LMFDB - Embedded newform 378.2.ba.a.47.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(47,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("378.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.ba (of order $18$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.17
Character	$\chi$	$=$	378.47
Dual form			378.2.ba.a.185.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-0.611133 + 1.62065i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-4.17040 - 1.51790i) q^{5} +(-0.883272 + 1.48991i) q^{6} +(-1.63543 - 2.07976i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.25303 - 1.98087i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-0.611133 + 1.62065i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-4.17040 - 1.51790i) q^{5} +(-0.883272 + 1.48991i) q^{6} +(-1.63543 - 2.07976i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.25303 - 1.98087i) q^{9} +(-3.84346 - 2.21902i) q^{10} +(-0.783948 - 2.15388i) q^{11} +(-1.12857 + 1.31390i) q^{12} +(-1.38518 + 3.80576i) q^{13} +(-1.24943 - 2.33215i) q^{14} +(5.00866 - 5.83113i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.86694 - 3.23363i) q^{17} +(-1.87483 - 2.34201i) q^{18} +(-5.69313 + 3.28693i) q^{19} +(-3.39974 - 2.85272i) q^{20} +(4.37002 - 1.37945i) q^{21} +(-0.398021 - 2.25729i) q^{22} +(-4.03640 + 0.711726i) q^{23} +(-1.33958 + 1.09796i) q^{24} +(11.2580 + 9.44655i) q^{25} +(-2.02500 + 3.50741i) q^{26} +(4.58720 - 2.44081i) q^{27} +(-0.825480 - 2.51368i) q^{28} +(-1.81552 - 4.98809i) q^{29} +(5.94513 - 4.87279i) q^{30} +(-0.0325436 + 0.0894127i) q^{31} +(0.642788 + 0.766044i) q^{32} +(3.96979 + 0.0457992i) q^{33} +(2.40009 - 2.86031i) q^{34} +(3.66351 + 11.1558i) q^{35} +(-1.43966 - 2.63199i) q^{36} -2.90601 q^{37} +(-6.17741 + 2.24839i) q^{38} +(-5.32129 - 4.57073i) q^{39} +(-2.85272 - 3.39974i) q^{40} +(-0.325419 - 0.118443i) q^{41} +(4.54317 - 0.599648i) q^{42} +(0.361225 - 2.04861i) q^{43} -2.29211i q^{44} +(6.38928 + 11.6809i) q^{45} -4.09867 q^{46} +(2.13553 - 0.777271i) q^{47} +(-1.50989 + 0.848664i) q^{48} +(-1.65076 + 6.80257i) q^{49} +(9.44655 + 11.2580i) q^{50} +(4.09964 + 5.00183i) q^{51} +(-2.60329 + 3.10248i) q^{52} +(-1.50502 + 0.868925i) q^{53} +(4.94136 - 1.60717i) q^{54} +10.1725i q^{55} +(-0.376443 - 2.61883i) q^{56} +(-1.84771 - 11.2353i) q^{57} +(-0.921762 - 5.22757i) q^{58} +(-9.34207 + 7.83893i) q^{59} +(6.70096 - 3.76640i) q^{60} +(-2.55352 - 7.01574i) q^{61} +(-0.0475755 + 0.0824032i) q^{62} +(-0.435054 + 7.92532i) q^{63} +(0.500000 + 0.866025i) q^{64} +(11.5535 - 13.7690i) q^{65} +(3.90152 + 0.734450i) q^{66} +(0.776252 + 4.40235i) q^{67} +(2.86031 - 2.40009i) q^{68} +(1.31332 - 6.97656i) q^{69} +(1.67067 + 11.6225i) q^{70} +(-3.12776 + 1.80581i) q^{71} +(-0.960749 - 2.84200i) q^{72} -13.5227i q^{73} +(-2.86186 - 0.504623i) q^{74} +(-22.1897 + 12.4721i) q^{75} +(-6.47399 + 1.14154i) q^{76} +(-3.19745 + 5.15293i) q^{77} +(-4.44674 - 5.42532i) q^{78} +(-0.353140 + 2.00276i) q^{79} +(-2.21902 - 3.84346i) q^{80} +(1.15231 + 8.92593i) q^{81} +(-0.299908 - 0.173152i) q^{82} +(0.970084 - 0.353082i) q^{83} +(4.57828 + 0.198376i) q^{84} +(-12.6942 + 10.6517i) q^{85} +(0.711474 - 1.95476i) q^{86} +(9.19349 + 0.106065i) q^{87} +(0.398021 - 2.25729i) q^{88} +(-3.13366 - 5.42765i) q^{89} +(4.26384 + 12.6129i) q^{90} +(10.1804 - 3.34320i) q^{91} +(-4.03640 - 0.711726i) q^{92} +(-0.125019 - 0.107385i) q^{93} +(2.23806 - 0.394631i) q^{94} +(28.7318 - 5.06620i) q^{95} +(-1.63432 + 0.573581i) q^{96} +(10.4891 + 1.84951i) q^{97} +(-2.80694 + 6.41257i) q^{98} +(-2.50029 + 6.40566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 18 q^{6} + 24 q^{9}+O(q^{10}) $ 144 * q - 18 * q^6 + 24 * q^9	$ 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51} - 90 q^{53} + 6 q^{56} - 6 q^{57} + 18 q^{60} + 54 q^{61} - 24 q^{63} + 72 q^{64} + 78 q^{65} - 72 q^{66} - 54 q^{68} + 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} - 36 q^{74} - 6 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 36 q^{91} - 42 q^{92} + 96 q^{93} - 66 q^{95} - 108 q^{99}+O(q^{100}) $ 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	−0.611133	+	1.62065i	−0.352838	+	0.935684i
$3$	−0.611133	+	1.62065i	−0.352838	+	0.935684i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	−4.17040	−	1.51790i	−1.86506	−	0.678825i	−0.974681	−	0.223601i	$-0.928219\pi$
$5$	−4.17040	−	1.51790i	−1.86506	−	0.678825i	−0.890377	−	0.455225i	$-0.849559\pi$
$6$	−0.883272	+	1.48991i	−0.360594	+	0.608253i
$7$	−1.63543	−	2.07976i	−0.618133	−	0.786074i
$7$	−1.63543	−	2.07976i	−0.618133	−	0.786074i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−2.25303	−	1.98087i	−0.751011	−	0.660290i
$10$	−3.84346	−	2.21902i	−1.21541	−	0.701716i
$11$	−0.783948	−	2.15388i	−0.236369	−	0.649419i	−0.999993	−	0.00375751i	$-0.998804\pi$
$11$	−0.783948	−	2.15388i	−0.236369	−	0.649419i	0.763624	−	0.645661i	$-0.223418\pi$
$12$	−1.12857	+	1.31390i	−0.325791	+	0.379289i
$13$	−1.38518	+	3.80576i	−0.384181	+	1.05553i	0.585397	+	0.810746i	$0.300938\pi$
$13$	−1.38518	+	3.80576i	−0.384181	+	1.05553i	−0.969578	+	0.244782i	$0.921284\pi$
$14$	−1.24943	−	2.33215i	−0.333925	−	0.623293i
$15$	5.00866	−	5.83113i	1.29323	−	1.50559i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	1.86694	−	3.23363i	0.452799	−	0.784270i	−0.545760	−	0.837941i	$-0.683759\pi$
$17$	1.86694	−	3.23363i	0.452799	−	0.784270i	0.998559	+	0.0536714i	$0.0170924\pi$
$18$	−1.87483	−	2.34201i	−0.441902	−	0.552017i
$19$	−5.69313	+	3.28693i	−1.30609	+	0.754073i	−0.981442	−	0.191760i	$-0.938580\pi$
$19$	−5.69313	+	3.28693i	−1.30609	+	0.754073i	−0.324652	+	0.945834i	$0.605247\pi$
$20$	−3.39974	−	2.85272i	−0.760204	−	0.637887i
$21$	4.37002	−	1.37945i	0.953618	−	0.301021i
$22$	−0.398021	−	2.25729i	−0.0848583	−	0.481255i
$23$	−4.03640	+	0.711726i	−0.841648	+	0.148405i	−0.577820	−	0.816165i	$-0.696096\pi$
$23$	−4.03640	+	0.711726i	−0.841648	+	0.148405i	−0.263828	+	0.964570i	$0.584985\pi$
$24$	−1.33958	+	1.09796i	−0.273441	+	0.224120i
$25$	11.2580	+	9.44655i	2.25159	+	1.88931i
$26$	−2.02500	+	3.50741i	−0.397136	+	0.687859i
$27$	4.58720	−	2.44081i	0.882808	−	0.469734i
$28$	−0.825480	−	2.51368i	−0.156001	−	0.475041i
$29$	−1.81552	−	4.98809i	−0.337133	−	0.926265i	−0.986204	−	0.165537i	$-0.947064\pi$
$29$	−1.81552	−	4.98809i	−0.337133	−	0.926265i	0.649071	−	0.760728i	$-0.275158\pi$
$30$	5.94513	−	4.87279i	1.08543	−	0.889646i
$31$	−0.0325436	+	0.0894127i	−0.00584500	+	0.0160590i	−0.942581	−	0.333978i	$-0.891609\pi$
$31$	−0.0325436	+	0.0894127i	−0.00584500	+	0.0160590i	0.936736	+	0.350037i	$0.113831\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	3.96979	+	0.0457992i	0.691051	+	0.00797262i
$34$	2.40009	−	2.86031i	0.411611	−	0.490539i
$35$	3.66351	+	11.1558i	0.619247	+	1.88568i
$36$	−1.43966	−	2.63199i	−0.239944	−	0.438665i
$37$	−2.90601			−0.477745			−0.238872	−	0.971051i	$-0.576778\pi$
$37$	−2.90601			−0.477745			−0.238872	+	0.971051i	$0.576778\pi$
$38$	−6.17741	+	2.24839i	−1.00211	+	0.364737i
$39$	−5.32129	−	4.57073i	−0.852088	−	0.731902i
$40$	−2.85272	−	3.39974i	−0.451054	−	0.537546i
$41$	−0.325419	−	0.118443i	−0.0508220	−	0.0184977i	0.316484	−	0.948598i	$-0.397498\pi$
$41$	−0.325419	−	0.118443i	−0.0508220	−	0.0184977i	−0.367306	+	0.930100i	$0.619720\pi$
$42$	4.54317	−	0.599648i	0.701027	−	0.0925276i
$43$	0.361225	−	2.04861i	0.0550862	−	0.312410i	−0.944798	−	0.327655i	$-0.893742\pi$
$43$	0.361225	−	2.04861i	0.0550862	−	0.312410i	0.999884	+	0.0152451i	$0.00485285\pi$
$44$		−	2.29211i		−	0.345549i
$45$	6.38928	+	11.6809i	0.952457	+	1.74128i
$46$	−4.09867			−0.604316
$47$	2.13553	−	0.777271i	0.311500	−	0.113377i	−0.181540	−	0.983384i	$-0.558108\pi$
$47$	2.13553	−	0.777271i	0.311500	−	0.113377i	0.493039	+	0.870007i	$0.335886\pi$
$48$	−1.50989	+	0.848664i	−0.217934	+	0.122494i
$49$	−1.65076	+	6.80257i	−0.235823	+	0.971796i
$50$	9.44655	+	11.2580i	1.33594	+	1.59212i
$51$	4.09964	+	5.00183i	0.574065	+	0.700397i
$52$	−2.60329	+	3.10248i	−0.361012	+	0.430237i
$53$	−1.50502	+	0.868925i	−0.206731	+	0.119356i	−0.599791	−	0.800157i	$-0.704750\pi$
$53$	−1.50502	+	0.868925i	−0.206731	+	0.119356i	0.393060	+	0.919513i	$0.371416\pi$
$54$	4.94136	−	1.60717i	0.672434	−	0.218708i
$55$			10.1725i			1.37166i
$56$	−0.376443	−	2.61883i	−0.0503043	−	0.349956i
$57$	−1.84771	−	11.2353i	−0.244736	−	1.48816i
$58$	−0.921762	−	5.22757i	−0.121033	−	0.686414i
$59$	−9.34207	+	7.83893i	−1.21623	+	1.02054i	−0.217221	+	0.976123i	$0.569699\pi$
$59$	−9.34207	+	7.83893i	−1.21623	+	1.02054i	−0.999013	+	0.0444186i	$0.985856\pi$
$60$	6.70096	−	3.76640i	0.865090	−	0.486241i
$61$	−2.55352	−	7.01574i	−0.326945	−	0.898274i	−0.988880	−	0.148713i	$-0.952487\pi$
$61$	−2.55352	−	7.01574i	−0.326945	−	0.898274i	0.661936	−	0.749561i	$-0.269735\pi$
$62$	−0.0475755	+	0.0824032i	−0.00604210	+	0.0104652i
$63$	−0.435054	+	7.92532i	−0.0548117	+	0.998497i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	11.5535	−	13.7690i	1.43304	−	1.70783i
$66$	3.90152	+	0.734450i	0.480244	+	0.0904045i
$67$	0.776252	+	4.40235i	0.0948343	+	0.537832i	0.994798	+	0.101867i	$0.0324817\pi$
$67$	0.776252	+	4.40235i	0.0948343	+	0.537832i	−0.899964	+	0.435965i	$0.856407\pi$
$68$	2.86031	−	2.40009i	0.346864	−	0.291053i
$69$	1.31332	−	6.97656i	0.158105	−	0.839880i
$70$	1.67067	+	11.6225i	0.199683	+	1.38915i
$71$	−3.12776	+	1.80581i	−0.371197	+	0.214311i	−0.673981	−	0.738749i	$-0.735417\pi$
$71$	−3.12776	+	1.80581i	−0.371197	+	0.214311i	0.302784	+	0.953059i	$0.402084\pi$
$72$	−0.960749	−	2.84200i	−0.113225	−	0.334933i
$73$		−	13.5227i		−	1.58271i	−0.611354	−	0.791357i	$-0.709375\pi$
$73$		−	13.5227i		−	1.58271i	0.611354	−	0.791357i	$-0.290625\pi$
$74$	−2.86186	−	0.504623i	−0.332684	−	0.0586612i
$75$	−22.1897	+	12.4721i	−2.56224	+	1.44016i
$76$	−6.47399	+	1.14154i	−0.742617	+	0.130943i
$77$	−3.19745	+	5.15293i	−0.364383	+	0.587231i
$78$	−4.44674	−	5.42532i	−0.503495	−	0.614297i
$79$	−0.353140	+	2.00276i	−0.0397313	+	0.225328i	−0.998208	−	0.0598443i	$-0.980940\pi$
$79$	−0.353140	+	2.00276i	−0.0397313	+	0.225328i	0.958476	+	0.285172i	$0.0920507\pi$
$80$	−2.21902	−	3.84346i	−0.248094	−	0.429712i
$81$	1.15231	+	8.92593i	0.128035	+	0.991770i
$82$	−0.299908	−	0.173152i	−0.0331193	−	0.0191214i
$83$	0.970084	−	0.353082i	0.106481	−	0.0387557i	−0.288230	−	0.957561i	$-0.593067\pi$
$83$	0.970084	−	0.353082i	0.106481	−	0.0387557i	0.394711	+	0.918805i	$0.370845\pi$
$84$	4.57828	+	0.198376i	0.499531	+	0.0216446i
$85$	−12.6942	+	10.6517i	−1.37688	+	1.15534i
$86$	0.711474	−	1.95476i	0.0767202	−	0.210787i
$87$	9.19349	+	0.106065i	0.985645	+	0.0113713i
$88$	0.398021	−	2.25729i	0.0424292	−	0.240628i
$89$	−3.13366	−	5.42765i	−0.332167	−	0.575330i	0.650770	−	0.759275i	$-0.274446\pi$
$89$	−3.13366	−	5.42765i	−0.332167	−	0.575330i	−0.982936	+	0.183945i	$0.941113\pi$
$90$	4.26384	+	12.6129i	0.449449	+	1.32952i
$91$	10.1804	−	3.34320i	1.06720	−	0.350462i
$92$	−4.03640	−	0.711726i	−0.420824	−	0.0742026i
$93$	−0.125019	−	0.107385i	−0.0129638	−	0.0111353i
$94$	2.23806	−	0.394631i	0.230838	−	0.0407031i
$95$	28.7318	−	5.06620i	2.94782	−	0.519781i
$96$	−1.63432	+	0.573581i	−0.166802	+	0.0585408i
$97$	10.4891	+	1.84951i	1.06500	+	0.187789i	0.678576	−	0.734531i	$-0.262598\pi$
$97$	10.4891	+	1.84951i	1.06500	+	0.187789i	0.386428	+	0.922320i	$0.373709\pi$
$98$	−2.80694	+	6.41257i	−0.283544	+	0.647768i
$99$	−2.50029	+	6.40566i	−0.251289	+	0.643793i
$100$	7.34811	+	12.7273i	0.734811	+	1.27273i
$101$	1.38681	−	7.86499i	0.137993	−	0.782596i	−0.834736	−	0.550650i	$-0.814380\pi$
$101$	1.38681	−	7.86499i	0.137993	−	0.782596i	0.972729	−	0.231945i	$-0.0745091\pi$
$102$	3.16880	+	5.63774i	0.313758	+	0.558219i
$103$	3.26410	−	8.96804i	0.321621	−	0.883647i	−0.668535	−	0.743681i	$-0.733078\pi$
$103$	3.26410	−	8.96804i	0.321621	−	0.883647i	0.990156	−	0.139967i	$-0.0446995\pi$
$104$	−3.10248	+	2.60329i	−0.304224	+	0.255274i
$105$	−20.3186	−	0.880401i	−1.98289	−	0.0859184i
$106$	−1.63305	+	0.594380i	−0.158615	+	0.0577313i
$107$	−2.19043	−	1.26464i	−0.211756	−	0.122258i	0.390371	−	0.920658i	$-0.372347\pi$
$107$	−2.19043	−	1.26464i	−0.211756	−	0.122258i	−0.602127	+	0.798400i	$0.705680\pi$
$108$	5.14537	−	0.724694i	0.495113	−	0.0697337i
$109$	5.53571	+	9.58813i	0.530225	+	0.918376i	0.999378	+	0.0352596i	$0.0112258\pi$
$109$	5.53571	+	9.58813i	0.530225	+	0.918376i	−0.469153	+	0.883117i	$0.655441\pi$
$110$	−1.76643	+	10.0179i	−0.168423	+	0.955173i
$111$	1.77596	−	4.70963i	0.168566	−	0.447018i
$112$	0.0840316	−	2.64442i	0.00794024	−	0.249874i
$113$	−3.47150	+	0.612119i	−0.326571	+	0.0575833i	−0.334530	−	0.942385i	$-0.608578\pi$
$113$	−3.47150	+	0.612119i	−0.326571	+	0.0575833i	0.00795916	+	0.999968i	$0.497466\pi$
$114$	0.131354	−	11.3855i	0.0123024	−	1.06635i
$115$	17.9137	+	3.15867i	1.67046	+	0.294548i
$116$		−	5.30822i		−	0.492855i
$117$	10.6596	−	5.83064i	0.985478	−	0.539042i
$118$	−10.5614	+	6.09760i	−0.972252	+	0.561330i
$119$	−9.77839	+	1.40559i	−0.896384	+	0.128850i
$120$	7.25319	−	2.54557i	0.662122	−	0.232378i
$121$	4.40187	−	3.69361i	0.400170	−	0.335782i
$122$	−1.29646	−	7.35257i	−0.117376	−	0.665670i
$123$	0.390829	−	0.455007i	0.0352399	−	0.0410266i
$124$	−0.0611619	+	0.0728899i	−0.00549250	+	0.00654571i
$125$	−21.5161	−	37.2670i	−1.92446	−	3.33326i
$126$	−1.80466	+	7.72937i	−0.160772	+	0.688587i
$127$	5.14801	−	8.91661i	0.456812	−	0.791222i	−0.541978	−	0.840392i	$-0.682325\pi$
$127$	5.14801	−	8.91661i	0.456812	−	0.791222i	0.998790	+	0.0491709i	$0.0156579\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	3.09932	+	1.83739i	0.272880	+	0.161773i
$130$	13.7690	−	11.5535i	1.20762	−	1.01331i
$131$	−0.245399	−	1.39173i	−0.0214406	−	0.121596i	0.972209	−	0.234115i	$-0.0752192\pi$
$131$	−0.245399	−	1.39173i	−0.0214406	−	0.121596i	−0.993650	+	0.112519i	$0.964108\pi$
$132$	3.71472	+	1.40078i	0.323324	+	0.121923i
$133$	16.1467	+	6.46478i	1.40010	+	0.560568i
$134$			4.47026i			0.386172i
$135$	−22.8354	+	3.21622i	−1.96535	+	0.276808i
$136$	3.23363	−	1.86694i	0.277281	−	0.160088i
$137$	3.60512	−	4.29642i	0.308006	−	0.367068i	−0.589730	−	0.807600i	$-0.700766\pi$
$137$	3.60512	−	4.29642i	0.308006	−	0.367068i	0.897737	+	0.440533i	$0.145210\pi$
$138$	2.50483	−	6.64252i	0.213225	−	0.565449i
$139$	6.84886	+	8.16215i	0.580913	+	0.692305i	0.973832	−	0.227268i	$-0.0729793\pi$
$139$	6.84886	+	8.16215i	0.580913	+	0.692305i	−0.392920	+	0.919573i	$0.628535\pi$
$140$	−0.372936	+	11.7360i	−0.0315188	+	0.991876i
$141$	−0.0454091	+	3.93598i	−0.00382414	+	0.331469i
$142$	−3.39382	+	1.23525i	−0.284803	+	0.103660i
$143$	9.28306			0.776288
$144$	−0.452645	−	2.96566i	−0.0377204	−	0.247138i
$145$			23.5581i			1.95639i
$146$	2.34819	−	13.3173i	0.194338	−	1.10215i
$147$	−10.0158	−	6.83259i	−0.826087	−	0.563542i
$148$	−2.73075	−	0.993913i	−0.224467	−	0.0816992i
$149$	−7.78092	−	9.27294i	−0.637438	−	0.759669i	0.346525	−	0.938041i	$-0.387361\pi$
$149$	−7.78092	−	9.27294i	−0.637438	−	0.759669i	−0.983963	+	0.178372i	$0.942917\pi$
$150$	−24.0183	+	8.42946i	−1.96109	+	0.688263i
$151$	−16.0562	+	5.84399i	−1.30664	+	0.475577i	−0.899153	−	0.437635i	$-0.855816\pi$
$151$	−16.0562	+	5.84399i	−1.30664	+	0.475577i	−0.407485	+	0.913212i	$0.633594\pi$
$152$	−6.57386			−0.533210
$153$	−10.6117	+	3.58731i	−0.857902	+	0.290017i
$154$	−4.04367	+	4.51941i	−0.325848	+	0.364185i
$155$	0.271439	−	0.323488i	0.0218025	−	0.0259832i
$156$	−3.43709	−	6.11507i	−0.275188	−	0.489597i
$157$	−11.8366	−	14.1063i	−0.944663	−	1.12581i	−0.991913	−	0.126922i	$-0.959490\pi$
$157$	−11.8366	−	14.1063i	−0.944663	−	1.12581i	0.0472500	−	0.998883i	$-0.484954\pi$
$158$	−0.695550	+	1.91101i	−0.0553349	+	0.152032i
$159$	−0.488457	−	2.97015i	−0.0387372	−	0.235548i
$160$	−1.51790	−	4.17040i	−0.120001	−	0.329699i
$161$	8.08145	+	7.23075i	0.636908	+	0.569863i
$162$	−0.415164	+	8.99042i	−0.0326184	+	0.706354i
$163$	2.31150	−	4.00364i	0.181051	−	0.313589i	−0.761188	−	0.648531i	$-0.775383\pi$
$163$	2.31150	−	4.00364i	0.181051	−	0.313589i	0.942239	+	0.334942i	$0.108717\pi$
$164$	−0.265284	−	0.222600i	−0.0207152	−	0.0173821i
$165$	−16.4861	−	6.21674i	−1.28344	−	0.483973i
$166$	1.01666	−	0.179264i	0.0789080	−	0.0139136i
$167$	2.53862	+	14.3973i	0.196445	+	1.11409i	0.910346	+	0.413847i	$0.135815\pi$
$167$	2.53862	+	14.3973i	0.196445	+	1.11409i	−0.713902	+	0.700246i	$0.753074\pi$
$168$	4.47428	+	0.990372i	0.345198	+	0.0764089i
$169$	−2.60650	−	2.18711i	−0.200500	−	0.168240i
$170$	−14.3510	+	8.28554i	−1.10067	+	0.635472i
$171$	19.3378	+	3.87179i	1.47880	+	0.296083i
$172$	1.04010	−	1.80151i	0.0793073	−	0.137364i
$173$	8.37219	+	7.02511i	0.636526	+	0.534109i	0.902949	−	0.429747i	$-0.141397\pi$
$173$	8.37219	+	7.02511i	0.636526	+	0.534109i	−0.266423	+	0.963856i	$0.585842\pi$
$174$	9.03540	+	1.70089i	0.684972	+	0.128944i
$175$	1.23495	−	38.8629i	0.0933532	−	2.93776i
$176$	0.783948	−	2.15388i	0.0590923	−	0.162355i
$177$	−6.99493	−	19.9309i	−0.525771	−	1.49810i
$178$	−2.14355	−	5.88935i	−0.160666	−	0.441425i
$179$	9.77399	+	5.64301i	0.730542	+	0.421779i	0.818620	−	0.574335i	$-0.194739\pi$
$179$	9.77399	+	5.64301i	0.730542	+	0.421779i	−0.0880784	+	0.996114i	$0.528073\pi$
$180$	2.00886	+	13.1617i	0.149731	+	0.981015i
$181$	−8.24437	−	4.75989i	−0.612800	−	0.353800i	0.161261	−	0.986912i	$-0.448444\pi$
$181$	−8.24437	−	4.75989i	−0.612800	−	0.353800i	−0.774060	+	0.633112i	$0.781777\pi$
$182$	10.6063	−	1.52460i	0.786191	−	0.113011i
$183$	12.9306	+	0.149180i	0.955859	+	0.0110277i
$184$	−3.85149	−	1.40183i	−0.283935	−	0.103344i
$185$	12.1192	+	4.41103i	0.891021	+	0.324305i
$186$	−0.104472	−	0.127463i	−0.00766026	−	0.00934602i
$187$	−8.42842	−	1.48616i	−0.616347	−	0.108679i
$188$	2.27259			0.165746
$189$	−12.5783	−	5.54850i	−0.914938	−	0.403594i
$190$	29.1751			2.11658
$191$	−3.42982	−	0.604769i	−0.248173	−	0.0437596i	0.0481778	−	0.998839i	$-0.484659\pi$
$191$	−3.42982	−	0.604769i	−0.248173	−	0.0437596i	−0.296351	+	0.955079i	$0.595770\pi$
$192$	−1.70909	+	0.281070i	−0.123343	+	0.0202845i
$193$	−21.6371	−	7.87526i	−1.55747	−	0.566874i	−0.587318	−	0.809357i	$-0.699816\pi$
$193$	−21.6371	−	7.87526i	−1.55747	−	0.566874i	−0.970156	+	0.242483i	$0.922038\pi$
$194$	10.0086	+	3.64282i	0.718572	+	0.261539i
$195$	15.2540	+	27.1389i	1.09236	+	1.94346i
$196$	−3.87783	+	5.82773i	−0.276988	+	0.416267i
$197$	−20.5300	−	11.8530i	−1.46270	−	0.844490i	−0.463564	−	0.886064i	$-0.653429\pi$
$197$	−20.5300	−	11.8530i	−1.46270	−	0.844490i	−0.999135	+	0.0415739i	$0.986763\pi$
$198$	−3.57464	+	5.87417i	−0.254039	+	0.417459i
$199$	−20.0387	−	11.5694i	−1.42051	−	0.820131i	−0.424166	−	0.905585i	$-0.639433\pi$
$199$	−20.0387	−	11.5694i	−1.42051	−	0.820131i	−0.996342	+	0.0854538i	$0.972766\pi$
$200$	5.02640	+	13.8099i	0.355420	+	0.976509i
$201$	−7.60907	−	1.43238i	−0.536702	−	0.101033i
$202$	2.73148	−	7.50469i	0.192186	−	0.528028i
$203$	−7.40486	+	11.9335i	−0.519720	+	0.837566i
$204$	2.14168	+	6.10235i	0.149947	+	0.427250i
$205$	1.17734	+	0.987908i	0.0822292	+	0.0689985i
$206$	4.77180	−	8.26499i	0.332467	−	0.575849i
$207$	10.5040	+	6.39204i	0.730077	+	0.444277i
$208$	−3.50741	+	2.02500i	−0.243195	+	0.140409i
$209$	11.5428	+	9.68553i	0.798430	+	0.669962i
$210$	−19.8570	−	4.39531i	−1.37027	−	0.303305i
$211$	4.46526	+	25.3238i	0.307401	+	1.74336i	0.611980	+	0.790873i	$0.290373\pi$
$211$	4.46526	+	25.3238i	0.307401	+	1.74336i	−0.304579	+	0.952487i	$0.598516\pi$
$212$	−1.71145	+	0.301775i	−0.117543	+	0.0207260i
$213$	−1.01512	−	6.17261i	−0.0695548	−	0.422940i
$214$	−1.93754	−	1.62579i	−0.132448	−	0.111137i
$215$	−4.61603	+	7.99520i	−0.314811	+	0.545268i
$216$	5.19304	+	0.179799i	0.353342	+	0.0122338i
$217$	0.239179	−	0.0785453i	0.0162365	−	0.00533200i
$218$	3.78665	+	10.4037i	0.256464	+	0.704630i
$219$	21.9156	+	8.26418i	1.48092	+	0.558441i
$220$	−3.47919	+	9.55901i	−0.234567	+	0.644468i
$221$	9.72036	+	11.5843i	0.653863	+	0.779243i
$222$	2.56680	−	4.32969i	0.172272	−	0.290590i
$223$	−9.07299	+	10.8128i	−0.607572	+	0.724076i	−0.978880	−	0.204433i	$-0.934465\pi$
$223$	−9.07299	+	10.8128i	−0.607572	+	0.724076i	0.371308	+	0.928510i	$0.378909\pi$
$224$	0.541953	−	2.58965i	0.0362108	−	0.173028i
$225$	−6.65217	−	43.5839i	−0.443478	−	2.90559i
$226$	−3.52505			−0.234483
$227$	−1.62000	+	0.589631i	−0.107523	+	0.0391352i	−0.395221	−	0.918586i	$-0.629332\pi$
$227$	−1.62000	+	0.589631i	−0.107523	+	0.0391352i	0.287698	+	0.957721i	$0.407110\pi$
$228$	2.10643	−	11.1897i	0.139502	−	0.741057i
$229$	3.61923	+	4.31324i	0.239166	+	0.285027i	0.872254	−	0.489053i	$-0.162657\pi$
$229$	3.61923	+	4.31324i	0.239166	+	0.285027i	−0.633088	+	0.774080i	$0.718213\pi$
$230$	17.0931	+	6.22137i	1.12708	+	0.410225i
$231$	−6.39704	−	8.33109i	−0.420895	−	0.548145i
$232$	0.921762	−	5.22757i	0.0605166	−	0.343207i
$233$			28.4124i			1.86136i	0.365834	+	0.930680i	$0.380784\pi$
$233$			28.4124i			1.86136i	−0.365834	+	0.930680i	$0.619216\pi$
$234$	11.5101	−	3.89104i	0.752440	−	0.254365i
$235$	−10.0858			−0.657928
$236$	−11.4597	+	4.17101i	−0.745966	+	0.271509i
$237$	−3.02996	−	1.79627i	−0.196817	−	0.116680i
$238$	−9.87391	−	0.313763i	−0.640031	−	0.0203383i
$239$	−13.0399	−	15.5403i	−0.843478	−	1.00522i	−0.999847	−	0.0175194i	$-0.994423\pi$
$239$	−13.0399	−	15.5403i	−0.843478	−	1.00522i	0.156368	−	0.987699i	$-0.450021\pi$
$240$	7.58503	−	1.24740i	0.489611	−	0.0805193i
$241$	7.11125	−	8.47486i	0.458076	−	0.545914i	−0.486726	−	0.873555i	$-0.661809\pi$
$241$	7.11125	−	8.47486i	0.458076	−	0.545914i	0.944802	+	0.327641i	$0.106254\pi$
$242$	4.97638	−	2.87312i	0.319894	−	0.184691i
$243$	−15.1700	−	3.58743i	−0.973159	−	0.230134i
$244$		−	7.46600i		−	0.477961i
$245$	17.2100	−	25.8637i	1.09950	−	1.65237i
$246$	0.463903	−	0.380228i	0.0295774	−	0.0242425i
$247$	−4.62324	−	26.2197i	−0.294170	−	1.66832i
$248$	−0.0728899	+	0.0611619i	−0.00462851	+	0.00388378i
$249$	−0.0206275	+	1.78795i	−0.00130721	+	0.113307i
$250$	−14.7179	−	40.4371i	−0.930841	−	2.55746i
$251$	−12.7923	+	22.1570i	−0.807446	+	1.39854i	0.107182	+	0.994239i	$0.465817\pi$
$251$	−12.7923	+	22.1570i	−0.807446	+	1.39854i	−0.914627	+	0.404298i	$0.867516\pi$
$252$	−3.11944	+	7.29857i	−0.196506	+	0.459767i
$253$	4.69730	+	8.13596i	0.295317	+	0.511504i
$254$	6.61815	−	7.88721i	0.415260	−	0.494887i
$255$	−9.50485	−	27.0825i	−0.595217	−	1.69597i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	9.16596	−	7.69116i	0.571757	−	0.479761i	−0.310471	−	0.950583i	$-0.600487\pi$
$257$	9.16596	−	7.69116i	0.571757	−	0.479761i	0.882228	+	0.470822i	$0.156042\pi$
$258$	2.73318	+	2.34767i	0.170160	+	0.146159i
$259$	4.75256	+	6.04378i	0.295310	+	0.375543i
$260$	15.5660	−	8.98705i	0.965364	−	0.557353i
$261$	−5.79034	+	14.8346i	−0.358413	+	0.918241i
$262$		−	1.41320i		−	0.0873076i
$263$	−20.8314	−	3.67314i	−1.28452	−	0.226496i	−0.510622	−	0.859805i	$-0.670585\pi$
$263$	−20.8314	−	3.67314i	−1.28452	−	0.226496i	−0.773898	+	0.633310i	$0.781696\pi$
$264$	3.41504	+	2.02456i	0.210181	+	0.124603i
$265$	7.59548	−	1.33929i	0.466587	−	0.0822718i
$266$	14.7788	+	9.17041i	0.906146	+	0.562274i
$267$	10.7114	−	1.76155i	0.655528	−	0.107805i
$268$	−0.776252	+	4.40235i	−0.0474172	+	0.268916i
$269$	4.68672	+	8.11764i	0.285754	+	0.494941i	0.972792	−	0.231681i	$-0.0744225\pi$
$269$	4.68672	+	8.11764i	0.285754	+	0.494941i	−0.687037	+	0.726622i	$0.741089\pi$
$270$	−23.0469	−	0.797957i	−1.40259	−	0.0485621i
$271$	−19.3806	−	11.1894i	−1.17729	−	0.679707i	−0.221901	−	0.975069i	$-0.571226\pi$
$271$	−19.3806	−	11.1894i	−1.17729	−	0.679707i	−0.955385	+	0.295363i	$0.904560\pi$
$272$	3.50869	−	1.27706i	0.212746	−	0.0774331i
$273$	−0.803424	+	18.5421i	−0.0486255	+	1.12222i
$274$	4.29642	−	3.60512i	0.259556	−	0.217793i
$275$	11.5211	−	31.6539i	0.694746	−	1.90880i
$276$	3.62024	−	6.10664i	0.217913	−	0.367577i
$277$	5.51809	−	31.2947i	0.331550	−	1.88031i	−0.127399	−	0.991852i	$-0.540663\pi$
$277$	5.51809	−	31.2947i	0.331550	−	1.88031i	0.458949	−	0.888463i	$-0.348226\pi$
$278$	5.32747	+	9.22744i	0.319520	+	0.553425i
$279$	0.250437	−	0.136985i	0.0149932	−	0.00820109i
$280$	−2.40521	+	11.4930i	−0.143739	+	0.686837i
$281$	−11.8961	−	2.09760i	−0.709661	−	0.125132i	−0.192845	−	0.981229i	$-0.561772\pi$
$281$	−11.8961	−	2.09760i	−0.709661	−	0.125132i	−0.516815	+	0.856097i	$0.672883\pi$
$282$	−0.728194	+	3.86829i	−0.0433633	+	0.230354i
$283$	−0.845383	+	0.149064i	−0.0502528	+	0.00886092i	−0.198718	−	0.980057i	$-0.563678\pi$
$283$	−0.845383	+	0.149064i	−0.0502528	+	0.00886092i	0.148465	+	0.988918i	$0.452567\pi$
$284$	−3.55676	+	0.627152i	−0.211055	+	0.0372146i
$285$	−9.34842	+	49.6604i	−0.553753	+	2.94163i
$286$	9.14203	+	1.61199i	0.540580	+	0.0953188i
$287$	0.285867	+	0.870497i	0.0168742	+	0.0513838i
$288$	0.0692124	−	2.99920i	0.00407838	−	0.176730i
$289$	1.52910	+	2.64848i	0.0899470	+	0.155793i
$290$	−4.09082	+	23.2002i	−0.240221	+	1.36236i
$291$	−9.40763	+	15.8688i	−0.551485	+	0.930248i
$292$	4.62504	−	12.7072i	0.270660	−	0.743632i
$293$	12.9783	−	10.8901i	0.758201	−	0.636206i	−0.179457	−	0.983766i	$-0.557434\pi$
$293$	12.9783	−	10.8901i	0.758201	−	0.636206i	0.937658	+	0.347560i	$0.112990\pi$
$294$	−8.67714	−	8.46801i	−0.506061	−	0.493864i
$295$	50.8588	−	18.5111i	2.96111	−	1.07776i
$296$	−2.51668	−	1.45300i	−0.146279	−	0.0844541i
$297$	−8.85334	−	7.96682i	−0.513723	−	0.462282i
$298$	−6.05248	−	10.4832i	−0.350611	−	0.607276i
$299$	2.88250	−	16.3474i	0.166699	−	0.945397i
$300$	−25.1172	+	4.13066i	−1.45014	+	0.238484i
$301$	−4.85136	+	2.59909i	−0.279628	+	0.149809i
$302$	−16.8271	+	2.96707i	−0.968291	+	0.170736i
$303$	11.8989	+	7.05409i	0.683574	+	0.405247i
$304$	−6.47399	−	1.14154i	−0.371309	−	0.0654717i
$305$			33.1344i			1.89727i
$306$	−11.0734	+	1.69012i	−0.633023	+	0.0966176i
$307$	8.02265	−	4.63188i	0.457877	−	0.264355i	−0.253274	−	0.967395i	$-0.581507\pi$
$307$	8.02265	−	4.63188i	0.457877	−	0.264355i	0.711151	+	0.703039i	$0.248174\pi$
$308$	−4.76703	+	3.74858i	−0.271627	+	0.213595i
$309$	12.5393	+	10.7706i	0.713335	+	0.612720i
$310$	0.323488	−	0.271439i	0.0183729	−	0.0154167i
$311$	3.00586	+	17.0471i	0.170446	+	0.966650i	0.943269	+	0.332028i	$0.107733\pi$
$311$	3.00586	+	17.0471i	0.170446	+	0.966650i	−0.772823	+	0.634622i	$0.781156\pi$
$312$	−2.32300	−	6.61901i	−0.131514	−	0.374728i
$313$	9.31940	−	11.1064i	0.526764	−	0.627773i	−0.435402	−	0.900236i	$-0.643394\pi$
$313$	9.31940	−	11.1064i	0.526764	−	0.627773i	0.962166	+	0.272463i	$0.0878383\pi$
$314$	−9.20723	−	15.9474i	−0.519594	−	0.899964i
$315$	13.8442	−	32.3914i	0.780032	−	1.82505i
$316$	−1.01683	+	1.76119i	−0.0572009	+	0.0990749i
$317$	2.70056	+	7.41973i	0.151679	+	0.416734i	0.992139	−	0.125139i	$-0.0399377\pi$
$317$	2.70056	+	7.41973i	0.151679	+	0.416734i	−0.840461	+	0.541873i	$0.817715\pi$
$318$	0.0347244	−	3.00985i	0.00194725	−	0.168784i
$319$	−9.32048	+	7.82081i	−0.521846	+	0.437881i
$320$	−0.770658	−	4.37062i	−0.0430811	−	0.244325i
$321$	3.38819	−	2.77705i	0.189110	−	0.155000i
$322$	6.70307	+	8.52423i	0.373547	+	0.475037i
$323$			24.5460i			1.36577i
$324$	−1.97003	+	8.78174i	−0.109446	+	0.487875i
$325$	−51.5456	+	29.7599i	−2.85924	+	1.65078i
$326$	2.97161	−	3.54143i	0.164582	−	0.196141i
$327$	−18.9221	+	3.11184i	−1.04639	+	0.172085i
$328$	−0.222600	−	0.265284i	−0.0122910	−	0.0146479i
$329$	−5.10904	−	3.17022i	−0.281671	−	0.174780i
$330$	−15.1561	−	8.98507i	−0.834315	−	0.494612i
$331$	−13.2715	+	4.83043i	−0.729467	+	0.265504i	−0.679939	−	0.733268i	$-0.737994\pi$
$331$	−13.2715	+	4.83043i	−0.729467	+	0.265504i	−0.0495279	+	0.998773i	$0.515772\pi$
$332$	1.03234			0.0566571
$333$	6.54733	+	5.75642i	0.358792	+	0.315450i
$334$			14.6194i			0.799935i
$335$	3.44504	−	19.5378i	0.188223	−	1.06746i
$336$	4.23433	+	1.75228i	0.231001	+	0.0955945i
$337$	3.60623	+	1.31256i	0.196444	+	0.0714996i	0.438368	−	0.898795i	$-0.355557\pi$
$337$	3.60623	+	1.31256i	0.196444	+	0.0714996i	−0.241925	+	0.970295i	$0.577779\pi$
$338$	−2.18711	−	2.60650i	−0.118963	−	0.141775i
$339$	1.12951	−	6.00018i	0.0613468	−	0.325885i
$340$	−15.5717	+	5.66764i	−0.844495	+	0.307371i
$341$	0.218097			0.0118106
$342$	18.3717	+	7.17094i	0.993426	+	0.387760i
$343$	16.8474	−	7.69192i	0.909673	−	0.415325i
$344$	1.33713	−	1.59353i	0.0720934	−	0.0859176i
$345$	−16.0668	+	27.1015i	−0.865006	+	1.45910i
$346$	7.02511	+	8.37219i	0.377672	+	0.450092i
$347$	2.56300	−	7.04179i	0.137589	−	0.378023i	−0.851693	−	0.524041i	$-0.824424\pi$
$347$	2.56300	−	7.04179i	0.137589	−	0.378023i	0.989282	+	0.146019i	$0.0466459\pi$
$348$	8.60278	+	3.24403i	0.461157	+	0.173898i
$349$	9.55564	+	26.2539i	0.511502	+	1.40534i	0.879672	+	0.475581i	$0.157762\pi$
$349$	9.55564	+	26.2539i	0.511502	+	1.40534i	−0.368171	+	0.929758i	$0.620016\pi$
$350$	7.96466	−	38.0581i	0.425729	−	2.03429i
$351$	2.93502	+	20.8388i	0.156660	+	1.11229i
$352$	1.14606	−	1.98503i	0.0610849	−	0.105802i
$353$	10.3572	+	8.69075i	0.551260	+	0.462562i	0.875367	−	0.483458i	$-0.160619\pi$
$353$	10.3572	+	8.69075i	0.551260	+	0.462562i	−0.324107	+	0.946020i	$0.605064\pi$
$354$	−3.42770	−	20.8427i	−0.182180	−	1.10778i
$355$	15.7850	−	2.78333i	0.837783	−	0.147724i
$356$	−1.08831	−	6.17210i	−0.0576802	−	0.327120i
$357$	3.69792	−	16.7064i	0.195715	−	0.884195i
$358$	8.64560	+	7.25452i	0.456934	+	0.383413i
$359$	3.83174	−	2.21226i	0.202231	−	0.116758i	−0.395464	−	0.918481i	$-0.629416\pi$
$359$	3.83174	−	2.21226i	0.202231	−	0.116758i	0.597696	+	0.801723i	$0.296083\pi$
$360$	−0.307168	+	13.3106i	−0.0161892	+	0.701529i
$361$	12.1078	−	20.9714i	0.637253	−	1.10376i
$362$	−7.29258	−	6.11920i	−0.383289	−	0.321618i
$363$	3.29593	+	9.39119i	0.172991	+	0.492909i
$364$	10.7099	+	0.340329i	0.561351	+	0.0178381i
$365$	−20.5261	+	56.3951i	−1.07439	+	2.95185i
$366$	12.7083	+	2.39229i	0.664272	+	0.125047i
$367$	11.7494	+	32.2811i	0.613312	+	1.68506i	0.722787	+	0.691070i	$0.242861\pi$
$367$	11.7494	+	32.2811i	0.613312	+	1.68506i	−0.109476	+	0.993989i	$0.534917\pi$
$368$	−3.54955	−	2.04933i	−0.185033	−	0.106829i
$369$	0.498560	+	0.911469i	0.0259540	+	0.0474492i
$370$	11.1691	+	6.44849i	0.580655	+	0.335241i
$371$	4.26851	+	1.70902i	0.221610	+	0.0887277i
$372$	−0.0807512	−	0.143668i	−0.00418675	−	0.00744882i
$373$	18.1745	+	6.61498i	0.941040	+	0.342511i	0.766577	−	0.642153i	$-0.221959\pi$
$373$	18.1745	+	6.61498i	0.941040	+	0.342511i	0.174464	+	0.984664i	$0.444181\pi$
$374$	−8.04231	−	2.92716i	−0.415858	−	0.151360i
$375$	73.5461	−	12.0951i	3.79790	−	0.624586i
$376$	2.23806	+	0.394631i	0.115419	+	0.0203515i
$377$	21.4983			1.10722
$378$	−11.4237	−	7.64841i	−0.587574	−	0.393392i
$379$	−13.1956			−0.677811			−0.338906	−	0.940820i	$-0.610057\pi$
$379$	−13.1956			−0.677811			−0.338906	+	0.940820i	$0.610057\pi$
$380$	28.7318	+	5.06620i	1.47391	+	0.259890i
$381$	11.3046	+	13.7924i	0.579153	+	0.706605i
$382$	−3.27269	−	1.19116i	−0.167446	−	0.0609452i
$383$	20.8771	+	7.59866i	1.06677	+	0.388273i	0.814969	−	0.579505i	$-0.196754\pi$
$383$	20.8771	+	7.59866i	1.06677	+	0.388273i	0.251803	+	0.967778i	$0.418976\pi$
$384$	−1.73194	−	0.0199812i	−0.0883825	−	0.00101966i
$385$	21.1563	−	16.6363i	1.07822	−	0.847867i
$386$	−19.9409	−	11.5129i	−1.01496	−	0.585989i
$387$	−4.87187	+	3.90004i	−0.247651	+	0.198250i
$388$	9.22393	+	5.32544i	0.468274	+	0.270358i
$389$	4.09862	+	11.2609i	0.207808	+	0.570948i	0.999184	−	0.0403815i	$-0.0128573\pi$
$389$	4.09862	+	11.2609i	0.207808	+	0.570948i	−0.791376	+	0.611329i	$0.790635\pi$
$390$	10.3096	+	29.3754i	0.522046	+	1.48748i
$391$	−5.23424	+	14.3810i	−0.264707	+	0.727277i
$392$	−4.83089	+	5.06582i	−0.243997	+	0.255862i
$393$	2.40548	+	0.452824i	0.121340	+	0.0228419i
$394$	−18.1598	−	15.2379i	−0.914878	−	0.767674i
$395$	4.51271	−	7.81625i	0.227059	−	0.393278i
$396$	−4.54037	+	5.16420i	−0.228162	+	0.259511i
$397$	6.31552	−	3.64627i	0.316967	−	0.183001i	−0.333073	−	0.942901i	$-0.608086\pi$
$397$	6.31552	−	3.64627i	0.316967	−	0.183001i	0.650040	+	0.759900i	$0.274752\pi$
$398$	−17.7253	−	14.8733i	−0.888489	−	0.745531i
$399$	−20.3450	+	22.2174i	−1.01852	+	1.11226i
$400$	2.55197	+	14.4729i	0.127599	+	0.723647i
$401$	−18.4176	+	3.24752i	−0.919732	+	0.162173i	−0.613419	−	0.789758i	$-0.710206\pi$
$401$	−18.4176	+	3.24752i	−0.919732	+	0.162173i	−0.306312	+	0.951931i	$0.599095\pi$
$402$	−7.24474	−	2.73192i	−0.361335	−	0.136256i
$403$	−0.295205	−	0.247706i	−0.0147052	−	0.0123391i
$404$	3.99316	−	6.91636i	0.198667	−	0.344102i
$405$	8.74306	−	38.9737i	0.434446	−	1.93662i
$406$	−9.36460	+	10.4663i	−0.464757	+	0.519436i
$407$	2.27816	+	6.25919i	0.112924	+	0.310257i
$408$	1.04948	+	6.38154i	0.0519569	+	0.315933i
$409$	2.42122	−	6.65225i	0.119722	−	0.328933i	−0.865327	−	0.501207i	$-0.832889\pi$
$409$	2.42122	−	6.65225i	0.119722	−	0.328933i	0.985049	+	0.172275i	$0.0551117\pi$
$410$	0.987908	+	1.17734i	0.0487893	+	0.0581448i
$411$	4.75979	+	8.46833i	0.234783	+	0.417712i
$412$	6.13450	−	7.31081i	0.302225	−	0.360178i
$413$	31.5813	+	6.60923i	1.55401	+	0.325219i
$414$	9.23443	+	8.11893i	0.453848	+	0.399023i
$415$	−4.58157			−0.224901
$416$	−3.80576	+	1.38518i	−0.186593	+	0.0679142i
$417$	−17.4136	+	6.11146i	−0.852747	+	0.299280i
$418$	9.68553	+	11.5428i	0.473735	+	0.564575i
$419$	−22.0538	−	8.02694i	−1.07740	−	0.392142i	−0.258461	−	0.966022i	$-0.583215\pi$
$419$	−22.0538	−	8.02694i	−1.07740	−	0.392142i	−0.818939	+	0.573880i	$0.805438\pi$
$420$	−18.7921	−	7.77668i	−0.916962	−	0.379463i
$421$	−0.682707	+	3.87182i	−0.0332731	+	0.188701i	−0.996914	−	0.0784989i	$-0.974987\pi$
$421$	−0.682707	+	3.87182i	−0.0332731	+	0.188701i	0.963641	+	0.267200i	$0.0860984\pi$
$422$			25.7144i			1.25176i
$423$	−6.35110	−	2.47900i	−0.308801	−	0.120533i
$424$	−1.73785			−0.0843975
$425$	51.5645	−	18.7679i	2.50125	−	0.910379i
$426$	0.0721648	−	6.25510i	0.00349639	−	0.303061i
$427$	−10.4149	+	16.7844i	−0.504014	+	0.812255i
$428$	−1.62579	−	1.93754i	−0.0785857	−	0.0936548i
$429$	−5.67318	+	15.0446i	−0.273904	+	0.726361i
$430$	−5.93425	+	7.07217i	−0.286175	+	0.341050i
$431$	−16.0564	+	9.27015i	−0.773408	+	0.446528i	−0.834089	−	0.551630i	$-0.814006\pi$
$431$	−16.0564	+	9.27015i	−0.773408	+	0.446528i	0.0606807	+	0.998157i	$0.480673\pi$
$432$	5.08292	+	1.07883i	0.244552	+	0.0519052i
$433$		−	22.3750i		−	1.07527i	−0.843177	−	0.537636i	$-0.819317\pi$
$433$		−	22.3750i		−	1.07527i	0.843177	−	0.537636i	$-0.180683\pi$
$434$	0.249185	−	0.0358189i	0.0119612	−	0.00171936i
$435$	−38.1795	−	14.3971i	−1.83057	−	0.690289i
$436$	1.92253	+	10.9032i	0.0920726	+	0.522169i
$437$	20.6404	−	17.3193i	0.987362	−	0.828495i
$438$	20.1476	+	11.9442i	0.962691	+	0.570718i
$439$	−5.99828	−	16.4801i	−0.286282	−	0.786554i	−0.996579	−	0.0826511i	$-0.973661\pi$
$439$	−5.99828	−	16.4801i	−0.286282	−	0.786554i	0.710296	−	0.703903i	$-0.248561\pi$
$440$	−5.08624	+	8.80963i	−0.242477	+	0.419983i
$441$	17.1942	−	12.0565i	0.818773	−	0.574118i
$442$	7.56110	+	13.0962i	0.359645	+	0.622923i
$443$	−9.20835	+	10.9741i	−0.437502	+	0.521394i	−0.939071	−	0.343723i	$-0.888312\pi$
$443$	−9.20835	+	10.9741i	−0.437502	+	0.521394i	0.501569	+	0.865117i	$0.332756\pi$
$444$	3.27964	−	3.81819i	0.155645	−	0.181203i
$445$	4.82995	+	27.3920i	0.228962	+	1.29851i
$446$	−10.8128	+	9.07299i	−0.511999	+	0.429618i
$447$	19.7834	−	6.94317i	0.935722	−	0.328401i
$448$	0.983408	−	2.45620i	0.0464616	−	0.116044i
$449$	−0.759364	+	0.438419i	−0.0358366	+	0.0206903i	−0.517811	−	0.855495i	$-0.673253\pi$
$449$	−0.759364	+	0.438419i	−0.0358366	+	0.0206903i	0.481975	+	0.876185i	$0.339920\pi$
$450$	1.01716	−	44.0769i	0.0479494	−	2.07781i
$451$			0.793767i			0.0373770i
$452$	−3.47150	−	0.612119i	−0.163285	−	0.0287916i
$453$	0.341413	−	29.5930i	0.0160410	−	1.39040i
$454$	−1.69778	+	0.299364i	−0.0796805	+	0.0140498i
$455$	−47.5310	−	1.51039i	−2.22829	−	0.0708083i
$456$	4.01750	−	10.6539i	0.188137	−	0.498917i
$457$	1.65699	−	9.39726i	0.0775107	−	0.439585i	−0.921212	−	0.389061i	$-0.872800\pi$
$457$	1.65699	−	9.39726i	0.0775107	−	0.439585i	0.998723	−	0.0505244i	$-0.0160893\pi$
$458$	2.81526	+	4.87618i	0.131549	+	0.227849i
$459$	0.671347	−	19.3902i	0.0313358	−	0.905055i
$460$	15.7531	+	9.09503i	0.734490	+	0.424058i
$461$	−33.3935	+	12.1542i	−1.55529	+	0.566079i	−0.969651	−	0.244493i	$-0.921378\pi$
$461$	−33.3935	+	12.1542i	−1.55529	+	0.566079i	−0.585638	+	0.810572i	$0.699156\pi$
$462$	−4.85318	−	9.31535i	−0.225790	−	0.433389i
$463$	10.6056	−	8.89912i	0.492882	−	0.413577i	−0.362176	−	0.932110i	$-0.617966\pi$
$463$	10.6056	−	8.89912i	0.492882	−	0.413577i	0.855058	+	0.518533i	$0.173522\pi$
$464$	1.81552	−	4.98809i	0.0842832	−	0.231566i
$465$	0.358377	+	0.637603i	0.0166193	+	0.0295681i
$466$	−4.93377	+	27.9808i	−0.228552	+	1.29618i
$467$	−1.40341	−	2.43078i	−0.0649422	−	0.112483i	0.831726	−	0.555186i	$-0.187353\pi$
$467$	−1.40341	−	2.43078i	−0.0649422	−	0.112483i	−0.896668	+	0.442703i	$0.854020\pi$
$468$	12.0109	−	1.83321i	0.555205	−	0.0847404i
$469$	7.88630	−	8.81413i	0.364155	−	0.406999i
$470$	−9.93261	−	1.75139i	−0.458157	−	0.0807855i
$471$	30.0951	−	10.5622i	1.38671	−	0.486680i
$472$	−12.0099	+	2.11767i	−0.552802	+	0.0974739i
$473$	−4.69563	+	0.827967i	−0.215905	+	0.0380700i
$474$	−2.67201	−	2.29512i	−0.122729	−	0.105419i
$475$	−95.1431	−	16.7763i	−4.36547	−	0.769749i
$476$	−9.66942	−	2.02358i	−0.443197	−	0.0927508i
$477$	5.11209	+	1.02354i	0.234067	+	0.0468645i
$478$	−10.1432	−	17.5686i	−0.463940	−	0.803567i
$479$	−3.29219	+	18.6709i	−0.150424	+	0.853097i	0.812427	+	0.583063i	$0.198146\pi$
$479$	−3.29219	+	18.6709i	−0.150424	+	0.853097i	−0.962851	+	0.270034i	$0.912965\pi$
$480$	7.68640	+	0.0886776i	0.350835	+	0.00404756i
$481$	4.02535	−	11.0596i	0.183540	−	0.504273i
$482$	8.47486	−	7.11125i	0.386019	−	0.323909i
$483$	−16.6574	+	8.67828i	−0.757937	+	0.394875i
$484$	5.39969	−	1.96533i	0.245440	−	0.0893330i
$485$	−40.9362	−	23.6345i	−1.85882	−	1.07319i
$486$	−14.3166	−	6.16718i	−0.649416	−	0.279749i
$487$	−3.93561	−	6.81667i	−0.178339	−	0.308893i	0.762973	−	0.646431i	$-0.223739\pi$
$487$	−3.93561	−	6.81667i	−0.178339	−	0.308893i	−0.941312	+	0.337538i	$0.890406\pi$
$488$	1.29646	−	7.35257i	0.0586878	−	0.332835i
$489$	5.07587	+	6.19290i	0.229539	+	0.280053i
$490$	21.4397	−	22.4823i	0.968546	−	1.01565i
$491$	22.1009	−	3.89698i	0.997399	−	0.175868i	0.348962	−	0.937137i	$-0.386534\pi$
$491$	22.1009	−	3.89698i	0.997399	−	0.175868i	0.648437	+	0.761268i	$0.275423\pi$
$492$	0.522881	−	0.293896i	0.0235733	−	0.0132498i
$493$	−19.5191	−	3.44174i	−0.879095	−	0.155008i
$494$		−	26.6242i		−	1.19788i
$495$	20.1504	−	22.9189i	0.905691	−	1.03013i
$496$	−0.0824032	+	0.0475755i	−0.00370001	+	0.00213620i
$497$	8.87087	+	3.55170i	0.397913	+	0.159316i
$498$	−0.330788	+	1.75720i	−0.0148230	+	0.0787422i
$499$	−4.21912	+	3.54026i	−0.188874	+	0.158484i	−0.732321	−	0.680959i	$-0.761563\pi$
$499$	−4.21912	+	3.54026i	−0.188874	+	0.158484i	0.543448	+	0.839443i	$0.317119\pi$
$500$	−7.47247	−	42.3785i	−0.334179	−	1.89522i
$501$	−24.8844	−	4.68441i	−1.11175	−	0.209284i
$502$	−16.4455	+	19.5990i	−0.734000	+	0.874747i
$503$	−0.608926	−	1.05469i	−0.0271507	−	0.0470263i	0.852131	−	0.523329i	$-0.175310\pi$
$503$	−0.608926	−	1.05469i	−0.0271507	−	0.0470263i	−0.879281	+	0.476303i	$0.841977\pi$
$504$	−4.33943	+	6.64600i	−0.193294	+	0.296037i
$505$	−17.7218	+	30.6951i	−0.788610	+	1.36591i
$506$	3.21314	+	8.82804i	0.142842	+	0.392454i
$507$	5.13747	−	2.88762i	0.228163	−	0.128244i
$508$	7.88721	−	6.61815i	0.349938	−	0.293633i
$509$	−4.99445	−	28.3249i	−0.221375	−	1.25548i	−0.869495	−	0.493942i	$-0.835556\pi$
$509$	−4.99445	−	28.3249i	−0.221375	−	1.25548i	0.648120	−	0.761538i	$-0.275555\pi$
$510$	−4.65763	−	28.3215i	−0.206243	−	1.25410i
$511$	−28.1239	+	22.1154i	−1.24413	+	0.978328i
$512$			1.00000i			0.0441942i
$513$	−18.0928	+	28.9737i	−0.798816	+	1.27922i
$514$	10.3623	−	5.98266i	0.457060	−	0.263884i
$515$	−27.2252	+	32.4457i	−1.19968	+	1.42973i
$516$	2.28399	+	2.78661i	0.100547	+	0.122674i
$517$	−3.34829	−	3.99034i	−0.147258	−	0.175495i
$518$	3.63087	+	6.77724i	0.159531	+	0.297775i
$519$	−16.5018	+	9.27515i	−0.724348	+	0.407134i
$520$	16.8901	−	6.14750i	0.740681	−	0.269586i
$521$	41.5476			1.82023			0.910116	−	0.414354i	$-0.135993\pi$
$521$	41.5476			1.82023			0.910116	+	0.414354i	$0.135993\pi$
$522$	−8.27838	+	13.6038i	−0.362335	+	0.595421i
$523$		−	10.1741i		−	0.444884i	−0.974946	−	0.222442i	$-0.928597\pi$
$523$		−	10.1741i		−	0.444884i	0.974946	−	0.222442i	$-0.0714029\pi$
$524$	0.245399	−	1.39173i	0.0107203	−	0.0607979i
$525$	62.2286	+	25.7518i	2.71588	+	1.12390i
$526$	−19.8771	−	7.23468i	−0.866683	−	0.315447i
$527$	0.228371	+	0.272162i	0.00994798	+	0.0118555i
$528$	3.01159	+	2.58681i	0.131063	+	0.112577i
$529$	−5.82696	+	2.12084i	−0.253346	+	0.0922104i
$530$	7.71265			0.335016
$531$	36.5759	+	0.844060i	1.58726	+	0.0366291i
$532$	12.9619	+	11.5974i	0.561967	+	0.502811i
$533$	0.901531	−	1.07440i	0.0390496	−	0.0465375i
$534$	10.8546	+	0.125229i	0.469724	+	0.00541917i
$535$	7.21534	+	8.59890i	0.311946	+	0.371763i
$536$	−1.52892	+	4.20067i	−0.0660392	+	0.181441i
$537$	−15.1186	+	12.3916i	−0.652415	+	0.534737i
$538$	3.20591	+	8.80816i	0.138216	+	0.379747i
$539$	15.9460	−	1.77732i	0.686844	−	0.0765546i
$540$	−22.5582	−	4.78789i	−0.970752	−	0.206038i
$541$	9.78093	−	16.9411i	0.420515	−	0.728353i	−0.575475	−	0.817819i	$-0.695183\pi$
$541$	9.78093	−	16.9411i	0.420515	−	0.728353i	0.995990	+	0.0894661i	$0.0285161\pi$
$542$	−17.1431	−	14.3848i	−0.736360	−	0.617880i
$543$	12.7525	−	10.4523i	0.547264	−	0.448553i
$544$	3.67715	−	0.648380i	0.157656	−	0.0277991i
$545$	−8.53228	−	48.3889i	−0.365483	−	2.07275i
$546$	−4.01101	+	18.1209i	−0.171656	+	0.775501i
$547$	−12.9816	−	10.8929i	−0.555055	−	0.465746i	0.321594	−	0.946878i	$-0.395782\pi$
$547$	−12.9816	−	10.8929i	−0.555055	−	0.465746i	−0.876648	+	0.481131i	$0.840226\pi$
$548$	4.85717	−	2.80429i	0.207488	−	0.119793i
$549$	−8.14410	+	20.8649i	−0.347582	+	0.890492i
$550$	16.8427	−	29.1724i	0.718174	−	1.24391i
$551$	26.7315	+	22.4304i	1.13880	+	0.955566i
$552$	4.62565	−	5.38522i	0.196881	−	0.229210i
$553$	4.74277	−	2.54091i	0.201683	−	0.108051i
$554$	10.8685	−	29.8610i	0.461759	−	1.26867i
$555$	−14.5552	+	16.9453i	−0.617834	+	0.719288i
$556$	3.64420	+	10.0124i	0.154549	+	0.424619i
$557$	15.0771	+	8.70475i	0.638836	+	0.368832i	0.784166	−	0.620551i	$-0.213091\pi$
$557$	15.0771	+	8.70475i	0.638836	+	0.368832i	−0.145330	+	0.989383i	$0.546424\pi$
$558$	0.270419	−	0.0914162i	0.0114478	−	0.00386996i
$559$	7.29614	+	4.21243i	0.308594	+	0.178167i
$560$	−4.36440	+	10.9007i	−0.184430	+	0.460639i
$561$	7.55944	−	12.7513i	0.319160	−	0.538361i
$562$	−11.3511	−	4.13146i	−0.478817	−	0.174275i
$563$	−25.3592	−	9.22998i	−1.06876	−	0.388997i	−0.253048	−	0.967454i	$-0.581433\pi$
$563$	−25.3592	−	9.22998i	−1.06876	−	0.388997i	−0.815713	+	0.578456i	$0.803655\pi$
$564$	−1.38885	+	3.68308i	−0.0584813	+	0.155086i
$565$	15.4067	+	2.71661i	0.648163	+	0.114289i
$566$	−0.858424			−0.0360823
$567$	16.6792	−	16.9942i	0.700461	−	0.713690i
$568$	−3.61163			−0.151540
$569$	2.64109	+	0.465696i	0.110720	+	0.0195230i	0.228734	−	0.973489i	$-0.426541\pi$
$569$	2.64109	+	0.465696i	0.110720	+	0.0195230i	−0.118013	+	0.993012i	$0.537653\pi$
$570$	−17.8298	+	47.2827i	−0.746810	+	1.98045i
$571$	3.92564	+	1.42882i	0.164283	+	0.0597941i	0.422852	−	0.906199i	$-0.361029\pi$
$571$	3.92564	+	1.42882i	0.164283	+	0.0597941i	−0.258569	+	0.965993i	$0.583251\pi$
$572$	8.72322	+	3.17499i	0.364736	+	0.132753i
$573$	3.07620	−	5.18895i	0.128510	−	0.216772i
$574$	0.130364	+	0.906913i	0.00544128	+	0.0378538i
$575$	−52.1650	−	30.1175i	−2.17543	−	1.25598i
$576$	0.588967	−	2.94162i	0.0245403	−	0.122567i
$577$	−29.0036	−	16.7452i	−1.20743	−	0.697112i	−0.245236	−	0.969463i	$-0.578865\pi$
$577$	−29.0036	−	16.7452i	−1.20743	−	0.697112i	−0.962198	+	0.272351i	$0.912199\pi$
$578$	1.04597	+	2.87377i	0.0435064	+	0.119533i
$579$	25.9862	−	30.2534i	1.07995	−	1.25729i
$580$	−8.05734	+	22.1374i	−0.334563	+	0.919204i
$581$	−2.32082	−	1.44010i	−0.0962840	−	0.0597453i
$582$	−12.0203	+	13.9941i	−0.498257	+	0.580076i
$583$	3.05142	+	2.56045i	0.126377	+	0.106043i
$584$	6.76136	−	11.7110i	0.279787	−	0.484605i
$585$	−53.3050	+	8.13588i	−2.20389	+	0.336377i
$586$	14.6722	−	8.47099i	0.606103	−	0.349933i
$587$	−17.4863	−	14.6728i	−0.721738	−	0.605610i	0.206127	−	0.978525i	$-0.433914\pi$
$587$	−17.4863	−	14.6728i	−0.721738	−	0.605610i	−0.927866	+	0.372915i	$0.878358\pi$
$588$	−7.07487	−	9.84613i	−0.291763	−	0.406048i
$589$	−0.108619	−	0.616007i	−0.00447555	−	0.0253821i
$590$	53.3006	−	9.39833i	2.19435	−	0.386923i
$591$	31.7561	−	26.0282i	1.30627	−	1.07066i
$592$	−2.22613	−	1.86795i	−0.0914934	−	0.0767721i
$593$	4.21343	−	7.29787i	0.173025	−	0.299688i	−0.766451	−	0.642303i	$-0.777979\pi$
$593$	4.21343	−	7.29787i	0.173025	−	0.299688i	0.939476	+	0.342615i	$0.111313\pi$
$594$	−7.33541	−	9.38315i	−0.300976	−	0.384995i
$595$	42.9133	+	8.98075i	1.75927	+	0.368175i
$596$	−4.14014	−	11.3749i	−0.169587	−	0.465936i
$597$	30.9963	−	25.4054i	1.26859	−	1.03977i
$598$	5.67741	−	15.5985i	0.232166	−	0.637872i
$599$	4.81563	+	5.73904i	0.196761	+	0.234491i	0.855399	−	0.517969i	$-0.173312\pi$
$599$	4.81563	+	5.73904i	0.196761	+	0.234491i	−0.658638	+	0.752460i	$0.728867\pi$
$600$	−25.4529	−	0.293649i	−1.03911	−	0.0119882i
$601$	−5.47801	+	6.52844i	−0.223453	+	0.266301i	−0.866110	−	0.499853i	$-0.833387\pi$
$601$	−5.47801	+	6.52844i	−0.223453	+	0.266301i	0.642658	+	0.766154i	$0.277832\pi$
$602$	−5.22898	+	1.71717i	−0.213117	+	0.0699867i
$603$	6.97155	−	11.4563i	0.283904	−	0.466536i
$604$	−17.0867			−0.695247
$605$	−23.9641	+	8.72220i	−0.974277	+	0.354608i
$606$	10.4932	+	9.01315i	0.426257	+	0.366134i
$607$	−15.8750	−	18.9191i	−0.644347	−	0.767902i	0.340703	−	0.940171i	$-0.389335\pi$
$607$	−15.8750	−	18.9191i	−0.644347	−	0.767902i	−0.985050	+	0.172268i	$0.944890\pi$
$608$	−6.17741	−	2.24839i	−0.250527	−	0.0911844i
$609$	−14.8147	−	19.2937i	−0.600321	−	0.781819i
$610$	−5.75373	+	32.6310i	−0.232962	+	1.32119i
$611$			9.20399i			0.372354i
$612$	−11.1986	−	0.258430i	−0.452678	−	0.0104464i
$613$	23.7513			0.959307			0.479654	−	0.877458i	$-0.340762\pi$
$613$	23.7513			0.959307			0.479654	+	0.877458i	$0.340762\pi$
$614$	8.70509	−	3.16839i	0.351309	−	0.127866i
$615$	−2.32057	+	1.30432i	−0.0935744	+	0.0525953i
$616$	−5.34554	+	2.86384i	−0.215378	+	0.115387i
$617$	−0.575029	−	0.685293i	−0.0231498	−	0.0275888i	0.754345	−	0.656478i	$-0.227954\pi$
$617$	−0.575029	−	0.685293i	−0.0231498	−	0.0275888i	−0.777495	+	0.628889i	$0.783510\pi$
$618$	10.4785	+	12.7844i	0.421506	+	0.514265i
$619$	11.7183	−	13.9653i	0.470998	−	0.561314i	−0.477281	−	0.878751i	$-0.658378\pi$
$619$	11.7183	−	13.9653i	0.470998	−	0.561314i	0.948280	+	0.317437i	$0.102822\pi$
$620$	0.365709	−	0.211142i	0.0146872	−	0.00847967i
$621$	−16.7786	+	13.1169i	−0.673302	+	0.526364i
$622$			17.3100i			0.694069i
$623$	−6.16332	+	15.3938i	−0.246928	+	0.616738i
$624$	−1.13833	−	6.92184i	−0.0455698	−	0.277095i
$625$	20.4033	+	115.713i	0.816130	+	4.62850i
$626$	11.1064	−	9.31940i	0.443902	−	0.372478i
$627$	−22.7511	+	12.7877i	−0.908589	+	0.510690i
$628$	−6.29812	−	17.3039i	−0.251322	−	0.690502i
$629$	−5.42533	+	9.39695i	−0.216322	+	0.374681i
$630$	19.2586	−	29.4952i	0.767280	−	1.17512i
$631$	4.92415	+	8.52887i	0.196027	+	0.339529i	0.947237	−	0.320535i	$-0.103863\pi$
$631$	4.92415	+	8.52887i	0.196027	+	0.339529i	−0.751210	+	0.660064i	$0.770529\pi$
$632$	−1.30721	+	1.55787i	−0.0519978	+	0.0619686i
$633$	−43.7699	−	8.23955i	−1.73970	−	0.327493i
$634$	1.37111	+	7.77596i	0.0544538	+	0.308823i
$635$	−35.0038	+	29.3716i	−1.38908	+	1.16558i
$636$	0.556851	−	2.95809i	0.0220806	−	0.117296i
$637$	−23.6023	−	15.7052i	−0.935159	−	0.622263i
$638$	−10.5369	+	6.08351i	−0.417162	+	0.240848i
$639$	10.6240	+	2.12713i	0.420280	+	0.0841479i
$640$		−	4.43804i		−	0.175429i
$641$	−26.2539	−	4.62927i	−1.03697	−	0.182845i	−0.370850	−	0.928693i	$-0.620933\pi$
$641$	−26.2539	−	4.62927i	−1.03697	−	0.182845i	−0.666116	+	0.745848i	$0.732045\pi$
$642$	3.81894	−	2.14651i	0.150722	−	0.0847161i
$643$	21.4634	−	3.78457i	0.846433	−	0.149249i	0.266421	−	0.963857i	$-0.414159\pi$
$643$	21.4634	−	3.78457i	0.846433	−	0.149249i	0.580012	+	0.814608i	$0.303048\pi$
$644$	5.12102	+	9.55870i	0.201796	+	0.376666i
$645$	−10.1364	−	12.3671i	−0.399122	−	0.486955i
$646$	−4.26236	+	24.1730i	−0.167700	+	0.951076i
$647$	−18.0575	−	31.2766i	−0.709915	−	1.22961i	−0.964888	−	0.262661i	$-0.915400\pi$
$647$	−18.0575	−	31.2766i	−0.709915	−	1.22961i	0.254973	−	0.966948i	$-0.417933\pi$
$648$	−3.46503	+	8.30624i	−0.136119	+	0.326300i
$649$	24.2078	+	13.9764i	0.950239	+	0.548621i
$650$	−55.9303	+	20.3570i	−2.19377	+	0.798465i
$651$	−0.0188757	+	0.435628i	−0.000739797	+	0.0170736i
$652$	3.54143	−	2.97161i	0.138693	−	0.116377i
$653$	−3.24305	+	8.91019i	−0.126910	+	0.348683i	−0.986833	−	0.161741i	$-0.948289\pi$
$653$	−3.24305	+	8.91019i	−0.126910	+	0.348683i	0.859923	+	0.510424i	$0.170511\pi$
$654$	−19.1750	−	0.221221i	−0.749801	−	0.00865041i
$655$	−1.08909	+	6.17655i	−0.0425543	+	0.241338i
$656$	−0.173152	−	0.299908i	−0.00676045	−	0.0117094i
$657$	−26.7867	+	30.4671i	−1.04505	+	1.18864i
$658$	−4.48092	−	4.00923i	−0.174684	−	0.156296i
$659$	29.4290	+	5.18912i	1.14639	+	0.202139i	0.714399	−	0.699739i	$-0.246700\pi$
$659$	29.4290	+	5.18912i	1.14639	+	0.202139i	0.431991	+	0.901878i	$0.357811\pi$
$660$	−13.3656	−	11.4804i	−0.520255	−	0.446874i
$661$	20.5503	−	3.62358i	0.799315	−	0.140941i	0.240952	−	0.970537i	$-0.422540\pi$
$661$	20.5503	−	3.62358i	0.799315	−	0.140941i	0.558364	+	0.829596i	$0.311429\pi$
$662$	−13.9087	+	2.45247i	−0.540576	+	0.0953180i
$663$	−24.7145	+	8.67380i	−0.959833	+	0.336863i
$664$	1.01666	+	0.179264i	0.0394540	+	0.00695680i
$665$	−57.5252	−	51.4698i	−2.23073	−	1.99591i
$666$	5.44827	+	6.80590i	0.211116	+	0.263723i
$667$	10.8783	+	18.8418i	0.421210	+	0.729557i
$668$	−2.53862	+	14.3973i	−0.0982223	+	0.557046i
$669$	−11.9789	−	21.3122i	−0.463132	−	0.823977i
$670$	6.78541	−	18.6428i	0.262143	−	0.720232i
$671$	−13.1092	+	11.0000i	−0.506076	+	0.424648i
$672$	3.86572	+	2.46094i	0.149123	+	0.0949328i
$673$	−7.45741	+	2.71428i	−0.287462	+	0.104628i	−0.481727	−	0.876322i	$-0.659990\pi$
$673$	−7.45741	+	2.71428i	−0.287462	+	0.104628i	0.194265	+	0.980949i	$0.437768\pi$
$674$	3.32352	+	1.91883i	0.128017	+	0.0739107i
$675$	74.6998	+	15.8547i	2.87520	+	0.610248i
$676$	−1.70127	−	2.94669i	−0.0654336	−	0.113334i
$677$	0.255032	−	1.44636i	0.00980167	−	0.0555881i	−0.979515	−	0.201373i	$-0.935460\pi$
$677$	0.255032	−	1.44636i	0.00980167	−	0.0555881i	0.989316	+	0.145785i	$0.0465708\pi$
$678$	2.15428	−	5.71288i	0.0827344	−	0.219402i
$679$	−13.3076	−	24.8394i	−0.510698	−	0.953250i
$680$	−16.3193	+	2.87754i	−0.625818	+	0.110349i
$681$	0.0344470	−	2.98580i	0.00132001	−	0.114416i
$682$	0.214783	+	0.0378721i	0.00822448	+	0.00145020i
$683$		−	33.6286i		−	1.28676i	−0.765545	−	0.643382i	$-0.777531\pi$
$683$		−	33.6286i		−	1.28676i	0.765545	−	0.643382i	$-0.222469\pi$
$684$	16.8473	+	10.2522i	0.644174	+	0.392003i
$685$	−21.5563	+	12.4455i	−0.823624	+	0.475520i
$686$	17.9271	−	4.64955i	0.684461	−	0.177521i
$687$	−9.20209	+	3.22956i	−0.351082	+	0.123215i
$688$	1.59353	−	1.33713i	0.0607529	−	0.0509777i
$689$	−1.22219	−	6.93138i	−0.0465617	−	0.264064i
$690$	−20.5288	+	23.8998i	−0.781519	+	0.909852i
$691$	−12.0406	+	14.3494i	−0.458045	+	0.545877i	−0.944794	−	0.327665i	$-0.893738\pi$
$691$	−12.0406	+	14.3494i	−0.458045	+	0.545877i	0.486749	+	0.873542i	$0.338183\pi$
$692$	5.46456	+	9.46490i	0.207731	+	0.359801i
$693$	17.4112	−	5.27598i	0.661399	−	0.200418i
$694$	3.74686	−	6.48974i	0.142229	−	0.246347i
$695$	−16.1731	−	44.4353i	−0.613482	−	1.68553i
$696$	7.90876	+	4.68860i	0.299781	+	0.177721i
$697$	−0.990537	+	0.831160i	−0.0375193	+	0.0314824i
$698$	4.85152	+	27.5144i	0.183633	+	1.04143i
$699$	−46.0467	−	17.3638i	−1.74165	−	0.656758i
$700$	14.4524	−	36.0968i	0.546248	−	1.36433i
$701$			4.38388i			0.165577i	0.996567	+	0.0827884i	$0.0263826\pi$
$701$			4.38388i			0.165577i	−0.996567	+	0.0827884i	$0.973617\pi$
$702$	−0.728188	+	21.0318i	−0.0274837	+	0.793796i
$703$	16.5443	−	9.55184i	0.623979	−	0.360255i
$704$	1.47334	−	1.75586i	0.0555286	−	0.0661764i
$705$	6.16379	−	16.3456i	0.232142	−	0.615613i
$706$	8.69075	+	10.3572i	0.327081	+	0.389800i
$707$	−18.6253	+	9.97839i	−0.700476	+	0.375276i
$708$	0.243675	−	21.1213i	0.00915788	−	0.793787i
$709$	19.6463	−	7.15068i	0.737833	−	0.268549i	0.0543564	−	0.998522i	$-0.482689\pi$
$709$	19.6463	−	7.15068i	0.737833	−	0.268549i	0.683477	+	0.729972i	$0.260467\pi$
$710$	16.0285			0.601541
$711$	4.76283	−	3.81275i	0.178620	−	0.142989i
$712$		−	6.26731i		−	0.234877i
$713$	0.0677215	−	0.384068i	0.00253619	−	0.0143834i
$714$	6.54278	−	15.8104i	0.244857	−	0.591691i
$715$	−38.7140	−	14.0908i	−1.44782	−	0.526964i
$716$	7.25452	+	8.64560i	0.271114	+	0.323101i
$717$	33.1545	−	11.6359i	1.23818	−	0.434550i
$718$	4.15768	−	1.51327i	0.155163	−	0.0564748i
$719$	46.1942			1.72275			0.861377	−	0.507967i	$-0.169603\pi$
$719$	46.1942			1.72275			0.861377	+	0.507967i	$0.169603\pi$
$720$	−2.61386	+	13.0550i	−0.0974128	+	0.486532i
$721$	−23.9895	+	7.87804i	−0.893417	+	0.293394i
$722$	15.5655	−	18.5502i	0.579288	−	0.690369i
$723$	9.38889	+	16.7041i	0.349177	+	0.621234i
$724$	−6.11920	−	7.29258i	−0.227418	−	0.271026i
$725$	26.6812	−	73.3061i	0.990916	−	2.72252i
$726$	1.61509	+	9.82084i	0.0599417	+	0.364486i
$727$	10.1538	+	27.8974i	0.376584	+	1.03466i	0.972762	+	0.231804i	$0.0744628\pi$
$727$	10.1538	+	27.8974i	0.376584	+	1.03466i	−0.596178	+	0.802852i	$0.703315\pi$
$728$	10.4881	+	2.19491i	0.388715	+	0.0813489i
$729$	15.0849	−	22.3930i	0.558700	−	0.829370i
$730$	−30.0072	+	51.9740i	−1.11062	+	1.92364i
$731$	−5.95005	−	4.99268i	−0.220071	−	0.184661i
$732$	12.0998	+	4.56272i	0.447221	+	0.168643i
$733$	−25.4331	+	4.48454i	−0.939393	+	0.165640i	−0.622322	−	0.782762i	$-0.713810\pi$
$733$	−25.4331	+	4.48454i	−0.939393	+	0.165640i	−0.317071	+	0.948402i	$0.602699\pi$
$734$	5.96531	+	33.8309i	0.220183	+	1.24872i
$735$	31.3985	+	43.6975i	1.15815	+	1.61181i
$736$	−3.13976	−	2.63457i	−0.115733	−	0.0971116i
$737$	8.87358	−	5.12316i	0.326863	−	0.188714i
$738$	0.332711	+	0.984196i	0.0122473	+	0.0362287i
$739$	19.2363	−	33.3182i	0.707618	−	1.22563i	−0.258120	−	0.966113i	$-0.583103\pi$
$739$	19.2363	−	33.3182i	0.707618	−	1.22563i	0.965738	−	0.259518i	$-0.0835636\pi$
$740$	9.87966	+	8.29002i	0.363184	+	0.304747i
$741$	45.3184	+	8.53105i	1.66481	+	0.313396i
$742$	3.90689	+	2.42427i	0.143426	+	0.0889978i
$743$	−1.29892	+	3.56875i	−0.0476527	+	0.130925i	−0.961236	−	0.275727i	$-0.911081\pi$
$743$	−1.29892	+	3.56875i	−0.0476527	+	0.130925i	0.913583	+	0.406652i	$0.133304\pi$
$744$	−0.0545768	−	0.155507i	−0.00200088	−	0.00570118i
$745$	18.3741	+	50.4825i	0.673176	+	1.84953i
$746$	16.7497	+	9.67045i	0.613251	+	0.354060i
$747$	−2.88504	−	1.12610i	−0.105558	−	0.0412020i
$748$	−7.41183	−	4.27922i	−0.271003	−	0.156464i
$749$	0.952132	+	6.62378i	0.0347901	+	0.242028i
$750$	74.5290	+	0.859837i	2.72141	+	0.0313968i
$751$	−19.5518	−	7.11627i	−0.713455	−	0.259676i	−0.0403105	−	0.999187i	$-0.512835\pi$
$751$	−19.5518	−	7.11627i	−0.713455	−	0.259676i	−0.673145	+	0.739511i	$0.735057\pi$
$752$	2.13553	+	0.777271i	0.0778749	+	0.0283442i
$753$	−28.0910	−	34.2728i	−1.02369	−	1.24897i
$754$	21.1717	+	3.73314i	0.771028	+	0.135953i
$755$	75.8314			2.75979
$756$	−9.92206	−	9.51592i	−0.360862	−	0.346091i
$757$	25.9352			0.942631			0.471315	−	0.881965i	$-0.343779\pi$
$757$	25.9352			0.942631			0.471315	+	0.881965i	$0.343779\pi$
$758$	−12.9951	−	2.29139i	−0.472004	−	0.0832270i
$759$	−16.0562	+	2.64054i	−0.582805	+	0.0958454i
$760$	27.4156	+	9.97846i	0.994468	+	0.361957i
$761$	−17.6643	−	6.42928i	−0.640331	−	0.233061i	0.00139071	−	0.999999i	$-0.499557\pi$
$761$	−17.6643	−	6.42928i	−0.640331	−	0.233061i	−0.641722	+	0.766938i	$0.721780\pi$
$762$	8.73786	+	15.5459i	0.316539	+	0.563167i
$763$	10.8877	−	27.1936i	0.394162	−	0.984474i
$764$	−3.01613	−	1.74136i	−0.109120	−	0.0630003i
$765$	49.7000	+	1.14692i	1.79691	+	0.0414672i
$766$	19.2405	+	11.1085i	0.695187	+	0.401366i
$767$	−16.8926	−	46.4120i	−0.609956	−	1.67584i
$768$	−1.70215	−	0.320425i	−0.0614212	−	0.0115623i
$769$	−9.66231	+	26.5470i	−0.348432	+	0.957309i	0.634433	+	0.772978i	$0.281234\pi$
$769$	−9.66231	+	26.5470i	−0.348432	+	0.957309i	−0.982864	+	0.184330i	$0.940988\pi$
$770$	23.7237	−	12.7099i	0.854944	−	0.458031i
$771$	6.86307	+	19.5552i	0.247168	+	0.704262i
$772$	−17.6387	−	14.8007i	−0.634832	−	0.532687i
$773$	−24.7695	+	42.9021i	−0.890898	+	1.54308i	−0.0520963	+	0.998642i	$0.516590\pi$
$773$	−24.7695	+	42.9021i	−0.890898	+	1.54308i	−0.838801	+	0.544438i	$0.816743\pi$
$774$	−5.47509	+	2.99480i	−0.196798	+	0.107646i
$775$	−1.21102	+	0.699180i	−0.0435010	+	0.0251153i
$776$	8.15905	+	6.84625i	0.292893	+	0.245766i
$777$	−12.6993	+	4.00870i	−0.455586	+	0.143811i
$778$	2.08092	+	11.8015i	0.0746046	+	0.423104i
$779$	2.24197	−	0.395319i	0.0803268	−	0.0141638i
$780$	5.05197	+	30.7194i	0.180890	+	1.09993i
$781$	6.34150	+	5.32115i	0.226917	+	0.190406i
$782$	−7.65195	+	13.2536i	−0.273633	+	0.473947i
$783$	−20.5031	−	18.4501i	−0.732722	−	0.659352i
$784$	−5.63717	+	4.14998i	−0.201327	+	0.148214i
$785$	27.9513	+	76.7956i	0.997625	+	2.74095i
$786$	2.29030	+	0.863652i	0.0816924	+	0.0308054i
$787$	8.42345	−	23.1432i	0.300264	−	0.824967i	−0.694190	−	0.719792i	$-0.744237\pi$
$787$	8.42345	−	23.1432i	0.300264	−	0.824967i	0.994454	−	0.105176i	$-0.0335405\pi$
$788$	−15.2379	−	18.1598i	−0.542828	−	0.646917i
$789$	18.6837	−	31.5157i	0.665156	−	1.12199i
$790$	5.80143	−	6.91388i	0.206406	−	0.245985i
$791$	6.95043	+	6.21879i	0.247129	+	0.221115i
$792$	−5.36815	+	4.29732i	−0.190749	+	0.152698i
$793$	30.2373			1.07376
$794$	6.85274	−	2.49419i	0.243195	−	0.0885157i
$795$	−2.47133	+	13.1281i	−0.0876490	+	0.465607i
$796$	−14.8733	−	17.7253i	−0.527170	−	0.628257i
$797$	7.44567	+	2.71000i	0.263739	+	0.0959932i	0.470505	−	0.882397i	$-0.344072\pi$
$797$	7.44567	+	2.71000i	0.263739	+	0.0959932i	−0.206766	+	0.978390i	$0.566294\pi$
$798$	−23.8939	+	18.3470i	−0.845834	+	0.649475i
$799$	1.47350	−	8.35664i	0.0521287	−	0.295637i
$800$			14.6962i			0.519590i
$801$	−3.69124	+	18.4360i	−0.130424	+	0.651405i
$802$	−18.7017			−0.660381
$803$	−29.1263	+	10.6011i	−1.02784	+	0.374105i
$804$	−6.66028	−	3.94846i	−0.234890	−	0.139251i
$805$	−22.7273	−	42.4219i	−0.801032	−	1.49518i
$806$	−0.247706	−	0.295205i	−0.00872507	−	0.0103981i
$807$	−16.0201	+	2.63459i	−0.563934	+	0.0927420i
$808$	5.13351	−	6.11788i	0.180596	−	0.215226i
$809$	−11.0858	+	6.40039i	−0.389756	+	0.225026i	−0.682054	−	0.731301i	$-0.738913\pi$
$809$	−11.0858	+	6.40039i	−0.389756	+	0.225026i	0.292298	+	0.956327i	$0.405580\pi$
$810$	15.3780	−	36.8634i	0.540326	−	1.29525i
$811$		−	4.20293i		−	0.147585i	−0.997274	−	0.0737925i	$-0.976490\pi$
$811$		−	4.20293i		−	0.147585i	0.997274	−	0.0737925i	$-0.0235102\pi$
$812$	−11.0398	+	8.68120i	−0.387421	+	0.304650i
$813$	29.9782	−	24.5710i	1.05138	−	0.861742i
$814$	1.15665	+	6.55970i	0.0405406	+	0.229917i
$815$	−15.7170	+	13.1881i	−0.550542	+	0.461960i
$816$	−0.0746074	+	6.46683i	−0.00261178	+	0.226384i
$817$	4.67713	+	12.8503i	0.163632	+	0.449575i
$818$	3.53959	−	6.13075i	0.123759	−	0.214357i
$819$	−29.5592	−	12.6337i	−1.03288	−	0.441459i
$820$	0.768456	+	1.33100i	0.0268356	+	0.0464807i
$821$	−4.13301	+	4.92554i	−0.144243	+	0.171902i	−0.833329	−	0.552778i	$-0.813568\pi$
$821$	−4.13301	+	4.92554i	−0.144243	+	0.171902i	0.689086	+	0.724680i	$0.258012\pi$
$822$	3.21697	+	9.16621i	0.112205	+	0.319708i
$823$	1.94174	+	11.0122i	0.0676850	+	0.383860i	0.999766	+	0.0216118i	$0.00687978\pi$
$823$	1.94174	+	11.0122i	0.0676850	+	0.383860i	−0.932081	+	0.362249i	$0.882009\pi$
$824$	7.31081	−	6.13450i	0.254684	−	0.213705i
$825$	44.2590	+	38.0164i	1.54090	+	1.32356i
$826$	29.9538	+	11.9929i	1.04223	+	0.417285i
$827$	35.2518	−	20.3526i	1.22583	−	0.707731i	0.259672	−	0.965697i	$-0.416386\pi$
$827$	35.2518	−	20.3526i	1.22583	−	0.707731i	0.966154	+	0.257966i	$0.0830523\pi$
$828$	7.68430	+	9.59912i	0.267048	+	0.333593i
$829$			15.6874i			0.544845i	0.962178	+	0.272422i	$0.0878248\pi$
$829$			15.6874i			0.544845i	−0.962178	+	0.272422i	$0.912175\pi$
$830$	−4.51197	−	0.795582i	−0.156613	−	0.0276151i
$831$	47.3455	+	28.0681i	1.64240	+	0.973672i
$832$	−3.98848	+	0.703276i	−0.138276	+	0.0243817i
$833$	18.9151	+	18.0379i	0.655370	+	0.624977i
$834$	−18.2103	+	2.99478i	−0.630570	+	0.103701i
$835$	11.2665	−	63.8956i	0.389894	−	2.21120i
$836$	7.53401	+	13.0493i	0.260569	+	0.451319i
$837$	0.0689554	+	0.489587i	0.00238345	+	0.0169226i
$838$	−20.3249	−	11.7346i	−0.702113	−	0.405365i
$839$	48.8534	−	17.7812i	1.68661	−	0.613875i	0.692415	−	0.721499i	$-0.256547\pi$
$839$	48.8534	−	17.7812i	1.68661	−	0.613875i	0.994192	+	0.107624i	$0.0343244\pi$
$840$	−17.1562	−	10.9217i	−0.591946	−	0.376836i
$841$	0.630335	−	0.528914i	0.0217357	−	0.0182384i
$842$	−1.34467	+	3.69445i	−0.0463404	+	0.127319i
$843$	10.6696	−	17.9975i	0.367479	−	0.619867i
$844$	−4.46526	+	25.3238i	−0.153701	+	0.871680i
$845$	7.55032	+	13.0775i	0.259739	+	0.449881i
$846$	−5.82414	−	3.54419i	−0.200238	−	0.121852i
$847$	−14.8807	−	3.11419i	−0.511308	−	0.107005i
$848$	−1.71145	−	0.301775i	−0.0587714	−	0.0103630i
$849$	0.275061	−	1.46117i	0.00944006	−	0.0501472i
$850$	54.0401	−	9.52873i	1.85356	−	0.326833i
$851$	11.7298	−	2.06828i	0.402093	−	0.0708998i
$852$	1.15726	−	6.14754i	0.0396469	−	0.210611i
$853$	−20.3551	−	3.58916i	−0.696947	−	0.122890i	−0.186060	−	0.982538i	$-0.559572\pi$
$853$	−20.3551	−	3.58916i	−0.696947	−	0.122890i	−0.510887	+	0.859648i	$0.670683\pi$
$854$	−13.1713	+	14.7209i	−0.450712	+	0.503739i
$855$	−74.7692	−	45.4997i	−2.55705	−	1.55606i
$856$	−1.26464	−	2.19043i	−0.0432246	−	0.0748672i
$857$	6.20618	−	35.1970i	0.211999	−	1.20231i	−0.674039	−	0.738695i	$-0.735442\pi$
$857$	6.20618	−	35.1970i	0.211999	−	1.20231i	0.886039	−	0.463612i	$-0.153447\pi$
$858$	−8.19947	+	13.8309i	−0.279925	+	0.472180i
$859$	−13.8195	+	37.9688i	−0.471515	+	1.29548i	0.445019	+	0.895521i	$0.353197\pi$
$859$	−13.8195	+	37.9688i	−0.471515	+	1.29548i	−0.916534	+	0.399957i	$0.869025\pi$
$860$	−7.07217	+	5.93425i	−0.241159	+	0.202356i
$861$	−1.58548	−	0.0686984i	−0.0540329	−	0.00234124i
$862$	−17.4222	+	6.34116i	−0.593402	+	0.215981i
$863$	19.7631	+	11.4102i	0.672743	+	0.388408i	0.797115	−	0.603827i	$-0.206358\pi$
$863$	19.7631	+	11.4102i	0.672743	+	0.388408i	−0.124372	+	0.992236i	$0.539692\pi$
$864$	4.81837	+	1.94508i	0.163924	+	0.0661730i
$865$	−24.2520	−	42.0056i	−0.824591	−	1.42823i
$866$	3.88537	−	22.0350i	0.132030	−	0.748781i
$867$	−5.22675	+	0.859567i	−0.177510	+	0.0291924i
$868$	0.251619	+	0.00799570i	0.00854050	+	0.000271392i
$869$	4.59054	−	0.809435i	0.155723	−	0.0274582i
$870$	−35.0994	−	20.8082i	−1.18998	−	0.705464i
$871$	−17.8295	−	3.14383i	−0.604131	−	0.106525i
$872$			11.0714i			0.374926i
$873$	−19.9686	−	24.9445i	−0.675834	−	0.844243i
$874$	23.3342	−	13.4720i	0.789293	−	0.455698i
$875$	−42.3182	+	105.696i	−1.43062	+	3.57316i
$876$	17.7674	+	15.2614i	0.600306	+	0.515634i
$877$	−36.8141	+	30.8907i	−1.24312	+	1.04310i	−0.245850	+	0.969308i	$0.579067\pi$
$877$	−36.8141	+	30.8907i	−1.24312	+	1.04310i	−0.997273	+	0.0737966i	$0.976488\pi$
$878$	−3.04541	−	17.2714i	−0.102777	−	0.582880i
$879$	9.71759	+	27.6886i	0.327766	+	0.933915i
$880$	−6.53875	+	7.79257i	−0.220421	+	0.262688i
$881$	4.50978	+	7.81117i	0.151938	+	0.263165i	0.931940	−	0.362613i	$-0.118115\pi$
$881$	4.50978	+	7.81117i	0.151938	+	0.263165i	−0.780002	+	0.625777i	$0.784782\pi$
$882$	19.0266	−	8.88756i	0.640659	−	0.299260i
$883$	22.3124	−	38.6463i	0.750873	−	1.30055i	−0.196527	−	0.980498i	$-0.562966\pi$
$883$	22.3124	−	38.6463i	0.750873	−	1.30055i	0.947400	−	0.320052i	$-0.103700\pi$
$884$	5.17210	+	14.2102i	0.173956	+	0.477942i
$885$	−1.08144	+	93.7372i	−0.0363522	+	3.15094i
$886$	−10.9741	+	9.20835i	−0.368681	+	0.309360i
$887$	9.93132	+	56.3233i	0.333461	+	1.89115i	0.441927	+	0.897051i	$0.354295\pi$
$887$	9.93132	+	56.3233i	0.333461	+	1.89115i	−0.108466	+	0.994100i	$0.534594\pi$
$888$	3.89284	−	3.19068i	0.130635	−	0.107072i
$889$	−26.9636	+	3.87587i	−0.904329	+	0.129992i
$890$			27.8146i			0.932347i
$891$	18.3220	−	9.47940i	0.613811	−	0.317572i
$892$	−12.2240	+	7.05753i	−0.409290	+	0.236304i
$893$	−9.60304	+	11.4445i	−0.321353	+	0.382974i
$894$	20.6885	−	3.40234i	0.691927	−	0.113791i
$895$	−32.1959	−	38.3695i	−1.07619	−	1.28255i
$896$	1.39498	−	2.24812i	0.0466031	−	0.0751043i
$897$	24.7319	+	14.6620i	0.825776	+	0.489550i
$898$	−0.823958	+	0.299896i	−0.0274958	+	0.0100077i
$899$	0.505082			0.0168454
$900$	8.65558	−	43.2307i	0.288519	−	1.44102i
$901$			6.48891i			0.216177i
$902$	−0.137836	+	0.781708i	−0.00458944	+	0.0260280i
$903$	−1.24739	−	9.45075i	−0.0415106	−	0.314501i
$904$	−3.31246	−	1.20564i	−0.110171	−	0.0400989i
$905$	27.1573	+	32.3648i	0.902738	+	1.07584i
$906$	5.47500	−	29.0842i	0.181895	−	0.966257i
$907$	−35.2862	+	12.8431i	−1.17166	+	0.426450i	−0.853249	−	0.521503i	$-0.825372\pi$
$907$	−35.2862	+	12.8431i	−1.17166	+	0.426450i	−0.318411	+	0.947953i	$0.603149\pi$
$908$	−1.72397			−0.0572118
$909$	−18.7040	+	14.9730i	−0.620374	+	0.496623i
$910$	−46.5466	−	9.74112i	−1.54301	−	0.322915i
$911$	7.90445	−	9.42015i	0.261886	−	0.312104i	−0.619038	−	0.785361i	$-0.712477\pi$
$911$	7.90445	−	9.42015i	0.261886	−	0.312104i	0.880924	+	0.473257i	$0.156922\pi$
$912$	5.80651	−	9.79446i	0.192273	−	0.324327i
$913$	−1.52099	−	1.81265i	−0.0503374	−	0.0599898i
$914$	3.26363	−	8.96676i	0.107951	−	0.296594i
$915$	−53.6994	−	20.2495i	−1.77525	−	0.669429i
$916$	1.92575	+	5.29097i	0.0636287	+	0.174818i
$917$	−2.49312	+	2.78644i	−0.0823301	+	0.0920163i
$918$	4.02821	−	18.9790i	0.132951	−	0.626400i
$919$	16.6202	−	28.7870i	0.548249	−	0.949595i	−0.450146	−	0.892955i	$-0.648628\pi$
$919$	16.6202	−	28.7870i	0.548249	−	0.949595i	0.998395	−	0.0566398i	$-0.0180387\pi$
$920$	13.9344	+	11.6923i	0.459403	+	0.385485i
$921$	2.60376	+	15.8326i	0.0857969	+	0.521703i
$922$	−34.9967	+	6.17087i	−1.15256	+	0.203227i
$923$	−2.53997	−	14.4049i	−0.0836041	−	0.474143i
$924$	−3.16185	−	10.0166i	−0.104017	−	0.329521i
$925$	−32.7157	−	27.4517i	−1.07569	−	0.902608i
$926$	11.9898	−	6.92229i	0.394008	−	0.227480i
$927$	−25.1186	+	13.7395i	−0.825004	+	0.451266i
$928$	2.65411	−	4.59705i	0.0871254	−	0.150906i
$929$	1.83181	+	1.53707i	0.0600997	+	0.0504296i	0.672343	−	0.740240i	$-0.265288\pi$
$929$	1.83181	+	1.53707i	0.0600997	+	0.0504296i	−0.612243	+	0.790670i	$0.709733\pi$
$930$	0.242214	+	0.690148i	0.00794251	+	0.0226308i
$931$	−12.9616	−	44.1539i	−0.424798	−	1.44708i
$932$	−9.71762	+	26.6990i	−0.318311	+	0.874553i
$933$	−29.4643	−	5.54657i	−0.964619	−	0.181587i
$934$	−0.959991	−	2.63755i	−0.0314119	−	0.0863034i
$935$	32.8940	+	18.9914i	1.07575	+	0.621084i
$936$	12.1468	+	0.280311i	0.397030	+	0.00916224i
$937$	16.4410	+	9.49219i	0.537103	+	0.310096i	0.743904	−	0.668287i	$-0.232972\pi$
$937$	16.4410	+	9.49219i	0.537103	+	0.310096i	−0.206801	+	0.978383i	$0.566305\pi$
$938$	9.29705	−	7.31078i	0.303559	−	0.238705i
$939$	12.3043	+	21.8910i	0.401535	+	0.714387i
$940$	−9.47759	−	3.44956i	−0.309125	−	0.112512i
$941$	−51.7568	−	18.8379i	−1.68722	−	0.614099i	−0.692951	−	0.720985i	$-0.743690\pi$
$941$	−51.7568	−	18.8379i	−1.68722	−	0.614099i	−0.994271	+	0.106886i	$0.965912\pi$
$942$	31.4720	−	5.17575i	1.02541	−	0.168635i
$943$	1.39782	+	0.246474i	0.0455193	+	0.00802629i
$944$	−12.1952			−0.396920
$945$	44.0345	+	42.2321i	1.43244	+	1.37381i
$946$	−4.76807			−0.155023
$947$	−46.0190	−	8.11439i	−1.49542	−	0.263682i	−0.634696	−	0.772762i	$-0.718875\pi$
$947$	−46.0190	−	8.11439i	−1.49542	−	0.263682i	−0.860719	+	0.509080i	$0.829986\pi$
$948$	−2.23287	−	2.72424i	−0.0725202	−	0.0884794i
$949$	51.4642	+	18.7314i	1.67060	+	0.608048i
$950$	−90.7845	−	33.0429i	−2.94544	−	1.07205i
$951$	−13.6752	−	0.157770i	−0.443449	−	0.00511605i
$952$	−9.17113	−	3.67192i	−0.297238	−	0.119008i
$953$	−20.0182	−	11.5575i	−0.648453	−	0.374385i	0.139410	−	0.990235i	$-0.455479\pi$
$953$	−20.0182	−	11.5575i	−0.648453	−	0.374385i	−0.787863	+	0.615850i	$0.788813\pi$
$954$	4.85669	+	1.89569i	0.157241	+	0.0613753i
$955$	13.3857	+	7.72825i	0.433152	+	0.250080i
$956$	−6.93836	−	19.0630i	−0.224403	−	0.616541i
$957$	−6.97876	−	19.8848i	−0.225591	−	0.642785i
$958$	−6.48435	+	17.8156i	−0.209500	+	0.575596i
$959$	−14.8314	−	0.471298i	−0.478931	−	0.0152190i
$960$	7.55423	+	1.42206i	0.243812	+	0.0458968i
$961$	23.7404	+	19.9206i	0.765821	+	0.642600i
$962$	5.88467	−	10.1926i	0.189730	−	0.328621i
$963$	2.43001	+	7.18823i	0.0783059	+	0.231637i
$964$	9.58097	−	5.53157i	0.308582	−	0.178160i
$965$	78.2814	+	65.6859i	2.51997	+	2.11450i
$966$	−17.9113	+	5.65391i	−0.576286	+	0.181912i
$967$	3.65717	+	20.7408i	0.117607	+	0.666980i	0.985427	+	0.170101i	$0.0544095\pi$
$967$	3.65717	+	20.7408i	0.117607	+	0.666980i	−0.867820	+	0.496879i	$0.834479\pi$
$968$	5.65893	−	0.997822i	0.181885	−	0.0320712i
$969$	−39.7805	−	15.0008i	−1.27793	−	0.481896i
$970$	−36.2102	−	30.3840i	−1.16264	−	0.975570i
$971$	14.9211	−	25.8441i	0.478841	−	0.829377i	−0.520865	−	0.853639i	$-0.674390\pi$
$971$	14.9211	−	25.8441i	0.478841	−	0.829377i	0.999706	+	0.0242623i	$0.00772370\pi$
$972$	−13.0282	−	8.55954i	−0.417880	−	0.274547i
$973$	5.77448	−	27.5926i	0.185121	−	0.884577i
$974$	−2.69211	−	7.39652i	−0.0862609	−	0.237000i
$975$	−16.7292	−	101.725i	−0.535763	−	3.25780i
$976$	2.55352	−	7.01574i	0.0817362	−	0.224568i
$977$	−27.7148	−	33.0292i	−0.886674	−	1.05670i	−0.998019	−	0.0629153i	$-0.979960\pi$
$977$	−27.7148	−	33.0292i	−0.886674	−	1.05670i	0.111345	−	0.993782i	$-0.464484\pi$
$978$	3.92337	+	6.98023i	0.125456	+	0.223203i
$979$	−9.23388	+	11.0045i	−0.295116	+	0.351706i
$980$	25.0180	−	18.4178i	0.799170	−	0.588335i
$981$	6.52070	−	32.5679i	0.208190	−	1.03981i
$982$	22.4418			0.716147
$983$	52.0862	−	18.9578i	1.66129	−	0.604661i	0.670728	−	0.741704i	$-0.265982\pi$
$983$	52.0862	−	18.9578i	1.66129	−	0.604661i	0.990565	+	0.137042i	$0.0437597\pi$
$984$	0.565972	−	0.198633i	0.0180425	−	0.00633220i
$985$	67.6264	+	80.5940i	2.15476	+	2.56794i
$986$	−18.6249	−	6.77891i	−0.593137	−	0.215884i
$987$	8.26013	−	6.34256i	0.262923	−	0.201886i
$988$	4.62324	−	26.2197i	0.147085	−	0.834159i
$989$			8.52609i			0.271114i
$990$	23.8241	−	19.0717i	0.757178	−	0.606137i
$991$	8.09739			0.257222			0.128611	−	0.991695i	$-0.458948\pi$
$991$	8.09739			0.257222			0.128611	+	0.991695i	$0.458948\pi$
$992$	−0.0894127	+	0.0325436i	−0.00283886	+	0.00103326i
$993$	0.282200	−	24.4605i	0.00895533	−	0.776231i
$994$	8.11935	+	5.03815i	0.257530	+	0.159800i
$995$	66.0083	+	78.6656i	2.09260	+	2.49387i
$996$	−0.630898	+	1.67307i	−0.0199908	+	0.0530132i
$997$	−21.2068	+	25.2732i	−0.671625	+	0.800411i	−0.989004	−	0.147887i	$-0.952753\pi$
$997$	−21.2068	+	25.2732i	−0.671625	+	0.800411i	0.317379	+	0.948299i	$0.397197\pi$
$998$	−4.76979	+	2.75384i	−0.150985	+	0.0871712i
$999$	−13.3305	+	7.09301i	−0.421757	+	0.224413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.ba.a.47.17	✓	144
7.3	odd	6		378.2.bf.a.101.1	yes	144
27.23	odd	18		378.2.bf.a.131.1	yes	144
189.185	even	18	inner	378.2.ba.a.185.17	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.17	✓	144	1.1	even	1	trivial
378.2.ba.a.185.17	yes	144	189.185	even	18	inner
378.2.bf.a.101.1	yes	144	7.3	odd	6
378.2.bf.a.131.1	yes	144	27.23	odd	18

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.611133 + 1.62065i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-4.17040 - 1.51790i) q^{5} +(-0.883272 + 1.48991i) q^{6} +(-1.63543 - 2.07976i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.25303 - 1.98087i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-0.611133 + 1.62065i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-4.17040 - 1.51790i) q^{5} +(-0.883272 + 1.48991i) q^{6} +(-1.63543 - 2.07976i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.25303 - 1.98087i) q^{9} +(-3.84346 - 2.21902i) q^{10} +(-0.783948 - 2.15388i) q^{11} +(-1.12857 + 1.31390i) q^{12} +(-1.38518 + 3.80576i) q^{13} +(-1.24943 - 2.33215i) q^{14} +(5.00866 - 5.83113i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.86694 - 3.23363i) q^{17} +(-1.87483 - 2.34201i) q^{18} +(-5.69313 + 3.28693i) q^{19} +(-3.39974 - 2.85272i) q^{20} +(4.37002 - 1.37945i) q^{21} +(-0.398021 - 2.25729i) q^{22} +(-4.03640 + 0.711726i) q^{23} +(-1.33958 + 1.09796i) q^{24} +(11.2580 + 9.44655i) q^{25} +(-2.02500 + 3.50741i) q^{26} +(4.58720 - 2.44081i) q^{27} +(-0.825480 - 2.51368i) q^{28} +(-1.81552 - 4.98809i) q^{29} +(5.94513 - 4.87279i) q^{30} +(-0.0325436 + 0.0894127i) q^{31} +(0.642788 + 0.766044i) q^{32} +(3.96979 + 0.0457992i) q^{33} +(2.40009 - 2.86031i) q^{34} +(3.66351 + 11.1558i) q^{35} +(-1.43966 - 2.63199i) q^{36} -2.90601 q^{37} +(-6.17741 + 2.24839i) q^{38} +(-5.32129 - 4.57073i) q^{39} +(-2.85272 - 3.39974i) q^{40} +(-0.325419 - 0.118443i) q^{41} +(4.54317 - 0.599648i) q^{42} +(0.361225 - 2.04861i) q^{43} -2.29211i q^{44} +(6.38928 + 11.6809i) q^{45} -4.09867 q^{46} +(2.13553 - 0.777271i) q^{47} +(-1.50989 + 0.848664i) q^{48} +(-1.65076 + 6.80257i) q^{49} +(9.44655 + 11.2580i) q^{50} +(4.09964 + 5.00183i) q^{51} +(-2.60329 + 3.10248i) q^{52} +(-1.50502 + 0.868925i) q^{53} +(4.94136 - 1.60717i) q^{54} +10.1725i q^{55} +(-0.376443 - 2.61883i) q^{56} +(-1.84771 - 11.2353i) q^{57} +(-0.921762 - 5.22757i) q^{58} +(-9.34207 + 7.83893i) q^{59} +(6.70096 - 3.76640i) q^{60} +(-2.55352 - 7.01574i) q^{61} +(-0.0475755 + 0.0824032i) q^{62} +(-0.435054 + 7.92532i) q^{63} +(0.500000 + 0.866025i) q^{64} +(11.5535 - 13.7690i) q^{65} +(3.90152 + 0.734450i) q^{66} +(0.776252 + 4.40235i) q^{67} +(2.86031 - 2.40009i) q^{68} +(1.31332 - 6.97656i) q^{69} +(1.67067 + 11.6225i) q^{70} +(-3.12776 + 1.80581i) q^{71} +(-0.960749 - 2.84200i) q^{72} -13.5227i q^{73} +(-2.86186 - 0.504623i) q^{74} +(-22.1897 + 12.4721i) q^{75} +(-6.47399 + 1.14154i) q^{76} +(-3.19745 + 5.15293i) q^{77} +(-4.44674 - 5.42532i) q^{78} +(-0.353140 + 2.00276i) q^{79} +(-2.21902 - 3.84346i) q^{80} +(1.15231 + 8.92593i) q^{81} +(-0.299908 - 0.173152i) q^{82} +(0.970084 - 0.353082i) q^{83} +(4.57828 + 0.198376i) q^{84} +(-12.6942 + 10.6517i) q^{85} +(0.711474 - 1.95476i) q^{86} +(9.19349 + 0.106065i) q^{87} +(0.398021 - 2.25729i) q^{88} +(-3.13366 - 5.42765i) q^{89} +(4.26384 + 12.6129i) q^{90} +(10.1804 - 3.34320i) q^{91} +(-4.03640 - 0.711726i) q^{92} +(-0.125019 - 0.107385i) q^{93} +(2.23806 - 0.394631i) q^{94} +(28.7318 - 5.06620i) q^{95} +(-1.63432 + 0.573581i) q^{96} +(10.4891 + 1.84951i) q^{97} +(-2.80694 + 6.41257i) q^{98} +(-2.50029 + 6.40566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 18 q^{6} + 24 q^{9}+O(q^{10}) \) 144 * q - 18 * q^6 + 24 * q^9	\( 144 q - 18 q^{6} + 24 q^{9} - 24 q^{11} + 6 q^{14} + 12 q^{15} - 30 q^{21} - 42 q^{23} - 6 q^{29} - 18 q^{30} + 6 q^{36} + 48 q^{39} - 48 q^{42} + 18 q^{45} - 54 q^{47} - 36 q^{49} + 12 q^{50} - 36 q^{51} - 90 q^{53} + 6 q^{56} - 6 q^{57} + 18 q^{60} + 54 q^{61} - 24 q^{63} + 72 q^{64} + 78 q^{65} - 72 q^{66} - 54 q^{68} + 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} - 36 q^{74} - 6 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 36 q^{91} - 42 q^{92} + 96 q^{93} - 66 q^{95} - 108 q^{99}+O(q^{100}) \) 144 * q - 18 * q^6 + 24 * q^9 - 24 * q^11 + 6 * q^14 + 12 * q^15 - 30 * q^21 - 42 * q^23 - 6 * q^29 - 18 * q^30 + 6 * q^36 + 48 * q^39 - 48 * q^42 + 18 * q^45 - 54 * q^47 - 36 * q^49 + 12 * q^50 - 36 * q^51 - 90 * q^53 + 6 * q^56 - 6 * q^57 + 18 * q^60 + 54 * q^61 - 24 * q^63 + 72 * q^64 + 78 * q^65 - 72 * q^66 - 54 * q^68 + 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 - 36 * q^74 - 6 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 36 * q^91 - 42 * q^92 + 96 * q^93 - 66 * q^95 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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