LMFDB - Embedded newform 210.2.t.f.59.1

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			59.1
Root			$-1.01575 + 1.40294i$ of defining polynomial
Character	$\chi$	$=$	210.59
Dual form			210.2.t.f.89.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.72286 - 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.20711 - 0.358719i) q^{5} +(-0.707107 - 1.58114i) q^{6} +(-1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.72286 - 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.20711 - 0.358719i) q^{5} +(-0.707107 - 1.58114i) q^{6} +(-1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +(-0.792893 - 2.09077i) q^{10} +(-4.05781 - 2.34278i) q^{11} +(1.01575 - 1.40294i) 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} +(0.936492 + 2.85008i) q^{18} +(-1.23861 + 0.715113i) q^{19} +(1.41421 - 1.73205i) q^{20} +(2.03803 + 4.10444i) q^{21} -4.68556i q^{22} +(2.23861 + 3.87739i) q^{23} +(1.72286 + 0.178197i) q^{24} +(4.74264 + 1.58346i) q^{25} +(-0.522278 - 0.904612i) q^{26} +(-4.94975 - 1.58114i) q^{27} +(2.64360 - 0.106711i) q^{28} +6.92163i q^{29} +(0.993475 + 3.74340i) q^{30} +(-5.73861 - 3.31319i) q^{31} +(0.500000 - 0.866025i) q^{32} +(6.57357 + 4.75937i) q^{33} -3.16228i q^{34} +(2.31920 + 5.44255i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(-2.30615 + 1.33146i) q^{37} +(-1.23861 - 0.715113i) q^{38} +(1.79962 + 0.186137i) q^{39} +(2.20711 + 0.358719i) q^{40} -1.04456 q^{41} +(-2.53553 + 3.81721i) q^{42} -6.92163i q^{43} +(4.05781 - 2.34278i) q^{44} +(-6.26089 - 2.40858i) 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} +(4.43649 + 3.21209i) q^{51} +(0.522278 - 0.904612i) q^{52} +(2.50000 - 4.33013i) q^{53} +(-1.10557 - 5.07718i) 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} +(-2.74514 + 2.73207i) q^{60} +(3.00000 - 1.73205i) q^{61} -6.62638i q^{62} +(-2.77984 - 7.43455i) q^{63} +1.00000 q^{64} +(2.30545 + 0.374703i) q^{65} +(-0.834952 + 8.07256i) q^{66} +(-12.3583 - 7.13505i) q^{67} +(2.73861 - 1.58114i) q^{68} +(-3.16588 - 7.07912i) q^{69} +(-3.55378 + 4.72976i) q^{70} -6.92163i q^{71} +(-2.93649 - 0.614017i) q^{72} +(-1.75166 + 3.03397i) q^{73} +(-2.30615 - 1.33146i) q^{74} +(-7.88874 - 3.57321i) q^{75} -1.43023i q^{76} +(0.500000 + 12.3867i) q^{77} +(0.738613 + 1.65159i) q^{78} +(-5.73861 - 9.93957i) q^{79} +(0.792893 + 2.09077i) q^{80} +(8.24597 + 3.60611i) q^{81} +(-0.522278 - 0.904612i) q^{82} +4.06775i q^{83} +(-4.57357 - 0.287233i) q^{84} +(5.47723 + 4.47214i) q^{85} +(5.99430 - 3.46081i) q^{86} +(1.23341 - 11.9250i) 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} +(9.29642 + 6.73076i) q^{93} +(9.71584 + 5.60944i) q^{94} +(2.99028 - 1.13402i) q^{95} +(-1.01575 + 1.40294i) 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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

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

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
$3$	−1.72286	−	0.178197i	−0.994694	−	0.102882i
$3$	−1.72286	−	0.178197i	−0.994694	−	0.102882i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.20711	−	0.358719i	−0.987048	−	0.160424i
$5$	−2.20711	−	0.358719i	−0.987048	−	0.160424i
$6$	−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
$9$	2.93649	+	0.614017i	0.978831	+	0.204672i
$10$	−0.792893	−	2.09077i	−0.250735	−	0.661160i
$11$	−4.05781	−	2.34278i	−1.22348	−	0.706374i	−0.257819	−	0.966193i	$-0.583004\pi$
$11$	−4.05781	−	2.34278i	−1.22348	−	0.706374i	−0.965657	+	0.259819i	$0.916337\pi$
$12$	1.01575	−	1.40294i	0.293223	−	0.404994i
$13$	−1.04456			−0.289708			−0.144854	−	0.989453i	$-0.546271\pi$
$13$	−1.04456			−0.289708			−0.144854	+	0.989453i	$0.546271\pi$
$14$	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	0.129668	−	0.991557i	$-0.458609\pi$
$17$	−2.73861	−	1.58114i	−0.664211	−	0.383482i	−0.793880	+	0.608075i	$0.791942\pi$
$18$	0.936492	+	2.85008i	0.220733	+	0.671771i
$19$	−1.23861	+	0.715113i	−0.284157	+	0.164058i	−0.635304	−	0.772262i	$-0.719125\pi$
$19$	−1.23861	+	0.715113i	−0.284157	+	0.164058i	0.351147	+	0.936320i	$0.385792\pi$
$20$	1.41421	−	1.73205i	0.316228	−	0.387298i
$21$	2.03803	+	4.10444i	0.444735	+	0.895662i
$22$		−	4.68556i		−	0.998964i
$23$	2.23861	+	3.87739i	0.466783	+	0.808492i	0.999280	−	0.0379400i	$-0.0120796\pi$
$23$	2.23861	+	3.87739i	0.466783	+	0.808492i	−0.532497	+	0.846432i	$0.678746\pi$
$24$	1.72286	+	0.178197i	0.351677	+	0.0363743i
$25$	4.74264	+	1.58346i	0.948528	+	0.316693i
$26$	−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	$0.777832\pi$
$30$	0.993475	+	3.74340i	0.181383	+	0.683447i
$31$	−5.73861	−	3.31319i	−1.03069	−	0.595066i	−0.113504	−	0.993537i	$-0.536208\pi$
$31$	−5.73861	−	3.31319i	−1.03069	−	0.595066i	−0.917181	+	0.398471i	$0.869541\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	6.57357	+	4.75937i	1.14431	+	0.828500i
$34$		−	3.16228i		−	0.542326i
$35$	2.31920	+	5.44255i	0.392016	+	0.919958i
$36$	−2.00000	+	2.23607i	−0.333333	+	0.372678i
$37$	−2.30615	+	1.33146i	−0.379129	+	0.218890i	−0.677439	−	0.735579i	$-0.736910\pi$
$37$	−2.30615	+	1.33146i	−0.379129	+	0.218890i	0.298310	+	0.954469i	$0.403577\pi$
$38$	−1.23861	−	0.715113i	−0.200930	−	0.116007i
$39$	1.79962	+	0.186137i	0.288170	+	0.0298057i
$40$	2.20711	+	0.358719i	0.348974	+	0.0567185i
$41$	−1.04456			−0.163132			−0.0815661	−	0.996668i	$-0.525992\pi$
$41$	−1.04456			−0.163132			−0.0815661	+	0.996668i	$0.525992\pi$
$42$	−2.53553	+	3.81721i	−0.391241	+	0.589008i
$43$		−	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
$45$	−6.26089	−	2.40858i	−0.933319	−	0.359050i
$46$	−2.23861	+	3.87739i	−0.330065	+	0.571690i
$47$	9.71584	−	5.60944i	1.41720	−	0.818221i	0.421149	−	0.906992i	$-0.361627\pi$
$47$	9.71584	−	5.60944i	1.41720	−	0.818221i	0.996052	+	0.0887705i	$0.0282938\pi$
$48$	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
$51$	4.43649	+	3.21209i	0.621233	+	0.449783i
$52$	0.522278	−	0.904612i	0.0724269	−	0.125447i
$53$	2.50000	−	4.33013i	0.343401	−	0.594789i	−0.641661	−	0.766989i	$-0.721754\pi$
$53$	2.50000	−	4.33013i	0.343401	−	0.594789i	0.985062	+	0.172200i	$0.0550875\pi$
$54$	−1.10557	−	5.07718i	−0.150449	−	0.690916i
$55$	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	0.284042	+	0.958812i	$0.408324\pi$
$59$	−5.28720	+	9.15769i	−0.688334	+	1.19223i	−0.972376	+	0.233418i	$0.925009\pi$
$60$	−2.74514	+	2.73207i	−0.354396	+	0.352709i
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	−0.295495	−	0.955344i	$-0.595484\pi$
$61$	3.00000	−	1.73205i	0.384111	−	0.221766i	0.679605	+	0.733578i	$0.262151\pi$
$62$		−	6.62638i		−	0.841551i
$63$	−2.77984	−	7.43455i	−0.350227	−	0.936665i
$64$	1.00000			0.125000
$65$	2.30545	+	0.374703i	0.285956	+	0.0464761i
$66$	−0.834952	+	8.07256i	−0.102776	+	0.993663i
$67$	−12.3583	−	7.13505i	−1.50980	−	0.871685i	−0.999935	−	0.0114319i	$-0.996361\pi$
$67$	−12.3583	−	7.13505i	−1.50980	−	0.871685i	−0.509868	−	0.860253i	$-0.670306\pi$
$68$	2.73861	−	1.58114i	0.332106	−	0.191741i
$69$	−3.16588	−	7.07912i	−0.381127	−	0.852225i
$70$	−3.55378	+	4.72976i	−0.424758	+	0.565314i
$71$		−	6.92163i		−	0.821446i	−0.911760	−	0.410723i	$-0.865276\pi$
$71$		−	6.92163i		−	0.821446i	0.911760	−	0.410723i	$-0.134724\pi$
$72$	−2.93649	−	0.614017i	−0.346069	−	0.0723626i
$73$	−1.75166	+	3.03397i	−0.205017	+	0.355099i	−0.950138	−	0.311830i	$-0.899058\pi$
$73$	−1.75166	+	3.03397i	−0.205017	+	0.355099i	0.745121	+	0.666929i	$0.232392\pi$
$74$	−2.30615	−	1.33146i	−0.268084	−	0.154779i
$75$	−7.88874	−	3.57321i	−0.910913	−	0.412599i
$76$		−	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	−0.984152	−	0.177325i	$-0.943256\pi$
$79$	−5.73861	−	9.93957i	−0.645644	−	1.11829i	0.338508	−	0.940964i	$-0.390078\pi$
$80$	0.792893	+	2.09077i	0.0886482	+	0.233755i
$81$	8.24597	+	3.60611i	0.916219	+	0.400679i
$82$	−0.522278	−	0.904612i	−0.0576760	−	0.0998977i
$83$			4.06775i			0.446494i	0.974762	+	0.223247i	$0.0716656\pi$
$83$			4.06775i			0.446494i	−0.974762	+	0.223247i	$0.928334\pi$
$84$	−4.57357	−	0.287233i	−0.499017	−	0.0313397i
$85$	5.47723	+	4.47214i	0.594089	+	0.485071i
$86$	5.99430	−	3.46081i	0.646382	−	0.373189i
$87$	1.23341	−	11.9250i	0.132236	−	1.27849i
$88$	4.05781	+	2.34278i	0.432564	+	0.249741i
$89$	−2.45877	−	4.25871i	−0.260629	−	0.451423i	0.705780	−	0.708431i	$-0.250597\pi$
$89$	−2.45877	−	4.25871i	−0.260629	−	0.451423i	−0.966409	+	0.257008i	$0.917263\pi$
$90$	−1.04456	−	6.62638i	−0.110106	−	0.698482i
$91$	1.47723	+	2.33570i	0.154855	+	0.244848i
$92$	−4.47723			−0.466783
$93$	9.29642	+	6.73076i	0.963994	+	0.697948i
$94$	9.71584	+	5.60944i	1.00211	+	0.578570i
$95$	2.99028	−	1.13402i	0.306796	−	0.116348i
$96$	−1.01575	+	1.40294i	−0.103670	+	0.143187i
$97$	11.9886			1.21726			0.608629	−	0.793455i	$-0.291720\pi$
$97$	11.9886			1.21726			0.608629	+	0.793455i	$0.291720\pi$
$98$	−6.97723	+	0.564201i	−0.704806	+	0.0569930i
$99$	−10.4772	−	9.37112i	−1.05300	−	0.941833i
$100$	−3.74264	+	3.31552i	−0.374264	+	0.331552i
$101$	5.65685	−	9.79796i	0.562878	−	0.974933i	−0.434366	−	0.900737i	$-0.643027\pi$
$101$	5.65685	−	9.79796i	0.562878	−	0.974933i	0.997244	−	0.0741967i	$-0.0236393\pi$
$102$	−0.563508	+	5.44816i	−0.0557956	+	0.539448i
$103$	2.45877	+	4.25871i	0.242270	+	0.419624i	0.961360	−	0.275293i	$-0.0887748\pi$
$103$	2.45877	+	4.25871i	0.242270	+	0.419624i	−0.719091	+	0.694916i	$0.755441\pi$
$104$	1.04456			0.102427
$105$	−3.02581	−	9.79002i	−0.295289	−	0.955408i
$106$	5.00000			0.485643
$107$	−2.73861	−	4.74342i	−0.264752	−	0.458563i	0.702747	−	0.711440i	$-0.251957\pi$
$107$	−2.73861	−	4.74342i	−0.264752	−	0.458563i	−0.967499	+	0.252877i	$0.918623\pi$
$108$	3.84418	−	3.49604i	0.369906	−	0.336406i
$109$	10.2158	−	17.6944i	0.978500	−	1.69481i	0.310634	−	0.950529i	$-0.399459\pi$
$109$	10.2158	−	17.6944i	0.978500	−	1.69481i	0.667866	−	0.744282i	$-0.267208\pi$
$110$	−1.68080	+	10.3415i	−0.160258	+	0.986026i
$111$	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	$0.807175\pi$
$114$	2.00653	+	1.45276i	0.187928	+	0.136063i
$115$	−3.54996	−	9.36085i	−0.331036	−	0.872904i
$116$	−5.99430	−	3.46081i	−0.556557	−	0.321328i
$117$	−3.06733	−	0.641375i	−0.283575	−	0.0592951i
$118$	−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
$123$	1.79962	+	0.186137i	0.162267	+	0.0167834i
$124$	5.73861	−	3.31319i	0.515343	−	0.297533i
$125$	−9.89949	−	5.19615i	−0.885438	−	0.464758i
$126$	5.04858	−	6.12469i	0.449764	−	0.545631i
$127$			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
$129$	−1.23341	+	11.9250i	−0.108596	+	1.04994i
$130$	0.828222	+	2.18393i	0.0726398	+	0.191543i
$131$	−6.88624	−	11.9273i	−0.601654	−	1.04209i	−0.992571	−	0.121669i	$-0.961175\pi$
$131$	−6.88624	−	11.9273i	−0.601654	−	1.04209i	0.390917	−	0.920426i	$-0.372158\pi$
$132$	−7.40852	+	3.31319i	−0.644829	+	0.288376i
$133$	3.35071	+	1.75830i	0.290543	+	0.152464i
$134$		−	14.2701i		−	1.23275i
$135$	10.3574	+	5.26531i	0.891426	+	0.453166i
$136$	2.73861	+	1.58114i	0.234834	+	0.135582i
$137$	−1.73861	+	3.01137i	−0.148540	+	0.257278i	−0.930688	−	0.365814i	$-0.880791\pi$
$137$	−1.73861	+	3.01137i	−0.148540	+	0.257278i	0.782148	+	0.623092i	$0.214124\pi$
$138$	4.54776	−	6.28129i	0.387131	−	0.534699i
$139$			20.1810i			1.71173i	0.517202	+	0.855863i	$0.326974\pi$
$139$			20.1810i			1.71173i	−0.517202	+	0.855863i	$0.673026\pi$
$140$	−5.87298	−	0.712788i	−0.496358	−	0.0602416i
$141$	−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
$144$	−0.936492	−	2.85008i	−0.0780410	−	0.237507i
$145$	2.48292	−	15.2768i	0.206195	−	1.26867i
$146$	−3.50333			−0.289937
$147$	6.29560	−	10.3617i	0.519252	−	0.854621i
$148$		−	2.66291i		−	0.218890i
$149$	−2.12132	+	1.22474i	−0.173785	+	0.100335i	−0.584370	−	0.811488i	$-0.698658\pi$
$149$	−2.12132	+	1.22474i	−0.173785	+	0.100335i	0.410584	+	0.911823i	$0.365325\pi$
$150$	−0.849876	−	8.61845i	−0.0693921	−	0.703694i
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	−0.822464	−	0.568818i	$-0.807401\pi$
$151$	1.00000	−	1.73205i	0.0813788	−	0.140952i	0.903842	+	0.427865i	$0.140734\pi$
$152$	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
$156$	−1.06101	+	1.46545i	−0.0849489	+	0.117330i
$157$	−7.22369	+	12.5118i	−0.576513	+	0.998550i	0.419362	+	0.907819i	$0.362254\pi$
$157$	−7.22369	+	12.5118i	−0.576513	+	0.998550i	−0.995875	+	0.0907311i	$0.971080\pi$
$158$	5.73861	−	9.93957i	0.456540	−	0.790750i
$159$	−5.07877	+	7.01471i	−0.402772	+	0.556303i
$160$	−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	$-0.861889\pi$
$163$	−12.7279	+	7.34847i	−0.996928	+	0.575577i	−0.0895899	+	0.995979i	$0.528556\pi$
$164$	0.522278	−	0.904612i	0.0407831	−	0.0706383i
$165$	−12.8013	−	12.8625i	−0.996578	−	1.00134i
$166$	−3.52277	+	2.03387i	−0.273420	+	0.157859i
$167$			4.29068i			0.332023i	0.986124	+	0.166011i	$0.0530889\pi$
$167$			4.29068i			0.332023i	−0.986124	+	0.166011i	$0.946911\pi$
$168$	−2.03803	−	4.10444i	−0.157238	−	0.316664i
$169$	−11.9089			−0.916069
$170$	−1.13437	+	6.97948i	−0.0870023	+	0.535302i
$171$	−4.07627	+	1.33940i	−0.311720	+	0.102426i
$172$	5.99430	+	3.46081i	0.457061	+	0.263885i
$173$	−0.977226	+	0.564201i	−0.0742971	+	0.0428954i	−0.536688	−	0.843781i	$-0.680325\pi$
$173$	−0.977226	+	0.564201i	−0.0742971	+	0.0428954i	0.462391	+	0.886676i	$0.346992\pi$
$174$	10.9441	−	4.89433i	0.829666	−	0.371038i
$175$	−3.16637	−	12.8442i	−0.239355	−	0.970932i
$176$			4.68556i			0.353187i
$177$	10.7410	−	14.8353i	0.807341	−	1.11509i
$178$	2.45877	−	4.25871i	0.184293	−	0.319204i
$179$	16.7857	+	9.69125i	1.25462	+	0.724358i	0.972024	−	0.234880i	$-0.0754697\pi$
$179$	16.7857	+	9.69125i	1.25462	+	0.724358i	0.282600	+	0.959238i	$0.408803\pi$
$180$	5.21633	−	4.21780i	0.388803	−	0.314376i
$181$			3.16228i			0.235050i	0.993070	+	0.117525i	$0.0374961\pi$
$181$			3.16228i			0.235050i	−0.993070	+	0.117525i	$0.962504\pi$
$182$	−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
$185$	5.56754	−	2.11140i	0.409333	−	0.155234i
$186$	−1.18080	+	11.4163i	−0.0865805	+	0.837085i
$187$	7.40852	+	12.8319i	0.541764	+	0.938364i
$188$			11.2189i			0.818221i
$189$	3.46447	+	13.3040i	0.252003	+	0.967726i
$190$	2.47723	+	2.02265i	0.179717	+	0.146738i
$191$	−14.1099	+	8.14637i	−1.02096	+	0.589451i	−0.914381	−	0.404854i	$-0.867322\pi$
$191$	−14.1099	+	8.14637i	−1.02096	+	0.589451i	−0.106577	+	0.994304i	$0.533989\pi$
$192$	−1.72286	−	0.178197i	−0.124337	−	0.0128603i
$193$	−6.36396	−	3.67423i	−0.458088	−	0.264477i	0.253152	−	0.967427i	$-0.418533\pi$
$193$	−6.36396	−	3.67423i	−0.458088	−	0.264477i	−0.711240	+	0.702949i	$0.751866\pi$
$194$	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	$0.603888\pi$
$198$	2.87701	−	13.7591i	0.204460	−	0.977817i
$199$	13.4317	+	7.75478i	0.952146	+	0.549722i	0.893747	−	0.448571i	$-0.148067\pi$
$199$	13.4317	+	7.75478i	0.952146	+	0.549722i	0.0583993	+	0.998293i	$0.481400\pi$
$200$	−4.74264	−	1.58346i	−0.335355	−	0.111968i
$201$	20.0201	+	14.4949i	1.41211	+	1.02239i
$202$	11.3137			0.796030
$203$	15.4772	−	9.78866i	1.08629	−	0.687029i
$204$	−5.00000	+	2.23607i	−0.350070	+	0.156556i
$205$	2.30545	+	0.374703i	0.161019	+	0.0261704i
$206$	−2.45877	+	4.25871i	−0.171311	+	0.296719i
$207$	4.19288	+	12.7605i	0.291426	+	0.886914i
$208$	0.522278	+	0.904612i	0.0362135	+	0.0627236i
$209$	6.70141			0.463546
$210$	6.96550	−	7.51544i	0.480665	−	0.518614i
$211$	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
$213$	−1.23341	+	11.9250i	−0.0845121	+	0.817087i
$214$	2.73861	−	4.74342i	0.187208	−	0.324253i
$215$	−2.48292	+	15.2768i	−0.169334	+	1.04187i
$216$	4.94975	+	1.58114i	0.336788	+	0.107583i
$217$	0.707107	+	17.5175i	0.0480015	+	1.18916i
$218$	20.4317			1.38381
$219$	3.55851	−	4.91496i	0.240462	−	0.332122i
$220$	−9.79642	+	3.71515i	−0.660475	+	0.250475i
$221$	2.86064	+	1.65159i	0.192427	+	0.111098i
$222$	3.73591	+	2.70486i	0.250738	+	0.181538i
$223$	21.8881			1.46574			0.732868	−	0.680371i	$-0.238181\pi$
$223$	21.8881			1.46574			0.732868	+	0.680371i	$0.238181\pi$
$224$	−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	0.170648	−	0.985332i	$-0.445414\pi$
$227$	−9.00000	−	5.19615i	−0.597351	−	0.344881i	−0.767999	+	0.640451i	$0.778747\pi$
$228$	−0.254862	+	2.46408i	−0.0168787	+	0.163188i
$229$	−11.7386	+	6.77729i	−0.775709	+	0.447856i	−0.834908	−	0.550390i	$-0.814479\pi$
$229$	−11.7386	+	6.77729i	−0.775709	+	0.447856i	0.0591982	+	0.998246i	$0.481146\pi$
$230$	6.33175	−	7.75478i	0.417503	−	0.511335i
$231$	1.34585	−	21.4297i	0.0885503	−	1.40997i
$232$		−	6.92163i		−	0.454427i
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	0.793047	−	0.609160i	$-0.208493\pi$
$233$	−2.00000	−	3.46410i	−0.131024	−	0.226941i	−0.924072	+	0.382219i	$0.875160\pi$
$234$	−0.978218	−	2.97707i	−0.0639481	−	0.194617i
$235$	−23.4561	+	8.89538i	−1.53011	+	0.580270i
$236$	−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			$\pi$
$240$	−0.993475	−	3.74340i	−0.0641285	−	0.241635i
$241$	−18.4545	−	10.6547i	−1.18876	−	0.686328i	−0.230732	−	0.973017i	$-0.574112\pi$
$241$	−18.4545	−	10.6547i	−1.18876	−	0.686328i	−0.958024	+	0.286689i	$0.907445\pi$
$242$	−5.47723	+	9.48683i	−0.352089	+	0.609837i
$243$	−13.5640	−	7.68223i	−0.870134	−	0.492815i
$244$			3.46410i			0.221766i
$245$	8.89006	−	12.8828i	0.567965	−	0.823053i
$246$	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
$249$	0.724861	−	7.00816i	0.0459362	−	0.444124i
$250$	−0.449747	−	11.1713i	−0.0284445	−	0.706534i
$251$	−8.85494			−0.558919			−0.279459	−	0.960158i	$-0.590155\pi$
$251$	−8.85494			−0.558919			−0.279459	+	0.960158i	$0.590155\pi$
$252$	7.82843	+	1.30986i	0.493145	+	0.0825133i
$253$		−	20.9783i		−	1.31889i
$254$	−7.56114	+	4.36543i	−0.474428	+	0.273911i
$255$	−8.63957	−	8.68089i	−0.541031	−	0.543618i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.52277	−	5.49798i	0.594014	−	0.342954i	−0.172669	−	0.984980i	$-0.555239\pi$
$257$	9.52277	−	5.49798i	0.594014	−	0.342954i	0.766683	+	0.642026i	$0.221906\pi$
$258$	−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
$261$	−4.24999	+	20.3253i	−0.263068	+	1.25810i
$262$	6.88624	−	11.9273i	0.425433	−	0.736872i
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	−0.895209	−	0.445647i	$-0.852974\pi$
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	0.833546	+	0.552450i	$0.186307\pi$
$264$	−6.57357	−	4.75937i	−0.404575	−	0.292919i
$265$	−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	−0.463148	−	0.886281i	$-0.653280\pi$
$269$	8.79052	−	15.2256i	0.535968	−	0.928323i	0.999116	−	0.0420423i	$-0.0133864\pi$
$270$	0.618823	+	11.6025i	0.0376604	+	0.706103i
$271$	−5.47723	+	3.16228i	−0.332718	+	0.192095i	−0.657047	−	0.753850i	$-0.728195\pi$
$271$	−5.47723	+	3.16228i	−0.332718	+	0.192095i	0.324329	+	0.945944i	$0.394861\pi$
$272$			3.16228i			0.191741i
$273$	−2.12884	−	4.28732i	−0.128843	−	0.259480i
$274$	−3.47723			−0.210067
$275$	−15.5350	−	17.5364i	−0.936798	−	1.05748i
$276$	7.71363	+	0.797828i	0.464306	+	0.0480236i
$277$	8.48528	+	4.89898i	0.509831	+	0.294351i	0.732764	−	0.680483i	$-0.238230\pi$
$277$	8.48528	+	4.89898i	0.509831	+	0.294351i	−0.222933	+	0.974834i	$0.571563\pi$
$278$	−17.4772	+	10.0905i	−1.04821	+	0.605187i
$279$	−14.8170	−	13.2528i	−0.887073	−	0.793422i
$280$	−2.31920	−	5.44255i	−0.138599	−	0.325254i
$281$		−	1.80922i		−	0.107929i	−0.998543	−	0.0539646i	$-0.982814\pi$
$281$		−	1.80922i		−	0.107929i	0.998543	−	0.0539646i	$-0.0171858\pi$
$282$	−15.7394	−	11.3956i	−0.937270	−	0.678599i
$283$	−4.61230	+	7.98873i	−0.274173	+	0.474881i	−0.969926	−	0.243400i	$-0.921737\pi$
$283$	−4.61230	+	7.98873i	−0.274173	+	0.474881i	0.695753	+	0.718281i	$0.255071\pi$
$284$	5.99430	+	3.46081i	0.355696	+	0.205361i
$285$	−5.35390	+	1.42089i	−0.317138	+	0.0841665i
$286$			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
$290$	14.4715	−	5.48811i	0.849797	−	0.322273i
$291$	−20.6547	−	2.13633i	−1.21080	−	0.125234i
$292$	−1.75166	−	3.03397i	−0.102508	−	0.177550i
$293$		−	8.05661i		−	0.470672i	−0.971914	−	0.235336i	$-0.924381\pi$
$293$		−	8.05661i		−	0.470672i	0.971914	−	0.235336i	$-0.0756190\pi$
$294$	12.1213	+	0.271281i	0.706930	+	0.0158214i
$295$	14.9545	−	18.3154i	0.870682	−	1.06636i
$296$	2.30615	−	1.33146i	0.134042	−	0.0773893i
$297$	16.3809	+	18.0121i	0.950515	+	1.04517i
$298$	−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
$303$	−11.4919	+	15.8725i	−0.660194	+	0.911850i
$304$	1.23861	+	0.715113i	0.0710393	+	0.0410146i
$305$	−7.24264	+	2.74666i	−0.414712	+	0.157273i
$306$	1.94169	−	9.28600i	0.110999	−	0.530845i
$307$	−11.9886			−0.684226			−0.342113	−	0.939659i	$-0.611143\pi$
$307$	−11.9886			−0.684226			−0.342113	+	0.939659i	$0.611143\pi$
$308$	−10.9772	−	5.76035i	−0.625485	−	0.328227i
$309$	−3.47723	−	7.77531i	−0.197812	−	0.442322i
$310$	−2.37701	+	14.6251i	−0.135005	+	0.830651i
$311$	8.79052	−	15.2256i	0.498465	−	0.863366i	−0.501534	−	0.865138i	$-0.667231\pi$
$311$	8.79052	−	15.2256i	0.498465	−	0.863366i	0.999998	+	0.00177176i	$0.000563970\pi$
$312$	−1.79962	−	0.186137i	−0.101884	−	0.0105379i
$313$	−11.6190	−	20.1246i	−0.656742	−	1.13751i	−0.981454	−	0.191697i	$-0.938601\pi$
$313$	−11.6190	−	20.1246i	−0.656742	−	1.13751i	0.324712	−	0.945813i	$-0.394733\pi$
$314$	−14.4474			−0.815313
$315$	3.46849	+	17.4060i	0.195427	+	0.980718i
$316$	11.4772			0.645644
$317$	−4.95445	−	8.58136i	−0.278270	−	0.481977i	0.692685	−	0.721240i	$-0.256428\pi$
$317$	−4.95445	−	8.58136i	−0.278270	−	0.481977i	−0.970955	+	0.239263i	$0.923094\pi$
$318$	−8.61430	−	0.890985i	−0.483066	−	0.0499640i
$319$	16.2158	−	28.0867i	0.907913	−	1.57255i
$320$	−2.20711	−	0.358719i	−0.123381	−	0.0200530i
$321$	3.87298	+	8.66025i	0.216169	+	0.483368i
$322$	11.8360	−	0.477769i	0.659594	−	0.0266250i
$323$	4.52277			0.251654
$324$	−7.24597	+	5.33816i	−0.402554	+	0.296565i
$325$	−4.95395	−	1.65402i	−0.274796	−	0.0917484i
$326$	−12.7279	−	7.34847i	−0.704934	−	0.406994i
$327$	−20.7535	+	28.6645i	−1.14767	+	1.58515i
$328$	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	−0.994364	−	0.106017i	$-0.966190\pi$
$331$	−10.7158	−	18.5604i	−0.588996	−	1.02017i	0.405369	−	0.914153i	$-0.367143\pi$
$332$	−3.52277	−	2.03387i	−0.193337	−	0.111623i
$333$	−7.58952	+	2.49379i	−0.415903	+	0.136659i
$334$	−3.71584	+	2.14534i	−0.203322	+	0.117388i
$335$	24.7165	+	20.1810i	1.35041	+	1.10260i
$336$	2.53553	−	3.81721i	0.138325	−	0.208246i
$337$		−	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
$339$	30.1108	+	3.11439i	1.63539	+	0.169150i
$340$	−6.61160	+	2.50735i	−0.358564	+	0.135980i
$341$	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
$345$	4.44801	+	16.7600i	0.239473	+	0.902329i
$346$	−0.977226	−	0.564201i	−0.0525360	−	0.0303317i
$347$	−8.73861	+	15.1357i	−0.469113	+	0.812528i	−0.999377	−	0.0353049i	$-0.988760\pi$
$347$	−8.73861	+	15.1357i	−0.469113	+	0.812528i	0.530263	+	0.847833i	$0.322093\pi$
$348$	9.71064	+	7.03066i	0.520545	+	0.376883i
$349$		−	11.7436i		−	0.628623i	−0.949320	−	0.314311i	$-0.898226\pi$
$349$		−	11.7436i		−	0.628623i	0.949320	−	0.314311i	$-0.101774\pi$
$350$	9.54024	−	9.16427i	0.509947	−	0.489851i
$351$	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	0.486023	−	0.873946i	$-0.338447\pi$
$353$	−0.522774	−	0.301824i	−0.0278245	−	0.0160645i	−0.513848	+	0.857881i	$0.671780\pi$
$354$	18.2182	+	1.88433i	0.968286	+	0.100151i
$355$	−2.48292	+	15.2768i	−0.131780	+	0.810807i
$356$	4.91754			0.260629
$357$	0.908312	−	14.4629i	0.0480730	−	0.765457i
$358$			19.3825i			1.02440i
$359$	9.86729	−	5.69688i	0.520775	−	0.300670i	−0.216476	−	0.976288i	$-0.569456\pi$
$359$	9.86729	−	5.69688i	0.520775	−	0.300670i	0.737252	+	0.675618i	$0.236123\pi$
$360$	6.26089	+	2.40858i	0.329978	+	0.126943i
$361$	−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
$366$	−4.85993	−	3.51867i	−0.254033	−	0.183924i
$367$	−0.184829	+	0.320133i	−0.00964798	+	0.0167108i	−0.870809	−	0.491621i	$-0.836404\pi$
$367$	−0.184829	+	0.320133i	−0.00964798	+	0.0167108i	0.861161	+	0.508332i	$0.169738\pi$
$368$	2.23861	−	3.87739i	0.116696	−	0.202123i
$369$	−3.06733	−	0.641375i	−0.159679	−	0.0333887i
$370$	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	$-0.461437\pi$
$373$	20.1042	−	11.6072i	1.04096	−	0.600997i	0.920104	+	0.391673i	$0.128104\pi$
$374$	−7.40852	+	12.8319i	−0.383085	+	0.663523i
$375$	16.1295	+	10.7163i	0.832924	+	0.553387i
$376$	−9.71584	+	5.60944i	−0.501056	+	0.289285i
$377$		−	7.23003i		−	0.372365i
$378$	−9.78940	+	9.65234i	−0.503513	+	0.496463i
$379$	−20.4772			−1.05184			−0.525922	−	0.850533i	$-0.676280\pi$
$379$	−20.4772			−1.05184			−0.525922	+	0.850533i	$0.676280\pi$
$380$	−0.513050	+	3.15666i	−0.0263189	+	0.161933i
$381$	1.55581	−	15.0420i	0.0797066	−	0.770627i
$382$	−14.1099	−	8.14637i	−0.721927	−	0.416805i
$383$	−15.7158	+	9.07354i	−0.803042	+	0.463636i	−0.844534	−	0.535502i	$-0.820122\pi$
$383$	−15.7158	+	9.07354i	−0.803042	+	0.463636i	0.0414919	+	0.999139i	$0.486789\pi$
$384$	−0.707107	−	1.58114i	−0.0360844	−	0.0806872i
$385$	3.33981	−	27.5182i	0.170212	−	1.40246i
$386$		−	7.34847i		−	0.374027i
$387$	4.24999	−	20.3253i	0.216039	−	1.03319i
$388$	−5.99430	+	10.3824i	−0.304315	+	0.527088i
$389$	6.36396	+	3.67423i	0.322666	+	0.186291i	0.652580	−	0.757720i	$-0.273687\pi$
$389$	6.36396	+	3.67423i	0.322666	+	0.186291i	−0.329914	+	0.944011i	$0.607020\pi$
$390$	−1.03774	−	3.91019i	−0.0525480	−	0.198000i
$391$		−	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
$395$	9.10021	+	23.9962i	0.457881	+	1.20738i
$396$	13.3542	−	4.38799i	0.671076	−	0.220505i
$397$	−7.44073	−	12.8877i	−0.373439	−	0.646816i	0.616653	−	0.787235i	$-0.288488\pi$
$397$	−7.44073	−	12.8877i	−0.373439	−	0.646816i	−0.990092	+	0.140419i	$0.955155\pi$
$398$			15.5096i			0.777424i
$399$	−5.45947	−	3.62639i	−0.273315	−	0.181547i
$400$	−1.00000	−	4.89898i	−0.0500000	−	0.244949i
$401$	−0.827520	+	0.477769i	−0.0413244	+	0.0238586i	−0.520520	−	0.853850i	$-0.674262\pi$
$401$	−0.827520	+	0.477769i	−0.0413244	+	0.0238586i	0.479195	+	0.877708i	$0.340928\pi$
$402$	−2.54289	+	24.5854i	−0.126828	+	1.22621i
$403$	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
$408$	−4.43649	−	3.21209i	−0.219639	−	0.159022i
$409$	13.4317	+	7.75478i	0.664154	+	0.383449i	0.793858	−	0.608103i	$-0.208069\pi$
$409$	13.4317	+	7.75478i	0.664154	+	0.383449i	−0.129704	+	0.991553i	$0.541403\pi$
$410$	0.828222	+	2.18393i	0.0409029	+	0.107856i
$411$	3.53200	−	4.87835i	0.174221	−	0.240631i
$412$	−4.91754			−0.242270
$413$	27.9545	−	1.12840i	1.37555	−	0.0555251i
$414$	−8.95445	+	10.0114i	−0.440087	+	0.492033i
$415$	1.45918	−	8.97796i	0.0716284	−	0.440711i
$416$	−0.522278	+	0.904612i	−0.0256068	+	0.0443523i
$417$	3.59619	−	34.7690i	0.176106	−	1.70264i
$418$	3.35071	+	5.80359i	0.163888	+	0.283863i
$419$	8.85494			0.432592			0.216296	−	0.976328i	$-0.430602\pi$
$419$	8.85494			0.432592			0.216296	+	0.976328i	$0.430602\pi$
$420$	9.99131	+	2.27458i	0.487526	+	0.110988i
$421$	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
$423$	31.9748	−	10.5064i	1.55467	−	0.510838i
$424$	−2.50000	+	4.33013i	−0.121411	+	0.210290i
$425$	−10.4846	−	11.8353i	−0.508577	−	0.574095i
$426$	−10.9441	+	4.89433i	−0.530241	+	0.237131i
$427$	−8.11562	−	4.25871i	−0.392743	−	0.206094i
$428$	5.47723			0.264752
$429$	−6.86646	−	4.97143i	−0.331516	−	0.240023i
$430$	−14.4715	+	5.48811i	−0.697879	+	0.264660i
$431$	6.63699	+	3.83187i	0.319693	+	0.184575i	0.651256	−	0.758858i	$-0.274243\pi$
$431$	6.63699	+	3.83187i	0.319693	+	0.184575i	−0.331563	+	0.943433i	$0.607576\pi$
$432$	1.10557	+	5.07718i	0.0531916	+	0.244276i
$433$		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
$438$	6.03574	+	0.624282i	0.288399	+	0.0298294i
$439$	−7.69306	+	4.44159i	−0.367170	+	0.211986i	−0.672221	−	0.740350i	$-0.734660\pi$
$439$	−7.69306	+	4.44159i	−0.367170	+	0.211986i	0.305051	+	0.952336i	$0.401326\pi$
$440$	−8.11562	−	6.62638i	−0.386897	−	0.315900i
$441$	−12.6929	+	16.7300i	−0.604422	+	0.796664i
$442$			3.30318i			0.157116i
$443$	−7.52277	−	13.0298i	−0.357418	−	0.619066i	0.630111	−	0.776505i	$-0.283009\pi$
$443$	−7.52277	−	13.0298i	−0.357418	−	0.619066i	−0.987529	+	0.157439i	$0.949676\pi$
$444$	−0.474523	+	4.58782i	−0.0225199	+	0.217728i
$445$	3.89908	+	10.2814i	0.184834	+	0.487387i
$446$	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	$-0.209077\pi$
$450$	−0.0715641	+	14.9998i	−0.00337357	+	0.707099i
$451$	4.23861	+	2.44716i	0.199588	+	0.115232i
$452$	8.73861	−	15.1357i	0.411030	−	0.711924i
$453$	−2.03151	+	2.80588i	−0.0954485	+	0.131832i
$454$		−	10.3923i		−	0.487735i
$455$	−2.42253	−	5.68505i	−0.113570	−	0.266519i
$456$	−2.26139	+	1.01132i	−0.105899	+	0.0473595i
$457$	−9.59425	+	5.53924i	−0.448800	+	0.259115i	−0.707323	−	0.706890i	$-0.750098\pi$
$457$	−9.59425	+	5.53924i	−0.448800	+	0.259115i	0.258523	+	0.966005i	$0.416764\pi$
$458$	−11.7386	−	6.77729i	−0.548509	−	0.316682i
$459$	11.0554	+	12.1564i	0.516024	+	0.567411i
$460$	9.88171	+	1.60607i	0.460737	+	0.0748833i
$461$	31.7876			1.48050			0.740248	−	0.672334i	$-0.234708\pi$
$461$	31.7876			1.48050			0.740248	+	0.672334i	$0.234708\pi$
$462$	19.2316	−	9.54931i	0.894735	−	0.444274i
$463$			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
$465$	−18.1037	−	18.1903i	−0.839541	−	0.843556i
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	24.2614	−	14.0073i	1.12268	−	0.648181i	0.180599	−	0.983557i	$-0.442197\pi$
$467$	24.2614	−	14.0073i	1.12268	−	0.648181i	0.942085	+	0.335375i	$0.108863\pi$
$468$	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
$471$	14.6750	−	20.2688i	0.676187	−	0.933938i
$472$	5.28720	−	9.15769i	0.243363	−	0.421517i
$473$	−16.2158	+	28.0867i	−0.745605	+	1.29143i
$474$	−11.6580	+	16.1019i	−0.535471	+	0.739584i
$475$	−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	−0.265844	+	0.964016i	$0.585651\pi$
$479$	−21.1810	+	36.6866i	−0.967784	+	1.67625i	−0.701940	+	0.712236i	$0.747683\pi$
$480$	2.74514	−	2.73207i	0.125298	−	0.124701i
$481$	2.40890	−	1.39078i	0.109836	−	0.0634141i
$482$		−	21.3094i		−	0.970615i
$483$	−11.3522	+	17.0905i	−0.516541	+	0.777644i
$484$	−10.9545			−0.497930
$485$	−26.4601	−	4.30055i	−1.20149	−	0.195278i
$486$	−0.129018	−	15.5879i	−0.00585235	−	0.707083i
$487$	14.7526	+	8.51743i	0.668505	+	0.385962i	0.795510	−	0.605941i	$-0.207203\pi$
$487$	14.7526	+	8.51743i	0.668505	+	0.385962i	−0.127005	+	0.991902i	$0.540536\pi$
$488$	−3.00000	+	1.73205i	−0.135804	+	0.0784063i
$489$	23.2379	−	10.3923i	1.05085	−	0.469956i
$490$	15.6019	+	1.25761i	0.704821	+	0.0568132i
$491$			13.8433i			0.624737i	0.949961	+	0.312369i	$0.101122\pi$
$491$			13.8433i			0.624737i	−0.949961	+	0.312369i	$0.898878\pi$
$492$	−1.06101	+	1.46545i	−0.0478341	+	0.0660677i
$493$	10.9441	−	18.9557i	0.492895	−	0.853720i
$494$	1.29380	+	0.746976i	0.0582108	+	0.0336080i
$495$	19.7628	+	24.4414i	0.888270	+	1.09856i
$496$			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	0.843871	−	0.536546i	$-0.180271\pi$
$499$	−0.954451	−	1.65316i	−0.0427271	−	0.0740055i	−0.886598	+	0.462541i	$0.846938\pi$
$500$	9.44975	−	5.97514i	0.422606	−	0.267216i
$501$	0.764586	−	7.39224i	0.0341592	−	0.330261i
$502$	−4.42747	−	7.66860i	−0.197608	−	0.342266i
$503$		−	15.5096i		−	0.691537i	−0.938320	−	0.345769i	$-0.887618\pi$
$503$		−	15.5096i		−	0.691537i	0.938320	−	0.345769i	$-0.112382\pi$
$504$	2.77984	+	7.43455i	0.123824	+	0.331161i
$505$	−16.0000	+	19.5959i	−0.711991	+	0.872007i
$506$	18.1677	−	10.4891i	0.807655	−	0.466300i
$507$	20.5174	+	2.12213i	0.911208	+	0.0942471i
$508$	−7.56114	−	4.36543i	−0.335471	−	0.193684i
$509$	−12.3583	−	21.4051i	−0.547770	−	0.948766i	−0.998427	−	0.0560688i	$-0.982143\pi$
$509$	−12.3583	−	21.4051i	−0.547770	−	0.948766i	0.450656	−	0.892697i	$-0.351190\pi$
$510$	3.19808	−	11.8225i	0.141614	−	0.523511i
$511$	9.26139	−	0.373843i	0.409700	−	0.0165378i
$512$	−1.00000			−0.0441942
$513$	7.26151	−	1.58121i	0.320604	−	0.0698122i
$514$	9.52277	+	5.49798i	0.420032	+	0.242505i
$515$	−3.89908	−	10.2814i	−0.171814	−	0.453055i
$516$	−9.71064	−	7.03066i	−0.427487	−	0.309508i
$517$	−52.5667			−2.31188
$518$	0.284162	+	7.03967i	0.0124853	+	0.309305i
$519$	1.78416	−	0.797901i	0.0783160	−	0.0350240i
$520$	−2.30545	−	0.374703i	−0.101101	−	0.0164318i
$521$	−17.7981	+	30.8272i	−0.779748	+	1.35056i	0.152339	+	0.988328i	$0.451320\pi$
$521$	−17.7981	+	30.8272i	−0.779748	+	1.35056i	−0.932087	+	0.362235i	$0.882014\pi$
$522$	−19.7272	+	6.48204i	−0.863437	+	0.283711i
$523$	8.45307	+	14.6412i	0.369627	+	0.640213i	0.989507	−	0.144484i	$-0.0461521\pi$
$523$	8.45307	+	14.6412i	0.369627	+	0.640213i	−0.619880	+	0.784697i	$0.712819\pi$
$524$	13.7725			0.601654
$525$	3.16641	+	22.6930i	0.138194	+	0.990405i
$526$	−2.00000			−0.0872041
$527$	10.4772	+	18.1471i	0.456395	+	0.790500i
$528$	0.834952	−	8.07256i	0.0363366	−	0.351313i
$529$	1.47723	−	2.55863i	0.0642272	−	0.111245i
$530$	−11.0355	−	1.79360i	−0.479353	−	0.0779089i
$531$	−21.1488	+	23.6451i	−0.917779	+	1.02611i
$532$	−3.19808	+	2.02265i	−0.138655	+	0.0876928i
$533$	1.09110			0.0472607
$534$	−4.99501	+	6.89902i	−0.216155	+	0.298550i
$535$	4.34286	+	11.4516i	0.187758	+	0.495097i
$536$	12.3583	+	7.13505i	0.533796	+	0.308187i
$537$	−27.1925	−	19.6878i	−1.17344	−	0.849593i
$538$	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	0.759761	−	0.650202i	$-0.225316\pi$
$541$	−4.26139	−	7.38094i	−0.183211	−	0.317331i	−0.942972	+	0.332871i	$0.891983\pi$
$542$	−5.47723	−	3.16228i	−0.235267	−	0.135831i
$543$	0.563508	−	5.44816i	0.0241825	−	0.233803i
$544$	−2.73861	+	1.58114i	−0.117417	+	0.0677908i
$545$	−28.8948	+	35.3887i	−1.23772	+	1.51589i
$546$	2.64851	−	3.98729i	0.113346	−	0.170640i
$547$		−	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
$549$	9.87298	−	3.24410i	0.421369	−	0.138455i
$550$	7.41941	−	22.2219i	0.316365	−	0.947546i
$551$	−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
$555$	−9.96833	+	2.64554i	−0.423132	+	0.112297i
$556$	−17.4772	−	10.0905i	−0.741199	−	0.427932i
$557$	13.9317	−	24.1304i	0.590304	−	1.02244i	−0.403887	−	0.914809i	$-0.632341\pi$
$557$	13.9317	−	24.1304i	0.590304	−	1.02244i	0.994191	−	0.107628i	$-0.0343255\pi$
$558$	4.06871	−	19.4583i	0.172242	−	0.823736i
$559$			7.23003i			0.305798i
$560$	3.55378	−	4.72976i	0.150175	−	0.199869i
$561$	−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	0.298211	−	0.954500i	$-0.403610\pi$
$563$	−9.00000	−	5.19615i	−0.379305	−	0.218992i	−0.677516	+	0.735508i	$0.736943\pi$
$564$	1.99917	−	19.3286i	0.0841803	−	0.813879i
$565$	38.5741	+	6.26942i	1.62282	+	0.263757i
$566$	−9.22460			−0.387739
$567$	−3.59805	−	23.5384i	−0.151104	−	0.988518i
$568$			6.92163i			0.290425i
$569$	−6.54879	+	3.78095i	−0.274540	+	0.158505i	−0.630949	−	0.775824i	$-0.717334\pi$
$569$	−6.54879	+	3.78095i	−0.274540	+	0.158505i	0.356409	+	0.934330i	$0.384001\pi$
$570$	−3.90748	−	3.92617i	−0.163666	−	0.164449i
$571$	−7.47723	+	12.9509i	−0.312912	+	0.541980i	−0.978991	−	0.203901i	$-0.934638\pi$
$571$	−7.47723	+	12.9509i	−0.312912	+	0.541980i	0.666079	+	0.745881i	$0.267971\pi$
$572$	−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
$576$	2.93649	+	0.614017i	0.122354	+	0.0255840i
$577$	0.337449	−	0.584480i	0.0140482	−	0.0243322i	−0.858916	−	0.512117i	$-0.828862\pi$
$577$	0.337449	−	0.584480i	0.0140482	−	0.0243322i	0.872964	+	0.487785i	$0.162195\pi$
$578$	3.50000	−	6.06218i	0.145581	−	0.252153i
$579$	10.3095	+	7.46423i	0.428447	+	0.310203i
$580$	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
$585$	6.53985	+	2.51589i	0.270390	+	0.104019i
$586$	6.97723	−	4.02830i	0.288227	−	0.166408i
$587$			21.0864i			0.870330i	0.900351	+	0.435165i	$0.143310\pi$
$587$			21.0864i			0.870330i	−0.900351	+	0.435165i	$0.856690\pi$
$588$	5.82572	+	10.6330i	0.240249	+	0.438498i
$589$	9.47723			0.390502
$590$	23.3388	+	3.79324i	0.960844	+	0.156165i
$591$	15.5057	+	1.60377i	0.637821	+	0.0659704i
$592$	2.30615	+	1.33146i	0.0947821	+	0.0547225i
$593$	1.43168	−	0.826579i	0.0587919	−	0.0339435i	−0.470316	−	0.882498i	$-0.655860\pi$
$593$	1.43168	−	0.826579i	0.0587919	−	0.0339435i	0.529108	+	0.848555i	$0.322527\pi$
$594$	−7.40852	+	23.1923i	−0.303975	+	0.951593i
$595$	2.25403	−	18.5720i	0.0924064	−	0.761378i
$596$		−	2.44949i		−	0.100335i
$597$	−21.7590	−	15.7539i	−0.890537	−	0.644764i
$598$	2.33836	−	4.05015i	0.0956225	−	0.165623i
$599$	−20.4739	−	11.8206i	−0.836540	−	0.482977i	0.0195464	−	0.999809i	$-0.493778\pi$
$599$	−20.4739	−	11.8206i	−0.836540	−	0.482977i	−0.856087	+	0.516832i	$0.827111\pi$
$600$	7.88874	+	3.57321i	0.322056	+	0.145876i
$601$		−	4.06775i		−	0.165927i	−0.996553	−	0.0829635i	$-0.973562\pi$
$601$		−	4.06775i		−	0.165927i	0.996553	−	0.0829635i	$-0.0264385\pi$
$602$	−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
$605$	−8.68571	−	22.9032i	−0.353124	−	0.931149i
$606$	−19.4919	−	2.01607i	−0.791806	−	0.0818972i
$607$	−6.14692	−	10.6468i	−0.249496	−	0.432140i	0.713890	−	0.700258i	$-0.246932\pi$
$607$	−6.14692	−	10.6468i	−0.249496	−	0.432140i	−0.963386	+	0.268118i	$0.913598\pi$
$608$			1.43023i			0.0580034i
$609$	−28.4094	+	14.1065i	−1.15121	+	0.571624i
$610$	−6.00000	−	4.89898i	−0.242933	−	0.198354i
$611$	−10.1487	+	5.85938i	−0.410574	+	0.237045i
$612$	9.01276	−	2.96145i	0.364319	−	0.119709i
$613$	−5.07016	−	2.92726i	−0.204782	−	0.118231i	0.394102	−	0.919067i	$-0.371056\pi$
$613$	−5.07016	−	2.92726i	−0.204782	−	0.118231i	−0.598884	+	0.800836i	$0.704389\pi$
$614$	−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	$0.594431\pi$
$618$	4.99501	−	6.89902i	0.200929	−	0.277519i
$619$	26.1475	+	15.0963i	1.05096	+	0.606771i	0.922917	−	0.384998i	$-0.125798\pi$
$619$	26.1475	+	15.0963i	1.05096	+	0.606771i	0.128040	+	0.991769i	$0.459131\pi$
$620$	−13.8542	+	5.25401i	−0.556400	+	0.211006i
$621$	−4.94987	−	22.7317i	−0.198632	−	0.912190i
$622$	17.5810			0.704936
$623$	−6.04555	+	11.5207i	−0.242210	+	0.461567i
$624$	−0.738613	−	1.65159i	−0.0295682	−	0.0661165i
$625$	19.9853	+	15.0196i	0.799411	+	0.600784i
$626$	11.6190	−	20.1246i	0.464387	−	0.804341i
$627$	−11.5456	−	1.19417i	−0.461086	−	0.0476906i
$628$	−7.22369	−	12.5118i	−0.288257	−	0.499275i
$629$	8.42087			0.335762
$630$	−13.3398	+	11.7068i	−0.531471	+	0.466411i
$631$	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
$633$	−42.1708	−	4.36177i	−1.67614	−	0.173365i
$634$	4.95445	−	8.58136i	0.196766	−	0.340809i
$635$	3.13193	−	19.2699i	0.124287	−	0.764703i
$636$	−3.53553	−	7.90569i	−0.140193	−	0.313481i
$637$	3.13367	−	6.60635i	0.124160	−	0.261753i
$638$	32.4317			1.28398
$639$	4.24999	−	20.3253i	0.168127	−	0.804056i
$640$	−0.792893	−	2.09077i	−0.0313419	−	0.0826450i
$641$	13.9251	+	8.03966i	0.550008	+	0.317547i	0.749125	−	0.662428i	$-0.230474\pi$
$641$	13.9251	+	8.03966i	0.550008	+	0.317547i	−0.199117	+	0.979976i	$0.563807\pi$
$642$	−5.56351	+	7.68423i	−0.219574	+	0.303272i
$643$	26.0663			1.02796			0.513978	−	0.857803i	$-0.328171\pi$
$643$	26.0663			1.02796			0.513978	+	0.857803i	$0.328171\pi$
$644$	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	0.110676	−	0.993857i	$-0.464698\pi$
$647$	−17.6703	−	10.2019i	−0.694691	−	0.401080i	−0.805367	+	0.592777i	$0.798032\pi$
$648$	−8.24597	−	3.60611i	−0.323932	−	0.141661i
$649$	42.9089	−	24.7735i	1.68432	−	0.972444i
$650$	−1.04456	−	5.11726i	−0.0409709	−	0.200715i
$651$	1.90332	−	30.3062i	0.0745969	−	1.18779i
$652$		−	14.6969i		−	0.575577i
$653$	19.9317	+	34.5227i	0.779987	+	1.35098i	0.931949	+	0.362590i	$0.118108\pi$
$653$	19.9317	+	34.5227i	0.779987	+	1.35098i	−0.151962	+	0.988386i	$0.548559\pi$
$654$	−35.2009	−	3.64086i	−1.37646	−	0.142369i
$655$	10.9201	+	28.7951i	0.426684	+	1.12512i
$656$	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	$-0.232819\pi$
$660$	17.5399	−	4.65498i	0.682739	−	0.181195i
$661$	0.522774	+	0.301824i	0.0203336	+	0.0117396i	0.510132	−	0.860096i	$-0.329596\pi$
$661$	0.522774	+	0.301824i	0.0203336	+	0.0117396i	−0.489799	+	0.871836i	$0.662930\pi$
$662$	10.7158	−	18.5604i	0.416483	−	0.721370i
$663$	−4.63416	−	3.35521i	−0.179976	−	0.130306i
$664$		−	4.06775i		−	0.157859i
$665$	−6.76463	−	5.08272i	−0.262321	−	0.197099i
$666$	−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
$669$	−37.7101	−	3.90039i	−1.45796	−	0.150798i
$670$	−5.11896	+	31.4956i	−0.197763	+	1.21678i
$671$	−16.2312			−0.626600
$672$	4.57357	+	0.287233i	0.176429	+	0.0110803i
$673$			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
$675$	−20.9712	−	15.3365i	−0.807182	−	0.590303i
$676$	5.95445	−	10.3134i	0.229017	−	0.396670i
$677$	28.5000	−	16.4545i	1.09534	−	0.632397i	0.160350	−	0.987060i	$-0.448738\pi$
$677$	28.5000	−	16.4545i	1.09534	−	0.632397i	0.934994	+	0.354663i	$0.115404\pi$
$678$	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
$681$	14.5798	+	10.5560i	0.558699	+	0.404507i
$682$	−15.5241	+	26.8886i	−0.594450	+	1.02962i
$683$	−9.47723	+	16.4150i	−0.362636	+	0.628104i	−0.988394	−	0.151913i	$-0.951456\pi$
$683$	−9.47723	+	16.4150i	−0.362636	+	0.628104i	0.625758	+	0.780017i	$0.284790\pi$
$684$	0.878183	−	4.19985i	0.0335782	−	0.160585i
$685$	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
$690$	−12.2906	+	12.2321i	−0.467895	+	0.465668i
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	−0.441851	−	0.897089i	$-0.645678\pi$
$691$	3.00000	−	1.73205i	0.114125	−	0.0658903i	0.555976	+	0.831198i	$0.312345\pi$
$692$		−	1.12840i		−	0.0428954i
$693$	−6.13742	+	36.6805i	−0.233141	+	1.39338i
$694$	−17.4772			−0.663426
$695$	7.23930	−	44.5415i	0.274602	−	1.68956i
$696$	−1.23341	+	11.9250i	−0.0467524	+	0.452016i
$697$	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
$700$	12.7066	+	3.67995i	0.480265	+	0.139089i
$701$			51.7546i			1.95474i	0.211531	+	0.977371i	$0.432155\pi$
$701$			51.7546i			1.95474i	−0.211531	+	0.977371i	$0.567845\pi$
$702$	1.15483	+	5.30340i	0.0435861	+	0.200164i
$703$	1.90428	−	3.29832i	0.0718214	−	0.124398i
$704$	−4.05781	−	2.34278i	−0.152935	−	0.0882968i
$705$	41.9967	−	11.1457i	1.58169	−	0.419771i
$706$		−	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	0.996059	−	0.0886924i	$-0.0282688\pi$
$709$	11.2158	+	19.4264i	0.421220	+	0.729574i	−0.574839	+	0.818266i	$0.694935\pi$
$710$	−14.4715	+	5.48811i	−0.543107	+	0.205965i
$711$	−10.7483	−	32.7111i	−0.403094	−	1.22676i
$712$	2.45877	+	4.25871i	0.0921463	+	0.159602i
$713$		−	29.6678i		−	1.11107i
$714$	12.9794	−	6.44482i	0.485741	−	0.241191i
$715$	−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	$-0.161896\pi$
$719$	0.401865	+	0.696051i	0.0149870	+	0.0259583i	−0.858435	+	0.512923i	$0.828563\pi$
$720$	1.04456	+	6.62638i	0.0389283	+	0.246951i
$721$	6.04555	−	11.5207i	0.225148	−	0.429054i
$722$	−16.9545			−0.630979
$723$	29.8958	+	21.6451i	1.11184	+	0.804988i
$724$	−2.73861	−	1.58114i	−0.101780	−	0.0587626i
$725$	−10.9601	+	32.8268i	−0.407050	+	1.21916i
$726$	11.1270	−	15.3685i	0.412962	−	0.570377i
$727$	15.1223			0.560854			0.280427	−	0.959875i	$-0.409524\pi$
$727$	15.1223			0.560854			0.280427	+	0.959875i	$0.409524\pi$
$728$	−1.47723	−	2.33570i	−0.0547496	−	0.0865668i
$729$	22.0000	+	15.6525i	0.814815	+	0.579721i
$730$	7.73221	+	1.25671i	0.286182	+	0.0465130i
$731$	−10.9441	+	18.9557i	−0.404780	+	0.701100i
$732$	0.617292	−	5.96816i	0.0228158	−	0.220590i
$733$	−1.19718	−	2.07357i	−0.0442187	−	0.0765891i	0.843069	−	0.537805i	$-0.180747\pi$
$733$	−1.19718	−	2.07357i	−0.0442187	−	0.0765891i	−0.887288	+	0.461216i	$0.847413\pi$
$734$	−0.369657			−0.0136443
$735$	−17.6120	+	20.6111i	−0.649629	+	0.760252i
$736$	4.47723			0.165033
$737$	33.4317	+	57.9054i	1.23147	+	2.13297i
$738$	−0.978218	−	2.97707i	−0.0360087	−	0.109588i
$739$	−3.23861	+	5.60944i	−0.119134	+	0.206347i	−0.919425	−	0.393266i	$-0.871345\pi$
$739$	−3.23861	+	5.60944i	−0.119134	+	0.206347i	0.800291	+	0.599612i	$0.204679\pi$
$740$	−0.955238	+	5.87733i	−0.0351153	+	0.216055i
$741$	−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	$0.579241\pi$
$744$	−9.29642	−	6.73076i	−0.340823	−	0.246762i
$745$	5.12132	−	1.94218i	0.187631	−	0.0711561i
$746$	20.1042	+	11.6072i	0.736068	+	0.424969i
$747$	−2.49767	+	11.9449i	−0.0913848	+	0.437041i
$748$	−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	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	−9.71584	−	5.60944i	−0.354300	−	0.204555i
$753$	15.2558	+	1.57792i	0.555953	+	0.0575027i
$754$	6.26139	−	3.61501i	0.228026	−	0.131651i
$755$	−2.82843	+	3.46410i	−0.102937	+	0.126072i
$756$	−13.2539	−	3.65170i	−0.482039	−	0.132811i
$757$			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
$759$	−3.73827	+	36.1427i	−0.135691	+	1.31190i
$760$	−2.99028	+	1.13402i	−0.108469	+	0.0411351i
$761$	−0.891935	−	1.54488i	−0.0323326	−	0.0560018i	0.849406	−	0.527739i	$-0.176960\pi$
$761$	−0.891935	−	1.54488i	−0.0323326	−	0.0560018i	−0.881739	+	0.471738i	$0.843627\pi$
$762$	13.8047	−	6.17364i	0.500091	−	0.223648i
$763$	−54.0131	+	2.18028i	−1.95541	+	0.0789315i
$764$		−	16.2927i		−	0.589451i
$765$	13.3379	+	16.4955i	0.482231	+	0.596396i
$766$	−15.7158	−	9.07354i	−0.567836	−	0.327840i
$767$	5.52277	−	9.56573i	0.199416	−	0.345398i
$768$	1.01575	−	1.40294i	0.0366528	−	0.0506243i
$769$		−	16.1921i		−	0.583902i	−0.956433	−	0.291951i	$-0.905696\pi$
$769$		−	16.1921i		−	0.583902i	0.956433	−	0.291951i	$-0.0943045\pi$
$770$	25.5014	−	10.8667i	0.919005	−	0.391610i
$771$	−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	0.730514	−	0.682898i	$-0.239281\pi$
$773$	14.0228	+	8.09605i	0.504364	+	0.291195i	−0.226150	+	0.974093i	$0.572614\pi$
$774$	19.7272	−	6.48204i	0.709080	−	0.232992i
$775$	−21.9699	−	24.8002i	−0.789181	−	0.890848i
$776$	−11.9886			−0.430366
$777$	−10.1649	−	6.75190i	−0.364663	−	0.242223i
$778$			7.34847i			0.263455i
$779$	1.29380	−	0.746976i	0.0463552	−	0.0267632i
$780$	2.86745	−	2.85380i	0.102671	−	0.102183i
$781$	−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
$786$	−13.9894	+	19.3220i	−0.498987	+	0.689192i
$787$	25.0862	−	43.4506i	0.894226	−	1.54884i	0.0594664	−	0.998230i	$-0.481060\pi$
$787$	25.0862	−	43.4506i	0.894226	−	1.54884i	0.834760	−	0.550615i	$-0.185607\pi$
$788$	4.50000	−	7.79423i	0.160306	−	0.277658i
$789$	2.03151	−	2.80588i	0.0723235	−	0.0998921i
$790$	−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
$795$	13.7257	−	13.6604i	0.486800	−	0.484483i
$796$	−13.4317	+	7.75478i	−0.476073	+	0.274861i
$797$		−	54.2183i		−	1.92051i	−0.279121	−	0.960256i	$-0.590043\pi$
$797$		−	54.2183i		−	1.92051i	0.279121	−	0.960256i	$-0.409957\pi$
$798$	0.410809	−	6.54124i	0.0145425	−	0.231557i
$799$	−35.4772			−1.25509
$800$	3.74264	−	3.31552i	0.132322	−	0.117221i
$801$	−4.60523	−	14.0154i	−0.162718	−	0.495210i
$802$	−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
$805$	−15.9111	+	21.1762i	−0.560792	+	0.746363i
$806$			6.92163i			0.243804i
$807$	−17.8580	+	24.6652i	−0.628631	+	0.868256i
$808$	−5.65685	+	9.79796i	−0.199007	+	0.344691i
$809$	7.65776	+	4.42121i	0.269233	+	0.155441i	0.628539	−	0.777778i	$-0.283653\pi$
$809$	7.65776	+	4.42121i	0.269233	+	0.155441i	−0.359306	+	0.933220i	$0.616987\pi$
$810$	1.00138	−	20.0997i	0.0351848	−	0.706231i
$811$		−	38.3280i		−	1.34588i	−0.739697	−	0.672940i	$-0.765031\pi$
$811$		−	38.3280i		−	1.34588i	0.739697	−	0.672940i	$-0.234969\pi$
$812$	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
$815$	30.7279	−	11.6531i	1.07635	−	0.408190i
$816$	0.563508	−	5.44816i	0.0197267	−	0.190724i
$817$	4.94975	+	8.57321i	0.173170	+	0.299939i
$818$			15.5096i			0.542279i
$819$	2.90370	+	7.76580i	0.101464	+	0.271359i
$820$	−1.47723	+	1.80922i	−0.0515870	+	0.0631809i
$821$	10.1403	−	5.85452i	0.353900	−	0.204324i	−0.312502	−	0.949917i	$-0.601167\pi$
$821$	10.1403	−	5.85452i	0.353900	−	0.204324i	0.666401	+	0.745593i	$0.267834\pi$
$822$	5.99077	+	0.619631i	0.208952	+	0.0216121i
$823$	2.76401	+	1.59580i	0.0963474	+	0.0556262i	0.547400	−	0.836871i	$-0.315618\pi$
$823$	2.76401	+	1.59580i	0.0963474	+	0.0556262i	−0.451052	+	0.892498i	$0.648951\pi$
$824$	−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	$0.478350\pi$
$828$	−13.1473	−	2.74909i	−0.456901	−	0.0955375i
$829$	−43.6931	−	25.2262i	−1.51752	−	0.876142i	−0.999788	−	0.0206012i	$-0.993442\pi$
$829$	−43.6931	−	25.2262i	−1.51752	−	0.876142i	−0.517735	−	0.855541i	$-0.673225\pi$
$830$	8.50473	−	3.22529i	0.295203	−	0.111951i
$831$	−13.7460	−	9.95231i	−0.476842	−	0.345242i
$832$	−1.04456			−0.0362135
$833$	18.2158	−	12.5771i	0.631141	−	0.435770i
$834$	31.9089	−	14.2701i	1.10491	−	0.494133i
$835$	1.53915	−	9.46999i	0.0532645	−	0.327723i
$836$	−3.35071	+	5.80359i	−0.115887	+	0.200721i
$837$	23.1661	+	25.4730i	0.800737	+	0.880476i
$838$	4.42747	+	7.66860i	0.152944	+	0.264907i
$839$	−40.1440			−1.38593			−0.692963	−	0.720973i	$-0.743695\pi$
$839$	−40.1440			−1.38593			−0.692963	+	0.720973i	$0.743695\pi$
$840$	3.02581	+	9.79002i	0.104400	+	0.337788i
$841$	−18.9089			−0.652031
$842$	9.47723	+	16.4150i	0.326607	+	0.565700i
$843$	−0.322398	+	3.11704i	−0.0111040	+	0.107357i
$844$	−12.2386	+	21.1979i	−0.421270	+	0.729662i
$845$	26.2842	+	4.27196i	0.904205	+	0.146960i
$846$	25.0862	+	22.4378i	0.862481	+	0.771426i
$847$	13.4672	−	25.6639i	0.462740	−	0.881821i
$848$	−5.00000			−0.171701
$849$	9.36991	−	12.9416i	0.321575	−	0.444154i
$850$	5.00735	−	14.9975i	0.171751	−	0.514412i
$851$	−10.3251	−	5.96123i	−0.353942	−	0.204348i
$852$	−9.71064	−	7.03066i	−0.332681	−	0.240867i
$853$	−31.2891			−1.07132			−0.535659	−	0.844434i	$-0.679937\pi$
$853$	−31.2891			−1.07132			−0.535659	+	0.844434i	$0.679937\pi$
$854$	−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	0.260354	−	0.965513i	$-0.416161\pi$
$857$	−13.0455	−	7.53185i	−0.445627	−	0.257283i	−0.705982	+	0.708230i	$0.749494\pi$
$858$	0.872155	−	8.43224i	0.0297749	−	0.287872i
$859$	−26.4772	+	15.2866i	−0.903391	+	0.521573i	−0.878299	−	0.478112i	$-0.841321\pi$
$859$	−26.4772	+	15.2866i	−0.903391	+	0.521573i	−0.0250924	+	0.999685i	$0.507988\pi$
$860$	−11.9886	−	9.78866i	−0.408808	−	0.333790i
$861$	−2.12884	−	4.28732i	−0.0725506	−	0.146111i
$862$			7.66374i			0.261028i
$863$	−13.2386	−	22.9299i	−0.450648	−	0.780545i	0.547779	−	0.836623i	$-0.315474\pi$
$863$	−13.2386	−	22.9299i	−0.450648	−	0.780545i	−0.998426	+	0.0560787i	$0.982140\pi$
$864$	−3.84418	+	3.49604i	−0.130782	+	0.118938i
$865$	2.35923	−	0.894703i	0.0802163	−	0.0304208i
$866$		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
$870$	−25.9104	+	6.87646i	−0.878444	+	0.233134i
$871$	12.9089	+	7.45296i	0.437401	+	0.252534i
$872$	−10.2158	+	17.6944i	−0.345952	+	0.599206i
$873$	35.2044	+	7.36121i	1.19149	+	0.249139i
$874$		−	6.40345i		−	0.216600i
$875$	2.38105	+	29.4844i	0.0804942	+	0.996755i
$876$	2.47723	+	5.53924i	0.0836977	+	0.187154i
$877$	48.2359	−	27.8490i	1.62881	−	0.940394i	0.644361	−	0.764721i	$-0.277123\pi$
$877$	48.2359	−	27.8490i	1.62881	−	0.940394i	0.984449	−	0.175673i	$-0.0562101\pi$
$878$	−7.69306	−	4.44159i	−0.259628	−	0.149896i
$879$	−1.43566	+	13.8804i	−0.0484237	+	0.468174i
$880$	1.68080	−	10.3415i	0.0566598	−	0.348613i
$881$	−18.7544			−0.631853			−0.315926	−	0.948784i	$-0.602315\pi$
$881$	−18.7544			−0.631853			−0.315926	+	0.948784i	$0.602315\pi$
$882$	−20.8350	−	2.62736i	−0.701551	−	0.0884678i
$883$		−	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
$885$	−29.0282	+	28.8900i	−0.975771	+	0.971127i
$886$	7.52277	−	13.0298i	0.252733	−	0.437746i
$887$	−3.00000	+	1.73205i	−0.100730	+	0.0581566i	−0.549519	−	0.835481i	$-0.685189\pi$
$887$	−3.00000	+	1.73205i	−0.100730	+	0.0581566i	0.448789	+	0.893638i	$0.351856\pi$
$888$	−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
$891$	−25.0123	−	33.9514i	−0.837942	−	1.13741i
$892$	−10.9441	+	18.9557i	−0.366434	+	0.634682i
$893$	−8.02277	+	13.8959i	−0.268472	+	0.465007i
$894$	3.43649	+	2.48808i	0.114933	+	0.0832137i
$895$	−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
$900$	−13.0260	+	7.43794i	−0.434201	+	0.247931i
$901$	−13.6931	+	7.90569i	−0.456182	+	0.263377i
$902$			4.89433i			0.162963i
$903$	28.4094	−	14.1065i	0.945406	−	0.469435i
$904$	17.4772			0.581284
$905$	1.13437	−	6.97948i	0.0377078	−	0.232006i
$906$	−3.44572	−	0.356394i	−0.114476	−	0.0118404i
$907$	8.48528	+	4.89898i	0.281749	+	0.162668i	0.634215	−	0.773157i	$-0.281323\pi$
$907$	8.48528	+	4.89898i	0.281749	+	0.162668i	−0.352466	+	0.935825i	$0.614657\pi$
$908$	9.00000	−	5.19615i	0.298675	−	0.172440i
$909$	22.6274	−	25.2982i	0.750504	−	0.839089i
$910$	3.71213	−	4.94050i	0.123056	−	0.163776i
$911$		−	24.0681i		−	0.797410i	−0.917079	−	0.398705i	$-0.869460\pi$
$911$		−	24.0681i		−	0.797410i	0.917079	−	0.398705i	$-0.130540\pi$
$912$	−2.00653	−	1.45276i	−0.0664427	−	0.0481056i
$913$	9.52984	−	16.5062i	0.315392	−	0.546274i
$914$	−9.59425	−	5.53924i	−0.317350	−	0.183222i
$915$	12.9675	−	3.44150i	0.428692	−	0.113772i
$916$		−	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	0.862444	−	0.506153i	$-0.168933\pi$
$919$	−0.215838	−	0.373843i	−0.00711985	−	0.0123319i	−0.869563	+	0.493821i	$0.835600\pi$
$920$	3.54996	+	9.36085i	0.117039	+	0.308618i
$921$	20.6547	+	2.13633i	0.680595	+	0.0703946i
$922$	15.8938	+	27.5289i	0.523434	+	0.906615i
$923$			7.23003i			0.237979i
$924$	17.8857	+	11.8804i	0.588398	+	0.390836i
$925$	−13.0455	+	2.66291i	−0.428935	+	0.0875560i
$926$	−19.5497	+	11.2871i	−0.642444	+	0.370916i
$927$	4.60523	+	14.0154i	0.151256	+	0.460326i
$928$	5.99430	+	3.46081i	0.196773	+	0.113607i
$929$	7.96300	+	13.7923i	0.261258	+	0.452512i	0.966576	−	0.256379i	$-0.0825294\pi$
$929$	7.96300	+	13.7923i	0.261258	+	0.452512i	−0.705319	+	0.708890i	$0.749196\pi$
$930$	6.70141	−	24.7735i	0.219748	−	0.812354i
$931$	−0.806936	−	9.97902i	−0.0264463	−	0.327049i
$932$	4.00000			0.131024
$933$	−17.8580	+	24.6652i	−0.584645	+	0.807502i
$934$	24.2614	+	14.0073i	0.793857	+	0.458333i
$935$	−11.7483	−	30.9790i	−0.384211	−	1.01312i
$936$	3.06733	+	0.641375i	0.100259	+	0.0209640i
$937$	53.6757			1.75351			0.876754	−	0.480938i	$-0.159704\pi$
$937$	53.6757			1.75351			0.876754	+	0.480938i	$0.159704\pi$
$938$	−31.9089	+	20.1810i	−1.04186	+	0.658932i
$939$	16.4317	+	36.7423i	0.536228	+	1.19904i
$940$	4.02443	−	24.7613i	0.131262	−	0.807624i
$941$	−10.2369	+	17.7309i	−0.333715	+	0.578011i	−0.983237	−	0.182331i	$-0.941636\pi$
$941$	−10.2369	+	17.7309i	−0.333715	+	0.578011i	0.649522	+	0.760343i	$0.274969\pi$
$942$	24.8908	+	2.57448i	0.810986	+	0.0838811i
$943$	−2.33836	−	4.05015i	−0.0761474	−	0.131891i
$944$	10.5744			0.344167
$945$	−2.87403	−	30.6062i	−0.0934922	−	0.995620i
$946$	−32.4317			−1.05444
$947$	16.4317	+	28.4605i	0.533958	+	0.924842i	0.999213	+	0.0396654i	$0.0126292\pi$
$947$	16.4317	+	28.4605i	0.533958	+	0.924842i	−0.465255	+	0.885177i	$0.654037\pi$
$948$	−19.7737	−	2.04521i	−0.642218	−	0.0664252i
$949$	1.82971	−	3.16915i	0.0593949	−	0.102875i
$950$	−4.74194	−	5.35283i	−0.153849	−	0.173669i
$951$	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	$0.775047\pi$
$954$	14.6825	+	3.07008i	0.475362	+	0.0993976i
$955$	34.0644	−	12.9184i	1.10230	−	0.418030i
$956$		0			0
$957$	−32.9426	+	45.4998i	−1.06488	+	1.47080i
$958$	−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
$963$	−5.12938	−	15.6106i	−0.165292	−	0.503043i
$964$	18.4545	−	10.6547i	0.594378	−	0.343164i
$965$	12.7279	+	10.3923i	0.409726	+	0.334540i
$966$	−20.4769	−	1.28601i	−0.658833	−	0.0413766i
$967$		−	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
$969$	−7.79211	−	0.805945i	−0.250319	−	0.0258907i
$970$	−9.50569	−	25.0654i	−0.305209	−	0.804802i
$971$	−18.8748	−	32.6922i	−0.605723	−	1.04914i	−0.991937	−	0.126733i	$-0.959551\pi$
$971$	−18.8748	−	32.6922i	−0.605723	−	1.04914i	0.386214	−	0.922409i	$-0.373783\pi$
$972$	13.4350	−	7.90569i	0.430929	−	0.253575i
$973$	45.1260	−	28.5402i	1.44667	−	0.914956i
$974$			17.0349i			0.545832i
$975$	8.24023	+	3.73242i	0.263899	+	0.119533i
$976$	−3.00000	−	1.73205i	−0.0960277	−	0.0554416i
$977$	1.95445	−	3.38521i	0.0625284	−	0.108302i	−0.833067	−	0.553173i	$-0.813417\pi$
$977$	1.95445	−	3.38521i	0.0625284	−	0.108302i	0.895595	+	0.444870i	$0.146750\pi$
$978$	20.6190	+	14.9285i	0.659321	+	0.477359i
$979$			23.0414i			0.736407i
$980$	6.71181	+	14.1404i	0.214401	+	0.451699i
$981$	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	0.998918	−	0.0464984i	$-0.0148062\pi$
$983$	45.7158	+	26.3941i	1.45811	+	0.841840i	0.459190	+	0.888338i	$0.348140\pi$
$984$	−1.79962	−	0.186137i	−0.0573699	−	0.00593382i
$985$	19.8640	+	3.22848i	0.632918	+	0.102868i
$986$	21.8881			0.697059
$987$	42.8248	+	28.4459i	1.36313	+	0.905442i
$988$			1.49395i			0.0475290i
$989$	26.8378	−	15.4948i	0.853394	−	0.492707i
$990$	−11.2855	+	29.3358i	−0.358678	+	0.932352i
$991$	−5.26139	+	9.11299i	−0.167133	+	0.289484i	−0.937411	−	0.348225i	$-0.886784\pi$
$991$	−5.26139	+	9.11299i	−0.167133	+	0.289484i	0.770277	+	0.637709i	$0.220118\pi$
$992$	−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
$996$	5.70682	+	4.13183i	0.180827	+	0.130922i
$997$	−7.74597	+	13.4164i	−0.245317	+	0.424902i	−0.962221	−	0.272270i	$-0.912225\pi$
$997$	−7.74597	+	13.4164i	−0.245317	+	0.424902i	0.716904	+	0.697172i	$0.245559\pi$
$998$	0.954451	−	1.65316i	0.0302126	−	0.0523298i
$999$	13.5201	−	2.94403i	0.427756	−	0.0931449i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.t.e.59.3	✓	8	3.2	odd	2
210.2.t.e.59.4	yes	8	5.4	even	2
210.2.t.e.89.3	yes	8	35.19	odd	6
210.2.t.e.89.4	yes	8	21.5	even	6
210.2.t.f.59.1	yes	8	1.1	even	1	trivial
210.2.t.f.59.2	yes	8	15.14	odd	2	inner
210.2.t.f.89.1	yes	8	105.89	even	6	inner
210.2.t.f.89.2	yes	8	7.5	odd	6	inner
1050.2.s.i.101.1		16	15.8	even	4
1050.2.s.i.101.2		16	5.2	odd	4
1050.2.s.i.101.7		16	5.3	odd	4
1050.2.s.i.101.8		16	15.2	even	4
1050.2.s.i.551.1		16	35.33	even	12
1050.2.s.i.551.2		16	105.47	odd	12
1050.2.s.i.551.7		16	105.68	odd	12
1050.2.s.i.551.8		16	35.12	even	12
1470.2.d.e.1469.2		8	7.3	odd	6
1470.2.d.e.1469.3		8	105.74	odd	6
1470.2.d.e.1469.6		8	105.59	even	6
1470.2.d.e.1469.7		8	7.4	even	3
1470.2.d.f.1469.2		8	35.4	even	6
1470.2.d.f.1469.3		8	21.17	even	6
1470.2.d.f.1469.6		8	21.11	odd	6
1470.2.d.f.1469.7		8	35.24	odd	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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.72286 - 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.20711 - 0.358719i) q^{5} +(-0.707107 - 1.58114i) q^{6} +(-1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.72286 - 0.178197i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.20711 - 0.358719i) q^{5} +(-0.707107 - 1.58114i) q^{6} +(-1.41421 - 2.23607i) q^{7} -1.00000 q^{8} +(2.93649 + 0.614017i) q^{9} +(-0.792893 - 2.09077i) q^{10} +(-4.05781 - 2.34278i) q^{11} +(1.01575 - 1.40294i) 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} +(0.936492 + 2.85008i) q^{18} +(-1.23861 + 0.715113i) q^{19} +(1.41421 - 1.73205i) q^{20} +(2.03803 + 4.10444i) q^{21} -4.68556i q^{22} +(2.23861 + 3.87739i) q^{23} +(1.72286 + 0.178197i) q^{24} +(4.74264 + 1.58346i) q^{25} +(-0.522278 - 0.904612i) q^{26} +(-4.94975 - 1.58114i) q^{27} +(2.64360 - 0.106711i) q^{28} +6.92163i q^{29} +(0.993475 + 3.74340i) q^{30} +(-5.73861 - 3.31319i) q^{31} +(0.500000 - 0.866025i) q^{32} +(6.57357 + 4.75937i) q^{33} -3.16228i q^{34} +(2.31920 + 5.44255i) q^{35} +(-2.00000 + 2.23607i) q^{36} +(-2.30615 + 1.33146i) q^{37} +(-1.23861 - 0.715113i) q^{38} +(1.79962 + 0.186137i) q^{39} +(2.20711 + 0.358719i) q^{40} -1.04456 q^{41} +(-2.53553 + 3.81721i) q^{42} -6.92163i q^{43} +(4.05781 - 2.34278i) q^{44} +(-6.26089 - 2.40858i) 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} +(4.43649 + 3.21209i) q^{51} +(0.522278 - 0.904612i) q^{52} +(2.50000 - 4.33013i) q^{53} +(-1.10557 - 5.07718i) 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} +(-2.74514 + 2.73207i) q^{60} +(3.00000 - 1.73205i) q^{61} -6.62638i q^{62} +(-2.77984 - 7.43455i) q^{63} +1.00000 q^{64} +(2.30545 + 0.374703i) q^{65} +(-0.834952 + 8.07256i) q^{66} +(-12.3583 - 7.13505i) q^{67} +(2.73861 - 1.58114i) q^{68} +(-3.16588 - 7.07912i) q^{69} +(-3.55378 + 4.72976i) q^{70} -6.92163i q^{71} +(-2.93649 - 0.614017i) q^{72} +(-1.75166 + 3.03397i) q^{73} +(-2.30615 - 1.33146i) q^{74} +(-7.88874 - 3.57321i) q^{75} -1.43023i q^{76} +(0.500000 + 12.3867i) q^{77} +(0.738613 + 1.65159i) q^{78} +(-5.73861 - 9.93957i) q^{79} +(0.792893 + 2.09077i) q^{80} +(8.24597 + 3.60611i) q^{81} +(-0.522278 - 0.904612i) q^{82} +4.06775i q^{83} +(-4.57357 - 0.287233i) q^{84} +(5.47723 + 4.47214i) q^{85} +(5.99430 - 3.46081i) q^{86} +(1.23341 - 11.9250i) 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} +(9.29642 + 6.73076i) q^{93} +(9.71584 + 5.60944i) q^{94} +(2.99028 - 1.13402i) q^{95} +(-1.01575 + 1.40294i) 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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