LMFDB - Embedded newform 210.2.u.a.187.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(73,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("210.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.u (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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			187.3
Root			$0.792206 - 1.03242i$ of defining polynomial
Character	$\chi$	$=$	210.187
Dual form			210.2.u.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.0488750 + 2.23553i) q^{5} -1.00000i q^{6} +(2.15951 - 1.52856i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.0488750 + 2.23553i) q^{5} -1.00000i q^{6} +(2.15951 - 1.52856i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.625808 + 2.14671i) q^{10} +(0.883028 + 1.52945i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-2.71395 - 2.71395i) q^{13} +(1.69031 - 2.03540i) q^{14} +(2.17201 + 0.531389i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.14529 - 0.574830i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.886994 + 1.53632i) q^{19} +(1.16009 + 1.91159i) q^{20} +(-0.917556 - 2.48155i) q^{21} +(1.24879 + 1.24879i) q^{22} +(1.04741 + 3.90900i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.99522 + 0.218523i) q^{25} +(-3.32389 - 1.91905i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.10591 - 2.40353i) q^{28} -3.84628i q^{29} +(2.23553 - 0.0488750i) q^{30} +(-8.94554 + 5.16471i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.70588 - 0.457089i) q^{33} -2.22097 q^{34} +(3.52270 + 4.75295i) q^{35} -1.00000 q^{36} +(3.21516 - 0.861499i) q^{37} +(-0.459142 + 1.71354i) q^{38} +(-3.32389 + 1.91905i) q^{39} +(1.61532 + 1.54620i) q^{40} +11.8993i q^{41} +(-1.52856 - 2.15951i) q^{42} +(3.46335 - 3.46335i) q^{43} +(1.52945 + 0.883028i) q^{44} +(1.07544 - 1.96047i) q^{45} +(2.02344 + 3.50471i) q^{46} +(1.59118 + 5.93837i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(2.32699 - 6.60190i) q^{49} +(-4.76846 + 1.50394i) q^{50} +(-1.11049 + 1.92342i) q^{51} +(-3.70732 - 0.993373i) q^{52} +(-0.396561 - 0.106258i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.37598 + 2.04879i) q^{55} +(0.446149 - 2.60786i) q^{56} +(1.25440 + 1.25440i) q^{57} +(-0.995491 - 3.71522i) q^{58} +(-5.18379 - 8.97859i) q^{59} +(2.14671 - 0.625808i) q^{60} +(-5.87936 - 3.39445i) q^{61} +(-7.30401 + 7.30401i) q^{62} +(-2.63447 + 0.244018i) q^{63} -1.00000i q^{64} +(5.93447 - 6.19976i) q^{65} +(1.52945 - 0.883028i) q^{66} +(1.97702 - 7.37834i) q^{67} +(-2.14529 + 0.574830i) q^{68} +4.04689 q^{69} +(4.63282 + 3.67926i) q^{70} -10.7193 q^{71} +(-0.965926 + 0.258819i) q^{72} +(2.75198 - 10.2705i) q^{73} +(2.88263 - 1.66429i) q^{74} +(-1.08178 + 4.88157i) q^{75} +1.77399i q^{76} +(4.24477 + 1.95310i) q^{77} +(-2.71395 + 2.71395i) q^{78} +(10.9907 + 6.34546i) q^{79} +(1.96047 + 1.07544i) q^{80} +(0.500000 + 0.866025i) q^{81} +(3.07978 + 11.4939i) q^{82} +(1.94227 + 1.94227i) q^{83} +(-2.03540 - 1.69031i) q^{84} +(1.18020 - 4.82397i) q^{85} +(2.44896 - 4.24172i) q^{86} +(-3.71522 - 0.995491i) q^{87} +(1.70588 + 0.457089i) q^{88} +(0.558127 - 0.966705i) q^{89} +(0.531389 - 2.17201i) q^{90} +(-10.0092 - 1.71236i) q^{91} +(2.86158 + 2.86158i) q^{92} +(2.67345 + 9.97746i) q^{93} +(3.07393 + 5.32419i) q^{94} +(-3.47785 - 1.90782i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(7.26720 - 7.26720i) q^{97} +(0.539001 - 6.97922i) q^{98} -1.76606i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 8 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 - 8 * q^7	$ 16 q + 12 q^{5} - 8 q^{7} + 8 q^{10} + 4 q^{11} - 16 q^{13} + 16 q^{14} + 4 q^{15} + 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{20} + 8 q^{21} + 4 q^{22} + 32 q^{23} - 8 q^{24} - 32 q^{25} - 12 q^{26} - 8 q^{28} - 4 q^{30} - 24 q^{31} + 8 q^{33} + 16 q^{34} + 4 q^{35} - 16 q^{36} - 8 q^{37} - 28 q^{38} - 12 q^{39} - 4 q^{42} - 24 q^{43} + 4 q^{45} - 4 q^{46} - 24 q^{47} + 52 q^{49} + 8 q^{51} - 8 q^{52} + 44 q^{53} - 8 q^{54} - 56 q^{55} + 8 q^{56} - 8 q^{57} + 48 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 16 q^{65} + 36 q^{67} - 12 q^{68} - 8 q^{69} + 32 q^{70} - 32 q^{71} - 40 q^{73} - 24 q^{74} - 24 q^{75} - 44 q^{77} - 16 q^{78} + 12 q^{79} + 12 q^{80} + 8 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{87} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 8 q^{92} + 40 q^{93} + 8 q^{94} - 48 q^{95} + 44 q^{97} - 8 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 - 8 * q^7 + 8 * q^10 + 4 * q^11 - 16 * q^13 + 16 * q^14 + 4 * q^15 + 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^20 + 8 * q^21 + 4 * q^22 + 32 * q^23 - 8 * q^24 - 32 * q^25 - 12 * q^26 - 8 * q^28 - 4 * q^30 - 24 * q^31 + 8 * q^33 + 16 * q^34 + 4 * q^35 - 16 * q^36 - 8 * q^37 - 28 * q^38 - 12 * q^39 - 4 * q^42 - 24 * q^43 + 4 * q^45 - 4 * q^46 - 24 * q^47 + 52 * q^49 + 8 * q^51 - 8 * q^52 + 44 * q^53 - 8 * q^54 - 56 * q^55 + 8 * q^56 - 8 * q^57 + 48 * q^58 + 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 16 * q^65 + 36 * q^67 - 12 * q^68 - 8 * q^69 + 32 * q^70 - 32 * q^71 - 40 * q^73 - 24 * q^74 - 24 * q^75 - 44 * q^77 - 16 * q^78 + 12 * q^79 + 12 * q^80 + 8 * q^81 + 12 * q^82 - 16 * q^83 + 4 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^87 + 8 * q^88 - 16 * q^89 + 8 * q^91 + 8 * q^92 + 40 * q^93 + 8 * q^94 - 48 * q^95 + 44 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	0.0488750	+	2.23553i	0.0218576	+	0.999761i
$5$	0.0488750	+	2.23553i	0.0218576	+	0.999761i
$6$		−	1.00000i		−	0.408248i
$7$	2.15951	−	1.52856i	0.816219	−	0.577743i
$7$	2.15951	−	1.52856i	0.816219	−	0.577743i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	0.625808	+	2.14671i	0.197898	+	0.678849i
$11$	0.883028	+	1.52945i	0.266243	+	0.461147i	0.967889	−	0.251380i	$-0.0808843\pi$
$11$	0.883028	+	1.52945i	0.266243	+	0.461147i	−0.701645	+	0.712526i	$0.747551\pi$
$12$	−0.258819	−	0.965926i	−0.0747146	−	0.278839i
$13$	−2.71395	−	2.71395i	−0.752713	−	0.752713i	0.222272	−	0.974985i	$-0.428653\pi$
$13$	−2.71395	−	2.71395i	−0.752713	−	0.752713i	−0.974985	+	0.222272i	$0.928653\pi$
$14$	1.69031	−	2.03540i	0.451754	−	0.543984i
$15$	2.17201	+	0.531389i	0.560810	+	0.137204i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.14529	−	0.574830i	−0.520310	−	0.139417i	−0.0109000	−	0.999941i	$-0.503470\pi$
$17$	−2.14529	−	0.574830i	−0.520310	−	0.139417i	−0.509410	+	0.860524i	$0.670136\pi$
$18$	−0.965926	−	0.258819i	−0.227671	−	0.0610042i
$19$	−0.886994	+	1.53632i	−0.203490	+	0.352456i	−0.949651	−	0.313311i	$-0.898562\pi$
$19$	−0.886994	+	1.53632i	−0.203490	+	0.352456i	0.746160	+	0.665766i	$0.231895\pi$
$20$	1.16009	+	1.91159i	0.259405	+	0.427445i
$21$	−0.917556	−	2.48155i	−0.200227	−	0.541519i
$22$	1.24879	+	1.24879i	0.266243	+	0.266243i
$23$	1.04741	+	3.90900i	0.218401	+	0.815082i	0.984942	+	0.172887i	$0.0553095\pi$
$23$	1.04741	+	3.90900i	0.218401	+	0.815082i	−0.766541	+	0.642195i	$0.778024\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.99522	+	0.218523i	−0.999044	+	0.0437047i
$26$	−3.32389	−	1.91905i	−0.651869	−	0.376356i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.10591	−	2.40353i	0.208998	−	0.454225i
$29$		−	3.84628i		−	0.714236i	−0.934059	−	0.357118i	$-0.883759\pi$
$29$		−	3.84628i		−	0.714236i	0.934059	−	0.357118i	$-0.116241\pi$
$30$	2.23553	−	0.0488750i	0.408151	−	0.00892331i
$31$	−8.94554	+	5.16471i	−1.60667	+	0.927610i	−0.616558	+	0.787310i	$0.711473\pi$
$31$	−8.94554	+	5.16471i	−1.60667	+	0.927610i	−0.990109	+	0.140300i	$0.955193\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	1.70588	−	0.457089i	0.296956	−	0.0795690i
$34$	−2.22097			−0.380893
$35$	3.52270	+	4.75295i	0.595445	+	0.803396i
$36$	−1.00000			−0.166667
$37$	3.21516	−	0.861499i	0.528569	−	0.141630i	0.0153416	−	0.999882i	$-0.495116\pi$
$37$	3.21516	−	0.861499i	0.528569	−	0.141630i	0.513227	+	0.858253i	$0.328450\pi$
$38$	−0.459142	+	1.71354i	−0.0744827	+	0.277973i
$39$	−3.32389	+	1.91905i	−0.532248	+	0.307294i
$40$	1.61532	+	1.54620i	0.255405	+	0.244476i
$41$			11.8993i			1.85836i	0.369622	+	0.929182i	$0.379487\pi$
$41$			11.8993i			1.85836i	−0.369622	+	0.929182i	$0.620513\pi$
$42$	−1.52856	−	2.15951i	−0.235862	−	0.333220i
$43$	3.46335	−	3.46335i	0.528155	−	0.528155i	−0.391867	−	0.920022i	$-0.628171\pi$
$43$	3.46335	−	3.46335i	0.528155	−	0.528155i	0.920022	+	0.391867i	$0.128171\pi$
$44$	1.52945	+	0.883028i	0.230573	+	0.133122i
$45$	1.07544	−	1.96047i	0.160317	−	0.292249i
$46$	2.02344	+	3.50471i	0.298341	+	0.516741i
$47$	1.59118	+	5.93837i	0.232098	+	0.866200i	0.979436	+	0.201756i	$0.0646648\pi$
$47$	1.59118	+	5.93837i	0.232098	+	0.866200i	−0.747338	+	0.664444i	$0.768668\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	2.32699	−	6.60190i	0.332427	−	0.943129i
$50$	−4.76846	+	1.50394i	−0.674362	+	0.212689i
$51$	−1.11049	+	1.92342i	−0.155499	+	0.269332i
$52$	−3.70732	−	0.993373i	−0.514113	−	0.137756i
$53$	−0.396561	−	0.106258i	−0.0544719	−	0.0145957i	0.231480	−	0.972840i	$-0.425643\pi$
$53$	−0.396561	−	0.106258i	−0.0544719	−	0.0145957i	−0.285952	+	0.958244i	$0.592310\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−3.37598	+	2.04879i	−0.455217	+	0.276259i
$56$	0.446149	−	2.60786i	0.0596191	−	0.348490i
$57$	1.25440	+	1.25440i	0.166149	+	0.166149i
$58$	−0.995491	−	3.71522i	−0.130714	−	0.487833i
$59$	−5.18379	−	8.97859i	−0.674872	−	1.16891i	−0.976506	−	0.215489i	$-0.930865\pi$
$59$	−5.18379	−	8.97859i	−0.674872	−	1.16891i	0.301634	−	0.953424i	$-0.402468\pi$
$60$	2.14671	−	0.625808i	0.277139	−	0.0807915i
$61$	−5.87936	−	3.39445i	−0.752775	−	0.434615i	0.0739204	−	0.997264i	$-0.476449\pi$
$61$	−5.87936	−	3.39445i	−0.752775	−	0.434615i	−0.826696	+	0.562649i	$0.809782\pi$
$62$	−7.30401	+	7.30401i	−0.927610	+	0.927610i
$63$	−2.63447	+	0.244018i	−0.331913	+	0.0307434i
$64$		−	1.00000i		−	0.125000i
$65$	5.93447	−	6.19976i	0.736081	−	0.768986i
$66$	1.52945	−	0.883028i	0.188262	−	0.108693i
$67$	1.97702	−	7.37834i	0.241532	−	0.901408i	−0.733563	−	0.679621i	$-0.762144\pi$
$67$	1.97702	−	7.37834i	0.241532	−	0.901408i	0.975095	−	0.221787i	$-0.0711891\pi$
$68$	−2.14529	+	0.574830i	−0.260155	+	0.0697083i
$69$	4.04689			0.487188
$70$	4.63282	+	3.67926i	0.553728	+	0.439756i
$71$	−10.7193			−1.27214			−0.636072	−	0.771629i	$-0.719442\pi$
$71$	−10.7193			−1.27214			−0.636072	+	0.771629i	$0.719442\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	2.75198	−	10.2705i	0.322095	−	1.20207i	−0.595106	−	0.803647i	$-0.702890\pi$
$73$	2.75198	−	10.2705i	0.322095	−	1.20207i	0.917200	−	0.398426i	$-0.130444\pi$
$74$	2.88263	−	1.66429i	0.335099	−	0.193470i
$75$	−1.08178	+	4.88157i	−0.124913	+	0.563675i
$76$			1.77399i			0.203490i
$77$	4.24477	+	1.95310i	0.483737	+	0.222577i
$78$	−2.71395	+	2.71395i	−0.307294	+	0.307294i
$79$	10.9907	+	6.34546i	1.23655	+	0.713920i	0.968386	−	0.249455i	$-0.0802515\pi$
$79$	10.9907	+	6.34546i	1.23655	+	0.713920i	0.268159	+	0.963375i	$0.413585\pi$
$80$	1.96047	+	1.07544i	0.219187	+	0.120238i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	3.07978	+	11.4939i	0.340104	+	1.26929i
$83$	1.94227	+	1.94227i	0.213191	+	0.213191i	0.805622	−	0.592430i	$-0.201831\pi$
$83$	1.94227	+	1.94227i	0.213191	+	0.213191i	−0.592430	+	0.805622i	$0.701831\pi$
$84$	−2.03540	−	1.69031i	−0.222081	−	0.184428i
$85$	1.18020	−	4.82397i	0.128011	−	0.523233i
$86$	2.44896	−	4.24172i	0.264078	−	0.457396i
$87$	−3.71522	−	0.995491i	−0.398314	−	0.106728i
$88$	1.70588	+	0.457089i	0.181847	+	0.0487259i
$89$	0.558127	−	0.966705i	0.0591614	−	0.102471i	−0.834928	−	0.550359i	$-0.814491\pi$
$89$	0.558127	−	0.966705i	0.0591614	−	0.102471i	0.894089	+	0.447889i	$0.147824\pi$
$90$	0.531389	−	2.17201i	0.0560133	−	0.228950i
$91$	−10.0092	−	1.71236i	−1.04925	−	0.179504i
$92$	2.86158	+	2.86158i	0.298341	+	0.298341i
$93$	2.67345	+	9.97746i	0.277224	+	1.03461i
$94$	3.07393	+	5.32419i	0.317051	+	0.549149i
$95$	−3.47785	−	1.90782i	−0.356819	−	0.195738i
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	7.26720	−	7.26720i	0.737872	−	0.737872i	−0.234293	−	0.972166i	$-0.575278\pi$
$97$	7.26720	−	7.26720i	0.737872	−	0.737872i	0.972166	+	0.234293i	$0.0752777\pi$
$98$	0.539001	−	6.97922i	0.0544473	−	0.705007i
$99$		−	1.76606i		−	0.177495i
$100$	−4.21673	+	2.68686i	−0.421673	+	0.268686i
$101$	15.8887	−	9.17333i	1.58098	−	0.912780i	0.586265	−	0.810119i	$-0.300598\pi$
$101$	15.8887	−	9.17333i	1.58098	−	0.912780i	0.994716	−	0.102661i	$-0.0327358\pi$
$102$	−0.574830	+	2.14529i	−0.0569166	+	0.212416i
$103$	8.80911	−	2.36040i	0.867988	−	0.232577i	0.202770	−	0.979226i	$-0.435006\pi$
$103$	8.80911	−	2.36040i	0.867988	−	0.232577i	0.665217	+	0.746650i	$0.268339\pi$
$104$	−3.83810			−0.376356
$105$	5.50274	−	2.17251i	0.537013	−	0.212015i
$106$	−0.410550			−0.0398762
$107$	14.2519	−	3.81880i	1.37779	−	0.369177i	0.507471	−	0.861669i	$-0.330581\pi$
$107$	14.2519	−	3.81880i	1.37779	−	0.369177i	0.870317	+	0.492492i	$0.163914\pi$
$108$	−0.258819	+	0.965926i	−0.0249049	+	0.0929463i
$109$	−17.4494	+	10.0744i	−1.67135	+	0.964955i	−0.704467	+	0.709736i	$0.748814\pi$
$109$	−17.4494	+	10.0744i	−1.67135	+	0.964955i	−0.966883	+	0.255218i	$0.917853\pi$
$110$	−2.73068	+	2.85275i	−0.260360	+	0.271999i
$111$		−	3.32858i		−	0.315935i
$112$	−0.244018	−	2.63447i	−0.0230576	−	0.248934i
$113$	−6.54677	+	6.54677i	−0.615869	+	0.615869i	−0.944469	−	0.328600i	$-0.893423\pi$
$113$	−6.54677	+	6.54677i	−0.615869	+	0.615869i	0.328600	+	0.944469i	$0.393423\pi$
$114$	1.53632	+	0.886994i	0.143889	+	0.0830746i
$115$	−8.68750	+	2.53258i	−0.810113	+	0.236164i
$116$	−1.92314	−	3.33098i	−0.178559	−	0.309273i
$117$	0.993373	+	3.70732i	0.0918374	+	0.342742i
$118$	−7.33099	−	7.33099i	−0.674872	−	0.674872i
$119$	−5.51145	+	2.03786i	−0.505234	+	0.186811i
$120$	1.91159	−	1.16009i	0.174504	−	0.105902i
$121$	3.94052	−	6.82518i	0.358229	−	0.620471i
$122$	−6.55758	−	1.75710i	−0.593695	−	0.159080i
$123$	11.4939	+	3.07978i	1.03637	+	0.277694i
$124$	−5.16471	+	8.94554i	−0.463805	+	0.803333i
$125$	−0.732658	−	11.1563i	−0.0655309	−	0.997851i
$126$	−2.48155	+	0.917556i	−0.221074	+	0.0817424i
$127$	12.5444	+	12.5444i	1.11313	+	1.11313i	0.992724	+	0.120409i	$0.0384206\pi$
$127$	12.5444	+	12.5444i	1.11313	+	1.11313i	0.120409	+	0.992724i	$0.461579\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−2.44896	−	4.24172i	−0.215619	−	0.373462i
$130$	4.12764	−	7.52446i	0.362018	−	0.659939i
$131$	0.830756	+	0.479637i	0.0725835	+	0.0419061i	0.535853	−	0.844312i	$-0.319990\pi$
$131$	0.830756	+	0.479637i	0.0725835	+	0.0419061i	−0.463269	+	0.886218i	$0.653324\pi$
$132$	1.24879	−	1.24879i	0.108693	−	0.108693i
$133$	0.432886	+	4.67353i	0.0375359	+	0.405246i
$134$		−	7.63862i		−	0.659877i
$135$	−1.61532	−	1.54620i	−0.139025	−	0.133076i
$136$	−1.92342	+	1.11049i	−0.164932	+	0.0952233i
$137$	2.88499	−	10.7669i	0.246481	−	0.919880i	−0.726152	−	0.687534i	$-0.758693\pi$
$137$	2.88499	−	10.7669i	0.246481	−	0.919880i	0.972633	−	0.232346i	$-0.0746402\pi$
$138$	3.90900	−	1.04741i	0.332756	−	0.0891616i
$139$	13.5695			1.15095			0.575477	−	0.817818i	$-0.304816\pi$
$139$	13.5695			1.15095			0.575477	+	0.817818i	$0.304816\pi$
$140$	5.42723	+	2.35483i	0.458684	+	0.199019i
$141$	6.14785			0.517742
$142$	−10.3540	+	2.77435i	−0.868891	+	0.232819i
$143$	1.75435	−	6.54733i	0.146706	−	0.547516i
$144$	−0.866025	+	0.500000i	−0.0721688	+	0.0416667i
$145$	8.59849	−	0.187987i	0.714066	−	0.0156115i
$146$		−	10.6328i		−	0.879979i
$147$	−5.77468	−	3.95640i	−0.476288	−	0.326318i
$148$	2.35366	−	2.35366i	0.193470	−	0.193470i
$149$	−8.74565	−	5.04930i	−0.716471	−	0.413655i	0.0969812	−	0.995286i	$-0.469081\pi$
$149$	−8.74565	−	5.04930i	−0.716471	−	0.413655i	−0.813453	+	0.581631i	$0.802415\pi$
$150$	0.218523	+	4.99522i	0.0178424	+	0.407858i
$151$	7.15497	+	12.3928i	0.582263	+	1.00851i	0.995211	+	0.0977541i	$0.0311659\pi$
$151$	7.15497	+	12.3928i	0.582263	+	1.00851i	−0.412948	+	0.910755i	$0.635501\pi$
$152$	0.459142	+	1.71354i	0.0372413	+	0.138987i
$153$	1.57046	+	1.57046i	0.126964	+	0.126964i
$154$	4.60563	+	0.787924i	0.371133	+	0.0634927i
$155$	−11.9831	−	19.7456i	−0.962506	−	1.58601i
$156$	−1.91905	+	3.32389i	−0.153647	+	0.266124i
$157$	−9.25683	−	2.48036i	−0.738776	−	0.197954i	−0.130242	−	0.991482i	$-0.541575\pi$
$157$	−9.25683	−	2.48036i	−0.738776	−	0.197954i	−0.608534	+	0.793528i	$0.708242\pi$
$158$	12.2585	+	3.28465i	0.975233	+	0.261313i
$159$	−0.205275	+	0.355547i	−0.0162794	+	0.0281967i
$160$	2.17201	+	0.531389i	0.171712	+	0.0420100i
$161$	8.23705	+	6.84049i	0.649170	+	0.539106i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	3.06537	+	11.4401i	0.240098	+	0.896058i	0.975784	+	0.218736i	$0.0701932\pi$
$163$	3.06537	+	11.4401i	0.240098	+	0.896058i	−0.735686	+	0.677323i	$0.763140\pi$
$164$	5.94967	+	10.3051i	0.464591	+	0.804695i
$165$	1.10521	+	3.79121i	0.0860407	+	0.295145i
$166$	2.37878	+	1.37339i	0.184629	+	0.106596i
$167$	−6.95883	+	6.95883i	−0.538490	+	0.538490i	−0.923085	−	0.384595i	$-0.874341\pi$
$167$	−6.95883	+	6.95883i	−0.538490	+	0.538490i	0.384595	+	0.923085i	$0.374341\pi$
$168$	−2.40353	−	1.10591i	−0.185436	−	0.0853229i
$169$			1.73100i			0.133154i
$170$	−0.108550	−	4.96506i	−0.00832540	−	0.380802i
$171$	1.53632	−	0.886994i	0.117485	−	0.0678301i
$172$	1.26767	−	4.73102i	0.0966592	−	0.360737i
$173$	−8.37084	+	2.24296i	−0.636423	+	0.170529i	−0.562583	−	0.826741i	$-0.690192\pi$
$173$	−8.37084	+	2.24296i	−0.636423	+	0.170529i	−0.0738403	+	0.997270i	$0.523526\pi$
$174$	−3.84628			−0.291586
$175$	−10.4532	+	8.10742i	−0.790189	+	0.612863i
$176$	1.76606			0.133122
$177$	−10.0143	+	2.68333i	−0.752722	+	0.201691i
$178$	0.288908	−	1.07822i	0.0216546	−	0.0808160i
$179$	−11.5646	+	6.67682i	−0.864378	+	0.499049i	−0.865476	−	0.500951i	$-0.832984\pi$
$179$	−11.5646	+	6.67682i	−0.864378	+	0.499049i	0.00109809	+	0.999999i	$0.499650\pi$
$180$	−0.0488750	−	2.23553i	−0.00364293	−	0.166627i
$181$			8.73922i			0.649581i	0.945786	+	0.324791i	$0.105294\pi$
$181$			8.73922i			0.649581i	−0.945786	+	0.324791i	$0.894706\pi$
$182$	−10.1114	+	0.936566i	−0.749505	+	0.0694229i
$183$	−4.80048	+	4.80048i	−0.354862	+	0.354862i
$184$	3.50471	+	2.02344i	0.258371	+	0.149170i
$185$	2.08305	+	7.14549i	0.153149	+	0.525347i
$186$	5.16471	+	8.94554i	0.378695	+	0.655919i
$187$	−1.01518	−	3.78871i	−0.0742374	−	0.277058i
$188$	4.34719	+	4.34719i	0.317051	+	0.317051i
$189$	−0.446149	+	2.60786i	−0.0324525	+	0.189694i
$190$	−3.85312	−	0.942678i	−0.279535	−	0.0683891i
$191$	5.43796	−	9.41883i	0.393477	−	0.681523i	−0.599428	−	0.800429i	$-0.704605\pi$
$191$	5.43796	−	9.41883i	0.393477	−	0.681523i	0.992906	+	0.118906i	$0.0379386\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−10.8195	−	2.89908i	−0.778806	−	0.208680i	−0.152548	−	0.988296i	$-0.548748\pi$
$193$	−10.8195	−	2.89908i	−0.778806	−	0.208680i	−0.626258	+	0.779616i	$0.715414\pi$
$194$	5.13869	−	8.90047i	0.368936	−	0.639016i
$195$	−4.45255	−	7.33688i	−0.318854	−	0.525405i
$196$	−1.28572	−	6.88091i	−0.0918371	−	0.491494i
$197$	−10.3775	−	10.3775i	−0.739367	−	0.739367i	0.233088	−	0.972456i	$-0.425117\pi$
$197$	−10.3775	−	10.3775i	−0.739367	−	0.739367i	−0.972456	+	0.233088i	$0.925117\pi$
$198$	−0.457089	−	1.70588i	−0.0324839	−	0.121232i
$199$	9.28152	+	16.0761i	0.657949	+	1.13960i	0.981146	+	0.193270i	$0.0619092\pi$
$199$	9.28152	+	16.0761i	0.657949	+	1.13960i	−0.323197	+	0.946332i	$0.604757\pi$
$200$	−3.37764	+	3.68668i	−0.238835	+	0.260687i
$201$	−6.61524	−	3.81931i	−0.466603	−	0.269394i
$202$	12.9730	−	12.9730i	0.912780	−	0.912780i
$203$	−5.87928	−	8.30609i	−0.412645	−	0.582973i
$204$			2.22097i			0.155499i
$205$	−26.6014	+	0.581580i	−1.85792	+	0.0406193i
$206$	7.89804	−	4.55993i	0.550282	−	0.317706i
$207$	1.04741	−	3.90900i	0.0728002	−	0.271694i
$208$	−3.70732	+	0.993373i	−0.257056	+	0.0688780i
$209$	−3.13296			−0.216712
$210$	4.75295	−	3.52270i	0.327985	−	0.243089i
$211$	−0.453133			−0.0311950			−0.0155975	−	0.999878i	$-0.504965\pi$
$211$	−0.453133			−0.0311950			−0.0155975	+	0.999878i	$0.504965\pi$
$212$	−0.396561	+	0.106258i	−0.0272359	+	0.00729784i
$213$	−2.77435	+	10.3540i	−0.190096	+	0.709446i
$214$	12.7779	−	7.37735i	0.873483	−	0.504305i
$215$	7.91170	+	7.57316i	0.539573	+	0.516485i
$216$			1.00000i			0.0680414i
$217$	−11.4234	+	24.8271i	−0.775473	+	1.68537i
$218$	−14.2474	+	14.2474i	−0.964955	+	0.964955i
$219$	−9.20830	−	5.31641i	−0.622239	−	0.359250i
$220$	−1.89929	+	3.46230i	−0.128050	+	0.233428i
$221$	4.26215	+	7.38226i	0.286703	+	0.496585i
$222$	−0.861499	−	3.21516i	−0.0578201	−	0.215787i
$223$	−4.67260	−	4.67260i	−0.312901	−	0.312901i	0.533132	−	0.846032i	$-0.321015\pi$
$223$	−4.67260	−	4.67260i	−0.312901	−	0.312901i	−0.846032	+	0.533132i	$0.821015\pi$
$224$	−0.917556	−	2.48155i	−0.0613068	−	0.165806i
$225$	4.43525	+	2.30836i	0.295683	+	0.153891i
$226$	−4.62927	+	8.01813i	−0.307934	+	0.533358i
$227$	−16.0416	−	4.29835i	−1.06472	−	0.285291i	−0.316399	−	0.948626i	$-0.602474\pi$
$227$	−16.0416	−	4.29835i	−1.06472	−	0.285291i	−0.748323	+	0.663335i	$0.769140\pi$
$228$	1.71354	+	0.459142i	0.113482	+	0.0304074i
$229$	6.77075	−	11.7273i	0.447423	−	0.774960i	−0.550794	−	0.834641i	$-0.685675\pi$
$229$	6.77075	−	11.7273i	0.447423	−	0.774960i	0.998217	+	0.0596810i	$0.0190084\pi$
$230$	−7.73600	+	4.69477i	−0.510097	+	0.309564i
$231$	2.98518	−	3.59463i	0.196410	−	0.236510i
$232$	−2.71973	−	2.71973i	−0.178559	−	0.178559i
$233$	2.99668	+	11.1838i	0.196319	+	0.732672i	0.991922	+	0.126853i	$0.0404877\pi$
$233$	2.99668	+	11.1838i	0.196319	+	0.732672i	−0.795603	+	0.605819i	$0.792846\pi$
$234$	1.91905	+	3.32389i	0.125452	+	0.217290i
$235$	−13.1977	+	3.84738i	−0.860920	+	0.250975i
$236$	−8.97859	−	5.18379i	−0.584456	−	0.337436i
$237$	8.97383	−	8.97383i	0.582913	−	0.582913i
$238$	−4.79621	+	3.39489i	−0.310892	+	0.220058i
$239$			17.0264i			1.10135i	0.834721	+	0.550673i	$0.185629\pi$
$239$			17.0264i			1.10135i	−0.834721	+	0.550673i	$0.814371\pi$
$240$	1.54620	−	1.61532i	0.0998069	−	0.104269i
$241$	16.3866	−	9.46081i	1.05555	−	0.609424i	0.131355	−	0.991335i	$-0.458067\pi$
$241$	16.3866	−	9.46081i	1.05555	−	0.609424i	0.924199	+	0.381911i	$0.124734\pi$
$242$	2.03976	−	7.61250i	0.131121	−	0.489350i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−6.78891			−0.434615
$245$	14.8725	+	4.87940i	0.950170	+	0.311733i
$246$	11.8993			0.758674
$247$	6.57674	−	1.76223i	0.418468	−	0.112128i
$248$	−2.67345	+	9.97746i	−0.169764	+	0.633569i
$249$	2.37878	−	1.37339i	0.150749	−	0.0870350i
$250$	−3.59516	−	10.5865i	−0.227378	−	0.669552i
$251$			18.1527i			1.14579i	0.819629	+	0.572894i	$0.194179\pi$
$251$			18.1527i			1.14579i	−0.819629	+	0.572894i	$0.805821\pi$
$252$	−2.15951	+	1.52856i	−0.136037	+	0.0962904i
$253$	−5.05372	+	5.05372i	−0.317725	+	0.317725i
$254$	15.3637	+	8.87021i	0.964002	+	0.556567i
$255$	−4.35414	−	2.38852i	−0.272667	−	0.149575i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.22983	−	23.2500i	−0.388606	−	1.45030i	−0.832403	−	0.554170i	$-0.813036\pi$
$257$	−6.22983	−	23.2500i	−0.388606	−	1.45030i	0.443797	−	0.896127i	$-0.353631\pi$
$258$	−3.46335	−	3.46335i	−0.215619	−	0.215619i
$259$	5.62632	−	6.77499i	0.349603	−	0.420978i
$260$	2.03952	−	8.33639i	0.126486	−	0.517001i
$261$	−1.92314	+	3.33098i	−0.119039	+	0.206182i
$262$	0.926588	+	0.248279i	0.0572448	+	0.0153387i
$263$	−13.5576	−	3.63274i	−0.835995	−	0.224004i	−0.184668	−	0.982801i	$-0.559121\pi$
$263$	−13.5576	−	3.63274i	−0.835995	−	0.224004i	−0.651328	+	0.758797i	$0.725788\pi$
$264$	0.883028	−	1.52945i	0.0543466	−	0.0941311i
$265$	0.218162	−	0.891719i	0.0134016	−	0.0547779i
$266$	1.62773	+	4.40224i	0.0998027	+	0.269919i
$267$	−0.789311	−	0.789311i	−0.0483051	−	0.0483051i
$268$	−1.97702	−	7.37834i	−0.120766	−	0.450704i
$269$	13.2762	+	22.9951i	0.809466	+	1.40204i	0.913234	+	0.407435i	$0.133577\pi$
$269$	13.2762	+	22.9951i	0.809466	+	1.40204i	−0.103768	+	0.994602i	$0.533090\pi$
$270$	−1.96047	−	1.07544i	−0.119310	−	0.0654492i
$271$	10.3582	+	5.98031i	0.629216	+	0.363278i	0.780448	−	0.625220i	$-0.214991\pi$
$271$	10.3582	+	5.98031i	0.629216	+	0.363278i	−0.151232	+	0.988498i	$0.548324\pi$
$272$	−1.57046	+	1.57046i	−0.0952233	+	0.0952233i
$273$	−4.24460	+	9.22499i	−0.256895	+	0.558322i
$274$		−	11.1467i		−	0.673399i
$275$	−4.74514	−	7.44698i	−0.286143	−	0.449070i
$276$	3.50471	−	2.02344i	0.210959	−	0.121797i
$277$	−0.611241	+	2.28118i	−0.0367259	+	0.137063i	−0.981855	−	0.189635i	$-0.939269\pi$
$277$	−0.611241	+	2.28118i	−0.0367259	+	0.137063i	0.945129	+	0.326698i	$0.105936\pi$
$278$	13.1072	−	3.51206i	0.786116	−	0.210639i
$279$	10.3294			0.618406
$280$	5.85177	+	0.869921i	0.349710	+	0.0519877i
$281$	−11.0306			−0.658033			−0.329017	−	0.944324i	$-0.606717\pi$
$281$	−11.0306			−0.658033			−0.329017	+	0.944324i	$0.606717\pi$
$282$	5.93837	−	1.59118i	0.353625	−	0.0947534i
$283$	6.05917	−	22.6131i	0.360180	−	1.34421i	−0.513658	−	0.857995i	$-0.671710\pi$
$283$	6.05917	−	22.6131i	0.360180	−	1.34421i	0.873838	−	0.486217i	$-0.161623\pi$
$284$	−9.28317	+	5.35964i	−0.550855	+	0.318036i
$285$	−2.74294	+	2.86556i	−0.162478	+	0.169741i
$286$		−	6.77830i		−	0.400809i
$287$	18.1889	+	25.6968i	1.07366	+	1.51683i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	−10.4506	−	6.03364i	−0.614740	−	0.354920i
$290$	8.25685	−	2.40703i	0.484859	−	0.141346i
$291$	−5.13869	−	8.90047i	−0.301235	−	0.521755i
$292$	−2.75198	−	10.2705i	−0.161047	−	0.601037i
$293$	15.4837	+	15.4837i	0.904565	+	0.904565i	0.995827	−	0.0912620i	$-0.0290901\pi$
$293$	15.4837	+	15.4837i	0.904565	+	0.904565i	−0.0912620	+	0.995827i	$0.529090\pi$
$294$	−6.60190	−	2.32699i	−0.385031	−	0.135713i
$295$	19.8186	−	12.0274i	1.15388	−	0.700261i
$296$	1.66429	−	2.88263i	0.0967348	−	0.167550i
$297$	−1.70588	−	0.457089i	−0.0989852	−	0.0265230i
$298$	−9.75450	−	2.61371i	−0.565063	−	0.151408i
$299$	7.76618	−	13.4514i	0.449130	−	0.777916i
$300$	1.50394	+	4.76846i	0.0868298	+	0.275307i
$301$	2.18520	−	12.7731i	0.125953	−	0.736228i
$302$	10.1186	+	10.1186i	0.582263	+	0.582263i
$303$	−4.74846	−	17.7215i	−0.272792	−	1.01807i
$304$	0.886994	+	1.53632i	0.0508726	+	0.0881139i
$305$	7.30106	−	13.3094i	0.418057	−	0.762095i
$306$	1.92342	+	1.11049i	0.109954	+	0.0634822i
$307$	−2.12149	+	2.12149i	−0.121080	+	0.121080i	−0.765050	−	0.643971i	$-0.777286\pi$
$307$	−2.12149	+	2.12149i	−0.121080	+	0.121080i	0.643971	+	0.765050i	$0.277286\pi$
$308$	4.65263	−	0.430950i	0.265108	−	0.0245557i
$309$		−	9.11987i		−	0.518811i
$310$	−16.6853	−	15.9714i	−0.947663	−	0.907113i
$311$	13.0082	−	7.51027i	0.737626	−	0.425868i	−0.0835796	−	0.996501i	$-0.526635\pi$
$311$	13.0082	−	7.51027i	0.737626	−	0.425868i	0.821205	+	0.570633i	$0.193302\pi$
$312$	−0.993373	+	3.70732i	−0.0562387	+	0.209886i
$313$	−12.8644	+	3.44701i	−0.727139	+	0.194836i	−0.603355	−	0.797473i	$-0.706170\pi$
$313$	−12.8644	+	3.44701i	−0.727139	+	0.194836i	−0.123784	+	0.992309i	$0.539503\pi$
$314$	−9.58338			−0.540821
$315$	−0.674271	−	5.87753i	−0.0379909	−	0.331161i
$316$	12.6909			0.713920
$317$	−13.4280	+	3.59802i	−0.754192	+	0.202085i	−0.615377	−	0.788233i	$-0.710996\pi$
$317$	−13.4280	+	3.59802i	−0.754192	+	0.202085i	−0.138815	+	0.990318i	$0.544329\pi$
$318$	−0.106258	+	0.396561i	−0.00595867	+	0.0222380i
$319$	5.88269	−	3.39638i	0.329368	−	0.190160i
$320$	2.23553	−	0.0488750i	0.124970	−	0.00273219i
$321$		−	14.7547i		−	0.823527i
$322$	9.72682	+	4.47550i	0.542055	+	0.249410i
$323$	2.78598	−	2.78598i	0.155016	−	0.155016i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	14.1498	+	12.9637i	0.784891	+	0.719097i
$326$	5.92183	+	10.2569i	0.327980	+	0.568078i
$327$	5.21491	+	19.4623i	0.288385	+	1.07627i
$328$	8.41410	+	8.41410i	0.464591	+	0.464591i
$329$	12.5133	+	10.3918i	0.689883	+	0.572916i
$330$	2.04879	+	3.37598i	0.112782	+	0.185842i
$331$	9.31631	−	16.1363i	0.512071	−	0.886932i	−0.487832	−	0.872938i	$-0.662212\pi$
$331$	9.31631	−	16.1363i	0.512071	−	0.886932i	0.999902	−	0.0139944i	$-0.00445470\pi$
$332$	2.65318	+	0.710918i	0.145612	+	0.0390167i
$333$	−3.21516	−	0.861499i	−0.176190	−	0.0472099i
$334$	−4.92063	+	8.52279i	−0.269245	+	0.466346i
$335$	16.5912	+	4.05908i	0.906472	+	0.221771i
$336$	−2.60786	−	0.446149i	−0.142271	−	0.0243394i
$337$	9.63568	+	9.63568i	0.524889	+	0.524889i	0.919044	−	0.394155i	$-0.128963\pi$
$337$	9.63568	+	9.63568i	0.524889	+	0.524889i	−0.394155	+	0.919044i	$0.628963\pi$
$338$	0.448015	+	1.67202i	0.0243688	+	0.0909456i
$339$	4.62927	+	8.01813i	0.251427	+	0.435485i
$340$	−1.38990	−	4.76778i	−0.0753780	−	0.258569i
$341$	−15.7983	−	9.12117i	−0.855528	−	0.493939i
$342$	1.25440	−	1.25440i	0.0678301	−	0.0678301i
$343$	−5.06626	−	17.8138i	−0.273552	−	0.961857i
$344$		−	4.89791i		−	0.264078i
$345$	0.197792	+	9.04696i	0.0106487	+	0.487072i
$346$	−7.50509	+	4.33306i	−0.403476	+	0.232947i
$347$	9.02693	−	33.6890i	0.484591	−	1.80852i	−0.0973042	−	0.995255i	$-0.531022\pi$
$347$	9.02693	−	33.6890i	0.484591	−	1.80852i	0.581895	−	0.813264i	$-0.302311\pi$
$348$	−3.71522	+	0.995491i	−0.199157	+	0.0533639i
$349$	1.49727			0.0801469			0.0400735	−	0.999197i	$-0.487241\pi$
$349$	1.49727			0.0801469			0.0400735	+	0.999197i	$0.487241\pi$
$350$	−7.99868	+	10.5367i	−0.427547	+	0.563208i
$351$	3.83810			0.204863
$352$	1.70588	−	0.457089i	0.0909237	−	0.0243629i
$353$	−1.54431	+	5.76343i	−0.0821951	+	0.306756i	−0.994768	−	0.102157i	$-0.967426\pi$
$353$	−1.54431	+	5.76343i	−0.0821951	+	0.306756i	0.912573	+	0.408913i	$0.134092\pi$
$354$	−8.97859	+	5.18379i	−0.477207	+	0.275515i
$355$	−0.523905	−	23.9633i	−0.0278060	−	1.27184i
$356$		−	1.11625i		−	0.0591614i
$357$	0.541957	+	5.85109i	0.0286834	+	0.309673i
$358$	−9.44244	+	9.44244i	−0.499049	+	0.499049i
$359$	−14.9989	−	8.65964i	−0.791613	−	0.457038i	0.0489170	−	0.998803i	$-0.484423\pi$
$359$	−14.9989	−	8.65964i	−0.791613	−	0.457038i	−0.840530	+	0.541765i	$0.817756\pi$
$360$	−0.625808	−	2.14671i	−0.0329830	−	0.113142i
$361$	7.92648	+	13.7291i	0.417183	+	0.722583i
$362$	2.26188	+	8.44144i	0.118882	+	0.443672i
$363$	−5.57274	−	5.57274i	−0.292493	−	0.292493i
$364$	−9.52443	+	3.52167i	−0.499216	+	0.184586i
$365$	23.0946	+	5.65017i	1.20883	+	0.295743i
$366$	−3.39445	+	5.87936i	−0.177431	+	0.307319i
$367$	5.29802	+	1.41960i	0.276554	+	0.0741025i	0.394430	−	0.918926i	$-0.370942\pi$
$367$	5.29802	+	1.41960i	0.276554	+	0.0741025i	−0.117876	+	0.993028i	$0.537609\pi$
$368$	3.90900	+	1.04741i	0.203770	+	0.0546001i
$369$	5.94967	−	10.3051i	0.309727	−	0.536464i
$370$	3.86146	+	6.36288i	0.200748	+	0.330790i
$371$	−1.01880	+	0.376703i	−0.0528935	+	0.0195574i
$372$	7.30401	+	7.30401i	0.378695	+	0.378695i
$373$	7.98224	+	29.7901i	0.413305	+	1.54247i	0.788207	+	0.615410i	$0.211009\pi$
$373$	7.98224	+	29.7901i	0.413305	+	1.54247i	−0.374903	+	0.927064i	$0.622324\pi$
$374$	−1.96118	−	3.39686i	−0.101410	−	0.175648i
$375$	−10.9658	−	2.17977i	−0.566271	−	0.112563i
$376$	5.32419	+	3.07393i	0.274574	+	0.158526i
$377$	−10.4386	+	10.4386i	−0.537615	+	0.537615i
$378$	0.244018	+	2.63447i	0.0125509	+	0.135503i
$379$			12.9203i			0.663670i	0.943337	+	0.331835i	$0.107668\pi$
$379$			12.9203i			0.663670i	−0.943337	+	0.331835i	$0.892332\pi$
$380$	−3.96581	+	0.0867037i	−0.203442	+	0.00444780i
$381$	15.3637	−	8.87021i	0.787104	−	0.454435i
$382$	2.81490	−	10.5053i	0.144023	−	0.537500i
$383$	−1.14948	+	0.308002i	−0.0587356	+	0.0157382i	−0.288067	−	0.957610i	$-0.593013\pi$
$383$	−1.14948	+	0.308002i	−0.0587356	+	0.0157382i	0.229332	+	0.973348i	$0.426346\pi$
$384$	−1.00000			−0.0510310
$385$	−4.15876	+	9.58479i	−0.211950	+	0.488486i
$386$	−11.2012			−0.570126
$387$	−4.73102	+	1.26767i	−0.240491	+	0.0644394i
$388$	2.65998	−	9.92718i	0.135040	−	0.503976i
$389$	8.25213	−	4.76437i	0.418400	−	0.241563i	−0.275993	−	0.961160i	$-0.589007\pi$
$389$	8.25213	−	4.76437i	0.418400	−	0.241563i	0.694392	+	0.719597i	$0.255673\pi$
$390$	−6.19976	−	5.93447i	−0.313937	−	0.300504i
$391$		−	8.98802i		−	0.454544i
$392$	−3.02282	−	6.31368i	−0.152675	−	0.318889i
$393$	0.678310	−	0.678310i	0.0342162	−	0.0342162i
$394$	−12.7098	−	7.33801i	−0.640311	−	0.369684i
$395$	−13.6483	+	24.8801i	−0.686721	+	1.25185i
$396$	−0.883028	−	1.52945i	−0.0443738	−	0.0768578i
$397$	−7.38494	−	27.5610i	−0.370639	−	1.38324i	−0.859613	−	0.510946i	$-0.829295\pi$
$397$	−7.38494	−	27.5610i	−0.370639	−	1.38324i	0.488974	−	0.872299i	$-0.337371\pi$
$398$	13.1260	+	13.1260i	0.657949	+	0.657949i
$399$	4.62632	+	0.791463i	0.231606	+	0.0396227i
$400$	−2.30836	+	4.43525i	−0.115418	+	0.221763i
$401$	−19.6150	+	33.9741i	−0.979526	+	1.69659i	−0.315415	+	0.948954i	$0.602144\pi$
$401$	−19.6150	+	33.9741i	−0.979526	+	1.69659i	−0.664111	+	0.747634i	$0.731190\pi$
$402$	−7.37834	−	1.97702i	−0.367998	−	0.0986049i
$403$	38.2945	+	10.2610i	1.90758	+	0.511135i
$404$	9.17333	−	15.8887i	0.456390	−	0.790491i
$405$	−1.91159	+	1.16009i	−0.0949877	+	0.0576455i
$406$	−7.82873	−	6.50140i	−0.388533	−	0.322659i
$407$	4.15670	+	4.15670i	0.206040	+	0.206040i
$408$	0.574830	+	2.14529i	0.0284583	+	0.106208i
$409$	−4.32912	−	7.49826i	−0.214061	−	0.370765i	0.738920	−	0.673793i	$-0.235336\pi$
$409$	−4.32912	−	7.49826i	−0.214061	−	0.370765i	−0.952982	+	0.303028i	$0.902003\pi$
$410$	−25.5444	+	7.44670i	−1.26155	+	0.367767i
$411$	−9.65336	−	5.57337i	−0.476165	−	0.274914i
$412$	6.44872	−	6.44872i	0.317706	−	0.317706i
$413$	−24.9188	−	11.4656i	−1.22617	−	0.564187i
$414$		−	4.04689i		−	0.198894i
$415$	−4.24707	+	4.43693i	−0.208481	+	0.217800i
$416$	−3.32389	+	1.91905i	−0.162967	+	0.0940891i
$417$	3.51206	−	13.1072i	0.171986	−	0.641861i
$418$	−3.02621	+	0.810871i	−0.148017	+	0.0396610i
$419$	−4.29623			−0.209884			−0.104942	−	0.994478i	$-0.533466\pi$
$419$	−4.29623			−0.209884			−0.104942	+	0.994478i	$0.533466\pi$
$420$	3.67926	−	4.63282i	0.179529	−	0.226059i
$421$	−18.8346			−0.917945			−0.458972	−	0.888451i	$-0.651782\pi$
$421$	−18.8346			−0.917945			−0.458972	+	0.888451i	$0.651782\pi$
$422$	−0.437693	+	0.117279i	−0.0213066	+	0.00570907i
$423$	1.59118	−	5.93837i	0.0773659	−	0.288733i
$424$	−0.355547	+	0.205275i	−0.0172669	+	0.00996904i
$425$	10.8418	+	2.40260i	0.525906	+	0.116543i
$426$			10.7193i			0.519351i
$427$	−17.8852	+	1.65662i	−0.865525	+	0.0801693i
$428$	10.4332	−	10.4332i	0.504305	−	0.504305i
$429$	−5.87018	−	3.38915i	−0.283415	−	0.163630i
$430$	9.60219	+	5.26741i	0.463059	+	0.254017i
$431$	−3.46231	−	5.99690i	−0.166774	−	0.288860i	0.770510	−	0.637428i	$-0.220002\pi$
$431$	−3.46231	−	5.99690i	−0.166774	−	0.288860i	−0.937284	+	0.348567i	$0.886668\pi$
$432$	0.258819	+	0.965926i	0.0124524	+	0.0464731i
$433$	−11.5154	−	11.5154i	−0.553393	−	0.553393i	0.374025	−	0.927419i	$-0.377977\pi$
$433$	−11.5154	−	11.5154i	−0.553393	−	0.553393i	−0.927419	+	0.374025i	$0.877977\pi$
$434$	−4.60846	+	26.9377i	−0.221213	+	1.29305i
$435$	2.04387	−	8.35416i	0.0979961	−	0.400551i
$436$	−10.0744	+	17.4494i	−0.482477	+	0.835675i
$437$	−6.93451	−	1.85810i	−0.331723	−	0.0888848i
$438$	−10.2705	−	2.75198i	−0.490745	−	0.131495i
$439$	−9.11194	+	15.7823i	−0.434889	+	0.753250i	−0.997287	−	0.0736169i	$-0.976546\pi$
$439$	−9.11194	+	15.7823i	−0.434889	+	0.753250i	0.562397	+	0.826867i	$0.309879\pi$
$440$	−0.938463	+	3.83589i	−0.0447395	+	0.182869i
$441$	−5.31618	+	4.55392i	−0.253152	+	0.216853i
$442$	6.02759	+	6.02759i	0.286703	+	0.286703i
$443$	−8.49765	−	31.7136i	−0.403735	−	1.50676i	−0.806376	−	0.591403i	$-0.798574\pi$
$443$	−8.49765	−	31.7136i	−0.403735	−	1.50676i	0.402641	−	0.915358i	$-0.368092\pi$
$444$	−1.66429	−	2.88263i	−0.0789837	−	0.136804i
$445$	2.18838	+	1.20047i	0.103739	+	0.0569075i
$446$	−5.72275	−	3.30403i	−0.270980	−	0.156450i
$447$	−7.14079	+	7.14079i	−0.337748	+	0.337748i
$448$	−1.52856	−	2.15951i	−0.0722178	−	0.102027i
$449$			8.14032i			0.384165i	0.981379	+	0.192083i	$0.0615242\pi$
$449$			8.14032i			0.384165i	−0.981379	+	0.192083i	$0.938476\pi$
$450$	4.88157	+	1.08178i	0.230120	+	0.0509957i
$451$	−18.1994	+	10.5075i	−0.856978	+	0.494777i
$452$	−2.39629	+	8.94306i	−0.112712	+	0.420646i
$453$	13.8223	−	3.70368i	0.649430	−	0.174014i
$454$	−16.6075			−0.779430
$455$	3.33884	−	22.4597i	0.156527	−	1.05293i
$456$	1.77399			0.0830746
$457$	−4.41041	+	1.18177i	−0.206310	+	0.0552806i	−0.360494	−	0.932762i	$-0.617392\pi$
$457$	−4.41041	+	1.18177i	−0.206310	+	0.0552806i	0.154184	+	0.988042i	$0.450725\pi$
$458$	3.50480	−	13.0801i	0.163768	−	0.611192i
$459$	1.92342	−	1.11049i	0.0897774	−	0.0518330i
$460$	−6.25731	+	6.53703i	−0.291748	+	0.304790i
$461$		−	7.54894i		−	0.351589i	−0.984427	−	0.175795i	$-0.943751\pi$
$461$		−	7.54894i		−	0.351589i	0.984427	−	0.175795i	$-0.0562495\pi$
$462$	1.95310	−	4.24477i	0.0908665	−	0.197485i
$463$	−8.87647	+	8.87647i	−0.412525	+	0.412525i	−0.882617	−	0.470092i	$-0.844221\pi$
$463$	−8.87647	+	8.87647i	−0.412525	+	0.412525i	0.470092	+	0.882617i	$0.344221\pi$
$464$	−3.33098	−	1.92314i	−0.154637	−	0.0892796i
$465$	−22.1743	+	6.46424i	−1.02831	+	0.299772i
$466$	5.78914	+	10.0271i	0.268177	+	0.464495i
$467$	2.97858	+	11.1162i	0.137832	+	0.514397i	0.999970	+	0.00772331i	$0.00245843\pi$
$467$	2.97858	+	11.1162i	0.137832	+	0.514397i	−0.862138	+	0.506674i	$0.830875\pi$
$468$	2.71395	+	2.71395i	0.125452	+	0.125452i
$469$	−7.00886	−	18.9556i	−0.323639	−	0.875290i
$470$	−11.7522	+	7.13208i	−0.542088	+	0.328979i
$471$	−4.79169	+	8.29945i	−0.220789	+	0.382418i
$472$	−10.0143	−	2.68333i	−0.460946	−	0.123510i
$473$	8.35525	+	2.23878i	0.384175	+	0.102939i
$474$	6.34546	−	10.9907i	0.291457	−	0.504817i
$475$	4.09501	−	7.86808i	0.187892	−	0.361012i
$476$	−3.75412	+	4.52057i	−0.172070	+	0.207200i
$477$	0.290303	+	0.290303i	0.0132921	+	0.0132921i
$478$	4.40676	+	16.4462i	0.201560	+	0.752233i
$479$	−6.17379	−	10.6933i	−0.282088	−	0.488590i	0.689811	−	0.723989i	$-0.257694\pi$
$479$	−6.17379	−	10.6933i	−0.282088	−	0.488590i	−0.971899	+	0.235399i	$0.924360\pi$
$480$	1.07544	−	1.96047i	0.0490869	−	0.0894826i
$481$	−11.0638	−	6.38770i	−0.504467	−	0.291254i
$482$	13.3796	−	13.3796i	0.609424	−	0.609424i
$483$	8.73931	−	6.18593i	0.397652	−	0.281469i
$484$		−	7.88104i		−	0.358229i
$485$	16.6013	+	15.8909i	0.753824	+	0.721568i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$	−4.03414	+	15.0556i	−0.182804	+	0.682235i	0.812286	+	0.583260i	$0.198223\pi$
$487$	−4.03414	+	15.0556i	−0.182804	+	0.682235i	−0.995090	+	0.0989752i	$0.968444\pi$
$488$	−6.55758	+	1.75710i	−0.296848	+	0.0795401i
$489$	11.8437			0.535589
$490$	15.6286	+	0.863846i	0.706029	+	0.0390246i
$491$	−2.67474			−0.120709			−0.0603547	−	0.998177i	$-0.519223\pi$
$491$	−2.67474			−0.120709			−0.0603547	+	0.998177i	$0.519223\pi$
$492$	11.4939	−	3.07978i	0.518184	−	0.138847i
$493$	−2.21096	+	8.25140i	−0.0995764	+	0.371624i
$494$	5.89654	−	3.40437i	0.265298	−	0.153170i
$495$	3.94808	−	0.0863160i	0.177453	−	0.00387962i
$496$			10.3294i			0.463805i
$497$	−23.1484	+	16.3851i	−1.03835	+	0.734972i
$498$	1.94227	−	1.94227i	0.0870350	−	0.0870350i
$499$	15.7413	+	9.08825i	0.704678	+	0.406846i	0.809087	−	0.587688i	$-0.199962\pi$
$499$	15.7413	+	9.08825i	0.704678	+	0.406846i	−0.104410	+	0.994534i	$0.533295\pi$
$500$	−6.21265	−	9.29532i	−0.277838	−	0.415699i
$501$	4.92063	+	8.52279i	0.219838	+	0.380770i
$502$	4.69827	+	17.5342i	0.209694	+	0.782588i
$503$	3.59630	+	3.59630i	0.160351	+	0.160351i	0.782722	−	0.622371i	$-0.213831\pi$
$503$	3.59630	+	3.59630i	0.160351	+	0.160351i	−0.622371	+	0.782722i	$0.713831\pi$
$504$	−1.69031	+	2.03540i	−0.0752923	+	0.0906640i
$505$	21.2838	+	35.0713i	0.947119	+	1.56065i
$506$	−3.57352	+	6.18952i	−0.158862	+	0.275158i
$507$	1.67202	+	0.448015i	0.0742568	+	0.0198971i
$508$	17.1359	+	4.59156i	0.760284	+	0.203718i
$509$	−2.40629	+	4.16782i	−0.106657	+	0.184735i	−0.914414	−	0.404780i	$-0.867348\pi$
$509$	−2.40629	+	4.16782i	−0.106657	+	0.184735i	0.807757	+	0.589516i	$0.200681\pi$
$510$	−4.82397	−	1.18020i	−0.213609	−	0.0522601i
$511$	−9.75621	−	26.3859i	−0.431589	−	1.16724i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.459142	−	1.71354i	−0.0202716	−	0.0756547i
$514$	−12.0351	−	20.8454i	−0.530846	−	0.919452i
$515$	5.70729	+	19.5777i	0.251493	+	0.862697i
$516$	−4.24172	−	2.44896i	−0.186731	−	0.107809i
$517$	−7.67738	+	7.67738i	−0.337651	+	0.337651i
$518$	3.68111	−	8.00034i	0.161739	−	0.351515i
$519$			8.66613i			0.380401i
$520$	−0.187587	−	8.58020i	−0.00822623	−	0.376267i
$521$	4.61481	−	2.66436i	0.202178	−	0.116728i	−0.395493	−	0.918469i	$-0.629426\pi$
$521$	4.61481	−	2.66436i	0.202178	−	0.116728i	0.597671	+	0.801741i	$0.296093\pi$
$522$	−0.995491	+	3.71522i	−0.0435714	+	0.162611i
$523$	5.91757	−	1.58561i	0.258757	−	0.0693338i	−0.127108	−	0.991889i	$-0.540570\pi$
$523$	5.91757	−	1.58561i	0.258757	−	0.0693338i	0.385866	+	0.922555i	$0.373903\pi$
$524$	0.959275			0.0419061
$525$	5.12567	+	12.1954i	0.223703	+	0.532250i
$526$	−14.0358			−0.611991
$527$	22.1596	−	5.93766i	0.965289	−	0.258648i
$528$	0.457089	−	1.70588i	0.0198923	−	0.0742389i
$529$	5.73541	−	3.31134i	0.249366	−	0.143971i
$530$	−0.0200656	−	0.917799i	−0.000871596	−	0.0398666i
$531$			10.3676i			0.449915i
$532$	2.71165	+	3.83095i	0.117565	+	0.166093i
$533$	32.2942	−	32.2942i	1.39881	−	1.39881i
$534$	−0.966705	−	0.558127i	−0.0418334	−	0.0241525i
$535$	9.23362	+	31.6741i	0.399204	+	1.36939i
$536$	−3.81931	−	6.61524i	−0.164969	−	0.285735i
$537$	3.45617	+	12.8986i	0.149145	+	0.556617i
$538$	18.7754	+	18.7754i	0.809466	+	0.809466i
$539$	12.1521	−	2.27065i	0.523427	−	0.0978040i
$540$	−2.17201	−	0.531389i	−0.0934684	−	0.0228673i
$541$	6.81239	−	11.7994i	0.292887	−	0.507296i	−0.681604	−	0.731721i	$-0.738717\pi$
$541$	6.81239	−	11.7994i	0.292887	−	0.507296i	0.974491	+	0.224426i	$0.0720506\pi$
$542$	11.5531	+	3.09564i	0.496247	+	0.132969i
$543$	8.44144	+	2.26188i	0.362257	+	0.0970664i
$544$	−1.11049	+	1.92342i	−0.0476117	+	0.0824658i
$545$	−23.3746	−	38.5164i	−1.00126	−	1.64986i
$546$	−1.71236	+	10.0092i	−0.0732823	+	0.428356i
$547$	−14.8290	−	14.8290i	−0.634042	−	0.634042i	0.315037	−	0.949079i	$-0.397983\pi$
$547$	−14.8290	−	14.8290i	−0.634042	−	0.634042i	−0.949079	+	0.315037i	$0.897983\pi$
$548$	−2.88499	−	10.7669i	−0.123241	−	0.459940i
$549$	3.39445	+	5.87936i	0.144872	+	0.250925i
$550$	−6.51088	−	5.96510i	−0.277625	−	0.254353i
$551$	5.90911	+	3.41163i	0.251737	+	0.145340i
$552$	2.86158	−	2.86158i	0.121797	−	0.121797i
$553$	33.4339	−	3.09681i	1.42175	−	0.131690i
$554$			2.36165i			0.100337i
$555$	7.44115	−	0.162684i	0.315859	−	0.00690556i
$556$	11.7516	−	6.78477i	0.498378	−	0.287738i
$557$	0.0103825	−	0.0387479i	0.000439920	−	0.00164180i	−0.965706	−	0.259640i	$-0.916396\pi$
$557$	0.0103825	−	0.0387479i	0.000439920	−	0.00164180i	0.966145	+	0.257998i	$0.0830628\pi$
$558$	9.97746	−	2.67345i	0.422379	−	0.113176i
$559$	−18.7987			−0.795099
$560$	5.87753	−	0.674271i	0.248371	−	0.0284931i
$561$	−3.92236			−0.165602
$562$	−10.6548	+	2.85494i	−0.449445	+	0.120428i
$563$	3.59929	−	13.4327i	0.151692	−	0.566122i	−0.847674	−	0.530518i	$-0.821998\pi$
$563$	3.59929	−	13.4327i	0.151692	−	0.566122i	0.999366	−	0.0356047i	$-0.0113357\pi$
$564$	5.32419	−	3.07393i	0.224189	−	0.129436i
$565$	−14.9555	−	14.3156i	−0.629183	−	0.602260i
$566$		−	23.4108i		−	0.984031i
$567$	2.40353	+	1.10591i	0.100939	+	0.0464439i
$568$	−7.57968	+	7.57968i	−0.318036	+	0.318036i
$569$	−17.1817	−	9.91984i	−0.720293	−	0.415861i	0.0945677	−	0.995518i	$-0.469853\pi$
$569$	−17.1817	−	9.91984i	−0.720293	−	0.415861i	−0.814860	+	0.579657i	$0.803186\pi$
$570$	−1.90782	+	3.47785i	−0.0799097	+	0.145671i
$571$	2.94454	+	5.10010i	0.123225	+	0.213432i	0.921038	−	0.389473i	$-0.127343\pi$
$571$	2.94454	+	5.10010i	0.123225	+	0.213432i	−0.797813	+	0.602906i	$0.794010\pi$
$572$	−1.75435	−	6.54733i	−0.0733532	−	0.273758i
$573$	−7.69044	−	7.69044i	−0.321273	−	0.321273i
$574$	24.2199	+	20.1135i	1.01092	+	0.839523i
$575$	−6.08626	−	19.2974i	−0.253815	−	0.804758i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	14.4051	+	3.85984i	0.599692	+	0.160687i	0.545879	−	0.837864i	$-0.316196\pi$
$577$	14.4051	+	3.85984i	0.599692	+	0.160687i	0.0538132	+	0.998551i	$0.482862\pi$
$578$	−11.6561	−	3.12324i	−0.484830	−	0.129910i
$579$	−5.60060	+	9.70052i	−0.232753	+	0.403140i
$580$	7.35252	−	4.46205i	0.305297	−	0.185276i
$581$	7.16322	+	1.22547i	0.297180	+	0.0508411i
$582$	−7.26720	−	7.26720i	−0.301235	−	0.301235i
$583$	−0.187658	−	0.700349i	−0.00777200	−	0.0290055i
$584$	−5.31641	−	9.20830i	−0.219995	−	0.381042i
$585$	−8.23928	+	2.40191i	−0.340652	+	0.0993069i
$586$	18.9635	+	10.9486i	0.783376	+	0.452282i
$587$	4.86057	−	4.86057i	0.200617	−	0.200617i	−0.599647	−	0.800264i	$-0.704692\pi$
$587$	4.86057	−	4.86057i	0.200617	−	0.200617i	0.800264	+	0.599647i	$0.204692\pi$
$588$	−6.97922	−	0.539001i	−0.287818	−	0.0222280i
$589$		−	18.3243i		−	0.755039i
$590$	16.0304	−	16.7470i	0.659960	−	0.689462i
$591$	−12.7098	+	7.33801i	−0.522812	+	0.301846i
$592$	0.861499	−	3.21516i	0.0354074	−	0.132142i
$593$	−20.4715	+	5.48532i	−0.840664	+	0.225255i	−0.653361	−	0.757047i	$-0.726641\pi$
$593$	−20.4715	+	5.48532i	−0.840664	+	0.225255i	−0.187304	+	0.982302i	$0.559975\pi$
$594$	−1.76606			−0.0724622
$595$	−4.82509	−	12.2214i	−0.197809	−	0.501030i
$596$	−10.0986			−0.413655
$597$	17.9305	−	4.80447i	0.733847	−	0.196634i
$598$	4.02007	−	15.0031i	0.164393	−	0.613523i
$599$	−10.0409	+	5.79712i	−0.410260	+	0.236864i	−0.690902	−	0.722949i	$-0.742786\pi$
$599$	−10.0409	+	5.79712i	−0.410260	+	0.236864i	0.280641	+	0.959813i	$0.409453\pi$
$600$	2.68686	+	4.21673i	0.109691	+	0.172147i
$601$			15.3561i			0.626387i	0.949689	+	0.313193i	$0.101399\pi$
$601$			15.3561i			0.626387i	−0.949689	+	0.313193i	$0.898601\pi$
$602$	−1.19518	−	12.9034i	−0.0487119	−	0.525904i
$603$	−5.40132	+	5.40132i	−0.219959	+	0.219959i
$604$	12.3928	+	7.15497i	0.504254	+	0.291131i
$605$	15.4505	+	8.47559i	0.628153	+	0.344582i
$606$	−9.17333	−	15.8887i	−0.372641	−	0.645433i
$607$	5.83734	+	21.7853i	0.236931	+	0.884237i	0.977269	+	0.212003i	$0.0679985\pi$
$607$	5.83734	+	21.7853i	0.236931	+	0.884237i	−0.740339	+	0.672234i	$0.765335\pi$
$608$	1.25440	+	1.25440i	0.0508726	+	0.0508726i
$609$	−9.54474	+	3.52918i	−0.386772	+	0.143009i
$610$	3.60755	−	14.7456i	0.146065	−	0.597031i
$611$	11.7980	−	20.4348i	0.477297	−	0.826703i
$612$	2.14529	+	0.574830i	0.0867183	+	0.0232361i
$613$	4.62200	+	1.23846i	0.186681	+	0.0500209i	0.350948	−	0.936395i	$-0.385859\pi$
$613$	4.62200	+	1.23846i	0.186681	+	0.0500209i	−0.164267	+	0.986416i	$0.552526\pi$
$614$	−1.50012	+	2.59828i	−0.0605399	+	0.104858i
$615$	−6.32318	+	25.8455i	−0.254975	+	1.04219i
$616$	4.38256	−	1.62046i	0.176578	−	0.0652900i
$617$	17.3498	+	17.3498i	0.698475	+	0.698475i	0.964082	−	0.265606i	$-0.0855722\pi$
$617$	17.3498	+	17.3498i	0.698475	+	0.698475i	−0.265606	+	0.964082i	$0.585572\pi$
$618$	−2.36040	−	8.80911i	−0.0949490	−	0.354355i
$619$	−10.4801	−	18.1521i	−0.421232	−	0.729596i	0.574828	−	0.818274i	$-0.305069\pi$
$619$	−10.4801	−	18.1521i	−0.421232	−	0.729596i	−0.996060	+	0.0886786i	$0.971736\pi$
$620$	−20.2505	−	11.1087i	−0.813279	−	0.446135i
$621$	−3.50471	−	2.02344i	−0.140639	−	0.0811980i
$622$	10.6211	−	10.6211i	0.425868	−	0.425868i
$623$	−0.272387	−	2.94074i	−0.0109129	−	0.117818i
$624$			3.83810i			0.153647i
$625$	24.9045	−	2.18315i	0.996180	−	0.0873258i
$626$	−11.5339	+	6.65911i	−0.460988	+	0.266152i
$627$	−0.810871	+	3.02621i	−0.0323831	+	0.120855i
$628$	−9.25683	+	2.48036i	−0.369388	+	0.0989772i
$629$	−7.39267			−0.294765
$630$	−2.17251	−	5.50274i	−0.0865550	−	0.219235i
$631$	−48.7823			−1.94199			−0.970996	−	0.239095i	$-0.923149\pi$
$631$	−48.7823			−1.94199			−0.970996	+	0.239095i	$0.923149\pi$
$632$	12.2585	−	3.28465i	0.487616	−	0.130656i
$633$	−0.117279	+	0.437693i	−0.00466144	+	0.0173967i
$634$	−12.0392	+	6.95084i	−0.478138	+	0.276053i
$635$	−27.4303	+	28.6565i	−1.08854	+	1.13720i
$636$			0.410550i			0.0162794i
$637$	−24.2325	+	11.6019i	−0.960128	+	0.459683i
$638$	4.80320	−	4.80320i	0.190160	−	0.190160i
$639$	9.28317	+	5.35964i	0.367237	+	0.212024i
$640$	2.14671	−	0.625808i	0.0848562	−	0.0247372i
$641$	−6.03196	−	10.4477i	−0.238248	−	0.412658i	0.721964	−	0.691931i	$-0.243240\pi$
$641$	−6.03196	−	10.4477i	−0.238248	−	0.412658i	−0.960212	+	0.279273i	$0.909906\pi$
$642$	−3.81880	−	14.2519i	−0.150716	−	0.562480i
$643$	−15.5935	−	15.5935i	−0.614947	−	0.614947i	0.329284	−	0.944231i	$-0.393193\pi$
$643$	−15.5935	−	15.5935i	−0.614947	−	0.614947i	−0.944231	+	0.329284i	$0.893193\pi$
$644$	10.5537	+	1.80551i	0.415875	+	0.0711472i
$645$	9.36281	−	5.68204i	0.368660	−	0.223730i
$646$	1.96999	−	3.41212i	0.0775082	−	0.134248i
$647$	−6.33226	−	1.69672i	−0.248947	−	0.0667051i	0.132188	−	0.991225i	$-0.457800\pi$
$647$	−6.33226	−	1.69672i	−0.248947	−	0.0667051i	−0.381135	+	0.924520i	$0.624467\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	9.15487	−	15.8567i	0.359360	−	0.622430i
$650$	17.0229	+	8.85973i	0.667694	+	0.347507i
$651$	21.0245	+	17.4599i	0.824016	+	0.684308i
$652$	8.37474	+	8.37474i	0.327980	+	0.327980i
$653$	−5.97625	−	22.3037i	−0.233869	−	0.872811i	−0.978655	−	0.205508i	$-0.934115\pi$
$653$	−5.97625	−	22.3037i	−0.233869	−	0.872811i	0.744787	−	0.667303i	$-0.232551\pi$
$654$	10.0744	+	17.4494i	0.393941	+	0.682326i
$655$	−1.03164	+	1.88063i	−0.0403096	+	0.0734821i
$656$	10.3051	+	5.94967i	0.402348	+	0.232296i
$657$	−7.51854	+	7.51854i	−0.293326	+	0.293326i
$658$	14.7765	+	6.79898i	0.576050	+	0.265052i
$659$			8.89429i			0.346472i	0.984880	+	0.173236i	$0.0554224\pi$
$659$			8.89429i			0.346472i	−0.984880	+	0.173236i	$0.944578\pi$
$660$	2.85275	+	2.73068i	0.111043	+	0.106292i
$661$	7.24046	−	4.18028i	0.281621	−	0.162594i	−0.352536	−	0.935798i	$-0.614681\pi$
$661$	7.24046	−	4.18028i	0.281621	−	0.162594i	0.634157	+	0.773204i	$0.281347\pi$
$662$	4.82248	−	17.9977i	0.187431	−	0.699501i
$663$	8.23385	−	2.20625i	0.319776	−	0.0856837i
$664$	2.74678			0.106596
$665$	−10.4267	+	1.19615i	−0.404329	+	0.0463847i
$666$	−3.32858			−0.128980
$667$	15.0351	−	4.02864i	0.582161	−	0.155990i
$668$	−2.54711	+	9.50594i	−0.0985506	+	0.367796i
$669$	−5.72275	+	3.30403i	−0.221254	+	0.127741i
$670$	17.0764	−	0.373338i	0.659719	−	0.0144233i
$671$		−	11.9896i		−	0.462853i
$672$	−2.63447	+	0.244018i	−0.101627	+	0.00941321i
$673$	−11.1305	+	11.1305i	−0.429048	+	0.429048i	−0.888304	−	0.459256i	$-0.848116\pi$
$673$	−11.1305	+	11.1305i	−0.429048	+	0.429048i	0.459256	+	0.888304i	$0.348116\pi$
$674$	11.8013	+	6.81346i	0.454567	+	0.262444i
$675$	3.37764	−	3.68668i	0.130005	−	0.141900i
$676$	0.865499	+	1.49909i	0.0332884	+	0.0576572i
$677$	11.2360	+	41.9335i	0.431836	+	1.61163i	0.748526	+	0.663106i	$0.230762\pi$
$677$	11.2360	+	41.9335i	0.431836	+	1.61163i	−0.316690	+	0.948529i	$0.602571\pi$
$678$	6.54677	+	6.54677i	0.251427	+	0.251427i
$679$	4.58524	−	26.8020i	0.175965	−	1.02857i
$680$	−2.57653	−	4.24559i	−0.0988056	−	0.162811i
$681$	−8.30377	+	14.3825i	−0.318201	+	0.551140i
$682$	−17.6208	−	4.72147i	−0.674734	−	0.180794i
$683$	17.2742	+	4.62860i	0.660977	+	0.177108i	0.573687	−	0.819075i	$-0.305513\pi$
$683$	17.2742	+	4.62860i	0.660977	+	0.177108i	0.0872904	+	0.996183i	$0.472179\pi$
$684$	0.886994	−	1.53632i	0.0339151	−	0.0587426i
$685$	24.2108	+	5.92326i	0.925048	+	0.226316i
$686$	−9.50420	−	15.8956i	−0.362872	−	0.606897i
$687$	−9.57528	−	9.57528i	−0.365320	−	0.365320i
$688$	−1.26767	−	4.73102i	−0.0483296	−	0.180368i
$689$	0.787866	+	1.36462i	0.0300153	+	0.0519880i
$690$	2.53258	+	8.68750i	0.0964136	+	0.330727i
$691$	30.5564	+	17.6417i	1.16242	+	0.671123i	0.951883	−	0.306463i	$-0.0991456\pi$
$691$	30.5564	+	17.6417i	1.16242	+	0.671123i	0.210537	+	0.977586i	$0.432479\pi$
$692$	−6.12788	+	6.12788i	−0.232947	+	0.232947i
$693$	−2.69953	−	3.81382i	−0.102547	−	0.144875i
$694$		−	34.8774i		−	1.32393i
$695$	0.663211	+	30.3352i	0.0251570	+	1.15068i
$696$	−3.33098	+	1.92314i	−0.126260	+	0.0728964i
$697$	6.84009	−	25.5276i	0.259087	−	0.966926i
$698$	1.44625	−	0.387522i	0.0547414	−	0.0146679i
$699$	11.5783			0.437930
$700$	−4.99904	+	12.2478i	−0.188946	+	0.462925i
$701$	−14.9862			−0.566020			−0.283010	−	0.959117i	$-0.591333\pi$
$701$	−14.9862			−0.566020			−0.283010	+	0.959117i	$0.591333\pi$
$702$	3.70732	−	0.993373i	0.139924	−	0.0374924i
$703$	−1.52829	+	5.70366i	−0.0576405	+	0.215117i
$704$	1.52945	−	0.883028i	0.0576433	−	0.0332804i
$705$	0.300476	+	13.7437i	0.0113166	+	0.517619i
$706$			5.96674i			0.224561i
$707$	20.2898	−	44.0968i	0.763075	−	1.65843i
$708$	−7.33099	+	7.33099i	−0.275515	+	0.275515i
$709$	−7.19605	−	4.15464i	−0.270253	−	0.156031i	0.358750	−	0.933434i	$-0.383203\pi$
$709$	−7.19605	−	4.15464i	−0.270253	−	0.156031i	−0.629003	+	0.777403i	$0.716537\pi$
$710$	−6.70822	−	23.0112i	−0.251755	−	0.863595i
$711$	−6.34546	−	10.9907i	−0.237973	−	0.412182i
$712$	−0.288908	−	1.07822i	−0.0108273	−	0.0404080i
$713$	−29.5585	−	29.5585i	−1.10697	−	1.10697i
$714$	2.03786	+	5.51145i	0.0762652	+	0.206261i
$715$	14.7225	+	3.60191i	0.550591	+	0.134704i
$716$	−6.67682	+	11.5646i	−0.249524	+	0.432189i
$717$	16.4462	+	4.40676i	0.614196	+	0.164573i
$718$	−16.7291	−	4.48256i	−0.624326	−	0.167288i
$719$	−7.07678	+	12.2574i	−0.263920	+	0.457122i	−0.967280	−	0.253711i	$-0.918349\pi$
$719$	−7.07678	+	12.2574i	−0.263920	+	0.457122i	0.703360	+	0.710833i	$0.251682\pi$
$720$	−1.16009	−	1.91159i	−0.0432341	−	0.0712408i
$721$	15.4154	−	18.5626i	0.574099	−	0.691307i
$722$	11.2097	+	11.2097i	0.417183	+	0.417183i
$723$	−4.89728	−	18.2769i	−0.182132	−	0.679725i
$724$	4.36961	+	7.56839i	0.162395	+	0.281277i
$725$	0.840502	+	19.2130i	0.0312155	+	0.713554i
$726$	−6.82518	−	3.94052i	−0.253306	−	0.146246i
$727$	−19.9622	+	19.9622i	−0.740357	+	0.740357i	−0.972647	−	0.232290i	$-0.925378\pi$
$727$	−19.9622	+	19.9622i	−0.740357	+	0.740357i	0.232290	+	0.972647i	$0.425378\pi$
$728$	−8.28842	+	5.86678i	−0.307189	+	0.217437i
$729$		−	1.00000i		−	0.0370370i
$730$	23.7700	−	0.519679i	0.879769	−	0.0192342i
$731$	−9.42073	+	5.43906i	−0.348438	+	0.201171i
$732$	−1.75710	+	6.55758i	−0.0649442	+	0.242375i
$733$	−44.8290	+	12.0119i	−1.65580	+	0.443670i	−0.961228	−	0.275755i	$-0.911072\pi$
$733$	−44.8290	+	12.0119i	−1.65580	+	0.443670i	−0.694570	+	0.719425i	$0.744405\pi$
$734$	5.48491			0.202452
$735$	8.56242	−	13.1029i	0.315830	−	0.483306i
$736$	4.04689			0.149170
$737$	13.0306	−	3.49153i	0.479987	−	0.128612i
$738$	3.07978	−	11.4939i	0.113368	−	0.423095i
$739$	−15.1424	+	8.74246i	−0.557022	+	0.321597i	−0.751949	−	0.659221i	$-0.770886\pi$
$739$	−15.1424	+	8.74246i	−0.557022	+	0.321597i	0.194927	+	0.980818i	$0.437553\pi$
$740$	5.37672	+	5.14665i	0.197652	+	0.189195i
$741$		−	6.80874i		−	0.250125i
$742$	−0.886588	+	0.627552i	−0.0325477	+	0.0230382i
$743$	−12.2427	+	12.2427i	−0.449143	+	0.449143i	−0.895069	−	0.445927i	$-0.852874\pi$
$743$	−12.2427	+	12.2427i	−0.449143	+	0.449143i	0.445927	+	0.895069i	$0.352874\pi$
$744$	8.94554	+	5.16471i	0.327960	+	0.189348i
$745$	10.8604	−	19.7980i	0.397896	−	0.725342i
$746$	15.4205	+	26.7091i	0.564585	+	0.977889i
$747$	−0.710918	−	2.65318i	−0.0260111	−	0.0970749i
$748$	−2.77353	−	2.77353i	−0.101410	−	0.101410i
$749$	24.9400	−	30.0317i	0.911287	−	1.09734i
$750$	−11.1563	+	0.732658i	−0.407371	+	0.0267529i
$751$	12.4732	−	21.6042i	0.455154	−	0.788350i	−0.543543	−	0.839381i	$-0.682917\pi$
$751$	12.4732	−	21.6042i	0.455154	−	0.788350i	0.998697	+	0.0510312i	$0.0162508\pi$
$752$	5.93837	+	1.59118i	0.216550	+	0.0580244i
$753$	17.5342	+	4.69827i	0.638981	+	0.171214i
$754$	−7.38120	+	12.7846i	−0.268808	+	0.465588i
$755$	−27.3547	+	16.6009i	−0.995541	+	0.604167i
$756$	0.917556	+	2.48155i	0.0333712	+	0.0902531i
$757$	−32.4637	−	32.4637i	−1.17991	−	1.17991i	−0.979765	−	0.200149i	$-0.935857\pi$
$757$	−32.4637	−	32.4637i	−1.17991	−	1.17991i	−0.200149	−	0.979765i	$-0.564143\pi$
$758$	3.34401	+	12.4800i	0.121460	+	0.453295i
$759$	3.57352	+	6.18952i	0.129711	+	0.224665i
$760$	−3.80824	+	1.11018i	−0.138139	+	0.0402703i
$761$	28.5750	+	16.4978i	1.03584	+	0.598045i	0.918653	−	0.395065i	$-0.129278\pi$
$761$	28.5750	+	16.4978i	1.03584	+	0.598045i	0.117191	+	0.993109i	$0.462611\pi$
$762$	12.5444	−	12.5444i	0.454435	−	0.454435i
$763$	−22.2828	+	48.4284i	−0.806693	+	1.75322i
$764$		−	10.8759i		−	0.393477i
$765$	−3.43407	+	3.58758i	−0.124159	+	0.129709i
$766$	−1.03059	+	0.595014i	−0.0372369	+	0.0214987i
$767$	−10.2989	+	38.4359i	−0.371871	+	1.38784i
$768$	−0.965926	+	0.258819i	−0.0348548	+	0.00933933i
$769$	−10.0980			−0.364144			−0.182072	−	0.983285i	$-0.558280\pi$
$769$	−10.0980			−0.364144			−0.182072	+	0.983285i	$0.558280\pi$
$770$	−1.53633	+	10.3346i	−0.0553655	+	0.372432i
$771$	−24.0702			−0.866867
$772$	−10.8195	+	2.89908i	−0.389403	+	0.104340i
$773$	−3.06094	+	11.4236i	−0.110094	+	0.410878i	−0.998873	−	0.0474585i	$-0.984888\pi$
$773$	−3.06094	+	11.4236i	−0.110094	+	0.410878i	0.888779	+	0.458336i	$0.151554\pi$
$774$	−4.24172	+	2.44896i	−0.152465	+	0.0880259i
$775$	43.5564	−	27.7537i	1.56459	−	0.996942i
$776$		−	10.2774i		−	0.368936i
$777$	−5.08794	−	7.18811i	−0.182529	−	0.257872i
$778$	6.73784	−	6.73784i	0.241563	−	0.241563i
$779$	−18.2812	−	10.5546i	−0.654991	−	0.378159i
$780$	−7.52446	−	4.12764i	−0.269419	−	0.147793i
$781$	−9.46543	−	16.3946i	−0.338700	−	0.586645i
$782$	−2.32627	−	8.68176i	−0.0831873	−	0.310459i
$783$	2.71973	+	2.71973i	0.0971953	+	0.0971953i
$784$	−4.55392	−	5.31618i	−0.162640	−	0.189864i
$785$	5.09250	−	20.8152i	0.181759	−	0.742926i
$786$	0.479637	−	0.830756i	0.0171081	−	0.0296321i
$787$	−8.47179	−	2.27001i	−0.301987	−	0.0809171i	0.104644	−	0.994510i	$-0.466630\pi$
$787$	−8.47179	−	2.27001i	−0.301987	−	0.0809171i	−0.406631	+	0.913593i	$0.633296\pi$
$788$	−14.1760	−	3.79843i	−0.504997	−	0.135314i
$789$	−7.01791	+	12.1554i	−0.249844	+	0.432743i
$790$	−6.74381	+	27.5648i	−0.239934	+	0.980711i
$791$	−4.13068	+	24.1450i	−0.146870	+	0.858497i
$792$	−1.24879	−	1.24879i	−0.0443738	−	0.0443738i
$793$	6.74391	+	25.1686i	0.239483	+	0.893764i
$794$	−14.2666	−	24.7105i	−0.506303	−	0.876942i
$795$	−0.804870	−	0.441522i	−0.0285458	−	0.0156592i
$796$	16.0761	+	9.28152i	0.569801	+	0.328975i
$797$	26.4972	−	26.4972i	0.938580	−	0.938580i	−0.0596400	−	0.998220i	$-0.518995\pi$
$797$	26.4972	−	26.4972i	0.938580	−	0.938580i	0.998220	+	0.0596400i	$0.0189953\pi$
$798$	4.67353	−	0.432886i	0.165441	−	0.0153240i
$799$		−	13.6542i		−	0.483051i
$800$	−1.08178	+	4.88157i	−0.0382467	+	0.172590i
$801$	−0.966705	+	0.558127i	−0.0341568	+	0.0197205i
$802$	−10.1535	+	37.8932i	−0.358531	+	1.33806i
$803$	18.1383	−	4.86015i	0.640088	−	0.171511i
$804$	−7.63862			−0.269394
$805$	−14.8896	+	18.7485i	−0.524788	+	0.660799i
$806$	39.6453			1.39645
$807$	25.6477	−	6.87229i	0.902842	−	0.241916i
$808$	4.74846	−	17.7215i	0.167050	−	0.623441i
$809$	34.0232	−	19.6433i	1.19619	−	0.690622i	0.236489	−	0.971634i	$-0.424003\pi$
$809$	34.0232	−	19.6433i	1.19619	−	0.690622i	0.959704	+	0.281012i	$0.0906701\pi$
$810$	−1.54620	+	1.61532i	−0.0543280	+	0.0567566i
$811$			9.61165i			0.337511i	0.985658	+	0.168755i	$0.0539748\pi$
$811$			9.61165i			0.337511i	−0.985658	+	0.168755i	$0.946025\pi$
$812$	−9.24465	−	4.25364i	−0.324424	−	0.149274i
$813$	8.45744	−	8.45744i	0.296615	−	0.296615i
$814$	5.09089	+	2.93923i	0.178436	+	0.103020i
$815$	−25.4249	+	7.41187i	−0.890596	+	0.259626i
$816$	1.11049	+	1.92342i	0.0388748	+	0.0673331i
$817$	2.24884	+	8.39277i	0.0786769	+	0.293626i
$818$	−6.12230	−	6.12230i	−0.214061	−	0.214061i
$819$	7.81207	+	6.48757i	0.272976	+	0.226694i
$820$	−22.7467	+	13.8043i	−0.794348	+	0.482069i
$821$	−25.9357	+	44.9219i	−0.905162	+	1.56779i	−0.0844618	+	0.996427i	$0.526917\pi$
$821$	−25.9357	+	44.9219i	−0.905162	+	1.56779i	−0.820700	+	0.571359i	$0.806416\pi$
$822$	−10.7669	−	2.88499i	−0.375540	−	0.100626i
$823$	−10.0490	−	2.69263i	−0.350287	−	0.0938592i	0.0793852	−	0.996844i	$-0.474704\pi$
$823$	−10.0490	−	2.69263i	−0.350287	−	0.0938592i	−0.429672	+	0.902985i	$0.641371\pi$
$824$	4.55993	−	7.89804i	0.158853	−	0.275141i
$825$	−8.42136	+	2.65604i	−0.293194	+	0.0924713i
$826$	−27.0372	−	4.62548i	−0.940746	−	0.160941i
$827$	7.55951	+	7.55951i	0.262870	+	0.262870i	0.826219	−	0.563349i	$-0.190487\pi$
$827$	7.55951	+	7.55951i	0.262870	+	0.262870i	−0.563349	+	0.826219i	$0.690487\pi$
$828$	−1.04741	−	3.90900i	−0.0364001	−	0.135847i
$829$	−16.1525	−	27.9770i	−0.561001	−	0.971682i	−0.997409	−	0.0719331i	$-0.977083\pi$
$829$	−16.1525	−	27.9770i	−0.561001	−	0.971682i	0.436409	−	0.899748i	$-0.356250\pi$
$830$	−2.95399	+	5.38497i	−0.102535	+	0.186915i
$831$	2.04525	+	1.18083i	0.0709490	+	0.0409624i
$832$	−2.71395	+	2.71395i	−0.0940891	+	0.0940891i
$833$	−8.78704	+	12.8254i	−0.304453	+	0.444374i
$834$		−	13.5695i		−	0.469875i
$835$	−15.8968	−	15.2166i	−0.550132	−	0.526592i
$836$	−2.71323	+	1.56648i	−0.0938389	+	0.0541779i
$837$	2.67345	−	9.97746i	0.0924080	−	0.344871i
$838$	−4.14984	+	1.11195i	−0.143354	+	0.0384115i
$839$	24.7218			0.853490			0.426745	−	0.904372i	$-0.359660\pi$
$839$	24.7218			0.853490			0.426745	+	0.904372i	$0.359660\pi$
$840$	2.35483	−	5.42723i	0.0812493	−	0.187257i
$841$	14.2061			0.489866
$842$	−18.1929	+	4.87477i	−0.626968	+	0.167996i
$843$	−2.85494	+	10.6548i	−0.0983294	+	0.366970i
$844$	−0.392425	+	0.226566i	−0.0135078	+	0.00779874i
$845$	−3.86970	+	0.0846025i	−0.133122	+	0.00291041i
$846$		−	6.14785i		−	0.211367i
$847$	−1.92312	−	20.7624i	−0.0660791	−	0.713405i
$848$	−0.290303	+	0.290303i	−0.00996904	+	0.00996904i
$849$	−20.2744	−	11.7054i	−0.695815	−	0.401729i
$850$	11.0942	−	0.485334i	0.380529	−	0.0166468i
$851$	6.73519	+	11.6657i	0.230879	+	0.399895i
$852$	2.77435	+	10.3540i	0.0950478	+	0.354723i
$853$	28.0435	+	28.0435i	0.960191	+	0.960191i	0.999237	−	0.0390463i	$-0.0124320\pi$
$853$	28.0435	+	28.0435i	0.960191	+	0.960191i	−0.0390463	+	0.999237i	$0.512432\pi$
$854$	−16.8470	+	6.22920i	−0.576493	+	0.213159i
$855$	2.05799	+	3.39114i	0.0703819	+	0.115975i
$856$	7.37735	−	12.7779i	0.252153	−	0.436741i
$857$	−45.9579	−	12.3144i	−1.56989	−	0.420652i	−0.634115	−	0.773239i	$-0.718635\pi$
$857$	−45.9579	−	12.3144i	−1.56989	−	0.420652i	−0.935779	+	0.352587i	$0.885302\pi$
$858$	−6.54733	−	1.75435i	−0.223522	−	0.0598926i
$859$	−26.8560	+	46.5160i	−0.916315	+	1.58710i	−0.111351	+	0.993781i	$0.535518\pi$
$859$	−26.8560	+	46.5160i	−0.916315	+	1.58710i	−0.804964	+	0.593324i	$0.797815\pi$
$860$	10.6383	+	2.60270i	0.362763	+	0.0887512i
$861$	29.5288	−	10.9183i	1.00634	−	0.372095i
$862$	−4.89645	−	4.89645i	−0.166774	−	0.166774i
$863$	10.3466	+	38.6139i	0.352201	+	1.31443i	0.883970	+	0.467544i	$0.154861\pi$
$863$	10.3466	+	38.6139i	0.352201	+	1.31443i	−0.531768	+	0.846890i	$0.678472\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−5.42334	−	18.6037i	−0.184399	−	0.632544i
$866$	−14.1034	−	8.14260i	−0.479253	−	0.276697i
$867$	−8.53286	+	8.53286i	−0.289791	+	0.289791i
$868$	2.52057	+	27.2126i	0.0855536	+	0.923656i
$869$			22.4129i			0.760305i
$870$	−0.187987	−	8.59849i	−0.00637335	−	0.291516i
$871$	−25.3900	+	14.6589i	−0.860306	+	0.496698i
$872$	−5.21491	+	19.4623i	−0.176599	+	0.659076i
$873$	−9.92718	+	2.65998i	−0.335984	+	0.0900267i
$874$	−7.17914			−0.242838
$875$	−18.6353	−	22.9723i	−0.629988	−	0.776605i
$876$	−10.6328			−0.359250
$877$	7.34780	−	1.96884i	0.248118	−	0.0664829i	−0.132617	−	0.991167i	$-0.542338\pi$
$877$	7.34780	−	1.96884i	0.248118	−	0.0664829i	0.380734	+	0.924685i	$0.375671\pi$
$878$	−4.71669	+	17.6029i	−0.159180	+	0.594070i
$879$	18.9635	−	10.9486i	0.639624	−	0.369287i
$880$	0.0863160	+	3.94808i	0.00290971	+	0.133090i
$881$		−	37.1659i		−	1.25215i	−0.779763	−	0.626075i	$-0.784660\pi$
$881$		−	37.1659i		−	1.25215i	0.779763	−	0.626075i	$-0.215340\pi$
$882$	−3.95640	+	5.77468i	−0.133219	+	0.194444i
$883$	25.7803	−	25.7803i	0.867577	−	0.867577i	−0.124627	−	0.992204i	$-0.539773\pi$
$883$	25.7803	−	25.7803i	0.867577	−	0.867577i	0.992204	+	0.124627i	$0.0397734\pi$
$884$	7.38226	+	4.26215i	0.248292	+	0.143352i
$885$	−6.48812	−	22.2562i	−0.218096	−	0.748134i
$886$	−16.4162	−	28.4337i	−0.551513	−	0.955248i
$887$	−3.85864	−	14.4006i	−0.129560	−	0.483526i	0.870401	−	0.492344i	$-0.163860\pi$
$887$	−3.85864	−	14.4006i	−0.129560	−	0.483526i	−0.999961	+	0.00881809i	$0.997193\pi$
$888$	−2.35366	−	2.35366i	−0.0789837	−	0.0789837i
$889$	46.2646	+	7.91487i	1.55167	+	0.265456i
$890$	2.42452	+	0.593166i	0.0812700	+	0.0198830i
$891$	−0.883028	+	1.52945i	−0.0295826	+	0.0512385i
$892$	−6.38289	−	1.71029i	−0.213715	−	0.0572648i
$893$	−10.5346	−	2.82274i	−0.352527	−	0.0944593i
$894$	−5.04930	+	8.74565i	−0.168874	+	0.292498i
$895$	−15.4915	−	25.5267i	−0.517823	−	0.853263i
$896$	−2.03540	−	1.69031i	−0.0679980	−	0.0564692i
$897$	−10.9830	−	10.9830i	−0.366713	−	0.366713i
$898$	2.10687	+	7.86295i	0.0703072	+	0.262390i
$899$	19.8649	+	34.4071i	0.662533	+	1.14754i
$900$	4.99522	−	0.218523i	0.166507	−	0.00728411i
$901$	0.789659	+	0.455910i	0.0263074	+	0.0151886i
$902$	−14.8598	+	14.8598i	−0.494777	+	0.494777i
$903$	−11.7723	−	5.41666i	−0.391757	−	0.180255i
$904$			9.25854i			0.307934i
$905$	−19.5368	+	0.427129i	−0.649426	+	0.0141983i
$906$	12.3928	−	7.15497i	0.411722	−	0.237708i
$907$	5.56795	−	20.7799i	0.184881	−	0.689984i	−0.809775	−	0.586740i	$-0.800411\pi$
$907$	5.56795	−	20.7799i	0.184881	−	0.689984i	0.994656	−	0.103244i	$-0.0329223\pi$
$908$	−16.0416	+	4.29835i	−0.532361	+	0.142646i
$909$	−18.3467			−0.608520
$910$	−2.58792	−	22.5585i	−0.0857886	−	0.747808i
$911$	23.6120			0.782301			0.391151	−	0.920327i	$-0.372077\pi$
$911$	23.6120			0.782301			0.391151	+	0.920327i	$0.372077\pi$
$912$	1.71354	−	0.459142i	0.0567410	−	0.0152037i
$913$	−1.25552	+	4.68567i	−0.0415517	+	0.155073i
$914$	−3.95426	+	2.28300i	−0.130795	+	0.0755148i
$915$	−10.9663	−	10.4970i	−0.362533	−	0.347021i
$916$		−	13.5415i		−	0.447423i
$917$	2.52719	−	0.234081i	0.0834550	−	0.00773002i
$918$	1.57046	−	1.57046i	0.0518330	−	0.0518330i
$919$	38.2901	+	22.1068i	1.26307	+	0.729236i	0.973668	−	0.227971i	$-0.0732090\pi$
$919$	38.2901	+	22.1068i	1.26307	+	0.729236i	0.289406	+	0.957207i	$0.406542\pi$
$920$	−4.35219	+	7.93379i	−0.143487	+	0.261569i
$921$	1.50012	+	2.59828i	0.0494306	+	0.0856163i
$922$	−1.95381	−	7.29172i	−0.0643453	−	0.240140i
$923$	29.0915	+	29.0915i	0.957560	+	0.957560i
$924$	0.787924	−	4.60563i	0.0259208	−	0.151514i
$925$	−15.8722	+	5.00597i	−0.521874	+	0.164595i
$926$	−6.27661	+	10.8714i	−0.206262	+	0.357257i
$927$	−8.80911	−	2.36040i	−0.289329	−	0.0775255i
$928$	−3.71522	−	0.995491i	−0.121958	−	0.0326786i
$929$	0.388224	−	0.672424i	0.0127372	−	0.0220615i	−0.859587	−	0.510990i	$-0.829279\pi$
$929$	0.388224	−	0.672424i	0.0127372	−	0.0220615i	0.872324	+	0.488929i	$0.162612\pi$
$930$	−19.7456	+	11.9831i	−0.647485	+	0.392941i
$931$	8.07860	+	9.43085i	0.264766	+	0.309084i
$932$	8.18707	+	8.18707i	0.268177	+	0.268177i
$933$	−3.88760	−	14.5087i	−0.127274	−	0.474995i
$934$	5.75418	+	9.96652i	0.188282	+	0.326115i
$935$	8.42017	−	2.45465i	0.275369	−	0.0802755i
$936$	3.32389	+	1.91905i	0.108645	+	0.0627261i
$937$	−0.494892	+	0.494892i	−0.0161674	+	0.0161674i	−0.715144	−	0.698977i	$-0.753639\pi$
$937$	−0.494892	+	0.494892i	−0.0161674	+	0.0161674i	0.698977	+	0.715144i	$0.253639\pi$
$938$	−11.6761	−	16.4957i	−0.381239	−	0.538604i
$939$			13.3182i			0.434624i
$940$	−9.50581	+	9.93075i	−0.310045	+	0.323905i
$941$	15.9777	−	9.22471i	0.520857	−	0.300717i	−0.216428	−	0.976299i	$-0.569441\pi$
$941$	15.9777	−	9.22471i	0.520857	−	0.300717i	0.737285	+	0.675582i	$0.236107\pi$
$942$	−2.48036	+	9.25683i	−0.0808145	+	0.301604i
$943$	−46.5145	+	12.4635i	−1.51472	+	0.405868i
$944$	−10.3676			−0.337436
$945$	−5.85177	−	0.869921i	−0.190358	−	0.0282985i
$946$	8.64999			0.281235
$947$	9.98459	−	2.67536i	0.324456	−	0.0869376i	−0.0929149	−	0.995674i	$-0.529618\pi$
$947$	9.98459	−	2.67536i	0.324456	−	0.0869376i	0.417370	+	0.908736i	$0.362952\pi$
$948$	3.28465	−	12.2585i	0.106680	−	0.398137i
$949$	−35.3424	+	20.4049i	−1.14726	+	0.662372i
$950$	1.91907	−	8.65985i	0.0622628	−	0.280963i
$951$			13.9017i			0.450793i
$952$	−2.45620	+	5.33817i	−0.0796058	+	0.173011i
$953$	11.1833	−	11.1833i	0.362263	−	0.362263i	−0.502383	−	0.864645i	$-0.667543\pi$
$953$	11.1833	−	11.1833i	0.362263	−	0.362263i	0.864645	+	0.502383i	$0.167543\pi$
$954$	0.355547	+	0.205275i	0.0115113	+	0.00664603i
$955$	21.3219	+	11.6964i	0.689960	+	0.378487i
$956$	8.51320	+	14.7453i	0.275336	+	0.476897i
$957$	−1.75809	−	6.56129i	−0.0568311	−	0.212096i
$958$	−8.73106	−	8.73106i	−0.282088	−	0.282088i
$959$	−10.2278	−	27.6612i	−0.330271	−	0.893227i
$960$	0.531389	−	2.17201i	0.0171505	−	0.0701013i
$961$	37.8485	−	65.5555i	1.22092	−	2.11469i
$962$	−12.3401	−	3.30652i	−0.397861	−	0.106606i
$963$	−14.2519	−	3.81880i	−0.459263	−	0.123059i
$964$	9.46081	−	16.3866i	0.304712	−	0.527777i
$965$	5.95219	−	24.3291i	0.191608	−	0.783181i
$966$	6.84049	−	8.23705i	0.220089	−	0.265023i
$967$	−3.47333	−	3.47333i	−0.111695	−	0.111695i	0.649051	−	0.760745i	$-0.275166\pi$
$967$	−3.47333	−	3.47333i	−0.111695	−	0.111695i	−0.760745	+	0.649051i	$0.775166\pi$
$968$	−2.03976	−	7.61250i	−0.0655605	−	0.244675i
$969$	−1.96999	−	3.41212i	−0.0632851	−	0.109613i
$970$	20.1484	+	11.0527i	0.646928	+	0.354881i
$971$	31.5326	+	18.2054i	1.01193	+	0.584238i	0.911756	−	0.410732i	$-0.134727\pi$
$971$	31.5326	+	18.2054i	1.01193	+	0.584238i	0.100174	+	0.994970i	$0.468060\pi$
$972$	0.707107	−	0.707107i	0.0226805	−	0.0226805i
$973$	29.3036	−	20.7419i	0.939430	−	0.664955i
$974$			15.5867i			0.499431i
$975$	16.1842	−	10.3124i	0.518310	−	0.330262i
$976$	−5.87936	+	3.39445i	−0.188194	+	0.108654i
$977$	−6.24191	+	23.2951i	−0.199697	+	0.745278i	0.791304	+	0.611422i	$0.209402\pi$
$977$	−6.24191	+	23.2951i	−0.199697	+	0.745278i	−0.991001	+	0.133855i	$0.957264\pi$
$978$	11.4401	−	3.06537i	0.365814	−	0.0980196i
$979$	1.97137			0.0630052
$980$	15.3197	−	3.21057i	0.489369	−	0.102558i
$981$	20.1488			0.643303
$982$	−2.58360	+	0.692274i	−0.0824460	+	0.0220913i
$983$	−6.62151	+	24.7118i	−0.211193	+	0.788184i	0.776279	+	0.630390i	$0.217105\pi$
$983$	−6.62151	+	24.7118i	−0.211193	+	0.788184i	−0.987472	+	0.157794i	$0.949562\pi$
$984$	10.3051	−	5.94967i	0.328516	−	0.189669i
$985$	22.6921	−	23.7065i	0.723030	−	0.755352i
$986$			8.54248i			0.272048i
$987$	13.2764	−	9.39738i	0.422591	−	0.299122i
$988$	4.81451	−	4.81451i	0.153170	−	0.153170i
$989$	17.1658	+	9.91066i	0.545839	+	0.315141i
$990$	3.79121	−	1.10521i	0.120493	−	0.0351260i
$991$	−13.1174	−	22.7201i	−0.416689	−	0.721726i	0.578915	−	0.815388i	$-0.303476\pi$
$991$	−13.1174	−	22.7201i	−0.416689	−	0.721726i	−0.995604	+	0.0936614i	$0.970143\pi$
$992$	2.67345	+	9.97746i	0.0848822	+	0.316785i
$993$	−13.1752	−	13.1752i	−0.418104	−	0.418104i
$994$	−18.1189	+	21.8180i	−0.574696	+	0.692026i
$995$	−35.4849	+	21.5349i	−1.12495	+	0.682701i
$996$	1.37339	−	2.37878i	0.0435175	−	0.0753745i
$997$	36.0450	+	9.65822i	1.14156	+	0.305879i	0.779577	−	0.626307i	$-0.215434\pi$
$997$	36.0450	+	9.65822i	1.14156	+	0.305879i	0.361980	+	0.932186i	$0.382101\pi$
$998$	17.5571	+	4.70442i	0.555762	+	0.148916i
$999$	−1.66429	+	2.88263i	−0.0526558	+	0.0912025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.u.a.187.3	yes	16
3.2	odd	2		630.2.bv.a.397.2		16
5.2	odd	4		1050.2.bc.g.943.4		16
5.3	odd	4		210.2.u.b.103.2	yes	16
5.4	even	2		1050.2.bc.h.607.1		16
7.2	even	3		1470.2.m.d.97.3		16
7.3	odd	6		210.2.u.b.157.2	yes	16
7.5	odd	6		1470.2.m.e.97.2		16
15.8	even	4		630.2.bv.b.523.3		16
21.17	even	6		630.2.bv.b.577.3		16
35.3	even	12	inner	210.2.u.a.73.3	✓	16
35.17	even	12		1050.2.bc.h.493.1		16
35.23	odd	12		1470.2.m.e.1273.2		16
35.24	odd	6		1050.2.bc.g.157.4		16
35.33	even	12		1470.2.m.d.1273.3		16
105.38	odd	12		630.2.bv.a.73.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.3	✓	16	35.3	even	12	inner
210.2.u.a.187.3	yes	16	1.1	even	1	trivial
210.2.u.b.103.2	yes	16	5.3	odd	4
210.2.u.b.157.2	yes	16	7.3	odd	6
630.2.bv.a.73.2		16	105.38	odd	12
630.2.bv.a.397.2		16	3.2	odd	2
630.2.bv.b.523.3		16	15.8	even	4
630.2.bv.b.577.3		16	21.17	even	6
1050.2.bc.g.157.4		16	35.24	odd	6
1050.2.bc.g.943.4		16	5.2	odd	4
1050.2.bc.h.493.1		16	35.17	even	12
1050.2.bc.h.607.1		16	5.4	even	2
1470.2.m.d.97.3		16	7.2	even	3
1470.2.m.d.1273.3		16	35.33	even	12
1470.2.m.e.97.2		16	7.5	odd	6
1470.2.m.e.1273.2		16	35.23	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.0488750 + 2.23553i) q^{5} -1.00000i q^{6} +(2.15951 - 1.52856i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(0.258819 - 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.0488750 + 2.23553i) q^{5} -1.00000i q^{6} +(2.15951 - 1.52856i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(0.625808 + 2.14671i) q^{10} +(0.883028 + 1.52945i) q^{11} +(-0.258819 - 0.965926i) q^{12} +(-2.71395 - 2.71395i) q^{13} +(1.69031 - 2.03540i) q^{14} +(2.17201 + 0.531389i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.14529 - 0.574830i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.886994 + 1.53632i) q^{19} +(1.16009 + 1.91159i) q^{20} +(-0.917556 - 2.48155i) q^{21} +(1.24879 + 1.24879i) q^{22} +(1.04741 + 3.90900i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.99522 + 0.218523i) q^{25} +(-3.32389 - 1.91905i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.10591 - 2.40353i) q^{28} -3.84628i q^{29} +(2.23553 - 0.0488750i) q^{30} +(-8.94554 + 5.16471i) q^{31} +(0.258819 - 0.965926i) q^{32} +(1.70588 - 0.457089i) q^{33} -2.22097 q^{34} +(3.52270 + 4.75295i) q^{35} -1.00000 q^{36} +(3.21516 - 0.861499i) q^{37} +(-0.459142 + 1.71354i) q^{38} +(-3.32389 + 1.91905i) q^{39} +(1.61532 + 1.54620i) q^{40} +11.8993i q^{41} +(-1.52856 - 2.15951i) q^{42} +(3.46335 - 3.46335i) q^{43} +(1.52945 + 0.883028i) q^{44} +(1.07544 - 1.96047i) q^{45} +(2.02344 + 3.50471i) q^{46} +(1.59118 + 5.93837i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(2.32699 - 6.60190i) q^{49} +(-4.76846 + 1.50394i) q^{50} +(-1.11049 + 1.92342i) q^{51} +(-3.70732 - 0.993373i) q^{52} +(-0.396561 - 0.106258i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-3.37598 + 2.04879i) q^{55} +(0.446149 - 2.60786i) q^{56} +(1.25440 + 1.25440i) q^{57} +(-0.995491 - 3.71522i) q^{58} +(-5.18379 - 8.97859i) q^{59} +(2.14671 - 0.625808i) q^{60} +(-5.87936 - 3.39445i) q^{61} +(-7.30401 + 7.30401i) q^{62} +(-2.63447 + 0.244018i) q^{63} -1.00000i q^{64} +(5.93447 - 6.19976i) q^{65} +(1.52945 - 0.883028i) q^{66} +(1.97702 - 7.37834i) q^{67} +(-2.14529 + 0.574830i) q^{68} +4.04689 q^{69} +(4.63282 + 3.67926i) q^{70} -10.7193 q^{71} +(-0.965926 + 0.258819i) q^{72} +(2.75198 - 10.2705i) q^{73} +(2.88263 - 1.66429i) q^{74} +(-1.08178 + 4.88157i) q^{75} +1.77399i q^{76} +(4.24477 + 1.95310i) q^{77} +(-2.71395 + 2.71395i) q^{78} +(10.9907 + 6.34546i) q^{79} +(1.96047 + 1.07544i) q^{80} +(0.500000 + 0.866025i) q^{81} +(3.07978 + 11.4939i) q^{82} +(1.94227 + 1.94227i) q^{83} +(-2.03540 - 1.69031i) q^{84} +(1.18020 - 4.82397i) q^{85} +(2.44896 - 4.24172i) q^{86} +(-3.71522 - 0.995491i) q^{87} +(1.70588 + 0.457089i) q^{88} +(0.558127 - 0.966705i) q^{89} +(0.531389 - 2.17201i) q^{90} +(-10.0092 - 1.71236i) q^{91} +(2.86158 + 2.86158i) q^{92} +(2.67345 + 9.97746i) q^{93} +(3.07393 + 5.32419i) q^{94} +(-3.47785 - 1.90782i) q^{95} +(-0.866025 - 0.500000i) q^{96} +(7.26720 - 7.26720i) q^{97} +(0.539001 - 6.97922i) q^{98} -1.76606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 8 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 - 8 * q^7	\( 16 q + 12 q^{5} - 8 q^{7} + 8 q^{10} + 4 q^{11} - 16 q^{13} + 16 q^{14} + 4 q^{15} + 8 q^{16} - 12 q^{17} - 8 q^{19} - 8 q^{20} + 8 q^{21} + 4 q^{22} + 32 q^{23} - 8 q^{24} - 32 q^{25} - 12 q^{26} - 8 q^{28} - 4 q^{30} - 24 q^{31} + 8 q^{33} + 16 q^{34} + 4 q^{35} - 16 q^{36} - 8 q^{37} - 28 q^{38} - 12 q^{39} - 4 q^{42} - 24 q^{43} + 4 q^{45} - 4 q^{46} - 24 q^{47} + 52 q^{49} + 8 q^{51} - 8 q^{52} + 44 q^{53} - 8 q^{54} - 56 q^{55} + 8 q^{56} - 8 q^{57} + 48 q^{58} + 8 q^{59} + 24 q^{61} + 8 q^{62} + 4 q^{63} + 16 q^{65} + 36 q^{67} - 12 q^{68} - 8 q^{69} + 32 q^{70} - 32 q^{71} - 40 q^{73} - 24 q^{74} - 24 q^{75} - 44 q^{77} - 16 q^{78} + 12 q^{79} + 12 q^{80} + 8 q^{81} + 12 q^{82} - 16 q^{83} + 4 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{87} + 8 q^{88} - 16 q^{89} + 8 q^{91} + 8 q^{92} + 40 q^{93} + 8 q^{94} - 48 q^{95} + 44 q^{97} - 8 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 - 8 * q^7 + 8 * q^10 + 4 * q^11 - 16 * q^13 + 16 * q^14 + 4 * q^15 + 8 * q^16 - 12 * q^17 - 8 * q^19 - 8 * q^20 + 8 * q^21 + 4 * q^22 + 32 * q^23 - 8 * q^24 - 32 * q^25 - 12 * q^26 - 8 * q^28 - 4 * q^30 - 24 * q^31 + 8 * q^33 + 16 * q^34 + 4 * q^35 - 16 * q^36 - 8 * q^37 - 28 * q^38 - 12 * q^39 - 4 * q^42 - 24 * q^43 + 4 * q^45 - 4 * q^46 - 24 * q^47 + 52 * q^49 + 8 * q^51 - 8 * q^52 + 44 * q^53 - 8 * q^54 - 56 * q^55 + 8 * q^56 - 8 * q^57 + 48 * q^58 + 8 * q^59 + 24 * q^61 + 8 * q^62 + 4 * q^63 + 16 * q^65 + 36 * q^67 - 12 * q^68 - 8 * q^69 + 32 * q^70 - 32 * q^71 - 40 * q^73 - 24 * q^74 - 24 * q^75 - 44 * q^77 - 16 * q^78 + 12 * q^79 + 12 * q^80 + 8 * q^81 + 12 * q^82 - 16 * q^83 + 4 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^87 + 8 * q^88 - 16 * q^89 + 8 * q^91 + 8 * q^92 + 40 * q^93 + 8 * q^94 - 48 * q^95 + 44 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more