0
$451$	−11685.8	+	20240.5i	−1.22010	+	2.11327i
$452$	−1419.94	−	2459.41i	−0.147762	−	0.255931i
$453$		0			0
$454$	−2918.89			−0.301741
$455$	−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	$0.141961\pi$
$458$	932.969	+	1615.95i	0.0951851	+	0.164865i
$459$		0			0
$460$		−	5886.99i		−	0.596700i
$461$	−237.086	−	136.882i	−0.0239527	−	0.0138291i	0.487976	−	0.872857i	$-0.337735\pi$
$461$	−237.086	−	136.882i	−0.0239527	−	0.0138291i	−0.511929	+	0.859028i	$0.671069\pi$
$462$		0			0
$463$			11579.2i			1.16227i	0.813808	+	0.581134i	$0.197391\pi$
$463$			11579.2i			1.16227i	−0.813808	+	0.581134i	$0.802609\pi$
$464$	−859.623	+	1488.91i	−0.0860064	+	0.148968i
$465$		0			0
$466$	−2219.92	+	1281.67i	−0.220678	+	0.127408i
$467$	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
$470$	835.372	−	482.302i	0.0819847	−	0.0473339i
$471$		0			0
$472$	−987.535	+	1710.46i	−0.0963030	+	0.166802i
$473$			26853.4i			2.61040i
$474$		0			0
$475$	−14560.6	−	8406.56i	−1.40650	−	0.812041i
$476$		−	6526.71i		−	0.628469i
$477$		0			0
$478$	−2519.94	−	4364.67i	−0.241128	−	0.417647i
$479$	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
$482$	−3725.70			−0.352077
$483$		0			0
$484$	10752.6	+	18624.0i	1.00982	+	1.74906i
$485$	4290.33	−	7431.07i	0.401678	−	0.695727i
$486$		0			0
$487$	9952.82	+	5746.26i	0.926089	+	0.534678i	0.885572	−	0.464501i	$-0.153766\pi$
$487$	9952.82	+	5746.26i	0.926089	+	0.534678i	0.0405163	+	0.999179i	$0.487100\pi$
$488$	−3213.42	−	1855.27i	−0.298084	−	0.172099i
$489$		0			0
$490$	572.467	−	991.543i	0.0527785	−	0.0914150i
$491$	−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
$494$	2595.92	−	5765.75i	0.236429	−	0.525128i
$495$		0			0
$496$	−3407.16	+	1967.13i	−0.308440	+	0.178078i
$497$	941.741	+	1631.14i	0.0849957	+	0.147217i
$498$		0			0
$499$		−	9019.80i		−	0.809181i	−0.914498	−	0.404591i	$-0.867414\pi$
$499$		−	9019.80i		−	0.809181i	0.914498	−	0.404591i	$-0.132586\pi$
$500$	1022.98	+	590.617i	0.0914980	+	0.0528264i
$501$		0			0
$502$		−	3275.83i		−	0.291250i
$503$	−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
$506$	−3210.87			−0.282096
$507$		0			0
$508$	−3134.44			−0.273757
$509$	19443.6	−	11225.8i	1.69317	−	0.977551i	0.741234	−	0.671246i	$-0.234241\pi$
$509$	19443.6	−	11225.8i	1.69317	−	0.977551i	0.951934	−	0.306304i	$-0.0990926\pi$
$510$		0			0
$511$	−649.742	+	1125.39i	−0.0562483	+	0.0974249i
$512$			11720.8i			1.01170i
$513$		0			0
$514$	5973.03	+	3448.53i	0.512566	+	0.295930i
$515$			17358.9i			1.48529i
$516$		0			0
$517$	2237.56	+	3875.56i	0.190344	+	0.329685i
$518$	1291.20	−	745.474i	0.109521	−	0.0632321i
$519$		0			0
$520$	4139.74	−	9194.69i	0.349115	−	0.775411i
$521$	−15674.7			−1.31808			−0.659040	−	0.752108i	$-0.729037\pi$
$521$	−15674.7			−1.31808			−0.659040	+	0.752108i	$0.729037\pi$
$522$		0			0
$523$	−6755.39	−	11700.7i	−0.564804	−	0.978270i	−0.997068	−	0.0765223i	$-0.975618\pi$
$523$	−6755.39	−	11700.7i	−0.564804	−	0.978270i	0.432264	−	0.901747i	$-0.357715\pi$
$524$	5932.33	−	10275.1i	0.494571	−	0.856622i
$525$		0			0
$526$	−3702.37	−	2137.57i	−0.306903	−	0.177191i
$527$	3390.72	+	1957.63i	0.280270	+	0.161814i
$528$		0			0
$529$	4670.58	−	8089.68i	0.383873	−	0.664887i
$530$	1607.77	+	2784.74i	0.131768	+	0.228229i
$531$		0			0
$532$	−21667.4			−1.76580
$533$	1670.17	+	16554.0i	0.135728	+	1.34528i
$534$		0			0
$535$	8075.59	−	4662.44i	0.652595	−	0.376776i
$536$	2858.97	+	4951.88i	0.230389	+	0.399046i
$537$		0			0
$538$		−	4905.60i		−	0.393114i
$539$	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	$0.840296\pi$
$542$	1363.71	−	2362.02i	0.108075	−	0.187191i
$543$		0			0
$544$	5833.97	−	3368.25i	0.459797	−	0.265464i
$545$	−21997.2			−1.72891
$546$		0			0
$547$	−15228.6			−1.19036			−0.595181	−	0.803592i	$-0.702920\pi$
$547$	−15228.6			−1.19036			−0.595181	+	0.803592i	$0.702920\pi$
$548$	−12196.8	+	7041.82i	−0.950768	+	0.548926i
$549$		0			0
$550$	−3452.98	+	5980.73i	−0.267701	+	0.463671i
$551$		−	5680.03i		−	0.439160i
$552$		0			0
$553$	−5118.03	−	2954.90i	−0.393564	−	0.227224i
$554$			701.014i			0.0537603i
$555$		0			0
$556$	−10111.8	−	17514.1i	−0.771284	−	1.33590i
$557$	−20435.5	+	11798.5i	−1.55454	+	0.897516i	−0.556781	+	0.830660i	$0.687964\pi$
$557$	−20435.5	+	11798.5i	−1.55454	+	0.897516i	−0.997763	+	0.0668564i	$0.978703\pi$
$558$		0			0
$559$	11171.9	+	15512.4i	0.845298	+	1.17371i
$560$	−14173.6			−1.06954
$561$		0			0
$562$	3229.31	+	5593.33i	0.242385	+	0.419823i
$563$	−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
$566$	−7178.16	−	4144.31i	−0.533075	−	0.307771i
$567$		0			0
$568$	−636.233	+	1101.99i	−0.0469995	+	0.0814056i
$569$	−1137.33	−	1969.91i	−0.0837948	−	0.145137i	0.821082	−	0.570810i	$-0.193371\pi$
$569$	−1137.33	−	1969.91i	−0.0837948	−	0.145137i	−0.904877	+	0.425673i	$0.860037\pi$
$570$		0			0
$571$	4499.84			0.329794			0.164897	−	0.986311i	$-0.447271\pi$
$571$	4499.84			0.329794			0.164897	+	0.986311i	$0.447271\pi$
$572$	20144.5	+	9069.67i	1.47252	+	0.662975i
$573$		0			0
$574$	−5804.70	+	3351.34i	−0.422097	+	0.243698i
$575$	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	$0.635303\pi$
$578$	2344.40	+	1353.54i	0.168709	+	0.0974044i
$579$		0			0
$580$		−	4277.55i		−	0.306234i
$581$	3847.15	−	6663.47i	0.274711	−	0.475813i
$582$		0			0
$583$	−12919.3	+	7458.98i	−0.917777	+	0.529879i
$584$	−877.921			−0.0622066
$585$		0			0
$586$	1637.73			0.115450
$587$	−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
$590$		−	2015.72i		−	0.140654i
$591$		0			0
$592$	−3043.64	−	1757.24i	−0.211305	−	0.121997i
$593$		−	12824.5i		−	0.888090i	−0.896005	−	0.444045i	$-0.853543\pi$
$593$		−	12824.5i		−	0.888090i	0.896005	−	0.444045i	$-0.146457\pi$
$594$		0			0
$595$	7052.59	+	12215.4i	0.485929	+	0.841654i
$596$	4944.99	−	2854.99i	0.339857	−	0.196216i
$597$		0			0
$598$	−1854.82	+	1335.83i	−0.126838	+	0.0913482i
$599$	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	$-0.349530\pi$
$602$	−3850.60	+	6669.43i	−0.260695	+	0.451538i
$603$		0			0
$604$	1004.22	+	579.787i	0.0676509	+	0.0390583i
$605$	−40249.2	−	23237.9i	−2.70473	−	1.56158i
$606$		0			0
$607$	4765.74	−	8254.50i	0.318674	−	0.551960i	−0.661537	−	0.749912i	$-0.730096\pi$
$607$	4765.74	−	8254.50i	0.318674	−	0.551960i	0.980212	+	0.197952i	$0.0634290\pi$
$608$	−11181.9	−	19367.7i	−0.745868	−	1.29188i
$609$		0			0
$610$	3786.91			0.251356
$611$	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	$0.442274\pi$
$614$	2441.65	+	4229.06i	0.160484	+	0.277966i
$615$		0			0
$616$			18846.0i			1.23267i
$617$	−6939.13	−	4006.31i	−0.452770	−	0.261407i	0.256230	−	0.966616i	$-0.417520\pi$
$617$	−6939.13	−	4006.31i	−0.452770	−	0.261407i	−0.708999	+	0.705209i	$0.750853\pi$
$618$		0			0
$619$			1886.59i			0.122501i	0.998122	+	0.0612506i	$0.0195089\pi$
$619$			1886.59i			0.122501i	−0.998122	+	0.0612506i	$0.980491\pi$
$620$	4894.29	−	8477.16i	0.317031	−	0.549114i
$621$		0			0
$622$	4977.86	−	2873.97i	0.320891	−	0.185266i
$623$	−2457.70			−0.158051
$624$		0			0
$625$	−16844.5			−1.07805
$626$	5715.23	−	3299.69i	0.364899	−	0.210674i
$627$		0			0
$628$	1224.09	−	2120.19i	0.0777812	−	0.134721i
$629$			3497.53i			0.221710i
$630$		0			0
$631$	−12952.3	−	7478.04i	−0.817154	−	0.471784i	0.0322798	−	0.999479i	$-0.489723\pi$
$631$	−12952.3	−	7478.04i	−0.817154	−	0.471784i	−0.849434	+	0.527695i	$0.823057\pi$
$632$		−	3992.61i		−	0.251293i
$633$		0			0
$634$	−4392.79	−	7608.53i	−0.275173	−	0.476614i
$635$	5866.45	−	3387.00i	0.366619	−	0.211667i
$636$		0			0
$637$	3762.26	−	379.583i	0.234013	−	0.0236101i
$638$	−2333.06			−0.144775
$639$		0			0
$640$	−10947.8	−	18962.1i	−0.676170	−	1.17116i
$641$	−11845.9	+	20517.6i	−0.729927	+	1.26427i	0.226986	+	0.973898i	$0.427113\pi$
$641$	−11845.9	+	20517.6i	−0.729927	+	1.26427i	−0.956913	+	0.290373i	$0.906221\pi$
$642$		0			0
$643$	11822.4	+	6825.65i	0.725083	+	0.418627i	0.816621	−	0.577175i	$-0.195845\pi$
$643$	11822.4	+	6825.65i	0.725083	+	0.418627i	−0.0915374	+	0.995802i	$0.529178\pi$
$644$	6783.25	+	3916.31i	0.415058	+	0.239634i
$645$		0			0
$646$	−2987.80	+	5175.02i	−0.181971	+	0.315184i
$647$	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
$650$	493.509	+	4891.43i	0.0297800	+	0.295166i
$651$		0			0
$652$	−3450.56	+	1992.18i	−0.207261	+	0.119662i
$653$	3181.74	+	5510.93i	0.190675	+	0.330259i	0.945474	−	0.325697i	$-0.105599\pi$
$653$	3181.74	+	5510.93i	0.190675	+	0.330259i	−0.754799	+	0.655956i	$0.772266\pi$
$654$		0			0
$655$			25641.3i			1.52960i
$656$	13682.9	+	7899.85i	0.814374	+	0.470179i
$657$		0			0
$658$			1283.40i			0.0760369i
$659$	−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	$0.256548\pi$
$662$	5296.12			0.310936
$663$		0			0
$664$	5198.21			0.303810
$665$	40553.0	−	23413.3i	2.36478	−	1.36530i
$666$		0			0
$667$	−1026.64	+	1778.20i	−0.0595979	+	0.103227i
$668$		−	22451.9i		−	1.30043i
$669$		0			0
$670$	−5053.80	−	2917.81i	−0.291411	−	0.168246i
$671$			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	$0.835068\pi$
$674$	−983.620	+	567.893i	−0.0562131	+	0.0324547i
$675$		0			0
$676$	15410.1	−	3141.51i	0.876770	−	0.178738i
$677$	−4861.93			−0.276010			−0.138005	−	0.990431i	$-0.544069\pi$
$677$	−4861.93			−0.276010			−0.138005	+	0.990431i	$0.544069\pi$
$678$		0			0
$679$	5708.27	+	9887.02i	0.322627	+	0.558806i
$680$	−4764.67	+	8252.66i	−0.268701	+	0.465404i
$681$		0			0
$682$	−4623.60	−	2669.44i	−0.259600	−	0.149880i
$683$	−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
$686$	−2476.70	−	4289.77i	−0.137844	−	0.238753i
$687$		0			0
$688$	18153.4			1.00595
$689$	−4359.91	+	9683.70i	−0.241073	+	0.535442i
$690$		0			0
$691$	19144.8	−	11053.2i	1.05398	−	0.608517i	0.130221	−	0.991485i	$-0.458431\pi$
$691$	19144.8	−	11053.2i	1.05398	−	0.608517i	0.923762	+	0.382968i	$0.125098\pi$
$692$	−11898.0	−	20607.9i	−0.653604	−	1.13208i
$693$		0			0
$694$		−	4999.66i		−	0.273465i
$695$	37850.5	+	21853.0i	2.06583	+	1.19271i
$696$		0			0
$697$		−	15723.4i		−	0.854474i
$698$	−630.251	+	1091.63i	−0.0341767	+	0.0591958i
$699$		0			0
$700$	14589.4	−	8423.20i	0.787754	−	0.454810i
$701$	229.971			0.0123907			0.00619535	−	0.999981i	$-0.498028\pi$
$701$	229.971			0.0123907			0.00619535	+	0.999981i	$0.498028\pi$
$702$		0			0
$703$	11611.1			0.622934
$704$	12349.0	−	7129.68i	0.661107	−	0.381690i
$705$		0			0
$706$	−2738.56	+	4743.33i	−0.145988	+	0.252858i
$707$			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	$0.626072\pi$
$710$		−	1298.66i		−	0.0686446i
$711$		0			0
$712$	−830.202	−	1437.95i	−0.0436982	−	0.0756876i
$713$	−4069.16	+	2349.33i	−0.213732	+	0.123398i
$714$		0			0
$715$	−47503.0	+	4792.69i	−2.48463	+	0.250681i
$716$	−23717.6			−1.23795
$717$		0			0
$718$	3584.05	+	6207.75i	0.186289	+	0.322662i
$719$	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
$722$	11730.8	+	6772.81i	0.604677	+	0.349110i
$723$		0			0
$724$	272.063	−	471.226i	0.0139656	−	0.0241892i
$725$	2208.11	+	3824.55i	0.113113	+	0.195918i
$726$		0			0
$727$	13498.2			0.688612			0.344306	−	0.938857i	$-0.388114\pi$
$727$	13498.2			0.688612			0.344306	+	0.938857i	$0.388114\pi$
$728$	7840.57	+	10886.7i	0.399163	+	0.554244i
$729$		0			0
$730$	775.950	−	447.995i	0.0393414	−	0.0227138i
$731$	−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	$0.858977\pi$
$734$	−1341.37	−	774.442i	−0.0674537	−	0.0389444i
$735$		0			0
$736$			8084.38i			0.404883i
$737$	13536.7	−	23446.2i	0.676567	−	1.17185i
$738$		0			0
$739$	11598.3	−	6696.31i	0.577337	−	0.333326i	−0.182737	−	0.983162i	$-0.558496\pi$
$739$	11598.3	−	6696.31i	0.577337	−	0.333326i	0.760074	+	0.649836i	$0.225162\pi$
$740$	8744.19			0.434382
$741$		0			0
$742$	−4278.27			−0.211672
$743$	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
$746$			1716.05i			0.0842214i
$747$		0			0
$748$	−18080.6	−	10438.8i	−0.883812	−	0.510269i
$749$			12406.7i			0.605250i
$750$		0			0
$751$	−6225.26	−	10782.5i	−0.302480	−	0.523911i	0.674217	−	0.738534i	$-0.264481\pi$
$751$	−6225.26	−	10782.5i	−0.302480	−	0.523911i	−0.976697	+	0.214622i	$0.931148\pi$
$752$	2619.95	−	1512.63i	0.127048	−	0.0733510i
$753$		0			0
$754$	−1347.73	+	970.630i	−0.0650949	+	0.0468810i
$755$	−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	$0.779357\pi$
$758$	5351.51	−	9269.10i	0.256432	−	0.444154i
$759$		0			0
$760$	27397.3	+	15817.8i	1.30764	+	0.754964i
$761$	15363.8	+	8870.29i	0.731849	+	0.422533i	0.819098	−	0.573653i	$-0.194474\pi$
$761$	15363.8	+	8870.29i	0.731849	+	0.422533i	−0.0872491	+	0.996187i	$0.527808\pi$
$762$		0			0
$763$	14633.6	−	25346.2i	0.694328	−	1.20261i
$764$	−14579.5	−	25252.5i	−0.690405	−	1.19582i
$765$		0			0
$766$	−6124.94			−0.288907
$767$	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	$0.603155\pi$
$770$	−9616.95	−	16657.0i	−0.450092	−	0.779582i
$771$		0			0
$772$			6210.51i			0.289535i
$773$	1849.06	+	1067.56i	0.0860364	+	0.0496732i	0.542401	−	0.840120i	$-0.317515\pi$
$773$	1849.06	+	1067.56i	0.0860364	+	0.0496732i	−0.456365	+	0.889793i	$0.650849\pi$
$774$		0			0
$775$			10105.9i			0.468405i
$776$	−3856.47	+	6679.59i	−0.178401	+	0.308999i
$777$		0			0
$778$	11349.2	−	6552.48i	0.522994	−	0.301951i
$779$	−52198.9			−2.40080
$780$		0			0
$781$	6024.89			0.276040
$782$	1870.73	−	1080.07i	0.0855464	−	0.0493902i
$783$		0			0
$784$	1795.41	−	3109.75i	0.0817882	−	0.141661i
$785$			5290.89i			0.240560i
$786$		0			0
$787$	10136.3	+	5852.18i	0.459109	+	0.265067i	0.711670	−	0.702514i	$-0.247939\pi$
$787$	10136.3	+	5852.18i	0.459109	+	0.265067i	−0.252560	+	0.967581i	$0.581273\pi$
$788$		−	13512.9i		−	0.610885i
$789$		0			0
$790$	2037.39	+	3528.87i	0.0917559	+	0.158926i
$791$	−7071.79	+	4082.90i	−0.317881	+	0.183529i
$792$		0			0
$793$	7309.17	+	10148.9i	0.327309	+	0.454474i
$794$	3274.37			0.146351
$795$		0			0
$796$	9972.46	+	17272.8i	0.444051	+	0.769119i
$797$	74.8667	−	129.673i	0.00332737	−	0.00576317i	−0.864357	−	0.502879i	$-0.832274\pi$
$797$	74.8667	−	129.673i	0.00332737	−	0.00576317i	0.867684	+	0.497116i	$0.165608\pi$
$798$		0			0
$799$	−2607.31	−	1505.33i	−0.115444	−	0.0666518i
$800$	15058.4	+	8693.94i	0.665491	+	0.384222i
$801$		0			0
$802$	229.045	−	396.717i	0.0100846	−	0.0174670i
$803$	2078.40	+	3599.89i	0.0913387	+	0.158203i
$804$		0			0
$805$	−16927.4			−0.741135
$806$	−3781.49	+	381.524i	−0.165257	+	0.0166732i
$807$		0			0
$808$	−5570.62	+	3216.20i	−0.242542	+	0.140031i
$809$	11760.4	+	20369.6i	0.511093	+	0.885239i	0.999917	+	0.0128565i	$0.00409245\pi$
$809$	11760.4	+	20369.6i	0.511093	+	0.885239i	−0.488825	+	0.872382i	$0.662574\pi$
$810$		0			0
$811$		−	29604.8i		−	1.28183i	−0.767612	−	0.640915i	$-0.778555\pi$
$811$		−	29604.8i		−	1.28183i	0.767612	−	0.640915i	$-0.221445\pi$
$812$	4928.79	+	2845.64i	0.213013	+	0.122983i
$813$		0			0
$814$		−	4769.25i		−	0.205359i
$815$	4305.39	−	7457.16i	0.185045	−	0.320507i
$816$		0			0
$817$	−51939.9	+	29987.5i	−2.22417	+	1.28413i
$818$	−9593.44			−0.410057
$819$		0			0
$820$	−39310.3			−1.67412
$821$	37269.2	−	21517.4i	1.58429	−	0.914691i	0.590068	−	0.807353i	$-0.299101\pi$
$821$	37269.2	−	21517.4i	1.58429	−	0.914691i	0.994223	−	0.107338i	$-0.0342326\pi$
$822$		0			0
$823$	2792.47	−	4836.71i	0.118274	−	0.204857i	−0.800810	−	0.598919i	$-0.795597\pi$
$823$	2792.47	−	4836.71i	0.118274	−	0.204857i	0.919084	+	0.394062i	$0.128931\pi$
$824$		−	15603.5i		−	0.659675i
$825$		0			0
$826$	2322.60	+	1340.96i	0.0978374	+	0.0564865i
$827$			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	$-0.404056\pi$
$830$	−4594.44	+	2652.60i	−0.192139	+	0.110931i
$831$		0			0
$832$	4167.42	−	9256.17i	0.173653	−	0.385697i
$833$	−3573.50			−0.148637
$834$		0			0
$835$	24260.9	+	42021.1i	1.00549	+	1.74156i
$836$	−34654.9	+	60024.1i	−1.43369	+	2.48323i
$837$		0			0
$838$	−1354.90	−	782.254i	−0.0558525	−	0.0322464i
$839$	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
$842$	−4020.65	−	6963.97i	−0.164562	−	0.285029i
$843$		0			0
$844$	5073.82			0.206929
$845$	−25447.1	+	22531.4i	−1.03598	+	0.917284i
$846$		0			0
$847$	53551.4	−	30917.9i	2.17243	−	1.25425i
$848$	5042.41	+	8733.72i	0.204195	+	0.353676i
$849$		0			0
$850$		−	4646.02i		−	0.187479i
$851$	−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	$0.691956\pi$
$854$	−2519.24	+	4363.44i	−0.100944	+	0.174841i
$855$		0			0
$856$	−7258.93	+	4190.95i	−0.289843	+	0.167341i
$857$	−39959.3			−1.59275			−0.796374	−	0.604804i	$-0.793251\pi$
$857$	−39959.3			−1.59275			−0.796374	+	0.604804i	$0.793251\pi$
$858$		0			0
$859$	−32570.5			−1.29371			−0.646853	−	0.762615i	$-0.723915\pi$
$859$	−32570.5			−1.29371			−0.646853	+	0.762615i	$0.723915\pi$
$860$	−39115.2	+	22583.2i	−1.55095	+	0.895442i
$861$		0			0
$862$	3706.36	−	6419.60i	0.146449	−	0.253657i
$863$		−	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
$866$			3783.69i			0.148470i
$867$		0			0
$868$	6511.84	+	11278.8i	0.254639	+	0.441047i
$869$	−16371.6	+	9452.13i	−0.639088	+	0.368978i
$870$		0			0
$871$	−1934.70	−	19175.9i	−0.0752639	−	0.745981i
$872$	19772.7			0.767876
$873$		0			0
$874$	−3585.62	−	6210.48i	−0.138771	−	0.240358i
$875$	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	$-0.678773\pi$
$878$	−4858.59	−	2805.11i	−0.186753	−	0.107822i
$879$		0			0
$880$	−22669.2	+	39264.3i	−0.868386	+	1.50409i
$881$	−18980.3	−	32874.8i	−0.725836	−	1.25718i	−0.958629	−	0.284658i	$-0.908120\pi$
$881$	−18980.3	−	32874.8i	−0.725836	−	1.25718i	0.232793	−	0.972526i	$-0.425213\pi$
$882$		0			0
$883$	−43172.9			−1.64539			−0.822697	−	0.568480i	$-0.807532\pi$
$883$	−43172.9			−1.64539			−0.822697	+	0.568480i	$0.807532\pi$
$884$	−14787.5	+	1491.95i	−0.562621	+	0.0567642i
$885$		0			0
$886$	8785.89	−	5072.54i	0.333146	−	0.192342i
$887$	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
$890$	1467.55	+	847.289i	0.0552723	+	0.0319115i
$891$		0			0
$892$		−	38631.4i		−	1.45008i
$893$	−4997.41	+	8655.78i	−0.187270	+	0.324361i
$894$		0			0
$895$	44390.1	−	25628.7i	1.65788	−	0.957175i
$896$	29131.9			1.08619
$897$		0			0
$898$	−222.015			−0.00825027
$899$	−2956.70	+	1707.05i	−0.109690	+	0.0633296i
$900$		0			0
$901$	5018.08	−	8691.57i	0.185545	−	0.321374i
$902$			21440.6i			0.791456i
$903$		0			0
$904$	−4777.65	−	2758.38i	−0.175777	−	0.101485i
$905$			1175.93i			0.0431927i
$906$		0			0
$907$	−11178.0	−	19360.9i	−0.409218	−	0.708786i	0.585585	−	0.810611i	$-0.300865\pi$
$907$	−11178.0	−	19360.9i	−0.409218	−	0.708786i	−0.994802	+	0.101826i	$0.967532\pi$
$908$	19725.1	−	11388.3i	0.720926	−	0.416227i
$909$		0			0
$910$	−12485.3	−	5621.28i	−0.454817	−	0.204773i
$911$	−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
$914$	5069.48	−	8780.60i	0.183461	−	0.317764i
$915$		0			0
$916$	−12609.5	−	7280.12i	−0.454837	−	0.262600i
$917$	−29545.0	−	17057.8i	−1.06397	−	0.614285i
$918$		0			0
$919$	−20312.6	+	35182.4i	−0.729108	+	1.26285i	0.228153	+	0.973625i	$0.426731\pi$
$919$	−20312.6	+	35182.4i	−0.729108	+	1.26285i	−0.957261	+	0.289227i	$0.906602\pi$
$920$	−5718.02	−	9903.91i	−0.204911	−	0.354915i
$921$		0			0
$922$	−251.143			−0.00897068
$923$	3480.39	−	2506.56i	0.124115	−	0.0893871i
$924$		0			0
$925$	−7818.17	+	4513.82i	−0.277902	+	0.160447i
$926$	5311.22	+	9199.30i	0.188485	+	0.326466i
$927$		0			0
$928$			5874.20i			0.207791i
$929$	−37077.8	−	21406.9i	−1.30946	−	0.756014i	−0.327450	−	0.944869i	$-0.606189\pi$
$929$	−37077.8	−	21406.9i	−1.30946	−	0.756014i	−0.982005	+	0.188854i	$0.939523\pi$
$930$		0			0
$931$			11863.3i			0.417621i
$932$	10001.1	−	17322.4i	0.351499	−	0.608814i
$933$		0			0
$934$	717.338	−	414.155i	0.0251306	−	0.0145092i
$935$	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	$0.226158\pi$
$938$	6724.06	−	3882.14i	0.234060	−	0.135135i
$939$		0			0
$940$	−3763.49	+	6518.55i	−0.130587	+	0.226183i
$941$		−	7108.58i		−	0.246263i	−0.992390	−	0.123131i	$-0.960706\pi$
$941$		−	7108.58i		−	0.246263i	0.992390	−	0.123131i	$-0.0392936\pi$
$942$		0			0
$943$	16341.5	+	9434.75i	0.564318	+	0.325809i
$944$		−	6321.85i		−	0.217965i
$945$		0			0
$946$	12317.3	+	21334.2i	0.423330	+	0.733229i
$947$	−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
$950$	−15423.9			−0.526756
$951$		0			0
$952$	−6339.39	−	10980.1i	−0.215820	−	0.373811i
$953$	23903.3	−	41401.8i	0.812492	−	1.40728i	−0.0986228	−	0.995125i	$-0.531444\pi$
$953$	23903.3	−	41401.8i	0.812492	−	1.40728i	0.911115	−	0.412153i	$-0.135223\pi$
$954$		0			0
$955$	54574.4	+	31508.5i	1.84920	+	1.06764i
$956$	34058.2	+	19663.5i	1.15222	+	0.665234i
$957$		0			0
$958$	5535.78	−	9588.26i	0.186694	−	0.323364i
$959$	20248.1	+	35070.7i	0.681797	+	1.18091i
$960$		0			0
$961$	21978.3			0.737750
$962$	−1984.17	−	2755.04i	−0.0664991	−	0.0923349i
$963$		0			0
$964$	25177.3	−	14536.1i	0.841190	−	0.485662i
$965$	−6710.92	−	11623.7i	−0.223867	−	0.387750i
$966$		0			0
$967$			2832.71i			0.0942025i	0.998890	+	0.0471013i	$0.0149983\pi$
$967$			2832.71i			0.0942025i	−0.998890	+	0.0471013i	$0.985002\pi$
$968$	36178.9	+	20887.9i	1.20128	+	0.693557i
$969$		0			0
$970$		−	7871.68i		−	0.260561i
$971$	−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
$974$	10542.9			0.346835
$975$		0			0
$976$	11876.8			0.389515
$977$	3705.63	−	2139.45i	0.121344	−	0.0700583i	−0.438099	−	0.898927i	$-0.644348\pi$
$977$	3705.63	−	2139.45i	0.121344	−	0.0700583i	0.559444	+	0.828868i	$0.311015\pi$
$978$		0			0
$979$	−3930.85	+	6808.43i	−0.128325	+	0.222266i
$980$			8934.12i			0.291214i
$981$		0			0
$982$	−12476.5	−	7203.29i	−0.405438	−	0.234080i
$983$		−	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
$986$	1359.30	−	784.790i	0.0439034	−	0.0253477i
$987$		0			0
$988$	4952.98	+	49091.7i	0.159489	+	1.58078i
$989$	21680.5			0.697068
$990$		0			0
$991$	−11030.1	−	19104.7i	−0.353565	−	0.612393i	0.633306	−	0.773901i	$-0.281697\pi$
$991$	−11030.1	−	19104.7i	−0.353565	−	0.612393i	−0.986871	+	0.161508i	$0.948364\pi$
$992$	−6721.15	+	11641.4i	−0.215118	+	0.372594i
$993$		0			0
$994$	1496.37	+	863.929i	0.0477484	+	0.0275676i
$995$	−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	$0.975160\pi$
$998$	−4137.26	−	7165.95i	−0.131225	−	0.227289i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.e.10.3		10
3.2	odd	2		39.4.j.c.10.3	yes	10
12.11	even	2		624.4.bv.h.49.4		10
13.2	odd	12		1521.4.a.bk.1.6		10
13.4	even	6	inner	117.4.q.e.82.3		10
13.11	odd	12		1521.4.a.bk.1.5		10
39.2	even	12		507.4.a.r.1.5		10
39.11	even	12		507.4.a.r.1.6		10
39.17	odd	6		39.4.j.c.4.3	✓	10
39.23	odd	6		507.4.b.i.337.6		10
39.29	odd	6		507.4.b.i.337.5		10
156.95	even	6		624.4.bv.h.433.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.c.4.3	✓	10	39.17	odd	6
39.4.j.c.10.3	yes	10	3.2	odd	2
117.4.q.e.10.3		10	1.1	even	1	trivial
117.4.q.e.82.3		10	13.4	even	6	inner
507.4.a.r.1.5		10	39.2	even	12
507.4.a.r.1.6		10	39.11	even	12
507.4.b.i.337.5		10	39.29	odd	6
507.4.b.i.337.6		10	39.23	odd	6
624.4.bv.h.49.4		10	12.11	even	2
624.4.bv.h.433.2		10	156.95	even	6
1521.4.a.bk.1.5		10	13.11	odd	12
1521.4.a.bk.1.6		10	13.2	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.794469 - 0.458687i) q^{2} +(-3.57921 + 6.19938i) q^{4} -15.4704i q^{5} +(17.8257 + 10.2917i) q^{7} +13.9059i q^{8} +O(q^{10})\)	\(q+(0.794469 - 0.458687i) q^{2} +(-3.57921 + 6.19938i) q^{4} -15.4704i q^{5} +(17.8257 + 10.2917i) q^{7} +13.9059i q^{8} +(-7.09608 - 12.2908i) q^{10} +(57.0209 - 32.9210i) q^{11} +(19.2429 - 42.7400i) q^{13} +18.8826 q^{14} +(-22.2552 - 38.5472i) q^{16} +(-22.1478 + 38.3611i) q^{17} +(127.352 + 73.5266i) q^{19} +(95.9069 + 55.3719i) q^{20} +(30.2009 - 52.3094i) q^{22} +(-26.5793 - 46.0367i) q^{23} -114.334 q^{25} +(-4.31639 - 42.7821i) q^{26} +(-127.604 + 73.6721i) q^{28} +(-19.3128 - 33.4508i) q^{29} -88.3894i q^{31} +(-131.705 - 76.0401i) q^{32} +40.6357i q^{34} +(159.216 - 275.771i) q^{35} +(68.3803 - 39.4794i) q^{37} +134.903 q^{38} +215.131 q^{40} +(-307.410 + 177.483i) q^{41} +(-203.923 + 353.205i) q^{43} +471.325i q^{44} +(-42.2329 - 24.3832i) q^{46} +67.9674i q^{47} +(40.3369 + 69.8656i) q^{49} +(-90.8345 + 52.4433i) q^{50} +(196.087 + 272.270i) q^{52} -226.572 q^{53} +(-509.302 - 882.136i) q^{55} +(-143.115 + 247.883i) q^{56} +(-30.6869 - 17.7171i) q^{58} +(123.002 + 71.0154i) q^{59} +(-133.416 + 231.083i) q^{61} +(-40.5431 - 70.2227i) q^{62} +216.569 q^{64} +(-661.206 - 297.696i) q^{65} +(356.098 - 205.593i) q^{67} +(-158.543 - 274.605i) q^{68} -292.122i q^{70} +(79.2458 + 45.7526i) q^{71} +63.1328i q^{73} +(36.2173 - 62.7303i) q^{74} +(-911.638 + 526.335i) q^{76} +1355.25 q^{77} -287.115 q^{79} +(-596.341 + 344.298i) q^{80} +(-162.818 + 282.010i) q^{82} -373.812i q^{83} +(593.463 + 342.636i) q^{85} +374.147i q^{86} +(457.798 + 792.929i) q^{88} +(-103.406 + 59.7013i) q^{89} +(782.885 - 563.829i) q^{91} +380.532 q^{92} +(31.1758 + 53.9980i) q^{94} +(1137.49 - 1970.18i) q^{95} +(480.341 + 277.325i) q^{97} +(64.0928 + 37.0040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 30 q^{4} + 30 q^{7}+O(q^{10}) \) 10 * q + 30 * q^4 + 30 * q^7	\( 10 q + 30 q^{4} + 30 q^{7} + 40 q^{10} - 60 q^{11} + 25 q^{13} + 60 q^{14} - 250 q^{16} - 105 q^{17} + 180 q^{19} - 510 q^{20} - 290 q^{22} + 60 q^{23} - 960 q^{25} + 30 q^{26} + 150 q^{28} + 495 q^{29} - 1440 q^{32} - 60 q^{35} - 405 q^{37} + 1380 q^{38} + 2000 q^{40} - 1065 q^{41} - 370 q^{43} - 390 q^{46} + 775 q^{49} + 4320 q^{50} + 2940 q^{52} - 330 q^{53} - 260 q^{55} + 2670 q^{56} + 2040 q^{58} - 780 q^{59} - 1375 q^{61} + 780 q^{62} - 3140 q^{64} - 1605 q^{65} + 1590 q^{67} + 600 q^{68} - 1620 q^{71} - 2190 q^{74} - 5190 q^{76} + 4320 q^{77} + 1100 q^{79} - 8430 q^{80} - 2390 q^{82} + 525 q^{85} + 3170 q^{88} - 2040 q^{89} + 4770 q^{91} + 1740 q^{92} - 3230 q^{94} + 1380 q^{95} - 3750 q^{97} - 180 q^{98}+O(q^{100}) \) 10 * q + 30 * q^4 + 30 * q^7 + 40 * q^10 - 60 * q^11 + 25 * q^13 + 60 * q^14 - 250 * q^16 - 105 * q^17 + 180 * q^19 - 510 * q^20 - 290 * q^22 + 60 * q^23 - 960 * q^25 + 30 * q^26 + 150 * q^28 + 495 * q^29 - 1440 * q^32 - 60 * q^35 - 405 * q^37 + 1380 * q^38 + 2000 * q^40 - 1065 * q^41 - 370 * q^43 - 390 * q^46 + 775 * q^49 + 4320 * q^50 + 2940 * q^52 - 330 * q^53 - 260 * q^55 + 2670 * q^56 + 2040 * q^58 - 780 * q^59 - 1375 * q^61 + 780 * q^62 - 3140 * q^64 - 1605 * q^65 + 1590 * q^67 + 600 * q^68 - 1620 * q^71 - 2190 * q^74 - 5190 * q^76 + 4320 * q^77 + 1100 * q^79 - 8430 * q^80 - 2390 * q^82 + 525 * q^85 + 3170 * q^88 - 2040 * q^89 + 4770 * q^91 + 1740 * q^92 - 3230 * q^94 + 1380 * q^95 - 3750 * q^97 - 180 * q^98

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