LMFDB - Embedded newform 182.2.m.b.43.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [182,2,Mod(43,182)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(182, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("182.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	182.m (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:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.4
Root			$0.500000 - 3.15681i$ of defining polynomial
Character	$\chi$	$=$	182.43
Dual form			182.2.m.b.127.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.14539 + 1.98388i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.901839i q^{5} +(-1.98388 + 1.14539i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.14539 + 1.98388i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.901839i q^{5} +(-1.98388 + 1.14539i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +(-0.450919 + 0.781015i) q^{10} +(-3.75609 - 2.16858i) q^{11} -2.29079 q^{12} +(-0.426876 + 3.58019i) q^{13} +1.00000 q^{14} +(-1.78914 - 1.03296i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.53296 + 4.38722i) q^{17} -2.24770i q^{18} +(5.34544 - 3.08619i) q^{19} +(-0.781015 + 0.450919i) q^{20} +2.29079i q^{21} +(-2.16858 - 3.75609i) q^{22} +(4.22559 - 7.31893i) q^{23} +(-1.98388 - 1.14539i) q^{24} +4.18669 q^{25} +(-2.15978 + 2.88710i) q^{26} -1.72335 q^{27} +(0.866025 + 0.500000i) q^{28} +(1.09643 - 1.89907i) q^{29} +(-1.03296 - 1.78914i) q^{30} +0.873062i q^{31} +(-0.866025 + 0.500000i) q^{32} +(8.60441 - 4.96776i) q^{33} +5.06592i q^{34} +(0.450919 + 0.781015i) q^{35} +(1.12385 - 1.94657i) q^{36} +(0.124973 + 0.0721531i) q^{37} +6.17238 q^{38} +(-6.61373 - 4.94760i) q^{39} -0.901839 q^{40} +(-3.46110 - 1.99827i) q^{41} +(-1.14539 + 1.98388i) q^{42} +(3.85426 + 6.67577i) q^{43} -4.33716i q^{44} +(1.75549 - 1.01353i) q^{45} +(7.31893 - 4.22559i) q^{46} -2.92115i q^{47} +(-1.14539 - 1.98388i) q^{48} +(0.500000 - 0.866025i) q^{49} +(3.62578 + 2.09334i) q^{50} -11.6049 q^{51} +(-3.31398 + 1.42041i) q^{52} +1.69699 q^{53} +(-1.49246 - 0.861675i) q^{54} +(1.95571 - 3.38739i) q^{55} +(0.500000 + 0.866025i) q^{56} +14.1396i q^{57} +(1.89907 - 1.09643i) q^{58} +(-7.40394 + 4.27467i) q^{59} -2.06592i q^{60} +(-4.16720 - 7.21780i) q^{61} +(-0.436531 + 0.756094i) q^{62} +(-1.94657 - 1.12385i) q^{63} -1.00000 q^{64} +(-3.22876 - 0.384973i) q^{65} +9.93552 q^{66} +(-8.99180 - 5.19142i) q^{67} +(-2.53296 + 4.38722i) q^{68} +(9.67992 + 16.7661i) q^{69} +0.901839i q^{70} +(-2.83932 + 1.63928i) q^{71} +(1.94657 - 1.12385i) q^{72} +0.539023i q^{73} +(0.0721531 + 0.124973i) q^{74} +(-4.79540 + 8.30588i) q^{75} +(5.34544 + 3.08619i) q^{76} -4.33716 q^{77} +(-3.25386 - 7.59161i) q^{78} +6.53349 q^{79} +(-0.781015 - 0.450919i) q^{80} +(5.34547 - 9.25862i) q^{81} +(-1.99827 - 3.46110i) q^{82} -13.2348i q^{83} +(-1.98388 + 1.14539i) q^{84} +(-3.95656 + 2.28432i) q^{85} +7.70851i q^{86} +(2.51168 + 4.35037i) q^{87} +(2.16858 - 3.75609i) q^{88} +(-6.74790 - 3.89590i) q^{89} +2.02707 q^{90} +(1.42041 + 3.31398i) q^{91} +8.45117 q^{92} +(-1.73205 - 1.00000i) q^{93} +(1.46057 - 2.52979i) q^{94} +(2.78325 + 4.82072i) q^{95} -2.29079i q^{96} +(10.1378 - 5.85305i) q^{97} +(0.866025 - 0.500000i) q^{98} +9.74866i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^9	$ 12 q - 2 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{9} - 2 q^{10} - 18 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} - 6 q^{15} - 6 q^{16} + 4 q^{17} + 12 q^{19} - 2 q^{22} - 6 q^{23} + 6 q^{24} - 24 q^{25} - 14 q^{26} + 40 q^{27} - 10 q^{29} + 14 q^{30} + 12 q^{33} + 2 q^{35} + 6 q^{36} - 6 q^{37} + 8 q^{38} - 54 q^{39} - 4 q^{40} - 24 q^{41} - 2 q^{42} + 26 q^{43} + 72 q^{45} - 6 q^{46} - 2 q^{48} + 6 q^{49} - 12 q^{50} - 36 q^{51} - 4 q^{52} + 36 q^{53} - 36 q^{54} - 6 q^{55} + 6 q^{56} + 24 q^{58} + 6 q^{59} - 28 q^{61} - 2 q^{62} - 12 q^{64} - 34 q^{65} - 42 q^{67} - 4 q^{68} + 32 q^{69} + 48 q^{71} - 48 q^{75} + 12 q^{76} - 4 q^{77} - 8 q^{78} + 44 q^{79} - 34 q^{81} + 6 q^{82} + 6 q^{84} + 54 q^{85} + 2 q^{87} + 2 q^{88} + 12 q^{89} + 12 q^{90} - 16 q^{91} - 12 q^{92} + 8 q^{94} + 32 q^{95} + 60 q^{97}+O(q^{100}) $ 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^9 - 2 * q^10 - 18 * q^11 - 4 * q^12 - 8 * q^13 + 12 * q^14 - 6 * q^15 - 6 * q^16 + 4 * q^17 + 12 * q^19 - 2 * q^22 - 6 * q^23 + 6 * q^24 - 24 * q^25 - 14 * q^26 + 40 * q^27 - 10 * q^29 + 14 * q^30 + 12 * q^33 + 2 * q^35 + 6 * q^36 - 6 * q^37 + 8 * q^38 - 54 * q^39 - 4 * q^40 - 24 * q^41 - 2 * q^42 + 26 * q^43 + 72 * q^45 - 6 * q^46 - 2 * q^48 + 6 * q^49 - 12 * q^50 - 36 * q^51 - 4 * q^52 + 36 * q^53 - 36 * q^54 - 6 * q^55 + 6 * q^56 + 24 * q^58 + 6 * q^59 - 28 * q^61 - 2 * q^62 - 12 * q^64 - 34 * q^65 - 42 * q^67 - 4 * q^68 + 32 * q^69 + 48 * q^71 - 48 * q^75 + 12 * q^76 - 4 * q^77 - 8 * q^78 + 44 * q^79 - 34 * q^81 + 6 * q^82 + 6 * q^84 + 54 * q^85 + 2 * q^87 + 2 * q^88 + 12 * q^89 + 12 * q^90 - 16 * q^91 - 12 * q^92 + 8 * q^94 + 32 * q^95 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.14539	+	1.98388i	−0.661293	+	1.14539i	0.318983	+	0.947760i	$0.396659\pi$
$3$	−1.14539	+	1.98388i	−0.661293	+	1.14539i	−0.980276	+	0.197633i	$0.936675\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$			0.901839i			0.403315i	0.979456	+	0.201657i	$0.0646327\pi$
$5$			0.901839i			0.403315i	−0.979456	+	0.201657i	$0.935367\pi$
$6$	−1.98388	+	1.14539i	−0.809915	+	0.467605i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$7$	0.866025	−	0.500000i	0.327327	−	0.188982i
$8$			1.00000i			0.353553i
$9$	−1.12385	−	1.94657i	−0.374617	−	0.648856i
$10$	−0.450919	+	0.781015i	−0.142593	+	0.246979i
$11$	−3.75609	−	2.16858i	−1.13251	−	0.653852i	−0.187941	−	0.982180i	$-0.560181\pi$
$11$	−3.75609	−	2.16858i	−1.13251	−	0.653852i	−0.944564	+	0.328328i	$0.893515\pi$
$12$	−2.29079			−0.661293
$13$	−0.426876	+	3.58019i	−0.118394	+	0.992967i
$13$	−0.426876	+	3.58019i	−0.118394	+	0.992967i
$14$	1.00000			0.267261
$15$	−1.78914	−	1.03296i	−0.461954	−	0.266709i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.53296	+	4.38722i	0.614333	+	1.06406i	0.990501	+	0.137505i	$0.0439082\pi$
$17$	2.53296	+	4.38722i	0.614333	+	1.06406i	−0.376168	+	0.926551i	$0.622758\pi$
$18$		−	2.24770i		−	0.529789i
$19$	5.34544	−	3.08619i	1.22633	−	0.708021i	0.260068	−	0.965590i	$-0.416255\pi$
$19$	5.34544	−	3.08619i	1.22633	−	0.708021i	0.966260	+	0.257570i	$0.0829217\pi$
$20$	−0.781015	+	0.450919i	−0.174640	+	0.100829i
$21$			2.29079i			0.499891i
$22$	−2.16858	−	3.75609i	−0.462343	−	0.800802i
$23$	4.22559	−	7.31893i	0.881096	−	1.52610i	0.0309711	−	0.999520i	$-0.490140\pi$
$23$	4.22559	−	7.31893i	0.881096	−	1.52610i	0.850124	−	0.526582i	$-0.176527\pi$
$24$	−1.98388	−	1.14539i	−0.404958	−	0.233802i
$25$	4.18669			0.837337
$26$	−2.15978	+	2.88710i	−0.423568	+	0.566207i
$27$	−1.72335			−0.331659
$28$	0.866025	+	0.500000i	0.163663	+	0.0944911i
$29$	1.09643	−	1.89907i	0.203602	−	0.352649i	−0.746085	−	0.665851i	$-0.768069\pi$
$29$	1.09643	−	1.89907i	0.203602	−	0.352649i	0.949686	+	0.313203i	$0.101402\pi$
$30$	−1.03296	−	1.78914i	−0.188592	−	0.326651i
$31$			0.873062i			0.156807i	0.996922	+	0.0784033i	$0.0249822\pi$
$31$			0.873062i			0.156807i	−0.996922	+	0.0784033i	$0.975018\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	8.60441	−	4.96776i	1.49784	−	0.864776i
$34$			5.06592i			0.868798i
$35$	0.450919	+	0.781015i	0.0762193	+	0.132016i
$36$	1.12385	−	1.94657i	0.187309	−	0.324428i
$37$	0.124973	+	0.0721531i	0.0205454	+	0.0118619i	0.510238	−	0.860034i	$-0.329557\pi$
$37$	0.124973	+	0.0721531i	0.0205454	+	0.0118619i	−0.489692	+	0.871895i	$0.662891\pi$
$38$	6.17238			1.00129
$39$	−6.61373	−	4.94760i	−1.05904	−	0.792250i
$40$	−0.901839			−0.142593
$41$	−3.46110	−	1.99827i	−0.540533	−	0.312077i	0.204762	−	0.978812i	$-0.434358\pi$
$41$	−3.46110	−	1.99827i	−0.540533	−	0.312077i	−0.745295	+	0.666735i	$0.767691\pi$
$42$	−1.14539	+	1.98388i	−0.176738	+	0.306119i
$43$	3.85426	+	6.67577i	0.587768	+	1.01804i	0.994524	+	0.104508i	$0.0333267\pi$
$43$	3.85426	+	6.67577i	0.587768	+	1.01804i	−0.406756	+	0.913537i	$0.633340\pi$
$44$		−	4.33716i		−	0.653852i
$45$	1.75549	−	1.01353i	0.261693	−	0.151089i
$46$	7.31893	−	4.22559i	1.07912	−	0.623029i
$47$		−	2.92115i		−	0.426093i	−0.977042	−	0.213047i	$-0.931661\pi$
$47$		−	2.92115i		−	0.426093i	0.977042	−	0.213047i	$-0.0683387\pi$
$48$	−1.14539	−	1.98388i	−0.165323	−	0.286348i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	3.62578	+	2.09334i	0.512762	+	0.296043i
$51$	−11.6049			−1.62502
$52$	−3.31398	+	1.42041i	−0.459566	+	0.196976i
$53$	1.69699			0.233099			0.116549	−	0.993185i	$-0.462817\pi$
$53$	1.69699			0.233099			0.116549	+	0.993185i	$0.462817\pi$
$54$	−1.49246	−	0.861675i	−0.203099	−	0.117259i
$55$	1.95571	−	3.38739i	0.263708	−	0.456756i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$			14.1396i			1.87284i
$58$	1.89907	−	1.09643i	0.249360	−	0.143968i
$59$	−7.40394	+	4.27467i	−0.963911	+	0.556514i	−0.897374	−	0.441270i	$-0.854528\pi$
$59$	−7.40394	+	4.27467i	−0.963911	+	0.556514i	−0.0665363	+	0.997784i	$0.521195\pi$
$60$		−	2.06592i		−	0.266709i
$61$	−4.16720	−	7.21780i	−0.533555	−	0.924145i	−0.999232	−	0.0391900i	$-0.987522\pi$
$61$	−4.16720	−	7.21780i	−0.533555	−	0.924145i	0.465676	−	0.884955i	$-0.345811\pi$
$62$	−0.436531	+	0.756094i	−0.0554395	+	0.0960241i
$63$	−1.94657	−	1.12385i	−0.245245	−	0.141592i
$64$	−1.00000			−0.125000
$65$	−3.22876	−	0.384973i	−0.400478	−	0.0477501i
$66$	9.93552			1.22298
$67$	−8.99180	−	5.19142i	−1.09852	−	0.634233i	−0.162691	−	0.986677i	$-0.552017\pi$
$67$	−8.99180	−	5.19142i	−1.09852	−	0.634233i	−0.935833	+	0.352444i	$0.885351\pi$
$68$	−2.53296	+	4.38722i	−0.307167	+	0.532028i
$69$	9.67992	+	16.7661i	1.16532	+	2.01840i
$70$			0.901839i			0.107790i
$71$	−2.83932	+	1.63928i	−0.336965	+	0.194547i	−0.658929	−	0.752205i	$-0.728990\pi$
$71$	−2.83932	+	1.63928i	−0.336965	+	0.194547i	0.321964	+	0.946752i	$0.395657\pi$
$72$	1.94657	−	1.12385i	0.229405	−	0.132447i
$73$			0.539023i			0.0630879i	0.999502	+	0.0315439i	$0.0100424\pi$
$73$			0.539023i			0.0630879i	−0.999502	+	0.0315439i	$0.989958\pi$
$74$	0.0721531	+	0.124973i	0.00838763	+	0.0145278i
$75$	−4.79540	+	8.30588i	−0.553725	+	0.959081i
$76$	5.34544	+	3.08619i	0.613164	+	0.354010i
$77$	−4.33716			−0.494266
$78$	−3.25386	−	7.59161i	−0.368427	−	0.859581i
$79$	6.53349			0.735075			0.367537	−	0.930009i	$-0.380201\pi$
$79$	6.53349			0.735075			0.367537	+	0.930009i	$0.380201\pi$
$80$	−0.781015	−	0.450919i	−0.0873202	−	0.0504143i
$81$	5.34547	−	9.25862i	0.593941	−	1.02874i
$82$	−1.99827	−	3.46110i	−0.220672	−	0.382215i
$83$		−	13.2348i		−	1.45271i	−0.687319	−	0.726356i	$-0.741212\pi$
$83$		−	13.2348i		−	1.45271i	0.687319	−	0.726356i	$-0.258788\pi$
$84$	−1.98388	+	1.14539i	−0.216459	+	0.124973i
$85$	−3.95656	+	2.28432i	−0.429149	+	0.247769i
$86$			7.70851i			0.831230i
$87$	2.51168	+	4.35037i	0.269281	+	0.466408i
$88$	2.16858	−	3.75609i	0.231172	−	0.400401i
$89$	−6.74790	−	3.89590i	−0.715276	−	0.412965i	0.0977357	−	0.995212i	$-0.468840\pi$
$89$	−6.74790	−	3.89590i	−0.715276	−	0.412965i	−0.813011	+	0.582248i	$0.802173\pi$
$90$	2.02707			0.213672
$91$	1.42041	+	3.31398i	0.148900	+	0.347399i
$92$	8.45117			0.881096
$93$	−1.73205	−	1.00000i	−0.179605	−	0.103695i
$94$	1.46057	−	2.52979i	0.150647	−	0.260928i
$95$	2.78325	+	4.82072i	0.285555	+	0.494596i
$96$		−	2.29079i		−	0.233802i
$97$	10.1378	−	5.85305i	1.02934	−	0.594287i	0.112541	−	0.993647i	$-0.464101\pi$
$97$	10.1378	−	5.85305i	1.02934	−	0.594287i	0.916794	+	0.399360i	$0.130768\pi$
$98$	0.866025	−	0.500000i	0.0874818	−	0.0505076i
$99$			9.74866i			0.979777i
$100$	2.09334	+	3.62578i	0.209334	+	0.362578i
$101$	−5.37145	+	9.30362i	−0.534479	+	0.925745i	0.464709	+	0.885463i	$0.346159\pi$
$101$	−5.37145	+	9.30362i	−0.534479	+	0.925745i	−0.999188	+	0.0402814i	$0.987175\pi$
$102$	−10.0502	−	5.80247i	−0.995116	−	0.574530i
$103$	4.81099			0.474041			0.237021	−	0.971505i	$-0.423829\pi$
$103$	4.81099			0.474041			0.237021	+	0.971505i	$0.423829\pi$
$104$	−3.58019	−	0.426876i	−0.351067	−	0.0418586i
$105$	−2.06592			−0.201613
$106$	1.46963	+	0.848493i	0.142743	+	0.0824129i
$107$	−6.82652	+	11.8239i	−0.659944	+	1.14306i	0.320686	+	0.947186i	$0.396087\pi$
$107$	−6.82652	+	11.8239i	−0.659944	+	1.14306i	−0.980630	+	0.195871i	$0.937247\pi$
$108$	−0.861675	−	1.49246i	−0.0829147	−	0.143612i
$109$			5.11747i			0.490165i	0.969502	+	0.245082i	$0.0788150\pi$
$109$			5.11747i			0.490165i	−0.969502	+	0.245082i	$0.921185\pi$
$110$	3.38739	−	1.95571i	0.322975	−	0.186470i
$111$	−0.286286	+	0.165287i	−0.0271731	+	0.0156884i
$112$			1.00000i			0.0944911i
$113$	−8.96603	−	15.5296i	−0.843453	−	1.46090i	−0.886958	−	0.461850i	$-0.847186\pi$
$113$	−8.96603	−	15.5296i	−0.843453	−	1.46090i	0.0435052	−	0.999053i	$-0.486147\pi$
$114$	−7.06980	+	12.2453i	−0.662148	+	1.14687i
$115$	6.60049	+	3.81080i	0.615499	+	0.355359i
$116$	2.19286			0.203602
$117$	7.44884	−	3.19266i	0.688645	−	0.295162i
$118$	−8.54933			−0.787030
$119$	4.38722	+	2.53296i	0.402175	+	0.232196i
$120$	1.03296	−	1.78914i	0.0942959	−	0.163325i
$121$	3.90550	+	6.76452i	0.355045	+	0.614956i
$122$		−	8.33440i		−	0.754561i
$123$	7.92864	−	4.57761i	0.714902	−	0.412749i
$124$	−0.756094	+	0.436531i	−0.0678993	+	0.0392017i
$125$			8.28491i			0.741025i
$126$	−1.12385	−	1.94657i	−0.100121	−	0.173414i
$127$	−9.75681	+	16.8993i	−0.865777	+	1.49957i	0.000496195		1.00000i	$0.499842\pi$
$127$	−9.75681	+	16.8993i	−0.865777	+	1.49957i	−0.866273	+	0.499570i	$0.833491\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−17.6586			−1.55475
$130$	−2.60370	−	1.94777i	−0.228359	−	0.170831i
$131$	−20.6496			−1.80417			−0.902083	−	0.431562i	$-0.857963\pi$
$131$	−20.6496			−1.80417			−0.902083	+	0.431562i	$0.857963\pi$
$132$	8.60441	+	4.96776i	0.748918	+	0.432388i
$133$	3.08619	−	5.34544i	0.267607	−	0.463508i
$134$	−5.19142	−	8.99180i	−0.448470	−	0.776773i
$135$		−	1.55418i		−	0.133763i
$136$	−4.38722	+	2.53296i	−0.376201	+	0.217200i
$137$	2.76224	−	1.59478i	0.235994	−	0.136251i	−0.377340	−	0.926075i	$-0.623161\pi$
$137$	2.76224	−	1.59478i	0.235994	−	0.136251i	0.613334	+	0.789823i	$0.289828\pi$
$138$			19.3598i			1.64802i
$139$	0.297855	+	0.515900i	0.0252637	+	0.0437581i	0.878381	−	0.477961i	$-0.158624\pi$
$139$	0.297855	+	0.515900i	0.0252637	+	0.0437581i	−0.853117	+	0.521719i	$0.825291\pi$
$140$	−0.450919	+	0.781015i	−0.0381096	+	0.0660078i
$141$	5.79521	+	3.34587i	0.488045	+	0.281773i
$142$	−3.27856			−0.275131
$143$	9.36733	−	12.5218i	0.783335	−	1.04713i
$144$	2.24770			0.187309
$145$	1.71266	+	0.988802i	0.142228	+	0.0821155i
$146$	−0.269511	+	0.466808i	−0.0223049	+	0.0386333i
$147$	1.14539	+	1.98388i	0.0944705	+	0.163628i
$148$			0.144306i			0.0118619i
$149$	9.70783	−	5.60482i	0.795297	−	0.459165i	−0.0465273	−	0.998917i	$-0.514815\pi$
$149$	9.70783	−	5.60482i	0.795297	−	0.459165i	0.841824	+	0.539752i	$0.181482\pi$
$150$	−8.30588	+	4.79540i	−0.678172	+	0.391543i
$151$		−	13.0731i		−	1.06387i	−0.846785	−	0.531935i	$-0.821465\pi$
$151$		−	13.0731i		−	1.06387i	0.846785	−	0.531935i	$-0.178535\pi$
$152$	3.08619	+	5.34544i	0.250323	+	0.433572i
$153$	5.69334	−	9.86116i	0.460280	−	0.797228i
$154$	−3.75609	−	2.16858i	−0.302675	−	0.174749i
$155$	−0.787362			−0.0632424
$156$	0.977882	−	8.20146i	0.0782932	−	0.656642i
$157$	17.9245			1.43053			0.715266	−	0.698853i	$-0.246306\pi$
$157$	17.9245			1.43053			0.715266	+	0.698853i	$0.246306\pi$
$158$	5.65817	+	3.26674i	0.450139	+	0.259888i
$159$	−1.94372	+	3.36661i	−0.154147	+	0.266990i
$160$	−0.450919	−	0.781015i	−0.0356483	−	0.0617447i
$161$		−	8.45117i		−	0.666046i
$162$	9.25862	−	5.34547i	0.727426	−	0.419980i
$163$	17.5958	−	10.1589i	1.37821	−	0.795710i	0.386266	−	0.922387i	$-0.373765\pi$
$163$	17.5958	−	10.1589i	1.37821	−	0.795710i	0.991944	+	0.126677i	$0.0404312\pi$
$164$		−	3.99654i		−	0.312077i
$165$	4.48012	+	7.75979i	0.348777	+	0.604099i
$166$	6.61742	−	11.4617i	0.513611	−	0.889601i
$167$	−2.79770	−	1.61525i	−0.216493	−	0.124992i	0.387833	−	0.921730i	$-0.373224\pi$
$167$	−2.79770	−	1.61525i	−0.216493	−	0.124992i	−0.604325	+	0.796738i	$0.706557\pi$
$168$	−2.29079			−0.176738
$169$	−12.6356	−	3.05660i	−0.971966	−	0.235123i
$170$	−4.56864			−0.350399
$171$	−12.0150	−	6.93684i	−0.918807	−	0.530474i
$172$	−3.85426	+	6.67577i	−0.293884	+	0.509022i
$173$	−4.58522	−	7.94183i	−0.348608	−	0.603806i	0.637395	−	0.770538i	$-0.280012\pi$
$173$	−4.58522	−	7.94183i	−0.348608	−	0.603806i	−0.986002	+	0.166731i	$0.946679\pi$
$174$			5.02337i			0.380821i
$175$	3.62578	−	2.09334i	0.274083	−	0.158242i
$176$	3.75609	−	2.16858i	0.283126	−	0.163463i
$177$		−	19.5847i		−	1.47208i
$178$	−3.89590	−	6.74790i	−0.292010	−	0.505776i
$179$	−8.47747	+	14.6834i	−0.633636	+	1.09749i	0.353166	+	0.935561i	$0.385105\pi$
$179$	−8.47747	+	14.6834i	−0.633636	+	1.09749i	−0.986802	+	0.161929i	$0.948228\pi$
$180$	1.75549	+	1.01353i	0.130847	+	0.0755443i
$181$	−2.65743			−0.197525			−0.0987626	−	0.995111i	$-0.531488\pi$
$181$	−2.65743			−0.197525			−0.0987626	+	0.995111i	$0.531488\pi$
$182$	−0.426876	+	3.58019i	−0.0316421	+	0.265382i
$183$	19.0923			1.41135
$184$	7.31893	+	4.22559i	0.539559	+	0.311514i
$185$	−0.0650705	+	0.112705i	−0.00478408	+	0.00828627i
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$		−	21.9717i		−	1.60673i
$188$	2.52979	−	1.46057i	0.184504	−	0.106523i
$189$	−1.49246	+	0.861675i	−0.108561	+	0.0626776i
$190$			5.56649i			0.403836i
$191$	12.2430	+	21.2056i	0.885875	+	1.53438i	0.844708	+	0.535228i	$0.179774\pi$
$191$	12.2430	+	21.2056i	0.885875	+	1.53438i	0.0411671	+	0.999152i	$0.486892\pi$
$192$	1.14539	−	1.98388i	0.0826616	−	0.143174i
$193$	10.6009	+	6.12046i	0.763072	+	0.440560i	0.830398	−	0.557171i	$-0.188113\pi$
$193$	10.6009	+	6.12046i	0.763072	+	0.440560i	−0.0673254	+	0.997731i	$0.521447\pi$
$194$	11.7061			0.840449
$195$	4.46194	−	5.96452i	0.319526	−	0.427128i
$196$	1.00000			0.0714286
$197$	4.72634	+	2.72876i	0.336738	+	0.194416i	0.658829	−	0.752293i	$-0.271052\pi$
$197$	4.72634	+	2.72876i	0.336738	+	0.194416i	−0.322091	+	0.946709i	$0.604386\pi$
$198$	−4.87433	+	8.44259i	−0.346404	+	0.599989i
$199$	−6.40832	−	11.0995i	−0.454274	−	0.786825i	0.544372	−	0.838844i	$-0.316768\pi$
$199$	−6.40832	−	11.0995i	−0.454274	−	0.786825i	−0.998646	+	0.0520184i	$0.983435\pi$
$200$			4.18669i			0.296043i
$201$	20.5983	−	11.8924i	1.45289	−	0.838828i
$202$	−9.30362	+	5.37145i	−0.654600	+	0.377934i
$203$		−	2.19286i		−	0.153908i
$204$	−5.80247	−	10.0502i	−0.406254	−	0.703653i
$205$	1.80212	−	3.12136i	0.125865	−	0.218005i
$206$	4.16644	+	2.40550i	0.290290	+	0.167599i
$207$	−18.9957			−1.32029
$208$	−2.88710	−	2.15978i	−0.200184	−	0.149754i
$209$	−26.7706			−1.85176
$210$	−1.78914	−	1.03296i	−0.123462	−	0.0712810i
$211$	9.65552	−	16.7239i	0.664713	−	1.15132i	−0.314649	−	0.949208i	$-0.601887\pi$
$211$	9.65552	−	16.7239i	0.664713	−	1.15132i	0.979363	−	0.202110i	$-0.0647797\pi$
$212$	0.848493	+	1.46963i	0.0582747	+	0.100935i
$213$		−	7.51048i		−	0.514610i
$214$	−11.8239	+	6.82652i	−0.808263	+	0.466651i
$215$	−6.02046	+	3.47592i	−0.410592	+	0.237056i
$216$		−	1.72335i		−	0.117259i
$217$	0.436531	+	0.756094i	0.0296337	+	0.0513270i
$218$	−2.55874	+	4.43186i	−0.173299	+	0.300163i
$219$	−1.06936	−	0.617393i	−0.0722604	−	0.0417196i
$220$	3.91142			0.263708
$221$	−16.7883	+	7.19569i	−1.12931	+	0.484034i
$222$	−0.330575			−0.0221867
$223$	−9.21079	−	5.31785i	−0.616800	−	0.356110i	0.158822	−	0.987307i	$-0.449230\pi$
$223$	−9.21079	−	5.31785i	−0.616800	−	0.356110i	−0.775622	+	0.631197i	$0.782564\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−4.70522	−	8.14967i	−0.313681	−	0.543312i
$226$		−	17.9321i		−	1.19282i
$227$	19.6776	−	11.3609i	1.30605	−	0.754047i	0.324613	−	0.945847i	$-0.394766\pi$
$227$	19.6776	−	11.3609i	1.30605	−	0.754047i	0.981434	+	0.191800i	$0.0614326\pi$
$228$	−12.2453	+	7.06980i	−0.810962	+	0.468209i
$229$			20.3094i			1.34208i	0.741420	+	0.671042i	$0.234153\pi$
$229$			20.3094i			1.34208i	−0.741420	+	0.671042i	$0.765847\pi$
$230$	3.81080	+	6.60049i	0.251277	+	0.435224i
$231$	4.96776	−	8.60441i	0.326855	−	0.566129i
$232$	1.89907	+	1.09643i	0.124680	+	0.0719841i
$233$	10.6446			0.697352			0.348676	−	0.937243i	$-0.386631\pi$
$233$	10.6446			0.697352			0.348676	+	0.937243i	$0.386631\pi$
$234$	8.04721	+	0.959491i	0.526063	+	0.0627239i
$235$	2.63441			0.171850
$236$	−7.40394	−	4.27467i	−0.481955	−	0.278257i
$237$	−7.48341	+	12.9617i	−0.486100	+	0.841950i
$238$	2.53296	+	4.38722i	0.164187	+	0.284381i
$239$		−	0.311564i		−	0.0201534i	−0.999949	−	0.0100767i	$-0.996792\pi$
$239$		−	0.311564i		−	0.0201534i	0.999949	−	0.0100767i	$-0.00320757\pi$
$240$	1.78914	−	1.03296i	0.115488	−	0.0666773i
$241$	−21.9100	+	12.6498i	−1.41135	+	0.814843i	−0.995516	−	0.0945983i	$-0.969843\pi$
$241$	−21.9100	+	12.6498i	−1.41135	+	0.814843i	−0.415833	+	0.909441i	$0.636510\pi$
$242$			7.81099i			0.502110i
$243$	9.66031	+	16.7321i	0.619709	+	1.07337i
$244$	4.16720	−	7.21780i	0.266778	−	0.462073i
$245$	0.781015	+	0.450919i	0.0498972	+	0.0288082i
$246$	9.15521			0.583715
$247$	8.76732	+	20.4551i	0.557851	+	1.30153i
$248$	−0.873062			−0.0554395
$249$	26.2563	+	15.1591i	1.66393	+	0.960669i
$250$	−4.14246	+	7.17494i	−0.261992	+	0.453783i
$251$	4.02015	+	6.96311i	0.253750	+	0.439507i	0.964555	−	0.263881i	$-0.0850027\pi$
$251$	4.02015	+	6.96311i	0.253750	+	0.439507i	−0.710805	+	0.703389i	$0.751669\pi$
$252$		−	2.24770i		−	0.141592i
$253$	−31.7434	+	18.3271i	−1.99569	+	1.15221i
$254$	−16.8993	+	9.75681i	−1.06036	+	0.612197i
$255$		−	10.4658i		−	0.655393i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−8.46634	+	14.6641i	−0.528116	+	0.914723i	0.471347	+	0.881948i	$0.343768\pi$
$257$	−8.46634	+	14.6641i	−0.528116	+	0.914723i	−0.999463	+	0.0327753i	$0.989565\pi$
$258$	−15.2928	−	8.82928i	−0.952085	−	0.549687i
$259$	0.144306			0.00896676
$260$	−1.28098	−	2.98867i	−0.0794431	−	0.185350i
$261$	−4.92890			−0.305091
$262$	−17.8831	−	10.3248i	−1.10482	−	0.637869i
$263$	−5.16045	+	8.93817i	−0.318207	+	0.551151i	−0.980114	−	0.198435i	$-0.936414\pi$
$263$	−5.16045	+	8.93817i	−0.318207	+	0.551151i	0.661907	+	0.749586i	$0.269747\pi$
$264$	4.96776	+	8.60441i	0.305744	+	0.529565i
$265$			1.53041i			0.0940122i
$266$	5.34544	−	3.08619i	0.327750	−	0.189226i
$267$	15.4580	−	8.92468i	0.946014	−	0.546181i
$268$		−	10.3828i		−	0.634233i
$269$	3.06999	+	5.31738i	0.187181	+	0.324207i	0.944309	−	0.329059i	$-0.106732\pi$
$269$	3.06999	+	5.31738i	0.187181	+	0.324207i	−0.757128	+	0.653266i	$0.773398\pi$
$270$	0.777092	−	1.34596i	0.0472923	−	0.0819127i
$271$	9.24673	+	5.33860i	0.561699	+	0.324297i	0.753827	−	0.657073i	$-0.228206\pi$
$271$	9.24673	+	5.33860i	0.561699	+	0.324297i	−0.192128	+	0.981370i	$0.561539\pi$
$272$	−5.06592			−0.307167
$273$	−8.20146	−	0.977882i	−0.496375	−	0.0591841i
$274$	3.18956			0.192689
$275$	−15.7256	−	9.07917i	−0.948289	−	0.547495i
$276$	−9.67992	+	16.7661i	−0.582662	+	1.00920i
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	0.981084	+	0.193585i	$0.0620114\pi$
$277$	10.9545	+	18.9737i	0.658191	+	1.14002i	−0.322892	+	0.946436i	$0.604655\pi$
$278$			0.595710i			0.0357283i
$279$	1.69948	−	0.981193i	0.101745	−	0.0587425i
$280$	−0.781015	+	0.450919i	−0.0466746	+	0.0269476i
$281$		−	25.7719i		−	1.53743i	−0.639594	−	0.768713i	$-0.720898\pi$
$281$		−	25.7719i		−	1.53743i	0.639594	−	0.768713i	$-0.279102\pi$
$282$	3.34587	+	5.79521i	0.199243	+	0.345100i
$283$	−5.66344	+	9.80937i	−0.336657	+	0.583107i	−0.983802	−	0.179260i	$-0.942630\pi$
$283$	−5.66344	+	9.80937i	−0.336657	+	0.583107i	0.647145	+	0.762367i	$0.275963\pi$
$284$	−2.83932	−	1.63928i	−0.168482	−	0.0972733i
$285$	−12.7516			−0.755342
$286$	14.3733	−	6.16055i	0.849908	−	0.364281i
$287$	−3.99654			−0.235908
$288$	1.94657	+	1.12385i	0.114703	+	0.0662236i
$289$	−4.33177	+	7.50285i	−0.254810	+	0.441344i
$290$	0.988802	+	1.71266i	0.0580645	+	0.100571i
$291$			26.8162i			1.57199i
$292$	−0.466808	+	0.269511i	−0.0273178	+	0.0157720i
$293$	20.5646	−	11.8730i	1.20140	−	0.693626i	0.240530	−	0.970642i	$-0.422679\pi$
$293$	20.5646	−	11.8730i	1.20140	−	0.693626i	0.960865	+	0.277016i	$0.0893454\pi$
$294$			2.29079i			0.133601i
$295$	−3.85506	−	6.67716i	−0.224450	−	0.388759i
$296$	−0.0721531	+	0.124973i	−0.00419382	+	0.00726390i
$297$	6.47306	+	3.73723i	0.375605	+	0.216856i
$298$	11.2096			0.649357
$299$	24.3994	+	18.2527i	1.41105	+	1.05558i
$300$	−9.59081			−0.553725
$301$	6.67577	+	3.85426i	0.384785	+	0.222156i
$302$	6.53653	−	11.3216i	0.376135	−	0.651485i
$303$	−12.3048	−	21.3126i	−0.706894	−	1.22438i
$304$			6.17238i			0.354010i
$305$	6.50930	−	3.75814i	0.372721	−	0.215191i
$306$	9.86116	−	5.69334i	0.563725	−	0.325467i
$307$		−	6.68810i		−	0.381710i	−0.981618	−	0.190855i	$-0.938874\pi$
$307$		−	6.68810i		−	0.381710i	0.981618	−	0.190855i	$-0.0611261\pi$
$308$	−2.16858	−	3.75609i	−0.123566	−	0.214023i
$309$	−5.51048	+	9.54443i	−0.313480	+	0.542964i
$310$	−0.681875	−	0.393681i	−0.0387279	−	0.0223596i
$311$	9.18724			0.520961			0.260480	−	0.965479i	$-0.416119\pi$
$311$	9.18724			0.520961			0.260480	+	0.965479i	$0.416119\pi$
$312$	4.94760	−	6.61373i	0.280103	−	0.374429i
$313$	−17.1631			−0.970118			−0.485059	−	0.874481i	$-0.661202\pi$
$313$	−17.1631			−0.970118			−0.485059	+	0.874481i	$0.661202\pi$
$314$	15.5231	+	8.96225i	0.876018	+	0.505769i
$315$	1.01353	−	1.75549i	0.0571061	−	0.0989107i
$316$	3.26674	+	5.65817i	0.183769	+	0.318297i
$317$		−	3.76247i		−	0.211322i	−0.994402	−	0.105661i	$-0.966304\pi$
$317$		−	3.76247i		−	0.211322i	0.994402	−	0.105661i	$-0.0336958\pi$
$318$	−3.36661	+	1.94372i	−0.188790	+	0.108998i
$319$	−8.23658	+	4.75539i	−0.461160	+	0.266251i
$320$		−	0.901839i		−	0.0504143i
$321$	−15.6381	−	27.0860i	−0.872833	−	1.51179i
$322$	4.22559	−	7.31893i	0.235483	−	0.407868i
$323$	27.0796	+	15.6344i	1.50675	+	0.869921i
$324$	10.6909			0.593941
$325$	−1.78720	+	14.9891i	−0.0991358	+	0.831448i
$326$	20.3179			1.12530
$327$	−10.1524	−	5.86152i	−0.561432	−	0.324143i
$328$	1.99827	−	3.46110i	0.110336	−	0.191107i
$329$	−1.46057	−	2.52979i	−0.0805241	−	0.139472i
$330$			8.96024i			0.493245i
$331$	−27.9083	+	16.1129i	−1.53398	+	0.885643i	−0.534806	+	0.844975i	$0.679615\pi$
$331$	−27.9083	+	16.1129i	−1.53398	+	0.885643i	−0.999173	+	0.0406683i	$0.987051\pi$
$332$	11.4617	−	6.61742i	0.629043	−	0.363178i
$333$		−	0.324358i		−	0.0177747i
$334$	−1.61525	−	2.79770i	−0.0883827	−	0.153083i
$335$	4.68182	−	8.10916i	0.255795	−	0.443051i
$336$	−1.98388	−	1.14539i	−0.108230	−	0.0624863i
$337$	−3.01703			−0.164348			−0.0821740	−	0.996618i	$-0.526186\pi$
$337$	−3.01703			−0.164348			−0.0821740	+	0.996618i	$0.526186\pi$
$338$	−9.41441	−	8.96487i	−0.512077	−	0.487624i
$339$	41.0785			2.23108
$340$	−3.95656	−	2.28432i	−0.214575	−	0.123885i
$341$	1.89331	−	3.27931i	0.102528	−	0.177584i
$342$	−6.93684	−	12.0150i	−0.375101	−	0.649695i
$343$		−	1.00000i		−	0.0539949i
$344$	−6.67577	+	3.85426i	−0.359933	+	0.207808i
$345$	−15.1203	+	8.72972i	−0.814051	+	0.469993i
$346$		−	9.17044i		−	0.493006i
$347$	−0.234270	−	0.405768i	−0.0125763	−	0.0217828i	0.859669	−	0.510852i	$-0.170670\pi$
$347$	−0.234270	−	0.405768i	−0.0125763	−	0.0217828i	−0.872245	+	0.489069i	$0.837337\pi$
$348$	−2.51168	+	4.35037i	−0.134640	+	0.233204i
$349$	−27.9044	−	16.1106i	−1.49369	−	0.862380i	−0.493712	−	0.869625i	$-0.664360\pi$
$349$	−27.9044	−	16.1106i	−1.49369	−	0.862380i	−0.999974	+	0.00724565i	$0.997694\pi$
$350$	4.18669			0.223788
$351$	0.735656	−	6.16992i	0.0392664	−	0.329326i
$352$	4.33716			0.231172
$353$	−11.3583	−	6.55771i	−0.604540	−	0.349031i	0.166285	−	0.986078i	$-0.446823\pi$
$353$	−11.3583	−	6.55771i	−0.604540	−	0.349031i	−0.770826	+	0.637046i	$0.780156\pi$
$354$	9.79235	−	16.9608i	0.520457	−	0.901459i
$355$	−1.47837	−	2.56060i	−0.0784635	−	0.135903i
$356$		−	7.79180i		−	0.412965i
$357$	−10.0502	+	5.80247i	−0.531912	+	0.307099i
$358$	−14.6834	+	8.47747i	−0.776043	+	0.448048i
$359$			4.37981i			0.231157i	0.993298	+	0.115579i	$0.0368722\pi$
$359$			4.37981i			0.231157i	−0.993298	+	0.115579i	$0.963128\pi$
$360$	1.01353	+	1.75549i	0.0534179	+	0.0925225i
$361$	9.54914	−	16.5396i	0.502586	−	0.870505i
$362$	−2.30140	−	1.32871i	−0.120959	−	0.0698357i
$363$	−17.8933			−0.939156
$364$	−2.15978	+	2.88710i	−0.113203	+	0.151325i
$365$	−0.486112			−0.0254443
$366$	16.5344	+	9.54617i	0.864269	+	0.498986i
$367$	−12.9094	+	22.3597i	−0.673865	+	1.16717i	0.302934	+	0.953011i	$0.402034\pi$
$367$	−12.9094	+	22.3597i	−0.673865	+	1.16717i	−0.976799	+	0.214157i	$0.931300\pi$
$368$	4.22559	+	7.31893i	0.220274	+	0.381526i
$369$			8.98303i			0.467638i
$370$	−0.112705	+	0.0650705i	−0.00585928	+	0.00338285i
$371$	1.46963	−	0.848493i	0.0762995	−	0.0440515i
$372$		−	2.00000i		−	0.103695i
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	−0.924138	−	0.382059i	$-0.875215\pi$
$373$	−15.3143	−	26.5251i	−0.792942	−	1.37342i	0.131196	−	0.991356i	$-0.458118\pi$
$374$	10.9859	−	19.0281i	0.568065	−	0.983918i
$375$	−16.4363	−	9.48948i	−0.848765	−	0.490035i
$376$	2.92115			0.150647
$377$	6.33100	+	4.73609i	0.326063	+	0.243921i
$378$	−1.72335			−0.0886395
$379$	−33.0409	−	19.0762i	−1.69720	−	0.979877i	−0.948400	−	0.317076i	$-0.897299\pi$
$379$	−33.0409	−	19.0762i	−1.69720	−	0.979877i	−0.748796	−	0.662801i	$-0.769368\pi$
$380$	−2.78325	+	4.82072i	−0.142778	+	0.247298i
$381$	−22.3508	−	38.7127i	−1.14507	−	1.98331i
$382$			24.4861i			1.25282i
$383$	−27.6783	+	15.9801i	−1.41430	+	0.816544i	−0.995790	−	0.0916693i	$-0.970780\pi$
$383$	−27.6783	+	15.9801i	−1.41430	+	0.816544i	−0.418507	+	0.908214i	$0.637446\pi$
$384$	1.98388	−	1.14539i	0.101239	−	0.0584506i
$385$		−	3.91142i		−	0.199345i
$386$	6.12046	+	10.6009i	0.311523	+	0.539574i
$387$	8.66323	−	15.0051i	0.440377	−	0.762754i
$388$	10.1378	+	5.85305i	0.514668	+	0.297144i
$389$	5.24585			0.265975			0.132988	−	0.991118i	$-0.457543\pi$
$389$	5.24585			0.265975			0.132988	+	0.991118i	$0.457543\pi$
$390$	6.84641	−	2.93446i	0.346681	−	0.148592i
$391$	42.8130			2.16514
$392$	0.866025	+	0.500000i	0.0437409	+	0.0252538i
$393$	23.6520	−	40.9664i	1.19308	−	2.06648i
$394$	2.72876	+	4.72634i	0.137473	+	0.238110i
$395$			5.89215i			0.296466i
$396$	−8.44259	+	4.87433i	−0.424256	+	0.244944i
$397$	21.2432	−	12.2648i	1.06617	−	0.615552i	0.139035	−	0.990287i	$-0.455600\pi$
$397$	21.2432	−	12.2648i	1.06617	−	0.615552i	0.927132	+	0.374736i	$0.122266\pi$
$398$		−	12.8166i		−	0.642440i
$399$	7.06980	+	12.2453i	0.353933	+	0.613030i
$400$	−2.09334	+	3.62578i	−0.104667	+	0.181289i
$401$	3.69916	+	2.13571i	0.184727	+	0.106652i	0.589512	−	0.807760i	$-0.299320\pi$
$401$	3.69916	+	2.13571i	0.184727	+	0.106652i	−0.404784	+	0.914412i	$0.632653\pi$
$402$	23.7849			1.18628
$403$	−3.12573	−	0.372689i	−0.155704	−	0.0185650i
$404$	−10.7429			−0.534479
$405$	8.34979	+	4.82075i	0.414904	+	0.239545i
$406$	1.09643	−	1.89907i	0.0544149	−	0.0942493i
$407$	−0.312940	−	0.542028i	−0.0155119	−	0.0268673i
$408$		−	11.6049i		−	0.574530i
$409$	−1.39990	+	0.808235i	−0.0692208	+	0.0399646i	−0.534211	−	0.845351i	$-0.679391\pi$
$409$	−1.39990	+	0.808235i	−0.0692208	+	0.0399646i	0.464990	+	0.885316i	$0.346058\pi$
$410$	3.12136	−	1.80212i	0.154153	−	0.0890001i
$411$			7.30661i			0.360408i
$412$	2.40550	+	4.16644i	0.118510	+	0.205266i
$413$	−4.27467	+	7.40394i	−0.210343	+	0.364324i
$414$	−16.4508	−	9.49787i	−0.808512	−	0.466795i
$415$	11.9357			0.585900
$416$	−1.42041	−	3.31398i	−0.0696414	−	0.162481i
$417$	−1.36464			−0.0668269
$418$	−23.1840	−	13.3853i	−1.13397	−	0.654697i
$419$	13.0156	−	22.5437i	0.635854	−	1.10133i	−0.350480	−	0.936570i	$-0.613982\pi$
$419$	13.0156	−	22.5437i	0.635854	−	1.10133i	0.986334	−	0.164761i	$-0.0526851\pi$
$420$	−1.03296	−	1.78914i	−0.0504033	−	0.0873011i
$421$			37.5391i			1.82954i	0.403971	+	0.914772i	$0.367630\pi$
$421$			37.5391i			1.82954i	−0.403971	+	0.914772i	$0.632370\pi$
$422$	16.7239	−	9.65552i	0.814104	−	0.470023i
$423$	−5.68622	+	3.28294i	−0.276473	+	0.159622i
$424$			1.69699i			0.0824129i
$425$	10.6047	+	18.3679i	0.514404	+	0.890974i
$426$	3.75524	−	6.50427i	0.181942	−	0.315133i
$427$	−7.21780	−	4.16720i	−0.349294	−	0.201665i
$428$	−13.6530			−0.659944
$429$	14.1125	+	32.9261i	0.681359	+	1.58969i
$430$	−6.95183			−0.335247
$431$	18.6662	+	10.7769i	0.899118	+	0.519106i	0.876914	−	0.480647i	$-0.159598\pi$
$431$	18.6662	+	10.7769i	0.899118	+	0.519106i	0.0222041	+	0.999753i	$0.492932\pi$
$432$	0.861675	−	1.49246i	0.0414573	−	0.0718062i
$433$	1.59958	+	2.77056i	0.0768710	+	0.133145i	0.901898	−	0.431948i	$-0.142174\pi$
$433$	1.59958	+	2.77056i	0.0768710	+	0.133145i	−0.825027	+	0.565093i	$0.808840\pi$
$434$			0.873062i			0.0419083i
$435$	−3.92333	+	2.26513i	−0.188109	+	0.108605i
$436$	−4.43186	+	2.55874i	−0.212248	+	0.122541i
$437$		−	52.1638i		−	2.49534i
$438$	−0.617393	−	1.06936i	−0.0295002	−	0.0510958i
$439$	13.3114	−	23.0560i	0.635317	−	1.10040i	−0.351131	−	0.936326i	$-0.614203\pi$
$439$	13.3114	−	23.0560i	0.635317	−	1.10040i	0.986448	−	0.164075i	$-0.0524638\pi$
$440$	3.38739	+	1.95571i	0.161488	+	0.0932349i
$441$	−2.24770			−0.107034
$442$	−18.1370	−	2.16252i	−0.862688	−	0.102861i
$443$	9.09867			0.432291			0.216145	−	0.976361i	$-0.430652\pi$
$443$	9.09867			0.432291			0.216145	+	0.976361i	$0.430652\pi$
$444$	−0.286286	−	0.165287i	−0.0135865	−	0.00784420i
$445$	3.51347	−	6.08551i	0.166555	−	0.288481i
$446$	−5.31785	−	9.21079i	−0.251808	−	0.436144i
$447$			25.6789i			1.21457i
$448$	−0.866025	+	0.500000i	−0.0409159	+	0.0236228i
$449$	6.08550	−	3.51346i	0.287192	−	0.165811i	−0.349483	−	0.936943i	$-0.613643\pi$
$449$	6.08550	−	3.51346i	0.287192	−	0.165811i	0.636675	+	0.771132i	$0.280309\pi$
$450$		−	9.41043i		−	0.443612i
$451$	8.66681	+	15.0114i	0.408104	+	0.706858i
$452$	8.96603	−	15.5296i	0.421726	−	0.730452i
$453$	25.9354	+	14.9738i	1.21855	+	0.703531i
$454$	22.7217			1.06638
$455$	−2.98867	+	1.28098i	−0.140111	+	0.0600533i
$456$	−14.1396			−0.662148
$457$	−16.5853	−	9.57556i	−0.775830	−	0.447926i	0.0591204	−	0.998251i	$-0.481170\pi$
$457$	−16.5853	−	9.57556i	−0.775830	−	0.447926i	−0.834950	+	0.550325i	$0.814504\pi$
$458$	−10.1547	+	17.5885i	−0.474498	+	0.821855i
$459$	−4.36518	−	7.56071i	−0.203749	−	0.352904i
$460$			7.62159i			0.355359i
$461$	−2.82026	+	1.62828i	−0.131353	+	0.0758365i	−0.564236	−	0.825613i	$-0.690829\pi$
$461$	−2.82026	+	1.62828i	−0.131353	+	0.0758365i	0.432884	+	0.901450i	$0.357496\pi$
$462$	8.60441	−	4.96776i	0.400313	−	0.231121i
$463$			21.2761i			0.988786i	0.869238	+	0.494393i	$0.164610\pi$
$463$			21.2761i			0.988786i	−0.869238	+	0.494393i	$0.835390\pi$
$464$	1.09643	+	1.89907i	0.0509004	+	0.0881621i
$465$	0.901839	−	1.56203i	0.0418218	−	0.0724374i
$466$	9.21851	+	5.32231i	0.427039	+	0.246551i
$467$	−3.33171			−0.154173			−0.0770866	−	0.997024i	$-0.524562\pi$
$467$	−3.33171			−0.154173			−0.0770866	+	0.997024i	$0.524562\pi$
$468$	6.48935	+	4.85455i	0.299970	+	0.224402i
$469$	−10.3828			−0.479435
$470$	2.28146	+	1.31720i	0.105236	+	0.0607580i
$471$	−20.5306	+	35.5601i	−0.946001	+	1.63852i
$472$	−4.27467	−	7.40394i	−0.196757	−	0.340794i
$473$		−	33.4331i		−	1.53725i
$474$	−12.9617	+	7.48341i	−0.595348	+	0.343725i
$475$	22.3797	−	12.9209i	1.02685	−	0.592852i
$476$			5.06592i			0.232196i
$477$	−1.90716	−	3.30330i	−0.0873229	−	0.151248i
$478$	0.155782	−	0.269822i	0.00712530	−	0.0123414i
$479$	−0.160402	−	0.0926079i	−0.00732894	−	0.00423136i	0.496331	−	0.868133i	$-0.334680\pi$
$479$	−0.160402	−	0.0926079i	−0.00732894	−	0.00423136i	−0.503660	+	0.863902i	$0.668014\pi$
$480$	2.06592			0.0942959
$481$	−0.311670	+	0.416627i	−0.0142109	+	0.0189965i
$482$	−25.2995			−1.15236
$483$	16.7661	+	9.67992i	0.762884	+	0.440451i
$484$	−3.90550	+	6.76452i	−0.177523	+	0.307478i
$485$	5.27851	+	9.14264i	0.239685	+	0.415146i
$486$			19.3206i			0.876401i
$487$	−27.0466	+	15.6154i	−1.22560	+	0.707601i	−0.966106	−	0.258144i	$-0.916889\pi$
$487$	−27.0466	+	15.6154i	−1.22560	+	0.707601i	−0.259494	+	0.965745i	$0.583556\pi$
$488$	7.21780	−	4.16720i	0.326735	−	0.188640i
$489$			46.5440i			2.10479i
$490$	0.450919	+	0.781015i	0.0203705	+	0.0352827i
$491$	13.4236	−	23.2504i	0.605799	−	1.04927i	−0.386126	−	0.922446i	$-0.626187\pi$
$491$	13.4236	−	23.2504i	0.605799	−	1.04927i	0.991925	−	0.126829i	$-0.0404798\pi$
$492$	7.92864	+	4.57761i	0.357451	+	0.206374i
$493$	11.1088			0.500317
$494$	−2.63484	+	22.0983i	−0.118547	+	0.994250i
$495$	−8.79172			−0.395158
$496$	−0.756094	−	0.436531i	−0.0339496	−	0.0196008i
$497$	−1.63928	+	2.83932i	−0.0735317	+	0.127361i
$498$	15.1591	+	26.2563i	0.679295	+	1.17657i
$499$		−	15.2869i		−	0.684337i	−0.939639	−	0.342168i	$-0.888839\pi$
$499$		−	15.2869i		−	0.684337i	0.939639	−	0.342168i	$-0.111161\pi$
$500$	−7.17494	+	4.14246i	−0.320873	+	0.185256i
$501$	6.40893	−	3.70020i	0.286330	−	0.165313i
$502$			8.04030i			0.358856i
$503$	13.0551	+	22.6121i	0.582097	+	1.00822i	0.995230	+	0.0975513i	$0.0311010\pi$
$503$	13.0551	+	22.6121i	0.582097	+	1.00822i	−0.413133	+	0.910671i	$0.635566\pi$
$504$	1.12385	−	1.94657i	0.0500603	−	0.0867071i
$505$	−8.39036	−	4.84418i	−0.373366	−	0.215563i
$506$	−36.6541			−1.62947
$507$	20.5366	−	21.5664i	0.912062	−	0.957798i
$508$	−19.5136			−0.865777
$509$	14.7459	+	8.51357i	0.653602	+	0.377357i	0.789835	−	0.613320i	$-0.210166\pi$
$509$	14.7459	+	8.51357i	0.653602	+	0.377357i	−0.136233	+	0.990677i	$0.543500\pi$
$510$	5.23289	−	9.06364i	0.231716	−	0.401345i
$511$	0.269511	+	0.466808i	0.0119225	+	0.0206504i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.21206	+	5.31858i	−0.406722	+	0.234821i
$514$	−14.6641	+	8.46634i	−0.646807	+	0.373434i
$515$			4.33874i			0.191188i
$516$	−8.82928	−	15.2928i	−0.388687	−	0.673226i
$517$	−6.33475	+	10.9721i	−0.278602	+	0.482553i
$518$	0.124973	+	0.0721531i	0.00549099	+	0.00317023i
$519$	21.0075			0.922128
$520$	0.384973	−	3.22876i	0.0168822	−	0.141590i
$521$	−18.7760			−0.822593			−0.411297	−	0.911502i	$-0.634924\pi$
$521$	−18.7760			−0.822593			−0.411297	+	0.911502i	$0.634924\pi$
$522$	−4.26855	−	2.46445i	−0.186829	−	0.107866i
$523$	1.51624	−	2.62620i	0.0663004	−	0.114836i	−0.830970	−	0.556318i	$-0.812214\pi$
$523$	1.51624	−	2.62620i	0.0663004	−	0.114836i	0.897270	+	0.441482i	$0.145547\pi$
$524$	−10.3248	−	17.8831i	−0.451042	−	0.781227i
$525$			9.59081i			0.418577i
$526$	−8.93817	+	5.16045i	−0.389723	+	0.225006i
$527$	−3.83031	+	2.21143i	−0.166851	+	0.0963315i
$528$			9.93552i			0.432388i
$529$	−24.2111	−	41.9349i	−1.05266	−	1.82326i
$530$	−0.765204	+	1.32537i	−0.0332383	+	0.0575705i
$531$	16.6419	+	9.60818i	0.722195	+	0.416960i
$532$	6.17238			0.267607
$533$	8.63164	−	11.5384i	0.373878	−	0.499783i
$534$	17.8494			0.772417
$535$	−10.6632	−	6.15642i	−0.461011	−	0.266165i
$536$	5.19142	−	8.99180i	0.224235	−	0.388387i
$537$	−19.4201	−	33.6366i	−0.838038	−	1.45153i
$538$			6.13999i			0.264714i
$539$	−3.75609	+	2.16858i	−0.161786	+	0.0934074i
$540$	1.34596	−	0.777092i	0.0579210	−	0.0334407i
$541$			6.11845i			0.263053i	0.991313	+	0.131526i	$0.0419878\pi$
$541$			6.11845i			0.263053i	−0.991313	+	0.131526i	$0.958012\pi$
$542$	5.33860	+	9.24673i	0.229313	+	0.397181i
$543$	3.04380	−	5.27202i	0.130622	−	0.226244i
$544$	−4.38722	−	2.53296i	−0.188100	−	0.108600i
$545$	−4.61513			−0.197691
$546$	−6.61373	−	4.94760i	−0.283041	−	0.211738i
$547$	−37.4754			−1.60233			−0.801166	−	0.598442i	$-0.795786\pi$
$547$	−37.4754			−1.60233			−0.801166	+	0.598442i	$0.795786\pi$
$548$	2.76224	+	1.59478i	0.117997	+	0.0681257i
$549$	−9.36663	+	16.2235i	−0.399758	+	0.692402i
$550$	−9.07917	−	15.7256i	−0.387137	−	0.670541i
$551$		−	13.5352i		−	0.576617i
$552$	−16.7661	+	9.67992i	−0.713613	+	0.412005i
$553$	5.65817	−	3.26674i	0.240610	−	0.138916i
$554$			21.9090i			0.930823i
$555$	−0.149063	−	0.258184i	−0.00632736	−	0.0109593i
$556$	−0.297855	+	0.515900i	−0.0126319	+	0.0218790i
$557$	−7.69941	−	4.44526i	−0.326234	−	0.188352i	0.327934	−	0.944701i	$-0.393648\pi$
$557$	−7.69941	−	4.44526i	−0.326234	−	0.188352i	−0.654168	+	0.756349i	$0.726981\pi$
$558$	1.96239			0.0830744
$559$	−25.5458	+	10.9493i	−1.08047	+	0.463104i
$560$	−0.901839			−0.0381096
$561$	43.5893	+	25.1663i	1.84034	+	1.06252i
$562$	12.8860	−	22.3192i	0.543562	−	0.941477i
$563$	8.89598	+	15.4083i	0.374921	+	0.649382i	0.990315	−	0.138838i	$-0.0443366\pi$
$563$	8.89598	+	15.4083i	0.374921	+	0.649382i	−0.615394	+	0.788219i	$0.711003\pi$
$564$			6.69173i			0.281773i
$565$	14.0052	−	8.08591i	0.589204	−	0.340177i
$566$	−9.80937	+	5.66344i	−0.412319	+	0.238052i
$567$		−	10.6909i		−	0.448977i
$568$	−1.63928	−	2.83932i	−0.0687826	−	0.119135i
$569$	5.58684	−	9.67669i	0.234212	−	0.405668i	−0.724831	−	0.688927i	$-0.758082\pi$
$569$	5.58684	−	9.67669i	0.234212	−	0.405668i	0.959044	+	0.283259i	$0.0914155\pi$
$570$	−11.0432	−	6.37582i	−0.462551	−	0.267054i
$571$	−16.7239			−0.699873			−0.349936	−	0.936773i	$-0.613797\pi$
$571$	−16.7239			−0.699873			−0.349936	+	0.936773i	$0.613797\pi$
$572$	15.5279	+	1.85143i	0.649253	+	0.0774122i
$573$	−56.0924			−2.34329
$574$	−3.46110	−	1.99827i	−0.144464	−	0.0834061i
$575$	17.6912	−	30.6421i	0.737774	−	1.27786i
$576$	1.12385	+	1.94657i	0.0468272	+	0.0811070i
$577$			0.798887i			0.0332581i	0.999862	+	0.0166291i	$0.00529344\pi$
$577$			0.798887i			0.0332581i	−0.999862	+	0.0166291i	$0.994707\pi$
$578$	−7.50285	+	4.33177i	−0.312078	+	0.180178i
$579$	−24.2845	+	14.0207i	−1.00923	+	0.582679i
$580$			1.97760i			0.0821155i
$581$	−6.61742	−	11.4617i	−0.274537	−	0.475512i
$582$	−13.4081	+	23.2235i	−0.555783	+	0.962645i
$583$	−6.37404	−	3.68005i	−0.263986	−	0.152412i
$584$	−0.539023			−0.0223049
$585$	2.87927	+	6.71765i	0.119043	+	0.277741i
$586$	23.7459			0.980935
$587$	6.94921	+	4.01213i	0.286825	+	0.165598i	0.636509	−	0.771269i	$-0.280378\pi$
$587$	6.94921	+	4.01213i	0.286825	+	0.165598i	−0.349684	+	0.936868i	$0.613711\pi$
$588$	−1.14539	+	1.98388i	−0.0472352	+	0.0818138i
$589$	2.69444	+	4.66690i	0.111022	+	0.192296i
$590$		−	7.71012i		−	0.317421i
$591$	−10.8270	+	6.25100i	−0.445365	+	0.257132i
$592$	−0.124973	+	0.0721531i	−0.00513635	+	0.00296548i
$593$		−	4.93120i		−	0.202500i	−0.994861	−	0.101250i	$-0.967716\pi$
$593$		−	4.93120i		−	0.202500i	0.994861	−	0.101250i	$-0.0322842\pi$
$594$	3.73723	+	6.47306i	0.153340	+	0.265593i
$595$	−2.28432	+	3.95656i	−0.0936481	+	0.162203i
$596$	9.70783	+	5.60482i	0.397648	+	0.229582i
$597$	29.3602			1.20163
$598$	12.0041	+	28.0070i	0.490886	+	1.14529i
$599$	−17.8249			−0.728306			−0.364153	−	0.931339i	$-0.618642\pi$
$599$	−17.8249			−0.728306			−0.364153	+	0.931339i	$0.618642\pi$
$600$	−8.30588	−	4.79540i	−0.339086	−	0.195772i
$601$	0.0809165	−	0.140152i	0.00330065	−	0.00571690i	−0.864370	−	0.502856i	$-0.832283\pi$
$601$	0.0809165	−	0.140152i	0.00330065	−	0.00571690i	0.867671	+	0.497139i	$0.165616\pi$
$602$	3.85426	+	6.67577i	0.157088	+	0.272084i
$603$			23.3375i			0.950378i
$604$	11.3216	−	6.53653i	0.460670	−	0.265968i
$605$	−6.10050	+	3.52213i	−0.248021	+	0.143195i
$606$		−	24.6097i		−	0.999700i
$607$	−3.09423	−	5.35937i	−0.125591	−	0.217530i	0.796373	−	0.604806i	$-0.206749\pi$
$607$	−3.09423	−	5.35937i	−0.125591	−	0.217530i	−0.921964	+	0.387276i	$0.873416\pi$
$608$	−3.08619	+	5.34544i	−0.125162	+	0.216786i
$609$	4.35037	+	2.51168i	0.176286	+	0.101779i
$610$	7.51629			0.304326
$611$	10.4583	+	1.24697i	0.423097	+	0.0504469i
$612$	11.3867			0.460280
$613$	32.2269	+	18.6062i	1.30163	+	0.751497i	0.980684	−	0.195600i	$-0.0626654\pi$
$613$	32.2269	+	18.6062i	1.30163	+	0.751497i	0.320947	+	0.947097i	$0.395999\pi$
$614$	3.34405	−	5.79207i	0.134955	−	0.233749i
$615$	4.12826	+	7.15036i	0.166468	+	0.288330i
$616$		−	4.33716i		−	0.174749i
$617$	−5.78536	+	3.34018i	−0.232910	+	0.134471i	−0.611914	−	0.790924i	$-0.709600\pi$
$617$	−5.78536	+	3.34018i	−0.232910	+	0.134471i	0.379004	+	0.925395i	$0.376267\pi$
$618$	−9.54443	+	5.51048i	−0.383933	+	0.221664i
$619$		−	23.7344i		−	0.953965i	−0.878913	−	0.476982i	$-0.841731\pi$
$619$		−	23.7344i		−	0.953965i	0.878913	−	0.476982i	$-0.158269\pi$
$620$	−0.393681	−	0.681875i	−0.0158106	−	0.0273848i
$621$	−7.28216	+	12.6131i	−0.292223	+	0.506145i
$622$	7.95639	+	4.59362i	0.319022	+	0.184187i
$623$	−7.79180			−0.312172
$624$	7.59161	−	3.25386i	0.303908	−	0.130259i
$625$	13.4618			0.538471
$626$	−14.8637	−	8.58157i	−0.594074	−	0.342989i
$627$	30.6629	−	53.1097i	1.22456	−	2.12100i
$628$	8.96225	+	15.5231i	0.357633	+	0.619438i
$629$			0.731044i			0.0291486i
$630$	1.75549	−	1.01353i	0.0699404	−	0.0403801i
$631$	19.9348	−	11.5093i	0.793590	−	0.458180i	−0.0476346	−	0.998865i	$-0.515168\pi$
$631$	19.9348	−	11.5093i	0.793590	−	0.458180i	0.841225	+	0.540685i	$0.181835\pi$
$632$			6.53349i			0.259888i
$633$	22.1187	+	38.3108i	0.879141	+	1.52272i
$634$	1.88124	−	3.25840i	0.0747135	−	0.129408i
$635$	−15.2404	−	8.79907i	−0.604798	−	0.349181i
$636$	−3.88743			−0.154147
$637$	2.88710	+	2.15978i	0.114391	+	0.0855737i
$638$	−9.51078			−0.376536
$639$	6.38194	+	3.68461i	0.252466	+	0.145761i
$640$	0.450919	−	0.781015i	0.0178242	−	0.0308723i
$641$	6.32539	+	10.9559i	0.249838	+	0.432732i	0.963481	−	0.267778i	$-0.0862893\pi$
$641$	6.32539	+	10.9559i	0.249838	+	0.432732i	−0.713643	+	0.700510i	$0.752956\pi$
$642$		−	31.2762i		−	1.23437i
$643$	−13.1971	+	7.61938i	−0.520445	+	0.300479i	−0.737117	−	0.675766i	$-0.763813\pi$
$643$	−13.1971	+	7.61938i	−0.520445	+	0.300479i	0.216672	+	0.976244i	$0.430480\pi$
$644$	7.31893	−	4.22559i	0.288406	−	0.166511i
$645$		−	15.9252i		−	0.627053i
$646$	15.6344	+	27.0796i	0.615127	+	1.06543i
$647$	−14.6821	+	25.4301i	−0.577213	+	0.999762i	0.418585	+	0.908178i	$0.362526\pi$
$647$	−14.6821	+	25.4301i	−0.577213	+	0.999762i	−0.995797	+	0.0915840i	$0.970807\pi$
$648$	9.25862	+	5.34547i	0.363713	+	0.209990i
$649$	37.0799			1.45551
$650$	−9.04233	+	12.0874i	−0.354669	+	0.474106i
$651$	−2.00000			−0.0783862
$652$	17.5958	+	10.1589i	0.689105	+	0.397855i
$653$	14.5106	−	25.1330i	0.567842	−	0.983532i	−0.428937	−	0.903335i	$-0.641112\pi$
$653$	14.5106	−	25.1330i	0.567842	−	0.983532i	0.996779	−	0.0801974i	$-0.0255551\pi$
$654$	−5.86152	−	10.1524i	−0.229204	−	0.396992i
$655$		−	18.6226i		−	0.727647i
$656$	3.46110	−	1.99827i	0.135133	−	0.0780192i
$657$	1.04925	−	0.605782i	0.0409350	−	0.0236338i
$658$		−	2.92115i		−	0.113878i
$659$	−3.98651	−	6.90484i	−0.155293	−	0.268975i	0.777873	−	0.628422i	$-0.216299\pi$
$659$	−3.98651	−	6.90484i	−0.155293	−	0.268975i	−0.933166	+	0.359447i	$0.882965\pi$
$660$	−4.48012	+	7.75979i	−0.174388	+	0.302049i
$661$	3.40668	+	1.96685i	0.132505	+	0.0765015i	0.564787	−	0.825237i	$-0.308958\pi$
$661$	3.40668	+	1.96685i	0.132505	+	0.0765015i	−0.432282	+	0.901738i	$0.642292\pi$
$662$	−32.2257			−1.25249
$663$	4.95387	−	41.5479i	0.192392	−	1.61359i
$664$	13.2348			0.513611
$665$	4.82072	+	2.78325i	0.186940	+	0.107930i
$666$	0.162179	−	0.280902i	0.00628430	−	0.0108847i
$667$	−9.26611	−	16.0494i	−0.358785	−	0.621434i
$668$		−	3.23051i		−	0.124992i
$669$	21.1000	−	12.1821i	0.815772	−	0.470986i
$670$	8.10916	−	4.68182i	0.313284	−	0.180875i
$671$			36.1477i			1.39547i
$672$	−1.14539	−	1.98388i	−0.0441845	−	0.0765298i
$673$	18.1599	−	31.4539i	0.700014	−	1.21246i	−0.268447	−	0.963295i	$-0.586510\pi$
$673$	18.1599	−	31.4539i	0.700014	−	1.21246i	0.968461	−	0.249166i	$-0.0801563\pi$
$674$	−2.61282	−	1.50851i	−0.100642	−	0.0581058i
$675$	−7.21513			−0.277710
$676$	−3.67069	−	12.4710i	−0.141180	−	0.479654i
$677$	−21.1068			−0.811201			−0.405600	−	0.914051i	$-0.632938\pi$
$677$	−21.1068			−0.811201			−0.405600	+	0.914051i	$0.632938\pi$
$678$	35.5750	+	20.5393i	1.36625	+	0.788805i
$679$	5.85305	−	10.1378i	0.224619	−	0.389052i
$680$	−2.28432	−	3.95656i	−0.0875997	−	0.151727i
$681$			52.0506i			1.99458i
$682$	3.27931	−	1.89331i	0.125571	−	0.0724985i
$683$	−22.8854	+	13.2129i	−0.875685	+	0.505577i	−0.869233	−	0.494402i	$-0.835387\pi$
$683$	−22.8854	+	13.2129i	−0.875685	+	0.505577i	−0.00645161	+	0.999979i	$0.502054\pi$
$684$		−	13.8737i		−	0.530474i
$685$	1.43824	+	2.49110i	0.0549522	+	0.0951799i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−40.2914	−	23.2623i	−1.53721	−	0.887511i
$688$	−7.70851			−0.293884
$689$	−0.724402	+	6.07553i	−0.0275975	+	0.231459i
$690$	−17.4594			−0.664670
$691$	0.675291	+	0.389880i	0.0256893	+	0.0148317i	0.512790	−	0.858514i	$-0.328612\pi$
$691$	0.675291	+	0.389880i	0.0256893	+	0.0148317i	−0.487100	+	0.873346i	$0.661945\pi$
$692$	4.58522	−	7.94183i	0.174304	−	0.301903i
$693$	4.87433	+	8.44259i	0.185161	+	0.320707i
$694$		−	0.468540i		−	0.0177855i
$695$	−0.465259	+	0.268617i	−0.0176483	+	0.0101892i
$696$	−4.35037	+	2.51168i	−0.164900	+	0.0952052i
$697$		−	20.2461i		−	0.766877i
$698$	−16.1106	−	27.9044i	−0.609795	−	1.05620i
$699$	−12.1923	+	21.1176i	−0.461154	+	0.798742i
$700$	3.62578	+	2.09334i	0.137041	+	0.0791209i
$701$	21.5491			0.813899			0.406950	−	0.913451i	$-0.366592\pi$
$701$	21.5491			0.813899			0.406950	+	0.913451i	$0.366592\pi$
$702$	3.72206	−	4.97548i	0.140480	−	0.187787i
$703$	0.890713			0.0335939
$704$	3.75609	+	2.16858i	0.141563	+	0.0817315i
$705$	−3.01743	+	5.22634i	−0.113643	+	0.196835i
$706$	−6.55771	−	11.3583i	−0.246803	−	0.427474i
$707$			10.7429i			0.404028i
$708$	16.9608	−	9.79235i	0.637428	−	0.368019i
$709$	−3.92952	+	2.26871i	−0.147576	+	0.0852031i	−0.571970	−	0.820275i	$-0.693821\pi$
$709$	−3.92952	+	2.26871i	−0.147576	+	0.0852031i	0.424394	+	0.905478i	$0.360487\pi$
$710$		−	2.95673i		−	0.110964i
$711$	−7.34267	−	12.7179i	−0.275372	−	0.476958i
$712$	3.89590	−	6.74790i	0.146005	−	0.252888i
$713$	6.38988	+	3.68920i	0.239303	+	0.138162i
$714$	−11.6049			−0.434304
$715$	11.2927	+	8.44782i	0.422322	+	0.315931i
$716$	−16.9549			−0.633636
$717$	0.618106	+	0.356863i	0.0230836	+	0.0133273i
$718$	−2.18990	+	3.79302i	−0.0817265	+	0.141554i
$719$	−7.30036	−	12.6446i	−0.272258	−	0.471564i	0.697182	−	0.716894i	$-0.254437\pi$
$719$	−7.30036	−	12.6446i	−0.272258	−	0.471564i	−0.969440	+	0.245330i	$0.921104\pi$
$720$			2.02707i			0.0755443i
$721$	4.16644	−	2.40550i	0.155166	−	0.0895854i
$722$	16.5396	−	9.54914i	0.615540	−	0.355382i
$723$		−	57.9558i		−	2.15540i
$724$	−1.32871	−	2.30140i	−0.0493813	−	0.0855309i
$725$	4.59040	−	7.95081i	0.170483	−	0.295286i
$726$	−15.4961	−	8.94666i	−0.575113	−	0.332042i
$727$	30.6315			1.13606			0.568030	−	0.823008i	$-0.307706\pi$
$727$	30.6315			1.13606			0.568030	+	0.823008i	$0.307706\pi$
$728$	−3.31398	+	1.42041i	−0.122824	+	0.0526439i
$729$	−12.1866			−0.451355
$730$	−0.420985	−	0.243056i	−0.0155814	−	0.00899590i
$731$	−19.5254	+	33.8189i	−0.722171	+	1.25084i
$732$	9.54617	+	16.5344i	0.352837	+	0.611131i
$733$			17.7195i			0.654484i	0.944941	+	0.327242i	$0.106119\pi$
$733$			17.7195i			0.654484i	−0.944941	+	0.327242i	$0.893881\pi$
$734$	−22.3597	+	12.9094i	−0.825313	+	0.476495i
$735$	−1.78914	+	1.03296i	−0.0659934	+	0.0381013i
$736$			8.45117i			0.311514i
$737$	22.5160	+	38.9989i	0.829389	+	1.43654i
$738$	−4.49151	+	7.77953i	−0.165335	+	0.286368i
$739$	−9.05014	−	5.22510i	−0.332915	−	0.192208i	0.324220	−	0.945982i	$-0.394898\pi$
$739$	−9.05014	−	5.22510i	−0.332915	−	0.192208i	−0.657134	+	0.753773i	$0.728232\pi$
$740$	−0.130141			−0.00478408
$741$	−50.6225	−	6.03586i	−1.85966	−	0.221733i
$742$	1.69699			0.0622983
$743$	42.0103	+	24.2547i	1.54121	+	0.889818i	0.998763	+	0.0497278i	$0.0158354\pi$
$743$	42.0103	+	24.2547i	1.54121	+	0.889818i	0.542447	+	0.840090i	$0.317498\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$	5.05464	+	8.75490i	0.185188	+	0.320755i
$746$		−	30.6285i		−	1.12139i
$747$	−25.7625	+	14.8740i	−0.942601	+	0.544211i
$748$	19.0281	−	10.9859i	0.695735	−	0.401683i
$749$			13.6530i			0.498871i
$750$	−9.48948	−	16.4363i	−0.346507	−	0.600168i
$751$	15.7278	−	27.2413i	0.573914	−	0.994049i	−0.422244	−	0.906482i	$-0.638758\pi$
$751$	15.7278	−	27.2413i	0.573914	−	0.994049i	0.996159	−	0.0875667i	$-0.0279091\pi$
$752$	2.52979	+	1.46057i	0.0922519	+	0.0532617i
$753$	−18.4186			−0.671212
$754$	3.11476	+	7.26708i	0.113433	+	0.264651i
$755$	11.7898			0.429075
$756$	−1.49246	−	0.861675i	−0.0542804	−	0.0313388i
$757$	−24.3442	+	42.1654i	−0.884805	+	1.53253i	−0.0388676	+	0.999244i	$0.512375\pi$
$757$	−24.3442	+	42.1654i	−0.884805	+	1.53253i	−0.845937	+	0.533283i	$0.820958\pi$
$758$	−19.0762	−	33.0409i	−0.692877	−	1.20010i
$759$		−	83.9668i		−	3.04780i
$760$	−4.82072	+	2.78325i	−0.174866	+	0.100959i
$761$	−40.3350	+	23.2874i	−1.46214	+	0.844169i	−0.999110	−	0.0421718i	$-0.986572\pi$
$761$	−40.3350	+	23.2874i	−1.46214	+	0.844169i	−0.463033	+	0.886341i	$0.653239\pi$
$762$		−	44.7016i		−	1.61937i
$763$	2.55874	+	4.43186i	0.0926325	+	0.160444i
$764$	−12.2430	+	21.2056i	−0.442937	+	0.767190i
$765$	8.89318	+	5.13448i	0.321534	+	0.185637i
$766$	−31.9602			−1.15477
$767$	−12.1436	−	28.3323i	−0.438479	−	1.02302i
$768$	2.29079			0.0826616
$769$	−24.1069	−	13.9181i	−0.869315	−	0.501899i	−0.00219468	−	0.999998i	$-0.500699\pi$
$769$	−24.1069	−	13.9181i	−0.869315	−	0.501899i	−0.867121	+	0.498098i	$0.834032\pi$
$770$	1.95571	−	3.38739i	0.0704789	−	0.122073i
$771$	−19.3946	−	33.5924i	−0.698479	−	1.20980i
$772$			12.2409i			0.440560i
$773$	24.6578	−	14.2362i	0.886880	−	0.512040i	0.0139594	−	0.999903i	$-0.495556\pi$
$773$	24.6578	−	14.2362i	0.886880	−	0.512040i	0.872921	+	0.487862i	$0.162223\pi$
$774$	15.0051	−	8.66323i	0.539349	−	0.311393i
$775$			3.65524i			0.131300i
$776$	5.85305	+	10.1378i	0.210112	+	0.363925i
$777$	−0.165287	+	0.286286i	−0.00592965	+	0.0102705i
$778$	4.54304	+	2.62292i	0.162876	+	0.0940364i
$779$	−24.6681			−0.883828
$780$	7.39639	+	0.881892i	0.264833	+	0.0315768i
$781$	14.2196			0.508819
$782$	37.0771	+	21.4065i	1.32587	+	0.765494i
$783$	−1.88953	+	3.27276i	−0.0675263	+	0.116959i
$784$	0.500000	+	0.866025i	0.0178571	+	0.0309295i
$785$			16.1650i			0.576954i
$786$	40.9664	−	23.6520i	1.46122	−	0.843637i
$787$	13.1046	−	7.56594i	0.467128	−	0.269697i	−0.247908	−	0.968783i	$-0.579743\pi$
$787$	13.1046	−	7.56594i	0.467128	−	0.269697i	0.715037	+	0.699087i	$0.246410\pi$
$788$			5.45751i			0.194416i
$789$	−11.8215	−	20.4754i	−0.420856	−	0.728945i
$790$	−2.94608	+	5.10275i	−0.104817	+	0.181548i
$791$	−15.5296	−	8.96603i	−0.552170	−	0.318795i
$792$	−9.74866			−0.346404
$793$	27.6200	−	11.8383i	0.980815	−	0.420389i
$794$	24.5296			0.870522
$795$	−3.03614	−	1.75292i	−0.107681	−	0.0621696i
$796$	6.40832	−	11.0995i	0.227137	−	0.393413i
$797$	6.97234	+	12.0764i	0.246973	+	0.427770i	0.962684	−	0.270626i	$-0.0872308\pi$
$797$	6.97234	+	12.0764i	0.246973	+	0.427770i	−0.715712	+	0.698396i	$0.753897\pi$
$798$			14.1396i			0.500537i
$799$	12.8157	−	7.39916i	0.453387	−	0.261763i
$800$	−3.62578	+	2.09334i	−0.128191	+	0.0740109i
$801$			17.5137i			0.618815i
$802$	2.13571	+	3.69916i	0.0754147	+	0.130622i
$803$	1.16892	−	2.02462i	0.0412501	−	0.0714473i
$804$	20.5983	+	11.8924i	0.726446	+	0.419414i
$805$	7.62159			0.268626
$806$	−2.52062	−	1.88562i	−0.0887850	−	0.0664183i
$807$	−14.0654			−0.495125
$808$	−9.30362	−	5.37145i	−0.327300	−	0.188967i
$809$	10.8714	−	18.8299i	0.382220	−	0.662024i	−0.609159	−	0.793048i	$-0.708493\pi$
$809$	10.8714	−	18.8299i	0.382220	−	0.662024i	0.991379	+	0.131024i	$0.0418264\pi$
$810$	4.82075	+	8.34979i	0.169384	+	0.293382i
$811$			21.1256i			0.741819i	0.928669	+	0.370910i	$0.120954\pi$
$811$			21.1256i			0.741819i	−0.928669	+	0.370910i	$0.879046\pi$
$812$	1.89907	−	1.09643i	0.0666443	−	0.0384771i
$813$	−21.1823	+	12.2296i	−0.742895	+	0.428911i
$814$		−	0.625880i		−	0.0219371i
$815$	9.16173	+	15.8686i	0.320921	+	0.555852i
$816$	5.80247	−	10.0502i	0.203127	−	0.351827i
$817$	41.2054	+	23.7899i	1.44159	+	0.832304i
$818$	−1.61647			−0.0565185
$819$	4.85455	−	6.48935i	0.169632	−	0.226756i
$820$	3.60423			0.125865
$821$	−14.0933	−	8.13678i	−0.491860	−	0.283976i	0.233486	−	0.972360i	$-0.424987\pi$
$821$	−14.0933	−	8.13678i	−0.491860	−	0.283976i	−0.725346	+	0.688385i	$0.758320\pi$
$822$	−3.65330	+	6.32771i	−0.127424	+	0.220704i
$823$	9.32713	+	16.1551i	0.325123	+	0.563130i	0.981537	−	0.191271i	$-0.0612609\pi$
$823$	9.32713	+	16.1551i	0.325123	+	0.563130i	−0.656414	+	0.754401i	$0.727928\pi$
$824$			4.81099i			0.167599i
$825$	36.0240	−	20.7985i	1.25419	−	0.724109i
$826$	−7.40394	+	4.27467i	−0.257616	+	0.148735i
$827$			47.3361i			1.64604i	0.568015	+	0.823018i	$0.307712\pi$
$827$			47.3361i			1.64604i	−0.568015	+	0.823018i	$0.692288\pi$
$828$	−9.49787	−	16.4508i	−0.330074	−	0.571704i
$829$	0.460988	−	0.798454i	0.0160108	−	0.0277315i	−0.857909	−	0.513802i	$-0.828237\pi$
$829$	0.460988	−	0.798454i	0.0160108	−	0.0277315i	0.873920	+	0.486070i	$0.161570\pi$
$830$	10.3366	+	5.96784i	0.358789	+	0.207147i
$831$	−50.1888			−1.74103
$832$	0.426876	−	3.58019i	0.0147993	−	0.124121i
$833$	5.06592			0.175524
$834$	−1.18182	−	0.682322i	−0.0409230	−	0.0236269i
$835$	1.45670	−	2.52307i	0.0504111	−	0.0873146i
$836$	−13.3853	−	23.1840i	−0.462941	−	0.801837i
$837$		−	1.50459i		−	0.0520063i
$838$	22.5437	−	13.0156i	0.778758	−	0.449616i
$839$	−14.3894	+	8.30775i	−0.496779	+	0.286815i	−0.727382	−	0.686232i	$-0.759263\pi$
$839$	−14.3894	+	8.30775i	−0.496779	+	0.286815i	0.230604	+	0.973048i	$0.425930\pi$
$840$		−	2.06592i		−	0.0712810i
$841$	12.0957	+	20.9503i	0.417093	+	0.722426i
$842$	−18.7696	+	32.5098i	−0.646841	+	1.12036i
$843$	51.1284	+	29.5190i	1.76096	+	1.01669i
$844$	19.3110			0.664713
$845$	2.75656	−	11.3952i	0.0948284	−	0.392008i
$846$	−6.56588			−0.225740
$847$	6.76452	+	3.90550i	0.232432	+	0.134194i
$848$	−0.848493	+	1.46963i	−0.0291374	+	0.0504674i
$849$	−12.9737	−	22.4712i	−0.445258	−	0.771209i
$850$			21.2094i			0.727477i
$851$	1.05617	−	0.609779i	0.0362050	−	0.0209029i
$852$	6.50427	−	3.75524i	0.222832	−	0.128652i
$853$		−	26.3277i		−	0.901445i	−0.892664	−	0.450722i	$-0.851166\pi$
$853$		−	26.3277i		−	0.901445i	0.892664	−	0.450722i	$-0.148834\pi$
$854$	−4.16720	−	7.21780i	−0.142599	−	0.246988i
$855$	6.25591	−	10.8356i	0.213948	−	0.370568i
$856$	−11.8239	−	6.82652i	−0.404132	−	0.233325i
$857$	14.1058			0.481845			0.240923	−	0.970544i	$-0.422550\pi$
$857$	14.1058			0.481845			0.240923	+	0.970544i	$0.422550\pi$
$858$	−4.24123	+	35.5711i	−0.144793	+	1.21438i
$859$	23.4719			0.800850			0.400425	−	0.916329i	$-0.368862\pi$
$859$	23.4719			0.800850			0.400425	+	0.916329i	$0.368862\pi$
$860$	−6.02046	−	3.47592i	−0.205296	−	0.118528i
$861$	4.57761	−	7.92864i	0.156004	−	0.270207i
$862$	10.7769	+	18.6662i	0.367063	+	0.635772i
$863$			11.9484i			0.406727i	0.979103	+	0.203364i	$0.0651874\pi$
$863$			11.9484i			0.406727i	−0.979103	+	0.203364i	$0.934813\pi$
$864$	1.49246	−	0.861675i	0.0507747	−	0.0293148i
$865$	7.16225	−	4.13513i	0.243524	−	0.140599i
$866$			3.19917i			0.108712i
$867$	−9.92317	−	17.1874i	−0.337009	−	0.583716i
$868$	−0.436531	+	0.756094i	−0.0148168	+	0.0256635i
$869$	−24.5404	−	14.1684i	−0.832476	−	0.480630i
$870$	−4.53027			−0.153591
$871$	22.4247	−	29.9763i	0.759831	−	1.01571i
$872$	−5.11747			−0.173299
$873$	−22.7867	−	13.1559i	−0.771214	−	0.445261i
$874$	26.0819	−	45.1752i	0.882234	−	1.52807i
$875$	4.14246	+	7.17494i	0.140041	+	0.242557i
$876$		−	1.23479i		−	0.0417196i
$877$	−28.3486	+	16.3671i	−0.957264	+	0.552677i	−0.895330	−	0.445403i	$-0.853060\pi$
$877$	−28.3486	+	16.3671i	−0.957264	+	0.552677i	−0.0619342	+	0.998080i	$0.519727\pi$
$878$	23.0560	−	13.3114i	0.778101	−	0.449237i
$879$			54.3969i			1.83476i
$880$	1.95571	+	3.38739i	0.0659270	+	0.114189i
$881$	−5.29540	+	9.17190i	−0.178407	+	0.309009i	−0.941335	−	0.337474i	$-0.890428\pi$
$881$	−5.29540	+	9.17190i	−0.178407	+	0.309009i	0.762928	+	0.646483i	$0.223761\pi$
$882$	−1.94657	−	1.12385i	−0.0655444	−	0.0378421i
$883$	−38.6713			−1.30139			−0.650696	−	0.759338i	$-0.725523\pi$
$883$	−38.6713			−1.30139			−0.650696	+	0.759338i	$0.725523\pi$
$884$	−14.6258	−	10.9413i	−0.491919	−	0.367995i
$885$	17.6622			0.593710
$886$	7.87968	+	4.54933i	0.264723	+	0.152838i
$887$	−2.36082	+	4.08906i	−0.0792685	+	0.137297i	−0.902935	−	0.429778i	$-0.858592\pi$
$887$	−2.36082	+	4.08906i	−0.0792685	+	0.137297i	0.823666	+	0.567075i	$0.191925\pi$
$888$	−0.165287	−	0.286286i	−0.00554668	−	0.00960714i
$889$			19.5136i			0.654466i
$890$	6.08551	−	3.51347i	0.203987	−	0.117772i
$891$	−40.1562	+	23.1842i	−1.34528	+	0.776699i
$892$		−	10.6357i		−	0.356110i
$893$	−9.01522	−	15.6148i	−0.301683	−	0.522530i
$894$	−12.8394	+	22.2386i	−0.429415	+	0.743769i
$895$	−13.2421	−	7.64531i	−0.442634	−	0.255555i
$896$	−1.00000			−0.0334077
$897$	−64.1580	+	27.4989i	−2.14217	+	0.918162i
$898$	7.02693			0.234492
$899$	1.65801	+	0.957251i	0.0552976	+	0.0319261i
$900$	4.70522	−	8.14967i	0.156841	−	0.271656i
$901$	4.29840	+	7.44504i	0.143200	+	0.248030i
$902$			17.3336i			0.577147i
$903$	−15.2928	+	8.82928i	−0.508911	+	0.293820i
$904$	15.5296	−	8.96603i	0.516507	−	0.298206i
$905$		−	2.39657i		−	0.0796648i
$906$	14.9738	+	25.9354i	0.497471	+	0.861646i
$907$	−20.9654	+	36.3132i	−0.696146	+	1.20576i	0.273646	+	0.961830i	$0.411770\pi$
$907$	−20.9654	+	36.3132i	−0.696146	+	1.20576i	−0.969793	+	0.243930i	$0.921563\pi$
$908$	19.6776	+	11.3609i	0.653023	+	0.377023i
$909$	24.1468			0.800900
$910$	−3.22876	−	0.384973i	−0.107032	−	0.0127617i
$911$	−54.1425			−1.79382			−0.896910	−	0.442213i	$-0.854194\pi$
$911$	−54.1425			−1.79382			−0.896910	+	0.442213i	$0.854194\pi$
$912$	−12.2453	−	7.06980i	−0.405481	−	0.234105i
$913$	−28.7008	+	49.7113i	−0.949859	+	1.64520i
$914$	−9.57556	−	16.5853i	−0.316731	−	0.548595i
$915$			17.2182i			0.569216i
$916$	−17.5885	+	10.1547i	−0.581139	+	0.335521i
$917$	−17.8831	+	10.3248i	−0.590552	+	0.340956i
$918$		−	8.73035i		−	0.288145i
$919$	12.9117	+	22.3636i	0.425916	+	0.737708i	0.996506	−	0.0835271i	$-0.0266185\pi$
$919$	12.9117	+	22.3636i	0.425916	+	0.737708i	−0.570589	+	0.821236i	$0.693285\pi$
$920$	−3.81080	+	6.60049i	−0.125638	+	0.217612i
$921$	13.2684	+	7.66051i	0.437208	+	0.252422i
$922$	−3.25656			−0.107249
$923$	−4.65690	−	10.8651i	−0.153284	−	0.357628i
$924$	9.93552			0.326855
$925$	0.523222	+	0.302083i	0.0172034	+	0.00993241i
$926$	−10.6381	+	18.4257i	−0.349589	+	0.605506i
$927$	−5.40684	−	9.36493i	−0.177584	−	0.307585i
$928$			2.19286i			0.0719841i
$929$	13.8843	−	8.01610i	0.455529	−	0.263000i	−0.254633	−	0.967038i	$-0.581955\pi$
$929$	13.8843	−	8.01610i	0.455529	−	0.263000i	0.710162	+	0.704038i	$0.248621\pi$
$930$	1.56203	−	0.901839i	0.0512210	−	0.0295725i
$931$		−	6.17238i		−	0.202292i
$932$	5.32231	+	9.21851i	0.174338	+	0.301962i
$933$	−10.5230	+	18.2264i	−0.344508	+	0.596705i
$934$	−2.88535	−	1.66586i	−0.0944115	−	0.0545085i
$935$	19.8150			0.648018
$936$	3.19266	+	7.44884i	0.104355	+	0.243473i
$937$	47.0232			1.53618			0.768091	−	0.640340i	$-0.221207\pi$
$937$	47.0232			1.53618			0.768091	+	0.640340i	$0.221207\pi$
$938$	−8.99180	−	5.19142i	−0.293593	−	0.169506i
$939$	19.6586	−	34.0496i	0.641533	−	1.11117i
$940$	1.31720	+	2.28146i	0.0429624	+	0.0744131i
$941$		−	52.8569i		−	1.72308i	−0.507686	−	0.861542i	$-0.669499\pi$
$941$		−	52.8569i		−	1.72308i	0.507686	−	0.861542i	$-0.330501\pi$
$942$	−35.5601	+	20.5306i	−1.15861	+	0.668923i
$943$	−29.2504	+	16.8877i	−0.952523	+	0.549939i
$944$		−	8.54933i		−	0.278257i
$945$	−0.777092	−	1.34596i	−0.0252788	−	0.0437842i
$946$	16.7165	−	28.9539i	0.543502	−	0.941372i
$947$	−33.4029	−	19.2852i	−1.08545	−	0.626684i	−0.153088	−	0.988213i	$-0.548922\pi$
$947$	−33.4029	−	19.2852i	−1.08545	−	0.626684i	−0.932361	+	0.361528i	$0.882255\pi$
$948$	−14.9668			−0.486100
$949$	−1.92981	−	0.230096i	−0.0626441	−	0.00746923i
$950$	25.8418			0.838419
$951$	7.46430	+	4.30951i	0.242046	+	0.139746i
$952$	−2.53296	+	4.38722i	−0.0820937	+	0.142190i
$953$	13.6505	+	23.6433i	0.442182	+	0.765882i	0.997851	−	0.0655217i	$-0.0208711\pi$
$953$	13.6505	+	23.6433i	0.442182	+	0.765882i	−0.555669	+	0.831404i	$0.687538\pi$
$954$		−	3.81432i		−	0.123493i
$955$	−19.1240	+	11.0412i	−0.618838	+	0.357286i
$956$	0.269822	−	0.155782i	0.00872668	−	0.00503835i
$957$		−	21.7872i		−	0.704279i
$958$	−0.0926079	−	0.160402i	−0.00299203	−	0.00518234i
$959$	1.59478	−	2.76224i	0.0514982	−	0.0891975i
$960$	1.78914	+	1.03296i	0.0577442	+	0.0333386i
$961$	30.2378			0.975412
$962$	−0.478227	+	0.204974i	−0.0154187	+	0.00660863i
$963$	30.6880			0.988906
$964$	−21.9100	−	12.6498i	−0.705674	−	0.407421i
$965$	−5.51966	+	9.56034i	−0.177684	+	0.307758i
$966$	9.67992	+	16.7661i	0.311446	+	0.539441i
$967$		−	25.2494i		−	0.811966i	−0.913881	−	0.405983i	$-0.866929\pi$
$967$		−	25.2494i		−	0.811966i	0.913881	−	0.405983i	$-0.133071\pi$
$968$	−6.76452	+	3.90550i	−0.217420	+	0.125527i
$969$	−62.0335	+	35.8151i	−1.99280	+	1.15055i
$970$			10.5570i			0.338965i
$971$	3.28682	+	5.69294i	0.105479	+	0.182695i	0.913934	−	0.405863i	$-0.133029\pi$
$971$	3.28682	+	5.69294i	0.105479	+	0.182695i	−0.808455	+	0.588558i	$0.799696\pi$
$972$	−9.66031	+	16.7321i	−0.309854	+	0.536684i
$973$	0.515900	+	0.297855i	0.0165390	+	0.00954879i
$974$	−31.2308			−1.00070
$975$	−27.6896	−	20.7140i	−0.886777	−	0.663380i
$976$	8.33440			0.266778
$977$	12.0773	+	6.97285i	0.386388	+	0.223081i	0.680594	−	0.732661i	$-0.261722\pi$
$977$	12.0773	+	6.97285i	0.386388	+	0.223081i	−0.294206	+	0.955742i	$0.595055\pi$
$978$	−23.2720	+	40.3083i	−0.744156	+	1.28892i
$979$	16.8972	+	29.2667i	0.540036	+	0.935369i
$980$			0.901839i			0.0288082i
$981$	9.96151	−	5.75128i	0.318047	−	0.183624i
$982$	23.2504	−	13.4236i	0.741949	−	0.428365i
$983$			47.1390i			1.50350i	0.659449	+	0.751750i	$0.270790\pi$
$983$			47.1390i			1.50350i	−0.659449	+	0.751750i	$0.729210\pi$
$984$	4.57761	+	7.92864i	0.145929	+	0.252756i
$985$	−2.46090	+	4.26240i	−0.0784107	+	0.135811i
$986$	9.62054	+	5.55442i	0.306380	+	0.176889i
$987$	6.69173			0.213000
$988$	−13.3310	+	17.8203i	−0.424115	+	0.566939i
$989$	65.1459			2.07152
$990$	−7.61385	−	4.39586i	−0.241984	−	0.139710i
$991$	−4.70805	+	8.15458i	−0.149556	+	0.259039i	−0.931063	−	0.364857i	$-0.881118\pi$
$991$	−4.70805	+	8.15458i	−0.149556	+	0.259039i	0.781507	+	0.623896i	$0.214451\pi$
$992$	−0.436531	−	0.756094i	−0.0138599	−	0.0240060i
$993$		−	73.8223i		−	2.34268i
$994$	−2.83932	+	1.63928i	−0.0900576	+	0.0519948i
$995$	10.0100	−	5.77927i	0.317338	−	0.183215i
$996$			30.3182i			0.960669i
$997$	−20.2607	−	35.0926i	−0.641664	−	1.11139i	−0.985061	−	0.172204i	$-0.944911\pi$
$997$	−20.2607	−	35.0926i	−0.641664	−	1.11139i	0.343398	−	0.939190i	$-0.388422\pi$
$998$	7.64346	−	13.2389i	0.241950	−	0.419069i
$999$	−0.215372	−	0.124345i	−0.00681407	−	0.00393410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.2.m.b.43.4	✓	12
3.2	odd	2		1638.2.bj.g.1135.2		12
4.3	odd	2		1456.2.cc.d.225.5		12
7.2	even	3		1274.2.o.d.459.1		12
7.3	odd	6		1274.2.v.d.667.1		12
7.4	even	3		1274.2.v.e.667.3		12
7.5	odd	6		1274.2.o.e.459.3		12
7.6	odd	2		1274.2.m.c.589.6		12
13.4	even	6		2366.2.d.r.337.11		12
13.6	odd	12		2366.2.a.bf.1.5		6
13.7	odd	12		2366.2.a.bh.1.5		6
13.9	even	3		2366.2.d.r.337.5		12
13.10	even	6	inner	182.2.m.b.127.4	yes	12
39.23	odd	6		1638.2.bj.g.127.2		12
52.23	odd	6		1456.2.cc.d.673.5		12
91.10	odd	6		1274.2.o.e.569.6		12
91.23	even	6		1274.2.v.e.361.3		12
91.62	odd	6		1274.2.m.c.491.6		12
91.75	odd	6		1274.2.v.d.361.1		12
91.88	even	6		1274.2.o.d.569.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.4	✓	12	1.1	even	1	trivial
182.2.m.b.127.4	yes	12	13.10	even	6	inner
1274.2.m.c.491.6		12	91.62	odd	6
1274.2.m.c.589.6		12	7.6	odd	2
1274.2.o.d.459.1		12	7.2	even	3
1274.2.o.d.569.4		12	91.88	even	6
1274.2.o.e.459.3		12	7.5	odd	6
1274.2.o.e.569.6		12	91.10	odd	6
1274.2.v.d.361.1		12	91.75	odd	6
1274.2.v.d.667.1		12	7.3	odd	6
1274.2.v.e.361.3		12	91.23	even	6
1274.2.v.e.667.3		12	7.4	even	3
1456.2.cc.d.225.5		12	4.3	odd	2
1456.2.cc.d.673.5		12	52.23	odd	6
1638.2.bj.g.127.2		12	39.23	odd	6
1638.2.bj.g.1135.2		12	3.2	odd	2
2366.2.a.bf.1.5		6	13.6	odd	12
2366.2.a.bh.1.5		6	13.7	odd	12
2366.2.d.r.337.5		12	13.9	even	3
2366.2.d.r.337.11		12	13.4	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:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.14539 + 1.98388i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.901839i q^{5} +(-1.98388 + 1.14539i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.14539 + 1.98388i) q^{3} +(0.500000 + 0.866025i) q^{4} +0.901839i q^{5} +(-1.98388 + 1.14539i) q^{6} +(0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-1.12385 - 1.94657i) q^{9} +(-0.450919 + 0.781015i) q^{10} +(-3.75609 - 2.16858i) q^{11} -2.29079 q^{12} +(-0.426876 + 3.58019i) q^{13} +1.00000 q^{14} +(-1.78914 - 1.03296i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.53296 + 4.38722i) q^{17} -2.24770i q^{18} +(5.34544 - 3.08619i) q^{19} +(-0.781015 + 0.450919i) q^{20} +2.29079i q^{21} +(-2.16858 - 3.75609i) q^{22} +(4.22559 - 7.31893i) q^{23} +(-1.98388 - 1.14539i) q^{24} +4.18669 q^{25} +(-2.15978 + 2.88710i) q^{26} -1.72335 q^{27} +(0.866025 + 0.500000i) q^{28} +(1.09643 - 1.89907i) q^{29} +(-1.03296 - 1.78914i) q^{30} +0.873062i q^{31} +(-0.866025 + 0.500000i) q^{32} +(8.60441 - 4.96776i) q^{33} +5.06592i q^{34} +(0.450919 + 0.781015i) q^{35} +(1.12385 - 1.94657i) q^{36} +(0.124973 + 0.0721531i) q^{37} +6.17238 q^{38} +(-6.61373 - 4.94760i) q^{39} -0.901839 q^{40} +(-3.46110 - 1.99827i) q^{41} +(-1.14539 + 1.98388i) q^{42} +(3.85426 + 6.67577i) q^{43} -4.33716i q^{44} +(1.75549 - 1.01353i) q^{45} +(7.31893 - 4.22559i) q^{46} -2.92115i q^{47} +(-1.14539 - 1.98388i) q^{48} +(0.500000 - 0.866025i) q^{49} +(3.62578 + 2.09334i) q^{50} -11.6049 q^{51} +(-3.31398 + 1.42041i) q^{52} +1.69699 q^{53} +(-1.49246 - 0.861675i) q^{54} +(1.95571 - 3.38739i) q^{55} +(0.500000 + 0.866025i) q^{56} +14.1396i q^{57} +(1.89907 - 1.09643i) q^{58} +(-7.40394 + 4.27467i) q^{59} -2.06592i q^{60} +(-4.16720 - 7.21780i) q^{61} +(-0.436531 + 0.756094i) q^{62} +(-1.94657 - 1.12385i) q^{63} -1.00000 q^{64} +(-3.22876 - 0.384973i) q^{65} +9.93552 q^{66} +(-8.99180 - 5.19142i) q^{67} +(-2.53296 + 4.38722i) q^{68} +(9.67992 + 16.7661i) q^{69} +0.901839i q^{70} +(-2.83932 + 1.63928i) q^{71} +(1.94657 - 1.12385i) q^{72} +0.539023i q^{73} +(0.0721531 + 0.124973i) q^{74} +(-4.79540 + 8.30588i) q^{75} +(5.34544 + 3.08619i) q^{76} -4.33716 q^{77} +(-3.25386 - 7.59161i) q^{78} +6.53349 q^{79} +(-0.781015 - 0.450919i) q^{80} +(5.34547 - 9.25862i) q^{81} +(-1.99827 - 3.46110i) q^{82} -13.2348i q^{83} +(-1.98388 + 1.14539i) q^{84} +(-3.95656 + 2.28432i) q^{85} +7.70851i q^{86} +(2.51168 + 4.35037i) q^{87} +(2.16858 - 3.75609i) q^{88} +(-6.74790 - 3.89590i) q^{89} +2.02707 q^{90} +(1.42041 + 3.31398i) q^{91} +8.45117 q^{92} +(-1.73205 - 1.00000i) q^{93} +(1.46057 - 2.52979i) q^{94} +(2.78325 + 4.82072i) q^{95} -2.29079i q^{96} +(10.1378 - 5.85305i) q^{97} +(0.866025 - 0.500000i) q^{98} +9.74866i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^9	\( 12 q - 2 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{9} - 2 q^{10} - 18 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{14} - 6 q^{15} - 6 q^{16} + 4 q^{17} + 12 q^{19} - 2 q^{22} - 6 q^{23} + 6 q^{24} - 24 q^{25} - 14 q^{26} + 40 q^{27} - 10 q^{29} + 14 q^{30} + 12 q^{33} + 2 q^{35} + 6 q^{36} - 6 q^{37} + 8 q^{38} - 54 q^{39} - 4 q^{40} - 24 q^{41} - 2 q^{42} + 26 q^{43} + 72 q^{45} - 6 q^{46} - 2 q^{48} + 6 q^{49} - 12 q^{50} - 36 q^{51} - 4 q^{52} + 36 q^{53} - 36 q^{54} - 6 q^{55} + 6 q^{56} + 24 q^{58} + 6 q^{59} - 28 q^{61} - 2 q^{62} - 12 q^{64} - 34 q^{65} - 42 q^{67} - 4 q^{68} + 32 q^{69} + 48 q^{71} - 48 q^{75} + 12 q^{76} - 4 q^{77} - 8 q^{78} + 44 q^{79} - 34 q^{81} + 6 q^{82} + 6 q^{84} + 54 q^{85} + 2 q^{87} + 2 q^{88} + 12 q^{89} + 12 q^{90} - 16 q^{91} - 12 q^{92} + 8 q^{94} + 32 q^{95} + 60 q^{97}+O(q^{100}) \) 12 * q - 2 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^9 - 2 * q^10 - 18 * q^11 - 4 * q^12 - 8 * q^13 + 12 * q^14 - 6 * q^15 - 6 * q^16 + 4 * q^17 + 12 * q^19 - 2 * q^22 - 6 * q^23 + 6 * q^24 - 24 * q^25 - 14 * q^26 + 40 * q^27 - 10 * q^29 + 14 * q^30 + 12 * q^33 + 2 * q^35 + 6 * q^36 - 6 * q^37 + 8 * q^38 - 54 * q^39 - 4 * q^40 - 24 * q^41 - 2 * q^42 + 26 * q^43 + 72 * q^45 - 6 * q^46 - 2 * q^48 + 6 * q^49 - 12 * q^50 - 36 * q^51 - 4 * q^52 + 36 * q^53 - 36 * q^54 - 6 * q^55 + 6 * q^56 + 24 * q^58 + 6 * q^59 - 28 * q^61 - 2 * q^62 - 12 * q^64 - 34 * q^65 - 42 * q^67 - 4 * q^68 + 32 * q^69 + 48 * q^71 - 48 * q^75 + 12 * q^76 - 4 * q^77 - 8 * q^78 + 44 * q^79 - 34 * q^81 + 6 * q^82 + 6 * q^84 + 54 * q^85 + 2 * q^87 + 2 * q^88 + 12 * q^89 + 12 * q^90 - 16 * q^91 - 12 * q^92 + 8 * q^94 + 32 * q^95 + 60 * q^97

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