LMFDB - Embedded newform 690.2.m.f.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 36 x^{18} - 172 x^{17} + 691 x^{16} - 2342 x^{15} + 7870 x^{14} - 23240 x^{13} + \cdots + 123904 $ x^20 - 6x^19 + 36x^18 - 172x^17 + 691x^16 - 2342x^15 + 7870x^14 - 23240x^13 + 63837x^12 - 154607x^11 + 334467x^10 - 664202x^9 + 1099560x^8 - 1331000x^7 + 1218096x^6 + 395648x^5 - 588544x^4 + 665984x^3 + 2323200x^2 + 991232*x + 123904
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			301.1
Root			$-0.245245 - 0.0720105i$ of defining polynomial
Character	$\chi$	$=$	690.301
Dual form			690.2.m.f.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 - 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.525067 + 0.605959i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.841254 - 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.525067 + 0.605959i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(-3.81286 + 2.45038i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(1.33714 + 1.54314i) q^{13} +(0.769321 - 0.225893i) q^{14} +(-0.142315 + 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.27417 + 4.97974i) q^{17} +(0.959493 + 0.281733i) q^{18} +(-1.39854 - 3.06237i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-0.674516 - 0.433485i) q^{21} +4.53236 q^{22} +(0.259300 - 4.78882i) q^{23} +1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.290588 - 2.02109i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-0.769321 - 0.225893i) q^{28} +(-2.36151 + 5.17098i) q^{29} +(0.654861 - 0.755750i) q^{30} +(-1.15750 + 8.05059i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-2.96807 - 3.42533i) q^{33} +(4.60541 - 2.95971i) q^{34} +(-0.674516 + 0.433485i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(4.13446 - 1.21399i) q^{37} +(-0.479117 + 3.33233i) q^{38} +(-1.33714 + 1.54314i) q^{39} +(0.415415 - 0.909632i) q^{40} +(-5.00816 - 1.47053i) q^{41} +(0.333079 + 0.729342i) q^{42} +(-1.78576 - 12.4202i) q^{43} +(-3.81286 - 2.45038i) q^{44} -1.00000 q^{45} +(-2.80717 + 3.88842i) q^{46} -5.18694 q^{47} +(-0.841254 - 0.540641i) q^{48} +(0.904712 + 6.29241i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(-5.25270 - 1.54233i) q^{51} +(-0.848224 + 1.85735i) q^{52} +(-6.06642 + 7.00102i) q^{53} +(-0.142315 + 0.989821i) q^{54} +(-4.34877 + 1.27691i) q^{55} +(0.525067 + 0.605959i) q^{56} +(2.83217 - 1.82012i) q^{57} +(4.78227 - 3.07338i) q^{58} +(1.99897 + 2.30693i) q^{59} +(-0.959493 + 0.281733i) q^{60} +(-2.18047 + 15.1655i) q^{61} +(5.32623 - 6.14679i) q^{62} +(0.333079 - 0.729342i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.848224 + 1.85735i) q^{65} +(0.645022 + 4.48623i) q^{66} +(11.4849 + 7.38088i) q^{67} -5.47446 q^{68} +(4.77698 - 0.424859i) q^{69} +0.801799 q^{70} +(-4.84158 - 3.11150i) q^{71} +(0.142315 + 0.989821i) q^{72} +(1.55454 + 3.40396i) q^{73} +(-4.13446 - 1.21399i) q^{74} +(-0.415415 + 0.909632i) q^{75} +(2.20465 - 2.54431i) q^{76} +(0.517178 - 3.59705i) q^{77} +(1.95916 - 0.575261i) q^{78} +(1.29853 + 1.49859i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(3.41810 + 3.94470i) q^{82} +(2.51187 - 0.737551i) q^{83} +(0.114108 - 0.793638i) q^{84} +(-3.58501 + 4.13732i) q^{85} +(-5.21261 + 11.4140i) q^{86} +(-5.45443 - 1.60156i) q^{87} +(1.88281 + 4.12278i) q^{88} +(-0.999078 - 6.94874i) q^{89} +(0.841254 + 0.540641i) q^{90} -1.63717 q^{91} +(4.46378 - 1.75348i) q^{92} -8.13337 q^{93} +(4.36354 + 2.80427i) q^{94} +(-0.479117 - 3.33233i) q^{95} +(0.415415 + 0.909632i) q^{96} +(0.760874 + 0.223413i) q^{97} +(2.64084 - 5.78264i) q^{98} +(2.96807 - 3.42533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$2$	−0.841254	−	0.540641i	−0.594856	−	0.382291i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$3$	0.142315	+	0.989821i	0.0821655	+	0.571474i
$4$	0.415415	+	0.909632i	0.207708	+	0.454816i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$6$	0.415415	−	0.909632i	0.169592	−	0.371356i
$7$	−0.525067	+	0.605959i	−0.198457	+	0.229031i	−0.846251	−	0.532784i	$-0.821146\pi$
$7$	−0.525067	+	0.605959i	−0.198457	+	0.229031i	0.647795	+	0.761815i	$0.275691\pi$
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	−0.959493	+	0.281733i	−0.319831	+	0.0939109i
$10$	−0.654861	−	0.755750i	−0.207085	−	0.238989i
$11$	−3.81286	+	2.45038i	−1.14962	+	0.738817i	−0.969564	−	0.244839i	$-0.921265\pi$
$11$	−3.81286	+	2.45038i	−1.14962	+	0.738817i	−0.180058	+	0.983656i	$0.557629\pi$
$12$	−0.841254	+	0.540641i	−0.242849	+	0.156070i
$13$	1.33714	+	1.54314i	0.370856	+	0.427991i	0.910248	−	0.414064i	$-0.135891\pi$
$13$	1.33714	+	1.54314i	0.370856	+	0.427991i	−0.539391	+	0.842055i	$0.681346\pi$
$14$	0.769321	−	0.225893i	0.205610	−	0.0603724i
$15$	−0.142315	+	0.989821i	−0.0367455	+	0.255571i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−2.27417	+	4.97974i	−0.551568	+	1.20776i	0.404478	+	0.914548i	$0.367453\pi$
$17$	−2.27417	+	4.97974i	−0.551568	+	1.20776i	−0.956046	+	0.293217i	$0.905274\pi$
$18$	0.959493	+	0.281733i	0.226155	+	0.0664050i
$19$	−1.39854	−	3.06237i	−0.320846	−	0.702555i	0.678644	−	0.734467i	$-0.262568\pi$
$19$	−1.39854	−	3.06237i	−0.320846	−	0.702555i	−0.999491	+	0.0319116i	$0.989841\pi$
$20$	0.142315	+	0.989821i	0.0318226	+	0.221331i
$21$	−0.674516	−	0.433485i	−0.147192	−	0.0945943i
$22$	4.53236			0.966303
$23$	0.259300	−	4.78882i	0.0540677	−	0.998537i
$23$	0.259300	−	4.78882i	0.0540677	−	0.998537i
$24$	1.00000			0.204124
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	−0.290588	−	2.02109i	−0.0569891	−	0.396368i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−0.769321	−	0.225893i	−0.145388	−	0.0426898i
$29$	−2.36151	+	5.17098i	−0.438521	+	0.960227i	0.553346	+	0.832951i	$0.313351\pi$
$29$	−2.36151	+	5.17098i	−0.438521	+	0.960227i	−0.991867	+	0.127276i	$0.959377\pi$
$30$	0.654861	−	0.755750i	0.119561	−	0.137980i
$31$	−1.15750	+	8.05059i	−0.207893	+	1.44593i	0.572123	+	0.820168i	$0.306120\pi$
$31$	−1.15750	+	8.05059i	−0.207893	+	1.44593i	−0.780016	+	0.625760i	$0.784789\pi$
$32$	0.959493	−	0.281733i	0.169616	−	0.0498038i
$33$	−2.96807	−	3.42533i	−0.516674	−	0.596273i
$34$	4.60541	−	2.95971i	0.789821	−	0.507587i
$35$	−0.674516	+	0.433485i	−0.114014	+	0.0732724i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	4.13446	−	1.21399i	0.679700	−	0.199578i	0.0763822	−	0.997079i	$-0.475663\pi$
$37$	4.13446	−	1.21399i	0.679700	−	0.199578i	0.603318	+	0.797501i	$0.293845\pi$
$38$	−0.479117	+	3.33233i	−0.0777231	+	0.540576i
$39$	−1.33714	+	1.54314i	−0.214114	+	0.247101i
$40$	0.415415	−	0.909632i	0.0656829	−	0.143825i
$41$	−5.00816	−	1.47053i	−0.782143	−	0.229658i	−0.133802	−	0.991008i	$-0.542719\pi$
$41$	−5.00816	−	1.47053i	−0.782143	−	0.229658i	−0.648341	+	0.761350i	$0.724537\pi$
$42$	0.333079	+	0.729342i	0.0513953	+	0.112540i
$43$	−1.78576	−	12.4202i	−0.272326	−	1.89407i	−0.424041	−	0.905643i	$-0.639389\pi$
$43$	−1.78576	−	12.4202i	−0.272326	−	1.89407i	0.151715	−	0.988424i	$-0.451520\pi$
$44$	−3.81286	−	2.45038i	−0.574811	−	0.369409i
$45$	−1.00000			−0.149071
$46$	−2.80717	+	3.88842i	−0.413894	+	0.573316i
$47$	−5.18694			−0.756594			−0.378297	−	0.925684i	$-0.623490\pi$
$47$	−5.18694			−0.756594			−0.378297	+	0.925684i	$0.623490\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	0.904712	+	6.29241i	0.129245	+	0.898916i
$50$	−0.415415	−	0.909632i	−0.0587486	−	0.128641i
$51$	−5.25270	−	1.54233i	−0.735525	−	0.215970i
$52$	−0.848224	+	1.85735i	−0.117627	+	0.257568i
$53$	−6.06642	+	7.00102i	−0.833287	+	0.961664i	−0.999702	−	0.0243914i	$-0.992235\pi$
$53$	−6.06642	+	7.00102i	−0.833287	+	0.961664i	0.166416	+	0.986056i	$0.446781\pi$
$54$	−0.142315	+	0.989821i	−0.0193666	+	0.134698i
$55$	−4.34877	+	1.27691i	−0.586388	+	0.172179i
$56$	0.525067	+	0.605959i	0.0701650	+	0.0809747i
$57$	2.83217	−	1.82012i	0.375129	−	0.241081i
$58$	4.78227	−	3.07338i	0.627943	−	0.403555i
$59$	1.99897	+	2.30693i	0.260243	+	0.300337i	0.870802	−	0.491634i	$-0.163600\pi$
$59$	1.99897	+	2.30693i	0.260243	+	0.300337i	−0.610558	+	0.791971i	$0.709055\pi$
$60$	−0.959493	+	0.281733i	−0.123870	+	0.0363715i
$61$	−2.18047	+	15.1655i	−0.279180	+	1.94174i	0.0531745	+	0.998585i	$0.483066\pi$
$61$	−2.18047	+	15.1655i	−0.279180	+	1.94174i	−0.332355	+	0.943155i	$0.607843\pi$
$62$	5.32623	−	6.14679i	0.676432	−	0.780644i
$63$	0.333079	−	0.729342i	0.0419641	−	0.0918885i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	0.848224	+	1.85735i	0.105209	+	0.230376i
$66$	0.645022	+	4.48623i	0.0793968	+	0.552217i
$67$	11.4849	+	7.38088i	1.40310	+	0.901718i	0.999910	−	0.0133985i	$-0.00426501\pi$
$67$	11.4849	+	7.38088i	1.40310	+	0.901718i	0.403190	+	0.915116i	$0.367901\pi$
$68$	−5.47446			−0.663875
$69$	4.77698	−	0.424859i	0.575080	−	0.0511471i
$70$	0.801799			0.0958333
$71$	−4.84158	−	3.11150i	−0.574590	−	0.369267i	0.220842	−	0.975310i	$-0.429120\pi$
$71$	−4.84158	−	3.11150i	−0.574590	−	0.369267i	−0.795432	+	0.606043i	$0.792756\pi$
$72$	0.142315	+	0.989821i	0.0167720	+	0.116652i
$73$	1.55454	+	3.40396i	0.181945	+	0.398403i	0.978525	−	0.206130i	$-0.0660870\pi$
$73$	1.55454	+	3.40396i	0.181945	+	0.398403i	−0.796580	+	0.604533i	$0.793360\pi$
$74$	−4.13446	−	1.21399i	−0.480621	−	0.141123i
$75$	−0.415415	+	0.909632i	−0.0479680	+	0.105035i
$76$	2.20465	−	2.54431i	0.252891	−	0.291852i
$77$	0.517178	−	3.59705i	0.0589379	−	0.409922i
$78$	1.95916	−	0.575261i	0.221831	−	0.0651355i
$79$	1.29853	+	1.49859i	0.146097	+	0.168604i	0.824081	−	0.566472i	$-0.191692\pi$
$79$	1.29853	+	1.49859i	0.146097	+	0.168604i	−0.677985	+	0.735076i	$0.737146\pi$
$80$	−0.841254	+	0.540641i	−0.0940550	+	0.0604455i
$81$	0.841254	−	0.540641i	0.0934726	−	0.0600712i
$82$	3.41810	+	3.94470i	0.377466	+	0.435620i
$83$	2.51187	−	0.737551i	0.275713	−	0.0809568i	−0.140953	−	0.990016i	$-0.545017\pi$
$83$	2.51187	−	0.737551i	0.275713	−	0.0809568i	0.416666	+	0.909060i	$0.363198\pi$
$84$	0.114108	−	0.793638i	0.0124502	−	0.0865930i
$85$	−3.58501	+	4.13732i	−0.388849	+	0.448755i
$86$	−5.21261	+	11.4140i	−0.562090	+	1.23081i
$87$	−5.45443	−	1.60156i	−0.584776	−	0.171706i
$88$	1.88281	+	4.12278i	0.200708	+	0.439490i
$89$	−0.999078	−	6.94874i	−0.105902	−	0.736565i	−0.971708	−	0.236185i	$-0.924103\pi$
$89$	−0.999078	−	6.94874i	−0.105902	−	0.736565i	0.865806	−	0.500380i	$-0.166806\pi$
$90$	0.841254	+	0.540641i	0.0886759	+	0.0569885i
$91$	−1.63717			−0.171622
$92$	4.46378	−	1.75348i	0.465381	−	0.182813i
$93$	−8.13337			−0.843392
$94$	4.36354	+	2.80427i	0.450064	+	0.289239i
$95$	−0.479117	−	3.33233i	−0.0491564	−	0.341890i
$96$	0.415415	+	0.909632i	0.0423981	+	0.0928389i
$97$	0.760874	+	0.223413i	0.0772551	+	0.0226841i	0.320132	−	0.947373i	$-0.396273\pi$
$97$	0.760874	+	0.223413i	0.0772551	+	0.0226841i	−0.242877	+	0.970057i	$0.578091\pi$
$98$	2.64084	−	5.78264i	0.266765	−	0.584135i
$99$	2.96807	−	3.42533i	0.298302	−	0.344259i
$100$	−0.142315	+	0.989821i	−0.0142315	+	0.0989821i
$101$	−8.19154	+	2.40525i	−0.815089	+	0.239332i	−0.662600	−	0.748974i	$-0.730547\pi$
$101$	−8.19154	+	2.40525i	−0.815089	+	0.239332i	−0.152489	+	0.988305i	$0.548729\pi$
$102$	3.58501	+	4.13732i	0.354969	+	0.409656i
$103$	16.3723	−	10.5219i	1.61321	−	1.03675i	0.653048	−	0.757317i	$-0.273490\pi$
$103$	16.3723	−	10.5219i	1.61321	−	1.03675i	0.960165	−	0.279433i	$-0.0901464\pi$
$104$	1.71773	−	1.10392i	0.168437	−	0.108248i
$105$	−0.525067	−	0.605959i	−0.0512413	−	0.0591356i
$106$	8.88844	−	2.60988i	0.863321	−	0.253494i
$107$	0.0557577	−	0.387804i	0.00539030	−	0.0374904i	−0.986949	−	0.161035i	$-0.948517\pi$
$107$	0.0557577	−	0.387804i	0.00539030	−	0.0374904i	0.992339	+	0.123544i	$0.0394260\pi$
$108$	0.654861	−	0.755750i	0.0630140	−	0.0727220i
$109$	3.06282	−	6.70663i	0.293365	−	0.642379i	−0.704357	−	0.709846i	$-0.748765\pi$
$109$	3.06282	−	6.70663i	0.293365	−	0.642379i	0.997721	+	0.0674671i	$0.0214918\pi$
$110$	4.34877	+	1.27691i	0.414639	+	0.121749i
$111$	1.79002	+	3.91960i	0.169902	+	0.372032i
$112$	−0.114108	−	0.793638i	−0.0107822	−	0.0749917i
$113$	13.9531	+	8.96710i	1.31260	+	0.843554i	0.994524	−	0.104512i	$-0.0333281\pi$
$113$	13.9531	+	8.96710i	1.31260	+	0.843554i	0.318072	+	0.948066i	$0.396964\pi$
$114$	−3.36660			−0.315311
$115$	1.59796	−	4.52178i	0.149011	−	0.421658i
$116$	−5.68470			−0.527811
$117$	−1.71773	−	1.10392i	−0.158804	−	0.102057i
$118$	−0.434417	−	3.02144i	−0.0399913	−	0.278146i
$119$	−1.82343	−	3.99275i	−0.167153	−	0.366015i
$120$	0.959493	+	0.281733i	0.0875893	+	0.0257185i
$121$	3.96401	−	8.67998i	0.360365	−	0.789089i
$122$	10.0334	−	11.5792i	0.908381	−	1.04833i
$123$	0.742825	−	5.16646i	0.0669783	−	0.465844i
$124$	−7.80391	+	2.29144i	−0.700812	+	0.205777i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	−0.674516	+	0.433485i	−0.0600907	+	0.0386179i
$127$	−6.94227	+	4.46152i	−0.616026	+	0.395896i	−0.811113	−	0.584890i	$-0.801138\pi$
$127$	−6.94227	+	4.46152i	−0.616026	+	0.395896i	0.195086	+	0.980786i	$0.437501\pi$
$128$	0.654861	+	0.755750i	0.0578821	+	0.0667995i
$129$	12.0397	−	3.53517i	1.06003	−	0.311254i
$130$	0.290588	−	2.02109i	0.0254863	−	0.177261i
$131$	−7.70990	+	8.89769i	−0.673617	+	0.777395i	−0.984938	−	0.172910i	$-0.944683\pi$
$131$	−7.70990	+	8.89769i	−0.673617	+	0.777395i	0.311321	+	0.950305i	$0.399229\pi$
$132$	1.88281	−	4.12278i	0.163878	−	0.358842i
$133$	2.59000	+	0.760491i	0.224581	+	0.0659430i
$134$	−5.67128	−	12.4184i	−0.489924	−	1.07278i
$135$	−0.142315	−	0.989821i	−0.0122485	−	0.0851903i
$136$	4.60541	+	2.95971i	0.394910	+	0.253793i
$137$	7.30745			0.624317			0.312159	−	0.950030i	$-0.398948\pi$
$137$	7.30745			0.624317			0.312159	+	0.950030i	$0.398948\pi$
$138$	−4.24834	−	2.22521i	−0.361643	−	0.189423i
$139$	−0.283114			−0.0240134			−0.0120067	−	0.999928i	$-0.503822\pi$
$139$	−0.283114			−0.0240134			−0.0120067	+	0.999928i	$0.503822\pi$
$140$	−0.674516	−	0.433485i	−0.0570070	−	0.0366362i
$141$	−0.738179	−	5.13415i	−0.0621659	−	0.432373i
$142$	2.39080	+	5.23512i	0.200631	+	0.439321i
$143$	−8.87962	−	2.60729i	−0.742551	−	0.218033i
$144$	0.415415	−	0.909632i	0.0346179	−	0.0758027i
$145$	−3.72269	+	4.29621i	−0.309152	+	0.356781i
$146$	0.532560	−	3.70404i	0.0440750	−	0.306548i
$147$	−6.09961	+	1.79101i	−0.503087	+	0.147720i
$148$	2.82180	+	3.25653i	0.231950	+	0.267685i
$149$	1.79233	−	1.15186i	0.146834	−	0.0943642i	−0.465161	−	0.885226i	$-0.654004\pi$
$149$	1.79233	−	1.15186i	0.146834	−	0.0943642i	0.611995	+	0.790862i	$0.290367\pi$
$150$	0.841254	−	0.540641i	0.0686881	−	0.0441431i
$151$	9.25100	+	10.6762i	0.752835	+	0.868818i	0.994840	−	0.101457i	$-0.0323504\pi$
$151$	9.25100	+	10.6762i	0.752835	+	0.868818i	−0.242005	+	0.970275i	$0.577805\pi$
$152$	−3.23023	+	0.948481i	−0.262006	+	0.0769320i
$153$	0.779096	−	5.41873i	0.0629862	−	0.438079i
$154$	−2.37979	+	2.74643i	−0.191769	+	0.221313i
$155$	−3.37873	+	7.39838i	−0.271386	+	0.594252i
$156$	−1.95916	−	0.575261i	−0.156858	−	0.0460578i
$157$	−9.68705	−	21.2117i	−0.773111	−	1.69288i	−0.719680	−	0.694306i	$-0.755712\pi$
$157$	−9.68705	−	21.2117i	−0.773111	−	1.69288i	−0.0534308	−	0.998572i	$-0.517016\pi$
$158$	−0.282199	−	1.96273i	−0.0224505	−	0.156147i
$159$	−7.79310	−	5.00832i	−0.618033	−	0.397186i
$160$	1.00000			0.0790569
$161$	2.76568	+	2.67157i	0.217966	+	0.210550i
$162$	−1.00000			−0.0785674
$163$	−12.3115	−	7.91210i	−0.964308	−	0.619723i	−0.0391212	−	0.999234i	$-0.512456\pi$
$163$	−12.3115	−	7.91210i	−0.964308	−	0.619723i	−0.925187	+	0.379511i	$0.876092\pi$
$164$	−0.742825	−	5.16646i	−0.0580049	−	0.403433i
$165$	−1.88281	−	4.12278i	−0.146577	−	0.320958i
$166$	−2.51187	−	0.737551i	−0.194959	−	0.0572451i
$167$	4.18410	−	9.16191i	0.323776	−	0.708970i	−0.675830	−	0.737058i	$-0.736215\pi$
$167$	4.18410	−	9.16191i	0.323776	−	0.708970i	0.999605	+	0.0280881i	$0.00894189\pi$
$168$	−0.525067	+	0.605959i	−0.0405098	+	0.0467508i
$169$	1.25675	−	8.74088i	0.0966730	−	0.672375i
$170$	5.25270	−	1.54233i	0.402864	−	0.118292i
$171$	2.20465	+	2.54431i	0.168594	+	0.194568i
$172$	10.5560	−	6.78393i	0.804888	−	0.517270i
$173$	18.8599	−	12.1205i	1.43389	−	0.921507i	0.434106	−	0.900862i	$-0.357064\pi$
$173$	18.8599	−	12.1205i	1.43389	−	0.921507i	0.999787	−	0.0206450i	$-0.00657197\pi$
$174$	3.72269	+	4.29621i	0.282216	+	0.325695i
$175$	−0.769321	+	0.225893i	−0.0581552	+	0.0170759i
$176$	0.645022	−	4.48623i	0.0486204	−	0.338162i
$177$	−1.99897	+	2.30693i	−0.150252	+	0.173400i
$178$	−2.91629	+	6.38579i	−0.218586	+	0.478636i
$179$	17.5304	+	5.14739i	1.31028	+	0.384734i	0.860978	−	0.508643i	$-0.169853\pi$
$179$	17.5304	+	5.14739i	1.31028	+	0.384734i	0.449307	+	0.893377i	$0.351671\pi$
$180$	−0.415415	−	0.909632i	−0.0309632	−	0.0678000i
$181$	0.917790	+	6.38337i	0.0682188	+	0.474472i	0.995081	+	0.0990692i	$0.0315865\pi$
$181$	0.917790	+	6.38337i	0.0682188	+	0.474472i	−0.926862	+	0.375403i	$0.877504\pi$
$182$	1.37728	+	0.885121i	0.102090	+	0.0656095i
$183$	−15.3214			−1.13259
$184$	−4.70317	−	0.938180i	−0.346722	−	0.0691635i
$185$	4.30900			0.316804
$186$	6.84223	+	4.39723i	0.501697	+	0.322421i
$187$	−3.53115	−	24.5597i	−0.258223	−	1.79598i
$188$	−2.15473	−	4.71821i	−0.157150	−	0.344111i
$189$	0.769321	+	0.225893i	0.0559598	+	0.0164313i
$190$	−1.39854	+	3.06237i	−0.101461	+	0.222168i
$191$	14.2975	−	16.5001i	1.03453	−	1.19391i	0.0537953	−	0.998552i	$-0.482868\pi$
$191$	14.2975	−	16.5001i	1.03453	−	1.19391i	0.980732	−	0.195356i	$-0.0625864\pi$
$192$	0.142315	−	0.989821i	0.0102707	−	0.0714342i
$193$	13.8448	−	4.06521i	0.996572	−	0.292620i	0.257524	−	0.966272i	$-0.417093\pi$
$193$	13.8448	−	4.06521i	0.996572	−	0.292620i	0.739049	+	0.673652i	$0.235275\pi$
$194$	−0.519302	−	0.599307i	−0.0372837	−	0.0430277i
$195$	−1.71773	+	1.10392i	−0.123009	+	0.0790533i
$196$	−5.34795	+	3.43692i	−0.381996	+	0.245494i
$197$	3.06054	+	3.53205i	0.218054	+	0.251648i	0.854229	−	0.519897i	$-0.174030\pi$
$197$	3.06054	+	3.53205i	0.218054	+	0.251648i	−0.636175	+	0.771545i	$0.719484\pi$
$198$	−4.34877	+	1.27691i	−0.309054	+	0.0907463i
$199$	0.554202	−	3.85456i	0.0392863	−	0.273242i	−0.960704	−	0.277574i	$-0.910470\pi$
$199$	0.554202	−	3.85456i	0.0392863	−	0.273242i	0.999991	+	0.00433145i	$0.00137875\pi$
$200$	0.654861	−	0.755750i	0.0463056	−	0.0534396i
$201$	−5.67128	+	12.4184i	−0.400022	+	0.875925i
$202$	8.19154	+	2.40525i	0.576355	+	0.169233i
$203$	−1.89346	−	4.14609i	−0.132895	−	0.290998i
$204$	−0.779096	−	5.41873i	−0.0545477	−	0.379387i
$205$	−4.39100	−	2.82192i	−0.306681	−	0.197092i
$206$	−19.4618			−1.35597
$207$	1.10037	+	4.66789i	0.0764810	+	0.324441i
$208$	−2.04187			−0.141578
$209$	12.8364	+	8.24945i	0.887912	+	0.570626i
$210$	0.114108	+	0.793638i	0.00787419	+	0.0547662i
$211$	−3.12818	−	6.84977i	−0.215353	−	0.471557i	0.770867	−	0.636996i	$-0.219823\pi$
$211$	−3.12818	−	6.84977i	−0.215353	−	0.471557i	−0.986220	+	0.165439i	$0.947096\pi$
$212$	−8.88844	−	2.60988i	−0.610460	−	0.179247i
$213$	2.39080	−	5.23512i	0.163815	−	0.358704i
$214$	−0.256569	+	0.296096i	−0.0175387	+	0.0202407i
$215$	1.78576	−	12.4202i	0.121788	−	0.847053i
$216$	−0.959493	+	0.281733i	−0.0652852	+	0.0191695i
$217$	−4.27056	−	4.92849i	−0.289905	−	0.334568i
$218$	−6.20248	+	3.98609i	−0.420085	+	0.269972i
$219$	−3.14808	+	2.02315i	−0.212727	+	0.136712i
$220$	−2.96807	−	3.42533i	−0.200107	−	0.230936i
$221$	−10.7253	+	3.14924i	−0.721464	+	0.211841i
$222$	0.613235	−	4.26514i	0.0411576	−	0.286258i
$223$	−5.87713	+	6.78257i	−0.393562	+	0.454194i	−0.917603	−	0.397499i	$-0.869878\pi$
$223$	−5.87713	+	6.78257i	−0.393562	+	0.454194i	0.524041	+	0.851693i	$0.324424\pi$
$224$	−0.333079	+	0.729342i	−0.0222548	+	0.0487312i
$225$	−0.959493	−	0.281733i	−0.0639662	−	0.0187822i
$226$	−6.89010	−	15.0872i	−0.458323	−	1.00359i
$227$	−0.167872	−	1.16757i	−0.0111420	−	0.0774946i	0.983492	−	0.180953i	$-0.0579182\pi$
$227$	−0.167872	−	1.16757i	−0.0111420	−	0.0774946i	−0.994634	+	0.103458i	$0.967009\pi$
$228$	2.83217	+	1.82012i	0.187565	+	0.120541i
$229$	17.8320			1.17837			0.589186	−	0.807998i	$-0.299449\pi$
$229$	17.8320			1.17837			0.589186	+	0.807998i	$0.299449\pi$
$230$	−3.78895	+	2.94004i	−0.249836	+	0.193861i
$231$	3.63404			0.239103
$232$	4.78227	+	3.07338i	0.313972	+	0.201777i
$233$	4.07310	+	28.3290i	0.266837	+	1.85590i	0.477889	+	0.878420i	$0.341402\pi$
$233$	4.07310	+	28.3290i	0.266837	+	1.85590i	−0.211052	+	0.977475i	$0.567689\pi$
$234$	0.848224	+	1.85735i	0.0554501	+	0.121419i
$235$	−4.97684	−	1.46133i	−0.324653	−	0.0953267i
$236$	−1.26806	+	2.77666i	−0.0825435	+	0.180745i
$237$	−1.29853	+	1.49859i	−0.0843489	+	0.0973438i
$238$	−0.624679	+	4.34474i	−0.0404919	+	0.281627i
$239$	18.9148	−	5.55389i	1.22350	−	0.359252i	0.394706	−	0.918808i	$-0.370846\pi$
$239$	18.9148	−	5.55389i	1.22350	−	0.359252i	0.828793	+	0.559556i	$0.189028\pi$
$240$	−0.654861	−	0.755750i	−0.0422711	−	0.0487834i
$241$	−10.0484	+	6.45769i	−0.647272	+	0.415976i	−0.822668	−	0.568522i	$-0.807516\pi$
$241$	−10.0484	+	6.45769i	−0.647272	+	0.415976i	0.175397	+	0.984498i	$0.443879\pi$
$242$	−8.02749	+	5.15896i	−0.516027	+	0.331630i
$243$	0.654861	+	0.755750i	0.0420093	+	0.0484814i
$244$	−14.7008	+	4.31654i	−0.941122	+	0.276338i
$245$	−0.904712	+	6.29241i	−0.0577999	+	0.402007i
$246$	−3.41810	+	3.94470i	−0.217930	+	0.251505i
$247$	2.85563	−	6.25296i	0.181699	−	0.397866i
$248$	7.80391	+	2.29144i	0.495549	+	0.145506i
$249$	1.08752	+	2.38134i	0.0689188	+	0.150911i
$250$	−0.142315	−	0.989821i	−0.00900078	−	0.0626018i
$251$	−0.187467	−	0.120478i	−0.0118328	−	0.00760450i	0.534711	−	0.845035i	$-0.320420\pi$
$251$	−0.187467	−	0.120478i	−0.0118328	−	0.00760450i	−0.546544	+	0.837430i	$0.684057\pi$
$252$	0.801799			0.0505086
$253$	10.7457	+	18.8945i	0.675579	+	1.18789i
$254$	8.25229			0.517795
$255$	−4.60541	−	2.95971i	−0.288402	−	0.185345i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−7.60579	−	16.6544i	−0.474436	−	1.03887i	−0.983956	−	0.178411i	$-0.942904\pi$
$257$	−7.60579	−	16.6544i	−0.474436	−	1.03887i	0.509520	−	0.860459i	$-0.329823\pi$
$258$	−12.0397	−	3.53517i	−0.749557	−	0.220090i
$259$	−1.43524	+	3.14274i	−0.0891814	+	0.195280i
$260$	−1.33714	+	1.54314i	−0.0829260	+	0.0957017i
$261$	0.809017	−	5.62684i	0.0500769	−	0.348292i
$262$	11.2964	−	3.31693i	0.697896	−	0.204921i
$263$	10.4734	+	12.0869i	0.645816	+	0.745312i	0.980392	−	0.197057i	$-0.0631384\pi$
$263$	10.4734	+	12.0869i	0.645816	+	0.745312i	−0.334576	+	0.942369i	$0.608593\pi$
$264$	−3.81286	+	2.45038i	−0.234666	+	0.150810i
$265$	−7.79310	+	5.00832i	−0.478727	+	0.307659i
$266$	−1.76769	−	2.04002i	−0.108384	−	0.125082i
$267$	6.73583	−	1.97782i	0.412226	−	0.121040i
$268$	−1.94290	+	13.5131i	−0.118681	+	0.825446i
$269$	−15.1193	+	17.4486i	−0.921842	+	1.06386i	0.0759276	+	0.997113i	$0.475808\pi$
$269$	−15.1193	+	17.4486i	−0.921842	+	1.06386i	−0.997770	+	0.0667492i	$0.978737\pi$
$270$	−0.415415	+	0.909632i	−0.0252814	+	0.0553584i
$271$	2.32878	+	0.683792i	0.141464	+	0.0415374i	0.351698	−	0.936114i	$-0.385604\pi$
$271$	2.32878	+	0.683792i	0.141464	+	0.0415374i	−0.210234	+	0.977651i	$0.567423\pi$
$272$	−2.27417	−	4.97974i	−0.137892	−	0.301941i
$273$	−0.232994	−	1.62051i	−0.0141014	−	0.0980775i
$274$	−6.14741	−	3.95070i	−0.371379	−	0.238671i
$275$	−4.53236			−0.273312
$276$	2.37089	+	4.16880i	0.142711	+	0.250932i
$277$	7.10519			0.426909			0.213455	−	0.976953i	$-0.431528\pi$
$277$	7.10519			0.426909			0.213455	+	0.976953i	$0.431528\pi$
$278$	0.238170	+	0.153063i	0.0142845	+	0.00918009i
$279$	−1.15750	−	8.05059i	−0.0692977	−	0.481976i
$280$	0.333079	+	0.729342i	0.0199053	+	0.0435865i
$281$	−1.82321	−	0.535341i	−0.108763	−	0.0319358i	0.226898	−	0.973919i	$-0.427142\pi$
$281$	−1.82321	−	0.535341i	−0.108763	−	0.0319358i	−0.335661	+	0.941983i	$0.608960\pi$
$282$	−2.15473	+	4.71821i	−0.128313	+	0.280965i
$283$	−10.0756	+	11.6279i	−0.598932	+	0.691205i	−0.971565	−	0.236774i	$-0.923910\pi$
$283$	−10.0756	+	11.6279i	−0.598932	+	0.691205i	0.372632	+	0.927979i	$0.378455\pi$
$284$	0.819051	−	5.69662i	0.0486017	−	0.338032i
$285$	3.23023	−	0.948481i	0.191342	−	0.0561832i
$286$	6.06041	+	6.99408i	0.358359	+	0.413569i
$287$	3.52070	−	2.26262i	0.207820	−	0.133558i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	−8.49333	−	9.80182i	−0.499608	−	0.576578i
$290$	5.45443	−	1.60156i	0.320295	−	0.0940471i
$291$	−0.112855	+	0.784925i	−0.00661568	+	0.0460131i
$292$	−2.45057	+	2.82811i	−0.143409	+	0.165503i
$293$	1.33818	−	2.93020i	0.0781771	−	0.171184i	−0.866508	−	0.499164i	$-0.833641\pi$
$293$	1.33818	−	2.93020i	0.0781771	−	0.171184i	0.944685	+	0.327980i	$0.106368\pi$
$294$	6.09961	+	1.79101i	0.355736	+	0.104454i
$295$	1.26806	+	2.77666i	0.0738291	+	0.161663i
$296$	−0.613235	−	4.26514i	−0.0356435	−	0.247906i
$297$	3.81286	+	2.45038i	0.221245	+	0.142185i
$298$	−2.13055			−0.123419
$299$	7.73655	−	6.00319i	0.447416	−	0.347173i
$300$	−1.00000			−0.0577350
$301$	8.46380	+	5.43935i	0.487845	+	0.313519i
$302$	−2.01043	−	13.9829i	−0.115687	−	0.804624i
$303$	−3.54655	−	7.76586i	−0.203744	−	0.446137i
$304$	3.23023	+	0.948481i	0.185266	+	0.0543991i
$305$	−6.36475	+	13.9369i	−0.364444	+	0.798022i
$306$	−3.58501	+	4.13732i	−0.204941	+	0.236515i
$307$	−3.05645	+	21.2581i	−0.174441	+	1.21326i	0.694921	+	0.719086i	$0.255439\pi$
$307$	−3.05645	+	21.2581i	−0.174441	+	1.21326i	−0.869362	+	0.494176i	$0.835470\pi$
$308$	3.48684	−	1.02383i	0.198681	−	0.0583380i
$309$	12.7448	+	14.7083i	0.725025	+	0.836724i
$310$	6.84223	−	4.39723i	0.388613	−	0.249746i
$311$	−17.9716	+	11.5496i	−1.01907	+	0.654919i	−0.939726	−	0.341928i	$-0.888920\pi$
$311$	−17.9716	+	11.5496i	−1.01907	+	0.654919i	−0.0793473	+	0.996847i	$0.525284\pi$
$312$	1.33714	+	1.54314i	0.0757007	+	0.0873633i
$313$	24.5917	−	7.22077i	1.39000	−	0.408142i	0.500765	−	0.865584i	$-0.333052\pi$
$313$	24.5917	−	7.22077i	1.39000	−	0.408142i	0.889240	+	0.457441i	$0.151234\pi$
$314$	−3.31864	+	23.0816i	−0.187282	+	1.30257i
$315$	0.525067	−	0.605959i	0.0295842	−	0.0341419i
$316$	−0.823734	+	1.80372i	−0.0463386	+	0.101467i
$317$	29.4491	+	8.64703i	1.65403	+	0.485666i	0.969860	−	0.243662i	$-0.0783487\pi$
$317$	29.4491	+	8.64703i	1.65403	+	0.485666i	0.684165	+	0.729327i	$0.260167\pi$
$318$	3.84827	+	8.42654i	0.215800	+	0.472537i
$319$	−3.66676	−	25.5029i	−0.205299	−	1.42789i
$320$	−0.841254	−	0.540641i	−0.0470275	−	0.0302227i
$321$	0.391791			0.0218677
$322$	−0.882275	−	3.74271i	−0.0491673	−	0.208573i
$323$	18.4303			1.02549
$324$	0.841254	+	0.540641i	0.0467363	+	0.0300356i
$325$	0.290588	+	2.02109i	0.0161189	+	0.112110i
$326$	6.07946	+	13.3122i	0.336710	+	0.737292i
$327$	7.07425	+	2.07719i	0.391207	+	0.114869i
$328$	−2.16830	+	4.74791i	−0.119724	+	0.262159i
$329$	2.72349	−	3.14308i	0.150151	−	0.173283i
$330$	−0.645022	+	4.48623i	−0.0355073	+	0.246959i
$331$	−24.1421	+	7.08875i	−1.32697	+	0.389633i	−0.867002	−	0.498304i	$-0.833956\pi$
$331$	−24.1421	+	7.08875i	−1.32697	+	0.389633i	−0.459965	+	0.887937i	$0.652138\pi$
$332$	1.71437	+	1.97849i	0.0940882	+	0.108584i
$333$	−3.62496	+	2.32962i	−0.198647	+	0.127662i
$334$	−8.47319	+	5.44539i	−0.463632	+	0.297958i
$335$	8.94022	+	10.3176i	0.488456	+	0.563709i
$336$	0.769321	−	0.225893i	0.0419699	−	0.0123235i
$337$	−3.52925	+	24.5465i	−0.192251	+	1.33713i	0.633783	+	0.773511i	$0.281501\pi$
$337$	−3.52925	+	24.5465i	−0.192251	+	1.33713i	−0.826033	+	0.563621i	$0.809408\pi$
$338$	−5.78292	+	6.67385i	−0.314549	+	0.363009i
$339$	−6.89010	+	15.0872i	−0.374219	+	0.819425i
$340$	−5.25270	−	1.54233i	−0.284868	−	0.0836447i
$341$	−15.3136	−	33.5321i	−0.829278	−	1.81587i
$342$	−0.479117	−	3.33233i	−0.0259077	−	0.180192i
$343$	−9.00960	−	5.79012i	−0.486472	−	0.312637i
$344$	−12.5480			−0.676540
$345$	4.70317	+	0.938180i	0.253210	+	0.0505099i
$346$	−22.4188			−1.20524
$347$	−15.4542	−	9.93180i	−0.829624	−	0.533167i	0.0555344	−	0.998457i	$-0.482314\pi$
$347$	−15.4542	−	9.93180i	−0.829624	−	0.533167i	−0.885158	+	0.465290i	$0.845950\pi$
$348$	−0.809017	−	5.62684i	−0.0433679	−	0.301630i
$349$	5.67353	+	12.4233i	0.303697	+	0.665004i	0.998532	−	0.0541654i	$-0.0172498\pi$
$349$	5.67353	+	12.4233i	0.303697	+	0.665004i	−0.694835	+	0.719169i	$0.744523\pi$
$350$	0.769321	+	0.225893i	0.0411219	+	0.0120745i
$351$	0.848224	−	1.85735i	0.0452748	−	0.0991381i
$352$	−2.96807	+	3.42533i	−0.158198	+	0.182571i
$353$	−1.81371	+	12.6146i	−0.0965339	+	0.671408i	0.882888	+	0.469584i	$0.155596\pi$
$353$	−1.81371	+	12.6146i	−0.0965339	+	0.671408i	−0.979422	+	0.201824i	$0.935313\pi$
$354$	2.92886	−	0.859991i	0.155667	−	0.0457080i
$355$	−3.76886	−	4.34949i	−0.200030	−	0.230847i
$356$	5.90576	−	3.79540i	0.313005	−	0.201156i
$357$	3.69261	−	2.37310i	0.195434	−	0.125598i
$358$	−11.9646	−	13.8079i	−0.632350	−	0.729771i
$359$	5.32255	−	1.56284i	0.280913	−	0.0824836i	−0.138241	−	0.990399i	$-0.544145\pi$
$359$	5.32255	−	1.56284i	0.280913	−	0.0824836i	0.419154	+	0.907915i	$0.362327\pi$
$360$	−0.142315	+	0.989821i	−0.00750065	+	0.0521682i
$361$	5.02016	−	5.79357i	0.264219	−	0.304925i
$362$	2.67902	−	5.86622i	0.140806	−	0.308322i
$363$	9.15577	+	2.68838i	0.480553	+	0.141103i
$364$	−0.680105	−	1.48922i	−0.0356472	−	0.0780565i
$365$	0.532560	+	3.70404i	0.0278755	+	0.193878i
$366$	12.8892	+	8.28339i	0.673729	+	0.432980i
$367$	−20.6544			−1.07815			−0.539075	−	0.842258i	$-0.681226\pi$
$367$	−20.6544			−1.07815			−0.539075	+	0.842258i	$0.681226\pi$
$368$	3.44934	+	3.33197i	0.179809	+	0.173691i
$369$	5.21959			0.271721
$370$	−3.62496	−	2.32962i	−0.188453	−	0.121111i
$371$	−1.05706	−	7.35201i	−0.0548798	−	0.381697i
$372$	−3.37873	−	7.39838i	−0.175179	−	0.383588i
$373$	−16.7161	−	4.90830i	−0.865529	−	0.254142i	−0.181316	−	0.983425i	$-0.558036\pi$
$373$	−16.7161	−	4.90830i	−0.865529	−	0.254142i	−0.684213	+	0.729283i	$0.739854\pi$
$374$	−10.3074	+	22.5700i	−0.532981	+	1.16707i
$375$	−0.654861	+	0.755750i	−0.0338169	+	0.0390267i
$376$	−0.738179	+	5.13415i	−0.0380687	+	0.264773i
$377$	−11.1372	+	3.27019i	−0.573597	+	0.168423i
$378$	−0.525067	−	0.605959i	−0.0270065	−	0.0311672i
$379$	−23.7006	+	15.2314i	−1.21742	+	0.782386i	−0.981884	−	0.189480i	$-0.939320\pi$
$379$	−23.7006	+	15.2314i	−1.21742	+	0.782386i	−0.235532	+	0.971867i	$0.575683\pi$
$380$	2.83217	−	1.82012i	0.145287	−	0.0933703i
$381$	−5.40410	−	6.23666i	−0.276860	−	0.319514i
$382$	−20.9484	+	6.15102i	−1.07182	+	0.314713i
$383$	−3.54819	+	24.6782i	−0.181304	+	1.26100i	0.672379	+	0.740207i	$0.265272\pi$
$383$	−3.54819	+	24.6782i	−0.181304	+	1.26100i	−0.853684	+	0.520792i	$0.825637\pi$
$384$	−0.654861	+	0.755750i	−0.0334182	+	0.0385667i
$385$	1.50964	−	3.30564i	0.0769382	−	0.168471i
$386$	−13.8448	−	4.06521i	−0.704683	−	0.206914i
$387$	5.21261	+	11.4140i	0.264972	+	0.580207i
$388$	0.112855	+	0.784925i	0.00572935	+	0.0398485i
$389$	8.07380	+	5.18872i	0.409358	+	0.263078i	0.729074	−	0.684435i	$-0.239951\pi$
$389$	8.07380	+	5.18872i	0.409358	+	0.263078i	−0.319716	+	0.947513i	$0.603587\pi$
$390$	2.04187			0.103394
$391$	23.2574	+	12.1818i	1.17618	+	0.616062i
$392$	6.35712			0.321083
$393$	−9.90436	−	6.36515i	−0.499609	−	0.321079i
$394$	−0.665118	−	4.62600i	−0.0335082	−	0.233054i
$395$	0.823734	+	1.80372i	0.0414465	+	0.0907553i
$396$	4.34877	+	1.27691i	0.218534	+	0.0641673i
$397$	1.97167	−	4.31736i	0.0989554	−	0.216682i	−0.853679	−	0.520799i	$-0.825634\pi$
$397$	1.97167	−	4.31736i	0.0989554	−	0.216682i	0.952635	+	0.304117i	$0.0983614\pi$
$398$	−2.55016	+	2.94304i	−0.127828	+	0.147521i
$399$	−0.384156	+	2.67186i	−0.0192318	+	0.133760i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	11.0065	+	12.7021i	0.549636	+	0.634314i	0.960798	−	0.277248i	$-0.0894224\pi$
$401$	11.0065	+	12.7021i	0.549636	+	0.634314i	−0.411162	+	0.911562i	$0.634877\pi$
$402$	11.4849	−	7.38088i	0.572813	−	0.368125i
$403$	−13.9709	+	8.97858i	−0.695942	+	0.447255i
$404$	−5.59078	−	6.45211i	−0.278152	−	0.321004i
$405$	0.959493	−	0.281733i	0.0476776	−	0.0139994i
$406$	−0.648669	+	4.51159i	−0.0321929	+	0.223907i
$407$	−12.7894	+	14.7597i	−0.633947	+	0.731614i
$408$	−2.27417	+	4.97974i	−0.112588	+	0.246534i
$409$	14.5689	+	4.27782i	0.720387	+	0.211525i	0.621321	−	0.783556i	$-0.286596\pi$
$409$	14.5689	+	4.27782i	0.720387	+	0.211525i	0.0990662	+	0.995081i	$0.468414\pi$
$410$	2.16830	+	4.74791i	0.107084	+	0.234482i
$411$	1.03996	+	7.23307i	0.0512973	+	0.356781i
$412$	16.3723	+	10.5219i	0.806607	+	0.518375i
$413$	−2.44750			−0.120433
$414$	1.59796	−	4.52178i	0.0785355	−	0.222233i
$415$	2.61791			0.128508
$416$	1.71773	+	1.10392i	0.0842187	+	0.0541241i
$417$	−0.0402913	−	0.280232i	−0.00197307	−	0.0137230i
$418$	−6.33867	−	13.8798i	−0.310035	−	0.678881i
$419$	13.4881	+	3.96046i	0.658936	+	0.193481i	0.594071	−	0.804413i	$-0.297520\pi$
$419$	13.4881	+	3.96046i	0.658936	+	0.193481i	0.0648656	+	0.997894i	$0.479338\pi$
$420$	0.333079	−	0.729342i	0.0162526	−	0.0355883i
$421$	18.0401	−	20.8194i	0.879221	−	1.01468i	−0.120537	−	0.992709i	$-0.538462\pi$
$421$	18.0401	−	20.8194i	0.879221	−	1.01468i	0.999759	−	0.0219669i	$-0.00699284\pi$
$422$	−1.07167	+	7.45361i	−0.0521680	+	0.362836i
$423$	4.97684	−	1.46133i	0.241982	−	0.0710523i
$424$	6.06642	+	7.00102i	0.294611	+	0.340000i
$425$	−4.60541	+	2.95971i	−0.223395	+	0.143567i
$426$	−4.84158	+	3.11150i	−0.234576	+	0.150753i
$427$	−8.04477	−	9.28416i	−0.389314	−	0.449292i
$428$	0.375921	−	0.110380i	0.0181708	−	0.00533544i
$429$	1.31705	−	9.16030i	0.0635879	−	0.442263i
$430$	−8.21716	+	9.48311i	−0.396267	+	0.457316i
$431$	9.79465	−	21.4473i	0.471792	−	1.03308i	−0.512848	−	0.858480i	$-0.671409\pi$
$431$	9.79465	−	21.4473i	0.471792	−	1.03308i	0.984639	−	0.174600i	$-0.0558633\pi$
$432$	0.959493	+	0.281733i	0.0461636	+	0.0135549i
$433$	−5.48636	−	12.0134i	−0.263658	−	0.577330i	0.730785	−	0.682607i	$-0.239154\pi$
$433$	−5.48636	−	12.0134i	−0.263658	−	0.577330i	−0.994443	+	0.105278i	$0.966427\pi$
$434$	0.928082	+	6.45495i	0.0445494	+	0.309848i
$435$	−4.78227	−	3.07338i	−0.229292	−	0.147357i
$436$	7.37291			0.353098
$437$	−15.0278	+	5.90326i	−0.718875	+	0.282391i
$438$	3.74213			0.178806
$439$	−23.7535	−	15.2654i	−1.13369	−	0.728579i	−0.167364	−	0.985895i	$-0.553525\pi$
$439$	−23.7535	−	15.2654i	−1.13369	−	0.728579i	−0.966327	+	0.257316i	$0.917162\pi$
$440$	0.645022	+	4.48623i	0.0307502	+	0.213873i
$441$	−2.64084	−	5.78264i	−0.125754	−	0.275364i
$442$	10.7253	+	3.14924i	0.510152	+	0.149794i
$443$	−1.97524	+	4.32516i	−0.0938463	+	0.205495i	−0.950734	−	0.310009i	$-0.899668\pi$
$443$	−1.97524	+	4.32516i	−0.0938463	+	0.205495i	0.856887	+	0.515504i	$0.172395\pi$
$444$	−2.82180	+	3.25653i	−0.133916	+	0.154548i
$445$	0.999078	−	6.94874i	0.0473608	−	0.329402i
$446$	8.61109	−	2.52844i	0.407747	−	0.119725i
$447$	1.39521	+	1.61016i	0.0659913	+	0.0761580i
$448$	0.674516	−	0.433485i	0.0318679	−	0.0204803i
$449$	−2.15313	+	1.38374i	−0.101613	+	0.0653025i	−0.590460	−	0.807067i	$-0.701054\pi$
$449$	−2.15313	+	1.38374i	−0.101613	+	0.0653025i	0.488848	+	0.872369i	$0.337417\pi$
$450$	0.654861	+	0.755750i	0.0308704	+	0.0356264i
$451$	22.6988	−	6.66497i	1.06884	−	0.313841i
$452$	−2.36044	+	16.4172i	−0.111026	+	0.772202i
$453$	−9.25100	+	10.6762i	−0.434650	+	0.501612i
$454$	−0.490016	+	1.07298i	−0.0229976	+	0.0503577i
$455$	−1.57085	−	0.461244i	−0.0736427	−	0.0216235i
$456$	−1.39854	−	3.06237i	−0.0654925	−	0.143409i
$457$	−2.85183	−	19.8349i	−0.133403	−	0.927839i	−0.941073	−	0.338204i	$-0.890181\pi$
$457$	−2.85183	−	19.8349i	−0.133403	−	0.927839i	0.807670	−	0.589635i	$-0.200728\pi$
$458$	−15.0012	−	9.64070i	−0.700961	−	0.450480i
$459$	5.47446			0.255526
$460$	4.77698	−	0.424859i	0.222728	−	0.0198092i
$461$	−12.6646			−0.589849			−0.294925	−	0.955521i	$-0.595295\pi$
$461$	−12.6646			−0.589849			−0.294925	+	0.955521i	$0.595295\pi$
$462$	−3.05715	−	1.96471i	−0.142232	−	0.0914067i
$463$	−2.29032	−	15.9295i	−0.106440	−	0.740308i	−0.971225	−	0.238165i	$-0.923454\pi$
$463$	−2.29032	−	15.9295i	−0.106440	−	0.740308i	0.864785	−	0.502143i	$-0.167455\pi$
$464$	−2.36151	−	5.17098i	−0.109630	−	0.240057i
$465$	−7.80391	−	2.29144i	−0.361898	−	0.106263i
$466$	11.8893	−	26.0340i	0.550762	−	1.20600i
$467$	−14.3314	+	16.5393i	−0.663177	+	0.765347i	−0.983293	−	0.182031i	$-0.941733\pi$
$467$	−14.3314	+	16.5393i	−0.663177	+	0.765347i	0.320116	+	0.947378i	$0.396278\pi$
$468$	0.290588	−	2.02109i	0.0134325	−	0.0934248i
$469$	−10.5028	+	3.08391i	−0.484976	+	0.142402i
$470$	3.39673	+	3.92003i	0.156679	+	0.180818i
$471$	19.6172	−	12.6072i	0.903912	−	0.580909i
$472$	2.56793	−	1.65031i	0.118199	−	0.0759617i
$473$	37.2431	+	42.9809i	1.71244	+	1.97626i
$474$	1.90260	−	0.558652i	0.0873891	−	0.0256598i
$475$	0.479117	−	3.33233i	0.0219834	−	0.152898i
$476$	2.87446	−	3.31730i	0.131750	−	0.152048i
$477$	3.84827	−	8.42654i	0.176200	−	0.385825i
$478$	−18.9148	−	5.55389i	−0.865144	−	0.254029i
$479$	−10.3040	−	22.5627i	−0.470803	−	1.03091i	−0.984891	−	0.173177i	$-0.944597\pi$
$479$	−10.3040	−	22.5627i	−0.470803	−	1.03091i	0.514088	−	0.857738i	$-0.328131\pi$
$480$	0.142315	+	0.989821i	0.00649575	+	0.0451790i
$481$	7.40170	+	4.75679i	0.337489	+	0.216891i
$482$	11.9445			0.544057
$483$	−2.25078	+	3.11773i	−0.102414	+	0.141862i
$484$	9.54230			0.433741
$485$	0.667111	+	0.428726i	0.0302919	+	0.0194674i
$486$	−0.142315	−	0.989821i	−0.00645553	−	0.0448992i
$487$	7.56252	+	16.5596i	0.342690	+	0.750387i	0.999995	−	0.00323794i	$-0.00103067\pi$
$487$	7.56252	+	16.5596i	0.342690	+	0.750387i	−0.657304	+	0.753625i	$0.728303\pi$
$488$	14.7008	+	4.31654i	0.665474	+	0.195401i
$489$	6.07946	−	13.3122i	0.274923	−	0.601997i
$490$	4.16303	−	4.80439i	0.188066	−	0.217040i
$491$	0.788382	−	5.48332i	0.0355792	−	0.247459i	−0.964268	−	0.264928i	$-0.914652\pi$
$491$	0.788382	−	5.48332i	0.0355792	−	0.247459i	0.999847	+	0.0174693i	$0.00556093\pi$
$492$	5.00816	−	1.47053i	0.225785	−	0.0662965i
$493$	−20.3797	−	23.5194i	−0.917855	−	1.05926i
$494$	−5.78291	+	3.71645i	−0.260186	+	0.167211i
$495$	3.81286	−	2.45038i	0.171376	−	0.110136i
$496$	−5.32623	−	6.14679i	−0.239155	−	0.275999i
$497$	4.42760	−	1.30006i	0.198605	−	0.0583156i
$498$	0.372568	−	2.59127i	0.0166952	−	0.116117i
$499$	−14.2523	+	16.4481i	−0.638023	+	0.736318i	−0.979024	−	0.203745i	$-0.934689\pi$
$499$	−14.2523	+	16.4481i	−0.638023	+	0.736318i	0.341001	+	0.940063i	$0.389234\pi$
$500$	−0.415415	+	0.909632i	−0.0185779	+	0.0406800i
$501$	9.66411	+	2.83764i	0.431761	+	0.126776i
$502$	0.0925722	+	0.202705i	0.00413170	+	0.00904716i
$503$	−5.49060	−	38.1879i	−0.244814	−	1.70272i	−0.627319	−	0.778762i	$-0.715848\pi$
$503$	−5.49060	−	38.1879i	−0.244814	−	1.70272i	0.382505	−	0.923953i	$-0.375061\pi$
$504$	−0.674516	−	0.433485i	−0.0300453	−	0.0193090i
$505$	−8.53736			−0.379908
$506$	1.17524	−	21.7046i	0.0522458	−	0.964889i
$507$	8.83076			0.392188
$508$	−6.94227	−	4.46152i	−0.308013	−	0.197948i
$509$	−1.68890	−	11.7465i	−0.0748590	−	0.520656i	−0.992404	−	0.123023i	$-0.960741\pi$
$509$	−1.68890	−	11.7465i	−0.0748590	−	0.520656i	0.917545	−	0.397632i	$-0.130168\pi$
$510$	2.27417	+	4.97974i	0.100702	+	0.220507i
$511$	−2.87889	−	0.845320i	−0.127355	−	0.0373947i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−2.20465	+	2.54431i	−0.0973379	+	0.112334i
$514$	−2.60563	+	18.1225i	−0.114929	+	0.799351i
$515$	18.6735	−	5.48303i	0.822852	−	0.241611i
$516$	8.21716	+	9.48311i	0.361740	+	0.417471i
$517$	19.7771	−	12.7100i	0.869797	−	0.558984i
$518$	2.90649	−	1.86789i	0.127704	−	0.0820703i
$519$	14.6812	+	16.9430i	0.644433	+	0.743716i
$520$	1.95916	−	0.575261i	0.0859149	−	0.0252269i
$521$	−0.491137	+	3.41593i	−0.0215171	+	0.149655i	−0.997748	−	0.0670803i	$-0.978632\pi$
$521$	−0.491137	+	3.41593i	−0.0215171	+	0.149655i	0.976230	+	0.216735i	$0.0695407\pi$
$522$	−3.72269	+	4.29621i	−0.162938	+	0.188040i
$523$	−17.8385	+	39.0609i	−0.780023	+	1.70801i	−0.0767966	+	0.997047i	$0.524469\pi$
$523$	−17.8385	+	39.0609i	−0.780023	+	1.70801i	−0.703227	+	0.710966i	$0.748258\pi$
$524$	−11.2964	−	3.31693i	−0.493487	−	0.144901i
$525$	−0.333079	−	0.729342i	−0.0145368	−	0.0318311i
$526$	−2.27608	−	15.8305i	−0.0992419	−	0.690243i
$527$	−37.4575	−	24.0725i	−1.63167	−	1.04861i
$528$	4.53236			0.197246
$529$	−22.8655	−	2.48348i	−0.994153	−	0.107977i
$530$	9.26368			0.402389
$531$	−2.56793	−	1.65031i	−0.111439	−	0.0716173i
$532$	0.384156	+	2.67186i	0.0166553	+	0.115840i
$533$	−4.42738	−	9.69461i	−0.191771	−	0.419920i
$534$	−6.73583	−	1.97782i	−0.291488	−	0.0855885i
$535$	0.162756	−	0.356386i	0.00703656	−	0.0154079i
$536$	8.94022	−	10.3176i	0.386159	−	0.445651i
$537$	−2.60016	+	18.0845i	−0.112205	+	0.780405i
$538$	22.1526	−	6.50460i	0.955068	−	0.280433i
$539$	−18.8683	−	21.7752i	−0.812717	−	0.937925i
$540$	0.841254	−	0.540641i	0.0362018	−	0.0232655i
$541$	−18.0400	+	11.5936i	−0.775602	+	0.498449i	−0.867571	−	0.497313i	$-0.834320\pi$
$541$	−18.0400	+	11.5936i	−0.775602	+	0.498449i	0.0919695	+	0.995762i	$0.470684\pi$
$542$	−1.58941	−	1.83428i	−0.0682711	−	0.0787890i
$543$	−6.18778	+	1.81690i	−0.265543	+	0.0779705i
$544$	−0.779096	+	5.41873i	−0.0334035	+	0.232326i
$545$	4.82823	−	5.57207i	0.206819	−	0.238681i
$546$	−0.680105	+	1.48922i	−0.0291058	+	0.0637328i
$547$	−24.5662	−	7.21330i	−1.05038	−	0.308418i	−0.289407	−	0.957206i	$-0.593458\pi$
$547$	−24.5662	−	7.21330i	−1.05038	−	0.308418i	−0.760969	+	0.648788i	$0.775276\pi$
$548$	3.03562	+	6.64709i	0.129675	+	0.283949i
$549$	−2.18047	−	15.1655i	−0.0930600	−	0.647247i
$550$	3.81286	+	2.45038i	0.162581	+	0.104485i
$551$	19.1381			0.815311
$552$	0.259300	−	4.78882i	0.0110365	−	0.203826i
$553$	−1.58990			−0.0676095
$554$	−5.97726	−	3.84135i	−0.253950	−	0.163203i
$555$	0.613235	+	4.26514i	0.0260304	+	0.181045i
$556$	−0.117610	−	0.257529i	−0.00498776	−	0.0109217i
$557$	−31.6666	−	9.29816i	−1.34176	−	0.393976i	−0.469461	−	0.882953i	$-0.655552\pi$
$557$	−31.6666	−	9.29816i	−1.34176	−	0.393976i	−0.872296	+	0.488977i	$0.837370\pi$
$558$	−3.37873	+	7.39838i	−0.143033	+	0.313198i
$559$	16.7784	−	19.3633i	0.709650	−	0.818979i
$560$	0.114108	−	0.793638i	0.00482194	−	0.0335373i
$561$	23.8071	−	6.99041i	1.00514	−	0.295135i
$562$	1.24435	+	1.43606i	0.0524898	+	0.0605764i
$563$	2.04050	−	1.31135i	0.0859967	−	0.0552667i	−0.496936	−	0.867787i	$-0.665542\pi$
$563$	2.04050	−	1.31135i	0.0859967	−	0.0552667i	0.582933	+	0.812521i	$0.301905\pi$
$564$	4.36354	−	2.80427i	0.183738	−	0.118081i
$565$	10.8616	+	12.5349i	0.456949	+	0.527348i
$566$	14.7626	−	4.33470i	0.620520	−	0.182201i
$567$	−0.114108	+	0.793638i	−0.00479208	+	0.0333297i
$568$	−3.76886	+	4.34949i	−0.158138	+	0.182501i
$569$	7.04411	−	15.4245i	0.295305	−	0.646627i	−0.702582	−	0.711603i	$-0.747970\pi$
$569$	7.04411	−	15.4245i	0.295305	−	0.646627i	0.997887	+	0.0649756i	$0.0206970\pi$
$570$	−3.23023	−	0.948481i	−0.135299	−	0.0397275i
$571$	12.5158	+	27.4059i	0.523772	+	1.14690i	0.967992	+	0.250983i	$0.0807537\pi$
$571$	12.5158	+	27.4059i	0.523772	+	1.14690i	−0.444220	+	0.895918i	$0.646519\pi$
$572$	−1.31705	−	9.16030i	−0.0550687	−	0.383011i
$573$	18.3669	+	11.8037i	0.767290	+	0.493107i
$574$	−4.18506			−0.174681
$575$	2.80717	−	3.88842i	0.117067	−	0.162158i
$576$	1.00000			0.0416667
$577$	−16.4260	−	10.5564i	−0.683824	−	0.439467i	0.152062	−	0.988371i	$-0.451409\pi$
$577$	−16.4260	−	10.5564i	−0.683824	−	0.439467i	−0.835885	+	0.548904i	$0.815045\pi$
$578$	1.84578	+	12.8377i	0.0767742	+	0.533976i
$579$	5.99415	+	13.1254i	0.249109	+	0.545472i
$580$	−5.45443	−	1.60156i	−0.226483	−	0.0665013i
$581$	−0.871973	+	1.90935i	−0.0361755	+	0.0792134i
$582$	0.519302	−	0.599307i	0.0215258	−	0.0248421i
$583$	5.97528	−	41.5590i	0.247471	−	1.72120i
$584$	3.59054	−	1.05428i	0.148578	−	0.0436264i
$585$	−1.33714	−	1.54314i	−0.0552840	−	0.0638011i
$586$	−2.70993	+	1.74157i	−0.111946	+	0.0719435i
$587$	5.12688	−	3.29484i	0.211609	−	0.135993i	−0.430543	−	0.902570i	$-0.641678\pi$
$587$	5.12688	−	3.29484i	0.211609	−	0.135993i	0.642152	+	0.766577i	$0.278042\pi$
$588$	−4.16303	−	4.80439i	−0.171680	−	0.198130i
$589$	26.2727	−	7.71435i	1.08255	−	0.317864i
$590$	0.434417	−	3.02144i	0.0178847	−	0.124391i
$591$	−3.06054	+	3.53205i	−0.125894	+	0.145289i
$592$	−1.79002	+	3.91960i	−0.0735695	+	0.161095i
$593$	26.7550	+	7.85599i	1.09870	+	0.322607i	0.780335	−	0.625362i	$-0.215049\pi$
$593$	26.7550	+	7.85599i	1.09870	+	0.322607i	0.318363	+	0.947969i	$0.396867\pi$
$594$	−1.88281	−	4.12278i	−0.0772527	−	0.169160i
$595$	−0.624679	−	4.34474i	−0.0256093	−	0.178117i
$596$	1.79233	+	1.15186i	0.0734168	+	0.0471821i
$597$	3.89420			0.159379
$598$	−9.75397	+	0.867508i	−0.398869	+	0.0354750i
$599$	19.7629			0.807489			0.403745	−	0.914872i	$-0.367708\pi$
$599$	19.7629			0.807489			0.403745	+	0.914872i	$0.367708\pi$
$600$	0.841254	+	0.540641i	0.0343440	+	0.0220716i
$601$	−0.728737	−	5.06848i	−0.0297258	−	0.206748i	0.969546	−	0.244910i	$-0.0787586\pi$
$601$	−0.728737	−	5.06848i	−0.0297258	−	0.206748i	−0.999272	+	0.0381628i	$0.987849\pi$
$602$	−4.17946	−	9.15175i	−0.170342	−	0.372997i
$603$	−13.0991	−	3.84624i	−0.533436	−	0.156631i
$604$	−5.86843	+	12.8501i	−0.238783	+	0.522862i
$605$	6.24888	−	7.21159i	0.254053	−	0.293193i
$606$	−1.21499	+	8.45047i	−0.0493557	+	0.343277i
$607$	−29.1790	+	8.56772i	−1.18434	+	0.347753i	−0.813845	−	0.581082i	$-0.802629\pi$
$607$	−29.1790	+	8.56772i	−1.18434	+	0.347753i	−0.370493	+	0.928835i	$0.620811\pi$
$608$	−2.20465	−	2.54431i	−0.0894106	−	0.103185i
$609$	3.83442	−	2.46423i	0.155379	−	0.0998558i
$610$	12.8892	−	8.28339i	0.521868	−	0.335385i
$611$	−6.93567	−	8.00420i	−0.280587	−	0.323815i
$612$	5.25270	−	1.54233i	0.212328	−	0.0623451i
$613$	2.65371	−	18.4570i	0.107182	−	0.745470i	−0.863369	−	0.504574i	$-0.831650\pi$
$613$	2.65371	−	18.4570i	0.107182	−	0.745470i	0.970551	−	0.240896i	$-0.0774413\pi$
$614$	14.0642	−	16.2310i	0.567586	−	0.655029i
$615$	2.16830	−	4.74791i	0.0874341	−	0.191454i
$616$	−3.48684	−	1.02383i	−0.140489	−	0.0412512i
$617$	10.9254	+	23.9234i	0.439841	+	0.963118i	0.991627	+	0.129133i	$0.0412193\pi$
$617$	10.9254	+	23.9234i	0.439841	+	0.963118i	−0.551786	+	0.833986i	$0.686053\pi$
$618$	−2.76971	−	19.2637i	−0.111414	−	0.774901i
$619$	29.0034	+	18.6394i	1.16575	+	0.749180i	0.972713	−	0.232012i	$-0.0745309\pi$
$619$	29.0034	+	18.6394i	1.16575	+	0.749180i	0.193034	+	0.981192i	$0.438167\pi$
$620$	−8.13337			−0.326644
$621$	−4.46378	+	1.75348i	−0.179125	+	0.0703647i
$622$	21.3628			0.856571
$623$	4.73524	+	3.04315i	0.189713	+	0.121921i
$624$	−0.290588	−	2.02109i	−0.0116328	−	0.0809082i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	−24.5917	−	7.22077i	−0.982882	−	0.288600i
$627$	−6.33867	+	13.8798i	−0.253142	+	0.554304i
$628$	15.2707	−	17.6233i	0.609367	−	0.703247i
$629$	−3.35713	+	23.3493i	−0.133857	+	0.930999i
$630$	−0.769321	+	0.225893i	−0.0306505	+	0.00899979i
$631$	8.11573	+	9.36605i	0.323082	+	0.372857i	0.893936	−	0.448195i	$-0.147933\pi$
$631$	8.11573	+	9.36605i	0.323082	+	0.372857i	−0.570854	+	0.821052i	$0.693388\pi$
$632$	1.66814	−	1.07205i	0.0663549	−	0.0426437i
$633$	6.33486	−	4.07117i	0.251788	−	0.161814i
$634$	−20.0992	−	23.1957i	−0.798241	−	0.921220i
$635$	−7.91801	+	2.32494i	−0.314217	+	0.0922623i
$636$	1.31836	−	9.16939i	0.0522763	−	0.363590i
$637$	−8.50036	+	9.80994i	−0.336797	+	0.388684i
$638$	−10.7032	+	23.4368i	−0.423744	+	0.927870i
$639$	5.52208	+	1.62143i	0.218450	+	0.0641427i
$640$	0.415415	+	0.909632i	0.0164207	+	0.0359564i
$641$	−4.91519	−	34.1859i	−0.194138	−	1.35026i	−0.820910	−	0.571058i	$-0.806533\pi$
$641$	−4.91519	−	34.1859i	−0.194138	−	1.35026i	0.626771	−	0.779203i	$-0.284376\pi$
$642$	−0.329596	−	0.211818i	−0.0130081	−	0.00835981i
$643$	9.77223			0.385379			0.192690	−	0.981260i	$-0.438279\pi$
$643$	9.77223			0.385379			0.192690	+	0.981260i	$0.438279\pi$
$644$	−1.28124	+	3.62556i	−0.0504881	+	0.142867i
$645$	12.5480			0.494075
$646$	−15.5046	−	9.96418i	−0.610019	−	0.392035i
$647$	−0.724304	−	5.03764i	−0.0284753	−	0.198050i	0.970618	−	0.240626i	$-0.0773527\pi$
$647$	−0.724304	−	5.03764i	−0.0284753	−	0.198050i	−0.999093	+	0.0425758i	$0.986444\pi$
$648$	−0.415415	−	0.909632i	−0.0163190	−	0.0357337i
$649$	−13.2746	−	3.89779i	−0.521075	−	0.153002i
$650$	0.848224	−	1.85735i	0.0332701	−	0.0728513i
$651$	4.27056	−	4.92849i	0.167377	−	0.193163i
$652$	2.08273	−	14.4857i	0.0815660	−	0.567304i
$653$	−13.0462	+	3.83071i	−0.510537	+	0.149907i	−0.526848	−	0.849960i	$-0.676626\pi$
$653$	−13.0462	+	3.83071i	−0.510537	+	0.149907i	0.0163104	+	0.999867i	$0.494808\pi$
$654$	−4.82823	−	5.57207i	−0.188799	−	0.217885i
$655$	−9.90436	+	6.36515i	−0.386995	+	0.248707i
$656$	4.39100	−	2.82192i	0.171440	−	0.110178i
$657$	−2.45057	−	2.82811i	−0.0956059	−	0.110335i
$658$	−3.99042	+	1.17169i	−0.155563	+	0.0456774i
$659$	−1.92160	+	13.3651i	−0.0748551	+	0.520628i	0.917550	+	0.397619i	$0.130164\pi$
$659$	−1.92160	+	13.3651i	−0.0748551	+	0.520628i	−0.992406	+	0.123009i	$0.960746\pi$
$660$	2.96807	−	3.42533i	0.115532	−	0.133331i
$661$	4.07611	−	8.92543i	0.158542	−	0.347159i	−0.813646	−	0.581361i	$-0.802520\pi$
$661$	4.07611	−	8.92543i	0.158542	−	0.347159i	0.972188	+	0.234202i	$0.0752477\pi$
$662$	24.1421	+	7.08875i	0.938308	+	0.275512i
$663$	−4.64356	−	10.1680i	−0.180341	−	0.394892i
$664$	−0.372568	−	2.59127i	−0.0144584	−	0.100561i
$665$	2.27083	+	1.45937i	0.0880589	+	0.0565920i
$666$	4.30900			0.166970
$667$	24.1506	+	12.6497i	0.935113	+	0.489797i
$668$	10.0721			0.389701
$669$	−7.54993	−	4.85205i	−0.291897	−	0.187591i
$670$	−1.94290	−	13.5131i	−0.0750606	−	0.522058i
$671$	−28.8473	−	63.1669i	−1.11364	−	2.43853i
$672$	−0.769321	−	0.225893i	−0.0296772	−	0.00871401i
$673$	−1.89115	+	4.14103i	−0.0728983	+	0.159625i	−0.942573	−	0.334000i	$-0.891601\pi$
$673$	−1.89115	+	4.14103i	−0.0728983	+	0.159625i	0.869675	+	0.493625i	$0.164329\pi$
$674$	16.2398	−	18.7418i	0.625535	−	0.721906i
$675$	0.142315	−	0.989821i	0.00547770	−	0.0380982i
$676$	8.47306	−	2.48791i	0.325887	−	0.0956890i
$677$	25.9019	+	29.8924i	0.995491	+	1.14886i	0.988855	+	0.148880i	$0.0475668\pi$
$677$	25.9019	+	29.8924i	0.995491	+	1.14886i	0.00663569	+	0.999978i	$0.497888\pi$
$678$	13.9531	−	8.96710i	0.535865	−	0.344380i
$679$	−0.534889	+	0.343752i	−0.0205272	+	0.0131920i
$680$	3.58501	+	4.13732i	0.137479	+	0.158659i
$681$	1.13180	−	0.332326i	0.0433707	−	0.0127348i
$682$	−5.24621	+	36.4882i	−0.200888	+	1.39720i
$683$	−14.1390	+	16.3173i	−0.541014	+	0.624364i	−0.958766	−	0.284197i	$-0.908273\pi$
$683$	−14.1390	+	16.3173i	−0.541014	+	0.624364i	0.417751	+	0.908561i	$0.362818\pi$
$684$	−1.39854	+	3.06237i	−0.0534744	+	0.117093i
$685$	7.01144	+	2.05875i	0.267893	+	0.0786606i
$686$	4.44898	+	9.74191i	0.169863	+	0.371948i
$687$	2.53776	+	17.6505i	0.0968215	+	0.673408i
$688$	10.5560	+	6.78393i	0.402444	+	0.258635i
$689$	−18.9152			−0.720613
$690$	−3.44934	−	3.33197i	−0.131314	−	0.126846i
$691$	21.0492			0.800749			0.400374	−	0.916352i	$-0.368880\pi$
$691$	21.0492			0.800749			0.400374	+	0.916352i	$0.368880\pi$
$692$	18.8599	+	12.1205i	0.716946	+	0.460753i
$693$	0.517178	+	3.59705i	0.0196460	+	0.136641i
$694$	7.63135	+	16.7103i	0.289682	+	0.634315i
$695$	−0.271645	−	0.0797623i	−0.0103041	−	0.00302556i
$696$	−2.36151	+	5.17098i	−0.0895128	+	0.196006i
$697$	18.7123	−	21.5951i	0.708777	−	0.817973i
$698$	1.94366	−	13.5185i	0.0735688	−	0.511682i
$699$	−27.4610	+	8.06328i	−1.03867	+	0.304981i
$700$	−0.525067	−	0.605959i	−0.0198457	−	0.0229031i
$701$	−38.1647	+	24.5270i	−1.44146	+	0.926372i	−0.441892	+	0.897068i	$0.645693\pi$
$701$	−38.1647	+	24.5270i	−1.44146	+	0.926372i	−0.999571	+	0.0293036i	$0.990671\pi$
$702$	−1.71773	+	1.10392i	−0.0648316	+	0.0416647i
$703$	−9.49986	−	10.9634i	−0.358294	−	0.413493i
$704$	4.34877	−	1.27691i	0.163900	−	0.0481255i
$705$	0.738179	−	5.13415i	0.0278014	−	0.193363i
$706$	8.34576	−	9.63152i	0.314097	−	0.362487i
$707$	2.84362	−	6.22666i	0.106945	−	0.234178i
$708$	−2.92886	−	0.859991i	−0.110073	−	0.0323204i
$709$	−9.24002	−	20.2328i	−0.347016	−	0.759860i	−0.999997	−	0.00248519i	$-0.999209\pi$
$709$	−9.24002	−	20.2328i	−0.347016	−	0.759860i	0.652981	−	0.757375i	$-0.273518\pi$
$710$	0.819051	+	5.69662i	0.0307384	+	0.213790i
$711$	−1.66814	−	1.07205i	−0.0625600	−	0.0402049i
$712$	−7.02020			−0.263093
$713$	38.2526	+	7.63057i	1.43257	+	0.285767i
$714$	−4.38941			−0.164270
$715$	−7.78538	−	5.00336i	−0.291157	−	0.187115i
$716$	2.60016	+	18.0845i	0.0971727	+	0.675851i
$717$	8.18922	+	17.9319i	0.305832	+	0.669679i
$718$	−5.32255	−	1.56284i	−0.198636	−	0.0583247i
$719$	−14.1594	+	31.0047i	−0.528055	+	1.15628i	0.438244	+	0.898856i	$0.355601\pi$
$719$	−14.1594	+	31.0047i	−0.528055	+	1.15628i	−0.966299	+	0.257423i	$0.917127\pi$
$720$	0.654861	−	0.755750i	0.0244052	−	0.0281651i
$721$	−2.22075	+	15.4456i	−0.0827050	+	0.575226i
$722$	−7.35547	+	2.15976i	−0.273742	+	0.0803780i
$723$	−7.82199	−	9.02706i	−0.290903	−	0.335720i
$724$	−5.42525	+	3.48660i	−0.201628	+	0.129578i
$725$	−4.78227	+	3.07338i	−0.177609	+	0.114142i
$726$	−6.24888	−	7.21159i	−0.231918	−	0.267647i
$727$	24.7683	−	7.27264i	0.918607	−	0.269727i	0.211947	−	0.977281i	$-0.432019\pi$
$727$	24.7683	−	7.27264i	0.918607	−	0.269727i	0.706659	+	0.707554i	$0.250201\pi$
$728$	−0.232994	+	1.62051i	−0.00863532	+	0.0600600i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	1.55454	−	3.40396i	0.0575359	−	0.125986i
$731$	65.9106	+	19.3531i	2.43779	+	0.715801i
$732$	−6.36475	−	13.9369i	−0.235248	−	0.515121i
$733$	3.40548	+	23.6856i	0.125784	+	0.874848i	0.950815	+	0.309760i	$0.100249\pi$
$733$	3.40548	+	23.6856i	0.125784	+	0.874848i	−0.825031	+	0.565088i	$0.808842\pi$
$734$	17.3756	+	11.1666i	0.641344	+	0.412167i
$735$	−6.35712			−0.234486
$736$	−1.10037	−	4.66789i	−0.0405602	−	0.172061i
$737$	−61.8762			−2.27924
$738$	−4.39100	−	2.82192i	−0.161635	−	0.103876i
$739$	−5.16632	−	35.9325i	−0.190046	−	1.32180i	−0.831880	−	0.554955i	$-0.812735\pi$
$739$	−5.16632	−	35.9325i	−0.190046	−	1.32180i	0.641834	−	0.766844i	$-0.278174\pi$
$740$	1.79002	+	3.91960i	0.0658026	+	0.144088i
$741$	6.59571	+	1.93668i	0.242300	+	0.0711456i
$742$	−3.08554	+	6.75639i	−0.113274	+	0.248035i
$743$	8.56759	−	9.88752i	0.314314	−	0.362738i	−0.576507	−	0.817092i	$-0.695585\pi$
$743$	8.56759	−	9.88752i	0.314314	−	0.362738i	0.890821	+	0.454354i	$0.150130\pi$
$744$	−1.15750	+	8.05059i	−0.0424360	+	0.295149i
$745$	2.04425	−	0.600245i	0.0748954	−	0.0219913i
$746$	11.4089	+	13.1666i	0.417709	+	0.482062i
$747$	−2.20233	+	1.41535i	−0.0805790	+	0.0517850i
$748$	20.8734	−	13.4145i	0.763206	−	0.490483i
$749$	0.205717	+	0.237410i	0.00751672	+	0.00867476i
$750$	0.959493	−	0.281733i	0.0350357	−	0.0102874i
$751$	0.608522	−	4.23236i	0.0222053	−	0.154441i	−0.975702	−	0.219102i	$-0.929687\pi$
$751$	0.608522	−	4.23236i	0.0222053	−	0.154441i	0.997907	+	0.0646605i	$0.0205964\pi$
$752$	3.39673	−	3.92003i	0.123866	−	0.142949i
$753$	0.0925722	−	0.202705i	0.00337352	−	0.00738698i
$754$	11.1372	+	3.27019i	0.405594	+	0.119093i
$755$	5.86843	+	12.8501i	0.213574	+	0.467662i
$756$	0.114108	+	0.793638i	0.00415007	+	0.0288643i
$757$	−8.09072	−	5.19959i	−0.294062	−	0.188982i	0.385288	−	0.922796i	$-0.374102\pi$
$757$	−8.09072	−	5.19959i	−0.294062	−	0.188982i	−0.679350	+	0.733814i	$0.737738\pi$
$758$	28.1729			1.02329
$759$	−17.1729	+	13.3253i	−0.623337	+	0.483679i
$760$	−3.36660			−0.122119
$761$	−8.81295	−	5.66374i	−0.319469	−	0.205310i	0.371071	−	0.928605i	$-0.378991\pi$
$761$	−8.81295	−	5.66374i	−0.319469	−	0.205310i	−0.690540	+	0.723294i	$0.742627\pi$
$762$	1.17442	+	8.16829i	0.0425449	+	0.295906i
$763$	2.45576	+	5.37737i	0.0889046	+	0.194674i
$764$	20.9484	+	6.15102i	0.757888	+	0.222536i
$765$	2.27417	−	4.97974i	0.0822228	−	0.180043i
$766$	16.3270	−	18.8424i	0.589918	−	0.680802i
$767$	−0.887023	+	6.16938i	−0.0320286	+	0.222763i
$768$	0.959493	−	0.281733i	0.0346227	−	0.0101661i
$769$	34.5477	+	39.8702i	1.24582	+	1.43776i	0.856088	+	0.516830i	$0.172888\pi$
$769$	34.5477	+	39.8702i	1.24582	+	1.43776i	0.389735	+	0.920927i	$0.372566\pi$
$770$	−3.05715	+	1.96471i	−0.110172	+	0.0708033i
$771$	15.4024	−	9.89853i	0.554704	−	0.356487i
$772$	9.44919	+	10.9049i	0.340084	+	0.392478i
$773$	−1.05860	+	0.310834i	−0.0380753	+	0.0111799i	−0.300715	−	0.953714i	$-0.597225\pi$
$773$	−1.05860	+	0.310834i	−0.0380753	+	0.0111799i	0.262639	+	0.964894i	$0.415407\pi$
$774$	1.78576	−	12.4202i	0.0641878	−	0.446436i
$775$	−5.32623	+	6.14679i	−0.191324	+	0.220799i
$776$	0.329423	−	0.721335i	0.0118256	−	0.0258944i
$777$	−3.31500	−	0.973373i	−0.118925	−	0.0349196i
$778$	−3.98688	−	8.73005i	−0.142937	−	0.312988i
$779$	2.50080	+	17.3934i	0.0896003	+	0.623184i
$780$	−1.71773	−	1.10392i	−0.0615046	−	0.0395266i
$781$	26.0847			0.933382
$782$	−12.9793	−	22.8219i	−0.464141	−	0.816109i
$783$	5.68470			0.203155
$784$	−5.34795	−	3.43692i	−0.190998	−	0.122747i
$785$	−3.31864	−	23.0816i	−0.118447	−	0.823819i
$786$	4.89082	+	10.7094i	0.174450	+	0.381992i
$787$	−0.228252	−	0.0670208i	−0.00813630	−	0.00238903i	0.277662	−	0.960679i	$-0.410441\pi$
$787$	−0.228252	−	0.0670208i	−0.00813630	−	0.00238903i	−0.285798	+	0.958290i	$0.592259\pi$
$788$	−1.94147	+	4.25123i	−0.0691620	+	0.151444i
$789$	−10.4734	+	12.0869i	−0.372862	+	0.430306i
$790$	0.282199	−	1.96273i	0.0100402	−	0.0698309i
$791$	−12.7600	+	3.74668i	−0.453694	+	0.133216i
$792$	−2.96807	−	3.42533i	−0.105466	−	0.121714i
$793$	−26.3181	+	16.9136i	−0.934582	+	0.600620i
$794$	−3.99282	+	2.56603i	−0.141700	+	0.0910649i
$795$	−6.06642	−	7.00102i	−0.215154	−	0.248301i
$796$	3.73645	−	1.09712i	0.132435	−	0.0388865i
$797$	−2.52654	+	17.5725i	−0.0894948	+	0.622450i	0.894872	+	0.446322i	$0.147266\pi$
$797$	−2.52654	+	17.5725i	−0.0894948	+	0.622450i	−0.984367	+	0.176128i	$0.943643\pi$
$798$	1.76769	−	2.04002i	0.0625756	−	0.0722161i
$799$	11.7960	−	25.8296i	0.417312	−	0.913787i
$800$	0.959493	+	0.281733i	0.0339232	+	0.00996075i
$801$	2.91629	+	6.38579i	0.103042	+	0.225631i
$802$	−2.39193	−	16.6363i	−0.0844621	−	0.587447i
$803$	−14.2682	−	9.16963i	−0.503515	−	0.323589i
$804$	−13.6521			−0.481472
$805$	1.90098	+	3.34254i	0.0670007	+	0.117809i
$806$	16.6073			0.584967
$807$	−19.4227	−	12.4822i	−0.683713	−	0.439396i
$808$	1.21499	+	8.45047i	0.0427433	+	0.297286i
$809$	−14.6059	−	31.9824i	−0.513514	−	1.12444i	−0.971837	−	0.235654i	$-0.924277\pi$
$809$	−14.6059	−	31.9824i	−0.513514	−	1.12444i	0.458323	−	0.888786i	$-0.348450\pi$
$810$	−0.959493	−	0.281733i	−0.0337131	−	0.00989907i
$811$	−14.7911	+	32.3879i	−0.519384	+	1.13729i	0.450288	+	0.892884i	$0.351321\pi$
$811$	−14.7911	+	32.3879i	−0.519384	+	1.13729i	−0.969672	+	0.244410i	$0.921406\pi$
$812$	2.98485	−	3.44470i	0.104748	−	0.120885i
$813$	−0.345412	+	2.40239i	−0.0121141	+	0.0842556i
$814$	18.7388	−	5.50222i	0.656796	−	0.192853i
$815$	−9.58367	−	11.0601i	−0.335701	−	0.387420i
$816$	4.60541	−	2.95971i	0.161221	−	0.103611i
$817$	−35.5379	+	22.8388i	−1.24331	+	0.799029i
$818$	−9.94340	−	11.4753i	−0.347663	−	0.401224i
$819$	1.57085	−	0.461244i	0.0548901	−	0.0161172i
$820$	0.742825	−	5.16646i	0.0259406	−	0.180421i
$821$	−3.24866	+	3.74915i	−0.113379	+	0.130846i	−0.809602	−	0.586979i	$-0.800317\pi$
$821$	−3.24866	+	3.74915i	−0.113379	+	0.130846i	0.696223	+	0.717826i	$0.254862\pi$
$822$	3.03562	−	6.64709i	0.105880	−	0.231844i
$823$	5.14456	+	1.51058i	0.179328	+	0.0526555i	0.370164	−	0.928967i	$-0.379302\pi$
$823$	5.14456	+	1.51058i	0.179328	+	0.0526555i	−0.190836	+	0.981622i	$0.561120\pi$
$824$	−8.08473	−	17.7031i	−0.281645	−	0.616717i
$825$	−0.645022	−	4.48623i	−0.0224568	−	0.156190i
$826$	2.05897	+	1.32322i	0.0716406	+	0.0460406i
$827$	14.5268			0.505145			0.252572	−	0.967578i	$-0.418723\pi$
$827$	14.5268			0.505145			0.252572	+	0.967578i	$0.418723\pi$
$828$	−3.78895	+	2.94004i	−0.131675	+	0.102174i
$829$	−42.9182			−1.49061			−0.745305	−	0.666723i	$-0.767696\pi$
$829$	−42.9182			−1.49061			−0.745305	+	0.666723i	$0.767696\pi$
$830$	−2.20233	−	1.41535i	−0.0764440	−	0.0491275i
$831$	1.01117	+	7.03287i	0.0350772	+	0.243967i
$832$	−0.848224	−	1.85735i	−0.0294069	−	0.0643921i
$833$	−33.3920	−	9.80479i	−1.15697	−	0.339716i
$834$	−0.117610	+	0.257529i	−0.00407249	+	0.00891751i
$835$	6.59582	−	7.61199i	0.228258	−	0.263424i
$836$	−2.17153	+	15.1033i	−0.0751040	+	0.522360i
$837$	7.80391	−	2.29144i	0.269743	−	0.0792036i
$838$	−9.20572	−	10.6240i	−0.318006	−	0.366999i
$839$	8.34492	−	5.36295i	0.288099	−	0.185150i	−0.388607	−	0.921404i	$-0.627043\pi$
$839$	8.34492	−	5.36295i	0.288099	−	0.185150i	0.676705	+	0.736254i	$0.263407\pi$
$840$	−0.674516	+	0.433485i	−0.0232730	+	0.0149567i
$841$	−2.17138	−	2.50591i	−0.0748752	−	0.0864105i
$842$	−26.4321	+	7.76117i	−0.910911	+	0.267468i
$843$	0.270423	−	1.88083i	0.00931387	−	0.0647794i
$844$	4.93127	−	5.69099i	0.169741	−	0.195892i
$845$	3.66843	−	8.03275i	0.126198	−	0.276335i
$846$	−4.97684	−	1.46133i	−0.171107	−	0.0502416i
$847$	3.17834	+	6.95960i	0.109209	+	0.239135i
$848$	−1.31836	−	9.16939i	−0.0452726	−	0.314878i
$849$	−12.9434	−	8.31823i	−0.444217	−	0.285481i
$850$	5.47446			0.187772
$851$	−4.74149	−	20.1139i	−0.162536	−	0.689497i
$852$	5.75520			0.197170
$853$	9.94524	+	6.39142i	0.340519	+	0.218838i	0.699712	−	0.714425i	$-0.253312\pi$
$853$	9.94524	+	6.39142i	0.340519	+	0.218838i	−0.359193	+	0.933263i	$0.616948\pi$
$854$	1.74830	+	12.1597i	0.0598254	+	0.416095i
$855$	1.39854	+	3.06237i	0.0478289	+	0.104731i
$856$	−0.375921	−	0.110380i	−0.0128487	−	0.00377272i
$857$	−18.0629	+	39.5523i	−0.617018	+	1.35108i	0.300651	+	0.953734i	$0.402796\pi$
$857$	−18.0629	+	39.5523i	−0.617018	+	1.35108i	−0.917669	+	0.397346i	$0.869931\pi$
$858$	−6.06041	+	6.99408i	−0.206899	+	0.238774i
$859$	−6.36242	+	44.2516i	−0.217083	+	1.50985i	0.531644	+	0.846968i	$0.321574\pi$
$859$	−6.36242	+	44.2516i	−0.217083	+	1.50985i	−0.748727	+	0.662878i	$0.769335\pi$
$860$	12.0397	−	3.53517i	0.410549	−	0.120548i
$861$	2.74063	+	3.16286i	0.0934005	+	0.107790i
$862$	−19.8351	+	12.7472i	−0.675585	+	0.434172i
$863$	34.5930	−	22.2315i	1.17756	−	0.756771i	0.202622	−	0.979257i	$-0.435054\pi$
$863$	34.5930	−	22.2315i	1.17756	−	0.756771i	0.974936	+	0.222486i	$0.0714173\pi$
$864$	−0.654861	−	0.755750i	−0.0222788	−	0.0257111i
$865$	21.5107	−	6.31611i	0.731386	−	0.214754i
$866$	−1.87954	+	13.0725i	−0.0638695	+	0.444222i
$867$	8.49333	−	9.80182i	0.288449	−	0.332887i
$868$	2.70906	−	5.93201i	0.0919515	−	0.201346i
$869$	−8.62325	−	2.53201i	−0.292524	−	0.0858927i
$870$	2.36151	+	5.17098i	0.0800626	+	0.175313i
$871$	3.96714	+	27.5921i	0.134421	+	0.934922i
$872$	−6.20248	−	3.98609i	−0.210043	−	0.134986i
$873$	−0.792996			−0.0268389
$874$	15.8337	+	3.15848i	0.535583	+	0.106837i
$875$	−0.801799			−0.0271058
$876$	−3.14808	−	2.02315i	−0.106364	−	0.0683558i
$877$	−0.264048	−	1.83649i	−0.00891626	−	0.0620139i	0.984878	−	0.173252i	$-0.0554275\pi$
$877$	−0.264048	−	1.83649i	−0.00891626	−	0.0620139i	−0.993794	+	0.111238i	$0.964518\pi$
$878$	11.7296	+	25.6842i	0.395854	+	0.866799i
$879$	3.09082	+	0.907545i	0.104251	+	0.0306107i
$880$	1.88281	−	4.12278i	0.0634695	−	0.138979i
$881$	29.6479	−	34.2155i	0.998863	−	1.15275i	0.0106063	−	0.999944i	$-0.496624\pi$
$881$	29.6479	−	34.2155i	0.998863	−	1.15275i	0.988256	−	0.152805i	$-0.0488307\pi$
$882$	−0.904712	+	6.29241i	−0.0304632	+	0.211877i
$883$	−1.75246	+	0.514568i	−0.0589749	+	0.0173166i	−0.311087	−	0.950381i	$-0.600693\pi$
$883$	−1.75246	+	0.514568i	−0.0589749	+	0.0173166i	0.252112	+	0.967698i	$0.418875\pi$
$884$	−7.32012	−	8.44787i	−0.246202	−	0.284133i
$885$	−2.56793	+	1.65031i	−0.0863201	+	0.0554746i
$886$	4.00003	−	2.57067i	0.134384	−	0.0863632i
$887$	23.6724	+	27.3195i	0.794843	+	0.917298i	0.998087	−	0.0618306i	$-0.0196939\pi$
$887$	23.6724	+	27.3195i	0.794843	+	0.917298i	−0.203244	+	0.979128i	$0.565148\pi$
$888$	4.13446	−	1.21399i	0.138743	−	0.0407387i
$889$	0.941651	−	6.54933i	0.0315820	−	0.219657i
$890$	−4.59725	+	5.30551i	−0.154100	+	0.177841i
$891$	−1.88281	+	4.12278i	−0.0630765	+	0.138118i
$892$	−8.61109	−	2.52844i	−0.288320	−	0.0846585i
$893$	7.25413	+	15.8843i	0.242750	+	0.531549i
$894$	−0.303209	−	2.10886i	−0.0101408	−	0.0705309i
$895$	15.3701	+	9.87778i	0.513766	+	0.330178i
$896$	−0.801799			−0.0267862
$897$	7.04311	+	6.80346i	0.235163	+	0.227161i
$898$	2.55944			0.0854095
$899$	−38.8960	−	24.9969i	−1.29725	−	0.833695i
$900$	−0.142315	−	0.989821i	−0.00474383	−	0.0329940i
$901$	−21.0672	−	46.1307i	−0.701850	−	1.53684i
$902$	−22.6988	−	6.66497i	−0.755787	−	0.221919i
$903$	−4.17946	+	9.15175i	−0.139084	+	0.304551i
$904$	10.8616	−	12.5349i	0.361250	−	0.416905i
$905$	−0.917790	+	6.38337i	−0.0305084	+	0.212190i
$906$	13.5544	−	3.97994i	0.450316	−	0.132225i
$907$	29.7225	+	34.3016i	0.986919	+	1.13896i	0.990297	+	0.138970i	$0.0443793\pi$
$907$	29.7225	+	34.3016i	0.986919	+	1.13896i	−0.00337792	+	0.999994i	$0.501075\pi$
$908$	0.992327	−	0.637730i	0.0329315	−	0.0211638i
$909$	7.18209	−	4.61565i	0.238215	−	0.153091i
$910$	1.07212	+	1.23729i	0.0355404	+	0.0410158i
$911$	−1.07924	+	0.316893i	−0.0357568	+	0.0104991i	−0.299562	−	0.954077i	$-0.596841\pi$
$911$	−1.07924	+	0.316893i	−0.0357568	+	0.0104991i	0.263805	+	0.964576i	$0.415022\pi$
$912$	−0.479117	+	3.33233i	−0.0158652	+	0.110345i
$913$	−7.77014	+	8.96722i	−0.257154	+	0.296772i
$914$	−8.32446	+	18.2280i	−0.275349	+	0.602929i
$915$	−14.7008	−	4.31654i	−0.485993	−	0.142701i
$916$	7.40768	+	16.2205i	0.244757	+	0.535942i
$917$	−1.34343	−	9.34377i	−0.0443640	−	0.308558i
$918$	−4.60541	−	2.95971i	−0.152001	−	0.0976851i
$919$	−11.3990			−0.376020			−0.188010	−	0.982167i	$-0.560204\pi$
$919$	−11.3990			−0.376020			−0.188010	+	0.982167i	$0.560204\pi$
$920$	−4.24834	−	2.22521i	−0.140064	−	0.0733631i
$921$	−21.4767			−0.707680
$922$	10.6541	+	6.84700i	0.350875	+	0.225494i
$923$	−1.67240	−	11.6318i	−0.0550476	−	0.382864i
$924$	1.50964	+	3.30564i	0.0496634	+	0.108748i
$925$	4.13446	+	1.21399i	0.135940	+	0.0399156i
$926$	−6.68541	+	14.6390i	−0.219696	+	0.481068i
$927$	−12.7448	+	14.7083i	−0.418594	+	0.483083i
$928$	−0.809017	+	5.62684i	−0.0265573	+	0.184710i
$929$	0.419324	−	0.123125i	0.0137576	−	0.00403959i	−0.274847	−	0.961488i	$-0.588627\pi$
$929$	0.419324	−	0.123125i	0.0137576	−	0.00403959i	0.288604	+	0.957449i	$0.406809\pi$
$930$	5.32623	+	6.14679i	0.174654	+	0.201561i
$931$	18.0044	−	11.5707i	0.590071	−	0.379215i
$932$	−24.0769	+	15.4733i	−0.788667	+	0.506845i
$933$	−13.9897	−	16.1449i	−0.458001	−	0.528562i
$934$	20.9981	−	6.16561i	0.687080	−	0.201745i
$935$	3.53115	−	24.5597i	0.115481	−	0.803187i
$936$	−1.33714	+	1.54314i	−0.0437058	+	0.0504392i
$937$	2.17563	−	4.76397i	0.0710748	−	0.155632i	−0.870760	−	0.491708i	$-0.836373\pi$
$937$	2.17563	−	4.76397i	0.0710748	−	0.155632i	0.941835	+	0.336076i	$0.109100\pi$
$938$	10.5028	+	3.08391i	0.342930	+	0.100693i
$939$	10.6470	+	23.3138i	0.347453	+	0.760816i
$940$	−0.738179	−	5.13415i	−0.0240767	−	0.167457i
$941$	−43.9936	−	28.2730i	−1.43415	−	0.921673i	−0.999781	−	0.0209391i	$-0.993334\pi$
$941$	−43.9936	−	28.2730i	−1.43415	−	0.921673i	−0.434371	−	0.900734i	$-0.643029\pi$
$942$	−23.3190			−0.759773
$943$	−8.34070	+	23.6018i	−0.271611	+	0.768582i
$944$	−3.05251			−0.0993506
$945$	0.674516	+	0.433485i	0.0219420	+	0.0141013i
$946$	−8.09371	−	56.2930i	−0.263149	−	1.83024i
$947$	3.80191	+	8.32503i	0.123546	+	0.270527i	0.961292	−	0.275533i	$-0.0888543\pi$
$947$	3.80191	+	8.32503i	0.123546	+	0.270527i	−0.837746	+	0.546060i	$0.816127\pi$
$948$	−1.90260	−	0.558652i	−0.0617934	−	0.0181442i
$949$	−3.17416	+	6.95044i	−0.103038	+	0.225621i
$950$	−2.20465	+	2.54431i	−0.0715285	+	0.0825482i
$951$	−4.36797	+	30.3799i	−0.141641	+	0.985137i
$952$	−4.21161	+	1.23664i	−0.136499	+	0.0400798i
$953$	−29.2292	−	33.7323i	−0.946828	−	1.09270i	−0.995583	−	0.0938866i	$-0.970071\pi$
$953$	−29.2292	−	33.7323i	−0.946828	−	1.09270i	0.0487553	−	0.998811i	$-0.484475\pi$
$954$	−7.79310	+	5.00832i	−0.252311	+	0.162150i
$955$	18.3669	−	11.8037i	0.594340	−	0.381959i
$956$	12.9095	+	14.8984i	0.417523	+	0.481847i
$957$	24.7214	−	7.25887i	0.799131	−	0.234646i
$958$	−3.53000	+	24.5517i	−0.114049	+	0.793230i
$959$	−3.83690	+	4.42802i	−0.123900	+	0.142988i
$960$	0.415415	−	0.909632i	0.0134075	−	0.0293582i
$961$	−33.7279	−	9.90340i	−1.08800	−	0.319464i
$962$	−3.65500	−	8.00333i	−0.117842	−	0.258038i
$963$	0.0557577	+	0.387804i	0.00179677	+	0.0124968i
$964$	−10.0484	−	6.45769i	−0.323636	−	0.207988i
$965$	14.4293			0.464496
$966$	3.57905	−	1.40594i	0.115154	−	0.0452353i
$967$	−30.7784			−0.989767			−0.494883	−	0.868959i	$-0.664789\pi$
$967$	−30.7784			−0.989767			−0.494883	+	0.868959i	$0.664789\pi$
$968$	−8.02749	−	5.15896i	−0.258013	−	0.165815i
$969$	2.62291	+	18.2427i	0.0842599	+	0.586040i
$970$	−0.329423	−	0.721335i	−0.0105771	−	0.0231607i
$971$	11.1912	+	3.28603i	0.359143	+	0.105454i	0.456326	−	0.889813i	$-0.349165\pi$
$971$	11.1912	+	3.28603i	0.359143	+	0.105454i	−0.0971832	+	0.995267i	$0.530983\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	0.148654	−	0.171555i	0.00476561	−	0.00549981i
$974$	2.59080	−	18.0194i	0.0830147	−	0.577380i
$975$	−1.95916	+	0.575261i	−0.0627434	+	0.0184231i
$976$	−10.0334	−	11.5792i	−0.321161	−	0.370640i
$977$	10.1836	−	6.54458i	0.325801	−	0.209380i	−0.367507	−	0.930021i	$-0.619789\pi$
$977$	10.1836	−	6.54458i	0.325801	−	0.209380i	0.693308	+	0.720641i	$0.256152\pi$
$978$	−12.3115	+	7.91210i	−0.393677	+	0.253001i
$979$	20.8364	+	24.0465i	0.665934	+	0.768529i
$980$	−6.09961	+	1.79101i	−0.194845	+	0.0572116i
$981$	−1.04927	+	7.29786i	−0.0335007	+	0.233003i
$982$	−3.62773	+	4.18663i	−0.115766	+	0.133601i
$983$	13.4326	−	29.4132i	0.428432	−	0.938135i	−0.565146	−	0.824991i	$-0.691180\pi$
$983$	13.4326	−	29.4132i	0.428432	−	0.938135i	0.993579	−	0.113145i	$-0.0360924\pi$
$984$	−5.00816	−	1.47053i	−0.159654	−	0.0468787i
$985$	1.94147	+	4.25123i	0.0618604	+	0.135455i
$986$	4.42893	+	30.8039i	0.141046	+	0.980995i
$987$	3.49868	+	2.24846i	0.111364	+	0.0715694i
$988$	6.87416			0.218696
$989$	−59.9413	+	5.33111i	−1.90602	+	0.169520i
$990$	−4.53236			−0.144048
$991$	40.5767	+	26.0771i	1.28896	+	0.828366i	0.991965	−	0.126512i	$-0.0403783\pi$
$991$	40.5767	+	26.0771i	1.28896	+	0.828366i	0.296997	+	0.954878i	$0.404015\pi$
$992$	1.15750	+	8.05059i	0.0367507	+	0.255606i
$993$	−10.4524	−	22.8875i	−0.331696	−	0.726313i
$994$	−4.42760	−	1.30006i	−0.140435	−	0.0412354i
$995$	1.61771	−	3.54229i	0.0512848	−	0.112298i
$996$	−1.71437	+	1.97849i	−0.0543219	+	0.0626908i
$997$	−1.34851	+	9.37909i	−0.0427077	+	0.297039i	0.957262	+	0.289223i	$0.0933970\pi$
$997$	−1.34851	+	9.37909i	−0.0427077	+	0.297039i	−0.999969	+	0.00781576i	$0.997512\pi$
$998$	20.8823	−	6.13161i	0.661019	−	0.194093i
$999$	−2.82180	−	3.25653i	−0.0892776	−	0.103032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.f.301.1	✓	20
23.12	even	11	inner	690.2.m.f.541.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.f.301.1	✓	20	1.1	even	1	trivial
690.2.m.f.541.1	yes	20	23.12	even	11	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.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.525067 + 0.605959i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.841254 - 0.540641i) q^{2} +(0.142315 + 0.989821i) q^{3} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.415415 - 0.909632i) q^{6} +(-0.525067 + 0.605959i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(-3.81286 + 2.45038i) q^{11} +(-0.841254 + 0.540641i) q^{12} +(1.33714 + 1.54314i) q^{13} +(0.769321 - 0.225893i) q^{14} +(-0.142315 + 0.989821i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-2.27417 + 4.97974i) q^{17} +(0.959493 + 0.281733i) q^{18} +(-1.39854 - 3.06237i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-0.674516 - 0.433485i) q^{21} +4.53236 q^{22} +(0.259300 - 4.78882i) q^{23} +1.00000 q^{24} +(0.841254 + 0.540641i) q^{25} +(-0.290588 - 2.02109i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-0.769321 - 0.225893i) q^{28} +(-2.36151 + 5.17098i) q^{29} +(0.654861 - 0.755750i) q^{30} +(-1.15750 + 8.05059i) q^{31} +(0.959493 - 0.281733i) q^{32} +(-2.96807 - 3.42533i) q^{33} +(4.60541 - 2.95971i) q^{34} +(-0.674516 + 0.433485i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(4.13446 - 1.21399i) q^{37} +(-0.479117 + 3.33233i) q^{38} +(-1.33714 + 1.54314i) q^{39} +(0.415415 - 0.909632i) q^{40} +(-5.00816 - 1.47053i) q^{41} +(0.333079 + 0.729342i) q^{42} +(-1.78576 - 12.4202i) q^{43} +(-3.81286 - 2.45038i) q^{44} -1.00000 q^{45} +(-2.80717 + 3.88842i) q^{46} -5.18694 q^{47} +(-0.841254 - 0.540641i) q^{48} +(0.904712 + 6.29241i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(-5.25270 - 1.54233i) q^{51} +(-0.848224 + 1.85735i) q^{52} +(-6.06642 + 7.00102i) q^{53} +(-0.142315 + 0.989821i) q^{54} +(-4.34877 + 1.27691i) q^{55} +(0.525067 + 0.605959i) q^{56} +(2.83217 - 1.82012i) q^{57} +(4.78227 - 3.07338i) q^{58} +(1.99897 + 2.30693i) q^{59} +(-0.959493 + 0.281733i) q^{60} +(-2.18047 + 15.1655i) q^{61} +(5.32623 - 6.14679i) q^{62} +(0.333079 - 0.729342i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.848224 + 1.85735i) q^{65} +(0.645022 + 4.48623i) q^{66} +(11.4849 + 7.38088i) q^{67} -5.47446 q^{68} +(4.77698 - 0.424859i) q^{69} +0.801799 q^{70} +(-4.84158 - 3.11150i) q^{71} +(0.142315 + 0.989821i) q^{72} +(1.55454 + 3.40396i) q^{73} +(-4.13446 - 1.21399i) q^{74} +(-0.415415 + 0.909632i) q^{75} +(2.20465 - 2.54431i) q^{76} +(0.517178 - 3.59705i) q^{77} +(1.95916 - 0.575261i) q^{78} +(1.29853 + 1.49859i) q^{79} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(3.41810 + 3.94470i) q^{82} +(2.51187 - 0.737551i) q^{83} +(0.114108 - 0.793638i) q^{84} +(-3.58501 + 4.13732i) q^{85} +(-5.21261 + 11.4140i) q^{86} +(-5.45443 - 1.60156i) q^{87} +(1.88281 + 4.12278i) q^{88} +(-0.999078 - 6.94874i) q^{89} +(0.841254 + 0.540641i) q^{90} -1.63717 q^{91} +(4.46378 - 1.75348i) q^{92} -8.13337 q^{93} +(4.36354 + 2.80427i) q^{94} +(-0.479117 - 3.33233i) q^{95} +(0.415415 + 0.909632i) q^{96} +(0.760874 + 0.223413i) q^{97} +(2.64084 - 5.78264i) q^{98} +(2.96807 - 3.42533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more