LMFDB - Embedded newform 370.2.o.b.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 25 x^{15} + 132 x^{14} - 135 x^{13} + 666 x^{12} - 297 x^{11} + 1845 x^{10} + \cdots + 9 $ x^18 - 3x^17 + 18x^16 - 25x^15 + 132x^14 - 135x^13 + 666x^12 - 297x^11 + 1845x^10 - 382x^9 + 3810x^8 - 63x^7 + 3325x^6 - 1329x^5 + 1332x^4 - 192x^3 + 117x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			81.1
Root			$-0.707815 + 1.22597i$ of defining polynomial
Character	$\chi$	$=$	370.81
Dual form			370.2.o.b.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 - 0.342020i) q^{2} +(-1.33026 - 0.484174i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{5} -1.41563 q^{6} +(0.162212 + 0.919948i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.762973 - 0.640210i) q^{9} +O(q^{10})$	\(q+(0.939693 - 0.342020i) q^{2} +(-1.33026 - 0.484174i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{5} -1.41563 q^{6} +(0.162212 + 0.919948i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.762973 - 0.640210i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.17112 - 3.76049i) q^{11} +(-1.33026 + 0.484174i) q^{12} +(2.10207 - 1.76385i) q^{13} +(0.467070 + 0.808989i) q^{14} +(-0.245822 + 1.39412i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-5.05778 - 4.24398i) q^{17} +(-0.935925 - 0.340649i) q^{18} +(-1.18186 - 0.430160i) q^{19} +(-0.766044 - 0.642788i) q^{20} +(0.229632 - 1.30231i) q^{21} +(0.754021 - 4.27627i) q^{22} +(-0.408767 - 0.708006i) q^{23} +(-1.08444 + 0.909950i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(1.37203 - 2.37643i) q^{26} +(2.82842 + 4.89897i) q^{27} +(0.715592 + 0.600453i) q^{28} +(-2.40316 + 4.16240i) q^{29} +(0.245822 + 1.39412i) q^{30} +7.21022 q^{31} +(-0.173648 - 0.984808i) q^{32} +(-4.70887 + 3.95122i) q^{33} +(-6.20429 - 2.25818i) q^{34} +(0.877804 - 0.319495i) q^{35} -0.995990 q^{36} +(-4.57469 + 4.00902i) q^{37} -1.25770 q^{38} +(-3.65031 + 1.32860i) q^{39} +(-0.939693 - 0.342020i) q^{40} +(7.00771 - 5.88016i) q^{41} +(-0.229632 - 1.30231i) q^{42} +8.15193 q^{43} +(-0.754021 - 4.27627i) q^{44} +(-0.497995 + 0.862553i) q^{45} +(-0.626268 - 0.525501i) q^{46} +(0.927468 + 1.60642i) q^{47} +(-0.707815 + 1.22597i) q^{48} +(5.75786 - 2.09569i) q^{49} +(-0.766044 + 0.642788i) q^{50} +(4.67333 + 8.09444i) q^{51} +(0.476502 - 2.70237i) q^{52} +(-2.04649 + 11.6062i) q^{53} +(4.33340 + 3.63615i) q^{54} +(-4.08037 - 1.48513i) q^{55} +(0.877804 + 0.319495i) q^{56} +(1.36390 + 1.14445i) q^{57} +(-0.834610 + 4.73331i) q^{58} +(1.25951 - 7.14302i) q^{59} +(0.707815 + 1.22597i) q^{60} +(1.93294 - 1.62193i) q^{61} +(6.77539 - 2.46604i) q^{62} +(0.465197 - 0.805745i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.10207 - 1.76385i) q^{65} +(-3.07350 + 5.32346i) q^{66} +(2.53952 + 14.4023i) q^{67} -6.60247 q^{68} +(0.200968 + 1.13974i) q^{69} +(0.715592 - 0.600453i) q^{70} +(6.86552 + 2.49884i) q^{71} +(-0.935925 + 0.340649i) q^{72} -16.7122 q^{73} +(-2.92763 + 5.33188i) q^{74} +1.41563 q^{75} +(-1.18186 + 0.430160i) q^{76} +(3.81163 + 1.38732i) q^{77} +(-2.97576 + 2.49696i) q^{78} +(1.42188 + 8.06388i) q^{79} -1.00000 q^{80} +(-0.871719 - 4.94377i) q^{81} +(4.57395 - 7.92232i) q^{82} +(1.77946 + 1.49314i) q^{83} +(-0.661198 - 1.14523i) q^{84} +(-3.30123 + 5.71790i) q^{85} +(7.66030 - 2.78812i) q^{86} +(5.21216 - 4.37352i) q^{87} +(-2.17112 - 3.76049i) q^{88} +(-0.313571 + 1.77835i) q^{89} +(-0.172952 + 0.980859i) q^{90} +(1.96363 + 1.64768i) q^{91} +(-0.768231 - 0.279613i) q^{92} +(-9.59145 - 3.49100i) q^{93} +(1.42096 + 1.19233i) q^{94} +(-0.218398 + 1.23860i) q^{95} +(-0.245822 + 1.39412i) q^{96} +(0.270746 + 0.468946i) q^{97} +(4.69385 - 3.93861i) q^{98} +(-4.06401 + 1.47918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$2$	0.939693	−	0.342020i	0.664463	−	0.241845i
$3$	−1.33026	−	0.484174i	−0.768025	−	0.279538i	−0.0718546	−	0.997415i	$-0.522892\pi$
$3$	−1.33026	−	0.484174i	−0.768025	−	0.279538i	−0.696170	+	0.717877i	$0.745114\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	−1.41563			−0.577929
$7$	0.162212	+	0.919948i	0.0613102	+	0.347708i	0.999996	+	0.00293293i	$0.000933582\pi$
$7$	0.162212	+	0.919948i	0.0613102	+	0.347708i	−0.938685	+	0.344775i	$0.887955\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−0.762973	−	0.640210i	−0.254324	−	0.213403i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	2.17112	−	3.76049i	0.654617	−	1.13383i	−0.327373	−	0.944895i	$-0.606163\pi$
$11$	2.17112	−	3.76049i	0.654617	−	1.13383i	0.981990	−	0.188934i	$-0.0605032\pi$
$12$	−1.33026	+	0.484174i	−0.384012	+	0.139769i
$13$	2.10207	−	1.76385i	0.583011	−	0.489204i	−0.302924	−	0.953015i	$-0.597963\pi$
$13$	2.10207	−	1.76385i	0.583011	−	0.489204i	0.885934	+	0.463811i	$0.153518\pi$
$14$	0.467070	+	0.808989i	0.124830	+	0.216211i
$15$	−0.245822	+	1.39412i	−0.0634709	+	0.359961i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−5.05778	−	4.24398i	−1.22669	−	1.02932i	−0.998447	−	0.0557136i	$-0.982257\pi$
$17$	−5.05778	−	4.24398i	−1.22669	−	1.02932i	−0.228246	−	0.973604i	$-0.573299\pi$
$18$	−0.935925	−	0.340649i	−0.220600	−	0.0802917i
$19$	−1.18186	−	0.430160i	−0.271136	−	0.0986855i	0.202874	−	0.979205i	$-0.434972\pi$
$19$	−1.18186	−	0.430160i	−0.271136	−	0.0986855i	−0.474010	+	0.880519i	$0.657194\pi$
$20$	−0.766044	−	0.642788i	−0.171293	−	0.143732i
$21$	0.229632	−	1.30231i	0.0501098	−	0.284187i
$22$	0.754021	−	4.27627i	0.160758	−	0.911703i
$23$	−0.408767	−	0.708006i	−0.0852339	−	0.147629i	0.820257	−	0.571995i	$-0.193830\pi$
$23$	−0.408767	−	0.708006i	−0.0852339	−	0.147629i	−0.905491	+	0.424366i	$0.860497\pi$
$24$	−1.08444	+	0.909950i	−0.221360	+	0.185743i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	1.37203	−	2.37643i	0.269078	−	0.466056i
$27$	2.82842	+	4.89897i	0.544330	+	0.942808i
$28$	0.715592	+	0.600453i	0.135234	+	0.113475i
$29$	−2.40316	+	4.16240i	−0.446257	+	0.772939i	−0.998139	−	0.0609831i	$-0.980576\pi$
$29$	−2.40316	+	4.16240i	−0.446257	+	0.772939i	0.551882	+	0.833922i	$0.313910\pi$
$30$	0.245822	+	1.39412i	0.0448807	+	0.254531i
$31$	7.21022			1.29499			0.647497	−	0.762068i	$-0.275816\pi$
$31$	7.21022			1.29499			0.647497	+	0.762068i	$0.275816\pi$
$32$	−0.173648	−	0.984808i	−0.0306970	−	0.174091i
$33$	−4.70887	+	3.95122i	−0.819710	+	0.687818i
$34$	−6.20429	−	2.25818i	−1.06403	−	0.387274i
$35$	0.877804	−	0.319495i	0.148376	−	0.0540044i
$36$	−0.995990			−0.165998
$37$	−4.57469	+	4.00902i	−0.752074	+	0.659079i
$37$	−4.57469	+	4.00902i	−0.752074	+	0.659079i
$38$	−1.25770			−0.204027
$39$	−3.65031	+	1.32860i	−0.584518	+	0.212747i
$40$	−0.939693	−	0.342020i	−0.148578	−	0.0540781i
$41$	7.00771	−	5.88016i	1.09442	−	0.918327i	0.0973824	−	0.995247i	$-0.468953\pi$
$41$	7.00771	−	5.88016i	1.09442	−	0.918327i	0.997037	+	0.0769199i	$0.0245086\pi$
$42$	−0.229632	−	1.30231i	−0.0354329	−	0.200950i
$43$	8.15193			1.24316			0.621578	−	0.783352i	$-0.286492\pi$
$43$	8.15193			1.24316			0.621578	+	0.783352i	$0.286492\pi$
$44$	−0.754021	−	4.27627i	−0.113673	−	0.644671i
$45$	−0.497995	+	0.862553i	−0.0742367	+	0.128582i
$46$	−0.626268	−	0.525501i	−0.0923381	−	0.0774809i
$47$	0.927468	+	1.60642i	0.135285	+	0.234321i	0.925706	−	0.378243i	$-0.123472\pi$
$47$	0.927468	+	1.60642i	0.135285	+	0.234321i	−0.790421	+	0.612564i	$0.790138\pi$
$48$	−0.707815	+	1.22597i	−0.102164	+	0.176954i
$49$	5.75786	−	2.09569i	0.822551	−	0.299384i
$50$	−0.766044	+	0.642788i	−0.108335	+	0.0909039i
$51$	4.67333	+	8.09444i	0.654397	+	1.13345i
$52$	0.476502	−	2.70237i	0.0660789	−	0.374752i
$53$	−2.04649	+	11.6062i	−0.281107	+	1.59424i	0.437760	+	0.899092i	$0.355772\pi$
$53$	−2.04649	+	11.6062i	−0.281107	+	1.59424i	−0.718867	+	0.695147i	$0.755339\pi$
$54$	4.33340	+	3.63615i	0.589700	+	0.494817i
$55$	−4.08037	−	1.48513i	−0.550196	−	0.200255i
$56$	0.877804	+	0.319495i	0.117302	+	0.0426943i
$57$	1.36390	+	1.14445i	0.180653	+	0.151586i
$58$	−0.834610	+	4.73331i	−0.109590	+	0.621514i
$59$	1.25951	−	7.14302i	0.163974	−	0.929943i	−0.786142	−	0.618046i	$-0.787925\pi$
$59$	1.25951	−	7.14302i	0.163974	−	0.929943i	0.950116	−	0.311897i	$-0.100964\pi$
$60$	0.707815	+	1.22597i	0.0913786	+	0.158272i
$61$	1.93294	−	1.62193i	0.247488	−	0.207667i	−0.510602	−	0.859817i	$-0.670577\pi$
$61$	1.93294	−	1.62193i	0.247488	−	0.207667i	0.758090	+	0.652150i	$0.226133\pi$
$62$	6.77539	−	2.46604i	0.860476	−	0.313188i
$63$	0.465197	−	0.805745i	0.0586093	−	0.101514i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.10207	−	1.76385i	−0.260730	−	0.218779i
$66$	−3.07350	+	5.32346i	−0.378322	+	0.655272i
$67$	2.53952	+	14.4023i	0.310252	+	1.75953i	0.597691	+	0.801727i	$0.296085\pi$
$67$	2.53952	+	14.4023i	0.310252	+	1.75953i	−0.287439	+	0.957799i	$0.592804\pi$
$68$	−6.60247			−0.800667
$69$	0.200968	+	1.13974i	0.0241937	+	0.137209i
$70$	0.715592	−	0.600453i	0.0855297	−	0.0717679i
$71$	6.86552	+	2.49884i	0.814787	+	0.296558i	0.715600	−	0.698511i	$-0.246154\pi$
$71$	6.86552	+	2.49884i	0.814787	+	0.296558i	0.0991872	+	0.995069i	$0.468376\pi$
$72$	−0.935925	+	0.340649i	−0.110300	+	0.0401458i
$73$	−16.7122			−1.95602			−0.978009	−	0.208564i	$-0.933121\pi$
$73$	−16.7122			−1.95602			−0.978009	+	0.208564i	$0.933121\pi$
$74$	−2.92763	+	5.33188i	−0.340331	+	0.619819i
$75$	1.41563			0.163463
$76$	−1.18186	+	0.430160i	−0.135568	+	0.0493427i
$77$	3.81163	+	1.38732i	0.434376	+	0.158100i
$78$	−2.97576	+	2.49696i	−0.336939	+	0.282725i
$79$	1.42188	+	8.06388i	0.159974	+	0.907258i	0.954096	+	0.299500i	$0.0968198\pi$
$79$	1.42188	+	8.06388i	0.159974	+	0.907258i	−0.794122	+	0.607758i	$0.792069\pi$
$80$	−1.00000			−0.111803
$81$	−0.871719	−	4.94377i	−0.0968577	−	0.549307i
$82$	4.57395	−	7.92232i	0.505109	−	0.874874i
$83$	1.77946	+	1.49314i	0.195321	+	0.163894i	0.735203	−	0.677847i	$-0.237087\pi$
$83$	1.77946	+	1.49314i	0.195321	+	0.163894i	−0.539882	+	0.841741i	$0.681531\pi$
$84$	−0.661198	−	1.14523i	−0.0721426	−	0.124955i
$85$	−3.30123	+	5.71790i	−0.358069	+	0.620194i
$86$	7.66030	−	2.78812i	0.826032	−	0.300651i
$87$	5.21216	−	4.37352i	0.558802	−	0.468890i
$88$	−2.17112	−	3.76049i	−0.231442	−	0.400869i
$89$	−0.313571	+	1.77835i	−0.0332385	+	0.188505i	−0.996906	−	0.0785986i	$-0.974955\pi$
$89$	−0.313571	+	1.77835i	−0.0332385	+	0.188505i	0.963668	+	0.267104i	$0.0860666\pi$
$90$	−0.172952	+	0.980859i	−0.0182307	+	0.103392i
$91$	1.96363	+	1.64768i	0.205844	+	0.172724i
$92$	−0.768231	−	0.279613i	−0.0800936	−	0.0291517i
$93$	−9.59145	−	3.49100i	−0.994587	−	0.362000i
$94$	1.42096	+	1.19233i	0.146561	+	0.122979i
$95$	−0.218398	+	1.23860i	−0.0224072	+	0.127077i
$96$	−0.245822	+	1.39412i	−0.0250891	+	0.142287i
$97$	0.270746	+	0.468946i	0.0274901	+	0.0476142i	0.879443	−	0.476004i	$-0.157915\pi$
$97$	0.270746	+	0.468946i	0.0274901	+	0.0476142i	−0.851953	+	0.523618i	$0.824582\pi$
$98$	4.69385	−	3.93861i	0.474150	−	0.397859i
$99$	−4.06401	+	1.47918i	−0.408448	+	0.148663i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−3.07797	−	5.33120i	−0.306269	−	0.530474i	0.671274	−	0.741209i	$-0.265747\pi$
$101$	−3.07797	−	5.33120i	−0.306269	−	0.530474i	−0.977543	+	0.210735i	$0.932414\pi$
$102$	7.15995	+	6.00791i	0.708941	+	0.594872i
$103$	−2.68825	+	4.65618i	−0.264881	+	0.458787i	−0.967532	−	0.252747i	$-0.918666\pi$
$103$	−2.68825	+	4.65618i	−0.264881	+	0.458787i	0.702651	+	0.711534i	$0.251999\pi$
$104$	−0.476502	−	2.70237i	−0.0467248	−	0.264990i
$105$	−1.32240			−0.129053
$106$	2.04649	+	11.6062i	0.198773	+	1.12730i
$107$	4.99534	−	4.19159i	0.482918	−	0.405216i	−0.368562	−	0.929603i	$-0.620150\pi$
$107$	4.99534	−	4.19159i	0.482918	−	0.405216i	0.851480	+	0.524387i	$0.175705\pi$
$108$	5.31570	+	1.93476i	0.511503	+	0.186172i
$109$	1.01462	−	0.369291i	0.0971829	−	0.0353717i	−0.292971	−	0.956121i	$-0.594644\pi$
$109$	1.01462	−	0.369291i	0.0971829	−	0.0353717i	0.390154	+	0.920750i	$0.372422\pi$
$110$	−4.34223			−0.414016
$111$	8.02658	−	3.11808i	0.761849	−	0.295955i
$112$	0.934140			0.0882679
$113$	7.55516	−	2.74985i	0.710729	−	0.258684i	0.0387444	−	0.999249i	$-0.487664\pi$
$113$	7.55516	−	2.74985i	0.710729	−	0.258684i	0.671985	+	0.740565i	$0.265442\pi$
$114$	1.67307	+	0.608948i	0.156697	+	0.0570332i
$115$	−0.626268	+	0.525501i	−0.0583998	+	0.0490032i
$116$	0.834610	+	4.73331i	0.0774916	+	0.439477i
$117$	−2.73306			−0.252672
$118$	−1.25951	−	7.14302i	−0.115947	−	0.657569i
$119$	3.08381	−	5.34132i	0.282693	−	0.489638i
$120$	1.08444	+	0.909950i	0.0989950	+	0.0830667i
$121$	−3.92750	−	6.80263i	−0.357046	−	0.618421i
$122$	1.26164	−	2.18522i	0.114223	−	0.197840i
$123$	−12.1691	+	4.42918i	−1.09725	+	0.399366i
$124$	5.52335	−	4.63464i	0.496011	−	0.416203i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	0.161561	−	0.916259i	0.0143930	−	0.0816269i
$127$	2.82523	−	16.0227i	0.250699	−	1.42178i	−0.556178	−	0.831063i	$-0.687733\pi$
$127$	2.82523	−	16.0227i	0.250699	−	1.42178i	0.806877	−	0.590720i	$-0.201156\pi$
$128$	−0.766044	−	0.642788i	−0.0677094	−	0.0568149i
$129$	−10.8442	−	3.94695i	−0.954775	−	0.347510i
$130$	−2.57858	−	0.938525i	−0.226156	−	0.0823141i
$131$	−14.9013	−	12.5037i	−1.30193	−	1.09245i	−0.989808	−	0.142411i	$-0.954515\pi$
$131$	−14.9013	−	12.5037i	−1.30193	−	1.09245i	−0.312125	−	0.950041i	$-0.601041\pi$
$132$	−1.06742	+	6.05361i	−0.0929066	+	0.526899i
$133$	0.204014	−	1.15702i	0.0176903	−	0.100327i
$134$	7.31226	+	12.6652i	0.631683	+	1.09411i
$135$	4.33340	−	3.63615i	0.372959	−	0.312950i
$136$	−6.20429	+	2.25818i	−0.532013	+	0.193637i
$137$	1.37108	−	2.37478i	0.117139	−	0.202891i	−0.801494	−	0.598003i	$-0.795961\pi$
$137$	1.37108	−	2.37478i	0.117139	−	0.202891i	0.918633	+	0.395112i	$0.129294\pi$
$138$	0.578663	+	1.00227i	0.0492591	+	0.0853193i
$139$	−3.29458	−	2.76448i	−0.279442	−	0.234480i	0.492284	−	0.870435i	$-0.336162\pi$
$139$	−3.29458	−	2.76448i	−0.279442	−	0.234480i	−0.771726	+	0.635955i	$0.780607\pi$
$140$	0.467070	−	0.808989i	0.0394746	−	0.0683720i
$141$	−0.455983	−	2.58601i	−0.0384007	−	0.217781i
$142$	7.30613			0.613117
$143$	−2.06908	−	11.7343i	−0.173025	−	0.981275i
$144$	−0.762973	+	0.640210i	−0.0635811	+	0.0533509i
$145$	4.51647	+	1.64386i	0.375073	+	0.136515i
$146$	−15.7043	+	5.71592i	−1.29970	+	0.473053i
$147$	−8.67411			−0.715429
$148$	−0.927466	+	6.01164i	−0.0762372	+	0.494154i
$149$	−0.712087			−0.0583364			−0.0291682	−	0.999575i	$-0.509286\pi$
$149$	−0.712087			−0.0583364			−0.0291682	+	0.999575i	$0.509286\pi$
$150$	1.33026	−	0.484174i	0.108615	−	0.0395327i
$151$	16.9685	+	6.17604i	1.38088	+	0.502599i	0.922445	−	0.386129i	$-0.126188\pi$
$151$	16.9685	+	6.17604i	1.38088	+	0.502599i	0.458435	+	0.888728i	$0.348410\pi$
$152$	−0.963457	+	0.808436i	−0.0781467	+	0.0655729i
$153$	1.14191	+	6.47609i	0.0923179	+	0.523561i
$154$	4.05625			0.326862
$155$	−1.25204	−	7.10068i	−0.100566	−	0.570341i
$156$	−1.94229	+	3.36414i	−0.155508	+	0.269347i
$157$	−10.9281	−	9.16980i	−0.872160	−	0.731829i	0.0923915	−	0.995723i	$-0.470549\pi$
$157$	−10.9281	−	9.16980i	−0.872160	−	0.731829i	−0.964552	+	0.263893i	$0.914993\pi$
$158$	4.09414	+	7.09126i	0.325712	+	0.564150i
$159$	8.34180	−	14.4484i	0.661548	−	1.14583i
$160$	−0.939693	+	0.342020i	−0.0742892	+	0.0270391i
$161$	0.585022	−	0.490891i	0.0461062	−	0.0386877i
$162$	−2.51002	−	4.34747i	−0.197205	−	0.341570i
$163$	−1.71764	+	9.74122i	−0.134536	+	0.762991i	0.840646	+	0.541585i	$0.182176\pi$
$163$	−1.71764	+	9.74122i	−0.134536	+	0.762991i	−0.975182	+	0.221406i	$0.928935\pi$
$164$	1.58852	−	9.00893i	0.124042	−	0.703479i
$165$	4.70887	+	3.95122i	0.366585	+	0.307602i
$166$	2.18283	+	0.794485i	0.169420	+	0.0616640i
$167$	6.81295	+	2.47971i	0.527202	+	0.191886i	0.591888	−	0.806020i	$-0.298383\pi$
$167$	6.81295	+	2.47971i	0.527202	+	0.191886i	−0.0646867	+	0.997906i	$0.520605\pi$
$168$	−1.01301	−	0.850020i	−0.0781558	−	0.0655805i
$169$	−0.949876	+	5.38701i	−0.0730674	+	0.414386i
$170$	−1.14651	+	6.50216i	−0.0879330	+	0.498693i
$171$	0.626331	+	1.08484i	0.0478967	+	0.0829595i
$172$	6.24474	−	5.23996i	0.476157	−	0.399543i
$173$	−6.00865	+	2.18697i	−0.456829	+	0.166272i	−0.560177	−	0.828373i	$-0.689267\pi$
$173$	−6.00865	+	2.18697i	−0.456829	+	0.166272i	0.103348	+	0.994645i	$0.467045\pi$
$174$	3.40199	−	5.89243i	0.257904	−	0.446704i
$175$	−0.467070	−	0.808989i	−0.0353072	−	0.0611538i
$176$	−3.32634	−	2.79113i	−0.250733	−	0.210390i
$177$	−5.13394	+	8.89224i	−0.385890	+	0.668382i
$178$	0.313571	+	1.77835i	0.0235032	+	0.133293i
$179$	6.73046			0.503058			0.251529	−	0.967850i	$-0.419067\pi$
$179$	6.73046			0.503058			0.251529	+	0.967850i	$0.419067\pi$
$180$	0.172952	+	0.980859i	0.0128911	+	0.0731089i
$181$	−6.79676	+	5.70316i	−0.505199	+	0.423913i	−0.859436	−	0.511243i	$-0.829185\pi$
$181$	−6.79676	+	5.70316i	−0.505199	+	0.423913i	0.354237	+	0.935156i	$0.384741\pi$
$182$	2.40875	+	0.876713i	0.178548	+	0.0649863i
$183$	−3.35660	+	1.22170i	−0.248127	+	0.0903109i
$184$	−0.817534			−0.0602694
$185$	4.74250	+	3.80903i	0.348675	+	0.280045i
$186$	−10.2070			−0.748414
$187$	−26.9405	+	9.80553i	−1.97008	+	0.717051i
$188$	1.74307	+	0.634425i	0.127126	+	0.0462702i
$189$	−4.04800	+	3.39667i	−0.294448	+	0.247072i
$190$	0.218398	+	1.23860i	0.0158443	+	0.0898572i
$191$	1.67927			0.121508			0.0607539	−	0.998153i	$-0.480650\pi$
$191$	1.67927			0.121508			0.0607539	+	0.998153i	$0.480650\pi$
$192$	0.245822	+	1.39412i	0.0177406	+	0.100612i
$193$	10.9336	−	18.9375i	0.787016	−	1.36315i	−0.140772	−	0.990042i	$-0.544958\pi$
$193$	10.9336	−	18.9375i	0.787016	−	1.36315i	0.927788	−	0.373109i	$-0.121708\pi$
$194$	0.414807	+	0.348064i	0.0297814	+	0.0249895i
$195$	1.94229	+	3.36414i	0.139090	+	0.240911i
$196$	3.06369	−	5.30647i	0.218835	−	0.379034i
$197$	13.9494	−	5.07716i	0.993852	−	0.361732i	0.206641	−	0.978417i	$-0.433747\pi$
$197$	13.9494	−	5.07716i	0.993852	−	0.361732i	0.787211	+	0.616684i	$0.211525\pi$
$198$	−3.31301	+	2.77994i	−0.235445	+	0.197562i
$199$	5.41946	+	9.38678i	0.384175	+	0.665411i	0.991654	−	0.128924i	$-0.0411524\pi$
$199$	5.41946	+	9.38678i	0.384175	+	0.665411i	−0.607479	+	0.794336i	$0.707819\pi$
$200$	−0.173648	+	0.984808i	−0.0122788	+	0.0696364i
$201$	3.59502	−	20.3884i	0.253573	−	1.43809i
$202$	−4.71572	−	3.95696i	−0.331797	−	0.278411i
$203$	−4.21902	−	1.53560i	−0.296117	−	0.107778i
$204$	8.78298	+	3.19674i	0.614932	+	0.223817i
$205$	−7.00771	−	5.88016i	−0.489439	−	0.410688i
$206$	−0.933619	+	5.29482i	−0.0650483	+	0.368907i
$207$	−0.141394	+	0.801886i	−0.00982757	+	0.0557349i
$208$	−1.37203	−	2.37643i	−0.0951333	−	0.164776i
$209$	−4.18356	+	3.51042i	−0.289383	+	0.242821i
$210$	−1.24265	+	0.452286i	−0.0857507	+	0.0312107i
$211$	−10.1333	+	17.5515i	−0.697608	+	1.20829i	0.271685	+	0.962386i	$0.412419\pi$
$211$	−10.1333	+	17.5515i	−0.697608	+	1.20829i	−0.969293	+	0.245907i	$0.920914\pi$
$212$	5.89264	+	10.2064i	0.404708	+	0.700975i
$213$	−7.92303	−	6.64821i	−0.542877	−	0.455528i
$214$	3.26048	−	5.64731i	0.222882	−	0.386042i
$215$	−1.41557	−	8.02808i	−0.0965409	−	0.547510i
$216$	5.65685			0.384900
$217$	1.16958	+	6.63303i	0.0793964	+	0.450279i
$218$	0.827126	−	0.694041i	0.0560200	−	0.0470064i
$219$	22.2316	+	8.09162i	1.50227	+	0.546781i
$220$	−4.08037	+	1.48513i	−0.275098	+	0.100128i
$221$	−18.1176			−1.21872
$222$	6.47607	−	5.67529i	0.434645	−	0.380901i
$223$	2.19824			0.147205			0.0736026	−	0.997288i	$-0.476550\pi$
$223$	2.19824			0.147205			0.0736026	+	0.997288i	$0.476550\pi$
$224$	0.877804	−	0.319495i	0.0586508	−	0.0213471i
$225$	0.935925	+	0.340649i	0.0623950	+	0.0227099i
$226$	6.15902	−	5.16803i	0.409692	−	0.343772i
$227$	−1.07333	−	6.08717i	−0.0712396	−	0.404020i	−0.999486	−	0.0320543i	$-0.989795\pi$
$227$	−1.07333	−	6.08717i	−0.0712396	−	0.404020i	0.928247	−	0.371966i	$-0.121316\pi$
$228$	1.78044			0.117913
$229$	−0.695349	−	3.94352i	−0.0459499	−	0.260595i	0.953175	−	0.302419i	$-0.0977942\pi$
$229$	−0.695349	−	3.94352i	−0.0459499	−	0.260595i	−0.999125	+	0.0418241i	$0.986683\pi$
$230$	−0.408767	+	0.708006i	−0.0269533	+	0.0466845i
$231$	−4.39875	−	3.69099i	−0.289416	−	0.242849i
$232$	2.40316	+	4.16240i	0.157776	+	0.273275i
$233$	7.58145	−	13.1315i	0.496677	−	0.860270i	−0.503315	−	0.864103i	$-0.667887\pi$
$233$	7.58145	−	13.1315i	0.496677	−	0.860270i	0.999993	+	0.00383255i	$0.00121994\pi$
$234$	−2.56824	+	0.934762i	−0.167891	+	0.0611073i
$235$	1.42096	−	1.19233i	0.0926934	−	0.0777790i
$236$	−3.62661	−	6.28147i	−0.236072	−	0.408889i
$237$	2.01286	−	11.4155i	0.130749	−	0.741515i
$238$	1.07100	−	6.07393i	0.0694224	−	0.393714i
$239$	−10.0277	−	8.41426i	−0.648639	−	0.544273i	0.258018	−	0.966140i	$-0.416931\pi$
$239$	−10.0277	−	8.41426i	−0.648639	−	0.544273i	−0.906658	+	0.421867i	$0.861375\pi$
$240$	1.33026	+	0.484174i	0.0858678	+	0.0312533i
$241$	27.2919	+	9.93345i	1.75803	+	0.639870i	0.999925	−	0.0122651i	$-0.00390422\pi$
$241$	27.2919	+	9.93345i	1.75803	+	0.639870i	0.758103	+	0.652135i	$0.226126\pi$
$242$	−6.01728	−	5.04910i	−0.386805	−	0.324568i
$243$	1.71287	−	9.71417i	0.109881	−	0.623164i
$244$	0.438162	−	2.48494i	0.0280504	−	0.159082i
$245$	−3.06369	−	5.30647i	−0.195732	−	0.339018i
$246$	−9.92032	+	8.32414i	−0.632497	+	0.530728i
$247$	−3.24308	+	1.18039i	−0.206353	+	0.0751062i
$248$	3.60511	−	6.24424i	0.228925	−	0.396509i
$249$	−1.64420	−	2.84783i	−0.104197	−	0.180474i
$250$	0.766044	+	0.642788i	0.0484489	+	0.0406535i
$251$	5.15846	−	8.93472i	0.325599	−	0.563955i	−0.656034	−	0.754731i	$-0.727767\pi$
$251$	5.15846	−	8.93472i	0.325599	−	0.563955i	0.981633	+	0.190777i	$0.0611006\pi$
$252$	−0.161561	−	0.916259i	−0.0101774	−	0.0577189i
$253$	−3.54993			−0.223182
$254$	−2.82523	−	16.0227i	−0.177271	−	1.00535i
$255$	7.15995	−	6.00791i	0.448374	−	0.376230i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−8.71612	+	3.17241i	−0.543696	+	0.197889i	−0.599244	−	0.800567i	$-0.704532\pi$
$257$	−8.71612	+	3.17241i	−0.543696	+	0.197889i	0.0555472	+	0.998456i	$0.482310\pi$
$258$	−11.5401			−0.718456
$259$	−4.43016	−	3.55816i	−0.275277	−	0.221094i
$260$	−2.74406			−0.170180
$261$	4.49836	−	1.63727i	0.278442	−	0.101344i
$262$	−18.2792	−	6.65307i	−1.12929	−	0.411028i
$263$	−14.0062	+	11.7526i	−0.863660	+	0.724697i	−0.962753	−	0.270381i	$-0.912850\pi$
$263$	−14.0062	+	11.7526i	−0.863660	+	0.724697i	0.0990934	+	0.995078i	$0.468406\pi$
$264$	1.06742	+	6.05361i	0.0656949	+	0.372574i
$265$	11.7853			0.723964
$266$	−0.204014	−	1.15702i	−0.0125089	−	0.0709416i
$267$	1.27816	−	2.21384i	0.0782223	−	0.135485i
$268$	11.2030	+	9.40046i	0.684334	+	0.574224i
$269$	1.19940	+	2.07743i	0.0731289	+	0.126663i	0.900271	−	0.435330i	$-0.143368\pi$
$269$	1.19940	+	2.07743i	0.0731289	+	0.126663i	−0.827142	+	0.561993i	$0.810035\pi$
$270$	2.82842	−	4.89897i	0.172132	−	0.298142i
$271$	8.83801	−	3.21677i	0.536871	−	0.195405i	−0.0593328	−	0.998238i	$-0.518897\pi$
$271$	8.83801	−	3.21677i	0.536871	−	0.195405i	0.596204	+	0.802833i	$0.296675\pi$
$272$	−5.05778	+	4.24398i	−0.306673	+	0.257329i
$273$	−1.81437	−	3.14258i	−0.109811	−	0.190198i
$274$	0.476171	−	2.70050i	0.0287666	−	0.163143i
$275$	−0.754021	+	4.27627i	−0.0454692	+	0.257869i
$276$	0.886564	+	0.743915i	0.0533649	+	0.0447784i
$277$	−27.8179	−	10.1249i	−1.67141	−	0.608344i	−0.679319	−	0.733843i	$-0.737725\pi$
$277$	−27.8179	−	10.1249i	−1.67141	−	0.608344i	−0.992094	+	0.125499i	$0.959947\pi$
$278$	−4.04140	−	1.47095i	−0.242387	−	0.0882216i
$279$	−5.50120	−	4.61606i	−0.329348	−	0.276356i
$280$	0.162212	−	0.919948i	0.00969400	−	0.0549774i
$281$	3.38660	−	19.2064i	0.202028	−	1.14575i	−0.700022	−	0.714122i	$-0.746826\pi$
$281$	3.38660	−	19.2064i	0.202028	−	1.14575i	0.902049	−	0.431633i	$-0.142063\pi$
$282$	−1.31295	−	2.27410i	−0.0781851	−	0.135421i
$283$	−7.39085	+	6.20166i	−0.439340	+	0.368650i	−0.835462	−	0.549548i	$-0.814800\pi$
$283$	−7.39085	+	6.20166i	−0.439340	+	0.368650i	0.396122	+	0.918198i	$0.370356\pi$
$284$	6.86552	−	2.49884i	0.407393	−	0.148279i
$285$	0.890222	−	1.54191i	0.0527322	−	0.0913348i
$286$	−5.95768	−	10.3190i	−0.352285	−	0.610176i
$287$	6.54618	+	5.49289i	0.386409	+	0.324235i
$288$	−0.497995	+	0.862553i	−0.0293447	+	0.0508264i
$289$	4.61775	+	26.1886i	0.271632	+	1.54050i
$290$	4.80633			0.282237
$291$	−0.133110	−	0.754906i	−0.00780307	−	0.0442534i
$292$	−12.8023	+	10.7424i	−0.749198	+	0.628652i
$293$	23.1103	+	8.41147i	1.35012	+	0.491403i	0.912985	−	0.407993i	$-0.133771\pi$
$293$	23.1103	+	8.41147i	1.35012	+	0.491403i	0.437135	+	0.899396i	$0.355993\pi$
$294$	−8.15100	+	2.96672i	−0.475376	+	0.173023i
$295$	−7.25322			−0.422299
$296$	1.18457	+	5.96631i	0.0688517	+	0.346784i
$297$	24.5634			1.42531
$298$	−0.669143	+	0.243548i	−0.0387624	+	0.0141084i
$299$	−2.10807	−	0.767276i	−0.121913	−	0.0443727i
$300$	1.08444	−	0.909950i	0.0626099	−	0.0525360i
$301$	1.32234	+	7.49935i	0.0762183	+	0.432255i
$302$	18.0575			1.03909
$303$	1.51326	+	8.58214i	0.0869347	+	0.493031i
$304$	−0.628852	+	1.08920i	−0.0360671	+	0.0624701i
$305$	−1.93294	−	1.62193i	−0.110680	−	0.0928714i
$306$	3.28800	+	5.69498i	0.187962	+	0.325560i
$307$	−2.59232	+	4.49002i	−0.147951	+	0.256259i	−0.930470	−	0.366368i	$-0.880601\pi$
$307$	−2.59232	+	4.49002i	−0.147951	+	0.256259i	0.782519	+	0.622627i	$0.213935\pi$
$308$	3.81163	−	1.38732i	0.217188	−	0.0790499i
$309$	5.83047	−	4.89234i	0.331684	−	0.278316i
$310$	−3.60511	−	6.24424i	−0.204757	−	0.354649i
$311$	−3.03298	+	17.2009i	−0.171985	+	0.975373i	0.769583	+	0.638547i	$0.220464\pi$
$311$	−3.03298	+	17.2009i	−0.171985	+	0.975373i	−0.941567	+	0.336825i	$0.890647\pi$
$312$	−0.674550	+	3.82556i	−0.0381889	+	0.216580i
$313$	6.05698	+	5.08241i	0.342360	+	0.287275i	0.797714	−	0.603036i	$-0.206043\pi$
$313$	6.05698	+	5.08241i	0.342360	+	0.287275i	−0.455353	+	0.890311i	$0.650487\pi$
$314$	−13.4053	−	4.87915i	−0.756507	−	0.275346i
$315$	−0.874285	−	0.318214i	−0.0492604	−	0.0179293i
$316$	6.27259	+	5.26332i	0.352861	+	0.296085i
$317$	0.622260	−	3.52901i	0.0349496	−	0.198209i	−0.962334	−	0.271871i	$-0.912358\pi$
$317$	0.622260	−	3.52901i	0.0349496	−	0.198209i	0.997283	+	0.0736622i	$0.0234687\pi$
$318$	2.89708	−	16.4301i	0.162460	−	0.921357i
$319$	10.4351	+	18.0741i	0.584254	+	1.01196i
$320$	−0.766044	+	0.642788i	−0.0428232	+	0.0359329i
$321$	−8.67455	+	3.15728i	−0.484166	+	0.176222i
$322$	0.381846	−	0.661376i	0.0212794	−	0.0368570i
$323$	4.15197	+	7.19143i	0.231022	+	0.400142i
$324$	−3.84557	−	3.22681i	−0.213643	−	0.179267i
$325$	−1.37203	+	2.37643i	−0.0761066	+	0.131821i
$326$	1.71764	+	9.74122i	0.0951313	+	0.539516i
$327$	−1.52851			−0.0845266
$328$	−1.58852	−	9.00893i	−0.0877112	−	0.497435i
$329$	−1.32738	+	1.11380i	−0.0731807	+	0.0614059i
$330$	5.77629	+	2.10240i	0.317974	+	0.115733i
$331$	−23.9357	+	8.71187i	−1.31562	+	0.478848i	−0.902053	−	0.431625i	$-0.857941\pi$
$331$	−23.9357	+	8.71187i	−1.31562	+	0.478848i	−0.413570	+	0.910472i	$0.635718\pi$
$332$	2.32292			0.127487
$333$	6.05698	−	0.130011i	0.331920	−	0.00712458i
$334$	7.25019			0.396713
$335$	13.7426	−	5.00188i	0.750836	−	0.273282i
$336$	−1.24265	−	0.452286i	−0.0677919	−	0.0246742i
$337$	−21.8562	+	18.3395i	−1.19058	+	0.999017i	−0.190733	+	0.981642i	$0.561087\pi$
$337$	−21.8562	+	18.3395i	−1.19058	+	0.999017i	−0.999849	+	0.0173753i	$0.994469\pi$
$338$	0.949876	+	5.38701i	0.0516664	+	0.293015i
$339$	−11.3817			−0.618170
$340$	1.14651	+	6.50216i	0.0621780	+	0.352629i
$341$	15.6542	−	27.1139i	0.847724	−	1.46830i
$342$	0.959594	+	0.805195i	0.0518889	+	0.0435400i
$343$	6.13140	+	10.6199i	0.331065	+	0.573421i
$344$	4.07596	−	7.05977i	0.219761	−	0.380638i
$345$	1.08753	−	0.395829i	0.0585507	−	0.0213107i
$346$	−4.89830	+	4.11016i	−0.263334	+	0.220963i
$347$	14.1867	+	24.5721i	0.761582	+	1.31910i	0.942035	+	0.335515i	$0.108910\pi$
$347$	14.1867	+	24.5721i	0.761582	+	1.31910i	−0.180453	+	0.983584i	$0.557756\pi$
$348$	1.18150	−	6.70062i	0.0633350	−	0.359191i
$349$	−5.47527	+	31.0518i	−0.293085	+	1.66217i	0.381802	+	0.924244i	$0.375304\pi$
$349$	−5.47527	+	31.0518i	−0.293085	+	1.66217i	−0.674887	+	0.737921i	$0.735807\pi$
$350$	−0.715592	−	0.600453i	−0.0382500	−	0.0320956i
$351$	14.5866	+	5.30909i	0.778575	+	0.283378i
$352$	−4.08037	−	1.48513i	−0.217484	−	0.0791578i
$353$	0.428980	+	0.359957i	0.0228323	+	0.0191586i	0.654132	−	0.756380i	$-0.273034\pi$
$353$	0.428980	+	0.359957i	0.0228323	+	0.0191586i	−0.631300	+	0.775539i	$0.717478\pi$
$354$	−1.78300	+	10.1119i	−0.0947653	+	0.537440i
$355$	1.26870	−	7.19513i	0.0673354	−	0.381878i
$356$	0.902893	+	1.56386i	0.0478532	+	0.0828842i
$357$	−6.68839	+	5.61223i	−0.353987	+	0.297031i
$358$	6.32456	−	2.30195i	0.334263	−	0.121662i
$359$	11.5961	−	20.0850i	0.612018	−	1.06005i	−0.378882	−	0.925445i	$-0.623691\pi$
$359$	11.5961	−	20.0850i	0.612018	−	1.06005i	0.990900	−	0.134601i	$-0.0429752\pi$
$360$	0.497995	+	0.862553i	0.0262467	+	0.0454605i
$361$	−13.3431	−	11.1962i	−0.702268	−	0.589273i
$362$	−4.43627	+	7.68385i	−0.233165	+	0.403854i
$363$	1.93093	+	10.9508i	0.101348	+	0.574770i
$364$	2.56334			0.134355
$365$	2.90205	+	16.4583i	0.151900	+	0.861468i
$366$	−2.73633	+	2.29605i	−0.143030	+	0.120017i
$367$	8.27220	+	3.01084i	0.431805	+	0.157164i	0.548773	−	0.835971i	$-0.315095\pi$
$367$	8.27220	+	3.01084i	0.431805	+	0.157164i	−0.116968	+	0.993136i	$0.537317\pi$
$368$	−0.768231	+	0.279613i	−0.0400468	+	0.0145758i
$369$	−9.11123			−0.474312
$370$	5.75926	+	1.95729i	0.299409	+	0.101754i
$371$	−11.0091			−0.571564
$372$	−9.59145	+	3.49100i	−0.497294	+	0.181000i
$373$	19.7487	+	7.18793i	1.02255	+	0.372177i	0.798239	−	0.602341i	$-0.205765\pi$
$373$	19.7487	+	7.18793i	1.02255	+	0.372177i	0.224309	+	0.974518i	$0.427988\pi$
$374$	−21.9621	+	18.4284i	−1.13563	+	0.952908i
$375$	−0.245822	−	1.39412i	−0.0126942	−	0.0719922i
$376$	1.85494			0.0956610
$377$	2.29022	+	12.9885i	0.117953	+	0.668942i
$378$	−2.64214	+	4.57632i	−0.135897	+	0.235381i
$379$	9.91429	+	8.31908i	0.509263	+	0.427322i	0.860870	−	0.508825i	$-0.169920\pi$
$379$	9.91429	+	8.31908i	0.509263	+	0.427322i	−0.351607	+	0.936148i	$0.614365\pi$
$380$	0.628852	+	1.08920i	0.0322594	+	0.0558750i
$381$	−11.5161	+	19.9464i	−0.589985	+	1.02188i
$382$	1.57800	−	0.574345i	0.0807374	−	0.0293860i
$383$	29.2415	−	24.5365i	1.49417	−	1.25376i	0.604965	−	0.796252i	$-0.293187\pi$
$383$	29.2415	−	24.5365i	1.49417	−	1.25376i	0.889206	−	0.457507i	$-0.151257\pi$
$384$	0.707815	+	1.22597i	0.0361205	+	0.0625626i
$385$	0.704361	−	3.99463i	0.0358976	−	0.203585i
$386$	3.79719	−	21.5349i	0.193272	−	1.09610i
$387$	−6.21970	−	5.21895i	−0.316165	−	0.265294i
$388$	0.508836	+	0.185201i	0.0258322	+	0.00940216i
$389$	4.34394	+	1.58106i	0.220246	+	0.0801631i	0.449787	−	0.893136i	$-0.351500\pi$
$389$	4.34394	+	1.58106i	0.220246	+	0.0801631i	−0.229540	+	0.973299i	$0.573722\pi$
$390$	2.97576	+	2.49696i	0.150683	+	0.126438i
$391$	−0.937308	+	5.31574i	−0.0474017	+	0.268829i
$392$	1.06401	−	6.03429i	0.0537406	−	0.304778i
$393$	13.7686	+	23.8479i	0.694535	+	1.20297i
$394$	11.3716	−	9.54193i	0.572895	−	0.480716i
$395$	7.69447	−	2.80056i	0.387151	−	0.140911i
$396$	−2.16241	+	3.74541i	−0.108665	+	0.188214i
$397$	−5.90355	−	10.2253i	−0.296291	−	0.513191i	0.678994	−	0.734144i	$-0.262416\pi$
$397$	−5.90355	−	10.2253i	−0.296291	−	0.513191i	−0.975284	+	0.220954i	$0.929083\pi$
$398$	8.30310	+	6.96713i	0.416197	+	0.349230i
$399$	−0.831592	+	1.44036i	−0.0416317	+	0.0721081i
$400$	0.173648	+	0.984808i	0.00868241	+	0.0492404i
$401$	−16.0771			−0.802851			−0.401425	−	0.915892i	$-0.631485\pi$
$401$	−16.0771			−0.802851			−0.401425	+	0.915892i	$0.631485\pi$
$402$	−3.59502	−	20.3884i	−0.179303	−	1.01688i
$403$	15.1564	−	12.7177i	0.754995	−	0.633516i
$404$	−5.78469	−	2.10545i	−0.287799	−	0.104750i
$405$	−4.71729	+	1.71695i	−0.234404	+	0.0853160i
$406$	−4.48978			−0.222824
$407$	5.14368	+	25.9071i	0.254963	+	1.28417i
$408$	9.34665			0.462728
$409$	−33.5851	+	12.2240i	−1.66068	+	0.604437i	−0.990469	−	0.137737i	$-0.956017\pi$
$409$	−33.5851	+	12.2240i	−1.66068	+	0.604437i	−0.670208	+	0.742174i	$0.733795\pi$
$410$	−8.59622	−	3.12877i	−0.424537	−	0.154519i
$411$	−2.97370	+	2.49523i	−0.146682	+	0.123081i
$412$	0.933619	+	5.29482i	0.0459961	+	0.260857i
$413$	6.77552			0.333401
$414$	0.141394	+	0.801886i	0.00694914	+	0.0394106i
$415$	1.16146	−	2.01171i	0.0570138	−	0.0987508i
$416$	−2.10207	−	1.76385i	−0.103063	−	0.0864799i
$417$	3.04415	+	5.27261i	0.149072	+	0.258201i
$418$	−2.73062	+	4.72958i	−0.133559	+	0.231331i
$419$	−35.2286	+	12.8222i	−1.72103	+	0.626404i	−0.997928	−	0.0643367i	$-0.979507\pi$
$419$	−35.2286	+	12.8222i	−1.72103	+	0.626404i	−0.723103	+	0.690741i	$0.757285\pi$
$420$	−1.01301	+	0.850020i	−0.0494300	+	0.0414767i
$421$	16.3331	+	28.2898i	0.796028	+	1.37876i	0.922184	+	0.386751i	$0.126403\pi$
$421$	16.3331	+	28.2898i	0.796028	+	1.37876i	−0.126156	+	0.992010i	$0.540264\pi$
$422$	−3.51927	+	19.9588i	−0.171316	+	0.971579i
$423$	0.320815	−	1.81943i	0.0155985	−	0.0884638i
$424$	9.02805	+	7.57543i	0.438441	+	0.367896i
$425$	6.20429	+	2.25818i	0.300952	+	0.109538i
$426$	−9.71903	−	3.53744i	−0.470889	−	0.171389i
$427$	1.80564	+	1.51511i	0.0873808	+	0.0733212i
$428$	1.13235	−	6.42188i	0.0547343	−	0.310413i
$429$	−2.92906	+	16.6115i	−0.141416	+	0.802011i
$430$	−4.07596	−	7.05977i	−0.196560	−	0.340453i
$431$	−26.7263	+	22.4260i	−1.28736	+	1.08022i	−0.295177	+	0.955443i	$0.595379\pi$
$431$	−26.7263	+	22.4260i	−1.28736	+	1.08022i	−0.992184	+	0.124782i	$0.960177\pi$
$432$	5.31570	−	1.93476i	0.255752	−	0.0930860i
$433$	3.99134	−	6.91320i	0.191812	−	0.332227i	−0.754039	−	0.656830i	$-0.771897\pi$
$433$	3.99134	−	6.91320i	0.191812	−	0.332227i	0.945851	+	0.324602i	$0.105230\pi$
$434$	3.36768	+	5.83299i	0.161654	+	0.279992i
$435$	−5.21216	−	4.37352i	−0.249904	−	0.209694i
$436$	0.539868	−	0.935079i	0.0258550	−	0.0447821i
$437$	0.178548	+	1.01260i	0.00854110	+	0.0484390i
$438$	23.6583			1.13044
$439$	−5.97499	−	33.8859i	−0.285171	−	1.61728i	−0.704675	−	0.709530i	$-0.748907\pi$
$439$	−5.97499	−	33.8859i	−0.285171	−	1.61728i	0.419504	−	0.907753i	$-0.362204\pi$
$440$	−3.32634	+	2.79113i	−0.158577	+	0.133062i
$441$	−5.73477	−	2.08729i	−0.273084	−	0.0993946i
$442$	−17.0250	+	6.19658i	−0.809795	+	0.294741i
$443$	−18.1687			−0.863219			−0.431609	−	0.902061i	$-0.642054\pi$
$443$	−18.1687			−0.863219			−0.431609	+	0.902061i	$0.642054\pi$
$444$	4.14445	−	7.54797i	0.196687	−	0.358211i
$445$	1.80579			0.0856024
$446$	2.06567	−	0.751843i	0.0978124	−	0.0356008i
$447$	0.947259	+	0.344774i	0.0448038	+	0.0163073i
$448$	0.715592	−	0.600453i	0.0338086	−	0.0283688i
$449$	1.61580	+	9.16367i	0.0762544	+	0.432460i	0.998903	+	0.0468194i	$0.0149085\pi$
$449$	1.61580	+	9.16367i	0.0762544	+	0.432460i	−0.922649	+	0.385641i	$0.873980\pi$
$450$	0.995990			0.0469514
$451$	−6.89772	−	39.1189i	−0.324801	−	1.84204i
$452$	4.02001	−	6.96287i	0.189086	−	0.327506i
$453$	−19.5822	−	16.4315i	−0.920054	−	0.772017i
$454$	−3.09054	−	5.35297i	−0.145046	−	0.251227i
$455$	1.28167	−	2.21992i	0.0600856	−	0.104071i
$456$	1.67307	−	0.608948i	0.0783487	−	0.0285166i
$457$	30.5691	−	25.6506i	1.42996	−	1.19988i	0.484230	−	0.874941i	$-0.339100\pi$
$457$	30.5691	−	25.6506i	1.42996	−	1.19988i	0.945734	−	0.324941i	$-0.105345\pi$
$458$	−2.00218	−	3.46787i	−0.0935556	−	0.162043i
$459$	6.48561	−	36.7817i	0.302722	−	1.71682i
$460$	−0.141963	+	0.805114i	−0.00661908	+	0.0375386i
$461$	16.8996	+	14.1805i	0.787095	+	0.660451i	0.945025	−	0.326999i	$-0.106038\pi$
$461$	16.8996	+	14.1805i	0.787095	+	0.660451i	−0.157930	+	0.987450i	$0.550482\pi$
$462$	−5.39586	−	1.96393i	−0.251038	−	0.0913704i
$463$	1.37972	+	0.502176i	0.0641209	+	0.0233381i	0.373881	−	0.927476i	$-0.378027\pi$
$463$	1.37972	+	0.502176i	0.0641209	+	0.0233381i	−0.309761	+	0.950815i	$0.600249\pi$
$464$	3.68186	+	3.08945i	0.170926	+	0.143424i
$465$	−1.77243	+	10.0519i	−0.0821944	+	0.466148i
$466$	2.63301	−	14.9325i	0.121972	−	0.691737i
$467$	−1.44158	−	2.49689i	−0.0667084	−	0.115542i	0.830742	−	0.556657i	$-0.187916\pi$
$467$	−1.44158	−	2.49689i	−0.0667084	−	0.115542i	−0.897451	+	0.441115i	$0.854583\pi$
$468$	−2.09365	+	1.75678i	−0.0967788	+	0.0812071i
$469$	−12.8375	+	4.67245i	−0.592779	+	0.215754i
$470$	0.927468	−	1.60642i	0.0427809	−	0.0740987i
$471$	10.0975	+	17.4893i	0.465266	+	0.805865i
$472$	−5.55629	−	4.66228i	−0.255749	−	0.214599i
$473$	17.6988	−	30.6552i	0.813791	−	1.40953i
$474$	−2.01286	−	11.4155i	−0.0924536	−	0.524330i
$475$	1.25770			0.0577074
$476$	−1.07100	−	6.07393i	−0.0490891	−	0.278398i
$477$	8.99185	−	7.54506i	0.411709	−	0.345465i
$478$	−12.3008	−	4.47713i	−0.562627	−	0.204779i
$479$	−3.22775	+	1.17481i	−0.147480	+	0.0536783i	−0.414705	−	0.909956i	$-0.636115\pi$
$479$	−3.22775	+	1.17481i	−0.147480	+	0.0536783i	0.267226	+	0.963634i	$0.413893\pi$
$480$	1.41563			0.0646144
$481$	−2.54502	+	16.4963i	−0.116043	+	0.752167i
$482$	29.0435			1.32289
$483$	−1.01591	+	0.369760i	−0.0462253	+	0.0168246i
$484$	−7.38129	−	2.68657i	−0.335513	−	0.122117i
$485$	0.414807	−	0.348064i	0.0188354	−	0.0158048i
$486$	−1.71287	−	9.71417i	−0.0776974	−	0.440644i
$487$	−23.2413			−1.05317			−0.526583	−	0.850124i	$-0.676527\pi$
$487$	−23.2413			−1.05317			−0.526583	+	0.850124i	$0.676527\pi$
$488$	−0.438162	−	2.48494i	−0.0198347	−	0.112488i
$489$	7.00135	−	12.1267i	0.316612	−	0.548388i
$490$	−4.69385	−	3.93861i	−0.212046	−	0.177928i
$491$	10.3759	+	17.9715i	0.468257	+	0.811044i	0.999342	−	0.0362740i	$-0.0115489\pi$
$491$	10.3759	+	17.9715i	0.468257	+	0.811044i	−0.531085	+	0.847318i	$0.678216\pi$
$492$	−6.47503	+	11.2151i	−0.291917	+	0.505615i
$493$	29.8199	−	10.8535i	1.34302	−	0.488819i
$494$	−2.64379	+	2.21840i	−0.118950	+	0.0998106i
$495$	2.16241	+	3.74541i	0.0971932	+	0.168344i
$496$	1.25204	−	7.10068i	0.0562183	−	0.318830i
$497$	−1.18514	+	6.72126i	−0.0531608	+	0.301490i
$498$	−2.51906	−	2.11374i	−0.112882	−	0.0947189i
$499$	1.53952	+	0.560339i	0.0689183	+	0.0250842i	0.376249	−	0.926518i	$-0.377214\pi$
$499$	1.53952	+	0.560339i	0.0689183	+	0.0250842i	−0.307331	+	0.951603i	$0.599436\pi$
$500$	0.939693	+	0.342020i	0.0420243	+	0.0152956i
$501$	−7.86236	−	6.59731i	−0.351265	−	0.294746i
$502$	1.79152	−	10.1602i	0.0799593	−	0.453472i
$503$	2.17209	−	12.3185i	0.0968485	−	0.549255i	−0.897317	−	0.441387i	$-0.854487\pi$
$503$	2.17209	−	12.3185i	0.0968485	−	0.549255i	0.994165	−	0.107868i	$-0.0344024\pi$
$504$	−0.465197	−	0.805745i	−0.0207215	−	0.0358907i
$505$	−4.71572	+	3.95696i	−0.209847	+	0.176082i
$506$	−3.33584	+	1.21415i	−0.148296	+	0.0539754i
$507$	3.87183	−	6.70621i	0.171954	−	0.297833i
$508$	−8.13493	−	14.0901i	−0.360929	−	0.625148i
$509$	9.10061	+	7.63632i	0.403378	+	0.338474i	0.821797	−	0.569780i	$-0.192971\pi$
$509$	9.10061	+	7.63632i	0.403378	+	0.338474i	−0.418420	+	0.908254i	$0.637416\pi$
$510$	4.67333	−	8.09444i	0.206938	−	0.358428i
$511$	−2.71092	−	15.3744i	−0.119924	−	0.680122i
$512$	−1.00000			−0.0441942
$513$	−1.23544	−	7.00655i	−0.0545462	−	0.309347i
$514$	−7.10544	+	5.96217i	−0.313408	+	0.262980i
$515$	5.05225	+	1.83887i	0.222629	+	0.0810303i
$516$	−10.8442	+	3.94695i	−0.477388	+	0.173755i
$517$	8.05457			0.354239
$518$	−5.37995	−	1.82838i	−0.236381	−	0.0803343i
$519$	9.05192			0.397335
$520$	−2.57858	+	0.938525i	−0.113078	+	0.0411570i
$521$	−38.3686	−	13.9650i	−1.68096	−	0.611818i	−0.687517	−	0.726168i	$-0.741299\pi$
$521$	−38.3686	−	13.9650i	−1.68096	−	0.611818i	−0.993441	+	0.114350i	$0.963521\pi$
$522$	3.66710	−	3.07706i	0.160505	−	0.134679i
$523$	1.13655	+	6.44569i	0.0496978	+	0.281850i	0.999521	−	0.0309359i	$-0.00984878\pi$
$523$	1.13655	+	6.44569i	0.0496978	+	0.281850i	−0.949824	+	0.312786i	$0.898738\pi$
$524$	−19.4523			−0.849776
$525$	0.229632	+	1.30231i	0.0100220	+	0.0568373i
$526$	−9.14190	+	15.8342i	−0.398606	+	0.690406i
$527$	−36.4677	−	30.6001i	−1.58856	−	1.33296i
$528$	3.07350	+	5.32346i	0.133757	+	0.231674i
$529$	11.1658	−	19.3398i	0.485470	−	0.840859i
$530$	11.0745	−	4.03080i	0.481047	−	0.175087i
$531$	−5.53401	+	4.64358i	−0.240156	+	0.201514i
$532$	−0.587436	−	1.01747i	−0.0254686	−	0.0441128i
$533$	4.35899	−	24.7211i	0.188809	−	1.07079i
$534$	0.443901	−	2.51749i	0.0192095	−	0.108942i
$535$	−4.99534	−	4.19159i	−0.215967	−	0.181218i
$536$	13.7426	+	5.00188i	0.593588	+	0.216048i
$537$	−8.95324	−	3.25871i	−0.386361	−	0.140624i
$538$	1.83759	+	1.54192i	0.0792242	+	0.0664770i
$539$	4.62018	−	26.2023i	0.199005	−	1.12861i
$540$	0.982301	−	5.57091i	0.0422715	−	0.239734i
$541$	−0.469544	−	0.813275i	−0.0201873	−	0.0349654i	0.855755	−	0.517381i	$-0.173093\pi$
$541$	−0.469544	−	0.813275i	−0.0201873	−	0.0349654i	−0.875943	+	0.482415i	$0.839760\pi$
$542$	7.20481	−	6.04555i	0.309473	−	0.259679i
$543$	11.8028	−	4.29586i	0.506505	−	0.184353i
$544$	−3.30123	+	5.71790i	−0.141539	+	0.245153i
$545$	−0.539868	−	0.935079i	−0.0231254	−	0.0400544i
$546$	−2.77978	−	2.33251i	−0.118963	−	0.0998222i
$547$	−10.6852	+	18.5073i	−0.456866	+	0.791315i	−0.998793	−	0.0491103i	$-0.984361\pi$
$547$	−10.6852	+	18.5073i	−0.456866	+	0.791315i	0.541927	+	0.840425i	$0.317695\pi$
$548$	−0.476171	−	2.70050i	−0.0203410	−	0.115360i
$549$	−2.51316			−0.107259
$550$	0.754021	+	4.27627i	0.0321516	+	0.182341i
$551$	4.63069	−	3.88561i	0.197274	−	0.165533i
$552$	1.08753	+	0.395829i	0.0462884	+	0.0168476i
$553$	−7.18771	+	2.61611i	−0.305652	+	0.111248i
$554$	−29.6031			−1.25772
$555$	−4.46451	−	7.36318i	−0.189508	−	0.312550i
$556$	−4.30076			−0.182393
$557$	15.1896	−	5.52855i	0.643603	−	0.234252i	0.000461495	−	1.00000i	$-0.499853\pi$
$557$	15.1896	−	5.52855i	0.643603	−	0.234252i	0.643141	+	0.765748i	$0.277631\pi$
$558$	−6.74823	−	2.45615i	−0.285675	−	0.103977i
$559$	17.1360	−	14.3788i	0.724774	−	0.608157i
$560$	−0.162212	−	0.919948i	−0.00685469	−	0.0388749i
$561$	40.5854			1.71352
$562$	−3.38660	−	19.2064i	−0.142855	−	0.810171i
$563$	−10.4915	+	18.1718i	−0.442164	+	0.765851i	−0.997850	−	0.0655417i	$-0.979122\pi$
$563$	−10.4915	+	18.1718i	−0.442164	+	0.765851i	0.555686	+	0.831392i	$0.312456\pi$
$564$	−2.01156	−	1.68790i	−0.0847019	−	0.0710733i
$565$	−4.02001	−	6.96287i	−0.169123	−	0.292930i
$566$	−4.82403	+	8.35547i	−0.202769	+	0.351207i
$567$	4.40660	−	1.60387i	0.185060	−	0.0673563i
$568$	5.59682	−	4.69629i	0.234837	−	0.197052i
$569$	3.26644	+	5.65763i	0.136936	+	0.237180i	0.926335	−	0.376700i	$-0.122941\pi$
$569$	3.26644	+	5.65763i	0.136936	+	0.237180i	−0.789399	+	0.613880i	$0.789608\pi$
$570$	0.309171	−	1.75339i	0.0129497	−	0.0734416i
$571$	−3.56452	+	20.2154i	−0.149171	+	0.845989i	0.814753	+	0.579809i	$0.196873\pi$
$571$	−3.56452	+	20.2154i	−0.149171	+	0.845989i	−0.963923	+	0.266180i	$0.914238\pi$
$572$	−9.12770	−	7.65905i	−0.381648	−	0.320241i
$573$	−2.23386	−	0.813060i	−0.0933210	−	0.0339661i
$574$	8.03007	+	2.92271i	0.335169	+	0.121991i
$575$	0.626268	+	0.525501i	0.0261172	+	0.0219149i
$576$	−0.172952	+	0.980859i	−0.00720633	+	0.0408691i
$577$	0.707232	−	4.01091i	0.0294424	−	0.166976i	−0.966541	−	0.256511i	$-0.917427\pi$
$577$	0.707232	−	4.01091i	0.0294424	−	0.166976i	0.995984	+	0.0895348i	$0.0285380\pi$
$578$	13.2963	+	23.0298i	0.553052	+	0.957915i
$579$	−23.7135	+	19.8980i	−0.985500	+	0.826933i
$580$	4.51647	−	1.64386i	0.187536	−	0.0682576i
$581$	−1.08496	+	1.87921i	−0.0450119	+	0.0779629i
$582$	−0.383276	−	0.663854i	−0.0158873	−	0.0275176i
$583$	39.2019	+	32.8943i	1.62358	+	1.36234i
$584$	−8.35611	+	14.4732i	−0.345778	+	0.598906i
$585$	0.474591	+	2.69154i	0.0196219	+	0.111281i
$586$	24.5935			1.01595
$587$	−0.445995	−	2.52936i	−0.0184082	−	0.104398i	0.974219	−	0.225603i	$-0.0724353\pi$
$587$	−0.445995	−	2.52936i	−0.0184082	−	0.104398i	−0.992627	+	0.121205i	$0.961324\pi$
$588$	−6.64475	+	5.57561i	−0.274025	+	0.229934i
$589$	−8.52144	−	3.10155i	−0.351120	−	0.127797i
$590$	−6.81579	+	2.48075i	−0.280602	+	0.102131i
$591$	−21.0145			−0.864420
$592$	3.15373	+	5.20135i	0.129617	+	0.213774i
$593$	−27.8349			−1.14304			−0.571521	−	0.820587i	$-0.693647\pi$
$593$	−27.8349			−1.14304			−0.571521	+	0.820587i	$0.693647\pi$
$594$	23.0820	−	8.40116i	0.947066	−	0.344704i
$595$	−5.79567	−	2.10945i	−0.237599	−	0.0864791i
$596$	−0.545490	+	0.457721i	−0.0223441	+	0.0187490i
$597$	−2.66444	−	15.1108i	−0.109048	−	0.618444i
$598$	−2.24337			−0.0917381
$599$	−5.80728	−	32.9347i	−0.237279	−	1.34568i	−0.837761	−	0.546038i	$-0.816135\pi$
$599$	−5.80728	−	32.9347i	−0.237279	−	1.34568i	0.600481	−	0.799639i	$-0.294976\pi$
$600$	0.707815	−	1.22597i	0.0288964	−	0.0500501i
$601$	−5.54170	−	4.65004i	−0.226051	−	0.189679i	0.522727	−	0.852500i	$-0.324915\pi$
$601$	−5.54170	−	4.65004i	−0.226051	−	0.189679i	−0.748778	+	0.662821i	$0.769359\pi$
$602$	3.80752	+	6.59482i	0.155183	+	0.268785i
$603$	7.28294	−	12.6144i	0.296584	−	0.513699i
$604$	16.9685	−	6.17604i	0.690440	−	0.251300i
$605$	−6.01728	+	5.04910i	−0.244637	+	0.205275i
$606$	4.35727	+	7.54701i	0.177002	+	0.306576i
$607$	4.72568	−	26.8006i	0.191809	−	1.08780i	−0.725081	−	0.688664i	$-0.758198\pi$
$607$	4.72568	−	26.8006i	0.191809	−	1.08780i	0.916890	−	0.399140i	$-0.130691\pi$
$608$	−0.218398	+	1.23860i	−0.00885721	+	0.0502317i
$609$	4.86888	+	4.08548i	0.197297	+	0.165552i
$610$	−2.37110	−	0.863010i	−0.0960031	−	0.0349423i
$611$	4.78309	+	1.74090i	0.193503	+	0.0704294i
$612$	5.03750	+	4.22697i	0.203629	+	0.170865i
$613$	2.04991	−	11.6256i	0.0827952	−	0.469555i	−0.915015	−	0.403419i	$-0.867822\pi$
$613$	2.04991	−	11.6256i	0.0827952	−	0.469555i	0.997811	−	0.0661359i	$-0.0210671\pi$
$614$	−0.900302	+	5.10586i	−0.0363332	+	0.206056i
$615$	6.47503	+	11.2151i	0.261098	+	0.452236i
$616$	3.10727	−	2.60731i	0.125195	−	0.105051i
$617$	14.0014	−	5.09608i	0.563674	−	0.205160i	−0.0444377	−	0.999012i	$-0.514150\pi$
$617$	14.0014	−	5.09608i	0.563674	−	0.205160i	0.608111	+	0.793852i	$0.291927\pi$
$618$	3.80557	−	6.59143i	0.153082	−	0.265146i
$619$	−19.7604	−	34.2260i	−0.794238	−	1.37566i	−0.923322	−	0.384027i	$-0.874537\pi$
$619$	−19.7604	−	34.2260i	−0.794238	−	1.37566i	0.129084	−	0.991634i	$-0.458796\pi$
$620$	−5.52335	−	4.63464i	−0.221823	−	0.186132i
$621$	2.31233	−	4.00508i	0.0927907	−	0.160718i
$622$	3.03298	+	17.2009i	0.121611	+	0.689693i
$623$	−1.68686			−0.0675825
$624$	0.674550	+	3.82556i	0.0270036	+	0.153145i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	7.42998	+	2.70429i	0.296962	+	0.108085i
$627$	7.26486	−	2.64419i	0.290131	−	0.105599i
$628$	−14.2657			−0.569262
$629$	40.1520	−	0.861851i	1.60096	−	0.0343643i
$630$	−0.930394			−0.0370678
$631$	1.30868	−	0.476319i	0.0520975	−	0.0189620i	−0.315840	−	0.948812i	$-0.602286\pi$
$631$	1.30868	−	0.476319i	0.0520975	−	0.0189620i	0.367937	+	0.929851i	$0.380064\pi$
$632$	7.69447	+	2.80056i	0.306069	+	0.111400i
$633$	21.9779	−	18.4417i	0.873544	−	0.732991i
$634$	−0.622260	−	3.52901i	−0.0247131	−	0.140155i
$635$	−16.2699			−0.645650
$636$	−2.89708	−	16.4301i	−0.114877	−	0.651497i
$637$	8.40696	−	14.5613i	0.333096	−	0.576939i
$638$	15.9875	+	13.4151i	0.632952	+	0.531109i
$639$	−3.63842	−	6.30192i	−0.143934	−	0.249300i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−27.1086	+	9.86674i	−1.07073	+	0.389713i	−0.816448	−	0.577418i	$-0.804060\pi$
$641$	−27.1086	+	9.86674i	−1.07073	+	0.389713i	−0.254278	+	0.967131i	$0.581838\pi$
$642$	−7.07155	+	5.93374i	−0.279092	+	0.234186i
$643$	8.92992	+	15.4671i	0.352161	+	0.609962i	0.986628	−	0.162989i	$-0.0521135\pi$
$643$	8.92992	+	15.4671i	0.352161	+	0.609962i	−0.634466	+	0.772950i	$0.718780\pi$
$644$	0.132614	−	0.752089i	0.00522571	−	0.0296365i
$645$	−2.00392	+	11.3648i	−0.0789043	+	0.447488i
$646$	6.36119	+	5.33767i	0.250278	+	0.210008i
$647$	7.22242	+	2.62874i	0.283942	+	0.103347i	0.480065	−	0.877233i	$-0.340613\pi$
$647$	7.22242	+	2.62874i	0.283942	+	0.103347i	−0.196123	+	0.980579i	$0.562835\pi$
$648$	−4.71729	−	1.71695i	−0.185313	−	0.0674482i
$649$	−24.1267	−	20.2447i	−0.947056	−	0.794674i
$650$	−0.476502	+	2.70237i	−0.0186899	+	0.105996i
$651$	1.65570	−	9.38992i	0.0648918	−	0.368020i
$652$	4.94575	+	8.56629i	0.193690	+	0.335482i
$653$	−36.3580	+	30.5080i	−1.42280	+	1.19387i	−0.472976	+	0.881075i	$0.656820\pi$
$653$	−36.3580	+	30.5080i	−1.42280	+	1.19387i	−0.949821	+	0.312793i	$0.898735\pi$
$654$	−1.43633	+	0.522780i	−0.0561648	+	0.0204423i
$655$	−9.72614	+	16.8462i	−0.380032	+	0.658234i
$656$	−4.57395	−	7.92232i	−0.178583	−	0.309315i
$657$	12.7510	+	10.6993i	0.497463	+	0.417421i
$658$	−0.866385	+	1.50062i	−0.0337752	+	0.0585003i
$659$	7.34340	+	41.6465i	0.286058	+	1.62232i	0.701481	+	0.712689i	$0.252523\pi$
$659$	7.34340	+	41.6465i	0.286058	+	1.62232i	−0.415422	+	0.909629i	$0.636366\pi$
$660$	6.14700			0.239272
$661$	−5.07850	−	28.8016i	−0.197531	−	1.12025i	−0.908768	−	0.417301i	$-0.862976\pi$
$661$	−5.07850	−	28.8016i	−0.197531	−	1.12025i	0.711238	−	0.702952i	$-0.248135\pi$
$662$	−19.5125	+	16.3730i	−0.758376	+	0.636353i
$663$	24.1011	+	8.77207i	0.936007	+	0.340679i
$664$	2.18283	−	0.794485i	0.0847102	−	0.0308320i
$665$	−1.17487			−0.0455595
$666$	5.64723	−	2.19378i	0.218826	−	0.0850072i
$667$	3.92934			0.152145
$668$	6.81295	−	2.47971i	0.263601	−	0.0959429i
$669$	−2.92423	−	1.06433i	−0.113057	−	0.0411494i
$670$	11.2030	−	9.40046i	0.432811	−	0.363171i
$671$	−1.90260	−	10.7902i	−0.0734491	−	0.416551i
$672$	−1.32240			−0.0510126
$673$	2.80538	+	15.9101i	0.108139	+	0.613289i	0.989920	+	0.141629i	$0.0452340\pi$
$673$	2.80538	+	15.9101i	0.108139	+	0.613289i	−0.881780	+	0.471660i	$0.843655\pi$
$674$	−14.2656	+	24.7088i	−0.549491	+	0.951746i
$675$	−4.33340	−	3.63615i	−0.166792	−	0.139955i
$676$	2.73506	+	4.73726i	0.105195	+	0.182202i
$677$	−9.02364	+	15.6294i	−0.346807	+	0.600687i	−0.985680	−	0.168625i	$-0.946067\pi$
$677$	−9.02364	+	15.6294i	−0.346807	+	0.600687i	0.638874	+	0.769312i	$0.279401\pi$
$678$	−10.6953	+	3.89277i	−0.410751	+	0.149501i
$679$	−0.387487	+	0.325141i	−0.0148704	+	0.0124777i
$680$	3.30123	+	5.71790i	0.126597	+	0.219272i
$681$	−1.51944	+	8.61719i	−0.0582252	+	0.330211i
$682$	5.43666	−	30.8328i	0.208180	−	1.18065i
$683$	−27.3820	−	22.9762i	−1.04774	−	0.879161i	−0.0548885	−	0.998492i	$-0.517480\pi$
$683$	−27.3820	−	22.9762i	−1.04774	−	0.879161i	−0.992854	+	0.119332i	$0.961925\pi$
$684$	1.17712	+	0.428435i	0.0450082	+	0.0163816i
$685$	−2.57679	−	0.937874i	−0.0984540	−	0.0358343i
$686$	9.39386	+	7.88238i	0.358659	+	0.300951i
$687$	−0.984357	+	5.58256i	−0.0375556	+	0.212988i
$688$	1.41557	−	8.02808i	0.0539680	−	0.306068i
$689$	16.1698	+	28.0069i	0.616019	+	1.06698i
$690$	0.886564	−	0.743915i	0.0337509	−	0.0283204i
$691$	−30.2856	+	11.0231i	−1.15212	+	0.419337i	−0.846276	−	0.532745i	$-0.821161\pi$
$691$	−30.2856	+	11.0231i	−1.15212	+	0.419337i	−0.305843	+	0.952082i	$0.598938\pi$
$692$	−3.19714	+	5.53760i	−0.121537	+	0.210508i
$693$	−2.01999	−	3.49873i	−0.0767333	−	0.132906i
$694$	21.7353	+	18.2381i	0.825060	+	0.692308i
$695$	−2.15038	+	3.72457i	−0.0815686	+	0.141281i
$696$	−1.18150	−	6.70062i	−0.0447846	−	0.253986i
$697$	−60.3988			−2.28777
$698$	5.47527	+	31.0518i	0.207242	+	1.17533i
$699$	−16.4432	+	13.7975i	−0.621939	+	0.521868i
$700$	−0.877804	−	0.319495i	−0.0331779	−	0.0120758i
$701$	3.26300	−	1.18763i	0.123242	−	0.0448563i	−0.279663	−	0.960098i	$-0.590223\pi$
$701$	3.26300	−	1.18763i	0.123242	−	0.0448563i	0.402905	+	0.915242i	$0.368001\pi$
$702$	15.5227			0.585868
$703$	7.13114	−	2.77023i	0.268956	−	0.104481i
$704$	−4.34223			−0.163654
$705$	−2.46754	+	0.898112i	−0.0929330	+	0.0338249i
$706$	0.526222	+	0.191529i	0.0198046	+	0.00720829i
$707$	4.40514	−	3.69635i	0.165672	−	0.139016i
$708$	1.78300	+	10.1119i	0.0670092	+	0.380028i
$709$	46.5387			1.74780			0.873899	−	0.486108i	$-0.161584\pi$
$709$	46.5387			1.74780			0.873899	+	0.486108i	$0.161584\pi$
$710$	−1.26870	−	7.19513i	−0.0476133	−	0.270029i
$711$	4.07772	−	7.06283i	0.152927	−	0.264877i
$712$	1.38331	+	1.16074i	0.0518418	+	0.0435004i
$713$	−2.94730	−	5.10488i	−0.110377	−	0.191179i
$714$	−4.36554	+	7.56134i	−0.163376	+	0.282976i
$715$	−11.1968	+	4.07530i	−0.418736	+	0.152407i
$716$	5.15583	−	4.32625i	0.192682	−	0.161680i
$717$	9.26549	+	16.0483i	0.346026	+	0.599335i
$718$	4.02728	−	22.8398i	0.150297	−	0.852374i
$719$	2.37450	−	13.4665i	0.0885541	−	0.502215i	−0.907979	−	0.419016i	$-0.862375\pi$
$719$	2.37450	−	13.4665i	0.0885541	−	0.502215i	0.996533	−	0.0831991i	$-0.0265137\pi$
$720$	0.762973	+	0.640210i	0.0284343	+	0.0238592i
$721$	−4.71951	−	1.71776i	−0.175764	−	0.0639728i
$722$	−16.3677	−	5.95737i	−0.609144	−	0.221710i
$723$	−31.4958	−	26.4281i	−1.17134	−	0.982871i
$724$	−1.54070	+	8.73775i	−0.0572597	+	0.324736i
$725$	0.834610	−	4.73331i	0.0309967	−	0.175791i
$726$	5.55989	+	9.63001i	0.206347	+	0.357403i
$727$	28.0849	−	23.5660i	1.04161	−	0.874015i	0.0494237	−	0.998778i	$-0.484262\pi$
$727$	28.0849	−	23.5660i	1.04161	−	0.874015i	0.992187	+	0.124763i	$0.0398171\pi$
$728$	2.40875	−	0.876713i	0.0892742	−	0.0324932i
$729$	−14.5120	+	25.1354i	−0.537480	+	0.930942i
$730$	8.35611	+	14.4732i	0.309273	+	0.535677i
$731$	−41.2307	−	34.5966i	−1.52497	−	1.27960i
$732$	−1.78601	+	3.09346i	−0.0660129	+	0.114338i
$733$	−2.43225	−	13.7940i	−0.0898371	−	0.509492i	−0.996208	−	0.0870080i	$-0.972269\pi$
$733$	−2.43225	−	13.7940i	−0.0898371	−	0.509492i	0.906370	−	0.422484i	$-0.138842\pi$
$734$	8.80309			0.324928
$735$	1.50624	+	8.54233i	0.0555586	+	0.315089i
$736$	−0.626268	+	0.525501i	−0.0230845	+	0.0193702i
$737$	59.6734	+	21.7193i	2.19810	+	0.800042i
$738$	−8.56176	+	3.11622i	−0.315163	+	0.114710i
$739$	45.4669			1.67253			0.836263	−	0.548328i	$-0.184736\pi$
$739$	45.4669			1.67253			0.836263	+	0.548328i	$0.184736\pi$
$740$	6.08136	−	0.130535i	0.223555	−	0.00479855i
$741$	4.88565			0.179479
$742$	−10.3452	+	3.76533i	−0.379783	+	0.138230i
$743$	−11.5251	−	4.19481i	−0.422817	−	0.153893i	0.121844	−	0.992549i	$-0.461119\pi$
$743$	−11.5251	−	4.19481i	−0.422817	−	0.153893i	−0.544661	+	0.838657i	$0.683342\pi$
$744$	−7.81902	+	6.56094i	−0.286659	+	0.240536i
$745$	0.123653	+	0.701269i	0.00453028	+	0.0256925i
$746$	21.0161			0.769454
$747$	−0.401753	−	2.27846i	−0.0146994	−	0.0833643i
$748$	−14.3347	+	24.8285i	−0.524130	+	0.907819i
$749$	4.66634	+	3.91553i	0.170505	+	0.143070i
$750$	−0.707815	−	1.22597i	−0.0258458	−	0.0447662i
$751$	−20.3151	+	35.1867i	−0.741307	+	1.28398i	0.210593	+	0.977574i	$0.432461\pi$
$751$	−20.3151	+	35.1867i	−0.741307	+	1.28398i	−0.951900	+	0.306408i	$0.900873\pi$
$752$	1.74307	−	0.634425i	0.0635632	−	0.0231351i
$753$	−11.1880	+	9.38789i	−0.407715	+	0.342114i
$754$	6.59444	+	11.4219i	0.240155	+	0.415961i
$755$	3.13566	−	17.7832i	0.114118	−	0.647197i
$756$	−0.917606	+	5.20400i	−0.0333730	+	0.189268i
$757$	−36.6211	−	30.7288i	−1.33102	−	1.11686i	−0.983839	−	0.179057i	$-0.942695\pi$
$757$	−36.6211	−	30.7288i	−1.33102	−	1.11686i	−0.347178	−	0.937799i	$-0.612860\pi$
$758$	12.1617	+	4.42649i	0.441732	+	0.160777i
$759$	4.72232	+	1.71878i	0.171409	+	0.0623879i
$760$	0.963457	+	0.808436i	0.0349483	+	0.0293251i
$761$	−6.07257	+	34.4393i	−0.220131	+	1.24842i	0.651648	+	0.758522i	$0.274078\pi$
$761$	−6.07257	+	34.4393i	−0.220131	+	1.24842i	−0.871778	+	0.489901i	$0.837033\pi$
$762$	−3.99948	+	22.6822i	−0.144886	+	0.821689i
$763$	0.504312	+	0.873494i	0.0182573	+	0.0316226i
$764$	1.28640	−	1.07941i	0.0465402	−	0.0390519i
$765$	6.17941	−	2.24912i	0.223417	−	0.0813172i
$766$	19.0860	−	33.0580i	0.689607	−	1.19443i
$767$	−9.95164	−	17.2368i	−0.359333	−	0.622383i
$768$	1.08444	+	0.909950i	0.0391312	+	0.0328350i
$769$	16.2692	−	28.1790i	0.586681	−	1.01616i	−0.407982	−	0.912990i	$-0.633767\pi$
$769$	16.2692	−	28.1790i	0.586681	−	1.01616i	0.994664	−	0.103172i	$-0.0328992\pi$
$770$	−0.704361	−	3.99463i	−0.0253834	−	0.143956i
$771$	13.1307			0.472890
$772$	−3.79719	−	21.5349i	−0.136664	−	0.775059i
$773$	−17.5112	+	14.6936i	−0.629833	+	0.528493i	−0.900877	−	0.434074i	$-0.857076\pi$
$773$	−17.5112	+	14.6936i	−0.629833	+	0.528493i	0.271044	+	0.962567i	$0.412631\pi$
$774$	−7.62959	−	2.77694i	−0.274240	−	0.0998152i
$775$	−6.77539	+	2.46604i	−0.243379	+	0.0885828i
$776$	0.541492			0.0194384
$777$	4.17048	+	6.87824i	0.149615	+	0.246756i
$778$	4.62272			0.165733
$779$	−10.8115	+	3.93507i	−0.387362	+	0.140988i
$780$	3.65031	+	1.32860i	0.130702	+	0.0475717i
$781$	24.3027	−	20.3924i	0.869619	−	0.729697i
$782$	0.937308	+	5.31574i	0.0335181	+	0.190090i
$783$	−27.1887			−0.971644
$784$	−1.06401	−	6.03429i	−0.0380003	−	0.215511i
$785$	−7.13284	+	12.3544i	−0.254582	+	0.440949i
$786$	21.0947	+	17.7006i	0.752424	+	0.631359i
$787$	6.60566	+	11.4413i	0.235467	+	0.407840i	0.959408	−	0.282021i	$-0.0910049\pi$
$787$	6.60566	+	11.4413i	0.235467	+	0.407840i	−0.723942	+	0.689861i	$0.757672\pi$
$788$	7.42231	−	12.8558i	0.264409	−	0.457969i
$789$	24.3222	−	8.85255i	0.865892	−	0.315159i
$790$	6.27259	−	5.26332i	0.223169	−	0.187261i
$791$	3.75525	+	6.50429i	0.133521	+	0.231266i
$792$	−0.750998	+	4.25912i	−0.0266855	+	0.151341i
$793$	1.20234	−	6.81883i	0.0426965	−	0.242144i
$794$	−9.04477	−	7.58946i	−0.320987	−	0.269340i
$795$	−15.6775	−	5.70613i	−0.556022	−	0.202376i
$796$	10.1853	+	3.70713i	0.361007	+	0.131396i
$797$	18.5597	+	15.5734i	0.657417	+	0.551638i	0.909311	−	0.416116i	$-0.136609\pi$
$797$	18.5597	+	15.5734i	0.657417	+	0.551638i	−0.251894	+	0.967755i	$0.581054\pi$
$798$	−0.288809	+	1.63792i	−0.0102237	+	0.0579816i
$799$	2.12670	−	12.0611i	0.0752371	−	0.426691i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	1.37777	−	1.15608i	0.0486810	−	0.0408482i
$802$	−15.1075	+	5.49868i	−0.533465	+	0.194165i
$803$	−36.2842	+	62.8461i	−1.28044	+	2.21779i
$804$	−10.3515	−	17.9292i	−0.365068	−	0.632316i
$805$	−0.585022	−	0.490891i	−0.0206193	−	0.0173016i
$806$	9.89265	−	17.1346i	0.348454	−	0.603540i
$807$	−0.589678	−	3.34423i	−0.0207577	−	0.117723i
$808$	−6.15594			−0.216565
$809$	−2.80850	−	15.9278i	−0.0987415	−	0.559991i	−0.993536	−	0.113514i	$-0.963789\pi$
$809$	−2.80850	−	15.9278i	−0.0987415	−	0.559991i	0.894795	−	0.446477i	$-0.147322\pi$
$810$	−3.84557	+	3.22681i	−0.135119	+	0.113379i
$811$	19.2849	+	7.01915i	0.677186	+	0.246476i	0.657639	−	0.753333i	$-0.271555\pi$
$811$	19.2849	+	7.01915i	0.677186	+	0.246476i	0.0195472	+	0.999809i	$0.493778\pi$
$812$	−4.21902	+	1.53560i	−0.148058	+	0.0538889i
$813$	−13.3143			−0.466953
$814$	13.6942	+	22.5855i	0.479982	+	0.791620i
$815$	9.89150			0.346484
$816$	8.78298	−	3.19674i	0.307466	−	0.111908i
$817$	−9.63439	−	3.50663i	−0.337065	−	0.122682i
$818$	−27.3788	+	22.9736i	−0.957278	+	0.803252i
$819$	−0.443334	−	2.51427i	−0.0154914	−	0.0878558i
$820$	−9.14791			−0.319459
$821$	0.662208	+	3.75557i	0.0231112	+	0.131070i	0.994180	−	0.107728i	$-0.0343576\pi$
$821$	0.662208	+	3.75557i	0.0231112	+	0.131070i	−0.971069	+	0.238798i	$0.923246\pi$
$822$	−1.94094	+	3.36181i	−0.0676982	+	0.117257i
$823$	−3.29773	−	2.76713i	−0.114952	−	0.0964559i	0.583500	−	0.812113i	$-0.301683\pi$
$823$	−3.29773	−	2.76713i	−0.114952	−	0.0964559i	−0.698452	+	0.715657i	$0.746127\pi$
$824$	2.68825	+	4.65618i	0.0936496	+	0.162206i
$825$	3.07350	−	5.32346i	0.107006	−	0.185339i
$826$	6.36690	−	2.31736i	0.221533	−	0.0806314i
$827$	−28.3775	+	23.8115i	−0.986782	+	0.828008i	−0.985099	−	0.171990i	$-0.944980\pi$
$827$	−28.3775	+	23.8115i	−0.986782	+	0.828008i	−0.00168342	+	0.999999i	$0.500536\pi$
$828$	0.407128	+	0.705167i	0.0141487	+	0.0245062i
$829$	−2.25213	+	12.7725i	−0.0782198	+	0.443606i	0.920395	+	0.390990i	$0.127867\pi$
$829$	−2.25213	+	12.7725i	−0.0782198	+	0.443606i	−0.998615	+	0.0526165i	$0.983244\pi$
$830$	0.403370	−	2.28763i	0.0140012	−	0.0794047i
$831$	32.1027	+	26.9374i	1.11363	+	0.934447i
$832$	−2.57858	−	0.938525i	−0.0893960	−	0.0325375i
$833$	−38.0161	−	13.8367i	−1.31718	−	0.479414i
$834$	4.66390	+	3.91348i	0.161498	+	0.135513i
$835$	1.25898	−	7.14004i	0.0435689	−	0.247091i
$836$	−0.948335	+	5.37828i	−0.0327989	+	0.186012i
$837$	20.3936	+	35.3227i	0.704904	+	1.22093i
$838$	−28.7186	+	24.0978i	−0.992069	+	0.832445i
$839$	−15.9153	+	5.79269i	−0.549457	+	0.199986i	−0.601805	−	0.798643i	$-0.705552\pi$
$839$	−15.9153	+	5.79269i	−0.549457	+	0.199986i	0.0523483	+	0.998629i	$0.483329\pi$
$840$	−0.661198	+	1.14523i	−0.0228135	+	0.0395142i
$841$	2.94960	+	5.10885i	0.101710	+	0.176167i
$842$	25.0238	+	20.9975i	0.862378	+	0.723621i
$843$	−13.8043	+	23.9097i	−0.475444	+	0.823493i
$844$	3.51927	+	19.9588i	0.121138	+	0.687010i
$845$	5.47012			0.188178
$846$	−0.320815	−	1.81943i	−0.0110298	−	0.0625533i
$847$	5.62098	−	4.71656i	0.193139	−	0.162063i
$848$	11.0745	+	4.03080i	0.380301	+	0.138418i
$849$	12.8344	−	4.67134i	0.440476	−	0.160320i
$850$	6.60247			0.226463
$851$	4.70839	+	1.60015i	0.161402	+	0.0548524i
$852$	−10.3428			−0.354338
$853$	25.6342	−	9.33010i	0.877699	−	0.319456i	0.136418	−	0.990651i	$-0.456441\pi$
$853$	25.6342	−	9.33010i	0.877699	−	0.319456i	0.741281	+	0.671195i	$0.234219\pi$
$854$	2.21494	+	0.806172i	0.0757937	+	0.0275866i
$855$	0.959594	−	0.805195i	0.0328174	−	0.0275371i
$856$	−1.13235	−	6.42188i	−0.0387030	−	0.219495i
$857$	43.4359			1.48374			0.741871	−	0.670542i	$-0.233938\pi$
$857$	43.4359			1.48374			0.741871	+	0.670542i	$0.233938\pi$
$858$	2.92906	+	16.6115i	0.0999963	+	0.567107i
$859$	14.4243	−	24.9836i	0.492151	−	0.852430i	−0.507808	−	0.861470i	$-0.669544\pi$
$859$	14.4243	−	24.9836i	0.492151	−	0.852430i	0.999959	+	0.00903978i	$0.00287749\pi$
$860$	−6.24474	−	5.23996i	−0.212944	−	0.178681i
$861$	−6.04858	−	10.4765i	−0.206135	−	0.357037i
$862$	−17.4444	+	30.2145i	−0.594157	+	1.02911i
$863$	−14.7143	+	5.35557i	−0.500881	+	0.182306i	−0.580090	−	0.814552i	$-0.696983\pi$
$863$	−14.7143	+	5.35557i	−0.500881	+	0.182306i	0.0792091	+	0.996858i	$0.474761\pi$
$864$	4.33340	−	3.63615i	0.147425	−	0.123704i
$865$	3.19714	+	5.53760i	0.108706	+	0.188284i
$866$	1.38618	−	7.86141i	0.0471042	−	0.267141i
$867$	6.53703	−	37.0733i	0.222009	−	1.25908i
$868$	5.15958	+	4.32940i	0.175128	+	0.146949i
$869$	33.4112	+	12.1607i	1.13340	+	0.412523i
$870$	−6.39366	−	2.32710i	−0.216765	−	0.0788961i
$871$	30.7418	+	25.7955i	1.04165	+	0.874046i
$872$	0.187494	−	1.06333i	0.00634935	−	0.0360090i
$873$	0.0936520	−	0.531127i	0.00316964	−	0.0179759i
$874$	0.514108	+	0.890461i	0.0173900	+	0.0301203i
$875$	−0.715592	+	0.600453i	−0.0241914	+	0.0202990i
$876$	22.2316	−	8.09162i	0.751135	−	0.273391i
$877$	−25.3673	+	43.9374i	−0.856593	+	1.48366i	0.0185671	+	0.999828i	$0.494090\pi$
$877$	−25.3673	+	43.9374i	−0.856593	+	1.48366i	−0.875160	+	0.483834i	$0.839244\pi$
$878$	−17.2043	−	29.7987i	−0.580617	−	1.00566i
$879$	−26.6701	−	22.3788i	−0.899559	−	0.754820i
$880$	−2.17112	+	3.76049i	−0.0731883	+	0.126766i
$881$	8.14472	+	46.1910i	0.274402	+	1.55621i	0.740853	+	0.671667i	$0.234421\pi$
$881$	8.14472	+	46.1910i	0.274402	+	1.55621i	−0.466451	+	0.884547i	$0.654468\pi$
$882$	−6.10282			−0.205492
$883$	−1.45256	−	8.23790i	−0.0488826	−	0.277227i	0.950563	−	0.310533i	$-0.100508\pi$
$883$	−1.45256	−	8.23790i	−0.0488826	−	0.277227i	−0.999445	+	0.0333059i	$0.989396\pi$
$884$	−13.8789	+	11.6458i	−0.466797	+	0.391689i
$885$	9.64865	+	3.51182i	0.324336	+	0.118049i
$886$	−17.0729	+	6.21405i	−0.573577	+	0.208765i
$887$	−18.5150			−0.621671			−0.310836	−	0.950464i	$-0.600609\pi$
$887$	−18.5150			−0.621671			−0.310836	+	0.950464i	$0.600609\pi$
$888$	1.31295	−	8.51026i	0.0440597	−	0.285586i
$889$	15.1983			0.509735
$890$	1.69688	−	0.617615i	0.0568797	−	0.0207025i
$891$	−20.4836	−	7.45541i	−0.686225	−	0.249766i
$892$	1.68395	−	1.41300i	0.0563828	−	0.0473108i
$893$	−0.405114	−	2.29752i	−0.0135566	−	0.0768835i
$894$	1.00805			0.0337143
$895$	−1.16873	−	6.62820i	−0.0390664	−	0.221556i
$896$	0.467070	−	0.808989i	0.0156037	−	0.0270264i
$897$	2.43279	+	2.04135i	0.0812284	+	0.0681587i
$898$	4.65252	+	8.05840i	0.155257	+	0.268912i
$899$	−17.3274	+	30.0119i	−0.577900	+	1.00095i
$900$	0.935925	−	0.340649i	0.0311975	−	0.0113550i
$901$	59.6074	−	50.0165i	1.98581	−	1.66629i
$902$	−19.8612	−	34.4006i	−0.661305	−	1.14541i
$903$	1.87194	−	10.6163i	0.0622943	−	0.353288i
$904$	1.39614	−	7.91788i	0.0464348	−	0.263345i
$905$	6.79676	+	5.70316i	0.225932	+	0.189579i
$906$	−24.0212	−	8.74299i	−0.798050	−	0.290466i
$907$	−10.4672	−	3.80973i	−0.347556	−	0.126500i	0.162343	−	0.986734i	$-0.448095\pi$
$907$	−10.4672	−	3.80973i	−0.347556	−	0.126500i	−0.509899	+	0.860234i	$0.670317\pi$
$908$	−4.73498	−	3.97312i	−0.157136	−	0.131853i
$909$	−1.06468	+	6.03811i	−0.0353132	+	0.200271i
$910$	0.445119	−	2.52440i	0.0147556	−	0.0836829i
$911$	−28.9077	−	50.0695i	−0.957753	−	1.65888i	−0.727938	−	0.685643i	$-0.759521\pi$
$911$	−28.9077	−	50.0695i	−0.957753	−	1.65888i	−0.229815	−	0.973234i	$-0.573812\pi$
$912$	1.36390	−	1.14445i	0.0451632	−	0.0378964i
$913$	9.47835	−	3.44984i	0.313688	−	0.114173i
$914$	19.9526	−	34.5589i	0.659973	−	1.14311i
$915$	1.78601	+	3.09346i	0.0590437	+	0.102267i
$916$	−3.06751	−	2.57395i	−0.101353	−	0.0850457i
$917$	9.08557	−	15.7367i	0.300032	−	0.519671i
$918$	−6.48561	−	36.7817i	−0.214057	−	1.21398i
$919$	30.6233			1.01017			0.505085	−	0.863070i	$-0.331461\pi$
$919$	30.6233			1.01017			0.505085	+	0.863070i	$0.331461\pi$
$920$	0.141963	+	0.805114i	0.00468039	+	0.0265438i
$921$	5.62240	−	4.71775i	0.185264	−	0.155455i
$922$	20.7305	+	7.54528i	0.682722	+	0.248490i
$923$	18.8394	−	6.85698i	0.620107	−	0.225700i
$924$	−5.74216			−0.188903
$925$	2.92763	−	5.33188i	0.0962600	−	0.175311i
$926$	1.46826			0.0482502
$927$	5.03200	−	1.83150i	0.165272	−	0.0601543i
$928$	4.51647	+	1.64386i	0.148260	+	0.0539624i
$929$	−41.2295	+	34.5956i	−1.35270	+	1.13505i	−0.374531	+	0.927215i	$0.622196\pi$
$929$	−41.2295	+	34.5956i	−1.35270	+	1.13505i	−0.978165	+	0.207831i	$0.933359\pi$
$930$	1.77243	+	10.0519i	0.0581202	+	0.329616i
$931$	−7.70643			−0.252568
$932$	−2.63301	−	14.9325i	−0.0862471	−	0.489132i
$933$	12.3629	−	21.4131i	0.404742	−	0.701034i
$934$	−2.20863	−	1.85326i	−0.0722686	−	0.0606406i
$935$	14.3347	+	24.8285i	0.468796	+	0.811978i
$936$	−1.36653	+	2.36690i	−0.0446664	+	0.0773646i
$937$	9.46502	−	3.44499i	0.309209	−	0.112543i	−0.182755	−	0.983158i	$-0.558502\pi$
$937$	9.46502	−	3.44499i	0.309209	−	0.112543i	0.491964	+	0.870616i	$0.336279\pi$
$938$	−10.4652	+	8.78134i	−0.341701	+	0.286721i
$939$	−5.59657	−	9.69354i	−0.182637	−	0.316337i
$940$	0.322106	−	1.82676i	0.0105059	−	0.0595822i
$941$	−7.84436	+	44.4876i	−0.255719	+	1.45025i	0.538502	+	0.842624i	$0.318990\pi$
$941$	−7.84436	+	44.4876i	−0.255719	+	1.45025i	−0.794221	+	0.607629i	$0.792121\pi$
$942$	15.4702	+	12.9810i	0.504047	+	0.422945i
$943$	−7.02771	−	2.55788i	−0.228854	−	0.0832959i
$944$	−6.81579	−	2.48075i	−0.221835	−	0.0807414i
$945$	4.04800	+	3.39667i	0.131681	+	0.110494i
$946$	6.14672	−	34.8598i	0.199847	−	1.13339i
$947$	−4.10520	+	23.2818i	−0.133401	+	0.756556i	0.842558	+	0.538605i	$0.181048\pi$
$947$	−4.10520	+	23.2818i	−0.133401	+	0.756556i	−0.975960	+	0.217951i	$0.930063\pi$
$948$	−5.79579	−	10.0386i	−0.188238	−	0.326039i
$949$	−35.1303	+	29.4778i	−1.14038	+	0.956891i
$950$	1.18186	−	0.430160i	0.0383444	−	0.0139562i
$951$	−2.53642	+	4.39321i	−0.0822491	+	0.142460i
$952$	−3.08381	−	5.34132i	−0.0999469	−	0.173113i
$953$	2.61337	+	2.19288i	0.0846554	+	0.0710343i	0.684133	−	0.729357i	$-0.260181\pi$
$953$	2.61337	+	2.19288i	0.0846554	+	0.0710343i	−0.599478	+	0.800391i	$0.704625\pi$
$954$	5.86901	−	10.1654i	0.190016	−	0.329118i
$955$	−0.291602	−	1.65376i	−0.00943603	−	0.0535144i
$956$	−13.0903			−0.423369
$957$	−5.13035	−	29.0957i	−0.165841	−	0.940529i
$958$	−2.63129	+	2.20791i	−0.0850131	+	0.0713344i
$959$	2.40708	+	0.876106i	0.0777287	+	0.0282909i
$960$	1.33026	−	0.484174i	0.0429339	−	0.0156267i
$961$	20.9873			0.677010
$962$	3.25053	+	16.3719i	0.104801	+	0.527852i
$963$	−6.49481			−0.209292
$964$	27.2919	−	9.93345i	0.879014	−	0.319935i
$965$	−20.5484	−	7.47900i	−0.661476	−	0.240758i
$966$	−0.828174	+	0.694921i	−0.0266461	+	0.0223587i
$967$	−2.11695	−	12.0058i	−0.0680767	−	0.386082i	−0.999741	−	0.0227616i	$-0.992754\pi$
$967$	−2.11695	−	12.0058i	−0.0680767	−	0.386082i	0.931664	−	0.363320i	$-0.118357\pi$
$968$	−7.85500			−0.252469
$969$	−2.04129	−	11.5767i	−0.0655757	−	0.371898i
$970$	0.270746	−	0.468946i	0.00869313	−	0.0150569i
$971$	17.4298	+	14.6253i	0.559348	+	0.469349i	0.878092	−	0.478492i	$-0.158817\pi$
$971$	17.4298	+	14.6253i	0.559348	+	0.469349i	−0.318744	+	0.947841i	$0.603261\pi$
$972$	−4.93201	−	8.54250i	−0.158194	−	0.274001i
$973$	2.00876	−	3.47927i	0.0643978	−	0.111540i
$974$	−21.8397	+	7.94900i	−0.699789	+	0.254702i
$975$	2.97576	−	2.49696i	0.0953006	−	0.0799667i
$976$	−1.26164	−	2.18522i	−0.0403840	−	0.0699472i
$977$	5.38066	−	30.5152i	0.172143	−	0.976269i	−0.769248	−	0.638950i	$-0.779369\pi$
$977$	5.38066	−	30.5152i	0.172143	−	0.976269i	0.941391	−	0.337319i	$-0.109520\pi$
$978$	2.43154	−	13.7900i	0.0777522	−	0.440955i
$979$	6.00667	+	5.04019i	0.191974	+	0.161085i
$980$	−5.75786	−	2.09569i	−0.183928	−	0.0669443i
$981$	−1.01055	−	0.367811i	−0.0322644	−	0.0117433i
$982$	15.8968	+	13.3390i	0.507286	+	0.425664i
$983$	−7.77060	+	44.0693i	−0.247844	+	1.40559i	0.565951	+	0.824439i	$0.308509\pi$
$983$	−7.77060	+	44.0693i	−0.247844	+	1.40559i	−0.813795	+	0.581152i	$0.802602\pi$
$984$	−2.24875	+	12.7533i	−0.0716877	+	0.406561i
$985$	−7.42231	−	12.8558i	−0.236494	−	0.409620i
$986$	24.3094	−	20.3980i	0.774168	−	0.649604i
$987$	2.30503	−	0.838962i	0.0733699	−	0.0267045i
$988$	−1.72561	+	2.98884i	−0.0548990	+	0.0950878i
$989$	−3.33224	−	5.77161i	−0.105959	−	0.183526i
$990$	3.31301	+	2.77994i	0.105294	+	0.0883524i
$991$	12.6823	−	21.9664i	0.402866	−	0.697785i	−0.591204	−	0.806522i	$-0.701347\pi$
$991$	12.6823	−	21.9664i	0.402866	−	0.697785i	0.994071	+	0.108737i	$0.0346807\pi$
$992$	−1.25204	−	7.10068i	−0.0397524	−	0.225447i
$993$	36.0587			1.14429
$994$	1.18514	+	6.72126i	0.0375903	+	0.213185i
$995$	8.30310	−	6.96713i	0.263226	−	0.220873i
$996$	−3.09008	−	1.12470i	−0.0979129	−	0.0356374i
$997$	43.9268	−	15.9880i	1.39117	−	0.506346i	0.465628	−	0.884980i	$-0.345828\pi$
$997$	43.9268	−	15.9880i	1.39117	−	0.506346i	0.925546	+	0.378634i	$0.123606\pi$
$998$	1.63832			0.0518601
$999$	−32.5792	−	11.0721i	−1.03076	−	0.350305i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.b.81.1	✓	18
37.16	even	9	inner	370.2.o.b.201.1	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.b.81.1	✓	18	1.1	even	1	trivial
370.2.o.b.201.1	yes	18	37.16	even	9	inner

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.33026 - 0.484174i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{5} -1.41563 q^{6} +(0.162212 + 0.919948i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.762973 - 0.640210i) q^{9} +O(q^{10})\)	\(q+(0.939693 - 0.342020i) q^{2} +(-1.33026 - 0.484174i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.173648 - 0.984808i) q^{5} -1.41563 q^{6} +(0.162212 + 0.919948i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.762973 - 0.640210i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.17112 - 3.76049i) q^{11} +(-1.33026 + 0.484174i) q^{12} +(2.10207 - 1.76385i) q^{13} +(0.467070 + 0.808989i) q^{14} +(-0.245822 + 1.39412i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-5.05778 - 4.24398i) q^{17} +(-0.935925 - 0.340649i) q^{18} +(-1.18186 - 0.430160i) q^{19} +(-0.766044 - 0.642788i) q^{20} +(0.229632 - 1.30231i) q^{21} +(0.754021 - 4.27627i) q^{22} +(-0.408767 - 0.708006i) q^{23} +(-1.08444 + 0.909950i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(1.37203 - 2.37643i) q^{26} +(2.82842 + 4.89897i) q^{27} +(0.715592 + 0.600453i) q^{28} +(-2.40316 + 4.16240i) q^{29} +(0.245822 + 1.39412i) q^{30} +7.21022 q^{31} +(-0.173648 - 0.984808i) q^{32} +(-4.70887 + 3.95122i) q^{33} +(-6.20429 - 2.25818i) q^{34} +(0.877804 - 0.319495i) q^{35} -0.995990 q^{36} +(-4.57469 + 4.00902i) q^{37} -1.25770 q^{38} +(-3.65031 + 1.32860i) q^{39} +(-0.939693 - 0.342020i) q^{40} +(7.00771 - 5.88016i) q^{41} +(-0.229632 - 1.30231i) q^{42} +8.15193 q^{43} +(-0.754021 - 4.27627i) q^{44} +(-0.497995 + 0.862553i) q^{45} +(-0.626268 - 0.525501i) q^{46} +(0.927468 + 1.60642i) q^{47} +(-0.707815 + 1.22597i) q^{48} +(5.75786 - 2.09569i) q^{49} +(-0.766044 + 0.642788i) q^{50} +(4.67333 + 8.09444i) q^{51} +(0.476502 - 2.70237i) q^{52} +(-2.04649 + 11.6062i) q^{53} +(4.33340 + 3.63615i) q^{54} +(-4.08037 - 1.48513i) q^{55} +(0.877804 + 0.319495i) q^{56} +(1.36390 + 1.14445i) q^{57} +(-0.834610 + 4.73331i) q^{58} +(1.25951 - 7.14302i) q^{59} +(0.707815 + 1.22597i) q^{60} +(1.93294 - 1.62193i) q^{61} +(6.77539 - 2.46604i) q^{62} +(0.465197 - 0.805745i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.10207 - 1.76385i) q^{65} +(-3.07350 + 5.32346i) q^{66} +(2.53952 + 14.4023i) q^{67} -6.60247 q^{68} +(0.200968 + 1.13974i) q^{69} +(0.715592 - 0.600453i) q^{70} +(6.86552 + 2.49884i) q^{71} +(-0.935925 + 0.340649i) q^{72} -16.7122 q^{73} +(-2.92763 + 5.33188i) q^{74} +1.41563 q^{75} +(-1.18186 + 0.430160i) q^{76} +(3.81163 + 1.38732i) q^{77} +(-2.97576 + 2.49696i) q^{78} +(1.42188 + 8.06388i) q^{79} -1.00000 q^{80} +(-0.871719 - 4.94377i) q^{81} +(4.57395 - 7.92232i) q^{82} +(1.77946 + 1.49314i) q^{83} +(-0.661198 - 1.14523i) q^{84} +(-3.30123 + 5.71790i) q^{85} +(7.66030 - 2.78812i) q^{86} +(5.21216 - 4.37352i) q^{87} +(-2.17112 - 3.76049i) q^{88} +(-0.313571 + 1.77835i) q^{89} +(-0.172952 + 0.980859i) q^{90} +(1.96363 + 1.64768i) q^{91} +(-0.768231 - 0.279613i) q^{92} +(-9.59145 - 3.49100i) q^{93} +(1.42096 + 1.19233i) q^{94} +(-0.218398 + 1.23860i) q^{95} +(-0.245822 + 1.39412i) q^{96} +(0.270746 + 0.468946i) q^{97} +(4.69385 - 3.93861i) q^{98} +(-4.06401 + 1.47918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more