LMFDB - Embedded newform 117.3.n.a.38.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(38,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("117.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			38.18
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.647986 - 1.12234i) q^{2} +(2.50362 - 1.65285i) q^{3} +(1.16023 + 2.00957i) q^{4} +(-2.25417 - 3.90433i) q^{5} +(-0.232759 - 3.88094i) q^{6} +(-0.162124 - 0.0936021i) q^{7} +8.19114 q^{8} +(3.53618 - 8.27620i) q^{9} -5.84268 q^{10} +(2.73142 - 4.73097i) q^{11} +(6.22629 + 3.11352i) q^{12} +(-7.06871 + 10.9102i) q^{13} +(-0.210108 + 0.121306i) q^{14} +(-12.0968 - 6.04915i) q^{15} +(0.666831 - 1.15499i) q^{16} +6.56267i q^{17} +(-6.99735 - 9.33167i) q^{18} +9.33560i q^{19} +(5.23069 - 9.05983i) q^{20} +(-0.560605 + 0.0336222i) q^{21} +(-3.53985 - 6.13120i) q^{22} +(-15.5066 + 8.95272i) q^{23} +(20.5075 - 13.5387i) q^{24} +(2.33746 - 4.04860i) q^{25} +(7.66463 + 15.0032i) q^{26} +(-4.82607 - 26.5652i) q^{27} -0.434399i q^{28} +(2.86081 + 1.65169i) q^{29} +(-14.6278 + 9.65706i) q^{30} +(-20.4651 + 11.8155i) q^{31} +(15.5181 + 26.8781i) q^{32} +(-0.981137 - 16.3592i) q^{33} +(7.36558 + 4.25252i) q^{34} +0.843979i q^{35} +(20.7344 - 2.49606i) q^{36} +54.9508i q^{37} +(10.4778 + 6.04934i) q^{38} +(0.335648 + 38.9986i) q^{39} +(-18.4642 - 31.9809i) q^{40} +(27.4123 + 47.4795i) q^{41} +(-0.325529 + 0.650979i) q^{42} +(-20.2961 + 35.1538i) q^{43} +12.6763 q^{44} +(-40.2842 + 4.84951i) q^{45} +23.2050i q^{46} +(16.2252 - 28.1029i) q^{47} +(-0.239528 - 3.99381i) q^{48} +(-24.4825 - 42.4049i) q^{49} +(-3.02929 - 5.24688i) q^{50} +(10.8471 + 16.4304i) q^{51} +(-30.1262 - 1.54673i) q^{52} -70.1519i q^{53} +(-32.9425 - 11.7974i) q^{54} -24.6283 q^{55} +(-1.32798 - 0.766708i) q^{56} +(15.4303 + 23.3727i) q^{57} +(3.70753 - 2.14054i) q^{58} +(-9.16783 - 15.8791i) q^{59} +(-1.87888 - 31.3279i) q^{60} +(-16.7182 + 28.9569i) q^{61} +30.6252i q^{62} +(-1.34797 + 1.01077i) q^{63} +45.5566 q^{64} +(58.5312 + 3.00509i) q^{65} +(-18.9964 - 9.49933i) q^{66} +(73.0282 - 42.1629i) q^{67} +(-13.1882 + 7.61420i) q^{68} +(-24.0250 + 48.0442i) q^{69} +(0.947236 + 0.546887i) q^{70} -52.1928 q^{71} +(28.9653 - 67.7915i) q^{72} -88.7509i q^{73} +(61.6737 + 35.6073i) q^{74} +(-0.839625 - 13.9996i) q^{75} +(-18.7606 + 10.8314i) q^{76} +(-0.885657 + 0.511334i) q^{77} +(43.9873 + 24.8938i) q^{78} +(22.4851 - 38.9453i) q^{79} -6.01260 q^{80} +(-55.9909 - 58.5322i) q^{81} +71.0512 q^{82} +(43.9891 - 76.1913i) q^{83} +(-0.717996 - 1.08757i) q^{84} +(25.6229 - 14.7934i) q^{85} +(26.3031 + 45.5584i) q^{86} +(9.89236 - 0.593292i) q^{87} +(22.3735 - 38.7520i) q^{88} -174.305 q^{89} +(-20.6608 + 48.3551i) q^{90} +(2.16723 - 1.10716i) q^{91} +(-35.9823 - 20.7744i) q^{92} +(-31.7074 + 63.4072i) q^{93} +(-21.0275 - 36.4206i) q^{94} +(36.4493 - 21.0440i) q^{95} +(83.2767 + 41.6434i) q^{96} +(7.09093 + 4.09395i) q^{97} -63.4572 q^{98} +(-29.4956 - 39.3354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.647986	−	1.12234i	0.323993	−	0.561172i	−0.657315	−	0.753616i	$-0.728308\pi$
$2$	0.647986	−	1.12234i	0.323993	−	0.561172i	0.981308	+	0.192443i	$0.0616412\pi$
$3$	2.50362	−	1.65285i	0.834538	−	0.550950i
$3$	2.50362	−	1.65285i	0.834538	−	0.550950i
$4$	1.16023	+	2.00957i	0.290057	+	0.502393i
$5$	−2.25417	−	3.90433i	−0.450833	−	0.780866i	0.547605	−	0.836737i	$-0.315540\pi$
$5$	−2.25417	−	3.90433i	−0.450833	−	0.780866i	−0.998438	+	0.0558709i	$0.982206\pi$
$6$	−0.232759	−	3.88094i	−0.0387931	−	0.646824i
$7$	−0.162124	−	0.0936021i	−0.0231605	−	0.0133717i	0.488375	−	0.872634i	$-0.337590\pi$
$7$	−0.162124	−	0.0936021i	−0.0231605	−	0.0133717i	−0.511536	+	0.859262i	$0.670923\pi$
$8$	8.19114			1.02389
$9$	3.53618	−	8.27620i	0.392909	−	0.919577i
$10$	−5.84268			−0.584268
$11$	2.73142	−	4.73097i	0.248311	−	0.430088i	−0.714746	−	0.699384i	$-0.753458\pi$
$11$	2.73142	−	4.73097i	0.248311	−	0.430088i	0.963057	+	0.269296i	$0.0867911\pi$
$12$	6.22629	+	3.11352i	0.518857	+	0.259460i
$13$	−7.06871	+	10.9102i	−0.543747	+	0.839249i
$13$	−7.06871	+	10.9102i	−0.543747	+	0.839249i
$14$	−0.210108	+	0.121306i	−0.0150077	+	0.00866470i
$15$	−12.0968	−	6.04915i	−0.806456	−	0.403276i
$16$	0.666831	−	1.15499i	0.0416770	−	0.0721866i
$17$			6.56267i			0.386040i	0.981195	+	0.193020i	$0.0618282\pi$
$17$			6.56267i			0.386040i	−0.981195	+	0.193020i	$0.938172\pi$
$18$	−6.99735	−	9.33167i	−0.388742	−	0.518426i
$19$			9.33560i			0.491347i	0.969353	+	0.245674i	$0.0790092\pi$
$19$			9.33560i			0.491347i	−0.969353	+	0.245674i	$0.920991\pi$
$20$	5.23069	−	9.05983i	0.261535	−	0.452991i
$21$	−0.560605	+	0.0336222i	−0.0266955	+	0.00160106i
$22$	−3.53985	−	6.13120i	−0.160902	−	0.278691i
$23$	−15.5066	+	8.95272i	−0.674199	+	0.389249i	−0.797666	−	0.603100i	$-0.793932\pi$
$23$	−15.5066	+	8.95272i	−0.674199	+	0.389249i	0.123467	+	0.992349i	$0.460599\pi$
$24$	20.5075	−	13.5387i	0.854477	−	0.564113i
$25$	2.33746	−	4.04860i	0.0934985	−	0.161944i
$26$	7.66463	+	15.0032i	0.294793	+	0.577047i
$27$	−4.82607	−	26.5652i	−0.178743	−	0.983896i
$28$		−	0.434399i		−	0.0155143i
$29$	2.86081	+	1.65169i	0.0986486	+	0.0569548i	0.548513	−	0.836142i	$-0.315194\pi$
$29$	2.86081	+	1.65169i	0.0986486	+	0.0569548i	−0.449864	+	0.893097i	$0.648528\pi$
$30$	−14.6278	+	9.65706i	−0.487594	+	0.321902i
$31$	−20.4651	+	11.8155i	−0.660164	+	0.381146i	−0.792339	−	0.610080i	$-0.791137\pi$
$31$	−20.4651	+	11.8155i	−0.660164	+	0.381146i	0.132175	+	0.991226i	$0.457804\pi$
$32$	15.5181	+	26.8781i	0.484940	+	0.839941i
$33$	−0.981137	−	16.3592i	−0.0297314	−	0.495732i
$34$	7.36558	+	4.25252i	0.216635	+	0.125074i
$35$			0.843979i			0.0241137i
$36$	20.7344	−	2.49606i	0.575956	−	0.0693350i
$37$			54.9508i			1.48516i	0.669760	+	0.742578i	$0.266397\pi$
$37$			54.9508i			1.48516i	−0.669760	+	0.742578i	$0.733603\pi$
$38$	10.4778	+	6.04934i	0.275731	+	0.159193i
$39$	0.335648	+	38.9986i	0.00860635	+	0.999963i
$40$	−18.4642	−	31.9809i	−0.461605	−	0.799523i
$41$	27.4123	+	47.4795i	0.668593	+	1.15804i	0.978298	+	0.207205i	$0.0664366\pi$
$41$	27.4123	+	47.4795i	0.668593	+	1.15804i	−0.309704	+	0.950833i	$0.600230\pi$
$42$	−0.325529	+	0.650979i	−0.00775069	+	0.0154995i
$43$	−20.2961	+	35.1538i	−0.472001	+	0.817530i	−0.999487	−	0.0320337i	$-0.989802\pi$
$43$	−20.2961	+	35.1538i	−0.472001	+	0.817530i	0.527485	+	0.849564i	$0.323135\pi$
$44$	12.6763			0.288098
$45$	−40.2842	+	4.84951i	−0.895203	+	0.107767i
$46$			23.2050i			0.504456i
$47$	16.2252	−	28.1029i	0.345218	−	0.597935i	−0.640176	−	0.768229i	$-0.721138\pi$
$47$	16.2252	−	28.1029i	0.345218	−	0.597935i	0.985393	+	0.170294i	$0.0544717\pi$
$48$	−0.239528	−	3.99381i	−0.00499017	−	0.0832044i
$49$	−24.4825	−	42.4049i	−0.499642	−	0.865406i
$50$	−3.02929	−	5.24688i	−0.0605857	−	0.104938i
$51$	10.8471	+	16.4304i	0.212688	+	0.322165i
$52$	−30.1262	−	1.54673i	−0.579351	−	0.0297448i
$53$		−	70.1519i		−	1.32362i	−0.749671	−	0.661810i	$-0.769788\pi$
$53$		−	70.1519i		−	1.32362i	0.749671	−	0.661810i	$-0.230212\pi$
$54$	−32.9425	−	11.7974i	−0.610047	−	0.218470i
$55$	−24.6283			−0.447788
$56$	−1.32798	−	0.766708i	−0.0237139	−	0.0136912i
$57$	15.4303	+	23.3727i	0.270708	+	0.410048i
$58$	3.70753	−	2.14054i	0.0639229	−	0.0369059i
$59$	−9.16783	−	15.8791i	−0.155387	−	0.269138i	0.777813	−	0.628496i	$-0.216329\pi$
$59$	−9.16783	−	15.8791i	−0.155387	−	0.269138i	−0.933200	+	0.359358i	$0.882996\pi$
$60$	−1.87888	−	31.3279i	−0.0313147	−	0.522131i
$61$	−16.7182	+	28.9569i	−0.274070	+	0.474703i	−0.969900	−	0.243504i	$-0.921703\pi$
$61$	−16.7182	+	28.9569i	−0.274070	+	0.474703i	0.695830	+	0.718206i	$0.255037\pi$
$62$			30.6252i			0.493954i
$63$	−1.34797	+	1.01077i	−0.0213963	+	0.0160440i
$64$	45.5566			0.711823
$65$	58.5312	+	3.00509i	0.900481	+	0.0462321i
$66$	−18.9964	−	9.49933i	−0.287824	−	0.143929i
$67$	73.0282	−	42.1629i	1.08997	−	0.629297i	0.156404	−	0.987693i	$-0.450010\pi$
$67$	73.0282	−	42.1629i	1.08997	−	0.629297i	0.933569	+	0.358396i	$0.116676\pi$
$68$	−13.1882	+	7.61420i	−0.193944	+	0.111973i
$69$	−24.0250	+	48.0442i	−0.348188	+	0.696292i
$70$	0.947236	+	0.546887i	0.0135319	+	0.00781267i
$71$	−52.1928			−0.735110			−0.367555	−	0.930002i	$-0.619805\pi$
$71$	−52.1928			−0.735110			−0.367555	+	0.930002i	$0.619805\pi$
$72$	28.9653	−	67.7915i	0.402296	−	0.941548i
$73$		−	88.7509i		−	1.21577i	−0.794026	−	0.607883i	$-0.792019\pi$
$73$		−	88.7509i		−	1.21577i	0.794026	−	0.607883i	$-0.207981\pi$
$74$	61.6737	+	35.6073i	0.833429	+	0.481180i
$75$	−0.839625	−	13.9996i	−0.0111950	−	0.186662i
$76$	−18.7606	+	10.8314i	−0.246850	+	0.142519i
$77$	−0.885657	+	0.511334i	−0.0115020	+	0.00664071i
$78$	43.9873	+	24.8938i	0.563940	+	0.319151i
$79$	22.4851	−	38.9453i	0.284622	−	0.492979i	−0.687896	−	0.725810i	$-0.741465\pi$
$79$	22.4851	−	38.9453i	0.284622	−	0.492979i	0.972517	+	0.232830i	$0.0747987\pi$
$80$	−6.01260			−0.0751574
$81$	−55.9909	−	58.5322i	−0.691245	−	0.722620i
$82$	71.0512			0.866478
$83$	43.9891	−	76.1913i	0.529989	−	0.917968i	−0.469399	−	0.882986i	$-0.655529\pi$
$83$	43.9891	−	76.1913i	0.529989	−	0.917968i	0.999388	−	0.0349817i	$-0.0111373\pi$
$84$	−0.717996	−	1.08757i	−0.00854758	−	0.0129472i
$85$	25.6229	−	14.7934i	0.301445	−	0.174040i
$86$	26.3031	+	45.5584i	0.305850	+	0.529748i
$87$	9.89236	−	0.593292i	0.113705	−	0.00681945i
$88$	22.3735	−	38.7520i	0.254244	−	0.440364i
$89$	−174.305			−1.95848			−0.979241	−	0.202698i	$-0.935029\pi$
$89$	−174.305			−1.95848			−0.979241	+	0.202698i	$0.935029\pi$
$90$	−20.6608	+	48.3551i	−0.229564	+	0.537279i
$91$	2.16723	−	1.10716i	0.0238157	−	0.0121666i
$92$	−35.9823	−	20.7744i	−0.391112	−	0.225809i
$93$	−31.7074	+	63.4072i	−0.340940	+	0.681798i
$94$	−21.0275	−	36.4206i	−0.223696	−	0.387453i
$95$	36.4493	−	21.0440i	0.383677	−	0.221516i
$96$	83.2767	+	41.6434i	0.867466	+	0.433785i
$97$	7.09093	+	4.09395i	0.0731024	+	0.0422057i	0.536106	−	0.844151i	$-0.319895\pi$
$97$	7.09093	+	4.09395i	0.0731024	+	0.0422057i	−0.463003	+	0.886357i	$0.653228\pi$
$98$	−63.4572			−0.647523
$99$	−29.4956	−	39.3354i	−0.297935	−	0.397327i
$100$	10.8480			0.108480
$101$	−60.0429	−	34.6658i	−0.594484	−	0.343226i	0.172384	−	0.985030i	$-0.444853\pi$
$101$	−60.0429	−	34.6658i	−0.594484	−	0.343226i	−0.766869	+	0.641804i	$0.778186\pi$
$102$	25.4694	−	1.52752i	0.249700	−	0.0149757i
$103$	81.5907	+	141.319i	0.792143	+	1.37203i	0.924637	+	0.380848i	$0.124368\pi$
$103$	81.5907	+	141.319i	0.792143	+	1.37203i	−0.132494	+	0.991184i	$0.542299\pi$
$104$	−57.9008	+	89.3673i	−0.556738	+	0.859301i
$105$	1.39497	+	2.11300i	0.0132854	+	0.0201238i
$106$	−78.7346	−	45.4574i	−0.742779	−	0.428844i
$107$		−	180.476i		−	1.68669i	−0.537373	−	0.843345i	$-0.680583\pi$
$107$		−	180.476i		−	1.68669i	0.537373	−	0.843345i	$-0.319417\pi$
$108$	47.7854	−	40.5200i	0.442457	−	0.375185i
$109$		−	149.717i		−	1.37355i	−0.726870	−	0.686775i	$-0.759026\pi$
$109$		−	149.717i		−	1.37355i	0.726870	−	0.686775i	$-0.240974\pi$
$110$	−15.9588	+	27.6415i	−0.145080	+	0.251286i
$111$	90.8253	+	137.576i	0.818246	+	1.23942i
$112$	−0.216218	+	0.124834i	−0.00193052	+	0.00111459i
$113$	53.6475	−	30.9734i	0.474757	−	0.274101i	−0.243472	−	0.969908i	$-0.578286\pi$
$113$	53.6475	−	30.9734i	0.474757	−	0.274101i	0.718229	+	0.695807i	$0.244953\pi$
$114$	36.2309	−	2.17294i	0.317815	−	0.0190609i
$115$	69.9088	+	40.3619i	0.607902	+	0.350973i
$116$			7.66534i			0.0660805i
$117$	65.2991	+	97.0826i	0.558112	+	0.829766i
$118$	−23.7625			−0.201377
$119$	0.614280	−	1.06396i	0.00516202	−	0.00894088i
$120$	−99.0868	−	49.5494i	−0.825724	−	0.412912i
$121$	45.5786	+	78.9445i	0.376683	+	0.652434i
$122$	21.6664	+	37.5273i	0.177593	+	0.307601i
$123$	147.106	+	73.5621i	1.19599	+	0.598066i
$124$	−47.4883	−	27.4174i	−0.382970	−	0.221108i
$125$	−133.784			−1.07028
$126$	0.260972	+	2.16785i	0.00207120	+	0.0172052i
$127$	−60.3333			−0.475065			−0.237533	−	0.971380i	$-0.576339\pi$
$127$	−60.3333			−0.475065			−0.237533	+	0.971380i	$0.576339\pi$
$128$	−32.5522	+	56.3821i	−0.254314	+	0.440485i
$129$	7.29041	+	121.558i	0.0565148	+	0.942310i
$130$	41.3002	−	63.7450i	0.317694	−	0.490346i
$131$	−168.986	+	97.5640i	−1.28997	+	0.744763i	−0.978648	−	0.205542i	$-0.934104\pi$
$131$	−168.986	+	97.5640i	−1.28997	+	0.744763i	−0.311319	+	0.950305i	$0.600771\pi$
$132$	31.7366	−	20.9520i	0.240429	−	0.158727i
$133$	0.873832	−	1.51352i	0.00657017	−	0.0113799i
$134$		−	109.284i		−	0.815551i
$135$	−92.8405	+	78.7249i	−0.687708	+	0.583148i
$136$			53.7557i			0.395263i
$137$	55.0447	−	95.3402i	0.401786	−	0.695914i	−0.592155	−	0.805824i	$-0.701723\pi$
$137$	55.0447	−	95.3402i	0.401786	−	0.695914i	0.993942	+	0.109910i	$0.0350562\pi$
$138$	38.3543	+	58.0963i	0.277930	+	0.420988i
$139$	110.129	+	190.749i	0.792296	+	1.37230i	0.924542	+	0.381080i	$0.124448\pi$
$139$	110.129	+	190.749i	0.792296	+	1.37230i	−0.132246	+	0.991217i	$0.542219\pi$
$140$	−1.69604	+	0.979208i	−0.0121146	+	0.00699435i
$141$	−5.82816	−	97.1768i	−0.0413345	−	0.689197i
$142$	−33.8202	+	58.5784i	−0.238171	+	0.412524i
$143$	32.3083	+	63.2423i	0.225932	+	0.442254i
$144$	−7.20085	−	9.60306i	−0.0500059	−	0.0666879i
$145$		−	14.8927i		−	0.102709i
$146$	−99.6092	−	57.5094i	−0.682255	−	0.393900i
$147$	−131.384	−	65.6997i	−0.893766	−	0.446937i
$148$	−110.428	+	63.7554i	−0.746133	+	0.430780i
$149$	−39.0386	−	67.6168i	−0.262004	−	0.453804i	0.704770	−	0.709436i	$-0.251050\pi$
$149$	−39.0386	−	67.6168i	−0.262004	−	0.453804i	−0.966774	+	0.255631i	$0.917717\pi$
$150$	−16.2565	−	8.12921i	−0.108376	−	0.0541948i
$151$	224.322	+	129.512i	1.48557	+	0.857696i	0.999865	−	0.0164251i	$-0.00522849\pi$
$151$	224.322	+	129.512i	1.48557	+	0.857696i	0.485708	+	0.874121i	$0.338562\pi$
$152$			76.4692i			0.503087i
$153$	54.3140	+	23.2068i	0.354993	+	0.151678i
$154$			1.32535i			0.00860617i
$155$	92.2634	+	53.2683i	0.595248	+	0.343667i
$156$	−77.9810	+	45.9217i	−0.499878	+	0.294370i
$157$	−68.2125	−	118.148i	−0.434475	−	0.752532i	0.562778	−	0.826608i	$-0.309733\pi$
$157$	−68.2125	−	118.148i	−0.434475	−	0.752532i	−0.997253	+	0.0740760i	$0.976399\pi$
$158$	−29.1401	−	50.4721i	−0.184431	−	0.319444i
$159$	−115.950	−	175.633i	−0.729248	−	1.10461i
$160$	69.9607	−	121.175i	0.437254	−	0.757346i
$161$	3.35197			0.0208197
$162$	−101.975	+	24.9130i	−0.629473	+	0.153784i
$163$			44.8906i			0.275402i	0.990474	+	0.137701i	$0.0439714\pi$
$163$			44.8906i			0.275402i	−0.990474	+	0.137701i	$0.956029\pi$
$164$	−63.6091	+	110.174i	−0.387860	+	0.671794i
$165$	−61.6599	+	40.7069i	−0.373696	+	0.246709i
$166$	−57.0086	−	98.7419i	−0.343426	−	0.594831i
$167$	50.4995	+	87.4677i	0.302392	+	0.523759i	0.976677	−	0.214712i	$-0.0688814\pi$
$167$	50.4995	+	87.4677i	0.302392	+	0.523759i	−0.674285	+	0.738471i	$0.735548\pi$
$168$	−4.59200	+	0.275404i	−0.0273333	+	0.00163931i
$169$	−69.0667	−	154.243i	−0.408678	−	0.912678i
$170$		−	38.3436i		−	0.225550i
$171$	77.2633	+	33.0124i	0.451832	+	0.193055i
$172$	−94.1922			−0.547629
$173$	−15.2225	−	8.78871i	−0.0879913	−	0.0508018i	0.455359	−	0.890308i	$-0.349511\pi$
$173$	−15.2225	−	8.78871i	−0.0879913	−	0.0508018i	−0.543350	+	0.839506i	$0.682844\pi$
$174$	5.74423	−	11.4871i	0.0330128	−	0.0660177i
$175$	−0.757916	+	0.437583i	−0.00433095	+	0.00250047i
$176$	−3.64280	−	6.30951i	−0.0206977	−	0.0358495i
$177$	−49.1985	−	24.6022i	−0.277958	−	0.138996i
$178$	−112.947	+	195.630i	−0.634535	+	1.09905i
$179$			104.441i			0.583468i	0.956499	+	0.291734i	$0.0942322\pi$
$179$			104.441i			0.583468i	−0.956499	+	0.291734i	$0.905768\pi$
$180$	−56.4843	−	75.3274i	−0.313801	−	0.418486i
$181$	90.6107			0.500612			0.250306	−	0.968167i	$-0.419469\pi$
$181$	90.6107			0.500612			0.250306	+	0.968167i	$0.419469\pi$
$182$	0.161716	−	3.14980i	0.000888549	−	0.0173066i
$183$	6.00525	+	100.130i	0.0328156	+	0.547156i
$184$	−127.016	+	73.3329i	−0.690306	+	0.398549i
$185$	214.546	−	123.868i	1.15971	−	0.669558i
$186$	50.6188	+	76.6737i	0.272144	+	0.412224i
$187$	31.0478	+	17.9254i	0.166031	+	0.0958580i
$188$	75.2999			0.400531
$189$	−1.70414	+	4.75858i	−0.00901660	+	0.0251776i
$190$		−	54.5449i		−	0.287078i
$191$	207.774	+	119.958i	1.08782	+	0.628054i	0.932995	−	0.359888i	$-0.117185\pi$
$191$	207.774	+	119.958i	1.08782	+	0.628054i	0.154825	+	0.987942i	$0.450519\pi$
$192$	114.056	−	75.2983i	0.594043	−	0.392178i
$193$	310.002	−	178.980i	1.60623	−	0.927357i	0.616027	−	0.787725i	$-0.288741\pi$
$193$	310.002	−	178.980i	1.60623	−	0.927357i	0.990203	−	0.139632i	$-0.0445919\pi$
$194$	9.18965	−	5.30564i	0.0473693	−	0.0273487i
$195$	151.507	−	89.2197i	0.776957	−	0.457537i
$196$	56.8105	−	98.3987i	0.289850	−	0.502034i
$197$	−41.0547			−0.208399			−0.104200	−	0.994556i	$-0.533228\pi$
$197$	−41.0547			−0.208399			−0.104200	+	0.994556i	$0.533228\pi$
$198$	−63.2606	+	7.61547i	−0.319498	+	0.0384620i
$199$	−144.402			−0.725640			−0.362820	−	0.931859i	$-0.618186\pi$
$199$	−144.402			−0.725640			−0.362820	+	0.931859i	$0.618186\pi$
$200$	19.1465	−	33.1627i	0.0957324	−	0.165813i
$201$	113.146	−	226.264i	0.562914	−	1.12569i
$202$	−77.8139	+	44.9259i	−0.385218	+	0.222405i
$203$	−0.309203	−	0.535556i	−0.00152317	−	0.00263821i
$204$	−20.4330	+	40.8611i	−0.100162	+	0.200299i
$205$	123.584	−	214.054i	0.602848	−	1.04416i
$206$	211.479			1.02660
$207$	19.2605	+	159.994i	0.0930458	+	0.772917i
$208$	7.88753	+	15.4395i	0.0379208	+	0.0742286i
$209$	44.1664	+	25.4995i	0.211323	+	0.122007i
$210$	3.27544	−	0.196444i	0.0155973	−	0.000935446i
$211$	8.28442	+	14.3490i	0.0392626	+	0.0680049i	0.884989	−	0.465612i	$-0.154166\pi$
$211$	8.28442	+	14.3490i	0.0392626	+	0.0680049i	−0.845726	+	0.533617i	$0.820832\pi$
$212$	140.975	−	81.3922i	0.664978	−	0.383925i
$213$	−130.671	+	86.2669i	−0.613478	+	0.405009i
$214$	−202.556	−	116.946i	−0.946524	−	0.546476i
$215$	183.003			0.851176
$216$	−39.5310	−	217.599i	−0.183014	−	1.00740i
$217$	4.42383			0.0203863
$218$	−168.034	−	97.0145i	−0.770799	−	0.445021i
$219$	−146.692	−	222.198i	−0.669826	−	1.01460i
$220$	−28.5745	−	49.4925i	−0.129884	−	0.224966i
$221$	−71.6003	−	46.3896i	−0.323983	−	0.209908i
$222$	213.261	−	12.7903i	0.960634	−	0.0576139i
$223$	250.650	+	144.713i	1.12399	+	0.648936i	0.942417	−	0.334441i	$-0.108548\pi$
$223$	250.650	+	144.713i	1.12399	+	0.648936i	0.181574	+	0.983377i	$0.441881\pi$
$224$		−	5.81010i		−	0.0259379i
$225$	−25.2414	−	33.6619i	−0.112184	−	0.149608i
$226$		−	80.2813i		−	0.355227i
$227$	152.915	−	264.857i	0.673636	−	1.16677i	−0.303230	−	0.952917i	$-0.598065\pi$
$227$	152.915	−	264.857i	0.673636	−	1.16677i	0.976866	−	0.213854i	$-0.0686016\pi$
$228$	−29.0666	+	58.1261i	−0.127485	+	0.254939i
$229$	−240.075	+	138.607i	−1.04836	+	0.605273i	−0.922191	−	0.386736i	$-0.873603\pi$
$229$	−240.075	+	138.607i	−1.04836	+	0.605273i	−0.126172	+	0.992008i	$0.540269\pi$
$230$	90.5998	−	52.3078i	0.393912	−	0.227425i
$231$	−1.37219	+	2.74404i	−0.00594020	+	0.0118790i
$232$	23.4333	+	13.5292i	0.101006	+	0.0583156i
$233$			203.054i			0.871476i	0.900073	+	0.435738i	$0.143513\pi$
$233$			203.054i			0.871476i	−0.900073	+	0.435738i	$0.856487\pi$
$234$	151.273	−	10.3799i	0.646466	−	0.0443585i
$235$	−146.298			−0.622543
$236$	21.2735	−	36.8468i	0.0901421	−	0.156131i
$237$	−8.07673	−	134.669i	−0.0340790	−	0.568222i
$238$	−0.796090	−	1.37887i	−0.00334492	−	0.00579357i
$239$	18.5820	+	32.1850i	0.0777490	+	0.134665i	0.902278	−	0.431154i	$-0.141893\pi$
$239$	18.5820	+	32.1850i	0.0777490	+	0.134665i	−0.824529	+	0.565819i	$0.808560\pi$
$240$	−15.0532	+	9.93791i	−0.0627218	+	0.0414080i
$241$	−239.107	−	138.048i	−0.992144	−	0.572814i	−0.0862292	−	0.996275i	$-0.527482\pi$
$241$	−239.107	−	138.048i	−0.992144	−	0.572814i	−0.905914	+	0.423461i	$0.860815\pi$
$242$	118.137			0.488171
$243$	−236.925	−	53.9977i	−0.974998	−	0.222213i
$244$	−77.5879			−0.317983
$245$	−110.375	+	191.175i	−0.450511	+	0.780308i
$246$	177.885	−	117.437i	0.723110	−	0.477386i
$247$	−101.854	−	65.9907i	−0.412363	−	0.267169i
$248$	−167.632	+	96.7825i	−0.675937	+	0.390252i
$249$	−15.8010	−	263.461i	−0.0634579	−	1.05808i
$250$	−86.6905	+	150.152i	−0.346762	+	0.600609i
$251$			179.821i			0.716417i	0.933642	+	0.358209i	$0.116612\pi$
$251$			179.821i			0.716417i	−0.933642	+	0.358209i	$0.883388\pi$
$252$	−3.59517	−	1.53611i	−0.0142666	−	0.00609569i
$253$			97.8147i			0.386619i
$254$	−39.0951	+	67.7147i	−0.153918	+	0.266593i
$255$	39.6986	−	79.3876i	0.155681	−	0.311324i
$256$	133.300	+	230.883i	0.520703	+	0.901885i
$257$	−271.324	+	156.649i	−1.05574	+	0.609530i	−0.924250	−	0.381788i	$-0.875309\pi$
$257$	−271.324	+	156.649i	−1.05574	+	0.609530i	−0.131487	+	0.991318i	$0.541975\pi$
$258$	141.154	+	70.5855i	0.547109	+	0.273587i
$259$	5.14351	−	8.90882i	0.0198591	−	0.0343970i
$260$	61.8706	+	121.109i	0.237964	+	0.465806i
$261$	23.7860	−	17.8360i	0.0911343	−	0.0683370i
$262$			252.880i			0.965192i
$263$	43.6126	+	25.1797i	0.165827	+	0.0957404i	0.580617	−	0.814177i	$-0.302811\pi$
$263$	43.6126	+	25.1797i	0.165827	+	0.0957404i	−0.414790	+	0.909917i	$0.636145\pi$
$264$	−8.03663	−	134.000i	−0.0304418	−	0.507576i
$265$	−273.896	+	158.134i	−1.03357	+	0.596732i
$266$	−1.13246	−	1.96148i	−0.00425738	−	0.00737399i
$267$	−436.393	+	288.100i	−1.63443	+	1.07903i
$268$	169.459	+	97.8371i	0.632309	+	0.365064i
$269$		−	501.502i		−	1.86432i	−0.362047	−	0.932160i	$-0.617922\pi$
$269$		−	501.502i		−	1.86432i	0.362047	−	0.932160i	$-0.382078\pi$
$270$	28.1972	+	155.212i	0.104434	+	0.574858i
$271$			229.102i			0.845396i	0.906270	+	0.422698i	$0.138917\pi$
$271$			229.102i			0.845396i	−0.906270	+	0.422698i	$0.861083\pi$
$272$	7.57979	+	4.37620i	0.0278669	+	0.0160890i
$273$	3.59593	−	6.35401i	0.0131719	−	0.0232747i
$274$	−71.3364	−	123.558i	−0.260352	−	0.450943i
$275$	−12.7692	−	22.1169i	−0.0464335	−	0.0804252i
$276$	−124.423	+	7.46223i	−0.450807	+	0.0270371i
$277$	−198.883	+	344.476i	−0.717990	+	1.24360i	0.243805	+	0.969824i	$0.421604\pi$
$277$	−198.883	+	344.476i	−0.717990	+	1.24360i	−0.961795	+	0.273771i	$0.911729\pi$
$278$	285.449			1.02679
$279$	25.4194	+	211.155i	0.0911089	+	0.756827i
$280$			6.91315i			0.0246898i
$281$	−97.3277	+	168.576i	−0.346362	+	0.599916i	−0.985600	−	0.169092i	$-0.945916\pi$
$281$	−97.3277	+	168.576i	−0.346362	+	0.599916i	0.639238	+	0.769009i	$0.279250\pi$
$282$	−112.842	−	56.4280i	−0.400151	−	0.200099i
$283$	−208.024	−	360.308i	−0.735067	−	1.27317i	−0.954694	−	0.297589i	$-0.903817\pi$
$283$	−208.024	−	360.308i	−0.735067	−	1.27317i	0.219627	−	0.975584i	$-0.429516\pi$
$284$	−60.5556	−	104.885i	−0.213224	−	0.369315i
$285$	56.4724	−	112.931i	0.198149	−	0.396250i
$286$	91.9151	+	4.71907i	0.321381	+	0.0165002i
$287$		−	10.2634i		−	0.0357610i
$288$	277.323	−	33.3849i	0.962928	−	0.115920i
$289$	245.931			0.850973
$290$	−16.7148	−	9.65029i	−0.0576372	−	0.0332768i
$291$	24.5196	−	1.47056i	0.0842599	−	0.00505347i
$292$	178.352	−	102.971i	0.610793	−	0.352642i
$293$	118.452	+	205.164i	0.404272	+	0.700219i	0.994236	−	0.107210i	$-0.0341916\pi$
$293$	118.452	+	205.164i	0.404272	+	0.700219i	−0.589965	+	0.807429i	$0.700858\pi$
$294$	−158.872	+	104.885i	−0.540383	+	0.356752i
$295$	−41.3316	+	71.5885i	−0.140107	+	0.242673i
$296$			450.109i			1.52064i
$297$	−138.861	−	49.7288i	−0.467546	−	0.167437i
$298$	−101.186			−0.339550
$299$	11.9351	−	232.465i	0.0399168	−	0.777473i
$300$	27.1591	−	17.9300i	0.0905304	−	0.0597668i
$301$	6.58094	−	3.79951i	0.0218636	−	0.0126230i
$302$	290.715	−	167.844i	0.962631	−	0.555775i
$303$	−207.622	+	12.4521i	−0.685220	+	0.0410959i
$304$	10.7825	+	6.22527i	0.0354687	+	0.0204779i
$305$	150.743			0.494239
$306$	61.2407	−	45.9213i	0.200133	−	0.150070i
$307$			249.037i			0.811195i	0.914052	+	0.405598i	$0.132937\pi$
$307$			249.037i			0.811195i	−0.914052	+	0.405598i	$0.867063\pi$
$308$	−2.05513	−	1.18653i	−0.00667249	−	0.00385237i
$309$	437.851	+	218.952i	1.41699	+	0.708583i
$310$	119.571	−	69.0343i	0.385712	−	0.222691i
$311$	−127.535	+	73.6323i	−0.410080	+	0.236760i	−0.690824	−	0.723023i	$-0.742752\pi$
$311$	−127.535	+	73.6323i	−0.410080	+	0.236760i	0.280744	+	0.959783i	$0.409419\pi$
$312$	2.74934	+	319.442i	0.00881197	+	1.02385i
$313$	83.8809	−	145.286i	0.267990	−	0.464172i	−0.700353	−	0.713797i	$-0.746974\pi$
$313$	83.8809	−	145.286i	0.267990	−	0.464172i	0.968343	+	0.249625i	$0.0803072\pi$
$314$	−176.803			−0.563067
$315$	6.98494	+	2.98446i	0.0221744	+	0.00947448i
$316$	104.351			0.330226
$317$	−20.0628	+	34.7498i	−0.0632896	+	0.109621i	−0.895934	−	0.444187i	$-0.853492\pi$
$317$	−20.0628	+	34.7498i	−0.0632896	+	0.109621i	0.832644	+	0.553808i	$0.186826\pi$
$318$	−272.255	+	16.3285i	−0.856149	+	0.0513474i
$319$	15.6282	−	9.02293i	0.0489911	−	0.0282850i
$320$	−102.692	−	177.868i	−0.320913	−	0.555838i
$321$	−298.299	−	451.842i	−0.929281	−	1.40761i
$322$	2.17203	−	3.76207i	0.00674545	−	0.0116835i
$323$	−61.2665			−0.189680
$324$	52.6627	−	180.429i	0.162539	−	0.556878i
$325$	27.6484	+	54.1207i	0.0850720	+	0.166525i
$326$	50.3827	+	29.0885i	0.154548	+	0.0892285i
$327$	−247.460	−	374.834i	−0.756757	−	1.14628i
$328$	224.538	+	388.911i	0.684567	+	1.18571i
$329$	−5.26099	+	3.03743i	−0.0159908	+	0.00923232i
$330$	5.73247	+	95.5812i	0.0173711	+	0.289640i
$331$	10.1298	+	5.84845i	0.0306037	+	0.0176690i	0.515224	−	0.857056i	$-0.327709\pi$
$331$	10.1298	+	5.84845i	0.0306037	+	0.0176690i	−0.484620	+	0.874725i	$0.661042\pi$
$332$	204.149			0.614908
$333$	454.783	+	194.316i	1.36572	+	0.583531i
$334$	130.892			0.391892
$335$	−329.236	−	190.084i	−0.982793	−	0.567416i
$336$	−0.334996	+	0.669912i	−0.000997012	+	0.00199378i
$337$	−172.531	−	298.833i	−0.511963	−	0.886745i	−0.999904	−	0.0138688i	$-0.995585\pi$
$337$	−172.531	−	298.833i	−0.511963	−	0.886745i	0.487941	−	0.872876i	$-0.337748\pi$
$338$	−217.868	−	22.4305i	−0.644579	−	0.0663624i
$339$	83.1183	−	166.217i	0.245187	−	0.490315i
$340$	59.4567	+	34.3273i	0.174873	+	0.100963i
$341$			129.093i			0.378571i
$342$	87.1168	−	65.3245i	0.254727	−	0.191007i
$343$			18.3395i			0.0534678i
$344$	−166.248	+	287.950i	−0.483278	+	0.837063i
$345$	241.737	−	14.4981i	0.700686	−	0.0420235i
$346$	−19.7279	+	11.3899i	−0.0570171	+	0.0329189i
$347$	508.170	−	293.392i	1.46447	−	0.845511i	0.465255	−	0.885177i	$-0.345963\pi$
$347$	508.170	−	293.392i	1.46447	−	0.845511i	0.999213	+	0.0396654i	$0.0126292\pi$
$348$	12.6697	+	19.1911i	0.0364071	+	0.0551468i
$349$	−501.880	−	289.761i	−1.43805	−	0.830260i	−0.440338	−	0.897832i	$-0.645141\pi$
$349$	−501.880	−	289.761i	−1.43805	−	0.830260i	−0.997714	+	0.0675725i	$0.978475\pi$
$350$			1.13419i			0.00324055i
$351$	323.947	+	135.128i	0.922925	+	0.384980i
$352$	169.546			0.481664
$353$	−189.372	+	328.001i	−0.536463	+	0.929182i	0.462628	+	0.886553i	$0.346907\pi$
$353$	−189.372	+	328.001i	−0.536463	+	0.929182i	−0.999091	+	0.0426291i	$0.986427\pi$
$354$	−59.4922	+	39.2758i	−0.168057	+	0.110949i
$355$	117.651	+	203.778i	0.331412	+	0.574023i
$356$	−202.233	−	350.279i	−0.568071	−	0.983929i
$357$	−0.220651	−	3.67907i	−0.000618071	−	0.0103055i
$358$	117.219	+	67.6762i	0.327426	+	0.189040i
$359$	−226.733			−0.631569			−0.315784	−	0.948831i	$-0.602268\pi$
$359$	−226.733			−0.631569			−0.315784	+	0.948831i	$0.602268\pi$
$360$	−329.973	+	39.7230i	−0.916592	+	0.110342i
$361$	273.847			0.758578
$362$	58.7145	−	101.696i	0.162195	−	0.280929i
$363$	244.595	+	122.312i	0.673815	+	0.336948i
$364$	4.73940	+	3.07064i	0.0130203	+	0.00843583i
$365$	−346.513	+	200.059i	−0.949351	+	0.548108i
$366$	116.271	+	58.1426i	0.317681	+	0.158860i
$367$	−226.025	+	391.487i	−0.615873	+	1.06672i	0.374358	+	0.927284i	$0.377863\pi$
$367$	−226.025	+	391.487i	−0.615873	+	1.06672i	−0.990231	+	0.139439i	$0.955470\pi$
$368$			23.8798i			0.0648908i
$369$	489.885	−	58.9736i	1.32760	−	0.159820i
$370$		−	321.060i		−	0.867729i
$371$	−6.56637	+	11.3733i	−0.0176991	+	0.0306557i
$372$	−164.209	+	9.84842i	−0.441423	+	0.0264742i
$373$	78.8574	+	136.585i	0.211414	+	0.366180i	0.952157	−	0.305609i	$-0.0988599\pi$
$373$	78.8574	+	136.585i	0.211414	+	0.366180i	−0.740743	+	0.671788i	$0.765527\pi$
$374$	40.2371	−	23.2309i	0.107586	−	0.0621147i
$375$	−334.945	+	221.126i	−0.893186	+	0.589668i
$376$	132.903	−	230.195i	0.353466	−	0.612221i
$377$	−38.2426	+	19.5368i	−0.101439	+	0.0518218i
$378$	4.23651	+	4.99612i	0.0112077	+	0.0132173i
$379$		−	514.875i		−	1.35851i	−0.733903	−	0.679255i	$-0.762303\pi$
$379$		−	514.875i		−	1.35851i	0.733903	−	0.679255i	$-0.237697\pi$
$380$	84.5789	+	48.8317i	0.222576	+	0.128504i
$381$	−151.051	+	99.7218i	−0.396460	+	0.261737i
$382$	269.269	−	155.463i	0.704893	−	0.406970i
$383$	89.2179	+	154.530i	0.232945	+	0.403473i	0.958673	−	0.284509i	$-0.0918305\pi$
$383$	89.2179	+	154.530i	0.232945	+	0.403473i	−0.725728	+	0.687981i	$0.758497\pi$
$384$	11.6929	+	194.963i	0.0304502	+	0.507716i
$385$	3.99284	+	2.30527i	0.0103710	+	0.00598770i
$386$		−	463.906i		−	1.20183i
$387$	219.169	+	292.284i	0.566329	+	0.755257i
$388$			18.9997i			0.0489682i
$389$	−524.201	−	302.648i	−1.34756	−	0.778014i	−0.359657	−	0.933085i	$-0.617106\pi$
$389$	−524.201	−	302.648i	−1.34756	−	0.778014i	−0.987903	+	0.155070i	$0.950440\pi$
$390$	−1.96108	−	227.856i	−0.00502841	−	0.584246i
$391$	−58.7538	−	101.765i	−0.150265	−	0.260267i
$392$	−200.539	−	347.344i	−0.511580	−	0.886082i
$393$	−261.817	+	523.571i	−0.666200	+	1.33224i
$394$	−26.6029	+	46.0775i	−0.0675200	+	0.116948i
$395$	−202.741			−0.513268
$396$	44.8257	−	104.912i	0.113196	−	0.264928i
$397$		−	511.953i		−	1.28955i	−0.764371	−	0.644777i	$-0.776950\pi$
$397$		−	511.953i		−	1.28955i	0.764371	−	0.644777i	$-0.223050\pi$
$398$	−93.5707	+	162.069i	−0.235102	+	0.407209i
$399$	−0.313883	−	5.23359i	−0.000786675	−	0.0131168i
$400$	−3.11739	−	5.39947i	−0.00779347	−	0.0134987i
$401$	−32.5050	−	56.3003i	−0.0810599	−	0.140400i	0.822646	−	0.568555i	$-0.192497\pi$
$401$	−32.5050	−	56.3003i	−0.0810599	−	0.140400i	−0.903705	+	0.428155i	$0.859164\pi$
$402$	−180.630	−	273.605i	−0.449328	−	0.680609i
$403$	15.7516	−	306.799i	0.0390858	−	0.761289i
$404$		−	160.881i		−	0.398220i
$405$	−102.316	+	350.548i	−0.252633	+	0.865551i
$406$	−0.801438			−0.00197398
$407$	259.970	+	150.094i	0.638748	+	0.368781i
$408$	88.8501	+	134.584i	0.217770	+	0.329862i
$409$	238.707	−	137.817i	0.583635	−	0.336962i	−0.178942	−	0.983860i	$-0.557267\pi$
$409$	238.707	−	137.817i	0.583635	−	0.336962i	0.762577	+	0.646898i	$0.223934\pi$
$410$	−160.161	−	277.408i	−0.390637	−	0.676604i
$411$	−19.7722	−	329.676i	−0.0481076	−	0.802131i
$412$	−189.328	+	327.925i	−0.459533	+	0.795935i
$413$			3.43251i			0.00831117i
$414$	192.049	+	82.0569i	0.463886	+	0.198205i
$415$	−396.635			−0.955747
$416$	−402.939	−	20.6876i	−0.968604	−	0.0497297i
$417$	591.001	+	295.536i	1.41727	+	0.708719i
$418$	57.2384	−	33.0466i	0.136934	−	0.0790589i
$419$	405.554	−	234.147i	0.967910	−	0.558823i	0.0693118	−	0.997595i	$-0.477920\pi$
$419$	405.554	−	234.147i	0.967910	−	0.558823i	0.898599	+	0.438772i	$0.144586\pi$
$420$	−2.62774	+	5.25486i	−0.00625653	+	0.0125116i
$421$	−123.688	−	71.4111i	−0.293795	−	0.169623i	0.345857	−	0.938287i	$-0.387588\pi$
$421$	−123.688	−	71.4111i	−0.293795	−	0.169623i	−0.639652	+	0.768665i	$0.720922\pi$
$422$	21.4727			0.0508833
$423$	−175.210	−	233.660i	−0.414208	−	0.552388i
$424$		−	574.624i		−	1.35524i
$425$	26.5697	+	15.3400i	0.0625169	+	0.0360941i
$426$	12.1483	+	202.557i	0.0285172	+	0.475487i
$427$	5.42085	−	3.12973i	0.0126952	−	0.00732957i
$428$	362.679	−	209.393i	0.847382	−	0.489236i
$429$	185.418	+	104.934i	0.432209	+	0.244601i
$430$	118.583	−	205.392i	0.275775	−	0.477657i
$431$	234.681			0.544504			0.272252	−	0.962226i	$-0.412232\pi$
$431$	234.681			0.544504			0.272252	+	0.962226i	$0.412232\pi$
$432$	−33.9006	−	12.1405i	−0.0784736	−	0.0281029i
$433$	−15.5025			−0.0358026			−0.0179013	−	0.999840i	$-0.505698\pi$
$433$	−15.5025			−0.0358026			−0.0179013	+	0.999840i	$0.505698\pi$
$434$	2.86658	−	4.96507i	0.00660503	−	0.0114402i
$435$	−24.6154	−	37.2857i	−0.0565872	−	0.0857142i
$436$	300.867	−	173.706i	0.690063	−	0.398408i
$437$	−83.5790	−	144.763i	−0.191256	−	0.331266i
$438$	−344.437	+	20.6576i	−0.786387	+	0.0471634i
$439$	313.874	−	543.645i	0.714974	−	1.23837i	−0.247995	−	0.968761i	$-0.579772\pi$
$439$	313.874	−	543.645i	0.714974	−	1.23837i	0.962969	−	0.269611i	$-0.0868950\pi$
$440$	−201.734			−0.458487
$441$	−437.526	+	52.6705i	−0.992122	+	0.119434i
$442$	−98.4612	+	50.3004i	−0.222763	+	0.113802i
$443$	495.766	+	286.231i	1.11911	+	0.646119i	0.941174	−	0.337923i	$-0.109724\pi$
$443$	495.766	+	286.231i	1.11911	+	0.646119i	0.177937	+	0.984042i	$0.443058\pi$
$444$	−171.090	+	342.139i	−0.385338	+	0.770584i
$445$	392.912	+	680.544i	0.882949	+	1.52931i
$446$	324.835	−	187.544i	0.728330	−	0.420502i
$447$	−209.498	−	104.762i	−0.468676	−	0.234366i
$448$	−7.38581	−	4.26420i	−0.0164862	−	0.00951830i
$449$	80.8219			0.180004			0.0900021	−	0.995942i	$-0.471313\pi$
$449$	80.8219			0.180004			0.0900021	+	0.995942i	$0.471313\pi$
$450$	−54.1363	+	6.51707i	−0.120303	+	0.0144824i
$451$	299.499			0.664077
$452$	124.487	+	71.8724i	0.275413	+	0.159010i
$453$	775.679	−	46.5212i	1.71232	−	0.102696i
$454$	−198.174	−	343.247i	−0.436507	−	0.756051i
$455$	−9.20802	−	5.96585i	−0.0202374	−	0.0131117i
$456$	126.392	+	191.449i	0.277175	+	0.419845i
$457$	213.732	+	123.398i	0.467686	+	0.270019i	0.715270	−	0.698848i	$-0.246303\pi$
$457$	213.732	+	123.398i	0.467686	+	0.270019i	−0.247585	+	0.968866i	$0.579637\pi$
$458$			359.263i			0.784416i
$459$	174.339	−	31.6719i	0.379823	−	0.0690020i
$460$			187.316i			0.407208i
$461$	−262.211	+	454.162i	−0.568787	+	0.985167i	0.427900	+	0.903826i	$0.359254\pi$
$461$	−262.211	+	454.162i	−0.568787	+	0.985167i	−0.996686	+	0.0813410i	$0.974080\pi$
$462$	2.19060	+	3.31817i	0.00474157	+	0.00718218i
$463$	43.9680	−	25.3849i	0.0949632	−	0.0548270i	−0.451766	−	0.892136i	$-0.649206\pi$
$463$	43.9680	−	25.3849i	0.0949632	−	0.0548270i	0.546730	+	0.837309i	$0.315873\pi$
$464$	3.81535	−	2.20280i	0.00822275	−	0.00474741i
$465$	319.037	−	19.1342i	0.686100	−	0.0411487i
$466$	227.897	+	131.576i	0.489049	+	0.282352i
$467$			101.615i			0.217592i	0.994064	+	0.108796i	$0.0346995\pi$
$467$			101.615i			0.217592i	−0.994064	+	0.108796i	$0.965301\pi$
$468$	−119.333	+	243.861i	−0.254985	+	0.521071i
$469$	−15.7861			−0.0336591
$470$	−94.7988	+	164.196i	−0.201700	+	0.349354i
$471$	−366.058	−	183.051i	−0.777193	−	0.388643i
$472$	−75.0949	−	130.068i	−0.159099	−	0.275568i
$473$	110.874	+	192.040i	0.234407	+	0.406004i
$474$	−156.378	−	78.1986i	−0.329912	−	0.164976i
$475$	37.7962	+	21.8216i	0.0795708	+	0.0459402i
$476$	2.85082			0.00598912
$477$	−580.591	−	248.070i	−1.21717	−	0.520062i
$478$	48.1635			0.100761
$479$	18.6148	−	32.2418i	0.0388618	−	0.0673106i	−0.845940	−	0.533278i	$-0.820960\pi$
$479$	18.6148	−	32.2418i	0.0388618	−	0.0673106i	0.884802	+	0.465967i	$0.154293\pi$
$480$	−25.1301	−	419.011i	−0.0523544	−	0.872940i
$481$	−599.526	−	388.431i	−1.24642	−	0.807549i
$482$	−309.876	+	178.907i	−0.642895	+	0.371176i
$483$	8.39206	−	5.54031i	0.0173749	−	0.0114706i
$484$	−105.763	+	183.187i	−0.218519	+	0.378486i
$485$		−	36.9138i		−	0.0761109i
$486$	−214.128	+	230.921i	−0.440592	+	0.475147i
$487$			540.371i			1.10959i	0.831987	+	0.554795i	$0.187203\pi$
$487$			540.371i			1.10959i	−0.831987	+	0.554795i	$0.812797\pi$
$488$	−136.941	+	237.190i	−0.280618	+	0.486044i
$489$	74.1974	+	112.389i	0.151733	+	0.229834i
$490$	143.043	+	247.758i	0.291925	+	0.505629i
$491$	−441.513	+	254.907i	−0.899211	+	0.519160i	−0.876944	−	0.480592i	$-0.840422\pi$
$491$	−441.513	+	254.907i	−0.899211	+	0.519160i	−0.0222668	+	0.999752i	$0.507088\pi$
$492$	22.8486	+	380.970i	0.0464402	+	0.774329i
$493$	−10.8395	+	18.7746i	−0.0219868	+	0.0380823i
$494$	−140.064	+	71.5539i	−0.283530	+	0.144846i
$495$	−87.0903	+	203.829i	−0.175940	+	0.411776i
$496$			31.5158i			0.0635400i
$497$	8.46169	+	4.88536i	0.0170255	+	0.00982970i
$498$	−305.933	−	152.985i	−0.614324	−	0.307199i
$499$	325.310	−	187.818i	0.651924	−	0.376389i	−0.137269	−	0.990534i	$-0.543832\pi$
$499$	325.310	−	187.818i	0.651924	−	0.376389i	0.789193	+	0.614145i	$0.210499\pi$
$500$	−155.220	−	268.850i	−0.310441	−	0.537699i
$501$	271.002	+	135.517i	0.540923	+	0.270494i
$502$	201.821	+	116.521i	0.402034	+	0.232114i
$503$		−	842.603i		−	1.67515i	−0.546319	−	0.837577i	$-0.683971\pi$
$503$		−	842.603i		−	1.67515i	0.546319	−	0.837577i	$-0.316029\pi$
$504$	−11.0414	+	8.27938i	−0.0219075	+	0.0164273i
$505$			312.570i			0.618950i
$506$	109.782	+	63.3826i	0.216960	+	0.125262i
$507$	−427.856	−	272.008i	−0.843898	−	0.536504i
$508$	−70.0003	−	121.244i	−0.137796	−	0.238670i
$509$	365.564	+	633.175i	0.718200	+	1.24396i	0.961712	+	0.274061i	$0.0883669\pi$
$509$	365.564	+	633.175i	0.718200	+	1.24396i	−0.243513	+	0.969898i	$0.578300\pi$
$510$	−63.3761	−	95.9976i	−0.124267	−	0.188230i
$511$	−8.30728	+	14.3886i	−0.0162569	+	0.0281578i
$512$	85.0886			0.166189
$513$	248.002	−	45.0543i	0.483435	−	0.0878251i
$514$			406.026i			0.789934i
$515$	367.838	−	637.115i	0.714249	−	1.23712i
$516$	−235.821	+	155.686i	−0.457018	+	0.301716i
$517$	−88.6360	−	153.522i	−0.171443	−	0.296948i
$518$	−6.66585	−	11.5456i	−0.0128684	−	0.0222888i
$519$	−52.6377	+	3.15693i	−0.101421	+	0.00608272i
$520$	479.437	+	24.6151i	0.921995	+	0.0473367i
$521$			530.709i			1.01864i	0.860579	+	0.509318i	$0.170102\pi$
$521$			530.709i			1.01864i	−0.860579	+	0.509318i	$0.829898\pi$
$522$	−4.60507	−	38.2536i	−0.00882197	−	0.0732828i
$523$	108.736			0.207909			0.103955	−	0.994582i	$-0.466850\pi$
$523$	108.736			0.207909			0.103955	+	0.994582i	$0.466850\pi$
$524$	−392.124	−	226.393i	−0.748328	−	0.432047i
$525$	−1.17427	+	2.34826i	−0.00223671	+	0.00447288i
$526$	56.5207	−	32.6322i	0.107454	−	0.0620385i
$527$	−77.5414	−	134.306i	−0.147137	−	0.254849i
$528$	−19.5488	−	9.77560i	−0.0370243	−	0.0185144i
$529$	−104.198	+	180.476i	−0.196971	+	0.341164i
$530$			409.875i			0.773348i
$531$	−163.838	+	19.7232i	−0.308546	+	0.0371436i
$532$	4.05538			0.00762289
$533$	−711.783	−	36.5441i	−1.33543	−	0.0685630i
$534$	40.5710	+	676.468i	0.0759757	+	1.26679i
$535$	−704.637	+	406.823i	−1.31708	+	0.760416i
$536$	598.184	−	345.362i	1.11602	−	0.644332i
$537$	172.625	+	261.480i	0.321462	+	0.486927i
$538$	−562.858	−	324.966i	−1.04620	−	0.604027i
$539$	−267.488			−0.496267
$540$	−265.920	−	95.2310i	−0.492444	−	0.176354i
$541$		−	199.865i		−	0.369436i	−0.982792	−	0.184718i	$-0.940863\pi$
$541$		−	199.865i		−	0.369436i	0.982792	−	0.184718i	$-0.0591372\pi$
$542$	257.132	+	148.455i	0.474413	+	0.273903i
$543$	226.854	−	149.766i	0.417780	−	0.275812i
$544$	−176.392	+	101.840i	−0.324250	+	0.187206i
$545$	−584.545	+	337.487i	−1.07256	+	0.619242i
$546$	−4.80127	−	8.15318i	−0.00879354	−	0.0149326i
$547$	−282.244	+	488.862i	−0.515986	+	0.893714i	0.483842	+	0.875156i	$0.339241\pi$
$547$	−282.244	+	488.862i	−0.515986	+	0.893714i	−0.999828	+	0.0185588i	$0.994092\pi$
$548$	255.458			0.466164
$549$	180.534	+	240.760i	0.328841	+	0.438543i
$550$	−33.0971			−0.0601765
$551$	−15.4195	+	26.7074i	−0.0279846	+	0.0484707i
$552$	−196.792	+	393.536i	−0.356507	+	0.712928i
$553$	−7.29074	+	4.20931i	−0.0131840	+	0.00761177i
$554$	257.747	+	446.431i	0.465248	+	0.805833i
$555$	332.405	−	664.731i	0.598928	−	1.19771i
$556$	−255.550	+	442.625i	−0.459622	+	0.796089i
$557$	504.734			0.906165			0.453083	−	0.891469i	$-0.350324\pi$
$557$	504.734			0.906165			0.453083	+	0.891469i	$0.350324\pi$
$558$	253.460	+	108.296i	0.454229	+	0.194079i
$559$	−240.069	−	469.927i	−0.429462	−	0.840657i
$560$	0.974784	+	0.562792i	0.00174069	+	0.00100499i
$561$	107.360	−	6.43888i	0.191372	−	0.0114775i
$562$	126.134	+	218.470i	0.224438	+	0.388737i
$563$	273.837	−	158.100i	0.486389	−	0.280817i	−0.236686	−	0.971586i	$-0.576061\pi$
$563$	273.837	−	158.100i	0.486389	−	0.280817i	0.723075	+	0.690769i	$0.242728\pi$
$564$	188.522	−	124.459i	0.334259	−	0.220673i
$565$	−241.861	−	139.638i	−0.428072	−	0.247148i
$566$	−539.186			−0.952626
$567$	3.59870	+	14.7303i	0.00634692	+	0.0259794i
$568$	−427.519			−0.752674
$569$	37.8576	+	21.8571i	0.0665336	+	0.0384132i	0.532898	−	0.846180i	$-0.321103\pi$
$569$	37.8576	+	21.8571i	0.0665336	+	0.0384132i	−0.466364	+	0.884593i	$0.654436\pi$
$570$	−90.1545	−	136.559i	−0.158166	−	0.239578i
$571$	94.3613	+	163.439i	0.165256	+	0.286232i	0.936746	−	0.350009i	$-0.113822\pi$
$571$	94.3613	+	163.439i	0.165256	+	0.286232i	−0.771490	+	0.636241i	$0.780488\pi$
$572$	−89.6051	+	138.301i	−0.156652	+	0.241786i
$573$	718.458	−	43.0894i	1.25385	−	0.0751996i
$574$	−11.5191	−	6.65055i	−0.0200681	−	0.0115863i
$575$			83.7066i			0.145577i
$576$	161.096	−	377.036i	0.279681	−	0.654576i
$577$			633.598i			1.09809i	0.835792	+	0.549045i	$0.185009\pi$
$577$			633.598i			1.09809i	−0.835792	+	0.549045i	$0.814991\pi$
$578$	159.360	−	276.020i	0.275710	−	0.477543i
$579$	480.300	−	960.484i	0.829533	−	1.65887i
$580$	29.9280	−	17.2790i	0.0516001	−	0.0297913i
$581$	−14.2633	+	8.23495i	−0.0245496	+	0.0141737i
$582$	14.2379	−	28.4724i	0.0244638	−	0.0489216i
$583$	−331.886	−	191.615i	−0.569273	−	0.328670i
$584$		−	726.971i		−	1.24481i
$585$	231.848	−	473.790i	0.396321	−	0.809897i
$586$	307.020			0.523925
$587$	525.602	−	910.370i	0.895404	−	1.55089i	0.0621006	−	0.998070i	$-0.480220\pi$
$587$	525.602	−	910.370i	0.895404	−	1.55089i	0.833304	−	0.552816i	$-0.186447\pi$
$588$	−20.4065	−	340.252i	−0.0347050	−	0.578659i
$589$	−110.305	−	191.054i	−0.187275	−	0.324370i
$590$	53.5646	+	92.7767i	0.0907875	+	0.157249i
$591$	−102.785	+	67.8572i	−0.173917	+	0.114818i
$592$	63.4674	+	36.6429i	0.107208	+	0.0618968i
$593$	692.941			1.16853			0.584267	−	0.811562i	$-0.301382\pi$
$593$	692.941			1.16853			0.584267	+	0.811562i	$0.301382\pi$
$594$	−145.793	+	123.626i	−0.245443	+	0.208125i
$595$	−5.53876			−0.00930884
$596$	90.5873	−	156.902i	0.151992	−	0.263258i
$597$	−361.528	+	238.675i	−0.605574	+	0.399791i
$598$	−253.172	−	164.029i	−0.423364	−	0.274296i
$599$	−919.094	+	530.639i	−1.53438	+	0.885875i	−0.535228	+	0.844708i	$0.679774\pi$
$599$	−919.094	+	530.639i	−1.53438	+	0.885875i	−0.999152	+	0.0411670i	$0.986892\pi$
$600$	−6.87748	−	114.673i	−0.0114625	−	0.191121i
$601$	−42.5965	+	73.7793i	−0.0708760	+	0.122761i	−0.899285	−	0.437362i	$-0.855913\pi$
$601$	−42.5965	+	73.7793i	−0.0708760	+	0.122761i	0.828409	+	0.560123i	$0.189246\pi$
$602$		−	9.84812i		−	0.0163590i
$603$	−90.7073	−	753.492i	−0.150427	−	1.24957i
$604$			601.054i			0.995123i
$605$	205.484	−	355.908i	0.339643	−	0.588278i
$606$	−120.560	+	241.092i	−0.198945	+	0.397841i
$607$	111.215	+	192.630i	0.183221	+	0.317348i	0.942976	−	0.332862i	$-0.108014\pi$
$607$	111.215	+	192.630i	0.183221	+	0.317348i	−0.759755	+	0.650210i	$0.774681\pi$
$608$	−250.923	+	144.871i	−0.412703	+	0.238274i
$609$	−1.65932	−	0.829759i	−0.00272466	−	0.00136249i
$610$	97.6793	−	169.186i	0.160130	−	0.277353i
$611$	191.918	+	375.673i	0.314105	+	0.614849i
$612$	16.3808	+	136.073i	0.0267661	+	0.222342i
$613$		−	1211.06i		−	1.97563i	−0.155644	−	0.987813i	$-0.549745\pi$
$613$		−	1211.06i		−	1.97563i	0.155644	−	0.987813i	$-0.450255\pi$
$614$	279.505	+	161.372i	0.455220	+	0.262822i
$615$	−44.3918	−	740.173i	−0.0721817	−	1.20353i
$616$	−7.25454	+	4.18841i	−0.0117768	+	0.00679937i
$617$	44.9906	+	77.9259i	0.0729182	+	0.126298i	0.900179	−	0.435520i	$-0.143435\pi$
$617$	44.9906	+	77.9259i	0.0729182	+	0.126298i	−0.827261	+	0.561818i	$0.810102\pi$
$618$	529.461	−	349.542i	0.856734	−	0.565603i
$619$	−467.089	−	269.674i	−0.754586	−	0.435661i	0.0727624	−	0.997349i	$-0.476819\pi$
$619$	−467.089	−	269.674i	−0.754586	−	0.435661i	−0.827349	+	0.561689i	$0.810152\pi$
$620$			247.214i			0.398732i
$621$	312.666	+	368.728i	0.503489	+	0.593765i
$622$			190.851i			0.306834i
$623$	28.2590	+	16.3153i	0.0453595	+	0.0261883i
$624$	45.2666	+	25.6178i	0.0725426	+	0.0410541i
$625$	243.136	+	421.124i	0.389018	+	0.673798i
$626$	−108.707	−	188.287i	−0.173654	−	0.300777i
$627$	152.722	−	9.15950i	0.243577	−	0.0146085i
$628$	158.284	−	274.156i	0.252045	−	0.436554i
$629$	−360.624			−0.573329
$630$	7.87574	−	5.90562i	0.0125012	−	0.00937400i
$631$			1068.00i			1.69255i	0.532744	+	0.846276i	$0.321161\pi$
$631$			1068.00i			1.69255i	−0.532744	+	0.846276i	$0.678839\pi$
$632$	184.179	−	319.007i	0.291422	−	0.504757i
$633$	44.4578	+	22.2316i	0.0702334	+	0.0351209i
$634$	26.0008	+	45.0347i	0.0410108	+	0.0710327i
$635$	136.001	+	235.561i	0.214175	+	0.370962i
$636$	218.419	−	436.786i	0.343426	−	0.686770i
$637$	635.707	+	32.6382i	0.997970	+	0.0512374i
$638$		−	23.3869i		−	0.0366566i
$639$	−184.563	+	431.958i	−0.288831	+	0.675991i
$640$	293.513			0.458614
$641$	−356.116	−	205.604i	−0.555564	−	0.320755i	0.195799	−	0.980644i	$-0.437270\pi$
$641$	−356.116	−	205.604i	−0.555564	−	0.320755i	−0.751363	+	0.659889i	$0.770603\pi$
$642$	−700.416	+	42.0073i	−1.09099	+	0.0654320i
$643$	−776.631	+	448.388i	−1.20782	+	0.697338i	−0.962284	−	0.272048i	$-0.912299\pi$
$643$	−776.631	+	448.388i	−1.20782	+	0.697338i	−0.245541	+	0.969386i	$0.578966\pi$
$644$	3.88905	+	6.73604i	0.00603890	+	0.0104597i
$645$	458.169	−	302.476i	0.710339	−	0.468955i
$646$	−39.6998	+	68.7621i	−0.0614549	+	0.106443i
$647$		−	39.9656i		−	0.0617706i	−0.999523	−	0.0308853i	$-0.990167\pi$
$647$		−	39.9656i		−	0.0617706i	0.999523	−	0.0308853i	$-0.00983266\pi$
$648$	−458.629	−	479.445i	−0.707761	−	0.739885i
$649$	−100.165			−0.154337
$650$	78.6579	+	4.03842i	0.121012	+	0.00621296i
$651$	11.0756	−	7.31193i	0.0170132	−	0.0112318i
$652$	−90.2110	+	52.0833i	−0.138360	+	0.0798824i
$653$	189.335	−	109.313i	0.289947	−	0.167401i	−0.347971	−	0.937505i	$-0.613129\pi$
$653$	189.335	−	109.313i	0.289947	−	0.167401i	0.637918	+	0.770104i	$0.279796\pi$
$654$	−581.043	+	34.8479i	−0.888445	+	0.0532843i
$655$	761.844	+	439.851i	1.16312	+	0.671528i
$656$	73.1176			0.111460
$657$	−734.520	−	313.839i	−1.11799	−	0.477685i
$658$			7.87286i			0.0119648i
$659$	839.444	+	484.653i	1.27382	+	0.735437i	0.975704	−	0.219094i	$-0.0703100\pi$
$659$	839.444	+	484.653i	1.27382	+	0.735437i	0.298111	+	0.954531i	$0.403643\pi$
$660$	−153.343	−	76.6808i	−0.232338	−	0.116183i
$661$	205.518	−	118.656i	0.310919	−	0.179509i	−0.336418	−	0.941713i	$-0.609216\pi$
$661$	205.518	−	118.656i	0.310919	−	0.179509i	0.647338	+	0.762203i	$0.275882\pi$
$662$	13.1280	−	7.57943i	0.0198308	−	0.0114493i
$663$	−255.935	+	2.20275i	−0.386025	+	0.00332239i
$664$	360.321	−	624.094i	0.542652	−	0.939900i
$665$	−7.87905			−0.0118482
$666$	512.783	−	384.510i	0.769944	−	0.577342i
$667$	−59.1484			−0.0886783
$668$	−117.182	+	202.965i	−0.175422	+	0.303840i
$669$	866.719	−	51.9813i	1.29554	−	0.0777000i
$670$	−426.680	+	246.344i	−0.636836	+	0.367678i
$671$	91.3293	+	158.187i	0.136109	+	0.235748i
$672$	−9.60322	−	14.5463i	−0.0142905	−	0.0216462i
$673$	545.331	−	944.541i	0.810299	−	1.40348i	−0.102356	−	0.994748i	$-0.532638\pi$
$673$	545.331	−	944.541i	0.810299	−	1.40348i	0.912655	−	0.408731i	$-0.134029\pi$
$674$	−447.192			−0.663489
$675$	−118.833	−	42.5563i	−0.176048	−	0.0630463i
$676$	229.829	−	317.751i	0.339984	−	0.470046i
$677$	1125.33	+	649.709i	1.66223	+	0.959689i	0.971647	+	0.236435i	$0.0759790\pi$
$677$	1125.33	+	649.709i	1.66223	+	0.959689i	0.690582	+	0.723254i	$0.257354\pi$
$678$	−132.693	−	200.994i	−0.195712	−	0.296451i
$679$	−0.766405	−	1.32745i	−0.00112873	−	0.00195501i
$680$	209.880	−	121.174i	0.308647	−	0.178198i
$681$	−54.9277	−	915.846i	−0.0806574	−	1.34485i
$682$	144.887	+	83.6504i	0.212444	+	0.122655i
$683$	−703.770			−1.03041			−0.515205	−	0.857067i	$-0.672284\pi$
$683$	−703.770			−1.03041			−0.515205	+	0.857067i	$0.672284\pi$
$684$	23.3022	+	193.568i	0.0340676	+	0.282994i
$685$	−496.320			−0.724554
$686$	20.5832	+	11.8837i	0.0300047	+	0.0173232i
$687$	−371.958	+	743.827i	−0.541424	+	1.08272i
$688$	27.0681	+	46.8833i	0.0393432	+	0.0681444i
$689$	765.374	+	495.883i	1.11085	+	0.719715i
$690$	140.370	−	280.707i	0.203435	−	0.406821i
$691$	267.940	+	154.695i	0.387757	+	0.223872i	0.681188	−	0.732109i	$-0.261464\pi$
$691$	267.940	+	154.695i	0.387757	+	0.223872i	−0.293431	+	0.955980i	$0.594797\pi$
$692$		−	40.7876i		−	0.0589417i
$693$	1.10006	+	9.13804i	0.00158739	+	0.0131862i
$694$		−	760.457i		−	1.09576i
$695$	496.499	−	859.961i	0.714387	−	1.23735i
$696$	81.0297	−	4.85974i	0.116422	−	0.00698238i
$697$	−311.593	+	179.898i	−0.447048	+	0.258103i
$698$	−650.423	+	375.522i	−0.931838	+	0.537997i
$699$	335.618	+	508.369i	0.480140	+	0.727280i
$700$	−1.75871	−	1.01539i	−0.00251244	−	0.00145056i
$701$		−	321.205i		−	0.458210i	−0.973402	−	0.229105i	$-0.926420\pi$
$701$		−	321.205i		−	0.458210i	0.973402	−	0.229105i	$-0.0735799\pi$
$702$	361.573	−	276.019i	0.515062	−	0.393189i
$703$	−512.998			−0.729727
$704$	124.435	−	215.527i	0.176754	−	0.306146i
$705$	−366.273	+	241.808i	−0.519536	+	0.342990i
$706$	245.420	+	425.080i	0.347621	+	0.602097i
$707$	6.48958	+	11.2403i	0.00917904	+	0.0158986i
$708$	−7.64152	−	127.412i	−0.0107931	−	0.179961i
$709$	−10.3769	−	5.99109i	−0.0146359	−	0.00845006i	0.492664	−	0.870220i	$-0.336023\pi$
$709$	−10.3769	−	5.99109i	−0.0146359	−	0.00845006i	−0.507300	+	0.861769i	$0.669356\pi$
$710$	304.946			0.429501
$711$	−242.808	−	323.809i	−0.341502	−	0.455427i
$712$	−1427.76			−2.00527
$713$	211.562	−	366.436i	0.296721	−	0.513936i
$714$	−4.27217	−	2.13634i	−0.00598342	−	0.00299207i
$715$	174.091	−	268.701i	0.243483	−	0.375806i
$716$	−209.881	+	121.175i	−0.293131	+	0.169239i
$717$	99.7191	+	49.8656i	0.139078	+	0.0695475i
$718$	−146.920	+	254.473i	−0.204624	+	0.354419i
$719$			366.091i			0.509167i	0.967051	+	0.254584i	$0.0819384\pi$
$719$			366.091i			0.509167i	−0.967051	+	0.254584i	$0.918062\pi$
$720$	−21.2616	+	49.7614i	−0.0295300	+	0.0691131i
$721$		−	30.5483i		−	0.0423693i
$722$	177.449	−	307.350i	0.245774	−	0.425693i
$723$	−826.804	+	49.5874i	−1.14357	+	0.0685856i
$724$	105.129	+	182.089i	0.145206	+	0.251504i
$725$	13.3741	−	7.72153i	0.0184470	−	0.0106504i
$726$	295.770	−	195.263i	0.407397	−	0.268957i
$727$	−19.9404	+	34.5377i	−0.0274283	+	0.0475072i	−0.879414	−	0.476058i	$-0.842065\pi$
$727$	−19.9404	+	34.5377i	−0.0274283	+	0.0475072i	0.851985	+	0.523565i	$0.175398\pi$
$728$	17.7520	−	9.06891i	0.0243847	−	0.0124573i
$729$	−682.418	+	256.411i	−0.936102	+	0.351730i
$730$			518.543i			0.710333i
$731$	−230.703	−	133.196i	−0.315599	−	0.182211i
$732$	−194.250	+	128.241i	−0.265369	+	0.175193i
$733$	517.367	−	298.702i	0.705821	−	0.407506i	−0.103691	−	0.994610i	$-0.533065\pi$
$733$	517.367	−	298.702i	0.705821	−	0.407506i	0.809512	+	0.587104i	$0.199732\pi$
$734$	292.923	+	507.357i	0.399077	+	0.691222i
$735$	39.6471	+	661.063i	0.0539417	+	0.899406i
$736$	−481.264	−	277.858i	−0.653892	−	0.377524i
$737$		−	460.659i		−	0.625046i
$738$	251.250	−	588.034i	0.340447	−	0.796794i
$739$			36.3743i			0.0492209i	0.999697	+	0.0246105i	$0.00783454\pi$
$739$			36.3743i			0.0492209i	−0.999697	+	0.0246105i	$0.992165\pi$
$740$	497.845	+	287.431i	0.672763	+	0.388420i
$741$	−364.075	+	3.13347i	−0.491329	+	0.00422871i
$742$	8.50983	+	14.7395i	0.0114688	+	0.0198645i
$743$	117.915	+	204.235i	0.158702	+	0.274879i	0.934401	−	0.356224i	$-0.115936\pi$
$743$	117.915	+	204.235i	0.158702	+	0.274879i	−0.775699	+	0.631103i	$0.782603\pi$
$744$	−259.720	+	519.377i	−0.349086	+	0.698088i
$745$	−175.999	+	304.839i	−0.236240	+	0.409180i
$746$	204.394			0.273987
$747$	−475.021	−	633.489i	−0.635905	−	0.848044i
$748$			83.1904i			0.111217i
$749$	−16.8929	+	29.2594i	−0.0225540	+	0.0390646i
$750$	31.1395	+	519.210i	0.0415194	+	0.692280i
$751$	−290.048	−	502.377i	−0.386215	−	0.668944i	0.605722	−	0.795677i	$-0.292884\pi$
$751$	−290.048	−	502.377i	−0.386215	−	0.668944i	−0.991937	+	0.126732i	$0.959551\pi$
$752$	−21.6390	−	37.4798i	−0.0287753	−	0.0498402i
$753$	297.217	+	450.202i	0.394710	+	0.597878i
$754$	−2.85362	+	55.5809i	−0.00378464	+	0.0737148i
$755$		−	1167.77i		−	1.54671i
$756$	−11.5399	+	2.09644i	−0.0152644	+	0.00277307i
$757$	−177.728			−0.234779			−0.117389	−	0.993086i	$-0.537453\pi$
$757$	−177.728			−0.234779			−0.117389	+	0.993086i	$0.537453\pi$
$758$	−577.867	−	333.632i	−0.762358	−	0.440148i
$759$	161.673	+	244.890i	0.213008	+	0.322649i
$760$	298.561	−	172.374i	0.392843	−	0.226808i
$761$	327.594	+	567.410i	0.430479	+	0.745611i	0.996915	−	0.0784949i	$-0.0250114\pi$
$761$	327.594	+	567.410i	0.430479	+	0.745611i	−0.566436	+	0.824106i	$0.691678\pi$
$762$	14.0431	+	234.150i	0.0184293	+	0.307283i
$763$	−14.0138	+	24.2727i	−0.0183667	+	0.0318121i
$764$			556.716i			0.728685i
$765$	−31.8258	−	264.372i	−0.0416023	−	0.345584i
$766$	231.248			0.301890
$767$	238.050	+	12.2219i	0.310365	+	0.0159346i
$768$	715.346	+	357.716i	0.931440	+	0.465776i
$769$	−500.571	+	289.005i	−0.650938	+	0.375819i	−0.788816	−	0.614630i	$-0.789305\pi$
$769$	−500.571	+	289.005i	−0.650938	+	0.375819i	0.137877	+	0.990449i	$0.455972\pi$
$770$	5.17461	−	2.98756i	0.00672027	−	0.00387995i
$771$	−420.374	+	840.648i	−0.545233

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.647986 - 1.12234i) q^{2} +(2.50362 - 1.65285i) q^{3} +(1.16023 + 2.00957i) q^{4} +(-2.25417 - 3.90433i) q^{5} +(-0.232759 - 3.88094i) q^{6} +(-0.162124 - 0.0936021i) q^{7} +8.19114 q^{8} +(3.53618 - 8.27620i) q^{9} -5.84268 q^{10} +(2.73142 - 4.73097i) q^{11} +(6.22629 + 3.11352i) q^{12} +(-7.06871 + 10.9102i) q^{13} +(-0.210108 + 0.121306i) q^{14} +(-12.0968 - 6.04915i) q^{15} +(0.666831 - 1.15499i) q^{16} +6.56267i q^{17} +(-6.99735 - 9.33167i) q^{18} +9.33560i q^{19} +(5.23069 - 9.05983i) q^{20} +(-0.560605 + 0.0336222i) q^{21} +(-3.53985 - 6.13120i) q^{22} +(-15.5066 + 8.95272i) q^{23} +(20.5075 - 13.5387i) q^{24} +(2.33746 - 4.04860i) q^{25} +(7.66463 + 15.0032i) q^{26} +(-4.82607 - 26.5652i) q^{27} -0.434399i q^{28} +(2.86081 + 1.65169i) q^{29} +(-14.6278 + 9.65706i) q^{30} +(-20.4651 + 11.8155i) q^{31} +(15.5181 + 26.8781i) q^{32} +(-0.981137 - 16.3592i) q^{33} +(7.36558 + 4.25252i) q^{34} +0.843979i q^{35} +(20.7344 - 2.49606i) q^{36} +54.9508i q^{37} +(10.4778 + 6.04934i) q^{38} +(0.335648 + 38.9986i) q^{39} +(-18.4642 - 31.9809i) q^{40} +(27.4123 + 47.4795i) q^{41} +(-0.325529 + 0.650979i) q^{42} +(-20.2961 + 35.1538i) q^{43} +12.6763 q^{44} +(-40.2842 + 4.84951i) q^{45} +23.2050i q^{46} +(16.2252 - 28.1029i) q^{47} +(-0.239528 - 3.99381i) q^{48} +(-24.4825 - 42.4049i) q^{49} +(-3.02929 - 5.24688i) q^{50} +(10.8471 + 16.4304i) q^{51} +(-30.1262 - 1.54673i) q^{52} -70.1519i q^{53} +(-32.9425 - 11.7974i) q^{54} -24.6283 q^{55} +(-1.32798 - 0.766708i) q^{56} +(15.4303 + 23.3727i) q^{57} +(3.70753 - 2.14054i) q^{58} +(-9.16783 - 15.8791i) q^{59} +(-1.87888 - 31.3279i) q^{60} +(-16.7182 + 28.9569i) q^{61} +30.6252i q^{62} +(-1.34797 + 1.01077i) q^{63} +45.5566 q^{64} +(58.5312 + 3.00509i) q^{65} +(-18.9964 - 9.49933i) q^{66} +(73.0282 - 42.1629i) q^{67} +(-13.1882 + 7.61420i) q^{68} +(-24.0250 + 48.0442i) q^{69} +(0.947236 + 0.546887i) q^{70} -52.1928 q^{71} +(28.9653 - 67.7915i) q^{72} -88.7509i q^{73} +(61.6737 + 35.6073i) q^{74} +(-0.839625 - 13.9996i) q^{75} +(-18.7606 + 10.8314i) q^{76} +(-0.885657 + 0.511334i) q^{77} +(43.9873 + 24.8938i) q^{78} +(22.4851 - 38.9453i) q^{79} -6.01260 q^{80} +(-55.9909 - 58.5322i) q^{81} +71.0512 q^{82} +(43.9891 - 76.1913i) q^{83} +(-0.717996 - 1.08757i) q^{84} +(25.6229 - 14.7934i) q^{85} +(26.3031 + 45.5584i) q^{86} +(9.89236 - 0.593292i) q^{87} +(22.3735 - 38.7520i) q^{88} -174.305 q^{89} +(-20.6608 + 48.3551i) q^{90} +(2.16723 - 1.10716i) q^{91} +(-35.9823 - 20.7744i) q^{92} +(-31.7074 + 63.4072i) q^{93} +(-21.0275 - 36.4206i) q^{94} +(36.4493 - 21.0440i) q^{95} +(83.2767 + 41.6434i) q^{96} +(7.09093 + 4.09395i) q^{97} -63.4572 q^{98} +(-29.4956 - 39.3354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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