LMFDB - Embedded newform 1110.2.x.c.841.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(751,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.x (of order $6$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 8 x^{13} + 398 x^{12} - 136 x^{11} + 32 x^{10} - 824 x^{9} + 17825 x^{8} - 11480 x^{7} + \cdots + 20736 $ x^16 - 8x^13 + 398x^12 - 136x^11 + 32x^10 - 824x^9 + 17825x^8 - 11480x^7 + 3104x^6 + 11296x^5 + 68320x^4 - 21120x^3 + 4608x^2 + 13824*x + 20736
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			841.6
Root			$-1.91988 - 1.91988i$ of defining polynomial
Character	$\chi$	$=$	1110.841
Dual form			1110.2.x.c.751.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-0.861658 - 1.49244i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-0.861658 - 1.49244i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +0.723316 q^{11} +(0.500000 - 0.866025i) q^{12} +(-4.82534 + 2.78591i) q^{13} -1.72332i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50680 + 0.869951i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-4.54250 + 2.62261i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-0.861658 + 1.49244i) q^{21} +(0.626410 + 0.361658i) q^{22} +7.63372i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -5.57182 q^{26} +1.00000 q^{27} +(0.861658 - 1.49244i) q^{28} -2.12877i q^{29} +(0.500000 + 0.866025i) q^{30} +2.74404i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.361658 - 0.626410i) q^{33} +(0.869951 + 1.50680i) q^{34} +(1.49244 + 0.861658i) q^{35} -1.00000 q^{36} +(5.42438 + 2.75248i) q^{37} -5.24522 q^{38} +(4.82534 + 2.78591i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.65513 - 2.86677i) q^{41} +(-1.49244 + 0.861658i) q^{42} +7.27054i q^{43} +(0.361658 + 0.626410i) q^{44} -1.00000i q^{45} +(-3.81686 + 6.61099i) q^{46} -13.3740 q^{47} +1.00000 q^{48} +(2.01509 - 3.49024i) q^{49} +(0.866025 - 0.500000i) q^{50} -1.73990i q^{51} +(-4.82534 - 2.78591i) q^{52} +(-3.06059 + 5.30109i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.626410 + 0.361658i) q^{55} +(1.49244 - 0.861658i) q^{56} +(4.54250 + 2.62261i) q^{57} +(1.06438 - 1.84357i) q^{58} +(-9.24989 - 5.34043i) q^{59} +1.00000i q^{60} +(-2.86677 + 1.65513i) q^{61} +(-1.37202 + 2.37641i) q^{62} +1.72332 q^{63} -1.00000 q^{64} +(2.78591 - 4.82534i) q^{65} -0.723316i q^{66} +(6.11068 + 10.5840i) q^{67} +1.73990i q^{68} +(6.61099 - 3.81686i) q^{69} +(0.861658 + 1.49244i) q^{70} +(-6.70422 - 11.6121i) q^{71} +(-0.866025 - 0.500000i) q^{72} +6.00559 q^{73} +(3.32141 + 5.09590i) q^{74} -1.00000 q^{75} +(-4.54250 - 2.62261i) q^{76} +(-0.623250 - 1.07950i) q^{77} +(2.78591 + 4.82534i) q^{78} +(-4.33399 + 2.50223i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -3.31026i q^{82} +(-2.14284 + 3.71150i) q^{83} -1.72332 q^{84} -1.73990 q^{85} +(-3.63527 + 6.29647i) q^{86} +(-1.84357 + 1.06438i) q^{87} +0.723316i q^{88} +(11.5748 + 6.68269i) q^{89} +(0.500000 - 0.866025i) q^{90} +(8.31558 + 4.80100i) q^{91} +(-6.61099 + 3.81686i) q^{92} +(2.37641 - 1.37202i) q^{93} +(-11.5822 - 6.68699i) q^{94} +(2.62261 - 4.54250i) q^{95} +(0.866025 + 0.500000i) q^{96} -10.8078i q^{97} +(3.49024 - 2.01509i) q^{98} +(-0.361658 + 0.626410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$		−	1.00000i		−	0.408248i
$7$	−0.861658	−	1.49244i	−0.325676	−	0.564087i	0.655973	−	0.754784i	$-0.272259\pi$
$7$	−0.861658	−	1.49244i	−0.325676	−	0.564087i	−0.981649	+	0.190697i	$0.938925\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	0.723316			0.218088			0.109044	−	0.994037i	$-0.465221\pi$
$11$	0.723316			0.218088			0.109044	+	0.994037i	$0.465221\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−4.82534	+	2.78591i	−1.33831	+	0.772672i	−0.986556	−	0.163421i	$-0.947747\pi$
$13$	−4.82534	+	2.78591i	−1.33831	+	0.772672i	−0.351751	+	0.936093i	$0.614414\pi$
$14$		−	1.72332i		−	0.460575i
$15$	0.866025	+	0.500000i	0.223607	+	0.129099i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50680	+	0.869951i	0.365452	+	0.210994i	0.671470	−	0.741032i	$-0.265663\pi$
$17$	1.50680	+	0.869951i	0.365452	+	0.210994i	−0.306017	+	0.952026i	$0.598997\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	−4.54250	+	2.62261i	−1.04212	+	0.601668i	−0.920433	−	0.390900i	$-0.872164\pi$
$19$	−4.54250	+	2.62261i	−1.04212	+	0.601668i	−0.121687	+	0.992569i	$0.538830\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−0.861658	+	1.49244i	−0.188029	+	0.325676i
$22$	0.626410	+	0.361658i	0.133551	+	0.0771057i
$23$			7.63372i			1.59174i	0.605467	+	0.795870i	$0.292986\pi$
$23$			7.63372i			1.59174i	−0.605467	+	0.795870i	$0.707014\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−5.57182			−1.09272
$27$	1.00000			0.192450
$28$	0.861658	−	1.49244i	0.162838	−	0.282044i
$29$		−	2.12877i		−	0.395302i	−0.980272	−	0.197651i	$-0.936669\pi$
$29$		−	2.12877i		−	0.395302i	0.980272	−	0.197651i	$-0.0633313\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$			2.74404i			0.492844i	0.969163	+	0.246422i	$0.0792548\pi$
$31$			2.74404i			0.492844i	−0.969163	+	0.246422i	$0.920745\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.361658	−	0.626410i	−0.0629565	−	0.109044i
$34$	0.869951	+	1.50680i	0.149195	+	0.258414i
$35$	1.49244	+	0.861658i	0.252268	+	0.145647i
$36$	−1.00000			−0.166667
$37$	5.42438	+	2.75248i	0.891762	+	0.452504i
$37$	5.42438	+	2.75248i	0.891762	+	0.452504i
$38$	−5.24522			−0.850887
$39$	4.82534	+	2.78591i	0.772672	+	0.446103i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−1.65513	−	2.86677i	−0.258488	−	0.447715i	0.707349	−	0.706865i	$-0.249891\pi$
$41$	−1.65513	−	2.86677i	−0.258488	−	0.447715i	−0.965837	+	0.259150i	$0.916558\pi$
$42$	−1.49244	+	0.861658i	−0.230288	+	0.132957i
$43$			7.27054i			1.10875i	0.832268	+	0.554374i	$0.187042\pi$
$43$			7.27054i			1.10875i	−0.832268	+	0.554374i	$0.812958\pi$
$44$	0.361658	+	0.626410i	0.0545220	+	0.0944348i
$45$		−	1.00000i		−	0.149071i
$46$	−3.81686	+	6.61099i	−0.562765	+	0.974738i
$47$	−13.3740			−1.95080			−0.975398	−	0.220449i	$-0.929248\pi$
$47$	−13.3740			−1.95080			−0.975398	+	0.220449i	$0.929248\pi$
$48$	1.00000			0.144338
$49$	2.01509	−	3.49024i	0.287870	−	0.498606i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		−	1.73990i		−	0.243635i
$52$	−4.82534	−	2.78591i	−0.669154	−	0.386336i
$53$	−3.06059	+	5.30109i	−0.420404	+	0.728161i	−0.995979	−	0.0895883i	$-0.971445\pi$
$53$	−3.06059	+	5.30109i	−0.420404	+	0.728161i	0.575575	+	0.817749i	$0.304778\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−0.626410	+	0.361658i	−0.0844651	+	0.0487659i
$56$	1.49244	−	0.861658i	0.199435	−	0.115144i
$57$	4.54250	+	2.62261i	0.601668	+	0.347373i
$58$	1.06438	−	1.84357i	0.139760	−	0.242072i
$59$	−9.24989	−	5.34043i	−1.20423	−	0.695265i	−0.242740	−	0.970091i	$-0.578046\pi$
$59$	−9.24989	−	5.34043i	−1.20423	−	0.695265i	−0.961494	+	0.274827i	$0.911379\pi$
$60$			1.00000i			0.129099i
$61$	−2.86677	+	1.65513i	−0.367053	+	0.211918i	−0.672170	−	0.740397i	$-0.734638\pi$
$61$	−2.86677	+	1.65513i	−0.367053	+	0.211918i	0.305117	+	0.952315i	$0.401304\pi$
$62$	−1.37202	+	2.37641i	−0.174247	+	0.301804i
$63$	1.72332			0.217117
$64$	−1.00000			−0.125000
$65$	2.78591	−	4.82534i	0.345550	−	0.598509i
$66$		−	0.723316i		−	0.0890340i
$67$	6.11068	+	10.5840i	0.746538	+	1.29304i	0.949473	+	0.313850i	$0.101619\pi$
$67$	6.11068	+	10.5840i	0.746538	+	1.29304i	−0.202935	+	0.979192i	$0.565048\pi$
$68$			1.73990i			0.210994i
$69$	6.61099	−	3.81686i	0.795870	−	0.459496i
$70$	0.861658	+	1.49244i	0.102988	+	0.178380i
$71$	−6.70422	−	11.6121i	−0.795645	−	1.37810i	−0.922429	−	0.386167i	$-0.873799\pi$
$71$	−6.70422	−	11.6121i	−0.795645	−	1.37810i	0.126784	−	0.991930i	$-0.459534\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$	6.00559			0.702901			0.351451	−	0.936206i	$-0.385689\pi$
$73$	6.00559			0.702901			0.351451	+	0.936206i	$0.385689\pi$
$74$	3.32141	+	5.09590i	0.386106	+	0.592387i
$75$	−1.00000			−0.115470
$76$	−4.54250	−	2.62261i	−0.521060	−	0.300834i
$77$	−0.623250	−	1.07950i	−0.0710260	−	0.123021i
$78$	2.78591	+	4.82534i	0.315442	+	0.546362i
$79$	−4.33399	+	2.50223i	−0.487612	+	0.281523i	−0.723583	−	0.690237i	$-0.757506\pi$
$79$	−4.33399	+	2.50223i	−0.487612	+	0.281523i	0.235971	+	0.971760i	$0.424173\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		−	3.31026i		−	0.365558i
$83$	−2.14284	+	3.71150i	−0.235207	+	0.407390i	−0.959333	−	0.282278i	$-0.908910\pi$
$83$	−2.14284	+	3.71150i	−0.235207	+	0.407390i	0.724126	+	0.689668i	$0.242243\pi$
$84$	−1.72332			−0.188029
$85$	−1.73990			−0.188719
$86$	−3.63527	+	6.29647i	−0.392001	+	0.678966i
$87$	−1.84357	+	1.06438i	−0.197651	+	0.114114i
$88$			0.723316i			0.0771057i
$89$	11.5748	+	6.68269i	1.22692	+	0.708364i	0.966385	−	0.257099i	$-0.0827668\pi$
$89$	11.5748	+	6.68269i	1.22692	+	0.708364i	0.260538	+	0.965464i	$0.416100\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$	8.31558	+	4.80100i	0.871709	+	0.503282i
$92$	−6.61099	+	3.81686i	−0.689244	+	0.397935i
$93$	2.37641	−	1.37202i	0.246422	−	0.142272i
$94$	−11.5822	−	6.68699i	−1.19461	−	0.689711i
$95$	2.62261	−	4.54250i	0.269074	−	0.466050i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$		−	10.8078i		−	1.09737i	−0.836031	−	0.548683i	$-0.815129\pi$
$97$		−	10.8078i		−	1.09737i	0.836031	−	0.548683i	$-0.184871\pi$
$98$	3.49024	−	2.01509i	0.352568	−	0.203555i
$99$	−0.361658	+	0.626410i	−0.0363480	+	0.0629565i
$100$	1.00000			0.100000
$101$	−3.98776			−0.396797			−0.198399	−	0.980121i	$-0.563574\pi$
$101$	−3.98776			−0.396797			−0.198399	+	0.980121i	$0.563574\pi$
$102$	0.869951	−	1.50680i	0.0861380	−	0.149195i
$103$			0.842408i			0.0830049i	0.999138	+	0.0415024i	$0.0132144\pi$
$103$			0.842408i			0.0830049i	−0.999138	+	0.0415024i	$0.986786\pi$
$104$	−2.78591	−	4.82534i	−0.273181	−	0.473163i
$105$		−	1.72332i		−	0.168178i
$106$	−5.30109	+	3.06059i	−0.514887	+	0.297270i
$107$	−2.49320	−	4.31835i	−0.241027	−	0.417471i	0.719980	−	0.693995i	$-0.244151\pi$
$107$	−2.49320	−	4.31835i	−0.241027	−	0.417471i	−0.961007	+	0.276524i	$0.910818\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	10.5157	+	6.07127i	1.00723	+	0.581522i	0.910378	−	0.413777i	$-0.135791\pi$
$109$	10.5157	+	6.07127i	1.00723	+	0.581522i	0.0968478	+	0.995299i	$0.469124\pi$
$110$	−0.723316			−0.0689654
$111$	−0.328476	−	6.07389i	−0.0311775	−	0.576508i
$112$	1.72332			0.162838
$113$	5.91219	+	3.41340i	0.556172	+	0.321106i	0.751607	−	0.659611i	$-0.229279\pi$
$113$	5.91219	+	3.41340i	0.556172	+	0.321106i	−0.195436	+	0.980716i	$0.562612\pi$
$114$	2.62261	+	4.54250i	0.245630	+	0.425444i
$115$	−3.81686	−	6.61099i	−0.355924	−	0.616478i
$116$	1.84357	−	1.06438i	0.171171	−	0.0988256i
$117$		−	5.57182i		−	0.515115i
$118$	−5.34043	−	9.24989i	−0.491626	−	0.851522i
$119$		−	2.99840i		−	0.274863i
$120$	−0.500000	+	0.866025i	−0.0456435	+	0.0790569i
$121$	−10.4768			−0.952438
$122$	−3.31026			−0.299697
$123$	−1.65513	+	2.86677i	−0.149238	+	0.258488i
$124$	−2.37641	+	1.37202i	−0.213408	+	0.123211i
$125$			1.00000i			0.0894427i
$126$	1.49244	+	0.861658i	0.132957	+	0.0767626i
$127$	4.74205	−	8.21347i	0.420789	−	0.728827i	−0.575228	−	0.817993i	$-0.695087\pi$
$127$	4.74205	−	8.21347i	0.420789	−	0.728827i	0.996017	+	0.0891657i	$0.0284201\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	6.29647	−	3.63527i	0.554374	−	0.320068i
$130$	4.82534	−	2.78591i	0.423210	−	0.244340i
$131$	7.21706	+	4.16677i	0.630557	+	0.364052i	0.780968	−	0.624571i	$-0.214726\pi$
$131$	7.21706	+	4.16677i	0.630557	+	0.364052i	−0.150411	+	0.988624i	$0.548060\pi$
$132$	0.361658	−	0.626410i	0.0314783	−	0.0545220i
$133$	7.82815	+	4.51959i	0.678787	+	0.391898i
$134$			12.2214i			1.05576i
$135$	−0.866025	+	0.500000i	−0.0745356	+	0.0430331i
$136$	−0.869951	+	1.50680i	−0.0745977	+	0.129207i
$137$	−2.93000			−0.250327			−0.125163	−	0.992136i	$-0.539945\pi$
$137$	−2.93000			−0.250327			−0.125163	+	0.992136i	$0.539945\pi$
$138$	7.63372			0.649825
$139$	7.94517	−	13.7614i	0.673901	−	1.16723i	−0.302888	−	0.953026i	$-0.597951\pi$
$139$	7.94517	−	13.7614i	0.673901	−	1.16723i	0.976789	−	0.214204i	$-0.0687158\pi$
$140$			1.72332i			0.145647i
$141$	6.68699	+	11.5822i	0.563147	+	0.975398i
$142$		−	13.4084i		−	1.12521i
$143$	−3.49024	+	2.01509i	−0.291869	+	0.168510i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.06438	+	1.84357i	0.0883923	+	0.153100i
$146$	5.20099	+	3.00280i	0.430437	+	0.248513i
$147$	−4.03018			−0.332404
$148$	0.328476	+	6.07389i	0.0270005	+	0.499270i
$149$	−9.97784			−0.817417			−0.408708	−	0.912665i	$-0.634021\pi$
$149$	−9.97784			−0.817417			−0.408708	+	0.912665i	$0.634021\pi$
$150$	−0.866025	−	0.500000i	−0.0707107	−	0.0408248i
$151$	−1.16473	−	2.01736i	−0.0947840	−	0.164171i	0.814734	−	0.579834i	$-0.196883\pi$
$151$	−1.16473	−	2.01736i	−0.0947840	−	0.164171i	−0.909518	+	0.415664i	$0.863549\pi$
$152$	−2.62261	−	4.54250i	−0.212722	−	0.368445i
$153$	−1.50680	+	0.869951i	−0.121817	+	0.0703313i
$154$		−	1.24650i		−	0.100446i
$155$	−1.37202	−	2.37641i	−0.110203	−	0.190877i
$156$			5.57182i			0.446103i
$157$	−1.28685	+	2.22888i	−0.102701	+	0.177884i	−0.912797	−	0.408414i	$-0.866082\pi$
$157$	−1.28685	+	2.22888i	−0.102701	+	0.177884i	0.810095	+	0.586298i	$0.199415\pi$
$158$	−5.00446			−0.398134
$159$	6.12117			0.485440
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	11.3928	−	6.57765i	0.897881	−	0.518392i
$162$		−	1.00000i		−	0.0785674i
$163$	8.84842	+	5.10864i	0.693061	+	0.400139i	0.804758	−	0.593603i	$-0.202295\pi$
$163$	8.84842	+	5.10864i	0.693061	+	0.400139i	−0.111696	+	0.993742i	$0.535628\pi$
$164$	1.65513	−	2.86677i	0.129244	−	0.223857i
$165$	0.626410	+	0.361658i	0.0487659	+	0.0281550i
$166$	−3.71150	+	2.14284i	−0.288068	+	0.166316i
$167$	13.4500	−	7.76536i	1.04079	−	0.600901i	0.120734	−	0.992685i	$-0.461475\pi$
$167$	13.4500	−	7.76536i	1.04079	−	0.600901i	0.920057	+	0.391784i	$0.128142\pi$
$168$	−1.49244	−	0.861658i	−0.115144	−	0.0664783i
$169$	9.02259	−	15.6276i	0.694045	−	1.20212i
$170$	−1.50680	−	0.869951i	−0.115566	−	0.0667222i
$171$		−	5.24522i		−	0.401112i
$172$	−6.29647	+	3.63527i	−0.480102	+	0.277187i
$173$	−4.27836	+	7.41035i	−0.325278	+	0.563398i	−0.981569	−	0.191110i	$-0.938791\pi$
$173$	−4.27836	+	7.41035i	−0.325278	+	0.563398i	0.656291	+	0.754508i	$0.272125\pi$
$174$	−2.12877			−0.161382
$175$	−1.72332			−0.130270
$176$	−0.361658	+	0.626410i	−0.0272610	+	0.0472174i
$177$			10.6809i			0.802822i
$178$	6.68269	+	11.5748i	0.500889	+	0.867565i
$179$		−	21.6487i		−	1.61810i	−0.587742	−	0.809049i	$-0.699983\pi$
$179$		−	21.6487i		−	1.61810i	0.587742	−	0.809049i	$-0.300017\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	7.63386	+	13.2222i	0.567421	+	0.982802i	0.996820	+	0.0796867i	$0.0253920\pi$
$181$	7.63386	+	13.2222i	0.567421	+	0.982802i	−0.429399	+	0.903115i	$0.641275\pi$
$182$	4.80100	+	8.31558i	0.355874	+	0.616392i
$183$	2.86677	+	1.65513i	0.211918	+	0.122351i
$184$	−7.63372			−0.562765
$185$	−6.07389	+	0.328476i	−0.446561	+	0.0241500i
$186$	2.74404			0.201203
$187$	1.08989	+	0.629249i	0.0797007	+	0.0460152i
$188$	−6.68699	−	11.5822i	−0.487699	−	0.844720i
$189$	−0.861658	−	1.49244i	−0.0626764	−	0.108559i
$190$	4.54250	−	2.62261i	0.329547	−	0.190264i
$191$		−	15.5398i		−	1.12442i	−0.826995	−	0.562209i	$-0.809952\pi$
$191$		−	15.5398i		−	1.12442i	0.826995	−	0.562209i	$-0.190048\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$			13.2627i			0.954674i	0.878720	+	0.477337i	$0.158398\pi$
$193$			13.2627i			0.954674i	−0.878720	+	0.477337i	$0.841602\pi$
$194$	5.40390	−	9.35983i	0.387977	−	0.671997i
$195$	−5.57182			−0.399006
$196$	4.03018			0.287870
$197$	12.6116	−	21.8438i	0.898536	−	1.55631i	0.0691693	−	0.997605i	$-0.477965\pi$
$197$	12.6116	−	21.8438i	0.898536	−	1.55631i	0.829367	−	0.558705i	$-0.188702\pi$
$198$	−0.626410	+	0.361658i	−0.0445170	+	0.0257019i
$199$			4.05123i			0.287184i	0.989637	+	0.143592i	$0.0458654\pi$
$199$			4.05123i			0.287184i	−0.989637	+	0.143592i	$0.954135\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	6.11068	−	10.5840i	0.431014	−	0.746538i
$202$	−3.45350	−	1.99388i	−0.242988	−	0.140289i
$203$	−3.17705	+	1.83427i	−0.222985	+	0.128741i
$204$	1.50680	−	0.869951i	0.105497	−	0.0609087i
$205$	2.86677	+	1.65513i	0.200224	+	0.115599i
$206$	−0.421204	+	0.729546i	−0.0293467	+	0.0508299i
$207$	−6.61099	−	3.81686i	−0.459496	−	0.265290i
$208$		−	5.57182i		−	0.386336i
$209$	−3.28566	+	1.89698i	−0.227274	+	0.131217i
$210$	0.861658	−	1.49244i	0.0594600	−	0.102988i
$211$	−14.1711			−0.975580			−0.487790	−	0.872961i	$-0.662197\pi$
$211$	−14.1711			−0.975580			−0.487790	+	0.872961i	$0.662197\pi$
$212$	−6.12117			−0.420404
$213$	−6.70422	+	11.6121i	−0.459366	+	0.795645i
$214$		−	4.98641i		−	0.340864i
$215$	−3.63527	−	6.29647i	−0.247923	−	0.429416i
$216$			1.00000i			0.0680414i
$217$	4.09530	−	2.36442i	0.278007	−	0.160507i
$218$	6.07127	+	10.5157i	0.411198	+	0.712216i
$219$	−3.00280	−	5.20099i	−0.202910	−	0.351451i
$220$	−0.626410	−	0.361658i	−0.0422325	−	0.0243830i
$221$	−9.69442			−0.652117
$222$	2.75248	−	5.42438i	0.184734	−	0.364060i
$223$	−10.1930			−0.682577			−0.341289	−	0.939959i	$-0.610863\pi$
$223$	−10.1930			−0.682577			−0.341289	+	0.939959i	$0.610863\pi$
$224$	1.49244	+	0.861658i	0.0997175	+	0.0575719i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	3.41340	+	5.91219i	0.227056	+	0.393273i
$227$	−16.8709	+	9.74040i	−1.11976	+	0.646493i	−0.941339	−	0.337461i	$-0.890432\pi$
$227$	−16.8709	+	9.74040i	−1.11976	+	0.646493i	−0.178420	+	0.983954i	$0.557098\pi$
$228$			5.24522i			0.347373i
$229$	11.8302	+	20.4905i	0.781763	+	1.35405i	0.930914	+	0.365238i	$0.119012\pi$
$229$	11.8302	+	20.4905i	0.781763	+	1.35405i	−0.149151	+	0.988814i	$0.547654\pi$
$230$		−	7.63372i		−	0.503353i
$231$	−0.623250	+	1.07950i	−0.0410069	+	0.0710260i
$232$	2.12877			0.139760
$233$	2.50440			0.164068			0.0820342	−	0.996630i	$-0.473858\pi$
$233$	2.50440			0.164068			0.0820342	+	0.996630i	$0.473858\pi$
$234$	2.78591	−	4.82534i	0.182121	−	0.315442i
$235$	11.5822	−	6.68699i	0.755540	−	0.436211i
$236$		−	10.6809i		−	0.695265i
$237$	4.33399	+	2.50223i	0.281523	+	0.162537i
$238$	1.49920	−	2.59669i	0.0971787	−	0.168318i
$239$	11.1286	+	6.42509i	0.719848	+	0.415604i	0.814697	−	0.579887i	$-0.196903\pi$
$239$	11.1286	+	6.42509i	0.719848	+	0.415604i	−0.0948489	+	0.995492i	$0.530237\pi$
$240$	−0.866025	+	0.500000i	−0.0559017	+	0.0322749i
$241$	19.3844	−	11.1916i	1.24866	−	0.720912i	0.277815	−	0.960635i	$-0.410390\pi$
$241$	19.3844	−	11.1916i	1.24866	−	0.720912i	0.970842	+	0.239722i	$0.0770564\pi$
$242$	−9.07319	−	5.23841i	−0.583247	−	0.336738i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.86677	−	1.65513i	−0.183526	−	0.105959i
$245$			4.03018i			0.257479i
$246$	−2.86677	+	1.65513i	−0.182779	+	0.105527i
$247$	14.6127	−	25.3100i	0.929785	−	1.61043i
$248$	−2.74404			−0.174247
$249$	4.28567			0.271593
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$		−	11.9814i		−	0.756262i	−0.925752	−	0.378131i	$-0.876567\pi$
$251$		−	11.9814i		−	0.756262i	0.925752	−	0.378131i	$-0.123433\pi$
$252$	0.861658	+	1.49244i	0.0542793	+	0.0940146i
$253$			5.52159i			0.347139i
$254$	8.21347	−	4.74205i	0.515359	−	0.297542i
$255$	0.869951	+	1.50680i	0.0544784	+	0.0943594i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.1399	−	12.2051i	−1.31867	−	0.761335i	−0.335155	−	0.942163i	$-0.608789\pi$
$257$	−21.1399	−	12.2051i	−1.31867	−	0.761335i	−0.983515	+	0.180828i	$0.942122\pi$
$258$	7.27054			0.452644
$259$	−0.566067	−	10.4672i	−0.0351737	−	0.650402i
$260$	5.57182			0.345550
$261$	1.84357	+	1.06438i	0.114114	+	0.0658837i
$262$	4.16677	+	7.21706i	0.257424	+	0.445871i
$263$	1.50316	+	2.60355i	0.0926888	+	0.160542i	0.908642	−	0.417577i	$-0.137121\pi$
$263$	1.50316	+	2.60355i	0.0926888	+	0.160542i	−0.815953	+	0.578118i	$0.803787\pi$
$264$	0.626410	−	0.361658i	0.0385528	−	0.0222585i
$265$		−	6.12117i		−	0.376021i
$266$	4.51959	+	7.82815i	0.277114	+	0.479975i
$267$		−	13.3654i		−	0.817949i
$268$	−6.11068	+	10.5840i	−0.373269	+	0.646521i
$269$	−12.9630			−0.790369			−0.395185	−	0.918602i	$-0.629319\pi$
$269$	−12.9630			−0.790369			−0.395185	+	0.918602i	$0.629319\pi$
$270$	−1.00000			−0.0608581
$271$	−11.5185	+	19.9506i	−0.699700	+	1.21192i	0.268871	+	0.963176i	$0.413350\pi$
$271$	−11.5185	+	19.9506i	−0.699700	+	1.21192i	−0.968571	+	0.248739i	$0.919984\pi$
$272$	−1.50680	+	0.869951i	−0.0913631	+	0.0527485i
$273$		−	9.60200i		−	0.581140i
$274$	−2.53745	−	1.46500i	−0.153293	−	0.0885038i
$275$	0.361658	−	0.626410i	0.0218088	−	0.0377739i
$276$	6.61099	+	3.81686i	0.397935	+	0.229748i
$277$	8.75567	−	5.05509i	0.526077	−	0.303731i	−0.213340	−	0.976978i	$-0.568434\pi$
$277$	8.75567	−	5.05509i	0.526077	−	0.303731i	0.739418	+	0.673247i	$0.235101\pi$
$278$	13.7614	−	7.94517i	0.825356	−	0.476520i
$279$	−2.37641	−	1.37202i	−0.142272	−	0.0821406i
$280$	−0.861658	+	1.49244i	−0.0514939	+	0.0891901i
$281$	16.9111	+	9.76363i	1.00883	+	0.582449i	0.910849	−	0.412739i	$-0.135428\pi$
$281$	16.9111	+	9.76363i	1.00883	+	0.582449i	0.0979823	+	0.995188i	$0.468761\pi$
$282$			13.3740i			0.796410i
$283$	−5.77985	+	3.33700i	−0.343576	+	0.198364i	−0.661852	−	0.749634i	$-0.730229\pi$
$283$	−5.77985	+	3.33700i	−0.343576	+	0.198364i	0.318276	+	0.947998i	$0.396896\pi$
$284$	6.70422	−	11.6121i	0.397822	−	0.689049i
$285$	−5.24522			−0.310700
$286$	−4.03018			−0.238310
$287$	−2.85232	+	4.94036i	−0.168367	+	0.291620i
$288$		−	1.00000i		−	0.0589256i
$289$	−6.98637	−	12.1008i	−0.410963	−	0.711809i
$290$			2.12877i			0.125006i
$291$	−9.35983	+	5.40390i	−0.548683	+	0.316782i
$292$	3.00280	+	5.20099i	0.175725	+	0.304365i
$293$	5.20554	+	9.01626i	0.304111	+	0.526736i	0.977063	−	0.212950i	$-0.0683073\pi$
$293$	5.20554	+	9.01626i	0.304111	+	0.526736i	−0.672952	+	0.739686i	$0.734974\pi$
$294$	−3.49024	−	2.01509i	−0.203555	−	0.117523i
$295$	10.6809			0.621864
$296$	−2.75248	+	5.42438i	−0.159984	+	0.315286i
$297$	0.723316			0.0419710
$298$	−8.64107	−	4.98892i	−0.500564	−	0.289000i
$299$	−21.2669	−	36.8353i	−1.22989	−	2.13024i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	10.8508	−	6.26472i	0.625430	−	0.361092i
$302$		−	2.32945i		−	0.134045i
$303$	1.99388	+	3.45350i	0.114545	+	0.198399i
$304$		−	5.24522i		−	0.300834i
$305$	1.65513	−	2.86677i	0.0947726	−	0.164151i
$306$	−1.73990			−0.0994635
$307$	10.8590			0.619757			0.309879	−	0.950776i	$-0.399712\pi$
$307$	10.8590			0.619757			0.309879	+	0.950776i	$0.399712\pi$
$308$	0.623250	−	1.07950i	0.0355130	−	0.0615103i
$309$	0.729546	−	0.421204i	0.0415024	−	0.0239615i
$310$		−	2.74404i		−	0.155851i
$311$	10.3720	+	5.98825i	0.588140	+	0.339563i	0.764362	−	0.644788i	$-0.223054\pi$
$311$	10.3720	+	5.98825i	0.588140	+	0.339563i	−0.176222	+	0.984350i	$0.556388\pi$
$312$	−2.78591	+	4.82534i	−0.157721	+	0.273181i
$313$	−18.4761	−	10.6672i	−1.04433	−	0.602943i	−0.123272	−	0.992373i	$-0.539339\pi$
$313$	−18.4761	−	10.6672i	−1.04433	−	0.602943i	−0.921056	+	0.389430i	$0.872672\pi$
$314$	−2.22888	+	1.28685i	−0.125783	+	0.0726209i
$315$	−1.49244	+	0.861658i	−0.0840892	+	0.0485489i
$316$	−4.33399	−	2.50223i	−0.243806	−	0.140762i
$317$	−15.1500	+	26.2406i	−0.850910	+	1.47382i	0.0294788	+	0.999565i	$0.490615\pi$
$317$	−15.1500	+	26.2406i	−0.850910	+	1.47382i	−0.880388	+	0.474253i	$0.842718\pi$
$318$	5.30109	+	3.06059i	0.297270	+	0.171629i
$319$		−	1.53977i		−	0.0862106i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−2.49320	+	4.31835i	−0.139157	+	0.241027i
$322$	13.1553			0.733117
$323$	−9.12617			−0.507794
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$			5.57182i			0.309069i
$326$	5.10864	+	8.84842i	0.282941	+	0.490068i
$327$		−	12.1425i		−	0.671484i
$328$	2.86677	−	1.65513i	0.158291	−	0.0913894i
$329$	11.5238	+	19.9598i	0.635328	+	1.10042i
$330$	0.361658	+	0.626410i	0.0199086	+	0.0344827i
$331$	21.7500	+	12.5573i	1.19549	+	0.690214i	0.959545	−	0.281554i	$-0.0908498\pi$
$331$	21.7500	+	12.5573i	1.19549	+	0.690214i	0.235940	+	0.971768i	$0.424183\pi$
$332$	−4.28567			−0.235207
$333$	−5.09590	+	3.32141i	−0.279254	+	0.182012i
$334$	15.5307			0.849803
$335$	−10.5840	−	6.11068i	−0.578266	−	0.333862i
$336$	−0.861658	−	1.49244i	−0.0470073	−	0.0814190i
$337$	14.6613	+	25.3941i	0.798651	+	1.38330i	0.920495	+	0.390755i	$0.127786\pi$
$337$	14.6613	+	25.3941i	0.798651	+	1.38330i	−0.121843	+	0.992549i	$0.538881\pi$
$338$	15.6276	−	9.02259i	0.850028	−	0.490764i
$339$		−	6.82680i		−	0.370781i
$340$	−0.869951	−	1.50680i	−0.0471797	−	0.0817176i
$341$			1.98480i			0.107483i
$342$	2.62261	−	4.54250i	0.141815	−	0.245630i
$343$	−19.0085			−1.02636
$344$	−7.27054			−0.392001
$345$	−3.81686	+	6.61099i	−0.205493	+	0.355924i
$346$	−7.41035	+	4.27836i	−0.398383	+	0.230006i
$347$			28.8595i			1.54926i	0.632415	+	0.774630i	$0.282064\pi$
$347$			28.8595i			1.54926i	−0.632415	+	0.774630i	$0.717936\pi$
$348$	−1.84357	−	1.06438i	−0.0988256	−	0.0570570i
$349$	4.85895	−	8.41596i	0.260094	−	0.450496i	−0.706173	−	0.708040i	$-0.749580\pi$
$349$	4.85895	−	8.41596i	0.260094	−	0.450496i	0.966267	+	0.257544i	$0.0829132\pi$
$350$	−1.49244	−	0.861658i	−0.0797740	−	0.0460575i
$351$	−4.82534	+	2.78591i	−0.257557	+	0.148701i
$352$	−0.626410	+	0.361658i	−0.0333877	+	0.0192764i
$353$	−5.53586	−	3.19613i	−0.294644	−	0.170113i	0.345390	−	0.938459i	$-0.387747\pi$
$353$	−5.53586	−	3.19613i	−0.294644	−	0.170113i	−0.640034	+	0.768346i	$0.721080\pi$
$354$	−5.34043	+	9.24989i	−0.283841	+	0.491626i
$355$	11.6121	+	6.70422i	0.616304	+	0.355823i
$356$			13.3654i			0.708364i
$357$	−2.59669	+	1.49920i	−0.137431	+	0.0793461i
$358$	10.8243	−	18.7483i	0.572084	−	0.990878i
$359$	12.2436			0.646192			0.323096	−	0.946366i	$-0.395276\pi$
$359$	12.2436			0.646192			0.323096	+	0.946366i	$0.395276\pi$
$360$	1.00000			0.0527046
$361$	4.25617	−	7.37191i	0.224009	−	0.387995i
$362$			15.2677i			0.802454i
$363$	5.23841	+	9.07319i	0.274945	+	0.476219i
$364$			9.60200i			0.503282i
$365$	−5.20099	+	3.00280i	−0.272232	+	0.157174i
$366$	1.65513	+	2.86677i	0.0865152	+	0.149849i
$367$	16.1097	+	27.9027i	0.840917	+	1.45651i	0.889120	+	0.457674i	$0.151317\pi$
$367$	16.1097	+	27.9027i	0.840917	+	1.45651i	−0.0482029	+	0.998838i	$0.515349\pi$
$368$	−6.61099	−	3.81686i	−0.344622	−	0.198968i
$369$	3.31026			0.172326
$370$	−5.42438	−	2.75248i	−0.282000	−	0.143094i
$371$	10.5487			0.547662
$372$	2.37641	+	1.37202i	0.123211	+	0.0711358i
$373$	−9.12545	−	15.8057i	−0.472498	−	0.818391i	0.527007	−	0.849861i	$-0.323314\pi$
$373$	−9.12545	−	15.8057i	−0.472498	−	0.818391i	−0.999505	+	0.0314705i	$0.989981\pi$
$374$	0.629249	+	1.08989i	0.0325377	+	0.0563569i
$375$	0.866025	−	0.500000i	0.0447214	−	0.0258199i
$376$		−	13.3740i		−	0.689711i
$377$	5.93056	+	10.2720i	0.305439	+	0.529036i
$378$		−	1.72332i		−	0.0886378i
$379$	−17.0202	+	29.4798i	−0.874267	+	1.51427i	−0.0167247	+	0.999860i	$0.505324\pi$
$379$	−17.0202	+	29.4798i	−0.874267	+	1.51427i	−0.857542	+	0.514414i	$0.828009\pi$
$380$	5.24522			0.269074
$381$	−9.48409			−0.485885
$382$	7.76989	−	13.4578i	0.397542	−	0.688563i
$383$	−33.0364	+	19.0736i	−1.68808	+	0.974615i	−0.732099	+	0.681199i	$0.761459\pi$
$383$	−33.0364	+	19.0736i	−1.68808	+	0.974615i	−0.955985	+	0.293417i	$0.905208\pi$
$384$			1.00000i			0.0510310i
$385$	1.07950	+	0.623250i	0.0550165	+	0.0317638i
$386$	−6.63137	+	11.4859i	−0.337528	+	0.584616i
$387$	−6.29647	−	3.63527i	−0.320068	−	0.184791i
$388$	9.35983	−	5.40390i	0.475173	−	0.274341i
$389$	8.32204	−	4.80473i	0.421944	−	0.243610i	−0.273965	−	0.961740i	$-0.588335\pi$
$389$	8.32204	−	4.80473i	0.421944	−	0.243610i	0.695909	+	0.718130i	$0.255002\pi$
$390$	−4.82534	−	2.78591i	−0.244340	−	0.141070i
$391$	−6.64096	+	11.5025i	−0.335848	+	0.581705i
$392$	3.49024	+	2.01509i	0.176284	+	0.101778i
$393$		−	8.33354i		−	0.420371i
$394$	21.8438	−	12.6116i	1.10048	−	0.635361i
$395$	2.50223	−	4.33399i	0.125901	−	0.218067i
$396$	−0.723316			−0.0363480
$397$	12.2929			0.616964			0.308482	−	0.951230i	$-0.400179\pi$
$397$	12.2929			0.616964			0.308482	+	0.951230i	$0.400179\pi$
$398$	−2.02562	+	3.50847i	−0.101535	+	0.175864i
$399$		−	9.03917i		−	0.452525i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$			2.72723i			0.136191i	0.997679	+	0.0680957i	$0.0216923\pi$
$401$			2.72723i			0.136191i	−0.997679	+	0.0680957i	$0.978308\pi$
$402$	10.5840	−	6.11068i	0.527882	−	0.304773i
$403$	−7.64464	−	13.2409i	−0.380807	−	0.659576i
$404$	−1.99388	−	3.45350i	−0.0991993	−	0.171818i
$405$	0.866025	+	0.500000i	0.0430331	+	0.0248452i
$406$	−3.66854			−0.182067
$407$	3.92354	+	1.99091i	0.194483	+	0.0986856i
$408$	1.73990			0.0861380
$409$	14.2710	+	8.23934i	0.705653	+	0.407409i	0.809450	−	0.587189i	$-0.199766\pi$
$409$	14.2710	+	8.23934i	0.705653	+	0.407409i	−0.103796	+	0.994599i	$0.533099\pi$
$410$	1.65513	+	2.86677i	0.0817412	+	0.141580i
$411$	1.46500	+	2.53745i	0.0722631	+	0.125163i
$412$	−0.729546	+	0.421204i	−0.0359422	+	0.0207512i
$413$			18.4065i			0.905724i
$414$	−3.81686	−	6.61099i	−0.187588	−	0.324913i
$415$		−	4.28567i		−	0.210375i
$416$	2.78591	−	4.82534i	0.136590	−	0.236582i
$417$	−15.8903			−0.778154
$418$	−3.79395			−0.185568
$419$	13.1952	−	22.8548i	0.644628	−	1.11653i	−0.339760	−	0.940512i	$-0.610346\pi$
$419$	13.1952	−	22.8548i	0.644628	−	1.11653i	0.984387	−	0.176015i	$-0.0563209\pi$
$420$	1.49244	−	0.861658i	0.0728234	−	0.0420446i
$421$			16.1776i			0.788449i	0.919014	+	0.394224i	$0.128987\pi$
$421$			16.1776i			0.788449i	−0.919014	+	0.394224i	$0.871013\pi$
$422$	−12.2725	−	7.08556i	−0.597418	−	0.344920i
$423$	6.68699	−	11.5822i	0.325133	−	0.563147i
$424$	−5.30109	−	3.06059i	−0.257444	−	0.148635i
$425$	1.50680	−	0.869951i	0.0730905	−	0.0421988i
$426$	−11.6121	+	6.70422i	−0.562606	+	0.324821i
$427$	4.94036	+	2.85232i	0.239081	+	0.138033i
$428$	2.49320	−	4.31835i	0.120513	−	0.208735i
$429$	3.49024	+	2.01509i	0.168510	+	0.0972895i
$430$		−	7.27054i		−	0.350617i
$431$	13.9153	−	8.03401i	0.670277	−	0.386985i	−0.125904	−	0.992042i	$-0.540183\pi$
$431$	13.9153	−	8.03401i	0.670277	−	0.386985i	0.796182	+	0.605058i	$0.206850\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	21.8303			1.04910			0.524548	−	0.851381i	$-0.324234\pi$
$433$	21.8303			1.04910			0.524548	+	0.851381i	$0.324234\pi$
$434$	4.72884			0.226992
$435$	1.06438	−	1.84357i	0.0510333	−	0.0883923i
$436$			12.1425i			0.581522i
$437$	−20.0203	−	34.6761i	−0.957700	−	1.65878i
$438$		−	6.00559i		−	0.286958i
$439$	−3.90649	+	2.25542i	−0.186447	+	0.107645i	−0.590318	−	0.807171i	$-0.700998\pi$
$439$	−3.90649	+	2.25542i	−0.186447	+	0.107645i	0.403871	+	0.914816i	$0.367664\pi$
$440$	−0.361658	−	0.626410i	−0.0172414	−	0.0298629i
$441$	2.01509	+	3.49024i	0.0959568	+	0.166202i
$442$	−8.39561	−	4.84721i	−0.399338	−	0.230558i
$443$	18.8698			0.896532			0.448266	−	0.893900i	$-0.352042\pi$
$443$	18.8698			0.896532			0.448266	+	0.893900i	$0.352042\pi$
$444$	5.09590	−	3.32141i	0.241841	−	0.157627i
$445$	−13.3654			−0.633580
$446$	−8.82744	−	5.09652i	−0.417991	−	0.241327i
$447$	4.98892	+	8.64107i	0.235968	+	0.408708i
$448$	0.861658	+	1.49244i	0.0407095	+	0.0705109i
$449$	−18.6878	+	10.7894i	−0.881933	+	0.509184i	−0.871295	−	0.490759i	$-0.836719\pi$
$449$	−18.6878	+	10.7894i	−0.881933	+	0.509184i	−0.0106377	+	0.999943i	$0.503386\pi$
$450$			1.00000i			0.0471405i
$451$	−1.19718	−	2.07358i	−0.0563731	−	0.0976412i
$452$			6.82680i			0.321106i
$453$	−1.16473	+	2.01736i	−0.0547236	+	0.0947840i
$454$	−19.4808			−0.914279
$455$	−9.60200			−0.450149
$456$	−2.62261	+	4.54250i	−0.122815	+	0.212722i
$457$	14.0737	−	8.12544i	0.658339	−	0.380092i	−0.133305	−	0.991075i	$-0.542559\pi$
$457$	14.0737	−	8.12544i	0.658339	−	0.380092i	0.791644	+	0.610983i	$0.209226\pi$
$458$			23.6604i			1.10558i
$459$	1.50680	+	0.869951i	0.0703313	+	0.0406058i
$460$	3.81686	−	6.61099i	0.177962	−	0.308239i
$461$	0.770127	+	0.444633i	0.0358684	+	0.0207086i	0.517827	−	0.855485i	$-0.326741\pi$
$461$	0.770127	+	0.444633i	0.0358684	+	0.0207086i	−0.481959	+	0.876194i	$0.660074\pi$
$462$	−1.07950	+	0.623250i	−0.0502230	+	0.0289962i
$463$	−32.0564	+	18.5078i	−1.48979	+	0.860130i	−0.999932	−	0.0116723i	$-0.996284\pi$
$463$	−32.0564	+	18.5078i	−1.48979	+	0.860130i	−0.489857	+	0.871803i	$0.662951\pi$
$464$	1.84357	+	1.06438i	0.0855855	+	0.0494128i
$465$	−1.37202	+	2.37641i	−0.0636258	+	0.110203i
$466$	2.16887	+	1.25220i	0.100471	+	0.0580069i
$467$			11.6331i			0.538313i	0.963096	+	0.269157i	$0.0867449\pi$
$467$			11.6331i			0.538313i	−0.963096	+	0.269157i	$0.913255\pi$
$468$	4.82534	−	2.78591i	0.223051	−	0.128779i
$469$	10.5306	−	18.2396i	0.486259	−	0.842226i
$470$	13.3740			0.616896
$471$	2.57369			0.118589
$472$	5.34043	−	9.24989i	0.245813	−	0.425761i
$473$			5.25890i			0.241804i
$474$	2.50223	+	4.33399i	0.114931	+	0.199067i
$475$			5.24522i			0.240667i
$476$	2.59669	−	1.49920i	0.119019	−	0.0687157i
$477$	−3.06059	−	5.30109i	−0.140135	−	0.242720i
$478$	6.42509	+	11.1286i	0.293877	+	0.509009i
$479$	−10.7189	−	6.18855i	−0.489759	−	0.282762i	0.234716	−	0.972064i	$-0.424584\pi$
$479$	−10.7189	−	6.18855i	−0.489759	−	0.282762i	−0.724474	+	0.689302i	$0.757917\pi$
$480$	−1.00000			−0.0456435
$481$	−33.8426	+	1.83021i	−1.54309	+	0.0834503i
$482$	22.3831			1.01952
$483$	−11.3928	−	6.57765i	−0.518392	−	0.299294i
$484$	−5.23841	−	9.07319i	−0.238109	−	0.412418i
$485$	5.40390	+	9.35983i	0.245378	+	0.425008i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$			3.20363i			0.145170i	0.997362	+	0.0725852i	$0.0231249\pi$
$487$			3.20363i			0.145170i	−0.997362	+	0.0725852i	$0.976875\pi$
$488$	−1.65513	−	2.86677i	−0.0749243	−	0.129773i
$489$		−	10.2173i		−	0.462041i
$490$	−2.01509	+	3.49024i	−0.0910326	+	0.157673i
$491$	−26.5283			−1.19720			−0.598602	−	0.801047i	$-0.704277\pi$
$491$	−26.5283			−1.19720			−0.598602	+	0.801047i	$0.704277\pi$
$492$	−3.31026			−0.149238
$493$	1.85192	−	3.20763i	0.0834064	−	0.144464i
$494$	25.3100	−	14.6127i	1.13875	−	0.657457i
$495$		−	0.723316i		−	0.0325106i
$496$	−2.37641	−	1.37202i	−0.106704	−	0.0616054i
$497$	−11.5535	+	20.0112i	−0.518245	+	0.897626i
$498$	3.71150	+	2.14284i	0.166316	+	0.0960228i
$499$	−21.0480	+	12.1521i	−0.942239	+	0.544002i	−0.890662	−	0.454667i	$-0.849758\pi$
$499$	−21.0480	+	12.1521i	−0.942239	+	0.544002i	−0.0515777	+	0.998669i	$0.516425\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	−13.4500	−	7.76536i	−0.600901	−	0.346931i
$502$	5.99072	−	10.3762i	0.267379	−	0.463114i
$503$	−27.6126	−	15.9421i	−1.23118	−	0.710824i	−0.263907	−	0.964548i	$-0.585011\pi$
$503$	−27.6126	−	15.9421i	−1.23118	−	0.710824i	−0.967277	+	0.253724i	$0.918345\pi$
$504$			1.72332i			0.0767626i
$505$	3.45350	−	1.99388i	0.153679	−	0.0887265i
$506$	−2.76079	+	4.78183i	−0.122732	+	0.212578i
$507$	−18.0452			−0.801414
$508$	9.48409			0.420789
$509$	−8.17955	+	14.1674i	−0.362552	+	0.627958i	−0.988380	−	0.152003i	$-0.951428\pi$
$509$	−8.17955	+	14.1674i	−0.362552	+	0.627958i	0.625828	+	0.779961i	$0.284761\pi$
$510$			1.73990i			0.0770441i
$511$	−5.17476	−	8.96295i	−0.228918	−	0.396498i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.54250	+	2.62261i	−0.200556	+	0.115791i
$514$	−12.2051	−	21.1399i	−0.538345	−	0.932441i
$515$	−0.421204	−	0.729546i	−0.0185605	−	0.0321477i
$516$	6.29647	+	3.63527i	0.277187	+	0.160034i
$517$	−9.67361			−0.425445
$518$	4.74338	−	9.34792i	0.208412	−	0.410724i
$519$	8.55673			0.375599
$520$	4.82534	+	2.78591i	0.211605	+	0.122170i
$521$	−6.21264	−	10.7606i	−0.272181	−	0.471430i	0.697239	−	0.716838i	$-0.254411\pi$
$521$	−6.21264	−	10.7606i	−0.272181	−	0.471430i	−0.969420	+	0.245408i	$0.921078\pi$
$522$	1.06438	+	1.84357i	0.0465868	+	0.0806908i
$523$	−31.6748	+	18.2875i	−1.38504	+	0.799656i	−0.992752	−	0.120185i	$-0.961651\pi$
$523$	−31.6748	+	18.2875i	−1.38504	+	0.799656i	−0.392293	+	0.919840i	$0.628318\pi$
$524$			8.33354i			0.364052i
$525$	0.861658	+	1.49244i	0.0376058	+	0.0651352i
$526$			3.00632i			0.131082i
$527$	−2.38718	+	4.13471i	−0.103987	+	0.180111i
$528$	0.723316			0.0314783
$529$	−35.2737			−1.53364
$530$	3.06059	−	5.30109i	0.132943	−	0.230265i
$531$	9.24989	−	5.34043i	0.401411	−	0.231755i
$532$			9.03917i			0.391898i
$533$	15.9731	+	9.22210i	0.691874	+	0.399453i
$534$	6.68269	−	11.5748i	0.289188	−	0.500889i
$535$	4.31835	+	2.49320i	0.186699	+	0.107791i
$536$	−10.5840	+	6.11068i	−0.457159	+	0.263941i
$537$	−18.7483	+	10.8243i	−0.809049	+	0.467104i
$538$	−11.2263	−	6.48151i	−0.484000	−	0.279438i
$539$	1.45755	−	2.52455i	0.0627810	−	0.108740i
$540$	−0.866025	−	0.500000i	−0.0372678	−	0.0215166i
$541$		−	1.91472i		−	0.0823203i	−0.999153	−	0.0411601i	$-0.986895\pi$
$541$		−	1.91472i		−	0.0823203i	0.999153	−	0.0411601i	$-0.0131054\pi$
$542$	−19.9506	+	11.5185i	−0.856954	+	0.494762i
$543$	7.63386	−	13.2222i	0.327601	−	0.567421i
$544$	−1.73990			−0.0745977
$545$	−12.1425			−0.520129
$546$	4.80100	−	8.31558i	0.205464	−	0.355874i
$547$		−	17.1763i		−	0.734407i	−0.930141	−	0.367203i	$-0.880315\pi$
$547$		−	17.1763i		−	0.734407i	0.930141	−	0.367203i	$-0.119685\pi$
$548$	−1.46500	−	2.53745i	−0.0625817	−	0.108395i
$549$		−	3.31026i		−	0.141279i
$550$	0.626410	−	0.361658i	0.0267102	−	0.0154211i
$551$	5.58293	+	9.66992i	0.237841	+	0.411952i
$552$	3.81686	+	6.61099i	0.162456	+	0.281383i
$553$	7.46884	+	4.31214i	0.317607	+	0.183371i
$554$	10.1102			0.429540
$555$	3.32141	+	5.09590i	0.140986	+	0.216309i
$556$	15.8903			0.673901
$557$	27.0889	+	15.6398i	1.14780	+	0.662680i	0.948349	−	0.317229i	$-0.102752\pi$
$557$	27.0889	+	15.6398i	1.14780	+	0.662680i	0.199446	+	0.979909i	$0.436086\pi$
$558$	−1.37202	−	2.37641i	−0.0580822	−	0.100601i
$559$	−20.2551	−	35.0828i	−0.856698	−	1.48385i
$560$	−1.49244	+	0.861658i	−0.0630669	+	0.0364117i
$561$		−	1.25850i		−	0.0531338i
$562$	9.76363	+	16.9111i	0.411854	+	0.713352i
$563$		−	35.7184i		−	1.50535i	−0.658392	−	0.752675i	$-0.728763\pi$
$563$		−	35.7184i		−	1.50535i	0.658392	−	0.752675i	$-0.271237\pi$
$564$	−6.68699	+	11.5822i	−0.281573	+	0.487699i
$565$	−6.82680			−0.287206
$566$	−6.67400			−0.280529
$567$	−0.861658	+	1.49244i	−0.0361862	+	0.0626764i
$568$	11.6121	−	6.70422i	0.487231	−	0.281303i
$569$			30.3880i			1.27393i	0.770893	+	0.636965i	$0.219810\pi$
$569$			30.3880i			1.27393i	−0.770893	+	0.636965i	$0.780190\pi$
$570$	−4.54250	−	2.62261i	−0.190264	−	0.109849i
$571$	16.0830	−	27.8565i	0.673051	−	1.16576i	−0.303984	−	0.952677i	$-0.598317\pi$
$571$	16.0830	−	27.8565i	0.673051	−	1.16576i	0.977035	−	0.213081i	$-0.0683498\pi$
$572$	−3.49024	−	2.01509i	−0.145934	−	0.0842552i
$573$	−13.4578	+	7.76989i	−0.562209	+	0.324592i
$574$	−4.94036	+	2.85232i	−0.206206	+	0.119053i
$575$	6.61099	+	3.81686i	0.275698	+	0.159174i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−3.46095	−	1.99818i	−0.144081	−	0.0831854i	0.426226	−	0.904617i	$-0.359843\pi$
$577$	−3.46095	−	1.99818i	−0.144081	−	0.0831854i	−0.570308	+	0.821431i	$0.693176\pi$
$578$		−	13.9727i		−	0.581189i
$579$	11.4859	−	6.63137i	0.477337	−	0.275591i
$580$	−1.06438	+	1.84357i	−0.0441961	+	0.0765500i
$581$	7.38557			0.306405
$582$	−10.8078			−0.447998
$583$	−2.21377	+	3.83436i	−0.0916849	+	0.158803i
$584$			6.00559i			0.248513i
$585$	2.78591	+	4.82534i	0.115183	+	0.199503i
$586$			10.4111i			0.430078i
$587$	−37.0247	+	21.3762i	−1.52817	+	0.882292i	−0.528736	+	0.848787i	$0.677334\pi$
$587$	−37.0247	+	21.3762i	−1.52817	+	0.882292i	−0.999439	+	0.0335052i	$0.989333\pi$
$588$	−2.01509	−	3.49024i	−0.0831010	−	0.143935i
$589$	−7.19654	−	12.4648i	−0.296528	−	0.513602i
$590$	9.24989	+	5.34043i	0.380812	+	0.219862i
$591$	−25.2231			−1.03754
$592$	−5.09590	+	3.32141i	−0.209440	+	0.136509i
$593$	17.8033			0.731094			0.365547	−	0.930793i	$-0.380882\pi$
$593$	17.8033			0.731094			0.365547	+	0.930793i	$0.380882\pi$
$594$	0.626410	+	0.361658i	0.0257019	+	0.0148390i
$595$	1.49920	+	2.59669i	0.0614612	+	0.106454i
$596$	−4.98892	−	8.64107i	−0.204354	−	0.353952i
$597$	3.50847	−	2.02562i	0.143592	−	0.0829030i
$598$		−	42.5337i		−	1.73933i
$599$	−16.2690	−	28.1788i	−0.664734	−	1.15135i	−0.979357	−	0.202136i	$-0.935212\pi$
$599$	−16.2690	−	28.1788i	−0.664734	−	1.15135i	0.314623	−	0.949217i	$-0.398122\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	13.2884	−	23.0162i	0.542046	−	0.938851i	−0.456741	−	0.889600i	$-0.650983\pi$
$601$	13.2884	−	23.0162i	0.542046	−	0.938851i	0.998786	−	0.0492508i	$-0.0156834\pi$
$602$	12.5294			0.510662
$603$	−12.2214			−0.497692
$604$	1.16473	−	2.01736i	0.0473920	−	0.0820854i
$605$	9.07319	−	5.23841i	0.368878	−	0.212972i
$606$			3.98776i			0.161992i
$607$	−17.7165	−	10.2286i	−0.719091	−	0.415167i	0.0953273	−	0.995446i	$-0.469610\pi$
$607$	−17.7165	−	10.2286i	−0.719091	−	0.415167i	−0.814418	+	0.580279i	$0.802944\pi$
$608$	2.62261	−	4.54250i	0.106361	−	0.184222i
$609$	3.17705	+	1.83427i	0.128741	+	0.0743284i
$610$	2.86677	−	1.65513i	0.116072	−	0.0670144i
$611$	64.5340	−	37.2587i	2.61077	−	1.50733i
$612$	−1.50680	−	0.869951i	−0.0609087	−	0.0351657i
$613$	−18.8427	+	32.6366i	−0.761051	+	1.31818i	0.181258	+	0.983436i	$0.441983\pi$
$613$	−18.8427	+	32.6366i	−0.761051	+	1.31818i	−0.942309	+	0.334744i	$0.891350\pi$
$614$	9.40419	+	5.42951i	0.379522	+	0.219117i
$615$		−	3.31026i		−	0.133483i
$616$	1.07950	−	0.623250i	0.0434944	−	0.0251115i
$617$	16.6566	−	28.8501i	0.670570	−	1.16146i	−0.307172	−	0.951654i	$-0.599383\pi$
$617$	16.6566	−	28.8501i	0.670570	−	1.16146i	0.977743	−	0.209808i	$-0.0672839\pi$
$618$	0.842408			0.0338866
$619$	21.6657			0.870817			0.435408	−	0.900233i	$-0.356604\pi$
$619$	21.6657			0.870817			0.435408	+	0.900233i	$0.356604\pi$
$620$	1.37202	−	2.37641i	0.0551016	−	0.0954387i
$621$			7.63372i			0.306331i
$622$	5.98825	+	10.3720i	0.240107	+	0.415878i
$623$		−	23.0328i		−	0.922789i
$624$	−4.82534	+	2.78591i	−0.193168	+	0.111526i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−10.6672	−	18.4761i	−0.426345	−	0.738452i
$627$	3.28566	+	1.89698i	0.131217	+	0.0757579i
$628$	−2.57369			−0.102701
$629$	5.77893	+	8.86637i	0.230421	+	0.353525i
$630$	−1.72332			−0.0686585
$631$	3.45834	+	1.99668i	0.137674	+	0.0794864i	0.567255	−	0.823542i	$-0.308005\pi$
$631$	3.45834	+	1.99668i	0.137674	+	0.0794864i	−0.429581	+	0.903028i	$0.641339\pi$
$632$	−2.50223	−	4.33399i	−0.0995335	−	0.172397i
$633$	7.08556	+	12.2725i	0.281626	+	0.487790i
$634$	−26.2406	+	15.1500i	−1.04215	+	0.601684i
$635$			9.48409i			0.376365i
$636$	3.06059	+	5.30109i	0.121360	+	0.210202i
$637$			22.4555i			0.889718i
$638$	0.769886	−	1.33348i	0.0304801	−	0.0527930i
$639$	13.4084			0.530430
$640$	1.00000			0.0395285
$641$	−9.15890	+	15.8637i	−0.361755	+	0.626577i	−0.988250	−	0.152848i	$-0.951156\pi$
$641$	−9.15890	+	15.8637i	−0.361755	+	0.626577i	0.626495	+	0.779425i	$0.284489\pi$
$642$	−4.31835	+	2.49320i	−0.170432	+	0.0983989i
$643$			33.5561i			1.32332i	0.749803	+	0.661662i	$0.230148\pi$
$643$			33.5561i			1.32332i	−0.749803	+	0.661662i	$0.769852\pi$
$644$	11.3928	+	6.57765i	0.448940	+	0.259196i
$645$	−3.63527	+	6.29647i	−0.143139	+	0.247923i
$646$	−7.90349	−	4.56308i	−0.310959	−	0.179532i
$647$	4.00408	−	2.31176i	0.157417	−	0.0908846i	−0.419222	−	0.907884i	$-0.637697\pi$
$647$	4.00408	−	2.31176i	0.157417	−	0.0908846i	0.576639	+	0.816999i	$0.304364\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−6.69059	−	3.86282i	−0.262629	−	0.151629i
$650$	−2.78591	+	4.82534i	−0.109272	+	0.189265i
$651$	−4.09530	−	2.36442i	−0.160507	−	0.0926689i
$652$			10.2173i			0.400139i
$653$	4.24347	−	2.44997i	0.166060	−	0.0958746i	−0.414667	−	0.909973i	$-0.636102\pi$
$653$	4.24347	−	2.44997i	0.166060	−	0.0958746i	0.580727	+	0.814099i	$0.302769\pi$
$654$	6.07127	−	10.5157i	0.237405	−	0.411198i
$655$	−8.33354			−0.325618
$656$	3.31026			0.129244
$657$	−3.00280	+	5.20099i	−0.117150	+	0.202910i
$658$			23.0476i			0.898489i
$659$	14.8348	+	25.6947i	0.577883	+	1.00092i	0.995722	+	0.0924018i	$0.0294544\pi$
$659$	14.8348	+	25.6947i	0.577883	+	1.00092i	−0.417839	+	0.908521i	$0.637212\pi$
$660$			0.723316i			0.0281550i
$661$	2.36111	−	1.36319i	0.0918365	−	0.0530218i	−0.453378	−	0.891318i	$-0.649781\pi$
$661$	2.36111	−	1.36319i	0.0918365	−	0.0530218i	0.545215	+	0.838296i	$0.316448\pi$
$662$	12.5573	+	21.7500i	0.488055	+	0.845336i
$663$	4.84721	+	8.39561i	0.188250	+	0.326059i
$664$	−3.71150	−	2.14284i	−0.144034	−	0.0831582i
$665$	−9.03917			−0.350524
$666$	−6.07389	+	0.328476i	−0.235358	+	0.0127282i
$667$	16.2504			0.629219
$668$	13.4500	+	7.76536i	0.520396	+	0.300451i
$669$	5.09652	+	8.82744i	0.197043	+	0.341289i
$670$	−6.11068	−	10.5840i	−0.236076	−	0.408896i
$671$	−2.07358	+	1.19718i	−0.0800497	+	0.0462167i
$672$		−	1.72332i		−	0.0664783i
$673$	17.2930	+	29.9523i	0.666595	+	1.15458i	0.978850	+	0.204579i	$0.0655824\pi$
$673$	17.2930	+	29.9523i	0.666595	+	1.15458i	−0.312255	+	0.949998i	$0.601084\pi$
$674$			29.3226i			1.12946i
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	18.0452			0.694045
$677$	−15.1428			−0.581985			−0.290993	−	0.956725i	$-0.593986\pi$
$677$	−15.1428			−0.581985			−0.290993	+	0.956725i	$0.593986\pi$
$678$	3.41340	−	5.91219i	0.131091	−	0.227056i
$679$	−16.1299	+	9.31263i	−0.619010	+	0.357386i
$680$		−	1.73990i		−	0.0667222i
$681$	16.8709	+	9.74040i	0.646493	+	0.373253i
$682$	−0.992402	+	1.71889i	−0.0380010	+	0.0658197i
$683$	−15.6497	−	9.03537i	−0.598820	−	0.345729i	0.169757	−	0.985486i	$-0.445702\pi$
$683$	−15.6497	−	9.03537i	−0.598820	−	0.345729i	−0.768577	+	0.639757i	$0.779035\pi$
$684$	4.54250	−	2.62261i	0.173687	−	0.100278i
$685$	2.53745	−	1.46500i	0.0969511	−	0.0559747i
$686$	−16.4618	−	9.50424i	−0.628516	−	0.362874i
$687$	11.8302	−	20.4905i	0.451351	−	0.781763i
$688$	−6.29647	−	3.63527i	−0.240051	−	0.138593i
$689$		−	34.1061i		−	1.29934i
$690$	−6.61099	+	3.81686i	−0.251676	+	0.145305i
$691$	−4.39339	+	7.60957i	−0.167132	+	0.289482i	−0.937410	−	0.348226i	$-0.886784\pi$
$691$	−4.39339	+	7.60957i	−0.167132	+	0.289482i	0.770278	+	0.637708i	$0.220117\pi$
$692$	−8.55673			−0.325278
$693$	1.24650			0.0473507
$694$	−14.4298	+	24.9931i	−0.547746	+	0.948724i
$695$			15.8903i			0.602755i
$696$	−1.06438	−	1.84357i	−0.0403454	−	0.0698802i
$697$		−	5.75953i		−	0.218158i
$698$	8.41596	−	4.85895i	0.318549	−	0.183914i
$699$	−1.25220	−	2.16887i	−0.0473625	−	0.0820342i
$700$	−0.861658	−	1.49244i	−0.0325676	−	0.0564087i
$701$	29.4526	+	17.0045i	1.11241	+	0.642249i	0.939452	−	0.342680i	$-0.111335\pi$
$701$	29.4526	+	17.0045i	1.11241	+	0.642249i	0.172957	+	0.984929i	$0.444668\pi$
$702$	−5.57182			−0.210295
$703$	−31.8589	+	1.72293i	−1.20158	+	0.0649815i
$704$	−0.723316			−0.0272610
$705$	−11.5822	−	6.68699i	−0.436211	−	0.251847i
$706$	−3.19613	−	5.53586i	−0.120288	−	0.208345i
$707$	3.43609	+	5.95148i	0.129227	+	0.223828i
$708$	−9.24989	+	5.34043i	−0.347632	+	0.200706i
$709$			27.6590i			1.03875i	0.854545	+	0.519377i	$0.173836\pi$
$709$			27.6590i			1.03875i	−0.854545	+	0.519377i	$0.826164\pi$
$710$	6.70422	+	11.6121i	0.251605	+	0.435793i
$711$		−	5.00446i		−	0.187682i
$712$	−6.68269	+	11.5748i	−0.250445	+	0.433783i
$713$	−20.9472			−0.784479
$714$	−2.99840			−0.112212
$715$	2.01509	−	3.49024i	0.0753602	−	0.130528i
$716$	18.7483	−	10.8243i	0.700657	−	0.404524i
$717$		−	12.8502i		−	0.479898i
$718$	10.6033	+	6.12179i	0.395710	+	0.228463i
$719$	7.50807	−	13.0044i	0.280004	−	0.484981i	−0.691382	−	0.722490i	$-0.742998\pi$
$719$	7.50807	−	13.0044i	0.280004	−	0.484981i	0.971385	+	0.237509i	$0.0763310\pi$
$720$	0.866025	+	0.500000i	0.0322749	+	0.0186339i
$721$	1.25724	−	0.725867i	0.0468220	−	0.0270327i
$722$	7.37191	−	4.25617i	0.274354	−	0.158398i
$723$	−19.3844	−	11.1916i	−0.720912	−	0.416219i
$724$	−7.63386	+	13.2222i	−0.283710	+	0.491401i
$725$	−1.84357	−	1.06438i	−0.0684684	−	0.0395302i
$726$			10.4768i			0.388831i
$727$	0.0210570	−	0.0121573i	0.000780960	−	0.000450888i	−0.499609	−	0.866251i	$-0.666523\pi$
$727$	0.0210570	−	0.0121573i	0.000780960	−	0.000450888i	0.500390	+	0.865800i	$0.333190\pi$
$728$	−4.80100	+	8.31558i	−0.177937	+	0.308196i
$729$	1.00000			0.0370370
$730$	−6.00559			−0.222277
$731$	−6.32501	+	10.9552i	−0.233939	+	0.405194i
$732$			3.31026i			0.122351i
$733$	−16.0376	−	27.7779i	−0.592361	−	1.02600i	−0.993914	−	0.110163i	$-0.964863\pi$
$733$	−16.0376	−	27.7779i	−0.592361	−	1.02600i	0.401553	−	0.915836i	$-0.368471\pi$
$734$			32.2193i			1.18924i
$735$	3.49024	−	2.01509i	0.128739	−	0.0743278i
$736$	−3.81686	−	6.61099i	−0.140691	−	0.243684i
$737$	4.41995	+	7.65558i	0.162811	+	0.281997i
$738$	2.86677	+	1.65513i	0.105527	+	0.0609263i
$739$	−30.9975			−1.14026			−0.570131	−	0.821554i	$-0.693108\pi$
$739$	−30.9975			−1.14026			−0.570131	+	0.821554i	$0.693108\pi$
$740$	−3.32141	−	5.09590i	−0.122098	−	0.187329i
$741$	−29.2254			−1.07362
$742$	9.13545	+	5.27435i	0.335373	+	0.193628i
$743$	12.9588	+	22.4454i	0.475414	+	0.823441i	0.999603	−	0.0281608i	$-0.00896503\pi$
$743$	12.9588	+	22.4454i	0.475414	+	0.823441i	−0.524190	+	0.851602i	$0.675632\pi$
$744$	1.37202	+	2.37641i	0.0503006	+	0.0871233i
$745$	8.64107	−	4.98892i	0.316584	−	0.182780i
$746$		−	18.2509i		−	0.668213i
$747$	−2.14284	−	3.71150i	−0.0784023	−	0.135797i
$748$			1.25850i			0.0460152i
$749$	−4.29657	+	7.44189i	−0.156993	+	0.271921i
$750$	1.00000			0.0365148
$751$	−46.3456			−1.69118			−0.845588	−	0.533836i	$-0.820750\pi$
$751$	−46.3456			−1.69118			−0.845588	+	0.533836i	$0.820750\pi$
$752$	6.68699	−	11.5822i	0.243850	−	0.422360i
$753$	−10.3762	+	5.99072i	−0.378131	+	0.218314i
$754$			11.8611i			0.431956i
$755$	2.01736	+	1.16473i	0.0734194	+	0.0423887i
$756$	0.861658	−	1.49244i	0.0313382	−	0.0542793i
$757$	8.85144	+	5.11038i	0.321711	+	0.185740i	0.652155	−	0.758086i	$-0.273865\pi$
$757$	8.85144	+	5.11038i	0.321711	+	0.185740i	−0.330444	+	0.943826i	$0.607198\pi$
$758$	−29.4798	+	17.0202i	−1.07075	+	0.618200i
$759$	4.78183	−	2.76079i	0.173570	−	0.100210i
$760$	4.54250	+	2.62261i	0.164774	+	0.0951321i
$761$	7.18408	−	12.4432i	0.260423	−	0.451065i	−0.705932	−	0.708280i	$-0.749471\pi$
$761$	7.18408	−	12.4432i	0.260423	−	0.451065i	0.966354	+	0.257215i	$0.0828047\pi$
$762$	−8.21347	−	4.74205i	−0.297542	−	0.171786i
$763$		−	20.9254i		−	0.757551i
$764$	13.4578	−	7.76989i	0.486888	−	0.281105i
$765$	0.869951	−	1.50680i	0.0314531	−	0.0544784i
$766$	−38.1472			−1.37831
$767$	59.5118			2.14885
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$		−	3.21254i		−	0.115847i	−0.998321	−	0.0579236i	$-0.981552\pi$
$769$		−	3.21254i		−	0.115847i	0.998321	−	0.0579236i	$-0.0184480\pi$
$770$	0.623250	+	1.07950i	0.0224604	+	0.0389025i
$771$			24.4102i			0.879113i
$772$	−11.4859	+	6.63137i	−0.413386	+	0.238668i
$773$	12.7515	+	22.0862i	0.458639	+	0.794386i	0.998889	−	0.0471185i	$-0.0150038\pi$
$773$	12.7515	+	22.0862i	0.458639	+	0.794386i	−0.540250	+	0.841504i	$0.681671\pi$
$774$	−3.63527	−	6.29647i	−0.130667	−	0.226322i
$775$	2.37641	+	1.37202i	0.0853630	+	0.0492844i
$776$	10.8078			0.387977
$777$	−8.78185	+	5.72384i	−0.315047	+	0.205342i
$778$	9.60947			0.344516
$779$	15.0369	+	8.68154i	0.538751	+	0.311048i
$780$	−2.78591	−	4.82534i	−0.0997516	−	0.172775i
$781$	−4.84927	−	8.39918i	−0.173520	−	0.300546i
$782$	−11.5025	+	6.64096i	−0.411328	+	0.237480i
$783$		−	2.12877i		−	0.0760760i
$784$	2.01509	+	3.49024i	0.0719676	+	0.124651i
$785$		−	2.57369i		−	0.0918590i
$786$	4.16677	−	7.21706i	0.148624	−	0.257424i
$787$	21.7749			0.776191			0.388095	−	0.921619i	$-0.373133\pi$
$787$	21.7749			0.776191			0.388095	+	0.921619i	$0.373133\pi$
$788$	25.2231			0.898536
$789$	1.50316	−	2.60355i	0.0535139	−	0.0926888i
$790$	4.33399	−	2.50223i	0.154197	−	0.0890254i
$791$		−	11.7647i		−	0.418306i
$792$	−0.626410	−	0.361658i	−0.0222585	−	0.0128509i
$793$	9.22210	−	15.9731i	0.327486	−	0.567223i
$794$	10.6460	+	6.14646i	0.377812	+	0.218130i
$795$	−5.30109	+	3.06059i	−0.188010	+	0.108548i
$796$	−3.50847	+	2.02562i	−0.124354	+	0.0717961i
$797$	−9.82629	−	5.67321i	−0.348065	−	0.200956i	0.315768	−	0.948837i	$-0.397738\pi$
$797$	−9.82629	−	5.67321i	−0.348065	−	0.200956i	−0.663833	+	0.747881i	$0.731071\pi$
$798$	4.51959	−	7.82815i	0.159992	−	0.277114i
$799$	−20.1519	−	11.6347i	−0.712923	−	0.411607i
$800$			1.00000i			0.0353553i
$801$	−11.5748	+	6.68269i	−0.408974	+	0.236121i
$802$	−1.36361	+	2.36185i	−0.0481509	+	0.0833998i
$803$	4.34394			0.153294
$804$	12.2214			0.431014
$805$	−6.57765	+	11.3928i	−0.231832	+	0.401544i
$806$		−	15.2893i		−	0.538542i
$807$	6.48151	+	11.2263i	0.228160	+	0.395185i
$808$		−	3.98776i		−	0.140289i
$809$	45.3442	−	26.1795i	1.59422	−	0.920421i	0.601644	−	0.798764i	$-0.294512\pi$
$809$	45.3442	−	26.1795i	1.59422	−	0.920421i	0.992572	−	0.121657i	$-0.0388209\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	−10.3045	−	17.8479i	−0.361839	−	0.626723i	0.626425	−	0.779482i	$-0.284518\pi$
$811$	−10.3045	−	17.8479i	−0.361839	−	0.626723i	−0.988263	+	0.152759i	$0.951184\pi$
$812$	−3.17705	−	1.83427i	−0.111493	−	0.0643703i
$813$	23.0370			0.807944
$814$	2.40243	+	3.68595i	0.0842051	+	0.129192i
$815$	−10.2173			−0.357895
$816$	1.50680	+	0.869951i	0.0527485	+	0.0304544i
$817$	−19.0678	−	33.0264i	−0.667098	−	1.15545i
$818$	8.23934	+	14.2710i	0.288082	+	0.498972i
$819$	−8.31558	+	4.80100i	−0.290570	+	0.167761i
$820$			3.31026i			0.115599i
$821$	18.3228	+	31.7360i	0.639470	+	1.10759i	0.985549	+	0.169389i	$0.0541794\pi$
$821$	18.3228	+	31.7360i	0.639470	+	1.10759i	−0.346079	+	0.938205i	$0.612487\pi$
$822$			2.93000i			0.102195i
$823$	−12.3166	+	21.3330i	−0.429329	+	0.743620i	−0.996814	−	0.0797639i	$-0.974583\pi$
$823$	−12.3166	+	21.3330i	−0.429329	+	0.743620i	0.567484	+	0.823384i	$0.307917\pi$
$824$	−0.842408			−0.0293467
$825$	−0.723316			−0.0251826
$826$	−9.20324	+	15.9405i	−0.320222	+	0.554640i
$827$	−10.9945	+	6.34768i	−0.382316	+	0.220730i	−0.678826	−	0.734300i	$-0.737511\pi$
$827$	−10.9945	+	6.34768i	−0.382316	+	0.220730i	0.296509	+	0.955030i	$0.404177\pi$
$828$		−	7.63372i		−	0.265290i
$829$	−14.7321	−	8.50559i	−0.511667	−	0.295411i	0.221851	−	0.975080i	$-0.428790\pi$
$829$	−14.7321	−	8.50559i	−0.511667	−	0.295411i	−0.733519	+	0.679669i	$0.762123\pi$
$830$	2.14284	−	3.71150i	0.0743789	−	0.128828i
$831$	−8.75567	−	5.05509i	−0.303731	−	0.175359i
$832$	4.82534	−	2.78591i	0.167288	−	0.0965840i
$833$	6.07268	−	3.50606i	0.210406	−	0.121478i
$834$	−13.7614	−	7.94517i	−0.476520	−	0.275119i
$835$	−7.76536	+	13.4500i	−0.268731	+	0.465456i
$836$	−3.28566	−	1.89698i	−0.113637	−	0.0656083i
$837$			2.74404i			0.0948478i
$838$	22.8548	−	13.1952i	0.789504	−	0.455820i
$839$	−13.0905	+	22.6735i	−0.451936	+	0.782775i	−0.998506	−	0.0546376i	$-0.982600\pi$
$839$	−13.0905	+	22.6735i	−0.451936	+	0.782775i	0.546571	+	0.837413i	$0.315933\pi$
$840$	1.72332			0.0594600
$841$	24.4683			0.843736
$842$	−8.08881	+	14.0102i	−0.278759	+	0.482824i
$843$		−	19.5273i		−	0.672554i
$844$	−7.08556	−	12.2725i	−0.243895	−	0.422438i
$845$			18.0452i			0.620773i
$846$	11.5822	−	6.68699i	0.398205	−	0.229904i
$847$	9.02743	+	15.6360i	0.310186	+	0.537258i
$848$	−3.06059	−	5.30109i	−0.105101	−	0.182040i
$849$	5.77985	+	3.33700i	0.198364	+	0.114525i
$850$	1.73990			0.0596781
$851$	−21.0116	+	41.4082i	−0.720269	+	1.41945i
$852$	−13.4084			−0.459366
$853$	41.5321	+	23.9786i	1.42203	+	0.821011i	0.996473	−	0.0839198i	$-0.0267440\pi$
$853$	41.5321	+	23.9786i	1.42203	+	0.821011i	0.425560	+	0.904930i	$0.360077\pi$
$854$	2.85232	+	4.94036i	0.0976042	+	0.169055i
$855$	2.62261	+	4.54250i	0.0896914	+	0.155350i
$856$	4.31835	−	2.49320i	0.147598	−	0.0852159i
$857$			9.79243i			0.334503i	0.985914	+	0.167251i	$0.0534892\pi$
$857$			9.79243i			0.334503i	−0.985914	+	0.167251i	$0.946511\pi$
$858$	2.01509	+	3.49024i	0.0687941	+	0.119155i
$859$			38.4001i			1.31019i	0.755545	+	0.655097i	$0.227372\pi$
$859$			38.4001i			1.31019i	−0.755545	+	0.655097i	$0.772628\pi$
$860$	3.63527	−	6.29647i	0.123962	−	0.214708i
$861$	5.70463			0.194413
$862$	16.0680			0.547279
$863$	7.56388	−	13.1010i	0.257478	−	0.445964i	−0.708088	−	0.706124i	$-0.750442\pi$
$863$	7.56388	−	13.1010i	0.257478	−	0.445964i	0.965566	+	0.260160i	$0.0837753\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		−	8.55673i		−	0.290938i
$866$	18.9056	+	10.9151i	0.642437	+	0.370911i
$867$	−6.98637	+	12.1008i	−0.237270	+	0.410963i
$868$	4.09530	+	2.36442i	0.139003	+	0.0802537i
$869$	−3.13484	+	1.80990i	−0.106342	+	0.0613968i
$870$	1.84357	−	1.06438i	0.0625028	−	0.0360860i
$871$	−58.9722	−	34.0476i	−1.99820	−	1.15366i
$872$	−6.07127	+	10.5157i	−0.205599	+	0.356108i
$873$	9.35983	+	5.40390i	0.316782	+	0.182894i
$874$		−	40.0405i		−	1.35439i
$875$	1.49244	−	0.861658i	0.0504535	−	0.0291293i
$876$	3.00280	−	5.20099i	0.101455	−	0.175725i
$877$	−24.9990			−0.844157			−0.422078	−	0.906559i	$-0.638699\pi$
$877$	−24.9990			−0.844157			−0.422078	+	0.906559i	$0.638699\pi$
$878$	−4.51083			−0.152233
$879$	5.20554	−	9.01626i	0.175579	−	0.304111i
$880$		−	0.723316i		−	0.0243830i
$881$	3.77350	+	6.53589i	0.127132	+	0.220200i	0.922564	−	0.385843i	$-0.126089\pi$
$881$	3.77350	+	6.53589i	0.127132	+	0.220200i	−0.795432	+	0.606043i	$0.792756\pi$
$882$			4.03018i			0.135703i
$883$	9.35638	−	5.40191i	0.314867	−	0.181789i	−0.334235	−	0.942490i	$-0.608478\pi$
$883$	9.35638	−	5.40191i	0.314867	−	0.181789i	0.649102	+	0.760701i	$0.275145\pi$
$884$	−4.84721	−	8.39561i	−0.163029	−	0.282375i
$885$	−5.34043	−	9.24989i	−0.179517	−	0.310932i
$886$	16.3417	+	9.43490i	0.549011	+	0.316972i
$887$	11.7764			0.395412			0.197706	−	0.980261i	$-0.436651\pi$
$887$	11.7764			0.395412			0.197706	+	0.980261i	$0.436651\pi$
$888$	6.07389	−	0.328476i	0.203826	−	0.0110229i
$889$	−16.3441			−0.548163
$890$	−11.5748	−	6.68269i	−0.387987	−	0.224004i
$891$	−0.361658	−	0.626410i	−0.0121160	−	0.0209855i
$892$	−5.09652	−	8.82744i	−0.170644	−	0.295565i
$893$	60.7513	−	35.0748i	2.03296	−	1.17373i
$894$			9.97784i			0.333709i
$895$	10.8243	+	18.7483i	0.361818	+	0.626686i
$896$			1.72332i			0.0575719i
$897$	−21.2669	+	36.8353i	−0.710079	+	1.22989i
$898$	−21.5788			−0.720095
$899$	5.84142			0.194822
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−9.22337	+	5.32512i	−0.307275	+	0.177405i
$902$		−	2.39437i		−	0.0797237i
$903$	−10.8508	−	6.26472i	−0.361092	−	0.208477i
$904$	−3.41340	+	5.91219i	−0.113528	+	0.196636i
$905$	−13.2222	−	7.63386i	−0.439522	−	0.253758i
$906$	−2.01736	+	1.16473i	−0.0670224	+	0.0386954i
$907$	37.5666	−	21.6891i	1.24738	−	0.720174i	0.276792	−	0.960930i	$-0.410729\pi$
$907$	37.5666	−	21.6891i	1.24738	−	0.720174i	0.970586	+	0.240756i	$0.0773952\pi$
$908$	−16.8709	−	9.74040i	−0.559880	−	0.323247i
$909$	1.99388	−	3.45350i	0.0661329	−	0.114545i
$910$	−8.31558	−	4.80100i	−0.275659	−	0.159152i
$911$		−	58.6687i		−	1.94378i	−0.235433	−	0.971891i	$-0.575651\pi$
$911$		−	58.6687i		−	1.94378i	0.235433	−	0.971891i	$-0.424349\pi$
$912$	−4.54250	+	2.62261i	−0.150417	+	0.0868433i
$913$	−1.54995	+	2.68459i	−0.0512958	+	0.0888468i
$914$	16.2509			0.537531
$915$	−3.31026			−0.109434
$916$	−11.8302	+	20.4905i	−0.390881	+	0.677026i
$917$		−	14.3613i		−	0.474252i
$918$	0.869951	+	1.50680i	0.0287127	+	0.0497318i
$919$			0.554287i			0.0182843i	0.999958	+	0.00914213i	$0.00291007\pi$
$919$			0.554287i			0.0182843i	−0.999958	+	0.00914213i	$0.997090\pi$
$920$	6.61099	−	3.81686i	0.217958	−	0.125838i
$921$	−5.42951	−	9.40419i	−0.178909	−	0.309879i
$922$	0.444633	+	0.770127i	0.0146432	+	0.0253628i
$923$	64.7003	+	37.3547i	2.12964	+	1.22955i
$924$	−1.24650			−0.0410069
$925$	5.09590	−	3.32141i	0.167552	−	0.109207i
$926$	−37.0156			−1.21641
$927$	−0.729546	−	0.421204i	−0.0239615	−	0.0138341i
$928$	1.06438	+	1.84357i	0.0349401	+	0.0605181i
$929$	−4.25726	−	7.37379i	−0.139676	−	0.241926i	0.787698	−	0.616062i	$-0.211273\pi$
$929$	−4.25726	−	7.37379i	−0.139676	−	0.241926i	−0.927374	+	0.374136i	$0.877939\pi$
$930$	−2.37641	+	1.37202i	−0.0779254	+	0.0449903i
$931$			21.1392i			0.692809i
$932$	1.25220	+	2.16887i	0.0410171	+	0.0710437i
$933$		−	11.9765i		−	0.392093i
$934$	−5.81653	+	10.0745i	−0.190323	+	0.329648i
$935$	−1.25850			−0.0411573
$936$	5.57182			0.182121
$937$	20.7777	−	35.9881i	0.678779	−	1.17568i	−0.296570	−	0.955011i	$-0.595843\pi$
$937$	20.7777	−	35.9881i	0.678779	−	1.17568i	0.975349	−	0.220669i	$-0.0708240\pi$
$938$	18.2396	−	10.5306i	0.595543	−	0.343837i
$939$			21.3343i			0.696219i
$940$	11.5822	+	6.68699i	0.377770	+	0.218106i
$941$	−3.16259	+	5.47777i	−0.103098	+	0.178570i	−0.912959	−	0.408051i	$-0.866209\pi$
$941$	−3.16259	+	5.47777i	−0.103098	+	0.178570i	0.809862	+	0.586621i	$0.199542\pi$
$942$	2.22888	+	1.28685i	0.0726209	+	0.0419277i
$943$	21.8841	−	12.6348i	0.712646	−	0.411446i
$944$	9.24989	−	5.34043i	0.301058	−	0.173816i
$945$	1.49244	+	0.861658i	0.0485489	+	0.0280297i
$946$	−2.62945	+	4.55434i	−0.0854907	+	0.148074i
$947$	28.4858	+	16.4463i	0.925665	+	0.534433i	0.885438	−	0.464757i	$-0.153858\pi$
$947$	28.4858	+	16.4463i	0.925665	+	0.534433i	0.0402273	+	0.999191i	$0.487192\pi$
$948$			5.00446i			0.162537i
$949$	−28.9790	+	16.7310i	−0.940698	+	0.543112i
$950$	−2.62261	+	4.54250i	−0.0850887	+	0.147378i
$951$	30.3000			0.982546
$952$	2.99840			0.0971787
$953$	17.7188	−	30.6899i	0.573968	−	0.994142i	−0.422185	−	0.906510i	$-0.638737\pi$
$953$	17.7188	−	30.6899i	0.573968	−	0.994142i	0.996153	−	0.0876324i	$-0.0279301\pi$
$954$		−	6.12117i		−	0.198180i
$955$	7.76989	+	13.4578i	0.251428	+	0.435485i
$956$			12.8502i			0.415604i
$957$	−1.33348	+	0.769886i	−0.0431053	+	0.0248869i
$958$	−6.18855	−	10.7189i	−0.199943	−	0.346312i
$959$	2.52466	+	4.37283i	0.0815254	+	0.141206i
$960$	−0.866025	−	0.500000i	−0.0279508	−	0.0161374i
$961$	23.4703			0.757105
$962$	−30.2237	−	15.3363i	−0.974450	−	0.494462i
$963$	4.98641			0.160685
$964$	19.3844	+	11.1916i	0.624328	+	0.360456i
$965$	−6.63137	−	11.4859i	−0.213471	−	0.369743i
$966$	−6.57765	−	11.3928i	−0.211633	−	0.366558i
$967$	33.4298	−	19.3007i	1.07503	−	0.620669i	0.145478	−	0.989361i	$-0.453528\pi$
$967$	33.4298	−	19.3007i	1.07503	−	0.620669i	0.929551	+	0.368693i	$0.120195\pi$
$968$		−	10.4768i		−	0.336738i
$969$	4.56308	+	7.90349i	0.146587	+	0.253897i
$970$			10.8078i			0.347018i
$971$	−7.92935	+	13.7340i	−0.254465	+	0.440746i	−0.964750	−	0.263168i	$-0.915233\pi$
$971$	−7.92935	+	13.7340i	−0.254465	+	0.440746i	0.710285	+	0.703914i	$0.248566\pi$
$972$	−1.00000			−0.0320750
$973$	−27.3841			−0.877893
$974$	−1.60182	+	2.77443i	−0.0513255	+	0.0888984i
$975$	4.82534	−	2.78591i	0.154534	−	0.0892205i
$976$		−	3.31026i		−	0.105959i
$977$	−18.9582	−	10.9455i	−0.606526	−	0.350178i	0.165079	−	0.986280i	$-0.447212\pi$
$977$	−18.9582	−	10.9455i	−0.606526	−	0.350178i	−0.771605	+	0.636103i	$0.780546\pi$
$978$	5.10864	−	8.84842i	0.163356	−	0.282941i
$979$	8.37221	+	4.83370i	0.267577	+	0.154486i
$980$	−3.49024	+	2.01509i	−0.111492	+	0.0643697i
$981$	−10.5157	+	6.07127i	−0.335742	+	0.193841i
$982$	−22.9742	−	13.2641i	−0.733135	−	0.423275i
$983$	14.3480	−	24.8515i	0.457631	−	0.792640i	−0.541205	−	0.840891i	$-0.682032\pi$
$983$	14.3480	−	24.8515i	0.457631	−	0.792640i	0.998835	+	0.0482514i	$0.0153649\pi$
$984$	−2.86677	−	1.65513i	−0.0913894	−	0.0527637i
$985$			25.2231i			0.803675i
$986$	3.20763	−	1.85192i	0.102152	−	0.0589773i
$987$	11.5238	−	19.9598i	0.366807	−	0.635328i
$988$	29.2254			0.929785
$989$	−55.5013			−1.76484
$990$	0.361658	−	0.626410i	0.0114942	−	0.0199086i
$991$			24.2074i			0.768972i	0.923131	+	0.384486i	$0.125621\pi$
$991$			24.2074i			0.768972i	−0.923131	+	0.384486i	$0.874379\pi$
$992$	−1.37202	−	2.37641i	−0.0435616	−	0.0754509i
$993$		−	25.1147i		−	0.796990i
$994$	−20.0112	+	11.5535i	−0.634718	+	0.366454i
$995$	−2.02562	−	3.50847i	−0.0642164	−	0.111226i
$996$	2.14284	+	3.71150i	0.0678984	+	0.117603i
$997$	19.4550	+	11.2323i	0.616145	+	0.355731i	0.775367	−	0.631511i	$-0.217565\pi$
$997$	19.4550	+	11.2323i	0.616145	+	0.355731i	−0.159222	+	0.987243i	$0.550898\pi$
$998$	−24.3042			−0.769335
$999$	5.42438	+	2.75248i	0.171620	+	0.0870845i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.x.c.841.6	yes	16
37.11	even	6	inner	1110.2.x.c.751.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.x.c.751.6	✓	16	37.11	even	6	inner
1110.2.x.c.841.6	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-0.861658 - 1.49244i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} -1.00000i q^{6} +(-0.861658 - 1.49244i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} +0.723316 q^{11} +(0.500000 - 0.866025i) q^{12} +(-4.82534 + 2.78591i) q^{13} -1.72332i q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50680 + 0.869951i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(-4.54250 + 2.62261i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-0.861658 + 1.49244i) q^{21} +(0.626410 + 0.361658i) q^{22} +7.63372i q^{23} +(0.866025 - 0.500000i) q^{24} +(0.500000 - 0.866025i) q^{25} -5.57182 q^{26} +1.00000 q^{27} +(0.861658 - 1.49244i) q^{28} -2.12877i q^{29} +(0.500000 + 0.866025i) q^{30} +2.74404i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.361658 - 0.626410i) q^{33} +(0.869951 + 1.50680i) q^{34} +(1.49244 + 0.861658i) q^{35} -1.00000 q^{36} +(5.42438 + 2.75248i) q^{37} -5.24522 q^{38} +(4.82534 + 2.78591i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-1.65513 - 2.86677i) q^{41} +(-1.49244 + 0.861658i) q^{42} +7.27054i q^{43} +(0.361658 + 0.626410i) q^{44} -1.00000i q^{45} +(-3.81686 + 6.61099i) q^{46} -13.3740 q^{47} +1.00000 q^{48} +(2.01509 - 3.49024i) q^{49} +(0.866025 - 0.500000i) q^{50} -1.73990i q^{51} +(-4.82534 - 2.78591i) q^{52} +(-3.06059 + 5.30109i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.626410 + 0.361658i) q^{55} +(1.49244 - 0.861658i) q^{56} +(4.54250 + 2.62261i) q^{57} +(1.06438 - 1.84357i) q^{58} +(-9.24989 - 5.34043i) q^{59} +1.00000i q^{60} +(-2.86677 + 1.65513i) q^{61} +(-1.37202 + 2.37641i) q^{62} +1.72332 q^{63} -1.00000 q^{64} +(2.78591 - 4.82534i) q^{65} -0.723316i q^{66} +(6.11068 + 10.5840i) q^{67} +1.73990i q^{68} +(6.61099 - 3.81686i) q^{69} +(0.861658 + 1.49244i) q^{70} +(-6.70422 - 11.6121i) q^{71} +(-0.866025 - 0.500000i) q^{72} +6.00559 q^{73} +(3.32141 + 5.09590i) q^{74} -1.00000 q^{75} +(-4.54250 - 2.62261i) q^{76} +(-0.623250 - 1.07950i) q^{77} +(2.78591 + 4.82534i) q^{78} +(-4.33399 + 2.50223i) q^{79} -1.00000i q^{80} +(-0.500000 - 0.866025i) q^{81} -3.31026i q^{82} +(-2.14284 + 3.71150i) q^{83} -1.72332 q^{84} -1.73990 q^{85} +(-3.63527 + 6.29647i) q^{86} +(-1.84357 + 1.06438i) q^{87} +0.723316i q^{88} +(11.5748 + 6.68269i) q^{89} +(0.500000 - 0.866025i) q^{90} +(8.31558 + 4.80100i) q^{91} +(-6.61099 + 3.81686i) q^{92} +(2.37641 - 1.37202i) q^{93} +(-11.5822 - 6.68699i) q^{94} +(2.62261 - 4.54250i) q^{95} +(0.866025 + 0.500000i) q^{96} -10.8078i q^{97} +(3.49024 - 2.01509i) q^{98} +(-0.361658 + 0.626410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q - 8 q^{3} + 8 q^{4} - 2 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} + 8 q^{12} - 12 q^{13} - 8 q^{16} - 6 q^{17} + 6 q^{19} - 2 q^{21} - 6 q^{22} + 8 q^{25} + 16 q^{27} + 2 q^{28} + 8 q^{30} + 6 q^{33} - 4 q^{34} - 6 q^{35} - 16 q^{36} + 18 q^{37} + 12 q^{38} + 12 q^{39} - 8 q^{40} + 6 q^{42} - 6 q^{44} - 4 q^{46} - 60 q^{47} + 16 q^{48} - 4 q^{49} - 12 q^{52} + 12 q^{53} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 12 q^{58} + 12 q^{59} - 4 q^{62} + 4 q^{63} - 16 q^{64} + 22 q^{67} - 6 q^{69} + 2 q^{70} + 2 q^{71} + 24 q^{73} - 8 q^{74} - 16 q^{75} + 6 q^{76} - 58 q^{77} - 36 q^{79} - 8 q^{81} - 8 q^{83} - 4 q^{84} + 8 q^{85} - 2 q^{86} - 42 q^{89} + 8 q^{90} + 6 q^{92} - 6 q^{93} + 6 q^{94} - 6 q^{95} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 + 8 * q^4 - 2 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 + 8 * q^12 - 12 * q^13 - 8 * q^16 - 6 * q^17 + 6 * q^19 - 2 * q^21 - 6 * q^22 + 8 * q^25 + 16 * q^27 + 2 * q^28 + 8 * q^30 + 6 * q^33 - 4 * q^34 - 6 * q^35 - 16 * q^36 + 18 * q^37 + 12 * q^38 + 12 * q^39 - 8 * q^40 + 6 * q^42 - 6 * q^44 - 4 * q^46 - 60 * q^47 + 16 * q^48 - 4 * q^49 - 12 * q^52 + 12 * q^53 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 12 * q^58 + 12 * q^59 - 4 * q^62 + 4 * q^63 - 16 * q^64 + 22 * q^67 - 6 * q^69 + 2 * q^70 + 2 * q^71 + 24 * q^73 - 8 * q^74 - 16 * q^75 + 6 * q^76 - 58 * q^77 - 36 * q^79 - 8 * q^81 - 8 * q^83 - 4 * q^84 + 8 * q^85 - 2 * q^86 - 42 * q^89 + 8 * q^90 + 6 * q^92 - 6 * q^93 + 6 * q^94 - 6 * q^95 - 12 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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