LMFDB - Embedded newform 690.2.e.b.551.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(551,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("690.551");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.e (of order $2$, degree $1$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 3x^14 - 12x^13 + 15x^12 - 4x^11 + 45x^10 - 66x^9 - 32x^8 - 198x^7 + 405x^6 - 108x^5 + 1215x^4 - 2916x^3 + 2187x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			551.1
Root			$-0.251873 + 1.71364i$ of defining polynomial
Character	$\chi$	$=$	690.551
Dual form			690.2.e.b.551.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.71364 - 0.251873i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-0.251873 + 1.71364i) q^{6} +0.194278i q^{7} +1.00000i q^{8} +(2.87312 + 0.863238i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.71364 - 0.251873i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-0.251873 + 1.71364i) q^{6} +0.194278i q^{7} +1.00000i q^{8} +(2.87312 + 0.863238i) q^{9} -1.00000i q^{10} -3.67639 q^{11} +(1.71364 + 0.251873i) q^{12} +3.85351 q^{13} +0.194278 q^{14} +(-1.71364 - 0.251873i) q^{15} +1.00000 q^{16} +3.71391 q^{17} +(0.863238 - 2.87312i) q^{18} +0.273524i q^{19} -1.00000 q^{20} +(0.0489334 - 0.332923i) q^{21} +3.67639i q^{22} +(4.59371 - 1.37760i) q^{23} +(0.251873 - 1.71364i) q^{24} +1.00000 q^{25} -3.85351i q^{26} +(-4.70607 - 2.20294i) q^{27} -0.194278i q^{28} -9.11317i q^{29} +(-0.251873 + 1.71364i) q^{30} +2.24052 q^{31} -1.00000i q^{32} +(6.30001 + 0.925983i) q^{33} -3.71391i q^{34} +0.194278i q^{35} +(-2.87312 - 0.863238i) q^{36} +11.7876i q^{37} +0.273524 q^{38} +(-6.60352 - 0.970593i) q^{39} +1.00000i q^{40} -9.65442i q^{41} +(-0.332923 - 0.0489334i) q^{42} -10.4535i q^{43} +3.67639 q^{44} +(2.87312 + 0.863238i) q^{45} +(-1.37760 - 4.59371i) q^{46} -4.64640i q^{47} +(-1.71364 - 0.251873i) q^{48} +6.96226 q^{49} -1.00000i q^{50} +(-6.36430 - 0.935432i) q^{51} -3.85351 q^{52} -4.09935 q^{53} +(-2.20294 + 4.70607i) q^{54} -3.67639 q^{55} -0.194278 q^{56} +(0.0688932 - 0.468721i) q^{57} -9.11317 q^{58} +2.49823i q^{59} +(1.71364 + 0.251873i) q^{60} -13.9867i q^{61} -2.24052i q^{62} +(-0.167708 + 0.558185i) q^{63} -1.00000 q^{64} +3.85351 q^{65} +(0.925983 - 6.30001i) q^{66} +10.9816i q^{67} -3.71391 q^{68} +(-8.21895 + 1.20368i) q^{69} +0.194278 q^{70} -9.72869i q^{71} +(-0.863238 + 2.87312i) q^{72} +11.0817 q^{73} +11.7876 q^{74} +(-1.71364 - 0.251873i) q^{75} -0.273524i q^{76} -0.714243i q^{77} +(-0.970593 + 6.60352i) q^{78} +6.43875i q^{79} +1.00000 q^{80} +(7.50964 + 4.96037i) q^{81} -9.65442 q^{82} +9.42725 q^{83} +(-0.0489334 + 0.332923i) q^{84} +3.71391 q^{85} -10.4535 q^{86} +(-2.29536 + 15.6167i) q^{87} -3.67639i q^{88} -9.92316 q^{89} +(0.863238 - 2.87312i) q^{90} +0.748652i q^{91} +(-4.59371 + 1.37760i) q^{92} +(-3.83945 - 0.564326i) q^{93} -4.64640 q^{94} +0.273524i q^{95} +(-0.251873 + 1.71364i) q^{96} +8.91482i q^{97} -6.96226i q^{98} +(-10.5627 - 3.17360i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 16 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q - 16 * q^4 + 16 * q^5 + 2 * q^6 + 2 * q^9	$ 16 q - 16 q^{4} + 16 q^{5} + 2 q^{6} + 2 q^{9} + 12 q^{11} + 12 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{20} + 4 q^{21} - 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} + 2 q^{30} + 4 q^{31} + 28 q^{33} - 2 q^{36} + 16 q^{38} - 8 q^{39} - 12 q^{44} + 2 q^{45} - 4 q^{46} - 4 q^{49} + 2 q^{51} + 8 q^{53} - 26 q^{54} + 12 q^{55} - 12 q^{56} - 28 q^{57} - 8 q^{58} - 16 q^{64} - 10 q^{66} - 22 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} + 24 q^{74} - 12 q^{78} + 16 q^{80} + 22 q^{81} - 16 q^{82} + 40 q^{83} - 4 q^{84} + 40 q^{86} + 20 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} + 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^4 + 16 * q^5 + 2 * q^6 + 2 * q^9 + 12 * q^11 + 12 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^20 + 4 * q^21 - 4 * q^23 - 2 * q^24 + 16 * q^25 + 24 * q^27 + 2 * q^30 + 4 * q^31 + 28 * q^33 - 2 * q^36 + 16 * q^38 - 8 * q^39 - 12 * q^44 + 2 * q^45 - 4 * q^46 - 4 * q^49 + 2 * q^51 + 8 * q^53 - 26 * q^54 + 12 * q^55 - 12 * q^56 - 28 * q^57 - 8 * q^58 - 16 * q^64 - 10 * q^66 - 22 * q^69 + 12 * q^70 - 8 * q^72 - 16 * q^73 + 24 * q^74 - 12 * q^78 + 16 * q^80 + 22 * q^81 - 16 * q^82 + 40 * q^83 - 4 * q^84 + 40 * q^86 + 20 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 - 4 * q^93 - 24 * q^94 + 2 * q^96 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.71364	−	0.251873i	−0.989370	−	0.145419i
$3$	−1.71364	−	0.251873i	−0.989370	−	0.145419i
$4$	−1.00000			−0.500000
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−0.251873	+	1.71364i	−0.102827	+	0.699590i
$7$			0.194278i			0.0734302i	0.999326	+	0.0367151i	$0.0116894\pi$
$7$			0.194278i			0.0734302i	−0.999326	+	0.0367151i	$0.988311\pi$
$8$			1.00000i			0.353553i
$9$	2.87312	+	0.863238i	0.957707	+	0.287746i
$10$		−	1.00000i		−	0.316228i
$11$	−3.67639			−1.10847			−0.554237	−	0.832359i	$-0.686990\pi$
$11$	−3.67639			−1.10847			−0.554237	+	0.832359i	$0.686990\pi$
$12$	1.71364	+	0.251873i	0.494685	+	0.0727094i
$13$	3.85351			1.06877			0.534385	−	0.845241i	$-0.320543\pi$
$13$	3.85351			1.06877			0.534385	+	0.845241i	$0.320543\pi$
$14$	0.194278			0.0519230
$15$	−1.71364	−	0.251873i	−0.442460	−	0.0650333i
$16$	1.00000			0.250000
$17$	3.71391			0.900754			0.450377	−	0.892838i	$-0.351290\pi$
$17$	3.71391			0.900754			0.450377	+	0.892838i	$0.351290\pi$
$18$	0.863238	−	2.87312i	0.203467	−	0.677201i
$19$			0.273524i			0.0627507i	0.999508	+	0.0313753i	$0.00998872\pi$
$19$			0.273524i			0.0627507i	−0.999508	+	0.0313753i	$0.990011\pi$
$20$	−1.00000			−0.223607
$21$	0.0489334	−	0.332923i	0.0106781	−	0.0726497i
$22$			3.67639i			0.783810i
$23$	4.59371	−	1.37760i	0.957856	−	0.287250i
$23$	4.59371	−	1.37760i	0.957856	−	0.287250i
$24$	0.251873	−	1.71364i	0.0514133	−	0.349795i
$25$	1.00000			0.200000
$26$		−	3.85351i		−	0.755735i
$27$	−4.70607	−	2.20294i	−0.905683	−	0.423956i
$28$		−	0.194278i		−	0.0367151i
$29$		−	9.11317i		−	1.69227i	−0.532967	−	0.846136i	$-0.678923\pi$
$29$		−	9.11317i		−	1.69227i	0.532967	−	0.846136i	$-0.321077\pi$
$30$	−0.251873	+	1.71364i	−0.0459855	+	0.312866i
$31$	2.24052			0.402410			0.201205	−	0.979549i	$-0.435514\pi$
$31$	2.24052			0.402410			0.201205	+	0.979549i	$0.435514\pi$
$32$		−	1.00000i		−	0.176777i
$33$	6.30001	+	0.925983i	1.09669	+	0.161193i
$34$		−	3.71391i		−	0.636930i
$35$			0.194278i			0.0328390i
$36$	−2.87312	−	0.863238i	−0.478853	−	0.143873i
$37$			11.7876i			1.93787i	0.247321	+	0.968934i	$0.420450\pi$
$37$			11.7876i			1.93787i	−0.247321	+	0.968934i	$0.579550\pi$
$38$	0.273524			0.0443714
$39$	−6.60352	−	0.970593i	−1.05741	−	0.155419i
$40$			1.00000i			0.158114i
$41$		−	9.65442i		−	1.50777i	−0.657008	−	0.753884i	$-0.728178\pi$
$41$		−	9.65442i		−	1.50777i	0.657008	−	0.753884i	$-0.271822\pi$
$42$	−0.332923	−	0.0489334i	−0.0513711	−	0.00755058i
$43$		−	10.4535i		−	1.59415i	−0.603882	−	0.797074i	$-0.706380\pi$
$43$		−	10.4535i		−	1.59415i	0.603882	−	0.797074i	$-0.293620\pi$
$44$	3.67639			0.554237
$45$	2.87312	+	0.863238i	0.428299	+	0.128684i
$46$	−1.37760	−	4.59371i	−0.203116	−	0.677306i
$47$		−	4.64640i		−	0.677747i	−0.940832	−	0.338874i	$-0.889954\pi$
$47$		−	4.64640i		−	0.677747i	0.940832	−	0.338874i	$-0.110046\pi$
$48$	−1.71364	−	0.251873i	−0.247343	−	0.0363547i
$49$	6.96226			0.994608
$50$		−	1.00000i		−	0.141421i
$51$	−6.36430	−	0.935432i	−0.891180	−	0.130987i
$52$	−3.85351			−0.534385
$53$	−4.09935			−0.563089			−0.281545	−	0.959548i	$-0.590847\pi$
$53$	−4.09935			−0.563089			−0.281545	+	0.959548i	$0.590847\pi$
$54$	−2.20294	+	4.70607i	−0.299782	+	0.640414i
$55$	−3.67639			−0.495725
$56$	−0.194278			−0.0259615
$57$	0.0688932	−	0.468721i	0.00912513	−	0.0620837i
$58$	−9.11317			−1.19662
$59$			2.49823i			0.325242i	0.986689	+	0.162621i	$0.0519947\pi$
$59$			2.49823i			0.325242i	−0.986689	+	0.162621i	$0.948005\pi$
$60$	1.71364	+	0.251873i	0.221230	+	0.0325166i
$61$		−	13.9867i		−	1.79082i	−0.445245	−	0.895409i	$-0.646883\pi$
$61$		−	13.9867i		−	1.79082i	0.445245	−	0.895409i	$-0.353117\pi$
$62$		−	2.24052i		−	0.284547i
$63$	−0.167708	+	0.558185i	−0.0211293	+	0.0703246i
$64$	−1.00000			−0.125000
$65$	3.85351			0.477968
$66$	0.925983	−	6.30001i	0.113981	−	0.775478i
$67$			10.9816i			1.34161i	0.741632	+	0.670807i	$0.234052\pi$
$67$			10.9816i			1.34161i	−0.741632	+	0.670807i	$0.765948\pi$
$68$	−3.71391			−0.450377
$69$	−8.21895	+	1.20368i	−0.989445	+	0.144906i
$70$	0.194278			0.0232207
$71$		−	9.72869i		−	1.15458i	−0.816538	−	0.577291i	$-0.804110\pi$
$71$		−	9.72869i		−	1.15458i	0.816538	−	0.577291i	$-0.195890\pi$
$72$	−0.863238	+	2.87312i	−0.101734	+	0.338600i
$73$	11.0817			1.29702			0.648508	−	0.761208i	$-0.275393\pi$
$73$	11.0817			1.29702			0.648508	+	0.761208i	$0.275393\pi$
$74$	11.7876			1.37028
$75$	−1.71364	−	0.251873i	−0.197874	−	0.0290838i
$76$		−	0.273524i		−	0.0313753i
$77$		−	0.714243i		−	0.0813955i
$78$	−0.970593	+	6.60352i	−0.109898	+	0.747701i
$79$			6.43875i			0.724416i	0.932097	+	0.362208i	$0.117977\pi$
$79$			6.43875i			0.724416i	−0.932097	+	0.362208i	$0.882023\pi$
$80$	1.00000			0.111803
$81$	7.50964	+	4.96037i	0.834404	+	0.551153i
$82$	−9.65442			−1.06615
$83$	9.42725			1.03477			0.517387	−	0.855751i	$-0.326905\pi$
$83$	9.42725			1.03477			0.517387	+	0.855751i	$0.326905\pi$
$84$	−0.0489334	+	0.332923i	−0.00533907	+	0.0363248i
$85$	3.71391			0.402830
$86$	−10.4535			−1.12723
$87$	−2.29536	+	15.6167i	−0.246088	+	1.67428i
$88$		−	3.67639i		−	0.391905i
$89$	−9.92316			−1.05185			−0.525926	−	0.850530i	$-0.676281\pi$
$89$	−9.92316			−1.05185			−0.525926	+	0.850530i	$0.676281\pi$
$90$	0.863238	−	2.87312i	0.0909933	−	0.302853i
$91$			0.748652i			0.0784800i
$92$	−4.59371	+	1.37760i	−0.478928	+	0.143625i
$93$	−3.83945	−	0.564326i	−0.398132	−	0.0585179i
$94$	−4.64640			−0.479240
$95$			0.273524i			0.0280630i
$96$	−0.251873	+	1.71364i	−0.0257067	+	0.174898i
$97$			8.91482i			0.905163i	0.891723	+	0.452582i	$0.149497\pi$
$97$			8.91482i			0.905163i	−0.891723	+	0.452582i	$0.850503\pi$
$98$		−	6.96226i		−	0.703294i
$99$	−10.5627	−	3.17360i	−1.06159	−	0.318959i
$100$	−1.00000			−0.100000
$101$			8.39174i			0.835009i	0.908675	+	0.417505i	$0.137095\pi$
$101$			8.39174i			0.835009i	−0.908675	+	0.417505i	$0.862905\pi$
$102$	−0.935432	+	6.36430i	−0.0926215	+	0.630159i
$103$			3.35240i			0.330322i	0.986267	+	0.165161i	$0.0528144\pi$
$103$			3.35240i			0.330322i	−0.986267	+	0.165161i	$0.947186\pi$
$104$			3.85351i			0.377867i
$105$	0.0489334	−	0.332923i	0.00477541	−	0.0324899i
$106$			4.09935i			0.398164i
$107$	17.6874			1.70991			0.854954	−	0.518704i	$-0.173585\pi$
$107$	17.6874			1.70991			0.854954	+	0.518704i	$0.173585\pi$
$108$	4.70607	+	2.20294i	0.452841	+	0.211978i
$109$			6.90800i			0.661667i	0.943689	+	0.330833i	$0.107330\pi$
$109$			6.90800i			0.661667i	−0.943689	+	0.330833i	$0.892670\pi$
$110$			3.67639i			0.350530i
$111$	2.96897	−	20.1997i	0.281802	−	1.91727i
$112$			0.194278i			0.0183576i
$113$	3.33657			0.313878			0.156939	−	0.987608i	$-0.449837\pi$
$113$	3.33657			0.313878			0.156939	+	0.987608i	$0.449837\pi$
$114$	−0.468721	−	0.0688932i	−0.0438998	−	0.00645244i
$115$	4.59371	−	1.37760i	0.428366	−	0.128462i
$116$			9.11317i			0.846136i
$117$	11.0716	+	3.32649i	1.02357	+	0.307534i
$118$	2.49823			0.229980
$119$			0.721531i			0.0661426i
$120$	0.251873	−	1.71364i	0.0229927	−	0.156433i
$121$	2.51586			0.228715
$122$	−13.9867			−1.26630
$123$	−2.43169	+	16.5442i	−0.219258	+	1.49174i
$124$	−2.24052			−0.201205
$125$	1.00000			0.0894427
$126$	0.558185	+	0.167708i	0.0497270	+	0.0149406i
$127$	13.8315			1.22734			0.613672	−	0.789561i	$-0.289692\pi$
$127$	13.8315			1.22734			0.613672	+	0.789561i	$0.289692\pi$
$128$			1.00000i			0.0883883i
$129$	−2.63296	+	17.9136i	−0.231819	+	1.57720i
$130$		−	3.85351i		−	0.337975i
$131$			11.1092i			0.970613i	0.874344	+	0.485306i	$0.161292\pi$
$131$			11.1092i			0.970613i	−0.874344	+	0.485306i	$0.838708\pi$
$132$	−6.30001	−	0.925983i	−0.548346	−	0.0805965i
$133$	−0.0531397			−0.00460780
$134$	10.9816			0.948665
$135$	−4.70607	−	2.20294i	−0.405034	−	0.189599i
$136$			3.71391i			0.318465i
$137$	−6.61230			−0.564927			−0.282463	−	0.959278i	$-0.591152\pi$
$137$	−6.61230			−0.564927			−0.282463	+	0.959278i	$0.591152\pi$
$138$	1.20368	+	8.21895i	0.102464	+	0.699644i
$139$	−2.36109			−0.200265			−0.100133	−	0.994974i	$-0.531927\pi$
$139$	−2.36109			−0.200265			−0.100133	+	0.994974i	$0.531927\pi$
$140$		−	0.194278i		−	0.0164195i
$141$	−1.17030	+	7.96226i	−0.0985572	+	0.670543i
$142$	−9.72869			−0.816413
$143$	−14.1670			−1.18470
$144$	2.87312	+	0.863238i	0.239427	+	0.0719365i
$145$		−	9.11317i		−	0.756807i
$146$		−	11.0817i		−	0.917128i
$147$	−11.9308	−	1.75360i	−0.984036	−	0.144635i
$148$		−	11.7876i		−	0.968934i
$149$	−9.03818			−0.740436			−0.370218	−	0.928945i	$-0.620717\pi$
$149$	−9.03818			−0.740436			−0.370218	+	0.928945i	$0.620717\pi$
$150$	−0.251873	+	1.71364i	−0.0205653	+	0.139918i
$151$	7.21414			0.587078			0.293539	−	0.955947i	$-0.405167\pi$
$151$	7.21414			0.587078			0.293539	+	0.955947i	$0.405167\pi$
$152$	−0.273524			−0.0221857
$153$	10.6705	+	3.20598i	0.862659	+	0.259189i
$154$	−0.714243			−0.0575553
$155$	2.24052			0.179963
$156$	6.60352	+	0.970593i	0.528705	+	0.0777096i
$157$		−	0.699510i		−	0.0558270i	−0.999610	−	0.0279135i	$-0.991114\pi$
$157$		−	0.699510i		−	0.0558270i	0.999610	−	0.0279135i	$-0.00888629\pi$
$158$	6.43875			0.512239
$159$	7.02481	+	1.03252i	0.557104	+	0.0818838i
$160$		−	1.00000i		−	0.0790569i
$161$	0.267638	+	0.892458i	0.0210928	+	0.0703356i
$162$	4.96037	−	7.50964i	0.389724	−	0.590013i
$163$	−13.2190			−1.03539			−0.517694	−	0.855566i	$-0.673210\pi$
$163$	−13.2190			−1.03539			−0.517694	+	0.855566i	$0.673210\pi$
$164$			9.65442i			0.753884i
$165$	6.30001	+	0.925983i	0.490455	+	0.0720877i
$166$		−	9.42725i		−	0.731696i
$167$			10.7904i			0.834986i	0.908680	+	0.417493i	$0.137091\pi$
$167$			10.7904i			0.834986i	−0.908680	+	0.417493i	$0.862909\pi$
$168$	0.332923	+	0.0489334i	0.0256855	+	0.00377529i
$169$	1.84950			0.142269
$170$		−	3.71391i		−	0.284844i
$171$	−0.236116	+	0.785867i	−0.0180563	+	0.0600968i
$172$			10.4535i			0.797074i
$173$		−	3.90535i		−	0.296918i	−0.988919	−	0.148459i	$-0.952569\pi$
$173$		−	3.90535i		−	0.296918i	0.988919	−	0.148459i	$-0.0474314\pi$
$174$	15.6167	+	2.29536i	1.18390	+	0.174011i
$175$			0.194278i			0.0146860i
$176$	−3.67639			−0.277119
$177$	0.629235	−	4.28106i	0.0472962	−	0.321784i
$178$			9.92316i			0.743772i
$179$		−	5.90397i		−	0.441284i	−0.975355	−	0.220642i	$-0.929185\pi$
$179$		−	5.90397i		−	0.441284i	0.975355	−	0.220642i	$-0.0708152\pi$
$180$	−2.87312	−	0.863238i	−0.214150	−	0.0643420i
$181$			3.65493i			0.271669i	0.990732	+	0.135834i	$0.0433715\pi$
$181$			3.65493i			0.271669i	−0.990732	+	0.135834i	$0.956628\pi$
$182$	0.748652			0.0554938
$183$	−3.52288	+	23.9682i	−0.260419	+	1.77178i
$184$	1.37760	+	4.59371i	0.101558	+	0.338653i
$185$			11.7876i			0.866641i
$186$	−0.564326	+	3.83945i	−0.0413784	+	0.281522i
$187$	−13.6538			−0.998463
$188$			4.64640i			0.338874i
$189$	0.427983	−	0.914286i	0.0311312	−	0.0665045i
$190$	0.273524			0.0198435
$191$	−12.5903			−0.911005			−0.455503	−	0.890234i	$-0.650540\pi$
$191$	−12.5903			−0.911005			−0.455503	+	0.890234i	$0.650540\pi$
$192$	1.71364	+	0.251873i	0.123671	+	0.0181773i
$193$	23.4908			1.69090			0.845452	−	0.534051i	$-0.179331\pi$
$193$	23.4908			1.69090			0.845452	+	0.534051i	$0.179331\pi$
$194$	8.91482			0.640047
$195$	−6.60352	−	0.970593i	−0.472888	−	0.0695056i
$196$	−6.96226			−0.497304
$197$		−	15.4325i		−	1.09952i	−0.835322	−	0.549761i	$-0.814719\pi$
$197$		−	15.4325i		−	1.09952i	0.835322	−	0.549761i	$-0.185281\pi$
$198$	−3.17360	+	10.5627i	−0.225538	+	0.750660i
$199$		−	21.1429i		−	1.49878i	−0.662127	−	0.749391i	$-0.730346\pi$
$199$		−	21.1429i		−	1.49878i	0.662127	−	0.749391i	$-0.269654\pi$
$200$			1.00000i			0.0707107i
$201$	2.76596	−	18.8185i	0.195096	−	1.32735i
$202$	8.39174			0.590441
$203$	1.77049			0.124264
$204$	6.36430	+	0.935432i	0.445590	+	0.0654933i
$205$		−	9.65442i		−	0.674294i
$206$	3.35240			0.233573
$207$	14.3875	+	0.00745181i	1.00000	+	0.000517937i
$208$	3.85351			0.267193
$209$		−	1.00558i		−	0.0695575i
$210$	−0.332923	−	0.0489334i	−0.0229739	−	0.00337672i
$211$	−0.599814			−0.0412929			−0.0206464	−	0.999787i	$-0.506572\pi$
$211$	−0.599814			−0.0412929			−0.0206464	+	0.999787i	$0.506572\pi$
$212$	4.09935			0.281545
$213$	−2.45039	+	16.6715i	−0.167898	+	1.14231i
$214$		−	17.6874i		−	1.20909i
$215$		−	10.4535i		−	0.712925i
$216$	2.20294	−	4.70607i	0.149891	−	0.320207i
$217$			0.435285i			0.0295490i
$218$	6.90800			0.467869
$219$	−18.9900	−	2.79118i	−1.28323	−	0.188610i
$220$	3.67639			0.247862
$221$	14.3116			0.962699
$222$	−20.1997	−	2.96897i	−1.35571	−	0.199264i
$223$	−10.6634			−0.714072			−0.357036	−	0.934091i	$-0.616213\pi$
$223$	−10.6634			−0.714072			−0.357036	+	0.934091i	$0.616213\pi$
$224$	0.194278			0.0129808
$225$	2.87312	+	0.863238i	0.191541	+	0.0575492i
$226$		−	3.33657i		−	0.221945i
$227$	−5.57422			−0.369974			−0.184987	−	0.982741i	$-0.559224\pi$
$227$	−5.57422			−0.369974			−0.184987	+	0.982741i	$0.559224\pi$
$228$	−0.0688932	+	0.468721i	−0.00456256	+	0.0310418i
$229$			14.9060i			0.985015i	0.870308	+	0.492508i	$0.163920\pi$
$229$			14.9060i			0.985015i	−0.870308	+	0.492508i	$0.836080\pi$
$230$	−1.37760	−	4.59371i	−0.0908364	−	0.302901i
$231$	−0.179898	+	1.22395i	−0.0118364	+	0.0805303i
$232$	9.11317			0.598309
$233$		−	15.3425i		−	1.00512i	−0.864543	−	0.502559i	$-0.832392\pi$
$233$		−	15.3425i		−	1.00512i	0.864543	−	0.502559i	$-0.167608\pi$
$234$	3.32649	−	11.0716i	0.217460	−	0.723772i
$235$		−	4.64640i		−	0.303098i
$236$		−	2.49823i		−	0.162621i
$237$	1.62174	−	11.0337i	0.105344	−	0.716715i
$238$	0.721531			0.0467699
$239$			11.6220i			0.751763i	0.926668	+	0.375881i	$0.122660\pi$
$239$			11.6220i			0.751763i	−0.926668	+	0.375881i	$0.877340\pi$
$240$	−1.71364	−	0.251873i	−0.110615	−	0.0162583i
$241$			6.44721i			0.415301i	0.978203	+	0.207651i	$0.0665817\pi$
$241$			6.44721i			0.415301i	−0.978203	+	0.207651i	$0.933418\pi$
$242$		−	2.51586i		−	0.161726i
$243$	−11.6194	−	10.3918i	−0.745387	−	0.666632i
$244$			13.9867i			0.895409i
$245$	6.96226			0.444802
$246$	16.5442	+	2.43169i	1.05482	+	0.155039i
$247$			1.05403i			0.0670661i
$248$			2.24052i			0.142273i
$249$	−16.1549	−	2.37447i	−1.02378	−	0.150476i
$250$		−	1.00000i		−	0.0632456i
$251$	0.366988			0.0231641			0.0115820	−	0.999933i	$-0.496313\pi$
$251$	0.366988			0.0231641			0.0115820	+	0.999933i	$0.496313\pi$
$252$	0.167708	−	0.558185i	0.0105646	−	0.0351623i
$253$	−16.8883	+	5.06461i	−1.06176	+	0.318409i
$254$		−	13.8315i		−	0.867863i
$255$	−6.36430	−	0.935432i	−0.398548	−	0.0585790i
$256$	1.00000			0.0625000
$257$			20.9857i			1.30905i	0.756040	+	0.654525i	$0.227131\pi$
$257$			20.9857i			1.30905i	−0.756040	+	0.654525i	$0.772869\pi$
$258$	17.9136	+	2.63296i	1.11525	+	0.163921i
$259$	−2.29007			−0.142298
$260$	−3.85351			−0.238984
$261$	7.86683	−	26.1832i	0.486945	−	1.62070i
$262$	11.1092			0.686327
$263$	−28.4952			−1.75709			−0.878544	−	0.477661i	$-0.841485\pi$
$263$	−28.4952			−1.75709			−0.878544	+	0.477661i	$0.841485\pi$
$264$	−0.925983	+	6.30001i	−0.0569903	+	0.387739i
$265$	−4.09935			−0.251821
$266$			0.0531397i			0.00325821i
$267$	17.0047	+	2.49937i	1.04067	+	0.152959i
$268$		−	10.9816i		−	0.670807i
$269$			5.95349i			0.362991i	0.983392	+	0.181495i	$0.0580938\pi$
$269$			5.95349i			0.362991i	−0.983392	+	0.181495i	$0.941906\pi$
$270$	−2.20294	+	4.70607i	−0.134067	+	0.286402i
$271$	−10.8969			−0.661937			−0.330969	−	0.943642i	$-0.607375\pi$
$271$	−10.8969			−0.661937			−0.330969	+	0.943642i	$0.607375\pi$
$272$	3.71391			0.225189
$273$	0.188565	−	1.28292i	0.0114125	−	0.0776458i
$274$			6.61230i			0.399463i
$275$	−3.67639			−0.221695
$276$	8.21895	−	1.20368i	0.494723	−	0.0724532i
$277$	−12.5927			−0.756623			−0.378312	−	0.925678i	$-0.623495\pi$
$277$	−12.5927			−0.756623			−0.378312	+	0.925678i	$0.623495\pi$
$278$			2.36109i			0.141609i
$279$	6.43729	+	1.93410i	0.385390	+	0.115792i
$280$	−0.194278			−0.0116103
$281$	10.5936			0.631961			0.315980	−	0.948766i	$-0.397667\pi$
$281$	10.5936			0.631961			0.315980	+	0.948766i	$0.397667\pi$
$282$	7.96226	+	1.17030i	0.474145	+	0.0696904i
$283$		−	31.7364i		−	1.88653i	−0.332039	−	0.943266i	$-0.607737\pi$
$283$		−	31.7364i		−	1.88653i	0.332039	−	0.943266i	$-0.392263\pi$
$284$			9.72869i			0.577291i
$285$	0.0688932	−	0.468721i	0.00408088	−	0.0277647i
$286$			14.1670i			0.837712i
$287$	1.87564			0.110716
$288$	0.863238	−	2.87312i	0.0508668	−	0.169300i
$289$	−3.20690			−0.188641
$290$	−9.11317			−0.535144
$291$	2.24540	−	15.2768i	0.131628	−	0.895542i
$292$	−11.0817			−0.648508
$293$	−6.77543			−0.395825			−0.197912	−	0.980220i	$-0.563416\pi$
$293$	−6.77543			−0.395825			−0.197912	+	0.980220i	$0.563416\pi$
$294$	−1.75360	+	11.9308i	−0.102272	+	0.695818i
$295$			2.49823i			0.145452i
$296$	−11.7876			−0.685139
$297$	17.3013	+	8.09887i	1.00393	+	0.469944i
$298$			9.03818i			0.523567i
$299$	17.7019	−	5.30860i	1.02373	−	0.307004i
$300$	1.71364	+	0.251873i	0.0989370	+	0.0145419i
$301$	2.03089			0.117059
$302$		−	7.21414i		−	0.415127i
$303$	2.11365	−	14.3804i	0.121426	−	0.826133i
$304$			0.273524i			0.0156877i
$305$		−	13.9867i		−	0.800878i
$306$	3.20598	−	10.6705i	0.183274	−	0.609992i
$307$	−13.5532			−0.773522			−0.386761	−	0.922180i	$-0.626406\pi$
$307$	−13.5532			−0.773522			−0.386761	+	0.922180i	$0.626406\pi$
$308$			0.714243i			0.0406978i
$309$	0.844379	−	5.74481i	0.0480350	−	0.326811i
$310$		−	2.24052i		−	0.127253i
$311$			3.63405i			0.206068i	0.994678	+	0.103034i	$0.0328550\pi$
$311$			3.63405i			0.206068i	−0.994678	+	0.103034i	$0.967145\pi$
$312$	0.970593	−	6.60352i	0.0549490	−	0.373851i
$313$			20.2986i			1.14734i	0.819085	+	0.573672i	$0.194481\pi$
$313$			20.2986i			1.14734i	−0.819085	+	0.573672i	$0.805519\pi$
$314$	−0.699510			−0.0394756
$315$	−0.167708	+	0.558185i	−0.00944929	+	0.0314501i
$316$		−	6.43875i		−	0.362208i
$317$			22.0942i			1.24093i	0.784233	+	0.620467i	$0.213057\pi$
$317$			22.0942i			1.24093i	−0.784233	+	0.620467i	$0.786943\pi$
$318$	1.03252	−	7.02481i	0.0579006	−	0.393932i
$319$			33.5036i			1.87584i
$320$	−1.00000			−0.0559017
$321$	−30.3099	−	4.45498i	−1.69173	−	0.248653i
$322$	0.892458	−	0.267638i	0.0497348	−	0.0149149i
$323$			1.01584i			0.0565230i
$324$	−7.50964	−	4.96037i	−0.417202	−	0.275576i
$325$	3.85351			0.213754
$326$			13.2190i			0.732130i
$327$	1.73994	−	11.8378i	0.0962188	−	0.654633i
$328$	9.65442			0.533076
$329$	0.902694			0.0497671
$330$	0.925983	−	6.30001i	0.0509737	−	0.346804i
$331$	−27.8332			−1.52985			−0.764925	−	0.644120i	$-0.777224\pi$
$331$	−27.8332			−1.52985			−0.764925	+	0.644120i	$0.777224\pi$
$332$	−9.42725			−0.517387
$333$	−10.1755	+	33.8672i	−0.557614	+	1.85591i
$334$	10.7904			0.590424
$335$			10.9816i			0.599988i
$336$	0.0489334	−	0.332923i	0.00266953	−	0.0181624i
$337$		−	27.7015i		−	1.50900i	−0.656302	−	0.754498i	$-0.727880\pi$
$337$		−	27.7015i		−	1.50900i	0.656302	−	0.754498i	$-0.272120\pi$
$338$		−	1.84950i		−	0.100600i
$339$	−5.71767	−	0.840390i	−0.310541	−	0.0456437i
$340$	−3.71391			−0.201415
$341$	−8.23704			−0.446061
$342$	0.785867	+	0.236116i	0.0424948	+	0.0127677i
$343$			2.71256i			0.146465i
$344$	10.4535			0.563616
$345$	−8.21895	+	1.20368i	−0.442493	+	0.0648041i
$346$	−3.90535			−0.209953
$347$			25.4305i			1.36518i	0.730801	+	0.682590i	$0.239147\pi$
$347$			25.4305i			1.36518i	−0.730801	+	0.682590i	$0.760853\pi$
$348$	2.29536	−	15.6167i	0.123044	−	0.837142i
$349$	−25.3679			−1.35791			−0.678955	−	0.734180i	$-0.737567\pi$
$349$	−25.3679			−1.35791			−0.678955	+	0.734180i	$0.737567\pi$
$350$	0.194278			0.0103846
$351$	−18.1348	−	8.48904i	−0.967967	−	0.453111i
$352$			3.67639i			0.195952i
$353$			6.58726i			0.350605i	0.984515	+	0.175302i	$0.0560903\pi$
$353$			6.58726i			0.350605i	−0.984515	+	0.175302i	$0.943910\pi$
$354$	−4.28106	−	0.629235i	−0.227536	−	0.0334435i
$355$		−	9.72869i		−	0.516345i
$356$	9.92316			0.525926
$357$	0.181734	−	1.23644i	0.00961838	−	0.0654395i
$358$	−5.90397			−0.312035
$359$	34.1462			1.80217			0.901083	−	0.433647i	$-0.142774\pi$
$359$	34.1462			1.80217			0.901083	+	0.433647i	$0.142774\pi$
$360$	−0.863238	+	2.87312i	−0.0454966	+	0.151427i
$361$	18.9252			0.996062
$362$	3.65493			0.192099
$363$	−4.31128	−	0.633677i	−0.226284	−	0.0332594i
$364$		−	0.748652i		−	0.0392400i
$365$	11.0817			0.580043
$366$	23.9682	+	3.52288i	1.25284	+	0.184144i
$367$			2.78712i			0.145487i	0.997351	+	0.0727433i	$0.0231754\pi$
$367$			2.78712i			0.145487i	−0.997351	+	0.0727433i	$0.976825\pi$
$368$	4.59371	−	1.37760i	0.239464	−	0.0718125i
$369$	8.33407	−	27.7383i	0.433854	−	1.44400i
$370$	11.7876			0.612807
$371$		−	0.796415i		−	0.0413478i
$372$	3.83945	+	0.564326i	0.199066	+	0.0292590i
$373$		−	36.8414i		−	1.90757i	−0.300485	−	0.953787i	$-0.597148\pi$
$373$		−	36.8414i		−	1.90757i	0.300485	−	0.953787i	$-0.402852\pi$
$374$			13.6538i			0.706020i
$375$	−1.71364	−	0.251873i	−0.0884920	−	0.0130067i
$376$	4.64640			0.239620
$377$		−	35.1176i		−	1.80865i
$378$	−0.914286	−	0.427983i	−0.0470258	−	0.0220131i
$379$			12.8044i			0.657717i	0.944379	+	0.328859i	$0.106664\pi$
$379$			12.8044i			0.657717i	−0.944379	+	0.328859i	$0.893336\pi$
$380$		−	0.273524i		−	0.0140315i
$381$	−23.7021	−	3.48377i	−1.21430	−	0.178479i
$382$			12.5903i			0.644178i
$383$	−14.2092			−0.726055			−0.363028	−	0.931778i	$-0.618257\pi$
$383$	−14.2092			−0.726055			−0.363028	+	0.931778i	$0.618257\pi$
$384$	0.251873	−	1.71364i	0.0128533	−	0.0874488i
$385$		−	0.714243i		−	0.0364012i
$386$		−	23.4908i		−	1.19565i
$387$	9.02388	−	30.0342i	0.458710	−	1.52673i
$388$		−	8.91482i		−	0.452582i
$389$	−7.98762			−0.404988			−0.202494	−	0.979283i	$-0.564905\pi$
$389$	−7.98762			−0.404988			−0.202494	+	0.979283i	$0.564905\pi$
$390$	−0.970593	+	6.60352i	−0.0491479	+	0.334382i
$391$	17.0606	−	5.11629i	0.862793	−	0.258742i
$392$			6.96226i			0.351647i
$393$	2.79810	−	19.0371i	0.141145	−	0.960295i
$394$	−15.4325			−0.777479
$395$			6.43875i			0.323968i
$396$	10.5627	+	3.17360i	0.530797	+	0.159479i
$397$	6.37102			0.319752			0.159876	−	0.987137i	$-0.448891\pi$
$397$	6.37102			0.319752			0.159876	+	0.987137i	$0.448891\pi$
$398$	−21.1429			−1.05980
$399$	0.0910623	+	0.0133844i	0.00455882	+	0.000670061i
$400$	1.00000			0.0500000
$401$	−4.08280			−0.203885			−0.101943	−	0.994790i	$-0.532506\pi$
$401$	−4.08280			−0.203885			−0.101943	+	0.994790i	$0.532506\pi$
$402$	−18.8185	−	2.76596i	−0.938580	−	0.137954i
$403$	8.63386			0.430083
$404$		−	8.39174i		−	0.417505i
$405$	7.50964	+	4.96037i	0.373157	+	0.246483i
$406$		−	1.77049i		−	0.0878679i
$407$		−	43.3358i		−	2.14808i
$408$	0.935432	−	6.36430i	0.0463108	−	0.315080i
$409$	−18.0794			−0.893971			−0.446985	−	0.894541i	$-0.647502\pi$
$409$	−18.0794			−0.893971			−0.446985	+	0.894541i	$0.647502\pi$
$410$	−9.65442			−0.476798
$411$	11.3311	+	1.66546i	0.558922	+	0.0821509i
$412$		−	3.35240i		−	0.165161i
$413$	−0.485351			−0.0238826
$414$	0.00745181	−	14.3875i	0.000366237	−	0.707107i
$415$	9.42725			0.462765
$416$		−	3.85351i		−	0.188934i
$417$	4.04606	+	0.594694i	0.198136	+	0.0291223i
$418$	−1.00558			−0.0491846
$419$	−25.7595			−1.25843			−0.629217	−	0.777229i	$-0.716624\pi$
$419$	−25.7595			−1.25843			−0.629217	+	0.777229i	$0.716624\pi$
$420$	−0.0489334	+	0.332923i	−0.00238770	+	0.0162450i
$421$		−	13.8562i		−	0.675308i	−0.941270	−	0.337654i	$-0.890367\pi$
$421$		−	13.8562i		−	0.675308i	0.941270	−	0.337654i	$-0.109633\pi$
$422$			0.599814i			0.0291985i
$423$	4.01095	−	13.3497i	0.195019	−	0.649083i
$424$		−	4.09935i		−	0.199082i
$425$	3.71391			0.180151
$426$	16.6715	+	2.45039i	0.807735	+	0.118722i
$427$	2.71732			0.131500
$428$	−17.6874			−0.854954
$429$	24.2771	+	3.56828i	1.17211	+	0.172278i
$430$	−10.4535			−0.504114
$431$	23.1260			1.11394			0.556970	−	0.830533i	$-0.311964\pi$
$431$	23.1260			1.11394			0.556970	+	0.830533i	$0.311964\pi$
$432$	−4.70607	−	2.20294i	−0.226421	−	0.105989i
$433$		−	15.8236i		−	0.760432i	−0.924898	−	0.380216i	$-0.875850\pi$
$433$		−	15.8236i		−	0.760432i	0.924898	−	0.380216i	$-0.124150\pi$
$434$	0.435285			0.0208943
$435$	−2.29536	+	15.6167i	−0.110054	+	0.748763i
$436$		−	6.90800i		−	0.330833i
$437$	0.376807	+	1.25649i	0.0180251	+	0.0601061i
$438$	−2.79118	+	18.9900i	−0.133368	+	0.907379i
$439$	31.7678			1.51619			0.758096	−	0.652143i	$-0.226130\pi$
$439$	31.7678			1.51619			0.758096	+	0.652143i	$0.226130\pi$
$440$		−	3.67639i		−	0.175265i
$441$	20.0034	+	6.01008i	0.952543	+	0.286194i
$442$		−	14.3116i		−	0.680731i
$443$		−	11.4636i		−	0.544652i	−0.962205	−	0.272326i	$-0.912207\pi$
$443$		−	11.4636i		−	0.544652i	0.962205	−	0.272326i	$-0.0877930\pi$
$444$	−2.96897	+	20.1997i	−0.140901	+	0.958634i
$445$	−9.92316			−0.470403
$446$			10.6634i			0.504925i
$447$	15.4882	+	2.27647i	0.732565	+	0.107673i
$448$		−	0.194278i		−	0.00917878i
$449$		−	6.54091i		−	0.308685i	−0.988017	−	0.154342i	$-0.950674\pi$
$449$		−	6.54091i		−	0.308685i	0.988017	−	0.154342i	$-0.0493259\pi$
$450$	0.863238	−	2.87312i	0.0406934	−	0.135440i
$451$			35.4935i			1.67132i
$452$	−3.33657			−0.156939
$453$	−12.3624	−	1.81704i	−0.580838	−	0.0853722i
$454$			5.57422i			0.261611i
$455$			0.748652i			0.0350973i
$456$	0.468721	+	0.0688932i	0.0219499	+	0.00322622i
$457$			30.6183i			1.43226i	0.697966	+	0.716131i	$0.254089\pi$
$457$			30.6183i			1.43226i	−0.697966	+	0.716131i	$0.745911\pi$
$458$	14.9060			0.696511
$459$	−17.4779	−	8.18151i	−0.815798	−	0.381880i
$460$	−4.59371	+	1.37760i	−0.214183	+	0.0642310i
$461$			22.9570i			1.06921i	0.845101	+	0.534606i	$0.179540\pi$
$461$			22.9570i			1.06921i	−0.845101	+	0.534606i	$0.820460\pi$
$462$	1.22395	+	0.179898i	0.0569435	+	0.00836963i
$463$	22.2784			1.03536			0.517682	−	0.855573i	$-0.326795\pi$
$463$	22.2784			1.03536			0.517682	+	0.855573i	$0.326795\pi$
$464$		−	9.11317i		−	0.423068i
$465$	−3.83945	−	0.564326i	−0.178050	−	0.0261700i
$466$	−15.3425			−0.710726
$467$	21.8911			1.01300			0.506500	−	0.862240i	$-0.330939\pi$
$467$	21.8911			1.01300			0.506500	+	0.862240i	$0.330939\pi$
$468$	−11.0716	−	3.32649i	−0.511784	−	0.153767i
$469$	−2.13348			−0.0985151
$470$	−4.64640			−0.214322
$471$	−0.176187	+	1.19871i	−0.00811829	+	0.0552335i
$472$	−2.49823			−0.114990
$473$			38.4313i			1.76707i
$474$	−11.0337	−	1.62174i	−0.506794	−	0.0744892i
$475$			0.273524i			0.0125501i
$476$		−	0.721531i		−	0.0330713i
$477$	−11.7779	−	3.53872i	−0.539275	−	0.162027i
$478$	11.6220			0.531576
$479$	−5.71132			−0.260957			−0.130478	−	0.991451i	$-0.541651\pi$
$479$	−5.71132			−0.260957			−0.130478	+	0.991451i	$0.541651\pi$
$480$	−0.251873	+	1.71364i	−0.0114964	+	0.0782166i
$481$			45.4235i			2.07113i
$482$	6.44721			0.293662
$483$	−0.233849	−	1.59676i	−0.0106405	−	0.0726552i
$484$	−2.51586			−0.114357
$485$			8.91482i			0.404801i
$486$	−10.3918	+	11.6194i	−0.471380	+	0.527068i
$487$	22.2185			1.00682			0.503409	−	0.864048i	$-0.332079\pi$
$487$	22.2185			1.00682			0.503409	+	0.864048i	$0.332079\pi$
$488$	13.9867			0.633150
$489$	22.6525	+	3.32949i	1.02438	+	0.150565i
$490$		−	6.96226i		−	0.314523i
$491$		−	9.94225i		−	0.448688i	−0.974510	−	0.224344i	$-0.927976\pi$
$491$		−	9.94225i		−	0.448688i	0.974510	−	0.224344i	$-0.0720239\pi$
$492$	2.43169	−	16.5442i	0.109629	−	0.745870i
$493$		−	33.8454i		−	1.52432i
$494$	1.05403			0.0474229
$495$	−10.5627	−	3.17360i	−0.474759	−	0.142643i
$496$	2.24052			0.100602
$497$	1.89007			0.0847813
$498$	−2.37447	+	16.1549i	−0.106402	+	0.723919i
$499$	5.95037			0.266375			0.133187	−	0.991091i	$-0.457479\pi$
$499$	5.95037			0.266375			0.133187	+	0.991091i	$0.457479\pi$
$500$	−1.00000			−0.0447214
$501$	2.71781	−	18.4908i	0.121423	−	0.826110i
$502$		−	0.366988i		−	0.0163795i
$503$	−27.9653			−1.24691			−0.623455	−	0.781859i	$-0.714272\pi$
$503$	−27.9653			−1.24691			−0.623455	+	0.781859i	$0.714272\pi$
$504$	−0.558185	−	0.167708i	−0.0248635	−	0.00747032i
$505$			8.39174i			0.373427i
$506$	5.06461	+	16.8883i	0.225149	+	0.750776i
$507$	−3.16938	−	0.465839i	−0.140757	−	0.0206886i
$508$	−13.8315			−0.613672
$509$			3.52122i			0.156075i	0.996950	+	0.0780376i	$0.0248654\pi$
$509$			3.52122i			0.156075i	−0.996950	+	0.0780376i	$0.975135\pi$
$510$	−0.935432	+	6.36430i	−0.0414216	+	0.281816i
$511$			2.15293i			0.0952402i
$512$		−	1.00000i		−	0.0441942i
$513$	0.602557	−	1.28722i	0.0266035	−	0.0568322i
$514$	20.9857			0.925638
$515$			3.35240i			0.147724i
$516$	2.63296	−	17.9136i	0.115910	−	0.788601i
$517$			17.0820i			0.751265i
$518$			2.29007i			0.100620i
$519$	−0.983651	+	6.69236i	−0.0431775	+	0.293762i
$520$			3.85351i			0.168987i
$521$	25.1110			1.10013			0.550067	−	0.835121i	$-0.314602\pi$
$521$	25.1110			1.10013			0.550067	+	0.835121i	$0.314602\pi$
$522$	−26.1832	−	7.86683i	−1.14601	−	0.344322i
$523$			23.9422i			1.04692i	0.852050	+	0.523460i	$0.175359\pi$
$523$			23.9422i			1.04692i	−0.852050	+	0.523460i	$0.824641\pi$
$524$		−	11.1092i		−	0.485306i
$525$	0.0489334	−	0.332923i	0.00213563	−	0.0145299i
$526$			28.4952i			1.24245i
$527$	8.32109			0.362472
$528$	6.30001	+	0.925983i	0.274173	+	0.0402982i
$529$	19.2044	−	12.6566i	0.834975	−	0.550288i
$530$			4.09935i			0.178065i
$531$	−2.15656	+	7.17771i	−0.0935869	+	0.311486i
$532$	0.0531397			0.00230390
$533$		−	37.2034i		−	1.61146i
$534$	2.49937	−	17.0047i	0.108158	−	0.735866i
$535$	17.6874			0.764694
$536$	−10.9816			−0.474332
$537$	−1.48705	+	10.1173i	−0.0641709	+	0.436593i
$538$	5.95349			0.256673
$539$	−25.5960			−1.10250
$540$	4.70607	+	2.20294i	0.202517	+	0.0947994i
$541$	−3.04910			−0.131091			−0.0655455	−	0.997850i	$-0.520879\pi$
$541$	−3.04910			−0.131091			−0.0655455	+	0.997850i	$0.520879\pi$
$542$			10.8969i			0.468060i
$543$	0.920578	−	6.26324i	0.0395058	−	0.268781i
$544$		−	3.71391i		−	0.159232i
$545$			6.90800i			0.295906i
$546$	−1.28292	−	0.188565i	−0.0549039	−	0.00806984i
$547$	23.7201			1.01420			0.507099	−	0.861888i	$-0.330718\pi$
$547$	23.7201			1.01420			0.507099	+	0.861888i	$0.330718\pi$
$548$	6.61230			0.282463
$549$	12.0739	−	40.1856i	0.515301	−	1.71508i
$550$			3.67639i			0.156762i
$551$	2.49267			0.106191
$552$	−1.20368	−	8.21895i	−0.0512321	−	0.349822i
$553$	−1.25091			−0.0531940
$554$			12.5927i			0.535013i
$555$	2.96897	−	20.1997i	0.126026	−	0.857428i
$556$	2.36109			0.100133
$557$	−3.97743			−0.168529			−0.0842645	−	0.996443i	$-0.526854\pi$
$557$	−3.97743			−0.168529			−0.0842645	+	0.996443i	$0.526854\pi$
$558$	1.93410	−	6.43729i	0.0818772	−	0.272512i
$559$		−	40.2827i		−	1.70378i
$560$			0.194278i			0.00820975i
$561$	23.3976	+	3.43901i	0.987849	+	0.145195i
$562$		−	10.5936i		−	0.446864i
$563$	−19.2899			−0.812971			−0.406486	−	0.913657i	$-0.633246\pi$
$563$	−19.2899			−0.812971			−0.406486	+	0.913657i	$0.633246\pi$
$564$	1.17030	−	7.96226i	0.0492786	−	0.335271i
$565$	3.33657			0.140370
$566$	−31.7364			−1.33398
$567$	−0.963692	+	1.45896i	−0.0404713	+	0.0612705i
$568$	9.72869			0.408207
$569$	−10.8881			−0.456454			−0.228227	−	0.973608i	$-0.573293\pi$
$569$	−10.8881			−0.456454			−0.228227	+	0.973608i	$0.573293\pi$
$570$	−0.468721	−	0.0688932i	−0.0196326	−	0.00288562i
$571$		−	4.04576i		−	0.169310i	−0.996410	−	0.0846549i	$-0.973021\pi$
$571$		−	4.04576i		−	0.169310i	0.996410	−	0.0846549i	$-0.0269788\pi$
$572$	14.1670			0.592352
$573$	21.5753	+	3.17116i	0.901321	+	0.132477i
$574$		−	1.87564i		−	0.0782879i
$575$	4.59371	−	1.37760i	0.191571	−	0.0574500i
$576$	−2.87312	−	0.863238i	−0.119713	−	0.0359683i
$577$	−35.0273			−1.45821			−0.729103	−	0.684404i	$-0.760062\pi$
$577$	−35.0273			−1.45821			−0.729103	+	0.684404i	$0.760062\pi$
$578$			3.20690i			0.133390i
$579$	−40.2548	−	5.91669i	−1.67293	−	0.245889i
$580$			9.11317i			0.378404i
$581$			1.83151i			0.0759838i
$582$	−15.2768	−	2.24540i	−0.633244	−	0.0930749i
$583$	15.0708			0.624170
$584$			11.0817i			0.458564i
$585$	11.0716	+	3.32649i	0.457754	+	0.137534i
$586$			6.77543i			0.279890i
$587$			39.2631i			1.62056i	0.586043	+	0.810280i	$0.300685\pi$
$587$			39.2631i			1.62056i	−0.586043	+	0.810280i	$0.699315\pi$
$588$	11.9308	+	1.75360i	0.492018	+	0.0723173i
$589$			0.612836i			0.0252515i
$590$	2.49823			0.102850
$591$	−3.88703	+	26.4458i	−0.159891	+	1.08783i
$592$			11.7876i			0.484467i
$593$			20.0039i			0.821461i	0.911757	+	0.410730i	$0.134726\pi$
$593$			20.0039i			0.821461i	−0.911757	+	0.410730i	$0.865274\pi$
$594$	8.09887	−	17.3013i	0.332301	−	0.709883i
$595$			0.721531i			0.0295799i
$596$	9.03818			0.370218
$597$	−5.32533	+	36.2314i	−0.217951	+	1.48285i
$598$	−5.30860	−	17.7019i	−0.217085	−	0.723885i
$599$		−	9.77816i		−	0.399525i	−0.979844	−	0.199762i	$-0.935983\pi$
$599$		−	9.77816i		−	0.399525i	0.979844	−	0.199762i	$-0.0640170\pi$
$600$	0.251873	−	1.71364i	0.0102827	−	0.0699590i
$601$	−33.3197			−1.35914			−0.679569	−	0.733612i	$-0.737833\pi$
$601$	−33.3197			−1.35914			−0.679569	+	0.733612i	$0.737833\pi$
$602$		−	2.03089i		−	0.0827730i
$603$	−9.47972	+	31.5514i	−0.386044	+	1.28487i
$604$	−7.21414			−0.293539
$605$	2.51586			0.102284
$606$	−14.3804	−	2.11365i	−0.584164	−	0.0858612i
$607$	−6.68091			−0.271170			−0.135585	−	0.990766i	$-0.543291\pi$
$607$	−6.68091			−0.271170			−0.135585	+	0.990766i	$0.543291\pi$
$608$	0.273524			0.0110929
$609$	−3.03398	−	0.445938i	−0.122943	−	0.0180703i
$610$	−13.9867			−0.566306
$611$		−	17.9049i		−	0.724356i
$612$	−10.6705	−	3.20598i	−0.431329	−	0.129594i
$613$		−	2.66775i		−	0.107749i	−0.998548	−	0.0538746i	$-0.982843\pi$
$613$		−	2.66775i		−	0.107749i	0.998548	−	0.0538746i	$-0.0171571\pi$
$614$			13.5532i			0.546962i
$615$	−2.43169	+	16.5442i	−0.0980550	+	0.667127i
$616$	0.714243			0.0287777
$617$	−39.4541			−1.58836			−0.794182	−	0.607680i	$-0.792100\pi$
$617$	−39.4541			−1.58836			−0.794182	+	0.607680i	$0.792100\pi$
$618$	−5.74481	−	0.844379i	−0.231090	−	0.0339659i
$619$		−	2.35902i		−	0.0948171i	−0.998876	−	0.0474086i	$-0.984904\pi$
$619$		−	2.35902i		−	0.0948171i	0.998876	−	0.0474086i	$-0.0150963\pi$
$620$	−2.24052			−0.0899815
$621$	−24.6531	−	3.63659i	−0.989295	−	0.145931i
$622$	3.63405			0.145712
$623$		−	1.92785i		−	0.0772378i
$624$	−6.60352	−	0.970593i	−0.264352	−	0.0388548i
$625$	1.00000			0.0400000
$626$	20.2986			0.811294
$627$	−0.253279	+	1.72320i	−0.0101150	+	0.0688181i
$628$			0.699510i			0.0279135i
$629$			43.7780i			1.74554i
$630$	0.558185	+	0.167708i	0.0222386	+	0.00668166i
$631$			0.472138i			0.0187955i	0.999956	+	0.00939776i	$0.00299144\pi$
$631$			0.472138i			0.0187955i	−0.999956	+	0.00939776i	$0.997009\pi$
$632$	−6.43875			−0.256120
$633$	1.02786	+	0.151077i	0.0408540	+	0.00600476i
$634$	22.0942			0.877472
$635$	13.8315			0.548884
$636$	−7.02481	−	1.03252i	−0.278552	−	0.0409419i
$637$	26.8291			1.06301
$638$	33.5036			1.32642
$639$	8.39817	−	27.9517i	0.332227	−	1.10575i
$640$			1.00000i			0.0395285i
$641$	17.5371			0.692675			0.346337	−	0.938110i	$-0.387425\pi$
$641$	17.5371			0.692675			0.346337	+	0.938110i	$0.387425\pi$
$642$	−4.45498	+	30.3099i	−0.175824	+	1.19623i
$643$			3.71442i			0.146482i	0.997314	+	0.0732412i	$0.0233343\pi$
$643$			3.71442i			0.146482i	−0.997314	+	0.0732412i	$0.976666\pi$
$644$	−0.267638	−	0.892458i	−0.0105464	−	0.0351678i
$645$	−2.63296	+	17.9136i	−0.103673	+	0.705346i
$646$	1.01584			0.0399678
$647$			37.9848i			1.49334i	0.665197	+	0.746668i	$0.268347\pi$
$647$			37.9848i			1.49334i	−0.665197	+	0.746668i	$0.731653\pi$
$648$	−4.96037	+	7.50964i	−0.194862	+	0.295007i
$649$		−	9.18446i		−	0.360522i
$650$		−	3.85351i		−	0.151147i
$651$	0.109636	−	0.745921i	0.00429699	−	0.0292349i
$652$	13.2190			0.517694
$653$			28.7963i			1.12689i	0.826155	+	0.563443i	$0.190524\pi$
$653$			28.7963i			1.12689i	−0.826155	+	0.563443i	$0.809476\pi$
$654$	−11.8378	−	1.73994i	−0.462896	−	0.0680369i
$655$			11.1092i			0.434071i
$656$		−	9.65442i		−	0.376942i
$657$	31.8391	+	9.56615i	1.24216	+	0.373211i
$658$		−	0.902694i		−	0.0351907i
$659$	6.49917			0.253172			0.126586	−	0.991956i	$-0.459598\pi$
$659$	6.49917			0.253172			0.126586	+	0.991956i	$0.459598\pi$
$660$	−6.30001	−	0.925983i	−0.245228	−	0.0360438i
$661$			39.1114i			1.52126i	0.649187	+	0.760629i	$0.275109\pi$
$661$			39.1114i			1.52126i	−0.649187	+	0.760629i	$0.724891\pi$
$662$			27.8332i			1.08177i
$663$	−24.5248	−	3.60469i	−0.952466	−	0.139995i
$664$			9.42725i			0.365848i
$665$	−0.0531397			−0.00206067
$666$	33.8672	+	10.1755i	1.31233	+	0.394292i
$667$	−12.5543	−	41.8633i	−0.486105	−	1.62095i
$668$		−	10.7904i		−	0.417493i
$669$	18.2732	+	2.68581i	0.706481	+	0.103839i
$670$	10.9816			0.424256
$671$			51.4207i			1.98507i
$672$	−0.332923	−	0.0489334i	−0.0128428	−	0.00188765i
$673$	−13.0249			−0.502071			−0.251036	−	0.967978i	$-0.580771\pi$
$673$	−13.0249			−0.502071			−0.251036	+	0.967978i	$0.580771\pi$
$674$	−27.7015			−1.06702
$675$	−4.70607	−	2.20294i	−0.181137	−	0.0847912i
$676$	−1.84950			−0.0711347
$677$	−26.1392			−1.00461			−0.502305	−	0.864691i	$-0.667515\pi$
$677$	−26.1392			−1.00461			−0.502305	+	0.864691i	$0.667515\pi$
$678$	−0.840390	+	5.71767i	−0.0322750	+	0.219586i
$679$	−1.73196			−0.0664664
$680$			3.71391i			0.142422i
$681$	9.55221	+	1.40399i	0.366041	+	0.0538012i
$682$			8.23704i			0.315413i
$683$			15.5123i			0.593560i	0.954946	+	0.296780i	$0.0959128\pi$
$683$			15.5123i			0.593560i	−0.954946	+	0.296780i	$0.904087\pi$
$684$	0.236116	−	0.785867i	0.00902813	−	0.0300484i
$685$	−6.61230			−0.252643
$686$	2.71256			0.103566
$687$	3.75441	−	25.5435i	0.143240	−	0.974545i
$688$		−	10.4535i		−	0.398537i
$689$	−15.7969			−0.601813
$690$	1.20368	+	8.21895i	0.0458234	+	0.312890i
$691$	31.1673			1.18566			0.592830	−	0.805327i	$-0.298010\pi$
$691$	31.1673			1.18566			0.592830	+	0.805327i	$0.298010\pi$
$692$			3.90535i			0.148459i
$693$	0.616562	−	2.05211i	0.0234212	−	0.0779530i
$694$	25.4305			0.965329
$695$	−2.36109			−0.0895612
$696$	−15.6167	−	2.29536i	−0.591949	−	0.0870053i
$697$		−	35.8556i		−	1.35813i
$698$			25.3679i			0.960188i
$699$	−3.86435	+	26.2915i	−0.146163	+	0.994434i
$700$		−	0.194278i		−	0.00734302i
$701$	−39.7108			−1.49986			−0.749929	−	0.661519i	$-0.769912\pi$
$701$	−39.7108			−1.49986			−0.749929	+	0.661519i	$0.769912\pi$
$702$	−8.48904	+	18.1348i	−0.320398	+	0.684456i
$703$	−3.22419			−0.121603
$704$	3.67639			0.138559
$705$	−1.17030	+	7.96226i	−0.0440761	+	0.299876i
$706$	6.58726			0.247915
$707$	−1.63033			−0.0613149
$708$	−0.629235	+	4.28106i	−0.0236481	+	0.160892i
$709$		−	29.9453i		−	1.12462i	−0.826926	−	0.562311i	$-0.809913\pi$
$709$		−	29.9453i		−	1.12462i	0.826926	−	0.562311i	$-0.190087\pi$
$710$	−9.72869			−0.365111
$711$	−5.55817	+	18.4993i	−0.208448	+	0.693778i
$712$		−	9.92316i		−	0.371886i
$713$	10.2923	−	3.08655i	0.385450	−	0.115592i
$714$	−1.23644	−	0.181734i	−0.0462727	−	0.00680122i
$715$	−14.1670			−0.529816
$716$			5.90397i			0.220642i
$717$	2.92726	−	19.9159i	0.109320	−	0.743772i
$718$		−	34.1462i		−	1.27432i
$719$			19.0401i			0.710077i	0.934852	+	0.355038i	$0.115532\pi$
$719$			19.0401i			0.710077i	−0.934852	+	0.355038i	$0.884468\pi$
$720$	2.87312	+	0.863238i	0.107075	+	0.0321710i
$721$	−0.651299			−0.0242556
$722$		−	18.9252i		−	0.704322i
$723$	1.62388	−	11.0482i	0.0603926	−	0.410886i
$724$		−	3.65493i		−	0.135834i
$725$		−	9.11317i		−	0.338454i
$726$	−0.633677	+	4.31128i	−0.0235180	+	0.160007i
$727$			28.0357i			1.03979i	0.854231	+	0.519893i	$0.174028\pi$
$727$			28.0357i			1.03979i	−0.854231	+	0.519893i	$0.825972\pi$
$728$	−0.748652			−0.0277469
$729$	17.2941	+	20.7344i	0.640523	+	0.767939i
$730$		−	11.0817i		−	0.410152i
$731$		−	38.8234i		−	1.43594i
$732$	3.52288	−	23.9682i	0.130209	−	0.885891i
$733$			33.0849i			1.22202i	0.791623	+	0.611010i	$0.209237\pi$
$733$			33.0849i			1.22202i	−0.791623	+	0.611010i	$0.790763\pi$
$734$	2.78712			0.102875
$735$	−11.9308	−	1.75360i	−0.440074	−	0.0646826i
$736$	−1.37760	−	4.59371i	−0.0507791	−	0.169327i
$737$		−	40.3726i		−	1.48714i
$738$	−27.7383	−	8.33407i	−1.02106	−	0.306781i
$739$	0.332871			0.0122449			0.00612243	−	0.999981i	$-0.498051\pi$
$739$	0.332871			0.0122449			0.00612243	+	0.999981i	$0.498051\pi$
$740$		−	11.7876i		−	0.433320i
$741$	0.265480	−	1.80622i	0.00975266	−	0.0663532i
$742$	−0.796415			−0.0292373
$743$	16.2658			0.596734			0.298367	−	0.954451i	$-0.403558\pi$
$743$	16.2658			0.596734			0.298367	+	0.954451i	$0.403558\pi$
$744$	0.564326	−	3.83945i	0.0206892	−	0.140761i
$745$	−9.03818			−0.331133
$746$	−36.8414			−1.34886
$747$	27.0856	+	8.13796i	0.991011	+	0.297752i
$748$	13.6538			0.499231
$749$			3.43628i			0.125559i
$750$	−0.251873	+	1.71364i	−0.00919709	+	0.0625733i
$751$			40.0221i			1.46043i	0.683218	+	0.730214i	$0.260580\pi$
$751$			40.0221i			1.46043i	−0.683218	+	0.730214i	$0.739420\pi$
$752$		−	4.64640i		−	0.169437i
$753$	−0.628885	−	0.0924342i	−0.0229178	−	0.00336849i
$754$	−35.1176			−1.27891
$755$	7.21414			0.262549
$756$	−0.427983	+	0.914286i	−0.0155656	+	0.0332523i
$757$		−	20.5788i		−	0.747950i	−0.927439	−	0.373975i	$-0.877995\pi$
$757$		−	20.5788i		−	0.747950i	0.927439	−	0.373975i	$-0.122005\pi$
$758$	12.8044			0.465076
$759$	30.2161	−	4.42521i	1.09677	−	0.160625i
$760$	−0.273524			−0.00992176
$761$			5.93470i			0.215133i	0.994198	+	0.107566i	$0.0343058\pi$
$761$			5.93470i			0.215133i	−0.994198	+	0.107566i	$0.965694\pi$
$762$	−3.48377	+	23.7021i	−0.126204	+	0.858637i
$763$	−1.34207			−0.0485864
$764$	12.5903			0.455503
$765$	10.6705	+	3.20598i	0.385793	+	0.115913i
$766$			14.2092i			0.513399i
$767$			9.62693i			0.347608i
$768$	−1.71364	−	0.251873i	−0.0618356	−	0.00908867i
$769$		−	9.97467i		−	0.359696i	−0.983694	−	0.179848i	$-0.942439\pi$
$769$		−	9.97467i		−	0.359696i	0.983694	−	0.179848i	$-0.0575606\pi$
$770$	−0.714243			−0.0257395
$771$	5.28572	−	35.9619i	0.190361	−	1.29514i
$772$	−23.4908			−0.845452
$773$	44.7513			1.60959			0.804796	−	0.593552i	$-0.202275\pi$
$773$	44.7513			1.60959			0.804796	+	0.593552i	$0.202275\pi$
$774$	−30.0342	−	9.02388i	−1.07956	−	0.324357i
$775$	2.24052			0.0804819
$776$	−8.91482			−0.320024
$777$	3.92436	+	0.576806i	0.140785	+	0.0206928i
$778$			7.98762i			0.286370i
$779$	2.64072			0.0946135
$780$	6.60352	+	0.970593i	0.236444	+	0.0347528i
$781$			35.7665i			1.27983i
$782$	−5.11629	−	17.0606i	−0.182958	−	0.610087i
$783$	−20.0758	+	42.8872i	−0.717449	+	1.53266i
$784$	6.96226			0.248652
$785$		−	0.699510i		−	0.0249666i
$786$	−19.0371	−	2.79810i	−0.679031	−	0.0998048i
$787$		−	23.8924i		−	0.851671i	−0.904801	−	0.425835i	$-0.859980\pi$
$787$		−	23.8924i		−	0.851671i	0.904801	−	0.425835i	$-0.140020\pi$
$788$			15.4325i			0.549761i
$789$	48.8305	+	7.17716i	1.73841	+	0.255514i
$790$	6.43875			0.229080
$791$			0.648222i			0.0230481i
$792$	3.17360	−	10.5627i	0.112769	−	0.375330i
$793$		−	53.8979i		−	1.91397i
$794$		−	6.37102i		−	0.226099i
$795$	7.02481	+	1.03252i	0.249144	+	0.0366195i
$796$			21.1429i			0.749391i
$797$	16.9611			0.600793			0.300396	−	0.953814i	$-0.402881\pi$
$797$	16.9611			0.600793			0.300396	+	0.953814i	$0.402881\pi$
$798$	0.0133844	−	0.0910623i	0.000473804	−	0.00322357i
$799$		−	17.2563i		−	0.610484i
$800$		−	1.00000i		−	0.0353553i
$801$	−28.5104	−	8.56605i	−1.00737	−	0.302666i
$802$			4.08280i			0.144169i
$803$	−40.7407			−1.43771
$804$	−2.76596	+	18.8185i	−0.0975480	+	0.663677i
$805$	0.267638	+	0.892458i	0.00943300	+	0.0314550i
$806$		−	8.63386i		−	0.304115i
$807$	1.49952	−	10.2021i	0.0527857	−	0.359132i
$808$	−8.39174			−0.295220
$809$		−	18.7429i		−	0.658965i	−0.944162	−	0.329483i	$-0.893126\pi$
$809$		−	18.7429i		−	0.658965i	0.944162	−	0.329483i	$-0.106874\pi$
$810$	4.96037	−	7.50964i	0.174290	−	0.263862i
$811$	−38.4375			−1.34972			−0.674861	−	0.737944i	$-0.735797\pi$
$811$	−38.4375			−1.34972			−0.674861	+	0.737944i	$0.735797\pi$
$812$	−1.77049			−0.0621320
$813$	18.6733	+	2.74462i	0.654901	+	0.0962581i
$814$	−43.3358			−1.51892
$815$	−13.2190			−0.463040
$816$	−6.36430	−	0.935432i	−0.222795	−	0.0327467i
$817$	2.85929			0.100034
$818$			18.0794i			0.632133i
$819$	−0.646265	+	2.15097i	−0.0225823	+	0.0751609i
$820$			9.65442i			0.337147i
$821$		−	32.7980i		−	1.14466i	−0.820023	−	0.572330i	$-0.806040\pi$
$821$		−	32.7980i		−	1.14466i	0.820023	−	0.572330i	$-0.193960\pi$
$822$	1.66546	−	11.3311i	0.0580895	−	0.395217i
$823$	36.3523			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$823$	36.3523			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$824$	−3.35240			−0.116786
$825$	6.30001	+	0.925983i	0.219338	+	0.0322386i
$826$			0.485351i			0.0168875i
$827$	−1.85363			−0.0644572			−0.0322286	−	0.999481i	$-0.510260\pi$
$827$	−1.85363			−0.0644572			−0.0322286	+	0.999481i	$0.510260\pi$
$828$	−14.3875	−	0.00745181i	−0.500000	−	0.000258968i
$829$	−23.4117			−0.813124			−0.406562	−	0.913623i	$-0.633272\pi$
$829$	−23.4117			−0.813124			−0.406562	+	0.913623i	$0.633272\pi$
$830$		−	9.42725i		−	0.327225i
$831$	21.5794	+	3.17176i	0.748580	+	0.110027i
$832$	−3.85351			−0.133596
$833$	25.8572			0.895898
$834$	0.594694	−	4.04606i	0.0205926	−	0.140103i
$835$			10.7904i			0.373417i
$836$			1.00558i			0.0347788i
$837$	−10.5440	−	4.93573i	−0.364456	−	0.170604i
$838$			25.7595i			0.889848i
$839$	19.0303			0.656998			0.328499	−	0.944504i	$-0.393457\pi$
$839$	19.0303			0.656998			0.328499	+	0.944504i	$0.393457\pi$
$840$	0.332923	+	0.0489334i	0.0114869	+	0.00168836i
$841$	−54.0498			−1.86379
$842$	−13.8562			−0.477515
$843$	−18.1536	−	2.66824i	−0.625243	−	0.0918990i
$844$	0.599814			0.0206464
$845$	1.84950			0.0636248
$846$	−13.3497	−	4.01095i	−0.458971	−	0.137899i
$847$			0.488777i			0.0167946i
$848$	−4.09935			−0.140772
$849$	−7.99352	+	54.3847i	−0.274337	+	1.86648i
$850$		−	3.71391i		−	0.127386i
$851$	16.2386	+	54.1488i	0.556652	+	1.85620i
$852$	2.45039	−	16.6715i	0.0839490	−	0.571155i
$853$	−8.98937			−0.307790			−0.153895	−	0.988087i	$-0.549182\pi$
$853$	−8.98937			−0.307790			−0.153895	+	0.988087i	$0.549182\pi$
$854$		−	2.71732i		−	0.0929847i
$855$	−0.236116	+	0.785867i	−0.00807501	+	0.0268761i
$856$			17.6874i			0.604544i
$857$			35.0879i			1.19858i	0.800532	+	0.599290i	$0.204550\pi$
$857$			35.0879i			1.19858i	−0.800532	+	0.599290i	$0.795450\pi$
$858$	3.56828	−	24.2771i	0.121819	−	0.828807i
$859$	−20.3531			−0.694439			−0.347220	−	0.937784i	$-0.612874\pi$
$859$	−20.3531			−0.694439			−0.347220	+	0.937784i	$0.612874\pi$
$860$			10.4535i			0.356462i
$861$	−3.21418	−	0.472424i	−0.109539	−	0.0161002i
$862$		−	23.1260i		−	0.787674i
$863$		−	55.7757i		−	1.89863i	−0.314333	−	0.949313i	$-0.601781\pi$
$863$		−	55.7757i		−	1.89863i	0.314333	−	0.949313i	$-0.398219\pi$
$864$	−2.20294	+	4.70607i	−0.0749455	+	0.160104i
$865$		−	3.90535i		−	0.132786i
$866$	−15.8236			−0.537707
$867$	5.49548	+	0.807732i	0.186636	+	0.0274320i
$868$		−	0.435285i		−	0.0147745i
$869$		−	23.6714i		−	0.802996i
$870$	15.6167	+	2.29536i	0.529455	+	0.0778199i
$871$			42.3176i			1.43388i
$872$	−6.90800			−0.233935
$873$	−7.69562	+	25.6134i	−0.260457	+	0.866881i
$874$	1.25649	−	0.376807i	0.0425014	−	0.0127457i
$875$			0.194278i			0.00656780i
$876$	18.9900	+	2.79118i	0.641614	+	0.0943052i
$877$	26.1377			0.882608			0.441304	−	0.897358i	$-0.354516\pi$
$877$	26.1377			0.882608			0.441304	+	0.897358i	$0.354516\pi$
$878$		−	31.7678i		−	1.07211i
$879$	11.6106	+	1.70655i	0.391617	+	0.0575604i
$880$	−3.67639			−0.123931
$881$	15.6301			0.526590			0.263295	−	0.964715i	$-0.415191\pi$
$881$	15.6301			0.526590			0.263295	+	0.964715i	$0.415191\pi$
$882$	6.01008	−	20.0034i	0.202370	−	0.673549i
$883$	26.2855			0.884577			0.442289	−	0.896873i	$-0.354167\pi$
$883$	26.2855			0.884577			0.442289	+	0.896873i	$0.354167\pi$
$884$	−14.3116			−0.481350
$885$	0.629235	−	4.28106i	0.0211515	−	0.143906i
$886$	−11.4636			−0.385127
$887$		−	21.1883i		−	0.711435i	−0.934594	−	0.355717i	$-0.884237\pi$
$887$		−	21.1883i		−	0.711435i	0.934594	−	0.355717i	$-0.115763\pi$
$888$	20.1997	+	2.96897i	0.677857	+	0.0996321i
$889$			2.68715i			0.0901241i
$890$			9.92316i			0.332625i
$891$	−27.6084	−	18.2363i	−0.924916	−	0.610938i
$892$	10.6634			0.357036
$893$	1.27090			0.0425291
$894$	2.27647	−	15.4882i	0.0761365	−	0.518002i
$895$		−	5.90397i		−	0.197348i
$896$	−0.194278			−0.00649038
$897$	−31.6718	+	4.63840i	−1.05749	+	0.154872i
$898$	−6.54091			−0.218273
$899$		−	20.4183i		−	0.680987i
$900$	−2.87312	−	0.863238i	−0.0957707	−	0.0287746i
$901$	−15.2246			−0.507205
$902$	35.4935			1.18180
$903$	−3.48022	−	0.511526i	−0.115814	−	0.0170225i
$904$			3.33657i			0.110973i
$905$			3.65493i			0.121494i
$906$	−1.81704	+	12.3624i	−0.0603672	+	0.410714i
$907$		−	30.7874i		−	1.02228i	−0.859498	−	0.511140i	$-0.829223\pi$
$907$		−	30.7874i		−	1.02228i	0.859498	−	0.511140i	$-0.170777\pi$
$908$	5.57422			0.184987
$909$	−7.24407	+	24.1105i	−0.240271	+	0.799694i
$910$	0.748652			0.0248176
$911$	43.6844			1.44733			0.723664	−	0.690152i	$-0.242456\pi$
$911$	43.6844			1.44733			0.723664	+	0.690152i	$0.242456\pi$
$912$	0.0688932	−	0.468721i	0.00228128	−	0.0155209i
$913$	−34.6583			−1.14702
$914$	30.6183			1.01276
$915$	−3.52288	+	23.9682i	−0.116463	+	0.792365i
$916$		−	14.9060i		−	0.492508i
$917$	−2.15827			−0.0712723
$918$	−8.18151	+	17.4779i	−0.270030	+	0.576856i
$919$			53.3411i			1.75956i	0.475381	+	0.879780i	$0.342310\pi$
$919$			53.3411i			1.75956i	−0.475381	+	0.879780i	$0.657690\pi$
$920$	1.37760	+	4.59371i	0.0454182	+	0.151450i
$921$	23.2253	+	3.41368i	0.765299	+	0.112485i
$922$	22.9570			0.756047
$923$		−	37.4895i		−	1.23398i
$924$	0.179898	−	1.22395i	0.00591822	−	0.0402652i
$925$			11.7876i			0.387573i
$926$		−	22.2784i		−	0.732114i
$927$	−2.89392	+	9.63185i	−0.0950488	+	0.316352i
$928$	−9.11317			−0.299154
$929$		−	40.8893i		−	1.34153i	−0.741668	−	0.670767i	$-0.765965\pi$
$929$		−	40.8893i		−	1.34153i	0.741668	−	0.670767i	$-0.234035\pi$
$930$	−0.564326	+	3.83945i	−0.0185050	+	0.125900i
$931$			1.90434i			0.0624123i
$932$			15.3425i			0.502559i
$933$	0.915317	−	6.22745i	0.0299661	−	0.203877i
$934$		−	21.8911i		−	0.716299i
$935$	−13.6538			−0.446526
$936$	−3.32649	+	11.0716i	−0.108730	+	0.361886i
$937$		−	12.8925i		−	0.421181i	−0.977574	−	0.210590i	$-0.932461\pi$
$937$		−	12.8925i		−	0.421181i	0.977574	−	0.210590i	$-0.0675386\pi$
$938$			2.13348i			0.0696607i
$939$	5.11266	−	34.7844i	0.166845	−	1.13515i
$940$			4.64640i			0.151549i
$941$	−28.2649			−0.921410			−0.460705	−	0.887553i	$-0.652403\pi$
$941$	−28.2649			−0.921410			−0.460705	+	0.887553i	$0.652403\pi$
$942$	1.19871	+	0.176187i	0.0390560	+	0.00574050i
$943$	−13.3000	−	44.3497i	−0.433106	−	1.44422i
$944$			2.49823i			0.0813104i
$945$	0.427983	−	0.914286i	0.0139223	−	0.0297417i
$946$	38.4313			1.24951
$947$		−	53.6576i		−	1.74364i	−0.489829	−	0.871818i	$-0.662941\pi$
$947$		−	53.6576i		−	1.74364i	0.489829	−	0.871818i	$-0.337059\pi$
$948$	−1.62174	+	11.0337i	−0.0526718	+	0.358358i
$949$	42.7034			1.38621
$950$	0.273524			0.00887429
$951$	5.56492	−	37.8615i	0.180455	−	1.22774i
$952$	−0.721531			−0.0233849
$953$	47.7407			1.54647			0.773236	−	0.634118i	$-0.218637\pi$
$953$	47.7407			1.54647			0.773236	+	0.634118i	$0.218637\pi$
$954$	−3.53872	+	11.7779i	−0.114570	+	0.381325i
$955$	−12.5903			−0.407414
$956$		−	11.6220i		−	0.375881i
$957$	8.43864	−	57.4130i	0.272782	−	1.85590i
$958$			5.71132i			0.184524i
$959$		−	1.28462i		−	0.0414827i
$960$	1.71364	+	0.251873i	0.0553075	+	0.00812916i
$961$	−25.9801			−0.838066
$962$	45.4235			1.46451
$963$	50.8181	+	15.2685i	1.63759	+	0.492019i
$964$		−	6.44721i		−	0.207651i
$965$	23.4908			0.756196
$966$	−1.59676	+	0.233849i	−0.0513750	+	0.00752398i
$967$	−7.74638			−0.249107			−0.124553	−	0.992213i	$-0.539750\pi$
$967$	−7.74638			−0.249107			−0.124553	+	0.992213i	$0.539750\pi$
$968$			2.51586i			0.0808629i
$969$	0.255863	−	1.74079i	0.00821950	−	0.0559221i
$970$	8.91482			0.286238
$971$	−54.7216			−1.75610			−0.878051	−	0.478568i	$-0.841156\pi$
$971$	−54.7216			−1.75610			−0.878051	+	0.478568i	$0.841156\pi$
$972$	11.6194	+	10.3918i	0.372693	+	0.333316i
$973$		−	0.458708i		−	0.0147055i
$974$		−	22.2185i		−	0.711928i
$975$	−6.60352	−	0.970593i	−0.211482	−	0.0310838i
$976$		−	13.9867i		−	0.447704i
$977$	−30.6187			−0.979578			−0.489789	−	0.871841i	$-0.662926\pi$
$977$	−30.6187			−0.979578			−0.489789	+	0.871841i	$0.662926\pi$
$978$	3.32949	−	22.6525i	0.106465	−	0.724348i
$979$	36.4814			1.16595
$980$	−6.96226			−0.222401
$981$	−5.96325	+	19.8475i	−0.190392	+	0.633683i
$982$	−9.94225			−0.317270
$983$	−18.1788			−0.579812			−0.289906	−	0.957055i	$-0.593624\pi$
$983$	−18.1788			−0.579812			−0.289906	+	0.957055i	$0.593624\pi$
$984$	−16.5442	−	2.43169i	−0.527410	−	0.0775193i
$985$		−	15.4325i		−	0.491721i
$986$	−33.8454			−1.07786
$987$	−1.54689	−	0.227364i	−0.0492381	−	0.00723708i
$988$		−	1.05403i		−	0.0335330i
$989$	−14.4008	−	48.0205i	−0.457919	−	1.52696i
$990$	−3.17360	+	10.5627i	−0.100864	+	0.335705i
$991$	28.0460			0.890912			0.445456	−	0.895304i	$-0.353042\pi$
$991$	28.0460			0.890912			0.445456	+	0.895304i	$0.353042\pi$
$992$		−	2.24052i		−	0.0711367i
$993$	47.6960	+	7.01042i	1.51359	+	0.222469i
$994$		−	1.89007i		−	0.0599494i
$995$		−	21.1429i		−	0.670276i
$996$	16.1549	+	2.37447i	0.511888	+	0.0752379i
$997$	−34.7005			−1.09898			−0.549488	−	0.835502i	$-0.685177\pi$
$997$	−34.7005			−1.09898			−0.549488	+	0.835502i	$0.685177\pi$
$998$		−	5.95037i		−	0.188356i
$999$	25.9673	−	55.4732i	0.821570	−	1.75509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.e.b.551.1	yes	16
3.2	odd	2		690.2.e.a.551.9	yes	16
23.22	odd	2		690.2.e.a.551.1	✓	16
69.68	even	2	inner	690.2.e.b.551.9	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.e.a.551.1	✓	16	23.22	odd	2
690.2.e.a.551.9	yes	16	3.2	odd	2
690.2.e.b.551.1	yes	16	1.1	even	1	trivial
690.2.e.b.551.9	yes	16	69.68	even	2	inner

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.71364 - 0.251873i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-0.251873 + 1.71364i) q^{6} +0.194278i q^{7} +1.00000i q^{8} +(2.87312 + 0.863238i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.71364 - 0.251873i) q^{3} -1.00000 q^{4} +1.00000 q^{5} +(-0.251873 + 1.71364i) q^{6} +0.194278i q^{7} +1.00000i q^{8} +(2.87312 + 0.863238i) q^{9} -1.00000i q^{10} -3.67639 q^{11} +(1.71364 + 0.251873i) q^{12} +3.85351 q^{13} +0.194278 q^{14} +(-1.71364 - 0.251873i) q^{15} +1.00000 q^{16} +3.71391 q^{17} +(0.863238 - 2.87312i) q^{18} +0.273524i q^{19} -1.00000 q^{20} +(0.0489334 - 0.332923i) q^{21} +3.67639i q^{22} +(4.59371 - 1.37760i) q^{23} +(0.251873 - 1.71364i) q^{24} +1.00000 q^{25} -3.85351i q^{26} +(-4.70607 - 2.20294i) q^{27} -0.194278i q^{28} -9.11317i q^{29} +(-0.251873 + 1.71364i) q^{30} +2.24052 q^{31} -1.00000i q^{32} +(6.30001 + 0.925983i) q^{33} -3.71391i q^{34} +0.194278i q^{35} +(-2.87312 - 0.863238i) q^{36} +11.7876i q^{37} +0.273524 q^{38} +(-6.60352 - 0.970593i) q^{39} +1.00000i q^{40} -9.65442i q^{41} +(-0.332923 - 0.0489334i) q^{42} -10.4535i q^{43} +3.67639 q^{44} +(2.87312 + 0.863238i) q^{45} +(-1.37760 - 4.59371i) q^{46} -4.64640i q^{47} +(-1.71364 - 0.251873i) q^{48} +6.96226 q^{49} -1.00000i q^{50} +(-6.36430 - 0.935432i) q^{51} -3.85351 q^{52} -4.09935 q^{53} +(-2.20294 + 4.70607i) q^{54} -3.67639 q^{55} -0.194278 q^{56} +(0.0688932 - 0.468721i) q^{57} -9.11317 q^{58} +2.49823i q^{59} +(1.71364 + 0.251873i) q^{60} -13.9867i q^{61} -2.24052i q^{62} +(-0.167708 + 0.558185i) q^{63} -1.00000 q^{64} +3.85351 q^{65} +(0.925983 - 6.30001i) q^{66} +10.9816i q^{67} -3.71391 q^{68} +(-8.21895 + 1.20368i) q^{69} +0.194278 q^{70} -9.72869i q^{71} +(-0.863238 + 2.87312i) q^{72} +11.0817 q^{73} +11.7876 q^{74} +(-1.71364 - 0.251873i) q^{75} -0.273524i q^{76} -0.714243i q^{77} +(-0.970593 + 6.60352i) q^{78} +6.43875i q^{79} +1.00000 q^{80} +(7.50964 + 4.96037i) q^{81} -9.65442 q^{82} +9.42725 q^{83} +(-0.0489334 + 0.332923i) q^{84} +3.71391 q^{85} -10.4535 q^{86} +(-2.29536 + 15.6167i) q^{87} -3.67639i q^{88} -9.92316 q^{89} +(0.863238 - 2.87312i) q^{90} +0.748652i q^{91} +(-4.59371 + 1.37760i) q^{92} +(-3.83945 - 0.564326i) q^{93} -4.64640 q^{94} +0.273524i q^{95} +(-0.251873 + 1.71364i) q^{96} +8.91482i q^{97} -6.96226i q^{98} +(-10.5627 - 3.17360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 16 q^{5} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q - 16 * q^4 + 16 * q^5 + 2 * q^6 + 2 * q^9	\( 16 q - 16 q^{4} + 16 q^{5} + 2 q^{6} + 2 q^{9} + 12 q^{11} + 12 q^{14} + 16 q^{16} + 8 q^{18} - 16 q^{20} + 4 q^{21} - 4 q^{23} - 2 q^{24} + 16 q^{25} + 24 q^{27} + 2 q^{30} + 4 q^{31} + 28 q^{33} - 2 q^{36} + 16 q^{38} - 8 q^{39} - 12 q^{44} + 2 q^{45} - 4 q^{46} - 4 q^{49} + 2 q^{51} + 8 q^{53} - 26 q^{54} + 12 q^{55} - 12 q^{56} - 28 q^{57} - 8 q^{58} - 16 q^{64} - 10 q^{66} - 22 q^{69} + 12 q^{70} - 8 q^{72} - 16 q^{73} + 24 q^{74} - 12 q^{78} + 16 q^{80} + 22 q^{81} - 16 q^{82} + 40 q^{83} - 4 q^{84} + 40 q^{86} + 20 q^{87} - 80 q^{89} + 8 q^{90} + 4 q^{92} - 4 q^{93} - 24 q^{94} + 2 q^{96} + 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^4 + 16 * q^5 + 2 * q^6 + 2 * q^9 + 12 * q^11 + 12 * q^14 + 16 * q^16 + 8 * q^18 - 16 * q^20 + 4 * q^21 - 4 * q^23 - 2 * q^24 + 16 * q^25 + 24 * q^27 + 2 * q^30 + 4 * q^31 + 28 * q^33 - 2 * q^36 + 16 * q^38 - 8 * q^39 - 12 * q^44 + 2 * q^45 - 4 * q^46 - 4 * q^49 + 2 * q^51 + 8 * q^53 - 26 * q^54 + 12 * q^55 - 12 * q^56 - 28 * q^57 - 8 * q^58 - 16 * q^64 - 10 * q^66 - 22 * q^69 + 12 * q^70 - 8 * q^72 - 16 * q^73 + 24 * q^74 - 12 * q^78 + 16 * q^80 + 22 * q^81 - 16 * q^82 + 40 * q^83 - 4 * q^84 + 40 * q^86 + 20 * q^87 - 80 * q^89 + 8 * q^90 + 4 * q^92 - 4 * q^93 - 24 * q^94 + 2 * q^96 + 8 * q^99

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