LMFDB - Embedded newform 630.2.t.b.311.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(311,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 0, 1]))

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

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

chi := DirichletCharacter("630.311");

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.t (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.6
Character	$\chi$	$=$	630.311
Dual form			630.2.t.b.551.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.65157 + 0.521832i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.16939 - 1.27771i) q^{6} +(-2.02958 + 1.69729i) q^{7} -1.00000i q^{8} +(2.45538 + 1.72369i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.65157 + 0.521832i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.16939 - 1.27771i) q^{6} +(-2.02958 + 1.69729i) q^{7} -1.00000i q^{8} +(2.45538 + 1.72369i) q^{9} +(0.866025 + 0.500000i) q^{10} +5.51168i q^{11} +(0.373866 + 1.69122i) q^{12} +(-5.67516 - 3.27655i) q^{13} +(2.60632 - 0.455105i) q^{14} +(-1.65157 - 0.521832i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.26666 - 2.19392i) q^{17} +(-1.26458 - 2.72045i) q^{18} +(-6.11706 + 3.53169i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-4.23770 + 1.74410i) q^{21} +(2.75584 - 4.77326i) q^{22} +4.21229i q^{23} +(0.521832 - 1.65157i) q^{24} +1.00000 q^{25} +(3.27655 + 5.67516i) q^{26} +(3.15576 + 4.12809i) q^{27} +(-2.48469 - 0.909025i) q^{28} +(6.29071 - 3.63194i) q^{29} +(1.16939 + 1.27771i) q^{30} +(-5.33881 + 3.08236i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.87617 + 9.10294i) q^{33} +(-2.19392 + 1.26666i) q^{34} +(2.02958 - 1.69729i) q^{35} +(-0.265066 + 2.98827i) q^{36} +(-1.00755 - 1.74514i) q^{37} +7.06338 q^{38} +(-7.66312 - 8.37294i) q^{39} +1.00000i q^{40} +(-2.97356 + 5.15035i) q^{41} +(4.54201 + 0.608421i) q^{42} +(2.74829 + 4.76018i) q^{43} +(-4.77326 + 2.75584i) q^{44} +(-2.45538 - 1.72369i) q^{45} +(2.10615 - 3.64795i) q^{46} +(2.69332 - 4.66497i) q^{47} +(-1.27771 + 1.16939i) q^{48} +(1.23841 - 6.88958i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(3.23684 - 2.96244i) q^{51} -6.55311i q^{52} +(2.56943 + 1.48346i) q^{53} +(-0.668926 - 5.15292i) q^{54} -5.51168i q^{55} +(1.69729 + 2.02958i) q^{56} +(-11.9457 + 2.64076i) q^{57} -7.26388 q^{58} +(-1.95873 - 3.39263i) q^{59} +(-0.373866 - 1.69122i) q^{60} +(0.512178 + 0.295706i) q^{61} +6.16472 q^{62} +(-7.90900 + 0.669129i) q^{63} -1.00000 q^{64} +(5.67516 + 3.27655i) q^{65} +(7.04231 - 6.44529i) q^{66} +(1.48818 + 2.57760i) q^{67} +2.53332 q^{68} +(-2.19811 + 6.95691i) q^{69} +(-2.60632 + 0.455105i) q^{70} +14.8483i q^{71} +(1.72369 - 2.45538i) q^{72} +(9.76683 + 5.63888i) q^{73} +2.01511i q^{74} +(1.65157 + 0.521832i) q^{75} +(-6.11706 - 3.53169i) q^{76} +(-9.35492 - 11.1864i) q^{77} +(2.44998 + 11.0827i) q^{78} +(-0.619617 + 1.07321i) q^{79} +(0.500000 - 0.866025i) q^{80} +(3.05780 + 8.46462i) q^{81} +(5.15035 - 2.97356i) q^{82} +(-4.32347 - 7.48846i) q^{83} +(-3.62928 - 2.79791i) q^{84} +(-1.26666 + 2.19392i) q^{85} -5.49658i q^{86} +(12.2848 - 2.71572i) q^{87} +5.51168 q^{88} +(7.84313 + 13.5847i) q^{89} +(1.26458 + 2.72045i) q^{90} +(17.0795 - 2.98235i) q^{91} +(-3.64795 + 2.10615i) q^{92} +(-10.4259 + 2.30478i) q^{93} +(-4.66497 + 2.69332i) q^{94} +(6.11706 - 3.53169i) q^{95} +(1.69122 - 0.373866i) q^{96} +(0.197336 - 0.113932i) q^{97} +(-4.51729 + 5.34735i) q^{98} +(-9.50042 + 13.5333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	$ 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) $ 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.65157	+	0.521832i	0.953536	+	0.301280i
$3$	1.65157	+	0.521832i	0.953536	+	0.301280i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.16939	−	1.27771i	−0.477400	−	0.521621i
$7$	−2.02958	+	1.69729i	−0.767110	+	0.641515i
$7$	−2.02958	+	1.69729i	−0.767110	+	0.641515i
$8$		−	1.00000i		−	0.353553i
$9$	2.45538	+	1.72369i	0.818461	+	0.574563i
$10$	0.866025	+	0.500000i	0.273861	+	0.158114i
$11$			5.51168i			1.66183i	0.556396	+	0.830917i	$0.312184\pi$
$11$			5.51168i			1.66183i	−0.556396	+	0.830917i	$0.687816\pi$
$12$	0.373866	+	1.69122i	0.107926	+	0.488213i
$13$	−5.67516	−	3.27655i	−1.57400	−	0.908752i	−0.995671	−	0.0929524i	$-0.970370\pi$
$13$	−5.67516	−	3.27655i	−1.57400	−	0.908752i	−0.578334	−	0.815800i	$-0.696297\pi$
$14$	2.60632	−	0.455105i	0.696567	−	0.121632i
$15$	−1.65157	−	0.521832i	−0.426434	−	0.134737i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.26666	−	2.19392i	0.307211	−	0.532104i	−0.670541	−	0.741873i	$-0.733938\pi$
$17$	1.26666	−	2.19392i	0.307211	−	0.532104i	0.977751	+	0.209769i	$0.0672711\pi$
$18$	−1.26458	−	2.72045i	−0.298064	−	0.641216i
$19$	−6.11706	+	3.53169i	−1.40335	+	0.810225i	−0.994735	−	0.102482i	$-0.967322\pi$
$19$	−6.11706	+	3.53169i	−1.40335	+	0.810225i	−0.408616	+	0.912707i	$0.633988\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−4.23770	+	1.74410i	−0.924743	+	0.380593i
$22$	2.75584	−	4.77326i	0.587547	−	1.01766i
$23$			4.21229i			0.878324i	0.898408	+	0.439162i	$0.144725\pi$
$23$			4.21229i			0.878324i	−0.898408	+	0.439162i	$0.855275\pi$
$24$	0.521832	−	1.65157i	0.106519	−	0.337126i
$25$	1.00000			0.200000
$26$	3.27655	+	5.67516i	0.642585	+	1.11299i
$27$	3.15576	+	4.12809i	0.607327	+	0.794452i
$28$	−2.48469	−	0.909025i	−0.469562	−	0.171790i
$29$	6.29071	−	3.63194i	1.16815	−	0.674435i	0.214910	−	0.976634i	$-0.431054\pi$
$29$	6.29071	−	3.63194i	1.16815	−	0.674435i	0.953245	+	0.302199i	$0.0977208\pi$
$30$	1.16939	+	1.27771i	0.213500	+	0.233276i
$31$	−5.33881	+	3.08236i	−0.958878	+	0.553608i	−0.895827	−	0.444402i	$-0.853416\pi$
$31$	−5.33881	+	3.08236i	−0.958878	+	0.553608i	−0.0630503	+	0.998010i	$0.520083\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−2.87617	+	9.10294i	−0.500678	+	1.58462i
$34$	−2.19392	+	1.26666i	−0.376255	+	0.217231i
$35$	2.02958	−	1.69729i	0.343062	−	0.286894i
$36$	−0.265066	+	2.98827i	−0.0441777	+	0.498045i
$37$	−1.00755	−	1.74514i	−0.165641	−	0.286899i	0.771242	−	0.636542i	$-0.219636\pi$
$37$	−1.00755	−	1.74514i	−0.165641	−	0.286899i	−0.936883	+	0.349644i	$0.886303\pi$
$38$	7.06338			1.14583
$39$	−7.66312	−	8.37294i	−1.22708	−	1.34074i
$40$			1.00000i			0.158114i
$41$	−2.97356	+	5.15035i	−0.464392	+	0.804350i	−0.999174	−	0.0406401i	$-0.987060\pi$
$41$	−2.97356	+	5.15035i	−0.464392	+	0.804350i	0.534782	+	0.844990i	$0.320394\pi$
$42$	4.54201	+	0.608421i	0.700847	+	0.0938814i
$43$	2.74829	+	4.76018i	0.419110	+	0.725920i	0.995850	−	0.0910078i	$-0.0290088\pi$
$43$	2.74829	+	4.76018i	0.419110	+	0.725920i	−0.576740	+	0.816928i	$0.695675\pi$
$44$	−4.77326	+	2.75584i	−0.719595	+	0.415459i
$45$	−2.45538	−	1.72369i	−0.366027	−	0.256952i
$46$	2.10615	−	3.64795i	0.310534	−	0.537861i
$47$	2.69332	−	4.66497i	0.392861	−	0.680456i	−0.599964	−	0.800027i	$-0.704819\pi$
$47$	2.69332	−	4.66497i	0.392861	−	0.680456i	0.992826	+	0.119571i	$0.0381518\pi$
$48$	−1.27771	+	1.16939i	−0.184421	+	0.168787i
$49$	1.23841	−	6.88958i	0.176916	−	0.984226i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	3.23684	−	2.96244i	0.453249	−	0.414824i
$52$		−	6.55311i		−	0.908752i
$53$	2.56943	+	1.48346i	0.352938	+	0.203769i	0.665979	−	0.745971i	$-0.268014\pi$
$53$	2.56943	+	1.48346i	0.352938	+	0.203769i	−0.313040	+	0.949740i	$0.601348\pi$
$54$	−0.668926	−	5.15292i	−0.0910293	−	0.701223i
$55$		−	5.51168i		−	0.743195i
$56$	1.69729	+	2.02958i	0.226810	+	0.271214i
$57$	−11.9457	+	2.64076i	−1.58225	+	0.349777i
$58$	−7.26388			−0.953795
$59$	−1.95873	−	3.39263i	−0.255005	−	0.441682i	0.709892	−	0.704311i	$-0.248744\pi$
$59$	−1.95873	−	3.39263i	−0.255005	−	0.441682i	−0.964897	+	0.262629i	$0.915411\pi$
$60$	−0.373866	−	1.69122i	−0.0482659	−	0.218336i
$61$	0.512178	+	0.295706i	0.0655776	+	0.0378613i	0.532430	−	0.846474i	$-0.321279\pi$
$61$	0.512178	+	0.295706i	0.0655776	+	0.0378613i	−0.466853	+	0.884335i	$0.654612\pi$
$62$	6.16472			0.782920
$63$	−7.90900	+	0.669129i	−0.996440	+	0.0843023i
$64$	−1.00000			−0.125000
$65$	5.67516	+	3.27655i	0.703916	+	0.406406i
$66$	7.04231	−	6.44529i	0.866848	−	0.793360i
$67$	1.48818	+	2.57760i	0.181810	+	0.314904i	0.942497	−	0.334215i	$-0.108471\pi$
$67$	1.48818	+	2.57760i	0.181810	+	0.314904i	−0.760687	+	0.649119i	$0.775138\pi$
$68$	2.53332			0.307211
$69$	−2.19811	+	6.95691i	−0.264622	+	0.837513i
$70$	−2.60632	+	0.455105i	−0.311514	+	0.0543955i
$71$			14.8483i			1.76217i	0.472960	+	0.881084i	$0.343185\pi$
$71$			14.8483i			1.76217i	−0.472960	+	0.881084i	$0.656815\pi$
$72$	1.72369	−	2.45538i	0.203139	−	0.289370i
$73$	9.76683	+	5.63888i	1.14312	+	0.659981i	0.947201	−	0.320639i	$-0.103898\pi$
$73$	9.76683	+	5.63888i	1.14312	+	0.659981i	0.195919	+	0.980620i	$0.437231\pi$
$74$			2.01511i			0.234252i
$75$	1.65157	+	0.521832i	0.190707	+	0.0602560i
$76$	−6.11706	−	3.53169i	−0.701675	−	0.405112i
$77$	−9.35492	−	11.1864i	−1.06609	−	1.27481i
$78$	2.44998	+	11.0827i	0.277406	+	1.25487i
$79$	−0.619617	+	1.07321i	−0.0697124	+	0.120745i	−0.898775	−	0.438411i	$-0.855541\pi$
$79$	−0.619617	+	1.07321i	−0.0697124	+	0.120745i	0.829062	+	0.559156i	$0.188875\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	3.05780	+	8.46462i	0.339756	+	0.940514i
$82$	5.15035	−	2.97356i	0.568761	−	0.328374i
$83$	−4.32347	−	7.48846i	−0.474562	−	0.821966i	0.525014	−	0.851094i	$-0.324060\pi$
$83$	−4.32347	−	7.48846i	−0.474562	−	0.821966i	−0.999576	+	0.0291281i	$0.990727\pi$
$84$	−3.62928	−	2.79791i	−0.395987	−	0.305277i
$85$	−1.26666	+	2.19392i	−0.137389	+	0.237964i
$86$		−	5.49658i		−	0.592711i
$87$	12.2848	−	2.71572i	1.31707	−	0.291156i
$88$	5.51168			0.587547
$89$	7.84313	+	13.5847i	0.831371	+	1.43998i	0.896952	+	0.442129i	$0.145777\pi$
$89$	7.84313	+	13.5847i	0.831371	+	1.43998i	−0.0655810	+	0.997847i	$0.520890\pi$
$90$	1.26458	+	2.72045i	0.133298	+	0.286760i
$91$	17.0795	−	2.98235i	1.79041	−	0.312635i
$92$	−3.64795	+	2.10615i	−0.380326	+	0.219581i
$93$	−10.4259	+	2.30478i	−1.08112	+	0.238995i
$94$	−4.66497	+	2.69332i	−0.481155	+	0.277795i
$95$	6.11706	−	3.53169i	0.627597	−	0.362344i
$96$	1.69122	−	0.373866i	0.172609	−	0.0381575i
$97$	0.197336	−	0.113932i	0.0200365	−	0.0115681i	−0.489948	−	0.871751i	$-0.662984\pi$
$97$	0.197336	−	0.113932i	0.0200365	−	0.0115681i	0.509985	+	0.860183i	$0.329651\pi$
$98$	−4.51729	+	5.34735i	−0.456315	+	0.540164i
$99$	−9.50042	+	13.5333i	−0.954828	+	1.36015i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	2.76769			0.275396			0.137698	−	0.990474i	$-0.456030\pi$
$101$	2.76769			0.275396			0.137698	+	0.990474i	$0.456030\pi$
$102$	−4.28441	+	0.947123i	−0.424219	+	0.0937792i
$103$			3.30139i			0.325295i	0.986684	+	0.162648i	$0.0520034\pi$
$103$			3.30139i			0.325295i	−0.986684	+	0.162648i	$0.947997\pi$
$104$	−3.27655	+	5.67516i	−0.321292	+	0.556495i
$105$	4.23770	−	1.74410i	0.413558	−	0.170206i
$106$	−1.48346	−	2.56943i	−0.144086	−	0.249565i
$107$	4.81501	−	2.77994i	0.465484	−	0.268747i	−0.248863	−	0.968539i	$-0.580057\pi$
$107$	4.81501	−	2.77994i	0.465484	−	0.268747i	0.714347	+	0.699791i	$0.246724\pi$
$108$	−1.99715	+	4.79702i	−0.192176	+	0.461593i
$109$	9.12223	−	15.8002i	0.873751	−	1.51338i	0.0156644	−	0.999877i	$-0.495014\pi$
$109$	9.12223	−	15.8002i	0.873751	−	1.51338i	0.858087	−	0.513504i	$-0.171653\pi$
$110$	−2.75584	+	4.77326i	−0.262759	+	0.455112i
$111$	−0.753381	−	3.40799i	−0.0715078	−	0.323472i
$112$	−0.455105	−	2.60632i	−0.0430034	−	0.246274i
$113$	1.41503	+	0.816970i	0.133115	+	0.0768540i	0.565079	−	0.825037i	$-0.308846\pi$
$113$	1.41503	+	0.816970i	0.133115	+	0.0768540i	−0.431964	+	0.901891i	$0.642179\pi$
$114$	11.6657	+	3.68590i	1.09259	+	0.345216i
$115$		−	4.21229i		−	0.392798i
$116$	6.29071	+	3.63194i	0.584077	+	0.337217i
$117$	−8.28692	−	17.8274i	−0.766126	−	1.64814i
$118$			3.91747i			0.360632i
$119$	1.15293	+	6.60264i	0.105689	+	0.605263i
$120$	−0.521832	+	1.65157i	−0.0476366	+	0.150767i
$121$	−19.3786			−1.76169
$122$	−0.295706	−	0.512178i	−0.0267720	−	0.0463704i
$123$	−7.59866	+	6.95448i	−0.685148	+	0.627064i
$124$	−5.33881	−	3.08236i	−0.479439	−	0.276804i
$125$	−1.00000			−0.0894427
$126$	7.18396	+	3.37502i	0.639998	+	0.300670i
$127$	−11.2316			−0.996643			−0.498322	−	0.866992i	$-0.666050\pi$
$127$	−11.2316			−0.996643			−0.498322	+	0.866992i	$0.666050\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	2.05498	+	9.29592i	0.180931	+	0.818460i
$130$	−3.27655	−	5.67516i	−0.287373	−	0.497744i
$131$	−4.16723			−0.364092			−0.182046	−	0.983290i	$-0.558272\pi$
$131$	−4.16723			−0.364092			−0.182046	+	0.983290i	$0.558272\pi$
$132$	−9.32146	+	2.06063i	−0.811329	+	0.179355i
$133$	6.42079	−	17.5503i	0.556753	−	1.52180i
$134$		−	2.97636i		−	0.257118i
$135$	−3.15576	−	4.12809i	−0.271605	−	0.355290i
$136$	−2.19392	−	1.26666i	−0.188127	−	0.108615i
$137$		−	9.27120i		−	0.792092i	−0.918231	−	0.396046i	$-0.870382\pi$
$137$		−	9.27120i		−	0.792092i	0.918231	−	0.396046i	$-0.129618\pi$
$138$	5.38208	−	4.92580i	0.458153	−	0.419312i
$139$	3.08961	+	1.78379i	0.262057	+	0.151299i	0.625273	−	0.780406i	$-0.284988\pi$
$139$	3.08961	+	1.78379i	0.262057	+	0.151299i	−0.363216	+	0.931705i	$0.618321\pi$
$140$	2.48469	+	0.909025i	0.209994	+	0.0768266i
$141$	6.88255	−	6.29907i	0.579615	−	0.530478i
$142$	7.42414	−	12.8590i	0.623020	−	1.07910i
$143$	18.0593	−	31.2796i	1.51020	−	2.61574i
$144$	−2.72045	+	1.26458i	−0.226704	+	0.105382i
$145$	−6.29071	+	3.63194i	−0.522415	+	0.301616i
$146$	−5.63888	−	9.76683i	−0.466677	−	0.808308i
$147$	5.64053	−	10.7324i	0.465223	−	0.885193i
$148$	1.00755	−	1.74514i	0.0828205	−	0.143449i
$149$		−	10.3904i		−	0.851216i	−0.904908	−	0.425608i	$-0.860060\pi$
$149$		−	10.3904i		−	0.851216i	0.904908	−	0.425608i	$-0.139940\pi$
$150$	−1.16939	−	1.27771i	−0.0954801	−	0.104324i
$151$	−8.76778			−0.713512			−0.356756	−	0.934198i	$-0.616117\pi$
$151$	−8.76778			−0.713512			−0.356756	+	0.934198i	$0.616117\pi$
$152$	3.53169	+	6.11706i	0.286458	+	0.496159i
$153$	6.89177	−	3.20359i	0.557167	−	0.258995i
$154$	2.50839	+	14.3652i	0.202132	+	1.15758i
$155$	5.33881	−	3.08236i	0.428823	−	0.247581i
$156$	3.41962	−	10.8229i	0.273789	−	0.866528i
$157$	10.3942	−	6.00109i	0.829547	−	0.478939i	−0.0241507	−	0.999708i	$-0.507688\pi$
$157$	10.3942	−	6.00109i	0.829547	−	0.478939i	0.853697	+	0.520769i	$0.174355\pi$
$158$	1.07321	−	0.619617i	0.0853799	−	0.0492941i
$159$	3.46948	+	3.79085i	0.275148	+	0.300634i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−7.14949	−	8.54920i	−0.563458	−	0.673771i
$162$	1.58418	−	8.85948i	0.124465	−	0.696066i
$163$	−5.40261	−	9.35760i	−0.423165	−	0.732944i	0.573082	−	0.819498i	$-0.305748\pi$
$163$	−5.40261	−	9.35760i	−0.423165	−	0.732944i	−0.996247	+	0.0865542i	$0.972414\pi$
$164$	−5.94711			−0.464392
$165$	2.87617	−	9.10294i	0.223910	−	0.708663i
$166$			8.64693i			0.671132i
$167$	10.7866	−	18.6830i	0.834695	−	1.44573i	−0.0595841	−	0.998223i	$-0.518977\pi$
$167$	10.7866	−	18.6830i	0.834695	−	1.44573i	0.894279	−	0.447510i	$-0.147689\pi$
$168$	1.74410	+	4.23770i	0.134560	+	0.326946i
$169$	14.9716	+	25.9316i	1.15166	+	1.99474i
$170$	2.19392	−	1.26666i	0.168266	−	0.0971485i
$171$	−21.1073	−	1.87226i	−1.61411	−	0.143176i
$172$	−2.74829	+	4.76018i	−0.209555	+	0.362960i
$173$	−0.639733	+	1.10805i	−0.0486380	+	0.0842435i	−0.889319	−	0.457286i	$-0.848821\pi$
$173$	−0.639733	+	1.10805i	−0.0486380	+	0.0842435i	0.840681	+	0.541530i	$0.182155\pi$
$174$	−11.9968	−	3.79053i	−0.909477	−	0.287359i
$175$	−2.02958	+	1.69729i	−0.153422	+	0.128303i
$176$	−4.77326	−	2.75584i	−0.359798	−	0.207729i
$177$	−1.46461	−	6.62530i	−0.110087	−	0.497988i
$178$		−	15.6863i		−	1.17574i
$179$	10.2660	+	5.92708i	0.767317	+	0.443010i	0.831917	−	0.554901i	$-0.187244\pi$
$179$	10.2660	+	5.92708i	0.767317	+	0.443010i	−0.0645999	+	0.997911i	$0.520577\pi$
$180$	0.265066	−	2.98827i	0.0197569	−	0.222732i
$181$			13.3188i			0.989978i	0.868899	+	0.494989i	$0.164828\pi$
$181$			13.3188i			0.989978i	−0.868899	+	0.494989i	$0.835172\pi$
$182$	−16.2824	−	5.95694i	−1.20693	−	0.441558i
$183$	0.691590	+	0.755651i	0.0511238	+	0.0558593i
$184$	4.21229			0.310534
$185$	1.00755	+	1.74514i	0.0740769	+	0.128305i
$186$	10.1815	+	3.21695i	0.746543	+	0.235878i
$187$	12.0922	+	6.98143i	0.884269	+	0.510533i
$188$	5.38665			0.392861
$189$	−13.4115	−	3.02206i	−0.975540	−	0.219822i
$190$	−7.06338			−0.512431
$191$	7.09826	+	4.09818i	0.513612	+	0.296534i	0.734317	−	0.678806i	$-0.237502\pi$
$191$	7.09826	+	4.09818i	0.513612	+	0.296534i	−0.220705	+	0.975341i	$0.570836\pi$
$192$	−1.65157	−	0.521832i	−0.119192	−	0.0376600i
$193$	−1.49743	−	2.59363i	−0.107787	−	0.186693i	0.807086	−	0.590434i	$-0.201043\pi$
$193$	−1.49743	−	2.59363i	−0.107787	−	0.186693i	−0.914874	+	0.403740i	$0.867710\pi$
$194$	−0.227864			−0.0163597
$195$	7.66312	+	8.37294i	0.548767	+	0.599599i
$196$	6.58576	−	2.37229i	0.470411	−	0.169450i
$197$			11.9427i			0.850883i	0.904986	+	0.425441i	$0.139881\pi$
$197$			11.9427i			0.850883i	−0.904986	+	0.425441i	$0.860119\pi$
$198$	14.9942	−	6.96996i	1.06559	−	0.495333i
$199$	−2.73876	−	1.58122i	−0.194145	−	0.112090i	0.399776	−	0.916613i	$-0.369088\pi$
$199$	−2.73876	−	1.58122i	−0.194145	−	0.112090i	−0.593922	+	0.804523i	$0.702421\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	1.11276	+	5.03367i	0.0784879	+	0.355048i
$202$	−2.39689	−	1.38385i	−0.168645	−	0.0973670i
$203$	−6.60305	+	18.0485i	−0.463443	+	1.26676i
$204$	4.18397	+	1.32197i	0.292936	+	0.0925564i
$205$	2.97356	−	5.15035i	0.207682	−	0.359716i
$206$	1.65069	−	2.85909i	0.115009	−	0.199202i
$207$	−7.26068	+	10.3428i	−0.504652	+	0.718874i
$208$	5.67516	−	3.27655i	0.393501	−	0.227188i
$209$	−19.4655	−	33.7153i	−1.34646	−	2.33214i
$210$	−4.54201	−	0.608421i	−0.313428	−	0.0419850i
$211$	6.04072	−	10.4628i	0.415860	−	0.720291i	−0.579658	−	0.814860i	$-0.696814\pi$
$211$	6.04072	−	10.4628i	0.415860	−	0.720291i	0.995518	+	0.0945689i	$0.0301473\pi$
$212$			2.96692i			0.203769i
$213$	−7.74832	+	24.5230i	−0.530906	+	1.68029i
$214$	−5.55989			−0.380066
$215$	−2.74829	−	4.76018i	−0.187432	−	0.324641i
$216$	4.12809	−	3.15576i	0.280881	−	0.214723i
$217$	5.60389	−	15.3174i	0.380417	−	1.03981i
$218$	−15.8002	+	9.12223i	−1.07012	+	0.617835i
$219$	13.1881	+	14.4097i	0.891167	+	0.973715i
$220$	4.77326	−	2.75584i	0.321813	−	0.185799i
$221$	−14.3770	+	8.30057i	−0.967102	+	0.558357i
$222$	−1.05155	+	3.32810i	−0.0705754	+	0.223367i
$223$	−13.6952	+	7.90695i	−0.917101	+	0.529488i	−0.882709	−	0.469920i	$-0.844283\pi$
$223$	−13.6952	+	7.90695i	−0.917101	+	0.529488i	−0.0343917	+	0.999408i	$0.510949\pi$
$224$	−0.909025	+	2.48469i	−0.0607368	+	0.166015i
$225$	2.45538	+	1.72369i	0.163692	+	0.114913i
$226$	−0.816970	−	1.41503i	−0.0543440	−	0.0941266i
$227$	2.12883			0.141296			0.0706478	−	0.997501i	$-0.477493\pi$
$227$	2.12883			0.141296			0.0706478	+	0.997501i	$0.477493\pi$
$228$	−8.25982	−	9.02492i	−0.547020	−	0.597690i
$229$		−	20.3062i		−	1.34187i	−0.741517	−	0.670934i	$-0.765893\pi$
$229$		−	20.3062i		−	1.34187i	0.741517	−	0.670934i	$-0.234107\pi$
$230$	−2.10615	+	3.64795i	−0.138875	+	0.240539i
$231$	−9.61290	−	23.3569i	−0.632482	−	1.53677i
$232$	−3.63194	−	6.29071i	−0.238449	−	0.413005i
$233$	−11.1623	+	6.44458i	−0.731269	+	0.422198i	−0.818886	−	0.573956i	$-0.805408\pi$
$233$	−11.1623	+	6.44458i	−0.731269	+	0.422198i	0.0876172	+	0.996154i	$0.472075\pi$
$234$	−1.73701	+	19.5824i	−0.113552	+	1.28014i
$235$	−2.69332	+	4.66497i	−0.175693	+	0.304309i
$236$	1.95873	−	3.39263i	0.127503	−	0.220841i
$237$	−1.58338	+	1.44915i	−0.102851	+	0.0941321i
$238$	2.30285	−	6.29452i	0.149272	−	0.408013i
$239$	−0.970335	−	0.560223i	−0.0627658	−	0.0362378i	0.468289	−	0.883576i	$-0.344871\pi$
$239$	−0.970335	−	0.560223i	−0.0627658	−	0.0362378i	−0.531054	+	0.847338i	$0.678204\pi$
$240$	1.27771	−	1.16939i	0.0824756	−	0.0754836i
$241$		−	1.45223i		−	0.0935465i	−0.998906	−	0.0467732i	$-0.985106\pi$
$241$		−	1.45223i		−	0.0935465i	0.998906	−	0.0467732i	$-0.0148938\pi$
$242$	16.7824	+	9.68931i	1.07881	+	0.622853i
$243$	0.633064	+	15.5756i	0.0406111	+	0.999175i
$244$			0.591412i			0.0378613i
$245$	−1.23841	+	6.88958i	−0.0791192	+	0.440159i
$246$	10.0579	−	2.22342i	0.641267	−	0.141760i
$247$	46.2871			2.94517
$248$	3.08236	+	5.33881i	0.195730	+	0.339014i
$249$	−3.23279	−	14.6239i	−0.204870	−	0.926750i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	14.7760			0.932653			0.466327	−	0.884613i	$-0.345577\pi$
$251$	14.7760			0.932653			0.466327	+	0.884613i	$0.345577\pi$
$252$	−4.53398	−	6.51483i	−0.285614	−	0.410396i
$253$	−23.2168			−1.45963
$254$	9.72685	+	5.61580i	0.610317	+	0.352367i
$255$	−3.23684	+	2.96244i	−0.202699	+	0.185515i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−17.7853			−1.10942			−0.554708	−	0.832045i	$-0.687170\pi$
$257$	−17.7853			−1.10942			−0.554708	+	0.832045i	$0.687170\pi$
$258$	2.86829	−	9.07799i	0.178572	−	0.565171i
$259$	5.00692	+	1.83179i	0.311115	+	0.113822i
$260$			6.55311i			0.406406i
$261$	21.7064	+	1.92541i	1.34359	+	0.119180i
$262$	3.60893	+	2.08361i	0.222960	+	0.128726i
$263$		−	7.71730i		−	0.475869i	−0.971281	−	0.237935i	$-0.923530\pi$
$263$		−	7.71730i		−	0.475869i	0.971281	−	0.237935i	$-0.0764704\pi$
$264$	9.10294	+	2.87617i	0.560247	+	0.177016i
$265$	−2.56943	−	1.48346i	−0.157839	−	0.0911282i
$266$	−14.3357	+	11.9886i	−0.878979	+	0.735068i
$267$	5.86456	+	26.5289i	0.358905	+	1.62354i
$268$	−1.48818	+	2.57760i	−0.0909049	+	0.157452i
$269$	−11.2244	+	19.4412i	−0.684361	+	1.18535i	0.289276	+	0.957246i	$0.406586\pi$
$269$	−11.2244	+	19.4412i	−0.684361	+	1.18535i	−0.973637	+	0.228103i	$0.926748\pi$
$270$	0.668926	+	5.15292i	0.0407095	+	0.313596i
$271$	−0.353310	+	0.203983i	−0.0214620	+	0.0123911i	−0.510693	−	0.859763i	$-0.670611\pi$
$271$	−0.353310	+	0.203983i	−0.0214620	+	0.0123911i	0.489231	+	0.872154i	$0.337278\pi$
$272$	1.26666	+	2.19392i	0.0768026	+	0.133026i
$273$	29.7642	+	3.98705i	1.80141	+	0.241307i
$274$	−4.63560	+	8.02909i	−0.280047	+	0.485055i
$275$			5.51168i			0.332367i
$276$	−7.12392	+	1.57483i	−0.428809	+	0.0947939i
$277$	25.7859			1.54932			0.774662	−	0.632376i	$-0.217920\pi$
$277$	25.7859			1.54932			0.774662	+	0.632376i	$0.217920\pi$
$278$	−1.78379	−	3.08961i	−0.106984	−	0.185302i
$279$	−18.4218	−	1.63406i	−1.10289	−	0.0978287i
$280$	−1.69729	−	2.02958i	−0.101432	−	0.121291i
$281$	11.9347	−	6.89052i	0.711966	−	0.411054i	−0.0998226	−	0.995005i	$-0.531828\pi$
$281$	11.9347	−	6.89052i	0.711966	−	0.411054i	0.811788	+	0.583952i	$0.198494\pi$
$282$	−9.11000	+	2.01388i	−0.542493	+	0.119925i
$283$	2.84397	−	1.64197i	0.169056	−	0.0976048i	−0.413084	−	0.910693i	$-0.635549\pi$
$283$	2.84397	−	1.64197i	0.169056	−	0.0976048i	0.582141	+	0.813088i	$0.302215\pi$
$284$	−12.8590	+	7.42414i	−0.763041	+	0.440542i
$285$	11.9457	−	2.64076i	0.707604	−	0.156425i
$286$	−31.2796	+	18.0593i	−1.84960	+	1.06787i
$287$	−2.70656	−	15.5001i	−0.159763	−	0.914939i
$288$	2.98827	+	0.265066i	0.176085	+	0.0156192i
$289$	5.29114	+	9.16452i	0.311243	+	0.539089i
$290$	7.26388			0.426550
$291$	0.385369	−	0.0851907i	0.0225907	−	0.00499397i
$292$			11.2778i			0.659981i
$293$	−5.22757	+	9.05442i	−0.305398	+	0.528965i	−0.977350	−	0.211630i	$-0.932123\pi$
$293$	−5.22757	+	9.05442i	−0.305398	+	0.528965i	0.671952	+	0.740595i	$0.265456\pi$
$294$	−10.2510	+	6.47426i	−0.597853	+	0.377587i
$295$	1.95873	+	3.39263i	0.114042	+	0.197526i
$296$	−1.74514	+	1.00755i	−0.101434	+	0.0585629i
$297$	−22.7527	+	17.3936i	−1.32025	+	1.00928i
$298$	−5.19521	+	8.99836i	−0.300950	+	0.521261i
$299$	13.8018	−	23.9054i	0.798179	−	1.38249i
$300$	0.373866	+	1.69122i	0.0215852	+	0.0976426i
$301$	−13.6573	−	4.99653i	−0.787192	−	0.287995i
$302$	7.59312	+	4.38389i	0.436935	+	0.252264i
$303$	4.57104	+	1.44427i	0.262599	+	0.0829712i
$304$		−	7.06338i		−	0.405112i
$305$	−0.512178	−	0.295706i	−0.0293272	−	0.0169321i
$306$	−7.57025	−	0.671499i	−0.432762	−	0.0383870i
$307$			32.9003i			1.87772i	0.344297	+	0.938861i	$0.388117\pi$
$307$			32.9003i			1.87772i	−0.344297	+	0.938861i	$0.611883\pi$
$308$	5.01026	−	13.6948i	0.285486	−	0.780334i
$309$	−1.72277	+	5.45248i	−0.0980050	+	0.310181i
$310$	−6.16472			−0.350133
$311$	12.9216	+	22.3808i	0.732715	+	1.26910i	0.955719	+	0.294282i	$0.0950804\pi$
$311$	12.9216	+	22.3808i	0.732715	+	1.26910i	−0.223004	+	0.974818i	$0.571586\pi$
$312$	−8.37294	+	7.66312i	−0.474025	+	0.433839i
$313$	−16.2102	−	9.35899i	−0.916257	−	0.529002i	−0.0338183	−	0.999428i	$-0.510767\pi$
$313$	−16.2102	−	9.35899i	−0.916257	−	0.529002i	−0.882439	+	0.470426i	$0.844100\pi$
$314$	−12.0022			−0.677322
$315$	7.90900	−	0.669129i	0.445622	−	0.0377011i
$316$	−1.23923			−0.0697124
$317$	−15.9904	−	9.23209i	−0.898113	−	0.518526i	−0.0215255	−	0.999768i	$-0.506852\pi$
$317$	−15.9904	−	9.23209i	−0.898113	−	0.518526i	−0.876587	+	0.481243i	$0.840186\pi$
$318$	−1.10923	−	5.01771i	−0.0622026	−	0.281379i
$319$	20.0181	+	34.6724i	1.12080	+	1.94128i
$320$	1.00000			0.0559017
$321$	9.40299	−	2.07865i	0.524824	−	0.116019i
$322$	1.91704	+	10.9786i	0.106832	+	0.611812i
$323$			17.8938i			0.995638i
$324$	−5.80168	+	6.88044i	−0.322315	+	0.382247i
$325$	−5.67516	−	3.27655i	−0.314801	−	0.181750i
$326$			10.8052i			0.598446i
$327$	23.3111	−	21.3348i	1.28910	−	1.17982i
$328$	5.15035	+	2.97356i	0.284381	+	0.164187i
$329$	2.45149	+	14.0393i	0.135155	+	0.774011i
$330$	−7.04231	+	6.44529i	−0.387666	+	0.354802i
$331$	−11.7514	+	20.3540i	−0.645913	+	1.11875i	0.338176	+	0.941083i	$0.390190\pi$
$331$	−11.7514	+	20.3540i	−0.645913	+	1.11875i	−0.984090	+	0.177672i	$0.943143\pi$
$332$	4.32347	−	7.48846i	0.237281	−	0.410983i
$333$	0.534138	−	6.02169i	0.0292706	−	0.329986i
$334$	−18.6830	+	10.7866i	−1.02229	+	0.590218i
$335$	−1.48818	−	2.57760i	−0.0813078	−	0.140829i
$336$	0.608421	−	4.54201i	0.0331921	−	0.247787i
$337$	−8.75258	+	15.1599i	−0.476783	+	0.825813i	−0.999646	−	0.0266040i	$-0.991531\pi$
$337$	−8.75258	+	15.1599i	−0.476783	+	0.825813i	0.522863	+	0.852417i	$0.324864\pi$
$338$		−	29.9432i		−	1.62869i
$339$	1.91071	+	2.08769i	0.103775	+	0.113388i
$340$	−2.53332			−0.137389
$341$	−16.9890	−	29.4258i	−0.920005	−	1.59350i
$342$	17.3433	+	12.1751i	0.937818	+	0.658352i
$343$	9.18016	+	16.0849i	0.495682	+	0.868504i
$344$	4.76018	−	2.74829i	0.256651	−	0.148178i
$345$	2.19811	−	6.95691i	0.118342	−	0.374547i
$346$	1.10805	−	0.639733i	0.0595691	−	0.0343923i
$347$	−8.88116	+	5.12754i	−0.476766	+	0.275261i	−0.719068	−	0.694940i	$-0.755431\pi$
$347$	−8.88116	+	5.12754i	−0.476766	+	0.275261i	0.242302	+	0.970201i	$0.422098\pi$
$348$	8.49429	+	9.28111i	0.455342	+	0.497520i
$349$	0.861681	−	0.497492i	0.0461247	−	0.0266301i	−0.476760	−	0.879033i	$-0.658189\pi$
$349$	0.861681	−	0.497492i	0.0461247	−	0.0266301i	0.522885	+	0.852403i	$0.324856\pi$
$350$	2.60632	−	0.455105i	0.139313	−	0.0243264i
$351$	−4.38354	−	33.7676i	−0.233976	−	1.80238i
$352$	2.75584	+	4.77326i	0.146887	+	0.254415i
$353$	13.3768			0.711976			0.355988	−	0.934491i	$-0.384144\pi$
$353$	13.3768			0.711976			0.355988	+	0.934491i	$0.384144\pi$
$354$	−2.04426	+	6.46998i	−0.108651	+	0.343876i
$355$		−	14.8483i		−	0.788065i
$356$	−7.84313	+	13.5847i	−0.415685	+	0.719988i
$357$	−1.54133	+	11.5064i	−0.0815756	+	0.608982i
$358$	−5.92708	−	10.2660i	−0.313256	−	0.542575i
$359$	−14.3453	+	8.28227i	−0.757116	+	0.437121i	−0.828259	−	0.560345i	$-0.810669\pi$
$359$	−14.3453	+	8.28227i	−0.757116	+	0.437121i	0.0711432	+	0.997466i	$0.477335\pi$
$360$	−1.72369	+	2.45538i	−0.0908463	+	0.129410i
$361$	15.4456	−	26.7526i	0.812929	−	1.40803i
$362$	6.65940	−	11.5344i	0.350010	−	0.606235i
$363$	−32.0052	−	10.1124i	−1.67984	−	0.530763i
$364$	11.1225	+	13.3001i	0.582979	+	0.697113i
$365$	−9.76683	−	5.63888i	−0.511219	−	0.295153i
$366$	−0.221109	−	1.00021i	−0.0115575	−	0.0522817i
$367$			11.4300i			0.596639i	0.954466	+	0.298319i	$0.0964260\pi$
$367$			11.4300i			0.596639i	−0.954466	+	0.298319i	$0.903574\pi$
$368$	−3.64795	−	2.10615i	−0.190163	−	0.109791i
$369$	−16.1788	+	7.52060i	−0.842236	+	0.391507i
$370$		−	2.01511i		−	0.104761i
$371$	−7.73273	+	1.35026i	−0.401463	+	0.0701020i
$372$	−7.20895	−	7.87670i	−0.373766	−	0.408388i
$373$	−23.5637			−1.22008			−0.610040	−	0.792371i	$-0.708847\pi$
$373$	−23.5637			−1.22008			−0.610040	+	0.792371i	$0.708847\pi$
$374$	−6.98143	−	12.0922i	−0.361001	−	0.625273i
$375$	−1.65157	−	0.521832i	−0.0852868	−	0.0269473i
$376$	−4.66497	−	2.69332i	−0.240578	−	0.138898i
$377$	−47.6010			−2.45158
$378$	10.1036	+	9.32291i	0.519675	+	0.479519i
$379$	17.5149			0.899678			0.449839	−	0.893110i	$-0.351481\pi$
$379$	17.5149			0.899678			0.449839	+	0.893110i	$0.351481\pi$
$380$	6.11706	+	3.53169i	0.313799	+	0.181172i
$381$	−18.5498	−	5.86101i	−0.950335	−	0.300269i
$382$	−4.09818	−	7.09826i	−0.209681	−	0.363179i
$383$	19.9087			1.01729			0.508645	−	0.860977i	$-0.330147\pi$
$383$	19.9087			1.01729			0.508645	+	0.860977i	$0.330147\pi$
$384$	1.16939	+	1.27771i	0.0596750	+	0.0652027i
$385$	9.35492	+	11.1864i	0.476771	+	0.570112i
$386$			2.99486i			0.152435i
$387$	−1.45696	+	16.4252i	−0.0740614	+	0.834942i
$388$	0.197336	+	0.113932i	0.0100182	+	0.00578403i
$389$			34.4294i			1.74564i	0.488044	+	0.872819i	$0.337711\pi$
$389$			34.4294i			1.74564i	−0.488044	+	0.872819i	$0.662289\pi$
$390$	−2.44998	−	11.0827i	−0.124060	−	0.561196i
$391$	9.24145	+	5.33555i	0.467360	+	0.269830i
$392$	−6.88958	−	1.23841i	−0.347976	−	0.0625493i
$393$	−6.88248	−	2.17459i	−0.347175	−	0.109694i
$394$	5.97136	−	10.3427i	0.300833	−	0.521057i
$395$	0.619617	−	1.07321i	0.0311763	−	0.0539990i
$396$	−16.4704	−	1.46096i	−0.827667	−	0.0734161i
$397$	−10.0202	+	5.78514i	−0.502897	+	0.290348i	−0.729909	−	0.683544i	$-0.760438\pi$
$397$	−10.0202	+	5.78514i	−0.502897	+	0.290348i	0.227012	+	0.973892i	$0.427104\pi$
$398$	1.58122	+	2.73876i	0.0792595	+	0.137282i
$399$	19.7627	−	25.6350i	0.989373	−	1.28335i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$			13.9512i			0.696687i	0.937367	+	0.348344i	$0.113256\pi$
$401$			13.9512i			0.696687i	−0.937367	+	0.348344i	$0.886744\pi$
$402$	1.55316	−	4.91567i	0.0774645	−	0.245171i
$403$	40.3981			2.01237
$404$	1.38385	+	2.39689i	0.0688489	+	0.119250i
$405$	−3.05780	−	8.46462i	−0.151943	−	0.420611i
$406$	14.7427	−	12.3289i	0.731665	−	0.611874i
$407$	9.61863	−	5.55332i	0.476778	−	0.275268i
$408$	−2.96244	−	3.23684i	−0.146662	−	0.160248i
$409$	−19.3854	+	11.1922i	−0.958546	+	0.553417i	−0.895725	−	0.444608i	$-0.853343\pi$
$409$	−19.3854	+	11.1922i	−0.958546	+	0.553417i	−0.0628208	+	0.998025i	$0.520010\pi$
$410$	−5.15035	+	2.97356i	−0.254358	+	0.146854i
$411$	4.83801	−	15.3121i	0.238641	−	0.755288i
$412$	−2.85909	+	1.65069i	−0.140857	+	0.0813239i
$413$	9.73368	+	3.56108i	0.478963	+	0.175229i
$414$	11.4593	−	5.32678i	0.563195	−	0.261797i
$415$	4.32347	+	7.48846i	0.212231	+	0.367594i
$416$	−6.55311			−0.321292
$417$	4.17187	+	4.55831i	0.204297	+	0.223221i
$418$			38.9311i			1.90418i
$419$	19.0389	−	32.9764i	0.930112	−	1.61100i	0.146985	−	0.989139i	$-0.453043\pi$
$419$	19.0389	−	32.9764i	0.930112	−	1.61100i	0.783127	−	0.621862i	$-0.213623\pi$
$420$	3.62928	+	2.79791i	0.177091	+	0.136524i
$421$	17.9992	+	31.1755i	0.877227	+	1.51940i	0.854371	+	0.519664i	$0.173943\pi$
$421$	17.9992	+	31.1755i	0.877227	+	1.51940i	0.0228566	+	0.999739i	$0.492724\pi$
$422$	−10.4628	+	6.04072i	−0.509323	+	0.294058i
$423$	14.6541	−	6.81184i	0.712506	−	0.331203i
$424$	1.48346	−	2.56943i	0.0720432	−	0.124782i
$425$	1.26666	−	2.19392i	0.0614421	−	0.106421i
$426$	18.9717	−	17.3634i	0.919184	−	0.841259i
$427$	−1.54141	+	0.269155i	−0.0745939	+	0.0130253i
$428$	4.81501	+	2.77994i	0.232742	+	0.134374i
$429$	46.1490	−	42.2367i	2.22809	−	2.03921i
$430$			5.49658i			0.265068i
$431$	23.2779	+	13.4395i	1.12126	+	0.647359i	0.941722	−	0.336392i	$-0.109207\pi$
$431$	23.2779	+	13.4395i	1.12126	+	0.647359i	0.179537	+	0.983751i	$0.442540\pi$
$432$	−5.15292	+	0.668926i	−0.247920	+	0.0321837i
$433$			26.3834i			1.26790i	0.773372	+	0.633952i	$0.218568\pi$
$433$			26.3834i			1.26790i	−0.773372	+	0.633952i	$0.781432\pi$
$434$	−12.5118	+	10.4633i	−0.600586	+	0.502255i
$435$	−12.2848	+	2.71572i	−0.589012	+	0.130209i
$436$	18.2445			0.873751
$437$	−14.8765	−	25.7669i	−0.711640	−	1.23260i
$438$	−4.21637	−	19.0732i	−0.201466	−	0.911351i
$439$	−21.6627	−	12.5070i	−1.03391	−	0.596926i	−0.115804	−	0.993272i	$-0.536945\pi$
$439$	−21.6627	−	12.5070i	−1.03391	−	0.596926i	−0.918101	+	0.396346i	$0.870278\pi$
$440$	−5.51168			−0.262759
$441$	14.9163	−	14.7819i	0.710298	−	0.703901i
$442$	16.6011			0.789635
$443$	−8.24251	−	4.75881i	−0.391613	−	0.226098i	0.291246	−	0.956648i	$-0.405930\pi$
$443$	−8.24251	−	4.75881i	−0.391613	−	0.226098i	−0.682859	+	0.730550i	$0.739264\pi$
$444$	2.57472	−	2.35644i	0.122191	−	0.111832i
$445$	−7.84313	−	13.5847i	−0.371800	−	0.643977i
$446$	15.8139			0.748810
$447$	5.42205	−	17.1605i	0.256454	−	0.811665i
$448$	2.02958	−	1.69729i	0.0958888	−	0.0801894i
$449$		−	26.9921i		−	1.27383i	−0.770932	−	0.636917i	$-0.780209\pi$
$449$		−	26.9921i		−	1.27383i	0.770932	−	0.636917i	$-0.219791\pi$
$450$	−1.26458	−	2.72045i	−0.0596128	−	0.128243i
$451$	−28.3871	−	16.3893i	−1.33670	−	0.771742i
$452$			1.63394i			0.0768540i
$453$	−14.4806	−	4.57531i	−0.680359	−	0.214967i
$454$	−1.84362	−	1.06442i	−0.0865256	−	0.0499556i
$455$	−17.0795	+	2.98235i	−0.800697	+	0.139815i
$456$	2.64076	+	11.9457i	0.123665	+	0.559410i
$457$	2.38587	−	4.13245i	0.111606	−	0.193308i	−0.804812	−	0.593530i	$-0.797734\pi$
$457$	2.38587	−	4.13245i	0.111606	−	0.193308i	0.916418	+	0.400222i	$0.131067\pi$
$458$	−10.1531	+	17.5856i	−0.474422	+	0.821723i
$459$	13.0540	−	1.69461i	0.609309	−	0.0790974i
$460$	3.64795	−	2.10615i	0.170087	−	0.0981996i
$461$	11.0704	+	19.1745i	0.515600	+	0.893046i	0.999836	+	0.0181082i	$0.00576434\pi$
$461$	11.0704	+	19.1745i	0.515600	+	0.893046i	−0.484236	+	0.874938i	$0.660902\pi$
$462$	−3.35342	+	25.0341i	−0.156015	+	1.16469i
$463$	10.8244	−	18.7483i	0.503051	−	0.871309i	−0.496943	−	0.867783i	$-0.665544\pi$
$463$	10.8244	−	18.7483i	0.503051	−	0.871309i	0.999994	−	0.00352608i	$-0.00112239\pi$
$464$			7.26388i			0.337217i
$465$	10.4259	−	2.30478i	0.483489	−	0.106882i
$466$	12.8892			0.597079
$467$	−1.97116	−	3.41416i	−0.0912146	−	0.157988i	0.816808	−	0.576910i	$-0.195742\pi$
$467$	−1.97116	−	3.41416i	−0.0912146	−	0.157988i	−0.908022	+	0.418921i	$0.862408\pi$
$468$	11.2955	−	16.0904i	0.522135	−	0.743778i
$469$	−7.39531	−	2.70558i	−0.341484	−	0.124932i
$470$	4.66497	−	2.69332i	0.215179	−	0.124234i
$471$	20.2983	−	4.48721i	0.935297	−	0.206760i
$472$	−3.39263	+	1.95873i	−0.156158	+	0.0901580i
$473$	−26.2366	+	15.1477i	−1.20636	+	0.696491i
$474$	2.09582	−	0.463308i	0.0962641	−	0.0212804i
$475$	−6.11706	+	3.53169i	−0.280670	+	0.162045i
$476$	−5.14159	+	4.29978i	−0.235664	+	0.197080i
$477$	3.75191	+	8.07135i	0.171788	+	0.369562i
$478$	0.560223	+	0.970335i	0.0256240	+	0.0443821i
$479$	6.94520			0.317334			0.158667	−	0.987332i	$-0.449280\pi$
$479$	6.94520			0.317334			0.158667	+	0.987332i	$0.449280\pi$
$480$	−1.69122	+	0.373866i	−0.0771933	+	0.0170646i
$481$			13.2052i			0.602106i
$482$	−0.726116	+	1.25767i	−0.0330737	+	0.0572853i
$483$	−7.34664	−	17.8505i	−0.334284	−	0.812224i
$484$	−9.68931	−	16.7824i	−0.440423	−	0.762836i
$485$	−0.197336	+	0.113932i	−0.00896058	+	0.00517339i
$486$	7.23955	−	13.8054i	0.328393	−	0.626225i
$487$	−9.68011	+	16.7664i	−0.438648	+	0.759760i	−0.997585	−	0.0694495i	$-0.977876\pi$
$487$	−9.68011	+	16.7664i	−0.438648	+	0.759760i	0.558938	+	0.829210i	$0.311209\pi$
$488$	0.295706	−	0.512178i	0.0133860	−	0.0231852i
$489$	−4.03971	−	18.2740i	−0.182682	−	0.826380i
$490$	4.51729	−	5.34735i	0.204070	−	0.241569i
$491$	−23.8914	−	13.7937i	−1.07820	−	0.622500i	−0.147792	−	0.989019i	$-0.547216\pi$
$491$	−23.8914	−	13.7937i	−1.07820	−	0.622500i	−0.930411	+	0.366518i	$0.880550\pi$
$492$	−9.82209	−	3.10340i	−0.442814	−	0.139912i
$493$		−	18.4018i		−	0.828774i
$494$	−40.0858	−	23.1435i	−1.80354	−	1.04128i
$495$	9.50042	−	13.5333i	0.427012	−	0.608276i
$496$		−	6.16472i		−	0.276804i
$497$	−25.2019	−	30.1358i	−1.13046	−	1.35178i
$498$	−4.51225	+	14.2810i	−0.202199	+	0.639949i
$499$	15.6163			0.699080			0.349540	−	0.936921i	$-0.386338\pi$
$499$	15.6163			0.699080			0.349540	+	0.936921i	$0.386338\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	27.5643	−	25.2275i	1.23148	−	1.12708i
$502$	−12.7964	−	7.38800i	−0.571131	−	0.329743i
$503$	−1.51651			−0.0676180			−0.0338090	−	0.999428i	$-0.510764\pi$
$503$	−1.51651			−0.0676180			−0.0338090	+	0.999428i	$0.510764\pi$
$504$	0.669129	+	7.90900i	0.0298054	+	0.352295i
$505$	−2.76769			−0.123161
$506$	20.1064	+	11.6084i	0.893837	+	0.516057i
$507$	11.1947	+	50.6405i	0.497176	+	2.24902i
$508$	−5.61580	−	9.72685i	−0.249161	−	0.431559i
$509$	−2.70222			−0.119774			−0.0598869	−	0.998205i	$-0.519074\pi$
$509$	−2.70222			−0.119774			−0.0598869	+	0.998205i	$0.519074\pi$
$510$	4.28441	−	0.947123i	0.189717	−	0.0419393i
$511$	−29.3934	+	5.13257i	−1.30029	+	0.227051i
$512$			1.00000i			0.0441942i
$513$	−33.8832	−	14.1066i	−1.49598	−	0.622823i
$514$	15.4025	+	8.89265i	0.679376	+	0.392238i
$515$		−	3.30139i		−	0.145477i
$516$	−7.02301	+	6.42763i	−0.309171	+	0.282961i
$517$	25.7118	+	14.8447i	1.13081	+	0.652871i
$518$	−3.42023	−	4.08983i	−0.150276	−	0.179697i
$519$	−1.63478	+	1.49619i	−0.0717589	+	0.0656755i
$520$	3.27655	−	5.67516i	0.143686	−	0.248872i
$521$	8.63108	−	14.9495i	0.378134	−	0.654948i	−0.612656	−	0.790349i	$-0.709899\pi$
$521$	8.63108	−	14.9495i	0.378134	−	0.654948i	0.990791	+	0.135401i	$0.0432324\pi$
$522$	−17.8356	−	12.5207i	−0.780643	−	0.548015i
$523$	−34.8556	+	20.1239i	−1.52413	+	0.879956i	−0.524536	+	0.851388i	$0.675761\pi$
$523$	−34.8556	+	20.1239i	−1.52413	+	0.879956i	−0.999592	+	0.0285673i	$0.990906\pi$
$524$	−2.08361	−	3.60893i	−0.0910231	−	0.157657i
$525$	−4.23770	+	1.74410i	−0.184949	+	0.0761186i
$526$	−3.85865	+	6.68338i	−0.168245	+	0.291409i
$527$			15.6172i			0.680297i
$528$	−6.44529	−	7.04231i	−0.280495	−	0.306477i
$529$	5.25657			0.228547
$530$	1.48346	+	2.56943i	0.0644374	+	0.111609i
$531$	1.03839	−	11.7064i	0.0450623	−	0.508016i
$532$	18.4094	−	3.21458i	0.798148	−	0.139370i
$533$	33.7508	−	19.4860i	1.46191	−	0.844034i
$534$	8.18560	−	25.9070i	0.354226	−	1.12111i
$535$	−4.81501	+	2.77994i	−0.208171	+	0.120187i
$536$	2.57760	−	1.48818i	0.111335	−	0.0642795i
$537$	13.8621	+	15.1461i	0.598194	+	0.653604i
$538$	19.4412	−	11.2244i	0.838168	−	0.483917i
$539$	37.9732	+	6.82573i	1.63562	+	0.294005i
$540$	1.99715	−	4.79702i	0.0859437	−	0.206431i
$541$	−9.02742	−	15.6359i	−0.388119	−	0.672242i	0.604077	−	0.796926i	$-0.293542\pi$
$541$	−9.02742	−	15.6359i	−0.388119	−	0.672242i	−0.992197	+	0.124684i	$0.960208\pi$
$542$	0.407967			0.0175237
$543$	−6.95018	+	21.9970i	−0.298261	+	0.943980i
$544$		−	2.53332i		−	0.108615i
$545$	−9.12223	+	15.8002i	−0.390753	+	0.676805i
$546$	−23.7831	−	18.3350i	−1.01782	−	0.784666i
$547$	−17.3408	−	30.0351i	−0.741438	−	1.28421i	−0.951841	−	0.306593i	$-0.900811\pi$
$547$	−17.3408	−	30.0351i	−0.741438	−	1.28421i	0.210403	−	0.977615i	$-0.432523\pi$
$548$	8.02909	−	4.63560i	0.342986	−	0.198023i
$549$	0.747887	+	1.60891i	0.0319190	+	0.0686664i
$550$	2.75584	−	4.77326i	0.117509	−	0.203532i
$551$	−25.6538	+	44.4336i	−1.09289	+	1.89294i
$552$	6.95691	+	2.19811i	0.296106	+	0.0935578i
$553$	−0.563982	−	3.22984i	−0.0239830	−	0.137347i
$554$	−22.3312	−	12.8929i	−0.948763	−	0.547769i
$555$	0.753381	+	3.40799i	0.0319792	+	0.144661i
$556$			3.56757i			0.151299i
$557$	22.4858	+	12.9822i	0.952753	+	0.550072i	0.893935	−	0.448196i	$-0.147934\pi$
$557$	22.4858	+	12.9822i	0.952753	+	0.550072i	0.0588180	+	0.998269i	$0.481267\pi$
$558$	15.1367	+	10.6261i	0.640790	+	0.449837i
$559$		−	36.0196i		−	1.52347i
$560$	0.455105	+	2.60632i	0.0192317	+	0.110137i
$561$	16.3280	+	17.8404i	0.689369	+	0.753224i
$562$	−13.7810			−0.581318
$563$	−5.60094	−	9.70110i	−0.236051	−	0.408853i	0.723526	−	0.690297i	$-0.242520\pi$
$563$	−5.60094	−	9.70110i	−0.236051	−	0.408853i	−0.959578	+	0.281444i	$0.909187\pi$
$564$	8.89643	+	2.81093i	0.374607	+	0.118361i
$565$	−1.41503	−	0.816970i	−0.0595309	−	0.0343702i
$566$	−3.28393			−0.138034
$567$	−20.5730	−	11.9897i	−0.863984	−	0.503519i
$568$	14.8483			0.623020
$569$	8.70803	+	5.02758i	0.365059	+	0.210767i	0.671298	−	0.741188i	$-0.265737\pi$
$569$	8.70803	+	5.02758i	0.365059	+	0.210767i	−0.306238	+	0.951955i	$0.599070\pi$
$570$	−11.6657	−	3.68590i	−0.488621	−	0.154385i
$571$	−0.983905	−	1.70417i	−0.0411752	−	0.0713175i	0.844703	−	0.535235i	$-0.179777\pi$
$571$	−0.983905	−	1.70417i	−0.0411752	−	0.0713175i	−0.885879	+	0.463917i	$0.846443\pi$
$572$	36.1186			1.51020
$573$	9.58473	+	10.4726i	0.400408	+	0.437497i
$574$	−5.40608	+	14.7767i	−0.225645	+	0.616768i
$575$			4.21229i			0.175665i
$576$	−2.45538	−	1.72369i	−0.102308	−	0.0718203i
$577$	−20.3522	−	11.7503i	−0.847272	−	0.489173i	0.0124575	−	0.999922i	$-0.496035\pi$
$577$	−20.3522	−	11.7503i	−0.847272	−	0.489173i	−0.859729	+	0.510750i	$0.829368\pi$
$578$		−	10.5823i		−	0.440165i
$579$	−1.11968	−	5.06497i	−0.0465322	−	0.210493i
$580$	−6.29071	−	3.63194i	−0.261207	−	0.150808i
$581$	21.4849	+	7.86028i	0.891345	+	0.326099i
$582$	−0.376334	−	0.118907i	−0.0155996	−	0.00492885i
$583$	−8.17636	+	14.1619i	−0.338630	+	0.586525i
$584$	5.63888	−	9.76683i	0.233339	−	0.404154i
$585$	8.28692	+	17.8274i	0.342622	+	0.737072i
$586$	9.05442	−	5.22757i	0.374035	−	0.215949i
$587$	−6.90407	−	11.9582i	−0.284962	−	0.493568i	0.687638	−	0.726053i	$-0.258648\pi$
$587$	−6.90407	−	11.9582i	−0.284962	−	0.493568i	−0.972600	+	0.232485i	$0.925314\pi$
$588$	12.1148	−	0.481354i	0.499606	−	0.0198507i
$589$	21.7719	−	37.7100i	0.897094	−	1.55381i
$590$		−	3.91747i		−	0.161280i
$591$	−6.23209	+	19.7242i	−0.256354	+	0.811347i
$592$	2.01511			0.0828205
$593$	14.5740	+	25.2428i	0.598480	+	1.03660i	0.993046	+	0.117731i	$0.0375619\pi$
$593$	14.5740	+	25.2428i	0.598480	+	1.03660i	−0.394565	+	0.918868i	$0.629105\pi$
$594$	28.4012	−	3.68691i	1.16532	−	0.151276i
$595$	−1.15293	−	6.60264i	−0.0472654	−	0.270682i
$596$	8.99836	−	5.19521i	0.368587	−	0.212804i
$597$	−3.69812	−	4.04068i	−0.151354	−	0.165374i
$598$	−23.9054	+	13.8018i	−0.977566	+	0.564398i
$599$	−1.79110	+	1.03409i	−0.0731824	+	0.0422519i	−0.536145	−	0.844126i	$-0.680120\pi$
$599$	−1.79110	+	1.03409i	−0.0731824	+	0.0422519i	0.462962	+	0.886378i	$0.346787\pi$
$600$	0.521832	−	1.65157i	0.0213037	−	0.0674252i
$601$	−16.7765	+	9.68589i	−0.684326	+	0.395096i	−0.801483	−	0.598018i	$-0.795955\pi$
$601$	−16.7765	+	9.68589i	−0.684326	+	0.395096i	0.117157	+	0.993113i	$0.462622\pi$
$602$	9.32929	+	11.1558i	0.380233	+	0.454675i
$603$	−0.788932	+	8.89414i	−0.0321278	+	0.362198i
$604$	−4.38389	−	7.59312i	−0.178378	−	0.308960i
$605$	19.3786			0.787853
$606$	−3.23650	−	3.53630i	−0.131474	−	0.143652i
$607$			36.2789i			1.47252i	0.676701	+	0.736258i	$0.263409\pi$
$607$			36.2789i			1.47252i	−0.676701	+	0.736258i	$0.736591\pi$
$608$	−3.53169	+	6.11706i	−0.143229	+	0.248080i
$609$	−20.3237	+	26.3627i	−0.823558	+	1.06827i
$610$	0.295706	+	0.512178i	0.0119728	+	0.0207375i
$611$	−30.5701	+	17.6496i	−1.23673	+	0.714027i
$612$	6.22028	+	4.36666i	0.251440	+	0.176512i
$613$	10.2743	−	17.7956i	0.414974	−	0.718756i	−0.580452	−	0.814295i	$-0.697124\pi$
$613$	10.2743	−	17.7956i	0.414974	−	0.718756i	0.995426	+	0.0955386i	$0.0304573\pi$
$614$	16.4502	−	28.4925i	0.663875	−	1.14986i
$615$	7.59866	−	6.95448i	0.306408	−	0.280432i
$616$	−11.1864	+	9.35492i	−0.450713	+	0.376921i
$617$	31.4987	+	18.1858i	1.26809	+	0.732132i	0.974626	−	0.223838i	$-0.0718588\pi$
$617$	31.4987	+	18.1858i	1.26809	+	0.732132i	0.293463	+	0.955970i	$0.405192\pi$
$618$	4.21820	−	3.86060i	0.169681	−	0.155296i
$619$		−	48.3608i		−	1.94378i	−0.235426	−	0.971892i	$-0.575649\pi$
$619$		−	48.3608i		−	1.94378i	0.235426	−	0.971892i	$-0.424351\pi$
$620$	5.33881	+	3.08236i	0.214412	+	0.123791i
$621$	−17.3887	+	13.2930i	−0.697786	+	0.533430i
$622$		−	25.8431i		−	1.03622i
$623$	−38.9755	−	14.2592i	−1.56152	−	0.571283i
$624$	11.0827	−	2.44998i	0.443665	−	0.0980778i
$625$	1.00000			0.0400000
$626$	9.35899	+	16.2102i	0.374061	+	0.647892i
$627$	−14.5550	−	65.8410i	−0.581271	−	2.62944i
$628$	10.3942	+	6.00109i	0.414773	+	0.239470i
$629$	−5.10492			−0.203547
$630$	−7.18396	−	3.37502i	−0.286216	−	0.134464i
$631$	−33.2300			−1.32287			−0.661433	−	0.750004i	$-0.730051\pi$
$631$	−33.2300			−1.32287			−0.661433	+	0.750004i	$0.730051\pi$
$632$	1.07321	+	0.619617i	0.0426900	+	0.0246471i
$633$	15.4365	−	14.1279i	0.613547	−	0.561533i
$634$	9.23209	+	15.9904i	0.366653	+	0.635062i
$635$	11.2316			0.445712
$636$	−1.54824	+	4.90008i	−0.0613915	+	0.194301i
$637$	−29.6023	+	35.0417i	−1.17288	+	1.38840i
$638$		−	40.0362i		−	1.58505i
$639$	−25.5938	+	36.4582i	−1.01248	+	1.44226i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$			10.7186i			0.423359i	0.977339	+	0.211679i	$0.0678932\pi$
$641$			10.7186i			0.423359i	−0.977339	+	0.211679i	$0.932107\pi$
$642$	−9.18256	−	2.90133i	−0.362407	−	0.114506i
$643$	22.4608	+	12.9678i	0.885768	+	0.511398i	0.872556	−	0.488515i	$-0.162461\pi$
$643$	22.4608	+	12.9678i	0.885768	+	0.511398i	0.0132119	+	0.999913i	$0.495794\pi$
$644$	3.82908	−	10.4662i	0.150887	−	0.412428i
$645$	−2.05498	−	9.29592i	−0.0809149	−	0.366026i
$646$	8.94691	−	15.4965i	0.352011	−	0.609702i
$647$	−0.701476	+	1.21499i	−0.0275779	+	0.0477663i	−0.879485	−	0.475927i	$-0.842113\pi$
$647$	−0.701476	+	1.21499i	−0.0275779	+	0.0477663i	0.851907	+	0.523693i	$0.175446\pi$
$648$	8.46462	−	3.05780i	0.332522	−	0.120122i
$649$	18.6991	−	10.7959i	0.734003	−	0.423777i
$650$	3.27655	+	5.67516i	0.128517	+	0.222598i
$651$	17.2483	−	22.3735i	0.676016	−	0.876887i
$652$	5.40261	−	9.35760i	0.211583	−	0.366472i
$653$			23.6102i			0.923939i	0.886896	+	0.461969i	$0.152857\pi$
$653$			23.6102i			0.923939i	−0.886896	+	0.461969i	$0.847143\pi$
$654$	−30.8554	+	6.82099i	−1.20654	+	0.266722i
$655$	4.16723			0.162827
$656$	−2.97356	−	5.15035i	−0.116098	−	0.201087i
$657$	14.2616	+	30.6806i	0.556399	+	1.19696i
$658$	4.89660	−	13.3841i	0.190889	−	0.521768i
$659$	−9.61215	+	5.54958i	−0.374436	+	0.216181i	−0.675395	−	0.737456i	$-0.736027\pi$
$659$	−9.61215	+	5.54958i	−0.374436	+	0.216181i	0.300958	+	0.953637i	$0.402693\pi$
$660$	9.32146	−	2.06063i	0.362837	−	0.0802099i
$661$	27.2557	−	15.7361i	1.06012	−	0.612063i	0.134657	−	0.990892i	$-0.457007\pi$
$661$	27.2557	−	15.7361i	1.06012	−	0.612063i	0.925466	+	0.378830i	$0.123673\pi$
$662$	20.3540	−	11.7514i	0.791079	−	0.456730i
$663$	−28.0762	+	6.20660i	−1.09039	+	0.241044i
$664$	−7.48846	+	4.32347i	−0.290609	+	0.167783i
$665$	−6.42079	+	17.5503i	−0.248987	+	0.680571i
$666$	−3.47342	+	4.94786i	−0.134592	+	0.191726i
$667$	15.2988	+	26.4983i	0.592372	+	1.02602i
$668$	21.5733			0.834695
$669$	−26.7448	+	5.91228i	−1.03401	+	0.228582i
$670$			2.97636i			0.114987i
$671$	−1.62984	+	2.82296i	−0.0629192	+	0.108979i
$672$	−2.79791	+	3.62928i	−0.107932	+	0.140003i
$673$	14.7243	+	25.5033i	0.567580	+	0.983078i	0.996804	+	0.0798801i	$0.0254538\pi$
$673$	14.7243	+	25.5033i	0.567580	+	0.983078i	−0.429224	+	0.903198i	$0.641213\pi$
$674$	15.1599	−	8.75258i	0.583938	−	0.337137i
$675$	3.15576	+	4.12809i	0.121465	+	0.158890i
$676$	−14.9716	+	25.9316i	−0.575831	+	0.997368i
$677$	5.29070	−	9.16376i	0.203338	−	0.352192i	−0.746264	−	0.665650i	$-0.768154\pi$
$677$	5.29070	−	9.16376i	0.203338	−	0.352192i	0.949602	+	0.313458i	$0.101488\pi$
$678$	−0.610874	−	2.76335i	−0.0234605	−	0.106126i
$679$	−0.207134	+	0.566172i	−0.00794909	+	0.0217277i
$680$	2.19392	+	1.26666i	0.0841331	+	0.0485743i
$681$	3.51592	+	1.11089i	0.134730	+	0.0425696i
$682$			33.9780i			1.30108i
$683$	16.4839	+	9.51701i	0.630741	+	0.364158i	0.781039	−	0.624482i	$-0.214690\pi$
$683$	16.4839	+	9.51701i	0.630741	+	0.364158i	−0.150298	+	0.988641i	$0.548023\pi$
$684$	−8.93220	−	19.2156i	−0.341531	−	0.734725i
$685$			9.27120i			0.354234i
$686$	0.0922085	−	18.5200i	0.00352054	−	0.707098i
$687$	10.5964	−	33.5371i	0.404278	−	1.27952i
$688$	−5.49658			−0.209555
$689$	−9.72127	−	16.8377i	−0.370351	−	0.641467i
$690$	−5.38208	+	4.92580i	−0.204892	+	0.187522i
$691$	−1.91825	−	1.10750i	−0.0729735	−	0.0421313i	0.463069	−	0.886322i	$-0.346748\pi$
$691$	−1.91825	−	1.10750i	−0.0729735	−	0.0421313i	−0.536043	+	0.844191i	$0.680081\pi$
$692$	−1.27947			−0.0486380
$693$	−3.68802	−	43.5919i	−0.140096	−	1.65592i
$694$	10.2551			0.389278
$695$	−3.08961	−	1.78379i	−0.117195	−	0.0676628i
$696$	−2.71572	−	12.2848i	−0.102939	−	0.465655i
$697$	7.53298	+	13.0475i	0.285332	+	0.494209i
$698$	−0.994983			−0.0376607
$699$	−21.7984	+	4.81882i	−0.824491	+	0.182264i
$700$	−2.48469	−	0.909025i	−0.0939124	−	0.0343579i
$701$		−	14.6720i		−	0.554154i	−0.960848	−	0.277077i	$-0.910634\pi$
$701$		−	14.6720i		−	0.554154i	0.960848	−	0.277077i	$-0.0893656\pi$
$702$	−13.0875	+	31.4354i	−0.493957	+	1.18645i
$703$	12.3266	+	7.11674i	0.464905	+	0.268413i
$704$		−	5.51168i		−	0.207729i
$705$	−6.88255	+	6.29907i	−0.259212	+	0.237237i
$706$	−11.5847	−	6.68840i	−0.435994	−	0.251721i
$707$	−5.61726	+	4.69757i	−0.211259	+	0.176670i
$708$	5.00537	−	4.58104i	0.188113	−	0.172166i
$709$	14.5615	−	25.2213i	0.546870	−	0.947207i	−0.451617	−	0.892212i	$-0.649152\pi$
$709$	14.5615	−	25.2213i	0.546870	−	0.947207i	0.998487	−	0.0549947i	$-0.0175142\pi$
$710$	−7.42414	+	12.8590i	−0.278623	+	0.482589i
$711$	−3.37127	+	1.56711i	−0.126433	+	0.0587712i
$712$	13.5847	−	7.84313i	0.509108	−	0.293934i
$713$	−12.9838	−	22.4886i	−0.486248	−	0.842205i
$714$	7.08801	−	9.19415i	0.265262	−	0.344082i
$715$	−18.0593	+	31.2796i	−0.675380	+	1.16979i
$716$			11.8542i			0.443010i
$717$	−1.31024	−	1.43160i	−0.0489317	−	0.0534641i
$718$	16.5645			0.618183
$719$	−17.5750	−	30.4408i	−0.655438	−	1.13525i	−0.981784	−	0.190001i	$-0.939151\pi$
$719$	−17.5750	−	30.4408i	−0.655438	−	1.13525i	0.326346	−	0.945250i	$-0.394183\pi$
$720$	2.72045	−	1.26458i	0.101385	−	0.0471281i
$721$	−5.60341	−	6.70044i	−0.208682	−	0.249537i
$722$	−26.7526	+	15.4456i	−0.995630	+	0.574827i
$723$	0.757822	−	2.39847i	0.0281837	−	0.0891999i
$724$	−11.5344	+	6.65940i	−0.428673	+	0.247495i
$725$	6.29071	−	3.63194i	0.233631	−	0.134887i
$726$	22.6611	+	24.7602i	0.841033	+	0.918937i
$727$	12.6948	−	7.32936i	0.470825	−	0.271831i	−0.245760	−	0.969331i	$-0.579038\pi$
$727$	12.6948	−	7.32936i	0.470825	−	0.271831i	0.716585	+	0.697500i	$0.245704\pi$
$728$	−2.98235	−	17.0795i	−0.110533	−	0.633007i
$729$	−7.08230	+	26.0546i	−0.262307	+	0.964984i
$730$	5.63888	+	9.76683i	0.208704	+	0.361487i
$731$	13.9246			0.515020
$732$	−0.308618	+	0.976760i	−0.0114068	+	0.0361021i
$733$		−	25.3896i		−	0.937785i	−0.883255	−	0.468893i	$-0.844653\pi$
$733$		−	25.3896i		−	0.937785i	0.883255	−	0.468893i	$-0.155347\pi$
$734$	5.71498	−	9.89863i	0.210944	−	0.365365i
$735$	−5.64053	+	10.7324i	−0.208054	+	0.395870i
$736$	2.10615	+	3.64795i	0.0776336	+	0.134465i
$737$	−14.2069	+	8.20236i	−0.523318	+	0.302138i
$738$	17.7716	+	1.57638i	0.654180	+	0.0580274i
$739$	6.28334	−	10.8831i	0.231136	−	0.400340i	−0.727006	−	0.686631i	$-0.759089\pi$
$739$	6.28334	−	10.8831i	0.231136	−	0.400340i	0.958143	+	0.286291i	$0.0924223\pi$
$740$	−1.00755	+	1.74514i	−0.0370385	+	0.0641525i
$741$	76.4464	+	24.1541i	2.80833	+	0.887322i
$742$	7.37187	+	2.69701i	0.270630	+	0.0990102i
$743$	−15.1504	−	8.74709i	−0.555814	−	0.320899i	0.195650	−	0.980674i	$-0.437318\pi$
$743$	−15.1504	−	8.74709i	−0.555814	−	0.320899i	−0.751464	+	0.659774i	$0.770652\pi$
$744$	2.30478	+	10.4259i	0.0844973	+	0.382232i
$745$			10.3904i			0.380675i
$746$	20.4067	+	11.7818i	0.747143	+	0.431363i
$747$	2.29201	−	25.8393i	0.0838603	−	0.945412i
$748$			13.9629i			0.510533i
$749$	−5.05408	+	13.8146i	−0.184672	+	0.504774i
$750$	1.16939	+	1.27771i	0.0427000	+	0.0466552i
$751$	−32.8476			−1.19863			−0.599313	−	0.800515i	$-0.704560\pi$
$751$	−32.8476			−1.19863			−0.599313	+	0.800515i	$0.704560\pi$
$752$	2.69332	+	4.66497i	0.0982154	+	0.170114i
$753$	24.4036	+	7.71060i	0.889318	+	0.280990i
$754$	41.2237	+	23.8005i	1.50128	+	0.866763i
$755$	8.76778			0.319092
$756$	−4.08855	−	13.1257i	−0.148699	−	0.477377i
$757$	−34.4952			−1.25375			−0.626874	−	0.779120i	$-0.715666\pi$
$757$	−34.4952			−1.25375			−0.626874	+	0.779120i	$0.715666\pi$
$758$	−15.1683	−	8.75743i	−0.550938	−	0.318084i
$759$	−38.3443	−	12.1153i	−1.39181	−	0.439757i
$760$	−3.53169	−	6.11706i	−0.128108	−	0.221889i
$761$	41.8797			1.51814			0.759069	−	0.651010i	$-0.225654\pi$
$761$	41.8797			1.51814			0.759069	+	0.651010i	$0.225654\pi$
$762$	13.1341	+	14.3507i	0.475798	+	0.519870i
$763$	8.30315	+	47.5508i	0.300594	+	1.72146i
$764$			8.19637i			0.296534i
$765$	−6.89177	+	3.20359i	−0.249173	+	0.115826i
$766$	−17.2415	−	9.95437i	−0.622960	−	0.359666i
$767$			25.6716i			0.926947i
$768$	−0.373866	−	1.69122i	−0.0134907	−	0.0610266i
$769$	40.9461	+	23.6402i	1.47655	+	0.852489i	0.999650	−	0.0264667i	$-0.00842558\pi$
$769$	40.9461	+	23.6402i	1.47655	+	0.852489i	0.476904	+	0.878955i	$0.341759\pi$
$770$	−2.50839	−	14.3652i	−0.0903962	−	0.517685i
$771$	−29.3737	−	9.28094i	−1.05787	−	0.334245i
$772$	1.49743	−	2.59363i	0.0538937	−	0.0933467i
$773$	3.88458	−	6.72829i	0.139719	−	0.242000i	−0.787671	−	0.616096i	$-0.788713\pi$
$773$	3.88458	−	6.72829i	0.139719	−	0.242000i	0.927390	+	0.374096i	$0.122047\pi$
$774$	9.47438	−	13.4962i	0.340550	−	0.485111i
$775$	−5.33881	+	3.08236i	−0.191776	+	0.110722i
$776$	−0.113932	−	0.197336i	−0.00408993	−	0.00708396i
$777$	7.31340	+	5.63810i	0.262367	+	0.202266i
$778$	17.2147	−	29.8167i	0.617176	−	1.06898i
$779$		−	42.0067i		−	1.50505i
$780$	−3.41962	+	10.8229i	−0.122442	+	0.387523i
$781$	−81.8390			−2.92843
$782$	−5.33555	−	9.24145i	−0.190799	−	0.330473i
$783$	34.8450	+	14.5071i	1.24526	+	0.518440i
$784$	5.34735	+	4.51729i	0.190977	+	0.161332i
$785$	−10.3942	+	6.00109i	−0.370985	+	0.214188i
$786$	4.87310	+	5.32449i	0.173818	+	0.189918i
$787$	24.8482	−	14.3461i	0.885743	−	0.511384i	0.0131953	−	0.999913i	$-0.495800\pi$
$787$	24.8482	−	14.3461i	0.885743	−	0.511384i	0.872548	+	0.488529i	$0.162466\pi$
$788$	−10.3427	+	5.97136i	−0.368443	+	0.212721i
$789$	4.02714	−	12.7457i	0.143370	−	0.453758i
$790$	−1.07321	+	0.619617i	−0.0381831	+	0.0220450i
$791$	−4.25856	+	0.743614i	−0.151417	+	0.0264399i
$792$	13.5333	+	9.50042i	0.480884	+	0.337583i
$793$	−1.93779	−	3.35635i	−0.0688130	−	0.119188i
$794$	11.5703			0.410614
$795$	−3.46948	−	3.79085i	−0.123050	−	0.134448i
$796$		−	3.16245i		−	0.112090i
$797$	−18.1502	+	31.4371i	−0.642914	+	1.11356i	0.341866	+	0.939749i	$0.388941\pi$
$797$	−18.1502	+	31.4371i	−0.642914	+	1.11356i	−0.984779	+	0.173810i	$0.944392\pi$
$798$	−29.9325	+	12.3192i	−1.05960	+	0.436095i
$799$	−6.82306	−	11.8179i	−0.241382	−	0.418087i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	−4.15790	+	46.8748i	−0.146912	+	1.65624i
$802$	6.97558	−	12.0821i	0.246316	−	0.426632i
$803$	−31.0797	+	53.8316i	−1.09678	+	1.89968i
$804$	−3.80291	+	3.48051i	−0.134118	+	0.122748i
$805$	7.14949	+	8.54920i	0.251986	+	0.301320i
$806$	−34.9858	−	20.1990i	−1.23232	−	0.711481i
$807$	−28.6829	+	26.2512i	−1.00968	+	0.924088i
$808$		−	2.76769i		−	0.0973670i
$809$	27.0602	+	15.6232i	0.951384	+	0.549282i	0.893511	−	0.449042i	$-0.148235\pi$
$809$	27.0602	+	15.6232i	0.951384	+	0.549282i	0.0578737	+	0.998324i	$0.481568\pi$
$810$	−1.58418	+	8.85948i	−0.0556624	+	0.311290i
$811$		−	21.8513i		−	0.767304i	−0.923478	−	0.383652i	$-0.874666\pi$
$811$		−	21.8513i		−	0.767304i	0.923478	−	0.383652i	$-0.125334\pi$
$812$	−18.9320	+	3.30583i	−0.664382	+	0.116012i
$813$	−0.689962	+	0.152525i	−0.0241980	+	0.00534928i
$814$	−11.1066			−0.389288
$815$	5.40261	+	9.35760i	0.189245	+	0.327783i
$816$	0.947123	+	4.28441i	0.0331560	+	0.149984i
$817$	−33.6229	−	19.4122i	−1.17632	−	0.679147i
$818$	22.3843			0.782650
$819$	47.0772	+	22.1168i	1.64501	+	0.772825i
$820$	5.94711			0.207682
$821$	−46.4550	−	26.8208i	−1.62129	−	0.936052i	−0.986576	−	0.163304i	$-0.947785\pi$
$821$	−46.4550	−	26.8208i	−1.62129	−	0.936052i	−0.634713	−	0.772748i	$-0.718882\pi$
$822$	−11.8459	+	10.8416i	−0.413172	+	0.378145i
$823$	−25.8325	−	44.7432i	−0.900464	−	1.55965i	−0.826894	−	0.562359i	$-0.809894\pi$
$823$	−25.8325	−	44.7432i	−0.900464	−	1.55965i	−0.0735700	−	0.997290i	$-0.523439\pi$
$824$	3.30139			0.115009
$825$	−2.87617	+	9.10294i	−0.100136	+	0.316924i
$826$	−6.64908	−	7.95082i	−0.231351	−	0.276645i
$827$			4.96328i			0.172590i	0.996270	+	0.0862950i	$0.0275028\pi$
$827$			4.96328i			0.172590i	−0.996270	+	0.0862950i	$0.972497\pi$
$828$	−12.5875	−	1.11654i	−0.437445	−	0.0388024i
$829$	−29.7958	−	17.2026i	−1.03485	−	0.597471i	−0.116480	−	0.993193i	$-0.537161\pi$
$829$	−29.7958	−	17.2026i	−1.03485	−	0.597471i	−0.918370	+	0.395722i	$0.870494\pi$
$830$		−	8.64693i		−	0.300139i
$831$	42.5873	+	13.4559i	1.47734	+	0.466780i
$832$	5.67516	+	3.27655i	0.196751	+	0.113594i
$833$	−13.5466	−	11.4437i	−0.469360	−	0.396502i
$834$	−1.33379	−	6.03355i	−0.0461855	−	0.208925i
$835$	−10.7866	+	18.6830i	−0.373287	+	0.646552i
$836$	19.4655	−	33.7153i	0.673230	−	1.16607i
$837$	−29.5723	−	12.3119i	−1.02217	−	0.425561i
$838$	−32.9764	+	19.0389i	−1.13915	+	0.657688i
$839$	14.9698	+	25.9285i	0.516815	+	0.895151i	0.999809	+	0.0195269i	$0.00621601\pi$
$839$	14.9698	+	25.9285i	0.516815	+	0.895151i	−0.482994	+	0.875624i	$0.660451\pi$
$840$	−1.74410	−	4.23770i	−0.0601770	−	0.146215i
$841$	11.8820	−	20.5802i	0.409724	−	0.709663i
$842$		−	35.9984i		−	1.24059i
$843$	23.3068	−	5.15226i	0.802727	−	0.177453i
$844$	12.0814			0.415860
$845$	−14.9716	−	25.9316i	−0.515039	−	0.892073i
$846$	−16.0967	−	1.42782i	−0.553417	−	0.0490894i
$847$	39.3305	−	32.8912i	1.35141	−	1.13015i
$848$	−2.56943	+	1.48346i	−0.0882345	+	0.0509422i
$849$	5.55385	−	1.22775i	0.190608	−	0.0421363i
$850$	−2.19392	+	1.26666i	−0.0752509	+	0.0434461i
$851$	7.35103	−	4.24412i	0.251990	−	0.145486i
$852$	−25.1117	+	5.55127i	−0.860313	+	0.190183i
$853$	31.4260	−	18.1438i	1.07600	−	0.621232i	0.146189	−	0.989257i	$-0.453299\pi$
$853$	31.4260	−	18.1438i	1.07600	−	0.621232i	0.929816	+	0.368025i	$0.119966\pi$
$854$	1.46947	+	0.537608i	0.0502844	+	0.0183966i
$855$	21.1073	+	1.87226i	0.721853	+	0.0640301i
$856$	−2.77994	−	4.81501i	−0.0950166	−	0.164573i
$857$	8.61419			0.294255			0.147128	−	0.989118i	$-0.452997\pi$
$857$	8.61419			0.294255			0.147128	+	0.989118i	$0.452997\pi$
$858$	−61.0845	+	13.5035i	−2.08539	+	0.461003i
$859$		−	46.3923i		−	1.58289i	−0.611244	−	0.791443i	$-0.709330\pi$
$859$		−	46.3923i		−	1.58289i	0.611244	−	0.791443i	$-0.290670\pi$
$860$	2.74829	−	4.76018i	0.0937159	−	0.162321i
$861$	3.61835	−	27.0118i	0.123313	−	0.920561i
$862$	−13.4395	−	23.2779i	−0.457752	−	0.792850i
$863$	1.40487	−	0.811104i	0.0478225	−	0.0276103i	−0.475898	−	0.879500i	$-0.657877\pi$
$863$	1.40487	−	0.811104i	0.0478225	−	0.0276103i	0.523721	+	0.851890i	$0.324544\pi$
$864$	4.79702	+	1.99715i	0.163198	+	0.0679445i
$865$	0.639733	−	1.10805i	0.0217516	−	0.0376748i
$866$	13.1917	−	22.8487i	0.448272	−	0.776430i
$867$	3.95635	+	17.8970i	0.134365	+	0.607812i
$868$	16.0672	−	2.80560i	0.545357	−	0.0952281i
$869$	−5.91518	−	3.41513i	−0.200659	−	0.115850i
$870$	11.9968	+	3.79053i	0.406731	+	0.128511i
$871$		−	19.5044i		−	0.660880i
$872$	−15.8002	−	9.12223i	−0.535061	−	0.308918i
$873$	0.680919	+	0.0603992i	0.0230456	+	0.00204420i
$874$			29.7530i			1.00641i
$875$	2.02958	−	1.69729i	0.0686124	−	0.0573789i
$876$	−5.88510	+	18.6260i	−0.198839	+	0.629316i
$877$	−33.5380			−1.13250			−0.566249	−	0.824234i	$-0.691606\pi$
$877$	−33.5380			−1.13250			−0.566249	+	0.824234i	$0.691606\pi$
$878$	12.5070	+	21.6627i	0.422090	+	0.731082i
$879$	−13.3586	+	12.2261i	−0.450574	+	0.412377i
$880$	4.77326	+	2.75584i	0.160906	+	0.0928994i
$881$	39.1144			1.31780			0.658899	−	0.752231i	$-0.271022\pi$
$881$	39.1144			1.31780			0.658899	+	0.752231i	$0.271022\pi$
$882$	−20.3088	+	5.34339i	−0.683834	+	0.179921i
$883$	1.14778			0.0386258			0.0193129	−	0.999813i	$-0.493852\pi$
$883$	1.14778			0.0386258			0.0193129	+	0.999813i	$0.493852\pi$
$884$	−14.3770	−	8.30057i	−0.483551	−	0.279178i
$885$	1.46461	+	6.62530i	0.0492323	+	0.222707i
$886$	4.75881	+	8.24251i	0.159875	+	0.276912i
$887$	18.3937			0.617599			0.308800	−	0.951127i	$-0.400073\pi$
$887$	18.3937			0.617599			0.308800	+	0.951127i	$0.400073\pi$
$888$	−3.40799	+	0.753381i	−0.114365	+	0.0252818i
$889$	22.7955	−	19.0633i	0.764535	−	0.639362i
$890$			15.6863i			0.525805i
$891$	−46.6543	+	16.8536i	−1.56298	+	0.564618i
$892$	−13.6952	−	7.90695i	−0.458550	−	0.264744i
$893$			38.0479i			1.27322i
$894$	−13.2759	+	12.1504i	−0.444012	+	0.406371i
$895$	−10.2660	−	5.92708i	−0.343154	−	0.198120i
$896$	−2.60632	+	0.455105i	−0.0870709	+	0.0152040i
$897$	35.2693	−	32.2793i	1.17761	−	1.07777i
$898$	−13.4960	+	23.3758i	−0.450369	+	0.780061i
$899$	−22.3899	+	38.7805i	−0.746745	+	1.29340i
$900$	−0.265066	+	2.98827i	−0.00883555	+	0.0996089i
$901$	6.50919	−	3.75808i	0.216853	−	0.125200i
$902$	16.3893	+	28.3871i	0.545704	+	0.945187i
$903$	−19.9486	−	15.3789i	−0.663849	−	0.511779i
$904$	0.816970	−	1.41503i	0.0271720	−	0.0470633i
$905$		−	13.3188i		−	0.442732i
$906$	10.2529	+	11.2026i	0.340631	+	0.372183i
$907$	17.7344			0.588861			0.294430	−	0.955673i	$-0.404870\pi$
$907$	17.7344			0.588861			0.294430	+	0.955673i	$0.404870\pi$
$908$	1.06442	+	1.84362i	0.0353239	+	0.0611828i
$909$	6.79574	+	4.77063i	0.225400	+	0.158232i
$910$	16.2824	+	5.95694i	0.539757	+	0.197471i
$911$	36.1849	−	20.8914i	1.19886	−	0.692162i	0.238559	−	0.971128i	$-0.423325\pi$
$911$	36.1849	−	20.8914i	1.19886	−	0.692162i	0.960301	+	0.278966i	$0.0899917\pi$
$912$	3.68590	−	11.6657i	0.122052	−	0.386289i
$913$	41.2740	−	23.8296i	1.36597	−	0.788644i
$914$	−4.13245	+	2.38587i	−0.136689	+	0.0789176i
$915$	−0.691590	−	0.755651i	−0.0228632	−	0.0249810i
$916$	17.5856	−	10.1531i	0.581046	−	0.335467i
$917$	8.45773	−	7.07300i	0.279299	−	0.233571i
$918$	−12.1524	−	5.05943i	−0.401089	−	0.166986i
$919$	14.9114	+	25.8273i	0.491882	+	0.851964i	0.999956	−	0.00934919i	$-0.00297598\pi$
$919$	14.9114	+	25.8273i	0.491882	+	0.851964i	−0.508075	+	0.861313i	$0.669643\pi$
$920$	−4.21229			−0.138875
$921$	−17.1685	+	54.3373i	−0.565720	+	1.79047i
$922$		−	22.1408i		−	0.729169i
$923$	48.6512	−	84.2663i	1.60137	−	2.77366i
$924$	15.4212	−	20.0034i	0.507320	−	0.658065i
$925$	−1.00755	−	1.74514i	−0.0331282	−	0.0573797i
$926$	−18.7483	+	10.8244i	−0.616109	+	0.355710i
$927$	−5.69056	+	8.10617i	−0.186903	+	0.266242i
$928$	3.63194	−	6.29071i	0.119224	−	0.206503i
$929$	−11.8119	+	20.4588i	−0.387535	+	0.671230i	−0.992117	−	0.125312i	$-0.960007\pi$
$929$	−11.8119	+	20.4588i	−0.387535	+	0.671230i	0.604582	+	0.796543i	$0.293340\pi$
$930$	−10.1815	−	3.21695i	−0.333864	−	0.105488i
$931$	16.7564	+	46.5177i	0.549169	+	1.52456i
$932$	−11.1623	−	6.44458i	−0.365634	−	0.211099i
$933$	9.66187	+	43.7064i	0.316315	+	1.43088i
$934$			3.94233i			0.128997i
$935$	−12.0922	−	6.98143i	−0.395457	−	0.228317i
$936$	−17.8274	+	8.28692i	−0.582706	+	0.270866i
$937$		−	45.0608i		−	1.47207i	−0.676943	−	0.736035i	$-0.736696\pi$
$937$		−	45.0608i		−	1.47207i	0.676943	−	0.736035i	$-0.263304\pi$
$938$	5.05174	+	6.04076i	0.164945	+	0.197238i
$939$	−21.8886	−	23.9161i	−0.714307	−	0.780472i
$940$	−5.38665			−0.175693
$941$	17.2029	+	29.7963i	0.560799	+	0.971332i	0.997427	+	0.0716900i	$0.0228392\pi$
$941$	17.2029	+	29.7963i	0.560799	+	0.971332i	−0.436628	+	0.899642i	$0.643827\pi$
$942$	−19.8225	−	6.26312i	−0.645851	−	0.204064i
$943$	−21.6948	−	12.5255i	−0.706480	−	0.407886i
$944$	3.91747			0.127503
$945$	13.4115	+	3.02206i	0.436275	+	0.0983075i
$946$	30.2954			0.984988
$947$	8.90645	+	5.14214i	0.289421	+	0.167097i	0.637681	−	0.770301i	$-0.279894\pi$
$947$	8.90645	+	5.14214i	0.289421	+	0.167097i	−0.348260	+	0.937398i	$0.613227\pi$
$948$	−2.04669	−	0.646673i	−0.0664733	−	0.0210030i
$949$	−36.9522	−	64.0031i	−1.19952	−	2.07763i
$950$	7.06338			0.229166
$951$	−21.5918	−	23.5918i	−0.700161	−	0.765016i
$952$	6.60264	−	1.15293i	0.213993	−	0.0373666i
$953$		−	21.5003i		−	0.696464i	−0.937408	−	0.348232i	$-0.886782\pi$
$953$		−	21.5003i		−	0.696464i	0.937408	−	0.348232i	$-0.113218\pi$
$954$	0.786431	−	8.86595i	0.0254617	−	0.287046i
$955$	−7.09826	−	4.09818i	−0.229694	−	0.132614i
$956$		−	1.12045i		−	0.0362378i
$957$	14.9682	+	67.7100i	0.483852	+	2.18875i
$958$	−6.01472	−	3.47260i	−0.194327	−	0.112195i
$959$	15.7359	+	18.8167i	0.508139	+	0.607622i
$960$	1.65157	+	0.521832i	0.0533043	+	0.0168421i
$961$	3.50189	−	6.06546i	0.112964	−	0.195660i
$962$	6.60261	−	11.4361i	0.212877	−	0.368713i
$963$	16.6144	+	1.47374i	0.535393	+	0.0474906i
$964$	1.25767	−	0.726116i	0.0405068	−	0.0233866i
$965$	1.49743	+	2.59363i	0.0482040	+	0.0834918i
$966$	−2.56285	+	19.1323i	−0.0824583	+	0.615571i
$967$	−19.1245	+	33.1246i	−0.615001	+	1.06521i	0.375383	+	0.926870i	$0.377511\pi$
$967$	−19.1245	+	33.1246i	−0.615001	+	1.06521i	−0.990384	+	0.138344i	$0.955822\pi$
$968$			19.3786i			0.622853i
$969$	−9.33757	+	29.5529i	−0.299966	+	0.949377i
$970$	0.227864			0.00731628
$971$	−0.760849	−	1.31783i	−0.0244168	−	0.0422911i	0.853559	−	0.520997i	$-0.174440\pi$
$971$	−0.760849	−	1.31783i	−0.0244168	−	0.0422911i	−0.877976	+	0.478705i	$0.841106\pi$
$972$	−13.1723	+	8.33605i	−0.422503	+	0.267379i
$973$	−9.29822	+	1.62362i	−0.298087	+	0.0520509i
$974$	16.7664	−	9.68011i	0.537232	−	0.310171i
$975$	−7.66312	−	8.37294i	−0.245416	−	0.268149i
$976$	−0.512178	+	0.295706i	−0.0163944	+	0.00946532i
$977$	−29.6515	+	17.1193i	−0.948637	+	0.547696i	−0.892657	−	0.450736i	$-0.851162\pi$
$977$	−29.6515	+	17.1193i	−0.948637	+	0.547696i	−0.0559798	+	0.998432i	$0.517828\pi$
$978$	−5.63852	+	17.8456i	−0.180300	+	0.570640i
$979$	−74.8746	+	43.2289i	−2.39300	+	1.38160i
$980$	−6.58576	+	2.37229i	−0.210374	+	0.0757802i
$981$	49.6331	−	23.0716i	1.58466	−	0.736619i
$982$	13.7937	+	23.8914i	0.440174	+	0.762404i
$983$	0.677174			0.0215985			0.0107992	−	0.999942i	$-0.496562\pi$
$983$	0.677174			0.0215985			0.0107992	+	0.999942i	$0.496562\pi$
$984$	6.95448	+	7.59866i	0.221701	+	0.242237i
$985$		−	11.9427i		−	0.380526i
$986$	−9.20088	+	15.9364i	−0.293016	+	0.507518i
$987$	−3.27735	+	24.4662i	−0.104319	+	0.778767i
$988$	23.1435	+	40.0858i	0.736294	+	1.27530i
$989$	−20.0513	+	11.5766i	−0.637593	+	0.368114i
$990$	−14.9942	+	6.96996i	−0.476548	+	0.221520i
$991$	24.5136	−	42.4589i	0.778701	−	1.34875i	−0.153989	−	0.988073i	$-0.549212\pi$
$991$	24.5136	−	42.4589i	0.778701	−	1.34875i	0.932691	−	0.360678i	$-0.117455\pi$
$992$	−3.08236	+	5.33881i	−0.0978650	+	0.169507i
$993$	−30.0296	+	27.4838i	−0.952960	+	0.872172i
$994$	6.75753	+	38.6993i	0.214336	+	1.22747i
$995$	2.73876	+	1.58122i	0.0868245	+	0.0501281i
$996$	11.0482	−	10.1116i	0.350077	−	0.320399i
$997$		−	3.64007i		−	0.115282i	−0.998337	−	0.0576411i	$-0.981642\pi$
$997$		−	3.64007i		−	0.115282i	0.998337	−	0.0576411i	$-0.0183579\pi$
$998$	−13.5241	−	7.80813i	−0.428097	−	0.247162i
$999$	4.02448	−	9.66652i	0.127329	−	0.305835i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.t.b.311.6	✓	28
3.2	odd	2		1890.2.t.b.1151.14		28
7.5	odd	6		630.2.bk.b.131.13	yes	28
9.2	odd	6		630.2.bk.b.101.6	yes	28
9.7	even	3		1890.2.bk.b.521.1		28
21.5	even	6		1890.2.bk.b.341.1		28
63.47	even	6	inner	630.2.t.b.551.6	yes	28
63.61	odd	6		1890.2.t.b.1601.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.t.b.311.6	✓	28	1.1	even	1	trivial
630.2.t.b.551.6	yes	28	63.47	even	6	inner
630.2.bk.b.101.6	yes	28	9.2	odd	6
630.2.bk.b.131.13	yes	28	7.5	odd	6
1890.2.t.b.1151.14		28	3.2	odd	2
1890.2.t.b.1601.14		28	63.61	odd	6
1890.2.bk.b.341.1		28	21.5	even	6
1890.2.bk.b.521.1		28	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.65157 + 0.521832i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.16939 - 1.27771i) q^{6} +(-2.02958 + 1.69729i) q^{7} -1.00000i q^{8} +(2.45538 + 1.72369i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.65157 + 0.521832i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-1.16939 - 1.27771i) q^{6} +(-2.02958 + 1.69729i) q^{7} -1.00000i q^{8} +(2.45538 + 1.72369i) q^{9} +(0.866025 + 0.500000i) q^{10} +5.51168i q^{11} +(0.373866 + 1.69122i) q^{12} +(-5.67516 - 3.27655i) q^{13} +(2.60632 - 0.455105i) q^{14} +(-1.65157 - 0.521832i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.26666 - 2.19392i) q^{17} +(-1.26458 - 2.72045i) q^{18} +(-6.11706 + 3.53169i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-4.23770 + 1.74410i) q^{21} +(2.75584 - 4.77326i) q^{22} +4.21229i q^{23} +(0.521832 - 1.65157i) q^{24} +1.00000 q^{25} +(3.27655 + 5.67516i) q^{26} +(3.15576 + 4.12809i) q^{27} +(-2.48469 - 0.909025i) q^{28} +(6.29071 - 3.63194i) q^{29} +(1.16939 + 1.27771i) q^{30} +(-5.33881 + 3.08236i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.87617 + 9.10294i) q^{33} +(-2.19392 + 1.26666i) q^{34} +(2.02958 - 1.69729i) q^{35} +(-0.265066 + 2.98827i) q^{36} +(-1.00755 - 1.74514i) q^{37} +7.06338 q^{38} +(-7.66312 - 8.37294i) q^{39} +1.00000i q^{40} +(-2.97356 + 5.15035i) q^{41} +(4.54201 + 0.608421i) q^{42} +(2.74829 + 4.76018i) q^{43} +(-4.77326 + 2.75584i) q^{44} +(-2.45538 - 1.72369i) q^{45} +(2.10615 - 3.64795i) q^{46} +(2.69332 - 4.66497i) q^{47} +(-1.27771 + 1.16939i) q^{48} +(1.23841 - 6.88958i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(3.23684 - 2.96244i) q^{51} -6.55311i q^{52} +(2.56943 + 1.48346i) q^{53} +(-0.668926 - 5.15292i) q^{54} -5.51168i q^{55} +(1.69729 + 2.02958i) q^{56} +(-11.9457 + 2.64076i) q^{57} -7.26388 q^{58} +(-1.95873 - 3.39263i) q^{59} +(-0.373866 - 1.69122i) q^{60} +(0.512178 + 0.295706i) q^{61} +6.16472 q^{62} +(-7.90900 + 0.669129i) q^{63} -1.00000 q^{64} +(5.67516 + 3.27655i) q^{65} +(7.04231 - 6.44529i) q^{66} +(1.48818 + 2.57760i) q^{67} +2.53332 q^{68} +(-2.19811 + 6.95691i) q^{69} +(-2.60632 + 0.455105i) q^{70} +14.8483i q^{71} +(1.72369 - 2.45538i) q^{72} +(9.76683 + 5.63888i) q^{73} +2.01511i q^{74} +(1.65157 + 0.521832i) q^{75} +(-6.11706 - 3.53169i) q^{76} +(-9.35492 - 11.1864i) q^{77} +(2.44998 + 11.0827i) q^{78} +(-0.619617 + 1.07321i) q^{79} +(0.500000 - 0.866025i) q^{80} +(3.05780 + 8.46462i) q^{81} +(5.15035 - 2.97356i) q^{82} +(-4.32347 - 7.48846i) q^{83} +(-3.62928 - 2.79791i) q^{84} +(-1.26666 + 2.19392i) q^{85} -5.49658i q^{86} +(12.2848 - 2.71572i) q^{87} +5.51168 q^{88} +(7.84313 + 13.5847i) q^{89} +(1.26458 + 2.72045i) q^{90} +(17.0795 - 2.98235i) q^{91} +(-3.64795 + 2.10615i) q^{92} +(-10.4259 + 2.30478i) q^{93} +(-4.66497 + 2.69332i) q^{94} +(6.11706 - 3.53169i) q^{95} +(1.69122 - 0.373866i) q^{96} +(0.197336 - 0.113932i) q^{97} +(-4.51729 + 5.34735i) q^{98} +(-9.50042 + 13.5333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9	\( 28 q - 2 q^{3} + 14 q^{4} - 28 q^{5} - 8 q^{6} - 4 q^{7} + 6 q^{9} - 4 q^{12} + 6 q^{14} + 2 q^{15} - 14 q^{16} - 6 q^{17} - 4 q^{18} - 6 q^{19} - 14 q^{20} + 6 q^{21} - 6 q^{22} - 4 q^{24} + 28 q^{25} + 12 q^{26} + 28 q^{27} - 8 q^{28} + 8 q^{30} - 12 q^{31} + 26 q^{33} + 4 q^{35} - 6 q^{36} + 4 q^{37} - 12 q^{38} + 54 q^{39} + 18 q^{41} - 32 q^{42} + 28 q^{43} - 6 q^{45} - 18 q^{46} + 30 q^{47} - 2 q^{48} - 14 q^{49} + 34 q^{51} - 42 q^{53} + 14 q^{54} + 6 q^{56} - 30 q^{57} - 12 q^{58} - 24 q^{59} + 4 q^{60} + 24 q^{61} - 12 q^{62} + 44 q^{63} - 28 q^{64} - 10 q^{66} - 40 q^{67} - 12 q^{68} + 8 q^{69} - 6 q^{70} + 4 q^{72} + 6 q^{73} - 2 q^{75} - 6 q^{76} - 24 q^{77} + 14 q^{78} + 2 q^{79} + 14 q^{80} - 46 q^{81} + 24 q^{82} - 18 q^{83} + 18 q^{84} + 6 q^{85} + 104 q^{87} - 12 q^{88} + 6 q^{89} + 4 q^{90} + 66 q^{91} - 30 q^{92} + 40 q^{93} + 42 q^{94} + 6 q^{95} + 4 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) 28 * q - 2 * q^3 + 14 * q^4 - 28 * q^5 - 8 * q^6 - 4 * q^7 + 6 * q^9 - 4 * q^12 + 6 * q^14 + 2 * q^15 - 14 * q^16 - 6 * q^17 - 4 * q^18 - 6 * q^19 - 14 * q^20 + 6 * q^21 - 6 * q^22 - 4 * q^24 + 28 * q^25 + 12 * q^26 + 28 * q^27 - 8 * q^28 + 8 * q^30 - 12 * q^31 + 26 * q^33 + 4 * q^35 - 6 * q^36 + 4 * q^37 - 12 * q^38 + 54 * q^39 + 18 * q^41 - 32 * q^42 + 28 * q^43 - 6 * q^45 - 18 * q^46 + 30 * q^47 - 2 * q^48 - 14 * q^49 + 34 * q^51 - 42 * q^53 + 14 * q^54 + 6 * q^56 - 30 * q^57 - 12 * q^58 - 24 * q^59 + 4 * q^60 + 24 * q^61 - 12 * q^62 + 44 * q^63 - 28 * q^64 - 10 * q^66 - 40 * q^67 - 12 * q^68 + 8 * q^69 - 6 * q^70 + 4 * q^72 + 6 * q^73 - 2 * q^75 - 6 * q^76 - 24 * q^77 + 14 * q^78 + 2 * q^79 + 14 * q^80 - 46 * q^81 + 24 * q^82 - 18 * q^83 + 18 * q^84 + 6 * q^85 + 104 * q^87 - 12 * q^88 + 6 * q^89 + 4 * q^90 + 66 * q^91 - 30 * q^92 + 40 * q^93 + 42 * q^94 + 6 * q^95 + 4 * q^96 - 72 * q^97 - 24 * q^98 - 42 * q^99

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