LMFDB - Embedded newform 370.2.q.c.267.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			267.1
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	370.267
Dual form			370.2.q.c.273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.465926 + 0.124844i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(-0.341081 - 0.341081i) q^{6} +(4.19798 - 1.12484i) q^{7} -1.00000 q^{8} +(-2.39658 + 1.38366i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.465926 + 0.124844i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(-0.341081 - 0.341081i) q^{6} +(4.19798 - 1.12484i) q^{7} -1.00000 q^{8} +(-2.39658 + 1.38366i) q^{9} +(-1.81431 - 1.30701i) q^{10} +3.56048i q^{11} +(0.124844 - 0.465926i) q^{12} +(-2.59077 + 4.48735i) q^{13} +(3.07313 + 3.07313i) q^{14} +(0.835475 - 0.682163i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.739357 + 0.426868i) q^{17} +(-2.39658 - 1.38366i) q^{18} +(0.530550 + 1.98004i) q^{19} +(0.224745 - 2.22474i) q^{20} +(-1.81552 + 1.04819i) q^{21} +(-3.08346 + 1.78024i) q^{22} -5.38134 q^{23} +(0.465926 - 0.124844i) q^{24} +(3.31552 - 3.74264i) q^{25} -5.18154 q^{26} +(1.96713 - 1.96713i) q^{27} +(-1.12484 + 4.19798i) q^{28} +(-2.49269 - 2.49269i) q^{29} +(1.00851 + 0.382461i) q^{30} +(3.87832 - 3.87832i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.444506 - 1.65892i) q^{33} +(-0.739357 - 0.426868i) q^{34} +(-7.52761 + 6.14626i) q^{35} -2.76733i q^{36} +(-2.05197 + 5.72620i) q^{37} +(-1.44949 + 1.44949i) q^{38} +(0.646887 - 2.41421i) q^{39} +(2.03906 - 0.917738i) q^{40} +(3.80046 + 2.19419i) q^{41} +(-1.81552 - 1.04819i) q^{42} +10.1633 q^{43} +(-3.08346 - 1.78024i) q^{44} +(3.61692 - 5.02080i) q^{45} +(-2.69067 - 4.66038i) q^{46} +(6.14867 + 6.14867i) q^{47} +(0.341081 + 0.341081i) q^{48} +(10.2956 - 5.94414i) q^{49} +(4.89898 + 1.00000i) q^{50} +(0.291193 - 0.291193i) q^{51} +(-2.59077 - 4.48735i) q^{52} +(12.8737 + 3.44949i) q^{53} +(2.68715 + 0.720019i) q^{54} +(-3.26758 - 7.26002i) q^{55} +(-4.19798 + 1.12484i) q^{56} +(-0.494394 - 0.856315i) q^{57} +(0.912389 - 3.40508i) q^{58} +(-6.39595 - 1.71379i) q^{59} +(0.173033 + 1.06462i) q^{60} +(-2.12957 - 7.94767i) q^{61} +(5.29788 + 1.41956i) q^{62} +(-8.50436 + 8.50436i) q^{63} +1.00000 q^{64} +(1.16452 - 11.5276i) q^{65} +(1.21441 - 1.21441i) q^{66} +(1.47443 + 5.50266i) q^{67} -0.853736i q^{68} +(2.50731 - 0.671831i) q^{69} +(-9.08662 - 3.44597i) q^{70} +(-0.748487 + 1.29642i) q^{71} +(2.39658 - 1.38366i) q^{72} +(3.61401 + 3.61401i) q^{73} +(-5.98502 + 1.08604i) q^{74} +(-1.07754 + 2.15772i) q^{75} +(-1.98004 - 0.530550i) q^{76} +(4.00498 + 14.9468i) q^{77} +(2.41421 - 0.646887i) q^{78} +(-0.864068 - 3.22474i) q^{79} +(1.81431 + 1.30701i) q^{80} +(3.48004 - 6.02761i) q^{81} +4.38839i q^{82} +(-15.3446 - 4.11157i) q^{83} -2.09638i q^{84} +(1.11584 - 1.54894i) q^{85} +(5.08164 + 8.80166i) q^{86} +(1.47261 + 0.850212i) q^{87} -3.56048i q^{88} +(2.96240 - 11.0558i) q^{89} +(6.15660 + 0.621943i) q^{90} +(-5.82843 + 21.7520i) q^{91} +(2.69067 - 4.66038i) q^{92} +(-1.32282 + 2.29119i) q^{93} +(-2.25057 + 8.39924i) q^{94} +(-2.89898 - 3.55051i) q^{95} +(-0.124844 + 0.465926i) q^{96} -8.46926i q^{97} +(10.2956 + 5.94414i) q^{98} +(-4.92650 - 8.53295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} + 12 q^{7} - 8 q^{8} - 12 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 + 12 * q^7 - 8 * q^8 - 12 * q^9	$ 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} + 12 q^{7} - 8 q^{8} - 12 q^{9} - 4 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{14} - 4 q^{16} + 12 q^{17} - 12 q^{18} + 4 q^{19} - 8 q^{20} + 12 q^{21} - 12 q^{22} - 8 q^{23} - 4 q^{24} - 8 q^{26} - 8 q^{27} - 24 q^{29} - 12 q^{30} - 8 q^{31} + 4 q^{32} - 12 q^{33} + 12 q^{34} + 8 q^{38} + 16 q^{39} - 4 q^{40} + 12 q^{41} + 12 q^{42} + 16 q^{43} - 12 q^{44} - 12 q^{45} - 4 q^{46} - 8 q^{47} + 4 q^{48} + 36 q^{49} + 20 q^{51} - 4 q^{52} + 16 q^{53} - 4 q^{54} + 16 q^{55} - 12 q^{56} + 4 q^{57} - 24 q^{58} - 8 q^{59} - 12 q^{60} + 20 q^{62} - 4 q^{63} + 8 q^{64} + 16 q^{65} - 16 q^{67} + 16 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 16 q^{73} - 20 q^{75} + 4 q^{76} + 4 q^{77} + 8 q^{78} - 32 q^{79} + 4 q^{80} + 8 q^{81} + 16 q^{85} + 8 q^{86} - 36 q^{87} + 8 q^{89} + 24 q^{90} - 24 q^{91} + 4 q^{92} + 20 q^{93} - 16 q^{94} + 16 q^{95} + 8 q^{96} + 36 q^{98} + 4 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 + 12 * q^7 - 8 * q^8 - 12 * q^9 - 4 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^14 - 4 * q^16 + 12 * q^17 - 12 * q^18 + 4 * q^19 - 8 * q^20 + 12 * q^21 - 12 * q^22 - 8 * q^23 - 4 * q^24 - 8 * q^26 - 8 * q^27 - 24 * q^29 - 12 * q^30 - 8 * q^31 + 4 * q^32 - 12 * q^33 + 12 * q^34 + 8 * q^38 + 16 * q^39 - 4 * q^40 + 12 * q^41 + 12 * q^42 + 16 * q^43 - 12 * q^44 - 12 * q^45 - 4 * q^46 - 8 * q^47 + 4 * q^48 + 36 * q^49 + 20 * q^51 - 4 * q^52 + 16 * q^53 - 4 * q^54 + 16 * q^55 - 12 * q^56 + 4 * q^57 - 24 * q^58 - 8 * q^59 - 12 * q^60 + 20 * q^62 - 4 * q^63 + 8 * q^64 + 16 * q^65 - 16 * q^67 + 16 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 16 * q^73 - 20 * q^75 + 4 * q^76 + 4 * q^77 + 8 * q^78 - 32 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 24 * q^90 - 24 * q^91 + 4 * q^92 + 20 * q^93 - 16 * q^94 + 16 * q^95 + 8 * q^96 + 36 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.465926	+	0.124844i	−0.269002	+	0.0720790i	−0.390799	−	0.920476i	$-0.627801\pi$
$3$	−0.465926	+	0.124844i	−0.269002	+	0.0720790i	0.121796	+	0.992555i	$0.461135\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.03906	+	0.917738i	−0.911894	+	0.410425i
$5$	−2.03906	+	0.917738i	−0.911894	+	0.410425i
$6$	−0.341081	−	0.341081i	−0.139246	−	0.139246i
$7$	4.19798	−	1.12484i	1.58669	−	0.425151i	0.645698	−	0.763592i	$-0.276566\pi$
$7$	4.19798	−	1.12484i	1.58669	−	0.425151i	0.940988	+	0.338441i	$0.109900\pi$
$8$	−1.00000			−0.353553
$9$	−2.39658	+	1.38366i	−0.798858	+	0.461221i
$10$	−1.81431	−	1.30701i	−0.573736	−	0.413312i
$11$			3.56048i			1.07352i	0.843734	+	0.536762i	$0.180353\pi$
$11$			3.56048i			1.07352i	−0.843734	+	0.536762i	$0.819647\pi$
$12$	0.124844	−	0.465926i	0.0360395	−	0.134501i
$13$	−2.59077	+	4.48735i	−0.718550	+	1.24457i	0.243024	+	0.970020i	$0.421861\pi$
$13$	−2.59077	+	4.48735i	−0.718550	+	1.24457i	−0.961574	+	0.274545i	$0.911473\pi$
$14$	3.07313	+	3.07313i	0.821329	+	0.821329i
$15$	0.835475	−	0.682163i	0.215719	−	0.176134i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.739357	+	0.426868i	−0.179320	+	0.103531i	−0.586973	−	0.809606i	$-0.699681\pi$
$17$	−0.739357	+	0.426868i	−0.179320	+	0.103531i	0.407653	+	0.913137i	$0.366347\pi$
$18$	−2.39658	−	1.38366i	−0.564878	−	0.326133i
$19$	0.530550	+	1.98004i	0.121717	+	0.454252i	0.999701	−	0.0244361i	$-0.00777903\pi$
$19$	0.530550	+	1.98004i	0.121717	+	0.454252i	−0.877985	+	0.478688i	$0.841112\pi$
$20$	0.224745	−	2.22474i	0.0502545	−	0.497468i
$21$	−1.81552	+	1.04819i	−0.396178	+	0.228733i
$22$	−3.08346	+	1.78024i	−0.657397	+	0.379548i
$23$	−5.38134			−1.12209			−0.561044	−	0.827786i	$-0.689600\pi$
$23$	−5.38134			−1.12209			−0.561044	+	0.827786i	$0.689600\pi$
$24$	0.465926	−	0.124844i	0.0951067	−	0.0254838i
$25$	3.31552	−	3.74264i	0.663103	−	0.748528i
$26$	−5.18154			−1.01618
$27$	1.96713	−	1.96713i	0.378574	−	0.378574i
$28$	−1.12484	+	4.19798i	−0.212576	+	0.793343i
$29$	−2.49269	−	2.49269i	−0.462882	−	0.462882i	0.436717	−	0.899599i	$-0.356141\pi$
$29$	−2.49269	−	2.49269i	−0.462882	−	0.462882i	−0.899599	+	0.436717i	$0.856141\pi$
$30$	1.00851	+	0.382461i	0.184128	+	0.0698276i
$31$	3.87832	−	3.87832i	0.696566	−	0.696566i	−0.267102	−	0.963668i	$-0.586066\pi$
$31$	3.87832	−	3.87832i	0.696566	−	0.696566i	0.963668	+	0.267102i	$0.0860661\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.444506	−	1.65892i	−0.0773785	−	0.288781i
$34$	−0.739357	−	0.426868i	−0.126799	−	0.0732072i
$35$	−7.52761	+	6.14626i	−1.27240	+	1.03891i
$36$		−	2.76733i		−	0.461221i
$37$	−2.05197	+	5.72620i	−0.337342	+	0.941382i
$37$	−2.05197	+	5.72620i	−0.337342	+	0.941382i
$38$	−1.44949	+	1.44949i	−0.235138	+	0.235138i
$39$	0.646887	−	2.41421i	0.103585	−	0.386584i
$40$	2.03906	−	0.917738i	0.322403	−	0.145107i
$41$	3.80046	+	2.19419i	0.593532	+	0.342676i	0.766493	−	0.642253i	$-0.222000\pi$
$41$	3.80046	+	2.19419i	0.593532	+	0.342676i	−0.172961	+	0.984929i	$0.555333\pi$
$42$	−1.81552	−	1.04819i	−0.280140	−	0.161739i
$43$	10.1633			1.54989			0.774943	−	0.632031i	$-0.217779\pi$
$43$	10.1633			1.54989			0.774943	+	0.632031i	$0.217779\pi$
$44$	−3.08346	−	1.78024i	−0.464850	−	0.268381i
$45$	3.61692	−	5.02080i	0.539178	−	0.748456i
$46$	−2.69067	−	4.66038i	−0.396718	−	0.687135i
$47$	6.14867	+	6.14867i	0.896875	+	0.896875i	0.995159	−	0.0982830i	$-0.0313350\pi$
$47$	6.14867	+	6.14867i	0.896875	+	0.896875i	−0.0982830	+	0.995159i	$0.531335\pi$
$48$	0.341081	+	0.341081i	0.0492309	+	0.0492309i
$49$	10.2956	−	5.94414i	1.47079	−	0.849163i
$50$	4.89898	+	1.00000i	0.692820	+	0.141421i
$51$	0.291193	−	0.291193i	0.0407752	−	0.0407752i
$52$	−2.59077	−	4.48735i	−0.359275	−	0.622283i
$53$	12.8737	+	3.44949i	1.76833	+	0.473824i	0.988379	−	0.152011i	$-0.0485748\pi$
$53$	12.8737	+	3.44949i	1.76833	+	0.473824i	0.779956	+	0.625835i	$0.215241\pi$
$54$	2.68715	+	0.720019i	0.365674	+	0.0979821i
$55$	−3.26758	−	7.26002i	−0.440601	−	0.978941i
$56$	−4.19798	+	1.12484i	−0.560978	+	0.150314i
$57$	−0.494394	−	0.856315i	−0.0654841	−	0.113422i
$58$	0.912389	−	3.40508i	0.119803	−	0.447109i
$59$	−6.39595	−	1.71379i	−0.832682	−	0.223117i	−0.182799	−	0.983150i	$-0.558516\pi$
$59$	−6.39595	−	1.71379i	−0.832682	−	0.223117i	−0.649883	+	0.760034i	$0.725182\pi$
$60$	0.173033	+	1.06462i	0.0223384	+	0.137442i
$61$	−2.12957	−	7.94767i	−0.272664	−	1.01759i	−0.957391	−	0.288795i	$-0.906745\pi$
$61$	−2.12957	−	7.94767i	−0.272664	−	1.01759i	0.684727	−	0.728799i	$-0.259921\pi$
$62$	5.29788	+	1.41956i	0.672831	+	0.180285i
$63$	−8.50436	+	8.50436i	−1.07145	+	1.07145i
$64$	1.00000			0.125000
$65$	1.16452	−	11.5276i	0.144442	−	1.42982i
$66$	1.21441	−	1.21441i	0.149484	−	0.149484i
$67$	1.47443	+	5.50266i	0.180131	+	0.672257i	0.995621	+	0.0934858i	$0.0298010\pi$
$67$	1.47443	+	5.50266i	0.180131	+	0.672257i	−0.815490	+	0.578771i	$0.803532\pi$
$68$		−	0.853736i		−	0.103531i
$69$	2.50731	−	0.671831i	0.301844	−	0.0808789i
$70$	−9.08662	−	3.44597i	−1.08606	−	0.411872i
$71$	−0.748487	+	1.29642i	−0.0888291	+	0.153856i	−0.907016	−	0.421095i	$-0.861646\pi$
$71$	−0.748487	+	1.29642i	−0.0888291	+	0.153856i	0.818187	+	0.574952i	$0.194979\pi$
$72$	2.39658	−	1.38366i	0.282439	−	0.163066i
$73$	3.61401	+	3.61401i	0.422988	+	0.422988i	0.886231	−	0.463243i	$-0.153314\pi$
$73$	3.61401	+	3.61401i	0.422988	+	0.422988i	−0.463243	+	0.886231i	$0.653314\pi$
$74$	−5.98502	+	1.08604i	−0.695745	+	0.126250i
$75$	−1.07754	+	2.15772i	−0.124423	+	0.249152i
$76$	−1.98004	−	0.530550i	−0.227126	−	0.0608583i
$77$	4.00498	+	14.9468i	0.456410	+	1.70335i
$78$	2.41421	−	0.646887i	0.273356	−	0.0732455i
$79$	−0.864068	−	3.22474i	−0.0972152	−	0.362812i	0.900131	−	0.435620i	$-0.143471\pi$
$79$	−0.864068	−	3.22474i	−0.0972152	−	0.362812i	−0.997346	+	0.0728076i	$0.976804\pi$
$80$	1.81431	+	1.30701i	0.202846	+	0.146128i
$81$	3.48004	−	6.02761i	0.386671	−	0.669734i
$82$			4.38839i			0.484617i
$83$	−15.3446	−	4.11157i	−1.68429	−	0.451303i	−0.715381	−	0.698734i	$-0.753747\pi$
$83$	−15.3446	−	4.11157i	−1.68429	−	0.451303i	−0.968905	+	0.247431i	$0.920414\pi$
$84$		−	2.09638i		−	0.228733i
$85$	1.11584	−	1.54894i	0.121030	−	0.168007i
$86$	5.08164	+	8.80166i	0.547967	+	0.949107i
$87$	1.47261	+	0.850212i	0.157880	+	0.0911522i
$88$		−	3.56048i		−	0.379548i
$89$	2.96240	−	11.0558i	0.314014	−	1.17192i	−0.610890	−	0.791715i	$-0.709188\pi$
$89$	2.96240	−	11.0558i	0.314014	−	1.17192i	0.924904	−	0.380201i	$-0.124145\pi$
$90$	6.15660	+	0.621943i	0.648962	+	0.0655585i
$91$	−5.82843	+	21.7520i	−0.610985	+	2.28023i
$92$	2.69067	−	4.66038i	0.280522	−	0.485878i
$93$	−1.32282	+	2.29119i	−0.137170	+	0.237586i
$94$	−2.25057	+	8.39924i	−0.232128	+	0.866315i
$95$	−2.89898	−	3.55051i	−0.297429	−	0.364275i
$96$	−0.124844	+	0.465926i	−0.0127419	+	0.0475534i
$97$		−	8.46926i		−	0.859923i	−0.902847	−	0.429962i	$-0.858527\pi$
$97$		−	8.46926i		−	0.859923i	0.902847	−	0.429962i	$-0.141473\pi$
$98$	10.2956	+	5.94414i	1.04001	+	0.600449i
$99$	−4.92650	−	8.53295i	−0.495132	−	0.857594i
$100$	1.58346	+	4.74264i	0.158346	+	0.474264i
$101$		−	11.0635i		−	1.10086i	−0.834881	−	0.550430i	$-0.814464\pi$
$101$		−	11.0635i		−	1.10086i	0.834881	−	0.550430i	$-0.185536\pi$
$102$	0.397777	+	0.106584i	0.0393858	+	0.0105534i
$103$		−	3.34555i		−	0.329647i	−0.986323	−	0.164823i	$-0.947295\pi$
$103$		−	3.34555i		−	0.329647i	0.986323	−	0.164823i	$-0.0527054\pi$
$104$	2.59077	−	4.48735i	0.254046	−	0.440020i
$105$	2.73998	−	3.80348i	0.267395	−	0.371182i
$106$	3.44949	+	12.8737i	0.335044	+	1.25040i
$107$	5.38280	−	1.44232i	0.520375	−	0.139434i	0.0109350	−	0.999940i	$-0.496519\pi$
$107$	5.38280	−	1.44232i	0.520375	−	0.139434i	0.509440	+	0.860506i	$0.329853\pi$
$108$	0.720019	+	2.68715i	0.0692838	+	0.258571i
$109$	11.3316	+	3.03629i	1.08537	+	0.290824i	0.756794	−	0.653654i	$-0.226765\pi$
$109$	11.3316	+	3.03629i	1.08537	+	0.290824i	0.328576	+	0.944478i	$0.393431\pi$
$110$	4.65357	−	6.45982i	0.443701	−	0.615920i
$111$	0.241181	−	2.92416i	0.0228919	−	0.277549i
$112$	−3.07313	−	3.07313i	−0.290384	−	0.290384i
$113$	−5.91928	+	3.41750i	−0.556839	+	0.321491i	−0.751876	−	0.659305i	$-0.770851\pi$
$113$	−5.91928	+	3.41750i	−0.556839	+	0.321491i	0.195037	+	0.980796i	$0.437517\pi$
$114$	0.494394	−	0.856315i	0.0463042	−	0.0802013i
$115$	10.9729	−	4.93866i	1.02323	−	0.460532i
$116$	3.40508	−	0.912389i	0.316154	−	0.0847132i
$117$		−	14.3390i		−	1.32564i
$118$	−1.71379	−	6.39595i	−0.157767	−	0.588795i
$119$	−2.62364	+	2.62364i	−0.240509	+	0.240509i
$120$	−0.835475	+	0.682163i	−0.0762681	+	0.0622727i
$121$	−1.67700			−0.152455
$122$	5.81809	−	5.81809i	0.526746	−	0.526746i
$123$	−2.04466	−	0.547866i	−0.184361	−	0.0493994i
$124$	1.41956	+	5.29788i	0.127480	+	0.475763i
$125$	−3.32577	+	10.6742i	−0.297465	+	0.954733i
$126$	−11.6172	−	3.11281i	−1.03494	−	0.277311i
$127$	−3.83453	+	14.3107i	−0.340260	+	1.26987i	0.557794	+	0.829980i	$0.311648\pi$
$127$	−3.83453	+	14.3107i	−0.340260	+	1.26987i	−0.898053	+	0.439887i	$0.855019\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.73533	+	1.26883i	−0.416923	+	0.111714i
$130$	10.5655	−	4.75529i	0.926652	−	0.417067i
$131$	12.9799	+	3.47796i	1.13406	+	0.303871i	0.776561	−	0.630043i	$-0.216963\pi$
$131$	12.9799	+	3.47796i	1.13406	+	0.303871i	0.357500	+	0.933913i	$0.383629\pi$
$132$	1.65892	+	0.444506i	0.144390	+	0.0386893i
$133$	4.45447	+	7.71537i	0.386252	+	0.669008i
$134$	−4.02823	+	4.02823i	−0.347986	+	0.347986i
$135$	−2.20578	+	5.81640i	−0.189843	+	0.500596i
$136$	0.739357	−	0.426868i	0.0633993	−	0.0366036i
$137$	6.06937	+	6.06937i	0.518541	+	0.518541i	0.917130	−	0.398589i	$-0.130500\pi$
$137$	6.06937	+	6.06937i	0.518541	+	0.518541i	−0.398589	+	0.917130i	$0.630500\pi$
$138$	1.83548	+	1.83548i	0.156246	+	0.156246i
$139$	0.889767	+	1.54112i	0.0754691	+	0.130716i	0.901290	−	0.433216i	$-0.142621\pi$
$139$	0.889767	+	1.54112i	0.0754691	+	0.130716i	−0.825821	+	0.563932i	$0.809288\pi$
$140$	−1.55902	−	9.59223i	−0.131761	−	0.810691i
$141$	−3.63245	−	2.09720i	−0.305908	−	0.176616i
$142$	−1.49697			−0.125623
$143$	−15.9771	−	9.22438i	−1.33607	−	0.771381i
$144$	2.39658	+	1.38366i	0.199715	+	0.115305i
$145$	7.37039	+	2.79511i	0.612077	+	0.232121i
$146$	−1.32282	+	4.93684i	−0.109477	+	0.408575i
$147$	−4.05487	+	4.05487i	−0.334440	+	0.334440i
$148$	−3.93305	−	4.64016i	−0.323295	−	0.381419i
$149$		−	1.80552i		−	0.147914i	−0.997261	−	0.0739571i	$-0.976437\pi$
$149$		−	1.80552i		−	0.147914i	0.997261	−	0.0739571i	$-0.0235628\pi$
$150$	−2.40741	+	0.145685i	−0.196564	+	0.0118951i
$151$	−8.66636	−	5.00352i	−0.705258	−	0.407181i	0.104045	−	0.994573i	$-0.466822\pi$
$151$	−8.66636	−	5.00352i	−0.705258	−	0.407181i	−0.809303	+	0.587392i	$0.800155\pi$
$152$	−0.530550	−	1.98004i	−0.0430333	−	0.160602i
$153$	1.18128	−	2.04604i	0.0955011	−	0.165413i
$154$	−10.9418	+	10.9418i	−0.881717	+	0.881717i
$155$	−4.34883	+	11.4674i	−0.349307	+	0.921083i
$156$	1.76733	+	1.76733i	0.141499	+	0.141499i
$157$	0.379259	−	1.41542i	0.0302682	−	0.112962i	−0.949139	−	0.314857i	$-0.898043\pi$
$157$	0.379259	−	1.41542i	0.0302682	−	0.112962i	0.979407	+	0.201895i	$0.0647100\pi$
$158$	2.36068	−	2.36068i	0.187805	−	0.187805i
$159$	−6.42883			−0.509839
$160$	−0.224745	+	2.22474i	−0.0177676	+	0.175882i
$161$	−22.5907	+	6.05317i	−1.78040	+	0.477057i
$162$	6.96008			0.546835
$163$	−20.6628	+	11.9297i	−1.61843	+	0.934403i	−0.631109	+	0.775694i	$0.717400\pi$
$163$	−20.6628	+	11.9297i	−1.61843	+	0.934403i	−0.987325	+	0.158709i	$0.949267\pi$
$164$	−3.80046	+	2.19419i	−0.296766	+	0.171338i
$165$	2.42883	+	2.97469i	0.189084	+	0.231579i
$166$	−4.11157	−	15.3446i	−0.319120	−	1.19097i
$167$	−6.14162	−	3.54587i	−0.475253	−	0.274387i	0.243183	−	0.969980i	$-0.421808\pi$
$167$	−6.14162	−	3.54587i	−0.475253	−	0.274387i	−0.718436	+	0.695593i	$0.755142\pi$
$168$	1.81552	−	1.04819i	0.140070	−	0.0808695i
$169$	−6.92418	−	11.9930i	−0.532629	−	0.922541i
$170$	1.89934	+	0.191873i	0.145673	+	0.0147160i
$171$	−4.01121	−	4.01121i	−0.306745	−	0.306745i
$172$	−5.08164	+	8.80166i	−0.387471	+	0.671120i
$173$	0.223178	−	0.832913i	0.0169679	−	0.0633252i	−0.956923	−	0.290343i	$-0.906231\pi$
$173$	0.223178	−	0.832913i	0.0169679	−	0.0633252i	0.973891	+	0.227017i	$0.0728974\pi$
$174$			1.70042i			0.128909i
$175$	9.70857	−	19.4410i	0.733899	−	1.46960i
$176$	3.08346	−	1.78024i	0.232425	−	0.134191i
$177$	3.19400			0.240076
$178$	11.0558	−	2.96240i	0.828670	−	0.222041i
$179$	10.3495	+	10.3495i	0.773555	+	0.773555i	0.978726	−	0.205171i	$-0.0657750\pi$
$179$	10.3495	+	10.3495i	0.773555	+	0.773555i	−0.205171	+	0.978726i	$0.565775\pi$
$180$	2.53968	+	5.64274i	0.189297	+	0.420585i
$181$	−6.72122	+	11.6415i	−0.499584	+	0.865306i	−1.00000		0.000479821i	$-0.999847\pi$
$181$	−6.72122	+	11.6415i	−0.499584	+	0.865306i	0.500415	+	0.865785i	$0.333181\pi$
$182$	−21.7520	+	5.82843i	−1.61236	+	0.432032i
$183$	1.98444	+	3.43716i	0.146694	+	0.254082i
$184$	5.38134			0.396718
$185$	−1.07107	−	13.5592i	−0.0787465	−	0.996895i
$186$	−2.64564			−0.193988
$187$	−1.51985	−	2.63246i	−0.111143	−	0.192505i
$188$	−8.39924	+	2.25057i	−0.612577	+	0.164140i
$189$	6.04524	−	10.4707i	0.439727	−	0.761629i
$190$	1.62534	−	4.28585i	0.117915	−	0.310928i
$191$	1.56014	+	1.56014i	0.112888	+	0.112888i	0.761294	−	0.648407i	$-0.224564\pi$
$191$	1.56014	+	1.56014i	0.112888	+	0.112888i	−0.648407	+	0.761294i	$0.724564\pi$
$192$	−0.465926	+	0.124844i	−0.0336253	+	0.00900987i
$193$	3.55067			0.255583			0.127792	−	0.991801i	$-0.459211\pi$
$193$	3.55067			0.255583			0.127792	+	0.991801i	$0.459211\pi$
$194$	7.33460	−	4.23463i	0.526593	−	0.304029i
$195$	0.896575	+	5.51639i	0.0642051	+	0.395037i
$196$			11.8883i			0.849163i
$197$	−4.76595	+	17.7868i	−0.339560	+	1.26725i	0.559281	+	0.828978i	$0.311077\pi$
$197$	−4.76595	+	17.7868i	−0.339560	+	1.26725i	−0.898840	+	0.438276i	$0.855589\pi$
$198$	4.92650	−	8.53295i	0.350111	−	0.606411i
$199$	−5.97576	−	5.97576i	−0.423610	−	0.423610i	0.462834	−	0.886445i	$-0.346832\pi$
$199$	−5.97576	−	5.97576i	−0.423610	−	0.423610i	−0.886445	+	0.462834i	$0.846832\pi$
$200$	−3.31552	+	3.74264i	−0.234442	+	0.264645i
$201$	−1.37395	−	2.37976i	−0.0969112	−	0.167855i
$202$	9.58128	−	5.53175i	0.674136	−	0.389213i
$203$	−13.2682	−	7.66038i	−0.931243	−	0.537653i
$204$	0.106584	+	0.397777i	0.00746238	+	0.0278500i
$205$	−9.76305	−	0.986268i	−0.681881	−	0.0688839i
$206$	2.89733	−	1.67277i	0.201867	−	0.116548i
$207$	12.8968	−	7.44597i	0.896389	−	0.517530i
$208$	5.18154			0.359275
$209$	−7.04989	+	1.88901i	−0.487651	+	0.130666i
$210$	4.66390	+	0.471150i	0.321840	+	0.0325124i
$211$	17.1087			1.17781			0.588907	−	0.808201i	$-0.299558\pi$
$211$	17.1087			1.17781			0.588907	+	0.808201i	$0.299558\pi$
$212$	−9.42418	+	9.42418i	−0.647255	+	0.647255i
$213$	0.186889	−	0.697479i	0.0128054	−	0.0477905i
$214$	3.94048	+	3.94048i	0.269366	+	0.269366i
$215$	−20.7235	+	9.32723i	−1.41333	+	0.636111i
$216$	−1.96713	+	1.96713i	−0.133846	+	0.133846i
$217$	11.9186	−	20.6436i	0.809086	−	1.40138i
$218$	3.03629	+	11.3316i	0.205643	+	0.767472i
$219$	−2.13505	−	1.23267i	−0.144273	−	0.0832963i
$220$	7.92116	+	0.800199i	0.534044	+	0.0539494i
$221$		−	4.42367i		−	0.297568i
$222$	2.65299	−	1.25321i	0.178057	−	0.0841101i
$223$	17.2354	−	17.2354i	1.15417	−	1.15417i	0.168460	−	0.985708i	$-0.446120\pi$
$223$	17.2354	−	17.2354i	1.15417	−	1.15417i	0.985708	−	0.168460i	$-0.0538795\pi$
$224$	1.12484	−	4.19798i	0.0751568	−	0.280489i
$225$	−2.76733	+	13.5571i	−0.184488	+	0.903805i
$226$	−5.91928	−	3.41750i	−0.393745	−	0.227329i
$227$	14.3768	+	8.30046i	0.954223	+	0.550921i	0.894390	−	0.447288i	$-0.147610\pi$
$227$	14.3768	+	8.30046i	0.954223	+	0.550921i	0.0598325	+	0.998208i	$0.480943\pi$
$228$	0.988788			0.0654841
$229$	−10.8212	−	6.24761i	−0.715083	−	0.412853i	0.0978571	−	0.995200i	$-0.468801\pi$
$229$	−10.8212	−	6.24761i	−0.715083	−	0.412853i	−0.812940	+	0.582347i	$0.802135\pi$
$230$	9.76344	+	7.03345i	0.643782	+	0.463772i
$231$	−3.73205	−	6.46410i	−0.245551	−	0.425307i
$232$	2.49269	+	2.49269i	0.163653	+	0.163653i
$233$	20.8106	+	20.8106i	1.36335	+	1.36335i	0.869610	+	0.493739i	$0.164370\pi$
$233$	20.8106	+	20.8106i	1.36335	+	1.36335i	0.493739	+	0.869610i	$0.335630\pi$
$234$	12.4180	−	7.16951i	0.811787	−	0.468685i
$235$	−18.1804	−	6.89463i	−1.18596	−	0.449756i
$236$	4.68216	−	4.68216i	0.304783	−	0.304783i
$237$	0.805183	+	1.39462i	0.0523023	+	0.0905902i
$238$	−3.58396	−	0.960320i	−0.232314	−	0.0622483i
$239$	6.23119	+	1.66964i	0.403062	+	0.108000i	0.454654	−	0.890668i	$-0.349763\pi$
$239$	6.23119	+	1.66964i	0.403062	+	0.108000i	−0.0515920	+	0.998668i	$0.516430\pi$
$240$	−1.00851	−	0.382461i	−0.0650989	−	0.0246878i
$241$	−20.7353	+	5.55601i	−1.33568	+	0.357894i	−0.854829	−	0.518909i	$-0.826338\pi$
$241$	−20.7353	+	5.55601i	−1.33568	+	0.357894i	−0.480849	+	0.876803i	$0.659672\pi$
$242$	−0.838502	−	1.45233i	−0.0539009	−	0.0933591i
$243$	−3.02898	+	11.3043i	−0.194309	+	0.725173i
$244$	7.94767	+	2.12957i	0.508797	+	0.136332i
$245$	−15.5381	+	21.5691i	−0.992691	+	1.37800i
$246$	−0.547866	−	2.04466i	−0.0349307	−	0.130363i
$247$	−10.2597	−	2.74907i	−0.652806	−	0.174919i
$248$	−3.87832	+	3.87832i	−0.246273	+	0.246273i
$249$	7.66274			0.485607
$250$	−10.9070	+	2.45692i	−0.689822	+	0.155389i
$251$	−4.47613	+	4.47613i	−0.282531	+	0.282531i	−0.834118	−	0.551587i	$-0.814023\pi$
$251$	−4.47613	+	4.47613i	−0.282531	+	0.282531i	0.551587	+	0.834118i	$0.314023\pi$
$252$	−3.11281	−	11.6172i	−0.196089	−	0.731813i
$253$		−	19.1601i		−	1.20459i
$254$	−14.3107	+	3.83453i	−0.897931	+	0.240600i
$255$	−0.326521	+	0.860999i	−0.0204475	+	0.0539179i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−19.1942	+	11.0818i	−1.19730	+	0.691262i	−0.959953	−	0.280163i	$-0.909612\pi$
$257$	−19.1942	+	11.0818i	−1.19730	+	0.691262i	−0.237348	+	0.971425i	$0.576278\pi$
$258$	−3.46651	−	3.46651i	−0.215815	−	0.215815i
$259$	−2.17303	+	26.3466i	−0.135026	+	1.63710i
$260$	9.40094	+	6.77231i	0.583021	+	0.420001i
$261$	9.42298	+	2.52488i	0.583268	+	0.156286i
$262$	3.47796	+	12.9799i	0.214869	+	0.801902i
$263$	3.57715	−	0.958496i	0.220577	−	0.0591034i	−0.146838	−	0.989161i	$-0.546910\pi$
$263$	3.57715	−	0.958496i	0.220577	−	0.0591034i	0.367415	+	0.930057i	$0.380243\pi$
$264$	0.444506	+	1.65892i	0.0273574	+	0.102099i
$265$	−29.4159	+	4.78094i	−1.80700	+	0.293691i
$266$	−4.45447	+	7.71537i	−0.273121	+	0.473060i
$267$			5.52104i			0.337882i
$268$	−5.50266	−	1.47443i	−0.336129	−	0.0900654i
$269$		−	15.1550i		−	0.924016i	−0.886876	−	0.462008i	$-0.847129\pi$
$269$		−	15.1550i		−	0.924016i	0.886876	−	0.462008i	$-0.152871\pi$
$270$	−6.14004	+	0.997936i	−0.373671	+	0.0607324i
$271$	−10.7474	−	18.6150i	−0.652856	−	1.13078i	−0.982427	−	0.186649i	$-0.940237\pi$
$271$	−10.7474	−	18.6150i	−0.652856	−	1.13078i	0.329571	−	0.944131i	$-0.393096\pi$
$272$	0.739357	+	0.426868i	0.0448301	+	0.0258827i
$273$		−	10.8625i		−	0.657426i
$274$	−2.22154	+	8.29091i	−0.134208	+	0.500872i
$275$	13.3256	+	11.8048i	0.803563	+	0.711857i
$276$	−0.671831	+	2.50731i	−0.0404395	+	0.150922i
$277$	13.9477	−	24.1581i	0.838034	−	1.45152i	−0.0535021	−	0.998568i	$-0.517038\pi$
$277$	13.9477	−	24.1581i	0.838034	−	1.45152i	0.891536	−	0.452950i	$-0.149628\pi$
$278$	−0.889767	+	1.54112i	−0.0533647	+	0.0924304i
$279$	−3.92839	+	14.6610i	−0.235187	+	0.877729i
$280$	7.52761	−	6.14626i	0.449860	−	0.367310i
$281$	−5.64004	+	21.0489i	−0.336456	+	1.25567i	0.565825	+	0.824525i	$0.308558\pi$
$281$	−5.64004	+	21.0489i	−0.336456	+	1.25567i	−0.902282	+	0.431147i	$0.858109\pi$
$282$		−	4.19439i		−	0.249772i
$283$	24.7788	+	14.3060i	1.47294	+	0.850405i	0.999537	−	0.0304389i	$-0.00969051\pi$
$283$	24.7788	+	14.3060i	1.47294	+	0.850405i	0.473407	+	0.880844i	$0.343024\pi$
$284$	−0.748487	−	1.29642i	−0.0444145	−	0.0769282i
$285$	1.79397	+	1.29235i	0.106266	+	0.0765524i
$286$		−	18.4488i		−	1.09090i
$287$	18.4224	+	4.93626i	1.08744	+	0.291378i
$288$			2.76733i			0.163066i
$289$	−8.13557	+	14.0912i	−0.478563	+	0.828895i
$290$	1.26456	+	7.78050i	0.0742574	+	0.456886i
$291$	1.05734	+	3.94605i	0.0619824	+	0.231321i
$292$	−4.93684	+	1.32282i	−0.288906	+	0.0774122i
$293$	−5.29543	−	19.7628i	−0.309362	−	1.15456i	−0.929125	−	0.369767i	$-0.879438\pi$
$293$	−5.29543	−	19.7628i	−0.309362	−	1.15456i	0.619762	−	0.784790i	$-0.287229\pi$
$294$	−5.53906	−	1.48419i	−0.323044	−	0.0865595i
$295$	14.6145	−	2.37529i	0.850891	−	0.138295i
$296$	2.05197	−	5.72620i	0.119268	−	0.332829i
$297$	7.00392	+	7.00392i	0.406408	+	0.406408i
$298$	1.56363	−	0.902761i	0.0905786	−	0.0522956i
$299$	13.9418	−	24.1479i	0.806276	−	1.39651i
$300$	−1.32987	−	2.01203i	−0.0767800	−	0.116165i
$301$	42.6652	−	11.4321i	2.45918	−	0.658936i
$302$		−	10.0070i		−	0.575841i
$303$	1.38122	+	5.15477i	0.0793488	+	0.296134i
$304$	1.44949	−	1.44949i	0.0831339	−	0.0831339i
$305$	11.6362	+	14.2514i	0.666286	+	0.816031i
$306$	2.36257			0.135059
$307$	8.09720	−	8.09720i	0.462131	−	0.462131i	−0.437222	−	0.899354i	$-0.644038\pi$
$307$	8.09720	−	8.09720i	0.462131	−	0.462131i	0.899354	+	0.437222i	$0.144038\pi$
$308$	−14.9468	−	4.00498i	−0.851673	−	0.228205i
$309$	0.417673	+	1.55878i	0.0237606	+	0.0886758i
$310$	−12.1055	+	1.96749i	−0.687544	+	0.111746i
$311$	11.1837	+	2.99666i	0.634170	+	0.169925i	0.561561	−	0.827435i	$-0.310201\pi$
$311$	11.1837	+	2.99666i	0.634170	+	0.169925i	0.0726086	+	0.997361i	$0.476868\pi$
$312$	−0.646887	+	2.41421i	−0.0366227	+	0.136678i
$313$	−2.06424	−	3.57537i	−0.116678	−	0.202092i	0.801771	−	0.597631i	$-0.203891\pi$
$313$	−2.06424	−	3.57537i	−0.116678	−	0.202092i	−0.918449	+	0.395539i	$0.870558\pi$
$314$	1.41542	−	0.379259i	0.0798765	−	0.0214028i
$315$	9.53611	−	25.1457i	0.537299	−	1.41680i
$316$	3.22474	+	0.864068i	0.181406	+	0.0486076i
$317$	−19.8213	−	5.31111i	−1.11328	−	0.298302i	−0.345117	−	0.938560i	$-0.612161\pi$
$317$	−19.8213	−	5.31111i	−1.11328	−	0.298302i	−0.768160	+	0.640258i	$0.778827\pi$
$318$	−3.21441	−	5.56753i	−0.180255	−	0.312211i
$319$	8.87518	−	8.87518i	0.496915	−	0.496915i
$320$	−2.03906	+	0.917738i	−0.113987	+	0.0513031i
$321$	−2.32792	+	1.34403i	−0.129932	+	0.0750162i
$322$	−16.5376	−	16.5376i	−0.921603	−	0.921603i
$323$	−1.23748	−	1.23748i	−0.0688553	−	0.0688553i
$324$	3.48004	+	6.02761i	0.193336	+	0.334867i
$325$	8.20478	+	24.5742i	0.455120	+	1.36313i
$326$	−20.6628	−	11.9297i	−1.14441	−	0.660723i
$327$	−5.65874			−0.312929
$328$	−3.80046	−	2.19419i	−0.209845	−	0.121154i
$329$	32.7283	+	18.8957i	1.80437	+	1.04175i
$330$	−1.36175	+	3.59077i	−0.0749616	+	0.197665i
$331$	−2.47355	+	9.23143i	−0.135959	+	0.507405i	0.864033	+	0.503435i	$0.167931\pi$
$331$	−2.47355	+	9.23143i	−0.135959	+	0.507405i	−0.999992	+	0.00397055i	$0.998736\pi$
$332$	11.2330	−	11.2330i	0.616492	−	0.616492i
$333$	−3.00544	−	16.5625i	−0.164697	−	0.907620i
$334$		−	7.09173i		−	0.388042i
$335$	−8.05646	−	9.86710i	−0.440171	−	0.539097i
$336$	1.81552	+	1.04819i	0.0990445	+	0.0571834i
$337$	−0.480404	−	1.79289i	−0.0261693	−	0.0976651i	0.951606	−	0.307321i	$-0.0994324\pi$
$337$	−0.480404	−	1.79289i	−0.0261693	−	0.0976651i	−0.977775	+	0.209656i	$0.932766\pi$
$338$	6.92418	−	11.9930i	0.376626	−	0.652335i
$339$	2.33129	−	2.33129i	0.126618	−	0.126618i
$340$	0.783505	+	1.74082i	0.0424915	+	0.0944090i
$341$	13.8087	+	13.8087i	0.747781	+	0.747781i
$342$	1.46821	−	5.47942i	0.0793915	−	0.296293i
$343$	15.0223	−	15.0223i	0.811130	−	0.811130i
$344$	−10.1633			−0.547967
$345$	−4.49598	+	3.67095i	−0.242055	+	0.197637i
$346$	0.832913	−	0.223178i	0.0447777	−	0.0119981i
$347$	−25.5468			−1.37142			−0.685712	−	0.727873i	$-0.740509\pi$
$347$	−25.5468			−1.37142			−0.685712	+	0.727873i	$0.740509\pi$
$348$	−1.47261	+	0.850212i	−0.0789402	+	0.0455761i
$349$	−2.42921	+	1.40250i	−0.130032	+	0.0750743i	−0.563605	−	0.826044i	$-0.690586\pi$
$349$	−2.42921	+	1.40250i	−0.130032	+	0.0750743i	0.433573	+	0.901119i	$0.357253\pi$
$350$	21.6906	−	1.31261i	1.15941	−	0.0701621i
$351$	3.73081	+	13.9236i	0.199136	+	0.743185i
$352$	3.08346	+	1.78024i	0.164349	+	0.0948871i
$353$	20.2461	−	11.6891i	1.07759	−	0.622148i	0.147346	−	0.989085i	$-0.452927\pi$
$353$	20.2461	−	11.6891i	1.07759	−	0.622148i	0.930246	+	0.366937i	$0.119593\pi$
$354$	1.59700	+	2.76608i	0.0848795	+	0.147016i
$355$	0.336437	−	3.33038i	0.0178562	−	0.176758i
$356$	8.09343	+	8.09343i	0.428951	+	0.428951i
$357$	0.894876	−	1.54997i	0.0473618	−	0.0820331i
$358$	−3.78817	+	14.1376i	−0.200211	+	0.747197i
$359$		−	11.3570i		−	0.599401i	−0.954033	−	0.299701i	$-0.903113\pi$
$359$		−	11.3570i		−	0.599401i	0.954033	−	0.299701i	$-0.0968868\pi$
$360$	−3.61692	+	5.02080i	−0.190628	+	0.264619i
$361$	12.8154	−	7.39898i	0.674495	−	0.389420i
$362$	−13.4424			−0.706519
$363$	0.781359	−	0.209365i	0.0410107	−	0.0109888i
$364$	−15.9236	−	15.9236i	−0.834621	−	0.834621i
$365$	−10.6859	−	4.05247i	−0.559326	−	0.212116i
$366$	−1.98444	+	3.43716i	−0.103729	+	0.179663i
$367$	−13.6336	+	3.65311i	−0.711669	+	0.190691i	−0.596451	−	0.802649i	$-0.703423\pi$
$367$	−13.6336	+	3.65311i	−0.711669	+	0.190691i	−0.115217	+	0.993340i	$0.536756\pi$
$368$	2.69067	+	4.66038i	0.140261	+	0.242939i
$369$	−12.1441			−0.632197
$370$	11.2071	−	7.70719i	0.582630	−	0.400678i
$371$	57.9235			3.00724
$372$	−1.32282	−	2.29119i	−0.0685851	−	0.118793i
$373$	20.5188	−	5.49800i	1.06242	−	0.284676i	0.315047	−	0.949076i	$-0.397980\pi$
$373$	20.5188	−	5.49800i	1.06242	−	0.284676i	0.747377	+	0.664400i	$0.231313\pi$
$374$	1.51985	−	2.63246i	0.0785898	−	0.136121i
$375$	0.216941	−	5.38860i	0.0112028	−	0.278266i
$376$	−6.14867	−	6.14867i	−0.317093	−	0.317093i
$377$	17.6436	−	4.72758i	0.908690	−	0.243483i
$378$	12.0905			0.621868
$379$	−20.1970	+	11.6607i	−1.03745	+	0.598971i	−0.919109	−	0.394002i	$-0.871090\pi$
$379$	−20.1970	+	11.6607i	−1.03745	+	0.598971i	−0.118339	+	0.992973i	$0.537757\pi$
$380$	4.52432	−	0.735335i	0.232093	−	0.0377219i
$381$		−	7.14643i		−	0.366123i
$382$	−0.571050	+	2.13119i	−0.0292175	+	0.109041i
$383$	−0.900980	+	1.56054i	−0.0460379	+	0.0797400i	−0.888126	−	0.459600i	$-0.847993\pi$
$383$	−0.900980	+	1.56054i	−0.0460379	+	0.0797400i	0.842088	+	0.539340i	$0.181326\pi$
$384$	−0.341081	−	0.341081i	−0.0174057	−	0.0174057i
$385$	−21.8836	−	26.8019i	−1.11529	−	1.36595i
$386$	1.77534	+	3.07497i	0.0903623	+	0.156512i
$387$	−24.3571	+	14.0626i	−1.23814	+	0.714840i
$388$	7.33460	+	4.23463i	0.372358	+	0.214981i
$389$	−9.18034	−	34.2615i	−0.465462	−	1.73713i	−0.655354	−	0.755322i	$-0.727481\pi$
$389$	−9.18034	−	34.2615i	−0.465462	−	1.73713i	0.189893	−	0.981805i	$-0.439186\pi$
$390$	−4.32905	+	3.53465i	−0.219210	+	0.178984i
$391$	3.97873	−	2.29712i	0.201213	−	0.116170i
$392$	−10.2956	+	5.94414i	−0.520004	+	0.300224i
$393$	−6.48188			−0.326968
$394$	−17.7868	+	4.76595i	−0.896084	+	0.240105i
$395$	4.72135	+	5.78245i	0.237557	+	0.290947i
$396$	9.85301			0.495132
$397$	−5.48440	+	5.48440i	−0.275254	+	0.275254i	−0.831211	−	0.555957i	$-0.812352\pi$
$397$	−5.48440	+	5.48440i	−0.275254	+	0.275254i	0.555957	+	0.831211i	$0.312352\pi$
$398$	2.18728	−	8.16304i	0.109638	−	0.409176i
$399$	−3.03868	−	3.03868i	−0.152124	−	0.152124i
$400$	−4.89898	−	1.00000i	−0.244949	−	0.0500000i
$401$	22.4765	−	22.4765i	1.12242	−	1.12242i	0.131045	−	0.991376i	$-0.458167\pi$
$401$	22.4765	−	22.4765i	1.12242	−	1.12242i	0.991376	−	0.131045i	$-0.0418333\pi$
$402$	1.37395	−	2.37976i	0.0685266	−	0.118692i
$403$	7.35552	+	27.4512i	0.366404	+	1.36744i
$404$	9.58128	+	5.53175i	0.476686	+	0.275215i
$405$	−1.56424	+	15.4844i	−0.0777278	+	0.769426i
$406$		−	15.3208i		−	0.760356i
$407$	−20.3880	−	7.30599i	−1.01060	−	0.362145i
$408$	−0.291193	+	0.291193i	−0.0144162	+	0.0144162i
$409$	−1.03359	+	3.85739i	−0.0511075	+	0.190736i	−0.986760	−	0.162187i	$-0.948145\pi$
$409$	−1.03359	+	3.85739i	−0.0511075	+	0.190736i	0.935653	+	0.352922i	$0.114812\pi$
$410$	−4.02739	−	8.94818i	−0.198899	−	0.441919i
$411$	−3.58560	−	2.07015i	−0.176865	−	0.102113i
$412$	2.89733	+	1.67277i	0.142741	+	0.0824117i
$413$	−28.7778			−1.41606
$414$	12.8968	+	7.44597i	0.633843	+	0.365949i
$415$	35.0618	−	5.69857i	1.72112	−	0.279732i
$416$	2.59077	+	4.48735i	0.127023	+	0.220010i
$417$	−0.606966	−	0.606966i	−0.0297233	−	0.0297233i
$418$	−5.16088	−	5.16088i	−0.252427	−	0.252427i
$419$	−13.2473	+	7.64835i	−0.647174	+	0.373646i	−0.787373	−	0.616477i	$-0.788559\pi$
$419$	−13.2473	+	7.64835i	−0.647174	+	0.373646i	0.140199	+	0.990123i	$0.455226\pi$
$420$	1.92392	+	4.27463i	0.0938779	+	0.208581i
$421$	23.9597	−	23.9597i	1.16773	−	1.16773i	0.184983	−	0.982742i	$-0.440777\pi$
$421$	23.9597	−	23.9597i	1.16773	−	1.16773i	0.982742	−	0.184983i	$-0.0592231\pi$
$422$	8.55437	+	14.8166i	0.416420	+	0.721261i
$423$	−23.2434	−	6.22806i	−1.13013	−	0.302819i
$424$	−12.8737	−	3.44949i	−0.625201	−	0.167522i
$425$	−0.853736	+	4.18243i	−0.0414123	+	0.202878i
$426$	0.697479	−	0.186889i	0.0337930	−	0.00905480i
$427$	−17.8798	−	30.9687i	−0.865263	−	1.49868i
$428$	−1.44232	+	5.38280i	−0.0697170	+	0.260188i
$429$	8.59575	+	2.30323i	0.415007	+	0.111201i
$430$	−18.4394	−	13.2835i	−0.889226	−	0.640586i
$431$	−2.22234	−	8.29389i	−0.107046	−	0.399503i	0.891523	−	0.452976i	$-0.149638\pi$
$431$	−2.22234	−	8.29389i	−0.107046	−	0.399503i	−0.998569	+	0.0534731i	$0.982971\pi$
$432$	−2.68715	−	0.720019i	−0.129285	−	0.0346419i
$433$	4.81916	−	4.81916i	0.231594	−	0.231594i	−0.581764	−	0.813358i	$-0.697637\pi$
$433$	4.81916	−	4.81916i	0.231594	−	0.231594i	0.813358	+	0.581764i	$0.197637\pi$
$434$	23.8372			1.14422
$435$	−3.78301	−	0.382161i	−0.181381	−	0.0183232i
$436$	−8.29530	+	8.29530i	−0.397273	+	0.397273i
$437$	−2.85507	−	10.6553i	−0.136577	−	0.509711i
$438$		−	2.46535i		−	0.117799i
$439$	−0.562542	+	0.150733i	−0.0268487	+	0.00719408i	−0.272218	−	0.962235i	$-0.587757\pi$
$439$	−0.562542	+	0.150733i	−0.0268487	+	0.00719408i	0.245370	+	0.969430i	$0.421091\pi$
$440$	3.26758	+	7.26002i	0.155776	+	0.346108i
$441$	−16.4494	+	28.4912i	−0.783304	+	1.35672i
$442$	3.83101	−	2.21183i	0.182222	−	0.105206i
$443$	−5.60697	−	5.60697i	−0.266395	−	0.266395i	0.561251	−	0.827646i	$-0.310320\pi$
$443$	−5.60697	−	5.60697i	−0.266395	−	0.266395i	−0.827646	+	0.561251i	$0.810320\pi$
$444$	2.41181	+	1.67095i	0.114459	+	0.0792998i
$445$	4.10585	+	25.2622i	0.194636	+	1.19754i
$446$	23.5440	+	6.30860i	1.11484	+	0.298721i
$447$	0.225409	+	0.841240i	0.0106615	+	0.0397893i
$448$	4.19798	−	1.12484i	0.198336	−	0.0531439i
$449$	−0.125424	−	0.468090i	−0.00591914	−	0.0220905i	0.962903	−	0.269847i	$-0.0869733\pi$
$449$	−0.125424	−	0.468090i	−0.00591914	−	0.0220905i	−0.968822	+	0.247757i	$0.920307\pi$
$450$	−13.1244	+	4.38196i	−0.618692	+	0.206568i
$451$	−7.81238	+	13.5314i	−0.367871	+	0.637171i
$452$		−	6.83500i		−	0.321491i
$453$	4.66254	+	1.24932i	0.219065	+	0.0586984i
$454$			16.6009i			0.779119i
$455$	−8.07812	−	49.7025i	−0.378708	−	2.33009i
$456$	0.494394	+	0.856315i	0.0231521	+	0.0401006i
$457$	35.5806	+	20.5425i	1.66439	+	0.960936i	0.970580	+	0.240779i	$0.0774030\pi$
$457$	35.5806	+	20.5425i	1.66439	+	0.960936i	0.693811	+	0.720157i	$0.255930\pi$
$458$		−	12.4952i		−	0.583863i
$459$	−0.614706	+	2.29411i	−0.0286920	+	0.107080i
$460$	−1.20943	+	11.9721i	−0.0563899	+	0.558203i
$461$	−0.202745	+	0.756655i	−0.00944278	+	0.0352409i	−0.970486	−	0.241156i	$-0.922474\pi$
$461$	−0.202745	+	0.756655i	−0.00944278	+	0.0352409i	0.961044	+	0.276396i	$0.0891403\pi$
$462$	3.73205	−	6.46410i	0.173631	−	0.300737i
$463$	−13.1422	+	22.7630i	−0.610770	+	1.05788i	0.380341	+	0.924846i	$0.375807\pi$
$463$	−13.1422	+	22.7630i	−0.610770	+	1.05788i	−0.991111	+	0.133038i	$0.957527\pi$
$464$	−0.912389	+	3.40508i	−0.0423566	+	0.158077i
$465$	0.594595	−	5.88588i	0.0275737	−	0.272951i
$466$	−7.61722	+	28.4278i	−0.352861	+	1.31689i
$467$		−	32.5145i		−	1.50459i	−0.658825	−	0.752296i	$-0.728946\pi$
$467$		−	32.5145i		−	1.50459i	0.658825	−	0.752296i	$-0.271054\pi$
$468$	12.4180	+	7.16951i	0.574020	+	0.331411i
$469$	12.3793	+	21.4415i	0.571622	+	0.990078i
$470$	−3.11926	−	19.1920i	−0.143881	−	0.885259i
$471$			0.706827i			0.0325689i
$472$	6.39595	+	1.71379i	0.294398	+	0.0788836i
$473$			36.1861i			1.66384i
$474$	−0.805183	+	1.39462i	−0.0369833	+	0.0640569i
$475$	9.16962	+	4.57919i	0.420731	+	0.210108i
$476$	−0.960320	−	3.58396i	−0.0440162	−	0.164271i
$477$	−35.6257	+	9.54587i	−1.63119	+	0.437075i
$478$	1.66964	+	6.23119i	0.0763676	+	0.285008i
$479$	17.6197	+	4.72118i	0.805064	+	0.215716i	0.637806	−	0.770197i	$-0.279842\pi$
$479$	17.6197	+	4.72118i	0.805064	+	0.215716i	0.167258	+	0.985913i	$0.446509\pi$
$480$	−0.173033	−	1.06462i	−0.00789782	−	0.0485932i
$481$	−20.3793	−	24.0432i	−0.929215	−	1.09627i
$482$	−15.1793	−	15.1793i	−0.691398	−	0.691398i
$483$	9.76991	−	5.64066i	0.444546	−	0.256659i
$484$	0.838502	−	1.45233i	0.0381137	−	0.0660149i
$485$	7.77256	+	17.2693i	0.352934	+	0.784159i
$486$	−11.3043	+	3.02898i	−0.512774	+	0.137397i
$487$		−	13.1697i		−	0.596775i	−0.954445	−	0.298388i	$-0.903551\pi$
$487$		−	13.1697i		−	0.596775i	0.954445	−	0.298388i	$-0.0964488\pi$
$488$	2.12957	+	7.94767i	0.0964011	+	0.359774i
$489$	8.13797	−	8.13797i	0.368012	−	0.368012i
$490$	−26.4484	−	2.67183i	−1.19482	−	0.120701i
$491$	18.4085			0.830763			0.415382	−	0.909647i	$-0.363648\pi$
$491$	18.4085			0.830763			0.415382	+	0.909647i	$0.363648\pi$
$492$	1.49680	−	1.49680i	0.0674809	−	0.0674809i
$493$	2.90704	+	0.778939i	0.130927	+	0.0350817i
$494$	−2.74907	−	10.2597i	−0.123686	−	0.461604i
$495$	17.8764	+	12.8780i	0.803486	+	0.578821i
$496$	−5.29788	−	1.41956i	−0.237882	−	0.0637402i
$497$	−1.68386	+	6.28426i	−0.0755316	+	0.281888i
$498$	3.83137	+	6.63613i	0.171688	+	0.297372i
$499$	−35.0542	+	9.39274i	−1.56924	+	0.420477i	−0.935575	−	0.353129i	$-0.885118\pi$
$499$	−35.0542	+	9.39274i	−1.56924	+	0.420477i	−0.633667	+	0.773606i	$0.718451\pi$
$500$	−7.58128	−	8.21731i	−0.339045	−	0.367489i
$501$	3.30422	+	0.885363i	0.147622	+	0.0395551i
$502$	−6.11451	−	1.63838i	−0.272904	−	0.0731244i
$503$	−1.47409	−	2.55321i	−0.0657266	−	0.113842i	0.831289	−	0.555840i	$-0.187603\pi$
$503$	−1.47409	−	2.55321i	−0.0657266	−	0.113842i	−0.897016	+	0.441998i	$0.854270\pi$
$504$	8.50436	−	8.50436i	0.378814	−	0.378814i
$505$	10.1534	+	22.5591i	0.451820	+	1.00387i
$506$	16.5932	−	9.58007i	0.737657	−	0.425886i
$507$	4.72342	+	4.72342i	0.209774	+	0.209774i
$508$	−10.4761	−	10.4761i	−0.464803	−	0.464803i
$509$	8.50094	+	14.7241i	0.376798	+	0.652633i	0.990594	−	0.136831i	$-0.0436918\pi$
$509$	8.50094	+	14.7241i	0.376798	+	0.652633i	−0.613797	+	0.789464i	$0.710359\pi$
$510$	−0.908908	+	0.147724i	−0.0402471	+	0.00654133i
$511$	19.2368	+	11.1063i	0.850984	+	0.491316i
$512$	−1.00000			−0.0441942
$513$	4.93865	+	2.85133i	0.218047	+	0.125889i
$514$	−19.1942	−	11.0818i	−0.846620	−	0.488796i
$515$	3.07034	+	6.82177i	0.135295	+	0.300603i
$516$	1.26883	−	4.73533i	0.0558571	−	0.208461i
$517$	−21.8922	+	21.8922i	−0.962818	+	0.962818i
$518$	−23.9034	+	11.2914i	−1.05025	+	0.496116i
$519$			0.415938i			0.0182577i
$520$	−1.16452	+	11.5276i	−0.0510678	+	0.505519i
$521$	−14.3851	−	8.30526i	−0.630224	−	0.363860i	0.150615	−	0.988593i	$-0.451875\pi$
$521$	−14.3851	−	8.30526i	−0.630224	−	0.363860i	−0.780839	+	0.624732i	$0.785208\pi$
$522$	2.52488	+	9.42298i	0.110511	+	0.412433i
$523$	4.30690	−	7.45977i	0.188328	−	0.326193i	−0.756365	−	0.654150i	$-0.773027\pi$
$523$	4.30690	−	7.45977i	0.188328	−	0.326193i	0.944693	+	0.327957i	$0.106360\pi$
$524$	−9.50196	+	9.50196i	−0.415095	+	0.415095i
$525$	−2.09638	+	10.2701i	−0.0914934	+	0.448224i
$526$	2.61866	+	2.61866i	0.114179	+	0.114179i
$527$	−1.21193	+	4.52299i	−0.0527925	+	0.197024i
$528$	−1.21441	+	1.21441i	−0.0528505	+	0.0528505i
$529$	5.95884			0.259080
$530$	−18.8484	−	23.0844i	−0.818721	−	1.00272i
$531$	17.6997	−	4.74262i	0.768101	−	0.205812i
$532$	−8.90895			−0.386252
$533$	−19.6922	+	11.3693i	−0.852965	+	0.492459i
$534$	−4.78136	+	2.76052i	−0.206910	+	0.119459i
$535$	−9.65217	+	7.88097i	−0.417300	+	0.340724i
$536$	−1.47443	−	5.50266i	−0.0636858	−	0.237679i
$537$	−6.11416	−	3.53001i	−0.263845	−	0.152331i
$538$	13.1246	−	7.57749i	0.565842	−	0.326689i
$539$	21.1640	+	36.6571i	0.911597	+	1.57893i
$540$	−3.93426	−	4.81846i	−0.169303	−	0.207353i
$541$	−21.8799	−	21.8799i	−0.940689	−	0.940689i	0.0576477	−	0.998337i	$-0.481640\pi$
$541$	−21.8799	−	21.8799i	−0.940689	−	0.940689i	−0.998337	+	0.0576477i	$0.981640\pi$
$542$	10.7474	−	18.6150i	0.461639	−	0.799582i
$543$	1.67821	−	6.26318i	0.0720191	−	0.268779i
$544$			0.853736i			0.0366036i
$545$	−25.8923	+	4.20825i	−1.10910	+	0.180262i
$546$	9.40717	−	5.43123i	0.402590	−	0.232435i
$547$	6.52719			0.279083			0.139541	−	0.990216i	$-0.455437\pi$
$547$	6.52719			0.279083			0.139541	+	0.990216i	$0.455437\pi$
$548$	−8.29091	+	2.22154i	−0.354170	+	0.0948996i
$549$	16.1006	+	16.1006i	0.687156	+	0.687156i
$550$	−3.56048	+	17.4427i	−0.151819	+	0.743760i
$551$	3.61313	−	6.25813i	0.153925	−	0.266605i
$552$	−2.50731	+	0.671831i	−0.106718	+	0.0285950i
$553$	−7.25467	−	12.5655i	−0.308500	−	0.534338i
$554$	27.8953			1.18516
$555$	2.19183	+	6.18388i	0.0930381	+	0.262491i
$556$	−1.77953			−0.0754691
$557$	−9.28303	−	16.0787i	−0.393335	−	0.681276i	0.599552	−	0.800336i	$-0.295345\pi$
$557$	−9.28303	−	16.0787i	−0.393335	−	0.681276i	−0.992887	+	0.119060i	$0.962012\pi$
$558$	−14.6610	+	3.92839i	−0.620648	+	0.166302i
$559$	−26.3307	+	45.6062i	−1.11367	+	1.92893i
$560$	9.08662	+	3.44597i	0.383980	+	0.145619i
$561$	1.03679	+	1.03679i	0.0437732	+	0.0437732i
$562$	−21.0489	+	5.64004i	−0.887894	+	0.237911i
$563$	37.7909			1.59269			0.796347	−	0.604839i	$-0.206763\pi$
$563$	37.7909			1.59269			0.796347	+	0.604839i	$0.206763\pi$
$564$	3.63245	−	2.09720i	0.152954	−	0.0883079i
$565$	8.93339	−	12.4008i	0.375830	−	0.521706i
$566$			28.6120i			1.20265i
$567$	7.82901	−	29.2183i	0.328787	−	1.22705i
$568$	0.748487	−	1.29642i	0.0314058	−	0.0543965i
$569$	−17.0143	−	17.0143i	−0.713277	−	0.713277i	0.253942	−	0.967219i	$-0.418273\pi$
$569$	−17.0143	−	17.0143i	−0.713277	−	0.713277i	−0.967219	+	0.253942i	$0.918273\pi$
$570$	−0.222225	+	2.19980i	−0.00930798	+	0.0921395i
$571$	−13.0962	−	22.6833i	−0.548060	−	0.949268i	−0.998407	−	0.0564144i	$-0.982033\pi$
$571$	−13.0962	−	22.6833i	−0.548060	−	0.949268i	0.450347	−	0.892853i	$-0.351300\pi$
$572$	15.9771	−	9.22438i	0.668036	−	0.385691i
$573$	−0.921683	−	0.532134i	−0.0385039	−	0.0222302i
$574$	4.93626	+	18.4224i	0.206035	+	0.768934i
$575$	−17.8419	+	20.1404i	−0.744059	+	0.839914i
$576$	−2.39658	+	1.38366i	−0.0998573	+	0.0576526i
$577$	−4.70169	+	2.71452i	−0.195734	+	0.113007i	−0.594664	−	0.803974i	$-0.702715\pi$
$577$	−4.70169	+	2.71452i	−0.195734	+	0.113007i	0.398930	+	0.916981i	$0.369382\pi$
$578$	−16.2711			−0.676790
$579$	−1.65435	+	0.443282i	−0.0687525	+	0.0184222i
$580$	−6.10583	+	4.98539i	−0.253531	+	0.207007i
$581$	−69.0411			−2.86431
$582$	−2.88871	+	2.88871i	−0.119741	+	0.119741i
$583$	−12.2818	+	45.8364i	−0.508662	+	1.89835i
$584$	−3.61401	−	3.61401i	−0.149549	−	0.149549i
$585$	13.1595	+	29.2381i	0.544077	+	1.20885i
$586$	14.4674	−	14.4674i	0.597642	−	0.597642i
$587$	−16.1544	+	27.9803i	−0.666764	+	1.15487i	0.312040	+	0.950069i	$0.398988\pi$
$587$	−16.1544	+	27.9803i	−0.666764	+	1.15487i	−0.978804	+	0.204800i	$0.934346\pi$
$588$	−1.48419	−	5.53906i	−0.0612068	−	0.228427i
$589$	9.73686	+	5.62158i	0.401200	+	0.231633i
$590$	9.36433	+	11.4689i	0.385523	+	0.472168i
$591$		−	8.88232i		−	0.365370i
$592$	5.98502	−	1.08604i	0.245983	−	0.0446361i
$593$	6.35042	−	6.35042i	0.260780	−	0.260780i	−0.564591	−	0.825371i	$-0.690966\pi$
$593$	6.35042	−	6.35042i	0.260780	−	0.260780i	0.825371	+	0.564591i	$0.190966\pi$
$594$	−2.56361	+	9.56753i	−0.105186	+	0.392560i
$595$	2.94194	−	7.75757i	0.120608	−	0.318030i
$596$	1.56363	+	0.902761i	0.0640487	+	0.0369785i
$597$	3.53030	+	2.03822i	0.144486	+	0.0834188i
$598$	27.8836			1.14025
$599$	12.2925	+	7.09708i	0.502258	+	0.289979i	0.729646	−	0.683826i	$-0.239685\pi$
$599$	12.2925	+	7.09708i	0.502258	+	0.289979i	−0.227387	+	0.973804i	$0.573018\pi$
$600$	1.07754	−	2.15772i	0.0439902	−	0.0880884i
$601$	10.1854	+	17.6417i	0.415473	+	0.719620i	0.995478	−	0.0949925i	$-0.0302827\pi$
$601$	10.1854	+	17.6417i	0.415473	+	0.719620i	−0.580005	+	0.814613i	$0.696949\pi$
$602$	31.2331	+	31.2331i	1.27297	+	1.27297i
$603$	−11.1474	−	11.1474i	−0.453958	−	0.453958i
$604$	8.66636	−	5.00352i	0.352629	−	0.203591i
$605$	3.41951	−	1.53905i	0.139023	−	0.0625712i
$606$	−3.77356	+	3.77356i	−0.153290	+	0.153290i
$607$	−7.70604	−	13.3472i	−0.312778	−	0.541748i	0.666184	−	0.745787i	$-0.267926\pi$
$607$	−7.70604	−	13.3472i	−0.312778	−	0.541748i	−0.978963	+	0.204039i	$0.934593\pi$
$608$	1.98004	+	0.530550i	0.0803012	+	0.0215166i
$609$	7.13834	+	1.91271i	0.289260	+	0.0775070i
$610$	−6.52395	+	17.2029i	−0.264147	+	0.696526i
$611$	−43.5210	+	11.6614i	−1.76067	+	0.471770i
$612$	1.18128	+	2.04604i	0.0477505	+	0.0827063i
$613$	4.48320	−	16.7315i	0.181075	−	0.675780i	−0.814362	−	0.580357i	$-0.802913\pi$
$613$	4.48320	−	16.7315i	0.181075	−	0.675780i	0.995437	−	0.0954229i	$-0.0304204\pi$
$614$	11.0610	+	2.96378i	0.446385	+	0.119608i
$615$	4.67199	−	0.759334i	0.188393	−	0.0306193i
$616$	−4.00498	−	14.9468i	−0.161365	−	0.602224i
$617$	25.5264	+	6.83977i	1.02765	+	0.275359i	0.732988	−	0.680242i	$-0.238125\pi$
$617$	25.5264	+	6.83977i	1.02765	+	0.275359i	0.294665	+	0.955601i	$0.404792\pi$
$618$	−1.14110	+	1.14110i	−0.0459020	+	0.0459020i
$619$	24.0311			0.965892			0.482946	−	0.875650i	$-0.339567\pi$
$619$	24.0311			0.965892			0.482946	+	0.875650i	$0.339567\pi$
$620$	−7.75663	−	9.49989i	−0.311514	−	0.381525i
$621$	−10.5858	+	10.5858i	−0.424793	+	0.424793i
$622$	2.99666	+	11.1837i	0.120155	+	0.448426i
$623$		−	49.7444i		−	1.99297i
$624$	−2.41421	+	0.646887i	−0.0966459	+	0.0258962i
$625$	−3.01472	−	24.8176i	−0.120589	−	0.992703i
$626$	2.06424	−	3.57537i	0.0825037	−	0.142901i
$627$	3.04889	−	1.76028i	0.121761	−	0.0702988i
$628$	1.03616	+	1.03616i	0.0413471	+	0.0413471i
$629$	−0.927195	−	5.10963i	−0.0369697	−	0.203734i
$630$	26.5448	−	4.31431i	1.05757	−	0.171886i
$631$	2.58625	+	0.692984i	0.102957	+	0.0275872i	0.309930	−	0.950759i	$-0.399694\pi$
$631$	2.58625	+	0.692984i	0.102957	+	0.0275872i	−0.206973	+	0.978347i	$0.566361\pi$
$632$	0.864068	+	3.22474i	0.0343708	+	0.128273i
$633$	−7.97141	+	2.13593i	−0.316835	+	0.0848957i
$634$	−5.31111	−	19.8213i	−0.210931	−	0.787206i
$635$	−5.31460	−	32.6994i	−0.210904	−	1.29763i
$636$	3.21441	−	5.56753i	0.127460	−	0.220767i
$637$			61.5996i			2.44067i
$638$	12.1237	+	3.24854i	0.479983	+	0.128611i
$639$		−	4.14262i		−	0.163879i
$640$	−1.81431	−	1.30701i	−0.0717170	−	0.0516640i
$641$	−8.59978	−	14.8952i	−0.339671	−	0.588327i	0.644700	−	0.764436i	$-0.276982\pi$
$641$	−8.59978	−	14.8952i	−0.339671	−	0.588327i	−0.984371	+	0.176109i	$0.943649\pi$
$642$	−2.32792	−	1.34403i	−0.0918757	−	0.0530445i
$643$			14.4135i			0.568412i	0.958763	+	0.284206i	$0.0917299\pi$
$643$			14.4135i			0.568412i	−0.958763	+	0.284206i	$0.908270\pi$
$644$	6.05317	−	22.5907i	0.238528	−	0.890200i
$645$	8.49117	−	6.93301i	0.334339	−	0.272987i
$646$	0.452949	−	1.69043i	0.0178211	−	0.0665091i
$647$	11.2871	−	19.5498i	0.443740	−	0.768580i	−0.554224	−	0.832368i	$-0.686985\pi$
$647$	11.2871	−	19.5498i	0.443740	−	0.768580i	0.997963	+	0.0637877i	$0.0203181\pi$
$648$	−3.48004	+	6.02761i	−0.136709	+	0.236787i
$649$	6.10191	−	22.7727i	0.239521	−	0.893905i
$650$	−17.1795	+	19.3926i	−0.673834	+	0.760642i
$651$	−2.97594	+	11.1063i	−0.116636	+	0.435292i
$652$		−	23.8593i		−	0.934403i
$653$	7.05249	+	4.07175i	0.275985	+	0.159340i	0.631604	−	0.775291i	$-0.282397\pi$
$653$	7.05249	+	4.07175i	0.275985	+	0.159340i	−0.355619	+	0.934631i	$0.615730\pi$
$654$	−2.82937	−	4.90062i	−0.110637	−	0.191629i
$655$	−29.6587	+	4.82040i	−1.15886	+	0.188349i
$656$		−	4.38839i		−	0.171338i
$657$	−13.6618	−	3.66068i	−0.532999	−	0.142817i
$658$			37.7913i			1.47326i
$659$	4.31784	−	7.47871i	0.168199	−	0.291329i	−0.769588	−	0.638541i	$-0.779538\pi$
$659$	4.31784	−	7.47871i	0.168199	−	0.291329i	0.937787	+	0.347212i	$0.112872\pi$
$660$	−3.79057	+	0.616079i	−0.147548	+	0.0239808i
$661$	−4.20119	−	15.6791i	−0.163407	−	0.609845i	−0.998238	−	0.0593378i	$-0.981101\pi$
$661$	−4.20119	−	15.6791i	−0.163407	−	0.609845i	0.834831	−	0.550507i	$-0.185566\pi$
$662$	−9.23143	+	2.47355i	−0.358790	+	0.0961374i
$663$	0.552270	+	2.06110i	0.0214484	+	0.0800465i
$664$	15.3446	+	4.11157i	0.595485	+	0.159560i
$665$	−16.1636	−	11.6441i	−0.626798	−	0.451537i
$666$	12.8408	−	10.8840i	0.497572	−	0.421748i
$667$	13.4140	+	13.4140i	0.519394	+	0.519394i
$668$	6.14162	−	3.54587i	0.237626	−	0.137194i
$669$	−5.87868	+	10.1822i	−0.227283	+	0.393666i
$670$	4.51693	−	11.9106i	0.174504	−	0.460148i
$671$	28.2975	−	7.58229i	1.09241	−	0.292711i
$672$			2.09638i			0.0808695i
$673$	−4.09744	−	15.2919i	−0.157945	−	0.589458i	−0.998835	−	0.0482527i	$-0.984635\pi$
$673$	−4.09744	−	15.2919i	−0.157945	−	0.589458i	0.840890	−	0.541206i	$-0.182032\pi$
$674$	1.31249	−	1.31249i	0.0505552	−	0.0505552i
$675$	−0.840211	−	13.8843i	−0.0323397	−	0.534407i
$676$	13.8484			0.532629
$677$	29.4703	−	29.4703i	1.13264	−	1.13264i	0.142898	−	0.989737i	$-0.454358\pi$
$677$	29.4703	−	29.4703i	1.13264	−	1.13264i	0.989737	−	0.142898i	$-0.0456422\pi$
$678$	3.18460	+	0.853311i	0.122304	+	0.0327712i
$679$	−9.52660	−	35.5538i	−0.365597	−	1.36443i
$680$	−1.11584	+	1.54894i	−0.0427905	+	0.0593993i
$681$	−7.73479	−	2.07253i	−0.296398	−	0.0794196i
$682$	−5.05432	+	18.8630i	−0.193540	+	0.722301i
$683$	−1.26026	−	2.18284i	−0.0482226	−	0.0835239i	0.840907	−	0.541180i	$-0.182022\pi$
$683$	−1.26026	−	2.18284i	−0.0482226	−	0.0835239i	−0.889129	+	0.457656i	$0.848689\pi$
$684$	5.47942	−	1.46821i	0.209511	−	0.0561382i
$685$	−17.9459	−	6.80571i	−0.685677	−	0.260033i
$686$	20.5209	+	5.49856i	0.783491	+	0.209936i
$687$	5.82184	+	1.55996i	0.222117	+	0.0595161i
$688$	−5.08164	−	8.80166i	−0.193736	−	0.335560i
$689$	−48.8318	+	48.8318i	−1.86034	+	1.86034i
$690$	−5.42713	−	2.05816i	−0.206607	−	0.0783527i
$691$	−13.1244	+	7.57738i	−0.499276	+	0.288257i	−0.728414	−	0.685137i	$-0.759742\pi$
$691$	−13.1244	+	7.57738i	−0.499276	+	0.288257i	0.229139	+	0.973394i	$0.426409\pi$
$692$	0.609735	+	0.609735i	0.0231786	+	0.0231786i
$693$	−30.2796	−	30.2796i	−1.15023	−	1.15023i
$694$	−12.7734	−	22.1242i	−0.484872	−	0.839823i
$695$	−3.22863	−	2.32586i	−0.122469	−	0.0882251i
$696$	−1.47261	−	0.850212i	−0.0558191	−	0.0322272i
$697$	−3.74652			−0.141910
$698$	−2.42921	−	1.40250i	−0.0919469	−	0.0530855i
$699$	−12.2943	−	7.09812i	−0.465013	−	0.268475i
$700$	11.9821	+	18.1283i	0.452880	+	0.685187i
$701$	−7.45591	+	27.8258i	−0.281606	+	1.05097i	0.669678	+	0.742651i	$0.266432\pi$
$701$	−7.45591	+	27.8258i	−0.281606	+	1.05097i	−0.951284	+	0.308316i	$0.900235\pi$
$702$	−10.1928	+	10.1928i	−0.384701	+	0.384701i
$703$	−12.4268	−	1.02494i	−0.468685	−	0.0386565i
$704$			3.56048i			0.134191i
$705$	9.33145	+	0.942668i	0.351443	+	0.0355029i
$706$	20.2461	+	11.6891i	0.761973	+	0.439925i
$707$	−12.4447	−	46.4443i	−0.468032	−	1.74672i
$708$	−1.59700	+	2.76608i	−0.0600189	+	0.103956i
$709$	−12.3845	+	12.3845i	−0.465110	+	0.465110i	−0.900326	−	0.435216i	$-0.856672\pi$
$709$	−12.3845	+	12.3845i	−0.465110	+	0.465110i	0.435216	+	0.900326i	$0.356672\pi$
$710$	3.05242	−	1.37383i	0.114555	−	0.0515589i
$711$	6.53277	+	6.53277i	0.244998	+	0.244998i
$712$	−2.96240	+	11.0558i	−0.111021	+	0.414335i
$713$	−20.8705	+	20.8705i	−0.781608	+	0.781608i
$714$	1.78975			0.0669798
$715$	41.0438	+	4.14626i	1.53495	+	0.155061i
$716$	−14.1376	+	3.78817i	−0.528348	+	0.141570i
$717$	−3.11172			−0.116209
$718$	9.83548	−	5.67851i	0.367057	−	0.211920i
$719$	38.5743	−	22.2709i	1.43858	−	0.830565i	0.440829	−	0.897591i	$-0.354684\pi$
$719$	38.5743	−	22.2709i	1.43858	−	0.830565i	0.997751	+	0.0670263i	$0.0213512\pi$
$720$	−6.15660	−	0.621943i	−0.229443	−	0.0231784i
$721$	−3.76322	−	14.0445i	−0.140150	−	0.523046i
$722$	12.8154	+	7.39898i	0.476940	+	0.275362i
$723$	8.96748	−	5.17738i	0.333504	−	0.192549i
$724$	−6.72122	−	11.6415i	−0.249792	−	0.432653i
$725$	−17.5938	+	1.06469i	−0.653418	+	0.0395417i
$726$	0.571995	+	0.571995i	0.0212287	+	0.0212287i
$727$	−9.03837	+	15.6549i	−0.335215	+	0.580609i	−0.983526	−	0.180766i	$-0.942142\pi$
$727$	−9.03837	+	15.6549i	−0.335215	+	0.580609i	0.648311	+	0.761375i	$0.275476\pi$
$728$	5.82843	−	21.7520i	0.216016	−	0.806182i
$729$			15.2351i			0.564263i
$730$	−1.83341	−	11.2805i	−0.0678576	−	0.417510i
$731$	−7.51429	+	4.33838i	−0.277926	+	0.160461i
$732$	−3.96889			−0.146694
$733$	27.2404	−	7.29904i	1.00615	−	0.269596i	0.282128	−	0.959377i	$-0.408960\pi$
$733$	27.2404	−	7.29904i	1.00615	−	0.269596i	0.724018	+	0.689781i	$0.242293\pi$
$734$	−9.98050	−	9.98050i	−0.368387	−	0.368387i
$735$	4.54681	−	11.9894i	0.167712	−	0.442237i
$736$	−2.69067	+	4.66038i	−0.0991794	+	0.171784i
$737$	−19.5921	+	5.24969i	−0.721684	+	0.193375i
$738$	−6.07205	−	10.5171i	−0.223515	−	0.387140i
$739$	−10.3182			−0.379563			−0.189781	−	0.981826i	$-0.560778\pi$
$739$	−10.3182			−0.379563			−0.189781	+	0.981826i	$0.560778\pi$
$740$	12.2782	+	5.85204i	0.451355	+	0.215125i
$741$	5.12344			0.188214
$742$	28.9618	+	50.1632i	1.06322	+	1.84155i
$743$	−14.1876	+	3.80155i	−0.520491	+	0.139465i	−0.509494	−	0.860474i	$-0.670167\pi$
$743$	−14.1876	+	3.80155i	−0.520491	+	0.139465i	−0.0109975	+	0.999940i	$0.503501\pi$
$744$	1.32282	−	2.29119i	0.0484970	−	0.0839992i
$745$	1.65700	+	3.68157i	0.0607076	+	0.134882i
$746$	15.0208	+	15.0208i	0.549951	+	0.549951i
$747$	42.4635	−	11.3781i	1.55366	−	0.416301i
$748$	3.03971			0.111143
$749$	20.9745	−	12.1096i	0.766391	−	0.442476i
$750$	4.77514	−	2.50643i	0.174363	−	0.0915217i
$751$			35.5383i			1.29681i	0.761295	+	0.648406i	$0.224564\pi$
$751$			35.5383i			1.29681i	−0.761295	+	0.648406i	$0.775436\pi$
$752$	2.25057	−	8.39924i	0.0820698	−	0.306289i
$753$	1.52673	−	2.64437i	0.0556370	−	0.0963661i
$754$	12.9160	+	12.9160i	0.470373	+	0.470373i
$755$	22.2631	+	2.24903i	0.810238	+	0.0818507i
$756$	6.04524	+	10.4707i	0.219863	+	0.380815i
$757$	−13.5809	+	7.84096i	−0.493608	+	0.284984i	−0.726070	−	0.687621i	$-0.758655\pi$
$757$	−13.5809	+	7.84096i	−0.493608	+	0.284984i	0.232462	+	0.972605i	$0.425322\pi$
$758$	−20.1970	−	11.6607i	−0.733586	−	0.423536i
$759$	2.39204	+	8.92721i	0.0868255	+	0.324037i
$760$	2.89898	+	3.55051i	0.105157	+	0.128791i
$761$	8.62460	−	4.97942i	0.312642	−	0.180504i	−0.335466	−	0.942052i	$-0.608894\pi$
$761$	8.62460	−	4.97942i	0.312642	−	0.180504i	0.648108	+	0.761548i	$0.275561\pi$
$762$	6.18899	−	3.57321i	0.224203	−	0.129444i
$763$	50.9851			1.84578
$764$	−2.13119	+	0.571050i	−0.0771037	+	0.0206599i
$765$	−0.530975	+	5.25611i	−0.0191974	+	0.190035i
$766$	−1.80196			−0.0651074
$767$	24.2608	−	24.2608i	0.876007	−	0.876007i
$768$	0.124844	−	0.465926i	0.00450494	−	0.0168127i
$769$	−29.5809	−	29.5809i	−1.06671	−	1.06671i	−0.997609	−	0.0691049i	$-0.977986\pi$
$769$	−29.5809	−	29.5809i	−1.06671	−	1.06671i	−0.0691049	−	0.997609i	$-0.522014\pi$
$770$	12.2693	−	32.3527i	0.442154	−	1.16591i
$771$	7.55957	−	7.55957i	0.272251	−	0.272251i
$772$	−1.77534	+	3.07497i	−0.0638958	+	0.110671i
$773$	5.20332	+	19.4190i	0.187150	+	0.698454i	0.994160	+	0.107916i	$0.0344178\pi$
$773$	5.20332	+	19.4190i	0.187150	+	0.698454i	−0.807010	+	0.590538i	$0.798916\pi$
$774$	−24.3571	−	14.0626i	−0.875497	−	0.505468i
$775$	−1.65653	−	27.3738i	−0.0595042	−	0.983294i
$776$			8.46926i			0.304029i
$777$	−2.27676	−	12.5469i	−0.0816782	−	0.450116i
$778$	25.0812	−	25.0812i	0.899203	−	0.899203i
$779$	−2.32826	+	8.68919i	−0.0834186	+	0.311322i
$780$	−5.22562	−	1.98174i	−0.187107	−	0.0709577i
$781$	−4.61587	−	2.66497i	−0.165169	−	0.0953602i
$782$	3.97873	+	2.29712i	0.142279	+	0.0821449i
$783$	−9.80690			−0.350470
$784$	−10.2956	−	5.94414i	−0.367698	−	0.212291i
$785$	0.525648	+	3.23418i	0.0187612	+	0.115433i
$786$	−3.24094	−	5.61347i	−0.115601	−	0.200226i
$787$	−30.8503	−	30.8503i	−1.09969	−	1.09969i	−0.994446	−	0.105247i	$-0.966437\pi$
$787$	−30.8503	−	30.8503i	−1.09969	−	1.09969i	−0.105247	−	0.994446i	$-0.533563\pi$
$788$	−13.0208	−	13.0208i	−0.463847	−	0.463847i
$789$	−1.54703	+	0.893176i	−0.0550756	+	0.0317979i
$790$	−2.64708	+	6.98004i	−0.0941787	+	0.248339i
$791$	−21.0048	+	21.0048i	−0.746846	+	0.746846i
$792$	4.92650	+	8.53295i	0.175056	+	0.303205i
$793$	41.1812	+	11.0345i	1.46239	+	0.391845i
$794$	−7.49183	−	2.00743i	−0.265875	−	0.0712410i
$795$	13.1087	−	5.89998i	0.464919	−	0.209251i
$796$	8.16304	−	2.18728i	0.289331	−	0.0775261i
$797$	−20.9272	−	36.2470i	−0.741280	−	1.28393i	−0.951913	−	0.306369i	$-0.900886\pi$
$797$	−20.9272	−	36.2470i	−0.741280	−	1.28393i	0.210633	−	0.977565i	$-0.432447\pi$
$798$	1.11223	−	4.15091i	0.0393726	−	0.146941i
$799$	−7.17073	−	1.92139i	−0.253682	−	0.0679739i
$800$	−1.58346	−	4.74264i	−0.0559839	−	0.167678i
$801$	8.19793	+	30.5951i	0.289660	+	1.08102i
$802$	30.7034	+	8.22696i	1.08418	+	0.290504i
$803$	−12.8676	+	12.8676i	−0.454088	+	0.454088i
$804$	2.74791			0.0969112
$805$	40.5086	−	33.0751i	1.42774	−	1.16575i
$806$	−20.0956	+	20.0956i	−0.707839	+	0.707839i
$807$	1.89202	+	7.06110i	0.0666021	+	0.248562i
$808$			11.0635i			0.389213i
$809$	31.9208	−	8.55316i	1.12228	−	0.300713i	0.350472	−	0.936573i	$-0.386021\pi$
$809$	31.9208	−	8.55316i	1.12228	−	0.300713i	0.771805	+	0.635860i	$0.219354\pi$
$810$	−14.1920	+	6.38753i	−0.498656	+	0.224435i
$811$	−20.7589	+	35.9554i	−0.728942	+	1.26256i	0.228389	+	0.973570i	$0.426654\pi$
$811$	−20.7589	+	35.9554i	−0.728942	+	1.26256i	−0.957331	+	0.288995i	$0.906679\pi$
$812$	13.2682	−	7.66038i	0.465621	−	0.268827i
$813$	7.33145	+	7.33145i	0.257125	+	0.257125i
$814$	−3.86684	−	21.3095i	−0.135533	−	0.746899i
$815$	31.1843	−	43.2883i	1.09234	−	1.51632i
$816$	−0.397777	−	0.106584i	−0.0139250	−	0.00373119i
$817$	5.39213	+	20.1237i	0.188647	+	0.704039i
$818$	−3.85739	+	1.03359i	−0.134871	+	0.0361385i
$819$	−16.1292	−	60.1949i	−0.563599	−	2.10338i
$820$	5.73566	−	7.96191i	0.200298	−	0.278042i
$821$	9.19250	−	15.9219i	0.320821	−	0.555678i	−0.659837	−	0.751409i	$-0.729375\pi$
$821$	9.19250	−	15.9219i	0.320821	−	0.555678i	0.980658	+	0.195731i	$0.0627080\pi$
$822$		−	4.14030i		−	0.144409i
$823$	−26.6681	−	7.14570i	−0.929592	−	0.249083i	−0.237911	−	0.971287i	$-0.576463\pi$
$823$	−26.6681	−	7.14570i	−0.929592	−	0.249083i	−0.691681	+	0.722204i	$0.743129\pi$
$824$			3.34555i			0.116548i
$825$	−7.68250	−	3.83654i	−0.267470	−	0.133571i
$826$	−14.3889	−	24.9223i	−0.500654	−	0.867158i
$827$	5.95080	+	3.43570i	0.206930	+	0.119471i	0.599884	−	0.800087i	$-0.295214\pi$
$827$	5.95080	+	3.43570i	0.206930	+	0.119471i	−0.392954	+	0.919558i	$0.628547\pi$
$828$			14.8919i			0.517530i
$829$	3.51177	−	13.1061i	0.121969	−	0.455194i	−0.877745	−	0.479129i	$-0.840953\pi$
$829$	3.51177	−	13.1061i	0.121969	−	0.455194i	0.999714	+	0.0239345i	$0.00761932\pi$
$830$	22.4660	+	27.5151i	0.779807	+	0.955065i
$831$	−3.48258	+	12.9972i	−0.120809	+	0.450866i
$832$	−2.59077	+	4.48735i	−0.0898188	+	0.155571i
$833$	−5.07473	+	8.78968i	−0.175829	+	0.304544i
$834$	0.222165	−	0.829131i	0.00769295	−	0.0287105i
$835$	15.7773	+	1.59383i	0.545996	+	0.0551568i
$836$	1.88901	−	7.04989i	0.0653328	−	0.243825i
$837$		−	15.2583i		−	0.527403i
$838$	−13.2473	−	7.64835i	−0.457621	−	0.264208i
$839$	−25.2573	−	43.7469i	−0.871979	−	1.51031i	−0.859947	−	0.510384i	$-0.829503\pi$
$839$	−25.2573	−	43.7469i	−0.871979	−	1.51031i	−0.0120317	−	0.999928i	$-0.503830\pi$
$840$	−2.73998	+	3.80348i	−0.0945383	+	0.131233i
$841$		−	16.5730i		−	0.571481i
$842$	32.7296	+	8.76986i	1.12794	+	0.302229i
$843$		−	10.5114i		−	0.362030i
$844$	−8.55437	+	14.8166i	−0.294454	+	0.510009i
$845$	25.1253	+	18.0999i	0.864335	+	0.622656i
$846$	−6.22806	−	23.2434i	−0.214125	−	0.799126i
$847$	−7.04002	+	1.88637i	−0.241898	+	0.0648164i
$848$	−3.44949	−	12.8737i	−0.118456	−	0.442084i
$849$	−13.3311	−	3.57205i	−0.457522	−	0.122593i
$850$	−4.04896	+	1.35186i	−0.138878	+	0.0463684i
$851$	11.0424	−	30.8147i	0.378527	−	1.05631i
$852$	0.510590	+	0.510590i	0.0174925	+	0.0174925i
$853$	−21.0602	+	12.1591i	−0.721089	+	0.416321i	−0.815153	−	0.579245i	$-0.803347\pi$
$853$	−21.0602	+	12.1591i	−0.721089	+	0.416321i	0.0940645	+	0.995566i	$0.470014\pi$
$854$	17.8798	−	30.9687i	0.611833	−	1.05973i
$855$	11.8603	+	4.49785i	0.405615	+	0.153823i
$856$	−5.38280	+	1.44232i	−0.183980	+	0.0492974i
$857$			2.09422i			0.0715372i	0.999360	+	0.0357686i	$0.0113879\pi$
$857$			2.09422i			0.0715372i	−0.999360	+	0.0357686i	$0.988612\pi$
$858$	2.30323	+	8.59575i	0.0786308	+	0.293454i
$859$	−25.6794	+	25.6794i	−0.876169	+	0.876169i	−0.993136	−	0.116967i	$-0.962683\pi$
$859$	−25.6794	+	25.6794i	−0.876169	+	0.876169i	0.116967	+	0.993136i	$0.462683\pi$
$860$	2.28415	−	22.6107i	0.0778887	−	0.771019i
$861$	−9.19972			−0.313525
$862$	6.07155	−	6.07155i	0.206798	−	0.206798i
$863$	−0.179617	−	0.0481282i	−0.00611423	−	0.00163830i	0.255761	−	0.966740i	$-0.417674\pi$
$863$	−0.179617	−	0.0481282i	−0.00611423	−	0.00163830i	−0.261875	+	0.965102i	$0.584341\pi$
$864$	−0.720019	−	2.68715i	−0.0244955	−	0.0914186i
$865$	0.309322	+	1.90318i	0.0105173	+	0.0647100i
$866$	6.58310	+	1.76394i	0.223703	+	0.0599410i
$867$	2.03136	−	7.58114i	0.0689886	−	0.257469i
$868$	11.9186	+	20.6436i	0.404543	+	0.700689i
$869$	11.4816	−	3.07649i	0.389488	−	0.104363i
$870$	−1.56054	−	3.46726i	−0.0529073	−	0.117551i
$871$	−28.5123	−	7.63984i	−0.966101	−	0.258866i
$872$	−11.3316	−	3.03629i	−0.383736	−	0.102822i
$873$	11.7186	+	20.2972i	0.396615	+	0.686957i
$874$	7.80020	−	7.80020i	0.263846	−	0.263846i
$875$	−1.95463	+	48.5512i	−0.0660786	+	1.64133i
$876$	2.13505	−	1.23267i	0.0721367	−	0.0416482i
$877$	18.2121	+	18.2121i	0.614977	+	0.614977i	0.944239	−	0.329261i	$-0.106800\pi$
$877$	18.2121	+	18.2121i	0.614977	+	0.614977i	−0.329261	+	0.944239i	$0.606800\pi$
$878$	−0.411810	−	0.411810i	−0.0138979	−	0.0138979i
$879$	4.93456	+	8.54690i	0.166438	+	0.288280i
$880$	−4.65357	+	6.45982i	−0.156872	+	0.217761i
$881$	5.94587	+	3.43285i	0.200321	+	0.115656i	0.596805	−	0.802386i	$-0.296436\pi$
$881$	5.94587	+	3.43285i	0.200321	+	0.115656i	−0.396484	+	0.918042i	$0.629770\pi$
$882$	−32.8988			−1.10776
$883$	31.6837	+	18.2926i	1.06624	+	0.615595i	0.927152	−	0.374685i	$-0.122249\pi$
$883$	31.6837	+	18.2926i	1.06624	+	0.615595i	0.139089	+	0.990280i	$0.455582\pi$
$884$	3.83101	+	2.21183i	0.128851	+	0.0743920i
$885$	−6.51275	+	2.93125i	−0.218924	+	0.0985329i
$886$	2.05229	−	7.65926i	0.0689481	−	0.257318i
$887$	14.7010	−	14.7010i	0.493612	−	0.493612i	−0.415830	−	0.909442i	$-0.636509\pi$
$887$	14.7010	−	14.7010i	0.493612	−	0.493612i	0.909442	+	0.415830i	$0.136509\pi$
$888$	−0.241181	+	2.92416i	−0.00809350	+	0.0981285i
$889$			64.3891i			2.15954i
$890$	−19.8248	+	16.1869i	−0.664528	+	0.542585i
$891$	21.4612	+	12.3906i	0.718976	+	0.415101i
$892$	6.30860	+	23.5440i	0.211228	+	0.788312i
$893$	−8.91243	+	15.4368i	−0.298243	+	0.516572i
$894$	−0.615830	+	0.615830i	−0.0205964	+	0.0205964i
$895$	−30.6013	−	11.6051i	−1.02289	−	0.387915i
$896$	3.07313	+	3.07313i	0.102666	+	0.102666i
$897$	−3.48112	+	12.9917i	−0.116231	+	0.433780i
$898$	0.342665	−	0.342665i	0.0114349	−	0.0114349i
$899$	−19.3349			−0.644855
$900$	−10.3571	−	9.17511i	−0.345237	−	0.305837i
$901$	−10.9907	+	2.94495i	−0.366154	+	0.0981106i
$902$	−15.6248			−0.520248
$903$	−18.4516	+	10.6530i	−0.614030	+	0.354511i
$904$	5.91928	−	3.41750i	0.196872	−	0.113664i
$905$	3.02112	−	29.9060i	0.100425	−	0.994109i
$906$	1.24932	+	4.66254i	0.0415060	+	0.154903i
$907$	27.4929	+	15.8730i	0.912887	+	0.527056i	0.881359	−	0.472447i	$-0.156629\pi$
$907$	27.4929	+	15.8730i	0.912887	+	0.527056i	0.0315282	+	0.999503i	$0.489963\pi$
$908$	−14.3768	+	8.30046i	−0.477111	+	0.275460i
$909$	15.3082	+	26.5145i	0.507740	+	0.879431i
$910$	39.0046	−	31.8471i	1.29299	−	1.05572i
$911$	−4.29511	−	4.29511i	−0.142303	−	0.142303i	0.632366	−	0.774670i	$-0.282084\pi$
$911$	−4.29511	−	4.29511i	−0.142303	−	0.142303i	−0.774670	+	0.632366i	$0.782084\pi$
$912$	−0.494394	+	0.856315i	−0.0163710	+	0.0283554i
$913$	14.6391	−	54.6340i	0.484485	−	1.80812i
$914$			41.0850i			1.35897i
$915$	−7.20081	−	5.18736i	−0.238051	−	0.171489i
$916$	10.8212	−	6.24761i	0.357542	−	0.206427i
$917$	58.4015			1.92859
$918$	−2.29411	+	0.614706i	−0.0757170	+	0.0202883i
$919$	14.0218	+	14.0218i	0.462538	+	0.462538i	0.899486	−	0.436949i	$-0.143941\pi$
$919$	14.0218	+	14.0218i	0.462538	+	0.462538i	−0.436949	+	0.899486i	$0.643941\pi$
$920$	−10.9729	+	4.93866i	−0.361765	+	0.162823i
$921$	−2.76180	+	4.78358i	−0.0910045	+	0.157624i
$922$	−0.756655	+	0.202745i	−0.0249191	+	0.00667706i
$923$	−3.87832	−	6.71744i	−0.127656	−	0.221107i
$924$	7.46410			0.245551
$925$	14.6278	+	26.6651i	0.480959	+	0.876743i
$926$	−26.2844			−0.863759
$927$	4.62912	+	8.01786i	0.152040	+	0.263341i
$928$	−3.40508	+	0.912389i	−0.111777	+	0.0299506i
$929$	11.4501	−	19.8321i	0.375665	−	0.650671i	−0.614761	−	0.788713i	$-0.710748\pi$
$929$	11.4501	−	19.8321i	0.375665	−	0.650671i	0.990426	+	0.138042i	$0.0440809\pi$
$930$	5.39462	−	2.42801i	0.176896	−	0.0796174i
$931$	17.2319	+	17.2319i	0.564754	+	0.564754i
$932$	−28.4278	+	7.61722i	−0.931185	+	0.249510i
$933$	−5.58489			−0.182841
$934$	28.1584	−	16.2573i	0.921371	−	0.531954i
$935$	5.51498	+	3.97292i	0.180359	+	0.129928i
$936$			14.3390i			0.468685i
$937$	−4.62560	+	17.2630i	−0.151112	+	0.563957i	0.848295	+	0.529524i	$0.177629\pi$
$937$	−4.62560	+	17.2630i	−0.151112	+	0.563957i	−0.999407	+	0.0344332i	$0.989037\pi$
$938$	−12.3793	+	21.4415i	−0.404198	+	0.700091i
$939$	1.40815	+	1.40815i	0.0459532	+	0.0459532i
$940$	15.0611	−	12.2973i	0.491239	−	0.401095i
$941$	−17.2579	−	29.8916i	−0.562592	−	0.974438i	−0.997269	−	0.0738515i	$-0.976471\pi$
$941$	−17.2579	−	29.8916i	−0.562592	−	0.974438i	0.434677	−	0.900586i	$-0.356862\pi$
$942$	−0.612130	+	0.353414i	−0.0199443	+	0.0115148i
$943$	−20.4516	−	11.8077i	−0.665994	−	0.384512i
$944$	1.71379	+	6.39595i	0.0557791	+	0.208171i
$945$	−2.71728	+	26.8983i	−0.0883930	+	0.875000i
$946$	−31.3381	+	18.0931i	−1.01889	+	0.588256i
$947$	−32.8079	+	18.9416i	−1.06611	+	0.615521i	−0.927117	−	0.374772i	$-0.877721\pi$
$947$	−32.8079	+	18.9416i	−1.06611	+	0.615521i	−0.138996	+	0.990293i	$0.544388\pi$
$948$	−1.61037			−0.0523023
$949$	−25.5804	+	6.85425i	−0.830375	+	0.222498i
$950$	0.619114	+	10.2307i	0.0200867	+	0.331929i
$951$	9.89834			0.320976
$952$	2.62364	−	2.62364i	0.0850327	−	0.0850327i
$953$	13.7776	−	51.4186i	0.446299	−	1.66561i	−0.266185	−	0.963922i	$-0.585763\pi$
$953$	13.7776	−	51.4186i	0.446299	−	1.66561i	0.712484	−	0.701689i	$-0.247570\pi$
$954$	−26.0798	−	26.0798i	−0.844364	−	0.844364i
$955$	−4.61301	−	1.74941i	−0.149274	−	0.0566097i
$956$	−4.56155	+	4.56155i	−0.147531	+	0.147531i
$957$	−3.02716	+	5.24319i	−0.0978542	+	0.169488i
$958$	4.72118	+	17.6197i	0.152534	+	0.569266i
$959$	32.3062	+	18.6520i	1.04322	+	0.602304i
$960$	0.835475	−	0.682163i	0.0269649	−	0.0220167i
$961$			0.917343i			0.0295917i
$962$	10.6324	−	29.6706i	0.342801	−	0.956617i
$963$	−10.9046	+	10.9046i	−0.351396	+	0.351396i
$964$	5.55601	−	20.7353i	0.178947	−	0.667839i
$965$	−7.24003	+	3.25859i	−0.233065	+	0.104898i
$966$	9.76991	+	5.64066i	0.314342	+	0.181485i
$967$	39.7822	+	22.9683i	1.27931	+	0.738610i	0.976722	−	0.214511i	$-0.0688157\pi$
$967$	39.7822	+	22.9683i	1.27931	+	0.738610i	0.302589	+	0.953121i	$0.402149\pi$
$968$	1.67700			0.0539009
$969$	0.731067	+	0.422082i	0.0234853	+	0.0135592i
$970$	−11.0694	+	15.3659i	−0.355417	+	0.493369i
$971$	−9.51508	−	16.4806i	−0.305354	−	0.528888i	0.671986	−	0.740563i	$-0.265441\pi$
$971$	−9.51508	−	16.4806i	−0.305354	−	0.528888i	−0.977340	+	0.211676i	$0.932108\pi$
$972$	−8.27534	−	8.27534i	−0.265432	−	0.265432i
$973$	5.46875	+	5.46875i	0.175320	+	0.175320i
$974$	11.4053	−	6.58484i	0.365449	−	0.210992i
$975$	−6.89077	−	10.4254i	−0.220681	−	0.333881i
$976$	−5.81809	+	5.81809i	−0.186233	+	0.186233i
$977$	25.9339	+	44.9188i	0.829699	+	1.43708i	0.898275	+	0.439434i	$0.144821\pi$
$977$	25.9339	+	44.9188i	0.829699	+	1.43708i	−0.0685760	+	0.997646i	$0.521846\pi$
$978$	11.1167	+	2.97870i	0.355472	+	0.0952485i
$979$	39.3641	+	10.5476i	1.25808	+	0.337102i
$980$	−10.9103	−	24.2409i	−0.348518	−	0.774347i
$981$	−31.3582	+	8.40241i	−1.00119	+	0.268268i
$982$	9.20424	+	15.9422i	0.293719	+	0.508737i
$983$	7.08756	−	26.4511i	0.226058	−	0.843660i	−0.755920	−	0.654664i	$-0.772810\pi$
$983$	7.08756	−	26.4511i	0.226058	−	0.843660i	0.981978	−	0.188996i	$-0.0605232\pi$
$984$	2.04466	+	0.547866i	0.0651815	+	0.0174653i
$985$	−6.60554	−	40.6421i	−0.210470	−	1.29497i
$986$	0.778939	+	2.90704i	0.0248065	+	0.0925790i
$987$	−17.6080	−	4.71804i	−0.560468	−	0.150177i
$988$	7.51059	−	7.51059i	0.238944	−	0.238944i
$989$	−54.6921			−1.73911
$990$	−2.21441	+	21.9204i	−0.0703787	+	0.696677i
$991$	−2.07730	+	2.07730i	−0.0659875	+	0.0659875i	−0.739330	−	0.673343i	$-0.764858\pi$
$991$	−2.07730	+	2.07730i	−0.0659875	+	0.0659875i	0.673343	+	0.739330i	$0.264858\pi$
$992$	−1.41956	−	5.29788i	−0.0450711	−	0.168208i
$993$		−	4.60997i		−	0.146293i
$994$	−6.28426	+	1.68386i	−0.199325	+	0.0534089i
$995$	17.6691	+	6.70074i	0.560148	+	0.212428i
$996$	−3.83137	+	6.63613i	−0.121402	+	0.210274i
$997$	−8.05340	+	4.64963i	−0.255054	+	0.147255i	−0.622076	−	0.782957i	$-0.713711\pi$
$997$	−8.05340	+	4.64963i	−0.255054	+	0.147255i	0.367022	+	0.930212i	$0.380377\pi$
$998$	−25.6614	−	25.6614i	−0.812299	−	0.812299i
$999$	7.22769	+	15.3007i	0.228674	+	0.484092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.q.c.267.1	✓	8
5.3	odd	4		370.2.r.c.193.1	yes	8
37.14	odd	12		370.2.r.c.347.1	yes	8
185.88	even	12	inner	370.2.q.c.273.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.c.267.1	✓	8	1.1	even	1	trivial
370.2.q.c.273.1	yes	8	185.88	even	12	inner
370.2.r.c.193.1	yes	8	5.3	odd	4
370.2.r.c.347.1	yes	8	37.14	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.465926 + 0.124844i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(-0.341081 - 0.341081i) q^{6} +(4.19798 - 1.12484i) q^{7} -1.00000 q^{8} +(-2.39658 + 1.38366i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.465926 + 0.124844i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +(-0.341081 - 0.341081i) q^{6} +(4.19798 - 1.12484i) q^{7} -1.00000 q^{8} +(-2.39658 + 1.38366i) q^{9} +(-1.81431 - 1.30701i) q^{10} +3.56048i q^{11} +(0.124844 - 0.465926i) q^{12} +(-2.59077 + 4.48735i) q^{13} +(3.07313 + 3.07313i) q^{14} +(0.835475 - 0.682163i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.739357 + 0.426868i) q^{17} +(-2.39658 - 1.38366i) q^{18} +(0.530550 + 1.98004i) q^{19} +(0.224745 - 2.22474i) q^{20} +(-1.81552 + 1.04819i) q^{21} +(-3.08346 + 1.78024i) q^{22} -5.38134 q^{23} +(0.465926 - 0.124844i) q^{24} +(3.31552 - 3.74264i) q^{25} -5.18154 q^{26} +(1.96713 - 1.96713i) q^{27} +(-1.12484 + 4.19798i) q^{28} +(-2.49269 - 2.49269i) q^{29} +(1.00851 + 0.382461i) q^{30} +(3.87832 - 3.87832i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.444506 - 1.65892i) q^{33} +(-0.739357 - 0.426868i) q^{34} +(-7.52761 + 6.14626i) q^{35} -2.76733i q^{36} +(-2.05197 + 5.72620i) q^{37} +(-1.44949 + 1.44949i) q^{38} +(0.646887 - 2.41421i) q^{39} +(2.03906 - 0.917738i) q^{40} +(3.80046 + 2.19419i) q^{41} +(-1.81552 - 1.04819i) q^{42} +10.1633 q^{43} +(-3.08346 - 1.78024i) q^{44} +(3.61692 - 5.02080i) q^{45} +(-2.69067 - 4.66038i) q^{46} +(6.14867 + 6.14867i) q^{47} +(0.341081 + 0.341081i) q^{48} +(10.2956 - 5.94414i) q^{49} +(4.89898 + 1.00000i) q^{50} +(0.291193 - 0.291193i) q^{51} +(-2.59077 - 4.48735i) q^{52} +(12.8737 + 3.44949i) q^{53} +(2.68715 + 0.720019i) q^{54} +(-3.26758 - 7.26002i) q^{55} +(-4.19798 + 1.12484i) q^{56} +(-0.494394 - 0.856315i) q^{57} +(0.912389 - 3.40508i) q^{58} +(-6.39595 - 1.71379i) q^{59} +(0.173033 + 1.06462i) q^{60} +(-2.12957 - 7.94767i) q^{61} +(5.29788 + 1.41956i) q^{62} +(-8.50436 + 8.50436i) q^{63} +1.00000 q^{64} +(1.16452 - 11.5276i) q^{65} +(1.21441 - 1.21441i) q^{66} +(1.47443 + 5.50266i) q^{67} -0.853736i q^{68} +(2.50731 - 0.671831i) q^{69} +(-9.08662 - 3.44597i) q^{70} +(-0.748487 + 1.29642i) q^{71} +(2.39658 - 1.38366i) q^{72} +(3.61401 + 3.61401i) q^{73} +(-5.98502 + 1.08604i) q^{74} +(-1.07754 + 2.15772i) q^{75} +(-1.98004 - 0.530550i) q^{76} +(4.00498 + 14.9468i) q^{77} +(2.41421 - 0.646887i) q^{78} +(-0.864068 - 3.22474i) q^{79} +(1.81431 + 1.30701i) q^{80} +(3.48004 - 6.02761i) q^{81} +4.38839i q^{82} +(-15.3446 - 4.11157i) q^{83} -2.09638i q^{84} +(1.11584 - 1.54894i) q^{85} +(5.08164 + 8.80166i) q^{86} +(1.47261 + 0.850212i) q^{87} -3.56048i q^{88} +(2.96240 - 11.0558i) q^{89} +(6.15660 + 0.621943i) q^{90} +(-5.82843 + 21.7520i) q^{91} +(2.69067 - 4.66038i) q^{92} +(-1.32282 + 2.29119i) q^{93} +(-2.25057 + 8.39924i) q^{94} +(-2.89898 - 3.55051i) q^{95} +(-0.124844 + 0.465926i) q^{96} -8.46926i q^{97} +(10.2956 + 5.94414i) q^{98} +(-4.92650 - 8.53295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} + 12 q^{7} - 8 q^{8} - 12 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 + 12 * q^7 - 8 * q^8 - 12 * q^9	\( 8 q + 4 q^{2} + 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} + 12 q^{7} - 8 q^{8} - 12 q^{9} - 4 q^{10} - 8 q^{12} - 4 q^{13} + 12 q^{14} - 4 q^{16} + 12 q^{17} - 12 q^{18} + 4 q^{19} - 8 q^{20} + 12 q^{21} - 12 q^{22} - 8 q^{23} - 4 q^{24} - 8 q^{26} - 8 q^{27} - 24 q^{29} - 12 q^{30} - 8 q^{31} + 4 q^{32} - 12 q^{33} + 12 q^{34} + 8 q^{38} + 16 q^{39} - 4 q^{40} + 12 q^{41} + 12 q^{42} + 16 q^{43} - 12 q^{44} - 12 q^{45} - 4 q^{46} - 8 q^{47} + 4 q^{48} + 36 q^{49} + 20 q^{51} - 4 q^{52} + 16 q^{53} - 4 q^{54} + 16 q^{55} - 12 q^{56} + 4 q^{57} - 24 q^{58} - 8 q^{59} - 12 q^{60} + 20 q^{62} - 4 q^{63} + 8 q^{64} + 16 q^{65} - 16 q^{67} + 16 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 16 q^{73} - 20 q^{75} + 4 q^{76} + 4 q^{77} + 8 q^{78} - 32 q^{79} + 4 q^{80} + 8 q^{81} + 16 q^{85} + 8 q^{86} - 36 q^{87} + 8 q^{89} + 24 q^{90} - 24 q^{91} + 4 q^{92} + 20 q^{93} - 16 q^{94} + 16 q^{95} + 8 q^{96} + 36 q^{98} + 4 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 + 12 * q^7 - 8 * q^8 - 12 * q^9 - 4 * q^10 - 8 * q^12 - 4 * q^13 + 12 * q^14 - 4 * q^16 + 12 * q^17 - 12 * q^18 + 4 * q^19 - 8 * q^20 + 12 * q^21 - 12 * q^22 - 8 * q^23 - 4 * q^24 - 8 * q^26 - 8 * q^27 - 24 * q^29 - 12 * q^30 - 8 * q^31 + 4 * q^32 - 12 * q^33 + 12 * q^34 + 8 * q^38 + 16 * q^39 - 4 * q^40 + 12 * q^41 + 12 * q^42 + 16 * q^43 - 12 * q^44 - 12 * q^45 - 4 * q^46 - 8 * q^47 + 4 * q^48 + 36 * q^49 + 20 * q^51 - 4 * q^52 + 16 * q^53 - 4 * q^54 + 16 * q^55 - 12 * q^56 + 4 * q^57 - 24 * q^58 - 8 * q^59 - 12 * q^60 + 20 * q^62 - 4 * q^63 + 8 * q^64 + 16 * q^65 - 16 * q^67 + 16 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 16 * q^73 - 20 * q^75 + 4 * q^76 + 4 * q^77 + 8 * q^78 - 32 * q^79 + 4 * q^80 + 8 * q^81 + 16 * q^85 + 8 * q^86 - 36 * q^87 + 8 * q^89 + 24 * q^90 - 24 * q^91 + 4 * q^92 + 20 * q^93 - 16 * q^94 + 16 * q^95 + 8 * q^96 + 36 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more