LMFDB - Embedded newform 920.2.bb.a.11.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))

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

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

chi := DirichletCharacter("920.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.6
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31653 + 0.516468i) q^{2} +(0.0200411 - 0.139389i) q^{3} +(1.46652 - 1.35990i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.0456052 + 0.193861i) q^{6} +(-0.0496235 - 0.0572686i) q^{7} +(-1.22838 + 2.54776i) q^{8} +(2.85945 + 0.839611i) q^{9} +(1.11770 - 0.866458i) q^{10} +(2.49402 - 3.88077i) q^{11} +(-0.160164 - 0.231671i) q^{12} +(-2.63757 - 2.28547i) q^{13} +(0.0949085 + 0.0497671i) q^{14} +(0.0200411 + 0.139389i) q^{15} +(0.301368 - 3.98863i) q^{16} +(0.337829 - 0.154281i) q^{17} +(-4.19820 + 0.371440i) q^{18} +(-5.76287 - 2.63181i) q^{19} +(-1.02399 + 1.71798i) q^{20} +(-0.00897712 + 0.00576924i) q^{21} +(-1.27916 + 6.39724i) q^{22} +(-0.651598 + 4.75136i) q^{23} +(0.330511 + 0.222283i) q^{24} +(0.841254 - 0.540641i) q^{25} +(4.65282 + 1.64667i) q^{26} +(0.349838 - 0.766038i) q^{27} +(-0.150653 - 0.0165028i) q^{28} +(7.29043 - 3.32943i) q^{29} +(-0.0983747 - 0.173160i) q^{30} +(-5.07753 + 0.730039i) q^{31} +(1.66324 + 5.40681i) q^{32} +(-0.490953 - 0.425413i) q^{33} +(-0.365081 + 0.377594i) q^{34} +(0.0637479 + 0.0409683i) q^{35} +(5.33523 - 2.65725i) q^{36} +(-1.54589 - 0.453913i) q^{37} +(8.94626 + 0.488533i) q^{38} +(-0.371428 + 0.321845i) q^{39} +(0.460836 - 2.79063i) q^{40} +(-1.65854 + 0.486992i) q^{41} +(0.00883905 - 0.0122318i) q^{42} +(8.92789 + 1.28364i) q^{43} +(-1.61991 - 9.08283i) q^{44} -2.98017 q^{45} +(-1.59608 - 6.59185i) q^{46} -9.97596i q^{47} +(-0.549931 - 0.121944i) q^{48} +(0.995387 - 6.92307i) q^{49} +(-0.828315 + 1.14625i) q^{50} +(-0.0147346 - 0.0501815i) q^{51} +(-6.97605 + 0.235133i) q^{52} +(-4.50859 - 5.20319i) q^{53} +(-0.0649390 + 1.18920i) q^{54} +(-1.29965 + 4.42621i) q^{55} +(0.206863 - 0.0560811i) q^{56} +(-0.482340 + 0.750536i) q^{57} +(-7.87855 + 8.14857i) q^{58} +(8.58147 - 9.90354i) q^{59} +(0.218945 + 0.177163i) q^{60} +(1.74562 + 12.1411i) q^{61} +(6.30770 - 3.58351i) q^{62} +(-0.0938127 - 0.205421i) q^{63} +(-4.98216 - 6.25924i) q^{64} +(3.17462 + 1.44980i) q^{65} +(0.866068 + 0.306509i) q^{66} +(-6.36129 - 9.89836i) q^{67} +(0.285627 - 0.685668i) q^{68} +(0.649228 + 0.186048i) q^{69} +(-0.105085 - 0.0210123i) q^{70} +(-6.65631 - 10.3574i) q^{71} +(-5.65162 + 6.25383i) q^{72} +(-1.14097 + 2.49837i) q^{73} +(2.26964 - 0.200809i) q^{74} +(-0.0584997 - 0.128096i) q^{75} +(-12.0304 + 3.97729i) q^{76} +(-0.346008 + 0.0497484i) q^{77} +(0.322776 - 0.615550i) q^{78} +(0.685921 - 0.791595i) q^{79} +(0.834566 + 3.91197i) q^{80} +(7.42147 + 4.76949i) q^{81} +(1.93201 - 1.49772i) q^{82} +(2.64527 - 9.00898i) q^{83} +(-0.00531956 + 0.0206687i) q^{84} +(-0.280678 + 0.243209i) q^{85} +(-12.4168 + 2.92102i) q^{86} +(-0.317977 - 1.08293i) q^{87} +(6.82366 + 11.1212i) q^{88} +(5.47373 + 0.787004i) q^{89} +(3.92349 - 1.53916i) q^{90} +0.264463i q^{91} +(5.50577 + 7.85408i) q^{92} +0.722383i q^{93} +(5.15227 + 13.1337i) q^{94} +(6.27090 + 0.901619i) q^{95} +(0.786983 - 0.123479i) q^{96} +(-1.20453 - 4.10225i) q^{97} +(2.26508 + 9.62853i) q^{98} +(10.3899 - 9.00286i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.31653	+	0.516468i	−0.930930	+	0.365198i
$2$	−1.31653	+	0.516468i	−0.930930	+	0.365198i
$3$	0.0200411	−	0.139389i	0.0115707	−	0.0804762i	−0.983218	−	0.182435i	$-0.941602\pi$
$3$	0.0200411	−	0.139389i	0.0115707	−	0.0804762i	0.994789	+	0.101959i	$0.0325111\pi$
$4$	1.46652	−	1.35990i	0.733261	−	0.679948i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	0.0456052	+	0.193861i	0.0186182	+	0.0791433i
$7$	−0.0496235	−	0.0572686i	−0.0187559	−	0.0216455i	0.746294	−	0.665616i	$-0.231831\pi$
$7$	−0.0496235	−	0.0572686i	−0.0187559	−	0.0216455i	−0.765050	+	0.643971i	$0.777286\pi$
$8$	−1.22838	+	2.54776i	−0.434298	+	0.900769i
$9$	2.85945	+	0.839611i	0.953150	+	0.279870i
$10$	1.11770	−	0.866458i	0.353447	−	0.273998i
$11$	2.49402	−	3.88077i	0.751975	−	1.17010i	−0.228518	−	0.973540i	$-0.573388\pi$
$11$	2.49402	−	3.88077i	0.751975	−	1.17010i	0.980493	−	0.196556i	$-0.0629756\pi$
$12$	−0.160164	−	0.231671i	−0.0462353	−	0.0668775i
$13$	−2.63757	−	2.28547i	−0.731530	−	0.633874i	0.207291	−	0.978279i	$-0.433535\pi$
$13$	−2.63757	−	2.28547i	−0.731530	−	0.633874i	−0.938821	+	0.344405i	$0.888081\pi$
$14$	0.0949085	+	0.0497671i	0.0253654	+	0.0133008i
$15$	0.0200411	+	0.139389i	0.00517459	+	0.0359901i
$16$	0.301368	−	3.98863i	0.0753421	−	0.997158i
$17$	0.337829	−	0.154281i	0.0819355	−	0.0374187i	−0.374026	−	0.927418i	$-0.622023\pi$
$17$	0.337829	−	0.154281i	0.0819355	−	0.0374187i	0.455961	+	0.890000i	$0.349296\pi$
$18$	−4.19820	+	0.371440i	−0.989524	+	0.0875493i
$19$	−5.76287	−	2.63181i	−1.32209	−	0.603780i	−0.375683	−	0.926748i	$-0.622592\pi$
$19$	−5.76287	−	2.63181i	−1.32209	−	0.603780i	−0.946410	+	0.322969i	$0.895319\pi$
$20$	−1.02399	+	1.71798i	−0.228971	+	0.384151i
$21$	−0.00897712	+	0.00576924i	−0.00195897	+	0.00125895i
$22$	−1.27916	+	6.39724i	−0.272719	+	1.36390i
$23$	−0.651598	+	4.75136i	−0.135868	+	0.990727i
$23$	−0.651598	+	4.75136i	−0.135868	+	0.990727i
$24$	0.330511	+	0.222283i	0.0674653	+	0.0453733i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	4.65282	+	1.64667i	0.912493	+	0.322939i
$27$	0.349838	−	0.766038i	0.0673264	−	0.147424i
$28$	−0.150653	−	0.0165028i	−0.0284708	−	0.00311874i
$29$	7.29043	−	3.32943i	1.35380	−	0.618259i	0.399395	−	0.916779i	$-0.369220\pi$
$29$	7.29043	−	3.32943i	1.35380	−	0.618259i	0.954403	+	0.298520i	$0.0964930\pi$
$30$	−0.0983747	−	0.173160i	−0.0179607	−	0.0316145i
$31$	−5.07753	+	0.730039i	−0.911952	+	0.131119i	−0.582291	−	0.812980i	$-0.697844\pi$
$31$	−5.07753	+	0.730039i	−0.911952	+	0.131119i	−0.329661	+	0.944099i	$0.606934\pi$
$32$	1.66324	+	5.40681i	0.294022	+	0.955799i
$33$	−0.490953	−	0.425413i	−0.0854639	−	0.0740549i
$34$	−0.365081	+	0.377594i	−0.0626109	+	0.0647568i
$35$	0.0637479	+	0.0409683i	0.0107754	+	0.00692490i
$36$	5.33523	−	2.65725i	0.889205	−	0.442875i
$37$	−1.54589	−	0.453913i	−0.254142	−	0.0746229i	0.152180	−	0.988353i	$-0.451371\pi$
$37$	−1.54589	−	0.453913i	−0.254142	−	0.0746229i	−0.406322	+	0.913730i	$0.633189\pi$
$38$	8.94626	+	0.488533i	1.45127	+	0.0792505i
$39$	−0.371428	+	0.321845i	−0.0594762	+	0.0515364i
$40$	0.460836	−	2.79063i	0.0728646	−	0.441238i
$41$	−1.65854	+	0.486992i	−0.259021	+	0.0760553i	−0.408665	−	0.912685i	$-0.634005\pi$
$41$	−1.65854	+	0.486992i	−0.259021	+	0.0760553i	0.149644	+	0.988740i	$0.452187\pi$
$42$	0.00883905	−	0.0122318i	0.00136389	−	0.00188741i
$43$	8.92789	+	1.28364i	1.36149	+	0.195753i	0.784059	−	0.620686i	$-0.213146\pi$
$43$	8.92789	+	1.28364i	1.36149	+	0.195753i	0.577431	+	0.816439i	$0.304055\pi$
$44$	−1.61991	−	9.08283i	−0.244210	−	1.36929i
$45$	−2.98017			−0.444257
$46$	−1.59608	−	6.59185i	−0.235328	−	0.971916i
$47$		−	9.97596i		−	1.45514i	−0.686032	−	0.727572i	$-0.740649\pi$
$47$		−	9.97596i		−	1.45514i	0.686032	−	0.727572i	$-0.259351\pi$
$48$	−0.549931	−	0.121944i	−0.0793757	−	0.0176011i
$49$	0.995387	−	6.92307i	0.142198	−	0.989009i
$50$	−0.828315	+	1.14625i	−0.117141	+	0.162105i
$51$	−0.0147346	−	0.0501815i	−0.00206326	−	0.00702682i
$52$	−6.97605	+	0.235133i	−0.967404	+	0.0326071i
$53$	−4.50859	−	5.20319i	−0.619303	−	0.714713i	0.356272	−	0.934382i	$-0.384048\pi$
$53$	−4.50859	−	5.20319i	−0.619303	−	0.714713i	−0.975574	+	0.219669i	$0.929502\pi$
$54$	−0.0649390	+	1.18920i	−0.00883708	+	0.161829i
$55$	−1.29965	+	4.42621i	−0.175245	+	0.596831i
$56$	0.206863	−	0.0560811i	0.0276433	−	0.00749416i
$57$	−0.482340	+	0.750536i	−0.0638875	+	0.0994109i
$58$	−7.87855	+	8.14857i	−1.03450	+	1.06996i
$59$	8.58147	−	9.90354i	1.11721	−	1.28933i	0.164191	−	0.986429i	$-0.447499\pi$
$59$	8.58147	−	9.90354i	1.11721	−	1.28933i	0.953021	−	0.302903i	$-0.0979559\pi$
$60$	0.218945	+	0.177163i	0.0282657	+	0.0228716i
$61$	1.74562	+	12.1411i	0.223504	+	1.55451i	0.724634	+	0.689134i	$0.242009\pi$
$61$	1.74562	+	12.1411i	0.223504	+	1.55451i	−0.501130	+	0.865372i	$0.667082\pi$
$62$	6.30770	−	3.58351i	0.801079	−	0.455106i
$63$	−0.0938127	−	0.205421i	−0.0118193	−	0.0258806i
$64$	−4.98216	−	6.25924i	−0.622770	−	0.782405i
$65$	3.17462	+	1.44980i	0.393763	+	0.179826i
$66$	0.866068	+	0.306509i	0.106606	+	0.0377287i
$67$	−6.36129	−	9.89836i	−0.777155	−	1.20928i	−0.973488	−	0.228740i	$-0.926539\pi$
$67$	−6.36129	−	9.89836i	−0.777155	−	1.20928i	0.196332	−	0.980537i	$-0.437097\pi$
$68$	0.285627	−	0.685668i	0.0346373	−	0.0831495i
$69$	0.649228	+	0.186048i	0.0781579	+	0.0223976i
$70$	−0.105085	−	0.0210123i	−0.0125601	−	0.00251146i
$71$	−6.65631	−	10.3574i	−0.789959	−	1.22920i	−0.969413	−	0.245434i	$-0.921070\pi$
$71$	−6.65631	−	10.3574i	−0.789959	−	1.22920i	0.179455	−	0.983766i	$-0.442567\pi$
$72$	−5.65162	+	6.25383i	−0.666050	+	0.737021i
$73$	−1.14097	+	2.49837i	−0.133540	+	0.292412i	−0.964575	−	0.263808i	$-0.915021\pi$
$73$	−1.14097	+	2.49837i	−0.133540	+	0.292412i	0.831035	+	0.556220i	$0.187749\pi$
$74$	2.26964	−	0.200809i	0.263841	−	0.0233436i
$75$	−0.0584997	−	0.128096i	−0.00675496	−	0.0147913i
$76$	−12.0304	+	3.97729i	−1.37998	+	0.456226i
$77$	−0.346008	+	0.0497484i	−0.0394313	+	0.00566936i
$78$	0.322776	−	0.615550i	0.0365471	−	0.0696973i
$79$	0.685921	−	0.791595i	0.0771721	−	0.0890614i	−0.715850	−	0.698254i	$-0.753961\pi$
$79$	0.685921	−	0.791595i	0.0771721	−	0.0890614i	0.793023	+	0.609192i	$0.208506\pi$
$80$	0.834566	+	3.91197i	0.0933074	+	0.437371i
$81$	7.42147	+	4.76949i	0.824607	+	0.529943i
$82$	1.93201	−	1.49772i	0.213355	−	0.165396i
$83$	2.64527	−	9.00898i	0.290357	−	0.988864i	−0.677113	−	0.735879i	$-0.736769\pi$
$83$	2.64527	−	9.00898i	0.290357	−	0.988864i	0.967470	−	0.252985i	$-0.0814124\pi$
$84$	−0.00531956	+	0.0206687i	−0.000580412	+	0.00225514i
$85$	−0.280678	+	0.243209i	−0.0304438	+	0.0263797i
$86$	−12.4168	+	2.92102i	−1.33894	+	0.314982i
$87$	−0.317977	−	1.08293i	−0.0340907	−	0.116102i
$88$	6.82366	+	11.1212i	0.727404	+	1.18553i
$89$	5.47373	+	0.787004i	0.580215	+	0.0834223i	0.426172	−	0.904642i	$-0.359862\pi$
$89$	5.47373	+	0.787004i	0.580215	+	0.0834223i	0.154042	+	0.988064i	$0.450771\pi$
$90$	3.92349	−	1.53916i	0.413572	−	0.162242i
$91$			0.264463i			0.0277232i
$92$	5.50577	+	7.85408i	0.574016	+	0.818844i
$93$			0.722383i			0.0749076i
$94$	5.15227	+	13.1337i	0.531416	+	1.35464i
$95$	6.27090	+	0.901619i	0.643381	+	0.0925042i
$96$	0.786983	−	0.123479i	0.0803211	−	0.0126025i
$97$	−1.20453	−	4.10225i	−0.122301	−	0.416520i	0.875468	−	0.483276i	$-0.160553\pi$
$97$	−1.20453	−	4.10225i	−0.122301	−	0.416520i	−0.997769	+	0.0667559i	$0.978735\pi$
$98$	2.26508	+	9.62853i	0.228808	+	0.972629i
$99$	10.3899	−	9.00286i	1.04422	−	0.904821i
$100$	0.498501	−	1.93688i	0.0498501	−	0.193688i
$101$	4.72857	−	16.1040i	0.470510	−	1.60241i	−0.292662	−	0.956216i	$-0.594541\pi$
$101$	4.72857	−	16.1040i	0.470510	−	1.60241i	0.763172	−	0.646195i	$-0.223641\pi$
$102$	0.0453158	+	0.0584557i	0.00448693	+	0.00578798i
$103$	−2.49825	−	1.60553i	−0.246160	−	0.158197i	0.411743	−	0.911300i	$-0.364920\pi$
$103$	−2.49825	−	1.60553i	−0.246160	−	0.158197i	−0.657903	+	0.753103i	$0.728556\pi$
$104$	9.06276	−	3.91247i	0.888677	−	0.383649i
$105$	0.00698810	−	0.00806470i	0.000681969	−	0.000787034i
$106$	8.62300	+	4.52163i	0.837539	+	0.439180i
$107$	7.91546	−	1.13807i	0.765217	−	0.110022i	0.251355	−	0.967895i	$-0.419124\pi$
$107$	7.91546	−	1.13807i	0.765217	−	0.110022i	0.513861	+	0.857873i	$0.328215\pi$
$108$	−0.528687	−	1.59915i	−0.0508730	−	0.153879i
$109$	−0.985048	−	2.15695i	−0.0943505	−	0.206599i	0.856572	−	0.516027i	$-0.172590\pi$
$109$	−0.985048	−	2.15695i	−0.0943505	−	0.206599i	−0.950923	+	0.309428i	$0.899862\pi$
$110$	−0.574961	−	6.49849i	−0.0548204	−	0.619607i
$111$	−0.0942518	+	0.206383i	−0.00894598	+	0.0195890i
$112$	−0.243378	+	0.180671i	−0.0229971	+	0.0170718i
$113$	5.64217	+	8.77939i	0.530771	+	0.825896i	0.998312	−	0.0580754i	$-0.0184964\pi$
$113$	5.64217	+	8.77939i	0.530771	+	0.825896i	−0.467541	+	0.883971i	$0.654860\pi$
$114$	0.247389	−	1.23722i	0.0231701	−	0.115876i
$115$	−0.713409	−	4.74247i	−0.0665257	−	0.442238i
$116$	6.16389	−	14.7969i	0.572303	−	1.37386i
$117$	−5.62310	−	8.74971i	−0.519856	−	0.808911i
$118$	−6.18293	+	17.4704i	−0.569185	+	1.60828i
$119$	−0.0255997	−	0.0116910i	−0.00234672	−	0.00107171i
$120$	−0.379748	−	0.120163i	−0.0346660	−	0.0109693i
$121$	−4.27066	−	9.35145i	−0.388242	−	0.850132i
$122$	−8.56865	−	15.0826i	−0.775769	−	1.36551i
$123$	0.0346422	+	0.240942i	0.00312359	+	0.0217250i
$124$	−6.45353	+	7.97553i	−0.579544	+	0.716224i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	0.229601	+	0.221993i	0.0204545	+	0.0197767i
$127$	2.06724	−	3.21668i	0.183438	−	0.285435i	−0.737340	−	0.675521i	$-0.763919\pi$
$127$	2.06724	−	3.21668i	0.183438	−	0.285435i	0.920778	+	0.390087i	$0.127555\pi$
$128$	9.79188	+	5.66737i	0.865488	+	0.500930i
$129$	0.357849	−	1.21872i	0.0315069	−	0.107303i
$130$	−4.92827	−	0.269120i	−0.432238	−	0.0236034i
$131$	3.61600	+	4.17308i	0.315931	+	0.364604i	0.891398	−	0.453221i	$-0.149725\pi$
$131$	3.61600	+	4.17308i	0.315931	+	0.364604i	−0.575467	+	0.817825i	$0.695180\pi$
$132$	−1.29851	+	0.0437674i	−0.113021	+	0.00380946i
$133$	0.135254	+	0.460631i	0.0117280	+	0.0399418i
$134$	13.4870	+	9.74612i	1.16510	+	0.841937i
$135$	−0.119849	+	0.833569i	−0.0103150	+	0.0717422i
$136$	−0.0219111	+	1.05022i	−0.00187886	+	0.0900558i
$137$			16.5427i			1.41334i	0.707542	+	0.706671i	$0.249804\pi$
$137$			16.5427i			1.41334i	−0.707542	+	0.706671i	$0.750196\pi$
$138$	−0.950818	+	0.0903672i	−0.0809390	+	0.00769256i
$139$	−18.0530			−1.53124			−0.765618	−	0.643296i	$-0.777566\pi$
$139$	−18.0530			−1.53124			−0.765618	+	0.643296i	$0.777566\pi$
$140$	0.149200	−	0.0266096i	0.0126097	−	0.00224892i
$141$	−1.39054	−	0.199929i	−0.117104	−	0.0168371i
$142$	14.1125	+	10.1981i	1.18430	+	0.855807i
$143$	−15.4475	+	4.53580i	−1.29179	+	0.379302i
$144$	4.21065	−	11.1523i	0.350887	−	0.929355i
$145$	−6.05711	+	5.24851i	−0.503015	+	0.435865i
$146$	0.211793	−	3.87845i	0.0175281	−	0.320983i
$147$	−0.945050	−	0.277492i	−0.0779464	−	0.0228871i
$148$	−2.88435	+	1.43657i	−0.237092	+	0.118085i
$149$	12.3913	+	7.96343i	1.01514	+	0.652390i	0.938718	−	0.344686i	$-0.112015\pi$
$149$	12.3913	+	7.96343i	1.01514	+	0.652390i	0.0764202	+	0.997076i	$0.475651\pi$
$150$	0.143175	+	0.138430i	0.0116902	+	0.0113028i
$151$	5.90088	+	5.11314i	0.480207	+	0.416101i	0.861036	−	0.508544i	$-0.169816\pi$
$151$	5.90088	+	5.11314i	0.480207	+	0.416101i	−0.380829	+	0.924645i	$0.624361\pi$
$152$	13.7842	−	11.4495i	1.11805	−	0.928680i
$153$	1.09554	−	0.157515i	0.0885692	−	0.0127343i
$154$	0.429838	−	0.244198i	0.0346373	−	0.0196780i
$155$	4.66618	−	2.13097i	0.374797	−	0.171164i
$156$	−0.107033	+	0.977096i	−0.00856947	+	0.0782303i
$157$	5.08429	−	11.1330i	0.405770	−	0.888513i	−0.590882	−	0.806758i	$-0.701220\pi$
$157$	5.08429	−	11.1330i	0.405770	−	0.888513i	0.996652	−	0.0817552i	$-0.0260526\pi$
$158$	−0.494204	+	1.39642i	−0.0393168	+	0.111093i
$159$	−0.815624	+	0.524170i	−0.0646832	+	0.0415694i
$160$	−3.11914	−	4.71921i	−0.246590	−	0.373086i
$161$	0.304438	−	0.198463i	0.0239931	−	0.0156411i
$162$	−12.2339	−	2.44624i	−0.961186	−	0.192195i
$163$	−8.85067	+	5.68798i	−0.693238	+	0.445517i	−0.839236	−	0.543768i	$-0.816997\pi$
$163$	−8.85067	+	5.68798i	−0.693238	+	0.445517i	0.145998	+	0.989285i	$0.453361\pi$
$164$	−1.77003	+	2.96963i	−0.138216	+	0.231889i
$165$	0.590919	+	0.269864i	0.0460030	+	0.0210088i
$166$	1.17026	+	13.2268i	0.0908297	+	1.02660i
$167$	10.1791	−	4.64863i	0.787681	−	0.359722i	0.0193813	−	0.999812i	$-0.493830\pi$
$167$	10.1791	−	4.64863i	0.787681	−	0.359722i	0.768300	+	0.640090i	$0.221103\pi$
$168$	−0.00367132	−	0.0299584i	−0.000283249	−	0.00231134i
$169$	−0.116680	−	0.811528i	−0.00897539	−	0.0624252i
$170$	0.243912	−	0.465154i	0.0187072	−	0.0356757i
$171$	−14.2689	−	12.3641i	−1.09117	−	0.945507i
$172$	14.8385	−	10.2585i	1.13143	−	0.782204i
$173$	−12.0873	+	18.8082i	−0.918980	+	1.42996i	−0.0161945	+	0.999869i	$0.505155\pi$
$173$	−12.0873	+	18.8082i	−0.918980	+	1.42996i	−0.902785	+	0.430092i	$0.858481\pi$
$174$	0.977926	+	1.26149i	0.0741364	+	0.0956332i
$175$	−0.0727077	−	0.0213489i	−0.00549619	−	0.00161383i
$176$	−14.7273	−	11.1173i	−1.11011	−	0.837995i
$177$	−1.20846	−	1.39464i	−0.0908336	−	0.104828i
$178$	−7.61282	+	1.79089i	−0.570605	+	0.134233i
$179$	−14.2048	+	4.17090i	−1.06172	+	0.311748i	−0.765542	−	0.643386i	$-0.777529\pi$
$179$	−14.2048	+	4.17090i	−1.06172	+	0.311748i	−0.296174	+	0.955134i	$0.595711\pi$
$180$	−4.37048	+	4.05272i	−0.325756	+	0.302072i
$181$	−3.48155	+	24.2147i	−0.258782	+	1.79987i	0.282757	+	0.959192i	$0.408751\pi$
$181$	−3.48155	+	24.2147i	−0.258782	+	1.79987i	−0.541539	+	0.840676i	$0.682158\pi$
$182$	−0.136587	−	0.348174i	−0.0101245	−	0.0258084i
$183$	1.72732			0.127687
$184$	−11.3049	−	7.49660i	−0.833409	−	0.552657i
$185$	1.61115			0.118454
$186$	−0.373088	−	0.951041i	−0.0273561	−	0.0697337i
$187$	0.243821	−	1.69581i	0.0178300	−	0.124010i
$188$	−13.5663	−	14.6300i	−0.989421	−	1.06700i
$189$	−0.0612301	+	0.0179788i	−0.00445384	+	0.00130776i
$190$	−8.72151	+	2.05171i	−0.632725	+	0.148847i
$191$	14.2565	+	16.4529i	1.03157	+	1.19049i	0.981444	+	0.191748i	$0.0614155\pi$
$191$	14.2565	+	16.4529i	1.03157	+	1.19049i	0.0501217	+	0.998743i	$0.484039\pi$
$192$	−0.972317	+	0.569016i	−0.0701709	+	0.0410652i
$193$	9.72347	+	2.85507i	0.699911	+	0.205512i	0.612280	−	0.790641i	$-0.290252\pi$
$193$	9.72347	+	2.85507i	0.699911	+	0.205512i	0.0876303	+	0.996153i	$0.472071\pi$
$194$	3.70448	+	4.77865i	0.265966	+	0.343087i
$195$	0.265709	−	0.413451i	0.0190278	−	0.0296078i
$196$	−7.95489	−	11.5064i	−0.568207	−	0.821889i
$197$	4.21918	+	3.65594i	0.300604	+	0.260475i	0.792081	−	0.610415i	$-0.208997\pi$
$197$	4.21918	+	3.65594i	0.300604	+	0.260475i	−0.491477	+	0.870890i	$0.663543\pi$
$198$	−9.02890	+	17.2186i	−0.641656	+	1.22367i
$199$	−2.35354	−	16.3692i	−0.166838	−	1.16038i	−0.885369	−	0.464889i	$-0.846094\pi$
$199$	−2.35354	−	16.3692i	−0.166838	−	1.16038i	0.718531	−	0.695495i	$-0.244815\pi$
$200$	0.344043	+	2.80742i	0.0243275	+	0.198515i
$201$	−1.50721	+	0.688319i	−0.106310	+	0.0485503i
$202$	2.09190	+	23.6437i	0.147186	+	1.66356i
$203$	−0.552448	−	0.252295i	−0.0387743	−	0.0177076i
$204$	−0.0898503	−	0.0535547i	−0.00629078	−	0.00374958i
$205$	1.45416	−	0.934530i	0.101563	−	0.0652704i
$206$	4.11823	+	0.823464i	0.286931	+	0.0573734i
$207$	−5.85251	+	13.0392i	−0.406777	+	0.906287i
$208$	−9.91076	+	9.83152i	−0.687188	+	0.681693i
$209$	−24.5862	+	15.8006i	−1.70066	+	1.09295i
$210$	−0.00503491	+	0.0142266i	−0.000347442	+	0.000981727i
$211$	6.93305	−	15.1813i	0.477291	−	1.04512i	−0.505909	−	0.862587i	$-0.668843\pi$
$211$	6.93305	−	15.1813i	0.477291	−	1.04512i	0.983200	−	0.182534i	$-0.0584299\pi$
$212$	−13.6877	−	1.49938i	−0.940078	−	0.102978i
$213$	−1.57711	+	0.720242i	−0.108062	+	0.0493502i
$214$	−9.83320	+	5.58640i	−0.672183	+	0.381878i
$215$	−8.92789	+	1.28364i	−0.608877	+	0.0875433i
$216$	1.52195	+	1.83229i	0.103555	+	0.124672i
$217$	0.293773	+	0.254556i	0.0199426	+	0.0172804i
$218$	2.41085	+	2.33096i	0.163283	+	0.157872i
$219$	0.325378	+	0.209108i	0.0219870	+	0.0141302i
$220$	4.11322	+	8.25853i	0.277313	+	0.556790i
$221$	−1.24365	−	0.365169i	−0.0836570	−	0.0245639i
$222$	0.0174956	−	0.320388i	0.00117423	−	0.0215030i
$223$	−17.7603	+	15.3894i	−1.18932	+	1.03055i	−0.190510	+	0.981685i	$0.561014\pi$
$223$	−17.7603	+	15.3894i	−1.18932	+	1.03055i	−0.998806	+	0.0488623i	$0.984440\pi$
$224$	0.227105	−	0.363557i	0.0151741	−	0.0242911i
$225$	2.85945	−	0.839611i	0.190630	−	0.0559740i
$226$	−11.9624	−	8.64436i	−0.795726	−	0.575015i
$227$	−15.2257	−	2.18913i	−1.01057	−	0.145298i	−0.382909	−	0.923786i	$-0.625078\pi$
$227$	−15.2257	−	2.18913i	−1.01057	−	0.145298i	−0.627659	+	0.778488i	$0.715987\pi$
$228$	0.313288	+	1.75661i	0.0207480	+	0.116334i
$229$	−12.7578			−0.843061			−0.421531	−	0.906814i	$-0.638507\pi$
$229$	−12.7578			−0.843061			−0.421531	+	0.906814i	$0.638507\pi$
$230$	3.38856	+	5.87517i	0.223435	+	0.387397i
$231$			0.0492267i			0.00323888i
$232$	−0.472846	+	22.6641i	−0.0310439	+	1.48797i
$233$	−3.24345	+	22.5587i	−0.212485	+	1.47787i	0.552334	+	0.833623i	$0.313737\pi$
$233$	−3.24345	+	22.5587i	−0.212485	+	1.47787i	−0.764819	+	0.644245i	$0.777172\pi$
$234$	11.9219	+	8.61514i	0.779362	+	0.563189i
$235$	2.81055	+	9.57186i	0.183340	+	0.624399i
$236$	−0.882879	−	26.1937i	−0.0574705	−	1.70506i
$237$	−0.0965929	−	0.111474i	−0.00627438	−	0.00724103i
$238$	0.0397409	+	0.00217015i	0.00257602	+	0.000140670i
$239$	5.46723	−	18.6197i	0.353646	−	1.20441i	−0.570156	−	0.821536i	$-0.693117\pi$
$239$	5.46723	−	18.6197i	0.353646	−	1.20441i	0.923802	−	0.382870i	$-0.125064\pi$
$240$	0.562011	−	0.0379291i	0.0362776	−	0.00244832i
$241$	−3.87908	+	6.03597i	−0.249874	+	0.388811i	−0.943420	−	0.331601i	$-0.892411\pi$
$241$	−3.87908	+	6.03597i	−0.249874	+	0.388811i	0.693546	+	0.720412i	$0.256047\pi$
$242$	10.4522	+	10.1058i	0.671893	+	0.649627i
$243$	2.46800	−	2.84823i	0.158322	−	0.182714i
$244$	19.0706	+	15.4313i	1.22087	+	0.987887i
$245$	0.995387	+	6.92307i	0.0635929	+	0.442298i
$246$	−0.170047	−	0.299317i	−0.0108418	−	0.0190837i
$247$	9.18504	+	20.1124i	0.584430	+	1.27972i
$248$	4.37718	−	13.8331i	0.277951	−	0.878403i
$249$	−1.20274	−	0.549272i	−0.0762204	−	0.0348087i
$250$	0.471825	−	1.33318i	0.0298409	−	0.0843180i
$251$	2.12816	+	3.31149i	0.134328	+	0.209019i	0.901901	−	0.431943i	$-0.142172\pi$
$251$	2.12816	+	3.31149i	0.134328	+	0.209019i	−0.767572	+	0.640962i	$0.778536\pi$
$252$	−0.416930	−	0.173679i	−0.0262641	−	0.0109408i
$253$	16.8138	+	14.3787i	1.05708	+	0.903980i
$254$	−1.06027	+	5.30253i	−0.0665274	+	0.332711i
$255$	0.0282755	+	0.0439976i	0.00177068	+	0.00275524i
$256$	−15.8184	−	2.40409i	−0.988647	−	0.150256i
$257$	−0.0627720	+	0.137451i	−0.00391561	+	0.00857399i	−0.911580	−	0.411123i	$-0.865137\pi$
$257$	−0.0627720	+	0.137451i	−0.00391561	+	0.00857399i	0.907664	+	0.419697i	$0.137864\pi$
$258$	0.158311	+	1.78931i	0.00985602	+	0.111397i
$259$	0.0507174	+	0.111056i	0.00315143	+	0.00690066i
$260$	6.62722	−	2.19099i	0.411003	−	0.135879i
$261$	23.6420	−	3.39921i	1.46341	−	0.210406i
$262$	−6.91584	−	3.62645i	−0.427262	−	0.224043i
$263$	9.32331	−	10.7597i	0.574900	−	0.663470i	−0.391601	−	0.920135i	$-0.628078\pi$
$263$	9.32331	−	10.7597i	0.574900	−	0.663470i	0.966500	+	0.256666i	$0.0826239\pi$
$264$	1.68693	−	0.728261i	0.103823	−	0.0448213i
$265$	5.79187	+	3.72221i	0.355792	+	0.228653i
$266$	−0.415967	−	0.536582i	−0.0255046	−	0.0329000i
$267$	0.219399	−	0.747205i	0.0134270	−	0.0457282i
$268$	−22.7897	−	5.86547i	−1.39210	−	0.358290i
$269$	1.88358	−	1.63213i	0.114844	−	0.0995130i	−0.595546	−	0.803321i	$-0.703064\pi$
$269$	1.88358	−	1.63213i	0.114844	−	0.0995130i	0.710390	+	0.703808i	$0.248519\pi$
$270$	−0.272727	−	1.15932i	−0.0165976	−	0.0705540i
$271$	1.49727	+	5.09922i	0.0909525	+	0.309756i	0.992387	−	0.123160i	$-0.0393029\pi$
$271$	1.49727	+	5.09922i	0.0909525	+	0.309756i	−0.901434	+	0.432916i	$0.857485\pi$
$272$	−0.513560	−	1.39397i	−0.0311391	−	0.0845218i
$273$	0.0368632	+	0.00530013i	0.00223106	+	0.000320778i
$274$	−8.54380	−	21.7791i	−0.516150	−	1.31572i
$275$		−	4.61308i		−	0.278179i
$276$	1.20511	−	0.610039i	0.0725393	−	0.0367200i
$277$		−	23.8905i		−	1.43544i	−0.696333	−	0.717719i	$-0.745186\pi$
$277$		−	23.8905i		−	1.43544i	0.696333	−	0.717719i	$-0.254814\pi$
$278$	23.7674	−	9.32380i	1.42547	−	0.559204i
$279$	−15.1319	−	2.17564i	−0.905924	−	0.130252i
$280$	−0.182684	+	0.112090i	−0.0109175	+	0.00669863i
$281$	6.39781	+	21.7889i	0.381661	+	1.29982i	0.896695	+	0.442649i	$0.145961\pi$
$281$	6.39781	+	21.7889i	0.381661	+	1.29982i	−0.515034	+	0.857170i	$0.672221\pi$
$282$	1.93395	−	0.454955i	0.115165	−	0.0270922i
$283$	−10.5750	+	9.16327i	−0.628617	+	0.544700i	−0.909849	−	0.414940i	$-0.863803\pi$
$283$	−10.5750	+	9.16327i	−0.628617	+	0.544700i	0.281231	+	0.959640i	$0.409257\pi$
$284$	−23.8466	−	6.13749i	−1.41504	−	0.364193i
$285$	0.251351	−	0.856024i	0.0148888	−	0.0507065i
$286$	17.9946	−	13.9497i	1.06404	−	0.824862i
$287$	0.110192	+	0.0708161i	0.00650443	+	0.00418014i
$288$	0.216335	+	16.8570i	0.0127476	+	0.993308i
$289$	−11.0423	+	12.7435i	−0.649547	+	0.749618i
$290$	5.26369	−	10.0381i	0.309095	−	0.589460i
$291$	−0.595948	+	0.0856844i	−0.0349351	+	0.00502291i
$292$	1.72427	+	5.21550i	0.100905	+	0.305214i
$293$	5.44594	+	11.9249i	0.318155	+	0.696663i	0.999373	−	0.0354183i	$-0.0112764\pi$
$293$	5.44594	+	11.9249i	0.318155	+	0.696663i	−0.681217	+	0.732081i	$0.738549\pi$
$294$	1.38751	−	0.122761i	0.0809210	−	0.00715958i
$295$	−5.44371	+	11.9201i	−0.316945	+	0.694013i
$296$	3.05540	−	3.38097i	0.177592	−	0.196515i
$297$	−2.10031	−	3.26815i	−0.121873	−	0.189637i
$298$	−20.4265	−	4.08439i	−1.18327	−	0.236602i
$299$	12.5777	−	11.0428i	0.727388	−	0.638623i
$300$	−0.259989	−	0.108303i	−0.0150105	−	0.00625286i
$301$	−0.369521	−	0.574986i	−0.0212989	−	0.0331417i
$302$	−10.4095	−	3.68400i	−0.598998	−	0.211991i
$303$	−2.14996	−	0.981853i	−0.123512	−	0.0564060i
$304$	−12.2341	+	22.1928i	−0.701673	+	1.27285i
$305$	−5.09545	−	11.1575i	−0.291765	−	0.638876i
$306$	−1.36096	+	0.773186i	−0.0778012	+	0.0442001i
$307$	−2.67317	−	18.5923i	−0.152566	−	1.06112i	−0.911899	−	0.410416i	$-0.865384\pi$
$307$	−2.67317	−	18.5923i	−0.152566	−	1.06112i	0.759333	−	0.650703i	$-0.225525\pi$
$308$	−0.439775	+	0.543492i	−0.0250585	+	0.0309683i
$309$	−0.273860	+	0.316051i	−0.0155794	+	0.0179795i
$310$	−5.04260	+	5.21543i	−0.286401	+	0.296217i
$311$	−4.00760	+	6.23594i	−0.227250	+	0.353608i	−0.936090	−	0.351762i	$-0.885583\pi$
$311$	−4.00760	+	6.23594i	−0.227250	+	0.353608i	0.708839	+	0.705370i	$0.249219\pi$
$312$	−0.363727	−	1.34166i	−0.0205920	−	0.0759564i
$313$	2.15708	−	7.34634i	0.121925	−	0.415240i	−0.875798	−	0.482678i	$-0.839664\pi$
$313$	2.15708	−	7.34634i	0.121925	−	0.415240i	0.997723	+	0.0674378i	$0.0214824\pi$
$314$	−0.943775	+	17.2829i	−0.0532603	+	0.975330i
$315$	0.147887	+	0.170670i	0.00833246	+	0.00961617i
$316$	−0.0705689	−	2.09367i	−0.00396981	−	0.117778i
$317$	−9.19105	−	31.3018i	−0.516221	−	1.75809i	−0.642701	−	0.766117i	$-0.722186\pi$
$317$	−9.19105	−	31.3018i	−0.516221	−	1.75809i	0.126480	−	0.991969i	$-0.459632\pi$
$318$	0.803080	−	1.11133i	0.0450345	−	0.0623204i
$319$	5.26172	−	36.5961i	0.294600	−	2.04899i
$320$	6.54378	+	4.60206i	0.365808	+	0.257263i
$321$		−	1.12614i		−	0.0628548i
$322$	−0.298303	+	0.418516i	−0.0166238	+	0.0233230i
$323$	−2.35290			−0.130919
$324$	17.3697	−	3.09787i	0.964986	−	0.172104i
$325$	−3.45448	−	0.496679i	−0.191620	−	0.0275508i
$326$	8.71454	−	12.0595i	0.482654	−	0.667914i
$327$	−0.320397	+	0.0940770i	−0.0177180	+	0.00520247i
$328$	0.796584	−	4.82378i	0.0439840	−	0.266348i
$329$	−0.571309	+	0.495042i	−0.0314973	+	0.0272926i
$330$	−0.917340	−	0.0500936i	−0.0504979	−	0.00275756i
$331$	−0.453645	−	0.133202i	−0.0249346	−	0.00732146i	0.269241	−	0.963073i	$-0.413227\pi$
$331$	−0.453645	−	0.133202i	−0.0249346	−	0.00732146i	−0.294176	+	0.955751i	$0.595045\pi$
$332$	−8.37192	−	16.8092i	−0.459469	−	0.922522i
$333$	−4.03928	−	2.59589i	−0.221351	−	0.142254i
$334$	−11.0002	+	11.3773i	−0.601906	+	0.622536i
$335$	8.89230	+	7.70523i	0.485838	+	0.420981i
$336$	0.0203060	+	0.0375451i	0.00110778	+	0.00204825i
$337$	−20.7608	+	2.98495i	−1.13091	+	0.162600i	−0.682262	−	0.731108i	$-0.739004\pi$
$337$	−20.7608	+	2.98495i	−1.13091	+	0.162600i	−0.448649	+	0.893708i	$0.648095\pi$
$338$	0.572742	+	1.00814i	0.0311530	+	0.0548357i
$339$	1.33683	−	0.610508i	0.0726064	−	0.0331582i
$340$	−0.0808816	+	0.738364i	−0.00438642	+	0.0400434i
$341$	−9.83035	+	21.5255i	−0.532343	+	1.16567i
$342$	25.1712	+	8.90831i	1.36110	+	0.481706i
$343$	−0.892104	+	0.573320i	−0.0481691	+	0.0309564i
$344$	−14.2372	+	21.1693i	−0.767621	+	1.14137i
$345$	−0.675346	+	0.00439688i	−0.0363594	+	0.000236720i
$346$	6.19949	−	31.0043i	0.333287	−	1.66680i
$347$	−3.08555	+	1.98296i	−0.165641	+	0.106451i	−0.620835	−	0.783941i	$-0.713206\pi$
$347$	−3.08555	+	1.98296i	−0.165641	+	0.106451i	0.455194	+	0.890392i	$0.349570\pi$
$348$	−1.93899	−	1.15572i	−0.103941	−	0.0619533i
$349$	20.1883	+	9.21970i	1.08066	+	0.493519i	0.874513	−	0.485002i	$-0.161181\pi$
$349$	20.1883	+	9.21970i	1.08066	+	0.493519i	0.206144	+	0.978522i	$0.433908\pi$
$350$	0.106748	−	0.00944467i	0.00570593	−	0.000504839i
$351$	−2.67348	+	1.22094i	−0.142700	+	0.0651687i
$352$	25.1307	+	7.03004i	1.33947	+	0.374702i
$353$	1.19064	+	8.28111i	0.0633716	+	0.440759i	0.996662	+	0.0816368i	$0.0260148\pi$
$353$	1.19064	+	8.28111i	0.0633716	+	0.440759i	−0.933291	+	0.359122i	$0.883076\pi$
$354$	2.31127	+	1.21196i	0.122843	+	0.0644148i
$355$	9.30471	+	8.06257i	0.493843	+	0.427917i
$356$	9.09759	−	6.28955i	0.482171	−	0.333345i
$357$	−0.00214264	+	0.00333402i	−0.000113401	+	0.000176455i
$358$	16.5470	−	12.8275i	0.874534	−	0.677952i
$359$	8.88137	+	2.60780i	0.468741	+	0.137635i	0.507569	−	0.861611i	$-0.330544\pi$
$359$	8.88137	+	2.60780i	0.468741	+	0.137635i	−0.0388282	+	0.999246i	$0.512363\pi$
$360$	3.66078	−	7.59275i	0.192940	−	0.400173i
$361$	13.8419	+	15.9744i	0.728519	+	0.840756i
$362$	−7.92256	−	33.6776i	−0.416401	−	1.77006i
$363$	−1.38908	+	0.407870i	−0.0729076	+	0.0214076i
$364$	0.359642	+	0.387840i	0.0188504	+	0.0203284i
$365$	0.390877	−	2.71861i	0.0204595	−	0.142299i
$366$	−2.27407	+	0.892104i	−0.118868	+	0.0466310i
$367$	6.47617			0.338053			0.169027	−	0.985612i	$-0.445938\pi$
$367$	6.47617			0.338053			0.169027	+	0.985612i	$0.445938\pi$
$368$	18.7550	+	4.03090i	0.977675	+	0.210125i
$369$	−5.15140			−0.268171
$370$	−2.12113	+	0.832108i	−0.110272	+	0.0432592i
$371$	−0.0742473	+	0.516401i	−0.00385473	+	0.0268102i
$372$	0.982365	+	1.05939i	0.0509332	+	0.0549268i
$373$	9.30713	−	2.73282i	0.481905	−	0.141500i	−0.0317519	−	0.999496i	$-0.510109\pi$
$373$	9.30713	−	2.73282i	0.481905	−	0.141500i	0.513657	+	0.857996i	$0.328290\pi$
$374$	0.554835	+	2.35852i	0.0286898	+	0.121956i
$375$	0.0922190	+	0.106426i	0.00476217	+	0.00549583i
$376$	25.4163	+	12.2543i	1.31075	+	0.631966i
$377$	−26.8383	−	7.88043i	−1.38224	−	0.405863i
$378$	0.0713261	−	0.0552931i	0.00366862	−	0.00284397i
$379$	−13.8562	+	21.5606i	−0.711743	+	1.10749i	0.277430	+	0.960746i	$0.410517\pi$
$379$	−13.8562	+	21.5606i	−0.711743	+	1.10749i	−0.989174	+	0.146749i	$0.953119\pi$
$380$	10.4225	−	7.20553i	0.534664	−	0.369636i
$381$	−0.406940	−	0.352616i	−0.0208482	−	0.0180651i
$382$	−27.2666	−	14.2978i	−1.39508	−	0.731537i
$383$	−2.22250	−	15.4578i	−0.113564	−	0.789856i	−0.964404	−	0.264432i	$-0.914816\pi$
$383$	−2.22250	−	15.4578i	−0.113564	−	0.789856i	0.850840	−	0.525425i	$-0.176093\pi$
$384$	0.986209	−	1.25130i	0.0503273	−	0.0638551i
$385$	0.317977	−	0.145215i	0.0162056	−	0.00740084i
$386$	−14.2758	+	1.26307i	−0.726620	+	0.0642886i
$387$	24.4511	+	11.1664i	1.24292	+	0.567622i
$388$	−7.34510	−	4.37800i	−0.372891	−	0.222259i
$389$	−22.2541	+	14.3019i	−1.12833	+	0.725134i	−0.965211	−	0.261473i	$-0.915792\pi$
$389$	−22.2541	+	14.3019i	−1.12833	+	0.725134i	−0.163119	+	0.986606i	$0.552156\pi$
$390$	−0.136280	+	0.681552i	−0.00690082	+	0.0345117i
$391$	0.512917	+	1.70567i	0.0259393	+	0.0862597i
$392$	16.4156	+	11.0402i	0.829113	+	0.557613i
$393$	0.654150	−	0.420396i	0.0329975	−	0.0212062i
$394$	−7.44287	−	2.63410i	−0.374966	−	0.132704i
$395$	−0.435118	+	0.952776i	−0.0218932	+	0.0479394i
$396$	2.99399	−	27.3320i	0.150454	−	1.37348i
$397$	34.2134	−	15.6247i	1.71712	−	0.784182i	0.721322	−	0.692600i	$-0.243535\pi$
$397$	34.2134	−	15.6247i	1.71712	−	0.784182i	0.995797	−	0.0915826i	$-0.0291926\pi$
$398$	11.5527	+	20.3351i	0.579085	+	1.01931i
$399$	0.0669175	−	0.00962129i	0.00335007	−	0.000481667i
$400$	−1.90289	−	3.51838i	−0.0951445	−	0.175919i
$401$	−13.3419	−	11.5608i	−0.666261	−	0.577318i	0.254678	−	0.967026i	$-0.418031\pi$
$401$	−13.3419	−	11.5608i	−0.666261	−	0.577318i	−0.920939	+	0.389708i	$0.872576\pi$
$402$	1.62880	−	1.68462i	0.0812370	−	0.0840213i
$403$	15.0608	+	9.67900i	0.750233	+	0.482146i
$404$	−14.9653	−	30.0473i	−0.744549	−	1.49491i
$405$	−8.46457	−	2.48542i	−0.420608	−	0.123502i
$406$	0.857619	+	0.0468324i	0.0425629	+	0.00232425i
$407$	−5.61700	+	4.86716i	−0.278424	+	0.241256i
$408$	0.145950	+	0.0241018i	0.00722561	+	0.00119322i
$409$	33.4359	−	9.81768i	1.65330	−	0.485453i	0.683622	−	0.729836i	$-0.260404\pi$
$409$	33.4359	−	9.81768i	1.65330	−	0.485453i	0.969679	+	0.244384i	$0.0785856\pi$
$410$	−1.43179	+	1.98137i	−0.0707112	+	0.0978527i
$411$	2.30587	+	0.331535i	0.113740	+	0.0163534i
$412$	−5.84708	+	1.04282i	−0.288065	+	0.0513759i
$413$	−0.993005			−0.0488626
$414$	0.970692	−	20.1892i	0.0477069	−	0.992243i
$415$			9.38931i			0.460903i
$416$	7.97018	−	18.0621i	0.390770	−	0.885568i
$417$	−0.361802	+	2.51639i	−0.0177175	+	0.123228i
$418$	24.2080	−	33.4999i	1.18405	−	1.63854i
$419$	11.0436	+	37.6111i	0.539516	+	1.83742i	0.546519	+	0.837447i	$0.315953\pi$
$419$	11.0436	+	37.6111i	0.539516	+	1.83742i	−0.00700339	+	0.999975i	$0.502229\pi$
$420$	−0.000718949	−	0.0213301i	−3.50811e−5	−	0.00104080i
$421$	−16.4018	−	18.9287i	−0.799375	−	0.922528i	0.198972	−	0.980005i	$-0.436240\pi$
$421$	−16.4018	−	18.9287i	−0.799375	−	0.922528i	−0.998347	+	0.0574774i	$0.981694\pi$
$422$	−1.28695	+	23.5673i	−0.0626479	+	1.14724i
$423$	8.37592	−	28.5258i	0.407251	−	1.38697i
$424$	18.7948	−	5.09530i	0.912754	−	0.247450i
$425$	0.200789	−	0.312434i	0.00973969	−	0.0151553i
$426$	1.70434	−	1.76275i	0.0825753	−	0.0854055i
$427$	0.608679	−	0.702453i	0.0294560	−	0.0339941i
$428$	10.0605	−	12.4332i	0.486294	−	0.600982i
$429$	0.322655	+	2.24411i	0.0155779	+	0.108347i
$430$	11.0909	−	6.30092i	0.534851	−	0.303857i
$431$	6.30982	+	13.8166i	0.303933	+	0.665521i	0.998548	−	0.0538604i	$-0.0171526\pi$
$431$	6.30982	+	13.8166i	0.303933	+	0.665521i	−0.694615	+	0.719382i	$0.744425\pi$
$432$	−2.95001	−	1.62623i	−0.141933	−	0.0782422i
$433$	−9.73083	−	4.44392i	−0.467634	−	0.213561i	0.167640	−	0.985848i	$-0.446385\pi$
$433$	−9.73083	−	4.44392i	−0.467634	−	0.213561i	−0.635274	+	0.772287i	$0.719113\pi$
$434$	−0.518233	−	0.183407i	−0.0248760	−	0.00880382i
$435$	0.610193	+	0.949479i	0.0292565	+	0.0455240i
$436$	−4.37783	−	1.82366i	−0.209660	−	0.0873373i
$437$	16.2598	−	25.6666i	0.777810	−	1.22780i
$438$	−0.536369	−	0.107250i	−0.0256287	−	0.00512461i
$439$	9.06287	+	14.1021i	0.432547	+	0.673056i	0.987283	−	0.158970i	$-0.0508172\pi$
$439$	9.06287	+	14.1021i	0.432547	+	0.673056i	−0.554736	+	0.832026i	$0.687181\pi$
$440$	−9.68046	−	8.74828i	−0.461498	−	0.417058i
$441$	8.65894	−	18.9604i	0.412330	−	0.902878i
$442$	1.82591	−	0.161549i	0.0868495	−	0.00768411i
$443$	−5.89183	−	12.9013i	−0.279929	−	0.612959i	0.716482	−	0.697606i	$-0.245751\pi$
$443$	−5.89183	−	12.9013i	−0.279929	−	0.612959i	−0.996411	+	0.0846463i	$0.973024\pi$
$444$	0.142437	+	0.430837i	0.00675974	+	0.0204466i
$445$	−5.47373	+	0.787004i	−0.259480	+	0.0373076i
$446$	15.4339	−	29.4332i	0.730815	−	1.39370i
$447$	1.35835	−	1.56762i	0.0642478	−	0.0741459i
$448$	−0.111226	+	0.595927i	−0.00525492	+	0.0281549i
$449$	24.7698	+	15.9186i	1.16896	+	0.751243i	0.973324	−	0.229434i	$-0.0736874\pi$
$449$	24.7698	+	15.9186i	1.16896	+	0.751243i	0.195633	+	0.980677i	$0.437324\pi$
$450$	−3.33093	+	2.58219i	−0.157022	+	0.121726i
$451$	−2.24653	+	7.65098i	−0.105785	+	0.360270i
$452$	20.2134	+	5.20240i	0.950760	+	0.244700i
$453$	0.830975	−	0.720044i	0.0390426	−	0.0338306i
$454$	21.1758	−	4.98155i	0.993830	−	0.233796i
$455$	−0.0745078	−	0.253750i	−0.00349298	−	0.0118960i
$456$	−1.31969	−	2.15083i	−0.0618000	−	0.100722i
$457$	−4.93307	−	0.709268i	−0.230759	−	0.0331782i	0.0259651	−	0.999663i	$-0.491734\pi$
$457$	−4.93307	−	0.709268i	−0.230759	−	0.0331782i	−0.256724	+	0.966485i	$0.582643\pi$
$458$	16.7961	−	6.58901i	0.784831	−	0.307884i
$459$		−	0.312763i		−	0.0145985i
$460$	−7.49550	−	5.98478i	−0.349479	−	0.279042i
$461$			10.1918i			0.474677i	0.971427	+	0.237339i	$0.0762751\pi$
$461$			10.1918i			0.474677i	−0.971427	+	0.237339i	$0.923725\pi$
$462$	−0.0254240	−	0.0648086i	−0.00118283	−	0.00301517i
$463$	22.8778	+	3.28933i	1.06322	+	0.152868i	0.651658	−	0.758513i	$-0.274074\pi$
$463$	22.8778	+	3.28933i	1.06322	+	0.152868i	0.411563	+	0.911381i	$0.364983\pi$
$464$	−11.0827	−	30.0822i	−0.514504	−	1.39653i
$465$	−0.203519	−	0.693121i	−0.00943795	−	0.0321427i
$466$	−7.38073	−	31.3744i	−0.341906	−	1.45339i
$467$	−14.7588	+	12.7885i	−0.682954	+	0.591783i	−0.925678	−	0.378312i	$-0.876505\pi$
$467$	−14.7588	+	12.7885i	−0.682954	+	0.591783i	0.242724	+	0.970095i	$0.421959\pi$
$468$	−20.1451	−	5.18481i	−0.931207	−	0.239668i
$469$	−0.251196	+	0.855494i	−0.0115991	+	0.0395030i
$470$	−8.64375	−	11.1501i	−0.398706	−	0.514317i
$471$	−1.44993	−	0.931812i	−0.0668091	−	0.0429356i
$472$	14.6905	+	34.0289i	0.676187	+	1.56630i
$473$	27.2478	−	31.4456i	1.25286	−	1.44587i
$474$	0.184741	+	0.0968723i	0.00848542	+	0.00444949i
$475$	−6.27090	+	0.901619i	−0.287729	+	0.0413691i
$476$	−0.0534411	+	0.0176678i	−0.00244947	+	0.000809804i
$477$	−8.52344	−	18.6637i	−0.390262	−	0.854554i
$478$	2.41868	+	27.3371i	0.110628	+	1.25037i
$479$	−3.46848	+	7.59492i	−0.158479	+	0.347021i	−0.972170	−	0.234277i	$-0.924728\pi$
$479$	−3.46848	+	7.59492i	−0.158479	+	0.347021i	0.813691	+	0.581298i	$0.197455\pi$
$480$	−0.720317	+	0.340196i	−0.0328778	+	0.0155277i
$481$	3.03998	+	4.73030i	0.138611	+	0.215683i
$482$	1.98955	−	9.94998i	0.0906217	−	0.453209i
$483$	−0.0215623	−	0.0464127i	−0.000981117	−	0.00211185i
$484$	−18.9800	−	7.90644i	−0.862728	−	0.359384i
$485$	2.31147	+	3.59672i	0.104959	+	0.163319i
$486$	−1.77819	+	5.02443i	−0.0806603	+	0.227913i
$487$	22.5672	+	10.3061i	1.02262	+	0.467014i	0.854884	−	0.518819i	$-0.173628\pi$
$487$	22.5672	+	10.3061i	1.02262	+	0.467014i	0.167733	+	0.985832i	$0.446355\pi$
$488$	−33.0768	−	10.4664i	−1.49732	−	0.473794i
$489$	0.615464	+	1.34768i	0.0278322	+	0.0609441i
$490$	−4.88600	−	8.60036i	−0.220727	−	0.388525i
$491$	4.61515	+	32.0991i	0.208279	+	1.44861i	0.778772	+	0.627307i	$0.215843\pi$
$491$	4.61515	+	32.0991i	0.208279	+	1.44861i	−0.570493	+	0.821302i	$0.693248\pi$
$492$	0.378460	+	0.306237i	0.0170623	+	0.0138062i
$493$	1.94925	−	2.24955i	0.0877897	−	0.101315i
$494$	−22.4798	−	21.7349i	−1.01142	−	0.977900i
$495$	−7.43259	+	11.5653i	−0.334070	+	0.519823i
$496$	1.38165	+	20.4724i	0.0620379	+	0.919239i
$497$	−0.262845	+	0.895169i	−0.0117902	+	0.0401538i
$498$	1.86713	+	0.101959i	0.0836679	+	0.00456889i
$499$	5.53301	+	6.38544i	0.247692	+	0.285851i	0.865957	−	0.500118i	$-0.166710\pi$
$499$	5.53301	+	6.38544i	0.247692	+	0.285851i	−0.618266	+	0.785969i	$0.712164\pi$
$500$	0.0673734	+	1.99886i	0.00301303	+	0.0893920i
$501$	−0.443968	−	1.51201i	−0.0198350	−	0.0675518i
$502$	−4.51208	−	3.26055i	−0.201384	−	0.145526i
$503$	3.47782	−	24.1888i	0.155068	−	1.07852i	−0.752492	−	0.658602i	$-0.771148\pi$
$503$	3.47782	−	24.1888i	0.155068	−	1.07852i	0.907560	−	0.419922i	$-0.137943\pi$
$504$	0.638602	+	0.0133233i	0.0284456	+	0.000593468i
$505$			16.7839i			0.746874i
$506$	−29.5621	−	10.2462i	−1.31420	−	0.455499i
$507$	−0.115456			−0.00512760
$508$	−1.34271	−	7.52856i	−0.0595730	−	0.334026i
$509$	−7.24038	−	1.04101i	−0.320924	−	0.0461419i	−0.0200297	−	0.999799i	$-0.506376\pi$
$509$	−7.24038	−	1.04101i	−0.320924	−	0.0461419i	−0.300894	+	0.953657i	$0.597285\pi$
$510$	−0.0599491	−	0.0433209i	−0.00265459	−	0.00191828i
$511$	0.199697	−	0.0586362i	0.00883406	−	0.00259391i
$512$	22.0670	−	5.00461i	0.975234	−	0.221174i
$513$	−4.03214	+	3.49387i	−0.178023	+	0.154258i
$514$	0.0116521	−	0.213379i	0.000513952	−	0.00941175i
$515$	2.84938	+	0.836653i	0.125559	+	0.0368674i
$516$	−1.13254	−	2.27392i	−0.0498574	−	0.100104i
$517$	−38.7144	−	24.8802i	−1.70266	−	1.09423i
$518$	−0.124128	−	0.120014i	−0.00545386	−	0.00527313i
$519$	2.37941	+	2.06177i	0.104445	+	0.0905017i
$520$	−7.59338	+	6.30726i	−0.332992	+	0.276592i
$521$	11.1973	−	1.60993i	0.490562	−	0.0705322i	0.107405	−	0.994215i	$-0.465746\pi$
$521$	11.1973	−	1.60993i	0.490562	−	0.0705322i	0.383157	+	0.923683i	$0.374837\pi$
$522$	−29.3700	+	16.6855i	−1.28549	+	0.730306i
$523$	−1.23731	+	0.565060i	−0.0541037	+	0.0247083i	−0.442283	−	0.896875i	$-0.645831\pi$
$523$	−1.23731	+	0.565060i	−0.0541037	+	0.0247083i	0.388179	+	0.921584i	$0.373104\pi$
$524$	10.9779	+	1.20254i	0.479571	+	0.0525330i
$525$	−0.00443294	+	0.00970679i	−0.000193470	+	0.000423639i
$526$	−6.71742	+	18.9807i	−0.292893	+	0.827596i
$527$	−1.60270	+	1.03000i	−0.0698149	+	0.0448673i
$528$	−1.84477	+	1.83002i	−0.0802835	+	0.0796416i
$529$	−22.1508	−	6.19196i	−0.963080	−	0.269216i
$530$	−9.54759	−	1.90910i	−0.414721	−	0.0829258i
$531$	32.8534	−	21.1136i	1.42572	−	0.916253i
$532$	0.824763	+	0.491595i	0.0357580	+	0.0213133i
$533$	5.48752	+	2.50607i	0.237691	+	0.108550i
$534$	0.0970613	+	1.09703i	0.00420025	+	0.0474733i
$535$	−7.27420	+	3.32202i	−0.314491	+	0.143623i
$536$	33.0327	−	4.04808i	1.42680	−	0.174850i
$537$	0.296698	+	2.06358i	0.0128035	+	0.0890501i
$538$	−1.63686	+	3.12157i	−0.0705698	+	0.134580i
$539$	−24.3843	−	21.1291i	−1.05031	−	0.910095i
$540$	0.957806	+	1.38543i	0.0412174	+	0.0596194i
$541$	−11.8897	+	18.5008i	−0.511179	+	0.795411i	−0.996898	−	0.0787046i	$-0.974922\pi$
$541$	−11.8897	+	18.5008i	−0.511179	+	0.795411i	0.485719	+	0.874115i	$0.338558\pi$
$542$	−4.60479	−	5.94001i	−0.197793	−	0.255145i
$543$	3.30549	+	0.970580i	0.141852	+	0.0416516i
$544$	1.39606	+	1.56997i	0.0598556	+	0.0673119i
$545$	1.55283	+	1.79206i	0.0665160	+	0.0767635i
$546$	−0.0512690	+	0.0120609i	−0.00219411	+	0.000516158i
$547$	1.90532	−	0.559451i	0.0814655	−	0.0239204i	−0.240746	−	0.970588i	$-0.577392\pi$
$547$	1.90532	−	0.559451i	0.0814655	−	0.0239204i	0.322211	+	0.946668i	$0.395574\pi$
$548$	22.4964	+	24.2603i	0.960999	+	1.03635i
$549$	−5.20225	+	36.1825i	−0.222027	+	1.54423i
$550$	2.38251	+	6.07327i	0.101590	+	0.258965i
$551$	−50.7762			−2.16314
$552$	−1.27151	+	1.42554i	−0.0541189	+	0.0606750i
$553$	−0.0793713			−0.00337521
$554$	12.3387	+	31.4526i	0.524220	+	1.33629i
$555$	0.0322892	−	0.224576i	0.00137060	−	0.00953274i
$556$	−26.4751	+	24.5502i	−1.12279	+	1.04116i
$557$	12.9213	−	3.79404i	0.547494	−	0.160759i	0.00372415	−	0.999993i	$-0.498815\pi$
$557$	12.9213	−	3.79404i	0.547494	−	0.160759i	0.543770	+	0.839234i	$0.316996\pi$
$558$	21.0453	−	4.95085i	0.890919	−	0.209586i
$559$	−20.6142	−	23.7901i	−0.871888	−	1.00621i
$560$	0.182619	−	0.241920i	0.00771706	−	0.0102230i
$561$	−0.231491	−	0.0679719i	−0.00977357	−	0.00286978i
$562$	−19.6762	−	25.3816i	−0.829991	−	1.07066i
$563$	−1.99416	+	3.10298i	−0.0840440	+	0.130775i	−0.880731	−	0.473618i	$-0.842948\pi$
$563$	−1.99416	+	3.10298i	−0.0840440	+	0.130775i	0.796687	+	0.604393i	$0.206584\pi$
$564$	−2.31114	+	1.59779i	−0.0973164	+	0.0672789i
$565$	−7.88707	−	6.83418i	−0.331811	−	0.287516i
$566$	9.18978	−	17.5254i	0.386275	−	0.736647i
$567$	−0.0951375	−	0.661696i	−0.00399540	−	0.0277886i
$568$	34.5647	−	4.23582i	1.45030	−	0.177731i
$569$	21.7002	−	9.91014i	0.909718	−	0.415454i	0.0951106	−	0.995467i	$-0.469680\pi$
$569$	21.7002	−	9.91014i	0.909718	−	0.415454i	0.814608	+	0.580012i	$0.196952\pi$
$570$	0.111197	+	1.25680i	0.00465752	+	0.0526416i
$571$	−4.61741	−	2.10870i	−0.193233	−	0.0882464i	0.316449	−	0.948610i	$-0.397509\pi$
$571$	−4.61741	−	2.10870i	−0.193233	−	0.0882464i	−0.509681	+	0.860363i	$0.670237\pi$
$572$	−16.4859	+	27.6588i	−0.689309	+	1.15647i
$573$	2.57907	−	1.65747i	0.107742	−	0.0692417i
$574$	−0.181646	−	0.0363211i	−0.00758175	−	0.00151601i
$575$	2.02062	+	4.34938i	0.0842657	+	0.181382i
$576$	−8.99091	−	22.0811i	−0.374621	−	0.920045i
$577$	27.9495	−	17.9620i	1.16355	−	0.747770i	0.191261	−	0.981539i	$-0.438742\pi$
$577$	27.9495	−	17.9620i	1.16355	−	0.747770i	0.972292	+	0.233769i	$0.0751061\pi$
$578$	7.95595	−	22.4802i	0.330924	−	0.935055i
$579$	0.592834	−	1.29813i	0.0246373	−	0.0539482i
$580$	−1.74545	+	15.9341i	−0.0724757	+	0.661627i
$581$	−0.647200	+	0.295566i	−0.0268504	+	0.0122621i
$582$	0.740332	−	0.420595i	0.0306878	−	0.0174342i
$583$	−31.4369	+	4.51994i	−1.30198	+	0.187197i
$584$	−4.96370	−	5.97585i	−0.205399	−	0.247283i
$585$	7.86040	+	6.81108i	0.324988	+	0.281603i
$586$	−13.3286	−	12.8869i	−0.550600	−	0.532355i
$587$	−19.8030	−	12.7266i	−0.817359	−	0.525284i	0.0638792	−	0.997958i	$-0.479653\pi$
$587$	−19.8030	−	12.7266i	−0.817359	−	0.525284i	−0.881238	+	0.472673i	$0.843289\pi$
$588$	−1.76330	+	0.878222i	−0.0727171	+	0.0362173i
$589$	31.1825	+	9.15600i	1.28485	+	0.377267i
$590$	1.01049	−	18.5047i	0.0416013	−	0.761825i
$591$	0.594154	−	0.514838i	0.0244402	−	0.0211776i
$592$	−2.27637	+	6.02918i	−0.0935584	+	0.247798i
$593$	−41.3971	+	12.1553i	−1.69997	+	0.499157i	−0.980692	−	0.195560i	$-0.937347\pi$
$593$	−41.3971	+	12.1553i	−1.69997	+	0.499157i	−0.719282	+	0.694718i	$0.755529\pi$
$594$	4.45303	+	3.21789i	0.182710	+	0.132032i
$595$	0.0278565	+	0.00400516i	0.00114200	+	0.000164195i
$596$	29.0016	−	5.17239i	1.18795	−	0.211869i
$597$	−2.32886			−0.0953138
$598$	−10.8557	+	21.0342i	−0.443923	+	0.860154i
$599$		−	3.74701i		−	0.153099i	−0.997066	−	0.0765493i	$-0.975610\pi$
$599$		−	3.74701i		−	0.153099i	0.997066	−	0.0765493i	$-0.0243903\pi$
$600$	0.398219	+	0.00830815i	0.0162572	+	0.000339179i
$601$	2.58501	−	17.9791i	0.105445	−	0.733385i	−0.866670	−	0.498881i	$-0.833744\pi$
$601$	2.58501	−	17.9791i	0.105445	−	0.733385i	0.972115	−	0.234504i	$-0.0753465\pi$
$602$	0.783449	+	0.566143i	0.0319310	+	0.0230743i
$603$	−9.87903	−	33.6449i	−0.402305	−	1.37013i
$604$	15.6071	−	0.526050i	0.635044	−	0.0214047i
$605$	6.73228	+	7.76946i	0.273706	+	0.315874i
$606$	3.33759	+	0.182257i	0.135580	+	0.00740370i
$607$	−2.88590e−5	0	9.82848e-5i	−1.17135e−6	0	3.98926e-6i	−0.959494	−	0.281731i	$-0.909092\pi$
$607$	−2.88590e−5	0	9.82848e-5i	−1.17135e−6	0	3.98926e-6i	0.959492	+	0.281735i	$0.0909098\pi$
$608$	4.64470	−	35.5361i	0.188367	−	1.44118i
$609$	−0.0462387	+	0.0719489i	−0.00187369	+	0.00291552i
$610$	12.4708	+	12.0576i	0.504929	+	0.488196i
$611$	−22.7997	+	26.3123i	−0.922378	+	1.06448i
$612$	1.39243	−	1.72082i	0.0562856	−	0.0695600i
$613$	−0.0706365	−	0.491287i	−0.00285298	−	0.0198429i	0.988345	−	0.152229i	$-0.0486452\pi$
$613$	−0.0706365	−	0.491287i	−0.00285298	−	0.0198429i	−0.991198	+	0.132386i	$0.957736\pi$
$614$	13.1216	+	23.0968i	0.529546	+	0.932110i
$615$	−0.101120	−	0.221422i	−0.00407756	−	0.00892861i
$616$	0.298283	−	0.942655i	0.0120182	−	0.0379807i
$617$	35.2689	+	16.1068i	1.41987	+	0.648434i	0.969653	−	0.244485i	$-0.0786188\pi$
$617$	35.2689	+	16.1068i	1.41987	+	0.648434i	0.450219	+	0.892918i	$0.351346\pi$
$618$	0.197316	−	0.557532i	0.00793719	−	0.0224272i
$619$	2.70404	+	4.20756i	0.108684	+	0.169116i	0.891335	−	0.453345i	$-0.149769\pi$
$619$	2.70404	+	4.20756i	0.108684	+	0.169116i	−0.782651	+	0.622461i	$0.786133\pi$
$620$	3.94515	−	9.47064i	0.158441	−	0.380350i
$621$	3.41177	+	2.16136i	0.136910	+	0.0867322i
$622$	2.05547	−	10.2796i	0.0824168	−	0.412175i
$623$	−0.226555	−	0.352527i	−0.00907675	−	0.0141237i
$624$	1.17178	+	1.57848i	0.0469088	+	0.0631900i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	0.954284	+	10.7858i	0.0381408	+	0.431086i
$627$	1.70969	+	3.74370i	0.0682784	+	0.149509i
$628$	−7.68355	−	23.2409i	−0.306607	−	0.927414i
$629$	−0.592275	+	0.0851563i	−0.0236156	+	0.00339540i
$630$	−0.282843	−	0.148314i	−0.0112687	−	0.00590898i
$631$	8.40288	−	9.69744i	0.334513	−	0.386049i	−0.563427	−	0.826166i	$-0.690518\pi$
$631$	8.40288	−	9.69744i	0.334513	−	0.386049i	0.897941	+	0.440117i	$0.145063\pi$
$632$	1.17422	+	2.71994i	0.0467080	+	0.108193i
$633$	−1.97715	−	1.27064i	−0.0785848	−	0.0505034i
$634$	28.2667	+	36.4630i	1.12262	+	1.44813i
$635$	−1.07725	+	3.66879i	−0.0427496	+	0.145592i
$636$	−0.483314	+	1.87787i	−0.0191646	+	0.0744624i
$637$	−18.4478	+	15.9851i	−0.730930	+	0.633354i
$638$	11.9735	+	50.8975i	0.474035	+	2.01505i
$639$	−10.3372	−	35.2053i	−0.408933	−	1.39270i
$640$	−10.9919	−	2.67911i	−0.434494	−	0.105901i
$641$	−35.3206	−	5.07833i	−1.39508	−	0.200582i	−0.596568	−	0.802563i	$-0.703469\pi$
$641$	−35.3206	−	5.07833i	−1.39508	−	0.200582i	−0.798511	+	0.601981i	$0.794378\pi$
$642$	0.581614	+	1.48260i	0.0229545	+	0.0585134i
$643$			29.3597i			1.15783i	0.815387	+	0.578916i	$0.196524\pi$
$643$			29.3597i			1.15783i	−0.815387	+	0.578916i	$0.803476\pi$
$644$	0.176576	−	0.705055i	0.00695808	−	0.0277830i
$645$			1.27017i			0.0500131i
$646$	3.09767	−	1.21520i	0.121876	−	0.0478114i
$647$	17.8462	+	2.56590i	0.701607	+	0.100876i	0.483881	−	0.875134i	$-0.339227\pi$
$647$	17.8462	+	2.56590i	0.701607	+	0.100876i	0.217726	+	0.976010i	$0.430136\pi$
$648$	−21.2679	+	13.0494i	−0.835482	+	0.512627i
$649$	−17.0310	−	58.0023i	−0.668526	−	2.27679i
$650$	4.80446	−	1.13023i	0.188446	−	0.0443314i
$651$	0.0413698	−	0.0358472i	0.00162141	−	0.00140496i
$652$	−5.24463	+	20.3775i	−0.205396	+	0.798045i
$653$	0.349077	−	1.18885i	0.0136604	−	0.0465231i	−0.952381	−	0.304911i	$-0.901373\pi$
$653$	0.349077	−	1.18885i	0.0136604	−	0.0465231i	0.966041	+	0.258388i	$0.0831914\pi$
$654$	0.373226	−	0.289330i	0.0145943	−	0.0113137i
$655$	−4.64521	−	2.98530i	−0.181504	−	0.116645i
$656$	1.44260	+	6.76207i	0.0563240	+	0.264015i
$657$	−5.36019	+	6.18599i	−0.209121	+	0.241338i
$658$	0.496474	−	0.946803i	0.0193546	−	0.0369102i
$659$	−11.7796	+	1.69365i	−0.458868	+	0.0659752i	−0.367873	−	0.929876i	$-0.619914\pi$
$659$	−11.7796	+	1.69365i	−0.458868	+	0.0659752i	−0.0909950	+	0.995851i	$0.529005\pi$
$660$	1.23358	−	0.407827i	0.0480171	−	0.0158746i
$661$	12.6749	+	27.7542i	0.492998	+	1.07951i	0.978682	+	0.205380i	$0.0658432\pi$
$661$	12.6749	+	27.7542i	0.492998	+	1.07951i	−0.485684	+	0.874134i	$0.661430\pi$
$662$	0.666034	−	0.0589281i	0.0258861	−	0.00229031i
$663$	−0.0758246	+	0.166033i	−0.00294478	+	0.00644818i
$664$	19.7033	+	17.8060i	0.764637	+	0.691006i
$665$	−0.259550	−	0.403867i	−0.0100649	−	0.0156613i
$666$	6.65854	+	1.33141i	0.258013	+	0.0515912i
$667$	11.0689	+	36.8089i	0.428588	+	1.42525i
$668$	8.60619	−	20.6598i	0.332983	−	0.799352i
$669$	1.78917	+	2.78400i	0.0691733	+	0.107636i
$670$	−15.6865	−	5.55160i	−0.606023	−	0.214477i
$671$	51.4703	+	23.5057i	1.98699	+	0.907428i
$672$	−0.0461243	−	0.0389420i	−0.00177928	−	0.00150222i
$673$	−5.15003	−	11.2770i	−0.198519	−	0.434696i	0.784024	−	0.620730i	$-0.213164\pi$
$673$	−5.15003	−	11.2770i	−0.198519	−	0.434696i	−0.982543	+	0.186034i	$0.940437\pi$
$674$	25.7906	−	14.6521i	0.993418	−	0.564376i
$675$	−0.119849	−	0.833569i	−0.00461300	−	0.0320841i
$676$	−1.27471	−	1.03145i	−0.0490272	−	0.0396712i
$677$	7.87437	−	9.08751i	0.302637	−	0.349261i	−0.583979	−	0.811769i	$-0.698505\pi$
$677$	7.87437	−	9.08751i	0.302637	−	0.349261i	0.886615	+	0.462508i	$0.153050\pi$
$678$	−1.44467	+	1.49418i	−0.0554821	+	0.0573837i
$679$	−0.175157	+	0.272550i	−0.00672191	+	0.0104595i
$680$	−0.274858	−	1.01385i	−0.0105403	−	0.0388795i
$681$	−0.610281	+	2.07843i	−0.0233860	+	0.0796455i
$682$	1.82477	−	33.4160i	0.0698739	−	1.27957i
$683$	0.0373984	+	0.0431600i	0.00143101	+	0.00165147i	0.756465	−	0.654035i	$-0.226925\pi$
$683$	0.0373984	+	0.0431600i	0.00143101	+	0.00165147i	−0.755034	+	0.655686i	$0.772379\pi$
$684$	−37.7396	+	1.27204i	−1.44301	+	0.0486378i
$685$	−4.66063	−	15.8726i	−0.178073	−	0.606463i
$686$	0.878383	−	1.21554i	0.0335368	−	0.0464095i
$687$	−0.255681	+	1.77830i	−0.00975484	+	0.0678464i
$688$	7.81054	−	35.2232i	0.297774	−	1.34287i
$689$			24.0280i			0.915394i
$690$	0.886844	−	0.354583i	0.0337616	−	0.0134988i
$691$	−0.584062			−0.0222188			−0.0111094	−	0.999938i	$-0.503536\pi$
$691$	−0.584062			−0.0222188			−0.0111094	+	0.999938i	$0.503536\pi$
$692$	7.85091	+	44.0201i	0.298447	+	1.67339i
$693$	−1.03116	−	0.148259i	−0.0391706	−	0.00563189i
$694$	3.03809	−	4.20423i	0.115324	−	0.159590i
$695$	17.3217	−	5.08612i	0.657050	−	0.192927i
$696$	3.14964	+	0.520122i	0.119387	+	0.0197152i
$697$	−0.485169	+	0.420401i	−0.0183771	+	0.0159238i
$698$	−31.3403	−	1.71142i	−1.18625	−	0.0647780i
$699$	3.07943	+	0.904201i	0.116475	+	0.0342000i
$700$	−0.135660	+	0.0675663i	−0.00512745	+	0.00255376i
$701$	26.5442	+	17.0589i	1.00256	+	0.644307i	0.935458	−	0.353439i	$-0.114988\pi$
$701$	26.5442	+	17.0589i	1.00256	+	0.644307i	0.0671037	+	0.997746i	$0.478624\pi$
$702$	2.88915	−	2.98817i	0.109044	−	0.112781i
$703$	7.71413	+	6.68433i	0.290944	+	0.252104i
$704$	−36.7162	+	3.72394i	−1.38380	+	0.140351i
$705$	1.39054	−	0.199929i	0.0523707	−	0.00752977i
$706$	−5.84445	−	10.2874i	−0.219959	−	0.387172i
$707$	−1.15690	+	0.528340i	−0.0435099	+	0.0198703i
$708$	−3.66880	−	0.401886i	−0.137882	−	0.0151038i
$709$	−8.75118	+	19.1624i	−0.328657	+	0.719659i	−0.999765	−	0.0217012i	$-0.993092\pi$
$709$	−8.75118	+	19.1624i	−0.328657	+	0.719659i	0.671107	+	0.741360i	$0.265819\pi$
$710$	−16.4140	−	5.80906i	−0.616007	−	0.218010i
$711$	2.62599	−	1.68762i	0.0984823	−	0.0632907i
$712$	−8.72893	+	12.9790i	−0.327130	+	0.486409i
$713$	−0.160165	−	24.6009i	−0.00599824	−	0.921310i
$714$	0.00109895	−	0.00549595i	4.11270e−5	−	0.000205681i
$715$	13.5439	−	8.70413i	0.506513	−	0.325516i
$716$	−15.1596	+	25.4338i	−0.566542	+	0.950504i
$717$	−2.48581	−	1.13523i	−0.0928342	−	0.0423959i
$718$	−13.0395	+	1.15368i	−0.486628	+	0.0430550i
$719$	−17.9514	+	8.19813i	−0.669474	+	0.305739i	−0.721002	−	0.692933i	$-0.756318\pi$
$719$	−17.9514	+	8.19813i	−0.669474	+	0.305739i	0.0515279	+	0.998672i	$0.483591\pi$
$720$	−0.898129	+	11.8868i	−0.0334713	+	0.442995i
$721$	0.0320256	+	0.222743i	0.00119270	+	0.00829538i
$722$	−26.4735	−	13.8819i	−0.985243	−	0.516631i
$723$	0.763606	+	0.661668i	0.0283988	+	0.0246077i
$724$	27.8237	+	40.2460i	1.03406	+	1.49573i
$725$	4.33307	−	6.74239i	0.160926	−	0.250406i
$726$	1.61811	−	1.25439i	0.0600539	−	0.0465547i
$727$	35.0541	+	10.2928i	1.30008	+	0.381739i	0.857267	−	0.514873i	$-0.172161\pi$
$727$	35.0541	+	10.2928i	1.30008	+	0.381739i	0.442817	+	0.896612i	$0.353979\pi$
$728$	−0.673788	−	0.324861i	−0.0249722	−	0.0120402i
$729$	16.9838	+	19.6004i	0.629031	+	0.725940i
$730$	0.889473	+	3.78102i	0.0329209	+	0.139942i
$731$	3.21414	−	0.943756i	0.118879	−	0.0349061i
$732$	2.53315	−	2.34897i	0.0936277	−	0.0868204i
$733$	3.21326	−	22.3487i	0.118685	−	0.825469i	−0.840322	−	0.542087i	$-0.817634\pi$
$733$	3.21326	−	22.3487i	0.118685	−	0.825469i	0.959007	−	0.283382i	$-0.0914565\pi$
$734$	−8.52609	+	3.34473i	−0.314704	+	0.123456i
$735$	0.984947			0.0363303
$736$	−26.7735	+	4.37958i	−0.986884	+	0.161433i
$737$	−54.2784			−1.99937
$738$	6.78199	−	2.66054i	0.249649	−	0.0979357i
$739$	2.90302	−	20.1910i	0.106789	−	0.742736i	−0.864119	−	0.503287i	$-0.832124\pi$
$739$	2.90302	−	20.1910i	0.106789	−	0.742736i	0.970909	−	0.239450i	$-0.0769670\pi$
$740$	2.36279	−	2.19100i	0.0868577	−	0.0805426i
$741$	2.98753	−	0.877218i	0.109750	−	0.0322254i
$742$	−0.168956	−	0.718206i	−0.00620257	−	0.0263662i
$743$	12.7984	+	14.7701i	0.469528	+	0.541864i	0.940280	−	0.340402i	$-0.110563\pi$
$743$	12.7984	+	14.7701i	0.469528	+	0.541864i	−0.470753	+	0.882265i	$0.656018\pi$
$744$	−1.84046	−	0.887361i	−0.0674744	−	0.0325322i
$745$	−14.1330	−	4.14981i	−0.517792	−	0.152037i
$746$	−10.8417	+	8.40469i	−0.396944	+	0.307717i
$747$	15.1281	−	23.5397i	0.553507	−	0.861274i
$748$	−1.94856	−	2.81852i	−0.0712464	−	0.103055i
$749$	−0.457969	−	0.396832i	−0.0167338	−	0.0144999i
$750$	−0.176375	−	0.0924857i	−0.00644031	−	0.00337710i
$751$	1.51089	+	10.5084i	0.0551330	+	0.383459i	0.998641	+	0.0521098i	$0.0165946\pi$
$751$	1.51089	+	10.5084i	0.0551330	+	0.383459i	−0.943508	+	0.331349i	$0.892496\pi$
$752$	−39.7904	−	3.00644i	−1.45101	−	0.109634i
$753$	0.504235	−	0.230277i	0.0183754	−	0.00839174i
$754$	39.4035	−	3.48627i	1.43499	−	0.126962i
$755$	−7.10239	−	3.24355i	−0.258482	−	0.118045i
$756$	−0.0653460	+	0.109633i	−0.00237661	+	0.00398731i
$757$	−44.8824	+	28.8442i	−1.63128	+	1.04836i	−0.683246	+	0.730188i	$0.739432\pi$
$757$	−44.8824	+	28.8442i	−1.63128	+	1.04836i	−0.948033	+	0.318172i	$0.896931\pi$
$758$	7.10673	−	35.5415i	0.258128	−	1.29093i
$759$	2.34120	−	2.05550i	0.0849800	−	0.0746098i
$760$	−10.0002	+	14.8692i	−0.362744	+	0.539363i
$761$	14.0486	−	9.02849i	0.509261	−	0.327282i	−0.260650	−	0.965433i	$-0.583937\pi$
$761$	14.0486	−	9.02849i	0.509261	−	0.327282i	0.769911	+	0.638151i	$0.220300\pi$
$762$	0.717865	+	0.254059i	0.0260055	+	0.00920358i
$763$	−0.0746442	+	0.163448i	−0.00270230	+	0.00591722i
$764$	43.2817	+	4.74115i	1.56588	+	0.171529i
$765$	−1.00679	+	0.459784i	−0.0364004	+	0.0166235i
$766$	10.9094	+	19.2029i	0.394174	+	0.693827i
$767$	−45.2684	+	6.50862i	−1.63455	+	0.235013i
$768$	−0.652121	+	2.15672i	−0.0235314	+	0.0778240i
$769$	−22.2076	−	19.2430i	−0.800825	−	0.693919i	0.154981	−	0.987918i	$-0.450468\pi$
$769$	−22.2076	−	19.2430i	−0.800825	−	0.693919i	−0.955806	+	0.293998i	$0.905014\pi$
$770$	−0.343628	+	0.355405i	−0.0123835	+	0.0128079i
$771$	0.0179012	+	0.0115044i	0.000644696	+	0.000414321i
$772$	18.1423	−	9.03588i	0.652954	−	0.325209i
$773$	33.3684	+	9.79785i	1.20018	+	0.352404i	0.819921	−	0.572476i	$-0.194017\pi$
$773$	33.3684	+	9.79785i	1.20018	+	0.352404i	0.380257	+	0.924881i	$0.375835\pi$
$774$	−37.9578	−	2.07278i	−1.36437	−	0.0745046i
$775$	−3.87680	+	3.35927i	−0.139259	+	0.120669i
$776$	11.9312	+	1.97028i	0.428304	+	0.0707288i
$777$	0.0164963	−	0.00484377i	0.000591803	−	0.000173769i
$778$	21.9119	−	30.3225i	0.785579	−	1.08711i
$779$	10.8396	+	1.55850i	0.388370	+	0.0558392i
$780$	−0.172583	−	0.967671i	−0.00617945	−	0.0346482i
$781$	−56.7957			−2.03231
$782$	−1.55620	−	1.98067i	−0.0556496	−	0.0708287i
$783$		−	6.74951i		−	0.241208i
$784$	−27.3136	−	6.05662i	−0.975485	−	0.216308i
$785$	−1.74180	+	12.1145i	−0.0621675	+	0.432384i
$786$	−0.644089	+	0.891314i	−0.0229739	+	0.0317921i
$787$	12.4300	+	42.3328i	0.443083	+	1.50900i	0.814293	+	0.580454i	$0.197125\pi$
$787$	12.4300	+	42.3328i	0.443083	+	1.50900i	−0.371210	+	0.928549i	$0.621057\pi$
$788$	11.1592	−	0.376130i	0.397530	−	0.0133991i
$789$	−1.31293	−	1.51520i	−0.0467415	−	0.0539426i
$790$	0.0807692	−	1.47909i	0.00287364	−	0.0526235i
$791$	0.222799	−	0.758784i	0.00792182	−	0.0269793i
$792$	10.1744	+	37.5298i	0.361532	+	1.33356i
$793$	23.1438	−	36.0125i	0.821861	−	1.27884i
$794$	−36.9734	+	38.2406i	−1.31214	+	1.35711i
$795$	0.634910	−	0.732725i	0.0225179	−	0.0259871i
$796$	−25.7120	−	20.8053i	−0.911336	−	0.737423i
$797$	−4.14669	−	28.8409i	−0.146883	−	1.02160i	−0.921281	−	0.388897i	$-0.872856\pi$
$797$	−4.14669	−	28.8409i	−0.146883	−	1.02160i	0.774398	−	0.632699i	$-0.218053\pi$
$798$	−0.0831301	+	0.0472275i	−0.00294277	+	0.00167184i
$799$	−1.53910	−	3.37016i	−0.0544495	−	0.119228i
$800$	4.32235	+	3.64929i	0.152818	+	0.129022i
$801$	14.9911	+	6.84620i	0.529684	+	0.241899i
$802$	23.5358	+	8.32952i	0.831078	+	0.294126i
$803$	6.84999	+	10.6588i	0.241731	+	0.376140i
$804$	−1.27431	+	3.05908i	−0.0449415	+	0.107885i
$805$	−0.236193	+	0.276194i	−0.00832471	+	0.00973456i
$806$	−24.8270	−	4.96430i	−0.874493	−	0.174860i
$807$	−0.189752	−	0.295260i	−0.00667960	−	0.0103937i
$808$	35.2207	+	31.8292i	1.23906	+	1.11975i
$809$	−1.50863	+	3.30344i	−0.0530406	+	0.116143i	−0.934297	−	0.356496i	$-0.883971\pi$
$809$	−1.50863	+	3.30344i	−0.0530406	+	0.116143i	0.881256	+	0.472639i	$0.156699\pi$
$810$	12.4275	−	1.09954i	0.436659	−	0.0386339i
$811$	11.4395	+	25.0490i	0.401695	+	0.879589i	0.997096	+	0.0761602i	$0.0242660\pi$
$811$	11.4395	+	25.0490i	0.401695	+	0.879589i	−0.595401	+	0.803429i	$0.703007\pi$
$812$	−1.15327	+	0.381276i	−0.0404719	+	0.0133802i
$813$	0.740782	−	0.106508i	0.0259804	−	0.00373541i
$814$	4.88124	−	9.30878i	0.171087	−	0.326273i
$815$	6.88966	−	7.95110i	0.241334	−	0.278515i
$816$	−0.204596	+	0.0436479i	−0.00716230	+	0.00152798i
$817$	−48.0720	−	30.8940i	−1.68183	−	1.08084i
$818$	−38.9490	+	30.1939i	−1.36182	+	1.05570i
$819$	−0.222046	+	0.756218i	−0.00775891	+	0.0264244i
$820$	0.861689	−	3.34801i	0.0300915	−	0.116918i
$821$	24.9000	−	21.5760i	0.869016	−	0.753007i	−0.101298	−	0.994856i	$-0.532299\pi$
$821$	24.9000	−	21.5760i	0.869016	−	0.753007i	0.970314	+	0.241849i	$0.0777540\pi$
$822$	−3.20699	+	0.754434i	−0.111857	+	0.0263139i
$823$	−2.45455	−	8.35943i	−0.0855602	−	0.291391i	0.905587	−	0.424161i	$-0.139431\pi$
$823$	−2.45455	−	8.35943i	−0.0855602	−	0.291391i	−0.991147	+	0.132770i	$0.957613\pi$
$824$	7.15930	−	4.39274i	0.249406	−	0.153028i
$825$	−0.643012	−	0.0924511i	−0.0223868	−	0.00321873i
$826$	1.30732	−	0.512856i	0.0454876	−	0.0178445i
$827$			16.4685i			0.572664i	0.958130	+	0.286332i	$0.0924361\pi$
$827$			16.4685i			0.572664i	−0.958130	+	0.286332i	$0.907564\pi$
$828$	9.14912	+	27.0810i	0.317954	+	0.941131i
$829$		−	28.8182i		−	1.00090i	−0.865766	−	0.500449i	$-0.833168\pi$
$829$		−	28.8182i		−	1.00090i	0.865766	−	0.500449i	$-0.166832\pi$
$830$	−4.84928	−	12.3613i	−0.168321	−	0.429069i
$831$	−3.33006	−	0.478791i	−0.115519	−	0.0166091i
$832$	−1.16450	+	27.8957i	−0.0403718	+	0.967111i
$833$	−0.731829	−	2.49238i	−0.0253564	−	0.0863558i
$834$	−0.823310	−	3.49977i	−0.0285089	−	0.121187i
$835$	−8.45709	+	7.32811i	−0.292670	+	0.253600i
$836$	−14.5690	+	56.6065i	−0.503879	+	1.95778i
$837$	−1.21708	+	4.14498i	−0.0420683	+	0.143272i
$838$	−33.9642	−	43.8126i	−1.17327	−	1.51348i
$839$	−25.1320	−	16.1514i	−0.867653	−	0.557607i	0.0293811	−	0.999568i	$-0.490646\pi$
$839$	−25.1320	−	16.1514i	−0.867653	−	0.557607i	−0.897034	+	0.441962i	$0.854283\pi$
$840$	0.0119629	+	0.0277105i	0.000412758	+	0.000956104i
$841$	23.0743	−	26.6291i	0.795665	−	0.918246i
$842$	31.3696	+	16.4492i	1.08107	+	0.566878i
$843$	3.16535	−	0.455109i	0.109021	−	0.0156748i
$844$	−10.4775	−	31.6919i	−0.360649	−	1.09088i
$845$	0.340588	+	0.745783i	0.0117166	+	0.0256557i
$846$	3.70547	+	41.8810i	0.127397	+	1.43990i
$847$	−0.323619	+	0.708627i	−0.0111197	+	0.0243487i
$848$	−22.1124	+	16.4150i	−0.759342	+	0.563694i
$849$	1.06532	+	1.65768i	0.0365618	+	0.0568913i
$850$	−0.102983	+	0.515030i	−0.00353230	+	0.0176654i
$851$	3.16400	−	7.04930i	0.108461	−	0.241647i
$852$	−1.33341	+	3.20095i	−0.0456819	+	0.109663i
$853$	8.27275	+	12.8727i	0.283254	+	0.440751i	0.953502	−	0.301385i	$-0.0974490\pi$
$853$	8.27275	+	12.8727i	0.283254	+	0.440751i	−0.670249	+	0.742136i	$0.733813\pi$
$854$	−0.438551	+	1.23917i	−0.0150069	+	0.0424034i
$855$	17.1743	+	7.84325i	0.587350	+	0.268234i
$856$	−6.82367	+	21.5647i	−0.233228	+	0.737066i
$857$	6.36320	+	13.9335i	0.217363	+	0.475958i	0.986631	−	0.162967i	$-0.0521065\pi$
$857$	6.36320	+	13.9335i	0.217363	+	0.475958i	−0.769269	+	0.638925i	$0.779379\pi$
$858$	−1.58380	−	2.78781i	−0.0540700	−	0.0951742i
$859$	3.30461	+	22.9841i	0.112752	+	0.784206i	0.965222	+	0.261431i	$0.0841942\pi$
$859$	3.30461	+	22.9841i	0.112752	+	0.784206i	−0.852471	+	0.522775i	$0.824897\pi$
$860$	−11.3473	+	14.0235i	−0.386941	+	0.478197i
$861$	0.0120793	−	0.0139403i	0.000411663	−	0.000475084i
$862$	−15.4429	−	14.9312i	−0.525988	−	0.508558i
$863$	29.7276	−	46.2570i	1.01194	−	1.57461i	0.209558	−	0.977796i	$-0.432798\pi$
$863$	29.7276	−	46.2570i	1.01194	−	1.57461i	0.802381	−	0.596812i	$-0.203566\pi$
$864$	4.72369	+	0.617403i	0.160703	+	0.0210045i
$865$	6.29879	−	21.4517i	0.214165	−	0.729380i
$866$	15.1061	+	0.824906i	0.513326	+	0.0280315i
$867$	1.55500	+	1.79457i	0.0528107	+	0.0609468i
$868$	0.776995	−	0.0261892i	0.0263729	−	0.000888921i
$869$	−1.36130	−	4.63615i	−0.0461788	−	0.157271i
$870$	−1.29372	−	0.934876i	−0.0438611	−	0.0316953i
$871$	−5.84403	+	40.6461i	−0.198017	+	1.37724i
$872$	6.70542	+	0.139897i	0.227074	+	0.00473751i
$873$		−	12.7415i		−	0.431235i
$874$	−8.15056	+	42.1886i	−0.275697	+	1.42705i
$875$	0.0757772			0.00256174
$876$	0.761539	−	0.135819i	0.0257300	−	0.00458891i
$877$	−39.7178	−	5.71056i	−1.34117	−	0.192832i	−0.565909	−	0.824468i	$-0.691475\pi$
$877$	−39.7178	−	5.71056i	−1.34117	−	0.192832i	−0.775265	+	0.631636i	$0.782384\pi$
$878$	−19.2149	−	13.8852i	−0.648470	−	0.468603i
$879$	1.77135	−	0.520115i	0.0597461	−	0.0175430i
$880$	17.2629	+	6.51776i	0.581931	+	0.219714i
$881$	11.7150	−	10.1511i	0.394689	−	0.342000i	−0.434796	−	0.900529i	$-0.643180\pi$
$881$	11.7150	−	10.1511i	0.394689	−	0.342000i	0.829485	+	0.558529i	$0.188634\pi$
$882$	−1.60732	+	29.4341i	−0.0541214	+	0.991098i
$883$	−35.1192	−	10.3119i	−1.18185	−	0.347024i	−0.368965	−	0.929443i	$-0.620288\pi$
$883$	−35.1192	−	10.3119i	−1.18185	−	0.347024i	−0.812888	+	0.582420i	$0.802106\pi$
$884$	−2.32043	+	1.15571i	−0.0780446	+	0.0388706i
$885$	1.55243	+	0.997684i	0.0521842	+	0.0335368i
$886$	14.4199	+	13.9421i	0.484446	+	0.468393i
$887$	25.5640	+	22.1513i	0.858354	+	0.743768i	0.968199	−	0.250181i	$-0.0804900\pi$
$887$	25.5640	+	22.1513i	0.858354	+	0.743768i	−0.109845	+	0.993949i	$0.535035\pi$
$888$	−0.410036	−	0.493647i	−0.0137599	−	0.0165657i
$889$	−0.286799	+	0.0412354i	−0.00961892	+	0.00138299i
$890$	6.79989	−	3.86313i	0.227933	−	0.129492i
$891$	37.0185	−	16.9058i	1.24017	−	0.566366i
$892$	−5.11789	+	46.7209i	−0.171359	+	1.56433i
$893$	−26.2549	+	57.4901i	−0.878586	+	1.92383i
$894$	−0.978688	+	2.76537i	−0.0327322	+	0.0924878i
$895$	12.4543	−	8.00391i	0.416302	−	0.267541i
$896$	−0.161345	−	0.842002i	−0.00539016	−	0.0281293i
$897$	−1.28718	−	1.97450i	−0.0429776	−	0.0659268i
$898$	−40.8317	−	8.16452i	−1.36257	−	0.272454i
$899$	−34.5868	+	22.2276i	−1.15353	+	0.741331i
$900$	3.05166	−	5.11986i	0.101722	−	0.170662i
$901$	−2.32589	−	1.06220i	−0.0774865	−	0.0353869i
$902$	−0.993855	−	11.2330i	−0.0330918	−	0.374019i
$903$	−0.0875523	+	0.0399838i	−0.00291356	+	0.00133058i
$904$	−29.2985	+	3.59046i	−0.974455	+	0.119417i
$905$	−3.48155	−	24.2147i	−0.115731	−	0.804925i
$906$	−0.722127	+	1.37713i	−0.0239911	+	0.0457522i
$907$	−4.41919	−	3.82925i	−0.146737	−	0.127148i	0.578399	−	0.815754i	$-0.303678\pi$
$907$	−4.41919	−	3.82925i	−0.146737	−	0.127148i	−0.725136	+	0.688606i	$0.758223\pi$
$908$	−25.3059	+	17.4950i	−0.839804	+	0.580592i
$909$	27.0422	−	42.0785i	0.896935	−	1.39566i
$910$	0.229146	+	0.295590i	0.00759611	+	0.00979870i
$911$	−33.9506	−	9.96879i	−1.12483	−	0.330281i	−0.334158	−	0.942517i	$-0.608452\pi$
$911$	−33.9506	−	9.96879i	−1.12483	−	0.330281i	−0.790675	+	0.612236i	$0.790270\pi$
$912$	2.84825	+	2.15006i	0.0943149	+	0.0711957i
$913$	−28.3644	−	32.7342i	−0.938724	−	1.08335i
$914$	6.86086	−	1.61400i	0.226937	−	0.0533863i
$915$	−1.65735	+	0.486641i	−0.0547902	+	0.0160879i
$916$	−18.7096	+	17.3493i	−0.618183	+	0.573238i
$917$	0.0595481	−	0.414166i	0.00196645	−	0.0136770i
$918$	0.161532	+	0.411763i	0.00533136	+	0.0135902i
$919$	−1.69576			−0.0559380			−0.0279690	−	0.999609i	$-0.508904\pi$
$919$	−1.69576			−0.0559380			−0.0279690	+	0.999609i	$0.508904\pi$
$920$	12.9590	+	4.00797i	0.427246	+	0.132139i
$921$	−2.64513			−0.0871601
$922$	−5.26372	−	13.4178i	−0.173351	−	0.441891i
$923$	−6.11506	+	42.5312i	−0.201280	+	1.39993i
$924$	0.0669432	+	0.0721920i	0.00220227	+	0.00237494i
$925$	−1.54589	+	0.453913i	−0.0508285	+	0.0149246i
$926$	−31.8182	+	7.48514i	−1.04561	+	0.245977i
$927$	−5.79560	−	6.68848i	−0.190352	−	0.219678i
$928$	30.1273	+	33.8803i	0.988977	+	1.11218i
$929$	−13.7548	−	4.03876i	−0.451279	−	0.132508i	0.0481919	−	0.998838i	$-0.484654\pi$
$929$	−13.7548	−	4.03876i	−0.451279	−	0.132508i	−0.499471	+	0.866331i	$0.666472\pi$
$930$	0.625914	+	0.807406i	0.0205245	+	0.0264759i
$931$	−23.9565	+	37.2771i	−0.785143	+	1.22171i
$932$	25.9208	+	37.4935i	0.849066	+	1.22814i
$933$	0.788905	+	0.683590i	0.0258276	+	0.0223797i
$934$	12.8255	−	24.4590i	0.419664	−	0.800322i
$935$	0.243821	+	1.69581i	0.00797381	+	0.0554590i
$936$	29.1995	−	3.57832i	0.954415	−	0.116961i
$937$	53.6544	−	24.5031i	1.75281	−	0.800483i	0.765157	−	0.643843i	$-0.222661\pi$
$937$	53.6544	−	24.5031i	1.75281	−	0.800483i	0.987656	−	0.156640i	$-0.0500662\pi$
$938$	−0.111128	−	1.25602i	−0.00362845	−	0.0410105i
$939$	−0.980769	−	0.447902i	−0.0320062	−	0.0146167i
$940$	17.1385	+	10.2153i	0.558995	+	0.333186i
$941$	−38.3250	+	24.6300i	−1.24936	+	0.802914i	−0.986791	−	0.161999i	$-0.948206\pi$
$941$	−38.3250	+	24.6300i	−1.24936	+	0.802914i	−0.262568	+	0.964914i	$0.584569\pi$
$942$	2.39013	+	0.477920i	0.0778746	+	0.0155715i
$943$	−1.23317	−	8.19765i	−0.0401575	−	0.266952i
$944$	−36.9154	−	37.2129i	−1.20149	−	1.21118i
$945$	0.0536847	−	0.0345011i	0.00174636	−	0.00112232i
$946$	−19.6320	+	55.4719i	−0.638290	+	1.80355i
$947$	16.2764	−	35.6404i	0.528913	−	1.15816i	−0.437041	−	0.899442i	$-0.643973\pi$
$947$	16.2764	−	35.6404i	0.528913	−	1.15816i	0.965954	−	0.258716i	$-0.0832993\pi$
$948$	−0.293249	−	0.0321229i	−0.00952428	−	0.00104330i
$949$	8.71931	−	3.98197i	0.283041	−	0.129260i
$950$	7.79019	−	4.42573i	0.252747	−	0.143590i
$951$	−4.54733	+	0.653807i	−0.147457	+	0.0212011i
$952$	0.0612321	−	0.0508609i	0.00198454	−	0.00164841i
$953$	18.4637	+	15.9989i	0.598097	+	0.518254i	0.900460	−	0.434939i	$-0.143230\pi$
$953$	18.4637	+	15.9989i	0.598097	+	0.518254i	−0.302363	+	0.953193i	$0.597775\pi$
$954$	20.8606	+	20.1693i	0.675388	+	0.653007i
$955$	−18.3144	−	11.7699i	−0.592639	−	0.380866i
$956$	−17.3030	−	34.7410i	−0.559619	−	1.12360i
$957$	−4.99564	−	1.46685i	−0.161486	−	0.0474166i
$958$	0.643840	−	11.7903i	0.0208015	−	0.380928i
$959$	0.947380	−	0.820909i	0.0305925	−	0.0265085i
$960$	0.772621	−	0.819900i	0.0249362	−	0.0264621i
$961$	−4.49589	+	1.32011i	−0.145029	+	0.0425843i
$962$	−6.44529	−	4.65755i	−0.207804	−	0.150165i
$963$	23.5894	+	3.39165i	0.760158	+	0.109294i
$964$	2.51953	+	14.1270i	0.0811487	+	0.455001i
$965$	−10.1340			−0.326224
$966$	0.0523582	+	0.0499677i	0.00168460	+	0.00160768i
$967$			2.02824i			0.0652239i	0.999468	+	0.0326119i	$0.0103825\pi$
$967$			2.02824i			0.0652239i	−0.999468	+	0.0326119i	$0.989617\pi$
$968$	29.0712	+	0.606521i	0.934385	+	0.0194943i
$969$	−0.0471547	+	0.327968i	−0.00151483	+	0.0105359i
$970$	−4.90073	−	3.54140i	−0.157353	−	0.113708i
$971$	−15.2489	−	51.9330i	−0.489361	−	1.66661i	−0.720316	−	0.693646i	$-0.756003\pi$
$971$	−15.2489	−	51.9330i	−0.489361	−	1.66661i	0.230955	−	0.972964i	$-0.425815\pi$
$972$	−0.253913	−	7.53321i	−0.00814427	−	0.241628i
$973$	0.895853	+	1.03387i	0.0287197	+	0.0331443i
$974$	−35.0332	−	1.91308i	−1.12254	−	0.0612989i
$975$	−0.138463	+	0.471562i	−0.00443437	+	0.0151021i
$976$	48.9524	−	3.30371i	1.56693	−	0.105749i
$977$	13.2723	−	20.6521i	0.424618	−	0.660719i	−0.561364	−	0.827569i	$-0.689723\pi$
$977$	13.2723	−	20.6521i	0.424618	−	0.660719i	0.985982	+	0.166850i	$0.0533596\pi$
$978$	−1.50631	−	1.45640i	−0.0481665	−	0.0465704i
$979$	16.7058	−	19.2795i	0.533919	−	0.616175i
$980$	10.8744	+	8.79920i	0.347370	+	0.281080i
$981$	−1.00570	−	6.99476i	−0.0321094	−	0.223326i
$982$	−22.6541	−	39.8759i	−0.722923	−	1.27249i
$983$	1.21004	+	2.64963i	0.0385944	+	0.0845100i	0.927947	−	0.372712i	$-0.121572\pi$
$983$	1.21004	+	2.64963i	0.0385944	+	0.0845100i	−0.889353	+	0.457222i	$0.848845\pi$
$984$	−0.656416	−	0.207709i	−0.0209258	−	0.00662151i
$985$	−5.07827	−	2.31917i	−0.161807	−	0.0738949i
$986$	−1.40443	+	3.96833i	−0.0447261	+	0.126377i
$987$	0.0575537	+	0.0895554i	0.00183196	+	0.00285058i
$988$	40.8209	+	17.0046i	1.29868	+	0.540989i
$989$	−11.9164	+	41.5832i	−0.378920	+	1.32227i
$990$	3.81213	−	19.0649i	0.121157	−	0.605921i
$991$	−8.54831	−	13.3014i	−0.271546	−	0.422534i	0.678520	−	0.734582i	$-0.262621\pi$
$991$	−8.54831	−	13.3014i	−0.271546	−	0.422534i	−0.950066	+	0.312048i	$0.898985\pi$
$992$	−12.3923	−	26.2390i	−0.393457	−	0.833091i
$993$	−0.0276585	+	0.0605636i	−0.000877715	+	0.00192193i
$994$	−0.116282	−	1.31427i	−0.00368823	−	0.0416862i
$995$	6.86995	+	15.0431i	0.217792	+	0.476898i
$996$	−2.51079	+	0.830079i	−0.0795575	+	0.0263020i
$997$	22.4400	−	3.22639i	0.710683	−	0.102181i	0.222514	−	0.974930i	$-0.428574\pi$
$997$	22.4400	−	3.22639i	0.710683	−	0.102181i	0.488170	+	0.872749i	$0.337665\pi$
$998$	−10.5823	−	5.54901i	−0.334976	−	0.175651i
$999$	−0.888525	+	1.02541i	−0.0281117	+	0.0324426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.6	✓	480
8.3	odd	2		920.2.bb.b.11.12	yes	480
23.21	odd	22		920.2.bb.b.251.12	yes	480
184.67	even	22	inner	920.2.bb.a.251.6	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.6	✓	480	1.1	even	1	trivial
920.2.bb.a.251.6	yes	480	184.67	even	22	inner
920.2.bb.b.11.12	yes	480	8.3	odd	2
920.2.bb.b.251.12	yes	480	23.21	odd	22

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31653 + 0.516468i) q^{2} +(0.0200411 - 0.139389i) q^{3} +(1.46652 - 1.35990i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(0.0456052 + 0.193861i) q^{6} +(-0.0496235 - 0.0572686i) q^{7} +(-1.22838 + 2.54776i) q^{8} +(2.85945 + 0.839611i) q^{9} +(1.11770 - 0.866458i) q^{10} +(2.49402 - 3.88077i) q^{11} +(-0.160164 - 0.231671i) q^{12} +(-2.63757 - 2.28547i) q^{13} +(0.0949085 + 0.0497671i) q^{14} +(0.0200411 + 0.139389i) q^{15} +(0.301368 - 3.98863i) q^{16} +(0.337829 - 0.154281i) q^{17} +(-4.19820 + 0.371440i) q^{18} +(-5.76287 - 2.63181i) q^{19} +(-1.02399 + 1.71798i) q^{20} +(-0.00897712 + 0.00576924i) q^{21} +(-1.27916 + 6.39724i) q^{22} +(-0.651598 + 4.75136i) q^{23} +(0.330511 + 0.222283i) q^{24} +(0.841254 - 0.540641i) q^{25} +(4.65282 + 1.64667i) q^{26} +(0.349838 - 0.766038i) q^{27} +(-0.150653 - 0.0165028i) q^{28} +(7.29043 - 3.32943i) q^{29} +(-0.0983747 - 0.173160i) q^{30} +(-5.07753 + 0.730039i) q^{31} +(1.66324 + 5.40681i) q^{32} +(-0.490953 - 0.425413i) q^{33} +(-0.365081 + 0.377594i) q^{34} +(0.0637479 + 0.0409683i) q^{35} +(5.33523 - 2.65725i) q^{36} +(-1.54589 - 0.453913i) q^{37} +(8.94626 + 0.488533i) q^{38} +(-0.371428 + 0.321845i) q^{39} +(0.460836 - 2.79063i) q^{40} +(-1.65854 + 0.486992i) q^{41} +(0.00883905 - 0.0122318i) q^{42} +(8.92789 + 1.28364i) q^{43} +(-1.61991 - 9.08283i) q^{44} -2.98017 q^{45} +(-1.59608 - 6.59185i) q^{46} -9.97596i q^{47} +(-0.549931 - 0.121944i) q^{48} +(0.995387 - 6.92307i) q^{49} +(-0.828315 + 1.14625i) q^{50} +(-0.0147346 - 0.0501815i) q^{51} +(-6.97605 + 0.235133i) q^{52} +(-4.50859 - 5.20319i) q^{53} +(-0.0649390 + 1.18920i) q^{54} +(-1.29965 + 4.42621i) q^{55} +(0.206863 - 0.0560811i) q^{56} +(-0.482340 + 0.750536i) q^{57} +(-7.87855 + 8.14857i) q^{58} +(8.58147 - 9.90354i) q^{59} +(0.218945 + 0.177163i) q^{60} +(1.74562 + 12.1411i) q^{61} +(6.30770 - 3.58351i) q^{62} +(-0.0938127 - 0.205421i) q^{63} +(-4.98216 - 6.25924i) q^{64} +(3.17462 + 1.44980i) q^{65} +(0.866068 + 0.306509i) q^{66} +(-6.36129 - 9.89836i) q^{67} +(0.285627 - 0.685668i) q^{68} +(0.649228 + 0.186048i) q^{69} +(-0.105085 - 0.0210123i) q^{70} +(-6.65631 - 10.3574i) q^{71} +(-5.65162 + 6.25383i) q^{72} +(-1.14097 + 2.49837i) q^{73} +(2.26964 - 0.200809i) q^{74} +(-0.0584997 - 0.128096i) q^{75} +(-12.0304 + 3.97729i) q^{76} +(-0.346008 + 0.0497484i) q^{77} +(0.322776 - 0.615550i) q^{78} +(0.685921 - 0.791595i) q^{79} +(0.834566 + 3.91197i) q^{80} +(7.42147 + 4.76949i) q^{81} +(1.93201 - 1.49772i) q^{82} +(2.64527 - 9.00898i) q^{83} +(-0.00531956 + 0.0206687i) q^{84} +(-0.280678 + 0.243209i) q^{85} +(-12.4168 + 2.92102i) q^{86} +(-0.317977 - 1.08293i) q^{87} +(6.82366 + 11.1212i) q^{88} +(5.47373 + 0.787004i) q^{89} +(3.92349 - 1.53916i) q^{90} +0.264463i q^{91} +(5.50577 + 7.85408i) q^{92} +0.722383i q^{93} +(5.15227 + 13.1337i) q^{94} +(6.27090 + 0.901619i) q^{95} +(0.786983 - 0.123479i) q^{96} +(-1.20453 - 4.10225i) q^{97} +(2.26508 + 9.62853i) q^{98} +(10.3899 - 9.00286i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more