LMFDB - Embedded newform 117.3.n.a.38.9

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			38.9
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.9

$q$-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} +(12.9829 - 0.666563i) 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} +(31.4025 - 23.1276i) 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} +(16.4026 + 25.3167i) 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} +(31.8681 + 49.1870i) 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} +(5.60878 + 50.2308i) 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	−0.981308	−	0.192443i	$-0.938359\pi$
$2$	−0.647986	+	1.12234i	−0.323993	+	0.561172i	0.657315	+	0.753616i	$0.271692\pi$
$3$	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	0.998438	−	0.0558709i	$-0.0177935\pi$
$5$	2.25417	+	3.90433i	0.450833	+	0.780866i	−0.547605	+	0.836737i	$0.684460\pi$
$6$	0.232759	+	3.88094i	0.0387931	+	0.646824i
$7$	0.162124	+	0.0936021i	0.0231605	+	0.0133717i	0.511536	−	0.859262i	$-0.329077\pi$
$7$	0.162124	+	0.0936021i	0.0231605	+	0.0133717i	−0.488375	+	0.872634i	$0.662410\pi$
$8$	−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	−0.963057	−	0.269296i	$-0.913209\pi$
$11$	−2.73142	+	4.73097i	−0.248311	+	0.430088i	0.714746	+	0.699384i	$0.246542\pi$
$12$	6.22629	+	3.11352i	0.518857	+	0.259460i
$13$	12.9829	−	0.666563i	0.998685	−	0.0512741i
$13$	12.9829	−	0.666563i	0.998685	−	0.0512741i
$14$	−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	$-0.920991\pi$
$19$		−	9.33560i		−	0.491347i	0.969353	−	0.245674i	$-0.0790092\pi$
$20$	−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	−0.132175	−	0.991226i	$-0.542196\pi$
$31$	20.4651	−	11.8155i	0.660164	−	0.381146i	0.792339	+	0.610080i	$0.208863\pi$
$32$	−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	$-0.733603\pi$
$37$		−	54.9508i		−	1.48516i	0.669760	−	0.742578i	$-0.266397\pi$
$38$	10.4778	+	6.04934i	0.275731	+	0.159193i
$39$	31.4025	−	23.1276i	0.805191	−	0.593015i
$40$	−18.4642	−	31.9809i	−0.461605	−	0.799523i
$41$	−27.4123	−	47.4795i	−0.668593	−	1.15804i	−0.978298	−	0.207205i	$-0.933563\pi$
$41$	−27.4123	−	47.4795i	−0.668593	−	1.15804i	0.309704	−	0.950833i	$-0.399770\pi$
$42$	−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	−0.985393	−	0.170294i	$-0.945528\pi$
$47$	−16.2252	+	28.1029i	−0.345218	+	0.597935i	0.640176	+	0.768229i	$0.278862\pi$
$48$	−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
$52$	16.4026	+	25.3167i	0.315435	+	0.486860i
$53$		−	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	0.933200	−	0.359358i	$-0.117004\pi$
$59$	9.16783	+	15.8791i	0.155387	+	0.269138i	−0.777813	+	0.628496i	$0.783671\pi$
$60$	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
$65$	31.8681	+	49.1870i	0.490279	+	0.756723i
$66$	−18.9964	−	9.49933i	−0.287824	−	0.143929i
$67$	−73.0282	+	42.1629i	−1.08997	+	0.629297i	−0.933569	−	0.358396i	$-0.883324\pi$
$67$	−73.0282	+	42.1629i	−1.08997	+	0.629297i	−0.156404	+	0.987693i	$0.549990\pi$
$68$	−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	$-0.380195\pi$
$71$	52.1928			0.735110			0.367555	+	0.930002i	$0.380195\pi$
$72$	−28.9653	+	67.7915i	−0.402296	+	0.941548i
$73$			88.7509i			1.21577i	0.794026	+	0.607883i	$0.207981\pi$
$73$			88.7509i			1.21577i	−0.794026	+	0.607883i	$0.792019\pi$
$74$	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
$78$	5.60878	+	50.2308i	0.0719074	+	0.643984i
$79$	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	$0.344471\pi$
$83$	−43.9891	+	76.1913i	−0.529989	+	0.917968i	−0.999388	+	0.0349817i	$0.988863\pi$
$84$	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	$-0.0649711\pi$
$89$	174.305			1.95848			0.979241	+	0.202698i	$0.0649711\pi$
$90$	−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	0.463003	−	0.886357i	$-0.346772\pi$
$97$	−7.09093	−	4.09395i	−0.0731024	−	0.0422057i	−0.536106	+	0.844151i	$0.680105\pi$
$98$	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	$0.542299\pi$
$104$	−106.345	+	5.45991i	−1.02255	+	0.0524991i
$105$	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	$0.240974\pi$
$109$			149.717i			1.37355i	−0.726870	+	0.686775i	$0.759026\pi$
$110$	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
$117$	40.3933	−	109.806i	0.345242	−	0.938514i
$118$	−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
$130$	−75.8549	+	3.89451i	−0.583499	+	0.0299578i
$131$	−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	−0.993942	−	0.109910i	$-0.964944\pi$
$137$	−55.0447	+	95.3402i	−0.401786	+	0.695914i	0.592155	+	0.805824i	$0.298277\pi$
$138$	−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	0.966774	−	0.255631i	$-0.0822833\pi$
$149$	39.0386	+	67.6168i	0.262004	+	0.453804i	−0.704770	+	0.709436i	$0.748950\pi$
$150$	16.2565	+	8.12921i	0.108376	+	0.0541948i
$151$	−224.322	−	129.512i	−1.48557	−	0.857696i	−0.485708	−	0.874121i	$-0.661438\pi$
$151$	−224.322	−	129.512i	−1.48557	−	0.857696i	−0.999865	+	0.0164251i	$0.994772\pi$
$152$			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
$156$	82.9106	+	36.2723i	0.531478	+	0.232515i
$157$	−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	$-0.956029\pi$
$163$		−	44.8906i		−	0.275402i	0.990474	−	0.137701i	$-0.0439714\pi$
$164$	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	0.674285	−	0.738471i	$-0.264452\pi$
$167$	−50.4995	−	87.4677i	−0.302392	−	0.523759i	−0.976677	+	0.214712i	$0.931119\pi$
$168$	−4.59200	+	0.275404i	−0.0273333	+	0.00163931i
$169$	168.111	−	17.3078i	0.994742	−	0.102413i
$170$		−	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	$0.419469\pi$
$182$	−2.64695	+	1.71495i	−0.0145437	+	0.00942281i
$183$	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	$0.711259\pi$
$193$	−310.002	+	178.980i	−1.60623	+	0.927357i	−0.990203	+	0.139632i	$0.955408\pi$
$194$	9.18965	−	5.30564i	0.0473693	−	0.0273487i
$195$	161.084	+	70.4722i	0.826073	+	0.361396i
$196$	56.8105	−	98.3987i	0.289850	−	0.502034i
$197$	41.0547			0.208399			0.104200	−	0.994556i	$-0.466772\pi$
$197$	41.0547			0.208399			0.104200	+	0.994556i	$0.466772\pi$
$198$	−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
$221$	4.37444	+	85.2025i	0.0197938	+	0.385532i
$222$	213.261	−	12.7903i	0.960634	−	0.0576139i
$223$	−250.650	−	144.713i	−1.12399	−	0.648936i	−0.181574	−	0.983377i	$-0.558119\pi$
$223$	−250.650	−	144.713i	−1.12399	−	0.648936i	−0.942417	+	0.334441i	$0.891452\pi$
$224$		−	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	$0.401935\pi$
$227$	−152.915	+	264.857i	−0.673636	+	1.16677i	−0.976866	+	0.213854i	$0.931398\pi$
$228$	29.0666	−	58.1261i	0.127485	−	0.254939i
$229$	240.075	−	138.607i	1.04836	−	0.605273i	0.126172	−	0.992008i	$-0.459731\pi$
$229$	240.075	−	138.607i	1.04836	−	0.605273i	0.922191	+	0.386736i	$0.126397\pi$
$230$	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	$0.856487\pi$
$234$	97.0661	+	116.488i	0.414812	+	0.497812i
$235$	−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	0.824529	−	0.565819i	$-0.191440\pi$
$239$	−18.5820	−	32.1850i	−0.0777490	−	0.134665i	−0.902278	+	0.431154i	$0.858107\pi$
$240$	15.0532	−	9.93791i	0.0627218	−	0.0414080i
$241$	239.107	+	138.048i	0.992144	+	0.572814i	0.905914	−	0.423461i	$-0.139185\pi$
$241$	239.107	+	138.048i	0.992144	+	0.572814i	0.0862292	+	0.996275i	$0.472518\pi$
$242$	−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
$247$	−6.22277	−	121.203i	−0.0251934	−	0.490701i
$248$	−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	$-0.861083\pi$
$271$		−	229.102i		−	0.845396i	0.906270	−	0.422698i	$-0.138917\pi$
$272$	7.57979	+	4.37620i	0.0278669	+	0.0160890i
$273$	7.25587	−	0.810193i	0.0265783	−	0.00296774i
$274$	−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	−0.639238	−	0.769009i	$-0.720750\pi$
$281$	97.3277	−	168.576i	0.346362	−	0.599916i	0.985600	+	0.169092i	$0.0540836\pi$
$282$	−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
$286$	−50.0444	−	77.2412i	−0.174980	−	0.270074i
$287$		−	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	0.589965	−	0.807429i	$-0.299142\pi$
$293$	−118.452	−	205.164i	−0.404272	−	0.700219i	−0.994236	+	0.107210i	$0.965808\pi$
$294$	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
$299$	−195.353	+	126.568i	−0.653353	+	0.423306i
$300$	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	$-0.867063\pi$
$307$		−	249.037i		−	0.811195i	0.914052	−	0.405598i	$-0.132937\pi$
$308$	−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	$0.409419\pi$
$312$	−257.222	+	189.441i	−0.824429	+	0.607184i
$313$	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	−0.832644	−	0.553808i	$-0.813174\pi$
$317$	20.0628	−	34.7498i	0.0632896	−	0.109621i	0.895934	+	0.444187i	$0.146508\pi$
$318$	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	0.484620	−	0.874725i	$-0.338958\pi$
$331$	−10.1298	−	5.84845i	−0.0306037	−	0.0176690i	−0.515224	+	0.857056i	$0.672291\pi$
$332$	−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	$-0.337748\pi$
$338$	−89.5085	+	199.894i	−0.264818	+	0.591403i
$339$	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	0.997714	−	0.0675725i	$-0.0215254\pi$
$349$	501.880	+	289.761i	1.43805	+	0.830260i	0.440338	+	0.897832i	$0.354859\pi$
$350$			1.13419i			0.00324055i
$351$	−80.3638	−	341.676i	−0.228957	−	0.973437i
$352$	169.546			0.481664
$353$	189.372	−	328.001i	0.536463	−	0.929182i	−0.462628	−	0.886553i	$-0.653093\pi$
$353$	189.372	−	328.001i	0.536463	−	0.929182i	0.999091	−	0.0426291i	$-0.0135734\pi$
$354$	−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	$-0.397732\pi$
$359$	226.733			0.631569			0.315784	+	0.948831i	$0.397732\pi$
$360$	−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
$364$	0.289555	+	5.63976i	0.000795480	+	0.0154939i
$365$	−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	$0.237697\pi$
$379$			514.875i			1.35851i	−0.733903	+	0.679255i	$0.762303\pi$
$380$	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	0.725728	−	0.687981i	$-0.241503\pi$
$383$	−89.2179	−	154.530i	−0.232945	−	0.403473i	−0.958673	+	0.284509i	$0.908170\pi$
$384$	−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	$0.950440\pi$
$390$	−183.474	+	135.127i	−0.470447	+	0.346480i
$391$	−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	$0.223050\pi$
$397$			511.953i			1.28955i	−0.764371	+	0.644777i	$0.776950\pi$
$398$	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	0.903705	−	0.428155i	$-0.140836\pi$
$401$	32.5050	+	56.3003i	0.0810599	+	0.140400i	−0.822646	+	0.568555i	$0.807503\pi$
$402$	−180.630	−	273.605i	−0.449328	−	0.680609i
$403$	257.820	−	167.041i	0.639753	−	0.414494i
$404$		−	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	−0.762577	−	0.646898i	$-0.776066\pi$
$409$	−238.707	+	137.817i	−0.583635	+	0.336962i	0.178942	+	0.983860i	$0.442733\pi$
$410$	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
$416$	−219.386	−	338.612i	−0.527369	−	0.813971i
$417$	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	0.639652	−	0.768665i	$-0.279078\pi$
$421$	123.688	+	71.4111i	0.293795	+	0.169623i	−0.345857	+	0.938287i	$0.612412\pi$
$422$	−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
$429$	23.6424	+	211.735i	0.0551105	+	0.493555i
$430$	118.583	−	205.392i	0.275775	−	0.477657i
$431$	−234.681			−0.544504			−0.272252	−	0.962226i	$-0.587768\pi$
$431$	−234.681			−0.544504			−0.272252	+	0.962226i	$0.587768\pi$
$432$	−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	$-0.528687\pi$
$449$	−80.8219			−0.180004			−0.0900021	+	0.995942i	$0.528687\pi$
$450$	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
$455$	0.562566	+	10.9573i	0.00123641	+	0.0240820i
$456$	126.392	+	191.449i	0.277175	+	0.419845i
$457$	−213.732	−	123.398i	−0.467686	−	0.270019i	0.247585	−	0.968866i	$-0.420363\pi$
$457$	−213.732	−	123.398i	−0.467686	−	0.270019i	−0.715270	+	0.698848i	$0.753697\pi$
$458$			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	$-0.640746\pi$
$461$	262.211	−	454.162i	0.568787	−	0.985167i	0.996686	−	0.0813410i	$-0.0259203\pi$
$462$	−2.19060	−	3.31817i	−0.00474157	−	0.00718218i
$463$	−43.9680	+	25.3849i	−0.0949632	+	0.0548270i	−0.546730	−	0.837309i	$-0.684127\pi$
$463$	−43.9680	+	25.3849i	−0.0949632	+	0.0548270i	0.451766	+	0.892136i	$0.350794\pi$
$464$	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	$0.965301\pi$
$468$	267.529	−	46.2269i	0.571643	−	0.0987754i
$469$	−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	−0.884802	−	0.465967i	$-0.845707\pi$
$479$	−18.6148	+	32.2418i	−0.0388618	+	0.0673106i	0.845940	+	0.533278i	$0.179040\pi$
$480$	−25.1301	−	419.011i	−0.0523544	−	0.872940i
$481$	−36.6282	−	713.420i	−0.0761500	−	1.48320i
$482$	−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	$-0.812797\pi$
$487$		−	540.371i		−	1.10959i	0.831987	−	0.554795i	$-0.187203\pi$
$488$	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	−0.789193	−	0.614145i	$-0.789501\pi$
$499$	−325.310	+	187.818i	−0.651924	+	0.376389i	0.137269	+	0.990534i	$0.456168\pi$
$500$	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
$507$	392.279	−	321.195i	0.773726	−	0.633521i
$508$	−70.0003	−	121.244i	−0.137796	−	0.238670i
$509$	−365.564	−	633.175i	−0.718200	−	1.24396i	−0.961712	−	0.274061i	$-0.911633\pi$
$509$	−365.564	−	633.175i	−0.718200	−	1.24396i	0.243513	−	0.969898i	$-0.421700\pi$
$510$	−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
$520$	−261.036	−	402.897i	−0.501992	−	0.774803i
$521$			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
$533$	−387.540	−	598.150i	−0.727091	−	1.12223i
$534$	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	$0.0591372\pi$
$541$			199.865i			0.369436i	−0.982792	+	0.184718i	$0.940863\pi$
$542$	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
$546$	−3.79239	+	8.66859i	−0.00694577	+	0.0158765i
$547$	−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	$-0.649676\pi$
$557$	−504.734			−0.906165			−0.453083	+	0.891469i	$0.649676\pi$
$558$	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	$0.780488\pi$
$572$	−164.575	+	8.44956i	−0.287719	+	0.0147720i
$573$	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	$-0.814991\pi$
$577$		−	633.598i		−	1.09809i	0.835792	−	0.549045i	$-0.185009\pi$
$578$	−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
$585$	519.773	−	89.8127i	0.888500	−	0.153526i
$586$	307.020			0.523925
$587$	−525.602	+	910.370i	−0.895404	+	1.55089i	−0.0621006	+	0.998070i	$0.519780\pi$
$587$	−525.602	+	910.370i	−0.895404	+	1.55089i	−0.833304	+	0.552816i	$0.813553\pi$
$588$	−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	$-0.698618\pi$
$593$	−692.941			−1.16853			−0.584267	+	0.811562i	$0.698618\pi$
$594$	−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
$598$	−15.4676	−	301.268i	−0.0258655	−	0.503792i
$599$	−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	$0.450255\pi$
$613$			1211.06i			1.97563i	−0.155644	+	0.987813i	$0.549745\pi$
$614$	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	0.827261	−	0.561818i	$-0.189898\pi$
$617$	−44.9906	−	77.9259i	−0.0729182	−	0.126298i	−0.900179	+	0.435520i	$0.856565\pi$
$618$	−529.461	+	349.542i	−0.856734	+	0.565603i
$619$	467.089	+	269.674i	0.754586	+	0.435661i	0.827349	−	0.561689i	$-0.189848\pi$
$619$	467.089	+	269.674i	0.754586	+	0.435661i	−0.0727624	+	0.997349i	$0.523181\pi$
$620$			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
$624$	−5.77190	−	51.6916i	−0.00924983	−	0.0828391i
$625$	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	$-0.678839\pi$
$631$		−	1068.00i		−	1.69255i	0.532744	−	0.846276i	$-0.321161\pi$
$632$	−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
$637$	−346.119	−	534.219i	−0.543358	−	0.838649i
$638$		−	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	0.245541	−	0.969386i	$-0.421034\pi$
$643$	776.631	−	448.388i	1.20782	−	0.697338i	0.962284	+	0.272048i	$0.0877011\pi$
$644$	−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
$650$	42.8263	+	66.1005i	0.0658866	+	0.101693i
$651$	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	−0.647338	−	0.762203i	$-0.724118\pi$
$661$	−205.518	+	118.656i	−0.310919	+	0.179509i	0.336418	+	0.941713i	$0.390784\pi$
$662$	13.1280	−	7.57943i	0.0198308	−	0.0114493i
$663$	151.779	+	206.084i	0.228927	+	0.310836i
$664$	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	$-0.327716\pi$
$683$	703.770			1.03041			0.515205	+	0.857067i	$0.327716\pi$
$684$	−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
$689$	−46.7607	−	910.775i	−0.0678674	−	1.32188i
$690$	140.370	−	280.707i	0.203435	−	0.406821i
$691$	−267.940	−	154.695i	−0.387757	−	0.223872i	0.293431	−	0.955980i	$-0.405203\pi$
$691$	−267.940	−	154.695i	−0.387757	−	0.223872i	−0.681188	+	0.732109i	$0.738536\pi$
$692$		−	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	$-0.0735799\pi$
$702$	435.553	+	131.206i	0.620446	+	0.186903i
$703$	−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	0.507300	−	0.861769i	$-0.330644\pi$
$709$	10.3769	+	5.99109i	0.0146359	+	0.00845006i	−0.492664	+	0.870220i	$0.663977\pi$
$710$	−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
$715$	−319.747	+	16.4164i	−0.447199	+	0.0229599i
$716$	−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	−0.809512	−	0.587104i	$-0.800268\pi$
$733$	−517.367	+	298.702i	−0.705821	+	0.407506i	0.103691	+	0.994610i	$0.466935\pi$
$734$	−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	$-0.992165\pi$
$739$		−	36.3743i		−	0.0492209i	0.999697	−	0.0246105i	$-0.00783454\pi$
$740$	497.845	+	287.431i	0.672763	+	0.388420i
$741$	−215.910	−	293.161i	−0.291376	−	0.395629i
$742$	8.50983	+	14.7395i	0.0114688	+	0.0198645i
$743$	−117.915	−	204.235i	−0.158702	−	0.274879i	0.775699	−	0.631103i	$-0.217397\pi$
$743$	−117.915	−	204.235i	−0.158702	−	0.274879i	−0.934401	+	0.356224i	$0.884064\pi$
$744$	−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
$754$	−46.7077	+	30.2618i	−0.0619465	+	0.0401350i
$755$		−	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	0.566436	−	0.824106i	$-0.308322\pi$
$761$	−327.594	−	567.410i	−0.430479	−	0.745611i	−0.996915	+	0.0784949i	$0.974989\pi$
$762$	−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
$767$	129.609	+	200.046i	0.168982	+	0.260817i
$768$	715.346	+	357.716i	0.931440	+	0.465776i
$769$	500.571	−	289.005i	0.650938	−	0.375819i	−0.137877	−	0.990449i	$-0.544028\pi$
$769$	500.571	−	289.005i	0.650938	−	0.375819i	0.788816	+	0.614630i	$0.210695\pi$
$770$	5.17461	−	2.98756i	0.00672027	−	0.00387995i
$771$	−420.374	+	840.648i	−0.545233	+	1.09033i
$772$	−719.347	−	415.315i	−0.931796	−	0.537973i
$773$	1155.12			1.49433			0.747166	−	0.664638i	$-0.231414\pi$
$773$	1155.12			1.49433			0.747166	+	0.664638i	$0.231414\pi$
$774$	−470.063	+	56.5874i	−0.607316	+	0.0731103i
$775$		−	110.473i		−	0.142546i
$776$	58.0828	+	33.5341i	0.0748489	+	0.0432140i
$777$	−1.84757	−	30.8057i	−0.00237782	−	0.0396470i
$778$	679.350	−	392.223i	0.873200	−	0.504142i
$779$	−443.250	+	255.910i	−0.568999	+	0.328512i
$780$	45.2754	+	405.474i	0.0580453	+	0.519839i
$781$	−142.561	+	246.923i	−0.182536	+	0.316162i
$782$	152.287			0.194740
$783$	30.0710	−	83.9691i	0.0384048	−	0.107240i
$784$	−65.3027			−0.0832943
$785$	307.525	−	532.649i	0.391751	−	0.678533i
$786$	−417.973	−	633.115i	−0.531772	−	0.805490i
$787$	−1117.20	+	645.018i	−1.41957	+	0.819591i	−0.996261	−	0.0863928i	$-0.972466\pi$
$787$	−1117.20	+	645.018i	−1.41957	+	0.819591i	−0.423312	+	0.905984i	$0.639133\pi$
$788$	47.6328	+	82.5024i	0.0604477	+	0.104699i
$789$	150.807	−	9.04464i	0.191137	−	0.0114634i
$790$	−131.373	+	227.545i	−0.166295	+	0.288032i
$791$	11.5967			0.0146608
$792$	−241.602	−	322.201i	−0.305054	−	0.406820i
$793$	−197.750	+	387.088i	−0.249369	+	0.488131i
$794$	−574.588	−	331.739i	−0.723662	−	0.417807i
$795$	424.359	−	848.616i	0.533785	−	1.06744i
$796$	−167.540	−	290.187i	−0.210477	−	0.364557i
$797$	725.010	−	418.585i	0.909674	−	0.525200i	0.0293476	−	0.999569i	$-0.490657\pi$
$797$	725.010	−	418.585i	0.909674	−	0.525200i	0.880326	+	0.474369i	$0.157324\pi$
$798$	6.07728	+	3.03901i	0.00761564	+	0.00380828i
$799$	−184.430	−	106.481i	−0.230826	−	0.133268i
$800$	−145.092			−0.181365
$801$	616.374	−	1442.58i	0.769505	−	1.80098i
$802$	−84.2512			−0.105051
$803$	−419.878	−	242.417i	−0.522886	−	0.301889i
$804$	−585.970	+	35.1434i	−0.728818	+	0.0437107i
$805$	−7.55591	−	13.0872i	−0.00938622	−	0.0162574i
$806$	20.4136	+	397.604i	0.0253271	+	0.493305i
$807$	−828.907	−	1255.57i	−1.02715	−	1.55585i
$808$	491.820	+	283.952i	0.608688	+	0.351426i
$809$			93.7927i			0.115937i	0.998318	+	0.0579683i	$0.0184622\pi$
$809$			93.7927i			0.115937i	−0.998318	+	0.0579683i	$0.981538\pi$
$810$	327.137	+	341.985i	0.403872	+	0.422204i
$811$		−	551.690i		−	0.680259i	−0.940379	−	0.340130i	$-0.889529\pi$
$811$		−	551.690i		−	0.680259i	0.940379	−	0.340130i	$-0.110471\pi$
$812$	−0.717493	+	1.24273i	−0.000883611	+	0.00153046i
$813$	−378.672	−	573.584i	−0.465771	−	0.705516i
$814$	−336.914	+	194.518i	−0.413900	+	0.238965i
$815$	175.268	−	101.191i	0.215053	−	0.124161i
$816$	26.2101	−	1.57194i	0.0321202	−	0.00192640i
$817$	328.182	+	189.476i	0.401691	+	0.231917i
$818$		−	357.215i		−	0.436693i
$819$	16.8268	−	14.0213i	0.0205455	−	0.0171200i
$820$	573.542			0.699441
$821$	306.896	−	531.559i	0.373807	−	0.647454i	−0.616340	−	0.787480i	$-0.711385\pi$
$821$	306.896	−	531.559i	0.373807	−	0.647454i	0.990148	+	0.140026i	$0.0447187\pi$
$822$	−382.822	−	191.434i	−0.465720	−	0.232888i
$823$	378.480	+	655.547i	0.459879	+	0.796534i	0.998954	−	0.0457239i	$-0.0145594\pi$
$823$	378.480	+	655.547i	0.459879	+	0.796534i	−0.539075	+	0.842258i	$0.681226\pi$
$824$	−668.321	−	1157.57i	−0.811069	−	1.40481i
$825$	68.5251	+	34.2667i	0.0830607	+	0.0415354i
$826$	−3.85246	−	2.22422i	−0.00466400	−	0.00269276i
$827$	884.560			1.06960			0.534800	−	0.844979i	$-0.320387\pi$
$827$	884.560			1.06960			0.534800	+	0.844979i	$0.320387\pi$
$828$	−299.173	+	224.335i	−0.361320	+	0.270936i
$829$	1282.82			1.54743			0.773716	−	0.633532i	$-0.218396\pi$
$829$	1282.82			1.54743			0.773716	+	0.633532i	$0.218396\pi$
$830$	257.014	−	445.161i	0.309655	−	0.536339i
$831$	71.4395	+	1191.16i	0.0859682	+	1.43340i
$832$	591.457	−	30.3664i	0.710886	−	0.0364981i
$833$	278.289	−	160.670i	0.334081	−	0.192882i
$834$	−714.654	+	471.804i	−0.856899	+	0.565712i
$835$	227.669	−	394.334i	0.272657	−	0.472256i
$836$			118.341i			0.141556i
$837$	−412.647	−	486.636i	−0.493008	−	0.581405i
$838$			606.896i			0.724219i
$839$	555.459	−	962.083i	0.662049	−	1.14670i	−0.318028	−	0.948081i	$-0.603020\pi$
$839$	555.459	−	962.083i	0.662049	−	1.14670i	0.980076	−	0.198621i	$-0.0636462\pi$
$840$	−11.4264	−	17.3079i	−0.0136028	−	0.0206046i
$841$	−415.044	−	718.877i	−0.493512	−	0.854788i
$842$	−160.296	+	92.5469i	−0.190375	+	0.109913i
$843$	−34.9604	−	582.919i	−0.0414714	−	0.691481i
$844$	−19.2236	+	33.2963i	−0.0227768	+	0.0394506i
$845$	446.527	+	617.348i	0.528434	+	0.730589i
$846$	−375.781	+	45.2375i	−0.444186	+	0.0534722i
$847$			17.0650i			0.0201476i
$848$	−81.0244	−	46.7795i	−0.0955477	−	0.0551645i
$849$	−1116.35	−	558.240i	−1.31490	−	0.657527i
$850$	−34.4336	+	19.8802i	−0.0405101	+	0.0233885i
$851$	491.959	+	852.098i	0.578095	+	1.00129i
$852$	324.968	+	162.503i	0.381417	+	0.190732i
$853$	735.083	+	424.401i	0.861762	+	0.497539i	0.864602	−	0.502457i	$-0.167571\pi$
$853$	735.083	+	424.401i	0.861762	+	0.497539i	−0.00283972	+	0.999996i	$0.500904\pi$
$854$		−	8.11208i		−	0.00949892i
$855$	−45.2731	−	376.077i	−0.0529510	−	0.439856i
$856$			1478.30i			1.72699i
$857$	56.1270	+	32.4049i	0.0654924	+	0.0378120i	0.532389	−	0.846500i	$-0.321295\pi$
$857$	56.1270	+	32.4049i	0.0654924	+	0.0378120i	−0.466896	+	0.884312i	$0.654628\pi$
$858$	−252.960	−	110.667i	−0.294825	−	0.128982i
$859$	−431.846	−	747.980i	−0.502732	−	0.870757i	−0.999995	−	0.00315695i	$-0.998995\pi$
$859$	−431.846	−	747.980i	−0.502732	−	0.870757i	0.497264	−	0.867600i	$-0.334338\pi$
$860$	−212.325	−	367.758i	−0.246890	−	0.427625i
$861$	−16.9639	−	25.6956i	−0.0197025	−	0.0298439i
$862$	152.070	−	263.393i	0.176415	−	0.305561i
$863$	1287.21			1.49155			0.745776	−	0.666197i	$-0.232079\pi$
$863$	1287.21			1.49155			0.745776	+	0.666197i	$0.232079\pi$
$864$	−639.130	+	541.956i	−0.739734	+	0.627264i
$865$		−	79.2449i		−	0.0916126i
$866$	10.0454	−	17.3992i	0.0115998	−	0.0200914i
$867$	615.717	−	406.487i	0.710170	−	0.468844i
$868$	5.13265	+	8.89002i	0.00591320	+	0.0102420i
$869$	122.833	+	212.753i	0.141350	+	0.244825i
$870$	−57.7979	+	3.46641i	−0.0664343	+	0.00398438i
$871$	−920.014	+	596.074i	−1.05627	+	0.684356i
$872$		−	1226.35i		−	1.40637i
$873$	−58.9571	+	44.2090i	−0.0675339	+	0.0506403i
$874$	−216.632			−0.247863
$875$	21.6896	+	12.5225i	0.0247881	+	0.0143114i
$876$	−276.328	+	552.589i	−0.315443	+	0.630809i
$877$	−713.137	+	411.730i	−0.813155	+	0.469475i	−0.848050	−	0.529916i	$-0.822224\pi$
$877$	−713.137	+	411.730i	−0.813155	+	0.469475i	0.0348953	+	0.999391i	$0.488890\pi$
$878$	406.772	+	704.549i	0.463294	+	0.802448i
$879$	−635.663	−	317.870i	−0.723166	−	0.361627i
$880$	−16.4230	+	28.4454i	−0.0186624	+	0.0323243i
$881$		−	436.907i		−	0.495922i	−0.968770	−	0.247961i	$-0.920240\pi$
$881$		−	436.907i		−	0.495922i	0.968770	−	0.247961i	$-0.0797604\pi$
$882$	224.396	−	525.184i	0.254417	−	0.595447i
$883$	1620.87			1.83564			0.917819	−	0.397000i	$-0.129949\pi$
$883$	1620.87			1.83564			0.917819	+	0.397000i	$0.129949\pi$
$884$	−166.145	+	107.645i	−0.187947	+	0.121770i
$885$	14.8465	+	247.545i	0.0167757	+	0.279712i
$886$	−642.499	+	370.947i	−0.725168	+	0.418676i
$887$	−344.471	+	198.880i	−0.388355	+	0.224217i	−0.681447	−	0.731867i	$-0.738649\pi$
$887$	−344.471	+	198.880i	−0.388355	+	0.224217i	0.293092	+	0.956084i	$0.405316\pi$
$888$	743.963	+	1126.90i	0.837796	+	1.26903i
$889$	−9.78145	−	5.64732i	−0.0110028	−	0.00635244i
$890$	−1018.41			−1.14428
$891$	429.849	−	105.015i	0.482434	−	0.117861i
$892$		−	671.599i		−	0.752914i
$893$	262.358	+	151.472i	0.293794	+	0.169622i
$894$	−253.331	+	167.245i	−0.283367	+	0.187075i
$895$	−407.771	+	235.427i	−0.455611	+	0.263047i
$896$	10.5550	−	6.09392i	0.0117801	−	0.00680125i
$897$	−279.889	+	639.767i	−0.312028	+	0.713230i
$898$	52.3715	−	90.7101i	0.0583201	−	0.101013i
$899$	78.0623			0.0868324
$900$	38.3603	−	89.7798i	0.0426226	−	0.0997554i
$901$	460.384			0.510970
$902$	−194.071	+	336.141i	−0.215156	+	0.372662i
$903$	−10.1961	+	20.3898i	−0.0112914	+	0.0225801i
$904$	−439.434	+	253.707i	−0.486099	+	0.280650i
$905$	204.252	+	353.774i	0.225692	+	0.390911i
$906$	450.416	−	900.724i	0.497148	−	0.994177i
$907$	−213.237	+	369.338i	−0.235102	+	0.407208i	−0.959302	−	0.282381i	$-0.908876\pi$
$907$	−213.237	+	369.338i	−0.235102	+	0.407208i	0.724201	+	0.689589i	$0.242209\pi$
$908$	−709.666			−0.781571
$909$	−499.223	+	374.342i	−0.549201	+	0.411818i
$910$	−12.6624	−	6.46879i	−0.0139147	−	0.00710856i
$911$	110.172	+	63.6081i	0.120936	+	0.0698223i	0.559248	−	0.829001i	$-0.311090\pi$
$911$	110.172	+	63.6081i	0.120936	+	0.0698223i	−0.438312	+	0.898823i	$0.644423\pi$
$912$	−37.2846	+	2.23614i	−0.0408823	+	0.00245191i
$913$	−240.306	−	416.222i	−0.263205	−	0.455884i
$914$	276.991	−	159.921i	0.303054	−	0.174968i
$915$	−377.402	+	249.155i	−0.412461	+	0.272301i
$916$	557.084	+	321.632i	0.608170	+	0.351127i
$917$	−36.5288			−0.0398351
$918$	−77.4222	+	216.191i	−0.0843379	+	0.235502i
$919$	1263.38			1.37474			0.687368	−	0.726309i	$-0.258766\pi$
$919$	1263.38			1.37474			0.687368	+	0.726309i	$0.258766\pi$
$920$	572.632	+	330.609i	0.622426	+	0.359358i
$921$	−411.620	−	623.493i	−0.446928	−	0.676973i
$922$	339.818	+	588.581i	0.368566	+	0.638375i
$923$	677.614	−	34.7898i	0.734143	−	0.0376921i
$924$	−7.10640	+	0.426205i	−0.00769091	+	0.000461261i
$925$	−222.474	−	128.445i	−0.240512	−	0.138860i
$926$		−	65.7963i		−	0.0710543i
$927$	1458.11	−	175.531i	1.57293	−	0.189353i
$928$		−	102.524i		−	0.110479i
$929$	463.793	−	803.312i	0.499239	−	0.864706i	−0.500761	−	0.865586i	$-0.666946\pi$
$929$	463.793	−	803.312i	0.499239	−	0.864706i	1.00000		0.000879046i	$0.000279809\pi$
$930$	−185.256	+	370.468i	−0.199200	+	0.398352i
$931$	−395.875	+	228.559i	−0.425215	+	0.245498i
$932$	−408.052	+	235.589i	−0.437824	+	0.252778i
$933$	−197.595	+	395.143i	−0.211785	+	0.423519i
$934$	−114.047	−	65.8453i	−0.122106	−	0.0704982i
$935$		−	161.628i		−	0.172864i
$936$	−330.867	+	899.437i	−0.353490	+	0.960937i
$937$	−249.827			−0.266625			−0.133312	−	0.991074i	$-0.542561\pi$
$937$	−249.827			−0.266625			−0.133312	+	0.991074i	$0.542561\pi$
$938$	10.2292	−	17.7175i	0.0109053	−	0.0188886i
$939$	−30.1303	−	502.383i	−0.0320876	−	0.535019i
$940$	−169.739	−	293.996i	−0.180573	−	0.312761i
$941$	817.021	+	1415.12i	0.868247	+	1.50385i	0.863786	+	0.503858i	$0.168087\pi$
$941$	817.021	+	1415.12i	0.868247	+	1.50385i	0.00446066	+	0.999990i	$0.498580\pi$
$942$	442.647	−	292.229i	0.469901	−	0.310222i
$943$	850.142	+	490.830i	0.901529	+	0.520498i
$944$	24.4536			0.0259042
$945$	22.4205	−	4.07310i	0.0237254	−	0.00431016i
$946$	287.380			0.303784
$947$	−942.757	+	1632.90i	−0.995520	+	1.72429i	−0.415877	+	0.909421i	$0.636525\pi$
$947$	−942.757	+	1632.90i	−0.995520	+	1.72429i	−0.579643	+	0.814870i	$0.696808\pi$
$948$	261.256	−	172.477i	0.275586	−	0.181938i
$949$	59.1581	+	1152.24i	0.0623373	+	1.21417i
$950$	48.9828	−	28.2802i	0.0515608	−	0.0297686i
$951$	−7.20662	−	120.161i	−0.00757794	−	0.126352i
$952$	5.03165	−	8.71508i	0.00528535	−	0.00915449i
$953$			1399.79i			1.46882i	0.678704	+	0.734412i	$0.262542\pi$
$953$			1399.79i			1.46882i	−0.678704	+	0.734412i	$0.737458\pi$
$954$	654.634	−	490.877i	0.686200	−	0.514547i
$955$			1081.62i			1.13259i
$956$	43.1187	−	74.6838i	0.0451033	−	0.0781212i
$957$	−24.2134	+	48.4210i	−0.0253014	+	0.0505966i
$958$	−24.1243	−	41.7844i	−0.0251819	−	0.0436163i
$959$	−17.8481	+	10.3046i	−0.0186112	+	0.0107452i
$960$	551.091	+	275.579i	0.574054	+	0.287061i
$961$	−201.287	+	348.639i	−0.209456	+	0.362788i
$962$	824.438	+	421.177i	0.857005	+	0.437814i
$963$	−1493.65	−	638.195i	−1.55104	−	0.662715i
$964$			640.670i			0.664595i
$965$	−1397.59	−	806.901i	−1.44828	−	0.836167i
$966$	−0.780202	−	13.0088i	−0.000807662	−	0.0134667i
$967$	486.020	−	280.604i	0.502606	−	0.290180i	−0.227183	−	0.973852i	$-0.572952\pi$
$967$	486.020	−	280.604i	0.502606	−	0.290180i	0.729789	+	0.683672i	$0.239618\pi$
$968$	−373.341	−	646.645i	−0.385683	−	0.668022i
$969$	153.388	−	101.264i	0.158295	−	0.104504i
$970$	41.4300	+	23.9196i	0.0427113	+	0.0246594i
$971$		−	242.009i		−	0.249237i	−0.992205	−	0.124619i	$-0.960229\pi$
$971$		−	242.009i		−	0.249237i	0.992205	−	0.124619i	$-0.0397707\pi$
$972$	−166.374	−	538.767i	−0.171167	−	0.554287i
$973$			41.2333i			0.0423775i
$974$	606.482	+	350.153i	0.622672	+	0.359500i
$975$	−20.2324	−	181.196i	−0.0207512	−	0.185842i
$976$	22.2965	+	38.6187i	0.0228448	+	0.0395683i
$977$	799.206	+	1384.27i	0.818021	+	1.41685i	0.907139	+	0.420832i	$0.138262\pi$
$977$	799.206	+	1384.27i	0.818021	+	1.41685i	−0.0891180	+	0.996021i	$0.528405\pi$
$978$	174.218	−	10.4487i	0.178137	−	0.0106837i
$979$	−476.101	+	824.631i	−0.486313	+	0.842320i
$980$	512.241			0.522695
$981$	1239.09	+	529.426i	1.26309	+	0.539680i
$982$		−	660.706i		−	0.672817i
$983$	330.372	−	572.221i	0.336086	−	0.582117i	−0.647607	−	0.761974i	$-0.724230\pi$
$983$	330.372	−	572.221i	0.336086	−	0.582117i	0.983693	+	0.179857i	$0.0575635\pi$
$984$	1204.97	+	602.557i	1.22456	+	0.612355i
$985$	92.5441	+	160.291i	0.0939535	+	0.162732i
$986$	−14.0477	−	24.3313i	−0.0142471	−	0.0246768i
$987$	−8.15107	+	16.3002i	−0.00825843	+	0.0165149i
$988$	236.347	−	153.128i	0.239217	−	0.154988i
$989$		−	726.820i		−	0.734904i
$990$	−172.333	−	229.824i	−0.174074	−	0.232145i
$991$	−146.509			−0.147839			−0.0739197	−	0.997264i	$-0.523551\pi$
$991$	−146.509			−0.147839			−0.0739197	+	0.997264i	$0.523551\pi$
$992$	−635.157	−	366.708i	−0.640280	−	0.369666i
$993$	−35.0278	+	2.10078i	−0.0352747	+	0.00211559i
$994$	−10.9661	+	6.33129i	−0.0110323	+	0.00636951i
$995$	−325.507	−	563.795i	−0.327143	−	0.566628i
$996$	−511.112	+	337.428i	−0.513164	+	0.338783i
$997$	145.897	−	252.700i	0.146336	−	0.253461i	−0.783535	−	0.621348i	$-0.786585\pi$
$997$	145.897	−	252.700i	0.146336	−	0.253461i	0.929870	+	0.367887i	$0.119919\pi$
$998$		−	486.814i		−	0.487789i
$999$	−1459.78	+	265.196i	−1.46124	+	0.265462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.n.a.38.9	✓	52
3.2	odd	2		351.3.n.a.116.18		52
9.4	even	3		351.3.n.a.233.9		52
9.5	odd	6	inner	117.3.n.a.77.18	yes	52
13.12	even	2	inner	117.3.n.a.38.18	yes	52
39.38	odd	2		351.3.n.a.116.9		52
117.77	odd	6	inner	117.3.n.a.77.9	yes	52
117.103	even	6		351.3.n.a.233.18		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.n.a.38.9	✓	52	1.1	even	1	trivial
117.3.n.a.38.18	yes	52	13.12	even	2	inner
117.3.n.a.77.9	yes	52	117.77	odd	6	inner
117.3.n.a.77.18	yes	52	9.5	odd	6	inner
351.3.n.a.116.9		52	39.38	odd	2
351.3.n.a.116.18		52	3.2	odd	2
351.3.n.a.233.9		52	9.4	even	3
351.3.n.a.233.18		52	117.103	even	6

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} +(12.9829 - 0.666563i) 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} +(31.4025 - 23.1276i) 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} +(16.4026 + 25.3167i) 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} +(31.8681 + 49.1870i) 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} +(5.60878 + 50.2308i) 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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