LMFDB - Embedded newform 57.2.i.b.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(4,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("57.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.i (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:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			28.2
Root			$0.500000 + 1.96356i$ of defining polynomial
Character	$\chi$	$=$	57.28
Dual form			57.2.i.b.55.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.131669 + 0.746734i) q^{2} +(0.766044 - 0.642788i) q^{3} +(1.33911 - 0.487396i) q^{4} +(-2.97104 - 1.08137i) q^{5} +(0.580856 + 0.487396i) q^{6} +(-1.89771 + 3.28694i) q^{7} +(1.29853 + 2.24912i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.131669 + 0.746734i) q^{2} +(0.766044 - 0.642788i) q^{3} +(1.33911 - 0.487396i) q^{4} +(-2.97104 - 1.08137i) q^{5} +(0.580856 + 0.487396i) q^{6} +(-1.89771 + 3.28694i) q^{7} +(1.29853 + 2.24912i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.416301 - 2.36096i) q^{10} +(-0.752542 - 1.30344i) q^{11} +(0.712526 - 1.23413i) q^{12} +(-2.32962 - 1.95478i) q^{13} +(-2.70434 - 0.984299i) q^{14} +(-2.97104 + 1.08137i) q^{15} +(0.674788 - 0.566214i) q^{16} +(0.685522 + 3.88779i) q^{17} +0.758254 q^{18} +(1.20199 - 4.18990i) q^{19} -4.50560 q^{20} +(0.659069 + 3.73777i) q^{21} +(0.874238 - 0.733573i) q^{22} +(6.29625 - 2.29165i) q^{23} +(2.44044 + 0.888246i) q^{24} +(3.82748 + 3.21164i) q^{25} +(1.15296 - 1.99699i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.939207 + 5.32651i) q^{28} +(-0.277237 + 1.57229i) q^{29} +(-1.19869 - 2.07619i) q^{30} +(-2.46399 + 4.26776i) q^{31} +(4.49058 + 3.76805i) q^{32} +(-1.41432 - 0.514769i) q^{33} +(-2.81288 + 1.02380i) q^{34} +(9.19257 - 7.71348i) q^{35} +(-0.247458 - 1.40340i) q^{36} -6.28205 q^{37} +(3.28700 + 0.345884i) q^{38} -3.04110 q^{39} +(-1.42585 - 8.08640i) q^{40} +(-0.0274747 + 0.0230540i) q^{41} +(-2.70434 + 0.984299i) q^{42} +(8.21934 + 2.99159i) q^{43} +(-1.64303 - 1.37867i) q^{44} +(-1.58086 + 2.73812i) q^{45} +(2.54028 + 4.39989i) q^{46} +(1.05678 - 5.99331i) q^{47} +(0.152962 - 0.867490i) q^{48} +(-3.70264 - 6.41315i) q^{49} +(-1.89428 + 3.28099i) q^{50} +(3.02416 + 2.53757i) q^{51} +(-4.07236 - 1.48222i) q^{52} +(-7.88225 + 2.86891i) q^{53} +(0.580856 - 0.487396i) q^{54} +(0.826330 + 4.68635i) q^{55} -9.85695 q^{56} +(-1.77244 - 3.98227i) q^{57} -1.21058 q^{58} +(-1.07489 - 6.09598i) q^{59} +(-3.45149 + 2.89614i) q^{60} +(-0.317422 + 0.115532i) q^{61} +(-3.51131 - 1.27801i) q^{62} +(2.90747 + 2.43965i) q^{63} +(-1.34158 + 2.32369i) q^{64} +(4.80754 + 8.32690i) q^{65} +(0.198174 - 1.12390i) q^{66} +(1.08766 - 6.16842i) q^{67} +(2.81288 + 4.87205i) q^{68} +(3.35016 - 5.80266i) q^{69} +(6.97030 + 5.84878i) q^{70} +(4.75246 + 1.72975i) q^{71} +(2.44044 - 0.888246i) q^{72} +(-2.53923 + 2.13067i) q^{73} +(-0.827154 - 4.69102i) q^{74} +4.99642 q^{75} +(-0.432546 - 6.19658i) q^{76} +5.71244 q^{77} +(-0.400419 - 2.27089i) q^{78} +(-1.87620 + 1.57432i) q^{79} +(-2.61711 + 0.952549i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-0.0208328 - 0.0174808i) q^{82} +(-4.27498 + 7.40448i) q^{83} +(2.70434 + 4.68405i) q^{84} +(2.16742 - 12.2921i) q^{85} +(-1.15169 + 6.53156i) q^{86} +(0.798271 + 1.38265i) q^{87} +(1.95440 - 3.38511i) q^{88} +(-11.1562 - 9.36114i) q^{89} +(-2.25280 - 0.819952i) q^{90} +(10.8462 - 3.94769i) q^{91} +(7.31443 - 6.13754i) q^{92} +(0.855735 + 4.85311i) q^{93} +4.61456 q^{94} +(-8.10197 + 11.1485i) q^{95} +5.86204 q^{96} +(3.00347 + 17.0336i) q^{97} +(4.30140 - 3.60930i) q^{98} +(-1.41432 + 0.514769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8} - 18 q^{10} - 9 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + 33 q^{16} + 12 q^{17} - 9 q^{19} - 18 q^{20} - 24 q^{22} + 9 q^{23} + 30 q^{24} - 12 q^{25} - 6 q^{27} + 30 q^{28} - 6 q^{30} - 3 q^{32} - 9 q^{33} + 21 q^{34} + 30 q^{35} - 3 q^{36} - 12 q^{37} + 18 q^{38} + 6 q^{39} - 3 q^{40} - 18 q^{41} - 3 q^{42} + 15 q^{43} + 15 q^{44} - 9 q^{45} + 27 q^{46} - 9 q^{47} - 12 q^{48} - 9 q^{49} + 9 q^{50} - 15 q^{51} - 27 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 78 q^{56} - 3 q^{57} - 24 q^{58} - 30 q^{59} - 15 q^{60} + 21 q^{61} + 3 q^{62} + 9 q^{63} - 21 q^{64} + 21 q^{65} + 30 q^{66} + 3 q^{67} - 21 q^{68} - 6 q^{69} + 18 q^{70} - 30 q^{71} + 30 q^{72} - 24 q^{73} + 39 q^{74} + 30 q^{75} - 60 q^{76} + 96 q^{77} + 9 q^{78} + 24 q^{79} + 42 q^{80} - 33 q^{82} + 3 q^{83} + 3 q^{84} + 3 q^{85} + 51 q^{86} + 15 q^{87} + 42 q^{88} + 3 q^{89} - 9 q^{90} + 24 q^{91} + 69 q^{92} - 6 q^{93} + 18 q^{94} - 54 q^{95} - 42 q^{96} - 27 q^{97} - 3 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8 - 18 * q^10 - 9 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 + 33 * q^16 + 12 * q^17 - 9 * q^19 - 18 * q^20 - 24 * q^22 + 9 * q^23 + 30 * q^24 - 12 * q^25 - 6 * q^27 + 30 * q^28 - 6 * q^30 - 3 * q^32 - 9 * q^33 + 21 * q^34 + 30 * q^35 - 3 * q^36 - 12 * q^37 + 18 * q^38 + 6 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 + 15 * q^43 + 15 * q^44 - 9 * q^45 + 27 * q^46 - 9 * q^47 - 12 * q^48 - 9 * q^49 + 9 * q^50 - 15 * q^51 - 27 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 78 * q^56 - 3 * q^57 - 24 * q^58 - 30 * q^59 - 15 * q^60 + 21 * q^61 + 3 * q^62 + 9 * q^63 - 21 * q^64 + 21 * q^65 + 30 * q^66 + 3 * q^67 - 21 * q^68 - 6 * q^69 + 18 * q^70 - 30 * q^71 + 30 * q^72 - 24 * q^73 + 39 * q^74 + 30 * q^75 - 60 * q^76 + 96 * q^77 + 9 * q^78 + 24 * q^79 + 42 * q^80 - 33 * q^82 + 3 * q^83 + 3 * q^84 + 3 * q^85 + 51 * q^86 + 15 * q^87 + 42 * q^88 + 3 * q^89 - 9 * q^90 + 24 * q^91 + 69 * q^92 - 6 * q^93 + 18 * q^94 - 54 * q^95 - 42 * q^96 - 27 * q^97 - 3 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	0.131669	+	0.746734i	0.0931043	+	0.528021i	0.995312	+	0.0967185i	$0.0308347\pi$
$2$	0.131669	+	0.746734i	0.0931043	+	0.528021i	−0.902207	+	0.431302i	$0.858054\pi$
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$	1.33911	−	0.487396i	0.669555	−	0.243698i
$5$	−2.97104	−	1.08137i	−1.32869	−	0.483603i	−0.422456	−	0.906383i	$-0.638832\pi$
$5$	−2.97104	−	1.08137i	−1.32869	−	0.483603i	−0.906232	+	0.422780i	$0.861054\pi$
$6$	0.580856	+	0.487396i	0.237134	+	0.198979i
$7$	−1.89771	+	3.28694i	−0.717268	+	1.24235i	0.244810	+	0.969571i	$0.421275\pi$
$7$	−1.89771	+	3.28694i	−0.717268	+	1.24235i	−0.962078	+	0.272774i	$0.912059\pi$
$8$	1.29853	+	2.24912i	0.459099	+	0.795183i
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$	0.416301	−	2.36096i	0.131646	−	0.746601i
$11$	−0.752542	−	1.30344i	−0.226900	−	0.393002i	0.729988	−	0.683460i	$-0.239526\pi$
$11$	−0.752542	−	1.30344i	−0.226900	−	0.393002i	−0.956888	+	0.290458i	$0.906192\pi$
$12$	0.712526	−	1.23413i	0.205688	−	0.356263i
$13$	−2.32962	−	1.95478i	−0.646119	−	0.542158i	0.259771	−	0.965670i	$-0.416353\pi$
$13$	−2.32962	−	1.95478i	−0.646119	−	0.542158i	−0.905891	+	0.423512i	$0.860797\pi$
$14$	−2.70434	−	0.984299i	−0.722765	−	0.263065i
$15$	−2.97104	+	1.08137i	−0.767119	+	0.279208i
$16$	0.674788	−	0.566214i	0.168697	−	0.141554i
$17$	0.685522	+	3.88779i	0.166263	+	0.942927i	0.947752	+	0.319007i	$0.103349\pi$
$17$	0.685522	+	3.88779i	0.166263	+	0.942927i	−0.781489	+	0.623919i	$0.785539\pi$
$18$	0.758254			0.178722
$19$	1.20199	−	4.18990i	0.275755	−	0.961228i
$19$	1.20199	−	4.18990i	0.275755	−	0.961228i
$20$	−4.50560			−1.00748
$21$	0.659069	+	3.73777i	0.143821	+	0.815648i
$22$	0.874238	−	0.733573i	0.186388	−	0.156398i
$23$	6.29625	−	2.29165i	1.31286	−	0.477842i	0.411696	−	0.911321i	$-0.364937\pi$
$23$	6.29625	−	2.29165i	1.31286	−	0.477842i	0.901163	+	0.433480i	$0.142714\pi$
$24$	2.44044	+	0.888246i	0.498152	+	0.181312i
$25$	3.82748	+	3.21164i	0.765497	+	0.642328i
$26$	1.15296	−	1.99699i	0.226114	−	0.391642i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−0.939207	+	5.32651i	−0.177493	+	1.00662i
$29$	−0.277237	+	1.57229i	−0.0514815	+	0.291966i	−0.999669	−	0.0257466i	$-0.991804\pi$
$29$	−0.277237	+	1.57229i	−0.0514815	+	0.291966i	0.948187	+	0.317713i	$0.102915\pi$
$30$	−1.19869	−	2.07619i	−0.218850	−	0.379059i
$31$	−2.46399	+	4.26776i	−0.442546	+	0.766512i	−0.997878	−	0.0651170i	$-0.979258\pi$
$31$	−2.46399	+	4.26776i	−0.442546	+	0.766512i	0.555332	+	0.831629i	$0.312591\pi$
$32$	4.49058	+	3.76805i	0.793831	+	0.666103i
$33$	−1.41432	−	0.514769i	−0.246201	−	0.0896098i
$34$	−2.81288	+	1.02380i	−0.482405	+	0.175581i
$35$	9.19257	−	7.71348i	1.55383	−	1.30382i
$36$	−0.247458	−	1.40340i	−0.0412429	−	0.233900i
$37$	−6.28205			−1.03276			−0.516382	−	0.856359i	$-0.672721\pi$
$37$	−6.28205			−1.03276			−0.516382	+	0.856359i	$0.672721\pi$
$38$	3.28700	+	0.345884i	0.533222	+	0.0561098i
$39$	−3.04110			−0.486965
$40$	−1.42585	−	8.08640i	−0.225447	−	1.27857i
$41$	−0.0274747	+	0.0230540i	−0.00429083	+	0.00360043i	−0.644931	−	0.764241i	$-0.723114\pi$
$41$	−0.0274747	+	0.0230540i	−0.00429083	+	0.00360043i	0.640640	+	0.767842i	$0.278669\pi$
$42$	−2.70434	+	0.984299i	−0.417289	+	0.151881i
$43$	8.21934	+	2.99159i	1.25344	+	0.456214i	0.881562	−	0.472069i	$-0.156493\pi$
$43$	8.21934	+	2.99159i	1.25344	+	0.456214i	0.371876	+	0.928283i	$0.378715\pi$
$44$	−1.64303	−	1.37867i	−0.247696	−	0.207842i
$45$	−1.58086	+	2.73812i	−0.235660	+	0.408175i
$46$	2.54028	+	4.39989i	0.374543	+	0.648728i
$47$	1.05678	−	5.99331i	0.154148	−	0.874215i	−0.805413	−	0.592714i	$-0.798057\pi$
$47$	1.05678	−	5.99331i	0.154148	−	0.874215i	0.959561	−	0.281501i	$-0.0908323\pi$
$48$	0.152962	−	0.867490i	0.0220782	−	0.125211i
$49$	−3.70264	−	6.41315i	−0.528948	−	0.916165i
$50$	−1.89428	+	3.28099i	−0.267892	+	0.464002i
$51$	3.02416	+	2.53757i	0.423467	+	0.355331i
$52$	−4.07236	−	1.48222i	−0.564735	−	0.205547i
$53$	−7.88225	+	2.86891i	−1.08271	+	0.394074i	−0.820916	−	0.571049i	$-0.806537\pi$
$53$	−7.88225	+	2.86891i	−1.08271	+	0.394074i	−0.261795	+	0.965124i	$0.584314\pi$
$54$	0.580856	−	0.487396i	0.0790445	−	0.0663262i
$55$	0.826330	+	4.68635i	0.111422	+	0.631907i
$56$	−9.85695			−1.31719
$57$	−1.77244	−	3.98227i	−0.234765	−	0.527464i
$58$	−1.21058			−0.158957
$59$	−1.07489	−	6.09598i	−0.139938	−	0.793630i	−0.971293	−	0.237887i	$-0.923545\pi$
$59$	−1.07489	−	6.09598i	−0.139938	−	0.793630i	0.831355	−	0.555742i	$-0.187566\pi$
$60$	−3.45149	+	2.89614i	−0.445586	+	0.373891i
$61$	−0.317422	+	0.115532i	−0.0406417	+	0.0147924i	−0.362261	−	0.932077i	$-0.617995\pi$
$61$	−0.317422	+	0.115532i	−0.0406417	+	0.0147924i	0.321619	+	0.946869i	$0.395773\pi$
$62$	−3.51131	−	1.27801i	−0.445937	−	0.162308i
$63$	2.90747	+	2.43965i	0.366306	+	0.307367i
$64$	−1.34158	+	2.32369i	−0.167698	+	0.290462i
$65$	4.80754	+	8.32690i	0.596302	+	1.03282i
$66$	0.198174	−	1.12390i	0.0243935	−	0.138342i
$67$	1.08766	−	6.16842i	0.132879	−	0.753593i	−0.843435	−	0.537232i	$-0.819470\pi$
$67$	1.08766	−	6.16842i	0.132879	−	0.753593i	0.976313	−	0.216361i	$-0.0694188\pi$
$68$	2.81288	+	4.87205i	0.341112	+	0.590823i
$69$	3.35016	−	5.80266i	0.403312	−	0.698558i
$70$	6.97030	+	5.84878i	0.833111	+	0.699063i
$71$	4.75246	+	1.72975i	0.564013	+	0.205284i	0.608262	−	0.793737i	$-0.291867\pi$
$71$	4.75246	+	1.72975i	0.564013	+	0.205284i	−0.0442487	+	0.999021i	$0.514089\pi$
$72$	2.44044	−	0.888246i	0.287608	−	0.104681i
$73$	−2.53923	+	2.13067i	−0.297195	+	0.249376i	−0.779175	−	0.626806i	$-0.784362\pi$
$73$	−2.53923	+	2.13067i	−0.297195	+	0.249376i	0.481981	+	0.876182i	$0.339917\pi$
$74$	−0.827154	−	4.69102i	−0.0961547	−	0.545320i
$75$	4.99642			0.576937
$76$	−0.432546	−	6.19658i	−0.0496164	−	0.710796i
$77$	5.71244			0.650993
$78$	−0.400419	−	2.27089i	−0.0453386	−	0.257128i
$79$	−1.87620	+	1.57432i	−0.211089	+	0.177125i	−0.742202	−	0.670176i	$-0.766218\pi$
$79$	−1.87620	+	1.57432i	−0.211089	+	0.177125i	0.531113	+	0.847301i	$0.321774\pi$
$80$	−2.61711	+	0.952549i	−0.292601	+	0.106498i
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$	−0.0208328	−	0.0174808i	−0.00230060	−	0.00193043i
$83$	−4.27498	+	7.40448i	−0.469240	+	0.812747i	−0.999382	−	0.0351618i	$-0.988805\pi$
$83$	−4.27498	+	7.40448i	−0.469240	+	0.812747i	0.530142	+	0.847909i	$0.322139\pi$
$84$	2.70434	+	4.68405i	0.295068	+	0.511072i
$85$	2.16742	−	12.2921i	0.235090	−	1.33326i
$86$	−1.15169	+	6.53156i	−0.124190	+	0.704317i
$87$	0.798271	+	1.38265i	0.0855836	+	0.148235i
$88$	1.95440	−	3.38511i	0.208339	−	0.360854i
$89$	−11.1562	−	9.36114i	−1.18255	−	0.992279i	−0.999959	−	0.00909074i	$-0.997106\pi$
$89$	−11.1562	−	9.36114i	−1.18255	−	0.992279i	−0.182594	−	0.983188i	$-0.558449\pi$
$90$	−2.25280	−	0.819952i	−0.237466	−	0.0864306i
$91$	10.8462	−	3.94769i	1.13699	−	0.413830i
$92$	7.31443	−	6.13754i	0.762582	−	0.639882i
$93$	0.855735	+	4.85311i	0.0887356	+	0.503245i
$94$	4.61456			0.475955
$95$	−8.10197	+	11.1485i	−0.831245	+	1.14382i
$96$	5.86204			0.598292
$97$	3.00347	+	17.0336i	0.304957	+	1.72950i	0.623709	+	0.781657i	$0.285625\pi$
$97$	3.00347	+	17.0336i	0.304957	+	1.72950i	−0.318752	+	0.947838i	$0.603264\pi$
$98$	4.30140	−	3.60930i	0.434507	−	0.364594i
$99$	−1.41432	+	0.514769i	−0.142144	+	0.0517363i
$100$	6.69076	+	2.43524i	0.669076	+	0.243524i
$101$	8.90176	+	7.46946i	0.885758	+	0.743239i	0.967355	−	0.253426i	$-0.0815575\pi$
$101$	8.90176	+	7.46946i	0.885758	+	0.743239i	−0.0815967	+	0.996665i	$0.526002\pi$
$102$	−1.49670	+	2.59237i	−0.148196	+	0.256682i
$103$	−1.06335	−	1.84177i	−0.104775	−	0.181475i	0.808871	−	0.587985i	$-0.200079\pi$
$103$	−1.06335	−	1.84177i	−0.104775	−	0.181475i	−0.913646	+	0.406511i	$0.866745\pi$
$104$	1.37146	−	7.77792i	0.134482	−	0.762688i
$105$	2.08379	−	11.8177i	0.203357	−	1.15329i
$106$	−3.18016	−	5.50820i	−0.308885	−	0.535004i
$107$	−3.48793	+	6.04128i	−0.337191	+	0.584032i	−0.983903	−	0.178702i	$-0.942810\pi$
$107$	−3.48793	+	6.04128i	−0.337191	+	0.584032i	0.646712	+	0.762734i	$0.276144\pi$
$108$	−1.09165	−	0.916005i	−0.105044	−	0.0881426i
$109$	−3.16836	−	1.15319i	−0.303474	−	0.110455i	0.185795	−	0.982589i	$-0.440514\pi$
$109$	−3.16836	−	1.15319i	−0.303474	−	0.110455i	−0.489269	+	0.872133i	$0.662736\pi$
$110$	−3.39066	+	1.23410i	−0.323286	+	0.117667i
$111$	−4.81233	+	4.03803i	−0.456766	+	0.383272i
$112$	0.580556	+	3.29250i	0.0548574	+	0.311112i
$113$	−13.3061			−1.25173			−0.625864	−	0.779932i	$-0.715254\pi$
$113$	−13.3061			−1.25173			−0.625864	+	0.779932i	$0.715254\pi$
$114$	2.74032	−	1.84788i	0.256655	−	0.173070i
$115$	−21.1845			−1.97547
$116$	0.395076	+	2.24059i	0.0366819	+	0.208033i
$117$	−2.32962	+	1.95478i	−0.215373	+	0.180719i
$118$	4.41055	−	1.60531i	0.406024	−	0.147781i
$119$	−14.0798	−	5.12464i	−1.29070	−	0.469775i
$120$	−6.29011	−	5.27803i	−0.574206	−	0.481816i
$121$	4.36736	−	7.56449i	0.397033	−	0.687681i
$122$	−0.128066	−	0.221818i	−0.0115946	−	0.0200824i
$123$	−0.00622801	+	0.0353208i	−0.000561561	+	0.00318477i
$124$	−1.21947	+	6.91594i	−0.109511	+	0.621069i
$125$	0.00565210	+	0.00978973i	0.000505539	+	0.000875620i
$126$	−1.43895	+	2.49233i	−0.128192	+	0.222035i
$127$	−11.8173	−	9.91587i	−1.04861	−	0.879891i	−0.0556663	−	0.998449i	$-0.517728\pi$
$127$	−11.8173	−	9.91587i	−1.04861	−	0.879891i	−0.992947	+	0.118558i	$0.962173\pi$
$128$	9.10521	+	3.31402i	0.804794	+	0.292921i
$129$	8.21934	−	2.99159i	0.723672	−	0.263395i
$130$	−5.58498	+	4.68635i	−0.489835	+	0.411020i
$131$	−2.26601	−	12.8512i	−0.197982	−	1.12281i	−0.908107	−	0.418738i	$-0.862473\pi$
$131$	−2.26601	−	12.8512i	−0.197982	−	1.12281i	0.710125	−	0.704076i	$-0.248638\pi$
$132$	−2.14482			−0.186683
$133$	11.4909	+	11.9021i	0.996387	+	1.03204i
$134$	4.74938			0.410284
$135$	0.549026	+	3.11368i	0.0472526	+	0.267983i
$136$	−7.85392	+	6.59022i	−0.673468	+	0.565107i
$137$	9.37493	−	3.41219i	0.800954	−	0.291523i	0.0910723	−	0.995844i	$-0.470971\pi$
$137$	9.37493	−	3.41219i	0.800954	−	0.291523i	0.709882	+	0.704321i	$0.248748\pi$
$138$	4.77416	+	1.73765i	0.406403	+	0.147919i
$139$	1.23044	+	1.03246i	0.104364	+	0.0875722i	0.693477	−	0.720479i	$-0.256078\pi$
$139$	1.23044	+	1.03246i	0.104364	+	0.0875722i	−0.589112	+	0.808051i	$0.700522\pi$
$140$	8.55034	−	14.8096i	0.722636	−	1.25164i
$141$	−3.04289	−	5.27043i	−0.256257	−	0.443850i
$142$	−0.665913	+	3.77658i	−0.0558821	+	0.316923i
$143$	−0.794807	+	4.50757i	−0.0664651	+	0.376942i
$144$	−0.440436	−	0.762858i	−0.0367030	−	0.0635715i
$145$	2.52390	−	4.37153i	0.209599	−	0.363036i
$146$	−1.92538	−	1.61559i	−0.159346	−	0.133707i
$147$	−6.95868	−	2.53275i	−0.573942	−	0.208898i
$148$	−8.41236	+	3.06185i	−0.691492	+	0.251682i
$149$	−8.46076	+	7.09942i	−0.693132	+	0.581607i	−0.919811	−	0.392363i	$-0.871658\pi$
$149$	−8.46076	+	7.09942i	−0.693132	+	0.581607i	0.226678	+	0.973970i	$0.427213\pi$
$150$	0.657876	+	3.73100i	0.0537154	+	0.304635i
$151$	15.9610			1.29888			0.649442	−	0.760411i	$-0.275002\pi$
$151$	15.9610			1.29888			0.649442	+	0.760411i	$0.275002\pi$
$152$	10.9844	−	2.73729i	0.890951	−	0.222023i
$153$	3.94776			0.319158
$154$	0.752154	+	4.26568i	0.0606103	+	0.343738i
$155$	11.9356	−	10.0152i	0.958693	−	0.804439i
$156$	−4.07236	+	1.48222i	−0.326050	+	0.118673i
$157$	2.59154	+	0.943242i	0.206827	+	0.0752789i	0.443356	−	0.896346i	$-0.353788\pi$
$157$	2.59154	+	0.943242i	0.206827	+	0.0752789i	−0.236529	+	0.971624i	$0.576010\pi$
$158$	−1.42264	−	1.19373i	−0.113179	−	0.0949683i
$159$	−4.19406	+	7.26432i	−0.332611	+	0.576098i
$160$	−9.26704	−	16.0510i	−0.732624	−	1.26894i
$161$	−4.41598	+	25.0443i	−0.348028	+	1.97376i
$162$	0.131669	−	0.746734i	0.0103449	−	0.0586690i
$163$	4.75734	+	8.23996i	0.372624	+	0.645404i	0.989968	−	0.141289i	$-0.0451248\pi$
$163$	4.75734	+	8.23996i	0.372624	+	0.645404i	−0.617344	+	0.786693i	$0.711791\pi$
$164$	−0.0255552	+	0.0442629i	−0.00199553	+	0.00345635i
$165$	3.64533	+	3.05880i	0.283789	+	0.238127i
$166$	−6.09206	−	2.21733i	−0.472836	−	0.172098i
$167$	17.1686	−	6.24886i	1.32855	−	0.483551i	0.422360	−	0.906428i	$-0.361202\pi$
$167$	17.1686	−	6.24886i	1.32855	−	0.483551i	0.906187	+	0.422877i	$0.138980\pi$
$168$	−7.55086	+	6.33592i	−0.582561	+	0.488827i
$169$	−0.651480	−	3.69473i	−0.0501139	−	0.284210i
$170$	9.46429			0.725878
$171$	−3.91752	−	1.91129i	−0.299580	−	0.146160i
$172$	12.4647			0.950424
$173$	−2.59235	−	14.7020i	−0.197093	−	1.11777i	−0.909407	−	0.415908i	$-0.863464\pi$
$173$	−2.59235	−	14.7020i	−0.197093	−	1.11777i	0.712314	−	0.701861i	$-0.247647\pi$
$174$	−0.927361	+	0.778148i	−0.0703031	+	0.0589913i
$175$	−17.8199	+	6.48592i	−1.34706	+	0.490290i
$176$	−1.24583	−	0.453446i	−0.0939082	−	0.0341798i
$177$	−4.74183	−	3.97887i	−0.356418	−	0.299070i
$178$	5.52136	−	9.56328i	0.413843	−	0.716798i
$179$	6.57096	+	11.3812i	0.491137	+	0.850674i	0.999948	−	0.0102041i	$-0.00324814\pi$
$179$	6.57096	+	11.3812i	0.491137	+	0.850674i	−0.508811	+	0.860878i	$0.669915\pi$
$180$	−0.782390	+	4.43715i	−0.0583159	+	0.330726i
$181$	1.54342	−	8.75317i	0.114722	−	0.650618i	−0.872166	−	0.489210i	$-0.837285\pi$
$181$	1.54342	−	8.75317i	0.114722	−	0.650618i	0.986888	−	0.161408i	$-0.0516036\pi$
$182$	4.37598	+	7.57943i	0.324369	+	0.561824i
$183$	−0.168897	+	0.292537i	−0.0124852	+	0.0216250i
$184$	13.3301	+	11.1852i	0.982704	+	0.824587i
$185$	18.6642	+	6.79322i	1.37222	+	0.499447i
$186$	−3.51131	+	1.27801i	−0.257462	+	0.0937085i
$187$	4.55162	−	3.81926i	0.332847	−	0.279292i
$188$	−1.50597	−	8.54078i	−0.109834	−	0.622900i
$189$	3.79543			0.276077
$190$	−9.39178	−	4.58210i	−0.681352	−	0.332420i
$191$	−4.40795			−0.318948			−0.159474	−	0.987202i	$-0.550980\pi$
$191$	−4.40795			−0.318948			−0.159474	+	0.987202i	$0.550980\pi$
$192$	0.465928	+	2.64241i	0.0336254	+	0.190699i
$193$	−0.522180	+	0.438161i	−0.0375873	+	0.0315395i	−0.661388	−	0.750044i	$-0.730032\pi$
$193$	−0.522180	+	0.438161i	−0.0375873	+	0.0315395i	0.623800	+	0.781584i	$0.285588\pi$
$194$	−12.3241	+	4.48559i	−0.884817	+	0.322047i
$195$	9.03522	+	3.28855i	0.647025	+	0.235498i
$196$	−8.08398	−	6.78327i	−0.577427	−	0.484519i
$197$	4.75933	−	8.24341i	0.339089	−	0.587319i	−0.645173	−	0.764037i	$-0.723215\pi$
$197$	4.75933	−	8.24341i	0.339089	−	0.587319i	0.984262	+	0.176718i	$0.0565480\pi$
$198$	−0.570618	−	0.988340i	−0.0405521	−	0.0702382i
$199$	−1.60085	+	9.07885i	−0.113481	+	0.643583i	0.874010	+	0.485908i	$0.161511\pi$
$199$	−1.60085	+	9.07885i	−0.113481	+	0.643583i	−0.987491	+	0.157675i	$0.949600\pi$
$200$	−2.25326	+	12.7789i	−0.159330	+	0.903603i
$201$	−3.13179	−	5.42442i	−0.220899	−	0.382609i
$202$	−4.40561	+	7.63075i	−0.309978	+	0.536898i
$203$	−4.64189	−	3.89501i	−0.325797	−	0.273376i
$204$	5.28649	+	1.92412i	0.370128	+	0.134716i
$205$	0.106558	−	0.0387840i	0.00744235	−	0.00270879i
$206$	1.23530	−	1.03654i	0.0860676	−	0.0722193i
$207$	−1.16350	−	6.59854i	−0.0808688	−	0.458630i
$208$	−2.67882			−0.185743
$209$	−6.36583	+	1.58635i	−0.440334	+	0.109730i
$210$	9.09908			0.627896
$211$	1.05360	+	5.97527i	0.0725329	+	0.411355i	0.999357	+	0.0358585i	$0.0114166\pi$
$211$	1.05360	+	5.97527i	0.0725329	+	0.411355i	−0.926824	+	0.375496i	$0.877472\pi$
$212$	−9.15691	+	7.68356i	−0.628899	+	0.527709i
$213$	4.75246	−	1.72975i	0.325633	−	0.118521i
$214$	−4.97048	−	1.80911i	−0.339775	−	0.123668i
$215$	−21.1849	−	17.7763i	−1.44480	−	1.21233i
$216$	1.29853	−	2.24912i	0.0883537	−	0.153033i
$217$	−9.35190	−	16.1980i	−0.634848	−	1.09959i
$218$	0.443949	−	2.51776i	0.0300680	−	0.170524i
$219$	−0.575597	+	3.26437i	−0.0388952	+	0.220586i
$220$	3.39066	+	5.87279i	0.228598	+	0.395943i
$221$	6.00276	−	10.3971i	0.403790	−	0.699384i
$222$	−3.64897	−	3.06185i	−0.244903	−	0.205498i
$223$	−1.05040	−	0.382313i	−0.0703397	−	0.0256016i	0.306611	−	0.951835i	$-0.400805\pi$
$223$	−1.05040	−	0.382313i	−0.0703397	−	0.0256016i	−0.376950	+	0.926233i	$0.623027\pi$
$224$	−20.9072	+	7.60959i	−1.39692	+	0.508437i
$225$	3.82748	−	3.21164i	0.255166	−	0.214109i
$226$	−1.75200	−	9.93609i	−0.116541	−	0.660939i
$227$	4.93647			0.327645			0.163823	−	0.986490i	$-0.447618\pi$
$227$	4.93647			0.327645			0.163823	+	0.986490i	$0.447618\pi$
$228$	−4.31443	−	4.46882i	−0.285730	−	0.295955i
$229$	29.2267			1.93135			0.965676	−	0.259748i	$-0.0836395\pi$
$229$	29.2267			1.93135			0.965676	+	0.259748i	$0.0836395\pi$
$230$	−2.78935	−	15.8192i	−0.183924	−	1.04309i
$231$	4.37598	−	3.67189i	0.287919	−	0.241592i
$232$	−3.89626	+	1.41812i	−0.255802	+	0.0931043i
$233$	−24.2430	−	8.82373i	−1.58821	−	0.578062i	−0.611243	−	0.791443i	$-0.709330\pi$
$233$	−24.2430	−	8.82373i	−1.58821	−	0.578062i	−0.976969	+	0.213381i	$0.931552\pi$
$234$	−1.76644	−	1.48222i	−0.115476	−	0.0968957i
$235$	−9.62073	+	16.6636i	−0.627587	+	1.08701i
$236$	−4.41055	−	7.63930i	−0.287102	−	0.497276i
$237$	−0.425300	+	2.41200i	−0.0276262	+	0.156676i
$238$	1.97286	−	11.1887i	0.127882	−	0.725253i
$239$	11.2784	+	19.5347i	0.729537	+	1.26359i	0.957079	+	0.289826i	$0.0935976\pi$
$239$	11.2784	+	19.5347i	0.729537	+	1.26359i	−0.227543	+	0.973768i	$0.573069\pi$
$240$	−1.39253	+	2.41194i	−0.0898876	+	0.155690i
$241$	8.35097	+	7.00730i	0.537933	+	0.451380i	0.870830	−	0.491584i	$-0.163582\pi$
$241$	8.35097	+	7.00730i	0.537933	+	0.451380i	−0.332897	+	0.942963i	$0.608026\pi$
$242$	6.22371	+	2.26525i	0.400075	+	0.145615i
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$	−0.368753	+	0.309420i	−0.0236070	+	0.0198086i
$245$	4.06568	+	23.0576i	0.259747	+	1.47310i
$246$	−0.0271953			−0.00173391
$247$	−10.9905	+	7.41123i	−0.699308	+	0.471565i
$248$	−12.7983			−0.812690
$249$	1.48468	+	8.42006i	0.0940880	+	0.533600i
$250$	−0.00656612	+	0.00550963i	−0.000415278	+	0.000348459i
$251$	2.18678	−	0.795921i	0.138028	−	0.0502381i	−0.272082	−	0.962274i	$-0.587712\pi$
$251$	2.18678	−	0.795921i	0.138028	−	0.0502381i	0.410111	+	0.912036i	$0.365490\pi$
$252$	5.08250	+	1.84988i	0.320167	+	0.116531i
$253$	−7.72522	−	6.48223i	−0.485681	−	0.407535i
$254$	5.84855	−	10.1300i	0.366970	−	0.635611i
$255$	−6.24084	−	10.8095i	−0.390817	−	0.676914i
$256$	−2.20767	+	12.5203i	−0.137980	+	0.782521i
$257$	−4.74371	+	26.9029i	−0.295904	+	1.67816i	0.367600	+	0.929984i	$0.380180\pi$
$257$	−4.74371	+	26.9029i	−0.295904	+	1.67816i	−0.663504	+	0.748172i	$0.730932\pi$
$258$	3.31616	+	5.74376i	0.206455	+	0.357591i
$259$	11.9215	−	20.6487i	0.740768	−	1.28305i
$260$	10.4963	+	8.80746i	0.650954	+	0.546215i
$261$	1.50026	+	0.546049i	0.0928637	+	0.0337996i
$262$	9.29806	−	3.38422i	0.574436	−	0.209078i
$263$	−9.85482	+	8.26917i	−0.607674	+	0.509899i	−0.893902	−	0.448262i	$-0.852043\pi$
$263$	−9.85482	+	8.26917i	−0.607674	+	0.509899i	0.286228	+	0.958162i	$0.407599\pi$
$264$	−0.678755	−	3.84941i	−0.0417745	−	0.236915i
$265$	26.5208			1.62916
$266$	−7.37469	+	10.1478i	−0.452171	+	0.622201i
$267$	−14.5634			−0.891263
$268$	−1.54997	−	8.79032i	−0.0946795	−	0.536954i
$269$	8.96367	−	7.52141i	0.546524	−	0.458588i	−0.327238	−	0.944942i	$-0.606118\pi$
$269$	8.96367	−	7.52141i	0.546524	−	0.458588i	0.873762	+	0.486354i	$0.161673\pi$
$270$	−2.25280	+	0.819952i	−0.137101	+	0.0499007i
$271$	−3.41974	−	1.24468i	−0.207734	−	0.0756092i	0.236057	−	0.971739i	$-0.424145\pi$
$271$	−3.41974	−	1.24468i	−0.207734	−	0.0756092i	−0.443792	+	0.896130i	$0.646367\pi$
$272$	2.66390	+	2.23528i	0.161523	+	0.135534i
$273$	5.77113	−	9.99590i	0.349285	−	0.604979i
$274$	3.78239	+	6.55130i	0.228503	+	0.395778i
$275$	1.30584	−	7.40580i	0.0787452	−	0.446586i
$276$	1.65805	−	9.40325i	0.0998027	−	0.566009i
$277$	−5.84247	−	10.1195i	−0.351040	−	0.608019i	0.635392	−	0.772190i	$-0.280839\pi$
$277$	−5.84247	−	10.1195i	−0.351040	−	0.608019i	−0.986432	+	0.164171i	$0.947505\pi$
$278$	−0.608963	+	1.05475i	−0.0365232	+	0.0632600i
$279$	3.77505	+	3.16765i	0.226007	+	0.189642i
$280$	29.2854	+	10.6590i	1.75014	+	0.636997i
$281$	19.7440	−	7.18623i	1.17783	−	0.428695i	0.322394	−	0.946605i	$-0.395512\pi$
$281$	19.7440	−	7.18623i	1.17783	−	0.428695i	0.855435	+	0.517911i	$0.173290\pi$
$282$	3.53496	−	2.96618i	0.210504	−	0.176634i
$283$	1.00588	+	5.70463i	0.0597934	+	0.339105i	0.999999	−	0.00150258i	$-0.000478286\pi$
$283$	1.00588	+	5.70463i	0.0597934	+	0.339105i	−0.940205	+	0.340608i	$0.889367\pi$
$284$	7.20714			0.427665
$285$	0.959674	+	13.7481i	0.0568462	+	0.814369i
$286$	−3.47061			−0.205222
$287$	−0.0236380	−	0.134058i	−0.00139530	−	0.00791317i
$288$	4.49058	−	3.76805i	0.264610	−	0.222034i
$289$	1.32983	−	0.484019i	0.0782254	−	0.0284717i
$290$	3.59669	+	1.30909i	0.211205	+	0.0768723i
$291$	13.2498	+	11.1179i	0.776714	+	0.651741i
$292$	−2.36183	+	4.09081i	−0.138216	+	0.239397i
$293$	−13.6326	−	23.6123i	−0.796423	−	1.37944i	−0.921932	−	0.387352i	$-0.873390\pi$
$293$	−13.6326	−	23.6123i	−0.796423	−	1.37944i	0.125509	−	0.992092i	$-0.459944\pi$
$294$	0.975048	−	5.52977i	0.0568659	−	0.322503i
$295$	−3.39848	+	19.2737i	−0.197867	+	1.12216i
$296$	−8.15743	−	14.1291i	−0.474141	−	0.821236i
$297$	−0.752542	+	1.30344i	−0.0436669	+	0.0756334i
$298$	−6.41540	−	5.38316i	−0.371634	−	0.311838i
$299$	−19.1475	−	6.96912i	−1.10733	−	0.403035i
$300$	6.69076	−	2.43524i	0.386291	−	0.140599i
$301$	−25.4311	+	21.3393i	−1.46583	+	1.22997i
$302$	2.10157	+	11.9186i	0.120932	+	0.685838i
$303$	11.6204			0.667576
$304$	−1.56129	−	3.50787i	−0.0895462	−	0.201190i
$305$	1.06800			0.0611538
$306$	0.519799	+	2.94793i	0.0297150	+	0.168522i
$307$	10.1688	−	8.53266i	0.580366	−	0.486985i	−0.304702	−	0.952448i	$-0.598557\pi$
$307$	10.1688	−	8.53266i	0.580366	−	0.486985i	0.885067	+	0.465463i	$0.154112\pi$
$308$	7.64959	−	2.78422i	0.435876	−	0.158646i
$309$	−1.99844	−	0.727372i	−0.113687	−	0.0413787i
$310$	9.05024	+	7.59405i	0.514019	+	0.431313i
$311$	−1.14404	+	1.98154i	−0.0648726	+	0.112363i	−0.896637	−	0.442765i	$-0.853997\pi$
$311$	−1.14404	+	1.98154i	−0.0648726	+	0.112363i	0.831765	+	0.555128i	$0.187331\pi$
$312$	−3.94895	−	6.83979i	−0.223565	−	0.387227i
$313$	3.97698	−	22.5546i	0.224792	−	1.27486i	−0.638290	−	0.769796i	$-0.720358\pi$
$313$	3.97698	−	22.5546i	0.224792	−	1.27486i	0.863082	−	0.505064i	$-0.168531\pi$
$314$	−0.363125	+	2.05938i	−0.0204923	+	0.116218i
$315$	−6.00003	−	10.3923i	−0.338063	−	0.585543i
$316$	−1.74512	+	3.02264i	−0.0981707	+	0.170037i
$317$	−14.6921	−	12.3281i	−0.825190	−	0.692417i	0.128991	−	0.991646i	$-0.458826\pi$
$317$	−14.6921	−	12.3281i	−0.825190	−	0.692417i	−0.954181	+	0.299229i	$0.903271\pi$
$318$	−5.97675	−	2.17536i	−0.335159	−	0.121988i
$319$	2.25802	−	0.821851i	0.126425	−	0.0460148i
$320$	6.49867	−	5.45303i	0.363287	−	0.304834i
$321$	1.21135	+	6.86989i	0.0676108	+	0.383440i
$322$	−19.2829			−1.07459
$323$	17.1134	+	1.80081i	0.952215	+	0.100200i
$324$	−1.42505			−0.0791695
$325$	−2.63852	−	14.9638i	−0.146359	−	0.830041i
$326$	−5.52666	+	4.63742i	−0.306094	+	0.256843i
$327$	−3.16836	+	1.15319i	−0.175211	+	0.0637714i
$328$	−0.0875279	−	0.0318576i	−0.00483292	−	0.00175904i
$329$	17.6942	+	14.8472i	0.975511	+	0.818551i
$330$	−1.80413	+	3.12485i	−0.0993141	+	0.172017i
$331$	−0.193669	−	0.335444i	−0.0106450	−	0.0184377i	0.860654	−	0.509191i	$-0.170055\pi$
$331$	−0.193669	−	0.335444i	−0.0106450	−	0.0184377i	−0.871299	+	0.490753i	$0.836722\pi$
$332$	−2.11575	+	11.9990i	−0.116117	+	0.658532i
$333$	−1.09087	+	6.18661i	−0.0597791	+	0.339024i
$334$	6.92682	+	11.9976i	0.379019	+	0.656480i
$335$	−9.90182	+	17.1505i	−0.540994	+	0.937029i
$336$	2.56111	+	2.14902i	0.139720	+	0.117239i
$337$	−19.0936	−	6.94951i	−1.04010	−	0.378564i	−0.235180	−	0.971952i	$-0.575568\pi$
$337$	−19.0936	−	6.94951i	−1.04010	−	0.378564i	−0.804917	+	0.593388i	$0.797790\pi$
$338$	2.67320	−	0.972965i	0.145403	−	0.0529223i
$339$	−10.1930	+	8.55297i	−0.553609	+	0.464534i
$340$	−3.08869	−	17.5168i	−0.167508	−	0.949983i
$341$	7.41703			0.401655
$342$	0.911412	−	3.17700i	0.0492835	−	0.171793i
$343$	1.53818			0.0830538
$344$	3.94460	+	22.3709i	0.212679	+	1.20616i
$345$	−16.2283	+	13.6171i	−0.873701	+	0.733122i
$346$	10.6371	−	3.87160i	0.571855	−	0.208138i
$347$	13.0924	+	4.76525i	0.702837	+	0.255812i	0.668622	−	0.743603i	$-0.266885\pi$
$347$	13.0924	+	4.76525i	0.702837	+	0.255812i	0.0342153	+	0.999414i	$0.489107\pi$
$348$	1.74287	+	1.46244i	0.0934276	+	0.0783950i
$349$	−8.64464	+	14.9730i	−0.462737	+	0.801484i	−0.999096	−	0.0425058i	$-0.986466\pi$
$349$	−8.64464	+	14.9730i	−0.462737	+	0.801484i	0.536359	+	0.843990i	$0.319799\pi$
$350$	−7.18960	−	12.4528i	−0.384300	−	0.665628i
$351$	−0.528081	+	2.99490i	−0.0281869	+	0.159856i
$352$	1.53208	−	8.68883i	0.0816599	−	0.463116i
$353$	−3.42597	−	5.93396i	−0.182346	−	0.315833i	0.760333	−	0.649534i	$-0.225036\pi$
$353$	−3.42597	−	5.93396i	−0.182346	−	0.315833i	−0.942679	+	0.333701i	$0.891702\pi$
$354$	2.34680	−	4.06479i	0.124731	−	0.216041i
$355$	−12.2492	−	10.2783i	−0.650121	−	0.545517i
$356$	−19.5019	−	7.09812i	−1.03360	−	0.376200i
$357$	−14.0798	+	5.12464i	−0.745184	+	0.271225i
$358$	−7.63357	+	6.40533i	−0.403447	+	0.338532i
$359$	−2.71139	−	15.3771i	−0.143102	−	0.811571i	−0.968872	−	0.247564i	$-0.920370\pi$
$359$	−2.71139	−	15.3771i	−0.143102	−	0.811571i	0.825770	−	0.564008i	$-0.190741\pi$
$360$	−8.21115			−0.432766
$361$	−16.1105	−	10.0724i	−0.847919	−	0.530127i
$362$	6.73951			0.354221
$363$	−1.51677	−	8.60202i	−0.0796097	−	0.451489i
$364$	12.6001	−	10.5728i	0.660427	−	0.554164i
$365$	9.84819	−	3.58445i	0.515478	−	0.187619i
$366$	−0.240686	−	0.0876026i	−0.0125809	−	0.00457906i
$367$	−8.42265	−	7.06744i	−0.439659	−	0.368918i	0.395923	−	0.918284i	$-0.370425\pi$
$367$	−8.42265	−	7.06744i	−0.439659	−	0.368918i	−0.835582	+	0.549366i	$0.814869\pi$
$368$	2.95107	−	5.11140i	0.153835	−	0.266450i
$369$	0.0179328	+	0.0310606i	0.000933546	+	0.00161695i
$370$	−2.61522	+	14.8317i	−0.135959	+	0.771062i
$371$	5.52835	−	31.3528i	0.287018	−	1.62776i
$372$	3.51131	+	6.08177i	0.182053	+	0.315325i
$373$	−8.59138	+	14.8807i	−0.444845	+	0.770494i	−0.998041	−	0.0625568i	$-0.980075\pi$
$373$	−8.59138	+	14.8807i	−0.444845	+	0.770494i	0.553196	+	0.833051i	$0.313408\pi$
$374$	3.45128	+	2.89597i	0.178462	+	0.149747i
$375$	0.0106225	+	0.00386627i	0.000548542	+	0.000199653i
$376$	14.8519	−	5.40566i	0.765930	−	0.278776i
$377$	3.71933	−	3.12089i	0.191555	−	0.160734i
$378$	0.499742	+	2.83418i	0.0257039	+	0.145774i
$379$	−16.4266			−0.843777			−0.421889	−	0.906648i	$-0.638633\pi$
$379$	−16.4266			−0.843777			−0.421889	+	0.906648i	$0.638633\pi$
$380$	−5.41568	+	18.8780i	−0.277818	+	0.968421i
$381$	−15.4264			−0.790316
$382$	−0.580393	−	3.29157i	−0.0296955	−	0.168411i
$383$	1.79184	−	1.50353i	0.0915587	−	0.0768268i	−0.595859	−	0.803089i	$-0.703188\pi$
$383$	1.79184	−	1.50353i	0.0915587	−	0.0768268i	0.687418	+	0.726262i	$0.258744\pi$
$384$	9.10521	−	3.31402i	0.464648	−	0.169118i
$385$	−16.9719	−	6.17726i	−0.864967	−	0.314822i
$386$	−0.395945	−	0.332237i	−0.0201531	−	0.0169104i
$387$	4.37342	−	7.57498i	0.222313	−	0.385058i
$388$	12.3241	+	21.3459i	0.625660	+	1.08367i
$389$	3.27782	−	18.5894i	0.166192	−	0.942522i	−0.781635	−	0.623736i	$-0.785614\pi$
$389$	3.27782	−	18.5894i	0.166192	−	0.942522i	0.947827	−	0.318786i	$-0.103275\pi$
$390$	−1.26601	+	7.17991i	−0.0641070	+	0.363569i
$391$	13.2257	+	22.9075i	0.668850	+	1.15848i
$392$	9.61596	−	16.6553i	0.485679	−	0.841221i
$393$	−9.99645	−	8.38802i	−0.504254	−	0.423120i
$394$	6.78229	+	2.46855i	0.341687	+	0.124364i
$395$	7.27668	−	2.64849i	0.366129	−	0.133260i
$396$	−1.64303	+	1.37867i	−0.0825653	+	0.0692806i
$397$	4.36263	+	24.7417i	0.218954	+	1.24175i	0.873911	+	0.486085i	$0.161576\pi$
$397$	4.36263	+	24.7417i	0.218954	+	1.24175i	−0.654957	+	0.755666i	$0.727313\pi$
$398$	−6.99027			−0.350391
$399$	16.4530	+	1.73132i	0.823683	+	0.0866743i
$400$	4.40121			0.220061
$401$	0.0509173	+	0.288767i	0.00254269	+	0.0144203i	0.986053	−	0.166433i	$-0.0532251\pi$
$401$	0.0509173	+	0.288767i	0.00254269	+	0.0144203i	−0.983510	+	0.180854i	$0.942114\pi$
$402$	3.63824	−	3.05285i	0.181459	−	0.152262i
$403$	14.0827	−	5.12568i	0.701508	−	0.255328i
$404$	15.5610	+	5.66375i	0.774190	+	0.281782i
$405$	2.42201	+	2.03231i	0.120351	+	0.100986i
$406$	2.29734	−	3.97911i	0.114015	−	0.197480i
$407$	4.72751	+	8.18829i	0.234334	+	0.405878i
$408$	−1.78034	+	10.0968i	−0.0881399	+	0.499866i
$409$	−2.04894	+	11.6201i	−0.101314	+	0.574578i	0.891315	+	0.453384i	$0.149783\pi$
$409$	−2.04894	+	11.6201i	−0.101314	+	0.574578i	−0.992629	+	0.121194i	$0.961328\pi$
$410$	0.0429918	+	0.0744640i	0.00212322	+	0.00367752i
$411$	4.98830	−	8.63998i	0.246054	−	0.426179i
$412$	−2.32161	−	1.94806i	−0.114377	−	0.0959741i
$413$	22.0769	+	8.03535i	1.08634	+	0.395394i
$414$	4.77416	−	1.73765i	0.234637	−	0.0854009i
$415$	20.7081	−	17.3762i	1.01652	−	0.852962i
$416$	−3.09563	−	17.5562i	−0.151776	−	0.860764i
$417$	1.60622			0.0786571
$418$	−2.02277	−	4.54471i	−0.0989369	−	0.222289i
$419$	21.3599			1.04350			0.521750	−	0.853099i	$-0.325279\pi$
$419$	21.3599			1.04350			0.521750	+	0.853099i	$0.325279\pi$
$420$	−2.96950	−	16.8409i	−0.144897	−	0.821751i
$421$	−13.0042	+	10.9118i	−0.633784	+	0.531808i	−0.902102	−	0.431522i	$-0.857977\pi$
$421$	−13.0042	+	10.9118i	−0.633784	+	0.531808i	0.268318	+	0.963330i	$0.413532\pi$
$422$	−4.32321	+	1.57352i	−0.210451	+	0.0765978i
$423$	−5.71875	−	2.08146i	−0.278055	−	0.101204i
$424$	−16.6878	−	14.0028i	−0.810433	−	0.680034i
$425$	−9.86235	+	17.0821i	−0.478394	+	0.828603i
$426$	1.91742	+	3.32107i	0.0928992	+	0.160906i
$427$	0.222629	−	1.26259i	0.0107738	−	0.0611011i
$428$	−1.72623	+	9.78994i	−0.0834405	+	0.473215i
$429$	2.28856	+	3.96389i	0.110492	+	0.191379i
$430$	10.4847	−	18.1601i	0.505620	−	0.875759i
$431$	20.6462	+	17.3242i	0.994493	+	0.834478i	0.986212	−	0.165487i	$-0.0529197\pi$
$431$	20.6462	+	17.3242i	0.994493	+	0.834478i	0.00828071	+	0.999966i	$0.497364\pi$
$432$	−0.827750	−	0.301276i	−0.0398251	−	0.0144952i
$433$	−17.5735	+	6.39622i	−0.844527	+	0.307383i	−0.727807	−	0.685782i	$-0.759460\pi$
$433$	−17.5735	+	6.39622i	−0.844527	+	0.307383i	−0.116720	+	0.993165i	$0.537238\pi$
$434$	10.8642	−	9.11616i	0.521499	−	0.437590i
$435$	−0.876542	−	4.97112i	−0.0420270	−	0.238347i
$436$	−4.80484			−0.230110
$437$	−2.03375	−	29.1352i	−0.0972875	−	1.39372i
$438$	−2.51341			−0.120095
$439$	2.57733	+	14.6167i	0.123009	+	0.697619i	0.982470	+	0.186418i	$0.0596880\pi$
$439$	2.57733	+	14.6167i	0.123009	+	0.697619i	−0.859461	+	0.511201i	$0.829201\pi$
$440$	−9.46714	+	7.94388i	−0.451328	+	0.378709i
$441$	−6.95868	+	2.53275i	−0.331366	+	0.120607i
$442$	8.55425	+	3.11349i	0.406884	+	0.148094i
$443$	−2.51311	−	2.10875i	−0.119402	−	0.100190i	0.581132	−	0.813809i	$-0.302610\pi$
$443$	−2.51311	−	2.10875i	−0.119402	−	0.100190i	−0.700533	+	0.713620i	$0.747055\pi$
$444$	−4.47612	+	7.75287i	−0.212427	+	0.367935i
$445$	23.0226	+	39.8763i	1.09137	+	1.89032i
$446$	0.147181	−	0.834705i	0.00696923	−	0.0395244i
$447$	−1.91790	+	10.8769i	−0.0907135	+	0.514462i
$448$	−5.09189	−	8.81941i	−0.240569	−	0.416678i
$449$	−14.4876	+	25.0933i	−0.683714	+	1.18423i	0.290125	+	0.956989i	$0.406303\pi$
$449$	−14.4876	+	25.0933i	−0.683714	+	1.18423i	−0.973839	+	0.227238i	$0.927030\pi$
$450$	2.90220	+	2.43524i	0.136811	+	0.114798i
$451$	0.0507254	+	0.0184626i	0.00238857	+	0.000869368i
$452$	−17.8183	+	6.48532i	−0.838101	+	0.305044i
$453$	12.2268	−	10.2595i	0.574465	−	0.482034i
$454$	0.649982	+	3.68623i	0.0305052	+	0.173004i
$455$	−36.4933			−1.71083
$456$	6.65503	−	9.15751i	0.311650	−	0.428840i
$457$	9.18203			0.429517			0.214759	−	0.976667i	$-0.431104\pi$
$457$	9.18203			0.429517			0.214759	+	0.976667i	$0.431104\pi$
$458$	3.84826	+	21.8246i	0.179817	+	1.01979i
$459$	3.02416	−	2.53757i	0.141156	−	0.118444i
$460$	−28.3684	+	10.3253i	−1.32268	+	0.481417i
$461$	8.78792	+	3.19854i	0.409294	+	0.148971i	0.538458	−	0.842652i	$-0.319007\pi$
$461$	8.78792	+	3.19854i	0.409294	+	0.148971i	−0.129164	+	0.991623i	$0.541229\pi$
$462$	3.31811	+	2.78422i	0.154372	+	0.129534i
$463$	17.7097	−	30.6742i	0.823041	−	1.42555i	−0.0803655	−	0.996765i	$-0.525609\pi$
$463$	17.7097	−	30.6742i	0.823041	−	1.42555i	0.903407	−	0.428784i	$-0.141058\pi$
$464$	0.703175	+	1.21793i	0.0326441	+	0.0565412i
$465$	2.70559	−	15.3442i	0.125469	−	0.711568i
$466$	3.39692	−	19.2649i	0.157359	−	0.892429i
$467$	−0.930946	−	1.61245i	−0.0430790	−	0.0746151i	0.843682	−	0.536843i	$-0.180383\pi$
$467$	−0.930946	−	1.61245i	−0.0430790	−	0.0746151i	−0.886761	+	0.462228i	$0.847050\pi$
$468$	−2.16686	+	3.75311i	−0.100163	+	0.173488i
$469$	18.2111	+	15.2810i	0.840913	+	0.705610i
$470$	−13.7100	−	4.99004i	−0.632396	−	0.230173i
$471$	2.59154	−	0.943242i	0.119412	−	0.0434623i
$472$	12.3148	−	10.3334i	0.566835	−	0.475631i
$473$	−2.28603	−	12.9647i	−0.105112	−	0.596119i
$474$	−1.85712			−0.0853003
$475$	18.0570	−	12.1764i	0.828513	−	0.558692i
$476$	−21.3522			−0.978675
$477$	1.45658	+	8.26068i	0.0666923	+	0.378231i
$478$	−13.1022	+	10.9941i	−0.599281	+	0.502857i
$479$	−12.0196	+	4.37477i	−0.549188	+	0.199888i	−0.601686	−	0.798733i	$-0.705504\pi$
$479$	−12.0196	+	4.37477i	−0.549188	+	0.199888i	0.0524975	+	0.998621i	$0.483282\pi$
$480$	−17.4163	−	6.33903i	−0.794944	−	0.289336i
$481$	14.6348	+	12.2800i	0.667288	+	0.559921i
$482$	−4.13302	+	7.15860i	−0.188254	+	0.326065i
$483$	12.7153	+	22.0236i	0.578567	+	1.00211i
$484$	2.16147	−	12.2583i	0.0982487	−	0.557196i
$485$	9.49612	−	53.8552i	0.431197	−	2.44544i
$486$	−0.379127	−	0.656667i	−0.0171975	−	0.0297870i
$487$	16.7764	−	29.0576i	0.760211	−	1.31672i	−0.182531	−	0.983200i	$-0.558429\pi$
$487$	16.7764	−	29.0576i	0.760211	−	1.31672i	0.942742	−	0.333524i	$-0.108238\pi$
$488$	−0.672027	−	0.563897i	−0.0304212	−	0.0255264i
$489$	8.94088	+	3.25421i	0.404321	+	0.147161i
$490$	−16.6826	+	6.07197i	−0.753643	+	0.274304i
$491$	−13.7080	+	11.5024i	−0.618635	+	0.519096i	−0.897374	−	0.441270i	$-0.854528\pi$
$491$	−13.7080	+	11.5024i	−0.618635	+	0.519096i	0.278739	+	0.960367i	$0.410084\pi$
$492$	0.00887523	+	0.0503339i	0.000400126	+	0.00226923i
$493$	−6.30277			−0.283862
$494$	−6.98133	−	7.23115i	−0.314105	−	0.325345i
$495$	4.75865			0.213885
$496$	0.753794	+	4.27498i	0.0338463	+	0.191952i
$497$	−14.7044	+	12.3384i	−0.659582	+	0.553455i
$498$	−6.09206	+	2.21733i	−0.272992	+	0.0993609i
$499$	−7.35122	−	2.67562i	−0.329086	−	0.119777i	0.172193	−	0.985063i	$-0.444915\pi$
$499$	−7.35122	−	2.67562i	−0.329086	−	0.119777i	−0.501279	+	0.865286i	$0.667137\pi$
$500$	0.0123403	+	0.0103547i	0.000551873	+	0.000463077i
$501$	9.13522	−	15.8227i	0.408132	−	0.706905i
$502$	0.882273	+	1.52814i	0.0393778	+	0.0682043i
$503$	−2.98432	+	16.9249i	−0.133064	+	0.754645i	0.843124	+	0.537720i	$0.180714\pi$
$503$	−2.98432	+	16.9249i	−0.133064	+	0.754645i	−0.976188	+	0.216926i	$0.930397\pi$
$504$	−1.71164	+	9.70720i	−0.0762425	+	0.432393i
$505$	−18.3702	−	31.8181i	−0.817464	−	1.41589i
$506$	3.82333	−	6.62220i	0.169968	−	0.294393i
$507$	−2.87399	−	2.41156i	−0.127638	−	0.107101i
$508$	−20.6576	−	7.51875i	−0.916532	−	0.333590i
$509$	−29.5175	+	10.7435i	−1.30834	+	0.476196i	−0.899703	−	0.436502i	$-0.856217\pi$
$509$	−29.5175	+	10.7435i	−1.30834	+	0.476196i	−0.408635	+	0.912698i	$0.633995\pi$
$510$	7.25006	−	6.08353i	0.321038	−	0.269383i
$511$	−2.18464	−	12.3897i	−0.0966426	−	0.548088i
$512$	9.73907			0.430410
$513$	−4.22955	+	1.05400i	−0.186739	+	0.0465351i
$514$	−20.7139			−0.913652
$515$	1.16761	+	6.62184i	0.0514510	+	0.291793i
$516$	9.54851	−	8.01215i	0.420350	−	0.352715i
$517$	−8.60721	+	3.13277i	−0.378545	+	0.137779i
$518$	16.9888	+	6.18342i	0.746445	+	0.271684i
$519$	−11.4361	−	9.59602i	−0.501989	−	0.421219i
$520$	−12.4855	+	21.6254i	−0.547523	+	0.948338i
$521$	9.56803	+	16.5723i	0.419183	+	0.726046i	0.995858	−	0.0909277i	$-0.0289832\pi$
$521$	9.56803	+	16.5723i	0.419183	+	0.726046i	−0.576674	+	0.816974i	$0.695650\pi$
$522$	−0.210216	+	1.19219i	−0.00920089	+	0.0521808i
$523$	−3.46972	+	19.6777i	−0.151720	+	0.860447i	0.810003	+	0.586425i	$0.199465\pi$
$523$	−3.46972	+	19.6777i	−0.151720	+	0.860447i	−0.961723	+	0.274022i	$0.911646\pi$
$524$	−9.29806	−	16.1047i	−0.406188	−	0.703537i
$525$	−9.48178	+	16.4229i	−0.413819	+	0.716756i
$526$	−7.47245	−	6.27013i	−0.325814	−	0.273391i
$527$	−18.2812	−	6.65383i	−0.796344	−	0.289845i
$528$	−1.24583	+	0.453446i	−0.0542179	+	0.0197337i
$529$	16.7721	−	14.0735i	0.729221	−	0.611889i
$530$	3.49198	+	19.8040i	0.151682	+	0.860231i
$531$	−6.19002			−0.268624
$532$	21.1886	+	10.3376i	0.918642	+	0.448191i
$533$	0.109071			0.00472439
$534$	−1.91755	−	10.8750i	−0.0829804	−	0.470605i
$535$	16.8956	−	14.1771i	0.730462	−	0.612930i
$536$	15.2859	−	5.56360i	0.660249	−	0.240311i
$537$	12.3494	+	4.49480i	0.532915	+	0.193965i
$538$	6.79674	+	5.70314i	0.293028	+	0.245880i
$539$	−5.57278	+	9.65234i	−0.240037	+	0.415756i
$540$	2.25280	+	3.90197i	0.0969451	+	0.167914i
$541$	4.13910	−	23.4740i	0.177954	−	1.00923i	−0.756725	−	0.653733i	$-0.773202\pi$
$541$	4.13910	−	23.4740i	0.177954	−	1.00923i	0.934679	−	0.355493i	$-0.115687\pi$
$542$	0.479173	−	2.71752i	0.0205822	−	0.116728i
$543$	−4.44410	−	7.69741i	−0.190715	−	0.330327i
$544$	−11.5710	+	20.0415i	−0.496101	+	0.859273i
$545$	8.16629	+	6.85233i	0.349805	+	0.293522i
$546$	8.22416	+	2.99335i	0.351962	+	0.128104i
$547$	−19.4454	+	7.07754i	−0.831424	+	0.302614i	−0.722443	−	0.691430i	$-0.756981\pi$
$547$	−19.4454	+	7.07754i	−0.831424	+	0.302614i	−0.108981	+	0.994044i	$0.534759\pi$
$548$	10.8910	−	9.13861i	0.465239	−	0.390382i
$549$	0.0586572	+	0.332661i	0.00250343	+	0.0141976i
$550$	5.70210			0.243138
$551$	6.25448	+	3.05146i	0.266450	+	0.129997i
$552$	17.4011			0.740642
$553$	−1.61420	−	9.15456i	−0.0686426	−	0.389291i
$554$	6.78727	−	5.69519i	0.288363	−	0.241966i
$555$	18.6642	−	6.79322i	0.792252	−	0.288356i
$556$	2.15091	+	0.782868i	0.0912189	+	0.0332010i
$557$	−9.63965	−	8.08863i	−0.408445	−	0.342726i	0.415302	−	0.909684i	$-0.363676\pi$
$557$	−9.63965	−	8.08863i	−0.408445	−	0.342726i	−0.823747	+	0.566957i	$0.808120\pi$
$558$	−1.86833	+	3.23604i	−0.0790927	+	0.136993i
$559$	−13.3000	−	23.0363i	−0.562530	−	0.974330i
$560$	1.83555	−	10.4099i	0.0775662	−	0.439900i
$561$	1.03177	−	5.85145i	0.0435613	−	0.247048i
$562$	7.96589	+	13.7973i	0.336021	+	0.582005i
$563$	−13.3788	+	23.1727i	−0.563848	+	0.976614i	0.433307	+	0.901246i	$0.357346\pi$
$563$	−13.3788	+	23.1727i	−0.563848	+	0.976614i	−0.997156	+	0.0753679i	$0.975987\pi$
$564$	−6.64355	−	5.57460i	−0.279744	−	0.234733i
$565$	39.5328	+	14.3888i	1.66316	+	0.605340i
$566$	−4.12740	+	1.50225i	−0.173488	+	0.0631443i
$567$	2.90747	−	2.43965i	0.122102	−	0.102456i
$568$	2.28078	+	12.9350i	0.0956996	+	0.542739i
$569$	23.9769			1.00516			0.502582	−	0.864530i	$-0.332384\pi$
$569$	23.9769			1.00516			0.502582	+	0.864530i	$0.332384\pi$
$570$	−10.1398	+	2.52683i	−0.424711	+	0.105837i
$571$	−41.2633			−1.72682			−0.863408	−	0.504506i	$-0.831675\pi$
$571$	−41.2633			−1.72682			−0.863408	+	0.504506i	$0.831675\pi$
$572$	1.13264	+	6.42352i	0.0473581	+	0.268581i
$573$	−3.37669	+	2.83338i	−0.141063	+	0.118366i
$574$	0.0969930	−	0.0353025i	0.00404841	−	0.00147350i
$575$	31.4587	+	11.4500i	1.31192	+	0.477500i
$576$	2.05543	+	1.72471i	0.0856428	+	0.0718629i
$577$	2.16004	−	3.74130i	0.0899236	−	0.155752i	−0.817555	−	0.575850i	$-0.804671\pi$
$577$	2.16004	−	3.74130i	0.0899236	−	0.155752i	0.907479	+	0.420098i	$0.138004\pi$
$578$	0.536532	+	0.929301i	0.0223168	+	0.0386538i
$579$	−0.118369	+	0.671301i	−0.00491923	+	0.0278983i
$580$	1.24912	−	7.08410i	0.0518668	−	0.294151i
$581$	−16.2254	−	28.1032i	−0.673142	−	1.16592i
$582$	−6.55750	+	11.3579i	−0.271817	+	0.470801i
$583$	9.67118	+	8.11509i	0.400539	+	0.336092i
$584$	−8.08939	−	2.94430i	−0.334741	−	0.121836i
$585$	9.03522	−	3.28855i	0.373560	−	0.135965i
$586$	15.8371	−	13.2889i	0.654225	−	0.548960i
$587$	4.74456	+	26.9077i	0.195829	+	1.11060i	0.911233	+	0.411891i	$0.135131\pi$
$587$	4.74456	+	26.9077i	0.195829	+	1.11060i	−0.715404	+	0.698711i	$0.753757\pi$
$588$	−10.5529			−0.435194
$589$	14.9198	+	15.4537i	0.614759	+	0.636757i
$590$	−14.8398			−0.610947
$591$	−1.65290	−	9.37406i	−0.0679912	−	0.385597i
$592$	−4.23905	+	3.55699i	−0.174224	+	0.146191i
$593$	−18.6476	+	6.78718i	−0.765766	+	0.278716i	−0.695224	−	0.718793i	$-0.744695\pi$
$593$	−18.6476	+	6.78718i	−0.765766	+	0.278716i	−0.0705417	+	0.997509i	$0.522473\pi$
$594$	−1.07241	−	0.390326i	−0.0440016	−	0.0160153i
$595$	36.2901	+	30.4510i	1.48775	+	1.24837i
$596$	−7.86966	+	13.6306i	−0.322354	+	0.558333i
$597$	4.60945	+	7.98381i	0.188652	+	0.326756i
$598$	2.68294	−	15.2157i	0.109714	−	0.622217i
$599$	7.71458	−	43.7516i	0.315209	−	1.78764i	−0.255835	−	0.966721i	$-0.582350\pi$
$599$	7.71458	−	43.7516i	0.315209	−	1.78764i	0.571044	−	0.820920i	$-0.306539\pi$
$600$	6.48800	+	11.2376i	0.264872	+	0.458771i
$601$	−22.3304	+	38.6774i	−0.910876	+	1.57768i	−0.0980463	+	0.995182i	$0.531259\pi$
$601$	−22.3304	+	38.6774i	−0.910876	+	1.57768i	−0.812830	+	0.582502i	$0.802074\pi$
$602$	−19.2833	−	16.1806i	−0.785927	−	0.659471i
$603$	−5.88584	−	2.14227i	−0.239690	−	0.0872400i
$604$	21.3735	−	7.77931i	0.869674	−	0.316536i
$605$	−21.1556	+	17.7517i	−0.860097	+	0.721707i
$606$	1.53005	+	8.67737i	0.0621542	+	0.352494i
$607$	0.987705			0.0400897			0.0200449	−	0.999799i	$-0.493619\pi$
$607$	0.987705			0.0400897			0.0200449	+	0.999799i	$0.493619\pi$
$608$	21.1854	−	14.2859i	0.859180	−	0.579371i
$609$	−6.05956			−0.245546
$610$	0.140624	+	0.797516i	0.00569368	+	0.0322905i
$611$	−14.1775	+	11.8963i	−0.573561	+	0.481274i
$612$	5.28649	−	1.92412i	0.213694	−	0.0777781i
$613$	−16.4570	−	5.98985i	−0.664692	−	0.241928i	−0.0124309	−	0.999923i	$-0.503957\pi$
$613$	−16.4570	−	5.98985i	−0.664692	−	0.241928i	−0.652261	+	0.757995i	$0.726179\pi$
$614$	7.71055	+	6.46992i	0.311173	+	0.261105i
$615$	0.0566985	−	0.0982046i	0.00228630	−	0.00395999i
$616$	7.41777	+	12.8480i	0.298871	+	0.517659i
$617$	2.55265	−	14.4768i	0.102766	−	0.582814i	−0.889323	−	0.457279i	$-0.848824\pi$
$617$	2.55265	−	14.4768i	0.102766	−	0.582814i	0.992089	−	0.125535i	$-0.0400647\pi$
$618$	0.280020	−	1.58807i	0.0112641	−	0.0638817i
$619$	−14.3746	−	24.8976i	−0.577765	−	1.00072i	−0.995735	−	0.0922574i	$-0.970592\pi$
$619$	−14.3746	−	24.8976i	−0.577765	−	1.00072i	0.417970	−	0.908461i	$-0.362742\pi$
$620$	11.1018	−	19.2288i	0.445857	−	0.772248i
$621$	−5.13275	−	4.30689i	−0.205970	−	0.172829i
$622$	−1.63032	−	0.593387i	−0.0653697	−	0.0237926i
$623$	51.9407	−	18.9049i	2.08096	−	0.757408i
$624$	−2.05210	+	1.72191i	−0.0821496	+	0.0689317i
$625$	−4.34431	−	24.6378i	−0.173772	−	0.985511i
$626$	17.3659			0.694082
$627$	−3.85682	+	5.30710i	−0.154027	+	0.211945i
$628$	3.93008			0.156827
$629$	−4.30648	−	24.4233i	−0.171711	−	0.973820i
$630$	6.97030	−	5.84878i	0.277704	−	0.233021i
$631$	38.3445	−	13.9562i	1.52647	−	0.555589i	0.563716	−	0.825969i	$-0.309371\pi$
$631$	38.3445	−	13.9562i	1.52647	−	0.555589i	0.962754	+	0.270379i	$0.0871491\pi$
$632$	−5.97713	−	2.17550i	−0.237757	−	0.0865366i
$633$	4.64794	+	3.90008i	0.184739	+	0.155014i
$634$	7.27134	−	12.5943i	0.288782	−	0.500185i
$635$	24.3868	+	42.2393i	0.967763	+	1.67621i
$636$	−2.07570	+	11.7719i	−0.0823070	+	0.466786i
$637$	−3.91058	+	22.1780i	−0.154943	+	0.878725i
$638$	0.911016	+	1.57793i	0.0360675	+	0.0624707i
$639$	2.52873	−	4.37989i	0.100035	−	0.173266i
$640$	−23.4682	−	19.6922i	−0.927663	−	0.778402i
$641$	14.6296	+	5.32474i	0.577834	+	0.210314i	0.614370	−	0.789018i	$-0.289410\pi$
$641$	14.6296	+	5.32474i	0.577834	+	0.210314i	−0.0365360	+	0.999332i	$0.511632\pi$
$642$	−4.97048	+	1.80911i	−0.196169	+	0.0713998i
$643$	32.2770	−	27.0837i	1.27288	−	1.06808i	0.278698	−	0.960379i	$-0.410097\pi$
$643$	32.2770	−	27.0837i	1.27288	−	1.06808i	0.994184	−	0.107696i	$-0.0343474\pi$
$644$	6.29300	+	35.6894i	0.247979	+	1.40636i
$645$	−27.6550			−1.08891
$646$	0.908588	+	13.0163i	0.0357479	+	0.512119i
$647$	8.69408			0.341800			0.170900	−	0.985288i	$-0.445333\pi$
$647$	8.69408			0.341800			0.170900	+	0.985288i	$0.445333\pi$
$648$	−0.450974	−	2.55760i	−0.0177159	−	0.100472i
$649$	−7.13686	+	5.98854i	−0.280146	+	0.235071i
$650$	10.8266	−	3.94054i	0.424652	−	0.154561i
$651$	−17.5758	−	6.39708i	−0.688851	−	0.250721i
$652$	10.3867	+	8.71550i	0.406776	+	0.341325i
$653$	−19.4857	+	33.7502i	−0.762535	+	1.32075i	0.179005	+	0.983848i	$0.442712\pi$
$653$	−19.4857	+	33.7502i	−0.762535	+	1.32075i	−0.941540	+	0.336901i	$0.890621\pi$
$654$	−1.27830	−	2.21408i	−0.0499855	−	0.0865774i
$655$	−7.16448	+	40.6318i	−0.279939	+	1.58761i
$656$	−0.00548608	+	0.0311131i	−0.000214196	+	0.00121476i
$657$	1.65737	+	2.87064i	0.0646600	+	0.111994i
$658$	−8.75711	+	15.1678i	−0.341388	+	0.591301i
$659$	−13.4827	−	11.3133i	−0.525211	−	0.440704i	0.341233	−	0.939979i	$-0.389155\pi$
$659$	−13.4827	−	11.3133i	−0.525211	−	0.440704i	−0.866444	+	0.499275i	$0.833600\pi$
$660$	6.37235	+	2.31935i	0.248043	+	0.0902804i
$661$	−35.6673	+	12.9818i	−1.38730	+	0.504935i	−0.924382	−	0.381469i	$-0.875418\pi$
$661$	−35.6673	+	12.9818i	−1.38730	+	0.504935i	−0.462914	+	0.886403i	$0.653196\pi$
$662$	0.224987	−	0.188787i	0.00874438	−	0.00733741i
$663$	−2.08474	−	11.8231i	−0.0809645	−	0.459173i
$664$	−22.2047			−0.861711
$665$	−21.2693	−	47.7874i	−0.824789	−	1.85312i
$666$	−4.76339			−0.184578
$667$	1.85758	+	10.5348i	0.0719256	+	0.407911i
$668$	19.9450	−	16.7358i	0.771695	−	0.647529i
$669$	−1.05040	+	0.382313i	−0.0406106	+	0.0147811i
$670$	−14.1106	−	5.13584i	−0.545140	−	0.198415i
$671$	0.389463	+	0.326798i	0.0150350	+	0.0126159i
$672$	−11.1245	+	19.2682i	−0.429136	+	0.743285i
$673$	−5.09142	−	8.81860i	−0.196260	−	0.339932i	0.751053	−	0.660242i	$-0.229546\pi$
$673$	−5.09142	−	8.81860i	−0.196260	−	0.339932i	−0.947313	+	0.320310i	$0.896213\pi$
$674$	2.67539	−	15.1729i	0.103052	−	0.584439i
$675$	0.867620	−	4.92052i	0.0333947	−	0.189391i
$676$	−2.67320	−	4.63012i	−0.102815	−	0.178081i
$677$	25.8543	−	44.7809i	0.993661	−	1.72107i	0.399475	−	0.916744i	$-0.369193\pi$
$677$	25.8543	−	44.7809i	0.993661	−	1.72107i	0.594186	−	0.804327i	$-0.297474\pi$
$678$	−7.72891	−	6.48532i	−0.296827	−	0.249067i
$679$	−61.6879	−	22.4526i	−2.36737	−	0.861651i
$680$	30.4608	−	11.0868i	1.16812	−	0.425160i
$681$	3.78156	−	3.17310i	0.144910	−	0.121594i
$682$	0.976596	+	5.53855i	0.0373958	+	0.212082i
$683$	−26.1742			−1.00153			−0.500763	−	0.865584i	$-0.666947\pi$
$683$	−26.1742			−1.00153			−0.500763	+	0.865584i	$0.666947\pi$
$684$	−6.17755	−	0.650050i	−0.236204	−	0.0248553i
$685$	−31.5431			−1.20520
$686$	0.202531	+	1.14861i	0.00773267	+	0.0438541i
$687$	22.3889	−	18.7865i	0.854191	−	0.716751i
$688$	7.24019	−	2.63521i	0.276030	−	0.100467i
$689$	23.9707	+	8.72462i	0.913211	+	0.332382i
$690$	−12.3052	−	10.3253i	−0.468449	−	0.393076i
$691$	−17.2276	+	29.8390i	−0.655368	+	1.13513i	0.326434	+	0.945220i	$0.394153\pi$
$691$	−17.2276	+	29.8390i	−0.655368	+	1.13513i	−0.981801	+	0.189910i	$0.939180\pi$
$692$	−10.6371	−	18.4240i	−0.404363	−	0.700377i
$693$	0.991955	−	5.62566i	0.0376813	−	0.213701i
$694$	−1.83450	+	10.4040i	−0.0696368	+	0.394930i
$695$	−2.53921	−	4.39804i	−0.0963177	−	0.166827i
$696$	−2.07316	+	3.59081i	−0.0785828	+	0.136109i
$697$	−0.108464	−	0.0910117i	−0.00410835	−	0.00344732i
$698$	−12.3191	−	4.48377i	−0.466283	−	0.169713i
$699$	−24.2430	+	8.82373i	−0.916955	+	0.333744i
$700$	−20.7016	+	17.3707i	−0.782448	+	0.656552i
$701$	1.56451	+	8.87275i	0.0590906	+	0.335119i	0.999994	−	0.00355663i	$-0.00113211\pi$
$701$	1.56451	+	8.87275i	0.0590906	+	0.335119i	−0.940903	+	0.338676i	$0.890021\pi$
$702$	−2.30592			−0.0870315
$703$	−7.55095	+	26.3211i	−0.284789	+	0.992721i
$704$	4.03840			0.152203
$705$	3.34124	+	18.9491i	0.125839	+	0.713666i
$706$	3.97999	−	3.33961i	0.149789	−	0.125688i
$707$	−41.4446	+	15.0846i	−1.55869	+	0.567315i
$708$	−8.28912	−	3.01699i	−0.311524	−	0.113386i
$709$	−21.1957	−	17.7853i	−0.796023	−	0.667943i	0.151205	−	0.988502i	$-0.451685\pi$
$709$	−21.1957	−	17.7853i	−0.796023	−	0.667943i	−0.947228	+	0.320560i	$0.896129\pi$
$710$	6.06233	−	10.5003i	0.227515	−	0.394068i
$711$	1.22460	+	2.12107i	0.0459262	+	0.0795465i
$712$	6.56770	−	37.2473i	0.246135	−	1.39590i
$713$	−5.73371	+	32.5175i	−0.214729	+	1.21779i
$714$	−5.68063	−	9.83913i	−0.212592	−	0.368220i
$715$	7.23575	−	12.5327i	0.270602	−	0.468696i
$716$	14.3464	+	12.0381i	0.536151	+	0.449884i
$717$	21.1964	+	7.71485i	0.791594	+	0.288117i
$718$	11.1256	−	4.04938i	0.415203	−	0.151122i
$719$	−7.11568	+	5.97077i	−0.265370	+	0.222672i	−0.765757	−	0.643130i	$-0.777636\pi$
$719$	−7.11568	+	5.97077i	−0.265370	+	0.222672i	0.500387	+	0.865802i	$0.333191\pi$
$720$	0.483622	+	2.74276i	0.0180235	+	0.102216i
$721$	8.07171			0.300606
$722$	5.40016	−	13.3565i	0.200973	−	0.497076i
$723$	10.9014			0.405428
$724$	−2.19945	−	12.4737i	−0.0817420	−	0.463582i
$725$	−6.11074	+	5.12752i	−0.226947	+	0.190431i
$726$	6.22371	−	2.26525i	0.230984	−	0.0840711i
$727$	21.4481	+	7.80646i	0.795465	+	0.289526i	0.707606	−	0.706607i	$-0.249775\pi$
$727$	21.4481	+	7.80646i	0.795465	+	0.289526i	0.0878593	+	0.996133i	$0.471997\pi$
$728$	22.9629	+	19.2682i	0.851062	+	0.714126i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	3.97334	+	6.88202i	0.147060	+	0.254715i
$731$	−5.99615	+	34.0058i	−0.221775	+	1.25775i
$732$	−0.0835894	+	0.474059i	−0.00308955	+	0.0175217i
$733$	16.5879	+	28.7311i	0.612689	+	1.06121i	0.990785	+	0.135442i	$0.0432453\pi$
$733$	16.5879	+	28.7311i	0.612689	+	1.06121i	−0.378097	+	0.925766i	$0.623421\pi$
$734$	4.16850	−	7.22005i	0.153862	−	0.266497i
$735$	17.9357	+	15.0498i	0.661567	+	0.555120i
$736$	36.9089	+	13.4337i	1.36048	+	0.495174i
$737$	−8.85869	+	3.22430i	−0.326314	+	0.118769i
$738$	−0.0208328	+	0.0174808i	−0.000766866	+	0.000643477i
$739$	−0.799134	−	4.53211i	−0.0293966	−	0.166716i	0.966575	−	0.256383i	$-0.0825309\pi$
$739$	−0.799134	−	4.53211i	−0.0293966	−	0.166716i	−0.995972	+	0.0896668i	$0.971420\pi$
$740$	28.3044			1.04049
$741$	−3.65536	+	12.7419i	−0.134283	+	0.468085i
$742$	24.1401			0.886213
$743$	1.43353	+	8.12998i	0.0525913	+	0.298260i	0.999746	−	0.0225157i	$-0.00716756\pi$
$743$	1.43353	+	8.12998i	0.0525913	+	0.298260i	−0.947155	+	0.320776i	$0.896056\pi$
$744$	−9.80403	+	8.22656i	−0.359433	+	0.301600i
$745$	32.8143	−	11.9434i	1.20222	−	0.437574i
$746$	−12.2432	−	4.45615i	−0.448254	−	0.163151i
$747$	6.54965	+	5.49581i	0.239639	+	0.201081i
$748$	4.23362	−	7.33285i	0.154797	−	0.268116i
$749$	−13.2382	−	22.9292i	−0.483713	−	0.837816i
$750$	−0.00148842	+	0.00844124i	−5.43493e−5	+	0.000308230i
$751$	8.93701	−	50.6843i	0.326116	−	1.84950i	−0.175597	−	0.984462i	$-0.556185\pi$
$751$	8.93701	−	50.6843i	0.326116	−	1.84950i	0.501713	−	0.865034i	$-0.332703\pi$
$752$	−2.68039	−	4.64258i	−0.0977439	−	0.169297i
$753$	1.16356	−	2.01534i	0.0424025	−	0.0734432i
$754$	2.82020	+	2.36642i	0.102705	+	0.0861801i
$755$	−47.4206	−	17.2597i	−1.72581	−	0.628144i
$756$	5.08250	−	1.84988i	0.184849	−	0.0672794i
$757$	−0.676738	+	0.567851i	−0.0245965	+	0.0206389i	−0.655003	−	0.755626i	$-0.727333\pi$
$757$	−0.676738	+	0.567851i	−0.0245965	+	0.0206389i	0.630407	+	0.776265i	$0.282888\pi$
$758$	−2.16288	−	12.2663i	−0.0785593	−	0.445532i
$759$	−10.0846			−0.366047
$760$	−35.5950	−	3.74559i	−1.29117	−	0.135867i
$761$	20.8496			0.755796			0.377898	−	0.925847i	$-0.376647\pi$
$761$	20.8496			0.755796			0.377898	+	0.925847i	$0.376647\pi$
$762$	−2.03118	−	11.5194i	−0.0735818	−	0.417303i
$763$	9.80309	−	8.22577i	0.354896	−	0.297793i
$764$	−5.90273	+	2.14842i	−0.213553	+	0.0777271i
$765$	−11.7289	−	4.26899i	−0.424061	−	0.154346i
$766$	1.35867	+	1.14006i	0.0490907	+	0.0411920i
$767$	−9.41223	+	16.3025i	−0.339856	+	0.588648i
$768$	6.35674	+	11.0102i	0.229379	+	0.397296i
$769$	1.33636	−	7.57888i	0.0481904	−	0.273301i	−0.951186	−	0.308619i	$-0.900133\pi$
$769$	1.33636	−	7.57888i	0.0481904	−	0.273301i	0.999376	+	0.0353177i	$0.0112443\pi$
$770$	2.37809	−	13.4868i	0.0857005	−	0.486032i
$771$	13.6590	+	23.6580i	0.491915	+	0.852022i
$772$	−0.485698	+	0.841254i	−0.0174807	+	0.0302774i
$773$	34.3671	+	28.8374i	1.23610	+	1.03721i	0.997819	+	0.0660122i	$0.0210276\pi$
$773$	34.3671	+	28.8374i	1.23610	+	1.03721i	0.238279	+	0.971197i	$0.423417\pi$
$774$	6.23235	+	2.26839i	0.224017	+	0.0815355i
$775$	−23.1374	+	8.42132i	−0.831119	+	0.302503i
$776$	−34.4104	+	28.8737i	−1.23526	+	1.03651i
$777$	−4.14031	−	23.4808i	−0.148533	−	0.842371i
$778$	14.3130			0.513145
$779$	0.0635697	+	0.142827i	0.00227762	+	0.00511730i
$780$	13.7020			0.490609
$781$	−1.32179	−	7.49626i	−0.0472975	−	0.268237i
$782$	−15.3644	+	12.8923i	−0.549430	+	0.461026i
$783$	1.50026	−	0.546049i	0.0536149	−	0.0195142i
$784$	−6.12971	−	2.23103i	−0.218918	−	0.0796797i
$785$	−6.67956	−	5.60481i	−0.238404	−	0.200044i
$786$	4.94739	−	8.56914i	0.176468	−	0.305651i
$787$	−13.0523	−	22.6073i	−0.465265	−	0.805863i	0.533948	−	0.845517i	$-0.320708\pi$
$787$	−13.0523	−	22.6073i	−0.465265	−	0.805863i	−0.999213	+	0.0396543i	$0.987374\pi$
$788$	2.35547	−	13.3585i	0.0839100	−	0.475877i
$789$	−2.23391	+	12.6691i	−0.0795292	+	0.451032i
$790$	2.93584	+	5.08502i	0.104452	+	0.180917i
$791$	25.2511	−	43.7362i	0.897825	−	1.55508i
$792$	−2.99431	−	2.51252i	−0.106398	−	0.0892786i
$793$	0.965310	+	0.351344i	0.0342792	+	0.0124766i
$794$	−17.9011	+	6.51546i	−0.635285	+	0.231225i
$795$	20.3161	−	17.0473i	0.720539	−	0.604604i
$796$	2.28129	+	12.9378i	0.0808581	+	0.458569i
$797$	15.5431			0.550564			0.275282	−	0.961363i	$-0.411229\pi$
$797$	15.5431			0.550564			0.275282	+	0.961363i	$0.411229\pi$
$798$	0.873528	+	12.5140i	0.0309226	+	0.442991i
$799$	24.0252			0.849949
$800$	5.08602	+	28.8443i	0.179818	+	1.01980i
$801$	−11.1562	+	9.36114i	−0.394184	+	0.330760i
$802$	−0.208928	+	0.0760434i	−0.00737749	+	0.00268519i
$803$	4.68808	+	1.70632i	0.165439	+	0.0602148i
$804$	−6.83765	−	5.73747i	−0.241145	−	0.202345i
$805$	40.2021	−	69.6322i	1.41694	−	2.45421i
$806$	5.68178	+	9.84112i	0.200132	+	0.346639i
$807$	2.03190	−	11.5235i	0.0715262	−	0.405645i
$808$	−5.24051	+	29.7204i	−0.184361	+	1.04556i
$809$	21.7801	+	37.7243i	0.765748	+	1.32631i	0.939850	+	0.341587i	$0.110964\pi$
$809$	21.7801	+	37.7243i	0.765748	+	1.32631i	−0.174102	+	0.984728i	$0.555702\pi$
$810$	−1.19869	+	2.07619i	−0.0421177	+	0.0729500i
$811$	34.0798	+	28.5963i	1.19670	+	1.00415i	0.999718	+	0.0237468i	$0.00755954\pi$
$811$	34.0798	+	28.5963i	1.19670	+	1.00415i	0.196985	+	0.980406i	$0.436885\pi$
$812$	−8.11441	−	2.95341i	−0.284760	−	0.103644i
$813$	−3.41974	+	1.24468i	−0.119936	+	0.0436530i
$814$	−5.49201	+	4.60834i	−0.192495	+	0.161522i
$815$	−5.22381	−	29.6257i	−0.182982	−	1.03774i
$816$	3.47748			0.121736
$817$	22.4140	−	30.8423i	0.784167	−	1.07904i
$818$	−8.94693			−0.312822
$819$	−2.00429	−	11.3669i	−0.0700357	−	0.397192i
$820$	0.123790	−	0.103872i	0.00432294	−	0.00362737i
$821$	13.4872	−	4.90893i	0.470706	−	0.171323i	−0.0957663	−	0.995404i	$-0.530530\pi$
$821$	13.4872	−	4.90893i	0.470706	−	0.171323i	0.566472	+	0.824081i	$0.308308\pi$
$822$	7.10858	+	2.58731i	0.247940	+	0.0902428i
$823$	−9.46645	−	7.94329i	−0.329980	−	0.276886i	0.462712	−	0.886509i	$-0.346876\pi$
$823$	−9.46645	−	7.94329i	−0.329980	−	0.276886i	−0.792692	+	0.609623i	$0.791321\pi$
$824$	2.76157	−	4.78318i	0.0962039	−	0.166630i
$825$	−3.76002	−	6.51255i	−0.130907	−	0.226738i
$826$	−3.09341	+	17.5436i	−0.107634	+	0.610421i
$827$	−6.86623	+	38.9403i	−0.238762	+	1.35409i	0.595782	+	0.803146i	$0.296842\pi$
$827$	−6.86623	+	38.9403i	−0.238762	+	1.35409i	−0.834544	+	0.550941i	$0.814269\pi$
$828$	−4.77416	−	8.26908i	−0.165913	−	0.287370i
$829$	−7.55451	+	13.0848i	−0.262379	+	0.454454i	−0.966874	−	0.255255i	$-0.917840\pi$
$829$	−7.55451	+	13.0848i	−0.262379	+	0.454454i	0.704495	+	0.709709i	$0.251174\pi$
$830$	15.7020	+	13.1755i	0.545024	+	0.457330i
$831$	−10.9803	−	3.99648i	−0.380901	−	0.138637i
$832$	7.66769	−	2.79081i	0.265829	−	0.0967539i
$833$	22.3947	−	18.7914i	0.775931	−	0.651084i
$834$	0.211491	+	1.19942i	0.00732332	+	0.0415326i
$835$	−57.7659			−1.99907
$836$	−7.75137	+	5.22698i	−0.268087	+	0.180779i
$837$	4.92798			0.170336
$838$	2.81245	+	15.9502i	0.0971543	+	0.550990i
$839$	−1.73358	+	1.45465i	−0.0598499	+	0.0502200i	−0.672222	−	0.740350i	$-0.734660\pi$
$839$	−1.73358	+	1.45465i	−0.0598499	+	0.0502200i	0.612372	+	0.790570i	$0.290215\pi$
$840$	29.2854	−	10.6590i	1.01044	−	0.367770i
$841$	24.8559	+	9.04679i	0.857099	+	0.311958i
$842$	−9.86046	−	8.27391i	−0.339814	−	0.285138i
$843$	10.5056	−	18.1962i	0.361831	−	0.626710i
$844$	4.32321	+	7.48802i	0.148811	+	0.257748i
$845$	−2.05979	+	11.6817i	−0.0708590	+	0.401862i
$846$	0.801310	−	4.54445i	0.0275496	−	0.156242i
$847$	16.5760	+	28.7105i	0.569558	+	0.986503i
$848$	−3.69443	+	6.39895i	−0.126867	+	0.219741i
$849$	4.43742	+	3.72343i	0.152292	+	0.127788i
$850$	−14.0543	−	5.11536i	−0.482060	−	0.175456i
$851$	−39.5534	+	14.3962i	−1.35587	+	0.493497i
$852$	5.52099	−	4.63266i	0.189146	−	0.158712i
$853$	0.193770	+	1.09892i	0.00663456	+	0.0376264i	0.987945	−	0.154803i	$-0.0494744\pi$
$853$	0.193770	+	1.09892i	0.00663456	+	0.0376264i	−0.981311	+	0.192430i	$0.938363\pi$
$854$	0.972134			0.0332657
$855$	9.57228	+	9.91481i	0.327365	+	0.339079i
$856$	−18.1167			−0.619217
$857$	−0.646750	−	3.66790i	−0.0220925	−	0.125293i	0.971767	−	0.235943i	$-0.0758179\pi$
$857$	−0.646750	−	3.66790i	−0.0220925	−	0.125293i	−0.993859	+	0.110650i	$0.964707\pi$
$858$	−2.65864	+	2.23087i	−0.0907646	+	0.0761605i
$859$	−32.0738	+	11.6739i	−1.09435	+	0.398309i	−0.825229	−	0.564799i	$-0.808954\pi$
$859$	−32.0738	+	11.6739i	−1.09435	+	0.398309i	−0.269116	+	0.963108i	$0.586732\pi$
$860$	−37.0331	−	13.4789i	−1.26282	−	0.459628i
$861$	−0.104278	−	0.0874998i	−0.00355379	−	0.00298199i
$862$	−10.2181	+	17.6983i	−0.348030	+	0.602806i
$863$	−9.98389	−	17.2926i	−0.339856	−	0.588647i	0.644550	−	0.764562i	$-0.277045\pi$
$863$	−9.98389	−	17.2926i	−0.339856	−	0.588647i	−0.984405	+	0.175915i	$0.943712\pi$
$864$	1.01793	−	5.77298i	0.0346308	−	0.196401i
$865$	−8.19627	+	46.4834i	−0.278682	+	1.58048i
$866$	−7.09017	−	12.2805i	−0.240934	−	0.417309i
$867$	0.707589	−	1.22558i	0.0240310	−	0.0416229i
$868$	−20.4180	−	17.1328i	−0.693034	−	0.581524i
$869$	3.46395	+	1.26078i	0.117507	+	0.0427689i
$870$	3.59669	−	1.30909i	0.121939	−	0.0443822i
$871$	−14.5917	+	12.2439i	−0.494422	+	0.414869i
$872$	−1.52055	−	8.62346i	−0.0514923	−	0.292027i
$873$	17.2963			0.585392
$874$	21.4884	−	5.35488i	0.726857	−	0.181132i
$875$	−0.0429043			−0.00145043
$876$	0.820255	+	4.65190i	0.0277139	+	0.157173i
$877$	13.1938	−	11.0709i	0.445522	−	0.373837i	−0.392249	−	0.919859i	$-0.628303\pi$
$877$	13.1938	−	11.0709i	0.445522	−	0.373837i	0.837771	+	0.546022i	$0.183859\pi$
$878$	−10.5755	+	3.84916i	−0.356905	+	0.129903i
$879$	−25.6208	−	9.32522i	−0.864169	−	0.314532i
$880$	3.21108	+	2.69441i	0.108245	+	0.0908286i
$881$	11.5526	−	20.0097i	0.389217	−	0.674143i	−0.603128	−	0.797645i	$-0.706079\pi$
$881$	11.5526	−	20.0097i	0.389217	−	0.674143i	0.992344	+	0.123501i	$0.0394123\pi$
$882$	−2.80754	−	4.86280i	−0.0945347	−	0.163739i
$883$	−9.56314	+	54.2353i	−0.321825	+	1.82516i	0.209280	+	0.977856i	$0.432888\pi$
$883$	−9.56314	+	54.2353i	−0.321825	+	1.82516i	−0.531105	+	0.847306i	$0.678223\pi$
$884$	2.97086	−	16.8486i	0.0999208	−	0.566679i
$885$	9.78554	+	16.9490i	0.328937	+	0.569736i
$886$	1.24378	−	2.15429i	0.0417855	−	0.0723747i
$887$	−13.7757	−	11.5592i	−0.462542	−	0.388118i	0.381524	−	0.924359i	$-0.375399\pi$
$887$	−13.7757	−	11.5592i	−0.462542	−	0.388118i	−0.844065	+	0.536241i	$0.819844\pi$
$888$	−15.3309	−	5.58001i	−0.514473	−	0.187253i
$889$	55.0186	−	20.0251i	1.84527	−	0.671622i
$890$	−26.7456	+	22.4422i	−0.896515	+	0.752265i
$891$	0.261355	+	1.48222i	0.00875573	+	0.0496562i
$892$	−1.59293			−0.0533354
$893$	−23.8411	−	11.6317i	−0.797813	−	0.389240i
$894$	−8.37471			−0.280092
$895$	−7.21525	−	40.9197i	−0.241179	−	1.36780i
$896$	−28.1721	+	23.6392i	−0.941163	+	0.789729i
$897$	−19.1475	+	6.96912i	−0.639317	+	0.232692i
$898$	−20.6456	−	7.51439i	−0.688953	−	0.250759i
$899$	−6.02703	−	5.05728i	−0.201013	−	0.168670i
$900$	3.56008	−	6.16624i	0.118669	−	0.205541i
$901$	−16.5571	−	28.6778i	−0.551599	−	0.955397i
$902$	−0.00710763	+	0.0403094i	−0.000236658	+	0.00134216i
$903$	−5.76477	+	32.6936i	−0.191840	+	1.08798i
$904$	−17.2783	−	29.9269i	−0.574668	−	0.995354i
$905$	−14.0510	+	24.3370i	−0.467070	+	0.808989i
$906$	9.27102	+	7.77931i	0.308009	+	0.258450i
$907$	41.8945	+	15.2484i	1.39108	+	0.506313i	0.925519	−	0.378700i	$-0.123629\pi$
$907$	41.8945	+	15.2484i	1.39108	+	0.506313i	0.465565	+	0.885014i	$0.345851\pi$
$908$	6.61048	−	2.40602i	0.219376	−	0.0798465i
$909$	8.90176	−	7.46946i	0.295253	−	0.247746i
$910$	−4.80505	−	27.2508i	−0.159286	−	0.903356i
$911$	29.0598			0.962794			0.481397	−	0.876503i	$-0.340130\pi$
$911$	29.0598			0.962794			0.481397	+	0.876503i	$0.340130\pi$
$912$	−3.45084	−	1.68361i	−0.114269	−	0.0557498i
$913$	12.8684			0.425882
$914$	1.20899	+	6.85654i	0.0399899	+	0.226794i
$915$	0.818139	−	0.686500i	0.0270468	−	0.0226950i
$916$	39.1377	−	14.2450i	1.29315	−	0.470667i
$917$	46.5413	+	16.9396i	1.53693	+	0.559396i
$918$	2.29308	+	1.92412i	0.0756830	+	0.0635056i
$919$	8.86330	−	15.3517i	0.292373	−	0.506405i	−0.681997	−	0.731355i	$-0.738888\pi$
$919$	8.86330	−	15.3517i	0.292373	−	0.506405i	0.974370	+	0.224950i	$0.0722217\pi$
$920$	−27.5087	−	47.6465i	−0.906935	−	1.57086i
$921$	2.30509	−	13.0728i	0.0759552	−	0.430763i
$922$	−1.23136	+	6.98339i	−0.0405527	+	0.229986i
$923$	−7.69011	−	13.3197i	−0.253123	−	0.438422i
$924$	4.07026	−	7.04990i	0.133902	−	0.231925i
$925$	−24.0445	−	20.1757i	−0.790577	−	0.663373i
$926$	25.2373	+	9.18562i	0.829349	+	0.301858i
$927$	−1.99844	+	0.727372i	−0.0656373	+	0.0238900i
$928$	−7.16940	+	6.01584i	−0.235347	+	0.197480i
$929$	−0.0515969	−	0.292621i	−0.00169284	−	0.00960058i	0.983950	−	0.178446i	$-0.0571071\pi$
$929$	−0.0515969	−	0.292621i	−0.00169284	−	0.00960058i	−0.985642	+	0.168846i	$0.945996\pi$
$930$	11.8142			0.387404
$931$	−31.3210	+	7.80513i	−1.02650	+	0.255803i
$932$	−36.7647			−1.20427
$933$	0.397321	+	2.25332i	0.0130077	+	0.0737704i
$934$	1.08149	−	0.907479i	0.0353875	−	0.0296936i
$935$	−17.6531	+	6.42519i	−0.577317	+	0.210126i
$936$	−7.42161	−	2.70124i	−0.242583	−	0.0882929i
$937$	−19.0541	−	15.9883i	−0.622472	−	0.522316i	0.276108	−	0.961127i	$-0.410955\pi$
$937$	−19.0541	−	15.9883i	−0.622472	−	0.522316i	−0.898579	+	0.438811i	$0.855400\pi$
$938$	−9.01297	+	15.6109i	−0.294284	+	0.509715i
$939$	−11.4513	−	19.8342i	−0.373698	−	0.647263i
$940$	−4.76144	+	27.0035i	−0.155301	+	0.880757i
$941$	8.08270	−	45.8392i	0.263488	−	1.49432i	−0.509817	−	0.860283i	$-0.670287\pi$
$941$	8.08270	−	45.8392i	0.263488	−	1.49432i	0.773305	−	0.634034i	$-0.218602\pi$
$942$	1.04558	+	1.81099i	0.0340667	+	0.0590053i
$943$	−0.120156	+	0.208116i	−0.00391282	+	0.00677719i
$944$	−4.17695	−	3.50488i	−0.135948	−	0.114074i
$945$	−11.2764	−	4.10426i	−0.366820	−	0.133512i
$946$	9.38021	−	3.41412i	0.304977	−	0.111003i
$947$	−13.6115	+	11.4214i	−0.442313	+	0.371145i	−0.836574	−	0.547854i	$-0.815445\pi$
$947$	−13.6115	+	11.4214i	−0.442313	+	0.371145i	0.394261	+	0.918999i	$0.371001\pi$
$948$	0.606074	+	3.43722i	0.0196844	+	0.111636i
$949$	10.0804			0.327224
$950$	11.4701	+	11.8805i	0.372139	+	0.385456i
$951$	−19.1792			−0.621927
$952$	−6.75715	−	38.3217i	−0.219000	−	1.24201i
$953$	5.86121	−	4.91814i	0.189863	−	0.159314i	−0.542901	−	0.839797i	$-0.682674\pi$
$953$	5.86121	−	4.91814i	0.189863	−	0.159314i	0.732764	+	0.680482i	$0.238230\pi$
$954$	−5.97675	+	2.17536i	−0.193504	+	0.0704298i
$955$	13.0962	+	4.76663i	0.423783	+	0.154244i
$956$	24.6241	+	20.6621i	0.796400	+	0.668259i
$957$	1.20147	−	2.08100i	0.0388379	−	0.0672691i
$958$	−4.84940	−	8.39940i	−0.156677	−	0.271372i
$959$	−6.57526	+	37.2902i	−0.212326	+	1.20416i
$960$	1.47313	−	8.35453i	0.0475450	−	0.269641i
$961$	3.35750	+	5.81536i	0.108306	+	0.187592i
$962$	−7.24297	+	12.5452i	−0.233523	+	0.404473i
$963$	5.34382	+	4.48400i	0.172202	+	0.144495i
$964$	14.5982	+	5.31331i	0.470176	+	0.171130i
$965$	2.02523	−	0.737123i	0.0651944	−	0.0237288i
$966$	−14.7715	+	12.3948i	−0.475266	+	0.398796i
$967$	7.81261	+	44.3075i	0.251237	+	1.42483i	0.805551	+	0.592527i	$0.201869\pi$
$967$	7.81261	+	44.3075i	0.251237	+	1.42483i	−0.554314	+	0.832308i	$0.687019\pi$
$968$	22.6846			0.729110
$969$	14.2672	−	9.62079i	0.458327	−	0.309064i
$970$	41.4659			1.33139
$971$	−4.52803	−	25.6797i	−0.145311	−	0.824101i	−0.967117	−	0.254333i	$-0.918144\pi$
$971$	−4.52803	−	25.6797i	−0.145311	−	0.824101i	0.821805	−	0.569768i	$-0.192967\pi$
$972$	−1.09165	+	0.916005i	−0.0350148	+	0.0293809i
$973$	−5.72866	+	2.08506i	−0.183652	+	0.0668440i
$974$	23.9072	+	8.70152i	0.766037	+	0.278815i
$975$	−11.6398	−	9.76691i	−0.372770	−	0.312791i
$976$	−0.148776	+	0.257688i	−0.00476222	+	0.00824840i
$977$	−17.5714	−	30.4346i	−0.562159	−	0.973688i	−0.997308	−	0.0733291i	$-0.976638\pi$
$977$	−17.5714	−	30.4346i	−0.562159	−	0.973688i	0.435149	−	0.900358i	$-0.356696\pi$
$978$	−1.25279	+	7.10494i	−0.0400599	+	0.227191i
$979$	−3.80621	+	21.5861i	−0.121647	+	0.689894i
$980$	16.6826	+	28.8951i	0.532906	+	0.923021i
$981$	−1.68585	+	2.91997i	−0.0538250	+	0.0932276i
$982$	−10.3942	−	8.72175i	−0.331691	−	0.278322i
$983$	41.6979	+	15.1768i	1.32996	+	0.484065i	0.906635	−	0.421915i	$-0.138642\pi$
$983$	41.6979	+	15.1768i	1.32996	+	0.484065i	0.423321	+	0.905980i	$0.360864\pi$
$984$	−0.0875279	+	0.0318576i	−0.00279029	+	0.00101558i
$985$	−23.0543	+	19.3449i	−0.734572	+	0.616379i
$986$	−0.829881	−	4.70649i	−0.0264288	−	0.149885i
$987$	23.0981			0.735221
$988$	−11.1053	+	15.2812i	−0.353306	+	0.486159i
$989$	58.6067			1.86358
$990$	0.626568	+	3.55344i	0.0199136	+	0.112936i
$991$	0.860481	−	0.722030i	0.0273341	−	0.0229360i	−0.629018	−	0.777391i	$-0.716543\pi$
$991$	0.860481	−	0.722030i	0.0273341	−	0.0229360i	0.656352	+	0.754455i	$0.272098\pi$
$992$	−27.1459	+	9.88029i	−0.861882	+	0.313700i
$993$	−0.363978	−	0.132477i	−0.0115505	−	0.00420404i
$994$	−11.1497	−	9.35568i	−0.353646	−	0.296744i
$995$	14.5738	−	25.2425i	0.462019	−	0.800241i
$996$	6.09206	+	10.5518i	0.193034	+	0.334345i
$997$	−2.90266	+	16.4618i	−0.0919283	+	0.521351i	0.903717	+	0.428130i	$0.140827\pi$
$997$	−2.90266	+	16.4618i	−0.0919283	+	0.521351i	−0.995645	+	0.0932211i	$0.970284\pi$
$998$	1.03005	−	5.84170i	0.0326057	−	0.184916i
$999$	3.14103	+	5.44042i	0.0993777	+	0.172127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.i.b.28.2	✓	12
3.2	odd	2		171.2.u.e.28.1		12
4.3	odd	2		912.2.bo.j.769.1		12
19.6	even	9		1083.2.a.q.1.4		6
19.13	odd	18		1083.2.a.p.1.3		6
19.17	even	9	inner	57.2.i.b.55.2	yes	12
57.17	odd	18		171.2.u.e.55.1		12
57.32	even	18		3249.2.a.bg.1.4		6
57.44	odd	18		3249.2.a.bh.1.3		6
76.55	odd	18		912.2.bo.j.625.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.i.b.28.2	✓	12	1.1	even	1	trivial
57.2.i.b.55.2	yes	12	19.17	even	9	inner
171.2.u.e.28.1		12	3.2	odd	2
171.2.u.e.55.1		12	57.17	odd	18
912.2.bo.j.625.1		12	76.55	odd	18
912.2.bo.j.769.1		12	4.3	odd	2
1083.2.a.p.1.3		6	19.13	odd	18
1083.2.a.q.1.4		6	19.6	even	9
3249.2.a.bg.1.4		6	57.32	even	18
3249.2.a.bh.1.3		6	57.44	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.131669 + 0.746734i) q^{2} +(0.766044 - 0.642788i) q^{3} +(1.33911 - 0.487396i) q^{4} +(-2.97104 - 1.08137i) q^{5} +(0.580856 + 0.487396i) q^{6} +(-1.89771 + 3.28694i) q^{7} +(1.29853 + 2.24912i) q^{8} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.131669 + 0.746734i) q^{2} +(0.766044 - 0.642788i) q^{3} +(1.33911 - 0.487396i) q^{4} +(-2.97104 - 1.08137i) q^{5} +(0.580856 + 0.487396i) q^{6} +(-1.89771 + 3.28694i) q^{7} +(1.29853 + 2.24912i) q^{8} +(0.173648 - 0.984808i) q^{9} +(0.416301 - 2.36096i) q^{10} +(-0.752542 - 1.30344i) q^{11} +(0.712526 - 1.23413i) q^{12} +(-2.32962 - 1.95478i) q^{13} +(-2.70434 - 0.984299i) q^{14} +(-2.97104 + 1.08137i) q^{15} +(0.674788 - 0.566214i) q^{16} +(0.685522 + 3.88779i) q^{17} +0.758254 q^{18} +(1.20199 - 4.18990i) q^{19} -4.50560 q^{20} +(0.659069 + 3.73777i) q^{21} +(0.874238 - 0.733573i) q^{22} +(6.29625 - 2.29165i) q^{23} +(2.44044 + 0.888246i) q^{24} +(3.82748 + 3.21164i) q^{25} +(1.15296 - 1.99699i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-0.939207 + 5.32651i) q^{28} +(-0.277237 + 1.57229i) q^{29} +(-1.19869 - 2.07619i) q^{30} +(-2.46399 + 4.26776i) q^{31} +(4.49058 + 3.76805i) q^{32} +(-1.41432 - 0.514769i) q^{33} +(-2.81288 + 1.02380i) q^{34} +(9.19257 - 7.71348i) q^{35} +(-0.247458 - 1.40340i) q^{36} -6.28205 q^{37} +(3.28700 + 0.345884i) q^{38} -3.04110 q^{39} +(-1.42585 - 8.08640i) q^{40} +(-0.0274747 + 0.0230540i) q^{41} +(-2.70434 + 0.984299i) q^{42} +(8.21934 + 2.99159i) q^{43} +(-1.64303 - 1.37867i) q^{44} +(-1.58086 + 2.73812i) q^{45} +(2.54028 + 4.39989i) q^{46} +(1.05678 - 5.99331i) q^{47} +(0.152962 - 0.867490i) q^{48} +(-3.70264 - 6.41315i) q^{49} +(-1.89428 + 3.28099i) q^{50} +(3.02416 + 2.53757i) q^{51} +(-4.07236 - 1.48222i) q^{52} +(-7.88225 + 2.86891i) q^{53} +(0.580856 - 0.487396i) q^{54} +(0.826330 + 4.68635i) q^{55} -9.85695 q^{56} +(-1.77244 - 3.98227i) q^{57} -1.21058 q^{58} +(-1.07489 - 6.09598i) q^{59} +(-3.45149 + 2.89614i) q^{60} +(-0.317422 + 0.115532i) q^{61} +(-3.51131 - 1.27801i) q^{62} +(2.90747 + 2.43965i) q^{63} +(-1.34158 + 2.32369i) q^{64} +(4.80754 + 8.32690i) q^{65} +(0.198174 - 1.12390i) q^{66} +(1.08766 - 6.16842i) q^{67} +(2.81288 + 4.87205i) q^{68} +(3.35016 - 5.80266i) q^{69} +(6.97030 + 5.84878i) q^{70} +(4.75246 + 1.72975i) q^{71} +(2.44044 - 0.888246i) q^{72} +(-2.53923 + 2.13067i) q^{73} +(-0.827154 - 4.69102i) q^{74} +4.99642 q^{75} +(-0.432546 - 6.19658i) q^{76} +5.71244 q^{77} +(-0.400419 - 2.27089i) q^{78} +(-1.87620 + 1.57432i) q^{79} +(-2.61711 + 0.952549i) q^{80} +(-0.939693 - 0.342020i) q^{81} +(-0.0208328 - 0.0174808i) q^{82} +(-4.27498 + 7.40448i) q^{83} +(2.70434 + 4.68405i) q^{84} +(2.16742 - 12.2921i) q^{85} +(-1.15169 + 6.53156i) q^{86} +(0.798271 + 1.38265i) q^{87} +(1.95440 - 3.38511i) q^{88} +(-11.1562 - 9.36114i) q^{89} +(-2.25280 - 0.819952i) q^{90} +(10.8462 - 3.94769i) q^{91} +(7.31443 - 6.13754i) q^{92} +(0.855735 + 4.85311i) q^{93} +4.61456 q^{94} +(-8.10197 + 11.1485i) q^{95} +5.86204 q^{96} +(3.00347 + 17.0336i) q^{97} +(4.30140 - 3.60930i) q^{98} +(-1.41432 + 0.514769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8	\( 12 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 3 q^{6} - 9 q^{7} + 3 q^{8} - 18 q^{10} - 9 q^{11} - 6 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + 33 q^{16} + 12 q^{17} - 9 q^{19} - 18 q^{20} - 24 q^{22} + 9 q^{23} + 30 q^{24} - 12 q^{25} - 6 q^{27} + 30 q^{28} - 6 q^{30} - 3 q^{32} - 9 q^{33} + 21 q^{34} + 30 q^{35} - 3 q^{36} - 12 q^{37} + 18 q^{38} + 6 q^{39} - 3 q^{40} - 18 q^{41} - 3 q^{42} + 15 q^{43} + 15 q^{44} - 9 q^{45} + 27 q^{46} - 9 q^{47} - 12 q^{48} - 9 q^{49} + 9 q^{50} - 15 q^{51} - 27 q^{52} - 30 q^{53} - 3 q^{54} + 15 q^{55} - 78 q^{56} - 3 q^{57} - 24 q^{58} - 30 q^{59} - 15 q^{60} + 21 q^{61} + 3 q^{62} + 9 q^{63} - 21 q^{64} + 21 q^{65} + 30 q^{66} + 3 q^{67} - 21 q^{68} - 6 q^{69} + 18 q^{70} - 30 q^{71} + 30 q^{72} - 24 q^{73} + 39 q^{74} + 30 q^{75} - 60 q^{76} + 96 q^{77} + 9 q^{78} + 24 q^{79} + 42 q^{80} - 33 q^{82} + 3 q^{83} + 3 q^{84} + 3 q^{85} + 51 q^{86} + 15 q^{87} + 42 q^{88} + 3 q^{89} - 9 q^{90} + 24 q^{91} + 69 q^{92} - 6 q^{93} + 18 q^{94} - 54 q^{95} - 42 q^{96} - 27 q^{97} - 3 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 3 * q^6 - 9 * q^7 + 3 * q^8 - 18 * q^10 - 9 * q^11 - 6 * q^12 - 3 * q^13 - 3 * q^14 + 6 * q^15 + 33 * q^16 + 12 * q^17 - 9 * q^19 - 18 * q^20 - 24 * q^22 + 9 * q^23 + 30 * q^24 - 12 * q^25 - 6 * q^27 + 30 * q^28 - 6 * q^30 - 3 * q^32 - 9 * q^33 + 21 * q^34 + 30 * q^35 - 3 * q^36 - 12 * q^37 + 18 * q^38 + 6 * q^39 - 3 * q^40 - 18 * q^41 - 3 * q^42 + 15 * q^43 + 15 * q^44 - 9 * q^45 + 27 * q^46 - 9 * q^47 - 12 * q^48 - 9 * q^49 + 9 * q^50 - 15 * q^51 - 27 * q^52 - 30 * q^53 - 3 * q^54 + 15 * q^55 - 78 * q^56 - 3 * q^57 - 24 * q^58 - 30 * q^59 - 15 * q^60 + 21 * q^61 + 3 * q^62 + 9 * q^63 - 21 * q^64 + 21 * q^65 + 30 * q^66 + 3 * q^67 - 21 * q^68 - 6 * q^69 + 18 * q^70 - 30 * q^71 + 30 * q^72 - 24 * q^73 + 39 * q^74 + 30 * q^75 - 60 * q^76 + 96 * q^77 + 9 * q^78 + 24 * q^79 + 42 * q^80 - 33 * q^82 + 3 * q^83 + 3 * q^84 + 3 * q^85 + 51 * q^86 + 15 * q^87 + 42 * q^88 + 3 * q^89 - 9 * q^90 + 24 * q^91 + 69 * q^92 - 6 * q^93 + 18 * q^94 - 54 * q^95 - 42 * q^96 - 27 * q^97 - 3 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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