LMFDB - Embedded newform 690.2.m.g.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.3
Character	$\chi$	$=$	690.121
Dual form			690.2.m.g.211.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.743473 - 5.17097i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.743473 - 5.17097i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(1.65538 + 3.62478i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.717955 - 4.99349i) q^{13} +(-4.39483 - 2.82439i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-1.53793 + 1.77487i) q^{17} +(0.841254 - 0.540641i) q^{18} +(1.97472 + 2.27895i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(-2.17019 + 4.75205i) q^{21} +3.98489 q^{22} +(-3.56624 - 3.20655i) q^{23} +1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-4.84049 - 1.42130i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-4.39483 + 2.82439i) q^{28} +(4.46963 - 5.15823i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-7.85431 + 2.30623i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.567109 - 3.94433i) q^{33} +(0.975595 + 2.13626i) q^{34} +(-2.17019 - 4.75205i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.311508 - 0.200194i) q^{37} +(2.89333 - 0.849559i) q^{38} +(-0.717955 + 4.99349i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(1.62078 - 1.04161i) q^{41} +(3.42109 + 3.94814i) q^{42} +(-10.6622 - 3.13069i) q^{43} +(1.65538 - 3.62478i) q^{44} +1.00000 q^{45} +(-4.39825 + 1.91192i) q^{46} +4.92653 q^{47} +(0.415415 - 0.909632i) q^{48} +(-19.4697 - 5.71683i) q^{49} +(-0.654861 - 0.755750i) q^{50} +(1.97567 - 1.26969i) q^{51} +(-3.30367 + 3.81263i) q^{52} +(-0.316357 + 2.20031i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(3.35230 + 2.15439i) q^{55} +(0.743473 + 5.17097i) q^{56} +(-1.25268 - 2.74298i) q^{57} +(-2.83534 - 6.20852i) q^{58} +(0.310817 + 2.16178i) q^{59} +(0.841254 + 0.540641i) q^{60} +(12.6607 - 3.71752i) q^{61} +(-1.16497 + 8.10258i) q^{62} +(3.42109 - 3.94814i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-3.30367 - 3.81263i) q^{65} +(-3.82347 - 1.12267i) q^{66} +(-0.852560 + 1.86685i) q^{67} +2.34848 q^{68} +(2.51839 + 4.08138i) q^{69} -5.22414 q^{70} +(3.15425 - 6.90685i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(9.98981 + 11.5289i) q^{73} +(-0.311508 + 0.200194i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.429148 - 2.98479i) q^{76} +(19.9744 - 5.86501i) q^{77} +(4.24399 + 2.72745i) q^{78} +(0.615851 + 4.28334i) q^{79} +(0.415415 + 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.274188 - 1.90702i) q^{82} +(-7.64258 - 4.91159i) q^{83} +(5.01253 - 1.47181i) q^{84} +(-0.334224 + 2.32458i) q^{85} +(-7.27700 + 8.39810i) q^{86} +(-5.74182 + 3.69004i) q^{87} +(-2.60955 - 3.01158i) q^{88} +(3.93784 + 1.15625i) q^{89} +(0.415415 - 0.909632i) q^{90} -26.3550 q^{91} +(-0.0879548 + 4.79502i) q^{92} +8.18590 q^{93} +(2.04655 - 4.48133i) q^{94} +(2.89333 + 0.849559i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(6.57851 - 4.22775i) q^{97} +(-13.2882 + 15.3354i) q^{98} +(-0.567109 + 3.94433i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{11}\right)$

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 $

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$5$	0.841254	−	0.540641i	0.376220	−	0.241782i
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	0.743473	−	5.17097i	0.281006	−	1.95444i	−0.0169292	−	0.999857i	$-0.505389\pi$
$7$	0.743473	−	5.17097i	0.281006	−	1.95444i	0.297936	−	0.954586i	$-0.403702\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−0.142315	−	0.989821i	−0.0450039	−	0.313009i
$11$	1.65538	+	3.62478i	0.499117	+	1.09291i	0.976755	+	0.214357i	$0.0687656\pi$
$11$	1.65538	+	3.62478i	0.499117	+	1.09291i	−0.477639	+	0.878556i	$0.658507\pi$
$12$	0.415415	+	0.909632i	0.119920	+	0.262588i
$13$	−0.717955	−	4.99349i	−0.199125	−	1.38494i	−0.806831	−	0.590783i	$-0.798819\pi$
$13$	−0.717955	−	4.99349i	−0.199125	−	1.38494i	0.607706	−	0.794162i	$-0.292090\pi$
$14$	−4.39483	−	2.82439i	−1.17457	−	0.754849i
$15$	−0.959493	+	0.281733i	−0.247740	+	0.0727430i
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	−1.53793	+	1.77487i	−0.373003	+	0.430468i	−0.910954	−	0.412508i	$-0.864653\pi$
$17$	−1.53793	+	1.77487i	−0.373003	+	0.430468i	0.537951	+	0.842976i	$0.319198\pi$
$18$	0.841254	−	0.540641i	0.198285	−	0.127430i
$19$	1.97472	+	2.27895i	0.453032	+	0.522827i	0.935614	−	0.353024i	$-0.114847\pi$
$19$	1.97472	+	2.27895i	0.453032	+	0.522827i	−0.482582	+	0.875851i	$0.660301\pi$
$20$	−0.959493	−	0.281733i	−0.214549	−	0.0629973i
$21$	−2.17019	+	4.75205i	−0.473574	+	1.03698i
$22$	3.98489			0.849581
$23$	−3.56624	−	3.20655i	−0.743612	−	0.668611i
$23$	−3.56624	−	3.20655i	−0.743612	−	0.668611i
$24$	1.00000			0.204124
$25$	0.415415	−	0.909632i	0.0830830	−	0.181926i
$26$	−4.84049	−	1.42130i	−0.949298	−	0.278739i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−4.39483	+	2.82439i	−0.830545	+	0.533759i
$29$	4.46963	−	5.15823i	0.829989	−	0.957859i	−0.169629	−	0.985508i	$-0.554257\pi$
$29$	4.46963	−	5.15823i	0.829989	−	0.957859i	0.999618	+	0.0276495i	$0.00880224\pi$
$30$	−0.142315	+	0.989821i	−0.0259830	+	0.180716i
$31$	−7.85431	+	2.30623i	−1.41068	+	0.414212i	−0.896336	−	0.443375i	$-0.853781\pi$
$31$	−7.85431	+	2.30623i	−1.41068	+	0.414212i	−0.514340	+	0.857587i	$0.671963\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$	−0.567109	−	3.94433i	−0.0987210	−	0.686620i
$34$	0.975595	+	2.13626i	0.167313	+	0.366365i
$35$	−2.17019	−	4.75205i	−0.366829	−	0.803243i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−0.311508	−	0.200194i	−0.0512117	−	0.0329117i	0.514784	−	0.857320i	$-0.327872\pi$
$37$	−0.311508	−	0.200194i	−0.0512117	−	0.0329117i	−0.565996	+	0.824408i	$0.691508\pi$
$38$	2.89333	−	0.849559i	0.469361	−	0.137817i
$39$	−0.717955	+	4.99349i	−0.114965	+	0.799598i
$40$	−0.654861	+	0.755750i	−0.103543	+	0.119494i
$41$	1.62078	−	1.04161i	0.253124	−	0.162673i	−0.407926	−	0.913015i	$-0.633748\pi$
$41$	1.62078	−	1.04161i	0.253124	−	0.162673i	0.661049	+	0.750342i	$0.270111\pi$
$42$	3.42109	+	3.94814i	0.527885	+	0.609212i
$43$	−10.6622	−	3.13069i	−1.62596	−	0.477426i	−0.663351	−	0.748308i	$-0.730866\pi$
$43$	−10.6622	−	3.13069i	−1.62596	−	0.477426i	−0.962612	+	0.270883i	$0.912684\pi$
$44$	1.65538	−	3.62478i	0.249558	−	0.546457i
$45$	1.00000			0.149071
$46$	−4.39825	+	1.91192i	−0.648486	+	0.281897i
$47$	4.92653			0.718608			0.359304	−	0.933221i	$-0.383014\pi$
$47$	4.92653			0.718608			0.359304	+	0.933221i	$0.383014\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−19.4697	−	5.71683i	−2.78139	−	0.816689i
$50$	−0.654861	−	0.755750i	−0.0926113	−	0.106879i
$51$	1.97567	−	1.26969i	0.276649	−	0.177792i
$52$	−3.30367	+	3.81263i	−0.458136	+	0.528717i
$53$	−0.316357	+	2.20031i	−0.0434550	+	0.302236i	0.956490	+	0.291764i	$0.0942423\pi$
$53$	−0.316357	+	2.20031i	−0.0434550	+	0.302236i	−0.999945	+	0.0104715i	$0.996667\pi$
$54$	−0.959493	+	0.281733i	−0.130570	+	0.0383389i
$55$	3.35230	+	2.15439i	0.452024	+	0.290498i
$56$	0.743473	+	5.17097i	0.0993508	+	0.691000i
$57$	−1.25268	−	2.74298i	−0.165921	−	0.363316i
$58$	−2.83534	−	6.20852i	−0.372298	−	0.815219i
$59$	0.310817	+	2.16178i	0.0404650	+	0.281440i	1.00000		0.000149215i	$-4.74966e-5\pi$
$59$	0.310817	+	2.16178i	0.0404650	+	0.281440i	−0.959535	+	0.281589i	$0.909138\pi$
$60$	0.841254	+	0.540641i	0.108605	+	0.0697964i
$61$	12.6607	−	3.71752i	1.62104	−	0.475980i	0.659740	−	0.751494i	$-0.270666\pi$
$61$	12.6607	−	3.71752i	1.62104	−	0.475980i	0.961297	+	0.275514i	$0.0888481\pi$
$62$	−1.16497	+	8.10258i	−0.147952	+	1.02903i
$63$	3.42109	−	3.94814i	0.431016	−	0.497419i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−3.30367	−	3.81263i	−0.409769	−	0.472899i
$66$	−3.82347	−	1.12267i	−0.470637	−	0.138192i
$67$	−0.852560	+	1.86685i	−0.104157	+	0.228071i	−0.954534	−	0.298102i	$-0.903646\pi$
$67$	−0.852560	+	1.86685i	−0.104157	+	0.228071i	0.850377	+	0.526173i	$0.176374\pi$
$68$	2.34848			0.284795
$69$	2.51839	+	4.08138i	0.303179	+	0.491341i
$70$	−5.22414			−0.624405
$71$	3.15425	−	6.90685i	0.374341	−	0.819692i	−0.624899	−	0.780706i	$-0.714860\pi$
$71$	3.15425	−	6.90685i	0.374341	−	0.819692i	0.999240	−	0.0389866i	$-0.0124130\pi$
$72$	−0.959493	−	0.281733i	−0.113077	−	0.0332025i
$73$	9.98981	+	11.5289i	1.16922	+	1.34935i	0.925154	+	0.379592i	$0.123936\pi$
$73$	9.98981	+	11.5289i	1.16922	+	1.34935i	0.244065	+	0.969759i	$0.421519\pi$
$74$	−0.311508	+	0.200194i	−0.0362121	+	0.0232721i
$75$	−0.654861	+	0.755750i	−0.0756168	+	0.0872664i
$76$	0.429148	−	2.98479i	0.0492266	−	0.342379i
$77$	19.9744	−	5.86501i	2.27629	−	0.668380i
$78$	4.24399	+	2.72745i	0.480537	+	0.308822i
$79$	0.615851	+	4.28334i	0.0692887	+	0.481913i	0.994689	+	0.102923i	$0.0328196\pi$
$79$	0.615851	+	4.28334i	0.0692887	+	0.481913i	−0.925401	+	0.378990i	$0.876271\pi$
$80$	0.415415	+	0.909632i	0.0464448	+	0.101700i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−0.274188	−	1.90702i	−0.0302790	−	0.210595i
$83$	−7.64258	−	4.91159i	−0.838882	−	0.539117i	0.0492068	−	0.998789i	$-0.484331\pi$
$83$	−7.64258	−	4.91159i	−0.838882	−	0.539117i	−0.888089	+	0.459672i	$0.847967\pi$
$84$	5.01253	−	1.47181i	0.546912	−	0.160588i
$85$	−0.334224	+	2.32458i	−0.0362517	+	0.252136i
$86$	−7.27700	+	8.39810i	−0.784699	+	0.905591i
$87$	−5.74182	+	3.69004i	−0.615587	+	0.395614i
$88$	−2.60955	−	3.01158i	−0.278179	−	0.321035i
$89$	3.93784	+	1.15625i	0.417410	+	0.122563i	0.483692	−	0.875238i	$-0.339295\pi$
$89$	3.93784	+	1.15625i	0.417410	+	0.122563i	−0.0662817	+	0.997801i	$0.521114\pi$
$90$	0.415415	−	0.909632i	0.0437886	−	0.0958836i
$91$	−26.3550			−2.76275
$92$	−0.0879548	+	4.79502i	−0.00916992	+	0.499916i
$93$	8.18590			0.848838
$94$	2.04655	−	4.48133i	0.211086	−	0.462214i
$95$	2.89333	+	0.849559i	0.296850	+	0.0871629i
$96$	−0.654861	−	0.755750i	−0.0668364	−	0.0771334i
$97$	6.57851	−	4.22775i	0.667947	−	0.429263i	−0.162238	−	0.986752i	$-0.551871\pi$
$97$	6.57851	−	4.22775i	0.667947	−	0.429263i	0.830185	+	0.557488i	$0.188235\pi$
$98$	−13.2882	+	15.3354i	−1.34231	+	1.54911i
$99$	−0.567109	+	3.94433i	−0.0569966	+	0.396420i
$100$	−0.959493	+	0.281733i	−0.0959493	+	0.0281733i
$101$	6.56202	+	4.21715i	0.652945	+	0.419622i	0.824741	−	0.565510i	$-0.191321\pi$
$101$	6.56202	+	4.21715i	0.652945	+	0.419622i	−0.171796	+	0.985133i	$0.554957\pi$
$102$	−0.334224	−	2.32458i	−0.0330931	−	0.230168i
$103$	4.74954	+	10.4000i	0.467986	+	1.02475i	0.985594	+	0.169129i	$0.0540954\pi$
$103$	4.74954	+	10.4000i	0.467986	+	1.02475i	−0.517608	+	0.855618i	$0.673177\pi$
$104$	2.09570	+	4.58895i	0.205500	+	0.449983i
$105$	0.743473	+	5.17097i	0.0725555	+	0.504635i
$106$	1.87005	+	1.20181i	0.181636	+	0.116730i
$107$	3.30926	−	0.971687i	0.319918	−	0.0939365i	−0.117831	−	0.993034i	$-0.537594\pi$
$107$	3.30926	−	0.971687i	0.319918	−	0.0939365i	0.437749	+	0.899097i	$0.355776\pi$
$108$	−0.142315	+	0.989821i	−0.0136943	+	0.0952456i
$109$	10.6664	−	12.3097i	1.02165	−	1.17905i	0.0379449	−	0.999280i	$-0.487919\pi$
$109$	10.6664	−	12.3097i	1.02165	−	1.17905i	0.983708	−	0.179771i	$-0.0575357\pi$
$110$	3.35230	−	2.15439i	0.319630	−	0.205413i
$111$	0.242489	+	0.279847i	0.0230160	+	0.0265619i
$112$	5.01253	+	1.47181i	0.473639	+	0.139073i
$113$	−6.12379	+	13.4092i	−0.576077	+	1.26143i	0.367420	+	0.930055i	$0.380241\pi$
$113$	−6.12379	+	13.4092i	−0.576077	+	1.26143i	−0.943498	+	0.331379i	$0.892486\pi$
$114$	−3.01548			−0.282426
$115$	−4.73370	−	0.769463i	−0.441420	−	0.0717528i
$116$	−6.82531			−0.633714
$117$	2.09570	−	4.58895i	0.193748	−	0.424248i
$118$	2.09555	+	0.615308i	0.192911	+	0.0566437i
$119$	8.03436	+	9.27215i	0.736509	+	0.849977i
$120$	0.841254	−	0.540641i	0.0767956	−	0.0493535i
$121$	−3.19530	+	3.68757i	−0.290481	+	0.335233i
$122$	1.87787	−	13.0609i	0.170015	−	1.18248i
$123$	−1.84859	+	0.542794i	−0.166681	+	0.0489421i
$124$	6.88641	+	4.42563i	0.618418	+	0.397433i
$125$	−0.142315	−	0.989821i	−0.0127290	−	0.0885323i
$126$	−2.17019	−	4.75205i	−0.193336	−	0.423346i
$127$	−1.08832	−	2.38309i	−0.0965727	−	0.211465i	0.855180	−	0.518332i	$-0.173447\pi$
$127$	−1.08832	−	2.38309i	−0.0965727	−	0.211465i	−0.951752	+	0.306867i	$0.900719\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$	9.34824	+	6.00775i	0.823067	+	0.528953i
$130$	−4.84049	+	1.42130i	−0.424539	+	0.124656i
$131$	0.681088	−	4.73707i	0.0595069	−	0.413880i	−0.938194	−	0.346110i	$-0.887503\pi$
$131$	0.681088	−	4.73707i	0.0595069	−	0.413880i	0.997701	−	0.0677700i	$-0.0215884\pi$
$132$	−2.60955	+	3.01158i	−0.227132	+	0.262124i
$133$	13.2525	−	8.51688i	1.14914	−	0.738507i
$134$	1.34398	+	1.55103i	0.116102	+	0.133989i
$135$	−0.959493	−	0.281733i	−0.0825800	−	0.0242477i
$136$	0.975595	−	2.13626i	0.0836566	−	0.183182i
$137$	20.3355			1.73737			0.868687	−	0.495361i	$-0.164964\pi$
$137$	20.3355			1.73737			0.868687	+	0.495361i	$0.164964\pi$
$138$	4.75874	−	0.595344i	0.405090	−	0.0506790i
$139$	12.9242			1.09622			0.548108	−	0.836407i	$-0.315348\pi$
$139$	12.9242			1.09622			0.548108	+	0.836407i	$0.315348\pi$
$140$	−2.17019	+	4.75205i	−0.183414	+	0.401621i
$141$	−4.72697	−	1.38796i	−0.398083	−	0.116888i
$142$	−4.97237	−	5.73842i	−0.417272	−	0.481557i
$143$	16.9118	−	10.8686i	1.41424	−	0.908876i
$144$	−0.654861	+	0.755750i	−0.0545717	+	0.0629791i
$145$	0.971343	−	6.75584i	0.0806657	−	0.561042i
$146$	14.6369	−	4.29779i	1.21136	−	0.355688i
$147$	17.0704	+	10.9705i	1.40795	+	0.904832i
$148$	0.0526979	+	0.366522i	0.00433174	+	0.0301279i
$149$	0.341269	+	0.747275i	0.0279578	+	0.0612191i	0.923096	−	0.384570i	$-0.125650\pi$
$149$	0.341269	+	0.747275i	0.0279578	+	0.0612191i	−0.895138	+	0.445789i	$0.852923\pi$
$150$	0.415415	+	0.909632i	0.0339185	+	0.0742711i
$151$	−1.75744	−	12.2233i	−0.143018	−	0.994714i	−0.927303	−	0.374313i	$-0.877879\pi$
$151$	−1.75744	−	12.2233i	−0.143018	−	0.994714i	0.784284	−	0.620402i	$-0.213030\pi$
$152$	−2.53678	−	1.63029i	−0.205760	−	0.132234i
$153$	−2.25335	+	0.661644i	−0.182173	+	0.0534908i
$154$	2.96266	−	20.6057i	0.238738	−	1.66046i
$155$	−5.36062	+	6.18649i	−0.430576	+	0.496911i
$156$	4.24399	−	2.72745i	0.339791	−	0.218370i
$157$	−6.51924	−	7.52360i	−0.520292	−	0.600449i	0.433412	−	0.901196i	$-0.357309\pi$
$157$	−6.51924	−	7.52360i	−0.520292	−	0.600449i	−0.953704	+	0.300747i	$0.902764\pi$
$158$	4.15210	+	1.21917i	0.330323	+	0.0969916i
$159$	0.923441	−	2.02205i	0.0732337	−	0.160359i
$160$	1.00000			0.0790569
$161$	−19.2324	+	16.0569i	−1.51572	+	1.26546i
$162$	1.00000			0.0785674
$163$	2.48216	−	5.43516i	0.194417	−	0.425715i	−0.787168	−	0.616739i	$-0.788454\pi$
$163$	2.48216	−	5.43516i	0.194417	−	0.425715i	0.981585	+	0.191024i	$0.0611808\pi$
$164$	−1.84859	−	0.542794i	−0.144350	−	0.0423851i
$165$	−2.60955	−	3.01158i	−0.203153	−	0.234451i
$166$	−7.64258	+	4.91159i	−0.593179	+	0.381213i
$167$	13.1985	−	15.2319i	1.02133	−	1.17868i	0.0375552	−	0.999295i	$-0.488043\pi$
$167$	13.1985	−	15.2319i	1.02133	−	1.17868i	0.983779	−	0.179387i	$-0.0574116\pi$
$168$	0.743473	−	5.17097i	0.0573602	−	0.398949i
$169$	−11.9461	+	3.50768i	−0.918928	+	0.269822i
$170$	1.97567	+	1.26969i	0.151527	+	0.0973805i
$171$	0.429148	+	2.98479i	0.0328177	+	0.228252i
$172$	4.61621	+	10.1081i	0.351983	+	0.770734i
$173$	7.50220	+	16.4275i	0.570382	+	1.24896i	0.946594	+	0.322428i	$0.104499\pi$
$173$	7.50220	+	16.4275i	0.570382	+	1.24896i	−0.376212	+	0.926533i	$0.622774\pi$
$174$	0.971343	+	6.75584i	0.0736373	+	0.512159i
$175$	−4.39483	−	2.82439i	−0.332218	−	0.213503i
$176$	−3.82347	+	1.12267i	−0.288205	+	0.0846247i
$177$	0.310817	−	2.16178i	0.0233625	−	0.162490i
$178$	2.68761	−	3.10166i	0.201445	−	0.232479i
$179$	0.999595	−	0.642401i	0.0747133	−	0.0480153i	−0.502751	−	0.864431i	$-0.667679\pi$
$179$	0.999595	−	0.642401i	0.0747133	−	0.0480153i	0.577464	+	0.816416i	$0.304042\pi$
$180$	−0.654861	−	0.755750i	−0.0488104	−	0.0563302i
$181$	−11.6144	−	3.41030i	−0.863293	−	0.253486i	−0.180032	−	0.983661i	$-0.557620\pi$
$181$	−11.6144	−	3.41030i	−0.863293	−	0.253486i	−0.683260	+	0.730175i	$0.739438\pi$
$182$	−10.9482	+	23.9733i	−0.811538	+	1.77702i
$183$	−13.1952			−0.975418
$184$	4.32517	+	2.07193i	0.318856	+	0.152745i
$185$	−0.370291			−0.0272243
$186$	3.40054	−	7.44615i	0.249340	−	0.545978i
$187$	−8.97937	−	2.63658i	−0.656636	−	0.192806i
$188$	−3.22619	−	3.72322i	−0.235294	−	0.271544i
$189$	−4.39483	+	2.82439i	−0.319677	+	0.205444i
$190$	1.97472	−	2.27895i	0.143261	−	0.165332i
$191$	−2.08139	+	14.4764i	−0.150604	+	1.04748i	0.764605	+	0.644499i	$0.222934\pi$
$191$	−2.08139	+	14.4764i	−0.150604	+	1.04748i	−0.915210	+	0.402978i	$0.867975\pi$
$192$	−0.959493	+	0.281733i	−0.0692454	+	0.0203323i
$193$	10.3420	+	6.64638i	0.744431	+	0.478417i	0.857058	−	0.515221i	$-0.172290\pi$
$193$	10.3420	+	6.64638i	0.744431	+	0.478417i	−0.112627	+	0.993637i	$0.535926\pi$
$194$	−1.11289	−	7.74030i	−0.0799006	−	0.555721i
$195$	2.09570	+	4.58895i	0.150076	+	0.328621i
$196$	8.42947	+	18.4580i	0.602105	+	1.31843i
$197$	−2.87809	−	20.0175i	−0.205055	−	1.42619i	−0.788998	−	0.614395i	$-0.789400\pi$
$197$	−2.87809	−	20.0175i	−0.205055	−	1.42619i	0.583943	−	0.811795i	$-0.301509\pi$
$198$	3.35230	+	2.15439i	0.238238	+	0.153106i
$199$	−21.2313	+	6.23408i	−1.50505	+	0.441922i	−0.927308	−	0.374298i	$-0.877884\pi$
$199$	−21.2313	+	6.23408i	−1.50505	+	0.441922i	−0.577741	+	0.816220i	$0.696066\pi$
$200$	−0.142315	+	0.989821i	−0.0100632	+	0.0699909i
$201$	1.34398	−	1.55103i	0.0947968	−	0.109401i
$202$	6.56202	−	4.21715i	0.461702	−	0.296718i
$203$	−23.3500	−	26.9473i	−1.63885	−	1.89133i
$204$	−2.25335	−	0.661644i	−0.157766	−	0.0463244i
$205$	0.800350	−	1.75252i	0.0558989	−	0.122401i
$206$	11.4332			0.796592
$207$	−1.26652	−	4.62557i	−0.0880294	−	0.321500i
$208$	5.04484			0.349797
$209$	−4.99178	+	10.9305i	−0.345288	+	0.756076i
$210$	5.01253	+	1.47181i	0.345897	+	0.101565i
$211$	−3.88368	−	4.48201i	−0.267364	−	0.308554i	0.606153	−	0.795348i	$-0.292712\pi$
$211$	−3.88368	−	4.48201i	−0.267364	−	0.308554i	−0.873517	+	0.486794i	$0.838166\pi$
$212$	1.87005	−	1.20181i	0.128436	−	0.0825407i
$213$	−4.97237	+	5.73842i	−0.340701	+	0.393190i
$214$	0.490840	−	3.41386i	0.0335531	−	0.233367i
$215$	−10.6622	+	3.13069i	−0.727153	+	0.213511i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	6.08599	+	42.3290i	0.413144	+	2.87348i
$218$	−6.76628	−	14.8161i	−0.458270	−	1.00347i
$219$	−6.33710	−	13.8763i	−0.428221	−	0.937674i
$220$	−0.567109	−	3.94433i	−0.0382345	−	0.265927i
$221$	9.96693	+	6.40536i	0.670449	+	0.430871i
$222$	0.355291	−	0.104323i	0.0238456	−	0.00700170i
$223$	0.456862	−	3.17755i	0.0305938	−	0.212784i	−0.968790	−	0.247883i	$-0.920265\pi$
$223$	0.456862	−	3.17755i	0.0305938	−	0.212784i	0.999384	+	0.0350982i	$0.0111744\pi$
$224$	3.42109	−	3.94814i	0.228581	−	0.263796i
$225$	0.841254	−	0.540641i	0.0560836	−	0.0360427i
$226$	9.65355	+	11.1408i	0.642144	+	0.741074i
$227$	18.0178	+	5.29051i	1.19588	+	0.351143i	0.818278	−	0.574823i	$-0.194929\pi$
$227$	18.0178	+	5.29051i	1.19588	+	0.351143i	0.377607	+	0.925966i	$0.376747\pi$
$228$	−1.25268	+	2.74298i	−0.0829605	+	0.181658i
$229$	19.7756			1.30681			0.653403	−	0.757010i	$-0.273341\pi$
$229$	19.7756			1.30681			0.653403	+	0.757010i	$0.273341\pi$
$230$	−2.66638	+	3.98628i	−0.175816	+	0.262848i
$231$	−20.8176			−1.36970
$232$	−2.83534	+	6.20852i	−0.186149	+	0.407609i
$233$	−17.8773	−	5.24924i	−1.17118	−	0.343889i	−0.362412	−	0.932018i	$-0.618047\pi$
$233$	−17.8773	−	5.24924i	−1.17118	−	0.343889i	−0.808767	+	0.588129i	$0.799865\pi$
$234$	−3.30367	−	3.81263i	−0.215967	−	0.249240i
$235$	4.14446	−	2.66348i	0.270355	−	0.173746i
$236$	1.43022	−	1.65057i	0.0930997	−	0.107443i
$237$	0.615851	−	4.28334i	0.0400038	−	0.278233i
$238$	11.7718	−	3.45652i	0.763055	−	0.224053i
$239$	14.0980	+	9.06023i	0.911923	+	0.586058i	0.910304	−	0.413941i	$-0.135848\pi$
$239$	14.0980	+	9.06023i	0.911923	+	0.586058i	0.00161968	+	0.999999i	$0.499484\pi$
$240$	−0.142315	−	0.989821i	−0.00918638	−	0.0638927i
$241$	−6.54823	−	14.3386i	−0.421808	−	0.923632i	−0.994586	−	0.103921i	$-0.966861\pi$
$241$	−6.54823	−	14.3386i	−0.421808	−	0.923632i	0.572777	−	0.819711i	$-0.305866\pi$
$242$	2.02696	+	4.43841i	0.130298	+	0.285312i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	−11.1005	−	7.13387i	−0.710638	−	0.456699i
$245$	−19.4697	+	5.71683i	−1.24387	+	0.365235i
$246$	−0.274188	+	1.90702i	−0.0174816	+	0.121587i
$247$	9.96214	−	11.4969i	0.633876	−	0.731532i
$248$	6.88641	−	4.42563i	0.437288	−	0.281028i
$249$	5.94925	+	6.86580i	0.377018	+	0.435102i
$250$	−0.959493	−	0.281733i	−0.0606837	−	0.0178183i
$251$	1.57738	−	3.45399i	0.0995636	−	0.218014i	−0.853295	−	0.521428i	$-0.825399\pi$
$251$	1.57738	−	3.45399i	0.0995636	−	0.218014i	0.952859	+	0.303414i	$0.0981267\pi$
$252$	−5.22414			−0.329090
$253$	5.71954	−	18.2349i	0.359584	−	1.14642i
$254$	−2.61984			−0.164383
$255$	0.975595	−	2.13626i	0.0610941	−	0.133778i
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	7.27999	+	8.40156i	0.454113	+	0.524075i	0.935925	−	0.352200i	$-0.114566\pi$
$257$	7.27999	+	8.40156i	0.454113	+	0.524075i	−0.481811	+	0.876275i	$0.660021\pi$
$258$	9.34824	−	6.00775i	0.581996	−	0.374026i
$259$	−1.26680	+	1.46196i	−0.0787149	+	0.0908419i
$260$	−0.717955	+	4.99349i	−0.0445257	+	0.309683i
$261$	6.54884	−	1.92291i	0.405363	−	0.119025i
$262$	−4.02606	−	2.58739i	−0.248731	−	0.159849i
$263$	−1.51364	−	10.5276i	−0.0933350	−	0.649160i	−0.981758	−	0.190134i	$-0.939108\pi$
$263$	−1.51364	−	10.5276i	−0.0933350	−	0.649160i	0.888423	−	0.459025i	$-0.151801\pi$
$264$	1.65538	+	3.62478i	0.101882	+	0.223090i
$265$	0.923441	+	2.02205i	0.0567265	+	0.124214i
$266$	−2.24193	−	15.5930i	−0.137461	−	0.956066i
$267$	−3.45258	−	2.21884i	−0.211294	−	0.135791i
$268$	1.96918	−	0.578202i	0.120287	−	0.0353193i
$269$	−3.59607	+	25.0112i	−0.219256	+	1.52496i	0.521538	+	0.853228i	$0.325358\pi$
$269$	−3.59607	+	25.0112i	−0.219256	+	1.52496i	−0.740794	+	0.671732i	$0.765551\pi$
$270$	−0.654861	+	0.755750i	−0.0398536	+	0.0459935i
$271$	−7.38832	+	4.74818i	−0.448808	+	0.288432i	−0.745455	−	0.666556i	$-0.767768\pi$
$271$	−7.38832	+	4.74818i	−0.448808	+	0.288432i	0.296647	+	0.954987i	$0.404132\pi$
$272$	−1.53793	−	1.77487i	−0.0932507	−	0.107617i
$273$	25.2874	+	7.42505i	1.53046	+	0.449384i
$274$	8.44765	−	18.4978i	0.510341	−	1.11749i
$275$	3.98489			0.240298
$276$	1.43531	−	4.57601i	0.0863953	−	0.275444i
$277$	−22.8747			−1.37441			−0.687203	−	0.726465i	$-0.741162\pi$
$277$	−22.8747			−1.37441			−0.687203	+	0.726465i	$0.741162\pi$
$278$	5.36891	−	11.7563i	0.322006	−	0.705094i
$279$	−7.85431	−	2.30623i	−0.470225	−	0.138071i
$280$	3.42109	+	3.94814i	0.204449	+	0.235947i
$281$	14.4470	−	9.28454i	0.861837	−	0.553869i	−0.0334087	−	0.999442i	$-0.510636\pi$
$281$	14.4470	−	9.28454i	0.861837	−	0.553869i	0.895246	+	0.445573i	$0.147000\pi$
$282$	−3.22619	+	3.72322i	−0.192117	+	0.221715i
$283$	−0.922750	+	6.41786i	−0.0548518	+	0.381502i	0.943842	+	0.330398i	$0.107183\pi$
$283$	−0.922750	+	6.41786i	−0.0548518	+	0.381502i	−0.998693	+	0.0511040i	$0.983726\pi$
$284$	−7.28545	+	2.13920i	−0.432312	+	0.126938i
$285$	−2.53678	−	1.63029i	−0.150266	−	0.0965702i
$286$	−2.86097	−	19.8985i	−0.169173	−	1.17662i
$287$	−4.18114	−	9.15543i	−0.246805	−	0.540428i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	1.63443	+	11.3677i	0.0961431	+	0.668690i
$290$	−5.74182	−	3.69004i	−0.337171	−	0.216687i
$291$	−7.50313	+	2.20312i	−0.439842	+	0.129149i
$292$	2.17099	−	15.0996i	0.127048	−	0.883637i
$293$	−3.01541	+	3.47997i	−0.176162	+	0.203302i	−0.836963	−	0.547259i	$-0.815671\pi$
$293$	−3.01541	+	3.47997i	−0.176162	+	0.203302i	0.660801	+	0.750561i	$0.270217\pi$
$294$	17.0704	−	10.9705i	0.995568	−	0.639813i
$295$	1.43022	+	1.65057i	0.0832709	+	0.0960997i
$296$	0.355291	+	0.104323i	0.0206509	+	0.00606365i
$297$	1.65538	−	3.62478i	0.0960551	−	0.210331i
$298$	0.821513			0.0475890
$299$	−13.4514	+	20.1101i	−0.777917	+	1.16300i
$300$	1.00000			0.0577350
$301$	−24.1157	+	52.8061i	−1.39001	+	3.04369i
$302$	−11.8487	−	3.47910i	−0.681818	−	0.200200i
$303$	−5.10810	−	5.89506i	−0.293453	−	0.338663i
$304$	−2.53678	+	1.63029i	−0.145495	+	0.0935037i
$305$	8.64102	−	9.97227i	0.494783	−	0.571011i
$306$	−0.334224	+	2.32458i	−0.0191063	+	0.132887i
$307$	−6.05704	+	1.77851i	−0.345693	+	0.101505i	−0.449970	−	0.893044i	$-0.648565\pi$
$307$	−6.05704	+	1.77851i	−0.345693	+	0.101505i	0.104277	+	0.994548i	$0.466747\pi$
$308$	−17.5129	−	11.2549i	−0.997891	−	0.641305i
$309$	−1.62712	−	11.3169i	−0.0925637	−	0.643794i
$310$	3.40054	+	7.44615i	0.193138	+	0.422913i
$311$	4.02332	+	8.80983i	0.228141	+	0.499560i	0.988737	−	0.149667i	$-0.0478200\pi$
$311$	4.02332	+	8.80983i	0.228141	+	0.499560i	−0.760595	+	0.649226i	$0.775093\pi$
$312$	−0.717955	−	4.99349i	−0.0406462	−	0.282701i
$313$	21.4214	+	13.7667i	1.21081	+	0.778140i	0.980794	−	0.195047i	$-0.0624859\pi$
$313$	21.4214	+	13.7667i	1.21081	+	0.778140i	0.230016	+	0.973187i	$0.426122\pi$
$314$	−9.55190	+	2.80469i	−0.539045	+	0.158278i
$315$	0.743473	−	5.17097i	0.0418900	−	0.291351i
$316$	2.83384	−	3.27042i	0.159416	−	0.183976i
$317$	−18.9242	+	12.1618i	−1.06289	+	0.683077i	−0.950543	−	0.310592i	$-0.899473\pi$
$317$	−18.9242	+	12.1618i	−1.06289	+	0.683077i	−0.112346	+	0.993669i	$0.535836\pi$
$318$	−1.45571	−	1.67998i	−0.0816324	−	0.0942088i
$319$	26.0964	+	7.66259i	1.46112	+	0.429023i
$320$	0.415415	−	0.909632i	0.0232224	−	0.0508500i
$321$	−3.44897			−0.192503
$322$	6.61650	+	24.1647i	0.368723	+	1.34664i
$323$	−7.08181			−0.394042
$324$	0.415415	−	0.909632i	0.0230786	−	0.0505351i
$325$	−4.84049	−	1.42130i	−0.268502	−	0.0788393i
$326$	−3.91287	−	4.51570i	−0.216714	−	0.250101i
$327$	−13.7023	+	8.80596i	−0.757741	+	0.486971i
$328$	−1.26167	+	1.45605i	−0.0696642	+	0.0803968i
$329$	3.66274	−	25.4749i	0.201933	−	1.40448i
$330$	−3.82347	+	1.12267i	−0.210475	+	0.0618011i
$331$	−0.395961	−	0.254469i	−0.0217640	−	0.0139869i	0.529714	−	0.848177i	$-0.322299\pi$
$331$	−0.395961	−	0.254469i	−0.0217640	−	0.0139869i	−0.551478	+	0.834190i	$0.685936\pi$
$332$	1.29289	+	8.99228i	0.0709568	+	0.493516i
$333$	−0.153824	−	0.336828i	−0.00842952	−	0.0184581i
$334$	−8.37258	−	18.3334i	−0.458127	−	1.00316i
$335$	0.292074	+	2.03142i	0.0159577	+	0.110988i
$336$	−4.39483	−	2.82439i	−0.239758	−	0.154083i
$337$	12.2209	−	3.58838i	0.665714	−	0.195471i	0.0686204	−	0.997643i	$-0.478140\pi$
$337$	12.2209	−	3.58838i	0.665714	−	0.195471i	0.597094	+	0.802172i	$0.296322\pi$
$338$	−1.77188	+	12.3237i	−0.0963773	+	0.670319i
$339$	9.65355	−	11.1408i	0.524309	−	0.605084i
$340$	1.97567	−	1.26969i	0.107146	−	0.0688584i
$341$	−21.3615	−	24.6525i	−1.15679	−	1.33501i
$342$	2.89333	+	0.849559i	0.156454	+	0.0459389i
$343$	−28.8454	+	63.1627i	−1.55751	+	3.41046i
$344$	11.1123			0.599134
$345$	4.32517	+	2.07193i	0.232859	+	0.111549i
$346$	18.0595			0.970886
$347$	−6.83353	+	14.9633i	−0.366843	+	0.803274i	0.632739	+	0.774365i	$0.281931\pi$
$347$	−6.83353	+	14.9633i	−0.366843	+	0.803274i	−0.999582	+	0.0289091i	$0.990797\pi$
$348$	6.54884	+	1.92291i	0.351055	+	0.103079i
$349$	−19.5775	−	22.5936i	−1.04796	−	1.20941i	−0.977290	−	0.211907i	$-0.932033\pi$
$349$	−19.5775	−	22.5936i	−1.04796	−	1.20941i	−0.0706674	−	0.997500i	$-0.522513\pi$
$350$	−4.39483	+	2.82439i	−0.234913	+	0.150970i
$351$	−3.30367	+	3.81263i	−0.176337	+	0.203503i
$352$	−0.567109	+	3.94433i	−0.0302270	+	0.210233i
$353$	−1.77382	+	0.520840i	−0.0944109	+	0.0277215i	−0.328597	−	0.944470i	$-0.606576\pi$
$353$	−1.77382	+	0.520840i	−0.0944109	+	0.0277215i	0.234186	+	0.972192i	$0.424758\pi$
$354$	−1.83731	−	1.18077i	−0.0976519	−	0.0627570i
$355$	−1.08060	−	7.51573i	−0.0573522	−	0.398894i
$356$	−1.70490	−	3.73321i	−0.0903595	−	0.197860i
$357$	−5.09665	−	11.1601i	−0.269743	−	0.590655i
$358$	−0.169102	−	1.17613i	−0.00893729	−	0.0621602i
$359$	20.8344	+	13.3895i	1.09960	+	0.706669i	0.959003	−	0.283398i	$-0.0914616\pi$
$359$	20.8344	+	13.3895i	1.09960	+	0.706669i	0.140597	+	0.990067i	$0.455098\pi$
$360$	−0.959493	+	0.281733i	−0.0505697	+	0.0148486i
$361$	1.40990	−	9.80604i	0.0742050	−	0.516107i
$362$	−7.92692	+	9.14815i	−0.416630	+	0.480816i
$363$	4.10477	−	2.63798i	0.215445	−	0.138458i
$364$	17.2588	+	19.9177i	0.904608	+	1.04397i
$365$	14.6369	+	4.29779i	0.766132	+	0.224957i
$366$	−5.48149	+	12.0028i	−0.286522	+	0.627395i
$367$	2.44948			0.127862			0.0639310	−	0.997954i	$-0.479636\pi$
$367$	2.44948			0.127862			0.0639310	+	0.997954i	$0.479636\pi$
$368$	3.68144	−	3.07360i	0.191908	−	0.160223i
$369$	1.92663			0.100296
$370$	−0.153824	+	0.336828i	−0.00799695	+	0.0175109i
$371$	11.1425	+	3.27174i	0.578492	+	0.169860i
$372$	−5.36062	−	6.18649i	−0.277935	−	0.320754i
$373$	−1.03596	+	0.665770i	−0.0536399	+	0.0344722i	−0.567186	−	0.823590i	$-0.691968\pi$
$373$	−1.03596	+	0.665770i	−0.0536399	+	0.0344722i	0.513546	+	0.858062i	$0.328332\pi$
$374$	−6.12848	+	7.07264i	−0.316896	+	0.365718i
$375$	−0.142315	+	0.989821i	−0.00734911	+	0.0511142i
$376$	−4.72697	+	1.38796i	−0.243775	+	0.0715787i
$377$	−28.9665	−	18.6157i	−1.49185	−	0.958755i
$378$	0.743473	+	5.17097i	0.0382401	+	0.265966i
$379$	−8.74017	−	19.1383i	−0.448952	−	0.983068i	−0.989868	−	0.141991i	$-0.954649\pi$
$379$	−8.74017	−	19.1383i	−0.448952	−	0.983068i	0.540916	−	0.841077i	$-0.318078\pi$
$380$	−1.25268	−	2.74298i	−0.0642609	−	0.140712i
$381$	0.372842	+	2.59317i	0.0191013	+	0.132852i
$382$	12.3036	+	7.90702i	0.629505	+	0.404559i
$383$	−18.0419	+	5.29758i	−0.921898	+	0.270694i	−0.708041	−	0.706171i	$-0.750421\pi$
$383$	−18.0419	+	5.29758i	−0.921898	+	0.270694i	−0.213857	+	0.976865i	$0.568603\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	13.6327	−	15.7329i	0.694784	−	0.801824i
$386$	10.3420	−	6.64638i	0.526392	−	0.338292i
$387$	−7.27700	−	8.39810i	−0.369910	−	0.426899i
$388$	−7.50313	−	2.20312i	−0.380914	−	0.111846i
$389$	8.13114	−	17.8047i	0.412265	−	0.902735i	−0.583613	−	0.812032i	$-0.698361\pi$
$389$	8.13114	−	17.8047i	0.412265	−	0.902735i	0.995878	−	0.0907030i	$-0.0289114\pi$
$390$	5.04484			0.255455
$391$	11.1758	−	1.39815i	0.565185	−	0.0707077i
$392$	20.2917			1.02488
$393$	−1.98809	+	4.35330i	−0.100286	+	0.219595i
$394$	−19.4042	−	5.69758i	−0.977569	−	0.287040i
$395$	2.83384	+	3.27042i	0.142586	+	0.164553i
$396$	3.35230	−	2.15439i	0.168460	−	0.108262i
$397$	4.18618	−	4.83111i	0.210098	−	0.242466i	−0.640913	−	0.767613i	$-0.721444\pi$
$397$	4.18618	−	4.83111i	0.210098	−	0.242466i	0.851012	+	0.525147i	$0.175990\pi$
$398$	−3.14909	+	21.9024i	−0.157850	+	1.09787i
$399$	−15.1152	+	4.43822i	−0.756706	+	0.222189i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	−2.23577	−	15.5501i	−0.111649	−	0.776537i	−0.966316	−	0.257360i	$-0.917147\pi$
$401$	−2.23577	−	15.5501i	−0.111649	−	0.776537i	0.854667	−	0.519177i	$-0.173762\pi$
$402$	−0.852560	−	1.86685i	−0.0425218	−	0.0931098i
$403$	17.1552	+	37.5646i	0.854561	+	1.87123i
$404$	−1.11010	−	7.72089i	−0.0552294	−	0.384129i
$405$	0.841254	+	0.540641i	0.0418022	+	0.0268647i
$406$	−34.2121	+	10.0456i	−1.69792	+	0.498553i
$407$	0.209995	−	1.46055i	0.0104091	−	0.0723967i
$408$	−1.53793	+	1.77487i	−0.0761389	+	0.0878689i
$409$	−17.0729	+	10.9721i	−0.844201	+	0.542535i	−0.889761	−	0.456426i	$-0.849129\pi$
$409$	−17.0729	+	10.9721i	−0.844201	+	0.542535i	0.0455598	+	0.998962i	$0.485493\pi$
$410$	−1.26167	−	1.45605i	−0.0623096	−	0.0719091i
$411$	−19.5117	−	5.72916i	−0.962442	−	0.282599i
$412$	4.74954	−	10.4000i	0.233993	−	0.512374i
$413$	11.4096			0.561430
$414$	−4.73370	−	0.769463i	−0.232649	−	0.0378170i
$415$	−9.08475			−0.445953
$416$	2.09570	−	4.58895i	0.102750	−	0.224992i
$417$	−12.4007	−	3.64117i	−0.607264	−	0.178309i
$418$	7.86904	+	9.08136i	0.384887	+	0.444184i
$419$	−19.6823	+	12.6491i	−0.961544	+	0.617947i	−0.924425	−	0.381364i	$-0.875454\pi$
$419$	−19.6823	+	12.6491i	−0.961544	+	0.617947i	−0.0371188	+	0.999311i	$0.511818\pi$
$420$	3.42109	−	3.94814i	0.166932	−	0.192650i
$421$	3.84670	−	26.7544i	0.187477	−	1.30393i	−0.651037	−	0.759046i	$-0.725666\pi$
$421$	3.84670	−	26.7544i	0.187477	−	1.30393i	0.838513	−	0.544881i	$-0.183425\pi$
$422$	−5.69031	+	1.67083i	−0.277000	+	0.0813346i
$423$	4.14446	+	2.66348i	0.201510	+	0.129503i
$424$	−0.316357	−	2.20031i	−0.0153636	−	0.106857i
$425$	0.975595	+	2.13626i	0.0473233	+	0.103624i
$426$	3.15425	+	6.90685i	0.152824	+	0.334638i
$427$	−9.81028	−	68.2320i	−0.474753	−	3.30198i
$428$	−2.90146	−	1.86465i	−0.140247	−	0.0901314i
$429$	−19.2888	+	5.66371i	−0.931272	+	0.273446i
$430$	−1.58144	+	10.9992i	−0.0762639	+	0.530427i
$431$	1.44038	−	1.66229i	0.0693807	−	0.0800696i	−0.719998	−	0.693976i	$-0.755857\pi$
$431$	1.44038	−	1.66229i	0.0693807	−	0.0800696i	0.789379	+	0.613906i	$0.210403\pi$
$432$	0.841254	−	0.540641i	0.0404748	−	0.0260116i
$433$	0.390582	+	0.450756i	0.0187702	+	0.0216620i	0.765057	−	0.643963i	$-0.222711\pi$
$433$	0.390582	+	0.450756i	0.0187702	+	0.0216620i	−0.746287	+	0.665624i	$0.768165\pi$
$434$	41.0320	+	12.0481i	1.96960	+	0.578327i
$435$	−2.83534	+	6.20852i	−0.135944	+	0.297676i
$436$	−16.2880			−0.780054
$437$	0.265226	−	14.4593i	0.0126875	−	0.691682i
$438$	−15.2549			−0.728906
$439$	−4.68102	+	10.2500i	−0.223413	+	0.489206i	−0.987834	−	0.155511i	$-0.950298\pi$
$439$	−4.68102	+	10.2500i	−0.223413	+	0.489206i	0.764421	+	0.644717i	$0.223025\pi$
$440$	−3.82347	−	1.12267i	−0.182277	−	0.0535214i
$441$	−13.2882	−	15.3354i	−0.632772	−	0.730258i
$442$	9.96693	−	6.40536i	0.474079	−	0.304672i
$443$	−23.0562	+	26.6082i	−1.09543	+	1.26420i	−0.133458	+	0.991054i	$0.542608\pi$
$443$	−23.0562	+	26.6082i	−1.09543	+	1.26420i	−0.961974	+	0.273141i	$0.911937\pi$
$444$	0.0526979	−	0.366522i	0.00250093	−	0.0173944i
$445$	3.93784	−	1.15625i	0.186672	−	0.0548117i
$446$	−2.70061	−	1.73558i	−0.127878	−	0.0821820i
$447$	−0.116914	−	0.813151i	−0.00552982	−	0.0384607i
$448$	−2.17019	−	4.75205i	−0.102532	−	0.224513i
$449$	−2.25009	−	4.92700i	−0.106188	−	0.232520i	0.849078	−	0.528268i	$-0.177158\pi$
$449$	−2.25009	−	4.92700i	−0.106188	−	0.232520i	−0.955266	+	0.295748i	$0.904431\pi$
$450$	−0.142315	−	0.989821i	−0.00670879	−	0.0466606i
$451$	6.45864	+	4.15072i	0.304125	+	0.195450i
$452$	14.1442	−	4.15312i	0.665289	−	0.195347i
$453$	−1.75744	+	12.2233i	−0.0825717	+	0.574299i
$454$	12.2973	−	14.1918i	0.577140	−	0.666056i
$455$	−22.1712	+	14.2486i	−1.03940	+	0.667983i
$456$	1.97472	+	2.27895i	0.0924747	+	0.106722i
$457$	23.5774	+	6.92294i	1.10290	+	0.323842i	0.782005	−	0.623272i	$-0.214197\pi$
$457$	23.5774	+	6.92294i	1.10290	+	0.323842i	0.320898	+	0.947114i	$0.396015\pi$
$458$	8.21507	−	17.9885i	0.383865	−	0.840547i
$459$	2.34848			0.109618
$460$	2.51839	+	4.08138i	0.117421	+	0.190295i
$461$	21.0443			0.980130			0.490065	−	0.871686i	$-0.336973\pi$
$461$	21.0443			0.980130			0.490065	+	0.871686i	$0.336973\pi$
$462$	−8.64796	+	18.9364i	−0.402339	+	0.881001i
$463$	−16.5129	−	4.84862i	−0.767418	−	0.225334i	−0.125486	−	0.992095i	$-0.540049\pi$
$463$	−16.5129	−	4.84862i	−0.767418	−	0.225334i	−0.641933	+	0.766761i	$0.721867\pi$
$464$	4.46963	+	5.15823i	0.207497	+	0.239465i
$465$	6.88641	−	4.42563i	0.319350	−	0.205234i
$466$	−12.2014	+	14.0811i	−0.565217	+	0.652295i
$467$	−0.469603	+	3.26616i	−0.0217306	+	0.151140i	−0.997798	−	0.0663296i	$-0.978871\pi$
$467$	−0.469603	+	3.26616i	−0.0217306	+	0.151140i	0.976067	+	0.217469i	$0.0697802\pi$
$468$	−4.84049	+	1.42130i	−0.223752	+	0.0656994i
$469$	9.01955	+	5.79651i	0.416484	+	0.267658i
$470$	−0.701118	−	4.87638i	−0.0323402	−	0.224931i
$471$	4.13552	+	9.05552i	0.190555	+	0.417256i
$472$	−0.907272	−	1.98665i	−0.0417606	−	0.0914429i
$473$	−6.30187	−	43.8305i	−0.289760	−	2.01533i
$474$	−3.64043	−	2.33956i	−0.167210	−	0.107460i
$475$	2.89333	−	0.849559i	0.132755	−	0.0389804i
$476$	1.74603	−	12.1439i	0.0800293	−	0.556616i
$477$	−1.45571	+	1.67998i	−0.0666526	+	0.0769212i
$478$	14.0980	−	9.06023i	0.644827	−	0.414405i
$479$	9.97618	+	11.5131i	0.455823	+	0.526048i	0.936414	−	0.350897i	$-0.114123\pi$
$479$	9.97618	+	11.5131i	0.455823	+	0.526048i	−0.480591	+	0.876945i	$0.659578\pi$
$480$	−0.959493	−	0.281733i	−0.0437947	−	0.0128593i
$481$	−0.776019	+	1.69924i	−0.0353834	+	0.0774789i
$482$	−15.7631			−0.717989
$483$	22.9771	−	9.98814i	1.04549	−	0.454476i
$484$	4.87935			0.221789
$485$	3.24850	−	7.11323i	0.147507	−	0.322995i
$486$	−0.959493	−	0.281733i	−0.0435235	−	0.0127796i
$487$	−7.78812	−	8.98797i	−0.352914	−	0.407284i	0.551339	−	0.834281i	$-0.314117\pi$
$487$	−7.78812	−	8.98797i	−0.352914	−	0.407284i	−0.904253	+	0.426997i	$0.859571\pi$
$488$	−11.1005	+	7.13387i	−0.502497	+	0.322935i
$489$	−3.91287	+	4.51570i	−0.176946	+	0.204207i
$490$	−2.88781	+	20.0851i	−0.130458	+	0.907354i
$491$	−8.67987	+	2.54864i	−0.391717	+	0.115018i	−0.471659	−	0.881781i	$-0.656345\pi$
$491$	−8.67987	+	2.54864i	−0.391717	+	0.115018i	0.0799421	+	0.996800i	$0.474526\pi$
$492$	1.62078	+	1.04161i	0.0730705	+	0.0469596i
$493$	2.28118	+	15.8660i	0.102739	+	0.714568i
$494$	−6.31955	−	13.8379i	−0.284330	−	0.622596i
$495$	1.65538	+	3.62478i	0.0744039	+	0.162922i
$496$	−1.16497	−	8.10258i	−0.0523089	−	0.363816i
$497$	−33.3700	−	21.4456i	−1.49685	−	0.961967i
$498$	8.71675	−	2.55947i	0.390607	−	0.114693i
$499$	4.57659	−	31.8309i	0.204876	−	1.42495i	−0.584678	−	0.811265i	$-0.698779\pi$
$499$	4.57659	−	31.8309i	0.204876	−	1.42495i	0.789555	−	0.613680i	$-0.210312\pi$
$500$	−0.654861	+	0.755750i	−0.0292863	+	0.0337981i
$501$	−16.9552	+	10.8965i	−0.757504	+	0.486818i
$502$	−2.48659	−	2.86968i	−0.110982	−	0.128080i
$503$	14.1439	+	4.15304i	0.630647	+	0.185175i	0.581408	−	0.813612i	$-0.302502\pi$
$503$	14.1439	+	4.15304i	0.630647	+	0.185175i	0.0492393	+	0.998787i	$0.484320\pi$
$504$	−2.17019	+	4.75205i	−0.0966678	+	0.211673i
$505$	7.80029			0.347108
$506$	−14.2111	−	12.7777i	−0.631759	−	0.568039i
$507$	12.4504			0.552941
$508$	−1.08832	+	2.38309i	−0.0482864	+	0.105732i
$509$	−8.28733	−	2.43338i	−0.367330	−	0.107858i	0.0928581	−	0.995679i	$-0.470400\pi$
$509$	−8.28733	−	2.43338i	−0.367330	−	0.107858i	−0.460188	+	0.887822i	$0.652218\pi$
$510$	−1.53793	−	1.77487i	−0.0681007	−	0.0785924i
$511$	67.0425	−	43.0856i	2.96579	−	1.90600i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	0.429148	−	2.98479i	0.0189473	−	0.131782i
$514$	10.6665	−	3.13198i	0.470481	−	0.138146i
$515$	9.61826	+	6.18128i	0.423831	+	0.272380i
$516$	−1.58144	−	10.9992i	−0.0696191	−	0.484212i
$517$	8.15529	+	17.8576i	0.358669	+	0.785376i
$518$	0.803601	+	1.75964i	0.0353082	+	0.0773141i
$519$	−2.57014	−	17.8757i	−0.112817	−	0.784656i
$520$	4.24399	+	2.72745i	0.186111	+	0.119606i
$521$	40.0350	−	11.7553i	1.75396	−	0.515011i	0.762683	−	0.646772i	$-0.223882\pi$
$521$	40.0350	−	11.7553i	1.75396	−	0.515011i	0.991281	+	0.131762i	$0.0420633\pi$
$522$	0.971343	−	6.75584i	0.0425145	−	0.295695i
$523$	−1.58198	+	1.82571i	−0.0691754	+	0.0798326i	−0.789282	−	0.614030i	$-0.789547\pi$
$523$	−1.58198	+	1.82571i	−0.0691754	+	0.0798326i	0.720107	+	0.693863i	$0.244093\pi$
$524$	−4.02606	+	2.58739i	−0.175879	+	0.113031i
$525$	3.42109	+	3.94814i	0.149308	+	0.172311i
$526$	−10.2050	−	2.99647i	−0.444960	−	0.130652i
$527$	7.98612	−	17.4872i	0.347881	−	0.761753i
$528$	3.98489			0.173420
$529$	2.43613	+	22.8706i	0.105919	+	0.994375i
$530$	2.22294			0.0965582
$531$	−0.907272	+	1.98665i	−0.0393722	+	0.0862132i
$532$	−15.1152	−	4.43822i	−0.655326	−	0.192421i
$533$	−6.36494	−	7.34553i	−0.275696	−	0.318170i
$534$	−3.45258	+	2.21884i	−0.149408	+	0.0960185i
$535$	2.25859	−	2.60656i	0.0976476	−	0.112691i
$536$	0.292074	−	2.03142i	0.0126157	−	0.0877439i
$537$	−1.14009	+	0.334761i	−0.0491985	+	0.0144460i
$538$	21.2571	+	13.6611i	0.916460	+	0.588973i
$539$	−11.5076	−	80.0371i	−0.495667	−	3.44744i
$540$	0.415415	+	0.909632i	0.0178766	+	0.0391443i
$541$	2.66013	+	5.82487i	0.114368	+	0.250431i	0.958156	−	0.286245i	$-0.0924071\pi$
$541$	2.66013	+	5.82487i	0.114368	+	0.250431i	−0.843789	+	0.536676i	$0.819680\pi$
$542$	1.24988	+	8.69312i	0.0536870	+	0.373401i
$543$	10.1832	+	6.54432i	0.437001	+	0.280844i
$544$	−2.25335	+	0.661644i	−0.0966117	+	0.0283678i
$545$	2.31802	−	16.1222i	0.0992933	−	0.690600i
$546$	17.2588	−	19.9177i	0.738610	−	0.852401i
$547$	−9.03781	+	5.80825i	−0.386429	+	0.248343i	−0.719402	−	0.694593i	$-0.755584\pi$
$547$	−9.03781	+	5.80825i	−0.386429	+	0.248343i	0.332974	+	0.942936i	$0.391948\pi$
$548$	−13.3169	−	15.3685i	−0.568869	−	0.656510i
$549$	12.6607	+	3.71752i	0.540346	+	0.158660i
$550$	1.65538	−	3.62478i	0.0705858	−	0.154561i
$551$	20.5816			0.876805
$552$	−3.56624	−	3.20655i	−0.151789	−	0.136480i
$553$	22.6069			0.961343
$554$	−9.50249	+	20.8076i	−0.403722	+	0.884028i
$555$	0.355291	+	0.104323i	0.0150813	+	0.00442826i
$556$	−8.46355	−	9.76746i	−0.358935	−	0.414233i
$557$	20.0948	−	12.9142i	0.851445	−	0.547190i	−0.0405803	−	0.999176i	$-0.512921\pi$
$557$	20.0948	−	12.9142i	0.851445	−	0.547190i	0.892025	+	0.451986i	$0.149284\pi$
$558$	−5.36062	+	6.18649i	−0.226933	+	0.261895i
$559$	−7.97812	+	55.4890i	−0.337439	+	2.34694i
$560$	5.01253	−	1.47181i	0.211818	−	0.0621954i
$561$	7.87283	+	5.05956i	0.332391	+	0.213615i
$562$	−2.44400	−	16.9984i	−0.103094	−	0.717035i
$563$	10.2196	+	22.3778i	0.430705	+	0.943112i	0.993212	+	0.116320i	$0.0371097\pi$
$563$	10.2196	+	22.3778i	0.430705	+	0.943112i	−0.562507	+	0.826793i	$0.690163\pi$
$564$	2.04655	+	4.48133i	0.0861755	+	0.188698i
$565$	2.09792	+	14.5913i	0.0882600	+	0.613862i
$566$	5.45457	+	3.50544i	0.229273	+	0.147345i
$567$	5.01253	−	1.47181i	0.210506	−	0.0618103i
$568$	−1.08060	+	7.51573i	−0.0453409	+	0.315353i
$569$	−4.94779	+	5.71006i	−0.207422	+	0.239378i	−0.849923	−	0.526907i	$-0.823352\pi$
$569$	−4.94779	+	5.71006i	−0.207422	+	0.239378i	0.642501	+	0.766285i	$0.277897\pi$
$570$	−2.53678	+	1.63029i	−0.106254	+	0.0682854i
$571$	20.1451	+	23.2487i	0.843048	+	0.972929i	0.999892	−	0.0146940i	$-0.00467742\pi$
$571$	20.1451	+	23.2487i	0.843048	+	0.972929i	−0.156844	+	0.987623i	$0.550132\pi$
$572$	−19.2888	−	5.66371i	−0.806506	−	0.236811i
$573$	6.07556	−	13.3036i	0.253810	−	0.555767i
$574$	−10.0650			−0.420104
$575$	−4.39825	+	1.91192i	−0.183420	+	0.0797325i
$576$	1.00000			0.0416667
$577$	−10.8543	+	23.7675i	−0.451869	+	0.989454i	0.537397	+	0.843329i	$0.319408\pi$
$577$	−10.8543	+	23.7675i	−0.451869	+	0.989454i	−0.989266	+	0.146125i	$0.953320\pi$
$578$	11.0194	+	3.23559i	0.458347	+	0.134583i
$579$	−8.05054	−	9.29082i	−0.334569	−	0.386113i
$580$	−5.74182	+	3.69004i	−0.238416	+	0.153221i
$581$	−31.0797	+	35.8679i	−1.28940	+	1.48805i
$582$	−1.11289	+	7.74030i	−0.0461307	+	0.320846i
$583$	−8.49934	+	2.49563i	−0.352007	+	0.103359i
$584$	−12.8332	−	8.24740i	−0.531042	−	0.341280i
$585$	−0.717955	−	4.99349i	−0.0296838	−	0.206455i
$586$	1.91285	+	4.18855i	0.0790190	+	0.173027i
$587$	14.2151	+	31.1267i	0.586719	+	1.28474i	0.937405	+	0.348242i	$0.113221\pi$
$587$	14.2151	+	31.1267i	0.586719	+	1.28474i	−0.350686	+	0.936493i	$0.614051\pi$
$588$	−2.88781	−	20.0851i	−0.119091	−	0.828297i
$589$	−20.7659	−	13.3454i	−0.855642	−	0.549888i
$590$	2.09555	−	0.615308i	0.0862722	−	0.0253318i
$591$	−2.87809	+	20.0175i	−0.118389	+	0.823411i
$592$	0.242489	−	0.279847i	0.00996623	−	0.0115016i
$593$	−23.2015	+	14.9107i	−0.952770	+	0.612308i	−0.921988	−	0.387218i	$-0.873436\pi$
$593$	−23.2015	+	14.9107i	−0.952770	+	0.612308i	−0.0307820	+	0.999526i	$0.509800\pi$
$594$	−2.60955	−	3.01158i	−0.107071	−	0.123567i
$595$	11.7718	+	3.45652i	0.482598	+	0.141704i
$596$	0.341269	−	0.747275i	0.0139789	−	0.0306096i
$597$	22.1277			0.905625
$598$	12.7049	+	20.5899i	0.519542	+	0.841984i
$599$	−45.5746			−1.86213			−0.931063	−	0.364857i	$-0.881118\pi$
$599$	−45.5746			−1.86213			−0.931063	+	0.364857i	$0.881118\pi$
$600$	0.415415	−	0.909632i	0.0169592	−	0.0371356i
$601$	26.1618	+	7.68180i	1.06716	+	0.313347i	0.767732	−	0.640771i	$-0.221385\pi$
$601$	26.1618	+	7.68180i	1.06716	+	0.313347i	0.299431	+	0.954118i	$0.403203\pi$
$602$	38.0161	+	43.8729i	1.54942	+	1.78813i
$603$	−1.72651	+	1.10956i	−0.0703090	+	0.0451848i
$604$	−8.08684	+	9.33271i	−0.329049	+	0.379743i
$605$	−0.694404	+	4.82969i	−0.0282315	+	0.196355i
$606$	−7.48432	+	2.19759i	−0.304030	+	0.0892712i
$607$	−6.91038	−	4.44103i	−0.280484	−	0.180256i	0.392834	−	0.919610i	$-0.371495\pi$
$607$	−6.91038	−	4.44103i	−0.280484	−	0.180256i	−0.673317	+	0.739354i	$0.735131\pi$
$608$	0.429148	+	2.98479i	0.0174042	+	0.121049i
$609$	14.8122	+	32.4342i	0.600221	+	1.31430i
$610$	−5.48149	−	12.0028i	−0.221939	−	0.485978i
$611$	−3.53703	−	24.6006i	−0.143093	−	0.995232i
$612$	1.97567	+	1.26969i	0.0798617	+	0.0513240i
$613$	19.4964	−	5.72465i	0.787451	−	0.231217i	0.136806	−	0.990598i	$-0.456316\pi$
$613$	19.4964	−	5.72465i	0.787451	−	0.231217i	0.650646	+	0.759381i	$0.274498\pi$
$614$	−0.898398	+	6.24849i	−0.0362564	+	0.252169i
$615$	−1.26167	+	1.45605i	−0.0508756	+	0.0587135i
$616$	−17.5129	+	11.2549i	−0.705615	+	0.453471i
$617$	13.9754	+	16.1285i	0.562628	+	0.649308i	0.963778	−	0.266705i	$-0.0859348\pi$
$617$	13.9754	+	16.1285i	0.562628	+	0.649308i	−0.401150	+	0.916012i	$0.631389\pi$
$618$	−10.9701	−	3.22112i	−0.441283	−	0.129572i
$619$	−1.13132	+	2.47725i	−0.0454718	+	0.0995693i	−0.931004	−	0.365008i	$-0.881066\pi$
$619$	−1.13132	+	2.47725i	−0.0454718	+	0.0995693i	0.885533	+	0.464577i	$0.153794\pi$
$620$	8.18590			0.328754
$621$	−0.0879548	+	4.79502i	−0.00352950	+	0.192418i
$622$	9.68505			0.388335
$623$	8.90664	−	19.5028i	0.356837	−	0.781364i
$624$	−4.84049	−	1.42130i	−0.193775	−	0.0568973i
$625$	−0.654861	−	0.755750i	−0.0261944	−	0.0302300i
$626$	21.4214	−	13.7667i	0.856172	−	0.550228i
$627$	7.86904	−	9.08136i	0.314259	−	0.362675i
$628$	−1.41677	+	9.85382i	−0.0565351	+	0.393210i
$629$	0.834396	−	0.245001i	0.0332695	−	0.00976882i
$630$	−4.39483	−	2.82439i	−0.175094	−	0.112526i
$631$	−1.52965	−	10.6390i	−0.0608945	−	0.423531i	−0.997351	−	0.0727456i	$-0.976824\pi$
$631$	−1.52965	−	10.6390i	−0.0608945	−	0.423531i	0.936456	−	0.350785i	$-0.114085\pi$
$632$	−1.79766	−	3.93633i	−0.0715071	−	0.156579i
$633$	2.46364	+	5.39461i	0.0979208	+	0.214417i
$634$	3.20141	+	22.2663i	0.127144	+	0.884307i
$635$	−2.20395	−	1.41639i	−0.0874609	−	0.0562077i
$636$	−2.13289	+	0.626274i	−0.0845747	+	0.0248334i
$637$	−14.5685	+	101.326i	−0.577226	+	4.01469i
$638$	17.8110	−	20.5550i	0.705143	−	0.813779i
$639$	6.38765	−	4.10509i	0.252692	−	0.162395i
$640$	−0.654861	−	0.755750i	−0.0258856	−	0.0298736i
$641$	8.35087	+	2.45204i	0.329839	+	0.0968496i	0.442459	−	0.896789i	$-0.354106\pi$
$641$	8.35087	+	2.45204i	0.329839	+	0.0968496i	−0.112620	+	0.993638i	$0.535924\pi$
$642$	−1.43275	+	3.13729i	−0.0565463	+	0.123819i
$643$	15.1774			0.598538			0.299269	−	0.954169i	$-0.403257\pi$
$643$	15.1774			0.598538			0.299269	+	0.954169i	$0.403257\pi$
$644$	24.7295	+	4.01978i	0.974480	+	0.158402i
$645$	11.1123			0.437546
$646$	−2.94189	+	6.44184i	−0.115747	+	0.253451i
$647$	8.46551	+	2.48570i	0.332813	+	0.0977228i	0.443870	−	0.896091i	$-0.353605\pi$
$647$	8.46551	+	2.48570i	0.332813	+	0.0977228i	−0.111056	+	0.993814i	$0.535423\pi$
$648$	−0.654861	−	0.755750i	−0.0257254	−	0.0296886i
$649$	−7.32147	+	4.70523i	−0.287393	+	0.184696i
$650$	−3.30367	+	3.81263i	−0.129580	+	0.149544i
$651$	6.08599	−	42.3290i	0.238529	−	1.65901i
$652$	−5.73309	+	1.68339i	−0.224525	+	0.0659265i
$653$	−39.0772	−	25.1134i	−1.52921	−	0.982762i	−0.990075	−	0.140542i	$-0.955115\pi$
$653$	−39.0772	−	25.1134i	−1.52921	−	0.982762i	−0.539133	−	0.842220i	$-0.681248\pi$
$654$	2.31802	+	16.1222i	0.0906419	+	0.630429i
$655$	−1.98809	−	4.35330i	−0.0776809	−	0.170098i
$656$	0.800350	+	1.75252i	0.0312484	+	0.0684245i
$657$	2.17099	+	15.0996i	0.0846985	+	0.589091i
$658$	−21.6512	−	13.9144i	−0.844054	−	0.542440i
$659$	−3.69138	+	1.08389i	−0.143796	+	0.0422222i	−0.352838	−	0.935684i	$-0.614783\pi$
$659$	−3.69138	+	1.08389i	−0.143796	+	0.0422222i	0.209043	+	0.977907i	$0.432965\pi$
$660$	−0.567109	+	3.94433i	−0.0220747	+	0.153533i
$661$	4.92887	−	5.68822i	0.191711	−	0.221246i	−0.651754	−	0.758430i	$-0.725967\pi$
$661$	4.92887	−	5.68822i	0.191711	−	0.221246i	0.843465	+	0.537184i	$0.180512\pi$
$662$	−0.395961	+	0.254469i	−0.0153895	+	0.00989020i
$663$	−7.75861	−	8.95391i	−0.301319	−	0.347741i
$664$	8.71675	+	2.55947i	0.338276	+	0.0993267i
$665$	6.54416	−	14.3297i	0.253772	−	0.555682i
$666$	−0.370291			−0.0143485
$667$	−32.4799	+	4.06341i	−1.25762	+	0.157336i
$668$	−20.1547			−0.779810
$669$	−1.33358	+	2.92012i	−0.0515590	+	0.112898i
$670$	1.96918	+	0.578202i	0.0760759	+	0.0223379i
$671$	34.4335	+	39.7384i	1.32929	+	1.53408i
$672$	−4.39483	+	2.82439i	−0.169534	+	0.108953i
$673$	15.2978	−	17.6546i	0.589687	−	0.680535i	−0.379972	−	0.924998i	$-0.624066\pi$
$673$	15.2978	−	17.6546i	0.589687	−	0.680535i	0.969659	+	0.244463i	$0.0786118\pi$
$674$	1.81264	−	12.6072i	0.0698202	−	0.485610i
$675$	−0.959493	+	0.281733i	−0.0369309	+	0.0108439i
$676$	10.4739	+	6.73119i	0.402844	+	0.258892i
$677$	−1.39345	−	9.69163i	−0.0535545	−	0.372480i	−0.998920	−	0.0464668i	$-0.985204\pi$
$677$	−1.39345	−	9.69163i	−0.0535545	−	0.372480i	0.945365	−	0.326013i	$-0.105705\pi$
$678$	−6.12379	−	13.4092i	−0.235183	−	0.514978i
$679$	−16.9706	−	37.1605i	−0.651273	−	1.42609i
$680$	−0.334224	−	2.32458i	−0.0128169	−	0.0891435i
$681$	−15.7975	−	10.1524i	−0.605360	−	0.389041i
$682$	−31.2986	+	9.19009i	−1.19848	+	0.351907i
$683$	−0.981028	+	6.82320i	−0.0375380	+	0.261082i	−0.999945	−	0.0105305i	$-0.996648\pi$
$683$	−0.981028	+	6.82320i	−0.0375380	+	0.261082i	0.962407	+	0.271613i	$0.0875571\pi$
$684$	1.97472	−	2.27895i	0.0755053	−	0.0871378i
$685$	17.1073	−	10.9942i	0.653635	−	0.420066i
$686$	45.4720	+	52.4774i	1.73613	+	2.00360i
$687$	−18.9745	−	5.57142i	−0.723923	−	0.212563i
$688$	4.61621	−	10.1081i	0.175991	−	0.385367i
$689$	11.2144			0.427233
$690$	3.68144	−	3.07360i	0.140150	−	0.117010i
$691$	−6.18352			−0.235232			−0.117616	−	0.993059i	$-0.537525\pi$
$691$	−6.18352			−0.235232			−0.117616	+	0.993059i	$0.537525\pi$
$692$	7.50220	−	16.4275i	0.285191	−	0.624481i
$693$	19.9744	+	5.86501i	0.758764	+	0.222793i
$694$	10.7724	+	12.4320i	0.408914	+	0.471912i
$695$	10.8725	−	6.98735i	0.412419	−	0.265045i
$696$	4.46963	−	5.15823i	0.169421	−	0.195522i
$697$	−0.643925	+	4.47860i	−0.0243904	+	0.169639i
$698$	−28.6846	+	8.42256i	−1.08573	+	0.318799i
$699$	15.6742	+	10.0732i	0.592854	+	0.381004i
$700$	0.743473	+	5.17097i	0.0281006	+	0.195444i
$701$	−6.85596	−	15.0125i	−0.258946	−	0.567013i	0.734850	−	0.678230i	$-0.237252\pi$
$701$	−6.85596	−	15.0125i	−0.258946	−	0.567013i	−0.993796	+	0.111217i	$0.964525\pi$
$702$	2.09570	+	4.58895i	0.0790972	+	0.173199i
$703$	−0.158909	−	1.10524i	−0.00599338	−	0.0416849i
$704$	3.35230	+	2.15439i	0.126345	+	0.0811968i
$705$	−4.72697	+	1.38796i	−0.178028	+	0.0522737i
$706$	−0.263098	+	1.82989i	−0.00990183	+	0.0688687i
$707$	26.6855	−	30.7967i	1.00361	−	1.15823i
$708$	−1.83731	+	1.18077i	−0.0690503	+	0.0443759i
$709$	22.7788	+	26.2881i	0.855476	+	0.987272i	0.999998	−	0.00222979i	$-0.000709766\pi$
$709$	22.7788	+	26.2881i	0.855476	+	0.987272i	−0.144522	+	0.989502i	$0.546164\pi$
$710$	−7.28545	−	2.13920i	−0.273418	−	0.0802827i
$711$	−1.79766	+	3.93633i	−0.0674176	+	0.147624i
$712$	−4.10409			−0.153807
$713$	35.4054	+	16.9606i	1.32594	+	0.635180i
$714$	−12.2688			−0.459149
$715$	8.35114	−	18.2864i	0.312315	−	0.683874i
$716$	−1.14009	−	0.334761i	−0.0426072	−	0.0125106i
$717$	−10.9744	−	12.6651i	−0.409845	−	0.472986i
$718$	20.8344	−	13.3895i	0.777534	−	0.499691i
$719$	28.7271	−	33.1528i	1.07134	−	1.23639i	0.100938	−	0.994893i	$-0.467816\pi$
$719$	28.7271	−	33.1528i	1.07134	−	1.23639i	0.970401	−	0.241498i	$-0.0776389\pi$
$720$	−0.142315	+	0.989821i	−0.00530376	+	0.0368885i
$721$	57.3095	−	16.8276i	2.13432	−	0.626692i
$722$	−8.33419	−	5.35606i	−0.310167	−	0.199332i
$723$	2.24332	+	15.6027i	0.0834301	+	0.580269i
$724$	5.02849	+	11.0109i	0.186882	+	0.409215i
$725$	−2.83534	−	6.20852i	−0.105302	−	0.230579i
$726$	−0.694404	−	4.82969i	−0.0257718	−	0.179246i
$727$	23.6408	+	15.1930i	0.876788	+	0.563478i	0.899822	−	0.436257i	$-0.143696\pi$
$727$	23.6408	+	15.1930i	0.876788	+	0.563478i	−0.0230339	+	0.999735i	$0.507333\pi$
$728$	25.2874	−	7.42505i	0.937213	−	0.275191i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	9.98981	−	11.5289i	0.369740	−	0.426702i
$731$	21.9542	−	14.1091i	0.812005	−	0.521844i
$732$	8.64102	+	9.97227i	0.319381	+	0.368586i
$733$	−33.4194	−	9.81281i	−1.23437	−	0.362444i	−0.401474	−	0.915870i	$-0.631502\pi$
$733$	−33.4194	−	9.81281i	−1.23437	−	0.362444i	−0.832898	+	0.553426i	$0.813320\pi$
$734$	1.01755	−	2.22813i	0.0375585	−	0.0822417i
$735$	20.2917			0.748470
$736$	−1.26652	−	4.62557i	−0.0466846	−	0.170501i
$737$	−8.17822			−0.301249
$738$	0.800350	−	1.75252i	0.0294613	−	0.0645112i
$739$	34.3640	+	10.0902i	1.26410	+	0.371174i	0.844020	−	0.536312i	$-0.180183\pi$
$739$	34.3640	+	10.0902i	1.26410	+	0.371174i	0.420082	+	0.907486i	$0.362001\pi$
$740$	0.242489	+	0.279847i	0.00891407	+	0.0102874i
$741$	−12.7977	+	8.22456i	−0.470134	+	0.302137i
$742$	7.60486	−	8.77647i	0.279183	−	0.322195i
$743$	−2.78611	+	19.3778i	−0.102213	+	0.710904i	0.872690	+	0.488274i	$0.162373\pi$
$743$	−2.78611	+	19.3778i	−0.102213	+	0.710904i	−0.974903	+	0.222630i	$0.928536\pi$
$744$	−7.85431	+	2.30623i	−0.287953	+	0.0845506i
$745$	0.691101	+	0.444144i	0.0253200	+	0.0162722i
$746$	0.175253	+	1.21891i	0.00641647	+	0.0446275i
$747$	−3.77394	−	8.26378i	−0.138081	−	0.302356i
$748$	3.88764	+	8.51274i	0.142146	+	0.311257i
$749$	−2.56422	−	17.8345i	−0.0936944	−	0.651659i
$750$	0.841254	+	0.540641i	0.0307182	+	0.0197414i
$751$	−15.3200	+	4.49836i	−0.559035	+	0.164147i	−0.549030	−	0.835802i	$-0.685003\pi$
$751$	−15.3200	+	4.49836i	−0.559035	+	0.164147i	−0.0100047	+	0.999950i	$0.503185\pi$
$752$	−0.701118	+	4.87638i	−0.0255671	+	0.177823i
$753$	−2.48659	+	2.86968i	−0.0906164	+	0.104577i
$754$	−28.9665	+	18.6157i	−1.05490	+	0.677943i
$755$	−8.08684	−	9.33271i	−0.294310	−	0.339652i
$756$	5.01253	+	1.47181i	0.182304	+	0.0535293i
$757$	7.42875	−	16.2667i	0.270003	−	0.591223i	−0.725257	−	0.688478i	$-0.758279\pi$
$757$	7.42875	−	16.2667i	0.270003	−	0.591223i	0.995259	+	0.0972552i	$0.0310063\pi$
$758$	−21.0396			−0.764193
$759$	−10.6252	+	15.8849i	−0.385671	+	0.576585i
$760$	−3.01548			−0.109383
$761$	−18.7709	+	41.1026i	−0.680446	+	1.48997i	0.181723	+	0.983350i	$0.441832\pi$
$761$	−18.7709	+	41.1026i	−0.680446	+	1.48997i	−0.862170	+	0.506620i	$0.830895\pi$
$762$	2.51371	+	0.738093i	0.0910623	+	0.0267383i
$763$	−55.7227	−	64.3074i	−2.01730	−	2.32808i
$764$	12.3036	−	7.90702i	0.445128	−	0.286066i
$765$	−1.53793	+	1.77487i	−0.0556040	+	0.0641704i
$766$	−2.67603	+	18.6122i	−0.0966888	+	0.672486i
$767$	10.5717	−	3.10413i	0.381721	−	0.112084i
$768$	0.841254	+	0.540641i	0.0303561	+	0.0195087i
$769$	5.71042	+	39.7169i	0.205923	+	1.43223i	0.786283	+	0.617867i	$0.212003\pi$
$769$	5.71042	+	39.7169i	0.205923	+	1.43223i	−0.580360	+	0.814360i	$0.697088\pi$
$770$	−8.64796	−	18.9364i	−0.311651	−	0.682420i
$771$	−4.61811	−	10.1122i	−0.166317	−	0.364184i
$772$	−1.74955	−	12.1684i	−0.0629677	−	0.437950i
$773$	−38.3117	−	24.6215i	−1.37798	−	0.885572i	−0.378775	−	0.925489i	$-0.623654\pi$
$773$	−38.3117	−	24.6215i	−1.37798	−	0.885572i	−0.999203	+	0.0399165i	$0.987291\pi$
$774$	−10.6622	+	3.13069i	−0.383243	+	0.112530i
$775$	−1.16497	+	8.10258i	−0.0418471	+	0.291053i
$776$	−5.12094	+	5.90988i	−0.183831	+	0.212152i
$777$	1.62737	−	1.04584i	0.0583814	−	0.0375194i
$778$	−12.8179	−	14.7927i	−0.459546	−	0.530344i
$779$	5.57437	+	1.63678i	0.199723	+	0.0586439i
$780$	2.09570	−	4.58895i	0.0750382	−	0.164311i
$781$	30.2573			1.08269
$782$	3.37079	−	10.7467i	0.120539	−	0.384301i
$783$	−6.82531			−0.243917
$784$	8.42947	−	18.4580i	0.301052	−	0.659213i
$785$	−9.55190	−	2.80469i	−0.340922	−	0.100104i
$786$	3.13402	+	3.61685i	0.111787	+	0.129009i
$787$	21.8992	−	14.0737i	0.780621	−	0.501675i	−0.0886186	−	0.996066i	$-0.528245\pi$
$787$	21.8992	−	14.0737i	0.780621	−	0.501675i	0.869240	+	0.494391i	$0.164609\pi$
$788$	−13.2435	+	15.2838i	−0.471780	+	0.544463i
$789$	−1.51364	+	10.5276i	−0.0538870	+	0.374792i
$790$	4.15210	−	1.21917i	0.147725	−	0.0433760i
$791$	64.7858	+	41.6353i	2.30352	+	1.48038i
$792$	−0.567109	−	3.94433i	−0.0201513	−	0.140156i
$793$	−27.6532	−	60.5521i	−0.981994	−	2.15027i
$794$	−2.65553	−	5.81480i	−0.0942412	−	0.206359i
$795$	−0.316357	−	2.20031i	−0.0112200	−	0.0780370i
$796$	18.6150	+	11.9631i	0.659790	+	0.424021i
$797$	−36.8049	+	10.8069i	−1.30370	+	0.382800i	−0.858583	−	0.512675i	$-0.828655\pi$
$797$	−36.8049	+	10.8069i	−1.30370	+	0.382800i	−0.445113	+	0.895474i	$0.646837\pi$
$798$	−2.24193	+	15.5930i	−0.0793634	+	0.551985i
$799$	−7.57665	+	8.74392i	−0.268043	+	0.309338i
$800$	0.841254	−	0.540641i	0.0297428	−	0.0191145i
$801$	2.68761	+	3.10166i	0.0949619	+	0.109592i
$802$	−15.0737	−	4.42603i	−0.532270	−	0.156289i
$803$	−25.2526	+	55.2956i	−0.891147	+	1.95134i
$804$	−2.05231			−0.0723793
$805$	−7.49825	+	23.9057i	−0.264279	+	0.842567i
$806$	41.2965			1.45461
$807$	10.4969	−	22.9849i	0.369507	−	0.809108i
$808$	−7.48432	−	2.19759i	−0.263297	−	0.0773111i
$809$	2.08327	+	2.40422i	0.0732439	+	0.0845279i	0.791189	−	0.611572i	$-0.209463\pi$
$809$	2.08327	+	2.40422i	0.0732439	+	0.0845279i	−0.717945	+	0.696100i	$0.754917\pi$
$810$	0.841254	−	0.540641i	0.0295586	−	0.0189962i
$811$	−9.61669	+	11.0982i	−0.337687	+	0.389712i	−0.899041	−	0.437864i	$-0.855735\pi$
$811$	−9.61669	+	11.0982i	−0.337687	+	0.389712i	0.561354	+	0.827576i	$0.310281\pi$
$812$	−5.07444	+	35.2935i	−0.178078	+	1.23856i
$813$	8.42676	−	2.47432i	0.295539	−	0.0867782i
$814$	−1.24133	−	0.797753i	−0.0435085	−	0.0279612i
$815$	−0.850349	−	5.91431i	−0.0297864	−	0.207169i
$816$	0.975595	+	2.13626i	0.0341527	+	0.0747839i
$817$	−13.9201	−	30.4807i	−0.487002	−	1.06639i
$818$	2.88822	+	20.0880i	0.100984	+	0.702362i
$819$	−22.1712	−	14.2486i	−0.774725	−	0.497885i
$820$	−1.84859	+	0.542794i	−0.0645554	+	0.0189552i
$821$	−7.49750	+	52.1463i	−0.261665	+	1.81992i	0.258682	+	0.965962i	$0.416712\pi$
$821$	−7.49750	+	52.1463i	−0.261665	+	1.81992i	−0.520347	+	0.853955i	$0.674197\pi$
$822$	−13.3169	+	15.3685i	−0.464480	+	0.536038i
$823$	15.1107	−	9.71104i	0.526725	−	0.338505i	−0.250102	−	0.968219i	$-0.580464\pi$
$823$	15.1107	−	9.71104i	0.526725	−	0.338505i	0.776827	+	0.629714i	$0.216828\pi$
$824$	−7.48718	−	8.64067i	−0.260828	−	0.301012i
$825$	−3.82347	−	1.12267i	−0.133116	−	0.0390865i
$826$	4.73972	−	10.3785i	0.164916	−	0.361115i
$827$	3.96427			0.137851			0.0689256	−	0.997622i	$-0.478043\pi$
$827$	3.96427			0.137851			0.0689256	+	0.997622i	$0.478043\pi$
$828$	−2.66638	+	3.98628i	−0.0926631	+	0.138533i
$829$	−15.7253			−0.546161			−0.273081	−	0.961991i	$-0.588043\pi$
$829$	−15.7253			−0.546161			−0.273081	+	0.961991i	$0.588043\pi$
$830$	−3.77394	+	8.26378i	−0.130995	+	0.286840i
$831$	21.9481	+	6.44455i	0.761371	+	0.223559i
$832$	−3.30367	−	3.81263i	−0.114534	−	0.132179i
$833$	40.0896	−	25.7641i	1.38902	−	0.892672i
$834$	−8.46355	+	9.76746i	−0.293069	+	0.338220i
$835$	2.86832	−	19.9496i	0.0992622	−	0.690384i
$836$	11.5296	−	3.38540i	0.398760	−	0.117087i
$837$	6.88641	+	4.42563i	0.238029	+	0.152972i
$838$	3.32966	+	23.1583i	0.115021	+	0.799989i
$839$	21.1195	+	46.2452i	0.729125	+	1.59656i	0.800657	+	0.599123i	$0.204484\pi$
$839$	21.1195	+	46.2452i	0.729125	+	1.59656i	−0.0715320	+	0.997438i	$0.522789\pi$
$840$	−2.17019	−	4.75205i	−0.0748786	−	0.163961i
$841$	−2.50259	−	17.4059i	−0.0862962	−	0.600203i
$842$	−22.7386	−	14.6132i	−0.783626	−	0.503606i
$843$	−16.4776	+	4.83825i	−0.567518	+	0.166638i
$844$	−0.844004	+	5.87018i	−0.0290518	+	0.202060i
$845$	−8.15327	+	9.40938i	−0.280481	+	0.323692i
$846$	4.14446	−	2.66348i	0.142489	−	0.0915724i
$847$	16.6927	+	19.2644i	0.573567	+	0.661932i
$848$	−2.13289	−	0.626274i	−0.0732438	−	0.0215063i
$849$	2.69349	−	5.89793i	0.0924404	−	0.202416i
$850$	2.34848			0.0805523
$851$	0.468982	+	1.71281i	0.0160765	+	0.0587143i
$852$	7.59302			0.260132
$853$	0.884624	−	1.93706i	0.0302889	−	0.0663235i	−0.893883	−	0.448301i	$-0.852029\pi$
$853$	0.884624	−	1.93706i	0.0302889	−	0.0663235i	0.924172	+	0.381977i	$0.124757\pi$
$854$	−66.1413	−	19.4209i	−2.26331	−	0.664568i
$855$	1.97472	+	2.27895i	0.0675340	+	0.0779384i
$856$	−2.90146	+	1.86465i	−0.0991698	+	0.0637326i
$857$	−36.9331	+	42.6230i	−1.26161	+	1.45597i	−0.427847	+	0.903851i	$0.640728\pi$
$857$	−36.9331	+	42.6230i	−1.26161	+	1.45597i	−0.833762	+	0.552123i	$0.813818\pi$
$858$	−2.86097	+	19.8985i	−0.0976720	+	0.679324i
$859$	−12.6116	+	3.70310i	−0.430302	+	0.126348i	−0.489709	−	0.871886i	$-0.662897\pi$
$859$	−12.6116	+	3.70310i	−0.430302	+	0.126348i	0.0594073	+	0.998234i	$0.481079\pi$
$860$	9.34824	+	6.00775i	0.318773	+	0.204863i
$861$	1.43240	+	9.96253i	0.0488159	+	0.339522i
$862$	−0.913715	−	2.00076i	−0.0311213	−	0.0681461i
$863$	14.1867	+	31.0645i	0.482920	+	1.05745i	0.981650	+	0.190691i	$0.0610727\pi$
$863$	14.1867	+	31.0645i	0.482920	+	1.05745i	−0.498730	+	0.866758i	$0.666200\pi$
$864$	−0.142315	−	0.989821i	−0.00484165	−	0.0336744i
$865$	15.1926	+	9.76372i	0.516565	+	0.331976i
$866$	0.572276	−	0.168035i	0.0194467	−	0.00571007i
$867$	1.63443	−	11.3677i	0.0555082	−	0.386068i
$868$	28.0047	−	32.3191i	0.950540	−	1.09698i
$869$	−14.5067	+	9.32290i	−0.492106	+	0.316258i
$870$	4.46963	+	5.15823i	0.151535	+	0.174880i
$871$	9.93417	+	2.91694i	0.336607	+	0.0988366i
$872$	−6.76628	+	14.8161i	−0.229135	+	0.501736i
$873$	7.81989			0.264663
$874$	−13.0425	−	6.24787i	−0.441168	−	0.211337i
$875$	−5.22414			−0.176608
$876$	−6.33710	+	13.8763i	−0.214111	+	0.468837i
$877$	−33.1499	−	9.73370i	−1.11939	−	0.328684i	−0.330863	−	0.943679i	$-0.607340\pi$
$877$	−33.1499	−	9.73370i	−1.11939	−	0.328684i	−0.788531	+	0.614995i	$0.789158\pi$
$878$	7.37916	+	8.51601i	0.249035	+	0.287401i
$879$	3.87369	−	2.48947i	0.130656	−	0.0839677i
$880$	−2.60955	+	3.01158i	−0.0879679	+	0.101520i
$881$	2.28644	−	15.9026i	0.0770322	−	0.535771i	−0.914366	−	0.404889i	$-0.867310\pi$
$881$	2.28644	−	15.9026i	0.0770322	−	0.535771i	0.991398	−	0.130882i	$-0.0417808\pi$
$882$	−19.4697	+	5.71683i	−0.655580	+	0.192496i
$883$	9.33427	+	5.99877i	0.314123	+	0.201875i	0.688196	−	0.725525i	$-0.258403\pi$
$883$	9.33427	+	5.99877i	0.314123	+	0.201875i	−0.374073	+	0.927399i	$0.622039\pi$
$884$	−1.68611	−	11.7271i	−0.0567099	−	0.394426i
$885$	−0.907272	−	1.98665i	−0.0304976	−	0.0667804i
$886$	14.6258	+	32.0261i	0.491364	+	1.07594i
$887$	3.74174	+	26.0244i	0.125635	+	0.873813i	0.950995	+	0.309206i	$0.100063\pi$
$887$	3.74174	+	26.0244i	0.125635	+	0.873813i	−0.825360	+	0.564607i	$0.809028\pi$
$888$	−0.311508	−	0.200194i	−0.0104535	−	0.00671808i
$889$	−13.1320	+	3.85590i	−0.440433	+	0.129323i
$890$	0.584072	−	4.06231i	0.0195782	−	0.136169i
$891$	−2.60955	+	3.01158i	−0.0874232	+	0.100892i
$892$	−2.70061	+	1.73558i	−0.0904232	+	0.0581114i
$893$	9.72851	+	11.2273i	0.325552	+	0.375707i
$894$	−0.788236	−	0.231447i	−0.0263626	−	0.00774075i
$895$	0.493605	−	1.08084i	0.0164994	−	0.0361286i
$896$	−5.22414			−0.174526
$897$	18.5722	−	15.5058i	0.620109	−	0.517724i
$898$	−5.41648			−0.180750
$899$	−23.2098	+	50.8223i	−0.774089	+	1.69502i
$900$	−0.959493	−	0.281733i	−0.0319831	−	0.00939109i
$901$	−3.41872	−	3.94541i	−0.113894	−	0.131441i
$902$	6.45864	−	4.15072i	0.215049	−	0.138204i
$903$	38.0161	−	43.8729i	1.26510	−	1.46000i
$904$	2.09792	−	14.5913i	0.0697756	−	0.485300i
$905$	−11.6144	+	3.41030i	−0.386076	+	0.113362i
$906$	10.3886	+	6.67635i	0.345138	+	0.221807i
$907$	−2.30878	−	16.0579i	−0.0766618	−	0.533195i	−0.991574	−	0.129542i	$-0.958649\pi$
$907$	−2.30878	−	16.0579i	−0.0766618	−	0.533195i	0.914912	−	0.403653i	$-0.132260\pi$
$908$	−7.80086	−	17.0815i	−0.258881	−	0.566870i
$909$	3.24036	+	7.09539i	0.107476	+	0.235339i
$910$	3.75070	+	26.0867i	0.124335	+	0.864766i
$911$	−22.9015	−	14.7179i	−0.758762	−	0.487627i	0.103162	−	0.994665i	$-0.467104\pi$
$911$	−22.9015	−	14.7179i	−0.758762	−	0.487627i	−0.861924	+	0.507038i	$0.830740\pi$
$912$	2.89333	−	0.849559i	0.0958078	−	0.0281317i
$913$	5.15204	−	35.8333i	0.170508	−	1.18591i
$914$	16.0917	−	18.5708i	0.532267	−	0.614269i
$915$	−11.1005	+	7.13387i	−0.366972	+	0.235838i
$916$	−12.9502	−	14.9454i	−0.427888	−	0.493809i
$917$	−23.9889	−	7.04377i	−0.792182	−	0.232606i
$918$	0.975595	−	2.13626i	0.0321994	−	0.0705069i
$919$	12.2739			0.404879			0.202440	−	0.979295i	$-0.435113\pi$
$919$	12.2739			0.404879			0.202440	+	0.979295i	$0.435113\pi$
$920$	4.75874	−	0.595344i	0.156891	−	0.0196279i
$921$	6.31275			0.208012
$922$	8.74211	−	19.1426i	0.287906	−	0.630426i
$923$	−36.7539	−	10.7919i	−1.20977	−	0.355220i
$924$	13.6327	+	15.7329i	0.448481	+	0.517575i
$925$	−0.311508	+	0.200194i	−0.0102423	+	0.00658235i
$926$	−11.2702	+	13.0064i	−0.370360	+	0.427418i
$927$	−1.62712	+	11.3169i	−0.0534417	+	0.371695i
$928$	6.54884	−	1.92291i	0.214976	−	0.0631227i
$929$	9.25653	+	5.94881i	0.303697	+	0.195174i	0.683609	−	0.729848i	$-0.260409\pi$
$929$	9.25653	+	5.94881i	0.303697	+	0.195174i	−0.379912	+	0.925023i	$0.624046\pi$
$930$	−1.16497	−	8.10258i	−0.0382010	−	0.265694i
$931$	−25.4189	−	55.6596i	−0.833071	−	1.82417i
$932$	7.74001	+	16.9483i	0.253532	+	0.555159i
$933$	−1.37833	−	9.58647i	−0.0451244	−	0.313847i
$934$	2.77592	+	1.78398i	0.0908310	+	0.0583735i
$935$	−8.97937	+	2.63658i	−0.293657	+	0.0862254i
$936$	−0.717955	+	4.99349i	−0.0234671	+	0.163217i
$937$	−6.18108	+	7.13334i	−0.201927	+	0.233036i	−0.847677	−	0.530513i	$-0.821999\pi$
$937$	−6.18108	+	7.13334i	−0.201927	+	0.233036i	0.645750	+	0.763549i	$0.276545\pi$
$938$	9.01955	−	5.79651i	0.294499	−	0.189263i
$939$	−16.6752	−	19.2442i	−0.544173	−	0.628009i
$940$	−4.72697	−	1.38796i	−0.154177	−	0.0452704i
$941$	−22.3634	+	48.9691i	−0.729027	+	1.59635i	0.0717765	+	0.997421i	$0.477133\pi$
$941$	−22.3634	+	48.9691i	−0.729027	+	1.59635i	−0.800804	+	0.598927i	$0.795594\pi$
$942$	9.95515			0.324356
$943$	−9.12008	−	1.48247i	−0.296991	−	0.0482758i
$944$	−2.18401			−0.0710836
$945$	−2.17019	+	4.75205i	−0.0705962	+	0.154584i
$946$	−42.4875	−	12.4755i	−1.38139	−	0.405612i
$947$	−8.48543	−	9.79271i	−0.275739	−	0.318220i	0.600941	−	0.799293i	$-0.294793\pi$
$947$	−8.48543	−	9.79271i	−0.275739	−	0.318220i	−0.876680	+	0.481073i	$0.840247\pi$
$948$	−3.64043	+	2.33956i	−0.118236	+	0.0759854i
$949$	50.3970	−	58.1612i	1.63596	−	1.88799i
$950$	0.429148	−	2.98479i	0.0139234	−	0.0968393i
$951$	21.5840	−	6.33764i	0.699910	−	0.205512i
$952$	−10.3212	−	6.63302i	−0.334511	−	0.214977i
$953$	2.30337	+	16.0203i	0.0746134	+	0.518948i	0.992513	+	0.122136i	$0.0389743\pi$
$953$	2.30337	+	16.0203i	0.0746134	+	0.518948i	−0.917900	+	0.396812i	$0.870117\pi$
$954$	0.923441	+	2.02205i	0.0298975	+	0.0654664i
$955$	6.07556	+	13.3036i	0.196601	+	0.430495i
$956$	−2.38496	−	16.5877i	−0.0771350	−	0.536486i
$957$	−22.8805	−	14.7044i	−0.739622	−	0.475326i
$958$	14.6170	−	4.29193i	0.472253	−	0.138666i
$959$	15.1189	−	105.154i	0.488213	−	3.39560i
$960$	−0.654861	+	0.755750i	−0.0211355	+	0.0243917i
$961$	30.2926	−	19.4679i	0.977181	−	0.627996i
$962$	1.22332	+	1.41178i	0.0394413	+	0.0455177i
$963$	3.30926	+	0.971687i	0.106639	+	0.0313122i
$964$	−6.54823	+	14.3386i	−0.210904	+	0.461816i
$965$	12.2935			0.395742
$966$	0.459488	−	25.0499i	0.0147838	−	0.805967i
$967$	−50.6541			−1.62893			−0.814463	−	0.580216i	$-0.802968\pi$
$967$	−50.6541			−1.62893			−0.814463	+	0.580216i	$0.802968\pi$
$968$	2.02696	−	4.43841i	0.0651488	−	0.142656i
$969$	6.79494	+	1.99518i	0.218285	+	0.0640943i
$970$	−5.12094	−	5.90988i	−0.164424	−	0.189755i
$971$	8.29995	−	5.33405i	0.266358	−	0.171178i	−0.400644	−	0.916234i	$-0.631214\pi$
$971$	8.29995	−	5.33405i	0.266358	−	0.171178i	0.667002	+	0.745056i	$0.267577\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	9.60880	−	66.8307i	0.308044	−	2.14249i
$974$	−11.4111	+	3.35059i	−0.365634	+	0.107360i
$975$	4.24399	+	2.72745i	0.135916	+	0.0873482i
$976$	1.87787	+	13.0609i	0.0601093	+	0.418069i
$977$	−3.50820	−	7.68189i	−0.112237	−	0.245765i	0.845175	−	0.534490i	$-0.179496\pi$
$977$	−3.50820	−	7.68189i	−0.112237	−	0.245765i	−0.957412	+	0.288724i	$0.906769\pi$
$978$	2.48216	+	5.43516i	0.0793706	+	0.173797i
$979$	2.32746	+	16.1879i	0.0743861	+	0.517367i
$980$	17.0704	+	10.9705i	0.545295	+	0.350440i
$981$	15.6282	−	4.58886i	0.498971	−	0.146511i
$982$	−1.28742	+	8.95423i	−0.0410833	+	0.285741i
$983$	−11.6939	+	13.4954i	−0.372976	+	0.430438i	−0.910945	−	0.412527i	$-0.864646\pi$
$983$	−11.6939	+	13.4954i	−0.372976	+	0.430438i	0.537969	+	0.842965i	$0.319192\pi$
$984$	1.62078	−	1.04161i	0.0516687	−	0.0332054i
$985$	−13.2435	−	15.2838i	−0.421973	−	0.486983i
$986$	15.3798	+	4.51593i	0.489794	+	0.143816i
$987$	−10.6915	+	23.4111i	−0.340314	+	0.745183i
$988$	−15.2126			−0.483978
$989$	27.9851	+	45.3535i	0.889874	+	1.44216i
$990$	3.98489			0.126648
$991$	5.78897	−	12.6761i	0.183893	−	0.402669i	−0.795125	−	0.606446i	$-0.792595\pi$
$991$	5.78897	−	12.6761i	0.183893	−	0.402669i	0.979017	+	0.203777i	$0.0653218\pi$
$992$	−7.85431	−	2.30623i	−0.249375	−	0.0732230i
$993$	0.308230	+	0.355716i	0.00978137	+	0.0112883i
$994$	−33.3700	+	21.4456i	−1.05843	+	0.680213i
$995$	−14.4905	+	16.7230i	−0.459381	+	0.530154i
$996$	1.29289	−	8.99228i	0.0409669	−	0.284931i
$997$	24.4088	−	7.16706i	0.773033	−	0.226983i	0.128654	−	0.991689i	$-0.458934\pi$
$997$	24.4088	−	7.16706i	0.773033	−	0.226983i	0.644379	+	0.764706i	$0.277116\pi$
$998$	−27.0532	−	17.3860i	−0.856354	−	0.550345i
$999$	0.0526979	+	0.366522i	0.00166729	+	0.0115962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.121.3	✓	30
23.4	even	11	inner	690.2.m.g.211.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.121.3	✓	30	1.1	even	1	trivial
690.2.m.g.211.3	yes	30	23.4	even	11	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.743473 - 5.17097i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(0.743473 - 5.17097i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-0.142315 - 0.989821i) q^{10} +(1.65538 + 3.62478i) q^{11} +(0.415415 + 0.909632i) q^{12} +(-0.717955 - 4.99349i) q^{13} +(-4.39483 - 2.82439i) q^{14} +(-0.959493 + 0.281733i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-1.53793 + 1.77487i) q^{17} +(0.841254 - 0.540641i) q^{18} +(1.97472 + 2.27895i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(-2.17019 + 4.75205i) q^{21} +3.98489 q^{22} +(-3.56624 - 3.20655i) q^{23} +1.00000 q^{24} +(0.415415 - 0.909632i) q^{25} +(-4.84049 - 1.42130i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-4.39483 + 2.82439i) q^{28} +(4.46963 - 5.15823i) q^{29} +(-0.142315 + 0.989821i) q^{30} +(-7.85431 + 2.30623i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-0.567109 - 3.94433i) q^{33} +(0.975595 + 2.13626i) q^{34} +(-2.17019 - 4.75205i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-0.311508 - 0.200194i) q^{37} +(2.89333 - 0.849559i) q^{38} +(-0.717955 + 4.99349i) q^{39} +(-0.654861 + 0.755750i) q^{40} +(1.62078 - 1.04161i) q^{41} +(3.42109 + 3.94814i) q^{42} +(-10.6622 - 3.13069i) q^{43} +(1.65538 - 3.62478i) q^{44} +1.00000 q^{45} +(-4.39825 + 1.91192i) q^{46} +4.92653 q^{47} +(0.415415 - 0.909632i) q^{48} +(-19.4697 - 5.71683i) q^{49} +(-0.654861 - 0.755750i) q^{50} +(1.97567 - 1.26969i) q^{51} +(-3.30367 + 3.81263i) q^{52} +(-0.316357 + 2.20031i) q^{53} +(-0.959493 + 0.281733i) q^{54} +(3.35230 + 2.15439i) q^{55} +(0.743473 + 5.17097i) q^{56} +(-1.25268 - 2.74298i) q^{57} +(-2.83534 - 6.20852i) q^{58} +(0.310817 + 2.16178i) q^{59} +(0.841254 + 0.540641i) q^{60} +(12.6607 - 3.71752i) q^{61} +(-1.16497 + 8.10258i) q^{62} +(3.42109 - 3.94814i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-3.30367 - 3.81263i) q^{65} +(-3.82347 - 1.12267i) q^{66} +(-0.852560 + 1.86685i) q^{67} +2.34848 q^{68} +(2.51839 + 4.08138i) q^{69} -5.22414 q^{70} +(3.15425 - 6.90685i) q^{71} +(-0.959493 - 0.281733i) q^{72} +(9.98981 + 11.5289i) q^{73} +(-0.311508 + 0.200194i) q^{74} +(-0.654861 + 0.755750i) q^{75} +(0.429148 - 2.98479i) q^{76} +(19.9744 - 5.86501i) q^{77} +(4.24399 + 2.72745i) q^{78} +(0.615851 + 4.28334i) q^{79} +(0.415415 + 0.909632i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-0.274188 - 1.90702i) q^{82} +(-7.64258 - 4.91159i) q^{83} +(5.01253 - 1.47181i) q^{84} +(-0.334224 + 2.32458i) q^{85} +(-7.27700 + 8.39810i) q^{86} +(-5.74182 + 3.69004i) q^{87} +(-2.60955 - 3.01158i) q^{88} +(3.93784 + 1.15625i) q^{89} +(0.415415 - 0.909632i) q^{90} -26.3550 q^{91} +(-0.0879548 + 4.79502i) q^{92} +8.18590 q^{93} +(2.04655 - 4.48133i) q^{94} +(2.89333 + 0.849559i) q^{95} +(-0.654861 - 0.755750i) q^{96} +(6.57851 - 4.22775i) q^{97} +(-13.2882 + 15.3354i) q^{98} +(-0.567109 + 3.94433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more