LMFDB - Embedded newform 630.2.bi.b.479.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(479,630)]

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([1, 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("630.479");

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.bi (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			479.19
Character	$\chi$	$=$	630.479
Dual form			630.2.bi.b.509.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.34174 - 1.09532i) q^{3} +1.00000 q^{4} +(-0.255938 + 2.22137i) q^{5} +(1.34174 - 1.09532i) q^{6} +(2.61687 - 0.389830i) q^{7} +1.00000 q^{8} +(0.600540 - 2.93928i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.34174 - 1.09532i) q^{3} +1.00000 q^{4} +(-0.255938 + 2.22137i) q^{5} +(1.34174 - 1.09532i) q^{6} +(2.61687 - 0.389830i) q^{7} +1.00000 q^{8} +(0.600540 - 2.93928i) q^{9} +(-0.255938 + 2.22137i) q^{10} +(-1.98187 + 1.14423i) q^{11} +(1.34174 - 1.09532i) q^{12} +(-2.02055 - 3.49969i) q^{13} +(2.61687 - 0.389830i) q^{14} +(2.08972 + 3.26084i) q^{15} +1.00000 q^{16} +(5.58838 + 3.22645i) q^{17} +(0.600540 - 2.93928i) q^{18} +(-0.177623 + 0.102551i) q^{19} +(-0.255938 + 2.22137i) q^{20} +(3.08418 - 3.38937i) q^{21} +(-1.98187 + 1.14423i) q^{22} +(-1.00425 + 1.73941i) q^{23} +(1.34174 - 1.09532i) q^{24} +(-4.86899 - 1.13707i) 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} +(2.08972 + 3.26084i) q^{30} -0.975100i q^{31} +1.00000 q^{32} +(-1.40585 + 3.70605i) 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} +(-0.177623 + 0.102551i) q^{38} +(-6.54434 - 2.48253i) q^{39} +(-0.255938 + 2.22137i) q^{40} +(-1.15662 - 2.00333i) q^{41} +(3.08418 - 3.38937i) q^{42} +(-2.12736 - 1.22823i) q^{43} +(-1.98187 + 1.14423i) q^{44} +(6.37553 + 2.08630i) q^{45} +(-1.00425 + 1.73941i) q^{46} -4.77784i q^{47} +(1.34174 - 1.09532i) q^{48} +(6.69607 - 2.04027i) q^{49} +(-4.86899 - 1.13707i) q^{50} +(11.0322 - 1.79201i) q^{51} +(-2.02055 - 3.49969i) q^{52} +(-2.35928 + 4.08640i) q^{53} +(-2.41369 - 4.60153i) q^{54} +(-2.03453 - 4.69532i) q^{55} +(2.61687 - 0.389830i) q^{56} +(-0.125998 + 0.332151i) q^{57} +(2.95397 + 1.70547i) q^{58} -9.07146 q^{59} +(2.08972 + 3.26084i) q^{60} -10.7821i q^{61} -0.975100i q^{62} +(0.425720 - 7.92583i) q^{63} +1.00000 q^{64} +(8.29125 - 3.59268i) q^{65} +(-1.40585 + 3.70605i) q^{66} +6.05164i q^{67} +(5.58838 + 3.22645i) q^{68} +(0.557771 + 3.43381i) q^{69} +(0.196198 + 5.91283i) q^{70} -11.0359i q^{71} +(0.600540 - 2.93928i) q^{72} +(-7.78631 + 13.4863i) q^{73} +(-7.40520 + 4.27539i) q^{74} +(-7.77838 + 3.80746i) q^{75} +(-0.177623 + 0.102551i) q^{76} +(-4.74025 + 3.76691i) q^{77} +(-6.54434 - 2.48253i) q^{78} -7.23402 q^{79} +(-0.255938 + 2.22137i) q^{80} +(-8.27870 - 3.53031i) q^{81} +(-1.15662 - 2.00333i) q^{82} +(-9.91029 - 5.72171i) q^{83} +(3.08418 - 3.38937i) q^{84} +(-8.59743 + 11.5881i) q^{85} +(-2.12736 - 1.22823i) q^{86} +(5.83150 - 0.947240i) q^{87} +(-1.98187 + 1.14423i) 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} +(-1.06805 - 1.30833i) q^{93} -4.77784i q^{94} +(-0.182343 - 0.420814i) q^{95} +(1.34174 - 1.09532i) 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 + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8}+O(q^{10}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8	$ 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39} - 3 q^{41} + 8 q^{42} + 6 q^{44} - 39 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 42 q^{55} + 3 q^{56} - 22 q^{57} - 3 q^{58} - 4 q^{60} - 43 q^{63} + 48 q^{64} + 12 q^{65} - 42 q^{69} - 12 q^{70} - 18 q^{73} + 18 q^{75} - 12 q^{77} - 18 q^{78} + 8 q^{81} - 3 q^{82} + 9 q^{83} + 8 q^{84} - 33 q^{85} - 15 q^{87} + 6 q^{88} - 33 q^{89} - 39 q^{90} + 3 q^{92} - 8 q^{93} - 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) $ 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.34174	−	1.09532i	0.774655	−	0.632384i
$3$	1.34174	−	1.09532i	0.774655	−	0.632384i
$4$	1.00000			0.500000
$5$	−0.255938	+	2.22137i	−0.114459	+	0.993428i
$5$	−0.255938	+	2.22137i	−0.114459	+	0.993428i
$6$	1.34174	−	1.09532i	0.547764	−	0.447163i
$7$	2.61687	−	0.389830i	0.989086	−	0.147342i
$7$	2.61687	−	0.389830i	0.989086	−	0.147342i
$8$	1.00000			0.353553
$9$	0.600540	−	2.93928i	0.200180	−	0.979759i
$10$	−0.255938	+	2.22137i	−0.0809348	+	0.702460i
$11$	−1.98187	+	1.14423i	−0.597556	+	0.344999i	−0.768080	−	0.640354i	$-0.778787\pi$
$11$	−1.98187	+	1.14423i	−0.597556	+	0.344999i	0.170523	+	0.985354i	$0.445454\pi$
$12$	1.34174	−	1.09532i	0.387327	−	0.316192i
$13$	−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	$-0.356019\pi$
$14$	2.61687	−	0.389830i	0.699389	−	0.104186i
$15$	2.08972	+	3.26084i	0.539562	+	0.841946i
$16$	1.00000			0.250000
$17$	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	$0.380596\pi$
$18$	0.600540	−	2.93928i	0.141549	−	0.692794i
$19$	−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
$21$	3.08418	−	3.38937i	0.673023	−	0.739621i
$22$	−1.98187	+	1.14423i	−0.422536	+	0.243951i
$23$	−1.00425	+	1.73941i	−0.209400	+	0.362692i	−0.951526	−	0.307569i	$-0.900484\pi$
$23$	−1.00425	+	1.73941i	−0.209400	+	0.362692i	0.742126	+	0.670261i	$0.233818\pi$
$24$	1.34174	−	1.09532i	0.273882	−	0.223582i
$25$	−4.86899	−	1.13707i	−0.973798	−	0.227414i
$26$	−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	$0.564092\pi$
$30$	2.08972	+	3.26084i	0.381528	+	0.595346i
$31$		−	0.975100i		−	0.175133i	−0.996159	−	0.0875665i	$-0.972091\pi$
$31$		−	0.975100i		−	0.175133i	0.996159	−	0.0875665i	$-0.0279090\pi$
$32$	1.00000			0.176777
$33$	−1.40585	+	3.70605i	−0.244728	+	0.645140i
$34$	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	−0.964363	−	0.264584i	$-0.914765\pi$
$37$	−7.40520	+	4.27539i	−1.21741	+	0.702870i	−0.253045	+	0.967455i	$0.581432\pi$
$38$	−0.177623	+	0.102551i	−0.0288143	+	0.0166359i
$39$	−6.54434	−	2.48253i	−1.04793	−	0.397523i
$40$	−0.255938	+	2.22137i	−0.0404674	+	0.351230i
$41$	−1.15662	−	2.00333i	−0.180634	−	0.312867i	0.761463	−	0.648209i	$-0.224482\pi$
$41$	−1.15662	−	2.00333i	−0.180634	−	0.312867i	−0.942097	+	0.335342i	$0.891148\pi$
$42$	3.08418	−	3.38937i	0.475899	−	0.522991i
$43$	−2.12736	−	1.22823i	−0.324419	−	0.187303i	0.328942	−	0.944350i	$-0.393308\pi$
$43$	−2.12736	−	1.22823i	−0.324419	−	0.187303i	−0.653360	+	0.757047i	$0.726641\pi$
$44$	−1.98187	+	1.14423i	−0.298778	+	0.172500i
$45$	6.37553	+	2.08630i	0.950408	+	0.311007i
$46$	−1.00425	+	1.73941i	−0.148068	+	0.256462i
$47$		−	4.77784i		−	0.696920i	−0.937324	−	0.348460i	$-0.886705\pi$
$47$		−	4.77784i		−	0.696920i	0.937324	−	0.348460i	$-0.113295\pi$
$48$	1.34174	−	1.09532i	0.193664	−	0.158096i
$49$	6.69607	−	2.04027i	0.956581	−	0.291467i
$50$	−4.86899	−	1.13707i	−0.688579	−	0.160806i
$51$	11.0322	−	1.79201i	1.54481	−	0.250931i
$52$	−2.02055	−	3.49969i	−0.280200	−	0.485320i
$53$	−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	$0.271719\pi$
$54$	−2.41369	−	4.60153i	−0.328461	−	0.626190i
$55$	−2.03453	−	4.69532i	−0.274336	−	0.633117i
$56$	2.61687	−	0.389830i	0.349695	−	0.0520932i
$57$	−0.125998	+	0.332151i	−0.0166889	+	0.0439945i
$58$	2.95397	+	1.70547i	0.387875	+	0.223940i
$59$	−9.07146			−1.18100			−0.590502	−	0.807036i	$-0.701070\pi$
$59$	−9.07146			−1.18100			−0.590502	+	0.807036i	$0.701070\pi$
$60$	2.08972	+	3.26084i	0.269781	+	0.420973i
$61$		−	10.7821i		−	1.38051i	−0.723568	−	0.690253i	$-0.757499\pi$
$61$		−	10.7821i		−	1.38051i	0.723568	−	0.690253i	$-0.242501\pi$
$62$		−	0.975100i		−	0.123838i
$63$	0.425720	−	7.92583i	0.0536356	−	0.998561i
$64$	1.00000			0.125000
$65$	8.29125	−	3.59268i	1.02840	−	0.445618i
$66$	−1.40585	+	3.70605i	−0.173049	+	0.456183i
$67$			6.05164i			0.739325i	0.929166	+	0.369662i	$0.120527\pi$
$67$			6.05164i			0.739325i	−0.929166	+	0.369662i	$0.879473\pi$
$68$	5.58838	+	3.22645i	0.677690	+	0.391265i
$69$	0.557771	+	3.43381i	0.0671478	+	0.413382i
$70$	0.196198	+	5.91283i	0.0234502	+	0.706718i
$71$		−	11.0359i		−	1.30973i	−0.755748	−	0.654863i	$-0.772726\pi$
$71$		−	11.0359i		−	1.30973i	0.755748	−	0.654863i	$-0.227274\pi$
$72$	0.600540	−	2.93928i	0.0707743	−	0.346397i
$73$	−7.78631	+	13.4863i	−0.911318	+	1.57845i	−0.0991142	+	0.995076i	$0.531601\pi$
$73$	−7.78631	+	13.4863i	−0.911318	+	1.57845i	−0.812204	+	0.583373i	$0.801732\pi$
$74$	−7.40520	+	4.27539i	−0.860837	+	0.497004i
$75$	−7.77838	+	3.80746i	−0.898170	+	0.439648i
$76$	−0.177623	+	0.102551i	−0.0203748	+	0.0117634i
$77$	−4.74025	+	3.76691i	−0.540201	+	0.429279i
$78$	−6.54434	−	2.48253i	−0.741001	−	0.281091i
$79$	−7.23402			−0.813891			−0.406946	−	0.913452i	$-0.633406\pi$
$79$	−7.23402			−0.813891			−0.406946	+	0.913452i	$0.633406\pi$
$80$	−0.255938	+	2.22137i	−0.0286148	+	0.248357i
$81$	−8.27870	−	3.53031i	−0.919856	−	0.392256i
$82$	−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	$0.882809\pi$
$84$	3.08418	−	3.38937i	0.336512	−	0.369811i
$85$	−8.59743	+	11.5881i	−0.932522	+	1.25691i
$86$	−2.12736	−	1.22823i	−0.229399	−	0.132443i
$87$	5.83150	−	0.947240i	0.625202	−	0.101555i
$88$	−1.98187	+	1.14423i	−0.211268	+	0.121976i
$89$	5.08916	+	8.81469i	0.539450	+	0.934355i	0.998934	+	0.0461690i	$0.0147013\pi$
$89$	5.08916	+	8.81469i	0.539450	+	0.934355i	−0.459483	+	0.888186i	$0.651965\pi$
$90$	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
$93$	−1.06805	−	1.30833i	−0.110751	−	0.135668i
$94$		−	4.77784i		−	0.492797i
$95$	−0.182343	−	0.420814i	−0.0187080	−	0.0431746i
$96$	1.34174	−	1.09532i	0.136941	−	0.111791i
$97$	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
$101$	−0.757545	−	1.31211i	−0.0753785	−	0.130559i	0.825872	−	0.563857i	$-0.190683\pi$
$101$	−0.757545	−	1.31211i	−0.0753785	−	0.130559i	−0.901251	+	0.433298i	$0.857350\pi$
$102$	11.0322	−	1.79201i	1.09235	−	0.177435i
$103$	9.38804	−	16.2606i	0.925031	−	1.60220i	0.133520	−	0.991046i	$-0.457372\pi$
$103$	9.38804	−	16.2606i	0.925031	−	1.60220i	0.791511	−	0.611155i	$-0.209295\pi$
$104$	−2.02055	−	3.49969i	−0.198131	−	0.343173i
$105$	6.73970	+	7.71858i	0.657727	+	0.753256i
$106$	−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	$0.497189\pi$
$108$	−2.41369	−	4.60153i	−0.232257	−	0.442783i
$109$	−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	$0.882158\pi$
$110$	−2.03453	−	4.69532i	−0.193985	−	0.447682i
$111$	−5.25293	+	13.8475i	−0.498586	+	1.31435i
$112$	2.61687	−	0.389830i	0.247271	−	0.0368354i
$113$	2.98673	+	5.17317i	0.280968	+	0.486651i	0.971623	−	0.236533i	$-0.0760112\pi$
$113$	2.98673	+	5.17317i	0.280968	+	0.486651i	−0.690655	+	0.723184i	$0.742678\pi$
$114$	−0.125998	+	0.332151i	−0.0118008	+	0.0311088i
$115$	−3.60685	−	2.67599i	−0.336340	−	0.249537i
$116$	2.95397	+	1.70547i	0.274269	+	0.158349i
$117$	−11.5000	+	3.83725i	−1.06317	+	0.354754i
$118$	−9.07146			−0.835096
$119$	15.8818	+	6.26470i	1.45589	+	0.574284i
$120$	2.08972	+	3.26084i	0.190764	+	0.297673i
$121$	−2.88146	+	4.99084i	−0.261951	+	0.453713i
$122$		−	10.7821i		−	0.976166i
$123$	−3.74618	−	1.42107i	−0.337781	−	0.128134i
$124$		−	0.975100i		−	0.0875665i
$125$	3.77201	−	10.5248i	0.337379	−	0.941369i
$126$	0.425720	−	7.92583i	0.0379261	−	0.706089i
$127$			11.8327i			1.04998i	0.851108	+	0.524991i	$0.175931\pi$
$127$			11.8327i			1.04998i	−0.851108	+	0.524991i	$0.824069\pi$
$128$	1.00000			0.0883883
$129$	−4.19967	+	0.682173i	−0.369760	+	0.0600620i
$130$	8.29125	−	3.59268i	0.727191	−	0.315099i
$131$	−1.47813	+	2.56020i	−0.129145	+	0.223685i	−0.923346	−	0.383970i	$-0.874557\pi$
$131$	−1.47813	+	2.56020i	−0.129145	+	0.223685i	0.794201	+	0.607656i	$0.207890\pi$
$132$	−1.40585	+	3.70605i	−0.122364	+	0.322570i
$133$	−0.424840	+	0.337605i	−0.0368383	+	0.0292741i
$134$			6.05164i			0.522782i
$135$	10.8395	−	4.18399i	0.932914	−	0.360100i
$136$	5.58838	+	3.22645i	0.479199	+	0.276666i
$137$	3.43092	+	5.94252i	0.293123	+	0.507704i	0.974547	−	0.224185i	$-0.0719721\pi$
$137$	3.43092	+	5.94252i	0.293123	+	0.507704i	−0.681423	+	0.731889i	$0.738639\pi$
$138$	0.557771	+	3.43381i	0.0474807	+	0.292305i
$139$	−1.44024	+	0.831524i	−0.122160	+	0.0705289i	−0.559835	−	0.828604i	$-0.689135\pi$
$139$	−1.44024	+	0.831524i	−0.122160	+	0.0705289i	0.437675	+	0.899133i	$0.355802\pi$
$140$	0.196198	+	5.91283i	0.0165818	+	0.499725i
$141$	−5.23327	−	6.41063i	−0.440721	−	0.539872i
$142$		−	11.0359i		−	0.926116i
$143$	8.00893	+	4.62396i	0.669740	+	0.386675i
$144$	0.600540	−	2.93928i	0.0500450	−	0.244940i
$145$	−4.54452	+	6.12536i	−0.377402	+	0.508684i
$146$	−7.78631	+	13.4863i	−0.644399	+	1.11613i
$147$	6.74964	−	10.0719i	0.556701	−	0.830713i
$148$	−7.40520	+	4.27539i	−0.608704	+	0.351435i
$149$	−10.1542	−	5.86255i	−0.831867	−	0.480278i	0.0226246	−	0.999744i	$-0.492798\pi$
$149$	−10.1542	−	5.86255i	−0.831867	−	0.480278i	−0.854491	+	0.519466i	$0.826131\pi$
$150$	−7.77838	+	3.80746i	−0.635102	+	0.310878i
$151$	−1.68168	−	2.91276i	−0.136853	−	0.237037i	0.789451	−	0.613814i	$-0.210366\pi$
$151$	−1.68168	−	2.91276i	−0.136853	−	0.237037i	−0.926304	+	0.376777i	$0.877032\pi$
$152$	−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
$156$	−6.54434	−	2.48253i	−0.523967	−	0.198762i
$157$	2.58329			0.206169			0.103084	−	0.994673i	$-0.467129\pi$
$157$	2.58329			0.206169			0.103084	+	0.994673i	$0.467129\pi$
$158$	−7.23402			−0.575508
$159$	1.31037	+	8.06706i	0.103919	+	0.639760i
$160$	−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	$-0.261147\pi$
$163$	21.1464	−	12.2089i	1.65631	−	0.956272i	0.974395	−	0.224841i	$-0.0721863\pi$
$164$	−1.15662	−	2.00333i	−0.0903170	−	0.156434i
$165$	−7.87271	−	4.07144i	−0.612889	−	0.316961i
$166$	−9.91029	−	5.72171i	−0.769188	−	0.444091i
$167$	−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	$0.333462\pi$
$168$	3.08418	−	3.38937i	0.237950	−	0.261496i
$169$	−1.66523	+	2.88426i	−0.128094	+	0.221866i
$170$	−8.59743	+	11.5881i	−0.659393	+	0.888766i
$171$	0.194756	+	0.583670i	0.0148933	+	0.0446343i
$172$	−2.12736	−	1.22823i	−0.162209	−	0.0936516i
$173$			18.2330i			1.38623i	0.720826	+	0.693116i	$0.243763\pi$
$173$			18.2330i			1.38623i	−0.720826	+	0.693116i	$0.756237\pi$
$174$	5.83150	−	0.947240i	0.442085	−	0.0718101i
$175$	−13.1848	−	1.07749i	−0.996677	−	0.0814505i
$176$	−1.98187	+	1.14423i	−0.149389	+	0.0862498i
$177$	−12.1716	+	9.93617i	−0.914870	+	0.746849i
$178$	5.08916	+	8.81469i	0.381449	+	0.660689i
$179$	13.5399	+	7.81725i	1.01202	+	0.584289i	0.911782	−	0.410675i	$-0.134707\pi$
$179$	13.5399	+	7.81725i	1.01202	+	0.584289i	0.100236	+	0.994964i	$0.468040\pi$
$180$	6.37553	+	2.08630i	0.475204	+	0.155503i
$181$		−	24.3098i		−	1.80693i	−0.428659	−	0.903467i	$-0.641014\pi$
$181$		−	24.3098i		−	1.80693i	0.428659	−	0.903467i	$-0.358986\pi$
$182$	−6.65180	−	8.37059i	−0.493065	−	0.620469i
$183$	−11.8099	−	14.4668i	−0.873011	−	1.06942i
$184$	−1.00425	+	1.73941i	−0.0740342	+	0.128231i
$185$	−7.60197	−	17.5439i	−0.558908	−	1.28986i
$186$	−1.06805	−	1.30833i	−0.0783131	−	0.0959315i
$187$	−14.7672			−1.07989
$188$		−	4.77784i		−	0.348460i
$189$	−8.11013	−	11.1007i	−0.589925	−	0.807458i
$190$	−0.182343	−	0.420814i	−0.0132286	−	0.0305291i
$191$			11.9399i			0.863943i	0.901887	+	0.431972i	$0.142182\pi$
$191$			11.9399i			0.863943i	−0.901887	+	0.431972i	$0.857818\pi$
$192$	1.34174	−	1.09532i	0.0968318	−	0.0790481i
$193$		−	12.4417i		−	0.895572i	−0.894141	−	0.447786i	$-0.852213\pi$
$193$		−	12.4417i		−	0.895572i	0.894141	−	0.447786i	$-0.147787\pi$
$194$	4.24029	−	7.34440i	0.304435	−	0.527297i
$195$	7.18957	−	13.9020i	0.514856	−	0.995546i
$196$	6.69607	−	2.04027i	0.478290	−	0.145734i
$197$	−23.0465			−1.64199			−0.820996	−	0.570934i	$-0.806581\pi$
$197$	−23.0465			−1.64199			−0.820996	+	0.570934i	$0.806581\pi$
$198$	2.17303	+	6.51242i	0.154430	+	0.462818i
$199$	−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	$0.758999\pi$
$200$	−4.86899	−	1.13707i	−0.344290	−	0.0804029i
$201$	6.62849	+	8.11973i	0.467538	+	0.572722i
$202$	−0.757545	−	1.31211i	−0.0533007	−	0.0923195i
$203$	8.39500	+	3.31147i	0.589214	+	0.232419i
$204$	11.0322	−	1.79201i	0.772406	−	0.125466i
$205$	4.74616	−	2.05656i	0.331486	−	0.143636i
$206$	9.38804	−	16.2606i	0.654096	−	1.13293i
$207$	4.50951	+	3.99635i	0.313433	+	0.277765i
$208$	−2.02055	−	3.49969i	−0.140100	−	0.242660i
$209$	0.234684	−	0.406485i	0.0162334	−	0.0281171i
$210$	6.73970	+	7.71858i	0.465083	+	0.532633i
$211$	−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	$-0.386067\pi$
$212$	−2.35928	+	4.08640i	−0.162036	+	0.280655i
$213$	−12.0879	−	14.8074i	−0.828250	−	1.01459i
$214$	9.00357	+	15.5946i	0.615471	+	1.06603i
$215$	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
$219$	4.32461	+	26.6236i	0.292230	+	1.79906i
$220$	−2.03453	−	4.69532i	−0.137168	−	0.316559i
$221$		−	26.0768i		−	1.75411i
$222$	−5.25293	+	13.8475i	−0.352553	+	0.929387i
$223$	−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
$225$	−6.26618	+	13.6285i	−0.417745	+	0.908564i
$226$	2.98673	+	5.17317i	0.198674	+	0.344114i
$227$	16.0856	−	9.28700i	1.06764	−	0.616400i	0.140102	−	0.990137i	$-0.455257\pi$
$227$	16.0856	−	9.28700i	1.06764	−	0.616400i	0.927535	+	0.373737i	$0.121924\pi$
$228$	−0.125998	+	0.332151i	−0.00834444	+	0.0219973i
$229$	1.36101	+	0.785777i	0.0899378	+	0.0519256i	0.544294	−	0.838894i	$-0.316797\pi$
$229$	1.36101	+	0.785777i	0.0899378	+	0.0519256i	−0.454357	+	0.890820i	$0.650131\pi$
$230$	−3.60685	−	2.67599i	−0.237829	−	0.176450i
$231$	−2.23421	+	10.2463i	−0.147000	+	0.674158i
$232$	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	$0.753700\pi$
$234$	−11.5000	+	3.83725i	−0.751777	+	0.250849i
$235$	10.6134	+	1.22283i	0.692340	+	0.0797688i
$236$	−9.07146			−0.590502
$237$	−9.70619	+	7.92359i	−0.630485	+	0.514692i
$238$	15.8818	+	6.26470i	1.02947	+	0.406080i
$239$	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	$0.151949\pi$
$240$	2.08972	+	3.26084i	0.134891	+	0.210486i
$241$	24.5697	−	14.1853i	1.58267	−	0.913757i	0.588207	−	0.808710i	$-0.299834\pi$
$241$	24.5697	−	14.1853i	1.58267	−	0.913757i	0.994467	−	0.105047i	$-0.0334994\pi$
$242$	−2.88146	+	4.99084i	−0.185227	+	0.320823i
$243$	−14.9747	+	4.33109i	−0.960627	+	0.277840i
$244$		−	10.7821i		−	0.690253i
$245$	2.81842	+	15.3966i	0.180062	+	0.983655i
$246$	−3.74618	−	1.42107i	−0.238847	−	0.0906044i
$247$	0.717793	+	0.414418i	0.0456720	+	0.0263688i
$248$		−	0.975100i		−	0.0619189i
$249$	−19.5642	+	3.17790i	−1.23983	+	0.201392i
$250$	3.77201	−	10.5248i	0.238563	−	0.665648i
$251$	9.95552			0.628387			0.314193	−	0.949359i	$-0.398266\pi$
$251$	9.95552			0.628387			0.314193	+	0.949359i	$0.398266\pi$
$252$	0.425720	−	7.92583i	0.0268178	−	0.499280i
$253$		−	4.59638i		−	0.288972i
$254$			11.8327i			0.742450i
$255$	1.15717	+	24.9652i	0.0724647	+	1.56338i
$256$	1.00000			0.0625000
$257$	16.2504	+	9.38216i	1.01367	+	0.585243i	0.912264	−	0.409602i	$-0.134332\pi$
$257$	16.2504	+	9.38216i	1.01367	+	0.585243i	0.101406	+	0.994845i	$0.467666\pi$
$258$	−4.19967	+	0.682173i	−0.261460	+	0.0424703i
$259$	−17.7118	+	14.0749i	−1.10056	+	0.874574i
$260$	8.29125	−	3.59268i	0.514202	−	0.222809i
$261$	6.78683	−	7.65832i	0.420094	−	0.474038i
$262$	−1.47813	+	2.56020i	−0.0913192	+	0.158170i
$263$	1.47472	+	2.55429i	0.0909351	+	0.157504i	0.907905	−	0.419176i	$-0.137681\pi$
$263$	1.47472	+	2.55429i	0.0909351	+	0.157504i	−0.816970	+	0.576681i	$0.804348\pi$
$264$	−1.40585	+	3.70605i	−0.0865243	+	0.228092i
$265$	−8.47358	−	6.28671i	−0.520528	−	0.386190i
$266$	−0.424840	+	0.337605i	−0.0260486	+	0.0206999i
$267$	16.4833	+	6.25276i	1.00876	+	0.382663i
$268$			6.05164i			0.369662i
$269$	13.8077	−	23.9156i	0.841869	−	1.45816i	−0.0464436	−	0.998921i	$-0.514789\pi$
$269$	13.8077	−	23.9156i	0.841869	−	1.45816i	0.888313	−	0.459239i	$-0.151878\pi$
$270$	10.8395	−	4.18399i	0.659670	−	0.254629i
$271$	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
$273$	−18.0935	−	3.94529i	−1.09507	−	0.238780i
$274$	3.43092	+	5.94252i	0.207269	+	0.359001i
$275$	10.9508	−	3.31774i	0.660357	−	0.200067i
$276$	0.557771	+	3.43381i	0.0335739	+	0.206691i
$277$	−6.88813	+	3.97687i	−0.413868	+	0.238947i	−0.692450	−	0.721466i	$-0.743469\pi$
$277$	−6.88813	+	3.97687i	−0.413868	+	0.238947i	0.278582	+	0.960412i	$0.410135\pi$
$278$	−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	$0.814255\pi$
$282$	−5.23327	−	6.41063i	−0.311637	−	0.381747i
$283$	29.8023			1.77156			0.885780	−	0.464105i	$-0.153624\pi$
$283$	29.8023			1.77156			0.885780	+	0.464105i	$0.153624\pi$
$284$		−	11.0359i		−	0.654863i
$285$	−0.705584	−	0.364899i	−0.0417952	−	0.0216148i
$286$	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
$290$	−4.54452	+	6.12536i	−0.266864	+	0.359694i
$291$	−2.35511	−	14.4988i	−0.138059	−	0.849933i
$292$	−7.78631	+	13.4863i	−0.455659	+	0.789225i
$293$	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	$0.309692\pi$
$294$	6.74964	−	10.0719i	0.393647	−	0.587403i
$295$	2.32173	−	20.1511i	0.135177	−	1.17324i
$296$	−7.40520	+	4.27539i	−0.430418	+	0.248502i
$297$	10.0488	+	6.35782i	0.583093	+	0.368918i
$298$	−10.1542	−	5.86255i	−0.588219	−	0.339608i
$299$	8.11653			0.469391
$300$	−7.77838	+	3.80746i	−0.449085	+	0.219824i
$301$	−6.04582	−	2.38482i	−0.348476	−	0.137459i
$302$	−1.68168	−	2.91276i	−0.0967699	−	0.167610i
$303$	−2.45361	−	0.930752i	−0.140956	−	0.0534703i
$304$	−0.177623	+	0.102551i	−0.0101874	+	0.00588169i
$305$	23.9511	+	2.75955i	1.37143	+	0.158012i
$306$	12.8395	−	14.4882i	0.733984	−	0.828234i
$307$	8.06299			0.460179			0.230089	−	0.973169i	$-0.426098\pi$
$307$	8.06299			0.460179			0.230089	+	0.973169i	$0.426098\pi$
$308$	−4.74025	+	3.76691i	−0.270101	+	0.214639i
$309$	−5.21423	−	32.1004i	−0.296627	−	1.82613i
$310$	2.16606	+	0.249565i	0.123024	+	0.0141744i
$311$	−0.763625			−0.0433012			−0.0216506	−	0.999766i	$-0.506892\pi$
$311$	−0.763625			−0.0433012			−0.0216506	+	0.999766i	$0.506892\pi$
$312$	−6.54434	−	2.48253i	−0.370500	−	0.140546i
$313$	3.83737			0.216901			0.108450	−	0.994102i	$-0.465411\pi$
$313$	3.83737			0.216901			0.108450	+	0.994102i	$0.465411\pi$
$314$	2.58329			0.145783
$315$	17.4973	+	2.97420i	0.985859	+	0.167577i
$316$	−7.23402			−0.406946
$317$	−17.3289			−0.973288			−0.486644	−	0.873600i	$-0.661779\pi$
$317$	−17.3289			−0.973288			−0.486644	+	0.873600i	$0.661779\pi$
$318$	1.31037	+	8.06706i	0.0734821	+	0.452378i
$319$	−7.80583			−0.437043
$320$	−0.255938	+	2.22137i	−0.0143074	+	0.124178i
$321$	29.1616	+	11.0622i	1.62764	+	0.617430i
$322$	−1.94992	+	4.94330i	−0.108665	+	0.275479i
$323$	−1.32350			−0.0736416
$324$	−8.27870	−	3.53031i	−0.459928	−	0.196128i
$325$	5.85864	+	19.3375i	0.324979	+	1.07265i
$326$	21.1464	−	12.2089i	1.17119	−	0.676186i
$327$	4.51986	+	27.8256i	0.249949	+	1.53876i
$328$	−1.15662	−	2.00333i	−0.0638638	−	0.110615i
$329$	−1.86254	−	12.5030i	−0.102685	−	0.689313i
$330$	−7.87271	−	4.07144i	−0.433378	−	0.224126i
$331$	−4.95873			−0.272556			−0.136278	−	0.990671i	$-0.543514\pi$
$331$	−4.95873			−0.272556			−0.136278	+	0.990671i	$0.543514\pi$
$332$	−9.91029	−	5.72171i	−0.543898	−	0.314020i
$333$	8.11945	+	24.3335i	0.444943	+	1.33347i
$334$	−0.00904075	+	0.00521968i	−0.000494688	+	0.000285608i
$335$	−13.4429	−	1.54885i	−0.734466	−	0.0846224i
$336$	3.08418	−	3.38937i	0.168256	−	0.184905i
$337$	−1.58895	+	0.917381i	−0.0865557	+	0.0499729i	−0.542653	−	0.839957i	$-0.682580\pi$
$337$	−1.58895	+	0.917381i	−0.0865557	+	0.0499729i	0.456097	+	0.889930i	$0.349247\pi$
$338$	−1.66523	+	2.88426i	−0.0905765	+	0.156883i
$339$	9.67370	+	3.66962i	0.525403	+	0.199307i
$340$	−8.59743	+	11.5881i	−0.466261	+	0.628453i
$341$	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
$345$	−7.77053	+	0.360174i	−0.418351	+	0.0193911i
$346$			18.2330i			0.980214i
$347$	6.78486			0.364230			0.182115	−	0.983277i	$-0.441706\pi$
$347$	6.78486			0.364230			0.182115	+	0.983277i	$0.441706\pi$
$348$	5.83150	−	0.947240i	0.312601	−	0.0507774i
$349$	−11.4343	−	6.60159i	−0.612064	−	0.353375i	0.161709	−	0.986838i	$-0.448299\pi$
$349$	−11.4343	−	6.60159i	−0.612064	−	0.353375i	−0.773773	+	0.633463i	$0.781633\pi$
$350$	−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
$353$	−26.8650	+	15.5105i	−1.42988	+	0.825543i	−0.997111	−	0.0759611i	$-0.975798\pi$
$353$	−26.8650	+	15.5105i	−1.42988	+	0.825543i	−0.432771	+	0.901504i	$0.642464\pi$
$354$	−12.1716	+	9.93617i	−0.646911	+	0.528102i
$355$	24.5149	+	2.82452i	1.30112	+	0.149910i
$356$	5.08916	+	8.81469i	0.269725	+	0.467178i
$357$	28.1712	−	8.99013i	1.49098	−	0.475808i
$358$	13.5399	+	7.81725i	0.715605	+	0.413155i
$359$	24.9912	−	14.4287i	1.31899	−	0.761517i	0.335420	−	0.942069i	$-0.391122\pi$
$359$	24.9912	−	14.4287i	1.31899	−	0.761517i	0.983565	+	0.180552i	$0.0577884\pi$
$360$	6.37553	+	2.08630i	0.336020	+	0.109957i
$361$	−9.47897	+	16.4181i	−0.498893	+	0.864108i
$362$		−	24.3098i		−	1.27769i
$363$	1.60040	+	9.85254i	0.0839991	+	0.517124i
$364$	−6.65180	−	8.37059i	−0.348649	−	0.438738i
$365$	−27.9652	−	20.7479i	−1.46377	−	1.08600i
$366$	−11.8099	−	14.4668i	−0.617312	−	0.756191i
$367$	6.18161	+	10.7069i	0.322677	+	0.558893i	0.981040	−	0.193808i	$-0.0620838\pi$
$367$	6.18161	+	10.7069i	0.322677	+	0.558893i	−0.658362	+	0.752701i	$0.728750\pi$
$368$	−1.00425	+	1.73941i	−0.0523501	+	0.0906730i
$369$	−6.58293	+	2.19655i	−0.342694	+	0.114348i
$370$	−7.60197	−	17.5439i	−0.395207	−	0.912066i
$371$	−4.58095	+	11.6133i	−0.237831	+	0.602933i
$372$	−1.06805	−	1.30833i	−0.0553757	−	0.0678338i
$373$	31.7495	+	18.3306i	1.64393	+	0.949123i	0.979417	+	0.201845i	$0.0646937\pi$
$373$	31.7495	+	18.3306i	1.64393	+	0.949123i	0.664512	+	0.747278i	$0.268640\pi$
$374$	−14.7672			−0.763596
$375$	−6.46700	−	18.2532i	−0.333955	−	0.942589i
$376$		−	4.77784i		−	0.246398i
$377$		−	13.7840i		−	0.709910i
$378$	−8.11013	−	11.1007i	−0.417140	−	0.570959i
$379$	19.2906			0.990893			0.495446	−	0.868639i	$-0.335004\pi$
$379$	19.2906			0.990893			0.495446	+	0.868639i	$0.335004\pi$
$380$	−0.182343	−	0.420814i	−0.00935400	−	0.0215873i
$381$	12.9606	+	15.8764i	0.663993	+	0.813374i
$382$			11.9399i			0.610900i
$383$	7.09201	+	4.09457i	0.362385	+	0.209223i	0.670126	−	0.742247i	$-0.266240\pi$
$383$	7.09201	+	4.09457i	0.362385	+	0.209223i	−0.307742	+	0.951470i	$0.599573\pi$
$384$	1.34174	−	1.09532i	0.0684705	−	0.0558954i
$385$	−7.15449	−	11.4940i	−0.364627	−	0.585786i
$386$		−	12.4417i		−	0.633265i
$387$	−4.88767	+	5.51529i	−0.248454	+	0.280358i
$388$	4.24029	−	7.34440i	0.215268	−	0.372855i
$389$	7.64611	−	4.41449i	0.387673	−	0.223823i	−0.293478	−	0.955966i	$-0.594813\pi$
$389$	7.64611	−	4.41449i	0.387673	−	0.223823i	0.681152	+	0.732142i	$0.261479\pi$
$390$	7.18957	−	13.9020i	0.364058	−	0.703957i
$391$	−11.2242	+	6.48032i	−0.567634	+	0.327724i
$392$	6.69607	−	2.04027i	0.338202	−	0.103049i
$393$	0.820971	+	5.05415i	0.0414125	+	0.254948i
$394$	−23.0465			−1.16106
$395$	1.85146	−	16.0695i	0.0931572	−	0.808542i
$396$	2.17303	+	6.51242i	0.109199	+	0.327262i
$397$	5.82466	+	10.0886i	0.292332	+	0.506333i	0.974361	−	0.224992i	$-0.0722356\pi$
$397$	5.82466	+	10.0886i	0.292332	+	0.506333i	−0.682029	+	0.731325i	$0.738902\pi$
$398$	−6.98847	−	4.03479i	−0.350300	−	0.202246i
$399$	−0.200239	+	0.918316i	−0.0100245	+	0.0459733i
$400$	−4.86899	−	1.13707i	−0.243450	−	0.0568534i
$401$	−2.28763	−	1.32076i	−0.114239	−	0.0659557i	0.441792	−	0.897118i	$-0.354343\pi$
$401$	−2.28763	−	1.32076i	−0.114239	−	0.0659557i	−0.556031	+	0.831162i	$0.687676\pi$
$402$	6.62849	+	8.11973i	0.330599	+	0.404975i
$403$	−3.41255	+	1.97024i	−0.169991	+	0.0981444i
$404$	−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
$408$	11.0322	−	1.79201i	0.546173	−	0.0887177i
$409$		−	4.00359i		−	0.197965i	−0.995089	−	0.0989824i	$-0.968441\pi$
$409$		−	4.00359i		−	0.197965i	0.995089	−	0.0989824i	$-0.0315588\pi$
$410$	4.74616	−	2.05656i	0.234396	−	0.101566i
$411$	11.1124	+	4.21537i	0.548133	+	0.207929i
$412$	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
$416$	−2.02055	−	3.49969i	−0.0990655	−	0.171587i
$417$	−1.02165	+	2.69322i	−0.0500302	+	0.131887i
$418$	0.234684	−	0.406485i	0.0114788	−	0.0198818i
$419$	10.3156	+	17.8671i	0.503949	+	0.872865i	0.999990	+	0.00456603i	$0.00145342\pi$
$419$	10.3156	+	17.8671i	0.503949	+	0.872865i	−0.496040	+	0.868299i	$0.665213\pi$
$420$	6.73970	+	7.71858i	0.328863	+	0.376628i
$421$	−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
$423$	−14.0434	−	2.86928i	−0.682814	−	0.139509i
$424$	−2.35928	+	4.08640i	−0.114577	+	0.198453i
$425$	−23.5411	−	22.0639i	−1.14191	−	1.07026i
$426$	−12.0879	−	14.8074i	−0.585661	−	0.717420i
$427$	−4.20318	−	28.2154i	−0.203406	−	1.36544i
$428$	9.00357	+	15.5946i	0.435204	+	0.753795i
$429$	15.8106	−	2.56820i	0.763344	−	0.123994i
$430$	3.27283	−	4.41130i	0.157830	−	0.212732i
$431$	−1.89577	−	1.09452i	−0.0913159	−	0.0527213i	0.453647	−	0.891182i	$-0.350123\pi$
$431$	−1.89577	−	1.09452i	−0.0913159	−	0.0527213i	−0.544963	+	0.838460i	$0.683456\pi$
$432$	−2.41369	−	4.60153i	−0.116129	−	0.221391i
$433$	23.8117			1.14432			0.572158	−	0.820143i	$-0.306106\pi$
$433$	23.8117			1.14432			0.572158	+	0.820143i	$0.306106\pi$
$434$	−0.380123	−	2.55171i	−0.0182465	−	0.122486i
$435$	0.611669	+	13.1964i	0.0293273	+	0.632717i
$436$	−8.13785	+	14.0952i	−0.389732	+	0.675036i
$437$		−	0.411946i		−	0.0197060i
$438$	4.32461	+	26.6236i	0.206638	+	1.27213i
$439$		−	14.3892i		−	0.686758i	−0.939197	−	0.343379i	$-0.888428\pi$
$439$		−	14.3892i		−	0.686758i	0.939197	−	0.343379i	$-0.111572\pi$
$440$	−2.03453	−	4.69532i	−0.0969925	−	0.223841i
$441$	−1.97567	−	20.9069i	−0.0940794	−	0.995565i
$442$		−	26.0768i		−	1.24035i
$443$	−36.6080			−1.73930			−0.869649	−	0.493670i	$-0.835655\pi$
$443$	−36.6080			−1.73930			−0.869649	+	0.493670i	$0.835655\pi$
$444$	−5.25293	+	13.8475i	−0.249293	+	0.657176i
$445$	−20.8832	+	9.04891i	−0.989960	+	0.428960i
$446$	−2.10769	+	3.65063i	−0.0998021	+	0.172862i
$447$	−20.0457	+	3.25613i	−0.948130	+	0.154010i
$448$	2.61687	−	0.389830i	0.123636	−	0.0184177i
$449$			0.350689i			0.0165500i	0.999966	+	0.00827501i	$0.00263405\pi$
$449$			0.350689i			0.0165500i	−0.999966	+	0.00827501i	$0.997366\pi$
$450$	−6.26618	+	13.6285i	−0.295391	+	0.642452i
$451$	4.58455	+	2.64689i	0.215878	+	0.124637i
$452$	2.98673	+	5.17317i	0.140484	+	0.243325i
$453$	−5.44679	−	2.06618i	−0.255912	−	0.0970778i
$454$	16.0856	−	9.28700i	0.754933	−	0.435861i
$455$	20.2966	−	12.6338i	0.951521	−	0.592281i
$456$	−0.125998	+	0.332151i	−0.00590041	+	0.0155544i
$457$			1.91541i			0.0895992i	0.998996	+	0.0447996i	$0.0142649\pi$
$457$			1.91541i			0.0895992i	−0.998996	+	0.0447996i	$0.985735\pi$
$458$	1.36101	+	0.785777i	0.0635956	+	0.0367169i
$459$	1.35804	−	33.5027i	0.0633877	−	1.56377i
$460$	−3.60685	−	2.67599i	−0.168170	−	0.124769i
$461$	−12.2091	+	21.1468i	−0.568636	+	0.984906i	0.428065	+	0.903748i	$0.359195\pi$
$461$	−12.2091	+	21.1468i	−0.568636	+	0.984906i	−0.996701	+	0.0811583i	$0.974138\pi$
$462$	−2.23421	+	10.2463i	−0.103945	+	0.476702i
$463$	4.09771	−	2.36581i	0.190437	−	0.109949i	−0.401750	−	0.915749i	$-0.631598\pi$
$463$	4.09771	−	2.36581i	0.190437	−	0.109949i	0.592187	+	0.805801i	$0.298265\pi$
$464$	2.95397	+	1.70547i	0.137134	+	0.0791746i
$465$	3.17965	−	2.03768i	0.147453	−	0.0944952i
$466$	3.77904	+	6.54549i	0.175061	+	0.303214i
$467$	−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
$471$	3.46610	−	2.82953i	0.159709	−	0.130378i
$472$	−9.07146			−0.417548
$473$	5.62152			0.258478
$474$	−9.70619	+	7.92359i	−0.445820	+	0.363942i
$475$	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
$479$	−20.7765	−	35.9860i	−0.949303	−	1.64424i	−0.746898	−	0.664938i	$-0.768458\pi$
$479$	−20.7765	−	35.9860i	−0.949303	−	1.64424i	−0.202404	−	0.979302i	$-0.564875\pi$
$480$	2.08972	+	3.26084i	0.0953820	+	0.148836i
$481$	29.9251	+	17.2773i	1.36447	+	0.787776i
$482$	24.5697	−	14.1853i	1.11912	−	0.646124i
$483$	2.79822	+	8.76842i	0.127323	+	0.398977i
$484$	−2.88146	+	4.99084i	−0.130976	+	0.226856i
$485$	15.2294	+	11.2990i	0.691531	+	0.513060i
$486$	−14.9747	+	4.33109i	−0.679266	+	0.196462i
$487$	−8.25200	−	4.76429i	−0.373934	−	0.215891i	0.301242	−	0.953548i	$-0.402599\pi$
$487$	−8.25200	−	4.76429i	−0.373934	−	0.215891i	−0.675176	+	0.737657i	$0.735932\pi$
$488$		−	10.7821i		−	0.488083i
$489$	15.0003	−	39.5432i	0.678338	−	1.78821i
$490$	2.81842	+	15.3966i	0.127323	+	0.695549i
$491$	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	$0.301159\pi$
$492$	−3.74618	−	1.42107i	−0.168891	−	0.0640670i
$493$	11.0052	+	19.0616i	0.495651	+	0.858493i
$494$	0.717793	+	0.414418i	0.0322950	+	0.0186455i
$495$	−15.0227	+	3.16032i	−0.675219	+	0.142046i
$496$		−	0.975100i		−	0.0437833i
$497$	−4.30214	−	28.8797i	−0.192977	−	1.29543i
$498$	−19.5642	+	3.17790i	−0.876691	+	0.142405i
$499$	17.8598	−	30.9342i	0.799516	−	1.38480i	−0.120415	−	0.992724i	$-0.538423\pi$
$499$	17.8598	−	30.9342i	0.799516	−	1.38480i	0.919931	−	0.392079i	$-0.128244\pi$
$500$	3.77201	−	10.5248i	0.168690	−	0.470684i
$501$	−0.00641312	+	0.0169060i	−0.000286517	+	0.000755304i
$502$	9.95552			0.444337
$503$		−	2.25896i		−	0.100722i	−0.998731	−	0.0503609i	$-0.983963\pi$
$503$		−	2.25896i		−	0.100722i	0.998731	−	0.0503609i	$-0.0160372\pi$
$504$	0.425720	−	7.92583i	0.0189631	−	0.353044i
$505$	3.10856	−	1.34697i	0.138329	−	0.0599394i
$506$		−	4.59638i		−	0.204334i
$507$	0.924888	+	5.69389i	0.0410757	+	0.252875i
$508$			11.8327i			0.524991i
$509$	−19.7072	+	34.1338i	−0.873506	+	1.51296i	−0.0151595	+	0.999885i	$0.504826\pi$
$509$	−19.7072	+	34.1338i	−0.873506	+	1.51296i	−0.858346	+	0.513071i	$0.828508\pi$
$510$	1.15717	+	24.9652i	0.0512403	+	1.10548i
$511$	−15.1184	+	38.3272i	−0.668800	+	1.69550i
$512$	1.00000			0.0441942
$513$	0.900618	+	0.569814i	0.0397633	+	0.0251579i
$514$	16.2504	+	9.38216i	0.716774	+	0.413829i
$515$	33.7180	+	25.0160i	1.48579	+	1.10234i
$516$	−4.19967	+	0.682173i	−0.184880	+	0.0300310i
$517$	5.46696	+	9.46906i	0.240437	+	0.416449i
$518$	−17.7118	+	14.0749i	−0.778212	+	0.618417i
$519$	19.9710	+	24.4640i	0.876632	+	1.07385i
$520$	8.29125	−	3.59268i	0.363596	−	0.157550i
$521$	−19.9940	+	34.6307i	−0.875954	+	1.51720i	−0.0202106	+	0.999796i	$0.506434\pi$
$521$	−19.9940	+	34.6307i	−0.875954	+	1.51720i	−0.855743	+	0.517401i	$0.826900\pi$
$522$	6.78683	−	7.65832i	0.297052	−	0.335196i
$523$	−14.4859	−	25.0903i	−0.633424	−	1.09712i	−0.986847	−	0.161659i	$-0.948315\pi$
$523$	−14.4859	−	25.0903i	−0.633424	−	1.09712i	0.353422	−	0.935464i	$-0.385018\pi$
$524$	−1.47813	+	2.56020i	−0.0645724	+	0.111843i
$525$	−18.8708	+	12.9959i	−0.823589	+	0.567187i
$526$	1.47472	+	2.55429i	0.0643008	+	0.111372i
$527$	3.14611	−	5.44922i	0.137047	−	0.237372i
$528$	−1.40585	+	3.70605i	−0.0611819	+	0.161285i
$529$	9.48297	+	16.4250i	0.412303	+	0.714130i
$530$	−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
$534$	16.4833	+	6.25276i	0.713301	+	0.270583i
$535$	−36.9458	+	16.0090i	−1.59731	+	0.692130i
$536$			6.05164i			0.261391i
$537$	26.7294	−	4.34180i	1.15346	−	0.187362i
$538$	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	$0.799506\pi$
$542$	12.8142	−	7.39828i	0.550417	−	0.317783i
$543$	−26.6271	−	32.6175i	−1.14268	−	1.39975i
$544$	5.58838	+	3.22645i	0.239600	+	0.138333i
$545$	−29.2278	−	21.6847i	−1.25198	−	0.928870i
$546$	−18.0935	−	3.94529i	−0.774330	−	0.168843i
$547$	12.6990	+	7.33178i	0.542971	+	0.313484i	0.746282	−	0.665630i	$-0.231837\pi$
$547$	12.6990	+	7.33178i	0.542971	+	0.313484i	−0.203311	+	0.979114i	$0.565170\pi$
$548$	3.43092	+	5.94252i	0.146562	+	0.253852i
$549$	−31.6916	−	6.47508i	−1.35256	−	0.276350i
$550$	10.9508	−	3.31774i	0.466943	−	0.141469i
$551$	−0.699591			−0.0298036
$552$	0.557771	+	3.43381i	0.0237403	+	0.146153i
$553$	−18.9305	+	2.82004i	−0.805008	+	0.119920i
$554$	−6.88813	+	3.97687i	−0.292649	+	0.168961i
$555$	−29.4161	−	15.2128i	−1.24865	−	0.645749i
$556$	−1.44024	+	0.831524i	−0.0610798	+	0.0352645i
$557$	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	$-0.0253790\pi$
$558$	−2.86609	−	0.585586i	−0.121331	−	0.0247898i
$559$			9.92679i			0.419858i
$560$	0.196198	+	5.91283i	0.00829090	+	0.249862i
$561$	−19.8138	+	16.1749i	−0.836540	+	0.682904i
$562$	−12.9850	−	7.49690i	−0.547740	−	0.316238i
$563$		−	18.5309i		−	0.780986i	−0.920606	−	0.390493i	$-0.872305\pi$
$563$		−	18.5309i		−	0.780986i	0.920606	−	0.390493i	$-0.127695\pi$
$564$	−5.23327	−	6.41063i	−0.220361	−	0.269936i
$565$	−12.2560	+	5.31063i	−0.515612	+	0.223420i
$566$	29.8023			1.25268
$567$	−23.0405	−	6.01108i	−0.967612	−	0.252442i
$568$		−	11.0359i		−	0.463058i
$569$			23.8266i			0.998863i	0.866353	+	0.499431i	$0.166458\pi$
$569$			23.8266i			0.998863i	−0.866353	+	0.499431i	$0.833542\pi$
$570$	−0.705584	−	0.364899i	−0.0295537	−	0.0152840i
$571$	44.5452			1.86416			0.932079	−	0.362255i	$-0.117993\pi$
$571$	44.5452			1.86416			0.932079	+	0.362255i	$0.117993\pi$
$572$	8.00893	+	4.62396i	0.334870	+	0.193337i
$573$	13.0781	+	16.0203i	0.546344	+	0.669258i
$574$	−3.80769	−	4.79157i	−0.158930	−	0.199996i
$575$	6.86750	−	7.32727i	0.286395	−	0.305568i
$576$	0.600540	−	2.93928i	0.0250225	−	0.122470i
$577$	1.24045	−	2.14853i	0.0516407	−	0.0894443i	−0.839050	−	0.544055i	$-0.816888\pi$
$577$	1.24045	−	2.14853i	0.0516407	−	0.0894443i	0.890690	+	0.454611i	$0.150222\pi$
$578$	12.3200	+	21.3388i	0.512443	+	0.887578i
$579$	−13.6276	−	16.6935i	−0.566346	−	0.693759i
$580$	−4.54452	+	6.12536i	−0.188701	+	0.254342i
$581$	−28.1645	−	11.1097i	−1.16846	−	0.460907i
$582$	−2.35511	−	14.4988i	−0.0976224	−	0.600993i
$583$		−	10.7983i		−	0.447219i
$584$	−7.78631	+	13.4863i	−0.322200	+	0.558066i
$585$	−5.58067	−	26.5278i	−0.230732	−	1.09679i
$586$	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	$0.741194\pi$
$588$	6.74964	−	10.0719i	0.278350	−	0.415357i
$589$	0.0999973	+	0.173200i	0.00412032	+	0.00713660i
$590$	2.32173	−	20.1511i	0.0955843	−	0.829608i
$591$	−30.9224	+	25.2433i	−1.27198	+	1.03837i
$592$	−7.40520	+	4.27539i	−0.304352	+	0.175718i
$593$	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
$595$	−17.9810	+	33.6761i	−0.737150	+	1.38059i
$596$	−10.1542	−	5.86255i	−0.415933	−	0.240139i
$597$	−13.7961	+	2.24097i	−0.564638	+	0.0917169i
$598$	8.11653			0.331909
$599$		−	13.5005i		−	0.551614i	−0.961213	−	0.275807i	$-0.911055\pi$
$599$		−	13.5005i		−	0.551614i	0.961213	−	0.275807i	$-0.0889451\pi$
$600$	−7.77838	+	3.80746i	−0.317551	+	0.155439i
$601$	−13.5297	−	7.81138i	−0.551889	−	0.318633i	0.197995	−	0.980203i	$-0.436557\pi$
$601$	−13.5297	−	7.81138i	−0.551889	−	0.318633i	−0.749883	+	0.661570i	$0.769890\pi$
$602$	−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
$605$	−10.3490	−	7.67815i	−0.420748	−	0.312161i
$606$	−2.45361	−	0.930752i	−0.0996710	−	0.0378092i
$607$	−4.07061	+	7.05051i	−0.165221	+	0.286171i	−0.936734	−	0.350043i	$-0.886167\pi$
$607$	−4.07061	+	7.05051i	−0.165221	+	0.286171i	0.771513	+	0.636214i	$0.219500\pi$
$608$	−0.177623	+	0.102551i	−0.00720357	+	0.00415899i
$609$	14.8910	−	4.75210i	0.603415	−	0.192565i
$610$	23.9511	+	2.75955i	0.969750	+	0.111731i
$611$	−16.7210	+	9.65386i	−0.676458	+	0.390553i
$612$	12.8395	−	14.4882i	0.519005	−	0.585650i
$613$	−14.5475	−	8.39900i	−0.587568	−	0.339232i	0.176567	−	0.984289i	$-0.443501\pi$
$613$	−14.5475	−	8.39900i	−0.587568	−	0.339232i	−0.764135	+	0.645056i	$0.776834\pi$
$614$	8.06299			0.325396
$615$	4.11552	−	7.95794i	0.165954	−	0.320895i
$616$	−4.74025	+	3.76691i	−0.190990	+	0.151773i
$617$	−13.7676	−	23.8461i	−0.554262	−	0.960009i	−0.997961	−	0.0638334i	$-0.979667\pi$
$617$	−13.7676	−	23.8461i	−0.554262	−	0.960009i	0.443699	−	0.896176i	$-0.353666\pi$
$618$	−5.21423	−	32.1004i	−0.209747	−	1.29127i
$619$	8.09495	−	4.67362i	0.325363	−	0.187849i	−0.328417	−	0.944533i	$-0.606515\pi$
$619$	8.09495	−	4.67362i	0.325363	−	0.187849i	0.653781	+	0.756684i	$0.273182\pi$
$620$	2.16606	+	0.249565i	0.0869911	+	0.0100228i
$621$	10.4279	+	0.422695i	0.418457	+	0.0169622i
$622$	−0.763625			−0.0306186
$623$	16.7539	+	21.0830i	0.671232	+	0.844674i
$624$	−6.54434	−	2.48253i	−0.261983	−	0.0993808i
$625$	22.4142	+	11.0728i	0.896566	+	0.442910i
$626$	3.83737			0.153372
$627$	−0.130346	−	0.802452i	−0.00520553	−	0.0320468i
$628$	2.58329			0.103084
$629$	−55.1774			−2.20007
$630$	17.4973	+	2.97420i	0.697108	+	0.118495i
$631$	−45.9246			−1.82823			−0.914115	−	0.405454i	$-0.867113\pi$
$631$	−45.9246			−1.82823			−0.914115	+	0.405454i	$0.867113\pi$
$632$	−7.23402			−0.287754
$633$	−29.9209	−	11.3502i	−1.18925	−	0.451130i
$634$	−17.3289			−0.688218
$635$	−26.2848	−	3.02844i	−1.04308	−	0.120180i
$636$	1.31037	+	8.06706i	0.0519597	+	0.319880i
$637$	−20.6700	−	19.3117i	−0.818977	−	0.765157i
$638$	−7.80583			−0.309036
$639$	−32.4377	−	6.62752i	−1.28322	−	0.262181i
$640$	−0.255938	+	2.22137i	−0.0101168	+	0.0878075i
$641$	16.2569	−	9.38590i	0.642107	−	0.370721i	−0.143318	−	0.989677i	$-0.545777\pi$
$641$	16.2569	−	9.38590i	0.642107	−	0.370721i	0.785426	+	0.618956i	$0.212444\pi$
$642$	29.1616	+	11.0622i	1.15092	+	0.436589i
$643$	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	$0.683330\pi$
$644$	−1.94992	+	4.94330i	−0.0768376	+	0.194793i
$645$	−0.440505	−	9.50362i	−0.0173449	−	0.374205i
$646$	−1.32350			−0.0520724
$647$	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	$0.558951\pi$
$648$	−8.27870	−	3.53031i	−0.325218	−	0.138683i
$649$	17.9785	−	10.3799i	0.705716	−	0.407445i
$650$	5.85864	+	19.3375i	0.229795	+	0.758478i
$651$	−3.30497	−	3.00738i	−0.129532	−	0.117869i
$652$	21.1464	−	12.2089i	0.828156	−	0.478136i
$653$	−10.8831	+	18.8501i	−0.425888	+	0.737660i	−0.996503	−	0.0835580i	$-0.973372\pi$
$653$	−10.8831	+	18.8501i	−0.425888	+	0.737660i	0.570615	+	0.821218i	$0.306705\pi$
$654$	4.51986	+	27.8256i	0.176740	+	1.08807i
$655$	−5.30884	−	3.93873i	−0.207434	−	0.153899i
$656$	−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	$0.823825\pi$
$660$	−7.87271	−	4.07144i	−0.306445	−	0.158481i
$661$			25.9481i			1.00926i	0.863335	+	0.504632i	$0.168372\pi$
$661$			25.9481i			1.00926i	−0.863335	+	0.504632i	$0.831628\pi$
$662$	−4.95873			−0.192727
$663$	−28.5625	−	34.9883i	−1.10927	−	1.35883i
$664$	−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
$668$	−0.00904075	+	0.00521968i	−0.000349797	+	0.000201955i
$669$	1.17064	+	7.20680i	0.0452595	+	0.278631i
$670$	−13.4429	−	1.54885i	−0.519346	−	0.0598371i
$671$	12.3372	+	21.3687i	0.476274	+	0.824930i
$672$	3.08418	−	3.38937i	0.118975	−	0.130748i
$673$	3.32531	+	1.91987i	0.128181	+	0.0740054i	0.562719	−	0.826648i	$-0.309755\pi$
$673$	3.32531	+	1.91987i	0.128181	+	0.0740054i	−0.434538	+	0.900653i	$0.643088\pi$
$674$	−1.58895	+	0.917381i	−0.0612041	+	0.0353362i
$675$	6.51996	+	25.1494i	0.250953	+	0.967999i
$676$	−1.66523	+	2.88426i	−0.0640472	+	0.110933i
$677$			16.2326i			0.623868i	0.950104	+	0.311934i	$0.100977\pi$
$677$			16.2326i			0.623868i	−0.950104	+	0.311934i	$0.899023\pi$
$678$	9.67370	+	3.66962i	0.371516	+	0.140931i
$679$	8.23324	−	20.8724i	0.315963	−	0.801008i
$680$	−8.59743	+	11.5881i	−0.329696	+	0.444383i
$681$	11.4104	−	30.0796i	0.437248	−	1.15265i
$682$	1.11574	+	1.93252i	0.0427239	+	0.0740000i
$683$	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	$0.108665\pi$
$684$	0.194756	+	0.583670i	0.00744666	+	0.0223172i
$685$	−14.0787	+	6.10043i	−0.537918	+	0.233085i
$686$	16.7274	−	7.94946i	0.638655	−	0.303512i
$687$	2.68680	−	0.436430i	0.102508	−	0.0166508i
$688$	−2.12736	−	1.22823i	−0.0811047	−	0.0468258i
$689$	19.0682			0.726440
$690$	−7.77053	+	0.360174i	−0.295819	+	0.0137116i
$691$			15.7754i			0.600123i	0.953920	+	0.300062i	$0.0970072\pi$
$691$			15.7754i			0.600123i	−0.953920	+	0.300062i	$0.902993\pi$
$692$			18.2330i			0.693116i
$693$	8.22527	+	16.1951i	0.312452	+	0.615200i
$694$	6.78486			0.257550
$695$	−1.47851	−	3.41213i	−0.0560831	−	0.129430i
$696$	5.83150	−	0.947240i	0.221042	−	0.0359050i
$697$		−	14.9271i		−	0.565405i
$698$	−11.4343	−	6.60159i	−0.432794	−	0.249874i
$699$	12.2399	+	4.64309i	0.462956	+	0.175618i
$700$	−13.1848	−	1.07749i	−0.498339	−	0.0407252i
$701$			3.43541i			0.129754i	0.997893	+	0.0648769i	$0.0206655\pi$
$701$			3.43541i			0.129754i	−0.997893	+	0.0648769i	$0.979335\pi$
$702$	−11.2270	+	17.7448i	−0.423735	+	0.669734i
$703$	0.876890	−	1.51882i	0.0330725	−	0.0572833i
$704$	−1.98187	+	1.14423i	−0.0746945	+	0.0431249i
$705$	15.5798	−	9.98433i	0.586769	−	0.376032i
$706$	−26.8650	+	15.5105i	−1.01108	+	0.583747i
$707$	−2.49390	−	3.13830i	−0.0937927	−	0.118028i
$708$	−12.1716	+	9.93617i	−0.457435	+	0.373424i
$709$	−25.8612			−0.971239			−0.485620	−	0.874170i	$-0.661406\pi$
$709$	−25.8612			−0.971239			−0.485620	+	0.874170i	$0.661406\pi$
$710$	24.5149	+	2.82452i	0.920030	+	0.106002i
$711$	−4.34432	+	21.2628i	−0.162925	+	0.797417i
$712$	5.08916	+	8.81469i	0.190724	+	0.330345i
$713$	1.69610	+	0.979242i	0.0635193	+	0.0366729i
$714$	28.1712	−	8.99013i	1.05428	−	0.336447i
$715$	−12.3213	+	16.6074i	−0.460791	+	0.621080i
$716$	13.5399	+	7.81725i	0.506009	+	0.292144i
$717$	10.2473	−	27.0136i	0.382693	−	1.00884i
$718$	24.9912	−	14.4287i	0.932664	−	0.538474i
$719$	−20.8858	−	36.1753i	−0.778909	−	1.34911i	−0.932571	−	0.360986i	$-0.882440\pi$
$719$	−20.8858	−	36.1753i	−0.778909	−	1.34911i	0.153663	−	0.988123i	$-0.450893\pi$
$720$	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
$723$	17.4287	−	45.9448i	0.648180	−	1.70871i
$724$		−	24.3098i		−	0.903467i
$725$	−12.4436	−	11.6628i	−0.462143	−	0.433145i
$726$	1.60040	+	9.85254i	0.0593964	+	0.365662i
$727$	−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
$731$	−7.92564	−	13.7276i	−0.293141	−	0.507734i
$732$	−11.8099	−	14.4668i	−0.436505	−	0.534708i
$733$	−2.36946	+	4.10402i	−0.0875179	+	0.151586i	−0.906461	−	0.422289i	$-0.861227\pi$
$733$	−2.36946	+	4.10402i	−0.0875179	+	0.151586i	0.818943	+	0.573874i	$0.194560\pi$
$734$	6.18161	+	10.7069i	0.228167	+	0.395197i
$735$	20.6459	+	17.5712i	0.761534	+	0.648125i
$736$	−1.00425	+	1.73941i	−0.0370171	+	0.0641155i
$737$	−6.92448	−	11.9936i	−0.255067	−	0.441788i
$738$	−6.58293	+	2.19655i	−0.242321	+	0.0808563i
$739$	−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	$0.985847\pi$
$740$	−7.60197	−	17.5439i	−0.279454	−	0.644928i
$741$	1.41701	−	0.230173i	0.0520553	−	0.00845560i
$742$	−4.58095	+	11.6133i	−0.168172	+	0.426338i
$743$	16.2571	+	28.1581i	0.596415	+	1.03302i	0.993346	+	0.115173i	$0.0367421\pi$
$743$	16.2571	+	28.1581i	0.596415	+	1.03302i	−0.396930	+	0.917849i	$0.629925\pi$
$744$	−1.06805	−	1.30833i	−0.0391565	−	0.0479658i
$745$	15.6218	−	21.0559i	0.572337	−	0.771427i
$746$	31.7495	+	18.3306i	1.16243	+	0.671131i
$747$	−22.7692	+	25.6930i	−0.833082	+	0.940057i
$748$	−14.7672			−0.539944
$749$	29.6405	+	37.2993i	1.08304	+	1.36289i
$750$	−6.46700	−	18.2532i	−0.236142	−	0.666511i
$751$	16.5978	−	28.7482i	0.605662	−	1.04904i	−0.386284	−	0.922380i	$-0.626242\pi$
$751$	16.5978	−	28.7482i	0.605662	−	1.04904i	0.991946	−	0.126658i	$-0.0404251\pi$
$752$		−	4.77784i		−	0.174230i
$753$	13.3577	−	10.9045i	0.486783	−	0.397382i
$754$		−	13.7840i		−	0.501982i
$755$	6.90072	−	2.99015i	0.251143	−	0.108823i
$756$	−8.11013	−	11.1007i	−0.294963	−	0.403729i
$757$			1.30712i			0.0475082i	0.999718	+	0.0237541i	$0.00756188\pi$
$757$			1.30712i			0.0475082i	−0.999718	+	0.0237541i	$0.992438\pi$
$758$	19.2906			0.700667
$759$	−5.03451	−	6.16715i	−0.182741	−	0.223853i
$760$	−0.182343	−	0.420814i	−0.00661428	−	0.0152645i
$761$	−11.3771	+	19.7057i	−0.412420	+	0.714332i	−0.995154	−	0.0983312i	$-0.968650\pi$
$761$	−11.3771	+	19.7057i	−0.412420	+	0.714332i	0.582734	+	0.812663i	$0.301983\pi$
$762$	12.9606	+	15.8764i	0.469514	+	0.575142i
$763$	−15.8010	+	40.0577i	−0.572035	+	1.45018i
$764$			11.9399i			0.431972i
$765$	28.8975	+	32.2293i	1.04479	+	1.16525i
$766$	7.09201	+	4.09457i	0.256245	+	0.147943i
$767$	18.3293	+	31.7473i	0.661834	+	1.14633i
$768$	1.34174	−	1.09532i	0.0484159	−	0.0395240i
$769$	−34.4497	+	19.8896i	−1.24229	+	0.717236i	−0.969560	−	0.244855i	$-0.921260\pi$
$769$	−34.4497	+	19.8896i	−1.24229	+	0.717236i	−0.272729	+	0.962091i	$0.587926\pi$
$770$	−7.15449	−	11.4940i	−0.257830	−	0.414213i
$771$	32.0803	−	5.21096i	1.15534	−	0.187668i
$772$		−	12.4417i		−	0.447786i
$773$	−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	$0.892521\pi$
$774$	−4.88767	+	5.51529i	−0.175684	+	0.198243i
$775$	−1.10876	+	4.74775i	−0.0398277	+	0.170544i
$776$	4.24029	−	7.34440i	0.152218	−	0.263649i
$777$	−8.34807	+	38.2850i	−0.299485	+	1.37347i
$778$	7.64611	−	4.41449i	0.274126	−	0.158267i
$779$	0.410886	+	0.237225i	0.0147215	+	0.00849947i
$780$	7.18957	−	13.9020i	0.257428	−	0.497773i
$781$	12.6277	+	21.8718i	0.451854	+	0.782635i
$782$	−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
$786$	0.820971	+	5.05415i	0.0292831	+	0.180276i
$787$	−17.1289			−0.610581			−0.305290	−	0.952259i	$-0.598754\pi$
$787$	−17.1289			−0.610581			−0.305290	+	0.952259i	$0.598754\pi$
$788$	−23.0465			−0.820996
$789$	4.77646	+	1.81190i	0.170046	+	0.0645054i
$790$	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
$794$	5.82466	+	10.0886i	0.206710	+	0.358032i
$795$	−18.2553	+	0.846158i	−0.647450	+	0.0300101i
$796$	−6.98847	−	4.03479i	−0.247700	−	0.143010i
$797$	−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	$0.595971\pi$
$798$	−0.200239	+	0.918316i	−0.00708839	+	0.0325080i
$799$	15.4155	−	26.7004i	0.545360	−	0.944591i
$800$	−4.86899	−	1.13707i	−0.172145	−	0.0402014i
$801$	28.9651	−	9.66489i	1.02343	−	0.341492i
$802$	−2.28763	−	1.32076i	−0.0807788	−	0.0466377i
$803$		−	35.6374i		−	1.25762i
$804$	6.62849	+	8.11973i	0.233769	+	0.286361i
$805$	−10.4819	−	5.59668i	−0.369437	−	0.197257i
$806$	−3.41255	+	1.97024i	−0.120202	+	0.0693986i
$807$	−7.66895	−	47.2124i	−0.269960	−	1.66196i
$808$	−0.757545	−	1.31211i	−0.0266503	−	0.0461597i
$809$	5.30390	+	3.06221i	0.186475	+	0.107661i	0.590331	−	0.807161i	$-0.298997\pi$
$809$	5.30390	+	3.06221i	0.186475	+	0.107661i	−0.403856	+	0.914822i	$0.632330\pi$
$810$	9.96096	−	17.4865i	0.349992	−	0.614415i
$811$		−	51.1448i		−	1.79594i	−0.440059	−	0.897969i	$-0.645043\pi$
$811$		−	51.1448i		−	1.79594i	0.440059	−	0.897969i	$-0.354957\pi$
$812$	8.39500	+	3.31147i	0.294607	+	0.116210i
$813$	9.08983	−	23.9622i	0.318794	−	0.840392i
$814$	9.78409	−	16.9465i	0.342932	−	0.593976i
$815$	21.7083	+	50.0987i	0.760407	+	1.75488i
$816$	11.0322	−	1.79201i	0.386203	−	0.0627329i
$817$	0.503824			0.0176266
$818$		−	4.00359i		−	0.139982i
$819$	−28.5981	+	14.5246i	−0.999300	+	0.507532i
$820$	4.74616	−	2.05656i	0.165743	−	0.0718182i
$821$			9.10905i			0.317908i	0.987286	+	0.158954i	$0.0508121\pi$
$821$			9.10905i			0.317908i	−0.987286	+	0.158954i	$0.949188\pi$
$822$	11.1124	+	4.21537i	0.387589	+	0.147028i
$823$		−	44.7216i		−	1.55890i	−0.626466	−	0.779449i	$-0.715499\pi$
$823$		−	44.7216i		−	1.55890i	0.626466	−	0.779449i	$-0.284501\pi$
$824$	9.38804	−	16.2606i	0.327048	−	0.566464i
$825$	11.0591	−	16.4462i	0.385029	−	0.572582i
$826$	−23.7389	+	3.53633i	−0.825981	+	0.123044i
$827$	34.3286			1.19372			0.596860	−	0.802345i	$-0.296415\pi$
$827$	34.3286			1.19372			0.596860	+	0.802345i	$0.296415\pi$
$828$	4.50951	+	3.99635i	0.156716	+	0.138883i
$829$	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	$0.361791\pi$
$830$	15.2465	−	20.5500i	0.529213	−	0.713302i
$831$	−4.88615	+	12.8807i	−0.169499	+	0.446825i
$832$	−2.02055	−	3.49969i	−0.0700499	−	0.121330i
$833$	44.0030	+	10.2027i	1.52461	+	0.353504i
$834$	−1.02165	+	2.69322i	−0.0353767	+	0.0932585i
$835$	−0.00928098	−	0.0214188i	−0.000321181	−	0.000741228i
$836$	0.234684	−	0.406485i	0.00811672	−	0.0140586i
$837$	−4.48696	+	2.35358i	−0.155092	+	0.0813518i
$838$	10.3156	+	17.8671i	0.356346	+	0.617209i
$839$	−7.97922	+	13.8204i	−0.275473	+	0.477134i	−0.970254	−	0.242087i	$-0.922168\pi$
$839$	−7.97922	+	13.8204i	−0.275473	+	0.477134i	0.694781	+	0.719221i	$0.255501\pi$
$840$	6.73970	+	7.71858i	0.232542	+	0.266316i
$841$	−8.68273	−	15.0389i	−0.299404	−	0.518583i
$842$	−2.08360	+	3.60891i	−0.0718058	+	0.124371i
$843$	−25.6341	+	4.16387i	−0.882884	+	0.143411i
$844$	−9.23801	−	16.0007i	−0.317985	−	0.550767i
$845$	−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
$849$	39.9869	−	32.6431i	1.37235	−	1.12031i
$850$	−23.5411	−	22.0639i	−0.807452	−	0.756786i
$851$		−	17.1742i		−	0.588725i
$852$	−12.0879	−	14.8074i	−0.414125	−	0.507293i
$853$	−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
$855$	−1.34639	+	0.283241i	−0.0460457	+	0.00968664i
$856$	9.00357	+	15.5946i	0.307736	+	0.533014i
$857$	27.0181	−	15.5989i	0.922921	−	0.532849i	0.0383555	−	0.999264i	$-0.487788\pi$
$857$	27.0181	−	15.5989i	0.922921	−	0.532849i	0.884566	+	0.466415i	$0.154455\pi$
$858$	15.8106	−	2.56820i	0.539766	−	0.0876769i
$859$	−13.8087	−	7.97243i	−0.471145	−	0.272016i	0.245574	−	0.969378i	$-0.421024\pi$
$859$	−13.8087	−	7.97243i	−0.471145	−	0.272016i	−0.716719	+	0.697362i	$0.754357\pi$
$860$	3.27283	−	4.41130i	0.111602	−	0.150424i
$861$	−10.3572	−	2.25840i	−0.352974	−	0.0769662i
$862$	−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	$0.567077\pi$
$864$	−2.41369	−	4.60153i	−0.0821153	−	0.156547i
$865$	−40.5024	−	4.66653i	−1.37712	−	0.158667i
$866$	23.8117			0.809154
$867$	39.9031	+	15.1368i	1.35518	+	0.514074i
$868$	−0.380123	−	2.55171i	−0.0129022	−	0.0866108i
$869$	14.3369	−	8.27741i	0.486346	−	0.280792i
$870$	0.611669	+	13.1964i	0.0207375	+	0.447399i
$871$	21.1789	−	12.2276i	0.717618	−	0.414317i
$872$	−8.13785	+	14.0952i	−0.275582	+	0.477323i
$873$	−19.0408	−	16.8740i	−0.644432	−	0.571098i
$874$		−	0.411946i		−	0.0139343i
$875$	5.76800	−	29.0126i	0.194994	−	0.980804i
$876$	4.32461	+	26.6236i	0.146115	+	0.899528i
$877$	−32.8047	−	18.9398i	−1.10774	−	0.639552i	−0.169494	−	0.985531i	$-0.554213\pi$
$877$	−32.8047	−	18.9398i	−1.10774	−	0.639552i	−0.938242	+	0.345980i	$0.887547\pi$
$878$		−	14.3892i		−	0.485611i
$879$	1.56054	−	4.11383i	0.0526357	−	0.138756i
$880$	−2.03453	−	4.69532i	−0.0685840	−	0.158279i
$881$	−16.7367			−0.563872			−0.281936	−	0.959433i	$-0.590977\pi$
$881$	−16.7367			−0.563872			−0.281936	+	0.959433i	$0.590977\pi$
$882$	−1.97567	−	20.9069i	−0.0665242	−	0.703971i
$883$		−	5.43664i		−	0.182957i	−0.995807	−	0.0914787i	$-0.970841\pi$
$883$		−	5.43664i		−	0.182957i	0.995807	−	0.0914787i	$-0.0291593\pi$
$884$		−	26.0768i		−	0.877057i
$885$	−18.9568	−	29.5806i	−0.637225	−	0.994341i
$886$	−36.6080			−1.22987
$887$	33.7618	+	19.4924i	1.13361	+	0.654490i	0.944840	−	0.327531i	$-0.106217\pi$
$887$	33.7618	+	19.4924i	1.13361	+	0.654490i	0.188770	+	0.982021i	$0.439550\pi$
$888$	−5.25293	+	13.8475i	−0.176277	+	0.464693i
$889$	4.61274	+	30.9647i	0.154706	+	1.03852i
$890$	−20.8832	+	9.04891i	−0.700007	+	0.303320i
$891$	20.4468	−	2.47616i	0.684994	−	0.0829545i
$892$	−2.10769	+	3.65063i	−0.0705708	+	0.122232i
$893$	0.489972	+	0.848656i	0.0163963	+	0.0283992i
$894$	−20.0457	+	3.25613i	−0.670429	+	0.108901i
$895$	−20.8304	+	28.0764i	−0.696284	+	0.938490i
$896$	2.61687	−	0.389830i	0.0874236	−	0.0130233i
$897$	10.8903	−	8.89021i	0.363616	−	0.296835i
$898$			0.350689i			0.0117026i
$899$	1.66301	−	2.88041i	0.0554644	−	0.0960671i
$900$	−6.26618	+	13.6285i	−0.208873	+	0.454282i
$901$	−26.3691	+	15.2242i	−0.878483	+	0.507192i
$902$	4.58455	+	2.64689i	0.152649	+	0.0881318i
$903$	−10.7241	+	3.42232i	−0.356875	+	0.113888i
$904$	2.98673	+	5.17317i	0.0993372	+	0.172057i
$905$	54.0011	+	6.22181i	1.79506	+	0.206820i
$906$	−5.44679	−	2.06618i	−0.180957	−	0.0686444i
$907$	2.39252	−	1.38132i	0.0794424	−	0.0458661i	−0.459753	−	0.888047i	$-0.652062\pi$
$907$	2.39252	−	1.38132i	0.0794424	−	0.0458661i	0.539195	+	0.842181i	$0.318729\pi$
$908$	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	$0.424369\pi$
$912$	−0.125998	+	0.332151i	−0.00417222	+	0.0109986i
$913$	26.1879			0.866692
$914$			1.91541i			0.0633562i
$915$	35.1587	−	22.5315i	1.16231	−	0.744869i
$916$	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	$0.961134\pi$
$920$	−3.60685	−	2.67599i	−0.118914	−	0.0882248i
$921$	10.8184	−	8.83157i	0.356480	−	0.291010i
$922$	−12.2091	+	21.1468i	−0.402086	+	0.696434i
$923$	−38.6224	+	22.2987i	−1.27127	+	0.733969i
$924$	−2.23421	+	10.2463i	−0.0735002	+	0.337079i
$925$	40.9173	−	12.3966i	1.34535	−	0.407599i
$926$	4.09771	−	2.36581i	0.134659	−	0.0777454i
$927$	−42.1564	−	37.3592i	−1.38460	−	1.22704i
$928$	2.95397	+	1.70547i	0.0969687	+	0.0559849i
$929$	−6.44893			−0.211583			−0.105791	−	0.994388i	$-0.533738\pi$
$929$	−6.44893			−0.211583			−0.105791	+	0.994388i	$0.533738\pi$
$930$	3.17965	−	2.03768i	0.104265	−	0.0668182i
$931$	−0.980146	+	1.04909i	−0.0321230	+	0.0343824i
$932$	3.77904	+	6.54549i	0.123787	+	0.214405i
$933$	−1.02459	+	0.836415i	−0.0335435	+	0.0273830i
$934$	−29.9337	+	17.2822i	−0.979461	+	0.565492i
$935$	3.77950	−	32.8036i	0.123603	−	1.07279i
$936$	−11.5000	+	3.83725i	−0.375889	+	0.125424i
$937$	38.6081			1.26127			0.630635	−	0.776079i	$-0.282794\pi$
$937$	38.6081			1.26127			0.630635	+	0.776079i	$0.282794\pi$
$938$	2.35911	+	15.8364i	0.0770276	+	0.517076i
$939$	5.14876	−	4.20315i	0.168023	−	0.137165i
$940$	10.6134	+	1.22283i	0.346170	+	0.0398844i
$941$	−10.4321			−0.340077			−0.170039	−	0.985437i	$-0.554389\pi$
$941$	−10.4321			−0.340077			−0.170039	+	0.985437i	$0.554389\pi$
$942$	3.46610	−	2.82953i	0.112932	−	0.0921910i
$943$	4.64614			0.151299
$944$	−9.07146			−0.295251
$945$	26.7345	−	15.1745i	0.869674	−	0.493627i
$946$	5.62152			0.182771
$947$	−34.1258			−1.10894			−0.554470	−	0.832204i	$-0.687079\pi$
$947$	−34.1258			−1.10894			−0.554470	+	0.832204i	$0.687079\pi$
$948$	−9.70619	+	7.92359i	−0.315242	+	0.257346i
$949$	62.9304			2.04281
$950$	0.981453	−	0.297349i	0.0318426	−	0.00964729i
$951$	−23.2509	+	18.9807i	−0.753962	+	0.615492i
$952$	15.8818	+	6.26470i	0.514734	+	0.203040i
$953$	44.3067			1.43523			0.717617	−	0.696438i	$-0.245233\pi$
$953$	44.3067			1.43523			0.717617	+	0.696438i	$0.245233\pi$
$954$	10.5942	+	9.38863i	0.343000	+	0.303968i
$955$	−26.5230	−	3.05589i	−0.858265	−	0.0988861i
$956$	14.4459	−	8.34037i	0.467215	−	0.269747i
$957$	−10.4734	+	8.54990i	−0.338557	+	0.276379i
$958$	−20.7765	−	35.9860i	−0.671258	−	1.16265i
$959$	11.2949	+	14.2134i	0.364730	+	0.458973i
$960$	2.08972	+	3.26084i	0.0674453	+	0.105243i
$961$	30.0492			0.969328
$962$	29.9251	+	17.2773i	0.964824	+	0.557042i
$963$	51.2440	−	17.0988i	1.65131	−	0.551001i
$964$	24.5697	−	14.1853i	0.791337	−	0.456879i
$965$	27.6376	+	3.18430i	0.889686	+	0.102506i
$966$	2.79822	+	8.76842i	0.0900312	+	0.282119i
$967$	−14.0448	+	8.10875i	−0.451649	+	0.260760i	−0.708526	−	0.705684i	$-0.750640\pi$
$967$	−14.0448	+	8.10875i	−0.451649	+	0.260760i	0.256877	+	0.966444i	$0.417306\pi$
$968$	−2.88146	+	4.99084i	−0.0926137	+	0.160412i
$969$	−1.77580	+	1.44966i	−0.0570468	+	0.0465698i
$970$	15.2294	+	11.2990i	0.488986	+	0.362788i
$971$	−18.1313	−	31.4043i	−0.581861	−	1.00781i	−0.995259	−	0.0972627i	$-0.968991\pi$
$971$	−18.1313	−	31.4043i	−0.581861	−	1.00781i	0.413397	−	0.910551i	$-0.364342\pi$
$972$	−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
$975$	29.0415	+	19.5288i	0.930074	+	0.625422i
$976$		−	10.7821i		−	0.345127i
$977$	−8.70634			−0.278541			−0.139270	−	0.990254i	$-0.544476\pi$
$977$	−8.70634			−0.278541			−0.139270	+	0.990254i	$0.544476\pi$
$978$	15.0003	−	39.5432i	0.479657	−	1.26445i
$979$	−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
$983$	9.66469	−	5.57991i	0.308256	−	0.177972i	−0.337890	−	0.941186i	$-0.609713\pi$
$983$	9.66469	−	5.57991i	0.308256	−	0.177972i	0.646146	+	0.763214i	$0.276380\pi$
$984$	−3.74618	−	1.42107i	−0.119424	−	0.0453022i
$985$	5.89847	−	51.1948i	0.187941	−	1.63120i
$986$	11.0052	+	19.0616i	0.350478	+	0.607047i
$987$	−16.1939	−	14.7357i	−0.515457	−	0.469043i
$988$	0.717793	+	0.414418i	0.0228360	+	0.0131844i
$989$	4.27279	−	2.46689i	0.135867	−	0.0784427i
$990$	−15.0227	+	3.16032i	−0.477452	+	0.100442i
$991$	−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	$0.884214\pi$
$992$		−	0.975100i		−	0.0309594i
$993$	−6.65333	+	5.43141i	−0.211137	+	0.172360i
$994$	−4.30214	−	28.8797i	−0.136456	−	0.916008i
$995$	10.7514	−	14.4913i	0.340842	−	0.459406i
$996$	−19.5642	+	3.17790i	−0.619914	+	0.100696i
$997$	8.97969	+	15.5533i	0.284390	+	0.492577i	0.972461	−	0.233066i	$-0.0748758\pi$
$997$	8.97969	+	15.5533i	0.284390	+	0.492577i	−0.688071	+	0.725643i	$0.741542\pi$
$998$	17.8598	−	30.9342i	0.565343	−	0.979204i
$999$	37.5472	+	23.7558i	1.18794	+	0.751601i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bi.b.479.19	yes	48
3.2	odd	2		1890.2.bi.a.899.14		48
5.4	even	2		630.2.bi.a.479.6	yes	48
7.5	odd	6		630.2.r.a.299.10	yes	48
9.4	even	3		1890.2.r.a.1529.22		48
9.5	odd	6		630.2.r.b.59.15	yes	48
15.14	odd	2		1890.2.bi.b.899.19		48
21.5	even	6		1890.2.r.b.89.22		48
35.19	odd	6		630.2.r.b.299.15	yes	48
45.4	even	6		1890.2.r.b.1529.22		48
45.14	odd	6		630.2.r.a.59.10	✓	48
63.5	even	6		630.2.bi.a.509.6	yes	48
63.40	odd	6		1890.2.bi.b.719.19		48
105.89	even	6		1890.2.r.a.89.22		48
315.194	even	6	inner	630.2.bi.b.509.19	yes	48
315.229	odd	6		1890.2.bi.a.719.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.r.a.59.10	✓	48	45.14	odd	6
630.2.r.a.299.10	yes	48	7.5	odd	6
630.2.r.b.59.15	yes	48	9.5	odd	6
630.2.r.b.299.15	yes	48	35.19	odd	6
630.2.bi.a.479.6	yes	48	5.4	even	2
630.2.bi.a.509.6	yes	48	63.5	even	6
630.2.bi.b.479.19	yes	48	1.1	even	1	trivial
630.2.bi.b.509.19	yes	48	315.194	even	6	inner
1890.2.r.a.89.22		48	105.89	even	6
1890.2.r.a.1529.22		48	9.4	even	3
1890.2.r.b.89.22		48	21.5	even	6
1890.2.r.b.1529.22		48	45.4	even	6
1890.2.bi.a.719.14		48	315.229	odd	6
1890.2.bi.a.899.14		48	3.2	odd	2
1890.2.bi.b.719.19		48	63.40	odd	6
1890.2.bi.b.899.19		48	15.14	odd	2

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.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.34174 - 1.09532i) q^{3} +1.00000 q^{4} +(-0.255938 + 2.22137i) q^{5} +(1.34174 - 1.09532i) q^{6} +(2.61687 - 0.389830i) q^{7} +1.00000 q^{8} +(0.600540 - 2.93928i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.34174 - 1.09532i) q^{3} +1.00000 q^{4} +(-0.255938 + 2.22137i) q^{5} +(1.34174 - 1.09532i) q^{6} +(2.61687 - 0.389830i) q^{7} +1.00000 q^{8} +(0.600540 - 2.93928i) q^{9} +(-0.255938 + 2.22137i) q^{10} +(-1.98187 + 1.14423i) q^{11} +(1.34174 - 1.09532i) q^{12} +(-2.02055 - 3.49969i) q^{13} +(2.61687 - 0.389830i) q^{14} +(2.08972 + 3.26084i) q^{15} +1.00000 q^{16} +(5.58838 + 3.22645i) q^{17} +(0.600540 - 2.93928i) q^{18} +(-0.177623 + 0.102551i) q^{19} +(-0.255938 + 2.22137i) q^{20} +(3.08418 - 3.38937i) q^{21} +(-1.98187 + 1.14423i) q^{22} +(-1.00425 + 1.73941i) q^{23} +(1.34174 - 1.09532i) q^{24} +(-4.86899 - 1.13707i) 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} +(2.08972 + 3.26084i) q^{30} -0.975100i q^{31} +1.00000 q^{32} +(-1.40585 + 3.70605i) 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} +(-0.177623 + 0.102551i) q^{38} +(-6.54434 - 2.48253i) q^{39} +(-0.255938 + 2.22137i) q^{40} +(-1.15662 - 2.00333i) q^{41} +(3.08418 - 3.38937i) q^{42} +(-2.12736 - 1.22823i) q^{43} +(-1.98187 + 1.14423i) q^{44} +(6.37553 + 2.08630i) q^{45} +(-1.00425 + 1.73941i) q^{46} -4.77784i q^{47} +(1.34174 - 1.09532i) q^{48} +(6.69607 - 2.04027i) q^{49} +(-4.86899 - 1.13707i) q^{50} +(11.0322 - 1.79201i) q^{51} +(-2.02055 - 3.49969i) q^{52} +(-2.35928 + 4.08640i) q^{53} +(-2.41369 - 4.60153i) q^{54} +(-2.03453 - 4.69532i) q^{55} +(2.61687 - 0.389830i) q^{56} +(-0.125998 + 0.332151i) q^{57} +(2.95397 + 1.70547i) q^{58} -9.07146 q^{59} +(2.08972 + 3.26084i) q^{60} -10.7821i q^{61} -0.975100i q^{62} +(0.425720 - 7.92583i) q^{63} +1.00000 q^{64} +(8.29125 - 3.59268i) q^{65} +(-1.40585 + 3.70605i) q^{66} +6.05164i q^{67} +(5.58838 + 3.22645i) q^{68} +(0.557771 + 3.43381i) q^{69} +(0.196198 + 5.91283i) q^{70} -11.0359i q^{71} +(0.600540 - 2.93928i) q^{72} +(-7.78631 + 13.4863i) q^{73} +(-7.40520 + 4.27539i) q^{74} +(-7.77838 + 3.80746i) q^{75} +(-0.177623 + 0.102551i) q^{76} +(-4.74025 + 3.76691i) q^{77} +(-6.54434 - 2.48253i) q^{78} -7.23402 q^{79} +(-0.255938 + 2.22137i) q^{80} +(-8.27870 - 3.53031i) q^{81} +(-1.15662 - 2.00333i) q^{82} +(-9.91029 - 5.72171i) q^{83} +(3.08418 - 3.38937i) q^{84} +(-8.59743 + 11.5881i) q^{85} +(-2.12736 - 1.22823i) q^{86} +(5.83150 - 0.947240i) q^{87} +(-1.98187 + 1.14423i) 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} +(-1.06805 - 1.30833i) q^{93} -4.77784i q^{94} +(-0.182343 - 0.420814i) q^{95} +(1.34174 - 1.09532i) q^{96} +(4.24029 - 7.34440i) q^{97} +(6.69607 - 2.04027i) q^{98} +(2.17303 + 6.51242i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8}+O(q^{10}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8	\( 48 q + 48 q^{2} + 48 q^{4} + 3 q^{7} + 48 q^{8} + 6 q^{11} + 3 q^{14} - 4 q^{15} + 48 q^{16} + 8 q^{21} + 6 q^{22} + 3 q^{23} - 18 q^{25} + 3 q^{28} - 3 q^{29} - 4 q^{30} + 48 q^{32} - 12 q^{35} - 18 q^{39} - 3 q^{41} + 8 q^{42} + 6 q^{44} - 39 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} - 42 q^{55} + 3 q^{56} - 22 q^{57} - 3 q^{58} - 4 q^{60} - 43 q^{63} + 48 q^{64} + 12 q^{65} - 42 q^{69} - 12 q^{70} - 18 q^{73} + 18 q^{75} - 12 q^{77} - 18 q^{78} + 8 q^{81} - 3 q^{82} + 9 q^{83} + 8 q^{84} - 33 q^{85} - 15 q^{87} + 6 q^{88} - 33 q^{89} - 39 q^{90} + 3 q^{92} - 8 q^{93} - 24 q^{97} + 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q + 48 * q^2 + 48 * q^4 + 3 * q^7 + 48 * q^8 + 6 * q^11 + 3 * q^14 - 4 * q^15 + 48 * q^16 + 8 * q^21 + 6 * q^22 + 3 * q^23 - 18 * q^25 + 3 * q^28 - 3 * q^29 - 4 * q^30 + 48 * q^32 - 12 * q^35 - 18 * q^39 - 3 * q^41 + 8 * q^42 + 6 * q^44 - 39 * q^45 + 3 * q^46 + 3 * q^49 - 18 * q^50 + 10 * q^51 - 42 * q^55 + 3 * q^56 - 22 * q^57 - 3 * q^58 - 4 * q^60 - 43 * q^63 + 48 * q^64 + 12 * q^65 - 42 * q^69 - 12 * q^70 - 18 * q^73 + 18 * q^75 - 12 * q^77 - 18 * q^78 + 8 * q^81 - 3 * q^82 + 9 * q^83 + 8 * q^84 - 33 * q^85 - 15 * q^87 + 6 * q^88 - 33 * q^89 - 39 * q^90 + 3 * q^92 - 8 * q^93 - 24 * q^97 + 3 * q^98 - 26 * q^99

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