LMFDB - Embedded newform 630.2.bi.a.479.6

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			479.6
Character	$\chi$	$=$	630.479
Dual form			630.2.bi.a.509.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.34174 + 1.09532i) q^{3} +1.00000 q^{4} +(-1.79580 + 1.33234i) q^{5} +(1.34174 - 1.09532i) q^{6} +(-2.61687 + 0.389830i) q^{7} -1.00000 q^{8} +(0.600540 - 2.93928i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.34174 + 1.09532i) q^{3} +1.00000 q^{4} +(-1.79580 + 1.33234i) q^{5} +(1.34174 - 1.09532i) q^{6} +(-2.61687 + 0.389830i) q^{7} -1.00000 q^{8} +(0.600540 - 2.93928i) q^{9} +(1.79580 - 1.33234i) 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} +(0.950157 - 3.75462i) q^{15} +1.00000 q^{16} +(-5.58838 - 3.22645i) q^{17} +(-0.600540 + 2.93928i) q^{18} +(-0.177623 + 0.102551i) q^{19} +(-1.79580 + 1.33234i) 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} +(1.44977 - 4.78520i) 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} +(-0.950157 + 3.75462i) q^{30} -0.975100i q^{31} -1.00000 q^{32} +(1.40585 - 3.70605i) 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} +(0.177623 - 0.102551i) q^{38} +(-6.54434 - 2.48253i) q^{39} +(1.79580 - 1.33234i) 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} +(2.83766 + 6.07846i) q^{45} +(-1.00425 + 1.73941i) q^{46} +4.77784i q^{47} +(-1.34174 + 1.09532i) q^{48} +(6.69607 - 2.04027i) q^{49} +(-1.44977 + 4.78520i) 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} +(0.950157 - 3.75462i) 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} +(-4.17999 + 4.18661i) q^{70} -11.0359i q^{71} +(-0.600540 + 2.93928i) q^{72} +(7.78631 - 13.4863i) q^{73} +(-7.40520 + 4.27539i) q^{74} +(3.29613 + 8.00847i) q^{75} +(-0.177623 + 0.102551i) q^{76} +(4.74025 - 3.76691i) q^{77} +(6.54434 + 2.48253i) q^{78} -7.23402 q^{79} +(-1.79580 + 1.33234i) 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} +(14.3343 - 1.65154i) 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} +(-2.83766 - 6.07846i) 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} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39} - 3 q^{41} - 8 q^{42} + 6 q^{44} + 15 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} + 6 q^{60} + 43 q^{63} + 48 q^{64} - 12 q^{65} - 42 q^{69} + 18 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} - 15 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 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * 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 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * 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 - 15 * 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
$5$	−1.79580	+	1.33234i	−0.803104	+	0.595838i
$5$	−1.79580	+	1.33234i	−0.803104	+	0.595838i
$6$	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
$10$	1.79580	−	1.33234i	0.567881	−	0.421321i
$11$	−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	$0.0226856\pi$
$13$	2.02055	+	3.49969i	0.560399	+	0.970640i	−0.437062	+	0.899431i	$0.643981\pi$
$14$	2.61687	−	0.389830i	0.699389	−	0.104186i
$15$	0.950157	−	3.75462i	0.245330	−	0.969440i
$16$	1.00000			0.250000
$17$	−5.58838	−	3.22645i	−1.35538	−	0.782529i	−0.366383	−	0.930464i	$-0.619404\pi$
$17$	−5.58838	−	3.22645i	−1.35538	−	0.782529i	−0.988997	+	0.147935i	$0.952737\pi$
$18$	−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	$0.340823\pi$
$20$	−1.79580	+	1.33234i	−0.401552	+	0.297919i
$21$	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	−0.742126	−	0.670261i	$-0.766182\pi$
$23$	1.00425	−	1.73941i	0.209400	−	0.362692i	0.951526	+	0.307569i	$0.0995155\pi$
$24$	1.34174	−	1.09532i	0.273882	−	0.223582i
$25$	1.44977	−	4.78520i	0.289953	−	0.957041i
$26$	−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	$0.564092\pi$
$30$	−0.950157	+	3.75462i	−0.173474	+	0.685497i
$31$		−	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
$35$	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	$0.0852348\pi$
$38$	0.177623	−	0.102551i	0.0288143	−	0.0166359i
$39$	−6.54434	−	2.48253i	−1.04793	−	0.397523i
$40$	1.79580	−	1.33234i	0.283940	−	0.210661i
$41$	−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	0.653360	−	0.757047i	$-0.273359\pi$
$43$	2.12736	+	1.22823i	0.324419	+	0.187303i	−0.328942	+	0.944350i	$0.606692\pi$
$44$	−1.98187	+	1.14423i	−0.298778	+	0.172500i
$45$	2.83766	+	6.07846i	0.423013	+	0.906124i
$46$	−1.00425	+	1.73941i	−0.148068	+	0.256462i
$47$			4.77784i			0.696920i	0.937324	+	0.348460i	$0.113295\pi$
$47$			4.77784i			0.696920i	−0.937324	+	0.348460i	$0.886705\pi$
$48$	−1.34174	+	1.09532i	−0.193664	+	0.158096i
$49$	6.69607	−	2.04027i	0.956581	−	0.291467i
$50$	−1.44977	+	4.78520i	−0.205028	+	0.676730i
$51$	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	−0.657252	−	0.753671i	$-0.728281\pi$
$53$	2.35928	−	4.08640i	0.324072	−	0.561310i	0.981324	+	0.192361i	$0.0616145\pi$
$54$	−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	$0.701070\pi$
$60$	0.950157	−	3.75462i	0.122665	−	0.484720i
$61$		−	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	$-0.879473\pi$
$67$		−	6.05164i		−	0.739325i	0.929166	−	0.369662i	$-0.120527\pi$
$68$	−5.58838	−	3.22645i	−0.677690	−	0.391265i
$69$	0.557771	+	3.43381i	0.0671478	+	0.413382i
$70$	−4.17999	+	4.18661i	−0.499604	+	0.500395i
$71$		−	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	$-0.468399\pi$
$73$	7.78631	−	13.4863i	0.911318	−	1.57845i	0.812204	−	0.583373i	$-0.198268\pi$
$74$	−7.40520	+	4.27539i	−0.860837	+	0.497004i
$75$	3.29613	+	8.00847i	0.380604	+	0.924738i
$76$	−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	$0.633406\pi$
$80$	−1.79580	+	1.33234i	−0.200776	+	0.148960i
$81$	−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	0.932989	−	0.359906i	$-0.117191\pi$
$83$	9.91029	+	5.72171i	1.08780	+	0.628039i	0.154807	+	0.987945i	$0.450524\pi$
$84$	3.08418	−	3.38937i	0.336512	−	0.369811i
$85$	14.3343	−	1.65154i	1.55477	−	0.179135i
$86$	−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	$0.651965\pi$
$90$	−2.83766	−	6.07846i	−0.299115	−	0.640726i
$91$	−6.65180	−	8.37059i	−0.697299	−	0.877476i
$92$	1.00425	−	1.73941i	0.104700	−	0.181346i
$93$	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	−0.996920	−	0.0784313i	$-0.975009\pi$
$97$	−4.24029	+	7.34440i	−0.430536	+	0.745711i	0.566383	+	0.824142i	$0.308342\pi$
$98$	−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
$101$	−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	$0.542628\pi$
$103$	−9.38804	+	16.2606i	−0.925031	+	1.60220i	−0.791511	+	0.611155i	$0.790705\pi$
$104$	−2.02055	−	3.49969i	−0.198131	−	0.343173i
$105$	−1.02278	+	10.1958i	−0.0998131	+	0.995006i
$106$	−2.35928	+	4.08640i	−0.229154	+	0.396906i
$107$	−9.00357	−	15.5946i	−0.870408	−	1.50759i	−0.861576	−	0.507629i	$-0.830522\pi$
$107$	−9.00357	−	15.5946i	−0.870408	−	1.50759i	−0.00883183	−	0.999961i	$-0.502811\pi$
$108$	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	0.690655	−	0.723184i	$-0.257322\pi$
$113$	−2.98673	−	5.17317i	−0.280968	−	0.486651i	−0.971623	+	0.236533i	$0.923989\pi$
$114$	−0.125998	+	0.332151i	−0.0118008	+	0.0311088i
$115$	0.514051	+	4.46162i	0.0479355	+	0.416048i
$116$	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
$120$	−0.950157	+	3.75462i	−0.0867371	+	0.342749i
$121$	−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	$-0.824069\pi$
$127$		−	11.8327i		−	1.04998i	0.851108	−	0.524991i	$-0.175931\pi$
$128$	−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
$135$	−10.4653	−	5.04758i	−0.900707	−	0.434426i
$136$	5.58838	+	3.22645i	0.479199	+	0.276666i
$137$	−3.43092	−	5.94252i	−0.293123	−	0.507704i	0.681423	−	0.731889i	$-0.261361\pi$
$137$	−3.43092	−	5.94252i	−0.293123	−	0.507704i	−0.974547	+	0.224185i	$0.928028\pi$
$138$	−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	$0.355802\pi$
$140$	4.17999	−	4.18661i	0.353274	−	0.353833i
$141$	−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
$145$	−7.57698	+	0.872991i	−0.629234	+	0.0724980i
$146$	−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	$0.826131\pi$
$150$	−3.29613	−	8.00847i	−0.269128	−	0.653889i
$151$	−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
$155$	1.29916	+	1.75108i	0.104351	+	0.140650i
$156$	−6.54434	−	2.48253i	−0.523967	−	0.198762i
$157$	−2.58329			−0.206169			−0.103084	−	0.994673i	$-0.532871\pi$
$157$	−2.58329			−0.206169			−0.103084	+	0.994673i	$0.532871\pi$
$158$	7.23402			0.575508
$159$	1.31037	+	8.06706i	0.103919	+	0.639760i
$160$	1.79580	−	1.33234i	0.141970	−	0.105330i
$161$	−1.94992	+	4.94330i	−0.153675	+	0.389587i
$162$	8.27870	+	3.53031i	0.650436	+	0.277367i
$163$	−21.1464	+	12.2089i	−1.65631	+	0.956272i	−0.681916	+	0.731431i	$0.738853\pi$
$163$	−21.1464	+	12.2089i	−1.65631	+	0.956272i	−0.974395	+	0.224841i	$0.927814\pi$
$164$	−1.15662	−	2.00333i	−0.0903170	−	0.156434i
$165$	2.41308	+	8.52838i	0.187858	+	0.663933i
$166$	−9.91029	−	5.72171i	−0.769188	−	0.444091i
$167$	0.00904075	−	0.00521968i	0.000699594	−	0.000403911i	−0.499650	−	0.866227i	$-0.666538\pi$
$167$	0.00904075	−	0.00521968i	0.000699594	−	0.000403911i	0.500350	+	0.865823i	$0.333205\pi$
$168$	−3.08418	+	3.38937i	−0.237950	+	0.261496i
$169$	−1.66523	+	2.88426i	−0.128094	+	0.221866i
$170$	−14.3343	+	1.65154i	−1.09939	+	0.126668i
$171$	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	$-0.756237\pi$
$173$		−	18.2330i		−	1.38623i	0.720826	−	0.693116i	$-0.243763\pi$
$174$	5.83150	−	0.947240i	0.442085	−	0.0718101i
$175$	−1.92844	+	13.0874i	−0.145776	+	0.989318i
$176$	−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	$0.468040\pi$
$180$	2.83766	+	6.07846i	0.211506	+	0.453062i
$181$		−	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	$0.147787\pi$
$193$			12.4417i			0.895572i	−0.894141	+	0.447786i	$0.852213\pi$
$194$	4.24029	−	7.34440i	0.304435	−	0.527297i
$195$	15.0599	−	4.26114i	1.07846	−	0.305147i
$196$	6.69607	−	2.04027i	0.478290	−	0.145734i
$197$	23.0465			1.64199			0.820996	−	0.570934i	$-0.193419\pi$
$197$	23.0465			1.64199			0.820996	+	0.570934i	$0.193419\pi$
$198$	−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	$0.758999\pi$
$200$	−1.44977	+	4.78520i	−0.102514	+	0.338365i
$201$	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
$210$	1.02278	−	10.1958i	0.0705785	−	0.703576i
$211$	−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
$215$	−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
$219$	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	−0.786785	−	0.617227i	$-0.788256\pi$
$223$	2.10769	−	3.65063i	0.141142	−	0.244464i	0.927927	+	0.372763i	$0.121589\pi$
$224$	2.61687	−	0.389830i	0.174847	−	0.0260466i
$225$	−13.1944	−	7.13497i	−0.879627	−	0.475665i
$226$	2.98673	+	5.17317i	0.198674	+	0.344114i
$227$	−16.0856	+	9.28700i	−1.06764	+	0.616400i	−0.927535	−	0.373737i	$-0.878076\pi$
$227$	−16.0856	+	9.28700i	−1.06764	+	0.616400i	−0.140102	+	0.990137i	$0.544743\pi$
$228$	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	$0.650131\pi$
$230$	−0.514051	−	4.46162i	−0.0338955	−	0.294190i
$231$	−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	0.715279	−	0.698839i	$-0.246300\pi$
$233$	−3.77904	−	6.54549i	−0.247573	−	0.428809i	−0.962852	+	0.270030i	$0.912966\pi$
$234$	−11.5000	+	3.83725i	−0.751777	+	0.250849i
$235$	−6.36569	−	8.58003i	−0.415252	−	0.559699i
$236$	−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	$0.151949\pi$
$240$	0.950157	−	3.75462i	0.0613324	−	0.242360i
$241$	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
$245$	−9.30644	+	12.5853i	−0.594567	+	0.804046i
$246$	−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
$255$	−17.4239	+	17.9166i	−1.09113	+	1.12198i
$256$	1.00000			0.0625000
$257$	−16.2504	−	9.38216i	−1.01367	−	0.585243i	−0.101406	−	0.994845i	$-0.532334\pi$
$257$	−16.2504	−	9.38216i	−1.01367	−	0.585243i	−0.912264	+	0.409602i	$0.865668\pi$
$258$	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	0.816970	−	0.576681i	$-0.195652\pi$
$263$	−1.47472	−	2.55429i	−0.0909351	−	0.157504i	−0.907905	+	0.419176i	$0.862319\pi$
$264$	−1.40585	+	3.70605i	−0.0865243	+	0.228092i
$265$	1.20766	+	10.4817i	0.0741861	+	0.643885i
$266$	−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	$-0.151878\pi$
$270$	10.4653	+	5.04758i	0.636896	+	0.307186i
$271$	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
$275$	2.60214	+	11.1425i	0.156915	+	0.671919i
$276$	0.557771	+	3.43381i	0.0335739	+	0.206691i
$277$	6.88813	−	3.97687i	0.413868	−	0.238947i	−0.278582	−	0.960412i	$-0.589865\pi$
$277$	6.88813	−	3.97687i	0.413868	−	0.238947i	0.692450	+	0.721466i	$0.256531\pi$
$278$	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	0.0598996	−	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	$-0.846376\pi$
$283$	−29.8023			−1.77156			−0.885780	+	0.464105i	$0.846376\pi$
$284$		−	11.0359i		−	0.654863i
$285$	0.216270	+	0.764348i	0.0128107	+	0.0452761i
$286$	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
$290$	7.57698	−	0.872991i	0.444936	−	0.0512638i
$291$	−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	−0.562882	−	0.826537i	$-0.690308\pi$
$293$	−2.19993	+	1.27013i	−0.128522	+	0.0742019i	0.434361	+	0.900739i	$0.356974\pi$
$294$	6.74964	−	10.0719i	0.393647	−	0.587403i
$295$	16.2905	−	12.0862i	0.948469	−	0.703688i
$296$	−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
$300$	3.29613	+	8.00847i	0.190302	+	0.462369i
$301$	−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
$305$	14.3654	+	19.3625i	0.822559	+	1.10869i
$306$	12.8395	−	14.4882i	0.733984	−	0.828234i
$307$	−8.06299			−0.460179			−0.230089	−	0.973169i	$-0.573902\pi$
$307$	−8.06299			−0.460179			−0.230089	+	0.973169i	$0.573902\pi$
$308$	4.74025	−	3.76691i	0.270101	−	0.214639i
$309$	−5.21423	−	32.1004i	−0.296627	−	1.82613i
$310$	−1.29916	−	1.75108i	−0.0737873	−	0.0994547i
$311$	−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	$-0.534589\pi$
$313$	−3.83737			−0.216901			−0.108450	+	0.994102i	$0.534589\pi$
$314$	2.58329			0.145783
$315$	−9.79536	−	14.8004i	−0.551906	−	0.833906i
$316$	−7.23402			−0.406946
$317$	17.3289			0.973288			0.486644	−	0.873600i	$-0.338221\pi$
$317$	17.3289			0.973288			0.486644	+	0.873600i	$0.338221\pi$
$318$	−1.31037	−	8.06706i	−0.0734821	−	0.452378i
$319$	−7.80583			−0.437043
$320$	−1.79580	+	1.33234i	−0.100388	+	0.0744798i
$321$	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
$325$	19.6761	−	4.59500i	1.09143	−	0.254885i
$326$	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
$330$	−2.41308	−	8.52838i	−0.132835	−	0.469472i
$331$	−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
$335$	8.06281	+	10.8675i	0.440518	+	0.593755i
$336$	3.08418	−	3.38937i	0.168256	−	0.184905i
$337$	1.58895	−	0.917381i	0.0865557	−	0.0499729i	−0.456097	−	0.889930i	$-0.650753\pi$
$337$	1.58895	−	0.917381i	0.0865557	−	0.0499729i	0.542653	+	0.839957i	$0.317420\pi$
$338$	1.66523	−	2.88426i	0.0905765	−	0.156883i
$339$	9.67370	+	3.66962i	0.525403	+	0.199307i
$340$	14.3343	−	1.65154i	0.777386	−	0.0895676i
$341$	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
$345$	−5.57663	−	5.42329i	−0.300236	−	0.291980i
$346$			18.2330i			0.980214i
$347$	−6.78486			−0.364230			−0.182115	−	0.983277i	$-0.558294\pi$
$347$	−6.78486			−0.364230			−0.182115	+	0.983277i	$0.558294\pi$
$348$	−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	$0.781633\pi$
$350$	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
$353$	26.8650	−	15.5105i	1.42988	−	0.825543i	0.432771	−	0.901504i	$-0.357536\pi$
$353$	26.8650	−	15.5105i	1.42988	−	0.825543i	0.997111	+	0.0759611i	$0.0242025\pi$
$354$	−12.1716	+	9.93617i	−0.646911	+	0.528102i
$355$	14.7036	+	19.8183i	0.780385	+	1.05185i
$356$	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	$0.0577884\pi$
$360$	−2.83766	−	6.07846i	−0.149558	−	0.320363i
$361$	−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
$365$	3.98563	+	34.5926i	0.208617	+	1.81066i
$366$	−11.8099	−	14.4668i	−0.617312	−	0.756191i
$367$	−6.18161	−	10.7069i	−0.322677	−	0.558893i	0.658362	−	0.752701i	$-0.271250\pi$
$367$	−6.18161	−	10.7069i	−0.322677	−	0.558893i	−0.981040	+	0.193808i	$0.937916\pi$
$368$	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	$-0.935306\pi$
$373$	−31.7495	−	18.3306i	−1.64393	−	0.949123i	−0.664512	−	0.747278i	$-0.731360\pi$
$374$	−14.7672			−0.763596
$375$	−16.5891	−	9.99002i	−0.856659	−	0.515883i
$376$		−	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	0.307742	−	0.951470i	$-0.400427\pi$
$383$	−7.09201	−	4.09457i	−0.362385	−	0.209223i	−0.670126	+	0.742247i	$0.733760\pi$
$384$	1.34174	−	1.09532i	0.0684705	−	0.0558954i
$385$	−3.49374	+	13.0802i	−0.178057	+	0.666628i
$386$		−	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	$0.261479\pi$
$390$	−15.0599	+	4.26114i	−0.762586	+	0.215771i
$391$	−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
$395$	12.9908	−	9.63815i	0.653640	−	0.484948i
$396$	2.17303	+	6.51242i	0.109199	+	0.327262i
$397$	−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
$399$	−0.200239	+	0.918316i	−0.0100245	+	0.0459733i
$400$	1.44977	−	4.78520i	0.0724883	−	0.239260i
$401$	−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
$405$	19.5704	−	4.69030i	0.972462	−	0.233063i
$406$	8.39500	+	3.31147i	0.416637	+	0.164345i
$407$	−9.78409	+	16.9465i	−0.484979	+	0.840009i
$408$	−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
$415$	−25.4201	+	2.92881i	−1.24782	+	0.143770i
$416$	−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	$0.665213\pi$
$420$	−1.02278	+	10.1958i	−0.0499065	+	0.497503i
$421$	−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
$430$	5.45671	−	0.628702i	0.263146	−	0.0303187i
$431$	−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	$-0.693894\pi$
$433$	−23.8117			−1.14432			−0.572158	+	0.820143i	$0.693894\pi$
$434$	−0.380123	−	2.55171i	−0.0182465	−	0.122486i
$435$	9.21014	−	9.47056i	0.441592	−	0.454079i
$436$	−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	$-0.164345\pi$
$443$	36.6080			1.73930			0.869649	+	0.493670i	$0.164345\pi$
$444$	−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	$0.997366\pi$
$450$	13.1944	+	7.13497i	0.621990	+	0.336346i
$451$	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
$455$	23.0977	+	6.16943i	1.08284	+	0.289227i
$456$	−0.125998	+	0.332151i	−0.00590041	+	0.0155544i
$457$		−	1.91541i		−	0.0895992i	−0.998996	−	0.0447996i	$-0.985735\pi$
$457$		−	1.91541i		−	0.0895992i	0.998996	−	0.0447996i	$-0.0142649\pi$
$458$	−1.36101	−	0.785777i	−0.0635956	−	0.0367169i
$459$	1.35804	−	33.5027i	0.0633877	−	1.56377i
$460$	0.514051	+	4.46162i	0.0239678	+	0.208024i
$461$	−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	−0.592187	−	0.805801i	$-0.701735\pi$
$463$	−4.09771	+	2.36581i	−0.190437	+	0.109949i	0.401750	+	0.915749i	$0.368402\pi$
$464$	2.95397	+	1.70547i	0.137134	+	0.0791746i
$465$	−3.66113	−	0.926498i	−0.169781	−	0.0429653i
$466$	3.77904	+	6.54549i	0.175061	+	0.303214i
$467$	29.9337	−	17.2822i	1.38517	−	0.799726i	0.392401	−	0.919794i	$-0.371645\pi$
$467$	29.9337	−	17.2822i	1.38517	−	0.799726i	0.992766	+	0.120068i	$0.0383112\pi$
$468$	11.5000	−	3.83725i	0.531587	−	0.177377i
$469$	2.35911	+	15.8364i	0.108933	+	0.731256i
$470$	6.36569	+	8.58003i	0.293627	+	0.395767i
$471$	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
$475$	0.233215	+	0.998638i	0.0107006	+	0.0458207i
$476$	15.8818	+	6.26470i	0.727943	+	0.287142i
$477$	−10.5942	−	9.38863i	−0.485076	−	0.429876i
$478$	−14.4459	+	8.34037i	−0.660742	+	0.381480i
$479$	−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	$-0.564875\pi$
$480$	−0.950157	+	3.75462i	−0.0433686	+	0.171374i
$481$	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
$485$	−2.17050	−	18.8385i	−0.0985576	−	0.855413i
$486$	−14.9747	+	4.33109i	−0.679266	+	0.196462i
$487$	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	$0.597401\pi$
$488$			10.7821i			0.488083i
$489$	15.0003	−	39.5432i	0.678338	−	1.78821i
$490$	9.30644	−	12.5853i	0.420422	−	0.568547i
$491$	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
$495$	−12.5790	−	8.79978i	−0.565386	−	0.395521i
$496$		−	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	$0.0160372\pi$
$503$			2.25896i			0.100722i	−0.998731	+	0.0503609i	$0.983963\pi$
$504$	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	$0.828508\pi$
$510$	17.4239	−	17.9166i	0.771545	−	0.793361i
$511$	−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
$515$	−4.80552	−	41.7087i	−0.211756	−	1.83790i
$516$	−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	$0.0516846\pi$
$523$	14.4859	+	25.0903i	0.633424	+	1.09712i	−0.353422	+	0.935464i	$0.614982\pi$
$524$	−1.47813	+	2.56020i	−0.0645724	+	0.111843i
$525$	−11.7475	−	19.6722i	−0.512703	−	0.858566i
$526$	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
$530$	−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
$534$	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
$540$	−10.4653	−	5.04758i	−0.450354	−	0.217213i
$541$	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
$545$	−4.16557	−	36.1544i	−0.178434	−	1.54868i
$546$	−18.0935	−	3.94529i	−0.774330	−	0.168843i
$547$	−12.6990	−	7.33178i	−0.542971	−	0.313484i	0.203311	−	0.979114i	$-0.434830\pi$
$547$	−12.6990	−	7.33178i	−0.542971	−	0.313484i	−0.746282	+	0.665630i	$0.768163\pi$
$548$	−3.43092	−	5.94252i	−0.146562	−	0.253852i
$549$	−31.6916	−	6.47508i	−1.35256	−	0.276350i
$550$	−2.60214	−	11.1425i	−0.110956	−	0.475119i
$551$	−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
$555$	−9.01639	−	31.8660i	−0.382724	−	1.35264i
$556$	−1.44024	+	0.831524i	−0.0610798	+	0.0352645i
$557$	−13.3908	+	23.1936i	−0.567387	+	0.982743i	0.429436	+	0.903097i	$0.358712\pi$
$557$	−13.3908	+	23.1936i	−0.567387	+	0.982743i	−0.996823	+	0.0796459i	$0.974621\pi$
$558$	2.86609	+	0.585586i	0.121331	+	0.0247898i
$559$			9.92679i			0.419858i
$560$	4.17999	−	4.18661i	0.176637	−	0.176917i
$561$	−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	$0.127695\pi$
$563$			18.5309i			0.780986i	−0.920606	+	0.390493i	$0.872305\pi$
$564$	−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	$0.833542\pi$
$570$	−0.216270	−	0.764348i	−0.00905854	−	0.0320150i
$571$	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	−0.890690	−	0.454611i	$-0.849778\pi$
$577$	−1.24045	+	2.14853i	−0.0516407	+	0.0894443i	0.839050	+	0.544055i	$0.183112\pi$
$578$	−12.3200	−	21.3388i	−0.512443	−	0.887578i
$579$	−13.6276	−	16.6935i	−0.566346	−	0.693759i
$580$	−7.57698	+	0.872991i	−0.314617	+	0.0362490i
$581$	−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
$585$	−15.5391	+	22.2127i	−0.642464	+	0.918384i
$586$	2.19993	−	1.27013i	0.0908784	−	0.0524687i
$587$	9.73573	+	5.62093i	0.401837	+	0.232001i	0.687276	−	0.726396i	$-0.258806\pi$
$587$	9.73573	+	5.62093i	0.401837	+	0.232001i	−0.285439	+	0.958397i	$0.592140\pi$
$588$	−6.74964	+	10.0719i	−0.278350	+	0.415357i
$589$	0.0999973	+	0.173200i	0.00412032	+	0.00713660i
$590$	−16.2905	+	12.0862i	−0.670669	+	0.497582i
$591$	−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	−0.920418	−	0.390935i	$-0.872152\pi$
$593$	−25.3760	+	14.6508i	−1.04207	+	0.601638i	−0.121649	+	0.992573i	$0.538818\pi$
$594$	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
$597$	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	$-0.0889451\pi$
$600$	−3.29613	−	8.00847i	−0.134564	−	0.326944i
$601$	−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
$605$	−1.47495	−	12.8016i	−0.0599654	−	0.520459i
$606$	−2.45361	−	0.930752i	−0.0996710	−	0.0378092i
$607$	4.07061	−	7.05051i	0.165221	−	0.286171i	−0.771513	−	0.636214i	$-0.780500\pi$
$607$	4.07061	−	7.05051i	0.165221	−	0.286171i	0.936734	+	0.350043i	$0.113833\pi$
$608$	0.177623	−	0.102551i	0.00720357	−	0.00415899i
$609$	14.8910	−	4.75210i	0.603415	−	0.192565i
$610$	−14.3654	−	19.3625i	−0.581637	−	0.783963i
$611$	−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	0.764135	−	0.645056i	$-0.223166\pi$
$613$	14.5475	+	8.39900i	0.587568	+	0.339232i	−0.176567	+	0.984289i	$0.556499\pi$
$614$	8.06299			0.325396
$615$	−8.62071	+	2.43920i	−0.347621	+	0.0983582i
$616$	−4.74025	+	3.76691i	−0.190990	+	0.151773i
$617$	13.7676	+	23.8461i	0.554262	+	0.960009i	0.997961	+	0.0638334i	$0.0203326\pi$
$617$	13.7676	+	23.8461i	0.554262	+	0.960009i	−0.443699	+	0.896176i	$0.646334\pi$
$618$	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	$0.273182\pi$
$620$	1.29916	+	1.75108i	0.0521755	+	0.0703251i
$621$	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
$625$	−20.7964	−	13.8748i	−0.831854	−	0.554994i
$626$	3.83737			0.153372
$627$	0.130346	+	0.802452i	0.00520553	+	0.0320468i
$628$	−2.58329			−0.103084
$629$	−55.1774			−2.20007
$630$	9.79536	+	14.8004i	0.390256	+	0.589661i
$631$	−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
$635$	15.7651	+	21.2491i	0.625620	+	0.843245i
$636$	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
$640$	1.79580	−	1.33234i	0.0709851	−	0.0526652i
$641$	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	0.544629	−	0.838677i	$-0.316670\pi$
$643$	−11.5123	−	19.9399i	−0.454001	−	0.786353i	−0.998630	+	0.0523244i	$0.983337\pi$
$644$	−1.94992	+	4.94330i	−0.0768376	+	0.194793i
$645$	6.63286	−	6.82041i	0.261169	−	0.268553i
$646$	−1.32350			−0.0520724
$647$	−14.6259	−	8.44426i	−0.575003	−	0.331978i	0.184142	−	0.982900i	$-0.441049\pi$
$647$	−14.6259	−	8.44426i	−0.575003	−	0.331978i	−0.759145	+	0.650922i	$0.774383\pi$
$648$	8.27870	+	3.53031i	0.325218	+	0.138683i
$649$	17.9785	−	10.3799i	0.705716	−	0.407445i
$650$	−19.6761	+	4.59500i	−0.771759	+	0.180231i
$651$	−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	−0.570615	−	0.821218i	$-0.693295\pi$
$653$	10.8831	−	18.8501i	0.425888	−	0.737660i	0.996503	+	0.0835580i	$0.0266284\pi$
$654$	4.51986	+	27.8256i	0.176740	+	1.08807i
$655$	−0.756620	−	6.56696i	−0.0295636	−	0.256592i
$656$	−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	$0.823825\pi$
$660$	2.41308	+	8.52838i	0.0939289	+	0.331967i
$661$			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
$665$	−0.313123	+	1.17230i	−0.0121424	+	0.0454599i
$666$	8.11945	+	24.3335i	0.314622	+	0.942903i
$667$	5.93303	−	3.42544i	0.229728	−	0.132633i
$668$	0.00904075	−	0.00521968i	0.000349797	−	0.000201955i
$669$	1.17064	+	7.20680i	0.0452595	+	0.278631i
$670$	−8.06281	−	10.8675i	−0.311493	−	0.419848i
$671$	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	0.434538	−	0.900653i	$-0.356912\pi$
$673$	−3.32531	−	1.91987i	−0.128181	−	0.0740054i	−0.562719	+	0.826648i	$0.690245\pi$
$674$	−1.58895	+	0.917381i	−0.0612041	+	0.0353362i
$675$	25.5186	−	4.87884i	0.982210	−	0.187786i
$676$	−1.66523	+	2.88426i	−0.0640472	+	0.110933i
$677$		−	16.2326i		−	0.623868i	−0.950104	−	0.311934i	$-0.899023\pi$
$677$		−	16.2326i		−	0.623868i	0.950104	−	0.311934i	$-0.100977\pi$
$678$	−9.67370	−	3.66962i	−0.371516	−	0.140931i
$679$	8.23324	−	20.8724i	0.315963	−	0.801008i
$680$	−14.3343	+	1.65154i	−0.549695	+	0.0633338i
$681$	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	−0.942293	−	0.334790i	$-0.891335\pi$
$683$	−4.73579	+	8.20262i	−0.181210	+	0.313865i	0.761083	+	0.648655i	$0.224668\pi$
$684$	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
$690$	5.57663	+	5.42329i	0.212299	+	0.206461i
$691$			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
$700$	−1.92844	+	13.0874i	−0.0728882	+	0.494659i
$701$			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
$705$	17.9390	+	4.53970i	0.675622	+	0.170975i
$706$	−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	$0.661406\pi$
$710$	−14.7036	−	19.8183i	−0.551816	−	0.743768i
$711$	−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
$715$	20.5431	−	2.36689i	0.768267	−	0.0885168i
$716$	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	$-0.450893\pi$
$720$	2.83766	+	6.07846i	0.105753	+	0.226531i
$721$	18.2285	−	46.2116i	0.678864	−	1.72101i
$722$	9.47897	−	16.4181i	0.352771	−	0.611017i
$723$	−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	$-0.540542\pi$
$727$	21.4490	−	37.1508i	0.795499	−	1.37785i	0.922522	−	0.385945i	$-0.126125\pi$
$728$	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
$731$	−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	−0.818943	−	0.573874i	$-0.805440\pi$
$733$	2.36946	−	4.10402i	0.0875179	−	0.151586i	0.906461	+	0.422289i	$0.138773\pi$
$734$	6.18161	+	10.7069i	0.228167	+	0.395197i
$735$	−1.29813	−	27.0798i	−0.0478823	−	0.998853i
$736$	−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	$-0.963258\pi$
$743$	−16.2571	−	28.1581i	−0.596415	−	1.03302i	0.396930	−	0.917849i	$-0.370075\pi$
$744$	−1.06805	−	1.30833i	−0.0391565	−	0.0479658i
$745$	26.0458	−	3.00090i	0.954244	−	0.109944i
$746$	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
$750$	16.5891	+	9.99002i	0.605750	+	0.364784i
$751$	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	$-0.992438\pi$
$757$		−	1.30712i		−	0.0475082i	0.999718	−	0.0237541i	$-0.00756188\pi$
$758$	−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
$765$	3.75397	−	43.1243i	0.135725	−	1.55916i
$766$	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	$0.587926\pi$
$770$	3.49374	−	13.0802i	0.125906	−	0.471377i
$771$	32.0803	−	5.21096i	1.15534	−	0.187668i
$772$			12.4417i			0.447786i
$773$	31.3729	+	18.1132i	1.12841	+	0.651486i	0.943534	−	0.331277i	$-0.107479\pi$
$773$	31.3729	+	18.1132i	1.12841	+	0.651486i	0.184872	+	0.982763i	$0.440813\pi$
$774$	−4.88767	+	5.51529i	−0.175684	+	0.198243i
$775$	−4.66605	−	1.41367i	−0.167610	−	0.0507804i
$776$	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
$780$	15.0599	−	4.26114i	0.539230	−	0.152573i
$781$	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
$785$	4.63905	−	3.44180i	0.165575	−	0.122843i
$786$	0.820971	+	5.05415i	0.0292831	+	0.180276i
$787$	17.1289			0.610581			0.305290	−	0.952259i	$-0.401246\pi$
$787$	17.1289			0.610581			0.305290	+	0.952259i	$0.401246\pi$
$788$	23.0465			0.820996
$789$	4.77646	+	1.81190i	0.170046	+	0.0645054i
$790$	−12.9908	+	9.63815i	−0.462193	+	0.342910i
$791$	9.83255	+	12.3732i	0.349605	+	0.439941i
$792$	−2.17303	−	6.51242i	−0.0772151	−	0.231409i
$793$	37.7340	−	21.7858i	1.33997	−	0.773635i
$794$	5.82466	+	10.0886i	0.206710	+	0.358032i
$795$	−13.1012	−	12.7409i	−0.464652	−	0.451875i
$796$	−6.98847	−	4.03479i	−0.247700	−	0.143010i
$797$	35.9212	−	20.7391i	1.27239	−	0.734616i	0.296955	−	0.954891i	$-0.404029\pi$
$797$	35.9212	−	20.7391i	1.27239	−	0.734616i	0.975438	+	0.220275i	$0.0706955\pi$
$798$	0.200239	−	0.918316i	0.00708839	−	0.0325080i
$799$	15.4155	−	26.7004i	0.545360	−	0.944591i
$800$	−1.44977	+	4.78520i	−0.0512570	+	0.169183i
$801$	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
$805$	−3.08448	−	11.4751i	−0.108714	−	0.404444i
$806$	−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	$0.632330\pi$
$810$	−19.5704	+	4.69030i	−0.687634	+	0.164800i
$811$		−	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	$0.284501\pi$
$823$			44.7216i			1.55890i	−0.626466	+	0.779449i	$0.715499\pi$
$824$	9.38804	−	16.2606i	0.327048	−	0.566464i
$825$	−15.6960	−	12.1002i	−0.546466	−	0.421275i
$826$	−23.7389	+	3.53633i	−0.825981	+	0.123044i
$827$	−34.3286			−1.19372			−0.596860	−	0.802345i	$-0.703585\pi$
$827$	−34.3286			−1.19372			−0.596860	+	0.802345i	$0.703585\pi$
$828$	−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	$0.361791\pi$
$830$	25.4201	−	2.92881i	0.882344	−	0.101660i
$831$	−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	$0.255501\pi$
$840$	1.02278	−	10.1958i	0.0352892	−	0.351788i
$841$	−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
$845$	−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
$849$	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	−0.770875	−	0.636987i	$-0.780181\pi$
$853$	4.85434	−	8.40796i	0.166209	−	0.287883i	0.937084	+	0.349104i	$0.113514\pi$
$854$	−4.20318	−	28.2154i	−0.143830	−	0.965511i
$855$	−1.12739	−	0.788672i	−0.0385558	−	0.0269720i
$856$	9.00357	+	15.5946i	0.307736	+	0.533014i
$857$	−27.0181	+	15.5989i	−0.922921	+	0.532849i	−0.884566	−	0.466415i	$-0.845545\pi$
$857$	−27.0181	+	15.5989i	−0.922921	+	0.532849i	−0.0383555	+	0.999264i	$0.512212\pi$
$858$	−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	$0.754357\pi$
$860$	−5.45671	+	0.628702i	−0.186072	+	0.0214386i
$861$	−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	$-0.900411\pi$
$863$	−21.8059	−	37.7689i	−0.742281	−	1.28567i	0.209174	−	0.977879i	$-0.432923\pi$
$864$	−2.41369	−	4.60153i	−0.0821153	−	0.156547i
$865$	24.2925	+	32.7428i	0.825971	+	1.11329i
$866$	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
$870$	−9.21014	+	9.47056i	−0.312253	+	0.321082i
$871$	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
$875$	−13.9738	−	26.0717i	−0.472400	−	0.881384i
$876$	4.32461	+	26.6236i	0.146115	+	0.899528i
$877$	32.8047	+	18.9398i	1.10774	+	0.639552i	0.938242	−	0.345980i	$-0.112453\pi$
$877$	32.8047	+	18.9398i	1.10774	+	0.639552i	0.169494	+	0.985531i	$0.445787\pi$
$878$			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	$0.0291593\pi$
$883$			5.43664i			0.182957i	−0.995807	+	0.0914787i	$0.970841\pi$
$884$		−	26.0768i		−	0.877057i
$885$	−8.61932	+	34.0599i	−0.289735	+	1.14491i
$886$	−36.6080			−1.22987
$887$	−33.7618	−	19.4924i	−1.13361	−	0.654490i	−0.188770	−	0.982021i	$-0.560450\pi$
$887$	−33.7618	−	19.4924i	−1.13361	−	0.654490i	−0.944840	+	0.327531i	$0.893783\pi$
$888$	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
$895$	−34.7301	+	4.00147i	−1.16090	+	0.133754i
$896$	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
$900$	−13.1944	−	7.13497i	−0.439813	−	0.237832i
$901$	−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
$905$	32.3888	+	43.6554i	1.07664	+	1.45116i
$906$	−5.44679	−	2.06618i	−0.180957	−	0.0686444i
$907$	−2.39252	+	1.38132i	−0.0794424	+	0.0458661i	−0.539195	−	0.842181i	$-0.681271\pi$
$907$	−2.39252	+	1.38132i	−0.0794424	+	0.0458661i	0.459753	+	0.888047i	$0.347938\pi$
$908$	−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	0.959381	−	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
$915$	−40.4827	−	10.2447i	−1.33832	−	0.338679i
$916$	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	$0.961134\pi$
$920$	−0.514051	−	4.46162i	−0.0169478	−	0.147095i
$921$	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
$925$	−9.72283	−	41.6337i	−0.319685	−	1.36891i
$926$	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	$0.533738\pi$
$930$	3.66113	+	0.926498i	0.120053	+	0.0303811i
$931$	−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
$935$	−26.5190	+	19.6749i	−0.867263	+	0.643439i
$936$	−11.5000	+	3.83725i	−0.375889	+	0.125424i
$937$	−38.6081			−1.26127			−0.630635	−	0.776079i	$-0.717206\pi$
$937$	−38.6081			−1.26127			−0.630635	+	0.776079i	$0.717206\pi$
$938$	−2.35911	−	15.8364i	−0.0770276	−	0.517076i
$939$	5.14876	−	4.20315i	0.168023	−	0.137165i
$940$	−6.36569	−	8.58003i	−0.207626	−	0.279850i
$941$	−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
$945$	29.3540	+	9.12920i	0.954886	+	0.296973i
$946$	5.62152			0.182771
$947$	34.1258			1.10894			0.554470	−	0.832204i	$-0.312921\pi$
$947$	34.1258			1.10894			0.554470	+	0.832204i	$0.312921\pi$
$948$	9.70619	−	7.92359i	0.315242	−	0.257346i
$949$	62.9304			2.04281
$950$	−0.233215	−	0.998638i	−0.00756648	−	0.0324001i
$951$	−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	$-0.754767\pi$
$953$	−44.3067			−1.43523			−0.717617	+	0.696438i	$0.754767\pi$
$954$	10.5942	+	9.38863i	0.343000	+	0.303968i
$955$	−15.9080	−	21.4417i	−0.514771	−	0.693837i
$956$	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
$960$	0.950157	−	3.75462i	0.0306662	−	0.121180i
$961$	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
$965$	−16.5765	−	22.3427i	−0.533616	−	0.719237i
$966$	2.79822	+	8.76842i	0.0900312	+	0.282119i
$967$	14.0448	−	8.10875i	0.451649	−	0.260760i	−0.256877	−	0.966444i	$-0.582694\pi$
$967$	14.0448	−	8.10875i	0.451649	−	0.260760i	0.708526	+	0.705684i	$0.249360\pi$
$968$	2.88146	−	4.99084i	0.0926137	−	0.160412i
$969$	−1.77580	+	1.44966i	−0.0570468	+	0.0465698i
$970$	2.17050	+	18.8385i	0.0696907	+	0.604869i
$971$	−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
$975$	−21.3672	+	27.7169i	−0.684297	+	0.887652i
$976$		−	10.7821i		−	0.345127i
$977$	8.70634			0.278541			0.139270	−	0.990254i	$-0.455524\pi$
$977$	8.70634			0.278541			0.139270	+	0.990254i	$0.455524\pi$
$978$	−15.0003	+	39.5432i	−0.479657	+	1.26445i
$979$	−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
$983$	−9.66469	+	5.57991i	−0.308256	+	0.177972i	−0.646146	−	0.763214i	$-0.723620\pi$
$983$	−9.66469	+	5.57991i	−0.308256	+	0.177972i	0.337890	+	0.941186i	$0.390287\pi$
$984$	−3.74618	−	1.42107i	−0.119424	−	0.0453022i
$985$	−41.3867	+	30.7056i	−1.31869	+	0.978362i
$986$	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
$990$	12.5790	+	8.79978i	0.399788	+	0.279675i
$991$	−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
$995$	17.9256	−	2.06532i	0.568279	−	0.0654749i
$996$	−19.5642	+	3.17790i	−0.619914	+	0.100696i
$997$	−8.97969	−	15.5533i	−0.284390	−	0.492577i	0.688071	−	0.725643i	$-0.258458\pi$
$997$	−8.97969	−	15.5533i	−0.284390	−	0.492577i	−0.972461	+	0.233066i	$0.925124\pi$
$998$	−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.a.479.6	yes	48
3.2	odd	2		1890.2.bi.b.899.19		48
5.4	even	2		630.2.bi.b.479.19	yes	48
7.5	odd	6		630.2.r.b.299.15	yes	48
9.4	even	3		1890.2.r.b.1529.22		48
9.5	odd	6		630.2.r.a.59.10	✓	48
15.14	odd	2		1890.2.bi.a.899.14		48
21.5	even	6		1890.2.r.a.89.22		48
35.19	odd	6		630.2.r.a.299.10	yes	48
45.4	even	6		1890.2.r.a.1529.22		48
45.14	odd	6		630.2.r.b.59.15	yes	48
63.5	even	6		630.2.bi.b.509.19	yes	48
63.40	odd	6		1890.2.bi.a.719.14		48
105.89	even	6		1890.2.r.b.89.22		48
315.194	even	6	inner	630.2.bi.a.509.6	yes	48
315.229	odd	6		1890.2.bi.b.719.19		48

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.34174 + 1.09532i) q^{3} +1.00000 q^{4} +(-1.79580 + 1.33234i) q^{5} +(1.34174 - 1.09532i) q^{6} +(-2.61687 + 0.389830i) q^{7} -1.00000 q^{8} +(0.600540 - 2.93928i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.34174 + 1.09532i) q^{3} +1.00000 q^{4} +(-1.79580 + 1.33234i) q^{5} +(1.34174 - 1.09532i) q^{6} +(-2.61687 + 0.389830i) q^{7} -1.00000 q^{8} +(0.600540 - 2.93928i) q^{9} +(1.79580 - 1.33234i) 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} +(0.950157 - 3.75462i) q^{15} +1.00000 q^{16} +(-5.58838 - 3.22645i) q^{17} +(-0.600540 + 2.93928i) q^{18} +(-0.177623 + 0.102551i) q^{19} +(-1.79580 + 1.33234i) 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} +(1.44977 - 4.78520i) 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} +(-0.950157 + 3.75462i) q^{30} -0.975100i q^{31} -1.00000 q^{32} +(1.40585 - 3.70605i) 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} +(0.177623 - 0.102551i) q^{38} +(-6.54434 - 2.48253i) q^{39} +(1.79580 - 1.33234i) 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} +(2.83766 + 6.07846i) q^{45} +(-1.00425 + 1.73941i) q^{46} +4.77784i q^{47} +(-1.34174 + 1.09532i) q^{48} +(6.69607 - 2.04027i) q^{49} +(-1.44977 + 4.78520i) 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} +(0.950157 - 3.75462i) 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} +(-4.17999 + 4.18661i) q^{70} -11.0359i q^{71} +(-0.600540 + 2.93928i) q^{72} +(7.78631 - 13.4863i) q^{73} +(-7.40520 + 4.27539i) q^{74} +(3.29613 + 8.00847i) q^{75} +(-0.177623 + 0.102551i) q^{76} +(4.74025 - 3.76691i) q^{77} +(6.54434 + 2.48253i) q^{78} -7.23402 q^{79} +(-1.79580 + 1.33234i) 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} +(14.3343 - 1.65154i) 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} +(-2.83766 - 6.07846i) 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	\( 48 q - 48 q^{2} + 48 q^{4} - 3 q^{7} - 48 q^{8} + 6 q^{11} + 3 q^{14} + 6 q^{15} + 48 q^{16} + 8 q^{21} - 6 q^{22} - 3 q^{23} + 18 q^{25} - 3 q^{28} - 3 q^{29} - 6 q^{30} - 48 q^{32} - 18 q^{35} - 18 q^{39} - 3 q^{41} - 8 q^{42} + 6 q^{44} + 15 q^{45} + 3 q^{46} + 3 q^{49} - 18 q^{50} + 10 q^{51} + 42 q^{55} + 3 q^{56} + 22 q^{57} + 3 q^{58} + 6 q^{60} + 43 q^{63} + 48 q^{64} - 12 q^{65} - 42 q^{69} + 18 q^{70} + 18 q^{73} + 18 q^{75} + 12 q^{77} + 18 q^{78} + 8 q^{81} + 3 q^{82} - 9 q^{83} + 8 q^{84} + 33 q^{85} + 15 q^{87} - 6 q^{88} - 33 q^{89} - 15 q^{90} - 3 q^{92} + 8 q^{93} + 24 q^{97} - 3 q^{98} - 26 q^{99}+O(q^{100}) \) 48 * q - 48 * q^2 + 48 * q^4 - 3 * q^7 - 48 * q^8 + 6 * q^11 + 3 * q^14 + 6 * q^15 + 48 * q^16 + 8 * q^21 - 6 * q^22 - 3 * q^23 + 18 * q^25 - 3 * q^28 - 3 * q^29 - 6 * q^30 - 48 * q^32 - 18 * q^35 - 18 * q^39 - 3 * q^41 - 8 * q^42 + 6 * q^44 + 15 * 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 + 6 * q^60 + 43 * q^63 + 48 * q^64 - 12 * q^65 - 42 * q^69 + 18 * 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 - 15 * q^90 - 3 * q^92 + 8 * q^93 + 24 * q^97 - 3 * q^98 - 26 * q^99

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