LMFDB - Embedded newform 350.2.q.c.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(11,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([24, 20]))

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

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

chi := DirichletCharacter("350.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.q (of order $15$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	350.11
Dual form			350.2.q.c.191.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 + 0.406737i) q^{2} +(-0.138897 - 0.154261i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.77975 - 1.35369i) q^{5} +(-0.0641452 - 0.197419i) q^{6} +(0.411507 - 2.61355i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309081 - 2.94071i) q^{9} +O(q^{10})$	\(q+(0.913545 + 0.406737i) q^{2} +(-0.138897 - 0.154261i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.77975 - 1.35369i) q^{5} +(-0.0641452 - 0.197419i) q^{6} +(0.411507 - 2.61355i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309081 - 2.94071i) q^{9} +(2.17648 - 0.512766i) q^{10} +(0.426271 + 4.05570i) q^{11} +(0.0216978 - 0.206441i) q^{12} +(-4.09048 - 2.97191i) q^{13} +(1.43896 - 2.22023i) q^{14} +(-0.456023 - 0.0865226i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(4.33844 + 0.922165i) q^{17} +(1.47846 - 2.56076i) q^{18} +(-2.91912 + 3.24201i) q^{19} +(2.19688 + 0.416819i) q^{20} +(-0.460325 + 0.299535i) q^{21} +(-1.26018 + 3.87845i) q^{22} +(4.45503 + 1.98351i) q^{23} +(0.103789 - 0.179768i) q^{24} +(1.33505 - 4.81847i) q^{25} +(-2.52805 - 4.37872i) q^{26} +(-1.00037 + 0.726811i) q^{27} +(2.21760 - 1.44300i) q^{28} +(-2.26620 + 6.97466i) q^{29} +(-0.381406 - 0.264524i) q^{30} +(4.40252 + 0.935784i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.566427 - 0.629081i) q^{33} +(3.58829 + 2.60704i) q^{34} +(-2.80556 - 5.20853i) q^{35} +(2.39219 - 1.73803i) q^{36} +(-1.16205 + 11.0562i) q^{37} +(-3.98539 + 1.77441i) q^{38} +(0.109707 + 1.04379i) q^{39} +(1.83741 + 1.27433i) q^{40} +(-8.12326 - 5.90189i) q^{41} +(-0.542360 + 0.0864078i) q^{42} -3.55966 q^{43} +(-2.72874 + 3.03057i) q^{44} +(-3.43073 - 5.65215i) q^{45} +(3.26311 + 3.62405i) q^{46} +(7.80164 - 1.65829i) q^{47} +(0.167934 - 0.122011i) q^{48} +(-6.66132 - 2.15099i) q^{49} +(3.17947 - 3.85888i) q^{50} +(-0.460342 - 0.797337i) q^{51} +(-0.528507 - 5.02841i) q^{52} +(-7.61081 - 8.45266i) q^{53} +(-1.20950 + 0.257088i) q^{54} +(6.24882 + 6.64111i) q^{55} +(2.61280 - 0.416266i) q^{56} +0.905570 q^{57} +(-4.90713 + 5.44992i) q^{58} +(-2.06084 + 0.917543i) q^{59} +(-0.240840 - 0.396786i) q^{60} +(1.28369 + 0.571535i) q^{61} +(3.64128 + 2.64555i) q^{62} +(-7.55852 - 2.01792i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-11.3031 + 0.247978i) q^{65} +(0.773327 - 0.344307i) q^{66} +(2.45488 + 0.521801i) q^{67} +(2.21768 + 3.84114i) q^{68} +(-0.312813 - 0.962739i) q^{69} +(-0.444506 - 5.89936i) q^{70} +(-4.35140 + 13.3922i) q^{71} +(2.89230 - 0.614776i) q^{72} +(0.535757 + 5.09738i) q^{73} +(-5.55855 + 9.62769i) q^{74} +(-0.928734 + 0.463325i) q^{75} -4.36255 q^{76} +(10.7752 + 0.554865i) q^{77} +(-0.324325 + 0.998169i) q^{78} +(-4.19375 + 0.891410i) q^{79} +(1.16024 + 1.91150i) q^{80} +(-8.42582 - 1.79096i) q^{81} +(-5.02045 - 8.69567i) q^{82} +(-3.89185 - 11.9779i) q^{83} +(-0.530616 - 0.141660i) q^{84} +(8.96969 - 4.23168i) q^{85} +(-3.25191 - 1.44784i) q^{86} +(1.39068 - 0.619172i) q^{87} +(-3.72547 + 1.65869i) q^{88} +(-2.20482 - 0.981651i) q^{89} +(-0.835189 - 6.55889i) q^{90} +(-9.45049 + 9.46772i) q^{91} +(1.50696 + 4.63796i) q^{92} +(-0.467141 - 0.809113i) q^{93} +(7.80164 + 1.65829i) q^{94} +(-0.806635 + 9.72155i) q^{95} +(0.203042 - 0.0431579i) q^{96} +(1.66969 - 5.13879i) q^{97} +(-5.21054 - 4.67443i) q^{98} +12.0584 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9}+O(q^{10}) $ 80 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 20 * q^8 + 4 * q^9	\( 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9} + 3 q^{10} + 10 q^{11} + 2 q^{12} - 12 q^{13} - 7 q^{14} + 22 q^{15} + 10 q^{16} - 8 q^{17} - 36 q^{18} + 8 q^{19} + 4 q^{20} + 17 q^{21} + 20 q^{22} + 5 q^{23} - 8 q^{24} + 32 q^{25} - 24 q^{26} + 32 q^{27} - 7 q^{28} + 12 q^{29} - 11 q^{30} - 9 q^{31} - 40 q^{32} + 33 q^{33} - 4 q^{34} - 22 q^{35} - 8 q^{36} - 14 q^{37} - 2 q^{38} - 2 q^{40} - 18 q^{41} - 19 q^{42} - 8 q^{43} - 10 q^{44} + 33 q^{45} - 10 q^{46} + 10 q^{47} - 4 q^{48} + 12 q^{49} + 36 q^{50} + 46 q^{51} + 6 q^{52} - 30 q^{53} + 14 q^{54} + 2 q^{55} - q^{56} - 52 q^{57} - 6 q^{58} + 40 q^{59} + 4 q^{60} + 16 q^{61} - 32 q^{62} - 100 q^{63} - 20 q^{64} - 25 q^{65} - 7 q^{66} + q^{67} + 12 q^{68} - 142 q^{69} + 25 q^{70} - 84 q^{71} + 14 q^{72} + 22 q^{73} + 6 q^{74} - 29 q^{75} + 24 q^{76} + 38 q^{77} - 30 q^{78} + 10 q^{79} + 3 q^{80} + 52 q^{81} - 6 q^{82} - 98 q^{83} + 2 q^{84} - 36 q^{85} - 26 q^{86} + 34 q^{87} + 10 q^{88} + 45 q^{89} + 24 q^{90} - 63 q^{91} + 20 q^{92} - 20 q^{93} + 10 q^{94} - 33 q^{95} + 2 q^{96} - 106 q^{97} - 55 q^{98} + 12 q^{99}+O(q^{100}) \) 80 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 20 * q^8 + 4 * q^9 + 3 * q^10 + 10 * q^11 + 2 * q^12 - 12 * q^13 - 7 * q^14 + 22 * q^15 + 10 * q^16 - 8 * q^17 - 36 * q^18 + 8 * q^19 + 4 * q^20 + 17 * q^21 + 20 * q^22 + 5 * q^23 - 8 * q^24 + 32 * q^25 - 24 * q^26 + 32 * q^27 - 7 * q^28 + 12 * q^29 - 11 * q^30 - 9 * q^31 - 40 * q^32 + 33 * q^33 - 4 * q^34 - 22 * q^35 - 8 * q^36 - 14 * q^37 - 2 * q^38 - 2 * q^40 - 18 * q^41 - 19 * q^42 - 8 * q^43 - 10 * q^44 + 33 * q^45 - 10 * q^46 + 10 * q^47 - 4 * q^48 + 12 * q^49 + 36 * q^50 + 46 * q^51 + 6 * q^52 - 30 * q^53 + 14 * q^54 + 2 * q^55 - q^56 - 52 * q^57 - 6 * q^58 + 40 * q^59 + 4 * q^60 + 16 * q^61 - 32 * q^62 - 100 * q^63 - 20 * q^64 - 25 * q^65 - 7 * q^66 + q^67 + 12 * q^68 - 142 * q^69 + 25 * q^70 - 84 * q^71 + 14 * q^72 + 22 * q^73 + 6 * q^74 - 29 * q^75 + 24 * q^76 + 38 * q^77 - 30 * q^78 + 10 * q^79 + 3 * q^80 + 52 * q^81 - 6 * q^82 - 98 * q^83 + 2 * q^84 - 36 * q^85 - 26 * q^86 + 34 * q^87 + 10 * q^88 + 45 * q^89 + 24 * q^90 - 63 * q^91 + 20 * q^92 - 20 * q^93 + 10 * q^94 - 33 * q^95 + 2 * q^96 - 106 * q^97 - 55 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$3$	−0.138897	−	0.154261i	−0.0801921	−	0.0890624i	0.701713	−	0.712459i	$-0.252419\pi$
$3$	−0.138897	−	0.154261i	−0.0801921	−	0.0890624i	−0.781905	+	0.623397i	$0.785752\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	1.77975	−	1.35369i	0.795930	−	0.605389i
$5$	1.77975	−	1.35369i	0.795930	−	0.605389i
$6$	−0.0641452	−	0.197419i	−0.0261872	−	0.0805958i
$7$	0.411507	−	2.61355i	0.155535	−	0.987830i
$7$	0.411507	−	2.61355i	0.155535	−	0.987830i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.309081	−	2.94071i	0.103027	−	0.980238i
$10$	2.17648	−	0.512766i	0.688264	−	0.162151i
$11$	0.426271	+	4.05570i	0.128526	+	1.22284i	0.848635	+	0.528979i	$0.177425\pi$
$11$	0.426271	+	4.05570i	0.128526	+	1.22284i	−0.720110	+	0.693860i	$0.755908\pi$
$12$	0.0216978	−	0.206441i	0.00626362	−	0.0595944i
$13$	−4.09048	−	2.97191i	−1.13449	−	0.824258i	−0.148152	−	0.988965i	$-0.547332\pi$
$13$	−4.09048	−	2.97191i	−1.13449	−	0.824258i	−0.986343	+	0.164706i	$0.947332\pi$
$14$	1.43896	−	2.22023i	0.384578	−	0.593380i
$15$	−0.456023	−	0.0865226i	−0.117745	−	0.0223400i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	4.33844	+	0.922165i	1.05223	+	0.223658i	0.701389	−	0.712778i	$-0.252564\pi$
$17$	4.33844	+	0.922165i	1.05223	+	0.223658i	0.350838	+	0.936436i	$0.385897\pi$
$18$	1.47846	−	2.56076i	0.348475	−	0.603577i
$19$	−2.91912	+	3.24201i	−0.669691	+	0.743767i	−0.978248	−	0.207439i	$-0.933487\pi$
$19$	−2.91912	+	3.24201i	−0.669691	+	0.743767i	0.308557	+	0.951206i	$0.400154\pi$
$20$	2.19688	+	0.416819i	0.491236	+	0.0932036i
$21$	−0.460325	+	0.299535i	−0.100451	+	0.0653639i
$22$	−1.26018	+	3.87845i	−0.268672	+	0.826887i
$23$	4.45503	+	1.98351i	0.928938	+	0.413590i	0.814713	−	0.579865i	$-0.196895\pi$
$23$	4.45503	+	1.98351i	0.928938	+	0.413590i	0.114226	+	0.993455i	$0.463561\pi$
$24$	0.103789	−	0.179768i	0.0211859	−	0.0366950i
$25$	1.33505	−	4.81847i	0.267009	−	0.963694i
$26$	−2.52805	−	4.37872i	−0.495792	−	0.858737i
$27$	−1.00037	+	0.726811i	−0.192521	+	0.139875i
$28$	2.21760	−	1.44300i	0.419087	−	0.272701i
$29$	−2.26620	+	6.97466i	−0.420823	+	1.29516i	0.486114	+	0.873895i	$0.338414\pi$
$29$	−2.26620	+	6.97466i	−0.420823	+	1.29516i	−0.906937	+	0.421266i	$0.861586\pi$
$30$	−0.381406	−	0.264524i	−0.0696349	−	0.0482952i
$31$	4.40252	+	0.935784i	0.790716	+	0.168072i	0.585529	−	0.810651i	$-0.300887\pi$
$31$	4.40252	+	0.935784i	0.790716	+	0.168072i	0.205186	+	0.978723i	$0.434220\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.566427	−	0.629081i	0.0986022	−	0.109509i
$34$	3.58829	+	2.60704i	0.615386	+	0.447104i
$35$	−2.80556	−	5.20853i	−0.474226	−	0.880403i
$36$	2.39219	−	1.73803i	0.398699	−	0.289671i
$37$	−1.16205	+	11.0562i	−0.191040	+	1.81763i	0.308375	+	0.951265i	$0.400215\pi$
$37$	−1.16205	+	11.0562i	−0.191040	+	1.81763i	−0.499415	+	0.866363i	$0.666452\pi$
$38$	−3.98539	+	1.77441i	−0.646515	+	0.287847i
$39$	0.109707	+	1.04379i	0.0175671	+	0.167140i
$40$	1.83741	+	1.27433i	0.290520	+	0.201490i
$41$	−8.12326	−	5.90189i	−1.26864	−	0.921721i	−0.269492	−	0.963003i	$-0.586856\pi$
$41$	−8.12326	−	5.90189i	−1.26864	−	0.921721i	−0.999148	+	0.0412818i	$0.986856\pi$
$42$	−0.542360	+	0.0864078i	−0.0836880	+	0.0133330i
$43$	−3.55966			−0.542843			−0.271421	−	0.962461i	$-0.587494\pi$
$43$	−3.55966			−0.542843			−0.271421	+	0.962461i	$0.587494\pi$
$44$	−2.72874	+	3.03057i	−0.411373	+	0.456876i
$45$	−3.43073	−	5.65215i	−0.511422	−	0.842572i
$46$	3.26311	+	3.62405i	0.481119	+	0.534337i
$47$	7.80164	−	1.65829i	1.13799	−	0.241887i	0.399878	−	0.916568i	$-0.369052\pi$
$47$	7.80164	−	1.65829i	1.13799	−	0.241887i	0.738109	+	0.674682i	$0.235719\pi$
$48$	0.167934	−	0.122011i	0.0242392	−	0.0176108i
$49$	−6.66132	−	2.15099i	−0.951618	−	0.307284i
$50$	3.17947	−	3.85888i	0.449645	−	0.545728i
$51$	−0.460342	−	0.797337i	−0.0644608	−	0.111649i
$52$	−0.528507	−	5.02841i	−0.0732908	−	0.697315i
$53$	−7.61081	−	8.45266i	−1.04542	−	1.16106i	−0.986661	−	0.162790i	$-0.947951\pi$
$53$	−7.61081	−	8.45266i	−1.04542	−	1.16106i	−0.0587638	−	0.998272i	$-0.518716\pi$
$54$	−1.20950	+	0.257088i	−0.164593	+	0.0349852i
$55$	6.24882	+	6.64111i	0.842590	+	0.895486i
$56$	2.61280	−	0.416266i	0.349150	−	0.0556259i
$57$	0.905570			0.119946
$58$	−4.90713	+	5.44992i	−0.644337	+	0.715609i
$59$	−2.06084	+	0.917543i	−0.268298	+	0.119454i	−0.536476	−	0.843915i	$-0.680245\pi$
$59$	−2.06084	+	0.917543i	−0.268298	+	0.119454i	0.268178	+	0.963369i	$0.413578\pi$
$60$	−0.240840	−	0.396786i	−0.0310924	−	0.0512249i
$61$	1.28369	+	0.571535i	0.164360	+	0.0731776i	0.487267	−	0.873253i	$-0.337994\pi$
$61$	1.28369	+	0.571535i	0.164360	+	0.0731776i	−0.322908	+	0.946430i	$0.604660\pi$
$62$	3.64128	+	2.64555i	0.462443	+	0.335985i
$63$	−7.55852	−	2.01792i	−0.952284	−	0.254235i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−11.3031	+	0.247978i	−1.40197	+	0.0307579i
$66$	0.773327	−	0.344307i	0.0951899	−	0.0423813i
$67$	2.45488	+	0.521801i	0.299911	+	0.0637481i	0.355410	−	0.934711i	$-0.384341\pi$
$67$	2.45488	+	0.521801i	0.299911	+	0.0637481i	−0.0554983	+	0.998459i	$0.517675\pi$
$68$	2.21768	+	3.84114i	0.268934	+	0.465807i
$69$	−0.312813	−	0.962739i	−0.0376582	−	0.115900i
$70$	−0.444506	−	5.89936i	−0.0531286	−	0.705108i
$71$	−4.35140	+	13.3922i	−0.516416	+	1.58937i	0.264273	+	0.964448i	$0.414868\pi$
$71$	−4.35140	+	13.3922i	−0.516416	+	1.58937i	−0.780690	+	0.624919i	$0.785132\pi$
$72$	2.89230	−	0.614776i	0.340860	−	0.0724521i
$73$	0.535757	+	5.09738i	0.0627056	+	0.596604i	0.980083	+	0.198586i	$0.0636350\pi$
$73$	0.535757	+	5.09738i	0.0627056	+	0.596604i	−0.917378	+	0.398017i	$0.869698\pi$
$74$	−5.55855	+	9.62769i	−0.646168	+	1.11920i
$75$	−0.928734	+	0.463325i	−0.107241	+	0.0535002i
$76$	−4.36255			−0.500419
$77$	10.7752	+	0.554865i	1.22795	+	0.0632327i
$78$	−0.324325	+	0.998169i	−0.0367226	+	0.113020i
$79$	−4.19375	+	0.891410i	−0.471834	+	0.100291i	−0.437691	−	0.899125i	$-0.644204\pi$
$79$	−4.19375	+	0.891410i	−0.471834	+	0.100291i	−0.0341433	+	0.999417i	$0.510870\pi$
$80$	1.16024	+	1.91150i	0.129719	+	0.213713i
$81$	−8.42582	−	1.79096i	−0.936202	−	0.198996i
$82$	−5.02045	−	8.69567i	−0.554416	−	0.960277i
$83$	−3.89185	−	11.9779i	−0.427186	−	1.31474i	−0.900885	−	0.434058i	$-0.857081\pi$
$83$	−3.89185	−	11.9779i	−0.427186	−	1.31474i	0.473699	−	0.880687i	$-0.342919\pi$
$84$	−0.530616	−	0.141660i	−0.0578949	−	0.0154564i
$85$	8.96969	−	4.23168i	0.972899	−	0.458990i
$86$	−3.25191	−	1.44784i	−0.350662	−	0.156125i
$87$	1.39068	−	0.619172i	0.149097	−	0.0663822i
$88$	−3.72547	+	1.65869i	−0.397137	+	0.176817i
$89$	−2.20482	−	0.981651i	−0.233711	−	0.104055i	0.286540	−	0.958068i	$-0.407495\pi$
$89$	−2.20482	−	0.981651i	−0.233711	−	0.104055i	−0.520251	+	0.854013i	$0.674162\pi$
$90$	−0.835189	−	6.55889i	−0.0880366	−	0.691368i
$91$	−9.45049	+	9.46772i	−0.990681	+	0.992487i
$92$	1.50696	+	4.63796i	0.157112	+	0.483541i
$93$	−0.467141	−	0.809113i	−0.0484403	−	0.0839011i
$94$	7.80164	+	1.65829i	0.804678	+	0.171040i
$95$	−0.806635	+	9.72155i	−0.0827590	+	0.997410i
$96$	0.203042	−	0.0431579i	0.0207229	−	0.00440479i
$97$	1.66969	−	5.13879i	0.169532	−	0.521765i	−0.829810	−	0.558046i	$-0.811551\pi$
$97$	1.66969	−	5.13879i	0.169532	−	0.521765i	0.999342	+	0.0362812i	$0.0115512\pi$
$98$	−5.21054	−	4.67443i	−0.526344	−	0.472189i
$99$	12.0584			1.21191
$100$	4.47414	−	2.23205i	0.447414	−	0.223205i
$101$	1.06865	−	1.85096i	0.106335	−	0.184177i	−0.807948	−	0.589254i	$-0.799422\pi$
$101$	1.06865	−	1.85096i	0.106335	−	0.184177i	0.914283	+	0.405077i	$0.132755\pi$
$102$	−0.0962378	−	0.915641i	−0.00952896	−	0.0906620i
$103$	9.86420	−	2.09670i	0.971948	−	0.206594i	0.305539	−	0.952180i	$-0.401164\pi$
$103$	9.86420	−	2.09670i	0.971948	−	0.206594i	0.666410	+	0.745586i	$0.267830\pi$
$104$	1.56242	−	4.80864i	0.153208	−	0.471526i
$105$	−0.413788	+	1.15624i	−0.0403816	+	0.112837i
$106$	−3.51481	−	10.8175i	−0.341389	−	1.05069i
$107$	1.84487	+	3.19541i	0.178351	+	0.308912i	0.941316	−	0.337527i	$-0.109591\pi$
$107$	1.84487	+	3.19541i	0.178351	+	0.308912i	−0.762965	+	0.646440i	$0.776257\pi$
$108$	−1.20950	−	0.257088i	−0.116385	−	0.0247383i
$109$	8.53325	−	3.79925i	0.817338	−	0.363902i	0.0448989	−	0.998992i	$-0.485703\pi$
$109$	8.53325	−	3.79925i	0.817338	−	0.363902i	0.772439	+	0.635089i	$0.219037\pi$
$110$	3.00740	+	8.60857i	0.286744	+	0.820795i
$111$	1.86694	−	1.35641i	0.177202	−	0.128745i
$112$	2.55622	+	0.682443i	0.241540	+	0.0644848i
$113$	4.79568	+	3.48427i	0.451140	+	0.327772i	0.790046	−	0.613048i	$-0.210057\pi$
$113$	4.79568	+	3.48427i	0.451140	+	0.327772i	−0.338906	+	0.940820i	$0.610057\pi$
$114$	0.827279	+	0.368328i	0.0774818	+	0.0344971i
$115$	10.6139	−	2.50058i	0.989753	−	0.233180i
$116$	−6.69956	+	2.98284i	−0.622039	+	0.276950i
$117$	−10.0038	+	11.1104i	−0.924853	+	1.02715i
$118$	−2.25587			−0.207669
$119$	4.19542	−	10.9593i	0.384594	−	1.00464i
$120$	−0.0586311	−	0.460441i	−0.00535226	−	0.0420323i
$121$	−5.50736	+	1.17063i	−0.500669	+	0.106421i
$122$	0.940244	+	1.04425i	0.0851257	+	0.0945417i
$123$	0.217866	+	2.07285i	0.0196443	+	0.186903i
$124$	2.25044	+	3.89787i	0.202095	+	0.350039i
$125$	−4.14666	−	10.3829i	−0.370889	−	0.928677i
$126$	−6.08429	−	4.91779i	−0.542032	−	0.438112i
$127$	−7.50941	+	5.45590i	−0.666352	+	0.484133i	−0.868802	−	0.495159i	$-0.835110\pi$
$127$	−7.50941	+	5.45590i	−0.666352	+	0.484133i	0.202450	+	0.979293i	$0.435110\pi$
$128$	−0.978148	+	0.207912i	−0.0864569	+	0.0183770i
$129$	0.494425	+	0.549115i	0.0435317	+	0.0483469i
$130$	−10.4267	−	4.37084i	−0.914486	−	0.383348i
$131$	3.65855	−	4.06323i	0.319649	−	0.355006i	−0.561810	−	0.827266i	$-0.689895\pi$
$131$	3.65855	−	4.06323i	0.319649	−	0.355006i	0.881459	+	0.472260i	$0.156562\pi$
$132$	0.846511			0.0736794
$133$	7.27192	+	8.96337i	0.630556	+	0.777223i
$134$	2.03041	+	1.47518i	0.175401	+	0.127436i
$135$	−0.796534	+	2.64773i	−0.0685548	+	0.227881i
$136$	0.463622	+	4.41107i	0.0397553	+	0.378246i
$137$	15.8876	−	7.07361i	1.35737	−	0.604340i	0.406420	−	0.913687i	$-0.366777\pi$
$137$	15.8876	−	7.07361i	1.35737	−	0.604340i	0.950949	+	0.309347i	$0.100110\pi$
$138$	0.105812	−	1.00674i	0.00900735	−	0.0856992i
$139$	−18.2562	+	13.2639i	−1.54847	+	1.12503i	−0.603744	+	0.797178i	$0.706325\pi$
$139$	−18.2562	+	13.2639i	−1.54847	+	1.12503i	−0.944729	+	0.327853i	$0.893675\pi$
$140$	1.99341	−	5.57013i	0.168474	−	0.470762i
$141$	−1.33943	−	0.973155i	−0.112801	−	0.0819544i
$142$	−9.42232	+	10.4645i	−0.790703	+	0.878165i
$143$	10.3095	−	17.8566i	0.862124	−	1.49324i
$144$	2.89230	+	0.614776i	0.241025	+	0.0512314i
$145$	5.40824	+	15.4809i	0.449130	+	1.28562i
$146$	−1.58385	+	4.87460i	−0.131081	+	0.403425i
$147$	0.593424	+	1.32635i	0.0489448	+	0.109395i
$148$	−8.99392	+	6.53447i	−0.739296	+	0.537130i
$149$	−3.80025	−	6.58223i	−0.311329	−	0.539238i	0.667321	−	0.744770i	$-0.267441\pi$
$149$	−3.80025	−	6.58223i	−0.311329	−	0.539238i	−0.978650	+	0.205532i	$0.934107\pi$
$150$	−1.03689	+	0.0455187i	−0.0846619	+	0.00371658i
$151$	−2.31955	+	4.01758i	−0.188762	+	0.326946i	−0.944838	−	0.327538i	$-0.893781\pi$
$151$	−2.31955	+	4.01758i	−0.188762	+	0.326946i	0.756075	+	0.654484i	$0.227114\pi$
$152$	−3.98539	−	1.77441i	−0.323258	−	0.143924i
$153$	4.05275	−	12.4731i	0.327646	−	1.00839i
$154$	9.61795	+	4.88956i	0.775037	+	0.394012i
$155$	9.10216	−	4.29418i	0.731103	−	0.344917i
$156$	−0.702278	+	0.779958i	−0.0562272	+	0.0624466i
$157$	6.56484	−	11.3706i	0.523931	−	0.907476i	−0.475681	−	0.879618i	$-0.657798\pi$
$157$	6.56484	−	11.3706i	0.523931	−	0.907476i	0.999612	−	0.0278576i	$-0.00886851\pi$
$158$	−4.19375	−	0.891410i	−0.333637	−	0.0709168i
$159$	−0.246795	+	2.34809i	−0.0195721	+	0.186216i
$160$	0.282453	+	2.21816i	0.0223299	+	0.175361i
$161$	7.01728	−	10.8272i	0.553039	−	0.853306i
$162$	−6.96892	−	5.06322i	−0.547530	−	0.397804i
$163$	1.26066	−	11.9944i	0.0987425	−	0.939473i	−0.827225	−	0.561870i	$-0.810082\pi$
$163$	1.26066	−	11.9944i	0.0987425	−	0.939473i	0.925968	−	0.377602i	$-0.123251\pi$
$164$	−1.04956	−	9.98589i	−0.0819568	−	0.779767i
$165$	0.156520	−	1.88637i	0.0121851	−	0.146854i
$166$	1.31646	−	12.5253i	0.102177	−	0.972153i
$167$	0.847256	+	2.60759i	0.0655627	+	0.201781i	0.978471	−	0.206383i	$-0.0661692\pi$
$167$	0.847256	+	2.60759i	0.0655627	+	0.201781i	−0.912909	+	0.408164i	$0.866169\pi$
$168$	−0.427123	−	0.345234i	−0.0329533	−	0.0266354i
$169$	3.88256	+	11.9493i	0.298658	+	0.919176i
$170$	9.91540	−	0.217534i	0.760476	−	0.0166841i
$171$	8.63157	+	9.58632i	0.660072	+	0.733085i
$172$	−2.38188	−	2.64534i	−0.181616	−	0.201705i
$173$	−9.94866	−	4.42943i	−0.756382	−	0.336763i	−0.00794486	−	0.999968i	$-0.502529\pi$
$173$	−9.94866	−	4.42943i	−0.756382	−	0.336763i	−0.748438	+	0.663205i	$0.769196\pi$
$174$	1.52229			0.115405
$175$	−12.0439	−	5.47205i	−0.910437	−	0.413648i
$176$	−4.07804			−0.307394
$177$	0.427784	+	0.190462i	0.0321542	+	0.0143160i
$178$	−1.61493	−	1.79357i	−0.121044	−	0.134433i
$179$	6.33636	+	7.03724i	0.473602	+	0.525988i	0.931854	−	0.362834i	$-0.118191\pi$
$179$	6.33636	+	7.03724i	0.473602	+	0.525988i	−0.458252	+	0.888822i	$0.651524\pi$
$180$	1.90476	−	6.33155i	0.141972	−	0.471926i
$181$	7.41921	+	22.8340i	0.551466	+	1.69724i	0.705099	+	0.709109i	$0.250903\pi$
$181$	7.41921	+	22.8340i	0.551466	+	1.69724i	−0.153633	+	0.988128i	$0.549097\pi$
$182$	−12.4843	+	4.80533i	−0.925400	+	0.356195i
$183$	−0.0901350	−	0.277407i	−0.00666297	−	0.0205065i
$184$	−0.509748	+	4.84992i	−0.0375791	+	0.357541i
$185$	12.8985	+	21.2504i	0.948316	+	1.56236i
$186$	−0.0976592	−	0.929165i	−0.00716072	−	0.0681297i
$187$	−1.89067	+	17.9885i	−0.138259	+	1.31545i
$188$	6.45267	+	4.68814i	0.470609	+	0.341918i
$189$	1.48790	+	2.91361i	0.108229	+	0.211934i
$190$	−4.69101	+	8.55299i	−0.340322	+	0.620499i
$191$	−1.22674	+	11.6717i	−0.0887639	+	0.844532i	0.856043	+	0.516904i	$0.172916\pi$
$191$	−1.22674	+	11.6717i	−0.0887639	+	0.844532i	−0.944807	+	0.327627i	$0.893751\pi$
$192$	0.203042	+	0.0431579i	0.0146533	+	0.00311465i
$193$	−0.893590	+	1.54774i	−0.0643220	+	0.111409i	−0.896393	−	0.443260i	$-0.853822\pi$
$193$	−0.893590	+	1.54774i	−0.0643220	+	0.111409i	0.832071	+	0.554669i	$0.187155\pi$
$194$	3.61548	−	4.01539i	0.259576	−	0.288288i
$195$	1.60822	+	1.70918i	0.115167	+	0.122397i
$196$	−2.85880	−	6.38962i	−0.204200	−	0.456402i
$197$	6.10863	−	18.8004i	0.435222	−	1.33947i	−0.457638	−	0.889139i	$-0.651304\pi$
$197$	6.10863	−	18.8004i	0.435222	−	1.33947i	0.892859	−	0.450336i	$-0.148696\pi$
$198$	11.0159	+	4.90459i	0.782866	+	0.348554i
$199$	−2.61528	+	4.52981i	−0.185393	+	0.321109i	−0.943709	−	0.330778i	$-0.892689\pi$
$199$	−2.61528	+	4.52981i	−0.185393	+	0.321109i	0.758316	+	0.651887i	$0.226022\pi$
$200$	4.99519	−	0.219284i	0.353213	−	0.0155058i
$201$	−0.260482	−	0.451168i	−0.0183730	−	0.0318229i
$202$	1.72911	−	1.25627i	0.121660	−	0.0883911i
$203$	17.2961	+	8.79296i	1.21395	+	0.617145i
$204$	0.284507	−	0.875623i	0.0199195	−	0.0613059i
$205$	−22.4467	+	0.492459i	−1.56775	+	0.0343948i
$206$	9.86420	+	2.09670i	0.687271	+	0.146084i
$207$	7.20989	−	12.4879i	0.501122	−	0.867969i
$208$	3.38320	−	3.75742i	0.234582	−	0.260530i
$209$	−14.3929	−	10.4571i	−0.995580	−	0.723331i
$210$	−0.848298	+	0.887972i	−0.0585381	+	0.0612759i
$211$	15.3571	−	11.1576i	1.05723	−	0.768120i	0.0836530	−	0.996495i	$-0.473341\pi$
$211$	15.3571	−	11.1576i	1.05723	−	0.768120i	0.973573	+	0.228375i	$0.0733413\pi$
$212$	1.18892	−	11.3119i	0.0816557	−	0.776902i
$213$	2.67029	−	1.18889i	0.182965	−	0.0814614i
$214$	0.385684	+	3.66953i	0.0263648	+	0.250844i
$215$	−6.33532	+	4.81867i	−0.432065	+	0.328631i
$216$	−1.00037	−	0.726811i	−0.0680665	−	0.0494532i
$217$	4.25739	−	11.1211i	0.289010	−	0.754952i
$218$	9.34081			0.632639
$219$	0.711911	−	0.790657i	0.0481065	−	0.0534276i
$220$	−0.754029	+	9.08754i	−0.0508366	+	0.612682i
$221$	−15.0057	−	16.6655i	−1.00939	−	1.12105i
$222$	2.25724	−	0.479791i	0.151496	−	0.0322015i
$223$	0.844320	−	0.613434i	0.0565398	−	0.0410786i	−0.559156	−	0.829062i	$-0.688875\pi$
$223$	0.844320	−	0.613434i	0.0565398	−	0.0410786i	0.615696	+	0.787984i	$0.288875\pi$
$224$	2.05765	+	1.66315i	0.137483	+	0.111124i
$225$	−13.7571	−	5.41529i	−0.917140	−	0.361019i
$226$	2.96389	+	5.13362i	0.197155	+	0.341483i
$227$	0.344655	+	3.27917i	0.0228755	+	0.217646i	0.999988	+	0.00492225i	$0.00156681\pi$
$227$	0.344655	+	3.27917i	0.0228755	+	0.217646i	−0.977112	+	0.212724i	$0.931767\pi$
$228$	0.605944	+	0.672969i	0.0401297	+	0.0445685i
$229$	1.38734	−	0.294888i	0.0916779	−	0.0194867i	−0.161844	−	0.986816i	$-0.551744\pi$
$229$	1.38734	−	0.294888i	0.0916779	−	0.0194867i	0.253522	+	0.967330i	$0.418411\pi$
$230$	10.7134	+	2.03268i	0.706419	+	0.134031i
$231$	−1.41105	−	1.73926i	−0.0928401	−	0.114435i
$232$	−7.33359			−0.481474
$233$	3.23840	−	3.59661i	0.212155	−	0.235622i	−0.627670	−	0.778480i	$-0.715991\pi$
$233$	3.23840	−	3.59661i	0.212155	−	0.235622i	0.839825	+	0.542858i	$0.182658\pi$
$234$	−13.6579	+	6.08090i	−0.892847	+	0.397521i
$235$	11.6402	−	13.5124i	0.759323	−	0.881449i
$236$	−2.06084	−	0.917543i	−0.134149	−	0.0597270i
$237$	0.720009	+	0.523117i	0.0467696	+	0.0339801i
$238$	8.29025	−	8.30536i	0.537377	−	0.538357i
$239$	15.1711	−	11.0224i	0.981335	−	0.712982i	0.0233284	−	0.999728i	$-0.492574\pi$
$239$	15.1711	−	11.0224i	0.981335	−	0.712982i	0.958007	+	0.286746i	$0.0925737\pi$
$240$	0.133716	−	0.444481i	0.00863133	−	0.0286911i
$241$	14.3437	−	6.38621i	0.923957	−	0.411372i	0.111083	−	0.993811i	$-0.464568\pi$
$241$	14.3437	−	6.38621i	0.923957	−	0.411372i	0.812874	+	0.582439i	$0.197902\pi$
$242$	−5.50736	−	1.17063i	−0.354027	−	0.0752507i
$243$	2.74883	+	4.76112i	0.176338	+	0.305426i
$244$	0.434222	+	1.33640i	0.0277982	+	0.0855542i
$245$	−14.7673	+	5.18914i	−0.943448	+	0.331522i
$246$	−0.644075	+	1.98226i	−0.0410647	+	0.126384i
$247$	21.5755	−	4.58602i	1.37282	−	0.291801i
$248$	0.470469	+	4.47622i	0.0298748	+	0.284240i
$249$	−1.30715	+	2.26405i	−0.0828373	+	0.143478i
$250$	0.434954	−	11.1719i	0.0275089	−	0.706571i
$251$	−13.4421			−0.848459			−0.424230	−	0.905555i	$-0.639455\pi$
$251$	−13.4421			−0.848459			−0.424230	+	0.905555i	$0.639455\pi$
$252$	−3.55803	−	6.96733i	−0.224135	−	0.438901i
$253$	−6.14546	+	18.9138i	−0.386362	+	1.18910i
$254$	−9.07930	+	1.92986i	−0.569686	+	0.121090i
$255$	−1.89864	−	0.795902i	−0.118898	−	0.0498413i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−11.0358	−	19.1145i	−0.688393	−	1.19233i	−0.972358	−	0.233496i	$-0.924983\pi$
$257$	−11.0358	−	19.1145i	−0.688393	−	1.19233i	0.283965	−	0.958835i	$-0.408350\pi$
$258$	0.228335	+	0.702743i	0.0142155	+	0.0437508i
$259$	28.4178	+	7.58679i	1.76579	+	0.471420i
$260$	−7.74752	−	8.23390i	−0.480481	−	0.510645i
$261$	19.8100	+	8.81999i	1.22621	+	0.545944i
$262$	4.99492	−	2.22388i	0.308587	−	0.137392i
$263$	−9.38667	+	4.17922i	−0.578807	+	0.257702i	−0.675191	−	0.737643i	$-0.735939\pi$
$263$	−9.38667	+	4.17922i	−0.578807	+	0.257702i	0.0963842	+	0.995344i	$0.469272\pi$
$264$	0.773327	+	0.344307i	0.0475950	+	0.0211906i
$265$	−24.9876	−	4.74097i	−1.53498	−	0.291236i
$266$	2.99750	+	11.1462i	0.183788	+	0.683418i
$267$	0.154813	+	0.476466i	0.00947441	+	0.0291592i
$268$	1.25486	+	2.17348i	0.0766529	+	0.132767i
$269$	−2.81259	−	0.597834i	−0.171486	−	0.0364506i	0.121368	−	0.992608i	$-0.461272\pi$
$269$	−2.81259	−	0.597834i	−0.171486	−	0.0364506i	−0.292855	+	0.956157i	$0.594605\pi$
$270$	−1.80460	+	2.09485i	−0.109825	+	0.127488i
$271$	−10.2353	+	2.17557i	−0.621749	+	0.132157i	−0.508006	−	0.861353i	$-0.669617\pi$
$271$	−10.2353	+	2.17557i	−0.621749	+	0.132157i	−0.113743	+	0.993510i	$0.536284\pi$
$272$	−1.37060	+	4.21828i	−0.0831051	+	0.255771i
$273$	2.77314	+	0.142802i	0.167838	+	0.00864276i
$274$	17.3911			1.05064
$275$	20.1114	+	3.36057i	1.21276	+	0.202650i
$276$	0.506142	−	0.876663i	0.0304662	−	0.0527689i
$277$	1.82889	+	17.4007i	0.109887	+	1.04551i	0.900995	+	0.433829i	$0.142838\pi$
$277$	1.82889	+	17.4007i	0.109887	+	1.04551i	−0.791108	+	0.611677i	$0.790495\pi$
$278$	−22.0728	+	4.69172i	−1.32384	+	0.281391i
$279$	4.11261	−	12.6573i	0.246216	−	0.757773i
$280$	4.08664	−	4.27777i	0.244224	−	0.255646i
$281$	−4.26081	−	13.1134i	−0.254179	−	0.782282i	−0.993990	−	0.109468i	$-0.965085\pi$
$281$	−4.26081	−	13.1134i	−0.254179	−	0.782282i	0.739811	−	0.672814i	$-0.234915\pi$
$282$	−0.827815	−	1.43382i	−0.0492957	−	0.0853826i
$283$	−19.7268	−	4.19305i	−1.17263	−	0.249251i	−0.419897	−	0.907572i	$-0.637934\pi$
$283$	−19.7268	−	4.19305i	−1.17263	−	0.249251i	−0.752738	+	0.658321i	$0.771267\pi$
$284$	−12.8640	+	5.72744i	−0.763340	+	0.339861i
$285$	1.61169	−	1.22586i	0.0954683	−	0.0726137i
$286$	16.6811	−	12.1195i	0.986376	−	0.716644i
$287$	−18.7677	+	18.8019i	−1.10782	+	1.10984i
$288$	2.39219	+	1.73803i	0.140961	+	0.102414i
$289$	2.44143	+	1.08699i	0.143614	+	0.0639409i
$290$	−1.35598	+	16.3422i	−0.0796258	+	0.959649i
$291$	−1.02463	+	0.456194i	−0.0600648	+	0.0267426i
$292$	−3.42960	+	3.80896i	−0.200702	+	0.222903i
$293$	16.1547			0.943768			0.471884	−	0.881661i	$-0.343574\pi$
$293$	16.1547			0.943768			0.471884	+	0.881661i	$0.343574\pi$
$294$	0.00264662	+	1.45304i	0.000154354	+	0.0847433i
$295$	−2.42571	+	4.42273i	−0.141230	+	0.257502i
$296$	−10.8742	+	2.31137i	−0.632048	+	0.134346i
$297$	−3.37415	−	3.74738i	−0.195788	−	0.217445i
$298$	−0.794470	−	7.55887i	−0.0460224	−	0.437874i
$299$	−12.3284	−	21.3534i	−0.712970	−	1.23490i
$300$	−0.965762	−	0.380159i	−0.0557583	−	0.0219485i
$301$	−1.46482	+	9.30336i	−0.0844310	+	0.536237i
$302$	−3.75311	+	2.72680i	−0.215967	+	0.156909i
$303$	−0.433962	+	0.0922415i	−0.0249305	+	0.00529913i
$304$	−2.91912	−	3.24201i	−0.167423	−	0.185942i
$305$	3.05833	−	0.720525i	0.175120	−	0.0412572i
$306$	8.77564	−	9.74633i	0.501670	−	0.557161i
$307$	−33.0544			−1.88651			−0.943257	−	0.332063i	$-0.892255\pi$
$307$	−33.0544			−1.88651			−0.943257	+	0.332063i	$0.892255\pi$
$308$	6.79767	+	8.37881i	0.387333	+	0.477427i
$309$	−1.69354	−	1.23043i	−0.0963424	−	0.0699968i
$310$	10.0618	−	0.220747i	0.571474	−	0.0125376i
$311$	0.357924	+	3.40542i	0.0202960	+	0.193104i	0.999972	−	0.00748287i	$-0.00238189\pi$
$311$	0.357924	+	3.40542i	0.0202960	+	0.193104i	−0.979676	+	0.200587i	$0.935715\pi$
$312$	−0.958800	+	0.426885i	−0.0542814	+	0.0241676i
$313$	0.686738	−	6.53388i	0.0388167	−	0.369317i	−0.957820	−	0.287369i	$-0.907219\pi$
$313$	0.686738	−	6.53388i	0.0388167	−	0.369317i	0.996637	−	0.0819474i	$-0.0261140\pi$
$314$	10.6221	−	7.71743i	0.599442	−	0.435520i
$315$	−16.1840	+	6.64049i	−0.911862	+	0.374149i
$316$	−3.46862	−	2.52010i	−0.195125	−	0.141767i
$317$	−11.5789	+	12.8597i	−0.650338	+	0.722273i	−0.974665	−	0.223672i	$-0.928196\pi$
$317$	−11.5789	+	12.8597i	−0.650338	+	0.722273i	0.324327	+	0.945945i	$0.394862\pi$
$318$	−1.18051	+	2.04471i	−0.0662000	+	0.114662i
$319$	−29.2531	−	6.21794i	−1.63786	−	0.348138i
$320$	−0.644172	+	2.14127i	−0.0360103	+	0.119701i
$321$	0.236679	−	0.728424i	0.0132102	−	0.0406567i
$322$	10.8144	−	7.03699i	0.602665	−	0.392156i
$323$	−15.6541	+	11.3734i	−0.871016	+	0.632830i
$324$	−4.30703	−	7.45999i	−0.239279	−	0.414444i
$325$	−19.7810	+	15.7422i	−1.09725	+	0.873221i
$326$	6.03023	−	10.4447i	0.333983	−	0.578476i
$327$	−1.77132	−	0.788641i	−0.0979540	−	0.0436119i
$328$	3.10281	−	9.54946i	0.171324	−	0.527281i
$329$	−1.12360	−	21.0724i	−0.0619462	−	1.16176i
$330$	0.910246	−	1.65963i	0.0501074	−	0.0913594i
$331$	5.46216	−	6.06635i	0.300228	−	0.333437i	−0.574089	−	0.818793i	$-0.694644\pi$
$331$	5.46216	−	6.06635i	0.300228	−	0.333437i	0.874316	+	0.485357i	$0.161310\pi$
$332$	6.29715	−	10.9070i	0.345601	−	0.598599i
$333$	32.1539	+	6.83453i	1.76203	+	0.374530i
$334$	−0.286594	+	2.72676i	−0.0156817	+	0.149202i
$335$	5.07544	−	2.39447i	0.277301	−	0.130824i
$336$	−0.249777	−	0.489114i	−0.0136265	−	0.0266833i
$337$	−14.4957	−	10.5318i	−0.789632	−	0.573701i	0.118222	−	0.992987i	$-0.462281\pi$
$337$	−14.4957	−	10.5318i	−0.789632	−	0.573701i	−0.907854	+	0.419286i	$0.862281\pi$
$338$	−1.31332	+	12.4954i	−0.0714352	+	0.679660i
$339$	−0.128620	−	1.22374i	−0.00698568	−	0.0664643i
$340$	9.14664	+	3.83423i	0.496046	+	0.207940i
$341$	−1.91859	+	18.2542i	−0.103898	+	0.988520i
$342$	3.98622	+	12.2683i	0.215550	+	0.663395i
$343$	−8.36291	+	16.5246i	−0.451554	+	0.892244i
$344$	−1.10000	−	3.38544i	−0.0593078	−	0.182531i
$345$	−1.85998	−	1.28999i	−0.100138	−	0.0694505i
$346$	−7.28694	−	8.09297i	−0.391748	−	0.435081i
$347$	2.80825	+	3.11887i	0.150755	+	0.167430i	0.813792	−	0.581156i	$-0.197400\pi$
$347$	2.80825	+	3.11887i	0.150755	+	0.167430i	−0.663037	+	0.748586i	$0.730733\pi$
$348$	1.39068	+	0.619172i	0.0745484	+	0.0331911i
$349$	−1.87070			−0.100136			−0.0500682	−	0.998746i	$-0.515944\pi$
$349$	−1.87070			−0.100136			−0.0500682	+	0.998746i	$0.515944\pi$
$350$	−8.77701	−	9.89768i	−0.469151	−	0.529053i
$351$	6.25200			0.333707
$352$	−3.72547	−	1.65869i	−0.198568	−	0.0884084i
$353$	1.28928	+	1.43189i	0.0686213	+	0.0762116i	0.776478	−	0.630145i	$-0.217004\pi$
$353$	1.28928	+	1.43189i	0.0686213	+	0.0762116i	−0.707857	+	0.706356i	$0.750338\pi$
$354$	0.313333	+	0.347991i	0.0166534	+	0.0184955i
$355$	10.3845	+	29.7253i	0.551153	+	1.57766i
$356$	−0.745807	−	2.29536i	−0.0395277	−	0.121654i
$357$	−2.27332	+	0.875020i	−0.120317	+	0.0463110i
$358$	2.92625	+	9.00607i	0.154657	+	0.475986i
$359$	3.67235	−	34.9401i	0.193819	−	1.84407i	−0.275823	−	0.961208i	$-0.588950\pi$
$359$	3.67235	−	34.9401i	0.193819	−	1.84407i	0.469642	−	0.882857i	$-0.344383\pi$
$360$	4.31536	−	5.00942i	0.227439	−	0.264020i
$361$	−0.00332797	−	0.0316635i	−0.000175156	−	0.00166650i
$362$	−2.50963	+	23.8776i	−0.131903	+	1.25498i
$363$	0.945536	+	0.686972i	0.0496278	+	0.0360567i
$364$	−13.3595	−	0.687942i	−0.700228	−	0.0360580i
$365$	7.85379	+	8.34684i	0.411086	+	0.436894i
$366$	0.0304892	−	0.290085i	0.00159370	−	0.0151630i
$367$	−15.8594	−	3.37103i	−0.827856	−	0.175966i	−0.225550	−	0.974232i	$-0.572418\pi$
$367$	−15.8594	−	3.37103i	−0.827856	−	0.175966i	−0.602306	+	0.798265i	$0.705751\pi$
$368$	−2.43832	+	4.22329i	−0.127106	+	0.220154i
$369$	−19.8665	+	22.0640i	−1.03421	+	1.14861i
$370$	3.14006	+	24.6595i	0.163244	+	1.28198i
$371$	−25.2234	+	16.4129i	−1.30953	+	0.852117i
$372$	0.288709	−	0.888556i	0.0149689	−	0.0460695i
$373$	5.61439	+	2.49969i	0.290702	+	0.129429i	0.546906	−	0.837194i	$-0.315805\pi$
$373$	5.61439	+	2.49969i	0.290702	+	0.129429i	−0.256204	+	0.966623i	$0.582472\pi$
$374$	−9.04380	+	15.6643i	−0.467644	+	0.809983i
$375$	−1.02572	+	2.08182i	−0.0529679	+	0.107505i
$376$	3.98797	+	6.90736i	0.205664	+	0.356220i
$377$	29.9979	−	21.7947i	1.54497	−	1.12249i
$378$	0.174194	+	3.26690i	0.00895959	+	0.168031i
$379$	4.07061	−	12.5281i	0.209093	−	0.643523i	−0.790427	−	0.612556i	$-0.790141\pi$
$379$	4.07061	−	12.5281i	0.209093	−	0.643523i	0.999520	−	0.0309669i	$-0.00985865\pi$
$380$	−7.76426	+	5.90554i	−0.398298	+	0.302948i
$381$	1.88466	+	0.400598i	0.0965543	+	0.0205232i
$382$	−5.86798	+	10.1636i	−0.300232	+	0.520017i
$383$	−14.3682	+	15.9575i	−0.734180	+	0.815389i	−0.988419	−	0.151752i	$-0.951508\pi$
$383$	−14.3682	+	15.9575i	−0.734180	+	0.815389i	0.254239	+	0.967142i	$0.418175\pi$
$384$	0.167934	+	0.122011i	0.00856986	+	0.00622637i
$385$	19.9283	−	13.5988i	1.01564	−	0.693057i
$386$	−1.44586	+	1.05048i	−0.0735922	+	0.0534679i
$387$	−1.10022	+	10.4679i	−0.0559275	+	0.532115i
$388$	4.93611	−	2.19770i	0.250593	−	0.111571i
$389$	1.78797	+	17.0114i	0.0906536	+	0.862511i	0.941481	+	0.337066i	$0.109435\pi$
$389$	1.78797	+	17.0114i	0.0906536	+	0.862511i	−0.850828	+	0.525445i	$0.823899\pi$
$390$	0.773993	+	2.21553i	0.0391927	+	0.112188i
$391$	17.4988	+	12.7136i	0.884951	+	0.642955i
$392$	−0.0127500	−	6.99999i	−0.000643972	−	0.353553i
$393$	−1.13496			−0.0572510
$394$	13.2273	−	14.6904i	0.666383	−	0.740093i
$395$	−6.25716	+	7.26353i	−0.314832	+	0.365468i
$396$	8.06864	+	8.96114i	0.405465	+	0.450314i
$397$	−0.780707	+	0.165944i	−0.0391825	+	0.00832851i	−0.227461	−	0.973787i	$-0.573043\pi$
$397$	−0.780707	+	0.165944i	−0.0391825	+	0.00832851i	0.188279	+	0.982116i	$0.439709\pi$
$398$	−4.23162	+	3.07445i	−0.212112	+	0.154108i
$399$	0.372648	−	2.36676i	0.0186557	−	0.118486i
$400$	4.65252	+	1.83140i	0.232626	+	0.0915700i
$401$	−10.4345	−	18.0731i	−0.521076	−	0.902530i	−0.999700	−	0.0245098i	$-0.992198\pi$
$401$	−10.4345	−	18.0731i	−0.521076	−	0.902530i	0.478624	−	0.878020i	$-0.341136\pi$
$402$	−0.0544555	−	0.518110i	−0.00271599	−	0.0258410i
$403$	−15.2273	−	16.9117i	−0.758528	−	0.842431i
$404$	2.09060	−	0.444370i	0.104011	−	0.0221082i
$405$	−17.4203	+	8.21848i	−0.865621	+	0.408379i
$406$	12.2243	+	15.0677i	0.606684	+	0.747798i
$407$	−45.3360			−2.24722
$408$	0.616059	−	0.684202i	0.0304994	−	0.0338731i
$409$	−17.9798	+	8.00511i	−0.889043	+	0.395827i	−0.799859	−	0.600188i	$-0.795092\pi$
$409$	−17.9798	+	8.00511i	−0.889043	+	0.395827i	−0.0891836	+	0.996015i	$0.528426\pi$
$410$	−20.7064	−	8.68002i	−1.02262	−	0.428676i
$411$	−3.29792	−	1.46833i	−0.162674	−	0.0724272i
$412$	8.15859	+	5.92756i	0.401945	+	0.292030i
$413$	1.55000	+	5.76368i	0.0762706	+	0.283612i
$414$	11.6659	−	8.47574i	0.573345	−	0.416560i
$415$	−23.1409	−	16.0493i	−1.13594	−	0.787831i
$416$	4.61898	−	2.05650i	0.226464	−	0.100828i
$417$	4.58183	+	0.973899i	0.224373	+	0.0476920i
$418$	−8.89532	−	15.4072i	−0.435084	−	0.753588i
$419$	−4.77956	−	14.7100i	−0.233497	−	0.718629i	−0.997317	−	0.0732001i	$-0.976679\pi$
$419$	−4.77956	−	14.7100i	−0.233497	−	0.718629i	0.763821	−	0.645429i	$-0.223321\pi$
$420$	−1.13613	+	0.466169i	−0.0554374	+	0.0227467i
$421$	8.66325	−	26.6627i	0.422221	−	1.29946i	−0.483410	−	0.875394i	$-0.660602\pi$
$421$	8.66325	−	26.6627i	0.422221	−	1.29946i	0.905630	−	0.424068i	$-0.139398\pi$
$422$	18.5676	−	3.94667i	0.903857	−	0.192121i
$423$	−2.46521	−	23.4549i	−0.119863	−	1.14042i
$424$	5.68709	−	9.85032i	0.276189	−	0.478374i
$425$	10.2354	−	19.6735i	0.496492	−	0.954306i
$426$	2.92300			0.141620
$427$	2.02198	−	3.11980i	0.0978507	−	0.150978i
$428$	−1.14019	+	3.50916i	−0.0551134	+	0.169622i
$429$	−4.18652	+	0.889873i	−0.202127	+	0.0429635i
$430$	−7.74753	+	1.82527i	−0.373619	+	0.0880225i
$431$	24.5985	+	5.22857i	1.18487	+	0.251851i	0.757872	−	0.652403i	$-0.226239\pi$
$431$	24.5985	+	5.22857i	1.18487	+	0.251851i	0.426994	+	0.904254i	$0.359572\pi$
$432$	−0.618262	−	1.07086i	−0.0297462	−	0.0515218i
$433$	2.80328	+	8.62762i	0.134717	+	0.414617i	0.995546	−	0.0942779i	$-0.0300542\pi$
$433$	2.80328	+	8.62762i	0.134717	+	0.414617i	−0.860829	+	0.508895i	$0.830054\pi$
$434$	8.41269	−	8.42803i	0.403822	−	0.404558i
$435$	1.63691	−	2.98453i	0.0784836	−	0.143097i
$436$	8.53325	+	3.79925i	0.408669	+	0.181951i
$437$	−19.4353	+	8.65315i	−0.929716	+	0.413936i
$438$	0.971952	−	0.432741i	0.0464417	−	0.0206772i
$439$	21.2615	+	9.46622i	1.01476	+	0.451798i	0.845615	−	0.533794i	$-0.179234\pi$
$439$	21.2615	+	9.46622i	1.01476	+	0.451798i	0.169141	+	0.985592i	$0.445901\pi$
$440$	−4.38508	+	7.99519i	−0.209050	+	0.381156i
$441$	−8.38433	+	18.9242i	−0.399254	+	0.901153i
$442$	−6.92992	−	21.3281i	−0.329623	−	1.01447i
$443$	−8.08209	−	13.9986i	−0.383992	−	0.665093i	0.607637	−	0.794215i	$-0.292118\pi$
$443$	−8.08209	−	13.9986i	−0.383992	−	0.665093i	−0.991629	+	0.129122i	$0.958784\pi$
$444$	2.25724	+	0.479791i	0.107124	+	0.0227699i
$445$	−5.25290	+	1.23755i	−0.249011	+	0.0586656i
$446$	1.02083	−	0.216984i	0.0483377	−	0.0102745i
$447$	−0.487536	+	1.50048i	−0.0230597	+	0.0709703i
$448$	1.20329	+	2.35629i	0.0568502	+	0.111324i
$449$	11.7540			0.554705			0.277353	−	0.960768i	$-0.410543\pi$
$449$	11.7540			0.554705			0.277353	+	0.960768i	$0.410543\pi$
$450$	−10.3651	−	10.5426i	−0.488617	−	0.496984i
$451$	20.4736	−	35.4613i	0.964064	−	1.66981i
$452$	0.619623	+	5.89532i	0.0291446	+	0.277292i
$453$	0.941933	−	0.200214i	0.0442559	−	0.00940687i
$454$	−1.01890	+	3.13585i	−0.0478194	+	0.147173i
$455$	−4.00319	+	29.6433i	−0.187672	+	1.38970i
$456$	0.279836	+	0.861248i	0.0131045	+	0.0403316i
$457$	−1.67076	−	2.89383i	−0.0781547	−	0.135368i	0.824299	−	0.566155i	$-0.191569\pi$
$457$	−1.67076	−	2.89383i	−0.0781547	−	0.135368i	−0.902454	+	0.430787i	$0.858236\pi$
$458$	1.38734	+	0.294888i	0.0648261	+	0.0137792i
$459$	−5.01028	+	2.23072i	−0.233860	+	0.104121i
$460$	8.96038	+	6.21446i	0.417780	+	0.289751i
$461$	15.1301	−	10.9926i	0.704678	−	0.511978i	−0.176774	−	0.984251i	$-0.556566\pi$
$461$	15.1301	−	10.9926i	0.704678	−	0.511978i	0.881452	+	0.472273i	$0.156566\pi$
$462$	−0.581636	−	2.16282i	−0.0270602	−	0.100623i
$463$	15.3264	+	11.1353i	0.712278	+	0.517500i	0.883908	−	0.467661i	$-0.154903\pi$
$463$	15.3264	+	11.1353i	0.712278	+	0.517500i	−0.171630	+	0.985162i	$0.554903\pi$
$464$	−6.69956	−	2.98284i	−0.311019	−	0.138475i
$465$	−1.92668	−	0.807657i	−0.0893479	−	0.0374542i
$466$	4.42130	−	1.96849i	0.204813	−	0.0911886i
$467$	23.6527	−	26.2690i	1.09452	−	1.21558i	0.119645	−	0.992817i	$-0.461824\pi$
$467$	23.6527	−	26.2690i	1.09452	−	1.21558i	0.974872	−	0.222767i	$-0.0715091\pi$
$468$	−14.9505			−0.691085
$469$	2.37395	−	6.20123i	0.109619	−	0.286346i
$470$	16.1298	−	7.60966i	0.744013	−	0.351007i
$471$	−2.66588	+	0.566650i	−0.122837	+	0.0261098i
$472$	−1.50947	−	1.67643i	−0.0694789	−	0.0771642i
$473$	−1.51738	−	14.4369i	−0.0697692	−	0.663810i
$474$	0.444990	+	0.770745i	0.0204391	+	0.0354015i
$475$	11.7244	+	18.3939i	0.537950	+	0.843970i
$476$	10.9516	−	4.21538i	0.501967	−	0.193212i
$477$	−27.2092	+	19.7686i	−1.24582	+	0.905144i
$478$	18.3427	−	3.89886i	0.838975	−	0.178330i
$479$	−14.8025	−	16.4398i	−0.676344	−	0.751156i	0.303081	−	0.952965i	$-0.401985\pi$
$479$	−14.8025	−	16.4398i	−0.676344	−	0.751156i	−0.979425	+	0.201809i	$0.935318\pi$
$480$	0.302942	−	0.351666i	0.0138274	−	0.0160513i
$481$	37.6113	−	41.7716i	1.71493	−	1.90462i
$482$	15.7011			0.715166
$483$	−2.64489	+	0.421380i	−0.120347	+	0.0191734i
$484$	−4.55509	−	3.30946i	−0.207049	−	0.150430i
$485$	−3.98468	−	11.4060i	−0.180935	−	0.517921i
$486$	0.574662	+	5.46755i	0.0260672	+	0.248013i
$487$	0.737758	−	0.328471i	0.0334310	−	0.0148845i	−0.389953	−	0.920835i	$-0.627509\pi$
$487$	0.737758	−	0.328471i	0.0334310	−	0.0148845i	0.423384	+	0.905950i	$0.360842\pi$
$488$	−0.146881	+	1.39747i	−0.00664897	+	0.0632607i
$489$	−2.02536	+	1.47151i	−0.0915901	+	0.0665441i
$490$	−15.6012	−	1.26588i	−0.704791	−	0.0571868i
$491$	−4.40519	−	3.20055i	−0.198803	−	0.144439i	0.483930	−	0.875107i	$-0.339209\pi$
$491$	−4.40519	−	3.20055i	−0.198803	−	0.144439i	−0.682733	+	0.730668i	$0.739209\pi$
$492$	−1.39465	+	1.54892i	−0.0628756	+	0.0698305i
$493$	−16.2636	+	28.1693i	−0.732474	+	1.26868i
$494$	21.5755	+	4.58602i	0.970728	+	0.206335i
$495$	21.4610	−	16.3233i	0.964599	−	0.733679i
$496$	−1.39085	+	4.28059i	−0.0624509	+	0.192204i
$497$	33.2107	+	16.8836i	1.48970	+	0.757334i
$498$	−2.11501	+	1.53665i	−0.0947761	+	0.0688588i
$499$	9.63747	+	16.6926i	0.431433	+	0.747263i	0.996997	−	0.0774410i	$-0.0246749\pi$
$499$	9.63747	+	16.6926i	0.431433	+	0.747263i	−0.565564	+	0.824704i	$0.691342\pi$
$500$	4.94136	−	10.0291i	0.220984	−	0.448515i
$501$	0.284567	−	0.492884i	0.0127135	−	0.0220204i
$502$	−12.2800	−	5.46740i	−0.548083	−	0.244022i
$503$	−7.41347	+	22.8163i	−0.330550	+	1.01733i	0.638322	+	0.769769i	$0.279629\pi$
$503$	−7.41347	+	22.8163i	−0.330550	+	1.01733i	−0.968873	+	0.247560i	$0.920371\pi$
$504$	−0.416552	−	7.81215i	−0.0185547	−	0.347981i
$505$	−0.603687	−	4.74087i	−0.0268637	−	0.210966i
$506$	−13.3071	+	14.7790i	−0.591572	+	0.657007i
$507$	1.30403	−	2.25864i	0.0579140	−	0.100310i
$508$	−9.07930	−	1.92986i	−0.402829	−	0.0856239i
$509$	−0.947768	+	9.01741i	−0.0420091	+	0.399690i	0.953231	+	0.302241i	$0.0977348\pi$
$509$	−0.947768	+	9.01741i	−0.0420091	+	0.399690i	−0.995241	+	0.0974486i	$0.968932\pi$
$510$	−1.41077	−	1.49934i	−0.0624701	−	0.0663919i
$511$	13.5428	+	0.697379i	0.599096	+	0.0308502i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	0.563868	−	5.36485i	0.0248954	−	0.236864i
$514$	−2.30711	−	21.9506i	−0.101762	−	0.968201i
$515$	14.7176	−	17.0847i	0.648533	−	0.752841i
$516$	−0.0772368	+	0.734859i	−0.00340016	+	0.0323504i
$517$	10.0511	+	30.9342i	0.442049	+	1.36049i
$518$	22.8751	+	18.4894i	1.00507	+	0.812379i
$519$	0.698551	+	2.14992i	0.0306630	+	0.0943710i
$520$	−3.72869	−	10.6732i	−0.163514	−	0.468053i
$521$	23.1923	+	25.7577i	1.01608	+	1.12847i	0.991675	+	0.128764i	$0.0411009\pi$
$521$	23.1923	+	25.7577i	1.01608	+	1.12847i	0.0244000	+	0.999702i	$0.492232\pi$
$522$	14.5099	+	16.1149i	0.635083	+	0.705331i
$523$	17.9171	+	7.97721i	0.783460	+	0.348819i	0.759175	−	0.650886i	$-0.225603\pi$
$523$	17.9171	+	7.97721i	0.783460	+	0.348819i	0.0242846	+	0.999705i	$0.492269\pi$
$524$	5.46762			0.238854
$525$	0.828745	+	2.61796i	0.0361694	+	0.114257i
$526$	−10.2750			−0.448011
$527$	18.2371	+	8.11969i	0.794422	+	0.353699i
$528$	0.566427	+	0.629081i	0.0246506	+	0.0273772i
$529$	0.522998	+	0.580848i	0.0227390	+	0.0252543i
$530$	−20.8990	−	14.4945i	−0.907795	−	0.629600i
$531$	2.06127	+	6.34392i	0.0894513	+	0.275303i
$532$	−1.79522	+	11.4018i	−0.0778326	+	0.494329i
$533$	15.6881	+	48.2831i	0.679529	+	2.09137i
$534$	−0.0523673	+	0.498241i	−0.00226615	+	0.0215610i
$535$	7.60902	+	3.18966i	0.328967	+	0.137901i
$536$	0.262337	+	2.49597i	0.0113313	+	0.107810i
$537$	0.205469	−	1.95490i	0.00886662	−	0.0843603i
$538$	−2.32626	−	1.69013i	−0.100292	−	0.0728667i
$539$	5.88423	−	27.9332i	0.253452	−	1.20317i
$540$	−2.50064	+	1.17974i	−0.107610	+	0.0507679i
$541$	0.0947842	−	0.901811i	0.00407509	−	0.0387719i	−0.992295	−	0.123895i	$-0.960462\pi$
$541$	0.0947842	−	0.901811i	0.00407509	−	0.0387719i	0.996370	+	0.0851227i	$0.0271282\pi$
$542$	−10.2353	−	2.17557i	−0.439643	−	0.0934489i
$543$	2.49188	−	4.31606i	0.106937	−	0.185220i
$544$	−2.96784	+	3.29612i	−0.127245	+	0.141320i
$545$	10.0441	−	18.3131i	0.430241	−	0.784447i
$546$	2.47531	+	1.25839i	0.105933	+	0.0538543i
$547$	8.48153	−	26.1035i	0.362644	−	1.11610i	−0.588799	−	0.808279i	$-0.700399\pi$
$547$	8.48153	−	26.1035i	0.362644	−	1.11610i	0.951443	−	0.307824i	$-0.0996009\pi$
$548$	15.8876	+	7.07361i	0.678684	+	0.302170i
$549$	2.07749	−	3.59831i	0.0886649	−	0.153572i
$550$	17.0058	+	11.2501i	0.725128	+	0.479704i
$551$	−15.9966	−	27.7069i	−0.681477	−	1.18035i
$552$	0.818955	−	0.595005i	0.0348570	−	0.0253251i
$553$	0.603990	+	11.3274i	0.0256843	+	0.481691i
$554$	−5.40673	+	16.6402i	−0.229710	+	0.706974i
$555$	1.48653	−	4.94134i	0.0630999	−	0.209748i
$556$	−22.0728	−	4.69172i	−0.936096	−	0.198973i
$557$	10.6053	−	18.3689i	0.449362	−	0.778317i	−0.548983	−	0.835833i	$-0.684985\pi$
$557$	10.6053	−	18.3689i	0.449362	−	0.778317i	0.998345	+	0.0575165i	$0.0183182\pi$
$558$	8.90525	−	9.89028i	0.376989	−	0.418689i
$559$	14.5607	+	10.5790i	0.615852	+	0.447443i
$560$	5.47326	−	2.24575i	0.231288	−	0.0949003i
$561$	3.03753	−	2.20689i	0.128244	−	0.0931751i
$562$	1.44127	−	13.7127i	0.0607962	−	0.578437i
$563$	−7.52585	+	3.35073i	−0.317177	+	0.141216i	−0.559150	−	0.829067i	$-0.688872\pi$
$563$	−7.52585	+	3.35073i	−0.317177	+	0.141216i	0.241973	+	0.970283i	$0.422206\pi$
$564$	−0.173060	−	1.64656i	−0.00728716	−	0.0693327i
$565$	13.2517	−	0.290730i	0.557505	−	0.0122311i
$566$	−16.3158	−	11.8541i	−0.685806	−	0.498267i
$567$	−8.14806	+	21.2843i	−0.342186	+	0.893858i
$568$	−14.0814			−0.590844
$569$	20.5416	−	22.8138i	0.861149	−	0.956403i	−0.138273	−	0.990394i	$-0.544155\pi$
$569$	20.5416	−	22.8138i	0.861149	−	0.956403i	0.999422	+	0.0339911i	$0.0108218\pi$
$570$	1.97096	−	0.464346i	0.0825542	−	0.0194493i
$571$	14.0194	+	15.5701i	0.586693	+	0.651588i	0.961270	−	0.275607i	$-0.0888790\pi$
$571$	14.0194	+	15.5701i	0.586693	+	0.651588i	−0.374578	+	0.927196i	$0.622212\pi$
$572$	20.1684	−	4.28693i	0.843284	−	0.179246i
$573$	1.97087	−	1.43192i	0.0823342	−	0.0598193i
$574$	−24.7926	+	9.54289i	−1.03482	+	0.398312i
$575$	15.5051	−	18.8184i	0.646609	−	0.784780i
$576$	1.47846	+	2.56076i	0.0616023	+	0.106698i
$577$	−2.01172	−	19.1403i	−0.0837492	−	0.796820i	−0.953106	−	0.302636i	$-0.902133\pi$
$577$	−2.01172	−	19.1403i	−0.0837492	−	0.796820i	0.869357	−	0.494184i	$-0.164533\pi$
$578$	1.78824	+	1.98604i	0.0743808	+	0.0826083i
$579$	0.362872	−	0.0771309i	0.0150805	−	0.00320545i
$580$	−7.88574	+	14.3779i	−0.327437	+	0.597008i
$581$	−32.9064	+	5.24258i	−1.36519	+	0.217499i
$582$	−1.12159			−0.0464916
$583$	31.0372	−	34.4703i	1.28543	−	1.42761i
$584$	−4.68234	+	2.08471i	−0.193757	+	0.0862660i
$585$	−2.76434	+	33.3158i	−0.114291	+	1.37744i
$586$	14.7581	+	6.57071i	0.609650	+	0.271434i
$587$	−16.8893	−	12.2708i	−0.697096	−	0.506470i	0.181889	−	0.983319i	$-0.441779\pi$
$587$	−16.8893	−	12.2708i	−0.697096	−	0.506470i	−0.878985	+	0.476849i	$0.841779\pi$
$588$	−0.588589	+	1.32850i	−0.0242730	+	0.0547864i
$589$	−15.8853	+	11.5413i	−0.654542	+	0.475552i
$590$	−4.01489	+	3.05374i	−0.165290	+	0.125721i
$591$	−3.74863	+	1.66900i	−0.154198	+	0.0686534i
$592$	−10.8742	−	2.31137i	−0.446925	−	0.0949969i
$593$	12.5462	+	21.7307i	0.515213	+	0.892375i	0.999844	+	0.0176561i	$0.00562041\pi$
$593$	12.5462	+	21.7307i	0.515213	+	0.892375i	−0.484631	+	0.874718i	$0.661046\pi$
$594$	−1.55825	−	4.79579i	−0.0639357	−	0.196774i
$595$	−7.36864	−	25.1841i	−0.302085	−	1.03245i
$596$	2.34869	−	7.22851i	0.0962060	−	0.296091i
$597$	1.06203	−	0.225740i	0.0434658	−	0.00923894i
$598$	−2.57734	−	24.5217i	−0.105395	−	1.00277i
$599$	13.1412	−	22.7612i	0.536934	−	0.929997i	−0.462133	−	0.886811i	$-0.652916\pi$
$599$	13.1412	−	22.7612i	0.536934	−	0.929997i	0.999067	−	0.0431865i	$-0.0137510\pi$
$600$	−0.727643	−	0.740103i	−0.0297059	−	0.0302146i
$601$	4.45058			0.181543			0.0907715	−	0.995872i	$-0.471067\pi$
$601$	4.45058			0.181543			0.0907715	+	0.995872i	$0.471067\pi$
$602$	−5.12220	+	7.90324i	−0.208765	+	0.322112i
$603$	2.29322	−	7.05782i	0.0933873	−	0.287416i
$604$	−4.53773	+	0.964523i	−0.184637	+	0.0392459i
$605$	−8.21708	+	9.53868i	−0.334072	+	0.387803i
$606$	−0.433962	−	0.0922415i	−0.0176285	−	0.00374705i
$607$	−21.5288	−	37.2890i	−0.873827	−	1.51351i	−0.858007	−	0.513638i	$-0.828297\pi$
$607$	−21.5288	−	37.2890i	−0.873827	−	1.51351i	−0.0158206	−	0.999875i	$-0.505036\pi$
$608$	−1.34810	−	4.14903i	−0.0546728	−	0.168265i
$609$	−1.04596	−	3.88942i	−0.0423846	−	0.157607i
$610$	3.08699	+	0.585703i	0.124989	+	0.0237144i
$611$	−36.8407	−	16.4026i	−1.49042	−	0.663576i
$612$	11.9811	−	5.33435i	0.484309	−	0.215628i
$613$	−19.8792	+	8.85080i	−0.802914	+	0.357480i	−0.766815	−	0.641868i	$-0.778160\pi$
$613$	−19.8792	+	8.85080i	−0.802914	+	0.357480i	−0.0360989	+	0.999348i	$0.511493\pi$
$614$	−30.1967	−	13.4444i	−1.21864	−	0.542573i
$615$	3.19375	+	3.39425i	0.128784	+	0.136869i
$616$	2.80201	+	10.4193i	0.112896	+	0.419805i
$617$	10.4621	+	32.1991i	0.421189	+	1.29629i	0.906597	+	0.421998i	$0.138671\pi$
$617$	10.4621	+	32.1991i	0.421189	+	1.29629i	−0.485408	+	0.874288i	$0.661329\pi$
$618$	−1.04667	−	1.81288i	−0.0421032	−	0.0729248i
$619$	−37.5306	−	7.97738i	−1.50848	−	0.320638i	−0.621859	−	0.783129i	$-0.713623\pi$
$619$	−37.5306	−	7.97738i	−1.50848	−	0.320638i	−0.886624	+	0.462491i	$0.846956\pi$
$620$	9.28173	+	3.89086i	0.372763	+	0.156261i
$621$	−5.89831	+	1.25372i	−0.236691	+	0.0503102i
$622$	−1.05813	+	3.25659i	−0.0424271	+	0.130577i
$623$	−3.47290	+	5.35847i	−0.139139	+	0.214683i
$624$	−1.04954			−0.0420151
$625$	−21.4353	−	12.8658i	−0.857412	−	0.514630i
$626$	3.28493	−	5.68967i	0.131292	−	0.227405i
$627$	0.386018	+	3.67272i	0.0154161	+	0.146674i
$628$	12.8428	−	2.72981i	0.512482	−	0.108931i
$629$	−15.2371	+	46.8951i	−0.607544	+	1.86983i
$630$	−17.4857	−	0.516217i	−0.696647	−	0.0205666i
$631$	−8.07910	−	24.8649i	−0.321624	−	0.989857i	−0.972942	−	0.231051i	$-0.925783\pi$
$631$	−8.07910	−	24.8649i	−0.321624	−	0.989857i	0.651318	−	0.758805i	$-0.274217\pi$
$632$	−2.14372	−	3.71304i	−0.0852727	−	0.147697i
$633$	−3.85423	−	0.819241i	−0.153192	−	0.0325619i
$634$	−15.8084	+	7.03835i	−0.627832	+	0.279529i
$635$	−5.97929	+	19.8756i	−0.237281	+	0.788738i
$636$	−1.91011	+	1.38778i	−0.0757409	+	0.0550290i
$637$	20.8555	+	28.5954i	0.826323	+	1.13299i
$638$	−24.1950	−	17.5787i	−0.957889	−	0.695947i
$639$	38.0378	+	16.9355i	1.50475	+	0.669959i
$640$	−1.45941	+	1.69414i	−0.0576884	+	0.0669668i
$641$	24.9073	−	11.0895i	0.983780	−	0.438007i	0.149148	−	0.988815i	$-0.452347\pi$
$641$	24.9073	−	11.0895i	0.983780	−	0.438007i	0.834632	+	0.550808i	$0.185680\pi$
$642$	0.512494	−	0.569183i	0.0202265	−	0.0224638i
$643$	17.5479			0.692023			0.346011	−	0.938230i	$-0.387536\pi$
$643$	17.5479			0.692023			0.346011	+	0.938230i	$0.387536\pi$
$644$	12.7417	−	2.02998i	0.502093	−	0.0799925i
$645$	1.62329	+	0.307991i	0.0639169	+	0.0121271i
$646$	−18.9267	+	4.02299i	−0.744660	+	0.158282i
$647$	−6.24227	−	6.93274i	−0.245409	−	0.272554i	0.607838	−	0.794061i	$-0.292037\pi$
$647$	−6.24227	−	6.93274i	−0.245409	−	0.272554i	−0.853247	+	0.521507i	$0.825370\pi$
$648$	−0.900414	−	8.56687i	−0.0353716	−	0.336538i
$649$	−4.59975	−	7.96701i	−0.180556	−	0.312732i
$650$	−24.4738	+	6.33556i	−0.959941	+	0.248501i
$651$	−2.30689	+	0.887944i	−0.0904142	+	0.0348013i
$652$	9.75711	−	7.08896i	0.382118	−	0.277625i
$653$	9.11310	−	1.93705i	0.356623	−	0.0758026i	−0.0261163	−	0.999659i	$-0.508314\pi$
$653$	9.11310	−	1.93705i	0.356623	−	0.0758026i	0.382739	+	0.923856i	$0.374981\pi$
$654$	−1.29741	−	1.44092i	−0.0507327	−	0.0563444i
$655$	1.01096	−	12.1841i	0.0395016	−	0.476072i
$656$	6.71867	−	7.46184i	0.262320	−	0.291336i
$657$	15.1555			0.591274
$658$	7.54446	−	19.7076i	0.294114	−	0.768283i
$659$	28.2796	+	20.5463i	1.10162	+	0.800372i	0.981323	−	0.192366i	$-0.0616161\pi$
$659$	28.2796	+	20.5463i	1.10162	+	0.800372i	0.120294	+	0.992738i	$0.461616\pi$
$660$	1.50658	−	1.14591i	0.0586436	−	0.0446046i
$661$	1.86277	+	17.7231i	0.0724535	+	0.689349i	0.969111	+	0.246624i	$0.0793213\pi$
$661$	1.86277	+	17.7231i	0.0724535	+	0.689349i	−0.896658	+	0.442724i	$0.854012\pi$
$662$	7.45734	−	3.32022i	0.289838	−	0.129044i
$663$	−0.486589	+	4.62958i	−0.0188975	+	0.179798i
$664$	10.1890	−	7.40275i	0.395410	−	0.287282i
$665$	25.0759	+	6.10867i	0.972400	+	0.236884i
$666$	26.5942	+	19.3218i	1.03051	+	0.748706i
$667$	−23.9303	+	26.5773i	−0.926584	+	1.02908i
$668$	−1.37089	+	2.37445i	−0.0530413	+	0.0918702i
$669$	−0.211902	−	0.0450412i	−0.00819261	−	0.00174139i
$670$	5.61056	−	0.123090i	0.216755	−	0.00475539i
$671$	−1.77077	+	5.44988i	−0.0683600	+	0.210390i
$672$	−0.0292424	−	0.548421i	−0.00112805	−	0.0211558i
$673$	−10.8809	+	7.90543i	−0.419428	+	0.304732i	−0.777407	−	0.628997i	$-0.783466\pi$
$673$	−10.8809	+	7.90543i	−0.419428	+	0.304732i	0.357980	+	0.933729i	$0.383466\pi$
$674$	−8.95885	−	15.5172i	−0.345082	−	0.597699i
$675$	2.16658	+	5.79057i	0.0833916	+	0.222879i
$676$	−6.28211	+	10.8809i	−0.241620	+	0.418498i
$677$	4.31356	+	1.92052i	0.165784	+	0.0738117i	0.487951	−	0.872871i	$-0.337745\pi$
$677$	4.31356	+	1.92052i	0.165784	+	0.0738117i	−0.322167	+	0.946683i	$0.604411\pi$
$678$	0.380239	−	1.17026i	0.0146030	−	0.0449434i
$679$	−12.7434	−	6.47848i	−0.489047	−	0.248621i
$680$	6.79635	+	7.22302i	0.260628	+	0.276990i
$681$	0.457975	−	0.508633i	0.0175496	−	0.0194909i
$682$	−9.17737	+	15.8957i	−0.351420	+	0.608677i
$683$	−11.8764	−	2.52441i	−0.454439	−	0.0965939i	−0.0249950	−	0.999688i	$-0.507957\pi$
$683$	−11.8764	−	2.52441i	−0.454439	−	0.0965939i	−0.429444	+	0.903094i	$0.641290\pi$
$684$	−1.34838	+	12.8290i	−0.0515567	+	0.490529i
$685$	18.7005	−	34.0962i	0.714510	−	1.30275i
$686$	−14.3610	+	11.6945i	−0.548307	+	0.446496i
$687$	−0.238186	−	0.173053i	−0.00908738	−	0.00660237i
$688$	0.372086	−	3.54016i	0.0141856	−	0.134967i
$689$	6.01133	+	57.1940i	0.229013	+	2.17892i
$690$	−1.17449	−	1.93498i	−0.0447121	−	0.0736635i
$691$	−2.52443	+	24.0184i	−0.0960340	+	0.913703i	0.835363	+	0.549698i	$0.185257\pi$
$691$	−2.52443	+	24.0184i	−0.0960340	+	0.913703i	−0.931397	+	0.364004i	$0.881409\pi$
$692$	−3.36524	−	10.3572i	−0.127927	−	0.393720i
$693$	4.96211	−	31.5153i	0.188495	−	1.19717i
$694$	1.29690	+	3.99145i	0.0492297	+	0.151513i
$695$	−14.5363	+	48.3198i	−0.551395	+	1.83287i
$696$	1.01861	+	1.13128i	0.0386104	+	0.0428812i
$697$	−29.7998	−	33.0960i	−1.12875	−	1.25360i
$698$	−1.70897	−	0.760884i	−0.0646856	−	0.0287999i
$699$	−1.00462			−0.0379982
$700$	−3.99245	−	12.6119i	−0.150900	−	0.476685i
$701$	−25.2801			−0.954815			−0.477408	−	0.878682i	$-0.658424\pi$
$701$	−25.2801			−0.954815			−0.477408	+	0.878682i	$0.658424\pi$
$702$	5.71149	+	2.54292i	0.215566	+	0.0959762i
$703$	−32.4521	−	36.0417i	−1.22395	−	1.35934i
$704$	−2.72874	−	3.03057i	−0.102843	−	0.114219i
$705$	−3.70121	+	0.0812009i	−0.139396	+	0.00305820i
$706$	0.595412	+	1.83249i	0.0224086	+	0.0689667i
$707$	−4.39782	−	3.55466i	−0.165397	−	0.133687i
$708$	0.144703	+	0.445350i	0.00543827	+	0.0167373i
$709$	−0.0974805	+	0.927465i	−0.00366096	+	0.0348317i	−0.996200	−	0.0870966i	$-0.972241\pi$
$709$	−0.0974805	+	0.927465i	−0.00366096	+	0.0348317i	0.992539	+	0.121928i	$0.0389078\pi$
$710$	−2.60366	+	31.3792i	−0.0977135	+	1.17764i
$711$	1.32517	+	12.6081i	0.0496977	+	0.472842i
$712$	0.252277	−	2.40026i	0.00945450	−	0.0899535i
$713$	17.7572	+	12.9014i	0.665013	+	0.483160i
$714$	−2.43268	−	0.125270i	−0.0910408	−	0.00468811i
$715$	−5.82390	−	45.7362i	−0.217802	−	1.71044i
$716$	−0.989837	+	9.41767i	−0.0369920	+	0.351955i
$717$	−3.80754	−	0.809318i	−0.142195	−	0.0302245i
$718$	17.5663	−	30.4256i	0.655567	−	1.13548i
$719$	−0.794659	+	0.882559i	−0.0296358	+	0.0329139i	−0.757780	−	0.652510i	$-0.773716\pi$
$719$	−0.794659	+	0.882559i	−0.0296358	+	0.0329139i	0.728145	+	0.685423i	$0.240383\pi$
$720$	5.97979	−	2.82112i	0.222854	−	0.105137i
$721$	−1.42065	−	26.6434i	−0.0529079	−	0.992253i
$722$	0.00983845	−	0.0302796i	0.000366149	−	0.00112689i
$723$	−2.97743	−	1.32564i	−0.110732	−	0.0493010i
$724$	−12.0045	+	20.7925i	−0.446145	+	0.772746i
$725$	30.5817	+	20.2311i	1.13578	+	0.751365i
$726$	0.584374	+	1.01216i	0.0216881	+	0.0375650i
$727$	−15.1852	+	11.0327i	−0.563188	+	0.409180i	−0.832625	−	0.553838i	$-0.813163\pi$
$727$	−15.1852	+	11.0327i	−0.563188	+	0.409180i	0.269436	+	0.963018i	$0.413163\pi$
$728$	−11.9247	−	6.06227i	−0.441959	−	0.224683i
$729$	−7.63302	+	23.4920i	−0.282705	+	0.870075i
$730$	3.77983	+	10.8196i	0.139898	+	0.400453i
$731$	−15.4434	−	3.28259i	−0.571194	−	0.121411i
$732$	0.145842	−	0.252605i	0.00539046	−	0.00933655i
$733$	−6.55192	+	7.27664i	−0.242001	+	0.268769i	−0.851894	−	0.523715i	$-0.824546\pi$
$733$	−6.55192	+	7.27664i	−0.242001	+	0.268769i	0.609893	+	0.792484i	$0.291212\pi$
$734$	−13.1172	−	9.53020i	−0.484165	−	0.351766i
$735$	2.85161	+	1.55726i	0.105183	+	0.0574403i
$736$	−3.94528	+	2.86642i	−0.145425	+	0.105658i
$737$	−1.06982	+	10.1787i	−0.0394074	+	0.374936i
$738$	−27.1232	+	12.0760i	−0.998419	+	0.444525i
$739$	−0.550233	−	5.23511i	−0.0202406	−	0.192577i	0.979729	−	0.200326i	$-0.0642001\pi$
$739$	−0.550233	−	5.23511i	−0.0202406	−	0.192577i	−0.999970	+	0.00774902i	$0.997533\pi$
$740$	−7.16132	+	23.8047i	−0.263255	+	0.875079i
$741$	−3.70421	−	2.69127i	−0.136078	−	0.0988662i
$742$	−29.7184	+	4.73468i	−1.09100	+	0.173816i
$743$	−14.6417			−0.537152			−0.268576	−	0.963259i	$-0.586553\pi$
$743$	−14.6417			−0.537152			−0.268576	+	0.963259i	$0.586553\pi$
$744$	0.625157	−	0.694307i	0.0229194	−	0.0254545i
$745$	−15.6738	−	6.57039i	−0.574244	−	0.240720i
$746$	4.11228	+	4.56716i	0.150561	+	0.167215i
$747$	−36.4264	+	7.74268i	−1.33277	+	0.283290i
$748$	−14.6332	+	10.6316i	−0.535042	+	0.388731i
$749$	9.11056	−	3.50674i	0.332893	−	0.128134i
$750$	−1.78379	+	1.48464i	−0.0651349	+	0.0542115i
$751$	17.6946	+	30.6480i	0.645687	+	1.11836i	0.984142	+	0.177380i	$0.0567621\pi$
$751$	17.6946	+	30.6480i	0.645687	+	1.11836i	−0.338456	+	0.940982i	$0.609905\pi$
$752$	0.833713	+	7.93224i	0.0304024	+	0.289259i
$753$	1.86707	+	2.07359i	0.0680398	+	0.0755658i
$754$	36.2691	−	7.70924i	1.32084	−	0.280754i
$755$	1.31033	+	10.2903i	0.0476878	+	0.374501i
$756$	−1.16963	+	3.05531i	−0.0425391	+	0.111120i
$757$	−0.997193			−0.0362436			−0.0181218	−	0.999836i	$-0.505769\pi$
$757$	−0.997193			−0.0362436			−0.0181218	+	0.999836i	$0.505769\pi$
$758$	8.81431	−	9.78928i	0.320150	−	0.355563i
$759$	3.77124	−	1.67906i	0.136887	−	0.0609461i
$760$	−9.49501	+	2.23697i	−0.344420	+	0.0811434i
$761$	28.5483	+	12.7105i	1.03488	+	0.460757i	0.852641	−	0.522498i	$-0.175000\pi$
$761$	28.5483	+	12.7105i	1.03488	+	0.460757i	0.182236	+	0.983255i	$0.441666\pi$
$762$	1.55879	+	1.13253i	0.0564689	+	0.0410271i
$763$	−6.41805	−	23.8655i	−0.232349	−	0.863990i
$764$	−9.49458	+	6.89822i	−0.343502	+	0.249569i
$765$	−9.67180	−	27.6852i	−0.349685	−	1.00096i
$766$	−19.6165	+	8.73382i	−0.708772	+	0.315566i
$767$	11.1567	+	2.37142i	0.402843	+	0.0856270i
$768$	0.103789	+	0.179768i	0.00374516	+	0.00648682i
$769$	5.09292	+	15.6744i	0.183655	+	0.565233i	0.999923	−	0.0124413i	$-0.00396028\pi$
$769$	5.09292	+	15.6744i	0.183655	+	0.565233i	−0.816267	+	0.577675i	$0.803960\pi$
$770$	23.7365	−	4.31751i	0.855405	−	0.155592i
$771$	−1.41578	+	4.35733i	−0.0509882	+	0.156925i
$772$	−1.74812	+	0.371575i	−0.0629164	+	0.0133733i
$773$	−1.07642	−	10.2415i	−0.0387163	−	0.368361i	−0.996677	−	0.0814601i	$-0.974042\pi$
$773$	−1.07642	−	10.2415i	−0.0387163	−	0.368361i	0.957960	−	0.286901i	$-0.0926250\pi$
$774$	−5.26280	+	9.11543i	−0.189167	+	0.327647i
$775$	10.3866	−	19.9641i	0.373098	−	0.717131i
$776$	5.40324			0.193965
$777$	−2.77680	−	5.43752i	−0.0996171	−	0.195070i
$778$	−5.28576	+	16.2679i	−0.189504	+	0.583232i
$779$	42.8467	−	9.10735i	1.53514	−	0.326305i
$780$	−0.194059	+	2.33880i	−0.00694844	+	0.0837425i
$781$	−56.1698	−	11.9393i	−2.00991	−	0.427220i
$782$	10.8148	+	18.7319i	0.386738	+	0.669850i
$783$	−2.80221	−	8.62433i	−0.100143	−	0.308208i
$784$	2.83550	−	6.39999i	0.101268	−	0.228571i
$785$	−3.70852	−	29.1237i	−0.132363	−	1.03947i
$786$	−1.03684	−	0.461629i	−0.0369827	−	0.0164658i
$787$	37.6891	−	16.7803i	1.34347	−	0.598152i	0.396076	−	0.918218i	$-0.370372\pi$
$787$	37.6891	−	16.7803i	1.34347	−	0.598152i	0.947395	+	0.320066i	$0.103705\pi$
$788$	18.0589	−	8.04034i	0.643322	−	0.286425i
$789$	1.94847	+	0.867514i	0.0693673	+	0.0308843i
$790$	−8.67054	+	4.09055i	−0.308484	+	0.145535i
$791$	11.0798	−	11.1000i	0.393951	−	0.394670i
$792$	3.72625	+	11.4682i	0.132407	+	0.407505i
$793$	−3.55235	−	6.15285i	−0.126148	−	0.218494i
$794$	−0.780707	−	0.165944i	−0.0277062	−	0.00588914i
$795$	2.73936	+	4.51311i	0.0971550	+	0.160064i
$796$	−5.11627	+	1.08750i	−0.181341	+	0.0385453i
$797$	8.85856	−	27.2638i	0.313786	−	0.965735i	−0.662465	−	0.749093i	$-0.730490\pi$
$797$	8.85856	−	27.2638i	0.313786	−	0.965735i	0.976251	−	0.216642i	$-0.0695104\pi$
$798$	1.30308	−	2.01057i	0.0461284	−	0.0711734i
$799$	35.3762			1.25152
$800$	3.50539	+	3.56542i	0.123934	+	0.126057i
$801$	−3.56822	+	6.18035i	−0.126077	+	0.218372i
$802$	−2.18141	−	20.7548i	−0.0770283	−	0.732876i
$803$	−20.4451	+	4.34574i	−0.721491	+	0.153358i
$804$	0.160987	−	0.495466i	0.00567756	−	0.0174737i
$805$	−2.16769	−	28.7690i	−0.0764012	−	1.01398i
$806$	−7.03227	−	21.6431i	−0.247701	−	0.762346i
$807$	0.298437	+	0.516908i	0.0105055	+	0.0181960i
$808$	2.09060	+	0.444370i	0.0735469	+	0.0156329i
$809$	6.67711	−	2.97284i	0.234755	−	0.104520i	−0.285988	−	0.958233i	$-0.592322\pi$
$809$	6.67711	−	2.97284i	0.234755	−	0.104520i	0.520743	+	0.853714i	$0.325655\pi$
$810$	−19.2570	+	0.422479i	−0.676622	+	0.0148444i
$811$	−40.0842	+	29.1229i	−1.40755	+	1.02264i	−0.413874	+	0.910334i	$0.635825\pi$
$811$	−40.0842	+	29.1229i	−1.40755	+	1.02264i	−0.993673	+	0.112309i	$0.964175\pi$
$812$	5.03889	+	18.7371i	0.176830	+	0.657544i
$813$	1.75725	+	1.27672i	0.0616296	+	0.0447765i
$814$	−41.4165	−	18.4398i	−1.45165	−	0.646315i
$815$	−13.9930	−	23.0536i	−0.490154	−	0.807532i
$816$	0.841088	−	0.374476i	0.0294440	−	0.0131093i
$817$	10.3911	−	11.5404i	0.363537	−	0.403749i
$818$	−19.6813			−0.688141
$819$	24.9209	+	30.7175i	0.870806	+	1.07336i
$820$	−15.3858	−	16.3517i	−0.537294	−	0.571024i
$821$	−20.0692	+	4.26585i	−0.700422	+	0.148879i	−0.544340	−	0.838865i	$-0.683220\pi$
$821$	−20.0692	+	4.26585i	−0.700422	+	0.148879i	−0.156082	+	0.987744i	$0.549886\pi$
$822$	−2.41557	−	2.68277i	−0.0842528	−	0.0935723i
$823$	3.34896	+	31.8632i	0.116737	+	1.11068i	0.883396	+	0.468627i	$0.155251\pi$
$823$	3.34896	+	31.8632i	0.116737	+	1.11068i	−0.766659	+	0.642055i	$0.778082\pi$
$824$	5.04228	+	8.73349i	0.175656	+	0.304246i
$825$	−2.27500	−	3.56916i	−0.0792053	−	0.124262i
$826$	−0.928304	+	5.89583i	−0.0322998	+	0.205142i
$827$	−27.2244	+	19.7797i	−0.946687	+	0.687808i	−0.950021	−	0.312186i	$-0.898939\pi$
$827$	−27.2244	+	19.7797i	−0.946687	+	0.687808i	0.00333436	+	0.999994i	$0.498939\pi$
$828$	14.1047	−	2.99804i	0.490172	−	0.104189i
$829$	11.8703	+	13.1833i	0.412273	+	0.457875i	0.913138	−	0.407650i	$-0.133652\pi$
$829$	11.8703	+	13.1833i	0.412273	+	0.457875i	−0.500866	+	0.865525i	$0.666985\pi$
$830$	−14.6124	−	24.0740i	−0.507204	−	0.835622i
$831$	2.43021	−	2.69903i	0.0843032	−	0.0936282i
$832$	5.05611			0.175289
$833$	−26.9162	−	15.4748i	−0.932591	−	0.536169i
$834$	3.78959	+	2.75330i	0.131223	+	0.0953390i
$835$	5.03777	+	3.49394i	0.174339	+	0.120913i
$836$	−1.85963	−	17.6932i	−0.0643166	−	0.611932i
$837$	−5.08428	+	2.26367i	−0.175739	+	0.0782438i
$838$	1.61674	−	15.3822i	0.0558493	−	0.531371i
$839$	−30.7399	+	22.3338i	−1.06126	+	0.771050i	−0.974321	−	0.225164i	$-0.927708\pi$
$839$	−30.7399	+	22.3338i	−1.06126	+	0.771050i	−0.0869384	+	0.996214i	$0.527708\pi$
$840$	−1.22751	−	0.0362390i	−0.0423532	−	0.00125036i
$841$	−20.0486	−	14.5662i	−0.691333	−	0.502283i
$842$	18.7590	−	20.8340i	0.646477	−	0.717986i
$843$	−1.43107	+	2.47869i	−0.0492888	+	0.0853706i
$844$	18.5676	+	3.94667i	0.639123	+	0.135850i
$845$	23.0856	+	16.0110i	0.794170	+	0.550796i
$846$	7.28790	−	22.4299i	0.250563	−	0.771154i
$847$	0.793177	+	14.8755i	0.0272539	+	0.511128i
$848$	9.20190	−	6.68557i	0.315994	−	0.229583i
$849$	2.09316	+	3.62547i	0.0718372	+	0.124426i
$850$	17.3525	−	13.8095i	0.595185	−	0.473663i
$851$	−27.1070	+	46.9508i	−0.929217	+	1.60945i
$852$	2.67029	+	1.18889i	0.0914827	+	0.0407307i
$853$	4.35681	−	13.4089i	0.149174	−	0.459112i	−0.848350	−	0.529436i	$-0.822403\pi$
$853$	4.35681	−	13.4089i	0.149174	−	0.459112i	0.997524	+	0.0703245i	$0.0224035\pi$
$854$	3.11611	−	2.02766i	0.106631	−	0.0693852i
$855$	28.3390	+	5.37683i	0.969172	+	0.183884i
$856$	−2.46892	+	2.74202i	−0.0843860	+	0.0937202i
$857$	19.7176	−	34.1519i	0.673541	−	1.16661i	−0.303352	−	0.952879i	$-0.598106\pi$
$857$	19.7176	−	34.1519i	0.673541	−	1.16661i	0.976893	−	0.213729i	$-0.0685610\pi$
$858$	−4.18652	−	0.889873i	−0.142926	−	0.0303798i
$859$	−2.04866	+	19.4917i	−0.0698992	+	0.665047i	0.902335	+	0.431036i	$0.141852\pi$
$859$	−2.04866	+	19.4917i	−0.0698992	+	0.665047i	−0.972234	+	0.234011i	$0.924815\pi$
$860$	−7.82013	−	1.48373i	−0.266664	−	0.0505949i
$861$	5.50717	+	0.283589i	0.187684	+	0.00966470i
$862$	20.3452	+	14.7816i	0.692959	+	0.503464i
$863$	−3.48587	+	33.1658i	−0.118660	+	1.12898i	0.759465	+	0.650548i	$0.225461\pi$
$863$	−3.48587	+	33.1658i	−0.118660	+	1.12898i	−0.878126	+	0.478430i	$0.841206\pi$
$864$	−0.129252	−	1.22975i	−0.00439724	−	0.0418370i
$865$	−23.7022	+	5.58411i	−0.805900	+	0.189865i
$866$	−0.948242	+	9.02192i	−0.0322226	+	0.306577i
$867$	−0.171427	−	0.527597i	−0.00582195	−	0.0179181i
$868$	11.1134	−	4.27764i	0.377212	−	0.145192i
$869$	−5.40297	−	16.6286i	−0.183283	−	0.564087i
$870$	2.70930	−	2.06071i	0.0918540	−	0.0698647i
$871$	−8.49088	−	9.43008i	−0.287703	−	0.319526i
$872$	6.25022	+	6.94157i	0.211659	+	0.235071i
$873$	−14.5956	−	6.49839i	−0.493987	−	0.219937i
$874$	−21.2746			−0.719623
$875$	−28.8427	+	6.56488i	−0.975062	+	0.221933i
$876$	1.06393			0.0359470
$877$	20.9093	+	9.30940i	0.706056	+	0.314356i	0.728167	−	0.685399i	$-0.240372\pi$
$877$	20.9093	+	9.30940i	0.706056	+	0.314356i	−0.0221118	+	0.999756i	$0.507039\pi$
$878$	15.5731	+	17.2957i	0.525566	+	0.583700i
$879$	−2.24384	−	2.49204i	−0.0756828	−	0.0840543i
$880$	−7.25790	+	5.52040i	−0.244664	+	0.186093i
$881$	7.25645	+	22.3331i	0.244476	+	0.752420i	0.995722	+	0.0923978i	$0.0294532\pi$
$881$	7.25645	+	22.3331i	0.244476	+	0.752420i	−0.751246	+	0.660022i	$0.770547\pi$
$882$	−15.3566	+	13.8779i	−0.517085	+	0.467294i
$883$	−13.3950	−	41.2254i	−0.450776	−	1.38735i	−0.876023	−	0.482269i	$-0.839813\pi$
$883$	−13.3950	−	41.2254i	−0.450776	−	1.38735i	0.425247	−	0.905077i	$-0.360187\pi$
$884$	2.34412	−	22.3028i	0.0788414	−	0.750126i
$885$	1.01918	−	0.240112i	0.0342593	−	0.00807129i
$886$	−1.68962	−	16.0756i	−0.0567638	−	0.540071i
$887$	0.458435	−	4.36172i	0.0153928	−	0.146452i	−0.984126	−	0.177471i	$-0.943208\pi$
$887$	0.458435	−	4.36172i	0.0153928	−	0.146452i	0.999519	+	0.0310186i	$0.00987512\pi$
$888$	1.86694	+	1.35641i	0.0626504	+	0.0455182i
$889$	11.1691	+	21.8714i	0.374600	+	0.733542i
$890$	−5.30212	−	1.00599i	−0.177727	−	0.0337207i
$891$	3.67192	−	34.9360i	0.123014	−	1.17040i
$892$	1.02083	+	0.216984i	0.0341799	+	0.00726517i
$893$	−17.3977	+	30.1337i	−0.582192	+	1.00839i
$894$	−1.05569	+	1.17246i	−0.0353075	+	0.0392129i
$895$	20.8034	+	3.94709i	0.695381	+	0.131937i
$896$	0.140874	+	2.64200i	0.00470627	+	0.0882630i
$897$	−1.58162	+	4.86771i	−0.0528086	+	0.162528i
$898$	10.7378	+	4.78078i	0.358325	+	0.159537i
$899$	−16.5038	+	28.5854i	−0.550432	+	0.953376i
$900$	−5.18095	−	13.8471i	−0.172698	−	0.461568i
$901$	−25.2243	−	43.6898i	−0.840344	−	1.45552i
$902$	33.1270	−	24.0681i	1.10301	−	0.801382i
$903$	1.63860	−	1.06624i	0.0545292	−	0.0354823i
$904$	−1.83179	+	5.63766i	−0.0609243	+	0.187506i
$905$	44.1145	+	30.5956i	1.46642	+	1.01703i
$906$	0.941933	+	0.200214i	0.0312936	+	0.00665166i
$907$	9.63310	−	16.6850i	0.319862	−	0.554017i	−0.660597	−	0.750741i	$-0.729697\pi$
$907$	9.63310	−	16.6850i	0.319862	−	0.554017i	0.980459	+	0.196724i	$0.0630302\pi$
$908$	−2.20628	+	2.45032i	−0.0732179	+	0.0813167i
$909$	−5.11283	−	3.71469i	−0.169582	−	0.123209i
$910$	−15.7141	+	25.4522i	−0.520917	+	0.843733i
$911$	−34.3662	+	24.9685i	−1.13860	+	0.827244i	−0.986924	−	0.161185i	$-0.948468\pi$
$911$	−34.3662	+	24.9685i	−1.13860	+	0.827244i	−0.151680	+	0.988430i	$0.548468\pi$
$912$	−0.0946578	+	0.900609i	−0.00313443	+	0.0298221i
$913$	46.9197	−	20.8900i	1.55282	−	0.691359i
$914$	−0.349283	−	3.32321i	−0.0115533	−	0.109922i
$915$	−0.535941	−	0.371701i	−0.0177177	−	0.0122881i
$916$	1.14745	+	0.833675i	0.0379130	+	0.0275454i
$917$	−9.11396	−	11.2339i	−0.300969	−	0.370975i
$918$	−5.48444			−0.181013
$919$	−34.9289	+	38.7924i	−1.15220	+	1.27964i	−0.198088	+	0.980184i	$0.563473\pi$
$919$	−34.9289	+	38.7924i	−1.15220	+	1.27964i	−0.954109	+	0.299460i	$0.903193\pi$
$920$	5.65807	+	9.32171i	0.186541	+	0.307328i
$921$	4.59115	+	5.09899i	0.151284	+	0.168018i
$922$	18.2931	−	3.88832i	0.602452	−	0.128055i
$923$	57.5998	−	41.8487i	1.89592	−	1.37747i
$924$	0.348345	−	2.21240i	0.0114597	−	0.0727827i
$925$	51.7226	+	20.3599i	1.70063	+	0.669428i
$926$	9.47223	+	16.4064i	0.311277	+	0.539147i
$927$	−3.11695	−	29.6558i	−0.102374	−	0.974025i
$928$	−4.90713	−	5.44992i	−0.161084	−	0.178902i
$929$	15.4582	−	3.28575i	0.507169	−	0.107802i	0.0527811	−	0.998606i	$-0.483191\pi$
$929$	15.4582	−	3.28575i	0.507169	−	0.107802i	0.454388	+	0.890804i	$0.349858\pi$
$930$	−1.43161	−	1.52148i	−0.0469444	−	0.0498914i
$931$	26.4187	−	15.3171i	0.865838	−	0.501997i
$932$	4.83972			0.158530
$933$	0.475608	−	0.528216i	0.0155707	−	0.0172930i
$934$	32.2924	−	14.3775i	1.05664	−	0.470446i
$935$	20.9859	+	34.5745i	0.686314	+	1.13071i
$936$	−13.6579	−	6.08090i	−0.446423	−	0.198760i
$937$	−2.20662	−	1.60320i	−0.0720870	−	0.0523743i	0.551158	−	0.834401i	$-0.314186\pi$
$937$	−2.20662	−	1.60320i	−0.0720870	−	0.0523743i	−0.623245	+	0.782027i	$0.714186\pi$
$938$	4.69098	−	4.69953i	0.153166	−	0.153445i
$939$	−1.10331	+	0.801598i	−0.0360050	+	0.0261592i
$940$	17.8304	−	0.391182i	0.581565	−	0.0127590i
$941$	15.4761	−	6.89038i	0.504505	−	0.224620i	−0.138671	−	0.990338i	$-0.544283\pi$
$941$	15.4761	−	6.89038i	0.504505	−	0.224620i	0.643176	+	0.765718i	$0.277616\pi$
$942$	−2.66588	−	0.566650i	−0.0868590	−	0.0184624i
$943$	−24.4829	−	42.4057i	−0.797274	−	1.38092i
$944$	−0.697101	−	2.14546i	−0.0226887	−	0.0698286i
$945$	6.59222	+	3.17135i	0.214445	+	0.103164i
$946$	4.48582	−	13.8059i	0.145847	−	0.448870i
$947$	−20.5618	+	4.37055i	−0.668169	+	0.142024i	−0.529493	−	0.848314i	$-0.677618\pi$
$947$	−20.5618	+	4.37055i	−0.668169	+	0.142024i	−0.138676	+	0.990338i	$0.544285\pi$
$948$	0.0930282	+	0.885104i	0.00302142	+	0.0287469i
$949$	12.9574	−	22.4430i	0.420616	−	0.728529i
$950$	3.22926	+	21.5724i	0.104771	+	0.699901i
$951$	3.59202			0.116479
$952$	11.7193	+	0.603483i	0.379826	+	0.0195590i
$953$	−3.89113	+	11.9757i	−0.126046	+	0.387930i	−0.994090	−	0.108557i	$-0.965377\pi$
$953$	−3.89113	+	11.9757i	−0.126046	+	0.387930i	0.868044	+	0.496487i	$0.165377\pi$
$954$	−32.8975	+	6.99257i	−1.06509	+	0.226393i
$955$	13.6165	+	22.4333i	0.440620	+	0.725925i
$956$	18.3427	+	3.89886i	0.593245	+	0.126098i
$957$	3.10398	+	5.37626i	0.100338	+	0.173790i
$958$	−6.83607	−	21.0393i	−0.220863	−	0.679748i
$959$	−11.9494	−	44.4339i	−0.385867	−	1.43485i
$960$	0.419787	−	0.198046i	0.0135486	−	0.00639189i
$961$	−9.81343	−	4.36922i	−0.316562	−	0.140943i
$962$	51.3497	−	22.8624i	1.65558	−	0.737112i
$963$	9.96701	−	4.43760i	0.321182	−	0.143000i
$964$	14.3437	+	6.38621i	0.461979	+	0.205686i
$965$	0.504794	+	3.96424i	0.0162499	+	0.127614i
$966$	−2.58762	−	0.690826i	−0.0832554	−	0.0222270i
$967$	−2.78301	−	8.56524i	−0.0894957	−	0.275439i	0.896284	−	0.443480i	$-0.146256\pi$
$967$	−2.78301	−	8.56524i	−0.0894957	−	0.275439i	−0.985780	+	0.168040i	$0.946256\pi$
$968$	−2.81520	−	4.87607i	−0.0904839	−	0.156723i
$969$	3.92876	+	0.835084i	0.126210	+	0.0268268i
$970$	0.999059	−	12.0406i	0.0320779	−	0.386602i
$971$	3.50623	−	0.745273i	0.112520	−	0.0239170i	−0.151307	−	0.988487i	$-0.548348\pi$
$971$	3.50623	−	0.745273i	0.112520	−	0.0239170i	0.263828	+	0.964570i	$0.415015\pi$
$972$	−1.69887	+	5.22859i	−0.0544913	+	0.167707i
$973$	27.1534	+	53.1718i	0.870499	+	1.70461i
$974$	0.807577			0.0258764
$975$	5.17592	+	0.864888i	0.165762	+	0.0276986i
$976$	−0.702586	+	1.21692i	−0.0224892	+	0.0389525i
$977$	1.59968	+	15.2200i	0.0511783	+	0.486929i	0.989850	+	0.142117i	$0.0453909\pi$
$977$	1.59968	+	15.2200i	0.0511783	+	0.486929i	−0.938672	+	0.344813i	$0.887942\pi$
$978$	−2.44878	+	0.520504i	−0.0783033	+	0.0166439i
$979$	3.04143	−	9.36055i	0.0972045	−	0.299165i
$980$	−13.7375	−	7.50202i	−0.438829	−	0.239643i
$981$	−8.53503	−	26.2681i	−0.272503	−	0.838677i
$982$	−2.72255	−	4.71560i	−0.0868802	−	0.150481i
$983$	−39.2947	−	8.35235i	−1.25331	−	0.266398i	−0.467012	−	0.884251i	$-0.654670\pi$
$983$	−39.2947	−	8.35235i	−1.25331	−	0.266398i	−0.786294	+	0.617852i	$0.788003\pi$
$984$	−1.90408	+	0.847749i	−0.0606997	+	0.0270253i
$985$	−14.5781	−	41.7293i	−0.464497	−	1.32961i
$986$	−26.3150	+	19.1190i	−0.838041	+	0.608872i
$987$	−3.09458	+	3.10022i	−0.0985015	+	0.0986811i
$988$	17.8449	+	12.9651i	0.567722	+	0.412474i
$989$	−15.8584	−	7.06061i	−0.504268	−	0.224514i
$990$	26.2449	−	6.18314i	0.834117	−	0.196513i
$991$	1.98076	−	0.881893i	0.0629210	−	0.0280142i	−0.375035	−	0.927011i	$-0.622369\pi$
$991$	1.98076	−	0.881893i	0.0629210	−	0.0280142i	0.437956	+	0.898996i	$0.355703\pi$
$992$	−3.01167	+	3.34480i	−0.0956207	+	0.106198i
$993$	−1.69448			−0.0537726
$994$	23.4723	+	28.9320i	0.744496	+	0.917666i
$995$	1.47739	+	11.6022i	0.0468364	+	0.367815i
$996$	−2.55717	+	0.543544i	−0.0810271	+	0.0172228i
$997$	29.5240	+	32.7897i	0.935034	+	1.03846i	0.999179	+	0.0405198i	$0.0129014\pi$
$997$	29.5240	+	32.7897i	0.935034	+	1.03846i	−0.0641447	+	0.997941i	$0.520432\pi$
$998$	2.01478	+	19.1694i	0.0637768	+	0.606795i
$999$	−6.87328	−	11.9049i	−0.217461	−	0.376654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.q.c.11.5	✓	80
7.2	even	3	inner	350.2.q.c.261.6	yes	80
25.16	even	5	inner	350.2.q.c.291.6	yes	80
175.16	even	15	inner	350.2.q.c.191.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.q.c.11.5	✓	80	1.1	even	1	trivial
350.2.q.c.191.5	yes	80	175.16	even	15	inner
350.2.q.c.261.6	yes	80	7.2	even	3	inner
350.2.q.c.291.6	yes	80	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.913545 + 0.406737i) q^{2} +(-0.138897 - 0.154261i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.77975 - 1.35369i) q^{5} +(-0.0641452 - 0.197419i) q^{6} +(0.411507 - 2.61355i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309081 - 2.94071i) q^{9} +O(q^{10})\)	\(q+(0.913545 + 0.406737i) q^{2} +(-0.138897 - 0.154261i) q^{3} +(0.669131 + 0.743145i) q^{4} +(1.77975 - 1.35369i) q^{5} +(-0.0641452 - 0.197419i) q^{6} +(0.411507 - 2.61355i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.309081 - 2.94071i) q^{9} +(2.17648 - 0.512766i) q^{10} +(0.426271 + 4.05570i) q^{11} +(0.0216978 - 0.206441i) q^{12} +(-4.09048 - 2.97191i) q^{13} +(1.43896 - 2.22023i) q^{14} +(-0.456023 - 0.0865226i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(4.33844 + 0.922165i) q^{17} +(1.47846 - 2.56076i) q^{18} +(-2.91912 + 3.24201i) q^{19} +(2.19688 + 0.416819i) q^{20} +(-0.460325 + 0.299535i) q^{21} +(-1.26018 + 3.87845i) q^{22} +(4.45503 + 1.98351i) q^{23} +(0.103789 - 0.179768i) q^{24} +(1.33505 - 4.81847i) q^{25} +(-2.52805 - 4.37872i) q^{26} +(-1.00037 + 0.726811i) q^{27} +(2.21760 - 1.44300i) q^{28} +(-2.26620 + 6.97466i) q^{29} +(-0.381406 - 0.264524i) q^{30} +(4.40252 + 0.935784i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.566427 - 0.629081i) q^{33} +(3.58829 + 2.60704i) q^{34} +(-2.80556 - 5.20853i) q^{35} +(2.39219 - 1.73803i) q^{36} +(-1.16205 + 11.0562i) q^{37} +(-3.98539 + 1.77441i) q^{38} +(0.109707 + 1.04379i) q^{39} +(1.83741 + 1.27433i) q^{40} +(-8.12326 - 5.90189i) q^{41} +(-0.542360 + 0.0864078i) q^{42} -3.55966 q^{43} +(-2.72874 + 3.03057i) q^{44} +(-3.43073 - 5.65215i) q^{45} +(3.26311 + 3.62405i) q^{46} +(7.80164 - 1.65829i) q^{47} +(0.167934 - 0.122011i) q^{48} +(-6.66132 - 2.15099i) q^{49} +(3.17947 - 3.85888i) q^{50} +(-0.460342 - 0.797337i) q^{51} +(-0.528507 - 5.02841i) q^{52} +(-7.61081 - 8.45266i) q^{53} +(-1.20950 + 0.257088i) q^{54} +(6.24882 + 6.64111i) q^{55} +(2.61280 - 0.416266i) q^{56} +0.905570 q^{57} +(-4.90713 + 5.44992i) q^{58} +(-2.06084 + 0.917543i) q^{59} +(-0.240840 - 0.396786i) q^{60} +(1.28369 + 0.571535i) q^{61} +(3.64128 + 2.64555i) q^{62} +(-7.55852 - 2.01792i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-11.3031 + 0.247978i) q^{65} +(0.773327 - 0.344307i) q^{66} +(2.45488 + 0.521801i) q^{67} +(2.21768 + 3.84114i) q^{68} +(-0.312813 - 0.962739i) q^{69} +(-0.444506 - 5.89936i) q^{70} +(-4.35140 + 13.3922i) q^{71} +(2.89230 - 0.614776i) q^{72} +(0.535757 + 5.09738i) q^{73} +(-5.55855 + 9.62769i) q^{74} +(-0.928734 + 0.463325i) q^{75} -4.36255 q^{76} +(10.7752 + 0.554865i) q^{77} +(-0.324325 + 0.998169i) q^{78} +(-4.19375 + 0.891410i) q^{79} +(1.16024 + 1.91150i) q^{80} +(-8.42582 - 1.79096i) q^{81} +(-5.02045 - 8.69567i) q^{82} +(-3.89185 - 11.9779i) q^{83} +(-0.530616 - 0.141660i) q^{84} +(8.96969 - 4.23168i) q^{85} +(-3.25191 - 1.44784i) q^{86} +(1.39068 - 0.619172i) q^{87} +(-3.72547 + 1.65869i) q^{88} +(-2.20482 - 0.981651i) q^{89} +(-0.835189 - 6.55889i) q^{90} +(-9.45049 + 9.46772i) q^{91} +(1.50696 + 4.63796i) q^{92} +(-0.467141 - 0.809113i) q^{93} +(7.80164 + 1.65829i) q^{94} +(-0.806635 + 9.72155i) q^{95} +(0.203042 - 0.0431579i) q^{96} +(1.66969 - 5.13879i) q^{97} +(-5.21054 - 4.67443i) q^{98} +12.0584 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9}+O(q^{10}) \) 80 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 20 * q^8 + 4 * q^9	\( 80 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{7} - 20 q^{8} + 4 q^{9} + 3 q^{10} + 10 q^{11} + 2 q^{12} - 12 q^{13} - 7 q^{14} + 22 q^{15} + 10 q^{16} - 8 q^{17} - 36 q^{18} + 8 q^{19} + 4 q^{20} + 17 q^{21} + 20 q^{22} + 5 q^{23} - 8 q^{24} + 32 q^{25} - 24 q^{26} + 32 q^{27} - 7 q^{28} + 12 q^{29} - 11 q^{30} - 9 q^{31} - 40 q^{32} + 33 q^{33} - 4 q^{34} - 22 q^{35} - 8 q^{36} - 14 q^{37} - 2 q^{38} - 2 q^{40} - 18 q^{41} - 19 q^{42} - 8 q^{43} - 10 q^{44} + 33 q^{45} - 10 q^{46} + 10 q^{47} - 4 q^{48} + 12 q^{49} + 36 q^{50} + 46 q^{51} + 6 q^{52} - 30 q^{53} + 14 q^{54} + 2 q^{55} - q^{56} - 52 q^{57} - 6 q^{58} + 40 q^{59} + 4 q^{60} + 16 q^{61} - 32 q^{62} - 100 q^{63} - 20 q^{64} - 25 q^{65} - 7 q^{66} + q^{67} + 12 q^{68} - 142 q^{69} + 25 q^{70} - 84 q^{71} + 14 q^{72} + 22 q^{73} + 6 q^{74} - 29 q^{75} + 24 q^{76} + 38 q^{77} - 30 q^{78} + 10 q^{79} + 3 q^{80} + 52 q^{81} - 6 q^{82} - 98 q^{83} + 2 q^{84} - 36 q^{85} - 26 q^{86} + 34 q^{87} + 10 q^{88} + 45 q^{89} + 24 q^{90} - 63 q^{91} + 20 q^{92} - 20 q^{93} + 10 q^{94} - 33 q^{95} + 2 q^{96} - 106 q^{97} - 55 q^{98} + 12 q^{99}+O(q^{100}) \) 80 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^7 - 20 * q^8 + 4 * q^9 + 3 * q^10 + 10 * q^11 + 2 * q^12 - 12 * q^13 - 7 * q^14 + 22 * q^15 + 10 * q^16 - 8 * q^17 - 36 * q^18 + 8 * q^19 + 4 * q^20 + 17 * q^21 + 20 * q^22 + 5 * q^23 - 8 * q^24 + 32 * q^25 - 24 * q^26 + 32 * q^27 - 7 * q^28 + 12 * q^29 - 11 * q^30 - 9 * q^31 - 40 * q^32 + 33 * q^33 - 4 * q^34 - 22 * q^35 - 8 * q^36 - 14 * q^37 - 2 * q^38 - 2 * q^40 - 18 * q^41 - 19 * q^42 - 8 * q^43 - 10 * q^44 + 33 * q^45 - 10 * q^46 + 10 * q^47 - 4 * q^48 + 12 * q^49 + 36 * q^50 + 46 * q^51 + 6 * q^52 - 30 * q^53 + 14 * q^54 + 2 * q^55 - q^56 - 52 * q^57 - 6 * q^58 + 40 * q^59 + 4 * q^60 + 16 * q^61 - 32 * q^62 - 100 * q^63 - 20 * q^64 - 25 * q^65 - 7 * q^66 + q^67 + 12 * q^68 - 142 * q^69 + 25 * q^70 - 84 * q^71 + 14 * q^72 + 22 * q^73 + 6 * q^74 - 29 * q^75 + 24 * q^76 + 38 * q^77 - 30 * q^78 + 10 * q^79 + 3 * q^80 + 52 * q^81 - 6 * q^82 - 98 * q^83 + 2 * q^84 - 36 * q^85 - 26 * q^86 + 34 * q^87 + 10 * q^88 + 45 * q^89 + 24 * q^90 - 63 * q^91 + 20 * q^92 - 20 * q^93 + 10 * q^94 - 33 * q^95 + 2 * q^96 - 106 * q^97 - 55 * q^98 + 12 * q^99

Introduction

L-functions

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