LMFDB - Embedded newform 378.2.v.a.205.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(67,378)]

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([8, 12]))

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

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

chi := DirichletCharacter("378.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.v (of order $9$, 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:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			205.9
Character	$\chi$	$=$	378.205
Dual form			378.2.v.a.319.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(1.03428 + 1.38934i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.29253 - 1.92366i) q^{5} +(1.44709 + 0.951806i) q^{6} +(1.08943 + 2.41105i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.860524 + 2.87393i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(1.03428 + 1.38934i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.29253 - 1.92366i) q^{5} +(1.44709 + 0.951806i) q^{6} +(1.08943 + 2.41105i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.860524 + 2.87393i) q^{9} +(1.49634 - 2.59174i) q^{10} +(-4.67540 - 3.92312i) q^{11} +(1.68536 + 0.399472i) q^{12} +(-0.776320 + 0.651410i) q^{13} +(1.84835 + 1.89304i) q^{14} +(5.04374 + 1.19549i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.495055 + 0.857460i) q^{17} +(0.174315 + 2.99493i) q^{18} +(-0.365316 - 0.632745i) q^{19} +(0.519675 - 2.94722i) q^{20} +(-2.22299 + 4.00728i) q^{21} +(-5.73522 - 2.08745i) q^{22} +(-4.48064 - 1.63082i) q^{23} +(1.72034 - 0.201045i) q^{24} +(0.686982 - 3.89607i) q^{25} +(-0.506707 + 0.877642i) q^{26} +(-4.88289 + 1.77690i) q^{27} +(2.38434 + 1.14670i) q^{28} +(4.40248 + 3.69412i) q^{29} +(5.14845 - 0.601664i) q^{30} +(-1.14255 + 0.958713i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.614872 - 10.5533i) q^{33} +(-0.171931 + 0.975067i) q^{34} +(7.13558 + 3.43171i) q^{35} +(1.18813 + 2.75470i) q^{36} +7.19761 q^{37} +(-0.559696 - 0.469641i) q^{38} +(-1.70796 - 0.404830i) q^{39} +(-0.519675 - 2.94722i) q^{40} +(4.68857 - 3.93417i) q^{41} +(-0.718353 + 4.52592i) q^{42} +(-8.13938 + 2.96249i) q^{43} -6.10330 q^{44} +(3.55570 + 8.24394i) q^{45} -4.76820 q^{46} +(-3.08123 - 2.58546i) q^{47} +(1.54783 - 0.777312i) q^{48} +(-4.62630 + 5.25332i) q^{49} +(-0.686982 - 3.89607i) q^{50} +(-1.70333 + 0.199056i) q^{51} +(-0.175977 + 0.998018i) q^{52} +(6.09840 + 10.5627i) q^{53} +(-3.98068 + 3.33979i) q^{54} -18.2653 q^{55} +(2.63274 + 0.262053i) q^{56} +(0.501258 - 1.16198i) q^{57} +(5.40044 + 1.96560i) q^{58} +(-2.45918 - 13.9467i) q^{59} +(4.63218 - 2.32625i) q^{60} +(-6.67203 - 5.59850i) q^{61} +(-0.745746 + 1.29167i) q^{62} +(-7.86667 + 1.05618i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.526645 + 2.98675i) q^{65} +(-3.03166 - 10.1272i) q^{66} +(11.7890 + 4.29083i) q^{67} +(0.171931 + 0.975067i) q^{68} +(-2.36848 - 7.91185i) q^{69} +(7.87897 + 0.784241i) q^{70} +(-3.48150 - 6.03014i) q^{71} +(2.05864 + 2.18220i) q^{72} -8.79100 q^{73} +(6.76355 - 2.46173i) q^{74} +(6.12349 - 3.07518i) q^{75} +(-0.686569 - 0.249891i) q^{76} +(4.36534 - 15.5466i) q^{77} +(-1.74342 + 0.203741i) q^{78} +(-4.97578 + 1.81103i) q^{79} +(-1.49634 - 2.59174i) q^{80} +(-7.51900 - 4.94618i) q^{81} +(3.06024 - 5.30050i) q^{82} +(7.68885 + 6.45171i) q^{83} +(0.872925 + 4.49867i) q^{84} +(0.514534 + 2.91807i) q^{85} +(-6.63529 + 5.56767i) q^{86} +(-0.578979 + 9.93729i) q^{87} +(-5.73522 + 2.08745i) q^{88} +(-6.93172 - 12.0061i) q^{89} +(6.16086 + 6.53065i) q^{90} +(-2.41632 - 1.16208i) q^{91} +(-4.48064 + 1.63082i) q^{92} +(-2.51370 - 0.595810i) q^{93} +(-3.77969 - 1.37570i) q^{94} +(-2.05469 - 0.747844i) q^{95} +(1.18863 - 1.25982i) q^{96} +(4.30379 - 1.56645i) q^{97} +(-2.55056 + 6.51879i) q^{98} +(15.2981 - 10.0608i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	1.03428	+	1.38934i	0.597143	+	0.802135i
$3$	1.03428	+	1.38934i	0.597143	+	0.802135i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	2.29253	−	1.92366i	1.02525	−	0.860288i	0.0349726	−	0.999388i	$-0.488866\pi$
$5$	2.29253	−	1.92366i	1.02525	−	0.860288i	0.990278	+	0.139101i	$0.0444211\pi$
$6$	1.44709	+	0.951806i	0.590771	+	0.388573i
$7$	1.08943	+	2.41105i	0.411765	+	0.911290i
$7$	1.08943	+	2.41105i	0.411765	+	0.911290i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.860524	+	2.87393i	−0.286841	+	0.957978i
$10$	1.49634	−	2.59174i	0.473185	−	0.819581i
$11$	−4.67540	−	3.92312i	−1.40969	−	1.18287i	−0.956602	−	0.291398i	$-0.905880\pi$
$11$	−4.67540	−	3.92312i	−1.40969	−	1.18287i	−0.453083	−	0.891468i	$-0.649676\pi$
$12$	1.68536	+	0.399472i	0.486520	+	0.115318i
$13$	−0.776320	+	0.651410i	−0.215312	+	0.180669i	−0.744065	−	0.668108i	$-0.767105\pi$
$13$	−0.776320	+	0.651410i	−0.215312	+	0.180669i	0.528752	+	0.848776i	$0.322660\pi$
$14$	1.84835	+	1.89304i	0.493993	+	0.505936i
$15$	5.04374	+	1.19549i	1.30229	+	0.308675i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−0.495055	+	0.857460i	−0.120068	+	0.207965i	−0.919794	−	0.392401i	$-0.871645\pi$
$17$	−0.495055	+	0.857460i	−0.120068	+	0.207965i	0.799726	+	0.600365i	$0.204978\pi$
$18$	0.174315	+	2.99493i	0.0410865	+	0.705912i
$19$	−0.365316	−	0.632745i	−0.0838092	−	0.145162i	0.821074	−	0.570822i	$-0.193375\pi$
$19$	−0.365316	−	0.632745i	−0.0838092	−	0.145162i	−0.904883	+	0.425660i	$0.860042\pi$
$20$	0.519675	−	2.94722i	0.116203	−	0.659019i
$21$	−2.22299	+	4.00728i	−0.485096	+	0.874461i
$22$	−5.73522	−	2.08745i	−1.22275	−	0.445046i
$23$	−4.48064	−	1.63082i	−0.934278	−	0.340049i	−0.170374	−	0.985379i	$-0.554498\pi$
$23$	−4.48064	−	1.63082i	−0.934278	−	0.340049i	−0.763904	+	0.645330i	$0.776720\pi$
$24$	1.72034	−	0.201045i	0.351164	−	0.0410381i
$25$	0.686982	−	3.89607i	0.137396	−	0.779214i
$26$	−0.506707	+	0.877642i	−0.0993734	+	0.172120i
$27$	−4.88289	+	1.77690i	−0.939713	+	0.341964i
$28$	2.38434	+	1.14670i	0.450598	+	0.216706i
$29$	4.40248	+	3.69412i	0.817520	+	0.685980i	0.952390	−	0.304883i	$-0.0986173\pi$
$29$	4.40248	+	3.69412i	0.817520	+	0.685980i	−0.134870	+	0.990863i	$0.543062\pi$
$30$	5.14845	−	0.601664i	0.939974	−	0.109848i
$31$	−1.14255	+	0.958713i	−0.205208	+	0.172190i	−0.739600	−	0.673047i	$-0.764985\pi$
$31$	−1.14255	+	0.958713i	−0.205208	+	0.172190i	0.534392	+	0.845237i	$0.320541\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	0.614872	−	10.5533i	0.107035	−	1.83710i
$34$	−0.171931	+	0.975067i	−0.0294859	+	0.167223i
$35$	7.13558	+	3.43171i	1.20613	+	0.580065i
$36$	1.18813	+	2.75470i	0.198022	+	0.459116i
$37$	7.19761			1.18328			0.591640	−	0.806202i	$-0.298481\pi$
$37$	7.19761			1.18328			0.591640	+	0.806202i	$0.298481\pi$
$38$	−0.559696	−	0.469641i	−0.0907947	−	0.0761858i
$39$	−1.70796	−	0.404830i	−0.273493	−	0.0648247i
$40$	−0.519675	−	2.94722i	−0.0821678	−	0.465997i
$41$	4.68857	−	3.93417i	0.732231	−	0.614415i	−0.198508	−	0.980099i	$-0.563610\pi$
$41$	4.68857	−	3.93417i	0.732231	−	0.614415i	0.930739	+	0.365685i	$0.119165\pi$
$42$	−0.718353	+	4.52592i	−0.110844	+	0.698365i
$43$	−8.13938	+	2.96249i	−1.24124	+	0.451776i	−0.877434	−	0.479697i	$-0.840747\pi$
$43$	−8.13938	+	2.96249i	−1.24124	+	0.451776i	−0.363810	+	0.931473i	$0.618524\pi$
$44$	−6.10330			−0.920107
$45$	3.55570	+	8.24394i	0.530052	+	1.22893i
$46$	−4.76820			−0.703032
$47$	−3.08123	−	2.58546i	−0.449444	−	0.377128i	0.389785	−	0.920906i	$-0.372549\pi$
$47$	−3.08123	−	2.58546i	−0.449444	−	0.377128i	−0.839230	+	0.543777i	$0.816994\pi$
$48$	1.54783	−	0.777312i	0.223410	−	0.112195i
$49$	−4.62630	+	5.25332i	−0.660900	+	0.750474i
$50$	−0.686982	−	3.89607i	−0.0971539	−	0.550987i
$51$	−1.70333	+	0.199056i	−0.238514	+	0.0278734i
$52$	−0.175977	+	0.998018i	−0.0244037	+	0.138400i
$53$	6.09840	+	10.5627i	0.837679	+	1.45090i	0.891830	+	0.452370i	$0.149421\pi$
$53$	6.09840	+	10.5627i	0.837679	+	1.45090i	−0.0541512	+	0.998533i	$0.517245\pi$
$54$	−3.98068	+	3.33979i	−0.541702	+	0.454487i
$55$	−18.2653			−2.46289
$56$	2.63274	+	0.262053i	0.351815	+	0.0350183i
$57$	0.501258	−	1.16198i	0.0663933	−	0.153909i
$58$	5.40044	+	1.96560i	0.709112	+	0.258096i
$59$	−2.45918	−	13.9467i	−0.320158	−	1.81570i	−0.541721	−	0.840558i	$-0.682227\pi$
$59$	−2.45918	−	13.9467i	−0.320158	−	1.81570i	0.221564	−	0.975146i	$-0.428884\pi$
$60$	4.63218	−	2.32625i	0.598012	−	0.300318i
$61$	−6.67203	−	5.59850i	−0.854266	−	0.716814i	0.106459	−	0.994317i	$-0.466049\pi$
$61$	−6.67203	−	5.59850i	−0.854266	−	0.716814i	−0.960725	+	0.277503i	$0.910493\pi$
$62$	−0.745746	+	1.29167i	−0.0947099	+	0.164042i
$63$	−7.86667	+	1.05618i	−0.991107	+	0.133066i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.526645	+	2.98675i	−0.0653223	+	0.370461i
$66$	−3.03166	−	10.1272i	−0.373171	−	1.24657i
$67$	11.7890	+	4.29083i	1.44025	+	0.524208i	0.939851	−	0.341586i	$-0.110964\pi$
$67$	11.7890	+	4.29083i	1.44025	+	0.524208i	0.500400	+	0.865794i	$0.333186\pi$
$68$	0.171931	+	0.975067i	0.0208497	+	0.118244i
$69$	−2.36848	−	7.91185i	−0.285132	−	0.952475i
$70$	7.87897	+	0.784241i	0.941717	+	0.0937348i
$71$	−3.48150	−	6.03014i	−0.413179	−	0.715646i	0.582057	−	0.813148i	$-0.302248\pi$
$71$	−3.48150	−	6.03014i	−0.413179	−	0.715646i	−0.995235	+	0.0975018i	$0.968915\pi$
$72$	2.05864	+	2.18220i	0.242613	+	0.257175i
$73$	−8.79100			−1.02891			−0.514455	−	0.857518i	$-0.672006\pi$
$73$	−8.79100			−1.02891			−0.514455	+	0.857518i	$0.672006\pi$
$74$	6.76355	−	2.46173i	0.786246	−	0.286170i
$75$	6.12349	−	3.07518i	0.707080	−	0.355091i
$76$	−0.686569	−	0.249891i	−0.0787549	−	0.0286644i
$77$	4.36534	−	15.5466i	0.497476	−	1.77169i
$78$	−1.74342	+	0.203741i	−0.197403	+	0.0230692i
$79$	−4.97578	+	1.81103i	−0.559819	+	0.203757i	−0.606404	−	0.795157i	$-0.707388\pi$
$79$	−4.97578	+	1.81103i	−0.559819	+	0.203757i	0.0465849	+	0.998914i	$0.485166\pi$
$80$	−1.49634	−	2.59174i	−0.167296	−	0.289766i
$81$	−7.51900	−	4.94618i	−0.835444	−	0.549575i
$82$	3.06024	−	5.30050i	0.337947	−	0.585342i
$83$	7.68885	+	6.45171i	0.843961	+	0.708167i	0.958451	−	0.285257i	$-0.0920789\pi$
$83$	7.68885	+	6.45171i	0.843961	+	0.708167i	−0.114490	+	0.993424i	$0.536523\pi$
$84$	0.872925	+	4.49867i	0.0952439	+	0.490845i
$85$	0.514534	+	2.91807i	0.0558091	+	0.316509i
$86$	−6.63529	+	5.56767i	−0.715501	+	0.600377i
$87$	−0.578979	+	9.93729i	−0.0620731	+	1.06539i
$88$	−5.73522	+	2.08745i	−0.611377	+	0.222523i
$89$	−6.93172	−	12.0061i	−0.734761	−	1.27264i	−0.954828	−	0.297159i	$-0.903961\pi$
$89$	−6.93172	−	12.0061i	−0.734761	−	1.27264i	0.220067	−	0.975485i	$-0.429373\pi$
$90$	6.16086	+	6.53065i	0.649411	+	0.688391i
$91$	−2.41632	−	1.16208i	−0.253300	−	0.121819i
$92$	−4.48064	+	1.63082i	−0.467139	+	0.170025i
$93$	−2.51370	−	0.595810i	−0.260658	−	0.0617826i
$94$	−3.77969	−	1.37570i	−0.389846	−	0.141892i
$95$	−2.05469	−	0.747844i	−0.210806	−	0.0767272i
$96$	1.18863	−	1.25982i	0.121314	−	0.128580i
$97$	4.30379	−	1.56645i	0.436984	−	0.159049i	−0.114155	−	0.993463i	$-0.536416\pi$
$97$	4.30379	−	1.56645i	0.436984	−	0.159049i	0.551138	+	0.834414i	$0.314194\pi$
$98$	−2.55056	+	6.51879i	−0.257645	+	0.658497i
$99$	15.2981	−	10.0608i	1.53752	−	1.01115i
$100$	−1.97809	−	3.42614i	−0.197809	−	0.342614i
$101$	−5.27683	+	1.92061i	−0.525064	+	0.191108i	−0.590933	−	0.806721i	$-0.701240\pi$
$101$	−5.27683	+	1.92061i	−0.525064	+	0.191108i	0.0658691	+	0.997828i	$0.479018\pi$
$102$	−1.53252	+	0.769624i	−0.151742	+	0.0762041i
$103$	−1.18369	+	0.993235i	−0.116633	+	0.0978663i	−0.699239	−	0.714888i	$-0.746478\pi$
$103$	−1.18369	+	0.993235i	−0.116633	+	0.0978663i	0.582606	+	0.812755i	$0.302033\pi$
$104$	0.175977	+	0.998018i	0.0172560	+	0.0978637i
$105$	2.61239	+	13.4631i	0.254943	+	1.31386i
$106$	9.34328	+	7.83995i	0.907500	+	0.761483i
$107$	−4.47689	+	7.75421i	−0.432798	+	0.749627i	−0.997113	−	0.0759319i	$-0.975807\pi$
$107$	−4.47689	+	7.75421i	−0.432798	+	0.749627i	0.564315	+	0.825559i	$0.309140\pi$
$108$	−2.59834	+	4.49985i	−0.250026	+	0.432998i
$109$	−0.656451	−	1.13701i	−0.0628766	−	0.108905i	0.832874	−	0.553463i	$-0.186694\pi$
$109$	−0.656451	−	1.13701i	−0.0628766	−	0.108905i	−0.895750	+	0.444558i	$0.853361\pi$
$110$	−17.1637	+	6.24709i	−1.63650	+	0.595636i
$111$	7.44436	+	9.99992i	0.706587	+	0.949151i
$112$	2.56360	−	0.654202i	0.242237	−	0.0618163i
$113$	11.2913	+	4.10969i	1.06219	+	0.386607i	0.813252	−	0.581912i	$-0.197695\pi$
$113$	11.2913	+	4.10969i	1.06219	+	0.386607i	0.248941	+	0.968519i	$0.419917\pi$
$114$	0.0736069	−	1.26335i	0.00689391	−	0.118323i
$115$	−13.4092	+	4.88053i	−1.25041	+	0.455112i
$116$	5.74703			0.533598
$117$	−1.20407	−	2.79165i	−0.111316	−	0.258088i
$118$	−7.08092	−	12.2645i	−0.651851	−	1.12904i
$119$	−2.60670	−	0.259461i	−0.238956	−	0.0237847i
$120$	3.55720	−	3.77026i	0.324726	−	0.344176i
$121$	4.55831	+	25.8514i	0.414391	+	2.35013i
$122$	−8.18446	−	2.97890i	−0.740986	−	0.269697i
$123$	10.3152	+	2.44496i	0.930090	+	0.220455i
$124$	−0.258995	+	1.46883i	−0.0232584	+	0.131905i
$125$	1.56193	+	2.70534i	0.139703	+	0.241973i
$126$	−7.03102	+	3.68304i	−0.626373	+	0.328111i
$127$	5.48073	−	9.49290i	0.486336	−	0.842359i	−0.513541	−	0.858065i	$-0.671666\pi$
$127$	5.48073	−	9.49290i	0.486336	−	0.842359i	0.999877	+	0.0157066i	$0.00499976\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−12.5343	−	8.24431i	−1.10359	−	0.725871i
$130$	0.526645	+	2.98675i	0.0461898	+	0.261956i
$131$	19.0319	+	6.92703i	1.66282	+	0.605217i	0.990802	−	0.135317i	$-0.0432053\pi$
$131$	19.0319	+	6.92703i	1.66282	+	0.605217i	0.672019	+	0.740534i	$0.265428\pi$
$132$	−6.31253	−	8.47955i	−0.549435	−	0.738050i
$133$	1.12759	−	1.57012i	0.0977749	−	0.136147i
$134$	12.5455			1.08377
$135$	−7.77603	+	13.4666i	−0.669254	+	1.15902i
$136$	0.495055	+	0.857460i	0.0424506	+	0.0735266i
$137$	1.54917	−	8.78576i	0.132354	−	0.750618i	−0.844311	−	0.535853i	$-0.819990\pi$
$137$	1.54917	−	8.78576i	0.132354	−	0.750618i	0.976666	−	0.214765i	$-0.0688987\pi$
$138$	−4.93166	−	6.62464i	−0.419811	−	0.563927i
$139$	−0.208152	−	1.18049i	−0.0176552	−	0.100128i	0.974707	−	0.223488i	$-0.0717442\pi$
$139$	−0.208152	−	1.18049i	−0.0176552	−	0.100128i	−0.992362	+	0.123360i	$0.960633\pi$
$140$	7.67204	−	1.95782i	0.648405	−	0.165466i
$141$	0.405220	−	6.95497i	0.0341257	−	0.585714i
$142$	−5.33397	−	4.47574i	−0.447617	−	0.375595i
$143$	6.18517			0.517230
$144$	2.68084	+	1.34650i	0.223404	+	0.112209i
$145$	17.1990			1.42830
$146$	−8.26084	+	3.00670i	−0.683672	+	0.248836i
$147$	−12.0835	−	0.994087i	−0.996633	−	0.0819909i
$148$	5.51369	−	4.62654i	0.453223	−	0.380299i
$149$	−0.268324	−	1.52174i	−0.0219820	−	0.124666i	0.971842	−	0.235633i	$-0.0757163\pi$
$149$	−0.268324	−	1.52174i	−0.0219820	−	0.124666i	−0.993824	+	0.110967i	$0.964605\pi$
$150$	4.70243	−	4.98408i	0.383951	−	0.406949i
$151$	−0.0692745	−	0.0581282i	−0.00563748	−	0.00473041i	0.639965	−	0.768404i	$-0.278949\pi$
$151$	−0.0692745	−	0.0581282i	−0.00563748	−	0.00473041i	−0.645602	+	0.763674i	$0.723393\pi$
$152$	−0.730632			−0.0592620
$153$	−2.03828	−	2.16062i	−0.164785	−	0.174676i
$154$	−1.21516	−	16.1020i	−0.0979206	−	1.29754i
$155$	−0.775091	+	4.39576i	−0.0622568	+	0.353076i
$156$	−1.56859	+	0.787739i	−0.125588	+	0.0630696i
$157$	0.475512	+	2.69676i	0.0379500	+	0.215225i	0.997886	−	0.0649959i	$-0.0207034\pi$
$157$	0.475512	+	2.69676i	0.0379500	+	0.215225i	−0.959936	+	0.280221i	$0.909592\pi$
$158$	−4.05629	+	3.40363i	−0.322701	+	0.270778i
$159$	−8.36775	+	19.3976i	−0.663606	+	1.53833i
$160$	−2.29253	−	1.92366i	−0.181240	−	0.152079i
$161$	−0.949345	−	12.5797i	−0.0748189	−	0.991419i
$162$	−8.75724	−	2.07624i	−0.688034	−	0.163125i
$163$	−5.00648	+	8.67147i	−0.392137	+	0.679202i	−0.992731	−	0.120352i	$-0.961598\pi$
$163$	−5.00648	+	8.67147i	−0.392137	+	0.679202i	0.600594	+	0.799554i	$0.294931\pi$
$164$	1.06281	−	6.02750i	0.0829916	−	0.470669i
$165$	−18.8914	−	25.3766i	−1.47069	−	1.97557i
$166$	9.43177	+	3.43288i	0.732048	+	0.266444i
$167$	21.9140	+	7.97603i	1.69575	+	0.617204i	0.995331	−	0.0965233i	$-0.0307722\pi$
$167$	21.9140	+	7.97603i	1.69575	+	0.617204i	0.700424	+	0.713727i	$0.252994\pi$
$168$	2.35892	+	3.92881i	0.181994	+	0.303114i
$169$	−2.07909	+	11.7911i	−0.159930	+	0.907007i
$170$	1.48154	+	2.56611i	0.113629	+	0.196811i
$171$	2.13283	−	0.505401i	0.163102	−	0.0386490i
$172$	−4.33088	+	7.50130i	−0.330226	+	0.571968i
$173$	−1.28070	+	7.26320i	−0.0973696	+	0.552211i	0.896626	+	0.442789i	$0.146011\pi$
$173$	−1.28070	+	7.26320i	−0.0973696	+	0.552211i	−0.993995	+	0.109422i	$0.965100\pi$
$174$	2.85469	+	9.53602i	0.216414	+	0.722924i
$175$	10.1420	−	2.58813i	0.766665	−	0.195645i
$176$	−4.67540	+	3.92312i	−0.352421	+	0.295717i
$177$	16.8332	−	17.8414i	1.26526	−	1.34104i
$178$	−10.6200	−	8.91125i	−0.796004	−	0.667927i
$179$	−2.05696	+	3.56276i	−0.153745	+	0.266293i	−0.932601	−	0.360909i	$-0.882467\pi$
$179$	−2.05696	+	3.56276i	−0.153745	+	0.266293i	0.778857	+	0.627202i	$0.215800\pi$
$180$	8.02293	+	4.02966i	0.597994	+	0.300353i
$181$	4.94612	−	8.56693i	0.367642	−	0.636775i	−0.621554	−	0.783371i	$-0.713498\pi$
$181$	4.94612	−	8.56693i	0.367642	−	0.636775i	0.989196	+	0.146596i	$0.0468318\pi$
$182$	−2.66806	−	0.265568i	−0.197770	−	0.0196852i
$183$	0.877453	−	15.0601i	0.0648632	−	1.11328i
$184$	−3.65265	+	3.06494i	−0.269277	+	0.225950i
$185$	16.5008	−	13.8458i	1.21316	−	1.01796i
$186$	−2.56588	+	0.299857i	−0.188139	+	0.0219866i
$187$	5.67850	−	2.06680i	0.415253	−	0.151140i
$188$	−4.02227			−0.293354
$189$	−9.60374	−	9.83708i	−0.698569	−	0.715543i
$190$	−2.18655			−0.158629
$191$	7.59272	−	2.76352i	0.549390	−	0.199962i	−0.0523855	−	0.998627i	$-0.516682\pi$
$191$	7.59272	−	2.76352i	0.549390	−	0.199962i	0.601775	+	0.798665i	$0.294460\pi$
$192$	0.686062	−	1.59038i	0.0495123	−	0.114776i
$193$	14.6870	−	12.3238i	1.05719	−	0.887090i	0.0633610	−	0.997991i	$-0.479818\pi$
$193$	14.6870	−	12.3238i	1.05719	−	0.887090i	0.993831	+	0.110901i	$0.0353736\pi$
$194$	3.50848	−	2.94397i	0.251894	−	0.211364i
$195$	−4.69431	+	2.35746i	−0.336167	+	0.168821i
$196$	−0.167183	+	6.99800i	−0.0119416	+	0.499857i
$197$	−0.976072	+	1.69061i	−0.0695422	+	0.120451i	−0.898700	−	0.438564i	$-0.855487\pi$
$197$	−0.976072	+	1.69061i	−0.0695422	+	0.120451i	0.829158	+	0.559015i	$0.188821\pi$
$198$	10.9345	−	14.6864i	0.777081	−	1.04371i
$199$	3.63983	−	6.30437i	0.258021	−	0.446905i	−0.707691	−	0.706522i	$-0.750263\pi$
$199$	3.63983	−	6.30437i	0.258021	−	0.446905i	0.965712	+	0.259617i	$0.0835964\pi$
$200$	−3.03060	−	2.54298i	−0.214296	−	0.179816i
$201$	6.23169	+	20.8168i	0.439549	+	1.46830i
$202$	−4.30171	+	3.60956i	−0.302667	+	0.253968i
$203$	−4.11052	+	14.6391i	−0.288502	+	1.02746i
$204$	−1.17687	+	1.24736i	−0.0823977	+	0.0873329i
$205$	3.18066	−	18.0384i	0.222147	−	1.25986i
$206$	−0.772600	+	1.33818i	−0.0538296	+	0.0932355i
$207$	8.54257	−	11.4737i	0.593749	−	0.797478i
$208$	0.506707	+	0.877642i	0.0351338	+	0.0608535i
$209$	−0.774343	+	4.39152i	−0.0535624	+	0.303767i
$210$	7.05950	+	11.7577i	0.487151	+	0.811357i
$211$	21.6947	+	7.89624i	1.49353	+	0.543599i	0.954375	−	0.298609i	$-0.0965228\pi$
$211$	21.6947	+	7.89624i	1.49353	+	0.543599i	0.539151	+	0.842209i	$0.318745\pi$
$212$	11.4612	+	4.17155i	0.787161	+	0.286503i
$213$	4.77706	−	11.0739i	0.327318	−	0.758768i
$214$	−1.55481	+	8.81776i	−0.106285	+	0.602770i
$215$	−12.9610	+	22.4490i	−0.883929	+	1.53101i
$216$	−0.902607	+	5.11716i	−0.0614147	+	0.348178i
$217$	−3.55623	−	1.71029i	−0.241412	−	0.116102i
$218$	−1.00574	−	0.843917i	−0.0681174	−	0.0571573i
$219$	−9.09237	−	12.2137i	−0.614406	−	0.825324i
$220$	−13.9920	+	11.7407i	−0.943340	+	0.791556i
$221$	−0.174237	−	0.988146i	−0.0117204	−	0.0664699i
$222$	10.4156	+	6.85073i	0.699048	+	0.459791i
$223$	2.10783	−	11.9541i	0.141150	−	0.800504i	−0.829227	−	0.558911i	$-0.811219\pi$
$223$	2.10783	−	11.9541i	0.141150	−	0.800504i	0.970378	−	0.241592i	$-0.0776697\pi$
$224$	2.18524	−	1.49155i	0.146008	−	0.0996584i
$225$	10.6059	+	5.32700i	0.707059	+	0.355133i
$226$	12.0159			0.799287
$227$	−11.8295	−	9.92610i	−0.785149	−	0.658818i	0.159391	−	0.987216i	$-0.449047\pi$
$227$	−11.8295	−	9.92610i	−0.785149	−	0.658818i	−0.944540	+	0.328397i	$0.893491\pi$
$228$	−0.362923	−	1.21233i	−0.0240352	−	0.0802888i
$229$	−3.69183	−	20.9374i	−0.243963	−	1.38358i	−0.822889	−	0.568202i	$-0.807639\pi$
$229$	−3.69183	−	20.9374i	−0.243963	−	1.38358i	0.578927	−	0.815380i	$-0.303472\pi$
$230$	−10.9312	+	9.17240i	−0.720785	+	0.604810i
$231$	26.1144	−	10.0146i	1.71820	−	0.658911i
$232$	5.40044	−	1.96560i	0.354556	−	0.129048i
$233$	−1.06740			−0.0699277			−0.0349638	−	0.999389i	$-0.511132\pi$
$233$	−1.06740			−0.0699277			−0.0349638	+	0.999389i	$0.511132\pi$
$234$	−2.08625	−	2.21147i	−0.136383	−	0.144569i
$235$	−12.0374			−0.785232
$236$	−10.8486	−	9.10305i	−0.706184	−	0.592558i
$237$	−7.66250	−	5.03992i	−0.497733	−	0.327378i
$238$	−2.53824	+	0.647731i	−0.164530	+	0.0419862i
$239$	−1.55288	−	8.80684i	−0.100448	−	0.569667i	−0.992941	−	0.118607i	$-0.962157\pi$
$239$	−1.55288	−	8.80684i	−0.100448	−	0.569667i	0.892494	−	0.451060i	$-0.148954\pi$
$240$	2.05317	−	4.75952i	0.132531	−	0.307226i
$241$	−4.18493	+	23.7339i	−0.269575	+	1.52884i	0.486108	+	0.873899i	$0.338416\pi$
$241$	−4.18493	+	23.7339i	−0.269575	+	1.52884i	−0.755683	+	0.654938i	$0.772695\pi$
$242$	13.1251	+	22.7334i	0.843715	+	1.46136i
$243$	−0.904842	−	15.5622i	−0.0580456	−	0.998314i
$244$	−8.70972			−0.557583
$245$	−0.500326	+	20.9428i	−0.0319647	+	1.33799i
$246$	10.5293	−	1.23049i	0.671326	−	0.0784533i
$247$	0.695779	+	0.253243i	0.0442713	+	0.0161134i
$248$	0.258995	+	1.46883i	0.0164462	+	0.0932710i
$249$	−1.01118	+	17.3553i	−0.0640808	+	1.09985i
$250$	2.39301	+	2.00797i	0.151347	+	0.126995i
$251$	−13.3184	+	23.0682i	−0.840653	+	1.45605i	0.0486912	+	0.998814i	$0.484495\pi$
$251$	−13.3184	+	23.0682i	−0.840653	+	1.45605i	−0.889344	+	0.457239i	$0.848838\pi$
$252$	−5.34732	+	5.86568i	−0.336850	+	0.369503i
$253$	14.5509	+	25.2028i	0.914805	+	1.58449i
$254$	1.90344	−	10.7949i	0.119432	−	0.677334i
$255$	−3.52201	+	3.73297i	−0.220557	+	0.233768i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−0.624844	−	3.54367i	−0.0389767	−	0.221048i	0.959098	−	0.283075i	$-0.0913546\pi$
$257$	−0.624844	−	3.54367i	−0.0389767	−	0.221048i	−0.998074	+	0.0620272i	$0.980243\pi$
$258$	−14.5981	−	3.46013i	−0.908840	−	0.215418i
$259$	7.84127	+	17.3538i	0.487233	+	1.07831i
$260$	1.51641	+	2.62651i	0.0940440	+	0.162889i
$261$	−14.4051	+	9.47356i	−0.891653	+	0.586398i
$262$	20.2533			1.25125
$263$	−28.5845	+	10.4039i	−1.76260	+	0.641532i	−0.999986	−	0.00532697i	$-0.998304\pi$
$263$	−28.5845	+	10.4039i	−1.76260	+	0.641532i	−0.762609	+	0.646859i	$0.776082\pi$
$264$	−8.83201	−	5.80916i	−0.543573	−	0.357529i
$265$	34.2999	+	12.4841i	2.10703	+	0.766894i
$266$	0.522579	−	1.86109i	0.0320413	−	0.114111i
$267$	9.51118	−	22.0482i	0.582075	−	1.34933i
$268$	11.7890	−	4.29083i	0.720125	−	0.262104i
$269$	−8.88215	−	15.3843i	−0.541555	−	0.938000i	−0.998815	−	0.0486672i	$-0.984503\pi$
$269$	−8.88215	−	15.3843i	−0.541555	−	0.938000i	0.457261	−	0.889333i	$-0.348831\pi$
$270$	−2.70122	+	15.3140i	−0.164391	+	0.931983i
$271$	1.08326	−	1.87627i	0.0658035	−	0.113975i	−0.831247	−	0.555904i	$-0.812372\pi$
$271$	1.08326	−	1.87627i	0.0658035	−	0.113975i	0.897050	+	0.441929i	$0.145706\pi$
$272$	0.758468	+	0.636430i	0.0459889	+	0.0385892i
$273$	−0.884634	−	4.55901i	−0.0535405	−	0.275924i
$274$	−1.54917	−	8.78576i	−0.0935886	−	0.530767i
$275$	−18.4967	+	15.5206i	−1.11539	+	0.935924i
$276$	−6.90000	−	4.53840i	−0.415331	−	0.273180i
$277$	7.55420	−	2.74950i	0.453888	−	0.165202i	−0.104952	−	0.994477i	$-0.533469\pi$
$277$	7.55420	−	2.74950i	0.453888	−	0.165202i	0.558840	+	0.829276i	$0.311247\pi$
$278$	−0.599350	−	1.03810i	−0.0359466	−	0.0622614i
$279$	−1.77209	−	4.10861i	−0.106092	−	0.245976i
$280$	6.53974	−	4.46374i	0.390824	−	0.266760i
$281$	1.37570	−	0.500713i	0.0820672	−	0.0298700i	−0.300660	−	0.953731i	$-0.597207\pi$
$281$	1.37570	−	0.500713i	0.0820672	−	0.0298700i	0.382728	+	0.923861i	$0.374985\pi$
$282$	−1.99796	−	6.67413i	−0.118977	−	0.397439i
$283$	12.2373	+	4.45400i	0.727429	+	0.264763i	0.679076	−	0.734068i	$-0.262381\pi$
$283$	12.2373	+	4.45400i	0.727429	+	0.264763i	0.0483529	+	0.998830i	$0.484603\pi$
$284$	−6.54309	−	2.38149i	−0.388261	−	0.141315i
$285$	−1.08611	−	3.62814i	−0.0643358	−	0.214912i
$286$	5.81215	−	2.11545i	0.343680	−	0.125089i
$287$	14.5933	+	7.01836i	0.861417	+	0.414281i
$288$	2.97970	+	0.348397i	0.175581	+	0.0205295i
$289$	8.00984	+	13.8735i	0.471167	+	0.816085i
$290$	16.1618	−	5.88242i	0.949055	−	0.345428i
$291$	6.62766	+	4.35927i	0.388520	+	0.255545i
$292$	−6.73430	+	5.65075i	−0.394095	+	0.330685i
$293$	−3.18854	−	18.0831i	−0.186276	−	1.05643i	−0.924304	−	0.381656i	$-0.875354\pi$
$293$	−3.18854	−	18.0831i	−0.186276	−	1.05643i	0.738028	−	0.674770i	$-0.235757\pi$
$294$	−11.6948	+	3.19868i	−0.682055	+	0.186551i
$295$	−32.4664	−	27.2426i	−1.89027	−	1.58612i
$296$	3.59881	−	6.23332i	0.209176	−	0.362304i
$297$	29.8004	+	10.8485i	1.72920	+	0.629493i
$298$	−0.772609	−	1.33820i	−0.0447560	−	0.0775197i
$299$	4.54074	−	1.65270i	0.262598	−	0.0955778i
$300$	2.71418	−	6.29183i	0.156703	−	0.363259i
$301$	−16.0100	−	16.3970i	−0.922799	−	0.945108i
$302$	−0.0849778	−	0.0309294i	−0.00488992	−	0.00177979i
$303$	−8.12610	−	5.34485i	−0.466832	−	0.307054i
$304$	−0.686569	+	0.249891i	−0.0393774	+	0.0143322i
$305$	−26.0655			−1.49250
$306$	−2.65433	−	1.33319i	−0.151738	−	0.0762132i
$307$	−0.923527	−	1.59960i	−0.0527085	−	0.0912937i	0.838467	−	0.544952i	$-0.183452\pi$
$307$	−0.923527	−	1.59960i	−0.0527085	−	0.0912937i	−0.891176	+	0.453658i	$0.850119\pi$
$308$	−6.64909	−	14.7153i	−0.378867	−	0.838484i
$309$	−2.60421	−	0.617264i	−0.148148	−	0.0351149i
$310$	0.775091	+	4.39576i	0.0440222	+	0.249662i
$311$	−13.2744	−	4.83150i	−0.752724	−	0.273969i	−0.0629725	−	0.998015i	$-0.520058\pi$
$311$	−13.2744	−	4.83150i	−0.752724	−	0.273969i	−0.689752	+	0.724046i	$0.742280\pi$
$312$	−1.20457	+	1.27672i	−0.0681956	+	0.0722802i
$313$	−2.37944	+	13.4945i	−0.134494	+	0.762753i	0.840717	+	0.541475i	$0.182134\pi$
$313$	−2.37944	+	13.4945i	−0.134494	+	0.762753i	−0.975211	+	0.221278i	$0.928977\pi$
$314$	1.36918	+	2.37149i	0.0772674	+	0.133831i
$315$	−16.0029	+	17.5541i	−0.901659	+	0.989063i
$316$	−2.64756	+	4.58570i	−0.148937	+	0.257966i
$317$	−3.55536	−	2.98330i	−0.199689	−	0.167559i	0.537460	−	0.843289i	$-0.319384\pi$
$317$	−3.55536	−	2.98330i	−0.199689	−	0.167559i	−0.737149	+	0.675730i	$0.763828\pi$
$318$	−1.22876	+	21.0897i	−0.0689052	+	1.18265i
$319$	−6.09085	−	34.5429i	−0.341022	−	1.93403i
$320$	−2.81221	−	1.02356i	−0.157207	−	0.0572187i
$321$	−15.4036	+	1.80011i	−0.859744	+	0.100472i
$322$	−5.19460	−	11.4964i	−0.289484	−	0.640667i
$323$	0.723405			0.0402513
$324$	−8.93923	+	1.04413i	−0.496624	+	0.0580070i
$325$	2.00462	+	3.47210i	0.111196	+	0.192598i
$326$	−1.73873	+	9.86083i	−0.0962994	+	0.546141i
$327$	0.900732	−	2.08802i	0.0498106	−	0.115468i
$328$	−1.06281	−	6.02750i	−0.0586839	−	0.332813i
$329$	2.87689	−	10.2457i	0.158608	−	0.564862i
$330$	−26.4314	−	17.3850i	−1.45500	−	0.957012i
$331$	13.7478	+	11.5358i	0.755648	+	0.634064i	0.936990	−	0.349356i	$-0.113600\pi$
$331$	13.7478	+	11.5358i	0.755648	+	0.634064i	−0.181342	+	0.983420i	$0.558044\pi$
$332$	10.0371			0.550856
$333$	−6.19372	+	20.6855i	−0.339414	+	1.13356i
$334$	23.3204			1.27603
$335$	35.2807	−	12.8411i	1.92759	−	0.701585i
$336$	3.56039	+	2.88507i	0.194235	+	0.157394i
$337$	9.39800	−	7.88586i	0.511942	−	0.429570i	−0.349870	−	0.936798i	$-0.613774\pi$
$337$	9.39800	−	7.88586i	0.511942	−	0.429570i	0.861812	+	0.507228i	$0.169330\pi$
$338$	2.07909	+	11.7911i	0.113087	+	0.641351i
$339$	5.96860	+	19.9380i	0.324170	+	1.08288i
$340$	2.26986	+	1.90464i	0.123100	+	0.103293i
$341$	9.10303			0.492956
$342$	1.83135	−	1.20439i	0.0990280	−	0.0651261i
$343$	−17.7060	−	5.43112i	−0.956035	−	0.293253i
$344$	−1.50410	+	8.53016i	−0.0810955	+	0.459915i
$345$	−20.6495	−	13.5820i	−1.11173	−	0.731231i
$346$	1.28070	+	7.26320i	0.0688507	+	0.390472i
$347$	−18.0320	+	15.1306i	−0.968007	+	0.812255i	−0.982237	−	0.187644i	$-0.939915\pi$
$347$	−18.0320	+	15.1306i	−0.968007	+	0.812255i	0.0142297	+	0.999899i	$0.495470\pi$
$348$	5.94404	+	7.98457i	0.318634	+	0.428018i
$349$	19.7740	+	16.5924i	1.05848	+	0.888169i	0.993960	−	0.109747i	$-0.0350041\pi$
$349$	19.7740	+	16.5924i	1.05848	+	0.888169i	0.0645193	+	0.997916i	$0.479449\pi$
$350$	8.64519	−	5.90083i	0.462105	−	0.315412i
$351$	2.63320	−	4.56020i	0.140550	−	0.243406i
$352$	−3.05165	+	5.28561i	−0.162653	+	0.281724i
$353$	3.62804	−	20.5757i	0.193101	−	1.09513i	−0.721996	−	0.691898i	$-0.756775\pi$
$353$	3.62804	−	20.5757i	0.193101	−	1.09513i	0.915097	−	0.403234i	$-0.132114\pi$
$354$	9.71590	−	22.5228i	0.516394	−	1.19707i
$355$	−19.5814	−	7.12705i	−1.03927	−	0.378265i
$356$	−13.0274	−	4.74158i	−0.690450	−	0.251303i
$357$	−2.33558	−	3.88995i	−0.123612	−	0.205878i
$358$	−0.714375	+	4.05142i	−0.0377559	+	0.214124i
$359$	7.97266	+	13.8091i	0.420781	+	0.728814i	0.996016	−	0.0891740i	$-0.0284227\pi$
$359$	7.97266	+	13.8091i	0.420781	+	0.728814i	−0.575235	+	0.817988i	$0.695089\pi$
$360$	8.91731	+	1.04264i	0.469984	+	0.0549521i
$361$	9.23309	−	15.9922i	0.485952	−	0.841694i
$362$	1.71777	−	9.74195i	0.0902839	−	0.512026i
$363$	−31.2018	+	33.0707i	−1.63767	+	1.73576i
$364$	−2.59798	+	0.662977i	−0.136171	+	0.0347494i
$365$	−20.1536	+	16.9109i	−1.05489	+	0.885158i
$366$	−4.32633	−	14.4520i	−0.226141	−	0.755418i
$367$	6.37077	+	5.34571i	0.332551	+	0.279044i	0.793738	−	0.608259i	$-0.208132\pi$
$367$	6.37077	+	5.34571i	0.332551	+	0.279044i	−0.461187	+	0.887303i	$0.652576\pi$
$368$	−2.38410	+	4.12938i	−0.124280	+	0.215259i
$369$	7.27193	+	16.8601i	0.378562	+	0.877701i
$370$	10.7701	−	18.6544i	0.559911	−	0.969794i
$371$	−18.8235	+	26.2108i	−0.977267	+	1.36080i
$372$	−2.30858	+	1.15936i	−0.119694	+	0.0601098i
$373$	−5.04700	+	4.23494i	−0.261324	+	0.219277i	−0.764030	−	0.645180i	$-0.776782\pi$
$373$	−5.04700	+	4.23494i	−0.261324	+	0.219277i	0.502706	+	0.864457i	$0.332338\pi$
$374$	4.62915	−	3.88432i	0.239368	−	0.200853i
$375$	−2.14316	+	4.96812i	−0.110672	+	0.256553i
$376$	−3.77969	+	1.37570i	−0.194923	+	0.0709461i
$377$	−5.82412			−0.299957
$378$	−12.3890	−	5.95916i	−0.637224	−	0.306506i
$379$	−13.1374			−0.674823			−0.337411	−	0.941357i	$-0.609551\pi$
$379$	−13.1374			−0.674823			−0.337411	+	0.941357i	$0.609551\pi$
$380$	−2.05469	+	0.747844i	−0.105403	+	0.0383636i
$381$	18.8575	−	2.20374i	0.966097	−	0.112901i
$382$	6.18964	−	5.19373i	0.316690	−	0.265734i
$383$	−20.2797	+	17.0167i	−1.03625	+	0.869514i	−0.991581	−	0.129488i	$-0.958666\pi$
$383$	−20.2797	+	17.0167i	−1.03625	+	0.869514i	−0.0446650	+	0.999002i	$0.514222\pi$
$384$	0.100744	−	1.72912i	0.00514108	−	0.0882387i
$385$	−19.8987	−	44.0384i	−1.01413	−	2.24440i
$386$	9.58625	−	16.6039i	0.487927	−	0.845115i
$387$	−1.50988	−	25.9413i	−0.0767514	−	1.31867i
$388$	2.29000	−	3.96639i	0.116257	−	0.201363i
$389$	11.2123	+	9.40824i	0.568486	+	0.477017i	0.881143	−	0.472849i	$-0.156775\pi$
$389$	11.2123	+	9.40824i	0.568486	+	0.477017i	−0.312657	+	0.949866i	$0.601219\pi$
$390$	−3.60491	+	3.82083i	−0.182542	+	0.193475i
$391$	3.61652	−	3.03462i	0.182895	−	0.153468i
$392$	2.23636	+	6.63315i	0.112953	+	0.335025i
$393$	10.0603	+	33.6062i	0.507475	+	1.69521i
$394$	−0.338986	+	1.92249i	−0.0170779	+	0.0968534i
$395$	−7.92330	+	13.7236i	−0.398665	+	0.690508i
$396$	5.25203	−	17.5405i	0.263925	−	0.881442i
$397$	−13.1070	−	22.7020i	−0.657823	−	1.13938i	−0.981178	−	0.193105i	$-0.938144\pi$
$397$	−13.1070	−	22.7020i	−0.657823	−	1.13938i	0.323355	−	0.946278i	$-0.395189\pi$
$398$	1.26410	−	7.16906i	0.0633636	−	0.359353i
$399$	3.34768	−	0.0573386i	0.167594	−	0.00287052i
$400$	−3.71758	−	1.35309i	−0.185879	−	0.0676545i
$401$	−34.4887	−	12.5529i	−1.72228	−	0.626860i	−0.724251	−	0.689536i	$-0.757814\pi$
$401$	−34.4887	−	12.5529i	−1.72228	−	0.626860i	−0.998034	+	0.0626759i	$0.980037\pi$
$402$	12.9756	+	17.4300i	0.647165	+	0.869330i
$403$	0.262469	−	1.48854i	0.0130745	−	0.0741493i
$404$	−2.80774	+	4.86315i	−0.139690	+	0.241951i
$405$	−26.7523	+	3.12474i	−1.32933	+	0.155270i
$406$	1.14423	+	15.1621i	0.0567871	+	0.752482i
$407$	−33.6517	−	28.2371i	−1.66805	−	1.39966i
$408$	−0.679276	+	1.57465i	−0.0336292	+	0.0779569i
$409$	−6.14404	+	5.15546i	−0.303803	+	0.254921i	−0.781925	−	0.623372i	$-0.785762\pi$
$409$	−6.14404	+	5.15546i	−0.303803	+	0.254921i	0.478122	+	0.878293i	$0.341318\pi$
$410$	−3.18066	−	18.0384i	−0.157082	−	0.890854i
$411$	13.8087	−	6.93463i	0.681132	−	0.342060i
$412$	−0.268321	+	1.52172i	−0.0132192	+	0.0749700i
$413$	30.9470	−	21.1231i	1.52280	−	1.03940i
$414$	4.10315	−	13.7035i	0.201659	−	0.673490i
$415$	30.0378			1.47450
$416$	0.776320	+	0.651410i	0.0380622	+	0.0319380i
$417$	1.42481	−	1.51015i	0.0697733	−	0.0739525i
$418$	0.774343	+	4.39152i	0.0378743	+	0.214796i
$419$	24.9680	−	20.9507i	1.21977	−	1.02351i	0.220932	−	0.975289i	$-0.429090\pi$
$419$	24.9680	−	20.9507i	1.21977	−	1.02351i	0.998837	−	0.0482182i	$-0.0153543\pi$
$420$	10.6551	+	8.63412i	0.519917	+	0.421302i
$421$	−36.2666	+	13.1999i	−1.76752	+	0.643326i	−0.767527	+	0.641017i	$0.778513\pi$
$421$	−36.2666	+	13.1999i	−1.76752	+	0.643326i	−0.999997	+	0.00230919i	$0.999265\pi$
$422$	23.0871			1.12386
$423$	10.0819	−	6.63041i	0.490200	−	0.322382i
$424$	12.1968			0.592329
$425$	3.00063	+	2.51783i	0.145552	+	0.122132i
$426$	0.701483	−	12.0399i	0.0339869	−	0.583334i
$427$	6.22956	−	22.1857i	0.301469	−	1.07364i
$428$	1.55481	+	8.81776i	0.0751545	+	0.426222i
$429$	6.39720	+	8.59329i	0.308860	+	0.414888i
$430$	−4.50129	+	25.5281i	−0.217072	+	1.23107i
$431$	−3.76972	−	6.52935i	−0.181581	−	0.314508i	0.760838	−	0.648942i	$-0.224788\pi$
$431$	−3.76972	−	6.52935i	−0.181581	−	0.314508i	−0.942419	+	0.334434i	$0.891455\pi$
$432$	0.901997	+	5.11726i	0.0433974	+	0.246205i
$433$	11.3329			0.544623			0.272311	−	0.962209i	$-0.412212\pi$
$433$	11.3329			0.544623			0.272311	+	0.962209i	$0.412212\pi$
$434$	−3.92672	−	0.390850i	−0.188488	−	0.0187614i
$435$	17.7887	+	23.8953i	0.852901	+	1.14569i
$436$	−1.23372	−	0.449039i	−0.0590847	−	0.0215051i
$437$	0.604955	+	3.43087i	0.0289389	+	0.164121i
$438$	−12.7214	−	8.36733i	−0.607850	−	0.399807i
$439$	12.0474	+	10.1090i	0.574993	+	0.482476i	0.883298	−	0.468811i	$-0.155318\pi$
$439$	12.0474	+	10.1090i	0.574993	+	0.482476i	−0.308306	+	0.951287i	$0.599762\pi$
$440$	−9.13263	+	15.8182i	−0.435381	+	0.754102i
$441$	−11.1167	−	17.8163i	−0.529364	−	0.848395i
$442$	−0.501695	−	0.868961i	−0.0238632	−	0.0413323i
$443$	−4.82450	+	27.3611i	−0.229219	+	1.29997i	0.625234	+	0.780437i	$0.285003\pi$
$443$	−4.82450	+	27.3611i	−0.229219	+	1.29997i	−0.854453	+	0.519529i	$0.826108\pi$
$444$	12.1305	+	2.87524i	0.575690	+	0.136453i
$445$	−38.9869	−	14.1901i	−1.84815	−	0.672673i
$446$	−2.10783	−	11.9541i	−0.0998084	−	0.566042i
$447$	1.83669	−	1.94670i	0.0868726	−	0.0920759i
$448$	1.54332	−	2.14899i	0.0729148	−	0.101530i
$449$	−11.7354	−	20.3263i	−0.553829	−	0.959260i	−0.997994	−	0.0633145i	$-0.979833\pi$
$449$	−11.7354	−	20.3263i	−0.553829	−	0.959260i	0.444165	−	0.895945i	$-0.353500\pi$
$450$	11.7882	+	1.37832i	0.555701	+	0.0649746i
$451$	−37.3552			−1.75899
$452$	11.2913	−	4.10969i	0.531097	−	0.193303i
$453$	0.00911044	−	0.156367i	0.000428046	−	0.00734675i
$454$	−14.5110	−	5.28157i	−0.681034	−	0.247876i
$455$	−7.77495	+	1.98408i	−0.364495	+	0.0930152i
$456$	−0.755679	−	1.01509i	−0.0353879	−	0.0475362i
$457$	−32.2349	+	11.7326i	−1.50789	+	0.548826i	−0.958089	−	0.286472i	$-0.907517\pi$
$457$	−32.2349	+	11.7326i	−1.50789	+	0.548826i	−0.549798	+	0.835298i	$0.685295\pi$
$458$	−10.6302	−	18.4120i	−0.496716	−	0.860338i
$459$	0.893680	−	5.06654i	0.0417134	−	0.236486i
$460$	−7.13486	+	12.3579i	−0.332665	+	0.576192i
$461$	0.802442	+	0.673329i	0.0373735	+	0.0313601i	0.661283	−	0.750136i	$-0.270012\pi$
$461$	0.802442	+	0.673329i	0.0373735	+	0.0313601i	−0.623910	+	0.781497i	$0.714457\pi$
$462$	21.1143	−	18.3423i	0.982328	−	0.853361i
$463$	−2.69301	−	15.2728i	−0.125155	−	0.709789i	−0.981216	−	0.192914i	$-0.938206\pi$
$463$	−2.69301	−	15.2728i	−0.125155	−	0.709789i	0.856061	−	0.516875i	$-0.172905\pi$
$464$	4.40248	−	3.69412i	0.204380	−	0.171495i
$465$	−6.90886	+	3.46959i	−0.320391	+	0.160898i
$466$	−1.00303	+	0.365072i	−0.0464644	+	0.0169116i
$467$	−5.75123	−	9.96143i	−0.266135	−	0.460960i	0.701725	−	0.712448i	$-0.252413\pi$
$467$	−5.75123	−	9.96143i	−0.266135	−	0.460960i	−0.967860	+	0.251488i	$0.919080\pi$
$468$	−2.71680	−	1.36457i	−0.125584	−	0.0630771i
$469$	2.49781	+	33.0983i	0.115338	+	1.52834i
$470$	−11.3114	+	4.11703i	−0.521758	+	0.189904i
$471$	−3.25490	+	3.44986i	−0.149978	+	0.158961i
$472$	−13.3078	−	4.84363i	−0.612540	−	0.222946i
$473$	49.6771	+	18.0810i	2.28415	+	0.831364i
$474$	−8.92414	−	2.11525i	−0.409900	−	0.0971566i
$475$	−2.71618	+	0.988610i	−0.124627	+	0.0453606i
$476$	−2.16363	+	1.47680i	−0.0991697	+	0.0676889i
$477$	−35.6044	+	8.43691i	−1.63021	+	0.386299i
$478$	−4.47135	−	7.74460i	−0.204515	−	0.354230i
$479$	16.7686	−	6.10327i	0.766177	−	0.278866i	0.0707804	−	0.997492i	$-0.477451\pi$
$479$	16.7686	−	6.10327i	0.766177	−	0.278866i	0.695396	+	0.718626i	$0.255229\pi$
$480$	0.301496	−	5.17471i	0.0137613	−	0.236192i
$481$	−5.58765	+	4.68860i	−0.254775	+	0.213782i
$482$	4.18493	+	23.7339i	0.190618	+	1.08105i
$483$	16.4956	−	14.3299i	0.750574	−	0.652033i
$484$	20.1089	+	16.8733i	0.914039	+	0.766970i
$485$	6.85325	−	11.8702i	0.311190	−	0.538997i
$486$	−6.17285	−	14.3142i	−0.280006	−	0.649305i
$487$	15.6670	+	27.1360i	0.709940	+	1.22965i	0.964879	+	0.262694i	$0.0846111\pi$
$487$	15.6670	+	27.1360i	0.709940	+	1.22965i	−0.254939	+	0.966957i	$0.582056\pi$
$488$	−8.18446	+	2.97890i	−0.370493	+	0.134848i
$489$	−17.2257	+	2.01305i	−0.778974	+	0.0910333i
$490$	6.69272	+	19.8509i	0.302346	+	0.896774i
$491$	27.4902	+	10.0056i	1.24061	+	0.451547i	0.877220	−	0.480089i	$-0.159396\pi$
$491$	27.4902	+	10.0056i	1.24061	+	0.451547i	0.363394	+	0.931636i	$0.381618\pi$
$492$	9.47349	−	4.75753i	0.427098	−	0.214486i
$493$	−5.34702	+	1.94616i	−0.240818	+	0.0876505i
$494$	0.740432			0.0333136
$495$	15.7177	−	52.4931i	0.706458	−	2.35939i
$496$	0.745746	+	1.29167i	0.0334850	+	0.0579977i
$497$	10.7461	−	14.9635i	0.482029	−	0.671203i
$498$	4.98567	+	16.6545i	0.223413	+	0.746306i
$499$	2.25528	+	12.7903i	0.100960	+	0.572573i	0.992757	+	0.120137i	$0.0383335\pi$
$499$	2.25528	+	12.7903i	0.100960	+	0.572573i	−0.891797	+	0.452435i	$0.850555\pi$
$500$	2.93546	+	1.06842i	0.131278	+	0.0477812i
$501$	11.5838	+	38.6954i	0.517526	+	1.72878i
$502$	−4.62545	+	26.2322i	−0.206444	+	1.17080i
$503$	−14.3814	−	24.9094i	−0.641236	−	1.11065i	−0.985157	−	0.171655i	$-0.945088\pi$
$503$	−14.3814	−	24.9094i	−0.641236	−	1.11065i	0.343921	−	0.938999i	$-0.388245\pi$
$504$	−3.01866	+	7.34082i	−0.134462	+	0.326986i
$505$	−8.40269	+	14.5539i	−0.373915	+	0.647639i
$506$	22.2932	+	18.7062i	0.991055	+	0.831593i
$507$	−18.5322	+	9.30675i	−0.823043	+	0.413327i
$508$	−1.90344	−	10.7949i	−0.0844514	−	0.478947i
$509$	6.80700	+	2.47754i	0.301715	+	0.109815i	0.488441	−	0.872597i	$-0.337566\pi$
$509$	6.80700	+	2.47754i	0.301715	+	0.109815i	−0.186727	+	0.982412i	$0.559788\pi$
$510$	−2.03286	+	4.71244i	−0.0900166	+	0.208670i
$511$	−9.57715	−	21.1955i	−0.423668	−	0.937635i
$512$	−1.00000			−0.0441942
$513$	2.90812	+	2.44050i	0.128397	+	0.107751i
$514$	−1.79917	−	3.11625i	−0.0793578	−	0.137452i
$515$	−0.803001	+	4.55404i	−0.0353844	+	0.200675i
$516$	−14.9012	+	1.74140i	−0.655988	+	0.0766608i
$517$	4.26290	+	24.1761i	0.187482	+	1.06326i
$518$	13.3037	+	13.6254i	0.584532	+	0.598664i
$519$	−11.4156	+	5.73287i	−0.501091	+	0.251645i
$520$	2.32328	+	1.94947i	0.101883	+	0.0854897i
$521$	8.53286			0.373832			0.186916	−	0.982376i	$-0.440151\pi$
$521$	8.53286			0.373832			0.186916	+	0.982376i	$0.440151\pi$
$522$	−10.2962	+	13.8291i	−0.450653	+	0.605282i
$523$	−1.22503			−0.0535668			−0.0267834	−	0.999641i	$-0.508526\pi$
$523$	−1.22503			−0.0535668			−0.0267834	+	0.999641i	$0.508526\pi$
$524$	19.0319	−	6.92703i	0.831410	−	0.302609i
$525$	14.0855	+	11.4138i	0.614742	+	0.498141i
$526$	−23.3023	+	19.5529i	−1.01603	+	0.852549i
$527$	−0.256433	−	1.45431i	−0.0111704	−	0.0633506i
$528$	−10.2862	−	2.43810i	−0.447650	−	0.106105i
$529$	−0.202455	−	0.169880i	−0.00880238	−	0.00738607i
$530$	36.5012			1.58551
$531$	42.1980	+	4.93394i	1.83124	+	0.214115i
$532$	−0.145468	−	1.92759i	−0.00630685	−	0.0835715i
$533$	−1.07707	+	6.10835i	−0.0466530	+	0.264582i
$534$	1.39666	−	23.9715i	0.0604395	−	1.03735i
$535$	4.65305	+	26.3888i	0.201169	+	1.14089i
$536$	9.61045	−	8.06412i	0.415108	−	0.348317i
$537$	−7.07736	+	0.827082i	−0.305411	+	0.0356912i
$538$	−13.6083	−	11.4187i	−0.586693	−	0.492294i
$539$	42.2392	−	6.41180i	1.81937	−	0.276176i
$540$	2.69940	+	15.3144i	0.116163	+	0.659026i
$541$	−2.64381	+	4.57921i	−0.113666	+	0.196875i	−0.917246	−	0.398322i	$-0.869593\pi$
$541$	−2.64381	+	4.57921i	−0.113666	+	0.196875i	0.803580	+	0.595197i	$0.202926\pi$
$542$	0.376213	−	2.13361i	0.0161597	−	0.0916464i
$543$	17.0180	−	1.98878i	0.730314	−	0.0853468i
$544$	0.930398	+	0.338637i	0.0398905	+	0.0145190i
$545$	−3.69215	−	1.34383i	−0.158154	−	0.0575635i
$546$	−2.39056	−	3.98151i	−0.102306	−	0.170393i
$547$	1.98058	−	11.2324i	0.0846836	−	0.480264i	−0.912741	−	0.408539i	$-0.866038\pi$
$547$	1.98058	−	11.2324i	0.0846836	−	0.480264i	0.997424	−	0.0717253i	$-0.0228505\pi$
$548$	−4.46065	−	7.72607i	−0.190549	−	0.330041i
$549$	21.8312	−	14.3573i	0.931731	−	0.612756i
$550$	−12.0728	+	20.9108i	−0.514788	+	0.891639i
$551$	0.729142	−	4.13517i	0.0310625	−	0.176164i
$552$	−8.03611	−	1.90476i	−0.342039	−	0.0810720i
$553$	−9.78724	−	10.0238i	−0.416196	−	0.426257i
$554$	6.15824	−	5.16738i	0.261639	−	0.219541i
$555$	36.3029	+	8.60471i	1.54097	+	0.365249i
$556$	−0.918258	−	0.770510i	−0.0389428	−	0.0326769i
$557$	7.19267	−	12.4581i	0.304763	−	0.527865i	−0.672445	−	0.740147i	$-0.734756\pi$
$557$	7.19267	−	12.4581i	0.304763	−	0.527865i	0.977209	+	0.212281i	$0.0680893\pi$
$558$	−3.07044	−	3.25474i	−0.129982	−	0.137784i
$559$	4.38897	−	7.60192i	0.185634	−	0.321527i
$560$	4.61866	−	6.43127i	0.195174	−	0.271771i
$561$	8.74466	+	5.75170i	0.369200	+	0.242837i
$562$	1.12148	−	0.941033i	0.0473067	−	0.0396951i
$563$	−1.72556	+	1.44792i	−0.0727236	+	0.0610224i	−0.678425	−	0.734670i	$-0.737337\pi$
$563$	−1.72556	+	1.44792i	−0.0727236	+	0.0610224i	0.605701	+	0.795692i	$0.292893\pi$
$564$	−4.16015	−	5.58829i	−0.175174	−	0.235309i
$565$	33.7912	−	12.2990i	1.42161	−	0.517423i
$566$	13.0226			0.547381
$567$	3.73408	−	23.5172i	0.156816	−	0.987628i
$568$	−6.96301			−0.292161
$569$	−4.40139	+	1.60198i	−0.184516	+	0.0671583i	−0.432626	−	0.901574i	$-0.642413\pi$
$569$	−4.40139	+	1.60198i	−0.184516	+	0.0671583i	0.248110	+	0.968732i	$0.420191\pi$
$570$	−2.26151	−	3.03786i	−0.0947242	−	0.127242i
$571$	−9.83447	+	8.25210i	−0.411560	+	0.345340i	−0.824941	−	0.565218i	$-0.808792\pi$
$571$	−9.83447	+	8.25210i	−0.411560	+	0.345340i	0.413382	+	0.910558i	$0.364348\pi$
$572$	4.73811	−	3.97575i	0.198110	−	0.166234i
$573$	11.6925	+	7.69060i	0.488460	+	0.321279i
$574$	16.1137	+	1.60389i	0.672571	+	0.0669451i
$575$	−9.43190	+	16.3365i	−0.393338	+	0.681281i
$576$	2.91916	−	0.691732i	0.121632	−	0.0288222i
$577$	9.85265	−	17.0653i	0.410171	−	0.710438i	−0.584737	−	0.811223i	$-0.698802\pi$
$577$	9.85265	−	17.0653i	0.410171	−	0.710438i	0.994908	+	0.100785i	$0.0321356\pi$
$578$	12.2718	+	10.2973i	0.510439	+	0.428309i
$579$	32.3125	+	7.65887i	1.34286	+	0.318292i
$580$	13.1752	−	11.0553i	0.547072	−	0.459048i
$581$	−7.17895	+	25.5669i	−0.297833	+	1.06069i
$582$	7.71892	+	1.82958i	0.319960	+	0.0758385i
$583$	12.9265	−	73.3097i	0.535360	−	3.03618i
$584$	−4.39550	+	7.61323i	−0.181887	+	0.315038i
$585$	−8.13054	−	4.08372i	−0.336157	−	0.168841i
$586$	−9.18103	−	15.9020i	−0.379265	−	0.656906i
$587$	4.46034	−	25.2958i	0.184098	−	1.04407i	−0.743011	−	0.669279i	$-0.766603\pi$
$587$	4.46034	−	25.2958i	0.184098	−	1.04407i	0.927109	−	0.374791i	$-0.122286\pi$
$588$	−9.89551	+	7.00563i	−0.408084	+	0.288907i
$589$	1.02401	+	0.372710i	0.0421937	+	0.0153573i
$590$	−39.8260	−	14.4955i	−1.63961	−	0.596769i
$591$	−3.35836	+	0.392468i	−0.138144	+	0.0161440i
$592$	1.24985	−	7.08827i	0.0513686	−	0.291326i
$593$	−11.8795	+	20.5759i	−0.487832	+	0.844950i	−0.999902	−	0.0139935i	$-0.995546\pi$
$593$	−11.8795	+	20.5759i	−0.487832	+	0.844950i	0.512070	+	0.858944i	$0.328879\pi$
$594$	31.7137	+	0.00189051i	1.30123	+	7.75686e-5i
$595$	−6.47506	+	4.41959i	−0.265451	+	0.181186i
$596$	−1.18371	−	0.993247i	−0.0484865	−	0.0406850i
$597$	12.5235	−	1.46354i	0.512553	−	0.0598986i
$598$	3.70165	−	3.10605i	0.151372	−	0.127016i
$599$	−6.09894	−	34.5888i	−0.249196	−	1.41326i	−0.810543	−	0.585679i	$-0.800828\pi$
$599$	−6.09894	−	34.5888i	−0.249196	−	1.41326i	0.561347	−	0.827581i	$-0.310283\pi$
$600$	0.398561	−	6.84069i	0.0162712	−	0.279270i
$601$	−3.75035	+	21.2693i	−0.152980	+	0.867592i	0.807630	+	0.589690i	$0.200750\pi$
$601$	−3.75035	+	21.2693i	−0.152980	+	0.867592i	−0.960609	+	0.277902i	$0.910361\pi$
$602$	−20.6526	−	9.93243i	−0.841736	−	0.404815i
$603$	−22.4762	+	30.1883i	−0.915303	+	1.22936i
$604$	−0.0904314			−0.00367960
$605$	60.1795	+	50.4966i	2.44664	+	2.05298i
$606$	−9.46408	−	2.24323i	−0.384452	−	0.0911249i
$607$	−0.274115	−	1.55458i	−0.0111260	−	0.0630985i	0.978739	−	0.205108i	$-0.0657547\pi$
$607$	−0.274115	−	1.55458i	−0.0111260	−	0.0630985i	−0.989865	+	0.142010i	$0.954644\pi$
$608$	−0.559696	+	0.469641i	−0.0226987	+	0.0190465i
$609$	−24.5900	+	9.43000i	−0.996438	+	0.382123i
$610$	−24.4935	+	8.91491i	−0.991714	+	0.360954i
$611$	4.07622			0.164906
$612$	−2.95023	−	0.344951i	−0.119256	−	0.0139438i
$613$	15.2593			0.616316			0.308158	−	0.951335i	$-0.400287\pi$
$613$	15.2593			0.616316			0.308158	+	0.951335i	$0.400287\pi$
$614$	−1.41493	−	1.18726i	−0.0571017	−	0.0479141i
$615$	28.3512	−	14.2378i	1.14323	−	0.574123i
$616$	−11.2810	−	11.5538i	−0.454526	−	0.465515i
$617$	−0.887004	−	5.03045i	−0.0357094	−	0.202518i	0.961733	−	0.273987i	$-0.0883425\pi$
$617$	−0.887004	−	5.03045i	−0.0357094	−	0.202518i	−0.997443	+	0.0714687i	$0.977231\pi$
$618$	−2.65827	+	0.310654i	−0.106931	+	0.0124963i
$619$	6.21322	−	35.2369i	0.249730	−	1.41629i	−0.559515	−	0.828820i	$-0.689013\pi$
$619$	6.21322	−	35.2369i	0.249730	−	1.41629i	0.809245	−	0.587471i	$-0.199876\pi$
$620$	2.23179	+	3.86557i	0.0896307	+	0.155245i
$621$	24.7763	+	0.00147696i	0.994238	+	5.92684e-5i
$622$	−14.1264			−0.566415
$623$	21.3957	−	29.7925i	0.857199	−	1.19361i
$624$	−0.695265	+	1.61172i	−0.0278329	+	0.0645203i
$625$	27.3728	+	9.96290i	1.09491	+	0.398516i
$626$	2.37944	+	13.4945i	0.0951016	+	0.539348i
$627$	−6.90219	+	3.46624i	−0.275647	+	0.138428i
$628$	2.09771	+	1.76019i	0.0837076	+	0.0702390i
$629$	−3.56321	+	6.17166i	−0.142075	+	0.246080i
$630$	−9.03390	+	21.9688i	−0.359919	+	0.875257i
$631$	10.5768	+	18.3196i	0.421056	+	0.729290i	0.996043	−	0.0888722i	$-0.0283263\pi$
$631$	10.5768	+	18.3196i	0.421056	+	0.729290i	−0.574987	+	0.818163i	$0.694993\pi$
$632$	−0.919487	+	5.21467i	−0.0365752	+	0.207428i
$633$	11.4679	+	38.3083i	0.455809	+	1.52262i
$634$	−4.36129	−	1.58738i	−0.173209	−	0.0630429i
$635$	−5.69639	−	32.3058i	−0.226054	−	1.28202i
$636$	6.05845	+	20.2381i	0.240233	+	0.802493i
$637$	0.169426	−	7.09187i	0.00671288	−	0.280990i
$638$	−17.5379	−	30.3765i	−0.694332	−	1.20262i
$639$	20.3262	−	4.81653i	0.804090	−	0.190539i
$640$	−2.99269			−0.118296
$641$	−13.5402	+	4.92824i	−0.534807	+	0.194654i	−0.595283	−	0.803516i	$-0.702960\pi$
$641$	−13.5402	+	4.92824i	−0.534807	+	0.194654i	0.0604764	+	0.998170i	$0.480738\pi$
$642$	−13.8590	+	6.95989i	−0.546970	+	0.274685i
$643$	−22.0254	−	8.01659i	−0.868596	−	0.316143i	−0.130998	−	0.991383i	$-0.541818\pi$
$643$	−22.0254	−	8.01659i	−0.868596	−	0.316143i	−0.737599	+	0.675239i	$0.764040\pi$
$644$	−8.81331	−	9.02638i	−0.347293	−	0.355689i
$645$	−44.5946	+	5.21146i	−1.75591	+	0.205201i
$646$	0.679778	−	0.247419i	0.0267455	−	0.00973457i
$647$	−19.7913	−	34.2796i	−0.778078	−	1.34767i	−0.933048	−	0.359752i	$-0.882861\pi$
$647$	−19.7913	−	34.2796i	−0.778078	−	1.34767i	0.154970	−	0.987919i	$-0.450472\pi$
$648$	−8.04301	+	4.03855i	−0.315959	+	0.158649i
$649$	−43.2170	+	74.8540i	−1.69641	+	2.93828i
$650$	3.07125	+	2.57709i	0.120465	+	0.101082i
$651$	−1.30196	−	6.70973i	−0.0510279	−	0.262975i
$652$	1.73873	+	9.86083i	0.0680940	+	0.386180i
$653$	−18.9932	+	15.9372i	−0.743261	+	0.623670i	−0.933711	−	0.358027i	$-0.883450\pi$
$653$	−18.9932	+	15.9372i	−0.743261	+	0.623670i	0.190450	+	0.981697i	$0.439005\pi$
$654$	0.132267	−	2.27016i	0.00517206	−	0.0887704i
$655$	56.9564	−	20.7304i	2.22547	−	0.810005i
$656$	−3.06024	−	5.30050i	−0.119482	−	0.206950i
$657$	7.56487	−	25.2648i	0.295134	−	0.985672i
$658$	−0.800830	−	10.6117i	−0.0312196	−	0.413689i
$659$	−25.4533	+	9.26426i	−0.991521	+	0.360884i	−0.786309	−	0.617833i	$-0.788011\pi$
$659$	−25.4533	+	9.26426i	−0.991521	+	0.360884i	−0.205212	+	0.978718i	$0.565788\pi$
$660$	−30.7834	−	7.29646i	−1.19824	−	0.284014i
$661$	−9.77460	−	3.55766i	−0.380188	−	0.138377i	0.144855	−	0.989453i	$-0.453728\pi$
$661$	−9.77460	−	3.55766i	−0.380188	−	0.138377i	−0.525043	+	0.851076i	$0.675951\pi$
$662$	16.8642	+	6.13806i	0.655445	+	0.238562i
$663$	1.19266	−	1.26410i	0.0463191	−	0.0490934i
$664$	9.43177	−	3.43288i	0.366024	−	0.133222i
$665$	−0.435341	−	5.76867i	−0.0168818	−	0.223699i
$666$	1.25466	+	21.5564i	0.0486169	+	0.835292i
$667$	−13.7015	−	23.7317i	−0.530523	−	0.918894i
$668$	21.9140	−	7.97603i	0.847877	−	0.308602i
$669$	18.7883	−	9.43539i	0.726399	−	0.364793i
$670$	28.7611	−	24.1334i	1.11114	−	0.932354i
$671$	9.23079	+	52.3504i	0.356351	+	2.02097i
$672$	4.33242	+	1.49336i	0.167127	+	0.0576075i
$673$	9.00090	+	7.55265i	0.346959	+	0.291133i	0.799568	−	0.600576i	$-0.205062\pi$
$673$	9.00090	+	7.55265i	0.346959	+	0.291133i	−0.452609	+	0.891709i	$0.649506\pi$
$674$	6.13411	−	10.6246i	0.236277	−	0.409244i
$675$	3.56846	+	20.2448i	0.137350	+	0.779222i
$676$	5.98650	+	10.3689i	0.230250	+	0.398804i
$677$	−11.6745	+	4.24917i	−0.448688	+	0.163309i	−0.556474	−	0.830865i	$-0.687846\pi$
$677$	−11.6745	+	4.24917i	−0.448688	+	0.163309i	0.107786	+	0.994174i	$0.465624\pi$
$678$	12.4278	+	16.6942i	0.477288	+	0.641136i
$679$	8.46545	+	8.67011i	0.324874	+	0.332728i
$680$	2.78439	+	1.01344i	0.106776	+	0.0388635i
$681$	1.55572	−	26.7015i	0.0596152	−	1.02320i
$682$	8.55405	−	3.11342i	0.327551	−	0.119219i
$683$	41.6664			1.59432			0.797161	−	0.603767i	$-0.206334\pi$
$683$	41.6664			1.59432			0.797161	+	0.603767i	$0.206334\pi$
$684$	1.30898	−	1.75812i	0.0500500	−	0.0672233i
$685$	−13.3493	−	23.1217i	−0.510051	−	0.883435i
$686$	−18.4958	+	0.952227i	−0.706172	+	0.0363562i
$687$	25.2707	−	26.7843i	0.964139	−	1.02189i
$688$	1.50410	+	8.53016i	0.0573432	+	0.325209i
$689$	−11.6150	−	4.22750i	−0.442495	−	0.161055i
$690$	−24.0495	−	5.70035i	−0.915551	−	0.217009i
$691$	0.513903	−	2.91449i	0.0195498	−	0.110872i	−0.973471	−	0.228809i	$-0.926517\pi$
$691$	0.513903	−	2.91449i	0.0195498	−	0.110872i	0.993021	+	0.117937i	$0.0376280\pi$
$692$	3.68762	+	6.38715i	0.140182	+	0.242803i
$693$	40.9233	+	25.9239i	1.55455	+	0.984767i
$694$	−11.7695	+	20.3854i	−0.446766	+	0.773821i
$695$	−2.74806	−	2.30589i	−0.104240	−	0.0874675i
$696$	8.31646	+	5.47006i	0.315234	+	0.207342i
$697$	1.05230	+	5.96789i	0.0398587	+	0.226050i
$698$	24.2564	+	8.82862i	0.918119	+	0.334168i
$699$	−1.10399	−	1.48298i	−0.0417568	−	0.0560915i
$700$	6.10562	−	8.50179i	0.230771	−	0.321338i
$701$	−30.7388			−1.16099			−0.580494	−	0.814265i	$-0.697140\pi$
$701$	−30.7388			−1.16099			−0.580494	+	0.814265i	$0.697140\pi$
$702$	0.914715	−	5.18580i	0.0345237	−	0.195725i
$703$	−2.62940	−	4.55426i	−0.0991698	−	0.171767i
$704$	−1.05983	+	6.01057i	−0.0399437	+	0.226532i
$705$	−12.4500	−	16.7240i	−0.468895	−	0.629862i
$706$	−3.62804	−	20.5757i	−0.136543	−	0.774375i
$707$	−10.3794	−	10.6303i	−0.390357	−	0.399794i
$708$	1.42672	−	24.4875i	0.0536195	−	0.920296i
$709$	8.23625	+	6.91103i	0.309319	+	0.259549i	0.784210	−	0.620495i	$-0.213068\pi$
$709$	8.23625	+	6.91103i	0.309319	+	0.259549i	−0.474892	+	0.880044i	$0.657513\pi$
$710$	−20.8381			−0.782040
$711$	−0.923020	−	15.8585i	−0.0346160	−	0.594740i
$712$	−13.8634			−0.519555
$713$	6.68284	−	2.43236i	0.250274	−	0.0910925i
$714$	−3.52517	−	2.85654i	−0.131926	−	0.106903i
$715$	14.1797	−	11.8982i	0.530290	−	0.444966i
$716$	0.714375	+	4.05142i	0.0266975	+	0.151409i
$717$	10.6296	−	11.2662i	0.396968	−	0.420745i
$718$	12.2148	+	10.2495i	0.455853	+	0.382506i
$719$	−42.5047			−1.58516			−0.792578	−	0.609770i	$-0.791262\pi$
$719$	−42.5047			−1.58516			−0.792578	+	0.609770i	$0.791262\pi$
$720$	8.73614	−	2.07014i	0.325577	−	0.0771494i
$721$	−3.68428	−	1.77188i	−0.137210	−	0.0659882i
$722$	3.20662	−	18.1856i	0.119338	−	0.676799i
$723$	−37.3029	+	18.7333i	−1.38731	+	0.696698i
$724$	−1.71777	−	9.74195i	−0.0638404	−	0.362057i
$725$	17.4170	−	14.6146i	0.646850	−	0.542771i
$726$	−18.0093	+	41.7479i	−0.668387	+	1.54941i
$727$	−27.6108	−	23.1682i	−1.02403	−	0.859261i	−0.0338987	−	0.999425i	$-0.510792\pi$
$727$	−27.6108	−	23.1682i	−1.02403	−	0.859261i	−0.990128	+	0.140165i	$0.955237\pi$
$728$	−2.21455	+	1.51156i	−0.0820768	+	0.0560220i
$729$	20.6853	−	17.3528i	0.766121	−	0.642696i
$730$	−13.1544	+	22.7840i	−0.486865	+	0.843274i
$731$	1.48922	−	8.44579i	0.0550808	−	0.312379i
$732$	−9.00830	−	12.1007i	−0.332956	−	0.447257i
$733$	21.4997	+	7.82526i	0.794111	+	0.289033i	0.707044	−	0.707170i	$-0.250028\pi$
$733$	21.4997	+	7.82526i	0.794111	+	0.289033i	0.0870670	+	0.996202i	$0.472251\pi$
$734$	7.81490	+	2.84439i	0.288453	+	0.104988i
$735$	−29.6142	+	20.9657i	−1.09233	+	0.773330i
$736$	−0.827989	+	4.69576i	−0.0305201	+	0.173088i
$737$	−38.2846	−	66.3109i	−1.41023	−	2.44259i
$738$	12.5999	+	13.3561i	0.463808	+	0.491646i
$739$	2.02957	−	3.51531i	0.0746588	−	0.129313i	−0.826279	−	0.563261i	$-0.809547\pi$
$739$	2.02957	−	3.51531i	0.0746588	−	0.129313i	0.900938	+	0.433948i	$0.142880\pi$
$740$	3.74042	−	21.2130i	0.137500	−	0.779804i
$741$	0.367791	+	1.22860i	0.0135111	+	0.0451336i
$742$	−8.72366	+	31.0681i	−0.320256	+	1.14055i
$743$	−1.21450	+	1.01908i	−0.0445556	+	0.0373866i	−0.664794	−	0.747027i	$-0.731480\pi$
$743$	−1.21450	+	1.01908i	−0.0445556	+	0.0373866i	0.620238	+	0.784414i	$0.287036\pi$
$744$	−1.77283	+	1.87902i	−0.0649952	+	0.0688882i
$745$	−3.54246	−	2.97248i	−0.129786	−	0.108903i
$746$	−3.29420	+	5.70572i	−0.120609	+	0.208901i
$747$	−25.1582	+	16.5454i	−0.920492	+	0.605365i
$748$	3.02147	−	5.23333i	0.110476	−	0.191350i
$749$	−23.5730	−	2.34636i	−0.861339	−	0.0857342i
$750$	−0.314710	+	5.40151i	−0.0114916	+	0.197235i
$751$	−22.4960	+	18.8764i	−0.820891	+	0.688810i	−0.953181	−	0.302402i	$-0.902212\pi$
$751$	−22.4960	+	18.8764i	−0.820891	+	0.688810i	0.132289	+	0.991211i	$0.457767\pi$
$752$	−3.08123	+	2.58546i	−0.112361	+	0.0942821i
$753$	−45.8246	+	5.35520i	−1.66994	+	0.195154i
$754$	−5.47288	+	1.99196i	−0.199310	+	0.0725431i
$755$	−0.270633			−0.00984934
$756$	−13.6800	−	1.36248i	−0.497538	−	0.0495529i
$757$	−2.96567			−0.107789			−0.0538945	−	0.998547i	$-0.517163\pi$
$757$	−2.96567			−0.107789			−0.0538945	+	0.998547i	$0.517163\pi$
$758$	−12.3451	+	4.49326i	−0.448395	+	0.163202i
$759$	−19.9656	+	46.2829i	−0.724705	+	1.67996i
$760$	−1.67500	+	1.40549i	−0.0607585	+	0.0509824i
$761$	4.30983	−	3.61637i	0.156231	−	0.131093i	−0.561321	−	0.827598i	$-0.689707\pi$
$761$	4.30983	−	3.61637i	0.156231	−	0.131093i	0.717552	+	0.696504i	$0.245262\pi$
$762$	16.9665	−	8.52047i	0.614631	−	0.308664i
$763$	2.02622	−	2.82142i	0.0733542	−	0.102142i
$764$	4.04000	−	6.99749i	0.146162	−	0.253160i
$765$	−8.82911	−	1.03233i	−0.319217	−	0.0373240i
$766$	−13.2367	+	22.9266i	−0.478260	+	0.828370i
$767$	10.9941	+	9.22516i	0.396975	+	0.333101i
$768$	−0.496725	−	1.65930i	−0.0179240	−	0.0598747i
$769$	15.6923	−	13.1674i	0.565880	−	0.474830i	−0.314396	−	0.949292i	$-0.601802\pi$
$769$	15.6923	−	13.1674i	0.565880	−	0.474830i	0.880276	+	0.474462i	$0.157357\pi$
$770$	−33.7606	−	34.5768i	−1.21665	−	1.24606i
$771$	4.27709	−	4.53327i	0.154036	−	0.163262i
$772$	3.32927	−	18.8812i	0.119823	−	0.679550i
$773$	−9.28957	+	16.0900i	−0.334123	+	0.578717i	−0.983316	−	0.181906i	$-0.941773\pi$
$773$	−9.28957	+	16.0900i	−0.334123	+	0.578717i	0.649193	+	0.760623i	$0.275107\pi$
$774$	−10.2913	−	23.8605i	−0.369913	−	0.857647i
$775$	2.95030	+	5.11007i	0.105978	+	0.183559i
$776$	0.795308	−	4.51042i	0.0285499	−	0.161915i
$777$	−16.0002	+	28.8429i	−0.574004	+	1.03473i
$778$	13.7539	+	5.00602i	0.493102	+	0.179475i
$779$	−4.20214	−	1.52945i	−0.150557	−	0.0547983i
$780$	−2.08071	+	4.82336i	−0.0745013	+	0.172704i
$781$	−7.37958	+	41.8517i	−0.264062	+	1.49757i
$782$	2.36052	−	4.08854i	0.0844120	−	0.146206i
$783$	−28.0609	−	10.2152i	−1.00281	−	0.365062i
$784$	4.37016	+	5.46824i	0.156077	+	0.195294i
$785$	6.27778	+	5.26768i	0.224064	+	0.188012i
$786$	20.9476	+	28.1387i	0.747176	+	1.00367i
$787$	−23.0738	+	19.3612i	−0.822491	+	0.690152i	−0.953554	−	0.301222i	$-0.902605\pi$
$787$	−23.0738	+	19.3612i	−0.822491	+	0.690152i	0.131063	+	0.991374i	$0.458161\pi$
$788$	0.338986	+	1.92249i	0.0120759	+	0.0684857i
$789$	−44.0190	−	28.9530i	−1.56712	−	1.03075i
$790$	−2.75173	+	15.6059i	−0.0979023	+	0.555232i
$791$	2.39236	+	31.7010i	0.0850626	+	1.12716i
$792$	−1.06390	−	18.2790i	−0.0378040	−	0.649514i
$793$	8.82655			0.313440
$794$	−20.0811	−	16.8501i	−0.712653	−	0.597987i
$795$	18.1310	+	60.5663i	0.643042	+	2.14806i
$796$	−1.26410	−	7.16906i	−0.0448048	−	0.254101i
$797$	11.4203	−	9.58280i	0.404529	−	0.339440i	−0.417712	−	0.908579i	$-0.637168\pi$
$797$	11.4203	−	9.58280i	0.404529	−	0.339440i	0.822241	+	0.569139i	$0.192723\pi$
$798$	3.12618	−	1.19886i	0.110666	−	0.0424390i
$799$	3.74231	−	1.36209i	0.132393	−	0.0481872i
$800$	−3.95617			−0.139872
$801$	40.4697	−	9.58979i	1.42992	−	0.338838i
$802$	−36.7021			−1.29600
$803$	41.1014	+	34.4882i	1.45044	+	1.21706i
$804$	18.1545	+	11.9409i	0.640260	+	0.421124i
$805$	−26.3755	−	27.0131i	−0.929614	−	0.952087i
$806$	−0.262469	−	1.48854i	−0.00924508	−	0.0524315i
$807$	12.1874	−	28.2521i	0.429017	−	0.994520i
$808$	−0.975118	+	5.53017i	−0.0343045	+	0.194551i
$809$	−15.8444	−	27.4433i	−0.557060	−	0.964856i	−0.997740	−	0.0671916i	$-0.978596\pi$
$809$	−15.8444	−	27.4433i	−0.557060	−	0.964856i	0.440680	−	0.897664i	$-0.354737\pi$
$810$	−24.0702	+	12.0861i	−0.845741	+	0.424663i
$811$	−9.32761			−0.327537			−0.163768	−	0.986499i	$-0.552365\pi$
$811$	−9.32761			−0.327537			−0.163768	+	0.986499i	$0.552365\pi$
$812$	6.26096	+	13.8564i	0.219717	+	0.486263i
$813$	3.72717	−	0.435568i	0.130717	−	0.0152760i
$814$	−41.2799	−	15.0247i	−1.44686	−	0.526614i
$815$	5.20348	+	29.5104i	0.182270	+	1.03370i
$816$	−0.0997477	+	1.71202i	−0.00349187	+	0.0599325i
$817$	4.84795	+	4.06791i	0.169608	+	0.142318i
$818$	−4.01024	+	6.94594i	−0.140215	+	0.242859i
$819$	5.41905	−	5.94436i	0.189357	−	0.207713i
$820$	−9.15835	−	15.8627i	−0.319823	−	0.553950i
$821$	1.20393	−	6.82781i	0.0420173	−	0.238292i	−0.956565	−	0.291519i	$-0.905839\pi$
$821$	1.20393	−	6.82781i	0.0420173	−	0.238292i	0.998582	+	0.0532266i	$0.0169506\pi$
$822$	10.6041	−	11.2393i	0.369861	−	0.392014i
$823$	−39.8184	−	14.4927i	−1.38798	−	0.505185i	−0.463395	−	0.886152i	$-0.653369\pi$
$823$	−39.8184	−	14.4927i	−1.38798	−	0.505185i	−0.924588	+	0.380968i	$0.875591\pi$
$824$	0.268321	+	1.52172i	0.00934741	+	0.0530118i
$825$	−40.6941	−	9.64552i	−1.41679	−	0.335814i
$826$	21.8562	−	30.4337i	0.760474	−	1.05892i
$827$	11.4873	+	19.8967i	0.399454	+	0.691875i	0.993659	−	0.112439i	$-0.0358664\pi$
$827$	11.4873	+	19.8967i	0.399454	+	0.691875i	−0.594205	+	0.804314i	$0.702533\pi$
$828$	−0.831171	−	14.2804i	−0.0288852	−	0.496279i
$829$	39.4232			1.36922			0.684612	−	0.728908i	$-0.259972\pi$
$829$	39.4232			1.36922			0.684612	+	0.728908i	$0.259972\pi$
$830$	28.2263	−	10.2735i	0.979750	−	0.356600i
$831$	11.6332	+	7.65158i	0.403550	+	0.265430i
$832$	0.952297	+	0.346608i	0.0330150	+	0.0120165i
$833$	−2.21424	−	6.56754i	−0.0767188	−	0.227552i
$834$	0.822383	−	1.90639i	0.0284768	−	0.0660130i
$835$	65.5817	−	23.8698i	2.26955	−	0.826047i
$836$	2.22963	+	3.86183i	0.0771134	+	0.133564i
$837$	3.87541	−	6.71149i	0.133954	−	0.231983i
$838$	16.2967	−	28.2268i	0.562961	−	0.975078i
$839$	−8.50270	−	7.13461i	−0.293546	−	0.246314i	0.484106	−	0.875009i	$-0.339145\pi$
$839$	−8.50270	−	7.13461i	−0.293546	−	0.246314i	−0.777652	+	0.628695i	$0.783589\pi$
$840$	12.9656	+	4.46915i	0.447355	+	0.154200i
$841$	0.699510	+	3.96712i	0.0241210	+	0.136797i
$842$	−29.5648	+	24.8078i	−1.01887	+	0.854933i
$843$	2.11852	+	1.39343i	0.0729656	+	0.0479923i
$844$	21.6947	−	7.89624i	0.746763	−	0.271800i
$845$	17.9157	+	31.0309i	0.616319	+	1.06750i
$846$	7.20618	−	9.67877i	0.247753	−	0.332763i
$847$	−57.3631	+	39.1535i	−1.97102	+	1.34533i
$848$	11.4612	−	4.17155i	0.393580	−	0.143252i
$849$	6.46865	+	21.6084i	0.222004	+	0.741597i
$850$	3.68081	+	1.33971i	0.126251	+	0.0459516i
$851$	−32.2499	−	11.7380i	−1.10551	−	0.402374i
$852$	−3.45870	−	11.5537i	−0.118493	−	0.395823i
$853$	−33.2935	+	12.1178i	−1.13995	+	0.414907i	−0.841895	−	0.539642i	$-0.818560\pi$
$853$	−33.2935	+	12.1178i	−1.13995	+	0.414907i	−0.298054	+	0.954549i	$0.596337\pi$
$854$	−1.73410	−	22.9784i	−0.0593397	−	0.786305i
$855$	3.91736	−	5.26149i	0.133971	−	0.179939i
$856$	4.47689	+	7.75421i	0.153017	+	0.265033i
$857$	−1.57640	+	0.573763i	−0.0538489	+	0.0195994i	−0.368804	−	0.929507i	$-0.620233\pi$
$857$	−1.57640	+	0.573763i	−0.0538489	+	0.0195994i	0.314955	+	0.949107i	$0.398010\pi$
$858$	8.95048	+	5.88708i	0.305564	+	0.200982i
$859$	−34.5187	+	28.9646i	−1.17776	+	0.988261i	−0.177772	+	0.984072i	$0.556889\pi$
$859$	−34.5187	+	28.9646i	−1.17776	+	0.988261i	−0.999991	+	0.00418888i	$0.998667\pi$
$860$	4.50129	+	25.5281i	0.153493	+	0.870501i
$861$	5.34273	+	27.5340i	0.182080	+	0.938357i
$862$	−5.77555	−	4.84626i	−0.196716	−	0.165064i
$863$	9.30512	−	16.1169i	0.316750	−	0.548627i	−0.663058	−	0.748568i	$-0.730742\pi$
$863$	9.30512	−	16.1169i	0.316750	−	0.548627i	0.979808	+	0.199941i	$0.0640750\pi$
$864$	2.59781	+	4.50015i	0.0883792	+	0.153098i
$865$	11.0359	+	19.1147i	0.375232	+	0.649920i
$866$	10.6494	−	3.87607i	0.361882	−	0.131714i
$867$	−10.9905	+	25.4774i	−0.373257	+	0.865259i
$868$	−3.82358	+	0.975737i	−0.129781	+	0.0331187i
$869$	30.3687	+	11.0533i	1.03019	+	0.374957i
$870$	24.8885	+	16.3702i	0.843801	+	0.555000i
$871$	−11.9471	+	4.34839i	−0.404812	+	0.147339i
$872$	−1.31290			−0.0444605
$873$	0.798364	+	13.7168i	0.0270205	+	0.464243i
$874$	1.74190	+	3.01706i	0.0589206	+	0.102053i
$875$	−4.82109	+	6.71314i	−0.162983	+	0.226946i
$876$	−14.8160	−	3.51176i	−0.500585	−	0.118651i
$877$	−5.70875	−	32.3759i	−0.192771	−	1.09326i	−0.915558	−	0.402187i	$-0.868250\pi$
$877$	−5.70875	−	32.3759i	−0.192771	−	1.09326i	0.722787	−	0.691071i	$-0.242861\pi$
$878$	14.7784	+	5.37889i	0.498746	+	0.181529i
$879$	21.8257	−	23.1330i	0.736163	−	0.780256i
$880$	−3.17173	+	17.9878i	−0.106919	+	0.606367i
$881$	−4.57875	−	7.93064i	−0.154262	−	0.267190i	0.778528	−	0.627610i	$-0.215967\pi$
$881$	−4.57875	−	7.93064i	−0.154262	−	0.267190i	−0.932790	+	0.360420i	$0.882633\pi$
$882$	−16.5398	−	12.9397i	−0.556923	−	0.435703i
$883$	27.2804	−	47.2510i	0.918058	−	1.59012i	0.115696	−	0.993285i	$-0.463090\pi$
$883$	27.2804	−	47.2510i	0.918058	−	1.59012i	0.802362	−	0.596838i	$-0.203576\pi$
$884$	−0.768641	−	0.644967i	−0.0258522	−	0.0216926i
$885$	4.26973	−	73.2834i	0.143525	−	2.46339i
$886$	4.82450	+	27.3611i	0.162082	+	0.919215i
$887$	−1.37551	−	0.500645i	−0.0461852	−	0.0168100i	0.318824	−	0.947814i	$-0.396712\pi$
$887$	−1.37551	−	0.500645i	−0.0461852	−	0.0168100i	−0.365009	+	0.931004i	$0.618934\pi$
$888$	12.3824	−	1.44704i	0.415525	−	0.0485595i
$889$	28.8587	+	2.87248i	0.967889	+	0.0963398i
$890$	−41.4890			−1.39071
$891$	15.7498	+	52.6233i	0.527639	+	1.76295i
$892$	−6.06924	−	10.5122i	−0.203213	−	0.351976i
$893$	−0.510316	+	2.89415i	−0.0170771	+	0.0968489i
$894$	1.06012	−	2.45749i	0.0354556	−	0.0821907i
$895$	2.13790	+	12.1246i	0.0714621	+	0.405282i
$896$	0.715242	−	2.54724i	0.0238946	−	0.0850973i
$897$	6.99256	+	4.59928i	0.233475	+	0.153565i
$898$	−17.9797	−	15.0868i	−0.599991	−	0.503452i
$899$	−8.57165			−0.285881
$900$	11.5487	−	2.73661i	0.384957	−	0.0912203i
$901$	−12.0762			−0.402315
$902$	−35.1024	+	12.7762i	−1.16878	+	0.425401i
$903$	6.22220	−	39.2024i	0.207062	−	1.30457i
$904$	9.20473	−	7.72368i	0.306145	−	0.256886i
$905$	−5.14074	−	29.1546i	−0.170884	−	0.969132i
$906$	−0.0449195	−	0.150053i	−0.00149235	−	0.00498516i
$907$	21.7830	+	18.2781i	0.723291	+	0.606914i	0.928294	−	0.371848i	$-0.121276\pi$
$907$	21.7830	+	18.2781i	0.723291	+	0.606914i	−0.205002	+	0.978762i	$0.565720\pi$
$908$	−15.4423			−0.512470
$909$	−0.978865	−	16.8180i	−0.0324669	−	0.557817i
$910$	−6.62746	+	4.52362i	−0.219698	+	0.149956i
$911$	2.18642	−	12.3998i	0.0724393	−	0.410823i	−0.926927	−	0.375241i	$-0.877560\pi$
$911$	2.18642	−	12.3998i	0.0724393	−	0.410823i	0.999367	−	0.0355829i	$-0.0113288\pi$
$912$	−1.05729	−	0.695420i	−0.0350103	−	0.0230276i
$913$	−10.6376	−	60.3286i	−0.352052	−	1.99659i
$914$	−26.2782	+	22.0500i	−0.869204	+	0.729349i
$915$	−26.9590	−	36.2137i	−0.891238	−	1.19719i
$916$	−16.2864	−	13.6659i	−0.538118	−	0.451534i
$917$	4.03241	+	53.4332i	0.133162	+	1.76452i
$918$	−0.893076	−	5.06665i	−0.0294759	−	0.167224i
$919$	21.7040	−	37.5924i	0.715949	−	1.24006i	−0.246644	−	0.969106i	$-0.579328\pi$
$919$	21.7040	−	37.5924i	0.715949	−	1.24006i	0.962593	−	0.270953i	$-0.0873388\pi$
$920$	−2.47791	+	14.0529i	−0.0816943	+	0.463311i
$921$	1.26719	−	2.93752i	0.0417554	−	0.0967947i
$922$	0.984341	+	0.358271i	0.0324175	+	0.0117990i
$923$	6.63086	+	2.41343i	0.218257	+	0.0794392i
$924$	13.5676	−	24.4576i	0.446340	−	0.804598i
$925$	4.94463	−	28.0424i	0.162578	−	0.922028i
$926$	−7.75422	−	13.4307i	−0.254820	−	0.441360i
$927$	−1.83590	−	4.25655i	−0.0602988	−	0.139804i
$928$	2.87351	−	4.97707i	0.0943277	−	0.163380i
$929$	−8.75480	+	49.6509i	−0.287236	+	1.62899i	0.409953	+	0.912107i	$0.365545\pi$
$929$	−8.75480	+	49.6509i	−0.287236	+	1.62899i	−0.697189	+	0.716888i	$0.745566\pi$
$930$	−5.30554	+	5.62332i	−0.173975	+	0.184396i
$931$	5.01407	+	1.00815i	0.164330	+	0.0330408i
$932$	−0.817676	+	0.686111i	−0.0267839	+	0.0224743i
$933$	−7.01691	−	23.4398i	−0.229723	−	0.767385i
$934$	−8.81140	−	7.39364i	−0.288318	−	0.241927i
$935$	9.04230	−	15.6617i	0.295715	−	0.512193i
$936$	−3.01967	−	0.353070i	−0.0987010	−	0.0115405i
$937$	26.7056	−	46.2555i	0.872435	−	1.51110i	0.0129639	−	0.999916i	$-0.495873\pi$
$937$	26.7056	−	46.2555i	0.872435	−	1.51110i	0.859471	−	0.511185i	$-0.170793\pi$
$938$	13.6675	+	30.2479i	0.446258	+	0.987629i
$939$	−21.2094	+	10.6512i	−0.692143	+	0.347590i
$940$	−9.22117	+	7.73748i	−0.300761	+	0.252369i
$941$	−32.0725	+	26.9120i	−1.04553	+	0.877307i	−0.992617	−	0.121292i	$-0.961296\pi$
$941$	−32.0725	+	26.9120i	−1.04553	+	0.877307i	−0.0529168	+	0.998599i	$0.516852\pi$
$942$	−1.87869	+	4.35505i	−0.0612109	+	0.141895i
$943$	−27.4237	+	9.98141i	−0.893039	+	0.325040i
$944$	−14.1618			−0.460929
$945$	−40.9401	−	4.07748i	−1.33178	−	0.132640i
$946$	52.8652			1.71880
$947$	23.4938	−	8.55105i	0.763447	−	0.277872i	0.0691939	−	0.997603i	$-0.477957\pi$
$947$	23.4938	−	8.55105i	0.763447	−	0.277872i	0.694253	+	0.719731i	$0.255735\pi$
$948$	−9.10941	+	1.06455i	−0.295860	+	0.0345751i
$949$	6.82463	−	5.72655i	0.221537	−	0.185892i
$950$	−2.21425	+	1.85798i	−0.0718399	+	0.0602808i
$951$	0.467573	−	8.02517i	0.0151621	−	0.260234i
$952$	−1.52805	+	2.12774i	−0.0495244	+	0.0689604i
$953$	−8.12353	+	14.0704i	−0.263147	+	0.455784i	−0.967076	−	0.254486i	$-0.918094\pi$
$953$	−8.12353	+	14.0704i	−0.263147	+	0.455784i	0.703929	+	0.710270i	$0.251427\pi$
$954$	−30.5716	+	20.1055i	−0.989792	+	0.650940i
$955$	12.0905	−	20.9413i	0.391238	−	0.677644i
$956$	−6.85050	−	5.74826i	−0.221561	−	0.185912i
$957$	41.6922	−	44.1894i	1.34772	−	1.42844i
$958$	13.6699	−	11.4704i	0.441654	−	0.370592i
$959$	22.8706	−	5.83633i	0.738530	−	0.188465i
$960$	−1.48654	−	4.96575i	−0.0479779	−	0.160269i
$961$	−4.99680	+	28.3383i	−0.161187	+	0.914138i
$962$	−3.64708	+	6.31693i	−0.117587	+	0.203666i
$963$	−18.4326	−	19.5390i	−0.593982	−	0.629635i
$964$	12.0500	+	20.8713i	0.388105	+	0.672218i
$965$	9.96346	−	56.5056i	0.320735	−	1.81898i
$966$	10.5996	−	19.1075i	0.341038	−	0.614775i
$967$	27.0140	+	9.83231i	0.868713	+	0.316186i	0.737646	−	0.675188i	$-0.235937\pi$
$967$	27.0140	+	9.83231i	0.868713	+	0.316186i	0.131067	+	0.991373i	$0.458160\pi$
$968$	24.6672	+	8.97811i	0.792832	+	0.288567i
$969$	0.748204	+	1.00505i	0.0240358	+	0.0322870i
$970$	2.38011	−	13.4983i	0.0764207	−	0.433403i
$971$	18.5178	−	32.0738i	0.594264	−	1.02930i	−0.399386	−	0.916783i	$-0.630777\pi$
$971$	18.5178	−	32.0738i	0.594264	−	1.02930i	0.993650	−	0.112513i	$-0.0358901\pi$
$972$	−10.6963	−	11.3397i	−0.343085	−	0.363721i
$973$	2.61945	−	1.78792i	0.0839757	−	0.0573181i
$974$	24.0032	+	20.1411i	0.769113	+	0.645363i
$975$	−2.75059	+	6.37623i	−0.0880892	+	0.204203i
$976$	−6.67203	+	5.59850i	−0.213567	+	0.179204i
$977$	−2.20271	−	12.4922i	−0.0704709	−	0.399660i	−0.999556	−	0.0297943i	$-0.990515\pi$
$977$	−2.20271	−	12.4922i	−0.0704709	−	0.399660i	0.929085	−	0.369866i	$-0.120596\pi$
$978$	−15.4984	+	7.78319i	−0.495583	+	0.248879i
$979$	−14.6929	+	83.3273i	−0.469586	+	2.66315i
$980$	13.0785	+	16.3647i	0.417778	+	0.522752i
$981$	3.83257	−	0.908176i	0.122365	−	0.0289958i
$982$	29.2544			0.933546
$983$	4.72804	+	3.96730i	0.150801	+	0.126537i	0.715067	−	0.699056i	$-0.246396\pi$
$983$	4.72804	+	3.96730i	0.150801	+	0.126537i	−0.564266	+	0.825593i	$0.690841\pi$
$984$	7.27500	−	7.71074i	0.231918	−	0.245809i
$985$	1.01448	+	5.75340i	0.0323240	+	0.183318i
$986$	−4.35893	+	3.65758i	−0.138817	+	0.116481i
$987$	17.2102	−	6.59993i	0.547808	−	0.210078i
$988$	0.695779	−	0.253243i	0.0221357	−	0.00805672i
$989$	41.3009			1.31329
$990$	−3.18392	−	54.7032i	−0.101192	−	1.73858i
$991$	−0.119112			−0.00378371			−0.00189185	−	0.999998i	$-0.500602\pi$
$991$	−0.119112			−0.00378371			−0.00189185	+	0.999998i	$0.500602\pi$
$992$	1.14255	+	0.958713i	0.0362760	+	0.0304392i
$993$	−1.80800	+	31.0316i	−0.0573753	+	0.984758i
$994$	4.98024	−	17.7365i	0.157964	−	0.562566i
$995$	−3.78305	−	21.4548i	−0.119931	−	0.680162i
$996$	10.3812	+	13.9449i	0.328940	+	0.441861i
$997$	−0.637380	+	3.61476i	−0.0201860	+	0.114481i	−0.993236	−	0.116114i	$-0.962956\pi$
$997$	−0.637380	+	3.61476i	−0.0201860	+	0.114481i	0.973050	+	0.230595i	$0.0740672\pi$
$998$	6.49381	+	11.2476i	0.205558	+	0.356037i
$999$	−35.1452	+	12.7894i	−1.11194	+	0.404639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.v.a.205.9	✓	72
7.4	even	3		378.2.w.b.151.8	yes	72
27.22	even	9		378.2.w.b.373.8	yes	72
189.130	even	9	inner	378.2.v.a.319.9	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.205.9	✓	72	1.1	even	1	trivial
378.2.v.a.319.9	yes	72	189.130	even	9	inner
378.2.w.b.151.8	yes	72	7.4	even	3
378.2.w.b.373.8	yes	72	27.22	even	9

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.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.03428 + 1.38934i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.29253 - 1.92366i) q^{5} +(1.44709 + 0.951806i) q^{6} +(1.08943 + 2.41105i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.860524 + 2.87393i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(1.03428 + 1.38934i) q^{3} +(0.766044 - 0.642788i) q^{4} +(2.29253 - 1.92366i) q^{5} +(1.44709 + 0.951806i) q^{6} +(1.08943 + 2.41105i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.860524 + 2.87393i) q^{9} +(1.49634 - 2.59174i) q^{10} +(-4.67540 - 3.92312i) q^{11} +(1.68536 + 0.399472i) q^{12} +(-0.776320 + 0.651410i) q^{13} +(1.84835 + 1.89304i) q^{14} +(5.04374 + 1.19549i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.495055 + 0.857460i) q^{17} +(0.174315 + 2.99493i) q^{18} +(-0.365316 - 0.632745i) q^{19} +(0.519675 - 2.94722i) q^{20} +(-2.22299 + 4.00728i) q^{21} +(-5.73522 - 2.08745i) q^{22} +(-4.48064 - 1.63082i) q^{23} +(1.72034 - 0.201045i) q^{24} +(0.686982 - 3.89607i) q^{25} +(-0.506707 + 0.877642i) q^{26} +(-4.88289 + 1.77690i) q^{27} +(2.38434 + 1.14670i) q^{28} +(4.40248 + 3.69412i) q^{29} +(5.14845 - 0.601664i) q^{30} +(-1.14255 + 0.958713i) q^{31} +(-0.173648 - 0.984808i) q^{32} +(0.614872 - 10.5533i) q^{33} +(-0.171931 + 0.975067i) q^{34} +(7.13558 + 3.43171i) q^{35} +(1.18813 + 2.75470i) q^{36} +7.19761 q^{37} +(-0.559696 - 0.469641i) q^{38} +(-1.70796 - 0.404830i) q^{39} +(-0.519675 - 2.94722i) q^{40} +(4.68857 - 3.93417i) q^{41} +(-0.718353 + 4.52592i) q^{42} +(-8.13938 + 2.96249i) q^{43} -6.10330 q^{44} +(3.55570 + 8.24394i) q^{45} -4.76820 q^{46} +(-3.08123 - 2.58546i) q^{47} +(1.54783 - 0.777312i) q^{48} +(-4.62630 + 5.25332i) q^{49} +(-0.686982 - 3.89607i) q^{50} +(-1.70333 + 0.199056i) q^{51} +(-0.175977 + 0.998018i) q^{52} +(6.09840 + 10.5627i) q^{53} +(-3.98068 + 3.33979i) q^{54} -18.2653 q^{55} +(2.63274 + 0.262053i) q^{56} +(0.501258 - 1.16198i) q^{57} +(5.40044 + 1.96560i) q^{58} +(-2.45918 - 13.9467i) q^{59} +(4.63218 - 2.32625i) q^{60} +(-6.67203 - 5.59850i) q^{61} +(-0.745746 + 1.29167i) q^{62} +(-7.86667 + 1.05618i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.526645 + 2.98675i) q^{65} +(-3.03166 - 10.1272i) q^{66} +(11.7890 + 4.29083i) q^{67} +(0.171931 + 0.975067i) q^{68} +(-2.36848 - 7.91185i) q^{69} +(7.87897 + 0.784241i) q^{70} +(-3.48150 - 6.03014i) q^{71} +(2.05864 + 2.18220i) q^{72} -8.79100 q^{73} +(6.76355 - 2.46173i) q^{74} +(6.12349 - 3.07518i) q^{75} +(-0.686569 - 0.249891i) q^{76} +(4.36534 - 15.5466i) q^{77} +(-1.74342 + 0.203741i) q^{78} +(-4.97578 + 1.81103i) q^{79} +(-1.49634 - 2.59174i) q^{80} +(-7.51900 - 4.94618i) q^{81} +(3.06024 - 5.30050i) q^{82} +(7.68885 + 6.45171i) q^{83} +(0.872925 + 4.49867i) q^{84} +(0.514534 + 2.91807i) q^{85} +(-6.63529 + 5.56767i) q^{86} +(-0.578979 + 9.93729i) q^{87} +(-5.73522 + 2.08745i) q^{88} +(-6.93172 - 12.0061i) q^{89} +(6.16086 + 6.53065i) q^{90} +(-2.41632 - 1.16208i) q^{91} +(-4.48064 + 1.63082i) q^{92} +(-2.51370 - 0.595810i) q^{93} +(-3.77969 - 1.37570i) q^{94} +(-2.05469 - 0.747844i) q^{95} +(1.18863 - 1.25982i) q^{96} +(4.30379 - 1.56645i) q^{97} +(-2.55056 + 6.51879i) q^{98} +(15.2981 - 10.0608i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} - 6 q^{7} + 36 q^{8} + 6 q^{10} + 12 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} + 18 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} - 18 q^{35} - 3 q^{36} - 48 q^{39} - 6 q^{41} + 36 q^{42} - 24 q^{43} - 45 q^{45} - 27 q^{47} + 6 q^{48} + 48 q^{49} + 6 q^{50} + 15 q^{51} - 6 q^{52} - 15 q^{53} - 63 q^{54} - 72 q^{55} - 3 q^{56} + 57 q^{57} - 3 q^{58} - 30 q^{59} + 21 q^{60} + 9 q^{61} - 24 q^{62} - 21 q^{63} - 36 q^{64} + 45 q^{65} + 6 q^{67} + 9 q^{68} - 39 q^{69} + 15 q^{70} + 12 q^{71} - 60 q^{73} - 18 q^{74} + 42 q^{75} + 3 q^{77} + 6 q^{78} - 27 q^{79} - 6 q^{80} + 12 q^{81} + 33 q^{82} + 18 q^{83} - 21 q^{84} + 51 q^{85} - 12 q^{86} - 117 q^{87} + 6 q^{88} - 36 q^{89} - 69 q^{90} - 3 q^{91} + 12 q^{92} - 30 q^{93} - 27 q^{94} + 3 q^{95} + 48 q^{97} - 12 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 6 * q^7 + 36 * q^8 + 6 * q^10 + 12 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 - 12 * q^17 + 18 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 - 18 * q^35 - 3 * q^36 - 48 * q^39 - 6 * q^41 + 36 * q^42 - 24 * q^43 - 45 * q^45 - 27 * q^47 + 6 * q^48 + 48 * q^49 + 6 * q^50 + 15 * q^51 - 6 * q^52 - 15 * q^53 - 63 * q^54 - 72 * q^55 - 3 * q^56 + 57 * q^57 - 3 * q^58 - 30 * q^59 + 21 * q^60 + 9 * q^61 - 24 * q^62 - 21 * q^63 - 36 * q^64 + 45 * q^65 + 6 * q^67 + 9 * q^68 - 39 * q^69 + 15 * q^70 + 12 * q^71 - 60 * q^73 - 18 * q^74 + 42 * q^75 + 3 * q^77 + 6 * q^78 - 27 * q^79 - 6 * q^80 + 12 * q^81 + 33 * q^82 + 18 * q^83 - 21 * q^84 + 51 * q^85 - 12 * q^86 - 117 * q^87 + 6 * q^88 - 36 * q^89 - 69 * q^90 - 3 * q^91 + 12 * q^92 - 30 * q^93 - 27 * q^94 + 3 * q^95 + 48 * q^97 - 12 * q^98 + 90 * q^99

Introduction

L-functions

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