LMFDB - Embedded newform 156.2.w.c.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(7,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("156.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.w (of order $12$, degree $4$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.3
Character	$\chi$	$=$	156.67
Dual form			156.2.w.c.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.400093 + 1.35644i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.67985 - 1.08540i) q^{4} +(1.23779 - 1.23779i) q^{5} +(0.331729 + 1.37476i) q^{6} +(1.04473 + 3.89897i) q^{7} +(2.14438 - 1.84435i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.400093 + 1.35644i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.67985 - 1.08540i) q^{4} +(1.23779 - 1.23779i) q^{5} +(0.331729 + 1.37476i) q^{6} +(1.04473 + 3.89897i) q^{7} +(2.14438 - 1.84435i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.18375 + 2.17421i) q^{10} +(1.58765 + 0.425411i) q^{11} +(-1.99750 - 0.100060i) q^{12} +(3.59225 + 0.309463i) q^{13} +(-5.70670 - 0.142843i) q^{14} +(0.453062 - 1.69085i) q^{15} +(1.64380 + 3.64663i) q^{16} +(-4.31983 - 2.49405i) q^{17} +(0.974664 + 1.02471i) q^{18} +(-4.61114 + 1.23555i) q^{19} +(-3.42280 + 0.735801i) q^{20} +(2.85424 + 2.85424i) q^{21} +(-1.21225 + 1.98335i) q^{22} +(-3.83701 - 6.64589i) q^{23} +(0.934909 - 2.66945i) q^{24} +1.93577i q^{25} +(-1.85700 + 4.74885i) q^{26} -1.00000i q^{27} +(2.47697 - 7.68363i) q^{28} +(1.36638 + 2.36664i) q^{29} +(2.11227 + 1.29105i) q^{30} +(-3.45413 - 3.45413i) q^{31} +(-5.60410 + 0.770727i) q^{32} +(1.58765 - 0.425411i) q^{33} +(5.11136 - 4.86173i) q^{34} +(6.11924 + 3.53294i) q^{35} +(-1.77991 + 0.912093i) q^{36} +(2.39736 - 8.94708i) q^{37} +(0.168934 - 6.74906i) q^{38} +(3.26571 - 1.52812i) q^{39} +(0.371366 - 4.93720i) q^{40} +(1.75957 + 0.471476i) q^{41} +(-5.01357 + 2.72964i) q^{42} +(-3.69979 + 6.40823i) q^{43} +(-2.20528 - 2.43787i) q^{44} +(-0.453062 - 1.69085i) q^{45} +(10.5499 - 2.54569i) q^{46} +(1.50583 - 1.50583i) q^{47} +(3.24689 + 2.33617i) q^{48} +(-8.04832 + 4.64670i) q^{49} +(-2.62575 - 0.774486i) q^{50} -4.98811 q^{51} +(-5.69855 - 4.41888i) q^{52} -9.46051 q^{53} +(1.35644 + 0.400093i) q^{54} +(2.49175 - 1.43861i) q^{55} +(9.43136 + 6.43402i) q^{56} +(-3.37559 + 3.37559i) q^{57} +(-3.75688 + 0.906535i) q^{58} +(-0.287565 - 1.07321i) q^{59} +(-2.59633 + 2.34862i) q^{60} +(-4.02608 + 6.97338i) q^{61} +(6.06730 - 3.30335i) q^{62} +(3.89897 + 1.04473i) q^{63} +(1.19672 - 7.90999i) q^{64} +(4.82949 - 4.06339i) q^{65} +(-0.0581655 + 2.32376i) q^{66} +(0.191899 - 0.716178i) q^{67} +(4.54962 + 8.87839i) q^{68} +(-6.64589 - 3.83701i) q^{69} +(-7.24048 + 6.88687i) q^{70} +(3.84898 - 1.03133i) q^{71} +(-0.525068 - 2.77926i) q^{72} +(1.77016 + 1.77016i) q^{73} +(11.1770 + 6.83154i) q^{74} +(0.967883 + 1.67642i) q^{75} +(9.08709 + 2.92940i) q^{76} +6.63465i q^{77} +(0.766215 + 5.04112i) q^{78} -0.311883i q^{79} +(6.54843 + 2.47907i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.34352 + 2.19812i) q^{82} +(1.59712 + 1.59712i) q^{83} +(-1.69670 - 7.89270i) q^{84} +(-8.43413 + 2.25992i) q^{85} +(-7.21211 - 7.58243i) q^{86} +(2.36664 + 1.36638i) q^{87} +(4.18914 - 2.01596i) q^{88} +(-2.76068 + 10.3030i) q^{89} +(2.47480 + 0.0619461i) q^{90} +(2.54632 + 14.3294i) q^{91} +(-0.767865 + 15.3288i) q^{92} +(-4.71844 - 1.26430i) q^{93} +(1.44010 + 2.64504i) q^{94} +(-4.17826 + 7.23695i) q^{95} +(-4.46793 + 3.46952i) q^{96} +(1.08064 + 4.03300i) q^{97} +(-3.08289 - 12.7762i) q^{98} +(1.16224 - 1.16224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−0.400093	+	1.35644i	−0.282908	+	0.959147i
$2$	−0.400093	+	1.35644i	−0.282908	+	0.959147i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.67985	−	1.08540i	−0.839926	−	0.542701i
$5$	1.23779	−	1.23779i	0.553555	−	0.553555i	−0.373910	−	0.927465i	$-0.621983\pi$
$5$	1.23779	−	1.23779i	0.553555	−	0.553555i	0.927465	+	0.373910i	$0.121983\pi$
$6$	0.331729	+	1.37476i	0.135428	+	0.561242i
$7$	1.04473	+	3.89897i	0.394869	+	1.47367i	0.822003	+	0.569483i	$0.192857\pi$
$7$	1.04473	+	3.89897i	0.394869	+	1.47367i	−0.427134	+	0.904188i	$0.640477\pi$
$8$	2.14438	−	1.84435i	0.758152	−	0.652078i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	1.18375	+	2.17421i	0.374335	+	0.687546i
$11$	1.58765	+	0.425411i	0.478696	+	0.128266i	0.490095	−	0.871669i	$-0.336962\pi$
$11$	1.58765	+	0.425411i	0.478696	+	0.128266i	−0.0113995	+	0.999935i	$0.503629\pi$
$12$	−1.99750	−	0.100060i	−0.576627	−	0.0288849i
$13$	3.59225	+	0.309463i	0.996310	+	0.0858296i
$13$	3.59225	+	0.309463i	0.996310	+	0.0858296i
$14$	−5.70670	−	0.142843i	−1.52518	−	0.0381764i
$15$	0.453062	−	1.69085i	0.116980	−	0.436575i
$16$	1.64380	+	3.64663i	0.410951	+	0.911658i
$17$	−4.31983	−	2.49405i	−1.04771	−	0.604897i	−0.125704	−	0.992068i	$-0.540119\pi$
$17$	−4.31983	−	2.49405i	−1.04771	−	0.604897i	−0.922008	+	0.387171i	$0.873452\pi$
$18$	0.974664	+	1.02471i	0.229730	+	0.241526i
$19$	−4.61114	+	1.23555i	−1.05787	+	0.283455i	−0.745499	−	0.666506i	$-0.767789\pi$
$19$	−4.61114	+	1.23555i	−1.05787	+	0.283455i	−0.312368	+	0.949961i	$0.601122\pi$
$20$	−3.42280	+	0.735801i	−0.765360	+	0.164530i
$21$	2.85424	+	2.85424i	0.622847	+	0.622847i
$22$	−1.21225	+	1.98335i	−0.258453	+	0.422852i
$23$	−3.83701	−	6.64589i	−0.800071	−	1.38576i	−0.919569	−	0.392929i	$-0.871462\pi$
$23$	−3.83701	−	6.64589i	−0.800071	−	1.38576i	0.119497	−	0.992835i	$-0.461872\pi$
$24$	0.934909	−	2.66945i	0.190838	−	0.544898i
$25$			1.93577i			0.387153i
$26$	−1.85700	+	4.74885i	−0.364187	+	0.931326i
$27$		−	1.00000i		−	0.192450i
$28$	2.47697	−	7.68363i	0.468103	−	1.45207i
$29$	1.36638	+	2.36664i	0.253730	+	0.439474i	0.964550	−	0.263901i	$-0.0850091\pi$
$29$	1.36638	+	2.36664i	0.253730	+	0.439474i	−0.710820	+	0.703374i	$0.751676\pi$
$30$	2.11227	+	1.29105i	0.385645	+	0.235712i
$31$	−3.45413	−	3.45413i	−0.620381	−	0.620381i	0.325248	−	0.945629i	$-0.394552\pi$
$31$	−3.45413	−	3.45413i	−0.620381	−	0.620381i	−0.945629	+	0.325248i	$0.894552\pi$
$32$	−5.60410	+	0.770727i	−0.990675	+	0.136247i
$33$	1.58765	−	0.425411i	0.276375	−	0.0740545i
$34$	5.11136	−	4.86173i	0.876591	−	0.833779i
$35$	6.11924	+	3.53294i	1.03434	+	0.597177i
$36$	−1.77991	+	0.912093i	−0.296652	+	0.152015i
$37$	2.39736	−	8.94708i	0.394124	−	1.47089i	−0.429143	−	0.903237i	$-0.641184\pi$
$37$	2.39736	−	8.94708i	0.394124	−	1.47089i	0.823267	−	0.567655i	$-0.192149\pi$
$38$	0.168934	−	6.74906i	0.0274047	−	1.09484i
$39$	3.26571	−	1.52812i	0.522932	−	0.244695i
$40$	0.371366	−	4.93720i	0.0587182	−	0.780640i
$41$	1.75957	+	0.471476i	0.274799	+	0.0736322i	0.393587	−	0.919288i	$-0.371234\pi$
$41$	1.75957	+	0.471476i	0.274799	+	0.0736322i	−0.118788	+	0.992920i	$0.537901\pi$
$42$	−5.01357	+	2.72964i	−0.773610	+	0.421193i
$43$	−3.69979	+	6.40823i	−0.564213	+	0.977246i	0.432909	+	0.901437i	$0.357487\pi$
$43$	−3.69979	+	6.40823i	−0.564213	+	0.977246i	−0.997122	+	0.0758082i	$0.975846\pi$
$44$	−2.20528	−	2.43787i	−0.332459	−	0.367523i
$45$	−0.453062	−	1.69085i	−0.0675384	−	0.252057i
$46$	10.5499	−	2.54569i	1.55550	−	0.375342i
$47$	1.50583	−	1.50583i	0.219648	−	0.219648i	−0.588702	−	0.808350i	$-0.700361\pi$
$47$	1.50583	−	1.50583i	0.219648	−	0.219648i	0.808350	+	0.588702i	$0.200361\pi$
$48$	3.24689	+	2.33617i	0.468648	+	0.337198i
$49$	−8.04832	+	4.64670i	−1.14976	+	0.663814i
$50$	−2.62575	−	0.774486i	−0.371337	−	0.109529i
$51$	−4.98811			−0.698475
$52$	−5.69855	−	4.41888i	−0.790247	−	0.612789i
$53$	−9.46051			−1.29950			−0.649750	−	0.760148i	$-0.725127\pi$
$53$	−9.46051			−1.29950			−0.649750	+	0.760148i	$0.725127\pi$
$54$	1.35644	+	0.400093i	0.184588	+	0.0544457i
$55$	2.49175	−	1.43861i	0.335987	−	0.193982i
$56$	9.43136	+	6.43402i	1.26032	+	0.859782i
$57$	−3.37559	+	3.37559i	−0.447107	+	0.447107i
$58$	−3.75688	+	0.906535i	−0.493302	+	0.119034i
$59$	−0.287565	−	1.07321i	−0.0374378	−	0.139720i	0.944677	−	0.328001i	$-0.106375\pi$
$59$	−0.287565	−	1.07321i	−0.0374378	−	0.139720i	−0.982115	+	0.188281i	$0.939708\pi$
$60$	−2.59633	+	2.34862i	−0.335184	+	0.303206i
$61$	−4.02608	+	6.97338i	−0.515487	+	0.892849i	0.484352	+	0.874873i	$0.339056\pi$
$61$	−4.02608	+	6.97338i	−0.515487	+	0.892849i	−0.999838	+	0.0179760i	$0.994278\pi$
$62$	6.06730	−	3.30335i	0.770547	−	0.419526i
$63$	3.89897	+	1.04473i	0.491224	+	0.131623i
$64$	1.19672	−	7.90999i	0.149590	−	0.988748i
$65$	4.82949	−	4.06339i	0.599024	−	0.504001i
$66$	−0.0581655	+	2.32376i	−0.00715967	+	0.286035i
$67$	0.191899	−	0.716178i	0.0234442	−	0.0874950i	−0.953213	−	0.302301i	$-0.902245\pi$
$67$	0.191899	−	0.716178i	0.0234442	−	0.0874950i	0.976657	+	0.214806i	$0.0689119\pi$
$68$	4.54962	+	8.87839i	0.551722	+	1.07666i
$69$	−6.64589	−	3.83701i	−0.800071	−	0.461921i
$70$	−7.24048	+	6.88687i	−0.865403	+	0.823138i
$71$	3.84898	−	1.03133i	0.456790	−	0.122397i	−0.0230848	−	0.999734i	$-0.507349\pi$
$71$	3.84898	−	1.03133i	0.456790	−	0.122397i	0.479875	+	0.877337i	$0.340682\pi$
$72$	−0.525068	−	2.77926i	−0.0618799	−	0.327539i
$73$	1.77016	+	1.77016i	0.207181	+	0.207181i	0.803068	−	0.595887i	$-0.203199\pi$
$73$	1.77016	+	1.77016i	0.207181	+	0.207181i	−0.595887	+	0.803068i	$0.703199\pi$
$74$	11.1770	+	6.83154i	1.29930	+	0.794150i
$75$	0.967883	+	1.67642i	0.111762	+	0.193577i
$76$	9.08709	+	2.92940i	1.04236	+	0.336025i
$77$			6.63465i			0.756089i
$78$	0.766215	+	5.04112i	0.0867568	+	0.570795i
$79$		−	0.311883i		−	0.0350895i	−0.999846	−	0.0175448i	$-0.994415\pi$
$79$		−	0.311883i		−	0.0350895i	0.999846	−	0.0175448i	$-0.00558496\pi$
$80$	6.54843	+	2.47907i	0.732137	+	0.277169i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.34352	+	2.19812i	−0.148367	+	0.242741i
$83$	1.59712	+	1.59712i	0.175307	+	0.175307i	0.789306	−	0.614000i	$-0.210440\pi$
$83$	1.59712	+	1.59712i	0.175307	+	0.175307i	−0.614000	+	0.789306i	$0.710440\pi$
$84$	−1.69670	−	7.89270i	−0.185125	−	0.861165i
$85$	−8.43413	+	2.25992i	−0.914810	+	0.245123i
$86$	−7.21211	−	7.58243i	−0.777702	−	0.817634i
$87$	2.36664	+	1.36638i	0.253730	+	0.146491i
$88$	4.18914	−	2.01596i	0.446564	−	0.214902i
$89$	−2.76068	+	10.3030i	−0.292631	+	1.09211i	0.650449	+	0.759550i	$0.274581\pi$
$89$	−2.76068	+	10.3030i	−0.292631	+	1.09211i	−0.943080	+	0.332565i	$0.892086\pi$
$90$	2.47480	+	0.0619461i	0.260867	+	0.00652969i
$91$	2.54632	+	14.3294i	0.266927	+	1.50212i
$92$	−0.767865	+	15.3288i	−0.0800554	+	1.59814i
$93$	−4.71844	−	1.26430i	−0.489279	−	0.131102i
$94$	1.44010	+	2.64504i	0.148535	+	0.272815i
$95$	−4.17826	+	7.23695i	−0.428680	+	0.742496i
$96$	−4.46793	+	3.46952i	−0.456006	+	0.354107i
$97$	1.08064	+	4.03300i	0.109722	+	0.409489i	0.998838	−	0.0481934i	$-0.0153464\pi$
$97$	1.08064	+	4.03300i	0.109722	+	0.409489i	−0.889116	+	0.457682i	$0.848680\pi$
$98$	−3.08289	−	12.7762i	−0.311419	−	1.29059i
$99$	1.16224	−	1.16224i	0.116810	−	0.116810i
$100$	2.10109	−	3.25180i	0.210109	−	0.325180i
$101$	5.07704	−	2.93123i	0.505185	−	0.291669i	−0.225667	−	0.974204i	$-0.572456\pi$
$101$	5.07704	−	2.93123i	0.505185	−	0.291669i	0.730852	+	0.682536i	$0.239123\pi$
$102$	1.99571	−	6.76606i	0.197604	−	0.669940i
$103$	7.33577			0.722815			0.361408	−	0.932408i	$-0.382296\pi$
$103$	7.33577			0.722815			0.361408	+	0.932408i	$0.382296\pi$
$104$	8.27389	−	5.96177i	0.811322	−	0.584599i
$105$	7.06589			0.689560
$106$	3.78508	−	12.8326i	0.367639	−	1.24641i
$107$	−14.0746	+	8.12595i	−1.36064	+	0.785565i	−0.989709	−	0.143095i	$-0.954294\pi$
$107$	−14.0746	+	8.12595i	−1.36064	+	0.785565i	−0.370930	+	0.928661i	$0.620961\pi$
$108$	−1.08540	+	1.67985i	−0.104443	+	0.161644i
$109$	11.6729	−	11.6729i	1.11806	−	1.11806i	0.126033	−	0.992026i	$-0.459775\pi$
$109$	11.6729	−	11.6729i	1.11806	−	1.11806i	0.992026	−	0.126033i	$-0.0402247\pi$
$110$	0.954457	+	3.95548i	0.0910039	+	0.377140i
$111$	−2.39736	−	8.94708i	−0.227548	−	0.849220i
$112$	−12.5008	+	10.2189i	−1.18121	+	0.965591i
$113$	8.98373	−	15.5603i	0.845118	−	1.46379i	−0.0403999	−	0.999184i	$-0.512863\pi$
$113$	8.98373	−	15.5603i	0.845118	−	1.46379i	0.885518	−	0.464604i	$-0.153803\pi$
$114$	−3.22823	−	5.92932i	−0.302351	−	0.555332i
$115$	−12.9756	−	3.47680i	−1.20998	−	0.324213i
$116$	0.273441	−	5.45867i	0.0253883	−	0.506825i
$117$	2.06413	−	2.95624i	0.190829	−	0.273305i
$118$	1.57079	+	0.0393182i	0.144603	+	0.00361953i
$119$	5.21120	−	19.4485i	0.477710	−	1.78284i
$120$	−2.14699	−	4.46142i	−0.195992	−	0.407271i
$121$	−7.18661	−	4.14919i	−0.653328	−	0.377199i
$122$	−7.84815	−	8.25113i	−0.710538	−	0.747022i
$123$	1.75957	−	0.471476i	0.158655	−	0.0425115i
$124$	2.05331	+	9.55156i	0.184392	+	0.857755i
$125$	8.58500	+	8.58500i	0.767866	+	0.767866i
$126$	−2.97705	+	4.87072i	−0.265217	+	0.433918i
$127$	−4.38567	−	7.59620i	−0.389165	−	0.674054i	0.603172	−	0.797611i	$-0.293903\pi$
$127$	−4.38567	−	7.59620i	−0.389165	−	0.674054i	−0.992337	+	0.123557i	$0.960570\pi$
$128$	10.2506	+	4.78800i	0.906035	+	0.423203i
$129$			7.39958i			0.651497i
$130$	3.57949	+	8.17663i	0.313942	+	0.717138i
$131$		−	5.55167i		−	0.485052i	−0.970145	−	0.242526i	$-0.922024\pi$
$131$		−	5.55167i		−	0.485052i	0.970145	−	0.242526i	$-0.0779760\pi$
$132$	−3.12877	−	1.00862i	−0.272324	−	0.0877889i
$133$	−9.63474	−	16.6879i	−0.835438	−	1.44702i
$134$	0.894673	+	0.546837i	0.0772880	+	0.0472395i
$135$	−1.23779	−	1.23779i	−0.106532	−	0.106532i
$136$	−13.8633	+	2.61910i	−1.18876	+	0.224586i
$137$	−12.6380	+	3.38635i	−1.07974	+	0.289315i	−0.754489	−	0.656312i	$-0.772115\pi$
$137$	−12.6380	+	3.38635i	−1.07974	+	0.289315i	−0.325251	+	0.945628i	$0.605449\pi$
$138$	7.86364	−	7.47958i	0.669397	−	0.636705i
$139$	8.15618	+	4.70897i	0.691798	+	0.399410i	0.804285	−	0.594243i	$-0.202548\pi$
$139$	8.15618	+	4.70897i	0.691798	+	0.399410i	−0.112487	+	0.993653i	$0.535882\pi$
$140$	−6.44475	−	12.5767i	−0.544680	−	1.06292i
$141$	0.551173	−	2.05700i	0.0464171	−	0.173231i
$142$	−0.141012	+	5.63353i	−0.0118334	+	0.472756i
$143$	5.57160	+	2.01950i	0.465920	+	0.168879i
$144$	3.97998	+	0.399740i	0.331665	+	0.0333117i
$145$	4.62068	+	1.23811i	0.383727	+	0.102819i
$146$	−3.10934	+	1.69288i	−0.257331	+	0.140104i
$147$	−4.64670	+	8.04832i	−0.383253	+	0.663814i
$148$	−13.7384	+	12.4277i	−1.12929	+	1.02155i
$149$	6.01395	+	22.4444i	0.492682	+	1.83871i	0.542644	+	0.839963i	$0.317423\pi$
$149$	6.01395	+	22.4444i	0.492682	+	1.83871i	−0.0499619	+	0.998751i	$0.515910\pi$
$150$	−2.66121	+	0.642150i	−0.217287	+	0.0524313i
$151$	14.7652	−	14.7652i	1.20157	−	1.20157i	0.227885	−	0.973688i	$-0.426819\pi$
$151$	14.7652	−	14.7652i	1.20157	−	1.20157i	0.973688	−	0.227885i	$-0.0731811\pi$
$152$	−7.60923	+	11.1541i	−0.617190	+	0.904713i
$153$	−4.31983	+	2.49405i	−0.349237	+	0.201632i
$154$	−8.99950	−	2.65448i	−0.725200	−	0.213904i
$155$	−8.55097			−0.686830
$156$	−7.14453	−	0.977592i	−0.572020	−	0.0782700i
$157$	7.31710			0.583968			0.291984	−	0.956423i	$-0.405685\pi$
$157$	7.31710			0.583968			0.291984	+	0.956423i	$0.405685\pi$
$158$	0.423050	+	0.124782i	0.0336560	+	0.00992712i
$159$	−8.19304	+	4.73025i	−0.649750	+	0.375133i
$160$	−5.98269	+	7.89068i	−0.472973	+	0.623813i
$161$	21.9035	−	21.9035i	1.72624	−	1.72624i
$162$	1.37476	−	0.331729i	0.108011	−	0.0260631i
$163$	−0.543410	−	2.02803i	−0.0425632	−	0.158848i	0.941373	−	0.337367i	$-0.109536\pi$
$163$	−0.543410	−	2.02803i	−0.0425632	−	0.158848i	−0.983937	+	0.178519i	$0.942870\pi$
$164$	−2.44408	−	2.70185i	−0.190850	−	0.210979i
$165$	1.43861	−	2.49175i	0.111996	−	0.193982i
$166$	−2.80539	+	1.52740i	−0.217741	+	0.118549i
$167$	6.79218	+	1.81996i	0.525594	+	0.140833i	0.511853	−	0.859073i	$-0.328959\pi$
$167$	6.79218	+	1.81996i	0.525594	+	0.140833i	0.0137413	+	0.999906i	$0.495626\pi$
$168$	11.3848	+	0.856342i	0.878357	+	0.0660682i
$169$	12.8085	+	2.22333i	0.985267	+	0.171026i
$170$	0.308994	−	12.3446i	0.0236987	−	0.946785i
$171$	−1.23555	+	4.61114i	−0.0944849	+	0.352622i
$172$	13.1706	−	6.74911i	1.00425	−	0.514615i
$173$	−1.94727	−	1.12426i	−0.148048	−	0.0854757i	0.424146	−	0.905594i	$-0.360574\pi$
$173$	−1.94727	−	1.12426i	−0.148048	−	0.0854757i	−0.572194	+	0.820118i	$0.693908\pi$
$174$	−2.80029	+	2.66352i	−0.212289	+	0.201921i
$175$	−7.54749	+	2.02234i	−0.570537	+	0.152875i
$176$	1.05848	+	6.48888i	0.0797856	+	0.489118i
$177$	−0.785643	−	0.785643i	−0.0590525	−	0.0590525i
$178$	−12.8708	−	7.86684i	−0.964711	−	0.589645i
$179$	8.30277	+	14.3808i	0.620578	+	1.07487i	0.989378	+	0.145364i	$0.0464353\pi$
$179$	8.30277	+	14.3808i	0.620578	+	1.07487i	−0.368800	+	0.929509i	$0.620231\pi$
$180$	−1.07418	+	3.33213i	−0.0800643	+	0.248362i
$181$			22.0751i			1.64083i	0.571771	+	0.820413i	$0.306257\pi$
$181$			22.0751i			1.64083i	−0.571771	+	0.820413i	$0.693743\pi$
$182$	−20.4557	−	2.27914i	−1.51627	−	0.168941i
$183$			8.05216i			0.595233i
$184$	−20.4854	−	7.17451i	−1.51020	−	0.528912i
$185$	−8.10716	−	14.0420i	−0.596050	−	1.03239i
$186$	3.60276	−	5.89443i	0.264167	−	0.432201i
$187$	−5.79739	−	5.79739i	−0.423948	−	0.423948i
$188$	−4.16401	+	0.895140i	−0.303691	+	0.0652848i
$189$	3.89897	−	1.04473i	0.283608	−	0.0759926i
$190$	−8.14479	−	8.56300i	−0.590885	−	0.621225i
$191$	−9.21941	−	5.32283i	−0.667093	−	0.385146i	0.127881	−	0.991789i	$-0.459182\pi$
$191$	−9.21941	−	5.32283i	−0.667093	−	0.385146i	−0.794974	+	0.606643i	$0.792516\pi$
$192$	−2.91861	−	7.44861i	−0.210632	−	0.537557i
$193$	−2.67260	+	9.97429i	−0.192378	+	0.717965i	0.800552	+	0.599264i	$0.204540\pi$
$193$	−2.67260	+	9.97429i	−0.192378	+	0.717965i	−0.992930	+	0.118702i	$0.962127\pi$
$194$	−5.90287	−	0.147753i	−0.423801	−	0.0106081i
$195$	2.15076	−	5.93374i	0.154019	−	0.424924i
$196$	18.5635	+	0.929901i	1.32597	+	0.0664215i
$197$	3.89735	+	1.04429i	0.277675	+	0.0744028i	0.394969	−	0.918694i	$-0.370755\pi$
$197$	3.89735	+	1.04429i	0.277675	+	0.0744028i	−0.117294	+	0.993097i	$0.537422\pi$
$198$	1.11151	+	2.04152i	0.0789914	+	0.145084i
$199$	13.1823	−	22.8324i	0.934468	−	1.61855i	0.158887	−	0.987297i	$-0.449210\pi$
$199$	13.1823	−	22.8324i	0.934468	−	1.61855i	0.775581	−	0.631248i	$-0.217457\pi$
$200$	3.57024	+	4.15102i	0.252454	+	0.293521i
$201$	−0.191899	−	0.716178i	−0.0135355	−	0.0505153i
$202$	1.94475	+	8.05946i	0.136832	+	0.567062i
$203$	−7.79996	+	7.79996i	−0.547450	+	0.547450i
$204$	8.37928	+	5.41410i	0.586667	+	0.379063i
$205$	2.76156	−	1.59439i	0.192876	−	0.111357i
$206$	−2.93499	+	9.95053i	−0.204490	+	0.693286i
$207$	−7.67401			−0.533381
$208$	4.77645	+	13.6083i	0.331187	+	0.943565i
$209$	−7.84651			−0.542754
$210$	−2.82701	+	9.58444i	−0.195082	+	0.661389i
$211$	17.2916	−	9.98329i	1.19040	−	0.687278i	0.232003	−	0.972715i	$-0.425472\pi$
$211$	17.2916	−	9.98329i	1.19040	−	0.687278i	0.958397	+	0.285437i	$0.0921388\pi$
$212$	15.8922	+	10.2685i	1.09148	+	0.705241i
$213$	2.81765	−	2.81765i	0.193062	−	0.193062i
$214$	−5.39122	−	22.3424i	−0.368537	−	1.52730i
$215$	3.35247	+	12.5116i	0.228636	+	0.853282i
$216$	−1.84435	−	2.14438i	−0.125492	−	0.145906i
$217$	9.85894	−	17.0762i	0.669268	−	1.15921i
$218$	11.1633	+	20.5038i	0.756075	+	1.38869i
$219$	2.41808	+	0.647923i	0.163399	+	0.0437826i
$220$	−5.74723	−	0.287896i	−0.387478	−	0.0194099i
$221$	−14.7461	−	10.2961i	−0.991928	−	0.692589i
$222$	13.0953	+	0.327786i	0.878901	+	0.0219996i
$223$	−3.29915	+	12.3126i	−0.220928	+	0.824513i	0.763068	+	0.646319i	$0.223692\pi$
$223$	−3.29915	+	12.3126i	−0.220928	+	0.824513i	−0.983995	+	0.178195i	$0.942974\pi$
$224$	−8.85979	−	21.0450i	−0.591970	−	1.40613i
$225$	1.67642	+	0.967883i	0.111762	+	0.0645255i
$226$	17.5122	+	18.4114i	1.16490	+	1.22471i
$227$	−11.7286	+	3.14267i	−0.778454	+	0.208586i	−0.626103	−	0.779740i	$-0.715351\pi$
$227$	−11.7286	+	3.14267i	−0.778454	+	0.208586i	−0.152351	+	0.988326i	$0.548684\pi$
$228$	9.33435	−	2.00661i	0.618183	−	0.132891i
$229$	7.55560	+	7.55560i	0.499288	+	0.499288i	0.911216	−	0.411928i	$-0.135145\pi$
$229$	7.55560	+	7.55560i	0.499288	+	0.499288i	−0.411928	+	0.911216i	$0.635145\pi$
$230$	9.90751	−	16.2096i	0.653282	−	1.06883i
$231$	3.31732	+	5.74578i	0.218264	+	0.378044i
$232$	7.29495	+	2.55488i	0.478937	+	0.167736i
$233$		−	14.9395i		−	0.978721i	−0.872082	−	0.489361i	$-0.837230\pi$
$233$		−	14.9395i		−	0.978721i	0.872082	−	0.489361i	$-0.162770\pi$
$234$	3.18412	+	3.98263i	0.208153	+	0.260353i
$235$		−	3.72780i		−	0.243175i
$236$	−0.681796	+	2.11495i	−0.0443811	+	0.137672i
$237$	−0.155941	−	0.270098i	−0.0101295	−	0.0175448i
$238$	24.2957	+	14.8499i	1.57486	+	0.962574i
$239$	5.90086	+	5.90086i	0.381695	+	0.381695i	0.871713	−	0.490017i	$-0.163010\pi$
$239$	5.90086	+	5.90086i	0.381695	+	0.381695i	−0.490017	+	0.871713i	$0.663010\pi$
$240$	6.91064	−	1.12727i	0.446080	−	0.0727652i
$241$	1.79957	−	0.482195i	0.115921	−	0.0310609i	−0.200392	−	0.979716i	$-0.564222\pi$
$241$	1.79957	−	0.482195i	0.115921	−	0.0310609i	0.316313	+	0.948655i	$0.397555\pi$
$242$	8.50343	−	8.08813i	0.546621	−	0.519925i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	14.3321	−	7.34432i	0.917521	−	0.470172i
$245$	−4.21048	+	15.7137i	−0.268998	+	1.00391i
$246$	−0.0644639	+	2.57539i	−0.00411007	+	0.164201i
$247$	−16.9467	+	3.01142i	−1.07829	+	0.191612i
$248$	−13.7776	−	1.03632i	−0.874880	−	0.0658067i
$249$	2.18171	+	0.584586i	0.138260	+	0.0370467i
$250$	−15.0798	+	8.21023i	−0.953732	+	0.519261i
$251$	−0.980655	+	1.69854i	−0.0618984	+	0.107211i	−0.895314	−	0.445436i	$-0.853049\pi$
$251$	−0.980655	+	1.69854i	−0.0618984	+	0.107211i	0.833416	+	0.552647i	$0.186382\pi$
$252$	−5.41574	−	5.98693i	−0.341159	−	0.377141i
$253$	−3.26461	−	12.1837i	−0.205244	−	0.765982i
$254$	12.0585	−	2.90971i	0.756615	−	0.182571i
$255$	−6.17421	+	6.17421i	−0.386644	+	0.386644i
$256$	−10.5958	+	11.9887i	−0.662239	+	0.749293i
$257$	−24.8063	+	14.3219i	−1.54737	+	0.893376i	−0.549032	+	0.835801i	$0.685004\pi$
$257$	−24.8063	+	14.3219i	−1.54737	+	0.893376i	−0.998341	+	0.0575751i	$0.981663\pi$
$258$	−10.0371	−	2.96052i	−0.624881	−	0.184314i
$259$	37.3890			2.32324
$260$	−12.5232	+	1.58395i	−0.776658	+	0.0982325i
$261$	2.73276			0.169154
$262$	7.53050	+	2.22118i	0.465236	+	0.137225i
$263$	6.05064	−	3.49334i	0.373098	−	0.215409i	−0.301713	−	0.953399i	$-0.597558\pi$
$263$	6.05064	−	3.49334i	0.373098	−	0.215409i	0.674811	+	0.737990i	$0.264225\pi$
$264$	2.61992	−	3.84044i	0.161245	−	0.236363i
$265$	−11.7101	+	11.7101i	−0.719345	+	0.719345i
$266$	26.4908	−	6.39224i	1.62426	−	0.391934i
$267$	2.76068	+	10.3030i	0.168951	+	0.630533i
$268$	−1.09970	+	0.994784i	−0.0671751	+	0.0607661i
$269$	−5.42128	+	9.38993i	−0.330541	+	0.572514i	−0.982618	−	0.185639i	$-0.940565\pi$
$269$	−5.42128	+	9.38993i	−0.330541	+	0.572514i	0.652077	+	0.758153i	$0.273898\pi$
$270$	2.17421	−	1.18375i	0.132318	−	0.0720409i
$271$	2.34308	+	0.627826i	0.142332	+	0.0381377i	0.329282	−	0.944232i	$-0.393193\pi$
$271$	2.34308	+	0.627826i	0.142332	+	0.0381377i	−0.186950	+	0.982369i	$0.559860\pi$
$272$	1.99395	−	19.8525i	0.120901	−	1.20374i
$273$	9.36986	+	11.1364i	0.567090	+	0.674007i
$274$	0.463008	−	18.4976i	0.0279714	−	1.11748i
$275$	−0.823496	+	3.07333i	−0.0496587	+	0.185329i
$276$	6.99941	+	13.6591i	0.421315	+	0.822179i
$277$	−13.3960	−	7.73419i	−0.804889	−	0.464703i	0.0402891	−	0.999188i	$-0.487172\pi$
$277$	−13.3960	−	7.73419i	−0.804889	−	0.464703i	−0.845178	+	0.534485i	$0.820505\pi$
$278$	−9.65067	+	9.17934i	−0.578808	+	0.550540i
$279$	−4.71844	+	1.26430i	−0.282485	+	0.0756917i
$280$	19.6380	−	3.71007i	1.17359	−	0.221719i
$281$	−5.64159	−	5.64159i	−0.336549	−	0.336549i	0.518518	−	0.855067i	$-0.326484\pi$
$281$	−5.64159	−	5.64159i	−0.336549	−	0.336549i	−0.855067	+	0.518518i	$0.826484\pi$
$282$	2.56968	+	1.57062i	0.153022	+	0.0935293i
$283$	−7.20563	−	12.4805i	−0.428330	−	0.741890i	0.568395	−	0.822756i	$-0.307565\pi$
$283$	−7.20563	−	12.4805i	−0.428330	−	0.741890i	−0.996725	+	0.0808661i	$0.974231\pi$
$284$	−7.58513	−	2.44521i	−0.450094	−	0.145097i
$285$			8.35651i			0.494997i
$286$	−4.96848	+	6.74954i	−0.293793	+	0.399109i
$287$			7.35308i			0.434038i
$288$	−2.13458	+	5.23866i	−0.125781	+	0.308691i
$289$	3.94060	+	6.82532i	0.231800	+	0.401489i
$290$	−3.52812	+	5.77231i	−0.207178	+	0.338962i
$291$	2.95236	+	2.95236i	0.173070	+	0.173070i
$292$	−1.05227	−	4.89494i	−0.0615794	−	0.286455i
$293$	−11.2297	+	3.00899i	−0.656047	+	0.175787i	−0.571461	−	0.820629i	$-0.693623\pi$
$293$	−11.2297	+	3.00899i	−0.656047	+	0.175787i	−0.0845857	+	0.996416i	$0.526957\pi$
$294$	−9.05794	−	9.52303i	−0.528270	−	0.555395i
$295$	−1.68435	−	0.972459i	−0.0980665	−	0.0566187i
$296$	−11.3607	−	23.6075i	−0.660329	−	1.37216i
$297$	0.425411	−	1.58765i	0.0246848	−	0.0921251i
$298$	−32.8505	−	0.822274i	−1.90298	−	0.0476331i
$299$	−11.7268	−	25.0611i	−0.678179	−	1.44932i
$300$	0.193693	−	3.86668i	0.0111829	−	0.223243i
$301$	−28.8507	−	7.73053i	−1.66293	−	0.445580i
$302$	14.1206	+	25.9355i	0.812550	+	1.49242i
$303$	2.93123	−	5.07704i	0.168395	−	0.291669i
$304$	−12.0854	−	14.7841i	−0.693145	−	0.847927i
$305$	3.64812	+	13.6150i	0.208891	+	0.779592i
$306$	−1.65470	−	6.85743i	−0.0945928	−	0.392013i
$307$	−7.26699	+	7.26699i	−0.414749	+	0.414749i	−0.883389	−	0.468640i	$-0.844744\pi$
$307$	−7.26699	+	7.26699i	−0.414749	+	0.414749i	0.468640	+	0.883389i	$0.344744\pi$
$308$	7.20127	−	11.1452i	0.410330	−	0.635058i
$309$	6.35297	−	3.66789i	0.361408	−	0.208659i
$310$	3.42118	−	11.5989i	0.194310	−	0.658771i
$311$	−20.8388			−1.18166			−0.590829	−	0.806797i	$-0.701199\pi$
$311$	−20.8388			−1.18166			−0.590829	+	0.806797i	$0.701199\pi$
$312$	4.18452	−	9.29999i	0.236902	−	0.526508i
$313$	1.26254			0.0713631			0.0356816	−	0.999363i	$-0.488640\pi$
$313$	1.26254			0.0713631			0.0356816	+	0.999363i	$0.488640\pi$
$314$	−2.92752	+	9.92520i	−0.165210	+	0.560112i
$315$	6.11924	−	3.53294i	0.344780	−	0.199059i
$316$	−0.338518	+	0.523916i	−0.0190431	+	0.0294726i
$317$	14.8065	−	14.8065i	0.831617	−	0.831617i	−0.156121	−	0.987738i	$-0.549899\pi$
$317$	14.8065	−	14.8065i	0.831617	−	0.831617i	0.987738	+	0.156121i	$0.0498990\pi$
$318$	−3.13832	−	13.0059i	−0.175988	−	0.729334i
$319$	1.16255	+	4.33868i	0.0650900	+	0.242919i
$320$	−8.30960	−	11.2722i	−0.464521	−	0.630133i
$321$	−8.12595	+	14.0746i	−0.453546	+	0.785565i
$322$	20.9473	+	38.4742i	1.16735	+	2.14408i
$323$	23.0008	+	6.16306i	1.27980	+	0.342922i
$324$	−0.100060	+	1.99750i	−0.00555891	+	0.110972i
$325$	−0.599048	+	6.95375i	−0.0332292	+	0.385725i
$326$	2.96832	+	0.0742993i	0.164400	+	0.00411506i
$327$	4.27257	−	15.9455i	0.236274	−	0.881786i
$328$	4.64276	−	2.23425i	0.256353	−	0.123366i
$329$	7.44437	+	4.29801i	0.410421	+	0.236957i
$330$	2.80432	+	2.94832i	0.154373	+	0.162299i
$331$	0.617419	−	0.165437i	0.0339364	−	0.00909324i	−0.241811	−	0.970323i	$-0.577741\pi$
$331$	0.617419	−	0.165437i	0.0339364	−	0.00909324i	0.275747	+	0.961230i	$0.411075\pi$
$332$	−0.949406	−	4.41644i	−0.0521055	−	0.242384i
$333$	−6.54972	−	6.54972i	−0.358922	−	0.358922i
$334$	−5.18616	+	8.48502i	−0.283774	+	0.464280i
$335$	−0.648945	−	1.12401i	−0.0354557	−	0.0614110i
$336$	−5.71655	+	15.1002i	−0.311864	+	0.823782i
$337$			6.26263i			0.341147i	0.985345	+	0.170574i	$0.0545621\pi$
$337$			6.26263i			0.341147i	−0.985345	+	0.170574i	$0.945438\pi$
$338$	−8.14039	+	16.4844i	−0.442779	+	0.896631i
$339$		−	17.9675i		−	0.975859i
$340$	16.6210	+	5.35810i	0.901401	+	0.290584i
$341$	−4.01455	−	6.95340i	−0.217400	−	0.376548i
$342$	−5.76039	−	3.52083i	−0.311486	−	0.190385i
$343$	−6.54591	−	6.54591i	−0.353446	−	0.353446i
$344$	3.88529	+	20.5654i	0.209481	+	1.10881i
$345$	−12.9756	+	3.47680i	−0.698583	+	0.187185i
$346$	2.30407	−	2.19155i	0.123868	−	0.117818i
$347$	−0.310641	−	0.179349i	−0.0166761	−	0.00962794i	0.491639	−	0.870799i	$-0.336398\pi$
$347$	−0.310641	−	0.179349i	−0.0166761	−	0.00962794i	−0.508315	+	0.861171i	$0.669731\pi$
$348$	−2.49253	−	4.86407i	−0.133614	−	0.260742i
$349$	−2.85508	+	10.6553i	−0.152829	+	0.570364i	0.846453	+	0.532464i	$0.178734\pi$
$349$	−2.85508	+	10.6553i	−0.152829	+	0.570364i	−0.999282	+	0.0379007i	$0.987933\pi$
$350$	0.276511	−	11.0468i	0.0147801	−	0.590478i
$351$	0.309463	−	3.59225i	0.0165179	−	0.191740i
$352$	−9.22526	−	1.16040i	−0.491708	−	0.0618494i
$353$	0.203032	+	0.0544022i	0.0108063	+	0.00289554i	0.264218	−	0.964463i	$-0.414886\pi$
$353$	0.203032	+	0.0544022i	0.0108063	+	0.00289554i	−0.253412	+	0.967358i	$0.581553\pi$
$354$	1.38001	−	0.751347i	0.0733465	−	0.0399336i
$355$	3.48765	−	6.04079i	0.185105	−	0.320612i
$356$	15.8204	−	14.3110i	0.838481	−	0.758484i
$357$	−5.21120	−	19.4485i	−0.275806	−	1.02932i
$358$	−22.8286	+	5.50853i	−1.20653	+	0.291135i
$359$	−5.55720	+	5.55720i	−0.293298	+	0.293298i	−0.838381	−	0.545084i	$-0.816498\pi$
$359$	−5.55720	+	5.55720i	−0.293298	+	0.293298i	0.545084	+	0.838381i	$0.316498\pi$
$360$	−4.09006	−	2.79021i	−0.215565	−	0.147057i
$361$	3.28151	−	1.89458i	0.172711	−	0.0997148i
$362$	−29.9435	−	8.83207i	−1.57379	−	0.464203i
$363$	−8.29838			−0.435552
$364$	11.2757	−	26.8350i	0.591006	−	1.40653i
$365$	4.38216			0.229373
$366$	−10.9223	−	3.22161i	−0.570916	−	0.168396i
$367$	−17.6277	+	10.1773i	−0.920157	+	0.531253i	−0.883685	−	0.468082i	$-0.844945\pi$
$367$	−17.6277	+	10.1773i	−0.920157	+	0.531253i	−0.0364716	+	0.999335i	$0.511612\pi$
$368$	17.9278	−	24.9167i	0.934552	−	1.29887i
$369$	1.28810	−	1.28810i	0.0670556	−	0.0670556i
$370$	22.2907	−	5.37876i	1.15884	−	0.279628i
$371$	−9.88363	−	36.8862i	−0.513132	−	1.91504i
$372$	6.55400	+	7.24524i	0.339809	+	0.375648i
$373$	6.70320	−	11.6103i	0.347079	−	0.601158i	−0.638651	−	0.769497i	$-0.720507\pi$
$373$	6.70320	−	11.6103i	0.347079	−	0.601158i	0.985729	+	0.168339i	$0.0538404\pi$
$374$	10.1833	−	5.54431i	0.526566	−	0.286690i
$375$	11.7273	+	3.14233i	0.605597	+	0.162269i
$376$	0.451786	−	6.00636i	0.0232991	−	0.309754i
$377$	4.17598	+	8.92439i	0.215074	+	0.459630i
$378$	−0.142843	+	5.70670i	−0.00734705	+	0.293521i
$379$	−8.97914	+	33.5106i	−0.461227	+	1.72132i	0.207877	+	0.978155i	$0.433345\pi$
$379$	−8.97914	+	33.5106i	−0.461227	+	1.72132i	−0.669104	+	0.743169i	$0.733322\pi$
$380$	14.8739	−	7.62192i	0.763013	−	0.390996i
$381$	−7.59620	−	4.38567i	−0.389165	−	0.224685i
$382$	10.9087	−	10.3759i	0.558138	−	0.530879i
$383$	25.5927	−	6.85754i	1.30773	−	0.350404i	0.463360	−	0.886170i	$-0.346644\pi$
$383$	25.5927	−	6.85754i	1.30773	−	0.350404i	0.844366	+	0.535766i	$0.179977\pi$
$384$	11.2713	−	0.978776i	0.575186	−	0.0499479i
$385$	8.21228	+	8.21228i	0.418537	+	0.418537i
$386$	−12.4602	−	7.61586i	−0.634209	−	0.387637i
$387$	3.69979	+	6.40823i	0.188071	+	0.325749i
$388$	2.56211	−	7.94777i	0.130072	−	0.403487i
$389$			10.7078i			0.542905i	0.962452	+	0.271453i	$0.0875041\pi$
$389$			10.7078i			0.542905i	−0.962452	+	0.271453i	$0.912496\pi$
$390$	7.18825	+	5.29142i	0.363991	+	0.267942i
$391$			38.2788i			1.93584i
$392$	−8.68848	+	24.8082i	−0.438835	+	1.25300i
$393$	−2.77584	−	4.80789i	−0.140022	−	0.242526i
$394$	−2.97582	+	4.86871i	−0.149920	+	0.245282i
$395$	−0.386044	−	0.386044i	−0.0194240	−	0.0194240i
$396$	−3.21390	+	0.690895i	−0.161505	+	0.0347188i
$397$	20.4263	−	5.47322i	1.02517	−	0.274693i	0.293214	−	0.956047i	$-0.405275\pi$
$397$	20.4263	−	5.47322i	1.02517	−	0.274693i	0.731954	+	0.681354i	$0.238608\pi$
$398$	25.6966	+	27.0160i	1.28805	+	1.35419i
$399$	−16.6879	−	9.63474i	−0.835438	−	0.482340i
$400$	−7.05902	+	3.18202i	−0.352951	+	0.159101i
$401$	9.14912	−	34.1450i	0.456885	−	1.70512i	−0.225601	−	0.974220i	$-0.572435\pi$
$401$	9.14912	−	34.1450i	0.456885	−	1.70512i	0.682486	−	0.730898i	$-0.260899\pi$
$402$	1.04823	+	0.0262380i	0.0522809	+	0.00130863i
$403$	−11.3392	−	13.4770i	−0.564845	−	0.671339i
$404$	−11.7102	−	0.586600i	−0.582607	−	0.0291845i
$405$	−1.69085	−	0.453062i	−0.0840189	−	0.0225128i
$406$	−7.45946	−	13.7009i	−0.370207	−	0.679963i
$407$	7.61237	−	13.1850i	0.377331	−	0.653557i
$408$	−10.6964	+	9.19983i	−0.529550	+	0.455460i
$409$	1.22807	+	4.58321i	0.0607241	+	0.226625i	0.989618	−	0.143719i	$-0.0459062\pi$
$409$	1.22807	+	4.58321i	0.0607241	+	0.226625i	−0.928894	+	0.370345i	$0.879240\pi$
$410$	1.05781	+	4.38379i	0.0522415	+	0.216500i
$411$	−9.25168	+	9.25168i	−0.456352	+	0.456352i
$412$	−12.3230	−	7.96227i	−0.607111	−	0.392273i
$413$	3.88398	−	2.24242i	0.191118	−	0.110342i
$414$	3.07032	−	10.4093i	0.150898	−	0.511591i
$415$	3.95379			0.194084
$416$	−20.3698	+	1.03438i	−0.998713	+	0.0507146i
$417$	9.41795			0.461199
$418$	3.13933	−	10.6433i	0.153550	−	0.520581i
$419$	13.0212	−	7.51779i	0.636127	−	0.367268i	−0.146994	−	0.989137i	$-0.546960\pi$
$419$	13.0212	−	7.51779i	0.636127	−	0.367268i	0.783121	+	0.621869i	$0.213626\pi$
$420$	−11.8696	−	7.66933i	−0.579179	−	0.374225i
$421$	2.07235	−	2.07235i	0.101000	−	0.101000i	−0.654801	−	0.755801i	$-0.727248\pi$
$421$	2.07235	−	2.07235i	0.101000	−	0.101000i	0.755801	+	0.654801i	$0.227248\pi$
$422$	6.62349	+	27.4492i	0.322426	+	1.33621i
$423$	−0.551173	−	2.05700i	−0.0267989	−	0.100015i
$424$	−20.2869	+	17.4485i	−0.985219	+	0.847375i
$425$	4.82790	−	8.36217i	0.234188	−	0.405625i
$426$	2.69465	+	4.94929i	0.130556	+	0.239794i
$427$	−31.3951	−	8.41230i	−1.51932	−	0.407100i
$428$	32.4631	+	1.62617i	1.56916	+	0.0786040i
$429$	5.83489	−	1.03686i	0.281711	−	0.0500601i
$430$	−18.3125	−	0.458375i	−0.883106	−	0.0221048i
$431$	−7.16677	+	26.7468i	−0.345211	+	1.28835i	0.547154	+	0.837032i	$0.315711\pi$
$431$	−7.16677	+	26.7468i	−0.345211	+	1.28835i	−0.892365	+	0.451314i	$0.850955\pi$
$432$	3.64663	−	1.64380i	0.175449	−	0.0790875i
$433$	−26.8759	−	15.5168i	−1.29157	−	0.745689i	−0.312639	−	0.949872i	$-0.601213\pi$
$433$	−26.8759	−	15.5168i	−1.29157	−	0.745689i	−0.978933	+	0.204183i	$0.934546\pi$
$434$	19.2183	+	20.2051i	0.922508	+	0.969876i
$435$	4.62068	−	1.23811i	0.221545	−	0.0593627i
$436$	−32.2785	+	6.93893i	−1.54586	+	0.332315i
$437$	25.9043	+	25.9043i	1.23917	+	1.23917i
$438$	−1.84632	+	3.02075i	−0.0882208	+	0.144337i
$439$	2.93883	+	5.09021i	0.140263	+	0.242942i	0.927596	−	0.373586i	$-0.121872\pi$
$439$	2.93883	+	5.09021i	0.140263	+	0.242942i	−0.787333	+	0.616528i	$0.788539\pi$
$440$	2.68994	−	7.68059i	0.128238	−	0.366158i
$441$			9.29340i			0.442543i
$442$	19.8658	−	15.8827i	0.944919	−	0.755465i
$443$			1.60011i			0.0760237i	0.999277	+	0.0380118i	$0.0121025\pi$
$443$			1.60011i			0.0760237i	−0.999277	+	0.0380118i	$0.987898\pi$
$444$	−5.68397	+	17.6319i	−0.269749	+	0.836772i
$445$	9.33578	+	16.1700i	0.442558	+	0.766533i
$446$	−15.3813	−	9.40129i	−0.728327	−	0.445164i
$447$	16.4304	+	16.4304i	0.777132	+	0.777132i
$448$	32.0910	−	3.59780i	1.51616	−	0.169980i
$449$	12.5599	−	3.36542i	0.592740	−	0.158824i	0.0500347	−	0.998747i	$-0.484067\pi$
$449$	12.5599	−	3.36542i	0.592740	−	0.158824i	0.542705	+	0.839923i	$0.317400\pi$
$450$	−1.98360	+	1.88672i	−0.0935077	+	0.0889409i
$451$	2.59302	+	1.49708i	0.122101	+	0.0704948i
$452$	−31.9805	+	16.3880i	−1.50424	+	0.770827i
$453$	5.40443	−	20.1696i	0.253922	−	0.947651i
$454$	0.429690	−	17.1665i	0.0201663	−	0.805663i
$455$	20.8885	+	14.5849i	0.979268	+	0.683750i
$456$	−1.01276	+	13.4643i	−0.0474267	+	0.630524i
$457$	9.12334	+	2.44459i	0.426772	+	0.114353i	0.465810	−	0.884885i	$-0.345763\pi$
$457$	9.12334	+	2.44459i	0.426772	+	0.114353i	−0.0390386	+	0.999238i	$0.512430\pi$
$458$	−13.2716	+	7.22577i	−0.620143	+	0.337638i
$459$	−2.49405	+	4.31983i	−0.116412	+	0.201632i
$460$	18.0233	+	19.9243i	0.840343	+	0.928973i
$461$	0.0408995	+	0.152639i	0.00190488	+	0.00710911i	0.966872	−	0.255263i	$-0.0821620\pi$
$461$	0.0408995	+	0.152639i	0.00190488	+	0.00710911i	−0.964967	+	0.262372i	$0.915495\pi$
$462$	−9.12103	+	2.20090i	−0.424349	+	0.102395i
$463$	1.95135	−	1.95135i	0.0906870	−	0.0906870i	−0.660308	−	0.750995i	$-0.729574\pi$
$463$	1.95135	−	1.95135i	0.0906870	−	0.0906870i	0.750995	+	0.660308i	$0.229574\pi$
$464$	−6.38420	+	8.87297i	−0.296379	+	0.411917i
$465$	−7.40535	+	4.27548i	−0.343415	+	0.198271i
$466$	20.2646	+	5.97720i	0.938737	+	0.276888i
$467$	30.3961			1.40656			0.703282	−	0.710911i	$-0.251717\pi$
$467$	30.3961			1.40656			0.703282	+	0.710911i	$0.251717\pi$
$468$	−6.67614	+	2.72565i	−0.308605	+	0.125993i
$469$	2.99283			0.138196
$470$	5.05653	+	1.49146i	0.233240	+	0.0687961i
$471$	6.33680	−	3.65855i	0.291984	−	0.168577i
$472$	−2.59602	−	1.77099i	−0.119492	−	0.0815165i
$473$	−8.60012	+	8.60012i	−0.395434	+	0.395434i
$474$	0.428763	−	0.103460i	0.0196937	−	0.00475210i
$475$	−2.39174	−	8.92608i	−0.109740	−	0.409557i
$476$	−29.8635	+	27.0143i	−1.36879	+	1.23820i
$477$	−4.73025	+	8.19304i	−0.216583	+	0.375133i
$478$	−10.3651	+	5.64327i	−0.474086	+	0.258117i
$479$	−33.8443	−	9.06854i	−1.54638	−	0.414352i	−0.618062	−	0.786130i	$-0.712082\pi$
$479$	−33.8443	−	9.06854i	−1.54638	−	0.414352i	−0.928322	+	0.371777i	$0.878748\pi$
$480$	−1.23582	+	9.82488i	−0.0564072	+	0.448442i
$481$	11.3807	−	31.3982i	0.518916	−	1.43164i
$482$	−0.0659294	+	2.63394i	−0.00300300	+	0.119972i
$483$	8.01723	−	29.9207i	0.364797	−	1.36144i
$484$	7.56889	+	14.7704i	0.344041	+	0.671381i
$485$	6.32959	+	3.65439i	0.287412	+	0.165937i
$486$	1.02471	−	0.974664i	0.0464818	−	0.0442117i
$487$	30.1918	−	8.08986i	1.36812	−	0.366586i	0.501328	−	0.865257i	$-0.332845\pi$
$487$	30.1918	−	8.08986i	1.36812	−	0.366586i	0.866791	+	0.498671i	$0.166178\pi$
$488$	4.22793	+	22.3791i	0.191390	+	1.01305i
$489$	−1.48462	−	1.48462i	−0.0671370	−	0.0671370i
$490$	−19.6301	−	11.9982i	−0.886799	−	0.542024i
$491$	16.6231	+	28.7920i	0.750188	+	1.29936i	0.947731	+	0.319070i	$0.103370\pi$
$491$	16.6231	+	28.7920i	0.750188	+	1.29936i	−0.197543	+	0.980294i	$0.563296\pi$
$492$	−3.46756	−	1.11783i	−0.156330	−	0.0503959i
$493$		−	13.6313i		−	0.613923i
$494$	2.69544	−	24.1920i	0.121273	−	1.08845i
$495$		−	2.87722i		−	0.129321i
$496$	6.91804	−	18.2739i	0.310629	−	0.820521i
$497$	8.04225	+	13.9296i	0.360744	+	0.624828i
$498$	−1.66584	+	2.72546i	−0.0746481	+	0.122131i
$499$	16.3106	+	16.3106i	0.730165	+	0.730165i	0.970652	−	0.240488i	$-0.0773074\pi$
$499$	16.3106	+	16.3106i	0.730165	+	0.730165i	−0.240488	+	0.970652i	$0.577307\pi$
$500$	−5.10335	−	23.7397i	−0.228229	−	1.06167i
$501$	6.79218	−	1.81996i	0.303452	−	0.0813097i
$502$	−1.91162	−	2.00977i	−0.0853197	−	0.0897006i
$503$	−30.7356	−	17.7452i	−1.37043	−	0.791219i	−0.379449	−	0.925213i	$-0.623886\pi$
$503$	−30.7356	−	17.7452i	−1.37043	−	0.791219i	−0.990982	+	0.133994i	$0.957220\pi$
$504$	10.2877	−	4.95079i	0.458251	−	0.220526i
$505$	2.65606	−	9.91254i	0.118193	−	0.441102i
$506$	17.8326	+	0.446363i	0.792754	+	0.0198432i
$507$	12.2041	−	4.47877i	0.542004	−	0.198909i
$508$	−0.877663	+	17.5207i	−0.0389400	+	0.777356i
$509$	33.2216	+	8.90169i	1.47252	+	0.394561i	0.903795	−	0.427967i	$-0.140770\pi$
$509$	33.2216	+	8.90169i	1.47252	+	0.394561i	0.568726	+	0.822527i	$0.307437\pi$
$510$	−5.90468	−	10.8452i	−0.261464	−	0.480233i
$511$	−5.05246	+	8.75112i	−0.223508	+	0.387127i
$512$	−12.0226	−	19.1692i	−0.531329	−	0.847166i
$513$	1.23555	+	4.61114i	0.0545509	+	0.203587i
$514$	−9.50198	−	39.3783i	−0.419115	−	1.73690i
$515$	9.08012	−	9.08012i	0.400118	−	0.400118i
$516$	8.03153	−	12.4302i	0.353568	−	0.547209i
$517$	3.03134	−	1.75014i	0.133318	−	0.0769712i
$518$	−14.9591	+	50.7158i	−0.657263	+	2.22833i
$519$	−2.24851			−0.0986988
$520$	2.86192	−	17.6207i	0.125504	−	0.772720i
$521$	−26.6513			−1.16762			−0.583808	−	0.811892i	$-0.698438\pi$
$521$	−26.6513			−1.16762			−0.583808	+	0.811892i	$0.698438\pi$
$522$	−1.09336	+	3.70682i	−0.0478549	+	0.162243i
$523$	−14.1580	+	8.17414i	−0.619088	+	0.357430i	−0.776514	−	0.630100i	$-0.783014\pi$
$523$	−14.1580	+	8.17414i	−0.619088	+	0.357430i	0.157426	+	0.987531i	$0.449680\pi$
$524$	−6.02580	+	9.32599i	−0.263238	+	0.407408i
$525$	−5.52515	+	5.52515i	−0.241137	+	0.241137i
$526$	2.31768	+	9.60498i	0.101056	+	0.418797i
$527$	6.30647	+	23.5361i	0.274714	+	1.02525i
$528$	4.16111	+	5.09030i	0.181089	+	0.221527i
$529$	−17.9452	+	31.0821i	−0.780228	+	1.35139i
$530$	−11.1989	−	20.5691i	−0.486449	−	0.893467i
$531$	−1.07321	−	0.287565i	−0.0465733	−	0.0124793i
$532$	−1.92811	+	38.4907i	−0.0835942	+	1.66878i
$533$	6.17491	+	2.23818i	0.267465	+	0.0969463i
$534$	−15.0799	−	0.377461i	−0.652571	−	0.0163344i
$535$	−7.36311	+	27.4795i	−0.318335	+	1.18804i
$536$	−0.909380	−	1.88969i	−0.0392793	−	0.0816220i
$537$	14.3808	+	8.30277i	0.620578	+	0.358291i
$538$	−10.5679	−	11.1105i	−0.455612	−	0.479007i
$539$	−14.7547	+	3.95351i	−0.635530	+	0.170290i
$540$	0.735801	+	3.42280i	0.0316639	+	0.147294i
$541$	−16.6651	−	16.6651i	−0.716490	−	0.716490i	0.251395	−	0.967885i	$-0.419111\pi$
$541$	−16.6651	−	16.6651i	−0.716490	−	0.716490i	−0.967885	+	0.251395i	$0.919111\pi$
$542$	−1.78906	+	2.92705i	−0.0768465	+	0.125728i
$543$	11.0375	+	19.1176i	0.473666	+	0.820413i
$544$	26.1310	+	10.6475i	1.12036	+	0.456509i
$545$		−	28.8971i		−	1.23782i
$546$	−18.8547	+	8.25404i	−0.806906	+	0.353240i
$547$		−	24.5736i		−	1.05069i	−0.850888	−	0.525346i	$-0.823936\pi$
$547$		−	24.5736i		−	1.05069i	0.850888	−	0.525346i	$-0.176064\pi$
$548$	24.9056	+	8.02879i	1.06391	+	0.342973i
$549$	4.02608	+	6.97338i	0.171829	+	0.297616i
$550$	−3.83931	−	2.34664i	−0.163709	−	0.100061i
$551$	−9.22466	−	9.22466i	−0.392984	−	0.392984i
$552$	−21.3281	+	4.02938i	−0.907784	+	0.171502i
$553$	1.21602	−	0.325832i	0.0517104	−	0.0138558i
$554$	15.8506	−	15.0765i	0.673428	−	0.640538i
$555$	−14.0420	−	8.10716i	−0.596050	−	0.344130i
$556$	−8.59005	−	16.7631i	−0.364299	−	0.710915i
$557$	0.0562477	−	0.209919i	0.00238329	−	0.00889457i	−0.964724	−	0.263264i	$-0.915201\pi$
$557$	0.0562477	−	0.209919i	0.00238329	−	0.00889457i	0.967107	+	0.254369i	$0.0818678\pi$
$558$	0.172865	−	6.90611i	0.00731796	−	0.292359i
$559$	−15.2737	+	21.8750i	−0.646008	+	0.925213i
$560$	−2.82452	+	28.1221i	−0.119358	+	1.18837i
$561$	−7.91939	−	2.12199i	−0.334357	−	0.0895907i
$562$	9.90963	−	5.39531i	0.418013	−	0.227587i
$563$	8.68923	−	15.0502i	0.366208	−	0.634290i	−0.622762	−	0.782412i	$-0.713989\pi$
$563$	8.68923	−	15.0502i	0.366208	−	0.634290i	0.988969	+	0.148122i	$0.0473227\pi$
$564$	−3.15857	+	2.85722i	−0.133000	+	0.120311i
$565$	−8.14037	−	30.3803i	−0.342468	−	1.27811i
$566$	19.8120	−	4.78063i	0.832760	−	0.200945i
$567$	2.85424	−	2.85424i	0.119867	−	0.119867i
$568$	6.35153	−	9.31045i	0.266504	−	0.390658i
$569$	26.8954	−	15.5281i	1.12751	−	0.650970i	0.184205	−	0.982888i	$-0.441029\pi$
$569$	26.8954	−	15.5281i	1.12751	−	0.650970i	0.943308	+	0.331918i	$0.107696\pi$
$570$	−11.3351	−	3.34338i	−0.474775	−	0.140039i
$571$	−3.95390			−0.165466			−0.0827328	−	0.996572i	$-0.526365\pi$
$571$	−3.95390			−0.165466			−0.0827328	+	0.996572i	$0.526365\pi$
$572$	−7.16749	−	9.43989i	−0.299688	−	0.394701i
$573$	−10.6457			−0.444729
$574$	−9.97400	−	2.94191i	−0.416307	−	0.122793i
$575$	12.8649	−	7.42755i	0.536503	−	0.309750i
$576$	−6.25189	−	4.99138i	−0.260495	−	0.207974i
$577$	−26.0276	+	26.0276i	−1.08354	+	1.08354i	−0.0873665	+	0.996176i	$0.527845\pi$
$577$	−26.0276	+	26.0276i	−1.08354	+	1.08354i	−0.996176	+	0.0873665i	$0.972155\pi$
$578$	−10.8347	+	2.61442i	−0.450666	+	0.108746i
$579$	2.67260	+	9.97429i	0.111070	+	0.414517i
$580$	−6.41821	−	7.09514i	−0.266502	−	0.294610i
$581$	−4.55857	+	7.89567i	−0.189121	+	0.327568i
$582$	−5.18591	+	2.82348i	−0.214963	+	0.117037i
$583$	−15.0200	−	4.02460i	−0.622065	−	0.166682i
$584$	7.06069	+	0.531091i	0.292173	+	0.0219767i
$585$	−1.10425	−	6.21415i	−0.0456553	−	0.256923i
$586$	0.411413	−	16.4363i	0.0169953	−	0.678977i
$587$	8.10015	−	30.2302i	0.334329	−	1.24773i	−0.570266	−	0.821460i	$-0.693160\pi$
$587$	8.10015	−	30.2302i	0.334329	−	1.24773i	0.904595	−	0.426273i	$-0.140174\pi$
$588$	16.5414	−	8.47644i	0.682157	−	0.349563i
$589$	20.1952	+	11.6597i	0.832130	+	0.480431i
$590$	1.99298	−	1.89564i	0.0820495	−	0.0780423i
$591$	3.89735	−	1.04429i	0.160316	−	0.0429565i
$592$	36.5675	−	5.96494i	1.50291	−	0.245158i
$593$	−23.8727	−	23.8727i	−0.980335	−	0.980335i	0.0194751	−	0.999810i	$-0.493800\pi$
$593$	−23.8727	−	23.8727i	−0.980335	−	0.980335i	−0.999810	+	0.0194751i	$0.993800\pi$
$594$	1.98335	+	1.21225i	0.0813779	+	0.0497393i
$595$	−17.6227	−	30.5234i	−0.722460	−	1.25134i
$596$	14.2586	−	44.2308i	0.584056	−	1.81176i
$597$		−	26.3646i		−	1.07903i
$598$	38.6856	−	5.87995i	1.58197	−	0.240449i
$599$		−	12.7693i		−	0.521741i	−0.965374	−	0.260871i	$-0.915990\pi$
$599$		−	12.7693i		−	0.521741i	0.965374	−	0.260871i	$-0.0840096\pi$
$600$	5.16742	+	1.80977i	0.210959	+	0.0738834i
$601$	8.94671	+	15.4962i	0.364944	+	0.632101i	0.988767	−	0.149464i	$-0.0477548\pi$
$601$	8.94671	+	15.4962i	0.364944	+	0.632101i	−0.623823	+	0.781565i	$0.714422\pi$
$602$	22.0290	−	36.0413i	0.897834	−	1.46893i
$603$	−0.524278	−	0.524278i	−0.0213503	−	0.0213503i
$604$	−40.8295	+	8.77715i	−1.66133	+	0.357137i
$605$	−14.0313	+	3.75968i	−0.570454	+	0.152853i
$606$	5.71393	+	6.00733i	0.232113	+	0.244031i
$607$	10.1673	+	5.87007i	0.412676	+	0.238259i	0.691939	−	0.721956i	$-0.256757\pi$
$607$	10.1673	+	5.87007i	0.412676	+	0.238259i	−0.279263	+	0.960215i	$0.590090\pi$
$608$	24.8890	−	10.4781i	1.00938	−	0.424942i
$609$	−2.85498	+	10.6549i	−0.115690	+	0.431760i
$610$	−19.9275	−	0.498800i	−0.806840	−	0.0201958i
$611$	5.87532	−	4.94332i	0.237690	−	0.199985i
$612$	9.96372	+	0.499112i	0.402759	+	0.0201754i
$613$	31.5862	+	8.46349i	1.27575	+	0.341837i	0.832232	−	0.554427i	$-0.187062\pi$
$613$	31.5862	+	8.46349i	1.27575	+	0.341837i	0.443521	+	0.896264i	$0.353729\pi$
$614$	−6.94976	−	12.7647i	−0.280469	−	0.515141i
$615$	1.59439	−	2.76156i	0.0642920	−	0.111357i
$616$	12.2366	+	14.2272i	0.493028	+	0.573230i
$617$	−2.41205	−	9.00188i	−0.0971053	−	0.362402i	0.900225	−	0.435425i	$-0.143402\pi$
$617$	−2.41205	−	9.00188i	−0.0971053	−	0.362402i	−0.997330	+	0.0730231i	$0.976735\pi$
$618$	2.43349	+	10.0849i	0.0978892	+	0.405674i
$619$	2.30979	−	2.30979i	0.0928383	−	0.0928383i	−0.659162	−	0.752001i	$-0.729089\pi$
$619$	2.30979	−	2.30979i	0.0928383	−	0.0928383i	0.752001	+	0.659162i	$0.229089\pi$
$620$	14.3644	+	9.28124i	0.576886	+	0.372744i
$621$	−6.64589	+	3.83701i	−0.266690	+	0.153974i
$622$	8.33744	−	28.2665i	0.334301	−	1.13338i
$623$	−43.0552			−1.72497
$624$	10.9407	+	9.39690i	0.437977	+	0.376177i
$625$	11.5740			0.462959
$626$	−0.505134	+	1.71256i	−0.0201892	+	0.0684477i
$627$	−6.79528	+	3.92325i	−0.271377	+	0.156680i
$628$	−12.2916	−	7.94200i	−0.490490	−	0.316920i
$629$	−32.6707	+	32.6707i	−1.30267	+	1.30267i
$630$	2.34396	+	9.71388i	0.0933856	+	0.387010i
$631$	−4.78745	−	17.8670i	−0.190585	−	0.711274i	−0.993366	−	0.114999i	$-0.963313\pi$
$631$	−4.78745	−	17.8670i	−0.190585	−	0.711274i	0.802780	−	0.596275i	$-0.203353\pi$
$632$	−0.575222	−	0.668794i	−0.0228811	−	0.0266032i
$633$	9.98329	−	17.2916i	0.396800	−	0.687278i
$634$	14.1602	+	26.0081i	0.562372	+	1.03291i
$635$	−14.8310	−	3.97396i	−0.588550	−	0.157702i
$636$	18.8973	+	0.946622i	0.749327	+	0.0375360i
$637$	−30.3495	+	14.2014i	−1.20249	+	0.562681i
$638$	−6.35028	−	0.158952i	−0.251410	−	0.00629298i
$639$	1.03133	−	3.84898i	0.0407988	−	0.152263i
$640$	18.6146	−	6.76155i	0.735807	−	0.267274i
$641$	11.2111	+	6.47274i	0.442813	+	0.255658i	0.704790	−	0.709416i	$-0.251041\pi$
$641$	11.2111	+	6.47274i	0.442813	+	0.255658i	−0.261977	+	0.965074i	$0.584375\pi$
$642$	−15.8401	−	16.6535i	−0.625161	−	0.657261i
$643$	23.6984	−	6.34998i	0.934575	−	0.250419i	0.240771	−	0.970582i	$-0.422600\pi$
$643$	23.6984	−	6.34998i	0.934575	−	0.250419i	0.693805	+	0.720163i	$0.255933\pi$
$644$	−60.5687	+	13.0205i	−2.38674	+	0.513080i
$645$	9.15911	+	9.15911i	0.360640	+	0.360640i
$646$	−17.5623	+	28.7334i	−0.690978	+	1.13050i
$647$	8.36046	+	14.4807i	0.328684	+	0.569297i	0.982251	−	0.187572i	$-0.0600617\pi$
$647$	8.36046	+	14.4807i	0.328684	+	0.569297i	−0.653567	+	0.756868i	$0.726728\pi$
$648$	−2.66945	−	0.934909i	−0.104866	−	0.0367267i
$649$		−	1.82622i		−	0.0716853i
$650$	−9.19266	−	3.59472i	−0.360566	−	0.140996i
$651$		−	19.7179i		−	0.772804i
$652$	−1.28838	+	3.99661i	−0.0504571	+	0.156520i
$653$	1.15599	+	2.00224i	0.0452375	+	0.0783536i	0.887758	−	0.460311i	$-0.152262\pi$
$653$	1.15599	+	2.00224i	0.0452375	+	0.0783536i	−0.842520	+	0.538665i	$0.818929\pi$
$654$	19.9196	+	12.1751i	0.778918	+	0.476086i
$655$	−6.87179	−	6.87179i	−0.268503	−	0.268503i
$656$	1.17309	+	7.19152i	0.0458015	+	0.280782i
$657$	2.41808	−	0.647923i	0.0943383	−	0.0252779i
$658$	−8.80842	+	8.37823i	−0.343388	+	0.326617i
$659$	−5.95953	−	3.44074i	−0.232150	−	0.134032i	0.379413	−	0.925227i	$-0.376126\pi$
$659$	−5.95953	−	3.44074i	−0.232150	−	0.134032i	−0.611564	+	0.791195i	$0.709459\pi$
$660$	−5.12120	+	2.62429i	−0.199342	+	0.102150i
$661$	1.33265	−	4.97351i	0.0518340	−	0.193447i	−0.935154	−	0.354242i	$-0.884739\pi$
$661$	1.33265	−	4.97351i	0.0518340	−	0.193447i	0.986988	+	0.160795i	$0.0514057\pi$
$662$	−0.0226198	+	0.903681i	−0.000879145	+	0.0351226i
$663$	−17.9185	−	1.54363i	−0.695897	−	0.0599498i
$664$	6.37048	+	0.479175i	0.247223	+	0.0185956i
$665$	−32.5818	−	8.73026i	−1.26347	−	0.338545i
$666$	11.5048	−	6.26380i	0.445801	−	0.242717i
$667$	10.4856	−	18.1616i	0.406005	−	0.703221i
$668$	−9.43446	−	10.4295i	−0.365030	−	0.403530i
$669$	3.29915	+	12.3126i	0.127553	+	0.476033i
$670$	1.78428	−	0.430548i	0.0689329	−	0.0166335i
$671$	−9.35857	+	9.35857i	−0.361284	+	0.361284i
$672$	−18.1953	−	13.7956i	−0.701899	−	0.532178i
$673$	4.23608	−	2.44570i	0.163289	−	0.0942748i	−0.416129	−	0.909306i	$-0.636613\pi$
$673$	4.23608	−	2.44570i	0.163289	−	0.0942748i	0.579417	+	0.815031i	$0.303280\pi$
$674$	−8.49488	−	2.50563i	−0.327210	−	0.0965134i
$675$	1.93577			0.0745077
$676$	−19.1031	−	17.6372i	−0.734735	−	0.678354i
$677$	−28.5839			−1.09857			−0.549284	−	0.835636i	$-0.685099\pi$
$677$	−28.5839			−1.09857			−0.549284	+	0.835636i	$0.685099\pi$
$678$	24.3718	+	7.18865i	0.935992	+	0.276079i
$679$	−14.5956	+	8.42675i	−0.560126	+	0.323389i
$680$	−13.9179	+	20.4016i	−0.533726	+	0.782367i
$681$	−8.58593	+	8.58593i	−0.329013	+	0.329013i
$682$	11.0380	−	2.66348i	0.422669	−	0.101990i
$683$	5.89800	+	22.0116i	0.225681	+	0.842251i	0.982131	+	0.188200i	$0.0602653\pi$
$683$	5.89800	+	22.0116i	0.225681	+	0.842251i	−0.756450	+	0.654051i	$0.773068\pi$
$684$	7.08048	−	6.40496i	0.270729	−	0.244900i
$685$	−11.4516	+	19.8348i	−0.437544	+	0.757848i
$686$	11.4981	−	6.26015i	0.438999	−	0.239014i
$687$	10.3211	+	2.76554i	0.393776	+	0.105512i
$688$	−29.4502	−	2.95791i	−1.12278	−	0.112769i
$689$	−33.9845	−	2.92768i	−1.29471	−	0.111536i
$690$	0.475375	−	18.9916i	0.0180972	−	0.722999i
$691$	−12.2869	+	45.8554i	−0.467416	+	1.74442i	0.181335	+	0.983421i	$0.441958\pi$
$691$	−12.2869	+	45.8554i	−0.467416	+	1.74442i	−0.648751	+	0.761001i	$0.724708\pi$
$692$	2.05085	+	4.00216i	0.0779618	+	0.152139i
$693$	5.74578	+	3.31732i	0.218264	+	0.126015i
$694$	0.367561	−	0.349609i	0.0139524	−	0.0132710i
$695$	15.9243	−	4.26691i	0.604044	−	0.161853i
$696$	7.59506	−	1.43488i	0.287890	−	0.0543892i
$697$	−6.42516	−	6.42516i	−0.243370	−	0.243370i
$698$	−13.3109	−	8.13584i	−0.503827	−	0.307946i
$699$	−7.46976	−	12.9380i	−0.282532	−	0.489361i
$700$	14.8737	+	4.79483i	0.562174	+	0.181227i
$701$		−	2.95818i		−	0.111729i	−0.998438	−	0.0558645i	$-0.982209\pi$
$701$		−	2.95818i		−	0.111729i	0.998438	−	0.0558645i	$-0.0177915\pi$
$702$	4.74885	+	1.85700i	0.179234	+	0.0700879i
$703$			44.2183i			1.66772i
$704$	5.26497	−	12.0492i	0.198431	−	0.454122i
$705$	−1.86390	−	3.22837i	−0.0701985	−	0.121587i
$706$	−0.155025	+	0.253634i	−0.00583443	+	0.00954565i
$707$	16.7329	+	16.7329i	0.629305	+	0.629305i
$708$	0.467025	+	2.17250i	0.0175519	+	0.0816476i
$709$	−8.97695	+	2.40537i	−0.337137	+	0.0903355i	−0.423416	−	0.905936i	$-0.639169\pi$
$709$	−8.97695	+	2.40537i	−0.337137	+	0.0903355i	0.0862790	+	0.996271i	$0.472502\pi$
$710$	6.79857	+	7.14766i	0.255146	+	0.268247i
$711$	−0.270098	−	0.155941i	−0.0101295	−	0.00584826i
$712$	13.0824	+	27.1852i	0.490284	+	1.01881i
$713$	−9.70226	+	36.2093i	−0.363353	+	1.35605i
$714$	28.4656	+	0.712516i	1.06530	+	0.0266652i
$715$	9.39616	−	4.39674i	0.351397	−	0.164429i
$716$	1.66156	−	33.1695i	0.0620952	−	1.23960i
$717$	8.06073	+	2.15987i	0.301033	+	0.0806617i
$718$	−5.31460	−	9.76139i	−0.198339	−	0.364292i
$719$	−23.5059	+	40.7134i	−0.876621	+	1.51835i	−0.0215954	+	0.999767i	$0.506875\pi$
$719$	−23.5059	+	40.7134i	−0.876621	+	1.51835i	−0.855026	+	0.518586i	$0.826459\pi$
$720$	5.42116	−	4.43157i	0.202035	−	0.165155i
$721$	7.66387	+	28.6019i	0.285417	+	1.06519i
$722$	1.25698	+	5.20918i	0.0467798	+	0.193866i
$723$	1.31738	−	1.31738i	0.0489939	−	0.0489939i
$724$	23.9603	−	37.0828i	0.890479	−	1.37817i
$725$	−4.58126	+	2.64499i	−0.170144	+	0.0982325i
$726$	3.32012	−	11.2562i	0.123221	−	0.417758i
$727$	18.6487			0.691641			0.345820	−	0.938301i	$-0.387601\pi$
$727$	18.6487			0.691641			0.345820	+	0.938301i	$0.387601\pi$
$728$	31.8887	+	26.0312i	1.18187	+	0.964782i
$729$	−1.00000			−0.0370370
$730$	−1.75327	+	5.94413i	−0.0648914	+	0.220002i
$731$	31.9649	−	18.4550i	1.18227	−	0.682581i
$732$	8.73984	−	13.5264i	0.323034	−	0.499951i
$733$	2.68470	−	2.68470i	0.0991618	−	0.0991618i	−0.655785	−	0.754947i	$-0.727662\pi$
$733$	2.68470	−	2.68470i	0.0991618	−	0.0991618i	0.754947	+	0.655785i	$0.227662\pi$
$734$	−6.75223	−	27.9827i	−0.249229	−	1.03286i
$735$	4.21048	+	15.7137i	0.155306	+	0.579609i
$736$	26.6252	+	34.2870i	0.981416	+	1.26383i
$737$	0.609339	−	1.05541i	0.0224453	−	0.0388764i
$738$	1.23187	+	2.26258i	0.0453456	+	0.0832868i
$739$	0.857164	+	0.229676i	0.0315313	+	0.00844878i	0.274550	−	0.961573i	$-0.411471\pi$
$739$	0.857164	+	0.229676i	0.0315313	+	0.00844878i	−0.243019	+	0.970022i	$0.578138\pi$
$740$	−1.62241	+	32.3880i	−0.0596410	+	1.19061i
$741$	−13.1706	+	11.0813i	−0.483832	+	0.407082i
$742$	53.9882	+	1.35137i	1.98197	+	0.0496102i
$743$	2.88342	−	10.7611i	0.105782	−	0.394785i	−0.892650	−	0.450750i	$-0.851157\pi$
$743$	2.88342	−	10.7611i	0.105782	−	0.394785i	0.998433	+	0.0559644i	$0.0178233\pi$
$744$	−12.4499	+	5.99133i	−0.456437	+	0.219653i
$745$	35.2253	+	20.3374i	1.29056	+	0.745103i
$746$	13.0667	+	13.7377i	0.478407	+	0.502972i
$747$	2.18171	−	0.584586i	0.0798245	−	0.0213889i
$748$	3.44626	+	16.0313i	0.126008	+	0.586161i
$749$	−46.3869	−	46.3869i	−1.69494	−	1.69494i
$750$	−8.95440	+	14.6502i	−0.326968	+	0.534949i
$751$	−22.0335	−	38.1632i	−0.804016	−	1.39260i	−0.916954	−	0.398994i	$-0.869360\pi$
$751$	−22.0335	−	38.1632i	−0.804016	−	1.39260i	0.112938	−	0.993602i	$-0.463974\pi$
$752$	7.96650	+	3.01592i	0.290508	+	0.109979i
$753$			1.96131i			0.0714741i
$754$	−13.7762	+	2.09388i	−0.501699	+	0.0762547i
$755$		−	36.5523i		−	1.33027i
$756$	−7.68363	−	2.47697i	−0.279451	−	0.0900864i
$757$	−14.9336	−	25.8658i	−0.542773	−	0.940110i	−0.998743	−	0.0501149i	$-0.984041\pi$
$757$	−14.9336	−	25.8658i	−0.542773	−	0.940110i	0.455971	−	0.889995i	$-0.349292\pi$
$758$	−41.8626	−	25.5870i	−1.52052	−	0.929362i
$759$	−8.91907	−	8.91907i	−0.323742	−	0.323742i
$760$	4.38774	+	23.2250i	0.159160	+	0.842458i
$761$	25.6539	−	6.87393i	0.929951	−	0.249180i	0.238117	−	0.971236i	$-0.423470\pi$
$761$	25.6539	−	6.87393i	0.929951	−	0.249180i	0.691834	+	0.722057i	$0.256803\pi$
$762$	8.98807	−	8.54911i	0.325604	−	0.309701i
$763$	57.7071	+	33.3172i	2.08914	+	1.20616i
$764$	9.70983	+	18.9483i	0.351289	+	0.685526i
$765$	−2.25992	+	8.43413i	−0.0817075	+	0.304937i
$766$	−0.937617	+	37.4586i	−0.0338775	+	1.35343i
$767$	−0.700887	−	3.94422i	−0.0253076	−	0.142418i
$768$	−3.18191	+	15.6804i	−0.114817	+	0.565818i
$769$	−16.4456	−	4.40659i	−0.593044	−	0.158906i	−0.0502000	−	0.998739i	$-0.515986\pi$
$769$	−16.4456	−	4.40659i	−0.593044	−	0.158906i	−0.542844	+	0.839833i	$0.682653\pi$
$770$	−14.4251	+	7.85378i	−0.519846	+	0.283031i
$771$	−14.3219	+	24.8063i	−0.515791	+	0.893376i
$772$	15.3157	−	13.8545i	0.551224	−	0.498634i
$773$	−2.31069	−	8.62360i	−0.0831097	−	0.310169i	0.911840	−	0.410546i	$-0.134662\pi$
$773$	−2.31069	−	8.62360i	−0.0831097	−	0.310169i	−0.994950	+	0.100377i	$0.967995\pi$
$774$	−10.1726	+	2.45466i	−0.365648	+	0.0882308i
$775$	6.68640	−	6.68640i	0.240182	−	0.240182i
$776$	9.75558	+	6.65519i	0.350205	+	0.238908i
$777$	32.3798	−	18.6945i	1.16162	−	0.670661i
$778$	−14.5244	−	4.28410i	−0.520726	−	0.153592i
$779$	−8.69616			−0.311572
$780$	−10.0535	+	7.63336i	−0.359972	+	0.273318i
$781$	6.54959			0.234363
$782$	−51.9228	−	15.3151i	−1.85676	−	0.547666i
$783$	2.36664	−	1.36638i	0.0845768	−	0.0488304i
$784$	−30.1746	−	21.7110i	−1.07767	−	0.775392i
$785$	9.05702	−	9.05702i	0.323259	−	0.323259i
$786$	7.63220	−	1.84165i	0.272232	−	0.0656895i
$787$	−3.49413	−	13.0403i	−0.124552	−	0.464836i	0.875271	−	0.483633i	$-0.160683\pi$
$787$	−3.49413	−	13.0403i	−0.124552	−	0.464836i	−0.999823	+	0.0187969i	$0.994016\pi$
$788$	−5.41350	−	5.98445i	−0.192848	−	0.213187i
$789$	3.49334	−	6.05064i	0.124366	−	0.215409i
$790$	0.678099	−	0.369192i	0.0241257	−	0.0131353i
$791$	70.0546	+	18.7711i	2.49085	+	0.667422i
$792$	0.348701	−	4.63588i	0.0123906	−	0.164729i
$793$	−16.6207	+	23.8042i	−0.590218	+	0.845311i
$794$	−0.748341	+	29.8969i	−0.0265576	+	1.06100i
$795$	−4.28619	+	15.9963i	−0.152016	+	0.567330i
$796$	−46.9266	+	24.0469i	−1.66327	+	0.852321i
$797$	−2.47176	−	1.42707i	−0.0875544	−	0.0505495i	0.455584	−	0.890193i	$-0.349431\pi$
$797$	−2.47176	−	1.42707i	−0.0875544	−	0.0505495i	−0.543138	+	0.839643i	$0.682764\pi$
$798$	19.7456	−	18.7813i	0.698988	−	0.664850i
$799$	−10.2606	+	2.74931i	−0.362992	+	0.0972635i
$800$	−1.49195	−	10.8482i	−0.0527483	−	0.383543i
$801$	7.54231	+	7.54231i	0.266494	+	0.266494i
$802$	42.6551	+	26.0714i	1.50620	+	0.920612i
$803$	2.05736	+	3.56344i	0.0726025	+	0.125751i
$804$	−0.454979	+	1.41136i	−0.0160459	+	0.0497748i
$805$		−	54.2237i		−	1.91114i
$806$	22.8175	−	9.98883i	0.803712	−	0.351842i
$807$			10.8426i			0.381676i
$808$	5.48087	−	15.6495i	0.192816	−	0.550549i
$809$	15.0908	+	26.1380i	0.530564	+	0.918964i	0.999364	+	0.0356593i	$0.0113531\pi$
$809$	15.0908	+	26.1380i	0.530564	+	0.918964i	−0.468800	+	0.883304i	$0.655314\pi$
$810$	1.29105	−	2.11227i	0.0453627	−	0.0742175i
$811$	−2.31939	−	2.31939i	−0.0814448	−	0.0814448i	0.665211	−	0.746656i	$-0.268342\pi$
$811$	−2.31939	−	2.31939i	−0.0814448	−	0.0814448i	−0.746656	+	0.665211i	$0.768342\pi$
$812$	21.5689	−	4.63668i	0.756919	−	0.162715i
$813$	2.34308	−	0.627826i	0.0821753	−	0.0220188i
$814$	14.8390	+	15.6009i	0.520107	+	0.546813i
$815$	−3.18290	−	1.83765i	−0.111492	−	0.0643700i
$816$	−8.19946	−	18.1898i	−0.287039	−	0.636770i
$817$	9.14256	−	34.1205i	0.319858	−	1.19372i
$818$	−6.70819	−	0.167911i	−0.234546	−	0.00587087i
$819$	13.6827	+	4.95950i	0.478114	+	0.173299i
$820$	−6.36957	−	0.319070i	−0.222435	−	0.0111424i
$821$	14.5182	+	3.89013i	0.506688	+	0.135767i	0.503102	−	0.864227i	$-0.332192\pi$
$821$	14.5182	+	3.89013i	0.506688	+	0.135767i	0.00358582	+	0.999994i	$0.498859\pi$
$822$	−8.84781	−	16.2509i	−0.308603	−	0.566814i
$823$	16.5212	−	28.6155i	0.575891	−	0.997473i	−0.420053	−	0.907500i	$-0.637989\pi$
$823$	16.5212	−	28.6155i	0.575891	−	0.997473i	0.995944	−	0.0899732i	$-0.0286781\pi$
$824$	15.7307	−	13.5298i	0.548004	−	0.471332i
$825$	0.823496	+	3.07333i	0.0286704	+	0.107000i
$826$	1.48775	+	6.16555i	0.0517654	+	0.214527i
$827$	−7.09994	+	7.09994i	−0.246889	+	0.246889i	−0.819693	−	0.572804i	$-0.805856\pi$
$827$	−7.09994	+	7.09994i	−0.246889	+	0.246889i	0.572804	+	0.819693i	$0.305856\pi$
$828$	12.8912	+	8.32939i	0.448000	+	0.289466i
$829$	−18.0617	+	10.4279i	−0.627310	+	0.362178i	−0.779709	−	0.626141i	$-0.784633\pi$
$829$	−18.0617	+	10.4279i	−0.627310	+	0.362178i	0.152400	+	0.988319i	$0.451300\pi$
$830$	−1.58188	+	5.36307i	−0.0549079	+	0.186155i
$831$	−15.4684			−0.536592
$832$	6.74675	−	28.0443i	0.233901	−	0.972260i
$833$	46.3564			1.60616
$834$	−3.76805	+	12.7749i	−0.130477	+	0.442358i
$835$	10.6600	−	6.15455i	0.368904	−	0.212987i
$836$	13.1810	+	8.51662i	0.455873	+	0.294553i
$837$	−3.45413	+	3.45413i	−0.119392	+	0.119392i
$838$	4.98774	+	20.6703i	0.172298	+	0.714042i
$839$	8.68355	+	32.4074i	0.299789	+	1.11883i	0.937339	+	0.348420i	$0.113282\pi$
$839$	8.68355	+	32.4074i	0.299789	+	1.11883i	−0.637549	+	0.770410i	$0.720052\pi$
$840$	15.1519	−	13.0320i	0.522792	−	0.449647i
$841$	10.7660	−	18.6473i	0.371242	−	0.643010i
$842$	1.98188	+	3.64014i	0.0683001	+	0.125448i
$843$	−7.70656	−	2.06497i	−0.265428	−	0.0711212i
$844$	−39.8831	−	1.99786i	−1.37283	−	0.0687693i
$845$	18.6062	−	13.1021i	0.640072	−	0.450727i
$846$	3.01072	+	0.0753606i	0.103511	+	0.00259095i
$847$	8.66953	−	32.3551i	0.297888	−	1.11173i
$848$	−15.5512	−	34.4990i	−0.534031	−	1.18470i
$849$	−12.4805	−	7.20563i	−0.428330	−	0.247297i
$850$	9.41117	+	9.89440i	0.322800	+	0.339375i
$851$	−68.6600	+	18.3974i	−2.35364	+	0.630655i
$852$	−7.79152	+	1.67495i	−0.266933	+	0.0573828i
$853$	−1.98153	−	1.98153i	−0.0678462	−	0.0678462i	0.672369	−	0.740216i	$-0.265277\pi$
$853$	−1.98153	−	1.98153i	−0.0678462	−	0.0678462i	−0.740216	+	0.672369i	$0.765277\pi$
$854$	23.9717	−	39.2198i	0.820295	−	1.34208i
$855$	4.17826	+	7.23695i	0.142893	+	0.247499i
$856$	−15.1941	+	43.3836i	−0.519322	+	1.48282i
$857$			16.4651i			0.562438i	0.959644	+	0.281219i	$0.0907388\pi$
$857$			16.4651i			0.562438i	−0.959644	+	0.281219i	$0.909261\pi$
$858$	−0.928062	+	8.32952i	−0.0316835	+	0.284365i
$859$		−	32.6817i		−	1.11508i	−0.830149	−	0.557542i	$-0.811745\pi$
$859$		−	32.6817i		−	1.11508i	0.830149	−	0.557542i	$-0.188255\pi$
$860$	7.94845	−	24.6564i	0.271040	−	0.840775i
$861$	3.67654	+	6.36795i	0.125296	+	0.217019i
$862$	−33.4130	−	20.4225i	−1.13805	−	0.695592i
$863$	−30.2258	−	30.2258i	−1.02890	−	1.02890i	−0.999570	−	0.0293286i	$-0.990663\pi$
$863$	−30.2258	−	30.2258i	−1.02890	−	1.02890i	−0.0293286	−	0.999570i	$-0.509337\pi$
$864$	0.770727	+	5.60410i	0.0262207	+	0.190655i
$865$	−3.80190	+	1.01872i	−0.129268	+	0.0346374i
$866$	31.8004	−	30.2473i	1.08062	−	1.02785i
$867$	6.82532	+	3.94060i	0.231800	+	0.133830i
$868$	−35.0961	+	17.9845i	−1.19124	+	0.610435i
$869$	0.132678	−	0.495162i	0.00450080	−	0.0167972i
$870$	−0.169284	+	6.76303i	−0.00573926	+	0.229288i
$871$	0.910980	−	2.51330i	0.0308674	−	0.0851599i
$872$	3.50215	−	46.5600i	0.118598	−	1.57672i
$873$	4.03300	+	1.08064i	0.136496	+	0.0365741i
$874$	−45.5017	+	24.7735i	−1.53912	+	0.837975i
$875$	−24.5037	+	42.4416i	−0.828375	+	1.43479i
$876$	−3.35876	−	3.71301i	−0.113482	−	0.125451i
$877$	5.78295	+	21.5823i	0.195276	+	0.728781i	0.992195	+	0.124695i	$0.0397951\pi$
$877$	5.78295	+	21.5823i	0.195276	+	0.728781i	−0.796919	+	0.604086i	$0.793538\pi$
$878$	−8.08036	+	1.94979i	−0.272699	+	0.0658022i
$879$	−8.22073	+	8.22073i	−0.277278	+	0.277278i
$880$	9.34202	+	6.72169i	0.314919	+	0.226588i
$881$	25.1107	−	14.4977i	0.846001	−	0.488439i	−0.0132987	−	0.999912i	$-0.504233\pi$
$881$	25.1107	−	14.4977i	0.846001	−	0.488439i	0.859299	+	0.511473i	$0.170900\pi$
$882$	−12.6059	−	3.71822i	−0.424463	−	0.125199i
$883$	3.11643			0.104876			0.0524382	−	0.998624i	$-0.483301\pi$
$883$	3.11643			0.104876			0.0524382	+	0.998624i	$0.483301\pi$
$884$	13.5958	+	33.3013i	0.457277	+	1.12004i
$885$	−1.94492			−0.0653777
$886$	−2.17046	−	0.640194i	−0.0729179	−	0.0215077i
$887$	−13.6739	+	7.89461i	−0.459123	+	0.265075i	−0.711676	−	0.702508i	$-0.752063\pi$
$887$	−13.6739	+	7.89461i	−0.459123	+	0.265075i	0.252552	+	0.967583i	$0.418730\pi$
$888$	−21.6424	−	14.7643i	−0.726273	−	0.495459i
$889$	25.0355	−	25.0355i	0.839664	−	0.839664i
$890$	−25.6688	+	6.19389i	−0.860421	+	0.207620i
$891$	−0.425411	−	1.58765i	−0.0142518	−	0.0531884i
$892$	18.9062	−	17.1024i	0.633027	−	0.572632i
$893$	−5.08306	+	8.80413i	−0.170098	+	0.294619i
$894$	−28.8605	+	15.7132i	−0.965241	+	0.525527i
$895$	28.0774	+	7.52333i	0.938525	+	0.251477i
$896$	−7.95919	+	44.9689i	−0.265898	+	1.50231i
$897$	−22.6863	−	15.8401i	−0.757472	−	0.528887i
$898$	−0.460147	+	18.3833i	−0.0153553	+	0.613457i
$899$	3.45503	−	12.8943i	0.115232	−	0.430051i
$900$	−1.76560	−	3.44549i	−0.0588533	−	0.114850i
$901$	40.8677	+	23.5950i	1.36150	+	0.786064i
$902$	−3.06815	+	2.91830i	−0.102158	+	0.0971689i
$903$	−28.8507	+	7.73053i	−0.960092	+	0.257256i
$904$	−9.43414	−	49.9363i	−0.313775	−	1.66086i
$905$	27.3242	+	27.3242i	0.908288	+	0.908288i
$906$	25.1966	+	15.4005i	0.837100	+	0.511647i
$907$	−21.0560	−	36.4701i	−0.699155	−	1.21097i	−0.968760	−	0.248000i	$-0.920227\pi$
$907$	−21.0560	−	36.4701i	−0.699155	−	1.21097i	0.269605	−	0.962971i	$-0.413107\pi$
$908$	23.1134	+	7.45103i	0.767044	+	0.247271i
$909$		−	5.86247i		−	0.194446i
$910$	−28.1408	+	22.4987i	−0.932860	+	0.745823i
$911$			34.8578i			1.15489i	0.816430	+	0.577445i	$0.195950\pi$
$911$			34.8578i			1.15489i	−0.816430	+	0.577445i	$0.804050\pi$
$912$	−17.8583	−	6.76072i	−0.591348	−	0.223870i
$913$	1.85624	+	3.21511i	0.0614327	+	0.106404i
$914$	−6.96612	+	11.3972i	−0.230419	+	0.376985i
$915$	9.96686	+	9.96686i	0.329494	+	0.329494i
$916$	−4.49142	−	20.8932i	−0.148401	−	0.690329i
$917$	21.6458	−	5.79997i	0.714807	−	0.191532i
$918$	−4.86173	−	5.11136i	−0.160461	−	0.168700i
$919$	19.2108	+	11.0914i	0.633706	+	0.365870i	0.782186	−	0.623045i	$-0.214105\pi$
$919$	19.2108	+	11.0914i	0.633706	+	0.365870i	−0.148480	+	0.988915i	$0.547438\pi$
$920$	−34.2370	+	16.4760i	−1.12876	+	0.543198i
$921$	−2.65990	+	9.92689i	−0.0876468	+	0.327102i
$922$	−0.223409	−	0.00559210i	−0.00735758	−	0.000184166i
$923$	14.1456	−	2.51368i	0.465610	−	0.0827388i
$924$	0.663865	−	13.2527i	0.0218396	−	0.435981i
$925$	17.3195	+	4.64074i	0.569460	+	0.152586i
$926$	1.86617	+	3.42761i	0.0613261	+	0.112638i
$927$	3.66789	−	6.35297i	0.120469	−	0.208659i
$928$	−9.48137	−	12.2098i	−0.311241	−	0.400806i
$929$	−11.2962	−	42.1581i	−0.370618	−	1.38316i	−0.859643	−	0.510894i	$-0.829314\pi$
$929$	−11.2962	−	42.1581i	−0.370618	−	1.38316i	0.489026	−	0.872269i	$-0.337352\pi$
$930$	−2.83660	−	11.7555i	−0.0930158	−	0.385478i
$931$	31.3707	−	31.3707i	1.02813	−	1.02813i
$932$	−16.2154	+	25.0962i	−0.531153	+	0.822053i
$933$	−18.0469	+	10.4194i	−0.590829	+	0.341115i
$934$	−12.1613	+	41.2305i	−0.397929	+	1.34910i
$935$	−14.3519			−0.469357
$936$	−1.02610	−	10.1463i	−0.0335390	−	0.331642i
$937$	−53.2966			−1.74113			−0.870563	−	0.492058i	$-0.836245\pi$
$937$	−53.2966			−1.74113			−0.870563	+	0.492058i	$0.836245\pi$
$938$	−1.19741	+	4.05960i	−0.0390969	+	0.132551i
$939$	1.09339	−	0.631271i	0.0356816	−	0.0206008i
$940$	−4.04616	+	6.26215i	−0.131971	+	0.204249i
$941$	−20.7292	+	20.7292i	−0.675754	+	0.675754i	−0.959037	−	0.283282i	$-0.908577\pi$
$941$	−20.7292	+	20.7292i	−0.675754	+	0.675754i	0.283282	+	0.959037i	$0.408577\pi$
$942$	2.42729	+	10.0592i	0.0790855	+	0.327748i
$943$	−3.61811	−	13.5030i	−0.117822	−	0.439717i
$944$	3.44089	−	2.81279i	0.111992	−	0.0915484i
$945$	3.53294	−	6.11924i	0.114927	−	0.199059i
$946$	−8.22469	−	15.1064i	−0.267408	−	0.491151i
$947$	−9.54008	−	2.55626i	−0.310011	−	0.0830672i	0.100459	−	0.994941i	$-0.467969\pi$
$947$	−9.54008	−	2.55626i	−0.310011	−	0.0830672i	−0.410470	+	0.911874i	$0.634635\pi$
$948$	−0.0312071	+	0.622984i	−0.00101356	+	0.0202336i
$949$	5.81105	+	6.90664i	0.188635	+	0.224199i
$950$	13.0646	+	0.327017i	0.423872	+	0.0106098i
$951$	5.41956	−	20.2261i	0.175741	−	0.655876i
$952$	−24.6951	−	51.3162i	−0.800372	−	1.66317i
$953$	22.4515	+	12.9624i	0.727275	+	0.419893i	0.817425	−	0.576036i	$-0.195401\pi$
$953$	22.4515	+	12.9624i	0.727275	+	0.419893i	−0.0901493	+	0.995928i	$0.528734\pi$
$954$	−9.22081	−	9.69427i	−0.298535	−	0.313864i
$955$	−18.0002	+	4.82314i	−0.582472	+	0.156073i
$956$	−3.50776	−	16.3174i	−0.113449	−	0.527742i
$957$	3.17613	+	3.17613i	0.102670	+	0.102670i
$958$	25.8418	−	42.2794i	0.834909	−	1.36599i
$959$	−26.4065	−	45.7375i	−0.852712	−	1.47694i
$960$	−12.8324	−	5.60718i	−0.414164	−	0.180971i
$961$		−	7.13791i		−	0.230255i
$962$	38.0364	+	27.9994i	1.22634	+	0.902738i
$963$			16.2519i			0.523710i
$964$	−3.54639	−	1.14325i	−0.114222	−	0.0368215i
$965$	9.03794	+	15.6542i	0.290941	+	0.503925i
$966$	37.3780	+	22.8460i	1.20262	+	0.735056i
$967$	−42.8649	−	42.8649i	−1.37844	−	1.37844i	−0.847253	−	0.531190i	$-0.821745\pi$
$967$	−42.8649	−	42.8649i	−1.37844	−	1.37844i	−0.531190	−	0.847253i	$-0.678255\pi$
$968$	−23.0634	+	4.35721i	−0.741285	+	0.140046i
$969$	23.0008	−	6.16306i	0.738893	−	0.197986i
$970$	−7.48938	+	7.12361i	−0.240470	+	0.228725i
$971$	−4.55610	−	2.63046i	−0.146212	−	0.0844156i	0.425109	−	0.905142i	$-0.360236\pi$
$971$	−4.55610	−	2.63046i	−0.146212	−	0.0844156i	−0.571321	+	0.820726i	$0.693569\pi$
$972$	0.912093	+	1.77991i	0.0292554	+	0.0570907i
$973$	−9.83917	+	36.7203i	−0.315429	+	1.17720i
$974$	−1.10611	+	44.1900i	−0.0354420	+	1.41594i
$975$	2.95808	+	6.32165i	0.0947345	+	0.202455i
$976$	−32.0474	−	3.21877i	−1.02581	−	0.103030i
$977$	−53.2861	−	14.2780i	−1.70477	−	0.456792i	−0.730638	−	0.682765i	$-0.760777\pi$
$977$	−53.2861	−	14.2780i	−1.70477	−	0.456792i	−0.974134	+	0.225972i	$0.927444\pi$
$978$	2.60779	−	1.41981i	0.0833879	−	0.0454006i
$979$	−8.76600	+	15.1832i	−0.280163	+	0.485256i
$980$	24.1287	−	21.8267i	0.770763	−	0.697227i
$981$	−4.27257	−	15.9455i	−0.136413	−	0.509099i
$982$	−45.7053	+	11.0287i	−1.45852	+	0.351940i
$983$	−7.92130	+	7.92130i	−0.252650	+	0.252650i	−0.822056	−	0.569406i	$-0.807173\pi$
$983$	−7.92130	+	7.92130i	−0.252650	+	0.252650i	0.569406	+	0.822056i	$0.307173\pi$
$984$	2.90362	−	4.25630i	0.0925640	−	0.135686i
$985$	6.11671	−	3.53148i	0.194894	−	0.112522i
$986$	18.4900	+	5.45378i	0.588842	+	0.173684i
$987$	8.59602			0.273614
$988$	31.7365	+	13.3352i	1.00967	+	0.424250i
$989$	56.7845			1.80564
$990$	3.90277	+	1.15116i	0.124038	+	0.0365861i
$991$	27.1512	−	15.6758i	0.862487	−	0.497957i	−0.00235703	−	0.999997i	$-0.500750\pi$
$991$	27.1512	−	15.6758i	0.862487	−	0.497957i	0.864844	+	0.502040i	$0.167417\pi$
$992$	22.0195	+	16.6951i	0.699121	+	0.530071i
$993$	0.451982	−	0.451982i	0.0143432	−	0.0143432i
$994$	−22.1123	+	5.33570i	−0.701359	+	0.169238i
$995$	−11.9448	−	44.5785i	−0.378675	−	1.41323i
$996$	−3.03043	−	3.35005i	−0.0960229	−	0.106150i
$997$	9.30826	−	16.1224i	0.294796	−	0.510601i	−0.680142	−	0.733081i	$-0.738082\pi$
$997$	9.30826	−	16.1224i	0.294796	−	0.510601i	0.974937	+	0.222480i	$0.0714151\pi$
$998$	−28.6502	+	15.5986i	−0.906905	+	0.493765i
$999$	−8.94708	−	2.39736i	−0.283073	−	0.0758492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.67.3	yes	24
3.2	odd	2		468.2.cb.h.379.4		24
4.3	odd	2		156.2.w.d.67.5	yes	24
12.11	even	2		468.2.cb.g.379.2		24
13.7	odd	12		156.2.w.d.7.5	yes	24
39.20	even	12		468.2.cb.g.163.2		24
52.7	even	12	inner	156.2.w.c.7.3	✓	24
156.59	odd	12		468.2.cb.h.163.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.7.3	✓	24	52.7	even	12	inner
156.2.w.c.67.3	yes	24	1.1	even	1	trivial
156.2.w.d.7.5	yes	24	13.7	odd	12
156.2.w.d.67.5	yes	24	4.3	odd	2
468.2.cb.g.163.2		24	39.20	even	12
468.2.cb.g.379.2		24	12.11	even	2
468.2.cb.h.163.4		24	156.59	odd	12
468.2.cb.h.379.4		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.400093 + 1.35644i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.67985 - 1.08540i) q^{4} +(1.23779 - 1.23779i) q^{5} +(0.331729 + 1.37476i) q^{6} +(1.04473 + 3.89897i) q^{7} +(2.14438 - 1.84435i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.400093 + 1.35644i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.67985 - 1.08540i) q^{4} +(1.23779 - 1.23779i) q^{5} +(0.331729 + 1.37476i) q^{6} +(1.04473 + 3.89897i) q^{7} +(2.14438 - 1.84435i) q^{8} +(0.500000 - 0.866025i) q^{9} +(1.18375 + 2.17421i) q^{10} +(1.58765 + 0.425411i) q^{11} +(-1.99750 - 0.100060i) q^{12} +(3.59225 + 0.309463i) q^{13} +(-5.70670 - 0.142843i) q^{14} +(0.453062 - 1.69085i) q^{15} +(1.64380 + 3.64663i) q^{16} +(-4.31983 - 2.49405i) q^{17} +(0.974664 + 1.02471i) q^{18} +(-4.61114 + 1.23555i) q^{19} +(-3.42280 + 0.735801i) q^{20} +(2.85424 + 2.85424i) q^{21} +(-1.21225 + 1.98335i) q^{22} +(-3.83701 - 6.64589i) q^{23} +(0.934909 - 2.66945i) q^{24} +1.93577i q^{25} +(-1.85700 + 4.74885i) q^{26} -1.00000i q^{27} +(2.47697 - 7.68363i) q^{28} +(1.36638 + 2.36664i) q^{29} +(2.11227 + 1.29105i) q^{30} +(-3.45413 - 3.45413i) q^{31} +(-5.60410 + 0.770727i) q^{32} +(1.58765 - 0.425411i) q^{33} +(5.11136 - 4.86173i) q^{34} +(6.11924 + 3.53294i) q^{35} +(-1.77991 + 0.912093i) q^{36} +(2.39736 - 8.94708i) q^{37} +(0.168934 - 6.74906i) q^{38} +(3.26571 - 1.52812i) q^{39} +(0.371366 - 4.93720i) q^{40} +(1.75957 + 0.471476i) q^{41} +(-5.01357 + 2.72964i) q^{42} +(-3.69979 + 6.40823i) q^{43} +(-2.20528 - 2.43787i) q^{44} +(-0.453062 - 1.69085i) q^{45} +(10.5499 - 2.54569i) q^{46} +(1.50583 - 1.50583i) q^{47} +(3.24689 + 2.33617i) q^{48} +(-8.04832 + 4.64670i) q^{49} +(-2.62575 - 0.774486i) q^{50} -4.98811 q^{51} +(-5.69855 - 4.41888i) q^{52} -9.46051 q^{53} +(1.35644 + 0.400093i) q^{54} +(2.49175 - 1.43861i) q^{55} +(9.43136 + 6.43402i) q^{56} +(-3.37559 + 3.37559i) q^{57} +(-3.75688 + 0.906535i) q^{58} +(-0.287565 - 1.07321i) q^{59} +(-2.59633 + 2.34862i) q^{60} +(-4.02608 + 6.97338i) q^{61} +(6.06730 - 3.30335i) q^{62} +(3.89897 + 1.04473i) q^{63} +(1.19672 - 7.90999i) q^{64} +(4.82949 - 4.06339i) q^{65} +(-0.0581655 + 2.32376i) q^{66} +(0.191899 - 0.716178i) q^{67} +(4.54962 + 8.87839i) q^{68} +(-6.64589 - 3.83701i) q^{69} +(-7.24048 + 6.88687i) q^{70} +(3.84898 - 1.03133i) q^{71} +(-0.525068 - 2.77926i) q^{72} +(1.77016 + 1.77016i) q^{73} +(11.1770 + 6.83154i) q^{74} +(0.967883 + 1.67642i) q^{75} +(9.08709 + 2.92940i) q^{76} +6.63465i q^{77} +(0.766215 + 5.04112i) q^{78} -0.311883i q^{79} +(6.54843 + 2.47907i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.34352 + 2.19812i) q^{82} +(1.59712 + 1.59712i) q^{83} +(-1.69670 - 7.89270i) q^{84} +(-8.43413 + 2.25992i) q^{85} +(-7.21211 - 7.58243i) q^{86} +(2.36664 + 1.36638i) q^{87} +(4.18914 - 2.01596i) q^{88} +(-2.76068 + 10.3030i) q^{89} +(2.47480 + 0.0619461i) q^{90} +(2.54632 + 14.3294i) q^{91} +(-0.767865 + 15.3288i) q^{92} +(-4.71844 - 1.26430i) q^{93} +(1.44010 + 2.64504i) q^{94} +(-4.17826 + 7.23695i) q^{95} +(-4.46793 + 3.46952i) q^{96} +(1.08064 + 4.03300i) q^{97} +(-3.08289 - 12.7762i) q^{98} +(1.16224 - 1.16224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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