LMFDB - Embedded newform 65.2.o.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(2,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("65.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.o (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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.4
Root			$0.274809i$ of defining polynomial
Character	$\chi$	$=$	65.2
Dual form			65.2.o.a.33.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.137404 - 0.237991i) q^{2} +(-2.28256 - 0.611610i) q^{3} +(0.962240 - 1.66665i) q^{4} +(1.69883 - 1.45395i) q^{5} +(0.168076 + 0.627267i) q^{6} +(-0.334376 - 0.193052i) q^{7} -1.07848 q^{8} +(2.23793 + 1.29207i) q^{9} +O(q^{10})$	\(q+(-0.137404 - 0.237991i) q^{2} +(-2.28256 - 0.611610i) q^{3} +(0.962240 - 1.66665i) q^{4} +(1.69883 - 1.45395i) q^{5} +(0.168076 + 0.627267i) q^{6} +(-0.334376 - 0.193052i) q^{7} -1.07848 q^{8} +(2.23793 + 1.29207i) q^{9} +(-0.579454 - 0.204528i) q^{10} +(-1.12873 + 4.21249i) q^{11} +(-3.21571 + 3.21571i) q^{12} +(3.34024 + 1.35750i) q^{13} +0.106105i q^{14} +(-4.76693 + 2.27970i) q^{15} +(-1.77629 - 3.07663i) q^{16} +(0.510514 + 1.90527i) q^{17} -0.710144i q^{18} +(4.83947 - 1.29673i) q^{19} +(-0.788538 - 4.23041i) q^{20} +(0.645159 + 0.645159i) q^{21} +(1.15763 - 0.310185i) q^{22} +(0.0863441 - 0.322241i) q^{23} +(2.46170 + 0.659609i) q^{24} +(0.772064 - 4.94003i) q^{25} +(-0.135891 - 0.981474i) q^{26} +(0.694880 + 0.694880i) q^{27} +(-0.643499 + 0.371524i) q^{28} +(-7.07031 + 4.08205i) q^{29} +(1.19755 + 0.821248i) q^{30} +(-2.54187 + 2.54187i) q^{31} +(-1.56662 + 2.71347i) q^{32} +(5.15280 - 8.92491i) q^{33} +(0.383290 - 0.383290i) q^{34} +(-0.848736 + 0.158202i) q^{35} +(4.30685 - 2.48656i) q^{36} +(4.17859 - 2.41251i) q^{37} +(-0.973575 - 0.973575i) q^{38} +(-6.79403 - 5.14149i) q^{39} +(-1.83216 + 1.56806i) q^{40} +(4.49768 + 1.20515i) q^{41} +(0.0648946 - 0.242190i) q^{42} +(-6.58600 + 1.76471i) q^{43} +(5.93462 + 5.93462i) q^{44} +(5.68048 - 1.05883i) q^{45} +(-0.0885545 + 0.0237281i) q^{46} -9.83310i q^{47} +(2.17280 + 8.10898i) q^{48} +(-3.42546 - 5.93307i) q^{49} +(-1.28177 + 0.495037i) q^{50} -4.66112i q^{51} +(5.47658 - 4.26077i) q^{52} +(-7.17155 + 7.17155i) q^{53} +(0.0698958 - 0.260855i) q^{54} +(4.20721 + 8.79743i) q^{55} +(0.360618 + 0.208203i) q^{56} -11.8395 q^{57} +(1.94298 + 1.12178i) q^{58} +(0.628209 + 2.34451i) q^{59} +(-0.787474 + 10.1384i) q^{60} +(-5.32338 + 9.22037i) q^{61} +(0.954209 + 0.255679i) q^{62} +(-0.498873 - 0.864073i) q^{63} -6.24413 q^{64} +(7.64824 - 2.55038i) q^{65} -2.83207 q^{66} +(3.18796 + 5.52170i) q^{67} +(3.66665 + 0.982475i) q^{68} +(-0.394171 + 0.682724i) q^{69} +(0.154271 + 0.180254i) q^{70} +(-1.12684 - 4.20542i) q^{71} +(-2.41357 - 1.39347i) q^{72} +6.08593 q^{73} +(-1.14831 - 0.662979i) q^{74} +(-4.78365 + 10.8037i) q^{75} +(2.49554 - 9.31346i) q^{76} +(1.19065 - 1.19065i) q^{77} +(-0.290100 + 2.32338i) q^{78} -3.34944i q^{79} +(-7.49088 - 2.64404i) q^{80} +(-5.03732 - 8.72489i) q^{81} +(-0.331185 - 1.23600i) q^{82} -5.18834i q^{83} +(1.69605 - 0.454456i) q^{84} +(3.63744 + 2.49447i) q^{85} +(1.32493 + 1.32493i) q^{86} +(18.6350 - 4.99324i) q^{87} +(1.21732 - 4.54309i) q^{88} +(-4.82829 - 1.29374i) q^{89} +(-1.03251 - 1.20642i) q^{90} +(-0.854827 - 1.09875i) q^{91} +(-0.453978 - 0.453978i) q^{92} +(7.35661 - 4.24734i) q^{93} +(-2.34019 + 1.35111i) q^{94} +(6.33607 - 9.23927i) q^{95} +(5.23549 - 5.23549i) q^{96} +(-7.37402 + 12.7722i) q^{97} +(-0.941346 + 1.63046i) q^{98} +(-7.96886 + 7.96886i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.137404	−	0.237991i	−0.0971595	−	0.168285i	0.813348	−	0.581777i	$-0.197642\pi$
$2$	−0.137404	−	0.237991i	−0.0971595	−	0.168285i	−0.910508	+	0.413492i	$0.864309\pi$
$3$	−2.28256	−	0.611610i	−1.31784	−	0.353113i	−0.469669	−	0.882842i	$-0.655627\pi$
$3$	−2.28256	−	0.611610i	−1.31784	−	0.353113i	−0.848167	+	0.529729i	$0.822293\pi$
$4$	0.962240	−	1.66665i	0.481120	−	0.833324i
$5$	1.69883	−	1.45395i	0.759741	−	0.650226i
$5$	1.69883	−	1.45395i	0.759741	−	0.650226i
$6$	0.168076	+	0.627267i	0.0686166	+	0.256081i
$7$	−0.334376	−	0.193052i	−0.126382	−	0.0729667i	0.435476	−	0.900200i	$-0.356580\pi$
$7$	−0.334376	−	0.193052i	−0.126382	−	0.0729667i	−0.561858	+	0.827234i	$0.689913\pi$
$8$	−1.07848			−0.381301
$9$	2.23793	+	1.29207i	0.745977	+	0.430690i
$10$	−0.579454	−	0.204528i	−0.183239	−	0.0646776i
$11$	−1.12873	+	4.21249i	−0.340326	+	1.27011i	0.557653	+	0.830074i	$0.311702\pi$
$11$	−1.12873	+	4.21249i	−0.340326	+	1.27011i	−0.897979	+	0.440039i	$0.854965\pi$
$12$	−3.21571	+	3.21571i	−0.928295	+	0.928295i
$13$	3.34024	+	1.35750i	0.926416	+	0.376502i
$13$	3.34024	+	1.35750i	0.926416	+	0.376502i
$14$			0.106105i			0.0283576i
$15$	−4.76693	+	2.27970i	−1.23082	+	0.588616i
$16$	−1.77629	−	3.07663i	−0.444073	−	0.769157i
$17$	0.510514	+	1.90527i	0.123818	+	0.462095i	0.999795	−	0.0202583i	$-0.00644886\pi$
$17$	0.510514	+	1.90527i	0.123818	+	0.462095i	−0.875977	+	0.482353i	$0.839782\pi$
$18$		−	0.710144i		−	0.167383i
$19$	4.83947	−	1.29673i	1.11025	−	0.297491i	0.343318	−	0.939219i	$-0.388449\pi$
$19$	4.83947	−	1.29673i	1.11025	−	0.297491i	0.766932	+	0.641728i	$0.221782\pi$
$20$	−0.788538	−	4.23041i	−0.176322	−	0.945947i
$21$	0.645159	+	0.645159i	0.140785	+	0.140785i
$22$	1.15763	−	0.310185i	0.246807	−	0.0661318i
$23$	0.0863441	−	0.322241i	0.0180040	−	0.0671918i	−0.956339	−	0.292258i	$-0.905593\pi$
$23$	0.0863441	−	0.322241i	0.0180040	−	0.0671918i	0.974343	+	0.225067i	$0.0722600\pi$
$24$	2.46170	+	0.659609i	0.502492	+	0.134642i
$25$	0.772064	−	4.94003i	0.154413	−	0.988006i
$26$	−0.135891	−	0.981474i	−0.0266504	−	0.192483i
$27$	0.694880	+	0.694880i	0.133730	+	0.133730i
$28$	−0.643499	+	0.371524i	−0.121610	+	0.0702115i
$29$	−7.07031	+	4.08205i	−1.31292	+	0.758017i	−0.982579	−	0.185843i	$-0.940498\pi$
$29$	−7.07031	+	4.08205i	−1.31292	+	0.758017i	−0.330345	+	0.943860i	$0.607165\pi$
$30$	1.19755	+	0.821248i	0.218641	+	0.149939i
$31$	−2.54187	+	2.54187i	−0.456534	+	0.456534i	−0.897516	−	0.440982i	$-0.854630\pi$
$31$	−2.54187	+	2.54187i	−0.456534	+	0.456534i	0.440982	+	0.897516i	$0.354630\pi$
$32$	−1.56662	+	2.71347i	−0.276942	+	0.479678i
$33$	5.15280	−	8.92491i	0.896987	−	1.55363i
$34$	0.383290	−	0.383290i	0.0657336	−	0.0657336i
$35$	−0.848736	+	0.158202i	−0.143462	+	0.0267411i
$36$	4.30685	−	2.48656i	0.717809	−	0.414427i
$37$	4.17859	−	2.41251i	0.686956	−	0.396614i	−0.115514	−	0.993306i	$-0.536852\pi$
$37$	4.17859	−	2.41251i	0.686956	−	0.396614i	0.802471	+	0.596691i	$0.203518\pi$
$38$	−0.973575	−	0.973575i	−0.157935	−	0.157935i
$39$	−6.79403	−	5.14149i	−1.08792	−	0.823297i
$40$	−1.83216	+	1.56806i	−0.289690	+	0.247931i
$41$	4.49768	+	1.20515i	0.702419	+	0.188213i	0.592314	−	0.805707i	$-0.298214\pi$
$41$	4.49768	+	1.20515i	0.702419	+	0.188213i	0.110105	+	0.993920i	$0.464881\pi$
$42$	0.0648946	−	0.242190i	0.0100135	−	0.0373707i
$43$	−6.58600	+	1.76471i	−1.00436	+	0.269116i	−0.723269	−	0.690566i	$-0.757362\pi$
$43$	−6.58600	+	1.76471i	−1.00436	+	0.269116i	−0.281087	+	0.959682i	$0.590695\pi$
$44$	5.93462	+	5.93462i	0.894678	+	0.894678i
$45$	5.68048	−	1.05883i	0.846795	−	0.157841i
$46$	−0.0885545	+	0.0237281i	−0.0130566	+	0.00349852i
$47$		−	9.83310i		−	1.43430i	−0.696917	−	0.717152i	$-0.745445\pi$
$47$		−	9.83310i		−	1.43430i	0.696917	−	0.717152i	$-0.254555\pi$
$48$	2.17280	+	8.10898i	0.313616	+	1.17043i
$49$	−3.42546	−	5.93307i	−0.489352	−	0.847582i
$50$	−1.28177	+	0.495037i	−0.181270	+	0.0700088i
$51$		−	4.66112i		−	0.652687i
$52$	5.47658	−	4.26077i	0.759466	−	0.590862i
$53$	−7.17155	+	7.17155i	−0.985088	+	0.985088i	−0.999890	−	0.0148021i	$-0.995288\pi$
$53$	−7.17155	+	7.17155i	−0.985088	+	0.985088i	0.0148021	+	0.999890i	$0.495288\pi$
$54$	0.0698958	−	0.260855i	0.00951161	−	0.0354978i
$55$	4.20721	+	8.79743i	0.567301	+	1.18625i
$56$	0.360618	+	0.208203i	0.0481896	+	0.0278223i
$57$	−11.8395			−1.56818
$58$	1.94298	+	1.12178i	0.255126	+	0.147297i
$59$	0.628209	+	2.34451i	0.0817858	+	0.305229i	0.994686	−	0.102954i	$-0.0328294\pi$
$59$	0.628209	+	2.34451i	0.0817858	+	0.305229i	−0.912900	+	0.408183i	$0.866163\pi$
$60$	−0.787474	+	10.1384i	−0.101662	+	1.30887i
$61$	−5.32338	+	9.22037i	−0.681589	+	1.18055i	0.292906	+	0.956141i	$0.405378\pi$
$61$	−5.32338	+	9.22037i	−0.681589	+	1.18055i	−0.974496	+	0.224406i	$0.927956\pi$
$62$	0.954209	+	0.255679i	0.121185	+	0.0324713i
$63$	−0.498873	−	0.864073i	−0.0628521	−	0.108863i
$64$	−6.24413			−0.780516
$65$	7.64824	−	2.55038i	0.948647	−	0.316335i
$66$	−2.83207			−0.348603
$67$	3.18796	+	5.52170i	0.389471	+	0.674583i	0.992378	−	0.123228i	$-0.0393246\pi$
$67$	3.18796	+	5.52170i	0.389471	+	0.674583i	−0.602908	+	0.797811i	$0.705991\pi$
$68$	3.66665	+	0.982475i	0.444646	+	0.119143i
$69$	−0.394171	+	0.682724i	−0.0474526	+	0.0821903i
$70$	0.154271	+	0.180254i	0.0184389	+	0.0215445i
$71$	−1.12684	−	4.20542i	−0.133731	−	0.499091i	0.866269	−	0.499578i	$-0.166512\pi$
$71$	−1.12684	−	4.20542i	−0.133731	−	0.499091i	−1.00000		0.000486883i	$0.999845\pi$
$72$	−2.41357	−	1.39347i	−0.284442	−	0.164222i
$73$	6.08593			0.712304			0.356152	−	0.934428i	$-0.384088\pi$
$73$	6.08593			0.712304			0.356152	+	0.934428i	$0.384088\pi$
$74$	−1.14831	−	0.662979i	−0.133489	−	0.0770697i
$75$	−4.78365	+	10.8037i	−0.552369	+	1.24751i
$76$	2.49554	−	9.31346i	0.286258	−	1.06833i
$77$	1.19065	−	1.19065i	0.135687	−	0.135687i
$78$	−0.290100	+	2.32338i	−0.0328474	+	0.263071i
$79$		−	3.34944i		−	0.376842i	−0.982088	−	0.188421i	$-0.939663\pi$
$79$		−	3.34944i		−	0.376842i	0.982088	−	0.188421i	$-0.0603369\pi$
$80$	−7.49088	−	2.64404i	−0.837506	−	0.295612i
$81$	−5.03732	−	8.72489i	−0.559702	−	0.969433i
$82$	−0.331185	−	1.23600i	−0.0365733	−	0.136493i
$83$		−	5.18834i		−	0.569494i	−0.958603	−	0.284747i	$-0.908090\pi$
$83$		−	5.18834i		−	0.569494i	0.958603	−	0.284747i	$-0.0919096\pi$
$84$	1.69605	−	0.454456i	0.185054	−	0.0495852i
$85$	3.63744	+	2.49447i	0.394536	+	0.270563i
$86$	1.32493	+	1.32493i	0.142871	+	0.142871i
$87$	18.6350	−	4.99324i	1.99788	−	0.535332i
$88$	1.21732	−	4.54309i	0.129766	−	0.484295i
$89$	−4.82829	−	1.29374i	−0.511798	−	0.137136i	−0.00632782	−	0.999980i	$-0.502014\pi$
$89$	−4.82829	−	1.29374i	−0.511798	−	0.137136i	−0.505470	+	0.862844i	$0.668681\pi$
$90$	−1.03251	−	1.20642i	−0.108836	−	0.127167i
$91$	−0.854827	−	1.09875i	−0.0896102	−	0.115181i
$92$	−0.453978	−	0.453978i	−0.0473305	−	0.0473305i
$93$	7.35661	−	4.24734i	0.762845	−	0.440429i
$94$	−2.34019	+	1.35111i	−0.241372	+	0.139356i
$95$	6.33607	−	9.23927i	0.650067	−	0.947929i
$96$	5.23549	−	5.23549i	0.534345	−	0.534345i
$97$	−7.37402	+	12.7722i	−0.748718	+	1.29682i	0.199719	+	0.979853i	$0.435997\pi$
$97$	−7.37402	+	12.7722i	−0.748718	+	1.29682i	−0.948437	+	0.316965i	$0.897336\pi$
$98$	−0.941346	+	1.63046i	−0.0950903	+	0.164701i
$99$	−7.96886	+	7.96886i	−0.800900	+	0.800900i
$100$	−7.49039	−	6.04026i	−0.749039	−	0.604026i
$101$	4.57218	−	2.63975i	0.454949	−	0.262665i	−0.254969	−	0.966949i	$-0.582065\pi$
$101$	4.57218	−	2.63975i	0.454949	−	0.262665i	0.709918	+	0.704284i	$0.248732\pi$
$102$	−1.10930	+	0.640458i	−0.109838	+	0.0634147i
$103$	1.21001	+	1.21001i	0.119226	+	0.119226i	0.764203	−	0.644976i	$-0.223133\pi$
$103$	1.21001	+	1.21001i	0.119226	+	0.119226i	−0.644976	+	0.764203i	$0.723133\pi$
$104$	−3.60238	−	1.46404i	−0.353243	−	0.143560i
$105$	2.03405	+	0.157989i	0.198503	+	0.0154181i
$106$	2.69217	+	0.721364i	0.261487	+	0.0700651i
$107$	1.04897	−	3.91480i	0.101408	−	0.378458i	−0.896505	−	0.443033i	$-0.853902\pi$
$107$	1.04897	−	3.91480i	0.101408	−	0.378458i	0.997913	+	0.0645749i	$0.0205692\pi$
$108$	1.82676	−	0.489479i	0.175780	−	0.0471002i
$109$	5.02898	+	5.02898i	0.481689	+	0.481689i	0.905671	−	0.423982i	$-0.139368\pi$
$109$	5.02898	+	5.02898i	0.481689	+	0.481689i	−0.423982	+	0.905671i	$0.639368\pi$
$110$	1.51562	−	2.21008i	0.144509	−	0.210723i
$111$	−11.0134	+	2.95103i	−1.04535	+	0.280099i
$112$			1.37167i			0.129610i
$113$	−1.02863	−	3.83891i	−0.0967655	−	0.361134i	0.900516	−	0.434824i	$-0.143189\pi$
$113$	−1.02863	−	3.83891i	−0.0967655	−	0.361134i	−0.997281	+	0.0736896i	$0.976523\pi$
$114$	1.62679	+	2.81769i	0.152363	+	0.263901i
$115$	−0.321837	−	0.672973i	−0.0300115	−	0.0627550i
$116$			15.7116i			1.45879i
$117$	5.72124	+	7.35381i	0.528929	+	0.679860i
$118$	0.471653	−	0.471653i	0.0434192	−	0.0434192i
$119$	0.197111	−	0.735630i	0.0180692	−	0.0674351i
$120$	5.14105	−	2.45861i	0.469311	−	0.224440i
$121$	−6.94473	−	4.00954i	−0.631339	−	0.364504i
$122$	2.92582			0.264892
$123$	−9.52914	−	5.50165i	−0.859213	−	0.496067i
$124$	1.79052	+	6.68231i	0.160793	+	0.600089i
$125$	−5.87095	−	9.51483i	−0.525113	−	0.851032i
$126$	−0.137095	+	0.237455i	−0.0122134	+	0.0211542i
$127$	−11.0154	−	2.95156i	−0.977455	−	0.261908i	−0.265483	−	0.964116i	$-0.585531\pi$
$127$	−11.0154	−	2.95156i	−0.977455	−	0.261908i	−0.711972	+	0.702207i	$0.752198\pi$
$128$	3.99121	+	6.91298i	0.352777	+	0.611027i
$129$	16.1123			1.41860
$130$	−1.65787	−	1.46978i	−0.145405	−	0.128908i
$131$	20.8627			1.82279			0.911393	−	0.411536i	$-0.135008\pi$
$131$	20.8627			1.82279			0.911393	+	0.411536i	$0.135008\pi$
$132$	−9.91645	−	17.1758i	−0.863117	−	1.49496i
$133$	−1.86854	−	0.500673i	−0.162023	−	0.0434138i
$134$	0.876078	−	1.51741i	0.0756816	−	0.131084i
$135$	2.19080	+	0.170165i	0.188554	+	0.0146454i
$136$	−0.550580	−	2.05479i	−0.0472119	−	0.176197i
$137$	0.211266	+	0.121975i	0.0180497	+	0.0104210i	0.508998	−	0.860768i	$-0.330016\pi$
$137$	0.211266	+	0.121975i	0.0180497	+	0.0104210i	−0.490948	+	0.871189i	$0.663349\pi$
$138$	0.216643			0.0184419
$139$	−10.1187	−	5.84202i	−0.858255	−	0.495514i	0.00517263	−	0.999987i	$-0.498353\pi$
$139$	−10.1187	−	5.84202i	−0.858255	−	0.495514i	−0.863428	+	0.504473i	$0.831687\pi$
$140$	−0.553020	+	1.56677i	−0.0467387	+	0.132416i
$141$	−6.01402	+	22.4446i	−0.506472	+	1.89018i
$142$	−0.846020	+	0.846020i	−0.0709965	+	0.0709965i
$143$	−9.48868	+	12.5385i	−0.793483	+	1.04852i
$144$		−	9.18038i		−	0.765032i
$145$	−6.07619	+	17.2146i	−0.504600	+	1.42959i
$146$	−0.836233	−	1.44840i	−0.0692071	−	0.119870i
$147$	4.19009	+	15.6376i	0.345593	+	1.28977i
$148$		−	9.28566i		−	0.763277i
$149$	2.44620	−	0.655457i	0.200400	−	0.0536971i	−0.157223	−	0.987563i	$-0.550254\pi$
$149$	2.44620	−	0.655457i	0.200400	−	0.0536971i	0.357623	+	0.933866i	$0.383587\pi$
$150$	3.22848	−	0.346009i	0.263605	−	0.0282515i
$151$	2.58498	+	2.58498i	0.210362	+	0.210362i	0.804421	−	0.594059i	$-0.202475\pi$
$151$	2.58498	+	2.58498i	0.210362	+	0.210362i	−0.594059	+	0.804421i	$0.702475\pi$
$152$	−5.21928	+	1.39850i	−0.423339	+	0.113433i
$153$	−1.31924	+	4.92348i	−0.106654	+	0.398039i
$154$	−0.446964	−	0.119764i	−0.0360174	−	0.00965083i
$155$	−0.622463	+	8.01398i	−0.0499974	+	0.643698i
$156$	−15.1066	+	6.37592i	−1.20949	+	0.510482i
$157$	−2.21767	−	2.21767i	−0.176990	−	0.176990i	0.613053	−	0.790042i	$-0.289941\pi$
$157$	−2.21767	−	2.21767i	−0.176990	−	0.176990i	−0.790042	+	0.613053i	$0.789941\pi$
$158$	−0.797137	+	0.460228i	−0.0634169	+	0.0366137i
$159$	20.7557	−	11.9833i	1.64603	−	0.950337i
$160$	1.28382	+	6.88752i	0.101495	+	0.544506i
$161$	−0.0910805	+	0.0910805i	−0.00717815	+	0.00717815i
$162$	−1.38430	+	2.39768i	−0.108761	+	0.188379i
$163$	−7.40642	+	12.8283i	−0.580116	+	1.00479i	0.415349	+	0.909662i	$0.363659\pi$
$163$	−7.40642	+	12.8283i	−0.580116	+	1.00479i	−0.995465	+	0.0951279i	$0.969674\pi$
$164$	6.33641	−	6.33641i	0.494790	−	0.494790i
$165$	−4.22262	−	22.6538i	−0.328730	−	1.76360i
$166$	−1.23478	+	0.712900i	−0.0958374	+	0.0553318i
$167$	3.00348	−	1.73406i	0.232417	−	0.134186i	−0.379270	−	0.925286i	$-0.623825\pi$
$167$	3.00348	−	1.73406i	0.232417	−	0.134186i	0.611686	+	0.791100i	$0.290491\pi$
$168$	−0.695792	−	0.695792i	−0.0536815	−	0.0536815i
$169$	9.31440	+	9.06873i	0.716492	+	0.697595i
$170$	0.0938613	−	1.20843i	0.00719883	−	0.0926823i
$171$	12.5059	+	3.35094i	0.956348	+	0.256253i
$172$	−3.39616	+	12.6746i	−0.258955	+	0.966432i
$173$	−3.77661	+	1.01194i	−0.287130	+	0.0769362i	−0.399509	−	0.916729i	$-0.630819\pi$
$173$	−3.77661	+	1.01194i	−0.287130	+	0.0769362i	0.112379	+	0.993665i	$0.464153\pi$
$174$	−3.74888	−	3.74888i	−0.284202	−	0.284202i
$175$	−1.21184	+	1.50278i	−0.0916066	+	0.113599i
$176$	14.9652	−	4.00992i	1.12805	−	0.302259i
$177$		−	5.73569i		−	0.431121i
$178$	0.355530	+	1.32686i	0.0266481	+	0.0994521i
$179$	3.24880	+	5.62708i	0.242827	+	0.420588i	0.961518	−	0.274741i	$-0.0885921\pi$
$179$	3.24880	+	5.62708i	0.242827	+	0.420588i	−0.718692	+	0.695329i	$0.755259\pi$
$180$	3.70129	−	10.4862i	0.275878	−	0.781595i
$181$		−	11.9845i		−	0.890802i	−0.895331	−	0.445401i	$-0.853061\pi$
$181$		−	11.9845i		−	0.890802i	0.895331	−	0.445401i	$-0.146939\pi$
$182$	−0.144037	+	0.354415i	−0.0106767	+	0.0262710i
$183$	17.7902	−	17.7902i	1.31509	−	1.31509i
$184$	−0.0931205	+	0.347530i	−0.00686493	+	0.0256203i
$185$	3.59106	−	10.1739i	0.264020	−	0.748001i
$186$	−2.02166	−	1.16721i	−0.148235	−	0.0855837i
$187$	−8.60214			−0.629051
$188$	−16.3883	−	9.46180i	−1.19524	−	0.690073i
$189$	−0.0982030	−	0.366499i	−0.00714322	−	0.0266588i
$190$	−3.06947	−	0.238412i	−0.222683	−	0.0172963i
$191$	2.59646	−	4.49719i	0.187873	−	0.325405i	−0.756668	−	0.653799i	$-0.773174\pi$
$191$	2.59646	−	4.49719i	0.187873	−	0.325405i	0.944541	+	0.328394i	$0.106507\pi$
$192$	14.2526	+	3.81897i	1.02859	+	0.275610i
$193$	−3.33706	−	5.77996i	−0.240207	−	0.416051i	0.720566	−	0.693386i	$-0.243882\pi$
$193$	−3.33706	−	5.77996i	−0.240207	−	0.416051i	−0.960773	+	0.277335i	$0.910549\pi$
$194$	4.05289			0.290980
$195$	−19.0174	+	1.14365i	−1.36186	+	0.0818982i
$196$	−13.1845			−0.941748
$197$	−9.79857	−	16.9716i	−0.698119	−	1.20918i	−0.969118	−	0.246598i	$-0.920687\pi$
$197$	−9.79857	−	16.9716i	−0.698119	−	1.20918i	0.270999	−	0.962580i	$-0.412646\pi$
$198$	2.99147	+	0.801563i	0.212595	+	0.0569646i
$199$	7.35302	−	12.7358i	0.521242	−	0.902817i	−0.478453	−	0.878113i	$-0.658802\pi$
$199$	7.35302	−	12.7358i	0.521242	−	0.902817i	0.999695	−	0.0247042i	$-0.00786439\pi$
$200$	−0.832657	+	5.32773i	−0.0588777	+	0.376727i
$201$	−3.89957	−	14.5534i	−0.275054	−	1.02652i
$202$	−1.25647	−	0.725425i	−0.0884052	−	0.0510408i
$203$	3.15219			0.221240
$204$	−7.76844	−	4.48511i	−0.543900	−	0.314021i
$205$	9.39303	−	4.49205i	0.656038	−	0.313738i
$206$	0.121712	−	0.454234i	0.00848005	−	0.0316480i
$207$	0.609590	−	0.609590i	0.0423694	−	0.0423694i
$208$	−1.75673	−	12.6880i	−0.121807	−	0.879754i
$209$			21.8499i			1.51139i
$210$	−0.241887	−	0.505794i	−0.0166918	−	0.0349031i
$211$	10.7072	+	18.5453i	0.737111	+	1.27671i	0.953791	+	0.300471i	$0.0971440\pi$
$211$	10.7072	+	18.5453i	0.737111	+	1.27671i	−0.216679	+	0.976243i	$0.569523\pi$
$212$	5.05170	+	18.8532i	0.346952	+	1.29484i
$213$			10.2883i			0.704943i
$214$	−1.07582	+	0.288265i	−0.0735416	+	0.0197054i
$215$	−8.62271	+	12.5737i	−0.588064	+	0.857517i
$216$	−0.749414	−	0.749414i	−0.0509912	−	0.0509912i
$217$	1.34065	−	0.359227i	0.0910095	−	0.0243859i
$218$	0.505850	−	1.88786i	0.0342605	−	0.127862i
$219$	−13.8915	−	3.72221i	−0.938700	−	0.251524i
$220$	18.7106	+	1.45329i	1.26147	+	0.0979809i
$221$	−0.881153	+	7.05707i	−0.0592728	+	0.474710i
$222$	2.21561	+	2.21561i	0.148702	+	0.148702i
$223$	23.6733	−	13.6678i	1.58528	−	0.915264i	0.591214	−	0.806515i	$-0.298649\pi$
$223$	23.6733	−	13.6678i	1.58528	−	0.915264i	0.994069	−	0.108749i	$-0.0346846\pi$
$224$	1.04768	−	0.604878i	0.0700010	−	0.0404151i
$225$	8.11070	−	10.0579i	0.540713	−	0.670526i
$226$	−0.772287	+	0.772287i	−0.0513718	+	0.0513718i
$227$	−3.46369	+	5.99928i	−0.229893	+	0.398186i	−0.957776	−	0.287515i	$-0.907171\pi$
$227$	−3.46369	+	5.99928i	−0.229893	+	0.398186i	0.727883	+	0.685701i	$0.240504\pi$
$228$	−11.3924	+	19.7322i	−0.754481	+	1.30680i
$229$	−4.56825	+	4.56825i	−0.301879	+	0.301879i	−0.841749	−	0.539870i	$-0.818473\pi$
$229$	−4.56825	+	4.56825i	−0.301879	+	0.301879i	0.539870	+	0.841749i	$0.318473\pi$
$230$	−0.115940	+	0.169064i	−0.00764484	+	0.0111477i
$231$	−3.44594	+	1.98951i	−0.226726	+	0.130900i
$232$	7.62520	−	4.40241i	0.500619	−	0.289032i
$233$	−5.49074	−	5.49074i	−0.359711	−	0.359711i	0.503996	−	0.863706i	$-0.331863\pi$
$233$	−5.49074	−	5.49074i	−0.359711	−	0.359711i	−0.863706	+	0.503996i	$0.831863\pi$
$234$	0.964019	−	2.37205i	0.0630199	−	0.155066i
$235$	−14.2968	−	16.7048i	−0.932622	−	1.08970i
$236$	4.51196	+	1.20898i	0.293703	+	0.0786976i
$237$	−2.04855	+	7.64529i	−0.133068	+	0.496615i
$238$	−0.202157	+	0.0541679i	−0.0131039	+	0.00351119i
$239$	−8.33949	−	8.33949i	−0.539437	−	0.539437i	0.383927	−	0.923363i	$-0.374571\pi$
$239$	−8.33949	−	8.33949i	−0.539437	−	0.539437i	−0.923363	+	0.383927i	$0.874571\pi$
$240$	15.4813	+	10.6167i	0.999311	+	0.685303i
$241$	−1.40952	+	0.377680i	−0.0907952	+	0.0243285i	−0.303931	−	0.952694i	$-0.598299\pi$
$241$	−1.40952	+	0.377680i	−0.0907952	+	0.0243285i	0.213135	+	0.977023i	$0.431632\pi$
$242$			2.20371i			0.141660i
$243$	5.39872	+	20.1483i	0.346328	+	1.29251i
$244$	10.2447	+	17.7444i	0.655853	+	1.13597i
$245$	−14.4457	−	5.09885i	−0.922900	−	0.325754i
$246$			3.02380i			0.192791i
$247$	17.9253	+	2.23817i	1.14056	+	0.142412i
$248$	2.74136	−	2.74136i	0.174077	−	0.174077i
$249$	−3.17324	+	11.8427i	−0.201096	+	0.750500i
$250$	−1.45775	+	2.70461i	−0.0921964	+	0.171055i
$251$	−11.2668	−	6.50488i	−0.711153	−	0.410585i	0.100335	−	0.994954i	$-0.468009\pi$
$251$	−11.2668	−	6.50488i	−0.711153	−	0.410585i	−0.811488	+	0.584369i	$0.801342\pi$
$252$	−1.92014			−0.120958
$253$	1.25997	+	0.727447i	0.0792139	+	0.0457342i
$254$	0.811113	+	3.02712i	0.0508938	+	0.189938i
$255$	−6.77703	−	7.91846i	−0.424394	−	0.495873i
$256$	−5.14731	+	8.91540i	−0.321707	+	0.557212i
$257$	−28.4576	−	7.62518i	−1.77513	−	0.475646i	−0.785452	−	0.618922i	$-0.787570\pi$
$257$	−28.4576	−	7.62518i	−1.77513	−	0.475646i	−0.989683	+	0.143276i	$0.954236\pi$
$258$	−2.21389	−	3.83458i	−0.137831	−	0.238730i
$259$	−1.86296			−0.115759
$260$	3.10886	−	15.2010i	0.192803	−	0.942726i
$261$	−21.0972			−1.30588
$262$	−2.86663	−	4.96515i	−0.177101	−	0.306748i
$263$	4.88034	+	1.30768i	0.300934	+	0.0806351i	0.406127	−	0.913817i	$-0.366879\pi$
$263$	4.88034	+	1.30768i	0.300934	+	0.0806351i	−0.105192	+	0.994452i	$0.533546\pi$
$264$	−5.55719	+	9.62534i	−0.342022	+	0.592399i
$265$	−1.75619	+	22.6103i	−0.107882	+	1.38894i
$266$	0.137589	+	0.513490i	0.00843614	+	0.0314841i
$267$	10.2296	+	5.90606i	0.626041	+	0.361445i
$268$	12.2703			0.749529
$269$	−7.49111	−	4.32499i	−0.456741	−	0.263699i	0.253932	−	0.967222i	$-0.418276\pi$
$269$	−7.49111	−	4.32499i	−0.456741	−	0.263699i	−0.710673	+	0.703523i	$0.751609\pi$
$270$	−0.260528	−	0.544773i	−0.0158552	−	0.0331539i
$271$	5.96047	−	22.2448i	0.362073	−	1.35127i	−0.509273	−	0.860605i	$-0.670086\pi$
$271$	5.96047	−	22.2448i	0.362073	−	1.35127i	0.871346	−	0.490669i	$-0.163248\pi$
$272$	4.95497	−	4.95497i	0.300439	−	0.300439i
$273$	1.27918	+	3.03079i	0.0774198	+	0.183432i
$274$		−	0.0670394i		−	0.00405000i
$275$	19.9384	+	8.82829i	1.20233	+	0.532366i
$276$	0.758574	+	1.31389i	0.0456608	+	0.0790868i
$277$	−5.60114	−	20.9037i	−0.336540	−	1.25598i	−0.902190	−	0.431338i	$-0.858042\pi$
$277$	−5.60114	−	20.9037i	−0.336540	−	1.25598i	0.565650	−	0.824645i	$-0.308625\pi$
$278$			3.21087i			0.192575i
$279$	−8.97282	+	2.40426i	−0.537189	+	0.143939i
$280$	0.915345	−	0.170618i	0.0547023	−	0.0101964i
$281$	8.17717	+	8.17717i	0.487809	+	0.487809i	0.907614	−	0.419805i	$-0.137902\pi$
$281$	8.17717	+	8.17717i	0.487809	+	0.487809i	−0.419805	+	0.907614i	$0.637902\pi$
$282$	6.16797	−	1.65270i	0.367298	−	0.0984171i
$283$	−1.16452	+	4.34603i	−0.0692233	+	0.258345i	−0.991861	−	0.127322i	$-0.959362\pi$
$283$	−1.16452	+	4.34603i	−0.0692233	+	0.258345i	0.922638	+	0.385667i	$0.126029\pi$
$284$	−8.09325	−	2.16858i	−0.480246	−	0.128681i
$285$	−20.1133	+	17.2140i	−1.19141	+	1.01967i
$286$	4.28783	+	0.535383i	0.253545	+	0.0316579i
$287$	−1.27126	−	1.27126i	−0.0750400	−	0.0750400i
$288$	−7.01198	+	4.04837i	−0.413185	+	0.238552i
$289$	11.3530	−	6.55467i	0.667825	−	0.385569i
$290$	4.93182	−	0.919279i	0.289606	−	0.0539819i
$291$	24.6432	−	24.6432i	1.44461	−	1.44461i
$292$	5.85613	−	10.1431i	0.342704	−	0.593580i
$293$	6.55274	−	11.3497i	0.382815	−	0.663056i	−0.608648	−	0.793440i	$-0.708288\pi$
$293$	6.55274	−	11.3497i	0.382815	−	0.663056i	0.991463	+	0.130385i	$0.0416212\pi$
$294$	3.14588	−	3.14588i	0.183472	−	0.183472i
$295$	4.47601	+	3.06954i	0.260604	+	0.178716i
$296$	−4.50653	+	2.60185i	−0.261937	+	0.151229i
$297$	−3.71150	+	2.14284i	−0.215363	+	0.124340i
$298$	−0.492111	−	0.492111i	−0.0285072	−	0.0285072i
$299$	0.725851	−	0.959149i	0.0419770	−	0.0554690i
$300$	13.4030	+	18.3684i	0.773821	+	1.06050i
$301$	2.54288	+	0.681363i	0.146569	+	0.0392731i
$302$	0.260015	−	0.970388i	0.0149622	−	0.0558396i
$303$	−12.0508	+	3.22899i	−0.692298	+	0.185501i
$304$	−12.5859	−	12.5859i	−0.721849	−	0.721849i
$305$	4.36241	+	23.4038i	0.249791	+	1.34010i
$306$	1.35301	−	0.362539i	0.0773466	−	0.0207250i
$307$			7.75447i			0.442571i	0.975209	+	0.221285i	$0.0710252\pi$
$307$			7.75447i			0.442571i	−0.975209	+	0.221285i	$0.928975\pi$
$308$	−0.838703	−	3.13008i	−0.0477896	−	0.178353i
$309$	−2.02187	−	3.50198i	−0.115020	−	0.199221i
$310$	1.99279	−	0.953014i	0.113183	−	0.0541276i
$311$		−	11.6030i		−	0.657947i	−0.944339	−	0.328974i	$-0.893297\pi$
$311$		−	11.6030i		−	0.657947i	0.944339	−	0.328974i	$-0.106703\pi$
$312$	7.32724	+	5.54500i	0.414823	+	0.313924i
$313$	−10.1565	+	10.1565i	−0.574078	+	0.574078i	−0.933265	−	0.359188i	$-0.883054\pi$
$313$	−10.1565	+	10.1565i	−0.574078	+	0.574078i	0.359188	+	0.933265i	$0.383054\pi$
$314$	−0.223069	+	0.832505i	−0.0125885	+	0.0469810i
$315$	−2.10382	−	0.742580i	−0.118537	−	0.0418397i
$316$	−5.58234	−	3.22297i	−0.314031	−	0.181306i
$317$	21.7686			1.22265			0.611323	−	0.791381i	$-0.290638\pi$
$317$	21.7686			1.22265			0.611323	+	0.791381i	$0.290638\pi$
$318$	−5.70384	−	3.29311i	−0.319855	−	0.184669i
$319$	−9.21508	−	34.3911i	−0.515945	−	1.92553i
$320$	−10.6077	+	9.07864i	−0.592990	+	0.507512i
$321$	−4.78866	+	8.29420i	−0.267277	+	0.462937i
$322$	0.0341912	+	0.00916151i	0.00190540	+	0.000510551i
$323$	4.94124	+	8.55848i	0.274938	+	0.476206i
$324$	−19.3884			−1.07714
$325$	9.28496	−	15.4528i	0.515037	−	0.857168i
$326$	4.07070			0.225455
$327$	−8.40318	−	14.5547i	−0.464697	−	0.804878i
$328$	−4.85066	−	1.29973i	−0.267833	−	0.0717656i
$329$	−1.89830	+	3.28795i	−0.104657	+	0.181270i
$330$	−4.81121	+	4.11768i	−0.264848	+	0.226671i
$331$	−5.07792	−	18.9511i	−0.279108	−	1.04164i	−0.953038	−	0.302850i	$-0.902062\pi$
$331$	−5.07792	−	18.9511i	−0.279108	−	1.04164i	0.673931	−	0.738795i	$-0.264605\pi$
$332$	−8.64714	−	4.99243i	−0.474573	−	0.273995i
$333$	12.4685			0.683272
$334$	−0.825383	−	0.476535i	−0.0451630	−	0.0260748i
$335$	13.4441	+	4.74532i	0.734528	+	0.259265i
$336$	0.838924	−	3.13091i	0.0457671	−	0.170805i
$337$	9.35946	−	9.35946i	0.509842	−	0.509842i	−0.404636	−	0.914478i	$-0.632602\pi$
$337$	9.35946	−	9.35946i	0.509842	−	0.509842i	0.914478	+	0.404636i	$0.132602\pi$
$338$	0.878441	−	3.46283i	0.0477809	−	0.188353i
$339$			9.39165i			0.510084i
$340$	7.65749	−	3.66206i	0.415286	−	0.198603i
$341$	−7.83852	−	13.5767i	−0.424480	−	0.735220i
$342$	−0.920867	−	3.43672i	−0.0497948	−	0.185837i
$343$			5.34789i			0.288759i
$344$	7.10288	−	1.90321i	0.382962	−	0.102614i
$345$	0.323016	+	1.73294i	0.0173906	+	0.0932983i
$346$	0.759754	+	0.759754i	0.0408446	+	0.0408446i
$347$	26.7102	−	7.15698i	1.43388	−	0.384207i	0.543493	−	0.839414i	$-0.317101\pi$
$347$	26.7102	−	7.15698i	1.43388	−	0.384207i	0.890386	+	0.455207i	$0.150435\pi$
$348$	9.60939	−	35.8627i	0.515118	−	1.92244i
$349$	28.5113	+	7.63958i	1.52618	+	0.408938i	0.921769	−	0.387739i	$-0.126744\pi$
$349$	28.5113	+	7.63958i	1.52618	+	0.408938i	0.604406	+	0.796676i	$0.293410\pi$
$350$	0.524160	+	0.0819196i	0.0280175	+	0.00437878i
$351$	1.37777	+	3.26436i	0.0735398	+	0.174239i
$352$	−9.66215	−	9.66215i	−0.514994	−	0.514994i
$353$	−13.5408	+	7.81777i	−0.720702	+	0.416098i	−0.815011	−	0.579445i	$-0.803269\pi$
$353$	−13.5408	+	7.81777i	−0.720702	+	0.416098i	0.0943088	+	0.995543i	$0.469936\pi$
$354$	−1.36504	+	0.788109i	−0.0725513	+	0.0418875i
$355$	−8.02878	−	5.50594i	−0.426123	−	0.292225i
$356$	−6.80218	+	6.80218i	−0.360515	+	0.360515i
$357$	−0.899837	+	1.55856i	−0.0476244	+	0.0824879i
$358$	0.892798	−	1.54637i	0.0471858	−	0.0817282i
$359$	−14.0592	+	14.0592i	−0.742017	+	0.742017i	−0.972966	−	0.230949i	$-0.925817\pi$
$359$	−14.0592	+	14.0592i	−0.742017	+	0.742017i	0.230949	+	0.972966i	$0.425817\pi$
$360$	−6.12628	+	1.14192i	−0.322884	+	0.0601847i
$361$	5.28447	−	3.05099i	0.278130	−	0.160578i
$362$	−2.85221	+	1.64672i	−0.149909	+	0.0865499i
$363$	13.3995	+	13.3995i	0.703290	+	0.703290i
$364$	−2.65378	+	0.367432i	−0.139096	+	0.0192587i
$365$	10.3390	−	8.84863i	0.541167	−	0.463159i
$366$	−6.67836	−	1.78946i	−0.349084	−	0.0935367i
$367$	−5.70052	+	21.2746i	−0.297565	+	1.11053i	0.641594	+	0.767045i	$0.278273\pi$
$367$	−5.70052	+	21.2746i	−0.297565	+	1.11053i	−0.939159	+	0.343483i	$0.888393\pi$
$368$	−1.14479	+	0.306745i	−0.0596761	+	0.0159902i
$369$	8.50836	+	8.50836i	0.442928	+	0.442928i
$370$	−2.91473	+	0.543299i	−0.151530	+	0.0282448i
$371$	3.78247	−	1.01351i	0.196376	−	0.0526188i
$372$		−	16.3479i		−	0.847597i
$373$	−0.301668	−	1.12584i	−0.0156198	−	0.0582937i	0.957676	−	0.287848i	$-0.0929398\pi$
$373$	−0.301668	−	1.12584i	−0.0156198	−	0.0582937i	−0.973296	+	0.229554i	$0.926273\pi$
$374$	1.18197	+	2.04723i	0.0611183	+	0.105860i
$375$	7.58142	+	25.3089i	0.391503	+	1.30695i
$376$			10.6048i			0.546901i
$377$	−29.1579	+	4.03708i	−1.50171	+	0.207920i
$378$	−0.0737299	+	0.0737299i	−0.00379226	+	0.00379226i
$379$	−6.82640	+	25.4765i	−0.350649	+	1.30864i	0.535224	+	0.844710i	$0.320227\pi$
$379$	−6.82640	+	25.4765i	−0.350649	+	1.30864i	−0.885873	+	0.463928i	$0.846440\pi$
$380$	−9.30181	−	19.4504i	−0.477173	−	0.997784i
$381$	23.3380	+	13.4742i	1.19564	+	0.690304i
$382$	−1.42706			−0.0730146
$383$	28.4058	+	16.4001i	1.45147	+	0.838004i	0.998565	−	0.0535563i	$-0.0170557\pi$
$383$	28.4058	+	16.4001i	1.45147	+	0.838004i	0.452901	+	0.891561i	$0.350389\pi$
$384$	−4.88213	−	18.2204i	−0.249140	−	0.929804i
$385$	0.291570	−	3.75386i	0.0148598	−	0.191314i
$386$	−0.917054	+	1.58838i	−0.0466768	+	0.0808466i
$387$	−17.0192	−	4.56027i	−0.865132	−	0.231812i
$388$	14.1912	+	24.5798i	0.720447	+	1.24785i
$389$	−9.36826			−0.474989			−0.237495	−	0.971389i	$-0.576326\pi$
$389$	−9.36826			−0.474989			−0.237495	+	0.971389i	$0.576326\pi$
$390$	2.88525	+	4.36883i	0.146100	+	0.221224i
$391$	0.658034			0.0332782
$392$	3.69430	+	6.39871i	0.186590	+	0.323184i
$393$	−47.6205	−	12.7599i	−2.40213	−	0.643650i
$394$	−2.69273	+	4.66395i	−0.135658	+	0.234966i
$395$	−4.86992	−	5.69014i	−0.245032	−	0.286302i
$396$	5.61333	+	20.9492i	0.282080	+	1.05274i
$397$	10.0909	+	5.82600i	0.506449	+	0.292399i	0.731373	−	0.681978i	$-0.238880\pi$
$397$	10.0909	+	5.82600i	0.506449	+	0.292399i	−0.224924	+	0.974376i	$0.572213\pi$
$398$	−4.04135			−0.202574
$399$	3.95883	+	2.28563i	0.198189	+	0.114425i
$400$	−16.5701	+	6.39959i	−0.828503	+	0.319979i
$401$	−5.33600	+	19.9142i	−0.266467	+	0.994469i	0.694879	+	0.719126i	$0.255458\pi$
$401$	−5.33600	+	19.9142i	−0.266467	+	0.994469i	−0.961346	+	0.275342i	$0.911209\pi$
$402$	−2.92776	+	2.92776i	−0.146024	+	0.146024i
$403$	−11.9411	+	5.03988i	−0.594827	+	0.251054i
$404$		−	10.1603i		−	0.505493i
$405$	−21.2431	−	7.49813i	−1.05558	−	0.372585i
$406$	−0.433124	−	0.750193i	−0.0214956	−	0.0372314i
$407$	5.44616	+	20.3253i	0.269956	+	1.00749i
$408$			5.02693i			0.248870i
$409$	−4.40250	+	1.17965i	−0.217689	+	0.0583297i	−0.366015	−	0.930609i	$-0.619278\pi$
$409$	−4.40250	+	1.17965i	−0.217689	+	0.0583297i	0.148326	+	0.988939i	$0.452612\pi$
$410$	−2.35971	−	1.61823i	−0.116538	−	0.0799188i
$411$	−0.407627	−	0.407627i	−0.0201067	−	0.0201067i
$412$	3.18099	−	0.852344i	0.156716	−	0.0419920i
$413$	0.242554	−	0.905223i	0.0119353	−	0.0445431i
$414$	−0.228837	−	0.0613168i	−0.0112467	−	0.00301355i
$415$	−7.54358	−	8.81412i	−0.370300	−	0.432668i
$416$	−8.91642	+	6.93695i	−0.437163	+	0.340112i
$417$	19.5234	+	19.5234i	0.956067	+	0.956067i
$418$	5.20008	−	3.00227i	0.254344	−	0.146846i
$419$	−0.564687	+	0.326022i	−0.0275868	+	0.0159272i	−0.513730	−	0.857952i	$-0.671737\pi$
$419$	−0.564687	+	0.326022i	−0.0275868	+	0.0159272i	0.486143	+	0.873879i	$0.338403\pi$
$420$	2.22055	−	3.23802i	0.108352	−	0.157999i
$421$	−5.58095	+	5.58095i	−0.271999	+	0.271999i	−0.829904	−	0.557906i	$-0.811605\pi$
$421$	−5.58095	+	5.58095i	−0.271999	+	0.271999i	0.557906	+	0.829904i	$0.311605\pi$
$422$	2.94242	−	5.09642i	0.143235	−	0.248090i
$423$	12.7051	−	22.0058i	0.617741	−	1.06996i
$424$	7.73438	−	7.73438i	0.375615	−	0.375615i
$425$	9.80622	−	1.05097i	0.475672	−	0.0509795i
$426$	2.44853	−	1.41366i	0.118631	−	0.0684919i
$427$	3.56002	−	2.05538i	0.172281	−	0.0994667i
$428$	−5.51524	−	5.51524i	−0.266589	−	0.266589i
$429$	29.3271	−	22.8164i	1.41593	−	1.10159i
$430$	4.17722	+	0.324454i	0.201443	+	0.0156466i
$431$	−34.5325	−	9.25295i	−1.66337	−	0.445699i	−0.700060	−	0.714084i	$-0.746843\pi$
$431$	−34.5325	−	9.25295i	−1.66337	−	0.445699i	−0.963312	+	0.268385i	$0.913510\pi$
$432$	0.903577	−	3.37220i	0.0434734	−	0.162245i
$433$	25.4810	−	6.82761i	1.22454	−	0.328114i	0.412087	−	0.911144i	$-0.364800\pi$
$433$	25.4810	−	6.82761i	1.22454	−	0.328114i	0.812450	+	0.583031i	$0.198133\pi$
$434$	−0.269705	−	0.269705i	−0.0129462	−	0.0129462i
$435$	24.3979	−	35.5771i	1.16979	−	1.70579i
$436$	13.2206	−	3.54246i	0.633154	−	0.169653i
$437$		−	1.67144i		−	0.0799558i
$438$	1.02290	+	3.81750i	0.0488759	+	0.182407i
$439$	0.864675	+	1.49766i	0.0412687	+	0.0714794i	0.885922	−	0.463834i	$-0.153527\pi$
$439$	0.864675	+	1.49766i	0.0412687	+	0.0714794i	−0.844653	+	0.535314i	$0.820193\pi$
$440$	−4.53740	−	9.48786i	−0.216312	−	0.452316i
$441$		−	17.7038i		−	0.843036i
$442$	1.80059	−	0.759965i	0.0856455	−	0.0361478i
$443$	2.86737	−	2.86737i	0.136233	−	0.136233i	−0.635702	−	0.771935i	$-0.719289\pi$
$443$	2.86737	−	2.86737i	0.136233	−	0.136233i	0.771935	+	0.635702i	$0.219289\pi$
$444$	−5.67920	+	21.1951i	−0.269523	+	1.00587i
$445$	−10.0835	+	4.82225i	−0.478003	+	0.228596i
$446$	−6.50564	−	3.75603i	−0.308051	−	0.177853i
$447$	−5.98448			−0.283056
$448$	2.08788	+	1.20544i	0.0986432	+	0.0569517i
$449$	5.22508	+	19.5003i	0.246587	+	0.920274i	0.972579	+	0.232571i	$0.0747139\pi$
$449$	5.22508	+	19.5003i	0.246587	+	0.920274i	−0.725993	+	0.687702i	$0.758619\pi$
$450$	−3.50813	−	0.548277i	−0.165375	−	0.0258460i
$451$	−10.1534	+	17.5861i	−0.478103	+	0.828098i
$452$	−7.38790	−	1.97958i	−0.347497	−	0.0931117i
$453$	−4.31936	−	7.48135i	−0.202941	−	0.351505i
$454$	1.90370			0.0893452
$455$	−3.04974	−	0.623723i	−0.142974	−	0.0292406i
$456$	12.7686			0.597946
$457$	7.39079	+	12.8012i	0.345727	+	0.598816i	0.985486	−	0.169759i	$-0.0542991\pi$
$457$	7.39079	+	12.8012i	0.345727	+	0.598816i	−0.639759	+	0.768576i	$0.720966\pi$
$458$	1.71490	+	0.459507i	0.0801321	+	0.0214713i
$459$	−0.969184	+	1.67868i	−0.0452377	+	0.0783539i
$460$	−1.43129	−	0.111172i	−0.0667344	−	0.00518341i
$461$	−1.57205	−	5.86696i	−0.0732175	−	0.273252i	0.919606	−	0.392843i	$-0.128508\pi$
$461$	−1.57205	−	5.86696i	−0.0732175	−	0.273252i	−0.992823	+	0.119591i	$0.961842\pi$
$462$	0.946973	+	0.546735i	0.0440572	+	0.0254364i
$463$	−36.0148			−1.67375			−0.836874	−	0.547396i	$-0.815619\pi$
$463$	−36.0148			−1.67375			−0.836874	+	0.547396i	$0.815619\pi$
$464$	25.1179	+	14.5018i	1.16607	+	0.673230i
$465$	6.32224	−	17.9117i	0.293187	−	0.830634i
$466$	−0.552297	+	2.06120i	−0.0255847	+	0.0954833i
$467$	−7.68952	+	7.68952i	−0.355829	+	0.355829i	−0.862273	−	0.506444i	$-0.830960\pi$
$467$	−7.68952	+	7.68952i	−0.355829	+	0.355829i	0.506444	+	0.862273i	$0.330960\pi$
$468$	17.7614	−	2.45917i	0.821022	−	0.113675i
$469$		−	2.46176i		−	0.113674i
$470$	−2.01115	+	5.69783i	−0.0927673	+	0.262821i
$471$	3.70562	+	6.41832i	0.170746	+	0.295741i
$472$	−0.677511	−	2.52851i	−0.0311850	−	0.116384i
$473$		−	29.7353i		−	1.36723i
$474$	2.10099	−	0.562959i	0.0965018	−	0.0258576i
$475$	−2.66952	−	24.9083i	−0.122486	−	1.14287i
$476$	−1.03637	−	1.03637i	−0.0475019	−	0.0475019i
$477$	−25.3156	+	6.78329i	−1.15912	+	0.310586i
$478$	−0.838843	+	3.13061i	−0.0383678	+	0.143191i
$479$	8.87096	+	2.37697i	0.405324	+	0.108606i	0.455720	−	0.890123i	$-0.349382\pi$
$479$	8.87096	+	2.37697i	0.405324	+	0.108606i	−0.0503960	+	0.998729i	$0.516048\pi$
$480$	1.28208	−	16.5064i	0.0585189	−	0.753408i
$481$	17.2325	−	2.38594i	0.785733	−	0.108789i
$482$	0.283559	+	0.283559i	0.0129157	+	0.0129157i
$483$	0.263602	−	0.152191i	0.0119943	−	0.00692492i
$484$	−13.3650	+	7.71629i	−0.607500	+	0.350740i
$485$	6.04287	+	32.4192i	0.274393	+	1.47208i
$486$	4.05331	−	4.05331i	0.183862	−	0.183862i
$487$	−12.8657	+	22.2840i	−0.582998	+	1.00978i	0.412123	+	0.911128i	$0.364787\pi$
$487$	−12.8657	+	22.2840i	−0.582998	+	1.00978i	−0.995122	+	0.0986549i	$0.968546\pi$
$488$	5.74117	−	9.94399i	0.259890	−	0.450143i
$489$	24.7515	−	24.7515i	1.11930	−	1.11930i
$490$	0.771416	+	4.13855i	0.0348490	+	0.186961i
$491$	11.4291	−	6.59859i	0.515788	−	0.297790i	−0.219422	−	0.975630i	$-0.570417\pi$
$491$	11.4291	−	6.59859i	0.515788	−	0.297790i	0.735210	+	0.677840i	$0.237084\pi$
$492$	−18.3386	+	10.5878i	−0.826769	+	0.477336i
$493$	−11.3869	−	11.3869i	−0.512839	−	0.512839i
$494$	−1.93035	−	4.57360i	−0.0868504	−	0.205776i
$495$	−1.95144	+	25.1241i	−0.0877108	+	1.12924i
$496$	12.3355	+	3.30529i	0.553881	+	0.148412i
$497$	−0.435076	+	1.62373i	−0.0195158	+	0.0728341i
$498$	3.25447	−	0.872033i	0.145836	−	0.0390767i
$499$	−16.7683	−	16.7683i	−0.750650	−	0.750650i	0.223950	−	0.974601i	$-0.428105\pi$
$499$	−16.7683	−	16.7683i	−0.750650	−	0.750650i	−0.974601	+	0.223950i	$0.928105\pi$
$500$	−21.5071	+	0.629257i	−0.961829	+	0.0281412i
$501$	−7.91620	+	2.12114i	−0.353670	+	0.0947655i
$502$			3.57520i			0.159569i
$503$	1.95124	+	7.28214i	0.0870017	+	0.324695i	0.995686	−	0.0927898i	$-0.0295785\pi$
$503$	1.95124	+	7.28214i	0.0870017	+	0.324695i	−0.908684	+	0.417485i	$0.862912\pi$
$504$	0.538025	+	0.931887i	0.0239655	+	0.0415095i
$505$	3.92931	−	11.1322i	0.174852	−	0.495377i
$506$		−	0.399817i		−	0.0177740i
$507$	−15.7141	−	26.3967i	−0.697889	−	1.17232i
$508$	−15.5186	+	15.5186i	−0.688528	+	0.688528i
$509$	7.93327	−	29.6074i	0.351636	−	1.31232i	−0.533030	−	0.846097i	$-0.678947\pi$
$509$	7.93327	−	29.6074i	0.351636	−	1.31232i	0.884666	−	0.466226i	$-0.154387\pi$
$510$	−0.953331	+	2.70090i	−0.0422142	+	0.119598i
$511$	−2.03499	−	1.17490i	−0.0900225	−	0.0519745i
$512$	18.7939			0.830581
$513$	4.26392	+	2.46178i	0.188257	+	0.108690i
$514$	2.09547	+	7.82039i	0.0924271	+	0.344942i
$515$	3.81491	+	0.296312i	0.168105	+	0.0130571i
$516$	15.5039	−	26.8535i	0.682519	−	1.18216i
$517$	41.4218	+	11.0989i	1.82173	+	0.488131i
$518$	0.255979	+	0.443368i	0.0112471	+	0.0194805i
$519$	9.23923			0.405557
$520$	−8.24848	+	2.75053i	−0.361720	+	0.120619i
$521$	−7.16076			−0.313719			−0.156859	−	0.987621i	$-0.550137\pi$
$521$	−7.16076			−0.313719			−0.156859	+	0.987621i	$0.550137\pi$
$522$	2.89884	+	5.02094i	0.126879	+	0.219761i
$523$	−10.3897	−	2.78390i	−0.454308	−	0.121731i	0.0244065	−	0.999702i	$-0.492230\pi$
$523$	−10.3897	−	2.78390i	−0.454308	−	0.121731i	−0.478714	+	0.877971i	$0.658897\pi$
$524$	20.0750	−	34.7709i	0.876979	−	1.51897i
$525$	3.68521	−	2.68900i	0.160836	−	0.117358i
$526$	−0.359362	−	1.34116i	−0.0156689	−	0.0584773i
$527$	−6.14061	−	3.54528i	−0.267489	−	0.154435i
$528$	−36.6115			−1.59331
$529$	19.8222	+	11.4444i	0.861835	+	0.497581i
$530$	5.62237	−	2.68880i	0.244220	−	0.116794i
$531$	−1.62338	+	6.05854i	−0.0704487	+	0.262918i
$532$	−2.63243	+	2.63243i	−0.114130	+	0.114130i
$533$	13.3873	+	10.1311i	0.579870	+	0.438826i
$534$		−	3.24607i		−	0.140471i
$535$	−3.90990	−	8.17573i	−0.169040	−	0.353468i
$536$	−3.43815	−	5.95505i	−0.148505	−	0.257219i
$537$	−3.97399	−	14.8311i	−0.171490	−	0.640011i
$538$			2.37709i			0.102484i
$539$	28.8594	−	7.73286i	1.24306	−	0.333078i
$540$	2.39168	−	3.48756i	0.102922	−	0.150081i
$541$	11.1986	+	11.1986i	0.481464	+	0.481464i	0.905599	−	0.424135i	$-0.139422\pi$
$541$	11.1986	+	11.1986i	0.481464	+	0.481464i	−0.424135	+	0.905599i	$0.639422\pi$
$542$	−6.11306	+	1.63799i	−0.262578	+	0.0703576i
$543$	−7.32985	+	27.3554i	−0.314554	+	1.17393i
$544$	−5.96966	−	1.59957i	−0.255947	−	0.0685808i
$545$	15.8553	+	1.23152i	0.679166	+	0.0527523i
$546$	0.545536	−	0.720878i	0.0233468	−	0.0308507i
$547$	−23.6205	−	23.6205i	−1.00994	−	1.00994i	−0.999950	−	0.00999077i	$-0.996820\pi$
$547$	−23.6205	−	23.6205i	−1.00994	−	1.00994i	−0.00999077	−	0.999950i	$-0.503180\pi$
$548$	0.406578	−	0.234738i	0.0173681	−	0.0100275i
$549$	−23.8267	+	13.7564i	−1.01690	+	0.587108i
$550$	−0.638563	−	5.95820i	−0.0272284	−	0.254059i
$551$	−28.9232	+	28.9232i	−1.23217	+	1.23217i
$552$	0.425106	−	0.736305i	0.0180937	−	0.0313392i
$553$	−0.646616	+	1.11997i	−0.0274969	+	0.0476260i
$554$	−4.20528	+	4.20528i	−0.178665	+	0.178665i
$555$	−14.4193	+	21.0262i	−0.612064	+	0.892514i
$556$	−19.4732	+	11.2429i	−0.825847	+	0.476803i
$557$	26.9736	−	15.5732i	1.14291	−	0.659859i	0.195759	−	0.980652i	$-0.437283\pi$
$557$	26.9736	−	15.5732i	1.14291	−	0.659859i	0.947149	+	0.320793i	$0.103950\pi$
$558$	1.80510	+	1.80510i	0.0764159	+	0.0764159i
$559$	−24.3944	−	3.04592i	−1.03177	−	0.128829i
$560$	1.99433	+	2.33023i	0.0842759	+	0.0984702i
$561$	19.6349	+	5.26115i	0.828986	+	0.222126i
$562$	0.822517	−	3.06967i	0.0346958	−	0.129486i
$563$	−20.1348	+	5.39509i	−0.848579	+	0.227376i	−0.656802	−	0.754063i	$-0.728091\pi$
$563$	−20.1348	+	5.39509i	−0.848579	+	0.227376i	−0.191776	+	0.981439i	$0.561425\pi$
$564$	31.6204	+	31.6204i	1.33146	+	1.33146i
$565$	−7.32905	−	5.02608i	−0.308335	−	0.211449i
$566$	1.19433	−	0.320019i	0.0502013	−	0.0134514i
$567$			3.88985i			0.163359i
$568$	1.21527	+	4.53546i	0.0509918	+	0.190304i
$569$	−20.8728	−	36.1527i	−0.875031	−	1.51560i	−0.856729	−	0.515766i	$-0.827507\pi$
$569$	−20.8728	−	36.1527i	−0.875031	−	1.51560i	−0.0183019	−	0.999833i	$-0.505826\pi$
$570$	6.86043	+	2.42151i	0.287352	+	0.101426i
$571$			19.2151i			0.804127i	0.915612	+	0.402064i	$0.131707\pi$
$571$			19.2151i			0.804127i	−0.915612	+	0.402064i	$0.868293\pi$
$572$	11.7668	+	27.8793i	0.491996	+	1.16569i
$573$	−8.67709	+	8.67709i	−0.362491	+	0.362491i
$574$	−0.127872	+	0.477224i	−0.00533727	+	0.0199190i
$575$	−1.52522	−	0.675333i	−0.0636059	−	0.0281633i
$576$	−13.9739	−	8.06785i	−0.582247	−	0.336160i
$577$	−21.8168			−0.908243			−0.454122	−	0.890940i	$-0.650047\pi$
$577$	−21.8168			−0.908243			−0.454122	+	0.890940i	$0.650047\pi$
$578$	−3.11991	−	1.80128i	−0.129771	−	0.0749233i
$579$	4.08196	+	15.2341i	0.169640	+	0.633107i
$580$	22.8439	+	26.6914i	0.948542	+	1.10830i
$581$	−1.00162	+	1.73485i	−0.0415541	+	0.0719738i
$582$	−9.25095	−	2.47879i	−0.383464	−	0.102749i
$583$	−22.1153	−	38.3048i	−0.915922	−	1.58642i
$584$	−6.56356			−0.271602
$585$	20.4115	+	4.17450i	0.843912	+	0.172594i
$586$	−3.60150			−0.148777
$587$	2.92765	+	5.07084i	0.120837	+	0.209296i	0.920098	−	0.391688i	$-0.128109\pi$
$587$	2.92765	+	5.07084i	0.120837	+	0.209296i	−0.799261	+	0.600984i	$0.794775\pi$
$588$	30.0943	+	8.06375i	1.24107	+	0.332543i
$589$	−9.00520	+	15.5975i	−0.371053	+	0.642682i
$590$	0.115500	−	1.48702i	0.00475507	−	0.0612197i
$591$	11.9858	+	44.7316i	0.493030	+	1.84001i
$592$	−14.8448	−	8.57065i	−0.610118	−	0.352252i
$593$	45.6277			1.87370			0.936852	−	0.349727i	$-0.113726\pi$
$593$	45.6277			1.87370			0.936852	+	0.349727i	$0.113726\pi$
$594$	1.01995	+	0.588870i	0.0418492	+	0.0241616i
$595$	−0.734709	−	1.53630i	−0.0301201	−	0.0629823i
$596$	1.26141	−	4.70766i	0.0516695	−	0.192833i
$597$	−24.5730	+	24.5730i	−1.00571	+	1.00571i
$598$	−0.328004	−	0.0409550i	−0.0134131	−	0.00167477i
$599$		−	12.7240i		−	0.519888i	−0.965624	−	0.259944i	$-0.916296\pi$
$599$		−	12.7240i		−	0.519888i	0.965624	−	0.259944i	$-0.0837041\pi$
$600$	5.15908	−	11.6516i	0.210619	−	0.475674i
$601$	12.3636	+	21.4144i	0.504321	+	0.873510i	0.999988	+	0.00499702i	$0.00159061\pi$
$601$	12.3636	+	21.4144i	0.504321	+	0.873510i	−0.495666	+	0.868513i	$0.665076\pi$
$602$	−0.187244	−	0.698805i	−0.00763151	−	0.0284812i
$603$			16.4763i			0.670965i
$604$	6.79561	−	1.82088i	0.276510	−	0.0740905i
$605$	−17.6276	+	3.28574i	−0.716664	+	0.133584i
$606$	2.42430	+	2.42430i	0.0984804	+	0.0984804i
$607$	−4.25169	+	1.13924i	−0.172571	+	0.0462402i	−0.344070	−	0.938944i	$-0.611806\pi$
$607$	−4.25169	+	1.13924i	−0.172571	+	0.0462402i	0.171499	+	0.985184i	$0.445139\pi$
$608$	−4.06298	+	15.1632i	−0.164775	+	0.614950i
$609$	−7.19505	−	1.92791i	−0.291558	−	0.0781228i
$610$	4.97048	−	4.25400i	0.201249	−	0.172239i
$611$	13.3484	−	32.8449i	0.540019	−	1.32876i
$612$	6.93628	+	6.93628i	0.280382	+	0.280382i
$613$	−1.00509	+	0.580288i	−0.0405951	+	0.0234376i	−0.520160	−	0.854069i	$-0.674128\pi$
$613$	−1.00509	+	0.580288i	−0.0405951	+	0.0234376i	0.479565	+	0.877506i	$0.340794\pi$
$614$	1.84550	−	1.06550i	0.0744781	−	0.0430000i
$615$	−24.1875	+	4.50850i	−0.975335	+	0.181800i
$616$	−1.28409	+	1.28409i	−0.0517375	+	0.0517375i
$617$	19.2380	−	33.3212i	0.774493	−	1.34146i	−0.160587	−	0.987022i	$-0.551339\pi$
$617$	19.2380	−	33.3212i	0.774493	−	1.34146i	0.935079	−	0.354439i	$-0.115328\pi$
$618$	−0.555628	+	0.962375i	−0.0223506	+	0.0387124i
$619$	−24.7229	+	24.7229i	−0.993698	+	0.993698i	−0.999980	−	0.00628240i	$-0.998000\pi$
$619$	−24.7229	+	24.7229i	−0.993698	+	0.993698i	0.00628240	+	0.999980i	$0.498000\pi$
$620$	12.7575	+	8.74880i	0.512355	+	0.351360i
$621$	0.283917	−	0.163920i	0.0113932	−	0.00657787i
$622$	−2.76142	+	1.59431i	−0.110723	+	0.0639258i
$623$	1.36470	+	1.36470i	0.0546757	+	0.0546757i
$624$	−3.75027	+	30.0355i	−0.150131	+	1.20238i
$625$	−23.8078	−	7.62804i	−0.952313	−	0.305122i
$626$	3.81269	+	1.02161i	0.152386	+	0.0408317i
$627$	13.3636	−	49.8736i	0.533690	−	1.99176i
$628$	−5.83002	+	1.56215i	−0.232643	+	0.0623365i
$629$	6.72971	+	6.72971i	0.268331	+	0.268331i
$630$	0.112346	+	0.602725i	0.00447599	+	0.0240131i
$631$	−7.05694	+	1.89090i	−0.280933	+	0.0752756i	−0.396534	−	0.918020i	$-0.629787\pi$
$631$	−7.05694	+	1.89090i	−0.280933	+	0.0752756i	0.115601	+	0.993296i	$0.463120\pi$
$632$			3.61231i			0.143690i
$633$	−13.0972	−	48.8794i	−0.520567	−	1.94278i
$634$	−2.99110	−	5.18074i	−0.118792	−	0.205753i
$635$	−23.0047	+	11.0016i	−0.912912	+	0.436584i
$636$		−	46.1232i		−	1.82891i
$637$	−3.38773	−	24.4679i	−0.134227	−	0.969455i
$638$	−6.91860	+	6.91860i	−0.273910	+	0.273910i
$639$	2.91191	−	10.8674i	0.115193	−	0.429907i
$640$	16.8315	+	5.94098i	0.665325	+	0.234838i
$641$	−7.19858	−	4.15610i	−0.284327	−	0.164156i	0.351054	−	0.936355i	$-0.385823\pi$
$641$	−7.19858	−	4.15610i	−0.284327	−	0.164156i	−0.635381	+	0.772199i	$0.719157\pi$
$642$	2.63193			0.103874
$643$	9.66101	+	5.57779i	0.380993	+	0.219967i	0.678250	−	0.734831i	$-0.262739\pi$
$643$	9.66101	+	5.57779i	0.380993	+	0.219967i	−0.297257	+	0.954797i	$0.596072\pi$
$644$	0.0641579	+	0.239440i	0.00252817	+	0.00943528i
$645$	27.3720	−	23.4264i	1.07777	−	0.922414i
$646$	1.35789	−	2.35194i	0.0534257	−	0.0925360i
$647$	40.6647	+	10.8961i	1.59870	+	0.428369i	0.944648	−	0.328085i	$-0.106403\pi$
$647$	40.6647	+	10.8961i	1.59870	+	0.428369i	0.654047	+	0.756454i	$0.273070\pi$
$648$	5.43265	+	9.40963i	0.213415	+	0.369645i
$649$	−10.5853			−0.415509
$650$	−4.95343	−	0.0864561i	−0.194289	−	0.00339109i
$651$	−3.27983			−0.128547
$652$	14.2535	+	24.6878i	0.558211	+	0.966849i
$653$	41.2678	+	11.0577i	1.61494	+	0.432721i	0.949508	−	0.313742i	$-0.101583\pi$
$653$	41.2678	+	11.0577i	1.61494	+	0.432721i	0.665427	+	0.746463i	$0.268250\pi$
$654$	−2.30926	+	3.99976i	−0.0902994	+	0.156403i
$655$	35.4423	−	30.3334i	1.38485	−	1.18522i
$656$	−4.28140	−	15.9784i	−0.167160	−	0.623851i
$657$	13.6199	+	7.86345i	0.531363	+	0.306782i
$658$	1.04334			0.0406735
$659$	−15.2491	−	8.80408i	−0.594021	−	0.342958i	0.172665	−	0.984981i	$-0.444762\pi$
$659$	−15.2491	−	8.80408i	−0.594021	−	0.342958i	−0.766686	+	0.642023i	$0.778096\pi$
$660$	−41.8191	−	14.7608i	−1.62781	−	0.574563i
$661$	7.21232	−	26.9167i	0.280527	−	1.04694i	−0.671520	−	0.740987i	$-0.734358\pi$
$661$	7.21232	−	26.9167i	0.280527	−	1.04694i	0.952047	−	0.305953i	$-0.0989751\pi$
$662$	−3.81246	+	3.81246i	−0.148175	+	0.148175i
$663$	6.32746	−	15.5692i	0.245738	−	0.604659i
$664$			5.59552i			0.217148i
$665$	−3.90228	+	1.86620i	−0.151324	+	0.0723680i
$666$	−1.71323	−	2.96740i	−0.0663863	−	0.114985i
$667$	0.704922	+	2.63080i	0.0272947	+	0.101865i
$668$		−	6.67434i		−	0.258238i
$669$	−62.3951	+	16.7187i	−2.41234	+	0.646383i
$670$	−0.717929	−	3.85160i	−0.0277360	−	0.148800i
$671$	−32.8320	−	32.8320i	−1.26747	−	1.26747i
$672$	−2.76134	+	0.739899i	−0.106521	+	0.0285422i
$673$	1.89027	−	7.05459i	0.0728646	−	0.271934i	−0.919876	−	0.392209i	$-0.871711\pi$
$673$	1.89027	−	7.05459i	0.0728646	−	0.271934i	0.992741	+	0.120275i	$0.0383776\pi$
$674$	−3.51350	−	0.941440i	−0.135335	−	0.0362629i
$675$	3.96922	−	2.89624i	0.152775	−	0.111476i
$676$	24.0771	−	6.79753i	0.926042	−	0.261444i
$677$	3.26988	+	3.26988i	0.125672	+	0.125672i	0.767145	−	0.641473i	$-0.221677\pi$
$677$	3.26988	+	3.26988i	0.125672	+	0.125672i	−0.641473	+	0.767145i	$0.721677\pi$
$678$	2.23513	−	1.29045i	0.0858397	−	0.0495595i
$679$	4.93138	−	2.84713i	0.189249	−	0.109263i
$680$	−3.92291	−	2.69023i	−0.150437	−	0.103166i
$681$	11.5753	−	11.5753i	0.443566	−	0.443566i
$682$	−2.15409	+	3.73100i	−0.0824845	+	0.142867i
$683$	13.5476	−	23.4651i	0.518384	−	0.897868i	−0.481388	−	0.876508i	$-0.659867\pi$
$683$	13.5476	−	23.4651i	0.518384	−	0.897868i	0.999772	−	0.0213600i	$-0.00679961\pi$
$684$	17.6185	−	17.6185i	0.673660	−	0.673660i
$685$	0.536251	−	0.0999559i	0.0204891	−	0.00381912i
$686$	1.27275	−	0.734823i	0.0485939	−	0.0280557i
$687$	13.2213	−	7.63332i	0.504424	−	0.291229i
$688$	17.1280	+	17.1280i	0.653000	+	0.653000i
$689$	−33.6901	+	14.2193i	−1.28349	+	0.541714i
$690$	0.368040	−	0.314988i	0.0140111	−	0.0119914i
$691$	−12.1374	−	3.25221i	−0.461729	−	0.123720i	0.0204532	−	0.999791i	$-0.493489\pi$
$691$	−12.1374	−	3.25221i	−0.461729	−	0.123720i	−0.482182	+	0.876071i	$0.660156\pi$
$692$	−1.94746	+	7.26800i	−0.0740311	+	0.276288i
$693$	4.20299	−	1.12619i	0.159658	−	0.0427804i
$694$	−5.37339	−	5.37339i	−0.203971	−	0.203971i
$695$	−25.6839	+	4.78743i	−0.974247	+	0.181597i
$696$	−20.0975	+	5.38511i	−0.761795	+	0.204122i
$697$			9.18452i			0.347889i
$698$	−2.09942	−	7.83515i	−0.0794643	−	0.296565i
$699$	9.17475	+	15.8911i	0.347021	+	0.601058i
$700$	1.33852	+	3.46575i	0.0505913	+	0.130993i
$701$			39.3955i			1.48795i	0.668208	+	0.743974i	$0.267062\pi$
$701$			39.3955i			1.48795i	−0.668208	+	0.743974i	$0.732938\pi$
$702$	0.587578	−	0.776434i	0.0221767	−	0.0293046i
$703$	17.0938	−	17.0938i	0.644705	−	0.644705i
$704$	7.04795	−	26.3033i	0.265630	−	0.991343i
$705$	22.4165	+	46.8737i	0.844255	+	1.76537i
$706$	3.72112	+	2.14839i	0.140046	+	0.0808557i
$707$	−2.03843			−0.0766631
$708$	−9.55939	−	5.51911i	−0.359264	−	0.207421i
$709$	6.62303	+	24.7175i	0.248733	+	0.928285i	0.971470	+	0.237162i	$0.0762171\pi$
$709$	6.62303	+	24.7175i	0.248733	+	0.928285i	−0.722737	+	0.691123i	$0.757116\pi$
$710$	−0.207176	+	2.66732i	−0.00777519	+	0.100103i
$711$	4.32771	−	7.49582i	0.162302	−	0.281115i
$712$	5.20722	+	1.39527i	0.195149	+	0.0522900i
$713$	0.599619	+	1.03857i	0.0224559	+	0.0388948i
$714$	0.494566			0.0185087
$715$	2.11061	+	35.0968i	0.0789324	+	1.31255i
$716$	12.5045			0.467315
$717$	13.9349	+	24.1359i	0.520407	+	0.901371i
$718$	5.27777	+	1.41417i	0.196965	+	0.0527765i
$719$	−4.34268	+	7.52174i	−0.161955	+	0.280514i	−0.935570	−	0.353142i	$-0.885113\pi$
$719$	−4.34268	+	7.52174i	−0.161955	+	0.280514i	0.773615	+	0.633656i	$0.218446\pi$
$720$	−13.3478	−	15.5959i	−0.497443	−	0.581226i
$721$	−0.171004	−	0.638194i	−0.00636851	−	0.0237676i
$722$	−1.45222	−	0.838438i	−0.0540460	−	0.0312034i
$723$	3.44830			0.128244
$724$	−19.9740	−	11.5320i	−0.742327	−	0.428583i
$725$	14.7067	+	38.0792i	0.546194	+	1.41423i
$726$	1.34781	−	5.03011i	0.0500220	−	0.186685i
$727$	17.4677	−	17.4677i	0.647841	−	0.647841i	−0.304630	−	0.952471i	$-0.598533\pi$
$727$	17.4677	−	17.4677i	0.647841	−	0.647841i	0.952471	+	0.304630i	$0.0985327\pi$
$728$	0.921915	+	1.18498i	0.0341684	+	0.0439184i
$729$		−	19.0676i		−	0.706209i
$730$	−3.52652	−	1.24475i	−0.130522	−	0.0460701i
$731$	−6.72450	−	11.6472i	−0.248715	−	0.430786i
$732$	−12.5316	−	46.7685i	−0.463180	−	1.72861i
$733$			34.2413i			1.26473i	0.774670	+	0.632365i	$0.217916\pi$
$733$			34.2413i			1.26473i	−0.774670	+	0.632365i	$0.782084\pi$
$734$	5.84646	−	1.56655i	0.215797	−	0.0578225i
$735$	29.8546	+	20.4735i	1.10120	+	0.755178i
$736$	0.739121	+	0.739121i	0.0272444	+	0.0272444i
$737$	−26.8584	+	7.19670i	−0.989344	+	0.265094i
$738$	0.855830	−	3.19400i	0.0315035	−	0.117573i
$739$	27.2869	+	7.31150i	1.00376	+	0.268958i	0.723022	−	0.690825i	$-0.242753\pi$
$739$	27.2869	+	7.31150i	1.00376	+	0.268958i	0.280743	+	0.959783i	$0.409419\pi$
$740$	−13.5009	−	15.7748i	−0.496302	−	0.579893i
$741$	−39.5467	−	16.0720i	−1.45278	−	0.590421i
$742$	−0.760935	−	0.760935i	−0.0279348	−	0.0279348i
$743$	−27.4329	+	15.8384i	−1.00642	+	0.581055i	−0.910141	−	0.414299i	$-0.864027\pi$
$743$	−27.4329	+	15.8384i	−1.00642	+	0.581055i	−0.0962765	+	0.995355i	$0.530693\pi$
$744$	−7.93397	+	4.58068i	−0.290873	+	0.167936i
$745$	3.20268	−	4.67016i	0.117337	−	0.171101i
$746$	−0.226489	+	0.226489i	−0.00829237	+	0.00829237i
$747$	6.70370	−	11.6111i	0.245275	−	0.424830i
$748$	−8.27733	+	14.3367i	−0.302649	+	0.524203i
$749$	−1.10651	+	1.10651i	−0.0404309	+	0.0404309i
$750$	4.98157	−	5.28186i	0.181901	−	0.192866i
$751$	2.11351	−	1.22024i	0.0771231	−	0.0445271i	−0.460943	−	0.887430i	$-0.652489\pi$
$751$	2.11351	−	1.22024i	0.0771231	−	0.0445271i	0.538066	+	0.842903i	$0.319155\pi$
$752$	−30.2528	+	17.4665i	−1.10321	+	0.636936i
$753$	21.7387	+	21.7387i	0.792201	+	0.792201i
$754$	4.96721	+	6.38462i	0.180895	+	0.232514i
$755$	8.14986	+	0.633018i	0.296604	+	0.0230379i
$756$	−0.705319	−	0.188990i	−0.0256522	−	0.00687349i
$757$	11.0493	−	41.2367i	0.401595	−	1.49877i	−0.408655	−	0.912689i	$-0.634002\pi$
$757$	11.0493	−	41.2367i	0.401595	−	1.49877i	0.810250	−	0.586084i	$-0.199331\pi$
$758$	7.00115	−	1.87595i	0.254293	−	0.0681377i
$759$	−2.43105	−	2.43105i	−0.0882416	−	0.0882416i
$760$	−6.83333	+	9.96438i	−0.247871	+	0.361446i
$761$	−38.5996	+	10.3427i	−1.39923	+	0.374923i	−0.878069	−	0.478533i	$-0.841169\pi$
$761$	−38.5996	+	10.3427i	−1.39923	+	0.374923i	−0.521164	+	0.853457i	$0.674502\pi$
$762$		−	7.40565i		−	0.268279i
$763$	−0.710715	−	2.65242i	−0.0257296	−	0.0960242i
$764$	−4.99683	−	8.65476i	−0.180779	−	0.313118i
$765$	4.91731	+	10.2823i	0.177786	+	0.371756i
$766$		−	9.01376i		−	0.325680i
$767$	−1.08429	+	8.68401i	−0.0391516	+	0.313561i
$768$	17.2018	−	17.2018i	0.620716	−	0.620716i
$769$	9.91969	−	37.0208i	0.357713	−	1.33500i	−0.519322	−	0.854579i	$-0.673816\pi$
$769$	9.91969	−	37.0208i	0.357713	−	1.33500i	0.877035	−	0.480426i	$-0.159518\pi$
$770$	−0.933448	+	0.446405i	−0.0336391	+	0.0160873i
$771$	60.2925	+	34.8099i	2.17138	+	1.25365i
$772$	−12.8442			−0.462274
$773$	−12.6256	−	7.28940i	−0.454111	−	0.262181i	0.255454	−	0.966821i	$-0.417775\pi$
$773$	−12.6256	−	7.28940i	−0.454111	−	0.262181i	−0.709565	+	0.704640i	$0.751109\pi$
$774$	1.25320	+	4.67701i	0.0450454	+	0.168112i
$775$	10.5945	+	14.5194i	0.380564	+	0.521553i
$776$	7.95274	−	13.7745i	0.285487	−	0.494477i
$777$	4.25231	+	1.13940i	0.152551	+	0.0408759i
$778$	1.28724	+	2.22956i	0.0461497	+	0.0799337i
$779$	23.3291			0.835853
$780$	−16.3932	+	32.7958i	−0.586972	+	1.17428i
$781$	18.9872			0.679414
$782$	−0.0904167	−	0.156606i	−0.00323329	−	0.00560023i
$783$	−7.74955	−	2.07649i	−0.276946	−	0.0742075i
$784$	−12.1692	+	21.0777i	−0.434616	+	0.752777i
$785$	−6.99184	−	0.543072i	−0.249549	−	0.0193831i
$786$	3.50652	+	13.0865i	0.125073	+	0.466780i
$787$	−0.820823	−	0.473902i	−0.0292592	−	0.0168928i	0.485299	−	0.874348i	$-0.338711\pi$
$787$	−0.820823	−	0.473902i	−0.0292592	−	0.0168928i	−0.514558	+	0.857455i	$0.672044\pi$
$788$	−37.7143			−1.34352
$789$	−10.3399	−	5.96972i	−0.368109	−	0.212528i
$790$	−0.685056	+	1.94085i	−0.0243732	+	0.0690522i
$791$	−0.397158	+	1.48222i	−0.0141213	+	0.0527015i
$792$	8.59426	−	8.59426i	0.305384	−	0.305384i
$793$	−30.2980	+	23.5718i	−1.07591	+	0.837058i
$794$		−	3.20207i		−	0.113637i
$795$	17.8373	−	50.5353i	0.632625	−	1.79230i
$796$	−14.1507	−	24.5098i	−0.501560	−	0.868727i
$797$	−1.21053	−	4.51774i	−0.0428790	−	0.160027i	0.941167	−	0.337943i	$-0.109731\pi$
$797$	−1.21053	−	4.51774i	−0.0428790	−	0.160027i	−0.984046	+	0.177916i	$0.943064\pi$
$798$		−	1.25622i		−	0.0444698i
$799$	18.7347	−	5.01994i	0.662785	−	0.177593i
$800$	12.1951	+	9.83413i	0.431161	+	0.347689i
$801$	−9.13379	−	9.13379i	−0.322726	−	0.322726i
$802$	5.47260	−	1.46638i	0.193244	−	0.0517796i
$803$	−6.86939	+	25.6369i	−0.242415	+	0.904707i
$804$	−28.0077	−	7.50465i	−0.987756	−	0.264668i
$805$	−0.0223041	+	0.287157i	−0.000786117	+	0.0101210i
$806$	2.84020	+	2.14937i	0.100042	+	0.0757082i
$807$	14.4537	+	14.4537i	0.508794	+	0.508794i
$808$	−4.93101	+	2.84692i	−0.173472	+	0.100154i
$809$	−21.1627	+	12.2183i	−0.744040	+	0.429572i	−0.823536	−	0.567263i	$-0.808002\pi$
$809$	−21.1627	+	12.2183i	−0.744040	+	0.429572i	0.0794964	+	0.996835i	$0.474669\pi$
$810$	1.13441	+	6.08595i	0.0398590	+	0.213838i
$811$	−9.34795	+	9.34795i	−0.328251	+	0.328251i	−0.851921	−	0.523670i	$-0.824562\pi$
$811$	−9.34795	+	9.34795i	−0.328251	+	0.328251i	0.523670	+	0.851921i	$0.324562\pi$
$812$	3.03316	−	5.25359i	0.106443	−	0.184365i
$813$	−27.2103	+	47.1295i	−0.954305	+	1.65291i
$814$	4.08893	−	4.08893i	0.143317	−	0.143317i
$815$	6.06942	+	32.5617i	0.212603	+	1.14059i
$816$	−14.3405	+	8.27951i	−0.502019	+	0.289841i
$817$	−29.5844	+	17.0806i	−1.03503	+	0.597573i
$818$	0.885667	+	0.885667i	0.0309666	+	0.0309666i
$819$	−0.493378	−	3.56343i	−0.0172400	−	0.124516i
$820$	1.55168	−	19.9773i	0.0541871	−	0.697638i
$821$	−1.89876	−	0.508771i	−0.0662672	−	0.0177562i	0.225533	−	0.974236i	$-0.427588\pi$
$821$	−1.89876	−	0.508771i	−0.0662672	−	0.0177562i	−0.291800	+	0.956479i	$0.594254\pi$
$822$	−0.0410019	+	0.153021i	−0.00143011	+	0.00533723i
$823$	15.8846	−	4.25627i	0.553703	−	0.148364i	0.0288913	−	0.999583i	$-0.490802\pi$
$823$	15.8846	−	4.25627i	0.553703	−	0.148364i	0.524812	+	0.851218i	$0.324136\pi$
$824$	−1.30498	−	1.30498i	−0.0454610	−	0.0454610i
$825$	−40.1110	−	32.3456i	−1.39649	−	1.12613i
$826$	−0.248763	+	0.0666558i	−0.00865557	+	0.00231925i
$827$			27.3262i			0.950225i	0.879925	+	0.475113i	$0.157593\pi$
$827$			27.3262i			0.950225i	−0.879925	+	0.475113i	$0.842407\pi$
$828$	−0.429400	−	1.60254i	−0.0149227	−	0.0556922i
$829$	−7.27764	−	12.6052i	−0.252763	−	0.437798i	0.711523	−	0.702663i	$-0.248006\pi$
$829$	−7.27764	−	12.6052i	−0.252763	−	0.437798i	−0.964286	+	0.264865i	$0.914673\pi$
$830$	−1.06116	+	3.00640i	−0.0368335	+	0.104354i
$831$			51.1397i			1.77402i
$832$	−20.8569	−	8.47639i	−0.723082	−	0.293866i
$833$	9.55534	−	9.55534i	0.331073	−	0.331073i
$834$	1.96380	−	7.32901i	0.0680009	−	0.253783i
$835$	2.58118	−	7.31279i	0.0893254	−	0.253070i
$836$	36.4161	+	21.0248i	1.25948	+	0.727159i
$837$	−3.53259			−0.122104
$838$	0.155181	+	0.0895937i	0.00536063	+	0.00309496i
$839$	6.33030	+	23.6250i	0.218546	+	0.815625i	0.984888	+	0.173192i	$0.0554082\pi$
$839$	6.33030	+	23.6250i	0.218546	+	0.815625i	−0.766342	+	0.642433i	$0.777925\pi$
$840$	−2.19368	−	0.170388i	−0.0756892	−	0.00587895i
$841$	18.8262	−	32.6080i	0.649180	−	1.12441i
$842$	2.09506	+	0.561370i	0.0722006	+	0.0193461i
$843$	−13.6636	−	23.6661i	−0.470601	−	0.815104i
$844$	41.2114			1.41856
$845$	29.0091	+	1.86360i	0.997943	+	0.0641097i
$846$	−6.98292			−0.240078
$847$	1.54810	+	2.68139i	0.0531933	+	0.0921335i
$848$	34.8030	+	9.32543i	1.19514	+	0.320237i
$849$	5.31615	−	9.20784i	0.182450	−	0.316012i
$850$	−1.59754	−	2.18939i	−0.0547951	−	0.0750954i
$851$	−0.416612	−	1.55482i	−0.0142813	−	0.0532985i
$852$	17.1470	+	9.89982i	0.587446	+	0.339162i
$853$	2.94669			0.100893			0.0504464	−	0.998727i	$-0.483936\pi$
$853$	2.94669			0.100893			0.0504464	+	0.998727i	$0.483936\pi$
$854$	−0.978324	−	0.564835i	−0.0334775	−	0.0193283i
$855$	26.1175	−	12.4902i	0.893199	−	0.427156i
$856$	−1.13129	+	4.22204i	−0.0386667	+	0.144306i
$857$	13.0632	−	13.0632i	0.446229	−	0.446229i	−0.447870	−	0.894099i	$-0.647817\pi$
$857$	13.0632	−	13.0632i	0.446229	−	0.446229i	0.894099	+	0.447870i	$0.147817\pi$
$858$	−9.45978	−	3.84452i	−0.322951	−	0.131250i
$859$		−	3.08382i		−	0.105219i	−0.998615	−	0.0526093i	$-0.983246\pi$
$859$		−	3.08382i		−	0.105219i	0.998615	−	0.0526093i	$-0.0167538\pi$
$860$	12.6588	+	26.4699i	0.431660	+	0.902617i
$861$	2.12421	+	3.67923i	0.0723928	+	0.125388i
$862$	2.54279	+	9.48982i	0.0866078	+	0.323225i
$863$		−	50.9818i		−	1.73544i	−0.497053	−	0.867720i	$-0.665585\pi$
$863$		−	50.9818i		−	1.73544i	0.497053	−	0.867720i	$-0.334415\pi$
$864$	−2.97415	+	0.796920i	−0.101183	+	0.0271118i
$865$	−4.94451	+	7.21011i	−0.168118	+	0.245151i
$866$	−5.12611	−	5.12611i	−0.174192	−	0.174192i
$867$	−29.9228	+	8.01780i	−1.01623	+	0.272299i
$868$	0.691326	−	2.58006i	0.0234651	−	0.0875730i
$869$	14.1095	+	3.78062i	0.478631	+	0.128249i
$870$	−11.8194	−	0.918039i	−0.400715	−	0.0311244i
$871$	3.15284	+	22.7715i	0.106830	+	0.771581i
$872$	−5.42366	−	5.42366i	−0.183668	−	0.183668i
$873$	−33.0051	+	19.0555i	−1.11705	+	0.644931i
$874$	−0.397788	+	0.229663i	−0.0134554	+	0.00776846i
$875$	0.126246	+	4.31492i	0.00426790	+	0.145871i
$876$	−19.5706	+	19.5706i	−0.661228	+	0.661228i
$877$	13.3844	−	23.1824i	0.451958	−	0.782814i	−0.546550	−	0.837427i	$-0.684059\pi$
$877$	13.3844	−	23.1824i	0.451958	−	0.782814i	0.998508	+	0.0546128i	$0.0173924\pi$
$878$	0.237620	−	0.411570i	0.00801929	−	0.0138898i
$879$	−21.8986	+	21.8986i	−0.738621	+	0.738621i
$880$	19.5932	−	28.5708i	0.660486	−	0.963123i
$881$	27.2630	−	15.7403i	0.918512	−	0.530303i	0.0353521	−	0.999375i	$-0.488745\pi$
$881$	27.2630	−	15.7403i	0.918512	−	0.530303i	0.883160	+	0.469072i	$0.155411\pi$
$882$	−4.21334	+	2.43257i	−0.141870	+	0.0819089i
$883$	−27.3576	−	27.3576i	−0.920657	−	0.920657i	0.0764191	−	0.997076i	$-0.475651\pi$
$883$	−27.3576	−	27.3576i	−0.920657	−	0.920657i	−0.997076	+	0.0764191i	$0.975651\pi$
$884$	10.9138	+	8.25917i	0.367070	+	0.277786i
$885$	−8.33941	−	9.74398i	−0.280326	−	0.327540i
$886$	−1.07640	−	0.288420i	−0.0361623	−	0.00968965i
$887$	−0.355489	+	1.32670i	−0.0119362	+	0.0445463i	−0.971637	−	0.236477i	$-0.924007\pi$
$887$	−0.355489	+	1.32670i	−0.0119362	+	0.0445463i	0.959701	+	0.281023i	$0.0906739\pi$
$888$	11.8777	−	3.18263i	0.398591	−	0.106802i
$889$	3.11346	+	3.11346i	0.104422	+	0.104422i
$890$	2.53317	+	1.73718i	0.0849120	+	0.0582305i
$891$	42.4393	−	11.3716i	1.42177	−	0.380962i
$892$		−	52.6068i		−	1.76141i
$893$	−12.7509	−	47.5870i	−0.426692	−	1.59244i
$894$	0.822293	+	1.42425i	0.0275016	+	0.0476341i
$895$	13.7007	+	4.83589i	0.457962	+	0.161646i
$896$		−	3.08204i		−	0.102964i
$897$	−2.24342	+	1.74538i	−0.0749057	+	0.0582764i
$898$	3.92294	−	3.92294i	0.130910	−	0.130910i
$899$	7.59580	−	28.3479i	0.253334	−	0.945456i
$900$	−8.95854	−	23.1958i	−0.298618	−	0.773193i
$901$	−17.3249	−	10.0025i	−0.577176	−	0.333233i
$902$	5.58046			0.185809
$903$	−5.38754	−	3.11050i	−0.179286	−	0.103511i
$904$	1.10936	+	4.14019i	0.0368968	+	0.137701i
$905$	−17.4249	−	20.3597i	−0.579223	−	0.676779i
$906$	−1.18700	+	2.05594i	−0.0394354	+	0.0683040i
$907$	−22.4903	−	6.02625i	−0.746777	−	0.200098i	−0.134689	−	0.990888i	$-0.543004\pi$
$907$	−22.4903	−	6.02625i	−0.746777	−	0.200098i	−0.612088	+	0.790790i	$0.709670\pi$
$908$	6.66580	+	11.5455i	0.221212	+	0.383151i
$909$	13.6430			0.452508
$910$	0.270607	+	0.811513i	0.00897053	+	0.0269014i
$911$	2.89704			0.0959832			0.0479916	−	0.998848i	$-0.484718\pi$
$911$	2.89704			0.0959832			0.0479916	+	0.998848i	$0.484718\pi$
$912$	21.0304	+	36.4256i	0.696385	+	1.20617i
$913$	21.8558	+	5.85624i	0.723322	+	0.193813i
$914$	2.03105	−	3.51789i	0.0671813	−	0.116361i
$915$	4.35653	−	56.0886i	0.144022	−	1.85423i
$916$	3.21792	+	12.0094i	0.106323	+	0.396803i
$917$	−6.97599	−	4.02759i	−0.230368	−	0.133003i
$918$	0.532680			0.0175811
$919$	14.3846	+	8.30494i	0.474503	+	0.273955i	0.718123	−	0.695916i	$-0.245002\pi$
$919$	14.3846	+	8.30494i	0.474503	+	0.273955i	−0.243620	+	0.969871i	$0.578335\pi$
$920$	0.347095	+	0.725788i	0.0114434	+	0.0239285i
$921$	4.74271	−	17.7000i	0.156278	−	0.583236i
$922$	−1.18028	+	1.18028i	−0.0388704	+	0.0388704i
$923$	1.94494	−	15.5768i	0.0640183	−	0.512716i
$924$			7.65756i			0.251915i
$925$	−8.69174	−	22.5050i	−0.285783	−	0.739960i
$926$	4.94858	+	8.57120i	0.162621	+	0.281667i
$927$	1.14451	+	4.27135i	0.0375905	+	0.140290i
$928$		−	25.5801i		−	0.839708i
$929$	−41.3672	+	11.0843i	−1.35721	+	0.363664i	−0.862792	−	0.505559i	$-0.831286\pi$
$929$	−41.3672	+	11.0843i	−1.35721	+	0.363664i	−0.494420	+	0.869223i	$0.664620\pi$
$930$	−5.13152	+	0.956504i	−0.168269	+	0.0313650i
$931$	−24.2710	−	24.2710i	−0.795451	−	0.795451i
$932$	−14.4346	+	3.86773i	−0.472820	+	0.126692i
$933$	−7.09653	+	26.4846i	−0.232330	+	0.867067i
$934$	2.88661	+	0.773465i	0.0944528	+	0.0253086i
$935$	−14.6136	+	12.5071i	−0.477916	+	0.409025i
$936$	−6.17025	−	7.93095i	−0.201681	−	0.259231i
$937$	27.9881	+	27.9881i	0.914331	+	0.914331i	0.996609	−	0.0822783i	$-0.0262196\pi$
$937$	27.9881	+	27.9881i	0.914331	+	0.914331i	−0.0822783	+	0.996609i	$0.526220\pi$
$938$	−0.585878	+	0.338257i	−0.0191296	+	0.0110445i
$939$	29.3945	−	16.9709i	0.959254	−	0.553826i
$940$	−41.5980	+	7.75377i	−1.35678	+	0.252900i
$941$	−4.15042	+	4.15042i	−0.135300	+	0.135300i	−0.771513	−	0.636213i	$-0.780500\pi$
$941$	−4.15042	+	4.15042i	−0.135300	+	0.135300i	0.636213	+	0.771513i	$0.280500\pi$
$942$	1.01834	−	1.76381i	0.0331792	−	0.0574680i
$943$	0.776696	−	1.34528i	0.0252927	−	0.0438083i
$944$	6.09729	−	6.09729i	0.198450	−	0.198450i
$945$	−0.699701	−	0.479837i	−0.0227613	−	0.0156091i
$946$	−7.07675	+	4.08576i	−0.230085	+	0.132840i
$947$	−21.5292	+	12.4299i	−0.699606	+	0.403918i	−0.807201	−	0.590277i	$-0.799018\pi$
$947$	−21.5292	+	12.4299i	−0.699606	+	0.403918i	0.107595	+	0.994195i	$0.465685\pi$
$948$	10.7708	+	10.7708i	0.349820	+	0.349820i
$949$	20.3285	+	8.26164i	0.659890	+	0.268184i
$950$	−5.56115	+	4.05783i	−0.180428	+	0.131653i
$951$	−49.6881	−	13.3139i	−1.61125	−	0.431732i
$952$	−0.212581	+	0.793363i	−0.00688979	+	0.0257130i
$953$	31.5904	−	8.46463i	1.02331	−	0.274196i	0.292131	−	0.956378i	$-0.405636\pi$
$953$	31.5904	−	8.46463i	1.02331	−	0.274196i	0.731182	+	0.682182i	$0.238969\pi$
$954$	5.09284	+	5.09284i	0.164887	+	0.164887i
$955$	−2.12775	−	11.4151i	−0.0688523	−	0.369384i
$956$	−21.9236	+	5.87441i	−0.709059	+	0.189992i
$957$			84.1358i			2.71973i
$958$	−0.653211	−	2.43782i	−0.0211043	−	0.0787622i
$959$	−0.0470949	−	0.0815707i	−0.00152077	−	0.00263405i
$960$	29.7653	−	14.2347i	0.960672	−	0.459424i
$961$			18.0777i			0.583153i
$962$	−2.93565	−	3.77334i	−0.0946491	−	0.121657i
$963$	7.40571	−	7.40571i	0.238646	−	0.238646i
$964$	−0.726837	+	2.71259i	−0.0234098	+	0.0873667i
$965$	−14.0729	−	4.96727i	−0.453022	−	0.159902i
$966$	−0.0724402	−	0.0418234i	−0.00233072	−	0.00134564i
$967$	30.0090			0.965023			0.482512	−	0.875890i	$-0.339725\pi$
$967$	30.0090			0.965023			0.482512	+	0.875890i	$0.339725\pi$
$968$	7.48976	+	4.32422i	0.240730	+	0.138986i
$969$	−6.04422	−	22.5573i	−0.194168	−	0.724646i
$970$	6.88518	−	5.89269i	0.221070	−	0.189203i
$971$	3.13659	−	5.43273i	0.100658	−	0.174345i	−0.811298	−	0.584633i	$-0.801239\pi$
$971$	3.13659	−	5.43273i	0.100658	−	0.174345i	0.911956	+	0.410288i	$0.134572\pi$
$972$	38.7750	+	10.3897i	1.24371	+	0.333251i
$973$	2.25563	+	3.90686i	0.0723120	+	0.125248i
$974$	7.07119			0.226575
$975$	−30.6446	+	29.5932i	−0.981411	+	0.947740i
$976$	37.8235			1.21070
$977$	7.78106	+	13.4772i	0.248938	+	0.431174i	0.963231	−	0.268673i	$-0.0865851\pi$
$977$	7.78106	+	13.4772i	0.248938	+	0.431174i	−0.714293	+	0.699847i	$0.753252\pi$
$978$	−9.29160	−	2.48968i	−0.297113	−	0.0796111i
$979$	10.8997	−	18.8788i	0.348356	−	0.603370i
$980$	−22.3982	+	19.1695i	−0.715484	+	0.612349i
$981$	4.75672	+	17.7523i	0.151870	+	0.566788i
$982$	−3.14082	−	1.81335i	−0.100227	−	0.0578663i
$983$	53.4558			1.70498			0.852488	−	0.522746i	$-0.175093\pi$
$983$	53.4558			1.70498			0.852488	+	0.522746i	$0.175093\pi$
$984$	10.2770	+	5.93342i	0.327619	+	0.189151i
$985$	−41.3220	−	14.5853i	−1.31663	−	0.464727i
$986$	−1.14537	+	4.27459i	−0.0364761	+	0.136131i
$987$	6.34391	−	6.34391i	0.201929	−	0.201929i
$988$	20.9787	−	27.7215i	0.667421	−	0.881939i
$989$			2.27465i			0.0723297i
$990$	6.24744	−	2.98773i	0.198557	−	0.0949562i
$991$	11.8198	+	20.4726i	0.375470	+	0.650333i	0.990397	−	0.138251i	$-0.0441480\pi$
$991$	11.8198	+	20.4726i	0.375470	+	0.650333i	−0.614927	+	0.788584i	$0.710815\pi$
$992$	−2.91514	−	10.8795i	−0.0925558	−	0.345423i
$993$			46.3626i			1.47127i
$994$	0.446214	−	0.119563i	0.0141531	−	0.00379230i
$995$	−6.02566	−	32.3269i	−0.191026	−	1.02483i
$996$	16.6842	+	16.6842i	0.528658	+	0.528658i
$997$	−49.9653	+	13.3882i	−1.58242	+	0.424007i	−0.939673	−	0.342075i	$-0.888870\pi$
$997$	−49.9653	+	13.3882i	−1.58242	+	0.424007i	−0.642743	+	0.766082i	$0.722204\pi$
$998$	−1.68667	+	6.29473i	−0.0533905	+	0.199256i
$999$	4.58002	+	1.22721i	0.144906	+	0.0388273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.o.a.2.4	✓	20
3.2	odd	2		585.2.cf.a.262.2		20
5.2	odd	4		325.2.x.b.93.2		20
5.3	odd	4		65.2.t.a.28.4	yes	20
5.4	even	2		325.2.s.b.132.2		20
13.2	odd	12		845.2.f.d.437.6		20
13.3	even	3		845.2.k.e.577.5		20
13.4	even	6		845.2.o.f.357.2		20
13.5	odd	4		845.2.t.e.427.4		20
13.6	odd	12		845.2.t.g.657.2		20
13.7	odd	12		65.2.t.a.7.4	yes	20
13.8	odd	4		845.2.t.f.427.2		20
13.9	even	3		845.2.o.e.357.4		20
13.10	even	6		845.2.k.d.577.6		20
13.11	odd	12		845.2.f.e.437.5		20
13.12	even	2		845.2.o.g.587.2		20
15.8	even	4		585.2.dp.a.28.2		20
39.20	even	12		585.2.dp.a.397.2		20
65.3	odd	12		845.2.f.e.408.6		20
65.7	even	12		325.2.s.b.293.2		20
65.8	even	4		845.2.o.e.258.4		20
65.18	even	4		845.2.o.f.258.2		20
65.23	odd	12		845.2.f.d.408.5		20
65.28	even	12		845.2.k.d.268.6		20
65.33	even	12	inner	65.2.o.a.33.4	yes	20
65.38	odd	4		845.2.t.g.418.2		20
65.43	odd	12		845.2.t.e.188.4		20
65.48	odd	12		845.2.t.f.188.2		20
65.58	even	12		845.2.o.g.488.2		20
65.59	odd	12		325.2.x.b.7.2		20
65.63	even	12		845.2.k.e.268.5		20
195.98	odd	12		585.2.cf.a.163.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.4	✓	20	1.1	even	1	trivial
65.2.o.a.33.4	yes	20	65.33	even	12	inner
65.2.t.a.7.4	yes	20	13.7	odd	12
65.2.t.a.28.4	yes	20	5.3	odd	4
325.2.s.b.132.2		20	5.4	even	2
325.2.s.b.293.2		20	65.7	even	12
325.2.x.b.7.2		20	65.59	odd	12
325.2.x.b.93.2		20	5.2	odd	4
585.2.cf.a.163.2		20	195.98	odd	12
585.2.cf.a.262.2		20	3.2	odd	2
585.2.dp.a.28.2		20	15.8	even	4
585.2.dp.a.397.2		20	39.20	even	12
845.2.f.d.408.5		20	65.23	odd	12
845.2.f.d.437.6		20	13.2	odd	12
845.2.f.e.408.6		20	65.3	odd	12
845.2.f.e.437.5		20	13.11	odd	12
845.2.k.d.268.6		20	65.28	even	12
845.2.k.d.577.6		20	13.10	even	6
845.2.k.e.268.5		20	65.63	even	12
845.2.k.e.577.5		20	13.3	even	3
845.2.o.e.258.4		20	65.8	even	4
845.2.o.e.357.4		20	13.9	even	3
845.2.o.f.258.2		20	65.18	even	4
845.2.o.f.357.2		20	13.4	even	6
845.2.o.g.488.2		20	65.58	even	12
845.2.o.g.587.2		20	13.12	even	2
845.2.t.e.188.4		20	65.43	odd	12
845.2.t.e.427.4		20	13.5	odd	4
845.2.t.f.188.2		20	65.48	odd	12
845.2.t.f.427.2		20	13.8	odd	4
845.2.t.g.418.2		20	65.38	odd	4
845.2.t.g.657.2		20	13.6	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.o (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.137404 - 0.237991i) q^{2} +(-2.28256 - 0.611610i) q^{3} +(0.962240 - 1.66665i) q^{4} +(1.69883 - 1.45395i) q^{5} +(0.168076 + 0.627267i) q^{6} +(-0.334376 - 0.193052i) q^{7} -1.07848 q^{8} +(2.23793 + 1.29207i) q^{9} +O(q^{10})\)	\(q+(-0.137404 - 0.237991i) q^{2} +(-2.28256 - 0.611610i) q^{3} +(0.962240 - 1.66665i) q^{4} +(1.69883 - 1.45395i) q^{5} +(0.168076 + 0.627267i) q^{6} +(-0.334376 - 0.193052i) q^{7} -1.07848 q^{8} +(2.23793 + 1.29207i) q^{9} +(-0.579454 - 0.204528i) q^{10} +(-1.12873 + 4.21249i) q^{11} +(-3.21571 + 3.21571i) q^{12} +(3.34024 + 1.35750i) q^{13} +0.106105i q^{14} +(-4.76693 + 2.27970i) q^{15} +(-1.77629 - 3.07663i) q^{16} +(0.510514 + 1.90527i) q^{17} -0.710144i q^{18} +(4.83947 - 1.29673i) q^{19} +(-0.788538 - 4.23041i) q^{20} +(0.645159 + 0.645159i) q^{21} +(1.15763 - 0.310185i) q^{22} +(0.0863441 - 0.322241i) q^{23} +(2.46170 + 0.659609i) q^{24} +(0.772064 - 4.94003i) q^{25} +(-0.135891 - 0.981474i) q^{26} +(0.694880 + 0.694880i) q^{27} +(-0.643499 + 0.371524i) q^{28} +(-7.07031 + 4.08205i) q^{29} +(1.19755 + 0.821248i) q^{30} +(-2.54187 + 2.54187i) q^{31} +(-1.56662 + 2.71347i) q^{32} +(5.15280 - 8.92491i) q^{33} +(0.383290 - 0.383290i) q^{34} +(-0.848736 + 0.158202i) q^{35} +(4.30685 - 2.48656i) q^{36} +(4.17859 - 2.41251i) q^{37} +(-0.973575 - 0.973575i) q^{38} +(-6.79403 - 5.14149i) q^{39} +(-1.83216 + 1.56806i) q^{40} +(4.49768 + 1.20515i) q^{41} +(0.0648946 - 0.242190i) q^{42} +(-6.58600 + 1.76471i) q^{43} +(5.93462 + 5.93462i) q^{44} +(5.68048 - 1.05883i) q^{45} +(-0.0885545 + 0.0237281i) q^{46} -9.83310i q^{47} +(2.17280 + 8.10898i) q^{48} +(-3.42546 - 5.93307i) q^{49} +(-1.28177 + 0.495037i) q^{50} -4.66112i q^{51} +(5.47658 - 4.26077i) q^{52} +(-7.17155 + 7.17155i) q^{53} +(0.0698958 - 0.260855i) q^{54} +(4.20721 + 8.79743i) q^{55} +(0.360618 + 0.208203i) q^{56} -11.8395 q^{57} +(1.94298 + 1.12178i) q^{58} +(0.628209 + 2.34451i) q^{59} +(-0.787474 + 10.1384i) q^{60} +(-5.32338 + 9.22037i) q^{61} +(0.954209 + 0.255679i) q^{62} +(-0.498873 - 0.864073i) q^{63} -6.24413 q^{64} +(7.64824 - 2.55038i) q^{65} -2.83207 q^{66} +(3.18796 + 5.52170i) q^{67} +(3.66665 + 0.982475i) q^{68} +(-0.394171 + 0.682724i) q^{69} +(0.154271 + 0.180254i) q^{70} +(-1.12684 - 4.20542i) q^{71} +(-2.41357 - 1.39347i) q^{72} +6.08593 q^{73} +(-1.14831 - 0.662979i) q^{74} +(-4.78365 + 10.8037i) q^{75} +(2.49554 - 9.31346i) q^{76} +(1.19065 - 1.19065i) q^{77} +(-0.290100 + 2.32338i) q^{78} -3.34944i q^{79} +(-7.49088 - 2.64404i) q^{80} +(-5.03732 - 8.72489i) q^{81} +(-0.331185 - 1.23600i) q^{82} -5.18834i q^{83} +(1.69605 - 0.454456i) q^{84} +(3.63744 + 2.49447i) q^{85} +(1.32493 + 1.32493i) q^{86} +(18.6350 - 4.99324i) q^{87} +(1.21732 - 4.54309i) q^{88} +(-4.82829 - 1.29374i) q^{89} +(-1.03251 - 1.20642i) q^{90} +(-0.854827 - 1.09875i) q^{91} +(-0.453978 - 0.453978i) q^{92} +(7.35661 - 4.24734i) q^{93} +(-2.34019 + 1.35111i) q^{94} +(6.33607 - 9.23927i) q^{95} +(5.23549 - 5.23549i) q^{96} +(-7.37402 + 12.7722i) q^{97} +(-0.941346 + 1.63046i) q^{98} +(-7.96886 + 7.96886i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} - 8 q^{6} - 6 q^{7} + 12 q^{8} - 12 q^{9} - 10 q^{10} - 16 q^{11} + 24 q^{12} + 2 q^{13} + 12 q^{15} - 2 q^{16} - 10 q^{17} + 20 q^{19} + 14 q^{20} + 4 q^{21} + 16 q^{22} - 2 q^{23} - 32 q^{24} - 18 q^{25} - 24 q^{26} + 4 q^{27} + 6 q^{28} + 14 q^{30} - 6 q^{32} - 18 q^{33} - 2 q^{34} - 20 q^{35} + 36 q^{36} + 42 q^{37} + 8 q^{38} - 4 q^{39} - 16 q^{40} + 10 q^{41} - 56 q^{42} - 22 q^{43} + 36 q^{44} + 52 q^{45} + 4 q^{46} + 28 q^{48} - 18 q^{49} + 44 q^{50} + 46 q^{52} - 10 q^{53} + 48 q^{54} + 26 q^{55} - 12 q^{57} - 90 q^{58} + 16 q^{59} - 92 q^{60} - 16 q^{61} - 40 q^{62} - 32 q^{63} - 20 q^{64} + 8 q^{65} - 32 q^{66} - 58 q^{67} + 28 q^{68} + 16 q^{69} + 32 q^{70} - 16 q^{71} - 66 q^{72} + 72 q^{73} - 18 q^{74} - 34 q^{75} - 64 q^{76} + 28 q^{77} + 32 q^{78} - 34 q^{80} - 14 q^{81} + 22 q^{82} + 40 q^{84} - 6 q^{85} + 60 q^{86} + 62 q^{87} + 50 q^{88} + 6 q^{89} - 46 q^{90} + 8 q^{91} - 8 q^{92} + 48 q^{93} + 48 q^{94} + 14 q^{95} + 56 q^{96} - 22 q^{97} + 4 q^{98} - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 - 8 * q^6 - 6 * q^7 + 12 * q^8 - 12 * q^9 - 10 * q^10 - 16 * q^11 + 24 * q^12 + 2 * q^13 + 12 * q^15 - 2 * q^16 - 10 * q^17 + 20 * q^19 + 14 * q^20 + 4 * q^21 + 16 * q^22 - 2 * q^23 - 32 * q^24 - 18 * q^25 - 24 * q^26 + 4 * q^27 + 6 * q^28 + 14 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 - 20 * q^35 + 36 * q^36 + 42 * q^37 + 8 * q^38 - 4 * q^39 - 16 * q^40 + 10 * q^41 - 56 * q^42 - 22 * q^43 + 36 * q^44 + 52 * q^45 + 4 * q^46 + 28 * q^48 - 18 * q^49 + 44 * q^50 + 46 * q^52 - 10 * q^53 + 48 * q^54 + 26 * q^55 - 12 * q^57 - 90 * q^58 + 16 * q^59 - 92 * q^60 - 16 * q^61 - 40 * q^62 - 32 * q^63 - 20 * q^64 + 8 * q^65 - 32 * q^66 - 58 * q^67 + 28 * q^68 + 16 * q^69 + 32 * q^70 - 16 * q^71 - 66 * q^72 + 72 * q^73 - 18 * q^74 - 34 * q^75 - 64 * q^76 + 28 * q^77 + 32 * q^78 - 34 * q^80 - 14 * q^81 + 22 * q^82 + 40 * q^84 - 6 * q^85 + 60 * q^86 + 62 * q^87 + 50 * q^88 + 6 * q^89 - 46 * q^90 + 8 * q^91 - 8 * q^92 + 48 * q^93 + 48 * q^94 + 14 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more