LMFDB - Embedded newform 350.4.j.d.249.2

Newspace parameters

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	350.j (of order $6$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$20.6506685020$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			249.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.249
Dual form			350.4.j.d.149.2

$q$-expansion

$f(q)$	$=$	$q+(1.73205 - 1.00000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.00000 - 3.46410i) q^{4} +2.00000 q^{6} +(-15.5885 + 10.0000i) q^{7} -8.00000i q^{8} +(-13.0000 - 22.5167i) q^{9} +O(q^{10})$	\(q+(1.73205 - 1.00000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.00000 - 3.46410i) q^{4} +2.00000 q^{6} +(-15.5885 + 10.0000i) q^{7} -8.00000i q^{8} +(-13.0000 - 22.5167i) q^{9} +(-17.5000 + 30.3109i) q^{11} +(3.46410 - 2.00000i) q^{12} +66.0000i q^{13} +(-17.0000 + 32.9090i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(51.0955 + 29.5000i) q^{17} +(-45.0333 - 26.0000i) q^{18} +(68.5000 + 118.645i) q^{19} +(-18.5000 + 0.866025i) q^{21} +70.0000i q^{22} +(-6.06218 + 3.50000i) q^{23} +(4.00000 - 6.92820i) q^{24} +(66.0000 + 114.315i) q^{26} -53.0000i q^{27} +(3.46410 + 74.0000i) q^{28} -106.000 q^{29} +(-37.5000 + 64.9519i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-30.3109 + 17.5000i) q^{33} +118.000 q^{34} -104.000 q^{36} +(-9.52628 + 5.50000i) q^{37} +(237.291 + 137.000i) q^{38} +(-33.0000 + 57.1577i) q^{39} -498.000 q^{41} +(-31.1769 + 20.0000i) q^{42} +260.000i q^{43} +(70.0000 + 121.244i) q^{44} +(-7.00000 + 12.1244i) q^{46} +(148.090 - 85.5000i) q^{47} -16.0000i q^{48} +(143.000 - 311.769i) q^{49} +(29.5000 + 51.0955i) q^{51} +(228.631 + 132.000i) q^{52} +(361.133 + 208.500i) q^{53} +(-53.0000 - 91.7987i) q^{54} +(80.0000 + 124.708i) q^{56} +137.000i q^{57} +(-183.597 + 106.000i) q^{58} +(-8.50000 + 14.7224i) q^{59} +(-25.5000 - 44.1673i) q^{61} +150.000i q^{62} +(427.817 + 221.000i) q^{63} -64.0000 q^{64} +(-35.0000 + 60.6218i) q^{66} +(380.185 + 219.500i) q^{67} +(204.382 - 118.000i) q^{68} -7.00000 q^{69} -784.000 q^{71} +(-180.133 + 104.000i) q^{72} +(-255.477 - 147.500i) q^{73} +(-11.0000 + 19.0526i) q^{74} +548.000 q^{76} +(-30.3109 - 647.500i) q^{77} +132.000i q^{78} +(-247.500 - 428.683i) q^{79} +(-324.500 + 562.050i) q^{81} +(-862.561 + 498.000i) q^{82} +932.000i q^{83} +(-34.0000 + 65.8179i) q^{84} +(260.000 + 450.333i) q^{86} +(-91.7987 - 53.0000i) q^{87} +(242.487 + 140.000i) q^{88} +(-436.500 - 756.040i) q^{89} +(-660.000 - 1028.84i) q^{91} +28.0000i q^{92} +(-64.9519 + 37.5000i) q^{93} +(171.000 - 296.181i) q^{94} +(-16.0000 - 27.7128i) q^{96} +290.000i q^{97} +(-64.0859 - 683.000i) q^{98} +910.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9}+O(q^{10}) $ 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9	$ 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9} - 70 q^{11} - 68 q^{14} - 32 q^{16} + 274 q^{19} - 74 q^{21} + 16 q^{24} + 264 q^{26} - 424 q^{29} - 150 q^{31} + 472 q^{34} - 416 q^{36} - 132 q^{39} - 1992 q^{41} + 280 q^{44} - 28 q^{46} + 572 q^{49} + 118 q^{51} - 212 q^{54} + 320 q^{56} - 34 q^{59} - 102 q^{61} - 256 q^{64} - 140 q^{66} - 28 q^{69} - 3136 q^{71} - 44 q^{74} + 2192 q^{76} - 990 q^{79} - 1298 q^{81} - 136 q^{84} + 1040 q^{86} - 1746 q^{89} - 2640 q^{91} + 684 q^{94} - 64 q^{96} + 3640 q^{99}+O(q^{100}) $ 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9 - 70 * q^11 - 68 * q^14 - 32 * q^16 + 274 * q^19 - 74 * q^21 + 16 * q^24 + 264 * q^26 - 424 * q^29 - 150 * q^31 + 472 * q^34 - 416 * q^36 - 132 * q^39 - 1992 * q^41 + 280 * q^44 - 28 * q^46 + 572 * q^49 + 118 * q^51 - 212 * q^54 + 320 * q^56 - 34 * q^59 - 102 * q^61 - 256 * q^64 - 140 * q^66 - 28 * q^69 - 3136 * q^71 - 44 * q^74 + 2192 * q^76 - 990 * q^79 - 1298 * q^81 - 136 * q^84 + 1040 * q^86 - 1746 * q^89 - 2640 * q^91 + 684 * q^94 - 64 * q^96 + 3640 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	0.866025	+	0.500000i	0.166667	+	0.0962250i	0.581013	−	0.813894i	$-0.302656\pi$
$3$	0.866025	+	0.500000i	0.166667	+	0.0962250i	−0.414346	+	0.910119i	$0.635990\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	2.00000			0.136083
$7$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$7$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$8$		−	8.00000i		−	0.353553i
$9$	−13.0000	−	22.5167i	−0.481481	−	0.833950i
$10$		0			0
$11$	−17.5000	+	30.3109i	−0.479677	+	0.830825i	−0.999728	−	0.0233099i	$-0.992580\pi$
$11$	−17.5000	+	30.3109i	−0.479677	+	0.830825i	0.520051	+	0.854135i	$0.325913\pi$
$12$	3.46410	−	2.00000i	0.0833333	−	0.0481125i
$13$			66.0000i			1.40809i	0.710158	+	0.704043i	$0.248624\pi$
$13$			66.0000i			1.40809i	−0.710158	+	0.704043i	$0.751376\pi$
$14$	−17.0000	+	32.9090i	−0.324532	+	0.628235i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	51.0955	+	29.5000i	0.728969	+	0.420871i	0.818045	−	0.575154i	$-0.195058\pi$
$17$	51.0955	+	29.5000i	0.728969	+	0.420871i	−0.0890757	+	0.996025i	$0.528391\pi$
$18$	−45.0333	−	26.0000i	−0.589692	−	0.340459i
$19$	68.5000	+	118.645i	0.827104	+	1.43259i	0.900301	+	0.435269i	$0.143347\pi$
$19$	68.5000	+	118.645i	0.827104	+	1.43259i	−0.0731965	+	0.997318i	$0.523320\pi$
$20$		0			0
$21$	−18.5000	+	0.866025i	−0.192240	+	0.00899915i
$22$			70.0000i			0.678366i
$23$	−6.06218	+	3.50000i	−0.0549588	+	0.0317305i	−0.527228	−	0.849724i	$-0.676768\pi$
$23$	−6.06218	+	3.50000i	−0.0549588	+	0.0317305i	0.472269	+	0.881455i	$0.343435\pi$
$24$	4.00000	−	6.92820i	0.0340207	−	0.0589256i
$25$		0			0
$26$	66.0000	+	114.315i	0.497833	+	0.862273i
$27$		−	53.0000i		−	0.377772i
$28$	3.46410	+	74.0000i	0.0233805	+	0.499453i
$29$	−106.000			−0.678748			−0.339374	−	0.940651i	$-0.610215\pi$
$29$	−106.000			−0.678748			−0.339374	+	0.940651i	$0.610215\pi$
$30$		0			0
$31$	−37.5000	+	64.9519i	−0.217264	+	0.376313i	−0.953971	−	0.299900i	$-0.903047\pi$
$31$	−37.5000	+	64.9519i	−0.217264	+	0.376313i	0.736706	+	0.676213i	$0.236380\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−30.3109	+	17.5000i	−0.159892	+	0.0923139i
$34$	118.000			0.595201
$35$		0			0
$36$	−104.000			−0.481481
$37$	−9.52628	+	5.50000i	−0.0423273	+	0.0244377i	−0.521014	−	0.853548i	$-0.674446\pi$
$37$	−9.52628	+	5.50000i	−0.0423273	+	0.0244377i	0.478687	+	0.877986i	$0.341113\pi$
$38$	237.291	+	137.000i	1.01299	+	0.584851i
$39$	−33.0000	+	57.1577i	−0.135493	+	0.234681i
$40$		0			0
$41$	−498.000			−1.89694			−0.948470	−	0.316867i	$-0.897369\pi$
$41$	−498.000			−1.89694			−0.948470	+	0.316867i	$0.897369\pi$
$42$	−31.1769	+	20.0000i	−0.114541	+	0.0734778i
$43$			260.000i			0.922084i	0.887378	+	0.461042i	$0.152524\pi$
$43$			260.000i			0.922084i	−0.887378	+	0.461042i	$0.847476\pi$
$44$	70.0000	+	121.244i	0.239839	+	0.415413i
$45$		0			0
$46$	−7.00000	+	12.1244i	−0.0224368	+	0.0388617i
$47$	148.090	−	85.5000i	0.459600	−	0.265350i	−0.252276	−	0.967655i	$-0.581179\pi$
$47$	148.090	−	85.5000i	0.459600	−	0.265350i	0.711876	+	0.702305i	$0.247846\pi$
$48$		−	16.0000i		−	0.0481125i
$49$	143.000	−	311.769i	0.416910	−	0.908948i
$50$		0			0
$51$	29.5000	+	51.0955i	0.0809966	+	0.140290i
$52$	228.631	+	132.000i	0.609719	+	0.352021i
$53$	361.133	+	208.500i	0.935951	+	0.540371i	0.888689	−	0.458511i	$-0.151617\pi$
$53$	361.133	+	208.500i	0.935951	+	0.540371i	0.0472619	+	0.998883i	$0.484950\pi$
$54$	−53.0000	−	91.7987i	−0.133563	−	0.231337i
$55$		0			0
$56$	80.0000	+	124.708i	0.190901	+	0.297585i
$57$			137.000i			0.318353i
$58$	−183.597	+	106.000i	−0.415647	+	0.239974i
$59$	−8.50000	+	14.7224i	−0.0187560	+	0.0324864i	−0.875251	−	0.483669i	$-0.839304\pi$
$59$	−8.50000	+	14.7224i	−0.0187560	+	0.0324864i	0.856495	+	0.516155i	$0.172637\pi$
$60$		0			0
$61$	−25.5000	−	44.1673i	−0.0535236	−	0.0927056i	0.838022	−	0.545636i	$-0.183712\pi$
$61$	−25.5000	−	44.1673i	−0.0535236	−	0.0927056i	−0.891546	+	0.452930i	$0.850379\pi$
$62$			150.000i			0.307258i
$63$	427.817	+	221.000i	0.855553	+	0.441958i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−35.0000	+	60.6218i	−0.0652758	+	0.113061i
$67$	380.185	+	219.500i	0.693239	+	0.400242i	0.804824	−	0.593513i	$-0.202260\pi$
$67$	380.185	+	219.500i	0.693239	+	0.400242i	−0.111585	+	0.993755i	$0.535593\pi$
$68$	204.382	−	118.000i	0.364485	−	0.210435i
$69$	−7.00000			−0.0122131
$70$		0			0
$71$	−784.000			−1.31047			−0.655237	−	0.755423i	$-0.727431\pi$
$71$	−784.000			−1.31047			−0.655237	+	0.755423i	$0.727431\pi$
$72$	−180.133	+	104.000i	−0.294846	+	0.170229i
$73$	−255.477	−	147.500i	−0.409608	−	0.236487i	0.281013	−	0.959704i	$-0.409329\pi$
$73$	−255.477	−	147.500i	−0.409608	−	0.236487i	−0.690621	+	0.723217i	$0.742663\pi$
$74$	−11.0000	+	19.0526i	−0.0172801	+	0.0299299i
$75$		0			0
$76$	548.000			0.827104
$77$	−30.3109	−	647.500i	−0.0448603	−	0.958305i
$78$			132.000i			0.191616i
$79$	−247.500	−	428.683i	−0.352480	−	0.610513i	0.634203	−	0.773166i	$-0.281328\pi$
$79$	−247.500	−	428.683i	−0.352480	−	0.610513i	−0.986683	+	0.162653i	$0.947995\pi$
$80$		0			0
$81$	−324.500	+	562.050i	−0.445130	+	0.770988i
$82$	−862.561	+	498.000i	−1.16163	+	0.670670i
$83$			932.000i			1.23253i	0.787537	+	0.616267i	$0.211356\pi$
$83$			932.000i			1.23253i	−0.787537	+	0.616267i	$0.788644\pi$
$84$	−34.0000	+	65.8179i	−0.0441631	+	0.0854920i
$85$		0			0
$86$	260.000	+	450.333i	0.326006	+	0.564659i
$87$	−91.7987	−	53.0000i	−0.113125	−	0.0653126i
$88$	242.487	+	140.000i	0.293741	+	0.169591i
$89$	−436.500	−	756.040i	−0.519875	−	0.900451i	−0.999733	−	0.0231042i	$-0.992645\pi$
$89$	−436.500	−	756.040i	−0.519875	−	0.900451i	0.479858	−	0.877346i	$-0.340688\pi$
$90$		0			0
$91$	−660.000	−	1028.84i	−0.760294	−	1.18518i
$92$			28.0000i			0.0317305i
$93$	−64.9519	+	37.5000i	−0.0724215	+	0.0418126i
$94$	171.000	−	296.181i	0.187631	−	0.324986i
$95$		0			0
$96$	−16.0000	−	27.7128i	−0.0170103	−	0.0294628i
$97$			290.000i			0.303557i	0.988415	+	0.151779i	$0.0485001\pi$
$97$			290.000i			0.303557i	−0.988415	+	0.151779i	$0.951500\pi$
$98$	−64.0859	−	683.000i	−0.0660577	−	0.704014i
$99$	910.000			0.923823
$100$		0			0
$101$	542.500	−	939.638i	0.534463	−	0.925717i	−0.464726	−	0.885454i	$-0.653847\pi$
$101$	542.500	−	939.638i	0.534463	−	0.925717i	0.999189	−	0.0402627i	$-0.0128195\pi$
$102$	102.191	+	59.0000i	0.0992002	+	0.0572732i
$103$	1344.94	−	776.500i	1.28661	−	0.742823i	0.308560	−	0.951205i	$-0.400153\pi$
$103$	1344.94	−	776.500i	1.28661	−	0.742823i	0.978048	+	0.208381i	$0.0668195\pi$
$104$	528.000			0.497833
$105$		0			0
$106$	834.000			0.764200
$107$	−111.717	+	64.5000i	−0.100936	+	0.0582752i	−0.549618	−	0.835416i	$-0.685227\pi$
$107$	−111.717	+	64.5000i	−0.100936	+	0.0582752i	0.448682	+	0.893691i	$0.351893\pi$
$108$	−183.597	−	106.000i	−0.163580	−	0.0944431i
$109$	−482.500	+	835.715i	−0.423992	+	0.734376i	−0.996326	−	0.0856452i	$-0.972705\pi$
$109$	−482.500	+	835.715i	−0.423992	+	0.734376i	0.572334	+	0.820021i	$0.306038\pi$
$110$		0			0
$111$	−11.0000			−0.00940607
$112$	263.272	+	136.000i	0.222115	+	0.114739i
$113$		−	50.0000i		−	0.0416248i	−0.999783	−	0.0208124i	$-0.993375\pi$
$113$		−	50.0000i		−	0.0416248i	0.999783	−	0.0208124i	$-0.00662527\pi$
$114$	137.000	+	237.291i	0.112555	+	0.194950i
$115$		0			0
$116$	−212.000	+	367.195i	−0.169687	+	0.293907i
$117$	1486.10	−	858.000i	1.17427	−	0.677967i
$118$			34.0000i			0.0265250i
$119$	−1091.50	+	51.0955i	−0.840821	+	0.0393606i
$120$		0			0
$121$	53.0000	+	91.7987i	0.0398197	+	0.0689697i
$122$	−88.3346	−	51.0000i	−0.0655528	−	0.0378469i
$123$	−431.281	−	249.000i	−0.316157	−	0.182533i
$124$	150.000	+	259.808i	0.108632	+	0.188157i
$125$		0			0
$126$	962.000	−	45.0333i	0.680173	−	0.0318404i
$127$		−	936.000i		−	0.653989i	−0.945026	−	0.326994i	$-0.893964\pi$
$127$		−	936.000i		−	0.653989i	0.945026	−	0.326994i	$-0.106036\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−130.000	+	225.167i	−0.0887276	+	0.153681i
$130$		0			0
$131$	377.500	+	653.849i	0.251773	+	0.436084i	0.964014	−	0.265851i	$-0.0856529\pi$
$131$	377.500	+	653.849i	0.251773	+	0.436084i	−0.712241	+	0.701935i	$0.752320\pi$
$132$			140.000i			0.0923139i
$133$	−2254.26	−	1164.50i	−1.46970	−	0.759210i
$134$	878.000			0.566027
$135$		0			0
$136$	236.000	−	408.764i	0.148800	−	0.257730i
$137$	−2041.22	−	1178.50i	−1.27294	−	0.734935i	−0.297403	−	0.954752i	$-0.596121\pi$
$137$	−2041.22	−	1178.50i	−1.27294	−	0.734935i	−0.975541	+	0.219817i	$0.929454\pi$
$138$	−12.1244	+	7.00000i	−0.00747894	+	0.00431797i
$139$	−28.0000			−0.0170858			−0.00854291	−	0.999964i	$-0.502719\pi$
$139$	−28.0000			−0.0170858			−0.00854291	+	0.999964i	$0.502719\pi$
$140$		0			0
$141$	171.000			0.102133
$142$	−1357.93	+	784.000i	−0.802498	+	0.463323i
$143$	−2000.52	−	1155.00i	−1.16987	−	0.675426i
$144$	−208.000	+	360.267i	−0.120370	+	0.208488i
$145$		0			0
$146$	−590.000			−0.334443
$147$	279.726	−	198.500i	0.156948	−	0.111374i
$148$			44.0000i			0.0244377i
$149$	1147.50	+	1987.53i	0.630919	+	1.09278i	0.987364	+	0.158467i	$0.0506551\pi$
$149$	1147.50	+	1987.53i	0.630919	+	1.09278i	−0.356446	+	0.934316i	$0.616012\pi$
$150$		0			0
$151$	554.500	−	960.422i	0.298838	−	0.517603i	−0.677032	−	0.735953i	$-0.736734\pi$
$151$	554.500	−	960.422i	0.298838	−	0.517603i	0.975870	+	0.218350i	$0.0700676\pi$
$152$	949.164	−	548.000i	0.506496	−	0.292425i
$153$		−	1534.00i		−	0.810566i
$154$	−700.000	−	1091.19i	−0.366283	−	0.570979i
$155$		0			0
$156$	132.000	+	228.631i	0.0677465	+	0.117340i
$157$	1350.13	+	779.500i	0.686321	+	0.396248i	0.802232	−	0.597012i	$-0.203646\pi$
$157$	1350.13	+	779.500i	0.686321	+	0.396248i	−0.115911	+	0.993260i	$0.536979\pi$
$158$	−857.365	−	495.000i	−0.431698	−	0.249241i
$159$	208.500	+	361.133i	0.103995	+	0.180124i
$160$		0			0
$161$	59.5000	−	115.181i	0.0291258	−	0.0563824i
$162$			1298.00i			0.629509i
$163$	−1949.42	+	1125.50i	−0.936752	+	0.540834i	−0.888941	−	0.458022i	$-0.848558\pi$
$163$	−1949.42	+	1125.50i	−0.936752	+	0.540834i	−0.0478115	+	0.998856i	$0.515225\pi$
$164$	−996.000	+	1725.12i	−0.474235	+	0.821399i
$165$		0			0
$166$	932.000	+	1614.27i	0.435766	+	0.754770i
$167$		−	2788.00i		−	1.29187i	−0.763393	−	0.645934i	$-0.776468\pi$
$167$		−	2788.00i		−	1.29187i	0.763393	−	0.645934i	$-0.223532\pi$
$168$	6.92820	+	148.000i	0.00318168	+	0.0679670i
$169$	−2159.00			−0.982704
$170$		0			0
$171$	1781.00	−	3084.78i	0.796471	−	1.37953i
$172$	900.666	+	520.000i	0.399274	+	0.230521i
$173$	1367.45	−	789.500i	0.600957	−	0.346963i	−0.168461	−	0.985708i	$-0.553880\pi$
$173$	1367.45	−	789.500i	0.600957	−	0.346963i	0.769418	+	0.638746i	$0.220546\pi$
$174$	−212.000			−0.0923660
$175$		0			0
$176$	560.000			0.239839
$177$	−14.7224	+	8.50000i	−0.00625201	+	0.00360960i
$178$	−1512.08	−	873.000i	−0.636715	−	0.367607i
$179$	1225.50	−	2122.63i	0.511722	−	0.886328i	−0.488186	−	0.872740i	$-0.662341\pi$
$179$	1225.50	−	2122.63i	0.511722	−	0.886328i	0.999908	−	0.0135883i	$-0.00432541\pi$
$180$		0			0
$181$	−1170.00			−0.480472			−0.240236	−	0.970715i	$-0.577225\pi$
$181$	−1170.00			−0.480472			−0.240236	+	0.970715i	$0.577225\pi$
$182$	−2171.99	−	1122.00i	−0.884608	−	0.456968i
$183$		−	51.0000i		−	0.0206012i
$184$	28.0000	+	48.4974i	0.0112184	+	0.0194309i
$185$		0			0
$186$	−75.0000	+	129.904i	−0.0295660	+	0.0512097i
$187$	−1788.34	+	1032.50i	−0.699340	+	0.403764i
$188$		−	684.000i		−	0.265350i
$189$	530.000	+	826.188i	0.203978	+	0.317970i
$190$		0			0
$191$	637.500	+	1104.18i	0.241507	+	0.418303i	0.961144	−	0.276048i	$-0.0890249\pi$
$191$	637.500	+	1104.18i	0.241507	+	0.418303i	−0.719637	+	0.694351i	$0.755692\pi$
$192$	−55.4256	−	32.0000i	−0.0208333	−	0.0120281i
$193$	−30.3109	−	17.5000i	−0.0113048	−	0.00652683i	0.494337	−	0.869270i	$-0.335411\pi$
$193$	−30.3109	−	17.5000i	−0.0113048	−	0.00652683i	−0.505642	+	0.862744i	$0.668744\pi$
$194$	290.000	+	502.295i	0.107324	+	0.185890i
$195$		0			0
$196$	−794.000	−	1118.90i	−0.289359	−	0.407764i
$197$			2734.00i			0.988779i	0.869241	+	0.494389i	$0.164608\pi$
$197$			2734.00i			0.988779i	−0.869241	+	0.494389i	$0.835392\pi$
$198$	1576.17	−	910.000i	0.565724	−	0.326621i
$199$	1121.50	−	1942.49i	0.399503	−	0.691959i	−0.594162	−	0.804345i	$-0.702516\pi$
$199$	1121.50	−	1942.49i	0.399503	−	0.691959i	0.993665	+	0.112387i	$0.0358495\pi$
$200$		0			0
$201$	219.500	+	380.185i	0.0770265	+	0.133414i
$202$		−	2170.00i		−	0.755845i
$203$	1652.38	−	1060.00i	0.571301	−	0.366490i
$204$	236.000			0.0809966
$205$		0			0
$206$	1553.00	−	2689.87i	0.525256	−	0.909769i
$207$	157.617	+	91.0000i	0.0529232	+	0.0305553i
$208$	914.523	−	528.000i	0.304859	−	0.176011i
$209$	−4795.00			−1.58697
$210$		0			0
$211$	1172.00			0.382388			0.191194	−	0.981552i	$-0.438764\pi$
$211$	1172.00			0.382388			0.191194	+	0.981552i	$0.438764\pi$
$212$	1444.53	−	834.000i	0.467975	−	0.270186i
$213$	−678.964	−	392.000i	−0.218412	−	0.126100i
$214$	−129.000	+	223.435i	−0.0412068	+	0.0713723i
$215$		0			0
$216$	−424.000			−0.133563
$217$	−64.9519	−	1387.50i	−0.0203190	−	0.434054i
$218$			1930.00i			0.599615i
$219$	−147.500	−	255.477i	−0.0455120	−	0.0788291i
$220$		0			0
$221$	−1947.00	+	3372.30i	−0.592622	+	1.02645i
$222$	−19.0526	+	11.0000i	−0.00576002	+	0.00332555i
$223$			2024.00i			0.607790i	0.952706	+	0.303895i	$0.0982871\pi$
$223$			2024.00i			0.607790i	−0.952706	+	0.303895i	$0.901713\pi$
$224$	592.000	−	27.7128i	0.176583	−	0.00826625i
$225$		0			0
$226$	−50.0000	−	86.6025i	−0.0147166	−	0.0254899i
$227$	2226.55	+	1285.50i	0.651019	+	0.375866i	0.788847	−	0.614590i	$-0.210679\pi$
$227$	2226.55	+	1285.50i	0.651019	+	0.375866i	−0.137827	+	0.990456i	$0.544012\pi$
$228$	474.582	+	274.000i	0.137851	+	0.0795881i
$229$	447.500	+	775.093i	0.129134	+	0.223666i	0.923341	−	0.383980i	$-0.125447\pi$
$229$	447.500	+	775.093i	0.129134	+	0.223666i	−0.794207	+	0.607647i	$0.792114\pi$
$230$		0			0
$231$	297.500	−	575.907i	0.0847362	−	0.164034i
$232$			848.000i			0.239974i
$233$	1547.59	−	893.500i	0.435132	−	0.251224i	−0.266398	−	0.963863i	$-0.585834\pi$
$233$	1547.59	−	893.500i	0.435132	−	0.251224i	0.701531	+	0.712639i	$0.252500\pi$
$234$	1716.00	−	2972.20i	0.479395	−	0.830336i
$235$		0			0
$236$	34.0000	+	58.8897i	0.00937801	+	0.0162432i
$237$		−	495.000i		−	0.135670i
$238$	−1839.44	+	1180.00i	−0.500979	+	0.321378i
$239$	5100.00			1.38030			0.690150	−	0.723667i	$-0.257545\pi$
$239$	5100.00			1.38030			0.690150	+	0.723667i	$0.257545\pi$
$240$		0			0
$241$	2088.50	−	3617.39i	0.558225	−	0.966873i	−0.439420	−	0.898282i	$-0.644816\pi$
$241$	2088.50	−	3617.39i	0.558225	−	0.966873i	0.997645	−	0.0685917i	$-0.0218506\pi$
$242$	183.597	+	106.000i	0.0487690	+	0.0281568i
$243$	−1801.33	+	1040.00i	−0.475537	+	0.274552i
$244$	−204.000			−0.0535236
$245$		0			0
$246$	−996.000			−0.258141
$247$	−7830.60	+	4521.00i	−2.01720	+	1.16463i
$248$	519.615	+	300.000i	0.133047	+	0.0768146i
$249$	−466.000	+	807.136i	−0.118601	+	0.205422i
$250$		0			0
$251$	−4680.00			−1.17689			−0.588444	−	0.808538i	$-0.700259\pi$
$251$	−4680.00			−1.17689			−0.588444	+	0.808538i	$0.700259\pi$
$252$	1621.20	−	1040.00i	0.405262	−	0.259976i
$253$		−	245.000i		−	0.0608815i
$254$	−936.000	−	1621.20i	−0.231220	−	0.400485i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	1514.68	−	874.500i	0.367638	−	0.212256i	−0.304788	−	0.952420i	$-0.598586\pi$
$257$	1514.68	−	874.500i	0.367638	−	0.212256i	0.672426	+	0.740164i	$0.265252\pi$
$258$			520.000i			0.125480i
$259$	93.5000	−	180.999i	0.0224317	−	0.0434237i
$260$		0			0
$261$	1378.00	+	2386.77i	0.326805	+	0.566043i
$262$	1307.70	+	755.000i	0.308358	+	0.178031i
$263$	3873.73	+	2236.50i	0.908230	+	0.524367i	0.879861	−	0.475231i	$-0.157635\pi$
$263$	3873.73	+	2236.50i	0.908230	+	0.524367i	0.0283689	+	0.999598i	$0.490969\pi$
$264$	140.000	+	242.487i	0.0326379	+	0.0565305i
$265$		0			0
$266$	−5069.00	+	237.291i	−1.16842	+	0.0546964i
$267$		−	873.000i		−	0.200100i
$268$	1520.74	−	878.000i	0.346619	−	0.200121i
$269$	987.500	−	1710.40i	0.223825	−	0.387676i	−0.732141	−	0.681153i	$-0.761479\pi$
$269$	987.500	−	1710.40i	0.223825	−	0.387676i	0.955966	+	0.293476i	$0.0948122\pi$
$270$		0			0
$271$	4219.50	+	7308.39i	0.945817	+	1.63820i	0.754107	+	0.656751i	$0.228070\pi$
$271$	4219.50	+	7308.39i	0.945817	+	1.63820i	0.191710	+	0.981452i	$0.438597\pi$
$272$		−	944.000i		−	0.210435i
$273$	−57.1577	−	1221.00i	−0.0126716	−	0.270690i
$274$	−4714.00			−1.03935
$275$		0			0
$276$	−14.0000	+	24.2487i	−0.00305326	+	0.00528841i
$277$	456.395	+	263.500i	0.0989969	+	0.0571559i	0.548681	−	0.836032i	$-0.315130\pi$
$277$	456.395	+	263.500i	0.0989969	+	0.0571559i	−0.449684	+	0.893188i	$0.648463\pi$
$278$	−48.4974	+	28.0000i	−0.0104629	+	0.00604075i
$279$	1950.00			0.418435
$280$		0			0
$281$	−202.000			−0.0428837			−0.0214418	−	0.999770i	$-0.506826\pi$
$281$	−202.000			−0.0428837			−0.0214418	+	0.999770i	$0.506826\pi$
$282$	296.181	−	171.000i	0.0625436	−	0.0361096i
$283$	6884.04	+	3974.50i	1.44598	+	0.834839i	0.998239	−	0.0593220i	$-0.0188939\pi$
$283$	6884.04	+	3974.50i	1.44598	+	0.834839i	0.447745	+	0.894161i	$0.352227\pi$
$284$	−1568.00	+	2715.86i	−0.327619	+	0.567452i
$285$		0			0
$286$	−4620.00			−0.955197
$287$	7763.05	−	4980.00i	1.59665	−	1.02425i
$288$			832.000i			0.170229i
$289$	−716.000	−	1240.15i	−0.145736	−	0.252422i
$290$		0			0
$291$	−145.000	+	251.147i	−0.0292098	+	0.0505929i
$292$	−1021.91	+	590.000i	−0.204804	+	0.118244i
$293$			318.000i			0.0634053i	0.999497	+	0.0317027i	$0.0100930\pi$
$293$			318.000i			0.0634053i	−0.999497	+	0.0317027i	$0.989907\pi$
$294$	286.000	−	623.538i	0.0567342	−	0.123692i
$295$		0			0
$296$	44.0000	+	76.2102i	0.00864003	+	0.0149650i
$297$	1606.48	+	927.500i	0.313863	+	0.181209i
$298$	3975.06	+	2295.00i	0.772714	+	0.446127i
$299$	−231.000	−	400.104i	−0.0446792	−	0.0773866i
$300$		0			0
$301$	−2600.00	−	4053.00i	−0.497879	−	0.776116i
$302$		−	2218.00i		−	0.422621i
$303$	939.638	−	542.500i	0.178154	−	0.102857i
$304$	1096.00	−	1898.33i	0.206776	−	0.358147i
$305$		0			0
$306$	−1534.00	−	2656.97i	−0.286578	−	0.496368i
$307$			8132.00i			1.51178i	0.654696	+	0.755892i	$0.272797\pi$
$307$			8132.00i			1.51178i	−0.654696	+	0.755892i	$0.727203\pi$
$308$	−2303.63	−	1190.00i	−0.426173	−	0.220151i
$309$	1553.00			0.285913
$310$		0			0
$311$	464.500	−	804.538i	0.0846925	−	0.146692i	−0.820568	−	0.571549i	$-0.806343\pi$
$311$	464.500	−	804.538i	0.0846925	−	0.146692i	0.905260	+	0.424858i	$0.139676\pi$
$312$	457.261	+	264.000i	0.0829722	+	0.0479040i
$313$	−180.999	+	104.500i	−0.0326859	+	0.0188712i	−0.516254	−	0.856436i	$-0.672674\pi$
$313$	−180.999	+	104.500i	−0.0326859	+	0.0188712i	0.483568	+	0.875307i	$0.339341\pi$
$314$	3118.00			0.560379
$315$		0			0
$316$	−1980.00			−0.352480
$317$	−6175.63	+	3565.50i	−1.09419	+	0.631730i	−0.934689	−	0.355468i	$-0.884322\pi$
$317$	−6175.63	+	3565.50i	−1.09419	+	0.631730i	−0.159500	+	0.987198i	$0.550988\pi$
$318$	722.265	+	417.000i	0.127367	+	0.0735352i
$319$	1855.00	−	3212.95i	0.325580	−	0.563921i
$320$		0			0
$321$	−129.000			−0.0224301
$322$	−12.1244	−	259.000i	−0.00209834	−	0.0448246i
$323$			8083.00i			1.39242i
$324$	1298.00	+	2248.20i	0.222565	+	0.385494i
$325$		0			0
$326$	−2251.00	+	3898.85i	−0.382427	+	0.662384i
$327$	−835.715	+	482.500i	−0.141331	+	0.0815973i
$328$			3984.00i			0.670670i
$329$	−1453.50	+	2813.72i	−0.243569	+	0.471505i
$330$		0			0
$331$	3285.50	+	5690.65i	0.545581	+	0.944975i	0.998570	+	0.0534583i	$0.0170244\pi$
$331$	3285.50	+	5690.65i	0.545581	+	0.944975i	−0.452989	+	0.891516i	$0.649642\pi$
$332$	3228.54	+	1864.00i	0.533703	+	0.308133i
$333$	247.683	+	143.000i	0.0407596	+	0.0235326i
$334$	−2788.00	−	4828.96i	−0.456744	−	0.791104i
$335$		0			0
$336$	160.000	+	249.415i	0.0259783	+	0.0404962i
$337$			11466.0i			1.85339i	0.375813	+	0.926696i	$0.377364\pi$
$337$			11466.0i			1.85339i	−0.375813	+	0.926696i	$0.622636\pi$
$338$	−3739.50	+	2159.00i	−0.601781	+	0.347438i
$339$	25.0000	−	43.3013i	0.00400535	−	0.00693747i
$340$		0			0
$341$	−1312.50	−	2273.32i	−0.208434	−	0.361018i
$342$		−	7124.00i		−	1.12638i
$343$	888.542	+	6290.00i	0.139874	+	0.990169i
$344$	2080.00			0.326006
$345$		0			0
$346$	1579.00	−	2734.91i	0.245340	−	0.424941i
$347$	−8467.13	−	4888.50i	−1.30991	−	0.756278i	−0.327831	−	0.944737i	$-0.606318\pi$
$347$	−8467.13	−	4888.50i	−1.30991	−	0.756278i	−0.982081	+	0.188459i	$0.939651\pi$
$348$	−367.195	+	212.000i	−0.0565624	+	0.0326563i
$349$	−11914.0			−1.82734			−0.913670	−	0.406456i	$-0.866764\pi$
$349$	−11914.0			−1.82734			−0.913670	+	0.406456i	$0.866764\pi$
$350$		0			0
$351$	3498.00			0.531936
$352$	969.948	−	560.000i	0.146871	−	0.0847957i
$353$	−7900.75	−	4561.50i	−1.19126	−	0.687774i	−0.232667	−	0.972556i	$-0.574745\pi$
$353$	−7900.75	−	4561.50i	−1.19126	−	0.687774i	−0.958592	+	0.284783i	$0.908079\pi$
$354$	−17.0000	+	29.4449i	−0.00255237	+	0.00442084i
$355$		0			0
$356$	−3492.00			−0.519875
$357$	−970.814	−	501.500i	−0.143924	−	0.0743479i
$358$		−	4902.00i		−	0.723684i
$359$	4074.50	+	7057.24i	0.599008	+	1.03751i	0.992968	+	0.118385i	$0.0377716\pi$
$359$	4074.50	+	7057.24i	0.599008	+	1.03751i	−0.393960	+	0.919128i	$0.628895\pi$
$360$		0			0
$361$	−5955.00	+	10314.4i	−0.868202	+	1.50377i
$362$	−2026.50	+	1170.00i	−0.294228	+	0.169872i
$363$			106.000i			0.0153266i
$364$	−4884.00	+	228.631i	−0.703272	+	0.0329217i
$365$		0			0
$366$	−51.0000	−	88.3346i	−0.00728364	−	0.0126156i
$367$	8375.33	+	4835.50i	1.19125	+	0.687769i	0.958590	−	0.284790i	$-0.0919237\pi$
$367$	8375.33	+	4835.50i	1.19125	+	0.687769i	0.232660	+	0.972558i	$0.425257\pi$
$368$	96.9948	+	56.0000i	0.0137397	+	0.00793261i
$369$	6474.00	+	11213.3i	0.913341	+	1.58195i
$370$		0			0
$371$	−7714.50	+	361.133i	−1.07956	+	0.0505366i
$372$			300.000i			0.0418126i
$373$	−3558.50	+	2054.50i	−0.493973	+	0.285196i	−0.726221	−	0.687461i	$-0.758725\pi$
$373$	−3558.50	+	2054.50i	−0.493973	+	0.285196i	0.232248	+	0.972657i	$0.425392\pi$
$374$	−2065.00	+	3576.68i	−0.285504	+	0.494508i
$375$		0			0
$376$	−684.000	−	1184.72i	−0.0938154	−	0.162493i
$377$		−	6996.00i		−	0.955736i
$378$	1744.18	+	901.000i	0.237330	+	0.122599i
$379$	3488.00			0.472735			0.236367	−	0.971664i	$-0.424043\pi$
$379$	3488.00			0.472735			0.236367	+	0.971664i	$0.424043\pi$
$380$		0			0
$381$	468.000	−	810.600i	0.0629301	−	0.108998i
$382$	2208.36	+	1275.00i	0.295785	+	0.170771i
$383$	7549.14	−	4358.50i	1.00716	−	0.581485i	0.0968028	−	0.995304i	$-0.469138\pi$
$383$	7549.14	−	4358.50i	1.00716	−	0.581485i	0.910360	+	0.413818i	$0.135805\pi$
$384$	−128.000			−0.0170103
$385$		0			0
$386$	−70.0000			−0.00923033
$387$	5854.33	−	3380.00i	0.768973	−	0.443967i
$388$	1004.59	+	580.000i	0.131444	+	0.0758893i
$389$	81.5000	−	141.162i	0.0106227	−	0.0183990i	−0.860665	−	0.509171i	$-0.829952\pi$
$389$	81.5000	−	141.162i	0.0106227	−	0.0183990i	0.871288	+	0.490772i	$0.163285\pi$
$390$		0			0
$391$	−413.000			−0.0534177
$392$	−2494.15	−	1144.00i	−0.321362	−	0.147400i
$393$			755.000i			0.0969077i
$394$	2734.00	+	4735.43i	0.349586	+	0.605501i
$395$		0			0
$396$	1820.00	−	3152.33i	0.230956	−	0.400027i
$397$	−865.159	+	499.500i	−0.109373	+	0.0631466i	−0.553689	−	0.832724i	$-0.686780\pi$
$397$	−865.159	+	499.500i	−0.109373	+	0.0631466i	0.444316	+	0.895870i	$0.353447\pi$
$398$		−	4486.00i		−	0.564982i
$399$	−1370.00	−	2135.62i	−0.171894	−	0.267957i
$400$		0			0
$401$	7378.50	+	12779.9i	0.918865	+	1.59152i	0.801143	+	0.598474i	$0.204226\pi$
$401$	7378.50	+	12779.9i	0.918865	+	1.59152i	0.117722	+	0.993047i	$0.462441\pi$
$402$	760.370	+	439.000i	0.0943379	+	0.0544660i
$403$	−4286.83	−	2475.00i	−0.529881	−	0.305927i
$404$	−2170.00	−	3758.55i	−0.267232	−	0.462859i
$405$		0			0
$406$	1802.00	−	3488.35i	0.220275	−	0.426414i
$407$		−	385.000i		−	0.0468888i
$408$	408.764	−	236.000i	0.0496001	−	0.0286366i
$409$	−66.5000	+	115.181i	−0.00803964	+	0.0139251i	−0.870017	−	0.493021i	$-0.835892\pi$
$409$	−66.5000	+	115.181i	−0.00803964	+	0.0139251i	0.861978	+	0.506946i	$0.169226\pi$
$410$		0			0
$411$	−1178.50	−	2041.22i	−0.141438	−	0.244978i
$412$		−	6212.00i		−	0.742823i
$413$	−14.7224	−	314.500i	−0.00175410	−	0.0374710i
$414$	364.000			0.0432117
$415$		0			0
$416$	1056.00	−	1829.05i	0.124458	−	0.215568i
$417$	−24.2487	−	14.0000i	−0.00284764	−	0.00164408i
$418$	−8305.18	+	4795.00i	−0.971818	+	0.561079i
$419$	6420.00			0.748538			0.374269	−	0.927320i	$-0.377894\pi$
$419$	6420.00			0.748538			0.374269	+	0.927320i	$0.377894\pi$
$420$		0			0
$421$	10266.0			1.18844			0.594221	−	0.804302i	$-0.297460\pi$
$421$	10266.0			1.18844			0.594221	+	0.804302i	$0.297460\pi$
$422$	2029.96	−	1172.00i	0.234164	−	0.135194i
$423$	−3850.35	−	2223.00i	−0.442578	−	0.255522i
$424$	1668.00	−	2889.06i	0.191050	−	0.330908i
$425$		0			0
$426$	−1568.00			−0.178333
$427$	839.179	+	433.500i	0.0951070	+	0.0491301i
$428$			516.000i			0.0582752i
$429$	−1155.00	−	2000.52i	−0.129986	−	0.225142i
$430$		0			0
$431$	7606.50	−	13174.8i	0.850098	−	1.47241i	−0.0310213	−	0.999519i	$-0.509876\pi$
$431$	7606.50	−	13174.8i	0.850098	−	1.47241i	0.881119	−	0.472894i	$-0.156791\pi$
$432$	−734.390	+	424.000i	−0.0817901	+	0.0472215i
$433$		−	1378.00i		−	0.152939i	−0.997072	−	0.0764693i	$-0.975635\pi$
$433$		−	1378.00i		−	0.152939i	0.997072	−	0.0764693i	$-0.0243647\pi$
$434$	−1500.00	−	2338.27i	−0.165904	−	0.258619i
$435$		0			0
$436$	1930.00	+	3342.86i	0.211996	+	0.367188i
$437$	−830.518	−	479.500i	−0.0909132	−	0.0524888i
$438$	−510.955	−	295.000i	−0.0557406	−	0.0321818i
$439$	−1381.50	−	2392.83i	−0.150195	−	0.260145i	0.781104	−	0.624401i	$-0.214657\pi$
$439$	−1381.50	−	2392.83i	−0.150195	−	0.260145i	−0.931299	+	0.364256i	$0.881323\pi$
$440$		0			0
$441$	−8879.00	+	833.116i	−0.958752	+	0.0899597i
$442$			7788.00i			0.838094i
$443$	5065.38	−	2924.50i	0.543259	−	0.313651i	−0.203140	−	0.979150i	$-0.565115\pi$
$443$	5065.38	−	2924.50i	0.543259	−	0.313651i	0.746399	+	0.665499i	$0.231781\pi$
$444$	−22.0000	+	38.1051i	−0.00235152	+	0.00407295i
$445$		0			0
$446$	2024.00	+	3505.67i	0.214886	+	0.372194i
$447$			2295.00i			0.242841i
$448$	997.661	−	640.000i	0.105212	−	0.0674937i
$449$	−4582.00			−0.481599			−0.240799	−	0.970575i	$-0.577410\pi$
$449$	−4582.00			−0.481599			−0.240799	+	0.970575i	$0.577410\pi$
$450$		0			0
$451$	8715.00	−	15094.8i	0.909919	−	1.57603i
$452$	−173.205	−	100.000i	−0.0180241	−	0.0104062i
$453$	960.422	−	554.500i	0.0996127	−	0.0575114i
$454$	5142.00			0.531555
$455$		0			0
$456$	1096.00			0.112555
$457$	−10003.5	+	5775.50i	−1.02394	+	0.591174i	−0.915244	−	0.402901i	$-0.868002\pi$
$457$	−10003.5	+	5775.50i	−1.02394	+	0.591174i	−0.108700	+	0.994075i	$0.534669\pi$
$458$	1550.19	+	895.000i	0.158156	+	0.0913114i
$459$	1563.50	−	2708.06i	0.158993	−	0.275384i
$460$		0			0
$461$	−9494.00			−0.959175			−0.479587	−	0.877494i	$-0.659214\pi$
$461$	−9494.00			−0.959175			−0.479587	+	0.877494i	$0.659214\pi$
$462$	−60.6218	−	1295.00i	−0.00610472	−	0.130409i
$463$		−	10160.0i		−	1.01982i	−0.860229	−	0.509908i	$-0.829679\pi$
$463$		−	10160.0i		−	1.01982i	0.860229	−	0.509908i	$-0.170321\pi$
$464$	848.000	+	1468.78i	0.0848436	+	0.146953i
$465$		0			0
$466$	1787.00	−	3095.17i	0.177642	−	0.307685i
$467$	1131.90	−	653.500i	0.112158	−	0.0647545i	−0.442872	−	0.896585i	$-0.646040\pi$
$467$	1131.90	−	653.500i	0.112158	−	0.0647545i	0.555030	+	0.831831i	$0.312707\pi$
$468$		−	6864.00i		−	0.677967i
$469$	−8121.50	+	380.185i	−0.799608	+	0.0374314i
$470$		0			0
$471$	779.500	+	1350.13i	0.0762579	+	0.132083i
$472$	117.779	+	68.0000i	0.0114857	+	0.00663126i
$473$	−7880.83	−	4550.00i	−0.766091	−	0.442303i
$474$	−495.000	−	857.365i	−0.0479665	−	0.0830803i
$475$		0			0
$476$	−2006.00	+	3883.26i	−0.193161	+	0.373926i
$477$		−	10842.0i		−	1.04072i
$478$	8833.46	−	5100.00i	0.845257	−	0.488010i
$479$	9143.50	−	15837.0i	0.872186	−	1.51067i	0.0124559	−	0.999922i	$-0.496035\pi$
$479$	9143.50	−	15837.0i	0.872186	−	1.51067i	0.859730	−	0.510748i	$-0.170632\pi$
$480$		0			0
$481$	−363.000	−	628.734i	−0.0344103	−	0.0596005i
$482$		−	8354.00i		−	0.789449i
$483$	109.119	−	70.0000i	0.0102797	−	0.00659443i
$484$	424.000			0.0398197
$485$		0			0
$486$	−2080.00	+	3602.67i	−0.194137	+	0.336256i
$487$	−12949.7	−	7476.50i	−1.20494	−	0.695673i	−0.243291	−	0.969953i	$-0.578227\pi$
$487$	−12949.7	−	7476.50i	−1.20494	−	0.695673i	−0.961650	+	0.274281i	$0.911560\pi$
$488$	−353.338	+	204.000i	−0.0327764	+	0.0189235i
$489$	−2251.00			−0.208167
$490$		0			0
$491$	14352.0			1.31914			0.659569	−	0.751644i	$-0.270739\pi$
$491$	14352.0			1.31914			0.659569	+	0.751644i	$0.270739\pi$
$492$	−1725.12	+	996.000i	−0.158078	+	0.0912666i
$493$	−5416.12	−	3127.00i	−0.494787	−	0.285665i
$494$	−9042.00	+	15661.2i	−0.823520	+	1.42638i
$495$		0			0
$496$	1200.00			0.108632
$497$	12221.4	−	7840.00i	1.10302	−	0.707590i
$498$			1864.00i			0.167727i
$499$	−2765.50	−	4789.99i	−0.248098	−	0.429718i	0.714900	−	0.699226i	$-0.246472\pi$
$499$	−2765.50	−	4789.99i	−0.248098	−	0.429718i	−0.962998	+	0.269509i	$0.913139\pi$
$500$		0			0
$501$	1394.00	−	2414.48i	0.124310	−	0.215311i
$502$	−8106.00	+	4680.00i	−0.720694	+	0.416093i
$503$			8400.00i			0.744607i	0.928111	+	0.372304i	$0.121432\pi$
$503$			8400.00i			0.744607i	−0.928111	+	0.372304i	$0.878568\pi$
$504$	1768.00	−	3422.53i	0.156256	−	0.302484i
$505$		0			0
$506$	−245.000	−	424.352i	−0.0215249	−	0.0372821i
$507$	−1869.75	−	1079.50i	−0.163784	−	0.0945607i
$508$	−3242.40	−	1872.00i	−0.283185	−	0.163497i
$509$	−1192.50	−	2065.47i	−0.103844	−	0.179863i	0.809421	−	0.587228i	$-0.199781\pi$
$509$	−1192.50	−	2065.47i	−0.103844	−	0.179863i	−0.913265	+	0.407365i	$0.866448\pi$
$510$		0			0
$511$	5457.50	−	255.477i	0.472457	−	0.0221167i
$512$			512.000i			0.0441942i
$513$	6288.21	−	3630.50i	0.541192	−	0.312457i
$514$	1749.00	−	3029.36i	0.150088	−	0.259960i
$515$		0			0
$516$	520.000	+	900.666i	0.0443638	+	0.0768404i
$517$			5985.00i			0.509130i
$518$	−19.0526	−	407.000i	−0.00161606	−	0.0345223i
$519$	1579.00			0.133546
$520$		0			0
$521$	4576.50	−	7926.73i	0.384837	−	0.666557i	−0.606910	−	0.794771i	$-0.707591\pi$
$521$	4576.50	−	7926.73i	0.384837	−	0.666557i	0.991747	+	0.128214i	$0.0409243\pi$
$522$	4773.53	+	2756.00i	0.400253	+	0.231086i
$523$	−11957.2	+	6903.50i	−0.999718	+	0.577187i	−0.908165	−	0.418613i	$-0.862516\pi$
$523$	−11957.2	+	6903.50i	−0.999718	+	0.577187i	−0.0915530	+	0.995800i	$0.529183\pi$
$524$	3020.00			0.251773
$525$		0			0
$526$	8946.00			0.741567
$527$	−3832.16	+	2212.50i	−0.316758	+	0.182880i
$528$	484.974	+	280.000i	0.0399731	+	0.0230785i
$529$	−6059.00	+	10494.5i	−0.497986	+	0.862538i
$530$		0			0
$531$	442.000			0.0361227
$532$	−8542.47	+	5480.00i	−0.696172	+	0.446594i
$533$		−	32868.0i		−	2.67105i
$534$	−873.000	−	1512.08i	−0.0707461	−	0.122536i
$535$		0			0
$536$	1756.00	−	3041.48i	0.141507	−	0.245097i
$537$	2122.63	−	1225.50i	0.170574	−	0.0984809i
$538$		−	3950.00i		−	0.316536i
$539$	6947.50	+	9790.42i	0.555195	+	0.782381i
$540$		0			0
$541$	−4087.50	−	7079.76i	−0.324834	−	0.562629i	0.656645	−	0.754200i	$-0.271975\pi$
$541$	−4087.50	−	7079.76i	−0.324834	−	0.562629i	−0.981479	+	0.191571i	$0.938642\pi$
$542$	14616.8	+	8439.00i	1.15838	+	0.668794i
$543$	−1013.25	−	585.000i	−0.0800787	−	0.0462334i
$544$	−944.000	−	1635.06i	−0.0744001	−	0.128865i
$545$		0			0
$546$	−1320.00	−	2057.68i	−0.103463	−	0.161283i
$547$		−	4656.00i		−	0.363942i	−0.983304	−	0.181971i	$-0.941752\pi$
$547$		−	4656.00i		−	0.363942i	0.983304	−	0.181971i	$-0.0582477\pi$
$548$	−8164.89	+	4714.00i	−0.636472	+	0.367467i
$549$	−663.000	+	1148.35i	−0.0515413	+	0.0892721i
$550$		0			0
$551$	−7261.00	−	12576.4i	−0.561396	−	0.972366i
$552$			56.0000i			0.00431797i
$553$	8144.97	+	4207.50i	0.626328	+	0.323546i
$554$	1054.00			0.0808306
$555$		0			0
$556$	−56.0000	+	96.9948i	−0.00427146	+	0.00739838i
$557$	6064.78	+	3501.50i	0.461352	+	0.266361i	0.712612	−	0.701558i	$-0.247512\pi$
$557$	6064.78	+	3501.50i	0.461352	+	0.266361i	−0.251261	+	0.967919i	$0.580845\pi$
$558$	3377.50	−	1950.00i	0.256238	−	0.147939i
$559$	−17160.0			−1.29837
$560$		0			0
$561$	−2065.00			−0.155409
$562$	−349.874	+	202.000i	−0.0262608	+	0.0151617i
$563$	17106.6	+	9876.50i	1.28056	+	0.739334i	0.976951	−	0.213462i	$-0.0684740\pi$
$563$	17106.6	+	9876.50i	1.28056	+	0.739334i	0.303612	+	0.952796i	$0.401807\pi$
$564$	342.000	−	592.361i	0.0255333	−	0.0442250i
$565$		0			0
$566$	15898.0			1.18064
$567$	−562.050	−	12006.5i	−0.0416295	−	0.889287i
$568$			6272.00i			0.463323i
$569$	−3448.50	−	5972.98i	−0.254075	−	0.440071i	0.710569	−	0.703628i	$-0.248438\pi$
$569$	−3448.50	−	5972.98i	−0.254075	−	0.440071i	−0.964644	+	0.263557i	$0.915104\pi$
$570$		0			0
$571$	−12457.5	+	21577.0i	−0.913013	+	1.58138i	−0.103227	+	0.994658i	$0.532917\pi$
$571$	−12457.5	+	21577.0i	−0.913013	+	1.58138i	−0.809785	+	0.586726i	$0.800416\pi$
$572$	−8002.07	+	4620.00i	−0.584936	+	0.337713i
$573$			1275.00i			0.0929562i
$574$	8466.00	−	16388.7i	0.615617	−	1.19172i
$575$		0			0
$576$	832.000	+	1441.07i	0.0601852	+	0.104244i
$577$	109.985	+	63.5000i	0.00793543	+	0.00458152i	0.503962	−	0.863726i	$-0.331875\pi$
$577$	109.985	+	63.5000i	0.00793543	+	0.00458152i	−0.496027	+	0.868307i	$0.665208\pi$
$578$	−2480.30	−	1432.00i	−0.178489	−	0.103051i
$579$	−17.5000	−	30.3109i	−0.00125609	−	0.00217561i
$580$		0			0
$581$	−9320.00	−	14528.4i	−0.665506	−	1.03742i
$582$			580.000i			0.0413089i
$583$	−12639.6	+	7297.50i	−0.897908	+	0.518407i
$584$	−1180.00	+	2043.82i	−0.0836109	+	0.144818i
$585$		0			0
$586$	318.000	+	550.792i	0.0224172	+	0.0388277i
$587$		−	9044.00i		−	0.635921i	−0.948104	−	0.317961i	$-0.897002\pi$
$587$		−	9044.00i		−	0.635921i	0.948104	−	0.317961i	$-0.102998\pi$
$588$	−128.172	−	1366.00i	−0.00898931	−	0.0958042i
$589$	−10275.0			−0.718801
$590$		0			0
$591$	−1367.00	+	2367.71i	−0.0951453	+	0.164796i
$592$	152.420	+	88.0000i	0.0105818	+	0.00610942i
$593$	−9267.34	+	5350.50i	−0.641760	+	0.370521i	−0.785292	−	0.619125i	$-0.787487\pi$
$593$	−9267.34	+	5350.50i	−0.641760	+	0.370521i	0.143532	+	0.989646i	$0.454154\pi$
$594$	3710.00			0.256268
$595$		0			0
$596$	9180.00			0.630919
$597$	1942.49	−	1121.50i	0.133168	−	0.0768843i
$598$	−800.207	−	462.000i	−0.0547206	−	0.0315930i
$599$	10399.5	−	18012.5i	0.709369	−	1.22866i	−0.255722	−	0.966750i	$-0.582313\pi$
$599$	10399.5	−	18012.5i	0.709369	−	1.22866i	0.965091	−	0.261913i	$-0.0843533\pi$
$600$		0			0
$601$	−1402.00			−0.0951560			−0.0475780	−	0.998868i	$-0.515150\pi$
$601$	−1402.00			−0.0951560			−0.0475780	+	0.998868i	$0.515150\pi$
$602$	−8556.33	−	4420.00i	−0.579286	−	0.299245i
$603$		−	11414.0i		−	0.770836i
$604$	−2218.00	−	3841.69i	−0.149419	−	0.258801i
$605$		0			0
$606$	1085.00	−	1879.28i	0.0727312	−	0.125974i
$607$	−5650.82	+	3262.50i	−0.377858	+	0.218156i	−0.676886	−	0.736088i	$-0.736671\pi$
$607$	−5650.82	+	3262.50i	−0.377858	+	0.218156i	0.299028	+	0.954244i	$0.403338\pi$
$608$		−	4384.00i		−	0.292425i
$609$	1961.00	−	91.7987i	0.130482	−	0.00610816i
$610$		0			0
$611$	5643.00	+	9773.96i	0.373636	+	0.647156i
$612$	−5313.93	−	3068.00i	−0.350985	−	0.202641i
$613$	−13034.5	−	7525.50i	−0.858826	−	0.495844i	0.00479285	−	0.999989i	$-0.498474\pi$
$613$	−13034.5	−	7525.50i	−0.858826	−	0.495844i	−0.863619	+	0.504145i	$0.831808\pi$
$614$	8132.00	+	14085.0i	0.534496	+	0.925775i
$615$		0			0
$616$	−5180.00	+	242.487i	−0.338812	+	0.0158605i
$617$		−	11150.0i		−	0.727524i	−0.931492	−	0.363762i	$-0.881492\pi$
$617$		−	11150.0i		−	0.727524i	0.931492	−	0.363762i	$-0.118508\pi$
$618$	2689.87	−	1553.00i	0.175085	−	0.101085i
$619$	1707.50	−	2957.48i	0.110873	−	0.192037i	−0.805250	−	0.592936i	$-0.797969\pi$
$619$	1707.50	−	2957.48i	0.110873	−	0.192037i	0.916122	+	0.400899i	$0.131302\pi$
$620$		0			0
$621$	185.500	+	321.295i	0.0119869	+	0.0207619i
$622$		−	1858.00i		−	0.119773i
$623$	14364.8	+	7420.50i	0.923775	+	0.477201i
$624$	1056.00			0.0677465
$625$		0			0
$626$	−209.000	+	361.999i	−0.0133440	+	0.0231124i
$627$	−4152.59	−	2397.50i	−0.264495	−	0.152706i
$628$	5400.53	−	3118.00i	0.343160	−	0.198124i
$629$	−649.000			−0.0411404
$630$		0			0
$631$	−21184.0			−1.33648			−0.668242	−	0.743944i	$-0.732953\pi$
$631$	−21184.0			−1.33648			−0.668242	+	0.743944i	$0.732953\pi$
$632$	−3429.46	+	1980.00i	−0.215849	+	0.124621i
$633$	1014.98	+	586.000i	0.0637313	+	0.0367953i
$634$	−7131.00	+	12351.3i	−0.446701	+	0.773708i
$635$		0			0
$636$	1668.00			0.103995
$637$	20576.8	+	9438.00i	1.27988	+	0.587044i
$638$		−	7420.00i		−	0.460440i
$639$	10192.0	+	17653.1i	0.630969	+	1.09287i
$640$		0			0
$641$	5352.50	−	9270.80i	0.329814	−	0.571255i	−0.652660	−	0.757651i	$-0.726347\pi$
$641$	5352.50	−	9270.80i	0.329814	−	0.571255i	0.982475	+	0.186395i	$0.0596805\pi$
$642$	−223.435	+	129.000i	−0.0137356	+	0.00793026i
$643$			6860.00i			0.420734i	0.977622	+	0.210367i	$0.0674659\pi$
$643$			6860.00i			0.420734i	−0.977622	+	0.210367i	$0.932534\pi$
$644$	−280.000	−	436.477i	−0.0171328	−	0.0267074i
$645$		0			0
$646$	8083.00	+	14000.2i	0.492293	+	0.852677i
$647$	12525.3	+	7231.50i	0.761084	+	0.439412i	0.829685	−	0.558232i	$-0.188520\pi$
$647$	12525.3	+	7231.50i	0.761084	+	0.439412i	−0.0686008	+	0.997644i	$0.521853\pi$
$648$	4496.40	+	2596.00i	0.272586	+	0.157377i
$649$	−297.500	−	515.285i	−0.0179937	−	0.0311660i
$650$		0			0
$651$	637.500	−	1234.09i	0.0383803	−	0.0742975i
$652$			9004.00i			0.540834i
$653$	5177.97	−	2989.50i	0.310305	−	0.179155i	−0.336758	−	0.941591i	$-0.609330\pi$
$653$	5177.97	−	2989.50i	0.310305	−	0.179155i	0.647063	+	0.762436i	$0.275997\pi$
$654$	−965.000	+	1671.43i	−0.0576980	+	0.0999359i
$655$		0			0
$656$	3984.00	+	6900.49i	0.237117	+	0.410700i
$657$			7670.00i			0.455457i
$658$	296.181	+	6327.00i	0.0175476	+	0.374851i
$659$	6940.00			0.410234			0.205117	−	0.978737i	$-0.434243\pi$
$659$	6940.00			0.410234			0.205117	+	0.978737i	$0.434243\pi$
$660$		0			0
$661$	−6699.50	+	11603.9i	−0.394221	+	0.682812i	−0.993001	−	0.118102i	$-0.962319\pi$
$661$	−6699.50	+	11603.9i	−0.394221	+	0.682812i	0.598780	+	0.800914i	$0.295652\pi$
$662$	11381.3	+	6571.00i	0.668198	+	0.385784i
$663$	−3372.30	+	1947.00i	−0.197541	+	0.114050i
$664$	7456.00			0.435766
$665$		0			0
$666$	572.000			0.0332801
$667$	642.591	−	371.000i	0.0373032	−	0.0215370i
$668$	−9657.92	−	5576.00i	−0.559395	−	0.322967i
$669$	−1012.00	+	1752.84i	−0.0584846	+	0.101298i
$670$		0			0
$671$	1785.00			0.102696
$672$	526.543	+	272.000i	0.0302260	+	0.0156140i
$673$			29510.0i			1.69023i	0.534582	+	0.845117i	$0.320469\pi$
$673$			29510.0i			1.69023i	−0.534582	+	0.845117i	$0.679531\pi$
$674$	11466.0	+	19859.7i	0.655273	+	1.13497i
$675$		0			0
$676$	−4318.00	+	7479.00i	−0.245676	+	0.425523i
$677$	22517.5	−	13000.5i	1.27831	−	0.738035i	0.301776	−	0.953379i	$-0.402421\pi$
$677$	22517.5	−	13000.5i	1.27831	−	0.738035i	0.976538	+	0.215344i	$0.0690872\pi$
$678$		−	100.000i		−	0.00566442i
$679$	−2900.00	−	4520.65i	−0.163905	−	0.255503i
$680$		0			0
$681$	1285.50	+	2226.55i	0.0723355	+	0.125289i
$682$	−4546.63	−	2625.00i	−0.255278	−	0.147385i
$683$	7625.35	+	4402.50i	0.427198	+	0.246643i	0.698152	−	0.715949i	$-0.254006\pi$
$683$	7625.35	+	4402.50i	0.427198	+	0.246643i	−0.270954	+	0.962592i	$0.587339\pi$
$684$	−7124.00	−	12339.1i	−0.398235	−	0.689764i
$685$		0			0
$686$	7829.00	+	10006.1i	0.435733	+	0.556899i
$687$			895.000i			0.0497036i
$688$	3602.67	−	2080.00i	0.199637	−	0.115261i
$689$	−13761.0	+	23834.8i	−0.760889	+	1.31790i
$690$		0			0
$691$	−14342.5	−	24841.9i	−0.789601	−	1.36763i	−0.926211	−	0.377004i	$-0.876954\pi$
$691$	−14342.5	−	24841.9i	−0.789601	−	1.36763i	0.136610	−	0.990625i	$-0.456379\pi$
$692$		−	6316.00i		−	0.346963i
$693$	−14185.5	+	9100.00i	−0.777579	+	0.498817i
$694$	−19554.0			−1.06954
$695$		0			0
$696$	−424.000	+	734.390i	−0.0230915	+	0.0399956i
$697$	−25445.6	−	14691.0i	−1.38281	−	0.798366i
$698$	−20635.7	+	11914.0i	−1.11901	+	0.646062i
$699$	1787.00			0.0966961
$700$		0			0
$701$	−3146.00			−0.169505			−0.0847523	−	0.996402i	$-0.527010\pi$
$701$	−3146.00			−0.169505			−0.0847523	+	0.996402i	$0.527010\pi$
$702$	6058.71	−	3498.00i	0.325743	−	0.188068i
$703$	−1305.10	−	753.500i	−0.0700182	−	0.0404250i
$704$	1120.00	−	1939.90i	0.0599596	−	0.103853i
$705$		0			0
$706$	−18246.0			−0.972659
$707$	939.638	+	20072.5i	0.0499840	+	1.06776i
$708$			68.0000i			0.00360960i
$709$	629.500	+	1090.33i	0.0333447	+	0.0577547i	0.882216	−	0.470845i	$-0.156051\pi$
$709$	629.500	+	1090.33i	0.0333447	+	0.0577547i	−0.848871	+	0.528599i	$0.822717\pi$
$710$		0			0
$711$	−6435.00	+	11145.7i	−0.339425	+	0.587902i
$712$	−6048.32	+	3492.00i	−0.318357	+	0.183804i
$713$		−	525.000i		−	0.0275756i
$714$	−2183.00	+	102.191i	−0.114421	+	0.00535631i
$715$		0			0
$716$	−4902.00	−	8490.51i	−0.255861	−	0.443164i
$717$	4416.73	+	2550.00i	0.230050	+	0.132819i
$718$	14114.5	+	8149.00i	0.733632	+	0.423563i
$719$	8212.50	+	14224.5i	0.425973	+	0.737807i	0.996511	−	0.0834645i	$-0.0265985\pi$
$719$	8212.50	+	14224.5i	0.425973	+	0.737807i	−0.570538	+	0.821271i	$0.693265\pi$
$720$		0			0
$721$	−13200.5	+	25553.8i	−0.681848	+	1.31994i
$722$			23820.0i			1.22782i
$723$	3617.39	−	2088.50i	0.186075	−	0.107430i
$724$	−2340.00	+	4053.00i	−0.120118	+	0.208050i
$725$		0			0
$726$	106.000	+	183.597i	0.00541877	+	0.00938559i
$727$			6032.00i			0.307723i	0.988092	+	0.153861i	$0.0491709\pi$
$727$			6032.00i			0.307723i	−0.988092	+	0.153861i	$0.950829\pi$
$728$	−8230.71	+	5280.00i	−0.419025	+	0.268805i
$729$	15443.0			0.784586
$730$		0			0
$731$	−7670.00	+	13284.8i	−0.388078	+	0.672171i
$732$	−176.669	−	102.000i	−0.00892060	−	0.00515031i
$733$	13200.8	−	7621.50i	0.665189	−	0.384047i	−0.129062	−	0.991636i	$-0.541197\pi$
$733$	13200.8	−	7621.50i	0.665189	−	0.384047i	0.794251	+	0.607589i	$0.207863\pi$
$734$	19342.0			0.972652
$735$		0			0
$736$	224.000			0.0112184
$737$	−13306.5	+	7682.50i	−0.665062	+	0.383974i
$738$	22426.6	+	12948.0i	1.11861	+	0.645830i
$739$	−5026.50	+	8706.15i	−0.250207	+	0.433371i	−0.963583	−	0.267411i	$-0.913832\pi$
$739$	−5026.50	+	8706.15i	−0.250207	+	0.433371i	0.713376	+	0.700782i	$0.247165\pi$
$740$		0			0
$741$	−9042.00			−0.448267
$742$	−13000.8	+	8340.00i	−0.643226	+	0.412629i
$743$			24384.0i			1.20399i	0.798501	+	0.601993i	$0.205627\pi$
$743$			24384.0i			1.20399i	−0.798501	+	0.601993i	$0.794373\pi$
$744$	300.000	+	519.615i	0.0147830	+	0.0256049i
$745$		0			0
$746$	−4109.00	+	7117.00i	−0.201664	+	0.349292i
$747$	20985.5	−	12116.0i	1.02787	−	0.593442i
$748$			8260.00i			0.403764i
$749$	1096.50	−	2122.63i	0.0534916	−	0.103550i
$750$		0			0
$751$	−5794.50	−	10036.4i	−0.281550	−	0.487660i	0.690216	−	0.723603i	$-0.257515\pi$
$751$	−5794.50	−	10036.4i	−0.281550	−	0.487660i	−0.971767	+	0.235943i	$0.924182\pi$
$752$	−2369.45	−	1368.00i	−0.114900	−	0.0663375i
$753$	−4053.00	−	2340.00i	−0.196148	−	0.113246i
$754$	−6996.00	−	12117.4i	−0.337904	−	0.585266i
$755$		0			0
$756$	3922.00	−	183.597i	0.188680	−	0.00883250i
$757$		−	14562.0i		−	0.699161i	−0.936906	−	0.349581i	$-0.886324\pi$
$757$		−	14562.0i		−	0.699161i	0.936906	−	0.349581i	$-0.113676\pi$
$758$	6041.39	−	3488.00i	0.289490	−	0.167137i
$759$	122.500	−	212.176i	0.00585832	−	0.0101469i
$760$		0			0
$761$	11382.5	+	19715.1i	0.542201	+	0.939120i	0.998777	+	0.0494360i	$0.0157424\pi$
$761$	11382.5	+	19715.1i	0.542201	+	0.939120i	−0.456576	+	0.889684i	$0.650924\pi$
$762$		−	1872.00i		−	0.0889966i
$763$	−835.715	−	17852.5i	−0.0396526	−	0.847056i
$764$	5100.00			0.241507
$765$		0			0
$766$	8717.00	−	15098.3i	0.411172	−	0.712171i
$767$	−971.681	−	561.000i	−0.0457436	−	0.0264101i
$768$	−221.703	+	128.000i	−0.0104167	+	0.00601407i
$769$	−3766.00			−0.176600			−0.0883000	−	0.996094i	$-0.528143\pi$
$769$	−3766.00			−0.176600			−0.0883000	+	0.996094i	$0.528143\pi$
$770$		0			0
$771$	1749.00			0.0816974
$772$	−121.244	+	70.0000i	−0.00565240	+	0.00326341i
$773$	23262.3	+	13430.5i	1.08239	+	0.624918i	0.931540	−	0.363639i	$-0.118466\pi$
$773$	23262.3	+	13430.5i	1.08239	+	0.624918i	0.150849	+	0.988557i	$0.451799\pi$
$774$	6760.00	−	11708.7i	0.313932	−	0.543746i
$775$		0			0
$776$	2320.00			0.107324
$777$	171.473	−	110.000i	0.00791707	−	0.00507880i
$778$		−

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.00000 - 3.46410i) q^{4} +2.00000 q^{6} +(-15.5885 + 10.0000i) q^{7} -8.00000i q^{8} +(-13.0000 - 22.5167i) q^{9} +O(q^{10})\)	\(q+(1.73205 - 1.00000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(2.00000 - 3.46410i) q^{4} +2.00000 q^{6} +(-15.5885 + 10.0000i) q^{7} -8.00000i q^{8} +(-13.0000 - 22.5167i) q^{9} +(-17.5000 + 30.3109i) q^{11} +(3.46410 - 2.00000i) q^{12} +66.0000i q^{13} +(-17.0000 + 32.9090i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(51.0955 + 29.5000i) q^{17} +(-45.0333 - 26.0000i) q^{18} +(68.5000 + 118.645i) q^{19} +(-18.5000 + 0.866025i) q^{21} +70.0000i q^{22} +(-6.06218 + 3.50000i) q^{23} +(4.00000 - 6.92820i) q^{24} +(66.0000 + 114.315i) q^{26} -53.0000i q^{27} +(3.46410 + 74.0000i) q^{28} -106.000 q^{29} +(-37.5000 + 64.9519i) q^{31} +(-27.7128 - 16.0000i) q^{32} +(-30.3109 + 17.5000i) q^{33} +118.000 q^{34} -104.000 q^{36} +(-9.52628 + 5.50000i) q^{37} +(237.291 + 137.000i) q^{38} +(-33.0000 + 57.1577i) q^{39} -498.000 q^{41} +(-31.1769 + 20.0000i) q^{42} +260.000i q^{43} +(70.0000 + 121.244i) q^{44} +(-7.00000 + 12.1244i) q^{46} +(148.090 - 85.5000i) q^{47} -16.0000i q^{48} +(143.000 - 311.769i) q^{49} +(29.5000 + 51.0955i) q^{51} +(228.631 + 132.000i) q^{52} +(361.133 + 208.500i) q^{53} +(-53.0000 - 91.7987i) q^{54} +(80.0000 + 124.708i) q^{56} +137.000i q^{57} +(-183.597 + 106.000i) q^{58} +(-8.50000 + 14.7224i) q^{59} +(-25.5000 - 44.1673i) q^{61} +150.000i q^{62} +(427.817 + 221.000i) q^{63} -64.0000 q^{64} +(-35.0000 + 60.6218i) q^{66} +(380.185 + 219.500i) q^{67} +(204.382 - 118.000i) q^{68} -7.00000 q^{69} -784.000 q^{71} +(-180.133 + 104.000i) q^{72} +(-255.477 - 147.500i) q^{73} +(-11.0000 + 19.0526i) q^{74} +548.000 q^{76} +(-30.3109 - 647.500i) q^{77} +132.000i q^{78} +(-247.500 - 428.683i) q^{79} +(-324.500 + 562.050i) q^{81} +(-862.561 + 498.000i) q^{82} +932.000i q^{83} +(-34.0000 + 65.8179i) q^{84} +(260.000 + 450.333i) q^{86} +(-91.7987 - 53.0000i) q^{87} +(242.487 + 140.000i) q^{88} +(-436.500 - 756.040i) q^{89} +(-660.000 - 1028.84i) q^{91} +28.0000i q^{92} +(-64.9519 + 37.5000i) q^{93} +(171.000 - 296.181i) q^{94} +(-16.0000 - 27.7128i) q^{96} +290.000i q^{97} +(-64.0859 - 683.000i) q^{98} +910.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9}+O(q^{10}) \) 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9	\( 4 q + 8 q^{4} + 8 q^{6} - 52 q^{9} - 70 q^{11} - 68 q^{14} - 32 q^{16} + 274 q^{19} - 74 q^{21} + 16 q^{24} + 264 q^{26} - 424 q^{29} - 150 q^{31} + 472 q^{34} - 416 q^{36} - 132 q^{39} - 1992 q^{41} + 280 q^{44} - 28 q^{46} + 572 q^{49} + 118 q^{51} - 212 q^{54} + 320 q^{56} - 34 q^{59} - 102 q^{61} - 256 q^{64} - 140 q^{66} - 28 q^{69} - 3136 q^{71} - 44 q^{74} + 2192 q^{76} - 990 q^{79} - 1298 q^{81} - 136 q^{84} + 1040 q^{86} - 1746 q^{89} - 2640 q^{91} + 684 q^{94} - 64 q^{96} + 3640 q^{99}+O(q^{100}) \) 4 * q + 8 * q^4 + 8 * q^6 - 52 * q^9 - 70 * q^11 - 68 * q^14 - 32 * q^16 + 274 * q^19 - 74 * q^21 + 16 * q^24 + 264 * q^26 - 424 * q^29 - 150 * q^31 + 472 * q^34 - 416 * q^36 - 132 * q^39 - 1992 * q^41 + 280 * q^44 - 28 * q^46 + 572 * q^49 + 118 * q^51 - 212 * q^54 + 320 * q^56 - 34 * q^59 - 102 * q^61 - 256 * q^64 - 140 * q^66 - 28 * q^69 - 3136 * q^71 - 44 * q^74 + 2192 * q^76 - 990 * q^79 - 1298 * q^81 - 136 * q^84 + 1040 * q^86 - 1746 * q^89 - 2640 * q^91 + 684 * q^94 - 64 * q^96 + 3640 * q^99

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