LMFDB - Embedded newform 920.2.bb.a.11.11

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			11.11
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12141 - 0.861644i) q^{2} +(-0.343783 + 2.39106i) q^{3} +(0.515140 + 1.93252i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(2.44577 - 2.38515i) q^{6} +(0.126712 + 0.146233i) q^{7} +(1.08746 - 2.61102i) q^{8} +(-2.72052 - 0.798818i) q^{9} +(1.31874 + 0.510802i) q^{10} +(-1.10464 + 1.71886i) q^{11} +(-4.79787 + 0.567365i) q^{12} +(1.28531 + 1.11373i) q^{13} +(-0.0160955 - 0.273169i) q^{14} +(-0.343783 - 2.39106i) q^{15} +(-3.46926 + 1.99103i) q^{16} +(-3.47889 + 1.58876i) q^{17} +(2.36254 + 3.23993i) q^{18} +(-7.40324 - 3.38094i) q^{19} +(-1.03873 - 1.70911i) q^{20} +(-0.393215 + 0.252704i) q^{21} +(2.71981 - 0.975744i) q^{22} +(4.76299 + 0.560257i) q^{23} +(5.86927 + 3.49781i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.481729 - 2.35643i) q^{26} +(-0.165200 + 0.361738i) q^{27} +(-0.217325 + 0.320204i) q^{28} +(-7.47291 + 3.41276i) q^{29} +(-1.67472 + 2.97759i) q^{30} +(8.02799 - 1.15425i) q^{31} +(5.60604 + 0.756493i) q^{32} +(-3.73015 - 3.23219i) q^{33} +(5.27023 + 1.21591i) q^{34} +(-0.162778 - 0.104611i) q^{35} +(0.142281 - 5.66897i) q^{36} +(-3.88204 - 1.13987i) q^{37} +(5.38892 + 10.1704i) q^{38} +(-3.10487 + 2.69038i) q^{39} +(-0.307799 + 2.81163i) q^{40} +(-7.99476 + 2.34747i) q^{41} +(0.658698 + 0.0554255i) q^{42} +(7.70183 + 1.10736i) q^{43} +(-3.89078 - 1.24929i) q^{44} +2.83538 q^{45} +(-4.85855 - 4.73228i) q^{46} -7.57518i q^{47} +(-3.56802 - 8.97971i) q^{48} +(0.990876 - 6.89169i) q^{49} +(-1.40923 - 0.118579i) q^{50} +(-2.60284 - 8.86445i) q^{51} +(-1.49019 + 3.05762i) q^{52} +(-3.07690 - 3.55093i) q^{53} +(0.496947 - 0.263314i) q^{54} +(0.575640 - 1.96045i) q^{55} +(0.519613 - 0.171825i) q^{56} +(10.6292 - 16.5393i) q^{57} +(11.3208 + 2.61187i) q^{58} +(-5.05100 + 5.82917i) q^{59} +(4.44368 - 1.89610i) q^{60} +(-1.52193 - 10.5853i) q^{61} +(-9.99726 - 5.62288i) q^{62} +(-0.227909 - 0.499051i) q^{63} +(-5.63487 - 5.67875i) q^{64} +(-1.54702 - 0.706501i) q^{65} +(1.39804 + 6.83869i) q^{66} +(5.14671 + 8.00844i) q^{67} +(-4.86242 - 5.90460i) q^{68} +(-2.97705 + 11.1960i) q^{69} +(0.0924041 + 0.257569i) q^{70} +(-8.17755 - 12.7245i) q^{71} +(-5.04419 + 6.23466i) q^{72} +(-3.61351 + 7.91248i) q^{73} +(3.37121 + 4.62320i) q^{74} +(1.00350 + 2.19735i) q^{75} +(2.72004 - 16.0486i) q^{76} +(-0.391327 + 0.0562643i) q^{77} +(5.79999 - 0.341744i) q^{78} +(2.22552 - 2.56839i) q^{79} +(2.76779 - 2.88779i) q^{80} +(-7.96395 - 5.11812i) q^{81} +(10.9881 + 4.25615i) q^{82} +(4.02554 - 13.7097i) q^{83} +(-0.690916 - 0.629718i) q^{84} +(2.89037 - 2.50452i) q^{85} +(-7.68280 - 7.87804i) q^{86} +(-5.59108 - 19.0415i) q^{87} +(3.28673 + 4.75344i) q^{88} +(-7.37940 - 1.06100i) q^{89} +(-3.17963 - 2.44308i) q^{90} +0.329078i q^{91} +(1.37090 + 9.49319i) q^{92} +19.5923i q^{93} +(-6.52711 + 8.49491i) q^{94} +(8.05587 + 1.15826i) q^{95} +(-3.73609 + 13.1443i) q^{96} +(-2.16039 - 7.35762i) q^{97} +(-7.04937 + 6.87466i) q^{98} +(4.37827 - 3.79379i) 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 $

$2$	−1.12141	−	0.861644i	−0.792960	−	0.609274i
$2$	−1.12141	−	0.861644i	−0.792960	−	0.609274i
$3$	−0.343783	+	2.39106i	−0.198483	+	1.38048i	0.610205	+	0.792244i	$0.291087\pi$
$3$	−0.343783	+	2.39106i	−0.198483	+	1.38048i	−0.808688	+	0.588238i	$0.799822\pi$
$4$	0.515140	+	1.93252i	0.257570	+	0.966260i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	2.44577	−	2.38515i	0.998481	−	0.973735i
$7$	0.126712	+	0.146233i	0.0478926	+	0.0552710i	0.779190	−	0.626787i	$-0.215630\pi$
$7$	0.126712	+	0.146233i	0.0478926	+	0.0552710i	−0.731298	+	0.682058i	$0.761085\pi$
$8$	1.08746	−	2.61102i	0.384475	−	0.923136i
$9$	−2.72052	−	0.798818i	−0.906841	−	0.266273i
$10$	1.31874	+	0.510802i	0.417023	+	0.161530i
$11$	−1.10464	+	1.71886i	−0.333063	+	0.518256i	−0.966881	−	0.255226i	$-0.917850\pi$
$11$	−1.10464	+	1.71886i	−0.333063	+	0.518256i	0.633819	+	0.773482i	$0.281487\pi$
$12$	−4.79787	+	0.567365i	−1.38503	+	0.163784i
$13$	1.28531	+	1.11373i	0.356482	+	0.308893i	0.814628	−	0.579984i	$-0.196941\pi$
$13$	1.28531	+	1.11373i	0.356482	+	0.308893i	−0.458147	+	0.888877i	$0.651487\pi$
$14$	−0.0160955	−	0.273169i	−0.00430170	−	0.0730074i
$15$	−0.343783	−	2.39106i	−0.0887644	−	0.617370i
$16$	−3.46926	+	1.99103i	−0.867316	+	0.497759i
$17$	−3.47889	+	1.58876i	−0.843756	+	0.385330i	−0.789913	−	0.613219i	$-0.789874\pi$
$17$	−3.47889	+	1.58876i	−0.843756	+	0.385330i	−0.0538430	+	0.998549i	$0.517147\pi$
$18$	2.36254	+	3.23993i	0.556855	+	0.763658i
$19$	−7.40324	−	3.38094i	−1.69842	−	0.775642i	−0.998087	−	0.0618242i	$-0.980308\pi$
$19$	−7.40324	−	3.38094i	−1.69842	−	0.775642i	−0.700332	−	0.713818i	$-0.746965\pi$
$20$	−1.03873	−	1.70911i	−0.232266	−	0.382168i
$21$	−0.393215	+	0.252704i	−0.0858065	+	0.0551445i
$22$	2.71981	−	0.975744i	0.579865	−	0.208029i
$23$	4.76299	+	0.560257i	0.993153	+	0.116822i
$23$	4.76299	+	0.560257i	0.993153	+	0.116822i
$24$	5.86927	+	3.49781i	1.19806	+	0.713987i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−0.481729	−	2.35643i	−0.0944749	−	0.462135i
$27$	−0.165200	+	0.361738i	−0.0317928	+	0.0696164i
$28$	−0.217325	+	0.320204i	−0.0410705	+	0.0605129i
$29$	−7.47291	+	3.41276i	−1.38768	+	0.633734i	−0.962478	−	0.271361i	$-0.912526\pi$
$29$	−7.47291	+	3.41276i	−1.38768	+	0.633734i	−0.425207	+	0.905096i	$0.639799\pi$
$30$	−1.67472	+	2.97759i	−0.305761	+	0.543631i
$31$	8.02799	−	1.15425i	1.44187	−	0.207310i	0.623420	−	0.781887i	$-0.285743\pi$
$31$	8.02799	−	1.15425i	1.44187	−	0.207310i	0.818450	+	0.574578i	$0.194834\pi$
$32$	5.60604	+	0.756493i	0.991018	+	0.133730i
$33$	−3.73015	−	3.23219i	−0.649335	−	0.562652i
$34$	5.27023	+	1.21591i	0.903836	+	0.208527i
$35$	−0.162778	−	0.104611i	−0.0275145	−	0.0176825i
$36$	0.142281	−	5.66897i	0.0237135	−	0.944828i
$37$	−3.88204	−	1.13987i	−0.638203	−	0.187393i	−0.0534061	−	0.998573i	$-0.517008\pi$
$37$	−3.88204	−	1.13987i	−0.638203	−	0.187393i	−0.584797	+	0.811179i	$0.698826\pi$
$38$	5.38892	+	10.1704i	0.874199	+	1.64986i
$39$	−3.10487	+	2.69038i	−0.497177	+	0.430806i
$40$	−0.307799	+	2.81163i	−0.0486673	+	0.444558i
$41$	−7.99476	+	2.34747i	−1.24857	+	0.366614i	−0.838230	−	0.545317i	$-0.816409\pi$
$41$	−7.99476	+	2.34747i	−1.24857	+	0.366614i	−0.410343	+	0.911931i	$0.634591\pi$
$42$	0.658698	+	0.0554255i	0.101639	+	0.00855234i
$43$	7.70183	+	1.10736i	1.17452	+	0.168870i	0.701820	−	0.712354i	$-0.252371\pi$
$43$	7.70183	+	1.10736i	1.17452	+	0.168870i	0.472698	+	0.881224i	$0.343280\pi$
$44$	−3.89078	−	1.24929i	−0.586557	−	0.188338i
$45$	2.83538			0.422673
$46$	−4.85855	−	4.73228i	−0.716354	−	0.697737i
$47$		−	7.57518i		−	1.10495i	−0.833528	−	0.552477i	$-0.813683\pi$
$47$		−	7.57518i		−	1.10495i	0.833528	−	0.552477i	$-0.186317\pi$
$48$	−3.56802	−	8.97971i	−0.514999	−	1.29611i
$49$	0.990876	−	6.89169i	0.141554	−	0.984527i
$50$	−1.40923	−	0.118579i	−0.199296	−	0.0167696i
$51$	−2.60284	−	8.86445i	−0.364470	−	1.24127i
$52$	−1.49019	+	3.05762i	−0.206652	+	0.424015i
$53$	−3.07690	−	3.55093i	−0.422644	−	0.487757i	0.503996	−	0.863706i	$-0.331862\pi$
$53$	−3.07690	−	3.55093i	−0.422644	−	0.487757i	−0.926641	+	0.375948i	$0.877317\pi$
$54$	0.496947	−	0.263314i	0.0676259	−	0.0358325i
$55$	0.575640	−	1.96045i	0.0776193	−	0.264347i
$56$	0.519613	−	0.171825i	0.0694362	−	0.0229611i
$57$	10.6292	−	16.5393i	1.40787	−	2.19068i
$58$	11.3208	+	2.61187i	1.48650	+	0.342955i
$59$	−5.05100	+	5.82917i	−0.657585	+	0.758893i	−0.982381	−	0.186891i	$-0.940159\pi$
$59$	−5.05100	+	5.82917i	−0.657585	+	0.758893i	0.324796	+	0.945784i	$0.394704\pi$
$60$	4.44368	−	1.89610i	0.573677	−	0.244785i
$61$	−1.52193	−	10.5853i	−0.194863	−	1.35530i	−0.818912	−	0.573919i	$-0.805422\pi$
$61$	−1.52193	−	10.5853i	−0.194863	−	1.35530i	0.624048	−	0.781386i	$-0.285487\pi$
$62$	−9.99726	−	5.62288i	−1.26965	−	0.714106i
$63$	−0.227909	−	0.499051i	−0.0287138	−	0.0628745i
$64$	−5.63487	−	5.67875i	−0.704359	−	0.709844i
$65$	−1.54702	−	0.706501i	−0.191884	−	0.0876307i
$66$	1.39804	+	6.83869i	0.172087	+	0.841784i
$67$	5.14671	+	8.00844i	0.628771	+	0.978386i	0.998781	+	0.0493586i	$0.0157177\pi$
$67$	5.14671	+	8.00844i	0.628771	+	0.978386i	−0.370011	+	0.929028i	$0.620646\pi$
$68$	−4.86242	−	5.90460i	−0.589655	−	0.716038i
$69$	−2.97705	+	11.1960i	−0.358394	+	1.34784i
$70$	0.0924041	+	0.257569i	0.0110444	+	0.0307854i
$71$	−8.17755	−	12.7245i	−0.970497	−	1.51012i	−0.856179	−	0.516679i	$-0.827168\pi$
$71$	−8.17755	−	12.7245i	−0.970497	−	1.51012i	−0.114318	−	0.993444i	$-0.536468\pi$
$72$	−5.04419	+	6.23466i	−0.594463	+	0.734762i
$73$	−3.61351	+	7.91248i	−0.422929	+	0.926085i	0.571493	+	0.820607i	$0.306365\pi$
$73$	−3.61351	+	7.91248i	−0.422929	+	0.926085i	−0.994422	+	0.105478i	$0.966363\pi$
$74$	3.37121	+	4.62320i	0.391896	+	0.537436i
$75$	1.00350	+	2.19735i	0.115874	+	0.253729i
$76$	2.72004	−	16.0486i	0.312010	−	1.84090i
$77$	−0.391327	+	0.0562643i	−0.0445958	+	0.00641191i
$78$	5.79999	−	0.341744i	0.656720	−	0.0386949i
$79$	2.22552	−	2.56839i	0.250391	−	0.288966i	−0.616615	−	0.787265i	$-0.711496\pi$
$79$	2.22552	−	2.56839i	0.250391	−	0.288966i	0.867005	+	0.498299i	$0.166042\pi$
$80$	2.76779	−	2.88779i	0.309449	−	0.322865i
$81$	−7.96395	−	5.11812i	−0.884884	−	0.568680i
$82$	10.9881	+	4.25615i	1.21344	+	0.470013i
$83$	4.02554	−	13.7097i	0.441861	−	1.50484i	−0.374461	−	0.927243i	$-0.622172\pi$
$83$	4.02554	−	13.7097i	0.441861	−	1.50484i	0.816322	−	0.577597i	$-0.196010\pi$
$84$	−0.690916	−	0.629718i	−0.0753851	−	0.0687078i
$85$	2.89037	−	2.50452i	0.313505	−	0.271653i
$86$	−7.68280	−	7.87804i	−0.828457	−	0.849511i
$87$	−5.59108	−	19.0415i	−0.599427	−	2.04146i
$88$	3.28673	+	4.75344i	0.350366	+	0.506718i
$89$	−7.37940	−	1.06100i	−0.782215	−	0.112466i	−0.260373	−	0.965508i	$-0.583846\pi$
$89$	−7.37940	−	1.06100i	−0.782215	−	0.112466i	−0.521841	+	0.853042i	$0.674755\pi$
$90$	−3.17963	−	2.44308i	−0.335163	−	0.257524i
$91$			0.329078i			0.0344968i
$92$	1.37090	+	9.49319i	0.142926	+	0.989733i
$93$			19.5923i			2.03162i
$94$	−6.52711	+	8.49491i	−0.673220	+	0.876183i
$95$	8.05587	+	1.15826i	0.826515	+	0.118835i
$96$	−3.73609	+	13.1443i	−0.381313	+	1.34154i
$97$	−2.16039	−	7.35762i	−0.219355	−	0.747053i	−0.993479	−	0.114019i	$-0.963628\pi$
$97$	−2.16039	−	7.35762i	−0.219355	−	0.747053i	0.774124	−	0.633034i	$-0.218191\pi$
$98$	−7.04937	+	6.87466i	−0.712093	+	0.694445i
$99$	4.37827	−	3.79379i	0.440032	−	0.381290i
$100$	1.47816	+	1.34723i	0.147816	+	0.134723i
$101$	−1.96616	+	6.69612i	−0.195640	+	0.666289i	0.801981	+	0.597350i	$0.203780\pi$
$101$	−1.96616	+	6.69612i	−0.195640	+	0.666289i	−0.997621	+	0.0689390i	$0.978039\pi$
$102$	−4.71914	+	12.1834i	−0.467264	+	1.20634i
$103$	1.27520	+	0.819521i	0.125649	+	0.0807498i	0.601956	−	0.798529i	$-0.294388\pi$
$103$	1.27520	+	0.819521i	0.125649	+	0.0807498i	−0.476307	+	0.879279i	$0.658025\pi$
$104$	4.30570	−	2.14484i	0.422208	−	0.210319i
$105$	0.306092	−	0.353249i	0.0298715	−	0.0344736i
$106$	0.390840	+	6.63325i	0.0379618	+	0.644278i
$107$	−1.93245	+	0.277844i	−0.186817	+	0.0268602i	−0.235088	−	0.971974i	$-0.575538\pi$
$107$	−1.93245	+	0.277844i	−0.186817	+	0.0268602i	0.0482712	+	0.998834i	$0.484629\pi$
$108$	−0.784166	−	0.132907i	−0.0754564	−	0.0127890i
$109$	2.56798	+	5.62308i	0.245968	+	0.538594i	0.991839	−	0.127496i	$-0.0406940\pi$
$109$	2.56798	+	5.62308i	0.245968	+	0.538594i	−0.745872	+	0.666090i	$0.767967\pi$
$110$	−2.33474	+	1.70248i	−0.222609	+	0.162325i
$111$	4.06008	−	8.89034i	0.385366	−	0.843834i
$112$	−0.730753	−	0.255034i	−0.0690497	−	0.0240985i
$113$	0.223206	+	0.347315i	0.0209974	+	0.0326726i	0.851594	−	0.524203i	$-0.175637\pi$
$113$	0.223206	+	0.347315i	0.0209974	+	0.0326726i	−0.830596	+	0.556875i	$0.812000\pi$
$114$	−26.1707	+	9.38885i	−2.45111	+	0.879347i
$115$	−4.72790	+	0.804328i	−0.440879	+	0.0750040i
$116$	−10.4448	−	12.6835i	−0.969778	−	1.17763i
$117$	−2.60706	−	4.05666i	−0.241022	−	0.375038i
$118$	10.6869	−	2.18475i	0.983812	−	0.201122i
$119$	−0.673147	−	0.307416i	−0.0617073	−	0.0281808i
$120$	−6.61697	−	1.70256i	−0.604044	−	0.155422i
$121$	2.83532	+	6.20849i	0.257757	+	0.564408i
$122$	−7.41402	+	13.1818i	−0.671234	+	1.19343i
$123$	−2.86450	−	19.9230i	−0.258283	−	1.79640i
$124$	6.36615	+	14.9197i	0.571697	+	1.33982i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−0.174424	+	0.756019i	−0.0155389	+	0.0673516i
$127$	−6.68361	+	10.3999i	−0.593075	+	0.922842i	0.406882	+	0.913481i	$0.366616\pi$
$127$	−6.68361	+	10.3999i	−0.593075	+	0.922842i	−0.999956	+	0.00936127i	$0.997020\pi$
$128$	1.42596	+	11.2235i	0.126038	+	0.992025i
$129$	−5.29552	+	18.0349i	−0.466245	+	1.58788i
$130$	1.12610	+	2.12526i	0.0987655	+	0.186398i
$131$	1.48539	+	1.71423i	0.129779	+	0.149773i	0.816920	−	0.576751i	$-0.195680\pi$
$131$	1.48539	+	1.71423i	0.129779	+	0.149773i	−0.687141	+	0.726525i	$0.741134\pi$
$132$	4.32473	−	8.87361i	0.376419	−	0.772349i
$133$	−0.443672	−	1.51101i	−0.0384712	−	0.131021i
$134$	1.12883	−	13.4154i	0.0975158	−	1.15891i
$135$	0.0565950	−	0.393627i	0.00487092	−	0.0338780i
$136$	0.365128	+	10.8112i	0.0313095	+	0.927051i
$137$			20.1475i			1.72132i	0.509180	+	0.860660i	$0.329949\pi$
$137$			20.1475i			1.72132i	−0.509180	+	0.860660i	$0.670051\pi$
$138$	12.9855	−	9.99022i	1.10540	−	0.850424i
$139$	−16.2423			−1.37765			−0.688827	−	0.724925i	$-0.741874\pi$
$139$	−16.2423			−1.37765			−0.688827	+	0.724925i	$0.741874\pi$
$140$	0.118309	−	0.368461i	0.00999897	−	0.0311406i
$141$	18.1127	+	2.60422i	1.52537	+	0.219315i
$142$	−1.79358	+	21.3156i	−0.150514	+	1.78877i
$143$	−3.33416	+	0.978997i	−0.278816	+	0.0818679i
$144$	11.0287	−	2.64535i	0.919057	−	0.220446i
$145$	6.20872	−	5.37989i	0.515606	−	0.446775i
$146$	10.8700	−	5.75961i	0.899606	−	0.476669i
$147$	16.1378	+	4.73849i	1.33103	+	0.390824i
$148$	0.203027	−	8.08931i	0.0166887	−	0.664937i
$149$	5.21117	+	3.34902i	0.426916	+	0.274362i	0.736405	−	0.676541i	$-0.236522\pi$
$149$	5.21117	+	3.34902i	0.426916	+	0.274362i	−0.309489	+	0.950903i	$0.600158\pi$
$150$	0.768000	−	3.32880i	0.0627069	−	0.271796i
$151$	15.4957	+	13.4271i	1.26103	+	1.09268i	0.991556	+	0.129676i	$0.0413936\pi$
$151$	15.4957	+	13.4271i	1.26103	+	1.09268i	0.269469	+	0.963009i	$0.413152\pi$
$152$	−16.8784	+	15.6534i	−1.36902	+	1.26966i
$153$	10.7335	−	1.54325i	0.867755	−	0.124764i
$154$	0.487319	+	0.274089i	0.0392693	+	0.0220867i
$155$	−7.37761	+	3.36924i	−0.592584	+	0.270624i
$156$	−6.79866	−	4.61429i	−0.544328	−	0.369439i
$157$	4.04179	−	8.85028i	0.322570	−	0.706329i	−0.676990	−	0.735992i	$-0.736716\pi$
$157$	4.04179	−	8.85028i	0.322570	−	0.706329i	0.999560	+	0.0296627i	$0.00944332\pi$
$158$	−4.70876	+	0.962620i	−0.374609	+	0.0765819i
$159$	9.54828	−	6.13631i	0.757228	−	0.486641i
$160$	−5.59209	+	0.853555i	−0.442093	+	0.0674794i
$161$	0.521600	+	0.767500i	0.0411078	+	0.0604875i
$162$	4.52089	+	12.6016i	0.355195	+	0.990077i
$163$	4.28623	−	2.75459i	0.335723	−	0.215756i	−0.361907	−	0.932214i	$-0.617874\pi$
$163$	4.28623	−	2.75459i	0.335723	−	0.215756i	0.697630	+	0.716458i	$0.254238\pi$
$164$	−8.65496	−	14.2408i	−0.675839	−	1.11202i
$165$	4.48966	+	2.05036i	0.349520	+	0.159620i
$166$	−16.3272	+	11.9057i	−1.26724	+	0.924063i
$167$	5.43697	−	2.48298i	0.420725	−	0.192139i	−0.193791	−	0.981043i	$-0.562078\pi$
$167$	5.43697	−	2.48298i	0.420725	−	0.192139i	0.614517	+	0.788904i	$0.289351\pi$
$168$	0.232210	+	1.30150i	0.0179154	+	0.100413i
$169$	−1.43846	−	10.0047i	−0.110651	−	0.769592i
$170$	−5.39931	+	0.318135i	−0.414108	+	0.0243998i
$171$	17.4399	+	15.1118i	1.33366	+	1.15563i
$172$	1.82753	+	15.4544i	0.139348	+	1.17839i
$173$	−9.50215	+	14.7856i	−0.722435	+	1.12413i	0.264714	+	0.964327i	$0.414723\pi$
$173$	−9.50215	+	14.7856i	−0.722435	+	1.12413i	−0.987149	+	0.159804i	$0.948914\pi$
$174$	−10.1370	+	26.1709i	−0.768487	+	1.98401i
$175$	0.185657	+	0.0545137i	0.0140343	+	0.00412085i
$176$	0.409990	−	8.16256i	0.0309042	−	0.615276i
$177$	−12.2015	−	14.0812i	−0.917119	−	1.05841i
$178$	7.36116	+	7.54823i	0.551742	+	0.565764i
$179$	−9.23790	+	2.71249i	−0.690473	+	0.202741i	−0.608100	−	0.793860i	$-0.708068\pi$
$179$	−9.23790	+	2.71249i	−0.690473	+	0.202741i	−0.0823729	+	0.996602i	$0.526250\pi$
$180$	1.46061	+	5.47942i	0.108868	+	0.408412i
$181$	−1.26580	+	8.80383i	−0.0940861	+	0.654383i	0.887137	+	0.461506i	$0.152691\pi$
$181$	−1.26580	+	8.80383i	−0.0940861	+	0.654383i	−0.981223	+	0.192877i	$0.938218\pi$
$182$	0.283548	−	0.369033i	0.0210180	−	0.0273546i
$183$	25.8333			1.90965
$184$	6.64240	−	11.8270i	0.489684	−	0.871900i
$185$	4.04593			0.297463
$186$	16.8816	−	21.9710i	1.23782	−	1.61099i
$187$	1.11209	−	7.73475i	0.0813240	−	0.565621i
$188$	14.6392	−	3.90228i	1.06767	−	0.284603i
$189$	−0.0738309	+	0.0216787i	−0.00537041	+	0.00157689i
$190$	−8.03596	−	8.24018i	−0.582990	−	0.597806i
$191$	−11.6471	−	13.4414i	−0.842752	−	0.972588i	0.157136	−	0.987577i	$-0.449774\pi$
$191$	−11.6471	−	13.4414i	−0.842752	−	0.972588i	−0.999888	+	0.0149893i	$0.995229\pi$
$192$	15.5154	−	11.5211i	1.11973	−	0.831462i
$193$	−8.10755	−	2.38059i	−0.583594	−	0.171359i	−0.0234088	−	0.999726i	$-0.507452\pi$
$193$	−8.10755	−	2.38059i	−0.583594	−	0.171359i	−0.560185	+	0.828367i	$0.689270\pi$
$194$	−3.91695	+	10.1124i	−0.281221	+	0.726030i
$195$	2.22113	−	3.45615i	0.159058	−	0.247500i
$196$	13.8288	−	1.63530i	0.987769	−	0.116807i
$197$	−7.99133	−	6.92453i	−0.569359	−	0.493352i	0.321945	−	0.946758i	$-0.395663\pi$
$197$	−7.99133	−	6.92453i	−0.569359	−	0.493352i	−0.891304	+	0.453406i	$0.850209\pi$
$198$	−8.17875	+	0.481903i	−0.581238	+	0.0342474i
$199$	−2.76688	−	19.2441i	−0.196139	−	1.36418i	−0.815357	−	0.578959i	$-0.803459\pi$
$199$	−2.76688	−	19.2441i	−0.196139	−	1.36418i	0.619218	−	0.785219i	$-0.287450\pi$
$200$	−0.496797	−	2.78446i	−0.0351288	−	0.196891i
$201$	−20.9180	+	9.55295i	−1.47544	+	0.673813i
$202$	7.97455	−	5.81500i	0.561087	−	0.409142i
$203$	−1.44597	−	0.660351i	−0.101487	−	0.0463476i
$204$	15.7899	−	9.59646i	1.10551	−	0.671887i
$205$	7.00956	−	4.50477i	0.489569	−	0.314627i
$206$	−0.723892	−	2.01779i	−0.0504359	−	0.140586i
$207$	−12.5103	−	5.32895i	−0.869525	−	0.370388i
$208$	−6.67656	−	1.30472i	−0.462936	−	0.0904659i
$209$	13.9893	−	8.99039i	0.967661	−	0.621878i
$210$	−0.647631	+	0.132396i	−0.0446908	+	0.00913620i
$211$	−8.85864	+	19.3977i	−0.609854	+	1.33539i	0.312820	+	0.949813i	$0.398727\pi$
$211$	−8.85864	+	19.3977i	−0.609854	+	1.33539i	−0.922674	+	0.385582i	$0.874001\pi$
$212$	5.27721	−	7.77539i	0.362440	−	0.534016i
$213$	33.2365	−	15.1786i	2.27732	−	1.04002i
$214$	2.40648	+	1.35351i	0.164504	+	0.0925237i
$215$	−7.70183	+	1.10736i	−0.525261	+	0.0755211i
$216$	0.764856	+	0.824715i	0.0520419	+	0.0561148i
$217$	1.18603	+	1.02770i	0.0805132	+	0.0697650i
$218$	1.96533	−	8.51849i	0.133109	−	0.576945i
$219$	−17.6770	−	11.3603i	−1.19450	−	0.767658i
$220$	4.08514	+	0.102530i	0.275420	+	0.00691256i
$221$	−6.24091	−	1.83250i	−0.419809	−	0.123267i
$222$	−12.2133	+	6.47141i	−0.819706	+	0.434332i
$223$	3.65567	−	3.16766i	0.244802	−	0.212122i	−0.523814	−	0.851833i	$-0.675491\pi$
$223$	3.65567	−	3.16766i	0.244802	−	0.212122i	0.768616	+	0.639711i	$0.220946\pi$
$224$	0.599728	+	0.915648i	0.0400710	+	0.0611793i
$225$	−2.72052	+	0.798818i	−0.181368	+	0.0532545i
$226$	0.0489557	−	0.581808i	0.00325648	−	0.0387013i
$227$	20.6718	+	2.97216i	1.37204	+	0.197269i	0.788608	−	0.614896i	$-0.210802\pi$
$227$	20.6718	+	2.97216i	1.37204	+	0.197269i	0.583428	+	0.812165i	$0.301711\pi$
$228$	37.4380	+	12.0210i	2.47939	+	0.796111i
$229$	2.87458			0.189958			0.0949788	−	0.995479i	$-0.469722\pi$
$229$	2.87458			0.189958			0.0949788	+	0.995479i	$0.469722\pi$
$230$	5.99498	+	3.17178i	0.395297	+	0.209141i
$231$		−	0.955030i		−	0.0628363i
$232$	0.784321	+	23.2232i	0.0514932	+	1.52468i
$233$	−2.16130	+	15.0322i	−0.141591	+	0.984790i	0.787862	+	0.615852i	$0.211188\pi$
$233$	−2.16130	+	15.0322i	−0.141591	+	0.984790i	−0.929454	+	0.368939i	$0.879721\pi$
$234$	−0.571805	+	6.79555i	−0.0373801	+	0.444239i
$235$	2.13417	+	7.26833i	0.139218	+	0.474134i
$236$	−13.8670	−	6.75833i	−0.902662	−	0.439930i
$237$	5.37608	+	6.20433i	0.349214	+	0.403015i
$238$	0.489994	+	0.924754i	0.0317616	+	0.0599429i
$239$	−5.14879	+	17.5352i	−0.333048	+	1.13426i	0.607422	+	0.794379i	$0.292204\pi$
$239$	−5.14879	+	17.5352i	−0.333048	+	1.13426i	−0.940470	+	0.339877i	$0.889614\pi$
$240$	5.95337	+	7.61074i	0.384288	+	0.491271i
$241$	−8.78866	+	13.6754i	−0.566128	+	0.880912i	−0.999797	−	0.0201604i	$-0.993582\pi$
$241$	−8.78866	+	13.6754i	−0.566128	+	0.880912i	0.433669	+	0.901072i	$0.357219\pi$
$242$	2.16994	−	9.40533i	0.139489	−	0.604597i
$243$	14.1944	−	16.3812i	0.910569	−	1.05085i
$244$	19.6722	−	8.39406i	1.25939	−	0.537374i
$245$	0.990876	+	6.89169i	0.0633047	+	0.440294i
$246$	−13.9543	+	24.8101i	−0.889691	+	1.58184i
$247$	−5.75001	−	12.5908i	−0.365865	−	0.801132i
$248$	5.71633	−	22.2165i	0.362988	−	1.41075i
$249$	31.3970	+	14.3385i	1.98970	+	0.908666i
$250$	1.38556	−	0.283252i	0.0876303	−	0.0179144i
$251$	6.16942	+	9.59980i	0.389410	+	0.605934i	0.979510	−	0.201396i	$-0.0645479\pi$
$251$	6.16942	+	9.59980i	0.389410	+	0.605934i	−0.590100	+	0.807330i	$0.700912\pi$
$252$	0.847021	−	0.697520i	0.0533573	−	0.0439396i
$253$	−6.22442	+	7.56804i	−0.391326	+	0.475799i
$254$	16.4561	−	5.90371i	1.03255	−	0.370431i
$255$	4.99481	+	7.77207i	0.312787	+	0.486706i
$256$	8.07156	−	13.8148i	0.504472	−	0.863428i
$257$	3.81795	−	8.36015i	0.238157	−	0.521492i	−0.752381	−	0.658728i	$-0.771095\pi$
$257$	3.81795	−	8.36015i	0.238157	−	0.521492i	0.990538	+	0.137236i	$0.0438219\pi$
$258$	21.4781	−	15.6617i	1.33717	−	0.975057i
$259$	−0.325214	−	0.712119i	−0.0202078	−	0.0442489i
$260$	0.568395	−	3.35360i	0.0352504	−	0.207981i
$261$	23.0564	−	3.31501i	1.42716	−	0.205194i
$262$	−0.188681	−	3.20225i	−0.0116567	−	0.197835i
$263$	−14.2246	+	16.4160i	−0.877124	+	1.01225i	0.122680	+	0.992446i	$0.460851\pi$
$263$	−14.2246	+	16.4160i	−0.877124	+	1.01225i	−0.999804	+	0.0198085i	$0.993694\pi$
$264$	−12.4957	+	6.22462i	−0.769057	+	0.383099i
$265$	3.95267	+	2.54023i	0.242811	+	0.156045i
$266$	−0.804410	+	2.07675i	−0.0493215	+	0.127334i
$267$	5.07383	−	17.2799i	0.310513	−	1.05751i
$268$	−12.8252	+	14.0716i	−0.783423	+	0.859558i
$269$	−1.50816	+	1.30683i	−0.0919544	+	0.0796789i	−0.699625	−	0.714510i	$-0.746650\pi$
$269$	−1.50816	+	1.30683i	−0.0919544	+	0.0796789i	0.607671	+	0.794189i	$0.292104\pi$
$270$	−0.402633	+	0.392654i	−0.0245034	+	0.0238962i
$271$	2.89614	+	9.86334i	0.175928	+	0.599155i	0.999490	+	0.0319294i	$0.0101652\pi$
$271$	2.89614	+	9.86334i	0.175928	+	0.599155i	−0.823562	+	0.567226i	$0.808017\pi$
$272$	8.90593	−	12.4384i	0.540001	−	0.754190i
$273$	−0.786848	−	0.113132i	−0.0476222	−	0.00684704i
$274$	17.3600	−	22.5937i	1.04876	−	1.36494i
$275$			2.04321i			0.123210i
$276$	−23.1701	+	0.0143137i	−1.39468	+	0.000861585i
$277$		−	6.06104i		−	0.364173i	−0.983283	−	0.182086i	$-0.941715\pi$
$277$		−	6.06104i		−	0.364173i	0.983283	−	0.182086i	$-0.0582851\pi$
$278$	18.2144	+	13.9951i	1.09242	+	0.839369i
$279$	−22.7624	−	3.27274i	−1.36275	−	0.195934i
$280$	−0.450156	+	0.311257i	−0.0269020	+	0.0186011i
$281$	−0.292351	−	0.995656i	−0.0174402	−	0.0593959i	0.950313	−	0.311296i	$-0.100763\pi$
$281$	−0.292351	−	0.995656i	−0.0174402	−	0.0593959i	−0.967753	+	0.251900i	$0.918945\pi$
$282$	−18.0680	−	18.5271i	−1.07593	−	1.10328i
$283$	−2.77850	+	2.40759i	−0.165165	+	0.143116i	−0.733522	−	0.679666i	$-0.762125\pi$
$283$	−2.77850	+	2.40759i	−0.165165	+	0.143116i	0.568357	+	0.822782i	$0.307579\pi$
$284$	20.3778	−	22.3582i	1.20920	−	1.32671i
$285$	−5.53895	+	18.8639i	−0.328099	+	1.11740i
$286$	4.58252	+	1.77500i	0.270970	+	0.104958i
$287$	−1.35631	−	0.871648i	−0.0800605	−	0.0514518i
$288$	−14.6471	−	6.53626i	−0.863087	−	0.385153i
$289$	−1.55407	+	1.79350i	−0.0914162	+	0.105500i
$290$	−11.5981	+	0.683376i	−0.681063	+	0.0401292i
$291$	18.3352	−	2.63621i	1.07483	−	0.154537i
$292$	−17.1525	−	2.90714i	−1.00377	−	0.170128i
$293$	−7.09948	−	15.5457i	−0.414756	−	0.908189i	−0.995559	−	0.0941446i	$-0.969988\pi$
$293$	−7.09948	−	15.5457i	−0.414756	−	0.908189i	0.580802	−	0.814045i	$-0.302739\pi$
$294$	−14.0143	−	19.2189i	−0.817330	−	1.12087i
$295$	3.20414	−	7.01608i	0.186552	−	0.408492i
$296$	−7.19778	+	8.89653i	−0.418363	+	0.517100i
$297$	−0.439289	−	0.683547i	−0.0254901	−	0.0396634i
$298$	−2.95822	−	8.24581i	−0.171365	−	0.477667i
$299$	5.49796	+	6.02479i	0.317955	+	0.348423i
$300$	−3.72949	+	3.07122i	−0.215322	+	0.177317i
$301$	0.813982	+	1.26658i	0.0469171	+	0.0730045i
$302$	−5.80773	−	28.4092i	−0.334198	−	1.63477i
$303$	−15.3349	−	7.00322i	−0.880968	−	0.402325i
$304$	32.4153	−	3.01072i	1.85915	−	0.172677i
$305$	4.44250	+	9.72771i	0.254377	+	0.557007i
$306$	−13.3665	−	7.51787i	−0.764111	−	0.429768i
$307$	2.64931	+	18.4264i	0.151204	+	1.05165i	0.914205	+	0.405252i	$0.132816\pi$
$307$	2.64931	+	18.4264i	0.151204	+	1.05165i	−0.763001	+	0.646398i	$0.776275\pi$
$308$	−0.310320	−	0.727262i	−0.0176821	−	0.0414396i
$309$	−2.39792	+	2.76735i	−0.136413	+	0.157429i
$310$	11.1764	+	2.57856i	0.634780	+	0.146452i
$311$	−11.4096	+	17.7537i	−0.646979	+	1.00672i	0.350555	+	0.936542i	$0.385993\pi$
$311$	−11.4096	+	17.7537i	−0.646979	+	1.00672i	−0.997535	+	0.0701774i	$0.977643\pi$
$312$	3.64823	+	11.0326i	0.206541	+	0.624596i
$313$	−7.46302	+	25.4167i	−0.421835	+	1.43664i	0.425200	+	0.905099i	$0.360204\pi$
$313$	−7.46302	+	25.4167i	−0.421835	+	1.43664i	−0.847035	+	0.531538i	$0.821614\pi$
$314$	−12.1583	+	6.44225i	−0.686133	+	0.363557i
$315$	0.359276	+	0.414627i	0.0202429	+	0.0233616i
$316$	6.10991	+	2.97778i	0.343709	+	0.167513i
$317$	3.20096	+	10.9015i	0.179784	+	0.612287i	0.999234	+	0.0391367i	$0.0124608\pi$
$317$	3.20096	+	10.9015i	0.179784	+	0.612287i	−0.819450	+	0.573151i	$0.805721\pi$
$318$	−15.9949	−	1.34588i	−0.896949	−	0.0754729i
$319$	2.38885	−	16.6148i	0.133750	−	0.930249i
$320$	7.00651	+	3.86120i	0.391676	+	0.215848i
$321$		−	4.71613i		−	0.263229i
$322$	0.0763819	−	1.31012i	0.00425660	−	0.0730101i
$323$	31.1266			1.73193
$324$	5.78832	−	18.0270i	0.321573	−	1.00150i
$325$	1.68340	+	0.242037i	0.0933783	+	0.0134258i
$326$	−7.18012	−	0.604164i	−0.397670	−	0.0334616i
$327$	−14.3280	+	4.20708i	−0.792339	+	0.232652i
$328$	−2.56467	+	23.4273i	−0.141610	+	1.29356i
$329$	1.10774	−	0.959866i	0.0610719	−	0.0529191i
$330$	−3.26809	−	6.16780i	−0.179903	−	0.339526i
$331$	−4.61403	−	1.35480i	−0.253610	−	0.0744665i	0.152456	−	0.988310i	$-0.451282\pi$
$331$	−4.61403	−	1.35480i	−0.253610	−	0.0744665i	−0.406066	+	0.913844i	$0.633100\pi$
$332$	28.5681	+	0.717008i	1.56788	+	0.0393509i
$333$	9.65063	+	6.20208i	0.528851	+	0.339872i
$334$	−8.23654	−	1.90028i	−0.450683	−	0.103979i
$335$	−7.19447	−	6.23404i	−0.393076	−	0.340602i
$336$	0.861023	−	1.65960i	0.0469727	−	0.0905386i
$337$	−1.56383	+	0.224845i	−0.0851873	+	0.0122481i	−0.184777	−	0.982781i	$-0.559156\pi$
$337$	−1.56383	+	0.224845i	−0.0851873	+	0.0122481i	0.0995894	+	0.995029i	$0.468247\pi$
$338$	−7.00738	+	12.4588i	−0.381151	+	0.677672i
$339$	−0.907187	+	0.414298i	−0.0492716	+	0.0225016i
$340$	6.32898	+	4.29552i	0.343237	+	0.232957i
$341$	−6.88408	+	15.0740i	−0.372794	+	0.816305i
$342$	−6.53640	−	31.9736i	−0.353448	−	1.72893i
$343$	2.27280	−	1.46064i	0.122719	−	0.0788670i
$344$	11.2668	−	18.9054i	0.607463	−	1.01931i
$345$	−0.297828	−	11.5812i	−0.0160345	−	0.623513i
$346$	23.3958	−	8.39335i	1.25777	−	0.451229i
$347$	−25.0326	+	16.0875i	−1.34382	+	0.863621i	−0.997229	−	0.0743958i	$-0.976297\pi$
$347$	−25.0326	+	16.0875i	−1.34382	+	0.863621i	−0.346591	+	0.938016i	$0.612661\pi$
$348$	33.9178	−	20.6139i	1.81819	−	1.10502i
$349$	12.3632	+	5.64609i	0.661787	+	0.302228i	0.717849	−	0.696199i	$-0.245127\pi$
$349$	12.3632	+	5.64609i	0.661787	+	0.302228i	−0.0560614	+	0.998427i	$0.517854\pi$
$350$	−0.161227	−	0.221102i	−0.00861792	−	0.0118184i
$351$	−0.615211	+	0.280958i	−0.0328376	+	0.0149964i
$352$	−7.49299	+	8.80035i	−0.399378	+	0.469060i
$353$	−3.27300	−	22.7642i	−0.174204	−	1.21162i	−0.869881	−	0.493262i	$-0.835804\pi$
$353$	−3.27300	−	22.7642i	−0.174204	−	1.21162i	0.695676	−	0.718355i	$-0.255105\pi$
$354$	1.54988	+	26.3042i	0.0823753	+	1.39805i
$355$	11.4312	+	9.90521i	0.606706	+	0.525714i
$356$	−1.75102	−	14.8074i	−0.0928041	−	0.784790i
$357$	0.966468	−	1.50385i	0.0511509	−	0.0795924i
$358$	12.6967	+	4.91795i	0.671042	+	0.259922i
$359$	−2.74995	−	0.807458i	−0.145137	−	0.0426160i	0.208357	−	0.978053i	$-0.433188\pi$
$359$	−2.74995	−	0.807458i	−0.145137	−	0.0426160i	−0.353494	+	0.935437i	$0.615007\pi$
$360$	3.08335	−	7.40323i	0.162507	−	0.390184i
$361$	30.9348	+	35.7006i	1.62815	+	1.87898i
$362$	9.00525	−	8.78207i	0.473305	−	0.461575i
$363$	−15.8196	+	4.64507i	−0.830316	+	0.243803i
$364$	−0.635950	+	0.169521i	−0.0333329	+	0.00888534i
$365$	1.23793	−	8.61001i	0.0647963	−	0.450668i
$366$	−28.9698	−	22.2591i	−1.51428	−	1.16350i
$367$	−25.0564			−1.30793			−0.653966	−	0.756524i	$-0.726896\pi$
$367$	−25.0564			−1.30793			−0.653966	+	0.756524i	$0.726896\pi$
$368$	−17.6396	+	7.53961i	−0.919526	+	0.393029i
$369$	23.6251			1.22988
$370$	−4.53716	−	3.48615i	−0.235876	−	0.181236i
$371$	0.129385	−	0.899890i	0.00671732	−	0.0467200i
$372$	−37.8624	+	10.0928i	−1.96308	+	0.523285i
$373$	−16.1705	+	4.74809i	−0.837277	+	0.245847i	−0.672140	−	0.740424i	$-0.734625\pi$
$373$	−16.1705	+	4.74809i	−0.837277	+	0.245847i	−0.165137	+	0.986271i	$0.552807\pi$
$374$	−7.91171	+	7.71563i	−0.409105	+	0.398966i
$375$	−1.58192	−	1.82563i	−0.0816898	−	0.0942750i
$376$	−19.7790	−	8.23769i	−1.02002	−	0.424826i
$377$	−13.4059	−	3.93633i	−0.690440	−	0.202732i
$378$	0.101474	+	0.0393051i	0.00521928	+	0.00202164i
$379$	−1.24669	+	1.93988i	−0.0640380	+	0.0996451i	−0.871796	−	0.489869i	$-0.837044\pi$
$379$	−1.24669	+	1.93988i	−0.0640380	+	0.0996451i	0.807758	+	0.589514i	$0.200681\pi$
$380$	1.91154	+	16.1648i	0.0980600	+	0.829237i
$381$	−22.5691	−	19.5563i	−1.15625	−	1.00190i
$382$	1.47946	+	25.1090i	0.0756957	+	1.28469i
$383$	−1.45937	−	10.1501i	−0.0745702	−	0.518647i	−0.992533	−	0.121980i	$-0.961076\pi$
$383$	−1.45937	−	10.1501i	−0.0745702	−	0.518647i	0.917962	−	0.396667i	$-0.129833\pi$
$384$	−27.3263	−	0.448890i	−1.39449	−	0.0229073i
$385$	0.359624	−	0.164235i	0.0183281	−	0.00837017i
$386$	7.04070	+	9.65545i	0.358362	+	0.491449i
$387$	−20.0684	−	9.16495i	−1.02014	−	0.465881i
$388$	13.1058	−	7.96520i	0.665348	−	0.404372i
$389$	−1.21083	+	0.778151i	−0.0613914	+	0.0394538i	−0.570976	−	0.820966i	$-0.693435\pi$
$389$	−1.21083	+	0.778151i	−0.0613914	+	0.0394538i	0.509585	+	0.860420i	$0.329799\pi$
$390$	−5.46877	+	1.96195i	−0.276922	+	0.0993471i
$391$	−17.4601	+	5.61817i	−0.882994	+	0.284123i
$392$	−16.9168	−	10.0816i	−0.854428	−	0.509199i
$393$	−4.60950	+	2.96234i	−0.232518	+	0.149431i
$394$	2.99511	+	14.6509i	0.150892	+	0.738104i
$395$	−1.41177	+	3.09135i	−0.0710340	+	0.155543i
$396$	9.58699	+	6.50675i	0.481765	+	0.326977i
$397$	−4.62180	+	2.11070i	−0.231961	+	0.105933i	−0.528005	−	0.849241i	$-0.677060\pi$
$397$	−4.62180	+	2.11070i	−0.231961	+	0.105933i	0.296044	+	0.955174i	$0.404333\pi$
$398$	−13.4787	+	23.9647i	−0.675628	+	1.20124i
$399$	3.76544	−	0.541389i	0.188508	−	0.0271033i
$400$	−1.84209	+	3.55059i	−0.0921047	+	0.177529i
$401$	8.44075	+	7.31395i	0.421511	+	0.365241i	0.839637	−	0.543148i	$-0.182768\pi$
$401$	8.44075	+	7.31395i	0.421511	+	0.365241i	−0.418126	+	0.908389i	$0.637313\pi$
$402$	31.6890	+	7.31109i	1.58050	+	0.364644i
$403$	11.6040	+	7.45744i	0.578036	+	0.371482i
$404$	−13.9532	−	0.350201i	−0.694199	−	0.0174232i
$405$	9.08330	+	2.66710i	0.451353	+	0.132529i
$406$	1.05254	+	1.98644i	0.0522367	+	0.0985852i
$407$	6.24755	−	5.41353i	0.309680	−	0.268339i
$408$	−25.9757	−	2.84366i	−1.28599	−	0.140782i
$409$	2.87210	−	0.843323i	0.142016	−	0.0416997i	−0.209952	−	0.977712i	$-0.567331\pi$
$409$	2.87210	−	0.843323i	0.142016	−	0.0416997i	0.351968	+	0.936012i	$0.385513\pi$
$410$	−11.7421	−	0.988030i	−0.579902	−	0.0487953i
$411$	−48.1741	−	6.92638i	−2.37625	−	0.341653i
$412$	−0.926835	+	2.88652i	−0.0456619	+	0.142208i
$413$	−1.49244			−0.0734383
$414$	9.43756	+	16.7554i	0.463831	+	0.823482i
$415$			14.2885i			0.701396i
$416$	6.36299	+	7.21595i	0.311971	+	0.353791i
$417$	5.58383	−	38.8364i	0.273441	−	1.90183i
$418$	−23.4343	−	1.97186i	−1.14621	−	0.0964468i
$419$	−9.78183	−	33.3138i	−0.477874	−	1.62749i	−0.747314	−	0.664471i	$-0.768657\pi$
$419$	−9.78183	−	33.3138i	−0.477874	−	1.62749i	0.269441	−	0.963017i	$-0.413161\pi$
$420$	0.840341	+	0.409556i	0.0410044	+	0.0199843i
$421$	−3.25612	−	3.75776i	−0.158693	−	0.183142i	0.670835	−	0.741607i	$-0.265936\pi$
$421$	−3.25612	−	3.75776i	−0.158693	−	0.183142i	−0.829528	+	0.558465i	$0.811391\pi$
$422$	26.6481	−	14.1199i	1.29721	−	0.687345i
$423$	−6.05119	+	20.6084i	−0.294219	+	1.00202i
$424$	−12.6175	+	4.17236i	−0.612762	+	0.202628i
$425$	−2.06769	+	3.21738i	−0.100297	+	0.156066i
$426$	−50.3504	−	11.6165i	−2.43948	−	0.562822i
$427$	1.35507	−	1.56384i	0.0655766	−	0.0756794i
$428$	−1.53242	−	3.59137i	−0.0740724	−	0.173595i
$429$	−1.19462	−	8.30875i	−0.0576767	−	0.401150i
$430$	9.59109	+	5.39443i	0.462524	+	0.260143i
$431$	−0.761535	−	1.66753i	−0.0366818	−	0.0803220i	0.890404	−	0.455171i	$-0.150422\pi$
$431$	−0.761535	−	1.66753i	−0.0366818	−	0.0803220i	−0.927086	+	0.374849i	$0.877695\pi$
$432$	−0.147110	−	1.58388i	−0.00707783	−	0.0762045i
$433$	−12.3605	−	5.64487i	−0.594010	−	0.271275i	0.0956424	−	0.995416i	$-0.469509\pi$
$433$	−12.3605	−	5.64487i	−0.594010	−	0.271275i	−0.689653	+	0.724140i	$0.742237\pi$
$434$	−0.444520	−	2.17442i	−0.0213376	−	0.104375i
$435$	10.7292	+	16.6950i	0.514426	+	0.800462i
$436$	−9.54385	+	7.85934i	−0.457068	+	0.376394i
$437$	−33.3674	−	20.2511i	−1.59618	−	0.968743i
$438$	10.0347	+	27.9709i	0.479476	+	1.33650i
$439$	−1.96594	−	3.05906i	−0.0938292	−	0.146001i	0.791166	−	0.611602i	$-0.209475\pi$
$439$	−1.96594	−	3.05906i	−0.0938292	−	0.146001i	−0.884995	+	0.465601i	$0.845838\pi$
$440$	−4.49279	−	3.63491i	−0.214185	−	0.173288i
$441$	−8.20090	+	17.9575i	−0.390519	+	0.855118i
$442$	5.41969	+	7.43243i	0.257788	+	0.353525i
$443$	8.05020	+	17.6275i	0.382476	+	0.837506i	0.998750	+	0.0499746i	$0.0159141\pi$
$443$	8.05020	+	17.6275i	0.382476	+	0.837506i	−0.616274	+	0.787532i	$0.711359\pi$
$444$	19.2723	+	3.26642i	0.914621	+	0.155017i
$445$	7.37940	−	1.06100i	0.349817	−	0.0502961i
$446$	−6.82892	+	0.402370i	−0.323359	+	0.0190527i
$447$	−9.79922	+	11.3089i	−0.463487	+	0.534893i
$448$	0.116418	−	1.54357i	0.00550025	−	0.0729269i
$449$	−0.748351	−	0.480936i	−0.0353169	−	0.0226968i	0.522863	−	0.852417i	$-0.324864\pi$
$449$	−0.748351	−	0.480936i	−0.0353169	−	0.0226968i	−0.558180	+	0.829720i	$0.688500\pi$
$450$	3.73913	+	1.44832i	0.176264	+	0.0682743i
$451$	4.79639	−	16.3350i	0.225853	−	0.769186i
$452$	−0.556211	+	0.610265i	−0.0261619	+	0.0287045i
$453$	−37.4323	+	32.4353i	−1.75872	+	1.52394i
$454$	−20.6207	−	21.1448i	−0.967779	−	0.992373i
$455$	−0.0927121	−	0.315748i	−0.00434641	−	0.0148025i
$456$	−31.6257	−	45.7388i	−1.48101	−	2.14191i
$457$	−32.0823	−	4.61274i	−1.50075	−	0.215775i	−0.657564	−	0.753399i	$-0.728413\pi$
$457$	−32.0823	−	4.61274i	−1.50075	−	0.215775i	−0.843185	+	0.537624i	$0.819322\pi$
$458$	−3.22359	−	2.47686i	−0.150629	−	0.115736i
$459$		−	1.52091i		−	0.0709900i
$460$	−3.98991	−	8.72242i	−0.186031	−	0.406685i
$461$			17.3190i			0.806625i	0.915062	+	0.403312i	$0.132141\pi$
$461$			17.3190i			0.806625i	−0.915062	+	0.403312i	$0.867859\pi$
$462$	−0.822895	+	1.07098i	−0.0382846	+	0.0498267i
$463$	35.2497	+	5.06815i	1.63819	+	0.235537i	0.898998	−	0.437953i	$-0.144296\pi$
$463$	35.2497	+	5.06815i	1.63819	+	0.235537i	0.739196	+	0.673490i	$0.235206\pi$
$464$	19.1306	−	26.7186i	0.888114	−	1.24038i
$465$	−5.51978	−	18.7986i	−0.255974	−	0.871766i
$466$	15.3761	−	14.9950i	0.712284	−	0.694631i
$467$	20.4562	−	17.7254i	0.946602	−	0.820235i	−0.0372345	−	0.999307i	$-0.511855\pi$
$467$	20.4562	−	17.7254i	0.946602	−	0.820235i	0.983836	+	0.179072i	$0.0573094\pi$
$468$	6.49657	−	7.12793i	0.300304	−	0.329489i
$469$	−0.518951	+	1.76739i	−0.0239629	+	0.0816103i
$470$	3.86942	−	9.98971i	0.178483	−	0.460791i
$471$	19.7721	+	12.7068i	0.911050	+	0.585496i
$472$	9.72733	+	19.5273i	0.447737	+	0.898815i
$473$	−10.4112	+	12.0151i	−0.478707	+	0.552457i
$474$	−0.682893	−	11.5899i	−0.0313663	−	0.532341i
$475$	−8.05587	+	1.15826i	−0.369629	+	0.0531446i
$476$	0.247323	−	1.45923i	0.0113360	−	0.0668838i
$477$	5.53422	+	12.1183i	0.253395	+	0.554857i
$478$	20.8830	−	15.2278i	0.955167	−	0.696502i
$479$	11.6681	−	25.5497i	0.533131	−	1.16739i	−0.431094	−	0.902307i	$-0.641872\pi$
$479$	11.6681	−	25.5497i	0.533131	−	1.16739i	0.964225	−	0.265087i	$-0.0854005\pi$
$480$	−0.118439	−	13.6645i	−0.00540596	−	0.623695i
$481$	−3.72013	−	5.78863i	−0.169623	−	0.263939i
$482$	21.6391	−	7.76312i	0.985633	−	0.353601i
$483$	−2.01446	+	0.983326i	−0.0916611	+	0.0447429i
$484$	−10.5374	+	8.67756i	−0.478975	+	0.394434i
$485$	4.14576	+	6.45093i	0.188249	+	0.292922i
$486$	−30.0325	+	6.13959i	−1.36230	+	0.278498i
$487$	33.9303	+	15.4955i	1.53753	+	0.702167i	0.990824	−	0.135158i	$-0.0431540\pi$
$487$	33.9303	+	15.4955i	1.53753	+	0.702167i	0.546707	+	0.837324i	$0.315881\pi$
$488$	−29.2934	−	7.53724i	−1.32605	−	0.341195i
$489$	5.11288	+	11.1956i	0.231212	+	0.506284i
$490$	4.82700	−	8.58222i	0.218062	−	0.387705i
$491$	1.03886	+	7.22543i	0.0468831	+	0.326079i	0.999743	+	0.0226686i	$0.00721627\pi$
$491$	1.03886	+	7.22543i	0.0468831	+	0.326079i	−0.952860	+	0.303411i	$0.901875\pi$
$492$	37.0260	−	15.7988i	1.66926	−	0.712266i
$493$	20.5754	−	23.7453i	0.926670	−	1.06943i
$494$	−4.40061	+	19.0739i	−0.197993	+	0.858177i
$495$	−3.13208	+	4.87362i	−0.140777	+	0.219053i
$496$	−25.5531	+	19.9884i	−1.14737	+	0.897506i
$497$	0.824556	−	2.80818i	0.0369864	−	0.125964i
$498$	−22.8543	−	43.1324i	−1.02413	−	1.93281i
$499$	9.02036	+	10.4101i	0.403807	+	0.466018i	0.920836	−	0.389950i	$-0.127508\pi$
$499$	9.02036	+	10.4101i	0.403807	+	0.466018i	−0.517029	+	0.855968i	$0.672962\pi$
$500$	−1.79785	−	0.876214i	−0.0804021	−	0.0391855i
$501$	4.06783	+	13.8538i	0.181737	+	0.618940i
$502$	1.35314	−	16.0812i	0.0603935	−	0.717739i
$503$	−4.83930	+	33.6581i	−0.215774	+	1.50074i	0.537629	+	0.843181i	$0.319320\pi$
$503$	−4.83930	+	33.6581i	−0.215774	+	1.50074i	−0.753403	+	0.657559i	$0.771589\pi$
$504$	−1.55087	+	0.0523780i	−0.0690815	+	0.00233310i
$505$		−	6.97881i		−	0.310553i
$506$	13.5011	−	3.12367i	0.600197	−	0.138864i
$507$	24.4164			1.08437
$508$	−23.5410	−	7.55881i	−1.04446	−	0.335368i
$509$	−28.5041	−	4.09826i	−1.26342	−	0.181652i	−0.522147	−	0.852856i	$-0.674869\pi$
$509$	−28.5041	−	4.09826i	−1.26342	−	0.181652i	−0.741273	+	0.671203i	$0.765778\pi$
$510$	1.09551	−	13.0195i	0.0485100	−	0.576511i
$511$	−1.61494	+	0.474190i	−0.0714409	+	0.0209769i
$512$	−20.9550	+	8.53735i	−0.926091	+	0.377301i
$513$	2.44603	−	2.11950i	0.107995	−	0.0935780i
$514$	−11.4850	+	6.08548i	−0.506581	+	0.268419i
$515$	−1.45443	−	0.427060i	−0.0640899	−	0.0188185i
$516$	−37.5807	−	0.943209i	−1.65440	−	0.0415225i
$517$	13.0207	+	8.36788i	0.572649	+	0.368019i
$518$	−0.248894	+	1.07880i	−0.0109358	+	0.0473997i
$519$	−32.0867	−	27.8033i	−1.40845	−	1.22043i
$520$	−3.52701	+	3.27102i	−0.154670	+	0.143444i
$521$	6.55725	−	0.942791i	0.287278	−	0.0413044i	0.00283087	−	0.999996i	$-0.499099\pi$
$521$	6.55725	−	0.942791i	0.287278	−	0.0413044i	0.284448	+	0.958692i	$0.408190\pi$
$522$	−28.7121	−	16.1489i	−1.25670	−	0.706819i
$523$	−4.12681	+	1.88465i	−0.180453	+	0.0824100i	−0.503593	−	0.863941i	$-0.667989\pi$
$523$	−4.12681	+	1.88465i	−0.180453	+	0.0824100i	0.323140	+	0.946351i	$0.395262\pi$
$524$	−2.54761	+	3.75362i	−0.111293	+	0.163978i
$525$	−0.194171	+	0.425176i	−0.00847434	+	0.0185562i
$526$	30.0964	−	6.15265i	1.31226	−	0.268268i
$527$	−26.0947	+	16.7701i	−1.13670	+	0.730515i
$528$	19.3763	+	3.78647i	0.843244	+	0.164785i
$529$	22.3722	+	5.33700i	0.972705	+	0.232043i
$530$	−2.24381	−	6.25444i	−0.0974649	−	0.271676i
$531$	18.3978	−	11.8236i	0.798397	−	0.513099i
$532$	2.69150	−	1.63578i	0.116691	−	0.0709202i
$533$	−12.8902	−	5.88677i	−0.558337	−	0.254984i
$534$	−20.5790	+	15.0061i	−0.890538	+	0.649376i
$535$	1.77590	−	0.811024i	0.0767786	−	0.0350636i
$536$	26.5070	−	4.72933i	1.14493	−	0.204276i
$537$	−3.30991	−	23.0209i	−0.142833	−	0.993426i
$538$	2.81730	−	0.165999i	0.121462	−	0.00715674i
$539$	10.7513	+	9.31605i	0.463091	+	0.401271i
$540$	0.789846	−	0.0934019i	0.0339896	−	0.00401938i
$541$	−0.401903	+	0.625373i	−0.0172791	+	0.0268869i	−0.849786	−	0.527128i	$-0.823269\pi$
$541$	−0.401903	+	0.625373i	−0.0172791	+	0.0268869i	0.832507	+	0.554015i	$0.186905\pi$
$542$	5.25092	−	13.5563i	0.225546	−	0.582294i
$543$	−20.6154	−	6.05322i	−0.884690	−	0.259768i
$544$	−20.7047	+	6.27488i	−0.887708	+	0.269033i
$545$	−4.04816	−	4.67183i	−0.173404	−	0.200119i
$546$	0.784903	+	0.804850i	0.0335908	+	0.0344444i
$547$	−12.4487	+	3.65527i	−0.532268	+	0.156288i	−0.536812	−	0.843702i	$-0.680372\pi$
$547$	−12.4487	+	3.65527i	−0.532268	+	0.156288i	0.00454455	+	0.999990i	$0.498553\pi$
$548$	−38.9355	+	10.3788i	−1.66324	+	0.443360i
$549$	−4.31525	+	30.0132i	−0.184170	+	1.28093i
$550$	1.76052	−	2.29129i	0.0750689	−	0.0977009i
$551$	66.8621			2.84842
$552$	25.9956	+	19.9483i	1.10645	+	0.849058i
$553$	0.657584			0.0279633
$554$	−5.22246	+	6.79694i	−0.221881	+	0.288774i
$555$	−1.39092	+	9.67408i	−0.0590414	+	0.410642i
$556$	−8.36706	−	31.3886i	−0.354842	−	1.33117i
$557$	−24.7029	+	7.25344i	−1.04670	+	0.307338i	−0.759482	−	0.650528i	$-0.774548\pi$
$557$	−24.7029	+	7.25344i	−1.04670	+	0.307338i	−0.287215	+	0.957866i	$0.592729\pi$
$558$	22.7061	+	23.2832i	0.961227	+	0.985655i
$559$	8.66597	+	10.0011i	0.366531	+	0.423000i
$560$	0.773004	+	0.0388265i	0.0326654	+	0.00164072i
$561$	18.1120	+	5.31815i	0.764688	+	0.224533i
$562$	−0.530054	+	1.36845i	−0.0223590	+	0.0577244i
$563$	−8.55089	+	13.3055i	−0.360377	+	0.560758i	−0.973344	−	0.229351i	$-0.926340\pi$
$563$	−8.55089	+	13.3055i	−0.360377	+	0.560758i	0.612967	+	0.790109i	$0.289976\pi$
$564$	4.29789	+	36.3448i	0.180974	+	1.53039i
$565$	−0.312014	−	0.270362i	−0.0131265	−	0.0113742i
$566$	5.19034	−	0.305822i	0.218166	−	0.0128546i
$567$	−0.260688	−	1.81312i	−0.0109479	−	0.0761440i
$568$	−42.1168	+	7.51438i	−1.76718	+	0.315296i
$569$	34.5559	−	15.7812i	1.44866	−	0.661580i	0.473038	−	0.881042i	$-0.343157\pi$
$569$	34.5559	−	15.7812i	1.44866	−	0.661580i	0.975621	+	0.219462i	$0.0704301\pi$
$570$	22.4654	−	16.3817i	0.940974	−	0.686153i
$571$	−17.0311	−	7.77782i	−0.712727	−	0.325492i	0.0258449	−	0.999666i	$-0.491772\pi$
$571$	−17.0311	−	7.77782i	−0.712727	−	0.325492i	−0.738572	+	0.674174i	$0.764500\pi$
$572$	−3.60949	−	5.93901i	−0.150920	−	0.248322i
$573$	36.1434	−	23.2279i	1.50991	−	0.970361i
$574$	0.769936	+	2.14614i	0.0321365	+	0.0895780i
$575$	4.30978	−	2.10375i	0.179730	−	0.0877325i
$576$	10.7935	+	19.9504i	0.449729	+	0.831267i
$577$	−0.175159	+	0.112568i	−0.00729197	+	0.00468627i	−0.544282	−	0.838902i	$-0.683198\pi$
$577$	−0.175159	+	0.112568i	−0.00729197	+	0.00468627i	0.536990	+	0.843589i	$0.319561\pi$
$578$	3.28812	−	0.672195i	0.136768	−	0.0279596i
$579$	8.47939	−	18.5673i	0.352391	−	0.771629i
$580$	13.5951	+	9.22708i	0.564505	+	0.383134i
$581$	2.51491	−	1.14852i	0.104336	−	0.0476486i
$582$	−22.8329	−	12.8422i	−0.946453	−	0.532325i
$583$	9.50243	−	1.36624i	0.393550	−	0.0565840i
$584$	16.7301	+	18.0394i	0.692297	+	0.746477i
$585$	3.64434	+	3.15784i	0.150675	+	0.130561i
$586$	−5.43339	+	23.5504i	−0.224451	+	0.972857i
$587$	4.54993	+	2.92406i	0.187796	+	0.120689i	0.631160	−	0.775652i	$-0.282579\pi$
$587$	4.54993	+	2.92406i	0.187796	+	0.120689i	−0.443365	+	0.896341i	$0.646215\pi$
$588$	−0.843995	+	33.6277i	−0.0348058	+	1.38678i
$589$	−63.3356	−	18.5970i	−2.60970	−	0.766276i
$590$	−9.63853	+	5.10711i	−0.396812	+	0.210256i
$591$	19.3043	−	16.7272i	0.794072	−	0.688067i
$592$	15.7373	−	3.77477i	0.646800	−	0.155142i
$593$	24.4186	−	7.16994i	1.00275	−	0.294434i	0.261166	−	0.965294i	$-0.415893\pi$
$593$	24.4186	−	7.16994i	1.00275	−	0.294434i	0.741584	+	0.670860i	$0.234075\pi$
$594$	−0.0963492	+	1.14505i	−0.00395326	+	0.0469820i
$595$	0.732489	+	0.105316i	0.0300291	+	0.00431754i
$596$	−3.78756	+	11.7959i	−0.155144	+	0.483179i
$597$	46.9651			1.92215
$598$	−0.974267	−	11.4936i	−0.0398407	−	0.470007i
$599$			30.8566i			1.26077i	0.776284	+	0.630384i	$0.217102\pi$
$599$			30.8566i			1.26077i	−0.776284	+	0.630384i	$0.782898\pi$
$600$	6.82860	−	0.230624i	0.278777	−	0.00941518i
$601$	2.78767	−	19.3887i	0.113711	−	0.790880i	−0.850544	−	0.525904i	$-0.823727\pi$
$601$	2.78767	−	19.3887i	0.113711	−	0.790880i	0.964255	−	0.264976i	$-0.0853640\pi$
$602$	0.178530	−	2.12172i	0.00727636	−	0.0864750i
$603$	−7.60446	−	25.8984i	−0.309678	−	1.05467i
$604$	−17.9657	+	36.8627i	−0.731015	+	1.49992i
$605$	−4.46961	−	5.15820i	−0.181715	−	0.209711i
$606$	11.1625	+	21.0668i	0.453446	+	0.855778i
$607$	−9.67032	+	32.9341i	−0.392506	+	1.33675i	0.492151	+	0.870510i	$0.336211\pi$
$607$	−9.67032	+	32.9341i	−0.392506	+	1.33675i	−0.884657	+	0.466243i	$0.845607\pi$
$608$	−38.9452	−	24.5542i	−1.57944	−	0.995805i
$609$	2.07604	−	3.23038i	0.0841255	−	0.130902i
$610$	3.39994	−	14.7366i	0.137660	−	0.596669i
$611$	8.43670	−	9.73647i	0.341312	−	0.393895i
$612$	8.51164	+	19.9478i	0.344062	+	0.806342i
$613$	−2.59752	−	18.0662i	−0.104913	−	0.729686i	−0.972585	−	0.232548i	$-0.925294\pi$
$613$	−2.59752	−	18.0662i	−0.104913	−	0.729686i	0.867672	−	0.497137i	$-0.165616\pi$
$614$	12.9060	−	22.9464i	0.520844	−	0.926041i
$615$	8.36143	+	18.3090i	0.337165	+	0.738289i
$616$	−0.278644	+	1.08295i	−0.0112269	+	0.0436332i
$617$	20.2155	+	9.23212i	0.813846	+	0.371671i	0.778453	−	0.627702i	$-0.216005\pi$
$617$	20.2155	+	9.23212i	0.813846	+	0.371671i	0.0353928	+	0.999373i	$0.488732\pi$
$618$	5.07353	−	1.03719i	0.204087	−	0.0417219i
$619$	−19.7962	−	30.8035i	−0.795677	−	1.23810i	−0.967475	−	0.252966i	$-0.918594\pi$
$619$	−19.7962	−	30.8035i	−0.795677	−	1.23810i	0.171798	−	0.985132i	$-0.445042\pi$
$620$	−10.3116	−	12.5217i	−0.414125	−	0.502886i
$621$	−0.989512	+	1.63040i	−0.0397078	+	0.0654257i
$622$	28.0923	−	10.0782i	1.12640	−	0.404100i
$623$	−0.779905	−	1.21356i	−0.0312462	−	0.0486201i
$624$	5.41495	−	15.5155i	0.216772	−	0.621119i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	30.2693	−	22.0722i	1.20980	−	0.882182i
$627$	16.6873	+	36.5401i	0.666427	+	1.45927i
$628$	19.1854	+	3.25170i	0.765582	+	0.129757i
$629$	15.3162	−	2.20214i	0.610696	−	0.0878049i
$630$	−0.0456368	−	0.774536i	−0.00181821	−	0.0308583i
$631$	7.31171	−	8.43817i	0.291075	−	0.335918i	−0.591312	−	0.806443i	$-0.701390\pi$
$631$	7.31171	−	8.43817i	0.291075	−	0.335918i	0.882387	+	0.470525i	$0.155935\pi$
$632$	−4.28595	−	8.60389i	−0.170486	−	0.342245i
$633$	−43.3358	−	27.8502i	−1.72244	−	1.10695i
$634$	5.80358	−	14.9831i	0.230490	−	0.595057i
$635$	3.48289	−	11.8616i	0.138214	−	0.470714i
$636$	16.7772	+	15.2912i	0.665261	+	0.606335i
$637$	8.94906	−	7.75441i	0.354575	−	0.307241i
$638$	−16.9949	+	16.5737i	−0.672835	+	0.656160i
$639$	12.0827	+	41.1497i	0.477982	+	1.62786i
$640$	−4.53022	−	10.3671i	−0.179073	−	0.409796i
$641$	−44.8658	−	6.45072i	−1.77209	−	0.254788i	−0.822609	−	0.568608i	$-0.807482\pi$
$641$	−44.8658	−	6.45072i	−1.77209	−	0.254788i	−0.949483	+	0.313820i	$0.898391\pi$
$642$	−4.06363	+	5.28874i	−0.160379	+	0.208730i
$643$		−	3.33612i		−	0.131564i	−0.997834	−	0.0657818i	$-0.979046\pi$
$643$		−	3.33612i		−	0.131564i	0.997834	−	0.0657818i	$-0.0209541\pi$
$644$	−1.21451	+	1.40337i	−0.0478585	+	0.0553006i
$645$		−	18.7963i		−	0.740102i
$646$	−34.9058	−	26.8200i	−1.37335	−	1.05522i
$647$	15.7010	+	2.25747i	0.617272	+	0.0887502i	0.443855	−	0.896098i	$-0.353610\pi$
$647$	15.7010	+	2.25747i	0.617272	+	0.0887502i	0.173416	+	0.984849i	$0.444519\pi$
$648$	−22.0240	+	15.2283i	−0.865184	+	0.598225i
$649$	−4.43997	−	15.1211i	−0.174284	−	0.593556i
$650$	−1.67924	−	1.72192i	−0.0658652	−	0.0675391i
$651$	−2.86504	+	2.48257i	−0.112290	+	0.0972997i
$652$	7.53131	+	6.86422i	0.294949	+	0.268824i
$653$	−2.05978	+	7.01496i	−0.0806053	+	0.274516i	−0.989927	−	0.141577i	$-0.954783\pi$
$653$	−2.05978	+	7.01496i	−0.0806053	+	0.274516i	0.909322	+	0.416093i	$0.136601\pi$
$654$	19.6926	+	7.62775i	0.770042	+	0.298268i
$655$	−1.90818	−	1.22631i	−0.0745587	−	0.0479160i
$656$	23.0620	−	24.0619i	0.900421	−	0.939458i
$657$	16.1513	−	18.6395i	0.630121	−	0.727198i
$658$	−2.06930	+	0.121926i	−0.0806698	+	0.00475318i
$659$	36.8030	−	5.29148i	1.43364	−	0.206127i	0.618681	−	0.785642i	$-0.287667\pi$
$659$	36.8030	−	5.29148i	1.43364	−	0.206127i	0.814961	+	0.579516i	$0.196758\pi$
$660$	−1.64956	+	9.73259i	−0.0642090	+	0.378840i
$661$	−12.0159	−	26.3111i	−0.467363	−	1.02338i	−0.985747	−	0.168234i	$-0.946193\pi$
$661$	−12.0159	−	26.3111i	−0.467363	−	1.02338i	0.518384	−	0.855148i	$-0.326534\pi$
$662$	4.00688	+	5.49494i	0.155732	+	0.213567i
$663$	6.52714	−	14.2924i	0.253493	−	0.555073i
$664$	−31.4188	−	25.4196i	−1.21929	−	0.986470i
$665$	0.851399	+	1.32480i	0.0330159	+	0.0513737i
$666$	−5.47837	−	15.2705i	−0.212282	−	0.591720i
$667$	−37.5055	+	12.0682i	−1.45222	+	0.467284i
$668$	7.59921	+	9.22797i	0.294022	+	0.357041i
$669$	6.31732	+	9.82994i	0.244242	+	0.380048i
$670$	2.69645	+	13.1900i	0.104173	+	0.509575i
$671$	19.8758	+	9.07697i	0.767297	+	0.350413i
$672$	−2.39555	+	1.11920i	−0.0924103	+	0.0431742i
$673$	10.6712	+	23.3666i	0.411344	+	0.900717i	0.995993	+	0.0894310i	$0.0285048\pi$
$673$	10.6712	+	23.3666i	0.411344	+	0.900717i	−0.584649	+	0.811286i	$0.698768\pi$
$674$	1.94744	+	1.09532i	0.0750125	+	0.0421902i
$675$	0.0565950	+	0.393627i	0.00217834	+	0.0151507i
$676$	18.5933	−	7.93367i	0.715126	−	0.305141i
$677$	−9.63031	+	11.1140i	−0.370123	+	0.427145i	−0.910006	−	0.414596i	$-0.863923\pi$
$677$	−9.63031	+	11.1140i	−0.370123	+	0.427145i	0.539883	+	0.841740i	$0.318469\pi$
$678$	1.37431	+	0.317072i	0.0527800	+	0.0121771i
$679$	0.802182	−	1.24822i	0.0307849	−	0.0479023i
$680$	−3.39620	−	10.2704i	−0.130238	−	0.393851i
$681$	−14.2132	+	48.4059i	−0.544653	+	1.85492i
$682$	20.7084	−	10.9726i	0.792964	−	0.420163i
$683$	12.6876	+	14.6422i	0.485476	+	0.560269i	0.944651	−	0.328077i	$-0.106400\pi$
$683$	12.6876	+	14.6422i	0.485476	+	0.560269i	−0.459175	+	0.888346i	$0.651855\pi$
$684$	−20.2198	+	41.4876i	−0.773123	+	1.58632i
$685$	−5.67622	−	19.3314i	−0.216877	−	0.738616i
$686$	−3.80730	−	0.320361i	−0.145363	−	0.0122315i
$687$	−0.988232	+	6.87331i	−0.0377034	+	0.262233i
$688$	−28.9245	+	11.4929i	−1.10273	+	0.438163i
$689$		−	7.99088i		−	0.304428i
$690$	−9.64491	+	13.2440i	−0.367175	+	0.504190i
$691$	6.74784			0.256700			0.128350	−	0.991729i	$-0.459032\pi$
$691$	6.74784			0.256700			0.128350	+	0.991729i	$0.459032\pi$
$692$	−33.4685	−	10.7464i	−1.27228	−	0.408518i
$693$	1.10956	+	0.159530i	0.0421486	+	0.00606006i
$694$	41.9336	+	3.52846i	1.59178	+	0.133939i
$695$	15.5844	−	4.57599i	0.591149	−	0.173577i
$696$	−55.7977	−	6.10837i	−2.11501	−	0.231537i
$697$	24.0834	−	20.8684i	0.912223	−	0.790446i
$698$	−8.99936	−	16.9843i	−0.340631	−	0.642865i
$699$	−35.1999	−	10.3356i	−1.33138	−	0.390929i
$700$	−0.00970969	+	0.386867i	−0.000366992	+	0.0146222i
$701$	14.0474	+	9.02773i	0.530564	+	0.340973i	0.778338	−	0.627845i	$-0.216063\pi$
$701$	14.0474	+	9.02773i	0.530564	+	0.340973i	−0.247774	+	0.968818i	$0.579699\pi$
$702$	0.931992	+	0.215023i	0.0351758	+	0.00811553i
$703$	24.8858	+	21.5637i	0.938586	+	0.813290i
$704$	15.9855	−	3.41255i	0.602477	−	0.128615i
$705$	−18.1127	+	2.60422i	−0.682165	+	0.0980806i
$706$	−15.9443	+	28.3483i	−0.600070	+	1.06690i
$707$	−1.22833	+	0.560960i	−0.0461962	+	0.0210971i
$708$	20.9268	−	30.8334i	0.786478	−	1.15879i
$709$	16.5366	−	36.2101i	0.621044	−	1.35990i	−0.293713	−	0.955894i	$-0.594891\pi$
$709$	16.5366	−	36.2101i	0.621044	−	1.35990i	0.914757	−	0.404004i	$-0.132382\pi$
$710$	−4.28437	−	20.9575i	−0.160790	−	0.786520i
$711$	−8.10625	+	5.20957i	−0.304008	+	0.195374i
$712$	−10.7951	+	18.1140i	−0.404563	+	0.678850i
$713$	38.8840	−	0.999956i	1.45622	−	0.0374486i
$714$	−2.37960	+	0.853692i	−0.0890542	+	0.0319486i
$715$	2.92329	−	1.87868i	0.109325	−	0.0702587i
$716$	−10.0008	−	16.4551i	−0.373746	−	0.614956i
$717$	−40.1577	−	18.3394i	−1.49972	−	0.684897i
$718$	2.38809	+	3.27497i	0.0891228	+	0.122221i
$719$	33.3165	−	15.2151i	1.24250	−	0.567429i	0.317809	−	0.948155i	$-0.397053\pi$
$719$	33.3165	−	15.2151i	1.24250	−	0.567429i	0.924688	+	0.380726i	$0.124326\pi$
$720$	−9.83666	+	5.64533i	−0.366591	+	0.210389i
$721$	0.0417417	+	0.290320i	0.00155454	+	0.0108121i
$722$	−3.92946	−	66.6899i	−0.146239	−	2.48194i
$723$	−29.6774	−	25.7156i	−1.10372	−	0.956375i
$724$	−17.6656	+	2.08902i	−0.656538	+	0.0776378i
$725$	−4.44153	+	6.91116i	−0.164954	+	0.256674i
$726$	21.7428	+	8.42185i	0.806950	+	0.312564i
$727$	4.83346	+	1.41923i	0.179263	+	0.0526364i	0.370132	−	0.928979i	$-0.379312\pi$
$727$	4.83346	+	1.41923i	0.179263	+	0.0526364i	−0.190869	+	0.981616i	$0.561131\pi$
$728$	0.859231	+	0.357859i	0.0318452	+	0.0132631i
$729$	15.6904	+	18.1077i	0.581126	+	0.670656i
$730$	−8.80700	+	8.58873i	−0.325962	+	0.317883i
$731$	−28.5532	+	8.38397i	−1.05608	+	0.310092i
$732$	13.3077	+	49.9233i	0.491868	+	1.84522i
$733$	5.27535	−	36.6908i	0.194849	−	1.35521i	−0.624101	−	0.781343i	$-0.714535\pi$
$733$	5.27535	−	36.6908i	0.194849	−	1.35521i	0.818951	−	0.573864i	$-0.194556\pi$
$734$	28.0986	+	21.5897i	1.03714	+	0.796889i
$735$	−16.8191			−0.620383
$736$	26.2777	+	6.74400i	0.968610	+	0.248587i
$737$	−19.4507			−0.716475
$738$	−26.4936	−	20.3565i	−0.975242	−	0.749332i
$739$	4.81911	−	33.5177i	0.177274	−	1.23297i	−0.685763	−	0.727825i	$-0.740531\pi$
$739$	4.81911	−	33.5177i	0.177274	−	1.23297i	0.863036	−	0.505142i	$-0.168560\pi$
$740$	2.08422	+	7.81883i	0.0766174	+	0.287426i
$741$	32.0821	−	9.42016i	1.17857	−	0.346058i
$742$	−0.920479	+	0.897666i	−0.0337918	+	0.0329544i
$743$	−18.9748	−	21.8981i	−0.696117	−	0.803362i	0.292106	−	0.956386i	$-0.405644\pi$
$743$	−18.9748	−	21.8981i	−0.696117	−	0.803362i	−0.988222	+	0.153024i	$0.951099\pi$
$744$	51.1558	+	21.3058i	1.87546	+	0.781107i
$745$	−5.94361	−	1.74520i	−0.217757	−	0.0639392i
$746$	22.2250	+	8.60865i	0.813715	+	0.315185i
$747$	−21.9032	+	34.0820i	−0.801395	+	1.24700i
$748$	15.5204	−	1.83534i	0.567483	−	0.0671068i
$749$	−0.285495	−	0.247383i	−0.0104318	−	0.00903916i
$750$	0.200942	+	3.41033i	0.00733735	+	0.124528i
$751$	0.528917	+	3.67870i	0.0193005	+	0.134238i	0.997193	−	0.0748684i	$-0.0238537\pi$
$751$	0.528917	+	3.67870i	0.0193005	+	0.134238i	−0.977893	+	0.209106i	$0.932945\pi$
$752$	15.0824	+	26.2803i	0.550000	+	0.958343i
$753$	−25.0747	+	11.4512i	−0.913772	+	0.417306i
$754$	11.6419	+	15.9654i	0.423972	+	0.581425i
$755$	−18.6509	−	8.51759i	−0.678776	−	0.309987i
$756$	−0.0799278	−	0.131512i	−0.00290695	−	0.00478305i
$757$	−20.3622	+	13.0860i	−0.740075	+	0.475618i	−0.855568	−	0.517691i	$-0.826792\pi$
$757$	−20.3622	+	13.0860i	−0.740075	+	0.475618i	0.115492	+	0.993308i	$0.463155\pi$
$758$	3.06954	−	1.10121i	0.111491	−	0.0399978i
$759$	−15.9558	−	17.4848i	−0.579159	−	0.634656i
$760$	11.7847	−	19.7745i	0.427475	−	0.717297i
$761$	17.7383	−	11.3997i	0.643013	−	0.413240i	−0.178094	−	0.984014i	$-0.556993\pi$
$761$	17.7383	−	11.3997i	0.643013	−	0.413240i	0.821107	+	0.570774i	$0.193357\pi$
$762$	8.45881	+	41.3772i	0.306430	+	1.49894i
$763$	−0.496889	+	1.08804i	−0.0179886	+	0.0393896i
$764$	19.9760	−	29.4324i	0.722705	−	1.06483i
$765$	−9.86397	+	4.50473i	−0.356633	+	0.162869i
$766$	−7.10923	+	12.6399i	−0.256867	+	0.456700i
$767$	−12.9842	+	1.86685i	−0.468834	+	0.0674081i
$768$	30.2573	+	24.0489i	1.09182	+	0.867791i
$769$	28.9916	+	25.1214i	1.04547	+	0.905901i	0.995679	−	0.0928590i	$-0.0296006\pi$
$769$	28.9916	+	25.1214i	1.04547	+	0.905901i	0.0497861	+	0.998760i	$0.484146\pi$
$770$	−0.544799	−	0.125692i	−0.0196332	−	0.00452964i
$771$	18.6771	+	12.0031i	0.672640	+	0.432280i
$772$	0.424018	−	16.8943i	0.0152607	−	0.608040i
$773$	−6.09293	−	1.78905i	−0.219148	−	0.0643475i	0.170316	−	0.985390i	$-0.445521\pi$
$773$	−6.09293	−	1.78905i	−0.219148	−	0.0643475i	−0.389463	+	0.921042i	$0.627339\pi$
$774$	14.6081	+	27.5696i	0.525078	+	0.990967i
$775$	6.12954	−	5.31128i	0.220180	−	0.190787i
$776$	−21.5602	−	2.36027i	−0.773967	−	0.0847289i
$777$	1.81453	−	0.532793i	0.0650957	−	0.0191138i
$778$	2.02833	+	0.170672i	0.0727191	+	0.00611888i
$779$	67.1238	+	9.65095i	2.40496	+	0.345781i
$780$	7.82326	+	2.51198i	0.280118	+	0.0899433i
$781$	30.9050			1.10587
$782$	24.4208	+	8.74406i	0.873287	+	0.312687i
$783$		−	3.26702i		−	0.116754i
$784$	10.2840	+	25.8820i	0.367285	+	0.924355i
$785$	−1.38465	+	9.63049i	−0.0494205	+	0.343727i
$786$	7.72164	+	0.649730i	0.275422	+	0.0231751i
$787$	−3.75029	−	12.7723i	−0.133683	−	0.455284i	0.865256	−	0.501330i	$-0.167156\pi$
$787$	−3.75029	−	12.7723i	−0.133683	−	0.455284i	−0.998939	+	0.0460467i	$0.985338\pi$
$788$	9.26513	−	19.0105i	0.330057	−	0.677221i
$789$	−34.3616	−	39.6554i	−1.22330	−	1.41177i
$790$	4.24682	−	2.25024i	0.151095	−	0.0800599i
$791$	−0.0225062	+	0.0766491i	−0.000800228	+	0.00272533i
$792$	−5.14449	−	15.5573i	−0.182801	−	0.552806i
$793$	9.83297	−	15.3004i	0.349179	−	0.543333i
$794$	7.00162	+	1.61537i	0.248478	+	0.0573273i
$795$	−7.43271	+	8.57781i	−0.263611	+	0.304223i
$796$	35.7643	−	15.2605i	1.26763	−	0.540893i
$797$	−3.47964	−	24.2014i	−0.123255	−	0.857258i	−0.953829	−	0.300350i	$-0.902897\pi$
$797$	−3.47964	−	24.2014i	−0.123255	−	0.857258i	0.830574	−	0.556908i	$-0.188012\pi$
$798$	−4.68910	−	2.63735i	−0.165992	−	0.0933611i
$799$	12.0351	+	26.3532i	0.425772	+	0.932311i
$800$	5.12509	−	2.39445i	0.181199	−	0.0846567i
$801$	19.2283	+	8.78126i	0.679398	+	0.310271i
$802$	−3.16355	−	15.4749i	−0.111709	−	0.546437i
$803$	−9.60880	−	14.9516i	−0.339087	−	0.527630i
$804$	−29.2370	−	35.5034i	−1.03111	−	1.25211i
$805$	−0.716701	−	0.589459i	−0.0252604	−	0.0207757i
$806$	−6.58724	−	18.3614i	−0.232025	−	0.646753i
$807$	−2.60624	−	4.05538i	−0.0917439	−	0.142756i
$808$	15.3456	+	12.4154i	0.539856	+	0.436773i
$809$	−22.5049	+	49.2788i	−0.791230	+	1.73255i	−0.118131	+	0.992998i	$0.537690\pi$
$809$	−22.5049	+	49.2788i	−0.791230	+	1.73255i	−0.673098	+	0.739553i	$0.735037\pi$
$810$	−7.88805	−	10.8175i	−0.277158	−	0.380088i
$811$	10.8429	+	23.7426i	0.380745	+	0.833716i	0.998865	+	0.0476321i	$0.0151675\pi$
$811$	10.8429	+	23.7426i	0.380745	+	0.833716i	−0.618120	+	0.786084i	$0.712105\pi$
$812$	0.531266	−	3.13453i	0.0186438	−	0.110001i
$813$	−24.5795	+	3.53400i	−0.862042	+	0.123943i
$814$	−11.6706	+	0.687650i	−0.409055	+	0.0241021i
$815$	−3.33655	+	3.85058i	−0.116874	+	0.134880i
$816$	26.6794	+	25.5708i	0.933964	+	0.895156i
$817$	−53.2746	−	34.2375i	−1.86384	−	1.19782i
$818$	−3.94745	−	1.52901i	−0.138019	−	0.0534605i
$819$	0.262874	−	0.895266i	0.00918555	−	0.0312831i
$820$	12.3165	+	11.2255i	0.430109	+	0.392012i
$821$	15.1449	−	13.1232i	0.528562	−	0.458002i	−0.349234	−	0.937035i	$-0.613558\pi$
$821$	15.1449	−	13.1232i	0.528562	−	0.458002i	0.877797	+	0.479034i	$0.159013\pi$
$822$	48.0550	+	49.2762i	1.67611	+	1.71871i
$823$	−8.41132	−	28.6463i	−0.293200	−	0.998548i	−0.965961	−	0.258688i	$-0.916710\pi$
$823$	−8.41132	−	28.6463i	−0.293200	−	0.998548i	0.672761	−	0.739860i	$-0.265108\pi$
$824$	3.52652	−	2.43838i	0.122852	−	0.0849450i
$825$	−4.88546	−	0.702422i	−0.170090	−	0.0244552i
$826$	1.67365	+	1.28595i	0.0582336	+	0.0447440i
$827$			44.9807i			1.56413i	0.623195	+	0.782066i	$0.285834\pi$
$827$			44.9807i			1.56413i	−0.623195	+	0.782066i	$0.714166\pi$
$828$	3.85376	−	26.9215i	0.133927	−	0.935588i
$829$		−	37.0132i		−	1.28552i	−0.766067	−	0.642760i	$-0.777789\pi$
$829$		−	37.0132i		−	1.28552i	0.766067	−	0.642760i	$-0.222211\pi$
$830$	12.3116	−	16.0234i	0.427343	−	0.556179i
$831$	14.4923	+	2.08369i	0.502734	+	0.0722822i
$832$	−0.917969	−	13.5747i	−0.0318248	−	0.470618i
$833$	7.50208	+	25.5497i	0.259932	+	0.885246i
$834$	−39.7249	+	38.7404i	−1.37556	+	1.34147i
$835$	−4.51720	+	3.91417i	−0.156324	+	0.135456i
$836$	24.5806	+	22.4033i	0.850136	+	0.774835i
$837$	−0.908688	+	3.09471i	−0.0314089	+	0.106969i
$838$	−17.7352	+	45.7871i	−0.612652	+	1.58169i
$839$	28.3554	+	18.2229i	0.978936	+	0.629124i	0.929176	−	0.369637i	$-0.120518\pi$
$839$	28.3554	+	18.2229i	0.978936	+	0.629124i	0.0497602	+	0.998761i	$0.484154\pi$
$840$	−0.589479	−	1.18336i	−0.0203389	−	0.0408297i
$841$	25.2065	−	29.0898i	0.869189	−	1.00310i
$842$	0.413606	+	7.01962i	0.0142538	+	0.241912i
$843$	2.48118	−	0.356740i	0.0854565	−	0.0122868i
$844$	−42.0499	−	7.12696i	−1.44742	−	0.245320i
$845$	4.19884	+	9.19418i	0.144444	+	0.316289i
$846$	24.5430	−	17.8966i	0.843807	−	0.615299i
$847$	−0.548619	+	1.20131i	−0.0188508	+	0.0412775i
$848$	17.7446	+	6.19289i	0.609352	+	0.212665i
$849$	−4.80149	−	7.47127i	−0.164787	−	0.256413i
$850$	5.09097	−	1.82641i	0.174619	−	0.0626453i
$851$	−17.8515	−	7.60413i	−0.611942	−	0.260666i
$852$	46.4543	+	56.4110i	1.59150	+	1.93261i
$853$	−9.52686	−	14.8241i	−0.326193	−	0.507567i	0.638964	−	0.769237i	$-0.279363\pi$
$853$	−9.52686	−	14.8241i	−0.326193	−	0.507567i	−0.965157	+	0.261670i	$0.915727\pi$
$854$	−2.86707	+	0.586119i	−0.0981091	+	0.0200566i
$855$	−20.9910	−	9.58625i	−0.717876	−	0.327843i
$856$	−1.37600	+	5.34782i	−0.0470308	+	0.182785i
$857$	−6.60334	−	14.4593i	−0.225566	−	0.493920i	0.762683	−	0.646772i	$-0.223881\pi$
$857$	−6.60334	−	14.4593i	−0.225566	−	0.493920i	−0.988249	+	0.152852i	$0.951154\pi$
$858$	−5.81952	+	10.3469i	−0.198675	+	0.353237i
$859$	1.32953	+	9.24708i	0.0453630	+	0.315506i	0.999851	+	0.0172574i	$0.00549348\pi$
$859$	1.32953	+	9.24708i	0.0453630	+	0.315506i	−0.954488	+	0.298249i	$0.903597\pi$
$860$	−6.10751	−	14.3135i	−0.208264	−	0.488086i
$861$	2.55044	−	2.94337i	0.0869189	−	0.100310i
$862$	−0.582820	+	2.52616i	−0.0198509	+	0.0860414i
$863$	18.5465	−	28.8589i	0.631330	−	0.982369i	−0.367303	−	0.930101i	$-0.619719\pi$
$863$	18.5465	−	28.8589i	0.631330	−	0.982369i	0.998633	−	0.0522676i	$-0.0166449\pi$
$864$	−1.19977	+	1.90294i	−0.0408170	+	0.0647395i
$865$	4.95165	−	16.8638i	0.168361	−	0.573386i
$866$	8.99743	+	16.9806i	0.305745	+	0.577025i
$867$	−3.75410	−	4.33247i	−0.127496	−	0.147138i
$868$	−1.37508	+	2.82144i	−0.0466734	+	0.0957660i
$869$	1.95629	+	6.66251i	0.0663626	+	0.226010i
$870$	2.35323	−	27.9667i	0.0797821	−	0.948161i
$871$	−2.30410	+	16.0254i	−0.0780715	+	0.542999i
$872$	17.4746	−	0.590172i	0.591763	−	0.0199858i
$873$			21.7423i			0.735866i
$874$	19.9694	+	51.4607i	0.675474	+	1.74068i
$875$	−0.193495			−0.00654131
$876$	12.8479	−	40.0132i	0.434090	−	1.35192i
$877$	32.8457	+	4.72250i	1.10912	+	0.159467i	0.672441	−	0.740150i	$-0.265246\pi$
$877$	32.8457	+	4.72250i	1.10912	+	0.159467i	0.436678	+	0.899618i	$0.356155\pi$
$878$	−0.431189	+	5.12442i	−0.0145519	+	0.172941i
$879$	39.6114	−	11.6310i	1.33606	−	0.392303i
$880$	1.90628	+	7.94743i	0.0642606	+	0.267908i
$881$	−16.4427	+	14.2477i	−0.553970	+	0.480018i	−0.886278	−	0.463153i	$-0.846718\pi$
$881$	−16.4427	+	14.2477i	−0.553970	+	0.480018i	0.332308	+	0.943171i	$0.392173\pi$
$882$	24.6696	−	13.0715i	0.830667	−	0.440141i
$883$	−31.5339	−	9.25918i	−1.06120	−	0.311596i	−0.295865	−	0.955230i	$-0.595608\pi$
$883$	−31.5339	−	9.25918i	−1.06120	−	0.311596i	−0.765334	+	0.643634i	$0.777426\pi$
$884$	0.326394	−	13.0047i	0.0109778	−	0.437395i
$885$	15.6744	+	10.0733i	0.526888	+	0.338610i
$886$	6.16100	−	26.7041i	0.206983	−	0.897142i
$887$	−33.9821	−	29.4457i	−1.14101	−	0.988689i	−0.141009	−	0.990008i	$-0.545035\pi$
$887$	−33.9821	−	29.4457i	−1.14101	−	0.988689i	−0.999999	+	0.00131896i	$0.999580\pi$
$888$	−18.7977	−	20.2688i	−0.630809	−	0.680178i
$889$	−2.36771	+	0.340425i	−0.0794103	+	0.0114175i
$890$	−9.18957	−	5.16860i	−0.308035	−	0.173252i
$891$	17.5947	−	8.03522i	0.589444	−	0.269190i
$892$	8.00475	+	5.43287i	0.268019	+	0.181906i
$893$	−25.6113	+	56.0808i	−0.857048	+	1.87667i
$894$	20.7332	−	4.23853i	0.693423	−	0.141758i
$895$	8.09950	−	5.20523i	0.270736	−	0.173992i
$896$	−1.46056	+	1.63067i	−0.0487940	+	0.0544769i
$897$	−16.2958	+	11.0748i	−0.544100	+	0.369775i
$898$	0.424816	+	1.18414i	0.0141763	+	0.0395153i
$899$	−56.0533	+	36.0233i	−1.86948	+	1.20144i
$900$	−2.94518	−	4.84596i	−0.0981727	−	0.161532i
$901$	16.3458	+	7.46486i	0.544556	+	0.248691i
$902$	−19.4537	+	14.1855i	−0.647737	+	0.472327i
$903$	−3.30831	+	1.51085i	−0.110094	+	0.0502781i
$904$	1.14957	−	0.205104i	0.0382342	−	0.00682167i
$905$	−1.26580	−	8.80383i	−0.0420766	−	0.292649i
$906$	69.9248	−	4.12007i	2.32310	−	0.136880i
$907$	29.7703	+	25.7961i	0.988507	+	0.856546i	0.989657	−	0.143453i	$-0.0458207\pi$
$907$	29.7703	+	25.7961i	0.988507	+	0.856546i	−0.00115020	+	0.999999i	$0.500366\pi$
$908$	4.90512	+	41.4798i	0.162782	+	1.37655i
$909$	10.6980	−	16.6463i	0.354829	−	0.552124i
$910$	−0.168094	+	0.433970i	−0.00557226	+	0.0143860i
$911$	−24.2464	−	7.11938i	−0.803319	−	0.235876i	−0.145800	−	0.989314i	$-0.546576\pi$
$911$	−24.2464	−	7.11938i	−0.803319	−	0.235876i	−0.657519	+	0.753438i	$0.728394\pi$
$912$	−3.94503	+	78.5422i	−0.130633	+	2.60079i
$913$	19.1183	+	22.0637i	0.632725	+	0.730203i
$914$	32.0030	+	32.8163i	1.05857	+	1.08547i
$915$	−24.7868	+	7.27808i	−0.819428	+	0.240606i
$916$	1.48081	+	5.55518i	0.0489273	+	0.183548i
$917$	−0.0624613	+	0.434428i	−0.00206265	+	0.0143461i
$918$	−1.31048	+	1.70557i	−0.0432524	+	0.0562922i
$919$	1.47001			0.0484912			0.0242456	−	0.999706i	$-0.492282\pi$
$919$	1.47001			0.0484912			0.0242456	+	0.999706i	$0.492282\pi$
$920$	−3.04128	+	13.2193i	−0.100268	+	0.435828i
$921$	−44.9695			−1.48179
$922$	14.9228	−	19.4217i	0.491456	−	0.639621i
$923$	3.66096	−	25.4626i	0.120502	−	0.838111i
$924$	1.84561	−	0.491974i	0.0607162	−	0.0161847i
$925$	−3.88204	+	1.13987i	−0.127641	+	0.0374787i
$926$	−35.1626	−	36.0562i	−1.15552	−	1.18488i
$927$	−2.81456	−	3.24818i	−0.0924424	−	0.106684i
$928$	−44.4752	+	13.4789i	−1.45997	+	0.442466i
$929$	−30.4041	−	8.92745i	−0.997527	−	0.292900i	−0.258086	−	0.966122i	$-0.583092\pi$
$929$	−30.4041	−	8.92745i	−0.997527	−	0.292900i	−0.739441	+	0.673222i	$0.764910\pi$
$930$	−10.0078	+	25.8371i	−0.328168	+	0.847233i
$931$	−30.6361	+	47.6707i	−1.00406	+	1.56234i
$932$	−30.1633	+	3.56692i	−0.988033	+	0.116838i
$933$	−38.5278	−	33.3845i	−1.26134	−	1.09296i
$934$	−38.2129	+	2.25156i	−1.25036	+	0.0736732i
$935$	1.11209	+	7.73475i	0.0363692	+	0.252953i
$936$	−13.4271	+	2.39563i	−0.438878	+	0.0783037i
$937$	−13.7036	+	6.25825i	−0.447679	+	0.204448i	−0.626480	−	0.779437i	$-0.715505\pi$
$937$	−13.7036	+	6.25825i	−0.447679	+	0.204448i	0.178802	+	0.983885i	$0.442778\pi$
$938$	2.10482	−	1.53482i	0.0687247	−	0.0501137i
$939$	−58.2073	−	26.5824i	−1.89952	−	0.867484i
$940$	−12.9468	+	7.86854i	−0.422278	+	0.256643i
$941$	16.4529	−	10.5736i	0.536348	−	0.344690i	−0.244261	−	0.969710i	$-0.578545\pi$
$941$	16.4529	−	10.5736i	0.536348	−	0.344690i	0.780609	+	0.625020i	$0.214909\pi$
$942$	−11.2240	−	31.2860i	−0.365698	−	1.01935i
$943$	−39.3942	+	6.70189i	−1.28285	+	0.218244i
$944$	5.91718	−	30.2796i	0.192588	−	0.985518i
$945$	0.0647327	−	0.0416012i	0.00210575	−	0.00135329i
$946$	22.0280	−	4.50322i	0.716193	−	0.146412i
$947$	14.4579	−	31.6584i	0.469818	−	1.02876i	−0.515320	−	0.856998i	$-0.672327\pi$
$947$	14.4579	−	31.6584i	0.469818	−	1.02876i	0.985139	−	0.171761i	$-0.0549457\pi$
$948$	−9.22055	+	13.5855i	−0.299470	+	0.441236i
$949$	−13.4568	+	6.14554i	−0.436828	+	0.199493i
$950$	10.0320	+	5.64241i	0.325480	+	0.183064i
$951$	−27.1665	+	3.90596i	−0.880935	+	0.126659i
$952$	−1.53469	+	1.42330i	−0.0497396	+	0.0461294i
$953$	16.6818	+	14.4549i	0.540377	+	0.468239i	0.881769	−	0.471682i	$-0.156353\pi$
$953$	16.6818	+	14.4549i	0.540377	+	0.468239i	−0.341392	+	0.939921i	$0.610898\pi$
$954$	4.23547	−	18.3581i	0.137128	−	0.594366i
$955$	14.9622	+	9.61560i	0.484164	+	0.311154i
$956$	−36.5394	−	0.917075i	−1.18177	−	0.0296603i
$957$	38.9058	+	11.4238i	1.25765	+	0.369278i
$958$	−35.0995	+	18.5980i	−1.13401	+	0.600873i
$959$	−2.94624	+	2.55293i	−0.0951392	+	0.0824385i
$960$	−11.6411	+	15.4256i	−0.375715	+	0.497859i
$961$	33.3721	−	9.79893i	1.07652	−	0.316094i
$962$	−0.815935	+	9.69688i	−0.0263068	+	0.312640i
$963$	5.47922	+	0.787794i	0.176566	+	0.0253863i
$964$	−30.9554	−	9.93951i	−0.997007	−	0.320130i
$965$	8.44983			0.272010
$966$	3.10632	+	0.633031i	0.0999442	+	0.0203674i
$967$			44.9487i			1.44545i	0.691134	+	0.722726i	$0.257111\pi$
$967$			44.9487i			1.44545i	−0.691134	+	0.722726i	$0.742889\pi$
$968$	19.2938	−	0.651614i	0.620126	−	0.0209437i
$969$	−10.7008	+	74.4257i	−0.343759	+	2.39090i
$970$	0.909289	−	10.8063i	0.0291955	−	0.346970i
$971$	6.03870	+	20.5659i	0.193791	+	0.659992i	0.997856	+	0.0654499i	$0.0208483\pi$
$971$	6.03870	+	20.5659i	0.193791	+	0.659992i	−0.804065	+	0.594542i	$0.797334\pi$
$972$	38.9690	+	18.9923i	1.24993	+	0.609178i
$973$	−2.05809	−	2.37517i	−0.0659795	−	0.0761444i
$974$	−24.6984	−	46.6127i	−0.791388	−	1.49357i
$975$	−1.15745	+	3.94191i	−0.0370681	+	0.126242i
$976$	26.3556	+	33.6929i	0.843623	+	1.07848i
$977$	26.4092	−	41.0935i	0.844906	−	1.31470i	−0.102522	−	0.994731i	$-0.532691\pi$
$977$	26.4092	−	41.0935i	0.844906	−	1.31470i	0.947428	−	0.319968i	$-0.103672\pi$
$978$	3.91300	−	16.9604i	0.125124	−	0.542334i
$979$	9.97532	−	11.5121i	0.318813	−	0.367929i
$980$	−12.8079	+	5.46507i	−0.409133	+	0.174575i
$981$	−2.49442	−	17.3491i	−0.0796407	−	0.553913i
$982$	5.06076	−	8.99783i	0.161495	−	0.287132i
$983$	−12.2599	−	26.8455i	−0.391031	−	0.856238i	−0.998102	−	0.0615901i	$-0.980383\pi$
$983$	−12.2599	−	26.8455i	−0.391031	−	0.856238i	0.607071	−	0.794648i	$-0.292344\pi$
$984$	−55.1345	−	14.1862i	−1.75762	−	0.452239i
$985$	9.61849	+	4.39262i	0.306471	+	0.139960i
$986$	−43.5336	+	8.89963i	−1.38639	+	0.283422i
$987$	1.91428	+	2.97867i	0.0609321	+	0.0948122i
$988$	21.3698	−	17.5980i	0.679865	−	0.559867i
$989$	36.0634	+	9.58933i	1.14675	+	0.304923i
$990$	7.71168	−	2.76660i	0.245093	−	0.0879284i
$991$	15.3966	+	23.9576i	0.489089	+	0.761037i	0.994820	−	0.101654i	$-0.0324135\pi$
$991$	15.3966	+	23.9576i	0.489089	+	0.761037i	−0.505731	+	0.862691i	$0.668777\pi$
$992$	45.8785	−	0.397657i	1.45664	−	0.0126256i
$993$	4.82564	−	10.5667i	0.153137	−	0.335323i
$994$	−3.34432	+	2.43866i	−0.106075	+	0.0773496i
$995$	8.07650	+	17.6851i	0.256042	+	0.560654i
$996$	−11.5356	+	68.0616i	−0.365520	+	2.15661i
$997$	34.3429	−	4.93777i	1.08765	−	0.156381i	0.424915	−	0.905233i	$-0.360304\pi$
$997$	34.3429	−	4.93777i	1.08765	−	0.156381i	0.662737	+	0.748852i	$0.269395\pi$
$998$	−1.14580	−	19.4463i	−0.0362698	−	0.615562i
$999$	1.05365	−	1.21597i	0.0333359	−	0.0384717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.11	✓	480
8.3	odd	2		920.2.bb.b.11.29	yes	480
23.21	odd	22		920.2.bb.b.251.29	yes	480
184.67	even	22	inner	920.2.bb.a.251.11	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.11	✓	480	1.1	even	1	trivial
920.2.bb.a.251.11	yes	480	184.67	even	22	inner
920.2.bb.b.11.29	yes	480	8.3	odd	2
920.2.bb.b.251.29	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+(-1.12141 - 0.861644i) q^{2} +(-0.343783 + 2.39106i) q^{3} +(0.515140 + 1.93252i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(2.44577 - 2.38515i) q^{6} +(0.126712 + 0.146233i) q^{7} +(1.08746 - 2.61102i) q^{8} +(-2.72052 - 0.798818i) q^{9} +(1.31874 + 0.510802i) q^{10} +(-1.10464 + 1.71886i) q^{11} +(-4.79787 + 0.567365i) q^{12} +(1.28531 + 1.11373i) q^{13} +(-0.0160955 - 0.273169i) q^{14} +(-0.343783 - 2.39106i) q^{15} +(-3.46926 + 1.99103i) q^{16} +(-3.47889 + 1.58876i) q^{17} +(2.36254 + 3.23993i) q^{18} +(-7.40324 - 3.38094i) q^{19} +(-1.03873 - 1.70911i) q^{20} +(-0.393215 + 0.252704i) q^{21} +(2.71981 - 0.975744i) q^{22} +(4.76299 + 0.560257i) q^{23} +(5.86927 + 3.49781i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.481729 - 2.35643i) q^{26} +(-0.165200 + 0.361738i) q^{27} +(-0.217325 + 0.320204i) q^{28} +(-7.47291 + 3.41276i) q^{29} +(-1.67472 + 2.97759i) q^{30} +(8.02799 - 1.15425i) q^{31} +(5.60604 + 0.756493i) q^{32} +(-3.73015 - 3.23219i) q^{33} +(5.27023 + 1.21591i) q^{34} +(-0.162778 - 0.104611i) q^{35} +(0.142281 - 5.66897i) q^{36} +(-3.88204 - 1.13987i) q^{37} +(5.38892 + 10.1704i) q^{38} +(-3.10487 + 2.69038i) q^{39} +(-0.307799 + 2.81163i) q^{40} +(-7.99476 + 2.34747i) q^{41} +(0.658698 + 0.0554255i) q^{42} +(7.70183 + 1.10736i) q^{43} +(-3.89078 - 1.24929i) q^{44} +2.83538 q^{45} +(-4.85855 - 4.73228i) q^{46} -7.57518i q^{47} +(-3.56802 - 8.97971i) q^{48} +(0.990876 - 6.89169i) q^{49} +(-1.40923 - 0.118579i) q^{50} +(-2.60284 - 8.86445i) q^{51} +(-1.49019 + 3.05762i) q^{52} +(-3.07690 - 3.55093i) q^{53} +(0.496947 - 0.263314i) q^{54} +(0.575640 - 1.96045i) q^{55} +(0.519613 - 0.171825i) q^{56} +(10.6292 - 16.5393i) q^{57} +(11.3208 + 2.61187i) q^{58} +(-5.05100 + 5.82917i) q^{59} +(4.44368 - 1.89610i) q^{60} +(-1.52193 - 10.5853i) q^{61} +(-9.99726 - 5.62288i) q^{62} +(-0.227909 - 0.499051i) q^{63} +(-5.63487 - 5.67875i) q^{64} +(-1.54702 - 0.706501i) q^{65} +(1.39804 + 6.83869i) q^{66} +(5.14671 + 8.00844i) q^{67} +(-4.86242 - 5.90460i) q^{68} +(-2.97705 + 11.1960i) q^{69} +(0.0924041 + 0.257569i) q^{70} +(-8.17755 - 12.7245i) q^{71} +(-5.04419 + 6.23466i) q^{72} +(-3.61351 + 7.91248i) q^{73} +(3.37121 + 4.62320i) q^{74} +(1.00350 + 2.19735i) q^{75} +(2.72004 - 16.0486i) q^{76} +(-0.391327 + 0.0562643i) q^{77} +(5.79999 - 0.341744i) q^{78} +(2.22552 - 2.56839i) q^{79} +(2.76779 - 2.88779i) q^{80} +(-7.96395 - 5.11812i) q^{81} +(10.9881 + 4.25615i) q^{82} +(4.02554 - 13.7097i) q^{83} +(-0.690916 - 0.629718i) q^{84} +(2.89037 - 2.50452i) q^{85} +(-7.68280 - 7.87804i) q^{86} +(-5.59108 - 19.0415i) q^{87} +(3.28673 + 4.75344i) q^{88} +(-7.37940 - 1.06100i) q^{89} +(-3.17963 - 2.44308i) q^{90} +0.329078i q^{91} +(1.37090 + 9.49319i) q^{92} +19.5923i q^{93} +(-6.52711 + 8.49491i) q^{94} +(8.05587 + 1.15826i) q^{95} +(-3.73609 + 13.1443i) q^{96} +(-2.16039 - 7.35762i) q^{97} +(-7.04937 + 6.87466i) q^{98} +(4.37827 - 3.79379i) 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

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