LMFDB - Embedded newform 210.2.t.f.89.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(59,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("210.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.2
Root			$-1.72286 - 0.178197i$ of defining polynomial
Character	$\chi$	$=$	210.89
Dual form			210.2.t.f.59.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.01575 + 1.40294i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.792893 - 2.09077i) q^{5} +(0.707107 + 1.58114i) q^{6} +(1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(-0.936492 - 2.85008i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.01575 + 1.40294i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.792893 - 2.09077i) q^{5} +(0.707107 + 1.58114i) q^{6} +(1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(-0.936492 - 2.85008i) q^{9} +(-2.20711 - 0.358719i) q^{10} +(4.05781 - 2.34278i) q^{11} +(1.72286 + 0.178197i) q^{12} +1.04456 q^{13} +(-1.22938 - 2.34278i) q^{14} +(3.73861 + 1.01132i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.73861 + 1.58114i) q^{17} +(-2.93649 - 0.614017i) q^{18} +(-1.23861 - 0.715113i) q^{19} +(-1.41421 + 1.73205i) q^{20} +(1.70058 + 4.25535i) q^{21} -4.68556i q^{22} +(2.23861 - 3.87739i) q^{23} +(1.01575 - 1.40294i) q^{24} +(-3.74264 + 3.31552i) q^{25} +(0.522278 - 0.904612i) q^{26} +(4.94975 + 1.58114i) q^{27} +(-2.64360 - 0.106711i) q^{28} +6.92163i q^{29} +(2.74514 - 2.73207i) q^{30} +(-5.73861 + 3.31319i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.834952 + 8.07256i) q^{33} +3.16228i q^{34} +(-5.79642 - 1.18383i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(2.30615 + 1.33146i) q^{37} +(-1.23861 + 0.715113i) q^{38} +(-1.06101 + 1.46545i) q^{39} +(0.792893 + 2.09077i) q^{40} +1.04456 q^{41} +(4.53553 + 0.654929i) q^{42} -6.92163i q^{43} +(-4.05781 - 2.34278i) q^{44} +(-5.21633 + 4.21780i) q^{45} +(-2.23861 - 3.87739i) q^{46} +(9.71584 + 5.60944i) q^{47} +(-0.707107 - 1.58114i) q^{48} +(-3.00000 - 6.32456i) q^{49} +(1.00000 + 4.89898i) q^{50} +(0.563508 - 5.44816i) q^{51} +(-0.522278 - 0.904612i) q^{52} +(2.50000 + 4.33013i) q^{53} +(3.84418 - 3.49604i) q^{54} +(-8.11562 - 6.62638i) q^{55} +(-1.41421 + 2.23607i) q^{56} +(2.26139 - 1.01132i) q^{57} +(5.99430 + 3.46081i) q^{58} +(5.28720 + 9.15769i) q^{59} +(-0.993475 - 3.74340i) q^{60} +(3.00000 + 1.73205i) q^{61} +6.62638i q^{62} +(-7.69738 - 1.93657i) q^{63} +1.00000 q^{64} +(-0.828222 - 2.18393i) q^{65} +(6.57357 + 4.75937i) q^{66} +(12.3583 - 7.13505i) q^{67} +(2.73861 + 1.58114i) q^{68} +(3.16588 + 7.07912i) q^{69} +(-3.92344 + 4.42793i) q^{70} -6.92163i q^{71} +(0.936492 + 2.85008i) q^{72} +(1.75166 + 3.03397i) q^{73} +(2.30615 - 1.33146i) q^{74} +(-0.849876 - 8.61845i) q^{75} +1.43023i q^{76} +(0.500000 - 12.3867i) q^{77} +(0.738613 + 1.65159i) q^{78} +(-5.73861 + 9.93957i) q^{79} +(2.20711 + 0.358719i) q^{80} +(-7.24597 + 5.33816i) q^{81} +(0.522278 - 0.904612i) q^{82} -4.06775i q^{83} +(2.83495 - 3.60042i) q^{84} +(5.47723 + 4.47214i) q^{85} +(-5.99430 - 3.46081i) q^{86} +(-9.71064 - 7.03066i) q^{87} +(-4.05781 + 2.34278i) q^{88} +(2.45877 - 4.25871i) q^{89} +(1.04456 + 6.62638i) q^{90} +(1.47723 - 2.33570i) q^{91} -4.47723 q^{92} +(1.18080 - 11.4163i) q^{93} +(9.71584 - 5.60944i) q^{94} +(-0.513050 + 3.15666i) q^{95} +(-1.72286 - 0.178197i) q^{96} -11.9886 q^{97} +(-6.97723 - 0.564201i) q^{98} +(-10.4772 - 9.37112i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 12 * q^5 - 8 * q^8 + 8 * q^9	$ 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9} - 12 q^{10} + 8 q^{15} - 4 q^{16} - 8 q^{18} + 12 q^{19} + 4 q^{21} - 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} + 4 q^{32} + 12 q^{33} + 8 q^{35} - 16 q^{36} + 12 q^{38} - 8 q^{39} + 12 q^{40} + 8 q^{42} - 24 q^{45} + 4 q^{46} + 12 q^{47} - 24 q^{49} + 8 q^{50} + 20 q^{51} + 20 q^{53} + 40 q^{57} - 4 q^{60} + 24 q^{61} - 20 q^{63} + 8 q^{64} - 16 q^{65} + 12 q^{66} - 8 q^{70} - 8 q^{72} - 24 q^{75} + 4 q^{77} - 16 q^{78} - 24 q^{79} + 12 q^{80} + 4 q^{81} + 4 q^{84} - 12 q^{87} - 32 q^{91} + 8 q^{92} + 20 q^{93} + 12 q^{94} - 12 q^{95} - 12 q^{98} - 40 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 12 * q^5 - 8 * q^8 + 8 * q^9 - 12 * q^10 + 8 * q^15 - 4 * q^16 - 8 * q^18 + 12 * q^19 + 4 * q^21 - 4 * q^23 + 4 * q^25 + 4 * q^30 - 24 * q^31 + 4 * q^32 + 12 * q^33 + 8 * q^35 - 16 * q^36 + 12 * q^38 - 8 * q^39 + 12 * q^40 + 8 * q^42 - 24 * q^45 + 4 * q^46 + 12 * q^47 - 24 * q^49 + 8 * q^50 + 20 * q^51 + 20 * q^53 + 40 * q^57 - 4 * q^60 + 24 * q^61 - 20 * q^63 + 8 * q^64 - 16 * q^65 + 12 * q^66 - 8 * q^70 - 8 * q^72 - 24 * q^75 + 4 * q^77 - 16 * q^78 - 24 * q^79 + 12 * q^80 + 4 * q^81 + 4 * q^84 - 12 * q^87 - 32 * q^91 + 8 * q^92 + 20 * q^93 + 12 * q^94 - 12 * q^95 - 12 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.01575	+	1.40294i	−0.586445	+	0.809989i
$3$	−1.01575	+	1.40294i	−0.586445	+	0.809989i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.792893	−	2.09077i	−0.354593	−	0.935021i
$5$	−0.792893	−	2.09077i	−0.354593	−	0.935021i
$6$	0.707107	+	1.58114i	0.288675	+	0.645497i
$7$	1.41421	−	2.23607i	0.534522	−	0.845154i
$7$	1.41421	−	2.23607i	0.534522	−	0.845154i
$8$	−1.00000			−0.353553
$9$	−0.936492	−	2.85008i	−0.312164	−	0.950028i
$10$	−2.20711	−	0.358719i	−0.697948	−	0.113437i
$11$	4.05781	−	2.34278i	1.22348	−	0.706374i	0.257819	−	0.966193i	$-0.416996\pi$
$11$	4.05781	−	2.34278i	1.22348	−	0.706374i	0.965657	+	0.259819i	$0.0836628\pi$
$12$	1.72286	+	0.178197i	0.497347	+	0.0514410i
$13$	1.04456			0.289708			0.144854	−	0.989453i	$-0.453729\pi$
$13$	1.04456			0.289708			0.144854	+	0.989453i	$0.453729\pi$
$14$	−1.22938	−	2.34278i	−0.328567	−	0.626134i
$15$	3.73861	+	1.01132i	0.965306	+	0.261123i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.73861	+	1.58114i	−0.664211	+	0.383482i	−0.793880	−	0.608075i	$-0.791942\pi$
$17$	−2.73861	+	1.58114i	−0.664211	+	0.383482i	0.129668	+	0.991557i	$0.458609\pi$
$18$	−2.93649	−	0.614017i	−0.692138	−	0.144725i
$19$	−1.23861	−	0.715113i	−0.284157	−	0.164058i	0.351147	−	0.936320i	$-0.385792\pi$
$19$	−1.23861	−	0.715113i	−0.284157	−	0.164058i	−0.635304	+	0.772262i	$0.719125\pi$
$20$	−1.41421	+	1.73205i	−0.316228	+	0.387298i
$21$	1.70058	+	4.25535i	0.371097	+	0.928594i
$22$		−	4.68556i		−	0.998964i
$23$	2.23861	−	3.87739i	0.466783	−	0.808492i	−0.532497	−	0.846432i	$-0.678746\pi$
$23$	2.23861	−	3.87739i	0.466783	−	0.808492i	0.999280	+	0.0379400i	$0.0120796\pi$
$24$	1.01575	−	1.40294i	0.207340	−	0.286374i
$25$	−3.74264	+	3.31552i	−0.748528	+	0.663103i
$26$	0.522278	−	0.904612i	0.102427	−	0.177409i
$27$	4.94975	+	1.58114i	0.952579	+	0.304290i
$28$	−2.64360	−	0.106711i	−0.499593	−	0.0201665i
$29$			6.92163i			1.28531i	0.766154	+	0.642657i	$0.222168\pi$
$29$			6.92163i			1.28531i	−0.766154	+	0.642657i	$0.777832\pi$
$30$	2.74514	−	2.73207i	0.501191	−	0.498806i
$31$	−5.73861	+	3.31319i	−1.03069	+	0.595066i	−0.917181	−	0.398471i	$-0.869541\pi$
$31$	−5.73861	+	3.31319i	−1.03069	+	0.595066i	−0.113504	+	0.993537i	$0.536208\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.834952	+	8.07256i	−0.145347	+	1.40525i
$34$			3.16228i			0.542326i
$35$	−5.79642	−	1.18383i	−0.979775	−	0.200104i
$36$	−2.00000	+	2.23607i	−0.333333	+	0.372678i
$37$	2.30615	+	1.33146i	0.379129	+	0.218890i	0.677439	−	0.735579i	$-0.263090\pi$
$37$	2.30615	+	1.33146i	0.379129	+	0.218890i	−0.298310	+	0.954469i	$0.596423\pi$
$38$	−1.23861	+	0.715113i	−0.200930	+	0.116007i
$39$	−1.06101	+	1.46545i	−0.169898	+	0.234660i
$40$	0.792893	+	2.09077i	0.125367	+	0.330580i
$41$	1.04456			0.163132			0.0815661	−	0.996668i	$-0.474008\pi$
$41$	1.04456			0.163132			0.0815661	+	0.996668i	$0.474008\pi$
$42$	4.53553	+	0.654929i	0.699848	+	0.101058i
$43$		−	6.92163i		−	1.05554i	−0.849388	−	0.527769i	$-0.823029\pi$
$43$		−	6.92163i		−	1.05554i	0.849388	−	0.527769i	$-0.176971\pi$
$44$	−4.05781	−	2.34278i	−0.611738	−	0.353187i
$45$	−5.21633	+	4.21780i	−0.777605	+	0.628753i
$46$	−2.23861	−	3.87739i	−0.330065	−	0.571690i
$47$	9.71584	+	5.60944i	1.41720	+	0.818221i	0.996052	−	0.0887705i	$-0.0282938\pi$
$47$	9.71584	+	5.60944i	1.41720	+	0.818221i	0.421149	+	0.906992i	$0.361627\pi$
$48$	−0.707107	−	1.58114i	−0.102062	−	0.228218i
$49$	−3.00000	−	6.32456i	−0.428571	−	0.903508i
$50$	1.00000	+	4.89898i	0.141421	+	0.692820i
$51$	0.563508	−	5.44816i	0.0789069	−	0.762895i
$52$	−0.522278	−	0.904612i	−0.0724269	−	0.125447i
$53$	2.50000	+	4.33013i	0.343401	+	0.594789i	0.985062	−	0.172200i	$-0.0550875\pi$
$53$	2.50000	+	4.33013i	0.343401	+	0.594789i	−0.641661	+	0.766989i	$0.721754\pi$
$54$	3.84418	−	3.49604i	0.523127	−	0.475750i
$55$	−8.11562	−	6.62638i	−1.09431	−	0.893501i
$56$	−1.41421	+	2.23607i	−0.188982	+	0.298807i
$57$	2.26139	−	1.01132i	0.299528	−	0.133953i
$58$	5.99430	+	3.46081i	0.787091	+	0.454427i
$59$	5.28720	+	9.15769i	0.688334	+	1.19223i	0.972376	+	0.233418i	$0.0749911\pi$
$59$	5.28720	+	9.15769i	0.688334	+	1.19223i	−0.284042	+	0.958812i	$0.591676\pi$
$60$	−0.993475	−	3.74340i	−0.128257	−	0.483270i
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	0.679605	−	0.733578i	$-0.262151\pi$
$61$	3.00000	+	1.73205i	0.384111	+	0.221766i	−0.295495	+	0.955344i	$0.595484\pi$
$62$			6.62638i			0.841551i
$63$	−7.69738	−	1.93657i	−0.969779	−	0.243985i
$64$	1.00000			0.125000
$65$	−0.828222	−	2.18393i	−0.102728	−	0.270883i
$66$	6.57357	+	4.75937i	0.809150	+	0.585838i
$67$	12.3583	−	7.13505i	1.50980	−	0.871685i	0.509868	−	0.860253i	$-0.329694\pi$
$67$	12.3583	−	7.13505i	1.50980	−	0.871685i	0.999935	−	0.0114319i	$-0.00363898\pi$
$68$	2.73861	+	1.58114i	0.332106	+	0.191741i
$69$	3.16588	+	7.07912i	0.381127	+	0.852225i
$70$	−3.92344	+	4.42793i	−0.468941	+	0.529239i
$71$		−	6.92163i		−	0.821446i	−0.911760	−	0.410723i	$-0.865276\pi$
$71$		−	6.92163i		−	0.821446i	0.911760	−	0.410723i	$-0.134724\pi$
$72$	0.936492	+	2.85008i	0.110367	+	0.335886i
$73$	1.75166	+	3.03397i	0.205017	+	0.355099i	0.950138	−	0.311830i	$-0.100942\pi$
$73$	1.75166	+	3.03397i	0.205017	+	0.355099i	−0.745121	+	0.666929i	$0.767608\pi$
$74$	2.30615	−	1.33146i	0.268084	−	0.154779i
$75$	−0.849876	−	8.61845i	−0.0981353	−	0.995173i
$76$			1.43023i			0.164058i
$77$	0.500000	−	12.3867i	0.0569803	−	1.41160i
$78$	0.738613	+	1.65159i	0.0836314	+	0.187006i
$79$	−5.73861	+	9.93957i	−0.645644	+	1.11829i	0.338508	+	0.940964i	$0.390078\pi$
$79$	−5.73861	+	9.93957i	−0.645644	+	1.11829i	−0.984152	+	0.177325i	$0.943256\pi$
$80$	2.20711	+	0.358719i	0.246762	+	0.0401061i
$81$	−7.24597	+	5.33816i	−0.805107	+	0.593129i
$82$	0.522278	−	0.904612i	0.0576760	−	0.0998977i
$83$		−	4.06775i		−	0.446494i	−0.974762	−	0.223247i	$-0.928334\pi$
$83$		−	4.06775i		−	0.446494i	0.974762	−	0.223247i	$-0.0716656\pi$
$84$	2.83495	−	3.60042i	0.309319	−	0.392838i
$85$	5.47723	+	4.47214i	0.594089	+	0.485071i
$86$	−5.99430	−	3.46081i	−0.646382	−	0.373189i
$87$	−9.71064	−	7.03066i	−1.04109	−	0.753766i
$88$	−4.05781	+	2.34278i	−0.432564	+	0.249741i
$89$	2.45877	−	4.25871i	0.260629	−	0.451423i	−0.705780	−	0.708431i	$-0.749403\pi$
$89$	2.45877	−	4.25871i	0.260629	−	0.451423i	0.966409	+	0.257008i	$0.0827367\pi$
$90$	1.04456	+	6.62638i	0.110106	+	0.698482i
$91$	1.47723	−	2.33570i	0.154855	−	0.244848i
$92$	−4.47723			−0.466783
$93$	1.18080	−	11.4163i	0.122443	−	1.18382i
$94$	9.71584	−	5.60944i	1.00211	−	0.578570i
$95$	−0.513050	+	3.15666i	−0.0526378	+	0.323867i
$96$	−1.72286	−	0.178197i	−0.175839	−	0.0181872i
$97$	−11.9886			−1.21726			−0.608629	−	0.793455i	$-0.708280\pi$
$97$	−11.9886			−1.21726			−0.608629	+	0.793455i	$0.708280\pi$
$98$	−6.97723	−	0.564201i	−0.704806	−	0.0569930i
$99$	−10.4772	−	9.37112i	−1.05300	−	0.941833i
$100$	4.74264	+	1.58346i	0.474264	+	0.158346i
$101$	−5.65685	−	9.79796i	−0.562878	−	0.974933i	−0.997244	−	0.0741967i	$-0.976361\pi$
$101$	−5.65685	−	9.79796i	−0.562878	−	0.974933i	0.434366	−	0.900737i	$-0.356973\pi$
$102$	−4.43649	−	3.21209i	−0.439278	−	0.318045i
$103$	−2.45877	+	4.25871i	−0.242270	+	0.419624i	−0.961360	−	0.275293i	$-0.911225\pi$
$103$	−2.45877	+	4.25871i	−0.242270	+	0.419624i	0.719091	+	0.694916i	$0.244559\pi$
$104$	−1.04456			−0.102427
$105$	7.54858	−	6.92957i	0.736666	−	0.676256i
$106$	5.00000			0.485643
$107$	−2.73861	+	4.74342i	−0.264752	+	0.458563i	−0.967499	−	0.252877i	$-0.918623\pi$
$107$	−2.73861	+	4.74342i	−0.264752	+	0.458563i	0.702747	+	0.711440i	$0.251957\pi$
$108$	−1.10557	−	5.07718i	−0.106383	−	0.488552i
$109$	10.2158	+	17.6944i	0.978500	+	1.69481i	0.667866	+	0.744282i	$0.267208\pi$
$109$	10.2158	+	17.6944i	0.978500	+	1.69481i	0.310634	+	0.950529i	$0.399459\pi$
$110$	−9.79642	+	3.71515i	−0.934052	+	0.354225i
$111$	−4.21043	+	1.88296i	−0.399637	+	0.178723i
$112$	1.22938	+	2.34278i	0.116166	+	0.221372i
$113$	−17.4772			−1.64412			−0.822060	−	0.569402i	$-0.807175\pi$
$113$	−17.4772			−1.64412			−0.822060	+	0.569402i	$0.807175\pi$
$114$	0.254862	−	2.46408i	0.0238700	−	0.230782i
$115$	−9.88171	−	1.60607i	−0.921475	−	0.149767i
$116$	5.99430	−	3.46081i	0.556557	−	0.321328i
$117$	−0.978218	−	2.97707i	−0.0904363	−	0.275231i
$118$	10.5744			0.973452
$119$	−0.337449	+	8.35979i	−0.0309339	+	0.766341i
$120$	−3.73861	−	1.01132i	−0.341287	−	0.0923207i
$121$	5.47723	−	9.48683i	0.497930	−	0.862439i
$122$	3.00000	−	1.73205i	0.271607	−	0.156813i
$123$	−1.06101	+	1.46545i	−0.0956682	+	0.132135i
$124$	5.73861	+	3.31319i	0.515343	+	0.297533i
$125$	9.89949	+	5.19615i	0.885438	+	0.464758i
$126$	−5.52581	+	5.69784i	−0.492278	+	0.507604i
$127$			8.73085i			0.774738i	0.921925	+	0.387369i	$0.126616\pi$
$127$			8.73085i			0.774738i	−0.921925	+	0.387369i	$0.873384\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	9.71064	+	7.03066i	0.854974	+	0.619015i
$130$	−2.30545	−	0.374703i	−0.202201	−	0.0328636i
$131$	6.88624	−	11.9273i	0.601654	−	1.04209i	−0.390917	−	0.920426i	$-0.627842\pi$
$131$	6.88624	−	11.9273i	0.601654	−	1.04209i	0.992571	−	0.121669i	$-0.0388245\pi$
$132$	7.40852	−	3.31319i	0.644829	−	0.288376i
$133$	−3.35071	+	1.75830i	−0.290543	+	0.152464i
$134$		−	14.2701i		−	1.23275i
$135$	−0.618823	−	11.6025i	−0.0532598	−	0.998581i
$136$	2.73861	−	1.58114i	0.234834	−	0.135582i
$137$	−1.73861	−	3.01137i	−0.148540	−	0.257278i	0.782148	−	0.623092i	$-0.214124\pi$
$137$	−1.73861	−	3.01137i	−0.148540	−	0.257278i	−0.930688	+	0.365814i	$0.880791\pi$
$138$	7.71363	+	0.797828i	0.656628	+	0.0679156i
$139$		−	20.1810i		−	1.71173i	−0.517202	−	0.855863i	$-0.673026\pi$
$139$		−	20.1810i		−	1.71173i	0.517202	−	0.855863i	$-0.326974\pi$
$140$	1.87298	+	5.61177i	0.158296	+	0.474281i
$141$	−17.7386	+	7.93295i	−1.49386	+	0.668075i
$142$	−5.99430	−	3.46081i	−0.503031	−	0.290425i
$143$	4.23861	−	2.44716i	0.354451	−	0.204642i
$144$	2.93649	+	0.614017i	0.244708	+	0.0511681i
$145$	14.4715	−	5.48811i	1.20180	−	0.455763i
$146$	3.50333			0.289937
$147$	11.9202	+	2.21536i	0.983165	+	0.182720i
$148$		−	2.66291i		−	0.218890i
$149$	2.12132	+	1.22474i	0.173785	+	0.100335i	0.584370	−	0.811488i	$-0.301342\pi$
$149$	2.12132	+	1.22474i	0.173785	+	0.100335i	−0.410584	+	0.911823i	$0.634675\pi$
$150$	−7.88874	−	3.57321i	−0.644113	−	0.291751i
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	1.23861	+	0.715113i	0.100465	+	0.0580034i
$153$	7.07107	+	6.32456i	0.571662	+	0.511310i
$154$	−10.4772	−	6.62638i	−0.844279	−	0.533969i
$155$	11.4772	+	9.37112i	0.921873	+	0.752706i
$156$	1.79962	+	0.186137i	0.144085	+	0.0149029i
$157$	7.22369	+	12.5118i	0.576513	+	0.998550i	0.995875	+	0.0907311i	$0.0289204\pi$
$157$	7.22369	+	12.5118i	0.576513	+	0.998550i	−0.419362	+	0.907819i	$0.637746\pi$
$158$	5.73861	+	9.93957i	0.456540	+	0.790750i
$159$	−8.61430	−	0.890985i	−0.683158	−	0.0706597i
$160$	1.41421	−	1.73205i	0.111803	−	0.136931i
$161$	−5.50423	−	10.4891i	−0.433794	−	0.826661i
$162$	1.00000	+	8.94427i	0.0785674	+	0.702728i
$163$	12.7279	+	7.34847i	0.996928	+	0.575577i	0.907338	−	0.420402i	$-0.138111\pi$
$163$	12.7279	+	7.34847i	0.996928	+	0.575577i	0.0895899	+	0.995979i	$0.471444\pi$
$164$	−0.522278	−	0.904612i	−0.0407831	−	0.0706383i
$165$	17.5399	−	4.65498i	1.36548	−	0.362390i
$166$	−3.52277	−	2.03387i	−0.273420	−	0.157859i
$167$		−	4.29068i		−	0.332023i	−0.986124	−	0.166011i	$-0.946911\pi$
$167$		−	4.29068i		−	0.332023i	0.986124	−	0.166011i	$-0.0530889\pi$
$168$	−1.70058	−	4.25535i	−0.131203	−	0.328308i
$169$	−11.9089			−0.916069
$170$	6.61160	−	2.50735i	0.507086	−	0.192305i
$171$	−0.878183	+	4.19985i	−0.0671564	+	0.321170i
$172$	−5.99430	+	3.46081i	−0.457061	+	0.263885i
$173$	−0.977226	−	0.564201i	−0.0742971	−	0.0428954i	0.462391	−	0.886676i	$-0.346992\pi$
$173$	−0.977226	−	0.564201i	−0.0742971	−	0.0428954i	−0.536688	+	0.843781i	$0.680325\pi$
$174$	−10.9441	+	4.89433i	−0.829666	+	0.371038i
$175$	2.12082	+	13.0576i	0.160319	+	0.987065i
$176$			4.68556i			0.353187i
$177$	−18.2182	−	1.88433i	−1.36936	−	0.141635i
$178$	−2.45877	−	4.25871i	−0.184293	−	0.319204i
$179$	−16.7857	+	9.69125i	−1.25462	+	0.724358i	−0.972024	−	0.234880i	$-0.924530\pi$
$179$	−16.7857	+	9.69125i	−1.25462	+	0.724358i	−0.282600	+	0.959238i	$0.591197\pi$
$180$	6.26089	+	2.40858i	0.466659	+	0.179525i
$181$		−	3.16228i		−	0.235050i	−0.993070	−	0.117525i	$-0.962504\pi$
$181$		−	3.16228i		−	0.235050i	0.993070	−	0.117525i	$-0.0374961\pi$
$182$	−1.28416	−	2.44716i	−0.0951884	−	0.181396i
$183$	−5.47723	+	2.44949i	−0.404888	+	0.181071i
$184$	−2.23861	+	3.87739i	−0.165033	+	0.285845i
$185$	0.955238	−	5.87733i	0.0702305	−	0.432110i
$186$	−9.29642	−	6.73076i	−0.681647	−	0.493524i
$187$	−7.40852	+	12.8319i	−0.541764	+	0.938364i
$188$		−	11.2189i		−	0.818221i
$189$	10.5355	−	8.83190i	0.766347	−	0.642426i
$190$	2.47723	+	2.02265i	0.179717	+	0.146738i
$191$	14.1099	+	8.14637i	1.02096	+	0.589451i	0.914381	−	0.404854i	$-0.132678\pi$
$191$	14.1099	+	8.14637i	1.02096	+	0.589451i	0.106577	+	0.994304i	$0.466011\pi$
$192$	−1.01575	+	1.40294i	−0.0733057	+	0.101249i
$193$	6.36396	−	3.67423i	0.458088	−	0.264477i	−0.253152	−	0.967427i	$-0.581467\pi$
$193$	6.36396	−	3.67423i	0.458088	−	0.264477i	0.711240	+	0.702949i	$0.248134\pi$
$194$	−5.99430	+	10.3824i	−0.430366	+	0.745416i
$195$	3.90519	+	1.05638i	0.279657	+	0.0756492i
$196$	−3.97723	+	5.76035i	−0.284088	+	0.411454i
$197$	−9.00000			−0.641223			−0.320612	−	0.947211i	$-0.603888\pi$
$197$	−9.00000			−0.641223			−0.320612	+	0.947211i	$0.603888\pi$
$198$	−13.3542	+	4.38799i	−0.949044	+	0.311841i
$199$	13.4317	−	7.75478i	0.952146	−	0.549722i	0.0583993	−	0.998293i	$-0.481400\pi$
$199$	13.4317	−	7.75478i	0.952146	−	0.549722i	0.893747	+	0.448571i	$0.148067\pi$
$200$	3.74264	−	3.31552i	0.264645	−	0.234442i
$201$	−2.54289	+	24.5854i	−0.179361	+	1.73412i
$202$	−11.3137			−0.796030
$203$	15.4772	+	9.78866i	1.08629	+	0.687029i
$204$	−5.00000	+	2.23607i	−0.350070	+	0.156556i
$205$	−0.828222	−	2.18393i	−0.0578455	−	0.152532i
$206$	2.45877	+	4.25871i	0.171311	+	0.296719i
$207$	−13.1473	−	2.74909i	−0.913803	−	0.191075i
$208$	−0.522278	+	0.904612i	−0.0362135	+	0.0627236i
$209$	−6.70141			−0.463546
$210$	−2.22689	−	10.0020i	−0.153670	−	0.690207i
$211$	24.4772			1.68508			0.842541	−	0.538632i	$-0.181059\pi$
$211$	24.4772			1.68508			0.842541	+	0.538632i	$0.181059\pi$
$212$	2.50000	−	4.33013i	0.171701	−	0.297394i
$213$	9.71064	+	7.03066i	0.665362	+	0.481733i
$214$	2.73861	+	4.74342i	0.187208	+	0.324253i
$215$	−14.4715	+	5.48811i	−0.986950	+	0.374286i
$216$	−4.94975	−	1.58114i	−0.336788	−	0.107583i
$217$	−0.707107	+	17.5175i	−0.0480015	+	1.18916i
$218$	20.4317			1.38381
$219$	−6.03574	−	0.624282i	−0.407857	−	0.0421851i
$220$	−1.68080	+	10.3415i	−0.113320	+	0.697226i
$221$	−2.86064	+	1.65159i	−0.192427	+	0.111098i
$222$	−0.474523	+	4.58782i	−0.0318479	+	0.307915i
$223$	−21.8881			−1.46574			−0.732868	−	0.680371i	$-0.761819\pi$
$223$	−21.8881			−1.46574			−0.732868	+	0.680371i	$0.761819\pi$
$224$	2.64360	+	0.106711i	0.176633	+	0.00712992i
$225$	12.9545	+	7.56189i	0.863630	+	0.504126i
$226$	−8.73861	+	15.1357i	−0.581284	+	1.00681i
$227$	−9.00000	+	5.19615i	−0.597351	+	0.344881i	−0.767999	−	0.640451i	$-0.778747\pi$
$227$	−9.00000	+	5.19615i	−0.597351	+	0.344881i	0.170648	+	0.985332i	$0.445414\pi$
$228$	−2.00653	−	1.45276i	−0.132885	−	0.0962112i
$229$	−11.7386	−	6.77729i	−0.775709	−	0.447856i	0.0591982	−	0.998246i	$-0.481146\pi$
$229$	−11.7386	−	6.77729i	−0.775709	−	0.447856i	−0.834908	+	0.550390i	$0.814479\pi$
$230$	−6.33175	+	7.75478i	−0.417503	+	0.511335i
$231$	16.8700	+	13.2833i	1.10996	+	0.873979i
$232$		−	6.92163i		−	0.454427i
$233$	−2.00000	+	3.46410i	−0.131024	+	0.226941i	−0.924072	−	0.382219i	$-0.875160\pi$
$233$	−2.00000	+	3.46410i	−0.131024	+	0.226941i	0.793047	+	0.609160i	$0.208493\pi$
$234$	−3.06733	−	0.641375i	−0.200518	−	0.0419280i
$235$	4.02443	−	24.7613i	0.262525	−	1.61525i
$236$	5.28720	−	9.15769i	0.344167	−	0.596115i
$237$	−8.11562	−	18.1471i	−0.527166	−	1.17878i
$238$	7.07107	+	4.47214i	0.458349	+	0.289886i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−2.74514	+	2.73207i	−0.177198	+	0.176354i
$241$	−18.4545	+	10.6547i	−1.18876	+	0.686328i	−0.958024	−	0.286689i	$-0.907445\pi$
$241$	−18.4545	+	10.6547i	−1.18876	+	0.686328i	−0.230732	+	0.973017i	$0.574112\pi$
$242$	−5.47723	−	9.48683i	−0.352089	−	0.609837i
$243$	−0.129018	−	15.5879i	−0.00827648	−	0.999966i
$244$		−	3.46410i		−	0.221766i
$245$	−10.8445	+	11.2870i	−0.692830	+	0.721100i
$246$	0.738613	+	1.65159i	0.0470922	+	0.105301i
$247$	−1.29380	−	0.746976i	−0.0823226	−	0.0475290i
$248$	5.73861	−	3.31319i	0.364402	−	0.210388i
$249$	5.70682	+	4.13183i	0.361655	+	0.261844i
$250$	9.44975	−	5.97514i	0.597655	−	0.377901i
$251$	8.85494			0.558919			0.279459	−	0.960158i	$-0.409845\pi$
$251$	8.85494			0.558919			0.279459	+	0.960158i	$0.409845\pi$
$252$	2.17157	+	7.63441i	0.136796	+	0.480923i
$253$		−	20.9783i		−	1.31889i
$254$	7.56114	+	4.36543i	0.474428	+	0.273911i
$255$	−11.8377	+	3.14164i	−0.741303	+	0.196737i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.52277	+	5.49798i	0.594014	+	0.342954i	0.766683	−	0.642026i	$-0.221906\pi$
$257$	9.52277	+	5.49798i	0.594014	+	0.342954i	−0.172669	+	0.984980i	$0.555239\pi$
$258$	10.9441	−	4.89433i	0.681347	−	0.304708i
$259$	6.23861	−	3.27374i	0.387649	−	0.203421i
$260$	−1.47723	+	1.80922i	−0.0916136	+	0.112203i
$261$	19.7272	−	6.48204i	1.22108	−	0.401229i
$262$	−6.88624	−	11.9273i	−0.425433	−	0.736872i
$263$	−1.00000	−	1.73205i	−0.0616626	−	0.106803i	0.833546	−	0.552450i	$-0.186307\pi$
$263$	−1.00000	−	1.73205i	−0.0616626	−	0.106803i	−0.895209	+	0.445647i	$0.852974\pi$
$264$	0.834952	−	8.07256i	0.0513878	−	0.496832i
$265$	7.07107	−	8.66025i	0.434372	−	0.531995i
$266$	−0.152621	+	3.78095i	−0.00935778	+	0.231825i
$267$	3.47723	+	7.77531i	0.212803	+	0.475841i
$268$	−12.3583	−	7.13505i	−0.754901	−	0.435842i
$269$	−8.79052	−	15.2256i	−0.535968	−	0.928323i	−0.999116	−	0.0420423i	$-0.986614\pi$
$269$	−8.79052	−	15.2256i	−0.535968	−	0.928323i	0.463148	−	0.886281i	$-0.346720\pi$
$270$	−10.3574	−	5.26531i	−0.630333	−	0.320437i
$271$	−5.47723	−	3.16228i	−0.332718	−	0.192095i	0.324329	−	0.945944i	$-0.394861\pi$
$271$	−5.47723	−	3.16228i	−0.332718	−	0.192095i	−0.657047	+	0.753850i	$0.728195\pi$
$272$		−	3.16228i		−	0.191741i
$273$	1.77635	+	4.44495i	0.107510	+	0.269021i
$274$	−3.47723			−0.210067
$275$	−7.41941	+	22.2219i	−0.447407	+	1.34003i
$276$	4.54776	−	6.28129i	0.273743	−	0.378089i
$277$	−8.48528	+	4.89898i	−0.509831	+	0.294351i	−0.732764	−	0.680483i	$-0.761770\pi$
$277$	−8.48528	+	4.89898i	−0.509831	+	0.294351i	0.222933	+	0.974834i	$0.428437\pi$
$278$	−17.4772	−	10.0905i	−1.04821	−	0.605187i
$279$	14.8170	+	13.2528i	0.887073	+	0.793422i
$280$	5.79642	+	1.18383i	0.346403	+	0.0707475i
$281$		−	1.80922i		−	0.107929i	−0.998543	−	0.0539646i	$-0.982814\pi$
$281$		−	1.80922i		−	0.107929i	0.998543	−	0.0539646i	$-0.0171858\pi$
$282$	−1.99917	+	19.3286i	−0.119049	+	1.15100i
$283$	4.61230	+	7.98873i	0.274173	+	0.474881i	0.969926	−	0.243400i	$-0.0782627\pi$
$283$	4.61230	+	7.98873i	0.274173	+	0.474881i	−0.695753	+	0.718281i	$0.744929\pi$
$284$	−5.99430	+	3.46081i	−0.355696	+	0.205361i
$285$	−3.90748	−	3.92617i	−0.231459	−	0.232566i
$286$		−	4.89433i		−	0.289408i
$287$	1.47723	−	2.33570i	0.0871979	−	0.137872i
$288$	2.00000	−	2.23607i	0.117851	−	0.131762i
$289$	−3.50000	+	6.06218i	−0.205882	+	0.356599i
$290$	2.48292	−	15.2768i	0.145802	−	0.897083i
$291$	12.1775	−	16.8193i	0.713856	−	0.985966i
$292$	1.75166	−	3.03397i	0.102508	−	0.177550i
$293$			8.05661i			0.470672i	0.971914	+	0.235336i	$0.0756190\pi$
$293$			8.05661i			0.470672i	−0.971914	+	0.235336i	$0.924381\pi$
$294$	7.87868	−	9.21555i	0.459494	−	0.537462i
$295$	14.9545	−	18.3154i	0.870682	−	1.06636i
$296$	−2.30615	−	1.33146i	−0.134042	−	0.0773893i
$297$	23.7894	−	5.18020i	1.38040	−	0.300586i
$298$	2.12132	−	1.22474i	0.122885	−	0.0709476i
$299$	2.33836	−	4.05015i	0.135231	−	0.234226i
$300$	−7.03886	+	5.04524i	−0.406389	+	0.291287i
$301$	−15.4772	−	9.78866i	−0.892092	−	0.564209i
$302$	2.00000			0.115087
$303$	19.4919	+	2.01607i	1.11978	+	0.115820i
$304$	1.23861	−	0.715113i	0.0710393	−	0.0410146i
$305$	1.24264	−	7.64564i	0.0711534	−	0.437788i
$306$	9.01276	−	2.96145i	0.515225	−	0.169295i
$307$	11.9886			0.684226			0.342113	−	0.939659i	$-0.388857\pi$
$307$	11.9886			0.684226			0.342113	+	0.939659i	$0.388857\pi$
$308$	−10.9772	+	5.76035i	−0.625485	+	0.328227i
$309$	−3.47723	−	7.77531i	−0.197812	−	0.442322i
$310$	13.8542	−	5.25401i	0.786868	−	0.298408i
$311$	−8.79052	−	15.2256i	−0.498465	−	0.863366i	0.501534	−	0.865138i	$-0.332769\pi$
$311$	−8.79052	−	15.2256i	−0.498465	−	0.863366i	−0.999998	+	0.00177176i	$0.999436\pi$
$312$	1.06101	−	1.46545i	0.0600679	−	0.0829649i
$313$	11.6190	−	20.1246i	0.656742	−	1.13751i	−0.324712	−	0.945813i	$-0.605267\pi$
$313$	11.6190	−	20.1246i	0.656742	−	1.13751i	0.981454	−	0.191697i	$-0.0613992\pi$
$314$	14.4474			0.815313
$315$	2.05428	+	17.6290i	0.115746	+	0.993279i
$316$	11.4772			0.645644
$317$	−4.95445	+	8.58136i	−0.278270	+	0.481977i	−0.970955	−	0.239263i	$-0.923094\pi$
$317$	−4.95445	+	8.58136i	−0.278270	+	0.481977i	0.692685	+	0.721240i	$0.256428\pi$
$318$	−5.07877	+	7.01471i	−0.284803	+	0.393365i
$319$	16.2158	+	28.0867i	0.907913	+	1.57255i
$320$	−0.792893	−	2.09077i	−0.0443241	−	0.116878i
$321$	−3.87298	−	8.66025i	−0.216169	−	0.483368i
$322$	−11.8360	−	0.477769i	−0.659594	−	0.0266250i
$323$	4.52277			0.251654
$324$	8.24597	+	3.60611i	0.458109	+	0.200339i
$325$	−3.90940	+	3.46324i	−0.216854	+	0.192106i
$326$	12.7279	−	7.34847i	0.704934	−	0.406994i
$327$	−35.2009	−	3.64086i	−1.94662	−	0.201340i
$328$	−1.04456			−0.0576760
$329$	26.2834	−	13.7923i	1.44905	−	0.760396i
$330$	4.73861	−	17.5175i	0.260852	−	0.964306i
$331$	−10.7158	+	18.5604i	−0.588996	+	1.02017i	0.405369	+	0.914153i	$0.367143\pi$
$331$	−10.7158	+	18.5604i	−0.588996	+	1.02017i	−0.994364	+	0.106017i	$0.966190\pi$
$332$	−3.52277	+	2.03387i	−0.193337	+	0.111623i
$333$	1.63507	−	7.81962i	0.0896014	−	0.428512i
$334$	−3.71584	−	2.14534i	−0.203322	−	0.117388i
$335$	−24.7165	−	20.1810i	−1.35041	−	1.10260i
$336$	−4.53553	−	0.654929i	−0.247434	−	0.0357293i
$337$		−	17.1464i		−	0.934025i	−0.884251	−	0.467013i	$-0.845330\pi$
$337$		−	17.1464i		−	0.934025i	0.884251	−	0.467013i	$-0.154670\pi$
$338$	−5.95445	+	10.3134i	−0.323879	+	0.560976i
$339$	17.7525	−	24.5195i	0.964186	−	1.33172i
$340$	1.13437	−	6.97948i	0.0615199	−	0.378516i
$341$	−15.5241	+	26.8886i	−0.840679	+	1.45610i
$342$	3.19808	+	2.86045i	0.172933	+	0.154676i
$343$	−18.3848	−	2.23607i	−0.992685	−	0.120736i
$344$			6.92163i			0.373189i
$345$	12.2906	−	12.2321i	0.661704	−	0.658554i
$346$	−0.977226	+	0.564201i	−0.0525360	+	0.0303317i
$347$	−8.73861	−	15.1357i	−0.469113	−	0.812528i	0.530263	−	0.847833i	$-0.322093\pi$
$347$	−8.73861	−	15.1357i	−0.469113	−	0.812528i	−0.999377	+	0.0353049i	$0.988760\pi$
$348$	−1.23341	+	11.9250i	−0.0661179	+	0.639247i
$349$			11.7436i			0.628623i	0.949320	+	0.314311i	$0.101774\pi$
$349$			11.7436i			0.628623i	−0.949320	+	0.314311i	$0.898226\pi$
$350$	12.3687	+	4.69214i	0.661133	+	0.250805i
$351$	5.17029	+	1.65159i	0.275970	+	0.0881553i
$352$	4.05781	+	2.34278i	0.216282	+	0.124871i
$353$	−0.522774	+	0.301824i	−0.0278245	+	0.0160645i	−0.513848	−	0.857881i	$-0.671780\pi$
$353$	−0.522774	+	0.301824i	−0.0278245	+	0.0160645i	0.486023	+	0.873946i	$0.338447\pi$
$354$	−10.7410	+	14.8353i	−0.570876	+	0.788485i
$355$	−14.4715	+	5.48811i	−0.768069	+	0.291279i
$356$	−4.91754			−0.260629
$357$	−11.3855	−	8.96491i	−0.602587	−	0.474473i
$358$			19.3825i			1.02440i
$359$	−9.86729	−	5.69688i	−0.520775	−	0.300670i	0.216476	−	0.976288i	$-0.430544\pi$
$359$	−9.86729	−	5.69688i	−0.520775	−	0.300670i	−0.737252	+	0.675618i	$0.763877\pi$
$360$	5.21633	−	4.21780i	0.274925	−	0.222298i
$361$	−8.47723	−	14.6830i	−0.446170	−	0.772789i
$362$	−2.73861	−	1.58114i	−0.143938	−	0.0831028i
$363$	7.74597	+	17.3205i	0.406558	+	0.909091i
$364$	−2.76139	−	0.111466i	−0.144736	−	0.00584238i
$365$	4.95445	−	6.06794i	0.259328	−	0.317610i
$366$	−0.617292	+	5.96816i	−0.0322664	+	0.311961i
$367$	0.184829	+	0.320133i	0.00964798	+	0.0167108i	0.870809	−	0.491621i	$-0.163596\pi$
$367$	0.184829	+	0.320133i	0.00964798	+	0.0167108i	−0.861161	+	0.508332i	$0.830262\pi$
$368$	2.23861	+	3.87739i	0.116696	+	0.202123i
$369$	−0.978218	−	2.97707i	−0.0509240	−	0.154980i
$370$	−4.61230	−	3.76593i	−0.239782	−	0.195781i
$371$	13.2180	+	0.533554i	0.686244	+	0.0277008i
$372$	−10.4772	+	4.68556i	−0.543219	+	0.242935i
$373$	−20.1042	−	11.6072i	−1.04096	−	0.600997i	−0.120853	−	0.992670i	$-0.538563\pi$
$373$	−20.1042	−	11.6072i	−1.04096	−	0.600997i	−0.920104	+	0.391673i	$0.871896\pi$
$374$	7.40852	+	12.8319i	0.383085	+	0.663523i
$375$	−17.3453	+	8.61041i	−0.895710	+	0.444640i
$376$	−9.71584	−	5.60944i	−0.501056	−	0.289285i
$377$			7.23003i			0.372365i
$378$	−2.38089	−	13.5400i	−0.122460	−	0.696422i
$379$	−20.4772			−1.05184			−0.525922	−	0.850533i	$-0.676280\pi$
$379$	−20.4772			−1.05184			−0.525922	+	0.850533i	$0.676280\pi$
$380$	2.99028	−	1.13402i	0.153398	−	0.0581739i
$381$	−12.2489	−	8.86839i	−0.627529	−	0.454341i
$382$	14.1099	−	8.14637i	0.721927	−	0.416805i
$383$	−15.7158	−	9.07354i	−0.803042	−	0.463636i	0.0414919	−	0.999139i	$-0.486789\pi$
$383$	−15.7158	−	9.07354i	−0.803042	−	0.463636i	−0.844534	+	0.535502i	$0.820122\pi$
$384$	0.707107	+	1.58114i	0.0360844	+	0.0806872i
$385$	−26.2943	+	8.77597i	−1.34008	+	0.447265i
$386$		−	7.34847i		−	0.374027i
$387$	−19.7272	+	6.48204i	−1.00279	+	0.329501i
$388$	5.99430	+	10.3824i	0.304315	+	0.527088i
$389$	−6.36396	+	3.67423i	−0.322666	+	0.186291i	−0.652580	−	0.757720i	$-0.726313\pi$
$389$	−6.36396	+	3.67423i	−0.322666	+	0.186291i	0.329914	+	0.944011i	$0.392980\pi$
$390$	2.86745	−	2.85380i	0.145199	−	0.144508i
$391$			14.1582i			0.716012i
$392$	3.00000	+	6.32456i	0.151523	+	0.319438i
$393$	9.73861	+	21.7762i	0.491248	+	1.09846i
$394$	−4.50000	+	7.79423i	−0.226707	+	0.392668i
$395$	25.3315	+	4.11710i	1.27456	+	0.207154i
$396$	−2.87701	+	13.7591i	−0.144575	+	0.691421i
$397$	7.44073	−	12.8877i	0.373439	−	0.646816i	−0.616653	−	0.787235i	$-0.711512\pi$
$397$	7.44073	−	12.8877i	0.373439	−	0.646816i	0.990092	+	0.140419i	$0.0448451\pi$
$398$		−	15.5096i		−	0.777424i
$399$	0.936697	−	6.48684i	0.0468935	−	0.324748i
$400$	−1.00000	−	4.89898i	−0.0500000	−	0.244949i
$401$	0.827520	+	0.477769i	0.0413244	+	0.0238586i	0.520520	−	0.853850i	$-0.325738\pi$
$401$	0.827520	+	0.477769i	0.0413244	+	0.0238586i	−0.479195	+	0.877708i	$0.659072\pi$
$402$	20.0201	+	14.4949i	0.998513	+	0.722939i
$403$	−5.99430	+	3.46081i	−0.298598	+	0.172395i
$404$	−5.65685	+	9.79796i	−0.281439	+	0.487467i
$405$	16.9061	+	10.9171i	0.840073	+	0.542473i
$406$	16.2158	−	8.50934i	0.804779	−	0.422312i
$407$	12.4772			0.618473
$408$	−0.563508	+	5.44816i	−0.0278978	+	0.269724i
$409$	13.4317	−	7.75478i	0.664154	−	0.383449i	−0.129704	−	0.991553i	$-0.541403\pi$
$409$	13.4317	−	7.75478i	0.664154	−	0.383449i	0.793858	+	0.608103i	$0.208069\pi$
$410$	−2.30545	−	0.374703i	−0.113858	−	0.0185052i
$411$	5.99077	+	0.619631i	0.295503	+	0.0305641i
$412$	4.91754			0.242270
$413$	27.9545	+	1.12840i	1.37555	+	0.0555251i
$414$	−8.95445	+	10.0114i	−0.440087	+	0.492033i
$415$	−8.50473	+	3.22529i	−0.417481	+	0.158323i
$416$	0.522278	+	0.904612i	0.0256068	+	0.0443523i
$417$	28.3127	+	20.4989i	1.38648	+	1.00383i
$418$	−3.35071	+	5.80359i	−0.163888	+	0.283863i
$419$	−8.85494			−0.432592			−0.216296	−	0.976328i	$-0.569398\pi$
$419$	−8.85494			−0.432592			−0.216296	+	0.976328i	$0.569398\pi$
$420$	−9.77547	−	3.07248i	−0.476994	−	0.149922i
$421$	18.9545			0.923783			0.461892	−	0.886936i	$-0.347171\pi$
$421$	18.9545			0.923783			0.461892	+	0.886936i	$0.347171\pi$
$422$	12.2386	−	21.1979i	0.595766	−	1.03190i
$423$	6.88858	−	32.9442i	0.334934	−	1.60180i
$424$	−2.50000	−	4.33013i	−0.121411	−	0.210290i
$425$	5.00735	−	14.9975i	0.242892	−	0.727488i
$426$	10.9441	−	4.89433i	0.530241	−	0.237131i
$427$	8.11562	−	4.25871i	0.392743	−	0.206094i
$428$	5.47723			0.264752
$429$	−0.872155	+	8.43224i	−0.0421080	+	0.407112i
$430$	−2.48292	+	15.2768i	−0.119737	+	0.736711i
$431$	−6.63699	+	3.83187i	−0.319693	+	0.184575i	−0.651256	−	0.758858i	$-0.725757\pi$
$431$	−6.63699	+	3.83187i	−0.319693	+	0.184575i	0.331563	+	0.943433i	$0.392424\pi$
$432$	−3.84418	+	3.49604i	−0.184953	+	0.168203i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	14.8170	+	9.37112i	0.711240	+	0.449828i
$435$	−7.00000	+	25.8773i	−0.335624	+	1.24072i
$436$	10.2158	−	17.6944i	0.489250	−	0.847406i
$437$	−5.54555	+	3.20172i	−0.265280	+	0.153159i
$438$	−3.55851	+	4.91496i	−0.170032	+	0.234846i
$439$	−7.69306	−	4.44159i	−0.367170	−	0.211986i	0.305051	−	0.952336i	$-0.401326\pi$
$439$	−7.69306	−	4.44159i	−0.367170	−	0.211986i	−0.672221	+	0.740350i	$0.734660\pi$
$440$	8.11562	+	6.62638i	0.386897	+	0.315900i
$441$	−15.2160	+	14.4731i	−0.724574	+	0.689198i
$442$			3.30318i			0.157116i
$443$	−7.52277	+	13.0298i	−0.357418	+	0.619066i	−0.987529	−	0.157439i	$-0.949676\pi$
$443$	−7.52277	+	13.0298i	−0.357418	+	0.619066i	0.630111	+	0.776505i	$0.283009\pi$
$444$	3.73591	+	2.70486i	0.177298	+	0.128367i
$445$	−10.8535	−	1.76402i	−0.514507	−	0.0836224i
$446$	−10.9441	+	18.9557i	−0.518216	+	0.897576i
$447$	−3.87298	+	1.73205i	−0.183186	+	0.0819232i
$448$	1.41421	−	2.23607i	0.0668153	−	0.105644i
$449$		−	25.8773i		−	1.22122i	−0.791930	−	0.610612i	$-0.790923\pi$
$449$		−	25.8773i		−	1.22122i	0.791930	−	0.610612i	$-0.209077\pi$
$450$	13.0260	−	7.43794i	0.614052	−	0.350628i
$451$	4.23861	−	2.44716i	0.199588	−	0.115232i
$452$	8.73861	+	15.1357i	0.411030	+	0.711924i
$453$	−3.44572	−	0.356394i	−0.161894	−	0.0167448i
$454$			10.3923i			0.487735i
$455$	−6.05469	−	1.23658i	−0.283848	−	0.0579717i
$456$	−2.26139	+	1.01132i	−0.105899	+	0.0473595i
$457$	9.59425	+	5.53924i	0.448800	+	0.259115i	0.707323	−	0.706890i	$-0.249902\pi$
$457$	9.59425	+	5.53924i	0.448800	+	0.259115i	−0.258523	+	0.966005i	$0.583236\pi$
$458$	−11.7386	+	6.77729i	−0.548509	+	0.316682i
$459$	−16.0554	+	3.49611i	−0.749404	+	0.163184i
$460$	3.54996	+	9.36085i	0.165518	+	0.436452i
$461$	−31.7876			−1.48050			−0.740248	−	0.672334i	$-0.765292\pi$
$461$	−31.7876			−1.48050			−0.740248	+	0.672334i	$0.765292\pi$
$462$	19.9387	−	7.96817i	0.927632	−	0.370713i
$463$			22.5741i			1.04911i	0.851377	+	0.524554i	$0.175768\pi$
$463$			22.5741i			1.04911i	−0.851377	+	0.524554i	$0.824232\pi$
$464$	−5.99430	−	3.46081i	−0.278279	−	0.160664i
$465$	−24.8052	+	6.58314i	−1.15031	+	0.305286i
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	24.2614	+	14.0073i	1.12268	+	0.648181i	0.942085	−	0.335375i	$-0.108863\pi$
$467$	24.2614	+	14.0073i	1.12268	+	0.648181i	0.180599	+	0.983557i	$0.442197\pi$
$468$	−2.08911	+	2.33570i	−0.0965693	+	0.107968i
$469$	1.52277	−	37.7244i	0.0703152	−	1.74195i
$470$	−19.4317	−	15.8659i	−0.896316	−	0.731839i
$471$	−24.8908	−	2.57448i	−1.14691	−	0.118626i
$472$	−5.28720	−	9.15769i	−0.243363	−	0.421517i
$473$	−16.2158	−	28.0867i	−0.745605	−	1.29143i
$474$	−19.7737	−	2.04521i	−0.908234	−	0.0939395i
$475$	7.00665	−	1.43023i	0.321487	−	0.0656233i
$476$	7.40852	−	3.88766i	0.339569	−	0.178190i
$477$	10.0000	−	11.1803i	0.457869	−	0.511913i
$478$		0			0
$479$	21.1810	+	36.6866i	0.967784	+	1.67625i	0.701940	+	0.712236i	$0.252317\pi$
$479$	21.1810	+	36.6866i	0.967784	+	1.67625i	0.265844	+	0.964016i	$0.414349\pi$
$480$	0.993475	+	3.74340i	0.0453457	+	0.170862i
$481$	2.40890	+	1.39078i	0.109836	+	0.0634141i
$482$			21.3094i			0.970615i
$483$	20.3066	+	2.93227i	0.923983	+	0.133423i
$484$	−10.9545			−0.497930
$485$	9.50569	+	25.0654i	0.431631	+	1.13816i
$486$	−13.5640	−	7.68223i	−0.615278	−	0.348473i
$487$	−14.7526	+	8.51743i	−0.668505	+	0.385962i	−0.795510	−	0.605941i	$-0.792797\pi$
$487$	−14.7526	+	8.51743i	−0.668505	+	0.385962i	0.127005	+	0.991902i	$0.459464\pi$
$488$	−3.00000	−	1.73205i	−0.135804	−	0.0784063i
$489$	−23.2379	+	10.3923i	−1.05085	+	0.469956i
$490$	4.35258	+	15.0351i	0.196629	+	0.679218i
$491$			13.8433i			0.624737i	0.949961	+	0.312369i	$0.101122\pi$
$491$			13.8433i			0.624737i	−0.949961	+	0.312369i	$0.898878\pi$
$492$	1.79962	+	0.186137i	0.0811333	+	0.00839169i
$493$	−10.9441	−	18.9557i	−0.492895	−	0.853720i
$494$	−1.29380	+	0.746976i	−0.0582108	+	0.0336080i
$495$	−11.2855	+	29.3358i	−0.507247	+	1.31854i
$496$		−	6.62638i		−	0.297533i
$497$	−15.4772	−	9.78866i	−0.694248	−	0.439081i
$498$	6.43168	−	2.87633i	0.288210	−	0.128892i
$499$	−0.954451	+	1.65316i	−0.0427271	+	0.0740055i	−0.886598	−	0.462541i	$-0.846938\pi$
$499$	−0.954451	+	1.65316i	−0.0427271	+	0.0740055i	0.843871	+	0.536546i	$0.180271\pi$
$500$	−0.449747	−	11.1713i	−0.0201133	−	0.499595i
$501$	6.01958	+	4.35827i	0.268935	+	0.194713i
$502$	4.42747	−	7.66860i	0.197608	−	0.342266i
$503$			15.5096i			0.691537i	0.938320	+	0.345769i	$0.112382\pi$
$503$			15.5096i			0.691537i	−0.938320	+	0.345769i	$0.887618\pi$
$504$	7.69738	+	1.93657i	0.342869	+	0.0862617i
$505$	−16.0000	+	19.5959i	−0.711991	+	0.872007i
$506$	−18.1677	−	10.4891i	−0.807655	−	0.466300i
$507$	12.0965	−	16.7075i	0.537225	−	0.742006i
$508$	7.56114	−	4.36543i	0.335471	−	0.193684i
$509$	12.3583	−	21.4051i	0.547770	−	0.948766i	−0.450656	−	0.892697i	$-0.648810\pi$
$509$	12.3583	−	21.4051i	0.547770	−	0.948766i	0.998427	−	0.0560688i	$-0.0178566\pi$
$510$	−3.19808	+	11.8225i	−0.141614	+	0.523511i
$511$	9.26139	+	0.373843i	0.409700	+	0.0165378i
$512$	−1.00000			−0.0441942
$513$	−5.00013	−	5.49805i	−0.220761	−	0.242745i
$514$	9.52277	−	5.49798i	0.420032	−	0.242505i
$515$	10.8535	+	1.76402i	0.478264	+	0.0777319i
$516$	1.23341	−	11.9250i	0.0542980	−	0.524968i
$517$	52.5667			2.31188
$518$	0.284162	−	7.03967i	0.0124853	−	0.309305i
$519$	1.78416	−	0.797901i	0.0783160	−	0.0350240i
$520$	0.828222	+	2.18393i	0.0363199	+	0.0957715i
$521$	17.7981	+	30.8272i	0.779748	+	1.35056i	0.932087	+	0.362235i	$0.117986\pi$
$521$	17.7981	+	30.8272i	0.779748	+	1.35056i	−0.152339	+	0.988328i	$0.548680\pi$
$522$	4.24999	−	20.3253i	0.186017	−	0.889614i
$523$	−8.45307	+	14.6412i	−0.369627	+	0.640213i	−0.989507	−	0.144484i	$-0.953848\pi$
$523$	−8.45307	+	14.6412i	−0.369627	+	0.640213i	0.619880	+	0.784697i	$0.287181\pi$
$524$	−13.7725			−0.601654
$525$	−20.4734	−	10.2879i	−0.893530	−	0.449003i
$526$	−2.00000			−0.0872041
$527$	10.4772	−	18.1471i	0.456395	−	0.790500i
$528$	−6.57357	−	4.75937i	−0.286078	−	0.207125i
$529$	1.47723	+	2.55863i	0.0642272	+	0.111245i
$530$	−3.96447	−	10.4539i	−0.172205	−	0.454086i
$531$	21.1488	−	23.6451i	0.917779	−	1.02611i
$532$	3.19808	+	2.02265i	0.138655	+	0.0876928i
$533$	1.09110			0.0472607
$534$	8.47223	+	0.876291i	0.366629	+	0.0379208i
$535$	12.0888	+	1.96479i	0.522645	+	0.0849452i
$536$	−12.3583	+	7.13505i	−0.533796	+	0.308187i
$537$	3.45390	−	33.3933i	0.149047	−	1.44103i
$538$	−17.5810			−0.757973
$539$	−26.9905	−	18.6355i	−1.16256	−	0.802689i
$540$	−9.73861	+	6.33715i	−0.419083	+	0.272707i
$541$	−4.26139	+	7.38094i	−0.183211	+	0.317331i	−0.942972	−	0.332871i	$-0.891983\pi$
$541$	−4.26139	+	7.38094i	−0.183211	+	0.317331i	0.759761	+	0.650202i	$0.225316\pi$
$542$	−5.47723	+	3.16228i	−0.235267	+	0.135831i
$543$	4.43649	+	3.21209i	0.190388	+	0.137844i
$544$	−2.73861	−	1.58114i	−0.117417	−	0.0677908i
$545$	28.8948	−	35.3887i	1.23772	−	1.51589i
$546$	4.73762	+	0.684110i	0.202751	+	0.0292772i
$547$		−	3.61845i		−	0.154714i	−0.997003	−	0.0773569i	$-0.975352\pi$
$547$		−	3.61845i		−	0.154714i	0.997003	−	0.0773569i	$-0.0246481\pi$
$548$	−1.73861	+	3.01137i	−0.0742699	+	0.128639i
$549$	2.12702	−	10.1723i	0.0907789	−	0.434143i
$550$	15.5350	+	17.5364i	0.662416	+	0.747753i
$551$	4.94975	−	8.57321i	0.210866	−	0.365231i
$552$	−3.16588	−	7.07912i	−0.134749	−	0.301307i
$553$	14.1099	+	26.8886i	0.600015	+	1.14342i
$554$			9.79796i			0.416275i
$555$	7.27527	+	7.31006i	0.308818	+	0.310295i
$556$	−17.4772	+	10.0905i	−0.741199	+	0.427932i
$557$	13.9317	+	24.1304i	0.590304	+	1.02244i	0.994191	+	0.107628i	$0.0343255\pi$
$557$	13.9317	+	24.1304i	0.590304	+	1.02244i	−0.403887	+	0.914809i	$0.632341\pi$
$558$	18.8857	−	6.20555i	0.799497	−	0.262702i
$559$		−	7.23003i		−	0.305798i
$560$	3.92344	−	4.42793i	0.165796	−	0.187114i
$561$	−10.4772	−	23.4278i	−0.442349	−	0.989122i
$562$	−1.56683	−	0.904612i	−0.0660929	−	0.0381588i
$563$	−9.00000	+	5.19615i	−0.379305	+	0.218992i	−0.677516	−	0.735508i	$-0.736943\pi$
$563$	−9.00000	+	5.19615i	−0.379305	+	0.218992i	0.298211	+	0.954500i	$0.403610\pi$
$564$	15.7394	+	11.3956i	0.662750	+	0.479842i
$565$	13.8576	+	36.5409i	0.582993	+	1.53729i
$566$	9.22460			0.387739
$567$	1.68915	+	23.7518i	0.0709375	+	0.997481i
$568$			6.92163i			0.290425i
$569$	6.54879	+	3.78095i	0.274540	+	0.158505i	0.630949	−	0.775824i	$-0.282666\pi$
$569$	6.54879	+	3.78095i	0.274540	+	0.158505i	−0.356409	+	0.934330i	$0.615999\pi$
$570$	−5.35390	+	1.42089i	−0.224250	+	0.0595147i
$571$	−7.47723	−	12.9509i	−0.312912	−	0.541980i	0.666079	−	0.745881i	$-0.267971\pi$
$571$	−7.47723	−	12.9509i	−0.312912	−	0.541980i	−0.978991	+	0.203901i	$0.934638\pi$
$572$	−4.23861	−	2.44716i	−0.177225	−	0.102321i
$573$	−25.7611	+	11.5207i	−1.07618	+	0.481284i
$574$	−1.28416	−	2.44716i	−0.0535999	−	0.102143i
$575$	4.47723	+	21.9338i	0.186713	+	0.914704i
$576$	−0.936492	−	2.85008i	−0.0390205	−	0.118754i
$577$	−0.337449	−	0.584480i	−0.0140482	−	0.0243322i	0.858916	−	0.512117i	$-0.171138\pi$
$577$	−0.337449	−	0.584480i	−0.0140482	−	0.0243322i	−0.872964	+	0.487785i	$0.837805\pi$
$578$	3.50000	+	6.06218i	0.145581	+	0.252153i
$579$	−1.30948	+	12.6604i	−0.0544199	+	0.526148i
$580$	−11.9886	−	9.78866i	−0.497800	−	0.406452i
$581$	−9.09576	−	5.75267i	−0.377356	−	0.238661i
$582$	−8.47723	−	18.9557i	−0.351392	−	0.785737i
$583$	20.2891	+	11.7139i	0.840287	+	0.485140i
$584$	−1.75166	−	3.03397i	−0.0724843	−	0.125547i
$585$	−5.44875	+	4.40573i	−0.225278	+	0.182155i
$586$	6.97723	+	4.02830i	0.288227	+	0.166408i
$587$		−	21.0864i		−	0.870330i	−0.900351	−	0.435165i	$-0.856690\pi$
$587$		−	21.0864i		−	0.870330i	0.900351	−	0.435165i	$-0.143310\pi$
$588$	−4.04156	−	11.4309i	−0.166671	−	0.471403i
$589$	9.47723			0.390502
$590$	−8.38437	−	22.1086i	−0.345179	−	0.910198i
$591$	9.14178	−	12.6265i	0.376042	−	0.519384i
$592$	−2.30615	+	1.33146i	−0.0947821	+	0.0547225i
$593$	1.43168	+	0.826579i	0.0587919	+	0.0339435i	0.529108	−	0.848555i	$-0.322527\pi$
$593$	1.43168	+	0.826579i	0.0587919	+	0.0339435i	−0.470316	+	0.882498i	$0.655860\pi$
$594$	7.40852	−	23.1923i	0.303975	−	0.951593i
$595$	17.7460	−	5.92289i	0.727514	−	0.242815i
$596$		−	2.44949i		−	0.100335i
$597$	−2.76376	+	26.7208i	−0.113113	+	1.09361i
$598$	−2.33836	−	4.05015i	−0.0956225	−	0.165623i
$599$	20.4739	−	11.8206i	0.836540	−	0.482977i	−0.0195464	−	0.999809i	$-0.506222\pi$
$599$	20.4739	−	11.8206i	0.836540	−	0.482977i	0.856087	+	0.516832i	$0.172889\pi$
$600$	0.849876	+	8.61845i	0.0346961	+	0.351847i
$601$			4.06775i			0.165927i	0.996553	+	0.0829635i	$0.0264385\pi$
$601$			4.06775i			0.165927i	−0.996553	+	0.0829635i	$0.973562\pi$
$602$	−16.2158	+	8.50934i	−0.660908	+	0.346815i
$603$	−31.9089	−	28.5402i	−1.29943	−	1.16225i
$604$	1.00000	−	1.73205i	0.0406894	−	0.0704761i
$605$	−24.1776	−	3.92957i	−0.982961	−	0.159760i
$606$	11.4919	−	15.8725i	0.466828	−	0.644775i
$607$	6.14692	−	10.6468i	0.249496	−	0.432140i	−0.713890	−	0.700258i	$-0.753068\pi$
$607$	6.14692	−	10.6468i	0.249496	−	0.432140i	0.963386	+	0.268118i	$0.0864017\pi$
$608$		−	1.43023i		−	0.0580034i
$609$	−29.4540	+	11.7708i	−1.19353	+	0.476976i
$610$	−6.00000	−	4.89898i	−0.242933	−	0.198354i
$611$	10.1487	+	5.85938i	0.410574	+	0.237045i
$612$	1.94169	−	9.28600i	0.0784882	−	0.375364i
$613$	5.07016	−	2.92726i	0.204782	−	0.118231i	−0.394102	−	0.919067i	$-0.628944\pi$
$613$	5.07016	−	2.92726i	0.204782	−	0.118231i	0.598884	+	0.800836i	$0.295611\pi$
$614$	5.99430	−	10.3824i	0.241910	−	0.419001i
$615$	3.90519	+	1.05638i	0.157473	+	0.0425975i
$616$	−0.500000	+	12.3867i	−0.0201456	+	0.499076i
$617$	−14.5228			−0.584665			−0.292332	−	0.956317i	$-0.594431\pi$
$617$	−14.5228			−0.584665			−0.292332	+	0.956317i	$0.594431\pi$
$618$	−8.47223	−	0.876291i	−0.340803	−	0.0352496i
$619$	26.1475	−	15.0963i	1.05096	−	0.606771i	0.128040	−	0.991769i	$-0.459131\pi$
$619$	26.1475	−	15.0963i	1.05096	−	0.606771i	0.922917	+	0.384998i	$0.125798\pi$
$620$	2.37701	−	14.6251i	0.0954631	−	0.587359i
$621$	17.2113	−	15.6525i	0.690664	−	0.628115i
$622$	−17.5810			−0.704936
$623$	−6.04555	−	11.5207i	−0.242210	−	0.461567i
$624$	−0.738613	−	1.65159i	−0.0295682	−	0.0661165i
$625$	3.01472	−	24.8176i	0.120589	−	0.992703i
$626$	−11.6190	−	20.1246i	−0.464387	−	0.804341i
$627$	6.80698	−	9.40169i	0.271845	−	0.375467i
$628$	7.22369	−	12.5118i	0.288257	−	0.499275i
$629$	−8.42087			−0.335762
$630$	16.2943	+	7.03542i	0.649179	+	0.280298i
$631$	3.47723			0.138426			0.0692131	−	0.997602i	$-0.477951\pi$
$631$	3.47723			0.138426			0.0692131	+	0.997602i	$0.477951\pi$
$632$	5.73861	−	9.93957i	0.228270	−	0.395375i
$633$	−24.8628	+	34.3401i	−0.988208	+	1.36490i
$634$	4.95445	+	8.58136i	0.196766	+	0.340809i
$635$	18.2542	−	6.92263i	0.724396	−	0.274716i
$636$	3.53553	+	7.90569i	0.140193	+	0.313481i
$637$	−3.13367	−	6.60635i	−0.124160	−	0.261753i
$638$	32.4317			1.28398
$639$	−19.7272	+	6.48204i	−0.780397	+	0.256426i
$640$	−2.20711	−	0.358719i	−0.0872436	−	0.0141796i
$641$	−13.9251	+	8.03966i	−0.550008	+	0.317547i	−0.749125	−	0.662428i	$-0.769526\pi$
$641$	−13.9251	+	8.03966i	−0.550008	+	0.317547i	0.199117	+	0.979976i	$0.436193\pi$
$642$	−9.43649	−	0.976025i	−0.372429	−	0.0385206i
$643$	−26.0663			−1.02796			−0.513978	−	0.857803i	$-0.671829\pi$
$643$	−26.0663			−1.02796			−0.513978	+	0.857803i	$0.671829\pi$
$644$	−6.33175	+	10.0114i	−0.249506	+	0.394504i
$645$	7.00000	−	25.8773i	0.275625	−	1.01892i
$646$	2.26139	−	3.91684i	0.0889731	−	0.154106i
$647$	−17.6703	+	10.2019i	−0.694691	+	0.401080i	−0.805367	−	0.592777i	$-0.798032\pi$
$647$	−17.6703	+	10.2019i	−0.694691	+	0.401080i	0.110676	+	0.993857i	$0.464698\pi$
$648$	7.24597	−	5.33816i	0.284648	−	0.209703i
$649$	42.9089	+	24.7735i	1.68432	+	0.972444i
$650$	1.04456	+	5.11726i	0.0409709	+	0.200715i
$651$	−23.8578	−	18.7855i	−0.935060	−	0.736261i
$652$		−	14.6969i		−	0.575577i
$653$	19.9317	−	34.5227i	0.779987	−	1.35098i	−0.151962	−	0.988386i	$-0.548559\pi$
$653$	19.9317	−	34.5227i	0.779987	−	1.35098i	0.931949	−	0.362590i	$-0.118108\pi$
$654$	−20.7535	+	28.6645i	−0.811528	+	1.12087i
$655$	−30.3973	−	4.94046i	−1.18772	−	0.193040i
$656$	−0.522278	+	0.904612i	−0.0203915	+	0.0353192i
$657$	7.00665	−	7.83368i	0.273356	−	0.305621i
$658$	1.19718	−	29.6582i	0.0466708	−	1.15620i
$659$		−	34.2929i		−	1.33586i	−0.744224	−	0.667930i	$-0.767181\pi$
$659$		−	34.2929i		−	1.33586i	0.744224	−	0.667930i	$-0.232819\pi$
$660$	−12.8013	−	12.8625i	−0.498289	−	0.500672i
$661$	0.522774	−	0.301824i	0.0203336	−	0.0117396i	−0.489799	−	0.871836i	$-0.662930\pi$
$661$	0.522774	−	0.301824i	0.0203336	−	0.0117396i	0.510132	+	0.860096i	$0.329596\pi$
$662$	10.7158	+	18.5604i	0.416483	+	0.721370i
$663$	0.588616	−	5.69091i	0.0228600	−	0.221017i
$664$			4.06775i			0.157859i
$665$	6.33295	+	5.61141i	0.245581	+	0.217601i
$666$	−5.95445	−	5.32582i	−0.230730	−	0.206371i
$667$	26.8378	+	15.4948i	1.03917	+	0.599963i
$668$	−3.71584	+	2.14534i	−0.143770	+	0.0830057i
$669$	22.2329	−	30.7077i	0.859574	−	1.18723i
$670$	−29.8355	+	11.3147i	−1.15265	+	0.437124i
$671$	16.2312			0.626600
$672$	−2.83495	+	3.60042i	−0.109361	+	0.138889i
$673$			14.1585i			0.545771i	0.962047	+	0.272885i	$0.0879780\pi$
$673$			14.1585i			0.545771i	−0.962047	+	0.272885i	$0.912022\pi$
$674$	−14.8492	−	8.57321i	−0.571971	−	0.330228i
$675$	−23.7674	+	10.4933i	−0.914808	+	0.403888i
$676$	5.95445	+	10.3134i	0.229017	+	0.396670i
$677$	28.5000	+	16.4545i	1.09534	+	0.632397i	0.934994	−	0.354663i	$-0.115404\pi$
$677$	28.5000	+	16.4545i	1.09534	+	0.632397i	0.160350	+	0.987060i	$0.448738\pi$
$678$	−12.3583	−	27.6339i	−0.474616	−	1.06127i
$679$	−16.9545	+	26.8073i	−0.650652	+	1.02877i
$680$	−5.47723	−	4.47214i	−0.210042	−	0.171499i
$681$	1.85188	−	17.9045i	0.0709641	−	0.686101i
$682$	15.5241	+	26.8886i	0.594450	+	1.02962i
$683$	−9.47723	−	16.4150i	−0.362636	−	0.628104i	0.625758	−	0.780017i	$-0.284790\pi$
$683$	−9.47723	−	16.4150i	−0.362636	−	0.628104i	−0.988394	+	0.151913i	$0.951456\pi$
$684$	4.07627	−	1.33940i	0.155860	−	0.0512131i
$685$	−4.91754	+	6.02273i	−0.187890	+	0.230117i
$686$	−11.1289	+	14.8036i	−0.424903	+	0.565206i
$687$	21.4317	−	9.58454i	0.817669	−	0.365673i
$688$	5.99430	+	3.46081i	0.228531	+	0.131942i
$689$	2.61139	+	4.52306i	0.0994861	+	0.172315i
$690$	−4.44801	−	16.7600i	−0.169333	−	0.638043i
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	0.555976	−	0.831198i	$-0.312345\pi$
$691$	3.00000	+	1.73205i	0.114125	+	0.0658903i	−0.441851	+	0.897089i	$0.645678\pi$
$692$			1.12840i			0.0428954i
$693$	−35.7715	+	10.1750i	−1.35885	+	0.386517i
$694$	−17.4772			−0.663426
$695$	−42.1938	+	16.0013i	−1.60050	+	0.606966i
$696$	9.71064	+	7.03066i	0.368081	+	0.266497i
$697$	−2.86064	+	1.65159i	−0.108354	+	0.0625584i
$698$	10.1703	+	5.87182i	0.384951	+	0.222252i
$699$	−2.82843	−	6.32456i	−0.106981	−	0.239217i
$700$	10.2478	−	8.36551i	0.387332	−	0.316187i
$701$			51.7546i			1.95474i	0.211531	+	0.977371i	$0.432155\pi$
$701$			51.7546i			1.95474i	−0.211531	+	0.977371i	$0.567845\pi$
$702$	4.01546	−	3.65181i	0.151554	−	0.137829i
$703$	−1.90428	−	3.29832i	−0.0718214	−	0.124398i
$704$	4.05781	−	2.34278i	0.152935	−	0.0882968i
$705$	30.6508	+	30.7974i	1.15438	+	1.15990i
$706$			0.603648i			0.0227186i
$707$	−29.9089	−	1.20730i	−1.12484	−	0.0454050i
$708$	7.47723	+	16.7196i	0.281011	+	0.628360i
$709$	11.2158	−	19.4264i	0.421220	−	0.729574i	−0.574839	−	0.818266i	$-0.694935\pi$
$709$	11.2158	−	19.4264i	0.421220	−	0.729574i	0.996059	+	0.0886924i	$0.0282688\pi$
$710$	−2.48292	+	15.2768i	−0.0931824	+	0.573327i
$711$	33.7028	+	7.04721i	1.26395	+	0.264291i
$712$	−2.45877	+	4.25871i	−0.0921463	+	0.159602i
$713$			29.6678i			1.11107i
$714$	−13.4566	+	5.37771i	−0.503601	+	0.201256i
$715$	−8.47723	−	6.92163i	−0.317030	−	0.258854i
$716$	16.7857	+	9.69125i	0.627312	+	0.362179i
$717$		0			0
$718$	−9.86729	+	5.69688i	−0.368244	+	0.212606i
$719$	−0.401865	+	0.696051i	−0.0149870	+	0.0259583i	−0.873422	−	0.486965i	$-0.838104\pi$
$719$	−0.401865	+	0.696051i	−0.0149870	+	0.0259583i	0.858435	+	0.512923i	$0.171437\pi$
$720$	−1.04456	−	6.62638i	−0.0389283	−	0.246951i
$721$	6.04555	+	11.5207i	0.225148	+	0.429054i
$722$	−16.9545			−0.630979
$723$	3.79726	−	36.7130i	0.141222	−	1.36537i
$724$	−2.73861	+	1.58114i	−0.101780	+	0.0587626i
$725$	−22.9488	−	25.9052i	−0.852295	−	0.962093i
$726$	18.8730	+	1.95205i	0.700442	+	0.0724474i
$727$	−15.1223			−0.560854			−0.280427	−	0.959875i	$-0.590476\pi$
$727$	−15.1223			−0.560854			−0.280427	+	0.959875i	$0.590476\pi$
$728$	−1.47723	+	2.33570i	−0.0547496	+	0.0865668i
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	−2.77776	−	7.32465i	−0.102810	−	0.271097i
$731$	10.9441	+	18.9557i	0.404780	+	0.701100i
$732$	4.85993	+	3.51867i	0.179628	+	0.130054i
$733$	1.19718	−	2.07357i	0.0442187	−	0.0765891i	−0.843069	−	0.537805i	$-0.819253\pi$
$733$	1.19718	−	2.07357i	0.0442187	−	0.0765891i	0.887288	+	0.461216i	$0.152587\pi$
$734$	0.369657			0.0136443
$735$	−4.81967	−	26.6790i	−0.177776	−	0.984071i
$736$	4.47723			0.165033
$737$	33.4317	−	57.9054i	1.23147	−	2.13297i
$738$	−3.06733	−	0.641375i	−0.112910	−	0.0236093i
$739$	−3.23861	−	5.60944i	−0.119134	−	0.206347i	0.800291	−	0.599612i	$-0.204679\pi$
$739$	−3.23861	−	5.60944i	−0.119134	−	0.206347i	−0.919425	+	0.393266i	$0.871345\pi$
$740$	−5.56754	+	2.11140i	−0.204667	+	0.0776168i
$741$	2.36215	−	1.05638i	0.0867756	−	0.0388072i
$742$	7.07107	−	11.1803i	0.259587	−	0.410443i
$743$	−13.4317			−0.492760			−0.246380	−	0.969173i	$-0.579241\pi$
$743$	−13.4317			−0.492760			−0.246380	+	0.969173i	$0.579241\pi$
$744$	−1.18080	+	11.4163i	−0.0432903	+	0.418543i
$745$	0.878680	−	5.40629i	0.0321923	−	0.198071i
$746$	−20.1042	+	11.6072i	−0.736068	+	0.424969i
$747$	−11.5934	+	3.80941i	−0.424181	+	0.139379i
$748$	14.8170			0.541764
$749$	6.73362	+	12.8319i	0.246041	+	0.468868i
$750$	−1.21584	+	19.3267i	−0.0443961	+	0.705712i
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	−0.411170	−	0.911559i	$-0.634880\pi$
$751$	16.0000	−	27.7128i	0.583848	−	1.01125i	0.995018	−	0.0996961i	$-0.0317870\pi$
$752$	−9.71584	+	5.60944i	−0.354300	+	0.204555i
$753$	−8.99443	+	12.4230i	−0.327775	+	0.452718i
$754$	6.26139	+	3.61501i	0.228026	+	0.131651i
$755$	2.82843	−	3.46410i	0.102937	−	0.126072i
$756$	−12.9164	−	4.70809i	−0.469766	−	0.171232i
$757$			48.1361i			1.74954i	0.484541	+	0.874768i	$0.338986\pi$
$757$			48.1361i			1.74954i	−0.484541	+	0.874768i	$0.661014\pi$
$758$	−10.2386	+	17.7338i	−0.371883	+	0.644121i
$759$	29.4313	+	21.3088i	1.06829	+	0.773459i
$760$	0.513050	−	3.15666i	0.0186103	−	0.114504i
$761$	0.891935	−	1.54488i	0.0323326	−	0.0560018i	−0.849406	−	0.527739i	$-0.823040\pi$
$761$	0.891935	−	1.54488i	0.0323326	−	0.0560018i	0.881739	+	0.471738i	$0.156373\pi$
$762$	−13.8047	+	6.17364i	−0.500091	+	0.223648i
$763$	54.0131	+	2.18028i	1.95541	+	0.0789315i
$764$		−	16.2927i		−	0.589451i
$765$	7.61659	−	19.7987i	0.275378	−	0.715823i
$766$	−15.7158	+	9.07354i	−0.567836	+	0.327840i
$767$	5.52277	+	9.56573i	0.199416	+	0.345398i
$768$	1.72286	+	0.178197i	0.0621683	+	0.00643013i
$769$			16.1921i			0.583902i	0.956433	+	0.291951i	$0.0943045\pi$
$769$			16.1921i			0.583902i	−0.956433	+	0.291951i	$0.905696\pi$
$770$	−5.54692	+	27.1595i	−0.199897	+	0.978760i
$771$	−17.3861	+	7.77531i	−0.626146	+	0.280021i
$772$	−6.36396	−	3.67423i	−0.229044	−	0.132239i
$773$	14.0228	−	8.09605i	0.504364	−	0.291195i	−0.226150	−	0.974093i	$-0.572614\pi$
$773$	14.0228	−	8.09605i	0.504364	−	0.291195i	0.730514	+	0.682898i	$0.239281\pi$
$774$	−4.24999	+	20.3253i	−0.152763	+	0.730578i
$775$	10.4926	−	31.4265i	0.376907	−	1.12887i
$776$	11.9886			0.430366
$777$	−1.74402	+	12.0777i	−0.0625663	+	0.433286i
$778$			7.34847i			0.263455i
$779$	−1.29380	−	0.746976i	−0.0463552	−	0.0267632i
$780$	−1.03774	−	3.91019i	−0.0371571	−	0.140007i
$781$	−16.2158	−	28.0867i	−0.580248	−	1.00502i
$782$	12.2614	+	7.07912i	0.438466	+	0.253149i
$783$	−10.9441	+	34.2603i	−0.391108	+	1.22436i
$784$	6.97723	+	0.564201i	0.249187	+	0.0201501i
$785$	20.4317	−	25.0236i	0.729238	−	0.893130i
$786$	23.7280	+	2.45421i	0.846351	+	0.0875389i
$787$	−25.0862	−	43.4506i	−0.894226	−	1.54884i	−0.834760	−	0.550615i	$-0.814393\pi$
$787$	−25.0862	−	43.4506i	−0.894226	−	1.54884i	−0.0594664	−	0.998230i	$-0.518940\pi$
$788$	4.50000	+	7.79423i	0.160306	+	0.277658i
$789$	3.44572	+	0.356394i	0.122671	+	0.0126880i
$790$	16.2312	−	19.8791i	0.577482	−	0.707268i
$791$	−24.7165	+	39.0803i	−0.878819	+	1.38953i
$792$	10.4772	+	9.37112i	0.372292	+	0.332988i
$793$	3.13367	+	1.80922i	0.111280	+	0.0642474i
$794$	−7.44073	−	12.8877i	−0.264061	−	0.457368i
$795$	4.96737	+	18.7170i	0.176175	+	0.663823i
$796$	−13.4317	−	7.75478i	−0.476073	−	0.274861i
$797$			54.2183i			1.92051i	0.279121	+	0.960256i	$0.409957\pi$
$797$			54.2183i			1.92051i	−0.279121	+	0.960256i	$0.590043\pi$
$798$	−5.14942	−	4.05462i	−0.182288	−	0.143532i
$799$	−35.4772			−1.25509
$800$	−4.74264	−	1.58346i	−0.167678	−	0.0559839i
$801$	−14.4403	−	3.01945i	−0.510223	−	0.106687i
$802$	0.827520	−	0.477769i	0.0292207	−	0.0168706i
$803$	14.2158	+	8.20752i	0.501666	+	0.289637i
$804$	22.5630	−	10.0905i	0.795736	−	0.355864i
$805$	−17.5661	+	19.8249i	−0.619125	+	0.698735i
$806$			6.92163i			0.243804i
$807$	30.2897	+	3.13289i	1.06625	+	0.110283i
$808$	5.65685	+	9.79796i	0.199007	+	0.344691i
$809$	−7.65776	+	4.42121i	−0.269233	+	0.155441i	−0.628539	−	0.777778i	$-0.716347\pi$
$809$	−7.65776	+	4.42121i	−0.269233	+	0.155441i	0.359306	+	0.933220i	$0.383013\pi$
$810$	17.9075	−	9.18262i	0.629206	−	0.322644i
$811$			38.3280i			1.34588i	0.739697	+	0.672940i	$0.234969\pi$
$811$			38.3280i			1.34588i	−0.739697	+	0.672940i	$0.765031\pi$
$812$	0.738613	−	18.2980i	0.0259202	−	0.642134i
$813$	10.0000	−	4.47214i	0.350715	−	0.156845i
$814$	6.23861	−	10.8056i	0.218663	−	0.378736i
$815$	5.27208	−	32.4377i	0.184673	−	1.13624i
$816$	4.43649	+	3.21209i	0.155308	+	0.112446i
$817$	−4.94975	+	8.57321i	−0.173170	+	0.299939i
$818$		−	15.5096i		−	0.542279i
$819$	−8.04035	−	2.02286i	−0.280953	−	0.0706843i
$820$	−1.47723	+	1.80922i	−0.0515870	+	0.0631809i
$821$	−10.1403	−	5.85452i	−0.353900	−	0.204324i	0.312502	−	0.949917i	$-0.398833\pi$
$821$	−10.1403	−	5.85452i	−0.353900	−	0.204324i	−0.666401	+	0.745593i	$0.732166\pi$
$822$	3.53200	−	4.87835i	0.123193	−	0.170152i
$823$	−2.76401	+	1.59580i	−0.0963474	+	0.0556262i	−0.547400	−	0.836871i	$-0.684382\pi$
$823$	−2.76401	+	1.59580i	−0.0963474	+	0.0556262i	0.451052	+	0.892498i	$0.351049\pi$
$824$	2.45877	−	4.25871i	0.0856553	−	0.148359i
$825$	−23.6398	−	32.9810i	−0.823031	−	1.14825i
$826$	14.9545	−	23.6451i	0.520332	−	0.822717i
$827$	3.90890			0.135926			0.0679629	−	0.997688i	$-0.478350\pi$
$827$	3.90890			0.135926			0.0679629	+	0.997688i	$0.478350\pi$
$828$	4.19288	+	12.7605i	0.145713	+	0.443457i
$829$	−43.6931	+	25.2262i	−1.51752	+	0.876142i	−0.517735	+	0.855541i	$0.673225\pi$
$829$	−43.6931	+	25.2262i	−1.51752	+	0.876142i	−0.999788	+	0.0206012i	$0.993442\pi$
$830$	−1.45918	+	8.97796i	−0.0506489	+	0.311629i
$831$	1.74597	−	16.8805i	0.0605669	−	0.585578i
$832$	1.04456			0.0362135
$833$	18.2158	+	12.5771i	0.631141	+	0.435770i
$834$	31.9089	−	14.2701i	1.10491	−	0.494133i
$835$	−8.97083	+	3.40205i	−0.310448	+	0.117733i
$836$	3.35071	+	5.80359i	0.115887	+	0.200721i
$837$	−33.6433	+	7.32591i	−1.16288	+	0.253220i
$838$	−4.42747	+	7.66860i	−0.152944	+	0.264907i
$839$	40.1440			1.38593			0.692963	−	0.720973i	$-0.256305\pi$
$839$	40.1440			1.38593			0.692963	+	0.720973i	$0.256305\pi$
$840$	−7.54858	+	6.92957i	−0.260451	+	0.239093i
$841$	−18.9089			−0.652031
$842$	9.47723	−	16.4150i	0.326607	−	0.565700i
$843$	2.53824	+	1.83773i	0.0874215	+	0.0632946i
$844$	−12.2386	−	21.1979i	−0.421270	−	0.729662i
$845$	9.44249	+	24.8988i	0.324831	+	0.856544i
$846$	−25.0862	−	22.4378i	−0.862481	−	0.771426i
$847$	−13.4672	−	25.6639i	−0.462740	−	0.881821i
$848$	−5.00000			−0.171701
$849$	−15.8927	−	1.64380i	−0.545436	−	0.0564149i
$850$	−10.4846	−	11.8353i	−0.359618	−	0.405946i
$851$	10.3251	−	5.96123i	0.353942	−	0.204348i
$852$	1.23341	−	11.9250i	0.0422560	−	0.408543i
$853$	31.2891			1.07132			0.535659	−	0.844434i	$-0.320063\pi$
$853$	31.2891			1.07132			0.535659	+	0.844434i	$0.320063\pi$
$854$	0.369657	−	9.15769i	0.0126494	−	0.313370i
$855$	9.47723	−	1.49395i	0.324114	−	0.0510921i
$856$	2.73861	−	4.74342i	0.0936039	−	0.162127i
$857$	−13.0455	+	7.53185i	−0.445627	+	0.257283i	−0.705982	−	0.708230i	$-0.749494\pi$
$857$	−13.0455	+	7.53185i	−0.445627	+	0.257283i	0.260354	+	0.965513i	$0.416161\pi$
$858$	6.86646	+	4.97143i	0.234417	+	0.169722i
$859$	−26.4772	−	15.2866i	−0.903391	−	0.521573i	−0.0250924	−	0.999685i	$-0.507988\pi$
$859$	−26.4772	−	15.2866i	−0.903391	−	0.521573i	−0.878299	+	0.478112i	$0.841321\pi$
$860$	11.9886	+	9.78866i	0.408808	+	0.333790i
$861$	1.77635	+	4.44495i	0.0605380	+	0.151484i
$862$			7.66374i			0.261028i
$863$	−13.2386	+	22.9299i	−0.450648	+	0.780545i	−0.998426	−	0.0560787i	$-0.982140\pi$
$863$	−13.2386	+	22.9299i	−0.450648	+	0.780545i	0.547779	+	0.836623i	$0.315474\pi$
$864$	1.10557	+	5.07718i	0.0376122	+	0.172729i
$865$	−0.404780	+	2.49051i	−0.0137629	+	0.0846797i
$866$		0			0
$867$	−4.94975	−	11.0680i	−0.168102	−	0.375888i
$868$	15.5241	−	8.14637i	0.526924	−	0.276506i
$869$			53.7772i			1.82427i
$870$	18.9104	+	19.0008i	0.641122	+	0.644188i
$871$	12.9089	−	7.45296i	0.437401	−	0.252534i
$872$	−10.2158	−	17.6944i	−0.345952	−	0.599206i
$873$	11.2272	+	34.1685i	0.379984	+	1.15643i
$874$			6.40345i			0.216600i
$875$	25.6190	−	14.7875i	0.866079	−	0.499908i
$876$	2.47723	+	5.53924i	0.0836977	+	0.187154i
$877$	−48.2359	−	27.8490i	−1.62881	−	0.940394i	−0.984449	−	0.175673i	$-0.943790\pi$
$877$	−48.2359	−	27.8490i	−1.62881	−	0.940394i	−0.644361	−	0.764721i	$-0.722877\pi$
$878$	−7.69306	+	4.44159i	−0.259628	+	0.149896i
$879$	−11.3029	−	8.18352i	−0.381239	−	0.276023i
$880$	9.79642	−	3.71515i	0.330237	−	0.125238i
$881$	18.7544			0.631853			0.315926	−	0.948784i	$-0.397685\pi$
$881$	18.7544			0.631853			0.315926	+	0.948784i	$0.397685\pi$
$882$	4.92609	+	20.4141i	0.165870	+	0.687377i
$883$		−	24.3833i		−	0.820564i	−0.911959	−	0.410282i	$-0.865430\pi$
$883$		−	24.3833i		−	0.820564i	0.911959	−	0.410282i	$-0.134570\pi$
$884$	2.86064	+	1.65159i	0.0962136	+	0.0555489i
$885$	10.5054	+	39.5841i	0.353135	+	1.33061i
$886$	7.52277	+	13.0298i	0.252733	+	0.437746i
$887$	−3.00000	−	1.73205i	−0.100730	−	0.0581566i	0.448789	−	0.893638i	$-0.351856\pi$
$887$	−3.00000	−	1.73205i	−0.100730	−	0.0581566i	−0.549519	+	0.835481i	$0.685189\pi$
$888$	4.21043	−	1.88296i	0.141293	−	0.0631881i
$889$	19.5228	+	12.3473i	0.654773	+	0.414115i
$890$	−6.95445	+	8.51743i	−0.233114	+	0.285505i
$891$	−16.8966	+	38.6370i	−0.566059	+	1.29439i
$892$	10.9441	+	18.9557i	0.366434	+	0.634682i
$893$	−8.02277	−	13.8959i	−0.268472	−	0.465007i
$894$	−0.436492	+	4.22013i	−0.0145985	+	0.141142i
$895$	33.5715	+	27.4110i	1.12217	+	0.916248i
$896$	−1.22938	−	2.34278i	−0.0410709	−	0.0782667i
$897$	3.30694	+	7.39453i	0.110415	+	0.246896i
$898$	−22.4104	−	12.9386i	−0.747844	−	0.431768i
$899$	−22.9327	−	39.7205i	−0.764847	−	1.32475i
$900$	0.0715641	−	14.9998i	0.00238547	−	0.499994i
$901$	−13.6931	−	7.90569i	−0.456182	−	0.263377i
$902$		−	4.89433i		−	0.162963i
$903$	29.4540	−	11.7708i	0.980166	−	0.391707i
$904$	17.4772			0.581284
$905$	−6.61160	+	2.50735i	−0.219777	+	0.0833471i
$906$	−2.03151	+	2.80588i	−0.0674923	+	0.0932192i
$907$	−8.48528	+	4.89898i	−0.281749	+	0.162668i	−0.634215	−	0.773157i	$-0.718677\pi$
$907$	−8.48528	+	4.89898i	−0.281749	+	0.162668i	0.352466	+	0.935825i	$0.385343\pi$
$908$	9.00000	+	5.19615i	0.298675	+	0.172440i
$909$	−22.6274	+	25.2982i	−0.750504	+	0.839089i
$910$	−4.09826	+	4.62523i	−0.135856	+	0.153325i
$911$		−	24.0681i		−	0.797410i	−0.917079	−	0.398705i	$-0.869460\pi$
$911$		−	24.0681i		−	0.797410i	0.917079	−	0.398705i	$-0.130540\pi$
$912$	−0.254862	+	2.46408i	−0.00843933	+	0.0815939i
$913$	−9.52984	−	16.5062i	−0.315392	−	0.546274i
$914$	9.59425	−	5.53924i	0.317350	−	0.183222i
$915$	9.46418	+	9.50944i	0.312876	+	0.314372i
$916$			13.5546i			0.447856i
$917$	−16.9317	−	32.2659i	−0.559133	−	1.06551i
$918$	−5.00000	+	15.6525i	−0.165025	+	0.516609i
$919$	−0.215838	+	0.373843i	−0.00711985	+	0.0123319i	−0.869563	−	0.493821i	$-0.835600\pi$
$919$	−0.215838	+	0.373843i	−0.00711985	+	0.0123319i	0.862444	+	0.506153i	$0.168933\pi$
$920$	9.88171	+	1.60607i	0.325790	+	0.0529505i
$921$	−12.1775	+	16.8193i	−0.401261	+	0.554215i
$922$	−15.8938	+	27.5289i	−0.523434	+	0.906615i
$923$		−	7.23003i		−	0.237979i
$924$	3.06871	−	21.2515i	0.100953	−	0.699123i
$925$	−13.0455	+	2.66291i	−0.428935	+	0.0875560i
$926$	19.5497	+	11.2871i	0.642444	+	0.370916i
$927$	14.4403	+	3.01945i	0.474282	+	0.0991718i
$928$	−5.99430	+	3.46081i	−0.196773	+	0.113607i
$929$	−7.96300	+	13.7923i	−0.261258	+	0.452512i	−0.966576	−	0.256379i	$-0.917471\pi$
$929$	−7.96300	+	13.7923i	−0.261258	+	0.452512i	0.705319	+	0.708890i	$0.250804\pi$
$930$	−6.70141	+	24.7735i	−0.219748	+	0.812354i
$931$	−0.806936	+	9.97902i	−0.0264463	+	0.327049i
$932$	4.00000			0.131024
$933$	30.2897	+	3.13289i	0.991640	+	0.102566i
$934$	24.2614	−	14.0073i	0.793857	−	0.458333i
$935$	32.7028	+	5.31516i	1.06950	+	0.173824i
$936$	0.978218	+	2.97707i	0.0319741	+	0.0973087i
$937$	−53.6757			−1.75351			−0.876754	−	0.480938i	$-0.840296\pi$
$937$	−53.6757			−1.75351			−0.876754	+	0.480938i	$0.840296\pi$
$938$	−31.9089	−	20.1810i	−1.04186	−	0.658932i
$939$	16.4317	+	36.7423i	0.536228	+	1.19904i
$940$	−23.4561	+	8.89538i	−0.765054	+	0.290135i
$941$	10.2369	+	17.7309i	0.333715	+	0.578011i	0.983237	−	0.182331i	$-0.0583644\pi$
$941$	10.2369	+	17.7309i	0.333715	+	0.578011i	−0.649522	+	0.760343i	$0.725031\pi$
$942$	−14.6750	+	20.2688i	−0.478136	+	0.660394i
$943$	2.33836	−	4.05015i	0.0761474	−	0.131891i
$944$	−10.5744			−0.344167
$945$	−26.8190	−	15.0246i	−0.872423	−	0.488751i
$946$	−32.4317			−1.05444
$947$	16.4317	−	28.4605i	0.533958	−	0.924842i	−0.465255	−	0.885177i	$-0.654037\pi$
$947$	16.4317	−	28.4605i	0.533958	−	0.924842i	0.999213	−	0.0396654i	$-0.0126292\pi$
$948$	−11.6580	+	16.1019i	−0.378635	+	0.522965i
$949$	1.82971	+	3.16915i	0.0593949	+	0.102875i
$950$	2.26471	−	6.78305i	0.0734770	−	0.220071i
$951$	−7.00665	−	15.6674i	−0.227206	−	0.508049i
$952$	0.337449	−	8.35979i	0.0109368	−	0.270942i
$953$	−46.9545			−1.52100			−0.760502	−	0.649336i	$-0.775047\pi$
$953$	−46.9545			−1.52100			−0.760502	+	0.649336i	$0.775047\pi$
$954$	−4.68246	−	14.2504i	−0.151600	−	0.461375i
$955$	5.84452	−	35.9598i	0.189124	−	1.16363i
$956$		0			0
$957$	−55.8752	−	5.77923i	−1.80619	−	0.186816i
$958$	42.3620			1.36865
$959$	−9.19239	−	0.371058i	−0.296838	−	0.0119821i
$960$	3.73861	+	1.01132i	0.120663	+	0.0326403i
$961$	6.45445	−	11.1794i	0.208208	−	0.360627i
$962$	2.40890	−	1.39078i	0.0776661	−	0.0448406i
$963$	16.0838	+	3.36311i	0.518294	+	0.108375i
$964$	18.4545	+	10.6547i	0.594378	+	0.343164i
$965$	−12.7279	−	10.3923i	−0.409726	−	0.334540i
$966$	12.6927	−	16.1199i	0.408382	−	0.518649i
$967$		−	7.23690i		−	0.232723i	−0.993207	−	0.116361i	$-0.962877\pi$
$967$		−	7.23690i		−	0.232723i	0.993207	−	0.116361i	$-0.0371231\pi$
$968$	−5.47723	+	9.48683i	−0.176045	+	0.304918i
$969$	−4.59402	+	6.34519i	−0.147581	+	0.203837i
$970$	26.4601	+	4.30055i	0.849584	+	0.138082i
$971$	18.8748	−	32.6922i	0.605723	−	1.04914i	−0.386214	−	0.922409i	$-0.626217\pi$
$971$	18.8748	−	32.6922i	0.605723	−	1.04914i	0.991937	−	0.126733i	$-0.0404492\pi$
$972$	−13.4350	+	7.90569i	−0.430929	+	0.253575i
$973$	−45.1260	−	28.5402i	−1.44667	−	0.914956i
$974$			17.0349i			0.545832i
$975$	−0.887744	−	9.00246i	−0.0284306	−	0.288309i
$976$	−3.00000	+	1.73205i	−0.0960277	+	0.0554416i
$977$	1.95445	+	3.38521i	0.0625284	+	0.108302i	0.895595	−	0.444870i	$-0.146750\pi$
$977$	1.95445	+	3.38521i	0.0625284	+	0.108302i	−0.833067	+	0.553173i	$0.813417\pi$
$978$	−2.61895	+	25.3208i	−0.0837448	+	0.809669i
$979$		−	23.0414i		−	0.736407i
$980$	15.1971	+	3.74812i	0.485453	+	0.119729i
$981$	40.8634	−	45.6866i	1.30467	−	1.45866i
$982$	11.9886	+	6.92163i	0.382572	+	0.220878i
$983$	45.7158	−	26.3941i	1.45811	−	0.841840i	0.459190	−	0.888338i	$-0.348140\pi$
$983$	45.7158	−	26.3941i	1.45811	−	0.841840i	0.998918	+	0.0464984i	$0.0148062\pi$
$984$	1.06101	−	1.46545i	0.0338238	−	0.0467169i
$985$	7.13604	+	18.8169i	0.227373	+	0.599557i
$986$	−21.8881			−0.697059
$987$	−7.34757	+	50.8836i	−0.233876	+	1.61964i
$988$			1.49395i			0.0475290i
$989$	−26.8378	−	15.4948i	−0.853394	−	0.492707i
$990$	19.7628	+	24.4414i	0.628102	+	0.776800i
$991$	−5.26139	−	9.11299i	−0.167133	−	0.289484i	0.770277	−	0.637709i	$-0.220118\pi$
$991$	−5.26139	−	9.11299i	−0.167133	−	0.289484i	−0.937411	+	0.348225i	$0.886784\pi$
$992$	−5.73861	−	3.31319i	−0.182201	−	0.105194i
$993$	−15.1545	−	33.8865i	−0.480913	−	1.07535i
$994$	−16.2158	+	8.50934i	−0.514335	+	0.269900i
$995$	−26.8634	−	21.9338i	−0.851626	−	0.695349i
$996$	0.724861	−	7.00816i	0.0229681	−	0.222062i
$997$	7.74597	+	13.4164i	0.245317	+	0.424902i	0.962221	−	0.272270i	$-0.0877745\pi$
$997$	7.74597	+	13.4164i	0.245317	+	0.424902i	−0.716904	+	0.697172i	$0.754441\pi$
$998$	0.954451	+	1.65316i	0.0302126	+	0.0523298i
$999$	9.30964	+	10.2367i	0.294544	+	0.323875i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.t.f.89.2	yes	8
3.2	odd	2		210.2.t.e.89.4	yes	8
5.2	odd	4		1050.2.s.i.551.8		16
5.3	odd	4		1050.2.s.i.551.1		16
5.4	even	2		210.2.t.e.89.3	yes	8
7.2	even	3		1470.2.d.e.1469.2		8
7.3	odd	6	inner	210.2.t.f.59.1	yes	8
7.5	odd	6		1470.2.d.e.1469.7		8
15.2	even	4		1050.2.s.i.551.2		16
15.8	even	4		1050.2.s.i.551.7		16
15.14	odd	2	inner	210.2.t.f.89.1	yes	8
21.2	odd	6		1470.2.d.f.1469.3		8
21.5	even	6		1470.2.d.f.1469.6		8
21.17	even	6		210.2.t.e.59.3	✓	8
35.3	even	12		1050.2.s.i.101.7		16
35.9	even	6		1470.2.d.f.1469.7		8
35.17	even	12		1050.2.s.i.101.2		16
35.19	odd	6		1470.2.d.f.1469.2		8
35.24	odd	6		210.2.t.e.59.4	yes	8
105.17	odd	12		1050.2.s.i.101.8		16
105.38	odd	12		1050.2.s.i.101.1		16
105.44	odd	6		1470.2.d.e.1469.6		8
105.59	even	6	inner	210.2.t.f.59.2	yes	8
105.89	even	6		1470.2.d.e.1469.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.3	✓	8	21.17	even	6
210.2.t.e.59.4	yes	8	35.24	odd	6
210.2.t.e.89.3	yes	8	5.4	even	2
210.2.t.e.89.4	yes	8	3.2	odd	2
210.2.t.f.59.1	yes	8	7.3	odd	6	inner
210.2.t.f.59.2	yes	8	105.59	even	6	inner
210.2.t.f.89.1	yes	8	15.14	odd	2	inner
210.2.t.f.89.2	yes	8	1.1	even	1	trivial
1050.2.s.i.101.1		16	105.38	odd	12
1050.2.s.i.101.2		16	35.17	even	12
1050.2.s.i.101.7		16	35.3	even	12
1050.2.s.i.101.8		16	105.17	odd	12
1050.2.s.i.551.1		16	5.3	odd	4
1050.2.s.i.551.2		16	15.2	even	4
1050.2.s.i.551.7		16	15.8	even	4
1050.2.s.i.551.8		16	5.2	odd	4
1470.2.d.e.1469.2		8	7.2	even	3
1470.2.d.e.1469.3		8	105.89	even	6
1470.2.d.e.1469.6		8	105.44	odd	6
1470.2.d.e.1469.7		8	7.5	odd	6
1470.2.d.f.1469.2		8	35.19	odd	6
1470.2.d.f.1469.3		8	21.2	odd	6
1470.2.d.f.1469.6		8	21.5	even	6
1470.2.d.f.1469.7		8	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.01575 + 1.40294i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.792893 - 2.09077i) q^{5} +(0.707107 + 1.58114i) q^{6} +(1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(-0.936492 - 2.85008i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.01575 + 1.40294i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.792893 - 2.09077i) q^{5} +(0.707107 + 1.58114i) q^{6} +(1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(-0.936492 - 2.85008i) q^{9} +(-2.20711 - 0.358719i) q^{10} +(4.05781 - 2.34278i) q^{11} +(1.72286 + 0.178197i) q^{12} +1.04456 q^{13} +(-1.22938 - 2.34278i) q^{14} +(3.73861 + 1.01132i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.73861 + 1.58114i) q^{17} +(-2.93649 - 0.614017i) q^{18} +(-1.23861 - 0.715113i) q^{19} +(-1.41421 + 1.73205i) q^{20} +(1.70058 + 4.25535i) q^{21} -4.68556i q^{22} +(2.23861 - 3.87739i) q^{23} +(1.01575 - 1.40294i) q^{24} +(-3.74264 + 3.31552i) q^{25} +(0.522278 - 0.904612i) q^{26} +(4.94975 + 1.58114i) q^{27} +(-2.64360 - 0.106711i) q^{28} +6.92163i q^{29} +(2.74514 - 2.73207i) q^{30} +(-5.73861 + 3.31319i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.834952 + 8.07256i) q^{33} +3.16228i q^{34} +(-5.79642 - 1.18383i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(2.30615 + 1.33146i) q^{37} +(-1.23861 + 0.715113i) q^{38} +(-1.06101 + 1.46545i) q^{39} +(0.792893 + 2.09077i) q^{40} +1.04456 q^{41} +(4.53553 + 0.654929i) q^{42} -6.92163i q^{43} +(-4.05781 - 2.34278i) q^{44} +(-5.21633 + 4.21780i) q^{45} +(-2.23861 - 3.87739i) q^{46} +(9.71584 + 5.60944i) q^{47} +(-0.707107 - 1.58114i) q^{48} +(-3.00000 - 6.32456i) q^{49} +(1.00000 + 4.89898i) q^{50} +(0.563508 - 5.44816i) q^{51} +(-0.522278 - 0.904612i) q^{52} +(2.50000 + 4.33013i) q^{53} +(3.84418 - 3.49604i) q^{54} +(-8.11562 - 6.62638i) q^{55} +(-1.41421 + 2.23607i) q^{56} +(2.26139 - 1.01132i) q^{57} +(5.99430 + 3.46081i) q^{58} +(5.28720 + 9.15769i) q^{59} +(-0.993475 - 3.74340i) q^{60} +(3.00000 + 1.73205i) q^{61} +6.62638i q^{62} +(-7.69738 - 1.93657i) q^{63} +1.00000 q^{64} +(-0.828222 - 2.18393i) q^{65} +(6.57357 + 4.75937i) q^{66} +(12.3583 - 7.13505i) q^{67} +(2.73861 + 1.58114i) q^{68} +(3.16588 + 7.07912i) q^{69} +(-3.92344 + 4.42793i) q^{70} -6.92163i q^{71} +(0.936492 + 2.85008i) q^{72} +(1.75166 + 3.03397i) q^{73} +(2.30615 - 1.33146i) q^{74} +(-0.849876 - 8.61845i) q^{75} +1.43023i q^{76} +(0.500000 - 12.3867i) q^{77} +(0.738613 + 1.65159i) q^{78} +(-5.73861 + 9.93957i) q^{79} +(2.20711 + 0.358719i) q^{80} +(-7.24597 + 5.33816i) q^{81} +(0.522278 - 0.904612i) q^{82} -4.06775i q^{83} +(2.83495 - 3.60042i) q^{84} +(5.47723 + 4.47214i) q^{85} +(-5.99430 - 3.46081i) q^{86} +(-9.71064 - 7.03066i) q^{87} +(-4.05781 + 2.34278i) q^{88} +(2.45877 - 4.25871i) q^{89} +(1.04456 + 6.62638i) q^{90} +(1.47723 - 2.33570i) q^{91} -4.47723 q^{92} +(1.18080 - 11.4163i) q^{93} +(9.71584 - 5.60944i) q^{94} +(-0.513050 + 3.15666i) q^{95} +(-1.72286 - 0.178197i) q^{96} -11.9886 q^{97} +(-6.97723 - 0.564201i) q^{98} +(-10.4772 - 9.37112i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 12 * q^5 - 8 * q^8 + 8 * q^9	\( 8 q + 4 q^{2} - 4 q^{4} - 12 q^{5} - 8 q^{8} + 8 q^{9} - 12 q^{10} + 8 q^{15} - 4 q^{16} - 8 q^{18} + 12 q^{19} + 4 q^{21} - 4 q^{23} + 4 q^{25} + 4 q^{30} - 24 q^{31} + 4 q^{32} + 12 q^{33} + 8 q^{35} - 16 q^{36} + 12 q^{38} - 8 q^{39} + 12 q^{40} + 8 q^{42} - 24 q^{45} + 4 q^{46} + 12 q^{47} - 24 q^{49} + 8 q^{50} + 20 q^{51} + 20 q^{53} + 40 q^{57} - 4 q^{60} + 24 q^{61} - 20 q^{63} + 8 q^{64} - 16 q^{65} + 12 q^{66} - 8 q^{70} - 8 q^{72} - 24 q^{75} + 4 q^{77} - 16 q^{78} - 24 q^{79} + 12 q^{80} + 4 q^{81} + 4 q^{84} - 12 q^{87} - 32 q^{91} + 8 q^{92} + 20 q^{93} + 12 q^{94} - 12 q^{95} - 12 q^{98} - 40 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 12 * q^5 - 8 * q^8 + 8 * q^9 - 12 * q^10 + 8 * q^15 - 4 * q^16 - 8 * q^18 + 12 * q^19 + 4 * q^21 - 4 * q^23 + 4 * q^25 + 4 * q^30 - 24 * q^31 + 4 * q^32 + 12 * q^33 + 8 * q^35 - 16 * q^36 + 12 * q^38 - 8 * q^39 + 12 * q^40 + 8 * q^42 - 24 * q^45 + 4 * q^46 + 12 * q^47 - 24 * q^49 + 8 * q^50 + 20 * q^51 + 20 * q^53 + 40 * q^57 - 4 * q^60 + 24 * q^61 - 20 * q^63 + 8 * q^64 - 16 * q^65 + 12 * q^66 - 8 * q^70 - 8 * q^72 - 24 * q^75 + 4 * q^77 - 16 * q^78 - 24 * q^79 + 12 * q^80 + 4 * q^81 + 4 * q^84 - 12 * q^87 - 32 * q^91 + 8 * q^92 + 20 * q^93 + 12 * q^94 - 12 * q^95 - 12 * q^98 - 40 * q^99

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