LMFDB - Embedded newform 630.2.r.b.299.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(59,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("630.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.r (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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			299.15
Character	$\chi$	$=$	630.299
Dual form			630.2.r.b.59.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.277706 + 1.70964i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.05173 - 0.889037i) q^{5} +(-1.34174 + 1.09532i) q^{6} +(-0.970835 - 2.46119i) q^{7} -1.00000 q^{8} +(-2.84576 + 0.949556i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.277706 + 1.70964i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.05173 - 0.889037i) q^{5} +(-1.34174 + 1.09532i) q^{6} +(-0.970835 - 2.46119i) q^{7} -1.00000 q^{8} +(-2.84576 + 0.949556i) q^{9} +(-0.255938 - 2.22137i) q^{10} -2.28847i q^{11} +(-1.61945 - 0.614321i) q^{12} +(-2.02055 - 3.49969i) q^{13} +(1.64604 - 2.07137i) q^{14} +(0.950157 - 3.75462i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.58838 + 3.22645i) q^{17} +(-2.24522 - 1.98972i) q^{18} +(-0.177623 - 0.102551i) q^{19} +(1.79580 - 1.33234i) q^{20} +(3.93816 - 2.34327i) q^{21} +(1.98187 - 1.14423i) q^{22} -2.00850 q^{23} +(-0.277706 - 1.70964i) q^{24} +(3.41923 + 3.64814i) q^{25} +(2.02055 - 3.49969i) q^{26} +(-2.41369 - 4.60153i) q^{27} +(2.61687 + 0.389830i) q^{28} +(2.95397 + 1.70547i) q^{29} +(3.72668 - 1.05445i) q^{30} +(-0.844461 - 0.487550i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.91246 - 0.635521i) q^{33} +(-5.58838 - 3.22645i) q^{34} +(-0.196198 + 5.91283i) q^{35} +(0.600540 - 2.93928i) q^{36} +(-7.40520 - 4.27539i) q^{37} -0.205102i q^{38} +(5.42211 - 4.42630i) q^{39} +(2.05173 + 0.889037i) q^{40} +(1.15662 + 2.00333i) q^{41} +(3.99841 + 2.23891i) q^{42} +(2.12736 + 1.22823i) q^{43} +(1.98187 + 1.14423i) q^{44} +(6.68293 + 0.581749i) q^{45} +(-1.00425 - 1.73941i) q^{46} +(-4.13773 + 2.38892i) q^{47} +(1.34174 - 1.09532i) q^{48} +(-5.11496 + 4.77883i) q^{49} +(-1.44977 + 4.78520i) q^{50} +(-7.06800 - 8.65812i) q^{51} +4.04110 q^{52} +(2.35928 + 4.08640i) q^{53} +(2.77820 - 4.39108i) q^{54} +(-2.03453 + 4.69532i) q^{55} +(0.970835 + 2.46119i) q^{56} +(0.125998 - 0.332151i) q^{57} +3.41095i q^{58} +(-4.53573 + 7.85612i) q^{59} +(2.77652 + 2.70017i) q^{60} +(9.33757 - 5.39105i) q^{61} -0.975100i q^{62} +(5.09980 + 6.08210i) q^{63} +1.00000 q^{64} +(1.03427 + 8.97678i) q^{65} +(2.50661 + 3.07053i) q^{66} +(5.24087 + 3.02582i) q^{67} -6.45290i q^{68} +(-0.557771 - 3.43381i) q^{69} +(-5.21876 + 2.78650i) q^{70} -11.0359i q^{71} +(2.84576 - 0.949556i) q^{72} +(-7.78631 - 13.4863i) q^{73} -8.55079i q^{74} +(-5.28747 + 6.85876i) q^{75} +(0.177623 - 0.102551i) q^{76} +(-5.63236 + 2.22172i) q^{77} +(6.54434 + 2.48253i) q^{78} +(3.61701 + 6.26485i) q^{79} +(0.255938 + 2.22137i) q^{80} +(7.19669 - 5.40442i) q^{81} +(-1.15662 + 2.00333i) q^{82} +(-9.91029 - 5.72171i) q^{83} +(0.0602522 + 4.58218i) q^{84} +(14.3343 - 1.65154i) q^{85} +2.45646i q^{86} +(-2.09542 + 5.52385i) q^{87} +2.28847i q^{88} +(-5.08916 + 8.81469i) q^{89} +(2.83766 + 6.07846i) q^{90} +(-6.65180 + 8.37059i) q^{91} +(1.00425 - 1.73941i) q^{92} +(0.599024 - 1.57912i) q^{93} +(-4.13773 - 2.38892i) q^{94} +(0.273264 + 0.368321i) q^{95} +(1.61945 + 0.614321i) q^{96} +(4.24029 - 7.34440i) q^{97} +(-6.69607 - 2.04027i) q^{98} +(2.17303 + 6.51242i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	$ 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.277706	+	1.70964i	0.160334	+	0.987063i
$3$	0.277706	+	1.70964i	0.160334	+	0.987063i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.05173	−	0.889037i	−0.917563	−	0.397590i
$5$	−2.05173	−	0.889037i	−0.917563	−	0.397590i
$6$	−1.34174	+	1.09532i	−0.547764	+	0.447163i
$7$	−0.970835	−	2.46119i	−0.366941	−	0.930244i
$7$	−0.970835	−	2.46119i	−0.366941	−	0.930244i
$8$	−1.00000			−0.353553
$9$	−2.84576	+	0.949556i	−0.948586	+	0.316519i
$10$	−0.255938	−	2.22137i	−0.0809348	−	0.702460i
$11$		−	2.28847i		−	0.689998i	−0.938603	−	0.344999i	$-0.887879\pi$
$11$		−	2.28847i		−	0.689998i	0.938603	−	0.344999i	$-0.112121\pi$
$12$	−1.61945	−	0.614321i	−0.467494	−	0.177339i
$13$	−2.02055	−	3.49969i	−0.560399	−	0.970640i	−0.997461	−	0.0712086i	$-0.977314\pi$
$13$	−2.02055	−	3.49969i	−0.560399	−	0.970640i	0.437062	−	0.899431i	$-0.356019\pi$
$14$	1.64604	−	2.07137i	0.439923	−	0.553596i
$15$	0.950157	−	3.75462i	0.245330	−	0.969440i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.58838	+	3.22645i	−1.35538	+	0.782529i	−0.988997	−	0.147935i	$-0.952737\pi$
$17$	−5.58838	+	3.22645i	−1.35538	+	0.782529i	−0.366383	+	0.930464i	$0.619404\pi$
$18$	−2.24522	−	1.98972i	−0.529203	−	0.468982i
$19$	−0.177623	−	0.102551i	−0.0407496	−	0.0235268i	0.479487	−	0.877549i	$-0.340823\pi$
$19$	−0.177623	−	0.102551i	−0.0407496	−	0.0235268i	−0.520236	+	0.854022i	$0.674156\pi$
$20$	1.79580	−	1.33234i	0.401552	−	0.297919i
$21$	3.93816	−	2.34327i	0.859376	−	0.511343i
$22$	1.98187	−	1.14423i	0.422536	−	0.243951i
$23$	−2.00850			−0.418800			−0.209400	−	0.977830i	$-0.567151\pi$
$23$	−2.00850			−0.418800			−0.209400	+	0.977830i	$0.567151\pi$
$24$	−0.277706	−	1.70964i	−0.0566865	−	0.348979i
$25$	3.41923	+	3.64814i	0.683845	+	0.729627i
$26$	2.02055	−	3.49969i	0.396262	−	0.686346i
$27$	−2.41369	−	4.60153i	−0.464514	−	0.885566i
$28$	2.61687	+	0.389830i	0.494543	+	0.0736709i
$29$	2.95397	+	1.70547i	0.548538	+	0.316698i	0.748532	−	0.663099i	$-0.230759\pi$
$29$	2.95397	+	1.70547i	0.548538	+	0.316698i	−0.199994	+	0.979797i	$0.564092\pi$
$30$	3.72668	−	1.05445i	0.680395	−	0.192516i
$31$	−0.844461	−	0.487550i	−0.151670	−	0.0875665i	0.422244	−	0.906482i	$-0.361242\pi$
$31$	−0.844461	−	0.487550i	−0.151670	−	0.0875665i	−0.573914	+	0.818915i	$0.694576\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.91246	−	0.635521i	0.681072	−	0.110630i
$34$	−5.58838	−	3.22645i	−0.958399	−	0.553332i
$35$	−0.196198	+	5.91283i	−0.0331636	+	0.999450i
$36$	0.600540	−	2.93928i	0.100090	−	0.489880i
$37$	−7.40520	−	4.27539i	−1.21741	−	0.702870i	−0.253045	−	0.967455i	$-0.581432\pi$
$37$	−7.40520	−	4.27539i	−1.21741	−	0.702870i	−0.964363	+	0.264584i	$0.914765\pi$
$38$		−	0.205102i		−	0.0332719i
$39$	5.42211	−	4.42630i	0.868232	−	0.708775i
$40$	2.05173	+	0.889037i	0.324408	+	0.140569i
$41$	1.15662	+	2.00333i	0.180634	+	0.312867i	0.942097	−	0.335342i	$-0.108852\pi$
$41$	1.15662	+	2.00333i	0.180634	+	0.312867i	−0.761463	+	0.648209i	$0.775518\pi$
$42$	3.99841	+	2.23891i	0.616968	+	0.345471i
$43$	2.12736	+	1.22823i	0.324419	+	0.187303i	0.653360	−	0.757047i	$-0.273359\pi$
$43$	2.12736	+	1.22823i	0.324419	+	0.187303i	−0.328942	+	0.944350i	$0.606692\pi$
$44$	1.98187	+	1.14423i	0.298778	+	0.172500i
$45$	6.68293	+	0.581749i	0.996233	+	0.0867220i
$46$	−1.00425	−	1.73941i	−0.148068	−	0.256462i
$47$	−4.13773	+	2.38892i	−0.603550	+	0.348460i	−0.770437	−	0.637516i	$-0.779962\pi$
$47$	−4.13773	+	2.38892i	−0.603550	+	0.348460i	0.166887	+	0.985976i	$0.446629\pi$
$48$	1.34174	−	1.09532i	0.193664	−	0.158096i
$49$	−5.11496	+	4.77883i	−0.730708	+	0.682690i
$50$	−1.44977	+	4.78520i	−0.205028	+	0.676730i
$51$	−7.06800	−	8.65812i	−0.989719	−	1.21238i
$52$	4.04110			0.560399
$53$	2.35928	+	4.08640i	0.324072	+	0.561310i	0.981324	−	0.192361i	$-0.0616145\pi$
$53$	2.35928	+	4.08640i	0.324072	+	0.561310i	−0.657252	+	0.753671i	$0.728281\pi$
$54$	2.77820	−	4.39108i	0.378065	−	0.597550i
$55$	−2.03453	+	4.69532i	−0.274336	+	0.633117i
$56$	0.970835	+	2.46119i	0.129733	+	0.328891i
$57$	0.125998	−	0.332151i	0.0166889	−	0.0439945i
$58$			3.41095i			0.447879i
$59$	−4.53573	+	7.85612i	−0.590502	+	1.02278i	0.403663	+	0.914908i	$0.367737\pi$
$59$	−4.53573	+	7.85612i	−0.590502	+	1.02278i	−0.994165	+	0.107872i	$0.965596\pi$
$60$	2.77652	+	2.70017i	0.358447	+	0.348591i
$61$	9.33757	−	5.39105i	1.19555	−	0.690253i	0.235993	−	0.971755i	$-0.424166\pi$
$61$	9.33757	−	5.39105i	1.19555	−	0.690253i	0.959561	+	0.281501i	$0.0908324\pi$
$62$		−	0.975100i		−	0.123838i
$63$	5.09980	+	6.08210i	0.642515	+	0.766273i
$64$	1.00000			0.125000
$65$	1.03427	+	8.97678i	0.128286	+	1.11343i
$66$	2.50661	+	3.07053i	0.308542	+	0.377956i
$67$	5.24087	+	3.02582i	0.640274	+	0.369662i	0.784720	−	0.619850i	$-0.212807\pi$
$67$	5.24087	+	3.02582i	0.640274	+	0.369662i	−0.144446	+	0.989513i	$0.546140\pi$
$68$		−	6.45290i		−	0.782529i
$69$	−0.557771	−	3.43381i	−0.0671478	−	0.413382i
$70$	−5.21876	+	2.78650i	−0.623761	+	0.333050i
$71$		−	11.0359i		−	1.30973i	−0.755748	−	0.654863i	$-0.772726\pi$
$71$		−	11.0359i		−	1.30973i	0.755748	−	0.654863i	$-0.227274\pi$
$72$	2.84576	−	0.949556i	0.335376	−	0.111906i
$73$	−7.78631	−	13.4863i	−0.911318	−	1.57845i	−0.812204	−	0.583373i	$-0.801732\pi$
$73$	−7.78631	−	13.4863i	−0.911318	−	1.57845i	−0.0991142	−	0.995076i	$-0.531601\pi$
$74$		−	8.55079i		−	0.994009i
$75$	−5.28747	+	6.85876i	−0.610545	+	0.791982i
$76$	0.177623	−	0.102551i	0.0203748	−	0.0117634i
$77$	−5.63236	+	2.22172i	−0.641867	+	0.253189i
$78$	6.54434	+	2.48253i	0.741001	+	0.281091i
$79$	3.61701	+	6.26485i	0.406946	+	0.704851i	0.994546	−	0.104301i	$-0.0332605\pi$
$79$	3.61701	+	6.26485i	0.406946	+	0.704851i	−0.587600	+	0.809151i	$0.699927\pi$
$80$	0.255938	+	2.22137i	0.0286148	+	0.248357i
$81$	7.19669	−	5.40442i	0.799632	−	0.600491i
$82$	−1.15662	+	2.00333i	−0.127728	+	0.221231i
$83$	−9.91029	−	5.72171i	−1.08780	−	0.628039i	−0.154807	−	0.987945i	$-0.549476\pi$
$83$	−9.91029	−	5.72171i	−1.08780	−	0.628039i	−0.932989	+	0.359906i	$0.882809\pi$
$84$	0.0602522	+	4.58218i	0.00657406	+	0.499957i
$85$	14.3343	−	1.65154i	1.55477	−	0.179135i
$86$			2.45646i			0.264887i
$87$	−2.09542	+	5.52385i	−0.224652	+	0.592219i
$88$			2.28847i			0.243951i
$89$	−5.08916	+	8.81469i	−0.539450	+	0.934355i	0.459483	+	0.888186i	$0.348035\pi$
$89$	−5.08916	+	8.81469i	−0.539450	+	0.934355i	−0.998934	+	0.0461690i	$0.985299\pi$
$90$	2.83766	+	6.07846i	0.299115	+	0.640726i
$91$	−6.65180	+	8.37059i	−0.697299	+	0.877476i
$92$	1.00425	−	1.73941i	0.104700	−	0.181346i
$93$	0.599024	−	1.57912i	0.0621159	−	0.163747i
$94$	−4.13773	−	2.38892i	−0.426774	−	0.246398i
$95$	0.273264	+	0.368321i	0.0280363	+	0.0377889i
$96$	1.61945	+	0.614321i	0.165284	+	0.0626989i
$97$	4.24029	−	7.34440i	0.430536	−	0.745711i	−0.566383	−	0.824142i	$-0.691658\pi$
$97$	4.24029	−	7.34440i	0.430536	−	0.745711i	0.996920	+	0.0784313i	$0.0249911\pi$
$98$	−6.69607	−	2.04027i	−0.676405	−	0.206098i
$99$	2.17303	+	6.51242i	0.218397	+	0.654523i
$100$	−4.86899	+	1.13707i	−0.486899	+	0.113707i
$101$	−1.51509			−0.150757			−0.0753785	−	0.997155i	$-0.524017\pi$
$101$	−1.51509			−0.150757			−0.0753785	+	0.997155i	$0.524017\pi$
$102$	3.96415	−	10.4501i	0.392510	−	1.03472i
$103$	−18.7761			−1.85006			−0.925031	−	0.379891i	$-0.875961\pi$
$103$	−18.7761			−1.85006			−0.925031	+	0.379891i	$0.875961\pi$
$104$	2.02055	+	3.49969i	0.198131	+	0.343173i
$105$	−10.1633	+	1.30660i	−0.991837	+	0.127511i
$106$	−2.35928	+	4.08640i	−0.229154	+	0.396906i
$107$	−9.00357	+	15.5946i	−0.870408	+	1.50759i	−0.00883183	+	0.999961i	$0.502811\pi$
$107$	−9.00357	+	15.5946i	−0.870408	+	1.50759i	−0.861576	+	0.507629i	$0.830522\pi$
$108$	5.19189	+	0.210454i	0.499590	+	0.0202509i
$109$	−8.13785	−	14.0952i	−0.779464	−	1.35007i	−0.932251	−	0.361813i	$-0.882158\pi$
$109$	−8.13785	−	14.0952i	−0.779464	−	1.35007i	0.152786	−	0.988259i	$-0.451175\pi$
$110$	−5.08354	+	0.585706i	−0.484696	+	0.0558449i
$111$	5.25293	−	13.8475i	0.498586	−	1.31435i
$112$	−1.64604	+	2.07137i	−0.155536	+	0.195726i
$113$	−2.98673	−	5.17317i	−0.280968	−	0.486651i	0.690655	−	0.723184i	$-0.257322\pi$
$113$	−2.98673	−	5.17317i	−0.280968	−	0.486651i	−0.971623	+	0.236533i	$0.923989\pi$
$114$	0.350651	−	0.0569580i	0.0328414	−	0.00533460i
$115$	4.12090	+	1.78563i	0.384276	+	0.166511i
$116$	−2.95397	+	1.70547i	−0.274269	+	0.158349i
$117$	9.07315	+	8.04065i	0.838813	+	0.743359i
$118$	−9.07146			−0.835096
$119$	13.3663	+	10.6217i	1.22529	+	0.973693i
$120$	−0.950157	+	3.75462i	−0.0867371	+	0.342749i
$121$	5.76292			0.523902
$122$	9.33757	+	5.39105i	0.845384	+	0.488083i
$123$	−3.10377	+	2.53375i	−0.279858	+	0.228460i
$124$	0.844461	−	0.487550i	0.0758349	−	0.0437833i
$125$	−3.77201	−	10.5248i	−0.337379	−	0.941369i
$126$	−2.71735	+	7.45761i	−0.242081	+	0.664377i
$127$		−	11.8327i		−	1.04998i	−0.851108	−	0.524991i	$-0.824069\pi$
$127$		−	11.8327i		−	1.04998i	0.851108	−	0.524991i	$-0.175931\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.50905	+	3.97811i	−0.132865	+	0.350253i
$130$	−7.25698	+	5.38409i	−0.636480	+	0.472216i
$131$	−2.95626			−0.258290			−0.129145	−	0.991626i	$-0.541223\pi$
$131$	−2.95626			−0.258290			−0.129145	+	0.991626i	$0.541223\pi$
$132$	−1.40585	+	3.70605i	−0.122364	+	0.322570i
$133$	−0.0799547	+	0.536725i	−0.00693295	+	0.0465400i
$134$			6.05164i			0.522782i
$135$	0.861307	+	11.5870i	0.0741295	+	0.997249i
$136$	5.58838	−	3.22645i	0.479199	−	0.276666i
$137$	6.86183			0.586246			0.293123	−	0.956075i	$-0.405305\pi$
$137$	6.86183			0.586246			0.293123	+	0.956075i	$0.405305\pi$
$138$	2.69488	−	2.19995i	0.229404	−	0.187272i
$139$	1.44024	−	0.831524i	0.122160	−	0.0705289i	−0.437675	−	0.899133i	$-0.644198\pi$
$139$	1.44024	−	0.831524i	0.122160	−	0.0705289i	0.559835	+	0.828604i	$0.310865\pi$
$140$	−5.02256	−	3.12633i	−0.424484	−	0.264223i
$141$	−5.23327	−	6.41063i	−0.440721	−	0.539872i
$142$	9.55741	−	5.51797i	0.802040	−	0.463058i
$143$	−8.00893	+	4.62396i	−0.669740	+	0.386675i
$144$	2.24522	+	1.98972i	0.187102	+	0.165810i
$145$	−4.54452	−	6.12536i	−0.377402	−	0.508684i
$146$	7.78631	−	13.4863i	0.644399	−	1.11613i
$147$	−9.59054	−	7.41764i	−0.791015	−	0.611797i
$148$	7.40520	−	4.27539i	0.608704	−	0.351435i
$149$			11.7251i			0.960557i	0.877116	+	0.480278i	$0.159464\pi$
$149$			11.7251i			0.960557i	−0.877116	+	0.480278i	$0.840536\pi$
$150$	−8.58360	−	1.14970i	−0.700848	−	0.0938728i
$151$	3.36336			0.273706			0.136853	−	0.990591i	$-0.456301\pi$
$151$	3.36336			0.273706			0.136853	+	0.990591i	$0.456301\pi$
$152$	0.177623	+	0.102551i	0.0144071	+	0.00831797i
$153$	12.8395	−	14.4882i	1.03801	−	1.17130i
$154$	−4.74025	−	3.76691i	−0.381980	−	0.303546i
$155$	1.29916	+	1.75108i	0.104351	+	0.140650i
$156$	1.12224	+	6.90883i	0.0898508	+	0.553149i
$157$	−1.29164	+	2.23719i	−0.103084	+	0.178547i	−0.912954	−	0.408063i	$-0.866204\pi$
$157$	−1.29164	+	2.23719i	−0.103084	+	0.178547i	0.809870	+	0.586610i	$0.199538\pi$
$158$	−3.61701	+	6.26485i	−0.287754	+	0.498405i
$159$	−6.33109	+	5.16835i	−0.502088	+	0.409877i
$160$	−1.79580	+	1.33234i	−0.141970	+	0.105330i
$161$	1.94992	+	4.94330i	0.153675	+	0.389587i
$162$	8.27870	+	3.53031i	0.650436	+	0.277367i
$163$	21.1464	+	12.2089i	1.65631	+	0.956272i	0.974395	+	0.224841i	$0.0721863\pi$
$163$	21.1464	+	12.2089i	1.65631	+	0.956272i	0.681916	+	0.731431i	$0.261147\pi$
$164$	−2.31324			−0.180634
$165$	−8.59233	−	2.17440i	−0.668912	−	0.169277i
$166$		−	11.4434i		−	0.888181i
$167$	−0.00904075	+	0.00521968i	−0.000699594	+	0.000403911i	−0.500350	−	0.865823i	$-0.666795\pi$
$167$	−0.00904075	+	0.00521968i	−0.000699594	+	0.000403911i	0.499650	+	0.866227i	$0.333462\pi$
$168$	−3.93816	+	2.34327i	−0.303835	+	0.180787i
$169$	−1.66523	+	2.88426i	−0.128094	+	0.221866i
$170$	8.59743	+	11.5881i	0.659393	+	0.888766i
$171$	0.602851	+	0.123172i	0.0461011	+	0.00941917i
$172$	−2.12736	+	1.22823i	−0.162209	+	0.0936516i
$173$	15.7903	−	9.11652i	1.20051	−	0.693116i	0.239843	−	0.970812i	$-0.422904\pi$
$173$	15.7903	−	9.11652i	1.20051	−	0.693116i	0.960669	+	0.277695i	$0.0895706\pi$
$174$	−5.83150	+	0.947240i	−0.442085	+	0.0718101i
$175$	5.65927	−	11.9571i	0.427801	−	0.903873i
$176$	−1.98187	+	1.14423i	−0.149389	+	0.0862498i
$177$	−14.6908	−	5.57279i	−1.10422	−	0.418877i
$178$	−10.1783			−0.762898
$179$	−13.5399	+	7.81725i	−1.01202	+	0.584289i	−0.911782	−	0.410675i	$-0.865293\pi$
$179$	−13.5399	+	7.81725i	−1.01202	+	0.584289i	−0.100236	+	0.994964i	$0.531960\pi$
$180$	−3.84527	+	5.49671i	−0.286610	+	0.409701i
$181$			24.3098i			1.80693i	0.428659	+	0.903467i	$0.358986\pi$
$181$			24.3098i			1.80693i	−0.428659	+	0.903467i	$0.641014\pi$
$182$	−10.5750	−	1.57534i	−0.783874	−	0.116772i
$183$	11.8099	+	14.4668i	0.873011	+	1.06942i
$184$	2.00850			0.148068
$185$	11.3925	+	15.3555i	0.837594	+	1.12896i
$186$	1.66707	−	0.270791i	0.122236	−	0.0198554i
$187$	7.38362	+	12.7888i	0.539944	+	0.935210i
$188$		−	4.77784i		−	0.348460i
$189$	−8.98198	+	10.4079i	−0.653343	+	0.757062i
$190$	−0.182343	+	0.420814i	−0.0132286	+	0.0305291i
$191$	10.3403	−	5.96997i	0.748197	−	0.431972i	−0.0768452	−	0.997043i	$-0.524485\pi$
$191$	10.3403	−	5.96997i	0.748197	−	0.431972i	0.825042	+	0.565071i	$0.191151\pi$
$192$	0.277706	+	1.70964i	0.0200417	+	0.123383i
$193$	−10.7748	−	6.22084i	−0.775588	−	0.447786i	0.0592765	−	0.998242i	$-0.481121\pi$
$193$	−10.7748	−	6.22084i	−0.775588	−	0.447786i	−0.834864	+	0.550456i	$0.814454\pi$
$194$	8.48058			0.608870
$195$	−15.0599	+	4.26114i	−1.07846	+	0.305147i
$196$	−1.58111	−	6.81910i	−0.112936	−	0.487078i
$197$	23.0465			1.64199			0.820996	−	0.570934i	$-0.193419\pi$
$197$	23.0465			1.64199			0.820996	+	0.570934i	$0.193419\pi$
$198$	−4.55341	+	5.13811i	−0.323597	+	0.365149i
$199$	−6.98847	+	4.03479i	−0.495399	+	0.286019i	−0.726812	−	0.686837i	$-0.758999\pi$
$199$	−6.98847	+	4.03479i	−0.495399	+	0.286019i	0.231412	+	0.972856i	$0.425665\pi$
$200$	−3.41923	−	3.64814i	−0.241776	−	0.257962i
$201$	−3.71765	+	9.80031i	−0.262223	+	0.691260i
$202$	−0.757545	−	1.31211i	−0.0533007	−	0.0923195i
$203$	1.32969	−	8.92602i	0.0933258	−	0.626484i
$204$	11.0322	−	1.79201i	0.772406	−	0.125466i
$205$	−0.592047	−	5.13858i	−0.0413504	−	0.358894i
$206$	−9.38804	−	16.2606i	−0.654096	−	1.13293i
$207$	5.71570	−	1.90718i	0.397268	−	0.132558i
$208$	−2.02055	+	3.49969i	−0.140100	+	0.242660i
$209$	−0.234684	+	0.406485i	−0.0162334	+	0.0281171i
$210$	−6.21320	−	8.14838i	−0.428752	−	0.562292i
$211$	−9.23801	−	16.0007i	−0.635971	−	1.10153i	−0.986309	−	0.164910i	$-0.947266\pi$
$211$	−9.23801	−	16.0007i	−0.635971	−	1.10153i	0.350338	−	0.936623i	$-0.386067\pi$
$212$	−4.71857			−0.324072
$213$	18.8675	−	3.06475i	1.29278	−	0.209993i
$214$	−18.0071			−1.23094
$215$	−3.27283	−	4.41130i	−0.223205	−	0.300848i
$216$	2.41369	+	4.60153i	0.164231	+	0.313095i
$217$	−0.380123	+	2.55171i	−0.0258044	+	0.173222i
$218$	8.13785	−	14.0952i	0.551165	−	0.954645i
$219$	20.8944	−	17.0570i	1.41191	−	1.15261i
$220$	−3.04900	−	4.10962i	−0.205564	−	0.277070i
$221$	22.5832	+	13.0384i	1.51911	+	0.877057i
$222$	14.6188	−	2.37460i	0.981149	−	0.159373i
$223$	−2.10769	+	3.65063i	−0.141142	+	0.244464i	−0.927927	−	0.372763i	$-0.878411\pi$
$223$	−2.10769	+	3.65063i	−0.141142	+	0.244464i	0.786785	+	0.617227i	$0.211744\pi$
$224$	−2.61687	−	0.389830i	−0.174847	−	0.0260466i
$225$	−13.1944	−	7.13497i	−0.879627	−	0.475665i
$226$	2.98673	−	5.17317i	0.198674	−	0.344114i
$227$			18.5740i			1.23280i	0.787433	+	0.616400i	$0.211410\pi$
$227$			18.5740i			1.23280i	−0.787433	+	0.616400i	$0.788590\pi$
$228$	0.224652	+	0.275193i	0.0148780	+	0.0182251i
$229$			1.57155i			0.103851i	0.998651	+	0.0519256i	$0.0165359\pi$
$229$			1.57155i			0.103851i	−0.998651	+	0.0519256i	$0.983464\pi$
$230$	0.514051	+	4.46162i	0.0338955	+	0.294190i
$231$	−5.36249	−	9.01234i	−0.352826	−	0.592968i
$232$	−2.95397	−	1.70547i	−0.193937	−	0.111970i
$233$	−3.77904	+	6.54549i	−0.247573	+	0.428809i	−0.962852	−	0.270030i	$-0.912966\pi$
$233$	−3.77904	+	6.54549i	−0.247573	+	0.428809i	0.715279	+	0.698839i	$0.246300\pi$
$234$	−2.42684	+	11.8779i	−0.158647	+	0.776483i
$235$	10.6134	−	1.22283i	0.692340	−	0.0797688i
$236$	−4.53573	−	7.85612i	−0.295251	−	0.511390i
$237$	−9.70619	+	7.92359i	−0.630485	+	0.514692i
$238$	−2.51553	+	16.8864i	−0.163058	+	1.09458i
$239$	14.4459	−	8.34037i	0.934430	−	0.539494i	0.0462202	−	0.998931i	$-0.485282\pi$
$239$	14.4459	−	8.34037i	0.934430	−	0.539494i	0.888210	+	0.459438i	$0.151949\pi$
$240$	−3.72668	+	1.05445i	−0.240556	+	0.0680645i
$241$		−	28.3707i		−	1.82751i	−0.406260	−	0.913757i	$-0.633167\pi$
$241$		−	28.3707i		−	1.82751i	0.406260	−	0.913757i	$-0.366833\pi$
$242$	2.88146	+	4.99084i	0.185227	+	0.320823i
$243$	11.2382	+	10.8029i	0.720930	+	0.693008i
$244$			10.7821i			0.690253i
$245$	14.7431	−	5.25750i	0.941902	−	0.335889i
$246$	−3.74618	−	1.42107i	−0.238847	−	0.0906044i
$247$			0.828835i			0.0527375i
$248$	0.844461	+	0.487550i	0.0536233	+	0.0309594i
$249$	7.02993	−	18.5320i	0.445504	−	1.17442i
$250$	7.22876	−	8.52907i	0.457187	−	0.539426i
$251$	−9.95552			−0.628387			−0.314193	−	0.949359i	$-0.601734\pi$
$251$	−9.95552			−0.628387			−0.314193	+	0.949359i	$0.601734\pi$
$252$	−7.81716	+	1.37551i	−0.492435	+	0.0866489i
$253$			4.59638i			0.288972i
$254$	10.2474	−	5.91635i	0.642980	−	0.371225i
$255$	6.80427	+	24.0479i	0.426100	+	1.50594i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		−	18.7643i		−	1.17049i	−0.810858	−	0.585243i	$-0.800999\pi$
$257$		−	18.7643i		−	1.17049i	0.810858	−	0.585243i	$-0.199001\pi$
$258$	−4.19967	+	0.682173i	−0.261460	+	0.0424703i
$259$	−3.33335	+	22.3763i	−0.207124	+	1.39040i
$260$	−8.29125	−	3.59268i	−0.514202	−	0.222809i
$261$	−10.0257	−	2.04841i	−0.620576	−	0.126793i
$262$	−1.47813	−	2.56020i	−0.0913192	−	0.158170i
$263$	2.94944			0.181870			0.0909351	−	0.995857i	$-0.471014\pi$
$263$	2.94944			0.181870			0.0909351	+	0.995857i	$0.471014\pi$
$264$	−3.91246	+	0.635521i	−0.240795	+	0.0391136i
$265$	−1.20766	−	10.4817i	−0.0741861	−	0.643885i
$266$	−0.504795	+	0.199120i	−0.0309510	+	0.0122088i
$267$	−16.4833	−	6.25276i	−1.00876	−	0.382663i
$268$	−5.24087	+	3.02582i	−0.320137	+	0.184831i
$269$	−13.8077	−	23.9156i	−0.841869	−	1.45816i	−0.888313	−	0.459239i	$-0.848122\pi$
$269$	−13.8077	−	23.9156i	−0.841869	−	1.45816i	0.0464436	−	0.998921i	$-0.485211\pi$
$270$	−9.60397	+	6.53940i	−0.584479	+	0.397976i
$271$	12.8142	+	7.39828i	0.778407	+	0.449413i	0.835865	−	0.548935i	$-0.184966\pi$
$271$	12.8142	+	7.39828i	0.778407	+	0.449413i	−0.0574587	+	0.998348i	$0.518300\pi$
$272$	5.58838	+	3.22645i	0.338845	+	0.195632i
$273$	−16.1580	−	9.04765i	−0.977924	−	0.547589i
$274$	3.43092	+	5.94252i	0.207269	+	0.359001i
$275$	8.34863	−	7.82478i	0.503442	−	0.471852i
$276$	3.25265	+	1.23386i	0.195787	+	0.0742698i
$277$			7.95373i			0.477893i	0.971033	+	0.238947i	$0.0768021\pi$
$277$			7.95373i			0.477893i	−0.971033	+	0.238947i	$0.923198\pi$
$278$	1.44024	+	0.831524i	0.0863799	+	0.0498715i
$279$	2.86609	+	0.585586i	0.171588	+	0.0350581i
$280$	0.196198	−	5.91283i	0.0117251	−	0.353359i
$281$	−12.9850	−	7.49690i	−0.774621	−	0.447228i	0.0598996	−	0.998204i	$-0.480922\pi$
$281$	−12.9850	−	7.49690i	−0.774621	−	0.447228i	−0.834521	+	0.550977i	$0.814255\pi$
$282$	2.93513	−	7.73746i	0.174784	−	0.460759i
$283$	−14.9011	+	25.8095i	−0.885780	+	1.53422i	−0.0409630	+	0.999161i	$0.513043\pi$
$283$	−14.9011	+	25.8095i	−0.885780	+	1.53422i	−0.844817	+	0.535055i	$0.820291\pi$
$284$	9.55741	+	5.51797i	0.567128	+	0.327431i
$285$	−0.553810	+	0.569469i	−0.0328049	+	0.0337324i
$286$	−8.00893	−	4.62396i	−0.473578	−	0.273420i
$287$	3.80769	−	4.79157i	0.224761	−	0.282838i
$288$	−0.600540	+	2.93928i	−0.0353871	+	0.173199i
$289$	12.3200	−	21.3388i	0.724704	−	1.25522i
$290$	3.03246	−	6.99835i	0.178072	−	0.410957i
$291$	13.7339	+	5.20980i	0.805093	+	0.305404i
$292$	15.5726			0.911318
$293$	2.19993	−	1.27013i	0.128522	−	0.0742019i	−0.434361	−	0.900739i	$-0.643026\pi$
$293$	2.19993	−	1.27013i	0.128522	−	0.0742019i	0.562882	+	0.826537i	$0.309692\pi$
$294$	1.62860	−	12.0145i	0.0949817	−	0.700699i
$295$	16.2905	−	12.0862i	0.948469	−	0.703688i
$296$	7.40520	+	4.27539i	0.430418	+	0.248502i
$297$	−10.5305	+	5.52364i	−0.611039	+	0.320514i
$298$	−10.1542	+	5.86255i	−0.588219	+	0.339608i
$299$	4.05826	+	7.02912i	0.234695	+	0.406504i
$300$	−3.29613	−	8.00847i	−0.190302	−	0.462369i
$301$	0.957600	−	6.42825i	0.0551952	−	0.370518i
$302$	1.68168	+	2.91276i	0.0967699	+	0.167610i
$303$	−0.420750	−	2.59026i	−0.0241714	−	0.148807i
$304$			0.205102i			0.0117634i
$305$	−23.9511	+	2.75955i	−1.37143	+	0.158012i
$306$	18.9669	+	3.87522i	1.08426	+	0.221532i
$307$	8.06299			0.460179			0.230089	−	0.973169i	$-0.426098\pi$
$307$	8.06299			0.460179			0.230089	+	0.973169i	$0.426098\pi$
$308$	0.892112	−	5.98863i	0.0508328	−	0.341234i
$309$	−5.21423	−	32.1004i	−0.296627	−	1.82613i
$310$	−0.866900	+	2.00065i	−0.0492366	+	0.113629i
$311$	−0.381813	+	0.661319i	−0.0216506	+	0.0374999i	−0.876648	−	0.481133i	$-0.840225\pi$
$311$	−0.381813	+	0.661319i	−0.0216506	+	0.0374999i	0.854997	+	0.518633i	$0.173559\pi$
$312$	−5.42211	+	4.42630i	−0.306966	+	0.250590i
$313$	−1.91868	−	3.32326i	−0.108450	−	0.187842i	0.806692	−	0.590972i	$-0.201256\pi$
$313$	−1.91868	−	3.32326i	−0.108450	−	0.187842i	−0.915143	+	0.403130i	$0.867922\pi$
$314$	−2.58329			−0.145783
$315$	−5.05623	−	17.0128i	−0.284886	−	0.958561i
$316$	−7.23402			−0.406946
$317$	−8.66445	−	15.0073i	−0.486644	−	0.842892i	0.513238	−	0.858246i	$-0.328446\pi$
$317$	−8.66445	−	15.0073i	−0.486644	−	0.842892i	−0.999882	+	0.0153543i	$0.995112\pi$
$318$	−7.64147	−	2.89871i	−0.428512	−	0.162552i
$319$	3.90292	−	6.76005i	0.218521	−	0.378490i
$320$	−2.05173	−	0.889037i	−0.114695	−	0.0496987i
$321$	−29.1616	−	11.0622i	−1.62764	−	0.617430i
$322$	−3.30606	+	4.16033i	−0.184240	+	0.231846i
$323$	1.32350			0.0736416
$324$	1.08202	+	8.93472i	0.0601121	+	0.496373i
$325$	5.85864	−	19.3375i	0.324979	−	1.07265i
$326$			24.4177i			1.35237i
$327$	21.8378	−	17.8271i	1.20763	−	0.985842i
$328$	−1.15662	−	2.00333i	−0.0638638	−	0.110615i
$329$	9.89665	+	7.86452i	0.545620	+	0.433585i
$330$	−2.41308	−	8.52838i	−0.132835	−	0.469472i
$331$	2.47937	+	4.29439i	0.136278	+	0.236041i	0.926085	−	0.377315i	$-0.123153\pi$
$331$	2.47937	+	4.29439i	0.136278	+	0.236041i	−0.789807	+	0.613356i	$0.789819\pi$
$332$	9.91029	−	5.72171i	0.543898	−	0.314020i
$333$	25.1331	+	5.13509i	1.37729	+	0.281401i
$334$	−0.00904075	−	0.00521968i	−0.000494688	−	0.000285608i
$335$	−8.06281	−	10.8675i	−0.440518	−	0.593755i
$336$	−3.99841	−	2.23891i	−0.218131	−	0.122143i
$337$	1.58895	−	0.917381i	0.0865557	−	0.0499729i	−0.456097	−	0.889930i	$-0.650753\pi$
$337$	1.58895	−	0.917381i	0.0865557	−	0.0499729i	0.542653	+	0.839957i	$0.317420\pi$
$338$	−3.33046			−0.181153
$339$	8.01484	−	6.54286i	0.435306	−	0.355359i
$340$	−5.73687	+	13.2396i	−0.311125	+	0.718020i
$341$	−1.11574	+	1.93252i	−0.0604208	+	0.104652i
$342$	0.194756	+	0.583670i	0.0105312	+	0.0315613i
$343$	16.7274	+	7.94946i	0.903195	+	0.429230i
$344$	−2.12736	−	1.22823i	−0.114699	−	0.0662217i
$345$	−1.90839	+	7.54115i	−0.102744	+	0.406002i
$346$	15.7903	+	9.11652i	0.848890	+	0.490107i
$347$	3.39243	−	5.87586i	0.182115	−	0.315433i	−0.760486	−	0.649355i	$-0.775039\pi$
$347$	3.39243	−	5.87586i	0.182115	−	0.315433i	0.942601	+	0.333922i	$0.108372\pi$
$348$	−3.73608	−	4.57661i	−0.200275	−	0.245332i
$349$	11.4343	+	6.60159i	0.612064	+	0.353375i	0.773773	−	0.633463i	$-0.218367\pi$
$349$	11.4343	+	6.60159i	0.612064	+	0.353375i	−0.161709	+	0.986838i	$0.551701\pi$
$350$	13.1848	−	1.07749i	0.704757	−	0.0575942i
$351$	−11.2270	+	17.7448i	−0.599252	+	0.947146i
$352$	−1.98187	−	1.14423i	−0.105634	−	0.0609878i
$353$		−	31.0211i		−	1.65109i	−0.564340	−	0.825543i	$-0.690869\pi$
$353$		−	31.0211i		−	1.65109i	0.564340	−	0.825543i	$-0.309131\pi$
$354$	−2.51920	−	15.5090i	−0.133894	−	0.824292i
$355$	−9.81137	+	22.6428i	−0.520733	+	1.20176i
$356$	−5.08916	−	8.81469i	−0.269725	−	0.467178i
$357$	−14.4475	+	25.8013i	−0.764641	+	1.36555i
$358$	−13.5399	−	7.81725i	−0.715605	−	0.413155i
$359$	−24.9912	−	14.4287i	−1.31899	−	0.761517i	−0.335420	−	0.942069i	$-0.608878\pi$
$359$	−24.9912	−	14.4287i	−1.31899	−	0.761517i	−0.983565	+	0.180552i	$0.942212\pi$
$360$	−6.68293	−	0.581749i	−0.352221	−	0.0306608i
$361$	−9.47897	−	16.4181i	−0.498893	−	0.864108i
$362$	−21.0529	+	12.1549i	−1.10652	+	0.638847i
$363$	1.60040	+	9.85254i	0.0839991	+	0.517124i
$364$	−3.92324	−	9.94592i	−0.205634	−	0.521308i
$365$	3.98563	+	34.5926i	0.208617	+	1.81066i
$366$	−6.62367	+	17.4610i	−0.346225	+	0.912703i
$367$	−12.3632			−0.645354			−0.322677	−	0.946509i	$-0.604583\pi$
$367$	−12.3632			−0.645354			−0.322677	+	0.946509i	$0.604583\pi$
$368$	1.00425	+	1.73941i	0.0523501	+	0.0906730i
$369$	−5.19374	−	4.60271i	−0.270375	−	0.239608i
$370$	−7.60197	+	17.5439i	−0.395207	+	0.912066i
$371$	7.76695	−	9.77387i	0.403240	−	0.507434i
$372$	1.06805	+	1.30833i	0.0553757	+	0.0678338i
$373$			36.6612i			1.89825i	0.314906	+	0.949123i	$0.398027\pi$
$373$			36.6612i			1.89825i	−0.314906	+	0.949123i	$0.601973\pi$
$374$	−7.38362	+	12.7888i	−0.381798	+	0.661294i
$375$	16.9462	−	9.37160i	0.875097	−	0.483947i
$376$	4.13773	−	2.38892i	0.213387	−	0.123199i
$377$		−	13.7840i		−	0.709910i
$378$	−13.5045	−	2.57468i	−0.694596	−	0.132427i
$379$	19.2906			0.990893			0.495446	−	0.868639i	$-0.335004\pi$
$379$	19.2906			0.990893			0.495446	+	0.868639i	$0.335004\pi$
$380$	−0.455607	+	0.0524934i	−0.0233722	+	0.00269285i
$381$	20.2297	−	3.28601i	1.03640	−	0.168347i
$382$	10.3403	+	5.96997i	0.529055	+	0.305450i
$383$		−	8.18915i		−	0.418446i	−0.977868	−	0.209223i	$-0.932907\pi$
$383$		−	8.18915i		−	0.418446i	0.977868	−	0.209223i	$-0.0670934\pi$
$384$	−1.34174	+	1.09532i	−0.0684705	+	0.0558954i
$385$	13.5313	+	0.448993i	0.689619	+	0.0228828i
$386$		−	12.4417i		−	0.633265i
$387$	−7.22021	−	1.47520i	−0.367024	−	0.0749887i
$388$	4.24029	+	7.34440i	0.215268	+	0.372855i
$389$			8.82897i			0.447647i	0.974630	+	0.223823i	$0.0718538\pi$
$389$			8.82897i			0.447647i	−0.974630	+	0.223823i	$0.928146\pi$
$390$	−11.2202	−	10.9117i	−0.568156	−	0.552533i
$391$	11.2242	−	6.48032i	0.567634	−	0.327724i
$392$	5.11496	−	4.77883i	0.258344	−	0.241367i
$393$	−0.820971	−	5.05415i	−0.0414125	−	0.254948i
$394$	11.5232	+	19.9588i	0.580532	+	1.00551i
$395$	−1.85146	−	16.0695i	−0.0931572	−	0.808542i
$396$	−6.72644	−	1.37431i	−0.338016	−	0.0690619i
$397$	5.82466	−	10.0886i	0.292332	−	0.506333i	−0.682029	−	0.731325i	$-0.738902\pi$
$397$	5.82466	−	10.0886i	0.292332	−	0.506333i	0.974361	+	0.224992i	$0.0722356\pi$
$398$	−6.98847	−	4.03479i	−0.350300	−	0.202246i
$399$	−0.939813	+	0.0123578i	−0.0470495	+	0.000618666i
$400$	1.44977	−	4.78520i	0.0724883	−	0.239260i
$401$			2.64152i			0.131911i	0.997823	+	0.0659557i	$0.0210096\pi$
$401$			2.64152i			0.131911i	−0.997823	+	0.0659557i	$0.978990\pi$
$402$	−10.3461	+	1.68058i	−0.516018	+	0.0838195i
$403$			3.94047i			0.196289i
$404$	0.757545	−	1.31211i	0.0376893	−	0.0652797i
$405$	−19.5704	+	4.69030i	−0.972462	+	0.233063i
$406$	8.39500	−	3.31147i	0.416637	−	0.164345i
$407$	−9.78409	+	16.9465i	−0.484979	+	0.840009i
$408$	7.06800	+	8.65812i	0.349918	+	0.428641i
$409$	−3.46721	−	2.00180i	−0.171443	−	0.0989824i	0.411823	−	0.911264i	$-0.364892\pi$
$409$	−3.46721	−	2.00180i	−0.171443	−	0.0989824i	−0.583266	+	0.812281i	$0.698225\pi$
$410$	4.15411	−	3.08202i	0.205157	−	0.152210i
$411$	1.90557	+	11.7313i	0.0939950	+	0.578662i
$412$	9.38804	−	16.2606i	0.462516	−	0.801100i
$413$	23.7389	+	3.53633i	1.16811	+	0.174011i
$414$	4.50951	+	3.99635i	0.221631	+	0.196410i
$415$	15.2465	+	20.5500i	0.748420	+	1.00876i
$416$	−4.04110			−0.198131
$417$	1.82157	+	2.23138i	0.0892028	+	0.109271i
$418$	−0.469368			−0.0229575
$419$	−10.3156	−	17.8671i	−0.503949	−	0.872865i	−0.999990	−	0.00456603i	$-0.998547\pi$
$419$	−10.3156	−	17.8671i	−0.503949	−	0.872865i	0.496040	−	0.868299i	$-0.334787\pi$
$420$	3.95011	−	9.45498i	0.192745	−	0.461356i
$421$	−2.08360	+	3.60891i	−0.101549	+	0.175887i	−0.912323	−	0.409472i	$-0.865713\pi$
$421$	−2.08360	+	3.60891i	−0.101549	+	0.175887i	0.810774	+	0.585359i	$0.199046\pi$
$422$	9.23801	−	16.0007i	0.449699	−	0.778902i
$423$	9.50657	−	10.7273i	0.462225	−	0.521579i
$424$	−2.35928	−	4.08640i	−0.114577	−	0.198453i
$425$	−30.8785	−	9.35519i	−1.49782	−	0.453794i
$426$	12.0879	+	14.8074i	0.585661	+	0.717420i
$427$	−22.3337	−	17.7478i	−1.08080	−	0.858875i
$428$	−9.00357	−	15.5946i	−0.435204	−	0.753795i
$429$	−10.1294	−	12.4083i	−0.489054	−	0.599079i
$430$	2.18388	−	5.04000i	0.105316	−	0.243050i
$431$	1.89577	−	1.09452i	0.0913159	−	0.0527213i	−0.453647	−	0.891182i	$-0.649877\pi$
$431$	1.89577	−	1.09452i	0.0913159	−	0.0527213i	0.544963	+	0.838460i	$0.316544\pi$
$432$	−2.77820	+	4.39108i	−0.133666	+	0.211266i
$433$	23.8117			1.14432			0.572158	−	0.820143i	$-0.306106\pi$
$433$	23.8117			1.14432			0.572158	+	0.820143i	$0.306106\pi$
$434$	−2.39991	+	0.946661i	−0.115199	+	0.0454412i
$435$	9.21014	−	9.47056i	0.441592	−	0.454079i
$436$	16.2757			0.779464
$437$	0.356756	+	0.205973i	0.0170659	+	0.00985302i
$438$	25.2190	+	9.56658i	1.20501	+	0.457109i
$439$	12.4614	−	7.19459i	0.594750	−	0.343379i	−0.172223	−	0.985058i	$-0.555095\pi$
$439$	12.4614	−	7.19459i	0.594750	−	0.343379i	0.766973	+	0.641679i	$0.221762\pi$
$440$	2.03453	−	4.69532i	0.0969925	−	0.223841i
$441$	10.0182	−	18.4563i	0.477056	−	0.878873i
$442$			26.0768i			1.24035i
$443$	−18.3040	−	31.7035i	−0.869649	−	1.50628i	−0.862355	−	0.506304i	$-0.831012\pi$
$443$	−18.3040	−	31.7035i	−0.869649	−	1.50628i	−0.00729415	−	0.999973i	$-0.502322\pi$
$444$	9.36586	+	11.4729i	0.444484	+	0.544482i
$445$	18.2782	−	13.5609i	0.866470	−	0.642850i
$446$	−4.21539			−0.199604
$447$	−20.0457	+	3.25613i	−0.948130	+	0.154010i
$448$	−0.970835	−	2.46119i	−0.0458676	−	0.116281i
$449$			0.350689i			0.0165500i	0.999966	+	0.00827501i	$0.00263405\pi$
$449$			0.350689i			0.0165500i	−0.999966	+	0.00827501i	$0.997366\pi$
$450$	−0.418137	−	14.9942i	−0.0197112	−	0.706832i
$451$	4.58455	−	2.64689i	0.215878	−	0.124637i
$452$	5.97346			0.280968
$453$	0.934026	+	5.75015i	0.0438843	+	0.270166i
$454$	−16.0856	+	9.28700i	−0.754933	+	0.435861i
$455$	21.0895	−	11.2605i	0.988691	−	0.527901i
$456$	−0.125998	+	0.332151i	−0.00590041	+	0.0155544i
$457$	−1.65880	+	0.957706i	−0.0775952	+	0.0447996i	−0.538296	−	0.842756i	$-0.680932\pi$
$457$	−1.65880	+	0.957706i	−0.0775952	+	0.0447996i	0.460700	+	0.887556i	$0.347598\pi$
$458$	−1.36101	+	0.785777i	−0.0635956	+	0.0367169i
$459$	28.3352	+	17.9275i	1.32257	+	0.836783i
$460$	−3.60685	+	2.67599i	−0.168170	+	0.124769i
$461$	12.2091	−	21.1468i	0.568636	−	0.984906i	−0.428065	−	0.903748i	$-0.640805\pi$
$461$	12.2091	−	21.1468i	0.568636	−	0.984906i	0.996701	−	0.0811583i	$-0.0258619\pi$
$462$	5.12367	−	9.15023i	0.238375	−	0.425707i
$463$	−4.09771	+	2.36581i	−0.190437	+	0.109949i	−0.592187	−	0.805801i	$-0.701735\pi$
$463$	−4.09771	+	2.36581i	−0.190437	+	0.109949i	0.401750	+	0.915749i	$0.368402\pi$
$464$		−	3.41095i		−	0.158349i
$465$	−2.63294	+	2.70738i	−0.122100	+	0.125552i
$466$	−7.55808			−0.350121
$467$	29.9337	+	17.2822i	1.38517	+	0.799726i	0.992766	−	0.120068i	$-0.0383112\pi$
$467$	29.9337	+	17.2822i	1.38517	+	0.799726i	0.392401	+	0.919794i	$0.371645\pi$
$468$	−11.5000	+	3.83725i	−0.531587	+	0.177377i
$469$	2.35911	−	15.8364i	0.108933	−	0.731256i
$470$	6.36569	+	8.58003i	0.293627	+	0.395767i
$471$	−4.18349	−	1.58697i	−0.192765	−	0.0731236i
$472$	4.53573	−	7.85612i	0.208774	−	0.361607i
$473$	2.81076	−	4.86838i	0.129239	−	0.223848i
$474$	−11.7151	−	4.44401i	−0.538093	−	0.204120i
$475$	−0.233215	−	0.998638i	−0.0107006	−	0.0458207i
$476$	−15.8818	+	6.26470i	−0.727943	+	0.287142i
$477$	−10.5942	−	9.38863i	−0.485076	−	0.429876i
$478$	14.4459	+	8.34037i	0.660742	+	0.381480i
$479$	−41.5530			−1.89861			−0.949303	−	0.314364i	$-0.898209\pi$
$479$	−41.5530			−1.89861			−0.949303	+	0.314364i	$0.898209\pi$
$480$	−2.77652	−	2.70017i	−0.126730	−	0.123245i
$481$			34.5545i			1.57555i
$482$	24.5697	−	14.1853i	1.11912	−	0.646124i
$483$	−7.90978	+	4.70645i	−0.359907	+	0.214151i
$484$	−2.88146	+	4.99084i	−0.130976	+	0.226856i
$485$	−15.2294	+	11.2990i	−0.691531	+	0.513060i
$486$	−3.73652	+	15.1340i	−0.169492	+	0.686493i
$487$	−8.25200	+	4.76429i	−0.373934	+	0.215891i	−0.675176	−	0.737657i	$-0.735932\pi$
$487$	−8.25200	+	4.76429i	−0.373934	+	0.215891i	0.301242	+	0.953548i	$0.402599\pi$
$488$	−9.33757	+	5.39105i	−0.422692	+	0.244041i
$489$	−15.0003	+	39.5432i	−0.678338	+	1.78821i
$490$	11.9247	+	10.1391i	0.538702	+	0.458040i
$491$	3.87273	−	2.23592i	0.174774	−	0.100906i	−0.410061	−	0.912058i	$-0.634493\pi$
$491$	3.87273	−	2.23592i	0.174774	−	0.100906i	0.584835	+	0.811152i	$0.301159\pi$
$492$	−0.642402	−	3.95482i	−0.0289617	−	0.178297i
$493$	−22.0105			−0.991303
$494$	−0.717793	+	0.414418i	−0.0322950	+	0.0186455i
$495$	1.33131	−	15.2937i	0.0598380	−	0.687399i
$496$			0.975100i			0.0437833i
$497$	−27.1616	+	10.7141i	−1.21836	+	0.480592i
$498$	19.5642	−	3.17790i	0.876691	−	0.142405i
$499$	−35.7197			−1.59903			−0.799516	−	0.600644i	$-0.794911\pi$
$499$	−35.7197			−1.59903			−0.799516	+	0.600644i	$0.794911\pi$
$500$	11.0008	+	1.99575i	0.491969	+	0.0892528i
$501$	−0.0114345	−	0.0140069i	−0.000510854	−	0.000625783i
$502$	−4.97776	−	8.62173i	−0.222168	−	0.384807i
$503$		−	2.25896i		−	0.100722i	−0.998731	−	0.0503609i	$-0.983963\pi$
$503$		−	2.25896i		−	0.100722i	0.998731	−	0.0503609i	$-0.0160372\pi$
$504$	−5.09980	−	6.08210i	−0.227163	−	0.270918i
$505$	3.10856	+	1.34697i	0.138329	+	0.0599394i
$506$	−3.98058	+	2.29819i	−0.176958	+	0.102167i
$507$	−5.39350	−	2.04597i	−0.239534	−	0.0908647i
$508$	10.2474	+	5.91635i	0.454656	+	0.262496i
$509$	−39.4144			−1.74701			−0.873506	−	0.486814i	$-0.838159\pi$
$509$	−39.4144			−1.74701			−0.873506	+	0.486814i	$0.838159\pi$
$510$	−17.4239	+	17.9166i	−0.771545	+	0.793361i
$511$	−25.6331	+	32.2566i	−1.13394	+	1.42695i
$512$	−1.00000			−0.0441942
$513$	−0.0431644	+	1.06487i	−0.00190575	+	0.0470149i
$514$	16.2504	−	9.38216i	0.716774	−	0.413829i
$515$	38.5235	+	16.6926i	1.69755	+	0.735565i
$516$	−2.69061	−	3.29593i	−0.118448	−	0.145095i
$517$	5.46696	+	9.46906i	0.240437	+	0.416449i
$518$	−21.0451	+	8.30140i	−0.924671	+	0.364743i
$519$	19.9710	+	24.4640i	0.876632	+	1.07385i
$520$	−1.03427	−	8.97678i	−0.0453558	−	0.393658i
$521$	19.9940	+	34.6307i	0.875954	+	1.51720i	0.855743	+	0.517401i	$0.173100\pi$
$521$	19.9940	+	34.6307i	0.875954	+	1.51720i	0.0202106	+	0.999796i	$0.493566\pi$
$522$	−3.23888	−	9.70673i	−0.141762	−	0.424852i
$523$	−14.4859	+	25.0903i	−0.633424	+	1.09712i	0.353422	+	0.935464i	$0.385018\pi$
$523$	−14.4859	+	25.0903i	−0.633424	+	1.09712i	−0.986847	+	0.161659i	$0.948315\pi$
$524$	1.47813	−	2.56020i	0.0645724	−	0.111843i
$525$	22.0140	+	6.35477i	0.960770	+	0.277345i
$526$	1.47472	+	2.55429i	0.0643008	+	0.111372i
$527$	6.29222			0.274094
$528$	−2.50661	−	3.07053i	−0.109086	−	0.133628i
$529$	−18.9659			−0.824606
$530$	8.47358	−	6.28671i	0.368069	−	0.273077i
$531$	5.44777	−	26.6636i	0.236413	−	1.15710i
$532$	−0.424840	−	0.337605i	−0.0184192	−	0.0146371i
$533$	4.67402	−	8.09564i	0.202454	−	0.350661i
$534$	−2.82658	−	17.4013i	−0.122318	−	0.753028i
$535$	32.3371	−	23.9915i	1.39806	−	1.03724i
$536$	−5.24087	−	3.02582i	−0.226371	−	0.130695i
$537$	−17.1248	−	20.9775i	−0.738990	−	0.905244i
$538$	13.8077	−	23.9156i	0.595291	−	1.03107i
$539$	10.9362	+	11.7054i	0.471055	+	0.504188i
$540$	−10.4653	−	5.04758i	−0.450354	−	0.217213i
$541$	2.46717	−	4.27326i	0.106072	−	0.183722i	−0.808104	−	0.589040i	$-0.799506\pi$
$541$	2.46717	−	4.27326i	0.106072	−	0.183722i	0.914176	+	0.405318i	$0.132839\pi$
$542$			14.7966i			0.635566i
$543$	−41.5611	+	6.75098i	−1.78356	+	0.289712i
$544$			6.45290i			0.276666i
$545$	4.16557	+	36.1544i	0.178434	+	1.54868i
$546$	−0.243485	−	18.5170i	−0.0104202	−	0.792456i
$547$	−12.6990	−	7.33178i	−0.542971	−	0.313484i	0.203311	−	0.979114i	$-0.434830\pi$
$547$	−12.6990	−	7.33178i	−0.542971	−	0.313484i	−0.746282	+	0.665630i	$0.768163\pi$
$548$	−3.43092	+	5.94252i	−0.146562	+	0.253852i
$549$	−21.4534	+	24.2082i	−0.915608	+	1.03318i
$550$	10.9508	+	3.31774i	0.466943	+	0.141469i
$551$	−0.349795	−	0.605863i	−0.0149018	−	0.0258106i
$552$	0.557771	+	3.43381i	0.0237403	+	0.146153i
$553$	11.9075	−	14.9843i	0.506358	−	0.637197i
$554$	−6.88813	+	3.97687i	−0.292649	+	0.168961i
$555$	−23.0886	+	23.7414i	−0.980056	+	1.00777i
$556$			1.66305i			0.0705289i
$557$	−13.3908	−	23.1936i	−0.567387	−	0.982743i	−0.996823	−	0.0796459i	$-0.974621\pi$
$557$	−13.3908	−	23.1936i	−0.567387	−	0.982743i	0.429436	−	0.903097i	$-0.358712\pi$
$558$	0.925912	+	2.77490i	0.0391970	+	0.117471i
$559$		−	9.92679i		−	0.419858i
$560$	5.21876	−	2.78650i	0.220533	−	0.117751i
$561$	−19.8138	+	16.1749i	−0.836540	+	0.682904i
$562$		−	14.9938i		−	0.632475i
$563$	16.0483	+	9.26547i	0.676354	+	0.390493i	0.798480	−	0.602022i	$-0.205638\pi$
$563$	16.0483	+	9.26547i	0.676354	+	0.390493i	−0.122126	+	0.992515i	$0.538971\pi$
$564$	8.16840	−	1.32684i	0.343952	−	0.0558698i
$565$	1.52884	+	13.2693i	0.0643186	+	0.558243i
$566$	−29.8023			−1.25268
$567$	−20.2881	−	12.4657i	−0.852021	−	0.523508i
$568$			11.0359i			0.463058i
$569$	20.6344	−	11.9133i	0.865041	−	0.499431i	−0.000656372	−	1.00000i	$-0.500209\pi$
$569$	20.6344	−	11.9133i	0.865041	−	0.499431i	0.865697	+	0.500568i	$0.166876\pi$
$570$	−0.770080	−	0.194879i	−0.0322551	−	0.00816258i
$571$	−22.2726	+	38.5773i	−0.932079	+	1.61441i	−0.152318	+	0.988332i	$0.548674\pi$
$571$	−22.2726	+	38.5773i	−0.932079	+	1.61441i	−0.779761	+	0.626077i	$0.784660\pi$
$572$		−	9.24791i		−	0.386675i
$573$	13.0781	+	16.0203i	0.546344	+	0.669258i
$574$	6.05347	+	0.901771i	0.252667	+	0.0376392i
$575$	−6.86750	−	7.32727i	−0.286395	−	0.305568i
$576$	−2.84576	+	0.949556i	−0.118573	+	0.0395648i
$577$	1.24045	+	2.14853i	0.0516407	+	0.0894443i	0.890690	−	0.454611i	$-0.150222\pi$
$577$	1.24045	+	2.14853i	0.0516407	+	0.0894443i	−0.839050	+	0.544055i	$0.816888\pi$
$578$	24.6399			1.02489
$579$	7.64319	−	20.1486i	0.317640	−	0.837349i
$580$	7.57698	−	0.872991i	0.314617	−	0.0362490i
$581$	−4.46098	+	29.9460i	−0.185073	+	1.24237i
$582$	2.35511	+	14.4988i	0.0976224	+	0.600993i
$583$	9.35158	−	5.39914i	0.387303	−	0.223609i
$584$	7.78631	+	13.4863i	0.322200	+	0.558066i
$585$	−11.4672	−	24.5636i	−0.474112	−	1.01558i
$586$	2.19993	+	1.27013i	0.0908784	+	0.0524687i
$587$	−9.73573	−	5.62093i	−0.401837	−	0.232001i	0.285439	−	0.958397i	$-0.407860\pi$
$587$	−9.73573	−	5.62093i	−0.401837	−	0.232001i	−0.687276	+	0.726396i	$0.741194\pi$
$588$	11.2191	−	4.59683i	0.462670	−	0.189570i
$589$	0.0999973	+	0.173200i	0.00412032	+	0.00713660i
$590$	18.6122	+	8.06487i	0.766253	+	0.332025i
$591$	6.40014	+	39.4012i	0.263266	+	1.62075i
$592$			8.55079i			0.351435i
$593$	−25.3760	−	14.6508i	−1.04207	−	0.601638i	−0.121649	−	0.992573i	$-0.538818\pi$
$593$	−25.3760	−	14.6508i	−1.04207	−	0.601638i	−0.920418	+	0.390935i	$0.872152\pi$
$594$	−10.0488	−	6.35782i	−0.412309	−	0.260865i
$595$	−17.9810	−	33.6761i	−0.737150	−	1.38059i
$596$	−10.1542	−	5.86255i	−0.415933	−	0.240139i
$597$	−8.83880	−	10.8273i	−0.361748	−	0.443132i
$598$	−4.05826	+	7.02912i	−0.165955	+	0.287442i
$599$	11.6918	+	6.75024i	0.477712	+	0.275807i	0.719463	−	0.694531i	$-0.244388\pi$
$599$	11.6918	+	6.75024i	0.477712	+	0.275807i	−0.241750	+	0.970338i	$0.577722\pi$
$600$	5.28747	−	6.85876i	0.215860	−	0.280008i
$601$	13.5297	+	7.81138i	0.551889	+	0.318633i	0.749883	−	0.661570i	$-0.230110\pi$
$601$	13.5297	+	7.81138i	0.551889	+	0.318633i	−0.197995	+	0.980203i	$0.563443\pi$
$602$	6.04582	−	2.38482i	0.246409	−	0.0971979i
$603$	−17.7874	−	3.63425i	−0.724360	−	0.147998i
$604$	−1.68168	+	2.91276i	−0.0684266	+	0.118518i
$605$	−11.8240	−	5.12345i	−0.480713	−	0.208298i
$606$	2.03286	−	1.65951i	0.0825792	−	0.0674130i
$607$	8.14122			0.330442			0.165221	−	0.986257i	$-0.447166\pi$
$607$	8.14122			0.330442			0.165221	+	0.986257i	$0.447166\pi$
$608$	−0.177623	+	0.102551i	−0.00720357	+	0.00415899i
$609$	15.6296	−	0.205517i	0.633342	−	0.00832797i
$610$	−14.3654	−	19.3625i	−0.581637	−	0.783963i
$611$	16.7210	+	9.65386i	0.676458	+	0.390553i
$612$	6.12739	+	18.3634i	0.247685	+	0.742297i
$613$	−14.5475	+	8.39900i	−0.587568	+	0.339232i	−0.764135	−	0.645056i	$-0.776834\pi$
$613$	−14.5475	+	8.39900i	−0.587568	+	0.339232i	0.176567	+	0.984289i	$0.443501\pi$
$614$	4.03149	+	6.98275i	0.162698	+	0.281801i
$615$	8.62071	−	2.43920i	0.347621	−	0.0983582i
$616$	5.63236	−	2.22172i	0.226934	−	0.0895158i
$617$	13.7676	+	23.8461i	0.554262	+	0.960009i	0.997961	+	0.0638334i	$0.0203326\pi$
$617$	13.7676	+	23.8461i	0.554262	+	0.960009i	−0.443699	+	0.896176i	$0.646334\pi$
$618$	25.1926	−	20.5659i	1.01340	−	0.827280i
$619$		−	9.34724i		−	0.375697i	−0.982198	−	0.187849i	$-0.939849\pi$
$619$		−	9.34724i		−	0.375697i	0.982198	−	0.187849i	$-0.0601514\pi$
$620$	−2.16606	+	0.249565i	−0.0869911	+	0.0100228i
$621$	4.84788	+	9.24217i	0.194539	+	0.370875i
$622$	−0.763625			−0.0306186
$623$	26.6354	+	3.96781i	1.06713	+	0.158967i
$624$	−6.54434	−	2.48253i	−0.261983	−	0.0993808i
$625$	−1.61779	+	24.9476i	−0.0647116	+	0.997904i
$626$	1.91868	−	3.32326i	0.0766860	−	0.132824i
$627$	−0.760117	−	0.288343i	−0.0303561	−	0.0115153i
$628$	−1.29164	−	2.23719i	−0.0515421	−	0.0892736i
$629$	55.1774			2.20007
$630$	12.2054	−	12.8852i	0.486274	−	0.513359i
$631$	−45.9246			−1.82823			−0.914115	−	0.405454i	$-0.867113\pi$
$631$	−45.9246			−1.82823			−0.914115	+	0.405454i	$0.867113\pi$
$632$	−3.61701	−	6.26485i	−0.143877	−	0.249202i
$633$	24.7900	−	20.2372i	0.985316	−	0.804356i
$634$	8.66445	−	15.0073i	0.344109	−	0.596015i
$635$	−10.5197	+	24.2776i	−0.417462	+	0.963425i
$636$	−1.31037	−	8.06706i	−0.0519597	−	0.319880i
$637$	27.0594	+	8.24493i	1.07213	+	0.326676i
$638$	7.80583			0.309036
$639$	10.4793	+	31.4056i	0.414553	+	1.24239i
$640$	−0.255938	−	2.22137i	−0.0101168	−	0.0878075i
$641$			18.7718i			0.741442i	0.928744	+	0.370721i	$0.120889\pi$
$641$			18.7718i			0.741442i	−0.928744	+	0.370721i	$0.879111\pi$
$642$	−5.00069	−	30.7858i	−0.197361	−	1.21502i
$643$	11.5123	+	19.9399i	0.454001	+	0.786353i	0.998630	−	0.0523244i	$-0.0166630\pi$
$643$	11.5123	+	19.9399i	0.454001	+	0.786353i	−0.544629	+	0.838677i	$0.683330\pi$
$644$	−5.25598	−	0.782971i	−0.207115	−	0.0308534i
$645$	6.63286	−	6.82041i	0.261169	−	0.268553i
$646$	0.661750	+	1.14619i	0.0260362	+	0.0450961i
$647$	−14.6259	+	8.44426i	−0.575003	+	0.331978i	−0.759145	−	0.650922i	$-0.774383\pi$
$647$	−14.6259	+	8.44426i	−0.575003	+	0.331978i	0.184142	+	0.982900i	$0.441049\pi$
$648$	−7.19669	+	5.40442i	−0.282713	+	0.212305i
$649$	17.9785	+	10.3799i	0.705716	+	0.407445i
$650$	19.6761	−	4.59500i	0.771759	−	0.180231i
$651$	−4.46808	+	0.0587520i	−0.175118	+	0.00230267i
$652$	−21.1464	+	12.2089i	−0.828156	+	0.478136i
$653$	−21.7662			−0.851776			−0.425888	−	0.904776i	$-0.640038\pi$
$653$	−21.7662			−0.851776			−0.425888	+	0.904776i	$0.640038\pi$
$654$	26.3576	+	9.99850i	1.03066	+	0.390972i
$655$	6.06546	+	2.62823i	0.236997	+	0.102693i
$656$	1.15662	−	2.00333i	0.0451585	−	0.0782168i
$657$	34.9639	+	30.9852i	1.36407	+	1.20885i
$658$	−1.86254	+	12.5030i	−0.0726095	+	0.487418i
$659$	−21.0718	−	12.1658i	−0.820841	−	0.473913i	0.0298654	−	0.999554i	$-0.490492\pi$
$659$	−21.0718	−	12.1658i	−0.820841	−	0.473913i	−0.850706	+	0.525641i	$0.823825\pi$
$660$	6.17925	−	6.35397i	0.240527	−	0.247328i
$661$	22.4717	+	12.9740i	0.874048	+	0.504632i	0.868691	−	0.495354i	$-0.164962\pi$
$661$	22.4717	+	12.9740i	0.874048	+	0.504632i	0.00535644	+	0.999986i	$0.498295\pi$
$662$	−2.47937	+	4.29439i	−0.0963633	+	0.166906i
$663$	−16.0195	+	42.2300i	−0.622147	+	1.64008i
$664$	9.91029	+	5.72171i	0.384594	+	0.222045i
$665$	0.641215	−	1.03013i	0.0248652	−	0.0399469i
$666$	8.11945	+	24.3335i	0.314622	+	0.942903i
$667$	−5.93303	−	3.42544i	−0.229728	−	0.132633i
$668$		−	0.0104394i		−	0.000403911i
$669$	−6.82659	−	2.58960i	−0.263931	−	0.100120i
$670$	5.38013	−	12.4163i	0.207853	−	0.479685i
$671$	−12.3372	−	21.3687i	−0.476274	−	0.824930i
$672$	−0.0602522	−	4.58218i	−0.00232428	−	0.176761i
$673$	−3.32531	−	1.91987i	−0.128181	−	0.0740054i	0.434538	−	0.900653i	$-0.356912\pi$
$673$	−3.32531	−	1.91987i	−0.128181	−	0.0740054i	−0.562719	+	0.826648i	$0.690245\pi$
$674$	1.58895	+	0.917381i	0.0612041	+	0.0353362i
$675$	8.53408	−	24.5391i	0.328477	−	0.944512i
$676$	−1.66523	−	2.88426i	−0.0640472	−	0.110933i
$677$	14.0578	−	8.11628i	0.540286	−	0.311934i	−0.204909	−	0.978781i	$-0.565690\pi$
$677$	14.0578	−	8.11628i	0.540286	−	0.311934i	0.745195	+	0.666847i	$0.232357\pi$
$678$	9.67370	+	3.66962i	0.371516	+	0.140931i
$679$	−22.1926	−	3.30598i	−0.851674	−	0.126872i
$680$	−14.3343	+	1.65154i	−0.549695	+	0.0633338i
$681$	−31.7549	+	5.15811i	−1.21685	+	0.197659i
$682$	−2.23148			−0.0854479
$683$	−4.73579	−	8.20262i	−0.181210	−	0.313865i	0.761083	−	0.648655i	$-0.224668\pi$
$683$	−4.73579	−	8.20262i	−0.181210	−	0.313865i	−0.942293	+	0.334790i	$0.891335\pi$
$684$	−0.408095	+	0.460498i	−0.0156039	+	0.0176076i
$685$	−14.0787	−	6.10043i	−0.537918	−	0.233085i
$686$	1.47927	+	18.4611i	0.0564789	+	0.704848i
$687$	−2.68680	+	0.436430i	−0.102508	+	0.0166508i
$688$		−	2.45646i		−	0.0936516i
$689$	9.53409	−	16.5135i	0.363220	−	0.629115i
$690$	−7.48502	+	2.11786i	−0.284950	+	0.0806256i
$691$	−13.6619	+	7.88768i	−0.519722	+	0.300062i	−0.736821	−	0.676088i	$-0.763674\pi$
$691$	−13.6619	+	7.88768i	−0.519722	+	0.300062i	0.217099	+	0.976150i	$0.430341\pi$
$692$			18.2330i			0.693116i
$693$	13.9187	−	11.6707i	0.528727	−	0.443334i
$694$	6.78486			0.257550
$695$	−3.69425	+	0.425637i	−0.140131	+	0.0161453i
$696$	2.09542	−	5.52385i	0.0794265	−	0.209381i
$697$	−12.9273	−	7.46357i	−0.489655	−	0.282703i
$698$			13.2032i			0.499748i
$699$	−12.2399	−	4.64309i	−0.462956	−	0.175618i
$700$	7.52553	+	10.8796i	0.284438	+	0.411211i
$701$			3.43541i			0.129754i	0.997893	+	0.0648769i	$0.0206655\pi$
$701$			3.43541i			0.129754i	−0.997893	+	0.0648769i	$0.979335\pi$
$702$	−20.9809	−	0.850463i	−0.791874	−	0.0320987i
$703$	0.876890	+	1.51882i	0.0330725	+	0.0572833i
$704$		−	2.28847i		−	0.0862498i
$705$	5.03800	+	17.8055i	0.189742	+	0.670593i
$706$	26.8650	−	15.5105i	1.01108	−	0.583747i
$707$	1.47090	+	3.72893i	0.0553190	+	0.140241i
$708$	12.1716	−	9.93617i	0.457435	−	0.373424i
$709$	12.9306	+	22.3965i	0.485620	+	0.841118i	0.999863	−	0.0165263i	$-0.00526071\pi$
$709$	12.9306	+	22.3965i	0.485620	+	0.841118i	−0.514244	+	0.857644i	$0.671927\pi$
$710$	−24.5149	+	2.82452i	−0.920030	+	0.106002i
$711$	−16.2420	−	14.3937i	−0.609121	−	0.539806i
$712$	5.08916	−	8.81469i	0.190724	−	0.330345i
$713$	1.69610	+	0.979242i	0.0635193	+	0.0366729i
$714$	−29.5684	+	0.388802i	−1.10657	+	0.0145505i
$715$	20.5431	−	2.36689i	0.768267	−	0.0885168i
$716$		−	15.6345i		−	0.584289i
$717$	18.2708	+	22.3812i	0.682335	+	0.835842i
$718$		−	28.8574i		−	1.07695i
$719$	20.8858	−	36.1753i	0.778909	−	1.34911i	−0.153663	−	0.988123i	$-0.549107\pi$
$719$	20.8858	−	36.1753i	0.778909	−	1.34911i	0.932571	−	0.360986i	$-0.117560\pi$
$720$	−2.83766	−	6.07846i	−0.105753	−	0.226531i
$721$	18.2285	+	46.2116i	0.678864	+	1.72101i
$722$	9.47897	−	16.4181i	0.352771	−	0.611017i
$723$	48.5037	−	7.87870i	1.80387	−	0.293012i
$724$	−21.0529	−	12.1549i	−0.782425	−	0.451733i
$725$	3.87848	+	16.6079i	0.144043	+	0.616801i
$726$	−7.73235	+	6.31226i	−0.286975	+	0.234270i
$727$	−21.4490	+	37.1508i	−0.795499	+	1.37785i	0.127022	+	0.991900i	$0.459458\pi$
$727$	−21.4490	+	37.1508i	−0.795499	+	1.37785i	−0.922522	+	0.385945i	$0.873875\pi$
$728$	6.65180	−	8.37059i	0.246532	−	0.310235i
$729$	−15.3482	+	22.2133i	−0.568453	+	0.822716i
$730$	−27.9652	+	20.7479i	−1.03504	+	0.767916i
$731$	−15.8513			−0.586281
$732$	−18.4335	+	2.99425i	−0.681323	+	0.110671i
$733$	4.73892			0.175036			0.0875179	−	0.996163i	$-0.472106\pi$
$733$	4.73892			0.175036			0.0875179	+	0.996163i	$0.472106\pi$
$734$	−6.18161	−	10.7069i	−0.228167	−	0.395197i
$735$	13.0827	+	23.7454i	0.482562	+	0.875862i
$736$	−1.00425	+	1.73941i	−0.0370171	+	0.0641155i
$737$	6.92448	−	11.9936i	0.255067	−	0.441788i
$738$	1.38919	−	6.79926i	0.0511370	−	0.250284i
$739$	−14.6252	−	25.3317i	−0.537998	−	0.931841i	−0.999012	−	0.0444475i	$-0.985847\pi$
$739$	−14.6252	−	25.3317i	−0.537998	−	0.931841i	0.461013	−	0.887393i	$-0.347486\pi$
$740$	−18.9945	+	2.18847i	−0.698251	+	0.0804499i
$741$	−1.41701	+	0.230173i	−0.0520553	+	0.00845560i
$742$	12.3479	+	1.83944i	0.453305	+	0.0675278i
$743$	−16.2571	−	28.1581i	−0.596415	−	1.03302i	−0.993346	−	0.115173i	$-0.963258\pi$
$743$	−16.2571	−	28.1581i	−0.596415	−	1.03302i	0.396930	−	0.917849i	$-0.370075\pi$
$744$	−0.599024	+	1.57912i	−0.0219613	+	0.0578934i
$745$	10.4240	−	24.0568i	0.381907	−	0.881372i
$746$	−31.7495	+	18.3306i	−1.16243	+	0.671131i
$747$	33.6354	+	6.87222i	1.23065	+	0.251442i
$748$	−14.7672			−0.539944
$749$	47.1224	+	7.01971i	1.72182	+	0.256495i
$750$	16.5891	+	9.99002i	0.605750	+	0.364784i
$751$	−33.1956			−1.21132			−0.605662	−	0.795722i	$-0.707092\pi$
$751$	−33.1956			−1.21132			−0.605662	+	0.795722i	$0.707092\pi$
$752$	4.13773	+	2.38892i	0.150888	+	0.0871150i
$753$	−2.76471	−	17.0204i	−0.100752	−	0.620257i
$754$	11.9373	−	6.89198i	0.434729	−	0.250991i
$755$	−6.90072	−	2.99015i	−0.251143	−	0.108823i
$756$	−4.52250	−	12.9826i	−0.164482	−	0.472171i
$757$		−	1.30712i		−	0.0475082i	−0.999718	−	0.0237541i	$-0.992438\pi$
$757$		−	1.30712i		−	0.0475082i	0.999718	−	0.0237541i	$-0.00756188\pi$
$758$	9.64531	+	16.7062i	0.350334	+	0.606795i
$759$	−7.85816	+	1.27644i	−0.285233	+	0.0463319i
$760$	−0.273264	−	0.368321i	−0.00991233	−	0.0133604i
$761$	−22.7542			−0.824839			−0.412420	−	0.910994i	$-0.635316\pi$
$761$	−22.7542			−0.824839			−0.412420	+	0.910994i	$0.635316\pi$
$762$	12.9606	+	15.8764i	0.469514	+	0.575142i
$763$	−26.7904	+	33.7129i	−0.969879	+	1.22049i
$764$			11.9399i			0.431972i
$765$	−39.2237	+	18.3111i	−1.41814	+	0.662040i
$766$	7.09201	−	4.09457i	0.256245	−	0.147943i
$767$	36.6587			1.32367
$768$	−1.61945	−	0.614321i	−0.0584368	−	0.0221674i
$769$	34.4497	−	19.8896i	1.24229	−	0.717236i	0.272729	−	0.962091i	$-0.412074\pi$
$769$	34.4497	−	19.8896i	1.24229	−	0.717236i	0.969560	+	0.244855i	$0.0787403\pi$
$770$	6.37681	+	11.9429i	0.229804	+	0.430394i
$771$	32.0803	−	5.21096i	1.15534	−	0.187668i
$772$	10.7748	−	6.22084i	0.387794	−	0.223893i
$773$	31.3729	−	18.1132i	1.12841	−	0.651486i	0.184872	−	0.982763i	$-0.440813\pi$
$773$	31.3729	−	18.1132i	1.12841	−	0.651486i	0.943534	+	0.331277i	$0.107479\pi$
$774$	−2.33255	−	6.99049i	−0.0838416	−	0.251268i
$775$	−1.10876	−	4.74775i	−0.0398277	−	0.170544i
$776$	−4.24029	+	7.34440i	−0.152218	+	0.263649i
$777$	−39.1812	+	0.515204i	−1.40562	+	0.0184828i
$778$	−7.64611	+	4.41449i	−0.274126	+	0.158267i
$779$		−	0.474450i		−	0.0169989i
$780$	3.83968	−	15.1728i	0.137483	−	0.543273i
$781$	−25.2554			−0.903709
$782$	11.2242	+	6.48032i	0.401378	+	0.231736i
$783$	0.717846	−	17.7093i	0.0256537	−	0.632877i
$784$	6.69607	+	2.04027i	0.239145	+	0.0728668i
$785$	4.63905	−	3.44180i	0.165575	−	0.122843i
$786$	3.96654	−	3.23806i	0.141482	−	0.115498i
$787$	8.56447	−	14.8341i	0.305290	−	0.528778i	−0.672036	−	0.740519i	$-0.734580\pi$
$787$	8.56447	−	14.8341i	0.305290	−	0.528778i	0.977326	+	0.211740i	$0.0679131\pi$
$788$	−11.5232	+	19.9588i	−0.410498	+	0.711003i
$789$	0.819077	+	5.04249i	0.0291599	+	0.179517i
$790$	12.9908	−	9.63815i	0.462193	−	0.342910i
$791$	−9.83255	+	12.3732i	−0.349605	+	0.439941i
$792$	−2.17303	−	6.51242i	−0.0772151	−	0.231409i
$793$	−37.7340	−	21.7858i	−1.33997	−	0.773635i
$794$	11.6493			0.413419
$795$	17.5846	−	4.97550i	0.623661	−	0.176463i
$796$		−	8.06959i		−	0.286019i
$797$	−35.9212	+	20.7391i	−1.27239	+	0.734616i	−0.975438	−	0.220275i	$-0.929305\pi$
$797$	−35.9212	+	20.7391i	−1.27239	+	0.734616i	−0.296955	+	0.954891i	$0.595971\pi$
$798$	−0.480609	−	0.807723i	−0.0170134	−	0.0285931i
$799$	15.4155	−	26.7004i	0.545360	−	0.944591i
$800$	4.86899	−	1.13707i	0.172145	−	0.0402014i
$801$	6.11249	−	29.9169i	0.215974	−	1.05706i
$802$	−2.28763	+	1.32076i	−0.0807788	+	0.0466377i
$803$	−30.8629	+	17.8187i	−1.08913	+	0.628808i
$804$	−6.62849	−	8.11973i	−0.233769	−	0.286361i
$805$	0.394064	−	11.8759i	0.0138889	−	0.418570i
$806$	−3.41255	+	1.97024i	−0.120202	+	0.0693986i
$807$	37.0527	−	30.2477i	1.30432	−	1.06477i
$808$	1.51509			0.0533007
$809$	−5.30390	+	3.06221i	−0.186475	+	0.107661i	−0.590331	−	0.807161i	$-0.701003\pi$
$809$	−5.30390	+	3.06221i	−0.186475	+	0.107661i	0.403856	+	0.914822i	$0.367670\pi$
$810$	−13.8471	−	14.6033i	−0.486538	−	0.513109i
$811$			51.1448i			1.79594i	0.440059	+	0.897969i	$0.354957\pi$
$811$			51.1448i			1.79594i	−0.440059	+	0.897969i	$0.645043\pi$
$812$	7.06531	+	5.61455i	0.247944	+	0.197032i
$813$	−9.08983	+	23.9622i	−0.318794	+	0.840392i
$814$	−19.5682			−0.685864
$815$	−32.5326	−	43.8492i	−1.13957	−	1.53597i
$816$	−3.96415	+	10.4501i	−0.138773	+	0.365828i
$817$	−0.251912	−	0.436324i	−0.00881328	−	0.0152651i
$818$		−	4.00359i		−	0.139982i
$819$	10.9811	−	30.1369i	0.383710	−	1.05307i
$820$	4.74616	+	2.05656i	0.165743	+	0.0718182i
$821$	7.88867	−	4.55452i	0.275316	−	0.158954i	−0.355985	−	0.934492i	$-0.615855\pi$
$821$	7.88867	−	4.55452i	0.275316	−	0.158954i	0.631301	+	0.775538i	$0.282521\pi$
$822$	−9.20681	+	7.51592i	−0.321124	+	0.262148i
$823$	−38.7300	−	22.3608i	−1.35004	−	0.779449i	−0.361789	−	0.932260i	$-0.617834\pi$
$823$	−38.7300	−	22.3608i	−1.35004	−	0.779449i	−0.988255	+	0.152811i	$0.951167\pi$
$824$	18.7761			0.654096
$825$	15.6960	+	12.1002i	0.546466	+	0.421275i
$826$	8.80689	+	22.3266i	0.306431	+	0.776843i
$827$	−34.3286			−1.19372			−0.596860	−	0.802345i	$-0.703585\pi$
$827$	−34.3286			−1.19372			−0.596860	+	0.802345i	$0.703585\pi$
$828$	−1.20618	+	5.90353i	−0.0419177	+	0.205162i
$829$	40.7898	−	23.5500i	1.41669	−	0.817925i	0.420682	−	0.907208i	$-0.361791\pi$
$829$	40.7898	−	23.5500i	1.41669	−	0.817925i	0.996006	+	0.0892828i	$0.0284575\pi$
$830$	−10.1736	+	23.4788i	−0.353132	+	0.814963i
$831$	−13.5980	+	2.20880i	−0.471711	+	0.0766224i
$832$	−2.02055	−	3.49969i	−0.0700499	−	0.121330i
$833$	13.1657	−	43.2091i	0.456163	−	1.49710i
$834$	−1.02165	+	2.69322i	−0.0353767	+	0.0932585i
$835$	0.0231897	−	0.00267183i	0.000802513	−	9.24625e-5i
$836$	−0.234684	−	0.406485i	−0.00811672	−	0.0140586i
$837$	−0.205213	+	5.06261i	−0.00709321	+	0.174989i
$838$	10.3156	−	17.8671i	0.356346	−	0.617209i
$839$	7.97922	−	13.8204i	0.275473	−	0.477134i	−0.694781	−	0.719221i	$-0.744499\pi$
$839$	7.97922	−	13.8204i	0.275473	−	0.477134i	0.970254	+	0.242087i	$0.0778321\pi$
$840$	10.1633	−	1.30660i	0.350667	−	0.0450819i
$841$	−8.68273	−	15.0389i	−0.299404	−	0.518583i
$842$	−4.16721			−0.143612
$843$	9.21101	−	24.2817i	0.317244	−	0.836305i
$844$	18.4760			0.635971
$845$	5.98082	−	4.43728i	0.205746	−	0.152647i
$846$	14.0434	+	2.86928i	0.482822	+	0.0986480i
$847$	−5.59485	−	14.1837i	−0.192241	−	0.487357i
$848$	2.35928	−	4.08640i	0.0810181	−	0.140327i
$849$	−48.2632	−	18.3082i	−1.65639	−	0.628334i
$850$	−7.33739	−	31.4191i	−0.251670	−	1.07767i
$851$	14.8733	+	8.58711i	0.509851	+	0.294362i
$852$	−6.77961	+	17.8721i	−0.232266	+	0.612289i
$853$	−4.85434	+	8.40796i	−0.166209	+	0.287883i	−0.937084	−	0.349104i	$-0.886486\pi$
$853$	−4.85434	+	8.40796i	−0.166209	+	0.287883i	0.770875	+	0.636987i	$0.219819\pi$
$854$	4.20318	−	28.2154i	0.143830	−	0.965511i
$855$	−1.12739	−	0.788672i	−0.0385558	−	0.0269720i
$856$	9.00357	−	15.5946i	0.307736	−	0.533014i
$857$			31.1978i			1.06570i	0.846210	+	0.532849i	$0.178879\pi$
$857$			31.1978i			1.06570i	−0.846210	+	0.532849i	$0.821121\pi$
$858$	5.68119	−	14.9765i	0.193953	−	0.511289i
$859$		−	15.9449i		−	0.544031i	−0.962293	−	0.272016i	$-0.912310\pi$
$859$		−	15.9449i		−	0.544031i	0.962293	−	0.272016i	$-0.0876903\pi$
$860$	5.45671	−	0.628702i	0.186072	−	0.0214386i
$861$	9.24930	+	5.17914i	0.315215	+	0.176505i
$862$	1.89577	+	1.09452i	0.0645701	+	0.0372796i
$863$	−21.8059	+	37.7689i	−0.742281	+	1.28567i	0.209174	+	0.977879i	$0.432923\pi$
$863$	−21.8059	+	37.7689i	−0.742281	+	1.28567i	−0.951454	+	0.307790i	$0.900411\pi$
$864$	−5.19189	−	0.210454i	−0.176632	−	0.00715978i
$865$	−40.5024	+	4.66653i	−1.37712	+	0.158667i
$866$	11.9058	+	20.6215i	0.404577	+	0.700748i
$867$	39.9031	+	15.1368i	1.35518	+	0.514074i
$868$	−2.01979	−	1.60505i	−0.0685561	−	0.0544790i
$869$	14.3369	−	8.27741i	0.486346	−	0.280792i
$870$	12.8068	+	3.24094i	0.434192	+	0.109878i
$871$		−	24.4552i		−	0.828634i
$872$	8.13785	+	14.0952i	0.275582	+	0.477323i
$873$	−5.09292	+	24.9268i	−0.172369	+	0.843644i
$874$			0.411946i			0.0139343i
$875$	−22.2416	+	19.5015i	−0.751905	+	0.659272i
$876$	4.32461	+	26.6236i	0.146115	+	0.899528i
$877$		−	37.8796i		−	1.27910i	−0.768748	−	0.639552i	$-0.779120\pi$
$877$		−	37.8796i		−	1.27910i	0.768748	−	0.639552i	$-0.220880\pi$
$878$	12.4614	+	7.19459i	0.420552	+	0.242806i
$879$	2.78241	+	3.40838i	0.0938483	+	0.114962i
$880$	5.08354	−	0.585706i	0.171366	−	0.0197441i
$881$	16.7367			0.563872			0.281936	−	0.959433i	$-0.409023\pi$
$881$	16.7367			0.563872			0.281936	+	0.959433i	$0.409023\pi$
$882$	20.9927	−	0.552173i	0.706862	−	0.0185926i
$883$			5.43664i			0.182957i	0.995807	+	0.0914787i	$0.0291593\pi$
$883$			5.43664i			0.182957i	−0.995807	+	0.0914787i	$0.970841\pi$
$884$	−22.5832	+	13.0384i	−0.759554	+	0.438529i
$885$	25.1871	+	24.4945i	0.846655	+	0.823374i
$886$	18.3040	−	31.7035i	0.614935	−	1.06510i
$887$		−	38.9848i		−	1.30898i	−0.756070	−	0.654490i	$-0.772883\pi$
$887$		−	38.9848i		−	1.30898i	0.756070	−	0.654490i	$-0.227117\pi$
$888$	−5.25293	+	13.8475i	−0.176277	+	0.464693i
$889$	−29.1226	+	11.4876i	−0.976740	+	0.385282i
$890$	20.8832	+	9.04891i	0.700007	+	0.303320i
$891$	−12.3678	−	16.4694i	−0.414338	−	0.551745i
$892$	−2.10769	−	3.65063i	−0.0705708	−	0.122232i
$893$	0.979943			0.0327925
$894$	−12.8428	−	15.7320i	−0.429526	−	0.526158i
$895$	34.7301	−	4.00147i	1.16090	−	0.133754i
$896$	1.64604	−	2.07137i	0.0549903	−	0.0691995i
$897$	−10.8903	+	8.89021i	−0.363616	+	0.296835i
$898$	−0.303705	+	0.175344i	−0.0101348	+	0.00585132i
$899$	−1.66301	−	2.88041i	−0.0554644	−	0.0960671i
$900$	12.7763	−	7.85920i	0.425875	−	0.261973i
$901$	−26.3691	−	15.2242i	−0.878483	−	0.507192i
$902$	4.58455	+	2.64689i	0.152649	+	0.0881318i
$903$	11.2559	−	0.148007i	0.374574	−	0.00492537i
$904$	2.98673	+	5.17317i	0.0993372	+	0.172057i
$905$	21.6123	−	49.8772i	0.718418	−	1.65798i
$906$	−4.51276	+	3.68396i	−0.149926	+	0.122391i
$907$		−	2.76265i		−	0.0917322i	−0.998948	−	0.0458661i	$-0.985395\pi$
$907$		−	2.76265i		−	0.0917322i	0.998948	−	0.0458661i	$-0.0146048\pi$
$908$	−16.0856	−	9.28700i	−0.533818	−	0.308200i
$909$	4.31158	−	1.43866i	0.143006	−	0.0477174i
$910$	20.2966	+	12.6338i	0.672827	+	0.418806i
$911$	36.0610	+	20.8198i	1.19475	+	0.689792i	0.959381	−	0.282113i	$-0.0910354\pi$
$911$	36.0610	+	20.8198i	1.19475	+	0.689792i	0.235373	+	0.971905i	$0.424369\pi$
$912$	−0.350651	+	0.0569580i	−0.0116112	+	0.00188607i
$913$	−13.0939	+	22.6794i	−0.433346	+	0.750577i
$914$	−1.65880	−	0.957706i	−0.0548681	−	0.0316781i
$915$	−11.3692	−	40.1814i	−0.375854	−	1.32836i
$916$	−1.36101	−	0.785777i	−0.0449689	−	0.0259628i
$917$	2.87004	+	7.27593i	0.0947771	+	0.240273i
$918$	−1.35804	+	33.5027i	−0.0448219	+	1.10576i
$919$	−11.8470	+	20.5196i	−0.390797	+	0.676880i	−0.992555	−	0.121798i	$-0.961134\pi$
$919$	−11.8470	+	20.5196i	−0.390797	+	0.676880i	0.601758	+	0.798679i	$0.294467\pi$
$920$	−4.12090	−	1.78563i	−0.135862	−	0.0588704i
$921$	2.23914	+	13.7848i	0.0737821	+	0.454226i
$922$	24.4183			0.804172
$923$	−38.6224	+	22.2987i	−1.27127	+	0.733969i
$924$	10.4862	−	0.137885i	0.344969	−	0.00453609i
$925$	−9.72283	−	41.6337i	−0.319685	−	1.36891i
$926$	−4.09771	−	2.36581i	−0.134659	−	0.0777454i
$927$	53.4322	−	17.8289i	1.75494	−	0.585579i
$928$	2.95397	−	1.70547i	0.0969687	−	0.0559849i
$929$	−3.22447	−	5.58494i	−0.105791	−	0.183236i	0.808270	−	0.588812i	$-0.200404\pi$
$929$	−3.22447	−	5.58494i	−0.105791	−	0.183236i	−0.914061	+	0.405576i	$0.867071\pi$
$930$	−3.66113	−	0.926498i	−0.120053	−	0.0303811i
$931$	1.39861	−	0.324288i	0.0458375	−	0.0106281i
$932$	−3.77904	−	6.54549i	−0.123787	−	0.214405i
$933$	−1.23665	−	0.469111i	−0.0404861	−	0.0153580i
$934$			34.5645i			1.13098i
$935$	−3.77950	−	32.8036i	−0.123603	−	1.07279i
$936$	−9.07315	−	8.04065i	−0.296565	−	0.262817i
$937$	38.6081			1.26127			0.630635	−	0.776079i	$-0.282794\pi$
$937$	38.6081			1.26127			0.630635	+	0.776079i	$0.282794\pi$
$938$	14.8943	−	5.87514i	0.486315	−	0.191830i
$939$	5.14876	−	4.20315i	0.168023	−	0.137165i
$940$	−4.24768	+	9.80286i	−0.138544	+	0.319734i
$941$	−5.21606	+	9.03447i	−0.170039	+	0.294515i	−0.938433	−	0.345461i	$-0.887723\pi$
$941$	−5.21606	+	9.03447i	−0.170039	+	0.294515i	0.768395	+	0.639976i	$0.221056\pi$
$942$	−0.717394	−	4.41650i	−0.0233739	−	0.143897i
$943$	−2.32307	−	4.02368i	−0.0756496	−	0.131029i
$944$	9.07146			0.295251
$945$	27.6816	−	13.3689i	0.900484	−	0.434890i
$946$	5.62152			0.182771
$947$	−17.0629	−	29.5538i	−0.554470	−	0.960369i	−0.997945	−	0.0640827i	$-0.979588\pi$
$947$	−17.0629	−	29.5538i	−0.554470	−	0.960369i	0.443475	−	0.896287i	$-0.353745\pi$
$948$	−2.00893	−	12.3676i	−0.0652471	−	0.401681i
$949$	−31.4652	+	54.4993i	−1.02140	+	1.76912i
$950$	0.748239	−	0.701289i	0.0242761	−	0.0227528i
$951$	23.2509	−	18.9807i	0.753962	−	0.615492i
$952$	−13.3663	−	10.6217i	−0.433205	−	0.344252i
$953$	−44.3067			−1.43523			−0.717617	−	0.696438i	$-0.754767\pi$
$953$	−44.3067			−1.43523			−0.717617	+	0.696438i	$0.754767\pi$
$954$	2.83369	−	13.8692i	0.0917440	−	0.449031i
$955$	−26.5230	+	3.05589i	−0.858265	+	0.0988861i
$956$			16.6807i			0.539494i
$957$	12.6411	+	4.79529i	0.408630	+	0.155010i
$958$	−20.7765	−	35.9860i	−0.671258	−	1.16265i
$959$	−6.66171	−	16.8883i	−0.215118	−	0.545352i
$960$	0.950157	−	3.75462i	0.0306662	−	0.121180i
$961$	−15.0246	−	26.0234i	−0.484664	−	0.839463i
$962$	−29.9251	+	17.2773i	−0.964824	+	0.557042i
$963$	10.8140	−	52.9280i	0.348476	−	1.70558i
$964$	24.5697	+	14.1853i	0.791337	+	0.456879i
$965$	16.5765	+	22.3427i	0.533616	+	0.719237i
$966$	−8.03079	−	4.49684i	−0.258387	−	0.144684i
$967$	14.0448	−	8.10875i	0.451649	−	0.260760i	−0.256877	−	0.966444i	$-0.582694\pi$
$967$	14.0448	−	8.10875i	0.451649	−	0.260760i	0.708526	+	0.705684i	$0.249360\pi$
$968$	−5.76292			−0.185227
$969$	0.367544	+	2.26271i	0.0118072	+	0.0726888i
$970$	−17.3999	−	7.53955i	−0.558677	−	0.242080i
$971$	18.1313	−	31.4043i	0.581861	−	1.00781i	−0.413397	−	0.910551i	$-0.635658\pi$
$971$	18.1313	−	31.4043i	0.581861	−	1.00781i	0.995259	−	0.0972627i	$-0.0310087\pi$
$972$	−14.9747	+	4.33109i	−0.480314	+	0.138920i
$973$	−3.44478	−	2.73744i	−0.110435	−	0.0877584i
$974$	−8.25200	−	4.76429i	−0.264411	−	0.152658i
$975$	34.6872	+	4.64606i	1.11088	+	0.148793i
$976$	−9.33757	−	5.39105i	−0.298888	−	0.172563i
$977$	−4.35317	+	7.53992i	−0.139270	+	0.241223i	−0.927221	−	0.374516i	$-0.877809\pi$
$977$	−4.35317	+	7.53992i	−0.139270	+	0.241223i	0.787950	+	0.615739i	$0.211142\pi$
$978$	−41.7456	+	6.78095i	−1.33488	+	0.216831i
$979$	20.1721	+	11.6464i	0.644704	+	0.372220i
$980$	−2.81842	+	15.3966i	−0.0900312	+	0.491828i
$981$	36.5425	+	32.3841i	1.16671	+	1.03394i
$982$	3.87273	+	2.23592i	0.123584	+	0.0713512i
$983$			11.1598i			0.355943i	0.984036	+	0.177972i	$0.0569535\pi$
$983$			11.1598i			0.355943i	−0.984036	+	0.177972i	$0.943046\pi$
$984$	3.10377	−	2.53375i	0.0989447	−	0.0807729i
$985$	−47.2852	−	20.4892i	−1.50663	−	0.652839i
$986$	−11.0052	−	19.0616i	−0.350478	−	0.607047i
$987$	−10.6972	+	19.1038i	−0.340494	+	0.608080i
$988$	−0.717793	−	0.414418i	−0.0228360	−	0.0131844i
$989$	−4.27279	−	2.46689i	−0.135867	−	0.0784427i
$990$	13.9104	−	6.49388i	0.442100	−	0.206389i
$991$	−24.4098	−	42.2790i	−0.775402	−	1.34304i	−0.934568	−	0.355785i	$-0.884214\pi$
$991$	−24.4098	−	42.2790i	−0.775402	−	1.34304i	0.159165	−	0.987252i	$-0.449120\pi$
$992$	−0.844461	+	0.487550i	−0.0268117	+	0.0154797i
$993$	−6.65333	+	5.43141i	−0.211137	+	0.172360i
$994$	−22.8595	−	18.1656i	−0.725058	−	0.576178i
$995$	17.9256	−	2.06532i	0.568279	−	0.0654749i
$996$	12.5342	+	15.3541i	0.397162	+	0.486513i
$997$	−17.9594			−0.568779			−0.284390	−	0.958709i	$-0.591791\pi$
$997$	−17.9594			−0.568779			−0.284390	+	0.958709i	$0.591791\pi$
$998$	−17.8598	−	30.9342i	−0.565343	−	0.979204i
$999$	−1.79954	+	44.3947i	−0.0569350	+	1.40459i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.r.b.299.15	yes	48
3.2	odd	2		1890.2.r.a.89.22		48
5.4	even	2		630.2.r.a.299.10	yes	48
7.3	odd	6		630.2.bi.a.479.6	yes	48
9.4	even	3		1890.2.bi.a.719.14		48
9.5	odd	6		630.2.bi.b.509.19	yes	48
15.14	odd	2		1890.2.r.b.89.22		48
21.17	even	6		1890.2.bi.b.899.19		48
35.24	odd	6		630.2.bi.b.479.19	yes	48
45.4	even	6		1890.2.bi.b.719.19		48
45.14	odd	6		630.2.bi.a.509.6	yes	48
63.31	odd	6		1890.2.r.b.1529.22		48
63.59	even	6		630.2.r.a.59.10	✓	48
105.59	even	6		1890.2.bi.a.899.14		48
315.59	even	6	inner	630.2.r.b.59.15	yes	48
315.94	odd	6		1890.2.r.a.1529.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.10	✓	48	63.59	even	6
630.2.r.a.299.10	yes	48	5.4	even	2
630.2.r.b.59.15	yes	48	315.59	even	6	inner
630.2.r.b.299.15	yes	48	1.1	even	1	trivial
630.2.bi.a.479.6	yes	48	7.3	odd	6
630.2.bi.a.509.6	yes	48	45.14	odd	6
630.2.bi.b.479.19	yes	48	35.24	odd	6
630.2.bi.b.509.19	yes	48	9.5	odd	6
1890.2.r.a.89.22		48	3.2	odd	2
1890.2.r.a.1529.22		48	315.94	odd	6
1890.2.r.b.89.22		48	15.14	odd	2
1890.2.r.b.1529.22		48	63.31	odd	6
1890.2.bi.a.719.14		48	9.4	even	3
1890.2.bi.a.899.14		48	105.59	even	6
1890.2.bi.b.719.19		48	45.4	even	6
1890.2.bi.b.899.19		48	21.17	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.277706 + 1.70964i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.05173 - 0.889037i) q^{5} +(-1.34174 + 1.09532i) q^{6} +(-0.970835 - 2.46119i) q^{7} -1.00000 q^{8} +(-2.84576 + 0.949556i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.277706 + 1.70964i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.05173 - 0.889037i) q^{5} +(-1.34174 + 1.09532i) q^{6} +(-0.970835 - 2.46119i) q^{7} -1.00000 q^{8} +(-2.84576 + 0.949556i) q^{9} +(-0.255938 - 2.22137i) q^{10} -2.28847i q^{11} +(-1.61945 - 0.614321i) q^{12} +(-2.02055 - 3.49969i) q^{13} +(1.64604 - 2.07137i) q^{14} +(0.950157 - 3.75462i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.58838 + 3.22645i) q^{17} +(-2.24522 - 1.98972i) q^{18} +(-0.177623 - 0.102551i) q^{19} +(1.79580 - 1.33234i) q^{20} +(3.93816 - 2.34327i) q^{21} +(1.98187 - 1.14423i) q^{22} -2.00850 q^{23} +(-0.277706 - 1.70964i) q^{24} +(3.41923 + 3.64814i) q^{25} +(2.02055 - 3.49969i) q^{26} +(-2.41369 - 4.60153i) q^{27} +(2.61687 + 0.389830i) q^{28} +(2.95397 + 1.70547i) q^{29} +(3.72668 - 1.05445i) q^{30} +(-0.844461 - 0.487550i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.91246 - 0.635521i) q^{33} +(-5.58838 - 3.22645i) q^{34} +(-0.196198 + 5.91283i) q^{35} +(0.600540 - 2.93928i) q^{36} +(-7.40520 - 4.27539i) q^{37} -0.205102i q^{38} +(5.42211 - 4.42630i) q^{39} +(2.05173 + 0.889037i) q^{40} +(1.15662 + 2.00333i) q^{41} +(3.99841 + 2.23891i) q^{42} +(2.12736 + 1.22823i) q^{43} +(1.98187 + 1.14423i) q^{44} +(6.68293 + 0.581749i) q^{45} +(-1.00425 - 1.73941i) q^{46} +(-4.13773 + 2.38892i) q^{47} +(1.34174 - 1.09532i) q^{48} +(-5.11496 + 4.77883i) q^{49} +(-1.44977 + 4.78520i) q^{50} +(-7.06800 - 8.65812i) q^{51} +4.04110 q^{52} +(2.35928 + 4.08640i) q^{53} +(2.77820 - 4.39108i) q^{54} +(-2.03453 + 4.69532i) q^{55} +(0.970835 + 2.46119i) q^{56} +(0.125998 - 0.332151i) q^{57} +3.41095i q^{58} +(-4.53573 + 7.85612i) q^{59} +(2.77652 + 2.70017i) q^{60} +(9.33757 - 5.39105i) q^{61} -0.975100i q^{62} +(5.09980 + 6.08210i) q^{63} +1.00000 q^{64} +(1.03427 + 8.97678i) q^{65} +(2.50661 + 3.07053i) q^{66} +(5.24087 + 3.02582i) q^{67} -6.45290i q^{68} +(-0.557771 - 3.43381i) q^{69} +(-5.21876 + 2.78650i) q^{70} -11.0359i q^{71} +(2.84576 - 0.949556i) q^{72} +(-7.78631 - 13.4863i) q^{73} -8.55079i q^{74} +(-5.28747 + 6.85876i) q^{75} +(0.177623 - 0.102551i) q^{76} +(-5.63236 + 2.22172i) q^{77} +(6.54434 + 2.48253i) q^{78} +(3.61701 + 6.26485i) q^{79} +(0.255938 + 2.22137i) q^{80} +(7.19669 - 5.40442i) q^{81} +(-1.15662 + 2.00333i) q^{82} +(-9.91029 - 5.72171i) q^{83} +(0.0602522 + 4.58218i) q^{84} +(14.3343 - 1.65154i) q^{85} +2.45646i q^{86} +(-2.09542 + 5.52385i) q^{87} +2.28847i q^{88} +(-5.08916 + 8.81469i) q^{89} +(2.83766 + 6.07846i) q^{90} +(-6.65180 + 8.37059i) q^{91} +(1.00425 - 1.73941i) q^{92} +(0.599024 - 1.57912i) q^{93} +(-4.13773 - 2.38892i) q^{94} +(0.273264 + 0.368321i) q^{95} +(1.61945 + 0.614321i) q^{96} +(4.24029 - 7.34440i) q^{97} +(-6.69607 - 2.04027i) q^{98} +(2.17303 + 6.51242i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9}+O(q^{10}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9	\( 48 q + 24 q^{2} - 3 q^{3} - 24 q^{4} - 48 q^{8} + 3 q^{9} + 3 q^{12} + 3 q^{14} + 6 q^{15} - 24 q^{16} + 3 q^{18} + 5 q^{21} - 6 q^{22} + 6 q^{23} + 3 q^{24} + 3 q^{28} - 3 q^{29} - 3 q^{30} + 24 q^{32} - 24 q^{33} + 12 q^{35} + 3 q^{41} - 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} - 42 q^{55} + 22 q^{57} - 9 q^{60} - 9 q^{61} + 10 q^{63} + 48 q^{64} - 21 q^{65} - 24 q^{66} + 33 q^{67} + 42 q^{69} + 12 q^{70} - 3 q^{72} - 18 q^{73} - 39 q^{75} - 6 q^{77} + 18 q^{78} - 37 q^{81} - 3 q^{82} + 9 q^{83} - 13 q^{84} + 33 q^{85} + 18 q^{87} + 33 q^{89} + 15 q^{90} - 3 q^{92} + 32 q^{93} + 33 q^{95} - 3 q^{96} - 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 3 * q^3 - 24 * q^4 - 48 * q^8 + 3 * q^9 + 3 * q^12 + 3 * q^14 + 6 * q^15 - 24 * q^16 + 3 * q^18 + 5 * q^21 - 6 * q^22 + 6 * q^23 + 3 * q^24 + 3 * q^28 - 3 * q^29 - 3 * q^30 + 24 * q^32 - 24 * q^33 + 12 * q^35 + 3 * q^41 - 8 * q^42 - 6 * q^44 + 9 * q^45 + 3 * q^46 - 6 * q^49 - 18 * q^50 - 8 * q^51 - 42 * q^55 + 22 * q^57 - 9 * q^60 - 9 * q^61 + 10 * q^63 + 48 * q^64 - 21 * q^65 - 24 * q^66 + 33 * q^67 + 42 * q^69 + 12 * q^70 - 3 * q^72 - 18 * q^73 - 39 * q^75 - 6 * q^77 + 18 * q^78 - 37 * q^81 - 3 * q^82 + 9 * q^83 - 13 * q^84 + 33 * q^85 + 18 * q^87 + 33 * q^89 + 15 * q^90 - 3 * q^92 + 32 * q^93 + 33 * q^95 - 3 * q^96 - 24 * q^97 - 3 * q^98 - 26 * q^99

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