LMFDB - Embedded newform 220.2.r.b.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(51,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

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

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

chi := DirichletCharacter("220.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			211.2
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	220.211
Dual form			220.2.r.b.171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41355 + 0.0434654i) q^{2} +(-0.722562 - 0.994522i) q^{3} +(1.99622 + 0.122881i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.978148 - 1.43721i) q^{6} +(-0.948903 - 0.689419i) q^{7} +(2.81641 + 0.260464i) q^{8} +(0.460074 - 1.41596i) q^{9} +(-0.395472 - 1.35779i) q^{10} +(3.11426 + 1.14079i) q^{11} +(-1.32019 - 2.07407i) q^{12} +(1.03536 + 0.336408i) q^{13} +(-1.31135 - 1.01577i) q^{14} +(-0.722562 + 0.994522i) q^{15} +(3.96980 + 0.490594i) q^{16} +(-4.70810 + 1.52976i) q^{17} +(0.711880 - 1.98153i) q^{18} +(-4.36984 + 3.17488i) q^{19} +(-0.500000 - 1.93649i) q^{20} +1.44185i q^{21} +(4.35256 + 1.74793i) q^{22} +3.28095i q^{23} +(-1.77599 - 2.98918i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(1.44890 + 0.520530i) q^{26} +(-5.24803 + 1.70519i) q^{27} +(-1.80951 - 1.49283i) q^{28} +(0.622602 - 0.856939i) q^{29} +(-1.06460 + 1.37440i) q^{30} +(6.07715 + 1.97459i) q^{31} +(5.59017 + 0.866025i) q^{32} +(-1.11570 - 3.92149i) q^{33} +(-6.72161 + 1.95774i) q^{34} +(-0.362449 + 1.11550i) q^{35} +(1.09240 - 2.77004i) q^{36} +(1.19710 + 0.869742i) q^{37} +(-6.31497 + 4.29789i) q^{38} +(-0.413545 - 1.27276i) q^{39} +(-0.622602 - 2.75905i) q^{40} +(3.01196 + 4.14561i) q^{41} +(-0.0626707 + 2.03813i) q^{42} -9.12165 q^{43} +(6.07656 + 2.65996i) q^{44} -1.48883 q^{45} +(-0.142608 + 4.63777i) q^{46} +(0.973579 + 1.34002i) q^{47} +(-2.38052 - 4.30254i) q^{48} +(-1.73800 - 5.34901i) q^{49} +(-1.16913 + 0.795697i) q^{50} +(4.92327 + 3.57697i) q^{51} +(2.02547 + 0.798771i) q^{52} +(-1.39344 + 4.28856i) q^{53} +(-7.49244 + 2.18225i) q^{54} +(0.122602 - 3.31436i) q^{55} +(-2.49293 - 2.18884i) q^{56} +(6.31497 + 2.05186i) q^{57} +(0.917324 - 1.18426i) q^{58} +(-2.36799 + 3.25926i) q^{59} +(-1.56460 + 1.89650i) q^{60} +(-13.2591 + 4.30815i) q^{61} +(8.50451 + 3.05531i) q^{62} +(-1.41276 + 1.02643i) q^{63} +(7.86432 + 1.46715i) q^{64} -1.08864i q^{65} +(-1.40664 - 5.59170i) q^{66} -10.3928i q^{67} +(-9.58639 + 2.47520i) q^{68} +(3.26298 - 2.37069i) q^{69} +(-0.560824 + 1.56106i) q^{70} +(14.9187 - 4.84738i) q^{71} +(1.66456 - 3.86809i) q^{72} +(8.53598 - 11.7488i) q^{73} +(1.65435 + 1.28145i) q^{74} +(1.16913 + 0.379874i) q^{75} +(-9.11330 + 5.80079i) q^{76} +(-2.16864 - 3.22953i) q^{77} +(-0.529244 - 1.81708i) q^{78} +(2.99070 - 9.20442i) q^{79} +(-0.760154 - 3.92711i) q^{80} +(1.87441 + 1.36184i) q^{81} +(4.07735 + 5.99092i) q^{82} +(-0.989908 - 3.04662i) q^{83} +(-0.177176 + 2.87826i) q^{84} +(2.90977 + 4.00495i) q^{85} +(-12.8939 - 0.396476i) q^{86} -1.30211 q^{87} +(8.47388 + 4.02410i) q^{88} -0.254342 q^{89} +(-2.10453 - 0.0647125i) q^{90} +(-0.750529 - 1.03301i) q^{91} +(-0.403165 + 6.54950i) q^{92} +(-2.42735 - 7.47062i) q^{93} +(1.31795 + 1.93649i) q^{94} +(4.36984 + 3.17488i) q^{95} +(-3.17797 - 6.18530i) q^{96} +(-0.00979012 + 0.0301309i) q^{97} +(-2.22424 - 7.63661i) q^{98} +(3.04811 - 3.88482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} + 5 q^{3} - q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 5 q^{8} + 3 q^{9} - 5 q^{10} - q^{11} - 10 q^{12} + 10 q^{13} + 5 q^{14} + 5 q^{15} + 7 q^{16} - 5 q^{17} - 10 q^{18} - 11 q^{19} - 4 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 + 5 * q^3 - q^4 + 2 * q^5 + q^6 - 3 * q^7 + 5 * q^8 + 3 * q^9 - 5 * q^10 - q^11 - 10 * q^12 + 10 * q^13 + 5 * q^14 + 5 * q^15 + 7 * q^16 - 5 * q^17 - 10 * q^18 - 11 * q^19 - 4 * q^20 + q^22 + 3 * q^24 - 2 * q^25 + 7 * q^26 - 10 * q^27 - 9 * q^28 - 5 * q^29 - 6 * q^30 + 10 * q^31 - 11 * q^33 - 14 * q^34 + 8 * q^35 - 26 * q^36 + 20 * q^37 - 5 * q^38 + 3 * q^39 + 5 * q^40 + 10 * q^41 + 29 * q^42 - 34 * q^43 + 32 * q^44 - 8 * q^45 - 10 * q^46 - 23 * q^49 - 5 * q^50 + 9 * q^51 - 5 * q^52 - 7 * q^53 - 26 * q^54 - 9 * q^55 + 15 * q^56 + 5 * q^57 + 18 * q^58 - 5 * q^59 - 10 * q^60 - 10 * q^61 - q^62 - 23 * q^63 + 11 * q^64 - 17 * q^66 - 15 * q^68 + 15 * q^69 + 15 * q^70 + 90 * q^71 + 10 * q^72 + 5 * q^73 + 35 * q^74 + 5 * q^75 - 18 * q^76 - 14 * q^77 - 21 * q^79 - 7 * q^80 - 10 * q^81 - 2 * q^82 + 19 * q^83 - 30 * q^84 - 30 * q^86 - 18 * q^87 + 43 * q^88 + 20 * q^89 - 15 * q^90 - 10 * q^91 + 25 * q^92 + 11 * q^93 + 11 * q^95 - 36 * q^96 - 44 * q^97 + 50 * q^98 - 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

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 $

$2$	1.41355	+	0.0434654i	0.999528	+	0.0307347i
$2$	1.41355	+	0.0434654i	0.999528	+	0.0307347i
$3$	−0.722562	−	0.994522i	−0.417172	−	0.574187i	0.547778	−	0.836624i	$-0.315474\pi$
$3$	−0.722562	−	0.994522i	−0.417172	−	0.574187i	−0.964949	+	0.262436i	$0.915474\pi$
$4$	1.99622	+	0.122881i	0.998111	+	0.0614403i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−0.978148	−	1.43721i	−0.399327	−	0.586738i
$7$	−0.948903	−	0.689419i	−0.358652	−	0.260576i	0.393838	−	0.919180i	$-0.371147\pi$
$7$	−0.948903	−	0.689419i	−0.358652	−	0.260576i	−0.752490	+	0.658604i	$0.771147\pi$
$8$	2.81641	+	0.260464i	0.995751	+	0.0920879i
$9$	0.460074	−	1.41596i	0.153358	−	0.471987i
$10$	−0.395472	−	1.35779i	−0.125059	−	0.429372i
$11$	3.11426	+	1.14079i	0.938983	+	0.343963i
$11$	3.11426	+	1.14079i	0.938983	+	0.343963i
$12$	−1.32019	−	2.07407i	−0.381105	−	0.598734i
$13$	1.03536	+	0.336408i	0.287157	+	0.0933028i	0.449054	−	0.893505i	$-0.351761\pi$
$13$	1.03536	+	0.336408i	0.287157	+	0.0933028i	−0.161897	+	0.986808i	$0.551761\pi$
$14$	−1.31135	−	1.01577i	−0.350474	−	0.271476i
$15$	−0.722562	+	0.994522i	−0.186565	+	0.256784i
$16$	3.96980	+	0.490594i	0.992450	+	0.122648i
$17$	−4.70810	+	1.52976i	−1.14188	+	0.371020i	−0.818080	−	0.575105i	$-0.804961\pi$
$17$	−4.70810	+	1.52976i	−1.14188	+	0.371020i	−0.323803	+	0.946125i	$0.604961\pi$
$18$	0.711880	−	1.98153i	0.167792	−	0.467051i
$19$	−4.36984	+	3.17488i	−1.00251	+	0.728366i	−0.962625	−	0.270838i	$-0.912699\pi$
$19$	−4.36984	+	3.17488i	−1.00251	+	0.728366i	−0.0398853	+	0.999204i	$0.512699\pi$
$20$	−0.500000	−	1.93649i	−0.111803	−	0.433013i
$21$			1.44185i			0.314638i
$22$	4.35256	+	1.74793i	0.927968	+	0.372659i
$23$			3.28095i			0.684125i	0.939677	+	0.342063i	$0.111126\pi$
$23$			3.28095i			0.684125i	−0.939677	+	0.342063i	$0.888874\pi$
$24$	−1.77599	−	2.98918i	−0.362523	−	0.610164i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	1.44890	+	0.520530i	0.284153	+	0.102084i
$27$	−5.24803	+	1.70519i	−1.00998	+	0.328164i
$28$	−1.80951	−	1.49283i	−0.341964	−	0.282119i
$29$	0.622602	−	0.856939i	0.115614	−	0.159130i	−0.747288	−	0.664501i	$-0.768644\pi$
$29$	0.622602	−	0.856939i	0.115614	−	0.159130i	0.862902	+	0.505371i	$0.168644\pi$
$30$	−1.06460	+	1.37440i	−0.194369	+	0.250929i
$31$	6.07715	+	1.97459i	1.09149	+	0.354646i	0.798822	−	0.601568i	$-0.205457\pi$
$31$	6.07715	+	1.97459i	1.09149	+	0.354646i	0.292667	+	0.956214i	$0.405457\pi$
$32$	5.59017	+	0.866025i	0.988212	+	0.153093i
$33$	−1.11570	−	3.92149i	−0.194218	−	0.682644i
$34$	−6.72161	+	1.95774i	−1.15275	+	0.335749i
$35$	−0.362449	+	1.11550i	−0.0612650	+	0.188554i
$36$	1.09240	−	2.77004i	0.182067	−	0.461673i
$37$	1.19710	+	0.869742i	0.196801	+	0.142985i	0.681822	−	0.731518i	$-0.261188\pi$
$37$	1.19710	+	0.869742i	0.196801	+	0.142985i	−0.485021	+	0.874503i	$0.661188\pi$
$38$	−6.31497	+	4.29789i	−1.02442	+	0.697210i
$39$	−0.413545	−	1.27276i	−0.0662203	−	0.203805i
$40$	−0.622602	−	2.75905i	−0.0984421	−	0.436244i
$41$	3.01196	+	4.14561i	0.470389	+	0.647435i	0.976623	−	0.214961i	$-0.0689626\pi$
$41$	3.01196	+	4.14561i	0.470389	+	0.647435i	−0.506233	+	0.862397i	$0.668963\pi$
$42$	−0.0626707	+	2.03813i	−0.00967030	+	0.314490i
$43$	−9.12165			−1.39104			−0.695519	−	0.718508i	$-0.744826\pi$
$43$	−9.12165			−1.39104			−0.695519	+	0.718508i	$0.744826\pi$
$44$	6.07656	+	2.65996i	0.916076	+	0.401004i
$45$	−1.48883			−0.221942
$46$	−0.142608	+	4.63777i	−0.0210264	+	0.683802i
$47$	0.973579	+	1.34002i	0.142011	+	0.195462i	0.874098	−	0.485750i	$-0.161453\pi$
$47$	0.973579	+	1.34002i	0.142011	+	0.195462i	−0.732087	+	0.681211i	$0.761453\pi$
$48$	−2.38052	−	4.30254i	−0.343599	−	0.621018i
$49$	−1.73800	−	5.34901i	−0.248286	−	0.764145i
$50$	−1.16913	+	0.795697i	−0.165340	+	0.112529i
$51$	4.92327	+	3.57697i	0.689396	+	0.500876i
$52$	2.02547	+	0.798771i	0.280882	+	0.110770i
$53$	−1.39344	+	4.28856i	−0.191403	+	0.589079i	0.808596	+	0.588364i	$0.200228\pi$
$53$	−1.39344	+	4.28856i	−0.191403	+	0.589079i	−1.00000		0.000715358i	$0.999772\pi$
$54$	−7.49244	+	2.18225i	−1.01959	+	0.296967i
$55$	0.122602	−	3.31436i	0.0165317	−	0.446908i
$56$	−2.49293	−	2.18884i	−0.333132	−	0.292496i
$57$	6.31497	+	2.05186i	0.836438	+	0.271775i
$58$	0.917324	−	1.18426i	0.120451	−	0.155501i
$59$	−2.36799	+	3.25926i	−0.308287	+	0.424320i	−0.934846	−	0.355054i	$-0.884463\pi$
$59$	−2.36799	+	3.25926i	−0.308287	+	0.424320i	0.626559	+	0.779374i	$0.284463\pi$
$60$	−1.56460	+	1.89650i	−0.201989	+	0.244837i
$61$	−13.2591	+	4.30815i	−1.69766	+	0.551603i	−0.988203	−	0.153148i	$-0.951059\pi$
$61$	−13.2591	+	4.30815i	−1.69766	+	0.551603i	−0.709455	+	0.704751i	$0.751059\pi$
$62$	8.50451	+	3.05531i	1.08007	+	0.388025i
$63$	−1.41276	+	1.02643i	−0.177990	+	0.129318i
$64$	7.86432	+	1.46715i	0.983040	+	0.183393i
$65$		−	1.08864i		−	0.135029i
$66$	−1.40664	−	5.59170i	−0.173146	−	0.688291i
$67$		−	10.3928i		−	1.26968i	−0.772643	−	0.634841i	$-0.781066\pi$
$67$		−	10.3928i		−	1.26968i	0.772643	−	0.634841i	$-0.218934\pi$
$68$	−9.58639	+	2.47520i	−1.16252	+	0.300162i
$69$	3.26298	−	2.37069i	0.392816	−	0.285398i
$70$	−0.560824	+	1.56106i	−0.0670312	+	0.186582i
$71$	14.9187	−	4.84738i	1.77052	−	0.575278i	0.772323	−	0.635230i	$-0.219095\pi$
$71$	14.9187	−	4.84738i	1.77052	−	0.575278i	0.998201	+	0.0599516i	$0.0190946\pi$
$72$	1.66456	−	3.86809i	0.196171	−	0.455859i
$73$	8.53598	−	11.7488i	0.999061	−	1.37509i	0.0731616	−	0.997320i	$-0.476691\pi$
$73$	8.53598	−	11.7488i	0.999061	−	1.37509i	0.925900	−	0.377770i	$-0.123309\pi$
$74$	1.65435	+	1.28145i	0.192314	+	0.148966i
$75$	1.16913	+	0.379874i	0.135000	+	0.0438640i
$76$	−9.11330	+	5.80079i	−1.04537	+	0.665396i
$77$	−2.16864	−	3.22953i	−0.247140	−	0.368039i
$78$	−0.529244	−	1.81708i	−0.0599251	−	0.205744i
$79$	2.99070	−	9.20442i	0.336480	−	1.03558i	−0.629509	−	0.776993i	$-0.716744\pi$
$79$	2.99070	−	9.20442i	0.336480	−	1.03558i	0.965989	−	0.258585i	$-0.0832562\pi$
$80$	−0.760154	−	3.92711i	−0.0849877	−	0.439064i
$81$	1.87441	+	1.36184i	0.208268	+	0.151315i
$82$	4.07735	+	5.99092i	0.450268	+	0.661587i
$83$	−0.989908	−	3.04662i	−0.108657	−	0.334410i	0.881915	−	0.471409i	$-0.156254\pi$
$83$	−0.989908	−	3.04662i	−0.108657	−	0.334410i	−0.990571	+	0.136999i	$0.956254\pi$
$84$	−0.177176	+	2.87826i	−0.0193315	+	0.314044i
$85$	2.90977	+	4.00495i	0.315609	+	0.434398i
$86$	−12.8939	−	0.396476i	−1.39038	−	0.0427531i
$87$	−1.30211			−0.139601
$88$	8.47388	+	4.02410i	0.903319	+	0.428970i
$89$	−0.254342			−0.0269602			−0.0134801	−	0.999909i	$-0.504291\pi$
$89$	−0.254342			−0.0269602			−0.0134801	+	0.999909i	$0.504291\pi$
$90$	−2.10453	−	0.0647125i	−0.221837	−	0.00682130i
$91$	−0.750529	−	1.03301i	−0.0786768	−	0.108289i
$92$	−0.403165	+	6.54950i	−0.0420329	+	0.682833i
$93$	−2.42735	−	7.47062i	−0.251705	−	0.774668i
$94$	1.31795	+	1.93649i	0.135937	+	0.199734i
$95$	4.36984	+	3.17488i	0.448336	+	0.325735i
$96$	−3.17797	−	6.18530i	−0.324350	−	0.631285i
$97$	−0.00979012	+	0.0301309i	−0.000994036	+	0.00305933i	−0.951552	−	0.307487i	$-0.900512\pi$
$97$	−0.00979012	+	0.0301309i	−0.000994036	+	0.00305933i	0.950558	+	0.310546i	$0.100512\pi$
$98$	−2.22424	−	7.63661i	−0.224683	−	0.771415i
$99$	3.04811	−	3.88482i	0.306346	−	0.390439i
$100$	−1.68720	+	1.07394i	−0.168720	+	0.107394i
$101$	4.37365	+	1.42109i	0.435195	+	0.141403i	0.518418	−	0.855128i	$-0.326521\pi$
$101$	4.37365	+	1.42109i	0.435195	+	0.141403i	−0.0832228	+	0.996531i	$0.526521\pi$
$102$	6.80380	+	5.27020i	0.673676	+	0.521827i
$103$	2.37868	−	3.27397i	0.234378	−	0.322593i	−0.675586	−	0.737281i	$-0.736109\pi$
$103$	2.37868	−	3.27397i	0.234378	−	0.322593i	0.909964	+	0.414688i	$0.136109\pi$
$104$	2.82837	+	1.21714i	0.277344	+	0.119350i
$105$	1.37128	−	0.445557i	0.133824	−	0.0434819i
$106$	−2.15609	+	6.00151i	−0.209418	+	0.582918i
$107$	−4.44417	+	3.22888i	−0.429634	+	0.312147i	−0.781503	−	0.623902i	$-0.785546\pi$
$107$	−4.44417	+	3.22888i	−0.429634	+	0.312147i	0.351868	+	0.936049i	$0.385546\pi$
$108$	−10.6858	+	2.75905i	−1.02824	+	0.265490i
$109$			15.2250i			1.45829i	0.684359	+	0.729145i	$0.260082\pi$
$109$			15.2250i			1.45829i	−0.684359	+	0.729145i	$0.739918\pi$
$110$	0.317364	−	4.67967i	0.0302595	−	0.446189i
$111$		−	1.81898i		−	0.172650i
$112$	−3.42873	−	3.20238i	−0.323985	−	0.302597i
$113$	−11.2728	+	8.19017i	−1.06046	+	0.770467i	−0.974173	−	0.225804i	$-0.927499\pi$
$113$	−11.2728	+	8.19017i	−1.06046	+	0.770467i	−0.0862836	+	0.996271i	$0.527499\pi$
$114$	8.83731	+	3.17488i	0.827690	+	0.297354i
$115$	3.12037	−	1.01387i	0.290976	−	0.0945438i
$116$	1.34815	−	1.63413i	0.125173	−	0.151726i
$117$	0.952682	−	1.31125i	0.0880755	−	0.121225i
$118$	−3.48893	+	4.50419i	−0.321182	+	0.414644i
$119$	5.52218	+	1.79426i	0.506217	+	0.164480i
$120$	−2.29407	+	2.61278i	−0.209419	+	0.238513i
$121$	8.39717	+	7.10545i	0.763380	+	0.645950i
$122$	−18.9296	+	5.51346i	−1.71381	+	0.499165i
$123$	1.94657	−	5.99092i	0.175516	−	0.540183i
$124$	11.8887	+	4.68848i	1.06764	+	0.421038i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	−2.04161	+	1.38950i	−0.181881	+	0.123786i
$127$	−5.16913	−	15.9089i	−0.458686	−	1.41169i	−0.866752	−	0.498739i	$-0.833797\pi$
$127$	−5.16913	−	15.9089i	−0.458686	−	1.41169i	0.408066	−	0.912952i	$-0.366203\pi$
$128$	11.0528	+	2.41570i	0.976939	+	0.213520i
$129$	6.59096	+	9.07168i	0.580302	+	0.798717i
$130$	0.0473181	−	1.53884i	0.00415008	−	0.134965i
$131$	5.02294			0.438857			0.219428	−	0.975629i	$-0.429581\pi$
$131$	5.02294			0.438857			0.219428	+	0.975629i	$0.429581\pi$
$132$	−1.74531	−	7.96526i	−0.151909	−	0.693287i
$133$	6.33537			0.549347
$134$	0.451727	−	14.6907i	0.0390233	−	1.26908i
$135$	3.24346	+	4.46424i	0.279153	+	0.384221i
$136$	−13.6584	+	3.08213i	−1.17120	+	0.264290i
$137$	−4.37723	−	13.4717i	−0.373972	−	1.15097i	−0.944169	−	0.329460i	$-0.893133\pi$
$137$	−4.37723	−	13.4717i	−0.373972	−	1.15097i	0.570197	−	0.821508i	$-0.306867\pi$
$138$	4.71541	−	3.20925i	0.401402	−	0.273190i
$139$	−13.5531	−	9.84690i	−1.14956	−	0.835204i	−0.161137	−	0.986932i	$-0.551516\pi$
$139$	−13.5531	−	9.84690i	−1.14956	−	0.835204i	−0.988422	+	0.151729i	$0.951516\pi$
$140$	−0.860602	+	2.18225i	−0.0727341	+	0.184434i
$141$	0.629204	−	1.93649i	0.0529886	−	0.163082i
$142$	21.2990	−	6.20355i	1.78737	−	0.520590i
$143$	2.84060	+	2.22879i	0.237543	+	0.186381i
$144$	2.52106	−	5.39537i	0.210089	−	0.449615i
$145$	−1.00739	−	0.327321i	−0.0836593	−	0.0271826i
$146$	12.5767	−	16.2364i	1.04085	−	1.34373i
$147$	−4.06390	+	5.59347i	−0.335185	+	0.461342i
$148$	2.28280	+	1.88330i	0.187645	+	0.154806i
$149$	−2.09086	+	0.679361i	−0.171290	+	0.0556554i	−0.393406	−	0.919365i	$-0.628703\pi$
$149$	−2.09086	+	0.679361i	−0.171290	+	0.0556554i	0.222117	+	0.975020i	$0.428703\pi$
$150$	1.63611	+	0.587785i	0.133588	+	0.0479925i
$151$	2.43950	−	1.77240i	0.198524	−	0.144236i	−0.484082	−	0.875022i	$-0.660847\pi$
$151$	2.43950	−	1.77240i	0.198524	−	0.144236i	0.682606	+	0.730787i	$0.260847\pi$
$152$	−13.1342	+	7.80356i	−1.06532	+	0.632952i
$153$			7.37029i			0.595853i
$154$	−2.92510	−	4.65935i	−0.235711	−	0.375461i
$155$		−	6.38990i		−	0.513249i
$156$	−0.669131	−	2.59153i	−0.0535733	−	0.207489i
$157$	12.6955	−	9.22381i	1.01321	−	0.736140i	0.0483303	−	0.998831i	$-0.484610\pi$
$157$	12.6955	−	9.22381i	1.01321	−	0.736140i	0.964880	+	0.262691i	$0.0846100\pi$
$158$	4.62756	−	12.8809i	0.368149	−	1.02475i
$159$	5.27191	−	1.71295i	0.418090	−	0.135846i
$160$	−0.903818	−	5.58418i	−0.0714531	−	0.441469i
$161$	2.26195	−	3.11330i	0.178267	−	0.245363i
$162$	2.59037	+	2.00649i	0.203519	+	0.157645i
$163$	−15.1523	−	4.92328i	−1.18682	−	0.385621i	−0.351924	−	0.936029i	$-0.614472\pi$
$163$	−15.1523	−	4.92328i	−1.18682	−	0.385621i	−0.834896	+	0.550407i	$0.814472\pi$
$164$	5.50313	+	8.64566i	0.429722	+	0.675113i
$165$	−3.38479	+	2.27290i	−0.263506	+	0.176945i
$166$	−1.26686	−	4.34957i	−0.0983272	−	0.337592i
$167$	−4.60542	+	14.1740i	−0.356378	+	1.09682i	0.598828	+	0.800878i	$0.295633\pi$
$167$	−4.60542	+	14.1740i	−0.356378	+	1.09682i	−0.955206	+	0.295941i	$0.904367\pi$
$168$	−0.375551	+	4.06085i	−0.0289744	+	0.313301i
$169$	−9.55843	−	6.94460i	−0.735263	−	0.534200i
$170$	3.93901	+	5.78765i	0.302108	+	0.443893i
$171$	2.48505	+	7.64820i	0.190037	+	0.584873i
$172$	−18.2088	−	1.12087i	−1.38841	−	0.0854658i
$173$	7.07542	+	9.73848i	0.537934	+	0.740403i	0.988314	−	0.152434i	$-0.0487112\pi$
$173$	7.07542	+	9.73848i	0.537934	+	0.740403i	−0.450379	+	0.892837i	$0.648711\pi$
$174$	−1.84060	−	0.0565969i	−0.139535	−	0.00429060i
$175$	1.17291			0.0886636
$176$	11.8033	+	6.05656i	0.889708	+	0.456531i
$177$	4.95243			0.372248
$178$	−0.359523	−	0.0110551i	−0.0269474	−	0.000828611i
$179$	4.24947	+	5.84890i	0.317620	+	0.437167i	0.937739	−	0.347341i	$-0.112915\pi$
$179$	4.24947	+	5.84890i	0.317620	+	0.437167i	−0.620118	+	0.784508i	$0.712915\pi$
$180$	−2.97203	−	0.182948i	−0.221522	−	0.0136362i
$181$	−7.81407	−	24.0492i	−0.580816	−	1.78757i	−0.615462	−	0.788167i	$-0.711030\pi$
$181$	−7.81407	−	24.0492i	−0.580816	−	1.78757i	0.0346463	−	0.999400i	$-0.488970\pi$
$182$	−1.01601	−	1.49283i	−0.0753114	−	0.110656i
$183$	13.8651	+	10.0736i	1.02494	+	0.744661i
$184$	−0.854569	+	9.24050i	−0.0629996	+	0.681219i
$185$	0.457250	−	1.40727i	0.0336177	−	0.103465i
$186$	−3.10646	−	10.6656i	−0.227777	−	0.782038i
$187$	−16.4074	−	0.606930i	−1.19983	−	0.0443831i
$188$	1.77882	+	2.79460i	0.129734	+	0.203817i
$189$	6.15546	+	2.00003i	0.447744	+	0.145481i
$190$	6.03897	+	4.67777i	0.438113	+	0.339361i
$191$	−1.02514	+	1.41099i	−0.0741767	+	0.102095i	−0.844493	−	0.535566i	$-0.820098\pi$
$191$	−1.02514	+	1.41099i	−0.0741767	+	0.102095i	0.770317	+	0.637662i	$0.220098\pi$
$192$	−4.22335	−	8.88134i	−0.304794	−	0.640955i
$193$	−10.9311	+	3.55173i	−0.786837	+	0.255659i	−0.674757	−	0.738040i	$-0.735751\pi$
$193$	−10.9311	+	3.55173i	−0.786837	+	0.255659i	−0.112080	+	0.993699i	$0.535751\pi$
$194$	−0.0151484	+	0.0421659i	−0.00108759	+	0.00302733i
$195$	−1.08268	+	0.786610i	−0.0775320	+	0.0563303i
$196$	−2.81214	−	10.8914i	−0.200867	−	0.777956i
$197$			11.4119i			0.813063i	0.913637	+	0.406532i	$0.133262\pi$
$197$			11.4119i			0.813063i	−0.913637	+	0.406532i	$0.866738\pi$
$198$	4.47749	−	5.35888i	0.318202	−	0.380839i
$199$			11.5940i			0.821875i	0.911664	+	0.410937i	$0.134799\pi$
$199$			11.5940i			0.821875i	−0.911664	+	0.410937i	$0.865201\pi$
$200$	−2.43162	+	1.44472i	−0.171941	+	0.102157i
$201$	−10.3359	+	7.50944i	−0.729036	+	0.529675i
$202$	6.12059	+	2.19887i	0.430643	+	0.154712i
$203$	−1.18158	+	0.383918i	−0.0829306	+	0.0269458i
$204$	9.38840	+	7.74539i	0.657320	+	0.542286i
$205$	3.01196	−	4.14561i	0.210364	−	0.289542i
$206$	3.50467	−	4.52451i	0.244182	−	0.315238i
$207$	4.64570	+	1.50948i	0.322898	+	0.104916i
$208$	3.94512	+	1.84341i	0.273545	+	0.127818i
$209$	−17.2307	+	4.90228i	−1.19187	+	0.339098i
$210$	1.95774	−	0.570212i	0.135097	−	0.0393484i
$211$	−7.35063	+	22.6229i	−0.506038	+	1.55742i	0.292981	+	0.956118i	$0.405353\pi$
$211$	−7.35063	+	22.6229i	−0.506038	+	1.55742i	−0.799019	+	0.601306i	$0.794647\pi$
$212$	−3.30859	+	8.38969i	−0.227235	+	0.576206i
$213$	−15.6005	−	11.3344i	−1.06893	−	0.776623i
$214$	−6.42238	+	4.37100i	−0.439025	+	0.298795i
$215$	2.81874	+	8.67520i	0.192237	+	0.591644i
$216$	−15.2247	+	3.43558i	−1.03591	+	0.233762i
$217$	−4.40531	−	6.06339i	−0.299052	−	0.411610i
$218$	−0.661760	+	21.5212i	−0.0448201	+	1.45760i
$219$	−17.8522			−1.20634
$220$	0.652012	−	6.60113i	0.0439586	−	0.445048i
$221$	−5.38919			−0.362516
$222$	0.0790627	−	2.57121i	0.00530634	−	0.172569i
$223$	3.65167	+	5.02609i	0.244534	+	0.336572i	0.913588	−	0.406642i	$-0.133300\pi$
$223$	3.65167	+	5.02609i	0.244534	+	0.336572i	−0.669054	+	0.743214i	$0.733300\pi$
$224$	−4.70748	−	4.67574i	−0.314532	−	0.312411i
$225$	0.460074	+	1.41596i	0.0306716	+	0.0943974i
$226$	−16.2906	+	11.0872i	−1.08364	+	0.737510i
$227$	9.21277	+	6.69347i	0.611473	+	0.444261i	0.849933	−	0.526891i	$-0.176642\pi$
$227$	9.21277	+	6.69347i	0.611473	+	0.444261i	−0.238460	+	0.971152i	$0.576642\pi$
$228$	12.3539	+	4.87195i	0.818159	+	0.322653i
$229$	6.37812	−	19.6298i	0.421478	−	1.29718i	−0.484848	−	0.874598i	$-0.661125\pi$
$229$	6.37812	−	19.6298i	0.421478	−	1.29718i	0.906326	−	0.422578i	$-0.138875\pi$
$230$	4.45485	−	1.29752i	0.293744	−	0.0855561i
$231$	−1.64486	+	4.49030i	−0.108224	+	0.295440i
$232$	1.97670	−	2.25132i	0.129777	−	0.147807i
$233$	11.2344	+	3.65029i	0.735992	+	0.239138i	0.652943	−	0.757407i	$-0.273534\pi$
$233$	11.2344	+	3.65029i	0.735992	+	0.239138i	0.0830489	+	0.996545i	$0.473534\pi$
$234$	1.40365	−	1.81211i	0.0917597	−	0.118461i
$235$	0.973579	−	1.34002i	0.0635093	−	0.0874131i
$236$	−5.12754	+	6.21523i	−0.333774	+	0.404577i
$237$	−11.3150	+	3.67646i	−0.734986	+	0.238811i
$238$	7.72786	+	2.77630i	0.500923	+	0.179961i
$239$	−17.0935	+	12.4192i	−1.10569	+	0.803329i	−0.981979	−	0.188990i	$-0.939479\pi$
$239$	−17.0935	+	12.4192i	−1.10569	+	0.803329i	−0.123709	+	0.992319i	$0.539479\pi$
$240$	−3.35634	+	3.59357i	−0.216651	+	0.231964i
$241$		−	5.64518i		−	0.363638i	−0.983332	−	0.181819i	$-0.941801\pi$
$241$		−	5.64518i		−	0.363638i	0.983332	−	0.181819i	$-0.0581985\pi$
$242$	11.5609	+	10.4089i	0.743166	+	0.669107i
$243$			13.7062i			0.879250i
$244$	−26.9976	+	6.97074i	−1.72834	+	0.446256i
$245$	−4.55014	+	3.30587i	−0.290698	+	0.211204i
$246$	3.01196	−	8.38383i	0.192036	−	0.534534i
$247$	−5.59240	+	1.81708i	−0.355836	+	0.115618i
$248$	16.6014	+	7.14412i	1.05419	+	0.453652i
$249$	−2.31466	+	3.18586i	−0.146686	+	0.201896i
$250$	1.11803	+	0.866025i	0.0707107	+	0.0547723i
$251$	−18.9217	−	6.14803i	−1.19433	−	0.388060i	−0.356656	−	0.934236i	$-0.616083\pi$
$251$	−18.9217	−	6.14803i	−1.19433	−	0.388060i	−0.837671	+	0.546176i	$0.816083\pi$
$252$	−2.94630	+	1.87538i	−0.185600	+	0.118138i
$253$	−3.74289	+	10.2177i	−0.235314	+	0.642382i
$254$	−6.61531	−	22.7127i	−0.415082	−	1.42512i
$255$	1.88052	−	5.78765i	0.117763	−	0.362437i
$256$	15.5186	+	3.89512i	0.969915	+	0.243445i
$257$	−2.53312	−	1.84042i	−0.158012	−	0.114802i	0.505970	−	0.862551i	$-0.331135\pi$
$257$	−2.53312	−	1.84042i	−0.158012	−	0.114802i	−0.663982	+	0.747749i	$0.731135\pi$
$258$	8.92232	+	13.1097i	0.555479	+	0.816175i
$259$	−0.536313	−	1.65060i	−0.0333249	−	0.102563i
$260$	0.133773	−	2.17317i	0.00829623	−	0.134774i
$261$	−0.926949	−	1.27584i	−0.0573767	−	0.0789722i
$262$	7.10016	+	0.218324i	0.438649	+	0.0134881i
$263$	27.6248			1.70342			0.851709	−	0.524015i	$-0.175566\pi$
$263$	27.6248			1.70342			0.851709	+	0.524015i	$0.175566\pi$
$264$	−2.12086	−	11.3351i	−0.130530	−	0.697628i
$265$	4.50926			0.277002
$266$	8.95534	+	0.275369i	0.549087	+	0.0168840i
$267$	0.183778	+	0.252948i	0.0112470	+	0.0154802i
$268$	1.27707	−	20.7463i	0.0780096	−	1.26728i
$269$	−4.34312	−	13.3667i	−0.264805	−	0.814985i	−0.991738	−	0.128277i	$-0.959055\pi$
$269$	−4.34312	−	13.3667i	−0.264805	−	0.814985i	0.726934	−	0.686708i	$-0.240945\pi$
$270$	4.39074	+	6.45138i	0.267212	+	0.392619i
$271$	−16.7063	−	12.1379i	−1.01484	−	0.737322i	−0.0496190	−	0.998768i	$-0.515801\pi$
$271$	−16.7063	−	12.1379i	−1.01484	−	0.737322i	−0.965218	+	0.261446i	$0.915801\pi$
$272$	−19.4407	+	3.76306i	−1.17877	+	0.228169i
$273$	−0.485051	+	1.49283i	−0.0293566	+	0.0903504i
$274$	−5.60186	−	19.2332i	−0.338421	−	1.16192i
$275$	−3.19003	+	0.907591i	−0.192366	+	0.0547298i
$276$	6.80494	−	4.33147i	0.409609	−	0.260724i
$277$	22.3792	+	7.27144i	1.34464	+	0.436899i	0.890885	−	0.454230i	$-0.150085\pi$
$277$	22.3792	+	7.27144i	1.34464	+	0.436899i	0.453751	+	0.891128i	$0.350085\pi$
$278$	−18.7299	−	14.5081i	−1.12335	−	0.870140i
$279$	5.59188	−	7.69656i	0.334777	−	0.460781i
$280$	−1.31135	+	3.04731i	−0.0783683	+	0.182111i
$281$	7.16953	−	2.32952i	0.427699	−	0.138968i	−0.0872545	−	0.996186i	$-0.527809\pi$
$281$	7.16953	−	2.32952i	0.427699	−	0.138968i	0.514953	+	0.857218i	$0.327809\pi$
$282$	0.973579	−	2.70997i	0.0579758	−	0.161376i
$283$	4.57587	−	3.32457i	0.272008	−	0.197625i	−0.443416	−	0.896316i	$-0.646234\pi$
$283$	4.57587	−	3.32457i	0.272008	−	0.197625i	0.715424	+	0.698691i	$0.246234\pi$
$284$	30.3767	−	7.84323i	1.80252	−	0.465410i
$285$		−	6.63995i		−	0.393317i
$286$	3.91844	+	3.27397i	0.231702	+	0.193594i
$287$		−	6.01028i		−	0.354776i
$288$	3.79815	−	7.51703i	0.223808	−	0.442945i
$289$	6.07278	−	4.41214i	0.357223	−	0.259537i
$290$	−1.40977	−	0.506470i	−0.0827844	−	0.0297410i
$291$	0.0370398	−	0.0120350i	0.00217131	−	0.000705502i
$292$	18.4834	−	22.4042i	1.08166	−	1.31111i
$293$	7.13351	−	9.81843i	0.416744	−	0.573599i	−0.548103	−	0.836411i	$-0.684650\pi$
$293$	7.13351	−	9.81843i	0.416744	−	0.573599i	0.964847	+	0.262812i	$0.0846499\pi$
$294$	−5.98763	+	7.72999i	−0.349205	+	0.450822i
$295$	3.83149	+	1.24493i	0.223078	+	0.0724825i
$296$	3.14498	+	2.76135i	0.182798	+	0.160500i
$297$	−18.2890	−	0.676533i	−1.06123	−	0.0392564i
$298$	−2.98505	+	0.869428i	−0.172919	+	0.0503646i
$299$	−1.10374	+	3.39696i	−0.0638308	+	0.196451i
$300$	2.28716	+	0.901975i	0.132050	+	0.0520756i
$301$	8.65556	+	6.28863i	0.498898	+	0.362471i
$302$	3.52538	−	2.39933i	0.202863	−	0.138066i
$303$	−1.74694	−	5.37652i	−0.100359	−	0.308873i
$304$	−18.9050	+	10.4598i	−1.08427	+	0.599911i
$305$	8.19460	+	11.2789i	0.469221	+	0.645828i
$306$	−0.320352	+	10.4182i	−0.0183133	+	0.595571i
$307$	−0.470760			−0.0268677			−0.0134339	−	0.999910i	$-0.504276\pi$
$307$	−0.470760			−0.0268677			−0.0134339	+	0.999910i	$0.504276\pi$
$308$	−3.93224	−	6.71334i	−0.224060	−	0.382528i
$309$	−4.97477			−0.283005
$310$	0.277739	−	9.03241i	0.0157745	−	0.513006i
$311$	−8.08609	−	11.1295i	−0.458520	−	0.631099i	0.515681	−	0.856781i	$-0.327539\pi$
$311$	−8.08609	−	11.1295i	−0.458520	−	0.631099i	−0.974201	+	0.225682i	$0.927539\pi$
$312$	−0.833205	−	3.69233i	−0.0471709	−	0.209037i
$313$	8.37201	+	25.7664i	0.473214	+	1.45640i	0.848351	+	0.529434i	$0.177596\pi$
$313$	8.37201	+	25.7664i	0.473214	+	1.45640i	−0.375137	+	0.926969i	$0.622404\pi$
$314$	18.3466	−	12.4865i	1.03536	−	0.704652i
$315$	1.41276	+	1.02643i	0.0795998	+	0.0578326i
$316$	7.10114	−	18.0066i	0.399470	−	1.01295i
$317$	−1.53670	+	4.72947i	−0.0863096	+	0.265634i	−0.984892	−	0.173172i	$-0.944598\pi$
$317$	−1.53670	+	4.72947i	−0.0863096	+	0.265634i	0.898582	+	0.438806i	$0.144598\pi$
$318$	7.52654	−	2.19219i	0.422068	−	0.122932i
$319$	2.91653	−	1.95846i	0.163295	−	0.109653i
$320$	−1.03487	−	7.93278i	−0.0578510	−	0.443456i
$321$	6.42238	+	2.08676i	0.358462	+	0.116471i
$322$	3.33269	−	4.30248i	0.185723	−	0.239768i
$323$	15.7169	−	21.6324i	0.874510	−	1.20366i
$324$	3.57439	+	2.94886i	0.198577	+	0.163825i
$325$	−1.03536	+	0.336408i	−0.0574313	+	0.0186606i
$326$	−21.2045	−	7.61788i	−1.17441	−	0.421916i
$327$	15.1416	−	11.0010i	0.837332	−	0.608357i
$328$	7.40313	+	12.4602i	0.408770	+	0.688001i
$329$		−	1.94275i		−	0.107107i
$330$	−4.88335	+	3.06573i	−0.268819	+	0.168763i
$331$		−	8.10096i		−	0.445269i	−0.974902	−	0.222634i	$-0.928534\pi$
$331$		−	8.10096i		−	0.445269i	0.974902	−	0.222634i	$-0.0714656\pi$
$332$	−1.60171	−	6.20338i	−0.0879050	−	0.340455i
$333$	1.78227	−	1.29490i	0.0976680	−	0.0709599i
$334$	−7.12605	+	19.8355i	−0.389920	+	1.08535i
$335$	−9.88414	+	3.21155i	−0.540028	+	0.175466i
$336$	−0.707364	+	5.72387i	−0.0385899	+	0.312263i
$337$	−7.07709	+	9.74078i	−0.385514	+	0.530614i	−0.957035	−	0.289973i	$-0.906354\pi$
$337$	−7.07709	+	9.74078i	−0.385514	+	0.530614i	0.571521	+	0.820587i	$0.306354\pi$
$338$	−13.2094	−	10.2320i	−0.718498	−	0.556546i
$339$	16.2906	+	5.29314i	0.884785	+	0.287484i
$340$	5.31641	+	8.35232i	0.288323	+	0.452968i
$341$	16.6732	+	13.0822i	0.902905	+	0.708438i
$342$	3.18030	+	10.9191i	0.171971	+	0.590437i
$343$	−4.57566	+	14.0824i	−0.247062	+	0.760379i
$344$	−25.6903	−	2.37586i	−1.38513	−	0.128098i
$345$	−3.26298	−	2.37069i	−0.175673	−	0.127634i
$346$	9.57814	+	14.0733i	0.514924	+	0.756586i
$347$	4.19742	+	12.9183i	0.225329	+	0.693492i	0.998258	+	0.0589994i	$0.0187910\pi$
$347$	4.19742	+	12.9183i	0.225329	+	0.693492i	−0.772929	+	0.634493i	$0.781209\pi$
$348$	−2.59931	−	0.160004i	−0.139337	−	0.00857714i
$349$	−2.59967	−	3.57814i	−0.139157	−	0.191533i	0.733750	−	0.679419i	$-0.237768\pi$
$349$	−2.59967	−	3.57814i	−0.139157	−	0.191533i	−0.872907	+	0.487886i	$0.837768\pi$
$350$	1.65796	+	0.0509809i	0.0886217	+	0.00272505i
$351$	−6.00723			−0.320642
$352$	16.4213	+	9.07426i	0.875256	+	0.483660i
$353$	27.1653			1.44586			0.722931	−	0.690921i	$-0.242795\pi$
$353$	27.1653			1.44586			0.722931	+	0.690921i	$0.242795\pi$
$354$	7.00049	+	0.215259i	0.372072	+	0.0114409i
$355$	−9.22027	−	12.6906i	−0.489361	−	0.673548i
$356$	−0.507722	−	0.0312536i	−0.0269092	−	0.00165644i
$357$	−2.20568	−	6.78839i	−0.116737	−	0.359280i
$358$	5.75260	+	8.45238i	0.304034	+	0.446722i
$359$	−4.54147	−	3.29957i	−0.239690	−	0.174145i	0.461455	−	0.887163i	$-0.347327\pi$
$359$	−4.54147	−	3.29957i	−0.239690	−	0.174145i	−0.701145	+	0.713019i	$0.747327\pi$
$360$	−4.19315	−	0.387786i	−0.220999	−	0.0204381i
$361$	3.14435	−	9.67732i	0.165492	−	0.509333i
$362$	−10.0002	−	34.3343i	−0.525601	−	1.80457i
$363$	0.999045	−	13.4853i	0.0524363	−	0.707795i
$364$	−1.37128	−	2.15435i	−0.0718748	−	0.112919i
$365$	−13.8115	−	4.48763i	−0.722927	−	0.234893i
$366$	19.1611	+	14.8421i	1.00157	+	0.775811i
$367$	20.6644	−	28.4421i	1.07867	−	1.48467i	0.217699	−	0.976016i	$-0.430145\pi$
$367$	20.6644	−	28.4421i	1.07867	−	1.48467i	0.860974	−	0.508650i	$-0.169855\pi$
$368$	−1.60961	+	13.0247i	−0.0839069	+	0.678960i
$369$	7.25574	−	2.35753i	0.377719	−	0.122728i
$370$	0.707512	−	1.96937i	0.0367818	−	0.102383i
$371$	4.27885	−	3.10877i	0.222147	−	0.161399i
$372$	−3.92754	−	15.2113i	−0.203633	−	0.788669i
$373$			0.260135i			0.0134693i	0.999977	+	0.00673465i	$0.00214372\pi$
$373$			0.260135i			0.0134693i	−0.999977	+	0.00673465i	$0.997856\pi$
$374$	−23.1662	−	1.57108i	−1.19789	−	0.0812384i
$375$		−	1.22930i		−	0.0634806i
$376$	2.39297	+	4.02762i	0.123408	+	0.207709i
$377$	0.932897	−	0.677790i	0.0480467	−	0.0349079i
$378$	8.61409	+	3.09468i	0.443061	+	0.159173i
$379$	18.0893	−	5.87758i	0.929186	−	0.301911i	0.194956	−	0.980812i	$-0.437544\pi$
$379$	18.0893	−	5.87758i	0.929186	−	0.301911i	0.734230	+	0.678901i	$0.237544\pi$
$380$	8.33304	+	6.87472i	0.427476	+	0.352666i
$381$	−12.0868	+	16.6360i	−0.619224	+	0.852289i
$382$	−1.51041	+	1.94994i	−0.0772795	+	0.0997675i
$383$	−7.47256	−	2.42798i	−0.381830	−	0.124064i	0.111812	−	0.993729i	$-0.464335\pi$
$383$	−7.47256	−	2.42798i	−0.381830	−	0.124064i	−0.493642	+	0.869665i	$0.664335\pi$
$384$	−5.58387	−	12.7377i	−0.284951	−	0.650020i
$385$	−2.40132	+	3.06048i	−0.122382	+	0.155977i
$386$	−15.6060	+	4.54540i	−0.794323	+	0.231355i
$387$	−4.19663	+	12.9159i	−0.213327	+	0.656552i
$388$	−0.0232458	+	0.0589449i	−0.00118012	+	0.00299248i
$389$	25.3393	+	18.4101i	1.28475	+	0.933428i	0.999685	−	0.0250786i	$-0.00798362\pi$
$389$	25.3393	+	18.4101i	1.28475	+	0.933428i	0.285069	+	0.958507i	$0.407984\pi$
$390$	−1.56460	+	1.06485i	−0.0792267	+	0.0539208i
$391$	−5.01905	−	15.4470i	−0.253824	−	0.781191i
$392$	−3.50169	−	15.5177i	−0.176862	−	0.783762i
$393$	−3.62939	−	4.99543i	−0.183079	−	0.251986i
$394$	−0.496022	+	16.1312i	−0.0249892	+	0.812679i
$395$	−9.67810			−0.486958
$396$	6.56207	−	7.38040i	0.329756	−	0.370879i
$397$	11.4928			0.576805			0.288403	−	0.957509i	$-0.406876\pi$
$397$	11.4928			0.576805			0.288403	+	0.957509i	$0.406876\pi$
$398$	−0.503936	+	16.3886i	−0.0252600	+	0.821487i
$399$	−4.57770	−	6.30067i	−0.229172	−	0.315428i
$400$	−3.50000	+	1.93649i	−0.175000	+	0.0968246i
$401$	−10.2784	−	31.6336i	−0.513277	−	1.57970i	−0.786395	−	0.617724i	$-0.788055\pi$
$401$	−10.2784	−	31.6336i	−0.513277	−	1.57970i	0.273118	−	0.961980i	$-0.411945\pi$
$402$	−14.9366	+	10.1657i	−0.744971	+	0.507018i
$403$	5.62776	+	4.08881i	0.280339	+	0.203678i
$404$	8.55616	+	3.37424i	0.425685	+	0.167875i
$405$	0.715961	−	2.20350i	0.0355764	−	0.109493i
$406$	−1.68690	+	0.491328i	−0.0837196	+	0.0243842i
$407$	2.73587	+	4.07424i	0.135612	+	0.201953i
$408$	12.9343	+	11.3565i	0.640342	+	0.562232i
$409$	6.59049	+	2.14138i	0.325879	+	0.105884i	0.467388	−	0.884053i	$-0.345195\pi$
$409$	6.59049	+	2.14138i	0.325879	+	0.105884i	−0.141509	+	0.989937i	$0.545195\pi$
$410$	4.43773	−	5.72909i	0.219164	−	0.282940i
$411$	−10.2351	+	14.0874i	−0.504861	+	0.694881i
$412$	5.15067	−	6.24327i	0.253755	−	0.307584i
$413$	4.49399	−	1.46019i	0.221135	−	0.0718511i
$414$	6.50130	+	2.33564i	0.319521	+	0.114791i
$415$	−2.59161	+	1.88292i	−0.127217	+	0.0924288i
$416$	5.49649	+	2.77723i	0.269488	+	0.136165i
$417$			20.5939i			1.00849i
$418$	−24.5694	+	6.18066i	−1.20173	+	0.302306i
$419$			14.0522i			0.686493i	0.939245	+	0.343246i	$0.111527\pi$
$419$			14.0522i			0.686493i	−0.939245	+	0.343246i	$0.888473\pi$
$420$	2.79214	−	0.720927i	0.136242	−	0.0351776i
$421$	−20.5969	+	14.9645i	−1.00383	+	0.729327i	−0.962906	−	0.269836i	$-0.913031\pi$
$421$	−20.5969	+	14.9645i	−1.00383	+	0.729327i	−0.0409255	+	0.999162i	$0.513031\pi$
$422$	−11.3738	+	31.6590i	−0.553666	+	1.54114i
$423$	2.34533	−	0.762044i	0.114034	−	0.0370518i
$424$	−5.04151	+	11.7154i	−0.244837	+	0.568950i
$425$	2.90977	−	4.00495i	0.141144	−	0.194269i
$426$	−21.5594	−	16.6998i	−1.04456	−	0.809110i
$427$	15.5518	+	5.05307i	0.752602	+	0.244535i
$428$	−9.26831	+	5.89945i	−0.448001	+	0.285161i
$429$	0.164074	−	4.43548i	0.00792157	−	0.214147i
$430$	3.60735	+	12.3853i	0.173962	+	0.597273i
$431$	7.68857	−	23.6630i	0.370345	−	1.13981i	−0.576220	−	0.817295i	$-0.695473\pi$
$431$	7.68857	−	23.6630i	0.370345	−	1.13981i	0.946566	−	0.322512i	$-0.104527\pi$
$432$	−21.6702	+	4.19461i	−1.04261	+	0.201813i
$433$	−21.8035	−	15.8411i	−1.04781	−	0.761277i	−0.0760133	−	0.997107i	$-0.524219\pi$
$433$	−21.8035	−	15.8411i	−1.04781	−	0.761277i	−0.971794	+	0.235830i	$0.924219\pi$
$434$	−5.96356	−	8.76236i	−0.286260	−	0.420607i
$435$	0.402375	+	1.23838i	0.0192924	+	0.0593759i
$436$	−1.87086	+	30.3925i	−0.0895978	+	1.45553i
$437$	−10.4166	−	14.3372i	−0.498294	−	0.685843i
$438$	−25.2349	−	0.775952i	−1.20577	−	0.0370764i
$439$	31.9624			1.52548			0.762742	−	0.646703i	$-0.223853\pi$
$439$	31.9624			1.52548			0.762742	+	0.646703i	$0.223853\pi$
$440$	1.20857	−	9.30265i	0.0576163	−	0.443487i
$441$	−8.37360			−0.398743
$442$	−7.61787	−	0.234243i	−0.362345	−	0.0111418i
$443$	−24.5259	−	33.7570i	−1.16526	−	1.60384i	−0.689549	−	0.724239i	$-0.742191\pi$
$443$	−24.5259	−	33.7570i	−1.16526	−	1.60384i	−0.475710	−	0.879602i	$-0.657809\pi$
$444$	0.223518	−	3.63109i	0.0106077	−	0.172324i
$445$	0.0785959	+	0.241893i	0.00372580	+	0.0114668i
$446$	4.94334	+	7.26333i	0.234074	+	0.343929i
$447$	2.18641	+	1.58852i	0.103414	+	0.0751346i
$448$	−6.45100	−	6.81399i	−0.304781	−	0.321931i
$449$	0.860114	−	2.64716i	0.0405913	−	0.124927i	−0.928707	−	0.370813i	$-0.879079\pi$
$449$	0.860114	−	2.64716i	0.0405913	−	0.124927i	0.969299	+	0.245886i	$0.0790790\pi$
$450$	0.588790	+	2.02152i	0.0277558	+	0.0952955i
$451$	4.65073	+	16.3465i	0.218994	+	0.769727i
$452$	−23.5094	+	14.9642i	−1.10579	+	0.703856i
$453$	−3.52538	−	1.14547i	−0.165637	−	0.0538187i
$454$	12.7317	+	9.86196i	0.597530	+	0.462845i
$455$	−0.750529	+	1.03301i	−0.0351853	+	0.0484284i
$456$	17.2511	+	7.42369i	0.807856	+	0.347646i
$457$	−5.57551	+	1.81159i	−0.260811	+	0.0847427i	−0.436504	−	0.899702i	$-0.643783\pi$
$457$	−5.57551	+	1.81159i	−0.260811	+	0.0847427i	0.175693	+	0.984445i	$0.443783\pi$
$458$	9.86899	−	27.4705i	0.461148	−	1.28361i
$459$	22.0997	−	16.0564i	1.03153	−	0.749448i
$460$	6.35353	−	1.64048i	0.296235	−	0.0764875i
$461$		−	37.8294i		−	1.76189i	−0.473219	−	0.880945i	$-0.656908\pi$
$461$		−	37.8294i		−	1.76189i	0.473219	−	0.880945i	$-0.343092\pi$
$462$	−2.52025	+	6.27575i	−0.117253	+	0.291974i
$463$			34.9685i			1.62513i	0.582873	+	0.812563i	$0.301928\pi$
$463$			34.9685i			1.62513i	−0.582873	+	0.812563i	$0.698072\pi$
$464$	2.89202	−	3.09643i	0.134258	−	0.143748i
$465$	−6.35489	+	4.61710i	−0.294701	+	0.214113i
$466$	15.7217	+	5.64815i	0.728294	+	0.261646i
$467$	24.6769	−	8.01802i	1.14191	−	0.371030i	0.323821	−	0.946118i	$-0.395033\pi$
$467$	24.6769	−	8.01802i	1.14191	−	0.371030i	0.818091	+	0.575089i	$0.195033\pi$
$468$	2.06289	−	2.50049i	0.0953572	−	0.115585i
$469$	−7.16499	+	9.86176i	−0.330848	+	0.455374i
$470$	1.43444	−	1.85186i	0.0661659	−	0.0854198i
$471$	−18.3466	−	5.96116i	−0.845365	−	0.274676i
$472$	−7.51816	+	8.56264i	−0.346051	+	0.394128i
$473$	−28.4071	−	10.4059i	−1.30616	−	0.478465i
$474$	−16.1540	+	4.70503i	−0.741979	+	0.216109i
$475$	1.66913	−	5.13706i	0.0765850	−	0.235704i
$476$	10.8030	+	4.26032i	0.495155	+	0.195271i
$477$	5.43135	+	3.94611i	0.248685	+	0.180680i
$478$	−24.7023	+	16.8121i	−1.12986	+	0.768967i
$479$	1.60201	+	4.93049i	0.0731979	+	0.225280i	0.980962	−	0.194202i	$-0.0622117\pi$
$479$	1.60201	+	4.93049i	0.0731979	+	0.225280i	−0.907764	+	0.419482i	$0.862212\pi$
$480$	−4.90053	+	4.93379i	−0.223677	+	0.225196i
$481$	0.946835	+	1.30321i	0.0431720	+	0.0594211i
$482$	0.245370	−	7.97972i	0.0111763	−	0.363466i
$483$	−4.73065			−0.215252
$484$	15.8895	+	15.2159i	0.722250	+	0.691632i
$485$	0.0316815			0.00143858
$486$	−0.595743	+	19.3743i	−0.0270235	+	0.878835i
$487$	13.4505	+	18.5131i	0.609502	+	0.838908i	0.996536	−	0.0831573i	$-0.0265004\pi$
$487$	13.4505	+	18.5131i	0.609502	+	0.838908i	−0.387034	+	0.922065i	$0.626500\pi$
$488$	−38.4653	+	8.68000i	−1.74124	+	0.392925i
$489$	6.05218	+	18.6267i	0.273689	+	0.842328i
$490$	−6.57552	+	4.47523i	−0.297052	+	0.202170i
$491$	−8.56332	−	6.22162i	−0.386457	−	0.280778i	0.377545	−	0.925991i	$-0.376768\pi$
$491$	−8.56332	−	6.22162i	−0.386457	−	0.280778i	−0.764002	+	0.645214i	$0.776768\pi$
$492$	4.62195	−	11.7200i	0.208374	−	0.528379i
$493$	−1.62037	+	4.98698i	−0.0729778	+	0.224602i
$494$	−7.98410	+	2.32545i	−0.359221	+	0.104627i
$495$	−4.63660	−	1.69845i	−0.208399	−	0.0763396i
$496$	23.1564	+	10.8201i	1.03975	+	0.485838i
$497$	−17.4983	−	5.68554i	−0.784905	−	0.255031i
$498$	−3.41036	+	4.40275i	−0.152822	+	0.197292i
$499$	−13.6423	+	18.7770i	−0.610713	+	0.840575i	−0.996636	−	0.0819562i	$-0.973883\pi$
$499$	−13.6423	+	18.7770i	−0.610713	+	0.840575i	0.385922	+	0.922531i	$0.373883\pi$
$500$	1.54275	+	1.27276i	0.0689939	+	0.0569196i
$501$	17.4241	−	5.66143i	0.778451	−	0.252934i
$502$	−26.4794	−	9.51296i	−1.18184	−	0.424584i
$503$	−10.6983	+	7.77275i	−0.477013	+	0.346570i	−0.800168	−	0.599776i	$-0.795256\pi$
$503$	−10.6983	+	7.77275i	−0.477013	+	0.346570i	0.323155	+	0.946346i	$0.395256\pi$
$504$	−4.24624	+	2.52287i	−0.189143	+	0.112377i
$505$		−	4.59873i		−	0.204641i
$506$	−5.73486	+	14.2805i	−0.254946	+	0.634847i
$507$			14.5240i			0.645032i
$508$	−8.36383	−	32.3930i	−0.371085	−	1.43721i
$509$	−1.56969	+	1.14045i	−0.0695754	+	0.0505495i	−0.622029	−	0.782994i	$-0.713692\pi$
$509$	−1.56969	+	1.14045i	−0.0695754	+	0.0505495i	0.552454	+	0.833543i	$0.313692\pi$
$510$	2.90977	−	8.09937i	0.128847	−	0.358646i
$511$	−16.1996	+	5.26358i	−0.716630	+	0.232847i
$512$	21.7670	+	6.18045i	0.961974	+	0.273140i
$513$	17.5193	−	24.1132i	0.773496	−	1.06463i
$514$	−3.50069	−	2.71162i	−0.154409	−	0.119605i
$515$	−3.84878	−	1.25054i	−0.169597	−	0.0551055i
$516$	12.0423	+	18.9190i	0.530132	+	0.832862i
$517$	1.50329	+	5.28381i	0.0661146	+	0.232382i
$518$	−0.686359	−	2.35651i	−0.0301569	−	0.103539i
$519$	4.57270	−	14.0733i	0.200719	−	0.617750i
$520$	0.283551	−	3.06605i	0.0124345	−	0.134455i
$521$	33.4080	+	24.2723i	1.46363	+	1.06339i	0.982399	+	0.186794i	$0.0598098\pi$
$521$	33.4080	+	24.2723i	1.46363	+	1.06339i	0.481230	+	0.876594i	$0.340190\pi$
$522$	−1.25483	−	1.84374i	−0.0549224	−	0.0806984i
$523$	1.72381	+	5.30533i	0.0753768	+	0.231986i	0.981645	−	0.190717i	$-0.0610813\pi$
$523$	1.72381	+	5.30533i	0.0753768	+	0.231986i	−0.906268	+	0.422703i	$0.861081\pi$
$524$	10.0269	+	0.617222i	0.438028	+	0.0269635i
$525$	−0.847500	−	1.16648i	−0.0369879	−	0.0509095i
$526$	39.0489	+	1.20072i	1.70261	+	0.0523540i
$527$	−31.6325			−1.37793
$528$	−2.50524	−	16.1149i	−0.109027	−	0.701311i
$529$	12.2354			0.531972
$530$	6.37404	+	0.195997i	0.276871	+	0.00851355i
$531$	3.52554	+	4.85249i	0.152995	+	0.210580i
$532$	12.6468	+	0.778495i	0.548309	+	0.0337520i
$533$	1.72384	+	5.30544i	0.0746678	+	0.229804i
$534$	0.248784	+	0.365542i	0.0107659	+	0.0158185i
$535$	4.44417	+	3.22888i	0.192138	+	0.139597i
$536$	2.70695	−	29.2704i	0.116922	−	1.26429i
$537$	2.74635	−	8.45238i	0.118514	−	0.364747i
$538$	−5.55820	−	19.0833i	−0.239631	−	0.822738i
$539$	0.689551	−	18.6409i	0.0297010	−	0.802920i
$540$	5.92610	+	9.31017i	0.255019	+	0.400646i
$541$	−1.33241	−	0.432925i	−0.0572847	−	0.0186129i	0.280234	−	0.959932i	$-0.409588\pi$
$541$	−1.33241	−	0.432925i	−0.0572847	−	0.0186129i	−0.337519	+	0.941319i	$0.609588\pi$
$542$	−23.0876	−	17.8836i	−0.991696	−	0.768165i
$543$	−18.2713	+	25.1483i	−0.784098	+	1.07922i
$544$	−27.6439	+	4.47425i	−1.18522	+	0.191832i
$545$	14.4798	−	4.70478i	0.620248	−	0.201531i
$546$	−0.750529	+	2.08911i	−0.0321197	+	0.0894055i
$547$	32.1360	−	23.3482i	1.37404	−	0.998296i	0.376627	−	0.926365i	$-0.377084\pi$
$547$	32.1360	−	23.3482i	1.37404	−	0.998296i	0.997410	−	0.0719306i	$-0.0229160\pi$
$548$	−7.08251	−	27.4304i	−0.302550	−	1.17177i
$549$			20.7565i			0.885865i
$550$	−4.54870	+	1.14427i	−0.193957	+	0.0487916i
$551$			5.72137i			0.243739i
$552$	9.80736	−	5.82695i	0.417429	−	0.248011i
$553$	−9.18358	+	6.67226i	−0.390526	+	0.283734i
$554$	31.3180	+	11.2512i	1.33057	+	0.478019i
$555$	−1.72995	+	0.562096i	−0.0734325	+	0.0238597i
$556$	−25.8450	−	21.3220i	−1.09607	−	0.904255i
$557$	−21.9168	+	30.1659i	−0.928646	+	1.27817i	0.0317396	+	0.999496i	$0.489895\pi$
$557$	−21.9168	+	30.1659i	−0.928646	+	1.27817i	−0.960385	+	0.278675i	$0.910105\pi$
$558$	8.23890	−	10.6364i	0.348781	−	0.450274i
$559$	−9.44417	−	3.06860i	−0.399446	−	0.129788i
$560$	−1.98611	+	4.25051i	−0.0839284	+	0.179617i
$561$	11.2517	+	16.7560i	0.475049	+	0.707440i
$562$	10.2357	−	2.98126i	0.431768	−	0.125757i
$563$	5.64739	−	17.3809i	0.238009	−	0.732517i	−0.758699	−	0.651442i	$-0.774165\pi$
$563$	5.64739	−	17.3809i	0.238009	−	0.732517i	0.996708	−	0.0810755i	$-0.0258355\pi$
$564$	1.49399	−	3.78835i	0.0629083	−	0.159518i
$565$	11.2728	+	8.19017i	0.474251	+	0.344563i
$566$	6.61271	−	4.50054i	0.277953	−	0.189172i
$567$	−0.839757	−	2.58451i	−0.0352665	−	0.108539i
$568$	43.2797	−	9.76642i	1.81598	−	0.409790i
$569$	−16.4429	−	22.6317i	−0.689321	−	0.948769i	0.310677	−	0.950515i	$-0.399444\pi$
$569$	−16.4429	−	22.6317i	−0.689321	−	0.948769i	−0.999998	+	0.00174640i	$0.999444\pi$
$570$	0.288608	−	9.38587i	0.0120885	−	0.393131i
$571$	2.95106			0.123498			0.0617489	−	0.998092i	$-0.480332\pi$
$571$	2.95106			0.123498			0.0617489	+	0.998092i	$0.480332\pi$
$572$	5.39658	+	4.79822i	0.225643	+	0.200624i
$573$	2.14399			0.0895664
$574$	0.261239	−	8.49581i	0.0109039	−	0.354608i
$575$	−1.92849	−	2.65434i	−0.0804238	−	0.110694i
$576$	5.69559	−	10.4606i	0.237316	−	0.435857i
$577$	13.2912	+	40.9060i	0.553318	+	1.70294i	0.700343	+	0.713806i	$0.253030\pi$
$577$	13.2912	+	40.9060i	0.553318	+	1.70294i	−0.147025	+	0.989133i	$0.546970\pi$
$578$	8.77593	−	5.97280i	0.365031	−	0.248436i
$579$	11.4307	+	8.30486i	0.475042	+	0.345138i
$580$	−1.97076	−	0.777195i	−0.0818312	−	0.0322713i
$581$	−1.16107	+	3.57341i	−0.0481694	+	0.148250i
$582$	0.0528806	−	0.0154020i	0.00219197	−	0.000638434i
$583$	−9.23189	+	11.7660i	−0.382346	+	0.487300i
$584$	27.1009	−	30.8660i	1.12145	−	1.27725i
$585$	−1.54147	−	0.500854i	−0.0637320	−	0.0207078i
$586$	10.5103	−	13.5687i	0.434176	−	0.560519i
$587$	−5.66886	+	7.80252i	−0.233979	+	0.322045i	−0.909820	−	0.415003i	$-0.863781\pi$
$587$	−5.66886	+	7.80252i	−0.233979	+	0.322045i	0.675841	+	0.737047i	$0.263781\pi$
$588$	−8.79977	+	10.6664i	−0.362896	+	0.439877i
$589$	−32.8253	+	10.6656i	−1.35254	+	0.439467i
$590$	5.36188	+	1.92630i	0.220745	+	0.0793045i
$591$	11.3494	−	8.24580i	0.466851	−	0.339187i
$592$	4.32555	+	4.03999i	0.177779	+	0.166043i
$593$		−	21.0743i		−	0.865419i	−0.901533	−	0.432710i	$-0.857558\pi$
$593$		−	21.0743i		−	0.865419i	0.901533	−	0.432710i	$-0.142442\pi$
$594$	−25.8229	−	1.75125i	−1.05953	−	0.0718545i
$595$		−	5.80636i		−	0.238038i
$596$	−4.25730	+	1.09923i	−0.174386	+	0.0450262i
$597$	11.5305	−	8.37737i	0.471910	−	0.342863i
$598$	−1.70783	+	4.75378i	−0.0698386	+	0.194397i
$599$	−26.9630	+	8.76080i	−1.10168	+	0.357957i	−0.802748	−	0.596319i	$-0.796630\pi$
$599$	−26.9630	+	8.76080i	−1.10168	+	0.357957i	−0.298929	+	0.954275i	$0.596630\pi$
$600$	3.19381	+	1.37440i	0.130387	+	0.0561095i
$601$	12.0497	−	16.5849i	0.491516	−	0.676514i	−0.489150	−	0.872199i	$-0.662693\pi$
$601$	12.0497	−	16.5849i	0.491516	−	0.676514i	0.980667	+	0.195685i	$0.0626931\pi$
$602$	11.9617	+	9.26549i	0.487522	+	0.377633i
$603$	−14.7158	−	4.78145i	−0.599274	−	0.194716i
$604$	5.08757	−	3.23834i	0.207010	−	0.131766i
$605$	4.16282	−	10.1819i	0.169243	−	0.413953i
$606$	−2.23568	−	7.67588i	−0.0908184	−	0.311811i
$607$	3.85789	−	11.8734i	0.156587	−	0.481925i	−0.841731	−	0.539897i	$-0.818463\pi$
$607$	3.85789	−	11.8734i	0.156587	−	0.481925i	0.998318	+	0.0579714i	$0.0184632\pi$
$608$	−27.1777	+	13.9637i	−1.10220	+	0.566303i
$609$	1.23558	+	0.897701i	0.0500682	+	0.0363767i
$610$	11.0932	+	16.2994i	0.449150	+	0.659944i
$611$	0.557210	+	1.71492i	0.0225423	+	0.0693781i
$612$	−0.905665	+	14.7127i	−0.0366094	+	0.594727i
$613$	−9.79969	−	13.4881i	−0.395806	−	0.544780i	0.563879	−	0.825857i	$-0.309308\pi$
$613$	−9.79969	−	13.4881i	−0.395806	−	0.544780i	−0.959685	+	0.281077i	$0.909308\pi$
$614$	−0.665441	−	0.0204618i	−0.0268550	−	0.000825770i
$615$	−6.29923			−0.254009
$616$	−5.26661	−	9.66053i	−0.212198	−	0.389234i
$617$	41.3214			1.66354			0.831769	−	0.555121i	$-0.187328\pi$
$617$	41.3214			1.66354			0.831769	+	0.555121i	$0.187328\pi$
$618$	−7.03207	−	0.216230i	−0.282871	−	0.00869806i
$619$	18.0636	+	24.8624i	0.726037	+	0.999304i	0.999302	+	0.0373650i	$0.0118964\pi$
$619$	18.0636	+	24.8624i	0.726037	+	0.999304i	−0.273265	+	0.961939i	$0.588104\pi$
$620$	0.785194	−	12.7556i	0.0315342	−	0.512279i
$621$	−5.59464	−	17.2185i	−0.224505	−	0.690955i
$622$	−10.9463	−	16.0836i	−0.438907	−	0.644893i
$623$	0.241346	+	0.175348i	0.00966931	+	0.00702516i
$624$	−1.01728	−	5.25549i	−0.0407240	−	0.210388i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	10.7143	+	36.7859i	0.428228	+	1.47026i
$627$	17.3257	+	13.5941i	0.691921	+	0.542895i
$628$	26.4764	−	16.8527i	1.05652	−	0.672498i
$629$	−6.96654	−	2.26357i	−0.277774	−	0.0902544i
$630$	1.95238	+	1.51231i	0.0777847	+	0.0602518i
$631$	−6.22294	+	8.56514i	−0.247731	+	0.340973i	−0.914715	−	0.404099i	$-0.867585\pi$
$631$	−6.22294	+	8.56514i	−0.247731	+	0.340973i	0.666984	+	0.745072i	$0.267585\pi$
$632$	10.8204	−	25.1444i	0.430414	−	1.00019i
$633$	27.8103	−	9.03610i	1.10536	−	0.359153i
$634$	−2.37776	+	6.61853i	−0.0944330	+	0.262856i
$635$	−13.5330	+	9.83227i	−0.537039	+	0.390182i
$636$	10.7344	−	2.77161i	0.425647	−	0.109901i
$637$		−	6.12282i		−	0.242595i
$638$	4.20778	−	2.64161i	0.166588	−	0.104582i
$639$		−	23.3545i		−	0.923888i
$640$	−1.11803	−	11.2583i	−0.0441942	−	0.445025i
$641$	−25.8134	+	18.7545i	−1.01957	+	0.740758i	−0.966194	−	0.257816i	$-0.916997\pi$
$641$	−25.8134	+	18.7545i	−1.01957	+	0.740758i	−0.0533724	+	0.998575i	$0.516997\pi$
$642$	8.98763	+	3.22888i	0.354713	+	0.127434i
$643$	−31.0930	+	10.1027i	−1.22619	+	0.398412i	−0.849332	−	0.527860i	$-0.822995\pi$
$643$	−31.0930	+	10.1027i	−1.22619	+	0.398412i	−0.376855	+	0.926272i	$0.622995\pi$
$644$	4.89791	−	5.93690i	0.193005	−	0.233947i
$645$	6.59096	−	9.07168i	0.259519	−	0.357197i
$646$	23.1568	−	29.8953i	0.911091	−	1.17621i
$647$	25.7250	+	8.35856i	1.01135	+	0.328609i	0.767394	−	0.641176i	$-0.221553\pi$
$647$	25.7250	+	8.35856i	1.01135	+	0.328609i	0.243961	+	0.969785i	$0.421553\pi$
$648$	4.92439	+	4.32371i	0.193448	+	0.169851i
$649$	−11.0927	+	7.44879i	−0.435426	+	0.292390i
$650$	−1.47815	+	0.430526i	−0.0579777	+	0.0168866i
$651$	−2.84706	+	8.76236i	−0.111585	+	0.343424i
$652$	−29.6424	−	11.6899i	−1.16089	−	0.457811i
$653$	8.43560	+	6.12882i	0.330111	+	0.239839i	0.740478	−	0.672081i	$-0.234599\pi$
$653$	8.43560	+	6.12882i	0.330111	+	0.239839i	−0.410367	+	0.911920i	$0.634599\pi$
$654$	21.8815	−	14.8923i	0.855634	−	0.582335i
$655$	−1.55218	−	4.77710i	−0.0606485	−	0.186657i
$656$	9.92307	+	17.9349i	0.387431	+	0.700240i
$657$	−12.7086	−	17.4919i	−0.495811	−	0.682425i
$658$	0.0844424	−	2.74617i	0.00329191	−	0.107057i
$659$	21.1112			0.822377			0.411189	−	0.911550i	$-0.365114\pi$
$659$	21.1112			0.822377			0.411189	+	0.911550i	$0.365114\pi$
$660$	−7.03608	+	4.12129i	−0.273879	+	0.160421i
$661$	−29.6003			−1.15132			−0.575659	−	0.817690i	$-0.695254\pi$
$661$	−29.6003			−1.15132			−0.575659	+	0.817690i	$0.695254\pi$
$662$	0.352111	−	11.4511i	0.0136852	−	0.445058i
$663$	3.89403	+	5.35967i	0.151232	+	0.208152i
$664$	−1.99445	−	8.83837i	−0.0773997	−	0.342995i
$665$	−1.95774	−	6.02530i	−0.0759178	−	0.233651i
$666$	2.57561	−	1.75293i	0.0998028	−	0.0679246i
$667$	2.81157	+	2.04273i	0.108865	+	0.0790947i
$668$	−10.9352	+	27.7286i	−0.423094	+	1.07285i
$669$	2.36000	−	7.26333i	0.0912428	−	0.280816i
$670$	−14.1113	+	4.11005i	−0.545166	+	0.158785i
$671$	−46.2071	−	1.70926i	−1.78380	−	0.0659852i
$672$	−1.24868	+	8.06020i	−0.0481689	+	0.310929i
$673$	−24.4137	−	7.93249i	−0.941078	−	0.305775i	−0.201993	−	0.979387i	$-0.564742\pi$
$673$	−24.4137	−	7.93249i	−0.941078	−	0.305775i	−0.739085	+	0.673612i	$0.764742\pi$
$674$	−10.4272	+	13.4614i	−0.401640	+	0.518515i
$675$	3.24346	−	4.46424i	0.124841	−	0.171829i
$676$	−18.2274	−	15.0375i	−0.701053	−	0.578366i
$677$	−13.0270	+	4.23272i	−0.500667	+	0.162677i	−0.548453	−	0.836181i	$-0.684783\pi$
$677$	−13.0270	+	4.23272i	−0.500667	+	0.162677i	0.0477867	+	0.998858i	$0.484783\pi$
$678$	22.7975	+	8.19017i	0.875531	+	0.314542i
$679$	0.0300627	−	0.0218418i	0.00115370	−	0.000838212i
$680$	7.15195	+	12.0375i	0.274265	+	0.461616i
$681$		−	13.9988i		−	0.536433i
$682$	22.9997	+	19.2169i	0.880705	+	0.735854i
$683$		−	33.6874i		−	1.28901i	−0.764599	−	0.644506i	$-0.777063\pi$
$683$		−	33.6874i		−	1.28901i	0.764599	−	0.644506i	$-0.222937\pi$
$684$	4.02090	+	15.5729i	0.153743	+	0.595444i
$685$	−11.4597	+	8.32599i	−0.437854	+	0.318120i
$686$	−7.08000	+	19.7073i	−0.270316	+	0.752427i
$687$	−24.1309	+	7.84061i	−0.920652	+	0.299138i
$688$	−36.2111	−	4.47502i	−1.38054	−	0.170609i
$689$	−2.88541	+	3.97143i	−0.109926	+	0.151300i
$690$	−4.50932	−	3.49291i	−0.171667	−	0.132973i
$691$	47.4696	+	15.4238i	1.80583	+	0.586749i	0.999986	−	0.00537974i	$-0.00171243\pi$
$691$	47.4696	+	15.4238i	1.80583	+	0.586749i	0.805843	+	0.592129i	$0.201712\pi$
$692$	12.9274	+	20.3096i	0.491427	+	0.772055i
$693$	−5.57062	+	1.58489i	−0.211611	+	0.0602051i
$694$	5.37174	+	18.4431i	0.203909	+	0.700090i
$695$	−5.17682	+	15.9326i	−0.196368	+	0.604359i
$696$	−3.66728	−	0.339153i	−0.139008	−	0.0128556i
$697$	−20.5224	−	14.9104i	−0.777341	−	0.564771i
$698$	−3.51923	−	5.17086i	−0.133205	−	0.195720i
$699$	−4.48728	−	13.8104i	−0.169725	−	0.522359i
$700$	2.34139	+	0.144128i	0.0884961	+	0.00544752i
$701$	9.05876	+	12.4683i	0.342144	+	0.470921i	0.945066	−	0.326879i	$-0.105997\pi$
$701$	9.05876	+	12.4683i	0.342144	+	0.470921i	−0.602922	+	0.797800i	$0.705997\pi$
$702$	−8.49149	−	0.261106i	−0.320491	−	0.00985483i
$703$	−7.99244			−0.301441
$704$	22.8178	+	13.5406i	0.859978	+	0.510332i
$705$	−2.03615			−0.0766858
$706$	38.3993	+	1.18075i	1.44518	+	0.0444381i
$707$	−3.17045	−	4.36375i	−0.119237	−	0.164116i
$708$	9.88615	+	0.608558i	0.371544	+	0.0228710i
$709$	7.62254	+	23.4598i	0.286270	+	0.881050i	0.986015	+	0.166657i	$0.0532972\pi$
$709$	7.62254	+	23.4598i	0.286270	+	0.881050i	−0.699745	+	0.714393i	$0.746703\pi$
$710$	−12.4817	−	18.3395i	−0.468428	−	0.688270i
$711$	−11.6572	−	8.46942i	−0.437178	−	0.317628i
$712$	−0.716330	−	0.0662468i	−0.0268456	−	0.00248270i
$713$	−6.47852	+	19.9388i	−0.242623	+	0.746715i
$714$	−2.82277	−	9.69157i	−0.105640	−	0.362698i
$715$	1.24191	−	3.39030i	0.0464450	−	0.126790i
$716$	7.76417	+	12.1979i	0.290161	+	0.455856i
$717$	24.7023	+	8.02625i	0.922523	+	0.299746i
$718$	−6.27616	−	4.86149i	−0.234224	−	0.181429i
$719$	−28.5063	+	39.2355i	−1.06310	+	1.46324i	−0.186237	+	0.982505i	$0.559629\pi$
$719$	−28.5063	+	39.2355i	−1.06310	+	1.46324i	−0.876867	+	0.480732i	$0.840371\pi$
$720$	−5.91036	−	0.730410i	−0.220266	−	0.0272208i
$721$	−4.51427	+	1.46677i	−0.168120	+	0.0546255i
$722$	4.86531	−	13.5427i	0.181068	−	0.504006i
$723$	−5.61426	+	4.07900i	−0.208796	+	0.151699i
$724$	−12.6434	−	48.9678i	−0.469890	−	1.81987i
$725$			1.05923i			0.0393390i
$726$	1.99834	−	19.0187i	0.0741653	−	0.705849i
$727$		−	3.60653i		−	0.133759i	−0.997761	−	0.0668795i	$-0.978696\pi$
$727$		−	3.60653i		−	0.133759i	0.997761	−	0.0668795i	$-0.0213043\pi$
$728$	−1.84473	−	3.10488i	−0.0683703	−	0.115074i
$729$	19.2543	−	13.9891i	0.713122	−	0.518114i
$730$	−19.3281	−	6.94379i	−0.715367	−	0.257001i
$731$	42.9456	−	13.9539i	1.58840	−	0.516103i
$732$	26.4400	+	21.8129i	0.977250	+	0.806227i
$733$	−0.0867563	+	0.119410i	−0.00320442	+	0.00441050i	−0.810616	−	0.585578i	$-0.800868\pi$
$733$	−0.0867563	+	0.119410i	−0.00320442	+	0.00441050i	0.807412	+	0.589988i	$0.200868\pi$
$734$	30.4463	−	39.3060i	1.12379	−	1.45081i
$735$	6.57552	+	2.13652i	0.242542	+	0.0788066i
$736$	−2.84139	+	18.3411i	−0.104735	+	0.676061i
$737$	11.8560	−	32.3658i	0.436723	−	1.19221i
$738$	10.3588	−	3.01711i	0.381312	−	0.111061i
$739$	−5.49675	+	16.9173i	−0.202201	+	0.622311i	0.797616	+	0.603166i	$0.206094\pi$
$739$	−5.49675	+	16.9173i	−0.202201	+	0.622311i	−0.999817	+	0.0191450i	$0.993906\pi$
$740$	1.08570	−	2.75304i	0.0399111	−	0.101204i
$741$	5.84799	+	4.24881i	0.214831	+	0.156084i
$742$	6.18348	−	4.20840i	0.227003	−	0.154495i
$743$	6.92700	+	21.3191i	0.254127	+	0.782123i	0.994000	+	0.109376i	$0.0348854\pi$
$743$	6.92700	+	21.3191i	0.254127	+	0.782123i	−0.739873	+	0.672746i	$0.765115\pi$
$744$	−4.89059	−	21.6726i	−0.179298	−	0.794555i
$745$	1.29222	+	1.77859i	0.0473433	+	0.0651625i
$746$	−0.0113069	+	0.367713i	−0.000413974	+	0.0134629i
$747$	−4.76933			−0.174501
$748$	−32.6782	−	3.22771i	−1.19483	−	0.118017i
$749$	6.44314			0.235427
$750$	0.0534318	−	1.73767i	0.00195106	−	0.0634506i
$751$	−15.1954	−	20.9146i	−0.554487	−	0.763186i	0.436125	−	0.899886i	$-0.356350\pi$
$751$	−15.1954	−	20.9146i	−0.554487	−	0.763186i	−0.990613	+	0.136700i	$0.956350\pi$
$752$	3.20751	+	5.79723i	0.116966	+	0.211403i
$753$	7.55775	+	23.2604i	0.275420	+	0.847655i
$754$	1.34815	−	0.917538i	0.0490969	−	0.0334148i
$755$	−2.43950	−	1.77240i	−0.0887825	−	0.0645042i
$756$	12.0419	+	4.74889i	0.437960	+	0.172715i
$757$	7.50828	−	23.1081i	0.272893	−	0.839879i	−0.716876	−	0.697201i	$-0.754429\pi$
$757$	7.50828	−	23.1081i	0.272893	−	0.839879i	0.989769	−	0.142678i	$-0.0455714\pi$
$758$	25.8255	−	7.52196i	0.938026	−	0.273210i
$759$	12.8662	−	3.66055i	0.467014	−	0.132870i
$760$	11.4803	+	10.0799i	0.416435	+	0.365638i
$761$	−39.2239	−	12.7446i	−1.42187	−	0.461992i	−0.505672	−	0.862726i	$-0.668755\pi$
$761$	−39.2239	−	12.7446i	−1.42187	−	0.461992i	−0.916195	+	0.400733i	$0.868755\pi$
$762$	−17.8083	+	22.9904i	−0.645127	+	0.832855i
$763$	10.4964	−	14.4470i	0.379995	−	0.523018i
$764$	−2.21979	+	2.69067i	−0.0803094	+	0.0973452i
$765$	7.00956	−	2.27754i	0.253431	−	0.0823448i
$766$	−10.4573	−	3.75686i	−0.377837	−	0.135741i
$767$	−3.54816	+	2.57789i	−0.128117	+	0.0930823i

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41355 + 0.0434654i) q^{2} +(-0.722562 - 0.994522i) q^{3} +(1.99622 + 0.122881i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.978148 - 1.43721i) q^{6} +(-0.948903 - 0.689419i) q^{7} +(2.81641 + 0.260464i) q^{8} +(0.460074 - 1.41596i) q^{9} +(-0.395472 - 1.35779i) q^{10} +(3.11426 + 1.14079i) q^{11} +(-1.32019 - 2.07407i) q^{12} +(1.03536 + 0.336408i) q^{13} +(-1.31135 - 1.01577i) q^{14} +(-0.722562 + 0.994522i) q^{15} +(3.96980 + 0.490594i) q^{16} +(-4.70810 + 1.52976i) q^{17} +(0.711880 - 1.98153i) q^{18} +(-4.36984 + 3.17488i) q^{19} +(-0.500000 - 1.93649i) q^{20} +1.44185i q^{21} +(4.35256 + 1.74793i) q^{22} +3.28095i q^{23} +(-1.77599 - 2.98918i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(1.44890 + 0.520530i) q^{26} +(-5.24803 + 1.70519i) q^{27} +(-1.80951 - 1.49283i) q^{28} +(0.622602 - 0.856939i) q^{29} +(-1.06460 + 1.37440i) q^{30} +(6.07715 + 1.97459i) q^{31} +(5.59017 + 0.866025i) q^{32} +(-1.11570 - 3.92149i) q^{33} +(-6.72161 + 1.95774i) q^{34} +(-0.362449 + 1.11550i) q^{35} +(1.09240 - 2.77004i) q^{36} +(1.19710 + 0.869742i) q^{37} +(-6.31497 + 4.29789i) q^{38} +(-0.413545 - 1.27276i) q^{39} +(-0.622602 - 2.75905i) q^{40} +(3.01196 + 4.14561i) q^{41} +(-0.0626707 + 2.03813i) q^{42} -9.12165 q^{43} +(6.07656 + 2.65996i) q^{44} -1.48883 q^{45} +(-0.142608 + 4.63777i) q^{46} +(0.973579 + 1.34002i) q^{47} +(-2.38052 - 4.30254i) q^{48} +(-1.73800 - 5.34901i) q^{49} +(-1.16913 + 0.795697i) q^{50} +(4.92327 + 3.57697i) q^{51} +(2.02547 + 0.798771i) q^{52} +(-1.39344 + 4.28856i) q^{53} +(-7.49244 + 2.18225i) q^{54} +(0.122602 - 3.31436i) q^{55} +(-2.49293 - 2.18884i) q^{56} +(6.31497 + 2.05186i) q^{57} +(0.917324 - 1.18426i) q^{58} +(-2.36799 + 3.25926i) q^{59} +(-1.56460 + 1.89650i) q^{60} +(-13.2591 + 4.30815i) q^{61} +(8.50451 + 3.05531i) q^{62} +(-1.41276 + 1.02643i) q^{63} +(7.86432 + 1.46715i) q^{64} -1.08864i q^{65} +(-1.40664 - 5.59170i) q^{66} -10.3928i q^{67} +(-9.58639 + 2.47520i) q^{68} +(3.26298 - 2.37069i) q^{69} +(-0.560824 + 1.56106i) q^{70} +(14.9187 - 4.84738i) q^{71} +(1.66456 - 3.86809i) q^{72} +(8.53598 - 11.7488i) q^{73} +(1.65435 + 1.28145i) q^{74} +(1.16913 + 0.379874i) q^{75} +(-9.11330 + 5.80079i) q^{76} +(-2.16864 - 3.22953i) q^{77} +(-0.529244 - 1.81708i) q^{78} +(2.99070 - 9.20442i) q^{79} +(-0.760154 - 3.92711i) q^{80} +(1.87441 + 1.36184i) q^{81} +(4.07735 + 5.99092i) q^{82} +(-0.989908 - 3.04662i) q^{83} +(-0.177176 + 2.87826i) q^{84} +(2.90977 + 4.00495i) q^{85} +(-12.8939 - 0.396476i) q^{86} -1.30211 q^{87} +(8.47388 + 4.02410i) q^{88} -0.254342 q^{89} +(-2.10453 - 0.0647125i) q^{90} +(-0.750529 - 1.03301i) q^{91} +(-0.403165 + 6.54950i) q^{92} +(-2.42735 - 7.47062i) q^{93} +(1.31795 + 1.93649i) q^{94} +(4.36984 + 3.17488i) q^{95} +(-3.17797 - 6.18530i) q^{96} +(-0.00979012 + 0.0301309i) q^{97} +(-2.22424 - 7.63661i) q^{98} +(3.04811 - 3.88482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} + 5 q^{3} - q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 5 q^{8} + 3 q^{9} - 5 q^{10} - q^{11} - 10 q^{12} + 10 q^{13} + 5 q^{14} + 5 q^{15} + 7 q^{16} - 5 q^{17} - 10 q^{18} - 11 q^{19} - 4 q^{20}+ \cdots - 6 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 + 5 * q^3 - q^4 + 2 * q^5 + q^6 - 3 * q^7 + 5 * q^8 + 3 * q^9 - 5 * q^10 - q^11 - 10 * q^12 + 10 * q^13 + 5 * q^14 + 5 * q^15 + 7 * q^16 - 5 * q^17 - 10 * q^18 - 11 * q^19 - 4 * q^20 + q^22 + 3 * q^24 - 2 * q^25 + 7 * q^26 - 10 * q^27 - 9 * q^28 - 5 * q^29 - 6 * q^30 + 10 * q^31 - 11 * q^33 - 14 * q^34 + 8 * q^35 - 26 * q^36 + 20 * q^37 - 5 * q^38 + 3 * q^39 + 5 * q^40 + 10 * q^41 + 29 * q^42 - 34 * q^43 + 32 * q^44 - 8 * q^45 - 10 * q^46 - 23 * q^49 - 5 * q^50 + 9 * q^51 - 5 * q^52 - 7 * q^53 - 26 * q^54 - 9 * q^55 + 15 * q^56 + 5 * q^57 + 18 * q^58 - 5 * q^59 - 10 * q^60 - 10 * q^61 - q^62 - 23 * q^63 + 11 * q^64 - 17 * q^66 - 15 * q^68 + 15 * q^69 + 15 * q^70 + 90 * q^71 + 10 * q^72 + 5 * q^73 + 35 * q^74 + 5 * q^75 - 18 * q^76 - 14 * q^77 - 21 * q^79 - 7 * q^80 - 10 * q^81 - 2 * q^82 + 19 * q^83 - 30 * q^84 - 30 * q^86 - 18 * q^87 + 43 * q^88 + 20 * q^89 - 15 * q^90 - 10 * q^91 + 25 * q^92 + 11 * q^93 + 11 * q^95 - 36 * q^96 - 44 * q^97 + 50 * q^98 - 6 * q^99

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