LMFDB - Embedded newform 630.2.r.a.59.10

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			59.10
Character	$\chi$	$=$	630.59
Dual form			630.2.r.a.299.10

$q$-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} +(1.79580 - 1.33234i) q^{10} +2.28847i q^{11} +(1.61945 - 0.614321i) q^{12} +(2.02055 - 3.49969i) q^{13} +(1.64604 + 2.07137i) q^{14} +(2.08972 - 3.26084i) 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} +(0.255938 + 2.22137i) 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} +(1.77911 + 3.44017i) 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} +(-4.17999 + 4.18661i) 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} +(4.99455 + 4.47822i) 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} +(-4.86899 + 1.13707i) 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} +(-3.86883 - 0.179325i) q^{60} +(9.33757 + 5.39105i) q^{61} -0.975100i q^{62} +(-5.09980 + 6.08210i) q^{63} +1.00000 q^{64} +(-7.25698 + 5.38409i) q^{65} +(2.50661 - 3.07053i) q^{66} +(-5.24087 + 3.02582i) q^{67} -6.45290i q^{68} +(-0.557771 + 3.43381i) q^{69} +(-1.53572 - 5.71328i) q^{70} +11.0359i q^{71} +(-2.84576 - 0.949556i) q^{72} +(7.78631 - 13.4863i) q^{73} +8.55079i q^{74} +(-7.18655 + 4.83255i) 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} +(1.79580 - 1.33234i) 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} +(-8.59743 - 11.5881i) q^{85} -2.45646i q^{86} +(2.09542 + 5.52385i) q^{87} +2.28847i q^{88} +(-5.08916 - 8.81469i) q^{89} +(-6.37553 + 2.08630i) 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} +(0.455607 - 0.0524934i) 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} - 4 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} + 5 q^{30} - 24 q^{32} + 24 q^{33} + 18 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} - q^{60} - 9 q^{61} - 10 q^{63} + 48 q^{64} - 33 q^{65} - 24 q^{66} - 33 q^{67} + 42 q^{69} - 6 q^{70} + 3 q^{72} + 18 q^{73} + 9 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} + 39 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 - 4 * 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 + 5 * q^30 - 24 * q^32 + 24 * q^33 + 18 * 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 - q^60 - 9 * q^61 - 10 * q^63 + 48 * q^64 - 33 * q^65 - 24 * q^66 - 33 * q^67 + 42 * q^69 - 6 * q^70 + 3 * q^72 + 18 * q^73 + 9 * 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 + 39 * 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.500000	+	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
$10$	1.79580	−	1.33234i	0.567881	−	0.421321i
$11$			2.28847i			0.689998i	0.938603	+	0.344999i	$0.112121\pi$
$11$			2.28847i			0.689998i	−0.938603	+	0.344999i	$0.887879\pi$
$12$	1.61945	−	0.614321i	0.467494	−	0.177339i
$13$	2.02055	−	3.49969i	0.560399	−	0.970640i	−0.437062	−	0.899431i	$-0.643981\pi$
$13$	2.02055	−	3.49969i	0.560399	−	0.970640i	0.997461	−	0.0712086i	$-0.0226856\pi$
$14$	1.64604	+	2.07137i	0.439923	+	0.553596i
$15$	2.08972	−	3.26084i	0.539562	−	0.841946i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.58838	+	3.22645i	1.35538	+	0.782529i	0.988997	−	0.147935i	$-0.0472626\pi$
$17$	5.58838	+	3.22645i	1.35538	+	0.782529i	0.366383	+	0.930464i	$0.380596\pi$
$18$	2.24522	−	1.98972i	0.529203	−	0.468982i
$19$	−0.177623	+	0.102551i	−0.0407496	+	0.0235268i	−0.520236	−	0.854022i	$-0.674156\pi$
$19$	−0.177623	+	0.102551i	−0.0407496	+	0.0235268i	0.479487	+	0.877549i	$0.340823\pi$
$20$	0.255938	+	2.22137i	0.0572295	+	0.496714i
$21$	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	$-0.432849\pi$
$23$	2.00850			0.418800			0.209400	+	0.977830i	$0.432849\pi$
$24$	−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	−0.199994	−	0.979797i	$-0.564092\pi$
$29$	2.95397	−	1.70547i	0.548538	−	0.316698i	0.748532	+	0.663099i	$0.230759\pi$
$30$	1.77911	+	3.44017i	0.324820	+	0.628086i
$31$	−0.844461	+	0.487550i	−0.151670	+	0.0875665i	−0.573914	−	0.818915i	$-0.694576\pi$
$31$	−0.844461	+	0.487550i	−0.151670	+	0.0875665i	0.422244	+	0.906482i	$0.361242\pi$
$32$	−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
$35$	−4.17999	+	4.18661i	−0.706547	+	0.707666i
$36$	0.600540	+	2.93928i	0.100090	+	0.489880i
$37$	7.40520	−	4.27539i	1.21741	−	0.702870i	0.253045	−	0.967455i	$-0.418568\pi$
$37$	7.40520	−	4.27539i	1.21741	−	0.702870i	0.964363	+	0.264584i	$0.0852348\pi$
$38$		−	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	−0.761463	−	0.648209i	$-0.775518\pi$
$41$	1.15662	−	2.00333i	0.180634	−	0.312867i	0.942097	+	0.335342i	$0.108852\pi$
$42$	−3.99841	+	2.23891i	−0.616968	+	0.345471i
$43$	−2.12736	+	1.22823i	−0.324419	+	0.187303i	−0.653360	−	0.757047i	$-0.726641\pi$
$43$	−2.12736	+	1.22823i	−0.324419	+	0.187303i	0.328942	+	0.944350i	$0.393308\pi$
$44$	1.98187	−	1.14423i	0.298778	−	0.172500i
$45$	4.99455	+	4.47822i	0.744544	+	0.667574i
$46$	−1.00425	+	1.73941i	−0.148068	+	0.256462i
$47$	4.13773	+	2.38892i	0.603550	+	0.348460i	0.770437	−	0.637516i	$-0.220038\pi$
$47$	4.13773	+	2.38892i	0.603550	+	0.348460i	−0.166887	+	0.985976i	$0.553371\pi$
$48$	−1.34174	−	1.09532i	−0.193664	−	0.158096i
$49$	−5.11496	−	4.77883i	−0.730708	−	0.682690i
$50$	−4.86899	+	1.13707i	−0.688579	+	0.160806i
$51$	−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	$-0.938385\pi$
$53$	−2.35928	+	4.08640i	−0.324072	+	0.561310i	0.657252	+	0.753671i	$0.271719\pi$
$54$	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	−0.994165	−	0.107872i	$-0.965596\pi$
$59$	−4.53573	−	7.85612i	−0.590502	−	1.02278i	0.403663	−	0.914908i	$-0.367737\pi$
$60$	−3.86883	−	0.179325i	−0.499464	−	0.0231508i
$61$	9.33757	+	5.39105i	1.19555	+	0.690253i	0.959561	−	0.281501i	$-0.0908324\pi$
$61$	9.33757	+	5.39105i	1.19555	+	0.690253i	0.235993	+	0.971755i	$0.424166\pi$
$62$		−	0.975100i		−	0.123838i
$63$	−5.09980	+	6.08210i	−0.642515	+	0.766273i
$64$	1.00000			0.125000
$65$	−7.25698	+	5.38409i	−0.900118	+	0.667815i
$66$	2.50661	−	3.07053i	0.308542	−	0.377956i
$67$	−5.24087	+	3.02582i	−0.640274	+	0.369662i	−0.784720	−	0.619850i	$-0.787193\pi$
$67$	−5.24087	+	3.02582i	−0.640274	+	0.369662i	0.144446	+	0.989513i	$0.453860\pi$
$68$		−	6.45290i		−	0.782529i
$69$	−0.557771	+	3.43381i	−0.0671478	+	0.413382i
$70$	−1.53572	−	5.71328i	−0.183553	−	0.682868i
$71$			11.0359i			1.30973i	0.755748	+	0.654863i	$0.227274\pi$
$71$			11.0359i			1.30973i	−0.755748	+	0.654863i	$0.772726\pi$
$72$	−2.84576	−	0.949556i	−0.335376	−	0.111906i
$73$	7.78631	−	13.4863i	0.911318	−	1.57845i	0.0991142	−	0.995076i	$-0.468399\pi$
$73$	7.78631	−	13.4863i	0.911318	−	1.57845i	0.812204	−	0.583373i	$-0.198268\pi$
$74$			8.55079i			0.994009i
$75$	−7.18655	+	4.83255i	−0.829831	+	0.558014i
$76$	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	−0.587600	−	0.809151i	$-0.699927\pi$
$79$	3.61701	−	6.26485i	0.406946	−	0.704851i	0.994546	+	0.104301i	$0.0332605\pi$
$80$	1.79580	−	1.33234i	0.200776	−	0.148960i
$81$	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	$-0.450524\pi$
$83$	9.91029	−	5.72171i	1.08780	−	0.628039i	0.932989	+	0.359906i	$0.117191\pi$
$84$	0.0602522	−	4.58218i	0.00657406	−	0.499957i
$85$	−8.59743	−	11.5881i	−0.932522	−	1.25691i
$86$		−	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	−0.998934	−	0.0461690i	$-0.985299\pi$
$89$	−5.08916	−	8.81469i	−0.539450	−	0.934355i	0.459483	−	0.888186i	$-0.348035\pi$
$90$	−6.37553	+	2.08630i	−0.672040	+	0.219915i
$91$	−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
$95$	0.455607	−	0.0524934i	0.0467443	−	0.00538571i
$96$	1.61945	−	0.614321i	0.165284	−	0.0626989i
$97$	−4.24029	−	7.34440i	−0.430536	−	0.745711i	0.566383	−	0.824142i	$-0.308342\pi$
$97$	−4.24029	−	7.34440i	−0.430536	−	0.745711i	−0.996920	+	0.0784313i	$0.975009\pi$
$98$	6.69607	−	2.04027i	0.676405	−	0.206098i
$99$	2.17303	−	6.51242i	0.218397	−	0.654523i
$100$	1.44977	−	4.78520i	0.144977	−	0.478520i
$101$	−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	$-0.124039\pi$
$103$	18.7761			1.85006			0.925031	+	0.379891i	$0.124039\pi$
$104$	2.02055	−	3.49969i	0.198131	−	0.343173i
$105$	−5.99680	−	8.30894i	−0.585228	−	0.810869i
$106$	−2.35928	−	4.08640i	−0.229154	−	0.396906i
$107$	9.00357	+	15.5946i	0.870408	+	1.50759i	0.861576	+	0.507629i	$0.169478\pi$
$107$	9.00357	+	15.5946i	0.870408	+	1.50759i	0.00883183	+	0.999961i	$0.497189\pi$
$108$	−5.19189	+	0.210454i	−0.499590	+	0.0202509i
$109$	−8.13785	+	14.0952i	−0.779464	+	1.35007i	0.152786	+	0.988259i	$0.451175\pi$
$109$	−8.13785	+	14.0952i	−0.779464	+	1.35007i	−0.932251	+	0.361813i	$0.882158\pi$
$110$	3.04900	+	4.10962i	0.290711	+	0.391837i
$111$	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	$-0.742678\pi$
$113$	2.98673	−	5.17317i	0.280968	−	0.486651i	0.971623	+	0.236533i	$0.0760112\pi$
$114$	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
$120$	2.08972	−	3.26084i	0.190764	−	0.297673i
$121$	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
$130$	−1.03427	−	8.97678i	−0.0907116	−	0.787316i
$131$	−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
$135$	−9.04318	+	7.29527i	−0.778313	+	0.627877i
$136$	5.58838	+	3.22645i	0.479199	+	0.276666i
$137$	−6.86183			−0.586246			−0.293123	−	0.956075i	$-0.594695\pi$
$137$	−6.86183			−0.586246			−0.293123	+	0.956075i	$0.594695\pi$
$138$	−2.69488	−	2.19995i	−0.229404	−	0.187272i
$139$	1.44024	+	0.831524i	0.122160	+	0.0705289i	0.559835	−	0.828604i	$-0.310865\pi$
$139$	1.44024	+	0.831524i	0.122160	+	0.0705289i	−0.437675	+	0.899133i	$0.644198\pi$
$140$	5.71570	+	1.52667i	0.483065	+	0.129027i
$141$	−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
$145$	−7.57698	+	0.872991i	−0.629234	+	0.0724980i
$146$	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	$-0.840536\pi$
$149$		−	11.7251i		−	0.960557i	0.877116	−	0.480278i	$-0.159464\pi$
$150$	−0.591833	−	8.64001i	−0.0483230	−	0.705454i
$151$	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
$155$	2.16606	−	0.249565i	0.173982	−	0.0200456i
$156$	1.12224	−	6.90883i	0.0898508	−	0.553149i
$157$	1.29164	+	2.23719i	0.103084	+	0.178547i	0.912954	−	0.408063i	$-0.133796\pi$
$157$	1.29164	+	2.23719i	0.103084	+	0.178547i	−0.809870	+	0.586610i	$0.800462\pi$
$158$	3.61701	+	6.26485i	0.287754	+	0.498405i
$159$	−6.33109	−	5.16835i	−0.502088	−	0.409877i
$160$	0.255938	+	2.22137i	0.0202337	+	0.175615i
$161$	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	−0.681916	+	0.731431i	$0.738853\pi$
$163$	−21.1464	+	12.2089i	−1.65631	+	0.956272i	−0.974395	+	0.224841i	$0.927814\pi$
$164$	−2.31324			−0.180634
$165$	7.46233	+	4.78224i	0.580941	+	0.372297i
$166$			11.4434i			0.888181i
$167$	0.00904075	+	0.00521968i	0.000699594	+	0.000403911i	0.500350	−	0.865823i	$-0.333205\pi$
$167$	0.00904075	+	0.00521968i	0.000699594	+	0.000403911i	−0.499650	+	0.866227i	$0.666538\pi$
$168$	3.93816	+	2.34327i	0.303835	+	0.180787i
$169$	−1.66523	−	2.88426i	−0.128094	−	0.221866i
$170$	14.3343	−	1.65154i	1.09939	−	0.126668i
$171$	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	$-0.577096\pi$
$173$	−15.7903	−	9.11652i	−1.20051	−	0.693116i	−0.960669	+	0.277695i	$0.910429\pi$
$174$	−5.83150	−	0.947240i	−0.442085	−	0.0718101i
$175$	12.2983	−	4.87364i	0.929662	−	0.368413i
$176$	−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	−0.100236	−	0.994964i	$-0.531960\pi$
$179$	−13.5399	−	7.81725i	−1.01202	−	0.584289i	−0.911782	+	0.410675i	$0.865293\pi$
$180$	1.38098	−	6.56452i	0.102932	−	0.489290i
$181$		−	24.3098i		−	1.80693i	−0.428659	−	0.903467i	$-0.641014\pi$
$181$		−	24.3098i		−	1.80693i	0.428659	−	0.903467i	$-0.358986\pi$
$182$	10.5750	−	1.57534i	0.783874	−	0.116772i
$183$	−11.8099	+	14.4668i	−0.873011	+	1.06942i
$184$	2.00850			0.148068
$185$	−18.9945	+	2.18847i	−1.39650	+	0.160900i
$186$	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	0.825042	−	0.565071i	$-0.191151\pi$
$191$	10.3403	+	5.96997i	0.748197	+	0.431972i	−0.0768452	+	0.997043i	$0.524485\pi$
$192$	−0.277706	+	1.70964i	−0.0200417	+	0.123383i
$193$	10.7748	−	6.22084i	0.775588	−	0.447786i	−0.0592765	−	0.998242i	$-0.518879\pi$
$193$	10.7748	−	6.22084i	0.775588	−	0.447786i	0.834864	+	0.550456i	$0.185546\pi$
$194$	8.48058			0.608870
$195$	−7.18957	−	13.9020i	−0.514856	−	0.995546i
$196$	−1.58111	+	6.81910i	−0.112936	+	0.487078i
$197$	−23.0465			−1.64199			−0.820996	−	0.570934i	$-0.806581\pi$
$197$	−23.0465			−1.64199			−0.820996	+	0.570934i	$0.806581\pi$
$198$	4.55341	+	5.13811i	0.323597	+	0.365149i
$199$	−6.98847	−	4.03479i	−0.495399	−	0.286019i	0.231412	−	0.972856i	$-0.425665\pi$
$199$	−6.98847	−	4.03479i	−0.495399	−	0.286019i	−0.726812	+	0.686837i	$0.758999\pi$
$200$	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
$205$	−4.15411	+	3.08202i	−0.290136	+	0.215257i
$206$	−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
$210$	10.1941	−	1.03891i	0.703463	−	0.0716918i
$211$	−9.23801	+	16.0007i	−0.635971	+	1.10153i	0.350338	+	0.936623i	$0.386067\pi$
$211$	−9.23801	+	16.0007i	−0.635971	+	1.10153i	−0.986309	+	0.164910i	$0.947266\pi$
$212$	4.71857			0.324072
$213$	−18.8675	−	3.06475i	−1.29278	−	0.209993i
$214$	−18.0071			−1.23094
$215$	5.45671	−	0.628702i	0.372145	−	0.0428771i
$216$	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
$220$	−5.08354	+	0.585706i	−0.342732	+	0.0394883i
$221$	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	$-0.121589\pi$
$223$	2.10769	+	3.65063i	0.141142	+	0.244464i	−0.786785	+	0.617227i	$0.788256\pi$
$224$	−2.61687	+	0.389830i	−0.174847	+	0.0260466i
$225$	−6.26618	−	13.6285i	−0.417745	−	0.908564i
$226$	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	$-0.983464\pi$
$229$		−	1.57155i		−	0.103851i	0.998651	−	0.0519256i	$-0.0165359\pi$
$230$	3.60685	−	2.67599i	0.237829	−	0.176450i
$231$	−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	$-0.0870336\pi$
$233$	3.77904	+	6.54549i	0.247573	+	0.428809i	−0.715279	+	0.698839i	$0.753700\pi$
$234$	−2.42684	−	11.8779i	−0.158647	−	0.776483i
$235$	−6.36569	−	8.58003i	−0.415252	−	0.559699i
$236$	−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	0.888210	−	0.459438i	$-0.151949\pi$
$239$	14.4459	+	8.34037i	0.934430	+	0.539494i	0.0462202	+	0.998931i	$0.485282\pi$
$240$	1.77911	+	3.44017i	0.114841	+	0.222062i
$241$			28.3707i			1.82751i	0.406260	+	0.913757i	$0.366833\pi$
$241$			28.3707i			1.82751i	−0.406260	+	0.913757i	$0.633167\pi$
$242$	−2.88146	+	4.99084i	−0.185227	+	0.320823i
$243$	−11.2382	+	10.8029i	−0.720930	+	0.693008i
$244$		−	10.7821i		−	0.690253i
$245$	6.24598	+	14.3523i	0.399041	+	0.916933i
$246$	−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
$250$	11.0008	+	1.99575i	0.695750	+	0.126222i
$251$	−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
$255$	22.1991	−	11.4805i	1.39016	−	0.718934i
$256$	−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	$-0.528986\pi$
$263$	−2.94944			−0.181870			−0.0909351	+	0.995857i	$0.528986\pi$
$264$	−3.91246	−	0.635521i	−0.240795	−	0.0391136i
$265$	8.47358	−	6.28671i	0.520528	−	0.386190i
$266$	−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	0.0464436	+	0.998921i	$0.485211\pi$
$269$	−13.8077	+	23.9156i	−0.841869	+	1.45816i	−0.888313	+	0.459239i	$0.848122\pi$
$270$	−1.79630	−	11.4793i	−0.109319	−	0.698605i
$271$	12.8142	−	7.39828i	0.778407	−	0.449413i	−0.0574587	−	0.998348i	$-0.518300\pi$
$271$	12.8142	−	7.39828i	0.778407	−	0.449413i	0.835865	+	0.548935i	$0.184966\pi$
$272$	−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
$280$	−4.17999	+	4.18661i	−0.249802	+	0.250198i
$281$	−12.9850	+	7.49690i	−0.774621	+	0.447228i	−0.834521	−	0.550977i	$-0.814255\pi$
$281$	−12.9850	+	7.49690i	−0.774621	+	0.447228i	0.0598996	+	0.998204i	$0.480922\pi$
$282$	−2.93513	−	7.73746i	−0.174784	−	0.460759i
$283$	14.9011	+	25.8095i	0.885780	+	1.53422i	0.844817	+	0.535055i	$0.179709\pi$
$283$	14.9011	+	25.8095i	0.885780	+	1.53422i	0.0409630	+	0.999161i	$0.486957\pi$
$284$	9.55741	−	5.51797i	0.567128	−	0.327431i
$285$	−0.0367799	+	0.793503i	−0.00217865	+	0.0470031i
$286$	−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	$-0.356974\pi$
$293$	−2.19993	−	1.27013i	−0.128522	−	0.0742019i	−0.562882	+	0.826537i	$0.690308\pi$
$294$	1.62860	+	12.0145i	0.0949817	+	0.700699i
$295$	2.32173	+	20.1511i	0.135177	+	1.17324i
$296$	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
$300$	7.77838	+	3.80746i	0.449085	+	0.219824i
$301$	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
$305$	−14.3654	−	19.3625i	−0.822559	−	1.10869i
$306$	18.9669	−	3.87522i	1.08426	−	0.221532i
$307$	−8.06299			−0.460179			−0.230089	−	0.973169i	$-0.573902\pi$
$307$	−8.06299			−0.460179			−0.230089	+	0.973169i	$0.573902\pi$
$308$	−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	0.854997	−	0.518633i	$-0.173559\pi$
$311$	−0.381813	−	0.661319i	−0.0216506	−	0.0374999i	−0.876648	+	0.481133i	$0.840225\pi$
$312$	5.42211	+	4.42630i	0.306966	+	0.250590i
$313$	1.91868	−	3.32326i	0.108450	−	0.187842i	−0.806692	−	0.590972i	$-0.798744\pi$
$313$	1.91868	−	3.32326i	0.108450	−	0.187842i	0.915143	+	0.403130i	$0.132078\pi$
$314$	−2.58329			−0.145783
$315$	15.8707	−	7.94494i	0.894210	−	0.447647i
$316$	−7.23402			−0.406946
$317$	8.66445	−	15.0073i	0.486644	−	0.842892i	−0.513238	−	0.858246i	$-0.671554\pi$
$317$	8.66445	−	15.0073i	0.486644	−	0.842892i	0.999882	+	0.0153543i	$0.00488761\pi$
$318$	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
$325$	19.6761	−	4.59500i	1.09143	−	0.254885i
$326$		−	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
$330$	−7.87271	+	4.07144i	−0.433378	+	0.224126i
$331$	2.47937	−	4.29439i	0.136278	−	0.236041i	−0.789807	−	0.613356i	$-0.789819\pi$
$331$	2.47937	−	4.29439i	0.136278	−	0.236041i	0.926085	+	0.377315i	$0.123153\pi$
$332$	−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
$335$	13.4429	−	1.54885i	0.734466	−	0.0846224i
$336$	−3.99841	+	2.23891i	−0.218131	+	0.122143i
$337$	−1.58895	−	0.917381i	−0.0865557	−	0.0499729i	0.456097	−	0.889930i	$-0.349247\pi$
$337$	−1.58895	−	0.917381i	−0.0865557	−	0.0499729i	−0.542653	+	0.839957i	$0.682580\pi$
$338$	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
$345$	4.19719	−	6.54939i	0.225969	−	0.352607i
$346$	15.7903	−	9.11652i	0.848890	−	0.490107i
$347$	−3.39243	−	5.87586i	−0.182115	−	0.315433i	0.760486	−	0.649355i	$-0.224961\pi$
$347$	−3.39243	−	5.87586i	−0.182115	−	0.315433i	−0.942601	+	0.333922i	$0.891628\pi$
$348$	3.73608	−	4.57661i	0.200275	−	0.245332i
$349$	11.4343	−	6.60159i	0.612064	−	0.353375i	−0.161709	−	0.986838i	$-0.551701\pi$
$349$	11.4343	−	6.60159i	0.612064	−	0.353375i	0.773773	+	0.633463i	$0.218367\pi$
$350$	−1.92844	+	13.0874i	−0.103079	+	0.699553i
$351$	−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	−0.983565	−	0.180552i	$-0.942212\pi$
$359$	−24.9912	+	14.4287i	−1.31899	+	0.761517i	−0.335420	+	0.942069i	$0.608878\pi$
$360$	4.99455	+	4.47822i	0.263236	+	0.236023i
$361$	−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
$365$	−27.9652	+	20.7479i	−1.46377	+	1.08600i
$366$	−6.62367	−	17.4610i	−0.346225	−	0.912703i
$367$	12.3632			0.645354			0.322677	−	0.946509i	$-0.395417\pi$
$367$	12.3632			0.645354			0.322677	+	0.946509i	$0.395417\pi$
$368$	−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
$375$	19.0412	−	3.52599i	0.983283	−	0.182081i
$376$	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	$0.335004\pi$
$380$	−0.273264	−	0.368321i	−0.0140182	−	0.0188945i
$381$	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
$385$	−9.58091	−	9.56576i	−0.488288	−	0.487516i
$386$			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	$-0.928146\pi$
$389$		−	8.82897i		−	0.447647i	0.974630	−	0.223823i	$-0.0718538\pi$
$390$	15.6343	+	0.724671i	0.791674	+	0.0366951i
$391$	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
$395$	−12.9908	+	9.63815i	−0.653640	+	0.484948i
$396$	−6.72644	+	1.37431i	−0.338016	+	0.0690619i
$397$	−5.82466	−	10.0886i	−0.292332	−	0.506333i	0.682029	−	0.731325i	$-0.261098\pi$
$397$	−5.82466	−	10.0886i	−0.292332	−	0.506333i	−0.974361	+	0.224992i	$0.927764\pi$
$398$	6.98847	−	4.03479i	0.350300	−	0.202246i
$399$	−0.939813	−	0.0123578i	−0.0470495	−	0.000618666i
$400$	−4.86899	+	1.13707i	−0.243450	+	0.0568534i
$401$		−	2.64152i		−	0.131911i	−0.997823	−	0.0659557i	$-0.978990\pi$
$401$		−	2.64152i		−	0.131911i	0.997823	−	0.0659557i	$-0.0210096\pi$
$402$	10.3461	+	1.68058i	0.516018	+	0.0838195i
$403$			3.94047i			0.196289i
$404$	0.757545	+	1.31211i	0.0376893	+	0.0652797i
$405$	−9.96096	−	17.4865i	−0.494964	−	0.868913i
$406$	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	−0.583266	−	0.812281i	$-0.698225\pi$
$409$	−3.46721	+	2.00180i	−0.171443	+	0.0989824i	0.411823	+	0.911264i	$0.364892\pi$
$410$	−0.592047	−	5.13858i	−0.0292391	−	0.253776i
$411$	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
$415$	−25.4201	+	2.92881i	−1.24782	+	0.143770i
$416$	−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	0.496040	+	0.868299i	$0.334787\pi$
$419$	−10.3156	+	17.8671i	−0.503949	+	0.872865i	−0.999990	+	0.00456603i	$0.998547\pi$
$420$	−4.19735	+	9.34785i	−0.204810	+	0.456128i
$421$	−2.08360	−	3.60891i	−0.101549	−	0.175887i	0.810774	−	0.585359i	$-0.199046\pi$
$421$	−2.08360	−	3.60891i	−0.101549	−	0.175887i	−0.912323	+	0.409472i	$0.865713\pi$
$422$	−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
$425$	7.33739	+	31.4191i	0.355916	+	1.52405i
$426$	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	0.544963	−	0.838460i	$-0.316544\pi$
$431$	1.89577	+	1.09452i	0.0913159	+	0.0527213i	−0.453647	+	0.891182i	$0.649877\pi$
$432$	2.77820	+	4.39108i	0.133666	+	0.211266i
$433$	−23.8117			−1.14432			−0.572158	−	0.820143i	$-0.693894\pi$
$433$	−23.8117			−1.14432			−0.572158	+	0.820143i	$0.693894\pi$
$434$	−2.39991	−	0.946661i	−0.115199	−	0.0454412i
$435$	0.611669	−	13.1964i	0.0293273	−	0.632717i
$436$	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	0.766973	−	0.641679i	$-0.221762\pi$
$439$	12.4614	+	7.19459i	0.594750	+	0.343379i	−0.172223	+	0.985058i	$0.555095\pi$
$440$	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	0.00729415	−	0.999973i	$-0.497678\pi$
$443$	18.3040	−	31.7035i	0.869649	−	1.50628i	0.862355	−	0.506304i	$-0.168988\pi$
$444$	9.36586	−	11.4729i	0.444484	−	0.544482i
$445$	2.60502	+	22.6099i	0.123490	+	1.07181i
$446$	−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	$-0.997366\pi$
$449$		−	0.350689i		−	0.0165500i	0.999966	−	0.00827501i	$-0.00263405\pi$
$450$	14.9357	+	1.38756i	0.704075	+	0.0654101i
$451$	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
$455$	6.20597	+	23.0879i	0.290940	+	1.08238i
$456$	−0.125998	−	0.332151i	−0.00590041	−	0.0155544i
$457$	1.65880	+	0.957706i	0.0775952	+	0.0447996i	0.538296	−	0.842756i	$-0.319068\pi$
$457$	1.65880	+	0.957706i	0.0775952	+	0.0447996i	−0.460700	+	0.887556i	$0.652402\pi$
$458$	1.36101	+	0.785777i	0.0635956	+	0.0367169i
$459$	28.3352	−	17.9275i	1.32257	−	0.836783i
$460$	0.514051	+	4.46162i	0.0239678	+	0.208024i
$461$	12.2091	+	21.1468i	0.568636	+	0.984906i	0.996701	+	0.0811583i	$0.0258619\pi$
$461$	12.2091	+	21.1468i	0.568636	+	0.984906i	−0.428065	+	0.903748i	$0.640805\pi$
$462$	−5.12367	−	9.15023i	−0.238375	−	0.425707i
$463$	4.09771	+	2.36581i	0.190437	+	0.109949i	0.592187	−	0.805801i	$-0.298265\pi$
$463$	4.09771	+	2.36581i	0.190437	+	0.109949i	−0.401750	+	0.915749i	$0.631598\pi$
$464$			3.41095i			0.158349i
$465$	−0.174860	+	3.77249i	−0.00810894	+	0.174945i
$466$	−7.55808			−0.350121
$467$	−29.9337	+	17.2822i	−1.38517	+	0.799726i	−0.992766	−	0.120068i	$-0.961689\pi$
$467$	−29.9337	+	17.2822i	−1.38517	+	0.799726i	−0.392401	+	0.919794i	$0.628355\pi$
$468$	11.5000	+	3.83725i	0.531587	+	0.177377i
$469$	2.35911	+	15.8364i	0.108933	+	0.731256i
$470$	10.6134	−	1.22283i	0.489558	−	0.0564050i
$471$	−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
$475$	−0.981453	−	0.297349i	−0.0450322	−	0.0136433i
$476$	−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	$0.898209\pi$
$480$	−3.86883	−	0.179325i	−0.176587	−	0.00818504i
$481$		−	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
$485$	2.17050	+	18.8385i	0.0985576	+	0.855413i
$486$	−3.73652	−	15.1340i	−0.169492	−	0.686493i
$487$	8.25200	+	4.76429i	0.373934	+	0.215891i	0.675176	−	0.737657i	$-0.264068\pi$
$487$	8.25200	+	4.76429i	0.373934	+	0.215891i	−0.301242	+	0.953548i	$0.597401\pi$
$488$	9.33757	+	5.39105i	0.422692	+	0.244041i
$489$	−15.0003	−	39.5432i	−0.678338	−	1.78821i
$490$	−15.5524	−	1.76696i	−0.702587	−	0.0798231i
$491$	3.87273	+	2.23592i	0.174774	+	0.100906i	0.584835	−	0.811152i	$-0.301159\pi$
$491$	3.87273	+	2.23592i	0.174774	+	0.100906i	−0.410061	+	0.912058i	$0.634493\pi$
$492$	0.642402	−	3.95482i	0.0289617	−	0.178297i
$493$	22.0105			0.991303
$494$	−0.717793	−	0.414418i	−0.0322950	−	0.0186455i
$495$	−10.2483	+	11.4299i	−0.460625	+	0.513734i
$496$		−	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	$0.794911\pi$
$500$	−7.22876	+	8.52907i	−0.323280	+	0.381432i
$501$	−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	$0.838159\pi$
$510$	−1.15717	+	24.9652i	−0.0512403	+	1.10548i
$511$	−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
$520$	−7.25698	+	5.38409i	−0.318240	+	0.236108i
$521$	19.9940	−	34.6307i	0.875954	−	1.51720i	0.0202106	−	0.999796i	$-0.493566\pi$
$521$	19.9940	−	34.6307i	0.875954	−	1.51720i	0.855743	−	0.517401i	$-0.173100\pi$
$522$	3.23888	−	9.70673i	0.141762	−	0.424852i
$523$	14.4859	+	25.0903i	0.633424	+	1.09712i	0.986847	+	0.161659i	$0.0516846\pi$
$523$	14.4859	+	25.0903i	0.633424	+	1.09712i	−0.353422	+	0.935464i	$0.614982\pi$
$524$	1.47813	+	2.56020i	0.0645724	+	0.111843i
$525$	4.91688	+	22.3791i	0.214590	+	0.976704i
$526$	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
$530$	1.20766	+	10.4817i	0.0524575	+	0.455296i
$531$	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
$535$	−4.60871	−	40.0005i	−0.199252	−	1.72937i
$536$	−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
$540$	10.8395	+	4.18399i	0.466457	+	0.180050i
$541$	2.46717	+	4.27326i	0.106072	+	0.183722i	0.914176	−	0.405318i	$-0.132839\pi$
$541$	2.46717	+	4.27326i	0.106072	+	0.183722i	−0.808104	+	0.589040i	$0.799506\pi$
$542$			14.7966i			0.635566i
$543$	41.5611	+	6.75098i	1.78356	+	0.289712i
$544$		−	6.45290i		−	0.276666i
$545$	29.2278	−	21.6847i	1.25198	−	0.928870i
$546$	−0.243485	+	18.5170i	−0.0104202	+	0.792456i
$547$	12.6990	−	7.33178i	0.542971	−	0.313484i	−0.203311	−	0.979114i	$-0.565170\pi$
$547$	12.6990	−	7.33178i	0.542971	−	0.313484i	0.746282	+	0.665630i	$0.231837\pi$
$548$	3.43092	+	5.94252i	0.146562	+	0.253852i
$549$	−21.4534	−	24.2082i	−0.915608	−	1.03318i
$550$	−2.60214	−	11.1425i	−0.110956	−	0.475119i
$551$	−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
$555$	1.53337	−	33.0815i	0.0650880	−	1.40423i
$556$		−	1.66305i		−	0.0705289i
$557$	13.3908	−	23.1936i	0.567387	−	0.982743i	−0.429436	−	0.903097i	$-0.641288\pi$
$557$	13.3908	−	23.1936i	0.567387	−	0.982743i	0.996823	−	0.0796459i	$-0.0253790\pi$
$558$	−0.925912	+	2.77490i	−0.0391970	+	0.117471i
$559$			9.92679i			0.419858i
$560$	−1.53572	−	5.71328i	−0.0648958	−	0.241430i
$561$	−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	$-0.794362\pi$
$563$	−16.0483	+	9.26547i	−0.676354	+	0.390493i	0.122126	+	0.992515i	$0.461029\pi$
$564$	8.16840	+	1.32684i	0.343952	+	0.0558698i
$565$	−10.7271	+	7.95865i	−0.451293	+	0.334823i
$566$	−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	0.865697	−	0.500568i	$-0.166876\pi$
$569$	20.6344	+	11.9133i	0.865041	+	0.499431i	−0.000656372		1.00000i	$0.500209\pi$
$570$	−0.668804	−	0.428604i	−0.0280131	−	0.0179522i
$571$	−22.2726	−	38.5773i	−0.932079	−	1.61441i	−0.779761	−	0.626077i	$-0.784660\pi$
$571$	−22.2726	−	38.5773i	−0.932079	−	1.61441i	−0.152318	−	0.988332i	$-0.548674\pi$
$572$		−	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	$-0.849778\pi$
$577$	−1.24045	+	2.14853i	−0.0516407	+	0.0894443i	0.839050	+	0.544055i	$0.183112\pi$
$578$	−24.6399			−1.02489
$579$	7.64319	+	20.1486i	0.317640	+	0.837349i
$580$	4.54452	+	6.12536i	0.188701	+	0.254342i
$581$	−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
$585$	25.7641	−	8.43092i	1.06522	−	0.348576i
$586$	2.19993	−	1.27013i	0.0908784	−	0.0524687i
$587$	9.73573	−	5.62093i	0.401837	−	0.232001i	−0.285439	−	0.958397i	$-0.592140\pi$
$587$	9.73573	−	5.62093i	0.401837	−	0.232001i	0.687276	+	0.726396i	$0.258806\pi$
$588$	−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	$-0.461182\pi$
$593$	25.3760	−	14.6508i	1.04207	−	0.601638i	0.920418	+	0.390935i	$0.127848\pi$
$594$	−10.0488	+	6.35782i	−0.412309	+	0.260865i
$595$	−36.8672	+	9.90982i	−1.51141	+	0.406263i
$596$	−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	−0.241750	−	0.970338i	$-0.577722\pi$
$599$	11.6918	−	6.75024i	0.477712	−	0.275807i	0.719463	+	0.694531i	$0.244388\pi$
$600$	−7.18655	+	4.83255i	−0.293390	+	0.197288i
$601$	13.5297	−	7.81138i	0.551889	−	0.318633i	−0.197995	−	0.980203i	$-0.563443\pi$
$601$	13.5297	−	7.81138i	0.551889	−	0.318633i	0.749883	+	0.661570i	$0.230110\pi$
$602$	−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	$-0.552834\pi$
$607$	−8.14122			−0.330442			−0.165221	+	0.986257i	$0.552834\pi$
$608$	0.177623	+	0.102551i	0.00720357	+	0.00415899i
$609$	15.6296	+	0.205517i	0.633342	+	0.00832797i
$610$	23.9511	−	2.75955i	0.969750	−	0.111731i
$611$	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	$-0.223166\pi$
$613$	14.5475	+	8.39900i	0.587568	+	0.339232i	−0.176567	+	0.984289i	$0.556499\pi$
$614$	4.03149	−	6.98275i	0.162698	−	0.281801i
$615$	−4.11552	−	7.95794i	−0.165954	−	0.320895i
$616$	5.63236	+	2.22172i	0.226934	+	0.0895158i
$617$	−13.7676	+	23.8461i	−0.554262	+	0.960009i	0.443699	+	0.896176i	$0.353666\pi$
$617$	−13.7676	+	23.8461i	−0.554262	+	0.960009i	−0.997961	+	0.0638334i	$0.979667\pi$
$618$	−25.1926	−	20.5659i	−1.01340	−	0.827280i
$619$			9.34724i			0.375697i	0.982198	+	0.187849i	$0.0601514\pi$
$619$			9.34724i			0.375697i	−0.982198	+	0.187849i	$0.939849\pi$
$620$	−1.29916	−	1.75108i	−0.0521755	−	0.0703251i
$621$	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
$630$	−1.05481	+	17.7169i	−0.0420245	+	0.705857i
$631$	−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
$640$	1.79580	−	1.33234i	0.0709851	−	0.0526652i
$641$		−	18.7718i		−	0.741442i	−0.928744	−	0.370721i	$-0.879111\pi$
$641$		−	18.7718i		−	0.741442i	0.928744	−	0.370721i	$-0.120889\pi$
$642$	5.00069	−	30.7858i	0.197361	−	1.21502i
$643$	−11.5123	+	19.9399i	−0.454001	+	0.786353i	−0.998630	−	0.0523244i	$-0.983337\pi$
$643$	−11.5123	+	19.9399i	−0.454001	+	0.786353i	0.544629	+	0.838677i	$0.316670\pi$
$644$	−5.25598	+	0.782971i	−0.207115	+	0.0308534i
$645$	−0.440505	+	9.50362i	−0.0173449	+	0.374205i
$646$	0.661750	−	1.14619i	0.0260362	−	0.0450961i
$647$	14.6259	+	8.44426i	0.575003	+	0.331978i	0.759145	−	0.650922i	$-0.225617\pi$
$647$	14.6259	+	8.44426i	0.575003	+	0.331978i	−0.184142	+	0.982900i	$0.558951\pi$
$648$	7.19669	+	5.40442i	0.282713	+	0.212305i
$649$	17.9785	−	10.3799i	0.705716	−	0.407445i
$650$	−5.85864	+	19.3375i	−0.229795	+	0.758478i
$651$	−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	$-0.359962\pi$
$653$	21.7662			0.851776			0.425888	+	0.904776i	$0.359962\pi$
$654$	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	−0.850706	−	0.525641i	$-0.823825\pi$
$659$	−21.0718	+	12.1658i	−0.820841	+	0.473913i	0.0298654	+	0.999554i	$0.490492\pi$
$660$	0.410380	−	8.85368i	0.0159740	−	0.344629i
$661$	22.4717	−	12.9740i	0.874048	−	0.504632i	0.00535644	−	0.999986i	$-0.498295\pi$
$661$	22.4717	−	12.9740i	0.874048	−	0.504632i	0.868691	+	0.495354i	$0.164962\pi$
$662$	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
$665$	0.313123	−	1.17230i	0.0121424	−	0.0454599i
$666$	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	$-0.643088\pi$
$673$	3.32531	−	1.91987i	0.128181	−	0.0740054i	0.562719	+	0.826648i	$0.309755\pi$
$674$	1.58895	−	0.917381i	0.0612041	−	0.0353362i
$675$	25.0400	−	6.92823i	0.963789	−	0.266668i
$676$	−1.66523	+	2.88426i	−0.0640472	+	0.110933i
$677$	−14.0578	−	8.11628i	−0.540286	−	0.311934i	0.204909	−	0.978781i	$-0.434310\pi$
$677$	−14.0578	−	8.11628i	−0.540286	−	0.311934i	−0.745195	+	0.666847i	$0.767643\pi$
$678$	−9.67370	+	3.66962i	−0.371516	+	0.140931i
$679$	−22.1926	+	3.30598i	−0.851674	+	0.126872i
$680$	−8.59743	−	11.5881i	−0.329696	−	0.444383i
$681$	−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	$-0.775332\pi$
$683$	4.73579	−	8.20262i	0.181210	−	0.313865i	0.942293	+	0.334790i	$0.108665\pi$
$684$	−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
$690$	3.57335	+	6.90956i	0.136035	+	0.263043i
$691$	−13.6619	−	7.88768i	−0.519722	−	0.300062i	0.217099	−	0.976150i	$-0.430341\pi$
$691$	−13.6619	−	7.88768i	−0.519722	−	0.300062i	−0.736821	+	0.676088i	$0.763674\pi$
$692$			18.2330i			0.693116i
$693$	−13.9187	−	11.6707i	−0.528727	−	0.443334i
$694$	6.78486			0.257550
$695$	−2.21574	−	2.98649i	−0.0840477	−	0.113284i
$696$	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
$700$	−10.3698	−	8.21380i	−0.391943	−	0.310452i
$701$		−	3.43541i		−	0.129754i	−0.997893	−	0.0648769i	$-0.979335\pi$
$701$		−	3.43541i		−	0.129754i	0.997893	−	0.0648769i	$-0.0206655\pi$
$702$	20.9809	−	0.850463i	0.791874	−	0.0320987i
$703$	−0.876890	+	1.51882i	−0.0330725	+	0.0572833i
$704$			2.28847i			0.0862498i
$705$	16.4366	−	8.50033i	0.619037	−	0.320141i
$706$	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	−0.514244	−	0.857644i	$-0.671927\pi$
$709$	12.9306	−	22.3965i	0.485620	−	0.841118i	0.999863	+	0.0165263i	$0.00526071\pi$
$710$	14.7036	+	19.8183i	0.551816	+	0.743768i
$711$	−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
$715$	−12.3213	−	16.6074i	−0.460791	−	0.621080i
$716$			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	0.932571	+	0.360986i	$0.117560\pi$
$719$	20.8858	+	36.1753i	0.778909	+	1.34911i	−0.153663	+	0.988123i	$0.549107\pi$
$720$	−6.37553	+	2.08630i	−0.237602	+	0.0777517i
$721$	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
$725$	16.3221	+	4.94507i	0.606187	+	0.183655i
$726$	−7.73235	−	6.31226i	−0.286975	−	0.234270i
$727$	21.4490	+	37.1508i	0.795499	+	1.37785i	0.922522	+	0.385945i	$0.126125\pi$
$727$	21.4490	+	37.1508i	0.795499	+	1.37785i	−0.127022	+	0.991900i	$0.540542\pi$
$728$	−6.65180	−	8.37059i	−0.246532	−	0.310235i
$729$	−15.3482	−	22.2133i	−0.568453	−	0.822716i
$730$	−3.98563	−	34.5926i	−0.147515	−	1.28033i
$731$	−15.8513			−0.586281
$732$	18.4335	+	2.99425i	0.681323	+	0.110671i
$733$	−4.73892			−0.175036			−0.0875179	−	0.996163i	$-0.527894\pi$
$733$	−4.73892			−0.175036			−0.0875179	+	0.996163i	$0.527894\pi$
$734$	−6.18161	+	10.7069i	−0.228167	+	0.395197i
$735$	−26.2718	+	6.69268i	−0.969050	+	0.246863i
$736$	−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	0.461013	+	0.887393i	$0.347486\pi$
$739$	−14.6252	+	25.3317i	−0.537998	+	0.931841i	−0.999012	+	0.0444475i	$0.985847\pi$
$740$	11.3925	+	15.3555i	0.418797	+	0.564478i
$741$	−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	−0.396930	−	0.917849i	$-0.629925\pi$
$743$	16.2571	−	28.1581i	0.596415	−	1.03302i	0.993346	−	0.115173i	$-0.0367421\pi$
$744$	−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
$750$	−6.46700	+	18.2532i	−0.236142	+	0.666511i
$751$	−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
$760$	0.455607	−	0.0524934i	0.0165266	−	0.00190413i
$761$	−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
$765$	13.4627	+	41.1407i	0.486744	+	1.48744i
$766$	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	0.969560	−	0.244855i	$-0.0787403\pi$
$769$	34.4497	+	19.8896i	1.24229	+	0.717236i	0.272729	+	0.962091i	$0.412074\pi$
$770$	13.0746	−	3.51443i	0.471178	−	0.126651i
$771$	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	$-0.559187\pi$
$773$	−31.3729	−	18.1132i	−1.12841	−	0.651486i	−0.943534	+	0.331277i	$0.892521\pi$
$774$	−2.33255	+	6.99049i	−0.0838416	+	0.251268i
$775$	−4.66605	−	1.41367i	−0.167610	−	0.0507804i
$776$	−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
$780$	−8.44474	+	13.1774i	−0.302370	+	0.471826i
$781$	−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
$785$	−0.661161	−	5.73844i	−0.0235979	−	0.204814i
$786$	3.96654	+	3.23806i	0.141482	+	0.115498i
$787$	−8.56447	−	14.8341i	−0.305290	−	0.528778i	0.672036	−	0.740519i	$-0.265420\pi$
$787$	−8.56447	−	14.8341i	−0.305290	−	0.528778i	−0.977326	+	0.211740i	$0.932087\pi$
$788$	11.5232	+	19.9588i	0.410498	+	0.711003i
$789$	0.819077	−	5.04249i	0.0291599	−	0.179517i
$790$	−1.85146	−	16.0695i	−0.0658721	−	0.571726i
$791$	−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
$795$	8.39487	+	16.2327i	0.297735	+	0.575713i
$796$			8.06959i			0.286019i
$797$	35.9212	+	20.7391i	1.27239	+	0.734616i	0.975438	−	0.220275i	$-0.0706955\pi$
$797$	35.9212	+	20.7391i	1.27239	+	0.734616i	0.296955	+	0.954891i	$0.404029\pi$
$798$	0.480609	−	0.807723i	0.0170134	−	0.0285931i
$799$	15.4155	+	26.7004i	0.545360	+	0.944591i
$800$	1.44977	−	4.78520i	0.0512570	−	0.169183i
$801$	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
$805$	−8.39549	+	8.40879i	−0.295902	+	0.296371i
$806$	−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	0.403856	−	0.914822i	$-0.367670\pi$
$809$	−5.30390	−	3.06221i	−0.186475	−	0.107661i	−0.590331	+	0.807161i	$0.701003\pi$
$810$	20.1243	+	0.116828i	0.707095	+	0.00410493i
$811$		−	51.1448i		−	1.79594i	−0.440059	−	0.897969i	$-0.645043\pi$
$811$		−	51.1448i		−	1.79594i	0.440059	−	0.897969i	$-0.354957\pi$
$812$	−7.06531	+	5.61455i	−0.247944	+	0.197032i
$813$	9.08983	+	23.9622i	0.318794	+	0.840392i
$814$	−19.5682			−0.685864
$815$	54.2409	−	6.24943i	1.89997	−	0.218908i
$816$	−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	0.631301	−	0.775538i	$-0.282521\pi$
$821$	7.88867	+	4.55452i	0.275316	+	0.158954i	−0.355985	+	0.934492i	$0.615855\pi$
$822$	9.20681	+	7.51592i	0.321124	+	0.262148i
$823$	38.7300	−	22.3608i	1.35004	−	0.779449i	0.361789	−	0.932260i	$-0.382166\pi$
$823$	38.7300	−	22.3608i	1.35004	−	0.779449i	0.988255	+	0.152811i	$0.0488327\pi$
$824$	18.7761			0.654096
$825$	−11.0591	−	16.4462i	−0.385029	−	0.572582i
$826$	8.80689	−	22.3266i	0.306431	−	0.776843i
$827$	34.3286			1.19372			0.596860	−	0.802345i	$-0.296415\pi$
$827$	34.3286			1.19372			0.596860	+	0.802345i	$0.296415\pi$
$828$	1.20618	+	5.90353i	0.0419177	+	0.205162i
$829$	40.7898	+	23.5500i	1.41669	+	0.817925i	0.996006	−	0.0892828i	$-0.0284575\pi$
$829$	40.7898	+	23.5500i	1.41669	+	0.817925i	0.420682	+	0.907208i	$0.361791\pi$
$830$	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
$835$	−0.0139087	−	0.0187470i	−0.000481331	−	0.000648765i
$836$	−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	0.970254	−	0.242087i	$-0.0778321\pi$
$839$	7.97922	+	13.8204i	0.275473	+	0.477134i	−0.694781	+	0.719221i	$0.744499\pi$
$840$	−5.99680	−	8.30894i	−0.206909	−	0.286686i
$841$	−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
$845$	0.852391	+	7.39818i	0.0293231	+	0.254505i
$846$	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
$850$	−30.8785	−	9.35519i	−1.05912	−	0.320881i
$851$	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	$-0.113514\pi$
$853$	4.85434	+	8.40796i	0.166209	+	0.287883i	−0.770875	+	0.636987i	$0.780181\pi$
$854$	4.20318	+	28.2154i	0.143830	+	0.965511i
$855$	−1.34639	−	0.283241i	−0.0460457	−	0.00968664i
$856$	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	$0.0876903\pi$
$859$			15.9449i			0.544031i	−0.962293	+	0.272016i	$0.912310\pi$
$860$	−3.27283	−	4.41130i	−0.111602	−	0.150424i
$861$	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	0.951454	+	0.307790i	$0.0995893\pi$
$863$	21.8059	+	37.7689i	0.742281	+	1.28567i	−0.209174	+	0.977879i	$0.567077\pi$
$864$	−5.19189	+	0.210454i	−0.176632	+	0.00715978i
$865$	24.2925	+	32.7428i	0.825971	+	1.11329i
$866$	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
$870$	11.1226	+	7.12790i	0.377090	+	0.241659i
$871$			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
$875$	−29.5656	−	0.934208i	−0.999501	−	0.0315820i
$876$	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
$880$	3.04900	+	4.10962i	0.102782	+	0.138535i
$881$	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
$885$	−35.0959	−	1.62674i	−1.17974	−	0.0546824i
$886$	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
$895$	20.8304	+	28.0764i	0.696284	+	0.938490i
$896$	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
$900$	−8.66950	+	12.2409i	−0.288983	+	0.408030i
$901$	−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
$910$	−23.0977	−	6.16943i	−0.765682	−	0.204515i
$911$	36.0610	−	20.8198i	1.19475	−	0.689792i	0.235373	−	0.971905i	$-0.424369\pi$
$911$	36.0610	−	20.8198i	1.19475	−	0.689792i	0.959381	+	0.282113i	$0.0910354\pi$
$912$	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
$915$	37.0922	−	19.1826i	1.22623	−	0.634157i
$916$	−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	0.601758	−	0.798679i	$-0.294467\pi$
$919$	−11.8470	−	20.5196i	−0.390797	−	0.676880i	−0.992555	+	0.121798i	$0.961134\pi$
$920$	−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
$925$	40.9173	+	12.3966i	1.34535	+	0.407599i
$926$	−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	−0.914061	−	0.405576i	$-0.867071\pi$
$929$	−3.22447	+	5.58494i	−0.105791	+	0.183236i	0.808270	+	0.588812i	$0.200404\pi$
$930$	−3.17965	−	2.03768i	−0.104265	−	0.0668182i
$931$	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
$935$	26.5190	−	19.6749i	0.867263	−	0.643439i
$936$	−9.07315	+	8.04065i	−0.296565	+	0.262817i
$937$	−38.6081			−1.26127			−0.630635	−	0.776079i	$-0.717206\pi$
$937$	−38.6081			−1.26127			−0.630635	+	0.776079i	$0.717206\pi$
$938$	−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	0.768395	−	0.639976i	$-0.221056\pi$
$941$	−5.21606	−	9.03447i	−0.170039	−	0.294515i	−0.938433	+	0.345461i	$0.887723\pi$
$942$	0.717394	−	4.41650i	0.0233739	−	0.143897i
$943$	2.32307	−	4.02368i	0.0756496	−	0.131029i
$944$	9.07146			0.295251
$945$	9.17564	+	29.3395i	0.298484	+	0.954415i
$946$	5.62152			0.182771
$947$	17.0629	−	29.5538i	0.554470	−	0.960369i	−0.443475	−	0.896287i	$-0.646255\pi$
$947$	17.0629	−	29.5538i	0.554470	−	0.960369i	0.997945	−	0.0640827i	$-0.0204122\pi$
$948$	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	$-0.245233\pi$
$953$	44.3067			1.43523			0.717617	+	0.696438i	$0.245233\pi$
$954$	2.83369	+	13.8692i	0.0917440	+	0.449031i
$955$	−15.9080	−	21.4417i	−0.514771	−	0.693837i
$956$		−	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
$960$	2.08972	−	3.26084i	0.0674453	−	0.105243i
$961$	−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
$965$	−27.6376	+	3.18430i	−0.889686	+	0.102506i
$966$	−8.03079	+	4.49684i	−0.258387	+	0.144684i
$967$	−14.0448	−	8.10875i	−0.451649	−	0.260760i	0.256877	−	0.966444i	$-0.417306\pi$
$967$	−14.0448	−	8.10875i	−0.451649	−	0.260760i	−0.708526	+	0.705684i	$0.750640\pi$
$968$	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	0.995259	+	0.0972627i	$0.0310087\pi$
$971$	18.1313	+	31.4043i	0.581861	+	1.00781i	−0.413397	+	0.910551i	$0.635658\pi$
$972$	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
$975$	2.39165	+	34.9151i	0.0765942	+	1.11818i
$976$	−9.33757	+	5.39105i	−0.298888	+	0.172563i
$977$	4.35317	+	7.53992i	0.139270	+	0.241223i	0.927221	−	0.374516i	$-0.122191\pi$
$977$	4.35317	+	7.53992i	0.139270	+	0.241223i	−0.787950	+	0.615739i	$0.788858\pi$
$978$	41.7456	+	6.78095i	1.33488	+	0.216831i
$979$	20.1721	−	11.6464i	0.644704	−	0.372220i
$980$	9.30644	−	12.5853i	0.297283	−	0.402023i
$981$	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
$990$	−4.77442	−	14.5902i	−0.151741	−	0.463706i
$991$	−24.4098	+	42.2790i	−0.775402	+	1.34304i	0.159165	+	0.987252i	$0.449120\pi$
$991$	−24.4098	+	42.2790i	−0.775402	+	1.34304i	−0.934568	+	0.355785i	$0.884214\pi$
$992$	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
$995$	10.7514	+	14.4913i	0.340842	+	0.459406i
$996$	12.5342	−	15.3541i	0.397162	−	0.486513i
$997$	17.9594			0.568779			0.284390	−	0.958709i	$-0.408209\pi$
$997$	17.9594			0.568779			0.284390	+	0.958709i	$0.408209\pi$
$998$	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.a.59.10	✓	48
3.2	odd	2		1890.2.r.b.1529.22		48
5.4	even	2		630.2.r.b.59.15	yes	48
7.5	odd	6		630.2.bi.b.509.19	yes	48
9.2	odd	6		630.2.bi.a.479.6	yes	48
9.7	even	3		1890.2.bi.b.899.19		48
15.14	odd	2		1890.2.r.a.1529.22		48
21.5	even	6		1890.2.bi.a.719.14		48
35.19	odd	6		630.2.bi.a.509.6	yes	48
45.29	odd	6		630.2.bi.b.479.19	yes	48
45.34	even	6		1890.2.bi.a.899.14		48
63.47	even	6		630.2.r.b.299.15	yes	48
63.61	odd	6		1890.2.r.a.89.22		48
105.89	even	6		1890.2.bi.b.719.19		48
315.124	odd	6		1890.2.r.b.89.22		48
315.299	even	6	inner	630.2.r.a.299.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.10	✓	48	1.1	even	1	trivial
630.2.r.a.299.10	yes	48	315.299	even	6	inner
630.2.r.b.59.15	yes	48	5.4	even	2
630.2.r.b.299.15	yes	48	63.47	even	6
630.2.bi.a.479.6	yes	48	9.2	odd	6
630.2.bi.a.509.6	yes	48	35.19	odd	6
630.2.bi.b.479.19	yes	48	45.29	odd	6
630.2.bi.b.509.19	yes	48	7.5	odd	6
1890.2.r.a.89.22		48	63.61	odd	6
1890.2.r.a.1529.22		48	15.14	odd	2
1890.2.r.b.89.22		48	315.124	odd	6
1890.2.r.b.1529.22		48	3.2	odd	2
1890.2.bi.a.719.14		48	21.5	even	6
1890.2.bi.a.899.14		48	45.34	even	6
1890.2.bi.b.719.19		48	105.89	even	6
1890.2.bi.b.899.19		48	9.7	even	3

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} +(1.79580 - 1.33234i) q^{10} +2.28847i q^{11} +(1.61945 - 0.614321i) q^{12} +(2.02055 - 3.49969i) q^{13} +(1.64604 + 2.07137i) q^{14} +(2.08972 - 3.26084i) 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} +(0.255938 + 2.22137i) 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} +(1.77911 + 3.44017i) 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} +(-4.17999 + 4.18661i) 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} +(4.99455 + 4.47822i) 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} +(-4.86899 + 1.13707i) 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} +(-3.86883 - 0.179325i) q^{60} +(9.33757 + 5.39105i) q^{61} -0.975100i q^{62} +(-5.09980 + 6.08210i) q^{63} +1.00000 q^{64} +(-7.25698 + 5.38409i) q^{65} +(2.50661 - 3.07053i) q^{66} +(-5.24087 + 3.02582i) q^{67} -6.45290i q^{68} +(-0.557771 + 3.43381i) q^{69} +(-1.53572 - 5.71328i) q^{70} +11.0359i q^{71} +(-2.84576 - 0.949556i) q^{72} +(7.78631 - 13.4863i) q^{73} +8.55079i q^{74} +(-7.18655 + 4.83255i) 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} +(1.79580 - 1.33234i) 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} +(-8.59743 - 11.5881i) q^{85} -2.45646i q^{86} +(2.09542 + 5.52385i) q^{87} +2.28847i q^{88} +(-5.08916 - 8.81469i) q^{89} +(-6.37553 + 2.08630i) 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} +(0.455607 - 0.0524934i) 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	\( 48 q - 24 q^{2} + 3 q^{3} - 24 q^{4} + 48 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{14} - 4 q^{15} - 24 q^{16} - 3 q^{18} + 5 q^{21} + 6 q^{22} - 6 q^{23} + 3 q^{24} - 3 q^{28} - 3 q^{29} + 5 q^{30} - 24 q^{32} + 24 q^{33} + 18 q^{35} + 3 q^{41} + 8 q^{42} - 6 q^{44} + 9 q^{45} + 3 q^{46} - 6 q^{49} - 18 q^{50} - 8 q^{51} + 42 q^{55} - 22 q^{57} - q^{60} - 9 q^{61} - 10 q^{63} + 48 q^{64} - 33 q^{65} - 24 q^{66} - 33 q^{67} + 42 q^{69} - 6 q^{70} + 3 q^{72} + 18 q^{73} + 9 q^{75} + 6 q^{77} - 18 q^{78} - 37 q^{81} + 3 q^{82} - 9 q^{83} - 13 q^{84} - 33 q^{85} - 18 q^{87} + 33 q^{89} + 39 q^{90} + 3 q^{92} - 32 q^{93} + 33 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 + 3 * q^3 - 24 * q^4 + 48 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^14 - 4 * 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 + 5 * q^30 - 24 * q^32 + 24 * q^33 + 18 * 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 - q^60 - 9 * q^61 - 10 * q^63 + 48 * q^64 - 33 * q^65 - 24 * q^66 - 33 * q^67 + 42 * q^69 - 6 * q^70 + 3 * q^72 + 18 * q^73 + 9 * 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 + 39 * 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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