LMFDB - Embedded newform 15.4.e.a.8.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,4,Mod(2,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("15.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	15.e (of order $4$, 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:	$0.885028650086$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.28356903014400.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 209x^{4} + 1600 $ x^8 + 209*x^4 + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.3
Root			$1.18766 - 1.18766i$ of defining polynomial
Character	$\chi$	$=$	15.8
Dual form			15.4.e.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18766 + 1.18766i) q^{2} +(-0.932827 + 5.11173i) q^{3} -5.17891i q^{4} +(2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 + 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(-25.2597 - 9.53673i) q^{9} +O(q^{10})$	\(q+(1.18766 + 1.18766i) q^{2} +(-0.932827 + 5.11173i) q^{3} -5.17891i q^{4} +(2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 + 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(-25.2597 - 9.53673i) q^{9} +(15.8945 - 10.0000i) q^{10} +28.7164i q^{11} +(26.4732 + 4.83102i) q^{12} +(14.1789 + 14.1789i) q^{13} -31.7292 q^{14} +(53.4105 + 22.8543i) q^{15} -4.25236 q^{16} +(18.5587 + 18.5587i) q^{17} +(-18.6736 - 41.3264i) q^{18} -49.0735i q^{19} +(-56.4577 - 12.8518i) q^{20} +(-55.8211 - 80.7421i) q^{21} +(-34.1055 + 34.1055i) q^{22} +(-37.7738 + 37.7738i) q^{23} +(65.4088 + 94.6102i) q^{24} +(-112.684 - 54.1055i) q^{25} +33.6796i q^{26} +(72.3121 - 120.225i) q^{27} +(69.1789 + 69.1789i) q^{28} +125.854 q^{29} +(36.2905 + 90.5770i) q^{30} +247.367 q^{31} +(-130.267 - 130.267i) q^{32} +(-146.791 - 26.7874i) q^{33} +44.0829i q^{34} +(112.471 + 178.768i) q^{35} +(-49.3898 + 130.818i) q^{36} +(-127.463 + 127.463i) q^{37} +(58.2828 - 58.2828i) q^{38} +(-85.7053 + 59.2524i) q^{39} +(-131.789 - 209.473i) q^{40} -390.328i q^{41} +(29.5978 - 162.191i) q^{42} +(-39.3993 - 39.3993i) q^{43} +148.720 q^{44} +(-166.648 + 251.701i) q^{45} -89.7251 q^{46} +(124.560 + 124.560i) q^{47} +(3.96671 - 21.7369i) q^{48} -13.8625i q^{49} +(-69.5712 - 198.089i) q^{50} +(-112.179 + 77.5549i) q^{51} +(73.4313 - 73.4313i) q^{52} +(-160.441 + 160.441i) q^{53} +(228.669 - 56.9040i) q^{54} +(313.051 + 71.2618i) q^{55} +418.156i q^{56} +(250.850 + 45.7770i) q^{57} +(149.473 + 149.473i) q^{58} -729.423 q^{59} +(118.360 - 276.608i) q^{60} +2.00000 q^{61} +(293.789 + 293.789i) q^{62} +(464.804 - 210.024i) q^{63} -275.409i q^{64} +(189.757 - 119.385i) q^{65} +(-142.524 - 206.153i) q^{66} +(-329.987 + 329.987i) q^{67} +(96.1136 - 96.1136i) q^{68} +(-157.853 - 228.326i) q^{69} +(-78.7382 + 345.895i) q^{70} +171.760i q^{71} +(-544.637 + 246.097i) q^{72} +(-279.927 - 279.927i) q^{73} -302.767 q^{74} +(381.687 - 525.538i) q^{75} -254.147 q^{76} +(-383.589 - 383.589i) q^{77} +(-172.161 - 31.4172i) q^{78} -48.0189i q^{79} +(-10.5525 + 46.3569i) q^{80} +(547.102 + 481.789i) q^{81} +(463.578 - 463.578i) q^{82} +(144.451 - 144.451i) q^{83} +(-418.156 + 289.092i) q^{84} +(248.371 - 156.262i) q^{85} -93.5862i q^{86} +(-117.400 + 643.334i) q^{87} +(449.473 + 449.473i) q^{88} +1417.21 q^{89} +(-496.858 + 101.015i) q^{90} -378.799 q^{91} +(195.627 + 195.627i) q^{92} +(-230.751 + 1264.48i) q^{93} +295.872i q^{94} +(-534.972 - 121.779i) q^{95} +(787.409 - 544.375i) q^{96} +(908.111 - 908.111i) q^{97} +(16.4640 - 16.4640i) q^{98} +(273.861 - 725.367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7}+O(q^{10}) $ 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7	$ 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7} - 100 q^{10} + 132 q^{12} + 68 q^{13} + 90 q^{15} + 284 q^{16} - 240 q^{18} - 492 q^{21} - 500 q^{22} - 220 q^{25} + 702 q^{27} + 508 q^{28} + 660 q^{30} + 616 q^{31} - 240 q^{33} - 804 q^{36} - 1156 q^{37} - 600 q^{40} + 540 q^{42} + 548 q^{43} + 180 q^{45} + 736 q^{46} - 1116 q^{48} - 852 q^{51} + 224 q^{52} + 460 q^{55} + 684 q^{57} + 60 q^{58} + 540 q^{60} + 16 q^{61} + 1428 q^{63} + 2040 q^{66} + 404 q^{67} - 2220 q^{70} - 1800 q^{72} - 2512 q^{73} - 2910 q^{75} - 1488 q^{76} - 360 q^{78} + 288 q^{81} + 2800 q^{82} + 4940 q^{85} - 1680 q^{87} + 2460 q^{88} + 600 q^{90} - 1304 q^{91} + 3408 q^{93} + 4164 q^{96} + 1904 q^{97}+O(q^{100}) $ 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7 - 100 * q^10 + 132 * q^12 + 68 * q^13 + 90 * q^15 + 284 * q^16 - 240 * q^18 - 492 * q^21 - 500 * q^22 - 220 * q^25 + 702 * q^27 + 508 * q^28 + 660 * q^30 + 616 * q^31 - 240 * q^33 - 804 * q^36 - 1156 * q^37 - 600 * q^40 + 540 * q^42 + 548 * q^43 + 180 * q^45 + 736 * q^46 - 1116 * q^48 - 852 * q^51 + 224 * q^52 + 460 * q^55 + 684 * q^57 + 60 * q^58 + 540 * q^60 + 16 * q^61 + 1428 * q^63 + 2040 * q^66 + 404 * q^67 - 2220 * q^70 - 1800 * q^72 - 2512 * q^73 - 2910 * q^75 - 1488 * q^76 - 360 * q^78 + 288 * q^81 + 2800 * q^82 + 4940 * q^85 - 1680 * q^87 + 2460 * q^88 + 600 * q^90 - 1304 * q^91 + 3408 * q^93 + 4164 * q^96 + 1904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.18766	+	1.18766i	0.419903	+	0.419903i	0.885170	−	0.465267i	$-0.154042\pi$
$2$	1.18766	+	1.18766i	0.419903	+	0.419903i	−0.465267	+	0.885170i	$0.654042\pi$
$3$	−0.932827	+	5.11173i	−0.179523	+	0.983754i
$3$	−0.932827	+	5.11173i	−0.179523	+	0.983754i
$4$		−	5.17891i		−	0.647364i
$5$	2.48157	−	10.9015i	0.221958	−	0.975056i
$5$	2.48157	−	10.9015i	0.221958	−	0.975056i
$6$	−7.17891	+	4.96314i	−0.488463	+	0.337699i
$7$	−13.3578	+	13.3578i	−0.721254	+	0.721254i	−0.968861	−	0.247606i	$-0.920356\pi$
$7$	−13.3578	+	13.3578i	−0.721254	+	0.721254i	0.247606	+	0.968861i	$0.420356\pi$
$8$	15.6521	−	15.6521i	0.691732	−	0.691732i
$9$	−25.2597	−	9.53673i	−0.935543	−	0.353212i
$10$	15.8945	−	10.0000i	0.502630	−	0.316228i
$11$			28.7164i			0.787121i	0.919299	+	0.393560i	$0.128757\pi$
$11$			28.7164i			0.787121i	−0.919299	+	0.393560i	$0.871243\pi$
$12$	26.4732	+	4.83102i	0.636846	+	0.116216i
$13$	14.1789	+	14.1789i	0.302502	+	0.302502i	0.841992	−	0.539490i	$-0.181383\pi$
$13$	14.1789	+	14.1789i	0.302502	+	0.302502i	−0.539490	+	0.841992i	$0.681383\pi$
$14$	−31.7292			−0.605713
$15$	53.4105	+	22.8543i	0.919369	+	0.393397i
$16$	−4.25236			−0.0664431
$17$	18.5587	+	18.5587i	0.264773	+	0.264773i	0.826990	−	0.562217i	$-0.190051\pi$
$17$	18.5587	+	18.5587i	0.264773	+	0.264773i	−0.562217	+	0.826990i	$0.690051\pi$
$18$	−18.6736	−	41.3264i	−0.244522	−	0.541152i
$19$		−	49.0735i		−	0.592538i	−0.955105	−	0.296269i	$-0.904258\pi$
$19$		−	49.0735i		−	0.592538i	0.955105	−	0.296269i	$-0.0957425\pi$
$20$	−56.4577	−	12.8518i	−0.631216	−	0.143688i
$21$	−55.8211	−	80.7421i	−0.580055	−	0.839018i
$22$	−34.1055	+	34.1055i	−0.330514	+	0.330514i
$23$	−37.7738	+	37.7738i	−0.342451	+	0.342451i	−0.857288	−	0.514837i	$-0.827852\pi$
$23$	−37.7738	+	37.7738i	−0.342451	+	0.342451i	0.514837	+	0.857288i	$0.327852\pi$
$24$	65.4088	+	94.6102i	0.556313	+	0.804676i
$25$	−112.684	−	54.1055i	−0.901469	−	0.432844i
$26$			33.6796i			0.254042i
$27$	72.3121	−	120.225i	0.515425	−	0.856935i
$28$	69.1789	+	69.1789i	0.466914	+	0.466914i
$29$	125.854			0.805882			0.402941	−	0.915226i	$-0.367988\pi$
$29$	125.854			0.805882			0.402941	+	0.915226i	$0.367988\pi$
$30$	36.2905	+	90.5770i	0.220857	+	0.551234i
$31$	247.367			1.43318			0.716588	−	0.697496i	$-0.245703\pi$
$31$	247.367			1.43318			0.716588	+	0.697496i	$0.245703\pi$
$32$	−130.267	−	130.267i	−0.719632	−	0.719632i
$33$	−146.791	−	26.7874i	−0.774333	−	0.141306i
$34$			44.0829i			0.222357i
$35$	112.471	+	178.768i	0.543175	+	0.863352i
$36$	−49.3898	+	130.818i	−0.228657	+	0.605637i
$37$	−127.463	+	127.463i	−0.566347	+	0.566347i	−0.931103	−	0.364756i	$-0.881152\pi$
$37$	−127.463	+	127.463i	−0.566347	+	0.566347i	0.364756	+	0.931103i	$0.381152\pi$
$38$	58.2828	−	58.2828i	0.248808	−	0.248808i
$39$	−85.7053	+	59.2524i	−0.351893	+	0.243281i
$40$	−131.789	−	209.473i	−0.520942	−	0.828014i
$41$		−	390.328i		−	1.48680i	−0.668845	−	0.743402i	$-0.733211\pi$
$41$		−	390.328i		−	1.48680i	0.668845	−	0.743402i	$-0.266789\pi$
$42$	29.5978	−	162.191i	0.108739	−	0.595873i
$43$	−39.3993	−	39.3993i	−0.139729	−	0.139729i	0.633783	−	0.773511i	$-0.281501\pi$
$43$	−39.3993	−	39.3993i	−0.139729	−	0.139729i	−0.773511	+	0.633783i	$0.781501\pi$
$44$	148.720			0.509553
$45$	−166.648	+	251.701i	−0.552053	+	0.833809i
$46$	−89.7251			−0.287592
$47$	124.560	+	124.560i	0.386575	+	0.386575i	0.873464	−	0.486889i	$-0.161868\pi$
$47$	124.560	+	124.560i	0.386575	+	0.386575i	−0.486889	+	0.873464i	$0.661868\pi$
$48$	3.96671	−	21.7369i	0.0119280	−	0.0653637i
$49$		−	13.8625i		−	0.0404155i
$50$	−69.5712	−	198.089i	−0.196777	−	0.560281i
$51$	−112.179	+	77.5549i	−0.308004	+	0.212938i
$52$	73.4313	−	73.4313i	0.195829	−	0.195829i
$53$	−160.441	+	160.441i	−0.415816	+	0.415816i	−0.883759	−	0.467943i	$-0.844995\pi$
$53$	−160.441	+	160.441i	−0.415816	+	0.415816i	0.467943	+	0.883759i	$0.344995\pi$
$54$	228.669	−	56.9040i	0.576257	−	0.143401i
$55$	313.051	+	71.2618i	0.767487	+	0.174708i
$56$			418.156i			0.997830i
$57$	250.850	+	45.7770i	0.582912	+	0.106374i
$58$	149.473	+	149.473i	0.338392	+	0.338392i
$59$	−729.423			−1.60954			−0.804769	−	0.593588i	$-0.797711\pi$
$59$	−729.423			−1.60954			−0.804769	+	0.593588i	$0.797711\pi$
$60$	118.360	−	276.608i	0.254671	−	0.595166i
$61$	2.00000			0.00419793			0.00209897	−	0.999998i	$-0.499332\pi$
$61$	2.00000			0.00419793			0.00209897	+	0.999998i	$0.499332\pi$
$62$	293.789	+	293.789i	0.601795	+	0.601795i
$63$	464.804	−	210.024i	0.929520	−	0.420009i
$64$		−	275.409i		−	0.537908i
$65$	189.757	−	119.385i	0.362099	−	0.227813i
$66$	−142.524	−	206.153i	−0.265810	−	0.384479i
$67$	−329.987	+	329.987i	−0.601706	+	0.601706i	−0.940765	−	0.339059i	$-0.889891\pi$
$67$	−329.987	+	329.987i	−0.601706	+	0.601706i	0.339059	+	0.940765i	$0.389891\pi$
$68$	96.1136	−	96.1136i	0.171404	−	0.171404i
$69$	−157.853	−	228.326i	−0.275410	−	0.398365i
$70$	−78.7382	+	345.895i	−0.134443	+	0.590604i
$71$			171.760i			0.287100i	0.989643	+	0.143550i	$0.0458518\pi$
$71$			171.760i			0.287100i	−0.989643	+	0.143550i	$0.954148\pi$
$72$	−544.637	+	246.097i	−0.891474	+	0.402817i
$73$	−279.927	−	279.927i	−0.448807	−	0.448807i	0.446151	−	0.894958i	$-0.352795\pi$
$73$	−279.927	−	279.927i	−0.448807	−	0.448807i	−0.894958	+	0.446151i	$0.852795\pi$
$74$	−302.767			−0.475621
$75$	381.687	−	525.538i	0.587646	−	0.809118i
$76$	−254.147			−0.383587
$77$	−383.589	−	383.589i	−0.567714	−	0.567714i
$78$	−172.161	−	31.4172i	−0.249915	−	0.0456064i
$79$		−	48.0189i		−	0.0683866i	−0.999415	−	0.0341933i	$-0.989114\pi$
$79$		−	48.0189i		−	0.0683866i	0.999415	−	0.0341933i	$-0.0108862\pi$
$80$	−10.5525	+	46.3569i	−0.0147476	+	0.0647858i
$81$	547.102	+	481.789i	0.750483	+	0.660890i
$82$	463.578	−	463.578i	0.624313	−	0.624313i
$83$	144.451	−	144.451i	0.191031	−	0.191031i	−0.605111	−	0.796141i	$-0.706871\pi$
$83$	144.451	−	144.451i	0.191031	−	0.191031i	0.796141	+	0.605111i	$0.206871\pi$
$84$	−418.156	+	289.092i	−0.543150	+	0.375507i
$85$	248.371	−	156.262i	0.316937	−	0.199400i
$86$		−	93.5862i		−	0.117345i
$87$	−117.400	+	643.334i	−0.144674	+	0.792789i
$88$	449.473	+	449.473i	0.544477	+	0.544477i
$89$	1417.21			1.68790			0.843952	−	0.536419i	$-0.180223\pi$
$89$	1417.21			1.68790			0.843952	+	0.536419i	$0.180223\pi$
$90$	−496.858	+	101.015i	−0.581927	+	0.118310i
$91$	−378.799			−0.436361
$92$	195.627	+	195.627i	0.221690	+	0.221690i
$93$	−230.751	+	1264.48i	−0.257288	+	1.40989i
$94$			295.872i			0.324647i
$95$	−534.972	−	121.779i	−0.577758	−	0.131519i
$96$	787.409	−	544.375i	0.837131	−	0.578751i
$97$	908.111	−	908.111i	0.950564	−	0.950564i	−0.0482702	−	0.998834i	$-0.515371\pi$
$97$	908.111	−	908.111i	0.950564	−	0.950564i	0.998834	+	0.0482702i	$0.0153708\pi$
$98$	16.4640	−	16.4640i	0.0169706	−	0.0169706i
$99$	273.861	−	725.367i	0.278020	−	0.736385i
$100$	−280.207	+	583.578i	−0.280207	+	0.583578i
$101$		−	337.668i		−	0.332665i	−0.986070	−	0.166333i	$-0.946807\pi$
$101$		−	337.668i		−	0.332665i	0.986070	−	0.166333i	$-0.0531926\pi$
$102$	−225.340	−	41.1217i	−0.218745	−	0.0399182i
$103$	−933.505	−	933.505i	−0.893019	−	0.893019i	0.101787	−	0.994806i	$-0.467544\pi$
$103$	−933.505	−	933.505i	−0.893019	−	0.893019i	−0.994806	+	0.101787i	$0.967544\pi$
$104$	443.860			0.418500
$105$	−1018.73	+	408.164i	−0.946838	+	0.379359i
$106$	−381.100			−0.349205
$107$	−596.188	−	596.188i	−0.538651	−	0.538651i	0.384481	−	0.923133i	$-0.374380\pi$
$107$	−596.188	−	596.188i	−0.538651	−	0.538651i	−0.923133	+	0.384481i	$0.874380\pi$
$108$	−622.632	−	374.498i	−0.554748	−	0.333667i
$109$			2074.60i			1.82303i	0.411264	+	0.911516i	$0.365087\pi$
$109$			2074.60i			1.82303i	−0.411264	+	0.911516i	$0.634913\pi$
$110$	287.164	+	456.434i	0.248909	+	0.395630i
$111$	−532.657	−	770.460i	−0.455474	−	0.658818i
$112$	56.8022	−	56.8022i	0.0479224	−	0.0479224i
$113$	271.193	−	271.193i	0.225767	−	0.225767i	−0.585154	−	0.810922i	$-0.698966\pi$
$113$	271.193	−	271.193i	0.225767	−	0.225767i	0.810922	+	0.585154i	$0.198966\pi$
$114$	243.558	+	352.294i	0.200099	+	0.289433i
$115$	318.051	+	505.527i	0.257899	+	0.409919i
$116$		−	651.788i		−	0.521698i
$117$	−222.934	−	493.375i	−0.176156	−	0.389851i
$118$	−866.309	−	866.309i	−0.675849	−	0.675849i
$119$	−495.806			−0.381937
$120$	1193.71	−	478.269i	0.908082	−	0.363832i
$121$	506.367			0.380441
$122$	2.37533	+	2.37533i	0.00176272	+	0.00176272i
$123$	1995.25	+	364.108i	1.46265	+	0.266915i
$124$		−	1281.09i		−	0.927786i
$125$	−869.461	+	1094.15i	−0.622135	+	0.782910i
$126$	801.469	+	302.593i	0.566671	+	0.213945i
$127$	105.588	−	105.588i	0.0737747	−	0.0737747i	−0.669257	−	0.743031i	$-0.733387\pi$
$127$	105.588	−	105.588i	0.0737747	−	0.0737747i	0.743031	+	0.669257i	$0.233387\pi$
$128$	−715.045	+	715.045i	−0.493763	+	0.493763i
$129$	238.151	−	164.646i	0.162543	−	0.112374i
$130$	367.156	+	83.5782i	0.247706	+	0.0563868i
$131$			1979.28i			1.32008i	0.751231	+	0.660039i	$0.229460\pi$
$131$			1979.28i			1.32008i	−0.751231	+	0.660039i	$0.770540\pi$
$132$	−138.730	+	760.216i	−0.0914763	+	0.501275i
$133$	655.514	+	655.514i	0.427371	+	0.427371i
$134$	−783.827			−0.505316
$135$	−1131.18	−	1086.65i	−0.721157	−	0.692772i
$136$	580.964			0.366304
$137$	507.451	+	507.451i	0.316456	+	0.316456i	0.847404	−	0.530948i	$-0.178164\pi$
$137$	507.451	+	507.451i	0.316456	+	0.316456i	−0.530948	+	0.847404i	$0.678164\pi$
$138$	83.6979	−	458.651i	0.0516293	−	0.282920i
$139$		−	68.4333i		−	0.0417585i	−0.999782	−	0.0208793i	$-0.993353\pi$
$139$		−	68.4333i		−	0.0417585i	0.999782	−	0.0208793i	$-0.00664656\pi$
$140$	925.823	−	582.479i	0.558903	−	0.351632i
$141$	−752.913	+	520.527i	−0.449693	+	0.310895i
$142$	−203.993	+	203.993i	−0.120554	+	0.120554i
$143$	−407.167	+	407.167i	−0.238105	+	0.238105i
$144$	107.413	+	40.5536i	0.0621604	+	0.0234685i
$145$	312.316	−	1372.00i	0.178872	−	0.785780i
$146$		−	664.917i		−	0.376911i
$147$	70.8616	+	12.9313i	0.0397590	+	0.00725550i
$148$	660.121	+	660.121i	0.366632	+	0.366632i
$149$	363.356			0.199780			0.0998902	−	0.994998i	$-0.468151\pi$
$149$	363.356			0.199780			0.0998902	+	0.994998i	$0.468151\pi$
$150$	1077.48	−	170.846i	0.586505	−	0.0929970i
$151$	−2083.14			−1.12267			−0.561337	−	0.827588i	$-0.689713\pi$
$151$	−2083.14			−1.12267			−0.561337	+	0.827588i	$0.689713\pi$
$152$	−768.103	−	768.103i	−0.409878	−	0.409878i
$153$	−291.797	−	645.774i	−0.154185	−	0.341227i
$154$		−	911.149i		−	0.476769i
$155$	613.859	−	2696.66i	0.318105	−	1.39743i
$156$	306.863	+	443.860i	0.157491	+	0.227803i
$157$	−1208.52	+	1208.52i	−0.614333	+	0.614333i	−0.944072	−	0.329739i	$-0.893039\pi$
$157$	−1208.52	+	1208.52i	−0.614333	+	0.614333i	0.329739	+	0.944072i	$0.393039\pi$
$158$	57.0303	−	57.0303i	0.0287157	−	0.0287157i
$159$	−670.468	−	969.795i	−0.334412	−	0.483709i
$160$	−1743.37	+	1096.84i	−0.861410	+	0.541953i
$161$		−	1009.15i		−	0.493989i
$162$	77.5696	+	1221.98i	0.0376200	+	0.592639i
$163$	626.062	+	626.062i	0.300840	+	0.300840i	0.841343	−	0.540502i	$-0.181766\pi$
$163$	626.062	+	626.062i	0.300840	+	0.300840i	−0.540502	+	0.841343i	$0.681766\pi$
$164$	−2021.47			−0.962502
$165$	−656.294	+	1533.76i	−0.309651	+	0.723654i
$166$	343.119			0.160429
$167$	3009.65	+	3009.65i	1.39457	+	1.39457i	0.814724	+	0.579848i	$0.196888\pi$
$167$	3009.65	+	3009.65i	1.39457	+	1.39457i	0.579848	+	0.814724i	$0.303112\pi$
$168$	−2137.50	−	390.067i	−0.981619	−	0.179133i
$169$		−	1794.92i		−	0.816985i
$170$	480.568	+	109.395i	0.216811	+	0.0493541i
$171$	−468.000	+	1239.58i	−0.209292	+	0.554345i
$172$	−204.045	+	204.045i	−0.0904552	+	0.0904552i
$173$	1839.23	−	1839.23i	0.808288	−	0.808288i	−0.176086	−	0.984375i	$-0.556344\pi$
$173$	1839.23	−	1839.23i	0.808288	−	0.808288i	0.984375	+	0.176086i	$0.0563438\pi$
$174$	−903.497	+	624.633i	−0.393643	+	0.272145i
$175$	2227.94	−	782.476i	0.962379	−	0.337998i
$176$		−	122.113i		−	0.0522987i
$177$	680.425	−	3728.61i	0.288948	−	1.58339i
$178$	1683.16	+	1683.16i	0.708755	+	0.708755i
$179$	−821.582			−0.343061			−0.171530	−	0.985179i	$-0.554871\pi$
$179$	−821.582			−0.343061			−0.171530	+	0.985179i	$0.554871\pi$
$180$	1303.54	+	863.054i	0.539777	+	0.357379i
$181$	2314.20			0.950350			0.475175	−	0.879891i	$-0.342385\pi$
$181$	2314.20			0.950350			0.475175	+	0.879891i	$0.342385\pi$
$182$	−449.885	−	449.885i	−0.183229	−	0.183229i
$183$	−1.86565	+	10.2235i	−0.000753623	+	0.00412973i
$184$			1182.48i			0.473769i
$185$	1073.23	+	1705.84i	0.426515	+	0.677925i
$186$	−1775.83	+	1227.72i	−0.700053	+	0.483982i
$187$	−532.938	+	532.938i	−0.208408	+	0.208408i
$188$	645.087	−	645.087i	0.250254	−	0.250254i
$189$	640.007	+	2571.87i	0.246316	+	0.989820i
$190$	−490.735	−	780.000i	−0.187377	−	0.297827i
$191$			931.167i			0.352758i	0.984322	+	0.176379i	$0.0564385\pi$
$191$			931.167i			0.352758i	−0.984322	+	0.176379i	$0.943562\pi$
$192$	1407.82	+	256.909i	0.529169	+	0.0965666i
$193$	−2623.28	−	2623.28i	−0.978382	−	0.978382i	0.0213891	−	0.999771i	$-0.493191\pi$
$193$	−2623.28	−	2623.28i	−0.978382	−	0.978382i	−0.999771	+	0.0213891i	$0.993191\pi$
$194$	2157.06			0.798289
$195$	433.254	+	1081.35i	0.159107	+	0.397114i
$196$	−71.7928			−0.0261636
$197$	−2995.05	−	2995.05i	−1.08319	−	1.08319i	−0.996210	−	0.0869796i	$-0.972279\pi$
$197$	−2995.05	−	2995.05i	−1.08319	−	1.08319i	−0.0869796	−	0.996210i	$-0.527721\pi$
$198$	1186.75	−	536.238i	0.425952	−	0.192469i
$199$			109.458i			0.0389912i	0.999810	+	0.0194956i	$0.00620603\pi$
$199$			109.458i			0.0389912i	−0.999810	+	0.0194956i	$0.993794\pi$
$200$	−2610.60	+	916.872i	−0.922987	+	0.324163i
$201$	−1378.98	−	1994.63i	−0.483911	−	0.699951i
$202$	401.036	−	401.036i	0.139687	−	0.139687i
$203$	−1681.14	+	1681.14i	−0.581246	+	0.581246i
$204$	401.650	+	580.964i	0.137849	+	0.199390i
$205$	−4255.14	−	968.625i	−1.44972	−	0.330008i
$206$		−	2217.38i		−	0.749962i
$207$	1314.39	−	593.915i	0.441336	−	0.199420i
$208$	−60.2938	−	60.2938i	−0.0200991	−	0.0200991i
$209$	1409.21			0.466399
$210$	−1694.67	−	725.148i	−0.556874	−	0.238286i
$211$	2714.94			0.885801			0.442901	−	0.896571i	$-0.353949\pi$
$211$	2714.94			0.885801			0.442901	+	0.896571i	$0.353949\pi$
$212$	830.909	+	830.909i	0.269184	+	0.269184i
$213$	−877.989	−	160.222i	−0.282436	−	0.0515409i
$214$		−	1416.14i		−	0.452362i
$215$	−527.281	+	331.737i	−0.167257	+	0.105229i
$216$	−749.932	−	3013.61i	−0.236233	−	0.949305i
$217$	−3304.29	+	3304.29i	−1.03368	+	1.03368i
$218$	−2463.93	+	2463.93i	−0.765496	+	0.765496i
$219$	1692.03	−	1169.79i	0.522087	−	0.360945i
$220$	369.058	−	1621.26i	0.113100	−	0.496843i
$221$			526.283i			0.160188i
$222$	282.429	−	1547.67i	0.0853847	−	0.467894i
$223$	2830.49	+	2830.49i	0.849971	+	0.849971i	0.990129	−	0.140158i	$-0.0447612\pi$
$223$	2830.49	+	2830.49i	0.849971	+	0.849971i	−0.140158	+	0.990129i	$0.544761\pi$
$224$	3480.17			1.03808
$225$	2330.36	+	2441.32i	0.690478	+	0.723354i
$226$	644.173			0.189601
$227$	−1398.96	−	1398.96i	−0.409042	−	0.409042i	0.472362	−	0.881404i	$-0.343401\pi$
$227$	−1398.96	−	1398.96i	−0.409042	−	0.409042i	−0.881404	+	0.472362i	$0.843401\pi$
$228$	237.075	−	1299.13i	0.0688626	−	0.377356i
$229$			3930.38i			1.13418i	0.823656	+	0.567089i	$0.191931\pi$
$229$			3930.38i			1.13418i	−0.823656	+	0.567089i	$0.808069\pi$
$230$	−222.659	+	978.134i	−0.0638335	+	0.280419i
$231$	2318.63	−	1602.98i	0.660408	−	0.456573i
$232$	1969.89	−	1969.89i	0.557454	−	0.557454i
$233$	−1980.71	+	1980.71i	−0.556912	+	0.556912i	−0.928427	−	0.371515i	$-0.878838\pi$
$233$	−1980.71	+	1980.71i	−0.556912	+	0.556912i	0.371515	+	0.928427i	$0.378838\pi$
$234$	321.193	−	850.735i	0.0897309	−	0.237668i
$235$	1667.00	−	1048.79i	0.462736	−	0.291129i
$236$			3777.61i			1.04196i
$237$	245.460	+	44.7933i	0.0672756	+	0.0122769i
$238$	−588.851	−	588.851i	−0.160376	−	0.160376i
$239$	−2976.20			−0.805500			−0.402750	−	0.915310i	$-0.631946\pi$
$239$	−2976.20			−0.805500			−0.402750	+	0.915310i	$0.631946\pi$
$240$	−227.121	−	97.1847i	−0.0610857	−	0.0261385i
$241$	1835.45			0.490587			0.245294	−	0.969449i	$-0.421116\pi$
$241$	1835.45			0.490587			0.245294	+	0.969449i	$0.421116\pi$
$242$	601.394	+	601.394i	0.159748	+	0.159748i
$243$	−2973.13	+	2347.21i	−0.784882	+	0.619645i
$244$		−	10.3578i		−	0.00271759i
$245$	−151.122	−	34.4008i	−0.0394074	−	0.00897057i
$246$	1937.25	+	2802.13i	0.502092	+	0.726248i
$247$	695.808	−	695.808i	0.179244	−	0.179244i
$248$	3871.82	−	3871.82i	0.991374	−	0.991374i
$249$	603.648	+	873.143i	0.153633	+	0.222222i
$250$	−2332.11	+	266.855i	−0.589982	+	0.0675095i
$251$		−	1542.14i		−	0.387805i	−0.981021	−	0.193902i	$-0.937885\pi$
$251$		−	1542.14i		−	0.387805i	0.981021	−	0.193902i	$-0.0621145\pi$
$252$	−1087.70	−	2407.18i	−0.271898	−	0.601738i
$253$	−1084.73	−	1084.73i	−0.269550	−	0.269550i
$254$	250.805			0.0619564
$255$	567.082	+	1415.37i	0.139263	+	0.347584i
$256$	−3901.74			−0.952572
$257$	−428.853	−	428.853i	−0.104090	−	0.104090i	0.653144	−	0.757234i	$-0.273450\pi$
$257$	−428.853	−	428.853i	−0.104090	−	0.104090i	−0.757234	+	0.653144i	$0.773450\pi$
$258$	478.388	+	87.2997i	0.115438	+	0.0210660i
$259$		−	3405.26i		−	0.816960i
$260$	−618.283	−	982.733i	−0.147478	−	0.234410i
$261$	−3179.04	−	1200.24i	−0.753937	−	0.284647i
$262$	−2350.72	+	2350.72i	−0.554304	+	0.554304i
$263$	5256.99	−	5256.99i	1.23255	−	1.23255i	0.269565	−	0.962982i	$-0.413120\pi$
$263$	5256.99	−	5256.99i	1.23255	−	1.23255i	0.962982	−	0.269565i	$-0.0868798\pi$
$264$	−2716.87	+	1878.31i	−0.633377	+	0.437885i
$265$	1350.89	+	2147.18i	0.313150	+	0.497738i
$266$			1557.06i			0.358908i
$267$	−1322.01	+	7244.38i	−0.303017	+	1.66048i
$268$	1708.97	+	1708.97i	0.389523	+	0.389523i
$269$	−1930.34			−0.437528			−0.218764	−	0.975778i	$-0.570203\pi$
$269$	−1930.34			−0.437528			−0.218764	+	0.975778i	$0.570203\pi$
$270$	−52.8785	−	2634.04i	−0.0119188	−	0.593712i
$271$	−3261.67			−0.731116			−0.365558	−	0.930789i	$-0.619122\pi$
$271$	−3261.67			−0.731116			−0.365558	+	0.930789i	$0.619122\pi$
$272$	−78.9180	−	78.9180i	−0.0175923	−	0.0175923i
$273$	353.353	−	1936.32i	0.0783367	−	0.429272i
$274$			1205.36i			0.265762i
$275$	1553.72	−	3235.87i	0.340700	−	0.709565i
$276$	−1182.48	+	817.507i	−0.257887	+	0.178290i
$277$	4865.57	−	4865.57i	1.05539	−	1.05539i	0.0570194	−	0.998373i	$-0.481840\pi$
$277$	4865.57	−	4865.57i	1.05539	−	1.05539i	0.998373	−	0.0570194i	$-0.0181597\pi$
$278$	81.2758	−	81.2758i	0.0175345	−	0.0175345i
$279$	−6248.41	−	2359.07i	−1.34080	−	0.506215i
$280$	4558.51	+	1037.68i	0.972940	+	0.221477i
$281$		−	3981.96i		−	0.845351i	−0.906281	−	0.422676i	$-0.861091\pi$
$281$		−	3981.96i		−	0.845351i	0.906281	−	0.422676i	$-0.138909\pi$
$282$	−1512.42	−	275.997i	−0.319373	−	0.0582815i
$283$	−4092.66	−	4092.66i	−0.859658	−	0.859658i	0.131640	−	0.991298i	$-0.457976\pi$
$283$	−4092.66	−	4092.66i	−0.859658	−	0.859658i	−0.991298	+	0.131640i	$0.957976\pi$
$284$	889.527			0.185858
$285$	1121.54	−	2621.04i	0.233103	−	0.544761i
$286$	−967.156			−0.199962
$287$	5213.93	+	5213.93i	1.07236	+	1.07236i
$288$	2048.19	+	4532.83i	0.419064	+	0.927429i
$289$		−	4224.15i		−	0.859791i
$290$	2000.40	−	1258.54i	0.405060	−	0.254842i
$291$	3794.91	+	5489.13i	0.764473	+	1.10577i
$292$	−1449.71	+	1449.71i	−0.290541	+	0.290541i
$293$	−4515.35	+	4515.35i	−0.900305	+	0.900305i	−0.995462	−	0.0951570i	$-0.969665\pi$
$293$	−4515.35	+	4515.35i	−0.900305	+	0.900305i	0.0951570	+	0.995462i	$0.469665\pi$
$294$	68.8017	+	99.5179i	0.0136483	+	0.0197415i
$295$	−1810.11	+	7951.77i	−0.357250	+	1.56939i
$296$			3990.14i			0.783521i
$297$	3452.42	+	2076.54i	0.674511	+	0.405701i
$298$	431.545	+	431.545i	0.0838883	+	0.0838883i
$299$	−1071.18			−0.207184
$300$	−2721.71	−	1976.72i	−0.523794	−	0.380420i
$301$	1052.58			0.201560
$302$	−2474.07	−	2474.07i	−0.471413	−	0.471413i
$303$	1726.07	+	314.986i	0.327261	+	0.0597210i
$304$			208.678i			0.0393701i
$305$	4.96314	−	21.8029i	0.000931766	−	0.00409322i
$306$	420.406	−	1113.52i	0.0785393	−	0.208025i
$307$	1831.07	−	1831.07i	0.340406	−	0.340406i	−0.516114	−	0.856520i	$-0.672622\pi$
$307$	1831.07	−	1831.07i	0.340406	−	0.340406i	0.856520	+	0.516114i	$0.172622\pi$
$308$	−1986.57	+	1986.57i	−0.367517	+	0.367517i
$309$	5642.63	−	3901.03i	1.03883	−	0.718194i
$310$	3931.79	−	2473.67i	0.720357	−	0.453210i
$311$		−	4010.21i		−	0.731184i	−0.930775	−	0.365592i	$-0.880866\pi$
$311$		−	4010.21i		−	0.731184i	0.930775	−	0.365592i	$-0.119134\pi$
$312$	−414.044	+	2268.89i	−0.0751303	+	0.411701i
$313$	6072.69	+	6072.69i	1.09664	+	1.09664i	0.994801	+	0.101841i	$0.0324733\pi$
$313$	6072.69	+	6072.69i	1.09664	+	1.09664i	0.101841	+	0.994801i	$0.467527\pi$
$314$	−2870.63			−0.515920
$315$	−1136.13	−	5588.23i	−0.203218	−	0.999559i
$316$	−248.685			−0.0442710
$317$	3112.10	+	3112.10i	0.551397	+	0.551397i	0.926844	−	0.375447i	$-0.122511\pi$
$317$	3112.10	+	3112.10i	0.551397	+	0.551397i	−0.375447	+	0.926844i	$0.622511\pi$
$318$	355.500	−	1948.08i	0.0626901	−	0.343531i
$319$			3614.09i			0.634326i
$320$	−3002.36	−	683.446i	−0.524490	−	0.119393i
$321$	3603.70	−	2491.42i	0.626600	−	0.433200i
$322$	1198.53	−	1198.53i	0.207427	−	0.207427i
$323$	910.737	−	910.737i	0.156888	−	0.156888i
$324$	2495.14	−	2833.39i	0.427836	−	0.485835i
$325$	−830.574	−	2364.89i	−0.141760	−	0.403632i
$326$			1487.10i			0.252647i
$327$	−10604.8	−	1935.24i	−1.79342	−	0.327275i
$328$	−6109.45	−	6109.45i	−1.02847	−	1.02847i
$329$	−3327.71			−0.557637
$330$	−2601.05	+	1042.13i	−0.433887	+	0.173841i
$331$	−9589.47			−1.59240			−0.796201	−	0.605033i	$-0.793160\pi$
$331$	−9589.47			−1.59240			−0.796201	+	0.605033i	$0.793160\pi$
$332$	−748.099	−	748.099i	−0.123666	−	0.123666i
$333$	4435.26	−	2004.10i	0.729883	−	0.329801i
$334$			7148.90i			1.17117i
$335$	2778.45	+	4416.22i	0.453144	+	0.720251i
$336$	237.371	+	343.345i	0.0385407	+	0.0557470i
$337$	−2561.34	+	2561.34i	−0.414021	+	0.414021i	−0.883137	−	0.469115i	$-0.844573\pi$
$337$	−2561.34	+	2561.34i	−0.414021	+	0.414021i	0.469115	+	0.883137i	$0.344573\pi$
$338$	2131.76	−	2131.76i	0.343054	−	0.343054i
$339$	1133.29	+	1639.24i	0.181569	+	0.262630i
$340$	−809.265	−	1286.29i	−0.129084	−	0.205173i
$341$			7103.50i			1.12808i
$342$	−2028.03	+	916.377i	−0.320653	+	0.144889i
$343$	−4396.56	−	4396.56i	−0.692104	−	0.692104i
$344$	−1233.36			−0.193310
$345$	−2880.81	+	1154.22i	−0.449558	+	0.180120i
$346$	4368.77			0.678805
$347$	−8177.44	−	8177.44i	−1.26509	−	1.26509i	−0.948592	−	0.316503i	$-0.897491\pi$
$347$	−8177.44	−	8177.44i	−1.26509	−	1.26509i	−0.316503	−	0.948592i	$-0.602509\pi$
$348$	3331.77	+	608.005i	0.513223	+	0.0936566i
$349$		−	2766.04i		−	0.424249i	−0.977243	−	0.212124i	$-0.931962\pi$
$349$		−	2766.04i		−	0.424249i	0.977243	−	0.212124i	$-0.0680382\pi$
$350$	3575.36	+	1716.72i	0.546032	+	0.262179i
$351$	2729.96	−	679.347i	0.415141	−	0.103307i
$352$	3740.81	−	3740.81i	0.566437	−	0.566437i
$353$	−6338.53	+	6338.53i	−0.955711	+	0.955711i	−0.999060	−	0.0433491i	$-0.986197\pi$
$353$	−6338.53	+	6338.53i	−0.955711	+	0.955711i	0.0433491	+	0.999060i	$0.486197\pi$
$354$	5236.46	−	3620.23i	0.786199	−	0.543539i
$355$	1872.43	+	426.233i	0.279939	+	0.0637242i
$356$		−	7339.58i		−	1.09269i
$357$	462.501	−	2534.43i	0.0685663	−	0.375732i
$358$	−975.763	−	975.763i	−0.144052	−	0.144052i
$359$	8827.47			1.29776			0.648880	−	0.760890i	$-0.275238\pi$
$359$	8827.47			1.29776			0.648880	+	0.760890i	$0.275238\pi$
$360$	1331.26	+	6548.05i	0.194900	+	0.958646i
$361$	4450.80			0.648899
$362$	2748.50	+	2748.50i	0.399055	+	0.399055i
$363$	−472.353	+	2588.42i	−0.0682978	+	0.374261i
$364$			1961.76i			0.282484i
$365$	−3746.27	+	2356.95i	−0.537229	+	0.337996i
$366$	−14.3578	+	9.92628i	−0.00205053	+	0.00141764i
$367$	6191.27	−	6191.27i	0.880605	−	0.880605i	−0.112991	−	0.993596i	$-0.536043\pi$
$367$	6191.27	−	6191.27i	0.880605	−	0.880605i	0.993596	+	0.112991i	$0.0360432\pi$
$368$	160.628	−	160.628i	0.0227535	−	0.0227535i
$369$	−3722.45	+	9859.55i	−0.525157	+	1.39097i
$370$	−751.338	+	3300.60i	−0.105568	+	0.463757i
$371$		−	4286.28i		−	0.599818i
$372$	6548.60	+	1195.04i	0.912713	+	0.166559i
$373$	3584.46	+	3584.46i	0.497577	+	0.497577i	0.910683	−	0.413106i	$-0.135556\pi$
$373$	3584.46	+	3584.46i	0.497577	+	0.497577i	−0.413106	+	0.910683i	$0.635556\pi$
$374$	−1265.90			−0.175022
$375$	−4781.95	−	5465.10i	−0.658503	−	0.752578i
$376$	3899.27			0.534812
$377$	1784.48	+	1784.48i	0.243781	+	0.243781i
$378$	−2294.40	+	3814.63i	−0.312200	+	0.519057i
$379$			7110.48i			0.963695i	0.876255	+	0.481848i	$0.160034\pi$
$379$			7110.48i			0.963695i	−0.876255	+	0.481848i	$0.839966\pi$
$380$	−630.683	+	2770.57i	−0.0851404	+	0.374019i
$381$	441.241	+	638.231i	0.0593319	+	0.0858203i
$382$	−1105.91	+	1105.91i	−0.148124	+	0.148124i
$383$	1695.77	−	1695.77i	0.226240	−	0.226240i	−0.584880	−	0.811120i	$-0.698858\pi$
$383$	1695.77	−	1695.77i	0.226240	−	0.226240i	0.811120	+	0.584880i	$0.198858\pi$
$384$	−2988.11	−	4322.14i	−0.397100	−	0.574383i
$385$	−5133.58	+	3229.77i	−0.679562	+	0.427544i
$386$		−	6231.15i		−	0.821650i
$387$	619.472	+	1370.95i	0.0813683	+	0.180076i
$388$	−4703.02	−	4703.02i	−0.615361	−	0.615361i
$389$	12362.2			1.61128			0.805640	−	0.592405i	$-0.201822\pi$
$389$	12362.2			1.61128			0.805640	+	0.592405i	$0.201822\pi$
$390$	−769.723	+	1798.84i	−0.0999395	+	0.233559i
$391$	−1402.06			−0.181343
$392$	−216.978	−	216.978i	−0.0279567	−	0.0279567i
$393$	−10117.5	−	1846.32i	−1.29863	−	0.236984i
$394$		−	7114.22i		−	0.909668i
$395$	−523.476	−	119.162i	−0.0666808	−	0.0151790i
$396$	−3756.61	−	1418.30i	−0.476709	−	0.179980i
$397$	−1340.12	+	1340.12i	−0.169417	+	0.169417i	−0.786723	−	0.617306i	$-0.788224\pi$
$397$	−1340.12	+	1340.12i	−0.169417	+	0.169417i	0.617306	+	0.786723i	$0.288224\pi$
$398$	−129.999	+	129.999i	−0.0163725	+	0.0163725i
$399$	−3962.30	+	2739.33i	−0.497150	+	0.343705i
$400$	479.171	+	230.076i	0.0598964	+	0.0287595i
$401$			2281.30i			0.284096i	0.989860	+	0.142048i	$0.0453688\pi$
$401$			2281.30i			0.284096i	−0.989860	+	0.142048i	$0.954631\pi$
$402$	731.175	−	4006.72i	0.0907156	−	0.497107i
$403$	3507.40	+	3507.40i	0.433538	+	0.433538i
$404$	−1748.75			−0.215356
$405$	6609.87	−	4768.61i	0.810981	−	0.585072i
$406$	−3993.26			−0.488133
$407$	−3660.29	−	3660.29i	−0.445783	−	0.445783i
$408$	−541.939	+	2969.74i	−0.0657597	+	0.360352i
$409$		−	4614.82i		−	0.557917i	−0.960303	−	0.278959i	$-0.910011\pi$
$409$		−	4614.82i		−	0.557917i	0.960303	−	0.278959i	$-0.0899892\pi$
$410$	−3903.28	−	6204.08i	−0.470169	−	0.747311i
$411$	−3067.32	+	2120.59i	−0.368126	+	0.254504i
$412$	−4834.54	+	4834.54i	−0.578108	+	0.578108i
$413$	9743.49	−	9743.49i	1.16089	−	1.16089i
$414$	2266.43	+	855.683i	0.269055	+	0.101581i
$415$	−1216.26	−	1933.19i	−0.143865	−	0.228667i
$416$		−	3694.10i		−	0.435380i
$417$	349.813	+	63.8364i	0.0410801	+	0.00749660i
$418$	1673.67	+	1673.67i	0.195842	+	0.195842i
$419$	2142.28			0.249779			0.124889	−	0.992171i	$-0.460142\pi$
$419$	2142.28			0.249779			0.124889	+	0.992171i	$0.460142\pi$
$420$	2113.84	+	5275.92i	0.245583	+	0.612948i
$421$	−8889.30			−1.02907			−0.514534	−	0.857470i	$-0.672035\pi$
$421$	−8889.30			−1.02907			−0.514534	+	0.857470i	$0.672035\pi$
$422$	3224.43	+	3224.43i	0.371950	+	0.371950i
$423$	−1958.46	−	4334.26i	−0.225115	−	0.498200i
$424$			5022.48i			0.575267i
$425$	−1087.13	−	3095.38i	−0.124079	−	0.353289i
$426$	−852.466	−	1233.05i	−0.0969534	−	0.140238i
$427$	−26.7156	+	26.7156i	−0.00302778	+	0.00302778i
$428$	−3087.60	+	3087.60i	−0.348703	+	0.348703i
$429$	−1701.52	−	2461.15i	−0.191492	−	0.276982i
$430$	−1020.23	−	232.241i	−0.114418	−	0.0260457i
$431$			15707.3i			1.75543i	0.479179	+	0.877717i	$0.340935\pi$
$431$			15707.3i			1.75543i	−0.479179	+	0.877717i	$0.659065\pi$
$432$	−307.497	+	511.238i	−0.0342464	+	0.0569374i
$433$	5430.81	+	5430.81i	0.602744	+	0.602744i	0.941040	−	0.338296i	$-0.109851\pi$
$433$	5430.81	+	5430.81i	0.602744	+	0.602744i	−0.338296	+	0.941040i	$0.609851\pi$
$434$	−7848.76			−0.868094
$435$	6721.94	+	2876.31i	0.740902	+	0.317031i
$436$	10744.2			1.18016
$437$	1853.69	+	1853.69i	0.202915	+	0.202915i
$438$	3398.88	+	620.253i	0.370787	+	0.0676640i
$439$		−	8221.92i		−	0.893874i	−0.894565	−	0.446937i	$-0.852515\pi$
$439$		−	8221.92i		−	0.893874i	0.894565	−	0.446937i	$-0.147485\pi$
$440$	6015.31	−	3784.51i	0.651747	−	0.410044i
$441$	−132.203	+	350.163i	−0.0142753	+	0.0378105i
$442$	−625.047	+	625.047i	−0.0672635	+	0.0672635i
$443$	1960.53	−	1960.53i	0.210265	−	0.210265i	−0.594115	−	0.804380i	$-0.702498\pi$
$443$	1960.53	−	1960.53i	0.210265	−	0.210265i	0.804380	+	0.594115i	$0.202498\pi$
$444$	−3990.14	+	2758.58i	−0.426495	+	0.294857i
$445$	3516.89	−	15449.6i	0.374644	−	1.64580i
$446$			6723.34i			0.713810i
$447$	−338.948	+	1857.38i	−0.0358651	+	0.196535i
$448$	3678.86	+	3678.86i	0.387968	+	0.387968i
$449$	−17849.2			−1.87607			−0.938036	−	0.346537i	$-0.887357\pi$
$449$	−17849.2			−1.87607			−0.938036	+	0.346537i	$0.887357\pi$
$450$	−131.779	+	5667.15i	−0.0138047	+	0.593672i
$451$	11208.8			1.17029
$452$	−1404.49	−	1404.49i	−0.146154	−	0.146154i
$453$	1943.21	−	10648.5i	0.201545	−	1.10443i
$454$		−	3323.00i		−	0.343516i
$455$	−940.015	+	4129.46i	−0.0968540	+	0.425477i
$456$	4642.85	−	3209.83i	0.476801	−	0.329636i
$457$	−6346.80	+	6346.80i	−0.649652	+	0.649652i	−0.952909	−	0.303257i	$-0.901926\pi$
$457$	−6346.80	+	6346.80i	−0.649652	+	0.649652i	0.303257	+	0.952909i	$0.401926\pi$
$458$	−4667.97	+	4667.97i	−0.476245	+	0.476245i
$459$	3573.22	−	889.192i	0.363363	−	0.0904225i
$460$	2618.08	−	1647.16i	0.265366	−	0.166954i
$461$			8848.20i			0.893930i	0.894552	+	0.446965i	$0.147495\pi$
$461$			8848.20i			0.893930i	−0.894552	+	0.446965i	$0.852505\pi$
$462$	4657.55	+	849.944i	0.469024	+	0.0855908i
$463$	1329.43	+	1329.43i	0.133443	+	0.133443i	0.770673	−	0.637230i	$-0.219920\pi$
$463$	1329.43	+	1329.43i	0.133443	+	0.133443i	−0.637230	+	0.770673i	$0.719920\pi$
$464$	−535.178			−0.0535453
$465$	13212.0	+	5653.40i	1.31762	+	0.563807i
$466$	−4704.83			−0.467697
$467$	1479.96	+	1479.96i	0.146647	+	0.146647i	0.776618	−	0.629971i	$-0.216933\pi$
$467$	1479.96	+	1479.96i	0.146647	+	0.146647i	−0.629971	+	0.776618i	$0.716933\pi$
$468$	−2555.14	+	1154.56i	−0.252375	+	0.114037i
$469$		−	8815.81i		−	0.867966i
$470$	3225.44	+	734.227i	0.316550	+	0.0720582i
$471$	−5050.29	−	7304.96i	−0.494066	−	0.714639i
$472$	−11417.0	+	11417.0i	−1.11337	+	1.11337i
$473$	1131.41	−	1131.41i	0.109983	−	0.109983i
$474$	238.324	+	344.723i	0.0230941	+	0.0334043i
$475$	−2655.14	+	5529.77i	−0.256476	+	0.534155i
$476$			2567.73i			0.247252i
$477$	5582.76	−	2522.60i	0.535885	−	0.242143i
$478$	−3534.73	−	3534.73i	−0.338231	−	0.338231i
$479$	5039.60			0.480720			0.240360	−	0.970684i	$-0.422734\pi$
$479$	5039.60			0.480720			0.240360	+	0.970684i	$0.422734\pi$
$480$	−3980.47	−	9934.81i	−0.378506	−	0.944708i
$481$	−3614.58			−0.342642
$482$	2179.89	+	2179.89i	0.205999	+	0.205999i
$483$	5158.51	+	941.362i	0.485963	+	0.0886821i
$484$		−	2622.43i		−	0.246284i
$485$	−7646.20	−	12153.3i	−0.715868	−	1.13784i
$486$	−6318.78	−	743.377i	−0.589765	−	0.0693833i
$487$	1292.93	−	1292.93i	0.120305	−	0.120305i	−0.644391	−	0.764696i	$-0.722889\pi$
$487$	1292.93	−	1292.93i	0.120305	−	0.120305i	0.764696	+	0.644391i	$0.222889\pi$
$488$	31.3042	−	31.3042i	0.00290384	−	0.00290384i
$489$	−3784.27	+	2616.26i	−0.349961	+	0.241945i
$490$	−138.625	−	220.339i	−0.0127805	−	0.0203140i
$491$		−	13865.7i		−	1.27444i	−0.770681	−	0.637221i	$-0.780084\pi$
$491$		−	13865.7i		−	1.27444i	0.770681	−	0.637221i	$-0.219916\pi$
$492$	1885.68	−	10333.2i	0.172791	−	0.946865i
$493$	2335.69	+	2335.69i	0.213375	+	0.213375i
$494$	1652.77			0.150530
$495$	−7227.96	−	4785.53i	−0.656308	−	0.434532i
$496$	−1051.89			−0.0952247
$497$	−2294.33	−	2294.33i	−0.207072	−	0.207072i
$498$	−320.070	+	1753.93i	−0.0288006	+	0.157822i
$499$			10884.3i			0.976453i	0.872717	+	0.488226i	$0.162356\pi$
$499$			10884.3i			0.976453i	−0.872717	+	0.488226i	$0.837644\pi$
$500$	5666.50	+	4502.86i	0.506827	+	0.402748i
$501$	−18192.0	+	12577.0i	−1.62227	+	1.12156i
$502$	1831.54	−	1831.54i	0.162840	−	0.162840i
$503$	−7880.86	+	7880.86i	−0.698589	+	0.698589i	−0.964106	−	0.265517i	$-0.914457\pi$
$503$	−7880.86	+	7880.86i	−0.698589	+	0.698589i	0.265517	+	0.964106i	$0.414457\pi$
$504$	3987.84	−	10562.5i	0.352445	−	0.933513i
$505$	−3681.07	−	837.946i	−0.324368	−	0.0738379i
$506$		−	2576.58i		−	0.226370i
$507$	9175.14	+	1674.35i	0.803713	+	0.146667i
$508$	−546.829	−	546.829i	−0.0477590	−	0.0477590i
$509$	1788.46			0.155741			0.0778704	−	0.996963i	$-0.475188\pi$
$509$	1788.46			0.155741			0.0778704	+	0.996963i	$0.475188\pi$
$510$	−1007.48	+	2354.49i	−0.0874747	+	0.204428i
$511$	7478.42			0.647408
$512$	1086.41	+	1086.41i	0.0937754	+	0.0937754i
$513$	−5899.84	−	3548.60i	−0.507766	−	0.305409i
$514$		−	1018.67i		−	0.0874153i
$515$	−12493.1	+	7860.01i	−1.06896	+	0.672531i
$516$	−852.686	−	1233.36i	−0.0727469	−	0.105224i
$517$	−3576.93	+	3576.93i	−0.304281	+	0.304281i
$518$	4044.31	−	4044.31i	0.343044	−	0.343044i
$519$	7685.96	+	11117.3i	0.650051	+	0.940263i
$520$	1101.47	−	4838.72i	0.0928896	−	0.408061i
$521$		−	18251.6i		−	1.53478i	−0.641183	−	0.767388i	$-0.721556\pi$
$521$		−	18251.6i		−	1.53478i	0.641183	−	0.767388i	$-0.278444\pi$
$522$	−2350.15	−	5201.11i	−0.197056	−	0.436104i
$523$	−2125.69	−	2125.69i	−0.177725	−	0.177725i	0.612639	−	0.790363i	$-0.290108\pi$
$523$	−2125.69	−	2125.69i	−0.177725	−	0.177725i	−0.790363	+	0.612639i	$0.790108\pi$
$524$	10250.5			0.854570
$525$	1921.53	+	12118.5i	0.159738	+	1.00742i
$526$	12487.1			1.03510
$527$	4590.80	+	4590.80i	0.379466	+	0.379466i
$528$	624.207	+	113.910i	0.0514491	+	0.00938880i
$529$			9313.29i			0.765455i
$530$	−945.725	+	4154.54i	−0.0775088	+	0.340494i
$531$	18425.0	+	6956.30i	1.50579	+	0.568508i
$532$	3394.85	−	3394.85i	0.276664	−	0.276664i
$533$	5534.42	−	5534.42i	0.449761	−	0.449761i
$534$	−10174.0	+	7033.79i	−0.824478	+	0.570003i
$535$	−7978.81	+	5019.84i	−0.644774	+	0.405657i
$536$			10330.0i			0.832439i
$537$	766.393	−	4199.71i	0.0615872	−	0.337488i
$538$	−2292.60	−	2292.60i	−0.183719	−	0.183719i
$539$	398.082			0.0318119
$540$	−5627.68	+	5858.26i	−0.448475	+	0.466851i
$541$	−2214.16			−0.175960			−0.0879798	−	0.996122i	$-0.528041\pi$
$541$	−2214.16			−0.175960			−0.0879798	+	0.996122i	$0.528041\pi$
$542$	−3873.77	−	3873.77i	−0.306998	−	0.306998i
$543$	−2158.75	+	11829.6i	−0.170609	+	0.934911i
$544$		−	4835.17i		−	0.381078i
$545$	22616.2	+	5148.26i	1.77756	+	0.404637i
$546$	2719.36	−	1880.03i	0.213146	−	0.147359i
$547$	12385.1	−	12385.1i	0.968098	−	0.968098i	−0.0314090	−	0.999507i	$-0.509999\pi$
$547$	12385.1	−	12385.1i	0.968098	−	0.968098i	0.999507	+	0.0314090i	$0.00999944\pi$
$548$	2628.04	−	2628.04i	0.204862	−	0.204862i
$549$	−50.5193	−	19.0735i	−0.00392735	−	0.00148276i
$550$	5688.42	−	1997.84i	0.441009	−	0.154887i
$551$		−	6176.11i		−	0.477516i
$552$	−6044.52	−	1103.05i	−0.466072	−	0.0850522i
$553$	641.427	+	641.427i	0.0493242	+	0.0493242i
$554$	11557.3			0.886324
$555$	−9720.96	+	3894.79i	−0.743481	+	0.297882i
$556$	−354.410			−0.0270329
$557$	−8716.96	−	8716.96i	−0.663105	−	0.663105i	0.293006	−	0.956111i	$-0.405344\pi$
$557$	−8716.96	−	8716.96i	−0.663105	−	0.663105i	−0.956111	+	0.293006i	$0.905344\pi$
$558$	−4619.23	−	10222.8i	−0.350444	−	0.775566i
$559$		−	1117.28i		−	0.0845363i
$560$	−478.268	−	760.186i	−0.0360902	−	0.0573638i
$561$	−2227.10	−	3221.38i	−0.167608	−	0.242436i
$562$	4729.23	−	4729.23i	0.354965	−	0.354965i
$563$	−11697.0	+	11697.0i	−0.875615	+	0.875615i	−0.993077	−	0.117462i	$-0.962524\pi$
$563$	−11697.0	+	11697.0i	−0.875615	+	0.875615i	0.117462	+	0.993077i	$0.462524\pi$
$564$	2695.76	+	3899.27i	0.201262	+	0.291115i
$565$	−2283.42	−	3629.39i	−0.170025	−	0.270247i
$566$		−	9721.40i		−	0.721945i
$567$	−13743.7	+	872.435i	−1.01796	+	0.0646188i
$568$	2688.40	+	2688.40i	0.198596	+	0.198596i
$569$	−11517.5			−0.848576			−0.424288	−	0.905527i	$-0.639476\pi$
$569$	−11517.5			−0.848576			−0.424288	+	0.905527i	$0.639476\pi$
$570$	4444.92	−	1780.90i	0.326627	−	0.130866i
$571$	−11093.9			−0.813072			−0.406536	−	0.913635i	$-0.633263\pi$
$571$	−11093.9			−0.813072			−0.406536	+	0.913635i	$0.633263\pi$
$572$	2108.68	+	2108.68i	0.154141	+	0.154141i
$573$	−4759.88	−	868.617i	−0.347027	−	0.0633281i
$574$			12384.8i			0.900577i
$575$	6300.25	−	2212.72i	0.456937	−	0.160481i
$576$	−2626.50	+	6956.73i	−0.189995	+	0.503236i
$577$	−14119.4	+	14119.4i	−1.01871	+	1.01871i	−0.0188920	+	0.999822i	$0.506014\pi$
$577$	−14119.4	+	14119.4i	−1.01871	+	1.01871i	−0.999822	+	0.0188920i	$0.993986\pi$
$578$	5016.87	−	5016.87i	0.361028	−	0.361028i
$579$	15856.6	−	10962.4i	1.13813	−	0.786846i
$580$	−7105.44	−	1617.46i	−0.508685	−	0.115795i
$581$			3859.10i			0.275564i
$582$	−2012.16	+	11026.3i	−0.143311	+	0.785320i
$583$	−4607.29	−	4607.29i	−0.327297	−	0.327297i
$584$	−8762.89			−0.620909
$585$	−5931.73	+	1205.96i	−0.419226	+	0.0852316i
$586$	−10725.4			−0.756081
$587$	−8524.33	−	8524.33i	−0.599381	−	0.599381i	0.340767	−	0.940148i	$-0.389313\pi$
$587$	−8524.33	−	8524.33i	−0.599381	−	0.599381i	−0.940148	+	0.340767i	$0.889313\pi$
$588$	66.9702	−	366.986i	0.00469695	−	0.0257385i
$589$		−	12139.2i		−	0.849211i
$590$	−11593.8	+	7294.23i	−0.809001	+	0.508981i
$591$	18103.8	−	12516.0i	1.26005	−	0.871135i
$592$	542.020	−	542.020i	0.0376298	−	0.0376298i
$593$	4580.53	−	4580.53i	0.317200	−	0.317200i	−0.530491	−	0.847691i	$-0.677992\pi$
$593$	4580.53	−	4580.53i	0.317200	−	0.317200i	0.847691	+	0.530491i	$0.177992\pi$
$594$	1634.08	+	6566.55i	0.112874	+	0.453584i
$595$	−1230.38	+	5405.01i	−0.0847740	+	0.372410i
$596$		−	1881.79i		−	0.129331i
$597$	−559.518	−	102.105i	−0.0383577	−	0.00699979i
$598$	−1272.20	−	1272.20i	−0.0869971	−	0.0869971i
$599$	10195.8			0.695477			0.347738	−	0.937592i	$-0.386950\pi$
$599$	10195.8			0.695477			0.347738	+	0.937592i	$0.386950\pi$
$600$	−2251.57	−	14200.0i	−0.153200	−	0.966187i
$601$	18915.8			1.28385			0.641923	−	0.766769i	$-0.278137\pi$
$601$	18915.8			1.28385			0.641923	+	0.766769i	$0.278137\pi$
$602$	1250.11	+	1250.11i	0.0846355	+	0.0846355i
$603$	11482.4	−	5188.36i	0.775452	−	0.350392i
$604$			10788.4i			0.726778i
$605$	1256.59	−	5520.14i	0.0844421	−	0.370952i
$606$	1675.89	+	2424.09i	0.112341	+	0.162495i
$607$	12758.2	−	12758.2i	0.853113	−	0.853113i	−0.137402	−	0.990515i	$-0.543875\pi$
$607$	12758.2	−	12758.2i	0.853113	−	0.853113i	0.990515	+	0.137402i	$0.0438753\pi$
$608$	−6392.67	+	6392.67i	−0.426409	+	0.426409i
$609$	−7025.33	−	10161.8i	−0.467456	−	0.676149i
$610$	31.7891	−	20.0000i	0.00211000	−	0.00132750i
$611$			3532.26i			0.233879i
$612$	−3344.41	+	1511.19i	−0.220898	+	0.0998140i
$613$	7340.02	+	7340.02i	0.483622	+	0.483622i	0.906286	−	0.422664i	$-0.138905\pi$
$613$	7340.02	+	7340.02i	0.483622	+	0.483622i	−0.422664	+	0.906286i	$0.638905\pi$
$614$	4349.39			0.285875
$615$	8920.67	−	20847.6i	0.584904	−	1.36692i
$616$	−12007.9			−0.785412
$617$	17118.9	+	17118.9i	1.11698	+	1.11698i	0.992182	+	0.124803i	$0.0398299\pi$
$617$	17118.9	+	17118.9i	1.11698	+	1.11698i	0.124803	+	0.992182i	$0.460170\pi$
$618$	11334.7	+	2068.43i	0.737778	+	0.134635i
$619$		−	3176.16i		−	0.206237i	−0.994669	−	0.103118i	$-0.967118\pi$
$619$		−	3176.16i		−	0.206237i	0.994669	−	0.103118i	$-0.0328820\pi$
$620$	−13965.8	−	3179.12i	−0.904644	−	0.205930i
$621$	1809.84	+	7272.84i	0.116950	+	0.469966i
$622$	4762.79	−	4762.79i	0.307026	−	0.307026i
$623$	−18930.8	+	18930.8i	−1.21741	+	1.21741i
$624$	364.450	−	251.962i	0.0233809	−	0.0161644i
$625$	9770.20	+	12193.6i	0.625293	+	0.780390i
$626$			14424.6i			0.920965i
$627$	−1314.55	+	7203.53i	−0.0837291	+	0.458822i
$628$	6258.80	+	6258.80i	0.397697	+	0.397697i
$629$	−4731.09			−0.299906
$630$	5287.60	−	7986.28i	0.334386	−	0.505049i
$631$	−11467.2			−0.723459			−0.361729	−	0.932283i	$-0.617814\pi$
$631$	−11467.2			−0.723459			−0.361729	+	0.932283i	$0.617814\pi$
$632$	−751.597	−	751.597i	−0.0473052	−	0.0473052i
$633$	−2532.57	+	13878.0i	−0.159021	+	0.871410i
$634$			7392.26i			0.463066i
$635$	−889.036	−	1413.08i	−0.0555596	−	0.0883094i
$636$	−5022.48	+	3472.29i	−0.313136	+	0.216486i
$637$	196.556	−	196.556i	0.0122258	−	0.0122258i
$638$	−4292.32	+	4292.32i	−0.266355	+	0.266355i
$639$	1638.02	−	4338.59i	0.101407	−	0.268595i
$640$	6020.60	+	9569.47i	0.371852	+	0.591042i
$641$			12383.2i			0.763035i	0.924362	+	0.381518i	$0.124598\pi$
$641$			12383.2i			0.763035i	−0.924362	+	0.381518i	$0.875402\pi$
$642$	7238.95	+	1321.02i	0.445013	+	0.0812092i
$643$	−11142.9	−	11142.9i	−0.683413	−	0.683413i	0.277354	−	0.960768i	$-0.410542\pi$
$643$	−11142.9	−	11142.9i	−0.683413	−	0.683413i	−0.960768	+	0.277354i	$0.910542\pi$
$644$	−5226.29			−0.319790
$645$	−1203.89	−	3004.78i	−0.0734933	−	0.183431i
$646$	2163.30			0.131755
$647$	2391.21	+	2391.21i	0.145299	+	0.145299i	0.776014	−	0.630716i	$-0.217239\pi$
$647$	2391.21	+	2391.21i	0.145299	+	0.145299i	−0.630716	+	0.776014i	$0.717239\pi$
$648$	16104.3	−	1022.28i	0.976292	−	0.0619738i
$649$		−	20946.4i		−	1.26690i
$650$	1822.25	−	3795.13i	0.109961	−	0.229011i
$651$	−13808.3	−	19973.0i	−0.831322	−	1.20246i
$652$	3242.32	−	3242.32i	0.194753	−	0.194753i
$653$	16623.3	−	16623.3i	0.996201	−	0.996201i	−0.00379136	−	0.999993i	$-0.501207\pi$
$653$	16623.3	−	16623.3i	0.996201	−	0.996201i	0.999993	+	0.00379136i	$0.00120683\pi$
$654$	−10296.5	−	14893.4i	−0.615636	−	0.890484i
$655$	21577.0	+	4911.71i	1.28715	+	0.293002i
$656$			1659.81i			0.0987878i
$657$	4401.27	+	9740.43i	0.261354	+	0.578403i
$658$	−3952.20	−	3952.20i	−0.234153	−	0.234153i
$659$	−20089.8			−1.18754			−0.593768	−	0.804636i	$-0.702360\pi$
$659$	−20089.8			−1.18754			−0.593768	+	0.804636i	$0.702360\pi$
$660$	7943.19	+	3398.88i	0.468467	+	0.200457i
$661$	541.434			0.0318598			0.0159299	−	0.999873i	$-0.494929\pi$
$661$	541.434			0.0318598			0.0159299	+	0.999873i	$0.494929\pi$
$662$	−11389.1	−	11389.1i	−0.668654	−	0.668654i
$663$	−2690.22	−	490.931i	−0.157586	−	0.0287574i
$664$		−	4521.93i		−	0.264284i
$665$	8772.76	−	5519.36i	0.511569	−	0.321852i
$666$	7647.80	+	2887.41i	0.444964	+	0.167995i
$667$	−4753.99	+	4753.99i	−0.275975	+	0.275975i
$668$	15586.7	−	15586.7i	0.902796	−	0.902796i
$669$	−17109.1	+	11828.3i	−0.988751	+	0.683573i
$670$	−1945.12	+	8544.86i	−0.112159	+	0.492711i
$671$			57.4328i			0.00330428i
$672$	−3246.40	+	17789.7i	−0.186358	+	1.02121i
$673$	−24314.3	−	24314.3i	−1.39264	−	1.39264i	−0.819354	−	0.573288i	$-0.805668\pi$
$673$	−24314.3	−	24314.3i	−1.39264	−	1.39264i	−0.573288	−	0.819354i	$-0.694332\pi$
$674$	−6084.03			−0.347697
$675$	−14653.2	+	9634.87i	−0.835558	+	0.549402i
$676$	−9295.71			−0.528887
$677$	14662.4	+	14662.4i	0.832380	+	0.832380i	0.987842	−	0.155462i	$-0.0496867\pi$
$677$	14662.4	+	14662.4i	0.832380	+	0.832380i	−0.155462	+	0.987842i	$0.549687\pi$
$678$	−600.902	+	3292.84i	−0.0340376	+	0.186520i
$679$			24260.8i			1.37120i
$680$	1441.70	−	6333.36i	0.0813041	−	0.357166i
$681$	8456.13	−	5846.14i	0.475829	−	0.328964i
$682$	−8436.57	+	8436.57i	−0.473685	+	0.473685i
$683$	15981.2	−	15981.2i	0.895320	−	0.895320i	−0.0996976	−	0.995018i	$-0.531788\pi$
$683$	15981.2	−	15981.2i	0.895320	−	0.895320i	0.995018	+	0.0996976i	$0.0317875\pi$
$684$	6419.67	+	2423.73i	0.358863	+	0.135488i
$685$	6791.23	−	4272.68i	0.378803	−	0.238322i
$686$		−	10443.3i		−	0.581233i
$687$	−20091.1	−	3666.36i	−1.11575	−	0.203611i
$688$	167.540	+	167.540i	0.00928400	+	0.00928400i
$689$	−4549.75			−0.251570
$690$	−4792.26	−	2050.60i	−0.264403	−	0.113138i
$691$	−16714.9			−0.920209			−0.460105	−	0.887865i	$-0.652188\pi$
$691$	−16714.9			−0.920209			−0.460105	+	0.887865i	$0.652188\pi$
$692$	−9525.19	−	9525.19i	−0.523256	−	0.523256i
$693$	6031.14	+	13347.5i	0.330598	+	0.731645i
$694$		−	19424.1i		−	1.06243i
$695$	−746.023	−	169.822i	−0.0407169	−	0.00926865i
$696$	8231.98	+	11907.1i	0.448322	+	0.648474i
$697$	7243.96	−	7243.96i	0.393665	−	0.393665i
$698$	3285.13	−	3285.13i	0.178143	−	0.178143i
$699$	−8277.19	−	11972.5i	−0.447886	−	0.647842i
$700$	−4052.37	−	11538.3i	−0.218808	−	0.623009i
$701$			6990.49i			0.376643i	0.982107	+	0.188322i	$0.0603048\pi$
$701$			6990.49i			0.376643i	−0.982107	+	0.188322i	$0.939695\pi$
$702$	4049.11	+	2435.44i	0.217698	+	0.130940i
$703$	6255.06	+	6255.06i	0.335582	+	0.335582i
$704$	7908.75			0.423398
$705$	3806.09	+	9499.58i	0.203327	+	0.507482i
$706$	−15056.1			−0.802611
$707$	4510.51	+	4510.51i	0.239936	+	0.239936i
$708$	−19310.2	−	3523.86i	−1.02503	−	0.187055i
$709$			28175.0i			1.49243i	0.665705	+	0.746215i	$0.268131\pi$
$709$			28175.0i			1.49243i	−0.665705	+	0.746215i	$0.731869\pi$
$710$	1717.60	+	2730.04i	0.0907890	+	0.144305i
$711$	−457.943	+	1212.94i	−0.0241550	+	0.0639787i
$712$	22182.3	−	22182.3i	1.16758	−	1.16758i
$713$	−9343.99	+	9343.99i	−0.490793	+	0.490793i
$714$	3559.35	−	2460.75i	0.186562	−	0.128980i
$715$	3428.31	+	5449.13i	0.179317	+	0.285015i
$716$			4254.90i			0.222085i
$717$	2776.28	−	15213.6i	0.144605	−	0.792414i
$718$	10484.1	+	10484.1i	0.544933	+	0.544933i
$719$	20143.8			1.04484			0.522418	−	0.852690i	$-0.325030\pi$
$719$	20143.8			1.04484			0.522418	+	0.852690i	$0.325030\pi$
$720$	708.646	−	1070.32i	0.0366801	−	0.0554008i
$721$	24939.2			1.28819
$722$	5286.05	+	5286.05i	0.272474	+	0.272474i
$723$	−1712.15	+	9382.32i	−0.0880715	+	0.482617i
$724$		−	11985.0i		−	0.615222i
$725$	−14181.7	−	6809.41i	−0.726477	−	0.348821i
$726$	−3635.16	+	2513.17i	−0.185831	+	0.128475i
$727$	−9805.90	+	9805.90i	−0.500249	+	0.500249i	−0.911515	−	0.411267i	$-0.865087\pi$
$727$	−9805.90	+	9805.90i	−0.500249	+	0.500249i	0.411267	+	0.911515i	$0.365087\pi$
$728$	−5929.00	+	5929.00i	−0.301845	+	0.301845i
$729$	−9224.92	−	17387.4i	−0.468674	−	0.883371i
$730$	−7248.57	−	1650.04i	−0.367509	−	0.0836585i
$731$		−	1462.39i		−	0.0739926i
$732$	52.9464	+	9.66205i	0.00267344	+	0.000487868i
$733$	16533.1	+	16533.1i	0.833100	+	0.833100i	0.987940	−	0.154840i	$-0.0494861\pi$
$733$	16533.1	+	16533.1i	0.833100	+	0.833100i	−0.154840	+	0.987940i	$0.549486\pi$
$734$	14706.3			0.739536
$735$	316.818	−	740.405i	0.0158994	−	0.0371568i
$736$	9841.37			0.492877
$737$	−9476.04	−	9476.04i	−0.473615	−	0.473615i
$738$	−16130.8	+	7288.81i	−0.804586	+	0.363557i
$739$			15250.1i			0.759114i	0.925168	+	0.379557i	$0.123924\pi$
$739$			15250.1i			0.759114i	−0.925168	+	0.379557i	$0.876076\pi$
$740$	8834.41	−	5558.14i	0.438864	−	0.276110i
$741$	2907.72	+	4205.85i	0.144153	+	0.208510i
$742$	5090.66	−	5090.66i	0.251865	−	0.251865i
$743$	5438.49	−	5438.49i	0.268531	−	0.268531i	−0.559977	−	0.828508i	$-0.689190\pi$
$743$	5438.49	−	5438.49i	0.268531	−	0.268531i	0.828508	+	0.559977i	$0.189190\pi$
$744$	16180.0	+	23403.5i	0.797294	+	1.15324i
$745$	901.693	−	3961.11i	0.0443429	−	0.194797i
$746$			8514.27i			0.417868i
$747$	−5026.38	+	2271.20i	−0.246192	+	0.111243i
$748$	2760.04	+	2760.04i	0.134916	+	0.134916i
$749$	15927.5			0.777009
$750$	811.363	−	12170.1i	0.0395024	−	0.592517i
$751$	2087.82			0.101446			0.0507228	−	0.998713i	$-0.483848\pi$
$751$	2087.82			0.101446			0.0507228	+	0.998713i	$0.483848\pi$
$752$	−529.676	−	529.676i	−0.0256852	−	0.0256852i
$753$	7883.01	+	1438.55i	0.381505	+	0.0696197i
$754$			4238.72i			0.204728i
$755$	−5169.46	+	22709.3i	−0.249187	+	1.09467i
$756$	13319.5	−	3314.54i	0.640774	−	0.159456i
$757$	−10258.6	+	10258.6i	−0.492546	+	0.492546i	−0.909107	−	0.416562i	$-0.863235\pi$
$757$	−10258.6	+	10258.6i	−0.492546	+	0.492546i	0.416562	+	0.909107i	$0.363235\pi$
$758$	−8444.86	+	8444.86i	−0.404658	+	0.404658i
$759$	6556.70	−	4532.98i	0.313561	−	0.216781i
$760$	−10279.5	+	6467.35i	−0.490629	+	0.308678i
$761$		−	26879.5i		−	1.28040i	−0.768210	−	0.640198i	$-0.778852\pi$
$761$		−	26879.5i		−	1.28040i	0.768210	−	0.640198i	$-0.221148\pi$
$762$	−233.958	+	1282.05i	−0.0111226	+	0.0609498i
$763$	−27712.1	−	27712.1i	−1.31487	−	1.31487i
$764$	4822.43			0.228363
$765$	−7763.99	+	1578.48i	−0.366938	+	0.0746012i
$766$	4028.02			0.189998
$767$	−10342.4	−	10342.4i	−0.486888	−	0.486888i
$768$	3639.64	−	19944.6i	0.171008	−	0.937097i
$769$		−	25180.9i		−	1.18082i	−0.807105	−	0.590408i	$-0.798967\pi$
$769$		−	25180.9i		−	1.18082i	0.807105	−	0.590408i	$-0.201033\pi$
$770$	−9932.85	−	2261.08i	−0.464877	−	0.105823i
$771$	2592.23	−	1792.14i	0.121085	−	0.0837124i
$772$	−13585.7	+	13585.7i	−0.633369	+	0.633369i
$773$	−18871.2	+	18871.2i	−0.878072	+	0.878072i	−0.993335	−	0.115263i	$-0.963229\pi$
$773$	−18871.2	+	18871.2i	−0.878072	+	0.878072i	0.115263	+	0.993335i	$0.463229\pi$
$774$	−892.506	+	2363.96i	−0.0414476	+	0.109781i
$775$	−27874.2	−	13383.9i	−1.29196	−	0.620341i
$776$		−	28427.7i		−	1.31507i
$777$	17406.8	+	3176.52i	0.803688	+	0.146663i
$778$	14682.1	+	14682.1i	0.676581	+	0.676581i
$779$	−19154.7			−0.880988
$780$	5600.22	−	2243.78i	0.257077	−	0.103000i
$781$	−4932.32			−0.225982
$782$	−1665.18	−	1665.18i	−0.0761465	−	0.0761465i
$783$	9100.79	−	15130.8i	0.415371	−	0.690588i
$784$			58.9485i			0.00268533i
$785$	10175.6	+	16173.6i	0.462653	+	0.735365i
$786$	−9823.43	−	14209.0i	−0.445789	−	0.644809i
$787$	14716.0	−	14716.0i	0.666542	−	0.666542i	−0.290372	−	0.956914i	$-0.593779\pi$
$787$	14716.0	−	14716.0i	0.666542	−	0.666542i	0.956914	+	0.290372i	$0.0937789\pi$
$788$	−15511.1	+	15511.1i	−0.701217	+	0.701217i
$789$	21968.5	+	31776.2i	0.991253	+	1.43379i
$790$	−480.189	−	763.238i	−0.0216258	−	0.0343731i
$791$			7245.10i			0.325672i
$792$	−7067.03	−	15640.0i	−0.317066	−	0.701697i
$793$	28.3578	+	28.3578i	0.00126988	+	0.00126988i
$794$	−3183.22			−0.142277
$795$	−12236.0	+	4902.46i	−0.545869	+	0.218708i
$796$	566.871			0.0252415
$797$	−17463.9	−	17463.9i	−0.776163	−	0.776163i	0.203013	−	0.979176i	$-0.434927\pi$
$797$	−17463.9	−	17463.9i	−0.776163	−	0.776163i	−0.979176	+	0.203013i	$0.934927\pi$
$798$	−7959.28	−	1452.47i	−0.353077	−	0.0644321i
$799$			4623.35i			0.204709i
$800$	7630.82	+	21727.2i	0.337238	+	0.960214i
$801$	−35798.1	−	13515.5i	−1.57911	−	0.596188i
$802$	−2709.42	+	2709.42i	−0.119293	+	0.119293i
$803$	8038.49	−	8038.49i	0.353265	−	0.353265i
$804$	−10330.0	+	7141.64i	−0.453122	+	0.313266i
$805$	−11001.2	−	2504.28i	−0.481667	−	0.109645i
$806$			8331.22i			0.364088i
$807$	1800.68	−	9867.40i	0.0785462	−	0.430420i
$808$	−5285.22	−	5285.22i	−0.230115	−	0.230115i
$809$	24097.9			1.04727			0.523633	−	0.851944i	$-0.324576\pi$
$809$	24097.9			1.04727			0.523633	+	0.851944i	$0.324576\pi$
$810$	13513.8	+	2186.80i	0.586207	+	0.0948596i
$811$	25302.7			1.09556			0.547780	−	0.836622i	$-0.315473\pi$
$811$	25302.7			1.09556			0.547780	+	0.836622i	$0.315473\pi$
$812$	8706.47	+	8706.47i	0.376277	+	0.376277i
$813$	3042.57	−	16672.8i	0.131252	−	0.719238i
$814$		−	8694.39i		−	0.374371i
$815$	8378.61	−	5271.38i	0.360110	−	0.226562i
$816$	477.025	−	329.791i	0.0204647	−	0.0141483i
$817$	−1933.46	+	1933.46i	−0.0827945	+	0.0827945i
$818$	5480.85	−	5480.85i	0.234271	−	0.234271i
$819$	9568.33	+	3612.50i	0.408235	+	0.154128i
$820$	−5016.42	+	22037.0i	−0.213635	+	0.938494i
$821$			27925.3i			1.18709i	0.804802	+	0.593544i	$0.202272\pi$
$821$			27925.3i			1.18709i	−0.804802	+	0.593544i	$0.797728\pi$
$822$	−6161.50	−	1124.39i	−0.261444	−	0.0477102i
$823$	997.907	+	997.907i	0.0422659	+	0.0422659i	0.727924	−	0.685658i	$-0.240485\pi$
$823$	997.907	+	997.907i	0.0422659	+	0.0422659i	−0.685658	+	0.727924i	$0.740485\pi$
$824$	−29222.6			−1.23546
$825$	15091.6	+	10960.7i	0.636874	+	0.462548i
$826$	23144.0			0.974918
$827$	18683.3	+	18683.3i	0.785590	+	0.785590i	0.980768	−	0.195178i	$-0.0625285\pi$
$827$	18683.3	+	18683.3i	0.785590	+	0.785590i	−0.195178	+	0.980768i	$0.562529\pi$
$828$	−3075.83	−	6807.11i	−0.129097	−	0.285705i
$829$			21146.9i			0.885962i	0.896531	+	0.442981i	$0.146079\pi$
$829$			21146.9i			0.885962i	−0.896531	+	0.442981i	$0.853921\pi$
$830$	851.473	−	3740.49i	0.0356085	−	0.156427i
$831$	20332.8	+	29410.2i	0.848780	+	1.22771i
$832$	3904.99	−	3904.99i	0.162718	−	0.162718i
$833$	257.270	−	257.270i	0.0107009	−	0.0107009i
$834$	339.644	+	491.276i	0.0141018	+	0.0203975i
$835$	40278.2	−	25340.9i	1.66932	−	1.05025i
$836$		−	7298.19i		−	0.301930i
$837$	17887.6	−	29739.6i	0.738695	−	1.22814i
$838$	2544.31	+	2544.31i	0.104883	+	0.104883i
$839$	−30903.4			−1.27164			−0.635820	−	0.771838i	$-0.719338\pi$
$839$	−30903.4			−1.27164			−0.635820	+	0.771838i	$0.719338\pi$
$840$	−9556.67	+	22333.9i	−0.392543	+	0.917374i
$841$	−8549.68			−0.350555
$842$	−10557.5	−	10557.5i	−0.432109	−	0.432109i
$843$	20354.7	+	3714.48i	0.831618	+	0.151760i
$844$		−	14060.4i		−	0.573435i
$845$	−19567.2	−	4454.21i	−0.796607	−	0.181337i
$846$	2821.65	−	7473.63i	0.114669	−	0.303722i
$847$	−6763.96	+	6763.96i	−0.274395	+	0.274395i
$848$	682.252	−	682.252i	0.0276281	−	0.0276281i
$849$	24738.3	−	17102.8i	1.00002	−	0.691364i
$850$	2385.12	−	4967.42i	0.0962460	−	0.200448i
$851$		−	9629.53i		−	0.387892i
$852$	−829.774	+	4547.02i	−0.0333657	+	0.182839i
$853$	181.224	+	181.224i	0.00727432	+	0.00727432i	0.710735	−	0.703460i	$-0.248363\pi$
$853$	181.224	+	181.224i	0.00727432	+	0.00727432i	−0.703460	+	0.710735i	$0.748363\pi$
$854$	−63.4584			−0.00254274
$855$	12351.8	+	8177.98i	0.494063	+	0.327112i
$856$	−18663.2			−0.745205
$857$	13852.9	+	13852.9i	0.552167	+	0.552167i	0.927066	−	0.374899i	$-0.122323\pi$
$857$	13852.9	+	13852.9i	0.552167	+	0.552167i	−0.374899	+	0.927066i	$0.622323\pi$
$858$	902.189	−	4943.85i	0.0358977	−	0.196713i
$859$		−	8910.47i		−	0.353925i	−0.984218	−	0.176962i	$-0.943373\pi$
$859$		−	8910.47i		−	0.353925i	0.984218	−	0.176962i	$-0.0566271\pi$
$860$	1718.04	+	2730.74i	0.0681216	+	0.108276i
$861$	−31515.9	+	21788.5i	−1.24746	+	0.862428i
$862$	−18655.0	+	18655.0i	−0.737112	+	0.737112i
$863$	6487.75	−	6487.75i	0.255905	−	0.255905i	−0.567481	−	0.823386i	$-0.692082\pi$
$863$	6487.75	−	6487.75i	0.255905	−	0.255905i	0.823386	+	0.567481i	$0.192082\pi$
$864$	−25081.2	+	6241.43i	−0.987594	+	0.245761i
$865$	−15486.1	−	24614.4i	−0.608720	−	0.967533i
$866$			12900.0i			0.506187i
$867$	21592.8	+	3940.40i	0.845823	+	0.154352i
$868$	17112.6	+	17112.6i	0.669170	+	0.669170i
$869$	1378.93			0.0538285
$870$	4567.32	+	11399.5i	0.177985	+	0.444229i
$871$	−9357.71			−0.364034
$872$	32471.9	+	32471.9i	1.26105	+	1.26105i
$873$	−31599.0	+	14278.2i	−1.22504	+	0.553543i
$874$			4403.12i			0.170409i
$875$	−3001.35	−	26229.5i	−0.115959	−	1.01339i
$876$	−6058.22	−	8762.89i	−0.233662	−	0.337980i
$877$	−20231.6	+	20231.6i	−0.778987	+	0.778987i	−0.979659	−	0.200672i	$-0.935688\pi$
$877$	−20231.6	+	20231.6i	−0.778987	+	0.778987i	0.200672	+	0.979659i	$0.435688\pi$
$878$	9764.88	−	9764.88i	0.375340	−	0.375340i
$879$	−18869.2	−	27293.3i	−0.724054	−	1.04730i
$880$	−1331.20	−	303.031i	−0.0509942	−	0.0116081i
$881$		−	33209.0i		−	1.26996i	−0.772527	−	0.634982i	$-0.781007\pi$
$881$		−	33209.0i		−	1.26996i	0.772527	−	0.634982i	$-0.218993\pi$
$882$	−572.889	+	258.863i	−0.0218709	+	0.00988251i
$883$	26984.3	+	26984.3i	1.02842	+	1.02842i	0.999584	+	0.0288331i	$0.00917914\pi$
$883$	26984.3	+	26984.3i	1.02842	+	1.02842i	0.0288331	+	0.999584i	$0.490821\pi$
$884$	2725.57			0.103700
$885$	−38958.8	−	16670.4i	−1.47976	−	0.633187i
$886$	4656.90			0.176582
$887$	−24008.9	−	24008.9i	−0.908838	−	0.908838i	0.0873406	−	0.996179i	$-0.472163\pi$
$887$	−24008.9	−	24008.9i	−0.908838	−	0.908838i	−0.996179	+	0.0873406i	$0.972163\pi$
$888$	−20396.5	−	3722.11i	−0.770792	−	0.140660i
$889$			2820.84i			0.106421i
$890$	22525.8	−	14172.1i	0.848390	−	0.533762i
$891$	−13835.3	+	15710.8i	−0.520200	+	0.590720i
$892$	14658.8	−	14658.8i	0.550240	−	0.550240i
$893$	6112.61	−	6112.61i	0.229060	−	0.229060i
$894$	−2608.50	+	1803.39i	−0.0975853	+	0.0674656i
$895$	−2038.81	+	8956.44i	−0.0761452	+	0.334504i
$896$		−	19102.9i		−	0.712258i
$897$	999.226	−	5475.59i	0.0371942	−	0.203818i
$898$	−21198.9	−	21198.9i	−0.787768	−	0.787768i
$899$	31132.2			1.15497
$900$	12643.4	−	12068.7i	0.468273	−	0.446990i
$901$	−5955.13			−0.220193
$902$	13312.3	+	13312.3i	0.491409	+	0.491409i
$903$	−981.871	+	5380.49i	−0.0361845	+	0.198285i
$904$		−	8489.50i		−	0.312341i
$905$	5742.86	−	25228.2i	0.210938	−	0.926645i
$906$	14954.7	−	10338.9i	0.548384	−	0.379125i
$907$	−23026.7	+	23026.7i	−0.842989	+	0.842989i	−0.989246	−	0.146258i	$-0.953277\pi$
$907$	−23026.7	+	23026.7i	−0.842989	+	0.842989i	0.146258	+	0.989246i	$0.453277\pi$
$908$	−7245.11	+	7245.11i	−0.264799	+	0.264799i
$909$	−3220.25	+	8529.38i	−0.117501	+	0.311223i
$910$	−6020.83	+	3787.99i	−0.219328	+	0.137990i
$911$			33422.1i			1.21550i	0.794127	+	0.607752i	$0.207929\pi$
$911$			33422.1i			1.21550i	−0.794127	+	0.607752i	$0.792071\pi$
$912$	−1066.71	−	194.660i	−0.0387304	−	0.00706781i
$913$	4148.12	+	4148.12i	0.150364	+	0.150364i
$914$	−15075.7			−0.545581
$915$	106.821	+	45.7086i	0.00385945	+	0.00165145i
$916$	20355.1			0.734226
$917$	−26438.8	−	26438.8i	−0.952112	−	0.952112i
$918$	5299.85	+	3187.73i	0.190546	+	0.114609i
$919$		−	42542.2i		−	1.52703i	−0.645792	−	0.763513i	$-0.723473\pi$
$919$		−	42542.2i		−	1.52703i	0.645792	−	0.763513i	$-0.276527\pi$
$920$	12890.7	+	2934.40i	0.461951	+	0.105157i
$921$	7651.86	+	11068.0i	0.273765	+	0.395986i
$922$	−10508.7	+	10508.7i	−0.375363	+	0.375363i
$923$	−2435.36	+	2435.36i	−0.0868482	+	0.0868482i
$924$	−8301.70	−	12007.9i	−0.295569	−	0.427524i
$925$	21259.5	−	7466.56i	0.755684	−	0.265404i
$926$			3157.84i			0.112066i
$927$	14677.4	+	32482.6i	0.520033	+	1.15088i
$928$	−16394.7	−	16394.7i	−0.579938	−	0.579938i
$929$	−5721.21			−0.202053			−0.101026	−	0.994884i	$-0.532213\pi$
$929$	−5721.21			−0.202053			−0.101026	+	0.994884i	$0.532213\pi$
$930$	8977.08	+	22405.8i	0.316527	+	0.790015i
$931$	−680.282			−0.0239477
$932$	10257.9	+	10257.9i	0.360524	+	0.360524i
$933$	20499.1	+	3740.83i	0.719305	+	0.131264i
$934$			3515.38i			0.123155i
$935$	4487.28	+	7132.32i	0.156952	+	0.249467i
$936$	−11211.8	−	4232.97i	−0.391525	−	0.147819i
$937$	1344.01	−	1344.01i	0.0468589	−	0.0468589i	−0.683289	−	0.730148i	$-0.739451\pi$
$937$	1344.01	−	1344.01i	0.0468589	−	0.0468589i	0.730148	+	0.683289i	$0.239451\pi$
$938$	10470.2	−	10470.2i	0.364461	−	0.364461i
$939$	−36706.8	+	25377.2i	−1.27570	+	0.881953i
$940$	−5431.56	−	8633.22i	−0.188466	−	0.299558i
$941$			9625.77i			0.333466i	0.986002	+	0.166733i	$0.0533217\pi$
$941$			9625.77i			0.333466i	−0.986002	+	0.166733i	$0.946678\pi$
$942$	2677.80	−	14673.9i	0.0926192	−	0.507538i
$943$	14744.1	+	14744.1i	0.509157	+	0.509157i
$944$	3101.77			0.106943
$945$	29625.4	−	594.731i	1.01980	−	0.0204726i
$946$	2687.46			0.0923645
$947$	2234.24	+	2234.24i	0.0766664	+	0.0766664i	0.744400	−	0.667734i	$-0.232736\pi$
$947$	2234.24	+	2234.24i	0.0766664	+	0.0766664i	−0.667734	+	0.744400i	$0.732736\pi$
$948$	231.980	−	1271.21i	0.00794765	−	0.0435518i
$949$		−	7938.11i		−	0.271530i
$950$	−9720.93	+	3414.10i	−0.331988	+	0.116598i
$951$	−18811.3	+	13005.2i	−0.641427	+	0.443451i
$952$	−7760.41	+	7760.41i	−0.264198	+	0.264198i
$953$	−6457.14	+	6457.14i	−0.219483	+	0.219483i	−0.808281	−	0.588798i	$-0.799602\pi$
$953$	−6457.14	+	6457.14i	−0.219483	+	0.219483i	0.588798	+	0.808281i	$0.299602\pi$
$954$	9626.45	+	3634.44i	0.326696	+	0.123343i
$955$	10151.1	+	2310.75i	0.343959	+	0.0782977i
$956$			15413.5i			0.521451i
$957$	−18474.3	−	3371.32i	−0.624021	−	0.113876i
$958$	5985.35	+	5985.35i	0.201856	+	0.201856i
$959$	−13556.9			−0.456491
$960$	6294.27	−	14709.7i	0.211611	−	0.494535i
$961$	31399.6			1.05399
$962$	−4292.91	−	4292.91i	−0.143876	−	0.143876i
$963$	9373.84	+	20745.2i	0.313674	+	0.694190i
$964$		−	9505.61i		−	0.317588i
$965$	−35107.4	+	22087.7i	−1.17114	+	0.736817i
$966$	5008.55	+	7244.59i	0.166819	+	0.241295i
$967$	13166.9	−	13166.9i	0.437869	−	0.437869i	−0.453425	−	0.891294i	$-0.649798\pi$
$967$	13166.9	−	13166.9i	0.437869	−	0.437869i	0.891294	+	0.453425i	$0.149798\pi$
$968$	7925.72	−	7925.72i	0.263163	−	0.263163i
$969$	3805.89	+	5505.01i	0.126174	+	0.182504i
$970$	5352.90	−	23515.1i	0.177187	−	0.778376i
$971$			21504.3i			0.710716i	0.934730	+	0.355358i	$0.115641\pi$
$971$			21504.3i			0.710716i	−0.934730	+	0.355358i	$0.884359\pi$
$972$	12156.0	+	15397.6i	0.401136	+	0.508104i
$973$	914.119	+	914.119i	0.0301185	+	0.0301185i
$974$	3071.14			0.101032
$975$	12863.5	−	2039.65i	0.422523	−	0.0669959i
$976$	−8.50472			−0.000278924
$977$	8996.19	+	8996.19i	0.294589	+	0.294589i	0.838890	−	0.544301i	$-0.183205\pi$
$977$	8996.19	+	8996.19i	0.294589	+	0.294589i	−0.544301	+	0.838890i	$0.683205\pi$
$978$	−7601.68	−	1387.21i	−0.248543	−	0.0453559i
$979$			40697.1i			1.32858i
$980$	−178.159	+	782.646i	−0.00580722	+	0.0255109i
$981$	19784.9	−	52403.7i	0.643917	−	1.70553i
$982$	16467.8	−	16467.8i	0.535142	−	0.535142i
$983$	16337.3	−	16337.3i	0.530090	−	0.530090i	−0.390509	−	0.920599i	$-0.627701\pi$
$983$	16337.3	−	16337.3i	0.530090	−	0.530090i	0.920599	+	0.390509i	$0.127701\pi$
$984$	36929.0	−	25530.8i	1.19639	−	0.827128i
$985$	−40082.8	+	25218.0i	−1.29659	+	0.815748i
$986$			5548.02i			0.179194i
$987$	3104.18	−	17010.4i	0.100108	−	0.548578i
$988$	−3603.53	−	3603.53i	−0.116036	−	0.116036i
$989$	2976.52			0.0957004
$990$	−2900.78	−	14268.0i	−0.0931242	−	0.458047i
$991$	−18296.9			−0.586500			−0.293250	−	0.956036i	$-0.594737\pi$
$991$	−18296.9			−0.586500			−0.293250	+	0.956036i	$0.594737\pi$
$992$	−32223.9	−	32223.9i	−1.03136	−	1.03136i
$993$	8945.31	−	49018.8i	0.285872	−	1.56653i
$994$		−	5449.79i		−	0.173900i
$995$	1193.25	+	271.627i	0.0380186	+	0.00865441i
$996$	4521.93	−	3126.24i	0.143858	−	0.0994564i
$997$	20406.0	−	20406.0i	0.648210	−	0.648210i	−0.304350	−	0.952560i	$-0.598439\pi$
$997$	20406.0	−	20406.0i	0.648210	−	0.648210i	0.952560	+	0.304350i	$0.0984393\pi$
$998$	−12926.9	+	12926.9i	−0.410015	+	0.410015i
$999$	6107.09	+	24541.4i	0.193413	+	0.777232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.4.e.a.8.3	yes	8
3.2	odd	2	inner	15.4.e.a.8.2	yes	8
4.3	odd	2		240.4.v.c.113.2		8
5.2	odd	4	inner	15.4.e.a.2.2	✓	8
5.3	odd	4		75.4.e.c.32.3		8
5.4	even	2		75.4.e.c.68.2		8
12.11	even	2		240.4.v.c.113.1		8
15.2	even	4	inner	15.4.e.a.2.3	yes	8
15.8	even	4		75.4.e.c.32.2		8
15.14	odd	2		75.4.e.c.68.3		8
20.7	even	4		240.4.v.c.17.1		8
60.47	odd	4		240.4.v.c.17.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.e.a.2.2	✓	8	5.2	odd	4	inner
15.4.e.a.2.3	yes	8	15.2	even	4	inner
15.4.e.a.8.2	yes	8	3.2	odd	2	inner
15.4.e.a.8.3	yes	8	1.1	even	1	trivial
75.4.e.c.32.2		8	15.8	even	4
75.4.e.c.32.3		8	5.3	odd	4
75.4.e.c.68.2		8	5.4	even	2
75.4.e.c.68.3		8	15.14	odd	2
240.4.v.c.17.1		8	20.7	even	4
240.4.v.c.17.2		8	60.47	odd	4
240.4.v.c.113.1		8	12.11	even	2
240.4.v.c.113.2		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18766 + 1.18766i) q^{2} +(-0.932827 + 5.11173i) q^{3} -5.17891i q^{4} +(2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 + 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(-25.2597 - 9.53673i) q^{9} +O(q^{10})\)	\(q+(1.18766 + 1.18766i) q^{2} +(-0.932827 + 5.11173i) q^{3} -5.17891i q^{4} +(2.48157 - 10.9015i) q^{5} +(-7.17891 + 4.96314i) q^{6} +(-13.3578 + 13.3578i) q^{7} +(15.6521 - 15.6521i) q^{8} +(-25.2597 - 9.53673i) q^{9} +(15.8945 - 10.0000i) q^{10} +28.7164i q^{11} +(26.4732 + 4.83102i) q^{12} +(14.1789 + 14.1789i) q^{13} -31.7292 q^{14} +(53.4105 + 22.8543i) q^{15} -4.25236 q^{16} +(18.5587 + 18.5587i) q^{17} +(-18.6736 - 41.3264i) q^{18} -49.0735i q^{19} +(-56.4577 - 12.8518i) q^{20} +(-55.8211 - 80.7421i) q^{21} +(-34.1055 + 34.1055i) q^{22} +(-37.7738 + 37.7738i) q^{23} +(65.4088 + 94.6102i) q^{24} +(-112.684 - 54.1055i) q^{25} +33.6796i q^{26} +(72.3121 - 120.225i) q^{27} +(69.1789 + 69.1789i) q^{28} +125.854 q^{29} +(36.2905 + 90.5770i) q^{30} +247.367 q^{31} +(-130.267 - 130.267i) q^{32} +(-146.791 - 26.7874i) q^{33} +44.0829i q^{34} +(112.471 + 178.768i) q^{35} +(-49.3898 + 130.818i) q^{36} +(-127.463 + 127.463i) q^{37} +(58.2828 - 58.2828i) q^{38} +(-85.7053 + 59.2524i) q^{39} +(-131.789 - 209.473i) q^{40} -390.328i q^{41} +(29.5978 - 162.191i) q^{42} +(-39.3993 - 39.3993i) q^{43} +148.720 q^{44} +(-166.648 + 251.701i) q^{45} -89.7251 q^{46} +(124.560 + 124.560i) q^{47} +(3.96671 - 21.7369i) q^{48} -13.8625i q^{49} +(-69.5712 - 198.089i) q^{50} +(-112.179 + 77.5549i) q^{51} +(73.4313 - 73.4313i) q^{52} +(-160.441 + 160.441i) q^{53} +(228.669 - 56.9040i) q^{54} +(313.051 + 71.2618i) q^{55} +418.156i q^{56} +(250.850 + 45.7770i) q^{57} +(149.473 + 149.473i) q^{58} -729.423 q^{59} +(118.360 - 276.608i) q^{60} +2.00000 q^{61} +(293.789 + 293.789i) q^{62} +(464.804 - 210.024i) q^{63} -275.409i q^{64} +(189.757 - 119.385i) q^{65} +(-142.524 - 206.153i) q^{66} +(-329.987 + 329.987i) q^{67} +(96.1136 - 96.1136i) q^{68} +(-157.853 - 228.326i) q^{69} +(-78.7382 + 345.895i) q^{70} +171.760i q^{71} +(-544.637 + 246.097i) q^{72} +(-279.927 - 279.927i) q^{73} -302.767 q^{74} +(381.687 - 525.538i) q^{75} -254.147 q^{76} +(-383.589 - 383.589i) q^{77} +(-172.161 - 31.4172i) q^{78} -48.0189i q^{79} +(-10.5525 + 46.3569i) q^{80} +(547.102 + 481.789i) q^{81} +(463.578 - 463.578i) q^{82} +(144.451 - 144.451i) q^{83} +(-418.156 + 289.092i) q^{84} +(248.371 - 156.262i) q^{85} -93.5862i q^{86} +(-117.400 + 643.334i) q^{87} +(449.473 + 449.473i) q^{88} +1417.21 q^{89} +(-496.858 + 101.015i) q^{90} -378.799 q^{91} +(195.627 + 195.627i) q^{92} +(-230.751 + 1264.48i) q^{93} +295.872i q^{94} +(-534.972 - 121.779i) q^{95} +(787.409 - 544.375i) q^{96} +(908.111 - 908.111i) q^{97} +(16.4640 - 16.4640i) q^{98} +(273.861 - 725.367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7}+O(q^{10}) \) 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7	\( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7} - 100 q^{10} + 132 q^{12} + 68 q^{13} + 90 q^{15} + 284 q^{16} - 240 q^{18} - 492 q^{21} - 500 q^{22} - 220 q^{25} + 702 q^{27} + 508 q^{28} + 660 q^{30} + 616 q^{31} - 240 q^{33} - 804 q^{36} - 1156 q^{37} - 600 q^{40} + 540 q^{42} + 548 q^{43} + 180 q^{45} + 736 q^{46} - 1116 q^{48} - 852 q^{51} + 224 q^{52} + 460 q^{55} + 684 q^{57} + 60 q^{58} + 540 q^{60} + 16 q^{61} + 1428 q^{63} + 2040 q^{66} + 404 q^{67} - 2220 q^{70} - 1800 q^{72} - 2512 q^{73} - 2910 q^{75} - 1488 q^{76} - 360 q^{78} + 288 q^{81} + 2800 q^{82} + 4940 q^{85} - 1680 q^{87} + 2460 q^{88} + 600 q^{90} - 1304 q^{91} + 3408 q^{93} + 4164 q^{96} + 1904 q^{97}+O(q^{100}) \) 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7 - 100 * q^10 + 132 * q^12 + 68 * q^13 + 90 * q^15 + 284 * q^16 - 240 * q^18 - 492 * q^21 - 500 * q^22 - 220 * q^25 + 702 * q^27 + 508 * q^28 + 660 * q^30 + 616 * q^31 - 240 * q^33 - 804 * q^36 - 1156 * q^37 - 600 * q^40 + 540 * q^42 + 548 * q^43 + 180 * q^45 + 736 * q^46 - 1116 * q^48 - 852 * q^51 + 224 * q^52 + 460 * q^55 + 684 * q^57 + 60 * q^58 + 540 * q^60 + 16 * q^61 + 1428 * q^63 + 2040 * q^66 + 404 * q^67 - 2220 * q^70 - 1800 * q^72 - 2512 * q^73 - 2910 * q^75 - 1488 * q^76 - 360 * q^78 + 288 * q^81 + 2800 * q^82 + 4940 * q^85 - 1680 * q^87 + 2460 * q^88 + 600 * q^90 - 1304 * q^91 + 3408 * q^93 + 4164 * q^96 + 1904 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more